Subgroups — #157×C₁₂₇⋊C₇ #44544784

Order 32004.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃⋊D₃×C₁₂₇⋊C₇	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₁₂₇⋊C₇	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₁₂₇⋊C₇	—	6	2	no	—
4	#157×C₁₂₇	C₇	1	1	yes	maximal, characteristic, complemented, Hall
5	C₄×C₁₂₇⋊C₇	—	9	1	no	maximal, Hall
6	C₃×C₁₂₇⋊C₇	—	2	2	no	—
7	C₃⋊D₃×C₁₂₇	C₂×C₇	1	1	yes	characteristic
8	C₂×C₁₂₇⋊C₇	—	9	1	no	—
9	C₃²×C₁₂₇	C₄×C₇	1	1	yes	characteristic, complemented, Hall
10	C₁₂₇⋊C₇	#157	1	1	yes	characteristic, direct product factor, Hall
11	D₃×C₁₂₇	—	6	2	no	—
12	C₄×C₁₂₇	—	9	1	no	Hall
13	C₃×C₁₂₇	—	2	2	no	—
14	C₂×C₁₂₇	—	9	1	no	—
15	C₇×#157	—	127	1	no	maximal, Hall
16	C₁₂₇	C₇×#157	1	1	yes	characteristic, complemented, Sylow
17	C₇×C₃⋊D₃	—	127	1	no	—
18	C₃²×C₇	—	127	1	no	Hall
19	D₃×C₇	—	762	2	no	—
20	#157	C₁₂₇⋊C₇	1	1	yes	characteristic, direct product factor, Hall
21	C₄×C₇	—	1143	1	no	Hall
22	C₃×C₇	—	254	2	no	—
23	C₃⋊D₃	C₂×C₁₂₇⋊C₇	1	1	yes	characteristic
24	C₂×C₇	—	1143	1	no	—
25	C₃²	C₄×C₁₂₇⋊C₇	1	1	yes	characteristic, complemented, Sylow
26	C₇	—	127	1	no	Sylow
27	D₃	—	6	2	no	—
28	C₄	—	9	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	9	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₁₂₇	C₄×C₇
prime radical	C₃⋊D₃×C₁₂₇⋊C₇	C₂
cosocle	C₃⋊D₃×C₁₂₇	C₂×C₇
LCS	G ▷ C₃²×C₁₂₇
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.