Finite Group Databasebeta

← #14916846

Subgroups — #14916846

Order 2816.

2614 conjugacy classes of subgroups.

The subgroup lattice has 710 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071782C212yesmaximal, complemented
2#13071773C212yesmaximal, complemented
3#13071600C214yesmaximal, complemented
4#13071556C212yesmaximal, complemented
5#13071526C212yesmaximal, complemented
6#13071476C212yesmaximal, complemented
7#13071446C212yesmaximal, complemented
8#13071351C212yesmaximal, complemented
9#13071321C212yesmaximal, complemented
10#13071288C214yesmaximal, complemented
11#13071259C212yesmaximal, complemented
12#13071249C212yesmaximal, complemented
13C2×#10622824C211yesmaximal, 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—
29C22×C22⋊Dic11C2212yes—
30C2×D4×Dic11C2214yes—
31C2×D4×Dic11C2214yes—
32C22×C4⋊Dic11C2212yes—
33#10622843C2214yescomplemented
34#10622834C2214yes—
35#10622833C2214yes—
36#10622833C2214yes—
37#10622833C2214yes—
38#10622833C2214yescomplemented
39#10622825C2211yescharacteristic
40#10622825C2211yescharacteristic
41#10622825C2212yes—
42#10622825C2212yes—
43#10622825C2212yes—
44#10622825C2212yescomplemented
45#10622824C2212yes—
46#10622824C2212yes—
47#10622824C2212yes—
48#10622824C2212yes—
49#10622824C2212yescomplemented
50C4×C22⋊Dic11C2212yescomplemented
51C2×C11⋊#95C2212yes—
52C2×C11⋊#95C2211yescharacteristic
53C2×C11⋊#95C2211yescharacteristic
54C2×C11⋊#95C2212yes—
55C2×C11⋊#95C2212yescomplemented
56#10622598C2214yescomplemented
57#10622598C2214yescomplemented
58#10622594C2214yescomplemented
59#10622594C2214yescomplemented
60#10622594C2214yescomplemented
61#10622594C2214yescomplemented
62#10622564C2214yes—
63#10622564C2214yes—
64#10622564C2214yescomplemented
65#10622564C2214yescomplemented
66#10622563C2214yes—
67#10622563C2214yes—
68#10622563C2214yescomplemented
69#10622563C2214yescomplemented
70C22⋊C4×Dic11C2214yes—
71C22⋊C4×Dic11C2214yes—
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×C11C2312yes—
91C23×C4×C11C2311yescharacteristic
92C23×C4×C11C2311yescharacteristic
93C23×Dic11C2314yes—
94C23×Dic11C2312yes—
95C23×Dic11C2312yes—
96C23×Dic11C2314yes—
97C11×#123C2×C4116yescomplemented
98C11×C22⋊Q8C2×C418yescomplemented
99C11×C22⋊Q8C2×C418yescomplemented
100C11×#121C2×C418yescomplemented
101C11×#121C2×C418yescomplemented
102C11×#120C2×C4116yescomplemented
103C4×D4×C11C2×C4116yescomplemented
104C4×D4×C11C2×C4116yescomplemented
105C11×#117C2×C418yescomplemented
106C2×C11×C4⋊C4C2311yescharacteristic
107C2×C11×C4⋊C4C2311yescharacteristic
108C2×C11×C4⋊C4C2312yes—
109C2×C11×C4⋊C4C2312yes—
110C2×C11×C22⋊C4C2312yes—
111C2×C11×C22⋊C4C2312yes—
112C2×C11×C22⋊C4C2312yes—
113C2×C11×C22⋊C4C2312yes—
114C2×C11×C22⋊C4C2312yes—
115C2×C42×C11C2312yes—
116C2×C22⋊Dic11—44no—
117C2×C22⋊Dic11—44no—
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2314yes—
124C2×C22⋊Dic11C2312yes—
125C2×C22⋊Dic11C2312yes—
126D4×Dic11—48no—
127D4×Dic11—48no—
128C2×C4⋊Dic11—44no—
129C2×C4⋊Dic11C2314yes—
130C2×C4⋊Dic11C2312yes—
131C2×C4⋊Dic11C2314yes—
132C2×C4⋊Dic11C2312yes—
133C2×C4⋊Dic11C2314yes—
134C2×C4⋊Dic11C2314yes—
135C2×C4×Dic11C2314yes—
136C2×C4×Dic11C2314yes—
137C2×C4×Dic11C2314yes—
138C11⋊#95C2312yes—
139C11⋊#95C2312yes—
140C11⋊#95C2314yes—
141C11⋊#95C2312yes—
142C11⋊#95C2312yes—
143C11⋊#95C2314yes—
144C11⋊#95C2314yes—
145C11⋊#95C2314yes—
146C11⋊#95C2314yes—
147C11⋊#95C2314yes—
148C11⋊#95C2312yes—
149C11⋊#95C2314yes—
150C11⋊#95C2312yes—
151C11⋊#95C2314yes—
152C11⋊#95C2314yes—
153#34386—111nomaximal, Sylow
154C24×C11—22no—
155C24×C11—24no—
156C24×C11—22no—
157C24×C11—42no—
158C24×C11C22×C414yes—
159C24×C11C2411yescharacteristic
160C24×C11C2412yes—
161C24×C11C2411yescharacteristic
162C24×C11C2411yescharacteristic
163C11×#41—416no—
164C2×Q8×C11—42no—
165C2×Q8×C11C22×C414yes—
166C2×D4×C11—24no—
167C2×D4×C11—28no—
168C2×D4×C11—24no—
169C2×D4×C11—44no—
170C2×D4×C11—42no—
171C2×D4×C11C22×C418yes—
172C2×D4×C11C22×C418yes—
173C2×D4×C11C22×C418yes—
174C2×D4×C11C22×C414yes—
175C22×C4×C11—24no—
176C22×C4×C11—24no—
177C22×C4×C11—416no—
178C22×C4×C11—42no—
179C22×C4×C11—42no—
180C22×C4×C11—42no—
181C22×C4×C11—42no—
182C22×C4×C11—44no—
183C22×C4×C11C22×C414yes—
184C22×C4×C11C22×C414yes—
185C22×C4×C11C22×C414yes—
186C22×C4×C11C22×C414yes—
187C22×C4×C11C22×C418yes—
188C22×C4×C11C22×C414yes—
189C22×C4×C11C22×C414yes—
190C22×C4×C11C2411yescharacteristic
191C22×C4×C11C2411yescharacteristic
192C22×C4×C11C2412yes—
193C22×C4×C11C2412yes—
194C22×C4×C11C2412yes—
195C22×C4×C11C2411yescharacteristic
196C22×C4×C11C2411yescharacteristic
197C22×Dic11—28no—
198C22×Dic11—24no—
199C22×Dic11—24no—
200C22×Dic11—44no—
201C22×Dic11—44no—
202C22×Dic11—44no—
203C22×Dic11—42no—
204C22×Dic11—42no—
205C22×Dic11—44no—
206C22×Dic11—42no—
207C22×Dic11—42no—
208C22×Dic11—44no—
209C22×Dic11C2414yes—
210C22×Dic11C2414yes—
211C22×Dic11C2414yes—
212C22×Dic11C2414yes—
213C11×C4⋊C4C22×C414yes—
214C11×C4⋊C4C22×C414yes—
215C11×C4⋊C4C22×C418yes—
216C11×C4⋊C4C22×C418yes—
217C11×C22⋊C4C22×C418yes—
218C11×C22⋊C4C22×C418yes—
219C11×C22⋊C4C22×C418yes—
220C11×C22⋊C4C22×C418yes—
221C11×C22⋊C4C22×C418yes—
222C42×C11C22×C418yes—
223C22⋊Dic11—28no—
224C22⋊Dic11—28no—
225C22⋊Dic11—44no—
226C22⋊Dic11—44no—
227C22⋊Dic11—42no—
228C22⋊Dic11—42no—
229C22⋊Dic11—44no—
230C22⋊Dic11—44no—
231C4⋊Dic11—42no—
232C4⋊Dic11—44no—
233C4⋊Dic11—42no—
234C4⋊Dic11—44no—
235C4⋊Dic11—44no—
236C4⋊Dic11—44no—
237C4×Dic11—44no—
238C4×Dic11—44no—
239C4×Dic11—44no—
240C2×#525D1111yescharacteristic
241#2378—112no—
242#2377—112no—
243#2358—114no—
244#2353—112no—
245#2349—112no—
246#2343—112no—
247#2339—112no—
248#2329—112no—
249#2325—112no—
250#2322—114no—
251#2319—112no—
252#2318—112no—
253C2×#381—111no—
254C2×#380—111no—
255C23×C11—21no—
256C23×C11—22no—
257C23×C11—21no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—28no—
261C23×C11—28no—
262C23×C11—21no—
263C23×C11—22no—
264C23×C11—22no—
265C23×C11—24no—
266C23×C11—22no—
267C23×C11—21no—
268C23×C11—24no—
269C23×C11—22no—
270C23×C11—44no—
271C23×C11—48no—
272C23×C11—48no—
273C23×C11C23×C412yes—
274C23×C11C23×C414yes—
275C23×C11C23×C412yes—
276C23×C11C23×C412yes—
277C23×C11H(5,𝔽2)14yes—
278C23×C11H(5,𝔽2)12yes—
279C23×C112−1+412yes—
280C23×C11C2511yescharacteristic
281Q8×C11—44no—
282D4×C11—216no—
283D4×C11—216no—
284D4×C11—48no—
285D4×C11—44no—
286C2×C4×C11—28no—
287C2×C4×C11—28no—
288C2×C4×C11—22no—
289C2×C4×C11—24no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—24no—
296C2×C4×C11—44no—
297C2×C4×C11—44no—
298C2×C4×C11—44no—
299C2×C4×C11—44no—
300C2×C4×C11—48no—
301C2×C4×C11C23×C412yes—
302C2×C4×C11C23×C414yes—
303C2×C4×C11C23×C414yes—
304C2×C4×C11C23×C412yes—
305C2×C4×C11C23×C412yes—
306C2×C4×C11C23×C414yes—
307C2×C4×C11C23×C412yes—
308C2×Dic11—24no—
309C2×Dic11—24no—
310C2×Dic11—24no—
311C2×Dic11—24no—
312C2×Dic11—24no—
313C2×Dic11—24no—
314C2×Dic11—24no—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—24no—
318C2×Dic11—24no—
319C2×Dic11—24no—
320C2×Dic11—88no—
321C2×Dic11—84no—
322C2×Dic11—84no—
323C2×Dic11—88no—
324C22×#41C2×D1111yescharacteristic
325C24×C4C2×D1111yescharacteristic
326#525Dic11116yescomplemented
327C2×#123C2×D1112yes—
328C2×C22⋊Q8C2×D1111yescharacteristic
329C2×C22⋊Q8C2×D1111yescharacteristic
330C2×#121C2×D1111yescharacteristic
331C2×#121C2×D1111yescharacteristic
332C2×#120C2×D1112yes—
333C2×C4×D4—114no—
334C2×C4×D4—114no—
335C2×C4×D4C2×D1112yes—
336C2×C4×D4C2×D1112yes—
337C2×#117C2×D1111yescharacteristic
338C22×C4⋊C4—112no—
339C22×C22⋊C4—112no—
340C22×C22⋊C4—112no—
341#391—114no—
342#390—114no—
343#389—114no—
344#389—114no—
345#388—114no—
346#388—114no—
347#388—114no—
348#388—114no—
349#387—114no—
350#387—114no—
351#387—114no—
352#387—114no—
353#386—114no—
354#386—114no—
355#386—114no—
356#386—114no—
357#385—114no—
358#385—114no—
359#385—114no—
360#385—114no—
361#383—112no—
362#382—112no—
363#381—112no—
364#381—112no—
365#381—112no—
366#381—112no—
367#381—112no—
368#380—111no—
369#380—111no—
370#380—112no—
371#380—112no—
372#380—112no—
373#380—112no—
374C4×C4⋊C4—112no—
375C4×C22⋊C4—112no—
376C4×C22⋊C4—114no—
377C4×C22⋊C4—114no—
378#376—112no—
379C2×#95—112no—
380C2×#95—112no—
381C2×#95—112no—
382C2×#95—111no—
383C2×#95—111no—
384C22×C11—22no—
385C22×C11—22no—
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—24no—
389C22×C11—24no—
390C22×C11—24no—
391C22×C11—24no—
392C22×C11—22no—
393C22×C11—24no—
394C22×C11—24no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—24no—
398C22×C11—416no—
399C22×C11—42no—
400C22×C11—44no—
401C22×C11—44no—
402C22×C11—42no—
403C22×C11#51814yes—
404C22×C11#52014yes—
405C22×C11C24×C411yescharacteristic
406C22×C11C2×H(5,𝔽2)12yes—
407C22×C11C2×H(5,𝔽2)11yescharacteristic
408C22×C11C2×2−1+411yescharacteristic
409C22×C11#58512yes—
410C4×C11—22no—
411C4×C11—22no—
412C4×C11—22no—
413C4×C11—22no—
414C4×C11—24no—
415C4×C11—24no—
416C4×C11—24no—
417Dic11—44no—
418Dic11—44no—
419Dic11—44no—
420Dic11—44no—
421C25C22×D1111yescharacteristic
422C2×#41—44no—
423C2×#41C2×Dic1118yescomplemented
424C22×Q8C22×D1111yescharacteristic
425C22×D4C22×D1112yes—
426C22×D4C22×D1112yes—
427C22×D4C22×D1112yes—
428C22×D4C22×D1111yescharacteristic
429C23×C4—44no—
430C23×C4—114no—
431C23×C4—112no—
432C23×C4—112no—
433C23×C4—114no—
434C23×C4C2×Dic1118yescomplemented
435C23×C4C22×D1111yescharacteristic
436C23×C4C22×D1111yescharacteristic
437C23×C4C22×D1111yescharacteristic
438C23×C4C22×D1111yescharacteristic
439C23×C4C22×D1112yes—
440C23×C4C22×D1111yescharacteristic
441C23×C4C22×D1111yescharacteristic
442#123C2×Dic11116yescomplemented
443C22⋊Q8C2×Dic1118yescomplemented
444C22⋊Q8C2×Dic1118yescomplemented
445#121C2×Dic1118yescomplemented
446#121C2×Dic1118yescomplemented
447#120C2×Dic11116yescomplemented
448C4×D4—448no—
449C4×D4—448no—
450C4×D4C2×Dic11116yescomplemented
451C4×D4C2×Dic11116yescomplemented
452#117C2×Dic1118yescomplemented
453C2×C4⋊C4—112no—
454C2×C4⋊C4—114no—
455C2×C4⋊C4—112no—
456C2×C4⋊C4—114no—
457C2×C4⋊C4—114no—
458C2×C4⋊C4—114no—
459C2×C4⋊C4—444no—
460C2×C4⋊C4C22×D1111yescharacteristic
461C2×C4⋊C4C22×D1111yescharacteristic
462C2×C4⋊C4C22×D1112yes—
463C2×C4⋊C4C22×D1112yes—
464C2×C22⋊C4—114no—
465C2×C22⋊C4—114no—
466C2×C22⋊C4—112no—
467C2×C22⋊C4—112no—
468C2×C22⋊C4—114no—
469C2×C22⋊C4—114no—
470C2×C22⋊C4—114no—
471C2×C22⋊C4—114no—
472C2×C22⋊C4—444no—
473C2×C22⋊C4—444no—
474C2×C22⋊C4C22×D1112yes—
475C2×C22⋊C4C22×D1112yes—
476C2×C22⋊C4C22×D1112yes—
477C2×C22⋊C4C22×D1112yes—
478C2×C22⋊C4C22×D1112yes—
479C2×C42—114no—
480C2×C42—114no—
481C2×C42—114no—
482C2×C42C22×D1112yes—
483#95—112no—
484#95—112no—
485#95—112no—
486#95—112no—
487#95—114no—
488#95—112no—
489#95—114no—
490#95—114no—
491#95—112no—
492#95—114no—
493#95—114no—
494#95—114no—
495#95—114no—
496#95—114no—
497#95—114no—
498C2×C11—24no—
499C2×C11—24no—
500C2×C11—44no—
501C2×C11—42no—
502C2×C11C2×#51811yescharacteristic
503C2×C11C2×#52011yescharacteristic
504C2×C11#342811yescharacteristic
505C2×C11#353412yes—
506C2×C11#353512yes—
507C24—24no—
508C24—22no—
509C24—22no—
510C24—42no—
511C24C22×Dic1114yes—
512C24C23×D1111yescharacteristic
513C24C23×D1112yes—
514C24C23×D1111yescharacteristic
515C24C23×D1111yescharacteristic
516#41—416no—
517C2×Q8—42no—
518C2×Q8C22×Dic1114yes—
519C2×D4—28no—
520C2×D4—24no—
521C2×D4—24no—
522C2×D4—42no—
523C2×D4—44no—
524C2×D4C22×Dic1118yes—
525C2×D4C22×Dic1118yes—
526C2×D4C22×Dic1118yes—
527C2×D4C22×Dic1114yes—
528C22×C4—24no—
529C22×C4—24no—
530C22×C4—42no—
531C22×C4—42no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—416no—
535C22×C4—44no—
536C22×C4—114no—
537C22×C4—114no—
538C22×C4—114no—
539C22×C4—114no—
540C22×C4—228no—
541C22×C4—224no—
542C22×C4—224no—
543C22×C4—442no—
544C22×C4—442no—
545C22×C4—444no—
546C22×C4—444no—
547C22×C4—444no—
548C22×C4—442no—
549C22×C4—444no—
550C22×C4—444no—
551C22×C4—442no—
552C22×C4C22×Dic1114yes—
553C22×C4C22×Dic1114yes—
554C22×C4C22×Dic1114yes—
555C22×C4C22×Dic1114yes—
556C22×C4C22×Dic1118yes—
557C22×C4C22×Dic1114yes—
558C22×C4C22×Dic1114yes—
559C22×C4C23×D1111yescharacteristic
560C22×C4C23×D1111yescharacteristic
561C22×C4C23×D1112yes—
562C22×C4C23×D1112yes—
563C22×C4C23×D1112yes—
564C22×C4C23×D1111yescharacteristic
565C22×C4C23×D1111yescharacteristic
566C4⋊C4—442no—
567C4⋊C4—444no—
568C4⋊C4—442no—
569C4⋊C4—444no—
570C4⋊C4—444no—
571C4⋊C4—444no—
572C4⋊C4C22×Dic1114yes—
573C4⋊C4C22×Dic1114yes—
574C4⋊C4C22×Dic1118yes—
575C4⋊C4C22×Dic1118yes—
576C22⋊C4—228no—
577C22⋊C4—228no—
578C22⋊C4—444no—
579C22⋊C4—442no—
580C22⋊C4—442no—
581C22⋊C4—444no—
582C22⋊C4—444no—
583C22⋊C4—444no—
584C22⋊C4C22×Dic1118yes—
585C22⋊C4C22×Dic1118yes—
586C22⋊C4C22×Dic1118yes—
587C22⋊C4C22×Dic1118yes—
588C22⋊C4C22×Dic1118yes—
589C42—444no—
590C42—444no—
591C42—444no—
592C42C22×Dic1118yes—
593C11#3438611yescharacteristic, complemented, Sylow
594C23—22no—
595C23—21no—
596C23—21no—
597C23—22no—
598C23—22no—
599C23—28no—
600C23—28no—
601C23—22no—
602C23—24no—
603C23—21no—
604C23—22no—
605C23—22no—
606C23—21no—
607C23—24no—
608C23—22no—
609C23—44no—
610C23—48no—
611C23—48no—
612C23#6703714yes—
613C23#6704212yes—
614C23#6704312yes—
615C23C23×Dic1112yes—
616C23C23×Dic1114yes—
617C23C23×Dic1112yes—
618C23C23×Dic1112yes—
619C23C24×D1111yescharacteristic
620Q8—44no—
621D4—216no—
622D4—216no—
623D4—48no—
624D4—44no—
625C2×C4—28no—
626C2×C4—28no—
627C2×C4—24no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—24no—
635C2×C4—44no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—44no—
639C2×C4—48no—
640C2×C4—224no—
641C2×C4—224no—
642C2×C4—224no—
643C2×C4—224no—
644C2×C4—224no—
645C2×C4—224no—
646C2×C4—224no—
647C2×C4—224no—
648C2×C4—224no—
649C2×C4—224no—
650C2×C4—224no—
651C2×C4—224no—
652C2×C4—884no—
653C2×C4—888no—
654C2×C4—884no—
655C2×C4—888no—
656C2×C4C23×Dic1112yes—
657C2×C4C23×Dic1114yes—
658C2×C4C23×Dic1114yes—
659C2×C4C23×Dic1112yes—
660C2×C4C23×Dic1112yes—
661C2×C4C23×Dic1114yes—
662C2×C4C23×Dic1112yes—
663C22—24no—
664C22—24no—
665C22—24no—
666C22—24no—
667C22—22no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—24no—
673C22—24no—
674C22—22no—
675C22—22no—
676C22—24no—
677C22—416no—
678C22—44no—
679C22—42no—
680C22—42no—
681C22—44no—
682C22#1062332914yes—
683C22#1062335814yes—
684C22C2×#6703712yes—
685C22C2×#6704211yescharacteristic
686C22C2×#6704311yescharacteristic
687C22#1062345312yes—
688C22C24×Dic1111yescharacteristic
689C4—22no—
690C4—22no—
691C4—22no—
692C4—22no—
693C4—24no—
694C4—24no—
695C4—24no—
696C4—444no—
697C4—444no—
698C4—444no—
699C4—444no—
700C2—24no—
701C2—24no—
702C2—42no—
703C2—44no—
704C2C2×#1062332911yescharacteristic
705C2C2×#1062335811yescharacteristic
706C2#1308181911yescharacteristic
707C2#1308280012yes—
708C2#1308281912yes—
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
Fitting, prime radicalC2×C11×#525C2
socle, cosocleC23×C11C25
hypercenterC2×#525D11
hypocenterC11#34386
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. #13071600C2semidirect
4. #13071556C2semidirect
5. #13071526C2semidirect
6. #13071476C2semidirect
7. #13071446C2semidirect
8. #13071351C2semidirect
9. #13071321C2semidirect
10. #13071288C2semidirect
11. #13071259C2semidirect
12. #13071249C2semidirect
13. C2×#10622824C2semidirect
14. C2×#10622825C2semidirect
18. C11×#525C4semidirect
33. #10622843C22semidirect
38. #10622833C22semidirect
44. #10622825C22semidirect
49. #10622824C22semidirect
50. C4×C22⋊Dic11C22semidirect
55. C2×C11⋊#95C22semidirect
56. #10622598C22semidirect
57. #10622598C22semidirect
58. #10622594C22semidirect
59. #10622594C22semidirect
60. #10622594C22semidirect
61. #10622594C22semidirect
64. #10622564C22semidirect
65. #10622564C22semidirect
68. #10622563C22semidirect
69. #10622563C22semidirect
72. #10622550C22semidirect
73. #10622549C22semidirect
74. C4×C4⋊Dic11C22semidirect
75. #10622545C22semidirect
78. C2×C11×#41C2×C4semidirect
85. C23×C4×C11C2×C4semidirect
97. C11×#123C2×C4semidirect
98. C11×C22⋊Q8C2×C4semidirect
99. C11×C22⋊Q8C2×C4semidirect
100. C11×#121C2×C4semidirect
101. C11×#121C2×C4semidirect
102. C11×#120C2×C4semidirect
103. C4×D4×C11C2×C4semidirect
104. C4×D4×C11C2×C4semidirect
105. C11×#117C2×C4semidirect
326. #525Dic11semidirect
423. C2×#41C2×Dic11semidirect
434. C23×C4C2×Dic11semidirect
442. #123C2×Dic11semidirect
443. C22⋊Q8C2×Dic11semidirect
444. C22⋊Q8C2×Dic11semidirect
445. #121C2×Dic11semidirect
446. #121C2×Dic11semidirect
447. #120C2×Dic11semidirect
450. C4×D4C2×Dic11semidirect
451. C4×D4C2×Dic11semidirect
452. #117C2×Dic11semidirect
593. C11#34386semidirect

Maximal subgroups

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

subgroupindex
#130717822
#130717732
#130716002
#130715562
#130715262
#130714762
#130714462
#130713512
#130713212
#130712882
#130712592
#130712492
C2×#106228242
C2×#106228252
C2×C11×#5252
#3438611