Finite Group Databasebeta

← C2×#20257870 #27123994

Subgroups — C2×#20257870 #27123994

Order 12032.

6446 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257870C2132yesmaximal, direct product factor
2C2×#15689874C214yesmaximal, complemented
3C2×#15689853C211yesmaximal, characteristic, complemented
4C2×#15689849C212yesmaximal, complemented
5C2×#15689848C211yesmaximal, characteristic, complemented
6C2×#15689847C211yesmaximal, characteristic, complemented
7C2×#15689845C212yesmaximal, complemented
8C2×#15689841C212yesmaximal, complemented
9C2×#15689834C211yesmaximal, characteristic, complemented
10C2×#15689812C212yesmaximal, complemented
11C2×#15689753C212yesmaximal, complemented
12C2×#15689746C212yesmaximal
13C2×#15689736C212yesmaximal, complemented
14C2×#15689733C212yesmaximal, complemented
15C2×#15689731C214yesmaximal, complemented
16C2×#15689680C211yesmaximal, characteristic, complemented
17C2×#15689657C211yesmaximal, characteristic
18C2×C47×#533C211yesmaximal, characteristic, complemented
19#15689874C22164yescomplemented
20#15689853C22116yescomplemented
21#15689849C22132yescomplemented
22#15689848C22116yescomplemented
23#15689847C22116yescomplemented
24#15689845C22132yescomplemented
25#15689841C22132yescomplemented
26#15689834C22116yescomplemented
27#15689812C22132yescomplemented
28#15689753C22132yescomplemented
29#15689746C22132yes—
30#15689736C22132yescomplemented
31#15689733C22132yescomplemented
32#15689731C22164yescomplemented
33#15689680C22116yescomplemented
34C2×#13094024C2211yescharacteristic
35C2×#13094024C2211yescharacteristic
36C2×#13094023C2212yes—
37C2×#13094023C2212yes—
38C2×#13094023C2214yes—
39C2×#13094022C2212yes—
40C2×#13094022C2214yes—
41#15689657C22116yes—
42C2×#13094019C2214yes—
43C2×#13094019C2214yes—
44C2×#13094019C2214yes—
45C2×#13094018C2212yes—
46C2×#13094018C2214yes—
47C2×#13094017C2214yes—
48C2×#13094017C2214yes—
49C2×#13094016C2214yes—
50C2×#13094016C2211yescharacteristic
51C2×#13094016C2212yes—
52C2×#13094015C2212yes—
53C2×#13094015C2212yes—
54C2×#13094015C2214yes—
55C2×#13094015C2214yes—
56C2×#13094014C2214yes—
57C2×#13094014C2214yes—
58C2×#13094013C2212yes—
59C2×#13094012C2211yescharacteristic
60C2×#13094010C2214yes—
61C2×#13094007C2212yes—
62C2×#13094006C2214yes—
63C2×#13094004C2214yes—
64C2×#13094004C2212yes—
65C2×#13094004C2212yes—
66C2×#13094003C2211yescharacteristic
67C2×#13094003C2211yescharacteristic
68C2×#13094003C2211yescharacteristic
69C2×#13094003C2212yes—
70C2×#13094002C2214yes—
71C2×#13094000C2214yes—
72C2×#13093998C2211yescharacteristic
73C2×Q8×Dic47C2212yes—
74C2×Q8×Dic47C2212yes—
75C2×C4×Dic94C2211yescharacteristic
76C2×C4×Dic94C2211yescharacteristic
77C2×C4×Dic94C2214yes—
78C2×C4×Dic94C2212yes—
79C2×C4×Dic94C2211yescharacteristic
80C2×#13093989C2212yes—
81C2×#13093989C2212yes—
82C2×#13093989C2212yes—
83C2×C4×D188C2211yescharacteristic
84C2×#13093986C2212yes—
85C2×C4×C22⋊D47C2212yes—
86C2×#13093983C2212yes—
87C2×#13093982C2212yes—
88C2×#13093981C2212yes—
89C2×#13093981C2214yes—
90C2×C4⋊C4×D47C2212yes—
91C47×#533C22116yescomplemented
92C2×C4⋊Q8×C47C2211yescharacteristic
93C2×C4⋊Q8×C47C2211yescharacteristic
94C2×#125×C47C2212yes—
95C2×C22⋊Q8×C47C2212yes—
96C2×C22⋊Q8×C47C2212yes—
97C2×C4×Q8×C47C2212yes—
98C2×C4×Q8×C47C2212yes—
99C2×#117×C47C2212yes—
100C22×C42×C47C2211yescharacteristic
101C22×Dic94C2311yescharacteristic
102C22×Dic94C2311yescharacteristic
103C22×Dic94C2311yescharacteristic
104C22×Dic94C2312yes—
105C22×Dic94C2314yes—
106C22×D188C2311yescharacteristic
107C22×C22⋊D47C2312yes—
108C22×C4×D47C2312yes—
109C22×C4×D47C2314yes—
110#13094024C2318yes—
111#13094024C2318yes—
112#13094023C23116yes—
113#13094023C23116yes—
114#13094023C23132yes—
115#13094022C23132yes—
116#13094022C23116yes—
117#13094019C23132yes—
118#13094019C23132yes—
119#13094019C23132yes—
120#13094018C23116yes—
121#13094018C23132yes—
122#13094017C23132yes—
123#13094017C23132yes—
124#13094016C23116yes—
125#13094016C23132yes—
126#13094016C2318yes—
127#13094015C23132yes—
128#13094015C23116yes—
129#13094015C23132yes—
130#13094015C23116yes—
131#13094014C23132yes—
132#13094014C23132yes—
133#13094013C23116yes—
134#13094012C2318yes—
135#13094010C23132yes—
136#13094007C23116yes—
137#13094006C23132yes—
138#13094004C23132yes—
139#13094004C23116yes—
140#13094004C23116yes—
141#13094003C2318yes—
142#13094003C2318yes—
143#13094003C2318yes—
144#13094003C23116yes—
145#13094002C23132yes—
146#13094000C23132yes—
147#13093998C2318yes—
148Q8×Dic47C23116yes—
149Q8×Dic47C23116yes—
150C4×Dic94C23132yes—
151C4×Dic94C2318yes—
152C4×Dic94C23116yes—
153C4×Dic94C2318yes—
154C4×Dic94C2318yes—
155#13093989C23116yes—
156#13093989C23116yes—
157#13093989C23116yes—
158C4×D188C2318yes—
159#13093986C23116yes—
160C4×C22⋊D47C23116yes—
161#13093983C23116yes—
162#13093982C23116yes—
163#13093981C23132yes—
164#13093981C23116yes—
165C2×C4⋊Dic47C2311yescharacteristic
166C2×C4⋊Dic47C2311yescharacteristic
167C2×C4⋊Dic47C2312yes—
168C2×C4⋊Dic47C2312yes—
169C2×C4⋊Dic47C2311yescharacteristic
170C2×C4⋊Dic47C2311yescharacteristic
171C2×C4⋊Dic47C2314yes—
172C2×C4⋊Dic47C2312yes—
173C2×C4⋊Dic47C2314yes—
174C2×C4⋊Dic47C2314yes—
175C2×Dic47⋊C4C2314yes—
176C2×Dic47⋊C4C2312yes—
177C2×Dic47⋊C4C2314yes—
178C2×Dic47⋊C4C2312yes—
179C2×Dic47⋊C4C2312yes—
180C2×Dic47⋊C4C2312yes—
181C2×Dic47⋊C4C2314yes—
182C2×Dic47⋊C4C2314yes—
183C2×Dic47⋊C4C2314yes—
184C2×Dic47⋊C4C2312yes—
185C2×Dic47⋊C4C2312yes—
186C2×Dic47⋊C4C2312yes—
187C2×Dic47⋊C4C2312yes—
188C4⋊C4×D47C23116yes—
189C2×C22⋊Dic47C2312yes—
190C2×C22⋊Dic47C2312yes—
191C2×C22⋊Dic47C2312yes—
192C2×(C2×D47)⋊C4C2312yes—
193C2×(C2×D47)⋊C4C2312yes—
194C2×(C2×D47)⋊C4C2312yes—
195C2×(C2×D47)⋊C4C2314yes—
196C2×(C2×D47)⋊C4C2314yes—
197C2×(C2×D47)⋊C4C2314yes—
198C2×(C2×D47)⋊C4C2312yes—
199C2×C4×Dic47C2312yes—
200C2×C4×Dic47C2314yes—
201C2×C4×Dic47C2314yes—
202C2×C4×Dic47C2312yes—
203C2×C4×Dic47C2312yes—
204C2×C4×Dic47C2314yes—
205C22×Q8×C47C2312yes—
206C22×Q8×C47C2312yes—
207C23×C4×C47C2311yescharacteristic
208C23×C4×C47C2311yescharacteristic
209C23×C4×C47C2311yescharacteristic
210C4⋊Q8×C47C2318yes—
211C4⋊Q8×C47C2318yes—
212#125×C47C23116yes—
213C22⋊Q8×C47C23116yes—
214C22⋊Q8×C47C23116yes—
215C4×Q8×C47C23116yes—
216C4×Q8×C47C23116yes—
217#117×C47C23116yes—
218C2×C4⋊C4×C47C2312yes—
219C2×C4⋊C4×C47C2312yes—
220C2×C4⋊C4×C47C2314yes—
221C2×C4⋊C4×C47C2314yes—
222C2×C4⋊C4×C47C2312yes—
223C2×C4⋊C4×C47C2312yes—
224C2×C22⋊C4×C47C2314yes—
225C2×C42×C47C2311yescharacteristic
226C2×C42×C47C2311yescharacteristic
227C2×C42×C47C2311yescharacteristic
228C2×C42×C47C2311yescharacteristic
229C2×C42×C47C2318yes—
230C2×C42×C47C2314yes—
231C24×C47C2411yescharacteristic
232C23×D47C2412yes—
233C2×Q8×C47—28no—
234C2×Q8×C47—44no—
235C2×Q8×C47C2418yes—
236C2×Q8×C47C2418yes—
237C22×C4×C47—24no—
238C22×C4×C47—24no—
239C22×C4×C47—42no—
240C22×C4×C47C2411yescharacteristic
241C22×C4×C47C2411yescharacteristic
242C22×C4×C47C2411yescharacteristic
243C22×C4×C47C2411yescharacteristic
244C22×C4×C47C2414yes—
245C22×C4×C47C2414yes—
246C22×C4×C47C2414yes—
247C22×C4×C47C2414yes—
248C22×C4×C47C2414yes—
249C22×C4×C47C2411yescharacteristic
250C22×C4×C47C2411yescharacteristic
251C2×C22⋊D47—44no—
252C2×C22⋊D47C2418yes—
253C22×Dic47C2412yes—
254C22×Dic47C2412yes—
255C22×Dic47C2412yes—
256C22×Dic47C2412yes—
257C22×Dic47C2412yes—
258C22×Dic47C2412yes—
259C22×Dic47C2412yes—
260C2×D188—24no—
261C2×D188C2414yes—
262C2×C4×D47—28no—
263C2×C4×D47—48no—
264C2×C4×D47C2418yes—
265C2×C4×D47C24116yes—
266C2×Dic94—24no—
267C2×Dic94—24no—
268C2×Dic94—24no—
269C2×Dic94—48no—
270C2×Dic94—44no—
271C2×Dic94C2414yes—
272C2×Dic94C2414yes—
273C2×Dic94C2414yes—
274C2×Dic94C2418yes—
275C2×Dic94C24116yes—
276C4⋊C4×C47C2418yes—
277C4⋊C4×C47C2418yes—
278C4⋊C4×C47C24116yes—
279C4⋊C4×C47C24116yes—
280C4⋊C4×C47C2418yes—
281C4⋊C4×C47C2418yes—
282C22⋊C4×C47C24116yes—
283C42×C47C2414yes—
284C42×C47C2414yes—
285C42×C47C2414yes—
286C42×C47C2414yes—
287C42×C47C24116yes—
288C22⋊Dic47C2418yes—
289C22⋊Dic47C2418yes—
290C22⋊Dic47C2418yes—
291(C2×D47)⋊C4C2418yes—
292(C2×D47)⋊C4C2418yes—
293(C2×D47)⋊C4C2418yes—
294(C2×D47)⋊C4C24116yes—
295(C2×D47)⋊C4C24116yes—
296(C2×D47)⋊C4C24116yes—
297(C2×D47)⋊C4C2418yes—
298C4⋊Dic47C2414yes—
299C4⋊Dic47C2414yes—
300C4⋊Dic47C2418yes—
301C4⋊Dic47C2418yes—
302C4⋊Dic47C2414yes—
303C4⋊Dic47C2414yes—
304C4⋊Dic47C24116yes—
305C4⋊Dic47C2418yes—
306C4⋊Dic47C24116yes—
307C4⋊Dic47C24116yes—
308Dic47⋊C4C24116yes—
309Dic47⋊C4C2418yes—
310Dic47⋊C4C24116yes—
311Dic47⋊C4C2418yes—
312Dic47⋊C4C2418yes—
313Dic47⋊C4C2418yes—
314Dic47⋊C4C24116yes—
315Dic47⋊C4C24116yes—
316Dic47⋊C4C24116yes—
317Dic47⋊C4C2418yes—
318Dic47⋊C4C2418yes—
319Dic47⋊C4C2418yes—
320Dic47⋊C4C2418yes—
321C4×Dic47C2418yes—
322C4×Dic47C24116yes—
323C4×Dic47C24116yes—
324C4×Dic47C2418yes—
325C4×Dic47C2418yes—
326C4×Dic47C24116yes—
327C23×C47—22no—
328C23×C47—22no—
329C23×C47—22no—
330C23×C47C2512yes—
331C23×C47C2511yescharacteristic
332C22×D47—24no—
333C22×D47—24no—
334C22×D47—24no—
335C22×D47C2514yes—
336Q8×C47—216no—
337Q8×C47—48no—
338C2×C4×C47—22no—
339C2×C4×C47—22no—
340C2×C4×C47—28no—
341C2×C4×C47—22no—
342C2×C4×C47—28no—
343C2×C4×C47—22no—
344C2×C4×C47—28no—
345C2×C4×C47—28no—
346C2×C4×C47—44no—
347C2×C4×C472−1+414yes—
348C2×C4×C472−1+414yes—
349C2×C4×C47C2518yes—
350C2×C4×C47C2518yes—
351C2×C4×C47C2512yes—
352C2×C4×C47C2512yes—
353C2×C4×C47C2512yes—
354C2×C4×C47C2512yes—
355C2×C4×C47C2512yes—
356C2×C4×C47C2512yes—
357C22⋊D47—48no—
358C2×Dic47—24no—
359C2×Dic47—24no—
360C2×Dic47—24no—
361C2×Dic47—24no—
362C2×Dic47—24no—
363C2×Dic47—24no—
364C2×Dic47—24no—
365C2×Dic47C2514yes—
366C2×Dic47C2514yes—
367C2×Dic47C2514yes—
368C2×Dic47C2514yes—
369C2×Dic47C2514yes—
370C2×Dic47C2514yes—
371C2×Dic47C2514yes—
372D188—28no—
373C4×D47—216no—
374C4×D47—416no—
375Dic94—28no—
376Dic94—28no—
377Dic94—28no—
378Dic94—416no—
379Dic94—48no—
380C2×#3555—471nomaximal, Sylow
381C22×C47—22no—
382C22×C47—22no—
383C22×C47—22no—
384C22×C47—44no—
385C22×C47C2×2−1+412yes—
386C22×C47C2×2−1+412yes—
387C22×C47#58512yes—
388C22×C47C2611yescharacteristic
389C2×D47—24no—
390C2×D47—24no—
391C2×D47—24no—
392C2×D47—48no—
393C4×C47—22no—
394C4×C47—22no—
395C4×C47—28no—
396C4×C47—22no—
397C4×C47—28no—
398C4×C47—22no—
399C4×C47C2×2−1+414yes—
400C4×C47C2×2−1+414yes—
401Dic47—24no—
402Dic47—24no—
403Dic47—24no—
404Dic47—24no—
405Dic47—24no—
406Dic47—24no—
407Dic47—24no—
408#3555—4732no—
409C2×#563—474no—
410C2×Q82—471no—
411C2×#557—471no—
412C2×#557—472no—
413C2×#556—471no—
414C2×#556—472no—
415C2×#556—472no—
416C2×#554—471no—
417C2×#552—472no—
418C2×#544—472no—
419C2×#542—472no—
420C2×#541—472no—
421C2×#541—472no—
422C2×#541—474no—
423C2×#533—471no—
424C2×#533D4711yescharacteristic, complemented
425C2×#529—471no—
426C2×C47—42no—
427C2×C47#355514yescomplemented
428C2×C47C22×2−1+411yescharacteristic
429C2×C47C22×2−1+411yescharacteristic
430C2×C47C2×#58511yescharacteristic
431D47—44no—
432#563—4764no—
433Q82—4716no—
434#557—4716no—
435#557—4732no—
436#556—4716no—
437#556—4732no—
438#556—4732no—
439#554—4716no—
440#552—4732no—
441#544—4732no—
442#542—4732no—
443#541—4732no—
444#541—4732no—
445#541—4764no—
446#533—4716no—
447#533C2×D47116yescomplemented
448C2×C4⋊Q8—472no—
449C2×C4⋊Q8—474no—
450C2×C4⋊Q8—472no—
451C2×C4⋊Q8—472no—
452C2×C4⋊Q8—474no—
453C2×C4⋊Q8—471no—
454C2×C4⋊Q8—471no—
455C2×C4⋊Q8C2×D4711yescharacteristic
456C2×C4⋊Q8C2×D4711yescharacteristic
457#529—4716no—
458C2×#126—474no—
459C2×#126—474no—
460C2×#126—474no—
461C2×#126—474no—
462C2×#126—474no—
463C2×#126—472no—
464C2×#126—474no—
465C2×#125—474no—
466C2×#125—474no—
467C2×#125—472no—
468C2×#125—474no—
469C2×#125—474no—
470C2×#125—472no—
471C2×#125—471no—
472C2×#125—472no—
473C2×#125—474no—
474C2×#125C2×D4712yes—
475C2×#124—472no—
476C2×#124—474no—
477C2×#124—471no—
478C2×#123—472no—
479C2×#123—474no—
480C2×C22⋊Q8—474no—
481C2×C22⋊Q8—471no—
482C2×C22⋊Q8—471no—
483C2×C22⋊Q8—471no—
484C2×C22⋊Q8—472no—
485C2×C22⋊Q8—474no—
486C2×C22⋊Q8—472no—
487C2×C22⋊Q8—472no—
488C2×C22⋊Q8—474no—
489C2×C22⋊Q8C2×D4712yes—
490C2×C22⋊Q8C2×D4712yes—
491C2×#121—471no—
492C2×C4×Q8—472no—
493C2×C4×Q8—472no—
494C2×C4×Q8—472no—
495C2×C4×Q8—472no—
496C2×C4×Q8—472no—
497C2×C4×Q8—471no—
498C2×C4×Q8—471no—
499C2×C4×Q8—472no—
500C2×C4×Q8—471no—
501C2×C4×Q8—474no—
502C2×C4×Q8C2×D4712yes—
503C2×C4×Q8C2×D4712yes—
504C2×C4×D4—472no—
505C2×C4×D4—472no—
506C2×C4×D4—471no—
507C2×#117—472no—
508C2×#117—472no—
509C2×#117—472no—
510C2×#117—474no—
511C2×#117C2×D4712yes—
512C22×C4⋊C4—472no—
513C22×C42C2×D4711yescharacteristic
514C47C2×#355511yescharacteristic, complemented, Sylow
515C22×Q8—471no—
516C22×Q8—471no—
517C22×Q8—471no—
518C22×Q8—472no—
519C22×Q8—474no—
520C22×Q8C22×D4712yes—
521C22×Q8C22×D4712yes—
522C22×D4—472no—
523C22×D4—471no—
524C23×C4—472no—
525C23×C4—474no—
526C23×C4C22×D4711yescharacteristic
527C23×C4C22×D4711yescharacteristic
528C23×C4C22×D4711yescharacteristic
529C4⋊Q8—4716no—
530C4⋊Q8—4732no—
531C4⋊Q8—4716no—
532C4⋊Q8—4716no—
533C4⋊Q8—4732no—
534C4⋊Q8—478no—
535C4⋊Q8—478no—
536C4⋊Q8C22×D4718yes—
537C4⋊Q8C22×D4718yes—
538#126—4732no—
539#126—4732no—
540#126—4732no—
541#126—4732no—
542#126—4732no—
543#126—4716no—
544#126—4732no—
545#125—4732no—
546#125—4732no—
547#125—4716no—
548#125—4732no—
549#125—4732no—
550#125—4716no—
551#125—478no—
552#125—4716no—
553#125—4732no—
554#125C22×D47116yes—
555#124—4716no—
556#124—4732no—
557#124—478no—
558#123—4716no—
559#123—4732no—
560C22⋊Q8—4732no—
561C22⋊Q8—478no—
562C22⋊Q8—478no—
563C22⋊Q8—478no—
564C22⋊Q8—4716no—
565C22⋊Q8—4732no—
566C22⋊Q8—4716no—
567C22⋊Q8—4716no—
568C22⋊Q8—4732no—
569C22⋊Q8C22×D47116yes—
570C22⋊Q8C22×D47116yes—
571#121—478no—
572C4×Q8—4716no—
573C4×Q8—4716no—
574C4×Q8—4716no—
575C4×Q8—4716no—
576C4×Q8—4716no—
577C4×Q8—478no—
578C4×Q8—478no—
579C4×Q8—4716no—
580C4×Q8—478no—
581C4×Q8—4732no—
582C4×Q8C22×D47116yes—
583C4×Q8C22×D47116yes—
584C4×D4—4716no—
585C4×D4—4716no—
586C4×D4—478no—
587#117—4716no—
588#117—4716no—
589#117—4716no—
590#117—4732no—
591#117C22×D47116yes—
592C2×C4⋊C4—471no—
593C2×C4⋊C4—474no—
594C2×C4⋊C4—472no—
595C2×C4⋊C4—471no—
596C2×C4⋊C4—472no—
597C2×C4⋊C4—472no—
598C2×C4⋊C4—474no—
599C2×C4⋊C4—472no—
600C2×C4⋊C4—472no—
601C2×C4⋊C4—471no—
602C2×C4⋊C4—472no—
603C2×C4⋊C4—471no—
604C2×C4⋊C4—472no—
605C2×C4⋊C4—472no—
606C2×C4⋊C4—474no—
607C2×C4⋊C4—474no—
608C2×C4⋊C4—474no—
609C2×C4⋊C4—472no—
610C2×C4⋊C4—474no—
611C2×C4⋊C4—472no—
612C2×C4⋊C4—474no—
613C2×C4⋊C4—472no—
614C2×C4⋊C4—474no—
615C2×C4⋊C4—4716no—
616C2×C4⋊C4C22×D4712yes—
617C2×C4⋊C4C22×D4712yes—
618C2×C4⋊C4C22×D4712yes—
619C2×C4⋊C4C22×D4714yes—
620C2×C4⋊C4C22×D4714yes—
621C2×C4⋊C4C22×D4712yes—
622C2×C22⋊C4—472no—
623C2×C22⋊C4—472no—
624C2×C22⋊C4—472no—
625C2×C22⋊C4—472no—
626C2×C22⋊C4—472no—
627C2×C22⋊C4—472no—
628C2×C22⋊C4—474no—
629C2×C22⋊C4—474no—
630C2×C22⋊C4—472no—
631C2×C22⋊C4—474no—
632C2×C22⋊C4C22×D4714yes—
633C2×C42—472no—
634C2×C42—472no—
635C2×C42—472no—
636C2×C42—474no—
637C2×C42—474no—
638C2×C42—474no—
639C2×C42C22×D4711yescharacteristic
640C2×C42C22×D4714yes—
641C2×C42C22×D4711yescharacteristic
642C2×C42C22×D4711yescharacteristic
643C2×C42C22×D4711yescharacteristic
644C2×C42C22×D4718yes—
645C24—472no—
646C24C23×D4711yescharacteristic
647C2×Q8—28no—
648C2×Q8—44no—
649C2×Q8—474no—
650C2×Q8—474no—
651C2×Q8—474no—
652C2×Q8—478no—
653C2×Q8—4716no—
654C2×Q8—944no—
655C2×Q8—944no—
656C2×Q8—944no—
657C2×Q8—1884no—
658C2×Q8—1888no—
659C2×Q8C23×D4718yes—
660C2×Q8C23×D4718yes—
661C2×D4—478no—
662C2×D4—474no—
663C2×D4—944no—
664C2×D4—1884no—
665C22×C4—24no—
666C22×C4—24no—
667C22×C4—42no—
668C22×C4—472no—
669C22×C4—472no—
670C22×C4—472no—
671C22×C4—472no—
672C22×C4—472no—
673C22×C4—472no—
674C22×C4—472no—
675C22×C4—478no—
676C22×C4—4716no—
677C22×C4—948no—
678C22×C4—1888no—
679C22×C4C23×D4714yes—
680C22×C4C23×D4714yes—
681C22×C4C23×D4714yes—
682C22×C4C23×D4714yes—
683C22×C4C23×D4711yescharacteristic
684C22×C4C23×D4711yescharacteristic
685C22×C4C23×D4711yescharacteristic
686C22×C4C23×D4711yescharacteristic
687C22×C4C23×D4714yes—
688C22×C4C23×D4711yescharacteristic
689C22×C4C23×D4711yescharacteristic
690C4⋊C4—4716no—
691C4⋊C4—478no—
692C4⋊C4—478no—
693C4⋊C4—4716no—
694C4⋊C4—478no—
695C4⋊C4—478no—
696C4⋊C4—478no—
697C4⋊C4—478no—
698C4⋊C4—4716no—
699C4⋊C4—478no—
700C4⋊C4—4716no—
701C4⋊C4—478no—
702C4⋊C4—4716no—
703C4⋊C4—474no—
704C4⋊C4—474no—
705C4⋊C4—478no—
706C4⋊C4—478no—
707C4⋊C4—474no—
708C4⋊C4—474no—
709C4⋊C4—4716no—
710C4⋊C4—4716no—
711C4⋊C4—4716no—
712C4⋊C4—478no—
713C4⋊C4C23×D4718yes—
714C4⋊C4C23×D4718yes—
715C4⋊C4C23×D4718yes—
716C4⋊C4C23×D47116yes—
717C4⋊C4C23×D47116yes—
718C4⋊C4C23×D4718yes—
719C22⋊C4—478no—
720C22⋊C4—478no—
721C22⋊C4—478no—
722C22⋊C4—478no—
723C22⋊C4—478no—
724C22⋊C4—478no—
725C22⋊C4—4716no—
726C22⋊C4—4716no—
727C22⋊C4—478no—
728C22⋊C4—4716no—
729C22⋊C4C23×D47116yes—
730C42—478no—
731C42—478no—
732C42—478no—
733C42—4716no—
734C42—4716no—
735C42—4716no—
736C42C23×D4714yes—
737C42C23×D4714yes—
738C42C23×D4714yes—
739C42C23×D4714yes—
740C42C23×D47116yes—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—474no—
745C23—944no—
746C23—944no—
747C23—944no—
748C23C24×D4712yes—
749C23C24×D4711yescharacteristic
750Q8—216no—
751Q8—48no—
752Q8—948no—
753Q8—948no—
754Q8—948no—
755Q8—1888no—
756Q8—18816no—
757D4—948no—
758D4—1888no—
759C2×C4—22no—
760C2×C4—28no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—28no—
765C2×C4—28no—
766C2×C4—28no—
767C2×C4—44no—
768C2×C4—474no—
769C2×C4—474no—
770C2×C4—474no—
771C2×C4—474no—
772C2×C4—474no—
773C2×C4—474no—
774C2×C4—474no—
775C2×C4—944no—
776C2×C4—944no—
777C2×C4—944no—
778C2×C4—944no—
779C2×C4—944no—
780C2×C4—944no—
781C2×C4—944no—
782C2×C4—9416no—
783C2×C4—18816no—
784C2×C4#1309407114yes—
785C2×C4#1309407214yes—
786C2×C4C24×D4718yes—
787C2×C4C24×D4718yes—
788C2×C4C24×D4712yes—
789C2×C4C24×D4712yes—
790C2×C4C24×D4712yes—
791C2×C4C24×D4712yes—
792C2×C4C24×D4712yes—
793C2×C4C24×D4712yes—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—44no—
798C22—944no—
799C22—944no—
800C22—944no—
801C22—1888no—
802C22C2×#1309407112yes—
803C22C2×#1309407212yes—
804C22#1568995912yes—
805C22C25×D4711yescharacteristic
806C4—22no—
807C4—28no—
808C4—22no—
809C4—22no—
810C4—22no—
811C4—28no—
812C4—944no—
813C4—944no—
814C4—944no—
815C4—944no—
816C4—944no—
817C4—944no—
818C4—944no—
819C4C2×#1309407114yes—
820C4C2×#1309407214yes—
821C2—42no—
822C2—1884no—
823C2#2025787014yesdirect product factor
824C2C22×#1309407111yescharacteristic
825C2C22×#1309407211yescharacteristic
826C2C2×#1568995911yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#533C2
socleC23×C47C25
prime radicalC2×#13093998C22
hypercenterC2×#533D47
hypocenterC47C2×#3555
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #20257870C2direct (N × H)
2. C2×#15689874C2semidirect
3. C2×#15689853C2semidirect
4. C2×#15689849C2semidirect
5. C2×#15689848C2semidirect
6. C2×#15689847C2semidirect
7. C2×#15689845C2semidirect
8. C2×#15689841C2semidirect
9. C2×#15689834C2semidirect
10. C2×#15689812C2semidirect
11. C2×#15689753C2semidirect
13. C2×#15689736C2semidirect
14. C2×#15689733C2semidirect
15. C2×#15689731C2semidirect
16. C2×#15689680C2semidirect
18. C2×C47×#533C2semidirect
19. #15689874C22semidirect
20. #15689853C22semidirect
21. #15689849C22semidirect
22. #15689848C22semidirect
23. #15689847C22semidirect
24. #15689845C22semidirect
25. #15689841C22semidirect
26. #15689834C22semidirect
27. #15689812C22semidirect
28. #15689753C22semidirect
30. #15689736C22semidirect
31. #15689733C22semidirect
32. #15689731C22semidirect
33. #15689680C22semidirect
91. C47×#533C22semidirect
424. C2×#533D47semidirect
427. C2×C47#3555semidirect
447. #533C2×D47semidirect
514. C47C2×#3555semidirect
823. C2#20257870direct (N × H)

Maximal subgroups

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

subgroupindex
#202578702
C2×#156898742
C2×#156898532
C2×#156898492
C2×#156898482
C2×#156898472
C2×#156898452
C2×#156898412
C2×#156898342
C2×#156898122
C2×#156897532
C2×#156897462
C2×#156897362
C2×#156897332
C2×#156897312
C2×#156896802
C2×#156896572
C2×C47×#5332
C2×#355547