Finite Group Databasebeta

← C2×#22574651 #31763437

Subgroups — C2×#22574651 #31763437

Order 17152.

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#22574651C2132yesmaximal, direct product factor
2C2×#16864147C214yesmaximal, complemented
3C2×#16864124C211yesmaximal, characteristic, complemented
4C2×#16864120C211yesmaximal, characteristic, complemented
5C2×#16864107C212yesmaximal, complemented
6C2×#16864096C212yesmaximal, complemented
7C2×Q8×C22⋊D67C212yesmaximal, complemented
8C2×#16864056C212yesmaximal, complemented
9C2×#16864051C211yesmaximal, characteristic, complemented
10C2×#16864023C212yesmaximal, complemented
11C2×#16864011C212yesmaximal, complemented
12C2×#16864006C212yesmaximal, complemented
13C2×#16863992C214yesmaximal, complemented
14C2×#16863970C212yesmaximal, complemented
15C2×C4⋊Q8×D67C211yesmaximal, characteristic, complemented
16C2×#16863933C211yesmaximal, characteristic, complemented
17C2×#16863928C211yesmaximal, characteristic, complemented
18C2×D4×Q8×C67C211yesmaximal, characteristic, complemented
19C22×#11761628C2212yes—
20C22×Q8×D67C2212yes—
21#16864147C22164yescomplemented
22#16864124C22116yescomplemented
23#16864120C22116yescomplemented
24#16864107C22132yescomplemented
25#16864096C22132yescomplemented
26Q8×C22⋊D67C22132yescomplemented
27#16864056C22132yescomplemented
28#16864051C22116yescomplemented
29#16864023C22132yescomplemented
30#16864011C22132yescomplemented
31#16864006C22132yescomplemented
32#16863992C22164yescomplemented
33#16863970C22132yescomplemented
34C2×#14524043C2211yescharacteristic
35C2×#14524042C2212yes—
36C2×#14524042C2212yes—
37C2×#14524041C2214yes—
38C2×#14524041C2212yes—
39C2×#14524041C2212yes—
40C4⋊Q8×D67C22116yescomplemented
41#16863933C22116yescomplemented
42#16863928C22116yescomplemented
43C2×#14524038C2212yes—
44C2×#14524038C2214yes—
45C2×#14524036C2212yes—
46C2×#14524036C2214yes—
47C2×#14524036C2214yes—
48C2×#14524035C2212yes—
49C2×#14524034C2214yes—
50C2×#14524034C2211yescharacteristic
51C2×#14524034C2211yescharacteristic
52C2×#14524033C2214yes—
53C2×#14524033C2214yes—
54C2×#14524032C2212yes—
55C2×#14524032C2211yescharacteristic
56C2×#14524030C2211yescharacteristic
57C2×#14524029C2214yes—
58C2×#14524028C2212yes—
59C2×#14524026C2214yes—
60C2×#14524026C2214yes—
61C2×#14524025C2214yes—
62C2×#14524025C2212yes—
63C2×#14524023C2212yes—
64C2×#14524023C2211yescharacteristic
65C2×#14524022C2214yes—
66C2×#14524022C2212yes—
67C2×#14524021C2214yes—
68C2×#14524019C2214yes—
69C2×#14524019C2214yes—
70C2×#14524019C2211yescharacteristic
71C2×#14524019C2214yes—
72C2×#14524018C2211yescharacteristic
73C2×#14524016C2214yes—
74C2×#14524014C2212yes—
75C2×#14524014C2211yescharacteristic
76C2×Q8×Dic67C2212yes—
77C2×C4×Dic134C2212yes—
78C2×C4×Dic134C2211yescharacteristic
79C2×#14524008C2212yes—
80C2×C4×D268C2211yescharacteristic
81C2×C4×D268C2212yes—
82C2×#14524005C2214yes—
83C2×C4×C22⋊D67C2212yes—
84C2×C4×C22⋊D67C2214yes—
85C2×#14524002C2212yes—
86C2×#14524001C2212yes—
87C2×#14524000C2212yes—
88C2×C4⋊C4×D67C2212yes—
89C2×C4⋊C4×D67C2212yes—
90C2×C4⋊C4×D67C2212yes—
91C2×C42×D67C2211yescharacteristic
92C23×Q8×C67C2212yes—
93D4×Q8×C67C22116yescomplemented
94C2×C4⋊Q8×C67C2212yes—
95C2×C4⋊Q8×C67C2211yescharacteristic
96C2×C22⋊Q8×C67C2214yes—
97C2×C22⋊Q8×C67C2212yes—
98C2×C4×Q8×C67C2211yescharacteristic
99C2×C4×D4×C67C2212yes—
100C2×C4×D4×C67C2211yescharacteristic
101C2×#11761628—48no—
102C2×#11761628C23116yes—
103C22×Dic134C2312yes—
104C22×Dic134C2311yescharacteristic
105C22×Dic134C2314yes—
106C2×Q8×D67—48no—
107C2×Q8×D67C23116yes—
108C22×D268C2312yes—
109C22×D268C2311yescharacteristic
110C22×C22⋊D67C2312yes—
111C22×C22⋊D67C2314yes—
112C22×C4×D67C2311yescharacteristic
113C22×C4×D67C2311yescharacteristic
114C22×C4×D67C2311yescharacteristic
115C22×C4×D67C2312yes—
116C22×C4×D67C2314yes—
117C22×C4×D67C2314yes—
118#14524043C2318yes—
119#14524042C23116yes—
120#14524042C23116yes—
121#14524041C23116yes—
122#14524041C23132yes—
123#14524041C23116yes—
124#14524038C23132yes—
125#14524038C23116yes—
126#14524036C23132yes—
127#14524036C23132yes—
128#14524036C23116yes—
129#14524035C23116yes—
130#14524034C2318yes—
131#14524034C23132yes—
132#14524034C2318yes—
133#14524033C23132yes—
134#14524033C23132yes—
135#14524032C23116yes—
136#14524032C2318yes—
137#14524030C2318yes—
138#14524029C23132yes—
139#14524028C23116yes—
140#14524026C23132yes—
141#14524026C23132yes—
142#14524025C23132yes—
143#14524025C23116yes—
144#14524023C23116yes—
145#14524023C2318yes—
146#14524022C23116yes—
147#14524022C23132yes—
148#14524021C23132yes—
149#14524019C23132yes—
150#14524019C2318yes—
151#14524019C23132yes—
152#14524019C23132yes—
153#14524018C2318yes—
154#14524016C23132yes—
155#14524014C23116yes—
156#14524014C2318yes—
157Q8×Dic67C23116yes—
158C4×Dic134C23116yes—
159C4×Dic134C2318yes—
160#14524008C23116yes—
161C4×D268C2318yes—
162C4×D268C23116yes—
163#14524005C23132yes—
164C4×C22⋊D67C23116yes—
165C4×C22⋊D67C23132yes—
166#14524002C23116yes—
167#14524001C23116yes—
168#14524000C23116yes—
169C2×C4⋊Dic67C2312yes—
170C2×C4⋊Dic67C2312yes—
171C2×C4⋊Dic67C2311yescharacteristic
172C2×C4⋊Dic67C2312yes—
173C2×C4⋊Dic67C2312yes—
174C2×C4⋊Dic67C2311yescharacteristic
175C2×C4⋊Dic67C2312yes—
176C2×C4⋊Dic67C2314yes—
177C2×Dic67⋊C4C2314yes—
178C2×Dic67⋊C4C2314yes—
179C2×Dic67⋊C4C2314yes—
180C2×Dic67⋊C4C2312yes—
181C2×Dic67⋊C4C2312yes—
182C2×Dic67⋊C4C2314yes—
183C2×Dic67⋊C4C2312yes—
184C2×Dic67⋊C4C2314yes—
185C2×Dic67⋊C4C2314yes—
186C2×Dic67⋊C4C2312yes—
187C4⋊C4×D67C23116yes—
188C4⋊C4×D67C23116yes—
189C4⋊C4×D67C23116yes—
190C2×C22⋊Dic67C2312yes—
191C2×C22⋊Dic67C2312yes—
192C2×C22⋊Dic67C2314yes—
193C2×C22⋊Dic67C2312yes—
194C2×(C2×D67)⋊C4C2312yes—
195C2×(C2×D67)⋊C4C2312yes—
196C2×(C2×D67)⋊C4C2314yes—
197C2×(C2×D67)⋊C4C2312yes—
198C2×(C2×D67)⋊C4C2312yes—
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×Dic67C2312yes—
207C2×C4×Dic67C2314yes—
208C42×D67C2318yes—
209C22×Q8×C67—48no—
210C22×Q8×C67C2311yescharacteristic
211C22×Q8×C67C2312yes—
212C22×Q8×C67C23116yes—
213C22×Q8×C67C2314yes—
214C22×D4×C67C2311yescharacteristic
215C23×C4×C67C2312yes—
216C23×C4×C67C2314yes—
217C4⋊Q8×C67C23116yes—
218C4⋊Q8×C67C2318yes—
219C22⋊Q8×C67C23116yes—
220C22⋊Q8×C67C23132yes—
221C4×Q8×C67C2318yes—
222C4×D4×C67C23116yes—
223C4×D4×C67C2318yes—
224C2×C4⋊C4×C67C2311yescharacteristic
225C2×C4⋊C4×C67C2312yes—
226C2×C4⋊C4×C67C2311yescharacteristic
227C2×C4⋊C4×C67C2312yes—
228C2×C4⋊C4×C67C2312yes—
229C2×C4⋊C4×C67C2314yes—
230C2×C22⋊C4×C67C2314yes—
231C2×C22⋊C4×C67C2312yes—
232C2×C42×C67C2311yescharacteristic
233C2×C42×C67C2312yes—
234C23×D67C2412yes—
235C23×D67C2411yescharacteristic
236#11761628—432no—
237C2×Dic134—28no—
238C2×Dic134—24no—
239C2×Dic134—48no—
240C2×Dic134C2418yes—
241C2×Dic134C2414yes—
242C2×Dic134C24116yes—
243Q8×D67—432no—
244C2×D268—28no—
245C2×D268—24no—
246C2×D268C2418yes—
247C2×D268C2414yes—
248C2×C22⋊D67—28no—
249C2×C22⋊D67—48no—
250C2×C22⋊D67C2418yes—
251C2×C22⋊D67C24116yes—
252C22×Dic67C2412yes—
253C22×Dic67C2412yes—
254C22×Dic67C2411yescharacteristic
255C22×Dic67C2411yescharacteristic
256C22×Dic67C2412yes—
257C22×Dic67C2411yescharacteristic
258C22×Dic67C2414yes—
259C2×C4×D67—24no—
260C2×C4×D67—24no—
261C2×C4×D67—24no—
262C2×C4×D67—28no—
263C2×C4×D67—48no—
264C2×C4×D67—48no—
265C2×C4×D67C2414yes—
266C2×C4×D67C2414yes—
267C2×C4×D67C2414yes—
268C2×C4×D67C2418yes—
269C2×C4×D67C24116yes—
270C2×C4×D67C24116yes—
271C4⋊Dic67C2418yes—
272C4⋊Dic67C2418yes—
273C4⋊Dic67C2414yes—
274C4⋊Dic67C2418yes—
275C4⋊Dic67C2418yes—
276C4⋊Dic67C2414yes—
277C4⋊Dic67C2418yes—
278C4⋊Dic67C24116yes—
279Dic67⋊C4C24116yes—
280Dic67⋊C4C24116yes—
281Dic67⋊C4C24116yes—
282Dic67⋊C4C2418yes—
283Dic67⋊C4C2418yes—
284Dic67⋊C4C24116yes—
285Dic67⋊C4C2418yes—
286Dic67⋊C4C24116yes—
287Dic67⋊C4C24116yes—
288Dic67⋊C4C2418yes—
289C22⋊Dic67C2418yes—
290C22⋊Dic67C2418yes—
291C22⋊Dic67C24116yes—
292C22⋊Dic67C2418yes—
293(C2×D67)⋊C4C2418yes—
294(C2×D67)⋊C4C2418yes—
295(C2×D67)⋊C4C24116yes—
296(C2×D67)⋊C4C2418yes—
297(C2×D67)⋊C4C2418yes—
298(C2×D67)⋊C4C24116yes—
299(C2×D67)⋊C4C2418yes—
300(C2×D67)⋊C4C2418yes—
301C4×Dic67C2414yes—
302C4×Dic67C2414yes—
303C4×Dic67C2414yes—
304C4×Dic67C24116yes—
305C4×Dic67C2418yes—
306C4×Dic67C24116yes—
307C24×C67C2412yes—
308C2×Q8×C67—24no—
309C2×Q8×C67—28no—
310C2×Q8×C67—48no—
311C2×Q8×C67—432no—
312C2×Q8×C67C2414yes—
313C2×Q8×C67C2418yes—
314C2×Q8×C67C24116yes—
315C2×D4×C67—24no—
316C2×D4×C67C2414yes—
317C22×C4×C67—28no—
318C22×C4×C67—48no—
319C22×C4×C67C2412yes—
320C22×C4×C67C2411yescharacteristic
321C22×C4×C67C2412yes—
322C22×C4×C67C2414yes—
323C22×C4×C67C2412yes—
324C22×C4×C67C2418yes—
325C22×C4×C67C24116yes—
326C22×C4×C67C2411yescharacteristic
327C22×C4×C67C2411yescharacteristic
328C4⋊C4×C67C2414yes—
329C4⋊C4×C67C2418yes—
330C4⋊C4×C67C2414yes—
331C4⋊C4×C67C2418yes—
332C4⋊C4×C67C2418yes—
333C4⋊C4×C67C24116yes—
334C22⋊C4×C67C24116yes—
335C22⋊C4×C67C2418yes—
336C42×C67C2414yes—
337C42×C67C2418yes—
338C23×C67—24no—
339C23×C67—24no—
340C23×C67—24no—
341C23×C67C2514yes—
342C23×C67C2511yescharacteristic
343C22×D67—22no—
344C22×D67—22no—
345C22×D67—24no—
346C22×D67—24no—
347C22×D67—24no—
348C22×D672−1+414yes—
349C22×D67C2514yes—
350C22×D67C2512yes—
351Q8×C67—28no—
352Q8×C67—216no—
353Q8×C67—416no—
354D4×C67—28no—
355C2×C4×C67—24no—
356C2×C4×C67—24no—
357C2×C4×C67—28no—
358C2×C4×C67—22no—
359C2×C4×C67—24no—
360C2×C4×C67—216no—
361C2×C4×C67—416no—
362C2×C4×C67H(5,𝔽2)14yes—
363C2×C4×C672−1+414yes—
364C2×C4×C67C2514yes—
365C2×C4×C67C2512yes—
366C2×C4×C67C2514yes—
367C2×C4×C67C2518yes—
368C2×C4×C67C2514yes—
369C2×C4×C67C2512yes—
370C2×C4×C67C2512yes—
371C22⋊D67—216no—
372C22⋊D67—416no—
373C2×Dic67—22no—
374C2×Dic67—28no—
375C2×Dic67—22no—
376C2×Dic67—22no—
377C2×Dic67—24no—
378C2×Dic67—24no—
379C2×Dic67—24no—
380C2×Dic67C2514yes—
381C2×Dic67C2514yes—
382C2×Dic67C2512yes—
383C2×Dic67C2512yes—
384C2×Dic67C2514yes—
385C2×Dic67C2512yes—
386C2×Dic67C2518yes—
387D268—216no—
388D268—28no—
389C4×D67—28no—
390C4×D67—28no—
391C4×D67—28no—
392C4×D67—216no—
393C4×D67—416no—
394C4×D67—416no—
395Dic134—216no—
396Dic134—28no—
397Dic134—416no—
398C22×C67—24no—
399C22×C67—24no—
400C22×C67—24no—
401C22×C67—48no—
402C22×C67C2×H(5,𝔽2)12yes—
403C22×C67C2×2−1+412yes—
404C22×C67C2×2−1+412yes—
405C22×C67C2611yescharacteristic
406C2×D67—22no—
407C2×D67—22no—
408C2×D67—28no—
409C2×D67—24no—
410C2×D67—24no—
411C2×D67—24no—
412C2×D67—48no—
413C2×D67C2×2−1+414yes—
414C4×C67—28no—
415C4×C67—24no—
416C4×C67—24no—
417C4×C67—22no—
418C4×C67—24no—
419C4×C67C2×H(5,𝔽2)14yes—
420C4×C67C2×2−1+414yes—
421Dic67—28no—
422Dic67—22no—
423Dic67—24no—
424Dic67—22no—
425Dic67—22no—
426Dic67—24no—
427Dic67—24no—
428C2×#3552—671nomaximal, Sylow
429C2×C67—44no—
430C2×C67#355214yescomplemented
431C2×C67C22×H(5,𝔽2)11yescharacteristic
432C2×C67C22×2−1+411yescharacteristic
433C2×C67C22×2−1+411yescharacteristic
434D67—24no—
435D67—44no—
436#3552—6732no—
437C2×#563—674no—
438C2×#557—671no—
439C2×#556—671no—
440C2×#554—672no—
441C2×#553—672no—
442C2×D4×Q8—672no—
443C2×D4×Q8D6711yescharacteristic, complemented
444C2×#548—672no—
445C2×#547—671no—
446C2×#544—672no—
447C2×#542—672no—
448C2×#541—672no—
449C2×#539—674no—
450C2×#536—672no—
451C22×C4⋊Q8—671no—
452C2×#529—671no—
453C2×#529—671no—
454C67C2×#355211yescharacteristic, complemented, Sylow
455C22×#41—672no—
456C23×Q8—672no—
457C23×Q8C2×D6712yes—
458#563—6764no—
459#557—6716no—
460#556—6716no—
461#554—6732no—
462#553—6732no—
463D4×Q8—6732no—
464D4×Q8C2×D67116yescomplemented
465#548—6732no—
466#547—6716no—
467#544—6732no—
468#542—6732no—
469#541—6732no—
470#539—6764no—
471#536—6732no—
472C2×C4⋊Q8—672no—
473C2×C4⋊Q8—672no—
474C2×C4⋊Q8—674no—
475C2×C4⋊Q8—6716no—
476C2×C4⋊Q8—672no—
477C2×C4⋊Q8—672no—
478C2×C4⋊Q8—671no—
479C2×C4⋊Q8C2×D6711yescharacteristic
480C2×C4⋊Q8C2×D6712yes—
481#529—6716no—
482#529—6716no—
483C2×#126—672no—
484C2×#126—674no—
485C2×#126—672no—
486C2×#126—674no—
487C2×#126—674no—
488C2×#125—671no—
489C2×#125—671no—
490C2×#125—674no—
491C2×#125—674no—
492C2×#125—674no—
493C2×#125—672no—
494C2×#124—671no—
495C2×#124—672no—
496C2×#124—671no—
497C2×#124—674no—
498C2×#123—674no—
499C2×#123—674no—
500C2×#123—672no—
501C2×#123—672no—
502C2×#123—674no—
503C2×C22⋊Q8—671no—
504C2×C22⋊Q8—674no—
505C2×C22⋊Q8—674no—
506C2×C22⋊Q8—674no—
507C2×C22⋊Q8—672no—
508C2×C22⋊Q8—674no—
509C2×C22⋊Q8—671no—
510C2×C22⋊Q8—672no—
511C2×C22⋊Q8—674no—
512C2×C22⋊Q8C2×D6714yes—
513C2×C22⋊Q8C2×D6712yes—
514C2×#121—671no—
515C2×#121—672no—
516C2×#121—671no—
517C2×#121—674no—
518C2×C4×Q8—672no—
519C2×C4×Q8—672no—
520C2×C4×Q8—671no—
521C2×C4×Q8—672no—
522C2×C4×Q8C2×D6711yescharacteristic
523C2×C4×D4—672no—
524C2×C4×D4—674no—
525C2×C4×D4—674no—
526C2×C4×D4—671no—
527C2×C4×D4—672no—
528C2×C4×D4C2×D6711yescharacteristic
529C2×C4×D4C2×D6712yes—
530C2×#117—672no—
531C2×#117—672no—
532C2×#117—672no—
533C22×C4⋊C4—672no—
534C22×C4⋊C4—672no—
535C22×C4⋊C4—672no—
536C22×C42—671no—
537C2×#41—2688no—
538C2×#41—6716no—
539C22×Q8—48no—
540C22×Q8—2688no—
541C22×Q8—6716no—
542C22×Q8—674no—
543C22×Q8—671no—
544C22×Q8—672no—
545C22×Q8C22×D6712yes—
546C22×Q8C22×D6711yescharacteristic
547C22×Q8C22×D6714yes—
548C22×Q8C22×D67116yes—
549C22×D4—674no—
550C22×D4—672no—
551C22×D4—672no—
552C22×D4—671no—
553C22×D4C22×D6711yescharacteristic
554C23×C4—674no—
555C23×C4—674no—
556C23×C4—671no—
557C23×C4—671no—
558C23×C4—672no—
559C23×C4—671no—
560C23×C4C22×D6712yes—
561C23×C4C22×D6714yes—
562C4⋊Q8—6716no—
563C4⋊Q8—6716no—
564C4⋊Q8—6732no—
565C4⋊Q8—6716no—
566C4⋊Q8—6716no—
567C4⋊Q8—678no—
568C4⋊Q8C22×D6718yes—
569C4⋊Q8C22×D67116yes—
570#126—6716no—
571#126—6732no—
572#126—6716no—
573#126—6732no—
574#126—6732no—
575#125—678no—
576#125—678no—
577#125—6732no—
578#125—6732no—
579#125—6732no—
580#125—6716no—
581#124—678no—
582#124—6716no—
583#124—678no—
584#124—6732no—
585#123—6732no—
586#123—6732no—
587#123—6716no—
588#123—6716no—
589#123—6732no—
590C22⋊Q8—678no—
591C22⋊Q8—6732no—
592C22⋊Q8—6732no—
593C22⋊Q8—6732no—
594C22⋊Q8—6716no—
595C22⋊Q8—6732no—
596C22⋊Q8—678no—
597C22⋊Q8—6716no—
598C22⋊Q8—6732no—
599C22⋊Q8C22×D67132yes—
600C22⋊Q8C22×D67116yes—
601#121—678no—
602#121—6716no—
603#121—678no—
604#121—6732no—
605C4×Q8—6716no—
606C4×Q8—6716no—
607C4×Q8—678no—
608C4×Q8—6716no—
609C4×Q8C22×D6718yes—
610C4×D4—6716no—
611C4×D4—6732no—
612C4×D4—6732no—
613C4×D4—678no—
614C4×D4—6716no—
615C4×D4C22×D6718yes—
616C4×D4C22×D67116yes—
617#117—6716no—
618#117—6716no—
619#117—6716no—
620C2×C4⋊C4—672no—
621C2×C4⋊C4—674no—
622C2×C4⋊C4—674no—
623C2×C4⋊C4—674no—
624C2×C4⋊C4—672no—
625C2×C4⋊C4—671no—
626C2×C4⋊C4—672no—
627C2×C4⋊C4—672no—
628C2×C4⋊C4—672no—
629C2×C4⋊C4—672no—
630C2×C4⋊C4—671no—
631C2×C4⋊C4—672no—
632C2×C4⋊C4—674no—
633C2×C4⋊C4—672no—
634C2×C4⋊C4—674no—
635C2×C4⋊C4—674no—
636C2×C4⋊C4—674no—
637C2×C4⋊C4—672no—
638C2×C4⋊C4—6716no—
639C2×C4⋊C4—6716no—
640C2×C4⋊C4—6716no—
641C2×C4⋊C4C22×D6711yescharacteristic
642C2×C4⋊C4C22×D6712yes—
643C2×C4⋊C4C22×D6712yes—
644C2×C4⋊C4C22×D6714yes—
645C2×C4⋊C4C22×D6711yescharacteristic
646C2×C4⋊C4C22×D6712yes—
647C2×C22⋊C4—672no—
648C2×C22⋊C4—672no—
649C2×C22⋊C4—674no—
650C2×C22⋊C4—672no—
651C2×C22⋊C4—674no—
652C2×C22⋊C4—672no—
653C2×C22⋊C4—672no—
654C2×C22⋊C4—672no—
655C2×C22⋊C4—672no—
656C2×C22⋊C4—672no—
657C2×C22⋊C4—674no—
658C2×C22⋊C4—672no—
659C2×C22⋊C4C22×D6714yes—
660C2×C22⋊C4C22×D6712yes—
661C2×C42—671no—
662C2×C42—671no—
663C2×C42—672no—
664C2×C42—674no—
665C2×C42—674no—
666C2×C42—671no—
667C2×C42—678no—
668C2×C42C22×D6712yes—
669C2×C42C22×D6711yescharacteristic
670C24—671no—
671C24—672no—
672C24C23×D6712yes—
673#41—26832no—
674C2×Q8—24no—
675C2×Q8—28no—
676C2×Q8—48no—
677C2×Q8—432no—
678C2×Q8—2688no—
679C2×Q8—26832no—
680C2×Q8—6716no—
681C2×Q8—674no—
682C2×Q8—678no—
683C2×Q8—1348no—
684C2×Q8—1344no—
685C2×Q8C23×D6718yes—
686C2×Q8C23×D6714yes—
687C2×Q8C23×D67116yes—
688C2×D4—24no—
689C2×D4—2688no—
690C2×D4—6716no—
691C2×D4—678no—
692C2×D4—678no—
693C2×D4—674no—
694C2×D4—1348no—
695C2×D4—1348no—
696C2×D4—1344no—
697C2×D4C23×D6714yes—
698C22×C4—28no—
699C22×C4—48no—
700C22×C4—2688no—
701C22×C4—2688no—
702C22×C4—6716no—
703C22×C4—6716no—
704C22×C4—672no—
705C22×C4—672no—
706C22×C4—671no—
707C22×C4—671no—
708C22×C4—672no—
709C22×C4—671no—
710C22×C4—674no—
711C22×C4—674no—
712C22×C4—674no—
713C22×C4—674no—
714C22×C4—678no—
715C22×C4—1344no—
716C22×C4—1344no—
717C22×C4—1348no—
718C22×C4—1344no—
719C22×C4C23×D6718yes—
720C22×C4C23×D6712yes—
721C22×C4C23×D6711yescharacteristic
722C22×C4C23×D6714yes—
723C22×C4C23×D6712yes—
724C22×C4C23×D6712yes—
725C22×C4C23×D67116yes—
726C22×C4C23×D6711yescharacteristic
727C22×C4C23×D6711yescharacteristic
728C4⋊C4—678no—
729C4⋊C4—6716no—
730C4⋊C4—6716no—
731C4⋊C4—6716no—
732C4⋊C4—678no—
733C4⋊C4—674no—
734C4⋊C4—678no—
735C4⋊C4—678no—
736C4⋊C4—678no—
737C4⋊C4—678no—
738C4⋊C4—674no—
739C4⋊C4—678no—
740C4⋊C4—6716no—
741C4⋊C4—678no—
742C4⋊C4—6716no—
743C4⋊C4—6716no—
744C4⋊C4—6716no—
745C4⋊C4—678no—
746C4⋊C4C23×D6714yes—
747C4⋊C4C23×D6718yes—
748C4⋊C4C23×D6718yes—
749C4⋊C4C23×D67116yes—
750C4⋊C4C23×D6714yes—
751C4⋊C4C23×D6718yes—
752C22⋊C4—678no—
753C22⋊C4—678no—
754C22⋊C4—6716no—
755C22⋊C4—678no—
756C22⋊C4—6716no—
757C22⋊C4—678no—
758C22⋊C4—678no—
759C22⋊C4—678no—
760C22⋊C4—678no—
761C22⋊C4—678no—
762C22⋊C4—6716no—
763C22⋊C4—678no—
764C22⋊C4C23×D67116yes—
765C22⋊C4C23×D6718yes—
766C42—674no—
767C42—674no—
768C42—674no—
769C42—678no—
770C42—6716no—
771C42—6716no—
772C42C23×D6714yes—
773C42C23×D6718yes—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—674no—
778C23—672no—
779C23—674no—
780C23—1344no—
781C23—1344no—
782C23—1344no—
783C23—1342no—
784C23—1342no—
785C23C24×D6714yes—
786C23C24×D6711yescharacteristic
787Q8—28no—
788Q8—216no—
789Q8—416no—
790Q8—26816no—
791Q8—13416no—
792Q8—1348no—
793D4—28no—
794D4—26816no—
795D4—13416no—
796D4—13416no—
797D4—1348no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—28no—
801C2×C4—22no—
802C2×C4—24no—
803C2×C4—216no—
804C2×C4—416no—
805C2×C4—26816no—
806C2×C4—26816no—
807C2×C4—674no—
808C2×C4—674no—
809C2×C4—672no—
810C2×C4—672no—
811C2×C4—674no—
812C2×C4—672no—
813C2×C4—678no—
814C2×C4—1348no—
815C2×C4—1348no—
816C2×C4—1342no—
817C2×C4—1342no—
818C2×C4—1344no—
819C2×C4—1342no—
820C2×C4—1344no—
821C2×C4—1344no—
822C2×C4—1348no—
823C2×C4—13416no—
824C2×C4—1348no—
825C2×C4#1452408814yes—
826C2×C4#1452409114yes—
827C2×C4C24×D6714yes—
828C2×C4C24×D6712yes—
829C2×C4C24×D6718yes—
830C2×C4C24×D6714yes—
831C2×C4C24×D6714yes—
832C2×C4C24×D6712yes—
833C2×C4C24×D6712yes—
834C22—24no—
835C22—24no—
836C22—24no—
837C22—48no—
838C22—2688no—
839C22—674no—
840C22—1344no—
841C22—1344no—
842C22—1344no—
843C22—1348no—
844C22—1342no—
845C22—1342no—
846C22C2×#1452408812yes—
847C222−1+4×D6712yes—
848C22C2×#1452409112yes—
849C22C25×D6711yescharacteristic
850C4—24no—
851C4—24no—
852C4—28no—
853C4—22no—
854C4—24no—
855C4—1348no—
856C4—1342no—
857C4—1342no—
858C4—1344no—
859C4—1342no—
860C4—1344no—
861C4—1344no—
862C4C2×#1452408814yes—
863C4C2×#1452409114yes—
864C2—44no—
865C2—2684no—
866C2—1344no—
867C2#2257465114yesdirect product factor
868C2C22×#1452408811yescharacteristic
869C2C2×2−1+4×D6711yescharacteristic
870C2C22×#1452409111yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×D4×Q8×C67C2
socleC23×C67C25
hypercenterC2×D4×Q8D67
hypocenterC67C2×#3552
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
1. #22574651C2direct (N × H)
2. C2×#16864147C2semidirect
3. C2×#16864124C2semidirect
4. C2×#16864120C2semidirect
5. C2×#16864107C2semidirect
6. C2×#16864096C2semidirect
7. C2×Q8×C22⋊D67C2semidirect
8. C2×#16864056C2semidirect
9. C2×#16864051C2semidirect
10. C2×#16864023C2semidirect
11. C2×#16864011C2semidirect
12. C2×#16864006C2semidirect
13. C2×#16863992C2semidirect
14. C2×#16863970C2semidirect
15. C2×C4⋊Q8×D67C2semidirect
16. C2×#16863933C2semidirect
17. C2×#16863928C2semidirect
18. C2×D4×Q8×C67C2semidirect
21. #16864147C22semidirect
22. #16864124C22semidirect
23. #16864120C22semidirect
24. #16864107C22semidirect
25. #16864096C22semidirect
26. Q8×C22⋊D67C22semidirect
27. #16864056C22semidirect
28. #16864051C22semidirect
29. #16864023C22semidirect
30. #16864011C22semidirect
31. #16864006C22semidirect
32. #16863992C22semidirect
33. #16863970C22semidirect
40. C4⋊Q8×D67C22semidirect
41. #16863933C22semidirect
42. #16863928C22semidirect
93. D4×Q8×C67C22semidirect
430. C2×C67#3552semidirect
443. C2×D4×Q8D67semidirect
454. C67C2×#3552semidirect
464. D4×Q8C2×D67semidirect
867. C2#22574651direct (N × H)

Maximal subgroups

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

subgroupindex
#225746512
C2×#168641472
C2×#168641242
C2×#168641202
C2×#168641072
C2×#168640962
C2×Q8×C22⋊D672
C2×#168640562
C2×#168640512
C2×#168640232
C2×#168640112
C2×#168640062
C2×#168639922
C2×#168639702
C2×C4⋊Q8×D672
C2×#168639332
C2×#168639282
C2×D4×Q8×C672
C2×#355267