Subgroups — C₂×C₁₃²×D₄₇ #44540972

Order 31772.

160 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₃²×D₄₇	C₂	1	2	yes	maximal, direct product factor
2	C₂×C₁₃²×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₃²×C₄₇	C₂²	1	1	yes	characteristic, complemented, Hall
4	C₂×C₁₃×D₄₇	C₁₃	1	14	yes	maximal, direct product factor
5	C₂×C₁₃×C₄₇	C₂×C₁₃	1	14	yes	complemented
6	C₁₃×D₄₇	C₂×C₁₃	1	28	yes	direct product factor
7	C₂²×C₁₃²	—	47	1	no	maximal, Hall
8	C₁₃×C₄₇	C₂²×C₁₃	1	14	yes	complemented
9	C₂×C₁₃²	—	47	2	no	—
10	C₂×C₁₃²	D₄₇	1	1	yes	characteristic, direct product factor
11	C₂×D₄₇	C₁₃²	1	1	yes	characteristic, direct product factor, Hall
12	C₁₃²	C₂×D₄₇	1	1	yes	characteristic, direct product factor, Sylow
13	C₂×C₄₇	C₂×C₁₃²	1	1	yes	characteristic, complemented
14	D₄₇	C₂×C₁₃²	1	2	yes	direct product factor
15	C₂²×C₁₃	—	47	14	no	—
16	C₄₇	C₂²×C₁₃²	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₁₃	—	47	28	no	—
18	C₂×C₁₃	C₁₃×D₄₇	1	14	yes	direct product factor
19	C₁₃	C₂×C₁₃×D₄₇	1	14	yes	direct product factor
20	C₂²	—	47	1	no	Sylow
21	C₂	—	47	2	no	—
22	C₂	C₁₃²×D₄₇	1	1	yes	characteristic, direct product factor

	subgroup	G/H
center, hypercenter	C₂×C₁₃²	D₄₇
commutator, cosocle, hypocenter	C₄₇	C₂²×C₁₃²
Frattini	C₁	G
Fitting, socle	C₂×C₁₃²×C₄₇	C₂
LCS	G ▷ C₄₇
UCS	C₁ ◁ C₂×C₁₃²

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.