Subgroups — C₂×C₈×D₄ #2926

Order 128.

308 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²×C₈	C₂²
commutator	C₂	C₂³×C₈
Frattini, cosocle	C₂×C₄	C₂⁴
socle	C₂³	C₂²×C₄
prime radical	C₂²×D₄	C₄
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₈ ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂³×C₈	C₂	semidirect
3. C₈×D₄	C₂	direct (N × H)
4. C₂×C₄⋊C₈	C₂	semidirect
5. C₂×C₂²⋊C₈	C₂	semidirect
6. C₂×C₄×C₈	C₂	semidirect
13. C₂²×C₈	C₂²	semidirect
19. C₄⋊C₈	C₂²	semidirect
20. C₂²⋊C₈	C₂²	semidirect
21. C₄×C₈	C₂²	semidirect
23. C₂×D₄	C₈	direct (N × H)
36. C₂×C₈	D₄	direct (N × H)
46. C₂³	C₂×C₈	semidirect
49. D₄	C₂×C₈	direct (N × H)
55. C₂×C₄	C₂×C₈	semidirect
65. C₈	C₂×D₄	direct (N × H)
71. C₂²	C₂²×C₈	semidirect
77. C₄	C₂²×C₈	semidirect
81. C₂	C₈×D₄	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₈	2
C₂×C₄×D₄	2
C₈×D₄	2
C₂×C₄⋊C₈	2
C₂×C₂²⋊C₈	2
C₂×C₄×C₈	2

Subgroups — C2×C8×D4 #2926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×D₄ #2926