Subgroups — #34063293

Order 19197.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20264238	C₃	1	1	yes	maximal, characteristic, complemented
2	#20264237	C₃	1	1	yes	maximal, characteristic, complemented
3	(C₇₉⋊C₉)⋊C₉	C₃	1	6	yes	maximal, complemented
4	C₃²⋊(C₇₉⋊C₉)	C₃	1	3	yes	maximal
5	C₉×C₇₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃×3₋¹⁺²×C₇₉	C₃	1	1	yes	maximal, characteristic
7	C₃×C₇₉⋊C₉	C₃²	1	3	yes	—
8	C₃×C₇₉⋊C₉	C₃²	1	3	yes	—
9	C₃×C₇₉⋊C₉	C₃²	1	3	yes	—
10	C₃³×C₇₉	C₃²	1	1	yes	characteristic
11	3₋¹⁺²×C₇₉	—	3	3	no	—
12	C₃×C₉×C₇₉	C₃²	1	2	yes	—
13	C₃×C₉×C₇₉	C₃²	1	1	yes	characteristic
14	C₃²×C₇₉	—	3	1	no	—
15	C₃²×C₇₉	—	3	3	no	—
16	C₃²×C₇₉	C₃³	1	1	yes	characteristic
17	C₉×C₇₉	—	3	2	no	—
18	C₉×C₇₉	3₋¹⁺²	1	3	yes	—
19	C₇₉⋊C₉	—	3	3	no	—
20	C₇₉⋊C₉	—	3	3	no	—
21	C₇₉⋊C₉	—	3	3	no	—
22	#6899	—	79	1	no	maximal, Sylow
23	C₃×C₇₉	—	9	1	no	—
24	C₃×C₇₉	C₃×3₋¹⁺²	1	1	yes	characteristic
25	C₃×C₇₉	#737	1	3	yes	—
26	C₃×3₋¹⁺²	C₇₉⋊C₃	1	1	yes	characteristic
27	C₉⋊C₉	—	79	6	no	—
28	C₉⋊C₉	—	79	1	no	—
29	C₉⋊C₉	—	79	1	no	—
30	C₃²⋊C₉	—	79	3	no	—
31	C₉²	—	79	1	no	—
32	C₇₉	#6899	1	1	yes	characteristic, complemented, Sylow
33	C₃³	C₃×C₇₉⋊C₃	1	1	yes	characteristic
34	3₋¹⁺²	—	3	3	no	—
35	C₃×C₉	—	79	3	no	—
36	C₃×C₉	—	79	3	no	—
37	C₃×C₉	—	79	3	no	—
38	C₃×C₉	C₃×C₇₉⋊C₃	1	2	yes	—
39	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
40	C₃²	—	3	1	no	—
41	C₃²	—	3	3	no	—
42	C₃²	C₃²×C₇₉⋊C₃	1	1	yes	characteristic
43	C₉	—	3	2	no	—
44	C₉	—	237	3	no	—
45	C₉	—	237	3	no	—
46	C₉	—	237	3	no	—
47	C₉	#14523840	1	3	yes	—
48	C₃	—	9	1	no	—
49	C₃	C₃×#14523840	1	1	yes	characteristic
50	C₃	#20264264	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₇₉⋊C₃
commutator, socle, cosocle	C₃²×C₇₉	C₃³
Fitting	C₃×3₋¹⁺²×C₇₉	C₃
prime radical	C₃³×C₇₉	C₃²
hypercenter	C₃×3₋¹⁺²	C₇₉⋊C₃
hypocenter	C₇₉	#6899
LCS	G ▷ C₃²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₃² ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
1. #20264238	C₃	semidirect
2. #20264237	C₃	semidirect
3. (C₇₉⋊C₉)⋊C₉	C₃	semidirect
5. C₉×C₇₉⋊C₉	C₃	semidirect
32. C₇₉	#6899	semidirect

Maximal subgroups

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

subgroup	index
#20264238	3
#20264237	3
(C₇₉⋊C₉)⋊C₉	3
C₃²⋊(C₇₉⋊C₉)	3
C₉×C₇₉⋊C₉	3
C₃×3₋¹⁺²×C₇₉	3
#6899	79