Subgroups — C₈×C₄⋊C₄ #1769

Order 128.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

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

	subgroup	G/H
center	C₂²×C₈	C₂²
commutator	C₂	C₂×C₄×C₈
Frattini, cosocle	C₂²×C₄	C₂³
socle, prime radical	C₂³	C₂²×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
12. C₄⋊C₈	C₄	semidirect
14. C₄×C₈	C₄	semidirect
29. C₄⋊C₄	C₈	direct (N × H)
50. C₈	C₄⋊C₄	direct (N × H)
58. C₄	C₄×C₈	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₈	2
C₂×C₄×C₈	2
C₄×C₄⋊C₄	2
#336	2

Subgroups — C8×C4⋊C4 #1769

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×C₄⋊C₄ #1769