Subgroups — #49138779

Order 36414.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₇×#14579585	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#27131472	C₃	1	1	yes	maximal, characteristic
3	C₇×C₁₇²⋊C₃	C₂×C₃	1	1	yes	characteristic
4	#19104523	—	7	1	no	maximal, Hall
5	C₇⋊(C₁₇⋊D₁₇)	C₉	1	1	yes	characteristic, complemented, Hall
6	#14579585	D₇	1	1	yes	characteristic, complemented, Hall
7	C₇×C₁₇²	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	(C₁₇⋊D₁₇)⋊C₃	—	7	1	no	—
9	C₁₇²⋊C₃	C₃×D₇	1	1	yes	characteristic
10	C₁₇⋊D₁₇	—	7	1	no	Hall
11	C₁₇²	C₉×D₇	1	1	yes	characteristic, complemented, Sylow
12	D₁₁₉	—	153	2	no	—
13	C₉×D₇	—	289	1	no	maximal, Hall
14	C₇×C₁₇	—	9	2	no	—
15	C₇×C₉	—	289	1	no	Hall
16	C₃×D₇	—	289	1	no	—
17	D₁₇	—	1071	2	no	—
18	C₃×C₇	—	289	1	no	—
19	C₂×C₉	—	2023	1	no	Hall
20	C₁₇	—	9	2	no	—
21	D₇	—	289	1	no	Hall
22	C₉	—	289	1	no	Sylow
23	C₇	#19104523	1	1	yes	characteristic, complemented, Sylow
24	C₂×C₃	—	2023	1	no	—
25	C₃	—	289	1	no	—
26	C₂	—	2023	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇×C₁₇²	C₂×C₉
prime radical	#27131472	C₃
cosocle	C₇×C₁₇²⋊C₃	C₂×C₃
LCS	G ▷ C₇×C₁₇²
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.