Finite Group Databasebeta

← C2×#20257251 #27124355

Subgroups — C2×#20257251 #27124355

Order 12032.

7130 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257251C2132yesmaximal, direct product factor
2C2×#15689856C212yesmaximal, complemented
3C2×#15689850C212yesmaximal, complemented
4C2×#15689846C211yesmaximal, characteristic, complemented
5C2×#15689844C214yesmaximal, complemented
6C2×#15689843C211yesmaximal, characteristic, complemented
7C2×#15689834C211yesmaximal, characteristic, complemented
8C2×#15689808C212yesmaximal, complemented
9C2×#15689807C212yesmaximal, complemented
10C2×#15689719C214yesmaximal, complemented
11C2×#15689696C212yesmaximal, complemented
12C2×#15689678C211yesmaximal, characteristic, complemented
13C2×#15689670C211yesmaximal, characteristic
14C2×#15689658C212yesmaximal, complemented
15C2×#15689655C212yesmaximal, complemented
16C2×#15689604C212yesmaximal, complemented
17C2×C4×Q8×D47C211yesmaximal, characteristic, complemented
18C2×C47×#554C211yesmaximal, characteristic, complemented
19C22×#10625350C2212yes—
20C22×Q8×D47C2211yescharacteristic
21#15689856C22132yescomplemented
22#15689850C22132yescomplemented
23#15689846C22116yescomplemented
24#15689844C22164yescomplemented
25#15689843C22116yescomplemented
26#15689834C22116yescomplemented
27#15689808C22132yescomplemented
28#15689807C22132yescomplemented
29#15689719C22164yescomplemented
30#15689696C22132yescomplemented
31#15689678C22116yescomplemented
32#15689670C22116yes—
33C2×#13094024C2211yescharacteristic
34C2×#13094023C2211yescharacteristic
35C2×#13094023C2214yes—
36C2×#13094020C2211yescharacteristic
37#15689658C22132yescomplemented
38#15689655C22132yescomplemented
39C2×#13094019C2214yes—
40C2×#13094019C2214yes—
41C2×#13094017C2214yes—
42C2×#13094017C2214yes—
43C2×#13094015C2212yes—
44C2×#13094015C2212yes—
45C2×#13094014C2214yes—
46C2×#13094014C2214yes—
47C2×#13094012C2212yes—
48C2×#13094011C2212yes—
49C2×#13094010C2212yes—
50C2×#13094010C2214yes—
51C2×#13094009C2214yes—
52C2×#13094007C2214yes—
53C2×#13094006C2214yes—
54C2×#13094006C2214yes—
55C2×#13094004C2212yes—
56C2×#13094004C2212yes—
57C2×#13094003C2212yes—
58C2×#13094000C2212yes—
59C2×#13094000C2214yes—
60C2×#13094000C2212yes—
61C2×#13093999C2211yescharacteristic
62C2×#13093997C2212yes—
63C2×#13093995C2211yescharacteristic
64#15689604C22132yescomplemented
65C2×Q8×Dic47C2211yescharacteristic
66C2×Q8×Dic47C2212yes—
67C2×C4×Dic94C2211yescharacteristic
68C2×C4×Dic94C2212yes—
69C2×C4×Dic94C2212yes—
70C2×#13093989C2211yescharacteristic
71C2×#13093989C2212yes—
72C2×#13093989C2214yes—
73C2×#13093989C2212yes—
74C2×#13093989C2212yes—
75C4×Q8×D47C22116yescomplemented
76C2×C4×D188C2211yescharacteristic
77C2×#13093986C2214yes—
78C2×#13093986C2212yes—
79C2×C4×C22⋊D47C2214yes—
80C2×C4×C22⋊D47C2214yes—
81C2×C4×C22⋊D47C2212yes—
82C2×#13093983C2212yes—
83C2×#13093983C2214yes—
84C2×#13093982C2212yes—
85C2×#13093982C2212yes—
86C2×#13093982C2214yes—
87C2×C4⋊C4×D47C2211yescharacteristic
88C2×C4⋊C4×D47C2212yes—
89C2×C4⋊C4×D47C2212yes—
90C2×C42×D47C2212yes—
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×C47C2212yes—
99C2×C4×D4×C47C2211yescharacteristic
100C22×C4⋊C4×C47C2212yes—
101C2×#10625350—216no—
102C2×#10625350C23116yes—
103C22×Dic94C2312yes—
104C22×Dic94C2312yes—
105C22×Dic94C2311yescharacteristic
106C22×Dic94C2312yes—
107C2×Q8×D47—28no—
108C2×Q8×D47C2318yes—
109C22×D188C2311yescharacteristic
110C22×D188C2312yes—
111C22×C22⋊D47C2312yes—
112C22×C22⋊D47C2312yes—
113C22×C22⋊D47C2312yes—
114C22×C4×D47C2311yescharacteristic
115C22×C4×D47C2312yes—
116C22×C4×D47C2312yes—
117C22×C4×D47C2312yes—
118C22×C4×D47C2311yescharacteristic
119C22×C4×D47C2314yes—
120C22×C4×D47C2311yescharacteristic
121#13094024C2318yes—
122#13094023C23132yes—
123#13094023C2318yes—
124#13094020C2318yes—
125#13094019C23132yes—
126#13094019C23132yes—
127#13094017C23132yes—
128#13094017C23132yes—
129#13094015C23116yes—
130#13094015C23116yes—
131#13094014C23132yes—
132#13094014C23132yes—
133#13094012C23116yes—
134#13094011C23116yes—
135#13094010C23116yes—
136#13094010C23132yes—
137#13094009C23132yes—
138#13094007C23132yes—
139#13094006C23132yes—
140#13094006C23132yes—
141#13094004C23116yes—
142#13094004C23116yes—
143#13094003C23116yes—
144#13094000C23116yes—
145#13094000C23132yes—
146#13094000C23116yes—
147#13093999C2318yes—
148#13093997C23116yes—
149#13093995C2318yes—
150Q8×Dic47C2318yes—
151Q8×Dic47C23116yes—
152C4×Dic94C2318yes—
153C4×Dic94C23116yes—
154C4×Dic94C23116yes—
155#13093989C2318yes—
156#13093989C23116yes—
157#13093989C23116yes—
158#13093989C23132yes—
159#13093989C23116yes—
160C4×D188C2318yes—
161#13093986C23116yes—
162#13093986C23132yes—
163C4×C22⋊D47C23116yes—
164C4×C22⋊D47C23132yes—
165C4×C22⋊D47C23132yes—
166#13093983C23116yes—
167#13093983C23132yes—
168#13093982C23132yes—
169#13093982C23116yes—
170#13093982C23116yes—
171C2×C4⋊Dic47C2311yescharacteristic
172C2×C4⋊Dic47C2312yes—
173C2×C4⋊Dic47C2312yes—
174C2×C4⋊Dic47C2314yes—
175C2×C4⋊Dic47C2314yes—
176C2×C4⋊Dic47C2311yescharacteristic
177C2×C4⋊Dic47C2312yes—
178C2×Dic47⋊C4C2312yes—
179C2×Dic47⋊C4C2314yes—
180C2×Dic47⋊C4C2312yes—
181C2×Dic47⋊C4C2312yes—
182C2×Dic47⋊C4C2312yes—
183C2×Dic47⋊C4C2314yes—
184C2×Dic47⋊C4C2314yes—
185C2×Dic47⋊C4C2314yes—
186C4⋊C4×D47C23116yes—
187C4⋊C4×D47C2318yes—
188C4⋊C4×D47C23116yes—
189C2×C22⋊Dic47C2312yes—
190C2×C22⋊Dic47C2314yes—
191C2×C22⋊Dic47C2314yes—
192C2×(C2×D47)⋊C4C2312yes—
193C2×(C2×D47)⋊C4C2314yes—
194C2×(C2×D47)⋊C4C2314yes—
195C2×(C2×D47)⋊C4C2314yes—
196C2×(C2×D47)⋊C4C2314yes—
197C2×(C2×D47)⋊C4C2312yes—
198C2×C4×Dic47C2312yes—
199C2×C4×Dic47C2312yes—
200C2×C4×Dic47C2311yescharacteristic
201C2×C4×Dic47C2312yes—
202C2×C4×Dic47C2311yescharacteristic
203C2×C4×Dic47C2311yescharacteristic
204C2×C4×Dic47C2314yes—
205C2×C4×Dic47C2314yes—
206C2×C4×Dic47C2314yes—
207C42×D47C23116yes—
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×C47C2312yes—
230C2×C22⋊C4×C47C2314yes—
231C2×C42×C47C2312yes—
232C2×C42×C47C2311yescharacteristic
233C24×C47C2412yes—
234C23×D47C2412yes—
235C23×D47C2411yescharacteristic
236C2×Q8×C47—24no—
237C2×Q8×C47—44no—
238C2×Q8×C47C2414yes—
239C2×Q8×C47C2418yes—
240C2×D4×C47—24no—
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—28no—
255C2×C22⋊D47—44no—
256C2×C22⋊D47C2418yes—
257C2×C22⋊D47C2418yes—
258C2×C22⋊D47C2418yes—
259C22×Dic47C2411yescharacteristic
260C22×Dic47C2412yes—
261C22×Dic47C2414yes—
262C22×Dic47C2412yes—
263C22×Dic47C2412yes—
264C22×Dic47C2411yescharacteristic
265C22×Dic47C2411yescharacteristic
266Q8×D47—232no—
267#10625350—264no—
268C2×D188—28no—
269C2×D188—24no—
270C2×D188C2414yes—
271C2×D188C2418yes—
272C2×C4×D47—28no—
273C2×C4×D47—28no—
274C2×C4×D47—24no—
275C2×C4×D47—44no—
276C2×C4×D47—48no—
277C2×C4×D47—42no—
278C2×C4×D47#4118yes—
279C2×C4×D47C2414yes—
280C2×C4×D47C2418yes—
281C2×C4×D47C2418yes—
282C2×C4×D47C2418yes—
283C2×C4×D47C2414yes—
284C2×C4×D47C24116yes—
285C2×C4×D47C2414yes—
286C2×Dic94—24no—
287C2×Dic94—28no—
288C2×Dic94—28no—
289C2×Dic94—28no—
290C2×Dic94C2418yes—
291C2×Dic94C2418yes—
292C2×Dic94C2414yes—
293C2×Dic94C2418yes—
294C4⋊C4×C47C2414yes—
295C4⋊C4×C47C24116yes—
296C4⋊C4×C47C2418yes—
297C4⋊C4×C47C2414yes—
298C4⋊C4×C47C2418yes—
299C4⋊C4×C47C2418yes—
300C4⋊C4×C47C24116yes—
301C22⋊C4×C47C2418yes—
302C22⋊C4×C47C24116yes—
303C42×C47C2418yes—
304C42×C47C2414yes—
305C22⋊Dic47C2418yes—
306C22⋊Dic47C24116yes—
307C22⋊Dic47C24116yes—
308(C2×D47)⋊C4C2418yes—
309(C2×D47)⋊C4C24116yes—
310(C2×D47)⋊C4C24116yes—
311(C2×D47)⋊C4C24116yes—
312(C2×D47)⋊C4C24116yes—
313(C2×D47)⋊C4C2418yes—
314C4⋊Dic47C2414yes—
315C4⋊Dic47C2418yes—
316C4⋊Dic47C2418yes—
317C4⋊Dic47C24116yes—
318C4⋊Dic47C24116yes—
319C4⋊Dic47C2414yes—
320C4⋊Dic47C2418yes—
321Dic47⋊C4C2418yes—
322Dic47⋊C4C24116yes—
323Dic47⋊C4C2418yes—
324Dic47⋊C4C2418yes—
325Dic47⋊C4C2418yes—
326Dic47⋊C4C24116yes—
327Dic47⋊C4C24116yes—
328Dic47⋊C4C24116yes—
329C4×Dic47C2418yes—
330C4×Dic47C2418yes—
331C4×Dic47C2414yes—
332C4×Dic47C2418yes—
333C4×Dic47C2414yes—
334C4×Dic47C2414yes—
335C4×Dic47C24116yes—
336C4×Dic47C24116yes—
337C4×Dic47C24116yes—
338C23×C47—24no—
339C23×C47—24no—
340C23×C47—24no—
341C23×C47C2514yes—
342C23×C47C2511yescharacteristic
343C22×D47—22no—
344C22×D47—22no—
345C22×D47—24no—
346C22×D47—24no—
347C22×D47—24no—
348C22×D47C2×#4114yes—
349C22×D47C2514yes—
350C22×D47C2512yes—
351Q8×C47—28no—
352Q8×C47—48no—
353D4×C47—28no—
354C2×C4×C47—24no—
355C2×C4×C47—24no—
356C2×C4×C47—24no—
357C2×C4×C47—28no—
358C2×C4×C47—22no—
359C2×C4×C47—216no—
360C2×C4×C47—416no—
361C2×C4×C47C2×#4114yes—
362C2×C4×C472−1+414yes—
363C2×C4×C47C2514yes—
364C2×C4×C47C2514yes—
365C2×C4×C47C2512yes—
366C2×C4×C47C2518yes—
367C2×C4×C47C2514yes—
368C2×C4×C47C2512yes—
369C2×C4×C47C2512yes—
370C22⋊D47—216no—
371C22⋊D47—216no—
372C22⋊D47—48no—
373C2×Dic47—24no—
374C2×Dic47—24no—
375C2×Dic47—28no—
376C2×Dic47—22no—
377C2×Dic47—24no—
378C2×Dic47—22no—
379C2×Dic47C2×#4114yes—
380C2×Dic47C2512yes—
381C2×Dic47C2514yes—
382C2×Dic47C2518yes—
383C2×Dic47C2512yes—
384C2×Dic47C2514yes—
385C2×Dic47C2514yes—
386C2×Dic47C2512yes—
387D188—216no—
388D188—28no—
389C4×D47—216no—
390C4×D47—216no—
391C4×D47—28no—
392C4×D47—48no—
393C4×D47—416no—
394C4×D47—44no—
395C4×D47C2×#41116yes—
396Dic94—28no—
397Dic94—216no—
398Dic94—216no—
399Dic94—216no—
400C2×#3507—471nomaximal, Sylow
401C22×C47—24no—
402C22×C47—24no—
403C22×C47—24no—
404C22×C47—48no—
405C22×C47C22×#4112yes—
406C22×C47C2×2−1+412yes—
407C22×C47#58512yes—
408C22×C47C2611yescharacteristic
409C2×D47—22no—
410C2×D47—22no—
411C2×D47—28no—
412C2×D47—24no—
413C2×D47—24no—
414C2×D47—24no—
415C2×D47—48no—
416C2×D47C22×#4114yes—
417C4×C47—24no—
418C4×C47—24no—
419C4×C47—24no—
420C4×C47—28no—
421C4×C47—22no—
422C4×C47C22×#4114yes—
423C4×C47C2×2−1+414yes—
424Dic47—24no—
425Dic47—24no—
426Dic47—28no—
427Dic47—22no—
428Dic47—24no—
429Dic47—22no—
430Dic47C22×#4114yes—
431#3507—4732no—
432C2×#559—472no—
433C2×#557—472no—
434C2×#556—474no—
435C2×#556—471no—
436C2×#556—471no—
437C2×#554—471no—
438C2×#554D4711yescharacteristic, complemented
439C2×#552—472no—
440C2×#552—472no—
441C2×#539—474no—
442C2×#536—472no—
443C2×#533—471no—
444C2×#532—471no—
445C2×#529—472no—
446C2×#529—472no—
447C2×#520—472no—
448C22×C4×Q8—471no—
449C2×C47—44no—
450C2×C47#350714yescomplemented
451C2×C47C23×#4111yescharacteristic
452C2×C47C22×2−1+411yescharacteristic
453C2×C47C2×#58511yescharacteristic
454D47—24no—
455D47—44no—
456C22×#41—472no—
457C23×Q8—471no—
458#559—4732no—
459#557—4732no—
460#556—4764no—
461#556—4716no—
462#556—4716no—
463#554—4716no—
464#554C2×D47116yescomplemented
465#552—4732no—
466#552—4732no—
467#539—4764no—
468#536—4732no—
469#533—4716no—
470#532—4716no—
471C2×C4⋊Q8—471no—
472C2×C4⋊Q8—474no—
473C2×C4⋊Q8—471no—
474C2×C4⋊Q8C2×D4711yescharacteristic
475C2×#127—471no—
476#529—4732no—
477#529—4732no—
478C2×#126—474no—
479C2×#126—474no—
480C2×#126—474no—
481C2×#126—474no—
482C2×#125—472no—
483C2×#125—472no—
484C2×#125—474no—
485C2×#125—474no—
486C2×#125C2×D4712yes—
487C2×#124—472no—
488C2×#124—472no—
489C2×#124—474no—
490C2×#124—472no—
491C2×#123—474no—
492C2×#123—474no—
493C2×#123—474no—
494C2×#123—474no—
495C2×C22⋊Q8—472no—
496C2×C22⋊Q8—472no—
497C2×C22⋊Q8—474no—
498C2×C22⋊Q8—472no—
499C2×C22⋊Q8—472no—
500C2×C22⋊Q8—472no—
501C2×C22⋊Q8C2×D4712yes—
502C2×C22⋊Q8C2×D4714yes—
503C2×#121—471no—
504C2×#121—471no—
505C2×#121—472no—
506#520—4732no—
507C2×C4×Q8—471no—
508C2×C4×Q8—472no—
509C2×C4×Q8—4716no—
510C2×C4×Q8—471no—
511C2×C4×Q8—472no—
512C2×C4×Q8—474no—
513C2×C4×Q8—472no—
514C2×C4×Q8—472no—
515C2×C4×Q8—471no—
516C2×C4×Q8—472no—
517C2×C4×Q8—472no—
518C2×C4×Q8C2×D4711yescharacteristic
519C2×C4×D4—474no—
520C2×C4×D4—474no—
521C2×C4×D4—472no—
522C2×C4×D4—474no—
523C2×C4×D4—472no—
524C2×C4×D4—471no—
525C2×C4×D4C2×D4712yes—
526C2×C4×D4C2×D4711yescharacteristic
527C2×#117—472no—
528C2×#117—474no—
529C2×#117—472no—
530C2×#117—472no—
531C2×#117—474no—
532C22×C4⋊C4—471no—
533C22×C4⋊C4—472no—
534C22×C4⋊C4—472no—
535C22×C4⋊C4C2×D4712yes—
536C22×C42—472no—
537C22×C42—471no—
538C47C2×#350711yescharacteristic, complemented, Sylow
539C2×#41—4716no—
540C2×#41—9416no—
541C22×Q8—478no—
542C22×Q8—472no—
543C22×Q8—471no—
544C22×Q8—472no—
545C22×Q8—472no—
546C22×Q8—948no—
547C22×Q8C22×D4711yescharacteristic
548C22×Q8C22×D4712yes—
549C22×D4—472no—
550C22×D4—472no—
551C22×D4—472no—
552C22×D4—471no—
553C22×D4—472no—
554C22×D4C22×D4711yescharacteristic
555C23×C4—471no—
556C23×C4—472no—
557C23×C4—472no—
558C23×C4—471no—
559C23×C4—472no—
560C23×C4—471no—
561C23×C4—474no—
562C23×C4C22×D4712yes—
563C23×C4C22×D4714yes—
564C4⋊Q8—478no—
565C4⋊Q8—4732no—
566C4⋊Q8—478no—
567C4⋊Q8C22×D4718yes—
568#127—478no—
569#126—4732no—
570#126—4732no—
571#126—4732no—
572#126—4732no—
573#125—4716no—
574#125—4716no—
575#125—4732no—
576#125—4732no—
577#125C22×D47116yes—
578#124—4716no—
579#124—4716no—
580#124—4732no—
581#124—4716no—
582#123—4732no—
583#123—4732no—
584#123—4732no—
585#123—4732no—
586C22⋊Q8—4716no—
587C22⋊Q8—4716no—
588C22⋊Q8—4732no—
589C22⋊Q8—4716no—
590C22⋊Q8—4716no—
591C22⋊Q8—4716no—
592C22⋊Q8C22×D47116yes—
593C22⋊Q8C22×D47132yes—
594#121—478no—
595#121—478no—
596#121—4716no—
597C4×Q8—478no—
598C4×Q8—4716no—
599C4×Q8—478no—
600C4×Q8—4716no—
601C4×Q8—4732no—
602C4×Q8—4716no—
603C4×Q8—4716no—
604C4×Q8—478no—
605C4×Q8—4716no—
606C4×Q8—4716no—
607C4×Q8C22×D4718yes—
608C4×D4—4732no—
609C4×D4—4732no—
610C4×D4—4716no—
611C4×D4—4732no—
612C4×D4—4716no—
613C4×D4—478no—
614C4×D4C22×D47116yes—
615C4×D4C22×D4718yes—
616#117—4716no—
617#117—4732no—
618#117—4716no—
619#117—4716no—
620#117—4732no—
621C2×C4⋊C4—471no—
622C2×C4⋊C4—472no—
623C2×C4⋊C4—474no—
624C2×C4⋊C4—472no—
625C2×C4⋊C4—472no—
626C2×C4⋊C4—472no—
627C2×C4⋊C4—472no—
628C2×C4⋊C4—474no—
629C2×C4⋊C4—474no—
630C2×C4⋊C4—471no—
631C2×C4⋊C4—472no—
632C2×C4⋊C4—474no—
633C2×C4⋊C4—474no—
634C2×C4⋊C4—474no—
635C2×C4⋊C4—472no—
636C2×C4⋊C4—478no—
637C2×C4⋊C4—4716no—
638C2×C4⋊C4—4716no—
639C2×C4⋊C4C22×D4711yescharacteristic
640C2×C4⋊C4C22×D4712yes—
641C2×C4⋊C4C22×D4712yes—
642C2×C4⋊C4C22×D4714yes—
643C2×C4⋊C4C22×D47116yes—
644C2×C4⋊C4C22×D4714yes—
645C2×C4⋊C4C22×D4712yes—
646C2×C4⋊C4C22×D4711yescharacteristic
647C2×C22⋊C4—472no—
648C2×C22⋊C4—474no—
649C2×C22⋊C4—474no—
650C2×C22⋊C4—472no—
651C2×C22⋊C4—474no—
652C2×C22⋊C4—474no—
653C2×C22⋊C4—474no—
654C2×C22⋊C4—472no—
655C2×C22⋊C4—474no—
656C2×C22⋊C4C22×D4712yes—
657C2×C22⋊C4C22×D4714yes—
658C2×C42—474no—
659C2×C42—474no—
660C2×C42—472no—
661C2×C42—472no—
662C2×C42—474no—
663C2×C42—471no—
664C2×C42—472no—
665C2×C42—471no—
666C2×C42—471no—
667C2×C42—4716no—
668C2×C42—478no—
669C2×C42C22×D4711yescharacteristic
670C2×C42C22×D4712yes—
671C24—471no—
672C24—472no—
673C24C23×D4712yes—
674#41—9464no—
675C2×Q8—24no—
676C2×Q8—44no—
677C2×Q8—478no—
678C2×Q8—474no—
679C2×Q8—478no—
680C2×Q8—478no—
681C2×Q8—948no—
682C2×Q8—948no—
683C2×Q8—9432no—
684C2×Q8—944no—
685C2×Q8—948no—
686C2×Q8C23×D4714yes—
687C2×Q8C23×D4718yes—
688C2×D4—24no—
689C2×D4—478no—
690C2×D4—478no—
691C2×D4—478no—
692C2×D4—474no—
693C2×D4—478no—
694C2×D4—948no—
695C2×D4—948no—
696C2×D4—948no—
697C2×D4—944no—
698C2×D4—1884no—
699C2×D4C23×D4714yes—
700C22×C4—28no—
701C22×C4—48no—
702C22×C4—471no—
703C22×C4—478no—
704C22×C4—474no—
705C22×C4—471no—
706C22×C4—472no—
707C22×C4—474no—
708C22×C4—472no—
709C22×C4—472no—
710C22×C4—471no—
711C22×C4—474no—
712C22×C4—478no—
713C22×C4—478no—
714C22×C4—478no—
715C22×C4—474no—
716C22×C4—4716no—
717C22×C4—948no—
718C22×C4—948no—
719C22×C4—944no—
720C22×C4—1884no—
721C22×C4—1888no—
722C22×C4—1882no—
723C22×C4C23×D4718yes—
724C22×C4C23×D4712yes—
725C22×C4C23×D4712yes—
726C22×C4C23×D4711yescharacteristic
727C22×C4C23×D4712yes—
728C22×C4C23×D4714yes—
729C22×C4C23×D47116yes—
730C22×C4C23×D4711yescharacteristic
731C22×C4C23×D4711yescharacteristic
732C4⋊C4—478no—
733C4⋊C4—4716no—
734C4⋊C4—478no—
735C4⋊C4—478no—
736C4⋊C4—478no—
737C4⋊C4—4716no—
738C4⋊C4—4716no—
739C4⋊C4—4716no—
740C4⋊C4—474no—
741C4⋊C4—478no—
742C4⋊C4—478no—
743C4⋊C4—4716no—
744C4⋊C4—4716no—
745C4⋊C4—474no—
746C4⋊C4—478no—
747C4⋊C4C23×D4714yes—
748C4⋊C4C23×D4718yes—
749C4⋊C4C23×D4718yes—
750C4⋊C4C23×D47116yes—
751C4⋊C4C23×D47116yes—
752C4⋊C4C23×D4718yes—
753C4⋊C4C23×D4714yes—
754C22⋊C4—478no—
755C22⋊C4—4716no—
756C22⋊C4—4716no—
757C22⋊C4—478no—
758C22⋊C4—4716no—
759C22⋊C4—4716no—
760C22⋊C4—4716no—
761C22⋊C4—478no—
762C22⋊C4—4716no—
763C22⋊C4C23×D4718yes—
764C22⋊C4C23×D47116yes—
765C42—478no—
766C42—478no—
767C42—474no—
768C42—478no—
769C42—474no—
770C42—474no—
771C42—4716no—
772C42—4716no—
773C42—4716no—
774C42C23×D4714yes—
775C42C23×D4718yes—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—474no—
780C23—472no—
781C23—474no—
782C23—942no—
783C23—942no—
784C23—944no—
785C23—944no—
786C23—944no—
787C23C24×D4714yes—
788C23C24×D4711yescharacteristic
789Q8—28no—
790Q8—48no—
791Q8—9416no—
792Q8—9416no—
793Q8—948no—
794Q8—9416no—
795D4—28no—
796D4—9416no—
797D4—9416no—
798D4—9416no—
799D4—948no—
800D4—1888no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—24no—
804C2×C4—28no—
805C2×C4—22no—
806C2×C4—216no—
807C2×C4—416no—
808C2×C4—474no—
809C2×C4—472no—
810C2×C4—4716no—
811C2×C4—472no—
812C2×C4—474no—
813C2×C4—478no—
814C2×C4—474no—
815C2×C4—474no—
816C2×C4—472no—
817C2×C4—9416no—
818C2×C4—944no—
819C2×C4—944no—
820C2×C4—942no—
821C2×C4—948no—
822C2×C4—944no—
823C2×C4—942no—
824C2×C4—9416no—
825C2×C4—948no—
826C2×C4—1888no—
827C2×C4—18816no—
828C2×C4—1884no—
829C2×C4#41×D4714yes—
830C2×C4#1309407214yes—
831C2×C4C24×D4714yes—
832C2×C4C24×D4714yes—
833C2×C4C24×D4712yes—
834C2×C4C24×D4714yes—
835C2×C4C24×D4718yes—
836C2×C4C24×D4712yes—
837C2×C4C24×D4712yes—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—48no—
842C22—474no—
843C22—942no—
844C22—942no—
845C22—948no—
846C22—944no—
847C22—944no—
848C22—944no—
849C22—1888no—
850C22C2×#41×D4712yes—
851C22C2×#1309407212yes—
852C22#1568995812yes—
853C22C25×D4711yescharacteristic
854C4—24no—
855C4—24no—
856C4—24no—
857C4—28no—
858C4—22no—
859C4—474no—
860C4—944no—
861C4—944no—
862C4—942no—
863C4—948no—
864C4—944no—
865C4—942no—
866C4C2×#41×D4714yes—
867C4C2×#1309407214yes—
868C2—44no—
869C2—944no—
870C2—1884no—
871C2#2025725114yesdirect product factor
872C2C22×#41×D4711yescharacteristic
873C2C22×#1309407211yescharacteristic
874C2C2×#1568995811yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#554C2
socleC23×C47C25
prime radicalC2×#15689670C2
hypercenterC2×#554D47
hypocenterC47C2×#3507
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #20257251C2direct (N × H)
2. C2×#15689856C2semidirect
3. C2×#15689850C2semidirect
4. C2×#15689846C2semidirect
5. C2×#15689844C2semidirect
6. C2×#15689843C2semidirect
7. C2×#15689834C2semidirect
8. C2×#15689808C2semidirect
9. C2×#15689807C2semidirect
10. C2×#15689719C2semidirect
11. C2×#15689696C2semidirect
12. C2×#15689678C2semidirect
14. C2×#15689658C2semidirect
15. C2×#15689655C2semidirect
16. C2×#15689604C2semidirect
17. C2×C4×Q8×D47C2semidirect
18. C2×C47×#554C2semidirect
21. #15689856C22semidirect
22. #15689850C22semidirect
23. #15689846C22semidirect
24. #15689844C22semidirect
25. #15689843C22semidirect
26. #15689834C22semidirect
27. #15689808C22semidirect
28. #15689807C22semidirect
29. #15689719C22semidirect
30. #15689696C22semidirect
31. #15689678C22semidirect
37. #15689658C22semidirect
38. #15689655C22semidirect
64. #15689604C22semidirect
75. C4×Q8×D47C22semidirect
92. C47×#554C22semidirect
438. C2×#554D47semidirect
450. C2×C47#3507semidirect
464. #554C2×D47semidirect
538. C47C2×#3507semidirect
871. C2#20257251direct (N × H)

Maximal subgroups

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

subgroupindex
#202572512
C2×#156898562
C2×#156898502
C2×#156898462
C2×#156898442
C2×#156898432
C2×#156898342
C2×#156898082
C2×#156898072
C2×#156897192
C2×#156896962
C2×#156896782
C2×#156896702
C2×#156896582
C2×#156896552
C2×#156896042
C2×C4×Q8×D472
C2×C47×#5542
C2×#350747