Subgroups — #45657455

Order 32634.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30654579	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇⋊D₇×C₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₇²×C₃₇⋊C₃	C₂×C₃	1	1	yes	characteristic
4	#17987954	—	7	8	no	maximal
5	C₃₇×C₇⋊D₇	C₉	1	1	yes	characteristic, complemented, Hall
6	#14556422	—	7	8	no	—
7	C₇²×C₃₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	D₇×C₃₇⋊C₃	—	7	8	no	—
9	#11725077	—	37	1	no	maximal, Hall
10	C₇×C₃₇⋊C₃	AGL(1,𝔽₇)	1	8	yes	—
11	C₂×#66526	—	49	1	no	Hall
12	D₇×C₃₇	—	7	8	no	—
13	#89204	—	37	1	no	Hall
14	#66526	—	49	1	no	Hall
15	C₃×C₇⋊D₇	—	37	1	no	—
16	C₇×C₃₇	D₇⋊C₉	1	8	yes	complemented
17	C₂×C₃₇⋊C₃	—	49	1	no	—
18	C₃×C₇²	—	37	1	no	—
19	D₇⋊C₉	—	259	8	no	—
20	C₃₇⋊C₃	#64424	1	1	yes	characteristic
21	C₇⋊D₇	#66526	1	1	yes	characteristic, complemented, Hall
22	C₂×C₃₇	—	49	1	no	Hall
23	C₇⋊C₉	—	259	8	no	—
24	C₇²	C₂×#66526	1	1	yes	characteristic, complemented, Sylow
25	C₃×D₇	—	259	8	no	—
26	C₃₇	#11725077	1	1	yes	characteristic, complemented, Sylow
27	C₃×C₇	—	37	8	no	—
28	C₂×C₉	—	1813	1	no	Hall
29	D₇	—	7	8	no	—
30	C₉	—	1813	1	no	Sylow
31	C₇	#17987954	1	8	yes	complemented
32	C₂×C₃	—	1813	1	no	—
33	C₃	—	37	1	no	—
34	C₂	—	49	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇²×C₃₇	C₂×C₉
prime radical	C₇⋊D₇×C₃₇⋊C₃	C₃
cosocle	C₇²×C₃₇⋊C₃	C₂×C₃
LCS	G ▷ C₇²×C₃₇
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.