Subgroups — #45657451

Order 32634.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#30654580	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₇²×D₃₇⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₇²×C₃₇⋊C₃	C₂×C₃	1	1	yes	characteristic
4	#17987959	—	7	8	no	maximal
5	C₇²×D₃₇	C₉	1	1	yes	characteristic, complemented, Hall
6	#14556423	—	7	8	no	—
7	C₇²×C₃₇	C₂×C₉	1	1	yes	characteristic, complemented, Hall
8	C₇×D₃₇⋊C₃	ΓL(1,𝔽₈)	1	8	yes	—
9	C₂×#89204	—	37	1	no	maximal, Hall
10	C₇×C₃₇⋊C₃	C₂×ΓL(1,𝔽₈)	1	8	yes	—
11	#66526⋊C₂	—	49	1	no	Hall
12	C₇×D₃₇	C₇⋊C₉	1	8	yes	complemented
13	#89204	—	37	1	no	Hall
14	#66526	—	49	1	no	Hall
15	C₂×C₃×C₇²	—	37	1	no	—
16	C₇×C₃₇	C₂×C₇⋊C₉	1	8	yes	complemented
17	D₃₇⋊C₃	#3861	1	1	yes	characteristic
18	C₃×C₇²	—	37	1	no	—
19	C₂×C₇⋊C₉	—	259	8	no	—
20	C₃₇⋊C₃	C₂×#3861	1	1	yes	characteristic
21	C₂×C₇²	—	37	1	no	Hall
22	D₃₇	#89204	1	1	yes	characteristic, complemented, Hall
23	C₇⋊C₉	—	259	8	no	—
24	C₇²	#66526⋊C₂	1	1	yes	characteristic, complemented, Sylow
25	C₂×C₃×C₇	—	37	8	no	—
26	C₃₇	C₂×#89204	1	1	yes	characteristic, complemented, Sylow
27	C₃×C₇	—	37	8	no	—
28	C₂×C₉	—	1813	1	no	Hall
29	C₂×C₇	—	37	8	no	—
30	C₉	—	1813	1	no	Sylow
31	C₇	#17987959	1	8	yes	complemented
32	C₂×C₃	—	37	1	no	—
33	C₃	—	37	1	no	—
34	C₂	—	37	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₇²×C₃₇	C₂×C₉
prime radical	C₇²×D₃₇⋊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.