Finite Group Databasebeta

← #15617114

Subgroups — #15617114

Order 2816.

1898 conjugacy classes of subgroups.

The subgroup lattice has 834 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076567C212yesmaximal, complemented
2#13075543C211yesmaximal, characteristic, complemented
3#13074990C211yesmaximal, characteristic, complemented
4#13074193C211yesmaximal, characteristic, complemented
5#13074028C211yesmaximal, characteristic, complemented
6#13074021C211yesmaximal, characteristic, complemented
7#13073881C212yesmaximal, complemented
8#13073873C212yesmaximal, complemented
9#13072823C212yesmaximal, complemented
10#13072820C212yesmaximal, complemented
11#13072710C212yesmaximal, complemented
12#13072707C212yesmaximal, complemented
13#13071949C212yesmaximal
14#13071748C212yesmaximal, complemented
15#13071624C212yesmaximal, complemented
16#13071617C212yesmaximal, complemented
17#13071104C211yesmaximal, characteristic
18#13071095C212yesmaximal, complemented
19C11×#2599C211yesmaximal, characteristic, complemented
20C22×#4339C2211yescharacteristic
21C2×C4×Q8×C11C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23C2×#66999C2212yes—
24C22×C4×Dic11C2211yescharacteristic
25C2×#66949C2212yes—
26C2×#66947C2212yes—
27C2×C4⋊C4×D11C2212yes—
28C2×#66936C2212yes—
29C2×#66930C2212yes—
30C2×#66930C2212yes—
31C2×C4×Dic22C2211yescharacteristic
32C11×#398C2211yescharacteristic
33C11×#397C2211yescharacteristic
34C11×#395C2211yescharacteristic
35C11×#393C2211yescharacteristic
36C11×#388C2212yes—
37C11×#387C2212yes—
38C11×#387C2212yes—
39C11×#385C2212yes—
40C11×#383C2211yescharacteristic
41#10622843C2212yes—
42#10622823C2212yes—
43#10622607C2212yes—
44#10622602C2212yes—
45#10622602C2212yes—
46#10622601C2211yescharacteristic
47#10622601C2211yescharacteristic
48#10622598C2212yes—
49#10622596C2211yescharacteristic
50#10622592C2211yescharacteristic
51#10622592C2212yes—
52#10622591C2212yes—
53#10622591C2212yes—
54C4⋊C4×Dic11C2212yes—
55C4⋊C4×Dic11C2212yes—
56#10622587C2211yescharacteristic
57#10622587C2211yescharacteristic
58#10622585C2212yes—
59#10622585C2212yes—
60#10622585C2212yes—
61#10622574C2212yes—
62#10622572C2212yes—
63#10622571C2212yes—
64#10622571C2212yes—
65#10622569C2212yes—
66#10622566C2211yescharacteristic
67#10622563C2212yes—
68#10622560C2211yescharacteristic
69#10622559C2212yes—
70#10622557C2212yes—
71C4×(C2×D11)⋊C4C2212yes—
72C4×(C2×D11)⋊C4C2212yes—
73C4×(C2×D11)⋊C4C2212yes—
74C4×(C2×D11)⋊C4C2212yes—
75#10622550C2211yescharacteristic
76#10622546C2212yes—
77#10622546C2212yes—
78#10622541C2212yes—
79#10622289C2212yes—
80#10622288C2212yes—
81#10622288C2212yes—
82#10622283C2212yes—
83#10622283C2212yes—
84#10622282C2212yes—
85#10622282C2212yes—
86#10622281C2212yes—
87#10622281C2212yes—
88#10622279C2212yes—
89#10622279C2212yes—
90#10622278C2212yes—
91#10622277C2212yes—
92#10622273C2212yes—
93#10622272C2212yes—
94#10622271C2212yes—
95#10622271C2212yes—
96#10622269C2212yes—
97#10622268C2212yes—
98#10622268C2212yes—
99#10622267C2212yes—
100#10622266C2212yes—
101#10622262C2212yes—
102#10622262C2212yes—
103#10622260C2212yes—
104#10622260C2212yes—
105#10622260C2212yes—
106#10622259C2212yes—
107C22×Q8×C11C2311yescharacteristic
108C23×C4×C11C2311yescharacteristic
109C22×C22⋊D11C2312yes—
110C23×Dic11C2312yes—
111C2×#4339—24no—
112C2×#4339—42no—
113C2×#4339—42no—
114C22×D44C2311yescharacteristic
115C22×C4×D11C2312yes—
116C22×C4×D11C2312yes—
117C22×C4×D11C2312yes—
118C22×Dic22C2311yescharacteristic
119C22×Dic22C2311yescharacteristic
120C4×Q8×C11—42no—
121C11×#117—42no—
122C2×C11×C4⋊C4C2312yes—
123C2×C11×C4⋊C4C2312yes—
124C2×C11×C4⋊C4C2312yes—
125C2×C11×C4⋊C4C2311yescharacteristic
126C2×C11×C4⋊C4C2311yescharacteristic
127C2×C11×C4⋊C4C2311yescharacteristic
128C2×C11×C22⋊C4C2312yes—
129C2×C11×C22⋊C4C2312yes—
130C2×C11×C22⋊C4C2311yescharacteristic
131C2×C11×C22⋊C4C2311yescharacteristic
132C2×C42×C11C2311yescharacteristic
133C2×C42×C11C2311yescharacteristic
134C2×C42×C11C2312yes—
135C2×C22⋊Dic11C2312yes—
136C2×C22⋊Dic11C2312yes—
137#66999—28no—
138C2×(C2×D11)⋊C4C2312yes—
139C2×(C2×D11)⋊C4C2312yes—
140C2×(C2×D11)⋊C4C2312yes—
141C2×(C2×D11)⋊C4C2312yes—
142C2×(C2×D11)⋊C4C2312yes—
143C2×(C2×D11)⋊C4C2312yes—
144C2×(C2×D11)⋊C4C2312yes—
145C2×(C2×D11)⋊C4C2312yes—
146C2×(C2×D11)⋊C4C2312yes—
147C2×(C2×D11)⋊C4C2312yes—
148C2×C4⋊Dic11C2312yes—
149C2×C4⋊Dic11C2312yes—
150C2×C4⋊Dic11C2311yescharacteristic
151C2×C4⋊Dic11C2312yes—
152C2×C4⋊Dic11C2312yes—
153C2×Dic11⋊C4C2312yes—
154C2×Dic11⋊C4C2312yes—
155C2×Dic11⋊C4C2312yes—
156C2×Dic11⋊C4C2312yes—
157C2×Dic11⋊C4C2312yes—
158C2×Dic11⋊C4C2312yes—
159C2×Dic11⋊C4C2312yes—
160C2×Dic11⋊C4C2312yes—
161C2×Dic11⋊C4C2312yes—
162C2×Dic11⋊C4C2312yes—
163C2×Dic11⋊C4C2312yes—
164C2×C4×Dic11—42no—
165C2×C4×Dic11C2312yes—
166C2×C4×Dic11C2312yes—
167C2×C4×Dic11C2312yes—
168C2×C4×Dic11C2312yes—
169C2×C4×Dic11C2312yes—
170C2×C4×Dic11C2311yescharacteristic
171C2×C4×Dic11C2312yes—
172C2×C4×Dic11C2311yescharacteristic
173#66949—28no—
174#66947—28no—
175C4⋊C4×D11—44no—
176#66936—44no—
177#66930—28no—
178#66930—44no—
179C4×Dic22—42no—
180C11×#95C2312yes—
181C11×#95C2312yes—
182C11×#95C2312yes—
183C11×#95C2312yes—
184C11×#95C2311yescharacteristic
185C11×#95C2311yescharacteristic
186C11×#95C2312yes—
187C11×#95C2312yes—
188C11⋊#95C2312yes—
189C11⋊#95C2312yes—
190C11⋊#95C2312yes—
191C11⋊#95C2312yes—
192C11⋊#95C2312yes—
193C11⋊#95C2312yes—
194C11⋊#95C2312yes—
195C11⋊#95C2312yes—
196C11⋊#95C2311yescharacteristic
197C11⋊#95C2312yes—
198C11⋊#95C2312yes—
199C11⋊#95C2312yes—
200C11⋊#95C2312yes—
201C11⋊#95C2312yes—
202C11⋊#95C2312yes—
203C11⋊#95C2312yes—
204C11⋊#95C2312yes—
205C11⋊#95C2312yes—
206C11⋊#95C2312yes—
207C11⋊#95C2311yescharacteristic
208#60046—111nomaximal, Sylow
209C24×C11C2411yescharacteristic
210C23×D11C2412yes—
211C2×Q8×C11—24no—
212C2×Q8×C11—41no—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—22no—
216C22×C4×C11C2411yescharacteristic
217C22×C4×C11C2411yescharacteristic
218C22×C4×C11C2411yescharacteristic
219C22×C4×C11C2411yescharacteristic
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2411yescharacteristic
224C22×C4×C11C2412yes—
225C22×C4×C11C2411yescharacteristic
226C2×C22⋊D11—24no—
227C2×C22⋊D11—24no—
228C2×C22⋊D11—42no—
229C22×Dic11—24no—
230C22×Dic11—24no—
231C22×Dic11—24no—
232C22×Dic11C2412yes—
233C22×Dic11C2412yes—
234C22×Dic11C2412yes—
235C22×Dic11C2412yes—
236C22×Dic11C2412yes—
237C22×Dic11C2412yes—
238C22×Dic11C2412yes—
239#4339—416no—
240C2×D44—41no—
241C2×D44—41no—
242C2×D44#4114yes—
243C2×C4×D11—24no—
244C2×C4×D11—24no—
245C2×C4×D11—24no—
246C2×C4×D11—24no—
247C2×C4×D11—24no—
248C2×C4×D11—42no—
249C2×C4×D11—42no—
250C2×C4×D11—42no—
251C2×C4×D11—42no—
252C2×Dic22—24no—
253C2×Dic22—22no—
254C2×Dic22—41no—
255C2×Dic22—41no—
256C2×Dic22—41no—
257C11×C4⋊C4—24no—
258C11×C4⋊C4—24no—
259C11×C4⋊C4—24no—
260C11×C4⋊C4—41no—
261C11×C4⋊C4—41no—
262C11×C4⋊C4—41no—
263C11×C22⋊C4—24no—
264C11×C22⋊C4—24no—
265C11×C22⋊C4—41no—
266C11×C22⋊C4—41no—
267C42×C11—22no—
268C42×C11—22no—
269C42×C11—42no—
270C22⋊Dic11—24no—
271C22⋊Dic11—24no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4—24no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—24no—
276(C2×D11)⋊C4—24no—
277(C2×D11)⋊C4—24no—
278(C2×D11)⋊C4—24no—
279(C2×D11)⋊C4—24no—
280(C2×D11)⋊C4—24no—
281(C2×D11)⋊C4—42no—
282C4⋊Dic11—24no—
283C4⋊Dic11—24no—
284C4⋊Dic11—41no—
285C4⋊Dic11—42no—
286C4⋊Dic11—42no—
287Dic11⋊C4—24no—
288Dic11⋊C4—24no—
289Dic11⋊C4—24no—
290Dic11⋊C4—24no—
291Dic11⋊C4—24no—
292Dic11⋊C4—24no—
293Dic11⋊C4—42no—
294Dic11⋊C4—42no—
295Dic11⋊C4—42no—
296Dic11⋊C4—42no—
297Dic11⋊C4#4118yescomplemented
298C4×Dic11—24no—
299C4×Dic11—24no—
300C4×Dic11—42no—
301C4×Dic11—42no—
302C4×Dic11—42no—
303C4×Dic11—41no—
304C4×Dic11—41no—
305C4×Dic11—42no—
306#2805—112no—
307#2724—111no—
308#2683—111no—
309#2599—111no—
310#2599D1111yescharacteristic, complemented
311#2586—111no—
312#2586—111no—
313#2573—112no—
314#2573—112no—
315#2477—112no—
316#2477—112no—
317#2470—112no—
318#2470—112no—
319#2406—112no—
320#2374—112no—
321#2360—112no—
322#2360—112no—
323#2297—111no—
324#2296—112no—
325C23×C11—22no—
326C23×C11—21no—
327C23×C11—21no—
328C23×C11—22no—
329C23×C11H(5,𝔽2)12yes—
330C23×C11C2511yescharacteristic
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11C2×#4114yes—
338Q8×C11—44no—
339C2×C4×C11—28no—
340C2×C4×C11—22no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—22no—
345C2×C4×C11—21no—
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—21no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—21no—
357C2×C4×C11—21no—
358C2×C4×C11—21no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11C2×#4114yes—
364C2×C4×C11C2×#4112yes—
365C2×C4×C11H(5,𝔽2)12yes—
366C22⋊D11—48no—
367C2×Dic11—216no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11—22no—
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×Dic11C2×#4114yes—
387C2×Dic11C2×#4114yes—
388C2×Dic112−1+414yes—
389D44—44no—
390C4×D11—48no—
391C4×D11—48no—
392C4×D11—84no—
393Dic22—44no—
394Dic22—44no—
395C22×#41—111no—
396C2×#123—112no—
397C2×#123—112no—
398C2×C22⋊Q8—112no—
399C2×C22⋊Q8—112no—
400C2×C4×Q8—111no—
401C2×C4×Q8C2×D1111yescharacteristic
402C2×#117—112no—
403C2×#117—112no—
404C2×#117C2×D1111yescharacteristic
405C22×C4⋊C4—112no—
406C22×C42—111no—
407#400—112no—
408#400—112no—
409#400—112no—
410#400—112no—
411#398—111no—
412#398C2×D1111yescharacteristic
413#397—111no—
414#397—112no—
415#397—112no—
416#397C2×D1111yescharacteristic
417#396—112no—
418#396—112no—
419#395—111no—
420#395—112no—
421#395—112no—
422#395C2×D1111yescharacteristic
423#394—112no—
424#394—112no—
425#393—111no—
426#393C2×D1111yescharacteristic
427#391—112no—
428#391—111no—
429#391—111no—
430#391—112no—
431#390—111no—
432#390—111no—
433#389—112no—
434#389—112no—
435#389—112no—
436#389—112no—
437#389—112no—
438#389—112no—
439#389—112no—
440#389—112no—
441#388—112no—
442#388—112no—
443#388—112no—
444#388—112no—
445#388—112no—
446#388C2×D1112yes—
447#387—112no—
448#387—112no—
449#387—112no—
450#387—112no—
451#387—112no—
452#387—112no—
453#387—112no—
454#387—112no—
455#387C2×D1112yes—
456#387C2×D1112yes—
457#386—112no—
458#386—112no—
459#386—112no—
460#386—112no—
461#385—112no—
462#385—112no—
463#385—112no—
464#385—112no—
465#385—112no—
466#385—112no—
467#385—112no—
468#385C2×D1112yes—
469#383—111no—
470#383C2×D1111yescharacteristic
471#381—112no—
472C4×C4⋊C4—112no—
473C4×C4⋊C4—112no—
474C4×C4⋊C4—112no—
475C4×C4⋊C4—112no—
476C4×C22⋊C4—112no—
477C4×C22⋊C4—112no—
478C4×C22⋊C4—112no—
479C4×C22⋊C4—112no—
480C4×C22⋊C4—112no—
481C4×C22⋊C4—112no—
482C22×C11—22no—
483C22×C11—24no—
484C22×C11—41no—
485C22×C11—42no—
486C22×C11—41no—
487C22×C11C22×#4112yes—
488C22×C11C22×#4111yescharacteristic
489C22×C11C2×H(5,𝔽2)11yescharacteristic
490C22×C11C2×H(5,𝔽2)11yescharacteristic
491C22×C11C2×2−1+412yes—
492C2×D11—24no—
493C2×D11—24no—
494C2×D11—24no—
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C4×C11—24no—
500C4×C11—22no—
501C4×C11—22no—
502C4×C11—41no—
503C4×C11—41no—
504C4×C11—42no—
505C4×C11—42no—
506C4×C11—42no—
507C4×C11—41no—
508C4×C11—41no—
509Dic11—24no—
510Dic11—24no—
511Dic11—24no—
512Dic11—42no—
513Dic11—42no—
514Dic11—42no—
515Dic11—42no—
516C2×#41—224no—
517C2×#41—442no—
518C2×#41—442no—
519C22×Q8—111no—
520C22×Q8—111no—
521C22×Q8C22×D1111yescharacteristic
522C22×D4—112no—
523C22×D4—111no—
524C23×C4—112no—
525C23×C4—112no—
526C23×C4—112no—
527C23×C4—112no—
528C23×C4C22×D1111yescharacteristic
529#123—228no—
530#123—444no—
531C22⋊Q8—228no—
532C22⋊Q8—228no—
533C4×Q8—42no—
534C4×Q8—442no—
535#117—42no—
536#117—228no—
537#117—444no—
538C2×C4⋊C4—112no—
539C2×C4⋊C4—112no—
540C2×C4⋊C4—112no—
541C2×C4⋊C4—112no—
542C2×C4⋊C4—112no—
543C2×C4⋊C4—112no—
544C2×C4⋊C4—112no—
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—111no—
552C2×C4⋊C4—112no—
553C2×C4⋊C4—112no—
554C2×C4⋊C4—444no—
555C2×C4⋊C4C22×D1112yes—
556C2×C4⋊C4C22×D1112yes—
557C2×C4⋊C4C22×D1112yes—
558C2×C4⋊C4C22×D1111yescharacteristic
559C2×C4⋊C4C22×D1111yescharacteristic
560C2×C4⋊C4C22×D1111yescharacteristic
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⋊C4C22×D1112yes—
574C2×C22⋊C4C22×D1112yes—
575C2×C22⋊C4C22×D1111yescharacteristic
576C2×C22⋊C4C22×D1111yescharacteristic
577C2×C42—112no—
578C2×C42—112no—
579C2×C42—112no—
580C2×C42—112no—
581C2×C42—112no—
582C2×C42—112no—
583C2×C42—111no—
584C2×C42—111no—
585C2×C42—442no—
586C2×C42C22×D1111yescharacteristic
587C2×C42C22×D1111yescharacteristic
588C2×C42C22×D1112yes—
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—111no—
604#95—111no—
605#95—112no—
606#95—112no—
607#95—112no—
608#95—112no—
609#95C22×D1112yes—
610#95C22×D1112yes—
611#95C22×D1112yes—
612#95C22×D1112yes—
613#95C22×D1111yescharacteristic
614#95C22×D1111yescharacteristic
615#95C22×D1112yes—
616#95C22×D1112yes—
617C2×C11—42no—
618C2×C11#348111yescharacteristic
619C2×C11#348212yes—
620C2×C11#349011yescharacteristic
621C2×C11#349212yes—
622C2×C11#355011yescharacteristic
623D11—44no—
624C24—112no—
625C24C23×D1111yescharacteristic
626#41—4416no—
627C2×Q8—24no—
628C2×Q8—41no—
629C2×Q8—224no—
630C2×Q8—222no—
631C2×Q8—441no—
632C2×Q8—441no—
633C2×Q8—441no—
634C2×D4—114no—
635C2×D4—224no—
636C2×D4—224no—
637C2×D4—441no—
638C2×D4—441no—
639C2×D4—442no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—112no—
644C22×C4—112no—
645C22×C4—112no—
646C22×C4—112no—
647C22×C4—112no—
648C22×C4—112no—
649C22×C4—112no—
650C22×C4—224no—
651C22×C4—224no—
652C22×C4—224no—
653C22×C4—224no—
654C22×C4—224no—
655C22×C4—224no—
656C22×C4—224no—
657C22×C4—224no—
658C22×C4—442no—
659C22×C4—442no—
660C22×C4—442no—
661C22×C4—442no—
662C22×C4C23×D1111yescharacteristic
663C22×C4C23×D1111yescharacteristic
664C22×C4C23×D1111yescharacteristic
665C22×C4C23×D1111yescharacteristic
666C22×C4C23×D1112yes—
667C22×C4C23×D1112yes—
668C22×C4C23×D1112yes—
669C22×C4C23×D1111yescharacteristic
670C22×C4C23×D1111yescharacteristic
671C22×C4C23×D1112yes—
672C4⋊C4—24no—
673C4⋊C4—24no—
674C4⋊C4—24no—
675C4⋊C4—41no—
676C4⋊C4—41no—
677C4⋊C4—41no—
678C4⋊C4—118no—
679C4⋊C4—224no—
680C4⋊C4—224no—
681C4⋊C4—224no—
682C4⋊C4—224no—
683C4⋊C4—224no—
684C4⋊C4—224no—
685C4⋊C4—224no—
686C4⋊C4—224no—
687C4⋊C4—442no—
688C4⋊C4—442no—
689C4⋊C4—442no—
690C4⋊C4—442no—
691C4⋊C4—441no—
692C4⋊C4—442no—
693C4⋊C4—442no—
694C22⋊C4—24no—
695C22⋊C4—24no—
696C22⋊C4—41no—
697C22⋊C4—41no—
698C22⋊C4—224no—
699C22⋊C4—224no—
700C22⋊C4—224no—
701C22⋊C4—224no—
702C22⋊C4—224no—
703C22⋊C4—224no—
704C22⋊C4—224no—
705C22⋊C4—224no—
706C22⋊C4—224no—
707C22⋊C4—224no—
708C22⋊C4—224no—
709C22⋊C4—442no—
710C42—22no—
711C42—22no—
712C42—42no—
713C42—224no—
714C42—224no—
715C42—442no—
716C42—441no—
717C42—441no—
718C42—442no—
719C42—442no—
720C42—442no—
721C11#6004611yescharacteristic, complemented, Sylow
722C23—21no—
723C23—22no—
724C23—21no—
725C23—22no—
726C23—114no—
727C23—222no—
728C23—222no—
729C23—222no—
730C23—222no—
731C23—222no—
732C23—222no—
733C23#6704212yes—
734C23C24×D1111yescharacteristic
735Q8—44no—
736Q8—444no—
737Q8—444no—
738D4—444no—
739D4—448no—
740C2×C4—28no—
741C2×C4—22no—
742C2×C4—21no—
743C2×C4—22no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—22no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—114no—
765C2×C4—114no—
766C2×C4—114no—
767C2×C4—2216no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—222no—
772C2×C4—222no—
773C2×C4—222no—
774C2×C4—222no—
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—448no—
787C2×C4—448no—
788C2×C4—884no—
789C2×C4#6703712yes—
790C2×C4#41×D1114yes—
791C2×C4#41×D1112yes—
792C22—22no—
793C22—24no—
794C22—41no—
795C22—42no—
796C22—41no—
797C22—224no—
798C22—224no—
799C22—224no—
800C22—442no—
801C22—442no—
802C22—442no—
803C22—442no—
804C22C2×#6703711yescharacteristic
805C22C2×#41×D1112yes—
806C22C2×#41×D1111yescharacteristic
807C22C2×#6704211yescharacteristic
808C22D11×2−1+412yes—
809C4—24no—
810C4—22no—
811C4—22no—
812C4—41no—
813C4—41no—
814C4—42no—
815C4—41no—
816C4—41no—
817C4—42no—
818C4—42no—
819C4—224no—
820C4—224no—
821C4—224no—
822C4—442no—
823C4—442no—
824C4—442no—
825C4—442no—
826C2—42no—
827C2—444no—
828C2#1308221811yescharacteristic
829C2#1308223512yes—
830C2#1308229911yescharacteristic
831C2#1308231612yes—
832C2#1308302511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2599C2
prime radicalC22×#4339C22
hypercenter#2599D11
hypocenterC11#60046
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2599

Complements

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

NH ≅ G/Ntype
1. #13076567C2semidirect
2. #13075543C2semidirect
3. #13074990C2semidirect
4. #13074193C2semidirect
5. #13074028C2semidirect
6. #13074021C2semidirect
7. #13073881C2semidirect
8. #13073873C2semidirect
9. #13072823C2semidirect
10. #13072820C2semidirect
11. #13072710C2semidirect
12. #13072707C2semidirect
14. #13071748C2semidirect
15. #13071624C2semidirect
16. #13071617C2semidirect
18. #13071095C2semidirect
19. C11×#2599C2semidirect
297. Dic11⋊C4#41semidirect
310. #2599D11semidirect
721. C11#60046semidirect

Maximal subgroups

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

subgroupindex
#130765672
#130755432
#130749902
#130741932
#130740282
#130740212
#130738812
#130738732
#130728232
#130728202
#130727102
#130727072
#130719492
#130717482
#130716242
#130716172
#130711042
#130710952
C11×#25992
#6004611