Subgroups — #34063264

Order 19197.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14523840	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃×C₃²⋊(C₇₉⋊C₃)	C₃	1	1	yes	maximal, characteristic
3	C₃²×C₇₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	(C₃×C₇₉⋊C₃)⋊C₉	C₃	1	9	yes	maximal, complemented
5	C₃×3₋¹⁺²×C₇₉	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃²×C₇₉⋊C₃	C₃²	1	3	yes	—
7	#14523840	—	3	3	no	—
8	C₃²⋊(C₇₉⋊C₃)	—	3	3	no	—
9	C₃×C₇₉⋊C₉	—	3	3	no	—
10	C₃×C₇₉⋊C₉	C₃²	1	3	yes	—
11	C₃×C₇₉⋊C₉	C₃²	1	3	yes	—
12	C₃³×C₇₉	C₃²	1	1	yes	characteristic
13	3₋¹⁺²×C₇₉	—	3	3	no	—
14	C₃×C₉×C₇₉	C₃²	1	3	yes	—
15	C₃²×C₇₉	—	3	3	no	—
16	C₃²×C₇₉	H(3,𝔽₃)	1	3	yes	—
17	C₃²×C₇₉	C₃³	1	1	yes	characteristic
18	C₃×C₇₉⋊C₃	—	3	3	no	—
19	C₃×C₇₉⋊C₃	—	3	9	no	—
20	C₉×C₇₉	—	3	3	no	—
21	C₇₉⋊C₉	—	3	3	no	—
22	C₇₉⋊C₉	—	3	3	no	—
23	#6893	—	79	1	no	maximal, Sylow
24	C₃×C₇₉	—	3	3	no	—
25	C₃×C₇₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
26	C₃×C₇₉	#737	1	3	yes	—
27	C₇₉⋊C₃	—	9	3	no	—
28	C₃×3₋¹⁺²	—	79	1	no	—
29	C₃×3₋¹⁺²	C₇₉⋊C₃	1	1	yes	characteristic, complemented
30	C₃×H(3,𝔽₃)	—	79	1	no	—
31	C₃²×C₉	—	79	1	no	—
32	C₃²⋊C₉	—	79	9	no	—
33	C₇₉	#6893	1	1	yes	characteristic, complemented, Sylow
34	C₃³	—	79	3	no	—
35	C₃³	C₃×C₇₉⋊C₃	1	1	yes	characteristic
36	3₋¹⁺²	—	3	3	no	—
37	3₋¹⁺²	—	237	3	no	—
38	H(3,𝔽₃)	—	237	3	no	—
39	C₃×C₉	—	79	3	no	—
40	C₃×C₉	—	79	3	no	—
41	C₃×C₉	—	237	3	no	—
42	C₃×C₉	C₃×C₇₉⋊C₃	1	3	yes	—
43	C₃²	—	3	3	no	—
44	C₃²	—	237	3	no	—
45	C₃²	—	237	9	no	—
46	C₃²	C₃²⋊(C₇₉⋊C₃)	1	3	yes	—
47	C₃²	C₃²×C₇₉⋊C₃	1	1	yes	characteristic
48	C₉	—	3	3	no	—
49	C₉	—	237	3	no	—
50	C₉	—	237	3	no	—
51	C₃	—	3	3	no	—
52	C₃	—	711	3	no	—
53	C₃	C₃×C₃²⋊(C₇₉⋊C₃)	1	1	yes	characteristic
54	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	C₃×C₃²⋊(C₇₉⋊C₃)	C₃
hypercenter	C₃×3₋¹⁺²	C₇₉⋊C₃
hypocenter	C₇₉	#6893
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. C₃×#14523840	C₃	semidirect
3. C₃²×C₇₉⋊C₉	C₃	semidirect
4. (C₃×C₇₉⋊C₃)⋊C₉	C₃	semidirect
5. C₃×3₋¹⁺²×C₇₉	C₃	semidirect
29. C₃×3₋¹⁺²	C₇₉⋊C₃	semidirect
33. 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×#14523840	3
C₃×C₃²⋊(C₇₉⋊C₃)	3
C₃²×C₇₉⋊C₉	3
(C₃×C₇₉⋊C₃)⋊C₉	3
C₃×3₋¹⁺²×C₇₉	3
#6893	79