Subgroups — C₂×#533 #3443

Order 128.

584 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#533	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₄⋊Q₈	C₂	1	2	yes	maximal, complemented
3	C₂×#125	C₂	1	2	yes	maximal, complemented
4	C₂×C₂²⋊Q₈	C₂	1	4	yes	maximal
5	C₂×C₄×Q₈	C₂	1	4	yes	maximal, complemented
6	C₂×#117	C₂	1	2	yes	maximal
7	C₂²×C₄²	C₂	1	1	yes	maximal, characteristic
8	C₂²×Q₈	C₂²	1	4	yes	—
9	C₂³×C₄	C₂²	1	2	yes	—
10	C₂³×C₄	C₂²	1	1	yes	characteristic
11	C₄⋊Q₈	C₂²	1	16	yes	complemented
12	#125	C₂²	1	16	yes	complemented
13	C₂²⋊Q₈	C₂²	1	32	yes	—
14	C₄×Q₈	C₂²	1	32	yes	complemented
15	#117	C₂²	1	16	yes	—
16	C₂×C₄⋊C₄	C₂²	1	4	yes	—
17	C₂×C₄⋊C₄	C₂²	1	8	yes	—
18	C₂×C₄⋊C₄	C₂²	1	4	yes	—
19	C₂×C₂²⋊C₄	C₂²	1	4	yes	—
20	C₂×C₄²	C₂²	1	1	yes	characteristic
21	C₂×C₄²	C₂²	1	1	yes	characteristic
22	C₂×C₄²	C₂²	1	8	yes	—
23	C₂×C₄²	C₂²	1	4	yes	—
24	C₂×C₄²	C₂²	1	2	yes	—
25	C₂⁴	C₂³	1	1	yes	characteristic
26	C₂×Q₈	—	2	16	no	—
27	C₂×Q₈	C₂³	1	16	yes	—
28	C₂²×C₄	—	2	8	no	—
29	C₂²×C₄	Q₈	1	8	yes	complemented
30	C₂²×C₄	C₂³	1	2	yes	—
31	C₂²×C₄	C₂³	1	8	yes	—
32	C₂²×C₄	C₂³	1	8	yes	—
33	C₂²×C₄	C₂³	1	1	yes	characteristic
34	C₂²×C₄	C₂³	1	4	yes	—
35	C₂²×C₄	C₂³	1	2	yes	—
36	C₂²×C₄	C₂³	1	1	yes	characteristic
37	C₄⋊C₄	C₂³	1	16	yes	—
38	C₄⋊C₄	C₂³	1	32	yes	—
39	C₄⋊C₄	C₂³	1	16	yes	—
40	C₂²⋊C₄	C₂³	1	16	yes	—
41	C₄²	C₂³	1	8	yes	—
42	C₄²	C₂³	1	4	yes	—
43	C₄²	C₂³	1	4	yes	—
44	C₄²	C₂³	1	16	yes	—
45	C₂³	—	2	4	no	—
46	C₂³	C₂×Q₈	1	4	yes	—
47	C₂³	C₂⁴	1	2	yes	—
48	C₂³	C₂⁴	1	1	yes	characteristic
49	Q₈	—	2	32	no	—
50	C₂×C₄	—	2	4	no	—
51	C₂×C₄	—	2	16	no	—
52	C₂×C₄	—	2	16	no	—
53	C₂×C₄	C₂×Q₈	1	4	yes	—
54	C₂×C₄	C₂×Q₈	1	4	yes	—
55	C₂×C₄	C₂×Q₈	1	16	yes	complemented
56	C₂×C₄	#41	1	8	yes	—
57	C₂×C₄	C₂⁴	1	4	yes	—
58	C₂×C₄	C₂⁴	1	16	yes	—
59	C₂×C₄	C₂⁴	1	2	yes	—
60	C₂×C₄	C₂⁴	1	2	yes	—
61	C₂×C₄	C₂⁴	1	4	yes	—
62	C₂²	—	2	8	no	—
63	C₂²	—	2	4	no	—
64	C₂²	C₂²×Q₈	1	4	yes	—
65	C₂²	C₂²×Q₈	1	2	yes	—
66	C₂²	C₂×#41	1	4	yes	—
67	C₂²	C₂⁵	1	1	yes	characteristic
68	C₄	—	2	4	no	—
69	C₄	—	2	16	no	—
70	C₄	C₂²×Q₈	1	4	yes	—
71	C₄	C₂²×Q₈	1	4	yes	—
72	C₄	C₂×#41	1	8	yes	—
73	C₂	—	2	4	no	—
74	C₂	#533	1	4	yes	direct product factor
75	C₂	C₂³×Q₈	1	1	yes	characteristic
76	C₂	C₂²×#41	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁵
socle	C₂³	C₂⁴
prime radical	C₂⁴	C₂³
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #533	C₂	direct (N × H)
2. C₂×C₄⋊Q₈	C₂	semidirect
3. C₂×#125	C₂	semidirect
5. C₂×C₄×Q₈	C₂	semidirect
11. C₄⋊Q₈	C₂²	semidirect
12. #125	C₂²	semidirect
14. C₄×Q₈	C₂²	semidirect
29. C₂²×C₄	Q₈	semidirect
55. C₂×C₄	C₂×Q₈	semidirect
74. C₂	#533	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#533	2
C₂×C₄⋊Q₈	2
C₂×#125	2
C₂×C₂²⋊Q₈	2
C₂×C₄×Q₈	2
C₂×#117	2
C₂²×C₄²	2

Subgroups — C2×#533 #3443

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#533 #3443