Subgroups — C₂×#486 #3128

Order 128.

264 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, complemented
2	C₂×#127	C₂	1	1	yes	maximal, characteristic
3	#486	C₂	1	8	yes	maximal, direct product factor
4	C₂×#102	C₂	1	4	yes	maximal, complemented
5	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×Q₈	—	2	1	no	—
7	C₂²×D₄	—	2	1	no	—
8	C₂²×D₄	—	2	1	no	—
9	C₂²×D₄	C₂²	1	2	yes	—
10	C₂²×C₈	C₂²	1	2	yes	—
11	C₄⋊Q₈	—	2	2	no	—
12	C₄⋊Q₈	C₂²	1	4	yes	complemented
13	#127	—	2	2	no	—
14	#127	C₂²	1	4	yes	—
15	C₂×C₄⋊C₄	—	2	1	no	—
16	C₂×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₄²	C₂²	1	1	yes	characteristic
18	#102	C₂²	1	16	yes	complemented
19	C₄×C₈	C₂²	1	4	yes	complemented
20	C₂⁴	—	2	2	no	—
21	C₂×Q₈	—	2	4	no	—
22	C₂×Q₈	—	4	4	no	—
23	C₂×D₄	—	2	2	no	—
24	C₂×D₄	—	2	4	no	—
25	C₂×D₄	—	2	4	no	—
26	C₂×D₄	—	2	8	no	—
27	C₂×D₄	—	4	4	no	—
28	C₂×D₄	—	4	4	no	—
29	C₂×D₄	C₂³	1	4	yes	—
30	C₂²×C₄	—	2	2	no	—
31	C₂²×C₄	D₄	1	1	yes	characteristic
32	C₂²×C₄	D₄	1	1	yes	characteristic
33	C₂²×C₄	C₂³	1	1	yes	characteristic
34	C₂×C₈	—	2	4	no	—
35	C₂×C₈	C₂³	1	4	yes	—
36	C₄⋊C₄	—	2	4	no	—
37	C₄⋊C₄	—	2	2	no	—
38	C₄⋊C₄	C₂³	1	4	yes	—
39	C₄²	D₄	1	2	yes	—
40	C₄²	C₂³	1	2	yes	—
41	C₂³	—	2	4	no	—
42	C₂³	—	4	4	no	—
43	C₂³	—	4	4	no	—
44	C₂³	—	4	4	no	—
45	C₂³	C₂×D₄	1	1	yes	characteristic
46	Q₈	—	4	8	no	—
47	D₄	—	2	8	no	—
48	D₄	—	4	4	no	—
49	D₄	—	4	8	no	—
50	D₄	—	4	8	no	—
51	C₂×C₄	—	2	4	no	—
52	C₂×C₄	—	4	4	no	—
53	C₂×C₄	D₈	1	4	yes	—
54	C₂×C₄	SD₁₆	1	4	yes	—
55	C₂×C₄	C₂×D₄	1	1	yes	characteristic
56	C₂×C₄	C₂×D₄	1	2	yes	—
57	C₂×C₄	C₂×D₄	1	2	yes	—
58	C₂×C₄	#41	1	4	yes	—
59	C₂×C₄	C₂⁴	1	1	yes	characteristic
60	C₈	—	2	4	no	—
61	C₂²	—	4	4	no	—
62	C₂²	—	4	4	no	—
63	C₂²	—	4	4	no	—
64	C₂²	—	8	8	no	—
65	C₂²	#124	1	2	yes	—
66	C₂²	C₂×D₈	1	2	yes	—
67	C₂²	C₂×SD₁₆	1	2	yes	—
68	C₂²	C₂²×D₄	1	1	yes	characteristic
69	C₄	—	4	4	no	—
70	C₄	#124	1	2	yes	—
71	C₄	C₂×D₈	1	4	yes	—
72	C₄	C₂×SD₁₆	1	4	yes	—
73	C₄	C₂×#41	1	2	yes	—
74	C₂	—	8	4	no	—
75	C₂	#486	1	4	yes	direct product factor
76	C₂	C₂×#124	1	1	yes	characteristic
77	C₂	C₂²×D₈	1	1	yes	characteristic
78	C₂	C₂²×SD₁₆	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴
prime radical	C₂×#127	C₂
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×C₄⋊Q₈	C₂	semidirect
3. #486	C₂	direct (N × H)
4. C₂×#102	C₂	semidirect
5. C₂×C₄×C₈	C₂	semidirect
12. C₄⋊Q₈	C₂²	semidirect
18. #102	C₂²	semidirect
19. C₄×C₈	C₂²	semidirect
75. C₂	#486	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×#127	2
#486	2
C₂×#102	2
C₂×C₄×C₈	2

Subgroups — C2×#486 #3128

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#486 #3128