Subgroups — C₂×#2866 #36637

Order 256.

1093 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#2866	C₂	1	16	yes	maximal, direct product factor
2	C₂×#388	C₂	1	7	yes	maximal
3	C₂×#387	C₂	1	7	yes	maximal, complemented
4	C₂×C₄³	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×C₄⋊C₄	C₂²	1	7	yes	—
6	C₂²×C₂²⋊C₄	C₂²	1	7	yes	—
7	C₂²×C₄²	C₂²	1	7	yes	—
8	#388	C₂²	1	56	yes	—
9	#387	C₂²	1	56	yes	complemented
10	C₂×#95	C₂²	1	14	yes	—
11	C₄³	C₂²	1	8	yes	complemented
12	C₂⁵	C₂³	1	1	yes	characteristic
13	C₂³×C₄	C₂³	1	7	yes	—
14	C₂³×C₄	C₂³	1	7	yes	—
15	C₂×C₄⋊C₄	—	2	28	no	—
16	C₂×C₄⋊C₄	C₂³	1	28	yes	—
17	C₂×C₂²⋊C₄	—	2	28	no	—
18	C₂×C₂²⋊C₄	C₂³	1	28	yes	—
19	C₂×C₄²	—	2	28	no	—
20	C₂×C₄²	C₂³	1	28	yes	—
21	#95	C₂³	1	56	yes	—
22	C₂⁴	—	2	14	no	—
23	C₂⁴	C₂⁴	1	2	yes	—
24	C₂⁴	C₂⁴	1	1	yes	characteristic
25	C₂²×C₄	—	2	28	no	—
26	C₂²×C₄	—	2	14	no	—
27	C₂²×C₄	—	2	28	no	—
28	C₂²×C₄	#41	1	28	yes	—
29	C₂²×C₄	C₂⁴	1	14	yes	—
30	C₂²×C₄	C₂⁴	1	14	yes	—
31	C₄⋊C₄	—	2	56	no	—
32	C₂²⋊C₄	—	2	56	no	—
33	C₄²	—	2	56	no	—
34	C₂³	—	2	14	no	—
35	C₂³	—	4	28	no	—
36	C₂³	C₂×#41	1	14	yes	—
37	C₂³	C₂⁵	1	1	yes	characteristic
38	C₂×C₄	—	2	56	no	—
39	C₂×C₄	—	2	28	no	—
40	C₂×C₄	—	2	14	no	—
41	C₂×C₄	—	2	28	no	—
42	C₂×C₄	—	4	28	no	—
43	C₂×C₄	C₂×#41	1	28	yes	—
44	C₂²	—	4	14	no	—
45	C₂²	—	8	8	no	—
46	C₂²	#529	1	28	yes	—
47	C₂²	C₂²×#41	1	7	yes	—
48	C₄	—	2	28	no	—
49	C₄	—	4	14	no	—
50	C₂	—	8	2	no	—
51	C₂	#2866	1	8	yes	direct product factor
52	C₂	C₂×#529	1	7	yes	—

	subgroup	G/H
center, socle	C₂⁴	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁵
prime radical	C₂⁵	C₂³
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.