Finite Group Databasebeta

← C2×#22564284 #31024037

Subgroups — C2×#22564284 #31024037

Order 17152.

2594 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524038C211yesmaximal, characteristic
2#22564284C2116yesmaximal, direct product factor
3C2×#16863335C211yesmaximal, characteristic, complemented
4C2×#16863318C211yesmaximal, characteristic
5C2×#16863315C211yesmaximal, characteristic, complemented
6C2×#16863307C211yesmaximal, characteristic
7C2×#16863294C211yesmaximal, characteristic, complemented
8C2×#16863287C211yesmaximal, characteristic
9C2×#16863287C211yesmaximal, characteristic
10C2×#16863287C211yesmaximal, characteristic
11C2×#16863286C211yesmaximal, characteristic
12C2×#16863282C211yesmaximal, characteristic, complemented
13C2×#16863280C211yesmaximal, characteristic, complemented
14C2×#16863277C211yesmaximal, characteristic, complemented
15C2×C4×Dic67⋊C4C211yesmaximal, characteristic, complemented
16C22×C4×Q8×C67C211yesmaximal, characteristic, complemented
17C2×#14524038—28no—
18C2×#14524038C2218yes—
19C22×C4⋊Dic67C2211yescharacteristic
20C22×C4⋊Dic67C2211yescharacteristic
21C22×Dic67⋊C4C2211yescharacteristic
22C22×Dic67⋊C4C2211yescharacteristic
23C22×Dic67⋊C4C2211yescharacteristic
24C22×Dic67⋊C4C2211yescharacteristic
25C22×Dic67⋊C4C2211yescharacteristic
26C22×(C2×D67)⋊C4C2211yescharacteristic
27C22×(C2×D67)⋊C4C2211yescharacteristic
28C22×(C2×D67)⋊C4C2211yescharacteristic
29C22×(C2×D67)⋊C4C2211yescharacteristic
30C22×(C2×D67)⋊C4C2211yescharacteristic
31C22×(C2×D67)⋊C4C2211yescharacteristic
32C22×(C2×D67)⋊C4C2211yescharacteristic
33C22×C4×Dic67C2211yescharacteristic
34C22×C4×Dic67C2211yescharacteristic
35#16863335C2218yescomplemented
36#16863318C2218yes—
37#16863315C2218yescomplemented
38#16863307C2218yes—
39#16863294C2218yescomplemented
40#16863287C2218yes—
41#16863287C2218yes—
42#16863287C2218yes—
43#16863286C2218yes—
44#16863282C2218yescomplemented
45#16863280C2218yescomplemented
46#16863277C2218yescomplemented
47C4×Dic67⋊C4C2218yescomplemented
48C2×C67⋊#95C2211yescharacteristic
49C2×C67⋊#95C2211yescharacteristic
50C2×C67⋊#95C2211yescharacteristic
51C2×C67⋊#95C2211yescharacteristic
52C2×C67⋊#95C2211yescharacteristic
53C2×C67⋊#95C2211yescharacteristic
54C2×C67⋊#95C2211yescharacteristic
55C2×C67⋊#95C2211yescharacteristic
56C2×C67⋊#95C2211yescharacteristic
57C2×C67⋊#95C2211yescharacteristic
58C2×C67⋊#95C2211yescharacteristic
59C2×C67⋊#95C2211yescharacteristic
60C23×Q8×C67C2211yescharacteristic
61C2×C4×Q8×C67—28no—
62C2×C4×Q8×C67C2218yescomplemented
63C22×C4⋊C4×C67C2211yescharacteristic
64C22×C4⋊C4×C67C2211yescharacteristic
65C22×C4⋊C4×C67C2211yescharacteristic
66C22×C42×C67C2211yescharacteristic
67C22×C42×C67C2211yescharacteristic
68C22×C42×C67C2211yescharacteristic
69C24×D67C2311yescharacteristic
70C23×Dic67C2311yescharacteristic
71C23×Dic67C2311yescharacteristic
72C23×Dic67C2311yescharacteristic
73C23×Dic67C2311yescharacteristic
74C23×Dic67C2311yescharacteristic
75C23×Dic67C2311yescharacteristic
76C23×Dic67C2311yescharacteristic
77#14524038—232no—
78C2×C4⋊Dic67—24no—
79C2×C4⋊Dic67—24no—
80C2×C4⋊Dic67C2314yes—
81C2×C4⋊Dic67C2314yes—
82C2×Dic67⋊C4—24no—
83C2×Dic67⋊C4—24no—
84C2×Dic67⋊C4—24no—
85C2×Dic67⋊C4—24no—
86C2×Dic67⋊C4—24no—
87C2×Dic67⋊C4C2314yes—
88C2×Dic67⋊C4C2314yes—
89C2×Dic67⋊C4C2314yes—
90C2×Dic67⋊C4C2314yes—
91C2×Dic67⋊C4C2314yes—
92C2×(C2×D67)⋊C4—24no—
93C2×(C2×D67)⋊C4—24no—
94C2×(C2×D67)⋊C4—24no—
95C2×(C2×D67)⋊C4—24no—
96C2×(C2×D67)⋊C4—24no—
97C2×(C2×D67)⋊C4—24no—
98C2×(C2×D67)⋊C4—24no—
99C2×(C2×D67)⋊C4C2314yes—
100C2×(C2×D67)⋊C4C2314yes—
101C2×(C2×D67)⋊C4C2314yes—
102C2×(C2×D67)⋊C4C2314yes—
103C2×(C2×D67)⋊C4C2314yes—
104C2×(C2×D67)⋊C4C2314yes—
105C2×(C2×D67)⋊C4C2314yes—
106C2×C4×Dic67—24no—
107C2×C4×Dic67—24no—
108C2×C4×Dic67C2314yes—
109C2×C4×Dic67C2314yes—
110C67⋊#95C2314yes—
111C67⋊#95C2314yes—
112C67⋊#95C2314yes—
113C67⋊#95C2314yes—
114C67⋊#95C2314yes—
115C67⋊#95C2314yes—
116C67⋊#95C2314yes—
117C67⋊#95C2314yes—
118C67⋊#95C2314yes—
119C67⋊#95C2314yes—
120C67⋊#95C2314yes—
121C67⋊#95C2314yes—
122C22×Q8×C67—24no—
123C22×Q8×C67—24no—
124C22×Q8×C67—24no—
125C22×Q8×C67C2314yes—
126C23×C4×C67C2311yescharacteristic
127C23×C4×C67C2311yescharacteristic
128C23×C4×C67C2311yescharacteristic
129C23×C4×C67C2311yescharacteristic
130C23×C4×C67C2311yescharacteristic
131C23×C4×C67C2311yescharacteristic
132C23×C4×C67C2311yescharacteristic
133C4×Q8×C67—232no—
134C2×C4⋊C4×C67—24no—
135C2×C4⋊C4×C67—24no—
136C2×C4⋊C4×C67D418yes—
137C2×C4⋊C4×C67C2314yes—
138C2×C4⋊C4×C67C2314yes—
139C2×C4⋊C4×C67C2314yes—
140C2×C42×C67—24no—
141C2×C42×C67—24no—
142C2×C42×C67—24no—
143C2×C42×C67C2314yes—
144C2×C42×C67C2314yes—
145C2×C42×C67C2314yes—
146C23×D67—22no—
147C23×D67—22no—
148C23×D67—22no—
149C23×D67—22no—
150C23×D67—22no—
151C23×D67—22no—
152C23×D67—22no—
153C23×D67C2412yes—
154C22×Dic67—22no—
155C22×Dic67—22no—
156C22×Dic67—22no—
157C22×Dic67—22no—
158C22×Dic67—22no—
159C22×Dic67—22no—
160C22×Dic67—22no—
161C22×Dic67—22no—
162C22×Dic67—22no—
163C22×Dic67—22no—
164C22×Dic67—22no—
165C22×Dic67—22no—
166C22×Dic67—22no—
167C22×Dic67—22no—
168C22×Dic67—22no—
169C22×Dic67—22no—
170C22×Dic67—22no—
171C22×Dic67—22no—
172C22×Dic67—22no—
173C22×Dic67—22no—
174C22×Dic67#4114yes—
175C22×Dic67C2412yes—
176C22×Dic67C2412yes—
177C22×Dic67C2412yes—
178C22×Dic67C2412yes—
179C22×Dic67C2412yes—
180C22×Dic67C2412yes—
181C22×Dic67C2412yes—
182C4⋊Dic67—28no—
183C4⋊Dic67—28no—
184Dic67⋊C4—28no—
185Dic67⋊C4—28no—
186Dic67⋊C4—28no—
187Dic67⋊C4—28no—
188Dic67⋊C4—28no—
189(C2×D67)⋊C4—28no—
190(C2×D67)⋊C4—28no—
191(C2×D67)⋊C4—28no—
192(C2×D67)⋊C4—28no—
193(C2×D67)⋊C4—28no—
194(C2×D67)⋊C4—28no—
195(C2×D67)⋊C4—28no—
196C4×Dic67—28no—
197C4×Dic67—28no—
198C24×C67C2411yescharacteristic
199C2×Q8×C67—232no—
200C2×Q8×C67—28no—
201C2×Q8×C67—28no—
202C2×Q8×C67—28no—
203C22×C4×C67—22no—
204C22×C4×C67—22no—
205C22×C4×C67—22no—
206C22×C4×C67—22no—
207C22×C4×C67—22no—
208C22×C4×C67—22no—
209C22×C4×C67—22no—
210C22×C4×C67—22no—
211C22×C4×C67—22no—
212C22×C4×C67—22no—
213C22×C4×C67—22no—
214C22×C4×C67—22no—
215C22×C4×C67—22no—
216C22×C4×C67—22no—
217C22×C4×C67—22no—
218C22×C4×C67C2×D414yes—
219C22×C4×C67C2×D414yes—
220C22×C4×C67C2×D414yes—
221C22×C4×C67#4114yes—
222C22×C4×C67#4114yes—
223C22×C4×C67#4114yes—
224C22×C4×C67C2412yes—
225C22×C4×C67C2412yes—
226C22×C4×C67C2412yes—
227C22×C4×C67C2412yes—
228C22×C4×C67C2412yes—
229C22×C4×C67C2412yes—
230C22×C4×C67C2412yes—
231C4⋊C4×C67—28no—
232C4⋊C4×C67—28no—
233C4⋊C4×C67C2×D4116yes—
234C42×C67—28no—
235C42×C67—28no—
236C42×C67—28no—
237C23×C67C22×D412yes—
238C23×C67C2×#4112yes—
239C23×C67C2×#4112yes—
240C23×C67C2×#4112yes—
241C23×C67C2×#4112yes—
242C23×C672−1+412yes—
243C23×C672−1+412yes—
244C23×C67C2511yescharacteristic
245C22×D67—22no—
246C22×D67—22no—
247C22×D67—22no—
248C22×D67—22no—
249C22×D67—22no—
250C22×D67—22no—
251C22×D67—22no—
252C22×D67—44no—
253C22×D67—44no—
254C22×D67—44no—
255C22×D67—44no—
256C22×D67—44no—
257C22×D67—44no—
258C22×D67—44no—
259Q8×C67—232no—
260C2×C4×C67—28no—
261C2×C4×C67—28no—
262C2×C4×C67—28no—
263C2×C4×C67—28no—
264C2×C4×C67—28no—
265C2×C4×C67—28no—
266C2×C4×C67—22no—
267C2×C4×C67—22no—
268C2×C4×C67—22no—
269C2×C4×C67—22no—
270C2×C4×C67—22no—
271C2×C4×C67—22no—
272C2×C4×C67—22no—
273C2×C4×C67—22no—
274C2×C4×C67—22no—
275C2×C4×C67—22no—
276C2×C4×C67—22no—
277C2×C4×C67—22no—
278C2×C4×C67—22no—
279C2×C4×C67—22no—
280C2×C4×C67—22no—
281C2×C4×C67—44no—
282C2×C4×C67C22×D414yes—
283C2×C4×C67C22×D414yes—
284C2×C4×C67C22×D414yes—
285C2×C4×C67C2×#4114yes—
286C2×C4×C67C2×#4114yes—
287C2×C4×C67C2×#4114yes—
288C2×Dic67—28no—
289C2×Dic67—22no—
290C2×Dic67—22no—
291C2×Dic67—22no—
292C2×Dic67—22no—
293C2×Dic67—22no—
294C2×Dic67—22no—
295C2×Dic67—22no—
296C2×Dic67—22no—
297C2×Dic67—22no—
298C2×Dic67—22no—
299C2×Dic67—22no—
300C2×Dic67—22no—
301C2×Dic67—22no—
302C2×Dic67—22no—
303C2×Dic67—22no—
304C2×Dic67—22no—
305C2×Dic67—22no—
306C2×Dic67—22no—
307C2×Dic67—22no—
308C2×Dic67—22no—
309C2×Dic67—44no—
310C2×Dic67—44no—
311C2×Dic67—44no—
312C2×Dic67—44no—
313C2×Dic67—44no—
314C2×Dic67—44no—
315C2×Dic67C2×#4114yes—
316C22×C67#52514yes—
317C22×C67#52914yes—
318C22×C67#54114yes—
319C22×C67#54714yes—
320C22×C67#54814yes—
321C22×C67#55614yes—
322C22×C67#55614yes—
323C22×C67C23×D411yescharacteristic
324C22×C67C22×#4111yescharacteristic
325C22×C67C22×#4111yescharacteristic
326C22×C67C22×#4111yescharacteristic
327C22×C67C22×#4111yescharacteristic
328C22×C67C2×2−1+411yescharacteristic
329C22×C67C2×2−1+411yescharacteristic
330C2×D67—42no—
331C2×D67—42no—
332C2×D67—42no—
333C2×D67—42no—
334C2×D67—42no—
335C2×D67—42no—
336C2×D67—42no—
337C2×D67—88no—
338C4×C67—24no—
339C4×C67—24no—
340C4×C67—24no—
341C4×C67—24no—
342C4×C67—24no—
343C4×C67—24no—
344C4×C67—42no—
345Dic67—24no—
346Dic67—42no—
347Dic67—42no—
348Dic67—42no—
349Dic67—42no—
350Dic67—42no—
351Dic67—42no—
352C2×#2469—671nomaximal, Sylow
353C2×C67#246918yescomplemented
354C2×C67C2×#52511yescharacteristic
355C2×C67C2×#52911yescharacteristic
356C2×C67C2×#54111yescharacteristic
357C2×C67C2×#54711yescharacteristic
358C2×C67C2×#54811yescharacteristic
359C2×C67C2×#55611yescharacteristic
360C2×C67C2×#55611yescharacteristic
361D67—82no—
362C22×#126—671no—
363C22×C4×Q8D6711yescharacteristic, complemented
364#2469—6716no—
365C2×#400—671no—
366C2×#396—671no—
367C2×#395—671no—
368C2×#393—671no—
369C2×#389—671no—
370C2×#388—671no—
371C2×#388—671no—
372C2×#388—671no—
373C2×#388—671no—
374C2×#387—671no—
375C2×#387—671no—
376C2×#387—671no—
377C2×C4×C4⋊C4—671no—
378C67C2×#246911yescharacteristic, complemented, Sylow
379C23×Q8C2×D6711yescharacteristic
380C2×#126—678no—
381C2×#126—1348no—
382C2×C4×Q8—28no—
383C2×C4×Q8C2×D6718yescomplemented
384C22×C4⋊C4—671no—
385C22×C4⋊C4—671no—
386C22×C4⋊C4—671no—
387C22×C4⋊C4—671no—
388C22×C4⋊C4—671no—
389C22×C4⋊C4—671no—
390C22×C4⋊C4—671no—
391C22×C4⋊C4C2×D6711yescharacteristic
392C22×C4⋊C4C2×D6711yescharacteristic
393C22×C4⋊C4C2×D6711yescharacteristic
394C22×C22⋊C4—671no—
395C22×C22⋊C4—671no—
396C22×C22⋊C4—671no—
397C22×C22⋊C4—671no—
398C22×C22⋊C4—671no—
399C22×C22⋊C4—671no—
400C22×C22⋊C4—671no—
401C22×C42—671no—
402C22×C42—671no—
403C22×C42C2×D6711yescharacteristic
404C22×C42C2×D6711yescharacteristic
405C22×C42C2×D6711yescharacteristic
406#400—678no—
407#396—678no—
408#395—678no—
409#393—678no—
410#389—678no—
411#388—678no—
412#388—678no—
413#388—678no—
414#388—678no—
415#387—678no—
416#387—678no—
417#387—678no—
418C4×C4⋊C4—678no—
419C2×#95—671no—
420C2×#95—671no—
421C2×#95—671no—
422C2×#95—671no—
423C2×#95—671no—
424C2×#95—671no—
425C2×#95—671no—
426C2×#95—671no—
427C2×#95—671no—
428C2×#95—671no—
429C2×#95—671no—
430C2×#95—671no—
431C25—671no—
432C22×Q8—24no—
433C22×Q8—24no—
434C22×Q8—24no—
435C22×Q8C22×D6714yes—
436C23×C4—671no—
437C23×C4—671no—
438C23×C4—671no—
439C23×C4—671no—
440C23×C4—671no—
441C23×C4—671no—
442C23×C4—671no—
443C23×C4C22×D6711yescharacteristic
444C23×C4C22×D6711yescharacteristic
445C23×C4C22×D6711yescharacteristic
446C23×C4C22×D6711yescharacteristic
447C23×C4C22×D6711yescharacteristic
448C23×C4C22×D6711yescharacteristic
449C23×C4C22×D6711yescharacteristic
450#126—13432no—
451C4×Q8—232no—
452C2×C4⋊C4—24no—
453C2×C4⋊C4—24no—
454C2×C4⋊C4—674no—
455C2×C4⋊C4—674no—
456C2×C4⋊C4—674no—
457C2×C4⋊C4—674no—
458C2×C4⋊C4—674no—
459C2×C4⋊C4—674no—
460C2×C4⋊C4—674no—
461C2×C4⋊C4—1344no—
462C2×C4⋊C4—1344no—
463C2×C4⋊C4—1344no—
464C2×C4⋊C4—1344no—
465C2×C4⋊C4—1344no—
466C2×C4⋊C4—1344no—
467C2×C4⋊C4—1344no—
468C2×C4⋊C4C22⋊D6718yes—
469C2×C4⋊C4C22×D6714yes—
470C2×C4⋊C4C22×D6714yes—
471C2×C4⋊C4C22×D6714yes—
472C2×C22⋊C4—674no—
473C2×C22⋊C4—674no—
474C2×C22⋊C4—674no—
475C2×C22⋊C4—674no—
476C2×C22⋊C4—674no—
477C2×C22⋊C4—674no—
478C2×C22⋊C4—674no—
479C2×C22⋊C4—1344no—
480C2×C22⋊C4—1344no—
481C2×C22⋊C4—1344no—
482C2×C22⋊C4—1344no—
483C2×C22⋊C4—1344no—
484C2×C22⋊C4—1344no—
485C2×C22⋊C4—1344no—
486C2×C42—24no—
487C2×C42—24no—
488C2×C42—24no—
489C2×C42—674no—
490C2×C42—674no—
491C2×C42—1344no—
492C2×C42—1344no—
493C2×C42C22×D6714yes—
494C2×C42C22×D6714yes—
495C2×C42C22×D6714yes—
496#95—674no—
497#95—674no—
498#95—674no—
499#95—674no—
500#95—674no—
501#95—674no—
502#95—674no—
503#95—674no—
504#95—674no—
505#95—674no—
506#95—674no—
507#95—674no—
508C24—672no—
509C24—1342no—
510C24—1342no—
511C24—1342no—
512C24—1342no—
513C24—1342no—
514C24—1342no—
515C24—1342no—
516C24C23×D6711yescharacteristic
517C2×Q8—232no—
518C2×Q8—28no—
519C2×Q8—28no—
520C2×Q8—28no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—22no—
532C22×C4—22no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—674no—
537C22×C4—672no—
538C22×C4—672no—
539C22×C4—672no—
540C22×C4—672no—
541C22×C4—672no—
542C22×C4—672no—
543C22×C4—672no—
544C22×C4—1342no—
545C22×C4—1342no—
546C22×C4—1342no—
547C22×C4—1342no—
548C22×C4—1342no—
549C22×C4—1342no—
550C22×C4—1342no—
551C22×C4—1342no—
552C22×C4—1342no—
553C22×C4—1342no—
554C22×C4—1342no—
555C22×C4—1342no—
556C22×C4—1342no—
557C22×C4—1342no—
558C22×C4—1342no—
559C22×C4—1342no—
560C22×C4—1342no—
561C22×C4—1342no—
562C22×C4—1342no—
563C22×C4—1342no—
564C22×C4C2×C22⋊D6714yes—
565C22×C4C2×C22⋊D6714yes—
566C22×C4C2×C22⋊D6714yes—
567C22×C4#1176162814yes—
568C22×C4#1176162814yes—
569C22×C4#1176162914yes—
570C22×C4C23×D6712yes—
571C22×C4C23×D6712yes—
572C22×C4C23×D6712yes—
573C22×C4C23×D6712yes—
574C22×C4C23×D6712yes—
575C22×C4C23×D6712yes—
576C22×C4C23×D6712yes—
577C4⋊C4—28no—
578C4⋊C4—28no—
579C4⋊C4—1348no—
580C4⋊C4—1348no—
581C4⋊C4—1348no—
582C4⋊C4—1348no—
583C4⋊C4—1348no—
584C4⋊C4—1348no—
585C4⋊C4—1348no—
586C4⋊C4C2×C22⋊D67116yes—
587C22⋊C4—1348no—
588C22⋊C4—1348no—
589C22⋊C4—1348no—
590C22⋊C4—1348no—
591C22⋊C4—1348no—
592C22⋊C4—1348no—
593C22⋊C4—1348no—
594C42—28no—
595C42—28no—
596C42—28no—
597C42—1348no—
598C42—1348no—
599C23—2684no—
600C23—2684no—
601C23—2684no—
602C23—2684no—
603C23—2684no—
604C23—2684no—
605C23—2684no—
606C23—1342no—
607C23—1342no—
608C23—1342no—
609C23—1342no—
610C23—1342no—
611C23—1342no—
612C23—1342no—
613C23C22×C22⋊D6712yes—
614C23#41×D6712yes—
615C23C2×#1176162812yes—
616C23C2×#1176162812yes—
617C23C2×#1176162912yes—
618C23#1452409012yes—
619C23#1452409112yes—
620C23C24×D6711yescharacteristic
621Q8—232no—
622C2×C4—28no—
623C2×C4—28no—
624C2×C4—28no—
625C2×C4—28no—
626C2×C4—28no—
627C2×C4—28no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—22no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—44no—
644C2×C4—2684no—
645C2×C4—2684no—
646C2×C4—2684no—
647C2×C4—2684no—
648C2×C4—2684no—
649C2×C4—2684no—
650C2×C4—674no—
651C2×C4—1342no—
652C2×C4—1342no—
653C2×C4—1342no—
654C2×C4—1342no—
655C2×C4—1342no—
656C2×C4—1342no—
657C2×C4—1342no—
658C2×C4—1342no—
659C2×C4—1342no—
660C2×C4—1342no—
661C2×C4—1342no—
662C2×C4—1342no—
663C2×C4—1342no—
664C2×C4—1342no—
665C2×C4—1342no—
666C2×C4—1342no—
667C2×C4—1342no—
668C2×C4—1342no—
669C2×C4—1348no—
670C2×C4—1342no—
671C2×C4—1342no—
672C2×C4C22×C22⋊D6714yes—
673C2×C4C22×C22⋊D6714yes—
674C2×C4C22×C22⋊D6714yes—
675C2×C4C2×#1176162814yes—
676C2×C4C2×#1176162814yes—
677C2×C4C2×#1176162914yes—
678C22—2682no—
679C22—2682no—
680C22—2682no—
681C22—2682no—
682C22—2682no—
683C22—2682no—
684C22—2682no—
685C22—5368no—
686C22#1686390714yes—
687C22#1686393314yes—
688C22#1686400414yes—
689C22#1686404514yes—
690C22#1686405714yes—
691C22#1686411814yes—
692C22#1686411914yes—
693C22C23×C22⋊D6711yescharacteristic
694C22C2×#41×D6711yescharacteristic
695C22C22×#1176162811yescharacteristic
696C22C22×#1176162811yescharacteristic
697C22C22×#1176162911yescharacteristic
698C22C2×#1452409011yescharacteristic
699C22C2×#1452409111yescharacteristic
700C4—24no—
701C4—24no—
702C4—24no—
703C4—24no—
704C4—24no—
705C4—24no—
706C4—42no—
707C4—2682no—
708C4—2682no—
709C4—2682no—
710C4—2682no—
711C4—2682no—
712C4—2682no—
713C4—1344no—
714C2—5362no—
715C2#2256428418yesdirect product factor
716C2C2×#1686390711yescharacteristic
717C2C2×#1686393311yescharacteristic
718C2C2×#1686400411yescharacteristic
719C2C2×#1686404511yescharacteristic
720C2C2×#1686405711yescharacteristic
721C2C2×#1686411811yescharacteristic
722C2C2×#1686411911yescharacteristic
subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC22×C4×Q8×C67C2
socleC24×C67C24
prime radicalC24×D67C23
hypercenterC22×C4×Q8D67
hypocenterC67C2×#2469
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. #22564284C2direct (N × H)
3. C2×#16863335C2semidirect
5. C2×#16863315C2semidirect
7. C2×#16863294C2semidirect
12. C2×#16863282C2semidirect
13. C2×#16863280C2semidirect
14. C2×#16863277C2semidirect
15. C2×C4×Dic67⋊C4C2semidirect
16. C22×C4×Q8×C67C2semidirect
35. #16863335C22semidirect
37. #16863315C22semidirect
39. #16863294C22semidirect
44. #16863282C22semidirect
45. #16863280C22semidirect
46. #16863277C22semidirect
47. C4×Dic67⋊C4C22semidirect
62. C2×C4×Q8×C67C22semidirect
353. C2×C67#2469semidirect
363. C22×C4×Q8D67semidirect
378. C67C2×#2469semidirect
383. C2×C4×Q8C2×D67semidirect
715. C2#22564284direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240382
#225642842
C2×#168633352
C2×#168633182
C2×#168633152
C2×#168633072
C2×#168632942
C2×#168632872
C2×#168632862
C2×#168632822
C2×#168632802
C2×#168632772
C2×C4×Dic67⋊C42
C22×C4×Q8×C672
C2×#246967