Subgroups — C₂×C₄×D₈ #2936

Order 128.

308 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×D₄	C₂	1	2	yes	maximal, complemented
3	C₄×D₈	C₂	1	8	yes	maximal, direct product factor
4	C₂×#107	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#102	C₂	1	2	yes	maximal, complemented
6	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×D₄	C₂²	1	2	yes	—
8	C₂³×C₄	—	2	2	no	—
9	C₂×D₈	C₄	1	8	yes	direct product factor
10	C₂×D₈	C₂²	1	4	yes	—
11	C₂²×C₈	C₂²	1	1	yes	characteristic
12	C₂²×C₈	C₂²	1	1	yes	characteristic
13	C₄×D₄	—	2	4	no	—
14	C₄×D₄	C₂²	1	8	yes	complemented
15	C₂×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₄	—	2	2	no	—
17	C₂×C₄²	C₂²	1	1	yes	characteristic
18	#107	C₂²	1	4	yes	complemented
19	#102	C₂²	1	8	yes	complemented
20	C₄×C₈	C₂²	1	4	yes	complemented
21	C₂⁴	—	2	2	no	—
22	C₂×D₄	—	2	2	no	—
23	C₂×D₄	—	2	4	no	—
24	C₂×D₄	C₂×C₄	1	8	yes	complemented
25	C₂×D₄	C₂³	1	4	yes	—
26	C₂²×C₄	—	2	2	no	—
27	C₂²×C₄	—	2	8	no	—
28	C₂²×C₄	—	4	8	no	—
29	C₂²×C₄	D₄	1	1	yes	characteristic
30	C₂²×C₄	D₄	1	1	yes	characteristic
31	C₂²×C₄	C₂³	1	1	yes	characteristic
32	D₈	C₂×C₄	1	16	yes	direct product factor
33	C₂×C₈	—	2	2	no	—
34	C₂×C₈	C₂×C₄	1	4	yes	complemented
35	C₂×C₈	C₂³	1	2	yes	—
36	C₂×C₈	C₂³	1	2	yes	—
37	C₄⋊C₄	—	2	2	no	—
38	C₄⋊C₄	C₂³	1	4	yes	—
39	C₂²⋊C₄	—	2	8	no	—
40	C₄²	D₄	1	2	yes	—
41	C₄²	C₂³	1	2	yes	—
42	C₂³	—	2	8	no	—
43	C₂³	—	2	4	no	—
44	C₂³	—	4	4	no	—
45	C₂³	—	4	4	no	—
46	C₂³	C₂×D₄	1	1	yes	characteristic
47	D₄	—	2	8	no	—
48	D₄	—	2	4	no	—
49	D₄	C₂²×C₄	1	8	yes	complemented
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	—	2	4	no	—
52	C₂×C₄	—	4	4	no	—
53	C₂×C₄	—	4	16	no	—
54	C₂×C₄	D₈	1	4	yes	direct product factor
55	C₂×C₄	C₂²×C₄	1	2	yes	—
56	C₂×C₄	C₂×D₄	1	2	yes	—
57	C₂×C₄	C₂×D₄	1	1	yes	characteristic
58	C₂×C₄	C₂×D₄	1	2	yes	—
59	C₂×C₄	#41	1	2	yes	—
60	C₂×C₄	C₂⁴	1	1	yes	characteristic
61	C₈	—	2	2	no	—
62	C₈	C₂²×C₄	1	4	yes	complemented
63	C₂²	—	2	8	no	—
64	C₂²	—	4	4	no	—
65	C₂²	—	4	4	no	—
66	C₂²	—	4	16	no	—
67	C₂²	C₄×D₄	1	2	yes	—
68	C₂²	C₂×D₈	1	2	yes	—
69	C₂²	#135	1	2	yes	—
70	C₂²	C₂²×D₄	1	1	yes	characteristic
71	C₄	—	2	2	no	—
72	C₄	—	4	4	no	—
73	C₄	C₄×D₄	1	2	yes	—
74	C₄	C₂×D₈	1	4	yes	direct product factor
75	C₄	C₂³×C₄	1	1	yes	characteristic
76	C₄	C₂×#41	1	1	yes	characteristic
77	C₂	—	4	8	no	—
78	C₂	C₄×D₈	1	4	yes	direct product factor
79	C₂	C₂×C₄×D₄	1	1	yes	characteristic
80	C₂	C₂²×D₈	1	1	yes	characteristic
81	C₂	C₂×#135	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄
commutator	C₄	C₂³×C₄
Frattini, cosocle	C₂×C₄	C₂⁴
socle	C₂³	C₂×D₄
prime radical	C₂²×D₈	C₂
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ G
LECS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×D₄	C₂	semidirect
3. C₄×D₈	C₂	direct (N × H)
4. C₂×#107	C₂	semidirect
5. C₂×#102	C₂	semidirect
6. C₂×C₄×C₈	C₂	semidirect
9. C₂×D₈	C₄	direct (N × H)
14. C₄×D₄	C₂²	semidirect
18. #107	C₂²	semidirect
19. #102	C₂²	semidirect
20. C₄×C₈	C₂²	semidirect
24. C₂×D₄	C₂×C₄	semidirect
32. D₈	C₂×C₄	direct (N × H)
34. C₂×C₈	C₂×C₄	semidirect
49. D₄	C₂²×C₄	semidirect
54. C₂×C₄	D₈	direct (N × H)
62. C₈	C₂²×C₄	semidirect
74. C₄	C₂×D₈	direct (N × H)
78. C₂	C₄×D₈	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×D₈	2
C₂×C₄×D₄	2
C₄×D₈	2
C₂×#107	2
C₂×#102	2
C₂×C₄×C₈	2

Subgroups — C2×C4×D8 #2936

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×D₈ #2936