Subgroups — #34063294

Order 19197.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14523838	C₃	1	1	yes	maximal, characteristic
2	#20264238	C₃	1	2	yes	maximal, complemented
3	(C₇₉⋊C₉)⋊C₉	C₃	1	6	yes	maximal, complemented
4	(C₃×C₇₉⋊C₃)⋊C₉	C₃	1	3	yes	maximal
5	C₉²×C₇₉	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃²×C₇₉⋊C₃	C₃²	1	1	yes	characteristic
7	#14523838	—	3	3	no	—
8	C₃×C₇₉⋊C₉	C₃²	1	6	yes	—
9	C₃×C₇₉⋊C₉	C₃²	1	2	yes	—
10	C₃×C₉×C₇₉	C₃²	1	3	yes	—
11	C₃×C₉×C₇₉	C₃²	1	1	yes	characteristic
12	C₃²×C₇₉	C₃³	1	1	yes	characteristic
13	C₃×C₇₉⋊C₃	—	3	1	no	—
14	C₃×C₇₉⋊C₃	—	3	3	no	—
15	C₉×C₇₉	—	3	3	no	—
16	C₉×C₇₉	3₋¹⁺²	1	3	yes	—
17	C₇₉⋊C₉	—	3	2	no	—
18	C₇₉⋊C₉	—	3	6	no	—
19	#6899	—	79	1	no	maximal, Sylow
20	C₃×C₇₉	C₃×3₋¹⁺²	1	1	yes	characteristic
21	C₃×C₇₉	#737	1	3	yes	—
22	C₇₉⋊C₃	—	9	1	no	—
23	C₃×3₋¹⁺²	—	79	1	no	—
24	C₉⋊C₉	—	79	6	no	—
25	C₉⋊C₉	—	79	2	no	—
26	C₃²⋊C₉	—	79	3	no	—
27	C₉²	C₇₉⋊C₃	1	1	yes	characteristic, complemented
28	C₇₉	#6899	1	1	yes	characteristic, complemented, Sylow
29	C₃³	—	79	1	no	—
30	3₋¹⁺²	—	237	3	no	—
31	C₃×C₉	—	79	6	no	—
32	C₃×C₉	—	79	2	no	—
33	C₃×C₉	C₃×C₇₉⋊C₃	1	3	yes	—
34	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
35	C₃²	—	237	1	no	—
36	C₃²	—	237	3	no	—
37	C₃²	C₃²×C₇₉⋊C₃	1	1	yes	characteristic
38	C₉	—	3	3	no	—
39	C₉	—	237	2	no	—
40	C₉	—	237	6	no	—
41	C₉	#14523838	1	3	yes	—
42	C₃	—	711	1	no	—
43	C₃	C₃×#14523838	1	1	yes	characteristic
44	C₃	#20264263	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₇₉⋊C₃
commutator, socle, cosocle	C₃²×C₇₉	C₃³
Fitting	C₉²×C₇₉	C₃
prime radical	C₃²×C₇₉⋊C₃	C₃²
hypercenter	C₉²	C₇₉⋊C₃
hypocenter	C₇₉	#6899
LCS	G ▷ C₃²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₃² ◁ C₉²

Complements

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

N	H ≅ G/N	type
2. #20264238	C₃	semidirect
3. (C₇₉⋊C₉)⋊C₉	C₃	semidirect
5. C₉²×C₇₉	C₃	semidirect
27. C₉²	C₇₉⋊C₃	semidirect
28. C₇₉	#6899	semidirect

Maximal subgroups

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

subgroup	index
C₃×#14523838	3
#20264238	3
(C₇₉⋊C₉)⋊C₉	3
(C₃×C₇₉⋊C₃)⋊C₉	3
C₉²×C₇₉	3
#6899	79