Subgroups — C₃₇×#10624535 #41004324

Order 26973.

64 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃₇×#6879	C₃	1	3	yes	maximal, complemented
2	C₉×C₂₇×C₃₇	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃₇×#732	—	3	3	no	—
4	C₃×C₂₇×C₃₇	—	3	1	no	—
5	C₉²×C₃₇	C₃²	1	1	yes	characteristic
6	H(3,𝔽₃)×C₃₇	—	9	3	no	—
7	C₃×C₉×C₃₇	—	3	1	no	—
8	C₃×C₉×C₃₇	H(3,𝔽₃)	1	1	yes	characteristic
9	C₂₇×C₃₇	—	3	3	no	—
10	#10624535	C₃₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
11	C₃²×C₃₇	—	27	3	no	—
12	C₃²×C₃₇	#732	1	1	yes	characteristic
13	C₉×C₃₇	—	3	3	no	—
14	C₉×C₃₇	—	3	1	no	—
15	#6879	C₃×C₃₇	1	3	yes	complemented
16	C₉×C₂₇	C₃×C₃₇	1	1	yes	characteristic, complemented
17	C₃×C₃₇	—	3	1	no	—
18	C₃×C₃₇	—	81	3	no	—
19	C₃×C₃₇	#6879	1	1	yes	characteristic
20	#732	—	3	3	no	—
21	C₃×C₂₇	—	3	1	no	—
22	C₉²	C₃²×C₃₇	1	1	yes	characteristic
23	C₃₇	#10624535	1	1	yes	characteristic, direct product factor, Sylow
24	H(3,𝔽₃)	—	9	3	no	—
25	C₃×C₉	—	3	1	no	—
26	C₃×C₉	H(3,𝔽₃)×C₃₇	1	1	yes	characteristic
27	C₂₇	—	3	3	no	—
28	C₃²	—	27	3	no	—
29	C₃²	C₃₇×#732	1	1	yes	characteristic
30	C₉	—	3	3	no	—
31	C₉	—	3	1	no	—
32	C₃	—	3	1	no	—
33	C₃	—	81	3	no	—
34	C₃	C₃₇×#6879	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₃×C₃₇	#6879
commutator, Frattini, cosocle	C₉²	C₃²×C₃₇
LCS	G ▷ C₉² ▷ C₃×C₉ ▷ C₃² ▷ C₃ ▷ C₁
UCS	C₁ ◁ C₃×C₃₇ ◁ C₃²×C₃₇ ◁ C₃×C₉×C₃₇ ◁ C₉²×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.