Subgroups — C₂×#477 #3074

Order 128.

208 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×Q₈	C₂	1	1	yes	maximal, characteristic
3	#477	C₂	1	8	yes	maximal, direct product factor
4	C₂×#107	C₂	1	2	yes	maximal
5	C₂×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₂×#103	C₂	1	2	yes	maximal
7	C₂²×Q₈	—	2	1	no	—
8	C₂²×Q₈	C₂²	1	1	yes	characteristic
9	C₂²×C₈	C₂²	1	2	yes	—
10	C₄⋊Q₈	—	2	2	no	—
11	C₄⋊Q₈	C₂²	1	4	yes	—
12	C₄×Q₈	—	2	2	no	—
13	C₄×Q₈	C₂²	1	4	yes	—
14	C₂×C₄⋊C₄	—	2	1	no	—
15	C₂×C₄⋊C₄	—	2	1	no	—
16	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₄²	—	2	1	no	—
19	C₂×C₄²	C₂²	1	1	yes	characteristic
20	#107	C₂²	1	8	yes	—
21	C₄⋊C₈	C₂²	1	4	yes	—
22	#103	C₂²	1	8	yes	—
23	C₂×Q₈	—	2	1	no	—
24	C₂×Q₈	—	2	4	no	—
25	C₂×Q₈	—	2	2	no	—
26	C₂×Q₈	—	4	4	no	—
27	C₂×Q₈	Q₈	1	4	yes	complemented
28	C₂×Q₈	C₂³	1	2	yes	—
29	C₂²×C₄	—	2	1	no	—
30	C₂²×C₄	—	2	1	no	—
31	C₂²×C₄	—	2	2	no	—
32	C₂²×C₄	D₄	1	1	yes	characteristic
33	C₂²×C₄	D₄	1	1	yes	characteristic
34	C₂²×C₄	C₂³	1	1	yes	characteristic
35	C₂×C₈	—	2	4	no	—
36	C₂×C₈	C₂³	1	4	yes	—
37	C₄⋊C₄	—	2	4	no	—
38	C₄⋊C₄	—	2	4	no	—
39	C₄⋊C₄	—	2	1	no	—
40	C₄⋊C₄	—	2	2	no	—
41	C₄⋊C₄	C₂³	1	4	yes	—
42	C₄⋊C₄	C₂³	1	2	yes	—
43	C₄²	—	2	4	no	—
44	C₄²	D₄	1	2	yes	—
45	C₄²	C₂³	1	2	yes	—
46	C₂³	C₂×D₄	1	1	yes	characteristic
47	Q₈	—	2	4	no	—
48	Q₈	—	2	2	no	—
49	Q₈	—	4	8	no	—
50	Q₈	C₂×Q₈	1	4	yes	complemented
51	C₂×C₄	—	2	4	no	—
52	C₂×C₄	—	2	2	no	—
53	C₂×C₄	—	2	2	no	—
54	C₂×C₄	—	2	2	no	—
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	4	2	no	—
57	C₂×C₄	—	4	4	no	—
58	C₂×C₄	Q₁₆	1	4	yes	—
59	C₂×C₄	C₂×D₄	1	2	yes	—
60	C₂×C₄	C₂×D₄	1	1	yes	characteristic
61	C₂×C₄	C₂×D₄	1	2	yes	—
62	C₂×C₄	C₂×Q₈	1	2	yes	—
63	C₂×C₄	#41	1	2	yes	—
64	C₂×C₄	C₂⁴	1	1	yes	characteristic
65	C₈	—	2	4	no	—
66	C₂²	C₂²⋊Q₈	1	2	yes	—
67	C₂²	C₂×Q₁₆	1	2	yes	—
68	C₂²	AGL(1,ℤ/8)	1	2	yes	—
69	C₂²	C₂²×D₄	1	1	yes	characteristic
70	C₄	—	2	4	no	—
71	C₄	—	2	2	no	—
72	C₄	—	4	2	no	—
73	C₄	—	4	4	no	—
74	C₄	C₂²⋊Q₈	1	2	yes	—
75	C₄	C₂×Q₁₆	1	4	yes	—
76	C₄	C₂²×Q₈	1	1	yes	characteristic
77	C₄	C₂×#41	1	1	yes	characteristic
78	C₂	#477	1	4	yes	direct product factor
79	C₂	C₂×C₂²⋊Q₈	1	1	yes	characteristic
80	C₂	C₂²×Q₁₆	1	1	yes	characteristic
81	C₂	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ 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
3. #477	C₂	direct (N × H)
27. C₂×Q₈	Q₈	semidirect
50. Q₈	C₂×Q₈	semidirect
78. C₂	#477	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×Q₈	2
#477	2
C₂×#107	2
C₂×C₄⋊C₈	2
C₂×#103	2

Subgroups — C2×#477 #3074

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#477 #3074