Finite Group Databasebeta

← #14916541

Subgroups — #14916541

Order 2816.

2714 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623359C211yesmaximal, characteristic
2#13071766C212yesmaximal, complemented
3#13071759C212yesmaximal, complemented
4#13071599C212yesmaximal, complemented
5#13071597C212yesmaximal, complemented
6#13071546C212yesmaximal, complemented
7#13071538C212yesmaximal, complemented
8C4⋊C4×C22⋊D11C212yesmaximal, complemented
9#13071512C212yesmaximal, complemented
10#13071348C214yesmaximal, complemented
11#13071318C214yesmaximal, complemented
12#13071223C212yesmaximal, complemented
13#13071208C211yesmaximal, characteristic, complemented
14D11×#380C212yesmaximal, complemented
15C11×#2311C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×C4×D11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic, complemented
19C22×C11×C4⋊C4C2211yescharacteristic, complemented
20#10623359C4116yescomplemented
21C2×#66999C2212yes—
22C2×#66991C2212yes—
23C2×#66990C2211yescharacteristic
24C2×#66990C2211yescharacteristic
25C2×#66988C2211yescharacteristic
26C2×#66988C2211yescharacteristic
27C2×C4×C22⋊D11C2214yes—
28C2×C4×C22⋊D11C2212yes—
29C2×C4×C22⋊D11C2212yes—
30C2×#66979C2211yescharacteristic
31C2×#66979C2211yescharacteristic, complemented
32C22×C4⋊Dic11C2211yescharacteristic, complemented
33C2×C4⋊C4×D11C2212yes—
34C2×C4⋊C4×D11C2212yes—
35C2×(C22⋊D11)⋊C4C2214yes—
36C2×C22⋊C4×D11C2214yes—
37C11×#391C2212yescomplemented
38C11×#390C2212yes—
39C11×#386C2212yes—
40C11×#386C2212yescomplemented
41C11×#380C2212yes—
42C11×#380C2212yescomplemented
43#10622843C2212yescomplemented
44#10622834C2212yes—
45#10622833C2212yes—
46#10622833C2212yescomplemented
47#10622825C2212yes—
48#10622825C2212yescomplemented
49#10622823C2214yescomplemented
50#10622602C2214yes—
51#10622600C2212yes—
52#10622600C2212yes—
53#10622590C2212yescomplemented
54#10622589C2212yescomplemented
55C4⋊C4×Dic11C2212yescomplemented
56C4⋊C4×Dic11C2212yescomplemented
57#10622585C2214yescomplemented
58#10622569C2214yes—
59#10622569C2214yes—
60#10622559C2214yescomplemented
61#10622558C2214yes—
62#10622558C2214yescomplemented
63#10622557C2214yes—
64#10622557C2214yescomplemented
65#10622555C2214yes—
66C4×(C2×D11)⋊C4C2214yes—
67#10622546C2214yescomplemented
68#10622281C2214yes—
69#10622280C2214yes—
70#10622279C2214yes—
71D11×#95C2214yes—
72#10622267C2214yescomplemented
73#10622266C2214yescomplemented
74#10622265C2214yescomplemented
75#10622260C2214yescomplemented
76C24×D11C2311yescharacteristic
77C2×C11×#41—42no—
78C2×C11×#41—42no—
79C2×C11×#41C2×C418yescomplemented
80C22×Q8×C11C2311yescharacteristic
81C22×D4×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2312yes—
88C22×C22⋊D11C2312yes—
89C22×C22⋊D11C2312yes—
90C23×Dic11C2312yes—
91C23×Dic11C2311yescharacteristic
92C22×C4×D11—42no—
93C22×C4×D11—42no—
94C22×C4×D11C2×C418yescomplemented
95C22×C4×D11C2312yes—
96C22×C4×D11C2314yes—
97C22×C4×D11C2314yes—
98C22×C4×D11C2312yes—
99C11×#117—42no—
100C2×C11×C4⋊C4—42no—
101C2×C11×C4⋊C4C2312yes—
102C2×C11×C4⋊C4C2312yes—
103C2×C11×C4⋊C4C2312yes—
104C2×C11×C22⋊C4C2314yes—
105C2×C11×C22⋊C4C2314yes—
106C2×C11×C22⋊C4C2312yes—
107C2×C42×C11C2312yes—
108C2×C22⋊Dic11C2314yes—
109C2×C22⋊Dic11C2312yes—
110C2×C22⋊Dic11C2314yes—
111C2×C22⋊Dic11C2311yescharacteristic
112C2×C22⋊Dic11C2311yescharacteristic
113C2×C22⋊Dic11C2312yes—
114C2×C22⋊Dic11C2312yes—
115#66999C2×C4116yescomplemented
116#66991C2×C4116yescomplemented
117#66990C2×C418yescomplemented
118#66990C2×C418yescomplemented
119#66988C2×C418yescomplemented
120#66988C2×C418yescomplemented
121C4×C22⋊D11—48no—
122C4×C22⋊D11C2×C4116yescomplemented
123C4×C22⋊D11C2×C4116yescomplemented
124C2×(C2×D11)⋊C4C2314yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2312yes—
127C2×(C2×D11)⋊C4C2312yes—
128#66979—42no—
129#66979C2×C418yescomplemented
130C2×C4⋊Dic11—42no—
131C2×C4⋊Dic11C2312yes—
132C2×C4⋊Dic11C2312yes—
133C2×C4⋊Dic11C2312yes—
134C2×C4⋊Dic11C2312yes—
135C2×Dic11⋊C4C2314yes—
136C2×Dic11⋊C4C2314yes—
137C2×Dic11⋊C4C2314yes—
138C2×Dic11⋊C4C2314yes—
139C2×Dic11⋊C4C2312yes—
140C2×Dic11⋊C4C2312yes—
141C2×C4×Dic11C2314yes—
142C2×C4×Dic11C2312yes—
143C2×C4×Dic11C2314yes—
144C2×C4×Dic11C2312yes—
145C4⋊C4×D11—44no—
146C4⋊C4×D11—44no—
147(C22⋊D11)⋊C4—48no—
148C22⋊C4×D11—48no—
149C11×#95C2314yes—
150C11×#95C2314yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159#34360—111nomaximal, Sylow
160C24×C11C2411yescharacteristic
161C24×C11C2411yescharacteristic
162C24×C11C2411yescharacteristic
163C23×D11—24no—
164C23×D11—24no—
165C23×D11—41no—
166C23×D11—41no—
167C23×D11C22×C414yes—
168C23×D11C2412yes—
169C11×#41—416no—
170C2×Q8×C11—41no—
171C2×Q8×C11—41no—
172C2×Q8×C11C22×C414yes—
173C2×D4×C11—41no—
174C2×D4×C11—41no—
175C2×D4×C11—41no—
176C2×D4×C11—41no—
177C2×D4×C11—41no—
178C2×D4×C11—41no—
179C2×D4×C11C22×C414yes—
180C2×D4×C11C22×C414yes—
181C2×D4×C11C22×C414yes—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—44no—
189C22×C4×C11—42no—
190C22×C4×C11C22×C414yes—
191C22×C4×C11C22×C414yes—
192C22×C4×C11C22×C414yes—
193C22×C4×C11C2414yes—
194C22×C4×C11C2414yes—
195C22×C4×C11C2411yescharacteristic
196C22×C4×C11C2411yescharacteristic
197C22×C4×C11C2411yescharacteristic
198C22×C4×C11C2411yescharacteristic
199C2×C22⋊D11—24no—
200C2×C22⋊D11—24no—
201C2×C22⋊D11—24no—
202C2×C22⋊D11—24no—
203C2×C22⋊D11C22×C418yes—
204C2×C22⋊D11C22×C418yes—
205C22×Dic11—41no—
206C22×Dic11—41no—
207C22×Dic11—44no—
208C22×Dic11—42no—
209C22×Dic11C22×C414yes—
210C22×Dic11C2414yes—
211C22×Dic11C2414yes—
212C22×Dic11C2412yes—
213C22×Dic11C2412yes—
214C22×Dic11C2412yes—
215C2×C4×D11—28no—
216C2×C4×D11—28no—
217C2×C4×D11—24no—
218C2×C4×D11—24no—
219C2×C4×D11—42no—
220C2×C4×D11—42no—
221C2×C4×D11—44no—
222C2×C4×D11—44no—
223C2×C4×D11—44no—
224C2×C4×D11—44no—
225C2×C4×D11—416no—
226C2×C4×D11C22×C418yes—
227C2×C4×D11C22×C418yes—
228C11×C4⋊C4—24no—
229C11×C4⋊C4—24no—
230C11×C4⋊C4—42no—
231C11×C22⋊C4—44no—
232C11×C22⋊C4—44no—
233C11×C22⋊C4—42no—
234C42×C11—42no—
235C22⋊Dic11—44no—
236C22⋊Dic11—42no—
237C22⋊Dic11—44no—
238C22⋊Dic11C22×C414yes—
239C22⋊Dic11C22×C414yes—
240C22⋊Dic11C22×C418yes—
241C22⋊Dic11C22×C418yes—
242(C2×D11)⋊C4—28no—
243(C2×D11)⋊C4—28no—
244(C2×D11)⋊C4C22×C418yes—
245(C2×D11)⋊C4C22×C418yes—
246C4⋊Dic11—24no—
247C4⋊Dic11—24no—
248C4⋊Dic11—42no—
249C4⋊Dic11C22×C418yes—
250Dic11⋊C4—44no—
251Dic11⋊C4—44no—
252Dic11⋊C4—44no—
253Dic11⋊C4—44no—
254Dic11⋊C4C22×C418yes—
255Dic11⋊C4C22×C418yes—
256C4×Dic11—44no—
257C4×Dic11—42no—
258C4×Dic11—44no—
259C4×Dic11C22×C418yes—
260C2×#525—111no—
261#2376—112no—
262#2376—112no—
263#2358—112no—
264#2358—112no—
265#2352—112no—
266#2352—112no—
267D4×C4⋊C4—112no—
268D4×C4⋊C4—112no—
269#2329—114no—
270#2325—114no—
271#2314—112no—
272#2311—111no—
273#2311D1111yescharacteristic, complemented
274C2×#380—112no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—21no—
278C23×C11—22no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—21no—
282C23×C11—21no—
283C23×C11—21no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11C23×C412yes—
288C23×C11C23×C412yes—
289C23×C11C23×C412yes—
290C23×C11C2511yescharacteristic
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—22no—
295C22×D11—216no—
296C22×D11—44no—
297C22×D11—48no—
298C22×D11—44no—
299C22×D11—44no—
300C22×D11C23×C414yes—
301C22×D11H(5,𝔽2)14yes—
302C22×D112−1+414yes—
303Q8×C11—44no—
304D4×C11—44no—
305D4×C11—44no—
306D4×C11—44no—
307C2×C4×C11—21no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—28no—
314C2×C4×C11—28no—
315C2×C4×C11—28no—
316C2×C4×C11—24no—
317C2×C4×C11—24no—
318C2×C4×C11—24no—
319C2×C4×C11—24no—
320C2×C4×C11—24no—
321C2×C4×C11—24no—
322C2×C4×C11—84no—
323C2×C4×C11C23×C412yes—
324C2×C4×C11C23×C412yes—
325C2×C4×C11C23×C412yes—
326C2×C4×C11C23×C412yes—
327C2×C4×C11H(5,𝔽2)12yes—
328C2×C4×C11H(5,𝔽2)12yes—
329C22⋊D11—216no—
330C22⋊D11—216no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—22no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—24no—
338C2×Dic11—24no—
339C2×Dic11—24no—
340C2×Dic11—24no—
341C2×Dic11—24no—
342C2×Dic11—24no—
343C2×Dic11—44no—
344C2×Dic11—84no—
345C2×Dic11C23×C414yes—
346C2×Dic11C23×C414yes—
347C2×Dic11C23×C414yes—
348C4×D11—216no—
349C4×D11—48no—
350C4×D11—88no—
351C4×D11—88no—
352C22×#41C2×D1111yescharacteristic
353C24×C4—111no—
354#525—1116no—
355C2×#123—111no—
356C2×#123—111no—
357C2×C22⋊Q8—112no—
358C2×#121—112no—
359C2×#120—111no—
360C2×#120—111no—
361C2×C4×D4—112no—
362C2×C4×D4—112no—
363C2×C4×D4—114no—
364C2×C4×D4—114no—
365C2×#117—111no—
366C2×#117—111no—
367C2×#117C2×D1111yescharacteristic, complemented
368C22×C4⋊C4—111no—
369C22×C4⋊C4—112no—
370C22×C4⋊C4—112no—
371C22×C4⋊C4C2×D1111yescharacteristic, complemented
372C22×C22⋊C4—114no—
373#391—112no—
374#391C2×D1112yescomplemented
375#390—112no—
376#390C2×D1112yes—
377#389—114no—
378#389—114no—
379#388—114no—
380#388—114no—
381#388—114no—
382#388—114no—
383#387—114no—
384#387—114no—
385#387—114no—
386#387—114no—
387#386—112no—
388#386—112no—
389#386—114no—
390#386—114no—
391#386C2×D1112yes—
392#386C2×D1112yescomplemented
393#385—114no—
394#385—114no—
395#385—114no—
396#385—114no—
397#384—112no—
398#382—112no—
399#380—112no—
400#380—112no—
401#380—112no—
402#380—112no—
403#380—114no—
404#380—114no—
405#380C2×D1112yes—
406#380C2×D1112yescomplemented
407C4×C4⋊C4—112no—
408C4×C4⋊C4—112no—
409C4×C22⋊C4—114no—
410C4×C22⋊C4—114no—
411C2×#95—114no—
412C22×C11—22no—
413C22×C11—22no—
414C22×C11—22no—
415C22×C11—24no—
416C22×C11—24no—
417C22×C11—24no—
418C22×C11—42no—
419C22×C11—42no—
420C22×C11—42no—
421C22×C11—41no—
422C22×C11—41no—
423C22×C11—41no—
424C22×C11—41no—
425C22×C11—41no—
426C22×C11—41no—
427C22×C11C24×C411yescharacteristic
428C22×C11C2×H(5,𝔽2)11yescharacteristic
429C22×C11C2×H(5,𝔽2)11yescharacteristic
430C22×C11C2×H(5,𝔽2)12yes—
431C22×C11C2×2−1+412yes—
432C2×D11—24no—
433C2×D11—24no—
434C2×D11—24no—
435C2×D11—24no—
436C2×D11—24no—
437C2×D11—24no—
438C2×D11—416no—
439C2×D11#52018yes—
440C4×C11—22no—
441C4×C11—22no—
442C4×C11—22no—
443C4×C11—44no—
444C4×C11—44no—
445C4×C11#51814yes—
446Dic11—24no—
447Dic11—24no—
448Dic11—24no—
449Dic11—44no—
450Dic11—44no—
451C25—111no—
452C2×#41—42no—
453C2×#41—42no—
454C2×#41C4×D1118yescomplemented
455C22×Q8C22×D1111yescharacteristic
456C22×D4—112no—
457C22×D4—112no—
458C22×D4C22×D1111yescharacteristic
459C22×D4C22×D1111yescharacteristic
460C22×D4C22×D1111yescharacteristic
461C23×C4—111no—
462C23×C4—112no—
463C23×C4—118no—
464C23×C4—112no—
465C23×C4—112no—
466C23×C4—114no—
467C23×C4—114no—
468C23×C4—442no—
469C23×C4—442no—
470C23×C4C22×D1111yescharacteristic
471C23×C4C22×D1111yescharacteristic
472C23×C4C22×D1111yescharacteristic
473C23×C4C22×D1112yes—
474#123—118no—
475#123—118no—
476C22⋊Q8—1116no—
477#121—1116no—
478#120—118no—
479#120—118no—
480C4×D4—1116no—
481C4×D4—1116no—
482C4×D4—448no—
483C4×D4—448no—
484#117—42no—
485#117—118no—
486#117—442no—
487C2×C4⋊C4—42no—
488C2×C4⋊C4—112no—
489C2×C4⋊C4—112no—
490C2×C4⋊C4—112no—
491C2×C4⋊C4—112no—
492C2×C4⋊C4—112no—
493C2×C4⋊C4—114no—
494C2×C4⋊C4—114no—
495C2×C4⋊C4—112no—
496C2×C4⋊C4—114no—
497C2×C4⋊C4—114no—
498C2×C4⋊C4—444no—
499C2×C4⋊C4—444no—
500C2×C4⋊C4—442no—
501C2×C4⋊C4C22×D1112yes—
502C2×C4⋊C4C22×D1112yes—
503C2×C4⋊C4C22×D1112yes—
504C2×C22⋊C4—111no—
505C2×C22⋊C4—111no—
506C2×C22⋊C4—112no—
507C2×C22⋊C4—112no—
508C2×C22⋊C4—112no—
509C2×C22⋊C4—112no—
510C2×C22⋊C4—114no—
511C2×C22⋊C4—114no—
512C2×C22⋊C4—114no—
513C2×C22⋊C4—112no—
514C2×C22⋊C4—114no—
515C2×C22⋊C4—448no—
516C2×C22⋊C4C22×D1114yes—
517C2×C22⋊C4C22×D1112yes—
518C2×C22⋊C4C22×D1114yes—
519C2×C42—112no—
520C2×C42—112no—
521C2×C42—114no—
522C2×C42—114no—
523C2×C42C22×D1112yes—
524#95—114no—
525#95—114no—
526#95—114no—
527#95—114no—
528#95—114no—
529#95—114no—
530#95—114no—
531#95—114no—
532#95C22×D1114yes—
533#95C22×D1114yes—
534C2×C11—42no—
535C2×C11—42no—
536C2×C11—42no—
537C2×C11C2×#51811yescharacteristic
538C2×C11C2×#52012yes—
539C2×C11#353612yes—
540C2×C11#353711yescharacteristic
541C2×C11#353811yescharacteristic
542D11—28no—
543C24—112no—
544C24—114no—
545C24—224no—
546C24—224no—
547C24—441no—
548C24—441no—
549C24C23×D1111yescharacteristic
550C24C23×D1111yescharacteristic
551C24C23×D1111yescharacteristic
552#41—416no—
553C2×Q8—41no—
554C2×Q8—41no—
555C2×Q8C2×C4×D1114yes—
556C2×D4—41no—
557C2×D4—41no—
558C2×D4—41no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—118no—
563C2×D4—118no—
564C2×D4—224no—
565C2×D4—224no—
566C2×D4—224no—
567C2×D4—224no—
568C2×D4C2×C4×D1114yes—
569C2×D4C2×C4×D1114yes—
570C2×D4C2×C4×D1114yes—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—42no—
578C22×C4—44no—
579C22×C4—112no—
580C22×C4—112no—
581C22×C4—112no—
582C22×C4—114no—
583C22×C4—118no—
584C22×C4—118no—
585C22×C4—114no—
586C22×C4—114no—
587C22×C4—228no—
588C22×C4—228no—
589C22×C4—224no—
590C22×C4—224no—
591C22×C4—4416no—
592C22×C4—442no—
593C22×C4—442no—
594C22×C4—444no—
595C22×C4—444no—
596C22×C4—444no—
597C22×C4—444no—
598C22×C4—441no—
599C22×C4—441no—
600C22×C4—442no—
601C22×C4—444no—
602C22×C4C2×C4×D1114yes—
603C22×C4C2×C4×D1114yes—
604C22×C4C2×C4×D1114yes—
605C22×C4C23×D1114yes—
606C22×C4C23×D1114yes—
607C22×C4C23×D1111yescharacteristic
608C22×C4C23×D1111yescharacteristic
609C22×C4C23×D1111yescharacteristic
610C22×C4C23×D1111yescharacteristic
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—42no—
614C4⋊C4—118no—
615C4⋊C4—118no—
616C4⋊C4—118no—
617C4⋊C4—224no—
618C4⋊C4—224no—
619C4⋊C4—444no—
620C4⋊C4—444no—
621C4⋊C4—442no—
622C4⋊C4—444no—
623C4⋊C4—444no—
624C22⋊C4—44no—
625C22⋊C4—42no—
626C22⋊C4—44no—
627C22⋊C4—114no—
628C22⋊C4—114no—
629C22⋊C4—118no—
630C22⋊C4—118no—
631C22⋊C4—118no—
632C22⋊C4—118no—
633C22⋊C4—228no—
634C22⋊C4—228no—
635C22⋊C4—444no—
636C22⋊C4—442no—
637C22⋊C4—444no—
638C42—42no—
639C42—118no—
640C42—442no—
641C42—444no—
642C42—444no—
643C11#3436011yescharacteristic, complemented, Sylow
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—114no—
657C23—114no—
658C23—114no—
659C23—2216no—
660C23—222no—
661C23—222no—
662C23—222no—
663C23—222no—
664C23—444no—
665C23—448no—
666C23—444no—
667C23—444no—
668C23C22×C4×D1112yes—
669C23C22×C4×D1112yes—
670C23C22×C4×D1112yes—
671C23C24×D1111yescharacteristic
672Q8—44no—
673D4—44no—
674D4—44no—
675D4—44no—
676D4—2216no—
677D4—2216no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—28no—
685C2×C4—28no—
686C2×C4—28no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—24no—
692C2×C4—24no—
693C2×C4—84no—
694C2×C4—114no—
695C2×C4—114no—
696C2×C4—114no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—2216no—
704C2×C4—224no—
705C2×C4—224no—
706C2×C4—224no—
707C2×C4—224no—
708C2×C4—224no—
709C2×C4—224no—
710C2×C4—448no—
711C2×C4—444no—
712C2×C4—888no—
713C2×C4—888no—
714C2×C4—884no—
715C2×C4C22×C4×D1112yes—
716C2×C4C22×C4×D1112yes—
717C2×C4C22×C4×D1112yes—
718C2×C4C22×C4×D1112yes—
719C2×C4#6703712yes—
720C2×C4#6703712yes—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—24no—
725C22—24no—
726C22—24no—
727C22—42no—
728C22—42no—
729C22—42no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—118no—
737C22—224no—
738C22—224no—
739C22—224no—
740C22—224no—
741C22—224no—
742C22—224no—
743C22—4416no—
744C22C23×C4×D1111yescharacteristic
745C22C2×#6703711yescharacteristic
746C22C2×#6703711yescharacteristic
747C22D11×H(5,𝔽2)12yes—
748C22D11×2−1+412yes—
749C4—22no—
750C4—22no—
751C4—22no—
752C4—44no—
753C4—44no—
754C4—224no—
755C4—224no—
756C4—224no—
757C4—444no—
758C4—444no—
759C4#1062301714yes—
760C2—42no—
761C2—42no—
762C2—42no—
763C2—228no—
764C2C2×#1062301711yescharacteristic
765C2D11×#52012yes—
766C2#1308283412yes—
767C2#1308284911yescharacteristic
768C2#1308285911yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2311C2
socle, cosocleC23×C11C25
prime radicalC2×#10623359C2
hypercenter#2311D11
hypocenterC11#34360
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2311

Complements

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

NH ≅ G/Ntype
2. #13071766C2semidirect
3. #13071759C2semidirect
4. #13071599C2semidirect
5. #13071597C2semidirect
6. #13071546C2semidirect
7. #13071538C2semidirect
8. C4⋊C4×C22⋊D11C2semidirect
9. #13071512C2semidirect
10. #13071348C2semidirect
11. #13071318C2semidirect
12. #13071223C2semidirect
13. #13071208C2semidirect
14. D11×#380C2semidirect
15. C11×#2311C2semidirect
18. C2×C11×#117C22semidirect
19. C22×C11×C4⋊C4C22semidirect
20. #10623359C4semidirect
31. C2×#66979C22semidirect
32. C22×C4⋊Dic11C22semidirect
37. C11×#391C22semidirect
40. C11×#386C22semidirect
42. C11×#380C22semidirect
43. #10622843C22semidirect
46. #10622833C22semidirect
48. #10622825C22semidirect
49. #10622823C22semidirect
53. #10622590C22semidirect
54. #10622589C22semidirect
55. C4⋊C4×Dic11C22semidirect
56. C4⋊C4×Dic11C22semidirect
57. #10622585C22semidirect
60. #10622559C22semidirect
62. #10622558C22semidirect
64. #10622557C22semidirect
67. #10622546C22semidirect
72. #10622267C22semidirect
73. #10622266C22semidirect
74. #10622265C22semidirect
75. #10622260C22semidirect
79. C2×C11×#41C2×C4semidirect
94. C22×C4×D11C2×C4semidirect
115. #66999C2×C4semidirect
116. #66991C2×C4semidirect
117. #66990C2×C4semidirect
118. #66990C2×C4semidirect
119. #66988C2×C4semidirect
120. #66988C2×C4semidirect
122. C4×C22⋊D11C2×C4semidirect
123. C4×C22⋊D11C2×C4semidirect
129. #66979C2×C4semidirect
273. #2311D11semidirect
367. C2×#117C2×D11semidirect
371. C22×C4⋊C4C2×D11semidirect
374. #391C2×D11semidirect
392. #386C2×D11semidirect
406. #380C2×D11semidirect
454. C2×#41C4×D11semidirect
643. C11#34360semidirect

Maximal subgroups

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

subgroupindex
C2×#106233592
#130717662
#130717592
#130715992
#130715972
#130715462
#130715382
C4⋊C4×C22⋊D112
#130715122
#130713482
#130713182
#130712232
#130712082
D11×#3802
C11×#23112
#3436011