Subgroups — C₂×#557 #3476

Order 128.

524 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#557	C₂	1	16	yes	maximal, direct product factor
2	C₂×C₄⋊Q₈	C₂	1	3	yes	maximal
3	C₂×#125	C₂	1	6	yes	maximal
4	C₂×C₄×Q₈	C₂	1	2	yes	maximal
5	C₂×C₄×Q₈	C₂	1	3	yes	maximal
6	C₂×C₄×Q₈	C₂	1	1	yes	maximal, characteristic
7	C₂²×Q₈	C₂²	1	3	yes	—
8	C₂²×Q₈	C₂²	1	1	yes	characteristic
9	C₄⋊Q₈	C₂²	1	24	yes	—
10	#125	C₂²	1	48	yes	—
11	C₄×Q₈	C₂²	1	16	yes	—
12	C₄×Q₈	C₂²	1	24	yes	—
13	C₄×Q₈	C₂²	1	8	yes	—
14	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₄	C₂²	1	6	yes	—
16	C₂×C₄⋊C₄	C₂²	1	3	yes	—
17	C₂×C₄⋊C₄	C₂²	1	6	yes	—
18	C₂×C₄⋊C₄	C₂²	1	6	yes	—
19	C₂×C₄²	C₂²	1	6	yes	—
20	C₂×C₄²	C₂²	1	3	yes	—
21	C₂×Q₈	—	2	12	no	—
22	C₂×Q₈	Q₈	1	8	yes	complemented
23	C₂×Q₈	C₂³	1	12	yes	—
24	C₂×Q₈	C₂³	1	4	yes	—
25	C₂²×C₄	C₂³	1	2	yes	—
26	C₂²×C₄	C₂³	1	3	yes	—
27	C₂²×C₄	C₂³	1	6	yes	—
28	C₂²×C₄	C₂³	1	3	yes	—
29	C₂²×C₄	C₂³	1	1	yes	characteristic
30	C₄⋊C₄	C₂³	1	4	yes	—
31	C₄⋊C₄	C₂³	1	24	yes	—
32	C₄⋊C₄	C₂³	1	12	yes	—
33	C₄⋊C₄	C₂³	1	24	yes	—
34	C₄⋊C₄	C₂³	1	24	yes	—
35	C₄²	C₂³	1	24	yes	—
36	C₄²	C₂³	1	12	yes	—
37	C₂³	C₂⁴	1	1	yes	characteristic
38	Q₈	—	2	24	no	—
39	Q₈	C₂×Q₈	1	16	yes	complemented
40	C₂×C₄	—	2	12	no	—
41	C₂×C₄	—	2	4	no	—
42	C₂×C₄	—	2	6	no	—
43	C₂×C₄	C₂×Q₈	1	12	yes	—
44	C₂×C₄	#41	1	4	yes	—
45	C₂×C₄	C₂⁴	1	4	yes	—
46	C₂×C₄	C₂⁴	1	6	yes	—
47	C₂×C₄	C₂⁴	1	12	yes	—
48	C₂×C₄	C₂⁴	1	6	yes	—
49	C₂×C₄	C₂⁴	1	2	yes	—
50	C₂²	C₂²×Q₈	1	2	yes	—
51	C₂²	C₂×#41	1	2	yes	—
52	C₂²	2₋¹⁺⁴	1	2	yes	—
53	C₂²	C₂⁵	1	1	yes	characteristic
54	C₄	—	2	12	no	—
55	C₄	—	2	4	no	—
56	C₄	—	2	6	no	—
57	C₄	C₂²×Q₈	1	12	yes	—
58	C₄	C₂×#41	1	4	yes	—
59	C₂	#557	1	4	yes	direct product factor
60	C₂	C₂³×Q₈	1	1	yes	characteristic
61	C₂	C₂²×#41	1	1	yes	characteristic
62	C₂	C₂×2₋¹⁺⁴	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. #557	C₂	direct (N × H)
22. C₂×Q₈	Q₈	semidirect
39. Q₈	C₂×Q₈	semidirect
59. C₂	#557	direct (N × H)

Maximal subgroups

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

subgroup	index
#557	2
C₂×C₄⋊Q₈	2
C₂×#125	2
C₂×C₄×Q₈	2

Subgroups — C2×#557 #3476

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#557 #3476