Finite Group Databasebeta

← C2×#20257365 #27124395

Subgroups — C2×#20257365 #27124395

Order 12032.

7142 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257365C2132yesmaximal, direct product factor
2C2×#15689833C211yesmaximal, characteristic, complemented
3C2×#15689833C211yesmaximal, characteristic, complemented
4C2×#15689826C212yesmaximal, complemented
5C2×#15689814C212yesmaximal, complemented
6C2×#15689814C212yesmaximal, complemented
7C2×#15689805C214yesmaximal, complemented
8C2×#15689776C211yesmaximal, characteristic, complemented
9C2×#15689776C212yesmaximal, complemented
10C2×#15689734C212yesmaximal, complemented
11C2×#15689721C214yesmaximal, complemented
12C2×#15689678C211yesmaximal, characteristic, complemented
13C2×#15689660C212yesmaximal, complemented
14C2×#15689660C211yesmaximal, characteristic, complemented
15C2×#125×D47C212yesmaximal, complemented
16C2×#15689605C212yesmaximal, complemented
17C2×C4×#10625354C211yesmaximal, characteristic, complemented
18C2×C47×#557C211yesmaximal, characteristic, complemented
19C22×#10625354C2211yescharacteristic
20C22×#10625354C2212yes—
21#15689833C22116yescomplemented
22#15689833C22116yescomplemented
23#15689826C22132yescomplemented
24#15689814C22132yescomplemented
25#15689814C22132yescomplemented
26#15689805C22164yescomplemented
27#15689776C22132yescomplemented
28#15689776C22116yescomplemented
29#15689734C22132yescomplemented
30#15689721C22164yescomplemented
31#15689678C22116yescomplemented
32C2×#13094024C2211yescharacteristic
33#15689660C22132yescomplemented
34#15689660C22116yescomplemented
35C2×#13094019C2212yes—
36C2×#13094019C2214yes—
37C2×#13094019C2214yes—
38C2×#13094018C2214yes—
39C2×#13094016C2212yes—
40C2×#13094016C2212yes—
41C2×#13094015C2211yescharacteristic
42C2×#13094015C2212yes—
43C2×#13094014C2214yes—
44C2×#13094014C2214yes—
45C2×#13094014C2214yes—
46#125×D47C22132yescomplemented
47C2×#13094013C2211yescharacteristic
48C2×#13094009C2214yes—
49C2×#13094009C2214yes—
50C2×#13094009C2214yes—
51C2×#13094009C2214yes—
52C2×#13094009C2212yes—
53C2×#13094004C2212yes—
54C2×#13094002C2214yes—
55C2×#13094002C2214yes—
56C2×#13094000C2212yes—
57C2×#13094000C2212yes—
58C2×#13094000C2212yes—
59C2×#13094000C2211yescharacteristic
60C2×#13094000C2212yes—
61C2×#13093999C2212yes—
62C2×#13093999C2214yes—
63C2×#13093999C2211yescharacteristic
64#15689605C22132yescomplemented
65C4×#10625354C22116yescomplemented
66C2×Q8×Dic47C2211yescharacteristic
67C2×Q8×Dic47C2212yes—
68C2×#13093989C2212yes—
69C2×C4×D188C2211yescharacteristic
70C2×C4×D188C2212yes—
71C2×C4×D188C2212yes—
72C2×C4×D188C2214yes—
73C2×C4×D188C2212yes—
74C2×C4×D188C2211yescharacteristic
75C2×C4×D188C2212yes—
76C2×#13093986C2211yescharacteristic
77C2×#13093986C2212yes—
78C2×#13093986C2214yes—
79C2×#13093982C2212yes—
80C2×#13093982C2211yescharacteristic
81C2×#13093982C2212yes—
82C2×#13093981C2214yes—
83C2×#13093981C2212yes—
84C2×#13093981C2214yes—
85C2×C4⋊C4×D47C2214yes—
86C2×C4⋊C4×D47C2212yes—
87C2×C4⋊C4×D47C2214yes—
88C2×C4⋊C4×D47C2212yes—
89C2×C4⋊C4×D47C2212yes—
90C2×C42×D47C2212yes—
91C2×C42×D47C2211yescharacteristic
92C47×#557C22116yescomplemented
93C2×C4⋊Q8×C47C2211yescharacteristic
94C2×C4⋊Q8×C47C2212yes—
95C2×#125×C47C2214yes—
96C2×#125×C47C2212yes—
97C2×C4×Q8×C47C2211yescharacteristic
98C2×C4×Q8×C47C2212yes—
99C2×C4×Q8×C47C2212yes—
100C2×C4×Q8×C47C2211yescharacteristic
101C2×#10625354—28no—
102C2×#10625354—216no—
103C2×#10625354C2318yes—
104C2×#10625354C23116yes—
105C22×Dic94C2312yes—
106C22×D188C2312yes—
107C22×D188C2314yes—
108C22×D188C2311yescharacteristic
109C22×D188C2312yes—
110C22×D188C2311yescharacteristic
111C22×C4×D47C2312yes—
112C22×C4×D47C2312yes—
113C22×C4×D47C2311yescharacteristic
114C22×C4×D47C2311yescharacteristic
115C22×C4×D47C2314yes—
116C22×C4×D47C2312yes—
117C22×C4×D47C2312yes—
118C22×C4×D47C2311yescharacteristic
119C22×C4×D47C2314yes—
120C22×C4×D47C2314yes—
121#13094024C2318yes—
122#13094019C23132yes—
123#13094019C23132yes—
124#13094019C23116yes—
125#13094018C23132yes—
126#13094016C23116yes—
127#13094016C23116yes—
128#13094015C2318yes—
129#13094015C23116yes—
130#13094014C23132yes—
131#13094014C23132yes—
132#13094014C23132yes—
133#13094013C2318yes—
134#13094009C23132yes—
135#13094009C23132yes—
136#13094009C23132yes—
137#13094009C23132yes—
138#13094009C23116yes—
139#13094004C23116yes—
140#13094002C23132yes—
141#13094002C23132yes—
142#13094000C23116yes—
143#13094000C23116yes—
144#13094000C23116yes—
145#13094000C2318yes—
146#13094000C23116yes—
147#13093999C23116yes—
148#13093999C23132yes—
149#13093999C2318yes—
150Q8×Dic47C2318yes—
151Q8×Dic47C23116yes—
152#13093989C23116yes—
153C4×D188C23116yes—
154C4×D188C2318yes—
155C4×D188C23116yes—
156C4×D188C2318yes—
157C4×D188C23116yes—
158C4×D188C23116yes—
159C4×D188C23132yes—
160#13093986C23132yes—
161#13093986C2318yes—
162#13093986C23116yes—
163#13093982C23116yes—
164#13093982C2318yes—
165#13093982C23116yes—
166#13093981C23116yes—
167#13093981C23132yes—
168#13093981C23132yes—
169C2×C4⋊Dic47C2311yescharacteristic
170C2×C4⋊Dic47C2312yes—
171C2×C4⋊Dic47C2312yes—
172C2×C4⋊Dic47C2312yes—
173C2×C4⋊Dic47C2314yes—
174C2×C4⋊Dic47C2311yescharacteristic
175C2×C4⋊Dic47C2312yes—
176C2×Dic47⋊C4C2314yes—
177C2×Dic47⋊C4C2312yes—
178C2×Dic47⋊C4C2314yes—
179C2×Dic47⋊C4C2314yes—
180C2×Dic47⋊C4C2314yes—
181C2×Dic47⋊C4C2314yes—
182C2×Dic47⋊C4C2312yes—
183C2×Dic47⋊C4C2314yes—
184C4⋊C4×D47C23132yes—
185C4⋊C4×D47C23116yes—
186C4⋊C4×D47C23116yes—
187C4⋊C4×D47C23116yes—
188C4⋊C4×D47C23132yes—
189C2×(C2×D47)⋊C4C2312yes—
190C2×(C2×D47)⋊C4C2312yes—
191C2×(C2×D47)⋊C4C2312yes—
192C2×(C2×D47)⋊C4C2314yes—
193C2×(C2×D47)⋊C4C2312yes—
194C2×(C2×D47)⋊C4C2314yes—
195C2×(C2×D47)⋊C4C2312yes—
196C2×(C2×D47)⋊C4C2312yes—
197C2×(C2×D47)⋊C4C2314yes—
198C2×(C2×D47)⋊C4C2314yes—
199C2×(C2×D47)⋊C4C2312yes—
200C2×(C2×D47)⋊C4C2312yes—
201C2×C4×Dic47C2311yescharacteristic
202C2×C4×Dic47C2312yes—
203C2×C4×Dic47C2311yescharacteristic
204C2×C4×Dic47C2311yescharacteristic
205C2×C4×Dic47C2312yes—
206C2×C4×Dic47C2314yes—
207C42×D47C23116yes—
208C42×D47C2318yes—
209C22×Q8×C47C2311yescharacteristic
210C22×Q8×C47C2311yescharacteristic
211C22×Q8×C47C2312yes—
212C4⋊Q8×C47C23116yes—
213C4⋊Q8×C47C2318yes—
214#125×C47C23132yes—
215#125×C47C23116yes—
216C4×Q8×C47C23116yes—
217C4×Q8×C47C23116yes—
218C4×Q8×C47C2318yes—
219C4×Q8×C47C2318yes—
220C2×C4⋊C4×C47C2311yescharacteristic
221C2×C4⋊C4×C47C2311yescharacteristic
222C2×C4⋊C4×C47C2314yes—
223C2×C4⋊C4×C47C2312yes—
224C2×C4⋊C4×C47C2312yes—
225C2×C4⋊C4×C47C2312yes—
226C2×C4⋊C4×C47C2314yes—
227C2×C4⋊C4×C47C2314yes—
228C2×C4⋊C4×C47C2312yes—
229C2×C42×C47C2312yes—
230C2×C42×C47C2314yes—
231C2×C42×C47C2311yescharacteristic
232C2×C42×C47C2312yes—
233C23×D47C2411yescharacteristic
234C23×D47C2412yes—
235C23×D47C2412yes—
236C2×Q8×C47—24no—
237C2×Q8×C47—28no—
238C2×Q8×C47—24no—
239C2×Q8×C47C2414yes—
240C2×Q8×C47C2418yes—
241C2×Q8×C47C2414yes—
242C22×C4×C47C2412yes—
243C22×C4×C47C2412yes—
244C22×C4×C47C2411yescharacteristic
245C22×C4×C47C2412yes—
246C22×C4×C47C2412yes—
247C22×C4×C47C2414yes—
248C22×C4×C47C2411yescharacteristic
249C22×C4×C47C2411yescharacteristic
250C22×Dic47C2411yescharacteristic
251C22×Dic47C2411yescharacteristic
252C22×Dic47C2411yescharacteristic
253C22×Dic47C2412yes—
254C22×Dic47C2414yes—
255C22×Dic47C2412yes—
256#10625354—232no—
257#10625354—264no—
258C2×D188—28no—
259C2×D188—216no—
260C2×D188—24no—
261C2×D188—44no—
262C2×D188#4118yes—
263C2×D188C24116yes—
264C2×D188C2418yes—
265C2×D188C2414yes—
266C2×D188C2418yes—
267C2×D188C2414yes—
268C2×C4×D47—28no—
269C2×C4×D47—216no—
270C2×C4×D47—24no—
271C2×C4×D47—28no—
272C2×C4×D47—28no—
273C2×C4×D47—24no—
274C2×C4×D47—48no—
275C2×C4×D47—48no—
276C2×C4×D47—42no—
277C2×C4×D47—44no—
278C2×C4×D47C2418yes—
279C2×C4×D47C2418yes—
280C2×C4×D47C2414yes—
281C2×C4×D47C2414yes—
282C2×C4×D47C24116yes—
283C2×C4×D47C2418yes—
284C2×C4×D47C2418yes—
285C2×C4×D47C2414yes—
286C2×C4×D47C24116yes—
287C2×C4×D47C24116yes—
288C2×Dic94—44no—
289C2×Dic94C2418yes—
290C4⋊C4×C47C2414yes—
291C4⋊C4×C47C2414yes—
292C4⋊C4×C47C24116yes—
293C4⋊C4×C47C2418yes—
294C4⋊C4×C47C2418yes—
295C4⋊C4×C47C2418yes—
296C4⋊C4×C47C24116yes—
297C4⋊C4×C47C24116yes—
298C4⋊C4×C47C2418yes—
299C42×C47C2418yes—
300C42×C47C24116yes—
301C42×C47C2414yes—
302C42×C47C2418yes—
303(C2×D47)⋊C4C2418yes—
304(C2×D47)⋊C4C2418yes—
305(C2×D47)⋊C4C2418yes—
306(C2×D47)⋊C4C24116yes—
307(C2×D47)⋊C4C2418yes—
308(C2×D47)⋊C4C24116yes—
309(C2×D47)⋊C4C2418yes—
310(C2×D47)⋊C4C2418yes—
311(C2×D47)⋊C4C24116yes—
312(C2×D47)⋊C4C24116yes—
313(C2×D47)⋊C4C2418yes—
314(C2×D47)⋊C4C2418yes—
315C4⋊Dic47C2414yes—
316C4⋊Dic47C2418yes—
317C4⋊Dic47C2418yes—
318C4⋊Dic47C2418yes—
319C4⋊Dic47C24116yes—
320C4⋊Dic47C2414yes—
321C4⋊Dic47C2418yes—
322Dic47⋊C4C24116yes—
323Dic47⋊C4C2418yes—
324Dic47⋊C4C24116yes—
325Dic47⋊C4C24116yes—
326Dic47⋊C4C24116yes—
327Dic47⋊C4C24116yes—
328Dic47⋊C4C2418yes—
329Dic47⋊C4C24116yes—
330C4×Dic47C2414yes—
331C4×Dic47C2418yes—
332C4×Dic47C2414yes—
333C4×Dic47C2414yes—
334C4×Dic47C2418yes—
335C4×Dic47C24116yes—
336C23×C47C2511yescharacteristic
337C22×D47—24no—
338C22×D47—24no—
339C22×D47—22no—
340C22×D47—24no—
341C22×D47—22no—
342C22×D47—24no—
343C22×D47—24no—
344C22×D47—22no—
345C22×D47C2×#4118yes—
346C22×D47C2512yes—
347C22×D47C2514yes—
348C22×D47C2514yes—
349Q8×C47—28no—
350Q8×C47—216no—
351Q8×C47—28no—
352C2×C4×C47—24no—
353C2×C4×C47—28no—
354C2×C4×C47—24no—
355C2×C4×C47—22no—
356C2×C4×C47—24no—
357C2×C4×C47—24no—
358C2×C4×C47C2×#4114yes—
359C2×C4×C472−1+414yes—
360C2×C4×C47C2514yes—
361C2×C4×C47C2518yes—
362C2×C4×C47C2514yes—
363C2×C4×C47C2512yes—
364C2×C4×C47C2514yes—
365C2×C4×C47C2514yes—
366C2×C4×C47C2512yes—
367C2×C4×C47C2512yes—
368C2×Dic47—22no—
369C2×Dic47—24no—
370C2×Dic47—22no—
371C2×Dic47—24no—
372C2×Dic47—28no—
373C2×Dic47—22no—
374C2×Dic47C2512yes—
375C2×Dic47C2512yes—
376C2×Dic47C2512yes—
377C2×Dic47C2514yes—
378C2×Dic47C2518yes—
379C2×Dic47C2514yes—
380D188—232no—
381D188—216no—
382D188—28no—
383D188—48no—
384D188C2×#41116yes—
385C4×D47—216no—
386C4×D47—232no—
387C4×D47—28no—
388C4×D47—216no—
389C4×D47—216no—
390C4×D47—28no—
391C4×D47—416no—
392C4×D47—416no—
393C4×D47—44no—
394C4×D47—48no—
395Dic94—48no—
396C2×#3515—471nomaximal, Sylow
397C22×C47C22×#4112yes—
398C22×C47C2×2−1+412yes—
399C22×C47#58512yes—
400C22×C47C2611yescharacteristic
401C2×D47—24no—
402C2×D47—24no—
403C2×D47—216no—
404C2×D47—22no—
405C2×D47—24no—
406C2×D47—22no—
407C2×D47—24no—
408C2×D47—24no—
409C2×D47—22no—
410C2×D47—44no—
411C2×D47—48no—
412C2×D47C22×#4118yes—
413C4×C47—24no—
414C4×C47—28no—
415C4×C47—24no—
416C4×C47—22no—
417C4×C47—24no—
418C4×C47—24no—
419C4×C47C22×#4114yes—
420C4×C47C2×2−1+414yes—
421Dic47—22no—
422Dic47—24no—
423Dic47—22no—
424Dic47—24no—
425Dic47—28no—
426Dic47—22no—
427#3515—4732no—
428C2×#557D4711yescharacteristic, complemented
429C2×#554—471no—
430C2×#554—471no—
431C2×#553—472no—
432C2×#552—474no—
433C2×#552—472no—
434C2×#552—472no—
435C2×#547—471no—
436C2×#547—472no—
437C2×#541—472no—
438C2×#539—474no—
439C2×#533—471no—
440C2×#529—471no—
441C2×#529—472no—
442C22×#125—472no—
443C2×#520—472no—
444C2×C4×#41—471no—
445C2×C47#351514yescomplemented
446C2×C47C23×#4111yescharacteristic
447C2×C47C22×2−1+411yescharacteristic
448C2×C47C2×#58511yescharacteristic
449D47—28no—
450D47—42no—
451D47—44no—
452C22×#41—471no—
453C22×#41—472no—
454#557C2×D47116yescomplemented
455#554—4716no—
456#554—4716no—
457#553—4732no—
458#552—4764no—
459#552—4732no—
460#552—4732no—
461#547—4716no—
462#547—4732no—
463#541—4732no—
464#539—4764no—
465#533—4716no—
466C2×C4⋊Q8—471no—
467C2×C4⋊Q8C2×D4711yescharacteristic
468C2×C4⋊Q8C2×D4712yes—
469#529—4732no—
470#529—4716no—
471C2×#126—474no—
472C2×#126—472no—
473C2×#126—474no—
474C2×#126—474no—
475C2×#125—4732no—
476C2×#125—471no—
477C2×#125—472no—
478C2×#125—474no—
479C2×#125—474no—
480C2×#125—474no—
481C2×#125—472no—
482C2×#125—472no—
483C2×#125C2×D4712yes—
484C2×#125C2×D4714yes—
485C2×#124—471no—
486C2×#123—472no—
487C2×#123—474no—
488C2×#123—474no—
489C2×#123—474no—
490C2×#123—474no—
491C2×C22⋊Q8—471no—
492C2×C22⋊Q8—472no—
493C2×C22⋊Q8—472no—
494C2×C22⋊Q8—472no—
495C2×C22⋊Q8—472no—
496C2×C22⋊Q8—472no—
497C2×C22⋊Q8—474no—
498C2×C22⋊Q8—474no—
499C2×#121—472no—
500C2×#121—471no—
501C2×#121—474no—
502#520—4732no—
503C4×#41—4716no—
504C2×C4×Q8—471no—
505C2×C4×Q8—472no—
506C2×C4×Q8—472no—
507C2×C4×Q8C2×D4711yescharacteristic
508C2×C4×Q8C2×D4712yes—
509C2×C4×Q8C2×D4712yes—
510C2×C4×Q8C2×D4711yescharacteristic
511C2×C4×D4—471no—
512C2×C4×D4—472no—
513C2×C4×D4—474no—
514C2×C4×D4—471no—
515C2×C4×D4—472no—
516C2×C4×D4—474no—
517C2×C4×D4—472no—
518C2×C4×D4—472no—
519C2×C4×D4—471no—
520C2×C4×D4—472no—
521C2×#117—471no—
522C2×#117—472no—
523C2×#117—472no—
524C2×#117—472no—
525C2×#117—474no—
526C2×#117—474no—
527C22×C4⋊C4—474no—
528C22×C4⋊C4—472no—
529C22×C4⋊C4—472no—
530C22×C4⋊C4—474no—
531C22×C4⋊C4—472no—
532C22×C42—472no—
533C22×C42—471no—
534C47C2×#351511yescharacteristic, complemented, Sylow
535C2×#41—478no—
536C2×#41—4716no—
537C2×#41—948no—
538C2×#41—9416no—
539C22×Q8—472no—
540C22×Q8C22×D4711yescharacteristic
541C22×Q8C22×D4712yes—
542C22×Q8C22×D4711yescharacteristic
543C22×D4—471no—
544C22×D4—471no—
545C22×D4—472no—
546C22×D4—474no—
547C22×D4—472no—
548C23×C4—474no—
549C23×C4—472no—
550C23×C4—472no—
551C23×C4—472no—
552C23×C4—471no—
553C23×C4—471no—
554C23×C4—474no—
555C23×C4—472no—
556C23×C4—474no—
557C23×C4—471no—
558C4⋊Q8—478no—
559C4⋊Q8C22×D4718yes—
560C4⋊Q8C22×D47116yes—
561#126—4732no—
562#126—4716no—
563#126—4732no—
564#126—4732no—
565#125—478no—
566#125—4716no—
567#125—4732no—
568#125—4732no—
569#125—4732no—
570#125—4716no—
571#125—4716no—
572#125C22×D47116yes—
573#125C22×D47132yes—
574#124—478no—
575#123—4716no—
576#123—4732no—
577#123—4732no—
578#123—4732no—
579#123—4732no—
580C22⋊Q8—478no—
581C22⋊Q8—4716no—
582C22⋊Q8—4716no—
583C22⋊Q8—4716no—
584C22⋊Q8—4716no—
585C22⋊Q8—4716no—
586C22⋊Q8—4732no—
587C22⋊Q8—4732no—
588#121—4716no—
589#121—478no—
590#121—4732no—
591C4×Q8—478no—
592C4×Q8—4716no—
593C4×Q8—4716no—
594C4×Q8C22×D4718yes—
595C4×Q8C22×D47116yes—
596C4×Q8C22×D47116yes—
597C4×Q8C22×D4718yes—
598C4×D4—478no—
599C4×D4—4716no—
600C4×D4—4732no—
601C4×D4—478no—
602C4×D4—4716no—
603C4×D4—4732no—
604C4×D4—4716no—
605C4×D4—4716no—
606C4×D4—478no—
607C4×D4—4716no—
608#117—478no—
609#117—4716no—
610#117—4716no—
611#117—4716no—
612#117—4732no—
613#117—4732no—
614C2×C4⋊C4—474no—
615C2×C4⋊C4—472no—
616C2×C4⋊C4—471no—
617C2×C4⋊C4—472no—
618C2×C4⋊C4—472no—
619C2×C4⋊C4—474no—
620C2×C4⋊C4—472no—
621C2×C4⋊C4—474no—
622C2×C4⋊C4—474no—
623C2×C4⋊C4—474no—
624C2×C4⋊C4—474no—
625C2×C4⋊C4—472no—
626C2×C4⋊C4—471no—
627C2×C4⋊C4—472no—
628C2×C4⋊C4—474no—
629C2×C4⋊C4—4732no—
630C2×C4⋊C4—4716no—
631C2×C4⋊C4—4732no—
632C2×C4⋊C4—4716no—
633C2×C4⋊C4—4716no—
634C2×C4⋊C4C22×D4711yescharacteristic
635C2×C4⋊C4C22×D4711yescharacteristic
636C2×C4⋊C4C22×D4712yes—
637C2×C4⋊C4C22×D4714yes—
638C2×C4⋊C4C22×D4714yes—
639C2×C4⋊C4C22×D4712yes—
640C2×C4⋊C4C22×D4712yes—
641C2×C4⋊C4C22×D4712yes—
642C2×C4⋊C4C22×D4714yes—
643C2×C22⋊C4—472no—
644C2×C22⋊C4—472no—
645C2×C22⋊C4—472no—
646C2×C22⋊C4—472no—
647C2×C22⋊C4—474no—
648C2×C22⋊C4—472no—
649C2×C22⋊C4—472no—
650C2×C22⋊C4—474no—
651C2×C22⋊C4—474no—
652C2×C22⋊C4—474no—
653C2×C22⋊C4—472no—
654C2×C22⋊C4—472no—
655C2×C42—472no—
656C2×C42—471no—
657C2×C42—474no—
658C2×C42—471no—
659C2×C42—472no—
660C2×C42—471no—
661C2×C42—4716no—
662C2×C42—478no—
663C2×C42C22×D4714yes—
664C2×C42C22×D4712yes—
665C2×C42C22×D4712yes—
666C2×C42C22×D4711yescharacteristic
667C24—472no—
668C24—471no—
669C24—472no—
670#41—9432no—
671#41—9464no—
672C2×Q8—24no—
673C2×Q8—28no—
674C2×Q8—24no—
675C2×Q8—478no—
676C2×Q8—1884no—
677C2×Q8C23×D4714yes—
678C2×Q8C23×D4718yes—
679C2×Q8C23×D4714yes—
680C2×D4—478no—
681C2×D4—474no—
682C2×D4—474no—
683C2×D4—478no—
684C2×D4—4716no—
685C2×D4—478no—
686C2×D4—948no—
687C2×D4—9416no—
688C2×D4—944no—
689C2×D4—1884no—
690C22×C4—471no—
691C22×C4—471no—
692C22×C4—471no—
693C22×C4—472no—
694C22×C4—474no—
695C22×C4—472no—
696C22×C4—478no—
697C22×C4—478no—
698C22×C4—474no—
699C22×C4—474no—
700C22×C4—4716no—
701C22×C4—478no—
702C22×C4—478no—
703C22×C4—474no—
704C22×C4—4716no—
705C22×C4—4716no—
706C22×C4—9416no—
707C22×C4—948no—
708C22×C4—948no—
709C22×C4—944no—
710C22×C4—948no—
711C22×C4—944no—
712C22×C4—1884no—
713C22×C4—1888no—
714C22×C4—1888no—
715C22×C4—1882no—
716C22×C4C23×D4712yes—
717C22×C4C23×D4711yescharacteristic
718C22×C4C23×D4714yes—
719C22×C4C23×D4712yes—
720C22×C4C23×D4712yes—
721C22×C4C23×D4712yes—
722C22×C4C23×D4711yescharacteristic
723C22×C4C23×D4711yescharacteristic
724C4⋊C4—4716no—
725C4⋊C4—478no—
726C4⋊C4—4716no—
727C4⋊C4—4716no—
728C4⋊C4—4716no—
729C4⋊C4—4716no—
730C4⋊C4—478no—
731C4⋊C4—4716no—
732C4⋊C4—474no—
733C4⋊C4—478no—
734C4⋊C4—478no—
735C4⋊C4—478no—
736C4⋊C4—4716no—
737C4⋊C4—474no—
738C4⋊C4—478no—
739C4⋊C4C23×D4714yes—
740C4⋊C4C23×D4714yes—
741C4⋊C4C23×D4718yes—
742C4⋊C4C23×D47116yes—
743C4⋊C4C23×D47116yes—
744C4⋊C4C23×D4718yes—
745C4⋊C4C23×D4718yes—
746C4⋊C4C23×D4718yes—
747C4⋊C4C23×D47116yes—
748C22⋊C4—478no—
749C22⋊C4—478no—
750C22⋊C4—478no—
751C22⋊C4—478no—
752C22⋊C4—4716no—
753C22⋊C4—478no—
754C22⋊C4—478no—
755C22⋊C4—4716no—
756C22⋊C4—4716no—
757C22⋊C4—4716no—
758C22⋊C4—478no—
759C22⋊C4—478no—
760C42—474no—
761C42—478no—
762C42—474no—
763C42—474no—
764C42—478no—
765C42—4716no—
766C42C23×D4718yes—
767C42C23×D4714yes—
768C42C23×D47116yes—
769C42C23×D4718yes—
770C23—478no—
771C23—474no—
772C23—472no—
773C23—474no—
774C23—944no—
775C23—944no—
776C23—942no—
777C23—944no—
778C23—942no—
779C23—944no—
780C23—944no—
781C23—942no—
782C23C24×D4711yescharacteristic
783Q8—28no—
784Q8—216no—
785Q8—28no—
786Q8—1888no—
787D4—4716no—
788D4—9416no—
789D4—9432no—
790D4—948no—
791D4—1888no—
792C2×C4—28no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—24no—
796C2×C4—24no—
797C2×C4—22no—
798C2×C4—472no—
799C2×C4—472no—
800C2×C4—472no—
801C2×C4—474no—
802C2×C4—478no—
803C2×C4—474no—
804C2×C4—9416no—
805C2×C4—9432no—
806C2×C4—942no—
807C2×C4—944no—
808C2×C4—942no—
809C2×C4—944no—
810C2×C4—942no—
811C2×C4—948no—
812C2×C4—948no—
813C2×C4—9416no—
814C2×C4—9416no—
815C2×C4—948no—
816C2×C4—1888no—
817C2×C4—18816no—
818C2×C4—18816no—
819C2×C4—1884no—
820C2×C4#41×D4714yes—
821C2×C4#1309407214yes—
822C2×C4C24×D4714yes—
823C2×C4C24×D4712yes—
824C2×C4C24×D4714yes—
825C2×C4C24×D4718yes—
826C2×C4C24×D4714yes—
827C2×C4C24×D4714yes—
828C2×C4C24×D4712yes—
829C2×C4C24×D4712yes—
830C22—478no—
831C22—9416no—
832C22—944no—
833C22—944no—
834C22—942no—
835C22—944no—
836C22—942no—
837C22—944no—
838C22—944no—
839C22—942no—
840C22—1884no—
841C22—1888no—
842C22C2×#41×D4712yes—
843C22C2×#1309407212yes—
844C22#1568996012yes—
845C22C25×D4711yescharacteristic
846C4—24no—
847C4—28no—
848C4—24no—
849C4—24no—
850C4—24no—
851C4—22no—
852C4—942no—
853C4—944no—
854C4—942no—
855C4—944no—
856C4—942no—
857C4—948no—
858C4C2×#41×D4714yes—
859C4C2×#1309407214yes—
860C2—948no—
861C2—1882no—
862C2—1884no—
863C2#2025736514yesdirect product factor
864C2C22×#41×D4711yescharacteristic
865C2C22×#1309407211yescharacteristic
866C2C2×#1568996011yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#557C2
socleC23×C47C25
hypercenterC2×#557D47
hypocenterC47C2×#3515
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #20257365C2direct (N × H)
2. C2×#15689833C2semidirect
3. C2×#15689833C2semidirect
4. C2×#15689826C2semidirect
5. C2×#15689814C2semidirect
6. C2×#15689814C2semidirect
7. C2×#15689805C2semidirect
8. C2×#15689776C2semidirect
9. C2×#15689776C2semidirect
10. C2×#15689734C2semidirect
11. C2×#15689721C2semidirect
12. C2×#15689678C2semidirect
13. C2×#15689660C2semidirect
14. C2×#15689660C2semidirect
15. C2×#125×D47C2semidirect
16. C2×#15689605C2semidirect
17. C2×C4×#10625354C2semidirect
18. C2×C47×#557C2semidirect
21. #15689833C22semidirect
22. #15689833C22semidirect
23. #15689826C22semidirect
24. #15689814C22semidirect
25. #15689814C22semidirect
26. #15689805C22semidirect
27. #15689776C22semidirect
28. #15689776C22semidirect
29. #15689734C22semidirect
30. #15689721C22semidirect
31. #15689678C22semidirect
33. #15689660C22semidirect
34. #15689660C22semidirect
46. #125×D47C22semidirect
64. #15689605C22semidirect
65. C4×#10625354C22semidirect
92. C47×#557C22semidirect
428. C2×#557D47semidirect
445. C2×C47#3515semidirect
454. #557C2×D47semidirect
534. C47C2×#3515semidirect
863. C2#20257365direct (N × H)

Maximal subgroups

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

subgroupindex
#202573652
C2×#156898332
C2×#156898262
C2×#156898142
C2×#156898052
C2×#156897762
C2×#156897342
C2×#156897212
C2×#156896782
C2×#156896602
C2×#125×D472
C2×#156896052
C2×C4×#106253542
C2×C47×#5572
C2×#351547