Finite Group Databasebeta

← #15633803

Subgroups — #15633803

Order 2816.

1776 conjugacy classes of subgroups.

The subgroup lattice has 842 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082428C211yesmaximal, characteristic, complemented
2#13081415C212yesmaximal, complemented
3#13081393C212yesmaximal, complemented
4#13081352C212yesmaximal, complemented
5#13081330C212yesmaximal, complemented
6#13081297C212yesmaximal, complemented
7#13081290C212yesmaximal, complemented
8#13081261C212yesmaximal, complemented
9#13081254C212yesmaximal, complemented
10#13078981C212yesmaximal, complemented
11C2×#10622694C211yesmaximal, characteristic, complemented
12#13078458C212yesmaximal, complemented
13#13078431C211yesmaximal, characteristic, complemented
14#13078162C212yesmaximal
15#13078099C211yesmaximal, characteristic, complemented
16#13077551C211yesmaximal, characteristic, complemented
17#13077459C212yesmaximal, complemented
18C4×#67003C211yesmaximal, characteristic
19C11×#3509C211yesmaximal, characteristic, complemented
20C11×#557C2212yes—
21C11×#557C2212yes—
22C11×#556C2212yes—
23C11×#556C2212yes—
24C11×#552—22no—
25C11×#552—22no—
26C11×#541—22no—
27C11×#536C2212yes—
28C11×#533—21no—
29C11×#533—21no—
30C11×#533C2211yescharacteristic
31C2×C11×C4⋊Q8C2211yescharacteristic
32C11×#519C2212yes—
33C4×C11×#41C2211yescharacteristic
34C2×#67003C2211yescharacteristic
35C2×#66995C2212yes—
36#10623259—21no—
37D11×C4⋊Q8—21no—
38#10623220—22no—
39#10623166—22no—
40#10623163—22no—
41#10623110C2212yes—
42Q8×D44C2212yes—
43#10623098C2212yes—
44Q8×Dic22C2212yes—
45#10623054C2212yes—
46#10623050C2212yes—
47C4×#4339C2211yescharacteristic
48C2×#66922C2211yescharacteristic
49#10622846C2211yescharacteristic
50#10622845C2212yes—
51#10622838C2212yes—
52C2×#66899C2212yes—
53C2×#66899C2212yes—
54#10622703C2212yes—
55#10622703C2212yes—
56#10622703C2214yes—
57#10622696C2212yes—
58#10622696C2214yes—
59#10622696C2212yes—
60#10622695C2214yes—
61#10622694C2212yes—
62#10622694C2212yes—
63#10622694C2212yes—
64#10622694C2212yes—
65#10622694C2214yes—
66#10622670C2214yes—
67#10622669C2214yes—
68#10622668C2214yes—
69#10622667C2214yes—
70#10622643C2214yes—
71C4×#4326C2211yescharacteristic
72C4×#4326C2211yescharacteristic
73C4×#4326C2214yes—
74#10622639C2214yes—
75C4×#4325C2211yescharacteristic
76C4×#4325C2211yescharacteristic
77C4×#4325C2214yes—
78#10622637C2212yes—
79#10622637C2212yes—
80Q8×C11⋊C8C2212yes—
81Q8×C11⋊C8C2212yes—
82#10622635C2214yes—
83#10622635C2214yes—
84#10622634C2212yes—
85#10622634C2214yes—
86#10622633C2214yes—
87#10622633C2212yes—
88C4×#4324C2211yescharacteristic
89C4×#4324C2211yescharacteristic
90C4×#4323C2211yescharacteristic
91C4×#4323C2211yescharacteristic
92#10622621C2212yes—
93#10622620C2212yes—
94#10622615C2211yescharacteristic
95#10622612C2212yes—
96#10622611C2211yescharacteristic
97#10622610C2212yes—
98#10622608C2212yes—
99#10622537C2211yescharacteristic
100C2×C4×C11⋊C8C2211yescharacteristic
101C2×C11×#41C2311yescharacteristic
102C22×Q8×C11C2312yes—
103C2×Q8×D11—22no—
104C2×#4339C2311yescharacteristic
105C22×Dic22—21no—
106C11×C4⋊Q8—21no—
107C11×C4⋊Q8—21no—
108C11×C4⋊Q8D411yescharacteristic
109C11×C4⋊Q8D411yescharacteristic
110C11×C4⋊Q8C2312yes—
111C11×C4⋊Q8C2312yes—
112C11×C4⋊Q8C2314yes—
113C11×#126—24no—
114C11×#126—24no—
115C11×#125—22no—
116C11×#125—22no—
117C11×#125—24no—
118C11×#125—24no—
119C11×#125D412yes—
120C11×#124C2314yes—
121C11×#123—24no—
122C11×C22⋊Q8—22no—
123C11×C22⋊Q8—22no—
124C11×C22⋊Q8—22no—
125C11×C22⋊Q8—22no—
126C11×C22⋊Q8D412yes—
127C11×C22⋊Q8D412yes—
128C4×Q8×C11—22no—
129C4×Q8×C11—22no—
130C4×Q8×C11—22no—
131C4×Q8×C11—22no—
132C4×Q8×C11C2311yescharacteristic
133C4×Q8×C11C2311yescharacteristic
134C4×Q8×C11C2314yes—
135C4×Q8×C11C2314yes—
136C4×Q8×C11C2312yes—
137C4×Q8×C11C2312yes—
138C4×D4×C11—21no—
139C4×D4×C11—21no—
140C4×D4×C11C2311yescharacteristic
141C4×D4×C11C2311yescharacteristic
142C11×#117—22no—
143C11×#117—22no—
144C11×#117—24no—
145C11×#117—21no—
146C11×#117C2311yescharacteristic
147C11×#117C2312yes—
148C2×C11×C4⋊C4—21no—
149C2×C11×C4⋊C4—21no—
150C2×C42×C11—21no—
151C2×C42×C11C2311yescharacteristic
152#67003—24no—
153#66999—22no—
154Q8×Dic11—22no—
155#66997—22no—
156C2×#4326C2314yes—
157C2×#4326C2311yescharacteristic
158#66995—28no—
159C2×#4325C2314yes—
160C2×#4325C2311yescharacteristic
161C2×#4324C2311yescharacteristic
162C2×#4323C2311yescharacteristic
163C4×C22⋊D11—21no—
164C4×C22⋊D11—21no—
165#66979C2311yescharacteristic
166C2×C4⋊Dic11—21no—
167C2×C4⋊Dic11C2312yes—
168C2×#4318C2312yes—
169C22×C11⋊C8C2311yescharacteristic
170C22×C11⋊C8C2311yescharacteristic
171#66950—22no—
172#66950—24no—
173#66949—24no—
174#66945—22no—
175C4⋊C4×D11—22no—
176C4⋊C4×D11—22no—
177#66943—22no—
178#66942—24no—
179#66941—22no—
180#66941—22no—
181#66941—24no—
182#66940—22no—
183(C22⋊D11)⋊C4—24no—
184#66931—24no—
185C4×D44C2311yescharacteristic
186C4×D44C2311yescharacteristic
187C4×D44C2314yes—
188#66925—21no—
189C42×D11—21no—
190#66923C2314yes—
191#66922—21no—
192#66922—21no—
193#66922C2312yes—
194#66922C2312yes—
195#66922C2314yes—
196C4×Dic22C2311yescharacteristic
197C4×Dic22C2311yescharacteristic
198C4×Dic22C2314yes—
199#66899C2314yes—
200#66899C2314yes—
201#66899C2314yes—
202#66899C2314yes—
203#66899C2314yes—
204#66899C2314yes—
205#66899C2314yes—
206#66899C2311yescharacteristic
207#66899C2311yescharacteristic
208#66896C2314yes—
209#66896C2311yescharacteristic
210#66896C2311yescharacteristic
211#66874C2311yescharacteristic
212#66874C2311yescharacteristic
213#66873C2311yescharacteristic
214#66873C2311yescharacteristic
215#66872C2314yes—
216#66872C2311yescharacteristic
217#66872C2311yescharacteristic
218#66871C2314yes—
219#66871C2311yescharacteristic
220#66871C2311yescharacteristic
221C4⋊(C11⋊C8)C2312yes—
222C4⋊(C11⋊C8)C2312yes—
223C4⋊(C11⋊C8)C2314yes—
224C4⋊(C11⋊C8)C2314yes—
225#66867C2314yes—
226C4×C11⋊C8C2311yescharacteristic
227C4×C11⋊C8C2311yescharacteristic
228C4×C11⋊C8C2311yescharacteristic
229C4×C11⋊C8C2311yescharacteristic
230C4×C11⋊C8C2314yes—
231#61330—111nomaximal, Sylow
232C11×#41—22no—
233C11×#41—22no—
234C2×Q8×C11—22no—
235C2×Q8×C11—24no—
236C2×Q8×C11—24no—
237C2×Q8×C11C2×D412yes—
238C2×Q8×C11C2×D412yes—
239C2×Q8×C11C2414yes—
240C2×Q8×C11C2411yescharacteristic
241C2×D4×C11—21no—
242C2×D4×C11C2411yescharacteristic
243C22×C4×C11—22no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11C2×D411yescharacteristic
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2411yescharacteristic
250C2×C22⋊D11—21no—
251C22×Dic11—22no—
252Q8×D11—84no—
253#4339—22no—
254#4339#4114yes—
255C2×D44C2411yescharacteristic
256C2×C4×D11—21no—
257C2×C4×D11—21no—
258C2×C4×D11—21no—
259C2×C4×D11—24no—
260C2×Dic22—22no—
261C2×Dic22—22no—
262C2×Dic22—24no—
263C2×Dic22—82no—
264C2×Dic22C2411yescharacteristic
265C11×C4⋊C4—22no—
266C11×C4⋊C4—22no—
267C11×C4⋊C4—22no—
268C11×C4⋊C4—22no—
269C11×C4⋊C4—21no—
270C11×C4⋊C4—21no—
271C11×C4⋊C4—24no—
272C11×C4⋊C4—24no—
273C11×C4⋊C4—24no—
274C11×C4⋊C4—24no—
275C11×C4⋊C4C2×D412yes—
276C11×C4⋊C4C2×D412yes—
277C11×C4⋊C4C2×D412yes—
278C11×C4⋊C4C2×D414yes—
279C11×C4⋊C4C2×D414yes—
280C11×C4⋊C4C2×D412yes—
281C11×C4⋊C4C2411yescharacteristic
282C11×C4⋊C4C2411yescharacteristic
283C11×C22⋊C4—21no—
284C11×C22⋊C4—21no—
285C11×C22⋊C4—21no—
286C11×C22⋊C4—24no—
287C11×C22⋊C4—24no—
288C11×C22⋊C4C2×D414yes—
289C42×C11—21no—
290C42×C11—21no—
291C42×C11—21no—
292C42×C11—24no—
293C42×C11—24no—
294C42×C11C2×D411yescharacteristic
295C42×C11C2×D411yescharacteristic
296C42×C11C2411yescharacteristic
297C42×C11C2411yescharacteristic
298C42×C11C2414yes—
299C22⋊Dic11—21no—
300#4326—28no—
301#4326—22no—
302#4325—28no—
303#4325—22no—
304#4324—22no—
305#4323—22no—
306(C2×D11)⋊C4—21no—
307(C2×D11)⋊C4—21no—
308(C2×D11)⋊C4—24no—
309C4⋊Dic11—22no—
310C4⋊Dic11—22no—
311C4⋊Dic11—22no—
312C4⋊Dic11—24no—
313C4⋊Dic11C2411yescharacteristic
314C4⋊Dic11C2414yes—
315C4⋊Dic11C2411yescharacteristic
316Dic11⋊C4—21no—
317Dic11⋊C4—21no—
318Dic11⋊C4—24no—
319Dic11⋊C4—24no—
320Dic11⋊C4—24no—
321C4×Dic11—21no—
322C4×Dic11—21no—
323C4×Dic11—24no—
324C4×Dic11—21no—
325#4318—24no—
326C2×C11⋊C8—22no—
327C2×C11⋊C8—22no—
328C2×C11⋊C8C2411yescharacteristic
329C2×C11⋊C8C2411yescharacteristic
330C2×C11⋊C8C2411yescharacteristic
331C2×C11⋊C8C2411yescharacteristic
332C2×C11⋊C8C2414yes—
333#3509D1111yescharacteristic, complemented
334#3503—111no—
335#3374—112no—
336#3372—112no—
337#3369—112no—
338#3367—112no—
339#3364—112no—
340#3363—112no—
341#3360—112no—
342#3359—112no—
343#3137—112no—
344C2×#487—111no—
345#3082—112no—
346#3079—111no—
347#3046—112no—
348#3039—111no—
349#2960—111no—
350#2947—112no—
351C4×#135—111no—
352C23×C11—21no—
353C23×C11C22×D411yescharacteristic
354C22×D11—21no—
355Q8×C11—24no—
356Q8×C11—24no—
357Q8×C11—24no—
358Q8×C11—21no—
359Q8×C11—24no—
360Q8×C11—21no—
361Q8×C11—44no—
362D4×C11—21no—
363D4×C11—21no—
364D4×C11—42no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—21no—
368C2×C4×C11—21no—
369C2×C4×C11—24no—
370C2×C4×C11—21no—
371C2×C4×C11—44no—
372C2×C4×C11—42no—
373C2×C4×C11—42no—
374C2×C4×C11—42no—
375C2×C4×C11C22×D414yes—
376C2×C4×C11C22×D414yes—
377C2×C4×C11C22×D411yescharacteristic
378C2×C4×C11C22×D411yescharacteristic
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C2×#4112yes—
383C2×C4×C112−1+412yes—
384C2×C4×C11C2511yescharacteristic
385C22⋊D11—24no—
386C2×Dic11—21no—
387C2×Dic11—21no—
388C2×Dic11—21no—
389C2×Dic11—24no—
390C2×Dic11—82no—
391D44—21no—
392D44C2×#4112yes—
393C4×D11—24no—
394C4×D11—42no—
395C4×D11—42no—
396C4×D11—84no—
397Dic22—21no—
398Dic22—44no—
399Dic22—82no—
400Dic22—84no—
401Dic22C2×#4112yes—
402C11⋊C8—21no—
403C11⋊C8—21no—
404C11⋊C8—24no—
405C11⋊C8—21no—
406C11⋊C8—21no—
407C2×#137—112no—
408C2×#135—111no—
409Q82—112no—
410#557—112no—
411#557C2×D1112yes—
412#557C2×D1112yes—
413#556C2×D1112yes—
414#556C2×D1112yes—
415#554—112no—
416#554—222no—
417#552—22no—
418#552—22no—
419D4×Q8—112no—
420D4×Q8—222no—
421#544—112no—
422#544—222no—
423#541—22no—
424#536C2×D1112yes—
425#533—21no—
426#533—21no—
427#533—221no—
428#533C2×D1111yescharacteristic
429C2×C4⋊Q8—111no—
430C2×C4⋊Q8—221no—
431C2×C4⋊Q8C2×D1111yescharacteristic
432#520—112no—
433#519C2×D1112yes—
434C4×#41—111no—
435C4×#41C2×D1111yescharacteristic
436#491—114no—
437#489—114no—
438#488—114no—
439#487—114no—
440#487—112no—
441#487—112no—
442#487—112no—
443#487—112no—
444#479—114no—
445#479—114no—
446#477—112no—
447#477—114no—
448#476—112no—
449#475—112no—
450#475—114no—
451#474—112no—
452#464—114no—
453#463—114no—
454#462—112no—
455#462—114no—
456#462—112no—
457#461—112no—
458#461—114no—
459#461—112no—
460#446—112no—
461#446—112no—
462C8×Q8—112no—
463C8×Q8—112no—
464#441—114no—
465#440—114no—
466C4×Q16—111no—
467C4×Q16—114no—
468C4×Q16—111no—
469C4×SD16—111no—
470C4×SD16—114no—
471C4×SD16—111no—
472C4×SD16—111no—
473C4×SD16—111no—
474C4×D8—111no—
475C4×D8—111no—
476#428—112no—
477#427—111no—
478#424—112no—
479#423—111no—
480#419—112no—
481#417—112no—
482#416—111no—
483#416—111no—
484C2×#103—112no—
485C2×#103—112no—
486#405—112no—
487C2×C4×C8—111no—
488C22×C11—21no—
489C22×C11—21no—
490C22×C11—41no—
491C22×C11—41no—
492C22×C11—41no—
493C22×C11#54812yes—
494C22×C11C23×D411yescharacteristic
495C2×D11—22no—
496C2×D11—41no—
497C2×D11—41no—
498C4×C11—21no—
499C4×C11—24no—
500C4×C11—21no—
501C4×C11—24no—
502C4×C11—41no—
503C4×C11—44no—
504C4×C11—41no—
505C4×C11—41no—
506C4×C11#54812yes—
507C4×C11#57712yes—
508C4×C11#57812yes—
509C4×C11C22×#4111yescharacteristic
510C4×C11C2×2−1+411yescharacteristic
511Dic11—22no—
512Dic11—44no—
513Dic11—41no—
514Dic11—41no—
515C2×#41—111no—
516C2×#41C22×D1111yescharacteristic
517C22×Q8—222no—
518C22×Q8—221no—
519C22×Q8C22×D1112yes—
520#137—228no—
521#135—224no—
522C2×Q16—111no—
523C2×Q16—114no—
524C2×SD16—111no—
525C2×SD16—114no—
526C2×SD16—111no—
527C2×D8—111no—
528C2×M16—112no—
529C22×C8—111no—
530C22×C8—111no—
531C4⋊Q8—21no—
532C4⋊Q8—21no—
533C4⋊Q8—112no—
534C4⋊Q8—112no—
535C4⋊Q8—114no—
536C4⋊Q8—222no—
537C4⋊Q8—222no—
538C4⋊Q8—222no—
539C4⋊Q8—224no—
540C4⋊Q8—221no—
541C4⋊Q8—221no—
542C4⋊Q8C22⋊D1111yescharacteristic
543C4⋊Q8C22⋊D1111yescharacteristic
544C4⋊Q8C22×D1112yes—
545C4⋊Q8C22×D1112yes—
546C4⋊Q8C22×D1114yes—
547#126—24no—
548#126—24no—
549#125—22no—
550#125—22no—
551#125—24no—
552#125—24no—
553#125—114no—
554#125—222no—
555#125—224no—
556#125C22⋊D1112yes—
557#124C22×D1114yes—
558#123—24no—
559C22⋊Q8—22no—
560C22⋊Q8—22no—
561C22⋊Q8—22no—
562C22⋊Q8—22no—
563C22⋊Q8—222no—
564C22⋊Q8—222no—
565C22⋊Q8—224no—
566C22⋊Q8—224no—
567C22⋊Q8—224no—
568C22⋊Q8C22⋊D1112yes—
569C22⋊Q8C22⋊D1112yes—
570C4×Q8—22no—
571C4×Q8—22no—
572C4×Q8—22no—
573C4×Q8—22no—
574C4×Q8—111no—
575C4×Q8—111no—
576C4×Q8—114no—
577C4×Q8—222no—
578C4×Q8—222no—
579C4×Q8C22×D1111yescharacteristic
580C4×Q8C22×D1111yescharacteristic
581C4×Q8C22×D1114yes—
582C4×Q8C22×D1114yes—
583C4×Q8C22×D1112yes—
584C4×Q8C22×D1112yes—
585C4×D4—21no—
586C4×D4—21no—
587C4×D4—111no—
588C4×D4—111no—
589C4×D4—114no—
590C4×D4—221no—
591C4×D4—221no—
592C4×D4—224no—
593C4×D4C22×D1111yescharacteristic
594C4×D4C22×D1111yescharacteristic
595#117—22no—
596#117—22no—
597#117—24no—
598#117—21no—
599#117—111no—
600#117—222no—
601#117—221no—
602#117C22×D1111yescharacteristic
603#117C22×D1112yes—
604C2×C4⋊C4—21no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—112no—
607C2×C4⋊C4—221no—
608C2×C4⋊C4—222no—
609C2×C4⋊C4—222no—
610C2×C42—21no—
611C2×C42—221no—
612C2×C42C22×D1111yescharacteristic
613#107—111no—
614#107—111no—
615#107—114no—
616#106—111no—
617#106—111no—
618#106—114no—
619C4⋊C8—112no—
620C4⋊C8—112no—
621C4⋊C8—114no—
622C4⋊C8—114no—
623#103—114no—
624#103—114no—
625#103—114no—
626#103—114no—
627#103—111no—
628#103—111no—
629#103—114no—
630#103—114no—
631#103—114no—
632#103—111no—
633#103—111no—
634#102—111no—
635#102—111no—
636#102—114no—
637#102—111no—
638#102—111no—
639#97—114no—
640C4×C8—111no—
641C4×C8—111no—
642C4×C8—111no—
643C4×C8—111no—
644C4×C8—114no—
645C2×C11—22no—
646C2×C11—81no—
647C2×C11C2×#54811yescharacteristic
648C2×C11C2×#57711yescharacteristic
649C2×C11C2×#57811yescharacteristic
650D11—42no—
651#41—22no—
652#41—22no—
653#41—114no—
654#41—222no—
655C2×Q8—22no—
656C2×Q8—24no—
657C2×Q8—24no—
658C2×Q8—111no—
659C2×Q8—222no—
660C2×Q8—224no—
661C2×Q8—222no—
662C2×Q8—882no—
663C2×Q8—884no—
664C2×Q8C2×C22⋊D1112yes—
665C2×Q8C2×C22⋊D1112yes—
666C2×Q8C23×D1114yes—
667C2×Q8C23×D1111yescharacteristic
668C2×D4—21no—
669C2×D4—111no—
670C2×D4—221no—
671C2×D4C23×D1111yescharacteristic
672C22×C4—22no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—221no—
677C22×C4—222no—
678C22×C4—221no—
679C22×C4—221no—
680C22×C4—224no—
681C22×C4C2×C22⋊D1111yescharacteristic
682C22×C4C2×C22⋊D1111yescharacteristic
683C22×C4C23×D1111yescharacteristic
684Q16—222no—
685Q16—228no—
686SD16—222no—
687SD16—222no—
688SD16—228no—
689D8—222no—
690M16—224no—
691C2×C8—111no—
692C2×C8—111no—
693C2×C8—111no—
694C2×C8—111no—
695C2×C8—114no—
696C2×C8—222no—
697C2×C8—222no—
698C4⋊C4—22no—
699C4⋊C4—22no—
700C4⋊C4—22no—
701C4⋊C4—22no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—24no—
705C4⋊C4—24no—
706C4⋊C4—24no—
707C4⋊C4—24no—
708C4⋊C4—114no—
709C4⋊C4—111no—
710C4⋊C4—111no—
711C4⋊C4—222no—
712C4⋊C4—222no—
713C4⋊C4—224no—
714C4⋊C4—224no—
715C4⋊C4—222no—
716C4⋊C4—221no—
717C4⋊C4—221no—
718C4⋊C4—224no—
719C4⋊C4—224no—
720C4⋊C4C2×C22⋊D1112yes—
721C4⋊C4C2×C22⋊D1112yes—
722C4⋊C4C2×C22⋊D1112yes—
723C4⋊C4C2×C22⋊D1112yes—
724C4⋊C4C2×C22⋊D1114yes—
725C4⋊C4C2×C22⋊D1114yes—
726C4⋊C4C23×D1111yescharacteristic
727C4⋊C4C23×D1111yescharacteristic
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—24no—
732C22⋊C4—24no—
733C22⋊C4—221no—
734C22⋊C4—221no—
735C22⋊C4—221no—
736C22⋊C4—224no—
737C22⋊C4C2×C22⋊D1114yes—
738C42—21no—
739C42—21no—
740C42—21no—
741C42—24no—
742C42—24no—
743C42—221no—
744C42—221no—
745C42—221no—
746C42—224no—
747C42C2×C22⋊D1111yescharacteristic
748C42C2×C22⋊D1111yescharacteristic
749C42C23×D1111yescharacteristic
750C42C23×D1111yescharacteristic
751C42C23×D1114yes—
752C11#6133011yescharacteristic, complemented, Sylow
753C23—21no—
754C23—221no—
755C23C22×C22⋊D1111yescharacteristic
756Q8—24no—
757Q8—24no—
758Q8—24no—
759Q8—21no—
760Q8—24no—
761Q8—21no—
762Q8—44no—
763Q8—112no—
764Q8—221no—
765Q8—444no—
766Q8—882no—
767Q8—884no—
768D4—21no—
769D4—21no—
770D4—42no—
771D4—112no—
772D4—224no—
773D4—221no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—24no—
779C2×C4—21no—
780C2×C4—44no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—221no—
785C2×C4—224no—
786C2×C4—221no—
787C2×C4—221no—
788C2×C4—224no—
789C2×C4—442no—
790C2×C4—442no—
791C2×C4—884no—
792C2×C4—882no—
793C2×C4#41×D1112yes—
794C2×C4#6704312yes—
795C2×C4C22×C22⋊D1114yes—
796C2×C4C22×C22⋊D1114yes—
797C2×C4C22×C22⋊D1111yescharacteristic
798C2×C4C22×C22⋊D1111yescharacteristic
799C2×C4C22×C22⋊D1111yescharacteristic
800C2×C4C22×C22⋊D1111yescharacteristic
801C2×C4C22×C22⋊D1111yescharacteristic
802C2×C4C24×D1111yescharacteristic
803C8—221no—
804C8—221no—
805C8—224no—
806C8—221no—
807C8—221no—
808C22—21no—
809C22—21no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—222no—
814C22—441no—
815C22—441no—
816C22#1062336212yes—
817C22C23×C22⋊D1111yescharacteristic
818C4—21no—
819C4—24no—
820C4—21no—
821C4—24no—
822C4—41no—
823C4—44no—
824C4—41no—
825C4—41no—
826C4—222no—
827C4—441no—
828C4—444no—
829C4—441no—
830C4#1062336212yes—
831C4#1062336812yes—
832C4#1062336912yes—
833C4C2×#41×D1111yescharacteristic
834C4C2×#6704311yescharacteristic
835C2—22no—
836C2—81no—
837C2—442no—
838C2C2×#1062336211yescharacteristic
839C2C2×#1062336811yescharacteristic
840C2C2×#1062336911yescharacteristic
subgroupG/H
centerC22C23×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3509C2
socleC22×C11C23×D4
prime radicalC2×#67003C22
hypercenter#3509D11
hypocenterC11#61330
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #533 ◁ #3509

Complements

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

NH ≅ G/Ntype
1. #13082428C2semidirect
2. #13081415C2semidirect
3. #13081393C2semidirect
4. #13081352C2semidirect
5. #13081330C2semidirect
6. #13081297C2semidirect
7. #13081290C2semidirect
8. #13081261C2semidirect
9. #13081254C2semidirect
10. #13078981C2semidirect
11. C2×#10622694C2semidirect
12. #13078458C2semidirect
13. #13078431C2semidirect
15. #13078099C2semidirect
16. #13077551C2semidirect
17. #13077459C2semidirect
19. C11×#3509C2semidirect
333. #3509D11semidirect
752. C11#61330semidirect

Maximal subgroups

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

subgroupindex
#130824282
#130814152
#130813932
#130813522
#130813302
#130812972
#130812902
#130812612
#130812542
#130789812
C2×#106226942
#130784582
#130784312
#130781622
#130780992
#130775512
#130774592
C4×#670032
C11×#35092
#6133011