Finite Group Databasebeta

← #14969054

Subgroups — #14969054

Order 2816.

1668 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076980C212yesmaximal, complemented
2#13076555C212yesmaximal, complemented
3#13076136C212yesmaximal, complemented
4#13075580C212yesmaximal, complemented
5#13075414C212yesmaximal, complemented
6#13075240C212yesmaximal, complemented
7#13075199C212yesmaximal, complemented
8#13075093C212yesmaximal, complemented
9#13075063C212yesmaximal, complemented
10#13074608C212yesmaximal, complemented
11#13074305C211yesmaximal, characteristic, complemented
12#13074268C211yesmaximal, characteristic, complemented
13#13074176C211yesmaximal, characteristic, complemented
14#13073750C212yesmaximal, complemented
15#13073393C212yesmaximal, complemented
16#13071431C211yesmaximal, characteristic, complemented
17#13071259C211yesmaximal, characteristic, complemented
18#13071109C211yesmaximal, characteristic, complemented
19C11×#2540C211yesmaximal, characteristic, complemented
20C2×C11×#124C2211yescharacteristic
21C2×C11×C22⋊Q8C2212yes—
22C2×C11×#121C2212yes—
23C2×C4×D4×C11C2211yescharacteristic
24C2×#66992C2212yes—
25C2×#66951C2212yes—
26C2×#66932C2212yes—
27C2×#66932C2212yes—
28C2×#66925C2211yescharacteristic
29C11×#399C2212yes—
30C11×#392C2212yes—
31C11×#390C2212yes—
32C11×#390C2212yes—
33C4×C11×C4⋊C4C2211yescharacteristic
34#10622844C2211yescharacteristic
35#10622843C2212yes—
36#10622842C2211yescharacteristic
37#10622836C2211yescharacteristic
38#10622836C2211yescharacteristic
39#10622836C2212yes—
40#10622835C2211yescharacteristic
41#10622835C2212yes—
42#10622835C2212yes—
43#10622835C2212yes—
44#10622835C2211yescharacteristic
45#10622834C2212yes—
46#10622834C2212yes—
47#10622834C2212yes—
48#10622833C2212yes—
49#10622833C2212yes—
50#10622826C2212yes—
51#10622825C2212yes—
52#10622824C2212yes—
53#10622823C2212yes—
54#10622607C2212yes—
55#10622605C2211yescharacteristic
56#10622603C2212yes—
57#10622599C2212yes—
58#10622599C2212yes—
59#10622598C2212yes—
60#10622598C2212yes—
61#10622597C2212yes—
62#10622597C2212yes—
63#10622595C2211yescharacteristic
64#10622595C2212yes—
65#10622591C2212yes—
66#10622586C2212yes—
67#10622585C2212yes—
68#10622574C2212yes—
69#10622574C2212yes—
70#10622574C2212yes—
71#10622572C2212yes—
72#10622570C2212yes—
73#10622569C2212yes—
74#10622569C2212yes—
75#10622566C2212yes—
76#10622565C2212yes—
77#10622565C2212yes—
78#10622564C2212yes—
79#10622564C2212yes—
80#10622564C2212yes—
81#10622564C2212yes—
82#10622564C2212yes—
83#10622563C2212yes—
84#10622563C2212yes—
85#10622561C2212yes—
86#10622558C2212yes—
87#10622558C2212yes—
88#10622558C2212yes—
89#10622557C2212yes—
90#10622557C2212yes—
91#10622557C2212yes—
92#10622556C2212yes—
93C22⋊C4×Dic11C2212yes—
94C4×(C2×D11)⋊C4C2211yescharacteristic
95C4×(C2×D11)⋊C4C2211yescharacteristic
96#10622550C2211yescharacteristic
97C4×C4⋊Dic11C2211yescharacteristic
98#10622546C2212yes—
99#10622545C2211yescharacteristic
100#10622545C2211yescharacteristic
101C42×Dic11C2211yescharacteristic
102#10622541C2212yes—
103#10622283C2212yes—
104#10622268C2212yes—
105#10622268C2212yes—
106#10622260C2212yes—
107C22×Q8×C11C2311yescharacteristic
108C22×D4×C11C2312yes—
109C22×D4×C11C2311yescharacteristic
110C22×D4×C11C2311yescharacteristic
111C22×D4×C11C2312yes—
112C23×C4×C11C2312yes—
113C22×C22⋊D11C2312yes—
114C22×C22⋊D11C2312yes—
115C23×Dic11C2312yes—
116C22×C4×D11C2311yescharacteristic
117C11×#124—24no—
118C11×C22⋊Q8—44no—
119C11×#121—44no—
120C4×D4×C11—24no—
121C2×C11×C4⋊C4C2312yes—
122C2×C11×C4⋊C4C2312yes—
123C2×C11×C4⋊C4C2311yescharacteristic
124C2×C11×C4⋊C4C2312yes—
125C2×C11×C22⋊C4C2312yes—
126C2×C11×C22⋊C4C2312yes—
127C2×C11×C22⋊C4C2312yes—
128C2×C11×C22⋊C4C2312yes—
129C2×C11×C22⋊C4C2312yes—
130C2×C11×C22⋊C4C2312yes—
131C2×C11×C22⋊C4C2312yes—
132C2×C42×C11C2311yescharacteristic
133C2×C42×C11C2311yescharacteristic
134C2×C42×C11C2311yescharacteristic
135C2×C22⋊Dic11C2312yes—
136C2×C22⋊Dic11C2312yes—
137C2×C22⋊Dic11C2312yes—
138C2×C22⋊Dic11C2312yes—
139C2×C22⋊Dic11C2312yes—
140C2×C22⋊Dic11C2312yes—
141C2×C22⋊Dic11C2312yes—
142C2×C22⋊Dic11C2312yes—
143C2×C22⋊Dic11C2312yes—
144C2×C22⋊Dic11C2312yes—
145C2×C22⋊Dic11C2312yes—
146C2×C22⋊Dic11C2312yes—
147C2×C22⋊Dic11C2312yes—
148#66992—44no—
149C2×(C2×D11)⋊C4C2311yescharacteristic
150C2×(C2×D11)⋊C4C2311yescharacteristic
151C2×(C2×D11)⋊C4C2312yes—
152C2×(C2×D11)⋊C4C2312yes—
153C2×(C2×D11)⋊C4C2312yes—
154C2×(C2×D11)⋊C4C2312yes—
155C2×C4⋊Dic11C2312yes—
156C2×C4⋊Dic11C2312yes—
157C2×C4⋊Dic11C2312yes—
158C2×C4⋊Dic11C2312yes—
159C2×C4⋊Dic11C2312yes—
160C2×C4⋊Dic11C2312yes—
161C2×Dic11⋊C4C2311yescharacteristic
162C2×Dic11⋊C4C2311yescharacteristic
163C2×Dic11⋊C4C2312yes—
164C2×Dic11⋊C4C2312yes—
165C2×Dic11⋊C4C2312yes—
166C2×Dic11⋊C4C2312yes—
167C2×Dic11⋊C4C2312yes—
168C2×Dic11⋊C4C2312yes—
169C2×C4×Dic11C2311yescharacteristic
170C2×C4×Dic11C2312yes—
171C2×C4×Dic11C2312yes—
172C2×C4×Dic11C2312yes—
173C2×C4×Dic11C2312yes—
174C2×C4×Dic11C2311yescharacteristic
175C2×C4×Dic11C2311yescharacteristic
176#66951—44no—
177#66932—44no—
178#66932—44no—
179#66925—24no—
180C11×#95C2312yes—
181C11⋊#95C2311yescharacteristic
182C11⋊#95C2311yescharacteristic
183C11⋊#95C2312yes—
184C11⋊#95C2312yes—
185C11⋊#95C2312yes—
186C11⋊#95C2312yes—
187C11⋊#95C2312yes—
188C11⋊#95C2312yes—
189C11⋊#95C2312yes—
190C11⋊#95C2312yes—
191C11⋊#95C2311yescharacteristic
192C11⋊#95C2311yescharacteristic
193C11⋊#95C2312yes—
194C11⋊#95C2312yes—
195C11⋊#95C2312yes—
196C11⋊#95C2312yes—
197C11⋊#95C2312yes—
198C11⋊#95C2312yes—
199C11⋊#95C2312yes—
200C11⋊#95C2312yes—
201C11⋊#95C2312yes—
202C11⋊#95C2312yes—
203#37027—111nomaximal, Sylow
204C24×C11C2412yes—
205C24×C11C2412yes—
206C23×D11C2411yescharacteristic
207C2×Q8×C11—22no—
208C2×Q8×C11—42no—
209C2×D4×C11—22no—
210C2×D4×C11—22no—
211C2×D4×C11—24no—
212C2×D4×C11—42no—
213C2×D4×C11—42no—
214C2×D4×C11—42no—
215C2×D4×C11—42no—
216C2×D4×C11—42no—
217C2×D4×C11—42no—
218C2×D4×C11—42no—
219C22×C4×C11—24no—
220C22×C4×C11—42no—
221C22×C4×C11—42no—
222C22×C4×C11C2412yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2411yescharacteristic
226C22×C4×C11C2411yescharacteristic
227C22×C4×C11C2411yescharacteristic
228C22×C4×C11C2412yes—
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×Dic11C2411yescharacteristic
239C22×Dic11C2412yes—
240C22×Dic11C2411yescharacteristic
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2411yescharacteristic
247C2×C4×D11—22no—
248C2×C4×D11—41no—
249C2×C4×D11—41no—
250C11×C4⋊C4—22no—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—24no—
253C11×C4⋊C4—42no—
254C11×C22⋊C4—24no—
255C11×C22⋊C4—24no—
256C11×C22⋊C4—24no—
257C11×C22⋊C4—24no—
258C11×C22⋊C4—24no—
259C11×C22⋊C4—42no—
260C11×C22⋊C4—42no—
261C42×C11—41no—
262C42×C11—41no—
263C42×C11#4114yes—
264C22⋊Dic11—42no—
265C22⋊Dic11—42no—
266C22⋊Dic11—42no—
267C22⋊Dic11—42no—
268C22⋊Dic11—42no—
269C22⋊Dic11—42no—
270C22⋊Dic11—42no—
271C22⋊Dic11—42no—
272C22⋊Dic11—42no—
273C22⋊Dic11—42no—
274C22⋊Dic11—42no—
275C22⋊Dic11—42no—
276C22⋊Dic11—42no—
277(C2×D11)⋊C4—22no—
278(C2×D11)⋊C4—22no—
279(C2×D11)⋊C4—24no—
280(C2×D11)⋊C4—42no—
281(C2×D11)⋊C4—42no—
282(C2×D11)⋊C4—42no—
283C4⋊Dic11—42no—
284C4⋊Dic11—42no—
285C4⋊Dic11—42no—
286C4⋊Dic11—42no—
287C4⋊Dic11—42no—
288C4⋊Dic11—42no—
289Dic11⋊C4—22no—
290Dic11⋊C4—22no—
291Dic11⋊C4—24no—
292Dic11⋊C4—24no—
293Dic11⋊C4—42no—
294Dic11⋊C4—42no—
295Dic11⋊C4—42no—
296Dic11⋊C4—42no—
297C4×Dic11—22no—
298C4×Dic11—24no—
299C4×Dic11—42no—
300C4×Dic11—41no—
301C4×Dic11—41no—
302C4×Dic11—42no—
303C4×Dic11—42no—
304#2860—112no—
305#2803—112no—
306#2771—112no—
307#2727—112no—
308#2714—112no—
309#2702—112no—
310#2699—112no—
311#2691—112no—
312#2689—112no—
313#2648—112no—
314#2610—111no—
315#2606—111no—
316#2598—111no—
317#2559—112no—
318#2540D1111yescharacteristic, complemented
319#2526—112no—
320#2337—111no—
321#2319—111no—
322#2298—111no—
323C23×C11—22no—
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—22no—
334C23×C11—22no—
335C23×C11—22no—
336C23×C11—22no—
337C23×C11C2511yescharacteristic
338C22×D11—21no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—21no—
342C22×D11—21no—
343Q8×C11—82no—
344D4×C11—44no—
345D4×C11—82no—
346D4×C11—84no—
347D4×C11—84no—
348C2×C4×C11—22no—
349C2×C4×C11—21no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
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—22no—
363C2×C4×C11—84no—
364C2×C4×C11C2×#4112yes—
365C2×C4×C11C2×#4112yes—
366C2×C4×C11C2×#4112yes—
367C2×C4×C11H(5,𝔽2)14yes—
368C22⋊D11—84no—
369C22⋊D11—84no—
370C2×Dic11—21no—
371C2×Dic11—21no—
372C2×Dic11—21no—
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—21no—
393C2×Dic11—21no—
394C2×Dic11—22no—
395C2×Dic11—84no—
396C4×D11—44no—
397C2×#126—112no—
398C2×#126—112no—
399C2×#126—112no—
400C2×#124C2×D1111yescharacteristic
401C2×C22⋊Q8C2×D1112yes—
402C2×#121—112no—
403C2×#121C2×D1112yes—
404C2×C4×D4C2×D1111yescharacteristic
405C2×#117—111no—
406#400—111no—
407#400—112no—
408#400—112no—
409#400—112no—
410#399—111no—
411#399C2×D1112yes—
412#398—112no—
413#398—112no—
414#397—112no—
415#397—112no—
416#397—112no—
417#396—112no—
418#396—112no—
419#395—111no—
420#394—111no—
421#394—111no—
422#394—112no—
423#394—112no—
424#394—112no—
425#394—112no—
426#394—112no—
427#394—112no—
428#394—112no—
429#393—111no—
430#392—111no—
431#392—111no—
432#392—112no—
433#392C2×D1112yes—
434#391—112no—
435#390—112no—
436#390—112no—
437#390—112no—
438#390—112no—
439#390C2×D1112yes—
440#390C2×D1112yes—
441#389—112no—
442#389—112no—
443#389—112no—
444#389—112no—
445#389—112no—
446#389—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#388—112no—
458#388—112no—
459#388—112no—
460#387—112no—
461#387—112no—
462#387—112no—
463#387—112no—
464#386—112no—
465#386—112no—
466#386—112no—
467#386—112no—
468#386—112no—
469#385—112no—
470#385—112no—
471#385—112no—
472#383—111no—
473#381—112no—
474#381—112no—
475#380—112no—
476C4×C4⋊C4—111no—
477C4×C4⋊C4C2×D1111yescharacteristic
478C4×C22⋊C4—112no—
479C4×C22⋊C4—111no—
480C4×C22⋊C4—111no—
481#376—111no—
482#376—111no—
483C43—111no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11—42no—
494C22×C11—42no—
495C22×C11—42no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11C22×#4111yescharacteristic
499C22×C11C2×H(5,𝔽2)12yes—
500C22×C11#58512yes—
501C22×C11#58511yescharacteristic
502C22×C11#58511yescharacteristic
503C2×D11—41no—
504C2×D11—41no—
505C2×D11—41no—
506C2×D11—42no—
507C2×D11—42no—
508C4×C11—22no—
509C4×C11—22no—
510C4×C11—22no—
511C4×C11—24no—
512C4×C11—42no—
513C4×C11—42no—
514C4×C11—42no—
515Dic11—41no—
516Dic11—41no—
517Dic11—41no—
518Dic11—42no—
519Dic11—42no—
520Dic11—42no—
521Dic11—42no—
522Dic11—42no—
523Dic11—42no—
524C22×Q8C22×D1111yescharacteristic
525C22×D4—112no—
526C22×D4—112no—
527C22×D4C22×D1111yescharacteristic
528C22×D4C22×D1112yes—
529C22×D4C22×D1111yescharacteristic
530C22×D4C22×D1112yes—
531C23×C4—112no—
532C23×C4—111no—
533C23×C4C22×D1112yes—
534#126—444no—
535#126—444no—
536#126—444no—
537#124—24no—
538C22⋊Q8—44no—
539#121—44no—
540#121—444no—
541C4×D4—24no—
542#117—224no—
543C2×C4⋊C4—111no—
544C2×C4⋊C4—111no—
545C2×C4⋊C4—112no—
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×D1112yes—
559C2×C4⋊C4C22×D1112yes—
560C2×C4⋊C4C22×D1112yes—
561C2×C22⋊C4—111no—
562C2×C22⋊C4—111no—
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⋊C4—112no—
579C2×C22⋊C4—112no—
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×C22⋊C4C22×D1112yes—
587C2×C42—111no—
588C2×C42—112no—
589C2×C42—112no—
590C2×C42—111no—
591C2×C42—112no—
592C2×C42—111no—
593C2×C42—112no—
594C2×C42C22×D1111yescharacteristic
595C2×C42C22×D1111yescharacteristic
596C2×C42C22×D1111yescharacteristic
597#95—111no—
598#95—111no—
599#95—112no—
600#95—112no—
601#95—112no—
602#95—112no—
603#95—112no—
604#95—112no—
605#95—112no—
606#95—112no—
607#95—112no—
608#95—112no—
609#95—112no—
610#95—112no—
611#95—111no—
612#95—112no—
613#95—111no—
614#95—112no—
615#95—112no—
616#95—112no—
617#95—112no—
618#95—112no—
619#95C22×D1112yes—
620C2×C11—82no—
621C2×C11—82no—
622C2×C11#345511yescharacteristic
623C2×C11#349311yescharacteristic
624C2×C11#350811yescharacteristic
625C2×C11#355112yes—
626C2×C11#356012yes—
627D11—81no—
628C24—111no—
629C24C23×D1112yes—
630C24C23×D1112yes—
631C2×Q8—22no—
632C2×Q8—42no—
633C2×D4—22no—
634C2×D4—22no—
635C2×D4—24no—
636C2×D4—42no—
637C2×D4—42no—
638C2×D4—42no—
639C2×D4—42no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—42no—
643C2×D4—442no—
644C2×D4—442no—
645C2×D4—442no—
646C2×D4—442no—
647C2×D4—442no—
648C2×D4—442no—
649C22×C4—24no—
650C22×C4—42no—
651C22×C4—42no—
652C22×C4—111no—
653C22×C4—112no—
654C22×C4—111no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—112no—
658C22×C4—112no—
659C22×C4—112no—
660C22×C4—111no—
661C22×C4—222no—
662C22×C4—441no—
663C22×C4—441no—
664C22×C4—442no—
665C22×C4—442no—
666C22×C4—442no—
667C22×C4C23×D1112yes—
668C22×C4C23×D1112yes—
669C22×C4C23×D1112yes—
670C22×C4C23×D1111yescharacteristic
671C22×C4C23×D1111yescharacteristic
672C22×C4C23×D1111yescharacteristic
673C22×C4C23×D1112yes—
674C4⋊C4—22no—
675C4⋊C4—24no—
676C4⋊C4—24no—
677C4⋊C4—42no—
678C4⋊C4—222no—
679C4⋊C4—222no—
680C4⋊C4—224no—
681C4⋊C4—224no—
682C4⋊C4—442no—
683C4⋊C4—442no—
684C4⋊C4—442no—
685C4⋊C4—442no—
686C4⋊C4—442no—
687C4⋊C4—442no—
688C4⋊C4—442no—
689C4⋊C4—442no—
690C4⋊C4—442no—
691C4⋊C4—442no—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—24no—
697C22⋊C4—42no—
698C22⋊C4—42no—
699C22⋊C4—222no—
700C22⋊C4—222no—
701C22⋊C4—224no—
702C22⋊C4—442no—
703C22⋊C4—442no—
704C22⋊C4—442no—
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—
718C42—41no—
719C42—41no—
720C42—222no—
721C42—224no—
722C42—442no—
723C42—442no—
724C42—442no—
725C42—441no—
726C42—441no—
727C42#434114yes—
728C11#3702711yescharacteristic, complemented, Sylow
729C23—22no—
730C23—22no—
731C23—22no—
732C23—22no—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—221no—
744C23—222no—
745C23—222no—
746C23—221no—
747C23—221no—
748C23C24×D1111yescharacteristic
749Q8—82no—
750D4—44no—
751D4—84no—
752D4—82no—
753D4—84no—
754D4—884no—
755D4—884no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—21no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—84no—
772C2×C4—221no—
773C2×C4—221no—
774C2×C4—221no—
775C2×C4—222no—
776C2×C4—222no—
777C2×C4—222no—
778C2×C4—222no—
779C2×C4—222no—
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—221no—
790C2×C4—222no—
791C2×C4—222no—
792C2×C4—222no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—221no—
796C2×C4—222no—
797C2×C4—444no—
798C2×C4—884no—
799C2×C4C2×#434112yes—
800C2×C4C2×#434112yes—
801C2×C4C2×#434112yes—
802C2×C4#6703714yes—
803C22—42no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—42no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—42no—
817C22—442no—
818C22—441no—
819C22—441no—
820C22—442no—
821C22—441no—
822C22C22×#434111yescharacteristic
823C22C2×#6703712yes—
824C22#1062345312yes—
825C22#1062345511yescharacteristic
826C22#1062345711yescharacteristic
827C4—24no—
828C4—22no—
829C4—22no—
830C4—22no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—442no—
835C4—442no—
836C4—441no—
837C4—441no—
838C4—442no—
839C4—442no—
840C4—442no—
841C4—442no—
842C4—441no—
843C2—82no—
844C2—82no—
845C2—881no—
846C2#1308200411yescharacteristic
847C2#1308233511yescharacteristic
848C2#1308249011yescharacteristic
849C2#1308303212yes—
850C2#1308316012yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2540C2
hypercenter#2540D11
hypocenterC11#37027
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2540

Complements

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

NH ≅ G/Ntype
1. #13076980C2semidirect
2. #13076555C2semidirect
3. #13076136C2semidirect
4. #13075580C2semidirect
5. #13075414C2semidirect
6. #13075240C2semidirect
7. #13075199C2semidirect
8. #13075093C2semidirect
9. #13075063C2semidirect
10. #13074608C2semidirect
11. #13074305C2semidirect
12. #13074268C2semidirect
13. #13074176C2semidirect
14. #13073750C2semidirect
15. #13073393C2semidirect
16. #13071431C2semidirect
17. #13071259C2semidirect
18. #13071109C2semidirect
19. C11×#2540C2semidirect
318. #2540D11semidirect
728. C11#37027semidirect

Maximal subgroups

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

subgroupindex
#130769802
#130765552
#130761362
#130755802
#130754142
#130752402
#130751992
#130750932
#130750632
#130746082
#130743052
#130742682
#130741762
#130737502
#130733932
#130714312
#130712592
#130711092
C11×#25402
#3702711