Finite Group Databasebeta

← #14959941

Subgroups — #14959941

Order 2816.

2570 conjugacy classes of subgroups.

The subgroup lattice has 798 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623322C211yesmaximal, characteristic, complemented
2#13076651C211yesmaximal, characteristic, complemented
3#13076644C211yesmaximal, characteristic, complemented
4#13076643C211yesmaximal, characteristic, complemented
5#13076638C211yesmaximal, characteristic, complemented
6#13076629C212yesmaximal, complemented
7#13076627C212yesmaximal, complemented
8#13076618C212yesmaximal, complemented
9#13076616C212yesmaximal, complemented
10#13076611C214yesmaximal, complemented
11#13071875C212yesmaximal, complemented
12#13071873C212yesmaximal, complemented
13#13071858C214yesmaximal, complemented
14#13071831C212yesmaximal, complemented
15#13071829C212yesmaximal, complemented
16#13070999C211yesmaximal, characteristic, complemented
17C2×C11×#525C211yesmaximal, characteristic, complemented
18C22×C11×#41C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C22×#4339C2211yescharacteristic
21C11×#525—28no—
22C2×C11×#123C2212yes—
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×C22⋊Q8C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic
26C2×C11×#121C2211yescharacteristic
27C2×C11×#120C2212yes—
28C2×C4×D4×C11C2212yes—
29C2×C4×D4×C11C2212yes—
30C2×C11×#117C2211yescharacteristic
31C2×#67006C2212yes—
32#10623322—28no—
33C2×#66983C2211yescharacteristic
34C2×#66983C2211yescharacteristic
35C2×#66982C2212yes—
36C2×C4×C22⋊D11C2212yes—
37C2×C4×C22⋊D11C2212yes—
38C2×C4×C22⋊D11C2214yescomplemented
39C2×#66979C2211yescharacteristic
40C2×#66979C2212yes—
41C2×#66977C2211yescharacteristic
42C2×#66977C2211yescharacteristic
43#10622860C2212yes—
44#10622844C2212yescomplemented
45#10622842C2212yescomplemented
46#10622836C2214yes—
47#10622836C2214yes—
48#10622836C2214yes—
49#10622836C2212yescomplemented
50#10622835C2214yes—
51#10622835C2214yes—
52#10622835C2214yes—
53#10622835C2212yescomplemented
54#10622825C2212yes—
55#10622825C2212yes—
56#10622824C2211yescharacteristic
57#10622824C2211yescharacteristic
58C4×C22⋊Dic11C2212yes—
59C4×C22⋊Dic11C2212yes—
60C4×C22⋊Dic11C2214yescomplemented
61#10622607C2214yescomplemented
62#10622606C2212yescomplemented
63#10622605C2212yescomplemented
64#10622604C2212yescomplemented
65#10622599C2212yescomplemented
66#10622597C2214yescomplemented
67#10622596C2212yescomplemented
68#10622595C2212yescomplemented
69#10622593C2212yescomplemented
70#10622592C2212yescomplemented
71#10622574C2214yescomplemented
72#10622573C2212yescomplemented
73#10622572C2214yes—
74#10622572C2214yes—
75#10622572C2214yes—
76#10622566C2212yescomplemented
77#10622565C2214yes—
78#10622565C2214yes—
79#10622565C2214yes—
80#10622562C2212yescomplemented
81#10622561C2214yescomplemented
82#10622560C2212yescomplemented
83C4×(C2×D11)⋊C4C2214yescomplemented
84C4×Dic11⋊C4C2214yescomplemented
85C25×C11C2311yescharacteristic
86C2×C11×#41—24no—
87C2×C11×#41—44no—
88C22×Q8×C11C2311yescharacteristic
89C22×D4×C11C2312yes—
90C22×D4×C11C2312yes—
91C22×D4×C11C2312yes—
92C22×D4×C11C2311yescharacteristic
93C23×C4×C11—44no—
94C23×C4×C11D418yescomplemented
95C23×C4×C11C2312yes—
96C23×C4×C11C2311yescharacteristic
97C23×C4×C11C2311yescharacteristic
98C23×C4×C11C2311yescharacteristic
99C23×C4×C11C2311yescharacteristic
100C23×C4×C11C2311yescharacteristic
101C23×C4×C11C2311yescharacteristic
102C22×C22⋊D11C2312yes—
103C22×C22⋊D11C2312yes—
104C22×C22⋊D11C2312yes—
105C22×C22⋊D11C2314yes—
106C2×#4339—24no—
107C2×#4339—44no—
108C22×D44C2311yescharacteristic
109C22×C4×D11C2312yes—
110C22×Dic22C2311yescharacteristic
111C11×#123—28no—
112C11×C22⋊Q8—24no—
113C11×C22⋊Q8—24no—
114C11×#121—24no—
115C11×#121—24no—
116C11×#120—28no—
117C4×D4×C11—28no—
118C4×D4×C11—28no—
119C11×#117—24no—
120C2×C11×C4⋊C4C2312yes—
121C2×C11×C4⋊C4C2311yescharacteristic
122C2×C11×C4⋊C4C2311yescharacteristic
123C2×C11×C4⋊C4C2312yes—
124C2×C11×C22⋊C4C2312yes—
125C2×C11×C22⋊C4C2312yes—
126C2×C11×C22⋊C4C2312yes—
127C2×C11×C22⋊C4C2312yes—
128C2×C11×C22⋊C4C2312yes—
129C2×C42×C11C2312yes—
130#67006—28no—
131C2×C22⋊Dic11C2312yes—
132C2×C22⋊Dic11C2312yes—
133C2×C22⋊Dic11C2312yes—
134C2×C22⋊Dic11C2312yes—
135C2×C22⋊Dic11C2312yes—
136C2×C22⋊Dic11C2314yes—
137C2×C22⋊Dic11C2314yes—
138C2×C22⋊Dic11C2314yes—
139C2×C22⋊Dic11C2314yes—
140C2×C22⋊Dic11C2314yes—
141#66983—24no—
142#66983—24no—
143#66982—28no—
144C4×C22⋊D11—28no—
145C4×C22⋊D11—28no—
146C4×C22⋊D11—48no—
147C2×(C2×D11)⋊C4C2312yes—
148C2×(C2×D11)⋊C4C2312yes—
149C2×(C2×D11)⋊C4C2314yes—
150C2×(C2×D11)⋊C4C2314yes—
151C2×(C2×D11)⋊C4C2314yes—
152#66979—24no—
153#66979—44no—
154C2×C4⋊Dic11C2311yescharacteristic
155C2×C4⋊Dic11C2311yescharacteristic
156C2×C4⋊Dic11C2314yes—
157#66977—24no—
158#66977—24no—
159C2×Dic11⋊C4C2312yes—
160C2×Dic11⋊C4C2312yes—
161C2×Dic11⋊C4C2314yes—
162C2×Dic11⋊C4C2314yes—
163C2×Dic11⋊C4C2314yes—
164C2×C4×Dic11C2312yes—
165C2×C4×Dic11C2314yes—
166C11⋊#95C2314yes—
167C11⋊#95C2314yes—
168C11⋊#95C2314yes—
169C11⋊#95C2314yes—
170C11⋊#95C2312yes—
171C11⋊#95C2314yes—
172C11⋊#95C2314yes—
173C11⋊#95C2312yes—
174C11⋊#95C2312yes—
175C11⋊#95C2312yes—
176#36652—111nomaximal, Sylow
177C24×C11—42no—
178C24×C11—42no—
179C24×C11—42no—
180C24×C11C2×D414yes—
181C24×C11C2412yes—
182C24×C11C2411yescharacteristic
183C24×C11C2411yescharacteristic
184C24×C11C2411yescharacteristic
185C23×D11C2412yes—
186C11×#41—416no—
187C2×Q8×C11—22no—
188C2×Q8×C11—42no—
189C2×D4×C11—24no—
190C2×D4×C11—24no—
191C2×D4×C11—24no—
192C2×D4×C11—22no—
193C2×D4×C11—42no—
194C2×D4×C11—44no—
195C2×D4×C11—42no—
196C2×D4×C11—42no—
197C2×D4×C11—44no—
198C22×C4×C11—24no—
199C22×C4×C11—24no—
200C22×C4×C11—24no—
201C22×C4×C11—24no—
202C22×C4×C11—28no—
203C22×C4×C11—416no—
204C22×C4×C11—42no—
205C22×C4×C11—42no—
206C22×C4×C11—42no—
207C22×C4×C11C2×D414yes—
208C22×C4×C11C2×D414yes—
209C22×C4×C11C2×D414yes—
210C22×C4×C11C2×D414yes—
211C22×C4×C11C2×D414yes—
212C22×C4×C11C2×D414yes—
213C22×C4×C11C2412yes—
214C22×C4×C11C2412yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2411yescharacteristic
217C22×C4×C11C2411yescharacteristic
218C22×C4×C11C2411yescharacteristic
219C22×C4×C11C2411yescharacteristic
220C2×C22⋊D11—24no—
221C2×C22⋊D11—24no—
222C2×C22⋊D11—24no—
223C2×C22⋊D11—44no—
224C2×C22⋊D11—44no—
225C2×C22⋊D11—42no—
226C2×C22⋊D11—44no—
227C2×C22⋊D11—44no—
228C2×C22⋊D11—42no—
229C2×C22⋊D11—44no—
230C22×Dic11C2414yes—
231C22×Dic11C2412yes—
232C22×Dic11C2412yes—
233C22×Dic11C2414yes—
234C22×Dic11C2412yes—
235#4339—416no—
236C2×D44—22no—
237C2×D44—42no—
238C2×C4×D11—24no—
239C2×C4×D11—28no—
240C2×Dic22—22no—
241C2×Dic22—42no—
242C11×C4⋊C4—22no—
243C11×C4⋊C4—22no—
244C11×C4⋊C4—24no—
245C11×C4⋊C4—24no—
246C11×C22⋊C4—24no—
247C11×C22⋊C4—24no—
248C11×C22⋊C4—24no—
249C11×C22⋊C4—24no—
250C11×C22⋊C4—24no—
251C42×C11—24no—
252C22⋊Dic11—24no—
253C22⋊Dic11—24no—
254C22⋊Dic11—24no—
255C22⋊Dic11—42no—
256C22⋊Dic11—42no—
257C22⋊Dic11—44no—
258C22⋊Dic11—44no—
259C22⋊Dic11—44no—
260C22⋊Dic11—44no—
261C22⋊Dic11—44no—
262(C2×D11)⋊C4—24no—
263(C2×D11)⋊C4—24no—
264(C2×D11)⋊C4—44no—
265(C2×D11)⋊C4—44no—
266(C2×D11)⋊C4—44no—
267C4⋊Dic11—22no—
268C4⋊Dic11—22no—
269C4⋊Dic11—44no—
270Dic11⋊C4—24no—
271Dic11⋊C4—24no—
272Dic11⋊C4—44no—
273Dic11⋊C4—44no—
274Dic11⋊C4—44no—
275C4×Dic11—24no—
276C4×Dic11—28no—
277C2×#525—111no—
278C2×#525D1111yescharacteristic, complemented
279#2817—111no—
280#2816—111no—
281#2816—111no—
282#2815—111no—
283#2814—112no—
284#2814—112no—
285#2813—112no—
286#2813—112no—
287#2812—114no—
288#2395—112no—
289#2395—112no—
290#2392—114no—
291#2388—112no—
292#2388—112no—
293#2280—111no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—22no—
297C23×C11—22no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—22no—
301C23×C11—22no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—24no—
305C23×C11—22no—
306C23×C11—24no—
307C23×C11—22no—
308C23×C11—44no—
309C23×C11—44no—
310C23×C11—44no—
311C23×C11—416no—
312C23×C11C22×D412yes—
313C23×C11C22×D412yes—
314C23×C11C22×D412yes—
315C23×C11C2511yescharacteristic
316C22×D11—22no—
317C22×D11—24no—
318C22×D11—22no—
319C22×D11—24no—
320C22×D11—22no—
321Q8×C11—44no—
322D4×C11—44no—
323D4×C11—48no—
324D4×C11—48no—
325D4×C11—48no—
326C2×C4×C11—22no—
327C2×C4×C11—22no—
328C2×C4×C11—22no—
329C2×C4×C11—28no—
330C2×C4×C11—28no—
331C2×C4×C11—28no—
332C2×C4×C11—22no—
333C2×C4×C11—22no—
334C2×C4×C11—22no—
335C2×C4×C11—24no—
336C2×C4×C11—22no—
337C2×C4×C11—24no—
338C2×C4×C11—22no—
339C2×C4×C11—44no—
340C2×C4×C11—44no—
341C2×C4×C11—44no—
342C2×C4×C11—48no—
343C2×C4×C11C22×D412yes—
344C2×C4×C11C22×D412yes—
345C2×C4×C11C22×D412yes—
346C2×C4×C11C22×D412yes—
347C2×C4×C11H(5,𝔽2)14yes—
348C22⋊D11—48no—
349C22⋊D11—48no—
350C22⋊D11—48no—
351C22⋊D11—416no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—24no—
356C2×Dic11—24no—
357C2×Dic11—24no—
358C2×Dic11—22no—
359C2×Dic11—24no—
360C2×Dic11—24no—
361C2×Dic11—24no—
362C2×Dic11—24no—
363C2×Dic11—22no—
364C2×Dic11—24no—
365D44—44no—
366C4×D11—48no—
367Dic22—44no—
368C22×#41—111no—
369C22×#41C2×D1111yescharacteristic
370C24×C4C2×D1111yescharacteristic
371#525—28no—
372#525—228no—
373C2×#123—112no—
374C2×#123C2×D1112yes—
375C2×C22⋊Q8—111no—
376C2×C22⋊Q8—111no—
377C2×C22⋊Q8C2×D1111yescharacteristic
378C2×C22⋊Q8C2×D1111yescharacteristic
379C2×#121—111no—
380C2×#121—111no—
381C2×#121C2×D1111yescharacteristic
382C2×#121C2×D1111yescharacteristic
383C2×#120—112no—
384C2×#120C2×D1112yes—
385C2×C4×D4—112no—
386C2×C4×D4—112no—
387C2×C4×D4—114no—
388C2×C4×D4C2×D1112yes—
389C2×C4×D4C2×D1112yes—
390C2×#117—111no—
391C2×#117—112no—
392C2×#117C2×D1111yescharacteristic
393#400—112no—
394#400—112no—
395#399—112no—
396#399—112no—
397#398—112no—
398#398—112no—
399#398—114no—
400#397—112no—
401#397—114no—
402#397—114no—
403#397—114no—
404#397—112no—
405#396—114no—
406#396—114no—
407#395—112no—
408#395—112no—
409#394—112no—
410#394—114no—
411#394—114no—
412#394—114no—
413#394—112no—
414#394—114no—
415#394—114no—
416#394—114no—
417#394—114no—
418#393—112no—
419#393—112no—
420#392—114no—
421#392—114no—
422#392—112no—
423#392—114no—
424#392—112no—
425#381—111no—
426#381—111no—
427#380—112no—
428#380—112no—
429#379—112no—
430C4×C4⋊C4—114no—
431C4×C22⋊C4—114no—
432C4×C22⋊C4—112no—
433C4×C22⋊C4—112no—
434C4×C22⋊C4—114no—
435C22×C11—22no—
436C22×C11—22no—
437C22×C11—22no—
438C22×C11—22no—
439C22×C11—22no—
440C22×C11—22no—
441C22×C11—22no—
442C22×C11—22no—
443C22×C11—22no—
444C22×C11—416no—
445C22×C11—44no—
446C22×C11—44no—
447C22×C11—44no—
448C22×C11—42no—
449C22×C11—42no—
450C22×C11—42no—
451C22×C11—44no—
452C22×C11—44no—
453C22×C11C23×D411yescharacteristic
454C22×C11C2×H(5,𝔽2)12yes—
455C22×C11#58512yes—
456C22×C11#58512yes—
457C2×D11—42no—
458C2×D11—42no—
459C2×D11—42no—
460C2×D11—44no—
461C2×D11—44no—
462C4×C11—22no—
463C4×C11—22no—
464C4×C11—22no—
465C4×C11—42no—
466C4×C11—42no—
467C4×C11—42no—
468C4×C11#53414yes—
469Dic11—42no—
470Dic11—42no—
471Dic11—42no—
472Dic11—44no—
473Dic11—44no—
474C25C22×D1111yescharacteristic
475C2×#41—24no—
476C2×#41—44no—
477C2×#41—224no—
478C2×#41—444no—
479C22×Q8—111no—
480C22×Q8C22×D1111yescharacteristic
481C22×D4—112no—
482C22×D4—112no—
483C22×D4—112no—
484C22×D4—114no—
485C22×D4—111no—
486C22×D4C22×D1112yes—
487C22×D4C22×D1112yes—
488C22×D4C22×D1112yes—
489C22×D4C22×D1111yescharacteristic
490C23×C4—44no—
491C23×C4—112no—
492C23×C4C22⋊D1118yescomplemented
493C23×C4C22×D1112yes—
494C23×C4C22×D1111yescharacteristic
495C23×C4C22×D1111yescharacteristic
496C23×C4C22×D1111yescharacteristic
497C23×C4C22×D1111yescharacteristic
498C23×C4C22×D1111yescharacteristic
499C23×C4C22×D1111yescharacteristic
500#123—28no—
501#123—228no—
502C22⋊Q8—24no—
503C22⋊Q8—24no—
504C22⋊Q8—224no—
505C22⋊Q8—224no—
506#121—24no—
507#121—24no—
508#121—224no—
509#121—224no—
510#120—28no—
511#120—228no—
512C4×D4—28no—
513C4×D4—28no—
514C4×D4—228no—
515C4×D4—228no—
516C4×D4—448no—
517#117—24no—
518#117—224no—
519#117—444no—
520C2×C4⋊C4—111no—
521C2×C4⋊C4—111no—
522C2×C4⋊C4—112no—
523C2×C4⋊C4—112no—
524C2×C4⋊C4—114no—
525C2×C4⋊C4—114no—
526C2×C4⋊C4—114no—
527C2×C4⋊C4—114no—
528C2×C4⋊C4C22×D1111yescharacteristic
529C2×C4⋊C4C22×D1111yescharacteristic
530C2×C4⋊C4C22×D1112yes—
531C2×C4⋊C4C22×D1112yes—
532C2×C22⋊C4—112no—
533C2×C22⋊C4—112no—
534C2×C22⋊C4—112no—
535C2×C22⋊C4—112no—
536C2×C22⋊C4—112no—
537C2×C22⋊C4—112no—
538C2×C22⋊C4—112no—
539C2×C22⋊C4—114no—
540C2×C22⋊C4—114no—
541C2×C22⋊C4—114no—
542C2×C22⋊C4—114no—
543C2×C22⋊C4—114no—
544C2×C22⋊C4—114no—
545C2×C22⋊C4—114no—
546C2×C22⋊C4—114no—
547C2×C22⋊C4C22×D1112yes—
548C2×C22⋊C4C22×D1112yes—
549C2×C22⋊C4C22×D1112yes—
550C2×C22⋊C4C22×D1112yes—
551C2×C22⋊C4C22×D1112yes—
552C2×C42—112no—
553C2×C42—114no—
554C2×C42C22×D1112yes—
555#95—112no—
556#95—112no—
557#95—112no—
558#95—112no—
559#95—114no—
560#95—114no—
561#95—114no—
562#95—114no—
563#95—114no—
564#95—114no—
565C2×C11—42no—
566C2×C11—42no—
567C2×C11—42no—
568C2×C11—82no—
569C2×C11C2×#53411yescharacteristic
570C2×C11#344911yescharacteristic
571C2×C11#344911yescharacteristic
572C2×C11#352914yes—
573D11—82no—
574C24—42no—
575C24—42no—
576C24—42no—
577C24—112no—
578C24C2×C22⋊D1114yes—
579C24C23×D1112yes—
580C24C23×D1111yescharacteristic
581C24C23×D1111yescharacteristic
582C24C23×D1111yescharacteristic
583#41—416no—
584#41—4416no—
585C2×Q8—22no—
586C2×Q8—42no—
587C2×Q8—222no—
588C2×Q8—442no—
589C2×D4—24no—
590C2×D4—24no—
591C2×D4—24no—
592C2×D4—22no—
593C2×D4—42no—
594C2×D4—44no—
595C2×D4—42no—
596C2×D4—44no—
597C2×D4—42no—
598C2×D4—224no—
599C2×D4—224no—
600C2×D4—224no—
601C2×D4—222no—
602C2×D4—442no—
603C2×D4—444no—
604C2×D4—444no—
605C2×D4—442no—
606C2×D4—444no—
607C2×D4—444no—
608C2×D4—444no—
609C2×D4—442no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—24no—
613C22×C4—28no—
614C22×C4—24no—
615C22×C4—416no—
616C22×C4—42no—
617C22×C4—42no—
618C22×C4—42no—
619C22×C4—114no—
620C22×C4—114no—
621C22×C4—112no—
622C22×C4—112no—
623C22×C4—112no—
624C22×C4—228no—
625C22×C4—224no—
626C22×C4C2×C22⋊D1114yes—
627C22×C4C2×C22⋊D1114yes—
628C22×C4C2×C22⋊D1114yes—
629C22×C4C2×C22⋊D1114yes—
630C22×C4C2×C22⋊D1114yes—
631C22×C4C2×C22⋊D1114yes—
632C22×C4C23×D1112yes—
633C22×C4C23×D1112yes—
634C22×C4C23×D1112yes—
635C22×C4C23×D1111yescharacteristic
636C22×C4C23×D1111yescharacteristic
637C22×C4C23×D1111yescharacteristic
638C22×C4C23×D1111yescharacteristic
639C4⋊C4—22no—
640C4⋊C4—22no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—222no—
644C4⋊C4—222no—
645C4⋊C4—224no—
646C4⋊C4—224no—
647C4⋊C4—444no—
648C4⋊C4—444no—
649C4⋊C4—444no—
650C4⋊C4—444no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—24no—
656C22⋊C4—224no—
657C22⋊C4—224no—
658C22⋊C4—224no—
659C22⋊C4—224no—
660C22⋊C4—224no—
661C22⋊C4—444no—
662C22⋊C4—444no—
663C22⋊C4—444no—
664C22⋊C4—442no—
665C22⋊C4—442no—
666C22⋊C4—444no—
667C22⋊C4—444no—
668C22⋊C4—444no—
669C22⋊C4—444no—
670C22⋊C4—444no—
671C42—24no—
672C42—228no—
673C42—224no—
674C11#3665211yescharacteristic, complemented, Sylow
675C23—22no—
676C23—22no—
677C23—22no—
678C23—22no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—24no—
685C23—22no—
686C23—24no—
687C23—22no—
688C23—22no—
689C23—44no—
690C23—44no—
691C23—44no—
692C23—416no—
693C23—224no—
694C23—222no—
695C23—224no—
696C23—222no—
697C23—222no—
698C23C22×C22⋊D1112yes—
699C23C22×C22⋊D1112yes—
700C23C22×C22⋊D1112yes—
701C23C24×D1111yescharacteristic
702Q8—44no—
703Q8—444no—
704D4—44no—
705D4—48no—
706D4—48no—
707D4—48no—
708D4—444no—
709D4—448no—
710D4—448no—
711D4—448no—
712D4—4416no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—28no—
717C2×C4—28no—
718C2×C4—28no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—24no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—44no—
727C2×C4—44no—
728C2×C4—44no—
729C2×C4—48no—
730C2×C4—224no—
731C2×C4—224no—
732C2×C4—224no—
733C2×C4—224no—
734C2×C4—224no—
735C2×C4—222no—
736C2×C4—224no—
737C2×C4—224no—
738C2×C4—224no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—448no—
744C2×C4#6703714yes—
745C2×C4C22×C22⋊D1112yes—
746C2×C4C22×C22⋊D1112yes—
747C2×C4C22×C22⋊D1112yes—
748C2×C4C22×C22⋊D1112yes—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—416no—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—44no—
766C22—44no—
767C22—442no—
768C22—442no—
769C22—442no—
770C22—444no—
771C22—444no—
772C22C2×#6703712yes—
773C22#1062345312yes—
774C22#1062345312yes—
775C22C23×C22⋊D1111yescharacteristic
776C4—22no—
777C4—22no—
778C4—22no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—442no—
783C4—442no—
784C4—442no—
785C4—444no—
786C4—444no—
787C4#1062333514yes—
788C2—42no—
789C2—42no—
790C2—42no—
791C2—82no—
792C2—882no—
793C2C2×#1062333511yescharacteristic
794C2#1308194511yescharacteristic
795C2#1308194511yescharacteristic
796C2#1308275414yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#525C2
hypercenterC2×#525D11
hypocenterC11#36652
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. C2×#10623322C2semidirect
2. #13076651C2semidirect
3. #13076644C2semidirect
4. #13076643C2semidirect
5. #13076638C2semidirect
6. #13076629C2semidirect
7. #13076627C2semidirect
8. #13076618C2semidirect
9. #13076616C2semidirect
10. #13076611C2semidirect
11. #13071875C2semidirect
12. #13071873C2semidirect
13. #13071858C2semidirect
14. #13071831C2semidirect
15. #13071829C2semidirect
16. #13070999C2semidirect
17. C2×C11×#525C2semidirect
38. C2×C4×C22⋊D11C22semidirect
44. #10622844C22semidirect
45. #10622842C22semidirect
49. #10622836C22semidirect
53. #10622835C22semidirect
60. C4×C22⋊Dic11C22semidirect
61. #10622607C22semidirect
62. #10622606C22semidirect
63. #10622605C22semidirect
64. #10622604C22semidirect
65. #10622599C22semidirect
66. #10622597C22semidirect
67. #10622596C22semidirect
68. #10622595C22semidirect
69. #10622593C22semidirect
70. #10622592C22semidirect
71. #10622574C22semidirect
72. #10622573C22semidirect
76. #10622566C22semidirect
80. #10622562C22semidirect
81. #10622561C22semidirect
82. #10622560C22semidirect
83. C4×(C2×D11)⋊C4C22semidirect
84. C4×Dic11⋊C4C22semidirect
94. C23×C4×C11D4semidirect
278. C2×#525D11semidirect
492. C23×C4C22⋊D11semidirect
674. C11#36652semidirect

Maximal subgroups

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

subgroupindex
C2×#106233222
#130766512
#130766442
#130766432
#130766382
#130766292
#130766272
#130766182
#130766162
#130766112
#130718752
#130718732
#130718582
#130718312
#130718292
#130709992
C2×C11×#5252
#3665211