Finite Group Databasebeta

← C2×#22572275 #31732565

Subgroups — C2×#22572275 #31732565

Order 17152.

2114 conjugacy classes of subgroups.

The subgroup lattice has 788 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864116C211yesmaximal, characteristic, complemented
2#22572275C2116yesmaximal, direct product factor
3C2×#16863755C211yesmaximal, characteristic, complemented
4C2×#16863734C211yesmaximal, characteristic, complemented
5C2×#16863717C211yesmaximal, characteristic, complemented
6C2×#16863691C211yesmaximal, characteristic, complemented
7C2×#16863640C211yesmaximal, characteristic, complemented
8C2×#16863635C211yesmaximal, characteristic, complemented
9C2×#16863615C211yesmaximal, characteristic, complemented
10C2×#16863558C211yesmaximal, characteristic, complemented
11C2×#16863552C211yesmaximal, characteristic, complemented
12C2×#16863501C211yesmaximal, characteristic, complemented
13C2×#16863468C211yesmaximal, characteristic, complemented
14C2×#16863405C211yesmaximal, characteristic, complemented
15C2×#16863392C211yesmaximal, characteristic, complemented
16C2×#548×C67C211yesmaximal, characteristic
17C22×#11761618C2211yescharacteristic
18C22×#11761618C2211yescharacteristic
19C22×#11761616C2211yescharacteristic
20C22×#11761612C2211yescharacteristic
21C23×C67⋊C8C2211yescharacteristic
22#16864116—24no—
23#16864116C2218yescomplemented
24C2×#14524043C2211yescharacteristic
25C2×#14524036—21no—
26C2×#14524036—21no—
27C2×#14524030—21no—
28C2×#14524022C2211yescharacteristic
29C2×#14524022C2211yescharacteristic
30C2×C4×Dic134C2211yescharacteristic
31C2×#14524008—21no—
32C2×#14524002C2211yescharacteristic
33C2×#14524002C2211yescharacteristic
34#16863755C2218yescomplemented
35#16863734C2218yescomplemented
36#16863717C2218yescomplemented
37#16863691C2218yescomplemented
38#16863640C2218yescomplemented
39#16863635C2218yescomplemented
40#16863615C2218yescomplemented
41#16863558C2218yescomplemented
42#16863552C2218yescomplemented
43#16863501C2218yescomplemented
44#16863468C2218yescomplemented
45C2×#14523976C2211yescharacteristic
46C2×#14523976C2211yescharacteristic
47C2×#14523974C2211yescharacteristic
48C2×C4⋊(C67⋊C8)C2211yescharacteristic
49#16863405C2218yescomplemented
50#16863392C2218yescomplemented
51C2×#14523967C2211yescharacteristic
52C2×#14523967C2211yescharacteristic
53C2×#14523967C2211yescharacteristic
54C2×#14523967C2211yescharacteristic
55C2×#14523967C2211yescharacteristic
56C2×#14523967C2211yescharacteristic
57C2×#14523966C2211yescharacteristic
58C2×#14523964C2211yescharacteristic
59C2×#14523964C2211yescharacteristic
60C2×#14523964C2211yescharacteristic
61C2×C22⋊(C67⋊C8)C2211yescharacteristic
62C2×C22⋊(C67⋊C8)C2211yescharacteristic
63C2×#14523954C2211yescharacteristic
64C22×#41×C67C2211yescharacteristic
65C23×Q8×C67C2211yescharacteristic
66#548×C67—24no—
67#548×C67C2218yes—
68C2×#124×C67—21no—
69C2×#124×C67C2211yescharacteristic
70C2×C22⋊Q8×C67—21no—
71C2×C22⋊Q8×C67C2211yescharacteristic
72C2×#121×C67—21no—
73C2×#121×C67C2211yescharacteristic
74C2×C4×Q8×C67C2211yescharacteristic
75C2×C4×D4×C67—21no—
76C2×C4×D4×C67C2211yescharacteristic
77C22×Dic134—21no—
78C22×Dic134C2311yescharacteristic
79C2×#11761618—24no—
80C2×#11761618—42no—
81C2×#11761618C2314yes—
82C2×#11761618C2314yes—
83C2×#11761616—42no—
84C2×#11761616C2314yes—
85C2×#11761612—42no—
86C2×#11761612C2314yes—
87C22×C67⋊C8—42no—
88C22×C67⋊C8C2311yescharacteristic
89C22×C67⋊C8C2311yescharacteristic
90C22×C67⋊C8C2311yescharacteristic
91C22×C67⋊C8C2311yescharacteristic
92C22×C67⋊C8C2314yes—
93#14524043—22no—
94#14524043C2314yes—
95#14524036—28no—
96#14524036—28no—
97#14524030—28no—
98#14524022—22no—
99#14524022—22no—
100#14524022C2314yes—
101#14524022C2314yes—
102C4×Dic134—22no—
103C4×Dic134C2314yes—
104#14524008—28no—
105#14524002—22no—
106#14524002—22no—
107#14524002C2314yes—
108#14524002C2314yes—
109C2×C4⋊Dic67—21no—
110C2×C4⋊Dic67C2311yescharacteristic
111C2×C4⋊Dic67C2311yescharacteristic
112C2×C4⋊Dic67C2311yescharacteristic
113C2×Dic67⋊C4—21no—
114C2×Dic67⋊C4—21no—
115C2×Dic67⋊C4—21no—
116C2×C22⋊Dic67—21no—
117C2×C22⋊Dic67—21no—
118C2×C22⋊Dic67—21no—
119C2×C22⋊Dic67—21no—
120C2×C4×Dic67—21no—
121C2×C4×Dic67—21no—
122C2×C4×Dic67—21no—
123#14523976C2314yes—
124#14523976C2314yes—
125#14523974C2314yes—
126C4⋊(C67⋊C8)C2314yes—
127#14523967C2314yes—
128#14523967C2314yes—
129#14523967C2314yes—
130#14523967C2314yes—
131#14523967C2314yes—
132#14523967C2314yes—
133#14523966C2314yes—
134#14523964C2314yes—
135#14523964C2314yes—
136#14523964C2314yes—
137C22⋊(C67⋊C8)C2314yes—
138C22⋊(C67⋊C8)C2314yes—
139#14523954C2314yes—
140C2×#41×C67—22no—
141C2×#41×C67—24no—
142C2×#41×C67—42no—
143C2×#41×C67C2314yes—
144C22×Q8×C67—21no—
145C22×Q8×C67—22no—
146C22×Q8×C67—24no—
147C22×Q8×C67—42no—
148C22×Q8×C67C2311yescharacteristic
149C22×Q8×C67C2314yes—
150C22×Q8×C67C2311yescharacteristic
151C22×D4×C67—21no—
152C22×D4×C67—21no—
153C22×D4×C67D411yescharacteristic
154C22×D4×C67C2311yescharacteristic
155C23×C4×C67—21no—
156C23×C4×C67—21no—
157C23×C4×C67C2311yescharacteristic
158C23×C4×C67C2311yescharacteristic
159#124×C67—28no—
160#124×C67—22no—
161#124×C67C2314yes—
162C22⋊Q8×C67—22no—
163C22⋊Q8×C67—28no—
164C22⋊Q8×C67C2314yes—
165#121×C67—28no—
166#121×C67—22no—
167#121×C67C2314yes—
168C4×Q8×C67—22no—
169C4×Q8×C67C2314yes—
170C4×D4×C67—28no—
171C4×D4×C67D414yes—
172C4×D4×C67C2314yes—
173C2×C4⋊C4×C67—21no—
174C2×C4⋊C4×C67—21no—
175C2×C4⋊C4×C67D411yescharacteristic
176C2×C4⋊C4×C67C2311yescharacteristic
177C2×C22⋊C4×C67—21no—
178C2×C22⋊C4×C67—21no—
179C2×C22⋊C4×C67—21no—
180C2×C22⋊C4×C67—21no—
181C2×C22⋊C4×C67D411yescharacteristic
182C2×C22⋊C4×C67D411yescharacteristic
183C2×C42×C67—21no—
184C2×C42×C67C2311yescharacteristic
185C2×Dic134—22no—
186C2×Dic134—22no—
187C2×Dic134—24no—
188C2×Dic134—21no—
189C2×Dic134—44no—
190C2×Dic134C2412yes—
191C22×Dic67—21no—
192C22×Dic67—21no—
193C22×Dic67—21no—
194C22×Dic67—21no—
195#11761618—28no—
196#11761618—44no—
197#11761616—44no—
198#11761612—44no—
199C2×C67⋊C8—22no—
200C2×C67⋊C8—22no—
201C2×C67⋊C8—22no—
202C2×C67⋊C8—22no—
203C2×C67⋊C8—44no—
204C2×C67⋊C8C2412yes—
205C2×C67⋊C8C2412yes—
206C2×C67⋊C8C2412yes—
207C2×C67⋊C8C2412yes—
208C4⋊Dic67—24no—
209C4⋊Dic67—21no—
210C4⋊Dic67—21no—
211C4⋊Dic67—21no—
212C4⋊Dic67C2412yes—
213C4⋊Dic67C2412yes—
214C4⋊Dic67C2412yes—
215Dic67⋊C4—24no—
216Dic67⋊C4—24no—
217Dic67⋊C4—24no—
218C22⋊Dic67—24no—
219C22⋊Dic67—24no—
220C22⋊Dic67—24no—
221C22⋊Dic67—24no—
222C4×Dic67—24no—
223C4×Dic67—24no—
224C4×Dic67—24no—
225C24×C67—21no—
226C24×C67C2×D411yescharacteristic
227C24×C67C2×D411yescharacteristic
228#41×C67—28no—
229#41×C67—44no—
230#41×C67—48no—
231C2×Q8×C67—21no—
232C2×Q8×C67—24no—
233C2×Q8×C67—21no—
234C2×Q8×C67—22no—
235C2×Q8×C67—28no—
236C2×Q8×C67—22no—
237C2×Q8×C67—22no—
238C2×Q8×C67—44no—
239C2×Q8×C67—44no—
240C2×Q8×C67—48no—
241C2×Q8×C67#4114yes—
242C2×Q8×C67C2412yes—
243C2×Q8×C67C2412yes—
244C2×D4×C67—24no—
245C2×D4×C67—24no—
246C2×D4×C67—21no—
247C2×D4×C67—22no—
248C2×D4×C67—22no—
249C2×D4×C67—42no—
250C2×D4×C67—44no—
251C2×D4×C67—44no—
252C2×D4×C67C2×D414yes—
253C2×D4×C67C2412yes—
254C22×C4×C67—21no—
255C22×C4×C67—22no—
256C22×C4×C67—22no—
257C22×C4×C67—22no—
258C22×C4×C67—22no—
259C22×C4×C67—21no—
260C22×C4×C67—21no—
261C22×C4×C67—24no—
262C22×C4×C67—24no—
263C22×C4×C67—44no—
264C22×C4×C67—44no—
265C22×C4×C67C2×D411yescharacteristic
266C22×C4×C67C2×D411yescharacteristic
267C22×C4×C67C2×D411yescharacteristic
268C22×C4×C67C2×D411yescharacteristic
269C22×C4×C67C2×D412yes—
270C22×C4×C67C2×D412yes—
271C22×C4×C67C2412yes—
272C22×C4×C67C2412yes—
273C22×C4×C67C2411yescharacteristic
274C4⋊C4×C67—24no—
275C4⋊C4×C67—24no—
276C4⋊C4×C67—21no—
277C4⋊C4×C67C2×D414yes—
278C4⋊C4×C67C2412yes—
279C22⋊C4×C67—24no—
280C22⋊C4×C67—24no—
281C22⋊C4×C67—24no—
282C22⋊C4×C67—24no—
283C22⋊C4×C67C2×D414yes—
284C22⋊C4×C67C2×D414yes—
285C42×C67—24no—
286C42×C67C2×D412yes—
287C42×C67C2412yes—
288C23×C67—22no—
289C23×C67—22no—
290C23×C67—22no—
291C23×C67—22no—
292C23×C67—22no—
293C23×C67—22no—
294C23×C67—22no—
295C23×C67—42no—
296C23×C67—42no—
297C23×C67—42no—
298C23×C67C22×D412yes—
299C23×C67C22×D412yes—
300C23×C67C22×D411yescharacteristic
301Q8×C67—24no—
302Q8×C67—22no—
303Q8×C67—22no—
304Q8×C67—22no—
305Q8×C67—48no—
306Q8×C67—42no—
307Q8×C67C2×#4114yes—
308D4×C67—22no—
309D4×C67—22no—
310D4×C67—44no—
311D4×C67—48no—
312D4×C67—48no—
313D4×C67—42no—
314C2×C4×C67—22no—
315C2×C4×C67—22no—
316C2×C4×C67—24no—
317C2×C4×C67—22no—
318C2×C4×C67—22no—
319C2×C4×C67—22no—
320C2×C4×C67—24no—
321C2×C4×C67—24no—
322C2×C4×C67—22no—
323C2×C4×C67—22no—
324C2×C4×C67—22no—
325C2×C4×C67—22no—
326C2×C4×C67—22no—
327C2×C4×C67—22no—
328C2×C4×C67—48no—
329C2×C4×C67—48no—
330C2×C4×C67—42no—
331C2×C4×C67—42no—
332C2×C4×C67C22×D412yes—
333C2×C4×C67C22×D412yes—
334C2×C4×C67C22×D412yes—
335C2×C4×C67C22×D412yes—
336C2×C4×C67C22×D411yescharacteristic
337C2×C4×C67C2×#4112yes—
338C2×C4×C67H(5,𝔽2)12yes—
339C2×C4×C67C2511yescharacteristic
340C2×Dic67—22no—
341C2×Dic67—22no—
342C2×Dic67—22no—
343C2×Dic67—22no—
344C2×Dic67—42no—
345C2×Dic67—42no—
346C2×Dic67—42no—
347C2×Dic67—42no—
348Dic134—22no—
349Dic134—22no—
350Dic134—48no—
351Dic134—42no—
352C67⋊C8—22no—
353C67⋊C8—22no—
354C67⋊C8—22no—
355C67⋊C8—22no—
356C22×C67—22no—
357C22×C67—22no—
358C22×C67—22no—
359C22×C67—22no—
360C22×C67—22no—
361C22×C67—22no—
362C22×C67—44no—
363C22×C67—44no—
364C22×C67—42no—
365C22×C67—42no—
366C22×C67—42no—
367C22×C67—84no—
368C22×C67#54612yes—
369C22×C67#57512yes—
370C22×C67#57812yes—
371C22×C67C23×D411yescharacteristic
372C4×C67—22no—
373C4×C67—22no—
374C4×C67—24no—
375C4×C67—22no—
376C4×C67—22no—
377C4×C67—42no—
378C4×C67—42no—
379C4×C67#54612yes—
380C4×C67C22×#4111yescharacteristic
381C4×C67C2×H(5,𝔽2)11yescharacteristic
382Dic67—42no—
383Dic67—42no—
384Dic67—42no—
385Dic67—42no—
386C2×#3313—671nomaximal, Sylow
387C2×C67—42no—
388C2×C67—42no—
389C2×C67—82no—
390C2×C67#331314yescomplemented
391C2×C67C2×#54611yescharacteristic
392C2×C67C2×#57511yescharacteristic
393C2×C67C2×#57811yescharacteristic
394C2×#556—671no—
395C2×#548D6711yescharacteristic
396#3313—6716no—
397C2×#489—671no—
398C2×#485—671no—
399C2×#482—671no—
400C2×#477—671no—
401C2×#468—671no—
402C2×#467—671no—
403C2×#464—671no—
404C2×#452—671no—
405C2×#451—671no—
406C2×#441—671no—
407C2×#435—671no—
408C2×#419—671no—
409C2×#416—671no—
410C67C2×#331311yescharacteristic, complemented, Sylow
411C22×#41C2×D6711yescharacteristic
412C23×Q8C2×D6711yescharacteristic
413C22×Q16—671no—
414C22×Q16—671no—
415C22×SD16—671no—
416C22×M16—671no—
417C23×C8—671no—
418#556—678no—
419#556—1344no—
420#548—24no—
421#548C2×D6718yes—
422C2×C4⋊Q8—671no—
423C2×#126—1341no—
424C2×#126—1341no—
425C2×#124—21no—
426C2×#124—1341no—
427C2×#124C2×D6711yescharacteristic
428C2×C22⋊Q8—21no—
429C2×C22⋊Q8—671no—
430C2×C22⋊Q8—671no—
431C2×C22⋊Q8C2×D6711yescharacteristic
432C2×#121—21no—
433C2×#121C2×D6711yescharacteristic
434C2×C4×Q8—671no—
435C2×C4×Q8—1341no—
436C2×C4×Q8C2×D6711yescharacteristic
437C2×C4×D4—21no—
438C2×C4×D4C2×D6711yescharacteristic
439C2×#117—671no—
440C2×#117—671no—
441#489—678no—
442#485—678no—
443#482—678no—
444#477—678no—
445#468—678no—
446#467—678no—
447#464—678no—
448#452—678no—
449#451—678no—
450#441—678no—
451#435—678no—
452C2×#107—671no—
453C2×#107—671no—
454C2×#106—671no—
455C2×C4⋊C8—671no—
456#419—678no—
457#416—678no—
458C2×#103—671no—
459C2×#103—671no—
460C2×#103—671no—
461C2×#103—671no—
462C2×#103—671no—
463C2×#103—671no—
464C2×#103—671no—
465C2×#102—671no—
466C2×#102—671no—
467C2×#102—671no—
468C2×C22⋊C8—671no—
469C2×C22⋊C8—671no—
470C2×#97—671no—
471C2×#41—22no—
472C2×#41—24no—
473C2×#41—42no—
474C2×#41C22×D6714yes—
475C22×Q8—21no—
476C22×Q8—22no—
477C22×Q8—24no—
478C22×Q8—42no—
479C22×Q8—671no—
480C22×Q8—1341no—
481C22×Q8C22×D6711yescharacteristic
482C22×Q8C22×D6714yes—
483C22×Q8C22×D6711yescharacteristic
484C22×D4—21no—
485C22×D4—21no—
486C22×D4C22⋊D6711yescharacteristic
487C22×D4C22×D6711yescharacteristic
488C23×C4—21no—
489C23×C4—21no—
490C23×C4C22×D6711yescharacteristic
491C23×C4C22×D6711yescharacteristic
492C2×Q16—2682no—
493C2×Q16—674no—
494C2×Q16—674no—
495C2×Q16—1344no—
496C2×SD16—2682no—
497C2×SD16—674no—
498C2×M16—2682no—
499C2×M16—674no—
500C22×C8—2682no—
501C22×C8—674no—
502C22×C8—671no—
503C22×C8—671no—
504C22×C8—671no—
505C22×C8—671no—
506C4⋊Q8—674no—
507C4⋊Q8—1342no—
508#126—1348no—
509#126—1348no—
510#124—28no—
511#124—22no—
512#124—1348no—
513#124C22×D6714yes—
514C22⋊Q8—22no—
515C22⋊Q8—28no—
516C22⋊Q8—674no—
517C22⋊Q8—674no—
518C22⋊Q8—1342no—
519C22⋊Q8—1342no—
520C22⋊Q8C22×D6714yes—
521#121—28no—
522#121—22no—
523#121C22×D6714yes—
524C4×Q8—22no—
525C4×Q8—674no—
526C4×Q8—1348no—
527C4×Q8—1342no—
528C4×Q8C22×D6714yes—
529C4×D4—28no—
530C4×D4C22⋊D6714yes—
531C4×D4C22×D6714yes—
532#117—674no—
533#117—674no—
534#117—1342no—
535#117—1342no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—671no—
539C2×C4⋊C4—671no—
540C2×C4⋊C4—671no—
541C2×C4⋊C4—1341no—
542C2×C4⋊C4—1341no—
543C2×C4⋊C4—1341no—
544C2×C4⋊C4—1341no—
545C2×C4⋊C4C22⋊D6711yescharacteristic
546C2×C4⋊C4C22×D6711yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—1341no—
552C2×C22⋊C4—1341no—
553C2×C22⋊C4—1341no—
554C2×C22⋊C4—1341no—
555C2×C22⋊C4C22⋊D6711yescharacteristic
556C2×C22⋊C4C22⋊D6711yescharacteristic
557C2×C42—21no—
558C2×C42—1341no—
559C2×C42—1341no—
560C2×C42—1341no—
561C2×C42C22×D6711yescharacteristic
562#107—674no—
563#107—674no—
564#106—674no—
565C4⋊C8—674no—
566#103—674no—
567#103—674no—
568#103—674no—
569#103—674no—
570#103—674no—
571#103—674no—
572#103—674no—
573#102—674no—
574#102—674no—
575#102—674no—
576C22⋊C8—674no—
577C22⋊C8—674no—
578#97—674no—
579C24—21no—
580C24C2×C22⋊D6711yescharacteristic
581C24C2×C22⋊D6711yescharacteristic
582#41—28no—
583#41—44no—
584#41—48no—
585C2×Q8—21no—
586C2×Q8—24no—
587C2×Q8—21no—
588C2×Q8—22no—
589C2×Q8—28no—
590C2×Q8—22no—
591C2×Q8—22no—
592C2×Q8—44no—
593C2×Q8—44no—
594C2×Q8—48no—
595C2×Q8—2684no—
596C2×Q8—672no—
597C2×Q8—1342no—
598C2×Q8—1342no—
599C2×Q8—1341no—
600C2×Q8—1344no—
601C2×Q8#1176162714yes—
602C2×Q8C23×D6712yes—
603C2×Q8C23×D6712yes—
604C2×D4—24no—
605C2×D4—24no—
606C2×D4—21no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—42no—
610C2×D4—44no—
611C2×D4—44no—
612C2×D4C2×C22⋊D6714yes—
613C2×D4C23×D6712yes—
614C22×C4—21no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—24no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—24no—
623C22×C4—44no—
624C22×C4—44no—
625C22×C4—1341no—
626C22×C4—1341no—
627C22×C4—1341no—
628C22×C4—1341no—
629C22×C4C2×C22⋊D6712yes—
630C22×C4C2×C22⋊D6712yes—
631C22×C4C2×C22⋊D6711yescharacteristic
632C22×C4C2×C22⋊D6711yescharacteristic
633C22×C4C2×C22⋊D6711yescharacteristic
634C22×C4C2×C22⋊D6711yescharacteristic
635C22×C4C23×D6712yes—
636C22×C4C23×D6712yes—
637C22×C4C23×D6711yescharacteristic
638Q16—2684no—
639Q16—1348no—
640SD16—2684no—
641M16—2684no—
642C2×C8—2684no—
643C2×C8—672no—
644C2×C8—672no—
645C2×C8—672no—
646C2×C8—672no—
647C2×C8—1342no—
648C2×C8—1342no—
649C2×C8—1342no—
650C2×C8—1342no—
651C4⋊C4—24no—
652C4⋊C4—24no—
653C4⋊C4—21no—
654C4⋊C4—672no—
655C4⋊C4—672no—
656C4⋊C4—672no—
657C4⋊C4—1341no—
658C4⋊C4—1341no—
659C4⋊C4—1341no—
660C4⋊C4—1344no—
661C4⋊C4—1344no—
662C4⋊C4—1344no—
663C4⋊C4—1344no—
664C4⋊C4C2×C22⋊D6714yes—
665C4⋊C4C23×D6712yes—
666C22⋊C4—24no—
667C22⋊C4—24no—
668C22⋊C4—24no—
669C22⋊C4—24no—
670C22⋊C4—1344no—
671C22⋊C4—1344no—
672C22⋊C4—1344no—
673C22⋊C4—1344no—
674C22⋊C4C2×C22⋊D6714yes—
675C22⋊C4C2×C22⋊D6714yes—
676C42—24no—
677C42—1344no—
678C42—1344no—
679C42—1344no—
680C42C2×C22⋊D6712yes—
681C42C23×D6712yes—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23C22×C22⋊D6712yes—
693C23C22×C22⋊D6712yes—
694C23C22×C22⋊D6711yescharacteristic
695Q8—24no—
696Q8—22no—
697Q8—22no—
698Q8—22no—
699Q8—48no—
700Q8—42no—
701Q8—2688no—
702Q8—2682no—
703Q8—1342no—
704Q8—1342no—
705Q8C2×#1176162714yes—
706D4—22no—
707D4—22no—
708D4—44no—
709D4—48no—
710D4—48no—
711D4—42no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—24no—
715C2×C4—22no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—24no—
719C2×C4—24no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—48no—
727C2×C4—48no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—2682no—
731C2×C4—2682no—
732C2×C4—2682no—
733C2×C4—2682no—
734C2×C4—1342no—
735C2×C4—1342no—
736C2×C4—1342no—
737C2×C4—1342no—
738C2×C4C22×C22⋊D6712yes—
739C2×C4C22×C22⋊D6712yes—
740C2×C4C22×C22⋊D6712yes—
741C2×C4C22×C22⋊D6712yes—
742C2×C4C22×C22⋊D6711yescharacteristic
743C2×C4C2×#1176162712yes—
744C2×C4#1452408812yes—
745C2×C4C24×D6711yescharacteristic
746C8—1342no—
747C8—1342no—
748C8—1342no—
749C8—1342no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—44no—
757C22—44no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—84no—
762C22#1686404012yes—
763C22#1686419412yes—
764C22#1686421112yes—
765C22C23×C22⋊D6711yescharacteristic
766C4—22no—
767C4—22no—
768C4—24no—
769C4—22no—
770C4—22no—
771C4—42no—
772C4—42no—
773C4—2682no—
774C4—2682no—
775C4—2682no—
776C4—2682no—
777C4#1686404012yes—
778C4C22×#1176162711yescharacteristic
779C4C2×#1452408811yescharacteristic
780C2—42no—
781C2—42no—
782C2—82no—
783C2#2257227514yesdirect product factor
784C2C2×#1686404011yescharacteristic
785C2C2×#1686419411yescharacteristic
786C2C2×#1686421111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
Fitting, prime radicalC2×#548×C67C2
socleC23×C67C22×D4
hypercenterC2×#548D67
hypocenterC67C2×#3313
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#16864116C2semidirect
2. #22572275C2direct (N × H)
3. C2×#16863755C2semidirect
4. C2×#16863734C2semidirect
5. C2×#16863717C2semidirect
6. C2×#16863691C2semidirect
7. C2×#16863640C2semidirect
8. C2×#16863635C2semidirect
9. C2×#16863615C2semidirect
10. C2×#16863558C2semidirect
11. C2×#16863552C2semidirect
12. C2×#16863501C2semidirect
13. C2×#16863468C2semidirect
14. C2×#16863405C2semidirect
15. C2×#16863392C2semidirect
23. #16864116C22semidirect
34. #16863755C22semidirect
35. #16863734C22semidirect
36. #16863717C22semidirect
37. #16863691C22semidirect
38. #16863640C22semidirect
39. #16863635C22semidirect
40. #16863615C22semidirect
41. #16863558C22semidirect
42. #16863552C22semidirect
43. #16863501C22semidirect
44. #16863468C22semidirect
49. #16863405C22semidirect
50. #16863392C22semidirect
390. C2×C67#3313semidirect
410. C67C2×#3313semidirect
783. C2#22572275direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168641162
#225722752
C2×#168637552
C2×#168637342
C2×#168637172
C2×#168636912
C2×#168636402
C2×#168636352
C2×#168636152
C2×#168635582
C2×#168635522
C2×#168635012
C2×#168634682
C2×#168634052
C2×#168633922
C2×#548×C672
C2×#331367