Finite Group Databasebeta

← #14916853

Subgroups — #14916853

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×#10623131C211yesmaximal, characteristic
2#13071784C211yesmaximal, characteristic, complemented
3#13071779C211yesmaximal, characteristic, complemented
4#13071773C211yesmaximal, characteristic
5#13071751C212yesmaximal, complemented
6#13071749C212yesmaximal, complemented
7#13071578C212yesmaximal, complemented
8#13071554C212yesmaximal, complemented
9#13071498C212yesmaximal, complemented
10#13071474C212yesmaximal, complemented
11#13071425C212yesmaximal, complemented
12#13071419C212yesmaximal, complemented
13#13071392C212yesmaximal, complemented
14#13071388C212yesmaximal, complemented
15#13071253C212yesmaximal, complemented
16#13071242C212yesmaximal, complemented
17#13071011C211yesmaximal, characteristic, complemented
18#13071007C211yesmaximal, characteristic, complemented
19C11×#2377C211yesmaximal, characteristic
20C2×C11×#121C2211yescharacteristic
21C2×#66989C2211yescharacteristic
22C2×#66988C2212yes—
23C2×D4×Dic11C2211yescharacteristic
24C2×D4×Dic11C2212yes—
25C2×#66977C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27#10623131C4116yescomplemented
28C2×#66943C2211yescharacteristic
29C2×#66940C2211yescharacteristic
30C2×#66932C2212yes—
31C2×#66930C2212yes—
32C11×#390C2212yes—
33C11×#388C2212yes—
34C11×#387C2212yes—
35C11×#386C2212yes—
36C11×#386C2212yes—
37C11×#385C2212yes—
38C11×#381C2211yescharacteristic
39C11×#380C2211yescharacteristic
40#10622834C2212yes—
41#10622833C2212yes—
42#10622833C2212yes—
43#10622825C2211yescharacteristic
44#10622824C2211yescharacteristic
45#10622823C2212yes—
46C4×C22⋊Dic11C2212yes—
47C4×C22⋊Dic11C2212yes—
48C2×C11⋊#95C2212yes—
49#10622594C2212yes—
50#10622591C2212yes—
51#10622591C2212yes—
52#10622591C2212yes—
53#10622590C2212yes—
54C4⋊C4×Dic11C2212yes—
55C4⋊C4×Dic11C2212yes—
56#10622586C2212yes—
57#10622585C2212yes—
58#10622564C2212yes—
59#10622563C2212yes—
60#10622559C2212yes—
61#10622558C2212yes—
62#10622558C2212yes—
63#10622558C2212yes—
64#10622558C2212yes—
65#10622558C2212yes—
66#10622557C2212yes—
67#10622557C2212yes—
68#10622557C2212yes—
69#10622557C2212yes—
70#10622557C2212yes—
71#10622556C2212yes—
72#10622556C2211yescharacteristic
73#10622556C2211yescharacteristic
74#10622555C2212yes—
75#10622555C2212yes—
76C22⋊C4×Dic11C2212yes—
77C22⋊C4×Dic11C2212yes—
78C22⋊C4×Dic11C2211yescharacteristic
79C22⋊C4×Dic11C2212yes—
80C22⋊C4×Dic11C2211yescharacteristic
81C22⋊C4×Dic11C2212yes—
82#10622545C2212yes—
83C4×Dic11⋊C4C2212yes—
84C4×Dic11⋊C4C2212yes—
85#10622541C2212yes—
86#10622268C2212yes—
87#10622268C2212yes—
88#10622268C2212yes—
89#10622267C2212yes—
90#10622267C2212yes—
91#10622266C2212yes—
92#10622266C2212yes—
93#10622264C2212yes—
94#10622264C2212yes—
95#10622264C2212yes—
96#10622263C2211yescharacteristic
97#10622263C2211yescharacteristic
98#10622263C2212yes—
99#10622262C2212yes—
100#10622262C2212yes—
101#10622262C2212yes—
102#10622261C2211yescharacteristic
103#10622261C2211yescharacteristic
104#10622261C2212yes—
105#10622260C2212yes—
106#10622259C2212yes—
107#10622259C2212yes—
108C22×D4×C11C2312yes—
109C22×D4×C11C2311yescharacteristic
110C23×C4×C11C2312yes—
111C23×C4×C11C2311yescharacteristic
112C23×Dic11C2312yes—
113C23×Dic11C2312yes—
114C23×Dic11C2311yescharacteristic
115C23×Dic11C2311yescharacteristic
116C22×Dic22C2311yescharacteristic
117C11×#121C2×C418yes—
118C2×C11×C4⋊C4C2312yes—
119C2×C11×C4⋊C4C2312yes—
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C22⋊C4C2312yes—
122C2×C11×C22⋊C4C2312yes—
123C2×C11×C22⋊C4C2311yescharacteristic
124C2×C11×C22⋊C4C2311yescharacteristic
125C2×C11×C22⋊C4C2312yes—
126C2×C11×C22⋊C4C2312yes—
127C2×C11×C22⋊C4C2312yes—
128C2×C42×C11C2312yes—
129C2×C22⋊Dic11C2312yes—
130C2×C22⋊Dic11C2311yescharacteristic
131C2×C22⋊Dic11C2311yescharacteristic
132C2×C22⋊Dic11C2312yes—
133C2×C22⋊Dic11C2312yes—
134C2×C22⋊Dic11C2312yes—
135C2×C22⋊Dic11C2312yes—
136C2×C22⋊Dic11C2312yes—
137C2×C22⋊Dic11C2312yes—
138C2×C22⋊Dic11C2312yes—
139#66989C2×C418yes—
140#66988C2×C4116yescomplemented
141D4×Dic11C2×C418yes—
142D4×Dic11C2×C4116yescomplemented
143C2×C4⋊Dic11C2312yes—
144C2×C4⋊Dic11C2312yes—
145C2×C4⋊Dic11C2312yes—
146C2×C4⋊Dic11C2311yescharacteristic
147#66977C2×C418yescomplemented
148C2×Dic11⋊C4C2312yes—
149C2×Dic11⋊C4C2312yes—
150C2×Dic11⋊C4C2312yes—
151C2×Dic11⋊C4C2312yes—
152C2×Dic11⋊C4C2312yes—
153C2×Dic11⋊C4C2312yes—
154C2×Dic11⋊C4C2312yes—
155C2×Dic11⋊C4C2312yes—
156C2×Dic11⋊C4C2312yes—
157C2×C4×Dic11C2×C418yescomplemented
158C2×C4×Dic11C2312yes—
159C2×C4×Dic11C2312yes—
160C2×C4×Dic11C2312yes—
161C2×C4×Dic11C2312yes—
162C2×C4×Dic11C2312yes—
163C2×C4×Dic11C2312yes—
164C2×C4×Dic11C2312yes—
165C2×C4×Dic11C2312yes—
166C2×C4×Dic11C2312yes—
167C2×C4×Dic11C2311yescharacteristic
168C2×C4×Dic11C2312yes—
169C2×C4×Dic11C2311yescharacteristic
170C2×C4×Dic11C2311yescharacteristic
171C2×C4×Dic11C2311yescharacteristic
172#66943C2×C418yescomplemented
173#66940C2×C418yescomplemented
174#66932C2×C4116yescomplemented
175#66930C2×C4116yescomplemented
176C11×#95C2312yes—
177C11×#95C2312yes—
178C11×#95C2311yescharacteristic
179C11×#95C2311yescharacteristic
180C11×#95C2312yes—
181C11×#95C2312yes—
182C11⋊#95C2312yes—
183C11⋊#95C2312yes—
184C11⋊#95C2312yes—
185C11⋊#95C2312yes—
186C11⋊#95C2312yes—
187C11⋊#95C2312yes—
188C11⋊#95C2312yes—
189C11⋊#95C2312yes—
190C11⋊#95C2311yescharacteristic
191C11⋊#95C2311yescharacteristic
192C11⋊#95C2312yes—
193C11⋊#95C2312yes—
194C11⋊#95C2312yes—
195C11⋊#95C2312yes—
196C11⋊#95C2312yes—
197C11⋊#95C2312yes—
198C11⋊#95C2312yes—
199C11⋊#95C2312yes—
200C11⋊#95C2312yes—
201C11⋊#95C2312yes—
202C11⋊#95C2312yes—
203C11⋊#95C2312yes—
204C11⋊#95C2312yes—
205C11⋊#95C2312yes—
206#34387—111nomaximal, Sylow
207C24×C11C2411yescharacteristic
208C24×C11C2412yes—
209C2×D4×C11—42no—
210C2×D4×C11—42no—
211C2×D4×C11—42no—
212C2×D4×C11C22×C414yes—
213C2×D4×C11C22×C418yes—
214C22×C4×C11—42no—
215C22×C4×C11—42no—
216C22×C4×C11—42no—
217C22×C4×C11—42no—
218C22×C4×C11C22×C414yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2412yes—
223C22×C4×C11C2411yescharacteristic
224C22×C4×C11C2412yes—
225C22×C4×C11C2411yescharacteristic
226C22×Dic11—41no—
227C22×Dic11—42no—
228C22×Dic11—41no—
229C22×Dic11—42no—
230C22×Dic11—42no—
231C22×Dic11—42no—
232C22×Dic11—42no—
233C22×Dic11—42no—
234C22×Dic11C22×C418yes—
235C22×Dic11C22×C414yes—
236C22×Dic11C22×C414yes—
237C22×Dic11C2412yes—
238C22×Dic11C2412yes—
239C22×Dic11C2412yes—
240C22×Dic11C2412yes—
241C22×Dic11C2411yescharacteristic
242C22×Dic11C2411yescharacteristic
243C22×Dic11C2411yescharacteristic
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2411yescharacteristic
247C2×Dic22—42no—
248C2×Dic22C22×C414yes—
249C11×C4⋊C4—42no—
250C11×C4⋊C4—42no—
251C11×C4⋊C4C22×C414yes—
252C11×C22⋊C4—42no—
253C11×C22⋊C4—42no—
254C11×C22⋊C4—41no—
255C11×C22⋊C4—42no—
256C11×C22⋊C4—41no—
257C11×C22⋊C4—42no—
258C11×C22⋊C4C22×C418yes—
259C42×C11—42no—
260C22⋊Dic11—41no—
261C22⋊Dic11—41no—
262C22⋊Dic11—42no—
263C22⋊Dic11—42no—
264C22⋊Dic11—42no—
265C22⋊Dic11—42no—
266C22⋊Dic11C22×C418yes—
267C22⋊Dic11C22×C418yes—
268C22⋊Dic11C22×C418yes—
269C22⋊Dic11C22×C418yes—
270C4⋊Dic11—42no—
271C4⋊Dic11—42no—
272C4⋊Dic11C22×C418yes—
273C4⋊Dic11C22×C414yes—
274Dic11⋊C4—42no—
275Dic11⋊C4—42no—
276Dic11⋊C4—42no—
277Dic11⋊C4—42no—
278Dic11⋊C4—42no—
279Dic11⋊C4—42no—
280Dic11⋊C4C22×C418yes—
281Dic11⋊C4C22×C418yes—
282Dic11⋊C4C22×C418yes—
283C4×Dic11—42no—
284C4×Dic11—42no—
285C4×Dic11—42no—
286C4×Dic11—42no—
287C4×Dic11—42no—
288C4×Dic11—42no—
289C4×Dic11—42no—
290C4×Dic11—42no—
291C4×Dic11—42no—
292C4×Dic11C22×C414yes—
293C4×Dic11C22×C418yes—
294C4×Dic11C22×C414yes—
295C4×Dic11C22×C414yes—
296C4×Dic11C22×C414yes—
297C2×#529—111no—
298#2378—111no—
299#2378—111no—
300#2377—111no—
301#2377D1111yescharacteristic
302#2374—112no—
303#2374—112no—
304#2356—112no—
305#2353—112no—
306#2346—112no—
307#2343—112no—
308#2337—112no—
309#2336—112no—
310#2334—112no—
311#2334—112no—
312#2319—112no—
313#2318—112no—
314#2283—111no—
315#2283—111no—
316C23×C11—21no—
317C23×C11—22no—
318C23×C11—22no—
319C23×C11—22no—
320C23×C11—22no—
321C23×C11—21no—
322C23×C11—22no—
323C23×C11—22no—
324C23×C11—22no—
325C23×C11—22no—
326C23×C11C23×C414yes—
327C23×C11C23×C412yes—
328C23×C11C2511yescharacteristic
329D4×C11—44no—
330D4×C11—48no—
331C2×C4×C11—22no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
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—44no—
348C2×C4×C11—84no—
349C2×C4×C11C23×C412yes—
350C2×C4×C11C23×C412yes—
351C2×C4×C11C23×C414yes—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—21no—
359C2×Dic11—21no—
360C2×Dic11—21no—
361C2×Dic11—21no—
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×Dic11—22no—
373C2×Dic11—22no—
374C2×Dic11—48no—
375C2×Dic11—44no—
376C2×Dic11—44no—
377C2×Dic11—84no—
378C2×Dic11C23×C412yes—
379C2×Dic11C23×C412yes—
380C2×Dic11C23×C412yes—
381C2×Dic11C23×C412yes—
382C2×Dic11C23×C414yes—
383C2×Dic11C23×C414yes—
384Dic22—44no—
385#529—1116no—
386C2×#126—112no—
387C2×#125—111no—
388C2×#124—111no—
389C2×#123—112no—
390C2×C22⋊Q8—111no—
391C2×#121C2×D1111yescharacteristic
392C2×C4×Q8—111no—
393C2×C4×D4—112no—
394C2×C4×D4—111no—
395C2×#117—112no—
396C22×C42—111no—
397#391—112no—
398#391—112no—
399#390—112no—
400#390C2×D1112yes—
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#388C2×D1112yes—
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#387—112no—
426#387—112no—
427#387—112no—
428#387C2×D1112yes—
429#386—112no—
430#386—112no—
431#386C2×D1112yes—
432#386C2×D1112yes—
433#385—112no—
434#385—112no—
435#385—112no—
436#385C2×D1112yes—
437#383—112no—
438#383—112no—
439#383—112no—
440#382—112no—
441#382—112no—
442#382—111no—
443#382—111no—
444#381—111no—
445#381—111no—
446#381—111no—
447#381—112no—
448#381C2×D1111yescharacteristic
449#380—111no—
450#380—112no—
451#380—112no—
452#380C2×D1111yescharacteristic
453C4×C4⋊C4—112no—
454C4×C4⋊C4—112no—
455C4×C4⋊C4—112no—
456C4×C4⋊C4—112no—
457C4×C4⋊C4—112no—
458C4×C4⋊C4—112no—
459C4×C4⋊C4—112no—
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—111no—
467C4×C22⋊C4—111no—
468#376—112no—
469#376—111no—
470#376—111no—
471#376—112no—
472C2×#95—112no—
473C22×C11—22no—
474C22×C11—22no—
475C22×C11—24no—
476C22×C11—24no—
477C22×C11—22no—
478C22×C11—24no—
479C22×C11—42no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—42no—
484C22×C11—42no—
485C22×C11C24×C411yescharacteristic
486C22×C11#58511yescharacteristic
487C22×C11#58512yes—
488C22×C11#58512yes—
489C22×C11#58511yescharacteristic
490C4×C11—22no—
491C4×C11—22no—
492C4×C11—24no—
493C4×C11—42no—
494C4×C11—42no—
495C4×C11—42no—
496C4×C11—42no—
497Dic11—24no—
498Dic11—22no—
499Dic11—22no—
500Dic11—22no—
501Dic11—24no—
502Dic11—22no—
503Dic11—42no—
504Dic11—42no—
505Dic11—42no—
506Dic11—42no—
507C22×Q8—111no—
508C22×D4C22×D1112yes—
509C22×D4C22×D1111yescharacteristic
510C23×C4—112no—
511C23×C4—111no—
512C23×C4—111no—
513C23×C4—112no—
514C23×C4C22×D1112yes—
515C23×C4C22×D1111yescharacteristic
516#126—1116no—
517#125—118no—
518#124—118no—
519#123—1116no—
520C22⋊Q8—118no—
521#121C4×D1118yes—
522C4×Q8—118no—
523C4×D4—118no—
524C4×D4—1116no—
525#117—1116no—
526C2×C4⋊C4—112no—
527C2×C4⋊C4—112no—
528C2×C4⋊C4—111no—
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⋊C4—112no—
537C2×C4⋊C4—112no—
538C2×C4⋊C4—112no—
539C2×C4⋊C4C22×D1112yes—
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—111no—
547C2×C22⋊C4—112no—
548C2×C22⋊C4—111no—
549C2×C22⋊C4—112no—
550C2×C22⋊C4—112no—
551C2×C22⋊C4—112no—
552C2×C22⋊C4C22×D1112yes—
553C2×C22⋊C4C22×D1112yes—
554C2×C22⋊C4C22×D1111yescharacteristic
555C2×C22⋊C4C22×D1111yescharacteristic
556C2×C22⋊C4C22×D1112yes—
557C2×C22⋊C4C22×D1112yes—
558C2×C22⋊C4C22×D1112yes—
559C2×C42—118no—
560C2×C42—111no—
561C2×C42—112no—
562C2×C42—111no—
563C2×C42—111no—
564C2×C42—111no—
565C2×C42—112no—
566C2×C42—112no—
567C2×C42—112no—
568C2×C42—112no—
569C2×C42—112no—
570C2×C42—112no—
571C2×C42—112no—
572C2×C42—112no—
573C2×C42—112no—
574C2×C42C22×D1112yes—
575#95—112no—
576#95—112no—
577#95—112no—
578#95—112no—
579#95—112no—
580#95—112no—
581#95—112no—
582#95—111no—
583#95—111no—
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#95C22×D1112yes—
600#95C22×D1111yescharacteristic
601#95C22×D1111yescharacteristic
602#95C22×D1112yes—
603#95C22×D1112yes—
604#95C22×D1112yes—
605C2×C11—42no—
606C2×C11—44no—
607C2×C11#342811yescharacteristic
608C2×C11#342811yescharacteristic
609C2×C11#342811yescharacteristic
610C2×C11#356612yes—
611C2×C11#356612yes—
612C24C23×D1111yescharacteristic
613C24C23×D1112yes—
614C2×Q8—114no—
615C2×Q8—442no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4C2×C4×D1118yes—
620C2×D4C2×C4×D1114yes—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4—42no—
624C22×C4—42no—
625C22×C4—111no—
626C22×C4—111no—
627C22×C4—111no—
628C22×C4—112no—
629C22×C4—111no—
630C22×C4—112no—
631C22×C4—114no—
632C22×C4—114no—
633C22×C4—118no—
634C22×C4—112no—
635C22×C4—112no—
636C22×C4—112no—
637C22×C4—112no—
638C22×C4—442no—
639C22×C4—442no—
640C22×C4—441no—
641C22×C4—442no—
642C22×C4—441no—
643C22×C4—442no—
644C22×C4—442no—
645C22×C4—442no—
646C22×C4C2×C4×D1114yes—
647C22×C4C23×D1112yes—
648C22×C4C23×D1112yes—
649C22×C4C23×D1112yes—
650C22×C4C23×D1112yes—
651C22×C4C23×D1111yescharacteristic
652C22×C4C23×D1112yes—
653C22×C4C23×D1111yescharacteristic
654C4⋊C4—42no—
655C4⋊C4—42no—
656C4⋊C4—118no—
657C4⋊C4—118no—
658C4⋊C4—114no—
659C4⋊C4—118no—
660C4⋊C4—118no—
661C4⋊C4—442no—
662C4⋊C4—442no—
663C4⋊C4—442no—
664C4⋊C4—442no—
665C4⋊C4—442no—
666C4⋊C4—442no—
667C4⋊C4—442no—
668C4⋊C4—442no—
669C4⋊C4C2×C4×D1114yes—
670C22⋊C4—42no—
671C22⋊C4—42no—
672C22⋊C4—41no—
673C22⋊C4—42no—
674C22⋊C4—41no—
675C22⋊C4—42no—
676C22⋊C4—118no—
677C22⋊C4—118no—
678C22⋊C4—118no—
679C22⋊C4—118no—
680C22⋊C4—442no—
681C22⋊C4—442no—
682C22⋊C4—442no—
683C22⋊C4—441no—
684C22⋊C4—441no—
685C22⋊C4—442no—
686C22⋊C4C2×C4×D1118yes—
687C42—42no—
688C42—114no—
689C42—114no—
690C42—114no—
691C42—114no—
692C42—118no—
693C42—442no—
694C42—442no—
695C42—442no—
696C42—442no—
697C42—442no—
698C42—442no—
699C42—442no—
700C42—442no—
701C42—442no—
702C11#3438711yescharacteristic, complemented, Sylow
703C23—21no—
704C23—22no—
705C23—22no—
706C23—22no—
707C23—22no—
708C23—22no—
709C23—22no—
710C23—22no—
711C23—21no—
712C23—22no—
713C23C22×C4×D1114yes—
714C23C22×C4×D1112yes—
715C23C24×D1111yescharacteristic
716Q8—444no—
717D4—44no—
718D4—48no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
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—44no—
736C2×C4—84no—
737C2×C4—112no—
738C2×C4—112no—
739C2×C4—112no—
740C2×C4—112no—
741C2×C4—114no—
742C2×C4—114no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—222no—
746C2×C4—222no—
747C2×C4—221no—
748C2×C4—222no—
749C2×C4—221no—
750C2×C4—222no—
751C2×C4—221no—
752C2×C4—221no—
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—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—444no—
766C2×C4—444no—
767C2×C4—448no—
768C2×C4—884no—
769C2×C4C22×C4×D1112yes—
770C2×C4C22×C4×D1112yes—
771C2×C4C22×C4×D1114yes—
772C22—22no—
773C22—22no—
774C22—24no—
775C22—24no—
776C22—22no—
777C22—24no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—42no—
782C22—42no—
783C22—42no—
784C22C23×C4×D1111yescharacteristic
785C22#1062345511yescharacteristic
786C22#1062345512yes—
787C22#1062345512yes—
788C22#1062345711yescharacteristic
789C4—22no—
790C4—22no—
791C4—24no—
792C4—42no—
793C4—42no—
794C4—42no—
795C4—42no—
796C4—222no—
797C4—222no—
798C4—224no—
799C4—222no—
800C4—222no—
801C4—224no—
802C4—442no—
803C4—442no—
804C4—442no—
805C4—442no—
806C2—42no—
807C2—44no—
808C2#1308181411yescharacteristic
809C2#1308181411yescharacteristic
810C2#1308181611yescharacteristic
811C2#1308327312yes—
812C2#1308328912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2377C2
socle, cosocleC23×C11C25
prime radicalC2×C11×#121C22
hypercenter#2377D11
hypocenterC11#34387
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2377

Complements

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

NH ≅ G/Ntype
2. #13071784C2semidirect
3. #13071779C2semidirect
5. #13071751C2semidirect
6. #13071749C2semidirect
7. #13071578C2semidirect
8. #13071554C2semidirect
9. #13071498C2semidirect
10. #13071474C2semidirect
11. #13071425C2semidirect
12. #13071419C2semidirect
13. #13071392C2semidirect
14. #13071388C2semidirect
15. #13071253C2semidirect
16. #13071242C2semidirect
17. #13071011C2semidirect
18. #13071007C2semidirect
27. #10623131C4semidirect
140. #66988C2×C4semidirect
142. D4×Dic11C2×C4semidirect
147. #66977C2×C4semidirect
157. C2×C4×Dic11C2×C4semidirect
172. #66943C2×C4semidirect
173. #66940C2×C4semidirect
174. #66932C2×C4semidirect
175. #66930C2×C4semidirect
702. C11#34387semidirect

Maximal subgroups

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

subgroupindex
C2×#106231312
#130717842
#130717792
#130717732
#130717512
#130717492
#130715782
#130715542
#130714982
#130714742
#130714252
#130714192
#130713922
#130713882
#130712532
#130712422
#130710112
#130710072
C11×#23772
#3438711