Subgroups — C₂×#446 #2959

Order 128.

200 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	#446	C₂	1	8	yes	maximal, direct product factor
3	C₂×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄⋊C₈	C₂	1	2	yes	maximal
5	C₂×#97	C₂	1	2	yes	maximal
6	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic
7	C₂²×Q₈	C₄	1	1	yes	characteristic
8	C₂²×C₈	C₂²	1	1	yes	characteristic
9	C₂²×C₈	C₂²	1	2	yes	—
10	C₂²×C₈	C₂²	1	1	yes	characteristic
11	C₄×Q₈	C₄	1	4	yes	—
12	C₄×Q₈	C₂²	1	4	yes	—
13	C₂×C₄⋊C₄	C₄	1	2	yes	—
14	C₂×C₄⋊C₄	C₄	1	1	yes	characteristic
15	C₂×C₄²	C₂²	1	1	yes	characteristic
16	C₂×C₄²	C₂²	1	2	yes	—
17	C₄⋊C₈	C₂²	1	4	yes	—
18	C₄⋊C₈	C₂²	1	8	yes	—
19	#97	C₂²	1	8	yes	—
20	C₄×C₈	C₂²	1	4	yes	—
21	C₂×Q₈	—	2	4	no	—
22	C₂×Q₈	C₂×C₄	1	4	yes	—
23	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
24	C₂²×C₄	C₂×C₄	1	2	yes	—
25	C₂²×C₄	C₂×C₄	1	2	yes	—
26	C₂²×C₄	C₂×C₄	1	1	yes	characteristic
27	C₂²×C₄	C₂³	1	1	yes	characteristic
28	C₂×C₈	—	2	2	no	—
29	C₂×C₈	—	2	4	no	—
30	C₂×C₈	Q₈	1	4	yes	complemented
31	C₂×C₈	C₂³	1	2	yes	—
32	C₂×C₈	C₂³	1	4	yes	—
33	C₂×C₈	C₂³	1	2	yes	—
34	C₄⋊C₄	C₂×C₄	1	8	yes	—
35	C₄⋊C₄	C₂×C₄	1	4	yes	—
36	C₄²	C₂×C₄	1	4	yes	—
37	C₄²	C₂×C₄	1	2	yes	—
38	C₄²	C₂³	1	2	yes	—
39	C₄²	C₂³	1	4	yes	—
40	C₂³	C₂²×C₄	1	1	yes	characteristic
41	Q₈	—	2	8	no	—
42	C₂×C₄	—	2	4	no	—
43	C₂×C₄	—	2	2	no	—
44	C₂×C₄	—	2	4	no	—
45	C₂×C₄	M₁₆	1	4	yes	—
46	C₂×C₄	C₂²×C₄	1	2	yes	—
47	C₂×C₄	C₂²×C₄	1	4	yes	—
48	C₂×C₄	C₂²×C₄	1	4	yes	—
49	C₂×C₄	C₂²×C₄	1	1	yes	characteristic
50	C₂×C₄	C₂²×C₄	1	2	yes	—
51	C₂×C₄	C₂×Q₈	1	2	yes	—
52	C₂×C₄	#41	1	2	yes	—
53	C₂×C₄	C₂⁴	1	1	yes	characteristic
54	C₈	—	2	2	no	—
55	C₈	—	2	4	no	—
56	C₈	C₂×Q₈	1	4	yes	complemented
57	C₂²	C₄×Q₈	1	2	yes	—
58	C₂²	C₂×M₁₆	1	2	yes	—
59	C₂²	#131	1	2	yes	—
60	C₂²	C₂³×C₄	1	1	yes	characteristic
61	C₄	—	2	4	no	—
62	C₄	—	2	2	no	—
63	C₄	—	2	4	no	—
64	C₄	C₄×Q₈	1	2	yes	—
65	C₄	C₂×M₁₆	1	4	yes	—
66	C₄	C₂²×Q₈	1	1	yes	characteristic
67	C₄	C₂×#41	1	1	yes	characteristic
68	C₂	#446	1	4	yes	direct product factor
69	C₂	C₂×C₄×Q₈	1	1	yes	characteristic
70	C₂	C₂²×M₁₆	1	1	yes	characteristic
71	C₂	C₂×#131	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. #446	C₂	direct (N × H)
30. C₂×C₈	Q₈	semidirect
56. C₈	C₂×Q₈	semidirect
68. C₂	#446	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
#446	2
C₂×C₄⋊C₈	2
C₂×#97	2
C₂×C₄×C₈	2

Subgroups — C2×#446 #2959

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#446 #2959