Subgroups — C₂³×2₋¹⁺⁴ #63099

Order 256.

29903 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×2₋¹⁺⁴	C₂	1	112	yes	maximal, direct product factor
2	C₂³×#41	C₂	1	10	yes	maximal, complemented
3	C₂⁴×Q₈	C₂	1	5	yes	maximal, complemented
4	C₂×2₋¹⁺⁴	C₂²	1	1792	yes	direct product factor
5	C₂²×#41	C₂²	1	560	yes	complemented
6	C₂³×Q₈	C₂²	1	10	yes	—
7	C₂³×Q₈	C₂²	1	280	yes	complemented
8	C₂³×D₄	C₂²	1	10	yes	—
9	C₂⁴×C₄	C₂²	1	15	yes	—
10	C₂⁵	C₂³	1	5	yes	—
11	2₋¹⁺⁴	C₂³	1	4096	yes	direct product factor
12	C₂×#41	C₂³	1	4480	yes	complemented
13	C₂²×Q₈	C₂³	1	280	yes	—
14	C₂²×Q₈	C₂³	1	2240	yes	complemented
15	C₂²×D₄	C₂³	1	280	yes	—
16	C₂³×C₄	C₂³	1	420	yes	—
17	C₂³×C₄	C₂³	1	10	yes	—
18	C₂⁴	—	2	40	no	—
19	C₂⁴	C₂⁴	1	70	yes	—
20	C₂⁴	C₂⁴	1	1	yes	characteristic
21	#41	C₂⁴	1	5120	yes	complemented
22	C₂×Q₈	C₂⁴	1	1120	yes	—
23	C₂×Q₈	C₂⁴	1	2560	yes	complemented
24	C₂×D₄	C₂⁴	1	1120	yes	—
25	C₂²×C₄	C₂⁴	1	140	yes	—
26	C₂²×C₄	C₂⁴	1	1680	yes	—
27	C₂³	—	2	280	no	—
28	C₂³	2₋¹⁺⁴	1	8	yes	direct product factor
29	C₂³	C₂⁵	1	140	yes	—
30	C₂³	C₂⁵	1	7	yes	—
31	Q₈	C₂⁵	1	640	yes	—
32	D₄	C₂⁵	1	640	yes	—
33	C₂×C₄	C₂⁵	1	280	yes	—
34	C₂×C₄	C₂⁵	1	960	yes	—
35	C₂²	—	2	280	no	—
36	C₂²	C₂×2₋¹⁺⁴	1	28	yes	direct product factor
37	C₂²	C₂⁶	1	40	yes	—
38	C₂²	C₂⁶	1	7	yes	—
39	C₄	C₂⁶	1	80	yes	—
40	C₂	—	2	40	no	—
41	C₂	C₂²×2₋¹⁺⁴	1	14	yes	direct product factor
42	C₂	C₂⁷	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴	C₂⁴
commutator, Frattini, cosocle	C₂	C₂⁷
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴ ◁ G
LECS	G ▷ C₂ ▷ 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.