Finite Group Databasebeta

← C2×#24921905 #36312010

Subgroups — C2×#24921905 #36312010

Order 21248.

7086 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921905C2132yesmaximal, direct product factor
2C2×#19128452C214yesmaximal, complemented
3C2×#19128429C211yesmaximal, characteristic, complemented
4C2×#19128425C211yesmaximal, characteristic, complemented
5C2×#19128412C212yesmaximal, complemented
6C2×#19128401C212yesmaximal, complemented
7C2×Q8×C22⋊D83C212yesmaximal, complemented
8C2×#19128361C212yesmaximal, complemented
9C2×#19128356C211yesmaximal, characteristic, complemented
10C2×#19128328C212yesmaximal, complemented
11C2×#19128316C212yesmaximal, complemented
12C2×#19128311C212yesmaximal, complemented
13C2×#19128297C214yesmaximal, complemented
14C2×#19128275C212yesmaximal, complemented
15C2×C4⋊Q8×D83C211yesmaximal, characteristic, complemented
16C2×#19128238C211yesmaximal, characteristic, complemented
17C2×#19128233C211yesmaximal, characteristic, complemented
18C2×D4×Q8×C83C211yesmaximal, characteristic, complemented
19C22×#13050590C2212yes—
20C22×Q8×D83C2212yes—
21#19128452C22164yescomplemented
22#19128429C22116yescomplemented
23#19128425C22116yescomplemented
24#19128412C22132yescomplemented
25#19128401C22132yescomplemented
26Q8×C22⋊D83C22132yescomplemented
27#19128361C22132yescomplemented
28#19128356C22116yescomplemented
29#19128328C22132yescomplemented
30#19128316C22132yescomplemented
31#19128311C22132yescomplemented
32#19128297C22164yescomplemented
33#19128275C22132yescomplemented
34C2×#14581792C2211yescharacteristic
35C2×#14581791C2212yes—
36C2×#14581791C2212yes—
37C2×#14581790C2214yes—
38C2×#14581790C2212yes—
39C2×#14581790C2212yes—
40C4⋊Q8×D83C22116yescomplemented
41#19128238C22116yescomplemented
42#19128233C22116yescomplemented
43C2×#14581787C2212yes—
44C2×#14581787C2214yes—
45C2×#14581785C2214yes—
46C2×#14581785C2212yes—
47C2×#14581785C2214yes—
48C2×#14581784C2212yes—
49C2×#14581783C2211yescharacteristic
50C2×#14581783C2211yescharacteristic
51C2×#14581783C2214yes—
52C2×#14581782C2214yes—
53C2×#14581782C2214yes—
54C2×#14581781C2212yes—
55C2×#14581781C2211yescharacteristic
56C2×#14581779C2211yescharacteristic
57C2×#14581778C2214yes—
58C2×#14581777C2212yes—
59C2×#14581775C2214yes—
60C2×#14581775C2214yes—
61C2×#14581774C2214yes—
62C2×#14581774C2212yes—
63C2×#14581772C2212yes—
64C2×#14581772C2211yescharacteristic
65C2×#14581771C2214yes—
66C2×#14581771C2212yes—
67C2×#14581770C2214yes—
68C2×#14581768C2214yes—
69C2×#14581768C2211yescharacteristic
70C2×#14581768C2214yes—
71C2×#14581768C2214yes—
72C2×#14581767C2211yescharacteristic
73C2×#14581765C2214yes—
74C2×#14581763C2212yes—
75C2×#14581763C2211yescharacteristic
76C2×Q8×Dic83C2212yes—
77C2×C4×Dic166C2212yes—
78C2×C4×Dic166C2211yescharacteristic
79C2×#14581757C2212yes—
80C2×C4×D332C2211yescharacteristic
81C2×C4×D332C2212yes—
82C2×#14581754C2214yes—
83C2×C4×C22⋊D83C2212yes—
84C2×C4×C22⋊D83C2214yes—
85C2×#14581751C2212yes—
86C2×#14581750C2212yes—
87C2×#14581749C2212yes—
88C2×C4⋊C4×D83C2212yes—
89C2×C4⋊C4×D83C2212yes—
90C2×C4⋊C4×D83C2212yes—
91C2×C42×D83C2211yescharacteristic
92C23×Q8×C83C2212yes—
93D4×Q8×C83C22116yescomplemented
94C2×C4⋊Q8×C83C2212yes—
95C2×C4⋊Q8×C83C2211yescharacteristic
96C2×C22⋊Q8×C83C2212yes—
97C2×C22⋊Q8×C83C2214yes—
98C2×C4×Q8×C83C2211yescharacteristic
99C2×C4×D4×C83C2212yes—
100C2×C4×D4×C83C2211yescharacteristic
101C2×#13050590—48no—
102C2×#13050590C23116yes—
103C22×Dic166C2312yes—
104C22×Dic166C2311yescharacteristic
105C22×Dic166C2314yes—
106C2×Q8×D83—48no—
107C2×Q8×D83C23116yes—
108C22×D332C2312yes—
109C22×D332C2311yescharacteristic
110C22×C22⋊D83C2312yes—
111C22×C22⋊D83C2314yes—
112C22×C4×D83C2311yescharacteristic
113C22×C4×D83C2311yescharacteristic
114C22×C4×D83C2311yescharacteristic
115C22×C4×D83C2312yes—
116C22×C4×D83C2314yes—
117C22×C4×D83C2314yes—
118#14581792C2318yes—
119#14581791C23116yes—
120#14581791C23116yes—
121#14581790C23132yes—
122#14581790C23116yes—
123#14581790C23116yes—
124#14581787C23132yes—
125#14581787C23116yes—
126#14581785C23132yes—
127#14581785C23116yes—
128#14581785C23132yes—
129#14581784C23116yes—
130#14581783C2318yes—
131#14581783C23132yes—
132#14581783C2318yes—
133#14581782C23132yes—
134#14581782C23132yes—
135#14581781C23116yes—
136#14581781C2318yes—
137#14581779C2318yes—
138#14581778C23132yes—
139#14581777C23116yes—
140#14581775C23132yes—
141#14581775C23132yes—
142#14581774C23132yes—
143#14581774C23116yes—
144#14581772C2318yes—
145#14581772C23116yes—
146#14581771C23116yes—
147#14581771C23132yes—
148#14581770C23132yes—
149#14581768C23132yes—
150#14581768C2318yes—
151#14581768C23132yes—
152#14581768C23132yes—
153#14581767C2318yes—
154#14581765C23132yes—
155#14581763C23116yes—
156#14581763C2318yes—
157Q8×Dic83C23116yes—
158C4×Dic166C23116yes—
159C4×Dic166C2318yes—
160#14581757C23116yes—
161C4×D332C2318yes—
162C4×D332C23116yes—
163#14581754C23132yes—
164C4×C22⋊D83C23116yes—
165C4×C22⋊D83C23132yes—
166#14581751C23116yes—
167#14581750C23116yes—
168#14581749C23116yes—
169C2×C4⋊Dic83C2312yes—
170C2×C4⋊Dic83C2312yes—
171C2×C4⋊Dic83C2311yescharacteristic
172C2×C4⋊Dic83C2312yes—
173C2×C4⋊Dic83C2312yes—
174C2×C4⋊Dic83C2311yescharacteristic
175C2×C4⋊Dic83C2312yes—
176C2×C4⋊Dic83C2314yes—
177C2×Dic83⋊C4C2314yes—
178C2×Dic83⋊C4C2314yes—
179C2×Dic83⋊C4C2314yes—
180C2×Dic83⋊C4C2312yes—
181C2×Dic83⋊C4C2312yes—
182C2×Dic83⋊C4C2314yes—
183C2×Dic83⋊C4C2312yes—
184C2×Dic83⋊C4C2314yes—
185C2×Dic83⋊C4C2314yes—
186C2×Dic83⋊C4C2312yes—
187C4⋊C4×D83C23116yes—
188C4⋊C4×D83C23116yes—
189C4⋊C4×D83C23116yes—
190C2×C22⋊Dic83C2312yes—
191C2×C22⋊Dic83C2312yes—
192C2×C22⋊Dic83C2314yes—
193C2×C22⋊Dic83C2312yes—
194C2×(C2×D83)⋊C4C2312yes—
195C2×(C2×D83)⋊C4C2312yes—
196C2×(C2×D83)⋊C4C2314yes—
197C2×(C2×D83)⋊C4C2312yes—
198C2×(C2×D83)⋊C4C2312yes—
199C2×(C2×D83)⋊C4C2314yes—
200C2×(C2×D83)⋊C4C2312yes—
201C2×(C2×D83)⋊C4C2312yes—
202C2×C4×Dic83C2311yescharacteristic
203C2×C4×Dic83C2311yescharacteristic
204C2×C4×Dic83C2311yescharacteristic
205C2×C4×Dic83C2314yes—
206C2×C4×Dic83C2312yes—
207C2×C4×Dic83C2314yes—
208C42×D83C2318yes—
209C22×Q8×C83—48no—
210C22×Q8×C83C2311yescharacteristic
211C22×Q8×C83C2312yes—
212C22×Q8×C83C23116yes—
213C22×Q8×C83C2314yes—
214C22×D4×C83C2311yescharacteristic
215C23×C4×C83C2312yes—
216C23×C4×C83C2314yes—
217C4⋊Q8×C83C23116yes—
218C4⋊Q8×C83C2318yes—
219C22⋊Q8×C83C23116yes—
220C22⋊Q8×C83C23132yes—
221C4×Q8×C83C2318yes—
222C4×D4×C83C2318yes—
223C4×D4×C83C23116yes—
224C2×C4⋊C4×C83C2311yescharacteristic
225C2×C4⋊C4×C83C2312yes—
226C2×C4⋊C4×C83C2311yescharacteristic
227C2×C4⋊C4×C83C2312yes—
228C2×C4⋊C4×C83C2312yes—
229C2×C4⋊C4×C83C2314yes—
230C2×C22⋊C4×C83C2314yes—
231C2×C22⋊C4×C83C2312yes—
232C2×C42×C83C2311yescharacteristic
233C2×C42×C83C2312yes—
234C23×D83C2412yes—
235C23×D83C2411yescharacteristic
236#13050590—432no—
237C2×Dic166—28no—
238C2×Dic166—24no—
239C2×Dic166—48no—
240C2×Dic166C2418yes—
241C2×Dic166C2414yes—
242C2×Dic166C24116yes—
243Q8×D83—432no—
244C2×D332—28no—
245C2×D332—24no—
246C2×D332C2418yes—
247C2×D332C2414yes—
248C2×C22⋊D83—28no—
249C2×C22⋊D83—48no—
250C2×C22⋊D83C2418yes—
251C2×C22⋊D83C24116yes—
252C22×Dic83C2414yes—
253C22×Dic83C2411yescharacteristic
254C22×Dic83C2411yescharacteristic
255C22×Dic83C2411yescharacteristic
256C22×Dic83C2412yes—
257C22×Dic83C2412yes—
258C22×Dic83C2412yes—
259C2×C4×D83—24no—
260C2×C4×D83—24no—
261C2×C4×D83—24no—
262C2×C4×D83—28no—
263C2×C4×D83—48no—
264C2×C4×D83—48no—
265C2×C4×D83C2414yes—
266C2×C4×D83C2418yes—
267C2×C4×D83C2414yes—
268C2×C4×D83C2414yes—
269C2×C4×D83C24116yes—
270C2×C4×D83C24116yes—
271C4⋊Dic83C2414yes—
272C4⋊Dic83C2418yes—
273C4⋊Dic83C2418yes—
274C4⋊Dic83C2418yes—
275C4⋊Dic83C2414yes—
276C4⋊Dic83C24116yes—
277C4⋊Dic83C2418yes—
278C4⋊Dic83C2418yes—
279Dic83⋊C4C24116yes—
280Dic83⋊C4C24116yes—
281Dic83⋊C4C2418yes—
282Dic83⋊C4C24116yes—
283Dic83⋊C4C24116yes—
284Dic83⋊C4C24116yes—
285Dic83⋊C4C24116yes—
286Dic83⋊C4C2418yes—
287Dic83⋊C4C2418yes—
288Dic83⋊C4C2418yes—
289C22⋊Dic83C24116yes—
290C22⋊Dic83C2418yes—
291C22⋊Dic83C2418yes—
292C22⋊Dic83C2418yes—
293(C2×D83)⋊C4C24116yes—
294(C2×D83)⋊C4C2418yes—
295(C2×D83)⋊C4C2418yes—
296(C2×D83)⋊C4C2418yes—
297(C2×D83)⋊C4C2418yes—
298(C2×D83)⋊C4C2418yes—
299(C2×D83)⋊C4C24116yes—
300(C2×D83)⋊C4C2418yes—
301C4×Dic83C24116yes—
302C4×Dic83C2414yes—
303C4×Dic83C2414yes—
304C4×Dic83C2418yes—
305C4×Dic83C24116yes—
306C4×Dic83C2414yes—
307C24×C83C2412yes—
308C2×Q8×C83—28no—
309C2×Q8×C83—24no—
310C2×Q8×C83—48no—
311C2×Q8×C83—432no—
312C2×Q8×C83C2414yes—
313C2×Q8×C83C2418yes—
314C2×Q8×C83C24116yes—
315C2×D4×C83—24no—
316C2×D4×C83C2414yes—
317C22×C4×C83—28no—
318C22×C4×C83—48no—
319C22×C4×C83C2418yes—
320C22×C4×C83C2412yes—
321C22×C4×C83C2414yes—
322C22×C4×C83C2411yescharacteristic
323C22×C4×C83C2412yes—
324C22×C4×C83C2412yes—
325C22×C4×C83C24116yes—
326C22×C4×C83C2411yescharacteristic
327C22×C4×C83C2411yescharacteristic
328C4⋊C4×C83C2414yes—
329C4⋊C4×C83C24116yes—
330C4⋊C4×C83C2414yes—
331C4⋊C4×C83C2418yes—
332C4⋊C4×C83C2418yes—
333C4⋊C4×C83C2418yes—
334C22⋊C4×C83C24116yes—
335C22⋊C4×C83C2418yes—
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×D832−1+414yes—
349C22×D83C2514yes—
350C22×D83C2512yes—
351Q8×C83—28no—
352Q8×C83—216no—
353Q8×C83—416no—
354D4×C83—28no—
355C2×C4×C83—24no—
356C2×C4×C83—24no—
357C2×C4×C83—28no—
358C2×C4×C83—22no—
359C2×C4×C83—24no—
360C2×C4×C83—216no—
361C2×C4×C83—416no—
362C2×C4×C83H(5,𝔽2)14yes—
363C2×C4×C832−1+414yes—
364C2×C4×C83C2514yes—
365C2×C4×C83C2512yes—
366C2×C4×C83C2514yes—
367C2×C4×C83C2518yes—
368C2×C4×C83C2514yes—
369C2×C4×C83C2512yes—
370C2×C4×C83C2512yes—
371C22⋊D83—216no—
372C22⋊D83—416no—
373C2×Dic83—22no—
374C2×Dic83—28no—
375C2×Dic83—22no—
376C2×Dic83—22no—
377C2×Dic83—24no—
378C2×Dic83—24no—
379C2×Dic83—24no—
380C2×Dic83C2514yes—
381C2×Dic83C2514yes—
382C2×Dic83C2512yes—
383C2×Dic83C2512yes—
384C2×Dic83C2514yes—
385C2×Dic83C2512yes—
386C2×Dic83C2518yes—
387D332—216no—
388D332—28no—
389C4×D83—28no—
390C4×D83—28no—
391C4×D83—28no—
392C4×D83—216no—
393C4×D83—416no—
394C4×D83—416no—
395Dic166—216no—
396Dic166—28no—
397Dic166—416no—
398C22×C83—24no—
399C22×C83—24no—
400C22×C83—24no—
401C22×C83—48no—
402C22×C83C2×H(5,𝔽2)12yes—
403C22×C83C2×2−1+412yes—
404C22×C83C2×2−1+412yes—
405C22×C83C2611yescharacteristic
406C2×D83—22no—
407C2×D83—22no—
408C2×D83—28no—
409C2×D83—24no—
410C2×D83—24no—
411C2×D83—24no—
412C2×D83—48no—
413C2×D83C2×2−1+414yes—
414C4×C83—28no—
415C4×C83—24no—
416C4×C83—24no—
417C4×C83—22no—
418C4×C83—24no—
419C4×C83C2×H(5,𝔽2)14yes—
420C4×C83C2×2−1+414yes—
421Dic83—28no—
422Dic83—22no—
423Dic83—24no—
424Dic83—22no—
425Dic83—22no—
426Dic83—24no—
427Dic83—24no—
428C2×#3552—831nomaximal, Sylow
429C2×C83—44no—
430C2×C83#355214yescomplemented
431C2×C83C22×H(5,𝔽2)11yescharacteristic
432C2×C83C22×2−1+411yescharacteristic
433C2×C83C22×2−1+411yescharacteristic
434D83—24no—
435D83—44no—
436#3552—8332no—
437C2×#563—834no—
438C2×#557—831no—
439C2×#556—831no—
440C2×#554—832no—
441C2×#553—832no—
442C2×D4×Q8—832no—
443C2×D4×Q8D8311yescharacteristic, complemented
444C2×#548—832no—
445C2×#547—831no—
446C2×#544—832no—
447C2×#542—832no—
448C2×#541—832no—
449C2×#539—834no—
450C2×#536—832no—
451C22×C4⋊Q8—831no—
452C2×#529—831no—
453C2×#529—831no—
454C83C2×#355211yescharacteristic, complemented, Sylow
455C22×#41—832no—
456C23×Q8—832no—
457C23×Q8C2×D8312yes—
458#563—8364no—
459#557—8316no—
460#556—8316no—
461#554—8332no—
462#553—8332no—
463D4×Q8—8332no—
464D4×Q8C2×D83116yescomplemented
465#548—8332no—
466#547—8316no—
467#544—8332no—
468#542—8332no—
469#541—8332no—
470#539—8364no—
471#536—8332no—
472C2×C4⋊Q8—832no—
473C2×C4⋊Q8—832no—
474C2×C4⋊Q8—834no—
475C2×C4⋊Q8—8316no—
476C2×C4⋊Q8—832no—
477C2×C4⋊Q8—832no—
478C2×C4⋊Q8—831no—
479C2×C4⋊Q8C2×D8311yescharacteristic
480C2×C4⋊Q8C2×D8312yes—
481#529—8316no—
482#529—8316no—
483C2×#126—832no—
484C2×#126—834no—
485C2×#126—832no—
486C2×#126—834no—
487C2×#126—834no—
488C2×#125—831no—
489C2×#125—831no—
490C2×#125—834no—
491C2×#125—834no—
492C2×#125—834no—
493C2×#125—832no—
494C2×#124—831no—
495C2×#124—832no—
496C2×#124—831no—
497C2×#124—834no—
498C2×#123—834no—
499C2×#123—834no—
500C2×#123—832no—
501C2×#123—832no—
502C2×#123—834no—
503C2×C22⋊Q8—831no—
504C2×C22⋊Q8—834no—
505C2×C22⋊Q8—834no—
506C2×C22⋊Q8—834no—
507C2×C22⋊Q8—832no—
508C2×C22⋊Q8—834no—
509C2×C22⋊Q8—831no—
510C2×C22⋊Q8—832no—
511C2×C22⋊Q8—834no—
512C2×C22⋊Q8C2×D8314yes—
513C2×C22⋊Q8C2×D8312yes—
514C2×#121—831no—
515C2×#121—832no—
516C2×#121—831no—
517C2×#121—834no—
518C2×C4×Q8—832no—
519C2×C4×Q8—832no—
520C2×C4×Q8—831no—
521C2×C4×Q8—832no—
522C2×C4×Q8C2×D8311yescharacteristic
523C2×C4×D4—832no—
524C2×C4×D4—834no—
525C2×C4×D4—834no—
526C2×C4×D4—831no—
527C2×C4×D4—832no—
528C2×C4×D4C2×D8311yescharacteristic
529C2×C4×D4C2×D8312yes—
530C2×#117—832no—
531C2×#117—832no—
532C2×#117—832no—
533C22×C4⋊C4—832no—
534C22×C4⋊C4—832no—
535C22×C4⋊C4—832no—
536C22×C42—831no—
537C2×#41—3328no—
538C2×#41—8316no—
539C22×Q8—48no—
540C22×Q8—3328no—
541C22×Q8—8316no—
542C22×Q8—834no—
543C22×Q8—831no—
544C22×Q8—832no—
545C22×Q8C22×D8312yes—
546C22×Q8C22×D8311yescharacteristic
547C22×Q8C22×D8314yes—
548C22×Q8C22×D83116yes—
549C22×D4—834no—
550C22×D4—832no—
551C22×D4—832no—
552C22×D4—831no—
553C22×D4C22×D8311yescharacteristic
554C23×C4—834no—
555C23×C4—834no—
556C23×C4—831no—
557C23×C4—831no—
558C23×C4—832no—
559C23×C4—831no—
560C23×C4C22×D8312yes—
561C23×C4C22×D8314yes—
562C4⋊Q8—8316no—
563C4⋊Q8—8316no—
564C4⋊Q8—8332no—
565C4⋊Q8—8316no—
566C4⋊Q8—8316no—
567C4⋊Q8—838no—
568C4⋊Q8C22×D8318yes—
569C4⋊Q8C22×D83116yes—
570#126—8316no—
571#126—8332no—
572#126—8316no—
573#126—8332no—
574#126—8332no—
575#125—838no—
576#125—838no—
577#125—8332no—
578#125—8332no—
579#125—8332no—
580#125—8316no—
581#124—838no—
582#124—8316no—
583#124—838no—
584#124—8332no—
585#123—8332no—
586#123—8332no—
587#123—8316no—
588#123—8316no—
589#123—8332no—
590C22⋊Q8—838no—
591C22⋊Q8—8332no—
592C22⋊Q8—8332no—
593C22⋊Q8—8332no—
594C22⋊Q8—8316no—
595C22⋊Q8—8332no—
596C22⋊Q8—8332no—
597C22⋊Q8—838no—
598C22⋊Q8—8316no—
599C22⋊Q8C22×D83132yes—
600C22⋊Q8C22×D83116yes—
601#121—838no—
602#121—8316no—
603#121—838no—
604#121—8332no—
605C4×Q8—8316no—
606C4×Q8—8316no—
607C4×Q8—838no—
608C4×Q8—8316no—
609C4×Q8C22×D8318yes—
610C4×D4—8316no—
611C4×D4—8332no—
612C4×D4—8332no—
613C4×D4—838no—
614C4×D4—8316no—
615C4×D4C22×D8318yes—
616C4×D4C22×D83116yes—
617#117—8316no—
618#117—8316no—
619#117—8316no—
620C2×C4⋊C4—832no—
621C2×C4⋊C4—834no—
622C2×C4⋊C4—834no—
623C2×C4⋊C4—834no—
624C2×C4⋊C4—832no—
625C2×C4⋊C4—831no—
626C2×C4⋊C4—832no—
627C2×C4⋊C4—832no—
628C2×C4⋊C4—832no—
629C2×C4⋊C4—832no—
630C2×C4⋊C4—831no—
631C2×C4⋊C4—832no—
632C2×C4⋊C4—834no—
633C2×C4⋊C4—832no—
634C2×C4⋊C4—834no—
635C2×C4⋊C4—834no—
636C2×C4⋊C4—834no—
637C2×C4⋊C4—832no—
638C2×C4⋊C4—8316no—
639C2×C4⋊C4—8316no—
640C2×C4⋊C4—8316no—
641C2×C4⋊C4C22×D8311yescharacteristic
642C2×C4⋊C4C22×D8312yes—
643C2×C4⋊C4C22×D8312yes—
644C2×C4⋊C4C22×D8314yes—
645C2×C4⋊C4C22×D8311yescharacteristic
646C2×C4⋊C4C22×D8312yes—
647C2×C22⋊C4—832no—
648C2×C22⋊C4—832no—
649C2×C22⋊C4—834no—
650C2×C22⋊C4—832no—
651C2×C22⋊C4—834no—
652C2×C22⋊C4—832no—
653C2×C22⋊C4—832no—
654C2×C22⋊C4—832no—
655C2×C22⋊C4—832no—
656C2×C22⋊C4—832no—
657C2×C22⋊C4—834no—
658C2×C22⋊C4—832no—
659C2×C22⋊C4C22×D8314yes—
660C2×C22⋊C4C22×D8312yes—
661C2×C42—831no—
662C2×C42—831no—
663C2×C42—832no—
664C2×C42—834no—
665C2×C42—834no—
666C2×C42—831no—
667C2×C42—838no—
668C2×C42C22×D8312yes—
669C2×C42C22×D8311yescharacteristic
670C24—831no—
671C24—832no—
672C24C23×D8312yes—
673#41—33232no—
674C2×Q8—24no—
675C2×Q8—28no—
676C2×Q8—48no—
677C2×Q8—432no—
678C2×Q8—3328no—
679C2×Q8—33232no—
680C2×Q8—8316no—
681C2×Q8—834no—
682C2×Q8—838no—
683C2×Q8—1668no—
684C2×Q8—1664no—
685C2×Q8C23×D8318yes—
686C2×Q8C23×D8314yes—
687C2×Q8C23×D83116yes—
688C2×D4—24no—
689C2×D4—3328no—
690C2×D4—8316no—
691C2×D4—838no—
692C2×D4—838no—
693C2×D4—834no—
694C2×D4—1668no—
695C2×D4—1668no—
696C2×D4—1664no—
697C2×D4C23×D8314yes—
698C22×C4—28no—
699C22×C4—48no—
700C22×C4—3328no—
701C22×C4—3328no—
702C22×C4—8316no—
703C22×C4—8316no—
704C22×C4—832no—
705C22×C4—832no—
706C22×C4—831no—
707C22×C4—831no—
708C22×C4—832no—
709C22×C4—831no—
710C22×C4—834no—
711C22×C4—834no—
712C22×C4—834no—
713C22×C4—834no—
714C22×C4—838no—
715C22×C4—1664no—
716C22×C4—1664no—
717C22×C4—1668no—
718C22×C4—1664no—
719C22×C4C23×D8318yes—
720C22×C4C23×D8312yes—
721C22×C4C23×D8311yescharacteristic
722C22×C4C23×D8314yes—
723C22×C4C23×D8312yes—
724C22×C4C23×D8312yes—
725C22×C4C23×D83116yes—
726C22×C4C23×D8311yescharacteristic
727C22×C4C23×D8311yescharacteristic
728C4⋊C4—838no—
729C4⋊C4—8316no—
730C4⋊C4—8316no—
731C4⋊C4—8316no—
732C4⋊C4—838no—
733C4⋊C4—834no—
734C4⋊C4—838no—
735C4⋊C4—838no—
736C4⋊C4—838no—
737C4⋊C4—838no—
738C4⋊C4—834no—
739C4⋊C4—838no—
740C4⋊C4—8316no—
741C4⋊C4—838no—
742C4⋊C4—8316no—
743C4⋊C4—8316no—
744C4⋊C4—8316no—
745C4⋊C4—838no—
746C4⋊C4C23×D8314yes—
747C4⋊C4C23×D8318yes—
748C4⋊C4C23×D8318yes—
749C4⋊C4C23×D83116yes—
750C4⋊C4C23×D8314yes—
751C4⋊C4C23×D8318yes—
752C22⋊C4—838no—
753C22⋊C4—838no—
754C22⋊C4—8316no—
755C22⋊C4—838no—
756C22⋊C4—8316no—
757C22⋊C4—838no—
758C22⋊C4—838no—
759C22⋊C4—838no—
760C22⋊C4—838no—
761C22⋊C4—838no—
762C22⋊C4—8316no—
763C22⋊C4—838no—
764C22⋊C4C23×D83116yes—
765C22⋊C4C23×D8318yes—
766C42—834no—
767C42—834no—
768C42—834no—
769C42—838no—
770C42—8316no—
771C42—8316no—
772C42C23×D8314yes—
773C42C23×D8318yes—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—834no—
778C23—832no—
779C23—834no—
780C23—1664no—
781C23—1664no—
782C23—1664no—
783C23—1662no—
784C23—1662no—
785C23C24×D8314yes—
786C23C24×D8311yescharacteristic
787Q8—28no—
788Q8—216no—
789Q8—416no—
790Q8—33216no—
791Q8—16616no—
792Q8—1668no—
793D4—28no—
794D4—33216no—
795D4—16616no—
796D4—16616no—
797D4—1668no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—28no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—216no—
804C2×C4—416no—
805C2×C4—33216no—
806C2×C4—33216no—
807C2×C4—834no—
808C2×C4—834no—
809C2×C4—832no—
810C2×C4—832no—
811C2×C4—834no—
812C2×C4—832no—
813C2×C4—838no—
814C2×C4—1668no—
815C2×C4—1668no—
816C2×C4—1662no—
817C2×C4—1662no—
818C2×C4—1664no—
819C2×C4—1662no—
820C2×C4—1664no—
821C2×C4—1664no—
822C2×C4—1668no—
823C2×C4—16616no—
824C2×C4—1668no—
825C2×C4#1458183714yes—
826C2×C4#1458184014yes—
827C2×C4C24×D8314yes—
828C2×C4C24×D8312yes—
829C2×C4C24×D8318yes—
830C2×C4C24×D8314yes—
831C2×C4C24×D8314yes—
832C2×C4C24×D8312yes—
833C2×C4C24×D8312yes—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—48no—
838C22—3328no—
839C22—834no—
840C22—1664no—
841C22—1664no—
842C22—1664no—
843C22—1668no—
844C22—1662no—
845C22—1662no—
846C22C2×#1458183712yes—
847C222−1+4×D8312yes—
848C22C2×#1458184012yes—
849C22C25×D8311yescharacteristic
850C4—24no—
851C4—24no—
852C4—28no—
853C4—22no—
854C4—24no—
855C4—1668no—
856C4—1662no—
857C4—1662no—
858C4—1664no—
859C4—1662no—
860C4—1664no—
861C4—1664no—
862C4C2×#1458183714yes—
863C4C2×#1458184014yes—
864C2—44no—
865C2—3324no—
866C2—1664no—
867C2#2492190514yesdirect product factor
868C2C22×#1458183711yescharacteristic
869C2C2×2−1+4×D8311yescharacteristic
870C2C22×#1458184011yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×D4×Q8×C83C2
socleC23×C83C25
hypercenterC2×D4×Q8D83
hypocenterC83C2×#3552
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #24921905C2direct (N × H)
2. C2×#19128452C2semidirect
3. C2×#19128429C2semidirect
4. C2×#19128425C2semidirect
5. C2×#19128412C2semidirect
6. C2×#19128401C2semidirect
7. C2×Q8×C22⋊D83C2semidirect
8. C2×#19128361C2semidirect
9. C2×#19128356C2semidirect
10. C2×#19128328C2semidirect
11. C2×#19128316C2semidirect
12. C2×#19128311C2semidirect
13. C2×#19128297C2semidirect
14. C2×#19128275C2semidirect
15. C2×C4⋊Q8×D83C2semidirect
16. C2×#19128238C2semidirect
17. C2×#19128233C2semidirect
18. C2×D4×Q8×C83C2semidirect
21. #19128452C22semidirect
22. #19128429C22semidirect
23. #19128425C22semidirect
24. #19128412C22semidirect
25. #19128401C22semidirect
26. Q8×C22⋊D83C22semidirect
27. #19128361C22semidirect
28. #19128356C22semidirect
29. #19128328C22semidirect
30. #19128316C22semidirect
31. #19128311C22semidirect
32. #19128297C22semidirect
33. #19128275C22semidirect
40. C4⋊Q8×D83C22semidirect
41. #19128238C22semidirect
42. #19128233C22semidirect
93. D4×Q8×C83C22semidirect
430. C2×C83#3552semidirect
443. C2×D4×Q8D83semidirect
454. C83C2×#3552semidirect
464. D4×Q8C2×D83semidirect
867. C2#24921905direct (N × H)

Maximal subgroups

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

subgroupindex
#249219052
C2×#191284522
C2×#191284292
C2×#191284252
C2×#191284122
C2×#191284012
C2×Q8×C22⋊D832
C2×#191283612
C2×#191283562
C2×#191283282
C2×#191283162
C2×#191283112
C2×#191282972
C2×#191282752
C2×C4⋊Q8×D832
C2×#191282382
C2×#191282332
C2×D4×Q8×C832
C2×#355283