Finite Group Databasebeta

← C2×#20257481 #27124496

Subgroups — C2×#20257481 #27124496

Order 12032.

7022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20257481C2132yesmaximal, direct product factor
2C2×#15689851C211yesmaximal, characteristic, complemented
3C2×#15689850C212yesmaximal, complemented
4C2×#15689846C211yesmaximal, characteristic, complemented
5C2×#15689845C212yesmaximal, complemented
6C2×#15689814C212yesmaximal, complemented
7C2×#15689805C214yesmaximal, complemented
8C2×#15689788C211yesmaximal, characteristic, complemented
9C2×#15689788C212yesmaximal, complemented
10C2×#15689734C212yesmaximal, complemented
11C2×#15689732C214yesmaximal, complemented
12C2×#15689678C211yesmaximal, characteristic, complemented
13C2×#15689677C212yesmaximal, complemented
14C2×#15689660C211yesmaximal, characteristic
15C2×#15689658C212yesmaximal
16C2×#15689599C212yesmaximal, complemented
17C2×C4×Q8×D47C211yesmaximal, characteristic, complemented
18C2×C47×#557C211yesmaximal, characteristic, complemented
19C22×Q8×D47C2211yescharacteristic
20C22×Q8×D47C2212yes—
21#15689851C22116yescomplemented
22#15689850C22132yescomplemented
23#15689846C22116yescomplemented
24#15689845C22132yescomplemented
25#15689814C22132yescomplemented
26#15689805C22164yescomplemented
27#15689788C22132yescomplemented
28#15689788C22116yescomplemented
29#15689734C22132yescomplemented
30#15689732C22164yescomplemented
31#15689678C22116yescomplemented
32#15689677C22132yescomplemented
33C2×#13094024C2211yescharacteristic
34C2×#13094023C2212yes—
35C2×#13094023C2214yes—
36C2×#13094022C2212yes—
37#15689660C22116yes—
38#15689658C22132yes—
39C2×#13094019C2214yes—
40C2×#13094019C2214yes—
41C2×#13094019C2214yes—
42C2×#13094019C2212yes—
43C2×#13094018C2214yes—
44C2×#13094016C2212yes—
45C2×#13094015C2211yescharacteristic
46C2×#13094015C2212yes—
47C2×#13094014C2214yes—
48C2×#13094014C2214yes—
49C2×#13094014C2214yes—
50C2×#13094014C2214yes—
51C2×#13094013C2211yescharacteristic
52C2×#13094012C2212yes—
53C2×#13094009C2212yes—
54C2×#13094009C2214yes—
55C2×#13094004C2212yes—
56C2×#13094002C2214yes—
57C2×#13094002C2214yes—
58C2×#13094002C2214yes—
59C2×#13094000C2212yes—
60C2×#13094000C2212yes—
61C2×#13094000C2212yes—
62C2×#13094000C2211yescharacteristic
63C2×#13093999C2211yescharacteristic
64#15689599C22132yescomplemented
65C2×Q8×Dic47C2211yescharacteristic
66C2×Q8×Dic47C2212yes—
67C2×C4×Dic94C2211yescharacteristic
68C2×C4×Dic94C2212yes—
69C2×C4×Dic94C2212yes—
70C2×C4×Dic94C2214yes—
71C2×C4×Dic94C2212yes—
72C2×#13093989C2211yescharacteristic
73C2×#13093989C2212yes—
74C2×#13093989C2214yes—
75C2×#13093989C2212yes—
76C2×#13093989C2212yes—
77C4×Q8×D47C22116yescomplemented
78C2×C4×D188C2212yes—
79C2×C4×D188C2211yescharacteristic
80C2×#13093986C2214yes—
81C2×#13093986C2212yes—
82C2×#13093982C2212yes—
83C2×#13093982C2214yes—
84C2×#13093982C2212yes—
85C2×#13093981C2214yes—
86C2×#13093981C2212yes—
87C2×#13093981C2214yes—
88C2×C4⋊C4×D47C2212yes—
89C2×C4⋊C4×D47C2211yescharacteristic
90C2×C42×D47C2212yes—
91C2×C42×D47C2211yescharacteristic
92C47×#557C22116yescomplemented
93C2×C4⋊Q8×C47C2211yescharacteristic
94C2×C4⋊Q8×C47C2212yes—
95C2×#125×C47C2214yes—
96C2×#125×C47C2212yes—
97C2×C4×Q8×C47C2211yescharacteristic
98C2×C4×Q8×C47C2212yes—
99C2×C4×Q8×C47C2211yescharacteristic
100C2×C4×Q8×C47C2212yes—
101C22×Dic94C2312yes—
102C22×Dic94C2312yes—
103C22×Dic94C2314yes—
104C22×Dic94C2311yescharacteristic
105C2×Q8×D47—28no—
106C2×Q8×D47—216no—
107C2×Q8×D47C2318yes—
108C2×Q8×D47C23116yes—
109C22×D188C2312yes—
110C22×D188C2311yescharacteristic
111C22×C4×D47C2311yescharacteristic
112C22×C4×D47C2312yes—
113C22×C4×D47C2311yescharacteristic
114C22×C4×D47C2312yes—
115C22×C4×D47C2311yescharacteristic
116C22×C4×D47C2314yes—
117C22×C4×D47C2312yes—
118#13094024C2318yes—
119#13094023C23132yes—
120#13094023C23116yes—
121#13094022C23116yes—
122#13094019C23116yes—
123#13094019C23132yes—
124#13094019C23132yes—
125#13094019C23132yes—
126#13094018C23132yes—
127#13094016C23116yes—
128#13094015C23116yes—
129#13094015C2318yes—
130#13094014C23132yes—
131#13094014C23132yes—
132#13094014C23132yes—
133#13094014C23132yes—
134#13094013C2318yes—
135#13094012C23116yes—
136#13094009C23116yes—
137#13094009C23132yes—
138#13094004C23116yes—
139#13094002C23132yes—
140#13094002C23132yes—
141#13094002C23132yes—
142#13094000C23116yes—
143#13094000C23116yes—
144#13094000C23116yes—
145#13094000C2318yes—
146#13093999C2318yes—
147Q8×Dic47C2318yes—
148Q8×Dic47C23116yes—
149C4×Dic94C23132yes—
150C4×Dic94C2318yes—
151C4×Dic94C23116yes—
152C4×Dic94C23116yes—
153C4×Dic94C23116yes—
154#13093989C23116yes—
155#13093989C23132yes—
156#13093989C2318yes—
157#13093989C23116yes—
158#13093989C23116yes—
159C4×D188C23116yes—
160C4×D188C2318yes—
161#13093986C23132yes—
162#13093986C23116yes—
163#13093982C23132yes—
164#13093982C23116yes—
165#13093982C23116yes—
166#13093981C23116yes—
167#13093981C23132yes—
168#13093981C23132yes—
169C2×C4⋊Dic47C2311yescharacteristic
170C2×C4⋊Dic47C2312yes—
171C2×C4⋊Dic47C2312yes—
172C2×C4⋊Dic47C2314yes—
173C2×C4⋊Dic47C2312yes—
174C2×C4⋊Dic47C2311yescharacteristic
175C2×C4⋊Dic47C2312yes—
176C2×Dic47⋊C4C2312yes—
177C2×Dic47⋊C4C2312yes—
178C2×Dic47⋊C4C2312yes—
179C2×Dic47⋊C4C2312yes—
180C2×Dic47⋊C4C2312yes—
181C2×Dic47⋊C4C2314yes—
182C2×Dic47⋊C4C2314yes—
183C2×Dic47⋊C4C2314yes—
184C2×Dic47⋊C4C2314yes—
185C2×Dic47⋊C4C2314yes—
186C2×Dic47⋊C4C2314yes—
187C4⋊C4×D47C23116yes—
188C4⋊C4×D47C2318yes—
189C2×(C2×D47)⋊C4C2312yes—
190C2×(C2×D47)⋊C4C2312yes—
191C2×(C2×D47)⋊C4C2312yes—
192C2×(C2×D47)⋊C4C2314yes—
193C2×(C2×D47)⋊C4C2314yes—
194C2×(C2×D47)⋊C4C2314yes—
195C2×(C2×D47)⋊C4C2314yes—
196C2×(C2×D47)⋊C4C2312yes—
197C2×(C2×D47)⋊C4C2312yes—
198C2×C4×Dic47C2311yescharacteristic
199C2×C4×Dic47C2312yes—
200C2×C4×Dic47C2312yes—
201C2×C4×Dic47C2311yescharacteristic
202C2×C4×Dic47C2311yescharacteristic
203C2×C4×Dic47C2312yes—
204C2×C4×Dic47C2314yes—
205C2×C4×Dic47C2314yes—
206C2×C4×Dic47C2314yes—
207C42×D47C23116yes—
208C42×D47C2318yes—
209C22×Q8×C47C2311yescharacteristic
210C22×Q8×C47C2311yescharacteristic
211C22×Q8×C47C2312yes—
212C4⋊Q8×C47C23116yes—
213C4⋊Q8×C47C2318yes—
214#125×C47C23132yes—
215#125×C47C23116yes—
216C4×Q8×C47C23116yes—
217C4×Q8×C47C2318yes—
218C4×Q8×C47C23116yes—
219C4×Q8×C47C2318yes—
220C2×C4⋊C4×C47C2311yescharacteristic
221C2×C4⋊C4×C47C2312yes—
222C2×C4⋊C4×C47C2314yes—
223C2×C4⋊C4×C47C2311yescharacteristic
224C2×C4⋊C4×C47C2312yes—
225C2×C4⋊C4×C47C2312yes—
226C2×C4⋊C4×C47C2314yes—
227C2×C4⋊C4×C47C2312yes—
228C2×C4⋊C4×C47C2314yes—
229C2×C42×C47C2312yes—
230C2×C42×C47C2314yes—
231C2×C42×C47C2311yescharacteristic
232C2×C42×C47C2312yes—
233C23×D47C2412yes—
234C23×D47C2411yescharacteristic
235C2×Q8×C47—24no—
236C2×Q8×C47—28no—
237C2×Q8×C47—24no—
238C2×Q8×C47C2414yes—
239C2×Q8×C47C2418yes—
240C2×Q8×C47C2414yes—
241C22×C4×C47C2412yes—
242C22×C4×C47C2412yes—
243C22×C4×C47C2412yes—
244C22×C4×C47C2411yescharacteristic
245C22×C4×C47C2412yes—
246C22×C4×C47C2414yes—
247C22×C4×C47C2411yescharacteristic
248C22×C4×C47C2411yescharacteristic
249C22×Dic47C2411yescharacteristic
250C22×Dic47C2411yescharacteristic
251C22×Dic47C2414yes—
252C22×Dic47C2412yes—
253C22×Dic47C2411yescharacteristic
254C22×Dic47C2412yes—
255C22×Dic47C2412yes—
256Q8×D47—232no—
257Q8×D47—264no—
258C2×D188—28no—
259C2×D188—24no—
260C2×D188C2418yes—
261C2×D188C2414yes—
262C2×C4×D47—28no—
263C2×C4×D47—24no—
264C2×C4×D47—24no—
265C2×C4×D47—28no—
266C2×C4×D47—24no—
267C2×C4×D47—28no—
268C2×C4×D47—216no—
269C2×C4×D47C2414yes—
270C2×C4×D47C2418yes—
271C2×C4×D47C2414yes—
272C2×C4×D47C2418yes—
273C2×C4×D47C2414yes—
274C2×C4×D47C24116yes—
275C2×C4×D47C2418yes—
276C2×Dic94—28no—
277C2×Dic94—28no—
278C2×Dic94—216no—
279C2×Dic94#4118yes—
280C2×Dic94C2418yes—
281C2×Dic94C2418yes—
282C2×Dic94C24116yes—
283C2×Dic94C2414yes—
284C4⋊C4×C47C2414yes—
285C4⋊C4×C47C2418yes—
286C4⋊C4×C47C24116yes—
287C4⋊C4×C47C2414yes—
288C4⋊C4×C47C2418yes—
289C4⋊C4×C47C2418yes—
290C4⋊C4×C47C24116yes—
291C4⋊C4×C47C2418yes—
292C4⋊C4×C47C24116yes—
293C42×C47C2418yes—
294C42×C47C24116yes—
295C42×C47C2414yes—
296C42×C47C2418yes—
297(C2×D47)⋊C4C2418yes—
298(C2×D47)⋊C4C2418yes—
299(C2×D47)⋊C4C2418yes—
300(C2×D47)⋊C4C24116yes—
301(C2×D47)⋊C4C24116yes—
302(C2×D47)⋊C4C24116yes—
303(C2×D47)⋊C4C24116yes—
304(C2×D47)⋊C4C2418yes—
305(C2×D47)⋊C4C2418yes—
306C4⋊Dic47C2414yes—
307C4⋊Dic47C2418yes—
308C4⋊Dic47C2418yes—
309C4⋊Dic47C24116yes—
310C4⋊Dic47C2418yes—
311C4⋊Dic47C2414yes—
312C4⋊Dic47C2418yes—
313Dic47⋊C4C2418yes—
314Dic47⋊C4C2418yes—
315Dic47⋊C4C2418yes—
316Dic47⋊C4C2418yes—
317Dic47⋊C4C2418yes—
318Dic47⋊C4C24116yes—
319Dic47⋊C4C24116yes—
320Dic47⋊C4C24116yes—
321Dic47⋊C4C24116yes—
322Dic47⋊C4C24116yes—
323Dic47⋊C4C24116yes—
324C4×Dic47C2414yes—
325C4×Dic47C2418yes—
326C4×Dic47C2418yes—
327C4×Dic47C2414yes—
328C4×Dic47C2414yes—
329C4×Dic47C2418yes—
330C4×Dic47C24116yes—
331C4×Dic47C24116yes—
332C4×Dic47C24116yes—
333C23×C47C2511yescharacteristic
334C22×D47—22no—
335C22×D47—22no—
336C22×D47—24no—
337C22×D47—24no—
338C22×D47—24no—
339C22×D472−1+414yes—
340C22×D47C2514yes—
341C22×D47C2512yes—
342Q8×C47—28no—
343Q8×C47—216no—
344Q8×C47—28no—
345C2×C4×C47—24no—
346C2×C4×C47—28no—
347C2×C4×C47—24no—
348C2×C4×C47—22no—
349C2×C4×C47—24no—
350C2×C4×C47—24no—
351C2×C4×C47C2×#4114yes—
352C2×C4×C472−1+414yes—
353C2×C4×C47C2514yes—
354C2×C4×C47C2514yes—
355C2×C4×C47C2512yes—
356C2×C4×C47C2514yes—
357C2×C4×C47C2518yes—
358C2×C4×C47C2514yes—
359C2×C4×C47C2512yes—
360C2×C4×C47C2512yes—
361C2×Dic47—22no—
362C2×Dic47—24no—
363C2×Dic47—28no—
364C2×Dic47—22no—
365C2×Dic47—24no—
366C2×Dic47—22no—
367C2×Dic47C2×#4118yes—
368C2×Dic47C2512yes—
369C2×Dic47C2512yes—
370C2×Dic47C2518yes—
371C2×Dic47C2514yes—
372C2×Dic47C2512yes—
373C2×Dic47C2514yes—
374C2×Dic47C2514yes—
375D188—216no—
376D188—28no—
377C4×D47—216no—
378C4×D47—28no—
379C4×D47—28no—
380C4×D47—216no—
381C4×D47—28no—
382C4×D47—216no—
383C4×D47—232no—
384Dic94—216no—
385Dic94—216no—
386Dic94—232no—
387Dic94C2×#41116yes—
388C2×#3523—471nomaximal, Sylow
389C22×C47C22×#4112yes—
390C22×C47C2×2−1+412yes—
391C22×C47C2×2−1+412yes—
392C22×C47C2611yescharacteristic
393C2×D47—22no—
394C2×D47—22no—
395C2×D47—28no—
396C2×D47—24no—
397C2×D47—24no—
398C2×D47—24no—
399C2×D47—48no—
400C2×D47C2×2−1+414yes—
401C4×C47—24no—
402C4×C47—28no—
403C4×C47—24no—
404C4×C47—22no—
405C4×C47—24no—
406C4×C47—24no—
407C4×C47C22×#4114yes—
408C4×C47C2×2−1+414yes—
409Dic47—22no—
410Dic47—24no—
411Dic47—28no—
412Dic47—22no—
413Dic47—24no—
414Dic47—22no—
415Dic47C22×#4118yes—
416#3523—4732no—
417C2×#557—472no—
418C2×#557—471no—
419C2×#557D4711yescharacteristic, complemented
420C2×#556—472no—
421C2×#556—471no—
422C2×#552—474no—
423C2×#552—472no—
424C2×D4×Q8—472no—
425C2×D4×Q8—471no—
426C2×#541—472no—
427C2×#541—474no—
428C2×#533—471no—
429C2×#533—472no—
430C2×#529—472no—
431C2×#529—471no—
432C2×#519—472no—
433C22×C4×Q8—471no—
434C2×C47#352314yescomplemented
435C2×C47C23×#4111yescharacteristic
436C2×C47C22×2−1+411yescharacteristic
437C2×C47C22×2−1+411yescharacteristic
438D47—24no—
439D47—44no—
440C23×Q8—471no—
441C23×Q8—472no—
442#557—4732no—
443#557—4716no—
444#557C2×D47116yescomplemented
445#556—4732no—
446#556—4716no—
447#552—4764no—
448#552—4732no—
449D4×Q8—4732no—
450D4×Q8—4716no—
451#541—4732no—
452#541—4764no—
453#533—4716no—
454#533—4732no—
455C2×C4⋊Q8—472no—
456C2×C4⋊Q8—472no—
457C2×C4⋊Q8—474no—
458C2×C4⋊Q8—471no—
459C2×C4⋊Q8C2×D4711yescharacteristic
460C2×C4⋊Q8C2×D4712yes—
461#529—4732no—
462#529—4716no—
463C2×#126—472no—
464C2×#126—474no—
465C2×#126—474no—
466C2×#126—474no—
467C2×#126—474no—
468C2×#125—471no—
469C2×#125—474no—
470C2×#125—472no—
471C2×#125—474no—
472C2×#125—474no—
473C2×#125—474no—
474C2×#125—472no—
475C2×#125C2×D4712yes—
476C2×#125C2×D4714yes—
477C2×#124—471no—
478C2×#124—472no—
479C2×#123—472no—
480C2×#123—474no—
481C2×C22⋊Q8—471no—
482C2×C22⋊Q8—472no—
483C2×C22⋊Q8—472no—
484C2×C22⋊Q8—472no—
485C2×C22⋊Q8—472no—
486C2×C22⋊Q8—474no—
487C2×C22⋊Q8—474no—
488C2×C22⋊Q8—474no—
489C2×#121—471no—
490#519—4732no—
491C2×C4×Q8—471no—
492C2×C4×Q8—472no—
493C2×C4×Q8—4716no—
494C2×C4×Q8—471no—
495C2×C4×Q8—472no—
496C2×C4×Q8—474no—
497C2×C4×Q8—472no—
498C2×C4×Q8—472no—
499C2×C4×Q8—471no—
500C2×C4×Q8—472no—
501C2×C4×Q8—474no—
502C2×C4×Q8—472no—
503C2×C4×Q8—472no—
504C2×C4×Q8C2×D4711yescharacteristic
505C2×C4×Q8C2×D4712yes—
506C2×C4×Q8C2×D4711yescharacteristic
507C2×C4×Q8C2×D4712yes—
508C2×C4×D4—474no—
509C2×C4×D4—472no—
510C2×C4×D4—472no—
511C2×C4×D4—471no—
512C2×#117—474no—
513C2×#117—472no—
514C2×#117—472no—
515C2×#117—472no—
516C2×#117—474no—
517C2×#117—474no—
518C22×C4⋊C4—472no—
519C22×C4⋊C4—471no—
520C22×C42—472no—
521C22×C42—471no—
522C47C2×#352311yescharacteristic, complemented, Sylow
523C22×Q8—478no—
524C22×Q8—4716no—
525C22×Q8—471no—
526C22×Q8—472no—
527C22×Q8—472no—
528C22×Q8—474no—
529C22×Q8—948no—
530C22×Q8—9416no—
531C22×Q8C22×D4711yescharacteristic
532C22×Q8C22×D4712yes—
533C22×Q8C22×D4711yescharacteristic
534C22×D4—472no—
535C22×D4—471no—
536C23×C4—471no—
537C23×C4—472no—
538C23×C4—472no—
539C23×C4—471no—
540C23×C4—474no—
541C23×C4—472no—
542C23×C4—471no—
543C4⋊Q8—4716no—
544C4⋊Q8—4716no—
545C4⋊Q8—4732no—
546C4⋊Q8—478no—
547C4⋊Q8C22×D4718yes—
548C4⋊Q8C22×D47116yes—
549#126—4716no—
550#126—4732no—
551#126—4732no—
552#126—4732no—
553#126—4732no—
554#125—478no—
555#125—4732no—
556#125—4716no—
557#125—4732no—
558#125—4732no—
559#125—4732no—
560#125—4716no—
561#125C22×D47116yes—
562#125C22×D47132yes—
563#124—478no—
564#124—4716no—
565#123—4716no—
566#123—4732no—
567C22⋊Q8—478no—
568C22⋊Q8—4716no—
569C22⋊Q8—4716no—
570C22⋊Q8—4716no—
571C22⋊Q8—4716no—
572C22⋊Q8—4732no—
573C22⋊Q8—4732no—
574C22⋊Q8—4732no—
575#121—478no—
576C4×Q8—478no—
577C4×Q8—4716no—
578C4×Q8—478no—
579C4×Q8—4716no—
580C4×Q8—4732no—
581C4×Q8—4716no—
582C4×Q8—4716no—
583C4×Q8—478no—
584C4×Q8—4716no—
585C4×Q8—4732no—
586C4×Q8—4716no—
587C4×Q8—4716no—
588C4×Q8C22×D4718yes—
589C4×Q8C22×D47116yes—
590C4×Q8C22×D4718yes—
591C4×Q8C22×D47116yes—
592C4×D4—4732no—
593C4×D4—4716no—
594C4×D4—4716no—
595C4×D4—478no—
596#117—4732no—
597#117—4716no—
598#117—4716no—
599#117—4716no—
600#117—4732no—
601#117—4732no—
602C2×C4⋊C4—472no—
603C2×C4⋊C4—472no—
604C2×C4⋊C4—471no—
605C2×C4⋊C4—472no—
606C2×C4⋊C4—472no—
607C2×C4⋊C4—474no—
608C2×C4⋊C4—472no—
609C2×C4⋊C4—472no—
610C2×C4⋊C4—474no—
611C2×C4⋊C4—472no—
612C2×C4⋊C4—474no—
613C2×C4⋊C4—474no—
614C2×C4⋊C4—472no—
615C2×C4⋊C4—471no—
616C2×C4⋊C4—472no—
617C2×C4⋊C4—474no—
618C2×C4⋊C4—474no—
619C2×C4⋊C4—474no—
620C2×C4⋊C4—4716no—
621C2×C4⋊C4—478no—
622C2×C4⋊C4C22×D4711yescharacteristic
623C2×C4⋊C4C22×D4712yes—
624C2×C4⋊C4C22×D4714yes—
625C2×C4⋊C4C22×D4712yes—
626C2×C4⋊C4C22×D4712yes—
627C2×C4⋊C4C22×D4714yes—
628C2×C4⋊C4C22×D4711yescharacteristic
629C2×C4⋊C4C22×D4714yes—
630C2×C4⋊C4C22×D4712yes—
631C2×C22⋊C4—472no—
632C2×C22⋊C4—472no—
633C2×C22⋊C4—474no—
634C2×C22⋊C4—474no—
635C2×C22⋊C4—472no—
636C2×C22⋊C4—474no—
637C2×C22⋊C4—472no—
638C2×C22⋊C4—474no—
639C2×C22⋊C4—472no—
640C2×C42—472no—
641C2×C42—471no—
642C2×C42—474no—
643C2×C42—474no—
644C2×C42—474no—
645C2×C42—472no—
646C2×C42—471no—
647C2×C42—472no—
648C2×C42—471no—
649C2×C42—4716no—
650C2×C42—478no—
651C2×C42C22×D4714yes—
652C2×C42C22×D4712yes—
653C2×C42C22×D4711yescharacteristic
654C2×C42C22×D4712yes—
655C24—471no—
656C24—472no—
657C2×Q8—24no—
658C2×Q8—28no—
659C2×Q8—24no—
660C2×Q8—478no—
661C2×Q8—474no—
662C2×Q8—478no—
663C2×Q8—478no—
664C2×Q8—4716no—
665C2×Q8—948no—
666C2×Q8—9416no—
667C2×Q8—9432no—
668C2×Q8—9464no—
669C2×Q8—948no—
670C2×Q8C23×D4714yes—
671C2×Q8C23×D4718yes—
672C2×Q8C23×D4714yes—
673C2×D4—478no—
674C2×D4—474no—
675C2×D4—948no—
676C2×D4—944no—
677C22×C4—472no—
678C22×C4—471no—
679C22×C4—471no—
680C22×C4—474no—
681C22×C4—472no—
682C22×C4—472no—
683C22×C4—471no—
684C22×C4—474no—
685C22×C4—474no—
686C22×C4—478no—
687C22×C4—478no—
688C22×C4—474no—
689C22×C4—4716no—
690C22×C4—478no—
691C22×C4—948no—
692C22×C4—9416no—
693C22×C4—948no—
694C22×C4—944no—
695C22×C4—944no—
696C22×C4—948no—
697C22×C4—944no—
698C22×C4C23×D4712yes—
699C22×C4C23×D4712yes—
700C22×C4C23×D4711yescharacteristic
701C22×C4C23×D4714yes—
702C22×C4C23×D4712yes—
703C22×C4C23×D4712yes—
704C22×C4C23×D4711yescharacteristic
705C22×C4C23×D4711yescharacteristic
706C4⋊C4—478no—
707C4⋊C4—478no—
708C4⋊C4—478no—
709C4⋊C4—4716no—
710C4⋊C4—478no—
711C4⋊C4—478no—
712C4⋊C4—4716no—
713C4⋊C4—4716no—
714C4⋊C4—4716no—
715C4⋊C4—4716no—
716C4⋊C4—4716no—
717C4⋊C4—474no—
718C4⋊C4—478no—
719C4⋊C4—478no—
720C4⋊C4—4716no—
721C4⋊C4—478no—
722C4⋊C4—474no—
723C4⋊C4—478no—
724C4⋊C4C23×D4714yes—
725C4⋊C4C23×D4718yes—
726C4⋊C4C23×D47116yes—
727C4⋊C4C23×D4718yes—
728C4⋊C4C23×D4718yes—
729C4⋊C4C23×D47116yes—
730C4⋊C4C23×D4714yes—
731C4⋊C4C23×D47116yes—
732C4⋊C4C23×D4718yes—
733C22⋊C4—478no—
734C22⋊C4—478no—
735C22⋊C4—4716no—
736C22⋊C4—4716no—
737C22⋊C4—478no—
738C22⋊C4—4716no—
739C22⋊C4—478no—
740C22⋊C4—4716no—
741C22⋊C4—478no—
742C42—478no—
743C42—474no—
744C42—478no—
745C42—474no—
746C42—478no—
747C42—474no—
748C42—4716no—
749C42—4716no—
750C42—4716no—
751C42C23×D4714yes—
752C42C23×D4718yes—
753C42C23×D47116yes—
754C42C23×D4718yes—
755C23—474no—
756C23—472no—
757C23—474no—
758C23—942no—
759C23—942no—
760C23—944no—
761C23—944no—
762C23—944no—
763C23C24×D4711yescharacteristic
764Q8—28no—
765Q8—216no—
766Q8—28no—
767Q8—4716no—
768Q8—9416no—
769Q8—9432no—
770Q8—9416no—
771D4—9416no—
772D4—948no—
773C2×C4—24no—
774C2×C4—28no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—478no—
780C2×C4—474no—
781C2×C4—472no—
782C2×C4—472no—
783C2×C4—478no—
784C2×C4—474no—
785C2×C4—472no—
786C2×C4—474no—
787C2×C4—9416no—
788C2×C4—9432no—
789C2×C4—9416no—
790C2×C4—948no—
791C2×C4—944no—
792C2×C4—942no—
793C2×C4—942no—
794C2×C4—944no—
795C2×C4—942no—
796C2×C4—948no—
797C2×C4—948no—
798C2×C4—9416no—
799C2×C4—948no—
800C2×C4#41×D4714yes—
801C2×C4#1309407214yes—
802C2×C4C24×D4714yes—
803C2×C4C24×D4714yes—
804C2×C4C24×D4712yes—
805C2×C4C24×D4714yes—
806C2×C4C24×D4718yes—
807C2×C4C24×D4714yes—
808C2×C4C24×D4712yes—
809C2×C4C24×D4712yes—
810C22—474no—
811C22—942no—
812C22—942no—
813C22—948no—
814C22—944no—
815C22—944no—
816C22—944no—
817C22—1888no—
818C22C2×#41×D4712yes—
819C222−1+4×D4712yes—
820C22C2×#1309407212yes—
821C22C25×D4711yescharacteristic
822C4—24no—
823C4—28no—
824C4—24no—
825C4—22no—
826C4—24no—
827C4—24no—
828C4—478no—
829C4—942no—
830C4—944no—
831C4—942no—
832C4—944no—
833C4—942no—
834C4—948no—
835C4C2×#41×D4714yes—
836C4C2×#1309407214yes—
837C2—944no—
838C2—1884no—
839C2#2025748114yesdirect product factor
840C2C22×#41×D4711yescharacteristic
841C2C2×2−1+4×D4711yescharacteristic
842C2C22×#1309407211yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#557C2
socleC23×C47C25
prime radicalC2×#13093999C22
hypercenterC2×#557D47
hypocenterC47C2×#3523
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #20257481C2direct (N × H)
2. C2×#15689851C2semidirect
3. C2×#15689850C2semidirect
4. C2×#15689846C2semidirect
5. C2×#15689845C2semidirect
6. C2×#15689814C2semidirect
7. C2×#15689805C2semidirect
8. C2×#15689788C2semidirect
9. C2×#15689788C2semidirect
10. C2×#15689734C2semidirect
11. C2×#15689732C2semidirect
12. C2×#15689678C2semidirect
13. C2×#15689677C2semidirect
16. C2×#15689599C2semidirect
17. C2×C4×Q8×D47C2semidirect
18. C2×C47×#557C2semidirect
21. #15689851C22semidirect
22. #15689850C22semidirect
23. #15689846C22semidirect
24. #15689845C22semidirect
25. #15689814C22semidirect
26. #15689805C22semidirect
27. #15689788C22semidirect
28. #15689788C22semidirect
29. #15689734C22semidirect
30. #15689732C22semidirect
31. #15689678C22semidirect
32. #15689677C22semidirect
64. #15689599C22semidirect
77. C4×Q8×D47C22semidirect
92. C47×#557C22semidirect
419. C2×#557D47semidirect
434. C2×C47#3523semidirect
444. #557C2×D47semidirect
522. C47C2×#3523semidirect
839. C2#20257481direct (N × H)

Maximal subgroups

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

subgroupindex
#202574812
C2×#156898512
C2×#156898502
C2×#156898462
C2×#156898452
C2×#156898142
C2×#156898052
C2×#156897882
C2×#156897342
C2×#156897322
C2×#156896782
C2×#156896772
C2×#156896602
C2×#156896582
C2×#156895992
C2×C4×Q8×D472
C2×C47×#5572
C2×#352347