Subgroups — #44565439

Order 32157.

26 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#24924308	C₃	1	2	yes	maximal
2	C₃×#16813208	C₃	1	1	yes	maximal, characteristic
3	3₋¹⁺²×C₃₉₇	C₃	1	1	yes	maximal, characteristic
4	C₃²×C₃₉₇	C₃²	1	1	yes	characteristic
5	C₉×C₃₉₇	—	3	1	no	—
6	#16813208	—	3	1	no	—
7	#16813208	—	3	2	no	—
8	C₃×C₃₉₇	—	3	1	no	—
9	C₃×C₃₉₇	H(3,𝔽₃)	1	1	yes	characteristic
10	C₃₉₇	#733	1	1	yes	characteristic, complemented, Sylow
11	#733	—	397	1	no	maximal, Sylow
12	3₋¹⁺²	—	397	2	no	—
13	3₋¹⁺²	C₃₉₇⋊C₃	1	1	yes	characteristic
14	C₃×C₉	—	397	1	no	—
15	C₃²	C₃×C₃₉₇⋊C₃	1	1	yes	characteristic
16	C₉	—	3	1	no	—
17	C₉	—	1191	1	no	—
18	C₉	—	1191	2	no	—
19	C₃	—	3	1	no	—
20	C₃	C₃²⋊(C₃₉₇⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃²⋊(C₃₉₇⋊C₃)
commutator, prime radical, cosocle	C₃²×C₃₉₇	C₃²
Frattini	C₃²	C₃×C₃₉₇⋊C₃
Fitting	3₋¹⁺²×C₃₉₇	C₃
socle	C₃×C₃₉₇	H(3,𝔽₃)
hypercenter	3₋¹⁺²	C₃₉₇⋊C₃
hypocenter	C₃₉₇	#733
LCS	G ▷ C₃²×C₃₉₇ ▷ C₃×C₃₉₇ ▷ C₃₉₇
UCS	C₁ ◁ C₃ ◁ C₃² ◁ 3₋¹⁺²

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
10. C₃₉₇	#733	semidirect

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.