Subgroups — C₉×#14523840 #34063243

Order 19197.

148 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14523840	C₃	1	1	yes	maximal, characteristic
2	(C₇₉⋊C₉)⋊C₉	C₃	1	6	yes	maximal, complemented
3	C₃²⋊(C₇₉⋊C₉)	C₃	1	2	yes	maximal
4	C₉×C₇₉⋊C₉	C₃	1	3	yes	maximal, complemented
5	C₃²×C₉×C₇₉	C₃	1	1	yes	maximal, characteristic
6	#14523840	C₉	1	9	yes	direct product factor
7	C₃×C₇₉⋊C₉	C₃²	1	6	yes	—
8	C₃×C₇₉⋊C₉	C₃²	1	3	yes	—
9	C₃³×C₇₉	C₃²	1	1	yes	characteristic
10	C₃×C₉×C₇₉	—	3	3	no	—
11	C₃×C₉×C₇₉	C₃²	1	2	yes	—
12	C₃×C₉×C₇₉	C₃²	1	1	yes	characteristic
13	C₃²×C₇₉	—	3	1	no	—
14	C₃²×C₇₉	—	3	2	no	—
15	C₃²×C₇₉	C₃×C₉	1	3	yes	—
16	C₃²×C₇₉	C₃³	1	1	yes	characteristic
17	C₉×C₇₉	—	3	2	no	—
18	C₉×C₇₉	3₋¹⁺²	1	3	yes	complemented
19	C₇₉⋊C₉	—	3	6	no	—
20	C₇₉⋊C₉	C₃×C₉	1	9	yes	complemented
21	C₉×3₋¹⁺²	—	79	1	no	maximal, Sylow
22	C₃×C₇₉	—	3	3	no	—
23	C₃×C₇₉	C₃²×C₉	1	1	yes	characteristic
24	C₃×C₇₉	C₃×3₋¹⁺²	1	1	yes	characteristic
25	C₃×C₇₉	#737	1	2	yes	—
26	C₃×3₋¹⁺²	—	79	1	no	—
27	C₃²×C₉	C₇₉⋊C₃	1	1	yes	characteristic
28	C₉⋊C₉	—	79	6	no	—
29	C₃²⋊C₉	—	79	2	no	—
30	C₉²	—	79	3	no	—
31	C₇₉	C₉×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
32	C₃³	C₃×C₇₉⋊C₃	1	1	yes	characteristic
33	3₋¹⁺²	—	79	9	no	—
34	C₃×C₉	—	3	3	no	—
35	C₃×C₉	—	79	3	no	—
36	C₃×C₉	—	79	6	no	—
37	C₃×C₉	C₃×C₇₉⋊C₃	1	2	yes	—
38	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
39	C₃²	—	3	1	no	—
40	C₃²	—	3	2	no	—
41	C₃²	C₉×C₇₉⋊C₃	1	3	yes	—
42	C₃²	C₃²×C₇₉⋊C₃	1	1	yes	characteristic
43	C₉	—	3	2	no	—
44	C₉	—	79	9	no	—
45	C₉	—	237	6	no	—
46	C₉	#14523840	1	3	yes	direct product factor
47	C₃	—	3	3	no	—
48	C₃	C₃×C₉×C₇₉⋊C₃	1	1	yes	characteristic
49	C₃	C₃×#14523840	1	1	yes	characteristic
50	C₃	#20264263	1	2	yes	—

	subgroup	G/H
center	C₃×C₉	C₃×C₇₉⋊C₃
commutator	C₃×C₇₉	C₃²×C₉
Frattini	C₃²	C₃²×C₇₉⋊C₃
Fitting	C₃²×C₉×C₇₉	C₃
socle, cosocle	C₃²×C₇₉	C₃³
prime radical	C₃³×C₇₉	C₃²
hypercenter	C₃²×C₉	C₇₉⋊C₃
hypocenter	C₇₉	C₉×3₋¹⁺²
LCS	G ▷ C₃×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₃×C₉ ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
2. (C₇₉⋊C₉)⋊C₉	C₃	semidirect
4. C₉×C₇₉⋊C₉	C₃	semidirect
6. #14523840	C₉	direct (N × H)
18. C₉×C₇₉	3₋¹⁺²	semidirect
20. C₇₉⋊C₉	C₃×C₉	semidirect
31. C₇₉	C₉×3₋¹⁺²	semidirect
46. C₉	#14523840	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#14523840	3
(C₇₉⋊C₉)⋊C₉	3
C₃²⋊(C₇₉⋊C₉)	3
C₉×C₇₉⋊C₉	3
C₃²×C₉×C₇₉	3
C₉×3₋¹⁺²	79

Subgroups — C9×#14523840 #34063243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#14523840 #34063243