Finite Group Databasebeta

← #28270094

Subgroups — #28270094

Order 13568.

2050 conjugacy classes of subgroups.

The subgroup lattice has 1868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20288985C211yesmaximal, characteristic, complemented
2#20288386C211yesmaximal, characteristic, complemented
3#20287003C211yesmaximal, characteristic, complemented
4#20286996C211yesmaximal, characteristic, complemented
5#20286904C211yesmaximal, characteristic, complemented
6#20286780C211yesmaximal, characteristic, complemented
7#20286752C211yesmaximal, characteristic, complemented
8#20286639C211yesmaximal, characteristic, complemented
9#20286629C211yesmaximal, characteristic, complemented
10#20286453C211yesmaximal, characteristic, complemented
11#20286428C211yesmaximal, characteristic, complemented
12#20286342C211yesmaximal, characteristic, complemented
13#20286326C211yesmaximal, characteristic, complemented
14#20286290C211yesmaximal, characteristic, complemented
15#20286268C211yesmaximal, characteristic, complemented
16#20286242C211yesmaximal, characteristic, complemented
17#20286232C211yesmaximal, characteristic, complemented
18#20285825C211yesmaximal, characteristic, complemented
19#20285821C211yesmaximal, characteristic, complemented
20#20285595C211yesmaximal, characteristic, complemented
21#20285560C211yesmaximal, characteristic, complemented
22#20285540C211yesmaximal, characteristic, complemented
23#20285500C211yesmaximal, characteristic, complemented
24#20284996C211yesmaximal, characteristic, complemented
25#20284982C211yesmaximal, characteristic, complemented
26#20284013C211yesmaximal, characteristic, complemented
27#20283998C211yesmaximal, characteristic, complemented
28#20283959C211yesmaximal, characteristic, complemented
29#20283928C211yesmaximal, characteristic, complemented
30#20283762C211yesmaximal, characteristic, complemented
31C53×#3319C211yesmaximal, characteristic, complemented
32C2×#13133264C2211yescharacteristic
33C22×#11719947C2211yescharacteristic, complemented
34C2×#13133250C2211yescharacteristic
35C2×#13133247C2211yescharacteristic, complemented
36C2×#13133243C2211yescharacteristic
37C2×#13133241C2211yescharacteristic, complemented
38C2×#13133236C2211yescharacteristic
39C2×#13133236C2211yescharacteristic
40C22×Dic212C2211yescharacteristic, complemented
41C2×SD16×D53C2211yescharacteristic, complemented
42#16811365—21no—
43#16811361—21no—
44#16811355—21no—
45#16811347C2211yescharacteristic, complemented
46#16811341C2211yescharacteristic
47#16811336C2211yescharacteristic, complemented
48#16811297—21no—
49D4×Dic106C2211yescharacteristic, complemented
50#16811286C2211yescharacteristic
51#16811282C2211yescharacteristic
52#16811281C2211yescharacteristic
53#16811279C2211yescharacteristic, complemented
54#16811279C2211yescharacteristic, complemented
55#16811277C2211yescharacteristic
56#16811273—21no—
57#16811272C2211yescharacteristic, complemented
58#16811271—21no—
59#16811270C2211yescharacteristic
60#16811268C2211yescharacteristic, complemented
61#16811267C2211yescharacteristic
62#16811263—21no—
63#16811260—21no—
64#16811247C2211yescharacteristic, complemented
65#16811244—21no—
66#16811242—21no—
67#16811238C2211yescharacteristic, complemented
68#16811210—21no—
69#16811207—21no—
70#16811202C2211yescharacteristic
71#16811200—21no—
72#16811199C2211yescharacteristic, complemented
73#16811195—21no—
74#16811193C2211yescharacteristic, complemented
75#16811189C2211yescharacteristic, complemented
76#16811135C2211yescharacteristic
77#16811133C2211yescharacteristic
78#16811132C2211yescharacteristic
79#16811129—21no—
80C2×#13133194—21no—
81C22⋊Q8×D53C2211yescharacteristic, complemented
82#16811102C2211yescharacteristic, complemented
83#16811017C2211yescharacteristic, complemented
84#16811014C2211yescharacteristic, complemented
85#16811006C2211yescharacteristic, complemented
86#16811005C2211yescharacteristic, complemented
87#16810981C2211yescharacteristic, complemented
88#16810975C2211yescharacteristic, complemented
89#16810972C2211yescharacteristic, complemented
90#16810966C2211yescharacteristic, complemented
91#16810966C2211yescharacteristic, complemented
92#16810964C2211yescharacteristic, complemented
93#16810964C2211yescharacteristic, complemented
94#16810962C2211yescharacteristic, complemented
95#16810960C2211yescharacteristic, complemented
96#16810955C2211yescharacteristic, complemented
97#16810946C2211yescharacteristic, complemented
98#16810940C2211yescharacteristic, complemented
99#16810938C2211yescharacteristic, complemented
100#16810915C2211yescharacteristic, complemented
101#16810911C2211yescharacteristic, complemented
102#16810907C2211yescharacteristic, complemented
103#16810882C2211yescharacteristic, complemented
104#16810881C2211yescharacteristic, complemented
105#16810879C2211yescharacteristic, complemented
106#16810874C2211yescharacteristic, complemented
107#16810868C2211yescharacteristic, complemented
108#16810867C2211yescharacteristic
109#16810867C2211yescharacteristic, complemented
110#16810865C2211yescharacteristic, complemented
111#16810865C2211yescharacteristic, complemented
112#16810863C2211yescharacteristic, complemented
113#16810855C2211yescharacteristic, complemented
114#16810853C2211yescharacteristic, complemented
115#16810852C2211yescharacteristic, complemented
116#16810851C2211yescharacteristic, complemented
117#16810846C2211yescharacteristic, complemented
118#16810844C2211yescharacteristic, complemented
119#16810844C2211yescharacteristic, complemented
120#16810842C2211yescharacteristic, complemented
121#16810838C2211yescharacteristic, complemented
122#16810837C2211yescharacteristic, complemented
123#16810836C2211yescharacteristic, complemented
124#16810834C2211yescharacteristic, complemented
125#16810832C2211yescharacteristic, complemented
126#16810828C2211yescharacteristic, complemented
127#16810827C2211yescharacteristic, complemented
128#16810787C2211yescharacteristic
129#16810786C2211yescharacteristic, complemented
130#16810786C2211yescharacteristic, complemented
131#16810786C2211yescharacteristic, complemented
132#16810786C2211yescharacteristic, complemented
133#16810786C2211yescharacteristic, complemented
134#16810786C2211yescharacteristic, complemented
135#16810786C2211yescharacteristic, complemented
136#16810786C2211yescharacteristic, complemented
137#16810786C2211yescharacteristic, complemented
138#16810783C2211yescharacteristic
139#16810782C2211yescharacteristic, complemented
140#16810781C2211yescharacteristic, complemented
141#16810781C2211yescharacteristic, complemented
142#16810780C2211yescharacteristic, complemented
143#16810780C2211yescharacteristic, complemented
144#16810780C2211yescharacteristic, complemented
145#16810780C2211yescharacteristic, complemented
146#16810775C2211yescharacteristic, complemented
147#16810774C2211yescharacteristic, complemented
148#16810769C2211yescharacteristic
149#16810769C2211yescharacteristic
150#16810769C2211yescharacteristic
151#16810769C2211yescharacteristic
152#16810768C2211yescharacteristic, complemented
153#16810765C2211yescharacteristic
154#16810765C2211yescharacteristic
155#16810764C2211yescharacteristic, complemented
156#16810763C2211yescharacteristic, complemented
157#16810761C2211yescharacteristic
158#16810761C2211yescharacteristic, complemented
159#16810761C2211yescharacteristic, complemented
160#16810760C2211yescharacteristic, complemented
161#16810755C2211yescharacteristic, complemented
162#16810731C2211yescharacteristic, complemented
163#16810722C2211yescharacteristic, complemented
164#16810720C2211yescharacteristic, complemented
165#16810717C2211yescharacteristic, complemented
166C4×#11719923C2211yescharacteristic, complemented
167C4×#11719923C2211yescharacteristic, complemented
168#16810703C2211yescharacteristic, complemented
169#16810701C2211yescharacteristic, complemented
170#16810698C2211yescharacteristic
171#16810697C2211yescharacteristic, complemented
172#16810696C2211yescharacteristic, complemented
173#16810692C2211yescharacteristic
174#16810688C2211yescharacteristic, complemented
175C8×C22⋊D53C2211yescharacteristic, complemented
176#16810685C2211yescharacteristic, complemented
177#16810683C2211yescharacteristic, complemented
178#16810631C2211yescharacteristic, complemented
179#16810631C2211yescharacteristic, complemented
180#16810630C2211yescharacteristic, complemented
181#16810616C2211yescharacteristic, complemented
182#16810616C2211yescharacteristic, complemented
183#16810616C2211yescharacteristic, complemented
184#16810589C2211yescharacteristic, complemented
185#16810588C2211yescharacteristic, complemented
186#16810586C2211yescharacteristic, complemented
187C22⋊C8×D53C2211yescharacteristic, complemented
188C53×#555C2211yescharacteristic
189C53×#546C2211yescharacteristic, complemented
190C53×#489C2211yescharacteristic, complemented
191C53×#485C2211yescharacteristic, complemented
192C53×#482C2211yescharacteristic, complemented
193C53×#474C2211yescharacteristic, complemented
194C53×#468C2211yescharacteristic
195C53×#466C2211yescharacteristic, complemented
196C53×#463C2211yescharacteristic, complemented
197C53×#449C2211yescharacteristic, complemented
198C53×#447C2211yescharacteristic
199C53×#442C2211yescharacteristic, complemented
200C53×#435C2211yescharacteristic, complemented
201C53×#418C2211yescharacteristic, complemented
202C53×#416C2211yescharacteristic, complemented
203#13133264—42no—
204#13133264—42no—
205C2×#11719945—21no—
206C2×#11719945C2311yescharacteristic
207C2×#11719945C2311yescharacteristic
208C2×#11719947—21no—
209C2×#11719947—21no—
210C2×#11719947—21no—
211C2×#11719947—21no—
212C2×#11719947—42no—
213C2×#11719947—42no—
214C2×#11719947C2311yescharacteristic
215C2×#11719947C2311yescharacteristic
216C2×#11719947C2311yescharacteristic
217C2×#11719947C2311yescharacteristic
218C2×#11719947C2311yescharacteristic
219C2×#11719947C2311yescharacteristic
220C22×Dic106—21no—
221C22×Dic106C2311yescharacteristic
222C22×Dic106C2311yescharacteristic
223C22×Dic106C2311yescharacteristic
224C2×Q8×D53C2311yescharacteristic
225C2×Q8×D53C2311yescharacteristic
226C22×C22⋊D53—21no—
227C2×D4×D53C2311yescharacteristic
228C23×Dic53—21no—
229C22×C4×D53C2311yescharacteristic
230#13133250—42no—
231#13133247—42no—
232#13133243—42no—
233#13133241—42no—
234#13133236—42no—
235#13133236—42no—
236C2×Dic212—42no—
237C2×Dic212C2311yescharacteristic
238C2×Dic212C2311yescharacteristic
239C2×Dic212C2311yescharacteristic
240C2×Dic212C2311yescharacteristic
241C2×Dic212C2311yescharacteristic
242C2×Dic212C2311yescharacteristic
243C2×#11719925C2311yescharacteristic
244C2×#11719925C2311yescharacteristic
245C2×#11719913C2311yescharacteristic
246C2×#11719913C2311yescharacteristic
247C2×#11719913C2311yescharacteristic
248C2×#11719923C2311yescharacteristic
249C2×#11719923C2311yescharacteristic
250C2×#11719923C2311yescharacteristic
251C2×#11719923C2311yescharacteristic
252C2×#11719923C2311yescharacteristic
253C2×#11719923C2311yescharacteristic
254C2×#11719923C2311yescharacteristic
255C2×#11719924C2311yescharacteristic
256SD16×D53—42no—
257C2×#11719922C2311yescharacteristic
258C2×#11719922C2311yescharacteristic
259C2×#11719917C2311yescharacteristic
260C2×#11719917C2311yescharacteristic
261C2×#11719912C2311yescharacteristic
262C2×C8×D53C2311yescharacteristic
263C2×C8×D53C2311yescharacteristic
264C2×C8×D53C2311yescharacteristic
265#13133217—21no—
266#13133217C2311yescharacteristic
267#13133216—21no—
268#13133216—21no—
269#13133216C2311yescharacteristic
270#13133215C2311yescharacteristic
271#13133213—21no—
272#13133212—21no—
273#13133212—21no—
274#13133212—21no—
275#13133211—21no—
276#13133210—21no—
277#13133210—21no—
278#13133206—21no—
279#13133206—21no—
280#13133205—21no—
281#13133205—21no—
282#13133205C2311yescharacteristic
283#13133204C2311yescharacteristic
284#13133204C2311yescharacteristic
285#13133203—21no—
286#13133203—21no—
287#13133203—21no—
288#13133203—21no—
289#13133203—21no—
290#13133203—21no—
291#13133203—21no—
292#13133203—21no—
293#13133202—21no—
294#13133202D411yescharacteristic
295#13133201—21no—
296#13133201—21no—
297#13133201—21no—
298#13133201—21no—
299#13133201—21no—
300#13133201—21no—
301#13133200—21no—
302#13133200—21no—
303#13133199—21no—
304#13133199—21no—
305#13133199—21no—
306#13133199—21no—
307#13133199D411yescharacteristic
308#13133198—21no—
309#13133198—21no—
310#13133197C2311yescharacteristic
311#13133197C2311yescharacteristic
312#13133197C2311yescharacteristic
313#13133197C2311yescharacteristic
314#13133197C2311yescharacteristic
315#13133197C2311yescharacteristic
316#13133197C2311yescharacteristic
317#13133196—21no—
318#13133196C2311yescharacteristic
319#13133196C2311yescharacteristic
320#13133196C2311yescharacteristic
321#13133195—21no—
322#13133195—21no—
323#13133195—21no—
324#13133195D411yescharacteristic
325#13133194—21no—
326#13133194—21no—
327#13133194—21no—
328#13133194—21no—
329#13133194—21no—
330#13133194—21no—
331#13133194—21no—
332#13133194—21no—
333#13133194—21no—
334#13133194—21no—
335#13133194D411yescharacteristic
336#13133193—21no—
337#13133193C2311yescharacteristic
338#13133192C2311yescharacteristic
339#13133192C2311yescharacteristic
340#13133191—21no—
341#13133191—21no—
342#13133191C2311yescharacteristic
343#13133190—21no—
344#13133190—21no—
345#13133190—21no—
346#13133190D411yescharacteristic
347#13133189—21no—
348#13133189—21no—
349#13133189—21no—
350#13133189—21no—
351#13133189—21no—
352#13133189—21no—
353#13133189D411yescharacteristic
354#13133188—21no—
355#13133188—21no—
356#13133188C2311yescharacteristic
357#13133188C2311yescharacteristic
358#13133187—21no—
359#13133187—21no—
360#13133187—21no—
361#13133187D411yescharacteristic
362#13133186—21no—
363#13133185—21no—
364#13133185—21no—
365#13133185—21no—
366#13133185D411yescharacteristic
367Q8×Dic53—21no—
368C4×Dic106—21no—
369C4×Dic106C2311yescharacteristic
370C4×Dic106C2311yescharacteristic
371#13133182C2311yescharacteristic
372#13133182C2311yescharacteristic
373C4×D212—21no—
374C4×D212—21no—
375C4×D212C2311yescharacteristic
376D4×Dic53—21no—
377D4×Dic53—21no—
378D4×Dic53—21no—
379D4×Dic53—21no—
380D4×Dic53C2311yescharacteristic
381#13133179C2311yescharacteristic
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#13133175C2311yescharacteristic
391#13133175C2311yescharacteristic
392#13133174—21no—
393#13133174C2311yescharacteristic
394#13133173—21no—
395C2×C4⋊Dic53—21no—
396C2×#11719919—21no—
397C2×#11719919—21no—
398C4⋊C4×D53—21no—
399C4⋊C4×D53C2311yescharacteristic
400C2×C22⋊Dic53—21no—
401C2×#11719921—21no—
402C22⋊C4×D53—21no—
403C22⋊C4×D53—21no—
404#13133150C2311yescharacteristic
405#13133150C2311yescharacteristic
406#13133149C2311yescharacteristic
407#13133148C2311yescharacteristic
408#13133148C2311yescharacteristic
409C4⋊#88322C2311yescharacteristic
410#13133146C2311yescharacteristic
411#13133146C2311yescharacteristic
412#13133142C2311yescharacteristic
413#13133142C2311yescharacteristic
414#13133142C2311yescharacteristic
415#13133142C2311yescharacteristic
416#13133142C2311yescharacteristic
417#13133141C2311yescharacteristic
418#13133140C2311yescharacteristic
419#13133140C2311yescharacteristic
420#13133140C2311yescharacteristic
421#13133140C2311yescharacteristic
422#13133140C2311yescharacteristic
423#13133140C2311yescharacteristic
424#13133140C2311yescharacteristic
425#13133140C2311yescharacteristic
426#13133140C2311yescharacteristic
427#13133140C2311yescharacteristic
428#13133140C2311yescharacteristic
429#13133139C2311yescharacteristic
430#13133138C2311yescharacteristic
431#13133138C2311yescharacteristic
432#13133138C2311yescharacteristic
433#13133137C2311yescharacteristic
434C22⋊#88322C2311yescharacteristic
435C22⋊#88322C2311yescharacteristic
436#13133129C2311yescharacteristic
437#13133129C2311yescharacteristic
438#13133129C2311yescharacteristic
439#13133129C2311yescharacteristic
440#13133129C2311yescharacteristic
441#13133129C2311yescharacteristic
442#13133129C2311yescharacteristic
443#13133129C2311yescharacteristic
444#13133127C2311yescharacteristic
445C4×#88322C2311yescharacteristic
446C8×Dic53C2311yescharacteristic
447C2×#41×C53C2311yescharacteristic
448C22×D4×C53C2311yescharacteristic
449C2×SD16×C53C2311yescharacteristic
450C2×D8×C53C2311yescharacteristic
451C2×D8×C53C2311yescharacteristic
452C2×M16×C53C2311yescharacteristic
453C22×C8×C53C2311yescharacteristic
454C4⋊Q8×C53C2311yescharacteristic
455#124×C53—21no—
456#124×C53—21no—
457#124×C53C2311yescharacteristic
458#123×C53—21no—
459C22⋊Q8×C53C2311yescharacteristic
460#121×C53—21no—
461#121×C53—21no—
462#121×C53C2311yescharacteristic
463#121×C53C2311yescharacteristic
464#121×C53C2311yescharacteristic
465#120×C53—21no—
466C4×D4×C53C2311yescharacteristic
467C4×D4×C53C2311yescharacteristic
468C4×D4×C53C2311yescharacteristic
469#117×C53—21no—
470#117×C53C2311yescharacteristic
471#117×C53C2311yescharacteristic
472C2×C22⋊C4×C53—21no—
473#107×C53C2311yescharacteristic
474#107×C53C2311yescharacteristic
475#106×C53C2311yescharacteristic
476C4⋊C8×C53C2311yescharacteristic
477#103×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
486#102×C53C2311yescharacteristic
487C22⋊C8×C53C2311yescharacteristic
488C22⋊C8×C53C2311yescharacteristic
489#97×C53C2311yescharacteristic
490C24×C53—21no—
491C23×D53—21no—
492C23×D53C2×D411yescharacteristic
493#41×C53—22no—
494#41×C53—41no—
495C2×Q8×C53—21no—
496C2×Q8×C53C2411yescharacteristic
497C2×D4×C53—22no—
498C2×D4×C53—21no—
499C2×D4×C53—21no—
500C2×D4×C53—21no—
501C2×D4×C53—21no—
502C2×D4×C53—21no—
503C2×D4×C53—41no—
504C2×D4×C53C2×D411yescharacteristic
505C2×D4×C53C2411yescharacteristic
506C2×D4×C53C2411yescharacteristic
507C2×D4×C53C2411yescharacteristic
508C22×C4×C53—21no—
509C22×C4×C53—21no—
510C22×C4×C53—21no—
511C22×C4×C53C2411yescharacteristic
512C22×C4×C53C2411yescharacteristic
513C2×C22⋊D53—21no—
514C2×C22⋊D53—21no—
515C2×C22⋊D53—21no—
516C2×C22⋊D53—21no—
517C2×C22⋊D53—21no—
518C2×C22⋊D53—21no—
519C2×C22⋊D53—21no—
520C2×C22⋊D53—21no—
521C2×C22⋊D53—21no—
522C2×C22⋊D53—21no—
523C2×C22⋊D53—21no—
524C2×C22⋊D53—44no—
525C2×C22⋊D53C2×D411yescharacteristic
526C2×C22⋊D53C2×D411yescharacteristic
527C2×C22⋊D53C2×D411yescharacteristic
528C2×C22⋊D53C2×D411yescharacteristic
529C22×Dic53—21no—
530C22×Dic53—21no—
531C22×Dic53—21no—
532C22×Dic53—21no—
533C22×Dic53—21no—
534C22×Dic53—21no—
535C22×Dic53—21no—
536C22×Dic53—21no—
537C22×Dic53—21no—
538C22×Dic53—21no—
539C22×Dic53—44no—
540C22×Dic53C2×D411yescharacteristic
541Q8×D53—22no—
542Q8×D53—41no—
543Q8×D53—41no—
544Q8×D53—41no—
545#11719947—22no—
546#11719947—22no—
547#11719947—22no—
548#11719947—22no—
549#11719947—22no—
550#11719947—41no—
551#11719947—41no—
552#11719947—41no—
553#11719947—41no—
554#11719947—41no—
555#11719947—41no—
556#11719947—41no—
557#11719947—44no—
558#11719947—44no—
559#11719947—44no—
560#11719947—44no—
561D4×D53—41no—
562D4×D53—41no—
563#11719945—41no—
564#11719945—41no—
565#11719945—41no—
566#11719945—41no—
567#11719945—44no—
568C2×D212—21no—
569C2×D212—21no—
570C2×D212C2×D411yescharacteristic
571C2×D212C2×D411yescharacteristic
572C2×D212C2411yescharacteristic
573C2×C4×D53—21no—
574C2×C4×D53—21no—
575C2×C4×D53—21no—
576C2×C4×D53—21no—
577C2×C4×D53—21no—
578C2×C4×D53—41no—
579C2×C4×D53—41no—
580C2×C4×D53C2×D411yescharacteristic
581C2×C4×D53C2×D411yescharacteristic
582C2×C4×D53C2411yescharacteristic
583C2×C4×D53C2411yescharacteristic
584C2×C4×D53C2411yescharacteristic
585C2×Dic106—22no—
586C2×Dic106—22no—
587C2×Dic106—21no—
588C2×Dic106—21no—
589C2×Dic106—21no—
590C2×Dic106—21no—
591C2×Dic106—21no—
592C2×Dic106—21no—
593C2×Dic106—41no—
594C2×Dic106—41no—
595C2×Dic106—41no—
596C2×Dic106—41no—
597C2×Dic106—44no—
598C2×Dic106C2×D411yescharacteristic
599C2×Dic106C2411yescharacteristic
600C2×Dic106C2411yescharacteristic
601C2×Dic106C2411yescharacteristic
602C2×Dic106C2411yescharacteristic
603C2×Dic106C2411yescharacteristic
604SD16×C53—41no—
605D8×C53—22no—
606D8×C53—41no—
607M16×C53—41no—
608C2×C8×C53—41no—
609C2×C8×C53C2411yescharacteristic
610C2×C8×C53C2411yescharacteristic
611C2×C8×C53C2411yescharacteristic
612C2×C8×C53C2411yescharacteristic
613C4⋊C4×C53—21no—
614C4⋊C4×C53—21no—
615C4⋊C4×C53C2×D411yescharacteristic
616C4⋊C4×C53C2411yescharacteristic
617C4⋊C4×C53C2411yescharacteristic
618C4⋊C4×C53C2411yescharacteristic
619C4⋊C4×C53C2411yescharacteristic
620C22⋊C4×C53—21no—
621C22⋊C4×C53—21no—
622C22⋊C4×C53—21no—
623C22⋊C4×C53—21no—
624C22⋊C4×C53—21no—
625C22⋊C4×C53—21no—
626C22⋊C4×C53—21no—
627C22⋊C4×C53—21no—
628C22⋊C4×C53—21no—
629C22⋊C4×C53—21no—
630C22⋊C4×C53C2×D411yescharacteristic
631C22⋊C4×C53C2×D411yescharacteristic
632C42×C53—21no—
633C42×C53—21no—
634C42×C53C2411yescharacteristic
635C22⋊Dic53—21no—
636C22⋊Dic53—21no—
637C22⋊Dic53—21no—
638C22⋊Dic53—21no—
639C22⋊Dic53—21no—
640C22⋊Dic53—21no—
641C22⋊Dic53—21no—
642C22⋊Dic53—21no—
643C22⋊Dic53—21no—
644C22⋊Dic53—21no—
645C22⋊Dic53C2×D411yescharacteristic
646C22⋊Dic53C2×D411yescharacteristic
647#11719925—41no—
648#11719925—41no—
649#11719924—41no—
650#11719923—22no—
651#11719923—22no—
652#11719923—22no—
653#11719923—41no—
654#11719923—41no—
655#11719923—41no—
656#11719923—41no—
657#11719922—22no—
658#11719922—41no—
659#11719921—21no—
660#11719921—21no—
661#11719921—21no—
662#11719921—21no—
663#11719921—21no—
664#11719921—21no—
665#11719921—21no—
666#11719921—21no—
667#11719921—21no—
668#11719921—21no—
669#11719921—21no—
670#11719921—21no—
671#11719921—21no—
672#11719921—21no—
673#11719921—21no—
674#11719921—21no—
675#11719921C2×D411yescharacteristic
676#11719921C2×D411yescharacteristic
677#11719921C2×D411yescharacteristic
678#11719921C2×D411yescharacteristic
679#11719921C2×D411yescharacteristic
680#11719921C2×D411yescharacteristic
681C4⋊Dic53—21no—
682C4⋊Dic53—21no—
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⋊Dic53C2411yescharacteristic
692C4⋊Dic53C2411yescharacteristic
693#11719919—21no—
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#11719919C2×D411yescharacteristic
706#11719919C2×D411yescharacteristic
707#11719919C2×D411yescharacteristic
708#11719919C2×D411yescharacteristic
709C4×Dic53—21no—
710C4×Dic53—21no—
711C4×Dic53—21no—
712C4×Dic53—21no—
713C4×Dic53—21no—
714C4×Dic53—21no—
715C4×Dic53C2411yescharacteristic
716#11719917—41no—
717#11719917—41no—
718C2×#88322C2411yescharacteristic
719C2×#88322C2411yescharacteristic
720C2×#88322C2411yescharacteristic
721C2×#88322C2411yescharacteristic
722Dic212—22no—
723Dic212—22no—
724Dic212—41no—
725Dic212—41no—
726Dic212—41no—
727Dic212—41no—
728#11719913—22no—
729#11719913—41no—
730#11719913—41no—
731#11719912—41no—
732C8×D53—41no—
733C8×D53—41no—
734C8×D53—41no—
735C23×C53—21no—
736C23×C53—21no—
737C23×C53—21no—
738C23×C53—42no—
739C23×C53—42no—
740C23×C53—81no—
741C23×C53C22×D411yescharacteristic
742C23×C53C22×D411yescharacteristic
743C22×D53—21no—
744C22×D53—41no—
745C22×D53—41no—
746C22×D53—41no—
747C22×D53—81no—
748C22×D53—81no—
749C22×D53—81no—
750C22×D53C22×D411yescharacteristic
751C22×D53C22×D411yescharacteristic
752C22×D53C22×D411yescharacteristic
753Q8×C53—21no—
754Q8×C53—21no—
755Q8×C53—81no—
756D4×C53—21no—
757D4×C53—21no—
758D4×C53—21no—
759D4×C53—21no—
760D4×C53—21no—
761D4×C53—41no—
762D4×C53—42no—
763D4×C53—42no—
764D4×C53—81no—
765D4×C53—81no—
766D4×C53—81no—
767D4×C53H(5,𝔽2)12yes—
768C2×C4×C53—21no—
769C2×C4×C53—21no—
770C2×C4×C53—21no—
771C2×C4×C53—21no—
772C2×C4×C53—21no—
773C2×C4×C53—21no—
774C2×C4×C53—21no—
775C2×C4×C53—21no—
776C2×C4×C53—21no—
777C2×C4×C53—42no—
778C2×C4×C53—81no—
779C2×C4×C53—81no—
780C2×C4×C53C22×D411yescharacteristic
781C2×C4×C53C22×D411yescharacteristic
782C2×C4×C53C22×D411yescharacteristic
783C2×C4×C53C22×D411yescharacteristic
784C2×C4×C53C2511yescharacteristic
785C22⋊D53—24no—
786C22⋊D53—41no—
787C22⋊D53—41no—
788C22⋊D53—41no—
789C22⋊D53—41no—
790C22⋊D53—42no—
791C22⋊D53—42no—
792C22⋊D53—42no—
793C22⋊D53—42no—
794C22⋊D53—81no—
795C22⋊D53—81no—
796C22⋊D53—81no—
797C22⋊D53—81no—
798C22⋊D53—81no—
799C22⋊D53—81no—
800C2×Dic53—24no—
801C2×Dic53—21no—
802C2×Dic53—21no—
803C2×Dic53—21no—
804C2×Dic53—21no—
805C2×Dic53—21no—
806C2×Dic53—21no—
807C2×Dic53—21no—
808C2×Dic53—41no—
809C2×Dic53—42no—
810C2×Dic53—42no—
811C2×Dic53—42no—
812C2×Dic53—42no—
813C2×Dic53—42no—
814C2×Dic53—42no—
815C2×Dic53—81no—
816C2×Dic53—81no—
817C2×Dic53—81no—
818C2×Dic53C22×D411yescharacteristic
819C2×Dic53C22×D411yescharacteristic
820C2×Dic53C22×D411yescharacteristic
821C2×Dic53C22×D411yescharacteristic
822C2×Dic53C22×D411yescharacteristic
823D212—21no—
824D212—21no—
825D212—41no—
826D212—41no—
827D212—81no—
828D212—81no—
829C4×D53—21no—
830C4×D53—21no—
831C4×D53—21no—
832C4×D53—21no—
833C4×D53—21no—
834C4×D53—21no—
835C4×D53—41no—
836C4×D53—41no—
837C4×D53—42no—
838C4×D53—42no—
839C4×D53—81no—
840C4×D53—81no—
841C4×D53—81no—
842Dic106—21no—
843Dic106—21no—
844Dic106—21no—
845Dic106—21no—
846Dic106—21no—
847Dic106—21no—
848Dic106—21no—
849Dic106—21no—
850Dic106—21no—
851Dic106—41no—
852Dic106—42no—
853Dic106—42no—
854Dic106—42no—
855Dic106—42no—
856Dic106—81no—
857Dic106—81no—
858Dic106H(5,𝔽2)12yes—
859C8×C53—21no—
860C8×C53—21no—
861C8×C53—21no—
862C8×C53—21no—
863#88322—21no—
864#88322—21no—
865#88322—21no—
866#88322—21no—
867#61627—531nomaximal, Sylow
868C22×C53—21no—
869C22×C53—21no—
870C22×C53—21no—
871C22×C53—21no—
872C22×C53—22no—
873C22×C53—21no—
874C22×C53—21no—
875C22×C53—41no—
876C22×C53—41no—
877C22×C53—41no—
878C22×C53—41no—
879C22×C53—41no—
880C22×C53—41no—
881C22×C53—41no—
882C22×C53—41no—
883C22×C53—84no—
884C22×C53C23×D411yescharacteristic
885C2×D53—21no—
886C2×D53—21no—
887C2×D53—21no—
888C2×D53—21no—
889C2×D53—21no—
890C2×D53—21no—
891C2×D53—21no—
892C2×D53—21no—
893C2×D53—21no—
894C2×D53—41no—
895C2×D53—41no—
896C2×D53—41no—
897C2×D53—82no—
898C2×D53—162no—
899C4×C53—21no—
900C4×C53—21no—
901C4×C53—21no—
902C4×C53—21no—
903C4×C53—41no—
904C4×C53—41no—
905C4×C53—41no—
906C4×C53—41no—
907C4×C53—41no—
908C4×C53C2×H(5,𝔽2)11yescharacteristic
909C4×C53C2×H(5,𝔽2)11yescharacteristic
910Dic53—21no—
911Dic53—21no—
912Dic53—22no—
913Dic53—21no—
914Dic53—21no—
915Dic53—21no—
916Dic53—41no—
917Dic53—41no—
918Dic53—41no—
919Dic53—41no—
920Dic53—41no—
921Dic53—41no—
922#3540—531no—
923#3489—531no—
924#3329—531no—
925#3328—531no—
926#3321—531no—
927#3319D5311yescharacteristic, complemented
928#3313—531no—
929#3311—531no—
930#3303—531no—
931#3302—531no—
932#3285—531no—
933#3282—531no—
934#3275—531no—
935#3273—531no—
936#3270—531no—
937#3269—531no—
938#3267—531no—
939#3266—531no—
940#3225—531no—
941#3225—531no—
942#3201—531no—
943#3198—531no—
944#3196—531no—
945#3190—531no—
946#3125—531no—
947#3124—531no—
948#3011—531no—
949#3010—531no—
950#3005—531no—
951#3002—531no—
952#2976—531no—
953C2×C53—41no—
954C2×C53—41no—
955C2×C53—42no—
956C2×C53—81no—
957C2×C53—81no—
958C2×C53#348411yescharacteristic
959C2×C53#358411yescharacteristic
960C2×C53#358611yescharacteristic
961D53—41no—
962D53—41no—
963D53—41no—
964D53—81no—
965C2×2−1+4—531no—
966C22×#41—531no—
967C2×#137—531no—
968C2×#137—531no—
969C2×AGL(1,ℤ/8)—531no—
970C2×AGL(1,ℤ/8)—531no—
971C2×#135—531no—
972C2×#135—531no—
973C22×Q16—531no—
974C22×SD16—531no—
975H(3,𝔽4)—1061no—
976#560—1061no—
977#559—1061no—
978#556—531no—
979#556—531no—
980#555—531no—
981#555C2×D5311yescharacteristic
982#551—1061no—
983D4×Q8—531no—
984D4×Q8—531no—
985#548—531no—
986#548—531no—
987#548—531no—
988#548—531no—
989#547—531no—
990#547—531no—
991#547—1061no—
992#547—1061no—
993#546—531no—
994#546—531no—
995#546—531no—
996#546—1061no—
997#546—1061no—
998#546C2×D5311yescharacteristic, complemented
999#542—531no—
1000#542—531no—
1001#542—1061no—
1002#542—1061no—
1003#538—1061no—
1004#538—1061no—
1005#537—531no—
1006#537—1061no—
1007#536—531no—
1008#536—531no—
1009#536—1061no—
1010#535—531no—
1011#525—531no—
1012#525—531no—
1013#525—531no—
1014#525—1061no—
1015C2×C22⋊Q8—531no—
1016C2×C22⋊Q8—1061no—
1017#520—531no—
1018#497—531no—
1019#497—531no—
1020#495—531no—
1021#495—531no—
1022#489—531no—
1023#489C2×D5311yescharacteristic, complemented
1024#487—531no—
1025#487—531no—
1026#485—531no—
1027#485—531no—
1028#485—531no—
1029#485—531no—
1030#485—531no—
1031#485C2×D5311yescharacteristic, complemented
1032#484—531no—
1033#483—531no—
1034#482—531no—
1035#482C2×D5311yescharacteristic, complemented
1036#481—531no—
1037#480—531no—
1038#477—531no—
1039#476—531no—
1040#475—531no—
1041#474C2×D5311yescharacteristic, complemented
1042#470—531no—
1043#470—531no—
1044#470—531no—
1045#469—531no—
1046#468—531no—
1047#468—531no—
1048#468—531no—
1049#468C2×D5311yescharacteristic
1050#467—531no—
1051#467—531no—
1052#467—531no—
1053#466C2×D5311yescharacteristic, complemented
1054#465—531no—
1055#465—531no—
1056#465—531no—
1057#465—531no—
1058#464—531no—
1059#464—531no—
1060#464—531no—
1061#464—531no—
1062#463—531no—
1063#463—531no—
1064#463—531no—
1065#463C2×D5311yescharacteristic, complemented
1066#462—531no—
1067#462—531no—
1068#461—531no—
1069#461—531no—
1070#452—531no—
1071#452—531no—
1072#452—531no—
1073#452—531no—
1074#452—531no—
1075#452—531no—
1076#452—531no—
1077#452—531no—
1078#452—531no—
1079#452—531no—
1080#452—531no—
1081#452—531no—
1082#451—531no—
1083#451—531no—
1084#451—531no—
1085#451—531no—
1086#451—531no—
1087#451—531no—
1088#450—531no—
1089#450—531no—
1090#449—531no—
1091#449—531no—
1092#449—531no—
1093#449—531no—
1094#449—531no—
1095#449—531no—
1096#449—531no—
1097#449C2×D5311yescharacteristic, complemented
1098#448—531no—
1099#448—531no—
1100#448—531no—
1101#448—531no—
1102#448—531no—
1103#448—531no—
1104#447—531no—
1105#447C2×D5311yescharacteristic
1106#442C2×D5311yescharacteristic, complemented
1107#441—531no—
1108#440—531no—
1109#440—531no—
1110C4×Q16—531no—
1111C4×SD16—531no—
1112C4×SD16—531no—
1113C4×D8—531no—
1114#436—531no—
1115#436—531no—
1116#435—531no—
1117#435—531no—
1118#435—531no—
1119#435C2×D5311yescharacteristic, complemented
1120C8×D4—531no—
1121C8×D4—531no—
1122#433—531no—
1123#433—531no—
1124#419—531no—
1125#419—531no—
1126#419—531no—
1127#418C2×D5311yescharacteristic, complemented
1128#416—531no—
1129#416—531no—
1130#416—531no—
1131#416C2×D5311yescharacteristic, complemented
1132#408—531no—
1133#408—531no—
1134#407—531no—
1135C2×C22⋊C8—531no—
1136C53#6162711yescharacteristic, complemented, Sylow
11372−1+4—2122no—
11382−1+4—2122no—
1139C2×#41—531no—
1140C2×#41—531no—
1141C2×#41—531no—
1142C2×#41—531no—
1143C2×#41—531no—
1144C2×#41—531no—
1145C2×#41—531no—
1146C2×#41—531no—
1147C2×#41—1061no—
1148C2×#41—1061no—
1149C2×#41—1061no—
1150C2×#41—1061no—
1151C2×#41—1061no—
1152C2×#41—2122no—
1153C2×#41—2122no—
1154C2×#41C22×D5311yescharacteristic
1155C22×Q8—531no—
1156C22×Q8—531no—
1157C22×Q8—531no—
1158C22×Q8—531no—
1159C22×Q8—531no—
1160C22×Q8—1061no—
1161C22×D4—531no—
1162C22×D4—1061no—
1163C22×D4C22×D5311yescharacteristic
1164C23×C4—531no—
1165C23×C4—1061no—
1166#137—2122no—
1167#137—2122no—
1168AGL(1,ℤ/8)—2122no—
1169AGL(1,ℤ/8)—2122no—
1170#135—2122no—
1171#135—2122no—
1172C2×Q16—531no—
1173C2×Q16—531no—
1174C2×Q16—531no—
1175C2×Q16—531no—
1176C2×Q16—531no—
1177C2×Q16—531no—
1178C2×Q16—531no—
1179C2×Q16—531no—
1180C2×Q16—2122no—
1181C2×SD16—531no—
1182C2×SD16—531no—
1183C2×SD16—531no—
1184C2×SD16—531no—
1185C2×SD16—531no—
1186C2×SD16—531no—
1187C2×SD16—531no—
1188C2×SD16—531no—
1189C2×SD16—531no—
1190C2×SD16—531no—
1191C2×SD16—531no—
1192C2×SD16—2122no—
1193C2×SD16C22×D5311yescharacteristic
1194C2×D8—531no—
1195C2×D8—531no—
1196C2×D8C22×D5311yescharacteristic
1197C2×D8C22×D5311yescharacteristic
1198C2×M16—531no—
1199C2×M16—531no—
1200C2×M16—531no—
1201C2×M16C22×D5311yescharacteristic
1202C22×C8—531no—
1203C22×C8—531no—
1204C22×C8—531no—
1205C22×C8C22×D5311yescharacteristic
1206C4⋊Q8—531no—
1207C4⋊Q8—531no—
1208C4⋊Q8—531no—
1209C4⋊Q8—1061no—
1210C4⋊Q8—1061no—
1211C4⋊Q8—1061no—
1212C4⋊Q8C22×D5311yescharacteristic
1213#127—1061no—
1214#126—1061no—
1215#126—1061no—
1216#126—1061no—
1217#126—1061no—
1218#126—1061no—
1219#126—1061no—
1220#124—21no—
1221#124—21no—
1222#124—531no—
1223#124—531no—
1224#124—531no—
1225#124—1061no—
1226#124—1061no—
1227#124—1061no—
1228#124—1061no—
1229#124—1061no—
1230#124—1061no—
1231#124—1061no—
1232#124—1061no—
1233#124—1061no—
1234#124—1061no—
1235#124—1061no—
1236#124—1061no—
1237#124C22×D5311yescharacteristic
1238#123—21no—
1239#123—531no—
1240#123—531no—
1241#123—1061no—
1242#123—1061no—
1243#123—1061no—
1244#123—1061no—
1245#123—1061no—
1246#123—1061no—
1247#123—1061no—
1248#123—1061no—
1249#123—1061no—
1250#123—1061no—
1251#123—1061no—
1252#123—1061no—
1253#123—1061no—
1254#123—1061no—
1255#123—1061no—
1256C22⋊Q8—531no—
1257C22⋊Q8—531no—
1258C22⋊Q8—531no—
1259C22⋊Q8—531no—
1260C22⋊Q8—531no—
1261C22⋊Q8—531no—
1262C22⋊Q8—531no—
1263C22⋊Q8—531no—
1264C22⋊Q8—531no—
1265C22⋊Q8—531no—
1266C22⋊Q8—531no—
1267C22⋊Q8—531no—
1268C22⋊Q8—531no—
1269C22⋊Q8—1061no—
1270C22⋊Q8—1061no—
1271C22⋊Q8—1061no—
1272C22⋊Q8—1061no—
1273C22⋊Q8—1061no—
1274C22⋊Q8—1061no—
1275C22⋊Q8—1061no—
1276C22⋊Q8—1061no—
1277C22⋊Q8—1061no—
1278C22⋊Q8—1061no—
1279C22⋊Q8—1061no—
1280C22⋊Q8—1061no—
1281C22⋊Q8—1061no—
1282C22⋊Q8—1061no—
1283C22⋊Q8—1061no—
1284C22⋊Q8C22×D5311yescharacteristic
1285#121—21no—
1286#121—21no—
1287#121—531no—
1288#121—531no—
1289#121—531no—
1290#121—531no—
1291#121—531no—
1292#121—531no—
1293#121—531no—
1294#121—1061no—
1295#121—1061no—
1296#121—1061no—
1297#121—1061no—
1298#121—1061no—
1299#121—1061no—
1300#121—1061no—
1301#121—1061no—
1302#121—1061no—
1303#121—1061no—
1304#121—1061no—
1305#121—1061no—
1306#121—1061no—
1307#121C22×D5311yescharacteristic
1308#121C22×D5311yescharacteristic
1309#121C22×D5311yescharacteristic
1310#120—21no—
1311#120—531no—
1312#120—531no—
1313#120—1061no—
1314#120—1061no—
1315#120—1061no—
1316#120—1061no—
1317#120—1061no—
1318#120—1061no—
1319#120—1061no—
1320C4×Q8—531no—
1321C4×Q8—531no—
1322C4×Q8—531no—
1323C4×Q8—531no—
1324C4×Q8—1061no—
1325C4×Q8—1061no—
1326C4×D4—531no—
1327C4×D4—531no—
1328C4×D4—531no—
1329C4×D4—531no—
1330C4×D4—531no—
1331C4×D4—1061no—
1332C4×D4—1061no—
1333C4×D4—1061no—
1334C4×D4—1061no—
1335C4×D4—1061no—
1336C4×D4—1061no—
1337C4×D4—1061no—
1338C4×D4—1061no—
1339C4×D4—1061no—
1340C4×D4—1061no—
1341C4×D4—1061no—
1342C4×D4—1061no—
1343C4×D4C22×D5311yescharacteristic
1344C4×D4C22×D5311yescharacteristic
1345C4×D4C22×D5311yescharacteristic
1346#117—21no—
1347#117—531no—
1348#117—531no—
1349#117—531no—
1350#117—1061no—
1351#117—1061no—
1352#117C22×D5311yescharacteristic
1353#117C22×D5311yescharacteristic
1354C2×C4⋊C4—531no—
1355C2×C4⋊C4—1061no—
1356C2×C4⋊C4—1061no—
1357C2×C4⋊C4—1061no—
1358C2×C4⋊C4—1061no—
1359C2×C22⋊C4—21no—
1360C2×C22⋊C4—1061no—
1361C2×C22⋊C4—1061no—
1362C2×C22⋊C4—1061no—
1363C2×C22⋊C4—1061no—
1364#107—531no—
1365#107—531no—
1366#107C22×D5311yescharacteristic
1367#107C22×D5311yescharacteristic
1368#106—531no—
1369#106—531no—
1370#106—531no—
1371#106C22×D5311yescharacteristic
1372C4⋊C8—531no—
1373C4⋊C8—531no—
1374C4⋊C8—531no—
1375C4⋊C8C22×D5311yescharacteristic
1376#103—531no—
1377#103—531no—
1378#103—531no—
1379#103—531no—
1380#103—531no—
1381#103—531no—
1382#103—531no—
1383#103—531no—
1384#103—531no—
1385#103—531no—
1386#103—531no—
1387#103—531no—
1388#103—531no—
1389#103—531no—
1390#103—531no—
1391#103—531no—
1392#103—531no—
1393#103C22×D5311yescharacteristic
1394#103C22×D5311yescharacteristic
1395#103C22×D5311yescharacteristic
1396#102—531no—
1397#102—531no—
1398#102—531no—
1399#102—531no—
1400#102—531no—
1401#102C22×D5311yescharacteristic
1402#102C22×D5311yescharacteristic
1403#102C22×D5311yescharacteristic
1404#102C22×D5311yescharacteristic
1405#102C22×D5311yescharacteristic
1406#102C22×D5311yescharacteristic
1407#102C22×D5311yescharacteristic
1408C22⋊C8—531no—
1409C22⋊C8—531no—
1410C22⋊C8—531no—
1411C22⋊C8—531no—
1412C22⋊C8—531no—
1413C22⋊C8—531no—
1414C22⋊C8—531no—
1415C22⋊C8—531no—
1416C22⋊C8—531no—
1417C22⋊C8—531no—
1418C22⋊C8C22×D5311yescharacteristic
1419C22⋊C8C22×D5311yescharacteristic
1420#97—531no—
1421#97C22×D5311yescharacteristic
1422C4×C8—531no—
1423C4×C8—531no—
1424C24—21no—
1425C24—531no—
1426C24—1061no—
1427#41—22no—
1428#41—41no—
1429#41—1062no—
1430#41—1062no—
1431#41—1062no—
1432#41—1062no—
1433#41—1062no—
1434#41—2121no—
1435#41—2121no—
1436#41—2121no—
1437#41—2121no—
1438#41—2124no—
1439#41—2121no—
1440#41—2121no—
1441#41—2121no—
1442#41—2121no—
1443#41—2121no—
1444#41—2121no—
1445#41—2121no—
1446#41—2124no—
1447#41—2124no—
1448#41—2124no—
1449#41—2124no—
1450C2×Q8—21no—
1451C2×Q8—531no—
1452C2×Q8—531no—
1453C2×Q8—531no—
1454C2×Q8—531no—
1455C2×Q8—531no—
1456C2×Q8—531no—
1457C2×Q8—1061no—
1458C2×Q8—1061no—
1459C2×Q8—1061no—
1460C2×Q8—1062no—
1461C2×Q8—1062no—
1462C2×Q8—1061no—
1463C2×Q8—1061no—
1464C2×Q8—1061no—
1465C2×Q8—1062no—
1466C2×Q8—2121no—
1467C2×Q8—2121no—
1468C2×Q8—2121no—
1469C2×Q8—2121no—
1470C2×Q8—2124no—
1471C2×Q8—2121no—
1472C2×Q8—2121no—
1473C2×Q8—2121no—
1474C2×Q8C23×D5311yescharacteristic
1475C2×D4—22no—
1476C2×D4—21no—
1477C2×D4—21no—
1478C2×D4—21no—
1479C2×D4—21no—
1480C2×D4—21no—
1481C2×D4—41no—
1482C2×D4—531no—
1483C2×D4—531no—
1484C2×D4—531no—
1485C2×D4—531no—
1486C2×D4—531no—
1487C2×D4—531no—
1488C2×D4—531no—
1489C2×D4—1061no—
1490C2×D4—1061no—
1491C2×D4—1061no—
1492C2×D4—1061no—
1493C2×D4—1061no—
1494C2×D4—1061no—
1495C2×D4—1061no—
1496C2×D4—1061no—
1497C2×D4—1061no—
1498C2×D4—1061no—
1499C2×D4—1061no—
1500C2×D4—1061no—
1501C2×D4—1061no—
1502C2×D4—2121no—
1503C2×D4—2121no—
1504C2×D4—2124no—
1505C2×D4D4×D5311yescharacteristic
1506C2×D4C23×D5311yescharacteristic
1507C2×D4C23×D5311yescharacteristic
1508C2×D4C23×D5311yescharacteristic
1509C22×C4—21no—
1510C22×C4—21no—
1511C22×C4—21no—
1512C22×C4—531no—
1513C22×C4—531no—
1514C22×C4—531no—
1515C22×C4—531no—
1516C22×C4—531no—
1517C22×C4—531no—
1518C22×C4—1061no—
1519C22×C4—1061no—
1520C22×C4—1061no—
1521C22×C4—1061no—
1522C22×C4—1061no—
1523C22×C4—1061no—
1524C22×C4—1061no—
1525C22×C4—1061no—
1526C22×C4—1061no—
1527C22×C4—1061no—
1528C22×C4—1061no—
1529C22×C4—1061no—
1530C22×C4—1061no—
1531C22×C4—1061no—
1532C22×C4—1061no—
1533C22×C4—2121no—
1534C22×C4—2121no—
1535C22×C4—2124no—
1536C22×C4C23×D5311yescharacteristic
1537C22×C4C23×D5311yescharacteristic
1538Q16—1062no—
1539Q16—1062no—
1540Q16—2121no—
1541Q16—2121no—
1542Q16—2121no—
1543Q16—2121no—
1544Q16—2121no—
1545Q16—2121no—
1546SD16—41no—
1547SD16—1062no—
1548SD16—1062no—
1549SD16—1062no—
1550SD16—1062no—
1551SD16—2121no—
1552SD16—2121no—
1553SD16—2121no—
1554SD16—2121no—
1555SD16—2121no—
1556SD16—2121no—
1557SD16—2121no—
1558D8—22no—
1559D8—41no—
1560D8—1062no—
1561D8—2121no—
1562M16—41no—
1563M16—2121no—
1564M16—2121no—
1565M16—2121no—
1566C2×C8—41no—
1567C2×C8—531no—
1568C2×C8—531no—
1569C2×C8—531no—
1570C2×C8—531no—
1571C2×C8—2121no—
1572C2×C8—2121no—
1573C2×C8—2121no—
1574C2×C8C23×D5311yescharacteristic
1575C2×C8C23×D5311yescharacteristic
1576C2×C8C23×D5311yescharacteristic
1577C2×C8C23×D5311yescharacteristic
1578C4⋊C4—21no—
1579C4⋊C4—21no—
1580C4⋊C4—531no—
1581C4⋊C4—531no—
1582C4⋊C4—531no—
1583C4⋊C4—531no—
1584C4⋊C4—531no—
1585C4⋊C4—531no—
1586C4⋊C4—531no—
1587C4⋊C4—1061no—
1588C4⋊C4—1061no—
1589C4⋊C4—1061no—
1590C4⋊C4—1061no—
1591C4⋊C4—1061no—
1592C4⋊C4—1061no—
1593C4⋊C4—1061no—
1594C4⋊C4—1061no—
1595C4⋊C4—1061no—
1596C4⋊C4—1061no—
1597C4⋊C4—1061no—
1598C4⋊C4—1061no—
1599C4⋊C4—1061no—
1600C4⋊C4—1061no—
1601C4⋊C4—1061no—
1602C4⋊C4—1061no—
1603C4⋊C4—1061no—
1604C4⋊C4—1061no—
1605C4⋊C4—1061no—
1606C4⋊C4—1061no—
1607C4⋊C4—1061no—
1608C4⋊C4D4×D5311yescharacteristic
1609C4⋊C4C23×D5311yescharacteristic
1610C4⋊C4C23×D5311yescharacteristic
1611C4⋊C4C23×D5311yescharacteristic
1612C4⋊C4C23×D5311yescharacteristic
1613C22⋊C4—21no—
1614C22⋊C4—21no—
1615C22⋊C4—21no—
1616C22⋊C4—21no—
1617C22⋊C4—21no—
1618C22⋊C4—21no—
1619C22⋊C4—21no—
1620C22⋊C4—21no—
1621C22⋊C4—21no—
1622C22⋊C4—21no—
1623C22⋊C4—531no—
1624C22⋊C4—531no—
1625C22⋊C4—531no—
1626C22⋊C4—531no—
1627C22⋊C4—531no—
1628C22⋊C4—531no—
1629C22⋊C4—531no—
1630C22⋊C4—531no—
1631C22⋊C4—1061no—
1632C22⋊C4—1061no—
1633C22⋊C4—1061no—
1634C22⋊C4—1061no—
1635C22⋊C4—1061no—
1636C22⋊C4—1061no—
1637C22⋊C4—1061no—
1638C22⋊C4—1061no—
1639C22⋊C4—1061no—
1640C22⋊C4—1061no—
1641C22⋊C4—1061no—
1642C22⋊C4—1061no—
1643C22⋊C4—1061no—
1644C22⋊C4—1061no—
1645C22⋊C4—1061no—
1646C22⋊C4—1061no—
1647C22⋊C4—1061no—
1648C22⋊C4—1061no—
1649C22⋊C4—1061no—
1650C22⋊C4—1061no—
1651C22⋊C4—1061no—
1652C22⋊C4—1061no—
1653C22⋊C4—1061no—
1654C22⋊C4—1061no—
1655C22⋊C4—1061no—
1656C22⋊C4—1061no—
1657C22⋊C4D4×D5311yescharacteristic
1658C22⋊C4D4×D5311yescharacteristic
1659C42—21no—
1660C42—21no—
1661C42—531no—
1662C42—1061no—
1663C42—1061no—
1664C42—1061no—
1665C42—1061no—
1666C42—1061no—
1667C42—1061no—
1668C42C23×D5311yescharacteristic
1669C23—21no—
1670C23—21no—
1671C23—21no—
1672C23—42no—
1673C23—42no—
1674C23—81no—
1675C23—531no—
1676C23—531no—
1677C23—531no—
1678C23—1061no—
1679C23—4241no—
1680C23—4241no—
1681C23—4241no—
1682C23—2121no—
1683C23—2121no—
1684C23—2121no—
1685C23C2×D4×D5311yescharacteristic
1686C23C2×D4×D5311yescharacteristic
1687Q8—21no—
1688Q8—21no—
1689Q8—81no—
1690Q8—532no—
1691Q8—1061no—
1692Q8—1061no—
1693Q8—1061no—
1694Q8—1061no—
1695Q8—1061no—
1696Q8—1061no—
1697Q8—1061no—
1698Q8—1061no—
1699Q8—1061no—
1700Q8—4241no—
1701Q8—4241no—
1702Q8—2121no—
1703Q8—2122no—
1704Q8—2122no—
1705Q8—2122no—
1706Q8—2122no—
1707D4—21no—
1708D4—21no—
1709D4—21no—
1710D4—21no—
1711D4—21no—
1712D4—41no—
1713D4—42no—
1714D4—42no—
1715D4—81no—
1716D4—81no—
1717D4—81no—
1718D4—1064no—
1719D4—1061no—
1720D4—1061no—
1721D4—4241no—
1722D4—4241no—
1723D4—4241no—
1724D4—4241no—
1725D4—4241no—
1726D4—4241no—
1727D4—4241no—
1728D4—4241no—
1729D4—2121no—
1730D4—2121no—
1731D4—2121no—
1732D4—2121no—
1733D4—2121no—
1734D4—2121no—
1735D4—2122no—
1736D4—2122no—
1737D4—2122no—
1738D4—2122no—
1739D4#1313326312yes—
1740C2×C4—21no—
1741C2×C4—21no—
1742C2×C4—21no—
1743C2×C4—21no—
1744C2×C4—21no—
1745C2×C4—21no—
1746C2×C4—21no—
1747C2×C4—21no—
1748C2×C4—21no—
1749C2×C4—42no—
1750C2×C4—81no—
1751C2×C4—81no—
1752C2×C4—531no—
1753C2×C4—531no—
1754C2×C4—531no—
1755C2×C4—531no—
1756C2×C4—531no—
1757C2×C4—1064no—
1758C2×C4—1061no—
1759C2×C4—1061no—
1760C2×C4—1061no—
1761C2×C4—1061no—
1762C2×C4—1061no—
1763C2×C4—1061no—
1764C2×C4—1061no—
1765C2×C4—1061no—
1766C2×C4—1061no—
1767C2×C4—1061no—
1768C2×C4—1061no—
1769C2×C4—1061no—
1770C2×C4—1061no—
1771C2×C4—4241no—
1772C2×C4—4241no—
1773C2×C4—4241no—
1774C2×C4—4241no—
1775C2×C4—4241no—
1776C2×C4—4241no—
1777C2×C4—2121no—
1778C2×C4—2121no—
1779C2×C4—2122no—
1780C2×C4—2122no—
1781C2×C4—2121no—
1782C2×C4—2122no—
1783C2×C4—2122no—
1784C2×C4—2122no—
1785C2×C4—2122no—
1786C2×C4—2122no—
1787C2×C4—2122no—
1788C2×C4C2×D4×D5311yescharacteristic
1789C2×C4C2×D4×D5311yescharacteristic
1790C2×C4C2×D4×D5311yescharacteristic
1791C2×C4C2×D4×D5311yescharacteristic
1792C2×C4C24×D5311yescharacteristic
1793C8—21no—
1794C8—21no—
1795C8—21no—
1796C8—21no—
1797C8—1061no—
1798C8—1061no—
1799C8—1061no—
1800C8—1061no—
1801C22—21no—
1802C22—21no—
1803C22—22no—
1804C22—21no—
1805C22—21no—
1806C22—21no—
1807C22—21no—
1808C22—41no—
1809C22—41no—
1810C22—41no—
1811C22—41no—
1812C22—41no—
1813C22—41no—
1814C22—41no—
1815C22—41no—
1816C22—84no—
1817C22—8482no—
1818C22—1061no—
1819C22—1061no—
1820C22—1061no—
1821C22—1061no—
1822C22—1061no—
1823C22—1061no—
1824C22—1061no—
1825C22—1061no—
1826C22—1061no—
1827C22—4242no—
1828C22—2121no—
1829C22—2121no—
1830C22—2121no—
1831C22C22×D4×D5311yescharacteristic
1832C4—21no—
1833C4—21no—
1834C4—21no—
1835C4—21no—
1836C4—41no—
1837C4—41no—
1838C4—41no—
1839C4—41no—
1840C4—41no—
1841C4—1061no—
1842C4—1061no—
1843C4—1061no—
1844C4—1062no—
1845C4—1061no—
1846C4—1061no—
1847C4—2121no—
1848C4—2121no—
1849C4—2121no—
1850C4—2121no—
1851C4—2121no—
1852C4—2121no—
1853C4H(5,𝔽2)×D5311yescharacteristic
1854C4C2×#1313326311yescharacteristic
1855C2—41no—
1856C2—41no—
1857C2—42no—
1858C2—81no—
1859C2—81no—
1860C2—4241no—
1861C2—2121no—
1862C2—2121no—
1863C2—2121no—
1864C2#2028834511yescharacteristic
1865C2#2028948311yescharacteristic
1866C2#2028949911yescharacteristic
subgroupG/H
centerC22C22×D4×D53
commutator, cosocleC2×C4×C53C25
FrattiniC2×C4C24×D53
FittingC53×#3319C2
socleC22×C53C23×D4
hypercenter#3319D53
hypocenterC53#61627
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22 ◁ C4×D4 ◁ #3319

Complements

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

NH ≅ G/Ntype
1. #20288985C2semidirect
2. #20288386C2semidirect
3. #20287003C2semidirect
4. #20286996C2semidirect
5. #20286904C2semidirect
6. #20286780C2semidirect
7. #20286752C2semidirect
8. #20286639C2semidirect
9. #20286629C2semidirect
10. #20286453C2semidirect
11. #20286428C2semidirect
12. #20286342C2semidirect
13. #20286326C2semidirect
14. #20286290C2semidirect
15. #20286268C2semidirect
16. #20286242C2semidirect
17. #20286232C2semidirect
18. #20285825C2semidirect
19. #20285821C2semidirect
20. #20285595C2semidirect
21. #20285560C2semidirect
22. #20285540C2semidirect
23. #20285500C2semidirect
24. #20284996C2semidirect
25. #20284982C2semidirect
26. #20284013C2semidirect
27. #20283998C2semidirect
28. #20283959C2semidirect
29. #20283928C2semidirect
30. #20283762C2semidirect
31. C53×#3319C2semidirect
33. C22×#11719947C22semidirect
35. C2×#13133247C22semidirect
37. C2×#13133241C22semidirect
40. C22×Dic212C22semidirect
41. C2×SD16×D53C22semidirect
45. #16811347C22semidirect
47. #16811336C22semidirect
49. D4×Dic106C22semidirect
53. #16811279C22semidirect
54. #16811279C22semidirect
57. #16811272C22semidirect
60. #16811268C22semidirect
64. #16811247C22semidirect
67. #16811238C22semidirect
72. #16811199C22semidirect
74. #16811193C22semidirect
75. #16811189C22semidirect
81. C22⋊Q8×D53C22semidirect
82. #16811102C22semidirect
83. #16811017C22semidirect
84. #16811014C22semidirect
85. #16811006C22semidirect
86. #16811005C22semidirect
87. #16810981C22semidirect
88. #16810975C22semidirect
89. #16810972C22semidirect
90. #16810966C22semidirect
91. #16810966C22semidirect
92. #16810964C22semidirect
93. #16810964C22semidirect
94. #16810962C22semidirect
95. #16810960C22semidirect
96. #16810955C22semidirect
97. #16810946C22semidirect
98. #16810940C22semidirect
99. #16810938C22semidirect
100. #16810915C22semidirect
101. #16810911C22semidirect
102. #16810907C22semidirect
103. #16810882C22semidirect
104. #16810881C22semidirect
105. #16810879C22semidirect
106. #16810874C22semidirect
107. #16810868C22semidirect
109. #16810867C22semidirect
110. #16810865C22semidirect
111. #16810865C22semidirect
112. #16810863C22semidirect
113. #16810855C22semidirect
114. #16810853C22semidirect
115. #16810852C22semidirect
116. #16810851C22semidirect
117. #16810846C22semidirect
118. #16810844C22semidirect
119. #16810844C22semidirect
120. #16810842C22semidirect
121. #16810838C22semidirect
122. #16810837C22semidirect
123. #16810836C22semidirect
124. #16810834C22semidirect
125. #16810832C22semidirect
126. #16810828C22semidirect
127. #16810827C22semidirect
129. #16810786C22semidirect
130. #16810786C22semidirect
131. #16810786C22semidirect
132. #16810786C22semidirect
133. #16810786C22semidirect
134. #16810786C22semidirect
135. #16810786C22semidirect
136. #16810786C22semidirect
137. #16810786C22semidirect
139. #16810782C22semidirect
140. #16810781C22semidirect
141. #16810781C22semidirect
142. #16810780C22semidirect
143. #16810780C22semidirect
144. #16810780C22semidirect
145. #16810780C22semidirect
146. #16810775C22semidirect
147. #16810774C22semidirect
152. #16810768C22semidirect
155. #16810764C22semidirect
156. #16810763C22semidirect
158. #16810761C22semidirect
159. #16810761C22semidirect
160. #16810760C22semidirect
161. #16810755C22semidirect
162. #16810731C22semidirect
163. #16810722C22semidirect
164. #16810720C22semidirect
165. #16810717C22semidirect
166. C4×#11719923C22semidirect
167. C4×#11719923C22semidirect
168. #16810703C22semidirect
169. #16810701C22semidirect
171. #16810697C22semidirect
172. #16810696C22semidirect
174. #16810688C22semidirect
175. C8×C22⋊D53C22semidirect
176. #16810685C22semidirect
177. #16810683C22semidirect
178. #16810631C22semidirect
179. #16810631C22semidirect
180. #16810630C22semidirect
181. #16810616C22semidirect
182. #16810616C22semidirect
183. #16810616C22semidirect
184. #16810589C22semidirect
185. #16810588C22semidirect
186. #16810586C22semidirect
187. C22⋊C8×D53C22semidirect
189. C53×#546C22semidirect
190. C53×#489C22semidirect
191. C53×#485C22semidirect
192. C53×#482C22semidirect
193. C53×#474C22semidirect
195. C53×#466C22semidirect
196. C53×#463C22semidirect
197. C53×#449C22semidirect
199. C53×#442C22semidirect
200. C53×#435C22semidirect
201. C53×#418C22semidirect
202. C53×#416C22semidirect
927. #3319D53semidirect
998. #546C2×D53semidirect
1023. #489C2×D53semidirect
1031. #485C2×D53semidirect
1035. #482C2×D53semidirect
1041. #474C2×D53semidirect
1053. #466C2×D53semidirect
1065. #463C2×D53semidirect
1097. #449C2×D53semidirect
1106. #442C2×D53semidirect
1119. #435C2×D53semidirect
1127. #418C2×D53semidirect
1131. #416C2×D53semidirect
1136. C53#61627semidirect

Maximal subgroups

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

subgroupindex
#202889852
#202883862
#202870032
#202869962
#202869042
#202867802
#202867522
#202866392
#202866292
#202864532
#202864282
#202863422
#202863262
#202862902
#202862682
#202862422
#202862322
#202858252
#202858212
#202855952
#202855602
#202855402
#202855002
#202849962
#202849822
#202840132
#202839982
#202839592
#202839282
#202837622
C53×#33192
#6162753