Finite Group Databasebeta

← #15633807

Subgroups — #15633807

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#13082502C211yesmaximal, characteristic, complemented
2#13082435C211yesmaximal, characteristic, complemented
3#13081417C212yesmaximal, complemented
4#13081395C212yesmaximal, complemented
5#13081354C212yesmaximal, complemented
6#13081332C212yesmaximal, complemented
7#13081299C212yesmaximal, complemented
8#13081292C212yesmaximal, complemented
9#13081263C212yesmaximal, complemented
10#13081256C212yesmaximal, complemented
11#13078985C212yesmaximal, complemented
12C2×#10622294C211yesmaximal, characteristic, complemented
13#13078461C212yesmaximal, complemented
14#13078431C211yesmaximal, characteristic, complemented
15#13078164C212yesmaximal
16#13078103C211yesmaximal, characteristic, complemented
17#13077550C211yesmaximal, characteristic, complemented
18#13077462C212yesmaximal, complemented
19C4×C11×#135C211yesmaximal, characteristic
20C2×C11×#135C2211yescharacteristic
21C4×C11×#41C2211yescharacteristic
22C4×C11×#41C2211yescharacteristic
23#10623358C2212yes—
24#10623356C2212yes—
25C2×#67004C2212yes—
26#10623101C2212yes—
27#10623098C2212yes—
28#10623098C2212yes—
29Q8×Dic22C2212yes—
30#10623074—22no—
31#10623074C2212yes—
32#10623073C2212yes—
33#10623073C2212yes—
34#10623072—22no—
35#10623072—22no—
36D4×Dic22—22no—
37D4×Dic22C2212yes—
38#10623050—22no—
39#10623050C2212yes—
40#10623049—22no—
41#10623047C2212yes—
42#10623001—21no—
43#10623001—21no—
44#10623001—21no—
45#10623001C2211yescharacteristic
46C2×#66922—21no—
47C2×#66922C2211yescharacteristic
48C2×#66922C2211yescharacteristic
49C4×C11×Q16C2211yescharacteristic
50C4×C11×Q16C2211yescharacteristic
51C4×C11×SD16C2211yescharacteristic
52C4×C11×SD16C2211yescharacteristic
53C4×C11×SD16C2211yescharacteristic
54C4×C11×SD16C2211yescharacteristic
55C4×C11×D8C2211yescharacteristic
56C4×C11×D8C2211yescharacteristic
57C11×#427C2211yescharacteristic
58C11×#416C2211yescharacteristic
59C11×#416C2211yescharacteristic
60C2×C4×C8×C11C2211yescharacteristic
61#10622845C2212yes—
62#10622795C2214yes—
63#10622779C2214yes—
64#10622775C2214yes—
65#10622766C2214yes—
66C2×#66880C2212yes—
67C2×#66880C2212yes—
68#10622715C2212yes—
69#10622714C2212yes—
70#10622644C2212yes—
71#10622644C2212yes—
72#10622634C2212yes—
73#10622633C2212yes—
74#10622632C2212yes—
75#10622632C2212yes—
76#10622621C2212yes—
77#10622620C2212yes—
78#10622617C2212yes—
79#10622608C2212yes—
80#10622537C2211yescharacteristic
81#10622490C2214yes—
82#10622488C2214yes—
83#10622470C2214yes—
84#10622467C2214yes—
85#10622410C2214yes—
86#10622405C2214yes—
87#10622403C2214yes—
88#10622402C2214yes—
89#10622381C2214yes—
90#10622378C2214yes—
91#10622371C2214yes—
92#10622370C2214yes—
93#10622294C2212yes—
94#10622294C2212yes—
95#10622294C2212yes—
96#10622294C2212yes—
97#10622292C2212yes—
98#10622292C2212yes—
99C8×Dic22C2212yes—
100C8×Dic22C2212yes—
101C2×C11×#41C2311yescharacteristic
102C2×C11×#41C2311yescharacteristic
103C22×Dic22—21no—
104C22×Dic22—22no—
105C22×Dic22C2312yes—
106C11×#135—24no—
107C2×C11×Q16C2311yescharacteristic
108C2×C11×SD16C2311yescharacteristic
109C2×C11×SD16C2311yescharacteristic
110C2×C11×D8C2311yescharacteristic
111C22×C8×C11C2311yescharacteristic
112C22×C8×C11C2311yescharacteristic
113C4×Q8×C11C2311yescharacteristic
114C4×Q8×C11C2311yescharacteristic
115C4×Q8×C11C2311yescharacteristic
116C4×Q8×C11C2311yescharacteristic
117C4×D4×C11—21no—
118C4×D4×C11—21no—
119C4×D4×C11—21no—
120C4×D4×C11—21no—
121C4×D4×C11C2311yescharacteristic
122C4×D4×C11C2311yescharacteristic
123C4×D4×C11C2311yescharacteristic
124C4×D4×C11C2311yescharacteristic
125C11×#117—21no—
126C11×#117—21no—
127C11×#117C2311yescharacteristic
128C11×#117C2311yescharacteristic
129C2×C42×C11—21no—
130C2×C42×C11—21no—
131C2×C42×C11C2311yescharacteristic
132#67004—28no—
133Q8×Dic11C2314yes—
134#66997C2314yes—
135C2×#4326C2314yes—
136#66989C2314yes—
137#66988—24no—
138D4×Dic11—24no—
139D4×Dic11C2314yes—
140C2×#4324C2314yes—
141#66979—22no—
142#66979—22no—
143#66979—22no—
144#66979C2312yes—
145C2×C4⋊Dic11—21no—
146C2×C4⋊Dic11—21no—
147C2×C4⋊Dic11—21no—
148C2×C4⋊Dic11—22no—
149C2×C4⋊Dic11—22no—
150C2×C4⋊Dic11C2312yes—
151#66977—22no—
152#66977—22no—
153#66977—22no—
154#66977—22no—
155#66977—22no—
156#66977—22no—
157#66977D412yes—
158#66977D412yes—
159C2×#4318C2312yes—
160#66943—24no—
161#66943C2314yes—
162#66942—24no—
163#66942—24no—
164#66941—24no—
165#66941C2314yes—
166#66940C2314yes—
167#66940C2314yes—
168#66932—24no—
169#66932—24no—
170#66931—24no—
171#66931—24no—
172#66931—24no—
173#66930—24no—
174#66923—22no—
175#66923—22no—
176#66923—22no—
177#66923D412yes—
178#66922—22no—
179#66922—21no—
180#66922—21no—
181#66922—21no—
182#66922—21no—
183#66922—22no—
184#66922—22no—
185#66922D411yescharacteristic
186#66922D411yescharacteristic
187#66922C2312yes—
188#66922C2312yes—
189#66922C2312yes—
190#66922C2312yes—
191C4×Dic22—22no—
192C4×Dic22—22no—
193C4×Dic22—22no—
194C4×Dic22—22no—
195C4×Dic22—22no—
196C4×Dic22—22no—
197C4×Dic22C2312yes—
198C4×Dic22C2312yes—
199C11×#107C2311yescharacteristic
200C11×#107C2311yescharacteristic
201C11×#106C2311yescharacteristic
202C11×#106C2311yescharacteristic
203C11×#103C2311yescharacteristic
204C11×#103C2311yescharacteristic
205C11×#103C2311yescharacteristic
206C11×#103C2311yescharacteristic
207C11×#102C2311yescharacteristic
208C11×#102C2311yescharacteristic
209C11×#102C2311yescharacteristic
210C11×#102C2311yescharacteristic
211C4×C8×C11C2311yescharacteristic
212C4×C8×C11C2311yescharacteristic
213C4×C8×C11C2311yescharacteristic
214C4×C8×C11C2311yescharacteristic
215#66899C2314yes—
216#66896C2314yes—
217#66880C2314yes—
218#66880C2314yes—
219#66880C2314yes—
220#66880C2314yes—
221#66879C2314yes—
222Dic11⋊C8C2314yes—
223Dic11⋊C8C2314yes—
224C8×Dic11C2314yes—
225#66874C2314yes—
226#66874C2314yes—
227#66872C2314yes—
228#66871C2314yes—
229C4⋊(C11⋊C8)C2312yes—
230C4⋊(C11⋊C8)C2312yes—
231#61330—111nomaximal, Sylow
232C11×#41—22no—
233C11×#41—22no—
234C11×#41—22no—
235C11×#41#4114yes—
236C2×Q8×C11C2411yescharacteristic
237C2×Q8×C11C2411yescharacteristic
238C2×D4×C11—21no—
239C2×D4×C11—21no—
240C2×D4×C11C2411yescharacteristic
241C2×D4×C11C2411yescharacteristic
242C22×C4×C11—21no—
243C22×C4×C11—21no—
244C22×C4×C11—21no—
245C22×C4×C11—21no—
246C22×C4×C11—21no—
247C22×C4×C11—21no—
248C22×C4×C11C2×D411yescharacteristic
249C22×C4×C11C2×D411yescharacteristic
250C22×C4×C11C2411yescharacteristic
251C22×Dic11—24no—
252C22×Dic11—22no—
253C22×Dic11—22no—
254C2×Dic22—24no—
255C2×Dic22—22no—
256C2×Dic22—22no—
257C2×Dic22—22no—
258C2×Dic22—24no—
259C2×Dic22—24no—
260C2×Dic22—82no—
261C2×Dic22—84no—
262C2×Dic22C2×D412yes—
263C2×Dic22C2×D412yes—
264C2×Dic22C2414yes—
265C11×Q16—22no—
266C11×SD16—22no—
267C11×SD16—22no—
268C11×D8—22no—
269C2×C8×C11—22no—
270C2×C8×C11—22no—
271C2×C8×C11C2411yescharacteristic
272C2×C8×C11C2411yescharacteristic
273C2×C8×C11C2411yescharacteristic
274C2×C8×C11C2411yescharacteristic
275C11×C4⋊C4—21no—
276C11×C4⋊C4—21no—
277C11×C4⋊C4—21no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4C2411yescharacteristic
280C11×C4⋊C4C2411yescharacteristic
281C11×C4⋊C4C2411yescharacteristic
282C11×C4⋊C4C2411yescharacteristic
283C11×C22⋊C4—21no—
284C11×C22⋊C4—21no—
285C11×C22⋊C4—21no—
286C11×C22⋊C4—21no—
287C11×C22⋊C4—21no—
288C11×C22⋊C4—21no—
289C42×C11—21no—
290C42×C11—21no—
291C42×C11—21no—
292C42×C11—21no—
293C42×C11—21no—
294C42×C11—21no—
295C42×C11C2×D411yescharacteristic
296C42×C11C2×D411yescharacteristic
297C42×C11C2411yescharacteristic
298C42×C11C2411yescharacteristic
299C22⋊Dic11—24no—
300C22⋊Dic11—24no—
301C22⋊Dic11—24no—
302C22⋊Dic11C2×D414yes—
303#4326—28no—
304#4324—28no—
305C4⋊Dic11—24no—
306C4⋊Dic11—24no—
307C4⋊Dic11—22no—
308C4⋊Dic11—22no—
309C4⋊Dic11—22no—
310C4⋊Dic11—22no—
311C4⋊Dic11—22no—
312C4⋊Dic11—22no—
313C4⋊Dic11—22no—
314C4⋊Dic11C2×D412yes—
315C4⋊Dic11C2×D412yes—
316C4⋊Dic11C2×D412yes—
317C4⋊Dic11C2×D412yes—
318C4⋊Dic11C2414yes—
319Dic11⋊C4—24no—
320Dic11⋊C4—24no—
321Dic11⋊C4—24no—
322Dic11⋊C4—24no—
323Dic11⋊C4—24no—
324Dic11⋊C4—24no—
325Dic11⋊C4C2×D414yes—
326Dic11⋊C4C2×D414yes—
327C4×Dic11—24no—
328C4×Dic11—24no—
329C4×Dic11—24no—
330C4×Dic11C2414yes—
331#4318—24no—
332C2×C11⋊C8C2414yes—
333#3509—111no—
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×#135D1111yescharacteristic
352C23×C11—21no—
353C23×C11—21no—
354C23×C11C22×D411yescharacteristic
355Q8×C11—21no—
356Q8×C11—21no—
357Q8×C11—21no—
358Q8×C11C2×#4112yes—
359D4×C11—24no—
360D4×C11—21no—
361D4×C11—21no—
362D4×C11—21no—
363D4×C11—42no—
364D4×C11C2×#4112yes—
365C2×C4×C11—21no—
366C2×C4×C11—24no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—21no—
370C2×C4×C11—21no—
371C2×C4×C11—21no—
372C2×C4×C11—21no—
373C2×C4×C11—21no—
374C2×C4×C11—42no—
375C2×C4×C11—42no—
376C2×C4×C11—42no—
377C2×C4×C11—42no—
378C2×C4×C11—42no—
379C2×C4×C11C22×D411yescharacteristic
380C2×C4×C11C22×D411yescharacteristic
381C2×C4×C11C22×D411yescharacteristic
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C2×#4112yes—
385C2×C4×C112−1+412yes—
386C2×C4×C11C2511yescharacteristic
387C2×Dic11—24no—
388C2×Dic11—24no—
389C2×Dic11—44no—
390C2×Dic11—84no—
391C2×Dic11—82no—
392C2×Dic11C22×D414yes—
393C2×Dic11C22×D414yes—
394Dic22—24no—
395Dic22—24no—
396Dic22—24no—
397Dic22—24no—
398Dic22—44no—
399Dic22—44no—
400Dic22—84no—
401Dic22—82no—
402C8×C11—21no—
403C8×C11—21no—
404C8×C11—21no—
405C8×C11—21no—
406C11⋊C8—24no—
407C2×#137—112no—
408C2×#135C2×D1111yescharacteristic
409Q82—112no—
410#557—112no—
411#557—112no—
412#557—112no—
413#556—112no—
414#556—112no—
415#554—112no—
416#554—222no—
417#552—222no—
418#552—222no—
419D4×Q8—112no—
420D4×Q8—222no—
421#544—112no—
422#544—222no—
423#541—222no—
424#536—112no—
425#533—111no—
426#533—221no—
427#533—221no—
428#533—221no—
429C2×C4⋊Q8—111no—
430C2×C4⋊Q8—111no—
431C2×C4⋊Q8—221no—
432#520—112no—
433#519—112no—
434C4×#41C2×D1111yescharacteristic
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—114no—
455#462—112no—
456#462—112no—
457#461—114no—
458#461—112no—
459#461—112no—
460#446—112no—
461#446—112no—
462C8×Q8—112no—
463C8×Q8—112no—
464#441—114no—
465#440—114no—
466C4×Q16—114no—
467C4×Q16C2×D1111yescharacteristic
468C4×Q16C2×D1111yescharacteristic
469C4×SD16—114no—
470C4×SD16C2×D1111yescharacteristic
471C4×SD16C2×D1111yescharacteristic
472C4×SD16C2×D1111yescharacteristic
473C4×SD16C2×D1111yescharacteristic
474C4×D8C2×D1111yescharacteristic
475C4×D8C2×D1111yescharacteristic
476#428—112no—
477#427C2×D1111yescharacteristic
478#424—112no—
479#423—111no—
480#419—112no—
481#417—112no—
482#416C2×D1111yescharacteristic
483#416C2×D1111yescharacteristic
484C2×#103—112no—
485C2×#103—112no—
486#405—112no—
487C2×C4×C8C2×D1111yescharacteristic
488C22×C11—21no—
489C22×C11—21no—
490C22×C11—22no—
491C22×C11—41no—
492C22×C11—41no—
493C22×C11—41no—
494C22×C11—41no—
495C22×C11—41no—
496C22×C11#54812yes—
497C22×C11C23×D411yescharacteristic
498C4×C11—22no—
499C4×C11—21no—
500C4×C11—21no—
501C4×C11—41no—
502C4×C11—41no—
503C4×C11—41no—
504C4×C11—41no—
505C4×C11—41no—
506C4×C11#54812yes—
507C4×C11#57712yes—
508C4×C11#57812yes—
509C4×C11C22×#4111yescharacteristic
510C4×C11C2×2−1+411yescharacteristic
511Dic11—24no—
512Dic11—24no—
513Dic11—44no—
514Dic11—44no—
515C2×#41C22×D1111yescharacteristic
516C2×#41C22×D1111yescharacteristic
517C22×Q8—112no—
518C22×Q8—222no—
519C22×Q8—221no—
520#137—228no—
521#135—24no—
522C2×Q16—114no—
523C2×Q16C22×D1111yescharacteristic
524C2×SD16—114no—
525C2×SD16C22×D1111yescharacteristic
526C2×SD16C22×D1111yescharacteristic
527C2×D8C22×D1111yescharacteristic
528C2×M16—112no—
529C22×C8C22×D1111yescharacteristic
530C22×C8C22×D1111yescharacteristic
531C4⋊Q8—114no—
532C4⋊Q8—114no—
533C4⋊Q8—111no—
534C4⋊Q8—111no—
535C4⋊Q8—112no—
536C4⋊Q8—112no—
537C4⋊Q8—112no—
538C4⋊Q8—112no—
539C4⋊Q8—222no—
540C4⋊Q8—222no—
541C4⋊Q8—222no—
542C4⋊Q8—224no—
543C4⋊Q8—221no—
544C4⋊Q8—221no—
545C4⋊Q8—221no—
546C4⋊Q8—221no—
547#126—224no—
548#126—224no—
549#125—114no—
550#125—112no—
551#125—222no—
552#125—222no—
553#125—222no—
554#125—224no—
555#125—224no—
556#125—224no—
557#124—114no—
558#123—224no—
559C22⋊Q8—112no—
560C22⋊Q8—112no—
561C22⋊Q8—224no—
562C22⋊Q8—224no—
563C22⋊Q8—224no—
564C22⋊Q8—222no—
565C22⋊Q8—222no—
566C22⋊Q8—222no—
567C22⋊Q8—222no—
568C22⋊Q8—222no—
569C22⋊Q8—222no—
570C4×Q8—112no—
571C4×Q8—112no—
572C4×Q8—114no—
573C4×Q8—114no—
574C4×Q8—114no—
575C4×Q8—222no—
576C4×Q8—222no—
577C4×Q8—222no—
578C4×Q8—222no—
579C4×Q8—222no—
580C4×Q8—222no—
581C4×Q8C22×D1111yescharacteristic
582C4×Q8C22×D1111yescharacteristic
583C4×Q8C22×D1111yescharacteristic
584C4×Q8C22×D1111yescharacteristic
585C4×D4—21no—
586C4×D4—21no—
587C4×D4—21no—
588C4×D4—21no—
589C4×D4—114no—
590C4×D4—224no—
591C4×D4C22×D1111yescharacteristic
592C4×D4C22×D1111yescharacteristic
593C4×D4C22×D1111yescharacteristic
594C4×D4C22×D1111yescharacteristic
595#117—21no—
596#117—21no—
597#117—112no—
598#117—224no—
599#117—222no—
600#117—222no—
601#117—222no—
602#117C22×D1111yescharacteristic
603#117C22×D1111yescharacteristic
604C2×C4⋊C4—112no—
605C2×C4⋊C4—222no—
606C2×C4⋊C4—222no—
607C2×C4⋊C4—221no—
608C2×C4⋊C4—221no—
609C2×C4⋊C4—221no—
610C2×C42—21no—
611C2×C42—21no—
612C2×C42C22×D1111yescharacteristic
613#107—114no—
614#107C22×D1111yescharacteristic
615#107C22×D1111yescharacteristic
616#106—114no—
617#106C22×D1111yescharacteristic
618#106C22×D1111yescharacteristic
619C4⋊C8—114no—
620C4⋊C8—114no—
621C4⋊C8—112no—
622C4⋊C8—112no—
623#103—114no—
624#103—114no—
625#103—114no—
626#103—114no—
627#103—114no—
628#103—114no—
629#103—114no—
630#103C22×D1111yescharacteristic
631#103C22×D1111yescharacteristic
632#103C22×D1111yescharacteristic
633#103C22×D1111yescharacteristic
634#102—114no—
635#102C22×D1111yescharacteristic
636#102C22×D1111yescharacteristic
637#102C22×D1111yescharacteristic
638#102C22×D1111yescharacteristic
639#97—114no—
640C4×C8—114no—
641C4×C8C22×D1111yescharacteristic
642C4×C8C22×D1111yescharacteristic
643C4×C8C22×D1111yescharacteristic
644C4×C8C22×D1111yescharacteristic
645C2×C11—22no—
646C2×C11—42no—
647C2×C11—81no—
648C2×C11C2×#54811yescharacteristic
649C2×C11C2×#57711yescharacteristic
650C2×C11C2×#57811yescharacteristic
651#41—22no—
652#41—22no—
653#41—22no—
654#41#433914yes—
655C2×Q8—112no—
656C2×Q8—112no—
657C2×Q8—114no—
658C2×Q8—224no—
659C2×Q8—222no—
660C2×Q8—222no—
661C2×Q8—222no—
662C2×Q8—224no—
663C2×Q8—224no—
664C2×Q8—882no—
665C2×Q8—884no—
666C2×Q8C23×D1111yescharacteristic
667C2×Q8C23×D1111yescharacteristic
668C2×D4—21no—
669C2×D4—21no—
670C2×D4C23×D1111yescharacteristic
671C2×D4C23×D1111yescharacteristic
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—224no—
679C22×C4—222no—
680C22×C4—222no—
681C22×C4D4×D1111yescharacteristic
682C22×C4D4×D1111yescharacteristic
683C22×C4C23×D1111yescharacteristic
684Q16—22no—
685Q16—228no—
686SD16—22no—
687SD16—22no—
688SD16—228no—
689D8—22no—
690M16—224no—
691C2×C8—22no—
692C2×C8—22no—
693C2×C8—114no—
694C2×C8C23×D1111yescharacteristic
695C2×C8C23×D1111yescharacteristic
696C2×C8C23×D1111yescharacteristic
697C2×C8C23×D1111yescharacteristic
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—112no—
703C4⋊C4—112no—
704C4⋊C4—112no—
705C4⋊C4—112no—
706C4⋊C4—114no—
707C4⋊C4—114no—
708C4⋊C4—114no—
709C4⋊C4—224no—
710C4⋊C4—224no—
711C4⋊C4—224no—
712C4⋊C4—224no—
713C4⋊C4—224no—
714C4⋊C4—224no—
715C4⋊C4—224no—
716C4⋊C4—224no—
717C4⋊C4—222no—
718C4⋊C4—222no—
719C4⋊C4—222no—
720C4⋊C4—222no—
721C4⋊C4—222no—
722C4⋊C4—222no—
723C4⋊C4—222no—
724C4⋊C4C23×D1111yescharacteristic
725C4⋊C4C23×D1111yescharacteristic
726C4⋊C4C23×D1111yescharacteristic
727C4⋊C4C23×D1111yescharacteristic
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—21no—
731C22⋊C4—21no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—114no—
735C22⋊C4—224no—
736C22⋊C4—224no—
737C22⋊C4—224no—
738C42—21no—
739C42—21no—
740C42—21no—
741C42—21no—
742C42—21no—
743C42—21no—
744C42—114no—
745C42—224no—
746C42—224no—
747C42—224no—
748C42D4×D1111yescharacteristic
749C42D4×D1111yescharacteristic
750C42C23×D1111yescharacteristic
751C42C23×D1111yescharacteristic
752C11#6133011yescharacteristic, complemented, Sylow
753C23—21no—
754C23—21no—
755C23C2×D4×D1111yescharacteristic
756Q8—21no—
757Q8—21no—
758Q8—21no—
759Q8—224no—
760Q8—224no—
761Q8—224no—
762Q8—224no—
763Q8—444no—
764Q8—444no—
765Q8—882no—
766Q8—884no—
767Q8C2×#433912yes—
768D4—24no—
769D4—21no—
770D4—21no—
771D4—21no—
772D4—42no—
773D4C2×#433912yes—
774C2×C4—21no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—114no—
789C2×C4—114no—
790C2×C4—224no—
791C2×C4—224no—
792C2×C4—444no—
793C2×C4—884no—
794C2×C4—882no—
795C2×C4C2×#433912yes—
796C2×C4C2×D4×D1111yescharacteristic
797C2×C4C2×D4×D1111yescharacteristic
798C2×C4C2×D4×D1111yescharacteristic
799C2×C4C2×D4×D1111yescharacteristic
800C2×C4C2×D4×D1111yescharacteristic
801C2×C4#6704312yes—
802C2×C4C24×D1111yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—224no—
808C22—21no—
809C22—21no—
810C22—22no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—41no—
815C22—41no—
816C22#1062308312yes—
817C22C22×D4×D1111yescharacteristic
818C4—22no—
819C4—21no—
820C4—21no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—224no—
827C4—224no—
828C4—444no—
829C4—444no—
830C4#1062308312yes—
831C4#1062330112yes—
832C4#1062330212yes—
833C4C22×#433911yescharacteristic
834C4C2×#6704311yescharacteristic
835C2—22no—
836C2—42no—
837C2—81no—
838C2C2×#1062308311yescharacteristic
839C2C2×#1062330111yescharacteristic
840C2C2×#1062330211yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC4×C11×#135C2
socleC22×C11C23×D4
prime radicalC2×C11×#135C22
hypercenterC4×#135D11
hypocenterC11#61330
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C2×C42 ◁ C4×#135

Complements

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

NH ≅ G/Ntype
1. #13082502C2semidirect
2. #13082435C2semidirect
3. #13081417C2semidirect
4. #13081395C2semidirect
5. #13081354C2semidirect
6. #13081332C2semidirect
7. #13081299C2semidirect
8. #13081292C2semidirect
9. #13081263C2semidirect
10. #13081256C2semidirect
11. #13078985C2semidirect
12. C2×#10622294C2semidirect
13. #13078461C2semidirect
14. #13078431C2semidirect
16. #13078103C2semidirect
17. #13077550C2semidirect
18. #13077462C2semidirect
752. C11#61330semidirect

Maximal subgroups

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

subgroupindex
#130825022
#130824352
#130814172
#130813952
#130813542
#130813322
#130812992
#130812922
#130812632
#130812562
#130789852
C2×#106222942
#130784612
#130784312
#130781642
#130781032
#130775502
#130774622
C4×C11×#1352
#6133011