Finite Group Databasebeta

← C2×#22574092 #31764270

Subgroups — C2×#22574092 #31764270

Order 17152.

7022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22574092C2132yesmaximal, direct product factor
2C2×#16864124C211yesmaximal, characteristic, complemented
3C2×#16864121C212yesmaximal, complemented
4C2×#16864120C211yesmaximal, characteristic, complemented
5C2×#16864119C211yesmaximal, characteristic, complemented
6C2×#16864118C212yesmaximal, complemented
7C2×#16864087C212yesmaximal, complemented
8C2×#16864084C212yesmaximal, complemented
9C2×#16864078C214yesmaximal, complemented
10C2×#16864005C214yesmaximal, complemented
11C2×#16863971C212yesmaximal
12C2×#16863952C212yesmaximal, complemented
13C2×#16863950C212yesmaximal, complemented
14C2×#16863950C211yesmaximal, characteristic, complemented
15C2×C4⋊Q8×D67C211yesmaximal, characteristic, complemented
16C2×#16863872C212yesmaximal, complemented
17C2×C4×#11761629C211yesmaximal, characteristic
18C2×#557×C67C211yesmaximal, characteristic, complemented
19C22×#11761629C2211yescharacteristic
20C22×Q8×D67C2212yes—
21#16864124C22116yescomplemented
22#16864121C22132yescomplemented
23#16864120C22116yescomplemented
24#16864119C22116yescomplemented
25#16864118C22132yescomplemented
26#16864087C22132yescomplemented
27#16864084C22132yescomplemented
28#16864078C22164yescomplemented
29#16864005C22164yescomplemented
30#16863971C22132yes—
31#16863952C22132yescomplemented
32#16863950C22132yescomplemented
33#16863950C22116yescomplemented
34C2×#14524043C2211yescharacteristic
35C2×#14524042C2212yes—
36C2×#14524042C2212yes—
37C2×#14524042C2211yescharacteristic
38C2×#14524041C2212yes—
39C2×#14524041C2211yescharacteristic
40C2×#14524041C2212yes—
41C4⋊Q8×D67C22116yescomplemented
42C2×#14524038C2214yes—
43C2×#14524038C2214yes—
44C2×#14524038C2214yes—
45C2×#14524037C2214yes—
46C2×#14524035C2212yes—
47C2×#14524034C2214yes—
48C2×#14524033C2212yes—
49C2×#14524033C2214yes—
50C2×#14524033C2214yes—
51C2×#14524033C2214yes—
52C2×#14524032C2212yes—
53C2×#14524031C2212yes—
54C2×#14524028C2214yes—
55C2×#14524028C2214yes—
56C2×#14524023C2211yescharacteristic
57C2×#14524023C2212yes—
58C2×#14524021C2214yes—
59C2×#14524021C2214yes—
60C2×#14524021C2212yes—
61C2×#14524021C2214yes—
62C2×#14524019C2211yescharacteristic
63C2×#14524019C2212yes—
64#16863872C22132yescomplemented
65C4×#11761629C22116yes—
66C2×Q8×Dic67C2211yescharacteristic
67C2×Q8×Dic67C2212yes—
68C2×C4×Dic134C2214yes—
69C2×C4×Dic134C2212yes—
70C2×C4×Dic134C2212yes—
71C2×C4×Dic134C2212yes—
72C2×C4×Dic134C2211yescharacteristic
73C2×#14524008C2214yes—
74C2×#14524008C2212yes—
75C2×#14524008C2214yes—
76C2×C4×D268C2212yes—
77C2×C4×D268C2211yescharacteristic
78C2×#14524005C2212yes—
79C2×#14524005C2211yescharacteristic
80C2×#14524001C2212yes—
81C2×#14524001C2211yescharacteristic
82C2×#14524001C2214yes—
83C2×#14524001C2212yes—
84C2×#14524001C2212yes—
85C2×#14524000C2214yes—
86C2×#14524000C2212yes—
87C2×#14524000C2214yes—
88C2×C4⋊C4×D67C2212yes—
89C2×C4⋊C4×D67C2212yes—
90C2×C42×D67C2211yescharacteristic
91C2×C42×D67C2212yes—
92#557×C67C22116yescomplemented
93C2×C4⋊Q8×C67C2211yescharacteristic
94C2×C4⋊Q8×C67C2212yes—
95C2×#125×C67C2214yes—
96C2×#125×C67C2212yes—
97C2×C4×Q8×C67C2211yescharacteristic
98C2×C4×Q8×C67C2212yes—
99C2×C4×Q8×C67C2212yes—
100C2×C4×Q8×C67C2211yescharacteristic
101C2×#11761629—28no—
102C2×#11761629C2318yes—
103C22×Dic134C2312yes—
104C22×Dic134C2314yes—
105C22×Dic134C2312yes—
106C22×Dic134C2311yescharacteristic
107C2×Q8×D67—216no—
108C2×Q8×D67C23116yes—
109C22×D268C2312yes—
110C22×D268C2311yescharacteristic
111C22×C4×D67C2311yescharacteristic
112C22×C4×D67C2311yescharacteristic
113C22×C4×D67C2312yes—
114C22×C4×D67C2312yes—
115C22×C4×D67C2312yes—
116C22×C4×D67C2314yes—
117C22×C4×D67C2311yescharacteristic
118#14524043C2318yes—
119#14524042C23116yes—
120#14524042C23116yes—
121#14524042C2318yes—
122#14524041C23116yes—
123#14524041C23116yes—
124#14524041C2318yes—
125#14524038C23132yes—
126#14524038C23132yes—
127#14524038C23132yes—
128#14524037C23132yes—
129#14524035C23116yes—
130#14524034C23132yes—
131#14524033C23116yes—
132#14524033C23132yes—
133#14524033C23132yes—
134#14524033C23132yes—
135#14524032C23116yes—
136#14524031C23116yes—
137#14524028C23132yes—
138#14524028C23132yes—
139#14524023C2318yes—
140#14524023C23116yes—
141#14524021C23132yes—
142#14524021C23132yes—
143#14524021C23116yes—
144#14524021C23132yes—
145#14524019C2318yes—
146#14524019C23116yes—
147Q8×Dic67C23116yes—
148Q8×Dic67C2318yes—
149C4×Dic134C23132yes—
150C4×Dic134C23116yes—
151C4×Dic134C23116yes—
152C4×Dic134C23116yes—
153C4×Dic134C2318yes—
154#14524008C23132yes—
155#14524008C23132yes—
156#14524008C23116yes—
157C4×D268C23116yes—
158C4×D268C2318yes—
159#14524005C23116yes—
160#14524005C2318yes—
161#14524001C23116yes—
162#14524001C23132yes—
163#14524001C23116yes—
164#14524001C23116yes—
165#14524001C2318yes—
166#14524000C23132yes—
167#14524000C23132yes—
168#14524000C23116yes—
169C2×C4⋊Dic67C2312yes—
170C2×C4⋊Dic67C2312yes—
171C2×C4⋊Dic67C2311yescharacteristic
172C2×C4⋊Dic67C2311yescharacteristic
173C2×C4⋊Dic67C2312yes—
174C2×C4⋊Dic67C2314yes—
175C2×C4⋊Dic67C2312yes—
176C2×Dic67⋊C4C2314yes—
177C2×Dic67⋊C4C2314yes—
178C2×Dic67⋊C4C2312yes—
179C2×Dic67⋊C4C2312yes—
180C2×Dic67⋊C4C2314yes—
181C2×Dic67⋊C4C2314yes—
182C2×Dic67⋊C4C2312yes—
183C2×Dic67⋊C4C2314yes—
184C2×Dic67⋊C4C2312yes—
185C2×Dic67⋊C4C2314yes—
186C2×Dic67⋊C4C2312yes—
187C4⋊C4×D67C23116yes—
188C4⋊C4×D67C23116yes—
189C2×(C2×D67)⋊C4C2312yes—
190C2×(C2×D67)⋊C4C2312yes—
191C2×(C2×D67)⋊C4C2312yes—
192C2×(C2×D67)⋊C4C2314yes—
193C2×(C2×D67)⋊C4C2314yes—
194C2×(C2×D67)⋊C4C2312yes—
195C2×(C2×D67)⋊C4C2312yes—
196C2×(C2×D67)⋊C4C2314yes—
197C2×(C2×D67)⋊C4C2314yes—
198C2×C4×Dic67C2311yescharacteristic
199C2×C4×Dic67C2312yes—
200C2×C4×Dic67C2311yescharacteristic
201C2×C4×Dic67C2312yes—
202C2×C4×Dic67C2311yescharacteristic
203C2×C4×Dic67C2314yes—
204C2×C4×Dic67C2314yes—
205C2×C4×Dic67C2312yes—
206C2×C4×Dic67C2314yes—
207C42×D67C2318yes—
208C42×D67C23116yes—
209C22×Q8×C67C2311yescharacteristic
210C22×Q8×C67C2312yes—
211C22×Q8×C67C2311yescharacteristic
212C4⋊Q8×C67C2318yes—
213C4⋊Q8×C67C23116yes—
214#125×C67C23132yes—
215#125×C67C23116yes—
216C4×Q8×C67C23116yes—
217C4×Q8×C67C23116yes—
218C4×Q8×C67C2318yes—
219C4×Q8×C67C2318yes—
220C2×C4⋊C4×C67C2311yescharacteristic
221C2×C4⋊C4×C67C2311yescharacteristic
222C2×C4⋊C4×C67C2312yes—
223C2×C4⋊C4×C67C2314yes—
224C2×C4⋊C4×C67C2312yes—
225C2×C4⋊C4×C67C2312yes—
226C2×C4⋊C4×C67C2314yes—
227C2×C4⋊C4×C67C2312yes—
228C2×C4⋊C4×C67C2314yes—
229C2×C42×C67C2312yes—
230C2×C42×C67C2314yes—
231C2×C42×C67C2311yescharacteristic
232C2×C42×C67C2312yes—
233C23×D67C2412yes—
234C23×D67C2411yescharacteristic
235#11761629—232no—
236C2×Dic134—28no—
237C2×Dic134—24no—
238C2×Dic134—216no—
239C2×Dic134—28no—
240C2×Dic134C2418yes—
241C2×Dic134C24116yes—
242C2×Dic134C2418yes—
243C2×Dic134C2414yes—
244Q8×D67—264no—
245C2×D268—28no—
246C2×D268—24no—
247C2×D268C2418yes—
248C2×D268C2414yes—
249C22×Dic67C2412yes—
250C22×Dic67C2412yes—
251C22×Dic67C2412yes—
252C22×Dic67C2411yescharacteristic
253C22×Dic67C2414yes—
254C22×Dic67C2411yescharacteristic
255C22×Dic67C2411yescharacteristic
256C2×C4×D67—216no—
257C2×C4×D67—24no—
258C2×C4×D67—28no—
259C2×C4×D67—28no—
260C2×C4×D67—24no—
261C2×C4×D67—28no—
262C2×C4×D67#4118yes—
263C2×C4×D67C2414yes—
264C2×C4×D67C2414yes—
265C2×C4×D67C2418yes—
266C2×C4×D67C2418yes—
267C2×C4×D67C2418yes—
268C2×C4×D67C24116yes—
269C2×C4×D67C2414yes—
270C4⋊Dic67C2418yes—
271C4⋊Dic67C2418yes—
272C4⋊Dic67C2414yes—
273C4⋊Dic67C2414yes—
274C4⋊Dic67C2418yes—
275C4⋊Dic67C24116yes—
276C4⋊Dic67C2418yes—
277Dic67⋊C4C24116yes—
278Dic67⋊C4C24116yes—
279Dic67⋊C4C2418yes—
280Dic67⋊C4C2418yes—
281Dic67⋊C4C24116yes—
282Dic67⋊C4C24116yes—
283Dic67⋊C4C2418yes—
284Dic67⋊C4C24116yes—
285Dic67⋊C4C2418yes—
286Dic67⋊C4C24116yes—
287Dic67⋊C4C2418yes—
288(C2×D67)⋊C4C2418yes—
289(C2×D67)⋊C4C2418yes—
290(C2×D67)⋊C4C2418yes—
291(C2×D67)⋊C4C24116yes—
292(C2×D67)⋊C4C24116yes—
293(C2×D67)⋊C4C2418yes—
294(C2×D67)⋊C4C2418yes—
295(C2×D67)⋊C4C24116yes—
296(C2×D67)⋊C4C24116yes—
297C4×Dic67C2414yes—
298C4×Dic67C2418yes—
299C4×Dic67C2414yes—
300C4×Dic67C2418yes—
301C4×Dic67C2414yes—
302C4×Dic67C24116yes—
303C4×Dic67C24116yes—
304C4×Dic67C2418yes—
305C4×Dic67C24116yes—
306C2×Q8×C67—28no—
307C2×Q8×C67—24no—
308C2×Q8×C67—24no—
309C2×Q8×C67C2414yes—
310C2×Q8×C67C2418yes—
311C2×Q8×C67C2414yes—
312C22×C4×C67C2412yes—
313C22×C4×C67C2412yes—
314C22×C4×C67C2412yes—
315C22×C4×C67C2411yescharacteristic
316C22×C4×C67C2414yes—
317C22×C4×C67C2412yes—
318C22×C4×C67C2411yescharacteristic
319C22×C4×C67C2411yescharacteristic
320C4⋊C4×C67C2414yes—
321C4⋊C4×C67C2414yes—
322C4⋊C4×C67C2418yes—
323C4⋊C4×C67C24116yes—
324C4⋊C4×C67C2418yes—
325C4⋊C4×C67C2418yes—
326C4⋊C4×C67C24116yes—
327C4⋊C4×C67C2418yes—
328C4⋊C4×C67C24116yes—
329C42×C67C2418yes—
330C42×C67C24116yes—
331C42×C67C2414yes—
332C42×C67C2418yes—
333C23×C67C2511yescharacteristic
334C22×D67—22no—
335C22×D67—22no—
336C22×D67—24no—
337C22×D67—24no—
338C22×D67—24no—
339C22×D67C2×#4114yes—
340C22×D67C2514yes—
341C22×D67C2512yes—
342Q8×C67—216no—
343Q8×C67—28no—
344Q8×C67—28no—
345C2×C4×C67—24no—
346C2×C4×C67—28no—
347C2×C4×C67—24no—
348C2×C4×C67—24no—
349C2×C4×C67—22no—
350C2×C4×C67—24no—
351C2×C4×C67C2×#4114yes—
352C2×C4×C672−1+414yes—
353C2×C4×C67C2514yes—
354C2×C4×C67C2514yes—
355C2×C4×C67C2514yes—
356C2×C4×C67C2512yes—
357C2×C4×C67C2518yes—
358C2×C4×C67C2514yes—
359C2×C4×C67C2512yes—
360C2×C4×C67C2512yes—
361C2×Dic67—28no—
362C2×Dic67—24no—
363C2×Dic67—22no—
364C2×Dic67—24no—
365C2×Dic67—24no—
366C2×Dic67C2×#4114yes—
367C2×Dic672−1+414yes—
368C2×Dic67C2514yes—
369C2×Dic67C2514yes—
370C2×Dic67C2514yes—
371C2×Dic67C2512yes—
372C2×Dic67C2518yes—
373C2×Dic67C2512yes—
374C2×Dic67C2512yes—
375D268—216no—
376D268—28no—
377C4×D67—232no—
378C4×D67—28no—
379C4×D67—216no—
380C4×D67—216no—
381C4×D67—28no—
382C4×D67—216no—
383C4×D67C2×#41116yes—
384Dic134—216no—
385Dic134—28no—
386Dic134—232no—
387Dic134—216no—
388C22×C67C22×#4112yes—
389C22×C67C2×2−1+412yes—
390C22×C67C2×2−1+412yes—
391C22×C67C2611yescharacteristic
392C2×D67—22no—
393C2×D67—22no—
394C2×D67—28no—
395C2×D67—24no—
396C2×D67—24no—
397C2×D67—24no—
398C2×D67—48no—
399C2×D67C22×#4114yes—
400C4×C67—28no—
401C4×C67—24no—
402C4×C67—24no—
403C4×C67—24no—
404C4×C67—22no—
405C4×C67—24no—
406C4×C67C22×#4114yes—
407C4×C67C2×2−1+414yes—
408Dic67—28no—
409Dic67—24no—
410Dic67—24no—
411Dic67—24no—
412Dic67—22no—
413Dic67C22×#4114yes—
414Dic67C2×2−1+414yes—
415C2×#3509—671nomaximal, Sylow
416C2×C67#350914yescomplemented
417C2×C67C23×#4111yescharacteristic
418C2×C67C22×2−1+411yescharacteristic
419C2×C67C22×2−1+411yescharacteristic
420D67—24no—
421D67—44no—
422#3509—6732no—
423C2×#557—672no—
424C2×#557—671no—
425C2×#557D6711yescharacteristic, complemented
426C2×#556—671no—
427C2×#556—672no—
428C2×#556—671no—
429C2×#552—674no—
430C2×#552—672no—
431C2×#552—672no—
432C2×#541—674no—
433C2×#536—672no—
434C2×#533—672no—
435C2×#533—671no—
436C2×#533—672no—
437C22×C4⋊Q8—671no—
438C2×#519—672no—
439C2×C4×#41—671no—
440C67C2×#350911yescharacteristic, complemented, Sylow
441C22×#41—671no—
442C23×Q8—672no—
443#557—6732no—
444#557—6716no—
445#557C2×D67116yescomplemented
446#556—6716no—
447#556—6732no—
448#556—6716no—
449#552—6764no—
450#552—6732no—
451#552—6732no—
452#541—6764no—
453#536—6732no—
454#533—6732no—
455#533—6716no—
456#533—6732no—
457C2×C4⋊Q8—672no—
458C2×C4⋊Q8—671no—
459C2×C4⋊Q8—672no—
460C2×C4⋊Q8—6716no—
461C2×C4⋊Q8—672no—
462C2×C4⋊Q8—672no—
463C2×C4⋊Q8—671no—
464C2×C4⋊Q8—671no—
465C2×C4⋊Q8C2×D6711yescharacteristic
466C2×C4⋊Q8C2×D6712yes—
467C2×#126—674no—
468C2×#126—674no—
469C2×#126—674no—
470C2×#126—674no—
471C2×#125—672no—
472C2×#125—674no—
473C2×#125—674no—
474C2×#125—674no—
475C2×#125—674no—
476C2×#125—672no—
477C2×#125C2×D6712yes—
478C2×#125C2×D6714yes—
479C2×#124—672no—
480C2×#124—672no—
481C2×#123—674no—
482C2×#123—674no—
483C2×C22⋊Q8—671no—
484C2×C22⋊Q8—672no—
485C2×C22⋊Q8—674no—
486C2×C22⋊Q8—674no—
487C2×C22⋊Q8—672no—
488C2×C22⋊Q8—671no—
489C2×C22⋊Q8—674no—
490C2×C22⋊Q8—672no—
491#519—6732no—
492C4×#41—6716no—
493C2×C4×Q8—671no—
494C2×C4×Q8—672no—
495C2×C4×Q8—674no—
496C2×C4×Q8—672no—
497C2×C4×Q8—674no—
498C2×C4×Q8—674no—
499C2×C4×Q8—672no—
500C2×C4×Q8—672no—
501C2×C4×Q8—671no—
502C2×C4×Q8—672no—
503C2×C4×Q8C2×D6711yescharacteristic
504C2×C4×Q8C2×D6712yes—
505C2×C4×Q8C2×D6712yes—
506C2×C4×Q8C2×D6711yescharacteristic
507C2×C4×D4—672no—
508C2×C4×D4—671no—
509C2×C4×D4—672no—
510C2×C4×D4—671no—
511C2×#117—671no—
512C2×#117—672no—
513C2×#117—674no—
514C2×#117—672no—
515C2×#117—672no—
516C2×#117—672no—
517C2×#117—674no—
518C2×#117—674no—
519C22×C4⋊C4—672no—
520C22×C4⋊C4—672no—
521C22×C42—671no—
522C22×C42—672no—
523C2×#41—678no—
524C2×#41—1348no—
525C22×Q8—6716no—
526C22×Q8—672no—
527C22×Q8—671no—
528C22×Q8—674no—
529C22×Q8—672no—
530C22×Q8—13416no—
531C22×Q8C22×D6712yes—
532C22×Q8C22×D6711yescharacteristic
533C22×Q8C22×D6711yescharacteristic
534C22×D4—672no—
535C22×D4—671no—
536C23×C4—671no—
537C23×C4—674no—
538C23×C4—671no—
539C23×C4—671no—
540C23×C4—672no—
541C23×C4—672no—
542C23×C4—672no—
543C4⋊Q8—6716no—
544C4⋊Q8—678no—
545C4⋊Q8—6716no—
546C4⋊Q8—6716no—
547C4⋊Q8—6716no—
548C4⋊Q8—678no—
549C4⋊Q8—678no—
550C4⋊Q8C22×D6718yes—
551C4⋊Q8C22×D67116yes—
552#126—6732no—
553#126—6732no—
554#126—6732no—
555#126—6732no—
556#125—6716no—
557#125—6732no—
558#125—6732no—
559#125—6732no—
560#125—6732no—
561#125—6716no—
562#125C22×D67116yes—
563#125C22×D67132yes—
564#124—6716no—
565#124—6716no—
566#123—6732no—
567#123—6732no—
568C22⋊Q8—678no—
569C22⋊Q8—6716no—
570C22⋊Q8—6732no—
571C22⋊Q8—6732no—
572C22⋊Q8—6716no—
573C22⋊Q8—678no—
574C22⋊Q8—6732no—
575C22⋊Q8—6716no—
576C4×Q8—678no—
577C4×Q8—6716no—
578C4×Q8—6732no—
579C4×Q8—6716no—
580C4×Q8—6732no—
581C4×Q8—6732no—
582C4×Q8—6716no—
583C4×Q8—6716no—
584C4×Q8—6716no—
585C4×Q8—678no—
586C4×Q8C22×D6718yes—
587C4×Q8C22×D67116yes—
588C4×Q8C22×D67116yes—
589C4×Q8C22×D6718yes—
590C4×D4—6716no—
591C4×D4—678no—
592C4×D4—6716no—
593C4×D4—678no—
594#117—678no—
595#117—6716no—
596#117—6732no—
597#117—6716no—
598#117—6716no—
599#117—6716no—
600#117—6732no—
601#117—6732no—
602C2×C4⋊C4—674no—
603C2×C4⋊C4—672no—
604C2×C4⋊C4—674no—
605C2×C4⋊C4—672no—
606C2×C4⋊C4—672no—
607C2×C4⋊C4—671no—
608C2×C4⋊C4—671no—
609C2×C4⋊C4—672no—
610C2×C4⋊C4—672no—
611C2×C4⋊C4—672no—
612C2×C4⋊C4—674no—
613C2×C4⋊C4—674no—
614C2×C4⋊C4—674no—
615C2×C4⋊C4—674no—
616C2×C4⋊C4—674no—
617C2×C4⋊C4—672no—
618C2×C4⋊C4—672no—
619C2×C4⋊C4—672no—
620C2×C4⋊C4—6716no—
621C2×C4⋊C4—6716no—
622C2×C4⋊C4C22×D6712yes—
623C2×C4⋊C4C22×D6712yes—
624C2×C4⋊C4C22×D6711yescharacteristic
625C2×C4⋊C4C22×D6711yescharacteristic
626C2×C4⋊C4C22×D6712yes—
627C2×C4⋊C4C22×D6714yes—
628C2×C4⋊C4C22×D6714yes—
629C2×C4⋊C4C22×D6714yes—
630C2×C4⋊C4C22×D6712yes—
631C2×C22⋊C4—672no—
632C2×C22⋊C4—672no—
633C2×C22⋊C4—672no—
634C2×C22⋊C4—672no—
635C2×C22⋊C4—672no—
636C2×C22⋊C4—674no—
637C2×C22⋊C4—674no—
638C2×C22⋊C4—674no—
639C2×C22⋊C4—674no—
640C2×C42—672no—
641C2×C42—674no—
642C2×C42—674no—
643C2×C42—674no—
644C2×C42—671no—
645C2×C42—672no—
646C2×C42—672no—
647C2×C42—671no—
648C2×C42—671no—
649C2×C42—678no—
650C2×C42—6716no—
651C2×C42C22×D6714yes—
652C2×C42C22×D6712yes—
653C2×C42C22×D6712yes—
654C2×C42C22×D6711yescharacteristic
655C24—671no—
656C24—672no—
657#41—13432no—
658C2×Q8—28no—
659C2×Q8—24no—
660C2×Q8—24no—
661C2×Q8—678no—
662C2×Q8—674no—
663C2×Q8—6716no—
664C2×Q8—678no—
665C2×Q8—13416no—
666C2×Q8—1348no—
667C2×Q8—13464no—
668C2×Q8—1348no—
669C2×Q8—1344no—
670C2×Q8C23×D6718yes—
671C2×Q8C23×D6714yes—
672C2×Q8C23×D6714yes—
673C2×D4—678no—
674C2×D4—674no—
675C2×D4—1348no—
676C2×D4—1344no—
677C22×C4—671no—
678C22×C4—671no—
679C22×C4—678no—
680C22×C4—674no—
681C22×C4—672no—
682C22×C4—672no—
683C22×C4—672no—
684C22×C4—671no—
685C22×C4—674no—
686C22×C4—674no—
687C22×C4—674no—
688C22×C4—678no—
689C22×C4—678no—
690C22×C4—678no—
691C22×C4—6716no—
692C22×C4—1348no—
693C22×C4—1348no—
694C22×C4—1344no—
695C22×C4—13416no—
696C22×C4—1348no—
697C22×C4—1344no—
698C22×C4C23×D6712yes—
699C22×C4C23×D6712yes—
700C22×C4C23×D6711yescharacteristic
701C22×C4C23×D6714yes—
702C22×C4C23×D6712yes—
703C22×C4C23×D6712yes—
704C22×C4C23×D6711yescharacteristic
705C22×C4C23×D6711yescharacteristic
706C4⋊C4—6716no—
707C4⋊C4—678no—
708C4⋊C4—6716no—
709C4⋊C4—678no—
710C4⋊C4—678no—
711C4⋊C4—674no—
712C4⋊C4—674no—
713C4⋊C4—678no—
714C4⋊C4—678no—
715C4⋊C4—678no—
716C4⋊C4—6716no—
717C4⋊C4—6716no—
718C4⋊C4—6716no—
719C4⋊C4—6716no—
720C4⋊C4—6716no—
721C4⋊C4—678no—
722C4⋊C4—678no—
723C4⋊C4—678no—
724C4⋊C4C23×D6718yes—
725C4⋊C4C23×D6718yes—
726C4⋊C4C23×D6714yes—
727C4⋊C4C23×D6714yes—
728C4⋊C4C23×D6718yes—
729C4⋊C4C23×D67116yes—
730C4⋊C4C23×D67116yes—
731C4⋊C4C23×D67116yes—
732C4⋊C4C23×D6718yes—
733C22⋊C4—678no—
734C22⋊C4—678no—
735C22⋊C4—678no—
736C22⋊C4—678no—
737C22⋊C4—678no—
738C22⋊C4—6716no—
739C22⋊C4—6716no—
740C22⋊C4—6716no—
741C22⋊C4—6716no—
742C42—674no—
743C42—678no—
744C42—674no—
745C42—678no—
746C42—674no—
747C42—6716no—
748C42—6716no—
749C42—6716no—
750C42—678no—
751C42C23×D6718yes—
752C42C23×D6714yes—
753C42C23×D67116yes—
754C42C23×D6718yes—
755C23—674no—
756C23—672no—
757C23—674no—
758C23—1344no—
759C23—1344no—
760C23—1344no—
761C23—1342no—
762C23—1342no—
763C23C24×D6711yescharacteristic
764Q8—216no—
765Q8—28no—
766Q8—28no—
767Q8—13432no—
768Q8—13416no—
769Q8—13416no—
770Q8—1348no—
771D4—13416no—
772D4—1348no—
773C2×C4—24no—
774C2×C4—28no—
775C2×C4—24no—
776C2×C4—22no—
777C2×C4—24no—
778C2×C4—24no—
779C2×C4—674no—
780C2×C4—674no—
781C2×C4—672no—
782C2×C4—672no—
783C2×C4—6716no—
784C2×C4—674no—
785C2×C4—674no—
786C2×C4—674no—
787C2×C4—672no—
788C2×C4—678no—
789C2×C4—13416no—
790C2×C4—13416no—
791C2×C4—1348no—
792C2×C4—13432no—
793C2×C4—1348no—
794C2×C4—1344no—
795C2×C4—1344no—
796C2×C4—1342no—
797C2×C4—1344no—
798C2×C4—13416no—
799C2×C4—1348no—
800C2×C4#41×D6714yes—
801C2×C4#1452409114yes—
802C2×C4C24×D6714yes—
803C2×C4C24×D6714yes—
804C2×C4C24×D6712yes—
805C2×C4C24×D6718yes—
806C2×C4C24×D6714yes—
807C2×C4C24×D6714yes—
808C2×C4C24×D6712yes—
809C2×C4C24×D6712yes—
810C22—2688no—
811C22—674no—
812C22—1344no—
813C22—1344no—
814C22—1344no—
815C22—1348no—
816C22—1342no—
817C22—1342no—
818C22C2×#41×D6712yes—
819C222−1+4×D6712yes—
820C22C2×#1452409112yes—
821C22C25×D6711yescharacteristic
822C4—24no—
823C4—28no—
824C4—24no—
825C4—22no—
826C4—24no—
827C4—24no—
828C4—674no—
829C4—674no—
830C4—1348no—
831C4—1344no—
832C4—1344no—
833C4—1342no—
834C4—1344no—
835C4C2×#41×D6714yes—
836C4C2×#1452409114yes—
837C2—2684no—
838C2—1344no—
839C2#2257409214yesdirect product factor
840C2C22×#41×D6711yescharacteristic
841C2C2×2−1+4×D6711yescharacteristic
842C2C22×#1452409111yescharacteristic
subgroupG/H
centerC23C24×D67
commutator, cosocleC22×C67C26
FrattiniC22C25×D67
FittingC2×#557×C67C2
socleC23×C67C25
prime radicalC22×#11761629C22
hypercenterC2×#557D67
hypocenterC67C2×#3509
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
1. #22574092C2direct (N × H)
2. C2×#16864124C2semidirect
3. C2×#16864121C2semidirect
4. C2×#16864120C2semidirect
5. C2×#16864119C2semidirect
6. C2×#16864118C2semidirect
7. C2×#16864087C2semidirect
8. C2×#16864084C2semidirect
9. C2×#16864078C2semidirect
10. C2×#16864005C2semidirect
12. C2×#16863952C2semidirect
13. C2×#16863950C2semidirect
14. C2×#16863950C2semidirect
15. C2×C4⋊Q8×D67C2semidirect
16. C2×#16863872C2semidirect
18. C2×#557×C67C2semidirect
21. #16864124C22semidirect
22. #16864121C22semidirect
23. #16864120C22semidirect
24. #16864119C22semidirect
25. #16864118C22semidirect
26. #16864087C22semidirect
27. #16864084C22semidirect
28. #16864078C22semidirect
29. #16864005C22semidirect
31. #16863952C22semidirect
32. #16863950C22semidirect
33. #16863950C22semidirect
41. C4⋊Q8×D67C22semidirect
64. #16863872C22semidirect
92. #557×C67C22semidirect
416. C2×C67#3509semidirect
425. C2×#557D67semidirect
440. C67C2×#3509semidirect
445. #557C2×D67semidirect
839. C2#22574092direct (N × H)

Maximal subgroups

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

subgroupindex
#225740922
C2×#168641242
C2×#168641212
C2×#168641202
C2×#168641192
C2×#168641182
C2×#168640872
C2×#168640842
C2×#168640782
C2×#168640052
C2×#168639712
C2×#168639522
C2×#168639502
C2×C4⋊Q8×D672
C2×#168638722
C2×C4×#117616292
C2×#557×C672
C2×#350967