Subgroups — C₇×C₃⋊#92150 #23779055

Order 10164.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₇×C₁₁⋊D₁₁	C₂	1	1	yes	maximal, characteristic
2	C₇×#92150	—	3	1	no	maximal, Hall
3	C₃×C₇×C₁₁²	C₄	1	1	yes	characteristic, complemented, Hall
4	C₇×C₁₁⋊D₁₁	D₃	1	1	yes	characteristic
5	C₃⋊#92150	C₇	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₇×C₁₁²	Dic₃	1	1	yes	characteristic, complemented, Hall
7	C₃×C₁₁⋊D₁₁	C₂×C₇	1	1	yes	characteristic
8	#92150	—	3	1	no	Hall
9	C₃×C₇×D₁₁	—	22	6	no	—
10	C₃×C₁₁²	C₄×C₇	1	1	yes	characteristic, complemented, Hall
11	C₁₁⋊D₁₁	D₃×C₇	1	1	yes	characteristic
12	C₃×C₇×C₁₁	—	2	6	no	—
13	C₇×D₁₁	—	22	6	no	—
14	C₁₁²	C₇×Dic₃	1	1	yes	characteristic, complemented, Sylow
15	C₇×Dic₃	—	121	1	no	maximal, Hall
16	C₇×C₁₁	—	2	6	no	—
17	C₃×D₁₁	—	22	6	no	—
18	C₂×C₃×C₇	—	121	1	no	—
19	C₃×C₁₁	—	2	6	no	—
20	C₄×C₇	—	363	1	no	Hall
21	D₁₁	—	22	6	no	—
22	C₃×C₇	#92150	1	1	yes	characteristic, complemented, Hall
23	C₂×C₇	—	121	1	no	—
24	Dic₃	—	121	1	no	Hall
25	C₁₁	—	2	6	no	—
26	C₇	C₃⋊#92150	1	1	yes	characteristic, direct product factor, Sylow
27	C₂×C₃	—	121	1	no	—
28	C₄	—	363	1	no	Sylow
29	C₃	C₇×#92150	1	1	yes	characteristic, complemented, Sylow
30	C₂	—	121	1	no	—

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