Finite Group Databasebeta

← C2×#22572658 #31734372

Subgroups — C2×#22572658 #31734372

Order 17152.

1878 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864086C211yesmaximal, characteristic
2#22572658C2116yesmaximal, direct product factor
3C2×#16863802C211yesmaximal, characteristic, complemented
4C2×#16863731C211yesmaximal, characteristic, complemented
5C2×#16863734C211yesmaximal, characteristic, complemented
6C2×#16863726C211yesmaximal, characteristic, complemented
7C2×#16863724C211yesmaximal, characteristic, complemented
8C2×#16863703C211yesmaximal, characteristic, complemented
9C2×#16863678C211yesmaximal, characteristic, complemented
10C2×#16863652C211yesmaximal, characteristic, complemented
11C2×#16863635C211yesmaximal, characteristic, complemented
12C2×#16863501C211yesmaximal, characteristic, complemented
13C2×#16863468C211yesmaximal, characteristic
14C2×#16863436C211yesmaximal, characteristic, complemented
15C22×#14523974C211yesmaximal, characteristic, complemented
16C2×#554×C67C211yesmaximal, characteristic
17C22×#11761618C2211yescharacteristic
18C22×#11761612C2211yescharacteristic
19C23×C67⋊C8C2211yescharacteristic
20#16864086—24no—
21#16864086C2218yes—
22C2×#14524036—21no—
23C2×#14524035C2211yescharacteristic
24C2×#14524033—21no—
25C2×#14524024—21no—
26C2×#14524022C2211yescharacteristic
27C2×#14524022C2211yescharacteristic
28C2×C4×Dic134C2211yescharacteristic
29C2×#14524002C2211yescharacteristic
30C2×#14523999—21no—
31C22×C4⋊Dic67C2211yescharacteristic
32#16863802C2218yescomplemented
33#16863734C2218yescomplemented
34#16863731C2218yescomplemented
35#16863726C2218yescomplemented
36#16863724C2218yescomplemented
37#16863703C2218yescomplemented
38#16863678C2218yescomplemented
39#16863652C2218yescomplemented
40#16863635C2218yescomplemented
41#16863501C2218yescomplemented
42#16863468C2218yes—
43#16863436C2218yescomplemented
44C2×#14523976C2211yescharacteristic
45C2×#14523976C2211yescharacteristic
46C2×#14523976C2211yescharacteristic
47C2×#14523974C2211yescharacteristic
48C2×#14523974C2211yescharacteristic
49C2×#14523974C2211yescharacteristic
50C2×#14523974C2211yescharacteristic
51C2×#14523974C2211yescharacteristic
52C2×#14523974C2211yescharacteristic
53C2×#14523974C2218yescomplemented
54C2×C4⋊(C67⋊C8)C2211yescharacteristic
55C2×#14523967C2211yescharacteristic
56C2×#14523967C2211yescharacteristic
57C2×#14523967C2211yescharacteristic
58C2×#14523966C2211yescharacteristic
59C2×#14523966C2211yescharacteristic
60C2×#14523966C2211yescharacteristic
61C2×C22⋊(C67⋊C8)C2211yescharacteristic
62C2×C22⋊(C67⋊C8)C2211yescharacteristic
63C2×#14523954C2211yescharacteristic
64#554×C67—24no—
65#554×C67C2218yes—
66C2×C4⋊Q8×C67C2211yescharacteristic
67C2×#125×C67—21no—
68C2×C22⋊Q8×C67—21no—
69C2×C22⋊Q8×C67—21no—
70C2×C22⋊Q8×C67C2211yescharacteristic
71C2×C22⋊Q8×C67C2211yescharacteristic
72C2×C4×Q8×C67C2211yescharacteristic
73C2×C4×D4×C67—21no—
74C2×C4×D4×C67C2211yescharacteristic
75C22×C4⋊C4×C67C2211yescharacteristic
76C22×C4⋊C4×C67C2211yescharacteristic
77C22×Dic134C2311yescharacteristic
78C23×Dic67—21no—
79C2×#11761618—24no—
80C2×#11761618C2314yes—
81C2×#11761612—24no—
82C2×#11761612C2314yes—
83C22×C67⋊C8—24no—
84C22×C67⋊C8C2311yescharacteristic
85C22×C67⋊C8C2311yescharacteristic
86C22×C67⋊C8C2311yescharacteristic
87C22×C67⋊C8C2314yes—
88C22×C67⋊C8C2311yescharacteristic
89#14524036—28no—
90#14524035—22no—
91#14524035C2314yes—
92#14524033—28no—
93#14524024—28no—
94#14524022—22no—
95#14524022—22no—
96#14524022C2314yes—
97#14524022C2314yes—
98C4×Dic134—22no—
99C4×Dic134C2314yes—
100#14524002—22no—
101#14524002C2314yes—
102#14523999—28no—
103C2×C4⋊Dic67—22no—
104C2×C4⋊Dic67—21no—
105C2×C4⋊Dic67C2314yes—
106C2×C4⋊Dic67C2311yescharacteristic
107C2×C4⋊Dic67C2311yescharacteristic
108C2×C4⋊Dic67C2311yescharacteristic
109C2×Dic67⋊C4—21no—
110C2×Dic67⋊C4—21no—
111C2×Dic67⋊C4—21no—
112C2×Dic67⋊C4—21no—
113C2×Dic67⋊C4—21no—
114C2×C22⋊Dic67—21no—
115C2×C22⋊Dic67—21no—
116C2×C22⋊Dic67—21no—
117C2×C4×Dic67—21no—
118C2×C4×Dic67—21no—
119#14523976C2314yes—
120#14523976C2314yes—
121#14523976C2314yes—
122#14523974C2314yes—
123#14523974C2314yes—
124#14523974C2314yes—
125#14523974C2314yes—
126#14523974C2314yes—
127#14523974C2314yes—
128C4⋊(C67⋊C8)C2314yes—
129#14523967C2314yes—
130#14523967C2314yes—
131#14523967C2314yes—
132#14523966C2314yes—
133#14523966C2314yes—
134#14523966C2314yes—
135C22⋊(C67⋊C8)C2314yes—
136C22⋊(C67⋊C8)C2314yes—
137#14523954C2314yes—
138C22×Q8×C67—21no—
139C22×Q8×C67C2311yescharacteristic
140C22×D4×C67D411yescharacteristic
141C23×C4×C67—21no—
142C23×C4×C67—21no—
143C23×C4×C67C2311yescharacteristic
144C23×C4×C67C2311yescharacteristic
145C4⋊Q8×C67—22no—
146C4⋊Q8×C67C2314yes—
147#125×C67—28no—
148C22⋊Q8×C67—22no—
149C22⋊Q8×C67—22no—
150C22⋊Q8×C67—28no—
151C22⋊Q8×C67—28no—
152C22⋊Q8×C67C2314yes—
153C22⋊Q8×C67C2314yes—
154C4×Q8×C67—22no—
155C4×Q8×C67C2314yes—
156C4×D4×C67—28no—
157C4×D4×C67D414yes—
158C4×D4×C67C2314yes—
159C2×C4⋊C4×C67—21no—
160C2×C4⋊C4×C67—21no—
161C2×C4⋊C4×C67—22no—
162C2×C4⋊C4×C67—22no—
163C2×C4⋊C4×C67—21no—
164C2×C4⋊C4×C67—21no—
165C2×C4⋊C4×C67—21no—
166C2×C4⋊C4×C67—21no—
167C2×C4⋊C4×C67D411yescharacteristic
168C2×C4⋊C4×C67C2311yescharacteristic
169C2×C4⋊C4×C67C2311yescharacteristic
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C4⋊C4×C67C2314yes—
172C2×C4⋊C4×C67C2314yes—
173C2×C22⋊C4×C67—21no—
174C2×C22⋊C4×C67—21no—
175C2×C22⋊C4×C67D411yescharacteristic
176C2×C22⋊C4×C67D411yescharacteristic
177C2×C42×C67—21no—
178C2×C42×C67C2311yescharacteristic
179C2×Dic134—22no—
180C2×Dic134—22no—
181C2×Dic134—21no—
182C2×Dic134C2412yes—
183C22×Dic67—21no—
184C22×Dic67—21no—
185C22×Dic67—21no—
186C22×Dic67—21no—
187C22×Dic67—24no—
188C22×Dic67—44no—
189#11761618—28no—
190#11761612—28no—
191C2×C67⋊C8—22no—
192C2×C67⋊C8—22no—
193C2×C67⋊C8—22no—
194C2×C67⋊C8—28no—
195C2×C67⋊C8#4114yes—
196C2×C67⋊C8C2412yes—
197C2×C67⋊C8C2412yes—
198C2×C67⋊C8C2412yes—
199C2×C67⋊C8C2412yes—
200C4⋊Dic67—21no—
201C4⋊Dic67—21no—
202C4⋊Dic67—24no—
203C4⋊Dic67—21no—
204C4⋊Dic67C2412yes—
205C4⋊Dic67C2412yes—
206C4⋊Dic67C2412yes—
207Dic67⋊C4—24no—
208Dic67⋊C4—24no—
209Dic67⋊C4—24no—
210Dic67⋊C4—24no—
211Dic67⋊C4—24no—
212C22⋊Dic67—24no—
213C22⋊Dic67—24no—
214C22⋊Dic67—24no—
215C4×Dic67—24no—
216C4×Dic67—24no—
217C24×C67C2×D411yescharacteristic
218C24×C67C2×D411yescharacteristic
219C2×Q8×C67—21no—
220C2×Q8×C67—24no—
221C2×Q8×C67—22no—
222C2×Q8×C67—22no—
223C2×Q8×C67—82no—
224C2×Q8×C67C2412yes—
225C2×D4×C67—24no—
226C2×D4×C67C2×D414yes—
227C22×C4×C67—22no—
228C22×C4×C67—22no—
229C22×C4×C67—22no—
230C22×C4×C67—22no—
231C22×C4×C67—21no—
232C22×C4×C67—21no—
233C22×C4×C67—21no—
234C22×C4×C67—21no—
235C22×C4×C67—24no—
236C22×C4×C67—24no—
237C22×C4×C67—82no—
238C22×C4×C67—82no—
239C22×C4×C67C2×D411yescharacteristic
240C22×C4×C67C2×D411yescharacteristic
241C22×C4×C67C2×D411yescharacteristic
242C22×C4×C67C2×D411yescharacteristic
243C22×C4×C67C2×D412yes—
244C22×C4×C67C2×D412yes—
245C22×C4×C67C2412yes—
246C22×C4×C67C2412yes—
247C22×C4×C67C2411yescharacteristic
248C4⋊C4×C67—21no—
249C4⋊C4×C67—24no—
250C4⋊C4×C67—24no—
251C4⋊C4×C67—21no—
252C4⋊C4×C67—21no—
253C4⋊C4×C67—24no—
254C4⋊C4×C67—24no—
255C4⋊C4×C67—24no—
256C4⋊C4×C67—24no—
257C4⋊C4×C67C2×D414yes—
258C4⋊C4×C67C2412yes—
259C4⋊C4×C67C2412yes—
260C4⋊C4×C67C2412yes—
261C22⋊C4×C67—24no—
262C22⋊C4×C67—24no—
263C22⋊C4×C67C2×D414yes—
264C22⋊C4×C67C2×D414yes—
265C42×C67—24no—
266C42×C67C2×D412yes—
267C42×C67C2412yes—
268C23×C67—22no—
269C23×C67—22no—
270C23×C67—22no—
271C23×C67—22no—
272C23×C67—22no—
273C23×C67#13714yes—
274C23×C67C22×D412yes—
275C23×C67C22×D412yes—
276C23×C67C22×D411yescharacteristic
277Q8×C67—22no—
278Q8×C67—22no—
279Q8×C67—42no—
280Q8×C67—84no—
281D4×C67—28no—
282C2×C4×C67—22no—
283C2×C4×C67—22no—
284C2×C4×C67—22no—
285C2×C4×C67—22no—
286C2×C4×C67—24no—
287C2×C4×C67—24no—
288C2×C4×C67—22no—
289C2×C4×C67—22no—
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—42no—
297C2×C4×C67—42no—
298C2×C4×C67—42no—
299C2×C4×C67—42no—
300C2×C4×C67—84no—
301C2×C4×C67—84no—
302C2×C4×C67C22×D412yes—
303C2×C4×C67C22×D412yes—
304C2×C4×C67C22×D412yes—
305C2×C4×C67C22×D412yes—
306C2×C4×C67C22×D411yescharacteristic
307C2×C4×C67C2×#4112yes—
308C2×C4×C672−1+412yes—
309C2×C4×C67C2511yescharacteristic
310C2×Dic67—22no—
311C2×Dic67—22no—
312C2×Dic67—22no—
313C2×Dic67—22no—
314C2×Dic67—42no—
315C2×Dic67—48no—
316C2×Dic67—42no—
317C2×Dic67—42no—
318C2×Dic67—42no—
319Dic134—22no—
320Dic134—22no—
321Dic134—42no—
322C67⋊C8—22no—
323C67⋊C8—22no—
324C67⋊C8—22no—
325C67⋊C8C2×#4114yes—
326C22×C67—28no—
327C22×C67—22no—
328C22×C67—22no—
329C22×C67—22no—
330C22×C67—22no—
331C22×C67—22no—
332C22×C67—44no—
333C22×C67#54712yes—
334C22×C67C2×#13714yes—
335C22×C67C2×#13712yes—
336C22×C67#57712yes—
337C22×C67C23×D411yescharacteristic
338C4×C67—22no—
339C4×C67—22no—
340C4×C67—22no—
341C4×C67—22no—
342C4×C67—42no—
343C4×C67—42no—
344C4×C67—42no—
345C4×C67—42no—
346C4×C67#54712yes—
347C4×C67C22×#4111yescharacteristic
348C4×C67C2×2−1+411yescharacteristic
349Dic67—42no—
350Dic67—42no—
351Dic67—42no—
352Dic67—42no—
353C2×#3344—671nomaximal, Sylow
354C2×C67—24no—
355C2×C67—42no—
356C2×C67#334414yescomplemented
357C2×C67C2×#54711yescharacteristic
358C2×C67C22×#13711yescharacteristic
359C2×C67C2×#57711yescharacteristic
360C2×#554D6711yescharacteristic
361C2×#552—671no—
362#3344—6716no—
363C2×#501—671no—
364C2×#484—671no—
365C2×#485—671no—
366C2×#483—671no—
367C2×#483—671no—
368C2×#479—671no—
369C2×#475—671no—
370C2×#470—671no—
371C2×#467—671no—
372C2×#441—671no—
373C2×#435—671no—
374C2×#428—671no—
375C22×#106—671no—
376C67C2×#334411yescharacteristic, complemented, Sylow
377C22×Q16—671no—
378C22×M16—671no—
379C23×C8—671no—
380#554—24no—
381#554C2×D6718yes—
382#552—678no—
383#552—1344no—
384C2×C4⋊Q8C2×D6711yescharacteristic
385C2×#126—1341no—
386C2×#125—21no—
387C2×#125—671no—
388C2×#125—1341no—
389C2×#123—1341no—
390C2×C22⋊Q8—21no—
391C2×C22⋊Q8—21no—
392C2×C22⋊Q8—671no—
393C2×C22⋊Q8—671no—
394C2×C22⋊Q8C2×D6711yescharacteristic
395C2×C22⋊Q8C2×D6711yescharacteristic
396C2×C4×Q8—671no—
397C2×C4×Q8C2×D6711yescharacteristic
398C2×C4×D4—21no—
399C2×C4×D4C2×D6711yescharacteristic
400C2×#117—671no—
401C2×#117—1341no—
402C22×C4⋊C4—671no—
403C22×C4⋊C4C2×D6711yescharacteristic
404C22×C4⋊C4C2×D6711yescharacteristic
405#501—678no—
406#485—678no—
407#484—678no—
408#483—678no—
409#483—678no—
410#479—678no—
411#475—678no—
412#470—678no—
413#467—678no—
414#441—678no—
415#435—678no—
416#428—678no—
417C2×#107—671no—
418C2×#107—671no—
419C2×#107—671no—
420C2×#106—671no—
421C2×#106—671no—
422C2×#106—671no—
423C2×#106—671no—
424C2×#106—678no—
425C2×#106—671no—
426C2×#106—671no—
427C2×C4⋊C8—671no—
428C2×#103—671no—
429C2×#103—671no—
430C2×#103—671no—
431C2×#103—671no—
432C2×#103—671no—
433C2×#103—671no—
434C2×C22⋊C8—671no—
435C2×C22⋊C8—671no—
436C2×#97—671no—
437C22×Q8—21no—
438C22×Q8—671no—
439C22×Q8C22×D6711yescharacteristic
440C22×D4C22⋊D6711yescharacteristic
441C23×C4—21no—
442C23×C4—21no—
443C23×C4—1341no—
444C23×C4C22×D6711yescharacteristic
445C23×C4C22×D6711yescharacteristic
446C2×Q16—674no—
447C2×Q16—1344no—
448C2×M16—674no—
449C2×M16—1344no—
450C22×C8—671no—
451C22×C8—671no—
452C22×C8—674no—
453C22×C8—671no—
454C22×C8—671no—
455C22×C8—1344no—
456C4⋊Q8—22no—
457C4⋊Q8C22×D6714yes—
458#126—1348no—
459#125—28no—
460#125—674no—
461#125—1348no—
462#125—1342no—
463#123—1348no—
464C22⋊Q8—22no—
465C22⋊Q8—22no—
466C22⋊Q8—28no—
467C22⋊Q8—28no—
468C22⋊Q8—674no—
469C22⋊Q8—674no—
470C22⋊Q8—1342no—
471C22⋊Q8—1342no—
472C22⋊Q8C22×D6714yes—
473C22⋊Q8C22×D6714yes—
474C4×Q8—22no—
475C4×Q8—674no—
476C4×Q8—1342no—
477C4×Q8C22×D6714yes—
478C4×D4—28no—
479C4×D4C22⋊D6714yes—
480C4×D4C22×D6714yes—
481#117—674no—
482#117—1342no—
483#117—1348no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—21no—
492C2×C4⋊C4—671no—
493C2×C4⋊C4—671no—
494C2×C4⋊C4—674no—
495C2×C4⋊C4—671no—
496C2×C4⋊C4—1341no—
497C2×C4⋊C4—1342no—
498C2×C4⋊C4—1341no—
499C2×C4⋊C4—1341no—
500C2×C4⋊C4—1341no—
501C2×C4⋊C4—1341no—
502C2×C4⋊C4—1341no—
503C2×C4⋊C4C22⋊D6711yescharacteristic
504C2×C4⋊C4C22×D6711yescharacteristic
505C2×C4⋊C4C22×D6711yescharacteristic
506C2×C4⋊C4C22×D6711yescharacteristic
507C2×C4⋊C4C22×D6714yes—
508C2×C4⋊C4C22×D6714yes—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—1341no—
512C2×C22⋊C4—1341no—
513C2×C22⋊C4—1341no—
514C2×C22⋊C4C22⋊D6711yescharacteristic
515C2×C22⋊C4C22⋊D6711yescharacteristic
516C2×C42—21no—
517C2×C42—1341no—
518C2×C42—1341no—
519C2×C42C22×D6711yescharacteristic
520#107—674no—
521#107—674no—
522#107—674no—
523#106—674no—
524#106—674no—
525#106—674no—
526#106—674no—
527#106—674no—
528#106—674no—
529C4⋊C8—674no—
530#103—674no—
531#103—674no—
532#103—674no—
533#103—674no—
534#103—674no—
535#103—674no—
536C22⋊C8—674no—
537C22⋊C8—674no—
538#97—674no—
539C24C2×C22⋊D6711yescharacteristic
540C24C2×C22⋊D6711yescharacteristic
541C2×Q8—21no—
542C2×Q8—24no—
543C2×Q8—22no—
544C2×Q8—22no—
545C2×Q8—82no—
546C2×Q8—672no—
547C2×Q8—1342no—
548C2×Q8—1342no—
549C2×Q8—1341no—
550C2×Q8C23×D6712yes—
551C2×D4—24no—
552C2×D4C2×C22⋊D6714yes—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—82no—
564C22×C4—82no—
565C22×C4—2684no—
566C22×C4—1344no—
567C22×C4—1341no—
568C22×C4—1341no—
569C22×C4—1341no—
570C22×C4—1341no—
571C22×C4C2×C22⋊D6712yes—
572C22×C4C2×C22⋊D6712yes—
573C22×C4C2×C22⋊D6711yescharacteristic
574C22×C4C2×C22⋊D6711yescharacteristic
575C22×C4C2×C22⋊D6711yescharacteristic
576C22×C4C2×C22⋊D6711yescharacteristic
577C22×C4C23×D6712yes—
578C22×C4C23×D6712yes—
579C22×C4C23×D6711yescharacteristic
580Q16—1348no—
581M16—1348no—
582C2×C8—674no—
583C2×C8—672no—
584C2×C8—672no—
585C2×C8—672no—
586C2×C8—672no—
587C2×C8—1348no—
588C2×C8—1342no—
589C2×C8—1342no—
590C2×C8—1342no—
591C4⋊C4—21no—
592C4⋊C4—24no—
593C4⋊C4—24no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—24no—
597C4⋊C4—24no—
598C4⋊C4—24no—
599C4⋊C4—24no—
600C4⋊C4—672no—
601C4⋊C4—672no—
602C4⋊C4—672no—
603C4⋊C4—1341no—
604C4⋊C4—1341no—
605C4⋊C4—1344no—
606C4⋊C4—1341no—
607C4⋊C4—1344no—
608C4⋊C4—1344no—
609C4⋊C4—1344no—
610C4⋊C4—1344no—
611C4⋊C4—1344no—
612C4⋊C4C2×C22⋊D6714yes—
613C4⋊C4C23×D6712yes—
614C4⋊C4C23×D6712yes—
615C4⋊C4C23×D6712yes—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—1344no—
619C22⋊C4—1344no—
620C22⋊C4—1344no—
621C22⋊C4C2×C22⋊D6714yes—
622C22⋊C4C2×C22⋊D6714yes—
623C42—24no—
624C42—1344no—
625C42—1344no—
626C42C2×C22⋊D6712yes—
627C42C23×D6712yes—
628C23—22no—
629C23—22no—
630C23—22no—
631C23—22no—
632C23—22no—
633C23#1452407414yes—
634C23C22×C22⋊D6712yes—
635C23C22×C22⋊D6712yes—
636C23C22×C22⋊D6711yescharacteristic
637Q8—22no—
638Q8—22no—
639Q8—42no—
640Q8—84no—
641Q8—2682no—
642Q8—1342no—
643Q8—1342no—
644D4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—84no—
664C2×C4—84no—
665C2×C4—2682no—
666C2×C4—2688no—
667C2×C4—2682no—
668C2×C4—2682no—
669C2×C4—2682no—
670C2×C4—1342no—
671C2×C4—1342no—
672C2×C4—1342no—
673C2×C4—1342no—
674C2×C4C22×C22⋊D6712yes—
675C2×C4C22×C22⋊D6712yes—
676C2×C4C22×C22⋊D6712yes—
677C2×C4C22×C22⋊D6712yes—
678C2×C4C22×C22⋊D6711yescharacteristic
679C2×C4#41×D6712yes—
680C2×C4#1452409012yes—
681C2×C4C24×D6711yescharacteristic
682C8—674no—
683C8—1342no—
684C8—1342no—
685C8—1342no—
686C22—22no—
687C22—28no—
688C22—22no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—44no—
693C22#1686404512yes—
694C22C2×#1452407414yes—
695C22C2×#1452407412yes—
696C22#1686420712yes—
697C22C23×C22⋊D6711yescharacteristic
698C4—22no—
699C4—22no—
700C4—22no—
701C4—22no—
702C4—42no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—2682no—
707C4—2682no—
708C4—2682no—
709C4—2682no—
710C4#1686404512yes—
711C4C2×#41×D6711yescharacteristic
712C4C2×#1452409011yescharacteristic
713C2—24no—
714C2—42no—
715C2#2257265814yesdirect product factor
716C2C2×#1686404511yescharacteristic
717C2C22×#1452407411yescharacteristic
718C2C2×#1686420711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#554×C67C2
socleC23×C67C22×D4
prime radicalC22×D4×C67D4
hypercenterC2×#554D67
hypocenterC67C2×#3344
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#554

Complements

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

NH ≅ G/Ntype
2. #22572658C2direct (N × H)
3. C2×#16863802C2semidirect
4. C2×#16863731C2semidirect
5. C2×#16863734C2semidirect
6. C2×#16863726C2semidirect
7. C2×#16863724C2semidirect
8. C2×#16863703C2semidirect
9. C2×#16863678C2semidirect
10. C2×#16863652C2semidirect
11. C2×#16863635C2semidirect
12. C2×#16863501C2semidirect
14. C2×#16863436C2semidirect
15. C22×#14523974C2semidirect
32. #16863802C22semidirect
33. #16863734C22semidirect
34. #16863731C22semidirect
35. #16863726C22semidirect
36. #16863724C22semidirect
37. #16863703C22semidirect
38. #16863678C22semidirect
39. #16863652C22semidirect
40. #16863635C22semidirect
41. #16863501C22semidirect
43. #16863436C22semidirect
53. C2×#14523974C22semidirect
356. C2×C67#3344semidirect
376. C67C2×#3344semidirect
715. C2#22572658direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640862
#225726582
C2×#168638022
C2×#168637312
C2×#168637342
C2×#168637262
C2×#168637242
C2×#168637032
C2×#168636782
C2×#168636522
C2×#168636352
C2×#168635012
C2×#168634682
C2×#168634362
C22×#145239742
C2×#554×C672
C2×#334467