Subgroups — C₃×(C₉₇⋊C₉)⋊C₉ #37555853

Order 23571.

180 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₉₇⋊C₉	C₃	1	1	yes	maximal, characteristic
2	C₃²×C₉₇⋊C₉	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₉₇⋊C₉	C₃	1	1	yes	maximal, characteristic
4	(C₉₇⋊C₉)⋊C₉	C₃	1	9	yes	maximal, direct product factor
5	C₃²×C₉×C₉₇	C₃	1	1	yes	maximal, characteristic
6	C₃×C₉₇⋊C₉	—	3	3	no	—
7	C₃×C₉₇⋊C₉	—	3	3	no	—
8	C₃×C₉₇⋊C₉	C₉	1	9	yes	complemented
9	C₃×C₉₇⋊C₉	C₃²	1	3	yes	—
10	C₃×C₉₇⋊C₉	C₃²	1	3	yes	—
11	C₃×C₉₇⋊C₉	C₃²	1	3	yes	—
12	C₃³×C₉₇	C₃²	1	1	yes	characteristic
13	C₃×C₉×C₉₇	—	3	3	no	—
14	C₃×C₉×C₉₇	C₃²	1	3	yes	—
15	C₃²×C₉₇	C₃×C₉	1	3	yes	—
16	C₃²×C₉₇	3₋¹⁺²	1	3	yes	—
17	C₃²×C₉₇	3₋¹⁺²	1	3	yes	—
18	C₃²×C₉₇	3₋¹⁺²	1	3	yes	—
19	C₃²×C₉₇	C₃³	1	1	yes	characteristic
20	C₉×C₉₇	—	3	3	no	—
21	C₉₇⋊C₉	—	3	3	no	—
22	C₉₇⋊C₉	—	3	3	no	—
23	C₉₇⋊C₉	C₃×C₉	1	9	yes	complemented
24	C₃×C₉₇	C₉⋊C₉	1	9	yes	complemented
25	C₃×C₉₇	C₃²×C₉	1	1	yes	characteristic
26	C₃×C₉₇	C₃×3₋¹⁺²	1	1	yes	characteristic
27	C₃×C₉₇	C₃×3₋¹⁺²	1	1	yes	characteristic
28	C₃×C₉₇	C₃×3₋¹⁺²	1	1	yes	characteristic
29	C₃×C₉⋊C₉	—	97	1	no	maximal, Sylow
30	C₉₇	C₃×C₉⋊C₉	1	1	yes	characteristic, complemented, Sylow
31	C₃²×C₉	—	97	1	no	—
32	C₃²×C₉	—	97	1	no	—
33	C₃²×C₉	—	97	1	no	—
34	C₃²×C₉	C₉₇⋊C₃	1	1	yes	characteristic
35	C₉⋊C₉	—	97	9	no	—
36	C₃³	C₃×C₉₇⋊C₃	1	1	yes	characteristic
37	C₃×C₉	—	3	3	no	—
38	C₃×C₉	—	291	3	no	—
39	C₃×C₉	—	291	3	no	—
40	C₃×C₉	—	97	3	no	—
41	C₃×C₉	—	97	3	no	—
42	C₃×C₉	—	97	9	no	—
43	C₃×C₉	—	97	3	no	—
44	C₃×C₉	C₃×C₉₇⋊C₃	1	3	yes	—
45	C₃²	C₉×C₉₇⋊C₃	1	3	yes	—
46	C₃²	#14579755	1	3	yes	—
47	C₃²	#14579756	1	3	yes	—
48	C₃²	#14579757	1	3	yes	—
49	C₃²	C₃²×C₉₇⋊C₃	1	1	yes	characteristic
50	C₉	—	3	3	no	—
51	C₉	—	291	3	no	—
52	C₉	—	291	3	no	—
53	C₉	—	97	9	no	—
54	C₃	(C₉₇⋊C₉)⋊C₉	1	9	yes	direct product factor
55	C₃	C₃×C₉×C₉₇⋊C₃	1	1	yes	characteristic
56	C₃	C₃×#14579755	1	1	yes	characteristic
57	C₃	C₃×#14579756	1	1	yes	characteristic
58	C₃	C₃×#14579757	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
4. (C₉₇⋊C₉)⋊C₉	C₃	direct (N × H)
8. C₃×C₉₇⋊C₉	C₉	semidirect
23. C₉₇⋊C₉	C₃×C₉	semidirect
24. C₃×C₉₇	C₉⋊C₉	semidirect
30. C₉₇	C₃×C₉⋊C₉	semidirect
54. C₃	(C₉₇⋊C₉)⋊C₉	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₉₇⋊C₉	3
(C₉₇⋊C₉)⋊C₉	3
C₃²×C₉×C₉₇	3
C₃×C₉⋊C₉	97

Subgroups — C3×(C97⋊C9)⋊C9 #37555853

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×(C₉₇⋊C₉)⋊C₉ #37555853