Subgroups — C₂⁷×D₆₁ #30593917

Order 15616.

834398 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁶×D₆₁	C₂	1	254	yes	maximal, direct product factor
2	C₂⁷×C₆₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂⁵×D₆₁	C₂²	1	10668	yes	direct product factor
4	C₂⁶×C₆₁	C₂²	1	127	yes	complemented
5	C₂⁴×D₆₁	C₂³	1	94488	yes	direct product factor
6	C₂⁵×C₆₁	C₂³	1	2667	yes	complemented
7	C₂⁴×C₆₁	C₂⁴	1	11811	yes	complemented
8	C₂³×D₆₁	C₂⁴	1	188976	yes	direct product factor
9	C₂³×C₆₁	C₂⁵	1	11811	yes	complemented
10	C₂²×D₆₁	C₂⁵	1	85344	yes	direct product factor
11	C₂⁸	—	61	1	no	maximal, Sylow
12	C₂²×C₆₁	C₂⁶	1	2667	yes	complemented
13	C₂×D₆₁	C₂⁶	1	8128	yes	direct product factor
14	C₂⁷	—	61	254	no	—
15	C₂⁷	D₆₁	1	1	yes	characteristic, direct product factor
16	C₂×C₆₁	C₂⁷	1	127	yes	complemented
17	D₆₁	C₂⁷	1	128	yes	direct product factor
18	C₂⁶	—	61	10668	no	—
19	C₂⁶	C₂×D₆₁	1	127	yes	direct product factor
20	C₆₁	C₂⁸	1	1	yes	characteristic, complemented, Sylow
21	C₂⁵	—	61	94488	no	—
22	C₂⁵	C₂²×D₆₁	1	2667	yes	direct product factor
23	C₂⁴	—	61	188976	no	—
24	C₂⁴	C₂³×D₆₁	1	11811	yes	direct product factor
25	C₂³	—	61	85344	no	—
26	C₂³	C₂⁴×D₆₁	1	11811	yes	direct product factor
27	C₂²	—	61	8128	no	—
28	C₂²	C₂⁵×D₆₁	1	2667	yes	direct product factor
29	C₂	—	61	128	no	—
30	C₂	C₂⁶×D₆₁	1	127	yes	direct product factor

	subgroup	G/H
center, hypercenter	C₂⁷	D₆₁
commutator, cosocle, hypocenter	C₆₁	C₂⁸
Frattini	C₁	G
Fitting, socle	C₂⁷×C₆₁	C₂
LCS	G ▷ C₆₁
UCS	C₁ ◁ C₂⁷

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.