Subgroups — C₆₇⋊#92150 #44569842

Order 32428.

36 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₆₇×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic
2	C₁₁²×C₆₇	C₄	1	1	yes	characteristic, complemented, Hall
3	D₁₁×C₆₇	—	22	6	no	—
4	C₁₁×C₆₇	—	2	6	no	—
5	#92150	—	67	1	no	maximal, Hall
6	Dic₆₇	—	121	1	no	maximal, Hall
7	C₁₁⋊D₁₁	D₆₇	1	1	yes	characteristic
8	C₂×C₆₇	—	121	1	no	—
9	C₁₁²	Dic₆₇	1	1	yes	characteristic, complemented, Sylow
10	C₆₇	#92150	1	1	yes	characteristic, complemented, Sylow
11	D₁₁	—	22	6	no	—
12	C₁₁	—	2	6	no	—
13	C₄	—	8107	1	no	Sylow
14	C₂	—	121	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₁₁²×C₆₇	C₄
prime radical, cosocle	C₆₇×C₁₁⋊D₁₁	C₂
LCS	G ▷ C₁₁²×C₆₇
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.