Subgroups — C₈×C₂²⋊C₄ #1751

Order 128.

192 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×C₈	C₂	semidirect
5. #336	C₂	semidirect
8. C₂²×C₈	C₄	semidirect
14. C₂²⋊C₈	C₄	semidirect
33. C₂²⋊C₄	C₈	direct (N × H)
48. C₂×C₄	C₂×C₈	semidirect
55. C₈	C₂²⋊C₄	direct (N × H)
59. C₂²	C₄×C₈	semidirect

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×C₂²⋊C₈	2
C₂×C₄×C₈	2
C₄×C₂²⋊C₄	2
#336	2

Subgroups — C8×C22⋊C4 #1751

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₂²⋊C₄ #1751