Subgroups — C₈×#95 #10695

Order 256.

587 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₈	C₂	1	3	yes	maximal
2	C₂×#336	C₂	1	3	yes	maximal
3	C₄×#95	C₂	1	1	yes	maximal, characteristic
4	C₂³×C₈	C₂²	1	3	yes	—
5	C₂³×C₈	C₂²	1	1	yes	characteristic
6	C₂²×C₄²	C₂²	1	3	yes	—
7	C₂×C₄×C₈	—	2	12	no	—
8	C₂×C₄×C₈	C₄	1	12	yes	complemented
9	C₂×#95	C₄	1	4	yes	—
10	#336	C₄	1	12	yes	complemented
11	C₂³×C₄	C₂×C₄	1	6	yes	—
12	C₂³×C₄	C₂³	1	1	yes	characteristic
13	C₂²×C₈	—	2	6	no	—
14	C₂²×C₈	—	2	3	no	—
15	C₂²×C₈	—	2	3	no	—
16	C₂²×C₈	C₂×C₄	1	12	yes	—
17	C₂²×C₈	C₂×C₄	1	6	yes	—
18	C₂²×C₈	C₂×C₄	1	6	yes	—
19	C₂²×C₈	D₄	1	6	yes	—
20	C₂²×C₈	Q₈	1	2	yes	—
21	C₂×C₄²	—	2	6	no	—
22	C₂×C₄²	—	2	6	no	—
23	C₂×C₄²	C₂×C₄	1	6	yes	—
24	C₂×C₄²	C₂×C₄	1	6	yes	—
25	C₄×C₈	—	2	24	no	—
26	#95	C₈	1	16	yes	direct product factor
27	C₂⁴	C₂²×C₄	1	1	yes	characteristic
28	C₂²×C₄	—	2	12	no	—
29	C₂²×C₄	—	2	12	no	—
30	C₂²×C₄	C₄²	1	12	yes	—
31	C₂²×C₄	C₂×C₈	1	24	yes	—
32	C₂²×C₄	C₂²×C₄	1	3	yes	—
33	C₂²×C₄	C₂²×C₄	1	3	yes	—
34	C₂²×C₄	C₂×D₄	1	3	yes	—
35	C₂²×C₄	C₂×Q₈	1	1	yes	characteristic
36	C₂²×C₄	#41	1	1	yes	characteristic
37	C₂²×C₄	#41	1	3	yes	—
38	C₂×C₈	—	2	6	no	—
39	C₂×C₈	—	2	6	no	—
40	C₂×C₈	—	2	12	no	—
41	C₂×C₈	—	2	12	no	—
42	C₂×C₈	C₄²	1	12	yes	—
43	C₂×C₈	C₄²	1	4	yes	—
44	C₂×C₈	C₂²⋊C₄	1	12	yes	—
45	C₂×C₈	C₄⋊C₄	1	12	yes	—
46	C₄²	—	2	6	no	—
47	C₄²	—	2	6	no	—
48	C₄²	—	2	12	no	—
49	C₂³	C₂×C₄²	1	3	yes	—
50	C₂³	C₄×D₄	1	3	yes	—
51	C₂³	C₄×Q₈	1	1	yes	characteristic
52	C₂³	C₂²×C₈	1	4	yes	—
53	C₂³	#131	1	4	yes	—
54	C₂×C₄	—	2	12	no	—
55	C₂×C₄	—	2	12	no	—
56	C₂×C₄	—	2	48	no	—
57	C₂×C₄	C₄×C₈	1	24	yes	complemented
58	C₂×C₄	C₂×C₄²	1	1	yes	characteristic
59	C₂×C₄	C₂×C₄²	1	3	yes	—
60	C₂×C₄	C₂×C₂²⋊C₄	1	3	yes	—
61	C₂×C₄	C₂×C₄⋊C₄	1	3	yes	—
62	C₂×C₄	#117	1	3	yes	—
63	C₂×C₄	#117	1	3	yes	—
64	C₂×C₄	C₄×D₄	1	3	yes	—
65	C₂×C₄	C₄×D₄	1	6	yes	—
66	C₂×C₄	C₄×Q₈	1	3	yes	—
67	C₈	—	2	12	no	—
68	C₈	#95	1	8	yes	direct product factor
69	C₂²	C₄³	1	1	yes	characteristic
70	C₂²	C₄×C₂²⋊C₄	1	3	yes	—
71	C₂²	C₄×C₄⋊C₄	1	3	yes	—
72	C₂²	C₂×C₄×C₈	1	6	yes	—
73	C₂²	#405	1	6	yes	—
74	C₂²	C₈×D₄	1	12	yes	—
75	C₂²	C₈×Q₈	1	4	yes	—
76	C₄	—	2	24	no	—
77	C₄	C₂×#95	1	1	yes	characteristic
78	C₄	#376	1	1	yes	characteristic
79	C₄	C₄×C₂²⋊C₄	1	3	yes	—
80	C₄	C₄×C₄⋊C₄	1	3	yes	—
81	C₂	C₄×#95	1	1	yes	characteristic
82	C₂	C₄²×C₈	1	1	yes	characteristic
83	C₂	#1726	1	1	yes	characteristic
84	C₂	C₈×C₂²⋊C₄	1	6	yes	—
85	C₂	C₈×C₄⋊C₄	1	6	yes	—

	subgroup	G/H
center	C₂³×C₈	C₂²
commutator	C₂	C₄²×C₈
Frattini, cosocle	C₂³×C₄	C₂³
socle, prime radical	C₂⁴	C₂²×C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₈ ◁ G
LECS	G ▷ C₂³×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
8. C₂×C₄×C₈	C₄	semidirect
10. #336	C₄	semidirect
26. #95	C₈	direct (N × H)
57. C₂×C₄	C₄×C₈	semidirect
68. C₈	#95	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₈	2
C₂×#336	2
C₄×#95	2

Subgroups — C8×#95 #10695

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#95 #10695