Finite Group Databasebeta

← #14916969

Subgroups — #14916969

Order 2816.

1990 conjugacy classes of subgroups.

The subgroup lattice has 814 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623222C211yesmaximal, characteristic
2#13071780C212yesmaximal, complemented
3#13071771C212yesmaximal
4#13071726C211yesmaximal, characteristic, complemented
5#13071726C211yesmaximal, characteristic, complemented
6#13071722C211yesmaximal, characteristic, complemented
7#13071585C212yesmaximal, complemented
8#13071555C212yesmaximal, complemented
9#13071505C212yesmaximal, complemented
10#13071475C212yesmaximal, complemented
11#13071412C212yesmaximal, complemented
12#13071400C212yesmaximal, complemented
13#13071397C212yesmaximal, complemented
14#13071385C212yesmaximal, complemented
15#13071265C212yesmaximal, complemented
16#13071248C212yesmaximal, complemented
17#13071008C211yesmaximal, characteristic, complemented
18#13071008C211yesmaximal, characteristic, complemented
19C11×#2371C211yesmaximal, characteristic, complemented
20C2×C11×#125C2211yescharacteristic
21#10623222C4116yescomplemented
22C2×#66951C2212yes—
23C2×#66950C2211yescharacteristic
24C2×#66948C2211yescharacteristic
25C2×#66947C2212yes—
26C2×#66946C2211yescharacteristic
27C2×#66946C2212yes—
28C2×#66945C2212yes—
29C2×#66940C2211yescharacteristic
30C2×#66928C2211yescharacteristic
31C2×C42×D11C2211yescharacteristic
32C11×#387C2212yes—
33C11×#387C2212yes—
34C11×#387C2212yes—
35C11×#387C2212yes—
36C4×C11×C4⋊C4C2212yes—
37C4×C11×C4⋊C4C2212yes—
38C11×#376C2211yescharacteristic
39C11×#376C2211yescharacteristic
40#10622603C2212yes—
41#10622602C2212yes—
42#10622602C2212yes—
43#10622601C2212yes—
44#10622600C2212yes—
45#10622594C2212yes—
46#10622594C2212yes—
47#10622594C2212yes—
48#10622594C2212yes—
49#10622590C2212yes—
50C4⋊C4×Dic11C2212yes—
51C4⋊C4×Dic11C2212yes—
52#10622586C2212yes—
53#10622585C2212yes—
54#10622553C2212yes—
55#10622553C2212yes—
56#10622553C2212yes—
57#10622553C2212yes—
58#10622553C2212yes—
59#10622552C2212yes—
60C4×(C2×D11)⋊C4C2212yes—
61C4×(C2×D11)⋊C4C2212yes—
62C4×(C2×D11)⋊C4C2212yes—
63C4×(C2×D11)⋊C4C2212yes—
64C4×(C2×D11)⋊C4C2212yes—
65#10622546C2212yes—
66#10622545C2211yescharacteristic
67#10622545C2211yescharacteristic
68C4×Dic11⋊C4C2212yes—
69C4×Dic11⋊C4C2212yes—
70C4×Dic11⋊C4C2212yes—
71#10622541C2212yes—
72#10622283C2212yes—
73#10622282C2212yes—
74#10622282C2212yes—
75#10622282C2212yes—
76#10622282C2212yes—
77#10622282C2212yes—
78#10622281C2212yes—
79#10622281C2212yes—
80#10622280C2211yescharacteristic
81#10622280C2211yescharacteristic
82#10622280C2212yes—
83#10622279C2212yes—
84#10622279C2212yes—
85#10622278C2212yes—
86#10622278C2212yes—
87#10622278C2212yes—
88#10622278C2212yes—
89#10622277C2212yes—
90#10622277C2212yes—
91#10622277C2211yescharacteristic
92#10622277C2211yescharacteristic
93D11×#95C2212yes—
94#10622267C2212yes—
95#10622266C2212yes—
96#10622265C2212yes—
97#10622264C2211yescharacteristic
98#10622264C2212yes—
99#10622264C2211yescharacteristic
100#10622264C2212yes—
101#10622263C2211yescharacteristic
102#10622263C2211yescharacteristic
103#10622263C2212yes—
104#10622261C2212yes—
105#10622260C2212yes—
106#10622259C2212yes—
107#10622259C2212yes—
108C22×D44C2311yescharacteristic
109C22×D44C2312yes—
110C22×C4×D11C2312yes—
111C22×C4×D11C2312yes—
112C22×C4×D11C2311yescharacteristic
113C22×C4×D11C2311yescharacteristic
114C22×C4×D11C2311yescharacteristic
115C22×C4×D11C2312yes—
116C22×Dic22C2311yescharacteristic
117C11×#125C2×C418yescomplemented
118C2×C11×C4⋊C4C2312yes—
119C2×C11×C4⋊C4C2312yes—
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C4⋊C4C2312yes—
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C4⋊C4C2312yes—
124C2×C42×C11C2312yes—
125C2×C42×C11C2312yes—
126C2×C42×C11C2312yes—
127C2×C42×C11C2312yes—
128C2×C42×C11C2311yescharacteristic
129C2×(C2×D11)⋊C4C2312yes—
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×(C2×D11)⋊C4C2312yes—
143C2×(C2×D11)⋊C4C2312yes—
144C2×C4⋊Dic11C2312yes—
145C2×C4⋊Dic11C2312yes—
146C2×C4⋊Dic11C2312yes—
147C2×Dic11⋊C4C2312yes—
148C2×Dic11⋊C4C2312yes—
149C2×Dic11⋊C4C2312yes—
150C2×Dic11⋊C4C2312yes—
151C2×Dic11⋊C4C2312yes—
152C2×Dic11⋊C4C2312yes—
153C2×Dic11⋊C4C2312yes—
154C2×C4×Dic11C2312yes—
155C2×C4×Dic11C2312yes—
156C2×C4×Dic11C2312yes—
157C2×C4×Dic11C2312yes—
158C2×C4×Dic11C2312yes—
159C2×C4×Dic11C2312yes—
160C2×C4×Dic11C2311yescharacteristic
161C2×C4×Dic11C2311yescharacteristic
162C2×C4×Dic11C2311yescharacteristic
163C2×C4×Dic11C2312yes—
164#66951C2×C4116yescomplemented
165#66950C2×C418yescomplemented
166#66948C2×C418yes—
167#66947C2×C4116yescomplemented
168#66946C2×C418yes—
169#66946C2×C4116yescomplemented
170#66945C2×C4116yescomplemented
171#66940C2×C418yescomplemented
172#66928C2×C418yes—
173C42×D11C2×C418yescomplemented
174C11×#95C2312yes—
175C11×#95C2312yes—
176C11×#95C2312yes—
177C11×#95C2312yes—
178C11×#95C2311yescharacteristic
179C11×#95C2311yescharacteristic
180C11×#95C2311yescharacteristic
181C11×#95C2311yescharacteristic
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⋊#95C2311yescharacteristic
197C11⋊#95C2311yescharacteristic
198C11⋊#95C2312yes—
199C11⋊#95C2312yes—
200C11⋊#95C2312yes—
201C11⋊#95C2312yes—
202C11⋊#95C2311yescharacteristic
203C11⋊#95C2311yescharacteristic
204C11⋊#95C2312yes—
205C11⋊#95C2312yes—
206#34395—111nomaximal, Sylow
207C23×D11C2411yescharacteristic
208C23×D11C2412yes—
209C22×C4×C11C2412yes—
210C22×C4×C11C2412yes—
211C22×C4×C11C2412yes—
212C22×C4×C11C2412yes—
213C22×C4×C11C2411yescharacteristic
214C22×C4×C11C2411yescharacteristic
215C22×C4×C11C2411yescharacteristic
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×Dic11C2412yes—
219C22×Dic11C2412yes—
220C22×Dic11C2412yes—
221C22×Dic11C2412yes—
222C22×Dic11C2411yescharacteristic
223C22×Dic11C2412yes—
224C22×Dic11C2411yescharacteristic
225C22×Dic11C2411yescharacteristic
226C2×D44—42no—
227C2×D44—42no—
228C2×D44—41no—
229C2×D44—41no—
230C2×D44C22×C414yes—
231C2×D44C22×C418yes—
232C2×C4×D11—42no—
233C2×C4×D11—42no—
234C2×C4×D11—42no—
235C2×C4×D11—42no—
236C2×C4×D11—41no—
237C2×C4×D11—41no—
238C2×C4×D11—42no—
239C2×C4×D11—42no—
240C2×C4×D11—42no—
241C2×C4×D11—42no—
242C2×C4×D11—42no—
243C2×C4×D11—42no—
244C2×C4×D11C22×C414yes—
245C2×C4×D11C22×C414yes—
246C2×C4×D11C22×C414yes—
247C2×C4×D11C22×C418yes—
248C2×Dic22—41no—
249C2×Dic22—41no—
250C2×Dic22C22×C414yes—
251C11×C4⋊C4—42no—
252C11×C4⋊C4—42no—
253C11×C4⋊C4C22×C414yes—
254C11×C4⋊C4C22×C418yes—
255C11×C4⋊C4C22×C414yes—
256C11×C4⋊C4C22×C418yes—
257C42×C11—42no—
258C42×C11—42no—
259C42×C11—42no—
260C42×C11—42no—
261C42×C11C22×C414yes—
262(C2×D11)⋊C4—42no—
263(C2×D11)⋊C4—42no—
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)⋊C4C22×C418yes—
273(C2×D11)⋊C4C22×C418yes—
274(C2×D11)⋊C4C22×C418yes—
275(C2×D11)⋊C4C22×C418yes—
276(C2×D11)⋊C4C22×C418yes—
277C4⋊Dic11—42no—
278C4⋊Dic11—42no—
279C4⋊Dic11C22×C418yes—
280Dic11⋊C4—42no—
281Dic11⋊C4—42no—
282Dic11⋊C4—42no—
283Dic11⋊C4—42no—
284Dic11⋊C4—42no—
285Dic11⋊C4—42no—
286Dic11⋊C4C22×C418yes—
287C4×Dic11—42no—
288C4×Dic11—42no—
289C4×Dic11—42no—
290C4×Dic11—42no—
291C4×Dic11—42no—
292C4×Dic11—42no—
293C4×Dic11C22×C414yes—
294C4×Dic11C22×C414yes—
295C4×Dic11C22×C414yes—
296C4×Dic11C22×C418yes—
297C2×#529—111no—
298#2378—112no—
299#2377—112no—
300#2372—111no—
301#2372—111no—
302#2371—111no—
303#2371D1111yescharacteristic, complemented
304#2357—112no—
305#2353—112no—
306#2347—112no—
307#2343—112no—
308#2335—112no—
309#2335—112no—
310#2334—112no—
311#2334—112no—
312#2320—112no—
313#2318—112no—
314#2283—111no—
315#2283—111no—
316C23×C11C2511yescharacteristic
317C22×D11—22no—
318C22×D11—21no—
319C22×D11—21no—
320C22×D11—22no—
321C22×D11—22no—
322C22×D11—22no—
323C22×D11—22no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—22no—
327C22×D11C23×C414yes—
328C22×D11C23×C412yes—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—22no—
340C2×C4×C11—22no—
341C2×C4×C11—22no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11C23×C414yes—
350C2×C4×C11C23×C412yes—
351C2×C4×C11C23×C412yes—
352C2×C4×C11C23×C412yes—
353C2×C4×C11C23×C414yes—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—21no—
358C2×Dic11—21no—
359C2×Dic11—22no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—22no—
369C2×Dic11—22no—
370C2×Dic11—22no—
371C2×Dic11—22no—
372C2×Dic11C23×C412yes—
373C2×Dic11C23×C412yes—
374C2×Dic11C23×C412yes—
375C2×Dic11C23×C414yes—
376D44—44no—
377D44—48no—
378C4×D11—44no—
379C4×D11—48no—
380C4×D11—44no—
381C4×D11—44no—
382C4×D11—84no—
383C4×D11—84no—
384Dic22—44no—
385#529—1116no—
386C2×#126—112no—
387C2×#125C2×D1111yescharacteristic
388C2×#124—111no—
389C2×#123—112no—
390C2×C22⋊Q8—111no—
391C2×#121—111no—
392C2×C4×Q8—111no—
393C2×C4×D4—111no—
394C2×C4×D4—112no—
395C2×#117—112no—
396C22×C42—111no—
397#391—112no—
398#391—112no—
399#390—112no—
400#390—112no—
401#389—112no—
402#389—112no—
403#389—112no—
404#389—112no—
405#388—112no—
406#388—112no—
407#388—112no—
408#388—112no—
409#388—112no—
410#388—112no—
411#388—112no—
412#388—112no—
413#388—112no—
414#388—112no—
415#388—112no—
416#388—112no—
417#387—112no—
418#387—112no—
419#387—112no—
420#387—112no—
421#387—112no—
422#387—112no—
423#387—112no—
424#387—112no—
425#387C2×D1112yes—
426#387C2×D1112yes—
427#387C2×D1112yes—
428#387C2×D1112yes—
429#386—112no—
430#386—112no—
431#386—112no—
432#386—112no—
433#385—112no—
434#385—112no—
435#385—112no—
436#385—112no—
437#383—112no—
438#383—112no—
439#383—111no—
440#383—111no—
441#382—112no—
442#382—112no—
443#382—111no—
444#382—111no—
445#381—112no—
446#381—111no—
447#381—111no—
448#381—112no—
449#380—112no—
450#380—111no—
451#380—111no—
452#380—112no—
453C4×C4⋊C4—112no—
454C4×C4⋊C4—112no—
455C4×C4⋊C4—112no—
456C4×C4⋊C4—112no—
457C4×C4⋊C4—112no—
458C4×C4⋊C4C2×D1112yes—
459C4×C4⋊C4C2×D1112yes—
460C4×C22⋊C4—112no—
461C4×C22⋊C4—112no—
462C4×C22⋊C4—112no—
463C4×C22⋊C4—112no—
464C4×C22⋊C4—112no—
465C4×C22⋊C4—112no—
466C4×C22⋊C4—112no—
467#376—111no—
468#376—111no—
469#376—112no—
470#376C2×D1111yescharacteristic
471#376C2×D1111yescharacteristic
472C2×#95—112no—
473C22×C11C24×C411yescharacteristic
474C22×C11#58512yes—
475C22×C11#58512yes—
476C22×C11#58511yescharacteristic
477C22×C11#58511yescharacteristic
478C2×D11—22no—
479C2×D11—24no—
480C2×D11—22no—
481C2×D11—22no—
482C2×D11—24no—
483C2×D11—24no—
484C2×D11—42no—
485C2×D11—42no—
486C2×D11—42no—
487C2×D11—42no—
488C2×D11—42no—
489C2×D11—42no—
490C4×C11—22no—
491C4×C11—22no—
492C4×C11—22no—
493C4×C11—24no—
494C4×C11—24no—
495C4×C11—42no—
496C4×C11—42no—
497C4×C11—42no—
498C4×C11—42no—
499Dic11—24no—
500Dic11—22no—
501Dic11—22no—
502Dic11—22no—
503Dic11—42no—
504Dic11—42no—
505Dic11—42no—
506Dic11—42no—
507C22×Q8—111no—
508C22×D4—112no—
509C22×D4—111no—
510C23×C4—112no—
511C23×C4—111no—
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—112no—
515C23×C4—112no—
516#126—1116no—
517#125C4×D1118yescomplemented
518#124—118no—
519#123—1116no—
520C22⋊Q8—118no—
521#121—118no—
522C4×Q8—118no—
523C4×D4—118no—
524C4×D4—1116no—
525#117—1116no—
526C2×C4⋊C4—112no—
527C2×C4⋊C4—112no—
528C2×C4⋊C4—112no—
529C2×C4⋊C4—112no—
530C2×C4⋊C4—112no—
531C2×C4⋊C4—112no—
532C2×C4⋊C4—112no—
533C2×C4⋊C4—112no—
534C2×C4⋊C4—112no—
535C2×C4⋊C4—112no—
536C2×C4⋊C4C22×D1112yes—
537C2×C4⋊C4C22×D1112yes—
538C2×C4⋊C4C22×D1112yes—
539C2×C4⋊C4C22×D1111yescharacteristic
540C2×C4⋊C4C22×D1112yes—
541C2×C4⋊C4C22×D1111yescharacteristic
542C2×C22⋊C4—112no—
543C2×C22⋊C4—112no—
544C2×C22⋊C4—112no—
545C2×C22⋊C4—112no—
546C2×C22⋊C4—112no—
547C2×C22⋊C4—112no—
548C2×C22⋊C4—112no—
549C2×C22⋊C4—112no—
550C2×C22⋊C4—112no—
551C2×C22⋊C4—112no—
552C2×C22⋊C4—112no—
553C2×C22⋊C4—112no—
554C2×C22⋊C4—112no—
555C2×C22⋊C4—112no—
556C2×C22⋊C4—112no—
557C2×C42—111no—
558C2×C42—112no—
559C2×C42—111no—
560C2×C42—111no—
561C2×C42—118no—
562C2×C42—112no—
563C2×C42—112no—
564C2×C42—112no—
565C2×C42—112no—
566C2×C42—112no—
567C2×C42—112no—
568C2×C42C22×D1112yes—
569C2×C42C22×D1112yes—
570C2×C42C22×D1112yes—
571C2×C42C22×D1112yes—
572C2×C42C22×D1111yescharacteristic
573#95—112no—
574#95—112no—
575#95—112no—
576#95—111no—
577#95—111no—
578#95—111no—
579#95—111no—
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#95C22×D1112yes—
596#95C22×D1112yes—
597#95C22×D1111yescharacteristic
598#95C22×D1111yescharacteristic
599#95C22×D1111yescharacteristic
600#95C22×D1111yescharacteristic
601#95C22×D1112yes—
602#95C22×D1112yes—
603#95C22×D1112yes—
604#95C22×D1112yes—
605C2×C11#342811yescharacteristic
606C2×C11#342811yescharacteristic
607C2×C11#342811yescharacteristic
608C2×C11#356612yes—
609C2×C11#356612yes—
610D11—42no—
611D11—44no—
612C24—112no—
613C24—111no—
614C2×Q8—114no—
615C2×Q8—441no—
616C2×Q8—441no—
617C2×D4—118no—
618C2×D4—114no—
619C2×D4—442no—
620C2×D4—442no—
621C2×D4—441no—
622C2×D4—441no—
623C22×C4—111no—
624C22×C4—112no—
625C22×C4—111no—
626C22×C4—111no—
627C22×C4—114no—
628C22×C4—114no—
629C22×C4—114no—
630C22×C4—118no—
631C22×C4—112no—
632C22×C4—112no—
633C22×C4—112no—
634C22×C4—112no—
635C22×C4—442no—
636C22×C4—442no—
637C22×C4—442no—
638C22×C4—442no—
639C22×C4—441no—
640C22×C4—441no—
641C22×C4—442no—
642C22×C4—442no—
643C22×C4—442no—
644C22×C4—442no—
645C22×C4—442no—
646C22×C4—442no—
647C22×C4C23×D1112yes—
648C22×C4C23×D1112yes—
649C22×C4C23×D1112yes—
650C22×C4C23×D1112yes—
651C22×C4C23×D1111yescharacteristic
652C22×C4C23×D1111yescharacteristic
653C22×C4C23×D1111yescharacteristic
654C22×C4C23×D1112yes—
655C22×C4C23×D1112yes—
656C4⋊C4—42no—
657C4⋊C4—42no—
658C4⋊C4—118no—
659C4⋊C4—118no—
660C4⋊C4—442no—
661C4⋊C4—442no—
662C4⋊C4—442no—
663C4⋊C4—442no—
664C4⋊C4—442no—
665C4⋊C4—442no—
666C4⋊C4—442no—
667C4⋊C4—442no—
668C4⋊C4C2×C4×D1118yes—
669C4⋊C4C2×C4×D1114yes—
670C4⋊C4C2×C4×D1118yes—
671C4⋊C4C2×C4×D1114yes—
672C22⋊C4—118no—
673C22⋊C4—118no—
674C22⋊C4—118no—
675C22⋊C4—118no—
676C22⋊C4—118no—
677C22⋊C4—442no—
678C22⋊C4—442no—
679C22⋊C4—442no—
680C22⋊C4—442no—
681C22⋊C4—442no—
682C22⋊C4—442no—
683C22⋊C4—442no—
684C22⋊C4—442no—
685C22⋊C4—442no—
686C22⋊C4—442no—
687C42—42no—
688C42—42no—
689C42—42no—
690C42—42no—
691C42—114no—
692C42—114no—
693C42—114no—
694C42—118no—
695C42—442no—
696C42—442no—
697C42—442no—
698C42—442no—
699C42—442no—
700C42—442no—
701C42C2×C4×D1114yes—
702C11#3439511yescharacteristic, complemented, Sylow
703C23—114no—
704C23—112no—
705C23—222no—
706C23—222no—
707C23—222no—
708C23—222no—
709C23—222no—
710C23—222no—
711C23—221no—
712C23—221no—
713C23—222no—
714C23—222no—
715C23C24×D1111yescharacteristic
716Q8—444no—
717D4—448no—
718D4—444no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—22no—
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—112no—
740C2×C4—112no—
741C2×C4—112no—
742C2×C4—114no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—221no—
748C2×C4—221no—
749C2×C4—222no—
750C2×C4—222no—
751C2×C4—222no—
752C2×C4—222no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—444no—
762C2×C4—448no—
763C2×C4—444no—
764C2×C4—444no—
765C2×C4—884no—
766C2×C4—884no—
767C2×C4C22×C4×D1112yes—
768C2×C4C22×C4×D1112yes—
769C2×C4C22×C4×D1112yes—
770C2×C4C22×C4×D1114yes—
771C2×C4C22×C4×D1114yes—
772C22—222no—
773C22—224no—
774C22—222no—
775C22—224no—
776C22—222no—
777C22—224no—
778C22—442no—
779C22—442no—
780C22—442no—
781C22—442no—
782C22—442no—
783C22—442no—
784C22C23×C4×D1111yescharacteristic
785C22#1062345312yes—
786C22#1062345312yes—
787C22#1062345711yescharacteristic
788C22#1062345711yescharacteristic
789C4—22no—
790C4—22no—
791C4—24no—
792C4—24no—
793C4—22no—
794C4—42no—
795C4—42no—
796C4—42no—
797C4—42no—
798C4—222no—
799C4—222no—
800C4—222no—
801C4—224no—
802C4—442no—
803C4—442no—
804C4—442no—
805C4—442no—
806C2—442no—
807C2—444no—
808C2#1308181511yescharacteristic
809C2#1308181511yescharacteristic
810C2#1308181811yescharacteristic
811C2#1308328612yes—
812C2#1308329412yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2371C2
socle, cosocleC23×C11C25
prime radicalC2×#66948C22
hypercenter#2371D11
hypocenterC11#34395
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2371

Complements

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

NH ≅ G/Ntype
2. #13071780C2semidirect
4. #13071726C2semidirect
5. #13071726C2semidirect
6. #13071722C2semidirect
7. #13071585C2semidirect
8. #13071555C2semidirect
9. #13071505C2semidirect
10. #13071475C2semidirect
11. #13071412C2semidirect
12. #13071400C2semidirect
13. #13071397C2semidirect
14. #13071385C2semidirect
15. #13071265C2semidirect
16. #13071248C2semidirect
17. #13071008C2semidirect
18. #13071008C2semidirect
19. C11×#2371C2semidirect
21. #10623222C4semidirect
117. C11×#125C2×C4semidirect
164. #66951C2×C4semidirect
165. #66950C2×C4semidirect
167. #66947C2×C4semidirect
169. #66946C2×C4semidirect
170. #66945C2×C4semidirect
171. #66940C2×C4semidirect
173. C42×D11C2×C4semidirect
303. #2371D11semidirect
517. #125C4×D11semidirect
702. C11#34395semidirect

Maximal subgroups

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

subgroupindex
C2×#106232222
#130717802
#130717712
#130717262
#130717222
#130715852
#130715552
#130715052
#130714752
#130714122
#130714002
#130713972
#130713852
#130712652
#130712482
#130710082
C11×#23712
#3439511