Finite Group Databasebeta

← C2×#20257268 #27124715

Subgroups — C2×#20257268 #27124715

Order 12032.

7022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257268C2132yesmaximal, direct product factor
2C2×#15689852C211yesmaximal, characteristic, complemented
3C2×#15689851C212yesmaximal, complemented
4C2×#15689848C211yesmaximal, characteristic, complemented
5C2×#15689843C211yesmaximal, characteristic, complemented
6C2×#15689842C212yesmaximal, complemented
7C2×#15689812C212yesmaximal, complemented
8C2×#15689809C214yesmaximal, complemented
9C2×#15689807C212yesmaximal, complemented
10C2×#15689730C214yesmaximal, complemented
11C2×#15689693C212yesmaximal
12C2×#15689677C211yesmaximal, characteristic, complemented
13C2×#15689676C212yesmaximal, complemented
14C2×#15689675C212yesmaximal, complemented
15C2×C4⋊Q8×D47C211yesmaximal, characteristic, complemented
16C2×#15689599C212yesmaximal, complemented
17C2×C4×#10625352C211yesmaximal, characteristic
18C2×C47×#556C211yesmaximal, characteristic, complemented
19C22×#10625352C2211yescharacteristic
20C22×Q8×D47C2212yes—
21#15689852C22116yescomplemented
22#15689851C22132yescomplemented
23#15689848C22116yescomplemented
24#15689843C22116yescomplemented
25#15689842C22132yescomplemented
26#15689812C22132yescomplemented
27#15689809C22164yescomplemented
28#15689807C22132yescomplemented
29#15689730C22164yescomplemented
30#15689693C22132yes—
31#15689677C22116yescomplemented
32#15689676C22132yescomplemented
33#15689675C22132yescomplemented
34C2×#13094024C2211yescharacteristic
35C2×#13094024C2212yes—
36C2×#13094023C2212yes—
37C2×#13094023C2212yes—
38C2×#13094023C2211yescharacteristic
39C2×#13094022C2212yes—
40C2×#13094022C2211yescharacteristic
41C2×#13094022C2212yes—
42C4⋊Q8×D47C22116yescomplemented
43C2×#13094017C2214yes—
44C2×#13094017C2214yes—
45C2×#13094017C2214yes—
46C2×#13094016C2214yes—
47C2×#13094015C2212yes—
48C2×#13094015C2214yes—
49C2×#13094015C2212yes—
50C2×#13094014C2214yes—
51C2×#13094014C2214yes—
52C2×#13094014C2214yes—
53C2×#13094014C2212yes—
54C2×#13094011C2212yes—
55C2×#13094006C2214yes—
56C2×#13094006C2214yes—
57C2×#13094004C2211yescharacteristic
58C2×#13094003C2212yes—
59C2×#13094002C2212yes—
60C2×#13094001C2214yes—
61C2×#13094001C2214yes—
62C2×#13094001C2214yes—
63C2×#13094000C2211yescharacteristic
64#15689599C22132yescomplemented
65C4×#10625352C22116yes—
66C2×Q8×Dic47C2212yes—
67C2×Q8×Dic47C2212yes—
68C2×C4×Dic94C2211yescharacteristic
69C2×C4×Dic94C2214yes—
70C2×C4×Dic94C2212yes—
71C2×C4×Dic94C2214yes—
72C2×C4×Dic94C2212yes—
73C2×C4×Dic94C2211yescharacteristic
74C2×#13093989C2211yescharacteristic
75C2×#13093989C2214yes—
76C2×#13093989C2212yes—
77C2×#13093989C2212yes—
78C2×D4×Dic47C2211yescharacteristic
79C2×C4×C22⋊D47C2212yes—
80C2×(C22⋊D47)⋊C4C2212yes—
81C2×#13093983C2212yes—
82C2×#13093982C2211yescharacteristic
83C2×#13093982C2214yes—
84C2×#13093981C2214yes—
85C2×#13093981C2212yes—
86C2×#13093980C2212yes—
87C2×#13093980C2214yes—
88C2×C4⋊C4×D47C2212yes—
89C2×C4⋊C4×D47C2212yes—
90C22×C4×Dic47C2212yes—
91C2×C42×D47C2211yescharacteristic
92C47×#556C22116yescomplemented
93C2×C4⋊Q8×C47C2211yescharacteristic
94C2×#126×C47C2214yes—
95C2×#124×C47C2212yes—
96C2×C22⋊Q8×C47C2212yes—
97C2×C4×Q8×C47C2212yes—
98C2×C4×Q8×C47C2211yescharacteristic
99C2×C4×D4×C47C2211yescharacteristic
100C2×#117×C47C2212yes—
101C2×#10625352—28no—
102C2×#10625352C2318yes—
103C22×Dic94C2311yescharacteristic
104C22×Dic94C2314yes—
105C22×Dic94C2312yes—
106C22×Dic94C2311yescharacteristic
107C22×Dic94C2312yes—
108C2×Q8×D47—216no—
109C2×Q8×D47C23116yes—
110C22×C22⋊D47C2312yes—
111C23×Dic47C2312yes—
112C23×Dic47C2312yes—
113C22×C4×D47C2311yescharacteristic
114C22×C4×D47C2311yescharacteristic
115C22×C4×D47C2314yes—
116C22×C4×D47C2311yescharacteristic
117#13094024C2318yes—
118#13094024C23116yes—
119#13094023C23116yes—
120#13094023C23116yes—
121#13094023C2318yes—
122#13094022C23116yes—
123#13094022C23116yes—
124#13094022C2318yes—
125#13094017C23132yes—
126#13094017C23132yes—
127#13094017C23132yes—
128#13094016C23132yes—
129#13094015C23132yes—
130#13094015C23116yes—
131#13094015C23116yes—
132#13094014C23116yes—
133#13094014C23132yes—
134#13094014C23132yes—
135#13094014C23132yes—
136#13094011C23116yes—
137#13094006C23132yes—
138#13094006C23132yes—
139#13094004C2318yes—
140#13094003C23116yes—
141#13094002C23116yes—
142#13094001C23132yes—
143#13094001C23132yes—
144#13094001C23132yes—
145#13094000C2318yes—
146Q8×Dic47C23116yes—
147Q8×Dic47C23116yes—
148C4×Dic94C23132yes—
149C4×Dic94C23132yes—
150C4×Dic94C23116yes—
151C4×Dic94C23116yes—
152C4×Dic94C2318yes—
153C4×Dic94C2318yes—
154#13093989C23132yes—
155#13093989C23116yes—
156#13093989C23116yes—
157#13093989C2318yes—
158D4×Dic47C2318yes—
159C4×C22⋊D47C23116yes—
160(C22⋊D47)⋊C4C23116yes—
161#13093983C23116yes—
162#13093982C23132yes—
163#13093982C2318yes—
164#13093981C23132yes—
165#13093981C23116yes—
166#13093980C23116yes—
167#13093980C23132yes—
168C2×C4⋊Dic47C2312yes—
169C2×C4⋊Dic47C2312yes—
170C2×C4⋊Dic47C2311yescharacteristic
171C2×C4⋊Dic47C2314yes—
172C2×C4⋊Dic47C2311yescharacteristic
173C2×C4⋊Dic47C2314yes—
174C2×C4⋊Dic47C2312yes—
175C2×C4⋊Dic47C2314yes—
176C2×Dic47⋊C4C2314yes—
177C2×Dic47⋊C4C2314yes—
178C2×Dic47⋊C4C2312yes—
179C2×Dic47⋊C4C2312yes—
180C2×Dic47⋊C4C2312yes—
181C2×Dic47⋊C4C2312yes—
182C2×Dic47⋊C4C2314yes—
183C2×Dic47⋊C4C2312yes—
184C2×Dic47⋊C4C2314yes—
185C2×Dic47⋊C4C2314yes—
186C2×Dic47⋊C4C2312yes—
187C2×Dic47⋊C4C2314yes—
188C2×Dic47⋊C4C2312yes—
189C4⋊C4×D47C23116yes—
190C4⋊C4×D47C23116yes—
191C2×C22⋊Dic47C2312yes—
192C2×C22⋊Dic47C2314yes—
193C2×C22⋊Dic47C2314yes—
194C2×(C2×D47)⋊C4C2312yes—
195C2×(C2×D47)⋊C4C2312yes—
196C2×(C2×D47)⋊C4C2312yes—
197C2×C4×Dic47C2311yescharacteristic
198C2×C4×Dic47C2311yescharacteristic
199C2×C4×Dic47C2311yescharacteristic
200C2×C4×Dic47C2312yes—
201C2×C4×Dic47C2312yes—
202C2×C4×Dic47C2312yes—
203C2×C4×Dic47C23116yes—
204C2×C4×Dic47C2314yes—
205C2×C4×Dic47C2314yes—
206C2×C4×Dic47C2312yes—
207C2×C4×Dic47C2314yes—
208C42×D47C2318yes—
209C22×Q8×C47C2311yescharacteristic
210C22×Q8×C47C2312yes—
211C22×D4×C47C2311yescharacteristic
212C23×C4×C47C2312yes—
213C4⋊Q8×C47C2318yes—
214#126×C47C23132yes—
215#124×C47C23116yes—
216C22⋊Q8×C47C23116yes—
217C4×Q8×C47C23116yes—
218C4×Q8×C47C2318yes—
219C4×D4×C47C2318yes—
220#117×C47C23116yes—
221C2×C4⋊C4×C47C2311yescharacteristic
222C2×C4⋊C4×C47C2312yes—
223C2×C4⋊C4×C47C2311yescharacteristic
224C2×C4⋊C4×C47C2314yes—
225C2×C4⋊C4×C47C2312yes—
226C2×C4⋊C4×C47C2312yes—
227C2×C22⋊C4×C47C2314yes—
228C2×C22⋊C4×C47C2312yes—
229C2×C22⋊C4×C47C2314yes—
230C2×C42×C47C2314yes—
231C2×C42×C47C2311yescharacteristic
232C2×C42×C47C2312yes—
233C24×C47C2412yes—
234C23×D47C2411yescharacteristic
235C2×Q8×C47—28no—
236C2×Q8×C47—24no—
237C2×Q8×C47C2414yes—
238C2×Q8×C47C2418yes—
239C2×D4×C47—24no—
240C2×D4×C47C2414yes—
241C22×C4×C47—28no—
242C22×C4×C47C2412yes—
243C22×C4×C47C2412yes—
244C22×C4×C47C2411yescharacteristic
245C22×C4×C47C2412yes—
246C22×C4×C47C2414yes—
247C22×C4×C47C2418yes—
248C22×C4×C47C2411yescharacteristic
249C22×C4×C47C2411yescharacteristic
250C2×C22⋊D47—28no—
251C2×C22⋊D47C2418yes—
252C22×Dic47—28no—
253C22×Dic47—28no—
254C22×Dic47C2412yes—
255C22×Dic47C2412yes—
256C22×Dic47C2412yes—
257C22×Dic47C2411yescharacteristic
258C22×Dic47C2414yes—
259C22×Dic47C2412yes—
260C22×Dic47C2418yes—
261C22×Dic47C2418yes—
262C22×Dic47C2411yescharacteristic
263C22×Dic47C2411yescharacteristic
264Q8×D47—264no—
265#10625352—232no—
266C2×C4×D47—216no—
267C2×C4×D47—24no—
268C2×C4×D47—24no—
269C2×C4×D47#4118yes—
270C2×C4×D47C2414yes—
271C2×C4×D47C2414yes—
272C2×C4×D47C24116yes—
273C2×C4×D47C2414yes—
274C2×Dic94—28no—
275C2×Dic94—24no—
276C2×Dic94—24no—
277C2×Dic94—216no—
278C2×Dic94—28no—
279C2×Dic94C2414yes—
280C2×Dic94C24116yes—
281C2×Dic94C2418yes—
282C2×Dic94C2414yes—
283C2×Dic94C2418yes—
284C4⋊C4×C47C2414yes—
285C4⋊C4×C47C2418yes—
286C4⋊C4×C47C2414yes—
287C4⋊C4×C47C24116yes—
288C4⋊C4×C47C2418yes—
289C4⋊C4×C47C2418yes—
290C22⋊C4×C47C24116yes—
291C22⋊C4×C47C2418yes—
292C22⋊C4×C47C24116yes—
293C42×C47C24116yes—
294C42×C47C2414yes—
295C42×C47C2418yes—
296C22⋊Dic47C2418yes—
297C22⋊Dic47C24116yes—
298C22⋊Dic47C24116yes—
299(C2×D47)⋊C4C2418yes—
300(C2×D47)⋊C4C2418yes—
301(C2×D47)⋊C4C2418yes—
302C4⋊Dic47C2418yes—
303C4⋊Dic47C2418yes—
304C4⋊Dic47C2414yes—
305C4⋊Dic47C24116yes—
306C4⋊Dic47C2414yes—
307C4⋊Dic47C24116yes—
308C4⋊Dic47C2418yes—
309C4⋊Dic47C24116yes—
310Dic47⋊C4C24116yes—
311Dic47⋊C4C24116yes—
312Dic47⋊C4C2418yes—
313Dic47⋊C4C2418yes—
314Dic47⋊C4C2418yes—
315Dic47⋊C4C2418yes—
316Dic47⋊C4C24116yes—
317Dic47⋊C4C2418yes—
318Dic47⋊C4C24116yes—
319Dic47⋊C4C24116yes—
320Dic47⋊C4C2418yes—
321Dic47⋊C4C24116yes—
322Dic47⋊C4C2418yes—
323C4×Dic47C2414yes—
324C4×Dic47C2414yes—
325C4×Dic47C2414yes—
326C4×Dic47C2418yes—
327C4×Dic47C2418yes—
328C4×Dic47C2418yes—
329C4×Dic47C24116yes—
330C4×Dic47C24116yes—
331C4×Dic47C2418yes—
332C4×Dic47C24116yes—
333C23×C47—24no—
334C23×C47—24no—
335C23×C47—24no—
336C23×C47C2514yes—
337C23×C47C2511yescharacteristic
338C22×D47—22no—
339C22×D47—22no—
340C22×D47C2×#4114yes—
341C22×D47C2512yes—
342Q8×C47—216no—
343Q8×C47—28no—
344D4×C47—28no—
345C2×C4×C47—28no—
346C2×C4×C47—24no—
347C2×C4×C47—22no—
348C2×C4×C47—24no—
349C2×C4×C47—24no—
350C2×C4×C47—216no—
351C2×C4×C47C2×#4114yes—
352C2×C4×C472−1+414yes—
353C2×C4×C47C2514yes—
354C2×C4×C47C2514yes—
355C2×C4×C47C2512yes—
356C2×C4×C47C2518yes—
357C2×C4×C47C2514yes—
358C2×C4×C47C2512yes—
359C2×C4×C47C2512yes—
360C22⋊D47—216no—
361C2×Dic47—28no—
362C2×Dic47—24no—
363C2×Dic47—24no—
364C2×Dic47—24no—
365C2×Dic47—22no—
366C2×Dic47—24no—
367C2×Dic47—216no—
368C2×Dic47—216no—
369C2×Dic47C2×#4114yes—
370C2×Dic472−1+414yes—
371C2×Dic47C2514yes—
372C2×Dic47C2514yes—
373C2×Dic47C2514yes—
374C2×Dic47C2512yes—
375C2×Dic47C2514yes—
376C2×Dic47C2518yes—
377C2×Dic47C2512yes—
378C2×Dic47C2512yes—
379C4×D47—232no—
380C4×D47—28no—
381C4×D47—28no—
382C4×D47C2×#41116yes—
383Dic94—28no—
384Dic94—216no—
385Dic94—28no—
386Dic94—232no—
387Dic94—216no—
388C2×#3509—471nomaximal, Sylow
389C22×C47—24no—
390C22×C47—24no—
391C22×C47—24no—
392C22×C47—48no—
393C22×C47C22×#4112yes—
394C22×C47C2×2−1+412yes—
395C22×C47C2×2−1+412yes—
396C22×C47C2611yescharacteristic
397C2×D47—22no—
398C2×D47—22no—
399C2×D47—28no—
400C2×D47C22×#4114yes—
401C4×C47—28no—
402C4×C47—24no—
403C4×C47—22no—
404C4×C47—24no—
405C4×C47—24no—
406C4×C47C22×#4114yes—
407C4×C47C2×2−1+414yes—
408Dic47—28no—
409Dic47—24no—
410Dic47—24no—
411Dic47—24no—
412Dic47—22no—
413Dic47—24no—
414Dic47C22×#4114yes—
415Dic47C2×2−1+414yes—
416#3509—4732no—
417C2×#557—471no—
418C2×#557—472no—
419C2×#557—471no—
420C2×#556—472no—
421C2×#556—471no—
422C2×#556D4711yescharacteristic, complemented
423C2×#552—474no—
424C2×#552—472no—
425C2×#552—472no—
426C2×#541—474no—
427C2×#536—472no—
428C2×#533—472no—
429C2×#533—471no—
430C2×#533—472no—
431C22×C4⋊Q8—471no—
432C2×#519—472no—
433C2×C4×#41—471no—
434C2×C47—44no—
435C2×C47#350914yescomplemented
436C2×C47C23×#4111yescharacteristic
437C2×C47C22×2−1+411yescharacteristic
438C2×C47C22×2−1+411yescharacteristic
439D47—24no—
440C22×#41—471no—
441C23×Q8—472no—
442#557—4716no—
443#557—4732no—
444#557—4716no—
445#556—4732no—
446#556—4716no—
447#556C2×D47116yescomplemented
448#552—4764no—
449#552—4732no—
450#552—4732no—
451#541—4764no—
452#536—4732no—
453#533—4732no—
454#533—4716no—
455#533—4732no—
456C2×C4⋊Q8—472no—
457C2×C4⋊Q8—471no—
458C2×C4⋊Q8—472no—
459C2×C4⋊Q8—4716no—
460C2×C4⋊Q8—472no—
461C2×C4⋊Q8—472no—
462C2×C4⋊Q8—471no—
463C2×C4⋊Q8—471no—
464C2×C4⋊Q8—472no—
465C2×C4⋊Q8C2×D4711yescharacteristic
466C2×#126—474no—
467C2×#126—474no—
468C2×#126—474no—
469C2×#126C2×D4714yes—
470C2×#125—472no—
471C2×#125—474no—
472C2×#125—472no—
473C2×#125—472no—
474C2×#125—474no—
475C2×#125—474no—
476C2×#125—474no—
477C2×#125—474no—
478C2×#124—472no—
479C2×#124C2×D4712yes—
480C2×#123—474no—
481C2×#123—474no—
482C2×C22⋊Q8—471no—
483C2×C22⋊Q8—472no—
484C2×C22⋊Q8—472no—
485C2×C22⋊Q8—471no—
486C2×C22⋊Q8—474no—
487C2×C22⋊Q8—474no—
488C2×C22⋊Q8—474no—
489C2×C22⋊Q8C2×D4712yes—
490#519—4732no—
491C4×#41—4716no—
492C2×C4×Q8—472no—
493C2×C4×Q8—472no—
494C2×C4×Q8—471no—
495C2×C4×Q8—474no—
496C2×C4×Q8—472no—
497C2×C4×Q8—472no—
498C2×C4×Q8—471no—
499C2×C4×Q8—474no—
500C2×C4×Q8—472no—
501C2×C4×Q8—474no—
502C2×C4×Q8—471no—
503C2×C4×Q8—472no—
504C2×C4×Q8C2×D4712yes—
505C2×C4×Q8C2×D4711yescharacteristic
506C2×C4×D4—471no—
507C2×C4×D4—472no—
508C2×C4×D4—472no—
509C2×C4×D4C2×D4711yescharacteristic
510C2×#117—472no—
511C2×#117—471no—
512C2×#117—474no—
513C2×#117—472no—
514C2×#117—474no—
515C2×#117—472no—
516C2×#117—474no—
517C2×#117C2×D4712yes—
518C22×C4⋊C4—472no—
519C22×C4⋊C4—472no—
520C22×C42—472no—
521C22×C42—471no—
522C47C2×#350911yescharacteristic, complemented, Sylow
523C2×#41—478no—
524C2×#41—948no—
525C22×Q8—4716no—
526C22×Q8—472no—
527C22×Q8—471no—
528C22×Q8—474no—
529C22×Q8—472no—
530C22×Q8—471no—
531C22×Q8—9416no—
532C22×Q8C22×D4711yescharacteristic
533C22×Q8C22×D4712yes—
534C22×D4—472no—
535C22×D4C22×D4711yescharacteristic
536C23×C4—471no—
537C23×C4—472no—
538C23×C4—472no—
539C23×C4—474no—
540C23×C4—471no—
541C23×C4—471no—
542C23×C4C22×D4712yes—
543C4⋊Q8—4716no—
544C4⋊Q8—478no—
545C4⋊Q8—4716no—
546C4⋊Q8—4716no—
547C4⋊Q8—4716no—
548C4⋊Q8—478no—
549C4⋊Q8—478no—
550C4⋊Q8—4716no—
551C4⋊Q8C22×D4718yes—
552#126—4732no—
553#126—4732no—
554#126—4732no—
555#126C22×D47132yes—
556#125—4716no—
557#125—4732no—
558#125—4716no—
559#125—4716no—
560#125—4732no—
561#125—4732no—
562#125—4732no—
563#125—4732no—
564#124—4716no—
565#124C22×D47116yes—
566#123—4732no—
567#123—4732no—
568C22⋊Q8—478no—
569C22⋊Q8—4716no—
570C22⋊Q8—4716no—
571C22⋊Q8—478no—
572C22⋊Q8—4732no—
573C22⋊Q8—4732no—
574C22⋊Q8—4732no—
575C22⋊Q8C22×D47116yes—
576C4×Q8—4716no—
577C4×Q8—4716no—
578C4×Q8—478no—
579C4×Q8—4732no—
580C4×Q8—4716no—
581C4×Q8—4716no—
582C4×Q8—478no—
583C4×Q8—4732no—
584C4×Q8—4716no—
585C4×Q8—4732no—
586C4×Q8—4716no—
587C4×Q8—478no—
588C4×Q8C22×D47116yes—
589C4×Q8C22×D4718yes—
590C4×D4—478no—
591C4×D4—4716no—
592C4×D4—4716no—
593C4×D4C22×D4718yes—
594#117—4716no—
595#117—478no—
596#117—4732no—
597#117—4716no—
598#117—4732no—
599#117—4716no—
600#117—4732no—
601#117C22×D47116yes—
602C2×C4⋊C4—474no—
603C2×C4⋊C4—472no—
604C2×C4⋊C4—474no—
605C2×C4⋊C4—472no—
606C2×C4⋊C4—472no—
607C2×C4⋊C4—471no—
608C2×C4⋊C4—471no—
609C2×C4⋊C4—472no—
610C2×C4⋊C4—472no—
611C2×C4⋊C4—472no—
612C2×C4⋊C4—472no—
613C2×C4⋊C4—474no—
614C2×C4⋊C4—474no—
615C2×C4⋊C4—474no—
616C2×C4⋊C4—474no—
617C2×C4⋊C4—474no—
618C2×C4⋊C4—474no—
619C2×C4⋊C4—474no—
620C2×C4⋊C4—472no—
621C2×C4⋊C4—472no—
622C2×C4⋊C4—472no—
623C2×C4⋊C4—4716no—
624C2×C4⋊C4—4716no—
625C2×C4⋊C4C22×D4712yes—
626C2×C4⋊C4C22×D4712yes—
627C2×C4⋊C4C22×D4711yescharacteristic
628C2×C4⋊C4C22×D4714yes—
629C2×C4⋊C4C22×D4711yescharacteristic
630C2×C4⋊C4C22×D4712yes—
631C2×C22⋊C4—472no—
632C2×C22⋊C4—474no—
633C2×C22⋊C4—474no—
634C2×C22⋊C4—472no—
635C2×C22⋊C4—472no—
636C2×C22⋊C4—472no—
637C2×C22⋊C4C22×D4712yes—
638C2×C22⋊C4C22×D4714yes—
639C2×C22⋊C4C22×D4714yes—
640C2×C42—472no—
641C2×C42—474no—
642C2×C42—474no—
643C2×C42—474no—
644C2×C42—471no—
645C2×C42—472no—
646C2×C42—472no—
647C2×C42—472no—
648C2×C42—471no—
649C2×C42—4716no—
650C2×C42—471no—
651C2×C42—478no—
652C2×C42C22×D4714yes—
653C2×C42C22×D4712yes—
654C2×C42C22×D4711yescharacteristic
655C24—471no—
656C24C23×D4712yes—
657#41—9432no—
658C2×Q8—28no—
659C2×Q8—24no—
660C2×Q8—478no—
661C2×Q8—474no—
662C2×Q8—4716no—
663C2×Q8—478no—
664C2×Q8—474no—
665C2×Q8—948no—
666C2×Q8—9416no—
667C2×Q8—9464no—
668C2×Q8—948no—
669C2×Q8—944no—
670C2×Q8—944no—
671C2×Q8C23×D4714yes—
672C2×Q8C23×D4718yes—
673C2×D4—24no—
674C2×D4—478no—
675C2×D4—948no—
676C2×D4C23×D4714yes—
677C22×C4—28no—
678C22×C4—471no—
679C22×C4—471no—
680C22×C4—478no—
681C22×C4—474no—
682C22×C4—478no—
683C22×C4—478no—
684C22×C4—472no—
685C22×C4—472no—
686C22×C4—472no—
687C22×C4—471no—
688C22×C4—474no—
689C22×C4—472no—
690C22×C4—474no—
691C22×C4—474no—
692C22×C4—4716no—
693C22×C4—944no—
694C22×C4—9416no—
695C22×C4—948no—
696C22×C4—948no—
697C22×C4—944no—
698C22×C4C23×D4718yes—
699C22×C4C23×D4712yes—
700C22×C4C23×D4712yes—
701C22×C4C23×D4711yescharacteristic
702C22×C4C23×D4714yes—
703C22×C4C23×D4712yes—
704C22×C4C23×D4711yescharacteristic
705C22×C4C23×D4711yescharacteristic
706C4⋊C4—4716no—
707C4⋊C4—4716no—
708C4⋊C4—478no—
709C4⋊C4—478no—
710C4⋊C4—478no—
711C4⋊C4—478no—
712C4⋊C4—478no—
713C4⋊C4—4716no—
714C4⋊C4—4716no—
715C4⋊C4—4716no—
716C4⋊C4—4716no—
717C4⋊C4—478no—
718C4⋊C4—478no—
719C4⋊C4—478no—
720C4⋊C4—478no—
721C4⋊C4—474no—
722C4⋊C4—474no—
723C4⋊C4—4716no—
724C4⋊C4—4716no—
725C4⋊C4—4716no—
726C4⋊C4—478no—
727C4⋊C4C23×D4718yes—
728C4⋊C4C23×D4718yes—
729C4⋊C4C23×D4714yes—
730C4⋊C4C23×D47116yes—
731C4⋊C4C23×D4714yes—
732C4⋊C4C23×D4718yes—
733C22⋊C4—478no—
734C22⋊C4—4716no—
735C22⋊C4—4716no—
736C22⋊C4—478no—
737C22⋊C4—478no—
738C22⋊C4—478no—
739C22⋊C4C23×D4718yes—
740C22⋊C4C23×D47116yes—
741C22⋊C4C23×D47116yes—
742C42—474no—
743C42—478no—
744C42—474no—
745C42—478no—
746C42—478no—
747C42—474no—
748C42—4716no—
749C42—4716no—
750C42—4716no—
751C42—478no—
752C42C23×D4714yes—
753C42C23×D47116yes—
754C42C23×D4718yes—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—474no—
759C23—472no—
760C23—942no—
761C23—942no—
762C23C24×D4714yes—
763C23C24×D4711yescharacteristic
764Q8—216no—
765Q8—28no—
766Q8—9416no—
767Q8—9432no—
768Q8—9416no—
769Q8—948no—
770Q8—948no—
771D4—28no—
772D4—9416no—
773C2×C4—28no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—24no—
778C2×C4—216no—
779C2×C4—474no—
780C2×C4—474no—
781C2×C4—472no—
782C2×C4—472no—
783C2×C4—4716no—
784C2×C4—474no—
785C2×C4—474no—
786C2×C4—474no—
787C2×C4—472no—
788C2×C4—478no—
789C2×C4—474no—
790C2×C4—948no—
791C2×C4—9432no—
792C2×C4—9416no—
793C2×C4—9416no—
794C2×C4—944no—
795C2×C4—948no—
796C2×C4—944no—
797C2×C4—944no—
798C2×C4—942no—
799C2×C4—944no—
800C2×C4—948no—
801C2×C4#41×D4714yes—
802C2×C4#1309407114yes—
803C2×C4C24×D4714yes—
804C2×C4C24×D4714yes—
805C2×C4C24×D4712yes—
806C2×C4C24×D4718yes—
807C2×C4C24×D4714yes—
808C2×C4C24×D4712yes—
809C2×C4C24×D4712yes—
810C22—24no—
811C22—24no—
812C22—24no—
813C22—48no—
814C22—474no—
815C22—942no—
816C22—942no—
817C22—948no—
818C22C2×#41×D4712yes—
819C222−1+4×D4712yes—
820C22C2×#1309407112yes—
821C22C25×D4711yescharacteristic
822C4—28no—
823C4—22no—
824C4—24no—
825C4—24no—
826C4—24no—
827C4—474no—
828C4—474no—
829C4—944no—
830C4—948no—
831C4—944no—
832C4—944no—
833C4—942no—
834C4—944no—
835C4C2×#41×D4714yes—
836C4C2×#1309407114yes—
837C2—44no—
838C2—944no—
839C2#2025726814yesdirect product factor
840C2C22×#41×D4711yescharacteristic
841C2C2×2−1+4×D4711yescharacteristic
842C2C22×#1309407111yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#556C2
socleC23×C47C25
prime radicalC22×#10625352C22
hypercenterC2×#556D47
hypocenterC47C2×#3509
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #20257268C2direct (N × H)
2. C2×#15689852C2semidirect
3. C2×#15689851C2semidirect
4. C2×#15689848C2semidirect
5. C2×#15689843C2semidirect
6. C2×#15689842C2semidirect
7. C2×#15689812C2semidirect
8. C2×#15689809C2semidirect
9. C2×#15689807C2semidirect
10. C2×#15689730C2semidirect
12. C2×#15689677C2semidirect
13. C2×#15689676C2semidirect
14. C2×#15689675C2semidirect
15. C2×C4⋊Q8×D47C2semidirect
16. C2×#15689599C2semidirect
18. C2×C47×#556C2semidirect
21. #15689852C22semidirect
22. #15689851C22semidirect
23. #15689848C22semidirect
24. #15689843C22semidirect
25. #15689842C22semidirect
26. #15689812C22semidirect
27. #15689809C22semidirect
28. #15689807C22semidirect
29. #15689730C22semidirect
31. #15689677C22semidirect
32. #15689676C22semidirect
33. #15689675C22semidirect
42. C4⋊Q8×D47C22semidirect
64. #15689599C22semidirect
92. C47×#556C22semidirect
422. C2×#556D47semidirect
435. C2×C47#3509semidirect
447. #556C2×D47semidirect
522. C47C2×#3509semidirect
839. C2#20257268direct (N × H)

Maximal subgroups

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

subgroupindex
#202572682
C2×#156898522
C2×#156898512
C2×#156898482
C2×#156898432
C2×#156898422
C2×#156898122
C2×#156898092
C2×#156898072
C2×#156897302
C2×#156896932
C2×#156896772
C2×#156896762
C2×#156896752
C2×C4⋊Q8×D472
C2×#156895992
C2×C4×#106253522
C2×C47×#5562
C2×#350947