Finite Group Databasebeta

← C2×#20257476 #27124493

Subgroups — C2×#20257476 #27124493

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#20257476C2132yesmaximal, direct product factor
2C2×#15689849C212yesmaximal, complemented
3C2×#15689848C211yesmaximal, characteristic, complemented
4C2×#15689848C211yesmaximal, characteristic, complemented
5C2×#15689847C211yesmaximal, characteristic, complemented
6C2×#15689845C212yesmaximal, complemented
7C2×#15689815C212yesmaximal, complemented
8C2×#15689806C214yesmaximal, complemented
9C2×#15689788C211yesmaximal, characteristic, complemented
10C2×#15689786C212yesmaximal, complemented
11C2×#15689732C214yesmaximal, complemented
12C2×#15689731C212yesmaximal, complemented
13C2×#15689675C212yesmaximal, complemented
14C2×#15689659C212yesmaximal
15C2×#15689657C211yesmaximal, characteristic
16C2×#15689599C212yesmaximal, complemented
17C22×C4×Dic94C211yesmaximal, characteristic, complemented
18C2×C47×#533C211yesmaximal, characteristic, complemented
19C23×Dic94C2211yescharacteristic
20C22×Q8×D47C2212yes—
21#15689849C22132yescomplemented
22#15689848C22116yescomplemented
23#15689848C22116yescomplemented
24#15689847C22116yescomplemented
25#15689845C22132yescomplemented
26#15689815C22132yescomplemented
27#15689806C22164yescomplemented
28#15689788C22116yescomplemented
29#15689786C22132yescomplemented
30#15689732C22164yescomplemented
31#15689731C22132yescomplemented
32#15689675C22132yescomplemented
33C2×#13094023C2214yes—
34C2×#13094023C2212yes—
35C2×#13094022C2212yes—
36C2×#13094022C2212yes—
37#15689659C22132yes—
38#15689657C22116yes—
39C2×#13094019C2214yes—
40C2×#13094019C2214yes—
41C2×#13094019C2214yes—
42C2×#13094018C2214yes—
43C2×#13094018C2212yes—
44C2×#13094016C2214yes—
45C2×#13094016C2211yescharacteristic
46C2×#13094015C2212yes—
47C2×#13094015C2214yes—
48C2×#13094015C2212yes—
49C2×#13094014C2214yes—
50C2×#13094014C2214yes—
51C2×#13094014C2214yes—
52C2×#13094013C2212yes—
53C2×#13094012C2211yescharacteristic
54C2×#13094008C2214yes—
55C2×#13094007C2212yes—
56C2×#13094004C2212yes—
57C2×#13094003C2211yescharacteristic
58C2×#13094002C2214yes—
59C2×#13094002C2214yes—
60C2×#13094001C2214yes—
61C2×#13094000C2212yes—
62C2×#13093998C2211yescharacteristic
63#15689599C22132yescomplemented
64C2×Q8×Dic47C2212yes—
65C2×Q8×Dic47C2212yes—
66C2×Q8×Dic47C2212yes—
67C2×C4×Dic94C2211yescharacteristic
68C2×C4×Dic94C2211yescharacteristic
69C2×C4×Dic94C2212yes—
70C2×C4×Dic94C2211yescharacteristic
71C2×C4×Dic94C2211yescharacteristic
72C2×C4×Dic94C2212yes—
73C2×C4×Dic94C2214yes—
74C2×C4×Dic94C2211yescharacteristic
75C2×C4×Dic94C22116yescomplemented
76C2×#13093989C2212yes—
77C2×#13093989C2214yes—
78C2×#13093989C2212yes—
79C2×C4×D188C2211yescharacteristic
80C2×#13093986C2212yes—
81C2×C4×C22⋊D47C2212yes—
82C2×(C22⋊D47)⋊C4C2214yes—
83C2×#13093982C2212yes—
84C2×#13093982C2214yes—
85C2×#13093981C2214yes—
86C2×#13093981C2212yes—
87C2×#13093980C2214yes—
88C22×C4⋊Dic47C2211yescharacteristic
89C22×Dic47⋊C4C2212yes—
90C22×C4×Dic47C2212yes—
91C47×#533C22116yescomplemented
92C2×C4⋊Q8×C47C2211yescharacteristic
93C2×C4⋊Q8×C47C2211yescharacteristic
94C2×#125×C47C2212yes—
95C2×C22⋊Q8×C47C2212yes—
96C2×C22⋊Q8×C47C2212yes—
97C2×C4×Q8×C47C2212yes—
98C2×C4×Q8×C47C2212yes—
99C2×#117×C47C2212yes—
100C22×C42×C47C2211yescharacteristic
101C22×Dic94—28no—
102C22×Dic94C2318yes—
103C22×Dic94C2311yescharacteristic
104C22×Dic94C2314yes—
105C22×Dic94C2312yes—
106C22×Dic94C2311yescharacteristic
107C22×Dic94C2311yescharacteristic
108C2×Q8×D47—216no—
109C2×Q8×D47C23116yes—
110C22×D188C2311yescharacteristic
111C22×C22⋊D47C2312yes—
112C23×Dic47C2312yes—
113C23×Dic47C2312yes—
114C22×C4×D47C2314yes—
115C22×C4×D47C2312yes—
116#13094023C23132yes—
117#13094023C23116yes—
118#13094022C23116yes—
119#13094022C23116yes—
120#13094019C23132yes—
121#13094019C23132yes—
122#13094019C23132yes—
123#13094018C23132yes—
124#13094018C23116yes—
125#13094016C23132yes—
126#13094016C2318yes—
127#13094015C23116yes—
128#13094015C23132yes—
129#13094015C23116yes—
130#13094014C23132yes—
131#13094014C23132yes—
132#13094014C23132yes—
133#13094013C23116yes—
134#13094012C2318yes—
135#13094008C23132yes—
136#13094007C23116yes—
137#13094004C23116yes—
138#13094003C2318yes—
139#13094002C23132yes—
140#13094002C23132yes—
141#13094001C23132yes—
142#13094000C23116yes—
143#13093998C2318yes—
144Q8×Dic47C23116yes—
145Q8×Dic47C23116yes—
146Q8×Dic47C23116yes—
147C4×Dic94C2318yes—
148C4×Dic94C23116yes—
149C4×Dic94C2318yes—
150C4×Dic94C23132yes—
151C4×Dic94C23116yes—
152C4×Dic94C2318yes—
153C4×Dic94C2318yes—
154C4×Dic94C2318yes—
155#13093989C23132yes—
156#13093989C23116yes—
157#13093989C23116yes—
158C4×D188C2318yes—
159#13093986C23116yes—
160C4×C22⋊D47C23116yes—
161(C22⋊D47)⋊C4C23132yes—
162#13093982C23132yes—
163#13093982C23116yes—
164#13093981C23116yes—
165#13093981C23132yes—
166#13093980C23132yes—
167C2×C4⋊Dic47C2318yes—
168C2×C4⋊Dic47C2311yescharacteristic
169C2×C4⋊Dic47C2311yescharacteristic
170C2×C4⋊Dic47C2312yes—
171C2×C4⋊Dic47C2314yes—
172C2×C4⋊Dic47C2311yescharacteristic
173C2×C4⋊Dic47C2311yescharacteristic
174C2×C4⋊Dic47C2314yes—
175C2×C4⋊Dic47C2314yes—
176C2×Dic47⋊C4C23116yes—
177C2×Dic47⋊C4C2312yes—
178C2×Dic47⋊C4C2312yes—
179C2×Dic47⋊C4C2312yes—
180C2×Dic47⋊C4C2312yes—
181C2×Dic47⋊C4C2314yes—
182C2×Dic47⋊C4C2314yes—
183C2×Dic47⋊C4C2314yes—
184C2×Dic47⋊C4C2312yes—
185C2×Dic47⋊C4C2312yes—
186C2×Dic47⋊C4C2314yes—
187C2×Dic47⋊C4C2312yes—
188C2×Dic47⋊C4C2314yes—
189C2×Dic47⋊C4C2312yes—
190C2×C22⋊Dic47C2312yes—
191C2×(C2×D47)⋊C4C2312yes—
192C2×(C2×D47)⋊C4C2312yes—
193C2×(C2×D47)⋊C4C2314yes—
194C2×(C2×D47)⋊C4C2314yes—
195C2×(C2×D47)⋊C4C2312yes—
196C2×(C2×D47)⋊C4C2314yes—
197C2×(C2×D47)⋊C4C2312yes—
198C2×C4×Dic47C2312yes—
199C2×C4×Dic47C2312yes—
200C2×C4×Dic47C2312yes—
201C2×C4×Dic47C2312yes—
202C2×C4×Dic47C23116yes—
203C2×C4×Dic47C2314yes—
204C2×C4×Dic47C2314yes—
205C2×C4×Dic47C2312yes—
206C2×C4×Dic47C2314yes—
207C22×Q8×C47C2312yes—
208C22×Q8×C47C2312yes—
209C23×C4×C47C2311yescharacteristic
210C23×C4×C47C2311yescharacteristic
211C23×C4×C47C2311yescharacteristic
212C4⋊Q8×C47C2318yes—
213C4⋊Q8×C47C2318yes—
214#125×C47C23116yes—
215C22⋊Q8×C47C23116yes—
216C22⋊Q8×C47C23116yes—
217C4×Q8×C47C23116yes—
218C4×Q8×C47C23116yes—
219#117×C47C23116yes—
220C2×C4⋊C4×C47C2312yes—
221C2×C4⋊C4×C47C2312yes—
222C2×C4⋊C4×C47C2314yes—
223C2×C4⋊C4×C47C2314yes—
224C2×C4⋊C4×C47C2312yes—
225C2×C4⋊C4×C47C2312yes—
226C2×C22⋊C4×C47C2314yes—
227C2×C42×C47C2311yescharacteristic
228C2×C42×C47C2311yescharacteristic
229C2×C42×C47C2311yescharacteristic
230C2×C42×C47C2311yescharacteristic
231C2×C42×C47C2318yes—
232C2×C42×C47C2314yes—
233C24×C47C2411yescharacteristic
234C23×D47C2412yes—
235C2×Q8×C47—28no—
236C2×Q8×C47—28no—
237C2×Q8×C47C2418yes—
238C2×Q8×C47C2418yes—
239C22×C4×C47—24no—
240C22×C4×C47—24no—
241C22×C4×C47—24no—
242C22×C4×C47C2411yescharacteristic
243C22×C4×C47C2411yescharacteristic
244C22×C4×C47C2411yescharacteristic
245C22×C4×C47C2411yescharacteristic
246C22×C4×C47C2414yes—
247C22×C4×C47C2414yes—
248C22×C4×C47C2414yes—
249C22×C4×C47C2414yes—
250C22×C4×C47C2414yes—
251C22×C4×C47C2411yescharacteristic
252C22×C4×C47C2411yescharacteristic
253C2×C22⋊D47—28no—
254C2×C22⋊D47C2418yes—
255C22×Dic47—28no—
256C22×Dic47—28no—
257C22×Dic47C2412yes—
258C22×Dic47C2412yes—
259C22×Dic47C2412yes—
260C22×Dic47C2412yes—
261C22×Dic47C2412yes—
262C22×Dic47C2412yes—
263C22×Dic47C2418yes—
264C22×Dic47C2418yes—
265C22×Dic47C2412yes—
266Q8×D47—264no—
267C2×D188—24no—
268C2×D188C2414yes—
269C2×C4×D47—28no—
270C2×C4×D47—216no—
271C2×C4×D47C24116yes—
272C2×C4×D47C2418yes—
273C2×Dic94—24no—
274C2×Dic94—24no—
275C2×Dic94—216no—
276C2×Dic94—28no—
277C2×Dic94—232no—
278C2×Dic94#4118yes—
279C2×Dic94C2414yes—
280C2×Dic94C24116yes—
281C2×Dic94C2418yes—
282C2×Dic94C2414yes—
283C2×Dic94C2414yes—
284C4⋊C4×C47C2418yes—
285C4⋊C4×C47C2418yes—
286C4⋊C4×C47C24116yes—
287C4⋊C4×C47C24116yes—
288C4⋊C4×C47C2418yes—
289C4⋊C4×C47C2418yes—
290C22⋊C4×C47C24116yes—
291C42×C47C2414yes—
292C42×C47C2414yes—
293C42×C47C2414yes—
294C42×C47C2414yes—
295C42×C47C24116yes—
296C22⋊Dic47C2418yes—
297(C2×D47)⋊C4C2418yes—
298(C2×D47)⋊C4C2418yes—
299(C2×D47)⋊C4C24116yes—
300(C2×D47)⋊C4C24116yes—
301(C2×D47)⋊C4C2418yes—
302(C2×D47)⋊C4C24116yes—
303(C2×D47)⋊C4C2418yes—
304C4⋊Dic47C2414yes—
305C4⋊Dic47C2414yes—
306C4⋊Dic47C2418yes—
307C4⋊Dic47C24116yes—
308C4⋊Dic47C2414yes—
309C4⋊Dic47C2414yes—
310C4⋊Dic47C24116yes—
311C4⋊Dic47C24116yes—
312Dic47⋊C4C2418yes—
313Dic47⋊C4C2418yes—
314Dic47⋊C4C2418yes—
315Dic47⋊C4C2418yes—
316Dic47⋊C4C24116yes—
317Dic47⋊C4C24116yes—
318Dic47⋊C4C24116yes—
319Dic47⋊C4C2418yes—
320Dic47⋊C4C2418yes—
321Dic47⋊C4C24116yes—
322Dic47⋊C4C2418yes—
323Dic47⋊C4C24116yes—
324Dic47⋊C4C2418yes—
325C4×Dic47C2418yes—
326C4×Dic47C2418yes—
327C4×Dic47C2418yes—
328C4×Dic47C2418yes—
329C4×Dic47C24116yes—
330C4×Dic47C24116yes—
331C4×Dic47C2418yes—
332C4×Dic47C24116yes—
333C23×C47—22no—
334C23×C47—22no—
335C23×C472−1+414yes—
336C23×C47C2512yes—
337C23×C47C2511yescharacteristic
338C22×D47—24no—
339C22×D47—24no—
340C22×D47—24no—
341C22×D47C2514yes—
342Q8×C47—216no—
343Q8×C47—216no—
344C2×C4×C47—22no—
345C2×C4×C47—28no—
346C2×C4×C47—22no—
347C2×C4×C47—28no—
348C2×C4×C47—22no—
349C2×C4×C47—22no—
350C2×C4×C47—28no—
351C2×C4×C47—28no—
352C2×C4×C47—28no—
353C2×C4×C47C2×#4114yes—
354C2×C4×C472−1+414yes—
355C2×C4×C47C2512yes—
356C2×C4×C47C2518yes—
357C2×C4×C47C2518yes—
358C2×C4×C47C2512yes—
359C2×C4×C47C2512yes—
360C2×C4×C47C2512yes—
361C2×C4×C47C2512yes—
362C2×C4×C47C2512yes—
363C22⋊D47—216no—
364C2×Dic47—24no—
365C2×Dic47—24no—
366C2×Dic47—24no—
367C2×Dic47—216no—
368C2×Dic47—24no—
369C2×Dic47—24no—
370C2×Dic47—24no—
371C2×Dic47—216no—
372C2×Dic47C2×#4118yes—
373C2×Dic47C2514yes—
374C2×Dic47C2514yes—
375C2×Dic47C2514yes—
376C2×Dic47C2514yes—
377C2×Dic47C2514yes—
378C2×Dic47C2514yes—
379C2×Dic47C2514yes—
380D188—28no—
381C4×D47—216no—
382C4×D47—232no—
383Dic94—28no—
384Dic94—28no—
385Dic94—216no—
386Dic94—232no—
387Dic94C2×#41116yes—
388C2×#3523—471nomaximal, Sylow
389C22×C47—22no—
390C22×C47—22no—
391C22×C47—28no—
392C22×C47C22×#4112yes—
393C22×C47C2×2−1+412yes—
394C22×C47C2×2−1+414yes—
395C22×C47C2×2−1+412yes—
396C22×C47C2611yescharacteristic
397C2×D47—24no—
398C2×D47—24no—
399C2×D47—24no—
400C2×D47—48no—
401C4×C47—22no—
402C4×C47—28no—
403C4×C47—22no—
404C4×C47—22no—
405C4×C47—22no—
406C4×C47—28no—
407C4×C47C22×#4114yes—
408C4×C47C2×2−1+414yes—
409Dic47—24no—
410Dic47—24no—
411Dic47—24no—
412Dic47—24no—
413Dic47—24no—
414Dic47—24no—
415Dic47C22×#4118yes—
416#3523—4732no—
417C2×#557—471no—
418C2×#557—471no—
419C2×#557—472no—
420C2×#556—471no—
421C2×#556—472no—
422C2×#552—472no—
423C2×#552—474no—
424C2×D4×Q8—471no—
425C2×D4×Q8—472no—
426C2×#541—474no—
427C2×#541—472no—
428C2×#533—472no—
429C2×#533D4711yescharacteristic, complemented
430C2×#529—471no—
431C2×#529—472no—
432C2×#519—472no—
433C22×C4×Q8—471no—
434C2×C47—24no—
435C2×C47#352314yescomplemented
436C2×C47C23×#4111yescharacteristic
437C2×C47C22×2−1+411yescharacteristic
438C2×C47C22×2−1+411yescharacteristic
439D47—44no—
440C23×Q8—472no—
441C23×Q8—471no—
442#557—4716no—
443#557—4716no—
444#557—4732no—
445#556—4716no—
446#556—4732no—
447#552—4732no—
448#552—4764no—
449D4×Q8—4716no—
450D4×Q8—4732no—
451#541—4764no—
452#541—4732no—
453#533—4732no—
454#533C2×D47116yescomplemented
455C2×C4⋊Q8—472no—
456C2×C4⋊Q8—472no—
457C2×C4⋊Q8—472no—
458C2×C4⋊Q8—474no—
459C2×C4⋊Q8C2×D4711yescharacteristic
460C2×C4⋊Q8C2×D4711yescharacteristic
461#529—4732no—
462#529—4716no—
463C2×#126—474no—
464C2×#126—474no—
465C2×#126—474no—
466C2×#126—472no—
467C2×#126—474no—
468C2×#125—472no—
469C2×#125—474no—
470C2×#125—474no—
471C2×#125—474no—
472C2×#125—474no—
473C2×#125—472no—
474C2×#125—471no—
475C2×#125—474no—
476C2×#125C2×D4712yes—
477C2×#124—472no—
478C2×#124—471no—
479C2×#123—472no—
480C2×#123—474no—
481C2×C22⋊Q8—472no—
482C2×C22⋊Q8—471no—
483C2×C22⋊Q8—474no—
484C2×C22⋊Q8—474no—
485C2×C22⋊Q8—472no—
486C2×C22⋊Q8—474no—
487C2×C22⋊Q8C2×D4712yes—
488C2×C22⋊Q8C2×D4712yes—
489C2×#121—471no—
490#519—4732no—
491C2×C4×Q8—472no—
492C2×C4×Q8—472no—
493C2×C4×Q8—472no—
494C2×C4×Q8—474no—
495C2×C4×Q8—472no—
496C2×C4×Q8—472no—
497C2×C4×Q8—471no—
498C2×C4×Q8—472no—
499C2×C4×Q8—471no—
500C2×C4×Q8—471no—
501C2×C4×Q8—472no—
502C2×C4×Q8—471no—
503C2×C4×Q8—4716no—
504C2×C4×Q8—474no—
505C2×C4×Q8—471no—
506C2×C4×Q8C2×D4712yes—
507C2×C4×Q8C2×D4712yes—
508C2×C4×D4—472no—
509C2×C4×D4—472no—
510C2×C4×D4—474no—
511C2×C4×D4—471no—
512C2×#117—474no—
513C2×#117—472no—
514C2×#117—474no—
515C2×#117—472no—
516C2×#117—474no—
517C2×#117C2×D4712yes—
518C22×C4⋊C4—472no—
519C22×C4⋊C4—471no—
520C22×C42—472no—
521C22×C42C2×D4711yescharacteristic
522C47C2×#352311yescharacteristic, complemented, Sylow
523C22×Q8—4716no—
524C22×Q8—471no—
525C22×Q8—471no—
526C22×Q8—474no—
527C22×Q8—472no—
528C22×Q8—471no—
529C22×Q8—478no—
530C22×Q8—948no—
531C22×Q8—9416no—
532C22×Q8C22×D4712yes—
533C22×Q8C22×D4712yes—
534C22×D4—472no—
535C22×D4—471no—
536C23×C4—472no—
537C23×C4—472no—
538C23×C4—474no—
539C23×C4—472no—
540C23×C4C22×D4711yescharacteristic
541C23×C4C22×D4711yescharacteristic
542C23×C4C22×D4711yescharacteristic
543C4⋊Q8—4716no—
544C4⋊Q8—4716no—
545C4⋊Q8—4716no—
546C4⋊Q8—4732no—
547C4⋊Q8C22×D4718yes—
548C4⋊Q8C22×D4718yes—
549#126—4732no—
550#126—4732no—
551#126—4732no—
552#126—4716no—
553#126—4732no—
554#125—4716no—
555#125—4732no—
556#125—4732no—
557#125—4732no—
558#125—4732no—
559#125—4716no—
560#125—478no—
561#125—4732no—
562#125C22×D47116yes—
563#124—4716no—
564#124—478no—
565#123—4716no—
566#123—4732no—
567C22⋊Q8—4716no—
568C22⋊Q8—478no—
569C22⋊Q8—4732no—
570C22⋊Q8—4732no—
571C22⋊Q8—4716no—
572C22⋊Q8—4732no—
573C22⋊Q8C22×D47116yes—
574C22⋊Q8C22×D47116yes—
575#121—478no—
576C4×Q8—4716no—
577C4×Q8—4716no—
578C4×Q8—4716no—
579C4×Q8—4732no—
580C4×Q8—4716no—
581C4×Q8—4716no—
582C4×Q8—478no—
583C4×Q8—4716no—
584C4×Q8—478no—
585C4×Q8—478no—
586C4×Q8—4716no—
587C4×Q8—478no—
588C4×Q8—4732no—
589C4×Q8—478no—
590C4×Q8C22×D47116yes—
591C4×Q8C22×D47116yes—
592C4×D4—4716no—
593C4×D4—4716no—
594C4×D4—4732no—
595C4×D4—478no—
596#117—4732no—
597#117—4716no—
598#117—4732no—
599#117—4716no—
600#117—4732no—
601#117C22×D47116yes—
602C2×C4⋊C4—472no—
603C2×C4⋊C4—471no—
604C2×C4⋊C4—472no—
605C2×C4⋊C4—471no—
606C2×C4⋊C4—472no—
607C2×C4⋊C4—472no—
608C2×C4⋊C4—472no—
609C2×C4⋊C4—4716no—
610C2×C4⋊C4—478no—
611C2×C4⋊C4—474no—
612C2×C4⋊C4—472no—
613C2×C4⋊C4—472no—
614C2×C4⋊C4—474no—
615C2×C4⋊C4—474no—
616C2×C4⋊C4—474no—
617C2×C4⋊C4—471no—
618C2×C4⋊C4—474no—
619C2×C4⋊C4—472no—
620C2×C4⋊C4—471no—
621C2×C4⋊C4—474no—
622C2×C4⋊C4—474no—
623C2×C4⋊C4—472no—
624C2×C4⋊C4—474no—
625C2×C4⋊C4C22×D4712yes—
626C2×C4⋊C4C22×D4714yes—
627C2×C4⋊C4C22×D4712yes—
628C2×C4⋊C4C22×D4712yes—
629C2×C4⋊C4C22×D4712yes—
630C2×C4⋊C4C22×D4714yes—
631C2×C22⋊C4—472no—
632C2×C22⋊C4—472no—
633C2×C22⋊C4—474no—
634C2×C22⋊C4—472no—
635C2×C22⋊C4—474no—
636C2×C22⋊C4—472no—
637C2×C22⋊C4—472no—
638C2×C22⋊C4—474no—
639C2×C22⋊C4C22×D4714yes—
640C2×C42—472no—
641C2×C42—474no—
642C2×C42—474no—
643C2×C42—474no—
644C2×C42—472no—
645C2×C42—472no—
646C2×C42—472no—
647C2×C42—472no—
648C2×C42—4716no—
649C2×C42C22×D4711yescharacteristic
650C2×C42C22×D4714yes—
651C2×C42C22×D4711yescharacteristic
652C2×C42C22×D4711yescharacteristic
653C2×C42C22×D4711yescharacteristic
654C2×C42C22×D4718yes—
655C24—472no—
656C24C23×D4711yescharacteristic
657C2×Q8—28no—
658C2×Q8—28no—
659C2×Q8—478no—
660C2×Q8—474no—
661C2×Q8—474no—
662C2×Q8—4716no—
663C2×Q8—478no—
664C2×Q8—474no—
665C2×Q8—948no—
666C2×Q8—9416no—
667C2×Q8—9432no—
668C2×Q8—9464no—
669C2×Q8—944no—
670C2×Q8—944no—
671C2×Q8C23×D4718yes—
672C2×Q8C23×D4718yes—
673C2×D4—478no—
674C2×D4—474no—
675C2×D4—948no—
676C2×D4—944no—
677C22×C4—24no—
678C22×C4—24no—
679C22×C4—24no—
680C22×C4—472no—
681C22×C4—478no—
682C22×C4—478no—
683C22×C4—472no—
684C22×C4—472no—
685C22×C4—472no—
686C22×C4—472no—
687C22×C4—472no—
688C22×C4—472no—
689C22×C4—4716no—
690C22×C4—478no—
691C22×C4—9416no—
692C22×C4—948no—
693C22×C4—948no—
694C22×C4—948no—
695C22×C4C23×D4714yes—
696C22×C4C23×D4714yes—
697C22×C4C23×D4714yes—
698C22×C4C23×D4711yescharacteristic
699C22×C4C23×D4714yes—
700C22×C4C23×D4714yes—
701C22×C4C23×D4711yescharacteristic
702C22×C4C23×D4711yescharacteristic
703C22×C4C23×D4711yescharacteristic
704C22×C4C23×D4711yescharacteristic
705C22×C4C23×D4711yescharacteristic
706C4⋊C4—478no—
707C4⋊C4—478no—
708C4⋊C4—478no—
709C4⋊C4—478no—
710C4⋊C4—4716no—
711C4⋊C4—478no—
712C4⋊C4—478no—
713C4⋊C4—4716no—
714C4⋊C4—4716no—
715C4⋊C4—4716no—
716C4⋊C4—478no—
717C4⋊C4—4716no—
718C4⋊C4—478no—
719C4⋊C4—474no—
720C4⋊C4—474no—
721C4⋊C4—478no—
722C4⋊C4—4716no—
723C4⋊C4—474no—
724C4⋊C4—474no—
725C4⋊C4—4716no—
726C4⋊C4—4716no—
727C4⋊C4C23×D4718yes—
728C4⋊C4C23×D47116yes—
729C4⋊C4C23×D4718yes—
730C4⋊C4C23×D4718yes—
731C4⋊C4C23×D4718yes—
732C4⋊C4C23×D47116yes—
733C22⋊C4—478no—
734C22⋊C4—478no—
735C22⋊C4—4716no—
736C22⋊C4—478no—
737C22⋊C4—4716no—
738C22⋊C4—478no—
739C22⋊C4—478no—
740C22⋊C4—4716no—
741C22⋊C4C23×D47116yes—
742C42—478no—
743C42—478no—
744C42—478no—
745C42—478no—
746C42—4716no—
747C42—4716no—
748C42—4716no—
749C42—478no—
750C42C23×D4714yes—
751C42C23×D4714yes—
752C42C23×D4714yes—
753C42C23×D4714yes—
754C42C23×D47116yes—
755C23—22no—
756C23—22no—
757C23—474no—
758C23—944no—
759C23—944no—
760C23—944no—
761C23#1309407214yes—
762C23C24×D4712yes—
763C23C24×D4711yescharacteristic
764Q8—216no—
765Q8—216no—
766Q8—4716no—
767Q8—9416no—
768Q8—9432no—
769Q8—948no—
770Q8—948no—
771D4—9416no—
772D4—948no—
773C2×C4—22no—
774C2×C4—28no—
775C2×C4—22no—
776C2×C4—28no—
777C2×C4—28no—
778C2×C4—22no—
779C2×C4—22no—
780C2×C4—28no—
781C2×C4—28no—
782C2×C4—478no—
783C2×C4—474no—
784C2×C4—474no—
785C2×C4—474no—
786C2×C4—474no—
787C2×C4—474no—
788C2×C4—474no—
789C2×C4—474no—
790C2×C4—9432no—
791C2×C4—9416no—
792C2×C4—944no—
793C2×C4—944no—
794C2×C4—944no—
795C2×C4—9416no—
796C2×C4—944no—
797C2×C4—944no—
798C2×C4—944no—
799C2×C4—9416no—
800C2×C4#41×D4714yes—
801C2×C4#1309407114yes—
802C2×C4C24×D4712yes—
803C2×C4C24×D4718yes—
804C2×C4C24×D4718yes—
805C2×C4C24×D4712yes—
806C2×C4C24×D4712yes—
807C2×C4C24×D4712yes—
808C2×C4C24×D4712yes—
809C2×C4C24×D4712yes—
810C22—22no—
811C22—22no—
812C22—28no—
813C22—944no—
814C22—944no—
815C22—944no—
816C22—1888no—
817C22C2×#41×D4712yes—
818C22C2×#1309407112yes—
819C22C2×#1309407214yes—
820C22C2×#1309407212yes—
821C22C25×D4711yescharacteristic
822C4—22no—
823C4—28no—
824C4—22no—
825C4—28no—
826C4—22no—
827C4—22no—
828C4—478no—
829C4—944no—
830C4—944no—
831C4—944no—
832C4—944no—
833C4—944no—
834C4—944no—
835C4C2×#41×D4714yes—
836C4C2×#1309407114yes—
837C2—24no—
838C2—1884no—
839C2#2025747614yesdirect product factor
840C2C22×#41×D4711yescharacteristic
841C2C22×#1309407111yescharacteristic
842C2C22×#1309407211yescharacteristic
subgroupG/H
centerC23C24×D47
commutator, cosocleC22×C47C26
FrattiniC22C25×D47
FittingC2×C47×#533C2
socleC23×C47C25
prime radicalC2×#13093998C22
hypercenterC2×#533D47
hypocenterC47C2×#3523
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #20257476C2direct (N × H)
2. C2×#15689849C2semidirect
3. C2×#15689848C2semidirect
4. C2×#15689848C2semidirect
5. C2×#15689847C2semidirect
6. C2×#15689845C2semidirect
7. C2×#15689815C2semidirect
8. C2×#15689806C2semidirect
9. C2×#15689788C2semidirect
10. C2×#15689786C2semidirect
11. C2×#15689732C2semidirect
12. C2×#15689731C2semidirect
13. C2×#15689675C2semidirect
16. C2×#15689599C2semidirect
17. C22×C4×Dic94C2semidirect
18. C2×C47×#533C2semidirect
21. #15689849C22semidirect
22. #15689848C22semidirect
23. #15689848C22semidirect
24. #15689847C22semidirect
25. #15689845C22semidirect
26. #15689815C22semidirect
27. #15689806C22semidirect
28. #15689788C22semidirect
29. #15689786C22semidirect
30. #15689732C22semidirect
31. #15689731C22semidirect
32. #15689675C22semidirect
63. #15689599C22semidirect
75. C2×C4×Dic94C22semidirect
91. C47×#533C22semidirect
429. C2×#533D47semidirect
435. C2×C47#3523semidirect
454. #533C2×D47semidirect
522. C47C2×#3523semidirect
839. C2#20257476direct (N × H)

Maximal subgroups

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

subgroupindex
#202574762
C2×#156898492
C2×#156898482
C2×#156898472
C2×#156898452
C2×#156898152
C2×#156898062
C2×#156897882
C2×#156897862
C2×#156897322
C2×#156897312
C2×#156896752
C2×#156896592
C2×#156896572
C2×#156895992
C22×C4×Dic942
C2×C47×#5332
C2×#352347