Subgroups — C₃₇⋊#10624391 #41001743

Order 26862.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×C₁₁²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented, Hall
2	C₁₁×D₄₀₇	—	3	1	no	maximal, Hall
3	C₁₁²×C₃₇	D₃	1	1	yes	characteristic, complemented, Hall
4	D₄₀₇	—	3	1	no	—
5	C₁₁×D₃₇	—	33	1	no	—
6	#10624391	—	37	1	no	maximal, Hall
7	C₁₁×C₃₇	—	3	1	no	—
8	C₁₁×C₃₇	—	6	1	no	—
9	C₁₁×C₃₇	—	6	1	no	—
10	C₁₁²⋊C₃	D₃₇	1	1	yes	characteristic, complemented, Hall
11	C₁₁×D₁₁	—	111	1	no	Hall
12	D₁₁₁	—	121	1	no	maximal, Hall
13	C₁₁²	D₁₁₁	1	1	yes	characteristic, complemented, Sylow
14	C₃×C₃₇	—	242	1	no	Hall
15	D₃₇	—	33	1	no	Hall
16	C₃₇	#10624391	1	1	yes	characteristic, complemented, Sylow
17	C₂×C₁₁	—	1221	1	no	—
18	D₁₁	—	111	1	no	—
19	C₁₁	—	3	1	no	—
20	C₁₁	—	6	1	no	—
21	C₁₁	—	6	1	no	—
22	D₃	—	4477	1	no	Hall
23	C₃	—	242	1	no	Sylow
24	C₂	—	1221	1	no	Sylow

	subgroup	G/H
center, Frattini, hypercenter	C₁	G
commutator, cosocle, hypocenter	C₃₇×C₁₁²⋊C₃	C₂
Fitting, socle	C₁₁²×C₃₇	D₃
LCS	G ▷ C₃₇×C₁₁²⋊C₃
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.