Subgroups — C₂×#460 #3032

Order 128.

292 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×SD₁₆	C₂	1	2	yes	maximal, complemented
2	C₂×#127	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#460	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₄⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#102	C₂	1	2	yes	maximal, complemented
7	C₂²×Q₈	C₂²	1	1	yes	characteristic
8	C₂²×D₄	—	2	1	no	—
9	C₂²×D₄	—	2	1	no	—
10	C₂²×D₄	C₂²	1	2	yes	—
11	C₂×SD₁₆	—	2	8	no	—
12	C₂×SD₁₆	C₂²	1	8	yes	complemented
13	C₂²×C₈	C₂²	1	2	yes	—
14	#127	—	2	2	no	—
15	#127	C₂²	1	4	yes	—
16	C₄×Q₈	—	2	2	no	—
17	C₄×Q₈	C₂²	1	4	yes	complemented
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	complemented
23	#102	C₂²	1	8	yes	complemented
24	C₂⁴	—	2	2	no	—
25	C₂×Q₈	—	2	1	no	—
26	C₂×Q₈	—	2	2	no	—
27	C₂×Q₈	D₄	1	4	yes	complemented
28	C₂×Q₈	C₂³	1	2	yes	—
29	C₂×D₄	—	2	4	no	—
30	C₂×D₄	—	2	2	no	—
31	C₂×D₄	—	2	4	no	—
32	C₂×D₄	—	2	4	no	—
33	C₂×D₄	—	2	4	no	—
34	C₂×D₄	—	4	4	no	—
35	C₂×D₄	—	4	4	no	—
36	C₂×D₄	C₂³	1	4	yes	—
37	C₂²×C₄	—	2	1	no	—
38	C₂²×C₄	—	2	1	no	—
39	C₂²×C₄	D₄	1	1	yes	characteristic
40	C₂²×C₄	D₄	1	1	yes	characteristic
41	C₂²×C₄	C₂³	1	1	yes	characteristic
42	SD₁₆	—	2	16	no	—
43	C₂×C₈	—	2	4	no	—
44	C₂×C₈	C₂³	1	4	yes	—
45	C₄⋊C₄	—	2	4	no	—
46	C₄⋊C₄	—	2	1	no	—
47	C₄⋊C₄	C₂³	1	2	yes	—
48	C₄²	—	2	4	no	—
49	C₄²	D₄	1	2	yes	—
50	C₄²	C₂³	1	2	yes	—
51	C₂³	—	2	4	no	—
52	C₂³	—	4	4	no	—
53	C₂³	—	4	4	no	—
54	C₂³	—	4	4	no	—
55	C₂³	C₂×D₄	1	1	yes	characteristic
56	Q₈	—	2	4	no	—
57	Q₈	—	2	2	no	—
58	Q₈	C₂×D₄	1	4	yes	complemented
59	D₄	—	2	4	no	—
60	D₄	—	2	4	no	—
61	D₄	—	4	8	no	—
62	D₄	—	4	4	no	—
63	D₄	—	4	8	no	—
64	C₂×C₄	—	2	4	no	—
65	C₂×C₄	—	2	2	no	—
66	C₂×C₄	—	2	2	no	—
67	C₂×C₄	—	2	2	no	—
68	C₂×C₄	—	4	2	no	—
69	C₂×C₄	SD₁₆	1	4	yes	complemented
70	C₂×C₄	C₂×D₄	1	2	yes	—
71	C₂×C₄	C₂×D₄	1	1	yes	characteristic
72	C₂×C₄	C₂×D₄	1	2	yes	—
73	C₂×C₄	C₂×D₄	1	2	yes	—
74	C₂×C₄	#41	1	2	yes	—
75	C₂×C₄	C₂⁴	1	1	yes	characteristic
76	C₈	—	2	4	no	—
77	C₂²	—	4	4	no	—
78	C₂²	—	4	4	no	—
79	C₂²	—	4	4	no	—
80	C₂²	—	8	8	no	—
81	C₂²	#121	1	2	yes	—
82	C₂²	C₂×SD₁₆	1	2	yes	—
83	C₂²	AGL(1,ℤ/8)	1	2	yes	—
84	C₂²	C₂²×D₄	1	1	yes	characteristic
85	C₄	—	2	4	no	—
86	C₄	—	2	2	no	—
87	C₄	—	4	2	no	—
88	C₄	#121	1	2	yes	—
89	C₄	C₂×SD₁₆	1	4	yes	complemented
90	C₄	C₂²×D₄	1	1	yes	characteristic
91	C₄	C₂×#41	1	1	yes	characteristic
92	C₂	—	8	4	no	—
93	C₂	#460	1	4	yes	direct product factor
94	C₂	C₂×#121	1	1	yes	characteristic
95	C₂	C₂²×SD₁₆	1	1	yes	characteristic
96	C₂	C₂×AGL(1,ℤ/8)	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. C₂²×SD₁₆	C₂	semidirect
3. C₂×C₄×Q₈	C₂	semidirect
4. #460	C₂	direct (N × H)
5. C₂×C₄⋊C₈	C₂	semidirect
6. C₂×#102	C₂	semidirect
12. C₂×SD₁₆	C₂²	semidirect
17. C₄×Q₈	C₂²	semidirect
22. C₄⋊C₈	C₂²	semidirect
23. #102	C₂²	semidirect
27. C₂×Q₈	D₄	semidirect
58. Q₈	C₂×D₄	semidirect
69. C₂×C₄	SD₁₆	semidirect
89. C₄	C₂×SD₁₆	semidirect
93. C₂	#460	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×SD₁₆	2
C₂×#127	2
C₂×C₄×Q₈	2
#460	2
C₂×C₄⋊C₈	2
C₂×#102	2

Subgroups — C2×#460 #3032

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#460 #3032