Subgroups — C₂×C₇²×D₁₆₃ #44543992

Order 31948.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇²×D₁₆₃	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₇²×C₁₆₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₇²×C₁₆₃	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₇×D₁₆₃	C₇	1	8	yes	maximal, direct product factor
5	C₂×C₇×C₁₆₃	C₂×C₇	1	8	yes	complemented
6	C₇×D₁₆₃	C₂×C₇	1	16	yes	direct product factor
7	C₇×C₁₆₃	C₂²×C₇	1	8	yes	complemented
8	C₂×D₁₆₃	C₇²	1	1	yes	characteristic, direct product factor, Hall
9	C₂×C₁₆₃	C₂×C₇²	1	1	yes	characteristic, complemented
10	D₁₆₃	C₂×C₇²	1	2	yes	direct product factor
11	C₂²×C₇²	—	163	1	no	maximal, Hall
12	C₁₆₃	C₂²×C₇²	1	1	yes	characteristic, complemented, Sylow
13	C₂×C₇²	—	163	2	no	—
14	C₂×C₇²	D₁₆₃	1	1	yes	characteristic, direct product factor
15	C₇²	C₂×D₁₆₃	1	1	yes	characteristic, direct product factor, Sylow
16	C₂²×C₇	—	163	8	no	—
17	C₂×C₇	—	163	16	no	—
18	C₂×C₇	C₇×D₁₆₃	1	8	yes	direct product factor
19	C₇	C₂×C₇×D₁₆₃	1	8	yes	direct product factor
20	C₂²	—	163	1	no	Sylow
21	C₂	—	163	2	no	—
22	C₂	C₇²×D₁₆₃	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₇²	D₁₆₃
commutator, cosocle, hypocenter	C₁₆₃	C₂²×C₇²
Frattini	C₁	G
Fitting, socle	C₂×C₇²×C₁₆₃	C₂
LCS	G ▷ C₁₆₃
UCS	C₁ ◁ C₂×C₇²

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.