Subgroups — D₆₇×D₁₂₁ #44569821

Order 32428.

30 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₈₁₀₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₂₁×D₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₆₇×D₁₂₁	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×C₁₂₁	C₂²	1	1	yes	characteristic, complemented, Hall
5	D₁₁×D₆₇	—	11	1	no	maximal
6	D₇₃₇	—	11	1	no	—
7	C₁₁×D₆₇	D₁₁	1	1	yes	characteristic
8	D₁₁×C₆₇	—	11	1	no	—
9	C₁₁×C₆₇	C₂×D₁₁	1	1	yes	characteristic
10	C₂×D₁₂₁	—	67	1	no	maximal, Hall
11	C₂×D₆₇	—	121	1	no	Hall
12	C₂×C₁₂₁	—	67	1	no	—
13	D₁₂₁	—	67	1	no	—
14	D₁₂₁	D₆₇	1	1	yes	characteristic, direct product factor
15	C₂×C₆₇	—	121	1	no	—
16	D₆₇	—	121	1	no	—
17	D₆₇	D₁₂₁	1	1	yes	characteristic, direct product factor
18	C₁₂₁	C₂×D₆₇	1	1	yes	characteristic, complemented, Sylow
19	C₆₇	C₂×D₁₂₁	1	1	yes	characteristic, complemented, Sylow
20	C₂×D₁₁	—	737	1	no	—
21	C₂×C₁₁	—	67	1	no	—
22	D₁₁	—	11	1	no	—
23	D₁₁	—	737	1	no	—
24	C₁₁	D₁₁×D₆₇	1	1	yes	characteristic
25	C₂²	—	8107	1	no	Sylow
26	C₂	—	67	1	no	—
27	C₂	—	121	1	no	—
28	C₂	—	8107	1	no	—

	subgroup	G/H
center, hypercenter	C₁	G
commutator, Fitting, cosocle, hypocenter	C₆₇×C₁₂₁	C₂²
Frattini	C₁₁	D₁₁×D₆₇
socle	C₁₁×C₆₇	C₂×D₁₁
LCS	G ▷ C₆₇×C₁₂₁
UCS	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.