Subgroups — #34063262

Order 19197.

156 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, complemented
2	C₃×#14523838	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×C₃²⋊(C₇₉⋊C₃)	C₃	1	1	yes	maximal, characteristic
4	C₃×C₉×C₇₉⋊C₃	C₃	1	1	yes	maximal, characteristic, complemented
5	C₃²⋊(C₇₉⋊C₉)	C₃	1	2	yes	maximal, complemented
6	(C₃×C₇₉⋊C₃)⋊C₉	C₃	1	2	yes	maximal, complemented
7	(C₃×C₇₉⋊C₃)⋊C₉	C₃	1	2	yes	maximal, complemented
8	(C₃×C₇₉⋊C₃)⋊C₉	C₃	1	2	yes	maximal, complemented
9	C₇₉×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
10	C₃²×C₇₉⋊C₃	C₃²	1	2	yes	—
11	C₃²×C₇₉⋊C₃	C₃²	1	1	yes	characteristic
12	#14523839	—	3	3	no	—
13	#14523838	—	3	3	no	—
14	C₃²⋊(C₇₉⋊C₃)	—	3	3	no	—
15	C₃×C₇₉⋊C₉	C₃²	1	2	yes	—
16	C₃×C₇₉⋊C₉	C₃²	1	2	yes	—
17	C₃×C₇₉⋊C₉	C₃²	1	2	yes	—
18	C₉×C₇₉⋊C₃	—	3	3	no	—
19	C₃³×C₇₉	C₃²	1	1	yes	characteristic
20	C₃×C₉×C₇₉	C₃²	1	1	yes	characteristic
21	C₃×C₉×C₇₉	C₃²	1	1	yes	characteristic
22	C₃×C₉×C₇₉	C₃²	1	1	yes	characteristic
23	C₃²×C₇₉	—	3	1	no	—
24	C₃²×C₇₉	—	3	1	no	—
25	C₃²×C₇₉	—	3	2	no	—
26	C₃²×C₇₉	C₃³	1	1	yes	characteristic
27	C₃×C₇₉⋊C₃	—	3	1	no	—
28	C₃×C₇₉⋊C₃	—	3	2	no	—
29	C₃×C₇₉⋊C₃	—	3	2	no	—
30	C₃×C₇₉⋊C₃	—	3	2	no	—
31	C₃×C₇₉⋊C₃	—	3	4	no	—
32	C₃×C₇₉⋊C₃	H(3,𝔽₃)	1	3	yes	—
33	C₉×C₇₉	—	3	1	no	—
34	C₉×C₇₉	—	3	1	no	—
35	C₉×C₇₉	—	3	1	no	—
36	C₇₉⋊C₉	—	3	2	no	—
37	C₇₉⋊C₉	—	3	2	no	—
38	C₇₉⋊C₉	—	3	2	no	—
39	#6893	—	79	1	no	maximal, Sylow
40	C₃×C₇₉	—	9	1	no	—
41	C₃×C₇₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
42	C₃×C₇₉	#737	1	1	yes	characteristic
43	C₃×C₇₉	#737	1	2	yes	—
44	C₇₉⋊C₃	—	3	3	no	—
45	C₇₉⋊C₃	—	9	2	no	—
46	C₃×3₋¹⁺²	—	79	1	no	—
47	C₃×3₋¹⁺²	—	79	1	no	—
48	C₃×H(3,𝔽₃)	—	79	1	no	—
49	C₃²×C₉	—	79	1	no	—
50	C₃²⋊C₉	—	79	2	no	—
51	C₃²⋊C₉	—	79	2	no	—
52	C₃²⋊C₉	—	79	2	no	—
53	C₃²⋊C₉	—	79	2	no	—
54	C₃²⋊C₉	C₇₉⋊C₃	1	1	yes	characteristic, complemented
55	C₇₉	#6893	1	1	yes	characteristic, complemented, Sylow
56	C₃³	—	79	1	no	—
57	C₃³	—	79	2	no	—
58	C₃³	C₃×C₇₉⋊C₃	1	1	yes	characteristic
59	3₋¹⁺²	—	237	3	no	—
60	3₋¹⁺²	—	237	3	no	—
61	H(3,𝔽₃)	—	237	3	no	—
62	C₃×C₉	—	79	2	no	—
63	C₃×C₉	—	79	2	no	—
64	C₃×C₉	—	79	2	no	—
65	C₃×C₉	—	237	3	no	—
66	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
67	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
68	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
69	C₃²	—	3	1	no	—
70	C₃²	—	3	1	no	—
71	C₃²	—	3	2	no	—
72	C₃²	—	79	3	no	—
73	C₃²	—	237	2	no	—
74	C₃²	—	237	2	no	—
75	C₃²	—	237	4	no	—
76	C₃²	—	237	1	no	—
77	C₃²	—	237	2	no	—
78	C₃²	C₃²×C₇₉⋊C₃	1	1	yes	characteristic
79	C₉	—	3	1	no	—
80	C₉	—	3	1	no	—
81	C₉	—	3	1	no	—
82	C₉	—	237	2	no	—
83	C₉	—	237	2	no	—
84	C₉	—	237	2	no	—
85	C₃	—	9	1	no	—
86	C₃	—	711	2	no	—
87	C₃	—	237	3	no	—
88	C₃	H(3,𝔽₃)×C₇₉⋊C₃	1	1	yes	characteristic
89	C₃	#20264263	1	1	yes	characteristic
90	C₃	#20264264	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₇₉⋊C₃
commutator, socle, cosocle	C₃²×C₇₉	C₃³
Fitting	C₇₉×C₃²⋊C₉	C₃
prime radical	C₃×C₃²⋊(C₇₉⋊C₃)	C₃
hypercenter	C₃²⋊C₉	C₇₉⋊C₃
hypocenter	C₇₉	#6893
LCS	G ▷ C₃²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₃² ◁ C₃²⋊C₉

Complements

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

N	H ≅ G/N	type
1. C₃×#14523839	C₃	semidirect
2. C₃×#14523838	C₃	semidirect
4. C₃×C₉×C₇₉⋊C₃	C₃	semidirect
5. C₃²⋊(C₇₉⋊C₉)	C₃	semidirect
6. (C₃×C₇₉⋊C₃)⋊C₉	C₃	semidirect
7. (C₃×C₇₉⋊C₃)⋊C₉	C₃	semidirect
8. (C₃×C₇₉⋊C₃)⋊C₉	C₃	semidirect
9. C₇₉×C₃²⋊C₉	C₃	semidirect
54. C₃²⋊C₉	C₇₉⋊C₃	semidirect
55. C₇₉	#6893	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
C₃×C₃²⋊(C₇₉⋊C₃)	3
C₃×C₉×C₇₉⋊C₃	3
C₃²⋊(C₇₉⋊C₉)	3
(C₃×C₇₉⋊C₃)⋊C₉	3
C₇₉×C₃²⋊C₉	3
#6893	79