Subgroups — C₂×#495 #3146

Order 128.

296 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×SD₁₆	C₂	1	2	yes	maximal, complemented
3	C₂²×D₈	C₂	1	1	yes	maximal, characteristic
4	C₂×#124	C₂	1	2	yes	maximal, complemented
5	#495	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄×C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×Q₈	C₂²	1	2	yes	—
8	C₂²×D₄	C₂²	1	2	yes	—
9	C₂×Q₁₆	—	2	4	no	—
10	C₂×Q₁₆	C₂²	1	4	yes	complemented
11	C₂×SD₁₆	—	2	8	no	—
12	C₂×SD₁₆	C₂²	1	8	yes	complemented
13	C₂×D₈	—	2	4	no	—
14	C₂×D₈	C₂²	1	4	yes	—
15	C₂²×C₈	C₂²	1	1	yes	characteristic
16	C₂²×C₈	C₂²	1	1	yes	characteristic
17	#124	—	2	4	no	—
18	#124	C₂²	1	8	yes	complemented
19	C₂×C₂²⋊C₄	—	2	4	no	—
20	C₂×C₄²	C₂²	1	1	yes	characteristic
21	C₄×C₈	C₂²	1	4	yes	complemented
22	C₂⁴	—	2	2	no	—
23	C₂×Q₈	—	2	2	no	—
24	C₂×Q₈	—	2	4	no	—
25	C₂×Q₈	—	2	4	no	—
26	C₂×Q₈	C₂³	1	4	yes	—
27	C₂×D₄	—	2	4	no	—
28	C₂×D₄	—	2	4	no	—
29	C₂×D₄	—	2	2	no	—
30	C₂×D₄	C₂³	1	4	yes	—
31	C₂²×C₄	—	2	2	no	—
32	C₂²×C₄	D₄	1	2	yes	—
33	C₂²×C₄	C₂³	1	1	yes	characteristic
34	Q₁₆	—	2	8	no	—
35	SD₁₆	—	2	16	no	—
36	D₈	—	2	8	no	—
37	C₂×C₈	D₄	1	4	yes	—
38	C₂×C₈	D₄	1	4	yes	—
39	C₂×C₈	C₂³	1	2	yes	—
40	C₂×C₈	C₂³	1	2	yes	—
41	C₂²⋊C₄	—	2	16	no	—
42	C₄²	D₄	1	2	yes	—
43	C₄²	C₂³	1	2	yes	—
44	C₂³	—	2	4	no	—
45	C₂³	—	4	4	no	—
46	C₂³	—	4	8	no	—
47	C₂³	C₂×D₄	1	1	yes	characteristic
48	Q₈	—	2	4	no	—
49	Q₈	—	2	4	no	—
50	Q₈	—	4	4	no	—
51	D₄	—	2	4	no	—
52	D₄	—	2	4	no	—
53	D₄	—	4	4	no	—
54	C₂×C₄	—	2	4	no	—
55	C₂×C₄	—	2	4	no	—
56	C₂×C₄	—	4	4	no	—
57	C₂×C₄	C₂×D₄	1	4	yes	—
58	C₂×C₄	C₂×D₄	1	1	yes	characteristic
59	C₂×C₄	C₂×D₄	1	2	yes	—
60	C₂×C₄	C₂×D₄	1	2	yes	—
61	C₂×C₄	C₂⁴	1	1	yes	characteristic
62	C₈	C₂×D₄	1	4	yes	—
63	C₈	C₂×D₄	1	4	yes	—
64	C₂²	—	4	4	no	—
65	C₂²	—	4	8	no	—
66	C₂²	—	8	8	no	—
67	C₂²	#127	1	2	yes	—
68	C₂²	#135	1	4	yes	—
69	C₂²	C₂²×D₄	1	1	yes	characteristic
70	C₄	—	2	4	no	—
71	C₄	—	4	4	no	—
72	C₄	#127	1	2	yes	—
73	C₄	C₂²×D₄	1	1	yes	characteristic
74	C₄	C₂²×D₄	1	1	yes	characteristic
75	C₂	—	8	4	no	—
76	C₂	#495	1	4	yes	direct product factor
77	C₂	C₂×#127	1	1	yes	characteristic
78	C₂	C₂×#135	1	2	yes	—

	subgroup	G/H
center, socle	C₂³	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴
prime radical	C₂²×D₈	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. C₂²×Q₁₆	C₂	semidirect
2. C₂²×SD₁₆	C₂	semidirect
4. C₂×#124	C₂	semidirect
5. #495	C₂	direct (N × H)
6. C₂×C₄×C₈	C₂	semidirect
10. C₂×Q₁₆	C₂²	semidirect
12. C₂×SD₁₆	C₂²	semidirect
18. #124	C₂²	semidirect
21. C₄×C₈	C₂²	semidirect
76. C₂	#495	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
C₂²×SD₁₆	2
C₂²×D₈	2
C₂×#124	2
#495	2
C₂×C₄×C₈	2

Subgroups — C2×#495 #3146

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#495 #3146