Subgroups — #34063280

Order 19197.

120 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	C₃×#14523838	C₃	1	1	yes	maximal, characteristic
3	#20264238	C₃	1	2	yes	maximal, complemented
4	#20264237	C₃	1	2	yes	maximal, complemented
5	(C₇₉⋊C₉)⋊C₉	C₃	1	4	yes	maximal, complemented
6	(C₃×C₇₉⋊C₃)⋊C₉	C₃	1	2	yes	maximal
7	C₉²×C₇₉	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₇₉⋊C₃	C₃²	1	1	yes	characteristic
9	#14523839	—	3	3	no	—
10	#14523838	—	3	3	no	—
11	C₃×C₇₉⋊C₉	C₃²	1	4	yes	—
12	C₃×C₇₉⋊C₉	C₃²	1	2	yes	—
13	C₃×C₇₉⋊C₉	C₃²	1	2	yes	—
14	C₃×C₉×C₇₉	C₃²	1	2	yes	—
15	C₃×C₉×C₇₉	C₃²	1	1	yes	characteristic
16	C₃×C₉×C₇₉	C₃²	1	1	yes	characteristic
17	C₃²×C₇₉	C₃³	1	1	yes	characteristic
18	C₃×C₇₉⋊C₃	—	3	1	no	—
19	C₃×C₇₉⋊C₃	—	3	1	no	—
20	C₃×C₇₉⋊C₃	—	3	2	no	—
21	C₉×C₇₉	—	3	2	no	—
22	C₉×C₇₉	3₋¹⁺²	1	3	yes	complemented
23	C₉×C₇₉	3₋¹⁺²	1	3	yes	complemented
24	C₇₉⋊C₉	—	3	2	no	—
25	C₇₉⋊C₉	—	3	2	no	—
26	C₇₉⋊C₉	—	3	4	no	—
27	#6896	—	79	1	no	maximal, Sylow
28	C₃×C₇₉	C₃×3₋¹⁺²	1	1	yes	characteristic
29	C₃×C₇₉	C₃×3₋¹⁺²	1	1	yes	characteristic
30	C₃×C₇₉	#737	1	2	yes	—
31	C₇₉⋊C₃	—	9	1	no	—
32	C₃×3₋¹⁺²	—	79	1	no	—
33	C₃×3₋¹⁺²	—	79	1	no	—
34	C₉⋊C₉	—	79	4	no	—
35	C₉⋊C₉	—	79	2	no	—
36	C₉⋊C₉	—	79	2	no	—
37	C₃²⋊C₉	—	79	2	no	—
38	C₉²	C₇₉⋊C₃	1	1	yes	characteristic, complemented
39	C₇₉	#6896	1	1	yes	characteristic, complemented, Sylow
40	C₃³	—	79	1	no	—
41	3₋¹⁺²	—	237	3	no	—
42	3₋¹⁺²	—	237	3	no	—
43	C₃×C₉	—	79	4	no	—
44	C₃×C₉	—	79	2	no	—
45	C₃×C₉	—	79	2	no	—
46	C₃×C₉	C₃×C₇₉⋊C₃	1	2	yes	—
47	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
48	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
49	C₃²	—	237	1	no	—
50	C₃²	—	237	1	no	—
51	C₃²	—	237	2	no	—
52	C₃²	C₃²×C₇₉⋊C₃	1	1	yes	characteristic
53	C₉	—	3	2	no	—
54	C₉	—	237	2	no	—
55	C₉	—	237	2	no	—
56	C₉	—	237	4	no	—
57	C₉	#14523838	1	3	yes	complemented
58	C₉	#14523839	1	3	yes	complemented
59	C₃	—	711	1	no	—
60	C₃	C₃×#14523838	1	1	yes	characteristic
61	C₃	C₃×#14523839	1	1	yes	characteristic
62	C₃	#20264263	1	2	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	#6896
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
3. #20264238	C₃	semidirect
4. #20264237	C₃	semidirect
5. (C₇₉⋊C₉)⋊C₉	C₃	semidirect
7. C₉²×C₇₉	C₃	semidirect
22. C₉×C₇₉	3₋¹⁺²	semidirect
23. C₉×C₇₉	3₋¹⁺²	semidirect
38. C₉²	C₇₉⋊C₃	semidirect
39. C₇₉	#6896	semidirect
57. C₉	#14523838	semidirect
58. C₉	#14523839	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
C₃×#14523838	3
#20264238	3
#20264237	3
(C₇₉⋊C₉)⋊C₉	3
(C₃×C₇₉⋊C₃)⋊C₉	3
C₉²×C₇₉	3
#6896	79