Subgroups — C₃₇×#10624562 #41004351

Order 26973.

2138 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×H(3,𝔽₃)×C₃₇	C₃	1	13	yes	maximal, complemented
2	C₃⁴×C₃₇	C₃²	1	13	yes	—
3	C₃×H(3,𝔽₃)×C₃₇	—	3	156	no	—
4	C₃³×C₃₇	—	3	156	no	—
5	C₃³×C₃₇	H(3,𝔽₃)	1	39	yes	complemented
6	C₃³×C₃₇	C₃³	1	1	yes	characteristic
7	H(3,𝔽₃)×C₃₇	—	3	351	no	—
8	#10624562	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
9	C₃²×C₃₇	—	3	156	no	—
10	C₃²×C₃₇	—	9	117	no	—
11	C₃²×C₃₇	C₃×H(3,𝔽₃)	1	13	yes	—
12	C₃²×H(3,𝔽₃)	C₃×C₃₇	1	13	yes	complemented
13	C₃×C₃₇	—	9	39	no	—
14	C₃×C₃₇	C₃²⋊H(3,𝔽₃)	1	13	yes	—
15	C₃⁴	C₃²×C₃₇	1	13	yes	—
16	C₃×H(3,𝔽₃)	—	3	156	no	—
17	C₃₇	#10624562	1	1	yes	characteristic, direct product factor, Sylow
18	C₃³	—	3	156	no	—
19	C₃³	H(3,𝔽₃)×C₃₇	1	39	yes	complemented
20	C₃³	C₃³×C₃₇	1	1	yes	characteristic
21	H(3,𝔽₃)	—	3	351	no	—
22	C₃²	—	3	156	no	—
23	C₃²	—	9	117	no	—
24	C₃²	C₃×H(3,𝔽₃)×C₃₇	1	13	yes	—
25	C₃	—	9	39	no	—
26	C₃	C₃₇×C₃²⋊H(3,𝔽₃)	1	13	yes	—

	subgroup	G/H
center, socle	C₃³×C₃₇	C₃³
commutator, Frattini, cosocle	C₃³	C₃³×C₃₇
LCS	G ▷ C₃³ ▷ C₁
UCS	C₁ ◁ C₃³×C₃₇ ◁ G

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.

subgroup	index
C₃²×H(3,𝔽₃)×C₃₇	3
#10624562	37