Subgroups — C₃×#21463357 #37555932

Order 23571.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#21463357	C₃	1	9	yes	maximal, direct product factor
2	C₃×C₉₇⋊C₂₇	C₃	1	3	yes	maximal, complemented
3	C₃²×C₉×C₉₇	C₃	1	1	yes	maximal, characteristic
4	C₉₇⋊C₂₇	C₃²	1	9	yes	complemented
5	C₃³×C₉₇	C₉	1	1	yes	characteristic
6	C₃×C₉×C₉₇	C₉	1	6	yes	—
7	C₃×C₉×C₉₇	C₉	1	2	yes	—
8	C₃×C₉×C₉₇	C₃²	1	3	yes	—
9	C₃×C₉×C₉₇	C₃²	1	1	yes	characteristic
10	C₃²×C₉₇	—	3	3	no	—
11	C₃²×C₉₇	C₃×C₉	1	3	yes	—
12	C₃²×C₉₇	C₃×C₉	1	1	yes	characteristic
13	C₉×C₉₇	C₃×C₉	1	6	yes	—
14	C₉×C₉₇	C₃×C₉	1	2	yes	—
15	C₉×C₉₇	C₃³	1	1	yes	characteristic
16	C₃×C₉₇	—	3	3	no	—
17	C₃×C₉₇	C₂₇⋊C₃	1	3	yes	complemented
18	C₃×C₉₇	C₃²×C₉	1	1	yes	characteristic
19	C₃×C₂₇⋊C₃	—	97	1	no	maximal, Sylow
20	C₉₇	C₃×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
21	C₃²×C₉	C₉₇⋊C₃	1	1	yes	characteristic
22	C₂₇⋊C₃	—	97	9	no	—
23	C₃×C₂₇	—	97	3	no	—
24	C₃³	C₉₇⋊C₉	1	1	yes	characteristic
25	C₃×C₉	C₉₇⋊C₉	1	2	yes	—
26	C₃×C₉	C₉₇⋊C₉	1	6	yes	—
27	C₃×C₉	C₃×C₉₇⋊C₃	1	3	yes	—
28	C₃×C₉	C₃×C₉₇⋊C₃	1	1	yes	characteristic
29	C₂₇	—	97	9	no	—
30	C₃²	—	3	3	no	—
31	C₃²	C₃×C₉₇⋊C₉	1	3	yes	—
32	C₃²	C₃×C₉₇⋊C₉	1	1	yes	characteristic
33	C₉	C₃×C₉₇⋊C₉	1	6	yes	—
34	C₉	C₃×C₉₇⋊C₉	1	2	yes	—
35	C₉	C₃²×C₉₇⋊C₃	1	1	yes	characteristic
36	C₃	—	3	3	no	—
37	C₃	#21463357	1	3	yes	direct product factor
38	C₃	C₃²×C₉₇⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₉	C₃×C₉₇⋊C₃
commutator	C₃×C₉₇	C₃²×C₉
Frattini	C₉	C₃²×C₉₇⋊C₃
Fitting	C₃²×C₉×C₉₇	C₃
socle	C₃²×C₉₇	C₃×C₉
prime radical	C₃³×C₉₇	C₉
cosocle	C₉×C₉₇	C₃³
hypercenter	C₃²×C₉	C₉₇⋊C₃
hypocenter	C₉₇	C₃×C₂₇⋊C₃
LCS	G ▷ C₃×C₉₇ ▷ C₉₇
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
1. #21463357	C₃	direct (N × H)
2. C₃×C₉₇⋊C₂₇	C₃	semidirect
4. C₉₇⋊C₂₇	C₃²	semidirect
17. C₃×C₉₇	C₂₇⋊C₃	semidirect
20. C₉₇	C₃×C₂₇⋊C₃	semidirect
37. C₃	#21463357	direct (N × H)

Maximal subgroups

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

subgroup	index
#21463357	3
C₃×C₉₇⋊C₂₇	3
C₃²×C₉×C₉₇	3
C₃×C₂₇⋊C₃	97

Subgroups — C3×#21463357 #37555932

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#21463357 #37555932