Subgroups — D₈×Dic₄₇ #15689206

Order 3008.

134 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×Dic₄₇	C₂	1	2	yes	maximal, complemented
2	#13093958	C₂	1	1	yes	maximal, characteristic, complemented
3	#13093945	C₂	1	2	yes	maximal, complemented
4	C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₂×D₄×C₄₇	C₂²	1	2	yes	—
7	C₂²×Dic₄₇	—	2	2	no	—
8	D₈×C₄₇	C₄	1	4	yes	complemented
9	C₂×C₈×C₄₇	C₂²	1	1	yes	characteristic
10	C₂²⋊Dic₄₇	—	2	2	no	—
11	C₄⋊Dic₄₇	C₂²	1	2	yes	—
12	C₄×Dic₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	C₂³×C₄₇	—	2	2	no	—
15	D₄×C₄₇	—	2	2	no	—
16	D₄×C₄₇	C₂×C₄	1	4	yes	complemented
17	C₂×C₄×C₄₇	C₂³	1	1	yes	characteristic
18	C₂×Dic₄₇	—	2	2	no	—
19	C₂×Dic₄₇	—	4	4	no	—
20	C₂×Dic₄₇	D₄	1	1	yes	characteristic
21	C₂×Dic₄₇	D₄	1	1	yes	characteristic
22	C₈×C₄₇	C₂×C₄	1	2	yes	complemented
23	C₄₇⋊C₈	—	2	1	no	—
24	C₂²×C₄₇	—	2	4	no	—
25	C₂²×C₄₇	—	4	2	no	—
26	C₂²×C₄₇	—	4	2	no	—
27	C₂²×C₄₇	C₂×D₄	1	1	yes	characteristic
28	C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
29	C₄×C₄₇	#41	1	1	yes	characteristic
30	Dic₄₇	—	2	1	no	—
31	Dic₄₇	—	4	2	no	—
32	Dic₄₇	D₈	1	2	yes	direct product factor
33	C₂×C₄₇	—	4	4	no	—
34	C₂×C₄₇	C₄×D₄	1	1	yes	characteristic
35	C₂×C₄₇	C₂×D₈	1	1	yes	characteristic
36	C₂×C₄₇	#135	1	1	yes	characteristic
37	C₄×D₈	—	47	1	no	maximal, Sylow
38	C₄₇	C₄×D₈	1	1	yes	characteristic, complemented, Sylow
39	C₂×D₈	D₄₇	1	1	yes	characteristic
40	C₄×D₄	—	47	2	no	—
41	#107	—	47	1	no	—
42	#102	—	47	2	no	—
43	C₄×C₈	—	47	1	no	—
44	C₂×D₄	C₂×D₄₇	1	2	yes	—
45	C₂²×C₄	—	94	2	no	—
46	D₈	Dic₄₇	1	4	yes	direct product factor
47	C₂×C₈	—	47	1	no	—
48	C₂×C₈	C₂×D₄₇	1	1	yes	characteristic
49	C₄⋊C₄	—	47	2	no	—
50	C₂²⋊C₄	—	94	2	no	—
51	C₄²	—	47	1	no	—
52	C₂³	—	2	2	no	—
53	D₄	—	2	2	no	—
54	D₄	C₂×Dic₄₇	1	4	yes	complemented
55	C₂×C₄	—	47	1	no	—
56	C₂×C₄	—	47	1	no	—
57	C₂×C₄	—	94	2	no	—
58	C₂×C₄	—	188	4	no	—
59	C₂×C₄	C₂²×D₄₇	1	1	yes	characteristic
60	C₈	—	94	1	no	—
61	C₈	C₂×Dic₄₇	1	2	yes	complemented
62	C₂²	—	2	4	no	—
63	C₂²	—	4	2	no	—
64	C₂²	—	4	2	no	—
65	C₂²	D₄×D₄₇	1	1	yes	characteristic
66	C₄	—	47	2	no	—
67	C₄	—	94	1	no	—
68	C₄	—	188	2	no	—
69	C₄	#10625352	1	1	yes	characteristic
70	C₄	C₂²×Dic₄₇	1	1	yes	characteristic
71	C₂	—	4	4	no	—
72	C₂	D₄×Dic₄₇	1	1	yes	characteristic
73	C₂	D₈×D₄₇	1	1	yes	characteristic
74	C₂	#13094043	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₄
Frattini	C₂×C₄	C₂²×D₄₇
Fitting, prime radical	C₂×D₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂×D₄
cosocle	C₂×C₄×C₄₇	C₂³
hypercenter	C₂×D₈	D₄₇
hypocenter	C₄₇	C₄×D₈
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×D₈

Complements

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

N	H ≅ G/N	type
1. D₄×Dic₄₇	C₂	semidirect
2. #13093958	C₂	semidirect
3. #13093945	C₂	semidirect
4. C₈×Dic₄₇	C₂	semidirect
8. D₈×C₄₇	C₄	semidirect
16. D₄×C₄₇	C₂×C₄	semidirect
22. C₈×C₄₇	C₂×C₄	semidirect
32. Dic₄₇	D₈	direct (N × H)
38. C₄₇	C₄×D₈	semidirect
46. D₈	Dic₄₇	direct (N × H)
54. D₄	C₂×Dic₄₇	semidirect
61. C₈	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
D₄×Dic₄₇	2
#13093958	2
#13093945	2
C₈×Dic₄₇	2
C₂×D₈×C₄₇	2
C₄×D₈	47

Subgroups — D8×Dic47 #15689206

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₈×Dic₄₇ #15689206