Subgroups — C₇²×D₃₉₃ #50310064

Order 38514.

80 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇²×C₁₃₁	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇²×D₁₃₁	—	3	1	no	maximal, Hall
3	C₇²×C₁₃₁	D₃	1	1	yes	characteristic, complemented, Hall
4	C₇×D₃₉₃	C₇	1	8	yes	maximal, direct product factor
5	C₃×C₇×C₁₃₁	C₂×C₇	1	8	yes	complemented
6	C₇×D₁₃₁	—	3	8	no	—
7	C₇×C₁₃₁	D₃×C₇	1	8	yes	complemented
8	D₃₉₃	C₇²	1	1	yes	characteristic, direct product factor, Hall
9	C₃×C₁₃₁	C₂×C₇²	1	1	yes	characteristic, complemented, Hall
10	D₃×C₇²	—	131	1	no	maximal, Hall
11	D₁₃₁	—	3	1	no	Hall
12	C₃×C₇²	D₁₃₁	1	1	yes	characteristic, complemented, Hall
13	C₁₃₁	D₃×C₇²	1	1	yes	characteristic, complemented, Sylow
14	C₂×C₇²	—	393	1	no	Hall
15	C₇²	D₃₉₃	1	1	yes	characteristic, direct product factor, Sylow
16	D₃×C₇	—	131	8	no	—
17	C₃×C₇	C₇×D₁₃₁	1	8	yes	complemented
18	C₂×C₇	—	393	8	no	—
19	C₇	C₇×D₃₉₃	1	8	yes	direct product factor
20	D₃	—	131	1	no	Hall
21	C₃	C₇²×D₁₃₁	1	1	yes	characteristic, complemented, Sylow
22	C₂	—	393	1	no	Sylow

	subgroup	G/H
center, hypercenter	C₇²	D₃₉₃
commutator, cosocle, hypocenter	C₃×C₁₃₁	C₂×C₇²
Frattini	C₁	G
Fitting, socle	C₃×C₇²×C₁₃₁	C₂
LCS	G ▷ C₃×C₁₃₁
UCS	C₁ ◁ 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.