Finite Group Databasebeta

← #14925792

Subgroups — #14925792

Order 2816.

2522 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623048C211yesmaximal, characteristic, complemented
2C2×#41×Dic11C211yesmaximal, characteristic
3#13073833C211yesmaximal, characteristic, complemented
4#13073826C211yesmaximal, characteristic, complemented
5#13073819C211yesmaximal, characteristic, complemented
6#13073818C211yesmaximal, characteristic, complemented
7#13073810C211yesmaximal, characteristic, complemented
8#13073809C211yesmaximal, characteristic, complemented
9#13073800C214yesmaximal, complemented
10#13073787C211yesmaximal, characteristic, complemented
11#13073567C211yesmaximal, characteristic, complemented
12#13072064C214yesmaximal, complemented
13#13071890C214yesmaximal, complemented
14C4×#66931C214yesmaximal, complemented
15#13071107C211yesmaximal, characteristic
16#13071023C211yesmaximal, characteristic, complemented
17#13071019C211yesmaximal, characteristic, complemented
18C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
19C11×#2297C211yesmaximal, characteristic
20C22×C11×#41C2211yescharacteristic
21C2×C11×#117C2211yescharacteristic
22C22×C42×C11C2211yescharacteristic
23#41×Dic11—28no—
24C2×Q8×Dic11C2211yescharacteristic
25C2×Q8×Dic11C2211yescharacteristic
26C2×D4×Dic11C2211yescharacteristic
27C2×D4×Dic11C2212yes—
28C2×D4×Dic11C2211yescharacteristic
29C2×D4×Dic11C2212yes—
30C2×#66979C2211yescharacteristic
31C2×#66979C2212yes—
32C2×#66979C2211yescharacteristic
33C22×Dic11⋊C4C2212yes—
34C22×C4×Dic11C2211yescharacteristic
35C22×C4×Dic11C2212yes—
36C22×C4×Dic11C2211yescharacteristic
37#10623048—28no—
38C2×#66943C2211yescharacteristic
39C2×#66943C2211yescharacteristic
40C2×#66941C2211yescharacteristic
41C2×#66941C2211yescharacteristic
42C2×#66931C2214yes—
43C2×#66931C2212yes—
44C2×#66931C2212yes—
45C2×C4×Dic22C2212yes—
46C2×C4×Dic22C2212yes—
47C11×#391C2211yescharacteristic
48C11×#391C2211yescharacteristic
49C11×#390C2211yescharacteristic
50C11×#390C2211yescharacteristic
51C11×#386C2214yes—
52C4×C11×C22⋊C4C2214yes—
53#10622843C2211yescharacteristic
54#10622843C2211yescharacteristic
55#10622834C2211yescharacteristic
56#10622834C2211yescharacteristic
57#10622833C2214yes—
58#10622825C2214yes—
59C4×C22⋊Dic11C2214yes—
60C2×C11⋊#95C2212yes—
61#10622590C2211yescharacteristic
62#10622590C2211yescharacteristic
63#10622589C2211yescharacteristic
64#10622589C2211yescharacteristic
65#10622563C2214yes—
66#10622562C2214yes—
67#10622561C2214yes—
68#10622561C2214yes—
69#10622560C2214yes—
70#10622559C2214yes—
71#10622555C2214yes—
72#10622555C2214yes—
73#10622549C2211yescharacteristic
74#10622549C2211yescharacteristic
75#10622548C2211yescharacteristic
76#10622548C2211yescharacteristic
77C4×C4⋊Dic11C2214yes—
78C4×Dic11⋊C4C2212yes—
79C4×Dic11⋊C4C2214yes—
80C4×Dic11⋊C4C2212yes—
81C4×Dic11⋊C4C2211yescharacteristic
82C4×Dic11⋊C4C2211yescharacteristic
83C4×Dic11⋊C4C2211yescharacteristic
84C4×Dic11⋊C4C2211yescharacteristic
85#10622274C2214yes—
86#10622273C2214yes—
87#10622270C2214yes—
88#10622269C2214yes—
89#10622268C2214yes—
90#10622267C2214yes—
91#10622260C2214yes—
92#10622259C2214yes—
93C2×C11×#41—24no—
94C2×C11×#41—24no—
95C2×C11×#41Q818yescomplemented
96C22×Q8×C11C2311yescharacteristic
97C22×D4×C11C2312yes—
98C22×D4×C11C2311yescharacteristic
99C23×C4×C11C2312yes—
100C23×C4×C11C2312yes—
101C23×C4×C11C2311yescharacteristic
102C23×Dic11C2312yes—
103C23×Dic11C2312yes—
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2312yes—
106C23×Dic11C2311yescharacteristic
107C22×Dic22C2312yes—
108C22×Dic22C2312yes—
109C11×#117—24no—
110C2×C11×C4⋊C4C2311yescharacteristic
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C22⋊C4C2312yes—
113C2×C11×C22⋊C4C2314yes—
114C2×C11×C22⋊C4C2314yes—
115C2×C42×C11—24no—
116C2×C42×C11C2312yes—
117C2×C42×C11C2312yes—
118C2×C42×C11C2311yescharacteristic
119C2×C42×C11C2311yescharacteristic
120C2×C22⋊Dic11C2312yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2312yes—
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2314yes—
126Q8×Dic11—24no—
127Q8×Dic11—24no—
128D4×Dic11—28no—
129D4×Dic11—28no—
130D4×Dic11—24no—
131D4×Dic11—24no—
132#66979—24no—
133#66979—24no—
134#66979—28no—
135C2×C4⋊Dic11C2312yes—
136C2×C4⋊Dic11C2312yes—
137C2×C4⋊Dic11C2314yes—
138C2×C4⋊Dic11C2311yescharacteristic
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2312yes—
141C2×C4⋊Dic11C2312yes—
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2311yescharacteristic
144C2×C4⋊Dic11C2314yes—
145C2×Dic11⋊C4—28no—
146C2×Dic11⋊C4C2312yes—
147C2×Dic11⋊C4C2312yes—
148C2×Dic11⋊C4C2312yes—
149C2×Dic11⋊C4C2312yes—
150C2×Dic11⋊C4C2314yes—
151C2×Dic11⋊C4C2312yes—
152C2×Dic11⋊C4C2312yes—
153C2×Dic11⋊C4C2312yes—
154C2×Dic11⋊C4C2314yes—
155C2×Dic11⋊C4C2312yes—
156C2×C4×Dic11—24no—
157C2×C4×Dic11—28no—
158C2×C4×Dic11D418yes—
159C2×C4×Dic11C2312yes—
160C2×C4×Dic11C2312yes—
161C2×C4×Dic11C2312yes—
162C2×C4×Dic11C2312yes—
163C2×C4×Dic11C2312yes—
164C2×C4×Dic11C2311yescharacteristic
165C2×C4×Dic11C2311yescharacteristic
166C2×C4×Dic11C2311yescharacteristic
167C2×C4×Dic11C2311yescharacteristic
168C2×C4×Dic11C2311yescharacteristic
169C2×C4×Dic11C2311yescharacteristic
170#66943—24no—
171#66943—24no—
172#66941—24no—
173#66941—24no—
174#66931—28no—
175#66931—28no—
176#66931—216no—
177C4×Dic22—28no—
178C4×Dic22—28no—
179C11×#95C2314yes—
180C11×#95C2314yes—
181C11⋊#95C2314yes—
182C11⋊#95C2314yes—
183C11⋊#95C2314yes—
184C11⋊#95C2314yes—
185C11⋊#95C2312yes—
186C11⋊#95C2314yes—
187C11⋊#95C2312yes—
188C11⋊#95C2314yes—
189C11⋊#95C2312yes—
190C11⋊#95C2312yes—
191#34947—111nomaximal, Sylow
192C24×C11C2412yes—
193C24×C11C2411yescharacteristic
194C11×#41—232no—
195C2×Q8×C11—22no—
196C2×Q8×C11—22no—
197C2×Q8×C11C2×Q814yes—
198C2×D4×C11—24no—
199C2×D4×C11—24no—
200C2×D4×C11—22no—
201C2×D4×C11—22no—
202C2×D4×C11C2×Q818yes—
203C2×D4×C11C2×Q814yes—
204C22×C4×C11—24no—
205C22×C4×C11—24no—
206C22×C4×C11—24no—
207C22×C4×C11—24no—
208C22×C4×C11—42no—
209C22×C4×C11C2×D414yes—
210C22×C4×C11C2×Q818yes—
211C22×C4×C11C2×Q814yes—
212C22×C4×C11#4114yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2412yes—
218C22×C4×C11C2411yescharacteristic
219C22×C4×C11C2411yescharacteristic
220C22×Dic11—24no—
221C22×Dic11—24no—
222C22×Dic11—24no—
223C22×Dic11—28no—
224C22×Dic11—24no—
225C22×Dic11—24no—
226C22×Dic11—42no—
227C22×Dic11—42no—
228C22×Dic11—44no—
229C22×Dic11C2×D414yes—
230C22×Dic11C2×D414yes—
231C22×Dic11C2412yes—
232C22×Dic11C2412yes—
233C22×Dic11C2412yes—
234C22×Dic11C2412yes—
235C22×Dic11C2412yes—
236C22×Dic11C2411yescharacteristic
237C22×Dic11C2411yescharacteristic
238C22×Dic11C2411yescharacteristic
239C22×Dic11C2412yes—
240C22×Dic11C2411yescharacteristic
241C2×Dic22—24no—
242C2×Dic22—24no—
243C2×Dic22—28no—
244C2×Dic22—44no—
245C11×C4⋊C4—22no—
246C11×C4⋊C4—22no—
247C11×C22⋊C4—24no—
248C11×C22⋊C4—28no—
249C11×C22⋊C4—44no—
250C42×C11—24no—
251C42×C11—22no—
252C42×C11—24no—
253C42×C11—22no—
254C22⋊Dic11—24no—
255C22⋊Dic11—24no—
256C22⋊Dic11—28no—
257C22⋊Dic11—24no—
258C22⋊Dic11—24no—
259C22⋊Dic11—44no—
260C4⋊Dic11—24no—
261C4⋊Dic11—24no—
262C4⋊Dic11—24no—
263C4⋊Dic11—24no—
264C4⋊Dic11—22no—
265C4⋊Dic11—22no—
266C4⋊Dic11—22no—
267C4⋊Dic11—22no—
268C4⋊Dic11—28no—
269C4⋊Dic11—44no—
270Dic11⋊C4—24no—
271Dic11⋊C4—24no—
272Dic11⋊C4—24no—
273Dic11⋊C4—24no—
274Dic11⋊C4—28no—
275Dic11⋊C4—24no—
276Dic11⋊C4—24no—
277Dic11⋊C4—24no—
278Dic11⋊C4—44no—
279Dic11⋊C4#4118yescomplemented
280C4×Dic11—24no—
281C4×Dic11—24no—
282C4×Dic11—24no—
283C4×Dic11—24no—
284C4×Dic11—24no—
285C4×Dic11—22no—
286C4×Dic11—22no—
287C4×Dic11C2×D414yes—
288C4×Dic11C2×D414yes—
289C4×Dic11C2×D414yes—
290C4×Dic11C2×D414yes—
291C2×#533—111no—
292C2×C4×#41—111no—
293#2568—111no—
294#2567—111no—
295#2566—111no—
296#2566—111no—
297#2565—111no—
298#2565—111no—
299#2564—114no—
300#2563—111no—
301#2542—111no—
302#2417—114no—
303#2396—114no—
304C4×C22⋊Q8—114no—
305#2297—111no—
306#2297D1111yescharacteristic
307#2285—111no—
308#2285—111no—
309C2×C4×C4⋊C4—111no—
310C23×C11—22no—
311C23×C11—22no—
312C23×C11—22no—
313C23×C11—24no—
314C23×C11—22no—
315C23×C11—24no—
316C23×C11C22×D412yes—
317C23×C11C22×Q814yes—
318C23×C11C22×Q812yes—
319C23×C11C2×#4112yes—
320C23×C11C2511yescharacteristic
321Q8×C11—28no—
322D4×C11—216no—
323D4×C11—28no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—216no—
329C2×C4×C11—22no—
330C2×C4×C11—22no—
331C2×C4×C11—22no—
332C2×C4×C11—24no—
333C2×C4×C11—22no—
334C2×C4×C11—24no—
335C2×C4×C11—22no—
336C2×C4×C11—48no—
337C2×C4×C11C22⋊Q8116yescomplemented
338C2×C4×C11C22×D412yes—
339C2×C4×C11C22×D412yes—
340C2×C4×C11C22×Q814yes—
341C2×C4×C11C22×Q812yes—
342C2×C4×C11C22×Q812yes—
343C2×C4×C11C2×#4112yes—
344C2×C4×C11C2×#4112yes—
345C2×C4×C11C2×#4114yes—
346C2×Dic11—22no—
347C2×Dic11—22no—
348C2×Dic11—22no—
349C2×Dic11—22no—
350C2×Dic11—22no—
351C2×Dic11—28no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—24no—
359C2×Dic11—24no—
360C2×Dic11—24no—
361C2×Dic11—24no—
362C2×Dic11—22no—
363C2×Dic11—44no—
364C2×Dic11—48no—
365C2×Dic11—48no—
366C2×Dic11—48no—
367C2×Dic11C22×D412yes—
368C2×Dic11C22×D412yes—
369C2×Dic11C22×D412yes—
370C2×Dic11C22×D412yes—
371C2×Dic11C2×#4114yes—
372C2×Dic11C2×#4114yes—
373Dic22—48no—
374Dic22—48no—
375C22×#41C2×D1111yescharacteristic
376#533—228no—
377C2×C4⋊Q8—111no—
378C2×C4⋊Q8—111no—
379C2×#125—111no—
380C2×#125—111no—
381C2×C22⋊Q8—112no—
382C2×C22⋊Q8—112no—
383C2×C22⋊Q8—114no—
384C4×#41—228no—
385C2×C4×Q8—111no—
386C2×C4×Q8—111no—
387C2×C4×Q8—112no—
388C2×C4×Q8—112no—
389C2×C4×D4—111no—
390C2×C4×D4—112no—
391C2×C4×D4—111no—
392C2×C4×D4—112no—
393C2×#117—112no—
394C2×#117—111no—
395C2×#117—111no—
396C2×#117C2×D1111yescharacteristic
397C22×C4⋊C4—112no—
398C22×C42—111no—
399C22×C42—112no—
400C22×C42—111no—
401C22×C42C2×D1111yescharacteristic
402#400—114no—
403#399—114no—
404#398—114no—
405#398—114no—
406#396—114no—
407#396—114no—
408#395—114no—
409#393—114no—
410#391—111no—
411#391—111no—
412#391—114no—
413#391C2×D1111yescharacteristic
414#391C2×D1111yescharacteristic
415#390—111no—
416#390—111no—
417#390C2×D1111yescharacteristic
418#390C2×D1111yescharacteristic
419#389—114no—
420#387—114no—
421#387—114no—
422#386—114no—
423#386C2×D1114yes—
424#385—114no—
425#385—114no—
426#384—111no—
427#384—111no—
428#384—111no—
429#384—111no—
430#382—111no—
431#382—111no—
432#382—111no—
433#382—111no—
434#380—114no—
435#380—114no—
436#380—114no—
437C4×C4⋊C4—111no—
438C4×C4⋊C4—111no—
439C4×C4⋊C4—111no—
440C4×C4⋊C4—111no—
441C4×C4⋊C4—112no—
442C4×C4⋊C4—114no—
443C4×C4⋊C4—112no—
444C4×C4⋊C4—114no—
445C4×C22⋊C4—114no—
446C4×C22⋊C4C2×D1114yes—
447C2×#95—112no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—24no—
451C22×C11—24no—
452C22×C11—24no—
453C22×C11—28no—
454C22×C11—42no—
455C22×C11—42no—
456C22×C11—44no—
457C22×C11C2×C22⋊Q814yes—
458C22×C11C23×D411yescharacteristic
459C22×C11C23×Q811yescharacteristic
460C22×C11C22×#4111yescharacteristic
461C22×C11C22×#4112yes—
462C22×C11#58512yes—
463C4×C11—24no—
464C4×C11—24no—
465C4×C11—42no—
466C4×C11—42no—
467C4×C11—42no—
468C4×C11C2×C22⋊Q814yes—
469C4×C11C2×C22⋊Q814yes—
470Dic11—22no—
471Dic11—22no—
472Dic11—22no—
473Dic11—24no—
474Dic11—42no—
475Dic11—42no—
476Dic11—42no—
477Dic11—42no—
478Dic11—42no—
479Dic11#53214yes—
480C2×#41—24no—
481C2×#41—24no—
482C2×#41Dic2218yescomplemented
483C22×Q8—112no—
484C22×Q8—112no—
485C22×Q8C22×D1111yescharacteristic
486C22×D4C22×D1112yes—
487C22×D4C22×D1111yescharacteristic
488C23×C4—111no—
489C23×C4—111no—
490C23×C4—112no—
491C23×C4—112no—
492C23×C4—112no—
493C23×C4C22×D1112yes—
494C23×C4C22×D1112yes—
495C23×C4C22×D1111yescharacteristic
496C4⋊Q8—224no—
497C4⋊Q8—224no—
498#125—224no—
499#125—224no—
500C22⋊Q8—2216no—
501C22⋊Q8—228no—
502C22⋊Q8—228no—
503C4×Q8—228no—
504C4×Q8—228no—
505C4×Q8—224no—
506C4×Q8—224no—
507C4×D4—224no—
508C4×D4—224no—
509C4×D4—228no—
510C4×D4—228no—
511#117—24no—
512#117—228no—
513#117—224no—
514#117—224no—
515C2×C4⋊C4—112no—
516C2×C4⋊C4—112no—
517C2×C4⋊C4—112no—
518C2×C4⋊C4—112no—
519C2×C4⋊C4—111no—
520C2×C4⋊C4—111no—
521C2×C4⋊C4—112no—
522C2×C4⋊C4—112no—
523C2×C4⋊C4—111no—
524C2×C4⋊C4—111no—
525C2×C4⋊C4—112no—
526C2×C4⋊C4—112no—
527C2×C4⋊C4—112no—
528C2×C4⋊C4—112no—
529C2×C4⋊C4—112no—
530C2×C4⋊C4—112no—
531C2×C4⋊C4—114no—
532C2×C4⋊C4—114no—
533C2×C4⋊C4—114no—
534C2×C4⋊C4—114no—
535C2×C4⋊C4—228no—
536C2×C4⋊C4C22×D1111yescharacteristic
537C2×C4⋊C4C22×D1111yescharacteristic
538C2×C22⋊C4—112no—
539C2×C22⋊C4—112no—
540C2×C22⋊C4—112no—
541C2×C22⋊C4—112no—
542C2×C22⋊C4—114no—
543C2×C22⋊C4—114no—
544C2×C22⋊C4C22×D1112yes—
545C2×C22⋊C4C22×D1114yes—
546C2×C22⋊C4C22×D1114yes—
547C2×C42—24no—
548C2×C42—118no—
549C2×C42—111no—
550C2×C42—111no—
551C2×C42—111no—
552C2×C42—111no—
553C2×C42—112no—
554C2×C42—112no—
555C2×C42—111no—
556C2×C42—111no—
557C2×C42—112no—
558C2×C42—112no—
559C2×C42—112no—
560C2×C42—228no—
561C2×C42—224no—
562C2×C42C22×D1111yescharacteristic
563C2×C42C22×D1111yescharacteristic
564C2×C42C22×D1112yes—
565C2×C42C22×D1112yes—
566#95—112no—
567#95—112no—
568#95—112no—
569#95—112no—
570#95—114no—
571#95—114no—
572#95—114no—
573#95—114no—
574#95—114no—
575#95—114no—
576#95C22×D1114yes—
577#95C22×D1114yes—
578C2×C11—24no—
579C2×C11—44no—
580C2×C11C22×C22⋊Q811yescharacteristic
581C2×C11C2×#53211yescharacteristic
582C2×C11#344911yescharacteristic
583C2×C11#347512yes—
584C2×C11Q8×#4112yes—
585C24C23×D1112yes—
586C24C23×D1111yescharacteristic
587#41—232no—
588C2×Q8—22no—
589C2×Q8—22no—
590C2×Q8—224no—
591C2×Q8—224no—
592C2×Q8—228no—
593C2×Q8—444no—
594C2×Q8C2×Dic2214yes—
595C2×D4—24no—
596C2×D4—24no—
597C2×D4—22no—
598C2×D4—22no—
599C2×D4C2×Dic2218yes—
600C2×D4C2×Dic2214yes—
601C22×C4—24no—
602C22×C4—24no—
603C22×C4—24no—
604C22×C4—24no—
605C22×C4—42no—
606C22×C4—111no—
607C22×C4—114no—
608C22×C4—111no—
609C22×C4—112no—
610C22×C4—111no—
611C22×C4—111no—
612C22×C4—114no—
613C22×C4—112no—
614C22×C4—112no—
615C22×C4—112no—
616C22×C4—112no—
617C22×C4—112no—
618C22×C4—224no—
619C22×C4—224no—
620C22×C4—224no—
621C22×C4—224no—
622C22×C4—228no—
623C22×C4—224no—
624C22×C4—442no—
625C22×C4—442no—
626C22×C4—444no—
627C22×C4C2×Dic2218yes—
628C22×C4C2×Dic2214yes—
629C22×C4D4×D1114yes—
630C22×C4#434114yes—
631C22×C4C23×D1112yes—
632C22×C4C23×D1112yes—
633C22×C4C23×D1112yes—
634C22×C4C23×D1112yes—
635C22×C4C23×D1112yes—
636C22×C4C23×D1111yescharacteristic
637C22×C4C23×D1111yescharacteristic
638C4⋊C4—22no—
639C4⋊C4—22no—
640C4⋊C4—118no—
641C4⋊C4—224no—
642C4⋊C4—224no—
643C4⋊C4—224no—
644C4⋊C4—224no—
645C4⋊C4—224no—
646C4⋊C4—224no—
647C4⋊C4—224no—
648C4⋊C4—224no—
649C4⋊C4—224no—
650C4⋊C4—224no—
651C4⋊C4—228no—
652C4⋊C4—222no—
653C4⋊C4—222no—
654C4⋊C4—222no—
655C4⋊C4—222no—
656C4⋊C4—224no—
657C4⋊C4—228no—
658C4⋊C4—444no—
659C4⋊C4—444no—
660C22⋊C4—24no—
661C22⋊C4—28no—
662C22⋊C4—44no—
663C22⋊C4—224no—
664C22⋊C4—224no—
665C22⋊C4—228no—
666C22⋊C4—224no—
667C22⋊C4—224no—
668C22⋊C4—444no—
669C42—24no—
670C42—22no—
671C42—24no—
672C42—22no—
673C42—114no—
674C42—114no—
675C42—114no—
676C42—114no—
677C42—224no—
678C42—224no—
679C42—224no—
680C42—224no—
681C42—222no—
682C42—224no—
683C42—222no—
684C11#3494711yescharacteristic, complemented, Sylow
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—24no—
690C23—24no—
691C23C22×Dic2214yes—
692C23C22×Dic2212yes—
693C23C2×D4×D1112yes—
694C23C2×#434112yes—
695C23C24×D1111yescharacteristic
696Q8—28no—
697Q8—448no—
698Q8—448no—
699D4—216no—
700D4—28no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—216no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—24no—
713C2×C4—48no—
714C2×C4—112no—
715C2×C4—114no—
716C2×C4—112no—
717C2×C4—112no—
718C2×C4—112no—
719C2×C4—114no—
720C2×C4—228no—
721C2×C4—222no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—222no—
725C2×C4—222no—
726C2×C4—222no—
727C2×C4—222no—
728C2×C4—222no—
729C2×C4—222no—
730C2×C4—222no—
731C2×C4—224no—
732C2×C4—224no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—224no—
736C2×C4—224no—
737C2×C4—448no—
738C2×C4—444no—
739C2×C4—448no—
740C2×C4—448no—
741C2×C4#66931116yescomplemented
742C2×C4C22×Dic2214yes—
743C2×C4C22×Dic2212yes—
744C2×C4C22×Dic2212yes—
745C2×C4C2×D4×D1112yes—
746C2×C4C2×D4×D1112yes—
747C2×C4C2×#434112yes—
748C2×C4C2×#434112yes—
749C2×C4#41×D1114yes—
750C22—22no—
751C22—24no—
752C22—24no—
753C22—22no—
754C22—28no—
755C22—24no—
756C22—42no—
757C22—44no—
758C22—42no—
759C22C2×#6693114yes—
760C22C23×Dic2211yescharacteristic
761C22C22×D4×D1111yescharacteristic
762C22C22×#434111yescharacteristic
763C22C2×#41×D1112yes—
764C22#1062345312yes—
765C4—24no—
766C4—24no—
767C4—42no—
768C4—42no—
769C4—42no—
770C4—114no—
771C4—222no—
772C4—224no—
773C4—222no—
774C4—222no—
775C4—442no—
776C4—442no—
777C4—442no—
778C4—442no—
779C4—442no—
780C4C2×#6693114yes—
781C4C2×#6693114yes—
782C2—24no—
783C2—44no—
784C2C22×#6693111yescharacteristic
785C2D11×#53211yescharacteristic
786C2#1308194311yescharacteristic
787C2#1308217612yes—
788C2#41×Dic2212yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC11×#2297C2
prime radicalC22×C11×#41C22
hypercenter#2297D11
hypocenterC11#34947
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ #2297

Complements

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

NH ≅ G/Ntype
1. C2×#10623048C2semidirect
3. #13073833C2semidirect
4. #13073826C2semidirect
5. #13073819C2semidirect
6. #13073818C2semidirect
7. #13073810C2semidirect
8. #13073809C2semidirect
9. #13073800C2semidirect
10. #13073787C2semidirect
11. #13073567C2semidirect
12. #13072064C2semidirect
13. #13071890C2semidirect
14. C4×#66931C2semidirect
16. #13071023C2semidirect
17. #13071019C2semidirect
18. C2×C4×Dic11⋊C4C2semidirect
95. C2×C11×#41Q8semidirect
279. Dic11⋊C4#41semidirect
337. C2×C4×C11C22⋊Q8semidirect
482. C2×#41Dic22semidirect
684. C11#34947semidirect
741. C2×C4#66931semidirect

Maximal subgroups

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

subgroupindex
C2×#106230482
C2×#41×Dic112
#130738332
#130738262
#130738192
#130738182
#130738102
#130738092
#130738002
#130737872
#130735672
#130720642
#130718902
C4×#669312
#130711072
#130710232
#130710192
C2×C4×Dic11⋊C42
C11×#22972
#3494711