Finite Group Databasebeta

← C2×#22572254 #31732431

Subgroups — C2×#22572254 #31732431

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×D4×Dic134C211yesmaximal, characteristic
2#22572254C2116yesmaximal, direct product factor
3C2×#16863766C211yesmaximal, characteristic, complemented
4C2×#16863737C211yesmaximal, characteristic, complemented
5C2×#16863726C211yesmaximal, characteristic, complemented
6C2×#16863700C211yesmaximal, characteristic, complemented
7C2×#16863652C211yesmaximal, characteristic, complemented
8C2×#16863635C211yesmaximal, characteristic, complemented
9C2×#16863606C211yesmaximal, characteristic, complemented
10C2×#16863551C211yesmaximal, characteristic, complemented
11C2×#16863551C211yesmaximal, characteristic, complemented
12C2×#16863501C211yesmaximal, characteristic, complemented
13C2×#16863468C211yesmaximal, characteristic
14C2×#16863404C211yesmaximal, characteristic, complemented
15C22×#14523966C211yesmaximal, characteristic, complemented
16C2×#552×C67C211yesmaximal, characteristic
17C23×Dic134C2211yescharacteristic
18C23×Dic134C2211yescharacteristic
19C22×#11761618C2211yescharacteristic
20C22×#11761618C2211yescharacteristic
21C22×#11761618C2211yescharacteristic
22C22×#11761612C2211yescharacteristic
23C23×C67⋊C8C2211yescharacteristic
24D4×Dic134—24no—
25D4×Dic134C2218yes—
26C2×#14524043C2211yescharacteristic
27C2×#14524042—21no—
28C2×#14524022C2211yescharacteristic
29C2×#14524022C2211yescharacteristic
30C2×#14524020—21no—
31C2×#14524020—21no—
32C2×C4×Dic134C2211yescharacteristic
33C2×D4×Dic67—21no—
34#16863766C2218yescomplemented
35#16863737C2218yescomplemented
36#16863726C2218yescomplemented
37#16863700C2218yescomplemented
38#16863652C2218yescomplemented
39#16863635C2218yescomplemented
40#16863606C2218yescomplemented
41#16863551C2218yescomplemented
42#16863551C2218yescomplemented
43#16863501C2218yescomplemented
44#16863468C2218yes—
45C2×#14523976C2211yescharacteristic
46C2×#14523974C2211yescharacteristic
47C2×#14523974C2211yescharacteristic
48C2×C4⋊(C67⋊C8)C2211yescharacteristic
49#16863404C2218yescomplemented
50C2×#14523967C2211yescharacteristic
51C2×#14523966C2211yescharacteristic
52C2×#14523966C2211yescharacteristic
53C2×#14523966C2211yescharacteristic
54C2×#14523966C2211yescharacteristic
55C2×#14523966C2211yescharacteristic
56C2×#14523966C2211yescharacteristic
57C2×#14523966C2211yescharacteristic
58C2×#14523966C2211yescharacteristic
59C2×#14523966C2211yescharacteristic
60C2×#14523966C2218yescomplemented
61C2×C22⋊(C67⋊C8)C2211yescharacteristic
62C2×C22⋊(C67⋊C8)C2211yescharacteristic
63C2×#14523954C2211yescharacteristic
64#552×C67—24no—
65#552×C67C2218yes—
66C2×#126×C67—21no—
67C2×#125×C67—21no—
68C2×#125×C67C2211yescharacteristic
69C2×#123×C67—21no—
70C2×C22⋊Q8×C67C2211yescharacteristic
71C2×C22⋊Q8×C67C2211yescharacteristic
72C2×C4×Q8×C67C2211yescharacteristic
73C2×C4×D4×C67C2211yescharacteristic
74C2×#117×C67—21no—
75C2×#117×C67C2211yescharacteristic
76C22×C4⋊C4×C67C2211yescharacteristic
77C22×Dic134—24no—
78C22×Dic134—24no—
79C22×Dic134—22no—
80C22×Dic134—22no—
81C22×Dic134—21no—
82C22×Dic134—21no—
83C22×Dic134—42no—
84C22×Dic134—42no—
85C22×Dic134C2311yescharacteristic
86C22×Dic134C2311yescharacteristic
87C22×Dic134C2314yes—
88C22×Dic134C2314yes—
89C22×Dic134C2311yescharacteristic
90C23×Dic67—21no—
91C23×Dic67—21no—
92C2×#11761618—24no—
93C2×#11761618—42no—
94C2×#11761618—42no—
95C2×#11761618C2314yes—
96C2×#11761618C2314yes—
97C2×#11761618C2314yes—
98C2×#11761612—42no—
99C2×#11761612C2314yes—
100C22×C67⋊C8—42no—
101C22×C67⋊C8C2311yescharacteristic
102C22×C67⋊C8C2311yescharacteristic
103C22×C67⋊C8C2311yescharacteristic
104C22×C67⋊C8C2311yescharacteristic
105C22×C67⋊C8C2314yes—
106#14524043—22no—
107#14524043C2314yes—
108#14524042—28no—
109#14524022—22no—
110#14524022—22no—
111#14524022C2314yes—
112#14524022C2314yes—
113#14524020—28no—
114#14524020—28no—
115C4×Dic134—22no—
116C4×Dic134C2314yes—
117D4×Dic67—28no—
118C2×C4⋊Dic67—21no—
119C2×C4⋊Dic67—21no—
120C2×C4⋊Dic67C2311yescharacteristic
121C2×Dic67⋊C4—21no—
122C2×Dic67⋊C4—21no—
123C2×Dic67⋊C4—21no—
124C2×C22⋊Dic67—21no—
125C2×C22⋊Dic67—21no—
126C2×C4×Dic67—21no—
127#14523976C2314yes—
128#14523974C2314yes—
129#14523974C2314yes—
130C4⋊(C67⋊C8)C2314yes—
131#14523967C2314yes—
132#14523966C2314yes—
133#14523966C2314yes—
134#14523966C2314yes—
135#14523966C2314yes—
136#14523966C2314yes—
137#14523966C2314yes—
138#14523966C2314yes—
139#14523966C2314yes—
140#14523966C2314yes—
141C22⋊(C67⋊C8)C2314yes—
142C22⋊(C67⋊C8)C2314yes—
143#14523954C2314yes—
144C22×Q8×C67C2311yescharacteristic
145C22×D4×C67D411yescharacteristic
146C23×C4×C67—21no—
147C23×C4×C67C2311yescharacteristic
148C23×C4×C67C2311yescharacteristic
149#126×C67—28no—
150#125×C67—28no—
151#125×C67—22no—
152#125×C67C2314yes—
153#123×C67—28no—
154C22⋊Q8×C67—22no—
155C22⋊Q8×C67—22no—
156C22⋊Q8×C67C2314yes—
157C22⋊Q8×C67C2314yes—
158C4×Q8×C67—22no—
159C4×Q8×C67C2314yes—
160C4×D4×C67D414yes—
161C4×D4×C67C2314yes—
162#117×C67—22no—
163#117×C67—28no—
164#117×C67C2314yes—
165C2×C4⋊C4×C67—21no—
166C2×C4⋊C4×C67—22no—
167C2×C4⋊C4×C67—21no—
168C2×C4⋊C4×C67—21no—
169C2×C4⋊C4×C67—21no—
170C2×C4⋊C4×C67—21no—
171C2×C4⋊C4×C67—21no—
172C2×C4⋊C4×C67D411yescharacteristic
173C2×C4⋊C4×C67C2311yescharacteristic
174C2×C4⋊C4×C67C2311yescharacteristic
175C2×C4⋊C4×C67C2314yes—
176C2×C4⋊C4×C67C2311yescharacteristic
177C2×C22⋊C4×C67—21no—
178C2×C22⋊C4×C67—21no—
179C2×C22⋊C4×C67—21no—
180C2×C22⋊C4×C67D411yescharacteristic
181C2×C22⋊C4×C67D411yescharacteristic
182C2×C42×C67—21no—
183C2×C42×C67—21no—
184C2×C42×C67C2311yescharacteristic
185C2×Dic134—21no—
186C2×Dic134—22no—
187C2×Dic134—22no—
188C2×Dic134—22no—
189C2×Dic134—22no—
190C2×Dic134—22no—
191C2×Dic134—28no—
192C2×Dic134—28no—
193C2×Dic134—24no—
194C2×Dic134—24no—
195C2×Dic134—21no—
196C2×Dic134—21no—
197C2×Dic134—44no—
198C2×Dic134—44no—
199C2×Dic134—48no—
200C2×Dic134—48no—
201C2×Dic134—44no—
202C2×Dic134—44no—
203C2×Dic134#4114yes—
204C2×Dic134C2412yes—
205C2×Dic134C2412yes—
206C2×Dic134C2412yes—
207C22×Dic67—21no—
208C22×Dic67—21no—
209C22×Dic67—21no—
210C22×Dic67—21no—
211C22×Dic67—24no—
212C22×Dic67—24no—
213C22×Dic67—44no—
214C22×Dic67—44no—
215#11761618—28no—
216#11761618—44no—
217#11761618—44no—
218#11761612—44no—
219C2×C67⋊C8—22no—
220C2×C67⋊C8—22no—
221C2×C67⋊C8—22no—
222C2×C67⋊C8—22no—
223C2×C67⋊C8—44no—
224C2×C67⋊C8C2412yes—
225C2×C67⋊C8C2412yes—
226C2×C67⋊C8C2412yes—
227C2×C67⋊C8C2412yes—
228C4⋊Dic67—24no—
229C4⋊Dic67—24no—
230C4⋊Dic67—21no—
231C4⋊Dic67C2412yes—
232Dic67⋊C4—24no—
233Dic67⋊C4—24no—
234Dic67⋊C4—24no—
235C22⋊Dic67—24no—
236C22⋊Dic67—24no—
237C4×Dic67—24no—
238C24×C67C2×D411yescharacteristic
239C24×C67C2×D411yescharacteristic
240C2×Q8×C67—21no—
241C2×Q8×C67—22no—
242C2×Q8×C67—22no—
243C2×Q8×C67C2412yes—
244C2×D4×C67—24no—
245C2×D4×C67C2×D414yes—
246C22×C4×C67—22no—
247C22×C4×C67—22no—
248C22×C4×C67—22no—
249C22×C4×C67—22no—
250C22×C4×C67—21no—
251C22×C4×C67—21no—
252C22×C4×C67—21no—
253C22×C4×C67—21no—
254C22×C4×C67—24no—
255C22×C4×C67—44no—
256C22×C4×C67C2×D411yescharacteristic
257C22×C4×C67C2×D411yescharacteristic
258C22×C4×C67C2×D411yescharacteristic
259C22×C4×C67C2×D411yescharacteristic
260C22×C4×C67C2×D412yes—
261C22×C4×C67C2×D412yes—
262C22×C4×C67C2412yes—
263C22×C4×C67C2412yes—
264C22×C4×C67C2411yescharacteristic
265C4⋊C4×C67—21no—
266C4⋊C4×C67—21no—
267C4⋊C4×C67—24no—
268C4⋊C4×C67—24no—
269C4⋊C4×C67—24no—
270C4⋊C4×C67—24no—
271C4⋊C4×C67—24no—
272C4⋊C4×C67—24no—
273C4⋊C4×C67—21no—
274C4⋊C4×C67C2×D414yes—
275C4⋊C4×C67C2412yes—
276C4⋊C4×C67C2412yes—
277C4⋊C4×C67C2412yes—
278C22⋊C4×C67—24no—
279C22⋊C4×C67—24no—
280C22⋊C4×C67—24no—
281C22⋊C4×C67C2×D414yes—
282C22⋊C4×C67C2×D414yes—
283C42×C67—24no—
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—22no—
297Q8×C67—22no—
298Q8×C67—42no—
299D4×C67—28no—
300C2×C4×C67—22no—
301C2×C4×C67—22no—
302C2×C4×C67—22no—
303C2×C4×C67—22no—
304C2×C4×C67—24no—
305C2×C4×C67—24no—
306C2×C4×C67—22no—
307C2×C4×C67—22no—
308C2×C4×C67—22no—
309C2×C4×C67—22no—
310C2×C4×C67—22no—
311C2×C4×C67—22no—
312C2×C4×C67—22no—
313C2×C4×C67—22no—
314C2×C4×C67—42no—
315C2×C4×C67—48no—
316C2×C4×C67—42no—
317C2×C4×C67—42no—
318C2×C4×C67—42no—
319C2×C4×C67C22×D412yes—
320C2×C4×C67C22×D412yes—
321C2×C4×C67C22×D412yes—
322C2×C4×C67C22×D412yes—
323C2×C4×C67C22×D411yescharacteristic
324C2×C4×C67C2×#4112yes—
325C2×C4×C67H(5,𝔽2)12yes—
326C2×C4×C67C2511yescharacteristic
327C2×Dic67—24no—
328C2×Dic67—22no—
329C2×Dic67—22no—
330C2×Dic67—22no—
331C2×Dic67—22no—
332C2×Dic67—48no—
333C2×Dic67—48no—
334C2×Dic67—42no—
335C2×Dic67—42no—
336C2×Dic67—42no—
337Dic134—24no—
338Dic134—22no—
339Dic134—22no—
340Dic134—22no—
341Dic134—22no—
342Dic134—22no—
343Dic134—48no—
344Dic134—48no—
345Dic134—42no—
346Dic134—42no—
347Dic134C2×#4114yes—
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—22no—
367C4×C67—22no—
368C4×C67—42no—
369C4×C67—42no—
370C4×C67—42no—
371C4×C67—42no—
372C4×C67#54612yes—
373C4×C67C22×#4111yescharacteristic
374C4×C67C2×H(5,𝔽2)11yescharacteristic
375Dic67—24no—
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×#552D6711yescharacteristic
387C2×D4×Q8—671no—
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×Q8—671no—
404C23×Q8—671no—
405C22×Q16—671no—
406C22×Q16—671no—
407C22×Q16—671no—
408C22×M16—671no—
409C23×C8—671no—
410#552—24no—
411#552C2×D6718yes—
412D4×Q8—678no—
413D4×Q8—1344no—
414C2×C4⋊Q8—671no—
415C2×C4⋊Q8—1341no—
416C2×#126—21no—
417C2×#125—21no—
418C2×#125C2×D6711yescharacteristic
419C2×#123—21no—
420C2×C22⋊Q8—671no—
421C2×C22⋊Q8—671no—
422C2×C22⋊Q8—1341no—
423C2×C22⋊Q8—1341no—
424C2×C22⋊Q8C2×D6711yescharacteristic
425C2×C22⋊Q8C2×D6711yescharacteristic
426C2×C4×Q8—671no—
427C2×C4×Q8C2×D6711yescharacteristic
428C2×C4×D4—1341no—
429C2×C4×D4C2×D6711yescharacteristic
430C2×#117—21no—
431C2×#117C2×D6711yescharacteristic
432C22×C4⋊C4C2×D6711yescharacteristic
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—671no—
459C2×#103—678no—
460C2×C22⋊C8—671no—
461C2×C22⋊C8—671no—
462C2×#97—671no—
463C22×Q8—2682no—
464C22×Q8—2682no—
465C22×Q8—674no—
466C22×Q8—674no—
467C22×Q8—671no—
468C22×Q8—671no—
469C22×Q8—671no—
470C22×Q8—1344no—
471C22×Q8—1344no—
472C22×Q8—1341no—
473C22×Q8—1341no—
474C22×Q8—1342no—
475C22×Q8—1342no—
476C22×Q8C22×D6711yescharacteristic
477C22×D4C22⋊D6711yescharacteristic
478C23×C4—21no—
479C23×C4—1341no—
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—674no—
498C4⋊Q8—1348no—
499C4⋊Q8—1342no—
500#126—28no—
501#125—28no—
502#125—22no—
503#125C22×D6714yes—
504#123—28no—
505C22⋊Q8—22no—
506C22⋊Q8—22no—
507C22⋊Q8—674no—
508C22⋊Q8—674no—
509C22⋊Q8—1342no—
510C22⋊Q8—1342no—
511C22⋊Q8—1348no—
512C22⋊Q8—1348no—
513C22⋊Q8C22×D6714yes—
514C22⋊Q8C22×D6714yes—
515C4×Q8—22no—
516C4×Q8—674no—
517C4×Q8—1342no—
518C4×Q8C22×D6714yes—
519C4×D4—1348no—
520C4×D4C22⋊D6714yes—
521C4×D4C22×D6714yes—
522#117—22no—
523#117—28no—
524#117C22×D6714yes—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—21no—
528C2×C4⋊C4—21no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—21no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—671no—
533C2×C4⋊C4—1341no—
534C2×C4⋊C4—1341no—
535C2×C4⋊C4—1341no—
536C2×C4⋊C4—1341no—
537C2×C4⋊C4—1341no—
538C2×C4⋊C4C22⋊D6711yescharacteristic
539C2×C4⋊C4C22×D6711yescharacteristic
540C2×C4⋊C4C22×D6711yescharacteristic
541C2×C4⋊C4C22×D6714yes—
542C2×C4⋊C4C22×D6711yescharacteristic
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—1341no—
547C2×C22⋊C4—1341no—
548C2×C22⋊C4C22⋊D6711yescharacteristic
549C2×C22⋊C4C22⋊D6711yescharacteristic
550C2×C42—21no—
551C2×C42—21no—
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—22no—
575C2×Q8—22no—
576C2×Q8—2688no—
577C2×Q8—2688no—
578C2×Q8—2684no—
579C2×Q8—2684no—
580C2×Q8—2684no—
581C2×Q8—2684no—
582C2×Q8—674no—
583C2×Q8—672no—
584C2×Q8—672no—
585C2×Q8—672no—
586C2×Q8—1348no—
587C2×Q8—1348no—
588C2×Q8—1342no—
589C2×Q8—1342no—
590C2×Q8—1342no—
591C2×Q8—1342no—
592C2×Q8—1341no—
593C2×Q8—1341no—
594C2×Q8—1344no—
595C2×Q8—1344no—
596C2×Q8—1341no—
597C2×Q8—1342no—
598C2×Q8C23×D6712yes—
599C2×D4—24no—
600C2×D4C2×C22⋊D6714yes—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—44no—
611C22×C4—2684no—
612C22×C4—2684no—
613C22×C4—1344no—
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—21no—
642C4⋊C4—21no—
643C4⋊C4—24no—
644C4⋊C4—24no—
645C4⋊C4—24no—
646C4⋊C4—24no—
647C4⋊C4—24no—
648C4⋊C4—24no—
649C4⋊C4—21no—
650C4⋊C4—672no—
651C4⋊C4—1341no—
652C4⋊C4—1344no—
653C4⋊C4—1344no—
654C4⋊C4—1344no—
655C4⋊C4—1344no—
656C4⋊C4—1344no—
657C4⋊C4C2×C22⋊D6714yes—
658C4⋊C4C23×D6712yes—
659C4⋊C4C23×D6712yes—
660C4⋊C4C23×D6712yes—
661C22⋊C4—24no—
662C22⋊C4—24no—
663C22⋊C4—24no—
664C22⋊C4—1344no—
665C22⋊C4—1344no—
666C22⋊C4C2×C22⋊D6714yes—
667C22⋊C4C2×C22⋊D6714yes—
668C42—24no—
669C42—24no—
670C42—1344no—
671C42C2×C22⋊D6712yes—
672C42C23×D6712yes—
673C23—22no—
674C23—22no—
675C23—22no—
676C23—22no—
677C23—22no—
678C23#1452407314yes—
679C23C22×C22⋊D6712yes—
680C23C22×C22⋊D6712yes—
681C23C22×C22⋊D6711yescharacteristic
682Q8—22no—
683Q8—22no—
684Q8—42no—
685Q8—2688no—
686Q8—2688no—
687Q8—2682no—
688Q8—2682no—
689Q8—674no—
690Q8—1342no—
691Q8—1342no—
692Q8—1342no—
693Q8—1342no—
694Q8—1344no—
695Q8—1342no—
696D4—28no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—42no—
712C2×C4—48no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—2682no—
717C2×C4—2682no—
718C2×C4—2682no—
719C2×C4—2688no—
720C2×C4—2688no—
721C2×C4—1342no—
722C2×C4—1342no—
723C2×C4—1342no—
724C2×C4—1344no—
725C2×C4—1342no—
726C2×C4C22×C22⋊D6712yes—
727C2×C4C22×C22⋊D6712yes—
728C2×C4C22×C22⋊D6712yes—
729C2×C4C22×C22⋊D6712yes—
730C2×C4C22×C22⋊D6711yescharacteristic
731C2×C4#41×D6712yes—
732C2×C4#1452408912yes—
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#1686403412yes—
746C22C2×#1452407314yes—
747C22C2×#1452407312yes—
748C22#1686421112yes—
749C22C23×C22⋊D6711yescharacteristic
750C4—22no—
751C4—22no—
752C4—22no—
753C4—22no—
754C4—42no—
755C4—42no—
756C4—42no—
757C4—42no—
758C4—2682no—
759C4—2682no—
760C4—2682no—
761C4—1344no—
762C4#1686403412yes—
763C4C2×#41×D6711yescharacteristic
764C4C2×#1452408911yescharacteristic
765C2—24no—
766C2—42no—
767C2#2257225414yesdirect product factor
768C2C2×#1686403411yescharacteristic
769C2C22×#1452407311yescharacteristic
770C2C2×#1686421111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D67
commutator, cosocleC2×C4×C67C25
FrattiniC2×C4C24×D67
FittingC2×#552×C67C2
socleC23×C67C22×D4
prime radicalC22×D4×C67D4
hypercenterC2×#552D67
hypocenterC67C2×#3312
LCSG ▷ C2×C4×C67 ▷ C2×C67 ▷ C67
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
2. #22572254C2direct (N × H)
3. C2×#16863766C2semidirect
4. C2×#16863737C2semidirect
5. C2×#16863726C2semidirect
6. C2×#16863700C2semidirect
7. C2×#16863652C2semidirect
8. C2×#16863635C2semidirect
9. C2×#16863606C2semidirect
10. C2×#16863551C2semidirect
11. C2×#16863551C2semidirect
12. C2×#16863501C2semidirect
14. C2×#16863404C2semidirect
15. C22×#14523966C2semidirect
34. #16863766C22semidirect
35. #16863737C22semidirect
36. #16863726C22semidirect
37. #16863700C22semidirect
38. #16863652C22semidirect
39. #16863635C22semidirect
40. #16863606C22semidirect
41. #16863551C22semidirect
42. #16863551C22semidirect
43. #16863501C22semidirect
49. #16863404C22semidirect
60. C2×#14523966C22semidirect
382. C2×C67#3312semidirect
402. C67C2×#3312semidirect
767. C2#22572254direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D4×Dic1342
#225722542
C2×#168637662
C2×#168637372
C2×#168637262
C2×#168637002
C2×#168636522
C2×#168636352
C2×#168636062
C2×#168635512
C2×#168635012
C2×#168634682
C2×#168634042
C22×#145239662
C2×#552×C672
C2×#331267