Subgroups — C₂×#508 #3411

Order 128.

184 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#135	C₂	1	2	yes	maximal, complemented
2	#508	C₂	1	8	yes	maximal, direct product factor
3	C₂×Q₃₂	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×SD₃₂	C₂	1	2	yes	maximal, complemented
5	C₂×D₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#41	—	2	2	no	—
8	#135	—	2	4	no	—
9	#135	C₂²	1	8	yes	complemented
10	C₂×Q₁₆	C₂²	1	2	yes	—
11	C₂×SD₁₆	—	2	2	no	—
12	C₂×D₈	C₂²	1	2	yes	—
13	C₂²×C₈	C₂²	1	1	yes	characteristic
14	Q₃₂	C₂²	1	4	yes	complemented
15	SD₃₂	C₂²	1	8	yes	complemented
16	D₁₆	C₂²	1	4	yes	complemented
17	C₂×C₁₆	C₂²	1	1	yes	characteristic
18	C₂×C₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₁₆	C₂²	1	4	yes	complemented
20	#41	—	2	8	no	—
21	#41	—	4	4	no	—
22	C₂×Q₈	—	2	2	no	—
23	C₂×D₄	—	2	2	no	—
24	C₂×D₄	—	4	2	no	—
25	C₂²×C₄	—	4	2	no	—
26	C₂²×C₄	D₄	1	1	yes	characteristic
27	Q₁₆	—	2	2	no	—
28	Q₁₆	C₂³	1	4	yes	—
29	SD₁₆	—	2	8	no	—
30	D₈	—	2	2	no	—
31	D₈	C₂³	1	4	yes	—
32	C₂×C₈	D₄	1	1	yes	characteristic
33	C₂×C₈	D₄	1	2	yes	—
34	C₂×C₈	C₂³	1	1	yes	characteristic
35	C₂×C₈	C₂³	1	2	yes	—
36	C₁₆	C₂³	1	2	yes	—
37	C₁₆	C₂³	1	2	yes	—
38	C₂³	—	4	2	no	—
39	C₂³	D₈	1	1	yes	characteristic
40	Q₈	—	2	4	no	—
41	Q₈	—	4	2	no	—
42	D₄	—	2	4	no	—
43	D₄	—	4	8	no	—
44	D₄	—	4	2	no	—
45	C₂×C₄	—	4	2	no	—
46	C₂×C₄	—	4	8	no	—
47	C₂×C₄	D₈	1	2	yes	—
48	C₂×C₄	D₈	1	1	yes	characteristic
49	C₂×C₄	C₂×D₄	1	1	yes	characteristic
50	C₂×C₄	C₂×D₄	1	2	yes	—
51	C₈	C₂×D₄	1	1	yes	characteristic
52	C₈	C₂×D₄	1	2	yes	—
53	C₈	C₂⁴	1	1	yes	characteristic
54	C₂²	—	2	2	no	—
55	C₂²	—	4	4	no	—
56	C₂²	—	8	4	no	—
57	C₂²	C₂×D₈	1	2	yes	—
58	C₂²	C₂×D₈	1	1	yes	characteristic
59	C₄	—	4	4	no	—
60	C₄	C₂×D₈	1	2	yes	—
61	C₄	C₂×D₈	1	1	yes	characteristic
62	C₄	C₂²×D₄	1	1	yes	characteristic
63	C₂	—	2	2	no	—
64	C₂	—	8	4	no	—
65	C₂	#508	1	2	yes	direct product factor
66	C₂	C₂²×D₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₈
commutator, Frattini, cosocle	C₈	C₂⁴
socle	C₂²	C₂×D₈
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ G
LECS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#135	C₂	semidirect
2. #508	C₂	direct (N × H)
3. C₂×Q₃₂	C₂	semidirect
4. C₂×SD₃₂	C₂	semidirect
5. C₂×D₁₆	C₂	semidirect
6. C₂²×C₁₆	C₂	semidirect
9. #135	C₂²	semidirect
14. Q₃₂	C₂²	semidirect
15. SD₃₂	C₂²	semidirect
16. D₁₆	C₂²	semidirect
19. C₂×C₁₆	C₂²	semidirect
65. C₂	#508	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×#135	2
#508	2
C₂×Q₃₂	2
C₂×SD₃₂	2
C₂×D₁₆	2
C₂²×C₁₆	2

Subgroups — C2×#508 #3411

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#508 #3411