Subgroups — C₂×#2867 #36642

Order 256.

4047 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#127	C₂	1	14	yes	maximal, complemented
2	#2867	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₄³	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×D₄	C₂²	1	28	yes	—
5	C₂×#127	—	2	112	no	—
6	C₂×#127	C₂²	1	112	yes	complemented
7	C₂²×C₄²	C₂²	1	7	yes	—
8	C₄³	C₂²	1	8	yes	complemented
9	C₂⁵	C₂³	1	8	yes	—
10	C₂²×D₄	—	2	336	no	—
11	C₂²×D₄	C₂³	1	112	yes	—
12	C₂³×C₄	C₂³	1	7	yes	—
13	#127	—	2	448	no	—
14	C₂×C₄²	D₄	1	56	yes	complemented
15	C₂×C₄²	C₂³	1	28	yes	—
16	C₂⁴	—	2	112	no	—
17	C₂⁴	C₂⁴	1	16	yes	—
18	C₂⁴	C₂⁴	1	1	yes	characteristic
19	C₂×D₄	—	2	672	no	—
20	C₂×D₄	—	4	448	no	—
21	C₂²×C₄	C₂×D₄	1	84	yes	—
22	C₂²×C₄	C₂⁴	1	14	yes	—
23	C₄²	C₂×D₄	1	112	yes	complemented
24	C₂³	—	2	112	no	—
25	C₂³	—	4	224	no	—
26	C₂³	C₂²×D₄	1	14	yes	—
27	C₂³	C₂⁵	1	1	yes	characteristic
28	D₄	—	4	448	no	—
29	C₂×C₄	#127	1	112	yes	complemented
30	C₂×C₄	C₂²×D₄	1	84	yes	—
31	C₂²	—	4	112	no	—
32	C₂²	—	8	64	no	—
33	C₂²	C₂×#127	1	28	yes	—
34	C₂²	C₂³×D₄	1	7	yes	—
35	C₄	C₂×#127	1	56	yes	complemented
36	C₂	—	8	16	no	—
37	C₂	#2867	1	8	yes	direct product factor
38	C₂	C₂²×#127	1	7	yes	—

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

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

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