Finite Group Databasebeta

← #14960747

Subgroups — #14960747

Order 2816.

2842 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623014C211yesmaximal, characteristic, complemented
2C22×#66991C211yesmaximal, characteristic
3#13076902C212yesmaximal, complemented
4#13074970C214yesmaximal, complemented
5#13074968C214yesmaximal, complemented
6#13074873C214yesmaximal, complemented
7#13074871C214yesmaximal, complemented
8#13074425C212yesmaximal, complemented
9#13073993C212yesmaximal, complemented
10#13072265C212yesmaximal, complemented
11#13071944C211yesmaximal, characteristic, complemented
12#13071943C211yesmaximal, characteristic, complemented
13#13071939C211yesmaximal, characteristic, complemented
14#13071212C211yesmaximal, characteristic, complemented
15C11×#2405C211yesmaximal, characteristic, complemented
16C23×D4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C2×C11×#123C2212yescomplemented
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C22×C22⋊Dic11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C2×#66991—28no—
26C2×#66991C2214yes—
27C2×#66991C2214yes—
28C2×#66988C2212yescomplemented
29C2×#66982C2212yescomplemented
30C22×C4⋊Dic11C2211yescharacteristic
31C2×#66977C2212yescomplemented
32C2×#66977C2212yescomplemented
33C2×#66949C2214yescomplemented
34C2×#66939C2212yescomplemented
35C2×#66938C2214yescomplemented
36#10623014—28no—
37C2×#66931C2212yes—
38C2×#66931C2212yes—
39C2×#66931C2212yescomplemented
40C2×#66931C2212yescomplemented
41C11×#394C2214yescomplemented
42C11×#386C2212yescomplemented
43C11×#385C2212yes—
44C11×#379C2211yescharacteristic
45C11×#379C2212yes—
46#10622860C2211yescharacteristic
47#10622860C2212yes—
48#10622835C2214yescomplemented
49#10622833C2212yescomplemented
50#10622826C2212yescomplemented
51#10622823C2212yes—
52#10622602C2214yescomplemented
53#10622598C2214yescomplemented
54#10622597C2214yescomplemented
55#10622574C2214yescomplemented
56#10622574C2214yescomplemented
57#10622572C2214yescomplemented
58#10622572C2214yescomplemented
59#10622571C2212yescomplemented
60#10622570C2214yescomplemented
61#10622568C2212yes—
62#10622568C2212yes—
63#10622563C2212yes—
64#10622562C2214yescomplemented
65#10622561C2214yescomplemented
66#10622561C2214yescomplemented
67#10622560C2214yescomplemented
68#10622559C2212yes—
69#10622558C2214yescomplemented
70#10622557C2214yescomplemented
71#10622555C2212yes—
72C22⋊C4×Dic11C2212yes—
73#10622281C2214yescomplemented
74#10622280C2214yescomplemented
75#10622269C2214yescomplemented
76#10622260C2214yescomplemented
77C25×C11C2311yescharacteristic
78C25×C11C2311yescharacteristic
79C24×D11C2311yescharacteristic
80C22×D4×C11—24no—
81C22×D4×C11—44no—
82C22×D4×C11C2312yes—
83C22×D4×C11C2312yes—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—44no—
90C22×C22⋊D11—44no—
91C22×C22⋊D11C2314yes—
92C22×C22⋊D11C2312yes—
93C22×C22⋊D11C2312yes—
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2311yescharacteristic
96C23×Dic11C2311yescharacteristic
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C22×C4×D11—24no—
100C22×C4×D11—44no—
101C22×C4×D11C2314yes—
102C22×Dic22C2312yes—
103C22×Dic22C2312yes—
104C11×#123—44no—
105C2×C11×C4⋊C4C2314yes—
106C2×C11×C22⋊C4—24no—
107C2×C11×C22⋊C4C2312yes—
108C2×C11×C22⋊C4C2312yes—
109C2×C11×C22⋊C4C2312yes—
110C2×C11×C22⋊C4C2314yes—
111C2×C11×C22⋊C4C2312yes—
112C2×C11×C22⋊C4C2312yes—
113C2×C11×C22⋊C4C2314yes—
114C2×C22⋊Dic11—24no—
115C2×C22⋊Dic11—24no—
116C2×C22⋊Dic11D418yes—
117C2×C22⋊Dic11C2312yes—
118C2×C22⋊Dic11C2312yes—
119C2×C22⋊Dic11C2312yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2312yes—
124C2×C22⋊Dic11C2314yes—
125C2×C22⋊Dic11C2312yes—
126C2×C22⋊Dic11C2312yes—
127#66991—216no—
128#66991—216no—
129#66988—44no—
130#66982—44no—
131C2×(C2×D11)⋊C4C2314yes—
132C2×(C2×D11)⋊C4C2314yes—
133C2×(C2×D11)⋊C4C2314yes—
134C2×(C2×D11)⋊C4C2314yes—
135C2×C4⋊Dic11—24no—
136C2×C4⋊Dic11C2312yes—
137C2×C4⋊Dic11C2312yes—
138C2×C4⋊Dic11C2314yes—
139C2×C4⋊Dic11C2314yes—
140#66977—28no—
141#66977—28no—
142C2×Dic11⋊C4C2312yes—
143C2×Dic11⋊C4C2312yes—
144C2×Dic11⋊C4C2312yes—
145C2×Dic11⋊C4C2312yes—
146C2×Dic11⋊C4C2314yes—
147C2×Dic11⋊C4C2314yes—
148C2×Dic11⋊C4C2314yes—
149C2×C4×Dic11C2314yes—
150#66949—48no—
151#66939—44no—
152#66938—48no—
153#66931—28no—
154#66931—28no—
155#66931—28no—
156#66931—28no—
157C11×#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2314yes—
162C11⋊#95C2314yes—
163#36718—111nomaximal, Sylow
164C24×C11—24no—
165C24×C11—22no—
166C24×C11—24no—
167C24×C11—42no—
168C24×C11—42no—
169C24×C11—42no—
170C24×C11—42no—
171C24×C11C2×D414yes—
172C24×C11C2412yes—
173C24×C11C2411yescharacteristic
174C24×C11C2411yescharacteristic
175C24×C11C2411yescharacteristic
176C23×D11—22no—
177C23×D11—24no—
178C23×D11—24no—
179C23×D11—42no—
180C23×D11C2412yes—
181C2×D4×C11—24no—
182C2×D4×C11—24no—
183C2×D4×C11—24no—
184C2×D4×C11—24no—
185C2×D4×C11—42no—
186C2×D4×C11—42no—
187C2×D4×C11—416no—
188C22×C4×C11—22no—
189C22×C4×C11—24no—
190C22×C4×C11—22no—
191C22×C4×C11—22no—
192C22×C4×C11—42no—
193C22×C4×C11—42no—
194C22×C4×C11C2414yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2412yes—
198C2×C22⋊D11—28no—
199C2×C22⋊D11—24no—
200C2×C22⋊D11—24no—
201C2×C22⋊D11—28no—
202C2×C22⋊D11—24no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—42no—
205C2×C22⋊D11—42no—
206C2×C22⋊D11—44no—
207C2×C22⋊D11—416no—
208C2×C22⋊D11—416no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—42no—
213C22×Dic11—42no—
214C22×Dic11—42no—
215C22×Dic11—42no—
216C22×Dic11—42no—
217C22×Dic11C2×D414yes—
218C22×Dic11C2×D414yes—
219C22×Dic11C2414yes—
220C22×Dic11C2412yes—
221C22×Dic11C2412yes—
222C22×Dic11C2412yes—
223C22×Dic11C2412yes—
224C22×Dic11C2412yes—
225C2×C4×D11—28no—
226C2×C4×D11—28no—
227C2×C4×D11—44no—
228C2×C4×D11—416no—
229C2×Dic22—24no—
230C2×Dic22—24no—
231C2×Dic22—44no—
232C2×Dic22—44no—
233C11×C4⋊C4—28no—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—24no—
236C11×C22⋊C4—24no—
237C11×C22⋊C4—44no—
238C11×C22⋊C4—42no—
239C11×C22⋊C4—42no—
240C11×C22⋊C4—44no—
241C22⋊Dic11—28no—
242C22⋊Dic11—24no—
243C22⋊Dic11—24no—
244C22⋊Dic11—24no—
245C22⋊Dic11—44no—
246C22⋊Dic11—42no—
247C22⋊Dic11—42no—
248C22⋊Dic11—44no—
249C22⋊Dic11C2×D418yes—
250C22⋊Dic11C2×D418yes—
251(C2×D11)⋊C4—28no—
252(C2×D11)⋊C4—28no—
253(C2×D11)⋊C4—44no—
254(C2×D11)⋊C4—44no—
255C4⋊Dic11—24no—
256C4⋊Dic11—24no—
257C4⋊Dic11—28no—
258C4⋊Dic11—44no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—24no—
263Dic11⋊C4—28no—
264Dic11⋊C4—44no—
265Dic11⋊C4—44no—
266C4×Dic11—44no—
267C2×#543—111no—
268C22×#121—111no—
269#2848—112no—
270#2681—114no—
271#2681—114no—
272#2672—114no—
273#2672—114no—
274#2626—112no—
275#2583—112no—
276#2435—112no—
277#2405—111no—
278#2405—111no—
279#2405—111no—
280#2405D1111yescharacteristic, complemented
281#2312—111no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—28no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—24no—
294C23×C11—22no—
295C23×C11—24no—
296C23×C11—44no—
297C23×C11—44no—
298C23×C11—44no—
299C23×C11—44no—
300C23×C11—44no—
301C23×C11—88no—
302C23×C11—88no—
303C23×C11C22×D412yes—
304C23×C11C22×D412yes—
305C23×C11C22×D412yes—
306C23×C112−1+414yes—
307C23×C11C2511yescharacteristic
308C22×D11—28no—
309C22×D11—22no—
310C22×D11—24no—
311C22×D11—22no—
312C22×D11—24no—
313C22×D11—416no—
314C22×D11—44no—
315C22×D11—44no—
316C22×D11H(5,𝔽2)14yes—
317D4×C11—48no—
318D4×C11—48no—
319C2×C4×C11—28no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—24no—
325C2×C4×C11—24no—
326C2×C4×C11—24no—
327C2×C4×C11—24no—
328C2×C4×C11—24no—
329C2×C4×C11—82no—
330C2×C4×C11—82no—
331C2×C4×C11H(5,𝔽2)14yes—
332C22⋊D11—416no—
333C22⋊D11—48no—
334C22⋊D11—48no—
335C2×Dic11—24no—
336C2×Dic11—24no—
337C2×Dic11—22no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—24no—
341C2×Dic11—24no—
342C2×Dic11—24no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—24no—
346C2×Dic11—24no—
347C2×Dic11—44no—
348C2×Dic11—44no—
349C2×Dic11—44no—
350C2×Dic11—82no—
351C2×Dic11—82no—
352C2×Dic11C22×D414yes—
353C2×Dic11C22×D414yes—
354C4×D11—416no—
355Dic22—84no—
356Dic22—84no—
357C23×D4—111no—
358C23×D4—111no—
359C23×D4C2×D1111yescharacteristic
360C24×C4—111no—
361#543—228no—
362C2×#124—114no—
363C2×#123—112no—
364C2×#123—112no—
365C2×#123—112no—
366C2×#123C2×D1112yescomplemented
367C2×C22⋊Q8—112no—
368C2×C22⋊Q8—112no—
369C2×C22⋊Q8—114no—
370C2×C22⋊Q8—112no—
371C2×C22⋊Q8—112no—
372C2×C22⋊Q8—112no—
373C2×C22⋊Q8—112no—
374C2×#121—114no—
375C2×#121—114no—
376C2×#121—228no—
377C22×C4⋊C4—111no—
378C22×C22⋊C4—111no—
379C22×C22⋊C4—111no—
380C22×C22⋊C4—111no—
381C22×C22⋊C4C2×D1111yescharacteristic
382#399—114no—
383#398—114no—
384#396—114no—
385#396—114no—
386#395—114no—
387#394—114no—
388#394—114no—
389#394—114no—
390#394—114no—
391#394—114no—
392#394C2×D1114yescomplemented
393#393—114no—
394#390—114no—
395#389—114no—
396#389—114no—
397#388—114no—
398#388—114no—
399#386—112no—
400#386—112no—
401#386—112no—
402#386C2×D1112yescomplemented
403#385—112no—
404#385—114no—
405#385—112no—
406#385—112no—
407#385—114no—
408#385C2×D1112yes—
409#380—112no—
410#380—114no—
411#379—111no—
412#379—112no—
413#379—112no—
414#379—112no—
415#379C2×D1111yescharacteristic
416#379C2×D1112yes—
417C4×C22⋊C4—112no—
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—28no—
421C22×C11—22no—
422C22×C11—22no—
423C22×C11—22no—
424C22×C11—22no—
425C22×C11—22no—
426C22×C11—22no—
427C22×C11—44no—
428C22×C11—44no—
429C22×C11—42no—
430C22×C11—42no—
431C22×C11—42no—
432C22×C11—44no—
433C22×C11—44no—
434C22×C11—88no—
435C22×C11—88no—
436C22×C11#53614yes—
437C22×C11C23×D411yescharacteristic
438C22×C11C2×H(5,𝔽2)12yes—
439C22×C11C2×H(5,𝔽2)12yes—
440C22×C11C2×2−1+412yes—
441C2×D11—24no—
442C2×D11—28no—
443C2×D11—416no—
444C2×D11—42no—
445C2×D11—42no—
446C2×D11—44no—
447C4×C11—24no—
448C4×C11—42no—
449C4×C11—42no—
450C4×C11—44no—
451Dic11—24no—
452Dic11—24no—
453Dic11—42no—
454Dic11—42no—
455Dic11—42no—
456Dic11—44no—
457C25—111no—
458C25C22×D1111yescharacteristic
459C25C22×D1111yescharacteristic
460C22×Q8—112no—
461C22×Q8—112no—
462C22×D4—24no—
463C22×D4—44no—
464C22×D4—112no—
465C22×D4—112no—
466C22×D4—114no—
467C22×D4—224no—
468C22×D4—224no—
469C22×D4—444no—
470C22×D4—444no—
471C22×D4C22×D1112yes—
472C22×D4C22×D1112yes—
473C23×C4—111no—
474C23×C4—111no—
475C23×C4—111no—
476C23×C4—111no—
477C23×C4—111no—
478C23×C4—114no—
479C23×C4—224no—
480C23×C4—444no—
481C23×C4C22×D1111yescharacteristic
482C23×C4C22×D1111yescharacteristic
483C23×C4C22×D1111yescharacteristic
484#124—448no—
485#123—44no—
486#123—444no—
487#123—444no—
488#123—444no—
489C22⋊Q8—228no—
490C22⋊Q8—228no—
491C22⋊Q8—228no—
492C22⋊Q8—228no—
493C22⋊Q8—228no—
494C22⋊Q8—228no—
495C22⋊Q8—448no—
496#121—2216no—
497#121—2216no—
498C2×C4⋊C4—114no—
499C2×C4⋊C4—112no—
500C2×C4⋊C4—112no—
501C2×C4⋊C4—112no—
502C2×C4⋊C4—112no—
503C2×C4⋊C4—112no—
504C2×C4⋊C4—112no—
505C2×C4⋊C4—114no—
506C2×C4⋊C4—114no—
507C2×C4⋊C4—114no—
508C2×C4⋊C4—114no—
509C2×C4⋊C4—224no—
510C2×C4⋊C4C22×D1114yes—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—118no—
513C2×C22⋊C4—112no—
514C2×C22⋊C4—112no—
515C2×C22⋊C4—114no—
516C2×C22⋊C4—112no—
517C2×C22⋊C4—112no—
518C2×C22⋊C4—112no—
519C2×C22⋊C4—114no—
520C2×C22⋊C4—114no—
521C2×C22⋊C4—112no—
522C2×C22⋊C4—112no—
523C2×C22⋊C4—114no—
524C2×C22⋊C4—114no—
525C2×C22⋊C4—114no—
526C2×C22⋊C4—114no—
527C2×C22⋊C4—224no—
528C2×C22⋊C4—224no—
529C2×C22⋊C4C22×D1112yes—
530C2×C22⋊C4C22×D1112yes—
531C2×C22⋊C4C22×D1112yes—
532C2×C22⋊C4C22×D1112yes—
533C2×C22⋊C4C22×D1112yes—
534C2×C22⋊C4C22×D1114yes—
535C2×C22⋊C4C22×D1114yes—
536C2×C42—114no—
537#95—114no—
538#95—114no—
539#95—114no—
540#95—114no—
541#95—114no—
542#95C22×D1114yes—
543C2×C11—24no—
544C2×C11—42no—
545C2×C11—42no—
546C2×C11—82no—
547C2×C11C2×#53611yescharacteristic
548C2×C11#348411yescharacteristic
549C2×C11#348411yescharacteristic
550C2×C11#353614yes—
551D11—44no—
552C24—24no—
553C24—22no—
554C24—24no—
555C24—42no—
556C24—42no—
557C24—42no—
558C24—42no—
559C24—112no—
560C24—224no—
561C24—222no—
562C24—224no—
563C24—442no—
564C24D4×D1114yes—
565C24C23×D1112yes—
566C24C23×D1111yescharacteristic
567C24C23×D1111yescharacteristic
568C24C23×D1111yescharacteristic
569C2×Q8—224no—
570C2×Q8—224no—
571C2×Q8—444no—
572C2×Q8—444no—
573C2×D4—24no—
574C2×D4—24no—
575C2×D4—24no—
576C2×D4—24no—
577C2×D4—42no—
578C2×D4—42no—
579C2×D4—416no—
580C2×D4—228no—
581C2×D4—224no—
582C2×D4—224no—
583C2×D4—228no—
584C2×D4—224no—
585C2×D4—224no—
586C2×D4—444no—
587C2×D4—442no—
588C2×D4—442no—
589C2×D4—4416no—
590C2×D4—4416no—
591C22×C4—22no—
592C22×C4—24no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—112no—
598C22×C4—112no—
599C22×C4—114no—
600C22×C4—114no—
601C22×C4—114no—
602C22×C4—112no—
603C22×C4—112no—
604C22×C4—112no—
605C22×C4—228no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—228no—
610C22×C4—444no—
611C22×C4—4416no—
612C22×C4—442no—
613C22×C4—442no—
614C22×C4—442no—
615C22×C4—442no—
616C22×C4—442no—
617C22×C4C23×D1114yes—
618C22×C4C23×D1112yes—
619C22×C4C23×D1112yes—
620C22×C4C23×D1112yes—
621C4⋊C4—28no—
622C4⋊C4—228no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4—224no—
626C4⋊C4—224no—
627C4⋊C4—224no—
628C4⋊C4—224no—
629C4⋊C4—228no—
630C4⋊C4—444no—
631C4⋊C4—444no—
632C4⋊C4—444no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—24no—
636C22⋊C4—42no—
637C22⋊C4—44no—
638C22⋊C4—42no—
639C22⋊C4—44no—
640C22⋊C4—118no—
641C22⋊C4—118no—
642C22⋊C4—228no—
643C22⋊C4—228no—
644C22⋊C4—228no—
645C22⋊C4—224no—
646C22⋊C4—224no—
647C22⋊C4—224no—
648C22⋊C4—444no—
649C22⋊C4—444no—
650C22⋊C4—442no—
651C22⋊C4—444no—
652C22⋊C4—442no—
653C22⋊C4—444no—
654C42—444no—
655C11#3671811yescharacteristic, complemented, Sylow
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—28no—
665C23—22no—
666C23—22no—
667C23—22no—
668C23—24no—
669C23—24no—
670C23—44no—
671C23—44no—
672C23—44no—
673C23—44no—
674C23—44no—
675C23—88no—
676C23—88no—
677C23—114no—
678C23—228no—
679C23—222no—
680C23—224no—
681C23—224no—
682C23—222no—
683C23—4416no—
684C23—444no—
685C23—444no—
686C23C2×D4×D1112yes—
687C23C2×D4×D1112yes—
688C23C2×D4×D1112yes—
689C23#6704314yes—
690C23C24×D1111yescharacteristic
691Q8—884no—
692Q8—884no—
693D4—48no—
694D4—48no—
695D4—4416no—
696D4—448no—
697D4—448no—
698C2×C4—28no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—82no—
709C2×C4—82no—
710C2×C4—114no—
711C2×C4—114no—
712C2×C4—224no—
713C2×C4—224no—
714C2×C4—222no—
715C2×C4—222no—
716C2×C4—222no—
717C2×C4—224no—
718C2×C4—224no—
719C2×C4—224no—
720C2×C4—224no—
721C2×C4—224no—
722C2×C4—222no—
723C2×C4—222no—
724C2×C4—4416no—
725C2×C4—444no—
726C2×C4—444no—
727C2×C4—444no—
728C2×C4—882no—
729C2×C4—882no—
730C2×C4#6703714yes—
731C22—22no—
732C22—22no—
733C22—28no—
734C22—22no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—22no—
739C22—22no—
740C22—44no—
741C22—44no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—44no—
746C22—44no—
747C22—88no—
748C22—88no—
749C22—224no—
750C22—228no—
751C22—4416no—
752C22—442no—
753C22—442no—
754C22—444no—
755C22#1062317914yes—
756C22C22×D4×D1111yescharacteristic
757C22C2×#6703712yes—
758C22C2×#6704312yes—
759C22D11×H(5,𝔽2)12yes—
760C4—24no—
761C4—42no—
762C4—42no—
763C4—44no—
764C4—224no—
765C4—224no—
766C4—442no—
767C4—442no—
768C4—442no—
769C4—444no—
770C2—24no—
771C2—42no—
772C2—42no—
773C2—82no—
774C2—444no—
775C2C2×#1062317911yescharacteristic
776C2#1308224511yescharacteristic
777C2#1308224811yescharacteristic
778C2#1308283614yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2405C2
prime radicalC22×#66991C2
hypercenter#2405D11
hypocenterC11#36718
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2405

Complements

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

NH ≅ G/Ntype
1. C2×#10623014C2semidirect
3. #13076902C2semidirect
4. #13074970C2semidirect
5. #13074968C2semidirect
6. #13074873C2semidirect
7. #13074871C2semidirect
8. #13074425C2semidirect
9. #13073993C2semidirect
10. #13072265C2semidirect
11. #13071944C2semidirect
12. #13071943C2semidirect
13. #13071939C2semidirect
14. #13071212C2semidirect
15. C11×#2405C2semidirect
20. C2×C11×#123C22semidirect
28. C2×#66988C22semidirect
29. C2×#66982C22semidirect
31. C2×#66977C22semidirect
32. C2×#66977C22semidirect
33. C2×#66949C22semidirect
34. C2×#66939C22semidirect
35. C2×#66938C22semidirect
39. C2×#66931C22semidirect
40. C2×#66931C22semidirect
41. C11×#394C22semidirect
42. C11×#386C22semidirect
48. #10622835C22semidirect
49. #10622833C22semidirect
50. #10622826C22semidirect
52. #10622602C22semidirect
53. #10622598C22semidirect
54. #10622597C22semidirect
55. #10622574C22semidirect
56. #10622574C22semidirect
57. #10622572C22semidirect
58. #10622572C22semidirect
59. #10622571C22semidirect
60. #10622570C22semidirect
64. #10622562C22semidirect
65. #10622561C22semidirect
66. #10622561C22semidirect
67. #10622560C22semidirect
69. #10622558C22semidirect
70. #10622557C22semidirect
73. #10622281C22semidirect
74. #10622280C22semidirect
75. #10622269C22semidirect
76. #10622260C22semidirect
280. #2405D11semidirect
366. C2×#123C2×D11semidirect
392. #394C2×D11semidirect
402. #386C2×D11semidirect
655. C11#36718semidirect

Maximal subgroups

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

subgroupindex
C2×#106230142
C22×#669912
#130769022
#130749702
#130749682
#130748732
#130748712
#130744252
#130739932
#130722652
#130719442
#130719432
#130719392
#130712122
C11×#24052
#3671811