Subgroups — C₂×C₁₁²×D₆₇ #44569848

Order 32428.

140 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₁²×D₆₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₁²×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₁²×C₆₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₁×D₆₇	C₁₁	1	12	yes	maximal, direct product factor
5	C₂×C₁₁×C₆₇	C₂×C₁₁	1	12	yes	complemented
6	C₁₁×D₆₇	C₂×C₁₁	1	24	yes	direct product factor
7	C₁₁×C₆₇	C₂²×C₁₁	1	12	yes	complemented
8	C₂²×C₁₁²	—	67	1	no	maximal, Hall
9	C₂×D₆₇	C₁₁²	1	1	yes	characteristic, direct product factor, Hall
10	C₂×C₁₁²	—	67	2	no	—
11	C₂×C₁₁²	D₆₇	1	1	yes	characteristic, direct product factor
12	C₂×C₆₇	C₂×C₁₁²	1	1	yes	characteristic, complemented
13	D₆₇	C₂×C₁₁²	1	2	yes	direct product factor
14	C₁₁²	C₂×D₆₇	1	1	yes	characteristic, direct product factor, Sylow
15	C₆₇	C₂²×C₁₁²	1	1	yes	characteristic, complemented, Sylow
16	C₂²×C₁₁	—	67	12	no	—
17	C₂×C₁₁	—	67	24	no	—
18	C₂×C₁₁	C₁₁×D₆₇	1	12	yes	direct product factor
19	C₁₁	C₂×C₁₁×D₆₇	1	12	yes	direct product factor
20	C₂²	—	67	1	no	Sylow
21	C₂	—	67	2	no	—
22	C₂	C₁₁²×D₆₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₁²	D₆₇
commutator, cosocle, hypocenter	C₆₇	C₂²×C₁₁²
Frattini	C₁	G
Fitting, socle	C₂×C₁₁²×C₆₇	C₂
LCS	G ▷ C₆₇
UCS	C₁ ◁ C₂×C₁₁²

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.