Subgroups — C₂×#462 #3033

Order 128.

240 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₁₆	C₂	1	2	yes	maximal
2	C₂×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×Q₈	C₂	1	1	yes	maximal, characteristic
4	#462	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₂×#103	C₂	1	2	yes	maximal
7	C₂²×Q₈	C₂²	1	2	yes	—
8	C₂²×Q₈	C₂²	1	1	yes	characteristic
9	C₂×Q₁₆	—	2	8	no	—
10	C₂×Q₁₆	C₂²	1	8	yes	—
11	C₂²×C₈	C₂²	1	2	yes	—
12	C₄⋊Q₈	—	2	2	no	—
13	C₄⋊Q₈	C₂²	1	4	yes	—
14	C₄×Q₈	—	2	2	no	—
15	C₄×Q₈	C₂²	1	4	yes	—
16	C₂×C₄⋊C₄	—	2	1	no	—
17	C₂×C₄⋊C₄	—	2	1	no	—
18	C₂×C₄⋊C₄	—	2	1	no	—
19	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₄²	—	2	1	no	—
21	C₂×C₄²	C₂²	1	1	yes	characteristic
22	C₄⋊C₈	C₂²	1	4	yes	—
23	#103	C₂²	1	8	yes	—
24	C₂×Q₈	—	2	1	no	—
25	C₂×Q₈	—	2	2	no	—
26	C₂×Q₈	—	2	2	no	—
27	C₂×Q₈	—	2	4	no	—
28	C₂×Q₈	—	2	4	no	—
29	C₂×Q₈	D₄	1	4	yes	—
30	C₂×Q₈	C₂³	1	4	yes	—
31	C₂×Q₈	C₂³	1	2	yes	—
32	C₂²×C₄	—	2	1	no	—
33	C₂²×C₄	—	2	1	no	—
34	C₂²×C₄	—	2	2	no	—
35	C₂²×C₄	D₄	1	1	yes	characteristic
36	C₂²×C₄	D₄	1	1	yes	characteristic
37	C₂²×C₄	C₂³	1	1	yes	characteristic
38	Q₁₆	—	2	16	no	—
39	C₂×C₈	—	2	4	no	—
40	C₂×C₈	C₂³	1	4	yes	—
41	C₄⋊C₄	—	2	4	no	—
42	C₄⋊C₄	—	2	4	no	—
43	C₄⋊C₄	—	2	4	no	—
44	C₄⋊C₄	—	2	1	no	—
45	C₄⋊C₄	C₂³	1	2	yes	—
46	C₄²	—	2	4	no	—
47	C₄²	D₄	1	2	yes	—
48	C₄²	C₂³	1	2	yes	—
49	C₂³	C₂×D₄	1	1	yes	characteristic
50	Q₈	—	2	4	no	—
51	Q₈	—	2	2	no	—
52	Q₈	—	2	4	no	—
53	Q₈	—	2	4	no	—
54	Q₈	—	4	4	no	—
55	Q₈	C₂×D₄	1	4	yes	—
56	C₂×C₄	—	2	4	no	—
57	C₂×C₄	—	2	2	no	—
58	C₂×C₄	—	2	2	no	—
59	C₂×C₄	—	2	2	no	—
60	C₂×C₄	—	2	4	no	—
61	C₂×C₄	—	4	4	no	—
62	C₂×C₄	—	4	2	no	—
63	C₂×C₄	Q₁₆	1	4	yes	complemented
64	C₂×C₄	C₂×D₄	1	2	yes	—
65	C₂×C₄	C₂×D₄	1	1	yes	characteristic
66	C₂×C₄	C₂×D₄	1	2	yes	—
67	C₂×C₄	C₂×D₄	1	2	yes	—
68	C₂×C₄	#41	1	2	yes	—
69	C₂×C₄	C₂⁴	1	1	yes	characteristic
70	C₈	—	2	4	no	—
71	C₂²	#121	1	2	yes	—
72	C₂²	C₂×Q₁₆	1	2	yes	—
73	C₂²	#137	1	2	yes	—
74	C₂²	C₂²×D₄	1	1	yes	characteristic
75	C₄	—	2	4	no	—
76	C₄	—	2	2	no	—
77	C₄	—	4	4	no	—
78	C₄	—	4	2	no	—
79	C₄	#121	1	2	yes	—
80	C₄	C₂×Q₁₆	1	4	yes	complemented
81	C₄	C₂²×D₄	1	1	yes	characteristic
82	C₄	C₂×#41	1	1	yes	characteristic
83	C₂	#462	1	4	yes	direct product factor
84	C₂	C₂×#121	1	1	yes	characteristic
85	C₂	C₂²×Q₁₆	1	1	yes	characteristic
86	C₂	C₂×#137	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
4. #462	C₂	direct (N × H)
63. C₂×C₄	Q₁₆	semidirect
80. C₄	C₂×Q₁₆	semidirect
83. C₂	#462	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×Q₁₆	2
C₂×C₄⋊Q₈	2
C₂×C₄×Q₈	2
#462	2
C₂×C₄⋊C₈	2
C₂×#103	2

Subgroups — C2×#462 #3033

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#462 #3033