Finite Group Databasebeta

← C2×#24921329 #36312485

Subgroups — C2×#24921329 #36312485

Order 21248.

7130 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921329C2132yesmaximal, direct product factor
2C2×#19128436C211yesmaximal, characteristic, complemented
3C2×#19128436C211yesmaximal, characteristic, complemented
4C2×#19128426C211yesmaximal, characteristic, complemented
5C2×#19128425C212yesmaximal, complemented
6C2×#19128423C212yesmaximal, complemented
7C2×#19128423C212yesmaximal, complemented
8C2×#19128407C212yesmaximal, complemented
9C2×#19128383C214yesmaximal, complemented
10C2×#19128299C214yesmaximal, complemented
11C2×#19128276C212yesmaximal, complemented
12C2×#19128255C211yesmaximal, characteristic, complemented
13C2×#19128252C211yesmaximal, characteristic
14C2×#19128238C212yesmaximal, complemented
15C2×#19128236C212yesmaximal, complemented
16C2×#19128183C212yesmaximal, complemented
17C2×C4×Q8×D83C211yesmaximal, characteristic, complemented
18C2×#557×C83C211yesmaximal, characteristic, complemented
19C22×#13050591C2212yes—
20C22×Q8×D83C2211yescharacteristic
21#19128436C22116yescomplemented
22#19128436C22116yescomplemented
23#19128426C22116yescomplemented
24#19128425C22132yescomplemented
25#19128423C22132yescomplemented
26#19128423C22132yescomplemented
27#19128407C22132yescomplemented
28#19128383C22164yescomplemented
29#19128299C22164yescomplemented
30#19128276C22132yescomplemented
31#19128255C22116yescomplemented
32#19128252C22116yes—
33C2×#14581791C2211yescharacteristic
34C2×#14581790C2211yescharacteristic
35C2×#14581790C2212yes—
36C2×#14581789C2211yescharacteristic
37#19128238C22132yescomplemented
38#19128236C22132yescomplemented
39C2×#14581787C2214yes—
40C2×#14581787C2214yes—
41C2×#14581787C2214yes—
42C2×#14581786C2214yes—
43C2×#14581783C2212yes—
44C2×#14581782C2212yes—
45C2×#14581782C2214yes—
46C2×#14581781C2212yes—
47C2×#14581781C2212yes—
48C2×#14581781C2212yes—
49C2×#14581780C2212yes—
50C2×#14581780C2212yes—
51C2×#14581777C2214yes—
52C2×#14581777C2214yes—
53C2×#14581777C2214yes—
54C2×#14581777C2214yes—
55C2×#14581772C2211yescharacteristic
56C2×#14581772C2214yes—
57C2×#14581770C2214yes—
58C2×#14581770C2214yes—
59C2×#14581770C2214yes—
60C2×#14581770C2212yes—
61C2×#14581768C2211yescharacteristic
62C2×#14581767C2212yes—
63C2×#14581767C2212yes—
64#19128183C22132yescomplemented
65C2×Q8×Dic83C2211yescharacteristic
66C2×Q8×Dic83C2212yes—
67C2×C4×Dic166C2212yes—
68C2×C4×Dic166C2211yescharacteristic
69C2×C4×Dic166C2212yes—
70C2×C4×Dic166C2211yescharacteristic
71C2×#14581757C2212yes—
72C2×#14581757C2211yescharacteristic
73C2×#14581757C2212yes—
74C4×Q8×D83C22116yescomplemented
75C2×C4×D332C2214yes—
76C2×C4×D332C2212yes—
77C2×C4×D332C2212yes—
78C2×#14581754C2214yes—
79C2×#14581754C2212yes—
80C2×#14581754C2212yes—
81C2×#14581754C2212yes—
82C2×#14581754C2212yes—
83C2×#14581750C2214yes—
84C2×#14581749C2214yes—
85C2×#14581749C2212yes—
86C2×#14581749C2214yes—
87C2×C4⋊C4×D83C2211yescharacteristic
88C2×C4⋊C4×D83C2212yes—
89C2×C4⋊C4×D83C2214yes—
90C2×C42×D83C2212yes—
91C2×C42×D83C2211yescharacteristic
92#557×C83C22116yescomplemented
93C2×C4⋊Q8×C83C2211yescharacteristic
94C2×C4⋊Q8×C83C2212yes—
95C2×#125×C83C2214yes—
96C2×#125×C83C2212yes—
97C2×C4×Q8×C83C2211yescharacteristic
98C2×C4×Q8×C83C2212yes—
99C2×C4×Q8×C83C2212yes—
100C2×C4×Q8×C83C2211yescharacteristic
101C2×#13050591—216no—
102C2×#13050591C23116yes—
103C22×Dic166C2311yescharacteristic
104C22×Dic166C2312yes—
105C22×Dic166C2311yescharacteristic
106C22×Dic166C2312yes—
107C2×Q8×D83—28no—
108C2×Q8×D83C2318yes—
109C22×D332C2312yes—
110C22×D332C2314yes—
111C22×D332C2312yes—
112C22×D332C2312yes—
113C22×C4×D83C2311yescharacteristic
114C22×C4×D83C2312yes—
115C22×C4×D83C2314yes—
116C22×C4×D83C2312yes—
117C22×C4×D83C2311yescharacteristic
118C22×C4×D83C2314yes—
119C22×C4×D83C2314yes—
120C22×C4×D83C2311yescharacteristic
121#14581791C2318yes—
122#14581790C2318yes—
123#14581790C23116yes—
124#14581789C2318yes—
125#14581787C23132yes—
126#14581787C23132yes—
127#14581787C23132yes—
128#14581786C23132yes—
129#14581783C23116yes—
130#14581782C23116yes—
131#14581782C23132yes—
132#14581781C23116yes—
133#14581781C23116yes—
134#14581781C23116yes—
135#14581780C23116yes—
136#14581780C23116yes—
137#14581777C23132yes—
138#14581777C23132yes—
139#14581777C23132yes—
140#14581777C23132yes—
141#14581772C23132yes—
142#14581772C2318yes—
143#14581770C23132yes—
144#14581770C23132yes—
145#14581770C23132yes—
146#14581770C23116yes—
147#14581768C2318yes—
148#14581767C23116yes—
149#14581767C23116yes—
150Q8×Dic83C2318yes—
151Q8×Dic83C23116yes—
152C4×Dic166C23116yes—
153C4×Dic166C2318yes—
154C4×Dic166C23116yes—
155C4×Dic166C2318yes—
156#14581757C23116yes—
157#14581757C2318yes—
158#14581757C23116yes—
159C4×D332C23116yes—
160C4×D332C23116yes—
161C4×D332C23132yes—
162#14581754C23116yes—
163#14581754C23116yes—
164#14581754C23116yes—
165#14581754C23116yes—
166#14581754C23132yes—
167#14581750C23132yes—
168#14581749C23132yes—
169#14581749C23132yes—
170#14581749C23116yes—
171C2×C4⋊Dic83C2311yescharacteristic
172C2×C4⋊Dic83C2314yes—
173C2×C4⋊Dic83C2312yes—
174C2×C4⋊Dic83C2312yes—
175C2×C4⋊Dic83C2311yescharacteristic
176C2×Dic83⋊C4C2312yes—
177C2×Dic83⋊C4C2312yes—
178C2×Dic83⋊C4C2312yes—
179C2×Dic83⋊C4C2312yes—
180C2×Dic83⋊C4C2312yes—
181C2×Dic83⋊C4C2312yes—
182C2×Dic83⋊C4C2314yes—
183C2×Dic83⋊C4C2314yes—
184C2×Dic83⋊C4C2312yes—
185C2×Dic83⋊C4C2312yes—
186C4⋊C4×D83C23132yes—
187C4⋊C4×D83C2318yes—
188C4⋊C4×D83C23116yes—
189C2×(C2×D83)⋊C4C2314yes—
190C2×(C2×D83)⋊C4C2312yes—
191C2×(C2×D83)⋊C4C2314yes—
192C2×(C2×D83)⋊C4C2312yes—
193C2×(C2×D83)⋊C4C2314yes—
194C2×(C2×D83)⋊C4C2314yes—
195C2×(C2×D83)⋊C4C2314yes—
196C2×(C2×D83)⋊C4C2314yes—
197C2×(C2×D83)⋊C4C2314yes—
198C2×(C2×D83)⋊C4C2314yes—
199C2×C4×Dic83C2312yes—
200C2×C4×Dic83C2312yes—
201C2×C4×Dic83C2311yescharacteristic
202C2×C4×Dic83C2311yescharacteristic
203C2×C4×Dic83C2312yes—
204C2×C4×Dic83C2311yescharacteristic
205C2×C4×Dic83C2314yes—
206C2×C4×Dic83C2312yes—
207C42×D83C23116yes—
208C42×D83C2318yes—
209C22×Q8×C83C2311yescharacteristic
210C22×Q8×C83C2311yescharacteristic
211C22×Q8×C83C2312yes—
212C4⋊Q8×C83C23116yes—
213C4⋊Q8×C83C2318yes—
214#125×C83C23132yes—
215#125×C83C23116yes—
216C4×Q8×C83C2318yes—
217C4×Q8×C83C23116yes—
218C4×Q8×C83C23116yes—
219C4×Q8×C83C2318yes—
220C2×C4⋊C4×C83C2311yescharacteristic
221C2×C4⋊C4×C83C2314yes—
222C2×C4⋊C4×C83C2312yes—
223C2×C4⋊C4×C83C2311yescharacteristic
224C2×C4⋊C4×C83C2312yes—
225C2×C4⋊C4×C83C2312yes—
226C2×C4⋊C4×C83C2314yes—
227C2×C4⋊C4×C83C2314yes—
228C2×C4⋊C4×C83C2312yes—
229C2×C42×C83C2312yes—
230C2×C42×C83C2314yes—
231C2×C42×C83C2311yescharacteristic
232C2×C42×C83C2312yes—
233C23×D83C2414yes—
234C23×D83C2411yescharacteristic
235#13050591—264no—
236C2×Dic166—24no—
237C2×Dic166—24no—
238C2×Dic166—28no—
239C2×Dic166—44no—
240C2×Dic166C2418yes—
241C2×Dic166C2414yes—
242C2×Dic166C2414yes—
243C2×Dic166C2418yes—
244Q8×D83—232no—
245C2×D332—216no—
246C2×D332—28no—
247C2×D332—28no—
248C2×D332—44no—
249C2×D332C24116yes—
250C2×D332C2418yes—
251C2×D332C2418yes—
252C2×D332C2418yes—
253C22×Dic83C2412yes—
254C22×Dic83C2412yes—
255C22×Dic83C2412yes—
256C22×Dic83C2411yescharacteristic
257C22×Dic83C2411yescharacteristic
258C22×Dic83C2412yes—
259C22×Dic83C2411yescharacteristic
260C2×C4×D83—28no—
261C2×C4×D83—24no—
262C2×C4×D83—216no—
263C2×C4×D83—44no—
264C2×C4×D83—48no—
265C2×C4×D83—48no—
266C2×C4×D83—42no—
267C2×C4×D83#4118yes—
268C2×C4×D83C2414yes—
269C2×C4×D83C24116yes—
270C2×C4×D83C2418yes—
271C2×C4×D83C2414yes—
272C2×C4×D83C24116yes—
273C2×C4×D83C24116yes—
274C2×C4×D83C2418yes—
275C2×C4×D83C2414yes—
276C4⋊Dic83C2414yes—
277C4⋊Dic83C2418yes—
278C4⋊Dic83C24116yes—
279C4⋊Dic83C2418yes—
280C4⋊Dic83C2414yes—
281Dic83⋊C4C2418yes—
282Dic83⋊C4C24116yes—
283Dic83⋊C4C2418yes—
284Dic83⋊C4C2418yes—
285Dic83⋊C4C2418yes—
286Dic83⋊C4C2418yes—
287Dic83⋊C4C24116yes—
288Dic83⋊C4C2418yes—
289Dic83⋊C4C2418yes—
290Dic83⋊C4C2418yes—
291(C2×D83)⋊C4C24116yes—
292(C2×D83)⋊C4C24116yes—
293(C2×D83)⋊C4C2418yes—
294(C2×D83)⋊C4C24116yes—
295(C2×D83)⋊C4C24116yes—
296(C2×D83)⋊C4C2418yes—
297(C2×D83)⋊C4C24116yes—
298(C2×D83)⋊C4C24116yes—
299(C2×D83)⋊C4C24116yes—
300(C2×D83)⋊C4C24116yes—
301C4×Dic83C2414yes—
302C4×Dic83C2418yes—
303C4×Dic83C2418yes—
304C4×Dic83C2414yes—
305C4×Dic83C24116yes—
306C4×Dic83C2418yes—
307C4×Dic83C2418yes—
308C4×Dic83C2414yes—
309C2×Q8×C83—24no—
310C2×Q8×C83—28no—
311C2×Q8×C83—24no—
312C2×Q8×C83C2414yes—
313C2×Q8×C83C2414yes—
314C2×Q8×C83C2418yes—
315C22×C4×C83C2412yes—
316C22×C4×C83C2412yes—
317C22×C4×C83C2411yescharacteristic
318C22×C4×C83C2414yes—
319C22×C4×C83C2412yes—
320C22×C4×C83C2412yes—
321C22×C4×C83C2411yescharacteristic
322C22×C4×C83C2411yescharacteristic
323C4⋊C4×C83C2418yes—
324C4⋊C4×C83C2418yes—
325C4⋊C4×C83C24116yes—
326C4⋊C4×C83C2418yes—
327C4⋊C4×C83C24116yes—
328C4⋊C4×C83C24116yes—
329C4⋊C4×C83C2414yes—
330C4⋊C4×C83C2418yes—
331C4⋊C4×C83C2414yes—
332C42×C83C2418yes—
333C42×C83C2418yes—
334C42×C83C24116yes—
335C42×C83C2414yes—
336C23×C83C2511yescharacteristic
337C22×D83—22no—
338C22×D83—22no—
339C22×D83—28no—
340C22×D83—28no—
341C22×D83—28no—
342C22×D83C2×#4114yes—
343C22×D83C2518yes—
344C22×D83C2512yes—
345Q8×C83—28no—
346Q8×C83—216no—
347Q8×C83—28no—
348C2×C4×C83—28no—
349C2×C4×C83—24no—
350C2×C4×C83—24no—
351C2×C4×C83—24no—
352C2×C4×C83—24no—
353C2×C4×C83—22no—
354C2×C4×C83C2×#4114yes—
355C2×C4×C832−1+414yes—
356C2×C4×C83C2514yes—
357C2×C4×C83C2514yes—
358C2×C4×C83C2512yes—
359C2×C4×C83C2514yes—
360C2×C4×C83C2514yes—
361C2×C4×C83C2518yes—
362C2×C4×C83C2512yes—
363C2×C4×C83C2512yes—
364C2×Dic83—24no—
365C2×Dic83—22no—
366C2×Dic83—24no—
367C2×Dic83—24no—
368C2×Dic83—24no—
369C2×Dic83—22no—
370C2×Dic83C2×#4114yes—
371C2×Dic83C2512yes—
372C2×Dic83C2514yes—
373C2×Dic83C2514yes—
374C2×Dic83C2514yes—
375C2×Dic83C2512yes—
376C2×Dic83C2514yes—
377C2×Dic83C2512yes—
378D332—232no—
379D332—216no—
380D332—216no—
381D332—48no—
382C4×D83—216no—
383C4×D83—28no—
384C4×D83—232no—
385C4×D83—44no—
386C4×D83—416no—
387C4×D83—416no—
388C4×D83—48no—
389C4×D83C2×#41116yes—
390Dic166—28no—
391Dic166—28no—
392Dic166—216no—
393Dic166—48no—
394C22×C83C22×#4112yes—
395C22×C83C2×2−1+412yes—
396C22×C83#58512yes—
397C22×C83C2611yescharacteristic
398C2×D83—22no—
399C2×D83—22no—
400C2×D83—28no—
401C2×D83—28no—
402C2×D83—28no—
403C2×D83—28no—
404C2×D83—416no—
405C2×D83C22×#4114yes—
406C4×C83—24no—
407C4×C83—28no—
408C4×C83—24no—
409C4×C83—24no—
410C4×C83—24no—
411C4×C83—22no—
412C4×C83C22×#4114yes—
413C4×C83C2×2−1+414yes—
414Dic83—24no—
415Dic83—24no—
416Dic83—22no—
417Dic83—22no—
418Dic83—24no—
419Dic83—24no—
420Dic83C22×#4114yes—
421C2×#3507—831nomaximal, Sylow
422C2×C83#350714yescomplemented
423C2×C83C23×#4111yescharacteristic
424C2×C83C22×2−1+411yescharacteristic
425C2×C83C2×#58511yescharacteristic
426D83—24no—
427D83—48no—
428#3507—8332no—
429C2×#559—831no—
430C2×#559—831no—
431C2×#557—831no—
432C2×#557D8311yescharacteristic, complemented
433C2×#556—832no—
434C2×#556—832no—
435C2×#556—832no—
436C2×#554—832no—
437C2×#552—834no—
438C2×#539—834no—
439C2×#536—832no—
440C2×#533—831no—
441C2×#532—831no—
442C2×#529—832no—
443C2×#529—832no—
444C2×#520—832no—
445C22×C4×Q8—831no—
446C83C2×#350711yescharacteristic, complemented, Sylow
447C22×#41—832no—
448C23×Q8—831no—
449#559—8316no—
450#559—8316no—
451#557—8316no—
452#557C2×D83116yescomplemented
453#556—8332no—
454#556—8332no—
455#556—8332no—
456#554—8332no—
457#552—8364no—
458#539—8364no—
459#536—8332no—
460#533—8316no—
461#532—8316no—
462C2×C4⋊Q8—831no—
463C2×C4⋊Q8—832no—
464C2×C4⋊Q8—831no—
465C2×C4⋊Q8C2×D8311yescharacteristic
466C2×C4⋊Q8C2×D8312yes—
467C2×#127—831no—
468#529—8332no—
469#529—8332no—
470C2×#126—834no—
471C2×#126—834no—
472C2×#126—834no—
473C2×#126—834no—
474C2×#125—832no—
475C2×#125—832no—
476C2×#125—834no—
477C2×#125C2×D8312yes—
478C2×#125C2×D8314yes—
479C2×#124—832no—
480C2×#124—832no—
481C2×#124—832no—
482C2×#124—832no—
483C2×#124—832no—
484C2×#123—834no—
485C2×#123—834no—
486C2×#123—834no—
487C2×#123—834no—
488C2×C22⋊Q8—831no—
489C2×C22⋊Q8—831no—
490C2×C22⋊Q8—832no—
491C2×C22⋊Q8—834no—
492C2×C22⋊Q8—834no—
493C2×C22⋊Q8—834no—
494C2×C22⋊Q8—834no—
495C2×#121—832no—
496C2×#121—832no—
497#520—8332no—
498C2×C4×Q8—831no—
499C2×C4×Q8—832no—
500C2×C4×Q8—8316no—
501C2×C4×Q8—832no—
502C2×C4×Q8—831no—
503C2×C4×Q8—832no—
504C2×C4×Q8—832no—
505C2×C4×Q8—831no—
506C2×C4×Q8—832no—
507C2×C4×Q8—831no—
508C2×C4×Q8C2×D8311yescharacteristic
509C2×C4×Q8C2×D8312yes—
510C2×C4×Q8C2×D8312yes—
511C2×C4×Q8C2×D8311yescharacteristic
512C2×C4×D4—834no—
513C2×C4×D4—832no—
514C2×C4×D4—832no—
515C2×C4×D4—832no—
516C2×C4×D4—832no—
517C2×C4×D4—834no—
518C2×C4×D4—832no—
519C2×C4×D4—832no—
520C2×#117—834no—
521C2×#117—832no—
522C2×#117—834no—
523C2×#117—834no—
524C22×C4⋊C4—831no—
525C22×C4⋊C4—832no—
526C22×C4⋊C4—834no—
527C22×C42—832no—
528C22×C42—831no—
529C2×#41—8316no—
530C2×#41—16616no—
531C22×Q8—838no—
532C22×Q8—832no—
533C22×Q8—831no—
534C22×Q8—832no—
535C22×Q8—831no—
536C22×Q8—1668no—
537C22×Q8C22×D8311yescharacteristic
538C22×Q8C22×D8312yes—
539C22×Q8C22×D8311yescharacteristic
540C22×D4—832no—
541C22×D4—832no—
542C22×D4—834no—
543C22×D4—832no—
544C23×C4—832no—
545C23×C4—831no—
546C23×C4—834no—
547C23×C4—834no—
548C23×C4—831no—
549C23×C4—834no—
550C23×C4—832no—
551C23×C4—831no—
552C4⋊Q8—838no—
553C4⋊Q8—8316no—
554C4⋊Q8—838no—
555C4⋊Q8C22×D8318yes—
556C4⋊Q8C22×D83116yes—
557#127—838no—
558#126—8332no—
559#126—8332no—
560#126—8332no—
561#126—8332no—
562#125—8316no—
563#125—8316no—
564#125—8332no—
565#125C22×D83116yes—
566#125C22×D83132yes—
567#124—8316no—
568#124—8316no—
569#124—8316no—
570#124—8316no—
571#124—8316no—
572#123—8332no—
573#123—8332no—
574#123—8332no—
575#123—8332no—
576C22⋊Q8—838no—
577C22⋊Q8—8316no—
578C22⋊Q8—8332no—
579C22⋊Q8—8332no—
580C22⋊Q8—8332no—
581C22⋊Q8—838no—
582C22⋊Q8—8332no—
583#121—8316no—
584#121—8316no—
585C4×Q8—838no—
586C4×Q8—8316no—
587C4×Q8—8316no—
588C4×Q8—838no—
589C4×Q8—8316no—
590C4×Q8—8316no—
591C4×Q8—838no—
592C4×Q8—8316no—
593C4×Q8—838no—
594C4×Q8C22×D8318yes—
595C4×Q8C22×D83116yes—
596C4×Q8C22×D83116yes—
597C4×Q8C22×D8318yes—
598C4×D4—8332no—
599C4×D4—8316no—
600C4×D4—8316no—
601C4×D4—8316no—
602C4×D4—8316no—
603C4×D4—8332no—
604C4×D4—8316no—
605C4×D4—8316no—
606#117—8332no—
607#117—8316no—
608#117—8332no—
609#117—8332no—
610C2×C4⋊C4—832no—
611C2×C4⋊C4—832no—
612C2×C4⋊C4—831no—
613C2×C4⋊C4—834no—
614C2×C4⋊C4—832no—
615C2×C4⋊C4—832no—
616C2×C4⋊C4—832no—
617C2×C4⋊C4—832no—
618C2×C4⋊C4—832no—
619C2×C4⋊C4—832no—
620C2×C4⋊C4—834no—
621C2×C4⋊C4—831no—
622C2×C4⋊C4—832no—
623C2×C4⋊C4—834no—
624C2×C4⋊C4—832no—
625C2×C4⋊C4—838no—
626C2×C4⋊C4—8316no—
627C2×C4⋊C4—8332no—
628C2×C4⋊C4C22×D8311yescharacteristic
629C2×C4⋊C4C22×D8314yes—
630C2×C4⋊C4C22×D8312yes—
631C2×C4⋊C4C22×D8314yes—
632C2×C4⋊C4C22×D8311yescharacteristic
633C2×C4⋊C4C22×D8312yes—
634C2×C4⋊C4C22×D8312yes—
635C2×C4⋊C4C22×D8312yes—
636C2×C4⋊C4C22×D8314yes—
637C2×C22⋊C4—834no—
638C2×C22⋊C4—832no—
639C2×C22⋊C4—832no—
640C2×C22⋊C4—834no—
641C2×C22⋊C4—834no—
642C2×C22⋊C4—834no—
643C2×C22⋊C4—834no—
644C2×C22⋊C4—834no—
645C2×C22⋊C4—834no—
646C2×C22⋊C4—834no—
647C2×C42—834no—
648C2×C42—832no—
649C2×C42—832no—
650C2×C42—832no—
651C2×C42—831no—
652C2×C42—831no—
653C2×C42—832no—
654C2×C42—831no—
655C2×C42—8316no—
656C2×C42—838no—
657C2×C42C22×D8314yes—
658C2×C42C22×D8312yes—
659C2×C42C22×D8312yes—
660C2×C42C22×D8311yescharacteristic
661C24—831no—
662C24—834no—
663#41—16664no—
664C2×Q8—24no—
665C2×Q8—28no—
666C2×Q8—24no—
667C2×Q8—3324no—
668C2×Q8—838no—
669C2×Q8—834no—
670C2×Q8—838no—
671C2×Q8—834no—
672C2×Q8—1668no—
673C2×Q8—16632no—
674C2×Q8—1664no—
675C2×Q8—1664no—
676C2×Q8C23×D8314yes—
677C2×Q8C23×D8318yes—
678C2×Q8C23×D8314yes—
679C2×D4—3324no—
680C2×D4—838no—
681C2×D4—838no—
682C2×D4—8316no—
683C2×D4—838no—
684C2×D4—16616no—
685C2×D4—1668no—
686C2×D4—1668no—
687C22×C4—3324no—
688C22×C4—3328no—
689C22×C4—3328no—
690C22×C4—3322no—
691C22×C4—838no—
692C22×C4—834no—
693C22×C4—8316no—
694C22×C4—8316no—
695C22×C4—831no—
696C22×C4—838no—
697C22×C4—834no—
698C22×C4—831no—
699C22×C4—832no—
700C22×C4—832no—
701C22×C4—832no—
702C22×C4—831no—
703C22×C4—832no—
704C22×C4—834no—
705C22×C4—838no—
706C22×C4—8316no—
707C22×C4—16616no—
708C22×C4—1668no—
709C22×C4—1664no—
710C22×C4C23×D8312yes—
711C22×C4C23×D8312yes—
712C22×C4C23×D8314yes—
713C22×C4C23×D8311yescharacteristic
714C22×C4C23×D8312yes—
715C22×C4C23×D8312yes—
716C22×C4C23×D8311yescharacteristic
717C22×C4C23×D8311yescharacteristic
718C4⋊C4—838no—
719C4⋊C4—838no—
720C4⋊C4—834no—
721C4⋊C4—8316no—
722C4⋊C4—838no—
723C4⋊C4—838no—
724C4⋊C4—838no—
725C4⋊C4—838no—
726C4⋊C4—838no—
727C4⋊C4—838no—
728C4⋊C4—8316no—
729C4⋊C4—834no—
730C4⋊C4—838no—
731C4⋊C4—8316no—
732C4⋊C4—838no—
733C4⋊C4C23×D8314yes—
734C4⋊C4C23×D83116yes—
735C4⋊C4C23×D8318yes—
736C4⋊C4C23×D83116yes—
737C4⋊C4C23×D8314yes—
738C4⋊C4C23×D8318yes—
739C4⋊C4C23×D8318yes—
740C4⋊C4C23×D8318yes—
741C4⋊C4C23×D83116yes—
742C22⋊C4—8316no—
743C22⋊C4—838no—
744C22⋊C4—838no—
745C22⋊C4—8316no—
746C22⋊C4—8316no—
747C22⋊C4—8316no—
748C22⋊C4—8316no—
749C22⋊C4—8316no—
750C22⋊C4—8316no—
751C22⋊C4—8316no—
752C42—838no—
753C42—838no—
754C42—834no—
755C42—834no—
756C42—838no—
757C42—834no—
758C42—8316no—
759C42—838no—
760C42C23×D8318yes—
761C42C23×D8314yes—
762C42C23×D83116yes—
763C42C23×D8318yes—
764C23—834no—
765C23—832no—
766C23—838no—
767C23—1668no—
768C23—1668no—
769C23—1668no—
770C23—1662no—
771C23—1662no—
772C23C24×D8311yescharacteristic
773Q8—28no—
774Q8—216no—
775Q8—28no—
776Q8—3328no—
777Q8—16616no—
778Q8—1668no—
779Q8—1668no—
780D4—3328no—
781D4—16632no—
782D4—16616no—
783D4—16616no—
784C2×C4—28no—
785C2×C4—24no—
786C2×C4—24no—
787C2×C4—24no—
788C2×C4—24no—
789C2×C4—22no—
790C2×C4—3328no—
791C2×C4—33216no—
792C2×C4—33216no—
793C2×C4—3324no—
794C2×C4—834no—
795C2×C4—832no—
796C2×C4—8316no—
797C2×C4—832no—
798C2×C4—834no—
799C2×C4—834no—
800C2×C4—834no—
801C2×C4—832no—
802C2×C4—834no—
803C2×C4—16632no—
804C2×C4—16616no—
805C2×C4—1664no—
806C2×C4—1662no—
807C2×C4—1664no—
808C2×C4—1664no—
809C2×C4—1664no—
810C2×C4—1662no—
811C2×C4—1668no—
812C2×C4#41×D8314yes—
813C2×C4#1458184014yes—
814C2×C4C24×D8314yes—
815C2×C4C24×D8314yes—
816C2×C4C24×D8318yes—
817C2×C4C24×D8312yes—
818C2×C4C24×D8314yes—
819C2×C4C24×D8314yes—
820C2×C4C24×D8312yes—
821C2×C4C24×D8312yes—
822C22—33216no—
823C22—834no—
824C22—1668no—
825C22—1668no—
826C22—1668no—
827C22—1662no—
828C22—1662no—
829C22—1668no—
830C22C2×#41×D8312yes—
831C22C2×#1458184012yes—
832C22#1912853812yes—
833C22C25×D8311yescharacteristic
834C4—28no—
835C4—24no—
836C4—24no—
837C4—24no—
838C4—24no—
839C4—22no—
840C4—834no—
841C4—1664no—
842C4—1662no—
843C4—1664no—
844C4—1664no—
845C4—1664no—
846C4—1662no—
847C4C2×#41×D8314yes—
848C4C2×#1458184014yes—
849C2—3328no—
850C2—1664no—
851C2#2492132914yesdirect product factor
852C2C22×#41×D8311yescharacteristic
853C2C22×#1458184011yescharacteristic
854C2C2×#1912853811yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#557×C83C2
socleC23×C83C25
prime radicalC2×#19128252C2
hypercenterC2×#557D83
hypocenterC83C2×#3507
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #24921329C2direct (N × H)
2. C2×#19128436C2semidirect
3. C2×#19128436C2semidirect
4. C2×#19128426C2semidirect
5. C2×#19128425C2semidirect
6. C2×#19128423C2semidirect
7. C2×#19128423C2semidirect
8. C2×#19128407C2semidirect
9. C2×#19128383C2semidirect
10. C2×#19128299C2semidirect
11. C2×#19128276C2semidirect
12. C2×#19128255C2semidirect
14. C2×#19128238C2semidirect
15. C2×#19128236C2semidirect
16. C2×#19128183C2semidirect
17. C2×C4×Q8×D83C2semidirect
18. C2×#557×C83C2semidirect
21. #19128436C22semidirect
22. #19128436C22semidirect
23. #19128426C22semidirect
24. #19128425C22semidirect
25. #19128423C22semidirect
26. #19128423C22semidirect
27. #19128407C22semidirect
28. #19128383C22semidirect
29. #19128299C22semidirect
30. #19128276C22semidirect
31. #19128255C22semidirect
37. #19128238C22semidirect
38. #19128236C22semidirect
64. #19128183C22semidirect
74. C4×Q8×D83C22semidirect
92. #557×C83C22semidirect
422. C2×C83#3507semidirect
432. C2×#557D83semidirect
446. C83C2×#3507semidirect
452. #557C2×D83semidirect
851. C2#24921329direct (N × H)

Maximal subgroups

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

subgroupindex
#249213292
C2×#191284362
C2×#191284262
C2×#191284252
C2×#191284232
C2×#191284072
C2×#191283832
C2×#191282992
C2×#191282762
C2×#191282552
C2×#191282522
C2×#191282382
C2×#191282362
C2×#191281832
C2×C4×Q8×D832
C2×#557×C832
C2×#350783