Finite Group Databasebeta

← #15617124

Subgroups — #15617124

Order 2816.

1854 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076599C211yesmaximal, characteristic, complemented
2#13075645C211yesmaximal, characteristic, complemented
3#13075581C212yesmaximal, complemented
4#13074317C211yesmaximal, characteristic, complemented
5#13074309C211yesmaximal, characteristic, complemented
6#13074112C211yesmaximal, characteristic, complemented
7#13073707C212yesmaximal, complemented
8#13073699C212yesmaximal, complemented
9#13072852C212yesmaximal, complemented
10#13072849C212yesmaximal, complemented
11#13072777C212yesmaximal, complemented
12#13072774C212yesmaximal, complemented
13#13072239C212yesmaximal
14#13071743C212yesmaximal, complemented
15#13071734C212yesmaximal, complemented
16#13071703C212yesmaximal, complemented
17#13071103C211yesmaximal, characteristic
18#13071096C212yesmaximal, complemented
19C11×#2593C211yesmaximal, characteristic, complemented
20C22×#4341C2211yescharacteristic
21C2×#66945C2211yescharacteristic
22C2×#66943C2211yescharacteristic
23C2×#66943C2211yescharacteristic
24C2×#66941C2212yes—
25C2×#66938C2212yes—
26C2×#66932C2212yes—
27C2×#66932C2212yes—
28C2×#66931C2212yes—
29C2×#66925C2212yes—
30C2×#66925C2212yes—
31C2×C42×D11C2211yescharacteristic
32C11×#400C2211yescharacteristic
33C11×#398C2211yescharacteristic
34C11×#394C2212yes—
35C11×#390C2211yescharacteristic
36C11×#388C2212yes—
37C11×#388C2212yes—
38C11×#388C2212yes—
39C11×#388C2212yes—
40C4×C11×C4⋊C4C2212yes—
41#10622835C2212yes—
42#10622834C2211yescharacteristic
43#10622606C2211yescharacteristic
44#10622605C2211yescharacteristic
45#10622602C2212yes—
46#10622602C2212yes—
47#10622599C2211yescharacteristic
48#10622598C2212yes—
49#10622597C2212yes—
50#10622596C2211yescharacteristic
51#10622592C2212yes—
52C4⋊C4×Dic11C2212yes—
53C4⋊C4×Dic11C2212yes—
54#10622587C2211yescharacteristic
55#10622585C2212yes—
56#10622585C2212yes—
57#10622574C2212yes—
58#10622572C2212yes—
59#10622570C2212yes—
60#10622569C2212yes—
61#10622569C2212yes—
62#10622564C2212yes—
63#10622564C2212yes—
64#10622563C2212yes—
65#10622562C2212yes—
66#10622562C2212yes—
67#10622561C2212yes—
68#10622561C2212yes—
69#10622559C2212yes—
70#10622558C2212yes—
71#10622558C2212yes—
72#10622558C2212yes—
73#10622557C2212yes—
74C22⋊C4×Dic11C2212yes—
75C22⋊C4×Dic11C2212yes—
76C22⋊C4×Dic11C2212yes—
77C4×C4⋊Dic11C2212yes—
78C4×Dic11⋊C4C2212yes—
79C4×Dic11⋊C4C2212yes—
80C4×Dic11⋊C4C2212yes—
81C4×Dic11⋊C4C2212yes—
82#10622542C2212yes—
83#10622542C2211yescharacteristic
84#10622541C2212yes—
85#10622290C2211yescharacteristic
86#10622287C2211yescharacteristic
87#10622283C2212yes—
88#10622282C2212yes—
89#10622281C2212yes—
90#10622281C2212yes—
91#10622270C2212yes—
92#10622269C2212yes—
93#10622268C2212yes—
94#10622268C2212yes—
95#10622267C2212yes—
96#10622266C2212yes—
97#10622265C2212yes—
98#10622265C2212yes—
99#10622261C2211yescharacteristic
100#10622261C2211yescharacteristic
101#10622260C2212yes—
102#10622260C2212yes—
103#10622260C2212yes—
104#10622260C2212yes—
105#10622259C2212yes—
106#10622259C2212yes—
107C22×D4×C11C2311yescharacteristic
108C22×C22⋊D11C2312yes—
109C23×Dic11C2312yes—
110C2×#4341—24no—
111C2×#4341—42no—
112C2×#4341—42no—
113C22×C4×D11C2312yes—
114C22×C4×D11C2311yescharacteristic
115C22×Dic22C2312yes—
116C22×Dic22C2311yescharacteristic
117C2×C11×C4⋊C4C2312yes—
118C2×C11×C4⋊C4C2312yes—
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C22⋊C4C2312yes—
123C2×C11×C22⋊C4C2312yes—
124C2×C11×C22⋊C4C2312yes—
125C2×C11×C22⋊C4C2312yes—
126C2×C11×C22⋊C4C2312yes—
127C2×C11×C22⋊C4C2312yes—
128C2×C42×C11C2312yes—
129C2×C42×C11C2311yescharacteristic
130C2×C42×C11C2312yes—
131C2×C22⋊Dic11C2312yes—
132C2×C22⋊Dic11C2312yes—
133C2×C22⋊Dic11C2312yes—
134C2×C22⋊Dic11C2312yes—
135C2×C22⋊Dic11C2312yes—
136C2×C22⋊Dic11C2312yes—
137C2×(C2×D11)⋊C4C2312yes—
138C2×(C2×D11)⋊C4C2312yes—
139C2×(C2×D11)⋊C4C2312yes—
140C2×(C2×D11)⋊C4C2312yes—
141C2×(C2×D11)⋊C4C2311yescharacteristic
142C2×(C2×D11)⋊C4C2311yescharacteristic
143C2×C4⋊Dic11C2312yes—
144C2×C4⋊Dic11C2312yes—
145C2×C4⋊Dic11C2312yes—
146C2×C4⋊Dic11C2312yes—
147C2×C4⋊Dic11C2311yescharacteristic
148C2×C4⋊Dic11C2312yes—
149C2×C4⋊Dic11C2311yescharacteristic
150C2×C4⋊Dic11C2311yescharacteristic
151C2×Dic11⋊C4C2312yes—
152C2×Dic11⋊C4C2312yes—
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×C4×Dic11C2312yes—
164C2×C4×Dic11C2312yes—
165C2×C4×Dic11C2312yes—
166C2×C4×Dic11C2312yes—
167C2×C4×Dic11C2311yescharacteristic
168C2×C4×Dic11C2311yescharacteristic
169C2×C4×Dic11C2311yescharacteristic
170C2×C4×Dic11C2312yes—
171C2×C4×Dic11C2312yes—
172C2×C4×Dic11C2312yes—
173#66945—42no—
174#66943—42no—
175#66943—42no—
176#66941—28no—
177#66938—44no—
178#66932—28no—
179#66932—28no—
180#66931—44no—
181#66925—28no—
182#66925—44no—
183C42×D11—42no—
184C11×#95C2312yes—
185C11×#95C2312yes—
186C11×#95C2311yescharacteristic
187C11×#95C2311yescharacteristic
188C11×#95C2312yes—
189C11×#95C2312yes—
190C11⋊#95C2312yes—
191C11⋊#95C2312yes—
192C11⋊#95C2312yes—
193C11⋊#95C2312yes—
194C11⋊#95C2312yes—
195C11⋊#95C2312yes—
196C11⋊#95C2312yes—
197C11⋊#95C2312yes—
198C11⋊#95C2311yescharacteristic
199C11⋊#95C2311yescharacteristic
200C11⋊#95C2312yes—
201C11⋊#95C2312yes—
202C11⋊#95C2312yes—
203C11⋊#95C2312yes—
204C11⋊#95C2312yes—
205C11⋊#95C2312yes—
206C11⋊#95C2312yes—
207C11⋊#95C2312yes—
208#60047—111nomaximal, Sylow
209C24×C11C2412yes—
210C23×D11C2411yescharacteristic
211C2×D4×C11—22no—
212C2×D4×C11—41no—
213C2×D4×C11—41no—
214C22×C4×C11C2411yescharacteristic
215C22×C4×C11C2411yescharacteristic
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2411yescharacteristic
221C22×C4×C11C2412yes—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—24no—
224C2×C22⋊D11—42no—
225C22×Dic11—24no—
226C22×Dic11—24no—
227C22×Dic11—42no—
228C22×Dic11C2412yes—
229C22×Dic11C2411yescharacteristic
230C22×Dic11C2411yescharacteristic
231C22×Dic11C2412yes—
232C22×Dic11C2412yes—
233C22×Dic11C2412yes—
234C22×Dic11C2412yes—
235C22×Dic11C2412yes—
236C22×Dic11C2411yescharacteristic
237#4341—416no—
238C2×C4×D11—24no—
239C2×C4×D11—22no—
240C2×C4×D11—24no—
241C2×C4×D11—22no—
242C2×C4×D11—22no—
243C2×C4×D11—24no—
244C2×Dic22—24no—
245C2×Dic22—41no—
246C2×Dic22—41no—
247C2×Dic22—42no—
248C2×Dic22—42no—
249C2×Dic22#4114yes—
250C11×C4⋊C4—24no—
251C11×C4⋊C4—24no—
252C11×C4⋊C4—41no—
253C11×C4⋊C4—41no—
254C11×C4⋊C4—41no—
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—24no—
262C42×C11—41no—
263C42×C11—42no—
264C22⋊Dic11—24no—
265C22⋊Dic11—24no—
266C22⋊Dic11—24no—
267C22⋊Dic11—24no—
268C22⋊Dic11—42no—
269C22⋊Dic11—42no—
270(C2×D11)⋊C4—24no—
271(C2×D11)⋊C4—24no—
272(C2×D11)⋊C4—24no—
273(C2×D11)⋊C4—24no—
274(C2×D11)⋊C4—41no—
275(C2×D11)⋊C4—41no—
276C4⋊Dic11—24no—
277C4⋊Dic11—24no—
278C4⋊Dic11—24no—
279C4⋊Dic11—24no—
280C4⋊Dic11—41no—
281C4⋊Dic11—41no—
282C4⋊Dic11—42no—
283C4⋊Dic11—41no—
284Dic11⋊C4—24no—
285Dic11⋊C4—24no—
286Dic11⋊C4—24no—
287Dic11⋊C4—24no—
288Dic11⋊C4—24no—
289Dic11⋊C4—24no—
290Dic11⋊C4—24no—
291Dic11⋊C4—42no—
292Dic11⋊C4—42no—
293Dic11⋊C4—42no—
294Dic11⋊C4—42no—
295Dic11⋊C4#4118yescomplemented
296C4×Dic11—24no—
297C4×Dic11—24no—
298C4×Dic11—24no—
299C4×Dic11—22no—
300C4×Dic11—22no—
301C4×Dic11—24no—
302C4×Dic11—42no—
303C4×Dic11—41no—
304C4×Dic11—42no—
305C4×Dic11—42no—
306#2809—111no—
307#2734—111no—
308#2727—112no—
309#2611—111no—
310#2611—111no—
311#2593—111no—
312#2593D1111yescharacteristic, complemented
313#2556—112no—
314#2556—112no—
315#2479—112no—
316#2479—112no—
317#2474—112no—
318#2474—112no—
319#2432—112no—
320#2373—112no—
321#2373—112no—
322#2369—112no—
323#2297—111no—
324#2296—112no—
325C23×C11—22no—
326C23×C11—22no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11C2511yescharacteristic
333C22×D11—22no—
334C22×D11—21no—
335C22×D11—21no—
336C22×D11—22no—
337C22×D11H(5,𝔽2)12yes—
338D4×C11—44no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—21no—
350C2×C4×C11—21no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—22no—
357C2×C4×C11—22no—
358C2×C4×C11C2×#4114yes—
359C2×C4×C11C2×#4112yes—
360C2×C4×C112−1+414yes—
361C22⋊D11—48no—
362C2×Dic11—22no—
363C2×Dic11—21no—
364C2×Dic11—22no—
365C2×Dic11—21no—
366C2×Dic11—22no—
367C2×Dic11—22no—
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—21no—
377C2×Dic11—21no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—48no—
384C2×Dic11C2×#4114yes—
385C2×Dic11C2×#4114yes—
386C2×Dic11C2×#4114yes—
387C2×Dic11H(5,𝔽2)12yes—
388C4×D11—216no—
389C4×D11—28no—
390Dic22—44no—
391Dic22—84no—
392C22×#41—111no—
393C2×C4⋊Q8—112no—
394C2×#126—112no—
395C2×#126—112no—
396C2×#125—111no—
397C2×#125—111no—
398C2×#124—112no—
399C2×C22⋊Q8—112no—
400C2×#117—111no—
401C2×#117—112no—
402C2×#117—112no—
403C22×C42—111no—
404#400—111no—
405#400C2×D1111yescharacteristic
406#399—111no—
407#399—112no—
408#399—112no—
409#399—111no—
410#398—111no—
411#398—112no—
412#398—112no—
413#398C2×D1111yescharacteristic
414#397—111no—
415#397—111no—
416#396—112no—
417#396—112no—
418#395—112no—
419#395—112no—
420#394—112no—
421#394—112no—
422#394—112no—
423#394C2×D1112yes—
424#391—111no—
425#391—111no—
426#391—112no—
427#391—112no—
428#391—112no—
429#390—111no—
430#390—112no—
431#390C2×D1111yescharacteristic
432#389—112no—
433#389—112no—
434#389—112no—
435#389—112no—
436#389—112no—
437#389—112no—
438#389—112no—
439#389—112no—
440#388—112no—
441#388—112no—
442#388—112no—
443#388—112no—
444#388—112no—
445#388—112no—
446#388—112no—
447#388—112no—
448#388C2×D1112yes—
449#388C2×D1112yes—
450#388C2×D1112yes—
451#388C2×D1112yes—
452#387—112no—
453#387—112no—
454#387—112no—
455#387—112no—
456#387—112no—
457#387—112no—
458#386—112no—
459#386—112no—
460#385—112no—
461#385—112no—
462#385—112no—
463#385—112no—
464#385—112no—
465#385—112no—
466C4×C4⋊C4—112no—
467C4×C4⋊C4—112no—
468C4×C4⋊C4—112no—
469C4×C4⋊C4—112no—
470C4×C4⋊C4—112no—
471C4×C4⋊C4—112no—
472C4×C4⋊C4—112no—
473C4×C4⋊C4C2×D1112yes—
474C4×C22⋊C4—112no—
475C4×C22⋊C4—112no—
476C4×C22⋊C4—112no—
477#376—111no—
478#376—111no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11—42no—
486C22×C11C22×#4111yescharacteristic
487C22×C11C22×#4112yes—
488C22×C11C2×H(5,𝔽2)11yescharacteristic
489C22×C11C2×H(5,𝔽2)11yescharacteristic
490C22×C11C2×2−1+412yes—
491C2×D11—22no—
492C2×D11—24no—
493C2×D11—42no—
494C2×D11—41no—
495C2×D11—41no—
496C4×C11—24no—
497C4×C11—22no—
498C4×C11—24no—
499C4×C11—42no—
500C4×C11—42no—
501C4×C11—42no—
502C4×C11—41no—
503C4×C11—41no—
504Dic11—24no—
505Dic11—24no—
506Dic11—22no—
507Dic11—24no—
508Dic11—42no—
509Dic11—41no—
510Dic11—41no—
511Dic11—42no—
512Dic11—42no—
513C2×#41—224no—
514C2×#41—442no—
515C2×#41—442no—
516C22×Q8—111no—
517C22×Q8—112no—
518C22×D4—112no—
519C22×D4C22×D1111yescharacteristic
520C23×C4—112no—
521C23×C4—112no—
522C23×C4—111no—
523C4⋊Q8—228no—
524#126—228no—
525#126—228no—
526#125—442no—
527#125—442no—
528#124—444no—
529C22⋊Q8—444no—
530#117—228no—
531#117—444no—
532#117—442no—
533C2×C4⋊C4—112no—
534C2×C4⋊C4—112no—
535C2×C4⋊C4—112no—
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—112no—
543C2×C4⋊C4—112no—
544C2×C4⋊C4—112no—
545C2×C4⋊C4—112no—
546C2×C4⋊C4—111no—
547C2×C4⋊C4—112no—
548C2×C4⋊C4—112no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—112no—
552C2×C4⋊C4—112no—
553C2×C4⋊C4C22×D1112yes—
554C2×C4⋊C4C22×D1112yes—
555C2×C4⋊C4C22×D1111yescharacteristic
556C2×C4⋊C4C22×D1111yescharacteristic
557C2×C4⋊C4C22×D1111yescharacteristic
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⋊C4—112no—
565C2×C22⋊C4—112no—
566C2×C22⋊C4—112no—
567C2×C22⋊C4—112no—
568C2×C22⋊C4—111no—
569C2×C22⋊C4—111no—
570C2×C22⋊C4C22×D1112yes—
571C2×C22⋊C4C22×D1112yes—
572C2×C22⋊C4C22×D1112yes—
573C2×C22⋊C4C22×D1112yes—
574C2×C22⋊C4C22×D1112yes—
575C2×C22⋊C4C22×D1112yes—
576C2×C42—111no—
577C2×C42—111no—
578C2×C42—112no—
579C2×C42—112no—
580C2×C42—112no—
581C2×C42—112no—
582C2×C42—112no—
583C2×C42—112no—
584C2×C42—112no—
585C2×C42—111no—
586C2×C42—442no—
587C2×C42C22×D1112yes—
588C2×C42C22×D1112yes—
589C2×C42C22×D1111yescharacteristic
590#95—112no—
591#95—112no—
592#95—111no—
593#95—111no—
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#95—112no—
607#95—112no—
608#95C22×D1111yescharacteristic
609#95C22×D1111yescharacteristic
610#95C22×D1112yes—
611#95C22×D1112yes—
612#95C22×D1112yes—
613#95C22×D1112yes—
614C2×C11—82no—
615C2×C11#348212yes—
616C2×C11#348311yescharacteristic
617C2×C11#349011yescharacteristic
618C2×C11#349212yes—
619C2×C11#355011yescharacteristic
620D11—42no—
621C24—111no—
622C24C23×D1112yes—
623#41—4416no—
624C2×Q8—114no—
625C2×Q8—224no—
626C2×Q8—441no—
627C2×Q8—441no—
628C2×Q8—442no—
629C2×Q8—442no—
630C2×D4—22no—
631C2×D4—41no—
632C2×D4—41no—
633C2×D4—224no—
634C2×D4—224no—
635C2×D4—442no—
636C22×C4—112no—
637C22×C4—111no—
638C22×C4—112no—
639C22×C4—112no—
640C22×C4—112no—
641C22×C4—111no—
642C22×C4—111no—
643C22×C4—112no—
644C22×C4—112no—
645C22×C4—224no—
646C22×C4—222no—
647C22×C4—224no—
648C22×C4—222no—
649C22×C4—224no—
650C22×C4—224no—
651C22×C4—222no—
652C22×C4—224no—
653C22×C4—442no—
654C22×C4C23×D1111yescharacteristic
655C22×C4C23×D1111yescharacteristic
656C22×C4C23×D1112yes—
657C22×C4C23×D1112yes—
658C22×C4C23×D1112yes—
659C22×C4C23×D1112yes—
660C22×C4C23×D1111yescharacteristic
661C22×C4C23×D1112yes—
662C4⋊C4—24no—
663C4⋊C4—24no—
664C4⋊C4—41no—
665C4⋊C4—41no—
666C4⋊C4—41no—
667C4⋊C4—118no—
668C4⋊C4—224no—
669C4⋊C4—224no—
670C4⋊C4—224no—
671C4⋊C4—224no—
672C4⋊C4—224no—
673C4⋊C4—224no—
674C4⋊C4—224no—
675C4⋊C4—224no—
676C4⋊C4—224no—
677C4⋊C4—224no—
678C4⋊C4—224no—
679C4⋊C4—442no—
680C4⋊C4—442no—
681C4⋊C4—441no—
682C4⋊C4—442no—
683C4⋊C4—442no—
684C4⋊C4—441no—
685C4⋊C4—441no—
686C4⋊C4—442no—
687C22⋊C4—24no—
688C22⋊C4—24no—
689C22⋊C4—24no—
690C22⋊C4—24no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—224no—
694C22⋊C4—224no—
695C22⋊C4—224no—
696C22⋊C4—224no—
697C22⋊C4—224no—
698C22⋊C4—224no—
699C22⋊C4—224no—
700C22⋊C4—224no—
701C22⋊C4—441no—
702C22⋊C4—441no—
703C22⋊C4—442no—
704C22⋊C4—442no—
705C42—24no—
706C42—41no—
707C42—42no—
708C42—224no—
709C42—222no—
710C42—222no—
711C42—224no—
712C42—224no—
713C42—224no—
714C42—442no—
715C42—441no—
716C42—442no—
717C42—442no—
718C11#6004711yescharacteristic, complemented, Sylow
719C23—22no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—112no—
727C23—222no—
728C23—221no—
729C23—222no—
730C23—221no—
731C23C24×D1111yescharacteristic
732Q8—444no—
733Q8—884no—
734D4—44no—
735D4—448no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—21no—
741C2×C4—21no—
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—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—114no—
756C2×C4—114no—
757C2×C4—114no—
758C2×C4—112no—
759C2×C4—228no—
760C2×C4—2216no—
761C2×C4—222no—
762C2×C4—221no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—221no—
767C2×C4—222no—
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—221no—
777C2×C4—221no—
778C2×C4—222no—
779C2×C4—222no—
780C2×C4—222no—
781C2×C4—222no—
782C2×C4—448no—
783C2×C4#41×D1114yes—
784C2×C4#41×D1112yes—
785C2×C4#6704314yes—
786C22—42no—
787C22—42no—
788C22—42no—
789C22—42no—
790C22—42no—
791C22—42no—
792C22—42no—
793C22—222no—
794C22—224no—
795C22—442no—
796C22—441no—
797C22—441no—
798C22C2×#41×D1111yescharacteristic
799C22C2×#41×D1112yes—
800C22C2×#6704312yes—
801C22D11×H(5,𝔽2)11yescharacteristic
802C22D11×H(5,𝔽2)11yescharacteristic
803C4—24no—
804C4—22no—
805C4—24no—
806C4—42no—
807C4—41no—
808C4—41no—
809C4—42no—
810C4—42no—
811C4—224no—
812C4—222no—
813C4—224no—
814C4—224no—
815C4—441no—
816C4—441no—
817C4—442no—
818C4—442no—
819C4—442no—
820C2—82no—
821C2—442no—
822C2#1308222912yes—
823C2#1308224111yescharacteristic
824C2#1308230211yescharacteristic
825C2#1308232012yes—
826C2#1308302811yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2593C2
prime radicalC22×#4341C22
hypercenter#2593D11
hypocenterC11#60047
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2593

Complements

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

NH ≅ G/Ntype
1. #13076599C2semidirect
2. #13075645C2semidirect
3. #13075581C2semidirect
4. #13074317C2semidirect
5. #13074309C2semidirect
6. #13074112C2semidirect
7. #13073707C2semidirect
8. #13073699C2semidirect
9. #13072852C2semidirect
10. #13072849C2semidirect
11. #13072777C2semidirect
12. #13072774C2semidirect
14. #13071743C2semidirect
15. #13071734C2semidirect
16. #13071703C2semidirect
18. #13071096C2semidirect
19. C11×#2593C2semidirect
295. Dic11⋊C4#41semidirect
312. #2593D11semidirect
718. C11#60047semidirect

Maximal subgroups

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

subgroupindex
#130765992
#130756452
#130755812
#130743172
#130743092
#130741122
#130737072
#130736992
#130728522
#130728492
#130727772
#130727742
#130722392
#130717432
#130717342
#130717032
#130711032
#130710962
C11×#25932
#6004711