Subgroups — C₂×#2868 #36643

Order 256.

1887 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊Q₈	C₂	1	6	yes	maximal
2	#2868	C₂	1	16	yes	maximal, direct product factor
3	C₂×#384	C₂	1	8	yes	maximal
4	C₂×C₄³	C₂	1	1	yes	maximal, characteristic
5	C₂³×Q₈	C₂²	1	4	yes	—
6	C₂×C₄⋊Q₈	—	2	48	no	—
7	C₂×C₄⋊Q₈	C₂²	1	48	yes	—
8	C₂²×C₄⋊C₄	C₂²	1	24	yes	—
9	C₂²×C₄²	C₂²	1	3	yes	—
10	C₂²×C₄²	C₂²	1	4	yes	—
11	#384	C₂²	1	64	yes	—
12	C₄³	C₂²	1	8	yes	—
13	C₂²×Q₈	—	2	48	no	—
14	C₂²×Q₈	C₂³	1	16	yes	—
15	C₂³×C₄	C₂³	1	8	yes	—
16	C₂³×C₄	C₂³	1	1	yes	characteristic
17	C₂³×C₄	C₂³	1	6	yes	—
18	C₄⋊Q₈	—	2	192	no	—
19	C₂×C₄⋊C₄	—	2	96	no	—
20	C₂×C₄⋊C₄	C₂³	1	96	yes	—
21	C₂×C₄²	D₄	1	24	yes	—
22	C₂×C₄²	Q₈	1	32	yes	complemented
23	C₂×C₄²	C₂³	1	12	yes	—
24	C₂×C₄²	C₂³	1	16	yes	—
25	C₂⁴	C₂⁴	1	1	yes	characteristic
26	C₂×Q₈	—	2	96	no	—
27	C₂×Q₈	—	4	64	no	—
28	C₂²×C₄	—	2	48	no	—
29	C₂²×C₄	C₂×D₄	1	12	yes	—
30	C₂²×C₄	C₂×D₄	1	24	yes	—
31	C₂²×C₄	C₂×Q₈	1	48	yes	—
32	C₂²×C₄	C₂⁴	1	16	yes	—
33	C₂²×C₄	C₂⁴	1	2	yes	—
34	C₂²×C₄	C₂⁴	1	12	yes	—
35	C₄⋊C₄	—	2	192	no	—
36	C₄²	C₂×D₄	1	48	yes	—
37	C₄²	C₂×Q₈	1	64	yes	complemented
38	C₂³	C₂²×D₄	1	6	yes	—
39	C₂³	C₂²×Q₈	1	8	yes	—
40	C₂³	C₂⁵	1	1	yes	characteristic
41	Q₈	—	4	64	no	—
42	C₂×C₄	—	2	48	no	—
43	C₂×C₄	—	4	32	no	—
44	C₂×C₄	#127	1	16	yes	—
45	C₂×C₄	C₄⋊Q₈	1	96	yes	complemented
46	C₂×C₄	C₂²×D₄	1	12	yes	—
47	C₂×C₄	C₂²×D₄	1	24	yes	—
48	C₂×C₄	C₂²×Q₈	1	48	yes	—
49	C₂²	C₂×#127	1	4	yes	—
50	C₂²	C₂×C₄⋊Q₈	1	24	yes	—
51	C₂²	C₂³×D₄	1	3	yes	—
52	C₂²	C₂³×Q₈	1	4	yes	—
53	C₄	—	4	16	no	—
54	C₄	C₂×#127	1	8	yes	—
55	C₄	C₂×C₄⋊Q₈	1	48	yes	complemented
56	C₂	#2868	1	8	yes	direct product factor
57	C₂	C₂²×#127	1	1	yes	characteristic
58	C₂	C₂²×C₄⋊Q₈	1	6	yes	—

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

Complements

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

N	H ≅ G/N	type
2. #2868	C₂	direct (N × H)
22. C₂×C₄²	Q₈	semidirect
37. C₄²	C₂×Q₈	semidirect
45. C₂×C₄	C₄⋊Q₈	semidirect
55. C₄	C₂×C₄⋊Q₈	semidirect
56. C₂	#2868	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×C₄⋊Q₈	2
#2868	2
C₂×#384	2
C₂×C₄³	2

Subgroups — C2×#2868 #36643

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2868 #36643