Finite Group Databasebeta

← Q8×(C22⋊D67)⋊C4 #31015690

Subgroups — Q8×(C22⋊D67)⋊C4 #31015690

Order 17152.

3148 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
1C2×Q8×C22⋊D67C211yesmaximal, characteristic
2C22×Q8×Dic67C211yesmaximal, characteristic, complemented
3C2×C4×Q8×D67C211yesmaximal, characteristic, complemented
4#22563266C213yesmaximal, complemented
5#22563219C213yesmaximal, complemented
6#22563212C213yesmaximal, complemented
7Q8×Dic67⋊C4C211yesmaximal, characteristic, complemented
8#22563105C213yesmaximal
9Q8×(C2×D67)⋊C4C211yesmaximal, characteristic, complemented
10#22562778C213yesmaximal, complemented
11#22562747C213yesmaximal, complemented
12#22562737C213yesmaximal, complemented
13C4×Q8×Dic67C211yesmaximal, characteristic, complemented
14C4×(C22⋊D67)⋊C4C213yesmaximal
15Q8×C22⋊C4×C67C211yesmaximal, characteristic, complemented
16C22×Q8×D67C2211yescharacteristic
17Q8×C22⋊D67C4116yescomplemented
18C2×#14524041C2213yes—
19C2×#14524022C2213yes—
20C2×#14524019C2213yes—
21C2×Q8×Dic67—28no—
22C2×Q8×Dic67C2211yescharacteristic
23C2×Q8×Dic67C2213yes—
24C2×Q8×Dic67C2213yes—
25C2×Q8×Dic67C2211yescharacteristic
26C2×Q8×Dic67C2211yescharacteristic
27C2×C4×Dic134C2213yes—
28C2×#14524008C2213yes—
29C4×Q8×D67—28no—
30C2×C4×C22⋊D67C2213yes—
31C2×(C22⋊D67)⋊C4C2213yes—
32C2×(C22⋊D67)⋊C4C2211yescharacteristic
33C22×C4⋊Dic67C2213yes—
34C2×C4⋊C4×D67C2213yes—
35C22×C4×Dic67C2213yes—
36C2×C42×D67C2213yes—
37#16863302C2213yes—
38#16863301C2213yes—
39#16863294C2213yes—
40#16863293C2216yes—
41#16863293C2216yes—
42#16863292C2213yes—
43#16863283C2216yes—
44#16863278C2216yes—
45#16863270C2216yes—
46#16863268C2216yes—
47#16863265C2213yes—
48#16863253C2213yes—
49C4⋊C4×Dic67C2213yes—
50C4⋊C4×Dic67C2213yes—
51C4×Dic67⋊C4C2213yes—
52C4×C4⋊Dic67C2213yes—
53#16863247C2216yes—
54#16863247C2213yes—
55#16863247C2213yes—
56C22⋊C4×Dic67C2213yes—
57C22⋊C4×Dic67C2213yes—
58C4×(C2×D67)⋊C4C2213yes—
59#16863243C2213yes—
60#16863243C2213yes—
61C42×Dic67C2213yes—
62C23×Q8×C67C2211yescharacteristic
63C2×C4×Q8×C67C2211yescharacteristic
64C2×C4×Q8×C67C2211yescharacteristic
65#391×C67C2213yes—
66#391×C67C2213yes—
67#380×C67C2213yes—
68C4×C22⋊C4×C67C2213yes—
69C22×Dic134C2313yes—
70C2×Q8×D67—24no—
71C2×Q8×D67—24no—
72C2×Q8×D67C2×C418yescomplemented
73C22×C22⋊D67C2311yescharacteristic
74C23×Dic67C2313yes—
75C23×Dic67C2311yescharacteristic
76C22×C4×D67C2313yes—
77C22×C4×D67C2313yes—
78C22×C4×D67C2311yescharacteristic
79#14524041C2×C4124yescomplemented
80#14524022C2×C4124yescomplemented
81#14524019C2×C4124yescomplemented
82Q8×Dic67—212no—
83Q8×Dic67—212no—
84Q8×Dic67—24no—
85Q8×Dic67C2×C418yescomplemented
86Q8×Dic67D418yescomplemented
87C4×Dic134—212no—
88#14524008—212no—
89C4×C22⋊D67C2×C4124yes—
90(C22⋊D67)⋊C4—212no—
91(C22⋊D67)⋊C4Q818yesdirect product factor
92C2×C4⋊Dic67—212no—
93C2×C4⋊Dic67C2313yes—
94C2×C4⋊Dic67C2316yes—
95C2×C4⋊Dic67C2313yes—
96C2×C4⋊Dic67C2313yes—
97C2×Dic67⋊C4C2313yes—
98C2×Dic67⋊C4C2316yes—
99C2×Dic67⋊C4C2316yes—
100C2×Dic67⋊C4C2313yes—
101C2×Dic67⋊C4C2316yes—
102C2×Dic67⋊C4C2311yescharacteristic
103C4⋊C4×D67—212no—
104C2×C22⋊Dic67C2313yes—
105C2×(C2×D67)⋊C4C2313yes—
106C2×(C2×D67)⋊C4C2313yes—
107C2×(C2×D67)⋊C4C2311yescharacteristic
108C2×C4×Dic67—212no—
109C2×C4×Dic67C2313yes—
110C2×C4×Dic67C2313yes—
111C2×C4×Dic67C2313yes—
112C2×C4×Dic67C2313yes—
113C2×C4×Dic67C2313yes—
114C2×C4×Dic67C2313yes—
115C2×C4×Dic67C2313yes—
116C2×C4×Dic67C2313yes—
117C2×C4×Dic67C2313yes—
118C2×C4×Dic67C2313yes—
119C2×C4×Dic67C2311yescharacteristic
120C42×D67—212no—
121C67⋊#95C2313yes—
122C67⋊#95C2313yes—
123C67⋊#95C2313yes—
124C67⋊#95C2313yes—
125C67⋊#95C2316yes—
126C67⋊#95C2316yes—
127C22×Q8×C67—24no—
128C22×Q8×C67—24no—
129C22×Q8×C67C2×C418yescomplemented
130C22×Q8×C67C2313yes—
131C22×Q8×C67C2311yescharacteristic
132C23×C4×C67C2313yes—
133C4×Q8×C67—24no—
134C4×Q8×C67—24no—
135C2×C4⋊C4×C67C2313yes—
136C2×C4⋊C4×C67C2313yes—
137C2×C22⋊C4×C67C2313yes—
138C2×C22⋊C4×C67C2311yescharacteristic
139C2×C42×C67C2313yes—
140C2×C42×C67C2313yes—
141#95×C67C2313yes—
142#95×C67C2313yes—
143#95×C67C2316yes—
144C23×D67C2411yescharacteristic
145C2×Dic134—26no—
146C2×Dic134—26no—
147C2×Dic134C22×C4112yes—
148Q8×D67—232no—
149C2×C22⋊D67C22×C414yes—
150C2×C22⋊D67C2×Q814yes—
151C2×C22⋊D67#4114yes—
152C22×Dic67—22no—
153C22×Dic67—22no—
154C22×Dic67—26no—
155C22×Dic67—26no—
156C22×Dic67—43no—
157C22×Dic67C2×Q814yescomplemented
158C22×Dic67C2413yes—
159C22×Dic67C2413yes—
160C22×Dic67C2413yes—
161C22×Dic67C2413yes—
162C22×Dic67C2411yescharacteristic
163C22×Dic67C2411yescharacteristic
164C22×Dic67C2411yescharacteristic
165C2×C4×D67—26no—
166C2×C4×D67—26no—
167C2×C4×D67—22no—
168C2×C4×D67—22no—
169C2×C4×D67—26no—
170C2×C4×D67—26no—
171C2×C4×D67—43no—
172C2×C4×D67C22×C4112yes—
173C2×C4×D67C2×Q814yescomplemented
174C4⋊Dic67—26no—
175C4⋊Dic67—212no—
176C4⋊Dic67C22×C4112yes—
177C4⋊Dic67C2×D4112yes—
178Dic67⋊C4—212no—
179Dic67⋊C4—26no—
180Dic67⋊C4—46no—
181Dic67⋊C4C22×C4112yes—
182Dic67⋊C4C22×C4124yes—
183Dic67⋊C4C2×Q814yescomplemented
184C22⋊Dic67C22×C4112yes—
185(C2×D67)⋊C4—26no—
186(C2×D67)⋊C4C22×C4112yes—
187(C2×D67)⋊C4C2×Q814yescomplemented
188C4×Dic67—26no—
189C4×Dic67—26no—
190C4×Dic67—26no—
191C4×Dic67—26no—
192C4×Dic67—26no—
193C4×Dic67—26no—
194C4×Dic67—26no—
195C4×Dic67—43no—
196C4×Dic67C22×C4112yes—
197C4×Dic67C2×D4112yes—
198C4×Dic67C2×Q814yescomplemented
199C24×C67C2411yescharacteristic
200C2×Q8×C67—232no—
201C2×Q8×C67—26no—
202C2×Q8×C67—26no—
203C2×Q8×C67C22×C4112yes—
204C2×Q8×C67C22×C414yes—
205C2×Q8×C67C2×D414yes—
206C2×Q8×C67#4114yes—
207C22×C4×C67—26no—
208C22×C4×C67—26no—
209C22×C4×C67C22×C4112yes—
210C22×C4×C67C2413yes—
211C22×C4×C67C2413yes—
212C22×C4×C67C2413yes—
213C22×C4×C67C2411yescharacteristic
214C22×C4×C67C2411yescharacteristic
215C22×C4×C67C2413yes—
216C4⋊C4×C67—26no—
217C4⋊C4×C67—26no—
218C22⋊C4×C67—26no—
219C22⋊C4×C67C2×Q814yescomplemented
220C42×C67—26no—
221C42×C67—26no—
222C23×C67—21no—
223C23×C67—21no—
224C23×C67—21no—
225C23×C67—21no—
226C23×C67C23×C412yes—
227C23×C67C22×Q812yes—
228C23×C67C2×#4112yes—
229C23×C67C2511yescharacteristic
230C22×D67—21no—
231C22×D67—21no—
232C22×D67—21no—
233C22×D67—21no—
234C22×D67C23×C412yes—
235C22×D67C22×Q812yes—
236C22×D67C2×#4112yes—
237Q8×C67—224no—
238Q8×C67C4×D4116yescomplemented
239C2×C4×C67—21no—
240C2×C4×C67—23no—
241C2×C4×C67—21no—
242C2×C4×C67—23no—
243C2×C4×C67—21no—
244C2×C4×C67—21no—
245C2×C4×C67—224no—
246C2×C4×C67—23no—
247C2×C4×C67—23no—
248C2×C4×C67—23no—
249C2×C4×C67—23no—
250C2×C4×C67—23no—
251C2×C4×C67—23no—
252C2×C4×C67C23×C416yes—
253C2×C4×C67C23×C416yes—
254C2×C4×C67C22×D416yes—
255C2×C4×C67C22×Q812yes—
256C2×C4×C67C22×Q812yes—
257C2×C4×C67C2×#4116yes—
258C22⋊D67C4×Q8116yescomplemented
259C2×Dic67—21no—
260C2×Dic67—23no—
261C2×Dic67—23no—
262C2×Dic67—23no—
263C2×Dic67—23no—
264C2×Dic67—21no—
265C2×Dic67—23no—
266C2×Dic67—23no—
267C2×Dic67—28no—
268C2×Dic67—23no—
269C2×Dic67—23no—
270C2×Dic67—23no—
271C2×Dic67—412no—
272C2×Dic67C23×C416yes—
273C2×Dic67C23×C416yes—
274C2×Dic67C23×C412yes—
275C2×Dic67C22×D416yes—
276C2×Dic67C22×D412yes—
277C2×Dic67C22×Q812yes—
278C2×Dic67C22×Q812yes—
279C2×Dic67C22×Q812yes—
280C2×Dic67C2×#4112yes—
281C2×Dic672−1+412yes—
282C4×D67—224no—
283C4×D67—28no—
284C4×D67—412no—
285Dic134—224no—
286C22×C67—22no—
287C22×C67—22no—
288C22×C67—22no—
289C22×C67—22no—
290C22×C67—22no—
291C22×C67—22no—
292C22×C67C2×C4×Q814yescomplemented
293C22×C67C24×C411yescharacteristic
294C22×C67C23×D411yescharacteristic
295C22×C67C23×Q811yescharacteristic
296C22×C67C22×#4111yescharacteristic
297C22×C67C22×#4111yescharacteristic
298C22×C67C2×2−1+411yescharacteristic
299C22×C67#58511yescharacteristic
300C2×D67—22no—
301C2×D67—22no—
302C2×D67—22no—
303C2×D67—22no—
304C2×D67—22no—
305C2×D67—22no—
306C2×D67C2×C4×Q814yescomplemented
307C4×C67—26no—
308C4×C67—22no—
309C4×C67—22no—
310C4×C67—43no—
311C4×C67—43no—
312C4×C67C2×C4×D4112yes—
313Dic67—26no—
314Dic67—26no—
315Dic67—22no—
316Dic67—26no—
317Dic67—43no—
318Dic67C2×C4×Q814yescomplemented
319Dic67D4×Q814yescomplemented
320C4×D4×Q8—671nomaximal, Sylow
321C2×C67—24no—
322C2×C67C22×C4×D411yescharacteristic
323C2×C67C22×C4×Q811yescharacteristic
324C2×C67C4×2−1+411yescharacteristic
325C2×C67C2×D4×Q811yescharacteristic
326C2×C67D4×#4111yescharacteristic
327C2×C67Q8×#4111yescharacteristic
328C2×C67#348211yescharacteristic
329D67—24no—
330C2×D4×Q8—671no—
331C22×C4×Q8—671no—
332C22×C4×Q8—671no—
333#2365—673no—
334#2360—673no—
335#2360—673no—
336Q8×C4⋊C4—671no—
337D4×C4⋊C4—673no—
338Q8×C22⋊C4—671no—
339Q8×C22⋊C4D6711yescharacteristic, complemented
340C4×C4⋊Q8—673no—
341C4×C22⋊Q8—673no—
342C4×C22⋊Q8—673no—
343C42×Q8—671no—
344C42×D4—673no—
345C67C4×D4×Q811yescharacteristic, complemented, Sylow
346C23×Q8—671no—
347C23×Q8C2×D6711yescharacteristic
348D4×Q8—6716no—
349C2×C4⋊Q8—673no—
350C2×C22⋊Q8—673no—
351C2×C22⋊Q8—673no—
352C2×C4×Q8—671no—
353C2×C4×Q8—671no—
354C2×C4×Q8—673no—
355C2×C4×Q8—671no—
356C2×C4×Q8—673no—
357C2×C4×Q8—673no—
358C2×C4×Q8—673no—
359C2×C4×Q8—1348no—
360C2×C4×Q8—1348no—
361C2×C4×Q8C2×D6711yescharacteristic
362C2×C4×Q8C2×D6711yescharacteristic
363C2×C4×D4—673no—
364C2×C4×D4—671no—
365C2×C4×D4—673no—
366C22×C4⋊C4—673no—
367C22×C4⋊C4—673no—
368C22×C42—673no—
369C22×C42—673no—
370#391—673no—
371#391—673no—
372#391C2×D6713yes—
373#391C2×D6713yes—
374#389—673no—
375#389—673no—
376#389—676no—
377#389—676no—
378#387—676no—
379#387—676no—
380#385—676no—
381#385—676no—
382#384—673no—
383#380—673no—
384#380C2×D6713yes—
385C4×C4⋊C4—673no—
386C4×C4⋊C4—673no—
387C4×C4⋊C4—673no—
388C4×C4⋊C4—673no—
389C4×C4⋊C4—673no—
390C4×C4⋊C4—676no—
391C4×C4⋊C4—673no—
392C4×C22⋊C4—673no—
393C4×C22⋊C4—673no—
394C4×C22⋊C4—673no—
395C4×C22⋊C4—673no—
396C4×C22⋊C4—673no—
397C4×C22⋊C4C2×D6713yes—
398C43—673no—
399C22×Q8—24no—
400C22×Q8—24no—
401C22×Q8—678no—
402C22×Q8—673no—
403C22×Q8—1344no—
404C22×Q8—1344no—
405C22×Q8C4×D6718yescomplemented
406C22×Q8C22×D6713yes—
407C22×Q8C22×D6711yescharacteristic
408C22×D4—671no—
409C23×C4—673no—
410C23×C4—673no—
411C23×C4—671no—
412C23×C4—673no—
413C23×C4—671no—
414C23×C4C22×D6713yes—
415C4⋊Q8—6724no—
416C22⋊Q8—6724no—
417C22⋊Q8—6724no—
418C4×Q8—24no—
419C4×Q8—24no—
420C4×Q8—678no—
421C4×Q8—678no—
422C4×Q8—13412no—
423C4×Q8—13412no—
424C4×Q8—13412no—
425C4×Q8—13412no—
426C4×Q8—1344no—
427C4×D4—6724no—
428C4×D4—678no—
429C4×D4—13412no—
430C2×C4⋊C4—676no—
431C2×C4⋊C4—673no—
432C2×C4⋊C4—673no—
433C2×C4⋊C4—671no—
434C2×C4⋊C4—673no—
435C2×C4⋊C4—676no—
436C2×C4⋊C4—676no—
437C2×C4⋊C4—673no—
438C2×C4⋊C4—676no—
439C2×C4⋊C4—673no—
440C2×C4⋊C4—13412no—
441C2×C4⋊C4—13412no—
442C2×C4⋊C4C22×D6713yes—
443C2×C4⋊C4C22×D6713yes—
444C2×C22⋊C4—673no—
445C2×C22⋊C4—673no—
446C2×C22⋊C4—671no—
447C2×C22⋊C4—673no—
448C2×C22⋊C4C22×D6713yes—
449C2×C22⋊C4C22×D6711yescharacteristic
450C2×C42—673no—
451C2×C42—673no—
452C2×C42—671no—
453C2×C42—673no—
454C2×C42—673no—
455C2×C42—673no—
456C2×C42—673no—
457C2×C42—673no—
458C2×C42—673no—
459C2×C42—673no—
460C2×C42—673no—
461C2×C42—13412no—
462C2×C42—13412no—
463C2×C42C22×D6713yes—
464C2×C42C22×D6713yes—
465#95—673no—
466#95—673no—
467#95—673no—
468#95—673no—
469#95—676no—
470#95—676no—
471#95C22×D6713yes—
472#95C22×D6713yes—
473#95C22×D6716yes—
474C24—671no—
475C24C23×D6711yescharacteristic
476C2×Q8—232no—
477C2×Q8—26no—
478C2×Q8—26no—
479C2×Q8—6712no—
480C2×Q8—13432no—
481C2×Q8—1346no—
482C2×Q8—1346no—
483C2×Q8C2×C4×D67112yes—
484C2×Q8C2×C4×D6714yes—
485C2×Q8D4×D6714yes—
486C2×Q8#1176162714yes—
487C2×D4—674no—
488C2×D4—674no—
489C2×D4—674no—
490C22×C4—26no—
491C22×C4—26no—
492C22×C4—2683no—
493C22×C4—2683no—
494C22×C4—671no—
495C22×C4—671no—
496C22×C4—674no—
497C22×C4—671no—
498C22×C4—673no—
499C22×C4—673no—
500C22×C4—673no—
501C22×C4—6712no—
502C22×C4—674no—
503C22×C4—673no—
504C22×C4—1346no—
505C22×C4—1346no—
506C22×C4—1342no—
507C22×C4—1342no—
508C22×C4—1346no—
509C22×C4—1346no—
510C22×C4—1342no—
511C22×C4—1342no—
512C22×C4—1346no—
513C22×C4—1346no—
514C22×C4C2×C4×D67112yes—
515C22×C4C23×D6713yes—
516C22×C4C23×D6713yes—
517C22×C4C23×D6713yes—
518C22×C4C23×D6711yescharacteristic
519C22×C4C23×D6711yescharacteristic
520C22×C4C23×D6713yes—
521C4⋊C4—26no—
522C4⋊C4—26no—
523C4⋊C4—2686no—
524C4⋊C4—6712no—
525C4⋊C4—6712no—
526C4⋊C4—6724no—
527C4⋊C4—6712no—
528C4⋊C4—674no—
529C4⋊C4—13412no—
530C4⋊C4—13412no—
531C4⋊C4—1346no—
532C4⋊C4—1346no—
533C22⋊C4—26no—
534C22⋊C4—6712no—
535C22⋊C4—6712no—
536C22⋊C4—674no—
537C22⋊C4—1346no—
538C22⋊C4Q8×D6714yescomplemented
539C42—26no—
540C42—26no—
541C42—2683no—
542C42—6712no—
543C42—6712no—
544C42—674no—
545C42—1346no—
546C42—1346no—
547C42—1346no—
548C42—1346no—
549C42—1346no—
550C42—1346no—
551C42—1346no—
552C23—21no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—672no—
557C23—672no—
558C23—672no—
559C23—1341no—
560C23—1341no—
561C23—1341no—
562C23—1341no—
563C23C22×C4×D6712yes—
564C23C2×Q8×D6712yes—
565C23#41×D6712yes—
566C23C24×D6711yescharacteristic
567Q8—224no—
568Q8—13424no—
569Q8(C22⋊D67)⋊C4116yesdirect product factor
570D4—6716no—
571C2×C4—21no—
572C2×C4—23no—
573C2×C4—21no—
574C2×C4—23no—
575C2×C4—21no—
576C2×C4—21no—
577C2×C4—224no—
578C2×C4—23no—
579C2×C4—23no—
580C2×C4—23no—
581C2×C4—23no—
582C2×C4—23no—
583C2×C4—23no—
584C2×C4—26812no—
585C2×C4—26812no—
586C2×C4—672no—
587C2×C4—672no—
588C2×C4—672no—
589C2×C4—672no—
590C2×C4—672no—
591C2×C4—672no—
592C2×C4—676no—
593C2×C4—676no—
594C2×C4—676no—
595C2×C4—672no—
596C2×C4—1348no—
597C2×C4—1343no—
598C2×C4—1343no—
599C2×C4—1343no—
600C2×C4—1348no—
601C2×C4—1341no—
602C2×C4—1343no—
603C2×C4—1343no—
604C2×C4—1343no—
605C2×C4—1343no—
606C2×C4—1341no—
607C2×C4—1343no—
608C2×C4—1343no—
609C2×C4—13424no—
610C2×C4C22×C4×D6716yes—
611C2×C4C22×C4×D6716yes—
612C2×C4C2×D4×D6716yes—
613C2×C4C2×Q8×D6712yes—
614C2×C4C2×Q8×D6712yes—
615C2×C4C2×#1176162716yes—
616C22—22no—
617C22—22no—
618C22—22no—
619C22—22no—
620C22—22no—
621C22—22no—
622C22—674no—
623C22—1342no—
624C22—1342no—
625C22—1342no—
626C22—1342no—
627C22—1342no—
628C22—1342no—
629C22C4×Q8×D6714yescomplemented
630C22C23×C4×D6711yescharacteristic
631C22C22×D4×D6711yescharacteristic
632C22C22×Q8×D6711yescharacteristic
633C22C2×#41×D6711yescharacteristic
634C22C22×#1176162711yescharacteristic
635C222−1+4×D6711yescharacteristic
636C22#1686423311yescharacteristic
637C4—26no—
638C4—22no—
639C4—22no—
640C4—43no—
641C4—43no—
642C4—2683no—
643C4—674no—
644C4—674no—
645C4—1346no—
646C4—1346no—
647C4—1342no—
648C4—1346no—
649C4C2×(C22⋊D67)⋊C4112yes—
650C2—24no—
651C2—1344no—
652C2C22×(C22⋊D67)⋊C411yescharacteristic
653C2C2×C4×Q8×D6711yescharacteristic
654C2#2257341811yescharacteristic
655C2D4×Q8×D6711yescharacteristic
656C2#2257369811yescharacteristic
657C2Q8×#1176162711yescharacteristic
658C2#2257382511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D67
commutatorC22×C67C24×C4
FittingQ8×C22⋊C4×C67C2
socle, cosocleC23×C67C25
prime radicalC22×C22⋊D67C23
hypercenterQ8×C22⋊C4D67
hypocenterC67C4×D4×Q8
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C23 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×Q8×Dic67C2semidirect
3. C2×C4×Q8×D67C2semidirect
4. #22563266C2semidirect
5. #22563219C2semidirect
6. #22563212C2semidirect
7. Q8×Dic67⋊C4C2semidirect
9. Q8×(C2×D67)⋊C4C2semidirect
10. #22562778C2semidirect
11. #22562747C2semidirect
12. #22562737C2semidirect
13. C4×Q8×Dic67C2semidirect
15. Q8×C22⋊C4×C67C2semidirect
17. Q8×C22⋊D67C4semidirect
72. C2×Q8×D67C2×C4semidirect
79. #14524041C2×C4semidirect
80. #14524022C2×C4semidirect
81. #14524019C2×C4semidirect
85. Q8×Dic67C2×C4semidirect
86. Q8×Dic67D4semidirect
91. (C22⋊D67)⋊C4Q8direct (N × H)
129. C22×Q8×C67C2×C4semidirect
157. C22×Dic67C2×Q8semidirect
173. C2×C4×D67C2×Q8semidirect
183. Dic67⋊C4C2×Q8semidirect
187. (C2×D67)⋊C4C2×Q8semidirect
198. C4×Dic67C2×Q8semidirect
219. C22⋊C4×C67C2×Q8semidirect
238. Q8×C67C4×D4semidirect
258. C22⋊D67C4×Q8semidirect
292. C22×C67C2×C4×Q8semidirect
306. C2×D67C2×C4×Q8semidirect
318. Dic67C2×C4×Q8semidirect
319. Dic67D4×Q8semidirect
339. Q8×C22⋊C4D67semidirect
345. C67C4×D4×Q8semidirect
405. C22×Q8C4×D67semidirect
538. C22⋊C4Q8×D67semidirect
569. Q8(C22⋊D67)⋊C4direct (N × H)
629. C22C4×Q8×D67semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D672
C22×Q8×Dic672
C2×C4×Q8×D672
#225632662
#225632192
#225632122
Q8×Dic67⋊C42
#225631052
Q8×(C2×D67)⋊C42
#225627782
#225627472
#225627372
C4×Q8×Dic672
C4×(C22⋊D67)⋊C42
Q8×C22⋊C4×C672
C4×D4×Q867