Subgroups — C₂×Q₈⋊C₈ #1475

Order 128.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic
4	Q₈⋊C₈	C₂	1	4	yes	maximal, direct product factor
5	C₂²×Q₈	C₄	1	1	yes	characteristic
6	C₂²×C₈	—	2	1	no	—
7	C₂²×C₈	—	2	1	no	—
8	C₄×Q₈	—	2	1	no	—
9	C₄×Q₈	—	2	1	no	—
10	C₄×Q₈	C₄	1	2	yes	—
11	C₄×Q₈	C₂²	1	2	yes	—
12	C₂×C₄⋊C₄	—	2	1	no	—
13	C₂×C₄⋊C₄	C₄	1	1	yes	characteristic
14	C₂×C₄²	—	2	1	no	—
15	C₂×C₄²	C₂²	1	1	yes	characteristic
16	C₄⋊C₈	—	2	1	no	—
17	C₄⋊C₈	C₂²	1	2	yes	—
18	C₄×C₈	—	2	1	no	—
19	C₄×C₈	C₂²	1	2	yes	—
20	C₂×Q₈	—	2	1	no	—
21	C₂×Q₈	—	2	2	no	—
22	C₂×Q₈	C₈	1	4	yes	complemented
23	C₂×Q₈	C₂×C₄	1	2	yes	—
24	C₂²×C₄	—	2	1	no	—
25	C₂²×C₄	—	2	1	no	—
26	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₄	D₄	1	1	yes	characteristic
28	C₂²×C₄	D₄	1	1	yes	characteristic
29	C₂×C₈	—	2	4	no	—
30	C₂×C₈	—	2	2	no	—
31	C₂×C₈	—	2	2	no	—
32	C₂×C₈	—	4	2	no	—
33	C₄⋊C₄	—	2	2	no	—
34	C₄⋊C₄	—	2	1	no	—
35	C₄⋊C₄	—	2	2	no	—
36	C₄⋊C₄	C₂×C₄	1	2	yes	—
37	C₄²	—	2	2	no	—
38	C₄²	—	2	2	no	—
39	C₄²	C₂×C₄	1	1	yes	characteristic
40	C₄²	D₄	1	1	yes	characteristic
41	C₄²	D₄	1	1	yes	characteristic
42	C₄²	C₂³	1	1	yes	characteristic
43	C₂³	C₂²⋊C₄	1	1	yes	characteristic
44	Q₈	—	2	4	no	—
45	Q₈	—	2	2	no	—
46	Q₈	C₂×C₈	1	4	yes	complemented
47	C₂×C₄	—	2	4	no	—
48	C₂×C₄	—	2	2	no	—
49	C₂×C₄	—	2	2	no	—
50	C₂×C₄	—	2	2	no	—
51	C₂×C₄	—	4	2	no	—
52	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
53	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
54	C₂×C₄	C₂²⋊C₄	1	1	yes	characteristic
55	C₂×C₄	C₂×C₈	1	2	yes	—
56	C₂×C₄	M₁₆	1	2	yes	—
57	C₂×C₄	SD₁₆	1	2	yes	—
58	C₂×C₄	Q₁₆	1	2	yes	—
59	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
60	C₂×C₄	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄	C₂×D₄	1	1	yes	characteristic
62	C₈	—	2	4	no	—
63	C₈	—	4	2	no	—
64	C₂²	C₂²⋊C₈	1	2	yes	—
65	C₂²	#103	1	2	yes	—
66	C₂²	#104	1	2	yes	—
67	C₂²	C₂×C₂²⋊C₄	1	1	yes	characteristic
68	C₄	—	2	4	no	—
69	C₄	—	2	1	no	—
70	C₄	—	2	1	no	—
71	C₄	—	4	2	no	—
72	C₄	C₂²⋊C₈	1	2	yes	—
73	C₄	#103	1	2	yes	—
74	C₄	C₂²×C₈	1	1	yes	characteristic
75	C₄	C₂×M₁₆	1	1	yes	characteristic
76	C₄	C₂×SD₁₆	1	1	yes	characteristic
77	C₄	C₂×Q₁₆	1	1	yes	characteristic
78	C₂	Q₈⋊C₈	1	4	yes	direct product factor
79	C₂	C₂×C₂²⋊C₈	1	1	yes	characteristic
80	C₂	C₂×#103	1	1	yes	characteristic
81	C₂	C₂×#104	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄
commutator	C₄	C₂²×C₈
Frattini, cosocle	C₄²	C₂³
socle, prime radical	C₂³	C₂²⋊C₄
LCS	G ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ G
LECS	G ▷ C₄² ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
4. Q₈⋊C₈	C₂	direct (N × H)
22. C₂×Q₈	C₈	semidirect
46. Q₈	C₂×C₈	semidirect
78. C₂	Q₈⋊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
C₂×C₄×Q₈	2
C₂×C₄⋊C₈	2
C₂×C₄×C₈	2
Q₈⋊C₈	2

Subgroups — C2×Q8⋊C8 #1475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×Q₈⋊C₈ #1475