Subgroups — #34063261

Order 19197.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14523840	C₃	1	2	yes	maximal, complemented
2	C₃²×C₇₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃²⋊(C₇₉⋊C₉)	C₃	1	9	yes	maximal, complemented
4	C₃×H(3,𝔽₃)×C₇₉	C₃	1	1	yes	maximal, characteristic
5	#14523840	—	3	6	no	—
6	C₃×C₇₉⋊C₉	—	3	3	no	—
7	C₃×C₇₉⋊C₉	C₃²	1	3	yes	—
8	C₃×C₇₉⋊C₉	C₃²	1	6	yes	—
9	C₃³×C₇₉	C₃²	1	3	yes	—
10	C₃³×C₇₉	C₃²	1	1	yes	characteristic
11	H(3,𝔽₃)×C₇₉	—	3	3	no	—
12	C₃²×C₇₉	—	3	3	no	—
13	C₃²×C₇₉	—	3	3	no	—
14	C₃²×C₇₉	—	3	9	no	—
15	C₃²×C₇₉	H(3,𝔽₃)	1	3	yes	—
16	C₃²×C₇₉	C₃³	1	1	yes	characteristic
17	C₇₉⋊C₉	—	3	3	no	—
18	C₇₉⋊C₉	—	3	6	no	—
19	#6893	—	79	1	no	maximal, Sylow
20	C₃×C₇₉	—	3	3	no	—
21	C₃×C₇₉	—	9	3	no	—
22	C₃×C₇₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
23	C₃×C₇₉	#737	1	3	yes	—
24	C₃×3₋¹⁺²	—	79	2	no	—
25	C₃×H(3,𝔽₃)	C₇₉⋊C₃	1	1	yes	characteristic
26	C₃²×C₉	—	79	1	no	—
27	C₃²⋊C₉	—	79	9	no	—
28	C₇₉	#6893	1	1	yes	characteristic, complemented, Sylow
29	C₃³	C₃×C₇₉⋊C₃	1	3	yes	—
30	C₃³	C₃×C₇₉⋊C₃	1	1	yes	characteristic
31	3₋¹⁺²	—	237	6	no	—
32	H(3,𝔽₃)	—	3	3	no	—
33	C₃×C₉	—	79	3	no	—
34	C₃×C₉	—	79	6	no	—
35	C₃×C₉	—	237	3	no	—
36	C₃²	—	3	3	no	—
37	C₃²	—	3	3	no	—
38	C₃²	—	3	9	no	—
39	C₃²	C₃²⋊(C₇₉⋊C₃)	1	3	yes	—
40	C₃²	C₃²×C₇₉⋊C₃	1	1	yes	characteristic
41	C₉	—	237	3	no	—
42	C₉	—	237	6	no	—
43	C₃	—	3	3	no	—
44	C₃	—	9	3	no	—
45	C₃	C₃×C₃²⋊(C₇₉⋊C₃)	1	1	yes	characteristic
46	C₃	#20264262	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₇₉⋊C₃
commutator, socle, cosocle	C₃²×C₇₉	C₃³
Fitting, prime radical	C₃×H(3,𝔽₃)×C₇₉	C₃
hypercenter	C₃×H(3,𝔽₃)	C₇₉⋊C₃
hypocenter	C₇₉	#6893
LCS	G ▷ C₃²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₃² ◁ C₃×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃×#14523840	C₃	semidirect
2. C₃²×C₇₉⋊C₉	C₃	semidirect
3. C₃²⋊(C₇₉⋊C₉)	C₃	semidirect
28. 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
C₃²×C₇₉⋊C₉	3
C₃²⋊(C₇₉⋊C₉)	3
C₃×H(3,𝔽₃)×C₇₉	3
#6893	79