Finite Group Databasebeta

← C2×#20257267 #27124714

Subgroups — C2×#20257267 #27124714

Order 12032.

7022 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257267C2132yesmaximal, direct product factor
2C2×#15689850C212yesmaximal, complemented
3C2×#15689849C212yesmaximal, complemented
4C2×#15689844C212yesmaximal, complemented
5C2×#15689841C212yesmaximal, complemented
6C2×#15689814C212yesmaximal, complemented
7C2×#15689812C212yesmaximal, complemented
8C2×#15689811C212yesmaximal, complemented
9C2×#15689807C212yesmaximal, complemented
10C2×#15689733C212yesmaximal, complemented
11C2×#15689731C212yesmaximal, complemented
12C2×#15689696C212yesmaximal
13C2×#15689680C211yesmaximal, characteristic, complemented
14C2×#15689678C211yesmaximal, characteristic, complemented
15C2×#15689678C211yesmaximal, characteristic, complemented
16C2×#15689678C211yesmaximal, characteristic, complemented
17C2×C4⋊Q8×D47C211yesmaximal, characteristic, complemented
18C2×#15689599C212yesmaximal, complemented
19C2×C4×#10625350C211yesmaximal, characteristic
20C2×C47×#533C211yesmaximal, characteristic, complemented
21C22×#10625350C2211yescharacteristic
22C22×Q8×D47C2212yes—
23#15689850C22132yescomplemented
24#15689849C22132yescomplemented
25#15689844C22132yescomplemented
26#15689841C22132yescomplemented
27#15689814C22132yescomplemented
28#15689812C22132yescomplemented
29#15689811C22132yescomplemented
30#15689807C22132yescomplemented
31#15689733C22132yescomplemented
32#15689731C22132yescomplemented
33#15689696C22132yes—
34#15689680C22116yescomplemented
35#15689678C22116yescomplemented
36#15689678C22116yescomplemented
37#15689678C22116yescomplemented
38C2×#13094024C2211yescharacteristic
39C2×#13094024C2211yescharacteristic
40C2×#13094023C2212yes—
41C2×#13094023C2212yes—
42C2×#13094023C2214yes—
43C2×#13094022C2212yes—
44C4⋊Q8×D47C22116yescomplemented
45C2×#13094019C2214yes—
46C2×#13094018C2214yes—
47C2×#13094017C2214yes—
48C2×#13094017C2214yes—
49C2×#13094016C2214yes—
50C2×#13094016C2212yes—
51C2×#13094015C2212yes—
52C2×#13094015C2214yes—
53C2×#13094015C2212yes—
54C2×#13094015C2212yes—
55C2×#13094014C2214yes—
56C2×#13094014C2214yes—
57C2×#13094010C2214yes—
58C2×#13094009C2214yes—
59C2×#13094006C2214yes—
60C2×#13094004C2212yes—
61C2×#13094004C2212yes—
62C2×#13094004C2212yes—
63C2×#13094003C2212yes—
64C2×#13094003C2212yes—
65C2×#13094000C2212yes—
66C2×#13094000C2212yes—
67C2×#13094000C2212yes—
68#15689599C22132yescomplemented
69C4×#10625350C22116yes—
70C2×Q8×Dic47C2212yes—
71C2×Q8×Dic47C2212yes—
72C2×Q8×Dic47C2212yes—
73C2×C4×Dic94C2211yescharacteristic
74C2×C4×Dic94C2211yescharacteristic
75C2×C4×Dic94C2214yes—
76C2×C4×Dic94C2212yes—
77C2×C4×Dic94C2212yes—
78C2×#13093989C2212yes—
79C2×#13093989C2214yes—
80C2×#13093989C2212yes—
81C2×#13093989C2212yes—
82C2×C4×D188C2211yescharacteristic
83C2×C4×D188C2211yescharacteristic
84C2×C4×C22⋊D47C2211yescharacteristic
85C2×C4×C22⋊D47C2211yescharacteristic
86C2×C4×C22⋊D47C2211yescharacteristic
87C2×C4×C22⋊D47C2211yescharacteristic
88C2×#13093983C2211yescharacteristic
89C2×#13093983C2212yes—
90C2×#13093982C2214yes—
91C2×#13093982C2212yes—
92C2×#13093982C2212yes—
93C2×#13093982C2212yes—
94C2×#13093981C2211yescharacteristic
95C2×#13093981C2211yescharacteristic
96C2×#13093981C2214yes—
97C2×C4⋊C4×D47C2212yes—
98C2×C4⋊C4×D47C2212yes—
99C2×C42×D47C2211yescharacteristic
100C2×C42×D47C2211yescharacteristic
101C47×#533C22116yescomplemented
102C2×C4⋊Q8×C47C2211yescharacteristic
103C2×C4⋊Q8×C47C2211yescharacteristic
104C2×#125×C47C2212yes—
105C2×C22⋊Q8×C47C2212yes—
106C2×C22⋊Q8×C47C2212yes—
107C2×C4×Q8×C47C2212yes—
108C2×C4×Q8×C47C2212yes—
109C2×#117×C47C2212yes—
110C22×C42×C47C2211yescharacteristic
111C2×#10625350—28no—
112C2×#10625350C2318yes—
113C22×Dic94C2312yes—
114C22×Dic94C2312yes—
115C22×Dic94C2314yes—
116C22×Dic94C2311yescharacteristic
117C2×Q8×D47—216no—
118C2×Q8×D47C23116yes—
119C22×D188C2311yescharacteristic
120C22×C22⋊D47C2311yescharacteristic
121C22×C22⋊D47C2311yescharacteristic
122C22×C4×D47C2311yescharacteristic
123C22×C4×D47C2311yescharacteristic
124C22×C4×D47C2311yescharacteristic
125C22×C4×D47C2311yescharacteristic
126C22×C4×D47C2311yescharacteristic
127C22×C4×D47C2314yes—
128C22×C4×D47C2311yescharacteristic
129#13094024C2318yes—
130#13094024C2318yes—
131#13094023C23116yes—
132#13094023C23116yes—
133#13094023C23132yes—
134#13094022C23116yes—
135#13094019C23132yes—
136#13094018C23132yes—
137#13094017C23132yes—
138#13094017C23132yes—
139#13094016C23132yes—
140#13094016C23116yes—
141#13094015C23116yes—
142#13094015C23132yes—
143#13094015C23116yes—
144#13094015C23116yes—
145#13094014C23132yes—
146#13094014C23132yes—
147#13094010C23132yes—
148#13094009C23132yes—
149#13094006C23132yes—
150#13094004C23116yes—
151#13094004C23116yes—
152#13094004C23116yes—
153#13094003C23116yes—
154#13094003C23116yes—
155#13094000C23116yes—
156#13094000C23116yes—
157#13094000C23116yes—
158Q8×Dic47C23116yes—
159Q8×Dic47C23116yes—
160Q8×Dic47C23116yes—
161C4×Dic94C23116yes—
162C4×Dic94C23116yes—
163C4×Dic94C23132yes—
164C4×Dic94C2318yes—
165C4×Dic94C2318yes—
166#13093989C23116yes—
167#13093989C23116yes—
168#13093989C23116yes—
169#13093989C23132yes—
170C4×D188C2318yes—
171C4×D188C2318yes—
172C4×C22⋊D47C2318yes—
173C4×C22⋊D47C2318yes—
174C4×C22⋊D47C2318yes—
175C4×C22⋊D47C2318yes—
176#13093983C2318yes—
177#13093983C23116yes—
178#13093982C23132yes—
179#13093982C23116yes—
180#13093982C23116yes—
181#13093982C23116yes—
182#13093981C2318yes—
183#13093981C23132yes—
184#13093981C2318yes—
185C2×C4⋊Dic47C2312yes—
186C2×C4⋊Dic47C2312yes—
187C2×C4⋊Dic47C2312yes—
188C2×C4⋊Dic47C2312yes—
189C2×C4⋊Dic47C2314yes—
190C2×C4⋊Dic47C2311yescharacteristic
191C2×C4⋊Dic47C2311yescharacteristic
192C2×C4⋊Dic47C2314yes—
193C2×C4⋊Dic47C2314yes—
194C2×Dic47⋊C4C2314yes—
195C2×Dic47⋊C4C2314yes—
196C2×Dic47⋊C4C2311yescharacteristic
197C2×Dic47⋊C4C2311yescharacteristic
198C2×Dic47⋊C4C2311yescharacteristic
199C2×Dic47⋊C4C2311yescharacteristic
200C2×Dic47⋊C4C2314yes—
201C2×Dic47⋊C4C2314yes—
202C2×Dic47⋊C4C2314yes—
203C2×Dic47⋊C4C2314yes—
204C2×Dic47⋊C4C2314yes—
205C4⋊C4×D47C23116yes—
206C4⋊C4×D47C23116yes—
207C2×C22⋊Dic47C2311yescharacteristic
208C2×C22⋊Dic47C2311yescharacteristic
209C2×C22⋊Dic47C2314yes—
210C2×(C2×D47)⋊C4C2311yescharacteristic
211C2×(C2×D47)⋊C4C2311yescharacteristic
212C2×(C2×D47)⋊C4C2314yes—
213C2×(C2×D47)⋊C4C2311yescharacteristic
214C2×(C2×D47)⋊C4C2311yescharacteristic
215C2×(C2×D47)⋊C4C2314yes—
216C2×(C2×D47)⋊C4C2314yes—
217C2×C4×Dic47C2311yescharacteristic
218C2×C4×Dic47C2311yescharacteristic
219C2×C4×Dic47C2311yescharacteristic
220C2×C4×Dic47C2311yescharacteristic
221C2×C4×Dic47C2311yescharacteristic
222C2×C4×Dic47C2311yescharacteristic
223C2×C4×Dic47C2314yes—
224C2×C4×Dic47C2314yes—
225C2×C4×Dic47C2314yes—
226C2×C4×Dic47C2314yes—
227C42×D47C2318yes—
228C42×D47C2318yes—
229C22×Q8×C47C2312yes—
230C22×Q8×C47C2312yes—
231C23×C4×C47C2311yescharacteristic
232C23×C4×C47C2311yescharacteristic
233C23×C4×C47C2311yescharacteristic
234C4⋊Q8×C47C2318yes—
235C4⋊Q8×C47C2318yes—
236#125×C47C23116yes—
237C22⋊Q8×C47C23116yes—
238C22⋊Q8×C47C23116yes—
239C4×Q8×C47C23116yes—
240C4×Q8×C47C23116yes—
241#117×C47C23116yes—
242C2×C4⋊C4×C47C2312yes—
243C2×C4⋊C4×C47C2312yes—
244C2×C4⋊C4×C47C2314yes—
245C2×C4⋊C4×C47C2314yes—
246C2×C4⋊C4×C47C2312yes—
247C2×C4⋊C4×C47C2312yes—
248C2×C22⋊C4×C47C2314yes—
249C2×C42×C47C2311yescharacteristic
250C2×C42×C47C2311yescharacteristic
251C2×C42×C47C2311yescharacteristic
252C2×C42×C47C2311yescharacteristic
253C2×C42×C47C2318yes—
254C2×C42×C47C2314yes—
255C24×C47C2411yescharacteristic
256C23×D47C2411yescharacteristic
257C23×D47C2411yescharacteristic
258C2×Q8×C47—28no—
259C2×Q8×C47—28no—
260C2×Q8×C47C2418yes—
261C2×Q8×C47C2418yes—
262C22×C4×C47—24no—
263C22×C4×C47—24no—
264C22×C4×C47—24no—
265C22×C4×C47C2411yescharacteristic
266C22×C4×C47C2411yescharacteristic
267C22×C4×C47C2411yescharacteristic
268C22×C4×C47C2414yes—
269C22×C4×C47C2414yes—
270C22×C4×C47C2414yes—
271C22×C4×C47C2414yes—
272C22×C4×C47C2414yes—
273C22×C4×C47C2411yescharacteristic
274C22×C4×C47C2411yescharacteristic
275C22×C4×C47C2411yescharacteristic
276C2×C22⋊D47—24no—
277C2×C22⋊D47—24no—
278C2×C22⋊D47C2414yes—
279C2×C22⋊D47C2414yes—
280C22×Dic47C2411yescharacteristic
281C22×Dic47C2411yescharacteristic
282C22×Dic47C2414yes—
283C22×Dic47C2411yescharacteristic
284C22×Dic47C2411yescharacteristic
285C22×Dic47C2414yes—
286C22×Dic47C2411yescharacteristic
287C22×Dic47C2411yescharacteristic
288Q8×D47—264no—
289#10625350—232no—
290C2×D188—24no—
291C2×D188C2414yes—
292C2×C4×D47—216no—
293C2×C4×D47—24no—
294C2×C4×D47—24no—
295C2×C4×D47—24no—
296C2×C4×D47—24no—
297C2×C4×D47—24no—
298C2×C4×D47#4118yes—
299C2×C4×D47C2414yes—
300C2×C4×D47C2414yes—
301C2×C4×D47C2414yes—
302C2×C4×D47C2414yes—
303C2×C4×D47C2414yes—
304C2×C4×D47C24116yes—
305C2×C4×D47C2414yes—
306C2×Dic94—28no—
307C2×Dic94—28no—
308C2×Dic94—216no—
309C2×Dic94—24no—
310C2×Dic94C2418yes—
311C2×Dic94C2418yes—
312C2×Dic94C24116yes—
313C2×Dic94C2414yes—
314C4⋊C4×C47C2418yes—
315C4⋊C4×C47C2418yes—
316C4⋊C4×C47C24116yes—
317C4⋊C4×C47C24116yes—
318C4⋊C4×C47C2418yes—
319C4⋊C4×C47C2418yes—
320C22⋊C4×C47C24116yes—
321C42×C47C2414yes—
322C42×C47C2414yes—
323C42×C47C2414yes—
324C42×C47C2414yes—
325C42×C47C24116yes—
326C22⋊Dic47C2414yes—
327C22⋊Dic47C2414yes—
328C22⋊Dic47C24116yes—
329(C2×D47)⋊C4C2414yes—
330(C2×D47)⋊C4C2414yes—
331(C2×D47)⋊C4C24116yes—
332(C2×D47)⋊C4C2414yes—
333(C2×D47)⋊C4C2414yes—
334(C2×D47)⋊C4C24116yes—
335(C2×D47)⋊C4C24116yes—
336C4⋊Dic47C2418yes—
337C4⋊Dic47C2418yes—
338C4⋊Dic47C2418yes—
339C4⋊Dic47C2418yes—
340C4⋊Dic47C24116yes—
341C4⋊Dic47C2414yes—
342C4⋊Dic47C2414yes—
343C4⋊Dic47C24116yes—
344C4⋊Dic47C24116yes—
345Dic47⋊C4C24116yes—
346Dic47⋊C4C24116yes—
347Dic47⋊C4C2414yes—
348Dic47⋊C4C2414yes—
349Dic47⋊C4C2414yes—
350Dic47⋊C4C2414yes—
351Dic47⋊C4C24116yes—
352Dic47⋊C4C24116yes—
353Dic47⋊C4C24116yes—
354Dic47⋊C4C24116yes—
355Dic47⋊C4C24116yes—
356C4×Dic47C2414yes—
357C4×Dic47C2414yes—
358C4×Dic47C2414yes—
359C4×Dic47C2414yes—
360C4×Dic47C2414yes—
361C4×Dic47C2414yes—
362C4×Dic47C24116yes—
363C4×Dic47C24116yes—
364C4×Dic47C24116yes—
365C4×Dic47C24116yes—
366C23×C47—22no—
367C23×C47—22no—
368C23×C47—22no—
369C23×C47C2512yes—
370C23×C47C2511yescharacteristic
371C22×D47—22no—
372C22×D47—22no—
373C22×D47—22no—
374C22×D47—22no—
375C22×D47—22no—
376C22×D47C2×#4114yes—
377C22×D47C2512yes—
378C22×D47C2512yes—
379Q8×C47—216no—
380Q8×C47—216no—
381C2×C4×C47—28no—
382C2×C4×C47—22no—
383C2×C4×C47—22no—
384C2×C4×C47—22no—
385C2×C4×C47—28no—
386C2×C4×C47—28no—
387C2×C4×C47—28no—
388C2×C4×C47—28no—
389C2×C4×C47C2×#4114yes—
390C2×C4×C472−1+414yes—
391C2×C4×C472−1+414yes—
392C2×C4×C47C2512yes—
393C2×C4×C47C2518yes—
394C2×C4×C47C2518yes—
395C2×C4×C47C2512yes—
396C2×C4×C47C2512yes—
397C2×C4×C47C2512yes—
398C2×C4×C47C2512yes—
399C2×C4×C47C2512yes—
400C22⋊D47—28no—
401C22⋊D47—28no—
402C2×Dic47—28no—
403C2×Dic47—22no—
404C2×Dic47—28no—
405C2×Dic47—22no—
406C2×Dic47—22no—
407C2×Dic47—22no—
408C2×Dic47—22no—
409C2×Dic47C2×#4114yes—
410C2×Dic47C2512yes—
411C2×Dic47C2512yes—
412C2×Dic47C2518yes—
413C2×Dic47C2512yes—
414C2×Dic47C2512yes—
415C2×Dic47C2512yes—
416C2×Dic47C2518yes—
417C2×Dic47C2512yes—
418D188—28no—
419C4×D47—232no—
420C4×D47—28no—
421C4×D47—28no—
422C4×D47—28no—
423C4×D47—28no—
424C4×D47—28no—
425C4×D47C2×#41116yes—
426Dic94—216no—
427Dic94—216no—
428Dic94—28no—
429Dic94—232no—
430C2×#3509—471nomaximal, Sylow
431C22×C47—22no—
432C22×C47—22no—
433C22×C47—22no—
434C22×C47—44no—
435C22×C47C22×#4112yes—
436C22×C47C2×2−1+412yes—
437C22×C47C2×2−1+412yes—
438C22×C47C2611yescharacteristic
439C2×D47—22no—
440C2×D47—22no—
441C2×D47—28no—
442C2×D47—22no—
443C2×D47—22no—
444C2×D47—22no—
445C2×D47—44no—
446C2×D47C22×#4114yes—
447C4×C47—28no—
448C4×C47—22no—
449C4×C47—22no—
450C4×C47—22no—
451C4×C47—28no—
452C4×C47C22×#4114yes—
453C4×C47C2×2−1+414yes—
454C4×C47C2×2−1+414yes—
455Dic47—28no—
456Dic47—22no—
457Dic47—28no—
458Dic47—22no—
459Dic47—22no—
460Dic47—22no—
461Dic47—22no—
462Dic47C22×#4114yes—
463#3509—4732no—
464C2×#557—472no—
465C2×#557—472no—
466C2×#556—472no—
467C2×#556—472no—
468C2×#552—472no—
469C2×#552—472no—
470C2×#552—472no—
471C2×#552—472no—
472C2×#541—472no—
473C2×#541—472no—
474C2×#536—472no—
475C2×#533—471no—
476C2×#533—471no—
477C2×#533—471no—
478C2×#533—471no—
479C2×#533D4711yescharacteristic, complemented
480C22×C4⋊Q8—471no—
481C2×#519—472no—
482C2×C4×#41—471no—
483C2×C47—42no—
484C2×C47#350914yescomplemented
485C2×C47C23×#4111yescharacteristic
486C2×C47C22×2−1+411yescharacteristic
487C2×C47C22×2−1+411yescharacteristic
488D47—24no—
489D47—42no—
490C22×#41—471no—
491C23×Q8—472no—
492#557—4732no—
493#557—4732no—
494#556—4732no—
495#556—4732no—
496#552—4732no—
497#552—4732no—
498#552—4732no—
499#552—4732no—
500#541—4732no—
501#541—4732no—
502#536—4732no—
503#533—4716no—
504#533—4716no—
505#533—4716no—
506#533—4716no—
507#533C2×D47116yescomplemented
508C2×C4⋊Q8—472no—
509C2×C4⋊Q8—4716no—
510C2×C4⋊Q8—472no—
511C2×C4⋊Q8—472no—
512C2×C4⋊Q8—474no—
513C2×C4⋊Q8—471no—
514C2×C4⋊Q8—471no—
515C2×C4⋊Q8C2×D4711yescharacteristic
516C2×C4⋊Q8C2×D4711yescharacteristic
517C2×#126—474no—
518C2×#126—474no—
519C2×#126—474no—
520C2×#126—474no—
521C2×#125—472no—
522C2×#125—472no—
523C2×#125—472no—
524C2×#125—474no—
525C2×#125—474no—
526C2×#125—474no—
527C2×#125—472no—
528C2×#125—474no—
529C2×#125C2×D4712yes—
530C2×#124—474no—
531C2×#123—474no—
532C2×#123—474no—
533C2×C22⋊Q8—472no—
534C2×C22⋊Q8—472no—
535C2×C22⋊Q8—472no—
536C2×C22⋊Q8—472no—
537C2×C22⋊Q8—472no—
538C2×C22⋊Q8—472no—
539C2×C22⋊Q8—472no—
540C2×C22⋊Q8—472no—
541C2×C22⋊Q8C2×D4712yes—
542C2×C22⋊Q8C2×D4712yes—
543#519—4732no—
544C4×#41—4716no—
545C2×C4×Q8—472no—
546C2×C4×Q8—472no—
547C2×C4×Q8—472no—
548C2×C4×Q8—472no—
549C2×C4×Q8—474no—
550C2×C4×Q8—472no—
551C2×C4×Q8—472no—
552C2×C4×Q8—471no—
553C2×C4×Q8—471no—
554C2×C4×Q8—472no—
555C2×C4×Q8—474no—
556C2×C4×Q8—472no—
557C2×C4×Q8C2×D4712yes—
558C2×C4×Q8C2×D4712yes—
559C2×C4×D4—471no—
560C2×C4×D4—471no—
561C2×C4×D4—471no—
562C2×C4×D4—471no—
563C2×C4×D4—471no—
564C2×C4×D4—471no—
565C2×#117—471no—
566C2×#117—472no—
567C2×#117—472no—
568C2×#117—474no—
569C2×#117—472no—
570C2×#117—472no—
571C2×#117—471no—
572C2×#117—471no—
573C2×#117—474no—
574C2×#117C2×D4712yes—
575C22×C4⋊C4—472no—
576C22×C4⋊C4—472no—
577C22×C42—471no—
578C22×C42—471no—
579C22×C42C2×D4711yescharacteristic
580C47C2×#350911yescharacteristic, complemented, Sylow
581C2×#41—478no—
582C2×#41—948no—
583C22×Q8—4716no—
584C22×Q8—472no—
585C22×Q8—472no—
586C22×Q8—474no—
587C22×Q8—471no—
588C22×Q8—9416no—
589C22×Q8C22×D4712yes—
590C22×Q8C22×D4712yes—
591C22×D4—471no—
592C22×D4—471no—
593C22×D4—471no—
594C23×C4—471no—
595C23×C4—474no—
596C23×C4—471no—
597C23×C4—471no—
598C23×C4—471no—
599C23×C4—471no—
600C23×C4—471no—
601C23×C4C22×D4711yescharacteristic
602C23×C4C22×D4711yescharacteristic
603C23×C4C22×D4711yescharacteristic
604C4⋊Q8—4716no—
605C4⋊Q8—4716no—
606C4⋊Q8—4716no—
607C4⋊Q8—4732no—
608C4⋊Q8—478no—
609C4⋊Q8—478no—
610C4⋊Q8C22×D4718yes—
611C4⋊Q8C22×D4718yes—
612#126—4732no—
613#126—4732no—
614#126—4732no—
615#126—4732no—
616#125—4716no—
617#125—4716no—
618#125—4716no—
619#125—4732no—
620#125—4732no—
621#125—4732no—
622#125—4716no—
623#125—4732no—
624#125C22×D47116yes—
625#124—4732no—
626#123—4732no—
627#123—4732no—
628C22⋊Q8—4716no—
629C22⋊Q8—4716no—
630C22⋊Q8—4716no—
631C22⋊Q8—4716no—
632C22⋊Q8—4716no—
633C22⋊Q8—4716no—
634C22⋊Q8—4716no—
635C22⋊Q8—4716no—
636C22⋊Q8C22×D47116yes—
637C22⋊Q8C22×D47116yes—
638C4×Q8—4716no—
639C4×Q8—4716no—
640C4×Q8—4716no—
641C4×Q8—4716no—
642C4×Q8—4732no—
643C4×Q8—4716no—
644C4×Q8—4716no—
645C4×Q8—478no—
646C4×Q8—478no—
647C4×Q8—4716no—
648C4×Q8—4732no—
649C4×Q8—4716no—
650C4×Q8C22×D47116yes—
651C4×Q8C22×D47116yes—
652C4×D4—478no—
653C4×D4—478no—
654C4×D4—478no—
655C4×D4—478no—
656C4×D4—478no—
657C4×D4—478no—
658#117—478no—
659#117—4716no—
660#117—4716no—
661#117—4732no—
662#117—4716no—
663#117—4716no—
664#117—478no—
665#117—478no—
666#117—4732no—
667#117C22×D47116yes—
668C2×C4⋊C4—472no—
669C2×C4⋊C4—472no—
670C2×C4⋊C4—474no—
671C2×C4⋊C4—474no—
672C2×C4⋊C4—472no—
673C2×C4⋊C4—471no—
674C2×C4⋊C4—471no—
675C2×C4⋊C4—471no—
676C2×C4⋊C4—471no—
677C2×C4⋊C4—471no—
678C2×C4⋊C4—471no—
679C2×C4⋊C4—472no—
680C2×C4⋊C4—474no—
681C2×C4⋊C4—474no—
682C2×C4⋊C4—474no—
683C2×C4⋊C4—474no—
684C2×C4⋊C4—474no—
685C2×C4⋊C4—474no—
686C2×C4⋊C4—474no—
687C2×C4⋊C4—474no—
688C2×C4⋊C4—4716no—
689C2×C4⋊C4—4716no—
690C2×C4⋊C4C22×D4712yes—
691C2×C4⋊C4C22×D4712yes—
692C2×C4⋊C4C22×D4712yes—
693C2×C4⋊C4C22×D4712yes—
694C2×C4⋊C4C22×D4714yes—
695C2×C4⋊C4C22×D4714yes—
696C2×C22⋊C4—471no—
697C2×C22⋊C4—471no—
698C2×C22⋊C4—474no—
699C2×C22⋊C4—471no—
700C2×C22⋊C4—471no—
701C2×C22⋊C4—474no—
702C2×C22⋊C4—471no—
703C2×C22⋊C4—471no—
704C2×C22⋊C4—474no—
705C2×C22⋊C4—474no—
706C2×C22⋊C4C22×D4714yes—
707C2×C42—471no—
708C2×C42—474no—
709C2×C42—474no—
710C2×C42—474no—
711C2×C42—471no—
712C2×C42—474no—
713C2×C42—471no—
714C2×C42—471no—
715C2×C42—471no—
716C2×C42—471no—
717C2×C42—478no—
718C2×C42—478no—
719C2×C42C22×D4711yescharacteristic
720C2×C42C22×D4714yes—
721C2×C42C22×D4711yescharacteristic
722C2×C42C22×D4711yescharacteristic
723C2×C42C22×D4718yes—
724C2×C42C22×D4711yescharacteristic
725C24—471no—
726C24—471no—
727C24C23×D4711yescharacteristic
728#41—9432no—
729C2×Q8—28no—
730C2×Q8—28no—
731C2×Q8—478no—
732C2×Q8—478no—
733C2×Q8—4716no—
734C2×Q8—474no—
735C2×Q8—9416no—
736C2×Q8—944no—
737C2×Q8—9464no—
738C2×Q8—948no—
739C2×Q8—948no—
740C2×Q8C23×D4718yes—
741C2×Q8C23×D4718yes—
742C2×D4—474no—
743C2×D4—474no—
744C2×D4—474no—
745C2×D4—944no—
746C2×D4—944no—
747C2×D4—944no—
748C22×C4—24no—
749C22×C4—24no—
750C22×C4—24no—
751C22×C4—471no—
752C22×C4—478no—
753C22×C4—474no—
754C22×C4—471no—
755C22×C4—471no—
756C22×C4—474no—
757C22×C4—471no—
758C22×C4—471no—
759C22×C4—474no—
760C22×C4—471no—
761C22×C4—474no—
762C22×C4—474no—
763C22×C4—474no—
764C22×C4—474no—
765C22×C4—474no—
766C22×C4—4716no—
767C22×C4—9416no—
768C22×C4—944no—
769C22×C4—944no—
770C22×C4—944no—
771C22×C4—944no—
772C22×C4—944no—
773C22×C4C23×D4714yes—
774C22×C4C23×D4714yes—
775C22×C4C23×D4714yes—
776C22×C4C23×D4711yescharacteristic
777C22×C4C23×D4714yes—
778C22×C4C23×D4714yes—
779C22×C4C23×D4711yescharacteristic
780C22×C4C23×D4711yescharacteristic
781C22×C4C23×D4711yescharacteristic
782C22×C4C23×D4711yescharacteristic
783C22×C4C23×D4711yescharacteristic
784C4⋊C4—4716no—
785C4⋊C4—4716no—
786C4⋊C4—474no—
787C4⋊C4—474no—
788C4⋊C4—474no—
789C4⋊C4—474no—
790C4⋊C4—4716no—
791C4⋊C4—4716no—
792C4⋊C4—4716no—
793C4⋊C4—4716no—
794C4⋊C4—4716no—
795C4⋊C4—478no—
796C4⋊C4—478no—
797C4⋊C4—478no—
798C4⋊C4—474no—
799C4⋊C4—474no—
800C4⋊C4—478no—
801C4⋊C4—4716no—
802C4⋊C4—4716no—
803C4⋊C4—4716no—
804C4⋊C4C23×D4718yes—
805C4⋊C4C23×D4718yes—
806C4⋊C4C23×D4718yes—
807C4⋊C4C23×D4718yes—
808C4⋊C4C23×D47116yes—
809C4⋊C4C23×D47116yes—
810C22⋊C4—474no—
811C22⋊C4—474no—
812C22⋊C4—4716no—
813C22⋊C4—474no—
814C22⋊C4—474no—
815C22⋊C4—4716no—
816C22⋊C4—474no—
817C22⋊C4—474no—
818C22⋊C4—4716no—
819C22⋊C4—4716no—
820C22⋊C4C23×D47116yes—
821C42—474no—
822C42—474no—
823C42—474no—
824C42—474no—
825C42—474no—
826C42—474no—
827C42—4716no—
828C42—4716no—
829C42—4716no—
830C42—4716no—
831C42C23×D4714yes—
832C42C23×D4714yes—
833C42C23×D4714yes—
834C42C23×D4714yes—
835C42C23×D47116yes—
836C23—22no—
837C23—22no—
838C23—22no—
839C23—474no—
840C23—472no—
841C23—472no—
842C23—942no—
843C23—942no—
844C23—942no—
845C23—942no—
846C23—942no—
847C23C24×D4712yes—
848C23C24×D4711yescharacteristic
849Q8—216no—
850Q8—216no—
851Q8—9432no—
852Q8—948no—
853Q8—9416no—
854Q8—9416no—
855D4—948no—
856D4—948no—
857D4—948no—
858C2×C4—22no—
859C2×C4—28no—
860C2×C4—22no—
861C2×C4—28no—
862C2×C4—22no—
863C2×C4—28no—
864C2×C4—28no—
865C2×C4—28no—
866C2×C4—474no—
867C2×C4—472no—
868C2×C4—4716no—
869C2×C4—472no—
870C2×C4—472no—
871C2×C4—478no—
872C2×C4—472no—
873C2×C4—472no—
874C2×C4—478no—
875C2×C4—472no—
876C2×C4—9432no—
877C2×C4—942no—
878C2×C4—948no—
879C2×C4—942no—
880C2×C4—942no—
881C2×C4—942no—
882C2×C4—942no—
883C2×C4—948no—
884C2×C4—948no—
885C2×C4—948no—
886C2×C4—948no—
887C2×C4—948no—
888C2×C4—948no—
889C2×C4#41×D4714yes—
890C2×C4#1309407114yes—
891C2×C4#1309407214yes—
892C2×C4C24×D4712yes—
893C2×C4C24×D4718yes—
894C2×C4C24×D4718yes—
895C2×C4C24×D4712yes—
896C2×C4C24×D4712yes—
897C2×C4C24×D4712yes—
898C2×C4C24×D4712yes—
899C2×C4C24×D4712yes—
900C22—22no—
901C22—22no—
902C22—22no—
903C22—44no—
904C22—474no—
905C22—942no—
906C22—942no—
907C22—948no—
908C22—942no—
909C22—942no—
910C22—942no—
911C22—1884no—
912C22C2×#41×D4712yes—
913C22C2×#1309407112yes—
914C22C2×#1309407212yes—
915C22C25×D4711yescharacteristic
916C4—22no—
917C4—28no—
918C4—22no—
919C4—28no—
920C4—22no—
921C4—474no—
922C4—942no—
923C4—948no—
924C4—942no—
925C4—942no—
926C4—942no—
927C4—942no—
928C4—948no—
929C4C2×#41×D4714yes—
930C4C2×#1309407114yes—
931C4C2×#1309407214yes—
932C2—42no—
933C2—944no—
934C2—1882no—
935C2#2025726714yesdirect product factor
936C2C22×#41×D4711yescharacteristic
937C2C22×#1309407111yescharacteristic
938C2C22×#1309407211yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#533C2
socleC23×C47C25
prime radicalC22×#10625350C22
hypercenterC2×#533D47
hypocenterC47C2×#3509
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #20257267C2direct (N × H)
2. C2×#15689850C2semidirect
3. C2×#15689849C2semidirect
4. C2×#15689844C2semidirect
5. C2×#15689841C2semidirect
6. C2×#15689814C2semidirect
7. C2×#15689812C2semidirect
8. C2×#15689811C2semidirect
9. C2×#15689807C2semidirect
10. C2×#15689733C2semidirect
11. C2×#15689731C2semidirect
13. C2×#15689680C2semidirect
14. C2×#15689678C2semidirect
15. C2×#15689678C2semidirect
16. C2×#15689678C2semidirect
17. C2×C4⋊Q8×D47C2semidirect
18. C2×#15689599C2semidirect
20. C2×C47×#533C2semidirect
23. #15689850C22semidirect
24. #15689849C22semidirect
25. #15689844C22semidirect
26. #15689841C22semidirect
27. #15689814C22semidirect
28. #15689812C22semidirect
29. #15689811C22semidirect
30. #15689807C22semidirect
31. #15689733C22semidirect
32. #15689731C22semidirect
34. #15689680C22semidirect
35. #15689678C22semidirect
36. #15689678C22semidirect
37. #15689678C22semidirect
44. C4⋊Q8×D47C22semidirect
68. #15689599C22semidirect
101. C47×#533C22semidirect
479. C2×#533D47semidirect
484. C2×C47#3509semidirect
507. #533C2×D47semidirect
580. C47C2×#3509semidirect
935. C2#20257267direct (N × H)

Maximal subgroups

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

subgroupindex
#202572672
C2×#156898502
C2×#156898492
C2×#156898442
C2×#156898412
C2×#156898142
C2×#156898122
C2×#156898112
C2×#156898072
C2×#156897332
C2×#156897312
C2×#156896962
C2×#156896802
C2×#156896782
C2×C4⋊Q8×D472
C2×#156895992
C2×C4×#106253502
C2×C47×#5332
C2×#350947