Finite Group Databasebeta

← C2×#24921346 #36312843

Subgroups — C2×#24921346 #36312843

Order 21248.

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#24921346C2132yesmaximal, direct product factor
2C2×#19128429C211yesmaximal, characteristic, complemented
3C2×#19128426C212yesmaximal, complemented
4C2×#19128425C211yesmaximal, characteristic, complemented
5C2×#19128424C211yesmaximal, characteristic, complemented
6C2×#19128423C212yesmaximal, complemented
7C2×#19128392C212yesmaximal, complemented
8C2×#19128389C212yesmaximal, complemented
9C2×#19128383C214yesmaximal, complemented
10C2×#19128310C214yesmaximal, complemented
11C2×#19128276C212yesmaximal
12C2×#19128257C212yesmaximal, complemented
13C2×#19128255C212yesmaximal, complemented
14C2×#19128255C211yesmaximal, characteristic, complemented
15C2×C4⋊Q8×D83C211yesmaximal, characteristic, complemented
16C2×#19128177C212yesmaximal, complemented
17C2×C4×#13050591C211yesmaximal, characteristic
18C2×#557×C83C211yesmaximal, characteristic, complemented
19C22×#13050591C2211yescharacteristic
20C22×Q8×D83C2212yes—
21#19128429C22116yescomplemented
22#19128426C22132yescomplemented
23#19128425C22116yescomplemented
24#19128424C22116yescomplemented
25#19128423C22132yescomplemented
26#19128392C22132yescomplemented
27#19128389C22132yescomplemented
28#19128383C22164yescomplemented
29#19128310C22164yescomplemented
30#19128276C22132yes—
31#19128257C22132yescomplemented
32#19128255C22116yescomplemented
33#19128255C22132yescomplemented
34C2×#14581792C2211yescharacteristic
35C2×#14581791C2212yes—
36C2×#14581791C2212yes—
37C2×#14581791C2211yescharacteristic
38C2×#14581790C2212yes—
39C2×#14581790C2211yescharacteristic
40C2×#14581790C2212yes—
41C4⋊Q8×D83C22116yescomplemented
42C2×#14581787C2214yes—
43C2×#14581787C2214yes—
44C2×#14581787C2214yes—
45C2×#14581786C2214yes—
46C2×#14581784C2212yes—
47C2×#14581783C2214yes—
48C2×#14581782C2214yes—
49C2×#14581782C2214yes—
50C2×#14581782C2214yes—
51C2×#14581782C2212yes—
52C2×#14581781C2212yes—
53C2×#14581780C2212yes—
54C2×#14581777C2214yes—
55C2×#14581777C2214yes—
56C2×#14581772C2211yescharacteristic
57C2×#14581772C2212yes—
58C2×#14581770C2212yes—
59C2×#14581770C2214yes—
60C2×#14581770C2214yes—
61C2×#14581770C2214yes—
62C2×#14581768C2211yescharacteristic
63C2×#14581768C2212yes—
64#19128177C22132yescomplemented
65C4×#13050591C22116yes—
66C2×Q8×Dic83C2211yescharacteristic
67C2×Q8×Dic83C2212yes—
68C2×C4×Dic166C2214yes—
69C2×C4×Dic166C2212yes—
70C2×C4×Dic166C2212yes—
71C2×C4×Dic166C2212yes—
72C2×C4×Dic166C2211yescharacteristic
73C2×#14581757C2214yes—
74C2×#14581757C2212yes—
75C2×#14581757C2214yes—
76C2×C4×D332C2212yes—
77C2×C4×D332C2211yescharacteristic
78C2×#14581754C2212yes—
79C2×#14581754C2211yescharacteristic
80C2×#14581750C2211yescharacteristic
81C2×#14581750C2212yes—
82C2×#14581750C2214yes—
83C2×#14581750C2212yes—
84C2×#14581750C2212yes—
85C2×#14581749C2214yes—
86C2×#14581749C2212yes—
87C2×#14581749C2214yes—
88C2×C4⋊C4×D83C2212yes—
89C2×C4⋊C4×D83C2212yes—
90C2×C42×D83C2211yescharacteristic
91C2×C42×D83C2212yes—
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—28no—
102C2×#13050591C2318yes—
103C22×Dic166C2312yes—
104C22×Dic166C2314yes—
105C22×Dic166C2312yes—
106C22×Dic166C2311yescharacteristic
107C2×Q8×D83—216no—
108C2×Q8×D83C23116yes—
109C22×D332C2312yes—
110C22×D332C2311yescharacteristic
111C22×C4×D83C2311yescharacteristic
112C22×C4×D83C2311yescharacteristic
113C22×C4×D83C2312yes—
114C22×C4×D83C2312yes—
115C22×C4×D83C2312yes—
116C22×C4×D83C2314yes—
117C22×C4×D83C2311yescharacteristic
118#14581792C2318yes—
119#14581791C23116yes—
120#14581791C23116yes—
121#14581791C2318yes—
122#14581790C23116yes—
123#14581790C23116yes—
124#14581790C2318yes—
125#14581787C23132yes—
126#14581787C23132yes—
127#14581787C23132yes—
128#14581786C23132yes—
129#14581784C23116yes—
130#14581783C23132yes—
131#14581782C23132yes—
132#14581782C23132yes—
133#14581782C23132yes—
134#14581782C23116yes—
135#14581781C23116yes—
136#14581780C23116yes—
137#14581777C23132yes—
138#14581777C23132yes—
139#14581772C2318yes—
140#14581772C23116yes—
141#14581770C23116yes—
142#14581770C23132yes—
143#14581770C23132yes—
144#14581770C23132yes—
145#14581768C2318yes—
146#14581768C23116yes—
147Q8×Dic83C23116yes—
148Q8×Dic83C2318yes—
149C4×Dic166C23116yes—
150C4×Dic166C23116yes—
151C4×Dic166C23116yes—
152C4×Dic166C2318yes—
153C4×Dic166C23132yes—
154#14581757C23132yes—
155#14581757C23116yes—
156#14581757C23132yes—
157C4×D332C23116yes—
158C4×D332C2318yes—
159#14581754C23116yes—
160#14581754C2318yes—
161#14581750C23132yes—
162#14581750C23116yes—
163#14581750C23116yes—
164#14581750C2318yes—
165#14581750C23116yes—
166#14581749C23132yes—
167#14581749C23132yes—
168#14581749C23116yes—
169C2×C4⋊Dic83C2312yes—
170C2×C4⋊Dic83C2312yes—
171C2×C4⋊Dic83C2311yescharacteristic
172C2×C4⋊Dic83C2311yescharacteristic
173C2×C4⋊Dic83C2312yes—
174C2×C4⋊Dic83C2314yes—
175C2×C4⋊Dic83C2312yes—
176C2×Dic83⋊C4C2314yes—
177C2×Dic83⋊C4C2314yes—
178C2×Dic83⋊C4C2312yes—
179C2×Dic83⋊C4C2312yes—
180C2×Dic83⋊C4C2314yes—
181C2×Dic83⋊C4C2314yes—
182C2×Dic83⋊C4C2312yes—
183C2×Dic83⋊C4C2314yes—
184C2×Dic83⋊C4C2312yes—
185C2×Dic83⋊C4C2314yes—
186C2×Dic83⋊C4C2312yes—
187C4⋊C4×D83C23116yes—
188C4⋊C4×D83C23116yes—
189C2×(C2×D83)⋊C4C2312yes—
190C2×(C2×D83)⋊C4C2312yes—
191C2×(C2×D83)⋊C4C2312yes—
192C2×(C2×D83)⋊C4C2314yes—
193C2×(C2×D83)⋊C4C2314yes—
194C2×(C2×D83)⋊C4C2312yes—
195C2×(C2×D83)⋊C4C2312yes—
196C2×(C2×D83)⋊C4C2314yes—
197C2×(C2×D83)⋊C4C2314yes—
198C2×C4×Dic83C2311yescharacteristic
199C2×C4×Dic83C2312yes—
200C2×C4×Dic83C2311yescharacteristic
201C2×C4×Dic83C2312yes—
202C2×C4×Dic83C2311yescharacteristic
203C2×C4×Dic83C2314yes—
204C2×C4×Dic83C2314yes—
205C2×C4×Dic83C2312yes—
206C2×C4×Dic83C2314yes—
207C42×D83C2318yes—
208C42×D83C23116yes—
209C22×Q8×C83C2311yescharacteristic
210C22×Q8×C83C2312yes—
211C22×Q8×C83C2311yescharacteristic
212C4⋊Q8×C83C2318yes—
213C4⋊Q8×C83C23116yes—
214#125×C83C23132yes—
215#125×C83C23116yes—
216C4×Q8×C83C23116yes—
217C4×Q8×C83C23116yes—
218C4×Q8×C83C2318yes—
219C4×Q8×C83C2318yes—
220C2×C4⋊C4×C83C2311yescharacteristic
221C2×C4⋊C4×C83C2311yescharacteristic
222C2×C4⋊C4×C83C2312yes—
223C2×C4⋊C4×C83C2314yes—
224C2×C4⋊C4×C83C2312yes—
225C2×C4⋊C4×C83C2312yes—
226C2×C4⋊C4×C83C2314yes—
227C2×C4⋊C4×C83C2312yes—
228C2×C4⋊C4×C83C2314yes—
229C2×C42×C83C2312yes—
230C2×C42×C83C2314yes—
231C2×C42×C83C2311yescharacteristic
232C2×C42×C83C2312yes—
233C23×D83C2412yes—
234C23×D83C2411yescharacteristic
235#13050591—232no—
236C2×Dic166—28no—
237C2×Dic166—24no—
238C2×Dic166—216no—
239C2×Dic166—28no—
240C2×Dic166C2418yes—
241C2×Dic166C24116yes—
242C2×Dic166C2414yes—
243C2×Dic166C2418yes—
244Q8×D83—264no—
245C2×D332—28no—
246C2×D332—24no—
247C2×D332C2418yes—
248C2×D332C2414yes—
249C22×Dic83C2414yes—
250C22×Dic83C2412yes—
251C22×Dic83C2411yescharacteristic
252C22×Dic83C2412yes—
253C22×Dic83C2412yes—
254C22×Dic83C2411yescharacteristic
255C22×Dic83C2411yescharacteristic
256C2×C4×D83—216no—
257C2×C4×D83—24no—
258C2×C4×D83—28no—
259C2×C4×D83—28no—
260C2×C4×D83—24no—
261C2×C4×D83—28no—
262C2×C4×D83#4118yes—
263C2×C4×D83C2414yes—
264C2×C4×D83C2418yes—
265C2×C4×D83C2418yes—
266C2×C4×D83C2414yes—
267C2×C4×D83C2418yes—
268C2×C4×D83C24116yes—
269C2×C4×D83C2414yes—
270C4⋊Dic83C2414yes—
271C4⋊Dic83C2418yes—
272C4⋊Dic83C2418yes—
273C4⋊Dic83C24116yes—
274C4⋊Dic83C2418yes—
275C4⋊Dic83C2418yes—
276C4⋊Dic83C2414yes—
277Dic83⋊C4C2418yes—
278Dic83⋊C4C24116yes—
279Dic83⋊C4C2418yes—
280Dic83⋊C4C2418yes—
281Dic83⋊C4C24116yes—
282Dic83⋊C4C24116yes—
283Dic83⋊C4C2418yes—
284Dic83⋊C4C2418yes—
285Dic83⋊C4C24116yes—
286Dic83⋊C4C24116yes—
287Dic83⋊C4C24116yes—
288(C2×D83)⋊C4C2418yes—
289(C2×D83)⋊C4C24116yes—
290(C2×D83)⋊C4C24116yes—
291(C2×D83)⋊C4C24116yes—
292(C2×D83)⋊C4C2418yes—
293(C2×D83)⋊C4C24116yes—
294(C2×D83)⋊C4C2418yes—
295(C2×D83)⋊C4C2418yes—
296(C2×D83)⋊C4C2418yes—
297C4×Dic83C2418yes—
298C4×Dic83C2414yes—
299C4×Dic83C2418yes—
300C4×Dic83C24116yes—
301C4×Dic83C24116yes—
302C4×Dic83C24116yes—
303C4×Dic83C2414yes—
304C4×Dic83C2414yes—
305C4×Dic83C2418yes—
306C2×Q8×C83—28no—
307C2×Q8×C83—24no—
308C2×Q8×C83—24no—
309C2×Q8×C83C2414yes—
310C2×Q8×C83C2418yes—
311C2×Q8×C83C2414yes—
312C22×C4×C83C2412yes—
313C22×C4×C83C2414yes—
314C22×C4×C83C2412yes—
315C22×C4×C83C2411yescharacteristic
316C22×C4×C83C2412yes—
317C22×C4×C83C2412yes—
318C22×C4×C83C2411yescharacteristic
319C22×C4×C83C2411yescharacteristic
320C4⋊C4×C83C24116yes—
321C4⋊C4×C83C24116yes—
322C4⋊C4×C83C2418yes—
323C4⋊C4×C83C24116yes—
324C4⋊C4×C83C2414yes—
325C4⋊C4×C83C2418yes—
326C4⋊C4×C83C2418yes—
327C4⋊C4×C83C2418yes—
328C4⋊C4×C83C2414yes—
329C42×C83C2418yes—
330C42×C83C2418yes—
331C42×C83C24116yes—
332C42×C83C2414yes—
333C23×C83C2511yescharacteristic
334C22×D83—22no—
335C22×D83—22no—
336C22×D83—24no—
337C22×D83—24no—
338C22×D83—24no—
339C22×D83C2×#4114yes—
340C22×D83C2514yes—
341C22×D83C2512yes—
342Q8×C83—216no—
343Q8×C83—28no—
344Q8×C83—28no—
345C2×C4×C83—24no—
346C2×C4×C83—28no—
347C2×C4×C83—24no—
348C2×C4×C83—24no—
349C2×C4×C83—22no—
350C2×C4×C83—24no—
351C2×C4×C83C2×#4114yes—
352C2×C4×C832−1+414yes—
353C2×C4×C83C2514yes—
354C2×C4×C83C2514yes—
355C2×C4×C83C2514yes—
356C2×C4×C83C2512yes—
357C2×C4×C83C2518yes—
358C2×C4×C83C2514yes—
359C2×C4×C83C2512yes—
360C2×C4×C83C2512yes—
361C2×Dic83—28no—
362C2×Dic83—24no—
363C2×Dic83—22no—
364C2×Dic83—24no—
365C2×Dic83—24no—
366C2×Dic83C2×#4114yes—
367C2×Dic832−1+414yes—
368C2×Dic83C2514yes—
369C2×Dic83C2514yes—
370C2×Dic83C2514yes—
371C2×Dic83C2512yes—
372C2×Dic83C2518yes—
373C2×Dic83C2512yes—
374C2×Dic83C2512yes—
375D332—216no—
376D332—28no—
377C4×D83—232no—
378C4×D83—28no—
379C4×D83—216no—
380C4×D83—216no—
381C4×D83—28no—
382C4×D83—216no—
383C4×D83C2×#41116yes—
384Dic166—216no—
385Dic166—28no—
386Dic166—232no—
387Dic166—216no—
388C22×C83C22×#4112yes—
389C22×C83C2×2−1+412yes—
390C22×C83C2×2−1+412yes—
391C22×C83C2611yescharacteristic
392C2×D83—22no—
393C2×D83—22no—
394C2×D83—28no—
395C2×D83—24no—
396C2×D83—24no—
397C2×D83—24no—
398C2×D83—48no—
399C2×D83C22×#4114yes—
400C4×C83—28no—
401C4×C83—24no—
402C4×C83—24no—
403C4×C83—24no—
404C4×C83—22no—
405C4×C83—24no—
406C4×C83C22×#4114yes—
407C4×C83C2×2−1+414yes—
408Dic83—28no—
409Dic83—24no—
410Dic83—24no—
411Dic83—24no—
412Dic83—22no—
413Dic83C22×#4114yes—
414Dic83C2×2−1+414yes—
415C2×#3509—831nomaximal, Sylow
416C2×C83#350914yescomplemented
417C2×C83C23×#4111yescharacteristic
418C2×C83C22×2−1+411yescharacteristic
419C2×C83C22×2−1+411yescharacteristic
420D83—24no—
421D83—44no—
422#3509—8332no—
423C2×#557—832no—
424C2×#557—831no—
425C2×#557D8311yescharacteristic, complemented
426C2×#556—831no—
427C2×#556—832no—
428C2×#556—831no—
429C2×#552—834no—
430C2×#552—832no—
431C2×#552—832no—
432C2×#541—834no—
433C2×#536—832no—
434C2×#533—832no—
435C2×#533—831no—
436C2×#533—832no—
437C22×C4⋊Q8—831no—
438C2×#519—832no—
439C2×C4×#41—831no—
440C83C2×#350911yescharacteristic, complemented, Sylow
441C22×#41—831no—
442C23×Q8—832no—
443#557—8332no—
444#557—8316no—
445#557C2×D83116yescomplemented
446#556—8316no—
447#556—8332no—
448#556—8316no—
449#552—8364no—
450#552—8332no—
451#552—8332no—
452#541—8364no—
453#536—8332no—
454#533—8332no—
455#533—8316no—
456#533—8332no—
457C2×C4⋊Q8—832no—
458C2×C4⋊Q8—831no—
459C2×C4⋊Q8—832no—
460C2×C4⋊Q8—8316no—
461C2×C4⋊Q8—832no—
462C2×C4⋊Q8—832no—
463C2×C4⋊Q8—831no—
464C2×C4⋊Q8—831no—
465C2×C4⋊Q8C2×D8311yescharacteristic
466C2×C4⋊Q8C2×D8312yes—
467C2×#126—834no—
468C2×#126—834no—
469C2×#126—834no—
470C2×#126—834no—
471C2×#125—832no—
472C2×#125—834no—
473C2×#125—834no—
474C2×#125—834no—
475C2×#125—834no—
476C2×#125—832no—
477C2×#125C2×D8312yes—
478C2×#125C2×D8314yes—
479C2×#124—832no—
480C2×#124—832no—
481C2×#123—834no—
482C2×#123—834no—
483C2×C22⋊Q8—831no—
484C2×C22⋊Q8—832no—
485C2×C22⋊Q8—834no—
486C2×C22⋊Q8—834no—
487C2×C22⋊Q8—832no—
488C2×C22⋊Q8—834no—
489C2×C22⋊Q8—831no—
490C2×C22⋊Q8—832no—
491#519—8332no—
492C4×#41—8316no—
493C2×C4×Q8—831no—
494C2×C4×Q8—832no—
495C2×C4×Q8—834no—
496C2×C4×Q8—832no—
497C2×C4×Q8—834no—
498C2×C4×Q8—834no—
499C2×C4×Q8—832no—
500C2×C4×Q8—832no—
501C2×C4×Q8—831no—
502C2×C4×Q8—832no—
503C2×C4×Q8C2×D8311yescharacteristic
504C2×C4×Q8C2×D8312yes—
505C2×C4×Q8C2×D8312yes—
506C2×C4×Q8C2×D8311yescharacteristic
507C2×C4×D4—832no—
508C2×C4×D4—831no—
509C2×C4×D4—832no—
510C2×C4×D4—831no—
511C2×#117—831no—
512C2×#117—832no—
513C2×#117—834no—
514C2×#117—832no—
515C2×#117—832no—
516C2×#117—832no—
517C2×#117—834no—
518C2×#117—834no—
519C22×C4⋊C4—832no—
520C22×C4⋊C4—832no—
521C22×C42—831no—
522C22×C42—832no—
523C2×#41—838no—
524C2×#41—1668no—
525C22×Q8—8316no—
526C22×Q8—832no—
527C22×Q8—831no—
528C22×Q8—834no—
529C22×Q8—832no—
530C22×Q8—16616no—
531C22×Q8C22×D8312yes—
532C22×Q8C22×D8311yescharacteristic
533C22×Q8C22×D8311yescharacteristic
534C22×D4—832no—
535C22×D4—831no—
536C23×C4—831no—
537C23×C4—834no—
538C23×C4—831no—
539C23×C4—831no—
540C23×C4—832no—
541C23×C4—832no—
542C23×C4—832no—
543C4⋊Q8—8316no—
544C4⋊Q8—838no—
545C4⋊Q8—8316no—
546C4⋊Q8—8316no—
547C4⋊Q8—8316no—
548C4⋊Q8—838no—
549C4⋊Q8—838no—
550C4⋊Q8C22×D8318yes—
551C4⋊Q8C22×D83116yes—
552#126—8332no—
553#126—8332no—
554#126—8332no—
555#126—8332no—
556#125—8316no—
557#125—8332no—
558#125—8332no—
559#125—8332no—
560#125—8332no—
561#125—8316no—
562#125C22×D83116yes—
563#125C22×D83132yes—
564#124—8316no—
565#124—8316no—
566#123—8332no—
567#123—8332no—
568C22⋊Q8—838no—
569C22⋊Q8—8316no—
570C22⋊Q8—8332no—
571C22⋊Q8—8332no—
572C22⋊Q8—8316no—
573C22⋊Q8—8332no—
574C22⋊Q8—838no—
575C22⋊Q8—8316no—
576C4×Q8—838no—
577C4×Q8—8316no—
578C4×Q8—8332no—
579C4×Q8—8316no—
580C4×Q8—8332no—
581C4×Q8—8332no—
582C4×Q8—8316no—
583C4×Q8—8316no—
584C4×Q8—8316no—
585C4×Q8—838no—
586C4×Q8C22×D8318yes—
587C4×Q8C22×D83116yes—
588C4×Q8C22×D83116yes—
589C4×Q8C22×D8318yes—
590C4×D4—8316no—
591C4×D4—838no—
592C4×D4—8316no—
593C4×D4—838no—
594#117—838no—
595#117—8316no—
596#117—8332no—
597#117—8316no—
598#117—8316no—
599#117—8316no—
600#117—8332no—
601#117—8332no—
602C2×C4⋊C4—834no—
603C2×C4⋊C4—832no—
604C2×C4⋊C4—834no—
605C2×C4⋊C4—832no—
606C2×C4⋊C4—832no—
607C2×C4⋊C4—831no—
608C2×C4⋊C4—831no—
609C2×C4⋊C4—832no—
610C2×C4⋊C4—832no—
611C2×C4⋊C4—832no—
612C2×C4⋊C4—834no—
613C2×C4⋊C4—834no—
614C2×C4⋊C4—834no—
615C2×C4⋊C4—834no—
616C2×C4⋊C4—834no—
617C2×C4⋊C4—832no—
618C2×C4⋊C4—832no—
619C2×C4⋊C4—832no—
620C2×C4⋊C4—8316no—
621C2×C4⋊C4—8316no—
622C2×C4⋊C4C22×D8312yes—
623C2×C4⋊C4C22×D8312yes—
624C2×C4⋊C4C22×D8311yescharacteristic
625C2×C4⋊C4C22×D8311yescharacteristic
626C2×C4⋊C4C22×D8312yes—
627C2×C4⋊C4C22×D8314yes—
628C2×C4⋊C4C22×D8314yes—
629C2×C4⋊C4C22×D8314yes—
630C2×C4⋊C4C22×D8312yes—
631C2×C22⋊C4—832no—
632C2×C22⋊C4—832no—
633C2×C22⋊C4—832no—
634C2×C22⋊C4—832no—
635C2×C22⋊C4—832no—
636C2×C22⋊C4—834no—
637C2×C22⋊C4—834no—
638C2×C22⋊C4—834no—
639C2×C22⋊C4—834no—
640C2×C42—832no—
641C2×C42—834no—
642C2×C42—834no—
643C2×C42—834no—
644C2×C42—831no—
645C2×C42—832no—
646C2×C42—832no—
647C2×C42—831no—
648C2×C42—831no—
649C2×C42—838no—
650C2×C42—8316no—
651C2×C42C22×D8314yes—
652C2×C42C22×D8312yes—
653C2×C42C22×D8312yes—
654C2×C42C22×D8311yescharacteristic
655C24—831no—
656C24—832no—
657#41—16632no—
658C2×Q8—28no—
659C2×Q8—24no—
660C2×Q8—24no—
661C2×Q8—838no—
662C2×Q8—834no—
663C2×Q8—8316no—
664C2×Q8—838no—
665C2×Q8—16616no—
666C2×Q8—1668no—
667C2×Q8—16664no—
668C2×Q8—1668no—
669C2×Q8—1664no—
670C2×Q8C23×D8318yes—
671C2×Q8C23×D8314yes—
672C2×Q8C23×D8314yes—
673C2×D4—838no—
674C2×D4—834no—
675C2×D4—1668no—
676C2×D4—1664no—
677C22×C4—831no—
678C22×C4—831no—
679C22×C4—838no—
680C22×C4—834no—
681C22×C4—832no—
682C22×C4—832no—
683C22×C4—832no—
684C22×C4—831no—
685C22×C4—834no—
686C22×C4—834no—
687C22×C4—834no—
688C22×C4—838no—
689C22×C4—838no—
690C22×C4—838no—
691C22×C4—8316no—
692C22×C4—1668no—
693C22×C4—1668no—
694C22×C4—1664no—
695C22×C4—16616no—
696C22×C4—1668no—
697C22×C4—1664no—
698C22×C4C23×D8312yes—
699C22×C4C23×D8312yes—
700C22×C4C23×D8311yescharacteristic
701C22×C4C23×D8314yes—
702C22×C4C23×D8312yes—
703C22×C4C23×D8312yes—
704C22×C4C23×D8311yescharacteristic
705C22×C4C23×D8311yescharacteristic
706C4⋊C4—8316no—
707C4⋊C4—838no—
708C4⋊C4—8316no—
709C4⋊C4—838no—
710C4⋊C4—838no—
711C4⋊C4—834no—
712C4⋊C4—834no—
713C4⋊C4—838no—
714C4⋊C4—838no—
715C4⋊C4—838no—
716C4⋊C4—8316no—
717C4⋊C4—8316no—
718C4⋊C4—8316no—
719C4⋊C4—8316no—
720C4⋊C4—8316no—
721C4⋊C4—838no—
722C4⋊C4—838no—
723C4⋊C4—838no—
724C4⋊C4C23×D8318yes—
725C4⋊C4C23×D8318yes—
726C4⋊C4C23×D8314yes—
727C4⋊C4C23×D8314yes—
728C4⋊C4C23×D8318yes—
729C4⋊C4C23×D83116yes—
730C4⋊C4C23×D83116yes—
731C4⋊C4C23×D83116yes—
732C4⋊C4C23×D8318yes—
733C22⋊C4—838no—
734C22⋊C4—838no—
735C22⋊C4—838no—
736C22⋊C4—838no—
737C22⋊C4—838no—
738C22⋊C4—8316no—
739C22⋊C4—8316no—
740C22⋊C4—8316no—
741C22⋊C4—8316no—
742C42—834no—
743C42—838no—
744C42—834no—
745C42—838no—
746C42—834no—
747C42—8316no—
748C42—8316no—
749C42—8316no—
750C42—838no—
751C42C23×D8318yes—
752C42C23×D8314yes—
753C42C23×D83116yes—
754C42C23×D8318yes—
755C23—834no—
756C23—832no—
757C23—834no—
758C23—1664no—
759C23—1664no—
760C23—1664no—
761C23—1662no—
762C23—1662no—
763C23C24×D8311yescharacteristic
764Q8—216no—
765Q8—28no—
766Q8—28no—
767Q8—16632no—
768Q8—16616no—
769Q8—16616no—
770Q8—1668no—
771D4—16616no—
772D4—1668no—
773C2×C4—24no—
774C2×C4—28no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—834no—
780C2×C4—834no—
781C2×C4—832no—
782C2×C4—832no—
783C2×C4—8316no—
784C2×C4—834no—
785C2×C4—834no—
786C2×C4—834no—
787C2×C4—832no—
788C2×C4—838no—
789C2×C4—16616no—
790C2×C4—16616no—
791C2×C4—1668no—
792C2×C4—16632no—
793C2×C4—1668no—
794C2×C4—1664no—
795C2×C4—1664no—
796C2×C4—1662no—
797C2×C4—1664no—
798C2×C4—16616no—
799C2×C4—1668no—
800C2×C4#41×D8314yes—
801C2×C4#1458184014yes—
802C2×C4C24×D8314yes—
803C2×C4C24×D8314yes—
804C2×C4C24×D8312yes—
805C2×C4C24×D8318yes—
806C2×C4C24×D8314yes—
807C2×C4C24×D8314yes—
808C2×C4C24×D8312yes—
809C2×C4C24×D8312yes—
810C22—3328no—
811C22—834no—
812C22—1664no—
813C22—1664no—
814C22—1664no—
815C22—1668no—
816C22—1662no—
817C22—1662no—
818C22C2×#41×D8312yes—
819C222−1+4×D8312yes—
820C22C2×#1458184012yes—
821C22C25×D8311yescharacteristic
822C4—24no—
823C4—28no—
824C4—24no—
825C4—22no—
826C4—24no—
827C4—24no—
828C4—834no—
829C4—834no—
830C4—1668no—
831C4—1664no—
832C4—1664no—
833C4—1662no—
834C4—1664no—
835C4C2×#41×D8314yes—
836C4C2×#1458184014yes—
837C2—3324no—
838C2—1664no—
839C2#2492134614yesdirect product factor
840C2C22×#41×D8311yescharacteristic
841C2C2×2−1+4×D8311yescharacteristic
842C2C22×#1458184011yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#557×C83C2
socleC23×C83C25
prime radicalC22×#13050591C22
hypercenterC2×#557D83
hypocenterC83C2×#3509
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #24921346C2direct (N × H)
2. C2×#19128429C2semidirect
3. C2×#19128426C2semidirect
4. C2×#19128425C2semidirect
5. C2×#19128424C2semidirect
6. C2×#19128423C2semidirect
7. C2×#19128392C2semidirect
8. C2×#19128389C2semidirect
9. C2×#19128383C2semidirect
10. C2×#19128310C2semidirect
12. C2×#19128257C2semidirect
13. C2×#19128255C2semidirect
14. C2×#19128255C2semidirect
15. C2×C4⋊Q8×D83C2semidirect
16. C2×#19128177C2semidirect
18. C2×#557×C83C2semidirect
21. #19128429C22semidirect
22. #19128426C22semidirect
23. #19128425C22semidirect
24. #19128424C22semidirect
25. #19128423C22semidirect
26. #19128392C22semidirect
27. #19128389C22semidirect
28. #19128383C22semidirect
29. #19128310C22semidirect
31. #19128257C22semidirect
32. #19128255C22semidirect
33. #19128255C22semidirect
41. C4⋊Q8×D83C22semidirect
64. #19128177C22semidirect
92. #557×C83C22semidirect
416. C2×C83#3509semidirect
425. C2×#557D83semidirect
440. C83C2×#3509semidirect
445. #557C2×D83semidirect
839. C2#24921346direct (N × H)

Maximal subgroups

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

subgroupindex
#249213462
C2×#191284292
C2×#191284262
C2×#191284252
C2×#191284242
C2×#191284232
C2×#191283922
C2×#191283892
C2×#191283832
C2×#191283102
C2×#191282762
C2×#191282572
C2×#191282552
C2×C4⋊Q8×D832
C2×#191281772
C2×C4×#130505912
C2×#557×C832
C2×#350983