Finite Group Databasebeta

← C2×#20257729 #27123961

Subgroups — C2×#20257729 #27123961

Order 12032.

7086 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#20257729C2132yesmaximal, direct product factor
2C2×#15689874C214yesmaximal, complemented
3C2×Q8×Dic94C211yesmaximal, characteristic, complemented
4C2×#15689838C211yesmaximal, characteristic, complemented
5C2×#15689834C211yesmaximal, characteristic, complemented
6C2×#15689811C212yesmaximal, complemented
7C2×#15689807C212yesmaximal, complemented
8C2×#15689778C212yesmaximal, complemented
9C2×#15689774C212yesmaximal, complemented
10C2×#15689754C212yesmaximal, complemented
11C2×#15689753C212yesmaximal, complemented
12C2×#15689746C212yesmaximal, complemented
13C2×#15689738C212yesmaximal, complemented
14C2×#15689696C214yesmaximal, complemented
15C2×C4⋊Q8×D47C211yesmaximal, characteristic, complemented
16C2×#15689660C211yesmaximal, characteristic, complemented
17C2×#15689655C211yesmaximal, characteristic, complemented
18C2×C47×#554C211yesmaximal, characteristic, complemented
19C22×#10625350C2214yes—
20C22×Q8×D47C2212yes—
21#15689874C22164yescomplemented
22Q8×Dic94C22116yescomplemented
23#15689838C22116yescomplemented
24#15689834C22116yescomplemented
25#15689811C22132yescomplemented
26#15689807C22132yescomplemented
27#15689778C22132yescomplemented
28#15689774C22132yescomplemented
29#15689754C22132yescomplemented
30#15689753C22132yescomplemented
31#15689746C22132yescomplemented
32#15689738C22132yescomplemented
33#15689696C22164yescomplemented
34C2×#13094024C2212yes—
35C2×#13094024C2211yescharacteristic
36C2×#13094023C2212yes—
37C2×#13094023C2214yes—
38C2×#13094023C2212yes—
39C2×#13094023C2212yes—
40C2×#13094023C2214yes—
41C2×#13094022C2212yes—
42C4⋊Q8×D47C22116yescomplemented
43#15689660C22116yescomplemented
44#15689655C22116yescomplemented
45C2×#13094019C2214yes—
46C2×#13094019C2212yes—
47C2×#13094017C2214yes—
48C2×#13094017C2212yes—
49C2×#13094015C2211yescharacteristic
50C2×#13094015C2211yescharacteristic
51C2×#13094015C2212yes—
52C2×#13094015C2214yes—
53C2×#13094014C2214yes—
54C2×#13094013C2211yescharacteristic
55C2×#13094011C2211yescharacteristic
56C2×#13094010C2214yes—
57C2×#13094010C2214yes—
58C2×#13094009C2214yes—
59C2×#13094009C2212yes—
60C2×#13094007C2214yes—
61C2×#13094006C2214yes—
62C2×#13094006C2214yes—
63C2×#13094006C2212yes—
64C2×#13094004C2214yes—
65C2×#13094004C2211yescharacteristic
66C2×#13094004C2212yes—
67C2×#13094003C2214yes—
68C2×#13094003C2214yes—
69C2×#13094002C2214yes—
70C2×#13094000C2211yescharacteristic
71C2×#13094000C2214yes—
72C2×#13093999C2211yescharacteristic
73C2×#13093998C2212yes—
74C2×#13093995C2211yescharacteristic
75C2×#13093995C2212yes—
76C2×Q8×Dic47C2212yes—
77C2×C4×Dic94C2212yes—
78C2×C4×Dic94C2211yescharacteristic
79C2×C4×D188C2212yes—
80C2×C4×D188C2211yescharacteristic
81C2×#13093986C2212yes—
82C2×C4×C22⋊D47C2212yes—
83C2×#13093983C2212yes—
84C2×#13093983C2212yes—
85C2×#13093982C2212yes—
86C2×#13093982C2214yes—
87C2×#13093981C2212yes—
88C2×C4⋊C4×D47C2212yes—
89C2×C4⋊C4×D47C2212yes—
90C2×C4⋊C4×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—416no—
102C2×#10625350C23132yes—
103C22×Dic94C2311yescharacteristic
104C22×Dic94C2314yes—
105C22×Dic94C2314yes—
106C22×Dic94C2312yes—
107C2×Q8×D47—48no—
108C2×Q8×D47C23116yes—
109C22×D188C2311yescharacteristic
110C22×D188C2312yes—
111C22×C22⋊D47C2312yes—
112C22×C22⋊D47C2314yes—
113C22×C4×D47C2311yescharacteristic
114C22×C4×D47C2311yescharacteristic
115C22×C4×D47C2311yescharacteristic
116C22×C4×D47C2314yes—
117C22×C4×D47C2312yes—
118C22×C4×D47C2314yes—
119#13094024C23116yes—
120#13094024C2318yes—
121#13094023C23116yes—
122#13094023C23116yes—
123#13094023C23132yes—
124#13094023C23116yes—
125#13094023C23132yes—
126#13094022C23116yes—
127#13094019C23132yes—
128#13094019C23116yes—
129#13094017C23132yes—
130#13094017C23116yes—
131#13094015C2318yes—
132#13094015C2318yes—
133#13094015C23116yes—
134#13094015C23132yes—
135#13094014C23132yes—
136#13094013C2318yes—
137#13094011C2318yes—
138#13094010C23132yes—
139#13094010C23132yes—
140#13094009C23132yes—
141#13094009C23116yes—
142#13094007C23132yes—
143#13094006C23132yes—
144#13094006C23132yes—
145#13094006C23116yes—
146#13094004C23116yes—
147#13094004C23132yes—
148#13094004C2318yes—
149#13094003C23132yes—
150#13094003C23132yes—
151#13094002C23132yes—
152#13094000C2318yes—
153#13094000C23132yes—
154#13093999C2318yes—
155#13093998C23116yes—
156#13093995C23116yes—
157#13093995C2318yes—
158Q8×Dic47C23116yes—
159C4×Dic94C23116yes—
160C4×Dic94C2318yes—
161C4×D188C23116yes—
162C4×D188C2318yes—
163#13093986C23116yes—
164C4×C22⋊D47C23116yes—
165#13093983C23116yes—
166#13093983C23116yes—
167#13093982C23116yes—
168#13093982C23132yes—
169#13093981C23116yes—
170C2×C4⋊Dic47C2311yescharacteristic
171C2×C4⋊Dic47C2312yes—
172C2×C4⋊Dic47C2312yes—
173C2×C4⋊Dic47C2314yes—
174C2×C4⋊Dic47C2311yescharacteristic
175C2×C4⋊Dic47C2312yes—
176C2×C4⋊Dic47C2312yes—
177C2×C4⋊Dic47C2312yes—
178C2×C4⋊Dic47C2314yes—
179C2×Dic47⋊C4C2314yes—
180C2×Dic47⋊C4C2314yes—
181C2×Dic47⋊C4C2314yes—
182C2×Dic47⋊C4C2312yes—
183C2×Dic47⋊C4C2312yes—
184C2×Dic47⋊C4C2312yes—
185C2×Dic47⋊C4C2312yes—
186C2×Dic47⋊C4C2314yes—
187C4⋊C4×D47C23116yes—
188C4⋊C4×D47C23116yes—
189C4⋊C4×D47C23116yes—
190C2×C22⋊Dic47C2312yes—
191C2×C22⋊Dic47C2314yes—
192C2×C22⋊Dic47C2312yes—
193C2×C22⋊Dic47C2312yes—
194C2×(C2×D47)⋊C4C2312yes—
195C2×(C2×D47)⋊C4C2312yes—
196C2×(C2×D47)⋊C4C2312yes—
197C2×(C2×D47)⋊C4C2312yes—
198C2×(C2×D47)⋊C4C2314yes—
199C2×(C2×D47)⋊C4C2314yes—
200C2×(C2×D47)⋊C4C2312yes—
201C2×(C2×D47)⋊C4C2312yes—
202C2×C4×Dic47C2311yescharacteristic
203C2×C4×Dic47C2311yescharacteristic
204C2×C4×Dic47C2311yescharacteristic
205C2×C4×Dic47C2314yes—
206C2×C4×Dic47C2314yes—
207C2×C4×Dic47C2312yes—
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×C47C23116yes—
220C4×D4×C47C2318yes—
221C2×C4⋊C4×C47C23116yes—
222C2×C4⋊C4×C47C2311yescharacteristic
223C2×C4⋊C4×C47C2314yes—
224C2×C4⋊C4×C47C2312yes—
225C2×C4⋊C4×C47C2311yescharacteristic
226C2×C4⋊C4×C47C2312yes—
227C2×C4⋊C4×C47C2312yes—
228C2×C4⋊C4×C47C2314yes—
229C2×C22⋊C4×C47C2314yes—
230C2×C22⋊C4×C47C2312yes—
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—48no—
255C2×C22⋊D47C2418yes—
256C2×C22⋊D47C24116yes—
257C22×Dic47C2412yes—
258C22×Dic47C2411yescharacteristic
259C22×Dic47C2411yescharacteristic
260C22×Dic47C2412yes—
261C22×Dic47C2411yescharacteristic
262C22×Dic47C2414yes—
263C22×Dic47C2412yes—
264Q8×D47—432no—
265#10625350—464no—
266C2×D188—28no—
267C2×D188—24no—
268C2×D188C2414yes—
269C2×D188C2418yes—
270C2×C4×D47—24no—
271C2×C4×D47—216no—
272C2×C4×D47—24no—
273C2×C4×D47—24no—
274C2×C4×D47—28no—
275C2×C4×D47—48no—
276C2×C4×D47C2414yes—
277C2×C4×D47C2414yes—
278C2×C4×D47C2414yes—
279C2×C4×D47C24116yes—
280C2×C4×D47C2418yes—
281C2×C4×D47C24116yes—
282C2×Dic94—24no—
283C2×Dic94—48no—
284C2×Dic94—44no—
285C2×Dic94—48no—
286C2×Dic94C2414yes—
287C2×Dic94C24116yes—
288C2×Dic94C24116yes—
289C2×Dic94C2418yes—
290C4⋊C4×C47C2414yes—
291C4⋊C4×C47C24116yes—
292C4⋊C4×C47C2418yes—
293C4⋊C4×C47C2414yes—
294C4⋊C4×C47C2418yes—
295C4⋊C4×C47C2418yes—
296C4⋊C4×C47C24116yes—
297C22⋊C4×C47C24116yes—
298C22⋊C4×C47C2418yes—
299C42×C47C2418yes—
300C42×C47C2414yes—
301C22⋊Dic47C2418yes—
302C22⋊Dic47C24116yes—
303C22⋊Dic47C2418yes—
304C22⋊Dic47C2418yes—
305(C2×D47)⋊C4C2418yes—
306(C2×D47)⋊C4C2418yes—
307(C2×D47)⋊C4C2418yes—
308(C2×D47)⋊C4C2418yes—
309(C2×D47)⋊C4C24116yes—
310(C2×D47)⋊C4C24116yes—
311(C2×D47)⋊C4C2418yes—
312(C2×D47)⋊C4C2418yes—
313C4⋊Dic47C2414yes—
314C4⋊Dic47C2418yes—
315C4⋊Dic47C2418yes—
316C4⋊Dic47C24116yes—
317C4⋊Dic47C2414yes—
318C4⋊Dic47C2418yes—
319C4⋊Dic47C2418yes—
320C4⋊Dic47C2418yes—
321C4⋊Dic47C24116yes—
322Dic47⋊C4C24116yes—
323Dic47⋊C4C24116yes—
324Dic47⋊C4C24116yes—
325Dic47⋊C4C2418yes—
326Dic47⋊C4C2418yes—
327Dic47⋊C4C2418yes—
328Dic47⋊C4C2418yes—
329Dic47⋊C4C24116yes—
330C4×Dic47C2414yes—
331C4×Dic47C2414yes—
332C4×Dic47C2414yes—
333C4×Dic47C24116yes—
334C4×Dic47C24116yes—
335C4×Dic47C2418yes—
336C23×C47—24no—
337C23×C47—24no—
338C23×C47—24no—
339C23×C47C2514yes—
340C23×C47C2511yescharacteristic
341C22×D47—22no—
342C22×D47—22no—
343C22×D47—24no—
344C22×D47—24no—
345C22×D47—24no—
346C22×D47H(5,𝔽2)14yes—
347C22×D47C2514yes—
348C22×D47C2512yes—
349Q8×C47—28no—
350Q8×C47—48no—
351D4×C47—28no—
352C2×C4×C47—22no—
353C2×C4×C47—24no—
354C2×C4×C47—28no—
355C2×C4×C47—24no—
356C2×C4×C47—24no—
357C2×C4×C47—216no—
358C2×C4×C47—416no—
359C2×C4×C472−1+414yes—
360C2×C4×C472−1+414yes—
361C2×C4×C47C2514yes—
362C2×C4×C47C2514yes—
363C2×C4×C47C2512yes—
364C2×C4×C47C2514yes—
365C2×C4×C47C2518yes—
366C2×C4×C47C2512yes—
367C2×C4×C47C2512yes—
368C22⋊D47—216no—
369C22⋊D47—416no—
370C2×Dic47—22no—
371C2×Dic47—28no—
372C2×Dic47—24no—
373C2×Dic47—24no—
374C2×Dic47—22no—
375C2×Dic47—22no—
376C2×Dic47—24no—
377C2×Dic47C2514yes—
378C2×Dic47C2512yes—
379C2×Dic47C2512yes—
380C2×Dic47C2514yes—
381C2×Dic47C2518yes—
382C2×Dic47C2512yes—
383C2×Dic47C2514yes—
384D188—216no—
385D188—28no—
386C4×D47—232no—
387C4×D47—28no—
388C4×D47—28no—
389C4×D47—28no—
390C4×D47—216no—
391C4×D47—416no—
392Dic94—28no—
393Dic94—416no—
394Dic94—416no—
395Dic94—48no—
396C2×#3544—471nomaximal, Sylow
397C22×C47—24no—
398C22×C47—24no—
399C22×C47—24no—
400C22×C47—48no—
401C22×C47C2×H(5,𝔽2)12yes—
402C22×C47C2×2−1+412yes—
403C22×C47C2×2−1+412yes—
404C22×C47C2611yescharacteristic
405C2×D47—22no—
406C2×D47—22no—
407C2×D47—28no—
408C2×D47—24no—
409C2×D47—24no—
410C2×D47—24no—
411C2×D47—48no—
412C2×D47C2×H(5,𝔽2)14yes—
413C4×C47—22no—
414C4×C47—24no—
415C4×C47—28no—
416C4×C47—24no—
417C4×C47—24no—
418C4×C47C2×2−1+414yes—
419C4×C47C2×2−1+414yes—
420Dic47—22no—
421Dic47—28no—
422Dic47—24no—
423Dic47—24no—
424Dic47—22no—
425Dic47—22no—
426Dic47—24no—
427#3544—4732no—
428C2×#563—474no—
429C2×Q82—471no—
430C2×#555—471no—
431C2×#554—471no—
432C2×#554D4711yescharacteristic, complemented
433C2×#552—472no—
434C2×#552—472no—
435C2×#547—472no—
436C2×#547—472no—
437C2×#544—472no—
438C2×#544—472no—
439C2×#542—472no—
440C2×#542—472no—
441C2×#536—474no—
442C22×C4⋊Q8—471no—
443C2×#529—471no—
444C2×#529—471no—
445C2×C47—44no—
446C2×C47#354414yescomplemented
447C2×C47C22×H(5,𝔽2)11yescharacteristic
448C2×C47C22×2−1+411yescharacteristic
449C2×C47C22×2−1+411yescharacteristic
450D47—24no—
451D47—44no—
452C22×#41—474no—
453C23×Q8—472no—
454#563—4764no—
455Q82—4716no—
456#555—4716no—
457#554—4716no—
458#554C2×D47116yescomplemented
459#552—4732no—
460#552—4732no—
461#547—4732no—
462#547—4732no—
463#544—4732no—
464#544—4732no—
465#542—4732no—
466#542—4732no—
467#536—4764no—
468C2×C4⋊Q8—472no—
469C2×C4⋊Q8—4716no—
470C2×C4⋊Q8—472no—
471C2×C4⋊Q8—472no—
472C2×C4⋊Q8—474no—
473C2×C4⋊Q8—474no—
474C2×C4⋊Q8—472no—
475C2×C4⋊Q8—471no—
476C2×C4⋊Q8—472no—
477C2×C4⋊Q8C2×D4711yescharacteristic
478#529—4716no—
479#529—4716no—
480C2×#126—472no—
481C2×#126—474no—
482C2×#126—472no—
483C2×#126—474no—
484C2×#125—471no—
485C2×#125—471no—
486C2×#125—472no—
487C2×#125—474no—
488C2×#125—474no—
489C2×#125C2×D4712yes—
490C2×#124—471no—
491C2×#124—471no—
492C2×#124—474no—
493C2×#124—474no—
494C2×#123—474no—
495C2×#123—472no—
496C2×#123—474no—
497C2×#123—472no—
498C2×#123—474no—
499C2×#123—474no—
500C2×C22⋊Q8—471no—
501C2×C22⋊Q8—474no—
502C2×C22⋊Q8—474no—
503C2×C22⋊Q8—474no—
504C2×C22⋊Q8—471no—
505C2×C22⋊Q8—474no—
506C2×C22⋊Q8—472no—
507C2×C22⋊Q8—474no—
508C2×C22⋊Q8C2×D4714yes—
509C2×C22⋊Q8C2×D4712yes—
510C2×#121—471no—
511C2×#121—472no—
512C2×#121—472no—
513C2×#121—471no—
514C2×C4×Q8—472no—
515C2×C4×Q8—471no—
516C2×C4×Q8—472no—
517C2×C4×Q8C2×D4711yescharacteristic
518C2×C4×D4—472no—
519C2×C4×D4—472no—
520C2×C4×D4—472no—
521C2×C4×D4—471no—
522C2×C4×D4C2×D4711yescharacteristic
523C2×C4×D4C2×D4712yes—
524C2×#117—472no—
525C2×#117—472no—
526C2×#117—474no—
527C2×#117—472no—
528C2×#117—472no—
529C22×C4⋊C4—472no—
530C22×C4⋊C4—472no—
531C22×C4⋊C4—472no—
532C22×C4⋊C4C2×D4712yes—
533C22×C42—471no—
534C47C2×#354411yescharacteristic, complemented, Sylow
535C2×#41—4732no—
536C2×#41—18816no—
537C22×Q8—4716no—
538C22×Q8—471no—
539C22×Q8—474no—
540C22×Q8—474no—
541C22×Q8—472no—
542C22×Q8—1888no—
543C22×Q8C22×D4711yescharacteristic
544C22×Q8C22×D4712yes—
545C22×D4—472no—
546C22×D4—474no—
547C22×D4—471no—
548C22×D4—472no—
549C22×D4C22×D4711yescharacteristic
550C23×C4—474no—
551C23×C4—471no—
552C23×C4—471no—
553C23×C4—472no—
554C23×C4—471no—
555C23×C4—474no—
556C23×C4C22×D4712yes—
557C23×C4C22×D4714yes—
558C4⋊Q8—4716no—
559C4⋊Q8—4716no—
560C4⋊Q8—4716no—
561C4⋊Q8—4732no—
562C4⋊Q8—4732no—
563C4⋊Q8—4716no—
564C4⋊Q8—478no—
565C4⋊Q8—4716no—
566C4⋊Q8C22×D4718yes—
567#126—4716no—
568#126—4732no—
569#126—4716no—
570#126—4732no—
571#125—478no—
572#125—478no—
573#125—4716no—
574#125—4732no—
575#125—4732no—
576#125C22×D47116yes—
577#124—478no—
578#124—478no—
579#124—4732no—
580#124—4732no—
581#123—4732no—
582#123—4716no—
583#123—4732no—
584#123—4716no—
585#123—4732no—
586#123—4732no—
587C22⋊Q8—478no—
588C22⋊Q8—4732no—
589C22⋊Q8—4732no—
590C22⋊Q8—4732no—
591C22⋊Q8—478no—
592C22⋊Q8—4732no—
593C22⋊Q8—4716no—
594C22⋊Q8—4732no—
595C22⋊Q8C22×D47132yes—
596C22⋊Q8C22×D47116yes—
597#121—478no—
598#121—4716no—
599#121—4716no—
600#121—478no—
601C4×Q8—4716no—
602C4×Q8—478no—
603C4×Q8—4716no—
604C4×Q8C22×D4718yes—
605C4×D4—4716no—
606C4×D4—4716no—
607C4×D4—4716no—
608C4×D4—478no—
609C4×D4C22×D4718yes—
610C4×D4C22×D47116yes—
611#117—4716no—
612#117—4716no—
613#117—4732no—
614#117—4716no—
615#117—4716no—
616C2×C4⋊C4—471no—
617C2×C4⋊C4—472no—
618C2×C4⋊C4—472no—
619C2×C4⋊C4—474no—
620C2×C4⋊C4—474no—
621C2×C4⋊C4—474no—
622C2×C4⋊C4—471no—
623C2×C4⋊C4—474no—
624C2×C4⋊C4—472no—
625C2×C4⋊C4—472no—
626C2×C4⋊C4—472no—
627C2×C4⋊C4—472no—
628C2×C4⋊C4—472no—
629C2×C4⋊C4—472no—
630C2×C4⋊C4—472no—
631C2×C4⋊C4—474no—
632C2×C4⋊C4—474no—
633C2×C4⋊C4—4716no—
634C2×C4⋊C4—4716no—
635C2×C4⋊C4—4716no—
636C2×C4⋊C4C22×D4712yes—
637C2×C4⋊C4C22×D4712yes—
638C2×C4⋊C4C22×D4711yescharacteristic
639C2×C4⋊C4C22×D4714yes—
640C2×C4⋊C4C22×D47116yes—
641C2×C4⋊C4C22×D4711yescharacteristic
642C2×C4⋊C4C22×D4714yes—
643C2×C4⋊C4C22×D4712yes—
644C2×C22⋊C4—472no—
645C2×C22⋊C4—474no—
646C2×C22⋊C4—472no—
647C2×C22⋊C4—472no—
648C2×C22⋊C4—472no—
649C2×C22⋊C4—472no—
650C2×C22⋊C4—472no—
651C2×C22⋊C4—474no—
652C2×C22⋊C4—472no—
653C2×C22⋊C4—474no—
654C2×C22⋊C4—472no—
655C2×C22⋊C4—472no—
656C2×C22⋊C4C22×D4714yes—
657C2×C22⋊C4C22×D4712yes—
658C2×C42—474no—
659C2×C42—471no—
660C2×C42—471no—
661C2×C42—472no—
662C2×C42—474no—
663C2×C42—471no—
664C2×C42—478no—
665C2×C42C22×D4712yes—
666C2×C42C22×D4711yescharacteristic
667C24—471no—
668C24—472no—
669C24C23×D4712yes—
670#41—18864no—
671C2×Q8—24no—
672C2×Q8—44no—
673C2×Q8—474no—
674C2×Q8—4716no—
675C2×Q8—4716no—
676C2×Q8—478no—
677C2×Q8—944no—
678C2×Q8—1888no—
679C2×Q8—1884no—
680C2×Q8—1888no—
681C2×Q8—18832no—
682C2×Q8C23×D4714yes—
683C2×Q8C23×D4718yes—
684C2×D4—24no—
685C2×D4—478no—
686C2×D4—4716no—
687C2×D4—474no—
688C2×D4—478no—
689C2×D4—948no—
690C2×D4—948no—
691C2×D4—944no—
692C2×D4—1888no—
693C2×D4C23×D4714yes—
694C22×C4—28no—
695C22×C4—48no—
696C22×C4—472no—
697C22×C4—471no—
698C22×C4—472no—
699C22×C4—471no—
700C22×C4—471no—
701C22×C4—474no—
702C22×C4—472no—
703C22×C4—474no—
704C22×C4—474no—
705C22×C4—474no—
706C22×C4—4716no—
707C22×C4—478no—
708C22×C4—4716no—
709C22×C4—944no—
710C22×C4—9416no—
711C22×C4—944no—
712C22×C4—944no—
713C22×C4—948no—
714C22×C4—1888no—
715C22×C4C23×D4718yes—
716C22×C4C23×D4712yes—
717C22×C4C23×D4712yes—
718C22×C4C23×D4711yescharacteristic
719C22×C4C23×D4712yes—
720C22×C4C23×D4714yes—
721C22×C4C23×D47116yes—
722C22×C4C23×D4711yescharacteristic
723C22×C4C23×D4711yescharacteristic
724C4⋊C4—4716no—
725C4⋊C4—4716no—
726C4⋊C4—4716no—
727C4⋊C4—478no—
728C4⋊C4—478no—
729C4⋊C4—478no—
730C4⋊C4—478no—
731C4⋊C4—4716no—
732C4⋊C4—474no—
733C4⋊C4—478no—
734C4⋊C4—478no—
735C4⋊C4—474no—
736C4⋊C4—4716no—
737C4⋊C4—478no—
738C4⋊C4—478no—
739C4⋊C4—478no—
740C4⋊C4—4716no—
741C4⋊C4C23×D4718yes—
742C4⋊C4C23×D4718yes—
743C4⋊C4C23×D4714yes—
744C4⋊C4C23×D47116yes—
745C4⋊C4C23×D4714yes—
746C4⋊C4C23×D47116yes—
747C4⋊C4C23×D4718yes—
748C22⋊C4—478no—
749C22⋊C4—4716no—
750C22⋊C4—478no—
751C22⋊C4—478no—
752C22⋊C4—478no—
753C22⋊C4—478no—
754C22⋊C4—478no—
755C22⋊C4—4716no—
756C22⋊C4—478no—
757C22⋊C4—4716no—
758C22⋊C4—478no—
759C22⋊C4—478no—
760C22⋊C4C23×D47116yes—
761C22⋊C4C23×D4718yes—
762C42—474no—
763C42—474no—
764C42—474no—
765C42—4716no—
766C42—478no—
767C42—4716no—
768C42C23×D4714yes—
769C42C23×D4718yes—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—474no—
774C23—472no—
775C23—474no—
776C23—942no—
777C23—942no—
778C23—944no—
779C23—944no—
780C23—944no—
781C23C24×D4714yes—
782C23C24×D4711yescharacteristic
783Q8—28no—
784Q8—48no—
785Q8—948no—
786Q8—18816no—
787Q8—1888no—
788Q8—18816no—
789D4—28no—
790D4—9416no—
791D4—9416no—
792D4—948no—
793D4—18816no—
794C2×C4—24no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—216no—
800C2×C4—416no—
801C2×C4—474no—
802C2×C4—472no—
803C2×C4—472no—
804C2×C4—474no—
805C2×C4—472no—
806C2×C4—478no—
807C2×C4—474no—
808C2×C4—948no—
809C2×C4—9432no—
810C2×C4—948no—
811C2×C4—942no—
812C2×C4—944no—
813C2×C4—942no—
814C2×C4—944no—
815C2×C4—942no—
816C2×C4—944no—
817C2×C4—948no—
818C2×C4—948no—
819C2×C4—9416no—
820C2×C4—18816no—
821C2×C4#1309407114yes—
822C2×C4#1309407214yes—
823C2×C4C24×D4714yes—
824C2×C4C24×D4714yes—
825C2×C4C24×D4712yes—
826C2×C4C24×D4714yes—
827C2×C4C24×D4718yes—
828C2×C4C24×D4712yes—
829C2×C4C24×D4712yes—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—48no—
834C22—474no—
835C22—942no—
836C22—942no—
837C22—948no—
838C22—944no—
839C22—944no—
840C22—944no—
841C22—1888no—
842C22H(5,𝔽2)×D4712yes—
843C22C2×#1309407112yes—
844C22C2×#1309407212yes—
845C22C25×D4711yescharacteristic
846C4—24no—
847C4—28no—
848C4—22no—
849C4—24no—
850C4—24no—
851C4—948no—
852C4—942no—
853C4—944no—
854C4—942no—
855C4—942no—
856C4—944no—
857C4—944no—
858C4C2×#1309407114yes—
859C4C2×#1309407214yes—
860C2—44no—
861C2—944no—
862C2—1884no—
863C2#2025772914yesdirect product factor
864C2C2×H(5,𝔽2)×D4711yescharacteristic
865C2C22×#1309407111yescharacteristic
866C2C22×#1309407211yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#554C2
socleC23×C47C25
hypercenterC2×#554D47
hypocenterC47C2×#3544
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #20257729C2direct (N × H)
2. C2×#15689874C2semidirect
3. C2×Q8×Dic94C2semidirect
4. C2×#15689838C2semidirect
5. C2×#15689834C2semidirect
6. C2×#15689811C2semidirect
7. C2×#15689807C2semidirect
8. C2×#15689778C2semidirect
9. C2×#15689774C2semidirect
10. C2×#15689754C2semidirect
11. C2×#15689753C2semidirect
12. C2×#15689746C2semidirect
13. C2×#15689738C2semidirect
14. C2×#15689696C2semidirect
15. C2×C4⋊Q8×D47C2semidirect
16. C2×#15689660C2semidirect
17. C2×#15689655C2semidirect
18. C2×C47×#554C2semidirect
21. #15689874C22semidirect
22. Q8×Dic94C22semidirect
23. #15689838C22semidirect
24. #15689834C22semidirect
25. #15689811C22semidirect
26. #15689807C22semidirect
27. #15689778C22semidirect
28. #15689774C22semidirect
29. #15689754C22semidirect
30. #15689753C22semidirect
31. #15689746C22semidirect
32. #15689738C22semidirect
33. #15689696C22semidirect
42. C4⋊Q8×D47C22semidirect
43. #15689660C22semidirect
44. #15689655C22semidirect
92. C47×#554C22semidirect
432. C2×#554D47semidirect
446. C2×C47#3544semidirect
458. #554C2×D47semidirect
534. C47C2×#3544semidirect
863. C2#20257729direct (N × H)

Maximal subgroups

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

subgroupindex
#202577292
C2×#156898742
C2×Q8×Dic942
C2×#156898382
C2×#156898342
C2×#156898112
C2×#156898072
C2×#156897782
C2×#156897742
C2×#156897542
C2×#156897532
C2×#156897462
C2×#156897382
C2×#156896962
C2×C4⋊Q8×D472
C2×#156896602
C2×#156896552
C2×C47×#5542
C2×#354447