Subgroups — #34063151

Order 19197.

72 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃²⋊(C₇₉⋊C₃)	C₃	1	1	yes	maximal, characteristic
2	C₃²⋊(C₇₉⋊C₉)	C₃	1	2	yes	maximal, complemented
3	C₇₉×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
4	C₃²×C₇₉⋊C₃	—	3	1	no	—
5	C₃²⋊(C₇₉⋊C₃)	—	3	3	no	—
6	C₃×C₇₉⋊C₉	—	3	2	no	—
7	C₃³×C₇₉	C₃²	1	1	yes	characteristic
8	C₃×C₉×C₇₉	—	3	1	no	—
9	C₃²×C₇₉	—	3	1	no	—
10	C₃²×C₇₉	—	3	2	no	—
11	C₃²×C₇₉	—	3	1	no	—
12	C₃²×C₇₉	H(3,𝔽₃)	1	1	yes	characteristic
13	C₃×C₇₉⋊C₃	—	3	3	no	—
14	C₃×C₇₉⋊C₃	—	9	2	no	—
15	C₃×C₇₉⋊C₃	—	9	1	no	—
16	C₉×C₇₉	—	9	1	no	—
17	C₇₉⋊C₉	—	9	2	no	—
18	#6859	—	79	1	no	maximal, Sylow
19	C₃×C₇₉	—	9	1	no	—
20	C₃×C₇₉	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
21	C₃×C₇₉	#731	1	2	yes	—
22	C₃×C₇₉	#732	1	1	yes	characteristic
23	C₇₉⋊C₃	—	9	3	no	—
24	C₃×H(3,𝔽₃)	—	79	1	no	—
25	C₃²⋊C₉	—	79	2	no	—
26	C₃²⋊C₉	C₇₉⋊C₃	1	1	yes	characteristic, complemented
27	C₇₉	#6859	1	1	yes	characteristic, complemented, Sylow
28	C₃³	—	237	1	no	—
29	C₃³	C₃×C₇₉⋊C₃	1	1	yes	characteristic
30	H(3,𝔽₃)	—	237	3	no	—
31	C₃×C₉	—	3	1	no	—
32	C₃×C₉	—	237	2	no	—
33	C₃²	—	3	1	no	—
34	C₃²	—	3	2	no	—
35	C₃²	—	3	1	no	—
36	C₃²	—	711	2	no	—
37	C₃²	—	711	1	no	—
38	C₃²	—	237	3	no	—
39	C₃²	C₃²⋊(C₇₉⋊C₃)	1	1	yes	characteristic
40	C₉	—	9	1	no	—
41	C₉	—	711	2	no	—
42	C₃	—	9	1	no	—
43	C₃	—	711	3	no	—
44	C₃	#20264244	1	1	yes	characteristic
45	C₃	#20264249	1	2	yes	—
46	C₃	#20264251	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²⋊(C₇₉⋊C₃)
commutator, cosocle	C₃³×C₇₉	C₃²
Frattini	C₃³	C₃×C₇₉⋊C₃
Fitting	C₇₉×C₃²⋊C₉	C₃
socle	C₃²×C₇₉	H(3,𝔽₃)
prime radical	C₃×C₃²⋊(C₇₉⋊C₃)	C₃
hypercenter	C₃²⋊C₉	C₇₉⋊C₃
hypocenter	C₇₉	#6859
LCS	G ▷ C₃³×C₇₉ ▷ C₃²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²⋊C₉

Complements

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

N	H ≅ G/N	type
2. C₃²⋊(C₇₉⋊C₉)	C₃	semidirect
3. C₇₉×C₃²⋊C₉	C₃	semidirect
26. C₃²⋊C₉	C₇₉⋊C₃	semidirect
27. C₇₉	#6859	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₃²⋊(C₇₉⋊C₃)	3
C₃²⋊(C₇₉⋊C₉)	3
C₇₉×C₃²⋊C₉	3
#6859	79