Finite Group Databasebeta

← C2×#22565128 #31027600

Subgroups — C2×#22565128 #31027600

Order 17152.

3614 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14524019C211yesmaximal, characteristic, complemented
2C22×Q8×Dic67C211yesmaximal, characteristic, complemented
3C22×C4×C22⋊D67C211yesmaximal, characteristic
4#22565128C2116yesmaximal, direct product factor
5C2×#16863319C212yesmaximal, complemented
6C2×#16863318C212yesmaximal, complemented
7C2×#16863296C212yesmaximal
8C2×#16863291C212yesmaximal, complemented
9C2×#16863265C211yesmaximal, characteristic, complemented
10C2×#16863256C211yesmaximal, characteristic, complemented
11C2×#16863253C211yesmaximal, characteristic, complemented
12C22×C22⋊Q8×C67C211yesmaximal, characteristic, complemented
13C23×C22⋊D67C2211yescharacteristic
14C23×C4×D67C2211yescharacteristic
15C2×#14524019—28no—
16C2×#14524019C2218yescomplemented
17C2×Q8×Dic67—28no—
18C2×Q8×Dic67C2218yescomplemented
19C2×C4×C22⋊D67—28no—
20C2×C4×C22⋊D67C2218yes—
21C22×C4⋊Dic67C2211yescharacteristic
22C22×C4⋊Dic67C2211yescharacteristic
23C22×C4⋊Dic67C2212yes—
24C22×Dic67⋊C4C2212yes—
25C22×Dic67⋊C4C2211yescharacteristic
26C22×Dic67⋊C4C2212yes—
27C22×Dic67⋊C4C2212yes—
28C22×C22⋊Dic67C2211yescharacteristic
29C22×C22⋊Dic67C2212yes—
30C22×(C2×D67)⋊C4C2211yescharacteristic
31C22×(C2×D67)⋊C4C2212yes—
32C22×(C2×D67)⋊C4C2212yes—
33C22×C4×Dic67C2212yes—
34C22×C4×Dic67C2211yescharacteristic
35#16863319C22116yescomplemented
36#16863318C22116yescomplemented
37#16863296C22116yes—
38#16863291C22116yescomplemented
39#16863265C2218yescomplemented
40#16863256C2218yescomplemented
41#16863253C2218yescomplemented
42C2×C67⋊#95C2212yes—
43C2×C67⋊#95C2212yes—
44C23×Q8×C67C2211yescharacteristic
45C24×C4×C67C2211yescharacteristic
46C2×C22⋊Q8×C67—28no—
47C2×C22⋊Q8×C67C2218yescomplemented
48C22×C4⋊C4×C67C2211yescharacteristic
49C22×C4⋊C4×C67C2212yes—
50C22×C22⋊C4×C67C2212yes—
51C24×D67C2311yescharacteristic
52C22×C22⋊D67—24no—
53C22×C22⋊D67—24no—
54C22×C22⋊D67Q818yescomplemented
55C22×C22⋊D67C2314yes—
56C23×Dic67C2312yes—
57C23×Dic67C2311yescharacteristic
58C23×Dic67C2312yes—
59C23×Dic67C2311yescharacteristic
60C23×Dic67C2311yescharacteristic
61C22×C4×D67—24no—
62C22×C4×D67—24no—
63C22×C4×D67—24no—
64C22×C4×D67C2314yes—
65#14524019—232no—
66Q8×Dic67—232no—
67C4×C22⋊D67—232no—
68C2×C4⋊Dic67—28no—
69C2×C4⋊Dic67—24no—
70C2×C4⋊Dic67—24no—
71C2×C4⋊Dic67C2314yes—
72C2×C4⋊Dic67C2314yes—
73C2×C4⋊Dic67C2318yes—
74C2×Dic67⋊C4—24no—
75C2×Dic67⋊C4—28no—
76C2×Dic67⋊C4—28no—
77C2×Dic67⋊C4—44no—
78C2×Dic67⋊C4C2318yes—
79C2×Dic67⋊C4C2314yes—
80C2×Dic67⋊C4C2318yes—
81C2×Dic67⋊C4C2318yes—
82C2×C22⋊Dic67—24no—
83C2×C22⋊Dic67—44no—
84C2×C22⋊Dic67C2314yes—
85C2×C22⋊Dic67C2318yes—
86C2×(C2×D67)⋊C4—24no—
87C2×(C2×D67)⋊C4—28no—
88C2×(C2×D67)⋊C4—44no—
89C2×(C2×D67)⋊C4C2318yes—
90C2×(C2×D67)⋊C4C2314yes—
91C2×(C2×D67)⋊C4C2318yes—
92C2×C4×Dic67—28no—
93C2×C4×Dic67D418yes—
94C2×C4×Dic67C2318yes—
95C2×C4×Dic67C2314yes—
96C67⋊#95C2318yes—
97C67⋊#95C2318yes—
98C25×C67C2311yescharacteristic
99C22×Q8×C67—24no—
100C22×Q8×C67—24no—
101C22×Q8×C67D418yescomplemented
102C22×Q8×C67C2314yes—
103C23×C4×C67—24no—
104C23×C4×C67—24no—
105C23×C4×C67—24no—
106C23×C4×C67C2311yescharacteristic
107C23×C4×C67C2312yes—
108C23×C4×C67C2314yes—
109C23×C4×C67C2312yes—
110C23×C4×C67C2311yescharacteristic
111C22⋊Q8×C67—232no—
112C2×C4⋊C4×C67—24no—
113C2×C4⋊C4×C67—28no—
114C2×C4⋊C4×C67C2314yes—
115C2×C4⋊C4×C67C2318yes—
116C2×C22⋊C4×C67—28no—
117C2×C22⋊C4×C67C2318yes—
118C23×D67—22no—
119C23×D67—22no—
120C23×D67—22no—
121C23×D67—22no—
122C23×D67—22no—
123C23×D67—22no—
124C23×D67C2×Q814yes—
125C23×D67C2412yes—
126C2×C22⋊D67—232no—
127C2×C22⋊D67—28no—
128C2×C22⋊D67—28no—
129C2×C22⋊D67C2×Q8116yescomplemented
130C22×Dic67—22no—
131C22×Dic67—22no—
132C22×Dic67—24no—
133C22×Dic67—24no—
134C22×Dic67—22no—
135C22×Dic67—22no—
136C22×Dic67—24no—
137C22×Dic67—22no—
138C22×Dic67—24no—
139C22×Dic67—24no—
140C22×Dic67—24no—
141C22×Dic67C2×D414yes—
142C22×Dic67C2×D414yes—
143C22×Dic67C2×Q814yes—
144C22×Dic67#4114yes—
145C22×Dic67C2414yes—
146C22×Dic67C2412yes—
147C22×Dic67C2414yes—
148C22×Dic67C2412yes—
149C22×Dic67C2412yes—
150C2×C4×D67—28no—
151C2×C4×D67—28no—
152C2×C4×D67—28no—
153C2×C4×D67—416no—
154C4⋊Dic67—28no—
155C4⋊Dic67—28no—
156C4⋊Dic67—216no—
157Dic67⋊C4—216no—
158Dic67⋊C4—28no—
159Dic67⋊C4—216no—
160Dic67⋊C4—48no—
161C22⋊Dic67—28no—
162C22⋊Dic67—48no—
163(C2×D67)⋊C4—216no—
164(C2×D67)⋊C4—28no—
165(C2×D67)⋊C4—48no—
166C4×Dic67—216no—
167C4×Dic67C2×D4116yes—
168C24×C67—22no—
169C24×C67—22no—
170C24×C67—22no—
171C24×C67—22no—
172C24×C67—22no—
173C24×C67—22no—
174C24×C67C2×Q814yes—
175C24×C67C2412yes—
176C24×C67C2411yescharacteristic
177C2×Q8×C67—232no—
178C2×Q8×C67—28no—
179C2×Q8×C67—28no—
180C2×Q8×C67C2×D4116yescomplemented
181C22×C4×C67—24no—
182C22×C4×C67—24no—
183C22×C4×C67—24no—
184C22×C4×C67—22no—
185C22×C4×C67—22no—
186C22×C4×C67—22no—
187C22×C4×C67—24no—
188C22×C4×C67—24no—
189C22×C4×C67—28no—
190C22×C4×C67—28no—
191C22×C4×C67—28no—
192C22×C4×C67—416no—
193C22×C4×C67C2×D414yes—
194C22×C4×C67C2×D418yes—
195C22×C4×C67C2×D414yes—
196C22×C4×C67#4114yes—
197C22×C4×C67C2414yes—
198C22×C4×C67C2412yes—
199C22×C4×C67C2414yes—
200C22×C4×C67C2412yes—
201C4⋊C4×C67—28no—
202C4⋊C4×C67—216no—
203C22⋊C4×C67—216no—
204C23×C67—28no—
205C23×C67—28no—
206C23×C67—28no—
207C23×C67—22no—
208C23×C67—22no—
209C23×C67—22no—
210C23×C67—22no—
211C23×C67—22no—
212C23×C67—22no—
213C23×C67—44no—
214C23×C67—44no—
215C23×C67—44no—
216C23×C67—44no—
217C23×C67C22×D412yes—
218C23×C67C22×D412yes—
219C23×C67C22×Q814yes—
220C23×C67C22×Q812yes—
221C23×C67C2×#4112yes—
222C23×C67C2×#4112yes—
223C23×C67H(5,𝔽2)12yes—
224C23×C672−1+412yes—
225C23×C67C2511yescharacteristic
226C22×D67—28no—
227C22×D67—28no—
228C22×D67—28no—
229C22×D67—22no—
230C22×D67—22no—
231C22×D67—22no—
232C22×D67—22no—
233C22×D67—22no—
234C22×D67—22no—
235C22×D67—44no—
236C22×D67—44no—
237C22×D67—44no—
238C22×D67—44no—
239C22×D67C22×Q814yes—
240Q8×C67—232no—
241C2×C4×C67—216no—
242C2×C4×C67—24no—
243C2×C4×C67—24no—
244C2×C4×C67—24no—
245C2×C4×C67—22no—
246C2×C4×C67—22no—
247C2×C4×C67—22no—
248C2×C4×C67—24no—
249C2×C4×C67—24no—
250C2×C4×C67—44no—
251C2×C4×C67—48no—
252C2×C4×C67—416no—
253C2×C4×C67#121116yes—
254C2×C4×C67C22×D414yes—
255C2×C4×C67C22×D418yes—
256C2×C4×C67C22×D414yes—
257C2×C4×C67C2×#4114yes—
258C22⋊D67—232no—
259C2×Dic67—28no—
260C2×Dic67—22no—
261C2×Dic67—22no—
262C2×Dic67—24no—
263C2×Dic67—24no—
264C2×Dic67—22no—
265C2×Dic67—22no—
266C2×Dic67—24no—
267C2×Dic67—22no—
268C2×Dic67—24no—
269C2×Dic67—24no—
270C2×Dic67—24no—
271C2×Dic67—44no—
272C2×Dic67—48no—
273C2×Dic67—48no—
274C2×Dic67C22⋊Q8116yescomplemented
275C2×Dic67C22×D414yes—
276C2×Dic67C22×D414yes—
277C2×Dic67C22×Q814yes—
278C2×Dic67C2×#4114yes—
279C4×D67—416no—
280C22×C67—24no—
281C22×C67—24no—
282C22×C67—24no—
283C22×C67—42no—
284C22×C67—42no—
285C22×C67—42no—
286C22×C67—42no—
287C22×C67—416no—
288C22×C67C2×#12114yes—
289C22×C67C2×C22⋊Q814yes—
290C22×C67#53714yes—
291C22×C67D4×Q814yes—
292C22×C67#55014yes—
293C22×C67#55414yes—
294C22×C67#55614yes—
295C22×C67C23×D411yescharacteristic
296C22×C67C23×D411yescharacteristic
297C22×C67C23×Q811yescharacteristic
298C22×C67C22×#4111yescharacteristic
299C22×C67C22×#4111yescharacteristic
300C22×C67C2×H(5,𝔽2)11yescharacteristic
301C22×C67C2×2−1+411yescharacteristic
302C2×D67—24no—
303C2×D67—24no—
304C2×D67—24no—
305C2×D67—42no—
306C2×D67—42no—
307C2×D67—42no—
308C2×D67—42no—
309C2×D67—416no—
310C4×C67—28no—
311C4×C67—42no—
312C4×C67—44no—
313C4×C67C2×#12118yes—
314Dic67—24no—
315Dic67—42no—
316Dic67—44no—
317Dic67—44no—
318Dic67C2×C22⋊Q818yescomplemented
319C2×#2538—671nomaximal, Sylow
320C2×C67—44no—
321C2×C67#253818yescomplemented
322C2×C67C22×#12111yescharacteristic
323C2×C67C22×C22⋊Q811yescharacteristic
324C2×C67C2×#53711yescharacteristic
325C2×C67C2×D4×Q811yescharacteristic
326C2×C67C2×#55011yescharacteristic
327C2×C67C2×#55411yescharacteristic
328C2×C67C2×#55611yescharacteristic
329D67—44no—
330C22×C22⋊Q8—671no—
331C22×C22⋊Q8D6711yescharacteristic, complemented
332C22×C4×Q8—671no—
333C22×C4×D4—671no—
334#2538—6716no—
335C2×#396—672no—
336C2×#396—672no—
337C2×#390—672no—
338C2×#389—672no—
339C2×#384—671no—
340C2×#380—671no—
341C2×#380—671no—
342C67C2×#253811yescharacteristic, complemented, Sylow
343C23×Q8C2×D6711yescharacteristic
344C23×D4—671no—
345C24×C4—671no—
346C24×C4C2×D6711yescharacteristic
347C2×C22⋊Q8—28no—
348C2×C22⋊Q8—678no—
349C2×C22⋊Q8—1348no—
350C2×C22⋊Q8C2×D6718yescomplemented
351C2×C4×Q8—678no—
352C2×C4×Q8—1348no—
353C2×C4×D4—678no—
354C2×C4×D4—1348no—
355C22×C4⋊C4—672no—
356C22×C4⋊C4—672no—
357C22×C4⋊C4—672no—
358C22×C4⋊C4—671no—
359C22×C4⋊C4—671no—
360C22×C4⋊C4—672no—
361C22×C4⋊C4—671no—
362C22×C4⋊C4C2×D6712yes—
363C22×C4⋊C4C2×D6711yescharacteristic
364C22×C22⋊C4—672no—
365C22×C22⋊C4—672no—
366C22×C22⋊C4—671no—
367C22×C22⋊C4—671no—
368C22×C22⋊C4—672no—
369C22×C22⋊C4C2×D6712yes—
370C22×C42—671no—
371C22×C42—672no—
372#396—6716no—
373#396—6716no—
374#390—6716no—
375#389—6716no—
376#384—678no—
377#380—678no—
378#380—678no—
379C2×#95—672no—
380C2×#95—672no—
381C25—671no—
382C25C22×D6711yescharacteristic
383C22×Q8—24no—
384C22×Q8—24no—
385C22×Q8C22⋊D6718yescomplemented
386C22×Q8C22×D6714yes—
387C22×D4—678no—
388C22×D4—674no—
389C22×D4—1344no—
390C22×D4—1344no—
391C23×C4—24no—
392C23×C4—24no—
393C23×C4—24no—
394C23×C4—671no—
395C23×C4—671no—
396C23×C4—672no—
397C23×C4—672no—
398C23×C4—671no—
399C23×C4—674no—
400C23×C4—1344no—
401C23×C4—1344no—
402C23×C4—1344no—
403C23×C4C22×D6714yes—
404C23×C4C22×D6712yes—
405C23×C4C22×D6711yescharacteristic
406C23×C4C22×D6712yes—
407C23×C4C22×D6711yescharacteristic
408C22⋊Q8—232no—
409C22⋊Q8—13432no—
410C4×Q8—13432no—
411C4×D4—13432no—
412C2×C4⋊C4—24no—
413C2×C4⋊C4—28no—
414C2×C4⋊C4—2684no—
415C2×C4⋊C4—678no—
416C2×C4⋊C4—674no—
417C2×C4⋊C4—674no—
418C2×C4⋊C4—678no—
419C2×C4⋊C4—678no—
420C2×C4⋊C4—674no—
421C2×C4⋊C4—678no—
422C2×C4⋊C4—1344no—
423C2×C4⋊C4—1348no—
424C2×C4⋊C4—1348no—
425C2×C4⋊C4—1344no—
426C2×C4⋊C4—1348no—
427C2×C4⋊C4—1344no—
428C2×C4⋊C4C22×D6714yes—
429C2×C4⋊C4C22×D6718yes—
430C2×C22⋊C4—28no—
431C2×C22⋊C4—2684no—
432C2×C22⋊C4—2684no—
433C2×C22⋊C4—678no—
434C2×C22⋊C4—678no—
435C2×C22⋊C4—674no—
436C2×C22⋊C4—674no—
437C2×C22⋊C4—678no—
438C2×C22⋊C4—1344no—
439C2×C22⋊C4—1344no—
440C2×C22⋊C4—1348no—
441C2×C22⋊C4C22×D6718yes—
442C2×C42—678no—
443C2×C42—674no—
444C2×C42—678no—
445C2×C42—1348no—
446#95—678no—
447#95—678no—
448C24—22no—
449C24—22no—
450C24—22no—
451C24—22no—
452C24—22no—
453C24—22no—
454C24—674no—
455C24—672no—
456C24—1342no—
457C24—1342no—
458C24—1342no—
459C24—1342no—
460C24—1342no—
461C24—1342no—
462C24Q8×D6714yes—
463C24C23×D6712yes—
464C24C23×D6711yescharacteristic
465C2×Q8—232no—
466C2×Q8—28no—
467C2×Q8—28no—
468C2×Q8C2×C22⋊D67116yescomplemented
469C2×D4—6716no—
470C2×D4—1348no—
471C2×D4—13432no—
472C2×D4—1348no—
473C22×C4—24no—
474C22×C4—24no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—22no—
480C22×C4—24no—
481C22×C4—28no—
482C22×C4—28no—
483C22×C4—28no—
484C22×C4—416no—
485C22×C4—26816no—
486C22×C4—674no—
487C22×C4—674no—
488C22×C4—674no—
489C22×C4—672no—
490C22×C4—674no—
491C22×C4—672no—
492C22×C4—674no—
493C22×C4—672no—
494C22×C4—674no—
495C22×C4—1344no—
496C22×C4—1342no—
497C22×C4—1344no—
498C22×C4—1342no—
499C22×C4—1344no—
500C22×C4—1342no—
501C22×C4—1344no—
502C22×C4—1344no—
503C22×C4—1344no—
504C22×C4—1348no—
505C22×C4—1348no—
506C22×C4—1348no—
507C22×C4—1342no—
508C22×C4—1342no—
509C22×C4D4×D6714yes—
510C22×C4C2×C22⋊D6718yes—
511C22×C4C2×C22⋊D6714yes—
512C22×C4#1176162714yes—
513C22×C4C23×D6712yes—
514C22×C4C23×D6714yes—
515C22×C4C23×D6714yes—
516C22×C4C23×D6712yes—
517C4⋊C4—28no—
518C4⋊C4—216no—
519C4⋊C4—2688no—
520C4⋊C4—1348no—
521C4⋊C4—13416no—
522C4⋊C4—13416no—
523C4⋊C4—1348no—
524C4⋊C4—13416no—
525C4⋊C4—1348no—
526C22⋊C4—216no—
527C22⋊C4—2688no—
528C22⋊C4—2688no—
529C22⋊C4—1348no—
530C22⋊C4—1348no—
531C22⋊C4—13416no—
532C42—6716no—
533C42—13416no—
534C23—28no—
535C23—28no—
536C23—28no—
537C23—22no—
538C23—22no—
539C23—22no—
540C23—22no—
541C23—22no—
542C23—22no—
543C23—44no—
544C23—44no—
545C23—44no—
546C23—44no—
547C23—2684no—
548C23—2684no—
549C23—2684no—
550C23—2684no—
551C23—674no—
552C23—1348no—
553C23—1348no—
554C23—1348no—
555C23—1342no—
556C23—1342no—
557C23—1342no—
558C23—1342no—
559C23—1342no—
560C23—1342no—
561C23C2×D4×D6712yes—
562C23C22×C22⋊D6712yes—
563C23C2×Q8×D6714yes—
564C23C2×Q8×D6712yes—
565C23#41×D6712yes—
566C23C2×#1176162712yes—
567C23#1452408912yes—
568C23#1452409112yes—
569C23C24×D6711yescharacteristic
570Q8—232no—
571D4—13432no—
572C2×C4—216no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—24no—
581C2×C4—48no—
582C2×C4—44no—
583C2×C4—416no—
584C2×C4—2688no—
585C2×C4—2684no—
586C2×C4—2688no—
587C2×C4—26816no—
588C2×C4—6716no—
589C2×C4—674no—
590C2×C4—674no—
591C2×C4—674no—
592C2×C4—674no—
593C2×C4—1344no—
594C2×C4—1342no—
595C2×C4—1344no—
596C2×C4—1342no—
597C2×C4—1344no—
598C2×C4—1342no—
599C2×C4—1344no—
600C2×C4—1344no—
601C2×C4—1344no—
602C2×C4—1342no—
603C2×C4—1342no—
604C2×C4—1348no—
605C2×C4#14524015116yes—
606C2×C4C2×D4×D6714yes—
607C2×C4C22×C22⋊D6718yes—
608C2×C4C22×C22⋊D6714yes—
609C2×C4C2×#1176162714yes—
610C22—24no—
611C22—24no—
612C22—24no—
613C22—416no—
614C22—42no—
615C22—42no—
616C22—42no—
617C22—42no—
618C22—26816no—
619C22—2682no—
620C22—2682no—
621C22—2682no—
622C22—2682no—
623C22—1344no—
624C22—1344no—
625C22—1344no—
626C22C2×#1452401514yes—
627C22C22⋊Q8×D6714yes—
628C22#1686397614yes—
629C22Q8×C22⋊D6714yes—
630C22#1686406514yes—
631C22#1686410414yes—
632C22#1686411714yes—
633C22C22×D4×D6711yescharacteristic
634C22C23×C22⋊D6711yescharacteristic
635C22C22×Q8×D6711yescharacteristic
636C22C2×#41×D6711yescharacteristic
637C22C22×#1176162711yescharacteristic
638C22C2×#1452408911yescharacteristic
639C22C2×#1452409111yescharacteristic
640C4—28no—
641C4—42no—
642C4—44no—
643C4—2682no—
644C4—2684no—
645C4—2684no—
646C4—678no—
647C4—1344no—
648C4C2×#1452401518yes—
649C2—44no—
650C2—2684no—
651C2#2256512818yesdirect product factor
652C2C22×#1452401511yescharacteristic
653C2C2×C22⋊Q8×D6711yescharacteristic
654C2C2×#1686397611yescharacteristic
655C2C2×Q8×C22⋊D6711yescharacteristic
656C2C2×#1686406511yescharacteristic
657C2C2×#1686410411yescharacteristic
658C2C2×#1686411711yescharacteristic
subgroupG/H
centerC24C23×D67
commutator, cosocleC23×C67C25
FrattiniC23C24×D67
FittingC22×C22⋊Q8×C67C2
socleC24×C67C24
prime radicalC23×C22⋊D67C22
hypercenterC22×C22⋊Q8D67
hypocenterC67C2×#2538
LCSG ▷ C23×C67 ▷ C67
UCSC1 ◁ C24 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14524019C2semidirect
2. C22×Q8×Dic67C2semidirect
4. #22565128C2direct (N × H)
5. C2×#16863319C2semidirect
6. C2×#16863318C2semidirect
8. C2×#16863291C2semidirect
9. C2×#16863265C2semidirect
10. C2×#16863256C2semidirect
11. C2×#16863253C2semidirect
12. C22×C22⋊Q8×C67C2semidirect
16. C2×#14524019C22semidirect
18. C2×Q8×Dic67C22semidirect
35. #16863319C22semidirect
36. #16863318C22semidirect
38. #16863291C22semidirect
39. #16863265C22semidirect
40. #16863256C22semidirect
41. #16863253C22semidirect
47. C2×C22⋊Q8×C67C22semidirect
54. C22×C22⋊D67Q8semidirect
101. C22×Q8×C67D4semidirect
129. C2×C22⋊D67C2×Q8semidirect
180. C2×Q8×C67C2×D4semidirect
274. C2×Dic67C22⋊Q8semidirect
318. Dic67C2×C22⋊Q8semidirect
321. C2×C67#2538semidirect
331. C22×C22⋊Q8D67semidirect
342. C67C2×#2538semidirect
350. C2×C22⋊Q8C2×D67semidirect
385. C22×Q8C22⋊D67semidirect
468. C2×Q8C2×C22⋊D67semidirect
651. C2#22565128direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145240192
C22×Q8×Dic672
C22×C4×C22⋊D672
#225651282
C2×#168633192
C2×#168633182
C2×#168632962
C2×#168632912
C2×#168632652
C2×#168632562
C2×#168632532
C22×C22⋊Q8×C672
C2×#253867