Subgroups — #34063298

Order 19197.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14523839	C₃	1	1	yes	maximal, characteristic
2	#20264238	C₃	1	1	yes	maximal, characteristic, complemented
3	#20264237	C₃	1	3	yes	maximal, complemented
4	(C₇₉⋊C₉)⋊C₉	C₃	1	3	yes	maximal, complemented
5	(C₃×C₇₉⋊C₃)⋊C₉	C₃	1	3	yes	maximal
6	C₉×C₇₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
7	C₇₉×C₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₇₉⋊C₃	C₃²	1	1	yes	characteristic
9	#14523839	—	3	3	no	—
10	C₃×C₇₉⋊C₉	C₃²	1	3	yes	—
11	C₃×C₇₉⋊C₉	C₃²	1	3	yes	—
12	C₃×C₇₉⋊C₉	C₃²	1	1	yes	characteristic
13	C₃×C₇₉⋊C₉	C₃²	1	1	yes	characteristic
14	C₃×C₉×C₇₉	C₃²	1	3	yes	—
15	C₃×C₉×C₇₉	C₃²	1	1	yes	characteristic
16	C₃²×C₇₉	C₃³	1	1	yes	characteristic
17	C₃×C₇₉⋊C₃	—	3	1	no	—
18	C₃×C₇₉⋊C₃	—	3	3	no	—
19	C₉×C₇₉	—	3	3	no	—
20	C₉×C₇₉	3₋¹⁺²	1	3	yes	—
21	C₇₉⋊C₉	—	3	1	no	—
22	C₇₉⋊C₉	—	3	1	no	—
23	C₇₉⋊C₉	—	3	3	no	—
24	C₇₉⋊C₉	—	3	3	no	—
25	#6899	—	79	1	no	maximal, Sylow
26	C₃×C₇₉	C₃×3₋¹⁺²	1	1	yes	characteristic
27	C₃×C₇₉	#737	1	3	yes	—
28	C₇₉⋊C₃	—	9	1	no	—
29	C₃×3₋¹⁺²	—	79	1	no	—
30	C₉⋊C₉	—	79	3	no	—
31	C₉⋊C₉	—	79	3	no	—
32	C₉⋊C₉	—	79	1	no	—
33	C₉⋊C₉	C₇₉⋊C₃	1	1	yes	characteristic, complemented
34	C₃²⋊C₉	—	79	3	no	—
35	C₉²	—	79	1	no	—
36	C₇₉	#6899	1	1	yes	characteristic, complemented, Sylow
37	C₃³	—	79	1	no	—
38	3₋¹⁺²	—	237	3	no	—
39	C₃×C₉	—	79	3	no	—
40	C₃×C₉	—	79	3	no	—
41	C₃×C₉	—	79	1	no	—
42	C₃×C₉	—	79	1	no	—
43	C₃×C₉	C₃×C₇₉⋊C₃	1	3	yes	—
44	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
45	C₃²	—	237	1	no	—
46	C₃²	—	237	3	no	—
47	C₃²	C₃²×C₇₉⋊C₃	1	1	yes	characteristic
48	C₉	—	3	3	no	—
49	C₉	—	237	1	no	—
50	C₉	—	237	1	no	—
51	C₉	—	237	3	no	—
52	C₉	—	237	3	no	—
53	C₉	#14523839	1	3	yes	—
54	C₃	—	711	1	no	—
55	C₃	C₃×#14523839	1	1	yes	characteristic
56	C₃	#20264264	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₇₉⋊C₃
commutator, socle, cosocle	C₃²×C₇₉	C₃³
Fitting	C₇₉×C₉⋊C₉	C₃
prime radical	C₃²×C₇₉⋊C₃	C₃²
hypercenter	C₉⋊C₉	C₇₉⋊C₃
hypocenter	C₇₉	#6899
LCS	G ▷ C₃²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₃² ◁ C₉⋊C₉

Complements

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

N	H ≅ G/N	type
2. #20264238	C₃	semidirect
3. #20264237	C₃	semidirect
4. (C₇₉⋊C₉)⋊C₉	C₃	semidirect
6. C₉×C₇₉⋊C₉	C₃	semidirect
7. C₇₉×C₉⋊C₉	C₃	semidirect
33. C₉⋊C₉	C₇₉⋊C₃	semidirect
36. 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×#14523839	3
#20264238	3
#20264237	3
(C₇₉⋊C₉)⋊C₉	3
(C₃×C₇₉⋊C₃)⋊C₉	3
C₉×C₇₉⋊C₉	3
C₇₉×C₉⋊C₉	3
#6899	79