Subgroups — C₂×C₆₁×D₁₂₁ #44443239

Order 29524.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₁×D₁₂₁	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₆₁×C₁₂₁	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₁×C₁₂₁	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×D₁₁×C₆₁	—	11	1	no	maximal
5	C₂×C₁₁×C₆₁	D₁₁	1	1	yes	characteristic
6	D₁₁×C₆₁	—	11	2	no	—
7	C₁₁×C₆₁	C₂×D₁₁	1	1	yes	characteristic
8	C₂×D₁₂₁	C₆₁	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₆₁	—	121	1	no	Hall
10	C₂×C₁₂₁	C₂×C₆₁	1	1	yes	characteristic, complemented
11	D₁₂₁	C₂×C₆₁	1	2	yes	direct product factor
12	C₂×C₆₁	—	121	2	no	—
13	C₂×C₆₁	D₁₂₁	1	1	yes	characteristic, direct product factor
14	C₁₂₁	C₂²×C₆₁	1	1	yes	characteristic, complemented, Sylow
15	C₆₁	C₂×D₁₂₁	1	1	yes	characteristic, direct product factor, Sylow
16	C₂×D₁₁	—	11	1	no	—
17	C₂×C₁₁	D₁₁×C₆₁	1	1	yes	characteristic
18	D₁₁	—	11	2	no	—
19	C₁₁	C₂×D₁₁×C₆₁	1	1	yes	characteristic
20	C₂²	—	121	1	no	Sylow
21	C₂	—	121	2	no	—
22	C₂	C₆₁×D₁₂₁	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₆₁	D₁₂₁
commutator, cosocle, hypocenter	C₁₂₁	C₂²×C₆₁
Frattini	C₁₁	C₂×D₁₁×C₆₁
Fitting	C₂×C₆₁×C₁₂₁	C₂
socle	C₂×C₁₁×C₆₁	D₁₁
LCS	G ▷ C₁₂₁
UCS	C₁ ◁ C₂×C₆₁

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.