Finite Group Databasebeta

← #14967758

Subgroups — #14967758

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#13076955C211yesmaximal, characteristic, complemented
2#13076947C211yesmaximal, characteristic
3#13076185C212yesmaximal, complemented
4#13076116C212yesmaximal, complemented
5#13076061C212yesmaximal, complemented
6#13076038C212yesmaximal, complemented
7#13075979C212yesmaximal, complemented
8#13075965C212yesmaximal, complemented
9#13075949C212yesmaximal, complemented
10#13075668C212yesmaximal, complemented
11#13074730C211yesmaximal, characteristic, complemented
12#13074544C211yesmaximal, characteristic
13#13073176C212yesmaximal, complemented
14#13072942C212yesmaximal, complemented
15#13072440C212yesmaximal, complemented
16#13072093C212yesmaximal, complemented
17#13071349C211yesmaximal, characteristic, complemented
18#13071319C211yesmaximal, characteristic
19C2×C11×#383C211yesmaximal, characteristic, complemented
20C22×C42×C11C2211yescharacteristic
21C2×#66983C2211yescharacteristic
22C2×#66982C2212yes—
23C2×C4×C22⋊D11C2212yes—
24C2×#66977C2211yescharacteristic
25C2×#66977C2212yes—
26C11×#383C2212yes—
27C11×#383C2212yes—
28C11×#383C2212yes—
29C11×#383C2212yes—
30C2×C11×#95C2211yescharacteristic
31C2×C11×#95C2211yescharacteristic
32C2×C11×#95C2211yescharacteristic
33C2×C11×#95C2211yescharacteristic
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2211yescharacteristic
36#10622826C2212yes—
37#10622826C2212yes—
38#10622826C2212yes—
39#10622826C2212yes—
40#10622825C2212yes—
41#10622825C2211yescharacteristic
42#10622825C2211yescharacteristic
43#10622824C2212yes—
44#10622823C2212yes—
45#10622823C2212yes—
46C4×C22⋊Dic11C2212yes—
47#10622553C2212yes—
48#10622553C2212yes—
49#10622552C2211yescharacteristic
50#10622552C2211yescharacteristic
51#10622546C2212yes—
52#10622546C2212yes—
53#10622542C2211yescharacteristic
54#10622542C2211yescharacteristic
55#10622541C2211yescharacteristic
56#10622541C2211yescharacteristic
57#10622541C2211yescharacteristic
58#10622541C2211yescharacteristic
59#10622289C2212yes—
60#10622288C2212yes—
61#10622288C2212yes—
62#10622288C2212yes—
63#10622287C2212yes—
64#10622287C2212yes—
65#10622287C2212yes—
66#10622286C2212yes—
67#10622286C2212yes—
68#10622286C2212yes—
69#10622285C2212yes—
70#10622283C2212yes—
71#10622283C2212yes—
72#10622283C2212yes—
73#10622282C2212yes—
74#10622282C2212yes—
75#10622281C2212yes—
76#10622281C2212yes—
77#10622281C2212yes—
78#10622280C2212yes—
79#10622278C2212yes—
80#10622277C2212yes—
81C11⋊#401C2212yes—
82#10622274C2212yes—
83#10622274C2212yes—
84#10622273C2212yes—
85#10622273C2212yes—
86#10622272C2212yes—
87#10622271C2212yes—
88#10622271C2212yes—
89#10622271C2212yes—
90#10622270C2212yes—
91#10622270C2212yes—
92#10622269C2212yes—
93#10622269C2212yes—
94#10622268C2212yes—
95#10622267C2212yes—
96#10622267C2212yes—
97#10622267C2212yes—
98#10622266C2212yes—
99#10622265C2212yes—
100#10622265C2212yes—
101#10622264C2212yes—
102#10622263C2212yes—
103#10622260C2212yes—
104#10622259C2212yes—
105#10622259C2212yes—
106#10622259C2212yes—
107C23×C4×C11C2311yescharacteristic
108C23×C4×C11C2311yescharacteristic
109C23×C4×C11C2311yescharacteristic
110C23×C4×C11C2311yescharacteristic
111C23×C4×C11C2311yescharacteristic
112C23×C4×C11C2311yescharacteristic
113C23×C4×C11C2311yescharacteristic
114C22×C22⋊D11C2312yes—
115C22×D44C2311yescharacteristic
116C22×C4×D11C2312yes—
117C22×Dic22C2311yescharacteristic
118C22×Dic22C2312yes—
119C2×C42×C11—24no—
120C2×C42×C11C2311yescharacteristic
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123C2×C42×C11C2311yescharacteristic
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2312yes—
126C2×C22⋊Dic11C2312yes—
127#66983—24no—
128#66982—44no—
129C4×C22⋊D11—44no—
130C2×(C2×D11)⋊C4C2312yes—
131C2×(C2×D11)⋊C4C2312yes—
132C2×(C2×D11)⋊C4C2312yes—
133C2×(C2×D11)⋊C4C2312yes—
134C2×(C2×D11)⋊C4C2312yes—
135C2×(C2×D11)⋊C4C2312yes—
136C2×(C2×D11)⋊C4C2312yes—
137C2×(C2×D11)⋊C4C2312yes—
138C2×(C2×D11)⋊C4C2312yes—
139C2×(C2×D11)⋊C4C2312yes—
140C2×(C2×D11)⋊C4C2312yes—
141C2×(C2×D11)⋊C4C2312yes—
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2311yescharacteristic
144C2×C4⋊Dic11C2311yescharacteristic
145C2×C4⋊Dic11C2312yes—
146C2×C4⋊Dic11C2312yes—
147C2×C4⋊Dic11C2311yescharacteristic
148C2×C4⋊Dic11C2311yescharacteristic
149C2×C4⋊Dic11C2312yes—
150C2×C4⋊Dic11C2311yescharacteristic
151#66977—24no—
152#66977—44no—
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—
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×C11C2411yescharacteristic
202C23×D11C2412yes—
203C22×C4×C11—22no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—41no—
212C22×C4×C11—41no—
213C22×C4×C11—41no—
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—41no—
221C22×C4×C11—41no—
222C22×C4×C11—41no—
223C22×C4×C11#4114yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2412yes—
226C22×C4×C11C2411yescharacteristic
227C22×C4×C11C2411yescharacteristic
228C22×C4×C11C2411yescharacteristic
229C22×C4×C11C2411yescharacteristic
230C22×C4×C11C2412yes—
231C22×C4×C11C2412yes—
232C22×C4×C11C2411yescharacteristic
233C22×C4×C11C2411yescharacteristic
234C2×C22⋊D11—24no—
235C2×C22⋊D11—24no—
236C2×C22⋊D11—24no—
237C22×Dic11C2412yes—
238C22×Dic11C2412yes—
239C22×Dic11C2412yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C2×D44—22no—
245C2×D44—41no—
246C2×D44—41no—
247C2×C4×D11—42no—
248C2×C4×D11—42no—
249C2×C4×D11—42no—
250C2×Dic22—22no—
251C2×Dic22—42no—
252C2×Dic22—41no—
253C2×Dic22—41no—
254C2×Dic22—42no—
255C2×Dic22—42no—
256C42×C11—22no—
257C42×C11—22no—
258C42×C11—22no—
259C42×C11—22no—
260C22⋊Dic11—24no—
261C22⋊Dic11—24no—
262C22⋊Dic11—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—42no—
265(C2×D11)⋊C4—42no—
266(C2×D11)⋊C4—42no—
267(C2×D11)⋊C4—42no—
268(C2×D11)⋊C4—42no—
269(C2×D11)⋊C4—42no—
270(C2×D11)⋊C4—42no—
271(C2×D11)⋊C4—42no—
272(C2×D11)⋊C4—42no—
273(C2×D11)⋊C4—42no—
274(C2×D11)⋊C4—42no—
275C4⋊Dic11—22no—
276C4⋊Dic11—22no—
277C4⋊Dic11—42no—
278C4⋊Dic11—41no—
279C4⋊Dic11—41no—
280C4⋊Dic11—41no—
281C4⋊Dic11—41no—
282C4⋊Dic11—42no—
283C4⋊Dic11—42no—
284Dic11⋊C4—24no—
285Dic11⋊C4—42no—
286Dic11⋊C4—42no—
287Dic11⋊C4—42no—
288Dic11⋊C4—42no—
289Dic11⋊C4—42no—
290Dic11⋊C4—42no—
291Dic11⋊C4—42no—
292Dic11⋊C4—42no—
293Dic11⋊C4—42no—
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#2639—111no—
309#2510—112no—
310#2488—112no—
311#2450—112no—
312#2419—112no—
313#2329—111no—
314#2325—111no—
315C2×#383D1111yescharacteristic, complemented
316C23×C11—21no—
317C23×C11—21no—
318C23×C11—21no—
319C23×C11—21no—
320C23×C11C2×#4112yes—
321C23×C11H(5,𝔽2)12yes—
322C23×C112−1+412yes—
323C23×C11C2511yescharacteristic
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
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—21no—
356C2×C4×C11—21no—
357C2×C4×C11—22no—
358C2×C4×C11—22no—
359C2×C4×C11—44no—
360C2×C4×C11—44no—
361C2×C4×C11—44no—
362C2×C4×C11—82no—
363C2×C4×C11—82no—
364C2×C4×C11—82no—
365C2×C4×C11—82no—
366C2×C4×C11C2×#4112yes—
367C2×C4×C11C2×#4112yes—
368C22⋊D11—48no—
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×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390D44—82no—
391C4×D11—84no—
392Dic22—82no—
393Dic22—84no—
394C2×#123—112no—
395C2×C22⋊Q8—111no—
396C2×C22⋊Q8—112no—
397C2×#121—111no—
398C2×C4×D4—112no—
399C22×C42C2×D1111yescharacteristic
400#401—112no—
401#400—112no—
402#400—112no—
403#400—112no—
404#400—112no—
405#400—112no—
406#400—112no—
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#397—112no—
417#396—112no—
418#395—112no—
419#395—112no—
420#394—112no—
421#393—112no—
422#393—112no—
423#393—112no—
424#391—111no—
425#391—111no—
426#391—112no—
427#391—112no—
428#391—112no—
429#390—111no—
430#390—111no—
431#389—111no—
432#389—111no—
433#389—111no—
434#389—111no—
435#389—112no—
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#386—112no—
456#386—112no—
457#385—112no—
458#385—112no—
459#385—112no—
460#385—112no—
461#385—112no—
462#383—112no—
463#383C2×D1112yes—
464#383C2×D1112yes—
465#383C2×D1112yes—
466#383C2×D1112yes—
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×#95C2×D1111yescharacteristic
476C2×#95C2×D1111yescharacteristic
477C2×#95C2×D1111yescharacteristic
478C2×#95C2×D1111yescharacteristic
479C2×#95C2×D1111yescharacteristic
480C2×#95C2×D1111yescharacteristic
481C22×C11—22no—
482C22×C11—22no—
483C22×C11—22no—
484C22×C11—22no—
485C22×C11—22no—
486C22×C11—22no—
487C22×C11#54214yes—
488C22×C11C22×#4111yescharacteristic
489C22×C11C2×H(5,𝔽2)11yescharacteristic
490C22×C11C2×2−1+411yescharacteristic
491C22×C11#58511yescharacteristic
492C22×C11#58511yescharacteristic
493C22×C11#58511yescharacteristic
494C22×C11#58511yescharacteristic
495C2×D11—42no—
496C2×D11—42no—
497C2×D11—42no—
498C2×D11—42no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—42no—
502C4×C11—22no—
503C4×C11—22no—
504C4×C11—41no—
505C4×C11—41no—
506C4×C11—41no—
507C4×C11—41no—
508C4×C11—42no—
509C4×C11—42no—
510C4×C11—42no—
511C4×C11—42no—
512Dic11—42no—
513Dic11—42no—
514Dic11—42no—
515Dic11—42no—
516Dic11—42no—
517Dic11—42no—
518Dic11—42no—
519C22×Q8—111no—
520C22×Q8—112no—
521C22×D4—112no—
522C22×D4—111no—
523C23×C4—112no—
524C23×C4C22×D1111yescharacteristic
525C23×C4C22×D1111yescharacteristic
526C23×C4C22×D1111yescharacteristic
527C23×C4C22×D1111yescharacteristic
528C23×C4C22×D1111yescharacteristic
529C23×C4C22×D1111yescharacteristic
530C23×C4C22×D1111yescharacteristic
531#123—444no—
532C22⋊Q8—224no—
533C22⋊Q8—444no—
534#121—224no—
535C4×D4—444no—
536C2×C4⋊C4—111no—
537C2×C4⋊C4—112no—
538C2×C4⋊C4—111no—
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—111no—
546C2×C4⋊C4—112no—
547C2×C4⋊C4—112no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4—112no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—112no—
553C2×C4⋊C4—112no—
554C2×C4⋊C4—112no—
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⋊C4—112no—
565C2×C22⋊C4—112no—
566C2×C22⋊C4—112no—
567C2×C22⋊C4—112no—
568C2×C22⋊C4—112no—
569C2×C22⋊C4—112no—
570C2×C42—24no—
571C2×C42—112no—
572C2×C42—112no—
573C2×C42—112no—
574C2×C42C22×D1111yescharacteristic
575C2×C42C22×D1111yescharacteristic
576C2×C42C22×D1111yescharacteristic
577C2×C42C22×D1111yescharacteristic
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#95C22×D1112yes—
601#95C22×D1112yes—
602#95C22×D1112yes—
603#95C22×D1112yes—
604#95C22×D1112yes—
605#95C22×D1112yes—
606#95C22×D1112yes—
607#95C22×D1112yes—
608#95C22×D1112yes—
609#95C22×D1112yes—
610#95C22×D1112yes—
611#95C22×D1112yes—
612C2×C11—24no—
613C2×C11C2×#54211yescharacteristic
614C2×C11#349111yescharacteristic
615C2×C11#349311yescharacteristic
616C2×C11#356011yescharacteristic
617C2×C11#356011yescharacteristic
618C2×C11#356411yescharacteristic
619C2×C11#356411yescharacteristic
620D11—82no—
621C24—112no—
622C24C23×D1111yescharacteristic
623C2×Q8—222no—
624C2×Q8—442no—
625C2×Q8—441no—
626C2×Q8—441no—
627C2×Q8—442no—
628C2×Q8—442no—
629C2×D4—224no—
630C2×D4—224no—
631C2×D4—224no—
632C2×D4—222no—
633C2×D4—441no—
634C2×D4—441no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—41no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4—41no—
653C22×C4—41no—
654C22×C4—41no—
655C22×C4—112no—
656C22×C4—112no—
657C22×C4—112no—
658C22×C4—112no—
659C22×C4—112no—
660C22×C4—112no—
661C22×C4—112no—
662C22×C4—442no—
663C22×C4—442no—
664C22×C4—442no—
665C22×C4#433914yes—
666C22×C4C23×D1112yes—
667C22×C4C23×D1112yes—
668C22×C4C23×D1111yescharacteristic
669C22×C4C23×D1111yescharacteristic
670C22×C4C23×D1111yescharacteristic
671C22×C4C23×D1111yescharacteristic
672C22×C4C23×D1112yes—
673C22×C4C23×D1112yes—
674C22×C4C23×D1111yescharacteristic
675C22×C4C23×D1111yescharacteristic
676C4⋊C4—222no—
677C4⋊C4—224no—
678C4⋊C4—222no—
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—442no—
688C4⋊C4—442no—
689C4⋊C4—441no—
690C4⋊C4—441no—
691C4⋊C4—441no—
692C4⋊C4—441no—
693C4⋊C4—442no—
694C4⋊C4—442no—
695C22⋊C4—224no—
696C22⋊C4—224no—
697C22⋊C4—224no—
698C22⋊C4—224no—
699C22⋊C4—442no—
700C22⋊C4—442no—
701C22⋊C4—442no—
702C22⋊C4—442no—
703C22⋊C4—442no—
704C22⋊C4—442no—
705C22⋊C4—442no—
706C22⋊C4—442no—
707C22⋊C4—442no—
708C22⋊C4—442no—
709C22⋊C4—442no—
710C42—22no—
711C42—22no—
712C42—22no—
713C42—22no—
714C42—442no—
715C42—442no—
716C42—442no—
717C11#3698011yescharacteristic, complemented, Sylow
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—222no—
723C23—222no—
724C23—222no—
725C23—222no—
726C23—222no—
727C23—222no—
728C23—222no—
729C23C2×#433912yes—
730C23#6704212yes—
731C23#6704312yes—
732C23C24×D1111yescharacteristic
733Q8—882no—
734Q8—884no—
735D4—448no—
736D4—882no—
737C2×C4—21no—
738C2×C4—21no—
739C2×C4—21no—
740C2×C4—21no—
741C2×C4—21no—
742C2×C4—21no—
743C2×C4—21no—
744C2×C4—21no—
745C2×C4—22no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—44no—
766C2×C4—44no—
767C2×C4—44no—
768C2×C4—82no—
769C2×C4—82no—
770C2×C4—82no—
771C2×C4—82no—
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—222no—
787C2×C4—222no—
788C2×C4—222no—
789C2×C4—222no—
790C2×C4—222no—
791C2×C4—222no—
792C2×C4—222no—
793C2×C4—884no—
794C2×C4C2×#433912yes—
795C2×C4C2×#433912yes—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—442no—
803C22—442no—
804C22—442no—
805C22—442no—
806C22—442no—
807C22—442no—
808C22—442no—
809C22#1062306514yes—
810C22C22×#433911yescharacteristic
811C22C2×#6704211yescharacteristic
812C22C2×#6704311yescharacteristic
813C22#1062345311yescharacteristic
814C22#1062345311yescharacteristic
815C22#1062345311yescharacteristic
816C22#1062345311yescharacteristic
817C4—22no—
818C4—22no—
819C4—42no—
820C4—42no—
821C4—42no—
822C4—42no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—442no—
828C4—442no—
829C4—442no—
830C4—442no—
831C4—442no—
832C4—442no—
833C4—442no—
834C2—24no—
835C2—882no—
836C2C2×#1062306511yescharacteristic
837C2#1308231411yescharacteristic
838C2#1308233611yescharacteristic
839C2#1308316811yescharacteristic
840C2#1308316811yescharacteristic
841C2#1308324011yescharacteristic
842C2#1308324011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC2×C11×#383C2
prime radicalC2×#66983C22
hypercenterC2×#383D11
hypocenterC11#36980
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#383

Complements

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

NH ≅ G/Ntype
1. #13076955C2semidirect
3. #13076185C2semidirect
4. #13076116C2semidirect
5. #13076061C2semidirect
6. #13076038C2semidirect
7. #13075979C2semidirect
8. #13075965C2semidirect
9. #13075949C2semidirect
10. #13075668C2semidirect
11. #13074730C2semidirect
13. #13073176C2semidirect
14. #13072942C2semidirect
15. #13072440C2semidirect
16. #13072093C2semidirect
17. #13071349C2semidirect
19. C2×C11×#383C2semidirect
315. C2×#383D11semidirect
717. C11#36980semidirect

Maximal subgroups

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

subgroupindex
#130769552
#130769472
#130761852
#130761162
#130760612
#130760382
#130759792
#130759652
#130759492
#130756682
#130747302
#130745442
#130731762
#130729422
#130724402
#130720932
#130713492
#130713192
C2×C11×#3832
#3698011