Finite Group Databasebeta

← C2×#22572260 #31732437

Subgroups — C2×#22572260 #31732437

Order 17152.

2094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16864086C211yesmaximal, characteristic
2#22572260C2116yesmaximal, direct product factor
3C2×#16863764C211yesmaximal, characteristic, complemented
4C2×#16863734C211yesmaximal, characteristic, complemented
5C2×#16863724C211yesmaximal, characteristic, complemented
6C2×#16863703C211yesmaximal, characteristic, complemented
7C2×#16863652C211yesmaximal, characteristic, complemented
8C2×#16863635C211yesmaximal, characteristic, complemented
9C2×#16863603C211yesmaximal, characteristic, complemented
10C2×#16863552C211yesmaximal, characteristic, complemented
11C2×#16863552C211yesmaximal, characteristic, complemented
12C2×#16863501C211yesmaximal, characteristic, complemented
13C2×#16863468C211yesmaximal, characteristic
14C2×#16863405C211yesmaximal, characteristic, complemented
15C22×#14523967C211yesmaximal, characteristic, complemented
16C2×D4×Q8×C67C211yesmaximal, characteristic
17C22×#11761618C2211yescharacteristic
18C22×#11761618C2211yescharacteristic
19C22×#11761618C2211yescharacteristic
20C22×#11761612C2211yescharacteristic
21C23×C67⋊C8C2211yescharacteristic
22#16864086—24no—
23#16864086C2218yes—
24C2×#14524036—21no—
25C2×#14524035C2211yescharacteristic
26C2×#14524033—21no—
27C2×#14524024—21no—
28C2×#14524022C2211yescharacteristic
29C2×#14524022C2211yescharacteristic
30C2×C4×Dic134C2211yescharacteristic
31C2×#14524002C2211yescharacteristic
32C2×#14523999—21no—
33C22×C4⋊Dic67C2211yescharacteristic
34#16863764C2218yescomplemented
35#16863734C2218yescomplemented
36#16863724C2218yescomplemented
37#16863703C2218yescomplemented
38#16863652C2218yescomplemented
39#16863635C2218yescomplemented
40#16863603C2218yescomplemented
41#16863552C2218yescomplemented
42#16863552C2218yescomplemented
43#16863501C2218yescomplemented
44#16863468C2218yes—
45C2×#14523976C2211yescharacteristic
46C2×#14523974C2211yescharacteristic
47C2×#14523974C2211yescharacteristic
48C2×C4⋊(C67⋊C8)C2211yescharacteristic
49#16863405C2218yescomplemented
50C2×#14523967C2211yescharacteristic
51C2×#14523967C2211yescharacteristic
52C2×#14523967C2211yescharacteristic
53C2×#14523967C2211yescharacteristic
54C2×#14523967C2211yescharacteristic
55C2×#14523967C2211yescharacteristic
56C2×#14523967C2211yescharacteristic
57C2×#14523967C2211yescharacteristic
58C2×#14523967C2211yescharacteristic
59C2×#14523967C2218yescomplemented
60C2×#14523966C2211yescharacteristic
61C2×C22⋊(C67⋊C8)C2211yescharacteristic
62C2×C22⋊(C67⋊C8)C2211yescharacteristic
63C2×#14523954C2211yescharacteristic
64C23×Q8×C67C2211yescharacteristic
65C23×Q8×C67C2211yescharacteristic
66D4×Q8×C67—24no—
67D4×Q8×C67C2218yes—
68C2×C4⋊Q8×C67—21no—
69C2×C4⋊Q8×C67C2211yescharacteristic
70C2×C22⋊Q8×C67—21no—
71C2×C22⋊Q8×C67—21no—
72C2×C22⋊Q8×C67C2211yescharacteristic
73C2×C22⋊Q8×C67C2211yescharacteristic
74C2×C4×Q8×C67C2211yescharacteristic
75C2×C4×D4×C67—21no—
76C2×C4×D4×C67C2211yescharacteristic
77C22×Dic134C2311yescharacteristic
78C23×Dic67—21no—
79C2×#11761618—24no—
80C2×#11761618—42no—
81C2×#11761618—42no—
82C2×#11761618C2314yes—
83C2×#11761618C2314yes—
84C2×#11761618C2314yes—
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#14524036—28no—
94#14524035—22no—
95#14524035C2314yes—
96#14524033—28no—
97#14524024—28no—
98#14524022—22no—
99#14524022—22no—
100#14524022C2314yes—
101#14524022C2314yes—
102C4×Dic134—22no—
103C4×Dic134C2314yes—
104#14524002—22no—
105#14524002C2314yes—
106#14523999—28no—
107C2×C4⋊Dic67—22no—
108C2×C4⋊Dic67—21no—
109C2×C4⋊Dic67C2314yes—
110C2×C4⋊Dic67C2311yescharacteristic
111C2×C4⋊Dic67C2311yescharacteristic
112C2×C4⋊Dic67C2311yescharacteristic
113C2×Dic67⋊C4—21no—
114C2×Dic67⋊C4—21no—
115C2×Dic67⋊C4—21no—
116C2×Dic67⋊C4—21no—
117C2×Dic67⋊C4—21no—
118C2×C22⋊Dic67—21no—
119C2×C22⋊Dic67—21no—
120C2×C22⋊Dic67—21no—
121C2×C4×Dic67—21no—
122C2×C4×Dic67—21no—
123#14523976C2314yes—
124#14523974C2314yes—
125#14523974C2314yes—
126C4⋊(C67⋊C8)C2314yes—
127#14523967C2314yes—
128#14523967C2314yes—
129#14523967C2314yes—
130#14523967C2314yes—
131#14523967C2314yes—
132#14523967C2314yes—
133#14523967C2314yes—
134#14523967C2314yes—
135#14523967C2314yes—
136#14523966C2314yes—
137C22⋊(C67⋊C8)C2314yes—
138C22⋊(C67⋊C8)C2314yes—
139#14523954C2314yes—
140C22×Q8×C67—21no—
141C22×Q8×C67—21no—
142C22×Q8×C67—22no—
143C22×Q8×C67—22no—
144C22×Q8×C67—24no—
145C22×Q8×C67—24no—
146C22×Q8×C67—42no—
147C22×Q8×C67—42no—
148C22×Q8×C67C2311yescharacteristic
149C22×Q8×C67C2311yescharacteristic
150C22×Q8×C67C2314yes—
151C22×Q8×C67C2314yes—
152C22×Q8×C67C2311yescharacteristic
153C22×D4×C67D411yescharacteristic
154C23×C4×C67—21no—
155C23×C4×C67—21no—
156C23×C4×C67C2311yescharacteristic
157C23×C4×C67C2311yescharacteristic
158C4⋊Q8×C67—28no—
159C4⋊Q8×C67—22no—
160C4⋊Q8×C67C2314yes—
161C22⋊Q8×C67—22no—
162C22⋊Q8×C67—22no—
163C22⋊Q8×C67—28no—
164C22⋊Q8×C67—28no—
165C22⋊Q8×C67C2314yes—
166C22⋊Q8×C67C2314yes—
167C4×Q8×C67—22no—
168C4×Q8×C67C2314yes—
169C4×D4×C67—28no—
170C4×D4×C67D414yes—
171C4×D4×C67C2314yes—
172C2×C4⋊C4×C67—21no—
173C2×C4⋊C4×C67—21no—
174C2×C4⋊C4×C67—21no—
175C2×C4⋊C4×C67—21no—
176C2×C4⋊C4×C67—21no—
177C2×C4⋊C4×C67D411yescharacteristic
178C2×C4⋊C4×C67C2311yescharacteristic
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—21no—
188C2×Dic134C2412yes—
189C22×Dic67—21no—
190C22×Dic67—21no—
191C22×Dic67—21no—
192C22×Dic67—21no—
193C22×Dic67—24no—
194C22×Dic67—44no—
195#11761618—28no—
196#11761618—44no—
197#11761618—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—21no—
209C4⋊Dic67—21no—
210C4⋊Dic67—24no—
211C4⋊Dic67—21no—
212C4⋊Dic67C2412yes—
213C4⋊Dic67C2412yes—
214C4⋊Dic67C2412yes—
215Dic67⋊C4—24no—
216Dic67⋊C4—24no—
217Dic67⋊C4—24no—
218Dic67⋊C4—24no—
219Dic67⋊C4—24no—
220C22⋊Dic67—24no—
221C22⋊Dic67—24no—
222C22⋊Dic67—24no—
223C4×Dic67—24no—
224C4×Dic67—24no—
225C24×C67C2×D411yescharacteristic
226C24×C67C2×D411yescharacteristic
227C2×Q8×C67—21no—
228C2×Q8×C67—24no—
229C2×Q8×C67—24no—
230C2×Q8×C67—21no—
231C2×Q8×C67—21no—
232C2×Q8×C67—22no—
233C2×Q8×C67—28no—
234C2×Q8×C67—28no—
235C2×Q8×C67—22no—
236C2×Q8×C67—22no—
237C2×Q8×C67—22no—
238C2×Q8×C67—22no—
239C2×Q8×C67—44no—
240C2×Q8×C67—44no—
241C2×Q8×C67—44no—
242C2×Q8×C67—44no—
243C2×Q8×C67—48no—
244C2×Q8×C67—48no—
245C2×Q8×C67#4114yes—
246C2×Q8×C67C2412yes—
247C2×Q8×C67C2412yes—
248C2×Q8×C67C2412yes—
249C2×D4×C67—24no—
250C2×D4×C67C2×D414yes—
251C22×C4×C67—21no—
252C22×C4×C67—22no—
253C22×C4×C67—22no—
254C22×C4×C67—22no—
255C22×C4×C67—22no—
256C22×C4×C67—21no—
257C22×C4×C67—21no—
258C22×C4×C67—21no—
259C22×C4×C67—24no—
260C22×C4×C67—24no—
261C22×C4×C67—44no—
262C22×C4×C67—44no—
263C22×C4×C67C2×D411yescharacteristic
264C22×C4×C67C2×D411yescharacteristic
265C22×C4×C67C2×D411yescharacteristic
266C22×C4×C67C2×D411yescharacteristic
267C22×C4×C67C2×D412yes—
268C22×C4×C67C2×D412yes—
269C22×C4×C67C2412yes—
270C22×C4×C67C2412yes—
271C22×C4×C67C2411yescharacteristic
272C4⋊C4×C67—24no—
273C4⋊C4×C67—24no—
274C4⋊C4×C67—24no—
275C4⋊C4×C67—24no—
276C4⋊C4×C67—24no—
277C4⋊C4×C67—21no—
278C4⋊C4×C67C2×D414yes—
279C4⋊C4×C67C2412yes—
280C22⋊C4×C67—24no—
281C22⋊C4×C67—24no—
282C22⋊C4×C67C2×D414yes—
283C22⋊C4×C67C2×D414yes—
284C42×C67—24no—
285C42×C67C2×D412yes—
286C42×C67C2412yes—
287C23×C67—22no—
288C23×C67—22no—
289C23×C67—22no—
290C23×C67—22no—
291C23×C67—22no—
292C23×C67#13714yes—
293C23×C67C22×D412yes—
294C23×C67C22×D412yes—
295C23×C67C22×D411yescharacteristic
296Q8×C67—24no—
297Q8×C67—22no—
298Q8×C67—22no—
299Q8×C67—22no—
300Q8×C67—22no—
301Q8×C67—22no—
302Q8×C67—48no—
303Q8×C67—48no—
304Q8×C67—42no—
305Q8×C67—42no—
306Q8×C67C2×#4114yes—
307D4×C67—28no—
308C2×C4×C67—22no—
309C2×C4×C67—22no—
310C2×C4×C67—24no—
311C2×C4×C67—22no—
312C2×C4×C67—22no—
313C2×C4×C67—22no—
314C2×C4×C67—24no—
315C2×C4×C67—24no—
316C2×C4×C67—22no—
317C2×C4×C67—22no—
318C2×C4×C67—22no—
319C2×C4×C67—22no—
320C2×C4×C67—22no—
321C2×C4×C67—22no—
322C2×C4×C67—22no—
323C2×C4×C67—48no—
324C2×C4×C67—48no—
325C2×C4×C67—42no—
326C2×C4×C67—42no—
327C2×C4×C67—42no—
328C2×C4×C67C22×D412yes—
329C2×C4×C67C22×D412yes—
330C2×C4×C67C22×D412yes—
331C2×C4×C67C22×D412yes—
332C2×C4×C67C22×D411yescharacteristic
333C2×C4×C67C2×#4112yes—
334C2×C4×C67H(5,𝔽2)12yes—
335C2×C4×C67C2511yescharacteristic
336C2×Dic67—22no—
337C2×Dic67—22no—
338C2×Dic67—22no—
339C2×Dic67—22no—
340C2×Dic67—42no—
341C2×Dic67—48no—
342C2×Dic67—42no—
343C2×Dic67—42no—
344C2×Dic67—42no—
345Dic134—22no—
346Dic134—22no—
347Dic134—42no—
348C67⋊C8—22no—
349C67⋊C8—22no—
350C67⋊C8—22no—
351C67⋊C8—22no—
352C22×C67—22no—
353C22×C67—28no—
354C22×C67—22no—
355C22×C67—22no—
356C22×C67—22no—
357C22×C67—22no—
358C22×C67—44no—
359C22×C67#54612yes—
360C22×C67C2×#13714yes—
361C22×C67C2×#13712yes—
362C22×C67#57812yes—
363C22×C67C23×D411yescharacteristic
364C4×C67—22no—
365C4×C67—22no—
366C4×C67—24no—
367C4×C67—22no—
368C4×C67—22no—
369C4×C67—42no—
370C4×C67—42no—
371C4×C67—42no—
372C4×C67#54612yes—
373C4×C67C22×#4111yescharacteristic
374C4×C67C2×H(5,𝔽2)11yescharacteristic
375Dic67—42no—
376Dic67—42no—
377Dic67—42no—
378Dic67—42no—
379C2×#3312—671nomaximal, Sylow
380C2×C67—24no—
381C2×C67—42no—
382C2×C67#331214yescomplemented
383C2×C67C2×#54611yescharacteristic
384C2×C67C22×#13711yescharacteristic
385C2×C67C2×#57811yescharacteristic
386C2×#552—671no—
387C2×D4×Q8D6711yescharacteristic
388#3312—6716no—
389C2×#491—671no—
390C2×#485—671no—
391C2×#483—671no—
392C2×#479—671no—
393C2×#470—671no—
394C2×#467—671no—
395C2×#462—671no—
396C2×#451—671no—
397C2×#451—671no—
398C2×#441—671no—
399C2×#435—671no—
400C2×#419—671no—
401C22×#103—671no—
402C67C2×#331211yescharacteristic, complemented, Sylow
403C23×Q8C2×D6711yescharacteristic
404C23×Q8C2×D6711yescharacteristic
405C22×Q16—671no—
406C22×Q16—671no—
407C22×Q16—671no—
408C22×M16—671no—
409C23×C8—671no—
410#552—678no—
411#552—1344no—
412D4×Q8—24no—
413D4×Q8C2×D6718yes—
414C2×C4⋊Q8—21no—
415C2×C4⋊Q8C2×D6711yescharacteristic
416C2×#126—1341no—
417C2×#125—671no—
418C2×#125—1341no—
419C2×#123—1341no—
420C2×C22⋊Q8—21no—
421C2×C22⋊Q8—21no—
422C2×C22⋊Q8—671no—
423C2×C22⋊Q8—671no—
424C2×C22⋊Q8C2×D6711yescharacteristic
425C2×C22⋊Q8C2×D6711yescharacteristic
426C2×C4×Q8—671no—
427C2×C4×Q8C2×D6711yescharacteristic
428C2×C4×D4—21no—
429C2×C4×D4C2×D6711yescharacteristic
430C2×#117—671no—
431C2×#117—1341no—
432C22×C4⋊C4—671no—
433#491—678no—
434#485—678no—
435#483—678no—
436#479—678no—
437#470—678no—
438#467—678no—
439#462—678no—
440#451—678no—
441#451—678no—
442#441—678no—
443#435—678no—
444C2×#107—671no—
445C2×#106—671no—
446C2×#106—671no—
447C2×C4⋊C8—671no—
448#419—678no—
449C2×#103—671no—
450C2×#103—671no—
451C2×#103—671no—
452C2×#103—671no—
453C2×#103—671no—
454C2×#103—671no—
455C2×#103—671no—
456C2×#103—671no—
457C2×#103—671no—
458C2×#103—678no—
459C2×#103—671no—
460C2×C22⋊C8—671no—
461C2×C22⋊C8—671no—
462C2×#97—671no—
463C22×Q8—21no—
464C22×Q8—21no—
465C22×Q8—22no—
466C22×Q8—22no—
467C22×Q8—24no—
468C22×Q8—24no—
469C22×Q8—42no—
470C22×Q8—42no—
471C22×Q8—671no—
472C22×Q8C22×D6711yescharacteristic
473C22×Q8C22×D6711yescharacteristic
474C22×Q8C22×D6714yes—
475C22×Q8C22×D6714yes—
476C22×Q8C22×D6711yescharacteristic
477C22×D4C22⋊D6711yescharacteristic
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—1341no—
481C23×C4C22×D6711yescharacteristic
482C23×C4C22×D6711yescharacteristic
483C2×Q16—2682no—
484C2×Q16—2682no—
485C2×Q16—674no—
486C2×Q16—674no—
487C2×Q16—674no—
488C2×Q16—1344no—
489C2×M16—2682no—
490C2×M16—674no—
491C22×C8—2682no—
492C22×C8—674no—
493C22×C8—671no—
494C22×C8—671no—
495C22×C8—671no—
496C22×C8—671no—
497C4⋊Q8—28no—
498C4⋊Q8—22no—
499C4⋊Q8C22×D6714yes—
500#126—1348no—
501#125—674no—
502#125—1348no—
503#125—1342no—
504#123—1348no—
505C22⋊Q8—22no—
506C22⋊Q8—22no—
507C22⋊Q8—28no—
508C22⋊Q8—28no—
509C22⋊Q8—674no—
510C22⋊Q8—674no—
511C22⋊Q8—1342no—
512C22⋊Q8—1342no—
513C22⋊Q8C22×D6714yes—
514C22⋊Q8C22×D6714yes—
515C4×Q8—22no—
516C4×Q8—674no—
517C4×Q8—1342no—
518C4×Q8C22×D6714yes—
519C4×D4—28no—
520C4×D4C22⋊D6714yes—
521C4×D4C22×D6714yes—
522#117—674no—
523#117—1342no—
524#117—1348no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—21no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—671no—
531C2×C4⋊C4—671no—
532C2×C4⋊C4—674no—
533C2×C4⋊C4—671no—
534C2×C4⋊C4—1341no—
535C2×C4⋊C4—1342no—
536C2×C4⋊C4—1341no—
537C2×C4⋊C4—1341no—
538C2×C4⋊C4—1341no—
539C2×C4⋊C4—1341no—
540C2×C4⋊C4—1341no—
541C2×C4⋊C4C22⋊D6711yescharacteristic
542C2×C4⋊C4C22×D6711yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—1341no—
546C2×C22⋊C4—1341no—
547C2×C22⋊C4—1341no—
548C2×C22⋊C4C22⋊D6711yescharacteristic
549C2×C22⋊C4C22⋊D6711yescharacteristic
550C2×C42—21no—
551C2×C42—1341no—
552C2×C42—1341no—
553C2×C42C22×D6711yescharacteristic
554#107—674no—
555#106—674no—
556#106—674no—
557C4⋊C8—674no—
558#103—674no—
559#103—674no—
560#103—674no—
561#103—674no—
562#103—674no—
563#103—674no—
564#103—674no—
565#103—674no—
566#103—674no—
567#103—674no—
568C22⋊C8—674no—
569C22⋊C8—674no—
570#97—674no—
571C24C2×C22⋊D6711yescharacteristic
572C24C2×C22⋊D6711yescharacteristic
573C2×Q8—21no—
574C2×Q8—24no—
575C2×Q8—24no—
576C2×Q8—21no—
577C2×Q8—21no—
578C2×Q8—22no—
579C2×Q8—28no—
580C2×Q8—28no—
581C2×Q8—22no—
582C2×Q8—22no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—44no—
586C2×Q8—44no—
587C2×Q8—44no—
588C2×Q8—44no—
589C2×Q8—48no—
590C2×Q8—48no—
591C2×Q8—672no—
592C2×Q8—1342no—
593C2×Q8—1342no—
594C2×Q8—1341no—
595C2×Q8#1176162714yes—
596C2×Q8C23×D6712yes—
597C2×Q8C23×D6712yes—
598C2×Q8C23×D6712yes—
599C2×D4—24no—
600C2×D4C2×C22⋊D6714yes—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—24no—
607C22×C4—24no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—44no—
612C22×C4—44no—
613C22×C4—2684no—
614C22×C4—1344no—
615C22×C4—1341no—
616C22×C4—1341no—
617C22×C4—1341no—
618C22×C4—1341no—
619C22×C4C2×C22⋊D6712yes—
620C22×C4C2×C22⋊D6712yes—
621C22×C4C2×C22⋊D6711yescharacteristic
622C22×C4C2×C22⋊D6711yescharacteristic
623C22×C4C2×C22⋊D6711yescharacteristic
624C22×C4C2×C22⋊D6711yescharacteristic
625C22×C4C23×D6712yes—
626C22×C4C23×D6712yes—
627C22×C4C23×D6711yescharacteristic
628Q16—2684no—
629Q16—2684no—
630Q16—1348no—
631M16—2684no—
632C2×C8—2684no—
633C2×C8—672no—
634C2×C8—672no—
635C2×C8—672no—
636C2×C8—672no—
637C2×C8—1342no—
638C2×C8—1342no—
639C2×C8—1342no—
640C2×C8—1342no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—21no—
647C4⋊C4—672no—
648C4⋊C4—672no—
649C4⋊C4—672no—
650C4⋊C4—1341no—
651C4⋊C4—1341no—
652C4⋊C4—1344no—
653C4⋊C4—1341no—
654C4⋊C4—1344no—
655C4⋊C4—1344no—
656C4⋊C4—1344no—
657C4⋊C4—1344no—
658C4⋊C4—1344no—
659C4⋊C4C2×C22⋊D6714yes—
660C4⋊C4C23×D6712yes—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—1344no—
664C22⋊C4—1344no—
665C22⋊C4—1344no—
666C22⋊C4C2×C22⋊D6714yes—
667C22⋊C4C2×C22⋊D6714yes—
668C42—24no—
669C42—1344no—
670C42—1344no—
671C42C2×C22⋊D6712yes—
672C42C23×D6712yes—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23#1452407414yes—
679C23C22×C22⋊D6712yes—
680C23C22×C22⋊D6712yes—
681C23C22×C22⋊D6711yescharacteristic
682Q8—24no—
683Q8—22no—
684Q8—22no—
685Q8—22no—
686Q8—22no—
687Q8—22no—
688Q8—48no—
689Q8—48no—
690Q8—42no—
691Q8—42no—
692Q8—2682no—
693Q8—1342no—
694Q8—1342no—
695Q8C2×#1176162714yes—
696D4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—24no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—48no—
713C2×C4—48no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—2682no—
718C2×C4—2688no—
719C2×C4—2682no—
720C2×C4—2682no—
721C2×C4—2682no—
722C2×C4—1342no—
723C2×C4—1342no—
724C2×C4—1342no—
725C2×C4—1342no—
726C2×C4C22×C22⋊D6712yes—
727C2×C4C22×C22⋊D6712yes—
728C2×C4C22×C22⋊D6712yes—
729C2×C4C22×C22⋊D6712yes—
730C2×C4C22×C22⋊D6711yescharacteristic
731C2×C4C2×#1176162712yes—
732C2×C4#1452408812yes—
733C2×C4C24×D6711yescharacteristic
734C8—1342no—
735C8—1342no—
736C8—1342no—
737C8—1342no—
738C22—22no—
739C22—22no—
740C22—28no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—44no—
745C22#1686404012yes—
746C22C2×#1452407414yes—
747C22C2×#1452407412yes—
748C22#1686421112yes—
749C22C23×C22⋊D6711yescharacteristic
750C4—22no—
751C4—22no—
752C4—24no—
753C4—22no—
754C4—22no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—2682no—
759C4—2682no—
760C4—2682no—
761C4—2682no—
762C4#1686404012yes—
763C4C22×#1176162711yescharacteristic
764C4C2×#1452408811yescharacteristic
765C2—24no—
766C2—42no—
767C2#2257226014yesdirect product factor
768C2C2×#1686404011yescharacteristic
769C2C22×#1452407411yescharacteristic
770C2C2×#1686421111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×D4×Q8×C67C2
socleC23×C67C22×D4
prime radicalC22×D4×C67D4
hypercenterC2×D4×Q8D67
hypocenterC67C2×#3312
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×D4×Q8

Complements

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

NH ≅ G/Ntype
2. #22572260C2direct (N × H)
3. C2×#16863764C2semidirect
4. C2×#16863734C2semidirect
5. C2×#16863724C2semidirect
6. C2×#16863703C2semidirect
7. C2×#16863652C2semidirect
8. C2×#16863635C2semidirect
9. C2×#16863603C2semidirect
10. C2×#16863552C2semidirect
11. C2×#16863552C2semidirect
12. C2×#16863501C2semidirect
14. C2×#16863405C2semidirect
15. C22×#14523967C2semidirect
34. #16863764C22semidirect
35. #16863734C22semidirect
36. #16863724C22semidirect
37. #16863703C22semidirect
38. #16863652C22semidirect
39. #16863635C22semidirect
40. #16863603C22semidirect
41. #16863552C22semidirect
42. #16863552C22semidirect
43. #16863501C22semidirect
49. #16863405C22semidirect
59. C2×#14523967C22semidirect
382. C2×C67#3312semidirect
402. C67C2×#3312semidirect
767. C2#22572260direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#168640862
#225722602
C2×#168637642
C2×#168637342
C2×#168637242
C2×#168637032
C2×#168636522
C2×#168636352
C2×#168636032
C2×#168635522
C2×#168635012
C2×#168634682
C2×#168634052
C22×#145239672
C2×D4×Q8×C672
C2×#331267