Finite Group Databasebeta

← #14917229

Subgroups — #14917229

Order 2816.

2766 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623361C211yesmaximal, characteristic
2#13071791C212yesmaximal, complemented
3#13071754C212yesmaximal, complemented
4#13071679C212yesmaximal, complemented
5#13071652C212yesmaximal, complemented
6#13071630C212yesmaximal, complemented
7#13071599C212yesmaximal, complemented
8#13071507C212yesmaximal, complemented
9C22⋊C4×D44C212yesmaximal, complemented
10#13071428C214yesmaximal, complemented
11#13071309C212yesmaximal, complemented
12#13071275C214yesmaximal, complemented
13#13071208C211yesmaximal, characteristic, complemented
14C4×#66983C212yesmaximal, complemented
15C11×#2297C211yesmaximal, characteristic, complemented
16C22×C11×#41C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic, complemented
19C22×C42×C11C2211yescharacteristic, complemented
20#10623361C4116yescomplemented
21C2×#67000C2212yes—
22C2×#66993C2212yes—
23C2×#66990C2212yes—
24C2×#66990C2212yes—
25C2×#66983C2212yes—
26C2×#66983C2212yes—
27C2×C4×C22⋊D11C2214yescomplemented
28C2×#66979C2211yescharacteristic
29C2×#66979C2211yescharacteristic, complemented
30C22×C4⋊Dic11C2211yescharacteristic, complemented
31C2×(C22⋊D11)⋊C4C2214yescomplemented
32C2×C22⋊C4×D11C2214yes—
33C2×C4×D44C2212yes—
34C2×C4×D44C2212yes—
35C11×#391C2212yescomplemented
36C11×#390C2212yes—
37C11×#386C2211yescharacteristic
38C11×#386C2211yescharacteristic
39C11×#386C2211yescharacteristic, complemented
40C11×#386C2211yescharacteristic, complemented
41C4×C11×C22⋊C4C2212yes—
42C4×C11×C22⋊C4C2212yescomplemented
43#10622843C2212yescomplemented
44#10622834C2212yes—
45#10622833C2212yes—
46#10622833C2212yescomplemented
47#10622826C2214yescomplemented
48#10622825C2212yes—
49#10622825C2212yescomplemented
50#10622603C2214yescomplemented
51#10622602C2214yescomplemented
52#10622571C2214yescomplemented
53#10622570C2214yescomplemented
54#10622570C2214yescomplemented
55#10622569C2214yescomplemented
56#10622569C2214yescomplemented
57#10622568C2214yes—
58#10622558C2214yes—
59#10622558C2214yes—
60#10622553C2214yescomplemented
61#10622552C2212yes—
62#10622552C2212yes—
63C4×(C2×D11)⋊C4C2214yescomplemented
64C4×C4⋊Dic11C2212yescomplemented
65C4×C4⋊Dic11C2212yescomplemented
66#10622541C2212yescomplemented
67#10622541C2212yescomplemented
68#10622283C2214yescomplemented
69#10622282C2214yescomplemented
70#10622281C2214yescomplemented
71#10622279C2214yescomplemented
72#10622278C2214yes—
73#10622278C2214yes—
74#10622264C2214yescomplemented
75#10622262C2214yescomplemented
76C24×D11C2312yes—
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×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C22×C22⋊D11C2314yes—
90C22×C22⋊D11C2314yes—
91C23×Dic11C2312yes—
92C22×D44—42no—
93C22×D44—42no—
94C22×D44C2×C418yescomplemented
95C22×D44C2312yes—
96C22×D44C2312yes—
97C22×C4×D11C2314yes—
98C22×C4×D11C2314yes—
99C11×#117—42no—
100C2×C11×C4⋊C4C2312yes—
101C2×C11×C22⋊C4C2312yes—
102C2×C11×C22⋊C4C2312yes—
103C2×C11×C22⋊C4C2312yes—
104C2×C11×C22⋊C4C2311yescharacteristic
105C2×C11×C22⋊C4C2312yes—
106C2×C11×C22⋊C4C2311yescharacteristic
107C2×C42×C11—42no—
108C2×C42×C11C2312yes—
109C2×C42×C11C2312yes—
110C2×C42×C11C2312yes—
111C2×C22⋊Dic11C2314yes—
112C2×C22⋊Dic11C2312yes—
113C2×C22⋊Dic11C2314yes—
114C2×C22⋊Dic11C2312yes—
115#67000C2×C4116yescomplemented
116#66993C2×C4116yescomplemented
117#66990C2×C4116yescomplemented
118#66990C2×C4116yescomplemented
119#66983C2×C4116yescomplemented
120#66983C2×C4116yescomplemented
121C4×C22⋊D11—48no—
122C2×(C2×D11)⋊C4C2314yes—
123C2×(C2×D11)⋊C4C2314yes—
124C2×(C2×D11)⋊C4C2314yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130#66979—42no—
131#66979C2×C418yescomplemented
132C2×C4⋊Dic11—42no—
133C2×C4⋊Dic11C2312yes—
134C2×C4⋊Dic11C2312yes—
135C2×C4⋊Dic11C2312yes—
136C2×C4⋊Dic11C2312yes—
137C2×Dic11⋊C4C2314yes—
138C2×Dic11⋊C4C2314yes—
139C2×C4×Dic11C2314yes—
140C2×C4×Dic11C2314yes—
141C2×C4×Dic11C2312yes—
142C2×C4×Dic11C2312yes—
143(C22⋊D11)⋊C4—48no—
144C22⋊C4×D11—48no—
145C4×D44—44no—
146C4×D44—44no—
147C11×#95C2312yes—
148C11×#95C2312yes—
149C11×#95C2312yes—
150C11×#95C2312yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157#34411—111nomaximal, Sylow
158C24×C11C2411yescharacteristic
159C24×C11C2411yescharacteristic
160C24×C11C2411yescharacteristic
161C23×D11—44no—
162C23×D11—42no—
163C23×D11—42no—
164C23×D11—44no—
165C23×D11C22×C418yes—
166C23×D11C2414yes—
167C11×#41—416no—
168C2×Q8×C11—41no—
169C2×Q8×C11—41no—
170C2×Q8×C11C22×C414yes—
171C2×D4×C11—41no—
172C2×D4×C11—41no—
173C2×D4×C11—41no—
174C2×D4×C11—41no—
175C2×D4×C11—41no—
176C2×D4×C11—41no—
177C2×D4×C11C22×C414yes—
178C2×D4×C11C22×C414yes—
179C2×D4×C11C22×C414yes—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—24no—
187C22×C4×C11—41no—
188C22×C4×C11—41no—
189C22×C4×C11—42no—
190C22×C4×C11C22×C414yes—
191C22×C4×C11C22×C414yes—
192C22×C4×C11C22×C414yes—
193C22×C4×C11C2412yes—
194C22×C4×C11C2412yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2411yescharacteristic
197C22×C4×C11C2411yescharacteristic
198C22×C4×C11C2411yescharacteristic
199C22×C4×C11C2412yes—
200C22×C4×C11C2411yescharacteristic
201C2×C22⋊D11—44no—
202C2×C22⋊D11—44no—
203C2×C22⋊D11—44no—
204C2×C22⋊D11—44no—
205C2×C22⋊D11C22×C4116yes—
206C2×C22⋊D11C22×C4116yes—
207C22×Dic11—44no—
208C22×Dic11—42no—
209C22×Dic11C2414yes—
210C22×Dic11C2414yes—
211C22×Dic11C2414yes—
212C2×D44—24no—
213C2×D44—24no—
214C2×D44—42no—
215C2×D44—42no—
216C2×D44—416no—
217C2×D44C22×C418yes—
218C2×D44C22×C418yes—
219C2×C4×D11—28no—
220C2×C4×D11—44no—
221C2×C4×D11—44no—
222C2×C4×D11—44no—
223C2×C4×D11—44no—
224C2×C4×D11—44no—
225C11×C4⋊C4—42no—
226C11×C22⋊C4—24no—
227C11×C22⋊C4—24no—
228C11×C22⋊C4—42no—
229C11×C22⋊C4—42no—
230C11×C22⋊C4—41no—
231C11×C22⋊C4—41no—
232C42×C11—24no—
233C42×C11—24no—
234C42×C11—42no—
235C22⋊Dic11—44no—
236C22⋊Dic11—42no—
237C22⋊Dic11—44no—
238C22⋊Dic11C22×C418yes—
239(C2×D11)⋊C4—28no—
240(C2×D11)⋊C4—44no—
241(C2×D11)⋊C4—44no—
242(C2×D11)⋊C4—44no—
243(C2×D11)⋊C4—44no—
244(C2×D11)⋊C4—44no—
245(C2×D11)⋊C4C22×C4116yes—
246(C2×D11)⋊C4C22×C4116yes—
247C4⋊Dic11—24no—
248C4⋊Dic11—24no—
249C4⋊Dic11—42no—
250C4⋊Dic11C22×C418yes—
251Dic11⋊C4—28no—
252Dic11⋊C4—44no—
253C4×Dic11—44no—
254C4×Dic11—42no—
255C4×Dic11—44no—
256C4×Dic11C22×C418yes—
257C2×#535—111no—
258#2380—112no—
259#2375—112no—
260#2366—112no—
261#2363—112no—
262#2361—112no—
263#2358—112no—
264#2347—112no—
265D4×C22⋊C4—112no—
266#2337—114no—
267#2324—112no—
268#2321—114no—
269#2311—111no—
270C4×#121—112no—
271#2297D1111yescharacteristic, complemented
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—21no—
275C23×C11—22no—
276C23×C11—21no—
277C23×C11—21no—
278C23×C11—21no—
279C23×C11—21no—
280C23×C11—21no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11C23×C412yes—
285C23×C11C23×C412yes—
286C23×C11C23×C412yes—
287C23×C11C2511yescharacteristic
288C22×D11—24no—
289C22×D11—24no—
290C22×D11—24no—
291C22×D11—24no—
292C22×D11—24no—
293C22×D11—24no—
294C22×D11—48no—
295C22×D11—416no—
296C22×D11—84no—
297C22×D11—84no—
298C22×D11—88no—
299C22×D11C23×C418yes—
300Q8×C11—44no—
301D4×C11—44no—
302D4×C11—44no—
303D4×C11—44no—
304C2×C4×C11—22no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
307C2×C4×C11—22no—
308C2×C4×C11—21no—
309C2×C4×C11—21no—
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—28no—
313C2×C4×C11—28no—
314C2×C4×C11—28no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—22no—
319C2×C4×C11—22no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—44no—
325C2×C4×C11—44no—
326C2×C4×C11C23×C412yes—
327C2×C4×C11C23×C412yes—
328C2×C4×C11C23×C412yes—
329C2×C4×C11C23×C412yes—
330C2×C4×C11H(5,𝔽2)12yes—
331C2×C4×C11H(5,𝔽2)12yes—
332C2×C4×C11H(5,𝔽2)14yes—
333C22⋊D11—416no—
334C22⋊D11—416no—
335C2×Dic11—24no—
336C2×Dic11—24no—
337C2×Dic11—24no—
338C2×Dic11—24no—
339C2×Dic11—24no—
340C2×Dic11—24no—
341C2×Dic11—24no—
342C2×Dic11—24no—
343C2×Dic11—84no—
344C2×Dic11C23×C418yes—
345D44—216no—
346D44—48no—
347C4×D11—88no—
348C4×D11—88no—
349C22×#41C2×D1111yescharacteristic
350C23×D4—111no—
351#535—1116no—
352C2×#127—112no—
353C2×#124—112no—
354C2×#121—112no—
355C2×#121—112no—
356C2×#120—112no—
357C2×#120—112no—
358C2×C4×D4—114no—
359C2×C4×D4—114no—
360C2×C4×D4—112no—
361C2×C4×D4—112no—
362C2×#117—111no—
363C2×#117—111no—
364C2×#117C2×D1111yescharacteristic, complemented
365C22×C4⋊C4—111no—
366C22×C22⋊C4—114no—
367C22×C42C2×D1111yescharacteristic, complemented
368#391—112no—
369#391C2×D1112yescomplemented
370#390—112no—
371#390—114no—
372#390—114no—
373#390—112no—
374#390—112no—
375#390C2×D1112yes—
376#389—112no—
377#389—112no—
378#388—114no—
379#388—114no—
380#388—114no—
381#388—114no—
382#388—114no—
383#388—114no—
384#386—112no—
385#386—112no—
386#386—114no—
387#386—114no—
388#386—114no—
389#386—114no—
390#386—114no—
391#386—114no—
392#386C2×D1111yescharacteristic
393#386C2×D1111yescharacteristic
394#386C2×D1111yescharacteristic, complemented
395#386C2×D1111yescharacteristic, complemented
396#385—114no—
397#385—114no—
398#383—114no—
399#380—112no—
400#380—112no—
401#379—114no—
402C4×C4⋊C4—112no—
403C4×C4⋊C4—112no—
404C4×C4⋊C4—114no—
405C4×C22⋊C4—114no—
406C4×C22⋊C4—114no—
407C4×C22⋊C4C2×D1112yes—
408C4×C22⋊C4C2×D1112yescomplemented
409C22×C11—22no—
410C22×C11—22no—
411C22×C11—22no—
412C22×C11—24no—
413C22×C11—24no—
414C22×C11—24no—
415C22×C11—41no—
416C22×C11—41no—
417C22×C11—41no—
418C22×C11—41no—
419C22×C11—41no—
420C22×C11—41no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11C24×C411yescharacteristic
425C22×C11C2×H(5,𝔽2)11yescharacteristic
426C22×C11C2×H(5,𝔽2)11yescharacteristic
427C22×C11C2×H(5,𝔽2)12yes—
428C22×C11#58512yes—
429C2×D11—28no—
430C2×D11—28no—
431C2×D11—28no—
432C2×D11—44no—
433C2×D11—44no—
434C2×D11—44no—
435C2×D11—44no—
436C2×D11—816no—
437C4×C11—22no—
438C4×C11—22no—
439C4×C11—22no—
440C4×C11—24no—
441C4×C11—42no—
442C4×C11—42no—
443C4×C11—42no—
444C4×C11#51814yes—
445Dic11—28no—
446Dic11—44no—
447Dic11—44no—
448C25—112no—
449C2×#41—42no—
450C2×#41—42no—
451C2×#41C4×D1118yescomplemented
452C22×Q8C22×D1111yescharacteristic
453C22×D4—114no—
454C22×D4—114no—
455C22×D4—118no—
456C22×D4—112no—
457C22×D4—112no—
458C22×D4—442no—
459C22×D4—442no—
460C22×D4C22×D1111yescharacteristic
461C22×D4C22×D1111yescharacteristic
462C22×D4C22×D1111yescharacteristic
463C23×C4—112no—
464C23×C4—114no—
465C23×C4—114no—
466C23×C4C22×D1111yescharacteristic
467C23×C4C22×D1111yescharacteristic
468C23×C4C22×D1111yescharacteristic
469C23×C4C22×D1111yescharacteristic
470C23×C4C22×D1111yescharacteristic
471#127—1116no—
472#124—1116no—
473#121—1116no—
474#121—1116no—
475#120—1116no—
476#120—1116no—
477C4×D4—444no—
478C4×D4—444no—
479C4×D4—448no—
480C4×D4—448no—
481#117—42no—
482#117—118no—
483#117—442no—
484C2×C4⋊C4—112no—
485C2×C4⋊C4—112no—
486C2×C4⋊C4—112no—
487C2×C4⋊C4—114no—
488C2×C4⋊C4—112no—
489C2×C4⋊C4—114no—
490C2×C4⋊C4—442no—
491C2×C4⋊C4C22×D1112yes—
492C2×C22⋊C4—112no—
493C2×C22⋊C4—114no—
494C2×C22⋊C4—114no—
495C2×C22⋊C4—114no—
496C2×C22⋊C4—114no—
497C2×C22⋊C4—112no—
498C2×C22⋊C4—114no—
499C2×C22⋊C4—114no—
500C2×C22⋊C4—114no—
501C2×C22⋊C4—114no—
502C2×C22⋊C4—114no—
503C2×C22⋊C4—114no—
504C2×C22⋊C4—448no—
505C2×C22⋊C4C22×D1112yes—
506C2×C22⋊C4C22×D1112yes—
507C2×C22⋊C4C22×D1111yescharacteristic
508C2×C22⋊C4C22×D1111yescharacteristic
509C2×C22⋊C4C22×D1112yes—
510C2×C22⋊C4C22×D1112yes—
511C2×C42—42no—
512C2×C42—112no—
513C2×C42—112no—
514C2×C42—114no—
515C2×C42—114no—
516C2×C42C22×D1112yes—
517C2×C42C22×D1112yes—
518C2×C42C22×D1112yes—
519#95—114no—
520#95—114no—
521#95—114no—
522#95—114no—
523#95—114no—
524#95—114no—
525#95C22×D1112yes—
526#95C22×D1112yes—
527#95C22×D1112yes—
528#95C22×D1112yes—
529C2×C11—42no—
530C2×C11—42no—
531C2×C11—42no—
532C2×C11C2×#51811yescharacteristic
533C2×C11C4×H(5,𝔽2)12yes—
534C2×C11#353711yescharacteristic
535C2×C11#354011yescharacteristic
536C2×C11#354612yes—
537D11—48no—
538C24—114no—
539C24—118no—
540C24—444no—
541C24—442no—
542C24—442no—
543C24—444no—
544C24C23×D1111yescharacteristic
545C24C23×D1111yescharacteristic
546C24C23×D1111yescharacteristic
547#41—416no—
548C2×Q8—41no—
549C2×Q8—41no—
550C2×Q8C2×C4×D1114yes—
551C2×D4—41no—
552C2×D4—41no—
553C2×D4—41no—
554C2×D4—41no—
555C2×D4—41no—
556C2×D4—41no—
557C2×D4—1116no—
558C2×D4—1116no—
559C2×D4—118no—
560C2×D4—118no—
561C2×D4—224no—
562C2×D4—224no—
563C2×D4—4416no—
564C2×D4—442no—
565C2×D4—442no—
566C2×D4—444no—
567C2×D4—444no—
568C2×D4—444no—
569C2×D4—444no—
570C2×D4C2×C4×D1114yes—
571C2×D4C2×C4×D1114yes—
572C2×D4C2×C4×D1114yes—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—24no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—42no—
583C22×C4—114no—
584C22×C4—114no—
585C22×C4—114no—
586C22×C4—228no—
587C22×C4—444no—
588C22×C4—444no—
589C22×C4—444no—
590C22×C4—444no—
591C22×C4—444no—
592C22×C4—442no—
593C22×C4—444no—
594C22×C4C2×C4×D1114yes—
595C22×C4C2×C4×D1114yes—
596C22×C4C2×C4×D1114yes—
597C22×C4C23×D1112yes—
598C22×C4C23×D1112yes—
599C22×C4C23×D1112yes—
600C22×C4C23×D1111yescharacteristic
601C22×C4C23×D1111yescharacteristic
602C22×C4C23×D1111yescharacteristic
603C22×C4C23×D1112yes—
604C22×C4C23×D1111yescharacteristic
605C4⋊C4—42no—
606C4⋊C4—118no—
607C4⋊C4—224no—
608C4⋊C4—224no—
609C4⋊C4—228no—
610C4⋊C4—442no—
611C4⋊C4—444no—
612C22⋊C4—24no—
613C22⋊C4—24no—
614C22⋊C4—41no—
615C22⋊C4—41no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—118no—
619C22⋊C4—1116no—
620C22⋊C4—1116no—
621C22⋊C4—228no—
622C22⋊C4—444no—
623C22⋊C4—444no—
624C22⋊C4—444no—
625C22⋊C4—444no—
626C22⋊C4—444no—
627C22⋊C4—444no—
628C22⋊C4—442no—
629C22⋊C4—444no—
630C42—24no—
631C42—24no—
632C42—42no—
633C42—118no—
634C42—442no—
635C42—444no—
636C42—444no—
637C11#3441111yescharacteristic, complemented, Sylow
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—118no—
651C23—224no—
652C23—224no—
653C23—224no—
654C23—224no—
655C23—224no—
656C23—224no—
657C23—448no—
658C23—4416no—
659C23—884no—
660C23—888no—
661C23—884no—
662C23C22×C4×D1112yes—
663C23C22×C4×D1112yes—
664C23C22×C4×D1112yes—
665C23C24×D1111yescharacteristic
666Q8—44no—
667D4—44no—
668D4—44no—
669D4—44no—
670D4—2216no—
671D4—448no—
672D4—4416no—
673D4—4416no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—22no—
682C2×C4—28no—
683C2×C4—28no—
684C2×C4—28no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—118no—
697C2×C4—224no—
698C2×C4—224no—
699C2×C4—224no—
700C2×C4—224no—
701C2×C4—224no—
702C2×C4—224no—
703C2×C4—224no—
704C2×C4—224no—
705C2×C4—888no—
706C2×C4—888no—
707C2×C4—884no—
708C2×C4C22×C4×D1112yes—
709C2×C4C22×C4×D1112yes—
710C2×C4C22×C4×D1112yes—
711C2×C4C22×C4×D1112yes—
712C2×C4#6703712yes—
713C2×C4#6703712yes—
714C2×C4#6704214yes—
715C22—22no—
716C22—22no—
717C22—22no—
718C22—24no—
719C22—24no—
720C22—24no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—42no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—228no—
731C22—228no—
732C22—228no—
733C22—444no—
734C22—444no—
735C22—444no—
736C22—444no—
737C22—8816no—
738C22C23×C4×D1111yescharacteristic
739C22C2×#6703711yescharacteristic
740C22C2×#6703711yescharacteristic
741C22C2×#6704212yes—
742C22#1062345312yes—
743C4—22no—
744C4—22no—
745C4—22no—
746C4—24no—
747C4—42no—
748C4—42no—
749C4—42no—
750C4—228no—
751C4—444no—
752C4—444no—
753C4#1062301714yes—
754C2—42no—
755C2—42no—
756C2—42no—
757C2—448no—
758C2C2×#1062301711yescharacteristic
759C2C4×#6704212yes—
760C2#1308285511yescharacteristic
761C2#1308289111yescharacteristic
762C2#1308298812yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC11×#2297C2
socle, cosocleC23×C11C25
prime radicalC2×#10623361C2
hypercenter#2297D11
hypocenterC11#34411
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2297

Complements

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

NH ≅ G/Ntype
2. #13071791C2semidirect
3. #13071754C2semidirect
4. #13071679C2semidirect
5. #13071652C2semidirect
6. #13071630C2semidirect
7. #13071599C2semidirect
8. #13071507C2semidirect
9. C22⋊C4×D44C2semidirect
10. #13071428C2semidirect
11. #13071309C2semidirect
12. #13071275C2semidirect
13. #13071208C2semidirect
14. C4×#66983C2semidirect
15. C11×#2297C2semidirect
18. C2×C11×#117C22semidirect
19. C22×C42×C11C22semidirect
20. #10623361C4semidirect
27. C2×C4×C22⋊D11C22semidirect
29. C2×#66979C22semidirect
30. C22×C4⋊Dic11C22semidirect
31. C2×(C22⋊D11)⋊C4C22semidirect
35. C11×#391C22semidirect
39. C11×#386C22semidirect
40. C11×#386C22semidirect
42. C4×C11×C22⋊C4C22semidirect
43. #10622843C22semidirect
46. #10622833C22semidirect
47. #10622826C22semidirect
49. #10622825C22semidirect
50. #10622603C22semidirect
51. #10622602C22semidirect
52. #10622571C22semidirect
53. #10622570C22semidirect
54. #10622570C22semidirect
55. #10622569C22semidirect
56. #10622569C22semidirect
60. #10622553C22semidirect
63. C4×(C2×D11)⋊C4C22semidirect
64. C4×C4⋊Dic11C22semidirect
65. C4×C4⋊Dic11C22semidirect
66. #10622541C22semidirect
67. #10622541C22semidirect
68. #10622283C22semidirect
69. #10622282C22semidirect
70. #10622281C22semidirect
71. #10622279C22semidirect
74. #10622264C22semidirect
75. #10622262C22semidirect
79. C2×C11×#41C2×C4semidirect
94. C22×D44C2×C4semidirect
115. #67000C2×C4semidirect
116. #66993C2×C4semidirect
117. #66990C2×C4semidirect
118. #66990C2×C4semidirect
119. #66983C2×C4semidirect
120. #66983C2×C4semidirect
131. #66979C2×C4semidirect
271. #2297D11semidirect
364. C2×#117C2×D11semidirect
367. C22×C42C2×D11semidirect
369. #391C2×D11semidirect
394. #386C2×D11semidirect
395. #386C2×D11semidirect
408. C4×C22⋊C4C2×D11semidirect
451. C2×#41C4×D11semidirect
637. C11#34411semidirect

Maximal subgroups

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

subgroupindex
C2×#106233612
#130717912
#130717542
#130716792
#130716522
#130716302
#130715992
#130715072
C22⋊C4×D442
#130714282
#130713092
#130712752
#130712082
C4×#669832
C11×#22972
#3441111