Finite Group Databasebeta

← #28270648

Subgroups — #28270648

Order 13568.

2100 conjugacy classes of subgroups.

The subgroup lattice has 1902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20289000C211yesmaximal, characteristic, complemented
2#20288380C211yesmaximal, characteristic, complemented
3#20287048C211yesmaximal, characteristic, complemented
4#20286981C211yesmaximal, characteristic, complemented
5#20286944C211yesmaximal, characteristic, complemented
6#20286911C211yesmaximal, characteristic, complemented
7#20286791C211yesmaximal, characteristic, complemented
8#20286784C211yesmaximal, characteristic, complemented
9#20286739C211yesmaximal, characteristic, complemented
10#20286716C211yesmaximal, characteristic, complemented
11#20286378C211yesmaximal, characteristic, complemented
12#20286365C211yesmaximal, characteristic, complemented
13#20286353C211yesmaximal, characteristic, complemented
14#20286308C211yesmaximal, characteristic, complemented
15#20286307C211yesmaximal, characteristic, complemented
16#20286268C211yesmaximal, characteristic, complemented
17#20286232C211yesmaximal, characteristic, complemented
18#20286213C211yesmaximal, characteristic, complemented
19#20285805C211yesmaximal, characteristic, complemented
20#20285783C211yesmaximal, characteristic, complemented
21#20285615C211yesmaximal, characteristic, complemented
22#20285604C211yesmaximal, characteristic, complemented
23#20285521C211yesmaximal, characteristic, complemented
24#20284972C211yesmaximal, characteristic, complemented
25#20284932C211yesmaximal, characteristic, complemented
26#20284014C211yesmaximal, characteristic, complemented
27#20283987C211yesmaximal, characteristic, complemented
28#20283977C211yesmaximal, characteristic, complemented
29#20283955C211yesmaximal, characteristic, complemented
30#20283775C211yesmaximal, characteristic, complemented
31C53×#3194C211yesmaximal, characteristic, complemented
32C2×#13133262C2211yescharacteristic
33C22×#11719945C2211yescharacteristic
34C2×#13133250C2211yescharacteristic, complemented
35C2×#13133250C2211yescharacteristic, complemented
36C2×#13133247C2211yescharacteristic, complemented
37C2×#13133246C2211yescharacteristic, complemented
38C2×#13133242C2211yescharacteristic, complemented
39C2×#13133241C2211yescharacteristic, complemented
40C2×#13133236C2211yescharacteristic, complemented
41C2×SD16×D53C2211yescharacteristic, complemented
42#16811376—21no—
43#16811370—21no—
44#16811341C2211yescharacteristic, complemented
45#16811332—21no—
46#16811331C2211yescharacteristic, complemented
47#16811325C2211yescharacteristic, complemented
48#16811322—21no—
49#16811312C2211yescharacteristic, complemented
50#16811291C2211yescharacteristic
51#16811291C2211yescharacteristic
52#16811286C2211yescharacteristic, complemented
53#16811280C2211yescharacteristic, complemented
54#16811279C2211yescharacteristic
55#16811279C2211yescharacteristic
56#16811279C2211yescharacteristic, complemented
57#16811272C2211yescharacteristic, complemented
58#16811270C2211yescharacteristic
59#16811270C2211yescharacteristic
60#16811263—21no—
61#16811263—21no—
62#16811257C2211yescharacteristic
63#16811257C2211yescharacteristic
64D4×C22⋊D53—21no—
65D4×C22⋊D53—21no—
66#16811240C2211yescharacteristic, complemented
67#16811238—21no—
68#16811233C2211yescharacteristic, complemented
69#16811215—21no—
70#16811208—21no—
71#16811208—21no—
72#16811204C2211yescharacteristic
73#16811202—21no—
74#16811202C2211yescharacteristic, complemented
75#16811196C2211yescharacteristic, complemented
76#16811190C2211yescharacteristic
77#16811189—21no—
78#16811134C2211yescharacteristic
79#16811133—21no—
80C2×#13133196C2211yescharacteristic, complemented
81#121×D53—21no—
82#16811104C2211yescharacteristic
83#16811014C2211yescharacteristic, complemented
84#16811011C2211yescharacteristic, complemented
85#16811006C2211yescharacteristic, complemented
86#16810994C2211yescharacteristic, complemented
87#16810986C2211yescharacteristic, complemented
88#16810981C2211yescharacteristic, complemented
89#16810976C2211yescharacteristic, complemented
90#16810968C2211yescharacteristic, complemented
91#16810967C2211yescharacteristic, complemented
92#16810960C2211yescharacteristic, complemented
93#16810958C2211yescharacteristic, complemented
94#16810958C2211yescharacteristic, complemented
95#16810949C2211yescharacteristic, complemented
96#16810938C2211yescharacteristic, complemented
97#16810934C2211yescharacteristic, complemented
98#16810934C2211yescharacteristic, complemented
99#16810933C2211yescharacteristic, complemented
100#16810922C2211yescharacteristic, complemented
101#16810917C2211yescharacteristic, complemented
102#16810902C2211yescharacteristic, complemented
103#16810882C2211yescharacteristic, complemented
104#16810872C2211yescharacteristic, complemented
105#16810870C2211yescharacteristic, complemented
106#16810868C2211yescharacteristic, complemented
107#16810867C2211yescharacteristic, complemented
108#16810867C2211yescharacteristic, complemented
109#16810867C2211yescharacteristic, complemented
110#16810867C2211yescharacteristic, complemented
111#16810865C2211yescharacteristic, complemented
112#16810863C2211yescharacteristic, complemented
113#16810858C2211yescharacteristic, complemented
114#16810853C2211yescharacteristic, complemented
115#16810844C2211yescharacteristic, complemented
116#16810844C2211yescharacteristic, complemented
117#16810844C2211yescharacteristic, complemented
118#16810843C2211yescharacteristic, complemented
119#16810837C2211yescharacteristic, complemented
120#16810836C2211yescharacteristic, complemented
121#16810832C2211yescharacteristic, complemented
122#16810827C2211yescharacteristic, complemented
123#16810822C2211yescharacteristic, complemented
124#16810822C2211yescharacteristic, complemented
125#16810821C2211yescharacteristic, complemented
126#16810816C2211yescharacteristic, complemented
127#16810787C2211yescharacteristic
128#16810787C2211yescharacteristic
129#16810787C2211yescharacteristic, complemented
130#16810787C2211yescharacteristic, complemented
131#16810786C2211yescharacteristic, complemented
132#16810786C2211yescharacteristic, complemented
133#16810786C2211yescharacteristic, complemented
134#16810783C2211yescharacteristic
135#16810783C2211yescharacteristic, complemented
136#16810783C2211yescharacteristic, complemented
137#16810783C2211yescharacteristic, complemented
138#16810782C2211yescharacteristic, complemented
139#16810781C2211yescharacteristic, complemented
140#16810781C2211yescharacteristic, complemented
141#16810780C2211yescharacteristic, complemented
142#16810776C2211yescharacteristic, complemented
143#16810776C2211yescharacteristic, complemented
144#16810775C2211yescharacteristic, complemented
145#16810775C2211yescharacteristic, complemented
146#16810774C2211yescharacteristic, complemented
147#16810774C2211yescharacteristic, complemented
148#16810772C2211yescharacteristic, complemented
149#16810769C2211yescharacteristic, complemented
150#16810766C2211yescharacteristic
151#16810766C2211yescharacteristic, complemented
152#16810766C2211yescharacteristic, complemented
153#16810766C2211yescharacteristic, complemented
154#16810765C2211yescharacteristic, complemented
155#16810763C2211yescharacteristic, complemented
156#16810761C2211yescharacteristic, complemented
157#16810761C2211yescharacteristic, complemented
158#16810755C2211yescharacteristic, complemented
159#16810729C2211yescharacteristic, complemented
160#16810726C2211yescharacteristic, complemented
161#16810722C2211yescharacteristic, complemented
162#16810720C2211yescharacteristic, complemented
163#16810717C2211yescharacteristic, complemented
164#16810715C2211yescharacteristic, complemented
165#16810710C2211yescharacteristic, complemented
166#16810703C2211yescharacteristic, complemented
167#16810699C2211yescharacteristic, complemented
168#16810699C2211yescharacteristic, complemented
169#16810698C2211yescharacteristic, complemented
170#16810698C2211yescharacteristic, complemented
171#16810697C2211yescharacteristic, complemented
172#16810697C2211yescharacteristic, complemented
173#16810692C2211yescharacteristic, complemented
174#16810692C2211yescharacteristic, complemented
175#16810681C2211yescharacteristic, complemented
176#16810681C2211yescharacteristic, complemented
177#16810631C2211yescharacteristic, complemented
178#16810627C2211yescharacteristic, complemented
179#16810626C2211yescharacteristic, complemented
180#16810625C2211yescharacteristic, complemented
181#16810625C2211yescharacteristic, complemented
182#16810621C2211yescharacteristic, complemented
183#16810616C2211yescharacteristic, complemented
184#102×D53C2211yescharacteristic, complemented
185#16810588C2211yescharacteristic, complemented
186#16810588C2211yescharacteristic, complemented
187#16810587C2211yescharacteristic, complemented
188C53×#525C2211yescharacteristic, complemented
189C2×#121×C53C2211yescharacteristic
190C53×#483C2211yescharacteristic, complemented
191C53×#482C2211yescharacteristic, complemented
192C53×#482C2211yescharacteristic, complemented
193C53×#480C2211yescharacteristic, complemented
194C53×#469C2211yescharacteristic, complemented
195C53×#469C2211yescharacteristic, complemented
196C53×#468C2211yescharacteristic, complemented
197C53×#468C2211yescharacteristic, complemented
198C53×#450C2211yescharacteristic, complemented
199C53×#449C2211yescharacteristic, complemented
200C53×#449C2211yescharacteristic, complemented
201C53×#447C2211yescharacteristic, complemented
202C53×#407C2211yescharacteristic, complemented
203#13133262—42no—
204#13133262—42no—
205C2×#11719945—21no—
206C2×#11719945—21no—
207C2×#11719945—42no—
208C2×#11719945—42no—
209C2×#11719945C2311yescharacteristic
210C2×#11719945C2311yescharacteristic
211C2×#11719945C2311yescharacteristic
212C2×#11719945C2311yescharacteristic
213C2×#11719945C2311yescharacteristic
214C2×#11719947—21no—
215C2×#11719947C2311yescharacteristic
216C2×#11719947C2311yescharacteristic
217C2×#11719947C2311yescharacteristic
218C22×Dic106C2311yescharacteristic
219C22×Dic106C2311yescharacteristic
220C2×Q8×D53C2311yescharacteristic
221C22×D212C2311yescharacteristic
222C22×C22⋊D53—21no—
223C22×C22⋊D53—21no—
224C22×C22⋊D53—21no—
225C2×D4×D53—21no—
226C2×D4×D53—21no—
227C2×D4×D53—21no—
228C2×D4×D53C2311yescharacteristic
229C2×D4×D53C2311yescharacteristic
230C22×C4×D53—21no—
231#13133250—42no—
232#13133250—42no—
233#13133247—42no—
234#13133246—42no—
235#13133242—42no—
236#13133241—42no—
237#13133236—42no—
238C2×Dic212C2311yescharacteristic
239C2×Dic212C2311yescharacteristic
240C2×Dic212C2311yescharacteristic
241C2×Dic212C2311yescharacteristic
242C2×#11719925C2311yescharacteristic
243C2×#11719925C2311yescharacteristic
244C2×#11719913C2311yescharacteristic
245C2×#11719913C2311yescharacteristic
246C2×#11719913C2311yescharacteristic
247C2×#11719913C2311yescharacteristic
248C2×#11719923C2311yescharacteristic
249C2×#11719923C2311yescharacteristic
250C2×#11719923C2311yescharacteristic
251C2×#11719923C2311yescharacteristic
252C2×#11719923C2311yescharacteristic
253C2×#11719923C2311yescharacteristic
254C2×#11719924C2311yescharacteristic
255C2×#11719924C2311yescharacteristic
256SD16×D53—42no—
257C2×#11719922C2311yescharacteristic
258C2×#11719922C2311yescharacteristic
259C2×#11719917C2311yescharacteristic
260C2×#11719917C2311yescharacteristic
261C2×#11719912C2311yescharacteristic
262C2×#11719912C2311yescharacteristic
263C2×C8×D53C2311yescharacteristic
264C2×C8×D53C2311yescharacteristic
265#13133216—21no—
266#13133216—21no—
267#13133216C2311yescharacteristic
268#13133215C2311yescharacteristic
269#13133213—21no—
270#13133213—21no—
271#13133213C2311yescharacteristic
272#13133213C2311yescharacteristic
273#13133211—21no—
274#13133210—21no—
275#13133210—21no—
276#13133210—21no—
277#13133210—21no—
278#13133210—21no—
279#13133210—21no—
280#13133209—21no—
281#13133208—21no—
282#13133208C2311yescharacteristic
283#13133207—21no—
284#13133207—21no—
285#13133204—21no—
286#13133204—21no—
287#13133204C2311yescharacteristic
288#13133204C2311yescharacteristic
289#13133204C2311yescharacteristic
290#13133203—21no—
291#13133203—21no—
292#13133203—21no—
293#13133203—21no—
294#13133203—21no—
295#13133202—21no—
296#13133201—21no—
297#13133200—21no—
298#13133200D411yescharacteristic
299#13133200D411yescharacteristic
300#13133199—21no—
301#13133199—21no—
302#13133199—21no—
303#13133199—21no—
304#13133198—21no—
305#13133198—21no—
306#13133197—21no—
307#13133197—21no—
308#13133197C2311yescharacteristic
309#13133197C2311yescharacteristic
310#13133197C2311yescharacteristic
311#13133197C2311yescharacteristic
312#13133196—21no—
313#13133196—21no—
314#13133196—21no—
315#13133196D411yescharacteristic
316#13133196D411yescharacteristic
317#13133196C2311yescharacteristic
318#13133196C2311yescharacteristic
319#13133196C2311yescharacteristic
320#13133196C2311yescharacteristic
321#13133195—21no—
322#13133194—21no—
323#13133194—21no—
324#13133194—21no—
325#13133194—21no—
326#13133194—21no—
327#13133194—21no—
328#13133194—21no—
329#13133193C2311yescharacteristic
330#13133192—21no—
331#13133192C2311yescharacteristic
332#13133192C2311yescharacteristic
333#13133191—21no—
334#13133191—21no—
335#13133191D411yescharacteristic
336#13133191D411yescharacteristic
337#13133190—21no—
338#13133190—21no—
339#13133190—21no—
340#13133190—21no—
341#13133190—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#13133188—21no—
351#13133188—21no—
352#13133188—21no—
353#13133188—21no—
354#13133188—21no—
355#13133188—21no—
356#13133188C2311yescharacteristic
357#13133187—21no—
358#13133187—21no—
359#13133186—21no—
360#13133186—21no—
361#13133186D411yescharacteristic
362#13133186D411yescharacteristic
363#13133185—21no—
364#13133185—21no—
365#13133185—21no—
366#13133185—21no—
367Q8×Dic53C2311yescharacteristic
368C4×Dic106—21no—
369#13133182C2311yescharacteristic
370#13133182C2311yescharacteristic
371#13133182C2311yescharacteristic
372#13133182C2311yescharacteristic
373D4×Dic53—21no—
374D4×Dic53—21no—
375D4×Dic53—21no—
376D4×Dic53—21no—
377D4×Dic53C2311yescharacteristic
378#13133179C2311yescharacteristic
379#13133179C2311yescharacteristic
380C4×C22⋊D53—21no—
381C4×C22⋊D53—21no—
382C4×C22⋊D53—21no—
383C4×C22⋊D53C2311yescharacteristic
384C4×C22⋊D53C2311yescharacteristic
385C4×C22⋊D53C2311yescharacteristic
386C4×C22⋊D53C2311yescharacteristic
387#13133177—21no—
388#13133177—21no—
389#13133177—21no—
390#13133177—21no—
391#13133176C2311yescharacteristic
392#13133175—21no—
393#13133175C2311yescharacteristic
394#13133174—21no—
395C2×C4⋊Dic53C2311yescharacteristic
396C2×#11719919—21no—
397C2×#11719919—21no—
398C4⋊C4×D53—21no—
399C4⋊C4×D53C2311yescharacteristic
400C2×C22⋊Dic53—21no—
401C22⋊C4×D53—21no—
402C22⋊C4×D53—21no—
403#13133150C2311yescharacteristic
404#13133150C2311yescharacteristic
405#13133150C2311yescharacteristic
406#13133150C2311yescharacteristic
407#13133146C2311yescharacteristic
408#13133146C2311yescharacteristic
409#13133146C2311yescharacteristic
410#13133146C2311yescharacteristic
411#13133142C2311yescharacteristic
412#13133142C2311yescharacteristic
413#13133142C2311yescharacteristic
414#13133142C2311yescharacteristic
415#13133140C2311yescharacteristic
416#13133140C2311yescharacteristic
417#13133140C2311yescharacteristic
418#13133140C2311yescharacteristic
419#13133140C2311yescharacteristic
420#13133140C2311yescharacteristic
421#13133140C2311yescharacteristic
422#13133140C2311yescharacteristic
423#13133139C2311yescharacteristic
424#13133139C2311yescharacteristic
425#13133139C2311yescharacteristic
426#13133139C2311yescharacteristic
427#13133138C2311yescharacteristic
428#13133138C2311yescharacteristic
429#13133138C2311yescharacteristic
430#13133138C2311yescharacteristic
431#13133137C2311yescharacteristic
432#13133137C2311yescharacteristic
433#13133137C2311yescharacteristic
434#13133137C2311yescharacteristic
435C22⋊#88322C2311yescharacteristic
436C22⋊#88322C2311yescharacteristic
437C22⋊#88322C2311yescharacteristic
438C22⋊#88322C2311yescharacteristic
439#13133129C2311yescharacteristic
440#13133129C2311yescharacteristic
441#13133129C2311yescharacteristic
442#13133129C2311yescharacteristic
443#13133127C2311yescharacteristic
444#13133127C2311yescharacteristic
445C8×Dic53C2311yescharacteristic
446C8×Dic53C2311yescharacteristic
447C2×#41×C53C2311yescharacteristic
448C22×D4×C53—21no—
449C22×D4×C53C2311yescharacteristic
450C23×C4×C53C2311yescharacteristic
451C2×SD16×C53C2311yescharacteristic
452C2×SD16×C53C2311yescharacteristic
453C2×D8×C53C2311yescharacteristic
454C2×D8×C53C2311yescharacteristic
455C2×M16×C53C2311yescharacteristic
456C2×M16×C53C2311yescharacteristic
457#123×C53—21no—
458C22⋊Q8×C53C2311yescharacteristic
459C22⋊Q8×C53C2311yescharacteristic
460#121×C53—21no—
461#121×C53—21no—
462#121×C53C2311yescharacteristic
463#121×C53C2311yescharacteristic
464#121×C53C2311yescharacteristic
465#121×C53C2311yescharacteristic
466#121×C53C2311yescharacteristic
467#121×C53C2311yescharacteristic
468#120×C53—21no—
469C4×D4×C53—21no—
470C4×D4×C53—21no—
471#117×C53C2311yescharacteristic
472C2×C4⋊C4×C53C2311yescharacteristic
473C2×C22⋊C4×C53—21no—
474#107×C53C2311yescharacteristic
475#107×C53C2311yescharacteristic
476#106×C53C2311yescharacteristic
477#106×C53C2311yescharacteristic
478#103×C53C2311yescharacteristic
479#103×C53C2311yescharacteristic
480#102×C53C2311yescharacteristic
481#102×C53C2311yescharacteristic
482#102×C53C2311yescharacteristic
483#102×C53C2311yescharacteristic
484#102×C53C2311yescharacteristic
485#102×C53C2311yescharacteristic
486C22⋊C8×C53C2311yescharacteristic
487C22⋊C8×C53C2311yescharacteristic
488C22⋊C8×C53C2311yescharacteristic
489C22⋊C8×C53C2311yescharacteristic
490C24×C53—21no—
491C24×C53C2×D411yescharacteristic
492C23×D53—21no—
493C23×D53—21no—
494C23×D53—21no—
495#41×C53—41no—
496#41×C53—41no—
497C2×Q8×C53C2411yescharacteristic
498C2×D4×C53—21no—
499C2×D4×C53—21no—
500C2×D4×C53—21no—
501C2×D4×C53—21no—
502C2×D4×C53—21no—
503C2×D4×C53—21no—
504C2×D4×C53—21no—
505C2×D4×C53—21no—
506C2×D4×C53—41no—
507C2×D4×C53—41no—
508C2×D4×C53—82no—
509C2×D4×C53C2411yescharacteristic
510C2×D4×C53C2411yescharacteristic
511C2×D4×C53C2411yescharacteristic
512C22×C4×C53—21no—
513C22×C4×C53—21no—
514C22×C4×C53—41no—
515C22×C4×C53—41no—
516C22×C4×C53C2×D411yescharacteristic
517C22×C4×C53C2×D411yescharacteristic
518C22×C4×C53C2×D411yescharacteristic
519C22×C4×C53C2411yescharacteristic
520C22×C4×C53C2411yescharacteristic
521C22×C4×C53C2411yescharacteristic
522C2×C22⋊D53—21no—
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—44no—
537C2×C22⋊D53—44no—
538C2×C22⋊D53—44no—
539C2×C22⋊D53C2×D411yescharacteristic
540C2×C22⋊D53C2×D411yescharacteristic
541C2×C22⋊D53C2×D411yescharacteristic
542C2×C22⋊D53C2×D411yescharacteristic
543C2×C22⋊D53C2×D411yescharacteristic
544C2×C22⋊D53C2×D411yescharacteristic
545C22×Dic53—21no—
546C22×Dic53—21no—
547C22×Dic53—21no—
548C22×Dic53—21no—
549C22×Dic53—21no—
550C22×Dic53—21no—
551C22×Dic53—21no—
552Q8×D53—41no—
553Q8×D53—41no—
554#11719947—22no—
555#11719947—22no—
556#11719947—41no—
557#11719947—41no—
558#11719947—41no—
559#11719947—41no—
560#11719947—44no—
561D4×D53—22no—
562D4×D53—22no—
563D4×D53—41no—
564D4×D53—41no—
565D4×D53—44no—
566D4×D53—82no—
567D4×D53—82no—
568#11719945—22no—
569#11719945—22no—
570#11719945—22no—
571#11719945—22no—
572#11719945—41no—
573#11719945—41no—
574#11719945—41no—
575#11719945—41no—
576#11719945—41no—
577#11719945—41no—
578#11719945—44no—
579#11719945—44no—
580C2×D212—22no—
581C2×D212—21no—
582C2×D212—21no—
583C2×D212—21no—
584C2×D212—41no—
585C2×D212C2×D411yescharacteristic
586C2×D212C2411yescharacteristic
587C2×D212C2411yescharacteristic
588C2×C4×D53—21no—
589C2×C4×D53—21no—
590C2×C4×D53—21no—
591C2×C4×D53—21no—
592C2×C4×D53—21no—
593C2×C4×D53—21no—
594C2×C4×D53—21no—
595C2×C4×D53—21no—
596C2×C4×D53—44no—
597C2×C4×D53C2411yescharacteristic
598C2×C4×D53C2411yescharacteristic
599C2×Dic106—22no—
600C2×Dic106—21no—
601C2×Dic106—21no—
602C2×Dic106—21no—
603C2×Dic106—21no—
604C2×Dic106—41no—
605C2×Dic106—41no—
606C2×Dic106—41no—
607C2×Dic106C2×D411yescharacteristic
608C2×Dic106C2411yescharacteristic
609C2×Dic106C2411yescharacteristic
610C2×Dic106C2411yescharacteristic
611C2×Dic106C2411yescharacteristic
612SD16×C53—41no—
613SD16×C53—41no—
614D8×C53—41no—
615D8×C53—41no—
616M16×C53—41no—
617M16×C53—41no—
618C2×C8×C53C2411yescharacteristic
619C2×C8×C53C2411yescharacteristic
620C2×C8×C53C2411yescharacteristic
621C2×C8×C53C2411yescharacteristic
622C4⋊C4×C53—21no—
623C4⋊C4×C53—21no—
624C4⋊C4×C53—21no—
625C4⋊C4×C53C2411yescharacteristic
626C4⋊C4×C53C2411yescharacteristic
627C4⋊C4×C53C2411yescharacteristic
628C4⋊C4×C53C2411yescharacteristic
629C22⋊C4×C53—21no—
630C22⋊C4×C53—21no—
631C22⋊C4×C53—21no—
632C22⋊C4×C53—21no—
633C22⋊C4×C53—21no—
634C22⋊C4×C53—21no—
635C22⋊C4×C53—21no—
636C22⋊C4×C53—21no—
637C22⋊C4×C53—21no—
638C42×C53—21no—
639C22⋊Dic53—21no—
640C22⋊Dic53—21no—
641C22⋊Dic53—21no—
642C22⋊Dic53—21no—
643C22⋊Dic53—21no—
644C22⋊Dic53—21no—
645C22⋊Dic53—21no—
646C22⋊Dic53—21no—
647C22⋊Dic53—21no—
648C22⋊Dic53—21no—
649C22⋊Dic53—21no—
650C22⋊Dic53—21no—
651C22⋊Dic53C2×D411yescharacteristic
652C22⋊Dic53C2×D411yescharacteristic
653C22⋊Dic53C2×D411yescharacteristic
654C22⋊Dic53C2×D411yescharacteristic
655C22⋊Dic53C2×D411yescharacteristic
656C22⋊Dic53C2×D411yescharacteristic
657#11719925—22no—
658#11719925—41no—
659#11719924—22no—
660#11719924—41no—
661#11719923—22no—
662#11719923—41no—
663#11719923—41no—
664#11719923—41no—
665#11719923—41no—
666#11719923—41no—
667#11719922—22no—
668#11719922—41no—
669#11719921—21no—
670#11719921—21no—
671#11719921—21no—
672#11719921—21no—
673#11719921—21no—
674#11719921—21no—
675#11719921—21no—
676#11719921—21no—
677#11719921—21no—
678#11719921—21no—
679#11719921C2×D411yescharacteristic
680#11719921C2×D411yescharacteristic
681#11719921C2×D411yescharacteristic
682#11719921C2×D411yescharacteristic
683C4⋊Dic53—21no—
684C4⋊Dic53—21no—
685C4⋊Dic53—21no—
686C4⋊Dic53—21no—
687C4⋊Dic53—21no—
688C4⋊Dic53—21no—
689C4⋊Dic53—21no—
690C4⋊Dic53C2×D411yescharacteristic
691C4⋊Dic53C2×D411yescharacteristic
692C4⋊Dic53C2411yescharacteristic
693C4⋊Dic53C2411yescharacteristic
694#11719919—21no—
695#11719919—21no—
696#11719919—21no—
697#11719919—21no—
698#11719919—21no—
699#11719919—21no—
700#11719919—21no—
701#11719919—21no—
702#11719919—21no—
703#11719919—21no—
704#11719919—21no—
705#11719919—21no—
706#11719919—21no—
707#11719919—21no—
708#11719919C2×D411yescharacteristic
709#11719919C2×D411yescharacteristic
710#11719919C2×D411yescharacteristic
711#11719919C2×D411yescharacteristic
712C4×Dic53—21no—
713C4×Dic53—21no—
714C4×Dic53—21no—
715C4×Dic53—21no—
716C4×Dic53—21no—
717C4×Dic53—21no—
718C4×Dic53C2411yescharacteristic
719C4×Dic53C2411yescharacteristic
720#11719917—41no—
721#11719917—41no—
722C2×#88322C2411yescharacteristic
723C2×#88322C2411yescharacteristic
724C2×#88322C2411yescharacteristic
725C2×#88322C2411yescharacteristic
726Dic212—22no—
727Dic212—22no—
728Dic212—41no—
729Dic212—41no—
730#11719913—22no—
731#11719913—22no—
732#11719913—41no—
733#11719913—41no—
734#11719912—41no—
735#11719912—41no—
736C8×D53—41no—
737C8×D53—41no—
738C23×C53—21no—
739C23×C53—21no—
740C23×C53—21no—
741C23×C53—41no—
742C23×C53—41no—
743C23×C53—41no—
744C23×C53—42no—
745C23×C53—81no—
746C23×C53—81no—
747C23×C53C22×D411yescharacteristic
748C23×C53C22×D411yescharacteristic
749C23×C53C22×D411yescharacteristic
750C22×D53—21no—
751C22×D53—21no—
752C22×D53—42no—
753C22×D53—42no—
754C22×D53—42no—
755C22×D53—42no—
756C22×D53—81no—
757C22×D53—81no—
758C22×D53—81no—
759C22×D53—81no—
760C22×D53—81no—
761C22×D53C22×D411yescharacteristic
762C22×D53C22×D411yescharacteristic
763Q8×C53—21no—
764Q8×C53—21no—
765D4×C53—21no—
766D4×C53—21no—
767D4×C53—21no—
768D4×C53—21no—
769D4×C53—21no—
770D4×C53—21no—
771D4×C53—42no—
772D4×C53—42no—
773D4×C53—42no—
774D4×C53—42no—
775D4×C53—81no—
776D4×C53—81no—
777D4×C53—81no—
778D4×C53—81no—
779C2×C4×C53—21no—
780C2×C4×C53—21no—
781C2×C4×C53—21no—
782C2×C4×C53—21no—
783C2×C4×C53—21no—
784C2×C4×C53—21no—
785C2×C4×C53—21no—
786C2×C4×C53—21no—
787C2×C4×C53—21no—
788C2×C4×C53—21no—
789C2×C4×C53—21no—
790C2×C4×C53—41no—
791C2×C4×C53—41no—
792C2×C4×C53—41no—
793C2×C4×C53—81no—
794C2×C4×C53—81no—
795C2×C4×C53C22×D411yescharacteristic
796C2×C4×C53C22×D411yescharacteristic
797C2×C4×C53C22×D411yescharacteristic
798C2×C4×C53C2511yescharacteristic
799C22⋊D53—24no—
800C22⋊D53—41no—
801C22⋊D53—41no—
802C22⋊D53—41no—
803C22⋊D53—41no—
804C22⋊D53—41no—
805C22⋊D53—41no—
806C22⋊D53—42no—
807C22⋊D53—42no—
808C22⋊D53—42no—
809C22⋊D53—42no—
810C22⋊D53—42no—
811C22⋊D53—42no—
812C22⋊D53—42no—
813C22⋊D53—81no—
814C22⋊D53—81no—
815C22⋊D53—81no—
816C22⋊D53—81no—
817C22⋊D53—81no—
818C22⋊D53—81no—
819C2×Dic53—21no—
820C2×Dic53—21no—
821C2×Dic53—21no—
822C2×Dic53—21no—
823C2×Dic53—21no—
824C2×Dic53—21no—
825C2×Dic53—42no—
826C2×Dic53—42no—
827C2×Dic53—42no—
828C2×Dic53—81no—
829C2×Dic53—81no—
830C2×Dic53—81no—
831C2×Dic53—81no—
832C2×Dic53C22×D411yescharacteristic
833C2×Dic53C22×D411yescharacteristic
834C2×Dic53C22×D411yescharacteristic
835C2×Dic53C22×D411yescharacteristic
836C2×Dic53C22×D411yescharacteristic
837C2×Dic53C22×D411yescharacteristic
838D212—21no—
839D212—21no—
840D212—21no—
841D212—41no—
842D212—42no—
843D212—81no—
844D212—81no—
845D212H(5,𝔽2)12yes—
846C4×D53—24no—
847C4×D53—21no—
848C4×D53—21no—
849C4×D53—21no—
850C4×D53—21no—
851C4×D53—42no—
852C4×D53—42no—
853C4×D53—42no—
854C4×D53—81no—
855C4×D53—81no—
856C4×D53—81no—
857C4×D53—81no—
858Dic106—21no—
859Dic106—21no—
860Dic106—21no—
861Dic106—21no—
862Dic106—21no—
863Dic106—21no—
864Dic106—21no—
865Dic106—41no—
866Dic106—42no—
867Dic106—81no—
868Dic106—81no—
869Dic106—81no—
870Dic106H(5,𝔽2)12yes—
871C8×C53—21no—
872C8×C53—21no—
873C8×C53—21no—
874C8×C53—21no—
875#88322—21no—
876#88322—21no—
877#88322—21no—
878#88322—21no—
879#61654—531nomaximal, Sylow
880C22×C53—21no—
881C22×C53—21no—
882C22×C53—21no—
883C22×C53—21no—
884C22×C53—21no—
885C22×C53—21no—
886C22×C53—21no—
887C22×C53—21no—
888C22×C53—21no—
889C22×C53—41no—
890C22×C53—41no—
891C22×C53—41no—
892C22×C53—41no—
893C22×C53—41no—
894C22×C53—41no—
895C22×C53—41no—
896C22×C53—41no—
897C22×C53—41no—
898C22×C53—82no—
899C22×C53—162no—
900C22×C53C23×D411yescharacteristic
901C2×D53—21no—
902C2×D53—21no—
903C2×D53—21no—
904C2×D53—21no—
905C2×D53—22no—
906C2×D53—21no—
907C2×D53—21no—
908C2×D53—41no—
909C2×D53—41no—
910C2×D53—41no—
911C2×D53—41no—
912C2×D53—41no—
913C2×D53—84no—
914C2×D53—162no—
915C2×D53—162no—
916C4×C53—21no—
917C4×C53—21no—
918C4×C53—21no—
919C4×C53—41no—
920C4×C53—41no—
921C4×C53—41no—
922C4×C53—41no—
923C4×C53—41no—
924C4×C53C2×H(5,𝔽2)11yescharacteristic
925C4×C53C2×H(5,𝔽2)11yescharacteristic
926Dic53—21no—
927Dic53—21no—
928Dic53—21no—
929Dic53—21no—
930Dic53—22no—
931Dic53—21no—
932Dic53—21no—
933Dic53—41no—
934Dic53—41no—
935Dic53—41no—
936Dic53—41no—
937Dic53—41no—
938#3541—531no—
939#3488—531no—
940#3333—531no—
941#3327—531no—
942#3324—531no—
943#3322—531no—
944#3314—531no—
945#3313—531no—
946#3310—531no—
947#3309—531no—
948#3278—531no—
949#3277—531no—
950#3275—531no—
951#3272—531no—
952#3271—531no—
953#3269—531no—
954#3266—531no—
955#3265—531no—
956#3224—531no—
957#3222—531no—
958#3203—531no—
959#3201—531no—
960#3194D5311yescharacteristic, complemented
961#3193—531no—
962#3124—531no—
963#3120—531no—
964#3012—531no—
965#3009—531no—
966#3007—531no—
967#3005—531no—
968#2978—531no—
969C2×C53—41no—
970C2×C53—41no—
971C2×C53—41no—
972C2×C53—81no—
973C2×C53—81no—
974C2×C53—81no—
975C2×C53#348411yescharacteristic
976C2×C53#358511yescharacteristic
977C2×C53#358611yescharacteristic
978D53—41no—
979D53—41no—
980D53—42no—
981D53—81no—
982C2×H(5,𝔽2)—531no—
983C22×#41—531no—
984C2×#137—531no—
985C2×#137—531no—
986C2×#137—531no—
987C2×#137—531no—
988C2×AGL(1,ℤ/8)—531no—
989C2×AGL(1,ℤ/8)—531no—
990C2×#135—531no—
991C22×SD16—531no—
992#563—1061no—
993#562—1061no—
994#556—531no—
995#554—531no—
996#554—1061no—
997#553—531no—
998#553—1061no—
999#552—531no—
1000#550—531no—
1001#550—531no—
1002D4×Q8—531no—
1003#548—531no—
1004#548—531no—
1005#548—531no—
1006#548—531no—
1007#547—531no—
1008#546—531no—
1009#546—531no—
1010#546—1061no—
1011#546—1061no—
1012D42—531no—
1013D42—531no—
1014D42—1061no—
1015D42—1061no—
1016#542—531no—
1017#542—1061no—
1018#541—531no—
1019#539—1061no—
1020#538—1061no—
1021#538—1061no—
1022#537—531no—
1023#537—531no—
1024#537—1061no—
1025#536—531no—
1026#535—531no—
1027#535—1061no—
1028#525—531no—
1029#525—1061no—
1030#525C2×D5311yescharacteristic, complemented
1031C2×C22⋊Q8—531no—
1032C2×#121—1061no—
1033C2×#121C2×D5311yescharacteristic
1034#520—531no—
1035#497—531no—
1036#496—531no—
1037#495—531no—
1038#492—531no—
1039#490—531no—
1040#489—531no—
1041#488—531no—
1042#486—531no—
1043#485—531no—
1044#484—531no—
1045#484—531no—
1046#484—531no—
1047#483C2×D5311yescharacteristic, complemented
1048#482—531no—
1049#482C2×D5311yescharacteristic, complemented
1050#482C2×D5311yescharacteristic, complemented
1051#480—531no—
1052#480—531no—
1053#480—531no—
1054#480C2×D5311yescharacteristic, complemented
1055#479—531no—
1056#478—531no—
1057#477—531no—
1058#474—531no—
1059#470—531no—
1060#469C2×D5311yescharacteristic, complemented
1061#469C2×D5311yescharacteristic, complemented
1062#468—531no—
1063#468—531no—
1064#468—531no—
1065#468—531no—
1066#468—531no—
1067#468—531no—
1068#468—531no—
1069#468C2×D5311yescharacteristic, complemented
1070#468C2×D5311yescharacteristic, complemented
1071#467—531no—
1072#467—531no—
1073#466—531no—
1074#465—531no—
1075#464—531no—
1076#464—531no—
1077#464—531no—
1078#464—531no—
1079#463—531no—
1080#463—531no—
1081#462—531no—
1082#461—531no—
1083#460—531no—
1084#460—531no—
1085#460—531no—
1086#459—531no—
1087#452—531no—
1088#452—531no—
1089#452—531no—
1090#452—531no—
1091#452—531no—
1092#452—531no—
1093#452—531no—
1094#452—531no—
1095#452—531no—
1096#452—531no—
1097#452—531no—
1098#452—531no—
1099#451—531no—
1100#451—531no—
1101#451—531no—
1102#450—531no—
1103#450—531no—
1104#450—531no—
1105#450—531no—
1106#450—531no—
1107#450—531no—
1108#450—531no—
1109#450C2×D5311yescharacteristic, complemented
1110#449—531no—
1111#449—531no—
1112#449—531no—
1113#449—531no—
1114#449—531no—
1115#449—531no—
1116#449C2×D5311yescharacteristic, complemented
1117#449C2×D5311yescharacteristic, complemented
1118#448—531no—
1119#448—531no—
1120#448—531no—
1121#447—531no—
1122#447C2×D5311yescharacteristic, complemented
1123#441—531no—
1124#440—531no—
1125#440—531no—
1126#440—531no—
1127C4×Q16—531no—
1128C4×Q16—531no—
1129C4×SD16—531no—
1130C4×D8—531no—
1131#436—531no—
1132#436—531no—
1133#436—531no—
1134#436—531no—
1135#435—531no—
1136#435—531no—
1137#435—531no—
1138#435—531no—
1139#433—531no—
1140#433—531no—
1141#419—531no—
1142#418—531no—
1143#418—531no—
1144#417—531no—
1145#417—531no—
1146#417—531no—
1147#416—531no—
1148C2×#102—531no—
1149#408—531no—
1150#408—531no—
1151#407—531no—
1152#407C2×D5311yescharacteristic, complemented
1153C53#6165411yescharacteristic, complemented, Sylow
1154H(5,𝔽2)—2122no—
1155H(5,𝔽2)—2122no—
1156C2×#41—531no—
1157C2×#41—531no—
1158C2×#41—531no—
1159C2×#41—531no—
1160C2×#41—531no—
1161C2×#41—531no—
1162C2×#41—531no—
1163C2×#41—531no—
1164C2×#41—1061no—
1165C2×#41—1061no—
1166C2×#41—1061no—
1167C2×#41—2122no—
1168C2×#41—2122no—
1169C2×#41C22×D5311yescharacteristic
1170C22×Q8—531no—
1171C22×Q8—531no—
1172C22×Q8—531no—
1173C22×D4—21no—
1174C22×D4—531no—
1175C22×D4—531no—
1176C22×D4—531no—
1177C22×D4—1061no—
1178C22×D4—1061no—
1179C22×D4—1061no—
1180C22×D4—1061no—
1181C22×D4—1061no—
1182C22×D4—1061no—
1183C22×D4C22×D5311yescharacteristic
1184C23×C4—1061no—
1185C23×C4C22×D5311yescharacteristic
1186#137—2122no—
1187#137—2122no—
1188#137—2122no—
1189#137—2122no—
1190AGL(1,ℤ/8)—2122no—
1191AGL(1,ℤ/8)—2122no—
1192#135—2122no—
1193C2×Q16—531no—
1194C2×Q16—531no—
1195C2×Q16—531no—
1196C2×Q16—531no—
1197C2×Q16—531no—
1198C2×Q16—531no—
1199C2×SD16—531no—
1200C2×SD16—531no—
1201C2×SD16—531no—
1202C2×SD16—531no—
1203C2×SD16—531no—
1204C2×SD16—531no—
1205C2×SD16—531no—
1206C2×SD16—531no—
1207C2×SD16—531no—
1208C2×SD16—531no—
1209C2×SD16—531no—
1210C2×SD16—531no—
1211C2×SD16—2122no—
1212C2×SD16C22×D5311yescharacteristic
1213C2×SD16C22×D5311yescharacteristic
1214C2×D8—531no—
1215C2×D8—531no—
1216C2×D8C22×D5311yescharacteristic
1217C2×D8C22×D5311yescharacteristic
1218C2×M16—531no—
1219C2×M16—531no—
1220C2×M16—531no—
1221C2×M16—531no—
1222C2×M16C22×D5311yescharacteristic
1223C2×M16C22×D5311yescharacteristic
1224C22×C8—531no—
1225C22×C8—531no—
1226C4⋊Q8—531no—
1227C4⋊Q8—531no—
1228C4⋊Q8—1061no—
1229C4⋊Q8—1061no—
1230#127—531no—
1231#127—531no—
1232#127—1061no—
1233#127—1061no—
1234#126—1061no—
1235#126—1061no—
1236#126—1061no—
1237#126—1061no—
1238#126—1061no—
1239#126—1061no—
1240#126—1061no—
1241#125—531no—
1242#125—1061no—
1243#125—1061no—
1244#125—1061no—
1245#125—1061no—
1246#124—531no—
1247#124—531no—
1248#124—531no—
1249#124—1061no—
1250#124—1061no—
1251#124—1061no—
1252#124—1061no—
1253#124—1061no—
1254#124—1061no—
1255#124—1061no—
1256#123—21no—
1257#123—531no—
1258#123—531no—
1259#123—1061no—
1260#123—1061no—
1261#123—1061no—
1262#123—1061no—
1263#123—1061no—
1264#123—1061no—
1265#123—1061no—
1266#123—1061no—
1267#123—1061no—
1268C22⋊Q8—531no—
1269C22⋊Q8—531no—
1270C22⋊Q8—531no—
1271C22⋊Q8—531no—
1272C22⋊Q8—531no—
1273C22⋊Q8—531no—
1274C22⋊Q8—531no—
1275C22⋊Q8—531no—
1276C22⋊Q8—531no—
1277C22⋊Q8—531no—
1278C22⋊Q8—531no—
1279C22⋊Q8—1061no—
1280C22⋊Q8—1061no—
1281C22⋊Q8—1061no—
1282C22⋊Q8—1061no—
1283C22⋊Q8—1061no—
1284C22⋊Q8—1061no—
1285C22⋊Q8—1061no—
1286C22⋊Q8—1061no—
1287C22⋊Q8—1061no—
1288C22⋊Q8—1061no—
1289C22⋊Q8—1061no—
1290C22⋊Q8—1061no—
1291C22⋊Q8—1061no—
1292C22⋊Q8C22×D5311yescharacteristic
1293C22⋊Q8C22×D5311yescharacteristic
1294#121—21no—
1295#121—21no—
1296#121—531no—
1297#121—531no—
1298#121—531no—
1299#121—531no—
1300#121—531no—
1301#121—1061no—
1302#121—1061no—
1303#121—1061no—
1304#121—1061no—
1305#121—1061no—
1306#121—1061no—
1307#121—1061no—
1308#121—1061no—
1309#121—1061no—
1310#121—1061no—
1311#121—1061no—
1312#121—1061no—
1313#121—1061no—
1314#121—1061no—
1315#121—1061no—
1316#121—1061no—
1317#121—1061no—
1318#121—1061no—
1319#121—1061no—
1320#121—1061no—
1321#121—1061no—
1322#121—1061no—
1323#121C22×D5311yescharacteristic
1324#121C22×D5311yescharacteristic
1325#121C22×D5311yescharacteristic
1326#121C22×D5311yescharacteristic
1327#121C22×D5311yescharacteristic
1328#121C22×D5311yescharacteristic
1329#120—21no—
1330#120—531no—
1331#120—531no—
1332#120—1061no—
1333#120—1061no—
1334#120—1061no—
1335#120—1061no—
1336#120—1061no—
1337#120—1061no—
1338#120—1061no—
1339#120—1061no—
1340C4×Q8—531no—
1341C4×Q8—531no—
1342C4×Q8—531no—
1343C4×Q8—531no—
1344C4×Q8—531no—
1345C4×Q8—1061no—
1346C4×D4—21no—
1347C4×D4—21no—
1348C4×D4—531no—
1349C4×D4—531no—
1350C4×D4—531no—
1351C4×D4—531no—
1352C4×D4—531no—
1353C4×D4—531no—
1354C4×D4—531no—
1355C4×D4—1061no—
1356C4×D4—1061no—
1357C4×D4—1061no—
1358C4×D4—1061no—
1359C4×D4—1061no—
1360C4×D4—1061no—
1361C4×D4—1061no—
1362C4×D4—1061no—
1363C4×D4—1061no—
1364C4×D4—1061no—
1365C4×D4—1061no—
1366#117—531no—
1367#117—531no—
1368#117—1061no—
1369#117—1061no—
1370#117C22×D5311yescharacteristic
1371C2×C4⋊C4—531no—
1372C2×C4⋊C4—531no—
1373C2×C4⋊C4—1061no—
1374C2×C4⋊C4—1061no—
1375C2×C4⋊C4—1061no—
1376C2×C4⋊C4C22×D5311yescharacteristic
1377C2×C22⋊C4—21no—
1378C2×C22⋊C4—1061no—
1379C2×C22⋊C4—1061no—
1380C2×C22⋊C4—1061no—
1381#107—531no—
1382#107—531no—
1383#107—531no—
1384#107—531no—
1385#107C22×D5311yescharacteristic
1386#107C22×D5311yescharacteristic
1387#106C22×D5311yescharacteristic
1388#106C22×D5311yescharacteristic
1389C4⋊C8—531no—
1390C4⋊C8—531no—
1391C4⋊C8—531no—
1392C4⋊C8—531no—
1393#103—531no—
1394#103—531no—
1395#103—531no—
1396#103—531no—
1397#103—531no—
1398#103—531no—
1399#103—531no—
1400#103—531no—
1401#103—531no—
1402#103—531no—
1403#103—531no—
1404#103—531no—
1405#103C22×D5311yescharacteristic
1406#103C22×D5311yescharacteristic
1407#102—531no—
1408#102—531no—
1409#102—531no—
1410#102—531no—
1411#102—531no—
1412#102—531no—
1413#102—531no—
1414#102—531no—
1415#102—531no—
1416#102—531no—
1417#102—531no—
1418#102—531no—
1419#102C22×D5311yescharacteristic
1420#102C22×D5311yescharacteristic
1421#102C22×D5311yescharacteristic
1422#102C22×D5311yescharacteristic
1423#102C22×D5311yescharacteristic
1424#102C22×D5311yescharacteristic
1425C22⋊C8—531no—
1426C22⋊C8—531no—
1427C22⋊C8—531no—
1428C22⋊C8—531no—
1429C22⋊C8—531no—
1430C22⋊C8—531no—
1431C22⋊C8—531no—
1432C22⋊C8—531no—
1433C22⋊C8C22×D5311yescharacteristic
1434C22⋊C8C22×D5311yescharacteristic
1435C22⋊C8C22×D5311yescharacteristic
1436C22⋊C8C22×D5311yescharacteristic
1437#97—531no—
1438#97—531no—
1439C4×C8—531no—
1440C4×C8—531no—
1441C24—21no—
1442C24—1061no—
1443C24—1061no—
1444C24—1061no—
1445C24D4×D5311yescharacteristic
1446#41—41no—
1447#41—41no—
1448#41—1062no—
1449#41—1062no—
1450#41—1062no—
1451#41—1062no—
1452#41—1062no—
1453#41—1062no—
1454#41—2121no—
1455#41—2121no—
1456#41—2121no—
1457#41—2121no—
1458#41—2121no—
1459#41—2121no—
1460#41—2124no—
1461#41—2124no—
1462#41—2121no—
1463#41—2121no—
1464#41—2121no—
1465#41—2121no—
1466#41—2124no—
1467C2×Q8—531no—
1468C2×Q8—531no—
1469C2×Q8—531no—
1470C2×Q8—531no—
1471C2×Q8—531no—
1472C2×Q8—1061no—
1473C2×Q8—1061no—
1474C2×Q8—1062no—
1475C2×Q8—1061no—
1476C2×Q8—1061no—
1477C2×Q8—2121no—
1478C2×Q8—2121no—
1479C2×Q8—2121no—
1480C2×Q8—2121no—
1481C2×Q8—2121no—
1482C2×Q8C23×D5311yescharacteristic
1483C2×D4—21no—
1484C2×D4—21no—
1485C2×D4—21no—
1486C2×D4—21no—
1487C2×D4—21no—
1488C2×D4—21no—
1489C2×D4—21no—
1490C2×D4—21no—
1491C2×D4—41no—
1492C2×D4—41no—
1493C2×D4—82no—
1494C2×D4—531no—
1495C2×D4—531no—
1496C2×D4—531no—
1497C2×D4—531no—
1498C2×D4—531no—
1499C2×D4—531no—
1500C2×D4—531no—
1501C2×D4—531no—
1502C2×D4—531no—
1503C2×D4—1062no—
1504C2×D4—1061no—
1505C2×D4—1061no—
1506C2×D4—1061no—
1507C2×D4—1061no—
1508C2×D4—1061no—
1509C2×D4—1061no—
1510C2×D4—1061no—
1511C2×D4—1061no—
1512C2×D4—1062no—
1513C2×D4—1062no—
1514C2×D4—1061no—
1515C2×D4—1061no—
1516C2×D4—1061no—
1517C2×D4—1061no—
1518C2×D4—1061no—
1519C2×D4—1061no—
1520C2×D4—1061no—
1521C2×D4—1061no—
1522C2×D4—1061no—
1523C2×D4—4242no—
1524C2×D4—4242no—
1525C2×D4—2121no—
1526C2×D4—2121no—
1527C2×D4—2121no—
1528C2×D4—2124no—
1529C2×D4—2124no—
1530C2×D4—2124no—
1531C2×D4—2124no—
1532C2×D4C23×D5311yescharacteristic
1533C2×D4C23×D5311yescharacteristic
1534C2×D4C23×D5311yescharacteristic
1535C22×C4—21no—
1536C22×C4—21no—
1537C22×C4—41no—
1538C22×C4—41no—
1539C22×C4—531no—
1540C22×C4—531no—
1541C22×C4—1061no—
1542C22×C4—1061no—
1543C22×C4—1061no—
1544C22×C4—1061no—
1545C22×C4—1061no—
1546C22×C4—1061no—
1547C22×C4—1061no—
1548C22×C4—1061no—
1549C22×C4—1061no—
1550C22×C4—1061no—
1551C22×C4—1061no—
1552C22×C4—1061no—
1553C22×C4—1061no—
1554C22×C4—1061no—
1555C22×C4—1061no—
1556C22×C4—2124no—
1557C22×C4D4×D5311yescharacteristic
1558C22×C4D4×D5311yescharacteristic
1559C22×C4D4×D5311yescharacteristic
1560C22×C4C23×D5311yescharacteristic
1561C22×C4C23×D5311yescharacteristic
1562C22×C4C23×D5311yescharacteristic
1563Q16—1062no—
1564Q16—1062no—
1565Q16—1062no—
1566Q16—2121no—
1567Q16—2121no—
1568Q16—2121no—
1569SD16—41no—
1570SD16—41no—
1571SD16—1062no—
1572SD16—1062no—
1573SD16—1062no—
1574SD16—1062no—
1575SD16—2121no—
1576SD16—2121no—
1577SD16—2121no—
1578SD16—2121no—
1579SD16—2121no—
1580SD16—2121no—
1581SD16—2121no—
1582SD16—2121no—
1583D8—41no—
1584D8—41no—
1585D8—1062no—
1586D8—2121no—
1587M16—41no—
1588M16—41no—
1589M16—2121no—
1590M16—2121no—
1591M16—2121no—
1592M16—2121no—
1593C2×C8—531no—
1594C2×C8—531no—
1595C2×C8—531no—
1596C2×C8—531no—
1597C2×C8—2121no—
1598C2×C8—2121no—
1599C2×C8C23×D5311yescharacteristic
1600C2×C8C23×D5311yescharacteristic
1601C2×C8C23×D5311yescharacteristic
1602C2×C8C23×D5311yescharacteristic
1603C4⋊C4—21no—
1604C4⋊C4—21no—
1605C4⋊C4—21no—
1606C4⋊C4—531no—
1607C4⋊C4—531no—
1608C4⋊C4—531no—
1609C4⋊C4—531no—
1610C4⋊C4—531no—
1611C4⋊C4—531no—
1612C4⋊C4—531no—
1613C4⋊C4—531no—
1614C4⋊C4—1061no—
1615C4⋊C4—1061no—
1616C4⋊C4—1061no—
1617C4⋊C4—1061no—
1618C4⋊C4—1061no—
1619C4⋊C4—1061no—
1620C4⋊C4—1061no—
1621C4⋊C4—1061no—
1622C4⋊C4—1061no—
1623C4⋊C4—1061no—
1624C4⋊C4—1061no—
1625C4⋊C4—1061no—
1626C4⋊C4—1061no—
1627C4⋊C4—1061no—
1628C4⋊C4—1061no—
1629C4⋊C4—1061no—
1630C4⋊C4—1061no—
1631C4⋊C4—1061no—
1632C4⋊C4—1061no—
1633C4⋊C4—1061no—
1634C4⋊C4—1061no—
1635C4⋊C4C23×D5311yescharacteristic
1636C4⋊C4C23×D5311yescharacteristic
1637C4⋊C4C23×D5311yescharacteristic
1638C4⋊C4C23×D5311yescharacteristic
1639C22⋊C4—21no—
1640C22⋊C4—21no—
1641C22⋊C4—21no—
1642C22⋊C4—21no—
1643C22⋊C4—21no—
1644C22⋊C4—21no—
1645C22⋊C4—21no—
1646C22⋊C4—21no—
1647C22⋊C4—21no—
1648C22⋊C4—531no—
1649C22⋊C4—531no—
1650C22⋊C4—531no—
1651C22⋊C4—531no—
1652C22⋊C4—531no—
1653C22⋊C4—531no—
1654C22⋊C4—531no—
1655C22⋊C4—531no—
1656C22⋊C4—531no—
1657C22⋊C4—531no—
1658C22⋊C4—1061no—
1659C22⋊C4—1061no—
1660C22⋊C4—1061no—
1661C22⋊C4—1061no—
1662C22⋊C4—1061no—
1663C22⋊C4—1061no—
1664C22⋊C4—1061no—
1665C22⋊C4—1061no—
1666C22⋊C4—1061no—
1667C22⋊C4—1061no—
1668C22⋊C4—1061no—
1669C22⋊C4—1061no—
1670C22⋊C4—1061no—
1671C22⋊C4—1061no—
1672C22⋊C4—1061no—
1673C22⋊C4—1061no—
1674C22⋊C4—1061no—
1675C22⋊C4—1061no—
1676C22⋊C4—1061no—
1677C22⋊C4—1061no—
1678C22⋊C4—1061no—
1679C22⋊C4—1061no—
1680C42—21no—
1681C42—531no—
1682C42—531no—
1683C42—1061no—
1684C42—1061no—
1685C42—1061no—
1686C42—1061no—
1687C42—1061no—
1688C42—1061no—
1689C23—21no—
1690C23—21no—
1691C23—21no—
1692C23—41no—
1693C23—41no—
1694C23—41no—
1695C23—42no—
1696C23—81no—
1697C23—81no—
1698C23—531no—
1699C23—531no—
1700C23—1061no—
1701C23—1061no—
1702C23—4241no—
1703C23—4241no—
1704C23—4241no—
1705C23—4241no—
1706C23—4241no—
1707C23—2122no—
1708C23—2122no—
1709C23—2122no—
1710C23—2122no—
1711C23C2×D4×D5311yescharacteristic
1712C23C2×D4×D5311yescharacteristic
1713C23C2×D4×D5311yescharacteristic
1714Q8—21no—
1715Q8—21no—
1716Q8—532no—
1717Q8—1061no—
1718Q8—1061no—
1719Q8—1061no—
1720Q8—1061no—
1721Q8—1061no—
1722Q8—1061no—
1723Q8—1061no—
1724Q8—4241no—
1725Q8—4241no—
1726Q8—4241no—
1727Q8—2121no—
1728Q8—2122no—
1729D4—21no—
1730D4—21no—
1731D4—21no—
1732D4—21no—
1733D4—21no—
1734D4—21no—
1735D4—42no—
1736D4—42no—
1737D4—42no—
1738D4—42no—
1739D4—81no—
1740D4—81no—
1741D4—81no—
1742D4—81no—
1743D4—532no—
1744D4—1064no—
1745D4—1061no—
1746D4—1061no—
1747D4—1061no—
1748D4—4241no—
1749D4—4241no—
1750D4—4241no—
1751D4—4241no—
1752D4—4241no—
1753D4—4241no—
1754D4—4241no—
1755D4—4241no—
1756D4—2121no—
1757D4—2122no—
1758D4—2121no—
1759D4—2121no—
1760D4—2121no—
1761D4—2121no—
1762D4—2121no—
1763D4—2121no—
1764D4—2122no—
1765D4—2122no—
1766D4—2122no—
1767D4—2122no—
1768D4—2122no—
1769D4—2122no—
1770D4—2122no—
1771C2×C4—21no—
1772C2×C4—21no—
1773C2×C4—21no—
1774C2×C4—21no—
1775C2×C4—21no—
1776C2×C4—21no—
1777C2×C4—21no—
1778C2×C4—21no—
1779C2×C4—21no—
1780C2×C4—21no—
1781C2×C4—21no—
1782C2×C4—41no—
1783C2×C4—41no—
1784C2×C4—41no—
1785C2×C4—81no—
1786C2×C4—81no—
1787C2×C4—531no—
1788C2×C4—531no—
1789C2×C4—531no—
1790C2×C4—531no—
1791C2×C4—531no—
1792C2×C4—531no—
1793C2×C4—1064no—
1794C2×C4—1061no—
1795C2×C4—1061no—
1796C2×C4—1061no—
1797C2×C4—1061no—
1798C2×C4—1061no—
1799C2×C4—1061no—
1800C2×C4—1061no—
1801C2×C4—1061no—
1802C2×C4—1061no—
1803C2×C4—1061no—
1804C2×C4—4241no—
1805C2×C4—4241no—
1806C2×C4—4241no—
1807C2×C4—4241no—
1808C2×C4—4241no—
1809C2×C4—4241no—
1810C2×C4—4241no—
1811C2×C4—4241no—
1812C2×C4—2122no—
1813C2×C4—2122no—
1814C2×C4—2122no—
1815C2×C4—2122no—
1816C2×C4—2122no—
1817C2×C4—2122no—
1818C2×C4C2×D4×D5311yescharacteristic
1819C2×C4C2×D4×D5311yescharacteristic
1820C2×C4C2×D4×D5311yescharacteristic
1821C2×C4C24×D5311yescharacteristic
1822C8—21no—
1823C8—21no—
1824C8—21no—
1825C8—21no—
1826C8—1061no—
1827C8—1061no—
1828C8—1061no—
1829C8—1061no—
1830C22—21no—
1831C22—21no—
1832C22—21no—
1833C22—21no—
1834C22—21no—
1835C22—21no—
1836C22—21no—
1837C22—21no—
1838C22—21no—
1839C22—41no—
1840C22—41no—
1841C22—41no—
1842C22—41no—
1843C22—41no—
1844C22—41no—
1845C22—41no—
1846C22—41no—
1847C22—41no—
1848C22—82no—
1849C22—162no—
1850C22—8482no—
1851C22—8482no—
1852C22—1061no—
1853C22—1062no—
1854C22—1061no—
1855C22—1061no—
1856C22—1061no—
1857C22—1061no—
1858C22—1061no—
1859C22—4244no—
1860C22—2121no—
1861C22—2121no—
1862C22—2121no—
1863C22—2121no—
1864C22—2121no—
1865C22C22×D4×D5311yescharacteristic
1866C4—21no—
1867C4—21no—
1868C4—21no—
1869C4—41no—
1870C4—41no—
1871C4—41no—
1872C4—41no—
1873C4—41no—
1874C4—1061no—
1875C4—1061no—
1876C4—1062no—
1877C4—1061no—
1878C4—1061no—
1879C4—1061no—
1880C4—1061no—
1881C4—2121no—
1882C4—2121no—
1883C4—2121no—
1884C4—2121no—
1885C4—2121no—
1886C4H(5,𝔽2)×D5311yescharacteristic
1887C4H(5,𝔽2)×D5311yescharacteristic
1888C2—41no—
1889C2—41no—
1890C2—41no—
1891C2—81no—
1892C2—81no—
1893C2—81no—
1894C2—4241no—
1895C2—2121no—
1896C2—2121no—
1897C2—2122no—
1898C2#2028834711yescharacteristic
1899C2#2028949111yescharacteristic
1900C2#2028949911yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3194C2
socleC22×C53C23×D4
hypercenter#3194D53
hypocenterC53#61654
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3194

Complements

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

NH ≅ G/Ntype
1. #20289000C2semidirect
2. #20288380C2semidirect
3. #20287048C2semidirect
4. #20286981C2semidirect
5. #20286944C2semidirect
6. #20286911C2semidirect
7. #20286791C2semidirect
8. #20286784C2semidirect
9. #20286739C2semidirect
10. #20286716C2semidirect
11. #20286378C2semidirect
12. #20286365C2semidirect
13. #20286353C2semidirect
14. #20286308C2semidirect
15. #20286307C2semidirect
16. #20286268C2semidirect
17. #20286232C2semidirect
18. #20286213C2semidirect
19. #20285805C2semidirect
20. #20285783C2semidirect
21. #20285615C2semidirect
22. #20285604C2semidirect
23. #20285521C2semidirect
24. #20284972C2semidirect
25. #20284932C2semidirect
26. #20284014C2semidirect
27. #20283987C2semidirect
28. #20283977C2semidirect
29. #20283955C2semidirect
30. #20283775C2semidirect
31. C53×#3194C2semidirect
34. C2×#13133250C22semidirect
35. C2×#13133250C22semidirect
36. C2×#13133247C22semidirect
37. C2×#13133246C22semidirect
38. C2×#13133242C22semidirect
39. C2×#13133241C22semidirect
40. C2×#13133236C22semidirect
41. C2×SD16×D53C22semidirect
44. #16811341C22semidirect
46. #16811331C22semidirect
47. #16811325C22semidirect
49. #16811312C22semidirect
52. #16811286C22semidirect
53. #16811280C22semidirect
56. #16811279C22semidirect
57. #16811272C22semidirect
66. #16811240C22semidirect
68. #16811233C22semidirect
74. #16811202C22semidirect
75. #16811196C22semidirect
80. C2×#13133196C22semidirect
83. #16811014C22semidirect
84. #16811011C22semidirect
85. #16811006C22semidirect
86. #16810994C22semidirect
87. #16810986C22semidirect
88. #16810981C22semidirect
89. #16810976C22semidirect
90. #16810968C22semidirect
91. #16810967C22semidirect
92. #16810960C22semidirect
93. #16810958C22semidirect
94. #16810958C22semidirect
95. #16810949C22semidirect
96. #16810938C22semidirect
97. #16810934C22semidirect
98. #16810934C22semidirect
99. #16810933C22semidirect
100. #16810922C22semidirect
101. #16810917C22semidirect
102. #16810902C22semidirect
103. #16810882C22semidirect
104. #16810872C22semidirect
105. #16810870C22semidirect
106. #16810868C22semidirect
107. #16810867C22semidirect
108. #16810867C22semidirect
109. #16810867C22semidirect
110. #16810867C22semidirect
111. #16810865C22semidirect
112. #16810863C22semidirect
113. #16810858C22semidirect
114. #16810853C22semidirect
115. #16810844C22semidirect
116. #16810844C22semidirect
117. #16810844C22semidirect
118. #16810843C22semidirect
119. #16810837C22semidirect
120. #16810836C22semidirect
121. #16810832C22semidirect
122. #16810827C22semidirect
123. #16810822C22semidirect
124. #16810822C22semidirect
125. #16810821C22semidirect
126. #16810816C22semidirect
129. #16810787C22semidirect
130. #16810787C22semidirect
131. #16810786C22semidirect
132. #16810786C22semidirect
133. #16810786C22semidirect
135. #16810783C22semidirect
136. #16810783C22semidirect
137. #16810783C22semidirect
138. #16810782C22semidirect
139. #16810781C22semidirect
140. #16810781C22semidirect
141. #16810780C22semidirect
142. #16810776C22semidirect
143. #16810776C22semidirect
144. #16810775C22semidirect
145. #16810775C22semidirect
146. #16810774C22semidirect
147. #16810774C22semidirect
148. #16810772C22semidirect
149. #16810769C22semidirect
151. #16810766C22semidirect
152. #16810766C22semidirect
153. #16810766C22semidirect
154. #16810765C22semidirect
155. #16810763C22semidirect
156. #16810761C22semidirect
157. #16810761C22semidirect
158. #16810755C22semidirect
159. #16810729C22semidirect
160. #16810726C22semidirect
161. #16810722C22semidirect
162. #16810720C22semidirect
163. #16810717C22semidirect
164. #16810715C22semidirect
165. #16810710C22semidirect
166. #16810703C22semidirect
167. #16810699C22semidirect
168. #16810699C22semidirect
169. #16810698C22semidirect
170. #16810698C22semidirect
171. #16810697C22semidirect
172. #16810697C22semidirect
173. #16810692C22semidirect
174. #16810692C22semidirect
175. #16810681C22semidirect
176. #16810681C22semidirect
177. #16810631C22semidirect
178. #16810627C22semidirect
179. #16810626C22semidirect
180. #16810625C22semidirect
181. #16810625C22semidirect
182. #16810621C22semidirect
183. #16810616C22semidirect
184. #102×D53C22semidirect
185. #16810588C22semidirect
186. #16810588C22semidirect
187. #16810587C22semidirect
188. C53×#525C22semidirect
190. C53×#483C22semidirect
191. C53×#482C22semidirect
192. C53×#482C22semidirect
193. C53×#480C22semidirect
194. C53×#469C22semidirect
195. C53×#469C22semidirect
196. C53×#468C22semidirect
197. C53×#468C22semidirect
198. C53×#450C22semidirect
199. C53×#449C22semidirect
200. C53×#449C22semidirect
201. C53×#447C22semidirect
202. C53×#407C22semidirect
960. #3194D53semidirect
1030. #525C2×D53semidirect
1047. #483C2×D53semidirect
1049. #482C2×D53semidirect
1050. #482C2×D53semidirect
1054. #480C2×D53semidirect
1060. #469C2×D53semidirect
1061. #469C2×D53semidirect
1069. #468C2×D53semidirect
1070. #468C2×D53semidirect
1109. #450C2×D53semidirect
1116. #449C2×D53semidirect
1117. #449C2×D53semidirect
1122. #447C2×D53semidirect
1152. #407C2×D53semidirect
1153. C53#61654semidirect

Maximal subgroups

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

subgroupindex
#202890002
#202883802
#202870482
#202869812
#202869442
#202869112
#202867912
#202867842
#202867392
#202867162
#202863782
#202863652
#202863532
#202863082
#202863072
#202862682
#202862322
#202862132
#202858052
#202857832
#202856152
#202856042
#202855212
#202849722
#202849322
#202840142
#202839872
#202839772
#202839552
#202837752
C53×#31942
#6165453