Finite Group Databasebeta

← C2×#20257367 #27124386

Subgroups — C2×#20257367 #27124386

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#20257367C2132yesmaximal, direct product factor
2C2×#15689852C211yesmaximal, characteristic, complemented
3C2×#15689834C211yesmaximal, characteristic, complemented
4C2×#15689821C212yesmaximal, complemented
5C2×#15689815C212yesmaximal, complemented
6C2×#15689815C214yesmaximal, complemented
7C2×#15689811C212yesmaximal, complemented
8C2×#15689777C211yesmaximal, characteristic, complemented
9C2×#15689777C212yesmaximal, complemented
10C2×#15689736C212yesmaximal, complemented
11C2×#15689722C214yesmaximal, complemented
12C2×#15689678C211yesmaximal, characteristic, complemented
13C2×#15689660C211yesmaximal, characteristic, complemented
14C2×#15689659C212yesmaximal, complemented
15C22×#13094015C212yesmaximal, complemented
16C2×#15689602C212yesmaximal, complemented
17C2×C4×#10625352C211yesmaximal, characteristic, complemented
18C2×C47×#554C211yesmaximal, characteristic, complemented
19C22×#10625352C2211yescharacteristic
20C22×#10625352C2212yes—
21#15689852C22116yescomplemented
22#15689834C22116yescomplemented
23#15689821C22132yescomplemented
24#15689815C22132yescomplemented
25#15689815C22164yescomplemented
26#15689811C22132yescomplemented
27#15689777C22116yescomplemented
28#15689777C22132yescomplemented
29#15689736C22132yescomplemented
30#15689722C22164yescomplemented
31#15689678C22116yescomplemented
32C2×#13094024C2211yescharacteristic
33C2×#13094024C2212yes—
34#15689660C22116yescomplemented
35#15689659C22132yescomplemented
36C2×#13094019C2214yes—
37C2×#13094019C2212yes—
38C2×#13094019C2214yes—
39C2×#13094019C2214yes—
40C2×#13094015C2211yescharacteristic
41C2×#13094015C2214yes—
42C2×#13094015C2212yes—
43C2×#13094015C2212yes—
44C2×#13094015C2212yes—
45C2×#13094015C2214yes—
46C2×#13094015C2214yes—
47C2×#13094015C2214yes—
48C2×#13094015C22132yescomplemented
49C2×#13094013C2211yescharacteristic
50C2×#13094009C2214yes—
51C2×#13094009C2212yes—
52C2×#13094008C2214yes—
53C2×#13094008C2214yes—
54C2×#13094008C2214yes—
55C2×#13094004C2212yes—
56C2×#13094004C2212yes—
57C2×#13094004C2212yes—
58C2×#13094000C2211yescharacteristic
59C2×#13094000C2214yes—
60C2×#13094000C2212yes—
61C2×#13093999C2211yescharacteristic
62C2×#13093998C2212yes—
63C2×#13093998C2214yes—
64#15689602C22132yescomplemented
65C4×#10625352C22116yescomplemented
66C2×Q8×Dic47C2212yes—
67C2×Q8×Dic47C2212yes—
68C2×C4×Dic94C2211yescharacteristic
69C2×C4×Dic94C2212yes—
70C2×#13093989C2211yescharacteristic
71C2×#13093989C2212yes—
72C2×C4×D188C2212yes—
73C2×C4×D188C2211yescharacteristic
74C2×D4×Dic47C2211yescharacteristic
75C2×#13093986C2212yes—
76C2×C4×C22⋊D47C2212yes—
77C2×C4×C22⋊D47C2214yes—
78C2×(C22⋊D47)⋊C4C2212yes—
79C2×(C22⋊D47)⋊C4C2214yes—
80C2×#13093982C2211yescharacteristic
81C2×#13093982C2214yes—
82C2×#13093982C2212yes—
83C2×#13093981C2212yes—
84C2×#13093980C2212yes—
85C2×#13093980C2214yes—
86C22×C4⋊Dic47C2212yes—
87C22×C4⋊Dic47C2214yes—
88C22×Dic47⋊C4C2214yes—
89C2×C4⋊C4×D47C2212yes—
90C22×C4×Dic47C2212yes—
91C2×C42×D47C2211yescharacteristic
92C47×#554C22116yescomplemented
93C2×C4⋊Q8×C47C2211yescharacteristic
94C2×#125×C47C2212yes—
95C2×C22⋊Q8×C47C2212yes—
96C2×C22⋊Q8×C47C2214yes—
97C2×C4×Q8×C47C2211yescharacteristic
98C2×C4×D4×C47C2211yescharacteristic
99C2×C4×D4×C47C2212yes—
100C22×C4⋊C4×C47C2212yes—
101C2×#10625352—28no—
102C2×#10625352—216no—
103C2×#10625352C2318yes—
104C2×#10625352C23116yes—
105C22×Dic94C2311yescharacteristic
106C22×Dic94C2312yes—
107C22×D188C2311yescharacteristic
108C22×D188C2312yes—
109C22×C22⋊D47C2312yes—
110C22×C22⋊D47C2314yes—
111C23×Dic47C2312yes—
112C23×Dic47C2314yes—
113C23×Dic47C2312yes—
114C22×C4×D47C2311yescharacteristic
115C22×C4×D47C2311yescharacteristic
116C22×C4×D47C2312yes—
117C22×C4×D47C2311yescharacteristic
118C22×C4×D47C2314yes—
119#13094024C23116yes—
120#13094024C2318yes—
121#13094019C23132yes—
122#13094019C23132yes—
123#13094019C23132yes—
124#13094019C23116yes—
125#13094015C23132yes—
126#13094015C23132yes—
127#13094015C23132yes—
128#13094015C23116yes—
129#13094015C23132yes—
130#13094015C23116yes—
131#13094015C2318yes—
132#13094015C23116yes—
133#13094013C2318yes—
134#13094009C23132yes—
135#13094009C23116yes—
136#13094008C23132yes—
137#13094008C23132yes—
138#13094008C23132yes—
139#13094004C23116yes—
140#13094004C23116yes—
141#13094004C23116yes—
142#13094000C2318yes—
143#13094000C23132yes—
144#13094000C23116yes—
145#13093999C2318yes—
146#13093998C23116yes—
147#13093998C23132yes—
148Q8×Dic47C23116yes—
149Q8×Dic47C23116yes—
150C4×Dic94C23116yes—
151C4×Dic94C2318yes—
152#13093989C2318yes—
153#13093989C23116yes—
154C4×D188C23116yes—
155C4×D188C2318yes—
156D4×Dic47C2318yes—
157#13093986C23116yes—
158C4×C22⋊D47C23116yes—
159C4×C22⋊D47C23132yes—
160(C22⋊D47)⋊C4C23116yes—
161(C22⋊D47)⋊C4C23132yes—
162#13093982C2318yes—
163#13093982C23132yes—
164#13093982C23116yes—
165#13093981C23116yes—
166#13093980C23116yes—
167#13093980C23132yes—
168C2×C4⋊Dic47C23116yes—
169C2×C4⋊Dic47C23132yes—
170C2×C4⋊Dic47C2311yescharacteristic
171C2×C4⋊Dic47C2311yescharacteristic
172C2×C4⋊Dic47C2312yes—
173C2×C4⋊Dic47C2312yes—
174C2×C4⋊Dic47C2314yes—
175C2×C4⋊Dic47C2314yes—
176C2×C4⋊Dic47C2314yes—
177C2×C4⋊Dic47C2314yes—
178C2×C4⋊Dic47C2312yes—
179C2×C4⋊Dic47C2314yes—
180C2×Dic47⋊C4C2314yes—
181C2×Dic47⋊C4C2312yes—
182C2×Dic47⋊C4C2314yes—
183C2×Dic47⋊C4C2314yes—
184C2×Dic47⋊C4C23132yes—
185C2×Dic47⋊C4C2312yes—
186C2×Dic47⋊C4C2312yes—
187C2×Dic47⋊C4C2312yes—
188C4⋊C4×D47C23116yes—
189C2×C22⋊Dic47C2312yes—
190C2×(C2×D47)⋊C4C2312yes—
191C2×(C2×D47)⋊C4C2312yes—
192C2×(C2×D47)⋊C4C2312yes—
193C2×(C2×D47)⋊C4C2312yes—
194C2×(C2×D47)⋊C4C2314yes—
195C2×(C2×D47)⋊C4C2314yes—
196C2×(C2×D47)⋊C4C2314yes—
197C2×(C2×D47)⋊C4C2312yes—
198C2×(C2×D47)⋊C4C2312yes—
199C2×C4×Dic47C2311yescharacteristic
200C2×C4×Dic47C2311yescharacteristic
201C2×C4×Dic47C2311yescharacteristic
202C2×C4×Dic47C2312yes—
203C2×C4×Dic47C2312yes—
204C2×C4×Dic47C2312yes—
205C2×C4×Dic47C23116yes—
206C2×C4×Dic47C2314yes—
207C2×C4×Dic47C2314yes—
208C42×D47C2318yes—
209C22×Q8×C47C2311yescharacteristic
210C22×Q8×C47C2312yes—
211C22×D4×C47C2311yescharacteristic
212C23×C4×C47C2312yes—
213C23×C4×C47C2314yes—
214C4⋊Q8×C47C2318yes—
215#125×C47C23116yes—
216C22⋊Q8×C47C23116yes—
217C22⋊Q8×C47C23132yes—
218C4×Q8×C47C2318yes—
219C4×D4×C47C2318yes—
220C4×D4×C47C23116yes—
221C2×C4⋊C4×C47C2311yescharacteristic
222C2×C4⋊C4×C47C2314yes—
223C2×C4⋊C4×C47C2312yes—
224C2×C4⋊C4×C47C23116yes—
225C2×C4⋊C4×C47C2311yescharacteristic
226C2×C4⋊C4×C47C2312yes—
227C2×C4⋊C4×C47C2312yes—
228C2×C4⋊C4×C47C2314yes—
229C2×C22⋊C4×C47C2314yes—
230C2×C22⋊C4×C47C2312yes—
231C2×C42×C47C2312yes—
232C2×C42×C47C2311yescharacteristic
233C24×C47C2412yes—
234C23×D47C2411yescharacteristic
235C23×D47C2412yes—
236C2×Q8×C47—24no—
237C2×Q8×C47—44no—
238C2×Q8×C47C2414yes—
239C2×Q8×C47C2418yes—
240C2×D4×C47#4118yes—
241C2×D4×C47C2414yes—
242C22×C4×C47—28no—
243C22×C4×C47—48no—
244C22×C4×C47C2412yes—
245C22×C4×C47C2411yescharacteristic
246C22×C4×C47C2412yes—
247C22×C4×C47C2412yes—
248C22×C4×C47C2414yes—
249C22×C4×C47C2418yes—
250C22×C4×C47C24116yes—
251C22×C4×C47C2411yescharacteristic
252C22×C4×C47C2411yescharacteristic
253C2×C22⋊D47—28no—
254C2×C22⋊D47—216no—
255C2×C22⋊D47C2418yes—
256C2×C22⋊D47C24116yes—
257C22×Dic47—28no—
258C22×Dic47—216no—
259C22×Dic47—44no—
260C22×Dic47C2411yescharacteristic
261C22×Dic47C2411yescharacteristic
262C22×Dic47C2411yescharacteristic
263C22×Dic47C2412yes—
264C22×Dic47C2412yes—
265C22×Dic47C2414yes—
266C22×Dic47C2418yes—
267C22×Dic47C2412yes—
268C22×Dic47C24116yes—
269C22×Dic47C2418yes—
270#10625352—232no—
271#10625352—264no—
272C2×D188—24no—
273C2×D188—44no—
274C2×D188C2414yes—
275C2×D188C2418yes—
276C2×C4×D47—24no—
277C2×C4×D47—28no—
278C2×C4×D47—24no—
279C2×C4×D47—48no—
280C2×C4×D47—42no—
281C2×C4×D47C2414yes—
282C2×C4×D47C2414yes—
283C2×C4×D47C2418yes—
284C2×C4×D47C2414yes—
285C2×C4×D47C24116yes—
286C2×Dic94—24no—
287C2×Dic94—28no—
288C2×Dic94C2414yes—
289C2×Dic94C2418yes—
290C4⋊C4×C47C2414yes—
291C4⋊C4×C47C24116yes—
292C4⋊C4×C47C2418yes—
293C4⋊C4×C47C2414yes—
294C4⋊C4×C47C2418yes—
295C4⋊C4×C47C2418yes—
296C4⋊C4×C47C24116yes—
297C22⋊C4×C47C24116yes—
298C22⋊C4×C47C2418yes—
299C42×C47C2418yes—
300C42×C47C2414yes—
301C22⋊Dic47C2418yes—
302(C2×D47)⋊C4C2418yes—
303(C2×D47)⋊C4C2418yes—
304(C2×D47)⋊C4C2418yes—
305(C2×D47)⋊C4C2418yes—
306(C2×D47)⋊C4C24116yes—
307(C2×D47)⋊C4C24116yes—
308(C2×D47)⋊C4C24116yes—
309(C2×D47)⋊C4C2418yes—
310(C2×D47)⋊C4C2418yes—
311C4⋊Dic47C2414yes—
312C4⋊Dic47C2414yes—
313C4⋊Dic47C2418yes—
314C4⋊Dic47C2418yes—
315C4⋊Dic47C24116yes—
316C4⋊Dic47C24116yes—
317C4⋊Dic47C24116yes—
318C4⋊Dic47C24116yes—
319C4⋊Dic47C2418yes—
320C4⋊Dic47C24116yes—
321Dic47⋊C4C24116yes—
322Dic47⋊C4C2418yes—
323Dic47⋊C4C24116yes—
324Dic47⋊C4C24116yes—
325Dic47⋊C4C2418yes—
326Dic47⋊C4C2418yes—
327Dic47⋊C4C2418yes—
328C4×Dic47C2414yes—
329C4×Dic47C2414yes—
330C4×Dic47C2414yes—
331C4×Dic47C2418yes—
332C4×Dic47C2418yes—
333C4×Dic47C2418yes—
334C4×Dic47C24116yes—
335C4×Dic47C24116yes—
336C23×C47—24no—
337C23×C47—24no—
338C23×C47C2×#4118yes—
339C23×C47C2514yes—
340C23×C47C2511yescharacteristic
341C22×D47—22no—
342C22×D47—24no—
343C22×D47—22no—
344C22×D47—24no—
345C22×D47—24no—
346C22×D47—22no—
347C22×D47C2512yes—
348C22×D47C2514yes—
349Q8×C47—28no—
350Q8×C47—48no—
351D4×C47C2×#41116yes—
352C2×C4×C47—24no—
353C2×C4×C47—24no—
354C2×C4×C47—28no—
355C2×C4×C47—22no—
356C2×C4×C47—24no—
357C2×C4×C47—216no—
358C2×C4×C47—416no—
359C2×C4×C47C2×#4114yes—
360C2×C4×C472−1+414yes—
361C2×C4×C47C2514yes—
362C2×C4×C47C2514yes—
363C2×C4×C47C2512yes—
364C2×C4×C47C2518yes—
365C2×C4×C47C2514yes—
366C2×C4×C47C2512yes—
367C2×C4×C47C2512yes—
368C22⋊D47—216no—
369C22⋊D47—232no—
370C2×Dic47—24no—
371C2×Dic47—28no—
372C2×Dic47—22no—
373C2×Dic47—24no—
374C2×Dic47—216no—
375C2×Dic47—232no—
376C2×Dic47—22no—
377C2×Dic47—24no—
378C2×Dic47—22no—
379C2×Dic47—48no—
380C2×Dic47C2512yes—
381C2×Dic47C2512yes—
382C2×Dic47C2514yes—
383C2×Dic47C2512yes—
384C2×Dic47C2514yes—
385C2×Dic47C2518yes—
386C2×Dic47C2514yes—
387D188—28no—
388D188—48no—
389C4×D47—28no—
390C4×D47—216no—
391C4×D47—28no—
392C4×D47—416no—
393C4×D47—44no—
394Dic94—28no—
395Dic94—216no—
396C2×#3515—471nomaximal, Sylow
397C22×C47—24no—
398C22×C47—24no—
399C22×C47—216no—
400C22×C47C22×#4118yes—
401C22×C47C22×#4112yes—
402C22×C47C2×2−1+412yes—
403C22×C47#58512yes—
404C22×C47C2611yescharacteristic
405C2×D47—22no—
406C2×D47—24no—
407C2×D47—22no—
408C2×D47—24no—
409C2×D47—24no—
410C2×D47—22no—
411C2×D47—44no—
412C2×D47—48no—
413C4×C47—24no—
414C4×C47—24no—
415C4×C47—28no—
416C4×C47—22no—
417C4×C47—24no—
418C4×C47C22×#4114yes—
419C4×C47C2×2−1+414yes—
420Dic47—24no—
421Dic47—28no—
422Dic47—22no—
423Dic47—24no—
424Dic47—22no—
425Dic47—24no—
426Dic47—22no—
427#3515—4732no—
428C2×#557—471no—
429C2×#554—471no—
430C2×#554D4711yescharacteristic, complemented
431C2×#553—472no—
432C2×#552—472no—
433C2×#552—474no—
434C2×#552—472no—
435C2×#547—472no—
436C2×#547—471no—
437C2×#541—472no—
438C2×#539—474no—
439C2×#533—471no—
440C2×#529—472no—
441C2×#529—471no—
442C22×#125—472no—
443C2×#520—472no—
444C2×C4×#41—471no—
445C2×C47—28no—
446C2×C47#351514yescomplemented
447C2×C47C23×#4111yescharacteristic
448C2×C47C22×2−1+411yescharacteristic
449C2×C47C2×#58511yescharacteristic
450D47—42no—
451D47—44no—
452C22×#41—471no—
453C22×#41—472no—
454#557—4716no—
455#554—4716no—
456#554C2×D47116yescomplemented
457#553—4732no—
458#552—4732no—
459#552—4764no—
460#552—4732no—
461#547—4732no—
462#547—4716no—
463#541—4732no—
464#539—4764no—
465#533—4716no—
466C2×C4⋊Q8—471no—
467C2×C4⋊Q8—472no—
468C2×C4⋊Q8C2×D4711yescharacteristic
469#529—4732no—
470#529—4716no—
471C2×#126—474no—
472C2×#126—472no—
473C2×#126—474no—
474C2×#126—474no—
475C2×#125—471no—
476C2×#125—472no—
477C2×#125—474no—
478C2×#125—474no—
479C2×#125—472no—
480C2×#125—472no—
481C2×#125—4732no—
482C2×#125—474no—
483C2×#125—474no—
484C2×#125C2×D4712yes—
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—474no—
494C2×C22⋊Q8—472no—
495C2×C22⋊Q8—472no—
496C2×C22⋊Q8—472no—
497C2×C22⋊Q8C2×D4712yes—
498C2×C22⋊Q8C2×D4714yes—
499C2×#121—472no—
500C2×#121—474no—
501C2×#121—471no—
502#520—4732no—
503C4×#41—4716no—
504C2×C4×Q8—472no—
505C2×C4×Q8—472no—
506C2×C4×Q8—471no—
507C2×C4×Q8—472no—
508C2×C4×Q8—471no—
509C2×C4×Q8—472no—
510C2×C4×Q8C2×D4711yescharacteristic
511C2×C4×D4—471no—
512C2×C4×D4—472no—
513C2×C4×D4—474no—
514C2×C4×D4—472no—
515C2×C4×D4—472no—
516C2×C4×D4—474no—
517C2×C4×D4—472no—
518C2×C4×D4—471no—
519C2×C4×D4C2×D4711yescharacteristic
520C2×C4×D4C2×D4712yes—
521C2×#117—471no—
522C2×#117—474no—
523C2×#117—472no—
524C2×#117—472no—
525C2×#117—474no—
526C2×#117—472no—
527C22×C4⋊C4—474no—
528C22×C4⋊C4—472no—
529C22×C4⋊C4—474no—
530C22×C4⋊C4—472no—
531C22×C4⋊C4C2×D4712yes—
532C22×C42—472no—
533C22×C42—471no—
534C47C2×#351511yescharacteristic, complemented, Sylow
535C2×#41—478no—
536C2×#41—4716no—
537C2×#41—948no—
538C2×#41—9416no—
539C22×Q8—471no—
540C22×Q8—472no—
541C22×Q8C22×D4711yescharacteristic
542C22×Q8C22×D4712yes—
543C22×D4—472no—
544C22×D4—474no—
545C22×D4—471no—
546C22×D4—472no—
547C22×D4C22×D4711yescharacteristic
548C23×C4—474no—
549C23×C4—472no—
550C23×C4—472no—
551C23×C4—472no—
552C23×C4—471no—
553C23×C4—471no—
554C23×C4—474no—
555C23×C4—471no—
556C23×C4C22×D4712yes—
557C23×C4C22×D4714yes—
558C4⋊Q8—478no—
559C4⋊Q8—4716no—
560C4⋊Q8C22×D4718yes—
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—4716no—
570#125—4716no—
571#125—4732no—
572#125—4732no—
573#125C22×D47116yes—
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—4732no—
583C22⋊Q8—4716no—
584C22⋊Q8—4716no—
585C22⋊Q8—4716no—
586C22⋊Q8C22×D47116yes—
587C22⋊Q8C22×D47132yes—
588#121—4716no—
589#121—4732no—
590#121—478no—
591C4×Q8—4716no—
592C4×Q8—4716no—
593C4×Q8—478no—
594C4×Q8—4716no—
595C4×Q8—478no—
596C4×Q8—4716no—
597C4×Q8C22×D4718yes—
598C4×D4—478no—
599C4×D4—4716no—
600C4×D4—4732no—
601C4×D4—4716no—
602C4×D4—4716no—
603C4×D4—4732no—
604C4×D4—4716no—
605C4×D4—478no—
606C4×D4C22×D4718yes—
607C4×D4C22×D47116yes—
608#117—478no—
609#117—4732no—
610#117—4716no—
611#117—4716no—
612#117—4732no—
613#117—4716no—
614C2×C4⋊C4—471no—
615C2×C4⋊C4—474no—
616C2×C4⋊C4—472no—
617C2×C4⋊C4—471no—
618C2×C4⋊C4—472no—
619C2×C4⋊C4—472no—
620C2×C4⋊C4—474no—
621C2×C4⋊C4—474no—
622C2×C4⋊C4—474no—
623C2×C4⋊C4—4732no—
624C2×C4⋊C4—474no—
625C2×C4⋊C4—474no—
626C2×C4⋊C4—474no—
627C2×C4⋊C4—4716no—
628C2×C4⋊C4—4732no—
629C2×C4⋊C4—472no—
630C2×C4⋊C4—472no—
631C2×C4⋊C4—472no—
632C2×C4⋊C4—472no—
633C2×C4⋊C4—474no—
634C2×C4⋊C4—4716no—
635C2×C4⋊C4C22×D4712yes—
636C2×C4⋊C4C22×D4711yescharacteristic
637C2×C4⋊C4C22×D4712yes—
638C2×C4⋊C4C22×D4714yes—
639C2×C4⋊C4C22×D47116yes—
640C2×C4⋊C4C22×D4711yescharacteristic
641C2×C4⋊C4C22×D4714yes—
642C2×C4⋊C4C22×D4712yes—
643C2×C22⋊C4—472no—
644C2×C22⋊C4—472no—
645C2×C22⋊C4—472no—
646C2×C22⋊C4—472no—
647C2×C22⋊C4—472no—
648C2×C22⋊C4—474no—
649C2×C22⋊C4—474no—
650C2×C22⋊C4—474no—
651C2×C22⋊C4—472no—
652C2×C22⋊C4—472no—
653C2×C22⋊C4C22×D4714yes—
654C2×C22⋊C4C22×D4712yes—
655C2×C42—472no—
656C2×C42—471no—
657C2×C42—474no—
658C2×C42—474no—
659C2×C42—471no—
660C2×C42—472no—
661C2×C42—472no—
662C2×C42—4716no—
663C2×C42—471no—
664C2×C42—478no—
665C2×C42C22×D4712yes—
666C2×C42C22×D4711yescharacteristic
667C24—471no—
668C24—472no—
669C24C23×D4712yes—
670#41—9432no—
671#41—9464no—
672C2×Q8—24no—
673C2×Q8—44no—
674C2×Q8—474no—
675C2×Q8—478no—
676C2×Q8—944no—
677C2×Q8—948no—
678C2×Q8C23×D4714yes—
679C2×Q8C23×D4718yes—
680C2×D4—478no—
681C2×D4—4716no—
682C2×D4—474no—
683C2×D4—478no—
684C2×D4—948no—
685C2×D4—9416no—
686C2×D4—944no—
687C2×D4—1884no—
688C2×D4#1062535418yes—
689C2×D4C23×D4714yes—
690C22×C4—28no—
691C22×C4—48no—
692C22×C4—478no—
693C22×C4—4716no—
694C22×C4—471no—
695C22×C4—471no—
696C22×C4—471no—
697C22×C4—472no—
698C22×C4—474no—
699C22×C4—472no—
700C22×C4—472no—
701C22×C4—478no—
702C22×C4—474no—
703C22×C4—474no—
704C22×C4—478no—
705C22×C4—474no—
706C22×C4—4716no—
707C22×C4—9416no—
708C22×C4—948no—
709C22×C4—948no—
710C22×C4—944no—
711C22×C4—944no—
712C22×C4—1888no—
713C22×C4—1882no—
714C22×C4—1884no—
715C22×C4C23×D4718yes—
716C22×C4C23×D4712yes—
717C22×C4C23×D4712yes—
718C22×C4C23×D4711yescharacteristic
719C22×C4C23×D4714yes—
720C22×C4C23×D4712yes—
721C22×C4C23×D47116yes—
722C22×C4C23×D4711yescharacteristic
723C22×C4C23×D4711yescharacteristic
724C4⋊C4—4716no—
725C4⋊C4—478no—
726C4⋊C4—4716no—
727C4⋊C4—4716no—
728C4⋊C4—478no—
729C4⋊C4—478no—
730C4⋊C4—478no—
731C4⋊C4—474no—
732C4⋊C4—474no—
733C4⋊C4—478no—
734C4⋊C4—478no—
735C4⋊C4—4716no—
736C4⋊C4—4716no—
737C4⋊C4—4716no—
738C4⋊C4—4716no—
739C4⋊C4—478no—
740C4⋊C4—4716no—
741C4⋊C4C23×D4718yes—
742C4⋊C4C23×D4714yes—
743C4⋊C4C23×D4718yes—
744C4⋊C4C23×D47116yes—
745C4⋊C4C23×D4714yes—
746C4⋊C4C23×D47116yes—
747C4⋊C4C23×D4718yes—
748C22⋊C4—478no—
749C22⋊C4—478no—
750C22⋊C4—478no—
751C22⋊C4—478no—
752C22⋊C4—478no—
753C22⋊C4—4716no—
754C22⋊C4—4716no—
755C22⋊C4—4716no—
756C22⋊C4—478no—
757C22⋊C4—478no—
758C22⋊C4C23×D47116yes—
759C22⋊C4C23×D4718yes—
760C42—474no—
761C42—478no—
762C42—474no—
763C42—474no—
764C42—478no—
765C42—478no—
766C42—4716no—
767C42—4716no—
768C42C23×D4714yes—
769C42C23×D4718yes—
770C23—24no—
771C23—24no—
772C23—472no—
773C23—474no—
774C23—942no—
775C23—944no—
776C23—942no—
777C23—944no—
778C23—944no—
779C23—942no—
780C23C2×#1062535418yes—
781C23C24×D4714yes—
782C23C24×D4711yescharacteristic
783Q8—28no—
784Q8—48no—
785Q8—948no—
786Q8—9416no—
787D4—9416no—
788D4—9432no—
789D4—948no—
790D4—1888no—
791D4C2×#10625354116yes—
792C2×C4—24no—
793C2×C4—24no—
794C2×C4—24no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—216no—
798C2×C4—416no—
799C2×C4—472no—
800C2×C4—472no—
801C2×C4—472no—
802C2×C4—474no—
803C2×C4—474no—
804C2×C4—478no—
805C2×C4—474no—
806C2×C4—942no—
807C2×C4—944no—
808C2×C4—948no—
809C2×C4—944no—
810C2×C4—9416no—
811C2×C4—9432no—
812C2×C4—942no—
813C2×C4—944no—
814C2×C4—942no—
815C2×C4—948no—
816C2×C4—9416no—
817C2×C4—948no—
818C2×C4—18816no—
819C2×C4—1884no—
820C2×C4—1888no—
821C2×C4C2×#1062535414yes—
822C2×C4#1309407114yes—
823C2×C4C24×D4714yes—
824C2×C4C24×D4714yes—
825C2×C4C24×D4712yes—
826C2×C4C24×D4718yes—
827C2×C4C24×D4714yes—
828C2×C4C24×D4712yes—
829C2×C4C24×D4712yes—
830C22—216no—
831C22—24no—
832C22—24no—
833C22—942no—
834C22—944no—
835C22—942no—
836C22—944no—
837C22—944no—
838C22—942no—
839C22—1884no—
840C22—1888no—
841C22C22×#1062535418yes—
842C22C22×#1062535412yes—
843C22C2×#1309407112yes—
844C22#1568995812yes—
845C22C25×D4711yescharacteristic
846C4—24no—
847C4—24no—
848C4—24no—
849C4—28no—
850C4—22no—
851C4—942no—
852C4—944no—
853C4—944no—
854C4—948no—
855C4—942no—
856C4—944no—
857C4—942no—
858C4C22×#1062535414yes—
859C4C2×#1309407114yes—
860C2—28no—
861C2—1882no—
862C2—1884no—
863C2#2025736714yesdirect product factor
864C2C23×#1062535411yescharacteristic
865C2C22×#1309407111yescharacteristic
866C2C2×#1568995811yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#554C2
socleC23×C47C25
hypercenterC2×#554D47
hypocenterC47C2×#3515
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #20257367C2direct (N × H)
2. C2×#15689852C2semidirect
3. C2×#15689834C2semidirect
4. C2×#15689821C2semidirect
5. C2×#15689815C2semidirect
6. C2×#15689815C2semidirect
7. C2×#15689811C2semidirect
8. C2×#15689777C2semidirect
9. C2×#15689777C2semidirect
10. C2×#15689736C2semidirect
11. C2×#15689722C2semidirect
12. C2×#15689678C2semidirect
13. C2×#15689660C2semidirect
14. C2×#15689659C2semidirect
15. C22×#13094015C2semidirect
16. C2×#15689602C2semidirect
17. C2×C4×#10625352C2semidirect
18. C2×C47×#554C2semidirect
21. #15689852C22semidirect
22. #15689834C22semidirect
23. #15689821C22semidirect
24. #15689815C22semidirect
25. #15689815C22semidirect
26. #15689811C22semidirect
27. #15689777C22semidirect
28. #15689777C22semidirect
29. #15689736C22semidirect
30. #15689722C22semidirect
31. #15689678C22semidirect
34. #15689660C22semidirect
35. #15689659C22semidirect
48. C2×#13094015C22semidirect
64. #15689602C22semidirect
65. C4×#10625352C22semidirect
92. C47×#554C22semidirect
430. C2×#554D47semidirect
446. C2×C47#3515semidirect
456. #554C2×D47semidirect
534. C47C2×#3515semidirect
863. C2#20257367direct (N × H)

Maximal subgroups

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

subgroupindex
#202573672
C2×#156898522
C2×#156898342
C2×#156898212
C2×#156898152
C2×#156898112
C2×#156897772
C2×#156897362
C2×#156897222
C2×#156896782
C2×#156896602
C2×#156896592
C22×#130940152
C2×#156896022
C2×C4×#106253522
C2×C47×#5542
C2×#351547