Subgroups — #34063360

Order 19197.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20264263	C₃	1	3	yes	maximal, complemented
2	#20264253	C₃	1	2	yes	maximal, complemented
3	#20264251	C₃	1	1	yes	maximal, characteristic, complemented
4	#20264248	C₃	1	3	yes	maximal, complemented
5	#20264245	C₃	1	3	yes	maximal, complemented
6	C₃×3₋¹⁺²×C₇₉	C₃	1	1	yes	maximal, characteristic, complemented
7	#14523840	C₃²	1	6	yes	—
8	#14523839	—	3	3	no	—
9	#14523838	—	3	3	no	—
10	C₃²⋊(C₇₉⋊C₃)	C₃²	1	3	yes	—
11	C₉×C₇₉⋊C₃	—	3	3	no	—
12	C₃³×C₇₉	C₃²	1	1	yes	characteristic
13	3₋¹⁺²×C₇₉	—	3	3	no	—
14	C₃×C₉×C₇₉	C₃²	1	1	yes	characteristic
15	C₃×C₉×C₇₉	C₃²	1	1	yes	characteristic
16	C₃×C₉×C₇₉	C₃²	1	1	yes	characteristic
17	C₃²×C₇₉	—	3	1	no	—
18	C₃²×C₇₉	—	9	1	no	—
19	C₃²×C₇₉	C₃³	1	1	yes	characteristic
20	C₃×C₇₉⋊C₃	—	3	3	no	—
21	C₉×C₇₉	—	3	1	no	—
22	C₉×C₇₉	—	3	1	no	—
23	C₉×C₇₉	H(3,𝔽₃)	1	3	yes	—
24	C₇₉⋊C₉	—	3	6	no	—
25	#6913	—	79	1	no	maximal, Sylow
26	C₃×C₇₉	—	3	1	no	—
27	C₃×C₇₉	—	9	1	no	—
28	C₃×C₇₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
29	C₇₉⋊C₃	—	9	3	no	—
30	#737	—	79	3	no	—
31	C₃×3₋¹⁺²	C₇₉⋊C₃	1	1	yes	characteristic, complemented
32	#733	—	79	2	no	—
33	#732	—	79	1	no	—
34	#731	—	79	3	no	—
35	AΣL(1,𝔽₂₇)	—	79	3	no	—
36	C₇₉	#6913	1	1	yes	characteristic, complemented, Sylow
37	C₃³	C₃×C₇₉⋊C₃	1	1	yes	characteristic
38	3₋¹⁺²	—	3	3	no	—
39	3₋¹⁺²	—	79	6	no	—
40	3₋¹⁺²	—	237	3	no	—
41	3₋¹⁺²	—	237	3	no	—
42	H(3,𝔽₃)	—	79	3	no	—
43	C₃×C₉	—	237	3	no	—
44	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
45	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
46	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
47	C₃²	—	3	1	no	—
48	C₃²	—	9	1	no	—
49	C₃²	—	237	3	no	—
50	C₃²	C₃²×C₇₉⋊C₃	1	1	yes	characteristic
51	C₉	—	3	1	no	—
52	C₉	—	3	1	no	—
53	C₉	—	237	6	no	—
54	C₉	C₃²⋊(C₇₉⋊C₃)	1	3	yes	—
55	C₃	—	3	1	no	—
56	C₃	—	9	1	no	—
57	C₃	—	711	3	no	—
58	C₃	C₃×C₃²⋊(C₇₉⋊C₃)	1	1	yes	characteristic

	subgroup	G/H
center	C₃	C₃×C₃²⋊(C₇₉⋊C₃)
commutator, cosocle	C₃²×C₇₉	C₃³
Frattini	C₃²	C₃²×C₇₉⋊C₃
Fitting	C₃×3₋¹⁺²×C₇₉	C₃
socle	C₃×C₇₉	C₃×H(3,𝔽₃)
hypercenter	C₃×3₋¹⁺²	C₇₉⋊C₃
hypocenter	C₇₉	#6913
LCS	G ▷ C₃²×C₇₉ ▷ C₃×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₃ ◁ C₃×C₉ ◁ C₃×3₋¹⁺²

Complements

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

N	H ≅ G/N	type
1. #20264263	C₃	semidirect
2. #20264253	C₃	semidirect
3. #20264251	C₃	semidirect
4. #20264248	C₃	semidirect
5. #20264245	C₃	semidirect
6. C₃×3₋¹⁺²×C₇₉	C₃	semidirect
31. C₃×3₋¹⁺²	C₇₉⋊C₃	semidirect
36. C₇₉	#6913	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20264263	3
#20264253	3
#20264251	3
#20264248	3
#20264245	3
C₃×3₋¹⁺²×C₇₉	3
#6913	79