Subgroups — C₇⋊#11760330 #20300676

Order 7308.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃⋊D₃×C₂₉	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇×C₂₉	C₄	1	1	yes	characteristic, complemented, Hall
3	D₃×C₇×C₂₉	—	6	2	no	—
4	#11760330	—	7	1	no	maximal, Hall
5	Dic₂₀₃	—	9	1	no	maximal, Hall
6	C₃×C₇×C₂₉	—	2	2	no	—
7	C₃⋊D₃×C₂₉	D₇	1	1	yes	characteristic
8	C₂×C₇×C₂₉	—	9	1	no	—
9	C₃²×C₂₉	Dic₇	1	1	yes	characteristic, complemented, Hall
10	C₇⋊#157	—	29	1	no	maximal, Hall
11	C₇×C₂₉	#157	1	1	yes	characteristic, complemented, Hall
12	D₃×C₂₉	—	6	2	no	—
13	C₇×C₃⋊D₃	D₂₉	1	1	yes	characteristic
14	Dic₂₉	—	63	1	no	Hall
15	C₃×C₂₉	—	2	2	no	—
16	C₃²×C₇	Dic₂₉	1	1	yes	characteristic, complemented, Hall
17	C₂×C₂₉	—	9	1	no	—
18	D₃×C₇	—	6	2	no	—
19	#157	—	203	1	no	Hall
20	C₂₉	C₇⋊#157	1	1	yes	characteristic, complemented, Sylow
21	Dic₇	—	261	1	no	Hall
22	C₃×C₇	—	2	2	no	—
23	C₃⋊D₃	D₂₀₃	1	1	yes	characteristic
24	C₂×C₇	—	9	1	no	—
25	C₃²	Dic₂₀₃	1	1	yes	characteristic, complemented, Sylow
26	C₇	#11760330	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	6	2	no	—
28	C₄	—	1827	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×C₇×C₂₉	C₄
LCS	G ▷ C₃²×C₇×C₂₉
UCS	C₁

Splittings G = N ⋊ H with N normal; H ≅ G/N.