Finite Group Databasebeta

← #28270332

Subgroups — #28270332

Order 13568.

2174 conjugacy classes of subgroups.

The subgroup lattice has 1952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289032C211yesmaximal, characteristic, complemented
2#20288375C211yesmaximal, characteristic, complemented
3#20286868C211yesmaximal, characteristic, complemented
4#20286732C211yesmaximal, characteristic, complemented
5#20286724C211yesmaximal, characteristic, complemented
6#20286700C211yesmaximal, characteristic, complemented
7#20286664C211yesmaximal, characteristic, complemented
8#20286600C211yesmaximal, characteristic, complemented
9#20286561C211yesmaximal, characteristic, complemented
10#20286472C211yesmaximal, characteristic, complemented
11#20286427C211yesmaximal, characteristic, complemented
12#20286401C211yesmaximal, characteristic, complemented
13#20286385C211yesmaximal, characteristic, complemented
14#20286261C211yesmaximal, characteristic, complemented
15#20286253C211yesmaximal, characteristic, complemented
16#20286207C211yesmaximal, characteristic, complemented
17#20286191C211yesmaximal, characteristic, complemented
18#20285812C211yesmaximal, characteristic, complemented
19#20285764C211yesmaximal, characteristic, complemented
20#20285615C211yesmaximal, characteristic, complemented
21#20285560C211yesmaximal, characteristic, complemented
22#20285475C211yesmaximal, characteristic, complemented
23#20285465C211yesmaximal, characteristic, complemented
24#20284982C211yesmaximal, characteristic, complemented
25#20284910C211yesmaximal, characteristic, complemented
26#20284024C211yesmaximal, characteristic, complemented
27#20283978C211yesmaximal, characteristic, complemented
28#20283928C211yesmaximal, characteristic, complemented
29C2×#16810769C211yesmaximal, characteristic, complemented
30#20283768C211yesmaximal, characteristic, complemented
31C53×#3294C211yesmaximal, characteristic, complemented
32C2×#13133262C2211yescharacteristic, complemented
33C22×#11719947C2211yescharacteristic, complemented
34C2×#13133243C2211yescharacteristic, complemented
35C2×#13133241C2211yescharacteristic, complemented
36C2×#13133239C2211yescharacteristic, complemented
37C2×#13133236C2211yescharacteristic, complemented
38C2×#13133236C2211yescharacteristic, complemented
39C22×#11719913C2211yescharacteristic, complemented
40C22×#11719922C2211yescharacteristic, complemented
41C2×D8×D53C2211yescharacteristic, complemented
42#16811369—21no—
43#16811363—21no—
44#16811339C2211yescharacteristic, complemented
45#16811321C2211yescharacteristic, complemented
46#16811308C2211yescharacteristic, complemented
47#16811296—21no—
48#16811293C2211yescharacteristic, complemented
49#16811291C2211yescharacteristic, complemented
50#16811291C2211yescharacteristic, complemented
51#16811282C2211yescharacteristic, complemented
52#16811279C2211yescharacteristic
53#16811269C2211yescharacteristic, complemented
54#16811268C2211yescharacteristic, complemented
55#16811268C2211yescharacteristic, complemented
56#16811267C2211yescharacteristic, complemented
57#16811262—21no—
58#16811261—21no—
59#16811260—21no—
60#16811257C2211yescharacteristic, complemented
61D4×C22⋊D53—21no—
62D4×C22⋊D53C2211yescharacteristic
63#16811255—21no—
64#16811247C2211yescharacteristic, complemented
65#16811225—21no—
66#16811224C2211yescharacteristic, complemented
67#16811213—21no—
68#16811204C2211yescharacteristic, complemented
69#16811202C2211yescharacteristic, complemented
70#16811200—21no—
71#16811189C2211yescharacteristic, complemented
72#16811188—21no—
73#16811187—21no—
74#16811186C2211yescharacteristic, complemented
75#16811184—21no—
76#16811133C2211yescharacteristic, complemented
77#16811132C2211yescharacteristic
78#16811129—21no—
79C2×#13133192C2211yescharacteristic, complemented
80C2×#13133189—21no—
81#121×D53C2211yescharacteristic, complemented
82#16811102C2211yescharacteristic, complemented
83#16811011C2211yescharacteristic, complemented
84#16811010C2211yescharacteristic, complemented
85#16811007C2211yescharacteristic, complemented
86#16810998C2211yescharacteristic, complemented
87#16810986C2211yescharacteristic, complemented
88#16810985C2211yescharacteristic, complemented
89#16810976C2211yescharacteristic, complemented
90#16810966C2211yescharacteristic, complemented
91#16810960C2211yescharacteristic, complemented
92#16810958C2211yescharacteristic, complemented
93#16810950C2211yescharacteristic, complemented
94#16810946C2211yescharacteristic, complemented
95#16810946C2211yescharacteristic, complemented
96#16810940C2211yescharacteristic, complemented
97#16810938C2211yescharacteristic, complemented
98#16810938C2211yescharacteristic, complemented
99#16810936C2211yescharacteristic, complemented
100#16810929C2211yescharacteristic, complemented
101#16810925C2211yescharacteristic, complemented
102#16810915C2211yescharacteristic, complemented
103#16810874C2211yescharacteristic, complemented
104#16810870C2211yescharacteristic, complemented
105#16810868C2211yescharacteristic, complemented
106#16810867C2211yescharacteristic, complemented
107#16810865C2211yescharacteristic, complemented
108#16810860C2211yescharacteristic, complemented
109#16810860C2211yescharacteristic, complemented
110#16810858C2211yescharacteristic, complemented
111#16810858C2211yescharacteristic, complemented
112#16810858C2211yescharacteristic, complemented
113#16810857C2211yescharacteristic, complemented
114#16810852C2211yescharacteristic, complemented
115#16810852C2211yescharacteristic, complemented
116#16810850C2211yescharacteristic, complemented
117#16810846C2211yescharacteristic, complemented
118#16810844C2211yescharacteristic, complemented
119#16810839C2211yescharacteristic, complemented
120#16810838C2211yescharacteristic, complemented
121#16810838C2211yescharacteristic, complemented
122#16810837C2211yescharacteristic, complemented
123#16810822C2211yescharacteristic, complemented
124#16810822C2211yescharacteristic, complemented
125#16810817C2211yescharacteristic, complemented
126#16810816C2211yescharacteristic, complemented
127#16810815C2211yescharacteristic, complemented
128#16810787C2211yescharacteristic, complemented
129#16810786C2211yescharacteristic, complemented
130#16810786C2211yescharacteristic, complemented
131#16810786C2211yescharacteristic, complemented
132#16810781C2211yescharacteristic, complemented
133#16810775C2211yescharacteristic, complemented
134#16810775C2211yescharacteristic, complemented
135#16810775C2211yescharacteristic, complemented
136#16810774C2211yescharacteristic, complemented
137#16810770C2211yescharacteristic, complemented
138#16810769C2211yescharacteristic
139#16810769C2211yescharacteristic, complemented
140#16810769C2211yescharacteristic, complemented
141#16810769C2211yescharacteristic, complemented
142#16810769C2211yescharacteristic, complemented
143#16810769C2211yescharacteristic, complemented
144#16810769C2211yescharacteristic, complemented
145#16810769C2211yescharacteristic, complemented
146#16810769C2211yescharacteristic, complemented
147#16810769C2211yescharacteristic, complemented
148#16810766C2211yescharacteristic, complemented
149#16810766C2211yescharacteristic, complemented
150#16810765C2211yescharacteristic, complemented
151#16810765C2211yescharacteristic, complemented
152#16810765C2211yescharacteristic, complemented
153#16810761C2211yescharacteristic, complemented
154#16810759C2211yescharacteristic, complemented
155#16810758C2211yescharacteristic, complemented
156#16810758C2211yescharacteristic, complemented
157#16810758C2211yescharacteristic, complemented
158#16810757C2211yescharacteristic, complemented
159#16810756C2211yescharacteristic, complemented
160#16810755C2211yescharacteristic, complemented
161#16810755C2211yescharacteristic, complemented
162#16810733C2211yescharacteristic, complemented
163#16810723C2211yescharacteristic, complemented
164#16810722C2211yescharacteristic, complemented
165#16810720C2211yescharacteristic, complemented
166#16810717C2211yescharacteristic, complemented
167C4×#11719913C2211yescharacteristic, complemented
168#16810703C2211yescharacteristic, complemented
169#16810697C2211yescharacteristic, complemented
170#16810695C2211yescharacteristic, complemented
171#16810694C2211yescharacteristic, complemented
172#16810693C2211yescharacteristic, complemented
173C8×D212C2211yescharacteristic, complemented
174C8×C22⋊D53C2211yescharacteristic, complemented
175#16810686C2211yescharacteristic, complemented
176#16810683C2211yescharacteristic, complemented
177#16810682C2211yescharacteristic, complemented
178#16810626C2211yescharacteristic, complemented
179#16810622C2211yescharacteristic, complemented
180#16810616C2211yescharacteristic, complemented
181#16810616C2211yescharacteristic, complemented
182#16810616C2211yescharacteristic, complemented
183C2×#13133140C2211yescharacteristic, complemented
184#16810589C2211yescharacteristic, complemented
185#16810588C2211yescharacteristic, complemented
186C2×#13133129C2211yescharacteristic, complemented
187C22⋊C8×D53C2211yescharacteristic, complemented
188C53×#547C2211yescharacteristic, complemented
189D42×C53C2211yescharacteristic, complemented
190C53×#486C2211yescharacteristic, complemented
191C53×#480C2211yescharacteristic, complemented
192C53×#480C2211yescharacteristic, complemented
193C53×#474C2211yescharacteristic, complemented
194C53×#466C2211yescharacteristic, complemented
195C53×#466C2211yescharacteristic, complemented
196C53×#459C2211yescharacteristic, complemented
197C53×#447C2211yescharacteristic, complemented
198C53×#447C2211yescharacteristic, complemented
199C4×D8×C53C2211yescharacteristic, complemented
200C8×D4×C53C2211yescharacteristic, complemented
201C2×#102×C53C2211yescharacteristic, complemented
202C2×#102×C53C2211yescharacteristic, complemented
203#13133262—42no—
204#13133262—42no—
205C2×#11719945C2311yescharacteristic
206C2×#11719945C2311yescharacteristic
207C2×#11719945C2311yescharacteristic
208C2×#11719947—21no—
209C2×#11719947—21no—
210C2×#11719947—21no—
211C2×#11719947—42no—
212C2×#11719947—42no—
213C2×#11719947C2311yescharacteristic
214C2×#11719947C2311yescharacteristic
215C2×#11719947C2311yescharacteristic
216C2×#11719947C2311yescharacteristic
217C2×#11719947C2311yescharacteristic
218C2×#11719947C2311yescharacteristic
219C22×Dic106C2311yescharacteristic
220C22×D212—21no—
221C22×D212C2311yescharacteristic
222C22×C22⋊D53—21no—
223C22×C22⋊D53—21no—
224C22×C22⋊D53—21no—
225C22×C22⋊D53—21no—
226C2×D4×D53—21no—
227C2×D4×D53—21no—
228C2×D4×D53—21no—
229C2×D4×D53C2311yescharacteristic
230C2×D4×D53C2311yescharacteristic
231C2×D4×D53C2311yescharacteristic
232C23×Dic53—21no—
233C22×C4×D53C2311yescharacteristic
234#13133243—42no—
235#13133241—42no—
236#13133239—42no—
237#13133236—42no—
238#13133236—42no—
239C2×Dic212C2311yescharacteristic
240C2×Dic212C2311yescharacteristic
241C2×#11719913—42no—
242C2×#11719913C2311yescharacteristic
243C2×#11719913C2311yescharacteristic
244C2×#11719913C2311yescharacteristic
245C2×#11719913C2311yescharacteristic
246C2×#11719913C2311yescharacteristic
247C2×#11719923C2311yescharacteristic
248C2×#11719923C2311yescharacteristic
249C2×#11719923C2311yescharacteristic
250C2×#11719923C2311yescharacteristic
251C2×#11719923C2311yescharacteristic
252C2×D424C2311yescharacteristic
253C2×D424C2311yescharacteristic
254C2×#11719922—42no—
255C2×#11719922C2311yescharacteristic
256C2×#11719922C2311yescharacteristic
257C2×#11719922C2311yescharacteristic
258C2×#11719922C2311yescharacteristic
259C2×#11719922C2311yescharacteristic
260C2×#11719922C2311yescharacteristic
261C2×#11719922C2311yescharacteristic
262D8×D53—42no—
263C2×#11719917C2311yescharacteristic
264C2×#11719912C2311yescharacteristic
265C22×#88322C2311yescharacteristic
266C2×C8×D53C2311yescharacteristic
267C2×C8×D53C2311yescharacteristic
268C2×C8×D53C2311yescharacteristic
269#13133213—21no—
270#13133213—21no—
271#13133213—21no—
272#13133213—21no—
273#13133213C2311yescharacteristic
274#13133213C2311yescharacteristic
275#13133212—21no—
276#13133212—21no—
277#13133212—21no—
278#13133208C2311yescharacteristic
279#13133207—21no—
280#13133206—21no—
281#13133206—21no—
282#13133206—21no—
283#13133205C2311yescharacteristic
284#13133205C2311yescharacteristic
285#13133204C2311yescharacteristic
286#13133203—21no—
287#13133203—21no—
288#13133203—21no—
289#13133202—21no—
290#13133202—21no—
291#13133202—21no—
292#13133202D411yescharacteristic
293#13133201—21no—
294#13133201—21no—
295#13133200—21no—
296#13133200—21no—
297#13133199—21no—
298#13133199—21no—
299#13133199D411yescharacteristic
300#13133198—21no—
301#13133197—21no—
302#13133197C2311yescharacteristic
303#13133197C2311yescharacteristic
304#13133197C2311yescharacteristic
305#13133196C2311yescharacteristic
306#13133196C2311yescharacteristic
307#13133195—21no—
308#13133195D411yescharacteristic
309#13133194—21no—
310#13133194—21no—
311#13133194D411yescharacteristic
312#13133193—21no—
313#13133192—21no—
314#13133192—21no—
315#13133192—21no—
316#13133192—21no—
317#13133192C2311yescharacteristic
318#13133192C2311yescharacteristic
319#13133192C2311yescharacteristic
320#13133192C2311yescharacteristic
321#13133192C2311yescharacteristic
322#13133192C2311yescharacteristic
323#13133191—21no—
324#13133191—21no—
325#13133191—21no—
326#13133191—21no—
327#13133191—21no—
328#13133191—21no—
329#13133191C2311yescharacteristic
330#13133191C2311yescharacteristic
331#13133190—21no—
332#13133190—21no—
333#13133190—21no—
334#13133190—21no—
335#13133190—21no—
336#13133190—21no—
337#13133190—21no—
338#13133190D411yescharacteristic
339#13133189—21no—
340#13133189—21no—
341#13133189—21no—
342#13133189—21no—
343#13133189—21no—
344#13133189—21no—
345#13133189—21no—
346#13133189—21no—
347#13133189—21no—
348#13133189—21no—
349#13133189—21no—
350#13133189—21no—
351#13133189D411yescharacteristic
352#13133188—21no—
353#13133188C2311yescharacteristic
354#13133188C2311yescharacteristic
355#13133188C2311yescharacteristic
356#13133187—21no—
357#13133187—21no—
358#13133187—21no—
359#13133187—21no—
360#13133187D411yescharacteristic
361#13133186—21no—
362#13133186—21no—
363#13133185—21no—
364#13133185—21no—
365#13133185—21no—
366#13133185—21no—
367#13133185—21no—
368#13133185—21no—
369#13133185—21no—
370#13133185D411yescharacteristic
371C4×Dic106C2311yescharacteristic
372#13133182C2311yescharacteristic
373#13133182C2311yescharacteristic
374C4×D212C2311yescharacteristic
375C4×D212C2311yescharacteristic
376D4×Dic53—21no—
377D4×Dic53—21no—
378D4×Dic53—21no—
379D4×Dic53C2311yescharacteristic
380#13133179C2311yescharacteristic
381C4×C22⋊D53—21no—
382C4×C22⋊D53—21no—
383C4×C22⋊D53C2311yescharacteristic
384C4×C22⋊D53C2311yescharacteristic
385#13133177—21no—
386#13133177—21no—
387#13133177—21no—
388#13133177—21no—
389#13133177—21no—
390#13133176—21no—
391#13133175—21no—
392#13133175C2311yescharacteristic
393#13133175C2311yescharacteristic
394#13133174C2311yescharacteristic
395#13133173—21no—
396C2×#11719919—21no—
397C4⋊C4×D53C2311yescharacteristic
398C2×C22⋊Dic53—21no—
399C2×#11719921—21no—
400C2×#11719921—21no—
401C2×#11719921—21no—
402C22⋊C4×D53—21no—
403C22⋊C4×D53—21no—
404#13133150C2311yescharacteristic
405#13133150C2311yescharacteristic
406#13133150C2311yescharacteristic
407#13133149C2311yescharacteristic
408#13133148C2311yescharacteristic
409C4⋊#88322C2311yescharacteristic
410#13133146C2311yescharacteristic
411#13133146C2311yescharacteristic
412#13133142C2311yescharacteristic
413#13133142C2311yescharacteristic
414#13133142C2311yescharacteristic
415#13133140C2311yescharacteristic
416#13133140C2311yescharacteristic
417#13133140C2311yescharacteristic
418#13133140C2311yescharacteristic
419#13133140C2311yescharacteristic
420#13133140C2311yescharacteristic
421#13133140C2311yescharacteristic
422#13133139C2311yescharacteristic
423#13133139C2311yescharacteristic
424#13133139C2311yescharacteristic
425#13133138C2311yescharacteristic
426#13133138C2311yescharacteristic
427#13133138C2311yescharacteristic
428#13133138C2311yescharacteristic
429#13133137C2311yescharacteristic
430#13133137C2311yescharacteristic
431#13133137C2311yescharacteristic
432#13133137C2311yescharacteristic
433#13133137C2311yescharacteristic
434C22⋊#88322C2311yescharacteristic
435C22⋊#88322C2311yescharacteristic
436#13133129C2311yescharacteristic
437#13133129C2311yescharacteristic
438#13133129C2311yescharacteristic
439#13133129C2311yescharacteristic
440#13133129C2311yescharacteristic
441#13133129C2311yescharacteristic
442#13133129C2311yescharacteristic
443#13133129C2311yescharacteristic
444#13133128C2311yescharacteristic
445#13133127C2311yescharacteristic
446C8×Dic53C2311yescharacteristic
447C2×#41×C53—21no—
448C22×D4×C53—21no—
449C22×D4×C53C2311yescharacteristic
450C22×D4×C53C2311yescharacteristic
451C2×D8×C53C2311yescharacteristic
452C2×D8×C53C2311yescharacteristic
453C2×D8×C53C2311yescharacteristic
454C22×C8×C53C2311yescharacteristic
455C22×C8×C53C2311yescharacteristic
456C4⋊Q8×C53C2311yescharacteristic
457#127×C53C2311yescharacteristic
458#123×C53—21no—
459#123×C53—21no—
460C22⋊Q8×C53—21no—
461#121×C53—21no—
462#121×C53C2311yescharacteristic
463#121×C53C2311yescharacteristic
464#121×C53C2311yescharacteristic
465#121×C53C2311yescharacteristic
466#120×C53—21no—
467#120×C53—21no—
468C4×D4×C53C2311yescharacteristic
469C4×D4×C53C2311yescharacteristic
470C4×D4×C53C2311yescharacteristic
471C2×C4⋊C4×C53C2311yescharacteristic
472C2×C4⋊C4×C53C2311yescharacteristic
473#107×C53C2311yescharacteristic
474#107×C53C2311yescharacteristic
475#107×C53C2311yescharacteristic
476C4⋊C8×C53C2311yescharacteristic
477#102×C53C2311yescharacteristic
478#102×C53C2311yescharacteristic
479#102×C53C2311yescharacteristic
480#102×C53C2311yescharacteristic
481#102×C53C2311yescharacteristic
482#102×C53C2311yescharacteristic
483#102×C53C2311yescharacteristic
484#102×C53C2311yescharacteristic
485#102×C53C2311yescharacteristic
486#102×C53C2311yescharacteristic
487C22⋊C8×C53C2311yescharacteristic
488C22⋊C8×C53C2311yescharacteristic
489C4×C8×C53C2311yescharacteristic
490C24×C53—21no—
491C24×C53—21no—
492C23×D53—21no—
493C23×D53—21no—
494C23×D53—21no—
495C23×D53—21no—
496C23×D53C2×D411yescharacteristic
497#41×C53—82no—
498C2×Q8×C53—21no—
499C2×D4×C53—22no—
500C2×D4×C53—22no—
501C2×D4×C53—21no—
502C2×D4×C53—21no—
503C2×D4×C53—21no—
504C2×D4×C53—21no—
505C2×D4×C53—21no—
506C2×D4×C53—21no—
507C2×D4×C53—21no—
508C2×D4×C53—21no—
509C2×D4×C53—41no—
510C2×D4×C53—41no—
511C2×D4×C53—82no—
512C2×D4×C53C2×D411yescharacteristic
513C2×D4×C53C2411yescharacteristic
514C2×D4×C53C2411yescharacteristic
515C2×D4×C53C2411yescharacteristic
516C2×D4×C53C2411yescharacteristic
517C22×C4×C53—21no—
518C22×C4×C53—21no—
519C22×C4×C53—21no—
520C22×C4×C53—21no—
521C22×C4×C53C2411yescharacteristic
522C22×C4×C53C2411yescharacteristic
523C2×C22⋊D53—21no—
524C2×C22⋊D53—21no—
525C2×C22⋊D53—21no—
526C2×C22⋊D53—21no—
527C2×C22⋊D53—21no—
528C2×C22⋊D53—21no—
529C2×C22⋊D53—21no—
530C2×C22⋊D53—21no—
531C2×C22⋊D53—21no—
532C2×C22⋊D53—21no—
533C2×C22⋊D53—21no—
534C2×C22⋊D53—21no—
535C2×C22⋊D53—21no—
536C2×C22⋊D53—21no—
537C2×C22⋊D53—21no—
538C2×C22⋊D53—21no—
539C2×C22⋊D53—21no—
540C2×C22⋊D53—21no—
541C2×C22⋊D53—21no—
542C2×C22⋊D53—21no—
543C2×C22⋊D53—44no—
544C2×C22⋊D53—44no—
545C2×C22⋊D53—44no—
546C2×C22⋊D53—82no—
547C2×C22⋊D53C2×D411yescharacteristic
548C2×C22⋊D53C2×D411yescharacteristic
549C2×C22⋊D53C2×D411yescharacteristic
550C2×C22⋊D53C2×D411yescharacteristic
551C22×Dic53—21no—
552C22×Dic53—21no—
553C22×Dic53—21no—
554C22×Dic53—21no—
555C22×Dic53—21no—
556C22×Dic53—21no—
557C22×Dic53—21no—
558C22×Dic53—21no—
559C22×Dic53—44no—
560C22×Dic53C2×D411yescharacteristic
561#11719947—22no—
562#11719947—22no—
563#11719947—22no—
564#11719947—22no—
565#11719947—22no—
566#11719947—41no—
567#11719947—41no—
568#11719947—41no—
569#11719947—41no—
570#11719947—41no—
571#11719947—41no—
572#11719947—41no—
573#11719947—44no—
574#11719947—44no—
575#11719947—44no—
576D4×D53—22no—
577D4×D53—41no—
578D4×D53—41no—
579D4×D53—41no—
580D4×D53—41no—
581D4×D53—41no—
582D4×D53—44no—
583D4×D53—82no—
584D4×D53—82no—
585#11719945—22no—
586#11719945—41no—
587#11719945—41no—
588#11719945—41no—
589#11719945—41no—
590#11719945—41no—
591C2×D212—21no—
592C2×D212—21no—
593C2×D212—21no—
594C2×D212—21no—
595C2×D212—21no—
596C2×D212—21no—
597C2×D212—21no—
598C2×D212—41no—
599C2×D212—41no—
600C2×D212—82no—
601C2×D212C2×D411yescharacteristic
602C2×D212C2×D411yescharacteristic
603C2×D212C2411yescharacteristic
604C2×D212C2411yescharacteristic
605C2×D212C2411yescharacteristic
606C2×C4×D53—21no—
607C2×C4×D53—21no—
608C2×C4×D53—21no—
609C2×C4×D53—21no—
610C2×C4×D53—21no—
611C2×C4×D53—41no—
612C2×C4×D53—41no—
613C2×C4×D53C2×D411yescharacteristic
614C2×C4×D53C2×D411yescharacteristic
615C2×C4×D53C2411yescharacteristic
616C2×C4×D53C2411yescharacteristic
617C2×C4×D53C2411yescharacteristic
618C2×Dic106—22no—
619C2×Dic106—21no—
620C2×Dic106—41no—
621C2×Dic106C2×D411yescharacteristic
622C2×Dic106C2411yescharacteristic
623C2×Dic106C2411yescharacteristic
624C2×Dic106C2411yescharacteristic
625D8×C53—22no—
626D8×C53—41no—
627D8×C53—41no—
628C2×C8×C53—41no—
629C2×C8×C53—41no—
630C2×C8×C53C2411yescharacteristic
631C2×C8×C53C2411yescharacteristic
632C2×C8×C53C2411yescharacteristic
633C2×C8×C53C2411yescharacteristic
634C4⋊C4×C53—21no—
635C4⋊C4×C53—21no—
636C4⋊C4×C53—21no—
637C4⋊C4×C53C2×D411yescharacteristic
638C4⋊C4×C53C2411yescharacteristic
639C4⋊C4×C53C2411yescharacteristic
640C4⋊C4×C53C2411yescharacteristic
641C4⋊C4×C53C2411yescharacteristic
642C22⋊C4×C53—21no—
643C22⋊C4×C53—21no—
644C22⋊C4×C53—21no—
645C22⋊C4×C53—21no—
646C22⋊C4×C53—21no—
647C22⋊C4×C53—21no—
648C22⋊C4×C53C2×D411yescharacteristic
649C22⋊C4×C53C2×D411yescharacteristic
650C42×C53C2411yescharacteristic
651C22⋊Dic53—21no—
652C22⋊Dic53—21no—
653C22⋊Dic53—21no—
654C22⋊Dic53—21no—
655C22⋊Dic53—21no—
656C22⋊Dic53—21no—
657C22⋊Dic53—21no—
658C22⋊Dic53—21no—
659C22⋊Dic53C2×D411yescharacteristic
660C22⋊Dic53C2×D411yescharacteristic
661#11719923—22no—
662#11719923—22no—
663#11719923—41no—
664#11719923—41no—
665#11719923—41no—
666#11719922—22no—
667#11719922—22no—
668#11719922—41no—
669#11719922—41no—
670#11719922—41no—
671#11719922—41no—
672#11719922—41no—
673#11719921—21no—
674#11719921—21no—
675#11719921—21no—
676#11719921—21no—
677#11719921—21no—
678#11719921—21no—
679#11719921—21no—
680#11719921—21no—
681#11719921—21no—
682#11719921—21no—
683#11719921—21no—
684#11719921—21no—
685#11719921—21no—
686#11719921—21no—
687#11719921—21no—
688#11719921—21no—
689#11719921—21no—
690#11719921—21no—
691#11719921—21no—
692#11719921C2×D411yescharacteristic
693#11719921C2×D411yescharacteristic
694#11719921C2×D411yescharacteristic
695#11719921C2×D411yescharacteristic
696#11719921C2×D411yescharacteristic
697#11719921C2×D411yescharacteristic
698C4⋊Dic53—21no—
699C4⋊Dic53—21no—
700C4⋊Dic53—21no—
701C4⋊Dic53—21no—
702C4⋊Dic53C2×D411yescharacteristic
703C4⋊Dic53C2411yescharacteristic
704C4⋊Dic53C2411yescharacteristic
705#11719919—21no—
706#11719919—21no—
707#11719919—21no—
708#11719919—21no—
709#11719919—21no—
710#11719919—21no—
711#11719919—21no—
712#11719919C2×D411yescharacteristic
713#11719919C2×D411yescharacteristic
714#11719919C2×D411yescharacteristic
715#11719919C2×D411yescharacteristic
716C4×Dic53—21no—
717C4×Dic53—21no—
718C4×Dic53—21no—
719C4×Dic53—21no—
720C4×Dic53—21no—
721C4×Dic53C2411yescharacteristic
722#11719917—41no—
723C2×#88322—41no—
724C2×#88322C2411yescharacteristic
725C2×#88322C2411yescharacteristic
726C2×#88322C2411yescharacteristic
727C2×#88322C2411yescharacteristic
728Dic212—22no—
729Dic212—41no—
730D424—41no—
731D424—41no—
732#11719913—22no—
733#11719913—22no—
734#11719913—41no—
735#11719913—41no—
736#11719913—41no—
737#11719912—41no—
738C8×D53—41no—
739C8×D53—41no—
740C8×D53—41no—
741C23×C53—21no—
742C23×C53—21no—
743C23×C53—21no—
744C23×C53—21no—
745C23×C53—42no—
746C23×C53—42no—
747C23×C53—42no—
748C23×C53—81no—
749C23×C53—81no—
750C23×C53—81no—
751C23×C53C22×D411yescharacteristic
752C23×C53C22×D411yescharacteristic
753C22×D53—22no—
754C22×D53—21no—
755C22×D53—21no—
756C22×D53—21no—
757C22×D53—41no—
758C22×D53—41no—
759C22×D53—42no—
760C22×D53—42no—
761C22×D53—42no—
762C22×D53—81no—
763C22×D53—81no—
764C22×D53—81no—
765C22×D53—81no—
766C22×D53—81no—
767C22×D53—81no—
768C22×D53—81no—
769C22×D53—81no—
770C22×D53—81no—
771C22×D53C22×D411yescharacteristic
772C22×D53C22×D411yescharacteristic
773C22×D53C22×D411yescharacteristic
774Q8×C53—81no—
775D4×C53—22no—
776D4×C53—21no—
777D4×C53—21no—
778D4×C53—21no—
779D4×C53—21no—
780D4×C53—21no—
781D4×C53—21no—
782D4×C53—21no—
783D4×C53—42no—
784D4×C53—42no—
785D4×C53—42no—
786D4×C53—42no—
787D4×C53—81no—
788D4×C53—81no—
789D4×C53—81no—
790D4×C53—81no—
791D4×C53H(5,𝔽2)12yes—
792C2×C4×C53—21no—
793C2×C4×C53—21no—
794C2×C4×C53—21no—
795C2×C4×C53—21no—
796C2×C4×C53—21no—
797C2×C4×C53—21no—
798C2×C4×C53—21no—
799C2×C4×C53—21no—
800C2×C4×C53—42no—
801C2×C4×C53—81no—
802C2×C4×C53—81no—
803C2×C4×C53—81no—
804C2×C4×C53C22×D411yescharacteristic
805C2×C4×C53C22×D411yescharacteristic
806C2×C4×C53C22×D411yescharacteristic
807C2×C4×C53C22×D411yescharacteristic
808C2×C4×C53C2511yescharacteristic
809C22⋊D53—24no—
810C22⋊D53—22no—
811C22⋊D53—41no—
812C22⋊D53—41no—
813C22⋊D53—41no—
814C22⋊D53—42no—
815C22⋊D53—42no—
816C22⋊D53—42no—
817C22⋊D53—42no—
818C22⋊D53—42no—
819C22⋊D53—42no—
820C22⋊D53—42no—
821C22⋊D53—42no—
822C22⋊D53—81no—
823C22⋊D53—81no—
824C22⋊D53—81no—
825C22⋊D53—81no—
826C22⋊D53—81no—
827C22⋊D53—81no—
828C22⋊D53—81no—
829C22⋊D53—81no—
830C22⋊D53—81no—
831C22⋊D53—81no—
832C22⋊D53—81no—
833C2×Dic53—24no—
834C2×Dic53—21no—
835C2×Dic53—21no—
836C2×Dic53—21no—
837C2×Dic53—21no—
838C2×Dic53—21no—
839C2×Dic53—41no—
840C2×Dic53—42no—
841C2×Dic53—42no—
842C2×Dic53—42no—
843C2×Dic53—42no—
844C2×Dic53—42no—
845C2×Dic53—81no—
846C2×Dic53—81no—
847C2×Dic53C22×D411yescharacteristic
848C2×Dic53C22×D411yescharacteristic
849C2×Dic53C22×D411yescharacteristic
850C2×Dic53C22×D411yescharacteristic
851C2×Dic53C22×D411yescharacteristic
852D212—21no—
853D212—21no—
854D212—21no—
855D212—21no—
856D212—21no—
857D212—21no—
858D212—41no—
859D212—41no—
860D212—81no—
861D212—81no—
862D212—81no—
863D212—81no—
864D212—81no—
865D212—81no—
866D212—81no—
867C4×D53—21no—
868C4×D53—21no—
869C4×D53—21no—
870C4×D53—21no—
871C4×D53—21no—
872C4×D53—21no—
873C4×D53—41no—
874C4×D53—41no—
875C4×D53—42no—
876C4×D53—81no—
877C4×D53—81no—
878C4×D53—81no—
879C4×D53—81no—
880Dic106—21no—
881Dic106—21no—
882Dic106—21no—
883Dic106—21no—
884Dic106—21no—
885Dic106—41no—
886Dic106—42no—
887Dic106H(5,𝔽2)12yes—
888C8×C53—21no—
889C8×C53—21no—
890C8×C53—21no—
891C8×C53—21no—
892#88322—21no—
893#88322—21no—
894#88322—21no—
895#88322—21no—
896#61639—531nomaximal, Sylow
897C22×C53—21no—
898C22×C53—21no—
899C22×C53—21no—
900C22×C53—22no—
901C22×C53—21no—
902C22×C53—21no—
903C22×C53—41no—
904C22×C53—41no—
905C22×C53—41no—
906C22×C53—41no—
907C22×C53—41no—
908C22×C53—41no—
909C22×C53—41no—
910C22×C53—41no—
911C22×C53—41no—
912C22×C53—41no—
913C22×C53—41no—
914C22×C53—84no—
915C22×C53—162no—
916C22×C53#57612yes—
917C22×C53C23×D411yescharacteristic
918C2×D53—21no—
919C2×D53—21no—
920C2×D53—21no—
921C2×D53—21no—
922C2×D53—21no—
923C2×D53—21no—
924C2×D53—21no—
925C2×D53—21no—
926C2×D53—21no—
927C2×D53—41no—
928C2×D53—41no—
929C2×D53—41no—
930C2×D53—41no—
931C2×D53—41no—
932C2×D53—41no—
933C2×D53—41no—
934C2×D53—41no—
935C2×D53—41no—
936C2×D53—82no—
937C2×D53—162no—
938C2×D53—162no—
939C2×D53—162no—
940C2×D53—162no—
941C4×C53—21no—
942C4×C53—21no—
943C4×C53—21no—
944C4×C53—21no—
945C4×C53—41no—
946C4×C53—41no—
947C4×C53—41no—
948C4×C53—41no—
949C4×C53C2×H(5,𝔽2)11yescharacteristic
950C4×C53C2×H(5,𝔽2)11yescharacteristic
951Dic53—21no—
952Dic53—22no—
953Dic53—21no—
954Dic53—21no—
955Dic53—21no—
956Dic53—21no—
957Dic53—41no—
958Dic53—41no—
959Dic53—41no—
960Dic53—41no—
961#3542—531no—
962#3488—531no—
963#3319—531no—
964#3310—531no—
965#3309—531no—
966#3308—531no—
967#3305—531no—
968#3300—531no—
969#3297—531no—
970#3294D5311yescharacteristic, complemented
971#3287—531no—
972#3282—531no—
973#3280—531no—
974D4×D8—531no—
975#3268—531no—
976#3268—531no—
977#3265—531no—
978#3264—531no—
979#3224—531no—
980#3220—531no—
981#3203—531no—
982#3198—531no—
983#3188—531no—
984#3186—531no—
985#3124—531no—
986#3119—531no—
987#3012—531no—
988#3008—531no—
989#3002—531no—
990C2×#449—531no—
991#2977—531no—
992C2×C53—22no—
993C2×C53—42no—
994C2×C53—41no—
995C2×C53—81no—
996C2×C53—81no—
997C2×C53—81no—
998C2×C53#348411yescharacteristic
999C2×C53C2×#57611yescharacteristic
1000C2×C53#358411yescharacteristic
1001D53—41no—
1002D53—41no—
1003D53—41no—
1004D53—81no—
1005D53—81no—
1006D53—81no—
1007C2×H(5,𝔽2)—531no—
1008C22×#41—531no—
1009C2×AGL(1,ℤ/8)—531no—
1010C2×AGL(1,ℤ/8)—531no—
1011C2×#135—531no—
1012C2×#135—531no—
1013C2×#135—531no—
1014C22×SD16—531no—
1015C22×D8—531no—
1016C22×D8—531no—
1017#562—1061no—
1018#560—1061no—
1019#555—531no—
1020#553—531no—
1021#552—531no—
1022#551—1061no—
1023#550—531no—
1024#550—531no—
1025#550—531no—
1026#548—531no—
1027#548—531no—
1028#547C2×D5311yescharacteristic, complemented
1029#546—531no—
1030#546—531no—
1031#546—531no—
1032#546—531no—
1033#546—1061no—
1034#546—1061no—
1035#546—1061no—
1036D42—531no—
1037D42—531no—
1038D42—1061no—
1039D42—1061no—
1040D42C2×D5311yescharacteristic, complemented
1041#542—531no—
1042#540—531no—
1043#540—1061no—
1044#538—1061no—
1045#537—531no—
1046#537—531no—
1047#537—1061no—
1048#535—531no—
1049#535—531no—
1050#535—1061no—
1051#535—1061no—
1052#534—1061no—
1053#525—531no—
1054#525—531no—
1055#525—1061no—
1056C2×#121—531no—
1057C2×#121—531no—
1058C2×#121—1061no—
1059#520—531no—
1060#496—531no—
1061#496—531no—
1062#495—531no—
1063#493—531no—
1064#490—531no—
1065#489—531no—
1066#488—531no—
1067#486C2×D5311yescharacteristic, complemented
1068#485—531no—
1069#484—531no—
1070#484—531no—
1071#482—531no—
1072#482—531no—
1073#482—531no—
1074#481—531no—
1075#480—531no—
1076#480—531no—
1077#480—531no—
1078#480C2×D5311yescharacteristic, complemented
1079#480C2×D5311yescharacteristic, complemented
1080#479—531no—
1081#478—531no—
1082#477—531no—
1083#474C2×D5311yescharacteristic, complemented
1084#469—531no—
1085#468—531no—
1086#468—531no—
1087#468—531no—
1088#467—531no—
1089#466—531no—
1090#466—531no—
1091#466—531no—
1092#466—531no—
1093#466—531no—
1094#466—531no—
1095#466C2×D5311yescharacteristic, complemented
1096#466C2×D5311yescharacteristic, complemented
1097#465—531no—
1098#465—531no—
1099#465—531no—
1100#464—531no—
1101#464—531no—
1102#463—531no—
1103#463—531no—
1104#463—531no—
1105#463—531no—
1106#460—531no—
1107#460—531no—
1108#459—531no—
1109#459—531no—
1110#459—531no—
1111#459C2×D5311yescharacteristic, complemented
1112#452—531no—
1113#452—531no—
1114#452—531no—
1115#452—531no—
1116#451—531no—
1117#450—531no—
1118#450—531no—
1119#450—531no—
1120#450—531no—
1121#449—531no—
1122#449—531no—
1123#449—531no—
1124#449—531no—
1125#449—531no—
1126#449—531no—
1127#449—531no—
1128#449—531no—
1129#449—531no—
1130#449—531no—
1131#449—531no—
1132#449—531no—
1133#449—531no—
1134#449—531no—
1135#449—531no—
1136#449—531no—
1137#448—531no—
1138#447—531no—
1139#447—531no—
1140#447—531no—
1141#447—531no—
1142#447—531no—
1143#447—531no—
1144#447—531no—
1145#447—531no—
1146#447C2×D5311yescharacteristic, complemented
1147#447C2×D5311yescharacteristic, complemented
1148#442—531no—
1149#440—531no—
1150#440—531no—
1151#440—531no—
1152C4×Q16—531no—
1153C4×SD16—531no—
1154C4×D8—531no—
1155C4×D8C2×D5311yescharacteristic, complemented
1156#435—531no—
1157#435—531no—
1158#435—531no—
1159#435—531no—
1160C8×D4—531no—
1161C8×D4—531no—
1162C8×D4—531no—
1163C8×D4C2×D5311yescharacteristic, complemented
1164#433—531no—
1165#433—531no—
1166#418—531no—
1167#417—531no—
1168#416—531no—
1169#416—531no—
1170#416—531no—
1171C2×#103—531no—
1172C2×#102C2×D5311yescharacteristic, complemented
1173C2×#102C2×D5311yescharacteristic, complemented
1174#408—531no—
1175#408—531no—
1176C2×C22⋊C8—531no—
1177C2×C22⋊C8—531no—
1178C53#6163911yescharacteristic, complemented, Sylow
1179H(5,𝔽2)—2122no—
1180H(5,𝔽2)—2122no—
1181C2×#41—21no—
1182C2×#41—531no—
1183C2×#41—531no—
1184C2×#41—531no—
1185C2×#41—531no—
1186C2×#41—531no—
1187C2×#41—531no—
1188C2×#41—531no—
1189C2×#41—531no—
1190C2×#41—531no—
1191C2×#41—1061no—
1192C2×#41—1061no—
1193C2×#41—1061no—
1194C2×#41—2122no—
1195C2×#41—2122no—
1196C22×Q8—531no—
1197C22×D4—21no—
1198C22×D4—531no—
1199C22×D4—531no—
1200C22×D4—531no—
1201C22×D4—531no—
1202C22×D4—1061no—
1203C22×D4—1061no—
1204C22×D4—1061no—
1205C22×D4—1061no—
1206C22×D4—1061no—
1207C22×D4—1061no—
1208C22×D4—1061no—
1209C22×D4—1061no—
1210C22×D4C22×D5311yescharacteristic
1211C22×D4C22×D5311yescharacteristic
1212C23×C4—531no—
1213C23×C4—1061no—
1214AGL(1,ℤ/8)—2122no—
1215AGL(1,ℤ/8)—2122no—
1216#135—2122no—
1217#135—2122no—
1218#135—2122no—
1219C2×Q16—531no—
1220C2×Q16—531no—
1221C2×SD16—531no—
1222C2×SD16—531no—
1223C2×SD16—531no—
1224C2×SD16—531no—
1225C2×SD16—531no—
1226C2×SD16—531no—
1227C2×SD16—531no—
1228C2×SD16—531no—
1229C2×SD16—531no—
1230C2×SD16—531no—
1231C2×SD16—2122no—
1232C2×D8—531no—
1233C2×D8—531no—
1234C2×D8—531no—
1235C2×D8—531no—
1236C2×D8—531no—
1237C2×D8—531no—
1238C2×D8—531no—
1239C2×D8—531no—
1240C2×D8—531no—
1241C2×D8—2122no—
1242C2×D8—2122no—
1243C2×D8C22×D5311yescharacteristic
1244C2×D8C22×D5311yescharacteristic
1245C2×D8C22×D5311yescharacteristic
1246C2×M16—531no—
1247C2×M16—531no—
1248C22×C8—531no—
1249C22×C8—531no—
1250C22×C8—531no—
1251C22×C8—531no—
1252C22×C8C22×D5311yescharacteristic
1253C22×C8C22×D5311yescharacteristic
1254C4⋊Q8C22×D5311yescharacteristic
1255#127—531no—
1256#127—531no—
1257#127—1061no—
1258#127—1061no—
1259#127—1061no—
1260#127—1061no—
1261#127C22×D5311yescharacteristic
1262#126—1061no—
1263#126—1061no—
1264#126—1061no—
1265#125—531no—
1266#125—1061no—
1267#124—531no—
1268#124—531no—
1269#124—531no—
1270#124—1061no—
1271#124—1061no—
1272#124—1061no—
1273#124—1061no—
1274#124—1061no—
1275#124—1061no—
1276#123—21no—
1277#123—21no—
1278#123—531no—
1279#123—531no—
1280#123—1061no—
1281#123—1061no—
1282#123—1061no—
1283#123—1061no—
1284#123—1061no—
1285#123—1061no—
1286#123—1061no—
1287#123—1061no—
1288#123—1061no—
1289#123—1061no—
1290C22⋊Q8—21no—
1291C22⋊Q8—531no—
1292C22⋊Q8—531no—
1293C22⋊Q8—531no—
1294C22⋊Q8—531no—
1295C22⋊Q8—531no—
1296C22⋊Q8—531no—
1297C22⋊Q8—531no—
1298C22⋊Q8—1061no—
1299C22⋊Q8—1061no—
1300C22⋊Q8—1061no—
1301C22⋊Q8—1061no—
1302C22⋊Q8—1061no—
1303#121—21no—
1304#121—531no—
1305#121—531no—
1306#121—531no—
1307#121—531no—
1308#121—531no—
1309#121—531no—
1310#121—531no—
1311#121—531no—
1312#121—531no—
1313#121—531no—
1314#121—531no—
1315#121—531no—
1316#121—531no—
1317#121—1061no—
1318#121—1061no—
1319#121—1061no—
1320#121—1061no—
1321#121—1061no—
1322#121—1061no—
1323#121—1061no—
1324#121—1061no—
1325#121—1061no—
1326#121—1061no—
1327#121—1061no—
1328#121—1061no—
1329#121—1061no—
1330#121—1061no—
1331#121—1061no—
1332#121—1061no—
1333#121—1061no—
1334#121—1061no—
1335#121—1061no—
1336#121—1061no—
1337#121—1061no—
1338#121—1061no—
1339#121—1061no—
1340#121—1061no—
1341#121—1061no—
1342#121—1061no—
1343#121—1061no—
1344#121—1061no—
1345#121—1061no—
1346#121—1061no—
1347#121C22×D5311yescharacteristic
1348#121C22×D5311yescharacteristic
1349#121C22×D5311yescharacteristic
1350#121C22×D5311yescharacteristic
1351#120—21no—
1352#120—21no—
1353#120—531no—
1354#120—531no—
1355#120—1061no—
1356#120—1061no—
1357#120—1061no—
1358#120—1061no—
1359#120—1061no—
1360#120—1061no—
1361#120—1061no—
1362#120—1061no—
1363#120—1061no—
1364#120—1061no—
1365#120—1061no—
1366#120—1061no—
1367#120—1061no—
1368C4×Q8—531no—
1369C4×Q8—531no—
1370C4×Q8—531no—
1371C4×D4—531no—
1372C4×D4—531no—
1373C4×D4—531no—
1374C4×D4—531no—
1375C4×D4—531no—
1376C4×D4—531no—
1377C4×D4—1061no—
1378C4×D4—1061no—
1379C4×D4—1061no—
1380C4×D4—1061no—
1381C4×D4—1061no—
1382C4×D4—1061no—
1383C4×D4—1061no—
1384C4×D4—1061no—
1385C4×D4—1061no—
1386C4×D4—1061no—
1387C4×D4C22×D5311yescharacteristic
1388C4×D4C22×D5311yescharacteristic
1389C4×D4C22×D5311yescharacteristic
1390#117—531no—
1391#117—531no—
1392#117—531no—
1393#117—1061no—
1394#117—1061no—
1395#117—1061no—
1396C2×C4⋊C4—531no—
1397C2×C4⋊C4—1061no—
1398C2×C4⋊C4C22×D5311yescharacteristic
1399C2×C4⋊C4C22×D5311yescharacteristic
1400C2×C22⋊C4—1061no—
1401C2×C22⋊C4—1061no—
1402C2×C22⋊C4—1061no—
1403C2×C22⋊C4—1061no—
1404C2×C22⋊C4—1061no—
1405C2×C22⋊C4—1061no—
1406#107—531no—
1407#107—531no—
1408#107—531no—
1409#107C22×D5311yescharacteristic
1410#107C22×D5311yescharacteristic
1411#107C22×D5311yescharacteristic
1412#106—531no—
1413#106—531no—
1414C4⋊C8—531no—
1415C4⋊C8—531no—
1416C4⋊C8—531no—
1417C4⋊C8C22×D5311yescharacteristic
1418#103—531no—
1419#103—531no—
1420#103—531no—
1421#103—531no—
1422#103—531no—
1423#103—531no—
1424#103—531no—
1425#103—531no—
1426#103—531no—
1427#103—531no—
1428#102—531no—
1429#102—531no—
1430#102—531no—
1431#102—531no—
1432#102—531no—
1433#102—531no—
1434#102—531no—
1435#102—531no—
1436#102—531no—
1437#102—531no—
1438#102—531no—
1439#102—531no—
1440#102C22×D5311yescharacteristic
1441#102C22×D5311yescharacteristic
1442#102C22×D5311yescharacteristic
1443#102C22×D5311yescharacteristic
1444#102C22×D5311yescharacteristic
1445#102C22×D5311yescharacteristic
1446#102C22×D5311yescharacteristic
1447#102C22×D5311yescharacteristic
1448#102C22×D5311yescharacteristic
1449#102C22×D5311yescharacteristic
1450C22⋊C8—531no—
1451C22⋊C8—531no—
1452C22⋊C8—531no—
1453C22⋊C8—531no—
1454C22⋊C8—531no—
1455C22⋊C8—531no—
1456C22⋊C8—531no—
1457C22⋊C8—531no—
1458C22⋊C8—531no—
1459C22⋊C8—531no—
1460C22⋊C8C22×D5311yescharacteristic
1461C22⋊C8C22×D5311yescharacteristic
1462#97—531no—
1463#97—531no—
1464C4×C8—531no—
1465C4×C8C22×D5311yescharacteristic
1466C24—21no—
1467C24—21no—
1468C24—531no—
1469C24—1061no—
1470C24—1061no—
1471C24—1061no—
1472C24—1061no—
1473#41—82no—
1474#41—1062no—
1475#41—1062no—
1476#41—1062no—
1477#41—1062no—
1478#41—1062no—
1479#41—1062no—
1480#41—2121no—
1481#41—2121no—
1482#41—2121no—
1483#41—2121no—
1484#41—2121no—
1485#41—2121no—
1486#41—2121no—
1487#41—2121no—
1488#41—2121no—
1489#41—2121no—
1490#41—2121no—
1491#41—2121no—
1492#41—2124no—
1493#41—2124no—
1494#41—2124no—
1495C2×Q8—21no—
1496C2×Q8—531no—
1497C2×Q8—531no—
1498C2×Q8—531no—
1499C2×Q8—531no—
1500C2×Q8—1062no—
1501C2×Q8—1061no—
1502C2×Q8—2121no—
1503C2×D4—22no—
1504C2×D4—22no—
1505C2×D4—21no—
1506C2×D4—21no—
1507C2×D4—21no—
1508C2×D4—21no—
1509C2×D4—21no—
1510C2×D4—21no—
1511C2×D4—21no—
1512C2×D4—21no—
1513C2×D4—41no—
1514C2×D4—41no—
1515C2×D4—82no—
1516C2×D4—531no—
1517C2×D4—531no—
1518C2×D4—531no—
1519C2×D4—531no—
1520C2×D4—531no—
1521C2×D4—531no—
1522C2×D4—531no—
1523C2×D4—531no—
1524C2×D4—531no—
1525C2×D4—1061no—
1526C2×D4—1061no—
1527C2×D4—1061no—
1528C2×D4—1061no—
1529C2×D4—1061no—
1530C2×D4—1061no—
1531C2×D4—1061no—
1532C2×D4—1061no—
1533C2×D4—1061no—
1534C2×D4—1061no—
1535C2×D4—1061no—
1536C2×D4—1061no—
1537C2×D4—1061no—
1538C2×D4—1061no—
1539C2×D4—1062no—
1540C2×D4—1061no—
1541C2×D4—1061no—
1542C2×D4—1061no—
1543C2×D4—1061no—
1544C2×D4—1061no—
1545C2×D4—1061no—
1546C2×D4—1061no—
1547C2×D4—1061no—
1548C2×D4—1061no—
1549C2×D4—1061no—
1550C2×D4—1061no—
1551C2×D4—1061no—
1552C2×D4—1061no—
1553C2×D4—4242no—
1554C2×D4—4242no—
1555C2×D4—4242no—
1556C2×D4—4242no—
1557C2×D4—2121no—
1558C2×D4—2121no—
1559C2×D4—2121no—
1560C2×D4—2121no—
1561C2×D4—2121no—
1562C2×D4—2121no—
1563C2×D4—2121no—
1564C2×D4—2124no—
1565C2×D4—2124no—
1566C2×D4—2124no—
1567C2×D4—2124no—
1568C2×D4D4×D5311yescharacteristic
1569C2×D4C23×D5311yescharacteristic
1570C2×D4C23×D5311yescharacteristic
1571C2×D4C23×D5311yescharacteristic
1572C2×D4C23×D5311yescharacteristic
1573C22×C4—21no—
1574C22×C4—21no—
1575C22×C4—21no—
1576C22×C4—21no—
1577C22×C4—531no—
1578C22×C4—531no—
1579C22×C4—531no—
1580C22×C4—531no—
1581C22×C4—531no—
1582C22×C4—531no—
1583C22×C4—1061no—
1584C22×C4—1061no—
1585C22×C4—1061no—
1586C22×C4—1061no—
1587C22×C4—1061no—
1588C22×C4—1061no—
1589C22×C4—1061no—
1590C22×C4—1061no—
1591C22×C4—1061no—
1592C22×C4—1061no—
1593C22×C4—1061no—
1594C22×C4—1061no—
1595C22×C4—1061no—
1596C22×C4—2121no—
1597C22×C4—2121no—
1598C22×C4—2124no—
1599C22×C4C23×D5311yescharacteristic
1600C22×C4C23×D5311yescharacteristic
1601Q16—1062no—
1602Q16—2121no—
1603SD16—1062no—
1604SD16—1062no—
1605SD16—1062no—
1606SD16—1062no—
1607SD16—2121no—
1608SD16—2121no—
1609SD16—2121no—
1610SD16—2121no—
1611SD16—2121no—
1612SD16—2121no—
1613D8—22no—
1614D8—41no—
1615D8—41no—
1616D8—1062no—
1617D8—1062no—
1618D8—2121no—
1619D8—2121no—
1620D8—2121no—
1621D8—2121no—
1622D8—2121no—
1623D8—2121no—
1624D8—2121no—
1625M16—2121no—
1626M16—2121no—
1627C2×C8—41no—
1628C2×C8—41no—
1629C2×C8—531no—
1630C2×C8—531no—
1631C2×C8—531no—
1632C2×C8—531no—
1633C2×C8—2121no—
1634C2×C8—2121no—
1635C2×C8—2121no—
1636C2×C8—2121no—
1637C2×C8C23×D5311yescharacteristic
1638C2×C8C23×D5311yescharacteristic
1639C2×C8C23×D5311yescharacteristic
1640C2×C8C23×D5311yescharacteristic
1641C4⋊C4—21no—
1642C4⋊C4—21no—
1643C4⋊C4—21no—
1644C4⋊C4—531no—
1645C4⋊C4—531no—
1646C4⋊C4—531no—
1647C4⋊C4—531no—
1648C4⋊C4—531no—
1649C4⋊C4—531no—
1650C4⋊C4—531no—
1651C4⋊C4—1061no—
1652C4⋊C4—1061no—
1653C4⋊C4—1061no—
1654C4⋊C4—1061no—
1655C4⋊C4—1061no—
1656C4⋊C4—1061no—
1657C4⋊C4—1061no—
1658C4⋊C4—1061no—
1659C4⋊C4—1061no—
1660C4⋊C4—1061no—
1661C4⋊C4—1061no—
1662C4⋊C4D4×D5311yescharacteristic
1663C4⋊C4C23×D5311yescharacteristic
1664C4⋊C4C23×D5311yescharacteristic
1665C4⋊C4C23×D5311yescharacteristic
1666C4⋊C4C23×D5311yescharacteristic
1667C22⋊C4—21no—
1668C22⋊C4—21no—
1669C22⋊C4—21no—
1670C22⋊C4—21no—
1671C22⋊C4—21no—
1672C22⋊C4—21no—
1673C22⋊C4—531no—
1674C22⋊C4—531no—
1675C22⋊C4—531no—
1676C22⋊C4—531no—
1677C22⋊C4—531no—
1678C22⋊C4—531no—
1679C22⋊C4—531no—
1680C22⋊C4—531no—
1681C22⋊C4—1061no—
1682C22⋊C4—1061no—
1683C22⋊C4—1061no—
1684C22⋊C4—1061no—
1685C22⋊C4—1061no—
1686C22⋊C4—1061no—
1687C22⋊C4—1061no—
1688C22⋊C4—1061no—
1689C22⋊C4—1061no—
1690C22⋊C4—1061no—
1691C22⋊C4—1061no—
1692C22⋊C4—1061no—
1693C22⋊C4—1061no—
1694C22⋊C4—1061no—
1695C22⋊C4—1061no—
1696C22⋊C4—1061no—
1697C22⋊C4—1061no—
1698C22⋊C4—1061no—
1699C22⋊C4—1061no—
1700C22⋊C4—1061no—
1701C22⋊C4—1061no—
1702C22⋊C4—1061no—
1703C22⋊C4—1061no—
1704C22⋊C4—1061no—
1705C22⋊C4—1061no—
1706C22⋊C4—1061no—
1707C22⋊C4—1061no—
1708C22⋊C4D4×D5311yescharacteristic
1709C22⋊C4D4×D5311yescharacteristic
1710C42—531no—
1711C42—1061no—
1712C42—1061no—
1713C42—1061no—
1714C42—1061no—
1715C42—1061no—
1716C42C23×D5311yescharacteristic
1717C23—21no—
1718C23—21no—
1719C23—21no—
1720C23—21no—
1721C23—42no—
1722C23—42no—
1723C23—42no—
1724C23—81no—
1725C23—81no—
1726C23—81no—
1727C23—531no—
1728C23—531no—
1729C23—531no—
1730C23—1062no—
1731C23—1061no—
1732C23—1061no—
1733C23—1061no—
1734C23—4241no—
1735C23—4241no—
1736C23—4241no—
1737C23—4241no—
1738C23—4241no—
1739C23—4241no—
1740C23—4241no—
1741C23—4241no—
1742C23—4241no—
1743C23—2122no—
1744C23—2121no—
1745C23—2121no—
1746C23—2122no—
1747C23—2122no—
1748C23C2×D4×D5311yescharacteristic
1749C23C2×D4×D5311yescharacteristic
1750Q8—81no—
1751Q8—532no—
1752Q8—1061no—
1753Q8—1061no—
1754Q8—1061no—
1755Q8—1061no—
1756Q8—1061no—
1757Q8—2121no—
1758Q8—2122no—
1759D4—22no—
1760D4—21no—
1761D4—21no—
1762D4—21no—
1763D4—21no—
1764D4—21no—
1765D4—21no—
1766D4—21no—
1767D4—42no—
1768D4—42no—
1769D4—42no—
1770D4—42no—
1771D4—81no—
1772D4—81no—
1773D4—81no—
1774D4—81no—
1775D4—1064no—
1776D4—1062no—
1777D4—1061no—
1778D4—1061no—
1779D4—1061no—
1780D4—1061no—
1781D4—1061no—
1782D4—1061no—
1783D4—4241no—
1784D4—4241no—
1785D4—4241no—
1786D4—4241no—
1787D4—4241no—
1788D4—4241no—
1789D4—4241no—
1790D4—4241no—
1791D4—4241no—
1792D4—4241no—
1793D4—4241no—
1794D4—4241no—
1795D4—4241no—
1796D4—4241no—
1797D4—4241no—
1798D4—4241no—
1799D4—4241no—
1800D4—4241no—
1801D4—2121no—
1802D4—2121no—
1803D4—2121no—
1804D4—2121no—
1805D4—2121no—
1806D4—2122no—
1807D4—2122no—
1808D4—2122no—
1809D4—2122no—
1810D4—2122no—
1811D4—2122no—
1812D4—2122no—
1813D4—2122no—
1814D4#1313326312yes—
1815C2×C4—21no—
1816C2×C4—21no—
1817C2×C4—21no—
1818C2×C4—21no—
1819C2×C4—21no—
1820C2×C4—21no—
1821C2×C4—21no—
1822C2×C4—21no—
1823C2×C4—42no—
1824C2×C4—81no—
1825C2×C4—81no—
1826C2×C4—81no—
1827C2×C4—531no—
1828C2×C4—531no—
1829C2×C4—531no—
1830C2×C4—531no—
1831C2×C4—531no—
1832C2×C4—1064no—
1833C2×C4—1061no—
1834C2×C4—1061no—
1835C2×C4—1061no—
1836C2×C4—1061no—
1837C2×C4—1061no—
1838C2×C4—1061no—
1839C2×C4—1061no—
1840C2×C4—1061no—
1841C2×C4—1061no—
1842C2×C4—1061no—
1843C2×C4—1061no—
1844C2×C4—4241no—
1845C2×C4—4241no—
1846C2×C4—4241no—
1847C2×C4—4241no—
1848C2×C4—4241no—
1849C2×C4—4241no—
1850C2×C4—2121no—
1851C2×C4—2121no—
1852C2×C4—2122no—
1853C2×C4—2121no—
1854C2×C4—2122no—
1855C2×C4—2122no—
1856C2×C4—2122no—
1857C2×C4—2122no—
1858C2×C4—2122no—
1859C2×C4C2×D4×D5311yescharacteristic
1860C2×C4C2×D4×D5311yescharacteristic
1861C2×C4C2×D4×D5311yescharacteristic
1862C2×C4C2×D4×D5311yescharacteristic
1863C2×C4C24×D5311yescharacteristic
1864C8—21no—
1865C8—21no—
1866C8—21no—
1867C8—21no—
1868C8—1061no—
1869C8—1061no—
1870C8—1061no—
1871C8—1061no—
1872C22—21no—
1873C22—21no—
1874C22—21no—
1875C22—22no—
1876C22—21no—
1877C22—21no—
1878C22—41no—
1879C22—41no—
1880C22—41no—
1881C22—41no—
1882C22—41no—
1883C22—41no—
1884C22—41no—
1885C22—41no—
1886C22—41no—
1887C22—41no—
1888C22—41no—
1889C22—84no—
1890C22—162no—
1891C22—8482no—
1892C22—8482no—
1893C22—8482no—
1894C22—8482no—
1895C22—1061no—
1896C22—1061no—
1897C22—1061no—
1898C22—1061no—
1899C22—1061no—
1900C22—1061no—
1901C22—1061no—
1902C22—1061no—
1903C22—1061no—
1904C22—4242no—
1905C22—2121no—
1906C22—2121no—
1907C22—2121no—
1908C22—2121no—
1909C22—2121no—
1910C22—2121no—
1911C22—2121no—
1912C22—2121no—
1913C22—2121no—
1914C22#1681142412yes—
1915C22C22×D4×D5311yescharacteristic
1916C4—21no—
1917C4—21no—
1918C4—21no—
1919C4—21no—
1920C4—41no—
1921C4—41no—
1922C4—41no—
1923C4—41no—
1924C4—1061no—
1925C4—1061no—
1926C4—1061no—
1927C4—1062no—
1928C4—1061no—
1929C4—1061no—
1930C4—2121no—
1931C4—2121no—
1932C4—2121no—
1933C4—2121no—
1934C4H(5,𝔽2)×D5311yescharacteristic
1935C4C2×#1313326311yescharacteristic
1936C2—22no—
1937C2—41no—
1938C2—42no—
1939C2—81no—
1940C2—81no—
1941C2—81no—
1942C2—4241no—
1943C2—4241no—
1944C2—4241no—
1945C2—2121no—
1946C2—2121no—
1947C2—2121no—
1948C2#2028834511yescharacteristic
1949C2C2×#1681142411yescharacteristic
1950C2#2028948711yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3294C2
socleC22×C53C23×D4
hypercenter#3294D53
hypocenterC53#61639
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3294

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20289032C2semidirect
2. #20288375C2semidirect
3. #20286868C2semidirect
4. #20286732C2semidirect
5. #20286724C2semidirect
6. #20286700C2semidirect
7. #20286664C2semidirect
8. #20286600C2semidirect
9. #20286561C2semidirect
10. #20286472C2semidirect
11. #20286427C2semidirect
12. #20286401C2semidirect
13. #20286385C2semidirect
14. #20286261C2semidirect
15. #20286253C2semidirect
16. #20286207C2semidirect
17. #20286191C2semidirect
18. #20285812C2semidirect
19. #20285764C2semidirect
20. #20285615C2semidirect
21. #20285560C2semidirect
22. #20285475C2semidirect
23. #20285465C2semidirect
24. #20284982C2semidirect
25. #20284910C2semidirect
26. #20284024C2semidirect
27. #20283978C2semidirect
28. #20283928C2semidirect
29. C2×#16810769C2semidirect
30. #20283768C2semidirect
31. C53×#3294C2semidirect
32. C2×#13133262C22semidirect
33. C22×#11719947C22semidirect
34. C2×#13133243C22semidirect
35. C2×#13133241C22semidirect
36. C2×#13133239C22semidirect
37. C2×#13133236C22semidirect
38. C2×#13133236C22semidirect
39. C22×#11719913C22semidirect
40. C22×#11719922C22semidirect
41. C2×D8×D53C22semidirect
44. #16811339C22semidirect
45. #16811321C22semidirect
46. #16811308C22semidirect
48. #16811293C22semidirect
49. #16811291C22semidirect
50. #16811291C22semidirect
51. #16811282C22semidirect
53. #16811269C22semidirect
54. #16811268C22semidirect
55. #16811268C22semidirect
56. #16811267C22semidirect
60. #16811257C22semidirect
64. #16811247C22semidirect
66. #16811224C22semidirect
68. #16811204C22semidirect
69. #16811202C22semidirect
71. #16811189C22semidirect
74. #16811186C22semidirect
76. #16811133C22semidirect
79. C2×#13133192C22semidirect
81. #121×D53C22semidirect
82. #16811102C22semidirect
83. #16811011C22semidirect
84. #16811010C22semidirect
85. #16811007C22semidirect
86. #16810998C22semidirect
87. #16810986C22semidirect
88. #16810985C22semidirect
89. #16810976C22semidirect
90. #16810966C22semidirect
91. #16810960C22semidirect
92. #16810958C22semidirect
93. #16810950C22semidirect
94. #16810946C22semidirect
95. #16810946C22semidirect
96. #16810940C22semidirect
97. #16810938C22semidirect
98. #16810938C22semidirect
99. #16810936C22semidirect
100. #16810929C22semidirect
101. #16810925C22semidirect
102. #16810915C22semidirect
103. #16810874C22semidirect
104. #16810870C22semidirect
105. #16810868C22semidirect
106. #16810867C22semidirect
107. #16810865C22semidirect
108. #16810860C22semidirect
109. #16810860C22semidirect
110. #16810858C22semidirect
111. #16810858C22semidirect
112. #16810858C22semidirect
113. #16810857C22semidirect
114. #16810852C22semidirect
115. #16810852C22semidirect
116. #16810850C22semidirect
117. #16810846C22semidirect
118. #16810844C22semidirect
119. #16810839C22semidirect
120. #16810838C22semidirect
121. #16810838C22semidirect
122. #16810837C22semidirect
123. #16810822C22semidirect
124. #16810822C22semidirect
125. #16810817C22semidirect
126. #16810816C22semidirect
127. #16810815C22semidirect
128. #16810787C22semidirect
129. #16810786C22semidirect
130. #16810786C22semidirect
131. #16810786C22semidirect
132. #16810781C22semidirect
133. #16810775C22semidirect
134. #16810775C22semidirect
135. #16810775C22semidirect
136. #16810774C22semidirect
137. #16810770C22semidirect
139. #16810769C22semidirect
140. #16810769C22semidirect
141. #16810769C22semidirect
142. #16810769C22semidirect
143. #16810769C22semidirect
144. #16810769C22semidirect
145. #16810769C22semidirect
146. #16810769C22semidirect
147. #16810769C22semidirect
148. #16810766C22semidirect
149. #16810766C22semidirect
150. #16810765C22semidirect
151. #16810765C22semidirect
152. #16810765C22semidirect
153. #16810761C22semidirect
154. #16810759C22semidirect
155. #16810758C22semidirect
156. #16810758C22semidirect
157. #16810758C22semidirect
158. #16810757C22semidirect
159. #16810756C22semidirect
160. #16810755C22semidirect
161. #16810755C22semidirect
162. #16810733C22semidirect
163. #16810723C22semidirect
164. #16810722C22semidirect
165. #16810720C22semidirect
166. #16810717C22semidirect
167. C4×#11719913C22semidirect
168. #16810703C22semidirect
169. #16810697C22semidirect
170. #16810695C22semidirect
171. #16810694C22semidirect
172. #16810693C22semidirect
173. C8×D212C22semidirect
174. C8×C22⋊D53C22semidirect
175. #16810686C22semidirect
176. #16810683C22semidirect
177. #16810682C22semidirect
178. #16810626C22semidirect
179. #16810622C22semidirect
180. #16810616C22semidirect
181. #16810616C22semidirect
182. #16810616C22semidirect
183. C2×#13133140C22semidirect
184. #16810589C22semidirect
185. #16810588C22semidirect
186. C2×#13133129C22semidirect
187. C22⋊C8×D53C22semidirect
188. C53×#547C22semidirect
189. D42×C53C22semidirect
190. C53×#486C22semidirect
191. C53×#480C22semidirect
192. C53×#480C22semidirect
193. C53×#474C22semidirect
194. C53×#466C22semidirect
195. C53×#466C22semidirect
196. C53×#459C22semidirect
197. C53×#447C22semidirect
198. C53×#447C22semidirect
199. C4×D8×C53C22semidirect
200. C8×D4×C53C22semidirect
201. C2×#102×C53C22semidirect
202. C2×#102×C53C22semidirect
970. #3294D53semidirect
1028. #547C2×D53semidirect
1040. D42C2×D53semidirect
1067. #486C2×D53semidirect
1078. #480C2×D53semidirect
1079. #480C2×D53semidirect
1083. #474C2×D53semidirect
1095. #466C2×D53semidirect
1096. #466C2×D53semidirect
1111. #459C2×D53semidirect
1146. #447C2×D53semidirect
1147. #447C2×D53semidirect
1155. C4×D8C2×D53semidirect
1163. C8×D4C2×D53semidirect
1172. C2×#102C2×D53semidirect
1173. C2×#102C2×D53semidirect
1178. C53#61639semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202890322
#202883752
#202868682
#202867322
#202867242
#202867002
#202866642
#202866002
#202865612
#202864722
#202864272
#202864012
#202863852
#202862612
#202862532
#202862072
#202861912
#202858122
#202857642
#202856152
#202855602
#202854752
#202854652
#202849822
#202849102
#202840242
#202839782
#202839282
C2×#168107692
#202837682
C53×#32942
#6163953