Subgroups — (C₂×#14524194)⋊C₈ #46831040

Order 34624.

118 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₅₄₁⋊C₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#14524194	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×D₅₄₁	C₂	1	1	yes	maximal, characteristic
4	C₂²×#14524194	C₄	1	2	yes	—
5	D₅₄₁⋊C₈	—	2	1	no	—
6	D₅₄₁⋊C₈	—	2	1	no	—
7	C₂×#16864520	C₄	1	2	yes	complemented
8	C₄×#14524194	—	2	1	no	—
9	C₄×#14524194	—	2	1	no	—
10	C₂×C₄×D₅₄₁	C₂²	1	1	yes	characteristic
11	C₂×#16864513	C₄	1	1	yes	characteristic, complemented
12	C₈×D₅₄₁	—	2	1	no	—
13	C₈×D₅₄₁	—	2	1	no	—
14	C₂×C₈×C₅₄₁	C₄	1	1	yes	characteristic, complemented
15	C₂×#14524194	—	2	2	no	—
16	C₂×#14524194	—	2	2	no	—
17	C₂×#14524194	C₈	1	4	yes	complemented
18	#16864520	—	2	2	no	—
19	C₂²×D₅₄₁	C₂×C₄	1	1	yes	characteristic
20	C₂×Dic₅₄₁	C₂×C₄	1	1	yes	characteristic
21	C₄×D₅₄₁	D₄	1	1	yes	characteristic
22	C₄×D₅₄₁	D₄	1	1	yes	characteristic
23	C₄×D₅₄₁	D₄	1	1	yes	characteristic
24	C₄×D₅₄₁	Q₈	1	1	yes	characteristic
25	#16864513	—	2	1	no	—
26	C₂×C₄×C₅₄₁	C₂×C₄	1	1	yes	characteristic
27	C₈×C₅₄₁	—	2	1	no	—
28	C₂²×C₅₄₁	C₄²	1	1	yes	characteristic
29	C₂×D₅₄₁	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×D₅₄₁	C₄⋊C₄	1	1	yes	characteristic
31	C₂×D₅₄₁	C₂×C₈	1	2	yes	—
32	C₂×D₅₄₁	M₁₆	1	2	yes	—
33	#14524194	—	2	4	no	—
34	C₄×C₅₄₁	C₂²⋊C₄	1	1	yes	characteristic
35	C₄×C₅₄₁	C₄⋊C₄	1	1	yes	characteristic
36	Dic₅₄₁	C₂²⋊C₄	1	1	yes	characteristic
37	Dic₅₄₁	C₄⋊C₄	1	1	yes	characteristic
38	C₂×C₅₄₁	#95	1	1	yes	characteristic
39	C₂×C₅₄₁	C₄×C₈	1	1	yes	characteristic
40	C₂×C₅₄₁	#97	1	1	yes	characteristic
41	D₅₄₁	C₂²⋊C₈	1	2	yes	—
42	D₅₄₁	C₄⋊C₈	1	2	yes	—
43	C₅₄₁	#336	1	1	yes	characteristic, complemented, Sylow
44	#336	—	541	1	no	maximal, Sylow
45	C₂²×C₈	—	541	1	no	—
46	C₂²×C₈	—	541	1	no	—
47	C₂×C₄²	—	541	1	no	—
48	C₂²×C₄	—	541	1	no	—
49	C₂²×C₄	—	541	2	no	—
50	C₂×C₈	—	541	2	no	—
51	C₂×C₈	—	541	1	no	—
52	C₂×C₈	—	1082	1	no	—
53	C₂×C₈	—	1082	1	no	—
54	C₂×C₈	—	1082	1	no	—
55	C₂×C₈	—	1082	1	no	—
56	C₂×C₈	#14524194	1	1	yes	characteristic, complemented
57	C₄²	—	1082	1	no	—
58	C₄²	—	1082	1	no	—
59	C₂³	—	541	1	no	—
60	C₂×C₄	—	541	1	no	—
61	C₂×C₄	—	541	1	no	—
62	C₂×C₄	—	541	1	no	—
63	C₂×C₄	—	541	1	no	—
64	C₂×C₄	—	541	1	no	—
65	C₂×C₄	—	541	4	no	—
66	C₂×C₄	—	1082	2	no	—
67	C₂×C₄	—	1082	2	no	—
68	C₂×C₄	C₂×#14524194	1	1	yes	characteristic
69	C₈	—	2	1	no	—
70	C₈	—	1082	2	no	—
71	C₈	—	1082	1	no	—
72	C₂²	—	541	1	no	—
73	C₂²	—	541	1	no	—
74	C₂²	—	541	2	no	—
75	C₂²	—	541	2	no	—
76	C₂²	C₄×#14524194	1	1	yes	characteristic
77	C₄	—	541	1	no	—
78	C₄	—	541	1	no	—
79	C₄	—	1082	4	no	—
80	C₄	C₂²⋊#14524194	1	1	yes	characteristic
81	C₄	C₄⋊#14524194	1	1	yes	characteristic
82	C₂	—	541	2	no	—
83	C₂	—	541	2	no	—
84	C₂	(C₂×#14524194)⋊C₄	1	1	yes	characteristic
85	C₂	C₈×#14524194	1	1	yes	characteristic
86	C₂	#31772682	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂×#14524194
commutator	C₂×C₅₄₁	C₄×C₈
Fitting	C₂×C₈×C₅₄₁	C₄
socle	C₂²×C₅₄₁	C₄²
prime radical	C₂²×D₅₄₁	C₂×C₄
cosocle	C₂×C₄×D₅₄₁	C₂²
hypercenter	C₂×C₈	#14524194
hypocenter	C₅₄₁	#336
LCS	G ▷ C₂×C₅₄₁ ▷ C₅₄₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₈

Complements

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

N	H ≅ G/N	type
7. C₂×#16864520	C₄	semidirect
11. C₂×#16864513	C₄	semidirect
14. C₂×C₈×C₅₄₁	C₄	semidirect
17. C₂×#14524194	C₈	semidirect
43. C₅₄₁	#336	semidirect
56. C₂×C₈	#14524194	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₅₄₁⋊C₈	2
C₂×C₄×#14524194	2
C₂×C₈×D₅₄₁	2
#336	541

Subgroups — (C2×#14524194)⋊C8 #46831040

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₂×#14524194)⋊C₈ #46831040