Subgroups — #34063348

Order 19197.

124 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	3₋¹⁺²×C₇₉⋊C₃	C₃	1	3	yes	maximal
3	#20264253	C₃	1	2	yes	maximal, complemented
4	#20264252	C₃	1	6	yes	maximal, complemented
5	C₇₉×#733	C₃	1	1	yes	maximal, characteristic, complemented
6	C₃²×C₇₉⋊C₃	C₃²	1	1	yes	characteristic
7	#14523840	C₃²	1	6	yes	—
8	#14523839	—	3	3	no	—
9	#14523839	—	3	3	no	—
10	#14523838	—	3	3	no	—
11	C₃×C₇₉⋊C₉	C₃²	1	2	yes	—
12	C₉×C₇₉⋊C₃	—	3	3	no	—
13	3₋¹⁺²×C₇₉	C₃²	1	3	yes	—
14	C₃×C₉×C₇₉	C₃²	1	1	yes	characteristic
15	C₃²×C₇₉	C₃³	1	1	yes	characteristic
16	C₃×C₇₉⋊C₃	—	9	1	no	—
17	C₃×C₇₉⋊C₃	H(3,𝔽₃)	1	3	yes	—
18	C₉×C₇₉	—	3	1	no	—
19	C₉×C₇₉	—	3	3	no	—
20	C₇₉⋊C₉	—	3	6	no	—
21	C₇₉⋊C₉	—	3	2	no	—
22	#6912	—	79	1	no	maximal, Sylow
23	C₃×C₇₉	—	3	1	no	—
24	C₃×C₇₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
25	C₇₉⋊C₃	—	3	3	no	—
26	C₃×3₋¹⁺²	—	79	1	no	—
27	C₃×3₋¹⁺²	—	79	3	no	—
28	#733	—	79	6	no	—
29	#733	—	79	2	no	—
30	#733	C₇₉⋊C₃	1	1	yes	characteristic, complemented
31	C₇₉	#6912	1	1	yes	characteristic, complemented, Sylow
32	C₃³	—	79	1	no	—
33	3₋¹⁺²	—	79	6	no	—
34	3₋¹⁺²	—	237	3	no	—
35	3₋¹⁺²	—	237	3	no	—
36	3₋¹⁺²	—	237	3	no	—
37	3₋¹⁺²	C₃×C₇₉⋊C₃	1	3	yes	—
38	C₃×C₉	—	79	2	no	—
39	C₃×C₉	—	237	3	no	—
40	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
41	C₃²	—	79	3	no	—
42	C₃²	—	711	1	no	—
43	C₃²	C₃²×C₇₉⋊C₃	1	1	yes	characteristic
44	C₉	—	3	3	no	—
45	C₉	—	3	1	no	—
46	C₉	—	237	2	no	—
47	C₉	—	237	6	no	—
48	C₃	—	3	1	no	—
49	C₃	—	237	3	no	—
50	C₃	H(3,𝔽₃)×C₇₉⋊C₃	1	1	yes	characteristic

	subgroup	G/H
center	C₃	H(3,𝔽₃)×C₇₉⋊C₃
commutator, cosocle	C₃²×C₇₉	C₃³
Frattini	C₃²	C₃²×C₇₉⋊C₃
Fitting	C₇₉×#733	C₃
socle	C₃×C₇₉	C₃×H(3,𝔽₃)
prime radical	C₃²×C₇₉⋊C₃	C₃²
hypercenter	#733	C₇₉⋊C₃
hypocenter	C₇₉	#6912
LCS	G ▷ C₃²×C₇₉ ▷ C₃×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₃ ◁ C₃² ◁ #733

Complements

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

N	H ≅ G/N	type
3. #20264253	C₃	semidirect
4. #20264252	C₃	semidirect
5. C₇₉×#733	C₃	semidirect
30. #733	C₇₉⋊C₃	semidirect
31. C₇₉	#6912	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
3₋¹⁺²×C₇₉⋊C₃	3
#20264253	3
#20264252	3
C₇₉×#733	3
#6912	79