Finite Group Databasebeta

← #14916570

Subgroups — #14916570

Order 2816.

2586 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071782C212yesmaximal, complemented
2#13071773C212yesmaximal, complemented
3#13071701C212yesmaximal, complemented
4#13071668C212yesmaximal, complemented
5#13071565C212yesmaximal, complemented
6#13071545C212yesmaximal, complemented
7#13071545C212yesmaximal, complemented
8D4×C4⋊Dic11C212yesmaximal, complemented
9#13071410C214yesmaximal, complemented
10#13071277C214yesmaximal, complemented
11#13071225C212yesmaximal, complemented
12#13071208C212yesmaximal, complemented
13#13070999C211yesmaximal, characteristic, complemented
14C2×#10622825C211yesmaximal, characteristic, complemented
15C2×C11×#525C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C11×#525C4116yescomplemented
19C2×C11×#123C2212yes—
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×#121C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×C11×#120C2212yes—
25C2×C4×D4×C11C2212yes—
26C2×C4×D4×C11C2212yes—
27C2×C11×#117C2211yescharacteristic
28C22×C22⋊Dic11C2212yes—
29C2×D4×Dic11C2214yes—
30C2×#66979C2212yes—
31C2×#66979C2212yescomplemented
32C22×C4⋊Dic11C2212yes—
33C22×C4⋊Dic11C2212yescomplemented
34#10622860C2212yes—
35#10622843C2214yescomplemented
36#10622834C2214yes—
37#10622834C2214yes—
38#10622833C2214yes—
39#10622833C2214yes—
40#10622833C2214yes—
41#10622833C2214yescomplemented
42#10622825C2212yes—
43#10622825C2212yes—
44#10622825C2212yes—
45#10622825C2212yes—
46#10622825C2211yescharacteristic
47#10622825C2211yescharacteristic
48#10622825C2211yescharacteristic
49#10622825C2211yescharacteristic
50#10622825C2212yescomplemented
51#10622825C2212yescomplemented
52#10622824C2212yes—
53C4×C22⋊Dic11C2212yes—
54C4×C22⋊Dic11C2212yes—
55C2×C11⋊#95C2212yes—
56#10622598C2214yescomplemented
57#10622594C2214yescomplemented
58#10622594C2214yescomplemented
59#10622594C2214yescomplemented
60#10622594C2214yescomplemented
61C4⋊C4×Dic11C2214yescomplemented
62#10622564C2214yes—
63#10622564C2214yes—
64#10622564C2214yes—
65#10622564C2214yes—
66#10622564C2214yescomplemented
67#10622564C2214yescomplemented
68#10622563C2214yes—
69#10622563C2214yescomplemented
70C22⋊C4×Dic11C2214yes—
71C22⋊C4×Dic11C2214yescomplemented
72#10622549C2212yescomplemented
73#10622548C2212yescomplemented
74C4×C4⋊Dic11C2212yescomplemented
75C4×C4⋊Dic11C2212yescomplemented
76C25×C11C2311yescharacteristic
77C2×C11×#41—44no—
78C2×C11×#41C2×C418yescomplemented
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2312yes—
81C22×D4×C11C2312yes—
82C22×D4×C11C2312yes—
83C22×D4×C11C2311yescharacteristic
84C23×C4×C11—44no—
85C23×C4×C11C2×C418yescomplemented
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2312yes—
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×Dic11C2314yes—
94C23×Dic11C2314yes—
95C11×#123C2×C4116yescomplemented
96C11×C22⋊Q8C2×C418yescomplemented
97C11×C22⋊Q8C2×C418yescomplemented
98C11×#121C2×C418yes—
99C11×#121C2×C418yescomplemented
100C11×#120C2×C4116yescomplemented
101C4×D4×C11C2×C4116yescomplemented
102C4×D4×C11C2×C4116yescomplemented
103C11×#117C2×C418yescomplemented
104C2×C11×C4⋊C4C2312yes—
105C2×C11×C4⋊C4C2311yescharacteristic
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2312yes—
108C2×C11×C22⋊C4C2312yes—
109C2×C11×C22⋊C4C2312yes—
110C2×C11×C22⋊C4C2312yes—
111C2×C11×C22⋊C4C2312yes—
112C2×C11×C22⋊C4C2312yes—
113C2×C42×C11C2312yes—
114C2×C22⋊Dic11—44no—
115C2×C22⋊Dic11C2312yes—
116C2×C22⋊Dic11C2312yes—
117C2×C22⋊Dic11C2314yes—
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2312yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2312yes—
125D4×Dic11—48no—
126#66979—44no—
127#66979—44no—
128C2×C4⋊Dic11—44no—
129C2×C4⋊Dic11—44no—
130C2×C4⋊Dic11C2312yes—
131C2×C4⋊Dic11C2312yes—
132C2×C4⋊Dic11C2312yes—
133C2×C4⋊Dic11C2312yes—
134C2×C4⋊Dic11C2314yes—
135C2×C4⋊Dic11C2314yes—
136C2×C4⋊Dic11C2314yes—
137C2×C4⋊Dic11C2314yes—
138C2×C4×Dic11C2314yes—
139C2×C4×Dic11C2314yes—
140C2×C4×Dic11C2314yes—
141C2×C4×Dic11C2314yes—
142C11⋊#95C2314yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2312yes—
148C11⋊#95C2314yes—
149C11⋊#95C2312yes—
150C11⋊#95C2312yes—
151C11⋊#95C2312yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154#34362—111nomaximal, Sylow
155C24×C11—22no—
156C24×C11—22no—
157C24×C11—42no—
158C24×C11—42no—
159C24×C11C22×C414yes—
160C24×C11C2411yescharacteristic
161C24×C11C2411yescharacteristic
162C24×C11C2412yes—
163C24×C11C2411yescharacteristic
164C11×#41—416no—
165C2×Q8×C11—42no—
166C2×Q8×C11C22×C414yes—
167C2×D4×C11—24no—
168C2×D4×C11—24no—
169C2×D4×C11—42no—
170C2×D4×C11—42no—
171C2×D4×C11—42no—
172C2×D4×C11—42no—
173C2×D4×C11—42no—
174C2×D4×C11C22×C418yes—
175C2×D4×C11C22×C418yes—
176C2×D4×C11C22×C418yes—
177C2×D4×C11C22×C414yes—
178C22×C4×C11—24no—
179C22×C4×C11—24no—
180C22×C4×C11—24no—
181C22×C4×C11—24no—
182C22×C4×C11—24no—
183C22×C4×C11—416no—
184C22×C4×C11—42no—
185C22×C4×C11—42no—
186C22×C4×C11—42no—
187C22×C4×C11C22×C414yes—
188C22×C4×C11C22×C414yes—
189C22×C4×C11C22×C414yes—
190C22×C4×C11C22×C418yes—
191C22×C4×C11C22×C414yes—
192C22×C4×C11C22×C414yes—
193C22×C4×C11C22×C414yes—
194C22×C4×C11C2411yescharacteristic
195C22×C4×C11C2411yescharacteristic
196C22×C4×C11C2412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2412yes—
199C22×C4×C11C2411yescharacteristic
200C22×C4×C11C2411yescharacteristic
201C22×Dic11—28no—
202C22×Dic11—44no—
203C22×Dic11—44no—
204C22×Dic11—44no—
205C22×Dic11—44no—
206C22×Dic11—44no—
207C22×Dic11C2414yes—
208C22×Dic11C2414yes—
209C22×Dic11C2414yes—
210C22×Dic11C2414yes—
211C11×C4⋊C4C22×C414yes—
212C11×C4⋊C4C22×C414yes—
213C11×C4⋊C4C22×C418yes—
214C11×C4⋊C4C22×C418yes—
215C11×C22⋊C4C22×C418yes—
216C11×C22⋊C4C22×C418yes—
217C11×C22⋊C4C22×C418yes—
218C11×C22⋊C4C22×C418yes—
219C11×C22⋊C4C22×C418yes—
220C42×C11C22×C418yes—
221C22⋊Dic11—24no—
222C22⋊Dic11—24no—
223C22⋊Dic11—44no—
224C22⋊Dic11—44no—
225C22⋊Dic11—44no—
226C22⋊Dic11—42no—
227C22⋊Dic11—44no—
228C22⋊Dic11—42no—
229C22⋊Dic11—44no—
230C22⋊Dic11—44no—
231C4⋊Dic11—24no—
232C4⋊Dic11—24no—
233C4⋊Dic11—24no—
234C4⋊Dic11—24no—
235C4⋊Dic11—44no—
236C4⋊Dic11—44no—
237C4⋊Dic11—44no—
238C4⋊Dic11—44no—
239C4×Dic11—44no—
240C4×Dic11—44no—
241C4×Dic11—44no—
242C4×Dic11—44no—
243C2×#525D1111yescharacteristic
244#2378—112no—
245#2377—112no—
246#2368—112no—
247#2364—112no—
248#2354—112no—
249#2352—112no—
250#2352—112no—
251D4×C4⋊C4—112no—
252#2335—114no—
253#2321—114no—
254#2314—112no—
255#2311—112no—
256#2280—111no—
257C2×#380—111no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—28no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—22no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—44no—
276C23×C11—44no—
277C23×C11—48no—
278C23×C11—48no—
279C23×C11C23×C412yes—
280C23×C11C23×C412yes—
281C23×C11C23×C414yes—
282C23×C11C23×C412yes—
283C23×C11H(5,𝔽2)12yes—
284C23×C112−1+412yes—
285C23×C11C2511yescharacteristic
286Q8×C11—44no—
287D4×C11—216no—
288D4×C11—48no—
289D4×C11—44no—
290D4×C11—48no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—28no—
301C2×C4×C11—28no—
302C2×C4×C11—28no—
303C2×C4×C11—216no—
304C2×C4×C11—44no—
305C2×C4×C11—44no—
306C2×C4×C11—44no—
307C2×C4×C11C23×C414yes—
308C2×C4×C11C23×C414yes—
309C2×C4×C11C23×C412yes—
310C2×C4×C11C23×C412yes—
311C2×C4×C11C23×C414yes—
312C2×C4×C11C23×C412yes—
313C2×C4×C11C23×C412yes—
314C2×C4×C11H(5,𝔽2)14yes—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—24no—
319C2×Dic11—24no—
320C2×Dic11—24no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—88no—
328C2×Dic11—88no—
329C22×#41C2×D1111yescharacteristic
330C24×C4C2×D1111yescharacteristic
331#525Dic11116yescomplemented
332C2×#123C2×D1112yes—
333C2×C22⋊Q8C2×D1111yescharacteristic
334C2×C22⋊Q8C2×D1111yescharacteristic
335C2×#121C2×D1111yescharacteristic
336C2×#121C2×D1111yescharacteristic
337C2×#120C2×D1112yes—
338C2×C4×D4—114no—
339C2×C4×D4C2×D1112yes—
340C2×C4×D4C2×D1112yes—
341C2×#117—112no—
342C2×#117—112no—
343C2×#117C2×D1111yescharacteristic
344C22×C4⋊C4—112no—
345C22×C4⋊C4—112no—
346C22×C22⋊C4—112no—
347#391—114no—
348#390—114no—
349#390—114no—
350#389—114no—
351#388—114no—
352#388—114no—
353#388—114no—
354#388—114no—
355#388—114no—
356#388—114no—
357#387—114no—
358#387—114no—
359#387—114no—
360#387—114no—
361#386—114no—
362#386—114no—
363#386—114no—
364#386—114no—
365#385—114no—
366#385—114no—
367#384—112no—
368#382—112no—
369#381—112no—
370#380—112no—
371#380—112no—
372#380—112no—
373#380—112no—
374#380—112no—
375#380—111no—
376#380—111no—
377#380—111no—
378#380—111no—
379#380—112no—
380#379—112no—
381C4×C4⋊C4—114no—
382C4×C4⋊C4—112no—
383C4×C4⋊C4—112no—
384C4×C22⋊C4—112no—
385C4×C22⋊C4—112no—
386C4×C22⋊C4—114no—
387C4×C22⋊C4—114no—
388C2×#95—112no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—24no—
392C22×C11—24no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—24no—
396C22×C11—24no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—22no—
400C22×C11—24no—
401C22×C11—22no—
402C22×C11—416no—
403C22×C11—42no—
404C22×C11—42no—
405C22×C11—42no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11#52014yes—
412C22×C11C24×C411yescharacteristic
413C22×C11C2×H(5,𝔽2)12yes—
414C22×C11C2×H(5,𝔽2)11yescharacteristic
415C22×C11C2×2−1+411yescharacteristic
416C22×C11#58512yes—
417C4×C11—22no—
418C4×C11—22no—
419C4×C11—22no—
420C4×C11—24no—
421C4×C11—24no—
422C4×C11—24no—
423C4×C11#51814yes—
424Dic11—44no—
425Dic11—44no—
426Dic11—44no—
427Dic11—44no—
428C25C22×D1111yescharacteristic
429C2×#41—44no—
430C2×#41C2×Dic1118yescomplemented
431C22×Q8C22×D1111yescharacteristic
432C22×D4C22×D1112yes—
433C22×D4C22×D1112yes—
434C22×D4C22×D1112yes—
435C22×D4C22×D1111yescharacteristic
436C23×C4—44no—
437C23×C4—114no—
438C23×C4—114no—
439C23×C4C2×Dic1118yescomplemented
440C23×C4C22×D1111yescharacteristic
441C23×C4C22×D1112yes—
442C23×C4C22×D1111yescharacteristic
443C23×C4C22×D1111yescharacteristic
444C23×C4C22×D1111yescharacteristic
445C23×C4C22×D1111yescharacteristic
446C23×C4C22×D1111yescharacteristic
447#123C2×Dic11116yescomplemented
448C22⋊Q8C2×Dic1118yescomplemented
449C22⋊Q8C2×Dic1118yescomplemented
450#121C2×Dic1118yes—
451#121C2×Dic1118yescomplemented
452#120C2×Dic11116yescomplemented
453C4×D4—448no—
454C4×D4C2×Dic11116yescomplemented
455C4×D4C2×Dic11116yescomplemented
456#117—444no—
457#117—444no—
458#117C2×Dic1118yescomplemented
459C2×C4⋊C4—112no—
460C2×C4⋊C4—112no—
461C2×C4⋊C4—112no—
462C2×C4⋊C4—112no—
463C2×C4⋊C4—114no—
464C2×C4⋊C4—114no—
465C2×C4⋊C4—114no—
466C2×C4⋊C4—114no—
467C2×C4⋊C4—444no—
468C2×C4⋊C4—444no—
469C2×C4⋊C4C22×D1111yescharacteristic
470C2×C4⋊C4C22×D1111yescharacteristic
471C2×C4⋊C4C22×D1112yes—
472C2×C4⋊C4C22×D1112yes—
473C2×C22⋊C4—112no—
474C2×C22⋊C4—112no—
475C2×C22⋊C4—112no—
476C2×C22⋊C4—114no—
477C2×C22⋊C4—112no—
478C2×C22⋊C4—114no—
479C2×C22⋊C4—114no—
480C2×C22⋊C4—114no—
481C2×C22⋊C4—114no—
482C2×C22⋊C4—114no—
483C2×C22⋊C4—444no—
484C2×C22⋊C4C22×D1112yes—
485C2×C22⋊C4C22×D1112yes—
486C2×C22⋊C4C22×D1112yes—
487C2×C22⋊C4C22×D1112yes—
488C2×C22⋊C4C22×D1112yes—
489C2×C42—114no—
490C2×C42—114no—
491C2×C42—114no—
492C2×C42—114no—
493C2×C42C22×D1112yes—
494#95—112no—
495#95—112no—
496#95—114no—
497#95—112no—
498#95—114no—
499#95—112no—
500#95—114no—
501#95—114no—
502#95—114no—
503#95—114no—
504#95—114no—
505#95—114no—
506C2×C11—24no—
507C2×C11—44no—
508C2×C11—42no—
509C2×C11—42no—
510C2×C11C2×#51811yescharacteristic
511C2×C11C2×#52011yescharacteristic
512C2×C11#342811yescharacteristic
513C2×C11#354112yes—
514C2×C11#354212yes—
515C24—22no—
516C24—22no—
517C24—42no—
518C24—42no—
519C24C22×Dic1114yes—
520C24C23×D1111yescharacteristic
521C24C23×D1111yescharacteristic
522C24C23×D1112yes—
523C24C23×D1111yescharacteristic
524#41—416no—
525C2×Q8—42no—
526C2×Q8C22×Dic1114yes—
527C2×D4—24no—
528C2×D4—24no—
529C2×D4—42no—
530C2×D4—42no—
531C2×D4—42no—
532C2×D4—42no—
533C2×D4—42no—
534C2×D4C22×Dic1118yes—
535C2×D4C22×Dic1118yes—
536C2×D4C22×Dic1118yes—
537C2×D4C22×Dic1114yes—
538C22×C4—24no—
539C22×C4—24no—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—416no—
544C22×C4—42no—
545C22×C4—42no—
546C22×C4—42no—
547C22×C4—114no—
548C22×C4—114no—
549C22×C4—114no—
550C22×C4—114no—
551C22×C4—228no—
552C22×C4—444no—
553C22×C4—444no—
554C22×C4—444no—
555C22×C4—444no—
556C22×C4—444no—
557C22×C4C22×Dic1114yes—
558C22×C4C22×Dic1114yes—
559C22×C4C22×Dic1114yes—
560C22×C4C22×Dic1118yes—
561C22×C4C22×Dic1114yes—
562C22×C4C22×Dic1114yes—
563C22×C4C22×Dic1114yes—
564C22×C4C23×D1111yescharacteristic
565C22×C4C23×D1111yescharacteristic
566C22×C4C23×D1112yes—
567C22×C4C23×D1112yes—
568C22×C4C23×D1112yes—
569C22×C4C23×D1111yescharacteristic
570C22×C4C23×D1111yescharacteristic
571C4⋊C4—224no—
572C4⋊C4—224no—
573C4⋊C4—224no—
574C4⋊C4—224no—
575C4⋊C4—444no—
576C4⋊C4—444no—
577C4⋊C4—444no—
578C4⋊C4—444no—
579C4⋊C4C22×Dic1114yes—
580C4⋊C4C22×Dic1114yes—
581C4⋊C4C22×Dic1118yes—
582C4⋊C4C22×Dic1118yes—
583C22⋊C4—224no—
584C22⋊C4—224no—
585C22⋊C4—442no—
586C22⋊C4—444no—
587C22⋊C4—442no—
588C22⋊C4—444no—
589C22⋊C4—444no—
590C22⋊C4—444no—
591C22⋊C4—444no—
592C22⋊C4—444no—
593C22⋊C4C22×Dic1118yes—
594C22⋊C4C22×Dic1118yes—
595C22⋊C4C22×Dic1118yes—
596C22⋊C4C22×Dic1118yes—
597C22⋊C4C22×Dic1118yes—
598C42—444no—
599C42—444no—
600C42—444no—
601C42—444no—
602C42C22×Dic1118yes—
603C11#3436211yescharacteristic, complemented, Sylow
604C23—22no—
605C23—22no—
606C23—28no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—21no—
612C23—21no—
613C23—22no—
614C23—22no—
615C23—21no—
616C23—21no—
617C23—22no—
618C23—22no—
619C23—22no—
620C23—22no—
621C23—44no—
622C23—44no—
623C23—48no—
624C23—48no—
625C23#6704212yes—
626C23#6704312yes—
627C23C23×Dic1112yes—
628C23C23×Dic1112yes—
629C23C23×Dic1114yes—
630C23C23×Dic1112yes—
631C23C24×D1111yescharacteristic
632Q8—44no—
633D4—216no—
634D4—48no—
635D4—44no—
636D4—48no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—28no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—216no—
650C2×C4—44no—
651C2×C4—44no—
652C2×C4—44no—
653C2×C4—224no—
654C2×C4—224no—
655C2×C4—224no—
656C2×C4—224no—
657C2×C4—224no—
658C2×C4—224no—
659C2×C4—224no—
660C2×C4—224no—
661C2×C4—224no—
662C2×C4—224no—
663C2×C4—224no—
664C2×C4—224no—
665C2×C4—888no—
666C2×C4—888no—
667C2×C4#6703714yes—
668C2×C4C23×Dic1114yes—
669C2×C4C23×Dic1114yes—
670C2×C4C23×Dic1112yes—
671C2×C4C23×Dic1112yes—
672C2×C4C23×Dic1114yes—
673C2×C4C23×Dic1112yes—
674C2×C4C23×Dic1112yes—
675C22—24no—
676C22—24no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—24no—
682C22—24no—
683C22—22no—
684C22—22no—
685C22—22no—
686C22—24no—
687C22—22no—
688C22—416no—
689C22—42no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—42no—
697C22#1062335814yes—
698C22C2×#6703712yes—
699C22C2×#6704211yescharacteristic
700C22C2×#6704311yescharacteristic
701C22#1062345312yes—
702C22C24×Dic1111yescharacteristic
703C4—22no—
704C4—22no—
705C4—22no—
706C4—24no—
707C4—24no—
708C4—24no—
709C4—444no—
710C4—444no—
711C4—444no—
712C4—444no—
713C4#1062332914yes—
714C2—24no—
715C2—42no—
716C2—42no—
717C2—44no—
718C2C2×#1062332911yescharacteristic
719C2C2×#1062335811yescharacteristic
720C2#1308181911yescharacteristic
721C2#1308290912yes—
722C2#1308293212yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
Fitting, prime radicalC2×C11×#525C2
socle, cosocleC23×C11C25
hypercenterC2×#525D11
hypocenterC11#34362
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. #13071782C2semidirect
2. #13071773C2semidirect
3. #13071701C2semidirect
4. #13071668C2semidirect
5. #13071565C2semidirect
6. #13071545C2semidirect
7. #13071545C2semidirect
8. D4×C4⋊Dic11C2semidirect
9. #13071410C2semidirect
10. #13071277C2semidirect
11. #13071225C2semidirect
12. #13071208C2semidirect
13. #13070999C2semidirect
14. C2×#10622825C2semidirect
18. C11×#525C4semidirect
31. C2×#66979C22semidirect
33. C22×C4⋊Dic11C22semidirect
35. #10622843C22semidirect
41. #10622833C22semidirect
50. #10622825C22semidirect
51. #10622825C22semidirect
56. #10622598C22semidirect
57. #10622594C22semidirect
58. #10622594C22semidirect
59. #10622594C22semidirect
60. #10622594C22semidirect
61. C4⋊C4×Dic11C22semidirect
66. #10622564C22semidirect
67. #10622564C22semidirect
69. #10622563C22semidirect
71. C22⋊C4×Dic11C22semidirect
72. #10622549C22semidirect
73. #10622548C22semidirect
74. C4×C4⋊Dic11C22semidirect
75. C4×C4⋊Dic11C22semidirect
78. C2×C11×#41C2×C4semidirect
85. C23×C4×C11C2×C4semidirect
95. C11×#123C2×C4semidirect
96. C11×C22⋊Q8C2×C4semidirect
97. C11×C22⋊Q8C2×C4semidirect
99. C11×#121C2×C4semidirect
100. C11×#120C2×C4semidirect
101. C4×D4×C11C2×C4semidirect
102. C4×D4×C11C2×C4semidirect
103. C11×#117C2×C4semidirect
331. #525Dic11semidirect
430. C2×#41C2×Dic11semidirect
439. C23×C4C2×Dic11semidirect
447. #123C2×Dic11semidirect
448. C22⋊Q8C2×Dic11semidirect
449. C22⋊Q8C2×Dic11semidirect
451. #121C2×Dic11semidirect
452. #120C2×Dic11semidirect
454. C4×D4C2×Dic11semidirect
455. C4×D4C2×Dic11semidirect
458. #117C2×Dic11semidirect
603. C11#34362semidirect

Maximal subgroups

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

subgroupindex
#130717822
#130717732
#130717012
#130716682
#130715652
#130715452
D4×C4⋊Dic112
#130714102
#130712772
#130712252
#130712082
#130709992
C2×#106228252
C2×C11×#5252
#3436211