Subgroups — #37590239

Order 24642.

32 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#27134470	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	#22551388	C₃	1	1	yes	maximal, characteristic
3	#16861552	C₂×C₃	1	1	yes	characteristic
4	C₃₇⋊D₃₇	C₉	1	1	yes	characteristic, complemented, Hall
5	C₃₇²	C₂×C₉	1	1	yes	characteristic, complemented, Sylow
6	#66526⋊C₂	—	37	1	no	maximal
7	#66526⋊C₂	—	37	1	no	maximal
8	#66526	—	37	1	no	—
9	#66526	—	37	1	no	—
10	D₃₇⋊C₃	—	37	1	no	—
11	D₃₇⋊C₃	—	37	1	no	—
12	C₃₇⋊C₃	—	37	1	no	—
13	C₃₇⋊C₃	—	37	1	no	—
14	D₃₇	—	37	1	no	—
15	D₃₇	—	333	4	no	—
16	D₃₇	—	333	1	no	—
17	C₃₇	—	9	4	no	—
18	C₃₇	#66526⋊C₂	1	1	yes	characteristic, complemented
19	C₃₇	#66526⋊C₂	1	1	yes	characteristic, complemented
20	C₂×C₉	—	1369	1	no	Hall
21	C₉	—	1369	1	no	Sylow
22	C₂×C₃	—	1369	1	no	—
23	C₃	—	1369	1	no	—
24	C₂	—	12321	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, hypocenter	C₃₇²	C₂×C₉
prime radical	#22551388	C₃
cosocle	#16861552	C₂×C₃
LCS	G ▷ C₃₇²
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.