Finite Group Databasebeta

← C2×#20257368 #27124393

Subgroups — C2×#20257368 #27124393

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#20257368C2132yesmaximal, direct product factor
2C2×#15689852C211yesmaximal, characteristic, complemented
3C2×#15689833C211yesmaximal, characteristic, complemented
4C2×#15689830C211yesmaximal, characteristic, complemented
5C2×#15689820C212yesmaximal, complemented
6C2×#15689813C212yesmaximal, complemented
7C2×#15689809C214yesmaximal, complemented
8C2×#15689807C212yesmaximal, complemented
9C2×#15689778C212yesmaximal, complemented
10C2×#15689778C211yesmaximal, characteristic, complemented
11C2×#15689735C212yesmaximal, complemented
12C2×#15689716C214yesmaximal, complemented
13C2×#15689680C211yesmaximal, characteristic, complemented
14C2×#15689652C212yesmaximal, complemented
15C2×#125×D47C212yesmaximal, complemented
16C2×#15689603C212yesmaximal, complemented
17C2×C4×#10625350C211yesmaximal, characteristic, complemented
18C2×C47×#529C211yesmaximal, characteristic, complemented
19C22×#10625350C2211yescharacteristic
20C22×#10625350C2212yes—
21#15689852C22116yescomplemented
22#15689833C22116yescomplemented
23#15689830C22116yescomplemented
24#15689820C22132yescomplemented
25#15689813C22132yescomplemented
26#15689809C22164yescomplemented
27#15689807C22132yescomplemented
28#15689778C22132yescomplemented
29#15689778C22116yescomplemented
30#15689735C22132yescomplemented
31#15689716C22164yescomplemented
32#15689680C22116yescomplemented
33C2×#13094024C2211yescharacteristic
34C2×#13094024C2212yes—
35C2×#13094024C2211yescharacteristic
36#15689652C22132yescomplemented
37C2×#13094017C2214yes—
38C2×#13094017C2214yes—
39C2×#13094017C2214yes—
40C2×#13094016C2212yes—
41C2×#13094016C2212yes—
42C2×#13094015C2212yes—
43C2×#13094015C2212yes—
44C2×#13094015C2214yes—
45C2×#13094014C2214yes—
46C2×#13094014C2214yes—
47C2×#13094014C2214yes—
48#125×D47C22132yescomplemented
49C2×#13094006C2214yes—
50C2×#13094006C2214yes—
51C2×#13094006C2214yes—
52C2×#13094005C2214yes—
53C2×#13094003C2212yes—
54C2×#13094003C2212yes—
55C2×#13094003C2212yes—
56C2×#13094003C2212yes—
57C2×#13094002C2214yes—
58C2×#13094001C2214yes—
59C2×#13094000C2212yes—
60C2×#13093995C2212yes—
61C2×#13093995C2214yes—
62#15689603C22132yescomplemented
63C4×#10625350C22116yescomplemented
64C2×Q8×Dic47C2212yes—
65C2×C4×Dic94C2211yescharacteristic
66C2×C4×Dic94C2211yescharacteristic
67C2×C4×Dic94C2212yes—
68C2×C4×Dic94C2212yes—
69C2×C4×Dic94C2212yes—
70C2×C4×D188C2211yescharacteristic
71C2×C4×D188C2211yescharacteristic
72C2×C4×D188C2212yes—
73C2×D4×Dic47C2212yes—
74C2×C4×C22⋊D47C2212yes—
75C2×C4×C22⋊D47C2212yes—
76C2×(C22⋊D47)⋊C4C2214yes—
77C2×(C22⋊D47)⋊C4C2214yes—
78C2×#13093983C2211yescharacteristic
79C2×#13093983C2212yes—
80C2×#13093982C2214yes—
81C2×#13093981C2212yes—
82C2×#13093980C2214yes—
83C22×C4⋊Dic47C2212yes—
84C2×C4⋊C4×D47C2214yes—
85C2×C4⋊C4×D47C2212yes—
86C2×C4⋊C4×D47C2214yes—
87C2×C4⋊C4×D47C2212yes—
88C2×C42×D47C2212yes—
89C47×#529C22116yescomplemented
90C2×#126×C47C2212yes—
91C2×#125×C47C2211yescharacteristic
92C2×#124×C47C2211yescharacteristic
93C2×#123×C47C2212yes—
94C2×C22⋊Q8×C47C2211yescharacteristic
95C2×#121×C47C2211yescharacteristic
96C2×C4×Q8×C47C2211yescharacteristic
97C2×C4×D4×C47C2212yes—
98C2×C4×D4×C47C2211yescharacteristic
99C2×#117×C47C2212yes—
100C22×C42×C47C2211yescharacteristic
101C2×#10625350—28no—
102C2×#10625350—216no—
103C2×#10625350C2318yes—
104C2×#10625350C23116yes—
105C22×Dic94C2311yescharacteristic
106C22×Dic94C2312yes—
107C22×Dic94C2312yes—
108C22×D188C2311yescharacteristic
109C22×C22⋊D47C2314yes—
110C22×C22⋊D47C2312yes—
111C23×Dic47C2314yes—
112C22×C4×D47C2312yes—
113C22×C4×D47C2312yes—
114C22×C4×D47C2314yes—
115C22×C4×D47C2312yes—
116C22×C4×D47C2314yes—
117#13094024C23116yes—
118#13094024C2318yes—
119#13094024C2318yes—
120#13094017C23132yes—
121#13094017C23132yes—
122#13094017C23132yes—
123#13094016C23116yes—
124#13094016C23116yes—
125#13094015C23116yes—
126#13094015C23132yes—
127#13094015C23116yes—
128#13094014C23132yes—
129#13094014C23132yes—
130#13094014C23132yes—
131#13094006C23132yes—
132#13094006C23132yes—
133#13094006C23132yes—
134#13094005C23132yes—
135#13094003C23116yes—
136#13094003C23116yes—
137#13094003C23116yes—
138#13094003C23116yes—
139#13094002C23132yes—
140#13094001C23132yes—
141#13094000C23116yes—
142#13093995C23116yes—
143#13093995C23132yes—
144Q8×Dic47C23116yes—
145C4×Dic94C2318yes—
146C4×Dic94C23116yes—
147C4×Dic94C23116yes—
148C4×Dic94C23116yes—
149C4×Dic94C2318yes—
150C4×D188C2318yes—
151C4×D188C23116yes—
152C4×D188C2318yes—
153D4×Dic47C23116yes—
154C4×C22⋊D47C23116yes—
155C4×C22⋊D47C23116yes—
156(C22⋊D47)⋊C4C23132yes—
157(C22⋊D47)⋊C4C23132yes—
158#13093983C23116yes—
159#13093983C2318yes—
160#13093982C23132yes—
161#13093981C23116yes—
162#13093980C23132yes—
163C2×C4⋊Dic47C23116yes—
164C2×C4⋊Dic47C2314yes—
165C2×C4⋊Dic47C2312yes—
166C2×C4⋊Dic47C2312yes—
167C2×C4⋊Dic47C2314yes—
168C2×C4⋊Dic47C2311yescharacteristic
169C2×C4⋊Dic47C2312yes—
170C2×C4⋊Dic47C2311yescharacteristic
171C2×C4⋊Dic47C2312yes—
172C2×C4⋊Dic47C2314yes—
173C2×Dic47⋊C4C2314yes—
174C2×Dic47⋊C4C2314yes—
175C2×Dic47⋊C4C2314yes—
176C2×Dic47⋊C4C2314yes—
177C2×Dic47⋊C4C2314yes—
178C2×Dic47⋊C4C2314yes—
179C2×Dic47⋊C4C2314yes—
180C2×Dic47⋊C4C2312yes—
181C2×Dic47⋊C4C2312yes—
182C4⋊C4×D47C23116yes—
183C4⋊C4×D47C23132yes—
184C4⋊C4×D47C23116yes—
185C4⋊C4×D47C23132yes—
186C2×C22⋊Dic47C2314yes—
187C2×C22⋊Dic47C2312yes—
188C2×C22⋊Dic47C2314yes—
189C2×C22⋊Dic47C2314yes—
190C2×(C2×D47)⋊C4C2312yes—
191C2×(C2×D47)⋊C4C2312yes—
192C2×(C2×D47)⋊C4C2314yes—
193C2×C4×Dic47C2312yes—
194C2×C4×Dic47C2312yes—
195C2×C4×Dic47C2312yes—
196C2×C4×Dic47C2314yes—
197C2×C4×Dic47C2314yes—
198C42×D47C23116yes—
199C22×Q8×C47C2311yescharacteristic
200C22×D4×C47C2311yescharacteristic
201C22×D4×C47C2312yes—
202C23×C4×C47C2311yescharacteristic
203C23×C4×C47C2311yescharacteristic
204C23×C4×C47C2312yes—
205C23×C4×C47C2311yescharacteristic
206#126×C47C23116yes—
207#125×C47C2318yes—
208#124×C47C2318yes—
209#123×C47C23116yes—
210C22⋊Q8×C47C2318yes—
211#121×C47C2318yes—
212C4×Q8×C47C2318yes—
213C4×D4×C47C23116yes—
214C4×D4×C47C2318yes—
215#117×C47C23116yes—
216C2×C4⋊C4×C47C2312yes—
217C2×C4⋊C4×C47C2312yes—
218C2×C4⋊C4×C47C2311yescharacteristic
219C2×C4⋊C4×C47C2312yes—
220C2×C4⋊C4×C47C2311yescharacteristic
221C2×C4⋊C4×C47C2312yes—
222C2×C22⋊C4×C47C2312yes—
223C2×C22⋊C4×C47C2312yes—
224C2×C22⋊C4×C47C2312yes—
225C2×C22⋊C4×C47C2312yes—
226C2×C22⋊C4×C47C2312yes—
227C2×C42×C47C2311yescharacteristic
228C2×C42×C47C2311yescharacteristic
229C2×C42×C47C2311yescharacteristic
230C2×C42×C47C2311yescharacteristic
231C2×C42×C47C2318yes—
232C2×C42×C47C2312yes—
233C24×C47C2412yes—
234C24×C47C2411yescharacteristic
235C23×D47C2412yes—
236C2×Q8×C47—24no—
237C2×Q8×C47C2414yes—
238C2×D4×C47—24no—
239C2×D4×C47—44no—
240C2×D4×C47C2414yes—
241C2×D4×C47C2418yes—
242C22×C4×C47—24no—
243C22×C4×C47—28no—
244C22×C4×C47—24no—
245C22×C4×C47—42no—
246C22×C4×C47C2411yescharacteristic
247C22×C4×C47C2411yescharacteristic
248C22×C4×C47C2411yescharacteristic
249C22×C4×C47C2411yescharacteristic
250C22×C4×C47C2414yes—
251C22×C4×C47C2414yes—
252C22×C4×C47C2412yes—
253C22×C4×C47C2412yes—
254C22×C4×C47C2412yes—
255C22×C4×C47C2418yes—
256C22×C4×C47C2414yes—
257C22×C4×C47C2411yescharacteristic
258C22×C4×C47C2411yescharacteristic
259C2×C22⋊D47—216no—
260C2×C22⋊D47—28no—
261C2×C22⋊D47C24116yes—
262C2×C22⋊D47C2418yes—
263C22×Dic47—48no—
264C22×Dic47C2412yes—
265C22×Dic47C2412yes—
266C22×Dic47C2412yes—
267C22×Dic47C2414yes—
268C22×Dic47C2414yes—
269C22×Dic47C24116yes—
270#10625350—232no—
271#10625350—264no—
272C2×D188#4118yes—
273C2×D188C2414yes—
274C2×C4×D47—28no—
275C2×C4×D47—216no—
276C2×C4×D47—28no—
277C2×C4×D47—48no—
278C2×C4×D47—44no—
279C2×C4×D47C2418yes—
280C2×C4×D47C2418yes—
281C2×C4×D47C24116yes—
282C2×C4×D47C2418yes—
283C2×C4×D47C24116yes—
284C2×Dic94—24no—
285C2×Dic94—28no—
286C2×Dic94—44no—
287C2×Dic94C2414yes—
288C2×Dic94C2418yes—
289C2×Dic94C2418yes—
290C4⋊C4×C47C2418yes—
291C4⋊C4×C47C2418yes—
292C4⋊C4×C47C2414yes—
293C4⋊C4×C47C2418yes—
294C4⋊C4×C47C2414yes—
295C4⋊C4×C47C2418yes—
296C22⋊C4×C47C2418yes—
297C22⋊C4×C47C2418yes—
298C22⋊C4×C47C2418yes—
299C22⋊C4×C47C2418yes—
300C22⋊C4×C47C2418yes—
301C42×C47C2414yes—
302C42×C47C2414yes—
303C42×C47C2414yes—
304C42×C47C2414yes—
305C42×C47C2418yes—
306C22⋊Dic47C24116yes—
307C22⋊Dic47C2418yes—
308C22⋊Dic47C24116yes—
309C22⋊Dic47C24116yes—
310(C2×D47)⋊C4C2418yes—
311(C2×D47)⋊C4C2418yes—
312(C2×D47)⋊C4C24116yes—
313C4⋊Dic47C24116yes—
314C4⋊Dic47C2418yes—
315C4⋊Dic47C2418yes—
316C4⋊Dic47C24116yes—
317C4⋊Dic47C2414yes—
318C4⋊Dic47C2418yes—
319C4⋊Dic47C2414yes—
320C4⋊Dic47C2418yes—
321C4⋊Dic47C24116yes—
322Dic47⋊C4C24116yes—
323Dic47⋊C4C24116yes—
324Dic47⋊C4C24116yes—
325Dic47⋊C4C24116yes—
326Dic47⋊C4C24116yes—
327Dic47⋊C4C24116yes—
328Dic47⋊C4C24116yes—
329Dic47⋊C4C2418yes—
330Dic47⋊C4C2418yes—
331C4×Dic47C2418yes—
332C4×Dic47C2418yes—
333C4×Dic47C2418yes—
334C4×Dic47C24116yes—
335C4×Dic47C24116yes—
336C23×C47—24no—
337C23×C47—22no—
338C23×C47—22no—
339C23×C47—24no—
340C23×C47—24no—
341C23×C47—22no—
342C23×C47C2512yes—
343C23×C47C2514yes—
344C23×C47C2511yescharacteristic
345C22×D47—24no—
346C22×D47—24no—
347C22×D47C2×#4118yes—
348C22×D47C2514yes—
349Q8×C47—28no—
350D4×C47—28no—
351D4×C47—48no—
352C2×C4×C47—22no—
353C2×C4×C47—24no—
354C2×C4×C47—22no—
355C2×C4×C47—24no—
356C2×C4×C47—22no—
357C2×C4×C47—22no—
358C2×C4×C47—24no—
359C2×C4×C47—28no—
360C2×C4×C47—216no—
361C2×C4×C47—28no—
362C2×C4×C47—44no—
363C2×C4×C47C2×#4114yes—
364C2×C4×C472−1+414yes—
365C2×C4×C47C2512yes—
366C2×C4×C47C2512yes—
367C2×C4×C47C2512yes—
368C2×C4×C47C2514yes—
369C2×C4×C47C2514yes—
370C2×C4×C47C2514yes—
371C2×C4×C47C2512yes—
372C2×C4×C47C2512yes—
373C2×C4×C47C2512yes—
374C22⋊D47—232no—
375C22⋊D47—216no—
376C2×Dic47—24no—
377C2×Dic47—28no—
378C2×Dic47—24no—
379C2×Dic47—28no—
380C2×Dic47—24no—
381C2×Dic47—416no—
382C2×Dic47C2514yes—
383C2×Dic47C2514yes—
384C2×Dic47C2514yes—
385C2×Dic47C2518yes—
386C2×Dic47C2518yes—
387D188C2×#41116yes—
388C4×D47—216no—
389C4×D47—232no—
390C4×D47—216no—
391C4×D47—416no—
392C4×D47—48no—
393Dic94—28no—
394Dic94—216no—
395Dic94—48no—
396C2×#3515—471nomaximal, Sylow
397C22×C47—22no—
398C22×C47—24no—
399C22×C47—22no—
400C22×C47—24no—
401C22×C47—24no—
402C22×C47—22no—
403C22×C47—44no—
404C22×C47—48no—
405C22×C47C22×#4112yes—
406C22×C47C2×2−1+412yes—
407C22×C47#58512yes—
408C22×C47C2611yescharacteristic
409C2×D47—24no—
410C2×D47—24no—
411C2×D47—216no—
412C2×D47C22×#4118yes—
413C4×C47—22no—
414C4×C47—24no—
415C4×C47—22no—
416C4×C47—24no—
417C4×C47—22no—
418C4×C47—22no—
419C4×C47—24no—
420C4×C47C22×#4114yes—
421C4×C47C2×2−1+414yes—
422Dic47—24no—
423Dic47—28no—
424Dic47—24no—
425Dic47—28no—
426Dic47—24no—
427#3515—4732no—
428C2×#557—471no—
429C2×#554—471no—
430C2×#554—471no—
431C2×#553—472no—
432C2×#552—474no—
433C2×#552—472no—
434C2×#552—472no—
435C2×#547—471no—
436C2×#547—472no—
437C2×#541—472no—
438C2×#539—474no—
439C2×#533—471no—
440C2×#529—472no—
441C2×#529D4711yescharacteristic, complemented
442C22×#125—472no—
443C2×#520—472no—
444C2×C4×#41—471no—
445C2×C47—42no—
446C2×C47—44no—
447C2×C47#351514yescomplemented
448C2×C47C23×#4111yescharacteristic
449C2×C47C22×2−1+411yescharacteristic
450C2×C47C2×#58511yescharacteristic
451D47—28no—
452C22×#41—471no—
453C22×#41—472no—
454#557—4716no—
455#554—4716no—
456#554—4716no—
457#553—4732no—
458#552—4764no—
459#552—4732no—
460#552—4732no—
461#547—4716no—
462#547—4732no—
463#541—4732no—
464#539—4764no—
465#533—4716no—
466C2×C4⋊Q8—471no—
467C2×C4⋊Q8—471no—
468C2×C4⋊Q8—472no—
469#529—4732no—
470#529C2×D47116yescomplemented
471C2×#126—474no—
472C2×#126—474no—
473C2×#126—474no—
474C2×#126C2×D4712yes—
475C2×#125—4732no—
476C2×#125—474no—
477C2×#125—474no—
478C2×#125—472no—
479C2×#125—472no—
480C2×#125—474no—
481C2×#125—474no—
482C2×#125—472no—
483C2×#125—472no—
484C2×#125C2×D4711yescharacteristic
485C2×#124C2×D4711yescharacteristic
486C2×#123—474no—
487C2×#123—474no—
488C2×#123—474no—
489C2×#123—474no—
490C2×#123C2×D4712yes—
491C2×C22⋊Q8—472no—
492C2×C22⋊Q8—472no—
493C2×C22⋊Q8—472no—
494C2×C22⋊Q8—472no—
495C2×C22⋊Q8—472no—
496C2×C22⋊Q8—474no—
497C2×C22⋊Q8—474no—
498C2×C22⋊Q8C2×D4711yescharacteristic
499C2×#121—472no—
500C2×#121—474no—
501C2×#121C2×D4711yescharacteristic
502#520—4732no—
503C4×#41—4716no—
504C2×C4×Q8—472no—
505C2×C4×Q8—471no—
506C2×C4×Q8—471no—
507C2×C4×Q8—472no—
508C2×C4×Q8—472no—
509C2×C4×Q8—472no—
510C2×C4×Q8C2×D4711yescharacteristic
511C2×C4×D4—472no—
512C2×C4×D4—472no—
513C2×C4×D4—472no—
514C2×C4×D4—474no—
515C2×C4×D4—474no—
516C2×C4×D4—471no—
517C2×C4×D4—471no—
518C2×C4×D4—472no—
519C2×C4×D4C2×D4712yes—
520C2×C4×D4C2×D4711yescharacteristic
521C2×#117—471no—
522C2×#117—472no—
523C2×#117—474no—
524C2×#117—474no—
525C2×#117—472no—
526C2×#117C2×D4712yes—
527C22×C4⋊C4—472no—
528C22×C4⋊C4—474no—
529C22×C4⋊C4—472no—
530C22×C4⋊C4—474no—
531C22×C4⋊C4—472no—
532C22×C42—472no—
533C22×C42C2×D4711yescharacteristic
534C47C2×#351511yescharacteristic, complemented, Sylow
535C2×#41—478no—
536C2×#41—4716no—
537C2×#41—948no—
538C2×#41—9416no—
539C22×Q8—471no—
540C22×Q8—472no—
541C22×Q8—472no—
542C22×Q8C22×D4711yescharacteristic
543C22×D4—472no—
544C22×D4—474no—
545C22×D4—471no—
546C22×D4C22×D4711yescharacteristic
547C22×D4C22×D4712yes—
548C23×C4—474no—
549C23×C4—474no—
550C23×C4—472no—
551C23×C4—472no—
552C23×C4—474no—
553C23×C4—472no—
554C23×C4C22×D4712yes—
555C23×C4C22×D4711yescharacteristic
556C23×C4C22×D4711yescharacteristic
557C23×C4C22×D4711yescharacteristic
558C4⋊Q8—478no—
559C4⋊Q8—478no—
560C4⋊Q8—4716no—
561#126—4732no—
562#126—4732no—
563#126—4732no—
564#126C22×D47116yes—
565#125—4732no—
566#125—4732no—
567#125—4716no—
568#125—4716no—
569#125—4732no—
570#125—4732no—
571#125—4716no—
572#125—4716no—
573#125C22×D4718yes—
574#124C22×D4718yes—
575#123—4732no—
576#123—4732no—
577#123—4732no—
578#123—4732no—
579#123C22×D47116yes—
580C22⋊Q8—4716no—
581C22⋊Q8—4716no—
582C22⋊Q8—4716no—
583C22⋊Q8—4716no—
584C22⋊Q8—4716no—
585C22⋊Q8—4732no—
586C22⋊Q8—4732no—
587C22⋊Q8C22×D4718yes—
588#121—4716no—
589#121—4732no—
590#121C22×D4718yes—
591C4×Q8—4716no—
592C4×Q8—478no—
593C4×Q8—478no—
594C4×Q8—4716no—
595C4×Q8—4716no—
596C4×Q8—4716no—
597C4×Q8C22×D4718yes—
598C4×D4—4716no—
599C4×D4—4716no—
600C4×D4—4716no—
601C4×D4—4732no—
602C4×D4—4732no—
603C4×D4—478no—
604C4×D4—478no—
605C4×D4—4716no—
606C4×D4C22×D47116yes—
607C4×D4C22×D4718yes—
608#117—478no—
609#117—4716no—
610#117—4732no—
611#117—4732no—
612#117—4716no—
613#117C22×D47116yes—
614C2×C4⋊C4—471no—
615C2×C4⋊C4—474no—
616C2×C4⋊C4—472no—
617C2×C4⋊C4—472no—
618C2×C4⋊C4—474no—
619C2×C4⋊C4—472no—
620C2×C4⋊C4—474no—
621C2×C4⋊C4—474no—
622C2×C4⋊C4—4716no—
623C2×C4⋊C4—474no—
624C2×C4⋊C4—474no—
625C2×C4⋊C4—474no—
626C2×C4⋊C4—474no—
627C2×C4⋊C4—472no—
628C2×C4⋊C4—471no—
629C2×C4⋊C4—472no—
630C2×C4⋊C4—474no—
631C2×C4⋊C4—472no—
632C2×C4⋊C4—474no—
633C2×C4⋊C4—4732no—
634C2×C4⋊C4—4732no—
635C2×C4⋊C4—4716no—
636C2×C4⋊C4—4716no—
637C2×C4⋊C4C22×D4712yes—
638C2×C4⋊C4C22×D4711yescharacteristic
639C2×C4⋊C4C22×D4712yes—
640C2×C4⋊C4C22×D4711yescharacteristic
641C2×C4⋊C4C22×D4712yes—
642C2×C4⋊C4C22×D4712yes—
643C2×C22⋊C4—472no—
644C2×C22⋊C4—474no—
645C2×C22⋊C4—474no—
646C2×C22⋊C4—474no—
647C2×C22⋊C4—472no—
648C2×C22⋊C4—472no—
649C2×C22⋊C4—474no—
650C2×C22⋊C4C22×D4712yes—
651C2×C22⋊C4C22×D4712yes—
652C2×C22⋊C4C22×D4712yes—
653C2×C22⋊C4C22×D4712yes—
654C2×C22⋊C4C22×D4712yes—
655C2×C42—472no—
656C2×C42—474no—
657C2×C42—474no—
658C2×C42—472no—
659C2×C42—472no—
660C2×C42—4716no—
661C2×C42C22×D4711yescharacteristic
662C2×C42C22×D4711yescharacteristic
663C2×C42C22×D4712yes—
664C2×C42C22×D4711yescharacteristic
665C2×C42C22×D4718yes—
666C2×C42C22×D4711yescharacteristic
667C24—472no—
668C24C23×D4711yescharacteristic
669C24C23×D4712yes—
670#41—9432no—
671#41—9464no—
672C2×Q8—24no—
673C2×Q8—474no—
674C2×Q8—478no—
675C2×Q8—478no—
676C2×Q8—944no—
677C2×Q8—948no—
678C2×Q8—1884no—
679C2×Q8C23×D4714yes—
680C2×D4—24no—
681C2×D4—44no—
682C2×D4—478no—
683C2×D4—4716no—
684C2×D4—478no—
685C2×D4—474no—
686C2×D4—948no—
687C2×D4—9416no—
688C2×D4C23×D4714yes—
689C2×D4C23×D4718yes—
690C22×C4—28no—
691C22×C4—24no—
692C22×C4—24no—
693C22×C4—42no—
694C22×C4—472no—
695C22×C4—472no—
696C22×C4—474no—
697C22×C4—472no—
698C22×C4—474no—
699C22×C4—4716no—
700C22×C4—478no—
701C22×C4—478no—
702C22×C4—4716no—
703C22×C4—478no—
704C22×C4—4716no—
705C22×C4—9416no—
706C22×C4—948no—
707C22×C4—948no—
708C22×C4—1884no—
709C22×C4—1888no—
710C22×C4—1888no—
711C22×C4C23×D4714yes—
712C22×C4C23×D4714yes—
713C22×C4C23×D4718yes—
714C22×C4C23×D4711yescharacteristic
715C22×C4C23×D4711yescharacteristic
716C22×C4C23×D4711yescharacteristic
717C22×C4C23×D4712yes—
718C22×C4C23×D4711yescharacteristic
719C22×C4C23×D4712yes—
720C22×C4C23×D4712yes—
721C22×C4C23×D4714yes—
722C22×C4C23×D4711yescharacteristic
723C22×C4C23×D4711yescharacteristic
724C4⋊C4—4716no—
725C4⋊C4—4716no—
726C4⋊C4—4716no—
727C4⋊C4—4716no—
728C4⋊C4—4716no—
729C4⋊C4—4716no—
730C4⋊C4—478no—
731C4⋊C4—478no—
732C4⋊C4—4716no—
733C4⋊C4—474no—
734C4⋊C4—4716no—
735C4⋊C4—478no—
736C4⋊C4—478no—
737C4⋊C4—478no—
738C4⋊C4—4716no—
739C4⋊C4—474no—
740C4⋊C4—478no—
741C4⋊C4—4716no—
742C4⋊C4C23×D4718yes—
743C4⋊C4C23×D4714yes—
744C4⋊C4C23×D4718yes—
745C4⋊C4C23×D4714yes—
746C4⋊C4C23×D4718yes—
747C4⋊C4C23×D4718yes—
748C22⋊C4—478no—
749C22⋊C4—4716no—
750C22⋊C4—4716no—
751C22⋊C4—4716no—
752C22⋊C4—478no—
753C22⋊C4—478no—
754C22⋊C4—4716no—
755C22⋊C4C23×D4718yes—
756C22⋊C4C23×D4718yes—
757C22⋊C4C23×D4718yes—
758C22⋊C4C23×D4718yes—
759C22⋊C4C23×D4718yes—
760C42—478no—
761C42—478no—
762C42—478no—
763C42—4716no—
764C42—4716no—
765C42C23×D4714yes—
766C42C23×D4714yes—
767C42C23×D4714yes—
768C42C23×D4714yes—
769C42C23×D4718yes—
770C23—22no—
771C23—24no—
772C23—22no—
773C23—24no—
774C23—22no—
775C23—24no—
776C23—478no—
777C23—474no—
778C23—944no—
779C23—944no—
780C23C24×D4712yes—
781C23C24×D4714yes—
782C23C24×D4711yescharacteristic
783Q8—28no—
784Q8—948no—
785Q8—9416no—
786Q8—1888no—
787D4—28no—
788D4—48no—
789D4—4716no—
790D4—9416no—
791D4—9432no—
792C2×C4—22no—
793C2×C4—24no—
794C2×C4—22no—
795C2×C4—24no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—28no—
800C2×C4—216no—
801C2×C4—28no—
802C2×C4—44no—
803C2×C4—474no—
804C2×C4—474no—
805C2×C4—474no—
806C2×C4—478no—
807C2×C4—478no—
808C2×C4—9416no—
809C2×C4—9432no—
810C2×C4—948no—
811C2×C4—944no—
812C2×C4—944no—
813C2×C4—944no—
814C2×C4—948no—
815C2×C4—9416no—
816C2×C4—1888no—
817C2×C4—18816no—
818C2×C4—18816no—
819C2×C4#41×D4714yes—
820C2×C4#1309407114yes—
821C2×C4C24×D4712yes—
822C2×C4C24×D4712yes—
823C2×C4C24×D4712yes—
824C2×C4C24×D4714yes—
825C2×C4C24×D4712yes—
826C2×C4C24×D4714yes—
827C2×C4C24×D4714yes—
828C2×C4C24×D4712yes—
829C2×C4C24×D4712yes—
830C22—22no—
831C22—24no—
832C22—22no—
833C22—24no—
834C22—22no—
835C22—24no—
836C22—44no—
837C22—48no—
838C22—478no—
839C22—9416no—
840C22—944no—
841C22—944no—
842C22C2×#41×D4712yes—
843C22C2×#1309407112yes—
844C22#1568995912yes—
845C22C25×D4711yescharacteristic
846C4—22no—
847C4—24no—
848C4—22no—
849C4—24no—
850C4—22no—
851C4—22no—
852C4—24no—
853C4—944no—
854C4—948no—
855C4—944no—
856C4—944no—
857C4—948no—
858C4C2×#41×D4714yes—
859C4C2×#1309407114yes—
860C2—42no—
861C2—44no—
862C2—948no—
863C2#2025736814yesdirect product factor
864C2C22×#41×D4711yescharacteristic
865C2C22×#1309407111yescharacteristic
866C2C2×#1568995911yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#529C2
socleC23×C47C25
hypercenterC2×#529D47
hypocenterC47C2×#3515
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. #20257368C2direct (N × H)
2. C2×#15689852C2semidirect
3. C2×#15689833C2semidirect
4. C2×#15689830C2semidirect
5. C2×#15689820C2semidirect
6. C2×#15689813C2semidirect
7. C2×#15689809C2semidirect
8. C2×#15689807C2semidirect
9. C2×#15689778C2semidirect
10. C2×#15689778C2semidirect
11. C2×#15689735C2semidirect
12. C2×#15689716C2semidirect
13. C2×#15689680C2semidirect
14. C2×#15689652C2semidirect
15. C2×#125×D47C2semidirect
16. C2×#15689603C2semidirect
17. C2×C4×#10625350C2semidirect
18. C2×C47×#529C2semidirect
21. #15689852C22semidirect
22. #15689833C22semidirect
23. #15689830C22semidirect
24. #15689820C22semidirect
25. #15689813C22semidirect
26. #15689809C22semidirect
27. #15689807C22semidirect
28. #15689778C22semidirect
29. #15689778C22semidirect
30. #15689735C22semidirect
31. #15689716C22semidirect
32. #15689680C22semidirect
36. #15689652C22semidirect
48. #125×D47C22semidirect
62. #15689603C22semidirect
63. C4×#10625350C22semidirect
89. C47×#529C22semidirect
441. C2×#529D47semidirect
447. C2×C47#3515semidirect
470. #529C2×D47semidirect
534. C47C2×#3515semidirect
863. C2#20257368direct (N × H)

Maximal subgroups

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

subgroupindex
#202573682
C2×#156898522
C2×#156898332
C2×#156898302
C2×#156898202
C2×#156898132
C2×#156898092
C2×#156898072
C2×#156897782
C2×#156897352
C2×#156897162
C2×#156896802
C2×#156896522
C2×#125×D472
C2×#156896032
C2×C4×#106253502
C2×C47×#5292
C2×#351547