Finite Group Databasebeta

← #14960765

Subgroups — #14960765

Order 2816.

2490 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623046C211yesmaximal, characteristic, complemented
2#13076903C211yesmaximal, characteristic, complemented
3#13076898C211yesmaximal, characteristic
4#13075270C214yesmaximal, complemented
5#13075240C214yesmaximal, complemented
6#13074986C214yesmaximal, complemented
7#13074971C214yesmaximal, complemented
8#13074429C211yesmaximal, characteristic, complemented
9#13074358C211yesmaximal, characteristic, complemented
10#13073506C212yesmaximal, complemented
11#13072023C212yesmaximal, complemented
12#13072001C212yesmaximal, complemented
13#13071975C212yesmaximal, complemented
14#13071234C211yesmaximal, characteristic, complemented
15C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
16C23×Q8×C11C2211yescharacteristic
17C24×C4×C11C2211yescharacteristic
18C2×C11×C22⋊Q8—28no—
19C2×C11×C22⋊Q8C2214yes—
20C2×C11×C22⋊Q8C2214yes—
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2211yescharacteristic
26C2×#67006C2212yes—
27C2×#66999C2214yescomplemented
28C2×#66983C2211yescharacteristic
29C2×#66983C2212yes—
30C2×#66982C2212yes—
31C2×#66982C2212yes—
32C2×C4×C22⋊D11C2212yes—
33C2×#66979C2212yes—
34C2×#66977C2211yescharacteristic
35C2×#66977C2212yes—
36#10623046—28no—
37C2×#66951C2212yescomplemented
38C2×#66949C2212yescomplemented
39C2×#66947C2212yescomplemented
40C2×#66942C2212yescomplemented
41#10622860C2212yes—
42#10622844C2214yescomplemented
43#10622843C2214yescomplemented
44#10622842C2214yescomplemented
45#10622826C2214yes—
46#10622826C2212yes—
47#10622826C2212yes—
48#10622825C2212yes—
49#10622825C2212yes—
50#10622825C2212yes—
51#10622825C2211yescharacteristic
52#10622825C2211yescharacteristic
53#10622824C2212yes—
54#10622823C2214yes—
55#10622823C2212yes—
56#10622823C2212yes—
57#10622607C2214yescomplemented
58#10622607C2214yescomplemented
59#10622604C2212yescomplemented
60#10622603C2214yescomplemented
61#10622599C2212yescomplemented
62#10622598C2214yescomplemented
63#10622598C2214yescomplemented
64#10622597C2214yescomplemented
65#10622597C2214yescomplemented
66#10622596C2212yescomplemented
67#10622592C2212yescomplemented
68#10622585C2214yescomplemented
69#10622574C2214yes—
70#10622574C2214yes—
71#10622570C2214yes—
72#10622569C2214yes—
73#10622561C2214yes—
74#10622561C2214yes—
75#10622558C2214yes—
76#10622557C2214yes—
77C25×C11C2311yescharacteristic
78C22×Q8×C11—24no—
79C22×Q8×C11—44no—
80C22×Q8×C11C2314yes—
81C23×C4×C11—24no—
82C23×C4×C11—44no—
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2312yes—
86C23×C4×C11C2312yes—
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C2311yescharacteristic
89C23×C4×C11C2311yescharacteristic
90C23×C4×C11C2311yescharacteristic
91C22×C22⋊D11C2312yes—
92C22×C22⋊D11C2314yes—
93C22×D44C2311yescharacteristic
94C22×C4×D11C2312yes—
95C22×Dic22C2311yescharacteristic
96C11×C22⋊Q8—216no—
97C11×C22⋊Q8—216no—
98C2×C11×C4⋊C4—24no—
99C2×C11×C4⋊C4—24no—
100C2×C11×C4⋊C4D418yescomplemented
101C2×C11×C4⋊C4C2314yes—
102C2×C11×C4⋊C4C2312yes—
103C2×C11×C4⋊C4C2312yes—
104C2×C11×C4⋊C4C2312yes—
105C2×C11×C4⋊C4C2312yes—
106C2×C11×C22⋊C4—24no—
107C2×C11×C22⋊C4—24no—
108C2×C11×C22⋊C4C2314yes—
109C2×C11×C22⋊C4C2314yes—
110#67006—44no—
111C2×C22⋊Dic11C2312yes—
112C2×C22⋊Dic11C2312yes—
113C2×C22⋊Dic11C2312yes—
114C2×C22⋊Dic11C2314yes—
115C2×C22⋊Dic11C2314yes—
116C2×C22⋊Dic11C2314yes—
117#66999—48no—
118#66983—24no—
119#66983—44no—
120#66982—28no—
121#66982—44no—
122C4×C22⋊D11—28no—
123C2×(C2×D11)⋊C4C2312yes—
124C2×(C2×D11)⋊C4C2312yes—
125C2×(C2×D11)⋊C4C2312yes—
126C2×(C2×D11)⋊C4C2312yes—
127C2×(C2×D11)⋊C4C2314yes—
128C2×(C2×D11)⋊C4C2314yes—
129C2×(C2×D11)⋊C4C2314yes—
130#66979—44no—
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×C4⋊Dic11C2312yes—
134C2×C4⋊Dic11C2314yes—
135C2×C4⋊Dic11C2312yes—
136C2×C4⋊Dic11C2314yes—
137#66977—24no—
138#66977—44no—
139C2×Dic11⋊C4C2312yes—
140C2×Dic11⋊C4C2312yes—
141C2×Dic11⋊C4C2312yes—
142C2×Dic11⋊C4C2312yes—
143C2×Dic11⋊C4C2314yes—
144C2×Dic11⋊C4C2314yes—
145C2×Dic11⋊C4C2314yes—
146C2×C4×Dic11C2312yes—
147C2×C4×Dic11C2314yes—
148#66951—28no—
149#66949—28no—
150#66947—28no—
151#66942—28no—
152C11⋊#95C2314yes—
153C11⋊#95C2314yes—
154C11⋊#95C2314yes—
155C11⋊#95C2314yes—
156C11⋊#95C2314yes—
157C11⋊#95C2314yes—
158C11⋊#95C2312yes—
159C11⋊#95C2314yes—
160C11⋊#95C2312yes—
161#36719—111nomaximal, Sylow
162C24×C11—22no—
163C24×C11—24no—
164C24×C11—22no—
165C24×C11—22no—
166C24×C11—42no—
167C24×C11C2412yes—
168C24×C11C2411yescharacteristic
169C23×D11C2412yes—
170C2×Q8×C11—28no—
171C2×Q8×C11—28no—
172C2×Q8×C11—44no—
173C2×Q8×C11—416no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—24no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—24no—
183C22×C4×C11—24no—
184C22×C4×C11—24no—
185C22×C4×C11—24no—
186C22×C4×C11—42no—
187C22×C4×C11—42no—
188C22×C4×C11—42no—
189C22×C4×C11—42no—
190C22×C4×C11—42no—
191C22×C4×C11—416no—
192C22×C4×C11C2×D414yes—
193C22×C4×C11C2×D414yes—
194C22×C4×C11C2×D414yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2412yes—
198C22×C4×C11C2411yescharacteristic
199C22×C4×C11C2411yescharacteristic
200C22×C4×C11C2412yes—
201C22×C4×C11C2412yes—
202C2×C22⋊D11—24no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—24no—
205C2×C22⋊D11—28no—
206C2×C22⋊D11—44no—
207C2×C22⋊D11—44no—
208C22×Dic11C2412yes—
209C22×Dic11C2414yes—
210C22×Dic11C2412yes—
211C22×Dic11C2414yes—
212C22×Dic11C2412yes—
213C2×D44—22no—
214C2×D44—42no—
215C2×C4×D11—24no—
216C2×C4×D11—44no—
217C2×Dic22—22no—
218C2×Dic22—42no—
219C11×C4⋊C4—28no—
220C11×C4⋊C4—24no—
221C11×C4⋊C4—24no—
222C11×C4⋊C4C2×D418yes—
223C11×C4⋊C4C2×D418yes—
224C11×C22⋊C4—28no—
225C11×C22⋊C4—28no—
226C22⋊Dic11—24no—
227C22⋊Dic11—24no—
228C22⋊Dic11—24no—
229C22⋊Dic11—28no—
230C22⋊Dic11—44no—
231C22⋊Dic11—44no—
232(C2×D11)⋊C4—24no—
233(C2×D11)⋊C4—24no—
234(C2×D11)⋊C4—24no—
235(C2×D11)⋊C4—24no—
236(C2×D11)⋊C4—28no—
237(C2×D11)⋊C4—44no—
238(C2×D11)⋊C4—44no—
239C4⋊Dic11—22no—
240C4⋊Dic11—22no—
241C4⋊Dic11—42no—
242C4⋊Dic11—44no—
243C4⋊Dic11—42no—
244C4⋊Dic11—44no—
245Dic11⋊C4—24no—
246Dic11⋊C4—24no—
247Dic11⋊C4—24no—
248Dic11⋊C4—24no—
249Dic11⋊C4—28no—
250Dic11⋊C4—44no—
251Dic11⋊C4—44no—
252C4×Dic11—24no—
253C4×Dic11—44no—
254C2×#539—111no—
255C22×C22⋊Q8D1111yescharacteristic, complemented
256#2848—111no—
257#2847—111no—
258#2704—114no—
259#2702—114no—
260#2683—114no—
261#2681—114no—
262#2627—111no—
263#2618—111no—
264#2534—112no—
265#2413—112no—
266#2411—112no—
267#2409—112no—
268#2316—111no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11—28no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—48no—
279C23×C11—48no—
280C23×C11—44no—
281C23×C11—44no—
282C23×C11C22×D412yes—
283C23×C11H(5,𝔽2)12yes—
284C23×C112−1+414yes—
285C23×C112−1+412yes—
286C23×C11C2511yescharacteristic
287C22×D11—22no—
288C22×D11—24no—
289C22×D11—22no—
290C22×D11—24no—
291C22×D11—22no—
292Q8×C11—416no—
293C2×C4×C11—28no—
294C2×C4×C11—28no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—24no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—24no—
306C2×C4×C11—22no—
307C2×C4×C11—44no—
308C2×C4×C11—44no—
309C2×C4×C11—48no—
310C2×C4×C11—48no—
311C2×C4×C11—44no—
312C2×C4×C11—44no—
313C2×C4×C11C22×D414yes—
314C2×C4×C11C22×D412yes—
315C2×C4×C11C22×D414yes—
316C2×C4×C11C22×D412yes—
317C2×C4×C11H(5,𝔽2)14yes—
318C22⋊D11—48no—
319C22⋊D11—88no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—22no—
328C2×Dic11—24no—
329C2×Dic11—24no—
330C2×Dic11—24no—
331C2×Dic11—24no—
332C2×Dic11—22no—
333D44—82no—
334C4×D11—84no—
335Dic22—82no—
336C23×Q8C2×D1111yescharacteristic
337C24×C4C2×D1111yescharacteristic
338#539—228no—
339C2×#126—112no—
340C2×#125—112no—
341C2×#123—112no—
342C2×#123—112no—
343C2×#123—112no—
344C2×C22⋊Q8—28no—
345C2×C22⋊Q8—111no—
346C2×C22⋊Q8—114no—
347C2×C22⋊Q8—112no—
348C2×C22⋊Q8—112no—
349C2×C22⋊Q8C2×D1114yes—
350C2×C22⋊Q8C2×D1114yes—
351C2×#121—111no—
352C2×#121—112no—
353C2×#120—112no—
354C2×C4×D4—112no—
355C2×#117—112no—
356C22×C4⋊C4C2×D1111yescharacteristic
357C22×C4⋊C4C2×D1111yescharacteristic
358C22×C4⋊C4C2×D1111yescharacteristic
359C22×C22⋊C4C2×D1111yescharacteristic
360C22×C22⋊C4C2×D1111yescharacteristic
361#400—112no—
362#398—112no—
363#398—114no—
364#398—114no—
365#396—114no—
366#396—114no—
367#396—114no—
368#396—114no—
369#395—114no—
370#395—112no—
371#394—112no—
372#394—114no—
373#394—114no—
374#393—114no—
375#391—114no—
376#390—114no—
377#389—114no—
378#389—114no—
379#389—114no—
380#388—114no—
381#388—114no—
382#388—114no—
383#386—112no—
384#386—114no—
385#386—112no—
386#386—114no—
387#385—112no—
388#385—114no—
389#385—112no—
390#381—112no—
391#380—111no—
392#380—111no—
393#380—112no—
394#380—112no—
395#380—112no—
396#379—112no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—24no—
400C22×C11—24no—
401C22×C11—24no—
402C22×C11—24no—
403C22×C11—24no—
404C22×C11—416no—
405C22×C11—42no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11—42no—
409C22×C11#53714yes—
410C22×C11C23×D411yescharacteristic
411C22×C11C2×H(5,𝔽2)12yes—
412C22×C11C2×H(5,𝔽2)11yescharacteristic
413C22×C11C2×2−1+412yes—
414C22×C11C2×2−1+411yescharacteristic
415C2×D11—42no—
416C2×D11—42no—
417C2×D11—42no—
418C2×D11—44no—
419C2×D11—44no—
420C4×C11—24no—
421C4×C11—24no—
422C4×C11—22no—
423C4×C11—22no—
424C4×C11—24no—
425C4×C11—42no—
426C4×C11—42no—
427Dic11—42no—
428Dic11—42no—
429Dic11—42no—
430Dic11—44no—
431Dic11—44no—
432C25C22×D1111yescharacteristic
433C22×Q8—24no—
434C22×Q8—44no—
435C22×Q8—111no—
436C22×Q8C22×D1114yes—
437C22×D4—112no—
438C22×D4—114no—
439C22×D4—111no—
440C23×C4—24no—
441C23×C4—44no—
442C23×C4—112no—
443C23×C4C22×D1111yescharacteristic
444C23×C4C22×D1111yescharacteristic
445C23×C4C22×D1112yes—
446C23×C4C22×D1112yes—
447C23×C4C22×D1111yescharacteristic
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1111yescharacteristic
450C23×C4C22×D1111yescharacteristic
451#126—228no—
452#125—228no—
453#123—228no—
454#123—228no—
455#123—444no—
456C22⋊Q8—216no—
457C22⋊Q8—216no—
458C22⋊Q8—224no—
459C22⋊Q8—228no—
460C22⋊Q8—448no—
461C22⋊Q8—444no—
462#121—224no—
463#121—444no—
464#120—444no—
465C4×D4—228no—
466#117—444no—
467C2×C4⋊C4—24no—
468C2×C4⋊C4—24no—
469C2×C4⋊C4—112no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—114no—
472C2×C4⋊C4—112no—
473C2×C4⋊C4—112no—
474C2×C4⋊C4—111no—
475C2×C4⋊C4—112no—
476C2×C4⋊C4—114no—
477C2×C4⋊C4—112no—
478C2×C4⋊C4—112no—
479C2×C4⋊C4—114no—
480C2×C4⋊C4—114no—
481C2×C4⋊C4—114no—
482C2×C4⋊C4C22⋊D1118yescomplemented
483C2×C4⋊C4C22×D1114yes—
484C2×C4⋊C4C22×D1112yes—
485C2×C4⋊C4C22×D1112yes—
486C2×C4⋊C4C22×D1112yes—
487C2×C4⋊C4C22×D1112yes—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—24no—
490C2×C22⋊C4—112no—
491C2×C22⋊C4—112no—
492C2×C22⋊C4—112no—
493C2×C22⋊C4—114no—
494C2×C22⋊C4—112no—
495C2×C22⋊C4—112no—
496C2×C22⋊C4—114no—
497C2×C22⋊C4—112no—
498C2×C22⋊C4—112no—
499C2×C22⋊C4—114no—
500C2×C22⋊C4—114no—
501C2×C22⋊C4—114no—
502C2×C22⋊C4—114no—
503C2×C22⋊C4C22×D1114yes—
504C2×C22⋊C4C22×D1114yes—
505C2×C42—112no—
506C2×C42—114no—
507#95—114no—
508#95—112no—
509#95—112no—
510#95—114no—
511#95—114no—
512#95—114no—
513#95—114no—
514#95—114no—
515#95—114no—
516C2×C11—24no—
517C2×C11—44no—
518C2×C11C2×#53711yescharacteristic
519C2×C11#348411yescharacteristic
520C2×C11#348611yescharacteristic
521C2×C11#353612yes—
522C2×C11#353812yes—
523D11—82no—
524C24—24no—
525C24—22no—
526C24—22no—
527C24—22no—
528C24—42no—
529C24—112no—
530C24C23×D1112yes—
531C24C23×D1111yescharacteristic
532C2×Q8—28no—
533C2×Q8—28no—
534C2×Q8—44no—
535C2×Q8—416no—
536C2×Q8—222no—
537C2×Q8—442no—
538C2×D4—224no—
539C2×D4—224no—
540C2×D4—224no—
541C2×D4—228no—
542C2×D4—222no—
543C2×D4—442no—
544C2×D4—444no—
545C2×D4—444no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—24no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—24no—
557C22×C4—24no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—42no—
562C22×C4—42no—
563C22×C4—416no—
564C22×C4—112no—
565C22×C4—114no—
566C22×C4—114no—
567C22×C4—112no—
568C22×C4—112no—
569C22×C4—224no—
570C22×C4—444no—
571C22×C4C2×C22⋊D1114yes—
572C22×C4C2×C22⋊D1114yes—
573C22×C4C2×C22⋊D1114yes—
574C22×C4C23×D1112yes—
575C22×C4C23×D1112yes—
576C22×C4C23×D1112yes—
577C22×C4C23×D1112yes—
578C22×C4C23×D1111yescharacteristic
579C22×C4C23×D1111yescharacteristic
580C22×C4C23×D1112yes—
581C4⋊C4—28no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—228no—
585C4⋊C4—224no—
586C4⋊C4—222no—
587C4⋊C4—224no—
588C4⋊C4—224no—
589C4⋊C4—222no—
590C4⋊C4—224no—
591C4⋊C4—444no—
592C4⋊C4—442no—
593C4⋊C4—444no—
594C4⋊C4—442no—
595C4⋊C4—444no—
596C4⋊C4—444no—
597C4⋊C4C2×C22⋊D1118yes—
598C4⋊C4C2×C22⋊D1118yes—
599C22⋊C4—28no—
600C22⋊C4—28no—
601C22⋊C4—228no—
602C22⋊C4—224no—
603C22⋊C4—224no—
604C22⋊C4—224no—
605C22⋊C4—228no—
606C22⋊C4—224no—
607C22⋊C4—224no—
608C22⋊C4—224no—
609C22⋊C4—224no—
610C22⋊C4—444no—
611C22⋊C4—444no—
612C22⋊C4—444no—
613C22⋊C4—444no—
614C42—224no—
615C42—444no—
616C11#3671911yescharacteristic, complemented, Sylow
617C23—22no—
618C23—22no—
619C23—28no—
620C23—22no—
621C23—22no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—48no—
627C23—48no—
628C23—44no—
629C23—44no—
630C23—224no—
631C23—224no—
632C23—222no—
633C23—222no—
634C23—222no—
635C23#6704014yes—
636C23#6704212yes—
637C23#6704312yes—
638C23C22×C22⋊D1112yes—
639C23C24×D1111yescharacteristic
640Q8—416no—
641Q8—882no—
642D4—448no—
643D4—882no—
644D4—888no—
645C2×C4—28no—
646C2×C4—28no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—48no—
662C2×C4—48no—
663C2×C4—44no—
664C2×C4—44no—
665C2×C4—224no—
666C2×C4—224no—
667C2×C4—224no—
668C2×C4—224no—
669C2×C4—224no—
670C2×C4—224no—
671C2×C4—224no—
672C2×C4—224no—
673C2×C4—222no—
674C2×C4—222no—
675C2×C4—222no—
676C2×C4—222no—
677C2×C4—222no—
678C2×C4—884no—
679C2×C4#6703714yes—
680C2×C4C22×C22⋊D1114yes—
681C2×C4C22×C22⋊D1114yes—
682C2×C4C22×C22⋊D1112yes—
683C2×C4C22×C22⋊D1112yes—
684C22—22no—
685C22—22no—
686C22—24no—
687C22—24no—
688C22—24no—
689C22—24no—
690C22—24no—
691C22—416no—
692C22—42no—
693C22—42no—
694C22—42no—
695C22—42no—
696C22—442no—
697C22—442no—
698C22—442no—
699C22—444no—
700C22—444no—
701C22#1062336414yes—
702C22C2×#6703712yes—
703C22C2×#6704012yes—
704C22C2×#6704211yescharacteristic
705C22C2×#6704311yescharacteristic
706C22C23×C22⋊D1111yescharacteristic
707C4—24no—
708C4—24no—
709C4—22no—
710C4—22no—
711C4—24no—
712C4—42no—
713C4—42no—
714C4—442no—
715C4—442no—
716C4—442no—
717C4—444no—
718C4—444no—
719C2—24no—
720C2—44no—
721C2—882no—
722C2C2×#1062336411yescharacteristic
723C2#1308225111yescharacteristic
724C2#1308226711yescharacteristic
725C2#1308284512yes—
726C2#1308286112yes—
subgroupG/H
center, FrattiniC23C24×D11
commutator, socle, cosocleC23×C11C25
FittingC22×C11×C22⋊Q8C2
prime radical#13076898C2
hypercenterC22×C22⋊Q8D11
hypocenterC11#36719
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#10623046C2semidirect
2. #13076903C2semidirect
4. #13075270C2semidirect
5. #13075240C2semidirect
6. #13074986C2semidirect
7. #13074971C2semidirect
8. #13074429C2semidirect
9. #13074358C2semidirect
10. #13073506C2semidirect
11. #13072023C2semidirect
12. #13072001C2semidirect
13. #13071975C2semidirect
14. #13071234C2semidirect
15. C22×C11×C22⋊Q8C2semidirect
27. C2×#66999C22semidirect
37. C2×#66951C22semidirect
38. C2×#66949C22semidirect
39. C2×#66947C22semidirect
40. C2×#66942C22semidirect
42. #10622844C22semidirect
43. #10622843C22semidirect
44. #10622842C22semidirect
57. #10622607C22semidirect
58. #10622607C22semidirect
59. #10622604C22semidirect
60. #10622603C22semidirect
61. #10622599C22semidirect
62. #10622598C22semidirect
63. #10622598C22semidirect
64. #10622597C22semidirect
65. #10622597C22semidirect
66. #10622596C22semidirect
67. #10622592C22semidirect
68. #10622585C22semidirect
100. C2×C11×C4⋊C4D4semidirect
255. C22×C22⋊Q8D11semidirect
482. C2×C4⋊C4C22⋊D11semidirect
616. C11#36719semidirect

Maximal subgroups

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

subgroupindex
C2×#106230462
#130769032
#130768982
#130752702
#130752402
#130749862
#130749712
#130744292
#130743582
#130735062
#130720232
#130720012
#130719752
#130712342
C22×C11×C22⋊Q82
#3671911