Subgroups — C₄×C₂²⋊C₈ #1748

Order 128.

218 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄²	C₂	1	1	yes	maximal, characteristic
2	C₂×C₂²⋊C₈	C₂	1	2	yes	maximal
3	C₂×C₄×C₈	C₂	1	2	yes	maximal, complemented
4	#336	C₂	1	2	yes	maximal, complemented
5	C₂³×C₄	C₄	1	2	yes	—
6	C₂³×C₄	C₂²	1	1	yes	characteristic
7	C₂²×C₈	C₂²	1	4	yes	—
8	C₂×C₄²	—	2	4	no	—
9	C₂×C₄²	C₄	1	2	yes	—
10	C₂×C₄²	C₂²	1	1	yes	characteristic
11	C₂×C₄²	C₂²	1	1	yes	characteristic
12	C₂²⋊C₈	C₄	1	8	yes	direct product factor
13	C₄×C₈	—	2	4	no	—
14	C₂⁴	C₂×C₄	1	1	yes	characteristic
15	C₂²×C₄	—	2	4	no	—
16	C₂²×C₄	—	2	4	no	—
17	C₂²×C₄	—	2	2	no	—
18	C₂²×C₄	—	2	2	no	—
19	C₂²×C₄	C₈	1	8	yes	complemented
20	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
21	C₂²×C₄	C₂×C₄	1	4	yes	—
22	C₂²×C₄	C₂×C₄	1	2	yes	—
23	C₂²×C₄	C₂×C₄	1	2	yes	—
24	C₂²×C₄	C₂³	1	1	yes	characteristic
25	C₂×C₈	—	2	4	no	—
26	C₂×C₈	—	2	4	no	—
27	C₂×C₈	C₂×C₄	1	8	yes	complemented
28	C₄²	—	2	4	no	—
29	C₄²	—	2	2	no	—
30	C₄²	D₄	1	4	yes	—
31	C₂³	—	2	1	no	—
32	C₂³	—	2	1	no	—
33	C₂³	—	2	2	no	—
34	C₂³	C₄²	1	2	yes	—
35	C₂³	C₂×C₈	1	4	yes	—
36	C₂³	C₂²×C₄	1	1	yes	characteristic
37	C₂×C₄	—	2	1	no	—
38	C₂×C₄	—	2	2	no	—
39	C₂×C₄	—	2	1	no	—
40	C₂×C₄	—	2	2	no	—
41	C₂×C₄	—	2	16	no	—
42	C₂×C₄	—	2	8	no	—
43	C₂×C₄	C₄²	1	2	yes	—
44	C₂×C₄	C₂²⋊C₄	1	4	yes	—
45	C₂×C₄	C₂×C₈	1	4	yes	—
46	C₂×C₄	C₂×C₈	1	4	yes	—
47	C₂×C₄	M₁₆	1	4	yes	—
48	C₂×C₄	C₂²×C₄	1	2	yes	—
49	C₂×C₄	C₂×D₄	1	2	yes	—
50	C₂×C₄	#41	1	2	yes	—
51	C₈	—	2	8	no	—
52	C₂²	—	2	2	no	—
53	C₂²	—	2	2	no	—
54	C₂²	—	2	4	no	—
55	C₂²	—	2	4	no	—
56	C₂²	C₄×C₈	1	4	yes	complemented
57	C₂²	C₂×C₄²	1	1	yes	characteristic
58	C₂²	C₂×C₂²⋊C₄	1	1	yes	characteristic
59	C₂²	#117	1	1	yes	characteristic
60	C₂²	C₂²×C₈	1	2	yes	—
61	C₂²	C₂×M₁₆	1	2	yes	—
62	C₄	—	2	2	no	—
63	C₄	—	2	4	no	—
64	C₄	C₂²⋊C₈	1	8	yes	direct product factor
65	C₄	C₄×D₄	1	4	yes	—
66	C₂	—	2	4	no	—
67	C₂	C₄×C₂²⋊C₄	1	1	yes	characteristic
68	C₂	C₂×C₄×C₈	1	1	yes	characteristic
69	C₂	C₄×M₁₆	1	1	yes	characteristic
70	C₂	C₂×C₂²⋊C₈	1	2	yes	—
71	C₂	#431	1	2	yes	—

	subgroup	G/H
center	C₂×C₄²	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 ◁ C₂×C₄² ◁ 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
4. #336	C₂	semidirect
12. C₂²⋊C₈	C₄	direct (N × H)
19. C₂²×C₄	C₈	semidirect
27. C₂×C₈	C₂×C₄	semidirect
56. C₂²	C₄×C₈	semidirect
64. C₄	C₂²⋊C₈	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×C₄²	2
C₂×C₂²⋊C₈	2
C₂×C₄×C₈	2
#336	2

Subgroups — C4×C22⋊C8 #1748

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₂²⋊C₈ #1748