Finite Group Databasebeta

← Dic11×#556 #14913730

Subgroups — Dic11×#556 #14913730

Order 2816.

2340 conjugacy classes of subgroups.

The subgroup lattice has 692 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13071740C214yesmaximal, complemented
2#13071691C212yesmaximal
3#13071676C211yesmaximal, characteristic, complemented
4#13071647C212yesmaximal, complemented
5#13071581C212yesmaximal, complemented
6#13071573C211yesmaximal, characteristic, complemented
7#13071565C211yesmaximal, characteristic
8#13071509C212yesmaximal, complemented
9C4⋊Q8×Dic11C211yesmaximal, characteristic, complemented
10#126×Dic11C214yesmaximal, complemented
11#124×Dic11C212yesmaximal
12C22⋊Q8×Dic11C212yesmaximal, complemented
13C4×Q8×Dic11C211yesmaximal, characteristic, complemented
14C4×Q8×Dic11C212yesmaximal, complemented
15C4×D4×Dic11C211yesmaximal, characteristic
16#117×Dic11C212yesmaximal, complemented
17C2×C11×#556C211yesmaximal, characteristic
18C11×#556C4116yescomplemented
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×#126C2214yes—
21C2×C11×#124C2212yes—
22C2×C11×C22⋊Q8C2212yes—
23C2×C4×Q8×C11C2211yescharacteristic
24C2×C4×Q8×C11C2212yes—
25C2×C4×D4×C11C2211yescharacteristic
26C2×C11×#117C2212yes—
27C2×Q8×Dic11C2211yescharacteristic
28C2×Q8×Dic11C2211yescharacteristic
29C2×Q8×Dic11C2212yes—
30C2×Q8×Dic11C2212yes—
31C2×D4×Dic11C2211yescharacteristic
32C2×D4×Dic11C2211yescharacteristic
33C2×#66979C2212yes—
34C22×C4×Dic11C2212yes—
35#10622843C2212yes—
36#10622843C2212yes—
37#10622843C2212yes—
38#10622834C2212yes—
39#10622825C2212yes—
40C4×C22⋊Dic11C2212yes—
41#10622598C2212yes—
42#10622598C2212yes—
43#10622598C2212yes—
44#10622594C2214yes—
45#10622594C2214yes—
46#10622594C2214yes—
47#10622594C2214yes—
48C4⋊C4×Dic11C2212yes—
49C4⋊C4×Dic11C2214yes—
50C4⋊C4×Dic11C2214yes—
51C4⋊C4×Dic11C2212yes—
52C4⋊C4×Dic11C2212yes—
53C4⋊C4×Dic11C2212yes—
54C4⋊C4×Dic11C2211yescharacteristic
55C4⋊C4×Dic11C2212yes—
56C4⋊C4×Dic11C2211yescharacteristic
57C4⋊C4×Dic11C2211yescharacteristic
58C4⋊C4×Dic11C2212yes—
59C4⋊C4×Dic11C2211yescharacteristic
60C4⋊C4×Dic11C2212yes—
61#10622564C2214yes—
62#10622564C2214yes—
63#10622564C2214yes—
64#10622564C2214yes—
65#10622564C2214yes—
66#10622563C2214yes—
67C22⋊C4×Dic11C2214yes—
68C22⋊C4×Dic11C2214yes—
69C22⋊C4×Dic11C2212yes—
70C22⋊C4×Dic11C2214yes—
71C22⋊C4×Dic11C2212yes—
72#10622550C2214yes—
73#10622549C2212yes—
74#10622548C2211yescharacteristic
75C4×C4⋊Dic11C2211yescharacteristic
76C4×C4⋊Dic11C2211yescharacteristic
77C4×C4⋊Dic11C2212yes—
78C4×C4⋊Dic11C2212yes—
79C4×C4⋊Dic11C2214yes—
80#10622545C2214yes—
81C42×Dic11C2212yes—
82C42×Dic11C2214yes—
83C42×Dic11C2211yescharacteristic
84C22×Q8×C11C2311yescharacteristic
85C22×Q8×C11C2312yes—
86C22×D4×C11C2311yescharacteristic
87C23×C4×C11C2312yes—
88C23×Dic11C2312yes—
89C23×Dic11C2312yes—
90C11×C4⋊Q8C2×C418yescomplemented
91C11×#126C2×C4132yescomplemented
92C11×#124C2×C4116yes—
93C11×C22⋊Q8C2×C4116yescomplemented
94C4×Q8×C11C2×C4116yescomplemented
95C4×Q8×C11C2×C418yescomplemented
96C4×D4×C11C2×C418yes—
97C11×#117C2×C4116yescomplemented
98C2×C11×C4⋊C4C2311yescharacteristic
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2314yes—
101C2×C11×C4⋊C4C2312yes—
102C2×C11×C4⋊C4C2312yes—
103C2×C11×C4⋊C4C2312yes—
104C2×C11×C22⋊C4C2314yes—
105C2×C11×C22⋊C4C2312yes—
106C2×C11×C22⋊C4C2314yes—
107C2×C42×C11C2314yes—
108C2×C42×C11C2311yescharacteristic
109C2×C42×C11C2312yes—
110C2×C22⋊Dic11C2314yes—
111C2×C22⋊Dic11C2312yes—
112C2×C22⋊Dic11C2312yes—
113C2×C22⋊Dic11C2314yes—
114Q8×Dic11—24no—
115Q8×Dic11—28no—
116Q8×Dic11—24no—
117Q8×Dic11—28no—
118D4×Dic11—24no—
119D4×Dic11—24no—
120#66979—28no—
121C2×C4⋊Dic11C2312yes—
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2312yes—
124C2×C4⋊Dic11C2314yes—
125C2×C4⋊Dic11C2312yes—
126C2×C4⋊Dic11C2314yes—
127C2×C4⋊Dic11C2311yescharacteristic
128C2×C4⋊Dic11C2312yes—
129C2×C4⋊Dic11C2312yes—
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4×Dic11—28no—
133C2×C4×Dic11C2312yes—
134C2×C4×Dic11C2312yes—
135C2×C4×Dic11C2314yes—
136C2×C4×Dic11C2311yescharacteristic
137C2×C4×Dic11C2312yes—
138C2×C4×Dic11C2312yes—
139C2×C4×Dic11C2314yes—
140C2×C4×Dic11C2311yescharacteristic
141C2×C4×Dic11C2314yes—
142C2×C4×Dic11C2312yes—
143C2×C4×Dic11C2311yescharacteristic
144C2×C4×Dic11C2312yes—
145C2×C4×Dic11C2312yes—
146C2×C4×Dic11C2314yes—
147C2×C4×Dic11C2312yes—
148C2×C4×Dic11C2311yescharacteristic
149C2×C4×Dic11C2311yescharacteristic
150C2×C4×Dic11C2311yescharacteristic
151C11⋊#95C2312yes—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2312yes—
156C11⋊#95C2312yes—
157C11⋊#95C2314yes—
158C11⋊#95C2312yes—
159C11⋊#95C2314yes—
160C11⋊#95C2312yes—
161C11⋊#95C2314yes—
162C11⋊#95C2312yes—
163C11⋊#95C2314yes—
164C11⋊#95C2314yes—
165C4×#556—111nomaximal, Sylow
166C24×C11C2412yes—
167C2×Q8×C11—24no—
168C2×Q8×C11—22no—
169C2×Q8×C11—22no—
170C2×Q8×C11—24no—
171C2×Q8×C11C22×C414yes—
172C2×Q8×C11C22×C418yes—
173C2×D4×C11—22no—
174C2×D4×C11—22no—
175C2×D4×C11C22×C414yes—
176C22×C4×C11—24no—
177C22×C4×C11—24no—
178C22×C4×C11C22×C418yes—
179C22×C4×C11C2412yes—
180C22×C4×C11C2412yes—
181C22×C4×C11C2411yescharacteristic
182C22×C4×C11C2414yes—
183C22×C4×C11C2412yes—
184C22×C4×C11C2411yescharacteristic
185C22×C4×C11C2411yescharacteristic
186C22×Dic11—24no—
187C22×Dic11—24no—
188C22×Dic11—24no—
189C22×Dic11—24no—
190C22×Dic11—24no—
191C22×Dic11—42no—
192C22×Dic11C2412yes—
193C22×Dic11C2411yescharacteristic
194C22×Dic11C2412yes—
195C22×Dic11C2414yes—
196C22×Dic11C2411yescharacteristic
197C22×Dic11C2412yes—
198C22×Dic11C2412yes—
199C22×Dic11C2411yescharacteristic
200C22×Dic11C2411yescharacteristic
201C11×C4⋊C4C22×C414yes—
202C11×C4⋊C4C22×C418yes—
203C11×C4⋊C4C22×C414yes—
204C11×C4⋊C4C22×C4116yes—
205C11×C4⋊C4C22×C418yes—
206C11×C4⋊C4C22×C418yes—
207C11×C22⋊C4C22×C4116yes—
208C11×C22⋊C4C22×C418yes—
209C11×C22⋊C4C22×C4116yes—
210C42×C11C22×C4116yes—
211C42×C11C22×C414yes—
212C42×C11C22×C418yes—
213C22⋊Dic11—28no—
214C22⋊Dic11—24no—
215C22⋊Dic11—24no—
216C22⋊Dic11—44no—
217C4⋊Dic11—24no—
218C4⋊Dic11—24no—
219C4⋊Dic11—28no—
220C4⋊Dic11—28no—
221C4⋊Dic11—24no—
222C4⋊Dic11—22no—
223C4⋊Dic11—22no—
224C4⋊Dic11—24no—
225C4⋊Dic11—42no—
226C4⋊Dic11#4114yes—
227C4⋊Dic11#4114yes—
228C4×Dic11—24no—
229C4×Dic11—24no—
230C4×Dic11—28no—
231C4×Dic11—24no—
232C4×Dic11—28no—
233C4×Dic11—24no—
234C4×Dic11—28no—
235C4×Dic11—24no—
236C4×Dic11—22no—
237C4×Dic11—24no—
238C4×Dic11—22no—
239C4×Dic11—24no—
240C4×Dic11—22no—
241C4×Dic11—42no—
242C4×Dic11—44no—
243C4×Dic11—41no—
244C4×Dic11#4114yes—
245C4×Dic11#4114yes—
246C2×#556D1111yescharacteristic
247#2373—114no—
248#2367—112no—
249#2365—111no—
250#2362—112no—
251#2356—112no—
252#2355—111no—
253#2354—111no—
254#2347—112no—
255C4×C4⋊Q8—111no—
256C4×#126—114no—
257C4×#124—112no—
258C4×C22⋊Q8—112no—
259C42×Q8—112no—
260C42×Q8—111no—
261C42×D4—111no—
262C4×#117—112no—
263C23×C11—22no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11C23×C414yes—
270C23×C11C2511yescharacteristic
271Q8×C11—28no—
272Q8×C11—216no—
273D4×C11—28no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—24no—
278C2×C4×C11—24no—
279C2×C4×C11—22no—
280C2×C4×C11—22no—
281C2×C4×C11—21no—
282C2×C4×C11—22no—
283C2×C4×C11—21no—
284C2×C4×C11—216no—
285C2×C4×C11C23×C414yes—
286C2×C4×C11C23×C414yes—
287C2×C4×C11C23×C412yes—
288C2×C4×C11C23×C418yes—
289C2×C4×C11C23×C414yes—
290C2×C4×C11C23×C412yes—
291C2×C4×C11C23×C412yes—
292C2×C4×C11C2×#4112yes—
293C2×C4×C11C2×#4112yes—
294C2×C4×C11C2×#4112yes—
295C2×C4×C11C2×#4112yes—
296C2×Dic11—21no—
297C2×Dic11—22no—
298C2×Dic11—22no—
299C2×Dic11—21no—
300C2×Dic11—22no—
301C2×Dic11—21no—
302C2×Dic11—22no—
303C2×Dic11—21no—
304C2×Dic11—22no—
305C2×Dic11—22no—
306C2×Dic11—22no—
307C2×Dic11—24no—
308C2×Dic11—21no—
309C2×Dic11—24no—
310C2×Dic11—21no—
311C2×Dic11—22no—
312C2×Dic11—21no—
313C2×Dic11—22no—
314C2×Dic11—24no—
315C2×Dic11—22no—
316C2×Dic11—48no—
317C2×Dic11—48no—
318C2×Dic11C2×#4114yes—
319C2×Dic11C2×#4112yes—
320C2×Dic11C2×#4114yes—
321C2×Dic11C2×#4112yes—
322C2×Dic11C2×#4112yes—
323C2×Dic11C2×#4112yes—
324C2×Dic112−1+412yes—
325#556Dic11116yesdirect product factor
326C2×C4⋊Q8C2×D1111yescharacteristic
327C2×#126C2×D1114yes—
328C2×#124C2×D1112yes—
329C2×C22⋊Q8C2×D1112yes—
330C2×C4×Q8—112no—
331C2×C4×Q8—111no—
332C2×C4×Q8—112no—
333C2×C4×Q8—111no—
334C2×C4×Q8C2×D1111yescharacteristic
335C2×C4×Q8C2×D1112yes—
336C2×C4×D4—111no—
337C2×C4×D4—111no—
338C2×C4×D4C2×D1111yescharacteristic
339C2×#117—112no—
340C2×#117C2×D1112yes—
341C22×C42—112no—
342#391—112no—
343#391—112no—
344#391—112no—
345#390—112no—
346#389—112no—
347#389—112no—
348#389—112no—
349#388—114no—
350#388—114no—
351#388—114no—
352#388—114no—
353#388—114no—
354#387—114no—
355#387—114no—
356#387—114no—
357#387—114no—
358#385—114no—
359#384—111no—
360#383—114no—
361#382—112no—
362#380—112no—
363C4×C4⋊C4—112no—
364C4×C4⋊C4—112no—
365C4×C4⋊C4—114no—
366C4×C4⋊C4—112no—
367C4×C4⋊C4—111no—
368C4×C4⋊C4—112no—
369C4×C4⋊C4—112no—
370C4×C4⋊C4—111no—
371C4×C4⋊C4—112no—
372C4×C4⋊C4—114no—
373C4×C4⋊C4—112no—
374C4×C4⋊C4—111no—
375C4×C4⋊C4—111no—
376C4×C4⋊C4—114no—
377C4×C4⋊C4—111no—
378C4×C4⋊C4—111no—
379C4×C4⋊C4—112no—
380C4×C4⋊C4—112no—
381C4×C22⋊C4—112no—
382C4×C22⋊C4—112no—
383C4×C22⋊C4—114no—
384C4×C22⋊C4—114no—
385C4×C22⋊C4—114no—
386C4×C22⋊C4—112no—
387#376—114no—
388C43—114no—
389C43—111no—
390C43—112no—
391C22×C11—24no—
392C22×C11—24no—
393C22×C11—24no—
394C22×C11—42no—
395C22×C11—42no—
396C22×C11—42no—
397C22×C11—42no—
398C22×C11C24×C411yescharacteristic
399C22×C11C22×#4111yescharacteristic
400C22×C11C22×#4111yescharacteristic
401C22×C11C22×#4111yescharacteristic
402C22×C11C22×#4111yescharacteristic
403C22×C11C2×2−1+411yescharacteristic
404C22×C11#58511yescharacteristic
405C4×C11—24no—
406C4×C11—24no—
407C4×C11—28no—
408C4×C11—24no—
409C4×C11—22no—
410C4×C11C4×#4114yes—
411C4×C11C4×#4114yes—
412Dic11—22no—
413Dic11—24no—
414Dic11—22no—
415Dic11—24no—
416Dic11—42no—
417Dic11—42no—
418Dic11—44no—
419Dic11—41no—
420Dic11#55614yesdirect product factor
421C22×Q8C22×D1111yescharacteristic
422C22×Q8C22×D1112yes—
423C22×D4C22×D1111yescharacteristic
424C23×C4—112no—
425C23×C4—112no—
426C23×C4C22×D1112yes—
427C4⋊Q8C2×Dic1118yescomplemented
428#126C2×Dic11132yescomplemented
429#124C2×Dic11116yes—
430C22⋊Q8C2×Dic11116yescomplemented
431C4×Q8—224no—
432C4×Q8—228no—
433C4×Q8—224no—
434C4×Q8—228no—
435C4×Q8C2×Dic11116yescomplemented
436C4×Q8C2×Dic1118yescomplemented
437C4×D4—224no—
438C4×D4—224no—
439C4×D4C2×Dic1118yes—
440#117—228no—
441#117C2×Dic11116yescomplemented
442C2×C4⋊C4—111no—
443C2×C4⋊C4—111no—
444C2×C4⋊C4—112no—
445C2×C4⋊C4—111no—
446C2×C4⋊C4—111no—
447C2×C4⋊C4—112no—
448C2×C4⋊C4—112no—
449C2×C4⋊C4—114no—
450C2×C4⋊C4—112no—
451C2×C4⋊C4—114no—
452C2×C4⋊C4—112no—
453C2×C4⋊C4C22×D1111yescharacteristic
454C2×C4⋊C4C22×D1112yes—
455C2×C4⋊C4C22×D1111yescharacteristic
456C2×C4⋊C4C22×D1114yes—
457C2×C4⋊C4C22×D1112yes—
458C2×C4⋊C4C22×D1112yes—
459C2×C22⋊C4—114no—
460C2×C22⋊C4—112no—
461C2×C22⋊C4—112no—
462C2×C22⋊C4—114no—
463C2×C22⋊C4C22×D1114yes—
464C2×C22⋊C4C22×D1112yes—
465C2×C22⋊C4C22×D1114yes—
466C2×C42—111no—
467C2×C42—111no—
468C2×C42—114no—
469C2×C42—111no—
470C2×C42—114no—
471C2×C42—112no—
472C2×C42—111no—
473C2×C42—114no—
474C2×C42—112no—
475C2×C42—112no—
476C2×C42—112no—
477C2×C42—112no—
478C2×C42—111no—
479C2×C42—112no—
480C2×C42—112no—
481C2×C42—111no—
482C2×C42—114no—
483C2×C42—112no—
484C2×C42—228no—
485C2×C42C22×D1114yes—
486C2×C42C22×D1111yescharacteristic
487C2×C42C22×D1112yes—
488#95—112no—
489#95—114no—
490#95—114no—
491#95—114no—
492#95—112no—
493#95—112no—
494#95—112no—
495#95—114no—
496#95—114no—
497#95—114no—
498#95—112no—
499#95—114no—
500#95—112no—
501#95—114no—
502C2×C11—44no—
503C2×C11C2×C4×#4111yescharacteristic
504C2×C11C2×C4×#4111yescharacteristic
505C2×C11C4×2−1+411yescharacteristic
506C2×C11C2×#55611yescharacteristic
507C2×C11#347511yescharacteristic
508C2×C11#348011yescharacteristic
509C2×C11#348211yescharacteristic
510C24C23×D1112yes—
511C2×Q8—22no—
512C2×Q8—24no—
513C2×Q8—24no—
514C2×Q8—22no—
515C2×Q8C22×Dic1114yes—
516C2×Q8C22×Dic1118yes—
517C2×D4—22no—
518C2×D4—22no—
519C2×D4C22×Dic1114yes—
520C22×C4—24no—
521C22×C4—24no—
522C22×C4—111no—
523C22×C4—111no—
524C22×C4—112no—
525C22×C4—112no—
526C22×C4—111no—
527C22×C4—112no—
528C22×C4—111no—
529C22×C4—114no—
530C22×C4—112no—
531C22×C4—224no—
532C22×C4—224no—
533C22×C4—224no—
534C22×C4—224no—
535C22×C4—224no—
536C22×C4—442no—
537C22×C4C22×Dic1118yes—
538C22×C4C23×D1112yes—
539C22×C4C23×D1112yes—
540C22×C4C23×D1111yescharacteristic
541C22×C4C23×D1114yes—
542C22×C4C23×D1112yes—
543C22×C4C23×D1111yescharacteristic
544C22×C4C23×D1111yescharacteristic
545C4⋊C4—114no—
546C4⋊C4—114no—
547C4⋊C4—224no—
548C4⋊C4—228no—
549C4⋊C4—224no—
550C4⋊C4—228no—
551C4⋊C4—224no—
552C4⋊C4—222no—
553C4⋊C4—222no—
554C4⋊C4—224no—
555C4⋊C4—442no—
556C4⋊C4C22×Dic1114yes—
557C4⋊C4C22×Dic1118yes—
558C4⋊C4C22×Dic1114yes—
559C4⋊C4C22×Dic11116yes—
560C4⋊C4C22×Dic1118yes—
561C4⋊C4C22×Dic1118yes—
562C22⋊C4—228no—
563C22⋊C4—224no—
564C22⋊C4—224no—
565C22⋊C4—444no—
566C22⋊C4C22×Dic11116yes—
567C22⋊C4C22×Dic1118yes—
568C22⋊C4C22×Dic11116yes—
569C42—114no—
570C42—114no—
571C42—224no—
572C42—224no—
573C42—228no—
574C42—224no—
575C42—228no—
576C42—224no—
577C42—228no—
578C42—224no—
579C42—222no—
580C42—224no—
581C42—222no—
582C42—224no—
583C42—222no—
584C42—442no—
585C42—444no—
586C42—441no—
587C42C22×Dic11116yes—
588C42C22×Dic1114yes—
589C42C22×Dic1118yes—
590C11C4×#55611yescharacteristic, complemented, Sylow
591C23—22no—
592C23—22no—
593C23—22no—
594C23—22no—
595C23—22no—
596C23—22no—
597C23C23×Dic1114yes—
598C23C24×D1111yescharacteristic
599Q8—28no—
600Q8—216no—
601D4—28no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—22no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—22no—
608C2×C4—22no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—21no—
612C2×C4—216no—
613C2×C4—112no—
614C2×C4—112no—
615C2×C4—112no—
616C2×C4—112no—
617C2×C4—112no—
618C2×C4—114no—
619C2×C4—114no—
620C2×C4—221no—
621C2×C4—222no—
622C2×C4—222no—
623C2×C4—221no—
624C2×C4—222no—
625C2×C4—221no—
626C2×C4—222no—
627C2×C4—221no—
628C2×C4—222no—
629C2×C4—221no—
630C2×C4—224no—
631C2×C4—222no—
632C2×C4—222no—
633C2×C4—224no—
634C2×C4—221no—
635C2×C4—222no—
636C2×C4—221no—
637C2×C4—222no—
638C2×C4—222no—
639C2×C4—224no—
640C2×C4—448no—
641C2×C4—448no—
642C2×C4#41×D1112yes—
643C2×C4#41×D1112yes—
644C2×C4#41×D1112yes—
645C2×C4#41×D1112yes—
646C2×C4C23×Dic1114yes—
647C2×C4C23×Dic1114yes—
648C2×C4C23×Dic1112yes—
649C2×C4C23×Dic1118yes—
650C2×C4C23×Dic1114yes—
651C2×C4C23×Dic1112yes—
652C2×C4C23×Dic1112yes—
653C22—24no—
654C22—24no—
655C22—24no—
656C22—42no—
657C22—42no—
658C22—42no—
659C22—42no—
660C22C2×#41×D1111yescharacteristic
661C22C2×#41×D1111yescharacteristic
662C22C2×#41×D1111yescharacteristic
663C22C2×#41×D1111yescharacteristic
664C22D11×2−1+411yescharacteristic
665C22#1062345711yescharacteristic
666C22C24×Dic1111yescharacteristic
667C4—24no—
668C4—24no—
669C4—28no—
670C4—24no—
671C4—22no—
672C4—114no—
673C4—222no—
674C4—224no—
675C4—222no—
676C4—224no—
677C4—442no—
678C4—442no—
679C4—444no—
680C4—441no—
681C4#41×Dic1114yes—
682C4#41×Dic1114yes—
683C2—44no—
684C2C2×#41×Dic1111yescharacteristic
685C2C2×#41×Dic1111yescharacteristic
686C22−1+4×Dic1111yescharacteristic
687C2D11×#55611yescharacteristic
688C2#1308217711yescharacteristic
689C2#1308220811yescharacteristic
690C2#1308223511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D11
commutatorC22×C11C24×C4
FittingC2×C11×#556C2
socle, cosocleC23×C11C25
prime radicalC22×D4×C11C23
hypercenterC2×#556D11
hypocenterC11C4×#556
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #13071740C2semidirect
3. #13071676C2semidirect
4. #13071647C2semidirect
5. #13071581C2semidirect
6. #13071573C2semidirect
8. #13071509C2semidirect
9. C4⋊Q8×Dic11C2semidirect
10. #126×Dic11C2semidirect
12. C22⋊Q8×Dic11C2semidirect
13. C4×Q8×Dic11C2semidirect
14. C4×Q8×Dic11C2semidirect
16. #117×Dic11C2semidirect
18. C11×#556C4semidirect
90. C11×C4⋊Q8C2×C4semidirect
91. C11×#126C2×C4semidirect
93. C11×C22⋊Q8C2×C4semidirect
94. C4×Q8×C11C2×C4semidirect
95. C4×Q8×C11C2×C4semidirect
97. C11×#117C2×C4semidirect
325. #556Dic11direct (N × H)
420. Dic11#556direct (N × H)
427. C4⋊Q8C2×Dic11semidirect
428. #126C2×Dic11semidirect
430. C22⋊Q8C2×Dic11semidirect
435. C4×Q8C2×Dic11semidirect
436. C4×Q8C2×Dic11semidirect
441. #117C2×Dic11semidirect
590. C11C4×#556semidirect

Maximal subgroups

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

subgroupindex
#130717402
#130716912
#130716762
#130716472
#130715812
#130715732
#130715652
#130715092
C4⋊Q8×Dic112
#126×Dic112
#124×Dic112
C22⋊Q8×Dic112
C4×Q8×Dic112
C4×D4×Dic112
#117×Dic112
C2×C11×#5562
C4×#55611