Finite Group Databasebeta

← #14916823

Subgroups — #14916823

Order 2816.

2090 conjugacy classes of subgroups.

The subgroup lattice has 830 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#13071743C212yesmaximal, complemented
6#13071731C212yesmaximal, complemented
7#13071570C212yesmaximal, complemented
8#13071564C212yesmaximal, complemented
9#13071543C212yesmaximal, complemented
10#13071543C212yesmaximal, complemented
11#13071425C212yesmaximal, complemented
12#13071416C212yesmaximal, complemented
13#13071407C212yesmaximal, complemented
14#13071403C212yesmaximal, complemented
15#13071235C212yesmaximal, complemented
16#13071220C212yesmaximal, complemented
17#13071018C211yesmaximal, 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×Dic11⋊C4C2212yes—
27C22×C4×Dic11C2211yescharacteristic
28#10623131C4116yescomplemented
29C2×#66943C2211yescharacteristic
30C2×#66940C2211yescharacteristic
31C2×#66932C2212yes—
32C2×#66930C2212yes—
33C2×#66930C2211yescharacteristic
34C2×#66930C2211yescharacteristic
35C2×#66930C2212yes—
36C11×#390C2212yes—
37C11×#388C2212yes—
38C11×#387C2212yes—
39C11×#386C2212yes—
40C11×#386C2212yes—
41C11×#385C2212yes—
42C11×#381C2211yescharacteristic
43C11×#380C2211yescharacteristic
44#10622834C2212yes—
45#10622833C2212yes—
46#10622833C2212yes—
47#10622825C2211yescharacteristic
48#10622824C2211yescharacteristic
49#10622823C2212yes—
50C4×C22⋊Dic11C2212yes—
51C4×C22⋊Dic11C2212yes—
52#10622594C2212yes—
53#10622591C2212yes—
54#10622591C2212yes—
55#10622589C2212yes—
56#10622589C2212yes—
57C4⋊C4×Dic11C2212yes—
58C4⋊C4×Dic11C2212yes—
59#10622585C2212yes—
60#10622585C2212yes—
61#10622564C2212yes—
62#10622563C2212yes—
63#10622559C2212yes—
64#10622558C2212yes—
65#10622558C2212yes—
66#10622558C2212yes—
67#10622558C2212yes—
68#10622558C2212yes—
69#10622557C2212yes—
70#10622557C2212yes—
71#10622557C2212yes—
72#10622557C2212yes—
73#10622557C2212yes—
74#10622555C2211yescharacteristic
75#10622555C2211yescharacteristic
76#10622555C2212yes—
77#10622555C2212yes—
78#10622555C2212yes—
79C22⋊C4×Dic11C2212yes—
80C22⋊C4×Dic11C2212yes—
81C22⋊C4×Dic11C2212yes—
82C4×C4⋊Dic11C2212yes—
83#10622546C2212yes—
84C4×Dic11⋊C4C2212yes—
85C4×Dic11⋊C4C2212yes—
86#10622268C2212yes—
87#10622268C2212yes—
88#10622267C2212yes—
89#10622267C2212yes—
90#10622266C2212yes—
91#10622266C2212yes—
92#10622265C2212yes—
93#10622264C2212yes—
94#10622263C2211yescharacteristic
95#10622263C2211yescharacteristic
96#10622263C2212yes—
97#10622263C2212yes—
98#10622262C2212yes—
99#10622262C2212yes—
100#10622262C2212yes—
101#10622262C2212yes—
102#10622261C2211yescharacteristic
103#10622261C2211yescharacteristic
104#10622260C2212yes—
105#10622260C2212yes—
106#10622259C2212yes—
107#10622259C2212yes—
108C22×D4×C11C2312yes—
109C22×D4×C11C2311yescharacteristic
110C23×C4×C11C2312yes—
111C23×C4×C11C2311yescharacteristic
112C23×Dic11C2311yescharacteristic
113C23×Dic11C2312yes—
114C23×Dic11C2312yes—
115C23×Dic11C2311yescharacteristic
116C22×Dic22C2311yescharacteristic
117C11×#121C2×C418yes—
118C2×C11×C4⋊C4C2312yes—
119C2×C11×C4⋊C4C2312yes—
120C2×C11×C4⋊C4C2311yescharacteristic
121C2×C11×C22⋊C4C2311yescharacteristic
122C2×C11×C22⋊C4C2311yescharacteristic
123C2×C11×C22⋊C4C2312yes—
124C2×C11×C22⋊C4C2312yes—
125C2×C11×C22⋊C4C2312yes—
126C2×C11×C22⋊C4C2312yes—
127C2×C11×C22⋊C4C2312yes—
128C2×C42×C11C2312yes—
129C2×C22⋊Dic11C2311yescharacteristic
130C2×C22⋊Dic11C2311yescharacteristic
131C2×C22⋊Dic11C2312yes—
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⋊C4—44no—
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×Dic11⋊C4C2312yes—
160C2×Dic11⋊C4C2312yes—
161C2×Dic11⋊C4C2312yes—
162C2×C4×Dic11C2×C418yescomplemented
163C2×C4×Dic11C2312yes—
164C2×C4×Dic11C2312yes—
165C2×C4×Dic11C2312yes—
166C2×C4×Dic11C2312yes—
167C2×C4×Dic11C2312yes—
168C2×C4×Dic11C2312yes—
169C2×C4×Dic11C2312yes—
170C2×C4×Dic11C2312yes—
171C2×C4×Dic11C2312yes—
172C2×C4×Dic11C2311yescharacteristic
173C2×C4×Dic11C2312yes—
174C2×C4×Dic11C2311yescharacteristic
175C2×C4×Dic11C2311yescharacteristic
176C2×C4×Dic11C2311yescharacteristic
177#66943C2×C418yescomplemented
178#66940C2×C418yescomplemented
179#66932C2×C4116yescomplemented
180#66930—42no—
181#66930—44no—
182#66930—42no—
183#66930C2×C4116yescomplemented
184C11×#95C2312yes—
185C11×#95C2312yes—
186C11×#95C2311yescharacteristic
187C11×#95C2312yes—
188C11×#95C2311yescharacteristic
189C11×#95C2312yes—
190C11⋊#95C2312yes—
191C11⋊#95C2312yes—
192C11⋊#95C2312yes—
193C11⋊#95C2312yes—
194C11⋊#95C2312yes—
195C11⋊#95C2312yes—
196C11⋊#95C2312yes—
197C11⋊#95C2311yescharacteristic
198C11⋊#95C2311yescharacteristic
199C11⋊#95C2312yes—
200C11⋊#95C2312yes—
201C11⋊#95C2312yes—
202C11⋊#95C2312yes—
203C11⋊#95C2312yes—
204C11⋊#95C2312yes—
205C11⋊#95C2312yes—
206C11⋊#95C2312yes—
207C11⋊#95C2312yes—
208C11⋊#95C2312yes—
209C11⋊#95C2312yes—
210#34385—111nomaximal, Sylow
211C24×C11C2411yescharacteristic
212C24×C11C2412yes—
213C2×D4×C11—42no—
214C2×D4×C11—42no—
215C2×D4×C11—42no—
216C2×D4×C11C22×C414yes—
217C2×D4×C11C22×C418yes—
218C22×C4×C11—42no—
219C22×C4×C11—42no—
220C22×C4×C11—42no—
221C22×C4×C11—42no—
222C22×C4×C11C22×C414yes—
223C22×C4×C11C2412yes—
224C22×C4×C11C2412yes—
225C22×C4×C11C2412yes—
226C22×C4×C11C2412yes—
227C22×C4×C11C2411yescharacteristic
228C22×C4×C11C2412yes—
229C22×C4×C11C2411yescharacteristic
230C22×Dic11—22no—
231C22×Dic11—24no—
232C22×Dic11—22no—
233C22×Dic11—24no—
234C22×Dic11—42no—
235C22×Dic11—42no—
236C22×Dic11—42no—
237C22×Dic11—42no—
238C22×Dic11C22×C418yes—
239C22×Dic11C22×C414yes—
240C22×Dic11C22×C414yes—
241C22×Dic11C2412yes—
242C22×Dic11C2412yes—
243C22×Dic11C2412yes—
244C22×Dic11C2412yes—
245C22×Dic11C2411yescharacteristic
246C22×Dic11C2411yescharacteristic
247C22×Dic11C2412yes—
248C22×Dic11C2411yescharacteristic
249C22×Dic11C2412yes—
250C22×Dic11C2411yescharacteristic
251C2×Dic22—42no—
252C2×Dic22C22×C414yes—
253C11×C4⋊C4—42no—
254C11×C4⋊C4—42no—
255C11×C4⋊C4C22×C414yes—
256C11×C22⋊C4—41no—
257C11×C22⋊C4—42no—
258C11×C22⋊C4—41no—
259C11×C22⋊C4—42no—
260C11×C22⋊C4—42no—
261C11×C22⋊C4—42no—
262C11×C22⋊C4C22×C418yes—
263C42×C11—42no—
264C22⋊Dic11—41no—
265C22⋊Dic11—41no—
266C22⋊Dic11—42no—
267C22⋊Dic11—42no—
268C22⋊Dic11—42no—
269C22⋊Dic11—42no—
270C22⋊Dic11C22×C418yes—
271C22⋊Dic11C22×C418yes—
272C22⋊Dic11C22×C418yes—
273C22⋊Dic11C22×C418yes—
274C4⋊Dic11—42no—
275C4⋊Dic11—42no—
276C4⋊Dic11C22×C418yes—
277C4⋊Dic11C22×C414yes—
278Dic11⋊C4—24no—
279Dic11⋊C4—24no—
280Dic11⋊C4—24no—
281Dic11⋊C4—24no—
282Dic11⋊C4—42no—
283Dic11⋊C4—42no—
284Dic11⋊C4—42no—
285Dic11⋊C4—42no—
286Dic11⋊C4—42no—
287Dic11⋊C4—42no—
288Dic11⋊C4C22×C418yes—
289Dic11⋊C4C22×C418yes—
290Dic11⋊C4C22×C418yes—
291C4×Dic11—42no—
292C4×Dic11—42no—
293C4×Dic11—42no—
294C4×Dic11—42no—
295C4×Dic11—42no—
296C4×Dic11—42no—
297C4×Dic11—42no—
298C4×Dic11—42no—
299C4×Dic11—42no—
300C4×Dic11C22×C414yes—
301C4×Dic11C22×C418yes—
302C4×Dic11C22×C414yes—
303C4×Dic11C22×C414yes—
304C4×Dic11C22×C414yes—
305C2×#529—111no—
306#2378—111no—
307#2378—111no—
308#2377—111no—
309#2377D1111yescharacteristic
310#2373—112no—
311#2373—112no—
312#2355—112no—
313#2354—112no—
314#2352—112no—
315#2352—112no—
316#2337—112no—
317#2336—112no—
318#2335—112no—
319#2335—112no—
320#2317—112no—
321#2314—112no—
322#2285—111no—
323#2283—111no—
324C23×C11—21no—
325C23×C11—22no—
326C23×C11—21no—
327C23×C11—22no—
328C23×C11—22no—
329C23×C11—22no—
330C23×C11—22no—
331C23×C11—22no—
332C23×C11—22no—
333C23×C11—22no—
334C23×C11C23×C414yes—
335C23×C11C23×C412yes—
336C23×C11C2511yescharacteristic
337D4×C11—44no—
338D4×C11—48no—
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×C11—22no—
350C2×C4×C11—22no—
351C2×C4×C11—22no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—44no—
356C2×C4×C11—84no—
357C2×C4×C11C23×C412yes—
358C2×C4×C11C23×C412yes—
359C2×C4×C11C23×C414yes—
360C2×Dic11—21no—
361C2×Dic11—22no—
362C2×Dic11—21no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—22no—
366C2×Dic11—22no—
367C2×Dic11—22no—
368C2×Dic11—28no—
369C2×Dic11—216no—
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—44no—
383C2×Dic11—84no—
384C2×Dic11C23×C412yes—
385C2×Dic11C23×C412yes—
386C2×Dic11C23×C412yes—
387C2×Dic11C23×C414yes—
388C2×Dic11C23×C414yes—
389C2×Dic11C23×C412yes—
390C2×Dic11H(5,𝔽2)12yes—
391C2×Dic112−1+412yes—
392Dic22—44no—
393#529—1116no—
394C2×#126—112no—
395C2×#125—111no—
396C2×#124—111no—
397C2×#123—112no—
398C2×C22⋊Q8—111no—
399C2×#121C2×D1111yescharacteristic
400C2×C4×Q8—111no—
401C2×C4×D4—111no—
402C2×C4×D4—112no—
403C2×#117—112no—
404C2×#117—112no—
405C2×#117—111no—
406C2×#117—111no—
407C22×C4⋊C4—112no—
408C22×C42—111no—
409#391—112no—
410#391—112no—
411#390—112no—
412#390C2×D1112yes—
413#389—112no—
414#389—112no—
415#389—112no—
416#389—112no—
417#388—112no—
418#388—112no—
419#388—112no—
420#388—112no—
421#388—112no—
422#388—112no—
423#388—112no—
424#388—112no—
425#388—112no—
426#388—112no—
427#388—112no—
428#388C2×D1112yes—
429#387—112no—
430#387—112no—
431#387—112no—
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#387C2×D1112yes—
441#386—112no—
442#386—112no—
443#386C2×D1112yes—
444#386C2×D1112yes—
445#385—112no—
446#385—112no—
447#385—112no—
448#385C2×D1112yes—
449#384—112no—
450#384—112no—
451#383—112no—
452#382—111no—
453#382—111no—
454#382—112no—
455#382—112no—
456#381—111no—
457#381C2×D1111yescharacteristic
458#380—111no—
459#380—112no—
460#380—112no—
461#380—111no—
462#380—111no—
463#380—112no—
464#380C2×D1111yescharacteristic
465C4×C4⋊C4—112no—
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×C4⋊C4—112no—
474C4×C22⋊C4—112no—
475C4×C22⋊C4—112no—
476C4×C22⋊C4—112no—
477C4×C22⋊C4—112no—
478C4×C22⋊C4—112no—
479#376—111no—
480#376—111no—
481C22×C11—22no—
482C22×C11—24no—
483C22×C11—22no—
484C22×C11—22no—
485C22×C11—24no—
486C22×C11—24no—
487C22×C11—42no—
488C22×C11—42no—
489C22×C11—42no—
490C22×C11—42no—
491C22×C11—42no—
492C22×C11—42no—
493C22×C11C24×C411yescharacteristic
494C22×C11C2×H(5,𝔽2)11yescharacteristic
495C22×C11C2×2−1+411yescharacteristic
496C22×C11#58512yes—
497C22×C11#58512yes—
498C4×C11—22no—
499C4×C11—22no—
500C4×C11—24no—
501C4×C11—42no—
502C4×C11—42no—
503C4×C11—42no—
504C4×C11—42no—
505Dic11—22no—
506Dic11—24no—
507Dic11—24no—
508Dic11—22no—
509Dic11—22no—
510Dic11—42no—
511Dic11—42no—
512Dic11—42no—
513Dic11—42no—
514Dic11#52014yes—
515C22×Q8—111no—
516C22×D4C22×D1112yes—
517C22×D4C22×D1111yescharacteristic
518C23×C4—112no—
519C23×C4—111no—
520C23×C4—111no—
521C23×C4—112no—
522C23×C4C22×D1112yes—
523C23×C4C22×D1111yescharacteristic
524#126—1116no—
525#125—118no—
526#124—118no—
527#123—1116no—
528C22⋊Q8—118no—
529#121C4×D1118yes—
530C4×Q8—118no—
531C4×D4—118no—
532C4×D4—1116no—
533#117—1116no—
534#117—442no—
535#117—444no—
536#117—442no—
537C2×C4⋊C4—112no—
538C2×C4⋊C4—112no—
539C2×C4⋊C4—111no—
540C2×C4⋊C4—112no—
541C2×C4⋊C4—112no—
542C2×C4⋊C4—112no—
543C2×C4⋊C4—112no—
544C2×C4⋊C4—112no—
545C2×C4⋊C4—112no—
546C2×C4⋊C4—112no—
547C2×C4⋊C4—112no—
548C2×C4⋊C4—112no—
549C2×C4⋊C4—112no—
550C2×C4⋊C4—112no—
551C2×C4⋊C4—112no—
552C2×C4⋊C4—112no—
553C2×C4⋊C4—112no—
554C2×C4⋊C4—444no—
555C2×C4⋊C4C22×D1112yes—
556C2×C4⋊C4C22×D1112yes—
557C2×C4⋊C4C22×D1111yescharacteristic
558C2×C22⋊C4—112no—
559C2×C22⋊C4—112no—
560C2×C22⋊C4—112no—
561C2×C22⋊C4—112no—
562C2×C22⋊C4—111no—
563C2×C22⋊C4—111no—
564C2×C22⋊C4—112no—
565C2×C22⋊C4—112no—
566C2×C22⋊C4—112no—
567C2×C22⋊C4—112no—
568C2×C22⋊C4C22×D1111yescharacteristic
569C2×C22⋊C4C22×D1111yescharacteristic
570C2×C22⋊C4C22×D1112yes—
571C2×C22⋊C4C22×D1112yes—
572C2×C22⋊C4C22×D1112yes—
573C2×C22⋊C4C22×D1112yes—
574C2×C22⋊C4C22×D1112yes—
575C2×C42—118no—
576C2×C42—111no—
577C2×C42—112no—
578C2×C42—111no—
579C2×C42—111no—
580C2×C42—111no—
581C2×C42—112no—
582C2×C42—112no—
583C2×C42—112no—
584C2×C42—112no—
585C2×C42—112no—
586C2×C42—112no—
587C2×C42—112no—
588C2×C42—112no—
589C2×C42—112no—
590C2×C42C22×D1112yes—
591#95—112no—
592#95—112no—
593#95—111no—
594#95—111no—
595#95—112no—
596#95—112no—
597#95—112no—
598#95—112no—
599#95—112no—
600#95—112no—
601#95—112no—
602#95—112no—
603#95—112no—
604#95—112no—
605#95—112no—
606#95—112no—
607#95—112no—
608#95—112no—
609#95—112no—
610#95—112no—
611#95C22×D1111yescharacteristic
612#95C22×D1111yescharacteristic
613#95C22×D1112yes—
614#95C22×D1112yes—
615#95C22×D1112yes—
616#95C22×D1112yes—
617C2×C11—42no—
618C2×C11—44no—
619C2×C11C2×#52011yescharacteristic
620C2×C11#342811yescharacteristic
621C2×C11#342811yescharacteristic
622C2×C11#356212yes—
623C2×C11#356512yes—
624C24C23×D1111yescharacteristic
625C24C23×D1112yes—
626C2×Q8—114no—
627C2×Q8—442no—
628C2×D4—42no—
629C2×D4—42no—
630C2×D4—42no—
631C2×D4C2×C4×D1118yes—
632C2×D4C2×C4×D1114yes—
633C22×C4—42no—
634C22×C4—42no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—111no—
638C22×C4—114no—
639C22×C4—118no—
640C22×C4—111no—
641C22×C4—111no—
642C22×C4—112no—
643C22×C4—111no—
644C22×C4—112no—
645C22×C4—114no—
646C22×C4—112no—
647C22×C4—112no—
648C22×C4—112no—
649C22×C4—112no—
650C22×C4—224no—
651C22×C4—222no—
652C22×C4—224no—
653C22×C4—222no—
654C22×C4—442no—
655C22×C4—442no—
656C22×C4—442no—
657C22×C4—442no—
658C22×C4C2×C4×D1114yes—
659C22×C4C23×D1112yes—
660C22×C4C23×D1112yes—
661C22×C4C23×D1112yes—
662C22×C4C23×D1112yes—
663C22×C4C23×D1111yescharacteristic
664C22×C4C23×D1112yes—
665C22×C4C23×D1111yescharacteristic
666C4⋊C4—42no—
667C4⋊C4—42no—
668C4⋊C4—118no—
669C4⋊C4—118no—
670C4⋊C4—114no—
671C4⋊C4—118no—
672C4⋊C4—118no—
673C4⋊C4—224no—
674C4⋊C4—224no—
675C4⋊C4—224no—
676C4⋊C4—224no—
677C4⋊C4—442no—
678C4⋊C4—442no—
679C4⋊C4—442no—
680C4⋊C4—442no—
681C4⋊C4—442no—
682C4⋊C4—442no—
683C4⋊C4—442no—
684C4⋊C4—442no—
685C4⋊C4C2×C4×D1114yes—
686C22⋊C4—41no—
687C22⋊C4—42no—
688C22⋊C4—41no—
689C22⋊C4—42no—
690C22⋊C4—42no—
691C22⋊C4—42no—
692C22⋊C4—118no—
693C22⋊C4—118no—
694C22⋊C4—118no—
695C22⋊C4—118no—
696C22⋊C4—441no—
697C22⋊C4—442no—
698C22⋊C4—441no—
699C22⋊C4—442no—
700C22⋊C4—442no—
701C22⋊C4—442no—
702C22⋊C4C2×C4×D1118yes—
703C42—42no—
704C42—114no—
705C42—114no—
706C42—114no—
707C42—114no—
708C42—118no—
709C42—442no—
710C42—442no—
711C42—442no—
712C42—442no—
713C42—442no—
714C42—442no—
715C42—442no—
716C42—442no—
717C42—442no—
718C11#3438511yescharacteristic, complemented, Sylow
719C23—21no—
720C23—22no—
721C23—22no—
722C23—22no—
723C23—22no—
724C23—22no—
725C23—22no—
726C23—22no—
727C23—21no—
728C23—22no—
729C23C22×C4×D1114yes—
730C23C22×C4×D1112yes—
731C23C24×D1111yescharacteristic
732Q8—444no—
733D4—44no—
734D4—48no—
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—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—44no—
752C2×C4—84no—
753C2×C4—112no—
754C2×C4—112no—
755C2×C4—112no—
756C2×C4—112no—
757C2×C4—112no—
758C2×C4—112no—
759C2×C4—114no—
760C2×C4—114no—
761C2×C4—228no—
762C2×C4—2216no—
763C2×C4—221no—
764C2×C4—222no—
765C2×C4—222no—
766C2×C4—222no—
767C2×C4—222no—
768C2×C4—222no—
769C2×C4—221no—
770C2×C4—222no—
771C2×C4—222no—
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—444no—
784C2×C4—884no—
785C2×C4C22×C4×D1112yes—
786C2×C4C22×C4×D1112yes—
787C2×C4C22×C4×D1114yes—
788C22—22no—
789C22—24no—
790C22—22no—
791C22—22no—
792C22—24no—
793C22—24no—
794C22—42no—
795C22—42no—
796C22—42no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22C23×C4×D1111yescharacteristic
801C22D11×H(5,𝔽2)11yescharacteristic
802C22#1062345512yes—
803C22#1062345512yes—
804C22D11×2−1+411yescharacteristic
805C4—22no—
806C4—22no—
807C4—24no—
808C4—42no—
809C4—42no—
810C4—42no—
811C4—42no—
812C4—114no—
813C4—222no—
814C4—224no—
815C4—222no—
816C4—222no—
817C4—224no—
818C4—442no—
819C4—442no—
820C4—442no—
821C4—442no—
822C2—42no—
823C2—44no—
824C2D11×#52011yescharacteristic
825C2#1308181411yescharacteristic
826C2#1308181411yescharacteristic
827C2#1308319312yes—
828C2#1308325012yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2377C2
socle, cosocleC23×C11C25
prime radicalC2×C11×#121C22
hypercenter#2377D11
hypocenterC11#34385
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. #13071743C2semidirect
6. #13071731C2semidirect
7. #13071570C2semidirect
8. #13071564C2semidirect
9. #13071543C2semidirect
10. #13071543C2semidirect
11. #13071425C2semidirect
12. #13071416C2semidirect
13. #13071407C2semidirect
14. #13071403C2semidirect
15. #13071235C2semidirect
16. #13071220C2semidirect
17. #13071018C2semidirect
18. #13071007C2semidirect
28. #10623131C4semidirect
140. #66988C2×C4semidirect
142. D4×Dic11C2×C4semidirect
147. #66977C2×C4semidirect
162. C2×C4×Dic11C2×C4semidirect
177. #66943C2×C4semidirect
178. #66940C2×C4semidirect
179. #66932C2×C4semidirect
183. #66930C2×C4semidirect
718. C11#34385semidirect

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
#130717432
#130717312
#130715702
#130715642
#130715432
#130714252
#130714162
#130714072
#130714032
#130712352
#130712202
#130710182
#130710072
C11×#23772
#3438511