Finite Group Databasebeta

← #14926837

Subgroups — #14926837

Order 2816.

1690 conjugacy classes of subgroups.

The subgroup lattice has 822 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13076955C211yesmaximal, characteristic
2#13076922C212yesmaximal
3#13074733C211yesmaximal, characteristic
4#13074732C211yesmaximal, characteristic
5#13074433C212yesmaximal
6#13074026C212yesmaximal, complemented
7#13074025C212yesmaximal, complemented
8#13074012C212yesmaximal, complemented
9#13074010C212yesmaximal, complemented
10#13073310C212yesmaximal, complemented
11#13073302C212yesmaximal, complemented
12#13072604C212yesmaximal, complemented
13#13072596C212yesmaximal, complemented
14#13071351C211yesmaximal, characteristic
15#13071346C211yesmaximal, characteristic
16#13071217C212yesmaximal
17#13071148C212yesmaximal
18C2×C4×C4⋊Dic11C211yesmaximal, characteristic
19C11×#2855C211yesmaximal, characteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×C4⋊Dic11C2211yescharacteristic
24C2×#66977C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C22×C4×Dic11C2211yescharacteristic
27C2×#66942C2212yes—
28C2×#66940C2212yes—
29C2×#66931C2212yes—
30C11×#391C2211yescharacteristic
31C11×#391C2211yescharacteristic
32C11×#389C2211yescharacteristic
33C11×#389C2211yescharacteristic
34C11×#387C2212yes—
35C11×#387C2212yes—
36C11×#385C2212yes—
37C11×#381C2212yes—
38C11×#380C2211yescharacteristic
39#10622843C2212yes—
40#10622842C2212yes—
41#10622825C2211yescharacteristic
42#10622824C2212yes—
43#10622823C2212yes—
44C2×C11⋊#95C2211yescharacteristic
45C2×C11⋊#95C2211yescharacteristic
46#10622598C2212yes—
47#10622597C2212yes—
48#10622596C2212yes—
49#10622594C2212yes—
50#10622594C2212yes—
51#10622594C2212yes—
52#10622593C2212yes—
53#10622592C2212yes—
54#10622592C2212yes—
55#10622591C2212yes—
56#10622591C2212yes—
57#10622591C2212yes—
58C4⋊C4×Dic11C2212yes—
59#10622585C2212yes—
60#10622585C2212yes—
61#10622585C2212yes—
62#10622563C2212yes—
63#10622559C2212yes—
64#10622555C2212yes—
65#10622555C2212yes—
66#10622555C2212yes—
67C22⋊C4×Dic11C2212yes—
68C22⋊C4×Dic11C2212yes—
69C4×C4⋊Dic11C2212yes—
70C4×C4⋊Dic11C2212yes—
71C4×C4⋊Dic11C2212yes—
72C4×C4⋊Dic11C2212yes—
73#10622546C2212yes—
74#10622546C2212yes—
75#10622542C2211yescharacteristic
76#10622542C2211yescharacteristic
77#10622541C2211yescharacteristic
78#10622541C2211yescharacteristic
79#10622274C2212yes—
80#10622274C2212yes—
81#10622273C2212yes—
82#10622273C2212yes—
83#10622270C2212yes—
84#10622270C2212yes—
85#10622270C2212yes—
86#10622269C2212yes—
87#10622269C2212yes—
88#10622269C2212yes—
89#10622267C2212yes—
90#10622267C2212yes—
91#10622267C2212yes—
92#10622267C2212yes—
93#10622266C2212yes—
94#10622266C2212yes—
95#10622266C2212yes—
96#10622266C2212yes—
97#10622266C2212yes—
98#10622266C2212yes—
99#10622266C2212yes—
100#10622265C2212yes—
101#10622263C2212yes—
102#10622262C2212yes—
103#10622262C2212yes—
104#10622260C2212yes—
105#10622259C2212yes—
106#10622259C2212yes—
107C22×Q8×C11C2311yescharacteristic
108C23×C4×C11C2311yescharacteristic
109C23×C4×C11C2311yescharacteristic
110C23×C4×C11C2311yescharacteristic
111C23×Dic11C2311yescharacteristic
112C23×Dic11C2311yescharacteristic
113C23×Dic11C2311yescharacteristic
114C23×Dic11C2311yescharacteristic
115C22×Dic22C2312yes—
116C22×Dic22C2311yescharacteristic
117C11×C22⋊Q8—24no—
118C2×C11×C4⋊C4C2312yes—
119C2×C11×C4⋊C4C2312yes—
120C2×C11×C4⋊C4C2312yes—
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C4⋊C4C2311yescharacteristic
124C2×C11×C22⋊C4C2312yes—
125C2×C11×C22⋊C4C2312yes—
126C2×C42×C11—24no—
127C2×C42×C11C2311yescharacteristic
128C2×C42×C11C2311yescharacteristic
129C2×C42×C11C2311yescharacteristic
130C2×C42×C11C2311yescharacteristic
131C2×C22⋊Dic11C2312yes—
132C2×C22⋊Dic11C2312yes—
133C2×C4⋊Dic11—24no—
134C2×C4⋊Dic11Q818yescomplemented
135C2×C4⋊Dic11C2312yes—
136C2×C4⋊Dic11C2311yescharacteristic
137C2×C4⋊Dic11C2312yes—
138C2×C4⋊Dic11C2312yes—
139C2×C4⋊Dic11C2312yes—
140C2×C4⋊Dic11C2312yes—
141C2×C4⋊Dic11C2311yescharacteristic
142C2×C4⋊Dic11C2311yescharacteristic
143C2×C4⋊Dic11C2312yes—
144C2×C4⋊Dic11C2312yes—
145#66977—24no—
146C2×Dic11⋊C4C2312yes—
147C2×Dic11⋊C4C2312yes—
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×Dic11⋊C4C2312yes—
158C2×Dic11⋊C4C2312yes—
159C2×C4×Dic11—42no—
160C2×C4×Dic11—42no—
161C2×C4×Dic11C2312yes—
162C2×C4×Dic11C2312yes—
163C2×C4×Dic11C2312yes—
164C2×C4×Dic11C2312yes—
165C2×C4×Dic11C2312yes—
166C2×C4×Dic11C2312yes—
167C2×C4×Dic11C2312yes—
168C2×C4×Dic11C2312yes—
169#66942—44no—
170#66940—44no—
171#66931—28no—
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—
200C11⋊#95C2312yes—
201C11⋊#95C2312yes—
202C11⋊#95C2312yes—
203C11⋊#95C2312yes—
204#35013—111nomaximal, Sylow
205C24×C11C2411yescharacteristic
206C2×Q8×C11—22no—
207C2×Q8×C11—41no—
208C2×Q8×C11—41no—
209C22×C4×C11—22no—
210C22×C4×C11—22no—
211C22×C4×C11—22no—
212C22×C4×C11—22no—
213C22×C4×C11—22no—
214C22×C4×C11—41no—
215C22×C4×C11—41no—
216C22×C4×C11C2×Q814yes—
217C22×C4×C11#4114yes—
218C22×C4×C11C2412yes—
219C22×C4×C11C2412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2412yes—
222C22×C4×C11C2411yescharacteristic
223C22×C4×C11C2411yescharacteristic
224C22×C4×C11C2411yescharacteristic
225C22×C4×C11C2411yescharacteristic
226C22×C4×C11C2411yescharacteristic
227C22×C4×C11C2411yescharacteristic
228C22×Dic11—22no—
229C22×Dic11—41no—
230C22×Dic11—41no—
231C22×Dic11—41no—
232C22×Dic11—41no—
233C22×Dic11—41no—
234C22×Dic11—41no—
235C22×Dic11—41no—
236C22×Dic11—41no—
237C22×Dic11C2×Q814yes—
238C22×Dic11C2×Q814yes—
239C22×Dic11#4114yes—
240C22×Dic11C2412yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2412yes—
246C22×Dic11C2412yes—
247C22×Dic11C2412yes—
248C2×Dic22—24no—
249C2×Dic22—22no—
250C2×Dic22—42no—
251C2×Dic22—42no—
252C2×Dic22—41no—
253C2×Dic22—41no—
254C11×C4⋊C4—22no—
255C11×C4⋊C4—24no—
256C11×C4⋊C4—24no—
257C11×C4⋊C4—24no—
258C11×C4⋊C4—41no—
259C11×C4⋊C4—41no—
260C11×C22⋊C4—24no—
261C11×C22⋊C4—24no—
262C42×C11—22no—
263C42×C11—22no—
264C42×C11—22no—
265C42×C11—22no—
266C22⋊Dic11—24no—
267C22⋊Dic11—24no—
268C4⋊Dic11—24no—
269C4⋊Dic11—24no—
270C4⋊Dic11—24no—
271C4⋊Dic11—22no—
272C4⋊Dic11—42no—
273C4⋊Dic11—41no—
274C4⋊Dic11—41no—
275C4⋊Dic11—42no—
276C4⋊Dic11C2×Q818yes—
277C4⋊Dic11C2×Q818yes—
278Dic11⋊C4—24no—
279Dic11⋊C4—24no—
280Dic11⋊C4—24no—
281Dic11⋊C4—24no—
282Dic11⋊C4—24no—
283Dic11⋊C4—42no—
284Dic11⋊C4—42no—
285Dic11⋊C4—42no—
286Dic11⋊C4—42no—
287Dic11⋊C4—42no—
288Dic11⋊C4—42no—
289Dic11⋊C4—42no—
290Dic11⋊C4—42no—
291C4×Dic11—24no—
292C4×Dic11—24no—
293C4×Dic11—42no—
294C4×Dic11—42no—
295C4×Dic11—42no—
296C4×Dic11—42no—
297C4×Dic11—42no—
298C4×Dic11—42no—
299#2855—111no—
300#2855D1111yescharacteristic
301#2851—112no—
302#2659—111no—
303#2659—111no—
304#2627—112no—
305#2586—112no—
306#2586—112no—
307#2585—112no—
308#2585—112no—
309#2520—112no—
310#2520—112no—
311#2462—112no—
312#2462—112no—
313#2329—111no—
314#2329—111no—
315#2313—112no—
316C4×C22⋊Q8—112no—
317C2×C4×C4⋊C4—111no—
318C23×C11—21no—
319C23×C11—21no—
320C23×C11—21no—
321C23×C11—21no—
322C23×C11C22×Q812yes—
323C23×C11C2×#4112yes—
324C23×C11C2×#4112yes—
325C23×C11C2511yescharacteristic
326Q8×C11—82no—
327C2×C4×C11—28no—
328C2×C4×C11—28no—
329C2×C4×C11—21no—
330C2×C4×C11—21no—
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—21no—
340C2×C4×C11—21no—
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×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—44no—
354C2×C4×C11C22×Q812yes—
355C2×C4×C11C22×Q812yes—
356C2×C4×C11C2×#4112yes—
357C2×C4×C11C2×#4112yes—
358C2×C4×C11H(5,𝔽2)12yes—
359C2×C4×C112−1+412yes—
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×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—44no—
382C2×Dic11—44no—
383C2×Dic11—44no—
384C2×Dic11—44no—
385C2×Dic11C22×Q814yes—
386C2×Dic11C22×Q814yes—
387C2×Dic11C2×#4114yes—
388Dic22—48no—
389Dic22—82no—
390C2×#125—112no—
391C2×C22⋊Q8—111no—
392C2×C22⋊Q8—112no—
393C2×C22⋊Q8C2×D1111yescharacteristic
394C2×C4×Q8—112no—
395C22×C4⋊C4—111no—
396C22×C4⋊C4—111no—
397C22×C42—111no—
398C22×C42—111no—
399C22×C42C2×D1111yescharacteristic
400#400—112no—
401#400—112no—
402#398—112no—
403#398—112no—
404#398—112no—
405#398—112no—
406#398—112no—
407#398—112no—
408#398—112no—
409#398—112no—
410#395—112no—
411#395—112no—
412#395—112no—
413#395—112no—
414#395—112no—
415#395—112no—
416#391—112no—
417#391—111no—
418#391—111no—
419#391—112no—
420#391—112no—
421#391C2×D1111yescharacteristic
422#391C2×D1111yescharacteristic
423#389—112no—
424#389—112no—
425#389—112no—
426#389—112no—
427#389—111no—
428#389—111no—
429#389—112no—
430#389C2×D1111yescharacteristic
431#389C2×D1111yescharacteristic
432#387—112no—
433#387—112no—
434#387—112no—
435#387—112no—
436#387—112no—
437#387—112no—
438#387—112no—
439#387—112no—
440#387—112no—
441#387—112no—
442#387—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#387C2×D1112yes—
453#387C2×D1112yes—
454#385—112no—
455#385—112no—
456#385—112no—
457#385C2×D1112yes—
458#382—112no—
459#381—112no—
460#381C2×D1112yes—
461#380—111no—
462#380—112no—
463#380—112no—
464#380—112no—
465#380C2×D1111yescharacteristic
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×C22⋊C4—112no—
474C4×C22⋊C4—112no—
475C2×#95—111no—
476C2×#95—111no—
477C22×C11—22no—
478C22×C11—22no—
479C22×C11—22no—
480C22×C11—22no—
481C22×C11—22no—
482C22×C11—22no—
483C22×C11#53314yes—
484C22×C11C23×Q811yescharacteristic
485C22×C11C22×#4111yescharacteristic
486C22×C11C22×#4111yescharacteristic
487C22×C11C2×H(5,𝔽2)11yescharacteristic
488C22×C11C2×2−1+411yescharacteristic
489C22×C11#58511yescharacteristic
490C22×C11#58511yescharacteristic
491C4×C11—22no—
492C4×C11—22no—
493C4×C11—22no—
494C4×C11—22no—
495C4×C11—22no—
496C4×C11—22no—
497C4×C11—42no—
498C4×C11—42no—
499C4×C11—42no—
500C4×C11—42no—
501Dic11—24no—
502Dic11—24no—
503Dic11—24no—
504Dic11—42no—
505Dic11—42no—
506Dic11—42no—
507Dic11—42no—
508Dic11—42no—
509C22×Q8—112no—
510C22×Q8—111no—
511C22×Q8C22×D1111yescharacteristic
512C23×C4—111no—
513C23×C4—111no—
514C23×C4—111no—
515C23×C4—111no—
516C23×C4C22×D1111yescharacteristic
517C23×C4C22×D1111yescharacteristic
518C23×C4C22×D1111yescharacteristic
519#125—444no—
520C22⋊Q8—24no—
521C22⋊Q8—228no—
522C22⋊Q8—224no—
523C4×Q8—444no—
524C2×C4⋊C4—118no—
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—112no—
532C2×C4⋊C4—112no—
533C2×C4⋊C4—112no—
534C2×C4⋊C4—111no—
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—111no—
545C2×C4⋊C4—111no—
546C2×C4⋊C4—112no—
547C2×C4⋊C4—112no—
548C2×C4⋊C4—224no—
549C2×C4⋊C4C22×D1112yes—
550C2×C4⋊C4C22×D1111yescharacteristic
551C2×C4⋊C4C22×D1112yes—
552C2×C4⋊C4C22×D1112yes—
553C2×C4⋊C4C22×D1111yescharacteristic
554C2×C4⋊C4C22×D1111yescharacteristic
555C2×C22⋊C4—112no—
556C2×C22⋊C4—112no—
557C2×C22⋊C4C22×D1112yes—
558C2×C22⋊C4C22×D1112yes—
559C2×C42—24no—
560C2×C42—112no—
561C2×C42—112no—
562C2×C42—112no—
563C2×C42—112no—
564C2×C42—112no—
565C2×C42—112no—
566C2×C42—112no—
567C2×C42—112no—
568C2×C42—442no—
569C2×C42—442no—
570C2×C42C22×D1111yescharacteristic
571C2×C42C22×D1111yescharacteristic
572C2×C42C22×D1111yescharacteristic
573C2×C42C22×D1111yescharacteristic
574#95—112no—
575#95—112no—
576#95—112no—
577#95—112no—
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#95C22×D1112yes—
600#95C22×D1112yes—
601#95C22×D1112yes—
602#95C22×D1112yes—
603#95C22×D1112yes—
604#95C22×D1112yes—
605#95C22×D1112yes—
606C2×C11—24no—
607C2×C11C2×#53311yescharacteristic
608C2×C11#345911yescharacteristic
609C2×C11#346111yescharacteristic
610C2×C11#349111yescharacteristic
611C2×C11#349211yescharacteristic
612C2×C11#350111yescharacteristic
613C2×C11#350211yescharacteristic
614C24C23×D1111yescharacteristic
615C2×Q8—22no—
616C2×Q8—41no—
617C2×Q8—41no—
618C2×Q8—224no—
619C2×Q8—222no—
620C2×Q8—442no—
621C2×Q8—442no—
622C2×Q8—441no—
623C2×Q8—441no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4—112no—
632C22×C4—112no—
633C22×C4—112no—
634C22×C4—114no—
635C22×C4—114no—
636C22×C4—114no—
637C22×C4—112no—
638C22×C4—112no—
639C22×C4—112no—
640C22×C4—112no—
641C22×C4—112no—
642C22×C4—222no—
643C22×C4—441no—
644C22×C4—441no—
645C22×C4—441no—
646C22×C4—441no—
647C22×C4—441no—
648C22×C4—441no—
649C22×C4—441no—
650C22×C4—441no—
651C22×C4#434114yes—
652C22×C4Q8×D1114yes—
653C22×C4C23×D1112yes—
654C22×C4C23×D1112yes—
655C22×C4C23×D1112yes—
656C22×C4C23×D1112yes—
657C22×C4C23×D1111yescharacteristic
658C22×C4C23×D1111yescharacteristic
659C22×C4C23×D1111yescharacteristic
660C22×C4C23×D1111yescharacteristic
661C22×C4C23×D1111yescharacteristic
662C22×C4C23×D1111yescharacteristic
663C4⋊C4—22no—
664C4⋊C4—24no—
665C4⋊C4—24no—
666C4⋊C4—24no—
667C4⋊C4—41no—
668C4⋊C4—41no—
669C4⋊C4—118no—
670C4⋊C4—118no—
671C4⋊C4—224no—
672C4⋊C4—224no—
673C4⋊C4—224no—
674C4⋊C4—224no—
675C4⋊C4—224no—
676C4⋊C4—224no—
677C4⋊C4—222no—
678C4⋊C4—224no—
679C4⋊C4—224no—
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—442no—
692C22⋊C4—24no—
693C22⋊C4—24no—
694C22⋊C4—224no—
695C22⋊C4—224no—
696C42—22no—
697C42—22no—
698C42—22no—
699C42—22no—
700C42—224no—
701C42—224no—
702C42—442no—
703C42—442no—
704C42—442no—
705C42—442no—
706C42—442no—
707C42—442no—
708C11#3501311yescharacteristic, complemented, Sylow
709C23—21no—
710C23—21no—
711C23—21no—
712C23—21no—
713C23C2×#434112yes—
714C23C2×Q8×D1112yes—
715C23#41×D1112yes—
716C23C24×D1111yescharacteristic
717Q8—82no—
718Q8—448no—
719Q8—882no—
720C2×C4—28no—
721C2×C4—28no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—44no—
747C2×C4—114no—
748C2×C4—114no—
749C2×C4—114no—
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—222no—
762C2×C4—222no—
763C2×C4—222no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—222no—
767C2×C4—222no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—444no—
772C2×C4—444no—
773C2×C4—444no—
774C2×C4—444no—
775C2×C4C2×#434112yes—
776C2×C4C2×#434112yes—
777C2×C4C2×Q8×D1112yes—
778C2×C4C2×Q8×D1112yes—
779C2×C4#6704212yes—
780C2×C4#6704312yes—
781C22—22no—
782C22—22no—
783C22—22no—
784C22—22no—
785C22—22no—
786C22—22no—
787C22#1062315314yes—
788C22C22×#434111yescharacteristic
789C22C22×Q8×D1111yescharacteristic
790C22C2×#41×D1111yescharacteristic
791C22C2×#6704211yescharacteristic
792C22C2×#6704311yescharacteristic
793C22#1062345311yescharacteristic
794C22#1062345311yescharacteristic
795C4—22no—
796C4—22no—
797C4—22no—
798C4—22no—
799C4—22no—
800C4—22no—
801C4—42no—
802C4—42no—
803C4—42no—
804C4—42no—
805C4—224no—
806C4—224no—
807C4—224no—
808C4—442no—
809C4—442no—
810C4—442no—
811C4—442no—
812C4—442no—
813C2—24no—
814C2C2×#1062315311yescharacteristic
815C2#1308202611yescharacteristic
816C2#1308204511yescharacteristic
817C2#1308231211yescharacteristic
818C2#1308232211yescharacteristic
819C2#1308241711yescharacteristic
820C2#1308242111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2855C2
prime radicalC24×C11C24
hypercenter#2855D11
hypocenterC11#35013
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2855

Complements

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

NH ≅ G/Ntype
6. #13074026C2semidirect
7. #13074025C2semidirect
8. #13074012C2semidirect
9. #13074010C2semidirect
10. #13073310C2semidirect
11. #13073302C2semidirect
12. #13072604C2semidirect
13. #13072596C2semidirect
134. C2×C4⋊Dic11Q8semidirect
708. C11#35013semidirect

Maximal subgroups

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

subgroupindex
#130769552
#130769222
#130747332
#130747322
#130744332
#130740262
#130740252
#130740122
#130740102
#130733102
#130733022
#130726042
#130725962
#130713512
#130713462
#130712172
#130711482
C2×C4×C4⋊Dic112
C11×#28552
#3501311