Finite Group Databasebeta

← C2×#24921318 #36312480

Subgroups — C2×#24921318 #36312480

Order 21248.

7130 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921318C2132yesmaximal, direct product factor
2C2×#19128433C212yesmaximal, complemented
3C2×#19128427C212yesmaximal, complemented
4C2×#19128425C211yesmaximal, characteristic, complemented
5C2×#19128418C214yesmaximal, complemented
6C2×#19128411C211yesmaximal, characteristic, complemented
7C2×#19128408C211yesmaximal, characteristic, complemented
8C2×#19128393C212yesmaximal, complemented
9C2×#19128390C212yesmaximal, complemented
10C2×#19128292C214yesmaximal, complemented
11C2×#19128274C212yesmaximal, complemented
12C2×#19128256C211yesmaximal, characteristic, complemented
13C2×#19128248C211yesmaximal, characteristic
14C2×#19128238C212yesmaximal, complemented
15C2×#19128230C212yesmaximal, complemented
16C2×#19128181C212yesmaximal, complemented
17C2×C4×Q8×D83C211yesmaximal, characteristic, complemented
18C2×#556×C83C211yesmaximal, characteristic, complemented
19C22×#13050590C2212yes—
20C22×Q8×D83C2211yescharacteristic
21#19128433C22132yescomplemented
22#19128427C22132yescomplemented
23#19128425C22116yescomplemented
24#19128418C22164yescomplemented
25#19128411C22116yescomplemented
26#19128408C22116yescomplemented
27#19128393C22132yescomplemented
28#19128390C22132yescomplemented
29#19128292C22164yescomplemented
30#19128274C22132yescomplemented
31#19128256C22116yescomplemented
32#19128248C22116yes—
33C2×#14581792C2211yescharacteristic
34C2×#14581791C2211yescharacteristic
35C2×#14581791C2214yes—
36C2×#14581788C2211yescharacteristic
37#19128238C22132yescomplemented
38#19128230C22132yescomplemented
39C2×#14581787C2214yes—
40C2×#14581787C2214yes—
41C2×#14581785C2214yes—
42C2×#14581784C2214yes—
43C2×#14581784C2212yes—
44C2×#14581783C2212yes—
45C2×#14581783C2214yes—
46C2×#14581783C2212yes—
47C2×#14581781C2212yes—
48C2×#14581778C2212yes—
49C2×#14581778C2214yes—
50C2×#14581777C2214yes—
51C2×#14581776C2214yes—
52C2×#14581774C2214yes—
53C2×#14581774C2214yes—
54C2×#14581772C2212yes—
55C2×#14581772C2212yes—
56C2×#14581771C2212yes—
57C2×#14581770C2214yes—
58C2×#14581769C2214yes—
59C2×#14581768C2212yes—
60C2×#14581768C2212yes—
61C2×#14581767C2211yescharacteristic
62C2×#14581765C2212yes—
63C2×#14581763C2211yescharacteristic
64#19128181C22132yescomplemented
65C2×Q8×Dic83C2211yescharacteristic
66C2×Q8×Dic83C2212yes—
67C2×Q8×Dic83C2212yes—
68C2×C4×Dic166C2211yescharacteristic
69C2×C4×Dic166C2212yes—
70C2×C4×Dic166C2214yes—
71C2×#14581757C2211yescharacteristic
72C2×#14581757C2212yes—
73C2×#14581757C2212yes—
74C4×Q8×D83C22116yescomplemented
75C2×C4×D332C2214yes—
76C2×C4×D332C2212yes—
77C2×C4×D332C2211yescharacteristic
78C2×D4×Dic83C2212yes—
79C2×C4×C22⋊D83C2212yes—
80C2×(C22⋊D83)⋊C4C2214yes—
81C2×(C22⋊D83)⋊C4C2214yes—
82C2×#14581750C2212yes—
83C2×#14581750C2212yes—
84C2×#14581749C2214yes—
85C2×#14581748C2214yes—
86C22×C4⋊Dic83C2212yes—
87C2×C4⋊C4×D83C2211yescharacteristic
88C2×C4⋊C4×D83C2212yes—
89C2×C4⋊C4×D83C2212yes—
90C2×C42×D83C2212yes—
91C2×C42×D83C2211yescharacteristic
92#556×C83C22116yescomplemented
93C2×C4⋊Q8×C83C2211yescharacteristic
94C2×#126×C83C2214yes—
95C2×#124×C83C2212yes—
96C2×C22⋊Q8×C83C2212yes—
97C2×C4×Q8×C83C2211yescharacteristic
98C2×C4×Q8×C83C2212yes—
99C2×C4×D4×C83C2211yescharacteristic
100C2×#117×C83C2212yes—
101C2×#13050590—216no—
102C2×#13050590C23116yes—
103C22×Dic166C2311yescharacteristic
104C22×Dic166C2312yes—
105C22×Dic166C2312yes—
106C22×Dic166C2312yes—
107C2×Q8×D83—28no—
108C2×Q8×D83C2318yes—
109C22×D332C2311yescharacteristic
110C22×D332C2312yes—
111C22×C22⋊D83C2312yes—
112C22×C22⋊D83C2312yes—
113C22×C22⋊D83C2312yes—
114C23×Dic83C2314yes—
115C22×C4×D83C2311yescharacteristic
116C22×C4×D83C2312yes—
117C22×C4×D83C2312yes—
118C22×C4×D83C2312yes—
119C22×C4×D83C2311yescharacteristic
120C22×C4×D83C2314yes—
121C22×C4×D83C2311yescharacteristic
122#14581792C2318yes—
123#14581791C23132yes—
124#14581791C2318yes—
125#14581788C2318yes—
126#14581787C23132yes—
127#14581787C23132yes—
128#14581785C23132yes—
129#14581784C23132yes—
130#14581784C23116yes—
131#14581783C23116yes—
132#14581783C23132yes—
133#14581783C23116yes—
134#14581781C23116yes—
135#14581778C23116yes—
136#14581778C23132yes—
137#14581777C23132yes—
138#14581776C23132yes—
139#14581774C23132yes—
140#14581774C23132yes—
141#14581772C23116yes—
142#14581772C23116yes—
143#14581771C23116yes—
144#14581770C23132yes—
145#14581769C23132yes—
146#14581768C23116yes—
147#14581768C23116yes—
148#14581767C2318yes—
149#14581765C23116yes—
150#14581763C2318yes—
151Q8×Dic83C2318yes—
152Q8×Dic83C23116yes—
153Q8×Dic83C23116yes—
154C4×Dic166C2318yes—
155C4×Dic166C23132yes—
156C4×Dic166C23116yes—
157#14581757C2318yes—
158#14581757C23116yes—
159#14581757C23116yes—
160C4×D332C2318yes—
161C4×D332C23116yes—
162C4×D332C23132yes—
163D4×Dic83C23116yes—
164C4×C22⋊D83C23116yes—
165(C22⋊D83)⋊C4C23132yes—
166(C22⋊D83)⋊C4C23132yes—
167#14581750C23116yes—
168#14581750C23116yes—
169#14581749C23132yes—
170#14581748C23132yes—
171C2×C4⋊Dic83C23116yes—
172C2×C4⋊Dic83C2311yescharacteristic
173C2×C4⋊Dic83C2312yes—
174C2×C4⋊Dic83C2312yes—
175C2×C4⋊Dic83C2314yes—
176C2×C4⋊Dic83C2312yes—
177C2×C4⋊Dic83C2311yescharacteristic
178C2×C4⋊Dic83C2314yes—
179C2×C4⋊Dic83C2314yes—
180C2×Dic83⋊C4C2312yes—
181C2×Dic83⋊C4C2314yes—
182C2×Dic83⋊C4C2312yes—
183C2×Dic83⋊C4C2312yes—
184C2×Dic83⋊C4C2314yes—
185C2×Dic83⋊C4C2314yes—
186C2×Dic83⋊C4C2314yes—
187C2×Dic83⋊C4C2312yes—
188C4⋊C4×D83C23116yes—
189C4⋊C4×D83C2318yes—
190C4⋊C4×D83C23116yes—
191C2×C22⋊Dic83C2312yes—
192C2×C22⋊Dic83C2314yes—
193C2×(C2×D83)⋊C4C2312yes—
194C2×(C2×D83)⋊C4C2314yes—
195C2×(C2×D83)⋊C4C2314yes—
196C2×(C2×D83)⋊C4C2314yes—
197C2×(C2×D83)⋊C4C2312yes—
198C2×(C2×D83)⋊C4C2314yes—
199C2×C4×Dic83C2312yes—
200C2×C4×Dic83C2312yes—
201C2×C4×Dic83C2311yescharacteristic
202C2×C4×Dic83C2312yes—
203C2×C4×Dic83C2311yescharacteristic
204C2×C4×Dic83C2311yescharacteristic
205C2×C4×Dic83C2314yes—
206C2×C4×Dic83C2314yes—
207C42×D83C23116yes—
208C42×D83C2318yes—
209C22×Q8×C83C2311yescharacteristic
210C22×Q8×C83C2312yes—
211C22×D4×C83C2311yescharacteristic
212C23×C4×C83C2312yes—
213C4⋊Q8×C83C2318yes—
214#126×C83C23132yes—
215#124×C83C23116yes—
216C22⋊Q8×C83C23116yes—
217C4×Q8×C83C2318yes—
218C4×Q8×C83C23116yes—
219C4×D4×C83C2318yes—
220#117×C83C23116yes—
221C2×C4⋊C4×C83C2311yescharacteristic
222C2×C4⋊C4×C83C2312yes—
223C2×C4⋊C4×C83C2311yescharacteristic
224C2×C4⋊C4×C83C2314yes—
225C2×C4⋊C4×C83C2312yes—
226C2×C4⋊C4×C83C2312yes—
227C2×C22⋊C4×C83C2314yes—
228C2×C22⋊C4×C83C2312yes—
229C2×C22⋊C4×C83C2314yes—
230C2×C42×C83C2314yes—
231C2×C42×C83C2311yescharacteristic
232C2×C42×C83C2312yes—
233C23×D83C2412yes—
234C23×D83C2411yescharacteristic
235#13050590—264no—
236C2×Dic166—24no—
237C2×Dic166—28no—
238C2×Dic166—28no—
239C2×Dic166—44no—
240C2×Dic166C2414yes—
241C2×Dic166C2418yes—
242C2×Dic166C2418yes—
243C2×Dic166C2418yes—
244Q8×D83—232no—
245C2×D332—28no—
246C2×D332—24no—
247C2×D332C2418yes—
248C2×D332C2414yes—
249C2×C22⋊D83—28no—
250C2×C22⋊D83—28no—
251C2×C22⋊D83—44no—
252C2×C22⋊D83C2418yes—
253C2×C22⋊D83C2418yes—
254C2×C22⋊D83C2418yes—
255C22×Dic83—48no—
256C22×Dic83C2412yes—
257C22×Dic83C2414yes—
258C22×Dic83C2411yescharacteristic
259C22×Dic83C2412yes—
260C22×Dic83C2412yes—
261C22×Dic83C2411yescharacteristic
262C22×Dic83C24116yes—
263C22×Dic83C2411yescharacteristic
264C2×C4×D83—28no—
265C2×C4×D83—28no—
266C2×C4×D83—24no—
267C2×C4×D83—44no—
268C2×C4×D83—48no—
269C2×C4×D83—42no—
270C2×C4×D83#4118yes—
271C2×C4×D83C2414yes—
272C2×C4×D83C2418yes—
273C2×C4×D83C2418yes—
274C2×C4×D83C2414yes—
275C2×C4×D83C24116yes—
276C2×C4×D83C2418yes—
277C2×C4×D83C2414yes—
278C4⋊Dic83C2414yes—
279C4⋊Dic83C2418yes—
280C4⋊Dic83C2418yes—
281C4⋊Dic83C24116yes—
282C4⋊Dic83C24116yes—
283C4⋊Dic83C24116yes—
284C4⋊Dic83C2418yes—
285C4⋊Dic83C2414yes—
286Dic83⋊C4C2418yes—
287Dic83⋊C4C24116yes—
288Dic83⋊C4C24116yes—
289Dic83⋊C4C2418yes—
290Dic83⋊C4C24116yes—
291Dic83⋊C4C24116yes—
292Dic83⋊C4C2418yes—
293Dic83⋊C4C2418yes—
294C22⋊Dic83C2418yes—
295C22⋊Dic83C24116yes—
296(C2×D83)⋊C4C2418yes—
297(C2×D83)⋊C4C2418yes—
298(C2×D83)⋊C4C24116yes—
299(C2×D83)⋊C4C24116yes—
300(C2×D83)⋊C4C24116yes—
301(C2×D83)⋊C4C24116yes—
302C4×Dic83C2414yes—
303C4×Dic83C24116yes—
304C4×Dic83C2418yes—
305C4×Dic83C2414yes—
306C4×Dic83C24116yes—
307C4×Dic83C2418yes—
308C4×Dic83C2418yes—
309C4×Dic83C2414yes—
310C24×C83C2412yes—
311C2×Q8×C83—24no—
312C2×Q8×C83—28no—
313C2×Q8×C83C2414yes—
314C2×Q8×C83C2418yes—
315C2×D4×C83—24no—
316C2×D4×C83C2414yes—
317C22×C4×C83—28no—
318C22×C4×C83C2418yes—
319C22×C4×C83C2412yes—
320C22×C4×C83C2411yescharacteristic
321C22×C4×C83C2412yes—
322C22×C4×C83C2412yes—
323C22×C4×C83C2414yes—
324C22×C4×C83C2411yescharacteristic
325C22×C4×C83C2411yescharacteristic
326C4⋊C4×C83C2414yes—
327C4⋊C4×C83C2418yes—
328C4⋊C4×C83C2418yes—
329C4⋊C4×C83C2418yes—
330C4⋊C4×C83C24116yes—
331C4⋊C4×C83C2414yes—
332C22⋊C4×C83C2418yes—
333C22⋊C4×C83C24116yes—
334C22⋊C4×C83C24116yes—
335C42×C83C24116yes—
336C42×C83C2418yes—
337C42×C83C2414yes—
338C23×C83—24no—
339C23×C83—24no—
340C23×C83—24no—
341C23×C83C2514yes—
342C23×C83C2511yescharacteristic
343C22×D83—22no—
344C22×D83—22no—
345C22×D83—24no—
346C22×D83—24no—
347C22×D83—24no—
348C22×D83C2×#4114yes—
349C22×D83C2514yes—
350C22×D83C2512yes—
351Q8×C83—28no—
352Q8×C83—216no—
353D4×C83—28no—
354C2×C4×C83—24no—
355C2×C4×C83—24no—
356C2×C4×C83—28no—
357C2×C4×C83—24no—
358C2×C4×C83—22no—
359C2×C4×C83—216no—
360C2×C4×C83C2×#4114yes—
361C2×C4×C832−1+414yes—
362C2×C4×C83C2514yes—
363C2×C4×C83C2514yes—
364C2×C4×C83C2512yes—
365C2×C4×C83C2518yes—
366C2×C4×C83C2514yes—
367C2×C4×C83C2512yes—
368C2×C4×C83C2512yes—
369C22⋊D83—216no—
370C22⋊D83—216no—
371C22⋊D83—48no—
372C2×Dic83—24no—
373C2×Dic83—24no—
374C2×Dic83—22no—
375C2×Dic83—24no—
376C2×Dic83—28no—
377C2×Dic83—22no—
378C2×Dic83—416no—
379C2×Dic83C2×#4114yes—
380C2×Dic83C2512yes—
381C2×Dic83C2514yes—
382C2×Dic83C2514yes—
383C2×Dic83C2514yes—
384C2×Dic83C2512yes—
385C2×Dic83C2518yes—
386C2×Dic83C2512yes—
387D332—216no—
388D332—28no—
389C4×D83—216no—
390C4×D83—216no—
391C4×D83—28no—
392C4×D83—416no—
393C4×D83—48no—
394C4×D83—44no—
395C4×D83C2×#41116yes—
396Dic166—28no—
397Dic166—216no—
398Dic166—216no—
399Dic166—48no—
400C22×C83—24no—
401C22×C83—24no—
402C22×C83—24no—
403C22×C83—48no—
404C22×C83C22×#4112yes—
405C22×C83C2×2−1+412yes—
406C22×C83#58512yes—
407C22×C83C2611yescharacteristic
408C2×D83—22no—
409C2×D83—22no—
410C2×D83—28no—
411C2×D83—24no—
412C2×D83—24no—
413C2×D83—24no—
414C2×D83—48no—
415C2×D83C22×#4114yes—
416C4×C83—24no—
417C4×C83—24no—
418C4×C83—28no—
419C4×C83—22no—
420C4×C83—24no—
421C4×C83C22×#4114yes—
422C4×C83C2×2−1+414yes—
423Dic83—24no—
424Dic83—24no—
425Dic83—22no—
426Dic83—28no—
427Dic83—24no—
428Dic83—22no—
429Dic83C22×#4114yes—
430C2×#3507—831nomaximal, Sylow
431C2×C83—44no—
432C2×C83#350714yescomplemented
433C2×C83C23×#4111yescharacteristic
434C2×C83C22×2−1+411yescharacteristic
435C2×C83C2×#58511yescharacteristic
436D83—24no—
437D83—44no—
438#3507—8332no—
439C2×#559—832no—
440C2×#557—832no—
441C2×#556—831no—
442C2×#556—834no—
443C2×#556D8311yescharacteristic, complemented
444C2×#554—831no—
445C2×#554—831no—
446C2×#552—832no—
447C2×#552—832no—
448C2×#539—834no—
449C2×#536—832no—
450C2×#533—831no—
451C2×#532—831no—
452C2×#529—832no—
453C2×#529—832no—
454C2×#520—832no—
455C22×C4×Q8—831no—
456C83C2×#350711yescharacteristic, complemented, Sylow
457C22×#41—832no—
458C23×Q8—831no—
459#559—8332no—
460#557—8332no—
461#556—8316no—
462#556—8364no—
463#556C2×D83116yescomplemented
464#554—8316no—
465#554—8316no—
466#552—8332no—
467#552—8332no—
468#539—8364no—
469#536—8332no—
470#533—8316no—
471#532—8316no—
472C2×C4⋊Q8—831no—
473C2×C4⋊Q8—834no—
474C2×C4⋊Q8—831no—
475C2×C4⋊Q8C2×D8311yescharacteristic
476C2×#127—831no—
477#529—8332no—
478#529—8332no—
479C2×#126—834no—
480C2×#126—834no—
481C2×#126—834no—
482C2×#126C2×D8314yes—
483C2×#125—832no—
484C2×#125—832no—
485C2×#125—834no—
486C2×#125—832no—
487C2×#125—834no—
488C2×#124—832no—
489C2×#124—832no—
490C2×#124—834no—
491C2×#124C2×D8312yes—
492C2×#123—834no—
493C2×#123—834no—
494C2×#123—834no—
495C2×#123—834no—
496C2×C22⋊Q8—832no—
497C2×C22⋊Q8—832no—
498C2×C22⋊Q8—832no—
499C2×C22⋊Q8—832no—
500C2×C22⋊Q8—832no—
501C2×C22⋊Q8—834no—
502C2×C22⋊Q8—834no—
503C2×C22⋊Q8C2×D8312yes—
504C2×#121—831no—
505C2×#121—831no—
506C2×#121—832no—
507#520—8332no—
508C2×C4×Q8—831no—
509C2×C4×Q8—832no—
510C2×C4×Q8—832no—
511C2×C4×Q8—8316no—
512C2×C4×Q8—831no—
513C2×C4×Q8—832no—
514C2×C4×Q8—832no—
515C2×C4×Q8—831no—
516C2×C4×Q8—832no—
517C2×C4×Q8—834no—
518C2×C4×Q8C2×D8311yescharacteristic
519C2×C4×Q8C2×D8312yes—
520C2×C4×D4—832no—
521C2×C4×D4—832no—
522C2×C4×D4—834no—
523C2×C4×D4—834no—
524C2×C4×D4—834no—
525C2×C4×D4—832no—
526C2×C4×D4—831no—
527C2×C4×D4C2×D8311yescharacteristic
528C2×#117—832no—
529C2×#117—832no—
530C2×#117—834no—
531C2×#117—834no—
532C2×#117C2×D8312yes—
533C22×C4⋊C4—832no—
534C22×C4⋊C4—831no—
535C22×C4⋊C4—832no—
536C22×C4⋊C4—832no—
537C22×C42—832no—
538C22×C42—831no—
539C2×#41—8316no—
540C2×#41—16616no—
541C22×Q8—838no—
542C22×Q8—832no—
543C22×Q8—831no—
544C22×Q8—832no—
545C22×Q8—832no—
546C22×Q8—1668no—
547C22×Q8C22×D8312yes—
548C22×Q8C22×D8311yescharacteristic
549C22×D4—832no—
550C22×D4—832no—
551C22×D4—832no—
552C22×D4—831no—
553C22×D4—832no—
554C22×D4C22×D8311yescharacteristic
555C23×C4—834no—
556C23×C4—832no—
557C23×C4—831no—
558C23×C4—834no—
559C23×C4—831no—
560C23×C4—832no—
561C23×C4—832no—
562C23×C4—831no—
563C23×C4C22×D8312yes—
564C4⋊Q8—838no—
565C4⋊Q8—8332no—
566C4⋊Q8—838no—
567C4⋊Q8C22×D8318yes—
568#127—838no—
569#126—8332no—
570#126—8332no—
571#126—8332no—
572#126C22×D83132yes—
573#125—8316no—
574#125—8316no—
575#125—8332no—
576#125—8316no—
577#125—8332no—
578#124—8316no—
579#124—8316no—
580#124—8332no—
581#124C22×D83116yes—
582#123—8332no—
583#123—8332no—
584#123—8332no—
585#123—8332no—
586C22⋊Q8—8316no—
587C22⋊Q8—8316no—
588C22⋊Q8—8316no—
589C22⋊Q8—8332no—
590C22⋊Q8—8316no—
591C22⋊Q8—8316no—
592C22⋊Q8—8332no—
593C22⋊Q8C22×D83116yes—
594#121—838no—
595#121—838no—
596#121—8316no—
597C4×Q8—838no—
598C4×Q8—8316no—
599C4×Q8—8316no—
600C4×Q8—838no—
601C4×Q8—8316no—
602C4×Q8—8316no—
603C4×Q8—838no—
604C4×Q8—8316no—
605C4×Q8—8332no—
606C4×Q8C22×D8318yes—
607C4×Q8C22×D83116yes—
608C4×D4—8316no—
609C4×D4—8316no—
610C4×D4—8332no—
611C4×D4—8332no—
612C4×D4—8332no—
613C4×D4—8316no—
614C4×D4—838no—
615C4×D4C22×D8318yes—
616#117—8316no—
617#117—8316no—
618#117—8332no—
619#117—8332no—
620#117C22×D83116yes—
621C2×C4⋊C4—831no—
622C2×C4⋊C4—832no—
623C2×C4⋊C4—832no—
624C2×C4⋊C4—834no—
625C2×C4⋊C4—834no—
626C2×C4⋊C4—832no—
627C2×C4⋊C4—832no—
628C2×C4⋊C4—832no—
629C2×C4⋊C4—8316no—
630C2×C4⋊C4—834no—
631C2×C4⋊C4—834no—
632C2×C4⋊C4—834no—
633C2×C4⋊C4—832no—
634C2×C4⋊C4—831no—
635C2×C4⋊C4—832no—
636C2×C4⋊C4—834no—
637C2×C4⋊C4—834no—
638C2×C4⋊C4—838no—
639C2×C4⋊C4—8316no—
640C2×C4⋊C4—8316no—
641C2×C4⋊C4C22×D8311yescharacteristic
642C2×C4⋊C4C22×D8312yes—
643C2×C4⋊C4C22×D8312yes—
644C2×C4⋊C4C22×D8311yescharacteristic
645C2×C4⋊C4C22×D8312yes—
646C2×C4⋊C4C22×D8314yes—
647C2×C22⋊C4—832no—
648C2×C22⋊C4—834no—
649C2×C22⋊C4—832no—
650C2×C22⋊C4—834no—
651C2×C22⋊C4—834no—
652C2×C22⋊C4—834no—
653C2×C22⋊C4—832no—
654C2×C22⋊C4—834no—
655C2×C22⋊C4C22×D8314yes—
656C2×C22⋊C4C22×D8314yes—
657C2×C22⋊C4C22×D8312yes—
658C2×C42—834no—
659C2×C42—832no—
660C2×C42—832no—
661C2×C42—834no—
662C2×C42—831no—
663C2×C42—832no—
664C2×C42—831no—
665C2×C42—831no—
666C2×C42—8316no—
667C2×C42—838no—
668C2×C42C22×D8314yes—
669C2×C42C22×D8311yescharacteristic
670C2×C42C22×D8312yes—
671C24—831no—
672C24—832no—
673C24C23×D8312yes—
674#41—16664no—
675C2×Q8—24no—
676C2×Q8—28no—
677C2×Q8—3324no—
678C2×Q8—838no—
679C2×Q8—834no—
680C2×Q8—838no—
681C2×Q8—838no—
682C2×Q8—1668no—
683C2×Q8—1668no—
684C2×Q8—16632no—
685C2×Q8—1664no—
686C2×Q8C23×D8318yes—
687C2×Q8C23×D8314yes—
688C2×D4—24no—
689C2×D4—3324no—
690C2×D4—838no—
691C2×D4—838no—
692C2×D4—838no—
693C2×D4—834no—
694C2×D4—838no—
695C2×D4—1668no—
696C2×D4—1668no—
697C2×D4—1668no—
698C2×D4—1664no—
699C2×D4C23×D8314yes—
700C22×C4—28no—
701C22×C4—3324no—
702C22×C4—3328no—
703C22×C4—3322no—
704C22×C4—3328no—
705C22×C4—8316no—
706C22×C4—838no—
707C22×C4—834no—
708C22×C4—8316no—
709C22×C4—831no—
710C22×C4—838no—
711C22×C4—834no—
712C22×C4—831no—
713C22×C4—832no—
714C22×C4—832no—
715C22×C4—832no—
716C22×C4—831no—
717C22×C4—834no—
718C22×C4—834no—
719C22×C4—838no—
720C22×C4—838no—
721C22×C4—1668no—
722C22×C4—1668no—
723C22×C4—1664no—
724C22×C4C23×D8318yes—
725C22×C4C23×D8314yes—
726C22×C4C23×D8312yes—
727C22×C4C23×D8312yes—
728C22×C4C23×D8311yescharacteristic
729C22×C4C23×D8312yes—
730C22×C4C23×D8311yescharacteristic
731C22×C4C23×D8311yescharacteristic
732C4⋊C4—834no—
733C4⋊C4—838no—
734C4⋊C4—838no—
735C4⋊C4—8316no—
736C4⋊C4—8316no—
737C4⋊C4—838no—
738C4⋊C4—838no—
739C4⋊C4—838no—
740C4⋊C4—8316no—
741C4⋊C4—8316no—
742C4⋊C4—8316no—
743C4⋊C4—838no—
744C4⋊C4—834no—
745C4⋊C4—838no—
746C4⋊C4—8316no—
747C4⋊C4—8316no—
748C4⋊C4C23×D8314yes—
749C4⋊C4C23×D8318yes—
750C4⋊C4C23×D8318yes—
751C4⋊C4C23×D8314yes—
752C4⋊C4C23×D8318yes—
753C4⋊C4C23×D83116yes—
754C22⋊C4—838no—
755C22⋊C4—8316no—
756C22⋊C4—838no—
757C22⋊C4—8316no—
758C22⋊C4—8316no—
759C22⋊C4—8316no—
760C22⋊C4—838no—
761C22⋊C4—8316no—
762C22⋊C4C23×D83116yes—
763C22⋊C4C23×D83116yes—
764C22⋊C4C23×D8318yes—
765C42—838no—
766C42—838no—
767C42—834no—
768C42—838no—
769C42—834no—
770C42—834no—
771C42—8316no—
772C42—8316no—
773C42C23×D8314yes—
774C42C23×D8318yes—
775C42C23×D83116yes—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—834no—
780C23—832no—
781C23—834no—
782C23—1664no—
783C23—1664no—
784C23—1664no—
785C23—1662no—
786C23—1662no—
787C23C24×D8314yes—
788C23C24×D8311yescharacteristic
789Q8—28no—
790Q8—216no—
791Q8—3328no—
792Q8—16616no—
793Q8—16616no—
794Q8—1668no—
795D4—28no—
796D4—3328no—
797D4—16616no—
798D4—16616no—
799D4—16616no—
800D4—1668no—
801C2×C4—24no—
802C2×C4—24no—
803C2×C4—28no—
804C2×C4—24no—
805C2×C4—22no—
806C2×C4—216no—
807C2×C4—3328no—
808C2×C4—33216no—
809C2×C4—3324no—
810C2×C4—33216no—
811C2×C4—834no—
812C2×C4—832no—
813C2×C4—8316no—
814C2×C4—832no—
815C2×C4—834no—
816C2×C4—834no—
817C2×C4—834no—
818C2×C4—832no—
819C2×C4—838no—
820C2×C4—16616no—
821C2×C4—1664no—
822C2×C4—1664no—
823C2×C4—1662no—
824C2×C4—1664no—
825C2×C4—1668no—
826C2×C4—1662no—
827C2×C4—16616no—
828C2×C4—1668no—
829C2×C4#41×D8314yes—
830C2×C4#1458183914yes—
831C2×C4C24×D8318yes—
832C2×C4C24×D8314yes—
833C2×C4C24×D8314yes—
834C2×C4C24×D8312yes—
835C2×C4C24×D8314yes—
836C2×C4C24×D8312yes—
837C2×C4C24×D8312yes—
838C22—24no—
839C22—24no—
840C22—24no—
841C22—48no—
842C22—3328no—
843C22—834no—
844C22—1664no—
845C22—1664no—
846C22—1664no—
847C22—1662no—
848C22—1662no—
849C22—1668no—
850C22C2×#41×D8312yes—
851C22C2×#1458183912yes—
852C22#1912853812yes—
853C22C25×D8311yescharacteristic
854C4—24no—
855C4—24no—
856C4—28no—
857C4—24no—
858C4—22no—
859C4—834no—
860C4—1664no—
861C4—1664no—
862C4—1662no—
863C4—1664no—
864C4—1668no—
865C4—1662no—
866C4C2×#41×D8314yes—
867C4C2×#1458183914yes—
868C2—44no—
869C2—3324no—
870C2—1664no—
871C2#2492131814yesdirect product factor
872C2C22×#41×D8311yescharacteristic
873C2C22×#1458183911yescharacteristic
874C2C2×#1912853811yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#556×C83C2
socleC23×C83C25
prime radicalC2×#19128248C2
hypercenterC2×#556D83
hypocenterC83C2×#3507
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. #24921318C2direct (N × H)
2. C2×#19128433C2semidirect
3. C2×#19128427C2semidirect
4. C2×#19128425C2semidirect
5. C2×#19128418C2semidirect
6. C2×#19128411C2semidirect
7. C2×#19128408C2semidirect
8. C2×#19128393C2semidirect
9. C2×#19128390C2semidirect
10. C2×#19128292C2semidirect
11. C2×#19128274C2semidirect
12. C2×#19128256C2semidirect
14. C2×#19128238C2semidirect
15. C2×#19128230C2semidirect
16. C2×#19128181C2semidirect
17. C2×C4×Q8×D83C2semidirect
18. C2×#556×C83C2semidirect
21. #19128433C22semidirect
22. #19128427C22semidirect
23. #19128425C22semidirect
24. #19128418C22semidirect
25. #19128411C22semidirect
26. #19128408C22semidirect
27. #19128393C22semidirect
28. #19128390C22semidirect
29. #19128292C22semidirect
30. #19128274C22semidirect
31. #19128256C22semidirect
37. #19128238C22semidirect
38. #19128230C22semidirect
64. #19128181C22semidirect
74. C4×Q8×D83C22semidirect
92. #556×C83C22semidirect
432. C2×C83#3507semidirect
443. C2×#556D83semidirect
456. C83C2×#3507semidirect
463. #556C2×D83semidirect
871. C2#24921318direct (N × H)

Maximal subgroups

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

subgroupindex
#249213182
C2×#191284332
C2×#191284272
C2×#191284252
C2×#191284182
C2×#191284112
C2×#191284082
C2×#191283932
C2×#191283902
C2×#191282922
C2×#191282742
C2×#191282562
C2×#191282482
C2×#191282382
C2×#191282302
C2×#191281812
C2×C4×Q8×D832
C2×#556×C832
C2×#350783