Finite Group Databasebeta

← C2×#24921804 #36312087

Subgroups — C2×#24921804 #36312087

Order 21248.

7086 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24921804C2132yesmaximal, direct product factor
2C2×#19128452C214yesmaximal, complemented
3C2×Q8×Dic166C211yesmaximal, characteristic, complemented
4C2×#19128416C211yesmaximal, characteristic, complemented
5C2×#19128412C211yesmaximal, characteristic, complemented
6C2×#19128389C212yesmaximal, complemented
7C2×#19128385C212yesmaximal, complemented
8C2×#19128356C212yesmaximal, complemented
9C2×#19128352C212yesmaximal, complemented
10C2×#19128332C212yesmaximal, complemented
11C2×#19128331C212yesmaximal, complemented
12C2×#19128324C212yesmaximal, complemented
13C2×#19128316C212yesmaximal, complemented
14C2×#19128274C214yesmaximal, complemented
15C2×C4⋊Q8×D83C211yesmaximal, characteristic, complemented
16C2×#19128238C211yesmaximal, characteristic, complemented
17C2×#19128233C211yesmaximal, characteristic, complemented
18C2×#554×C83C211yesmaximal, characteristic, complemented
19C22×#13050590C2214yes—
20C22×Q8×D83C2212yes—
21#19128452C22164yescomplemented
22Q8×Dic166C22116yescomplemented
23#19128416C22116yescomplemented
24#19128412C22116yescomplemented
25#19128389C22132yescomplemented
26#19128385C22132yescomplemented
27#19128356C22132yescomplemented
28#19128352C22132yescomplemented
29#19128332C22132yescomplemented
30#19128331C22132yescomplemented
31#19128324C22132yescomplemented
32#19128316C22132yescomplemented
33#19128274C22164yescomplemented
34C2×#14581792C2212yes—
35C2×#14581792C2211yescharacteristic
36C2×#14581791C2212yes—
37C2×#14581791C2212yes—
38C2×#14581791C2214yes—
39C2×#14581791C2212yes—
40C2×#14581791C2214yes—
41C2×#14581790C2212yes—
42C4⋊Q8×D83C22116yescomplemented
43#19128238C22116yescomplemented
44#19128233C22116yescomplemented
45C2×#14581787C2214yes—
46C2×#14581787C2212yes—
47C2×#14581785C2214yes—
48C2×#14581785C2212yes—
49C2×#14581783C2211yescharacteristic
50C2×#14581783C2211yescharacteristic
51C2×#14581783C2212yes—
52C2×#14581783C2214yes—
53C2×#14581782C2214yes—
54C2×#14581781C2211yescharacteristic
55C2×#14581779C2211yescharacteristic
56C2×#14581778C2214yes—
57C2×#14581778C2214yes—
58C2×#14581777C2214yes—
59C2×#14581777C2212yes—
60C2×#14581775C2214yes—
61C2×#14581774C2214yes—
62C2×#14581774C2214yes—
63C2×#14581774C2212yes—
64C2×#14581772C2212yes—
65C2×#14581772C2214yes—
66C2×#14581772C2211yescharacteristic
67C2×#14581771C2214yes—
68C2×#14581771C2214yes—
69C2×#14581770C2214yes—
70C2×#14581768C2211yescharacteristic
71C2×#14581768C2214yes—
72C2×#14581767C2211yescharacteristic
73C2×#14581766C2212yes—
74C2×#14581763C2212yes—
75C2×#14581763C2211yescharacteristic
76C2×Q8×Dic83C2212yes—
77C2×C4×Dic166C2212yes—
78C2×C4×Dic166C2211yescharacteristic
79C2×C4×D332C2212yes—
80C2×C4×D332C2211yescharacteristic
81C2×#14581754C2212yes—
82C2×C4×C22⋊D83C2212yes—
83C2×#14581751C2212yes—
84C2×#14581751C2212yes—
85C2×#14581750C2212yes—
86C2×#14581750C2214yes—
87C2×#14581749C2212yes—
88C2×C4⋊C4×D83C2212yes—
89C2×C4⋊C4×D83C2212yes—
90C2×C4⋊C4×D83C2212yes—
91C2×C42×D83C2211yescharacteristic
92#554×C83C22116yescomplemented
93C2×C4⋊Q8×C83C2211yescharacteristic
94C2×#125×C83C2212yes—
95C2×C22⋊Q8×C83C2212yes—
96C2×C22⋊Q8×C83C2214yes—
97C2×C4×Q8×C83C2211yescharacteristic
98C2×C4×D4×C83C2212yes—
99C2×C4×D4×C83C2211yescharacteristic
100C22×C4⋊C4×C83C2212yes—
101C2×#13050590—416no—
102C2×#13050590C23132yes—
103C22×Dic166C2311yescharacteristic
104C22×Dic166C2314yes—
105C22×Dic166C2314yes—
106C22×Dic166C2312yes—
107C2×Q8×D83—48no—
108C2×Q8×D83C23116yes—
109C22×D332C2311yescharacteristic
110C22×D332C2312yes—
111C22×C22⋊D83C2312yes—
112C22×C22⋊D83C2314yes—
113C22×C4×D83C2311yescharacteristic
114C22×C4×D83C2311yescharacteristic
115C22×C4×D83C2311yescharacteristic
116C22×C4×D83C2314yes—
117C22×C4×D83C2312yes—
118C22×C4×D83C2314yes—
119#14581792C23116yes—
120#14581792C2318yes—
121#14581791C23116yes—
122#14581791C23132yes—
123#14581791C23116yes—
124#14581791C23116yes—
125#14581791C23132yes—
126#14581790C23116yes—
127#14581787C23132yes—
128#14581787C23116yes—
129#14581785C23132yes—
130#14581785C23116yes—
131#14581783C2318yes—
132#14581783C2318yes—
133#14581783C23116yes—
134#14581783C23132yes—
135#14581782C23132yes—
136#14581781C2318yes—
137#14581779C2318yes—
138#14581778C23132yes—
139#14581778C23132yes—
140#14581777C23132yes—
141#14581777C23116yes—
142#14581775C23132yes—
143#14581774C23132yes—
144#14581774C23132yes—
145#14581774C23116yes—
146#14581772C23132yes—
147#14581772C2318yes—
148#14581772C23116yes—
149#14581771C23132yes—
150#14581771C23132yes—
151#14581770C23132yes—
152#14581768C2318yes—
153#14581768C23132yes—
154#14581767C2318yes—
155#14581766C23116yes—
156#14581763C2318yes—
157#14581763C23116yes—
158Q8×Dic83C23116yes—
159C4×Dic166C23116yes—
160C4×Dic166C2318yes—
161C4×D332C23116yes—
162C4×D332C2318yes—
163#14581754C23116yes—
164C4×C22⋊D83C23116yes—
165#14581751C23116yes—
166#14581751C23116yes—
167#14581750C23116yes—
168#14581750C23132yes—
169#14581749C23116yes—
170C2×C4⋊Dic83C2311yescharacteristic
171C2×C4⋊Dic83C2312yes—
172C2×C4⋊Dic83C2312yes—
173C2×C4⋊Dic83C2314yes—
174C2×C4⋊Dic83C2311yescharacteristic
175C2×C4⋊Dic83C2312yes—
176C2×C4⋊Dic83C2312yes—
177C2×C4⋊Dic83C2312yes—
178C2×C4⋊Dic83C2314yes—
179C2×Dic83⋊C4C2314yes—
180C2×Dic83⋊C4C2314yes—
181C2×Dic83⋊C4C2314yes—
182C2×Dic83⋊C4C2312yes—
183C2×Dic83⋊C4C2312yes—
184C2×Dic83⋊C4C2312yes—
185C2×Dic83⋊C4C2312yes—
186C2×Dic83⋊C4C2314yes—
187C4⋊C4×D83C23116yes—
188C4⋊C4×D83C23116yes—
189C4⋊C4×D83C23116yes—
190C2×C22⋊Dic83C2312yes—
191C2×C22⋊Dic83C2314yes—
192C2×C22⋊Dic83C2312yes—
193C2×C22⋊Dic83C2312yes—
194C2×(C2×D83)⋊C4C2312yes—
195C2×(C2×D83)⋊C4C2312yes—
196C2×(C2×D83)⋊C4C2312yes—
197C2×(C2×D83)⋊C4C2312yes—
198C2×(C2×D83)⋊C4C2314yes—
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×Dic83C2314yes—
207C2×C4×Dic83C2312yes—
208C42×D83C2318yes—
209C22×Q8×C83C2311yescharacteristic
210C22×Q8×C83C2312yes—
211C22×D4×C83C2311yescharacteristic
212C23×C4×C83C2312yes—
213C23×C4×C83C2314yes—
214C4⋊Q8×C83C2318yes—
215#125×C83C23116yes—
216C22⋊Q8×C83C23116yes—
217C22⋊Q8×C83C23132yes—
218C4×Q8×C83C2318yes—
219C4×D4×C83C23116yes—
220C4×D4×C83C2318yes—
221C2×C4⋊C4×C83C23116yes—
222C2×C4⋊C4×C83C2311yescharacteristic
223C2×C4⋊C4×C83C2314yes—
224C2×C4⋊C4×C83C2312yes—
225C2×C4⋊C4×C83C2311yescharacteristic
226C2×C4⋊C4×C83C2312yes—
227C2×C4⋊C4×C83C2312yes—
228C2×C4⋊C4×C83C2314yes—
229C2×C22⋊C4×C83C2314yes—
230C2×C22⋊C4×C83C2312yes—
231C2×C42×C83C2312yes—
232C2×C42×C83C2311yescharacteristic
233C23×D83C2412yes—
234C23×D83C2411yescharacteristic
235#13050590—464no—
236C2×Dic166—24no—
237C2×Dic166—44no—
238C2×Dic166—48no—
239C2×Dic166—48no—
240C2×Dic166C2414yes—
241C2×Dic166C24116yes—
242C2×Dic166C24116yes—
243C2×Dic166C2418yes—
244Q8×D83—432no—
245C2×D332—28no—
246C2×D332—24no—
247C2×D332C2414yes—
248C2×D332C2418yes—
249C2×C22⋊D83—28no—
250C2×C22⋊D83—48no—
251C2×C22⋊D83C2418yes—
252C2×C22⋊D83C24116yes—
253C22×Dic83C2412yes—
254C22×Dic83C2414yes—
255C22×Dic83C2411yescharacteristic
256C22×Dic83C2411yescharacteristic
257C22×Dic83C2411yescharacteristic
258C22×Dic83C2412yes—
259C22×Dic83C2412yes—
260C2×C4×D83—24no—
261C2×C4×D83—216no—
262C2×C4×D83—24no—
263C2×C4×D83—24no—
264C2×C4×D83—28no—
265C2×C4×D83—48no—
266C2×C4×D83C2414yes—
267C2×C4×D83C2418yes—
268C2×C4×D83C2414yes—
269C2×C4×D83C2414yes—
270C2×C4×D83C24116yes—
271C2×C4×D83C24116yes—
272C4⋊Dic83C2414yes—
273C4⋊Dic83C2418yes—
274C4⋊Dic83C2418yes—
275C4⋊Dic83C24116yes—
276C4⋊Dic83C2414yes—
277C4⋊Dic83C2418yes—
278C4⋊Dic83C2418yes—
279C4⋊Dic83C24116yes—
280C4⋊Dic83C2418yes—
281Dic83⋊C4C2418yes—
282Dic83⋊C4C24116yes—
283Dic83⋊C4C2418yes—
284Dic83⋊C4C2418yes—
285Dic83⋊C4C24116yes—
286Dic83⋊C4C2418yes—
287Dic83⋊C4C24116yes—
288Dic83⋊C4C24116yes—
289C22⋊Dic83C2418yes—
290C22⋊Dic83C24116yes—
291C22⋊Dic83C2418yes—
292C22⋊Dic83C2418yes—
293(C2×D83)⋊C4C24116yes—
294(C2×D83)⋊C4C2418yes—
295(C2×D83)⋊C4C2418yes—
296(C2×D83)⋊C4C24116yes—
297(C2×D83)⋊C4C2418yes—
298(C2×D83)⋊C4C2418yes—
299(C2×D83)⋊C4C2418yes—
300(C2×D83)⋊C4C2418yes—
301C4×Dic83C24116yes—
302C4×Dic83C24116yes—
303C4×Dic83C2414yes—
304C4×Dic83C2414yes—
305C4×Dic83C2418yes—
306C4×Dic83C2414yes—
307C24×C83C2412yes—
308C2×Q8×C83—24no—
309C2×Q8×C83—44no—
310C2×Q8×C83C2414yes—
311C2×Q8×C83C2418yes—
312C2×D4×C83—24no—
313C2×D4×C83C2414yes—
314C22×C4×C83—28no—
315C22×C4×C83—48no—
316C22×C4×C83C2418yes—
317C22×C4×C83C2414yes—
318C22×C4×C83C2411yescharacteristic
319C22×C4×C83C2412yes—
320C22×C4×C83C2412yes—
321C22×C4×C83C2412yes—
322C22×C4×C83C24116yes—
323C22×C4×C83C2411yescharacteristic
324C22×C4×C83C2411yescharacteristic
325C4⋊C4×C83C2414yes—
326C4⋊C4×C83C24116yes—
327C4⋊C4×C83C24116yes—
328C4⋊C4×C83C2414yes—
329C4⋊C4×C83C2418yes—
330C4⋊C4×C83C2418yes—
331C4⋊C4×C83C2418yes—
332C22⋊C4×C83C24116yes—
333C22⋊C4×C83C2418yes—
334C42×C83C2418yes—
335C42×C83C2414yes—
336C23×C83—24no—
337C23×C83—24no—
338C23×C83—24no—
339C23×C83C2514yes—
340C23×C83C2511yescharacteristic
341C22×D83—22no—
342C22×D83—22no—
343C22×D83—24no—
344C22×D83—24no—
345C22×D83—24no—
346C22×D83H(5,𝔽2)14yes—
347C22×D83C2514yes—
348C22×D83C2512yes—
349Q8×C83—28no—
350Q8×C83—48no—
351D4×C83—28no—
352C2×C4×C83—24no—
353C2×C4×C83—28no—
354C2×C4×C83—22no—
355C2×C4×C83—24no—
356C2×C4×C83—24no—
357C2×C4×C83—216no—
358C2×C4×C83—416no—
359C2×C4×C832−1+414yes—
360C2×C4×C832−1+414yes—
361C2×C4×C83C2514yes—
362C2×C4×C83C2512yes—
363C2×C4×C83C2514yes—
364C2×C4×C83C2514yes—
365C2×C4×C83C2518yes—
366C2×C4×C83C2512yes—
367C2×C4×C83C2512yes—
368C22⋊D83—216no—
369C22⋊D83—416no—
370C2×Dic83—28no—
371C2×Dic83—22no—
372C2×Dic83—24no—
373C2×Dic83—22no—
374C2×Dic83—22no—
375C2×Dic83—24no—
376C2×Dic83—24no—
377C2×Dic83C2514yes—
378C2×Dic83C2512yes—
379C2×Dic83C2514yes—
380C2×Dic83C2512yes—
381C2×Dic83C2512yes—
382C2×Dic83C2518yes—
383C2×Dic83C2514yes—
384D332—216no—
385D332—28no—
386C4×D83—28no—
387C4×D83—232no—
388C4×D83—28no—
389C4×D83—28no—
390C4×D83—216no—
391C4×D83—416no—
392Dic166—28no—
393Dic166—416no—
394Dic166—48no—
395Dic166—416no—
396C22×C83—24no—
397C22×C83—24no—
398C22×C83—24no—
399C22×C83—48no—
400C22×C83C2×H(5,𝔽2)12yes—
401C22×C83C2×2−1+412yes—
402C22×C83C2×2−1+412yes—
403C22×C83C2611yescharacteristic
404C2×D83—22no—
405C2×D83—22no—
406C2×D83—28no—
407C2×D83—24no—
408C2×D83—24no—
409C2×D83—24no—
410C2×D83—48no—
411C2×D83C2×H(5,𝔽2)14yes—
412C4×C83—22no—
413C4×C83—24no—
414C4×C83—28no—
415C4×C83—24no—
416C4×C83—24no—
417C4×C83C2×2−1+414yes—
418C4×C83C2×2−1+414yes—
419Dic83—22no—
420Dic83—28no—
421Dic83—24no—
422Dic83—24no—
423Dic83—22no—
424Dic83—22no—
425Dic83—24no—
426C2×#3544—831nomaximal, Sylow
427C2×C83—44no—
428C2×C83#354414yescomplemented
429C2×C83C22×H(5,𝔽2)11yescharacteristic
430C2×C83C22×2−1+411yescharacteristic
431C2×C83C22×2−1+411yescharacteristic
432D83—24no—
433D83—44no—
434#3544—8332no—
435C2×#563—834no—
436C2×Q82—831no—
437C2×#555—831no—
438C2×#554—831no—
439C2×#554D8311yescharacteristic, complemented
440C2×#552—832no—
441C2×#552—832no—
442C2×#547—832no—
443C2×#547—832no—
444C2×#544—832no—
445C2×#544—832no—
446C2×#542—832no—
447C2×#542—832no—
448C2×#536—834no—
449C22×C4⋊Q8—831no—
450C2×#529—831no—
451C2×#529—831no—
452C83C2×#354411yescharacteristic, complemented, Sylow
453C22×#41—834no—
454C23×Q8—832no—
455#563—8364no—
456Q82—8316no—
457#555—8316no—
458#554—8316no—
459#554C2×D83116yescomplemented
460#552—8332no—
461#552—8332no—
462#547—8332no—
463#547—8332no—
464#544—8332no—
465#544—8332no—
466#542—8332no—
467#542—8332no—
468#536—8364no—
469C2×C4⋊Q8—832no—
470C2×C4⋊Q8—8316no—
471C2×C4⋊Q8—832no—
472C2×C4⋊Q8—832no—
473C2×C4⋊Q8—834no—
474C2×C4⋊Q8—834no—
475C2×C4⋊Q8—832no—
476C2×C4⋊Q8—831no—
477C2×C4⋊Q8—832no—
478C2×C4⋊Q8C2×D8311yescharacteristic
479#529—8316no—
480#529—8316no—
481C2×#126—832no—
482C2×#126—834no—
483C2×#126—832no—
484C2×#126—834no—
485C2×#125—831no—
486C2×#125—831no—
487C2×#125—832no—
488C2×#125—834no—
489C2×#125—834no—
490C2×#125C2×D8312yes—
491C2×#124—831no—
492C2×#124—831no—
493C2×#124—834no—
494C2×#124—834no—
495C2×#123—834no—
496C2×#123—832no—
497C2×#123—834no—
498C2×#123—832no—
499C2×#123—834no—
500C2×#123—834no—
501C2×C22⋊Q8—831no—
502C2×C22⋊Q8—834no—
503C2×C22⋊Q8—834no—
504C2×C22⋊Q8—834no—
505C2×C22⋊Q8—831no—
506C2×C22⋊Q8—834no—
507C2×C22⋊Q8—832no—
508C2×C22⋊Q8—834no—
509C2×C22⋊Q8C2×D8314yes—
510C2×C22⋊Q8C2×D8312yes—
511C2×#121—831no—
512C2×#121—832no—
513C2×#121—832no—
514C2×#121—831no—
515C2×C4×Q8—832no—
516C2×C4×Q8—831no—
517C2×C4×Q8—832no—
518C2×C4×Q8C2×D8311yescharacteristic
519C2×C4×D4—832no—
520C2×C4×D4—832no—
521C2×C4×D4—832no—
522C2×C4×D4—831no—
523C2×C4×D4C2×D8311yescharacteristic
524C2×C4×D4C2×D8312yes—
525C2×#117—832no—
526C2×#117—832no—
527C2×#117—834no—
528C2×#117—832no—
529C2×#117—832no—
530C22×C4⋊C4—832no—
531C22×C4⋊C4—832no—
532C22×C4⋊C4—832no—
533C22×C4⋊C4C2×D8312yes—
534C22×C42—831no—
535C2×#41—33216no—
536C2×#41—8332no—
537C22×Q8—3328no—
538C22×Q8—8316no—
539C22×Q8—834no—
540C22×Q8—834no—
541C22×Q8—832no—
542C22×Q8—831no—
543C22×Q8C22×D8311yescharacteristic
544C22×Q8C22×D8312yes—
545C22×D4—834no—
546C22×D4—832no—
547C22×D4—831no—
548C22×D4—832no—
549C22×D4C22×D8311yescharacteristic
550C23×C4—834no—
551C23×C4—834no—
552C23×C4—831no—
553C23×C4—831no—
554C23×C4—832no—
555C23×C4—831no—
556C23×C4C22×D8312yes—
557C23×C4C22×D8314yes—
558C4⋊Q8—8316no—
559C4⋊Q8—8316no—
560C4⋊Q8—8316no—
561C4⋊Q8—8332no—
562C4⋊Q8—8332no—
563C4⋊Q8—8316no—
564C4⋊Q8—838no—
565C4⋊Q8—8316no—
566C4⋊Q8C22×D8318yes—
567#126—8316no—
568#126—8332no—
569#126—8316no—
570#126—8332no—
571#125—838no—
572#125—838no—
573#125—8332no—
574#125—8316no—
575#125—8332no—
576#125C22×D83116yes—
577#124—838no—
578#124—838no—
579#124—8332no—
580#124—8332no—
581#123—8332no—
582#123—8316no—
583#123—8332no—
584#123—8316no—
585#123—8332no—
586#123—8332no—
587C22⋊Q8—838no—
588C22⋊Q8—8332no—
589C22⋊Q8—8332no—
590C22⋊Q8—8332no—
591C22⋊Q8—8332no—
592C22⋊Q8—838no—
593C22⋊Q8—8332no—
594C22⋊Q8—8316no—
595C22⋊Q8C22×D83132yes—
596C22⋊Q8C22×D83116yes—
597#121—838no—
598#121—8316no—
599#121—8316no—
600#121—838no—
601C4×Q8—8316no—
602C4×Q8—838no—
603C4×Q8—8316no—
604C4×Q8C22×D8318yes—
605C4×D4—8316no—
606C4×D4—8316no—
607C4×D4—8316no—
608C4×D4—838no—
609C4×D4C22×D8318yes—
610C4×D4C22×D83116yes—
611#117—8316no—
612#117—8316no—
613#117—8332no—
614#117—8316no—
615#117—8316no—
616C2×C4⋊C4—831no—
617C2×C4⋊C4—832no—
618C2×C4⋊C4—832no—
619C2×C4⋊C4—834no—
620C2×C4⋊C4—834no—
621C2×C4⋊C4—834no—
622C2×C4⋊C4—831no—
623C2×C4⋊C4—834no—
624C2×C4⋊C4—832no—
625C2×C4⋊C4—832no—
626C2×C4⋊C4—832no—
627C2×C4⋊C4—832no—
628C2×C4⋊C4—832no—
629C2×C4⋊C4—832no—
630C2×C4⋊C4—832no—
631C2×C4⋊C4—834no—
632C2×C4⋊C4—834no—
633C2×C4⋊C4—8316no—
634C2×C4⋊C4—8316no—
635C2×C4⋊C4—8316no—
636C2×C4⋊C4C22×D8312yes—
637C2×C4⋊C4C22×D8312yes—
638C2×C4⋊C4C22×D8311yescharacteristic
639C2×C4⋊C4C22×D8314yes—
640C2×C4⋊C4C22×D83116yes—
641C2×C4⋊C4C22×D8311yescharacteristic
642C2×C4⋊C4C22×D8314yes—
643C2×C4⋊C4C22×D8312yes—
644C2×C22⋊C4—832no—
645C2×C22⋊C4—834no—
646C2×C22⋊C4—832no—
647C2×C22⋊C4—832no—
648C2×C22⋊C4—832no—
649C2×C22⋊C4—832no—
650C2×C22⋊C4—832no—
651C2×C22⋊C4—834no—
652C2×C22⋊C4—832no—
653C2×C22⋊C4—834no—
654C2×C22⋊C4—832no—
655C2×C22⋊C4—832no—
656C2×C22⋊C4C22×D8314yes—
657C2×C22⋊C4C22×D8312yes—
658C2×C42—834no—
659C2×C42—831no—
660C2×C42—831no—
661C2×C42—832no—
662C2×C42—834no—
663C2×C42—831no—
664C2×C42—838no—
665C2×C42C22×D8312yes—
666C2×C42C22×D8311yescharacteristic
667C24—831no—
668C24—832no—
669C24C23×D8312yes—
670#41—33264no—
671C2×Q8—24no—
672C2×Q8—44no—
673C2×Q8—3328no—
674C2×Q8—3324no—
675C2×Q8—3328no—
676C2×Q8—33232no—
677C2×Q8—8316no—
678C2×Q8—8316no—
679C2×Q8—838no—
680C2×Q8—834no—
681C2×Q8—1664no—
682C2×Q8C23×D8314yes—
683C2×Q8C23×D8318yes—
684C2×D4—24no—
685C2×D4—3328no—
686C2×D4—8316no—
687C2×D4—838no—
688C2×D4—834no—
689C2×D4—838no—
690C2×D4—1668no—
691C2×D4—1668no—
692C2×D4—1664no—
693C2×D4C23×D8314yes—
694C22×C4—28no—
695C22×C4—48no—
696C22×C4—3328no—
697C22×C4—8316no—
698C22×C4—832no—
699C22×C4—831no—
700C22×C4—832no—
701C22×C4—831no—
702C22×C4—831no—
703C22×C4—834no—
704C22×C4—832no—
705C22×C4—834no—
706C22×C4—834no—
707C22×C4—834no—
708C22×C4—8316no—
709C22×C4—838no—
710C22×C4—1664no—
711C22×C4—16616no—
712C22×C4—1664no—
713C22×C4—1668no—
714C22×C4—1664no—
715C22×C4C23×D8318yes—
716C22×C4C23×D8312yes—
717C22×C4C23×D8312yes—
718C22×C4C23×D8311yescharacteristic
719C22×C4C23×D8312yes—
720C22×C4C23×D8314yes—
721C22×C4C23×D83116yes—
722C22×C4C23×D8311yescharacteristic
723C22×C4C23×D8311yescharacteristic
724C4⋊C4—834no—
725C4⋊C4—838no—
726C4⋊C4—838no—
727C4⋊C4—8316no—
728C4⋊C4—8316no—
729C4⋊C4—8316no—
730C4⋊C4—834no—
731C4⋊C4—8316no—
732C4⋊C4—838no—
733C4⋊C4—838no—
734C4⋊C4—838no—
735C4⋊C4—838no—
736C4⋊C4—838no—
737C4⋊C4—838no—
738C4⋊C4—838no—
739C4⋊C4—8316no—
740C4⋊C4—8316no—
741C4⋊C4C23×D8318yes—
742C4⋊C4C23×D8318yes—
743C4⋊C4C23×D8314yes—
744C4⋊C4C23×D83116yes—
745C4⋊C4C23×D8314yes—
746C4⋊C4C23×D83116yes—
747C4⋊C4C23×D8318yes—
748C22⋊C4—838no—
749C22⋊C4—8316no—
750C22⋊C4—838no—
751C22⋊C4—838no—
752C22⋊C4—838no—
753C22⋊C4—838no—
754C22⋊C4—838no—
755C22⋊C4—8316no—
756C22⋊C4—838no—
757C22⋊C4—8316no—
758C22⋊C4—838no—
759C22⋊C4—838no—
760C22⋊C4C23×D83116yes—
761C22⋊C4C23×D8318yes—
762C42—834no—
763C42—834no—
764C42—834no—
765C42—8316no—
766C42—838no—
767C42—8316no—
768C42C23×D8314yes—
769C42C23×D8318yes—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—834no—
774C23—832no—
775C23—834no—
776C23—1664no—
777C23—1664no—
778C23—1664no—
779C23—1662no—
780C23—1662no—
781C23C24×D8314yes—
782C23C24×D8311yescharacteristic
783Q8—28no—
784Q8—48no—
785Q8—33216no—
786Q8—3328no—
787Q8—33216no—
788Q8—1668no—
789D4—28no—
790D4—33216no—
791D4—16616no—
792D4—16616no—
793D4—1668no—
794C2×C4—24no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—216no—
800C2×C4—416no—
801C2×C4—33216no—
802C2×C4—834no—
803C2×C4—832no—
804C2×C4—832no—
805C2×C4—834no—
806C2×C4—832no—
807C2×C4—838no—
808C2×C4—834no—
809C2×C4—1668no—
810C2×C4—16632no—
811C2×C4—1664no—
812C2×C4—1668no—
813C2×C4—1662no—
814C2×C4—1662no—
815C2×C4—1664no—
816C2×C4—1662no—
817C2×C4—1664no—
818C2×C4—1668no—
819C2×C4—16616no—
820C2×C4—1668no—
821C2×C4#1458183914yes—
822C2×C4#1458184014yes—
823C2×C4C24×D8314yes—
824C2×C4C24×D8314yes—
825C2×C4C24×D8312yes—
826C2×C4C24×D8314yes—
827C2×C4C24×D8318yes—
828C2×C4C24×D8312yes—
829C2×C4C24×D8312yes—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—48no—
834C22—3328no—
835C22—834no—
836C22—1664no—
837C22—1664no—
838C22—1664no—
839C22—1662no—
840C22—1662no—
841C22—1668no—
842C22H(5,𝔽2)×D8312yes—
843C22C2×#1458183912yes—
844C22C2×#1458184012yes—
845C22C25×D8311yescharacteristic
846C4—24no—
847C4—28no—
848C4—22no—
849C4—24no—
850C4—24no—
851C4—1664no—
852C4—1668no—
853C4—1662no—
854C4—1662no—
855C4—1662no—
856C4—1664no—
857C4—1664no—
858C4C2×#1458183914yes—
859C4C2×#1458184014yes—
860C2—44no—
861C2—3324no—
862C2—1664no—
863C2#2492180414yesdirect product factor
864C2C2×H(5,𝔽2)×D8311yescharacteristic
865C2C22×#1458183911yescharacteristic
866C2C22×#1458184011yescharacteristic
subgroupG/H
centerC23C24×D83
commutator, cosocleC22×C83C26
FrattiniC22C25×D83
FittingC2×#554×C83C2
socleC23×C83C25
hypercenterC2×#554D83
hypocenterC83C2×#3544
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #24921804C2direct (N × H)
2. C2×#19128452C2semidirect
3. C2×Q8×Dic166C2semidirect
4. C2×#19128416C2semidirect
5. C2×#19128412C2semidirect
6. C2×#19128389C2semidirect
7. C2×#19128385C2semidirect
8. C2×#19128356C2semidirect
9. C2×#19128352C2semidirect
10. C2×#19128332C2semidirect
11. C2×#19128331C2semidirect
12. C2×#19128324C2semidirect
13. C2×#19128316C2semidirect
14. C2×#19128274C2semidirect
15. C2×C4⋊Q8×D83C2semidirect
16. C2×#19128238C2semidirect
17. C2×#19128233C2semidirect
18. C2×#554×C83C2semidirect
21. #19128452C22semidirect
22. Q8×Dic166C22semidirect
23. #19128416C22semidirect
24. #19128412C22semidirect
25. #19128389C22semidirect
26. #19128385C22semidirect
27. #19128356C22semidirect
28. #19128352C22semidirect
29. #19128332C22semidirect
30. #19128331C22semidirect
31. #19128324C22semidirect
32. #19128316C22semidirect
33. #19128274C22semidirect
42. C4⋊Q8×D83C22semidirect
43. #19128238C22semidirect
44. #19128233C22semidirect
92. #554×C83C22semidirect
428. C2×C83#3544semidirect
439. C2×#554D83semidirect
452. C83C2×#3544semidirect
459. #554C2×D83semidirect
863. C2#24921804direct (N × H)

Maximal subgroups

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

subgroupindex
#249218042
C2×#191284522
C2×Q8×Dic1662
C2×#191284162
C2×#191284122
C2×#191283892
C2×#191283852
C2×#191283562
C2×#191283522
C2×#191283322
C2×#191283312
C2×#191283242
C2×#191283162
C2×#191282742
C2×C4⋊Q8×D832
C2×#191282382
C2×#191282332
C2×#554×C832
C2×#354483