Subgroups — C₂×#2844 #36688

Order 256.

935 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2844	C₂	1	16	yes	maximal, direct product factor
2	C₂×#400	C₂	1	6	yes	maximal
3	C₂×#395	C₂	1	6	yes	maximal
4	C₂×#382	C₂	1	3	yes	maximal
5	C₂³×Q₈	C₂²	1	2	yes	—
6	C₂²×C₄⋊C₄	C₂²	1	6	yes	—
7	C₂²×C₄⋊C₄	C₂²	1	3	yes	—
8	C₂²×C₄⋊C₄	C₂²	1	3	yes	—
9	C₂²×C₄²	C₂²	1	1	yes	characteristic
10	#400	C₂²	1	48	yes	—
11	#395	C₂²	1	48	yes	—
12	#382	C₂²	1	24	yes	—
13	C₂×#95	C₂²	1	6	yes	—
14	C₂×#95	C₂²	1	12	yes	—
15	C₂×#95	C₂²	1	2	yes	—
16	C₂²×Q₈	—	4	12	no	—
17	C₂²×Q₈	C₂³	1	8	yes	—
18	C₂³×C₄	C₂³	1	6	yes	—
19	C₂³×C₄	C₂³	1	6	yes	—
20	C₂³×C₄	C₂³	1	3	yes	—
21	C₂×C₄⋊C₄	—	4	6	no	—
22	C₂×C₄⋊C₄	—	4	6	no	—
23	C₂×C₄⋊C₄	—	4	12	no	—
24	C₂×C₄⋊C₄	C₂³	1	12	yes	—
25	C₂×C₄⋊C₄	C₂³	1	12	yes	—
26	C₂×C₄⋊C₄	C₂³	1	24	yes	—
27	C₂×C₄²	Q₈	1	8	yes	complemented
28	C₂×C₄²	C₂³	1	4	yes	—
29	#95	C₂³	1	48	yes	—
30	#95	C₂³	1	24	yes	—
31	#95	C₂³	1	8	yes	—
32	C₂⁴	C₂⁴	1	1	yes	characteristic
33	C₂×Q₈	—	4	24	no	—
34	C₂×Q₈	—	4	32	no	—
35	C₂²×C₄	—	2	6	no	—
36	C₂²×C₄	—	2	6	no	—
37	C₂²×C₄	—	2	12	no	—
38	C₂²×C₄	—	2	12	no	—
39	C₂²×C₄	—	2	24	no	—
40	C₂²×C₄	—	2	24	no	—
41	C₂²×C₄	C₂×Q₈	1	12	yes	—
42	C₂²×C₄	C₂⁴	1	12	yes	—
43	C₂²×C₄	C₂⁴	1	12	yes	—
44	C₂²×C₄	C₂⁴	1	6	yes	—
45	C₄⋊C₄	—	4	12	no	—
46	C₄⋊C₄	—	4	12	no	—
47	C₄⋊C₄	—	4	24	no	—
48	C₄²	C₂×Q₈	1	16	yes	complemented
49	C₂³	C₂²×Q₈	1	2	yes	—
50	C₂³	H(5,𝔽₂)	1	6	yes	—
51	C₂³	2₋¹⁺⁴	1	6	yes	—
52	C₂³	C₂⁵	1	1	yes	characteristic
53	Q₈	—	4	32	no	—
54	C₂×C₄	—	2	24	no	—
55	C₂×C₄	—	2	6	no	—
56	C₂×C₄	—	2	6	no	—
57	C₂×C₄	—	2	12	no	—
58	C₂×C₄	—	2	12	no	—
59	C₂×C₄	—	2	24	no	—
60	C₂×C₄	—	2	24	no	—
61	C₂×C₄	—	4	24	no	—
62	C₂×C₄	—	4	24	no	—
63	C₂×C₄	C₂²×Q₈	1	12	yes	—
64	C₂²	#544	1	12	yes	—
65	C₂²	H(3,𝔽₄)	1	4	yes	—
66	C₂²	#563	1	12	yes	—
67	C₂²	C₂³×Q₈	1	1	yes	characteristic
68	C₂²	C₂×H(5,𝔽₂)	1	3	yes	—
69	C₂²	C₂×2₋¹⁺⁴	1	3	yes	—
70	C₄	—	2	12	no	—
71	C₄	—	4	12	no	—
72	C₄	—	4	12	no	—
73	C₂	#2844	1	8	yes	direct product factor
74	C₂	C₂×#544	1	3	yes	—
75	C₂	C₂×H(3,𝔽₄)	1	1	yes	characteristic
76	C₂	C₂×#563	1	3	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
1. #2844	C₂	direct (N × H)
27. C₂×C₄²	Q₈	semidirect
48. C₄²	C₂×Q₈	semidirect
73. C₂	#2844	direct (N × H)

Maximal subgroups

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

subgroup	index
#2844	2
C₂×#400	2
C₂×#395	2
C₂×#382	2

Subgroups — C2×#2844 #36688

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2844 #36688