Subgroups — C₂×#1311 #11397

Order 256.

183 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₆	C₂	1	2	yes	maximal
2	C₂×C₈²	C₂	1	1	yes	maximal, characteristic
3	#1311	C₂	1	4	yes	maximal, direct product factor
4	C₂²×C₁₆	C₄	1	4	yes	—
5	C₂×C₄×C₈	C₄	1	2	yes	—
6	C₂×C₄×C₈	C₂²	1	1	yes	characteristic
7	C₄×C₁₆	C₄	1	4	yes	—
8	C₄×C₁₆	C₂²	1	4	yes	—
9	C₈²	C₄	1	2	yes	—
10	C₈²	C₂²	1	2	yes	—
11	C₂²×C₈	C₈	1	4	yes	—
12	C₂²×C₈	C₂×C₄	1	2	yes	—
13	C₂×C₄²	C₂×C₄	1	1	yes	characteristic
14	C₂×C₁₆	C₈	1	16	yes	complemented
15	C₂×C₁₆	C₂×C₄	1	8	yes	—
16	C₄×C₈	C₈	1	4	yes	—
17	C₄×C₈	C₂×C₄	1	2	yes	—
18	C₄×C₈	C₂×C₄	1	1	yes	characteristic
19	C₄×C₈	C₂×C₄	1	4	yes	—
20	C₄×C₈	C₂³	1	1	yes	characteristic
21	C₂²×C₄	C₄²	1	1	yes	characteristic
22	C₂²×C₄	C₂×C₈	1	2	yes	—
23	C₂×C₈	—	2	8	no	—
24	C₂×C₈	C₄²	1	2	yes	—
25	C₂×C₈	C₂×C₈	1	8	yes	—
26	C₂×C₈	C₂×C₈	1	8	yes	—
27	C₂×C₈	C₂²×C₄	1	2	yes	—
28	C₄²	C₄²	1	1	yes	characteristic
29	C₄²	C₂×C₈	1	2	yes	—
30	C₄²	C₂²×C₄	1	1	yes	characteristic
31	C₁₆	C₂×C₈	1	16	yes	complemented
32	C₂³	C₄×C₈	1	1	yes	characteristic
33	C₂×C₄	C₄×C₈	1	1	yes	characteristic
34	C₂×C₄	C₄×C₈	1	4	yes	—
35	C₂×C₄	C₄×C₈	1	2	yes	—
36	C₂×C₄	M₃₂	1	8	yes	—
37	C₂×C₄	C₂×C₄²	1	1	yes	characteristic
38	C₂×C₄	C₂²×C₈	1	2	yes	—
39	C₈	—	2	8	no	—
40	C₈	C₄×C₈	1	4	yes	—
41	C₈	C₂²×C₈	1	4	yes	—
42	C₂²	C₈²	1	2	yes	—
43	C₂²	#346	1	4	yes	—
44	C₂²	C₂×C₄×C₈	1	1	yes	characteristic
45	C₄	C₈²	1	2	yes	—
46	C₄	#346	1	4	yes	—
47	C₄	C₂×C₄×C₈	1	2	yes	—
48	C₄	C₂×M₃₂	1	4	yes	—
49	C₂	#1311	1	4	yes	direct product factor
50	C₂	C₂×C₈²	1	1	yes	characteristic
51	C₂	C₂×#346	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₈	C₂²
commutator	C₂	C₂×C₈²
Frattini, cosocle	C₄×C₈	C₂³
socle, prime radical	C₂³	C₄×C₈
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₈ ◁ G
LECS	G ▷ C₄×C₈ ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
3. #1311	C₂	direct (N × H)
14. C₂×C₁₆	C₈	semidirect
31. C₁₆	C₂×C₈	semidirect
49. C₂	#1311	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×C₄×C₁₆	2
C₂×C₈²	2
#1311	2

Subgroups — C2×#1311 #11397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#1311 #11397