Subgroups — #49176129

Order 37518.

48 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇⋊#92789	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₃₇×C₁₃⋊D₁₃	C₃	1	1	yes	maximal, characteristic, complemented, Hall
3	C₁₃²×C₃₇	C₂×C₃	1	1	yes	characteristic, complemented, Hall
4	#15668364	—	13	1	no	maximal
5	#15668363	—	13	1	no	maximal
6	#13089650	—	13	1	no	—
7	#13089649	—	13	1	no	—
8	#11759816	—	37	1	no	maximal, Hall
9	D₁₃×C₃₇	—	13	1	no	—
10	D₁₃×C₃₇	—	13	1	no	—
11	D₁₃×C₃₇	—	39	4	no	—
12	#92789	—	37	1	no	Hall
13	C₁₃×C₃₇	—	3	4	no	—
14	C₁₃×C₃₇	D₁₃⋊C₃	1	1	yes	characteristic, complemented
15	C₁₃×C₃₇	D₁₃⋊C₃	1	1	yes	characteristic, complemented
16	C₁₃⋊D₁₃	C₃₇⋊C₃	1	1	yes	characteristic, complemented, Hall
17	C₂×C₃₇⋊C₃	—	169	1	no	Hall
18	C₁₃²	C₂×C₃₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
19	C₃₇⋊C₃	—	169	1	no	Hall
20	D₁₃⋊C₃	—	481	1	no	—
21	D₁₃⋊C₃	—	481	1	no	—
22	C₂×C₃₇	—	169	1	no	Hall
23	C₁₃⋊C₃	—	481	1	no	—
24	C₁₃⋊C₃	—	481	1	no	—
25	C₃₇	#11759816	1	1	yes	characteristic, complemented, Sylow
26	D₁₃	—	13	1	no	—
27	D₁₃	—	13	1	no	—
28	D₁₃	—	39	4	no	—
29	C₁₃	—	3	4	no	—
30	C₁₃	#15668363	1	1	yes	characteristic, complemented
31	C₁₃	#15668364	1	1	yes	characteristic, complemented
32	C₂×C₃	—	6253	1	no	Hall
33	C₃	—	6253	1	no	Sylow
34	C₂	—	169	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, Fitting, socle, cosocle, hypocenter	C₁₃²×C₃₇	C₂×C₃
LCS	G ▷ C₁₃²×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.