Finite Group Databasebeta

← C4×Q8×C22⋊D67 #31015693

Subgroups — C4×Q8×C22⋊D67 #31015693

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
2C2×C4×Q8×D67C211yesmaximal, characteristic, complemented
3#22563263C213yesmaximal, complemented
4#22563214C213yesmaximal, complemented
5#22563210C213yesmaximal, complemented
6Q8×Dic67⋊C4C211yesmaximal, characteristic, complemented
7C4⋊C4×C22⋊D67C213yesmaximal
8Q8×C22⋊Dic67C211yesmaximal, characteristic, complemented
9Q8×(C2×D67)⋊C4C211yesmaximal, characteristic, complemented
10C4×#14524041C213yesmaximal, complemented
11C4×#14524022C213yesmaximal, complemented
12C4×#14524019C213yesmaximal, complemented
13C4×Q8×Dic67C211yesmaximal, characteristic, complemented
14C42×C22⋊D67C213yesmaximal
15C22×C4×Q8×C67C211yesmaximal, characteristic, complemented
16C22×Q8×D67C2211yescharacteristic
17Q8×C22⋊D67C4116yesdirect product factor
18C2×#14524041C2213yes—
19C2×#14524022C2213yes—
20C2×#14524019C2213yes—
21C2×Q8×Dic67C2211yescharacteristic
22C2×Q8×Dic67C2211yescharacteristic
23C2×Q8×Dic67C2211yescharacteristic
24C2×C4×Dic134C2213yes—
25C2×#14524008C2213yes—
26C4×Q8×D67—28no—
27C2×C4×C22⋊D67C2213yes—
28C2×C4×C22⋊D67C2213yes—
29C2×C4×C22⋊D67C2211yescharacteristic
30C2×C4⋊C4×D67C2213yes—
31C2×C42×D67C2213yes—
32#16863303C2213yes—
33#16863303C2213yes—
34#16863302C2213yes—
35#16863301C2213yes—
36#16863294C2213yes—
37#16863292C2213yes—
38#16863291C2216yes—
39#16863291C2216yes—
40#16863280C2216yes—
41#16863277C2216yes—
42#16863269C2216yes—
43#16863267C2216yes—
44#16863265C2213yes—
45#16863256C2213yes—
46#16863253C2213yes—
47C4⋊C4×Dic67C2213yes—
48C4⋊C4×Dic67C2213yes—
49C4×Dic67⋊C4C2213yes—
50C4×Dic67⋊C4C2216yes—
51C4×Dic67⋊C4C2213yes—
52C4×Dic67⋊C4C2213yes—
53C4×C4⋊Dic67C2213yes—
54C4×(C2×D67)⋊C4C2213yes—
55C4×(C2×D67)⋊C4C2213yes—
56C4×(C2×D67)⋊C4C2213yes—
57C4×C22⋊Dic67C2213yes—
58C4×C22⋊Dic67C2213yes—
59C4×C22⋊Dic67C2213yes—
60C42×Dic67C2213yes—
61C23×Q8×C67C2211yescharacteristic
62C2×C4×Q8×C67—28no—
63C2×C4×Q8×C67C2211yescharacteristic
64C2×C4×Q8×C67C2213yes—
65C2×C4×Q8×C67C2213yes—
66C2×C4×Q8×C67C2211yescharacteristic
67C22×C4⋊C4×C67C2213yes—
68C22×C42×C67C2213yes—
69C22×Dic134C2313yes—
70C2×Q8×D67—24no—
71C2×Q8×D67—24no—
72C2×Q8×D67C2×C418yescomplemented
73C22×C22⋊D67C2311yescharacteristic
74C22×C4×D67C2313yes—
75C22×C4×D67C2313yes—
76C22×C4×D67C2311yescharacteristic
77#14524041C2×C4124yescomplemented
78#14524022C2×C4124yescomplemented
79#14524019C2×C4124yescomplemented
80Q8×Dic67—24no—
81Q8×Dic67—24no—
82Q8×Dic67C2×C418yescomplemented
83C4×Dic134—212no—
84#14524008—212no—
85C4×C22⋊D67—212no—
86C4×C22⋊D67C2×C4124yes—
87C4×C22⋊D67Q818yesdirect product factor
88C2×C4⋊Dic67C2313yes—
89C2×C4⋊Dic67C2313yes—
90C2×C4⋊Dic67C2313yes—
91C2×Dic67⋊C4C2313yes—
92C2×Dic67⋊C4C2316yes—
93C2×Dic67⋊C4C2316yes—
94C2×Dic67⋊C4C2313yes—
95C2×Dic67⋊C4C2316yes—
96C2×Dic67⋊C4C2311yescharacteristic
97C4⋊C4×D67—212no—
98C2×C22⋊Dic67C2313yes—
99C2×C22⋊Dic67C2313yes—
100C2×C22⋊Dic67C2311yescharacteristic
101C2×(C2×D67)⋊C4C2313yes—
102C2×(C2×D67)⋊C4C2313yes—
103C2×(C2×D67)⋊C4C2311yescharacteristic
104C2×C4×Dic67C2313yes—
105C2×C4×Dic67C2313yes—
106C2×C4×Dic67C2313yes—
107C2×C4×Dic67C2313yes—
108C2×C4×Dic67C2313yes—
109C2×C4×Dic67C2313yes—
110C2×C4×Dic67C2313yes—
111C2×C4×Dic67C2313yes—
112C2×C4×Dic67C2311yescharacteristic
113C42×D67—212no—
114C67⋊#95C2313yes—
115C67⋊#95C2313yes—
116C67⋊#95C2313yes—
117C67⋊#95C2313yes—
118C67⋊#95C2313yes—
119C67⋊#95C2313yes—
120C67⋊#95C2316yes—
121C67⋊#95C2316yes—
122C67⋊#95C2316yes—
123C22×Q8×C67—24no—
124C22×Q8×C67—24no—
125C22×Q8×C67C2×C418yescomplemented
126C22×Q8×C67C2313yes—
127C22×Q8×C67C2311yescharacteristic
128C23×C4×C67C2313yes—
129C23×C4×C67C2313yes—
130C23×C4×C67C2311yescharacteristic
131C4×Q8×C67—24no—
132C4×Q8×C67—212no—
133C4×Q8×C67—212no—
134C4×Q8×C67D418yescomplemented
135C2×C4⋊C4×C67—212no—
136C2×C4⋊C4×C67C2313yes—
137C2×C4⋊C4×C67C2316yes—
138C2×C4⋊C4×C67C2313yes—
139C2×C42×C67—212no—
140C2×C42×C67C2313yes—
141C2×C42×C67C2313yes—
142C2×C42×C67C2313yes—
143C2×C42×C67C2313yes—
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×Dic67C2413yes—
153C22×Dic67C2413yes—
154C22×Dic67C2413yes—
155C22×Dic67C2413yes—
156C22×Dic67C2411yescharacteristic
157C22×Dic67C2411yescharacteristic
158C22×Dic67C2411yescharacteristic
159C2×C4×D67—22no—
160C2×C4×D67—26no—
161C2×C4×D67—26no—
162C2×C4×D67—22no—
163C2×C4×D67—26no—
164C2×C4×D67—26no—
165C2×C4×D67—43no—
166C2×C4×D67C22×C4112yes—
167C2×C4×D67C2×Q814yescomplemented
168C4⋊Dic67—26no—
169C4⋊Dic67—26no—
170C4⋊Dic67C22×C4112yes—
171Dic67⋊C4—212no—
172Dic67⋊C4—26no—
173Dic67⋊C4—46no—
174Dic67⋊C4C22×C4112yes—
175Dic67⋊C4C22×C4124yes—
176Dic67⋊C4C2×Q814yescomplemented
177C22⋊Dic67—26no—
178C22⋊Dic67C22×C4112yes—
179C22⋊Dic67C2×Q814yescomplemented
180(C2×D67)⋊C4—26no—
181(C2×D67)⋊C4C22×C4112yes—
182(C2×D67)⋊C4C2×Q814yescomplemented
183C4×Dic67—26no—
184C4×Dic67—26no—
185C4×Dic67—26no—
186C4×Dic67—26no—
187C4×Dic67—26no—
188C4×Dic67—26no—
189C4×Dic67—43no—
190C4×Dic67C22×C4112yes—
191C4×Dic67C2×Q814yescomplemented
192C24×C67C2411yescharacteristic
193C2×Q8×C67—232no—
194C2×Q8×C67—26no—
195C2×Q8×C67—26no—
196C2×Q8×C67C22×C4112yes—
197C2×Q8×C67C22×C414yes—
198C2×Q8×C67C2×D414yes—
199C2×Q8×C67#4114yes—
200C22×C4×C67—22no—
201C22×C4×C67—26no—
202C22×C4×C67—26no—
203C22×C4×C67—22no—
204C22×C4×C67—26no—
205C22×C4×C67—26no—
206C22×C4×C67—43no—
207C22×C4×C67C22×C4112yes—
208C22×C4×C67C2×Q814yescomplemented
209C22×C4×C67C2413yes—
210C22×C4×C67C2413yes—
211C22×C4×C67C2413yes—
212C22×C4×C67C2411yescharacteristic
213C22×C4×C67C2413yes—
214C22×C4×C67C2411yescharacteristic
215C4⋊C4×C67—212no—
216C4⋊C4×C67—26no—
217C4⋊C4×C67C2×D4112yes—
218C42×C67—26no—
219C42×C67—26no—
220C42×C67—26no—
221C42×C67C2×D4112yes—
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—23no—
242C2×C4×C67—23no—
243C2×C4×C67—21no—
244C2×C4×C67—23no—
245C2×C4×C67—224no—
246C2×C4×C67—28no—
247C2×C4×C67—23no—
248C2×C4×C67—23no—
249C2×C4×C67—23no—
250C2×C4×C67—412no—
251C2×C4×C67C23×C416yes—
252C2×C4×C67C23×C416yes—
253C2×C4×C67C22×D416yes—
254C2×C4×C67C22×D416yes—
255C2×C4×C67C22×D412yes—
256C2×C4×C67C22×Q812yes—
257C2×C4×C67C22×Q812yes—
258C2×C4×C67C2×#4116yes—
259C2×C4×C672−1+412yes—
260C22⋊D67C4×Q8116yesdirect product factor
261C2×Dic67—21no—
262C2×Dic67—23no—
263C2×Dic67—21no—
264C2×Dic67—23no—
265C2×Dic67—23no—
266C2×Dic67—21no—
267C2×Dic67—21no—
268C2×Dic67—23no—
269C2×Dic67—23no—
270C2×Dic67—23no—
271C2×Dic67—23no—
272C2×Dic67—23no—
273C2×Dic67—23no—
274C2×Dic67—23no—
275C2×Dic67C23×C416yes—
276C2×Dic67C23×C416yes—
277C2×Dic67C23×C412yes—
278C2×Dic67C22×Q812yes—
279C2×Dic67C22×Q812yes—
280C2×Dic67C22×Q812yes—
281C2×Dic67C2×#4112yes—
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—26no—
310C4×C67—43no—
311C4×C67C2×C4×D4112yes—
312C4×C67D4×Q814yescomplemented
313Dic67—26no—
314Dic67—26no—
315Dic67—22no—
316Dic67—22no—
317Dic67—43no—
318Dic67—43no—
319Dic67C2×C4×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×Q8D6711yescharacteristic, complemented
333#2365—673no—
334#2360—673no—
335#2360—673no—
336Q8×C4⋊C4—671no—
337D4×C4⋊C4—673no—
338Q8×C22⋊C4—671no—
339Q8×C22⋊C4—671no—
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—28no—
353C2×C4×Q8—671no—
354C2×C4×Q8—671no—
355C2×C4×Q8—671no—
356C2×C4×Q8—673no—
357C2×C4×Q8—673no—
358C2×C4×Q8—1348no—
359C2×C4×Q8C2×D6713yes—
360C2×C4×Q8C2×D6711yescharacteristic
361C2×C4×Q8C2×D6713yes—
362C2×C4×Q8C2×D6711yescharacteristic
363C2×C4×D4—673no—
364C2×C4×D4—671no—
365C2×C4×D4—673no—
366C22×C4⋊C4—673no—
367C22×C4⋊C4C2×D6713yes—
368C22×C42—673no—
369C22×C42C2×D6713yes—
370#391—673no—
371#391—673no—
372#391—673no—
373#391—673no—
374#389—676no—
375#389—676no—
376#389—673no—
377#389—673no—
378#387—676no—
379#387—676no—
380#385—676no—
381#385—676no—
382#384—673no—
383#380—673no—
384#380—673no—
385C4×C4⋊C4—673no—
386C4×C4⋊C4—673no—
387C4×C4⋊C4—673no—
388C4×C4⋊C4—676no—
389C4×C4⋊C4—673no—
390C4×C4⋊C4—673no—
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⋊C4—673no—
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×C4C22×D6713yes—
413C23×C4C22×D6713yes—
414C23×C4C22×D6711yescharacteristic
415C4⋊Q8—6724no—
416C22⋊Q8—6724no—
417C22⋊Q8—6724no—
418C4×Q8—24no—
419C4×Q8—212no—
420C4×Q8—212no—
421C4×Q8—678no—
422C4×Q8—1344no—
423C4×Q8—1344no—
424C4×Q8—13412no—
425C4×Q8—13412no—
426C4×Q8C22⋊D6718yesdirect product factor
427C4×D4—6724no—
428C4×D4—678no—
429C4×D4—13412no—
430C2×C4⋊C4—212no—
431C2×C4⋊C4—676no—
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—673no—
439C2×C4⋊C4—673no—
440C2×C4⋊C4—13412no—
441C2×C4⋊C4C22×D6713yes—
442C2×C4⋊C4C22×D6716yes—
443C2×C4⋊C4C22×D6713yes—
444C2×C22⋊C4—673no—
445C2×C22⋊C4—671no—
446C2×C22⋊C4—673no—
447C2×C22⋊C4—671no—
448C2×C22⋊C4—673no—
449C2×C22⋊C4—673no—
450C2×C42—212no—
451C2×C42—673no—
452C2×C42—673no—
453C2×C42—671no—
454C2×C42—673no—
455C2×C42—673no—
456C2×C42—673no—
457C2×C42—673no—
458C2×C42—673no—
459C2×C42—673no—
460C2×C42—13412no—
461C2×C42C22×D6713yes—
462C2×C42C22×D6713yes—
463C2×C42C22×D6713yes—
464C2×C42C22×D6713yes—
465#95—673no—
466#95—673no—
467#95—673no—
468#95—673no—
469#95—673no—
470#95—673no—
471#95—676no—
472#95—676no—
473#95—676no—
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×Q8C2×C22⋊D6714yes—
486C2×Q8#1176162814yes—
487C2×D4—674no—
488C2×D4—674no—
489C2×D4—674no—
490C22×C4—22no—
491C22×C4—26no—
492C22×C4—26no—
493C22×C4—22no—
494C22×C4—26no—
495C22×C4—26no—
496C22×C4—43no—
497C22×C4—2683no—
498C22×C4—671no—
499C22×C4—671no—
500C22×C4—671no—
501C22×C4—673no—
502C22×C4—673no—
503C22×C4—6712no—
504C22×C4—674no—
505C22×C4—673no—
506C22×C4—673no—
507C22×C4—1346no—
508C22×C4—1346no—
509C22×C4—1342no—
510C22×C4—1346no—
511C22×C4—1346no—
512C22×C4—1342no—
513C22×C4C2×C4×D67112yes—
514C22×C4Q8×D6714yescomplemented
515C22×C4C23×D6713yes—
516C22×C4C23×D6713yes—
517C22×C4C23×D6713yes—
518C22×C4C23×D6711yescharacteristic
519C22×C4C23×D6713yes—
520C22×C4C23×D6711yescharacteristic
521C4⋊C4—212no—
522C4⋊C4—26no—
523C4⋊C4—2686no—
524C4⋊C4—6712no—
525C4⋊C4—6712no—
526C4⋊C4—6724no—
527C4⋊C4—674no—
528C4⋊C4—1346no—
529C4⋊C4—13412no—
530C4⋊C4—1346no—
531C4⋊C4—1346no—
532C4⋊C4C2×C22⋊D67112yes—
533C22⋊C4—6712no—
534C22⋊C4—674no—
535C22⋊C4—6712no—
536C22⋊C4—674no—
537C22⋊C4—1346no—
538C22⋊C4—1346no—
539C42—26no—
540C42—26no—
541C42—26no—
542C42—2683no—
543C42—6712no—
544C42—674no—
545C42—1346no—
546C42—1346no—
547C42—1346no—
548C42—1346no—
549C42—1346no—
550C42—1346no—
551C42C2×C22⋊D67112yes—
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—
569Q8C4×C22⋊D67116yesdirect product factor
570D4—6716no—
571C2×C4—21no—
572C2×C4—23no—
573C2×C4—23no—
574C2×C4—23no—
575C2×C4—21no—
576C2×C4—23no—
577C2×C4—28no—
578C2×C4—224no—
579C2×C4—23no—
580C2×C4—23no—
581C2×C4—23no—
582C2×C4—412no—
583C2×C4—26812no—
584C2×C4—672no—
585C2×C4—672no—
586C2×C4—672no—
587C2×C4—676no—
588C2×C4—676no—
589C2×C4—672no—
590C2×C4—672no—
591C2×C4—1343no—
592C2×C4—1343no—
593C2×C4—1343no—
594C2×C4—1343no—
595C2×C4—1343no—
596C2×C4—1343no—
597C2×C4—1341no—
598C2×C4—1343no—
599C2×C4—1341no—
600C2×C4—1343no—
601C2×C4—1343no—
602C2×C4—1341no—
603C2×C4—1341no—
604C2×C4—1343no—
605C2×C4—1348no—
606C2×C4—13424no—
607C2×C4C22×C4×D6716yes—
608C2×C4C22×C4×D6716yes—
609C2×C4C22×C22⋊D6716yes—
610C2×C4C22×C22⋊D6712yes—
611C2×C4C22×C22⋊D6716yes—
612C2×C4C2×Q8×D6712yes—
613C2×C4C2×Q8×D6712yes—
614C2×C4C2×#1176162816yes—
615C2×C4#1452409112yes—
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
631C22C23×C22⋊D6711yescharacteristic
632C22C22×Q8×D6711yescharacteristic
633C22C2×#41×D6711yescharacteristic
634C22C22×#1176162811yescharacteristic
635C22C2×#1452409111yescharacteristic
636C22#1686423211yescharacteristic
637C4—26no—
638C4—22no—
639C4—26no—
640C4—43no—
641C4—2683no—
642C4—2683no—
643C4—674no—
644C4—1346no—
645C4—1346no—
646C4—1342no—
647C4—1342no—
648C4C2×C4×C22⋊D67112yes—
649C4Q8×C22⋊D6714yesdirect product factor
650C2—24no—
651C2—1344no—
652C2C22×C4×C22⋊D6711yescharacteristic
653C2C2×C4×Q8×D6711yescharacteristic
654C2C4×#1452409111yescharacteristic
655C2C2×Q8×C22⋊D6711yescharacteristic
656C2#41×C22⋊D6711yescharacteristic
657C2Q8×#1176162811yescharacteristic
658C2#2257382611yescharacteristic
subgroupG/H
centerC22×C4C23×D67
commutatorC22×C67C24×C4
FrattiniC23C24×D67
FittingC22×C4×Q8×C67C2
socle, cosocleC23×C67C25
prime radicalC22×C22⋊D67C23
hypercenterC22×C4×Q8D67
hypocenterC67C4×D4×Q8
LCSG ▷ C22×C67 ▷ C67
UCSC1 ◁ C22×C4 ◁ C22×C4×Q8

Complements

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

NH ≅ G/Ntype
2. C2×C4×Q8×D67C2semidirect
3. #22563263C2semidirect
4. #22563214C2semidirect
5. #22563210C2semidirect
6. Q8×Dic67⋊C4C2semidirect
8. Q8×C22⋊Dic67C2semidirect
9. Q8×(C2×D67)⋊C4C2semidirect
10. C4×#14524041C2semidirect
11. C4×#14524022C2semidirect
12. C4×#14524019C2semidirect
13. C4×Q8×Dic67C2semidirect
15. C22×C4×Q8×C67C2semidirect
17. Q8×C22⋊D67C4direct (N × H)
72. C2×Q8×D67C2×C4semidirect
77. #14524041C2×C4semidirect
78. #14524022C2×C4semidirect
79. #14524019C2×C4semidirect
82. Q8×Dic67C2×C4semidirect
87. C4×C22⋊D67Q8direct (N × H)
125. C22×Q8×C67C2×C4semidirect
134. C4×Q8×C67D4semidirect
167. C2×C4×D67C2×Q8semidirect
176. Dic67⋊C4C2×Q8semidirect
179. C22⋊Dic67C2×Q8semidirect
182. (C2×D67)⋊C4C2×Q8semidirect
191. C4×Dic67C2×Q8semidirect
208. C22×C4×C67C2×Q8semidirect
238. Q8×C67C4×D4semidirect
260. C22⋊D67C4×Q8direct (N × H)
292. C22×C67C2×C4×Q8semidirect
306. C2×D67C2×C4×Q8semidirect
312. C4×C67D4×Q8semidirect
319. Dic67C2×C4×Q8semidirect
332. C22×C4×Q8D67semidirect
345. C67C4×D4×Q8semidirect
405. C22×Q8C4×D67semidirect
426. C4×Q8C22⋊D67direct (N × H)
514. C22×C4Q8×D67semidirect
569. Q8C4×C22⋊D67direct (N × H)
629. C22C4×Q8×D67semidirect
649. C4Q8×C22⋊D67direct (N × H)

Maximal subgroups

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

subgroupindex
C2×Q8×C22⋊D672
C2×C4×Q8×D672
#225632632
#225632142
#225632102
Q8×Dic67⋊C42
C4⋊C4×C22⋊D672
Q8×C22⋊Dic672
Q8×(C2×D67)⋊C42
C4×#145240412
C4×#145240222
C4×#145240192
C4×Q8×Dic672
C42×C22⋊D672
C22×C4×Q8×C672
C4×D4×Q867