Finite Group Databasebeta

← C2×#20257829 #27123885

Subgroups — C2×#20257829 #27123885

Order 12032.

7086 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257829C2132yesmaximal, direct product factor
2C2×#15689872C214yesmaximal, complemented
3C2×#15689848C211yesmaximal, characteristic, complemented
4C2×#15689847C211yesmaximal, characteristic, complemented
5C2×#15689828C212yesmaximal, complemented
6C2×#15689821C212yesmaximal, complemented
7C2×#15689788C211yesmaximal, characteristic, complemented
8C2×Q8×C22⋊D47C212yesmaximal, complemented
9C2×#15689784C212yesmaximal, complemented
10C2×#15689776C211yesmaximal, characteristic, complemented
11C2×#15689750C212yesmaximal, complemented
12C2×#15689747C212yesmaximal, complemented
13C2×#15689734C212yesmaximal, complemented
14C2×#15689720C214yesmaximal, complemented
15C2×#15689698C212yesmaximal, complemented
16C2×#15689657C211yesmaximal, characteristic, complemented
17C2×#15689657C211yesmaximal, characteristic, complemented
18C22×C4⋊Q8×C47C211yesmaximal, characteristic, complemented
19C22×#10625354C2212yes—
20C22×Q8×D47C2212yes—
21#15689872C22164yescomplemented
22#15689848C22116yescomplemented
23#15689847C22116yescomplemented
24#15689828C22132yescomplemented
25#15689821C22132yescomplemented
26#15689788C22116yescomplemented
27Q8×C22⋊D47C22132yescomplemented
28#15689784C22132yescomplemented
29#15689776C22116yescomplemented
30#15689750C22132yescomplemented
31#15689747C22132yescomplemented
32#15689734C22132yescomplemented
33#15689720C22164yescomplemented
34#15689698C22132yescomplemented
35C2×#13094023C2212yes—
36C2×#13094022C2214yes—
37C2×#13094022C2212yes—
38#15689657C22116yescomplemented
39#15689657C22116yescomplemented
40C2×#13094019C2214yes—
41C2×#13094019C2214yes—
42C2×#13094019C2214yes—
43C2×#13094018C2212yes—
44C2×#13094018C2212yes—
45C2×#13094016C2211yescharacteristic
46C2×#13094016C2211yescharacteristic
47C2×#13094015C2212yes—
48C2×#13094014C2214yes—
49C2×#13094014C2214yes—
50C2×#13094014C2214yes—
51C2×#13094013C2214yes—
52C2×#13094013C2212yes—
53C2×#13094012C2211yescharacteristic
54C2×#13094012C2211yescharacteristic
55C2×#13094009C2214yes—
56C2×#13094009C2214yes—
57C2×#13094009C2214yes—
58C2×#13094007C2212yes—
59C2×#13094007C2212yes—
60C2×#13094004C2212yes—
61C2×#13094003C2211yescharacteristic
62C2×#13094003C2214yes—
63C2×#13094003C2211yescharacteristic
64C2×#13094002C2214yes—
65C2×#13094002C2214yes—
66C2×#13094002C2214yes—
67C2×#13094000C2214yes—
68C2×#13094000C2214yes—
69C2×#13094000C2212yes—
70C2×#13094000C2212yes—
71C2×#13093999C2212yes—
72C2×#13093998C2211yescharacteristic
73C2×#13093998C2214yes—
74C2×#13093998C2211yescharacteristic
75C2×Q8×Dic47C2212yes—
76C2×Q8×Dic47C2212yes—
77C2×C4×Dic94C2211yescharacteristic
78C2×C4×Dic94C2211yescharacteristic
79C2×#13093989C2212yes—
80C2×C4×D188C2211yescharacteristic
81C2×C4×D188C2211yescharacteristic
82C2×#13093986C2212yes—
83C2×C4×C22⋊D47C2212yes—
84C2×C4×C22⋊D47C2214yes—
85C2×C4×C22⋊D47C2214yes—
86C2×C4×C22⋊D47C2212yes—
87C2×#13093982C2212yes—
88C2×#13093981C2212yes—
89C2×#13093981C2212yes—
90C2×C4⋊C4×D47C2212yes—
91C23×Q8×C47C2212yes—
92C2×C4⋊Q8×C47C2212yes—
93C2×C4⋊Q8×C47C2211yescharacteristic
94C2×C4⋊Q8×C47C2211yescharacteristic
95C2×C4⋊Q8×C47C2212yes—
96C2×C4⋊Q8×C47C2212yes—
97C2×C4⋊Q8×C47C22116yescomplemented
98C22×C4⋊C4×C47C2212yes—
99C22×C4⋊C4×C47C2212yes—
100C22×C42×C47C2211yescharacteristic
101C2×#10625354—48no—
102C2×#10625354C23116yes—
103C22×Dic94C2311yescharacteristic
104C22×Dic94C2311yescharacteristic
105C22×Dic94C2314yes—
106C2×Q8×D47—48no—
107C2×Q8×D47C23116yes—
108C22×D188C2311yescharacteristic
109C22×D188C2311yescharacteristic
110C22×D188C2314yes—
111C22×C22⋊D47C2312yes—
112C22×C22⋊D47C2312yes—
113C22×C4×D47C2312yes—
114C22×C4×D47C2312yes—
115C22×C4×D47C2314yes—
116C22×C4×D47C2314yes—
117#13094023C23116yes—
118#13094022C23132yes—
119#13094022C23116yes—
120#13094019C23132yes—
121#13094019C23132yes—
122#13094019C23132yes—
123#13094018C23116yes—
124#13094018C23116yes—
125#13094016C2318yes—
126#13094016C2318yes—
127#13094015C23116yes—
128#13094014C23132yes—
129#13094014C23132yes—
130#13094014C23132yes—
131#13094013C23132yes—
132#13094013C23116yes—
133#13094012C2318yes—
134#13094012C2318yes—
135#13094009C23132yes—
136#13094009C23132yes—
137#13094009C23132yes—
138#13094007C23116yes—
139#13094007C23116yes—
140#13094004C23116yes—
141#13094003C2318yes—
142#13094003C23132yes—
143#13094003C2318yes—
144#13094002C23132yes—
145#13094002C23132yes—
146#13094002C23132yes—
147#13094000C23116yes—
148#13094000C23116yes—
149#13094000C23132yes—
150#13094000C23132yes—
151#13093999C23116yes—
152#13093998C2318yes—
153#13093998C23132yes—
154#13093998C2318yes—
155Q8×Dic47C23116yes—
156Q8×Dic47C23116yes—
157C4×Dic94C2318yes—
158C4×Dic94C2318yes—
159#13093989C23116yes—
160C4×D188C2318yes—
161C4×D188C2318yes—
162#13093986C23116yes—
163C4×C22⋊D47C23116yes—
164C4×C22⋊D47C23132yes—
165C4×C22⋊D47C23132yes—
166C4×C22⋊D47C23116yes—
167#13093982C23116yes—
168#13093981C23116yes—
169#13093981C23116yes—
170C2×C4⋊Dic47C2311yescharacteristic
171C2×C4⋊Dic47C2311yescharacteristic
172C2×C4⋊Dic47C2311yescharacteristic
173C2×C4⋊Dic47C2311yescharacteristic
174C2×C4⋊Dic47C2314yes—
175C2×C4⋊Dic47C2314yes—
176C2×Dic47⋊C4C2314yes—
177C2×Dic47⋊C4C2312yes—
178C2×Dic47⋊C4C2312yes—
179C2×Dic47⋊C4C2312yes—
180C2×Dic47⋊C4C2312yes—
181C2×Dic47⋊C4C2314yes—
182C2×Dic47⋊C4C2312yes—
183C2×Dic47⋊C4C2314yes—
184C2×Dic47⋊C4C2312yes—
185C2×Dic47⋊C4C2314yes—
186C2×Dic47⋊C4C2312yes—
187C2×Dic47⋊C4C2312yes—
188C4⋊C4×D47C23116yes—
189C2×C22⋊Dic47C2312yes—
190C2×C22⋊Dic47C2312yes—
191C2×(C2×D47)⋊C4C2312yes—
192C2×(C2×D47)⋊C4C2312yes—
193C2×(C2×D47)⋊C4C2312yes—
194C2×(C2×D47)⋊C4C2312yes—
195C2×(C2×D47)⋊C4C2314yes—
196C2×(C2×D47)⋊C4C2314yes—
197C2×(C2×D47)⋊C4C2312yes—
198C2×(C2×D47)⋊C4C2312yes—
199C2×(C2×D47)⋊C4C2314yes—
200C2×(C2×D47)⋊C4C2314yes—
201C2×(C2×D47)⋊C4C2312yes—
202C2×(C2×D47)⋊C4C2312yes—
203C2×C4×Dic47C2312yes—
204C2×C4×Dic47C2312yes—
205C2×C4×Dic47C2314yes—
206C2×C4×Dic47C2314yes—
207C22×Q8×C47—48no—
208C22×Q8×C47C2312yes—
209C22×Q8×C47C2312yes—
210C22×Q8×C47C23116yes—
211C22×Q8×C47C2314yes—
212C23×C4×C47C2311yescharacteristic
213C23×C4×C47C2311yescharacteristic
214C23×C4×C47C2311yescharacteristic
215C23×C4×C47C2314yes—
216C4⋊Q8×C47C23116yes—
217C4⋊Q8×C47C23116yes—
218C4⋊Q8×C47C2318yes—
219C4⋊Q8×C47C2318yes—
220C4⋊Q8×C47C23116yes—
221C2×C4⋊C4×C47C2312yes—
222C2×C4⋊C4×C47C2312yes—
223C2×C4⋊C4×C47C2312yes—
224C2×C4⋊C4×C47C2314yes—
225C2×C4⋊C4×C47C2314yes—
226C2×C4⋊C4×C47C2312yes—
227C2×C4⋊C4×C47C23116yes—
228C2×C4⋊C4×C47C23116yes—
229C2×C42×C47C2311yescharacteristic
230C2×C42×C47C2311yescharacteristic
231C2×C42×C47C2311yescharacteristic
232C2×C42×C47C2311yescharacteristic
233C2×C42×C47C2318yes—
234C24×C47C2411yescharacteristic
235C23×D47C2412yes—
236C23×D47C2412yes—
237C2×Q8×C47—28no—
238C2×Q8×C47—28no—
239C2×Q8×C47—48no—
240C2×Q8×C47—432no—
241C2×Q8×C47C2418yes—
242C2×Q8×C47C2418yes—
243C2×Q8×C47C24116yes—
244C22×C4×C47—24no—
245C22×C4×C47—24no—
246C22×C4×C47—24no—
247C22×C4×C47—48no—
248C22×C4×C47C2411yescharacteristic
249C22×C4×C47C2411yescharacteristic
250C22×C4×C47C2411yescharacteristic
251C22×C4×C47C2414yes—
252C22×C4×C47C2414yes—
253C22×C4×C47C2411yescharacteristic
254C22×C4×C47C2414yes—
255C22×C4×C47C2414yes—
256C22×C4×C47C2414yes—
257C22×C4×C47C24116yes—
258C22×C4×C47C2411yescharacteristic
259C22×C4×C47C2411yescharacteristic
260C2×C22⋊D47—28no—
261C2×C22⋊D47—28no—
262C2×C22⋊D47C2418yes—
263C2×C22⋊D47C2418yes—
264C22×Dic47C2412yes—
265C22×Dic47C2412yes—
266C22×Dic47C2412yes—
267C22×Dic47C2412yes—
268C22×Dic47C2412yes—
269C22×Dic47C2412yes—
270#10625354—432no—
271Q8×D47—432no—
272C2×D188—24no—
273C2×D188—24no—
274C2×D188—48no—
275C2×D188C2414yes—
276C2×D188C2414yes—
277C2×D188C24116yes—
278C2×C4×D47—28no—
279C2×C4×D47—28no—
280C2×C4×D47—48no—
281C2×C4×D47—48no—
282C2×C4×D47C2418yes—
283C2×C4×D47C2418yes—
284C2×C4×D47C24116yes—
285C2×C4×D47C24116yes—
286C2×Dic94—24no—
287C2×Dic94—24no—
288C2×Dic94—48no—
289C2×Dic94C2414yes—
290C2×Dic94C2414yes—
291C2×Dic94C24116yes—
292C4⋊C4×C47C2418yes—
293C4⋊C4×C47C2418yes—
294C4⋊C4×C47C2418yes—
295C4⋊C4×C47C24116yes—
296C4⋊C4×C47C24116yes—
297C4⋊C4×C47C2418yes—
298C42×C47C2414yes—
299C42×C47C2414yes—
300C42×C47C2414yes—
301C42×C47C2414yes—
302C22⋊Dic47C2418yes—
303C22⋊Dic47C2418yes—
304(C2×D47)⋊C4C2418yes—
305(C2×D47)⋊C4C2418yes—
306(C2×D47)⋊C4C2418yes—
307(C2×D47)⋊C4C2418yes—
308(C2×D47)⋊C4C24116yes—
309(C2×D47)⋊C4C24116yes—
310(C2×D47)⋊C4C2418yes—
311(C2×D47)⋊C4C2418yes—
312(C2×D47)⋊C4C24116yes—
313(C2×D47)⋊C4C24116yes—
314(C2×D47)⋊C4C2418yes—
315(C2×D47)⋊C4C2418yes—
316C4⋊Dic47C2414yes—
317C4⋊Dic47C2414yes—
318C4⋊Dic47C2414yes—
319C4⋊Dic47C2414yes—
320C4⋊Dic47C24116yes—
321C4⋊Dic47C24116yes—
322Dic47⋊C4C24116yes—
323Dic47⋊C4C2418yes—
324Dic47⋊C4C2418yes—
325Dic47⋊C4C2418yes—
326Dic47⋊C4C2418yes—
327Dic47⋊C4C24116yes—
328Dic47⋊C4C2418yes—
329Dic47⋊C4C24116yes—
330Dic47⋊C4C2418yes—
331Dic47⋊C4C24116yes—
332Dic47⋊C4C2418yes—
333Dic47⋊C4C2418yes—
334C4×Dic47C2418yes—
335C4×Dic47C2418yes—
336C4×Dic47C24116yes—
337C4×Dic47C24116yes—
338C23×C47—22no—
339C23×C47—22no—
340C23×C472−1+414yes—
341C23×C47C2512yes—
342C23×C47C2511yescharacteristic
343C22×D47—24no—
344C22×D47—24no—
345C22×D47—24no—
346C22×D47—24no—
347C22×D47—24no—
348C22×D47—24no—
349C22×D47C2514yes—
350C22×D47C2514yes—
351Q8×C47—216no—
352Q8×C47—216no—
353Q8×C47—416no—
354C2×C4×C47—28no—
355C2×C4×C47—28no—
356C2×C4×C47—22no—
357C2×C4×C47—28no—
358C2×C4×C47—22no—
359C2×C4×C47—22no—
360C2×C4×C47—22no—
361C2×C4×C47—28no—
362C2×C4×C47—28no—
363C2×C4×C47—416no—
364C2×C4×C47H(5,𝔽2)14yes—
365C2×C4×C472−1+414yes—
366C2×C4×C47C2518yes—
367C2×C4×C47C2518yes—
368C2×C4×C47C2512yes—
369C2×C4×C47C2512yes—
370C2×C4×C47C2512yes—
371C2×C4×C47C2512yes—
372C2×C4×C47C2512yes—
373C2×C4×C47C2512yes—
374C22⋊D47—216no—
375C22⋊D47—216no—
376C2×Dic47—24no—
377C2×Dic47—24no—
378C2×Dic47—24no—
379C2×Dic47—24no—
380C2×Dic47—24no—
381C2×Dic47—24no—
382C2×Dic47C2514yes—
383C2×Dic47C2514yes—
384C2×Dic47C2514yes—
385C2×Dic47C2514yes—
386C2×Dic47C2514yes—
387C2×Dic47C2514yes—
388D188—28no—
389D188—28no—
390D188—416no—
391C4×D47—216no—
392C4×D47—216no—
393C4×D47—416no—
394C4×D47—416no—
395Dic94—28no—
396Dic94—28no—
397Dic94—416no—
398C2×#3552—471nomaximal, Sylow
399C22×C47—22no—
400C22×C47—22no—
401C22×C47—28no—
402C22×C47C2×H(5,𝔽2)12yes—
403C22×C47C2×2−1+414yes—
404C22×C47C2×2−1+412yes—
405C22×C47C2×2−1+412yes—
406C22×C47C2611yescharacteristic
407C2×D47—24no—
408C2×D47—24no—
409C2×D47—24no—
410C2×D47—24no—
411C2×D47—24no—
412C2×D47—24no—
413C2×D47—48no—
414C2×D47—48no—
415C4×C47—28no—
416C4×C47—28no—
417C4×C47—22no—
418C4×C47—22no—
419C4×C47—22no—
420C4×C47—22no—
421C4×C47C2×H(5,𝔽2)14yes—
422C4×C47C2×2−1+414yes—
423Dic47—24no—
424Dic47—24no—
425Dic47—24no—
426Dic47—24no—
427Dic47—24no—
428Dic47—24no—
429#3552—4732no—
430C2×#563—474no—
431C2×#557—471no—
432C2×#556—471no—
433C2×#554—472no—
434C2×#553—472no—
435C2×D4×Q8—472no—
436C2×D4×Q8—471no—
437C2×#548—472no—
438C2×#547—471no—
439C2×#544—472no—
440C2×#542—472no—
441C2×#541—472no—
442C2×#539—474no—
443C2×#536—472no—
444C22×C4⋊Q8D4711yescharacteristic, complemented
445C2×#529—471no—
446C2×#529—471no—
447C2×C47—24no—
448C2×C47#355214yescomplemented
449C2×C47C22×H(5,𝔽2)11yescharacteristic
450C2×C47C22×2−1+411yescharacteristic
451C2×C47C22×2−1+411yescharacteristic
452D47—44no—
453D47—44no—
454C22×#41—472no—
455C23×Q8—472no—
456C23×Q8C2×D4712yes—
457#563—4764no—
458#557—4716no—
459#556—4716no—
460#554—4732no—
461#553—4732no—
462D4×Q8—4732no—
463D4×Q8—4716no—
464#548—4732no—
465#547—4716no—
466#544—4732no—
467#542—4732no—
468#541—4732no—
469#539—4764no—
470#536—4732no—
471C2×C4⋊Q8—472no—
472C2×C4⋊Q8—474no—
473C2×C4⋊Q8—472no—
474C2×C4⋊Q8C2×D4712yes—
475C2×C4⋊Q8C2×D4712yes—
476C2×C4⋊Q8C2×D4711yescharacteristic
477C2×C4⋊Q8C2×D4711yescharacteristic
478C2×C4⋊Q8C2×D4712yes—
479C2×C4⋊Q8C2×D47116yescomplemented
480#529—4716no—
481#529—4716no—
482C2×#126—474no—
483C2×#126—474no—
484C2×#126—474no—
485C2×#126—472no—
486C2×#126—472no—
487C2×#125—474no—
488C2×#125—474no—
489C2×#125—474no—
490C2×#125—472no—
491C2×#125—471no—
492C2×#125—471no—
493C2×#124—472no—
494C2×#124—474no—
495C2×#124—471no—
496C2×#124—471no—
497C2×#123—472no—
498C2×#123—472no—
499C2×#123—474no—
500C2×#123—474no—
501C2×#123—474no—
502C2×C22⋊Q8—472no—
503C2×C22⋊Q8—472no—
504C2×C22⋊Q8—474no—
505C2×C22⋊Q8—474no—
506C2×C22⋊Q8—471no—
507C2×C22⋊Q8—471no—
508C2×C22⋊Q8—474no—
509C2×C22⋊Q8—474no—
510C2×C22⋊Q8—474no—
511C2×C22⋊Q8—474no—
512C2×C22⋊Q8—472no—
513C2×#121—471no—
514C2×#121—471no—
515C2×#121—474no—
516C2×#121—472no—
517C2×C4×Q8—472no—
518C2×C4×Q8—472no—
519C2×C4×Q8—472no—
520C2×C4×Q8—471no—
521C2×C4×Q8—471no—
522C2×C4×D4—472no—
523C2×C4×D4—472no—
524C2×C4×D4—474no—
525C2×C4×D4—474no—
526C2×C4×D4—472no—
527C2×C4×D4—471no—
528C2×C4×D4—471no—
529C2×#117—472no—
530C2×#117—472no—
531C2×#117—472no—
532C22×C4⋊C4—472no—
533C22×C4⋊C4C2×D4712yes—
534C22×C4⋊C4C2×D4712yes—
535C22×C42C2×D4711yescharacteristic
536C47C2×#355211yescharacteristic, complemented, Sylow
537C2×#41—4716no—
538C2×#41—1888no—
539C22×Q8—48no—
540C22×Q8—4716no—
541C22×Q8—471no—
542C22×Q8—471no—
543C22×Q8—474no—
544C22×Q8—1888no—
545C22×Q8C22×D4712yes—
546C22×Q8C22×D4712yes—
547C22×Q8C22×D4714yes—
548C22×Q8C22×D47116yes—
549C22×D4—472no—
550C22×D4—472no—
551C22×D4—471no—
552C22×D4—471no—
553C22×D4—474no—
554C23×C4—472no—
555C23×C4—472no—
556C23×C4—474no—
557C23×C4—474no—
558C23×C4C22×D4711yescharacteristic
559C23×C4C22×D4711yescharacteristic
560C23×C4C22×D4711yescharacteristic
561C23×C4C22×D4714yes—
562C4⋊Q8—4716no—
563C4⋊Q8—4732no—
564C4⋊Q8—4716no—
565C4⋊Q8C22×D47116yes—
566C4⋊Q8C22×D47116yes—
567C4⋊Q8C22×D4718yes—
568C4⋊Q8C22×D4718yes—
569C4⋊Q8C22×D47116yes—
570#126—4732no—
571#126—4732no—
572#126—4732no—
573#126—4716no—
574#126—4716no—
575#125—4732no—
576#125—4732no—
577#125—4732no—
578#125—4716no—
579#125—478no—
580#125—478no—
581#124—4716no—
582#124—4732no—
583#124—478no—
584#124—478no—
585#123—4716no—
586#123—4716no—
587#123—4732no—
588#123—4732no—
589#123—4732no—
590C22⋊Q8—4716no—
591C22⋊Q8—4716no—
592C22⋊Q8—4732no—
593C22⋊Q8—4732no—
594C22⋊Q8—478no—
595C22⋊Q8—478no—
596C22⋊Q8—4732no—
597C22⋊Q8—4732no—
598C22⋊Q8—4732no—
599C22⋊Q8—4732no—
600C22⋊Q8—4716no—
601#121—478no—
602#121—478no—
603#121—4732no—
604#121—4716no—
605C4×Q8—4716no—
606C4×Q8—4716no—
607C4×Q8—4716no—
608C4×Q8—478no—
609C4×Q8—478no—
610C4×D4—4716no—
611C4×D4—4716no—
612C4×D4—4732no—
613C4×D4—4732no—
614C4×D4—4716no—
615C4×D4—478no—
616C4×D4—478no—
617#117—4716no—
618#117—4716no—
619#117—4716no—
620C2×C4⋊C4—471no—
621C2×C4⋊C4—474no—
622C2×C4⋊C4—471no—
623C2×C4⋊C4—472no—
624C2×C4⋊C4—472no—
625C2×C4⋊C4—472no—
626C2×C4⋊C4—472no—
627C2×C4⋊C4—471no—
628C2×C4⋊C4—474no—
629C2×C4⋊C4—472no—
630C2×C4⋊C4—474no—
631C2×C4⋊C4—472no—
632C2×C4⋊C4—471no—
633C2×C4⋊C4—474no—
634C2×C4⋊C4—474no—
635C2×C4⋊C4—474no—
636C2×C4⋊C4—472no—
637C2×C4⋊C4—472no—
638C2×C4⋊C4—4716no—
639C2×C4⋊C4C22×D4712yes—
640C2×C4⋊C4C22×D4712yes—
641C2×C4⋊C4C22×D4712yes—
642C2×C4⋊C4C22×D4714yes—
643C2×C4⋊C4C22×D4714yes—
644C2×C4⋊C4C22×D4712yes—
645C2×C4⋊C4C22×D47116yes—
646C2×C4⋊C4C22×D47116yes—
647C2×C22⋊C4—472no—
648C2×C22⋊C4—472no—
649C2×C22⋊C4—474no—
650C2×C22⋊C4—472no—
651C2×C22⋊C4—472no—
652C2×C22⋊C4—472no—
653C2×C22⋊C4—472no—
654C2×C22⋊C4—474no—
655C2×C22⋊C4—474no—
656C2×C22⋊C4—472no—
657C2×C22⋊C4—472no—
658C2×C22⋊C4—474no—
659C2×C22⋊C4—472no—
660C2×C22⋊C4—472no—
661C2×C42—472no—
662C2×C42—472no—
663C2×C42—474no—
664C2×C42—474no—
665C2×C42C22×D4711yescharacteristic
666C2×C42C22×D4711yescharacteristic
667C2×C42C22×D4711yescharacteristic
668C2×C42C22×D4711yescharacteristic
669C2×C42C22×D4718yes—
670C24—472no—
671C24—472no—
672C24C23×D4711yescharacteristic
673#41—18832no—
674C2×Q8—28no—
675C2×Q8—28no—
676C2×Q8—48no—
677C2×Q8—432no—
678C2×Q8—474no—
679C2×Q8—474no—
680C2×Q8—4716no—
681C2×Q8—944no—
682C2×Q8—944no—
683C2×Q8—1888no—
684C2×Q8—18832no—
685C2×Q8C23×D4718yes—
686C2×Q8C23×D4718yes—
687C2×Q8C23×D47116yes—
688C2×D4—478no—
689C2×D4—478no—
690C2×D4—474no—
691C2×D4—474no—
692C2×D4—4716no—
693C2×D4—948no—
694C2×D4—948no—
695C2×D4—944no—
696C2×D4—944no—
697C2×D4—1888no—
698C22×C4—24no—
699C22×C4—24no—
700C22×C4—24no—
701C22×C4—48no—
702C22×C4—472no—
703C22×C4—472no—
704C22×C4—472no—
705C22×C4—472no—
706C22×C4—472no—
707C22×C4—472no—
708C22×C4—478no—
709C22×C4—478no—
710C22×C4—4716no—
711C22×C4—4716no—
712C22×C4—948no—
713C22×C4—948no—
714C22×C4—1888no—
715C22×C4—1888no—
716C22×C4C23×D4714yes—
717C22×C4C23×D4714yes—
718C22×C4C23×D4714yes—
719C22×C4C23×D4714yes—
720C22×C4C23×D4714yes—
721C22×C4C23×D4711yescharacteristic
722C22×C4C23×D4711yescharacteristic
723C22×C4C23×D4711yescharacteristic
724C22×C4C23×D4711yescharacteristic
725C22×C4C23×D47116yes—
726C22×C4C23×D4711yescharacteristic
727C22×C4C23×D4711yescharacteristic
728C4⋊C4—4716no—
729C4⋊C4—478no—
730C4⋊C4—478no—
731C4⋊C4—478no—
732C4⋊C4—478no—
733C4⋊C4—4716no—
734C4⋊C4—478no—
735C4⋊C4—4716no—
736C4⋊C4—478no—
737C4⋊C4—4716no—
738C4⋊C4—478no—
739C4⋊C4—478no—
740C4⋊C4—474no—
741C4⋊C4—474no—
742C4⋊C4—474no—
743C4⋊C4—474no—
744C4⋊C4—4716no—
745C4⋊C4—4716no—
746C4⋊C4C23×D4718yes—
747C4⋊C4C23×D4718yes—
748C4⋊C4C23×D4718yes—
749C4⋊C4C23×D47116yes—
750C4⋊C4C23×D47116yes—
751C4⋊C4C23×D4718yes—
752C22⋊C4—478no—
753C22⋊C4—478no—
754C22⋊C4—4716no—
755C22⋊C4—478no—
756C22⋊C4—478no—
757C22⋊C4—478no—
758C22⋊C4—478no—
759C22⋊C4—4716no—
760C22⋊C4—4716no—
761C22⋊C4—478no—
762C22⋊C4—478no—
763C22⋊C4—4716no—
764C22⋊C4—478no—
765C22⋊C4—478no—
766C42—478no—
767C42—478no—
768C42—4716no—
769C42—4716no—
770C42C23×D4714yes—
771C42C23×D4714yes—
772C42C23×D4714yes—
773C42C23×D4714yes—
774C23—22no—
775C23—22no—
776C23—474no—
777C23—474no—
778C23—944no—
779C23—944no—
780C23—944no—
781C23—944no—
782C23—944no—
783C23—944no—
784C23#1309407214yes—
785C23C24×D4712yes—
786C23C24×D4711yescharacteristic
787Q8—216no—
788Q8—216no—
789Q8—416no—
790Q8—948no—
791Q8—948no—
792Q8—18816no—
793D4—9416no—
794D4—9416no—
795D4—948no—
796D4—948no—
797D4—18816no—
798C2×C4—22no—
799C2×C4—28no—
800C2×C4—28no—
801C2×C4—28no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—28no—
806C2×C4—28no—
807C2×C4—416no—
808C2×C4—474no—
809C2×C4—474no—
810C2×C4—474no—
811C2×C4—474no—
812C2×C4—474no—
813C2×C4—474no—
814C2×C4—944no—
815C2×C4—944no—
816C2×C4—944no—
817C2×C4—944no—
818C2×C4—944no—
819C2×C4—944no—
820C2×C4—9416no—
821C2×C4—9416no—
822C2×C4—18816no—
823C2×C4—18816no—
824C2×C4#1309406914yes—
825C2×C4#1309407214yes—
826C2×C4C24×D4718yes—
827C2×C4C24×D4718yes—
828C2×C4C24×D4712yes—
829C2×C4C24×D4712yes—
830C2×C4C24×D4712yes—
831C2×C4C24×D4712yes—
832C2×C4C24×D4712yes—
833C2×C4C24×D4712yes—
834C22—28no—
835C22—22no—
836C22—22no—
837C22—944no—
838C22—944no—
839C22—944no—
840C22—944no—
841C22—944no—
842C22—944no—
843C22—1888no—
844C22—1888no—
845C22C2×#1309406912yes—
846C22C2×#1309407214yes—
847C22C2×#1309407212yes—
848C22C2×#1309407212yes—
849C22C25×D4711yescharacteristic
850C4—22no—
851C4—28no—
852C4—28no—
853C4—22no—
854C4—22no—
855C4—22no—
856C4—944no—
857C4—944no—
858C4—944no—
859C4—944no—
860C4—944no—
861C4—944no—
862C4C2×#1309406914yes—
863C4C2×#1309407214yes—
864C2—24no—
865C2—1884no—
866C2—1884no—
867C2#2025782914yesdirect product factor
868C2C22×#1309406911yescharacteristic
869C2C22×#1309407211yescharacteristic
870C2C22×#1309407211yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC22×C4⋊Q8×C47C2
socleC23×C47C25
hypercenterC22×C4⋊Q8D47
hypocenterC47C2×#3552
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4⋊Q8

Complements

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

NH ≅ G/Ntype
1. #20257829C2direct (N × H)
2. C2×#15689872C2semidirect
3. C2×#15689848C2semidirect
4. C2×#15689847C2semidirect
5. C2×#15689828C2semidirect
6. C2×#15689821C2semidirect
7. C2×#15689788C2semidirect
8. C2×Q8×C22⋊D47C2semidirect
9. C2×#15689784C2semidirect
10. C2×#15689776C2semidirect
11. C2×#15689750C2semidirect
12. C2×#15689747C2semidirect
13. C2×#15689734C2semidirect
14. C2×#15689720C2semidirect
15. C2×#15689698C2semidirect
16. C2×#15689657C2semidirect
17. C2×#15689657C2semidirect
18. C22×C4⋊Q8×C47C2semidirect
21. #15689872C22semidirect
22. #15689848C22semidirect
23. #15689847C22semidirect
24. #15689828C22semidirect
25. #15689821C22semidirect
26. #15689788C22semidirect
27. Q8×C22⋊D47C22semidirect
28. #15689784C22semidirect
29. #15689776C22semidirect
30. #15689750C22semidirect
31. #15689747C22semidirect
32. #15689734C22semidirect
33. #15689720C22semidirect
34. #15689698C22semidirect
38. #15689657C22semidirect
39. #15689657C22semidirect
97. C2×C4⋊Q8×C47C22semidirect
444. C22×C4⋊Q8D47semidirect
448. C2×C47#3552semidirect
479. C2×C4⋊Q8C2×D47semidirect
536. C47C2×#3552semidirect
867. C2#20257829direct (N × H)

Maximal subgroups

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

subgroupindex
#202578292
C2×#156898722
C2×#156898482
C2×#156898472
C2×#156898282
C2×#156898212
C2×#156897882
C2×Q8×C22⋊D472
C2×#156897842
C2×#156897762
C2×#156897502
C2×#156897472
C2×#156897342
C2×#156897202
C2×#156896982
C2×#156896572
C22×C4⋊Q8×C472
C2×#355247