Finite Group Databasebeta

← #14960748

Subgroups — #14960748

Order 2816.

2842 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623165C211yesmaximal, characteristic, complemented
2C22×#66983C211yesmaximal, characteristic
3#13076903C211yesmaximal, characteristic, complemented
4#13074971C214yesmaximal, complemented
5#13074969C214yesmaximal, complemented
6#13074870C214yesmaximal, complemented
7#13074868C214yesmaximal, complemented
8#13074424C211yesmaximal, characteristic, complemented
9#13074423C211yesmaximal, characteristic, complemented
10#13073993C212yesmaximal, complemented
11#13072265C212yesmaximal, complemented
12#13071945C212yesmaximal, complemented
13#13071941C212yesmaximal, complemented
14#13071213C211yesmaximal, characteristic, complemented
15C11×#2848C211yesmaximal, characteristic, complemented
16C24×C4×C11C2211yescharacteristic
17C23×C22⋊D11C2211yescharacteristic
18C23×C22⋊D11C2211yescharacteristic
19C23×D44C2211yescharacteristic
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×C22⋊Q8C2212yescomplemented
22C2×#66999C2212yescomplemented
23C2×#66983—28no—
24C2×#66983C2214yes—
25C2×#66983C2214yes—
26C22×(C2×D11)⋊C4C2211yescharacteristic
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×C4⋊Dic11C2211yescharacteristic
29C2×#66977C2211yescharacteristic
30C2×#66977C2212yescomplemented
31#10623165—28no—
32C2×#66950C2212yescomplemented
33C2×#66949C2212yescomplemented
34C2×#66949C2212yescomplemented
35C2×#66947C2214yescomplemented
36C2×#66938C2214yescomplemented
37C2×#66936C2214yescomplemented
38C2×C22⋊C4×D11C2212yes—
39C2×#66931C2212yes—
40C11×#385C2212yes—
41C11×#385C2214yescomplemented
42C11×#380C2211yescharacteristic
43C11×#380C2212yescomplemented
44C11×#379C2212yes—
45#10622860C2212yes—
46#10622844C2212yescomplemented
47#10622825C2211yescharacteristic
48#10622825C2212yescomplemented
49#10622823C2212yes—
50#10622823C2214yescomplemented
51#10622607C2214yescomplemented
52#10622607C2214yescomplemented
53#10622605C2212yescomplemented
54#10622604C2214yescomplemented
55#10622603C2214yescomplemented
56#10622598C2214yescomplemented
57#10622597C2214yescomplemented
58#10622574C2214yescomplemented
59#10622574C2214yescomplemented
60#10622572C2214yescomplemented
61#10622572C2214yescomplemented
62#10622570C2214yescomplemented
63#10622569C2214yescomplemented
64#10622568C2212yes—
65#10622568C2212yes—
66#10622568C2212yes—
67#10622563C2212yes—
68#10622559C2212yes—
69C22⋊C4×Dic11C2212yes—
70#10622290C2212yescomplemented
71#10622286C2212yescomplemented
72#10622285C2214yescomplemented
73#10622283C2214yescomplemented
74#10622278C2214yescomplemented
75#10622269C2214yescomplemented
76#10622260C2214yescomplemented
77C25×C11C2311yescharacteristic
78C24×D11C2311yescharacteristic
79C24×D11C2311yescharacteristic
80C22×Q8×C11C2311yescharacteristic
81C23×C4×C11—24no—
82C23×C4×C11—44no—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2312yes—
85C23×C4×C11C2312yes—
86C23×C4×C11C2311yescharacteristic
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—44no—
90C22×C22⋊D11—44no—
91C22×C22⋊D11C2314yes—
92C22×C22⋊D11C2314yes—
93C23×Dic11C2311yescharacteristic
94C23×Dic11C2311yescharacteristic
95C22×D44—24no—
96C22×D44—44no—
97C22×D44C2314yes—
98C22×C4×D11C2312yes—
99C22×C4×D11C2312yes—
100C22×Dic22C2312yes—
101C22×Dic22C2311yescharacteristic
102C11×C22⋊Q8—24no—
103C11×C22⋊Q8—44no—
104C2×C11×C4⋊C4C2314yes—
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2312yes—
107C2×C11×C4⋊C4C2312yes—
108C2×C11×C22⋊C4C2312yes—
109C2×C11×C22⋊C4C2314yes—
110C2×C11×C22⋊C4C2312yes—
111C2×C11×C22⋊C4C2314yes—
112C2×C22⋊Dic11C2312yes—
113C2×C22⋊Dic11C2314yes—
114C2×C22⋊Dic11C2312yes—
115C2×C22⋊Dic11C2314yes—
116#66999—28no—
117#66983—216no—
118#66983—216no—
119C2×(C2×D11)⋊C4—24no—
120C2×(C2×D11)⋊C4D418yes—
121C2×(C2×D11)⋊C4C2312yes—
122C2×(C2×D11)⋊C4C2312yes—
123C2×(C2×D11)⋊C4C2312yes—
124C2×(C2×D11)⋊C4C2312yes—
125C2×(C2×D11)⋊C4C2314yes—
126C2×(C2×D11)⋊C4C2314yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130C2×(C2×D11)⋊C4C2314yes—
131C2×(C2×D11)⋊C4C2312yes—
132C2×(C2×D11)⋊C4C2312yes—
133C2×C4⋊Dic11—24no—
134C2×C4⋊Dic11C2312yes—
135C2×C4⋊Dic11C2314yes—
136C2×C4⋊Dic11C2311yescharacteristic
137C2×C4⋊Dic11C2314yes—
138C2×C4⋊Dic11C2312yes—
139#66977—24no—
140#66977—44no—
141C2×Dic11⋊C4C2312yes—
142C2×Dic11⋊C4C2312yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2312yes—
145C2×Dic11⋊C4C2314yes—
146C2×C4×Dic11C2314yes—
147#66950—28no—
148#66949—28no—
149#66949—28no—
150#66947—48no—
151#66938—48no—
152#66936—48no—
153C22⋊C4×D11—28no—
154#66931—28no—
155C11×#95C2314yes—
156C11×#95C2312yes—
157C11⋊#95C2314yes—
158C11⋊#95C2314yes—
159C11⋊#95C2314yes—
160C11⋊#95C2314yes—
161C11⋊#95C2312yes—
162#36718—111nomaximal, Sylow
163C24×C11—22no—
164C24×C11—24no—
165C24×C11—22no—
166C24×C11—22no—
167C24×C11—42no—
168C24×C11C2412yes—
169C24×C11C2411yescharacteristic
170C23×D11—22no—
171C23×D11—22no—
172C23×D11—22no—
173C23×D11—22no—
174C23×D11—22no—
175C23×D11—42no—
176C23×D11—42no—
177C23×D11—42no—
178C23×D11—42no—
179C23×D11C2×D414yes—
180C23×D11C2412yes—
181C23×D11C2412yes—
182C2×Q8×C11—22no—
183C2×Q8×C11—42no—
184C22×C4×C11—22no—
185C22×C4×C11—24no—
186C22×C4×C11—24no—
187C22×C4×C11—24no—
188C22×C4×C11—24no—
189C22×C4×C11—24no—
190C22×C4×C11—42no—
191C22×C4×C11—42no—
192C22×C4×C11—42no—
193C22×C4×C11—416no—
194C22×C4×C11C2×D414yes—
195C22×C4×C11C2414yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2411yescharacteristic
199C22×C4×C11C2411yescharacteristic
200C22×C4×C11C2412yes—
201C2×C22⋊D11—28no—
202C2×C22⋊D11—28no—
203C2×C22⋊D11—28no—
204C2×C22⋊D11—28no—
205C2×C22⋊D11—44no—
206C2×C22⋊D11—44no—
207C2×C22⋊D11—416no—
208C2×C22⋊D11—416no—
209C22×Dic11—22no—
210C22×Dic11—42no—
211C22×Dic11—42no—
212C22×Dic11C2×D414yes—
213C22×Dic11C2414yes—
214C22×Dic11C2412yes—
215C22×Dic11C2412yes—
216C22×Dic11C2412yes—
217C22×Dic11C2412yes—
218C2×D44—28no—
219C2×D44—28no—
220C2×D44—44no—
221C2×D44—416no—
222C2×C4×D11—24no—
223C2×C4×D11—24no—
224C2×C4×D11—44no—
225C2×C4×D11—44no—
226C2×Dic22—24no—
227C2×Dic22—22no—
228C2×Dic22—44no—
229C2×Dic22—42no—
230C11×C4⋊C4—22no—
231C11×C4⋊C4—24no—
232C11×C4⋊C4—28no—
233C11×C4⋊C4—42no—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—28no—
236C11×C22⋊C4—24no—
237C11×C22⋊C4—44no—
238C22⋊Dic11—24no—
239C22⋊Dic11—28no—
240C22⋊Dic11—24no—
241C22⋊Dic11—44no—
242(C2×D11)⋊C4—24no—
243(C2×D11)⋊C4—24no—
244(C2×D11)⋊C4—24no—
245(C2×D11)⋊C4—24no—
246(C2×D11)⋊C4—44no—
247(C2×D11)⋊C4—44no—
248(C2×D11)⋊C4—44no—
249(C2×D11)⋊C4—44no—
250(C2×D11)⋊C4—44no—
251(C2×D11)⋊C4—44no—
252(C2×D11)⋊C4C2×D418yes—
253(C2×D11)⋊C4C2×D418yes—
254C4⋊Dic11—24no—
255C4⋊Dic11—28no—
256C4⋊Dic11—22no—
257C4⋊Dic11—44no—
258C4⋊Dic11—42no—
259Dic11⋊C4—24no—
260Dic11⋊C4—24no—
261Dic11⋊C4—24no—
262Dic11⋊C4—28no—
263Dic11⋊C4—44no—
264C4×Dic11—44no—
265C2×#543—111no—
266C22×#121—111no—
267#2848—111no—
268#2848D1111yescharacteristic, complemented
269#2681—114no—
270#2681—114no—
271#2672—114no—
272#2672—114no—
273#2626—111no—
274#2626—111no—
275#2583—112no—
276#2435—112no—
277#2405—112no—
278#2405—112no—
279#2312—111no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—28no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—48no—
290C23×C11—48no—
291C23×C11—44no—
292C23×C11—44no—
293C23×C11C22×D412yes—
294C23×C11H(5,𝔽2)14yes—
295C23×C112−1+412yes—
296C23×C112−1+412yes—
297C23×C11C2511yescharacteristic
298C22×D11—24no—
299C22×D11—24no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—28no—
303C22×D11—22no—
304C22×D11—24no—
305C22×D11—24no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—44no—
309C22×D11—44no—
310C22×D11—44no—
311C22×D11—44no—
312C22×D11—44no—
313C22×D11—84no—
314C22×D11—84no—
315C22×D11—84no—
316C22×D11—84no—
317C22×D11C22×D414yes—
318Q8×C11—82no—
319C2×C4×C11—28no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—22no—
326C2×C4×C11—24no—
327C2×C4×C11—24no—
328C2×C4×C11—24no—
329C2×C4×C11—24no—
330C2×C4×C11—24no—
331C2×C4×C11—44no—
332C2×C4×C11—48no—
333C2×C4×C11—48no—
334C2×C4×C11C22×D412yes—
335C2×C4×C11C22×D412yes—
336C2×C4×C11H(5,𝔽2)14yes—
337C22⋊D11—416no—
338C22⋊D11—416no—
339C2×Dic11—24no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—22no—
343C2×Dic11—24no—
344C2×Dic11—24no—
345C2×Dic11—24no—
346C2×Dic11—24no—
347C2×Dic11—24no—
348C2×Dic11—24no—
349C2×Dic11—44no—
350C2×Dic11—44no—
351C2×Dic11C22×D414yes—
352D44—416no—
353C4×D11—84no—
354C4×D11—84no—
355Dic22—84no—
356Dic22—82no—
357C23×D4—111no—
358C23×D4—111no—
359C23×D4—111no—
360C24×C4C2×D1111yescharacteristic
361#543—228no—
362C2×#124—114no—
363C2×#123—114no—
364C2×#123—114no—
365C2×C22⋊Q8—112no—
366C2×C22⋊Q8—111no—
367C2×C22⋊Q8—112no—
368C2×C22⋊Q8—112no—
369C2×C22⋊Q8—112no—
370C2×C22⋊Q8—112no—
371C2×C22⋊Q8—112no—
372C2×C22⋊Q8C2×D1111yescharacteristic
373C2×C22⋊Q8C2×D1112yescomplemented
374C2×#121—114no—
375C2×#121—114no—
376C2×#121—228no—
377C22×C4⋊C4—111no—
378C22×C22⋊C4—111no—
379C22×C22⋊C4—111no—
380C22×C22⋊C4—112no—
381#399—112no—
382#399—112no—
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#394—114no—
393#393—112no—
394#393—112no—
395#390—114no—
396#389—114no—
397#389—114no—
398#388—114no—
399#388—114no—
400#386—114no—
401#386—114no—
402#385—112no—
403#385—114no—
404#385—112no—
405#385—112no—
406#385C2×D1112yes—
407#385C2×D1114yescomplemented
408#380—111no—
409#380—112no—
410#380C2×D1111yescharacteristic
411#380C2×D1112yescomplemented
412#379—112no—
413#379—112no—
414#379—112no—
415#379—112no—
416#379C2×D1112yes—
417C4×C22⋊C4—112no—
418C22×C11—22no—
419C22×C11—22no—
420C22×C11—24no—
421C22×C11—24no—
422C22×C11—24no—
423C22×C11—24no—
424C22×C11—24no—
425C22×C11—416no—
426C22×C11—42no—
427C22×C11—42no—
428C22×C11—42no—
429C22×C11—42no—
430C22×C11#53614yes—
431C22×C11C23×D411yescharacteristic
432C22×C11C2×H(5,𝔽2)12yes—
433C22×C11C2×H(5,𝔽2)12yes—
434C22×C11C2×2−1+411yescharacteristic
435C22×C11C2×2−1+411yescharacteristic
436C2×D11—24no—
437C2×D11—24no—
438C2×D11—24no—
439C2×D11—44no—
440C2×D11—44no—
441C2×D11—42no—
442C2×D11—42no—
443C2×D11—42no—
444C2×D11—44no—
445C2×D11—44no—
446C2×D11—88no—
447C2×D11—88no—
448C4×C11—24no—
449C4×C11—22no—
450C4×C11—22no—
451C4×C11—42no—
452C4×C11—42no—
453C4×C11—44no—
454Dic11—24no—
455Dic11—42no—
456Dic11—42no—
457Dic11—42no—
458Dic11—44no—
459C25—111no—
460C25—111no—
461C25C22×D1111yescharacteristic
462C22×Q8—111no—
463C22×Q8—112no—
464C22×Q8C22×D1111yescharacteristic
465C22×D4—114no—
466C22×D4—114no—
467C22×D4—114no—
468C22×D4—224no—
469C22×D4—224no—
470C22×D4—224no—
471C22×D4—444no—
472C22×D4—444no—
473C22×D4—444no—
474C23×C4—24no—
475C23×C4—44no—
476C23×C4—111no—
477C23×C4—111no—
478C23×C4—112no—
479C23×C4—112no—
480C23×C4C22×D1111yescharacteristic
481C23×C4C22×D1112yes—
482C23×C4C22×D1112yes—
483C23×C4C22×D1111yescharacteristic
484#124—448no—
485#123—448no—
486#123—448no—
487C22⋊Q8—24no—
488C22⋊Q8—44no—
489C22⋊Q8—228no—
490C22⋊Q8—228no—
491C22⋊Q8—228no—
492C22⋊Q8—228no—
493C22⋊Q8—228no—
494C22⋊Q8—224no—
495C22⋊Q8—444no—
496#121—2216no—
497#121—2216no—
498C2×C4⋊C4—114no—
499C2×C4⋊C4—111no—
500C2×C4⋊C4—112no—
501C2×C4⋊C4—112no—
502C2×C4⋊C4—112no—
503C2×C4⋊C4—112no—
504C2×C4⋊C4—114no—
505C2×C4⋊C4—112no—
506C2×C4⋊C4—114no—
507C2×C4⋊C4—114no—
508C2×C4⋊C4—224no—
509C2×C4⋊C4C22×D1111yescharacteristic
510C2×C4⋊C4C22×D1112yes—
511C2×C4⋊C4C22×D1114yes—
512C2×C4⋊C4C22×D1112yes—
513C2×C22⋊C4—118no—
514C2×C22⋊C4—112no—
515C2×C22⋊C4—112no—
516C2×C22⋊C4—112no—
517C2×C22⋊C4—114no—
518C2×C22⋊C4—112no—
519C2×C22⋊C4—112no—
520C2×C22⋊C4—112no—
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—114no—
528C2×C22⋊C4—114no—
529C2×C22⋊C4—114no—
530C2×C22⋊C4—228no—
531C2×C22⋊C4—224no—
532C2×C22⋊C4C22×D1112yes—
533C2×C22⋊C4C22×D1114yes—
534C2×C22⋊C4C22×D1112yes—
535C2×C22⋊C4C22×D1114yes—
536C2×C42—114no—
537#95—114no—
538#95—114no—
539#95—112no—
540#95—114no—
541#95—114no—
542#95C22×D1112yes—
543#95C22×D1114yes—
544C2×C11—24no—
545C2×C11—44no—
546C2×C11C2×#53611yescharacteristic
547C2×C11#348411yescharacteristic
548C2×C11#348411yescharacteristic
549C2×C11#353612yes—
550C2×C11#353612yes—
551D11—44no—
552D11—82no—
553C24—22no—
554C24—24no—
555C24—22no—
556C24—22no—
557C24—42no—
558C24—112no—
559C24—114no—
560C24—112no—
561C24—222no—
562C24—222no—
563C24—222no—
564C24—222no—
565C24—222no—
566C24—442no—
567C24—442no—
568C24—442no—
569C24—442no—
570C24C23×D1112yes—
571C24C23×D1111yescharacteristic
572C2×Q8—22no—
573C2×Q8—42no—
574C2×Q8—224no—
575C2×Q8—222no—
576C2×Q8—442no—
577C2×Q8—444no—
578C2×D4—228no—
579C2×D4—228no—
580C2×D4—228no—
581C2×D4—228no—
582C2×D4—228no—
583C2×D4—228no—
584C2×D4—444no—
585C2×D4—4416no—
586C2×D4—444no—
587C2×D4—444no—
588C2×D4—4416no—
589C2×D4—4416no—
590C22×C4—22no—
591C22×C4—24no—
592C22×C4—24no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—24no—
596C22×C4—42no—
597C22×C4—42no—
598C22×C4—42no—
599C22×C4—416no—
600C22×C4—112no—
601C22×C4—114no—
602C22×C4—114no—
603C22×C4—112no—
604C22×C4—112no—
605C22×C4—112no—
606C22×C4—224no—
607C22×C4—224no—
608C22×C4—222no—
609C22×C4—444no—
610C22×C4—444no—
611C22×C4—442no—
612C22×C4—442no—
613C22×C4D4×D1114yes—
614C22×C4C23×D1114yes—
615C22×C4C23×D1112yes—
616C22×C4C23×D1112yes—
617C22×C4C23×D1111yescharacteristic
618C22×C4C23×D1111yescharacteristic
619C22×C4C23×D1112yes—
620C4⋊C4—22no—
621C4⋊C4—24no—
622C4⋊C4—28no—
623C4⋊C4—42no—
624C4⋊C4—228no—
625C4⋊C4—224no—
626C4⋊C4—224no—
627C4⋊C4—224no—
628C4⋊C4—224no—
629C4⋊C4—222no—
630C4⋊C4—228no—
631C4⋊C4—442no—
632C4⋊C4—444no—
633C4⋊C4—444no—
634C22⋊C4—24no—
635C22⋊C4—28no—
636C22⋊C4—24no—
637C22⋊C4—44no—
638C22⋊C4—118no—
639C22⋊C4—118no—
640C22⋊C4—224no—
641C22⋊C4—224no—
642C22⋊C4—224no—
643C22⋊C4—224no—
644C22⋊C4—228no—
645C22⋊C4—224no—
646C22⋊C4—224no—
647C22⋊C4—444no—
648C22⋊C4—444no—
649C22⋊C4—444no—
650C22⋊C4—444no—
651C22⋊C4—444no—
652C22⋊C4—444no—
653C22⋊C4—444no—
654C42—444no—
655C11#3671811yescharacteristic, complemented, Sylow
656C23—22no—
657C23—22no—
658C23—28no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—48no—
666C23—48no—
667C23—44no—
668C23—44no—
669C23—114no—
670C23—224no—
671C23—222no—
672C23—224no—
673C23—222no—
674C23—228no—
675C23—222no—
676C23—224no—
677C23—222no—
678C23—224no—
679C23—222no—
680C23—444no—
681C23—444no—
682C23—444no—
683C23—444no—
684C23—444no—
685C23—884no—
686C23—884no—
687C23—884no—
688C23—884no—
689C23C2×D4×D1112yes—
690C23#6704012yes—
691C23#6704214yes—
692C23#6704312yes—
693C23C24×D1111yescharacteristic
694Q8—82no—
695Q8—882no—
696Q8—884no—
697D4—4416no—
698D4—4416no—
699D4—4416no—
700C2×C4—28no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—44no—
713C2×C4—48no—
714C2×C4—48no—
715C2×C4—114no—
716C2×C4—224no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—222no—
720C2×C4—224no—
721C2×C4—224no—
722C2×C4—224no—
723C2×C4—224no—
724C2×C4—224no—
725C2×C4—224no—
726C2×C4—444no—
727C2×C4—444no—
728C2×C4—884no—
729C2×C4—884no—
730C2×C4C2×D4×D1112yes—
731C2×C4C2×D4×D1112yes—
732C2×C4#6703714yes—
733C22—22no—
734C22—22no—
735C22—24no—
736C22—24no—
737C22—24no—
738C22—24no—
739C22—24no—
740C22—416no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—224no—
746C22—224no—
747C22—224no—
748C22—444no—
749C22—444no—
750C22—442no—
751C22—442no—
752C22—442no—
753C22—444no—
754C22—444no—
755C22—888no—
756C22—888no—
757C22#1062315914yes—
758C22C22×D4×D1111yescharacteristic
759C22C2×#6703712yes—
760C22C2×#6704011yescharacteristic
761C22C2×#6704212yes—
762C22C2×#6704311yescharacteristic
763C4—24no—
764C4—22no—
765C4—22no—
766C4—42no—
767C4—42no—
768C4—44no—
769C4—224no—
770C4—442no—
771C4—442no—
772C4—442no—
773C4—444no—
774C2—24no—
775C2—44no—
776C2—444no—
777C2—882no—
778C2C2×#1062315911yescharacteristic
779C2#1308224511yescharacteristic
780C2#1308224911yescharacteristic
781C2#1308284312yes—
782C2#1308284512yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC11×#2848C2
prime radicalC22×#66983C2
hypercenter#2848D11
hypocenterC11#36718
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ #2848

Complements

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

NH ≅ G/Ntype
1. C2×#10623165C2semidirect
3. #13076903C2semidirect
4. #13074971C2semidirect
5. #13074969C2semidirect
6. #13074870C2semidirect
7. #13074868C2semidirect
8. #13074424C2semidirect
9. #13074423C2semidirect
10. #13073993C2semidirect
11. #13072265C2semidirect
12. #13071945C2semidirect
13. #13071941C2semidirect
14. #13071213C2semidirect
15. C11×#2848C2semidirect
21. C2×C11×C22⋊Q8C22semidirect
22. C2×#66999C22semidirect
30. C2×#66977C22semidirect
32. C2×#66950C22semidirect
33. C2×#66949C22semidirect
34. C2×#66949C22semidirect
35. C2×#66947C22semidirect
36. C2×#66938C22semidirect
37. C2×#66936C22semidirect
41. C11×#385C22semidirect
43. C11×#380C22semidirect
46. #10622844C22semidirect
48. #10622825C22semidirect
50. #10622823C22semidirect
51. #10622607C22semidirect
52. #10622607C22semidirect
53. #10622605C22semidirect
54. #10622604C22semidirect
55. #10622603C22semidirect
56. #10622598C22semidirect
57. #10622597C22semidirect
58. #10622574C22semidirect
59. #10622574C22semidirect
60. #10622572C22semidirect
61. #10622572C22semidirect
62. #10622570C22semidirect
63. #10622569C22semidirect
70. #10622290C22semidirect
71. #10622286C22semidirect
72. #10622285C22semidirect
73. #10622283C22semidirect
74. #10622278C22semidirect
75. #10622269C22semidirect
76. #10622260C22semidirect
268. #2848D11semidirect
373. C2×C22⋊Q8C2×D11semidirect
407. #385C2×D11semidirect
411. #380C2×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×#106231652
C22×#669832
#130769032
#130749712
#130749692
#130748702
#130748682
#130744242
#130744232
#130739932
#130722652
#130719452
#130719412
#130712132
C11×#28482
#3671811