Finite Group Databasebeta

← #14914269

Subgroups — #14914269

Order 2816.

3014 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071701C212yesmaximal, complemented
2#13071668C212yesmaximal, complemented
3#13071612C214yesmaximal, complemented
4#13071556C212yesmaximal, complemented
5#13071526C212yesmaximal, complemented
6#13071476C212yesmaximal, complemented
7#13071446C212yesmaximal, complemented
8#13071351C212yesmaximal, complemented
9#13071321C212yesmaximal, complemented
10#13071249C212yesmaximal, complemented
11#120×Dic11C214yesmaximal, complemented
12#13070999C211yesmaximal, characteristic, complemented
13#13070977C212yesmaximal, complemented
14C22×C11⋊#95C211yesmaximal, characteristic, complemented
15C2×C11×#525C211yesmaximal, characteristic
16C22×C11×#41C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C24×Dic11C2212yes—
19C11×#525C4116yescomplemented
20C2×C11×#123C2212yes—
21C2×C11×C22⋊Q8C2211yescharacteristic
22C2×C11×C22⋊Q8C2211yescharacteristic
23C2×C11×#121C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C2×C11×#120C2212yes—
26C2×C4×D4×C11C2212yes—
27C2×C4×D4×C11C2212yes—
28C2×C11×#117C2211yescharacteristic
29C2×D4×Dic11C2214yes—
30C2×D4×Dic11C2214yes—
31C2×D4×Dic11C2214yes—
32C2×#66979C2212yes—
33#10622860C2212yes—
34#10622843C2214yescomplemented
35#10622833C2214yes—
36#10622833C2214yes—
37#10622833C2214yes—
38#10622833C2214yescomplemented
39#10622825C2211yescharacteristic
40#10622825C2211yescharacteristic
41#10622825C2212yes—
42#10622825C2212yescomplemented
43#10622824C2212yes—
44#10622824C2212yescomplemented
45C4×C22⋊Dic11C2212yes—
46C4×C22⋊Dic11C2212yes—
47C4×C22⋊Dic11C2212yescomplemented
48C2×C11⋊#95C2212yes—
49C2×C11⋊#95C2212yes—
50C2×C11⋊#95C2211yescharacteristic
51C2×C11⋊#95C2211yescharacteristic
52C2×C11⋊#95C2212yes—
53C2×C11⋊#95C2212yes—
54C2×C11⋊#95C2212yes—
55C2×C11⋊#95C2212yescomplemented
56#10622598C2214yescomplemented
57#10622594C2214yescomplemented
58#10622594C2214yescomplemented
59#10622594C2214yescomplemented
60#10622594C2214yescomplemented
61C4⋊C4×Dic11C2214yescomplemented
62#10622564C2214yescomplemented
63#10622564C2214yescomplemented
64#10622563C2214yes—
65#10622563C2214yes—
66#10622563C2214yes—
67#10622563C2214yescomplemented
68C22⋊C4×Dic11C2214yes—
69C22⋊C4×Dic11C2214yes—
70C22⋊C4×Dic11C2214yes—
71C22⋊C4×Dic11C2214yescomplemented
72#10622550C2212yescomplemented
73#10622549C2212yescomplemented
74C4×C4⋊Dic11C2212yescomplemented
75#10622545C2212yescomplemented
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×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2312yes—
93C23×Dic11—28no—
94C23×Dic11—44no—
95C23×Dic11—44no—
96C23×Dic11C2314yes—
97C23×Dic11C2314yes—
98C23×Dic11C2314yes—
99C23×Dic11C2312yes—
100C23×Dic11C2312yes—
101C11×#123C2×C4116yescomplemented
102C11×C22⋊Q8C2×C418yescomplemented
103C11×C22⋊Q8C2×C418yescomplemented
104C11×#121C2×C418yescomplemented
105C11×#121C2×C418yescomplemented
106C11×#120C2×C4116yescomplemented
107C4×D4×C11C2×C4116yescomplemented
108C4×D4×C11C2×C4116yescomplemented
109C11×#117C2×C418yescomplemented
110C2×C11×C4⋊C4C2312yes—
111C2×C11×C4⋊C4C2311yescharacteristic
112C2×C11×C4⋊C4C2311yescharacteristic
113C2×C11×C4⋊C4C2312yes—
114C2×C11×C22⋊C4C2312yes—
115C2×C11×C22⋊C4C2312yes—
116C2×C11×C22⋊C4C2312yes—
117C2×C11×C22⋊C4C2312yes—
118C2×C11×C22⋊C4C2312yes—
119C2×C42×C11C2312yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2312yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2314yes—
126C2×C22⋊Dic11C2314yes—
127D4×Dic11—216no—
128D4×Dic11—48no—
129D4×Dic11—48no—
130#66979—44no—
131C2×C4⋊Dic11C2314yes—
132C2×C4⋊Dic11C2314yes—
133C2×C4⋊Dic11C2312yes—
134C2×C4⋊Dic11C2312yes—
135C2×C4⋊Dic11C2314yes—
136C2×C4×Dic11C2314yes—
137C2×C4×Dic11C2314yes—
138C2×C4×Dic11C2314yes—
139C2×C4×Dic11C2314yes—
140C11⋊#95C2312yes—
141C11⋊#95C2312yes—
142C11⋊#95C2314yes—
143C11⋊#95C2312yes—
144C11⋊#95C2312yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2314yes—
149C11⋊#95C2314yes—
150C11⋊#95C2312yes—
151C11⋊#95C2314yes—
152C11⋊#95C2312yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155#34218—111nomaximal, Sylow
156C24×C11—24no—
157C24×C11—22no—
158C24×C11—24no—
159C24×C11—22no—
160C24×C11C22×C414yes—
161C24×C11C2412yes—
162C24×C11C2411yescharacteristic
163C24×C11C2411yescharacteristic
164C24×C11C2411yescharacteristic
165C11×#41—416no—
166C2×Q8×C11—42no—
167C2×Q8×C11C22×C414yescomplemented
168C2×D4×C11—28no—
169C2×D4×C11—24no—
170C2×D4×C11—28no—
171C2×D4×C11—24no—
172C2×D4×C11—42no—
173C2×D4×C11C22×C418yes—
174C2×D4×C11C22×C418yes—
175C2×D4×C11C22×C418yes—
176C2×D4×C11C22×C414yescomplemented
177C22×C4×C11—24no—
178C22×C4×C11—24no—
179C22×C4×C11—416no—
180C22×C4×C11—42no—
181C22×C4×C11—42no—
182C22×C4×C11—42no—
183C22×C4×C11—42no—
184C22×C4×C11—44no—
185C22×C4×C11C22×C414yes—
186C22×C4×C11C22×C414yes—
187C22×C4×C11C22×C414yes—
188C22×C4×C11C22×C414yes—
189C22×C4×C11C22×C414yes—
190C22×C4×C11C22×C414yes—
191C22×C4×C11C22×C418yescomplemented
192C22×C4×C11C2411yescharacteristic
193C22×C4×C11C2411yescharacteristic
194C22×C4×C11C2411yescharacteristic
195C22×C4×C11C2412yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2411yescharacteristic
199C22×Dic11—28no—
200C22×Dic11—28no—
201C22×Dic11—28no—
202C22×Dic11—24no—
203C22×Dic11—28no—
204C22×Dic11—28no—
205C22×Dic11—42no—
206C22×Dic11—44no—
207C22×Dic11—42no—
208C22×Dic11—42no—
209C22×Dic11—44no—
210C22×Dic11—42no—
211C22×Dic11—44no—
212C22×Dic11—44no—
213C22×Dic11—432no—
214C22×Dic11#4118yescomplemented
215C22×Dic11C2414yes—
216C22×Dic11C2414yes—
217C22×Dic11C2414yes—
218C22×Dic11C2414yes—
219C11×C4⋊C4C22×C414yescomplemented
220C11×C4⋊C4C22×C414yescomplemented
221C11×C4⋊C4C22×C418yescomplemented
222C11×C4⋊C4C22×C418yescomplemented
223C11×C22⋊C4C22×C418yes—
224C11×C22⋊C4C22×C418yes—
225C11×C22⋊C4C22×C418yes—
226C11×C22⋊C4C22×C418yescomplemented
227C11×C22⋊C4C22×C418yescomplemented
228C42×C11C22×C418yescomplemented
229C22⋊Dic11—28no—
230C22⋊Dic11—28no—
231C22⋊Dic11—28no—
232C22⋊Dic11—24no—
233C22⋊Dic11—24no—
234C22⋊Dic11—44no—
235C22⋊Dic11—44no—
236C4⋊Dic11—28no—
237C4⋊Dic11—42no—
238C4⋊Dic11—42no—
239C4⋊Dic11—44no—
240C4⋊Dic11—44no—
241C4×Dic11—28no—
242C4×Dic11—44no—
243C4×Dic11—44no—
244C4×Dic11—44no—
245C2×#525D1111yescharacteristic
246#2368—112no—
247#2364—112no—
248#2359—114no—
249#2353—112no—
250#2349—112no—
251#2343—112no—
252#2339—112no—
253#2329—112no—
254#2325—112no—
255#2318—112no—
256C4×#120—114no—
257#2280—111no—
258#2275—112no—
259C22×#95—111no—
260C23×C11—216no—
261C23×C11—216no—
262C23×C11—28no—
263C23×C11—28no—
264C23×C11—28no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11—21no—
272C23×C11—21no—
273C23×C11—24no—
274C23×C11—22no—
275C23×C11—24no—
276C23×C11—22no—
277C23×C11C23×C414yes—
278C23×C11C23×C412yes—
279C23×C11C23×C412yes—
280C23×C11C23×C412yes—
281C23×C11C2×#4114yes—
282C23×C11H(5,𝔽2)14yes—
283C23×C11H(5,𝔽2)12yes—
284C23×C112−1+412yes—
285C23×C11C2511yescharacteristic
286Q8×C11—44no—
287D4×C11—216no—
288D4×C11—216no—
289D4×C11—216no—
290D4×C11—44no—
291C2×C4×C11—28no—
292C2×C4×C11—28no—
293C2×C4×C11—24no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—24no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—44no—
302C2×C4×C11—44no—
303C2×C4×C11—44no—
304C2×C4×C11—44no—
305C2×C4×C11—48no—
306C2×C4×C11C23×C412yes—
307C2×C4×C11C23×C414yes—
308C2×C4×C11C23×C414yes—
309C2×C4×C11C23×C414yes—
310C2×C4×C11C23×C412yes—
311C2×C4×C11C23×C412yes—
312C2×C4×C11C23×C412yes—
313C2×Dic11—24no—
314C2×Dic11—24no—
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—48no—
325C2×Dic11—416no—
326C2×Dic11—416no—
327C2×Dic11—48no—
328C2×Dic11—88no—
329C2×Dic11C2×#4118yes—
330C22×#41C2×D1111yescharacteristic
331C24×C4—112no—
332C24×C4C2×D1111yescharacteristic
333#525Dic11116yescomplemented
334C2×#123C2×D1112yes—
335C2×C22⋊Q8C2×D1111yescharacteristic
336C2×C22⋊Q8C2×D1111yescharacteristic
337C2×#121C2×D1111yescharacteristic
338C2×#121C2×D1111yescharacteristic
339C2×#120C2×D1112yes—
340C2×C4×D4—114no—
341C2×C4×D4—114no—
342C2×C4×D4—114no—
343C2×C4×D4C2×D1112yes—
344C2×C4×D4C2×D1112yes—
345C2×#117—112no—
346C2×#117C2×D1111yescharacteristic
347#391—114no—
348#389—114no—
349#388—114no—
350#388—114no—
351#387—114no—
352#387—114no—
353#387—114no—
354#387—114no—
355#386—114no—
356#386—114no—
357#386—114no—
358#386—114no—
359#385—114no—
360#385—114no—
361#385—114no—
362#385—114no—
363#383—112no—
364#382—112no—
365#381—112no—
366#381—112no—
367#380—112no—
368#380—112no—
369#380—111no—
370#380—111no—
371#379—112no—
372C4×C4⋊C4—114no—
373C4×C4⋊C4—112no—
374C4×C22⋊C4—112no—
375C4×C22⋊C4—112no—
376C4×C22⋊C4—112no—
377C4×C22⋊C4—114no—
378C4×C22⋊C4—114no—
379C4×C22⋊C4—114no—
380C4×C22⋊C4—114no—
381#376—112no—
382C2×#95—111no—
383C2×#95—112no—
384C2×#95—112no—
385C2×#95—112no—
386C2×#95—112no—
387C2×#95—112no—
388C2×#95—112no—
389C2×#95—111no—
390C22×C11—232no—
391C22×C11—22no—
392C22×C11—22no—
393C22×C11—22no—
394C22×C11—22no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—24no—
398C22×C11—24no—
399C22×C11—24no—
400C22×C11—24no—
401C22×C11—24no—
402C22×C11—24no—
403C22×C11—24no—
404C22×C11—24no—
405C22×C11—24no—
406C22×C11—44no—
407C22×C11—44no—
408C22×C11C4×#4114yes—
409C22×C11#51814yes—
410C22×C11#52014yes—
411C22×C11C24×C411yescharacteristic
412C22×C11C22×#4112yes—
413C22×C11C2×H(5,𝔽2)12yes—
414C22×C11C2×H(5,𝔽2)11yescharacteristic
415C22×C11C2×2−1+411yescharacteristic
416C4×C11—24no—
417C4×C11—22no—
418C4×C11—22no—
419C4×C11—22no—
420C4×C11—22no—
421C4×C11—24no—
422C4×C11—24no—
423Dic11—28no—
424Dic11—44no—
425Dic11—44no—
426Dic11—44no—
427C25C22×D1111yescharacteristic
428C2×#41—44no—
429C2×#41C2×Dic1118yescomplemented
430C22×Q8C22×D1111yescharacteristic
431C22×D4C22×D1112yes—
432C22×D4C22×D1112yes—
433C22×D4C22×D1112yes—
434C22×D4C22×D1111yescharacteristic
435C23×C4—44no—
436C23×C4—112no—
437C23×C4—114no—
438C23×C4—114no—
439C23×C4—114no—
440C23×C4—112no—
441C23×C4—228no—
442C23×C4—444no—
443C23×C4—444no—
444C23×C4C2×Dic1118yescomplemented
445C23×C4C22×D1111yescharacteristic
446C23×C4C22×D1111yescharacteristic
447C23×C4C22×D1111yescharacteristic
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1111yescharacteristic
450C23×C4C22×D1111yescharacteristic
451C23×C4C22×D1112yes—
452#123C2×Dic11116yescomplemented
453C22⋊Q8C2×Dic1118yescomplemented
454C22⋊Q8C2×Dic1118yescomplemented
455#121C2×Dic1118yescomplemented
456#121C2×Dic1118yescomplemented
457#120C2×Dic11116yescomplemented
458C4×D4—2216no—
459C4×D4—448no—
460C4×D4—448no—
461C4×D4C2×Dic11116yescomplemented
462C4×D4C2×Dic11116yescomplemented
463#117—444no—
464#117C2×Dic1118yescomplemented
465C2×C4⋊C4—114no—
466C2×C4⋊C4—112no—
467C2×C4⋊C4—112no—
468C2×C4⋊C4—114no—
469C2×C4⋊C4—114no—
470C2×C4⋊C4C22×D1111yescharacteristic
471C2×C4⋊C4C22×D1111yescharacteristic
472C2×C4⋊C4C22×D1112yes—
473C2×C4⋊C4C22×D1112yes—
474C2×C22⋊C4—114no—
475C2×C22⋊C4—112no—
476C2×C22⋊C4—114no—
477C2×C22⋊C4—114no—
478C2×C22⋊C4—112no—
479C2×C22⋊C4—114no—
480C2×C22⋊C4—114no—
481C2×C22⋊C4C22×D1112yes—
482C2×C22⋊C4C22×D1112yes—
483C2×C22⋊C4C22×D1112yes—
484C2×C22⋊C4C22×D1112yes—
485C2×C22⋊C4C22×D1112yes—
486C2×C42—114no—
487C2×C42—114no—
488C2×C42—114no—
489C2×C42—114no—
490C2×C42C22×D1112yes—
491#95—112no—
492#95—112no—
493#95—112no—
494#95—114no—
495#95—114no—
496#95—112no—
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—24no—
508C2×C11—24no—
509C2×C11—44no—
510C2×C11C2×C4×#4111yescharacteristic
511C2×C11C2×#51811yescharacteristic
512C2×C11C2×#52011yescharacteristic
513C2×C11#349012yes—
514C2×C11#349212yes—
515C24—24no—
516C24—24no—
517C24—22no—
518C24—22no—
519C24C22×Dic1114yes—
520C24C23×D1112yes—
521C24C23×D1111yescharacteristic
522C24C23×D1111yescharacteristic
523C24C23×D1111yescharacteristic
524#41—416no—
525C2×Q8—42no—
526C2×Q8C22×Dic1114yescomplemented
527C2×D4—28no—
528C2×D4—28no—
529C2×D4—24no—
530C2×D4—24no—
531C2×D4—42no—
532C2×D4C22×Dic1118yes—
533C2×D4C22×Dic1118yes—
534C2×D4C22×Dic1118yes—
535C2×D4C22×Dic1114yescomplemented
536C22×C4—24no—
537C22×C4—24no—
538C22×C4—42no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—416no—
543C22×C4—44no—
544C22×C4—114no—
545C22×C4—118no—
546C22×C4—114no—
547C22×C4—114no—
548C22×C4—114no—
549C22×C4—228no—
550C22×C4—228no—
551C22×C4—228no—
552C22×C4—228no—
553C22×C4—224no—
554C22×C4—228no—
555C22×C4—442no—
556C22×C4—444no—
557C22×C4—442no—
558C22×C4—444no—
559C22×C4—442no—
560C22×C4—442no—
561C22×C4—444no—
562C22×C4—444no—
563C22×C4—4432no—
564C22×C4C22×Dic1114yes—
565C22×C4C22×Dic1114yes—
566C22×C4C22×Dic1114yes—
567C22×C4C22×Dic1114yes—
568C22×C4C22×Dic1114yes—
569C22×C4C22×Dic1114yes—
570C22×C4C22×Dic1118yescomplemented
571C22×C4C23×D1111yescharacteristic
572C22×C4C23×D1111yescharacteristic
573C22×C4C23×D1111yescharacteristic
574C22×C4C23×D1112yes—
575C22×C4C23×D1112yes—
576C22×C4C23×D1112yes—
577C22×C4C23×D1111yescharacteristic
578C4⋊C4—228no—
579C4⋊C4—442no—
580C4⋊C4—442no—
581C4⋊C4—444no—
582C4⋊C4—444no—
583C4⋊C4C22×Dic1114yescomplemented
584C4⋊C4C22×Dic1114yescomplemented
585C4⋊C4C22×Dic1118yescomplemented
586C4⋊C4C22×Dic1118yescomplemented
587C22⋊C4—228no—
588C22⋊C4—228no—
589C22⋊C4—228no—
590C22⋊C4—224no—
591C22⋊C4—224no—
592C22⋊C4—444no—
593C22⋊C4—444no—
594C22⋊C4C22×Dic1118yes—
595C22⋊C4C22×Dic1118yes—
596C22⋊C4C22×Dic1118yes—
597C22⋊C4C22×Dic1118yescomplemented
598C22⋊C4C22×Dic1118yescomplemented
599C42—228no—
600C42—444no—
601C42—444no—
602C42—444no—
603C42C22×Dic1118yescomplemented
604C11#3421811yescharacteristic, complemented, Sylow
605C23—216no—
606C23—216no—
607C23—28no—
608C23—28no—
609C23—28no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—24no—
619C23—24no—
620C23—22no—
621C23—22no—
622C23#6703714yes—
623C23#41×D1114yes—
624C23#6704212yes—
625C23#6704312yes—
626C23C23×Dic1114yes—
627C23C23×Dic1112yes—
628C23C23×Dic1112yes—
629C23C23×Dic1112yes—
630C23C24×D1111yescharacteristic
631Q8—44no—
632D4—216no—
633D4—216no—
634D4—216no—
635D4—44no—
636C2×C4—28no—
637C2×C4—28no—
638C2×C4—22no—
639C2×C4—24no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—44no—
647C2×C4—44no—
648C2×C4—44no—
649C2×C4—44no—
650C2×C4—48no—
651C2×C4—118no—
652C2×C4—224no—
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—448no—
664C2×C4—4416no—
665C2×C4—4416no—
666C2×C4—448no—
667C2×C4—888no—
668C2×C4C23×Dic1112yes—
669C2×C4C23×Dic1114yes—
670C2×C4C23×Dic1114yes—
671C2×C4C23×Dic1114yes—
672C2×C4C23×Dic1112yes—
673C2×C4C23×Dic1112yes—
674C2×C4C23×Dic1112yes—
675C22—232no—
676C22—24no—
677C22—24no—
678C22—24no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—24no—
684C22—24no—
685C22—24no—
686C22—22no—
687C22—22no—
688C22—24no—
689C22—24no—
690C22—24no—
691C22—44no—
692C22—44no—
693C22#1062332914yes—
694C22#41×Dic1114yes—
695C22#1062335814yes—
696C22C2×#6703712yes—
697C22C2×#41×D1112yes—
698C22C2×#6704211yescharacteristic
699C22C2×#6704311yescharacteristic
700C22C24×Dic1111yescharacteristic
701C4—24no—
702C4—22no—
703C4—22no—
704C4—22no—
705C4—22no—
706C4—24no—
707C4—24no—
708C4—228no—
709C4—444no—
710C4—444no—
711C4—444no—
712C2—24no—
713C2—24no—
714C2—24no—
715C2—44no—
716C2C2×#41×Dic1111yescharacteristic
717C2C2×#1062332911yescharacteristic
718C2C2×#1062335811yescharacteristic
719C2#1308229912yes—
720C2#1308231712yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
Fitting, prime radicalC2×C11×#525C2
socle, cosocleC23×C11C25
hypercenterC2×#525D11
hypocenterC11#34218
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#525

Complements

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

NH ≅ G/Ntype
1. #13071701C2semidirect
2. #13071668C2semidirect
3. #13071612C2semidirect
4. #13071556C2semidirect
5. #13071526C2semidirect
6. #13071476C2semidirect
7. #13071446C2semidirect
8. #13071351C2semidirect
9. #13071321C2semidirect
10. #13071249C2semidirect
11. #120×Dic11C2semidirect
12. #13070999C2semidirect
13. #13070977C2semidirect
14. C22×C11⋊#95C2semidirect
19. C11×#525C4semidirect
34. #10622843C22semidirect
38. #10622833C22semidirect
42. #10622825C22semidirect
44. #10622824C22semidirect
47. C4×C22⋊Dic11C22semidirect
55. C2×C11⋊#95C22semidirect
56. #10622598C22semidirect
57. #10622594C22semidirect
58. #10622594C22semidirect
59. #10622594C22semidirect
60. #10622594C22semidirect
61. C4⋊C4×Dic11C22semidirect
62. #10622564C22semidirect
63. #10622564C22semidirect
67. #10622563C22semidirect
71. C22⋊C4×Dic11C22semidirect
72. #10622550C22semidirect
73. #10622549C22semidirect
74. C4×C4⋊Dic11C22semidirect
75. #10622545C22semidirect
78. C2×C11×#41C2×C4semidirect
85. C23×C4×C11C2×C4semidirect
101. C11×#123C2×C4semidirect
102. C11×C22⋊Q8C2×C4semidirect
103. C11×C22⋊Q8C2×C4semidirect
104. C11×#121C2×C4semidirect
105. C11×#121C2×C4semidirect
106. C11×#120C2×C4semidirect
107. C4×D4×C11C2×C4semidirect
108. C4×D4×C11C2×C4semidirect
109. C11×#117C2×C4semidirect
167. C2×Q8×C11C22×C4semidirect
176. C2×D4×C11C22×C4semidirect
191. C22×C4×C11C22×C4semidirect
214. C22×Dic11#41semidirect
219. C11×C4⋊C4C22×C4semidirect
220. C11×C4⋊C4C22×C4semidirect
221. C11×C4⋊C4C22×C4semidirect
222. C11×C4⋊C4C22×C4semidirect
226. C11×C22⋊C4C22×C4semidirect
227. C11×C22⋊C4C22×C4semidirect
228. C42×C11C22×C4semidirect
333. #525Dic11semidirect
429. C2×#41C2×Dic11semidirect
444. C23×C4C2×Dic11semidirect
452. #123C2×Dic11semidirect
453. C22⋊Q8C2×Dic11semidirect
454. C22⋊Q8C2×Dic11semidirect
455. #121C2×Dic11semidirect
456. #121C2×Dic11semidirect
457. #120C2×Dic11semidirect
461. C4×D4C2×Dic11semidirect
462. C4×D4C2×Dic11semidirect
464. #117C2×Dic11semidirect
526. C2×Q8C22×Dic11semidirect
535. C2×D4C22×Dic11semidirect
570. C22×C4C22×Dic11semidirect
583. C4⋊C4C22×Dic11semidirect
584. C4⋊C4C22×Dic11semidirect
585. C4⋊C4C22×Dic11semidirect
586. C4⋊C4C22×Dic11semidirect
597. C22⋊C4C22×Dic11semidirect
598. C22⋊C4C22×Dic11semidirect
603. C42C22×Dic11semidirect
604. C11#34218semidirect

Maximal subgroups

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

subgroupindex
#130717012
#130716682
#130716122
#130715562
#130715262
#130714762
#130714462
#130713512
#130713212
#130712492
#120×Dic112
#130709992
#130709772
C22×C11⋊#952
C2×C11×#5252
#3421811