Subgroups — C₄⋊Q₈×D₄₇ #15689664

Order 3008.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×D₄₇	C₂	1	2	yes	maximal
2	#13094024	C₂	1	1	yes	maximal, characteristic, complemented
3	#13094023	C₂	1	4	yes	maximal, complemented
4	#13094022	C₂	1	2	yes	maximal, complemented
5	C₄⋊C₄×D₄₇	C₂	1	4	yes	maximal
6	C₄²×D₄₇	C₂	1	1	yes	maximal, characteristic
7	C₄⋊Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×Q₈×C₄₇	C₂²	1	2	yes	—
9	Q₈×D₄₇	—	2	8	no	—
10	C₂×C₄×D₄₇	C₂²	1	4	yes	—
11	C₂×C₄×D₄₇	C₂²	1	1	yes	characteristic
12	C₂×C₄×D₄₇	C₂²	1	2	yes	—
13	C₂×Dic₉₄	C₂²	1	2	yes	—
14	C₂×Dic₉₄	C₂²	1	4	yes	—
15	C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
16	C₄²×C₄₇	C₂²	1	1	yes	characteristic
17	C₄⋊Dic₄₇	C₂²	1	4	yes	—
18	Dic₄₇⋊C₄	C₂²	1	8	yes	—
19	C₄×Dic₄₇	C₂²	1	1	yes	characteristic
20	C₄×Dic₄₇	C₂²	1	2	yes	—
21	C₂²×D₄₇	C₂³	1	1	yes	characteristic
22	Q₈×C₄₇	—	2	4	no	—
23	C₂×C₄×C₄₇	C₂³	1	4	yes	—
24	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
25	C₂×C₄×C₄₇	C₂³	1	2	yes	—
26	C₂×Dic₄₇	C₂³	1	4	yes	—
27	C₂×Dic₄₇	C₂³	1	1	yes	characteristic
28	C₂×Dic₄₇	C₂³	1	2	yes	—
29	C₄×D₄₇	—	2	8	no	—
30	C₄×D₄₇	D₄	1	4	yes	—
31	C₄×D₄₇	Q₈	1	8	yes	complemented
32	Dic₉₄	—	2	4	no	—
33	Dic₉₄	—	2	8	no	—
34	C₂²×C₄₇	C₂⁴	1	1	yes	characteristic
35	C₂×D₄₇	C₂×D₄	1	2	yes	—
36	C₂×D₄₇	C₂×Q₈	1	4	yes	—
37	C₄×C₄₇	—	2	4	no	—
38	C₄×C₄₇	C₂×D₄	1	2	yes	—
39	C₄×C₄₇	C₂×Q₈	1	4	yes	complemented
40	Dic₄₇	—	2	4	no	—
41	Dic₄₇	C₂×D₄	1	2	yes	—
42	Dic₄₇	C₂×Q₈	1	4	yes	complemented
43	C₂×C₄₇	C₂²×D₄	1	1	yes	characteristic
44	C₂×C₄₇	C₂²×Q₈	1	2	yes	—
45	D₄₇	C₄⋊Q₈	1	4	yes	direct product factor
46	C₂×C₄⋊Q₈	—	47	1	no	maximal, Sylow
47	C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic, complemented, Sylow
48	C₂²×Q₈	—	47	2	no	—
49	C₄⋊Q₈	—	47	2	no	—
50	C₄⋊Q₈	—	47	4	no	—
51	C₄⋊Q₈	—	47	1	no	—
52	C₄⋊Q₈	D₄₇	1	1	yes	characteristic, direct product factor
53	C₂×C₄⋊C₄	—	47	4	no	—
54	C₂×C₄²	—	47	1	no	—
55	C₂×Q₈	—	47	4	no	—
56	C₂×Q₈	—	47	2	no	—
57	C₂×Q₈	—	94	8	no	—
58	C₂×Q₈	C₂×D₄₇	1	2	yes	—
59	C₂²×C₄	—	47	2	no	—
60	C₂²×C₄	—	47	1	no	—
61	C₂²×C₄	—	47	4	no	—
62	C₄⋊C₄	—	47	8	no	—
63	C₄⋊C₄	—	47	4	no	—
64	C₄⋊C₄	C₂×D₄₇	1	4	yes	—
65	C₄²	—	47	1	no	—
66	C₄²	—	47	2	no	—
67	C₄²	C₂×D₄₇	1	1	yes	characteristic
68	C₂³	—	47	1	no	—
69	Q₈	—	2	4	no	—
70	Q₈	—	94	8	no	—
71	Q₈	—	94	4	no	—
72	C₂×C₄	—	47	2	no	—
73	C₂×C₄	—	47	1	no	—
74	C₂×C₄	—	47	4	no	—
75	C₂×C₄	—	47	8	no	—
76	C₂×C₄	—	47	4	no	—
77	C₂×C₄	—	94	8	no	—
78	C₂×C₄	C₂²×D₄₇	1	4	yes	—
79	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
80	C₂×C₄	C₂²×D₄₇	1	2	yes	—
81	C₂²	—	47	2	no	—
82	C₂²	—	47	4	no	—
83	C₂²	C₂³×D₄₇	1	1	yes	characteristic
84	C₄	—	2	4	no	—
85	C₄	—	47	2	no	—
86	C₄	—	47	4	no	—
87	C₄	—	94	4	no	—
88	C₄	D₄×D₄₇	1	2	yes	—
89	C₄	Q₈×D₄₇	1	4	yes	complemented
90	C₂	—	47	4	no	—
91	C₂	C₂×D₄×D₄₇	1	1	yes	characteristic
92	C₂	C₂×Q₈×D₄₇	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²	C₂³×D₄₇
commutator, socle, cosocle	C₂²×C₄₇	C₂⁴
Fitting	C₄⋊Q₈×C₄₇	C₂
prime radical	C₂²×D₄₇	C₂³
hypercenter	C₄⋊Q₈	D₄₇
hypocenter	C₄₇	C₂×C₄⋊Q₈
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
2. #13094024	C₂	semidirect
3. #13094023	C₂	semidirect
4. #13094022	C₂	semidirect
7. C₄⋊Q₈×C₄₇	C₂	semidirect
31. C₄×D₄₇	Q₈	semidirect
39. C₄×C₄₇	C₂×Q₈	semidirect
42. Dic₄₇	C₂×Q₈	semidirect
45. D₄₇	C₄⋊Q₈	direct (N × H)
47. C₄₇	C₂×C₄⋊Q₈	semidirect
52. C₄⋊Q₈	D₄₇	direct (N × H)
89. C₄	Q₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₈×D₄₇	2
#13094024	2
#13094023	2
#13094022	2
C₄⋊C₄×D₄₇	2
C₄²×D₄₇	2
C₄⋊Q₈×C₄₇	2
C₂×C₄⋊Q₈	47

Subgroups — C4⋊Q8×D47 #15689664

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊Q₈×D₄₇ #15689664