Finite Group Databasebeta

← C2×#22572962 #31735580

Subgroups — C2×#22572962 #31735580

Order 17152.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864131C211yesmaximal, characteristic, complemented
2#22572962C2116yesmaximal, direct product factor
3C2×#16863762C211yesmaximal, characteristic, complemented
4C2×#16863758C211yesmaximal, characteristic, complemented
5C2×#16863753C211yesmaximal, characteristic, complemented
6C2×#16863700C211yesmaximal, characteristic, complemented
7C2×#16863693C211yesmaximal, characteristic, complemented
8C2×#16863673C211yesmaximal, characteristic, complemented
9C2×#16863611C211yesmaximal, characteristic, complemented
10C2×#16863611C211yesmaximal, characteristic, complemented
11C2×#16863591C211yesmaximal, characteristic
12C2×#16863527C211yesmaximal, characteristic, complemented
13C2×#16863506C211yesmaximal, characteristic, complemented
14C2×#16863496C211yesmaximal, characteristic, complemented
15C2×C4×#11761613C211yesmaximal, characteristic, complemented
16C2×#554×C67C211yesmaximal, characteristic, complemented
17C22×#11761616C2211yescharacteristic
18C22×#11761613C2211yescharacteristic
19C22×#11761613C2211yescharacteristic
20#16864131—24no—
21#16864131C2218yescomplemented
22C2×#14524040C2211yescharacteristic
23C2×#14524032—21no—
24C2×#14524031C2211yescharacteristic
25C2×#14524031C2211yescharacteristic
26C2×#14524028—21no—
27C2×#14524028—21no—
28C2×C4×Dic134C2211yescharacteristic
29C2×C4×D268C2211yescharacteristic
30C2×C4×D268C2211yescharacteristic
31C2×#14524005—21no—
32#16863762C2218yescomplemented
33#16863758C2218yescomplemented
34#16863753C2218yescomplemented
35#16863700C2218yescomplemented
36#16863693C2218yescomplemented
37#16863673C2218yescomplemented
38#16863611C2218yescomplemented
39#16863611C2218yescomplemented
40#16863591C2218yes—
41#16863527C2218yescomplemented
42#16863506C2218yescomplemented
43#16863496C2218yescomplemented
44C4×#11761613C2218yescomplemented
45C2×#14523976C2211yescharacteristic
46C2×#14523976C2211yescharacteristic
47C2×#14523974C2211yescharacteristic
48C2×C4⋊(C67⋊C8)C2211yescharacteristic
49C2×C4⋊(C67⋊C8)C2211yescharacteristic
50C2×C4⋊(C67⋊C8)C2211yescharacteristic
51C2×#14523966C2211yescharacteristic
52C2×#14523966C2211yescharacteristic
53C2×#14523966C2211yescharacteristic
54C2×#14523964C2211yescharacteristic
55C2×#14523963C2211yescharacteristic
56C2×#14523963C2211yescharacteristic
57C2×#14523963C2211yescharacteristic
58C2×#14523963C2211yescharacteristic
59C2×#14523963C2211yescharacteristic
60C2×#14523963C2211yescharacteristic
61C2×#14523954C2211yescharacteristic
62C2×#14523954C2211yescharacteristic
63C2×C4×C67⋊C8C2211yescharacteristic
64#554×C67—24no—
65#554×C67C2218yescomplemented
66C2×C4⋊Q8×C67C2211yescharacteristic
67C2×#125×C67C2211yescharacteristic
68C2×#125×C67C2211yescharacteristic
69C2×C22⋊Q8×C67—21no—
70C2×C22⋊Q8×C67—21no—
71C2×C22⋊Q8×C67—21no—
72C2×C4×Q8×C67C2211yescharacteristic
73C2×C4×D4×C67C2211yescharacteristic
74C2×C4×D4×C67C2211yescharacteristic
75C2×C4×D4×C67C2211yescharacteristic
76C22×C4⋊C4×C67—21no—
77C22×Dic134C2311yescharacteristic
78C22×D268—21no—
79C22×D268—21no—
80C22×D268C2311yescharacteristic
81C22×D268C2311yescharacteristic
82C22×C4×D67—21no—
83C22×C4×D67—21no—
84C2×#11761616—24no—
85C2×#11761616C2314yes—
86C2×#11761613—24no—
87C2×#11761613—24no—
88C2×#11761613C2314yes—
89C2×#11761613C2314yes—
90C22×C67⋊C8C2311yescharacteristic
91C22×C67⋊C8C2311yescharacteristic
92C22×C67⋊C8C2311yescharacteristic
93C22×C67⋊C8C2311yescharacteristic
94#14524040—22no—
95#14524040C2314yes—
96#14524032—28no—
97#14524031—22no—
98#14524031—22no—
99#14524031C2314yes—
100#14524031C2314yes—
101#14524028—28no—
102#14524028—28no—
103C4×Dic134—22no—
104C4×Dic134C2314yes—
105C4×D268—22no—
106C4×D268—22no—
107C4×D268C2314yes—
108C4×D268C2314yes—
109#14524005—28no—
110C2×C4⋊Dic67C2311yescharacteristic
111C2×Dic67⋊C4—21no—
112C2×(C2×D67)⋊C4—21no—
113C2×(C2×D67)⋊C4—21no—
114C2×(C2×D67)⋊C4—21no—
115C2×(C2×D67)⋊C4—21no—
116C2×(C2×D67)⋊C4—21no—
117C2×(C2×D67)⋊C4—21no—
118C2×C4×Dic67—21no—
119#14523976C2314yes—
120#14523976C2314yes—
121#14523974C2314yes—
122C4⋊(C67⋊C8)C2314yes—
123C4⋊(C67⋊C8)C2314yes—
124C4⋊(C67⋊C8)C2314yes—
125#14523966C2314yes—
126#14523966C2314yes—
127#14523966C2314yes—
128#14523964C2314yes—
129#14523963C2314yes—
130#14523963C2314yes—
131#14523963C2314yes—
132#14523963C2314yes—
133#14523963C2314yes—
134#14523963C2314yes—
135#14523954C2314yes—
136#14523954C2314yes—
137C4×C67⋊C8C2314yes—
138C22×Q8×C67—21no—
139C22×Q8×C67D411yescharacteristic
140C22×D4×C67C2311yescharacteristic
141C23×C4×C67—21no—
142C23×C4×C67—21no—
143C23×C4×C67—21no—
144C4⋊Q8×C67—22no—
145C4⋊Q8×C67C2314yes—
146#125×C67—22no—
147#125×C67—22no—
148#125×C67C2314yes—
149#125×C67C2314yes—
150C22⋊Q8×C67—28no—
151C22⋊Q8×C67—28no—
152C22⋊Q8×C67—28no—
153C4×Q8×C67D414yes—
154C4×Q8×C67C2314yes—
155C4×D4×C67—22no—
156C4×D4×C67—22no—
157C4×D4×C67—22no—
158C4×D4×C67C2314yes—
159C4×D4×C67C2314yes—
160C4×D4×C67C2314yes—
161C2×C4⋊C4×C67—21no—
162C2×C4⋊C4×C67—21no—
163C2×C4⋊C4×C67—21no—
164C2×C4⋊C4×C67—21no—
165C2×C4⋊C4×C67—21no—
166C2×C4⋊C4×C67—28no—
167C2×C4⋊C4×C67D411yescharacteristic
168C2×C4⋊C4×C67D411yescharacteristic
169C2×C4⋊C4×C67D411yescharacteristic
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C4⋊C4×C67C2311yescharacteristic
172C2×C4⋊C4×C67C2311yescharacteristic
173C2×C22⋊C4×C67—21no—
174C2×C22⋊C4×C67—21no—
175C2×C22⋊C4×C67—21no—
176C2×C42×C67C2311yescharacteristic
177C2×C42×C67C2311yescharacteristic
178C2×C42×C67C2311yescharacteristic
179C23×D67—21no—
180C23×D67—21no—
181C2×Dic134—22no—
182C2×Dic134—22no—
183C2×Dic134—21no—
184C2×Dic134C2412yes—
185C2×D268—22no—
186C2×D268—22no—
187C2×D268—22no—
188C2×D268—22no—
189C2×D268—24no—
190C2×D268—21no—
191C2×D268—21no—
192C2×D268—24no—
193C2×D268—44no—
194C2×D268—82no—
195C2×D268C2412yes—
196C2×D268C2412yes—
197C22×Dic67—21no—
198C22×Dic67—21no—
199C2×C4×D67—24no—
200C2×C4×D67—24no—
201C2×C4×D67—82no—
202C2×C4×D67—82no—
203#11761616—28no—
204#11761613—28no—
205#11761613—28no—
206C2×C67⋊C8—22no—
207C2×C67⋊C8—22no—
208C2×C67⋊C8—22no—
209C2×C67⋊C8—22no—
210C2×C67⋊C8C2412yes—
211C2×C67⋊C8C2412yes—
212C2×C67⋊C8C2412yes—
213C2×C67⋊C8C2412yes—
214C4⋊Dic67—21no—
215C4⋊Dic67C2412yes—
216Dic67⋊C4—24no—
217(C2×D67)⋊C4—24no—
218(C2×D67)⋊C4—24no—
219(C2×D67)⋊C4—24no—
220(C2×D67)⋊C4—24no—
221(C2×D67)⋊C4—24no—
222(C2×D67)⋊C4—24no—
223C4×Dic67—24no—
224C24×C67—21no—
225C2×Q8×C67—24no—
226C2×Q8×C67—42no—
227C2×Q8×C67—82no—
228C2×Q8×C67C2×D414yes—
229C2×D4×C67—21no—
230C2×D4×C67—22no—
231C2×D4×C67#4114yes—
232C2×D4×C67C2412yes—
233C22×C4×C67—21no—
234C22×C4×C67—21no—
235C22×C4×C67—21no—
236C22×C4×C67—24no—
237C22×C4×C67—24no—
238C22×C4×C67—24no—
239C22×C4×C67—44no—
240C22×C4×C67—82no—
241C22×C4×C67—82no—
242C22×C4×C67C2×D411yescharacteristic
243C22×C4×C67C2×D411yescharacteristic
244C22×C4×C67C2×D411yescharacteristic
245C22×C4×C67C2×D411yescharacteristic
246C22×C4×C67C2×D411yescharacteristic
247C22×C4×C67C2×D411yescharacteristic
248C22×C4×C67C2411yescharacteristic
249C4⋊C4×C67—24no—
250C4⋊C4×C67—24no—
251C4⋊C4×C67—24no—
252C4⋊C4×C67—24no—
253C4⋊C4×C67—24no—
254C4⋊C4×C67—21no—
255C4⋊C4×C67—21no—
256C4⋊C4×C67—21no—
257C4⋊C4×C67C2×D414yes—
258C4⋊C4×C67C2×D414yes—
259C4⋊C4×C67C2×D414yes—
260C4⋊C4×C67C2412yes—
261C4⋊C4×C67C2412yes—
262C4⋊C4×C67C2412yes—
263C22⋊C4×C67—24no—
264C22⋊C4×C67—24no—
265C22⋊C4×C67—24no—
266C42×C67C2×D412yes—
267C42×C67C2×D412yes—
268C42×C67C2×D412yes—
269C42×C67C2412yes—
270C42×C67C2412yes—
271C42×C67C2412yes—
272C23×C67—24no—
273C23×C67—22no—
274C23×C67—42no—
275C23×C67—42no—
276C23×C67C22×D411yescharacteristic
277C22×D67—22no—
278C22×D67—22no—
279C22×D67—42no—
280C22×D67—42no—
281C22×D67—42no—
282C22×D67—42no—
283C22×D67—42no—
284C22×D67—42no—
285Q8×C67—44no—
286Q8×C67—84no—
287D4×C67—24no—
288D4×C67—22no—
289D4×C67C2×#4114yes—
290C2×C4×C67—22no—
291C2×C4×C67—22no—
292C2×C4×C67—22no—
293C2×C4×C67—22no—
294C2×C4×C67—22no—
295C2×C4×C67—22no—
296C2×C4×C67—22no—
297C2×C4×C67—22no—
298C2×C4×C67—22no—
299C2×C4×C67—48no—
300C2×C4×C67—42no—
301C2×C4×C67—42no—
302C2×C4×C67—42no—
303C2×C4×C67—84no—
304C2×C4×C67—84no—
305C2×C4×C67C22×D412yes—
306C2×C4×C67C22×D412yes—
307C2×C4×C67C22×D412yes—
308C2×C4×C67C22×D412yes—
309C2×C4×C67C22×D412yes—
310C2×C4×C67C22×D412yes—
311C2×C4×C67C22×D411yescharacteristic
312C2×C4×C67C2×#4112yes—
313C2×C4×C672−1+412yes—
314C2×C4×C67C2511yescharacteristic
315C2×Dic67—22no—
316C2×Dic67—22no—
317C2×Dic67—42no—
318C2×Dic67—42no—
319D268—22no—
320D268—22no—
321D268—22no—
322D268—22no—
323D268—48no—
324D268—42no—
325D268—42no—
326D268—84no—
327C4×D67—84no—
328C4×D67—84no—
329Dic134—22no—
330Dic134—22no—
331Dic134—42no—
332C67⋊C8—22no—
333C67⋊C8—22no—
334C67⋊C8—22no—
335C67⋊C8—22no—
336C22×C67—24no—
337C22×C67—48no—
338C22×C67—42no—
339C22×C67—42no—
340C22×C67#54812yes—
341C22×C67#57512yes—
342C22×C67#57612yes—
343C22×C67C23×D411yescharacteristic
344C2×D67—42no—
345C2×D67—42no—
346C2×D67—42no—
347C2×D67—42no—
348C2×D67—42no—
349C2×D67—42no—
350C2×D67—84no—
351C2×D67—84no—
352C4×C67—22no—
353C4×C67—22no—
354C4×C67—22no—
355C4×C67—22no—
356C4×C67—22no—
357C4×C67—22no—
358C4×C67—42no—
359C4×C67—42no—
360C4×C67—42no—
361C4×C67#54812yes—
362C4×C67C22×#4111yescharacteristic
363C4×C67C2×2−1+411yescharacteristic
364Dic67—42no—
365Dic67—42no—
366C2×#3370—671nomaximal, Sylow
367C2×C67—44no—
368C2×C67#337014yescomplemented
369C2×C67C2×#54811yescharacteristic
370C2×C67C2×#57511yescharacteristic
371C2×C67C2×#57611yescharacteristic
372D67—82no—
373D67—82no—
374C2×#559—671no—
375C2×#554D6711yescharacteristic, complemented
376#3370—6716no—
377C2×#490—671no—
378C2×#489—671no—
379C2×#488—671no—
380C2×#479—671no—
381C2×#478—671no—
382C2×#474—671no—
383C2×#463—671no—
384C2×#463—671no—
385C2×#459—671no—
386C2×#446—671no—
387C2×#442—671no—
388C2×#440—671no—
389C2×C4×D8—671no—
390C67C2×#337011yescharacteristic, complemented, Sylow
391C22×SD16—671no—
392C22×D8—671no—
393C22×D8—671no—
394#559—678no—
395#559—1344no—
396#554—24no—
397#554C2×D6718yescomplemented
398C2×C4⋊Q8C2×D6711yescharacteristic
399C2×#127—671no—
400C2×#125C2×D6711yescharacteristic
401C2×#125C2×D6711yescharacteristic
402C2×#124—671no—
403C2×#124—671no—
404C2×#124—1341no—
405C2×#123—1341no—
406C2×#123—1341no—
407C2×C22⋊Q8—21no—
408C2×C22⋊Q8—21no—
409C2×C22⋊Q8—21no—
410C2×C4×Q8—671no—
411C2×C4×Q8C2×D6711yescharacteristic
412C2×C4×D4—671no—
413C2×C4×D4—671no—
414C2×C4×D4—1341no—
415C2×C4×D4C2×D6711yescharacteristic
416C2×C4×D4C2×D6711yescharacteristic
417C2×C4×D4C2×D6711yescharacteristic
418C22×C4⋊C4—21no—
419#490—678no—
420#489—678no—
421#488—678no—
422#479—678no—
423#478—678no—
424#474—678no—
425#463—678no—
426#463—678no—
427#459—678no—
428#446—678no—
429#442—678no—
430#440—678no—
431C4×D8—678no—
432C2×#107—671no—
433C2×#107—671no—
434C2×#106—671no—
435C2×C4⋊C8—671no—
436C2×C4⋊C8—671no—
437C2×C4⋊C8—671no—
438C2×#103—671no—
439C2×#103—671no—
440C2×#103—671no—
441C2×#102—671no—
442C2×#102—671no—
443C2×#102—671no—
444C2×#102—671no—
445C2×#102—671no—
446C2×#102—671no—
447C2×#102—671no—
448C2×#97—671no—
449C2×#97—671no—
450C2×C4×C8—671no—
451C22×Q8—21no—
452C22×Q8—671no—
453C22×Q8C22⋊D6711yescharacteristic
454C22×D4—671no—
455C22×D4—671no—
456C22×D4—1341no—
457C22×D4—1341no—
458C22×D4C22×D6711yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—21no—
462C23×C4—1341no—
463C23×C4—1341no—
464C2×SD16—674no—
465C2×SD16—1344no—
466C2×D8—674no—
467C2×D8—674no—
468C2×D8—1344no—
469C2×D8—1344no—
470C22×C8—671no—
471C22×C8—671no—
472C22×C8—671no—
473C22×C8—671no—
474C4⋊Q8—22no—
475C4⋊Q8C22×D6714yes—
476#127—674no—
477#127—1342no—
478#125—22no—
479#125—22no—
480#125C22×D6714yes—
481#125C22×D6714yes—
482#124—674no—
483#124—674no—
484#124—1348no—
485#124—1342no—
486#124—1342no—
487#123—1348no—
488#123—1348no—
489C22⋊Q8—28no—
490C22⋊Q8—28no—
491C22⋊Q8—28no—
492C4×Q8—674no—
493C4×Q8—1342no—
494C4×Q8C22⋊D6714yes—
495C4×Q8C22×D6714yes—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—674no—
500C4×D4—674no—
501C4×D4—1348no—
502C4×D4—1342no—
503C4×D4—1342no—
504C4×D4C22×D6714yes—
505C4×D4C22×D6714yes—
506C4×D4C22×D6714yes—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—28no—
513C2×C4⋊C4—671no—
514C2×C4⋊C4—1341no—
515C2×C4⋊C4C22⋊D6711yescharacteristic
516C2×C4⋊C4C22⋊D6711yescharacteristic
517C2×C4⋊C4C22⋊D6711yescharacteristic
518C2×C4⋊C4C22×D6711yescharacteristic
519C2×C4⋊C4C22×D6711yescharacteristic
520C2×C4⋊C4C22×D6711yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—1341no—
525C2×C22⋊C4—1341no—
526C2×C22⋊C4—1341no—
527C2×C22⋊C4—1341no—
528C2×C22⋊C4—1341no—
529C2×C22⋊C4—1341no—
530C2×C42—1341no—
531C2×C42C22×D6711yescharacteristic
532C2×C42C22×D6711yescharacteristic
533C2×C42C22×D6711yescharacteristic
534#107—674no—
535#107—674no—
536#106—674no—
537C4⋊C8—674no—
538C4⋊C8—674no—
539C4⋊C8—674no—
540#103—674no—
541#103—674no—
542#103—674no—
543#102—674no—
544#102—674no—
545#102—674no—
546#102—674no—
547#102—674no—
548#102—674no—
549#102—674no—
550#97—674no—
551#97—674no—
552C4×C8—674no—
553C24—21no—
554C24—1341no—
555C24—1341no—
556C2×Q8—24no—
557C2×Q8—42no—
558C2×Q8—82no—
559C2×Q8—672no—
560C2×Q8—1342no—
561C2×Q8—1342no—
562C2×Q8—1341no—
563C2×Q8C2×C22⋊D6714yes—
564C2×D4—21no—
565C2×D4—22no—
566C2×D4—2684no—
567C2×D4—5362no—
568C2×D4—672no—
569C2×D4—672no—
570C2×D4—1344no—
571C2×D4—1341no—
572C2×D4—1341no—
573C2×D4—1344no—
574C2×D4—1342no—
575C2×D4—1342no—
576C2×D4—1342no—
577C2×D4—1342no—
578C2×D4#1176162914yes—
579C2×D4C23×D6712yes—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—24no—
584C22×C4—24no—
585C22×C4—24no—
586C22×C4—44no—
587C22×C4—82no—
588C22×C4—82no—
589C22×C4—5362no—
590C22×C4—5362no—
591C22×C4—1341no—
592C22×C4—1341no—
593C22×C4—1344no—
594C22×C4—1344no—
595C22×C4C2×C22⋊D6711yescharacteristic
596C22×C4C2×C22⋊D6711yescharacteristic
597C22×C4C2×C22⋊D6711yescharacteristic
598C22×C4C2×C22⋊D6711yescharacteristic
599C22×C4C2×C22⋊D6711yescharacteristic
600C22×C4C2×C22⋊D6711yescharacteristic
601C22×C4C23×D6711yescharacteristic
602SD16—1348no—
603D8—1348no—
604D8—1348no—
605C2×C8—672no—
606C2×C8—672no—
607C2×C8—672no—
608C2×C8—672no—
609C2×C8—1342no—
610C2×C8—1342no—
611C2×C8—1342no—
612C2×C8—1342no—
613C4⋊C4—24no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—672no—
622C4⋊C4—1341no—
623C4⋊C4—1344no—
624C4⋊C4C2×C22⋊D6714yes—
625C4⋊C4C2×C22⋊D6714yes—
626C4⋊C4C2×C22⋊D6714yes—
627C4⋊C4C23×D6712yes—
628C4⋊C4C23×D6712yes—
629C4⋊C4C23×D6712yes—
630C22⋊C4—24no—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—1344no—
634C22⋊C4—1344no—
635C22⋊C4—1344no—
636C22⋊C4—1344no—
637C22⋊C4—1344no—
638C22⋊C4—1344no—
639C42—1344no—
640C42C2×C22⋊D6712yes—
641C42C2×C22⋊D6712yes—
642C42C2×C22⋊D6712yes—
643C42C23×D6712yes—
644C42C23×D6712yes—
645C42C23×D6712yes—
646C23—24no—
647C23—22no—
648C23—42no—
649C23—42no—
650C23—2682no—
651C23—2682no—
652C23—2682no—
653C23—2682no—
654C23—2682no—
655C23—2682no—
656C23—1342no—
657C23—1342no—
658C23C22×C22⋊D6711yescharacteristic
659Q8—44no—
660Q8—84no—
661Q8—2682no—
662Q8—1342no—
663Q8—1342no—
664D4—24no—
665D4—22no—
666D4—2688no—
667D4—2682no—
668D4—2682no—
669D4—5364no—
670D4—1342no—
671D4—1342no—
672D4—1342no—
673D4—1342no—
674D4C2×#1176162914yes—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—48no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—84no—
689C2×C4—84no—
690C2×C4—2682no—
691C2×C4—2682no—
692C2×C4—5364no—
693C2×C4—5364no—
694C2×C4—1342no—
695C2×C4—1342no—
696C2×C4C22×C22⋊D6712yes—
697C2×C4C22×C22⋊D6712yes—
698C2×C4C22×C22⋊D6712yes—
699C2×C4C22×C22⋊D6712yes—
700C2×C4C22×C22⋊D6712yes—
701C2×C4C22×C22⋊D6712yes—
702C2×C4C22×C22⋊D6711yescharacteristic
703C2×C4C2×#1176162912yes—
704C2×C4#1452409112yes—
705C2×C4C24×D6711yescharacteristic
706C8—1342no—
707C8—1342no—
708C8—1342no—
709C8—1342no—
710C22—24no—
711C22—42no—
712C22—42no—
713C22—48no—
714C22—2682no—
715C22—2682no—
716C22—2682no—
717C22—2682no—
718C22—2682no—
719C22—2682no—
720C22—5364no—
721C22—5364no—
722C22#1686405712yes—
723C22#1686419412yes—
724C22#1686419912yes—
725C22C23×C22⋊D6711yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—42no—
733C4—42no—
734C4—42no—
735C4—2682no—
736C4—2682no—
737C4#1686405712yes—
738C4C22×#1176162911yescharacteristic
739C4C2×#1452409111yescharacteristic
740C2—44no—
741C2—5362no—
742C2—5362no—
743C2#2257296214yesdirect product factor
744C2C2×#1686405711yescharacteristic
745C2C2×#1686419411yescharacteristic
746C2C2×#1686419911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#554×C67C2
socleC23×C67C22×D4
prime radicalC2×#16863591C2
hypercenterC2×#554D67
hypocenterC67C2×#3370
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
1. C2×#16864131C2semidirect
2. #22572962C2direct (N × H)
3. C2×#16863762C2semidirect
4. C2×#16863758C2semidirect
5. C2×#16863753C2semidirect
6. C2×#16863700C2semidirect
7. C2×#16863693C2semidirect
8. C2×#16863673C2semidirect
9. C2×#16863611C2semidirect
10. C2×#16863611C2semidirect
12. C2×#16863527C2semidirect
13. C2×#16863506C2semidirect
14. C2×#16863496C2semidirect
15. C2×C4×#11761613C2semidirect
16. C2×#554×C67C2semidirect
21. #16864131C22semidirect
32. #16863762C22semidirect
33. #16863758C22semidirect
34. #16863753C22semidirect
35. #16863700C22semidirect
36. #16863693C22semidirect
37. #16863673C22semidirect
38. #16863611C22semidirect
39. #16863611C22semidirect
41. #16863527C22semidirect
42. #16863506C22semidirect
43. #16863496C22semidirect
44. C4×#11761613C22semidirect
65. #554×C67C22semidirect
368. C2×C67#3370semidirect
375. C2×#554D67semidirect
390. C67C2×#3370semidirect
397. #554C2×D67semidirect
743. C2#22572962direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168641312
#225729622
C2×#168637622
C2×#168637582
C2×#168637532
C2×#168637002
C2×#168636932
C2×#168636732
C2×#168636112
C2×#168635912
C2×#168635272
C2×#168635062
C2×#168634962
C2×C4×#117616132
C2×#554×C672
C2×#337067