Finite Group Databasebeta

← #14968957

Subgroups — #14968957

Order 2816.

1676 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076985C212yesmaximal, complemented
2#13076484C212yesmaximal, complemented
3#13076471C212yesmaximal, complemented
4#13075641C212yesmaximal, complemented
5#13075266C212yesmaximal, complemented
6#13075221C212yesmaximal, complemented
7#13075131C212yesmaximal, complemented
8#13075081C212yesmaximal, complemented
9#13075021C212yesmaximal, complemented
10#13074604C212yesmaximal, complemented
11#13074264C211yesmaximal, characteristic, complemented
12#13074182C211yesmaximal, characteristic, complemented
13#13073712C212yesmaximal, complemented
14#13073556C211yesmaximal, characteristic, complemented
15#13073460C212yesmaximal, complemented
16#13071431C211yesmaximal, characteristic, complemented
17#13071260C211yesmaximal, characteristic, complemented
18#13071114C211yesmaximal, characteristic, complemented
19C11×#2610C211yesmaximal, characteristic, complemented
20C2×C11×#124C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C2×#66999C2212yes—
23C2×#66991C2212yes—
24C2×#66988C2212yes—
25C2×#66942C2212yes—
26C2×#66938C2212yes—
27C2×#66938C2212yes—
28C2×C4×D44C2211yescharacteristic
29C11×#395C2211yescharacteristic
30C11×#394C2211yescharacteristic
31C11×#393C2211yescharacteristic
32C11×#392C2211yescharacteristic
33C11×#390C2212yes—
34C11×#388C2212yes—
35C11×#388C2212yes—
36C11×#386C2212yes—
37C11×#376C2211yescharacteristic
38#10622843C2212yes—
39#10622836C2212yes—
40#10622836C2212yes—
41#10622835C2212yes—
42#10622833C2212yes—
43#10622826C2212yes—
44C4×C22⋊Dic11C2211yescharacteristic
45C4×C22⋊Dic11C2211yescharacteristic
46#10622604C2211yescharacteristic
47#10622603C2212yes—
48#10622603C2212yes—
49#10622602C2212yes—
50#10622599C2211yescharacteristic
51#10622594C2212yes—
52#10622594C2212yes—
53#10622593C2212yes—
54#10622574C2212yes—
55#10622574C2212yes—
56#10622573C2211yescharacteristic
57#10622573C2212yes—
58#10622572C2212yes—
59#10622571C2212yes—
60#10622571C2212yes—
61#10622570C2212yes—
62#10622570C2212yes—
63#10622570C2212yes—
64#10622569C2212yes—
65#10622566C2212yes—
66#10622565C2212yes—
67#10622565C2212yes—
68#10622564C2212yes—
69#10622564C2212yes—
70#10622564C2212yes—
71#10622564C2212yes—
72#10622563C2212yes—
73#10622562C2212yes—
74#10622562C2211yescharacteristic
75#10622561C2212yes—
76#10622560C2212yes—
77#10622558C2212yes—
78#10622557C2212yes—
79#10622555C2212yes—
80C22⋊C4×Dic11C2212yes—
81#10622553C2212yes—
82#10622552C2212yes—
83#10622550C2211yescharacteristic
84C4×C4⋊Dic11C2211yescharacteristic
85C4×C4⋊Dic11C2211yescharacteristic
86#10622546C2212yes—
87#10622545C2211yescharacteristic
88C42×Dic11C2211yescharacteristic
89#10622542C2212yes—
90#10622541C2212yes—
91#10622288C2212yes—
92#10622288C2212yes—
93#10622287C2212yes—
94#10622283C2212yes—
95#10622282C2212yes—
96#10622282C2212yes—
97#10622280C2212yes—
98#10622277C2212yes—
99#10622273C2212yes—
100#10622271C2212yes—
101#10622269C2212yes—
102#10622268C2212yes—
103#10622266C2212yes—
104#10622265C2212yes—
105#10622259C2212yes—
106#10622259C2212yes—
107C22×Q8×C11C2311yescharacteristic
108C22×D4×C11C2311yescharacteristic
109C22×D4×C11C2312yes—
110C23×C4×C11C2311yescharacteristic
111C22×C22⋊D11C2312yes—
112C22×C22⋊D11C2312yes—
113C22×C22⋊D11C2312yes—
114C23×Dic11C2312yes—
115C22×D44C2311yescharacteristic
116C22×C4×D11C2312yes—
117C22×Dic22C2312yes—
118C11×#124—24no—
119C11×#117—24no—
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C4⋊C4C2312yes—
123C2×C11×C22⋊C4C2312yes—
124C2×C11×C22⋊C4C2312yes—
125C2×C11×C22⋊C4C2311yescharacteristic
126C2×C11×C22⋊C4C2311yescharacteristic
127C2×C11×C22⋊C4C2312yes—
128C2×C11×C22⋊C4C2312yes—
129C2×C11×C22⋊C4C2312yes—
130C2×C11×C22⋊C4C2312yes—
131C2×C42×C11C2311yescharacteristic
132C2×C42×C11C2312yes—
133C2×C42×C11C2311yescharacteristic
134C2×C22⋊Dic11C2312yes—
135C2×C22⋊Dic11C2312yes—
136C2×C22⋊Dic11C2312yes—
137C2×C22⋊Dic11C2312yes—
138C2×C22⋊Dic11C2312yes—
139C2×C22⋊Dic11C2312yes—
140C2×C22⋊Dic11C2312yes—
141C2×C22⋊Dic11C2312yes—
142#66999—44no—
143#66991—44no—
144#66988—44no—
145C2×(C2×D11)⋊C4C2312yes—
146C2×(C2×D11)⋊C4C2312yes—
147C2×(C2×D11)⋊C4C2312yes—
148C2×(C2×D11)⋊C4C2312yes—
149C2×(C2×D11)⋊C4C2312yes—
150C2×(C2×D11)⋊C4C2312yes—
151C2×(C2×D11)⋊C4C2312yes—
152C2×(C2×D11)⋊C4C2312yes—
153C2×(C2×D11)⋊C4C2312yes—
154C2×(C2×D11)⋊C4C2312yes—
155C2×C4⋊Dic11C2311yescharacteristic
156C2×C4⋊Dic11C2312yes—
157C2×C4⋊Dic11C2312yes—
158C2×C4⋊Dic11C2312yes—
159C2×C4⋊Dic11C2312yes—
160C2×Dic11⋊C4C2312yes—
161C2×Dic11⋊C4C2312yes—
162C2×Dic11⋊C4C2312yes—
163C2×Dic11⋊C4C2312yes—
164C2×Dic11⋊C4C2312yes—
165C2×Dic11⋊C4C2312yes—
166C2×Dic11⋊C4C2312yes—
167C2×C4×Dic11C2312yes—
168C2×C4×Dic11C2312yes—
169C2×C4×Dic11C2311yescharacteristic
170C2×C4×Dic11C2312yes—
171C2×C4×Dic11C2311yescharacteristic
172C2×C4×Dic11C2311yescharacteristic
173C2×C4×Dic11C2311yescharacteristic
174#66942—44no—
175#66938—44no—
176#66938—44no—
177C4×D44—24no—
178C11×#95C2312yes—
179C11×#95C2312yes—
180C11×#95C2312yes—
181C11×#95C2311yescharacteristic
182C11×#95C2311yescharacteristic
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⋊#95C2311yescharacteristic
199C11⋊#95C2312yes—
200C11⋊#95C2312yes—
201C11⋊#95C2312yes—
202C11⋊#95C2311yescharacteristic
203#37022—111nomaximal, Sylow
204C24×C11C2411yescharacteristic
205C24×C11C2412yes—
206C23×D11C2412yes—
207C2×Q8×C11—22no—
208C2×Q8×C11—42no—
209C2×D4×C11—22no—
210C2×D4×C11—42no—
211C2×D4×C11—42no—
212C2×D4×C11—42no—
213C2×D4×C11—42no—
214C22×C4×C11—22no—
215C22×C4×C11—41no—
216C22×C4×C11—41no—
217C22×C4×C11C2411yescharacteristic
218C22×C4×C11C2411yescharacteristic
219C22×C4×C11C2412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2411yescharacteristic
223C22×C4×C11C2411yescharacteristic
224C22×C4×C11C2411yescharacteristic
225C22×C4×C11C2411yescharacteristic
226C2×C22⋊D11—24no—
227C2×C22⋊D11—42no—
228C2×C22⋊D11—42no—
229C2×C22⋊D11—42no—
230C2×C22⋊D11—42no—
231C2×C22⋊D11—42no—
232C2×C22⋊D11—42no—
233C2×C22⋊D11—42no—
234C2×C22⋊D11—42no—
235C22×Dic11—42no—
236C22×Dic11—42no—
237C22×Dic11—42no—
238C22×Dic11C2412yes—
239C22×Dic11C2412yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C2×D44—22no—
246C2×D44—42no—
247C2×C4×D11—24no—
248C2×C4×D11—42no—
249C2×C4×D11—42no—
250C2×Dic22—24no—
251C2×Dic22—42no—
252C2×Dic22—42no—
253C11×C4⋊C4—22no—
254C11×C4⋊C4—22no—
255C11×C4⋊C4—42no—
256C11×C22⋊C4—22no—
257C11×C22⋊C4—22no—
258C11×C22⋊C4—24no—
259C11×C22⋊C4—24no—
260C11×C22⋊C4—42no—
261C11×C22⋊C4—42no—
262C11×C22⋊C4—42no—
263C11×C22⋊C4—42no—
264C42×C11—22no—
265C42×C11—42no—
266C42×C11#4114yes—
267C22⋊Dic11—24no—
268C22⋊Dic11—24no—
269C22⋊Dic11—42no—
270C22⋊Dic11—42no—
271C22⋊Dic11—42no—
272C22⋊Dic11—42no—
273C22⋊Dic11—42no—
274C22⋊Dic11—42no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4—42no—
278(C2×D11)⋊C4—42no—
279(C2×D11)⋊C4—42no—
280(C2×D11)⋊C4—42no—
281(C2×D11)⋊C4—42no—
282(C2×D11)⋊C4—42no—
283(C2×D11)⋊C4—42no—
284(C2×D11)⋊C4—42no—
285C4⋊Dic11—24no—
286C4⋊Dic11—22no—
287C4⋊Dic11—42no—
288C4⋊Dic11—42no—
289C4⋊Dic11—42no—
290Dic11⋊C4—24no—
291Dic11⋊C4—24no—
292Dic11⋊C4—42no—
293Dic11⋊C4—42no—
294Dic11⋊C4—42no—
295Dic11⋊C4—42no—
296Dic11⋊C4—42no—
297C4×Dic11—24no—
298C4×Dic11—42no—
299C4×Dic11—41no—
300C4×Dic11—41no—
301C4×Dic11—41no—
302C4×Dic11—41no—
303C4×Dic11—42no—
304#2861—112no—
305#2798—112no—
306#2797—112no—
307#2733—112no—
308#2703—112no—
309#2700—112no—
310#2694—112no—
311#2690—112no—
312#2686—112no—
313#2648—112no—
314#2610D1111yescharacteristic, complemented
315#2605—111no—
316#2598—111no—
317#2557—112no—
318#2540—111no—
319#2531—112no—
320#2337—111no—
321#2319—111no—
322#2298—111no—
323C23×C11—21no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—21no—
334C23×C11—21no—
335C23×C11C2511yescharacteristic
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343Q8×C11—82no—
344D4×C11—82no—
345D4×C11—84no—
346C2×C4×C11—22no—
347C2×C4×C11—21no—
348C2×C4×C11—21no—
349C2×C4×C11—22no—
350C2×C4×C11—21no—
351C2×C4×C11—21no—
352C2×C4×C11—22no—
353C2×C4×C11—21no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—21no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—21no—
366C2×C4×C11—44no—
367C2×C4×C11C2×#4112yes—
368C2×C4×C11C2×#4112yes—
369C2×C4×C11C2×#4112yes—
370C22⋊D11—84no—
371C22⋊D11—84no—
372C22⋊D11—84no—
373C2×Dic11—22no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
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—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—84no—
394C2×Dic11H(5,𝔽2)14yes—
395D44—44no—
396C4×D11—84no—
397Dic22—84no—
398C2×#125—112no—
399C2×#124—112no—
400C2×#124—112no—
401C2×#124C2×D1111yescharacteristic
402C2×#123—112no—
403C2×C22⋊Q8—112no—
404C2×#121—112no—
405C2×C4×D4—111no—
406C2×#117C2×D1111yescharacteristic
407#400—111no—
408#400—112no—
409#400—112no—
410#399—111no—
411#399—112no—
412#398—112no—
413#397—112no—
414#397—112no—
415#397—112no—
416#397—112no—
417#397—112no—
418#397—112no—
419#396—112no—
420#395—112no—
421#395C2×D1111yescharacteristic
422#394—112no—
423#394—111no—
424#394—112no—
425#394—112no—
426#394—112no—
427#394C2×D1111yescharacteristic
428#393—112no—
429#393C2×D1111yescharacteristic
430#392—112no—
431#392—112no—
432#392—111no—
433#392—112no—
434#392C2×D1111yescharacteristic
435#391—112no—
436#391—112no—
437#391—112no—
438#391—112no—
439#390—112no—
440#390—112no—
441#390—112no—
442#390—112no—
443#390C2×D1112yes—
444#389—112no—
445#388—112no—
446#388—112no—
447#388—112no—
448#388—112no—
449#388—112no—
450#388—112no—
451#388—112no—
452#388—112no—
453#388—112no—
454#388—112no—
455#388—112no—
456#388—112no—
457#388C2×D1112yes—
458#388C2×D1112yes—
459#387—112no—
460#387—112no—
461#387—112no—
462#387—112no—
463#387—112no—
464#387—112no—
465#386—112no—
466#386—112no—
467#386—112no—
468#386—112no—
469#386—112no—
470#386C2×D1112yes—
471#385—112no—
472#385—112no—
473#383—111no—
474#381—112no—
475#380—112no—
476#380—112no—
477C4×C4⋊C4—111no—
478C4×C4⋊C4—111no—
479C4×C22⋊C4—111no—
480C4×C22⋊C4—111no—
481C4×C22⋊C4—112no—
482#376—111no—
483#376C2×D1111yescharacteristic
484C43—111no—
485C22×C11—41no—
486C22×C11—42no—
487C22×C11—41no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—41no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11C22×#4111yescharacteristic
498C22×C11C2×H(5,𝔽2)12yes—
499C22×C11#58512yes—
500C22×C11#58511yescharacteristic
501C22×C11#58511yescharacteristic
502C2×D11—42no—
503C2×D11—42no—
504C2×D11—42no—
505C2×D11—42no—
506C2×D11—42no—
507C2×D11—42no—
508C2×D11—42no—
509C4×C11—22no—
510C4×C11—22no—
511C4×C11—22no—
512C4×C11—41no—
513C4×C11—41no—
514C4×C11—41no—
515C4×C11—42no—
516C4×C11—42no—
517C4×C11—42no—
518Dic11—24no—
519Dic11—42no—
520Dic11—42no—
521Dic11—42no—
522Dic11—42no—
523Dic11—42no—
524Dic11—42no—
525C22×Q8—112no—
526C22×Q8C22×D1111yescharacteristic
527C22×D4—112no—
528C22×D4—112no—
529C22×D4—112no—
530C22×D4—111no—
531C22×D4C22×D1111yescharacteristic
532C22×D4C22×D1112yes—
533C23×C4—112no—
534C23×C4—112no—
535C23×C4C22×D1111yescharacteristic
536#125—444no—
537#124—24no—
538#124—444no—
539#124—444no—
540#123—444no—
541C22⋊Q8—444no—
542#121—444no—
543C4×D4—224no—
544#117—24no—
545C2×C4⋊C4—111no—
546C2×C4⋊C4—112no—
547C2×C4⋊C4—112no—
548C2×C4⋊C4—112no—
549C2×C4⋊C4—112no—
550C2×C4⋊C4—112no—
551C2×C4⋊C4—112no—
552C2×C4⋊C4—112no—
553C2×C4⋊C4—112no—
554C2×C4⋊C4—112no—
555C2×C4⋊C4—112no—
556C2×C4⋊C4—112no—
557C2×C4⋊C4C22×D1111yescharacteristic
558C2×C4⋊C4C22×D1111yescharacteristic
559C2×C4⋊C4C22×D1112yes—
560C2×C22⋊C4—112no—
561C2×C22⋊C4—112no—
562C2×C22⋊C4—112no—
563C2×C22⋊C4—112no—
564C2×C22⋊C4—112no—
565C2×C22⋊C4—112no—
566C2×C22⋊C4—112no—
567C2×C22⋊C4—112no—
568C2×C22⋊C4—112no—
569C2×C22⋊C4—112no—
570C2×C22⋊C4—112no—
571C2×C22⋊C4—112no—
572C2×C22⋊C4—112no—
573C2×C22⋊C4—112no—
574C2×C22⋊C4—112no—
575C2×C22⋊C4—112no—
576C2×C22⋊C4—112no—
577C2×C22⋊C4—112no—
578C2×C22⋊C4C22×D1111yescharacteristic
579C2×C22⋊C4C22×D1111yescharacteristic
580C2×C22⋊C4C22×D1112yes—
581C2×C22⋊C4C22×D1112yes—
582C2×C22⋊C4C22×D1112yes—
583C2×C22⋊C4C22×D1112yes—
584C2×C22⋊C4C22×D1112yes—
585C2×C22⋊C4C22×D1112yes—
586C2×C42—112no—
587C2×C42—112no—
588C2×C42—111no—
589C2×C42—111no—
590C2×C42—112no—
591C2×C42—111no—
592C2×C42—111no—
593C2×C42C22×D1111yescharacteristic
594C2×C42C22×D1112yes—
595C2×C42C22×D1111yescharacteristic
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#95—111no—
607#95—112no—
608#95—111no—
609#95—112no—
610#95—112no—
611#95—112no—
612#95—112no—
613#95—112no—
614#95—112no—
615#95—112no—
616#95C22×D1111yescharacteristic
617#95C22×D1111yescharacteristic
618#95C22×D1112yes—
619#95C22×D1112yes—
620#95C22×D1112yes—
621C2×C11—81no—
622C2×C11—82no—
623C2×C11#345511yescharacteristic
624C2×C11#349311yescharacteristic
625C2×C11#350811yescharacteristic
626C2×C11#354512yes—
627C2×C11#356212yes—
628D11—82no—
629C24—112no—
630C24C23×D1111yescharacteristic
631C24C23×D1112yes—
632C2×Q8—22no—
633C2×Q8—42no—
634C2×Q8—224no—
635C2×Q8—442no—
636C2×Q8—442no—
637C2×D4—22no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—224no—
643C2×D4—222no—
644C2×D4—442no—
645C2×D4—442no—
646C2×D4—442no—
647C2×D4—442no—
648C2×D4—442no—
649C2×D4—442no—
650C2×D4—442no—
651C2×D4—442no—
652C2×D4—442no—
653C22×C4—22no—
654C22×C4—41no—
655C22×C4—41no—
656C22×C4—112no—
657C22×C4—112no—
658C22×C4—112no—
659C22×C4—112no—
660C22×C4—112no—
661C22×C4—112no—
662C22×C4—112no—
663C22×C4—224no—
664C22×C4—442no—
665C22×C4—442no—
666C22×C4—442no—
667C22×C4—442no—
668C22×C4—442no—
669C22×C4C23×D1111yescharacteristic
670C22×C4C23×D1111yescharacteristic
671C22×C4C23×D1112yes—
672C22×C4C23×D1112yes—
673C22×C4C23×D1112yes—
674C22×C4C23×D1111yescharacteristic
675C22×C4C23×D1111yescharacteristic
676C22×C4C23×D1111yescharacteristic
677C22×C4C23×D1111yescharacteristic
678C4⋊C4—22no—
679C4⋊C4—22no—
680C4⋊C4—42no—
681C4⋊C4—224no—
682C4⋊C4—224no—
683C4⋊C4—224no—
684C4⋊C4—222no—
685C4⋊C4—442no—
686C4⋊C4—442no—
687C4⋊C4—442no—
688C4⋊C4—442no—
689C4⋊C4—442no—
690C4⋊C4—442no—
691C4⋊C4—442no—
692C4⋊C4—442no—
693C22⋊C4—22no—
694C22⋊C4—22no—
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—224no—
704C22⋊C4—224no—
705C22⋊C4—442no—
706C22⋊C4—442no—
707C22⋊C4—442no—
708C22⋊C4—442no—
709C22⋊C4—442no—
710C22⋊C4—442no—
711C22⋊C4—442no—
712C22⋊C4—442no—
713C22⋊C4—442no—
714C22⋊C4—442no—
715C22⋊C4—442no—
716C22⋊C4—442no—
717C22⋊C4—442no—
718C22⋊C4—442no—
719C42—22no—
720C42—42no—
721C42—224no—
722C42—442no—
723C42—441no—
724C42—441no—
725C42—441no—
726C42—441no—
727C42—442no—
728C42#434114yes—
729C11#3702211yescharacteristic, complemented, Sylow
730C23—21no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—21no—
737C23—21no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—222no—
743C23—222no—
744C23—222no—
745C23—222no—
746C23—222no—
747C23—222no—
748C23—222no—
749C23C24×D1111yescharacteristic
750Q8—82no—
751Q8—884no—
752D4—82no—
753D4—84no—
754D4—444no—
755D4—884no—
756D4—884no—
757D4—884no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—22no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—21no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—22no—
778C2×C4—44no—
779C2×C4—114no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—222no—
783C2×C4—222no—
784C2×C4—222no—
785C2×C4—222no—
786C2×C4—222no—
787C2×C4—222no—
788C2×C4—222no—
789C2×C4—222no—
790C2×C4—222no—
791C2×C4—222no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—222no—
799C2×C4—222no—
800C2×C4—884no—
801C2×C4—884no—
802C2×C4C2×#434112yes—
803C2×C4C2×#434112yes—
804C2×C4C2×#434112yes—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—41no—
813C22—41no—
814C22—42no—
815C22—41no—
816C22—42no—
817C22—442no—
818C22—442no—
819C22—442no—
820C22—442no—
821C22—442no—
822C22—442no—
823C22—442no—
824C22C22×#434111yescharacteristic
825C22#1062345311yescharacteristic
826C22#1062345312yes—
827C22#1062345311yescharacteristic
828C22D11×H(5,𝔽2)12yes—
829C4—22no—
830C4—22no—
831C4—22no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—224no—
839C4—442no—
840C4—442no—
841C4—442no—
842C4—442no—
843C4—442no—
844C4—442no—
845C2—82no—
846C2—81no—
847C2—882no—
848C2#1308200511yescharacteristic
849C2#1308233311yescharacteristic
850C2#1308249111yescharacteristic
851C2#1308296212yes—
852C2#1308319712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2610C2
hypercenter#2610D11
hypocenterC11#37022
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2610

Complements

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

NH ≅ G/Ntype
1. #13076985C2semidirect
2. #13076484C2semidirect
3. #13076471C2semidirect
4. #13075641C2semidirect
5. #13075266C2semidirect
6. #13075221C2semidirect
7. #13075131C2semidirect
8. #13075081C2semidirect
9. #13075021C2semidirect
10. #13074604C2semidirect
11. #13074264C2semidirect
12. #13074182C2semidirect
13. #13073712C2semidirect
14. #13073556C2semidirect
15. #13073460C2semidirect
16. #13071431C2semidirect
17. #13071260C2semidirect
18. #13071114C2semidirect
19. C11×#2610C2semidirect
314. #2610D11semidirect
729. C11#37022semidirect

Maximal subgroups

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

subgroupindex
#130769852
#130764842
#130764712
#130756412
#130752662
#130752212
#130751312
#130750812
#130750212
#130746042
#130742642
#130741822
#130737122
#130735562
#130734602
#130714312
#130712602
#130711142
C11×#26102
#3702211