Subgroups — C₂×#470 #3053

Order 128.

246 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×M₁₆	C₂	1	1	yes	maximal, characteristic
3	C₂×C₂²⋊Q₈	C₂	1	2	yes	maximal
4	#470	C₂	1	8	yes	maximal, direct product factor
5	C₂×#106	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#103	C₂	1	2	yes	maximal, complemented
7	C₂²×Q₈	C₂²	1	2	yes	—
8	C₂³×C₄	C₂²	1	1	yes	characteristic
9	C₂×Q₁₆	—	2	4	no	—
10	C₂×Q₁₆	C₂²	1	4	yes	complemented
11	C₂×M₁₆	—	2	4	no	—
12	C₂×M₁₆	C₂²	1	4	yes	—
13	C₂²×C₈	C₂²	1	1	yes	characteristic
14	C₂²×C₈	C₂²	1	1	yes	characteristic
15	C₂²⋊Q₈	—	2	4	no	—
16	C₂²⋊Q₈	C₂²	1	8	yes	—
17	C₂×C₄⋊C₄	—	2	2	no	—
18	C₂×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₂²⋊C₄	—	2	2	no	—
20	#106	C₂²	1	4	yes	complemented
21	#103	C₂²	1	8	yes	complemented
22	C₂⁴	D₄	1	1	yes	characteristic
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	C₂²×C₄	—	2	2	no	—
28	C₂²×C₄	—	2	2	no	—
29	C₂²×C₄	—	2	2	no	—
30	C₂²×C₄	—	2	2	no	—
31	C₂²×C₄	D₄	1	2	yes	—
32	C₂²×C₄	D₄	1	1	yes	characteristic
33	C₂²×C₄	C₂³	1	2	yes	—
34	C₂²×C₄	C₂³	1	1	yes	characteristic
35	Q₁₆	—	2	8	no	—
36	M₁₆	—	2	8	no	—
37	C₂×C₈	—	2	2	no	—
38	C₂×C₈	D₄	1	4	yes	—
39	C₂×C₈	C₂³	1	2	yes	—
40	C₂×C₈	C₂³	1	2	yes	—
41	C₄⋊C₄	—	2	8	no	—
42	C₄⋊C₄	—	2	2	no	—
43	C₄⋊C₄	C₂³	1	4	yes	—
44	C₂²⋊C₄	—	2	8	no	—
45	C₂³	—	2	2	no	—
46	C₂³	—	2	4	no	—
47	C₂³	C₂×D₄	1	2	yes	—
48	C₂³	C₂×D₄	1	1	yes	characteristic
49	Q₈	—	2	4	no	—
50	Q₈	—	2	4	no	—
51	Q₈	—	4	4	no	—
52	C₂×C₄	—	2	2	no	—
53	C₂×C₄	—	2	4	no	—
54	C₂×C₄	—	2	2	no	—
55	C₂×C₄	—	2	2	no	—
56	C₂×C₄	—	2	4	no	—
57	C₂×C₄	—	2	4	no	—
58	C₂×C₄	—	4	4	no	—
59	C₂×C₄	—	4	4	no	—
60	C₂×C₄	C₂×D₄	1	2	yes	—
61	C₂×C₄	C₂×D₄	1	1	yes	characteristic
62	C₂×C₄	C₂×D₄	1	2	yes	—
63	C₂×C₄	#41	1	2	yes	—
64	C₂×C₄	C₂⁴	1	1	yes	characteristic
65	C₈	—	2	2	no	—
66	C₈	C₂×D₄	1	4	yes	—
67	C₂²	—	2	2	no	—
68	C₂²	—	2	4	no	—
69	C₂²	—	4	4	no	—
70	C₂²	#121	1	2	yes	—
71	C₂²	#137	1	4	yes	—
72	C₂²	C₂²×D₄	1	1	yes	characteristic
73	C₄	—	2	2	no	—
74	C₄	—	4	4	no	—
75	C₄	—	4	4	no	—
76	C₄	#121	1	2	yes	—
77	C₄	C₂²×D₄	1	1	yes	characteristic
78	C₄	C₂×#41	1	1	yes	characteristic
79	C₂	—	4	2	no	—
80	C₂	#470	1	4	yes	direct product factor
81	C₂	C₂×#121	1	1	yes	characteristic
82	C₂	C₂×#137	1	2	yes	—

	subgroup	G/H
center, socle	C₂³	C₂×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴
prime radical	C₂⁴	D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ 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
4. #470	C₂	direct (N × H)
5. C₂×#106	C₂	semidirect
6. C₂×#103	C₂	semidirect
10. C₂×Q₁₆	C₂²	semidirect
20. #106	C₂²	semidirect
21. #103	C₂²	semidirect
80. C₂	#470	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×M₁₆	2
C₂×C₂²⋊Q₈	2
#470	2
C₂×#106	2
C₂×#103	2

Subgroups — C2×#470 #3053

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#470 #3053