Subgroups — #34063359

Order 19197.

126 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20264264	C₃	1	2	yes	maximal, complemented
2	#20264262	C₃	1	1	yes	maximal, characteristic, complemented
3	C₃×#14523839	C₃	1	1	yes	maximal, characteristic, complemented
4	#20264252	C₃	1	2	yes	maximal, complemented
5	#20264250	C₃	1	1	yes	maximal, characteristic, complemented
6	#20264248	C₃	1	2	yes	maximal, complemented
7	#20264246	C₃	1	2	yes	maximal, complemented
8	#20264244	C₃	1	1	yes	maximal, characteristic, complemented
9	C₇₉×#731	C₃	1	1	yes	maximal, characteristic, complemented
10	C₃²×C₇₉⋊C₃	C₃²	1	1	yes	characteristic
11	#14523840	—	3	2	no	—
12	#14523840	C₃²	1	2	yes	—
13	#14523840	C₃²	1	2	yes	—
14	#14523839	—	3	2	no	—
15	#14523839	—	3	1	no	—
16	#14523839	—	3	2	no	—
17	#14523838	—	3	2	no	—
18	C₃²⋊(C₇₉⋊C₃)	C₃²	1	2	yes	—
19	C₃×C₇₉⋊C₉	—	3	1	no	—
20	C₃×C₇₉⋊C₉	C₃²	1	1	yes	characteristic
21	C₃×C₇₉⋊C₉	C₃²	1	1	yes	characteristic
22	C₉×C₇₉⋊C₃	—	3	2	no	—
23	3₋¹⁺²×C₇₉	C₃²	1	2	yes	—
24	H(3,𝔽₃)×C₇₉	C₃²	1	1	yes	characteristic
25	C₃×C₉×C₇₉	C₃²	1	1	yes	characteristic
26	C₃²×C₇₉	—	3	1	no	—
27	C₃²×C₇₉	C₃³	1	1	yes	characteristic
28	C₃×C₇₉⋊C₃	—	3	2	no	—
29	C₃×C₇₉⋊C₃	—	3	1	no	—
30	C₃×C₇₉⋊C₃	—	9	1	no	—
31	C₉×C₇₉	—	3	1	no	—
32	C₉×C₇₉	—	3	2	no	—
33	C₇₉⋊C₉	—	3	2	no	—
34	C₇₉⋊C₉	—	3	2	no	—
35	C₇₉⋊C₉	—	3	1	no	—
36	C₇₉⋊C₉	H(3,𝔽₃)	1	2	yes	—
37	C₇₉⋊C₉	H(3,𝔽₃)	1	1	yes	characteristic
38	#6913	—	79	1	no	maximal, Sylow
39	C₃×C₇₉	—	3	1	no	—
40	C₃×C₇₉	—	9	1	no	—
41	C₃×C₇₉	C₃×H(3,𝔽₃)	1	1	yes	characteristic
42	C₇₉⋊C₃	—	9	2	no	—
43	C₇₉⋊C₃	—	9	1	no	—
44	#737	—	79	2	no	—
45	#737	—	79	1	no	—
46	C₃×3₋¹⁺²	—	79	1	no	—
47	#733	—	79	2	no	—
48	#732	—	79	1	no	—
49	#731	—	79	2	no	—
50	#731	C₇₉⋊C₃	1	1	yes	characteristic, complemented
51	AΣL(1,𝔽₂₇)	—	79	2	no	—
52	AΣL(1,𝔽₂₇)	—	79	1	no	—
53	C₇₉	#6913	1	1	yes	characteristic, complemented, Sylow
54	C₃³	—	79	1	no	—
55	3₋¹⁺²	—	79	2	no	—
56	3₋¹⁺²	—	79	2	no	—
57	3₋¹⁺²	—	237	2	no	—
58	3₋¹⁺²	—	237	2	no	—
59	3₋¹⁺²	—	237	1	no	—
60	3₋¹⁺²	—	237	2	no	—
61	3₋¹⁺²	—	237	2	no	—
62	3₋¹⁺²	C₃×C₇₉⋊C₃	1	2	yes	—
63	H(3,𝔽₃)	—	79	2	no	—
64	H(3,𝔽₃)	C₃×C₇₉⋊C₃	1	1	yes	characteristic
65	C₃×C₉	—	79	1	no	—
66	C₃×C₉	—	79	1	no	—
67	C₃×C₉	—	237	2	no	—
68	C₃×C₉	—	237	1	no	—
69	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
70	C₃²	—	3	1	no	—
71	C₃²	—	711	1	no	—
72	C₃²	—	237	2	no	—
73	C₃²	—	237	1	no	—
74	C₃²	C₃²×C₇₉⋊C₃	1	1	yes	characteristic
75	C₉	—	3	2	no	—
76	C₉	—	3	1	no	—
77	C₉	—	79	2	no	—
78	C₉	—	79	1	no	—
79	C₉	—	237	1	no	—
80	C₉	—	237	2	no	—
81	C₉	—	237	2	no	—
82	C₃	—	3	1	no	—
83	C₃	—	9	1	no	—
84	C₃	—	711	1	no	—
85	C₃	—	711	2	no	—
86	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×#731	C₃
socle	C₃×C₇₉	C₃×H(3,𝔽₃)
hypercenter	#731	C₇₉⋊C₃
hypocenter	C₇₉	#6913
LCS	G ▷ C₃²×C₇₉ ▷ C₃×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₃ ◁ C₃² ◁ #731

Complements

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

N	H ≅ G/N	type
1. #20264264	C₃	semidirect
2. #20264262	C₃	semidirect
3. C₃×#14523839	C₃	semidirect
4. #20264252	C₃	semidirect
5. #20264250	C₃	semidirect
6. #20264248	C₃	semidirect
7. #20264246	C₃	semidirect
8. #20264244	C₃	semidirect
9. C₇₉×#731	C₃	semidirect
50. #731	C₇₉⋊C₃	semidirect
53. 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
#20264262	3
C₃×#14523839	3
#20264252	3
#20264250	3
#20264248	3
#20264246	3
#20264244	3
C₇₉×#731	3
#6913	79