Subgroups — C₂³×#127 #62664

Order 256.

12015 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄	C₂	1	6	yes	maximal, complemented
2	C₂²×#127	C₂	1	56	yes	maximal, direct product factor
3	C₂³×C₄²	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁶	C₂²	1	4	yes	—
5	C₂³×D₄	—	2	96	no	—
6	C₂³×D₄	C₂²	1	168	yes	complemented
7	C₂⁴×C₄	C₂²	1	3	yes	—
8	C₂×#127	C₂²	1	448	yes	direct product factor
9	C₂²×C₄²	C₂²	1	28	yes	complemented
10	C₂⁵	—	2	96	no	—
11	C₂⁵	C₂³	1	56	yes	—
12	C₂⁵	C₂³	1	1	yes	characteristic
13	C₂²×D₄	—	2	1344	no	—
14	C₂²×D₄	C₂³	1	672	yes	complemented
15	C₂³×C₄	D₄	1	48	yes	complemented
16	C₂³×C₄	C₂³	1	42	yes	—
17	#127	C₂³	1	512	yes	direct product factor
18	C₂×C₄²	C₂³	1	112	yes	complemented
19	C₂⁴	—	2	672	no	—
20	C₂⁴	—	4	256	no	—
21	C₂⁴	C₂×D₄	1	24	yes	—
22	C₂⁴	C₂⁴	1	112	yes	—
23	C₂⁴	C₂⁴	1	7	yes	—
24	C₂×D₄	—	2	2688	no	—
25	C₂×D₄	C₂⁴	1	384	yes	complemented
26	C₂²×C₄	C₂×D₄	1	336	yes	complemented
27	C₂²×C₄	C₂⁴	1	84	yes	—
28	C₄²	C₂⁴	1	64	yes	complemented
29	C₂³	—	2	672	no	—
30	C₂³	—	4	896	no	—
31	C₂³	#127	1	64	yes	direct product factor
32	C₂³	C₂²×D₄	1	84	yes	—
33	C₂³	C₂⁵	1	32	yes	—
34	C₂³	C₂⁵	1	7	yes	—
35	D₄	—	2	768	no	—
36	C₂×C₄	C₂²×D₄	1	336	yes	complemented
37	C₂×C₄	C₂⁵	1	24	yes	—
38	C₂²	—	2	96	no	—
39	C₂²	—	4	448	no	—
40	C₂²	C₂×#127	1	112	yes	direct product factor
41	C₂²	C₂³×D₄	1	42	yes	—
42	C₂²	C₂⁶	1	1	yes	characteristic
43	C₄	C₂³×D₄	1	48	yes	complemented
44	C₂	—	4	32	no	—
45	C₂	C₂²×#127	1	28	yes	direct product factor
46	C₂	C₂⁴×D₄	1	3	yes	—

	subgroup	G/H
center, socle	C₂⁵	C₂³
commutator, Frattini, cosocle	C₂²	C₂⁶
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂⁵ ◁ G
LECS	G ▷ C₂² ▷ 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.