Finite Group Databasebeta

← C2×#22574550 #31763514

Subgroups — C2×#22574550 #31763514

Order 17152.

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#22574550C2132yesmaximal, direct product factor
2C2×#16864147C214yesmaximal, complemented
3C2×Q8×Dic134C211yesmaximal, characteristic, complemented
4C2×#16864111C211yesmaximal, characteristic, complemented
5C2×#16864107C211yesmaximal, characteristic, complemented
6C2×#16864084C212yesmaximal, complemented
7C2×#16864080C212yesmaximal, complemented
8C2×#16864051C212yesmaximal, complemented
9C2×#16864047C212yesmaximal, complemented
10C2×#16864027C212yesmaximal, complemented
11C2×#16864026C212yesmaximal, complemented
12C2×#16864019C212yesmaximal, complemented
13C2×#16864011C212yesmaximal, complemented
14C2×#16863969C214yesmaximal, complemented
15C2×C4⋊Q8×D67C211yesmaximal, characteristic, complemented
16C2×#16863933C211yesmaximal, characteristic, complemented
17C2×#16863928C211yesmaximal, characteristic, complemented
18C2×#554×C67C211yesmaximal, characteristic, complemented
19C22×#11761628C2214yes—
20C22×Q8×D67C2212yes—
21#16864147C22164yescomplemented
22Q8×Dic134C22116yescomplemented
23#16864111C22116yescomplemented
24#16864107C22116yescomplemented
25#16864084C22132yescomplemented
26#16864080C22132yescomplemented
27#16864051C22132yescomplemented
28#16864047C22132yescomplemented
29#16864027C22132yescomplemented
30#16864026C22132yescomplemented
31#16864019C22132yescomplemented
32#16864011C22132yescomplemented
33#16863969C22164yescomplemented
34C2×#14524043C2212yes—
35C2×#14524043C2211yescharacteristic
36C2×#14524042C2214yes—
37C2×#14524042C2212yes—
38C2×#14524042C2212yes—
39C2×#14524042C2214yes—
40C2×#14524042C2212yes—
41C2×#14524041C2212yes—
42C4⋊Q8×D67C22116yescomplemented
43#16863933C22116yescomplemented
44#16863928C22116yescomplemented
45C2×#14524038C2212yes—
46C2×#14524038C2214yes—
47C2×#14524036C2212yes—
48C2×#14524036C2214yes—
49C2×#14524034C2214yes—
50C2×#14524034C2211yescharacteristic
51C2×#14524034C2211yescharacteristic
52C2×#14524034C2212yes—
53C2×#14524033C2214yes—
54C2×#14524032C2211yescharacteristic
55C2×#14524030C2211yescharacteristic
56C2×#14524029C2214yes—
57C2×#14524029C2214yes—
58C2×#14524028C2214yes—
59C2×#14524028C2212yes—
60C2×#14524026C2214yes—
61C2×#14524025C2214yes—
62C2×#14524025C2214yes—
63C2×#14524025C2212yes—
64C2×#14524023C2212yes—
65C2×#14524023C2214yes—
66C2×#14524023C2211yescharacteristic
67C2×#14524022C2214yes—
68C2×#14524022C2214yes—
69C2×#14524021C2214yes—
70C2×#14524019C2214yes—
71C2×#14524019C2211yescharacteristic
72C2×#14524018C2211yescharacteristic
73C2×#14524017C2212yes—
74C2×#14524014C2212yes—
75C2×#14524014C2211yescharacteristic
76C2×Q8×Dic67C2212yes—
77C2×C4×Dic134C2212yes—
78C2×C4×Dic134C2211yescharacteristic
79C2×C4×D268C2212yes—
80C2×C4×D268C2211yescharacteristic
81C2×#14524005C2212yes—
82C2×C4×C22⋊D67C2212yes—
83C2×#14524002C2212yes—
84C2×#14524002C2212yes—
85C2×#14524001C2212yes—
86C2×#14524001C2214yes—
87C2×#14524000C2212yes—
88C2×C4⋊C4×D67C2212yes—
89C2×C4⋊C4×D67C2212yes—
90C2×C4⋊C4×D67C2212yes—
91C2×C42×D67C2211yescharacteristic
92#554×C67C22116yescomplemented
93C2×C4⋊Q8×C67C2211yescharacteristic
94C2×#125×C67C2212yes—
95C2×C22⋊Q8×C67C2214yes—
96C2×C22⋊Q8×C67C2212yes—
97C2×C4×Q8×C67C2211yescharacteristic
98C2×C4×D4×C67C2212yes—
99C2×C4×D4×C67C2211yescharacteristic
100C22×C4⋊C4×C67C2212yes—
101C2×#11761628—416no—
102C2×#11761628C23132yes—
103C22×Dic134C2311yescharacteristic
104C22×Dic134C2314yes—
105C22×Dic134C2314yes—
106C22×Dic134C2312yes—
107C2×Q8×D67—48no—
108C2×Q8×D67C23116yes—
109C22×D268C2311yescharacteristic
110C22×D268C2312yes—
111C22×C22⋊D67C2312yes—
112C22×C22⋊D67C2314yes—
113C22×C4×D67C2311yescharacteristic
114C22×C4×D67C2311yescharacteristic
115C22×C4×D67C2311yescharacteristic
116C22×C4×D67C2314yes—
117C22×C4×D67C2312yes—
118C22×C4×D67C2314yes—
119#14524043C23116yes—
120#14524043C2318yes—
121#14524042C23116yes—
122#14524042C23116yes—
123#14524042C23132yes—
124#14524042C23116yes—
125#14524042C23132yes—
126#14524041C23116yes—
127#14524038C23132yes—
128#14524038C23116yes—
129#14524036C23132yes—
130#14524036C23116yes—
131#14524034C2318yes—
132#14524034C2318yes—
133#14524034C23116yes—
134#14524034C23132yes—
135#14524033C23132yes—
136#14524032C2318yes—
137#14524030C2318yes—
138#14524029C23132yes—
139#14524029C23132yes—
140#14524028C23132yes—
141#14524028C23116yes—
142#14524026C23132yes—
143#14524025C23132yes—
144#14524025C23132yes—
145#14524025C23116yes—
146#14524023C23116yes—
147#14524023C23132yes—
148#14524023C2318yes—
149#14524022C23132yes—
150#14524022C23132yes—
151#14524021C23132yes—
152#14524019C2318yes—
153#14524019C23132yes—
154#14524018C2318yes—
155#14524017C23116yes—
156#14524014C23116yes—
157#14524014C2318yes—
158Q8×Dic67C23116yes—
159C4×Dic134C23116yes—
160C4×Dic134C2318yes—
161C4×D268C23116yes—
162C4×D268C2318yes—
163#14524005C23116yes—
164C4×C22⋊D67C23116yes—
165#14524002C23116yes—
166#14524002C23116yes—
167#14524001C23116yes—
168#14524001C23132yes—
169#14524000C23116yes—
170C2×C4⋊Dic67C2311yescharacteristic
171C2×C4⋊Dic67C2312yes—
172C2×C4⋊Dic67C2312yes—
173C2×C4⋊Dic67C2314yes—
174C2×C4⋊Dic67C2311yescharacteristic
175C2×C4⋊Dic67C2312yes—
176C2×C4⋊Dic67C2312yes—
177C2×C4⋊Dic67C2312yes—
178C2×C4⋊Dic67C2314yes—
179C2×Dic67⋊C4C2314yes—
180C2×Dic67⋊C4C2314yes—
181C2×Dic67⋊C4C2314yes—
182C2×Dic67⋊C4C2312yes—
183C2×Dic67⋊C4C2312yes—
184C2×Dic67⋊C4C2312yes—
185C2×Dic67⋊C4C2312yes—
186C2×Dic67⋊C4C2314yes—
187C4⋊C4×D67C23116yes—
188C4⋊C4×D67C23116yes—
189C4⋊C4×D67C23116yes—
190C2×C22⋊Dic67C2312yes—
191C2×C22⋊Dic67C2314yes—
192C2×C22⋊Dic67C2312yes—
193C2×C22⋊Dic67C2312yes—
194C2×(C2×D67)⋊C4C2312yes—
195C2×(C2×D67)⋊C4C2312yes—
196C2×(C2×D67)⋊C4C2312yes—
197C2×(C2×D67)⋊C4C2312yes—
198C2×(C2×D67)⋊C4C2314yes—
199C2×(C2×D67)⋊C4C2314yes—
200C2×(C2×D67)⋊C4C2312yes—
201C2×(C2×D67)⋊C4C2312yes—
202C2×C4×Dic67C2311yescharacteristic
203C2×C4×Dic67C2311yescharacteristic
204C2×C4×Dic67C2311yescharacteristic
205C2×C4×Dic67C2314yes—
206C2×C4×Dic67C2314yes—
207C2×C4×Dic67C2312yes—
208C42×D67C2318yes—
209C22×Q8×C67C2311yescharacteristic
210C22×Q8×C67C2312yes—
211C22×D4×C67C2311yescharacteristic
212C23×C4×C67C2312yes—
213C23×C4×C67C2314yes—
214C4⋊Q8×C67C2318yes—
215#125×C67C23116yes—
216C22⋊Q8×C67C23116yes—
217C22⋊Q8×C67C23132yes—
218C4×Q8×C67C2318yes—
219C4×D4×C67C23116yes—
220C4×D4×C67C2318yes—
221C2×C4⋊C4×C67C23116yes—
222C2×C4⋊C4×C67C2311yescharacteristic
223C2×C4⋊C4×C67C2314yes—
224C2×C4⋊C4×C67C2312yes—
225C2×C4⋊C4×C67C2311yescharacteristic
226C2×C4⋊C4×C67C2312yes—
227C2×C4⋊C4×C67C2312yes—
228C2×C4⋊C4×C67C2314yes—
229C2×C22⋊C4×C67C2314yes—
230C2×C22⋊C4×C67C2312yes—
231C2×C42×C67C2312yes—
232C2×C42×C67C2311yescharacteristic
233C23×D67C2412yes—
234C23×D67C2411yescharacteristic
235#11761628—464no—
236C2×Dic134—24no—
237C2×Dic134—44no—
238C2×Dic134—48no—
239C2×Dic134—48no—
240C2×Dic134C2414yes—
241C2×Dic134C24116yes—
242C2×Dic134C24116yes—
243C2×Dic134C2418yes—
244Q8×D67—432no—
245C2×D268—28no—
246C2×D268—24no—
247C2×D268C2414yes—
248C2×D268C2418yes—
249C2×C22⋊D67—28no—
250C2×C22⋊D67—48no—
251C2×C22⋊D67C2418yes—
252C2×C22⋊D67C24116yes—
253C22×Dic67C2412yes—
254C22×Dic67C2411yescharacteristic
255C22×Dic67C2411yescharacteristic
256C22×Dic67C2412yes—
257C22×Dic67C2411yescharacteristic
258C22×Dic67C2414yes—
259C22×Dic67C2412yes—
260C2×C4×D67—24no—
261C2×C4×D67—216no—
262C2×C4×D67—24no—
263C2×C4×D67—24no—
264C2×C4×D67—28no—
265C2×C4×D67—48no—
266C2×C4×D67C2414yes—
267C2×C4×D67C2414yes—
268C2×C4×D67C2414yes—
269C2×C4×D67C24116yes—
270C2×C4×D67C2418yes—
271C2×C4×D67C24116yes—
272C4⋊Dic67C2414yes—
273C4⋊Dic67C2418yes—
274C4⋊Dic67C2418yes—
275C4⋊Dic67C24116yes—
276C4⋊Dic67C2414yes—
277C4⋊Dic67C2418yes—
278C4⋊Dic67C2418yes—
279C4⋊Dic67C2418yes—
280C4⋊Dic67C24116yes—
281Dic67⋊C4C24116yes—
282Dic67⋊C4C24116yes—
283Dic67⋊C4C24116yes—
284Dic67⋊C4C2418yes—
285Dic67⋊C4C2418yes—
286Dic67⋊C4C2418yes—
287Dic67⋊C4C2418yes—
288Dic67⋊C4C24116yes—
289C22⋊Dic67C2418yes—
290C22⋊Dic67C24116yes—
291C22⋊Dic67C2418yes—
292C22⋊Dic67C2418yes—
293(C2×D67)⋊C4C2418yes—
294(C2×D67)⋊C4C2418yes—
295(C2×D67)⋊C4C2418yes—
296(C2×D67)⋊C4C2418yes—
297(C2×D67)⋊C4C24116yes—
298(C2×D67)⋊C4C24116yes—
299(C2×D67)⋊C4C2418yes—
300(C2×D67)⋊C4C2418yes—
301C4×Dic67C2414yes—
302C4×Dic67C2414yes—
303C4×Dic67C2414yes—
304C4×Dic67C24116yes—
305C4×Dic67C24116yes—
306C4×Dic67C2418yes—
307C24×C67C2412yes—
308C2×Q8×C67—24no—
309C2×Q8×C67—44no—
310C2×Q8×C67C2414yes—
311C2×Q8×C67C2418yes—
312C2×D4×C67—24no—
313C2×D4×C67C2414yes—
314C22×C4×C67—28no—
315C22×C4×C67—48no—
316C22×C4×C67C2412yes—
317C22×C4×C67C2411yescharacteristic
318C22×C4×C67C2412yes—
319C22×C4×C67C2412yes—
320C22×C4×C67C2414yes—
321C22×C4×C67C2418yes—
322C22×C4×C67C24116yes—
323C22×C4×C67C2411yescharacteristic
324C22×C4×C67C2411yescharacteristic
325C4⋊C4×C67C2414yes—
326C4⋊C4×C67C24116yes—
327C4⋊C4×C67C2418yes—
328C4⋊C4×C67C2414yes—
329C4⋊C4×C67C2418yes—
330C4⋊C4×C67C2418yes—
331C4⋊C4×C67C24116yes—
332C22⋊C4×C67C24116yes—
333C22⋊C4×C67C2418yes—
334C42×C67C2418yes—
335C42×C67C2414yes—
336C23×C67—24no—
337C23×C67—24no—
338C23×C67—24no—
339C23×C67C2514yes—
340C23×C67C2511yescharacteristic
341C22×D67—22no—
342C22×D67—22no—
343C22×D67—24no—
344C22×D67—24no—
345C22×D67—24no—
346C22×D67H(5,𝔽2)14yes—
347C22×D67C2514yes—
348C22×D67C2512yes—
349Q8×C67—28no—
350Q8×C67—48no—
351D4×C67—28no—
352C2×C4×C67—24no—
353C2×C4×C67—28no—
354C2×C4×C67—22no—
355C2×C4×C67—24no—
356C2×C4×C67—24no—
357C2×C4×C67—216no—
358C2×C4×C67—416no—
359C2×C4×C672−1+414yes—
360C2×C4×C672−1+414yes—
361C2×C4×C67C2514yes—
362C2×C4×C67C2512yes—
363C2×C4×C67C2514yes—
364C2×C4×C67C2514yes—
365C2×C4×C67C2518yes—
366C2×C4×C67C2512yes—
367C2×C4×C67C2512yes—
368C22⋊D67—216no—
369C22⋊D67—416no—
370C2×Dic67—28no—
371C2×Dic67—22no—
372C2×Dic67—24no—
373C2×Dic67—22no—
374C2×Dic67—22no—
375C2×Dic67—24no—
376C2×Dic67—24no—
377C2×Dic67C2514yes—
378C2×Dic67C2512yes—
379C2×Dic67C2512yes—
380C2×Dic67C2514yes—
381C2×Dic67C2512yes—
382C2×Dic67C2518yes—
383C2×Dic67C2514yes—
384D268—216no—
385D268—28no—
386C4×D67—28no—
387C4×D67—232no—
388C4×D67—28no—
389C4×D67—28no—
390C4×D67—216no—
391C4×D67—416no—
392Dic134—28no—
393Dic134—416no—
394Dic134—48no—
395Dic134—416no—
396C22×C67—24no—
397C22×C67—24no—
398C22×C67—24no—
399C22×C67—48no—
400C22×C67C2×H(5,𝔽2)12yes—
401C22×C67C2×2−1+412yes—
402C22×C67C2×2−1+412yes—
403C22×C67C2611yescharacteristic
404C2×D67—22no—
405C2×D67—22no—
406C2×D67—28no—
407C2×D67—24no—
408C2×D67—24no—
409C2×D67—24no—
410C2×D67—48no—
411C2×D67C2×H(5,𝔽2)14yes—
412C4×C67—22no—
413C4×C67—24no—
414C4×C67—28no—
415C4×C67—24no—
416C4×C67—24no—
417C4×C67C2×2−1+414yes—
418C4×C67C2×2−1+414yes—
419Dic67—22no—
420Dic67—28no—
421Dic67—24no—
422Dic67—24no—
423Dic67—22no—
424Dic67—22no—
425Dic67—24no—
426C2×#3544—671nomaximal, Sylow
427C2×C67—44no—
428C2×C67#354414yescomplemented
429C2×C67C22×H(5,𝔽2)11yescharacteristic
430C2×C67C22×2−1+411yescharacteristic
431C2×C67C22×2−1+411yescharacteristic
432D67—24no—
433D67—44no—
434#3544—6732no—
435C2×#563—674no—
436C2×Q82—671no—
437C2×#555—671no—
438C2×#554—671no—
439C2×#554D6711yescharacteristic, complemented
440C2×#552—672no—
441C2×#552—672no—
442C2×#547—672no—
443C2×#547—672no—
444C2×#544—672no—
445C2×#544—672no—
446C2×#542—672no—
447C2×#542—672no—
448C2×#536—674no—
449C22×C4⋊Q8—671no—
450C2×#529—671no—
451C2×#529—671no—
452C67C2×#354411yescharacteristic, complemented, Sylow
453C22×#41—674no—
454C23×Q8—672no—
455#563—6764no—
456Q82—6716no—
457#555—6716no—
458#554—6716no—
459#554C2×D67116yescomplemented
460#552—6732no—
461#552—6732no—
462#547—6732no—
463#547—6732no—
464#544—6732no—
465#544—6732no—
466#542—6732no—
467#542—6732no—
468#536—6764no—
469C2×C4⋊Q8—672no—
470C2×C4⋊Q8—6716no—
471C2×C4⋊Q8—672no—
472C2×C4⋊Q8—672no—
473C2×C4⋊Q8—674no—
474C2×C4⋊Q8—674no—
475C2×C4⋊Q8—672no—
476C2×C4⋊Q8—671no—
477C2×C4⋊Q8—672no—
478C2×C4⋊Q8C2×D6711yescharacteristic
479#529—6716no—
480#529—6716no—
481C2×#126—672no—
482C2×#126—674no—
483C2×#126—672no—
484C2×#126—674no—
485C2×#125—671no—
486C2×#125—671no—
487C2×#125—672no—
488C2×#125—674no—
489C2×#125—674no—
490C2×#125C2×D6712yes—
491C2×#124—671no—
492C2×#124—671no—
493C2×#124—674no—
494C2×#124—674no—
495C2×#123—674no—
496C2×#123—672no—
497C2×#123—674no—
498C2×#123—672no—
499C2×#123—674no—
500C2×#123—674no—
501C2×C22⋊Q8—671no—
502C2×C22⋊Q8—674no—
503C2×C22⋊Q8—674no—
504C2×C22⋊Q8—674no—
505C2×C22⋊Q8—671no—
506C2×C22⋊Q8—674no—
507C2×C22⋊Q8—672no—
508C2×C22⋊Q8—674no—
509C2×C22⋊Q8C2×D6714yes—
510C2×C22⋊Q8C2×D6712yes—
511C2×#121—671no—
512C2×#121—672no—
513C2×#121—672no—
514C2×#121—671no—
515C2×C4×Q8—672no—
516C2×C4×Q8—671no—
517C2×C4×Q8—672no—
518C2×C4×Q8C2×D6711yescharacteristic
519C2×C4×D4—672no—
520C2×C4×D4—672no—
521C2×C4×D4—672no—
522C2×C4×D4—671no—
523C2×C4×D4C2×D6711yescharacteristic
524C2×C4×D4C2×D6712yes—
525C2×#117—672no—
526C2×#117—672no—
527C2×#117—674no—
528C2×#117—672no—
529C2×#117—672no—
530C22×C4⋊C4—672no—
531C22×C4⋊C4—672no—
532C22×C4⋊C4—672no—
533C22×C4⋊C4C2×D6712yes—
534C22×C42—671no—
535C2×#41—26816no—
536C2×#41—6732no—
537C22×Q8—2688no—
538C22×Q8—6716no—
539C22×Q8—674no—
540C22×Q8—674no—
541C22×Q8—672no—
542C22×Q8—671no—
543C22×Q8C22×D6711yescharacteristic
544C22×Q8C22×D6712yes—
545C22×D4—674no—
546C22×D4—672no—
547C22×D4—671no—
548C22×D4—672no—
549C22×D4C22×D6711yescharacteristic
550C23×C4—674no—
551C23×C4—674no—
552C23×C4—671no—
553C23×C4—671no—
554C23×C4—672no—
555C23×C4—671no—
556C23×C4C22×D6712yes—
557C23×C4C22×D6714yes—
558C4⋊Q8—6716no—
559C4⋊Q8—6716no—
560C4⋊Q8—6716no—
561C4⋊Q8—6732no—
562C4⋊Q8—6732no—
563C4⋊Q8—6716no—
564C4⋊Q8—678no—
565C4⋊Q8—6716no—
566C4⋊Q8C22×D6718yes—
567#126—6716no—
568#126—6732no—
569#126—6716no—
570#126—6732no—
571#125—678no—
572#125—678no—
573#125—6716no—
574#125—6732no—
575#125—6732no—
576#125C22×D67116yes—
577#124—678no—
578#124—678no—
579#124—6732no—
580#124—6732no—
581#123—6732no—
582#123—6716no—
583#123—6732no—
584#123—6716no—
585#123—6732no—
586#123—6732no—
587C22⋊Q8—678no—
588C22⋊Q8—6732no—
589C22⋊Q8—6732no—
590C22⋊Q8—6732no—
591C22⋊Q8—678no—
592C22⋊Q8—6732no—
593C22⋊Q8—6716no—
594C22⋊Q8—6732no—
595C22⋊Q8C22×D67132yes—
596C22⋊Q8C22×D67116yes—
597#121—678no—
598#121—6716no—
599#121—6716no—
600#121—678no—
601C4×Q8—6716no—
602C4×Q8—678no—
603C4×Q8—6716no—
604C4×Q8C22×D6718yes—
605C4×D4—6716no—
606C4×D4—6716no—
607C4×D4—6716no—
608C4×D4—678no—
609C4×D4C22×D6718yes—
610C4×D4C22×D67116yes—
611#117—6716no—
612#117—6716no—
613#117—6732no—
614#117—6716no—
615#117—6716no—
616C2×C4⋊C4—671no—
617C2×C4⋊C4—672no—
618C2×C4⋊C4—672no—
619C2×C4⋊C4—674no—
620C2×C4⋊C4—674no—
621C2×C4⋊C4—674no—
622C2×C4⋊C4—671no—
623C2×C4⋊C4—674no—
624C2×C4⋊C4—672no—
625C2×C4⋊C4—672no—
626C2×C4⋊C4—672no—
627C2×C4⋊C4—672no—
628C2×C4⋊C4—672no—
629C2×C4⋊C4—672no—
630C2×C4⋊C4—672no—
631C2×C4⋊C4—674no—
632C2×C4⋊C4—674no—
633C2×C4⋊C4—6716no—
634C2×C4⋊C4—6716no—
635C2×C4⋊C4—6716no—
636C2×C4⋊C4C22×D6712yes—
637C2×C4⋊C4C22×D6712yes—
638C2×C4⋊C4C22×D6711yescharacteristic
639C2×C4⋊C4C22×D6714yes—
640C2×C4⋊C4C22×D67116yes—
641C2×C4⋊C4C22×D6711yescharacteristic
642C2×C4⋊C4C22×D6714yes—
643C2×C4⋊C4C22×D6712yes—
644C2×C22⋊C4—672no—
645C2×C22⋊C4—674no—
646C2×C22⋊C4—672no—
647C2×C22⋊C4—672no—
648C2×C22⋊C4—672no—
649C2×C22⋊C4—672no—
650C2×C22⋊C4—672no—
651C2×C22⋊C4—674no—
652C2×C22⋊C4—672no—
653C2×C22⋊C4—674no—
654C2×C22⋊C4—672no—
655C2×C22⋊C4—672no—
656C2×C22⋊C4C22×D6714yes—
657C2×C22⋊C4C22×D6712yes—
658C2×C42—674no—
659C2×C42—671no—
660C2×C42—671no—
661C2×C42—672no—
662C2×C42—674no—
663C2×C42—671no—
664C2×C42—678no—
665C2×C42C22×D6712yes—
666C2×C42C22×D6711yescharacteristic
667C24—671no—
668C24—672no—
669C24C23×D6712yes—
670#41—26864no—
671C2×Q8—24no—
672C2×Q8—44no—
673C2×Q8—2688no—
674C2×Q8—2684no—
675C2×Q8—2688no—
676C2×Q8—26832no—
677C2×Q8—6716no—
678C2×Q8—6716no—
679C2×Q8—678no—
680C2×Q8—674no—
681C2×Q8—1344no—
682C2×Q8C23×D6714yes—
683C2×Q8C23×D6718yes—
684C2×D4—24no—
685C2×D4—2688no—
686C2×D4—6716no—
687C2×D4—678no—
688C2×D4—674no—
689C2×D4—678no—
690C2×D4—1348no—
691C2×D4—1348no—
692C2×D4—1344no—
693C2×D4C23×D6714yes—
694C22×C4—28no—
695C22×C4—48no—
696C22×C4—2688no—
697C22×C4—6716no—
698C22×C4—672no—
699C22×C4—671no—
700C22×C4—672no—
701C22×C4—671no—
702C22×C4—671no—
703C22×C4—674no—
704C22×C4—672no—
705C22×C4—674no—
706C22×C4—674no—
707C22×C4—674no—
708C22×C4—6716no—
709C22×C4—678no—
710C22×C4—1344no—
711C22×C4—13416no—
712C22×C4—1344no—
713C22×C4—1348no—
714C22×C4—1344no—
715C22×C4C23×D6718yes—
716C22×C4C23×D6712yes—
717C22×C4C23×D6712yes—
718C22×C4C23×D6711yescharacteristic
719C22×C4C23×D6712yes—
720C22×C4C23×D6714yes—
721C22×C4C23×D67116yes—
722C22×C4C23×D6711yescharacteristic
723C22×C4C23×D6711yescharacteristic
724C4⋊C4—674no—
725C4⋊C4—678no—
726C4⋊C4—678no—
727C4⋊C4—6716no—
728C4⋊C4—6716no—
729C4⋊C4—6716no—
730C4⋊C4—674no—
731C4⋊C4—6716no—
732C4⋊C4—678no—
733C4⋊C4—678no—
734C4⋊C4—678no—
735C4⋊C4—678no—
736C4⋊C4—678no—
737C4⋊C4—678no—
738C4⋊C4—678no—
739C4⋊C4—6716no—
740C4⋊C4—6716no—
741C4⋊C4C23×D6718yes—
742C4⋊C4C23×D6718yes—
743C4⋊C4C23×D6714yes—
744C4⋊C4C23×D67116yes—
745C4⋊C4C23×D6714yes—
746C4⋊C4C23×D67116yes—
747C4⋊C4C23×D6718yes—
748C22⋊C4—678no—
749C22⋊C4—6716no—
750C22⋊C4—678no—
751C22⋊C4—678no—
752C22⋊C4—678no—
753C22⋊C4—678no—
754C22⋊C4—678no—
755C22⋊C4—6716no—
756C22⋊C4—678no—
757C22⋊C4—6716no—
758C22⋊C4—678no—
759C22⋊C4—678no—
760C22⋊C4C23×D67116yes—
761C22⋊C4C23×D6718yes—
762C42—674no—
763C42—674no—
764C42—674no—
765C42—6716no—
766C42—678no—
767C42—6716no—
768C42C23×D6714yes—
769C42C23×D6718yes—
770C23—24no—
771C23—24no—
772C23—24no—
773C23—674no—
774C23—672no—
775C23—674no—
776C23—1344no—
777C23—1344no—
778C23—1344no—
779C23—1342no—
780C23—1342no—
781C23C24×D6714yes—
782C23C24×D6711yescharacteristic
783Q8—28no—
784Q8—48no—
785Q8—26816no—
786Q8—2688no—
787Q8—26816no—
788Q8—1348no—
789D4—28no—
790D4—26816no—
791D4—13416no—
792D4—13416no—
793D4—1348no—
794C2×C4—24no—
795C2×C4—28no—
796C2×C4—22no—
797C2×C4—24no—
798C2×C4—24no—
799C2×C4—216no—
800C2×C4—416no—
801C2×C4—26816no—
802C2×C4—674no—
803C2×C4—672no—
804C2×C4—672no—
805C2×C4—674no—
806C2×C4—672no—
807C2×C4—678no—
808C2×C4—674no—
809C2×C4—1348no—
810C2×C4—13432no—
811C2×C4—1344no—
812C2×C4—1348no—
813C2×C4—1342no—
814C2×C4—1342no—
815C2×C4—1344no—
816C2×C4—1342no—
817C2×C4—1344no—
818C2×C4—1348no—
819C2×C4—13416no—
820C2×C4—1348no—
821C2×C4#1452409014yes—
822C2×C4#1452409114yes—
823C2×C4C24×D6714yes—
824C2×C4C24×D6714yes—
825C2×C4C24×D6712yes—
826C2×C4C24×D6714yes—
827C2×C4C24×D6718yes—
828C2×C4C24×D6712yes—
829C2×C4C24×D6712yes—
830C22—24no—
831C22—24no—
832C22—24no—
833C22—48no—
834C22—2688no—
835C22—674no—
836C22—1344no—
837C22—1344no—
838C22—1344no—
839C22—1342no—
840C22—1342no—
841C22—1348no—
842C22H(5,𝔽2)×D6712yes—
843C22C2×#1452409012yes—
844C22C2×#1452409112yes—
845C22C25×D6711yescharacteristic
846C4—24no—
847C4—28no—
848C4—22no—
849C4—24no—
850C4—24no—
851C4—1344no—
852C4—1348no—
853C4—1342no—
854C4—1342no—
855C4—1342no—
856C4—1344no—
857C4—1344no—
858C4C2×#1452409014yes—
859C4C2×#1452409114yes—
860C2—44no—
861C2—2684no—
862C2—1344no—
863C2#2257455014yesdirect product factor
864C2C2×H(5,𝔽2)×D6711yescharacteristic
865C2C22×#1452409011yescharacteristic
866C2C22×#1452409111yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#554×C67C2
socleC23×C67C25
hypercenterC2×#554D67
hypocenterC67C2×#3544
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. #22574550C2direct (N × H)
2. C2×#16864147C2semidirect
3. C2×Q8×Dic134C2semidirect
4. C2×#16864111C2semidirect
5. C2×#16864107C2semidirect
6. C2×#16864084C2semidirect
7. C2×#16864080C2semidirect
8. C2×#16864051C2semidirect
9. C2×#16864047C2semidirect
10. C2×#16864027C2semidirect
11. C2×#16864026C2semidirect
12. C2×#16864019C2semidirect
13. C2×#16864011C2semidirect
14. C2×#16863969C2semidirect
15. C2×C4⋊Q8×D67C2semidirect
16. C2×#16863933C2semidirect
17. C2×#16863928C2semidirect
18. C2×#554×C67C2semidirect
21. #16864147C22semidirect
22. Q8×Dic134C22semidirect
23. #16864111C22semidirect
24. #16864107C22semidirect
25. #16864084C22semidirect
26. #16864080C22semidirect
27. #16864051C22semidirect
28. #16864047C22semidirect
29. #16864027C22semidirect
30. #16864026C22semidirect
31. #16864019C22semidirect
32. #16864011C22semidirect
33. #16863969C22semidirect
42. C4⋊Q8×D67C22semidirect
43. #16863933C22semidirect
44. #16863928C22semidirect
92. #554×C67C22semidirect
428. C2×C67#3544semidirect
439. C2×#554D67semidirect
452. C67C2×#3544semidirect
459. #554C2×D67semidirect
863. C2#22574550direct (N × H)

Maximal subgroups

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

subgroupindex
#225745502
C2×#168641472
C2×Q8×Dic1342
C2×#168641112
C2×#168641072
C2×#168640842
C2×#168640802
C2×#168640512
C2×#168640472
C2×#168640272
C2×#168640262
C2×#168640192
C2×#168640112
C2×#168639692
C2×C4⋊Q8×D672
C2×#168639332
C2×#168639282
C2×#554×C672
C2×#354467