Subgroups — C₂×#488 #3130

Order 128.

206 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#124	C₂	1	1	yes	maximal, characteristic
3	#488	C₂	1	8	yes	maximal, direct product factor
4	C₂×#103	C₂	1	2	yes	maximal, complemented
5	C₂×#102	C₂	1	2	yes	maximal
6	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×Q₈	C₂²	1	1	yes	characteristic
8	C₂²×D₄	C₂²	1	1	yes	characteristic
9	C₂²×C₈	C₂²	1	2	yes	—
10	#125	—	2	2	no	—
11	#125	C₂²	1	4	yes	complemented
12	#124	—	2	2	no	—
13	#124	C₂²	1	4	yes	—
14	C₂×C₄⋊C₄	—	2	2	no	—
15	C₂×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₂²⋊C₄	—	2	2	no	—
17	C₂×C₄²	C₂²	1	1	yes	characteristic
18	#103	C₂²	1	8	yes	complemented
19	#102	C₂²	1	8	yes	—
20	C₄×C₈	C₂²	1	4	yes	complemented
21	C₂⁴	—	2	1	no	—
22	C₂×Q₈	—	2	1	no	—
23	C₂×Q₈	—	2	4	no	—
24	C₂×Q₈	C₂³	1	2	yes	—
25	C₂×D₄	—	2	1	no	—
26	C₂×D₄	—	2	4	no	—
27	C₂×D₄	C₂³	1	2	yes	—
28	C₂²×C₄	—	2	1	no	—
29	C₂²×C₄	—	2	2	no	—
30	C₂²×C₄	D₄	1	2	yes	—
31	C₂²×C₄	C₂³	1	1	yes	characteristic
32	C₂×C₈	—	2	4	no	—
33	C₂×C₈	C₂³	1	4	yes	—
34	C₄⋊C₄	—	2	8	no	—
35	C₄⋊C₄	—	2	2	no	—
36	C₄⋊C₄	C₂³	1	4	yes	—
37	C₂²⋊C₄	—	2	8	no	—
38	C₄²	D₄	1	2	yes	—
39	C₄²	C₂³	1	2	yes	—
40	C₂³	—	2	2	no	—
41	C₂³	—	4	2	no	—
42	C₂³	—	4	4	no	—
43	C₂³	C₂×D₄	1	1	yes	characteristic
44	Q₈	—	2	4	no	—
45	Q₈	—	4	2	no	—
46	D₄	—	2	4	no	—
47	D₄	—	4	2	no	—
48	C₂×C₄	—	2	4	no	—
49	C₂×C₄	—	2	2	no	—
50	C₂×C₄	—	2	4	no	—
51	C₂×C₄	—	4	2	no	—
52	C₂×C₄	—	4	4	no	—
53	C₂×C₄	C₂×D₄	1	4	yes	—
54	C₂×C₄	C₂×D₄	1	1	yes	characteristic
55	C₂×C₄	#41	1	4	yes	—
56	C₂×C₄	C₂⁴	1	1	yes	characteristic
57	C₈	—	2	4	no	—
58	C₂²	—	4	2	no	—
59	C₂²	—	4	4	no	—
60	C₂²	—	8	4	no	—
61	C₂²	#124	1	2	yes	—
62	C₂²	#135	1	4	yes	—
63	C₂²	C₂²×D₄	1	1	yes	characteristic
64	C₄	—	2	4	no	—
65	C₄	—	4	2	no	—
66	C₄	—	4	4	no	—
67	C₄	#124	1	2	yes	—
68	C₄	C₂×#41	1	2	yes	—
69	C₂	—	8	2	no	—
70	C₂	#488	1	4	yes	direct product factor
71	C₂	C₂×#124	1	1	yes	characteristic
72	C₂	C₂×#135	1	2	yes	—

	subgroup	G/H
center, socle	C₂³	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴
prime radical	C₂²×D₄	C₂²
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
1. C₂×#125	C₂	semidirect
3. #488	C₂	direct (N × H)
4. C₂×#103	C₂	semidirect
6. C₂×C₄×C₈	C₂	semidirect
11. #125	C₂²	semidirect
18. #103	C₂²	semidirect
20. C₄×C₈	C₂²	semidirect
70. C₂	#488	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×#125	2
C₂×#124	2
#488	2
C₂×#103	2
C₂×#102	2
C₂×C₄×C₈	2

Subgroups — C2×#488 #3130

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#488 #3130