Subgroups — C₂×#2262 #33978

Order 256.

235 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#508	C₂	1	2	yes	maximal, complemented
2	#2262	C₂	1	8	yes	maximal, direct product factor
3	C₂×Q₆₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×SD₆₄	C₂	1	2	yes	maximal, complemented
5	C₂×D₃₂	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×C₃₂	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#135	—	2	2	no	—
8	#508	—	2	4	no	—
9	#508	C₂²	1	8	yes	complemented
10	C₂×Q₃₂	C₂²	1	2	yes	—
11	C₂×SD₃₂	—	2	2	no	—
12	C₂×D₁₆	C₂²	1	2	yes	—
13	C₂²×C₁₆	C₂²	1	1	yes	characteristic
14	Q₆₄	C₂²	1	4	yes	complemented
15	SD₆₄	C₂²	1	8	yes	complemented
16	D₃₂	C₂²	1	4	yes	complemented
17	C₂×C₃₂	C₂²	1	1	yes	characteristic
18	C₂×C₃₂	C₂²	1	1	yes	characteristic
19	C₂×C₃₂	C₂²	1	4	yes	complemented
20	C₂×#41	—	4	2	no	—
21	#135	—	2	8	no	—
22	#135	—	4	4	no	—
23	C₂×Q₁₆	—	2	2	no	—
24	C₂×SD₁₆	—	4	2	no	—
25	C₂×D₈	—	2	2	no	—
26	C₂²×C₈	D₄	1	1	yes	characteristic
27	Q₃₂	—	2	2	no	—
28	Q₃₂	C₂³	1	4	yes	—
29	SD₃₂	—	2	8	no	—
30	D₁₆	—	2	2	no	—
31	D₁₆	C₂³	1	4	yes	—
32	C₂×C₁₆	D₄	1	1	yes	characteristic
33	C₂×C₁₆	D₄	1	2	yes	—
34	C₂×C₁₆	C₂³	1	1	yes	characteristic
35	C₂×C₁₆	C₂³	1	2	yes	—
36	C₃₂	C₂³	1	2	yes	—
37	C₃₂	C₂³	1	2	yes	—
38	#41	—	4	8	no	—
39	#41	—	8	4	no	—
40	C₂×Q₈	—	4	2	no	—
41	C₂×D₄	—	4	2	no	—
42	C₂×D₄	—	8	2	no	—
43	C₂²×C₄	—	8	2	no	—
44	C₂²×C₄	D₈	1	1	yes	characteristic
45	Q₁₆	—	2	4	no	—
46	Q₁₆	—	4	2	no	—
47	SD₁₆	—	4	8	no	—
48	D₈	—	2	4	no	—
49	D₈	—	4	2	no	—
50	C₂×C₈	D₈	1	1	yes	characteristic
51	C₂×C₈	D₈	1	2	yes	—
52	C₂×C₈	C₂×D₄	1	1	yes	characteristic
53	C₂×C₈	C₂×D₄	1	2	yes	—
54	C₁₆	C₂×D₄	1	1	yes	characteristic
55	C₁₆	C₂×D₄	1	2	yes	—
56	C₁₆	C₂⁴	1	1	yes	characteristic
57	C₂³	—	8	2	no	—
58	C₂³	D₁₆	1	1	yes	characteristic
59	Q₈	—	4	4	no	—
60	Q₈	—	8	2	no	—
61	D₄	—	4	4	no	—
62	D₄	—	8	8	no	—
63	D₄	—	8	2	no	—
64	C₂×C₄	—	8	2	no	—
65	C₂×C₄	—	8	8	no	—
66	C₂×C₄	D₁₆	1	2	yes	—
67	C₂×C₄	D₁₆	1	1	yes	characteristic
68	C₂×C₄	C₂×D₈	1	1	yes	characteristic
69	C₂×C₄	C₂×D₈	1	2	yes	—
70	C₈	C₂×D₈	1	1	yes	characteristic
71	C₈	C₂×D₈	1	2	yes	—
72	C₈	C₂²×D₄	1	1	yes	characteristic
73	C₂²	—	2	2	no	—
74	C₂²	—	8	4	no	—
75	C₂²	—	16	4	no	—
76	C₂²	C₂×D₁₆	1	2	yes	—
77	C₂²	C₂×D₁₆	1	1	yes	characteristic
78	C₄	—	8	4	no	—
79	C₄	C₂×D₁₆	1	2	yes	—
80	C₄	C₂×D₁₆	1	1	yes	characteristic
81	C₄	C₂²×D₈	1	1	yes	characteristic
82	C₂	—	2	2	no	—
83	C₂	—	16	4	no	—
84	C₂	#2262	1	2	yes	direct product factor
85	C₂	C₂²×D₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₁₆
commutator, Frattini, cosocle	C₁₆	C₂⁴
socle	C₂²	C₂×D₁₆
LCS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂²×C₈ ◁ C₂²×C₁₆ ◁ G
LECS	G ▷ C₁₆ ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. C₂×#508	C₂	semidirect
2. #2262	C₂	direct (N × H)
3. C₂×Q₆₄	C₂	semidirect
4. C₂×SD₆₄	C₂	semidirect
5. C₂×D₃₂	C₂	semidirect
6. C₂²×C₃₂	C₂	semidirect
9. #508	C₂²	semidirect
14. Q₆₄	C₂²	semidirect
15. SD₆₄	C₂²	semidirect
16. D₃₂	C₂²	semidirect
19. C₂×C₃₂	C₂²	semidirect
84. C₂	#2262	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#508	2
#2262	2
C₂×Q₆₄	2
C₂×SD₆₄	2
C₂×D₃₂	2
C₂²×C₃₂	2

Subgroups — C2×#2262 #33978

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2262 #33978