Subgroups — C₇⋊#13093287 #23780232

Order 10332.

40 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×C₃⋊D₁₂₃	C₂	1	1	yes	maximal, characteristic
2	C₃²×C₇×C₄₁	C₄	1	1	yes	characteristic, complemented, Hall
3	C₇×D₁₂₃	—	6	2	no	—
4	#13093287	—	7	1	no	maximal, Hall
5	C₇⋊#4223	—	9	1	no	maximal, Hall
6	C₃×C₇×C₄₁	—	2	2	no	—
7	C₃⋊D₁₂₃	D₇	1	1	yes	characteristic
8	C₇×D₄₁	—	9	1	no	—
9	C₃²×C₄₁	Dic₇	1	1	yes	characteristic, complemented, Hall
10	C₇×C₄₁	#157	1	1	yes	characteristic, complemented, Hall
11	C₇⋊#157	—	41	1	no	maximal, Hall
12	D₁₂₃	—	6	2	no	—
13	#4223	—	63	1	no	Hall
14	C₇×C₃⋊D₃	—	41	1	no	—
15	C₃×C₄₁	—	2	2	no	—
16	D₄₁	—	9	1	no	—
17	C₃²×C₇	#4223	1	1	yes	characteristic, complemented, Hall
18	D₃×C₇	—	246	2	no	—
19	C₄₁	C₇⋊#157	1	1	yes	characteristic, complemented, Sylow
20	#157	—	287	1	no	Hall
21	Dic₇	—	369	1	no	Hall
22	C₃×C₇	—	2	2	no	—
23	C₃⋊D₃	—	41	1	no	—
24	C₂×C₇	—	369	1	no	—
25	C₃²	C₇⋊#4223	1	1	yes	characteristic, complemented, Sylow
26	C₇	#13093287	1	1	yes	characteristic, complemented, Sylow
27	D₃	—	246	2	no	—
28	C₄	—	2583	1	no	Sylow
29	C₃	—	2	2	no	—
30	C₂	—	369	1	no	—

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃²×C₇×C₄₁	C₄
prime radical, cosocle	C₇×C₃⋊D₁₂₃	C₂
LCS	G ▷ C₃²×C₇×C₄₁
UCS	C₁

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