Subgroups — C₂×#2253 #33724

Order 256.

247 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#499	C₂	1	2	yes	maximal
2	#2253	C₂	1	8	yes	maximal, direct product factor
3	C₂×#367	C₂	1	2	yes	maximal
4	C₂×#366	C₂	1	2	yes	maximal
5	C₂×C₄×C₁₆	C₂	1	1	yes	maximal, characteristic
6	C₂×#125	—	2	2	no	—
7	C₂²×C₁₆	C₂²	1	1	yes	characteristic
8	C₂²×C₁₆	C₂²	1	1	yes	characteristic
9	#499	—	2	4	no	—
10	#499	C₂²	1	8	yes	—
11	C₂×#107	C₂²	1	4	yes	—
12	C₂×#106	—	2	2	no	—
13	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
14	#367	C₂²	1	8	yes	—
15	#366	C₂²	1	8	yes	—
16	C₄×C₁₆	C₂²	1	4	yes	—
17	C₂²×C₈	D₄	1	1	yes	characteristic
18	C₂²×C₈	C₂³	1	1	yes	characteristic
19	#125	—	2	8	no	—
20	#125	—	4	4	no	—
21	C₂×C₄⋊C₄	—	2	4	no	—
22	C₂×C₄⋊C₄	—	4	4	no	—
23	C₂×C₄²	D₄	1	1	yes	characteristic
24	C₂×C₁₆	Q₈	1	4	yes	—
25	C₂×C₁₆	Q₈	1	4	yes	—
26	C₂×C₁₆	C₂³	1	2	yes	—
27	C₂×C₁₆	C₂³	1	2	yes	—
28	#107	—	2	4	no	—
29	#107	C₂³	1	8	yes	—
30	#106	—	2	8	no	—
31	C₄×C₈	D₄	1	2	yes	—
32	C₄×C₈	C₂³	1	2	yes	—
33	C₂²×C₄	—	4	4	no	—
34	C₂²×C₄	D₈	1	2	yes	—
35	C₂²×C₄	C₂×D₄	1	1	yes	characteristic
36	C₂×C₈	Q₁₆	1	4	yes	—
37	C₂×C₈	C₂×D₄	1	1	yes	characteristic
38	C₂×C₈	C₂×D₄	1	2	yes	—
39	C₂×C₈	C₂×Q₈	1	2	yes	—
40	C₂×C₈	C₂×Q₈	1	2	yes	—
41	C₂×C₈	C₂⁴	1	1	yes	characteristic
42	C₄⋊C₄	—	2	8	no	—
43	C₄⋊C₄	—	4	4	no	—
44	C₄⋊C₄	—	4	16	no	—
45	C₄²	D₈	1	2	yes	—
46	C₄²	C₂×D₄	1	2	yes	—
47	C₁₆	C₂×Q₈	1	4	yes	—
48	C₁₆	C₂×Q₈	1	4	yes	—
49	C₂³	C₂×D₈	1	1	yes	characteristic
50	C₂×C₄	—	2	4	no	—
51	C₂×C₄	—	4	8	no	—
52	C₂×C₄	—	8	8	no	—
53	C₂×C₄	C₄⋊Q₈	1	2	yes	—
54	C₂×C₄	C₂×D₈	1	4	yes	—
55	C₂×C₄	C₂×D₈	1	1	yes	characteristic
56	C₂×C₄	C₂×Q₁₆	1	2	yes	—
57	C₂×C₄	C₂²×D₄	1	1	yes	characteristic
58	C₈	C₄⋊Q₈	1	2	yes	—
59	C₈	C₂×Q₁₆	1	4	yes	—
60	C₈	C₂²×Q₈	1	1	yes	characteristic
61	C₈	C₂²×Q₈	1	1	yes	characteristic
62	C₂²	#500	1	2	yes	—
63	C₂²	#508	1	4	yes	—
64	C₂²	C₂²×D₈	1	1	yes	characteristic
65	C₄	—	2	4	no	—
66	C₄	—	8	8	no	—
67	C₄	#500	1	2	yes	—
68	C₄	C₂×C₄⋊Q₈	1	1	yes	characteristic
69	C₄	C₂²×Q₁₆	1	1	yes	characteristic
70	C₂	#2253	1	4	yes	direct product factor
71	C₂	C₂×#500	1	1	yes	characteristic
72	C₂	C₂×#508	1	2	yes	—

	subgroup	G/H
center, socle, prime radical	C₂³	C₂×D₈
commutator, Frattini, cosocle	C₂×C₈	C₂⁴
LCS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ G
LECS	G ▷ C₂×C₈ ▷ C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. #2253	C₂	direct (N × H)
70. C₂	#2253	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×#499	2
#2253	2
C₂×#367	2
C₂×#366	2
C₂×C₄×C₁₆	2

Subgroups — C2×#2253 #33724

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#2253 #33724