Subgroups — #34063362

Order 19197.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20264264	C₃	1	3	yes	maximal, complemented
2	C₃×#14523838	C₃	1	1	yes	maximal, characteristic, complemented
3	#20264253	C₃	1	1	yes	maximal, characteristic, complemented
4	#20264251	C₃	1	1	yes	maximal, characteristic, complemented
5	#20264249	C₃	1	3	yes	maximal, complemented
6	#20264246	C₃	1	3	yes	maximal, complemented
7	C₇₉×#733	C₃	1	1	yes	maximal, characteristic, complemented
8	C₃²×C₇₉⋊C₃	C₃²	1	1	yes	characteristic
9	#14523840	C₃²	1	3	yes	—
10	#14523839	—	3	3	no	—
11	#14523838	—	3	3	no	—
12	#14523838	—	3	3	no	—
13	C₃²⋊(C₇₉⋊C₃)	C₃²	1	3	yes	—
14	C₃×C₇₉⋊C₉	C₃²	1	1	yes	characteristic
15	C₃×C₇₉⋊C₉	C₃²	1	1	yes	characteristic
16	C₉×C₇₉⋊C₃	—	3	3	no	—
17	3₋¹⁺²×C₇₉	C₃²	1	3	yes	—
18	C₃×C₉×C₇₉	C₃²	1	1	yes	characteristic
19	C₃²×C₇₉	C₃³	1	1	yes	characteristic
20	C₃×C₇₉⋊C₃	—	3	3	no	—
21	C₃×C₇₉⋊C₃	—	3	1	no	—
22	C₃×C₇₉⋊C₃	—	9	1	no	—
23	C₉×C₇₉	—	3	1	no	—
24	C₉×C₇₉	—	3	3	no	—
25	C₇₉⋊C₉	—	3	3	no	—
26	C₇₉⋊C₉	—	3	1	no	—
27	C₇₉⋊C₉	H(3,𝔽₃)	1	3	yes	—
28	#6913	—	79	1	no	maximal, Sylow
29	C₃×C₇₉	—	3	1	no	—
30	C₃×C₇₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
31	C₇₉⋊C₃	—	9	3	no	—
32	C₇₉⋊C₃	—	9	1	no	—
33	#737	—	79	3	no	—
34	C₃×3₋¹⁺²	—	79	1	no	—
35	#733	—	79	1	no	—
36	#733	C₇₉⋊C₃	1	1	yes	characteristic, complemented
37	#732	—	79	1	no	—
38	#731	—	79	3	no	—
39	AΣL(1,𝔽₂₇)	—	79	3	no	—
40	C₇₉	#6913	1	1	yes	characteristic, complemented, Sylow
41	C₃³	—	79	1	no	—
42	3₋¹⁺²	—	79	3	no	—
43	3₋¹⁺²	—	237	3	no	—
44	3₋¹⁺²	—	237	3	no	—
45	3₋¹⁺²	—	237	3	no	—
46	3₋¹⁺²	C₃×C₇₉⋊C₃	1	3	yes	—
47	H(3,𝔽₃)	—	79	3	no	—
48	C₃×C₉	—	79	1	no	—
49	C₃×C₉	—	79	1	no	—
50	C₃×C₉	—	237	3	no	—
51	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
52	C₃²	—	711	1	no	—
53	C₃²	—	237	3	no	—
54	C₃²	—	237	1	no	—
55	C₃²	C₃²×C₇₉⋊C₃	1	1	yes	characteristic
56	C₉	—	3	3	no	—
57	C₉	—	3	1	no	—
58	C₉	—	79	3	no	—
59	C₉	—	237	1	no	—
60	C₉	—	237	3	no	—
61	C₃	—	3	1	no	—
62	C₃	—	711	1	no	—
63	C₃	—	711	3	no	—
64	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)
hypercenter	#733	C₇₉⋊C₃
hypocenter	C₇₉	#6913
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
1. #20264264	C₃	semidirect
2. C₃×#14523838	C₃	semidirect
3. #20264253	C₃	semidirect
4. #20264251	C₃	semidirect
5. #20264249	C₃	semidirect
6. #20264246	C₃	semidirect
7. C₇₉×#733	C₃	semidirect
36. #733	C₇₉⋊C₃	semidirect
40. C₇₉	#6913	semidirect

Maximal subgroups

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

subgroup	index
#20264264	3
C₃×#14523838	3
#20264253	3
#20264251	3
#20264249	3
#20264246	3
C₇₉×#733	3
#6913	79