Finite Group Databasebeta

← C2×#22572643 #31734356

Subgroups — C2×#22572643 #31734356

Order 17152.

2094 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×#16864086C211yesmaximal, characteristic, complemented
2#22572643C2116yesmaximal, direct product factor
3C2×#16863802C211yesmaximal, characteristic, complemented
4C2×#16863731C211yesmaximal, characteristic, complemented
5C2×#16863717C211yesmaximal, characteristic, complemented
6C2×#16863726C211yesmaximal, characteristic, complemented
7C2×#16863707C211yesmaximal, characteristic, complemented
8C2×#16863688C211yesmaximal, characteristic, complemented
9C2×#16863696C211yesmaximal, characteristic, complemented
10C2×#16863640C211yesmaximal, characteristic, complemented
11C2×#16863623C211yesmaximal, characteristic, complemented
12C2×#16863496C211yesmaximal, characteristic, complemented
13C2×#16863468C211yesmaximal, characteristic, complemented
14C2×#16863436C211yesmaximal, characteristic, complemented
15C22×#14523976C211yesmaximal, characteristic, complemented
16C2×#547×C67C211yesmaximal, characteristic
17C22×#11761616C2211yescharacteristic
18C22×#11761612C2211yescharacteristic
19C23×C67⋊C8C2211yescharacteristic
20#16864086—24no—
21#16864086C2218yescomplemented
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#16863731C2218yescomplemented
34#16863726C2218yescomplemented
35#16863717C2218yescomplemented
36#16863707C2218yescomplemented
37#16863696C2218yescomplemented
38#16863688C2218yescomplemented
39#16863640C2218yescomplemented
40#16863623C2218yescomplemented
41#16863496C2218yescomplemented
42#16863468C2218yescomplemented
43#16863436C2218yescomplemented
44C2×#14523976C2211yescharacteristic
45C2×#14523976C2211yescharacteristic
46C2×#14523976C2211yescharacteristic
47C2×#14523976C2211yescharacteristic
48C2×#14523976C2211yescharacteristic
49C2×#14523976C2211yescharacteristic
50C2×#14523976C2218yescomplemented
51C2×#14523974C2211yescharacteristic
52C2×#14523974C2211yescharacteristic
53C2×#14523974C2211yescharacteristic
54C2×C4⋊(C67⋊C8)C2211yescharacteristic
55C2×#14523966C2211yescharacteristic
56C2×#14523966C2211yescharacteristic
57C2×#14523966C2211yescharacteristic
58C2×#14523964C2211yescharacteristic
59C2×#14523964C2211yescharacteristic
60C2×#14523964C2211yescharacteristic
61C2×C22⋊(C67⋊C8)C2211yescharacteristic
62C2×C22⋊(C67⋊C8)C2211yescharacteristic
63C2×#14523954C2211yescharacteristic
64C22×#41×C67—21no—
65#547×C67—24no—
66#547×C67C2218yes—
67C2×C4⋊Q8×C67C2211yescharacteristic
68C2×#123×C67—21no—
69C2×#123×C67—21no—
70C2×C22⋊Q8×C67—21no—
71C2×#121×C67C2211yescharacteristic
72C2×#121×C67C2211yescharacteristic
73C2×C4×D4×C67C2211yescharacteristic
74C2×C4×D4×C67C2211yescharacteristic
75C22×C4⋊C4×C67C2211yescharacteristic
76C22×C4⋊C4×C67C2211yescharacteristic
77C22×Dic134C2311yescharacteristic
78C23×Dic67—21no—
79C2×#11761616—24no—
80C2×#11761616C2314yes—
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#14523976C2314yes—
123#14523976C2314yes—
124#14523976C2314yes—
125#14523974C2314yes—
126#14523974C2314yes—
127#14523974C2314yes—
128C4⋊(C67⋊C8)C2314yes—
129#14523966C2314yes—
130#14523966C2314yes—
131#14523966C2314yes—
132#14523964C2314yes—
133#14523964C2314yes—
134#14523964C2314yes—
135C22⋊(C67⋊C8)C2314yes—
136C22⋊(C67⋊C8)C2314yes—
137#14523954C2314yes—
138C2×#41×C67—28no—
139C2×#41×C67—48no—
140C22×Q8×C67—21no—
141C22×D4×C67—21no—
142C22×D4×C67—21no—
143C22×D4×C67D411yescharacteristic
144C22×D4×C67C2311yescharacteristic
145C23×C4×C67—21no—
146C23×C4×C67—21no—
147C23×C4×C67—21no—
148C23×C4×C67C2311yescharacteristic
149C23×C4×C67C2311yescharacteristic
150C4⋊Q8×C67—22no—
151C4⋊Q8×C67C2314yes—
152#123×C67—28no—
153#123×C67—28no—
154C22⋊Q8×C67—28no—
155#121×C67—22no—
156#121×C67—22no—
157#121×C67C2314yes—
158#121×C67C2314yes—
159C4×D4×C67—22no—
160C4×D4×C67D414yes—
161C4×D4×C67C2314yes—
162C4×D4×C67C2314yes—
163C2×C4⋊C4×C67—21no—
164C2×C4⋊C4×C67—21no—
165C2×C4⋊C4×C67—22no—
166C2×C4⋊C4×C67—22no—
167C2×C4⋊C4×C67—21no—
168C2×C4⋊C4×C67D411yescharacteristic
169C2×C4⋊C4×C67C2311yescharacteristic
170C2×C4⋊C4×C67C2311yescharacteristic
171C2×C4⋊C4×C67C2311yescharacteristic
172C2×C4⋊C4×C67C2314yes—
173C2×C4⋊C4×C67C2314yes—
174C2×C22⋊C4×C67—21no—
175C2×C22⋊C4×C67—21no—
176C2×C22⋊C4×C67—21no—
177C2×C22⋊C4×C67D411yescharacteristic
178C2×C22⋊C4×C67D411yescharacteristic
179C2×C42×C67C2311yescharacteristic
180C2×Dic134—22no—
181C2×Dic134—22no—
182C2×Dic134—21no—
183C2×Dic134C2412yes—
184C22×Dic67—21no—
185C22×Dic67—21no—
186C22×Dic67—21no—
187C22×Dic67—21no—
188C22×Dic67—24no—
189C22×Dic67—44no—
190#11761616—28no—
191#11761612—28no—
192C2×C67⋊C8—22no—
193C2×C67⋊C8—22no—
194C2×C67⋊C8—22no—
195C2×C67⋊C8—28no—
196C2×C67⋊C8#4114yescomplemented
197C2×C67⋊C8C2412yes—
198C2×C67⋊C8C2412yes—
199C2×C67⋊C8C2412yes—
200C2×C67⋊C8C2412yes—
201C4⋊Dic67—21no—
202C4⋊Dic67—21no—
203C4⋊Dic67—24no—
204C4⋊Dic67—21no—
205C4⋊Dic67C2412yes—
206C4⋊Dic67C2412yes—
207C4⋊Dic67C2412yes—
208Dic67⋊C4—24no—
209Dic67⋊C4—24no—
210Dic67⋊C4—24no—
211Dic67⋊C4—24no—
212Dic67⋊C4—24no—
213C22⋊Dic67—24no—
214C22⋊Dic67—24no—
215C22⋊Dic67—24no—
216C4×Dic67—24no—
217C4×Dic67—24no—
218C24×C67—21no—
219C24×C67C2×D411yescharacteristic
220C24×C67C2×D411yescharacteristic
221#41×C67—432no—
222C2×Q8×C67—24no—
223C2×Q8×C67—44no—
224C2×D4×C67—24no—
225C2×D4×C67—24no—
226C2×D4×C67—24no—
227C2×D4×C67—21no—
228C2×D4×C67—22no—
229C2×D4×C67—22no—
230C2×D4×C67—44no—
231C2×D4×C67—44no—
232C2×D4×C67C2×D414yes—
233C2×D4×C67C2412yes—
234C22×C4×C67—22no—
235C22×C4×C67—22no—
236C22×C4×C67—22no—
237C22×C4×C67—22no—
238C22×C4×C67—21no—
239C22×C4×C67—21no—
240C22×C4×C67—21no—
241C22×C4×C67—24no—
242C22×C4×C67—24no—
243C22×C4×C67—24no—
244C22×C4×C67—44no—
245C22×C4×C67—44no—
246C22×C4×C67—44no—
247C22×C4×C67C2×D411yescharacteristic
248C22×C4×C67C2×D411yescharacteristic
249C22×C4×C67C2×D411yescharacteristic
250C22×C4×C67C2×D411yescharacteristic
251C22×C4×C67C2×D412yes—
252C22×C4×C67C2×D412yes—
253C22×C4×C67C2412yes—
254C22×C4×C67C2412yes—
255C22×C4×C67C2411yescharacteristic
256C4⋊C4×C67—21no—
257C4⋊C4×C67—21no—
258C4⋊C4×C67—21no—
259C4⋊C4×C67—24no—
260C4⋊C4×C67—24no—
261C4⋊C4×C67—24no—
262C4⋊C4×C67C2×D414yes—
263C4⋊C4×C67C2412yes—
264C4⋊C4×C67C2412yes—
265C4⋊C4×C67C2412yes—
266C22⋊C4×C67—24no—
267C22⋊C4×C67—24no—
268C22⋊C4×C67—24no—
269C22⋊C4×C67C2×D414yes—
270C22⋊C4×C67C2×D414yes—
271C42×C67C2×D412yes—
272C42×C67C2412yes—
273C23×C67—22no—
274C23×C67—22no—
275C23×C67—22no—
276C23×C67—22no—
277C23×C67—22no—
278C23×C67—22no—
279C23×C67—42no—
280C23×C67—42no—
281C23×C67—42no—
282C23×C67AGL(1,ℤ/8)14yes—
283C23×C67C22×D412yes—
284C23×C67C22×D412yes—
285C23×C67C22×D411yescharacteristic
286Q8×C67—48no—
287D4×C67—28no—
288D4×C67—22no—
289D4×C67—22no—
290D4×C67—48no—
291D4×C67—48no—
292D4×C67—42no—
293C2×C4×C67—22no—
294C2×C4×C67—22no—
295C2×C4×C67—22no—
296C2×C4×C67—22no—
297C2×C4×C67—24no—
298C2×C4×C67—24no—
299C2×C4×C67—22no—
300C2×C4×C67—22no—
301C2×C4×C67—22no—
302C2×C4×C67—22no—
303C2×C4×C67—22no—
304C2×C4×C67—22no—
305C2×C4×C67—22no—
306C2×C4×C67—48no—
307C2×C4×C67—48no—
308C2×C4×C67—42no—
309C2×C4×C67—42no—
310C2×C4×C67—42no—
311C2×C4×C67—48no—
312C2×C4×C67C22×D412yes—
313C2×C4×C67C22×D412yes—
314C2×C4×C67C22×D412yes—
315C2×C4×C67C22×D412yes—
316C2×C4×C67C22×D411yescharacteristic
317C2×C4×C67C2×#4112yes—
318C2×C4×C672−1+412yes—
319C2×C4×C67C2511yescharacteristic
320C2×Dic67—22no—
321C2×Dic67—22no—
322C2×Dic67—22no—
323C2×Dic67—22no—
324C2×Dic67—42no—
325C2×Dic67—48no—
326C2×Dic67—42no—
327C2×Dic67—42no—
328C2×Dic67—42no—
329Dic134—22no—
330Dic134—22no—
331Dic134—42no—
332C67⋊C8—22no—
333C67⋊C8—22no—
334C67⋊C8—22no—
335C67⋊C8C2×#4114yescomplemented
336C22×C67—28no—
337C22×C67—22no—
338C22×C67—22no—
339C22×C67—22no—
340C22×C67—22no—
341C22×C67—22no—
342C22×C67—44no—
343C22×C67—42no—
344C22×C67—42no—
345C22×C67—42no—
346C22×C67—84no—
347C22×C67#54712yes—
348C22×C67C2×AGL(1,ℤ/8)14yes—
349C22×C67C2×AGL(1,ℤ/8)12yes—
350C22×C67#57812yes—
351C22×C67C23×D411yescharacteristic
352C4×C67—22no—
353C4×C67—22no—
354C4×C67—22no—
355C4×C67—22no—
356C4×C67—42no—
357C4×C67—42no—
358C4×C67—42no—
359C4×C67#54712yes—
360C4×C67C22×#4111yescharacteristic
361C4×C67C2×2−1+411yescharacteristic
362Dic67—42no—
363Dic67—42no—
364Dic67—42no—
365Dic67—42no—
366C2×#3343—671nomaximal, Sylow
367C2×C67—24no—
368C2×C67—42no—
369C2×C67—82no—
370C2×C67#334314yescomplemented
371C2×C67C2×#54711yescharacteristic
372C2×C67C22×AGL(1,ℤ/8)11yescharacteristic
373C2×C67C2×#57811yescharacteristic
374C2×#552—671no—
375C2×#547D6711yescharacteristic
376#3343—6716no—
377C2×#501—671no—
378C2×#484—671no—
379C2×#482—671no—
380C2×#483—671no—
381C2×#480—671no—
382C2×#477—671no—
383C2×#478—671no—
384C2×#468—671no—
385C2×#465—671no—
386C2×#440—671no—
387C2×#435—671no—
388C2×#428—671no—
389C22×#107—671no—
390C67C2×#334311yescharacteristic, complemented, Sylow
391C22×#41—21no—
392C22×SD16—671no—
393C22×M16—671no—
394C23×C8—671no—
395#552—678no—
396#552—1344no—
397#547—24no—
398#547C2×D6718yes—
399C2×C4⋊Q8C2×D6711yescharacteristic
400C2×#126—1341no—
401C2×#125—671no—
402C2×#125—1341no—
403C2×#123—21no—
404C2×#123—21no—
405C2×#123—1341no—
406C2×C22⋊Q8—21no—
407C2×C22⋊Q8—671no—
408C2×C22⋊Q8—671no—
409C2×#121C2×D6711yescharacteristic
410C2×#121C2×D6711yescharacteristic
411C2×C4×Q8—671no—
412C2×C4×D4C2×D6711yescharacteristic
413C2×C4×D4C2×D6711yescharacteristic
414C2×#117—671no—
415C2×#117—1341no—
416C22×C4⋊C4—671no—
417C22×C4⋊C4C2×D6711yescharacteristic
418C22×C4⋊C4C2×D6711yescharacteristic
419#501—678no—
420#484—678no—
421#483—678no—
422#482—678no—
423#480—678no—
424#478—678no—
425#477—678no—
426#468—678no—
427#465—678no—
428#440—678no—
429#435—678no—
430#428—678no—
431C2×#107—671no—
432C2×#107—671no—
433C2×#107—671no—
434C2×#107—671no—
435C2×#107—678no—
436C2×#107—671no—
437C2×#107—671no—
438C2×#106—671no—
439C2×#106—671no—
440C2×#106—671no—
441C2×C4⋊C8—671no—
442C2×#103—671no—
443C2×#103—671no—
444C2×#103—671no—
445C2×#102—671no—
446C2×#102—671no—
447C2×#102—671no—
448C2×C22⋊C8—671no—
449C2×C22⋊C8—671no—
450C2×#97—671no—
451C2×#41—28no—
452C2×#41—48no—
453C22×Q8—21no—
454C22×Q8—671no—
455C22×D4—21no—
456C22×D4—21no—
457C22×D4C22⋊D6711yescharacteristic
458C22×D4C22×D6711yescharacteristic
459C23×C4—21no—
460C23×C4—21no—
461C23×C4—21no—
462C23×C4—1341no—
463C23×C4C22×D6711yescharacteristic
464C23×C4C22×D6711yescharacteristic
465C2×SD16—674no—
466C2×SD16—1344no—
467C2×M16—674no—
468C2×M16—1344no—
469C22×C8—671no—
470C22×C8—671no—
471C22×C8—674no—
472C22×C8—671no—
473C22×C8—671no—
474C22×C8—1344no—
475C4⋊Q8—22no—
476C4⋊Q8C22×D6714yes—
477#126—1348no—
478#125—674no—
479#125—1348no—
480#125—1342no—
481#123—28no—
482#123—28no—
483#123—1348no—
484C22⋊Q8—28no—
485C22⋊Q8—674no—
486C22⋊Q8—674no—
487C22⋊Q8—1342no—
488C22⋊Q8—1342no—
489#121—22no—
490#121—22no—
491#121C22×D6714yes—
492#121C22×D6714yes—
493C4×Q8—674no—
494C4×Q8—1342no—
495C4×D4—22no—
496C4×D4C22⋊D6714yes—
497C4×D4C22×D6714yes—
498C4×D4C22×D6714yes—
499#117—674no—
500#117—1342no—
501#117—1348no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—21no—
504C2×C4⋊C4—22no—
505C2×C4⋊C4—22no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—671no—
508C2×C4⋊C4—671no—
509C2×C4⋊C4—674no—
510C2×C4⋊C4—671no—
511C2×C4⋊C4—1341no—
512C2×C4⋊C4—1342no—
513C2×C4⋊C4—1341no—
514C2×C4⋊C4—1341no—
515C2×C4⋊C4—1341no—
516C2×C4⋊C4—1341no—
517C2×C4⋊C4—1341no—
518C2×C4⋊C4C22⋊D6711yescharacteristic
519C2×C4⋊C4C22×D6711yescharacteristic
520C2×C4⋊C4C22×D6711yescharacteristic
521C2×C4⋊C4C22×D6711yescharacteristic
522C2×C4⋊C4C22×D6714yes—
523C2×C4⋊C4C22×D6714yes—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—1341no—
528C2×C22⋊C4—1341no—
529C2×C22⋊C4—1341no—
530C2×C22⋊C4C22⋊D6711yescharacteristic
531C2×C22⋊C4C22⋊D6711yescharacteristic
532C2×C42—1341no—
533C2×C42—1341no—
534C2×C42C22×D6711yescharacteristic
535#107—674no—
536#107—674no—
537#107—674no—
538#107—674no—
539#107—674no—
540#107—674no—
541#106—674no—
542#106—674no—
543#106—674no—
544C4⋊C8—674no—
545#103—674no—
546#103—674no—
547#103—674no—
548#102—674no—
549#102—674no—
550#102—674no—
551C22⋊C8—674no—
552C22⋊C8—674no—
553#97—674no—
554C24—21no—
555C24C2×C22⋊D6711yescharacteristic
556C24C2×C22⋊D6711yescharacteristic
557#41—432no—
558C2×Q8—24no—
559C2×Q8—44no—
560C2×Q8—672no—
561C2×Q8—1342no—
562C2×Q8—1342no—
563C2×Q8—1341no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4C2×C22⋊D6714yes—
573C2×D4C23×D6712yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—24no—
579C22×C4—24no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—24no—
584C22×C4—44no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—2684no—
588C22×C4—1344no—
589C22×C4—1341no—
590C22×C4—1341no—
591C22×C4—1341no—
592C22×C4—1341no—
593C22×C4C2×C22⋊D6712yes—
594C22×C4C2×C22⋊D6712yes—
595C22×C4C2×C22⋊D6711yescharacteristic
596C22×C4C2×C22⋊D6711yescharacteristic
597C22×C4C2×C22⋊D6711yescharacteristic
598C22×C4C2×C22⋊D6711yescharacteristic
599C22×C4C23×D6712yes—
600C22×C4C23×D6712yes—
601C22×C4C23×D6711yescharacteristic
602SD16—1348no—
603M16—1348no—
604C2×C8—674no—
605C2×C8—672no—
606C2×C8—672no—
607C2×C8—672no—
608C2×C8—672no—
609C2×C8—1348no—
610C2×C8—1342no—
611C2×C8—1342no—
612C2×C8—1342no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—672no—
620C4⋊C4—672no—
621C4⋊C4—672no—
622C4⋊C4—1341no—
623C4⋊C4—1341no—
624C4⋊C4—1344no—
625C4⋊C4—1341no—
626C4⋊C4—1344no—
627C4⋊C4—1344no—
628C4⋊C4—1344no—
629C4⋊C4—1344no—
630C4⋊C4—1344no—
631C4⋊C4C2×C22⋊D6714yes—
632C4⋊C4C23×D6712yes—
633C4⋊C4C23×D6712yes—
634C4⋊C4C23×D6712yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—1344no—
639C22⋊C4—1344no—
640C22⋊C4—1344no—
641C22⋊C4C2×C22⋊D6714yes—
642C22⋊C4C2×C22⋊D6714yes—
643C42—1344no—
644C42—1344no—
645C42C2×C22⋊D6712yes—
646C42C23×D6712yes—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—22no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23#1452406914yes—
657C23C22×C22⋊D6712yes—
658C23C22×C22⋊D6712yes—
659C23C22×C22⋊D6711yescharacteristic
660Q8—48no—
661Q8—2682no—
662Q8—1342no—
663Q8—1342no—
664D4—28no—
665D4—22no—
666D4—22no—
667D4—48no—
668D4—48no—
669D4—42no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—48no—
684C2×C4—48no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—42no—
688C2×C4—48no—
689C2×C4—2682no—
690C2×C4—2688no—
691C2×C4—2682no—
692C2×C4—2682no—
693C2×C4—2682no—
694C2×C4—1342no—
695C2×C4—1342no—
696C2×C4—1342no—
697C2×C4—1342no—
698C2×C4C22×C22⋊D6712yes—
699C2×C4C22×C22⋊D6712yes—
700C2×C4C22×C22⋊D6712yes—
701C2×C4C22×C22⋊D6712yes—
702C2×C4C22×C22⋊D6711yescharacteristic
703C2×C4#41×D6712yes—
704C2×C4#1452409012yes—
705C2×C4C24×D6711yescharacteristic
706C8—674no—
707C8—1342no—
708C8—1342no—
709C8—1342no—
710C22—22no—
711C22—28no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—22no—
716C22—44no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—84no—
721C22#1686404512yes—
722C22C2×#1452406914yes—
723C22C2×#1452406912yes—
724C22#1686421112yes—
725C22C23×C22⋊D6711yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—42no—
731C4—42no—
732C4—42no—
733C4—2682no—
734C4—2682no—
735C4—2682no—
736C4—2682no—
737C4#1686404512yes—
738C4C2×#41×D6711yescharacteristic
739C4C2×#1452409011yescharacteristic
740C2—24no—
741C2—42no—
742C2—82no—
743C2#2257264314yesdirect product factor
744C2C2×#1686404511yescharacteristic
745C2C22×#1452406911yescharacteristic
746C2C2×#1686421111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
Fitting, prime radicalC2×#547×C67C2
socleC23×C67C22×D4
hypercenterC2×#547D67
hypocenterC67C2×#3343
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#16864086C2semidirect
2. #22572643C2direct (N × H)
3. C2×#16863802C2semidirect
4. C2×#16863731C2semidirect
5. C2×#16863717C2semidirect
6. C2×#16863726C2semidirect
7. C2×#16863707C2semidirect
8. C2×#16863688C2semidirect
9. C2×#16863696C2semidirect
10. C2×#16863640C2semidirect
11. C2×#16863623C2semidirect
12. C2×#16863496C2semidirect
13. C2×#16863468C2semidirect
14. C2×#16863436C2semidirect
15. C22×#14523976C2semidirect
21. #16864086C22semidirect
32. #16863802C22semidirect
33. #16863731C22semidirect
34. #16863726C22semidirect
35. #16863717C22semidirect
36. #16863707C22semidirect
37. #16863696C22semidirect
38. #16863688C22semidirect
39. #16863640C22semidirect
40. #16863623C22semidirect
41. #16863496C22semidirect
42. #16863468C22semidirect
43. #16863436C22semidirect
50. C2×#14523976C22semidirect
196. C2×C67⋊C8#41semidirect
335. C67⋊C8C2×#41semidirect
370. C2×C67#3343semidirect
390. C67C2×#3343semidirect
743. C2#22572643direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640862
#225726432
C2×#168638022
C2×#168637312
C2×#168637172
C2×#168637262
C2×#168637072
C2×#168636882
C2×#168636962
C2×#168636402
C2×#168636232
C2×#168634962
C2×#168634682
C2×#168634362
C22×#145239762
C2×#547×C672
C2×#334367