Finite Group Databasebeta

← #14967755

Subgroups — #14967755

Order 2816.

1562 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076950C211yesmaximal, characteristic, complemented
2#13076942C211yesmaximal, characteristic
3#13076191C212yesmaximal, complemented
4#13076122C212yesmaximal, complemented
5#13076072C212yesmaximal, complemented
6#13076042C212yesmaximal, complemented
7#13075985C212yesmaximal, complemented
8#13075975C212yesmaximal, complemented
9#13075955C212yesmaximal, complemented
10#13075673C212yesmaximal, complemented
11#13074730C211yesmaximal, characteristic, complemented
12#13073180C212yesmaximal, complemented
13#13072940C212yesmaximal, complemented
14#13072444C212yesmaximal, complemented
15#13072091C212yesmaximal, complemented
16#13071351C211yesmaximal, characteristic, complemented
17#13071321C211yesmaximal, characteristic
18C2×#10622264C211yesmaximal, characteristic, complemented
19C11×#2639C211yesmaximal, characteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×#66988C2212yes—
23C2×D4×Dic11C2212yes—
24C2×#66977C2212yes—
25C22×C4×Dic11C2211yescharacteristic
26C11×#400C2212yes—
27C11×#397C2212yes—
28C11×#394C2212yes—
29C11×#393C2212yes—
30C11×#386C2212yes—
31C11×#386C2212yes—
32C2×C11×#95C2211yescharacteristic
33#10622843C2211yescharacteristic
34#10622843C2212yes—
35#10622843C2211yescharacteristic
36#10622834C2211yescharacteristic
37#10622834C2211yescharacteristic
38#10622833C2212yes—
39#10622833C2212yes—
40#10622833C2212yes—
41#10622825C2212yes—
42#10622825C2211yescharacteristic
43#10622825C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2211yescharacteristic
48C2×C11⋊#95C2211yescharacteristic
49#10622598C2212yes—
50#10622594C2212yes—
51#10622594C2212yes—
52#10622594C2212yes—
53#10622591C2212yes—
54#10622591C2212yes—
55#10622586C2211yescharacteristic
56#10622586C2211yescharacteristic
57#10622586C2211yescharacteristic
58#10622586C2211yescharacteristic
59#10622566C2212yes—
60#10622566C2212yes—
61#10622566C2212yes—
62#10622565C2212yes—
63#10622565C2212yes—
64#10622564C2212yes—
65#10622564C2212yes—
66#10622564C2212yes—
67#10622563C2212yes—
68#10622563C2212yes—
69#10622563C2212yes—
70#10622563C2212yes—
71#10622561C2212yes—
72#10622560C2212yes—
73#10622560C2212yes—
74#10622559C2212yes—
75#10622558C2212yes—
76#10622557C2212yes—
77#10622557C2212yes—
78#10622557C2212yes—
79#10622556C2212yes—
80#10622556C2212yes—
81#10622555C2212yes—
82C22⋊C4×Dic11C2212yes—
83C11⋊#401C2212yes—
84#10622274C2212yes—
85#10622274C2212yes—
86#10622274C2212yes—
87#10622274C2212yes—
88#10622273C2212yes—
89#10622273C2212yes—
90#10622273C2212yes—
91#10622272C2212yes—
92#10622271C2212yes—
93#10622269C2212yes—
94#10622269C2212yes—
95#10622267C2212yes—
96#10622266C2212yes—
97#10622266C2212yes—
98#10622266C2212yes—
99#10622264C2212yes—
100#10622264C2212yes—
101#10622264C2212yes—
102#10622264C2212yes—
103#10622264C2212yes—
104#10622263C2212yes—
105#10622259C2212yes—
106#10622259C2212yes—
107C22×Q8×C11C2311yescharacteristic
108C22×D4×C11C2312yes—
109C22×D4×C11C2311yescharacteristic
110C23×C4×C11C2311yescharacteristic
111C23×C4×C11C2311yescharacteristic
112C23×C4×C11C2311yescharacteristic
113C23×Dic11C2311yescharacteristic
114C23×Dic11C2311yescharacteristic
115C23×Dic11C2311yescharacteristic
116C23×Dic11C2311yescharacteristic
117C23×Dic11C2312yes—
118C22×Dic22C2312yes—
119C11×C22⋊Q8—24no—
120C11×#121—24no—
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C4⋊C4C2312yes—
124C2×C11×C22⋊C4C2312yes—
125C2×C11×C22⋊C4C2312yes—
126C2×C11×C22⋊C4C2312yes—
127C2×C11×C22⋊C4C2312yes—
128C2×C11×C22⋊C4C2312yes—
129C2×C11×C22⋊C4C2312yes—
130C2×C22⋊Dic11C2312yes—
131C2×C22⋊Dic11C2312yes—
132C2×C22⋊Dic11C2312yes—
133C2×C22⋊Dic11C2312yes—
134C2×C22⋊Dic11C2312yes—
135C2×C22⋊Dic11C2312yes—
136C2×C22⋊Dic11C2312yes—
137C2×C22⋊Dic11C2312yes—
138C2×C22⋊Dic11C2312yes—
139#66988—44no—
140D4×Dic11—44no—
141C2×C4⋊Dic11C2312yes—
142C2×C4⋊Dic11C2312yes—
143C2×C4⋊Dic11C2312yes—
144C2×C4⋊Dic11C2312yes—
145C2×C4⋊Dic11C2311yescharacteristic
146C2×C4⋊Dic11C2311yescharacteristic
147C2×C4⋊Dic11C2312yes—
148C2×C4⋊Dic11C2312yes—
149C2×C4⋊Dic11C2311yescharacteristic
150C2×C4⋊Dic11C2311yescharacteristic
151#66977—44no—
152C2×Dic11⋊C4C2312yes—
153C2×Dic11⋊C4C2312yes—
154C2×Dic11⋊C4C2312yes—
155C2×Dic11⋊C4C2312yes—
156C2×Dic11⋊C4C2312yes—
157C2×Dic11⋊C4C2312yes—
158C2×C4×Dic11—24no—
159C2×C4×Dic11C2311yescharacteristic
160C2×C4×Dic11C2311yescharacteristic
161C2×C4×Dic11C2311yescharacteristic
162C2×C4×Dic11C2311yescharacteristic
163C2×C4×Dic11C2312yes—
164C2×C4×Dic11C2312yes—
165C2×C4×Dic11C2312yes—
166C11×#95C2312yes—
167C11×#95C2312yes—
168C11×#95C2312yes—
169C11×#95C2312yes—
170C11×#95C2312yes—
171C11×#95C2312yes—
172C11⋊#95C2312yes—
173C11⋊#95C2312yes—
174C11⋊#95C2312yes—
175C11⋊#95C2312yes—
176C11⋊#95C2312yes—
177C11⋊#95C2312yes—
178C11⋊#95C2312yes—
179C11⋊#95C2312yes—
180C11⋊#95C2312yes—
181C11⋊#95C2312yes—
182C11⋊#95C2312yes—
183C11⋊#95C2312yes—
184C11⋊#95C2312yes—
185C11⋊#95C2312yes—
186C11⋊#95C2312yes—
187C11⋊#95C2312yes—
188C11⋊#95C2312yes—
189C11⋊#95C2312yes—
190C11⋊#95C2312yes—
191C11⋊#95C2312yes—
192C11⋊#95C2312yes—
193C11⋊#95C2312yes—
194C11⋊#95C2312yes—
195C11⋊#95C2312yes—
196C11⋊#95C2312yes—
197C11⋊#95C2312yes—
198C11⋊#95C2312yes—
199C11⋊#95C2312yes—
200#36980—111nomaximal, Sylow
201C24×C11C2412yes—
202C24×C11C2411yescharacteristic
203C2×Q8×C11—22no—
204C2×Q8×C11—41no—
205C2×Q8×C11—41no—
206C2×D4×C11—24no—
207C2×D4×C11—24no—
208C2×D4×C11—24no—
209C2×D4×C11—22no—
210C2×D4×C11—41no—
211C2×D4×C11—41no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—41no—
215C22×C4×C11—41no—
216C22×C4×C11—41no—
217C22×C4×C11—41no—
218C22×C4×C11—41no—
219C22×C4×C11—41no—
220C22×C4×C11#4114yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2412yes—
226C22×C4×C11C2411yescharacteristic
227C22×C4×C11C2411yescharacteristic
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—41no—
235C22×Dic11—41no—
236C22×Dic11—42no—
237C22×Dic11—41no—
238C22×Dic11—41no—
239C22×Dic11—41no—
240C22×Dic11—41no—
241C22×Dic11—42no—
242C22×Dic11—42no—
243C22×Dic11C2412yes—
244C22×Dic11C2411yescharacteristic
245C22×Dic11C2411yescharacteristic
246C22×Dic11C2411yescharacteristic
247C22×Dic11C2411yescharacteristic
248C22×Dic11C2412yes—
249C22×Dic11C2412yes—
250C22×Dic11C2412yes—
251C22×Dic11C2412yes—
252C22×Dic11C2412yes—
253C2×Dic22—42no—
254C2×Dic22—42no—
255C2×Dic22—42no—
256C11×C4⋊C4—22no—
257C11×C4⋊C4—22no—
258C11×C4⋊C4—24no—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—24no—
261C11×C22⋊C4—42no—
262C11×C22⋊C4—42no—
263C11×C22⋊C4—42no—
264C11×C22⋊C4—42no—
265C22⋊Dic11—24no—
266C22⋊Dic11—24no—
267C22⋊Dic11—42no—
268C22⋊Dic11—42no—
269C22⋊Dic11—42no—
270C22⋊Dic11—42no—
271C22⋊Dic11—42no—
272C22⋊Dic11—42no—
273C22⋊Dic11—42no—
274C4⋊Dic11—42no—
275C4⋊Dic11—41no—
276C4⋊Dic11—41no—
277C4⋊Dic11—41no—
278C4⋊Dic11—41no—
279C4⋊Dic11—42no—
280C4⋊Dic11—42no—
281C4⋊Dic11—42no—
282C4⋊Dic11—42no—
283C4⋊Dic11—42no—
284Dic11⋊C4—42no—
285Dic11⋊C4—42no—
286Dic11⋊C4—42no—
287Dic11⋊C4—42no—
288Dic11⋊C4—42no—
289Dic11⋊C4—42no—
290C4×Dic11—22no—
291C4×Dic11—22no—
292C4×Dic11—22no—
293C4×Dic11—22no—
294C4×Dic11—42no—
295C4×Dic11—42no—
296C4×Dic11—42no—
297#2855—111no—
298#2854—111no—
299#2775—112no—
300#2770—112no—
301#2766—112no—
302#2764—112no—
303#2759—112no—
304#2758—112no—
305#2757—112no—
306#2737—112no—
307#2659—111no—
308#2639D1111yescharacteristic
309#2510—112no—
310#2488—112no—
311#2450—112no—
312#2419—112no—
313#2329—111no—
314#2325—111no—
315C2×#383—111no—
316C23×C11—21no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—21no—
320C23×C11—22no—
321C23×C11—22no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11C2×#4112yes—
328C23×C11H(5,𝔽2)12yes—
329C23×C112−1+412yes—
330C23×C11C2511yescharacteristic
331Q8×C11—82no—
332D4×C11—48no—
333D4×C11—82no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—44no—
354C2×C4×C11—82no—
355C2×C4×C11—82no—
356C2×C4×C11C2×#4112yes—
357C2×C4×C11C2×#4112yes—
358C2×Dic11—21no—
359C2×Dic11—21no—
360C2×Dic11—21no—
361C2×Dic11—21no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—21no—
367C2×Dic11—21no—
368C2×Dic11—22no—
369C2×Dic11—21no—
370C2×Dic11—21no—
371C2×Dic11—22no—
372C2×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—21no—
377C2×Dic11—21no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—21no—
387C2×Dic11—21no—
388C2×Dic11—44no—
389C2×Dic11—44no—
390C2×Dic11—82no—
391C2×Dic11—82no—
392C2×Dic11—84no—
393Dic22—84no—
394C2×#123—112no—
395C2×C22⋊Q8—112no—
396C2×C22⋊Q8C2×D1111yescharacteristic
397C2×#121C2×D1111yescharacteristic
398C2×C4×D4—112no—
399C22×C42—111no—
400#401—112no—
401#400—112no—
402#400—112no—
403#400—112no—
404#400—112no—
405#400—112no—
406#400C2×D1112yes—
407#398—112no—
408#398—112no—
409#398—112no—
410#398—112no—
411#397—112no—
412#397—112no—
413#397—112no—
414#397—112no—
415#397—112no—
416#397C2×D1112yes—
417#396—112no—
418#395—112no—
419#395—112no—
420#394C2×D1112yes—
421#393—112no—
422#393—112no—
423#393C2×D1112yes—
424#391—112no—
425#391—111no—
426#391—111no—
427#391—112no—
428#391—112no—
429#390—111no—
430#390—111no—
431#389—112no—
432#389—111no—
433#389—111no—
434#389—111no—
435#389—111no—
436#388—112no—
437#388—112no—
438#388—112no—
439#388—112no—
440#388—112no—
441#388—112no—
442#388—112no—
443#387—112no—
444#387—112no—
445#387—112no—
446#387—112no—
447#387—112no—
448#387—112no—
449#387—112no—
450#387—112no—
451#387—112no—
452#386—112no—
453#386—112no—
454#386—112no—
455#386C2×D1112yes—
456#386C2×D1112yes—
457#385—112no—
458#385—112no—
459#385—112no—
460#385—112no—
461#385—112no—
462#383—112no—
463#383—112no—
464#383—112no—
465#383—112no—
466#383—112no—
467#382—112no—
468#381—112no—
469#381—112no—
470#380—111no—
471#380—111no—
472#380—112no—
473#380—112no—
474C4×C22⋊C4—112no—
475C2×#95—111no—
476C2×#95—111no—
477C2×#95—111no—
478C2×#95—111no—
479C2×#95—111no—
480C2×#95C2×D1111yescharacteristic
481C22×C11—22no—
482C22×C11—22no—
483C22×C11—22no—
484C22×C11—22no—
485C22×C11—22no—
486C22×C11—22no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11#54214yes—
495C22×C11C22×#4111yescharacteristic
496C22×C11C2×H(5,𝔽2)11yescharacteristic
497C22×C11C2×2−1+411yescharacteristic
498C22×C11#58511yescharacteristic
499C22×C11#58511yescharacteristic
500C22×C11#58511yescharacteristic
501C22×C11#58511yescharacteristic
502C4×C11—22no—
503C4×C11—22no—
504C4×C11—42no—
505C4×C11—42no—
506C4×C11—42no—
507C4×C11—42no—
508C4×C11—42no—
509Dic11—41no—
510Dic11—41no—
511Dic11—41no—
512Dic11—41no—
513Dic11—42no—
514Dic11—42no—
515Dic11—42no—
516Dic11—42no—
517Dic11—42no—
518Dic11—42no—
519C22×Q8—112no—
520C22×Q8C22×D1111yescharacteristic
521C22×D4C22×D1112yes—
522C22×D4C22×D1111yescharacteristic
523C23×C4—111no—
524C23×C4—111no—
525C23×C4—111no—
526C23×C4—111no—
527C23×C4—112no—
528C23×C4C22×D1111yescharacteristic
529C23×C4C22×D1111yescharacteristic
530C23×C4C22×D1111yescharacteristic
531#123—444no—
532C22⋊Q8—24no—
533C22⋊Q8—444no—
534#121—24no—
535C4×D4—444no—
536C2×C4⋊C4—112no—
537C2×C4⋊C4—112no—
538C2×C4⋊C4—112no—
539C2×C4⋊C4—112no—
540C2×C4⋊C4—112no—
541C2×C4⋊C4—112no—
542C2×C4⋊C4—111no—
543C2×C4⋊C4—112no—
544C2×C4⋊C4—112no—
545C2×C4⋊C4—111no—
546C2×C4⋊C4—112no—
547C2×C4⋊C4—111no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4—112no—
550C2×C4⋊C4—112no—
551C2×C4⋊C4—112no—
552C2×C4⋊C4C22×D1111yescharacteristic
553C2×C4⋊C4C22×D1112yes—
554C2×C4⋊C4C22×D1111yescharacteristic
555C2×C22⋊C4—112no—
556C2×C22⋊C4—112no—
557C2×C22⋊C4—112no—
558C2×C22⋊C4—112no—
559C2×C22⋊C4—112no—
560C2×C22⋊C4—112no—
561C2×C22⋊C4—112no—
562C2×C22⋊C4—112no—
563C2×C22⋊C4—112no—
564C2×C22⋊C4C22×D1112yes—
565C2×C22⋊C4C22×D1112yes—
566C2×C22⋊C4C22×D1112yes—
567C2×C22⋊C4C22×D1112yes—
568C2×C22⋊C4C22×D1112yes—
569C2×C22⋊C4C22×D1112yes—
570C2×C42—111no—
571C2×C42—111no—
572C2×C42—111no—
573C2×C42—111no—
574C2×C42—112no—
575C2×C42—112no—
576C2×C42—112no—
577C2×C42—224no—
578#95—112no—
579#95—112no—
580#95—112no—
581#95—112no—
582#95—112no—
583#95—112no—
584#95—112no—
585#95—112no—
586#95—112no—
587#95—112no—
588#95—112no—
589#95—112no—
590#95—112no—
591#95—112no—
592#95—112no—
593#95—112no—
594#95—112no—
595#95—112no—
596#95—112no—
597#95—112no—
598#95—112no—
599#95—112no—
600#95—112no—
601#95—112no—
602#95—112no—
603#95—112no—
604#95—112no—
605#95—112no—
606#95C22×D1112yes—
607#95C22×D1112yes—
608#95C22×D1112yes—
609#95C22×D1112yes—
610#95C22×D1112yes—
611#95C22×D1112yes—
612C2×C11—24no—
613C2×C11—82no—
614C2×C11C2×#54211yescharacteristic
615C2×C11#349111yescharacteristic
616C2×C11#349311yescharacteristic
617C2×C11#356011yescharacteristic
618C2×C11#356011yescharacteristic
619C2×C11#356411yescharacteristic
620C2×C11#356411yescharacteristic
621C24C23×D1112yes—
622C24C23×D1111yescharacteristic
623C2×Q8—22no—
624C2×Q8—41no—
625C2×Q8—41no—
626C2×Q8—442no—
627C2×Q8—442no—
628C2×Q8—442no—
629C2×D4—24no—
630C2×D4—24no—
631C2×D4—24no—
632C2×D4—22no—
633C2×D4—41no—
634C2×D4—41no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—41no—
638C22×C4—41no—
639C22×C4—41no—
640C22×C4—41no—
641C22×C4—41no—
642C22×C4—41no—
643C22×C4—112no—
644C22×C4—111no—
645C22×C4—111no—
646C22×C4—111no—
647C22×C4—111no—
648C22×C4—112no—
649C22×C4—112no—
650C22×C4—112no—
651C22×C4—112no—
652C22×C4—112no—
653C22×C4—222no—
654C22×C4—222no—
655C22×C4—222no—
656C22×C4—222no—
657C22×C4—222no—
658C22×C4—222no—
659C22×C4—441no—
660C22×C4—441no—
661C22×C4—442no—
662C22×C4—441no—
663C22×C4—442no—
664C22×C4—441no—
665C22×C4—441no—
666C22×C4—442no—
667C22×C4—441no—
668C22×C4#434114yes—
669C22×C4C23×D1112yes—
670C22×C4C23×D1112yes—
671C22×C4C23×D1112yes—
672C22×C4C23×D1112yes—
673C22×C4C23×D1112yes—
674C22×C4C23×D1111yescharacteristic
675C22×C4C23×D1111yescharacteristic
676C4⋊C4—22no—
677C4⋊C4—22no—
678C4⋊C4—24no—
679C4⋊C4—442no—
680C4⋊C4—442no—
681C4⋊C4—442no—
682C4⋊C4—442no—
683C4⋊C4—442no—
684C4⋊C4—442no—
685C4⋊C4—442no—
686C4⋊C4—442no—
687C4⋊C4—441no—
688C4⋊C4—441no—
689C4⋊C4—441no—
690C4⋊C4—441no—
691C4⋊C4—442no—
692C4⋊C4—442no—
693C4⋊C4—442no—
694C4⋊C4—442no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—42no—
700C22⋊C4—42no—
701C22⋊C4—224no—
702C22⋊C4—224no—
703C22⋊C4—442no—
704C22⋊C4—442no—
705C22⋊C4—442no—
706C22⋊C4—442no—
707C22⋊C4—442no—
708C22⋊C4—442no—
709C22⋊C4—442no—
710C42—222no—
711C42—222no—
712C42—222no—
713C42—222no—
714C42—442no—
715C42—442no—
716C42—442no—
717C11#3698011yescharacteristic, complemented, Sylow
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—22no—
728C23—22no—
729C23C2×#434112yes—
730C23#6704212yes—
731C23#6704312yes—
732C23C24×D1111yescharacteristic
733Q8—82no—
734Q8—884no—
735D4—48no—
736D4—82no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—44no—
757C2×C4—82no—
758C2×C4—82no—
759C2×C4—221no—
760C2×C4—221no—
761C2×C4—221no—
762C2×C4—221no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—222no—
767C2×C4—222no—
768C2×C4—221no—
769C2×C4—221no—
770C2×C4—222no—
771C2×C4—221no—
772C2×C4—221no—
773C2×C4—222no—
774C2×C4—222no—
775C2×C4—221no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—221no—
781C2×C4—222no—
782C2×C4—222no—
783C2×C4—222no—
784C2×C4—222no—
785C2×C4—221no—
786C2×C4—222no—
787C2×C4—221no—
788C2×C4—222no—
789C2×C4—444no—
790C2×C4—444no—
791C2×C4—882no—
792C2×C4—882no—
793C2×C4—884no—
794C2×C4C2×#434112yes—
795C2×C4C2×#434112yes—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—42no—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22#1062321314yes—
810C22C22×#434111yescharacteristic
811C22C2×#6704211yescharacteristic
812C22C2×#6704311yescharacteristic
813C22#1062345511yescharacteristic
814C22#1062345511yescharacteristic
815C22#1062345511yescharacteristic
816C22#1062345711yescharacteristic
817C4—22no—
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—42no—
824C4—442no—
825C4—442no—
826C4—442no—
827C4—442no—
828C4—442no—
829C4—442no—
830C4—441no—
831C4—441no—
832C4—441no—
833C4—441no—
834C2—24no—
835C2—82no—
836C2C2×#1062321311yescharacteristic
837C2#1308231311yescharacteristic
838C2#1308233511yescharacteristic
839C2#1308317011yescharacteristic
840C2#1308317311yescharacteristic
841C2#1308324211yescharacteristic
842C2#1308324511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2639C2
prime radicalC2×C11×#121C22
hypercenter#2639D11
hypocenterC11#36980
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2639

Complements

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

NH ≅ G/Ntype
1. #13076950C2semidirect
3. #13076191C2semidirect
4. #13076122C2semidirect
5. #13076072C2semidirect
6. #13076042C2semidirect
7. #13075985C2semidirect
8. #13075975C2semidirect
9. #13075955C2semidirect
10. #13075673C2semidirect
11. #13074730C2semidirect
12. #13073180C2semidirect
13. #13072940C2semidirect
14. #13072444C2semidirect
15. #13072091C2semidirect
16. #13071351C2semidirect
18. C2×#10622264C2semidirect
717. C11#36980semidirect

Maximal subgroups

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

subgroupindex
#130769502
#130769422
#130761912
#130761222
#130760722
#130760422
#130759852
#130759752
#130759552
#130756732
#130747302
#130731802
#130729402
#130724442
#130720912
#130713512
#130713212
C2×#106222642
C11×#26392
#3698011