Subgroups — #34063278

Order 19197.

120 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14523840	C₃	1	2	yes	maximal
2	#20264238	C₃	1	1	yes	maximal, characteristic, complemented
3	#20264237	C₃	1	1	yes	maximal, characteristic, complemented
4	(C₇₉⋊C₉)⋊C₉	C₃	1	2	yes	maximal, complemented
5	(C₇₉⋊C₉)⋊C₉	C₃	1	2	yes	maximal, complemented
6	(C₇₉⋊C₉)⋊C₉	C₃	1	2	yes	maximal, complemented
7	C₃²⋊(C₇₉⋊C₉)	C₃	1	1	yes	maximal, characteristic
8	C₉×C₇₉⋊C₉	C₃	1	1	yes	maximal, characteristic, complemented
9	C₇₉×C₃²⋊C₉	C₃	1	1	yes	maximal, characteristic
10	#14523840	—	3	6	no	—
11	C₃×C₇₉⋊C₉	C₃²	1	1	yes	characteristic
12	C₃×C₇₉⋊C₉	C₃²	1	2	yes	—
13	C₃×C₇₉⋊C₉	C₃²	1	2	yes	—
14	C₃×C₇₉⋊C₉	C₃²	1	2	yes	—
15	C₃×C₇₉⋊C₉	C₃²	1	2	yes	—
16	C₃³×C₇₉	C₃²	1	1	yes	characteristic
17	C₃×C₉×C₇₉	C₃²	1	1	yes	characteristic
18	C₃×C₉×C₇₉	C₃²	1	1	yes	characteristic
19	C₃×C₉×C₇₉	C₃²	1	1	yes	characteristic
20	C₃²×C₇₉	—	3	2	no	—
21	C₃²×C₇₉	—	3	1	no	—
22	C₃²×C₇₉	—	3	1	no	—
23	C₃²×C₇₉	C₃³	1	1	yes	characteristic
24	C₉×C₇₉	—	3	1	no	—
25	C₉×C₇₉	—	3	1	no	—
26	C₉×C₇₉	—	3	1	no	—
27	C₇₉⋊C₉	—	3	2	no	—
28	C₇₉⋊C₉	—	3	2	no	—
29	C₇₉⋊C₉	—	3	1	no	—
30	C₇₉⋊C₉	—	3	2	no	—
31	C₇₉⋊C₉	3₋¹⁺²	1	6	yes	complemented
32	#6896	—	79	1	no	maximal, Sylow
33	C₃×C₇₉	—	9	1	no	—
34	C₃×C₇₉	C₃×3₋¹⁺²	1	2	yes	—
35	C₃×C₇₉	#737	1	1	yes	characteristic
36	C₃×C₇₉	#737	1	1	yes	characteristic
37	C₃×3₋¹⁺²	—	79	2	no	—
38	C₉⋊C₉	—	79	2	no	—
39	C₉⋊C₉	—	79	2	no	—
40	C₉⋊C₉	—	79	2	no	—
41	C₉⋊C₉	—	79	1	no	—
42	C₉⋊C₉	—	79	1	no	—
43	C₃²⋊C₉	—	79	1	no	—
44	C₃²⋊C₉	C₇₉⋊C₃	1	1	yes	characteristic
45	C₉²	—	79	1	no	—
46	C₇₉	#6896	1	1	yes	characteristic, complemented, Sylow
47	C₃³	C₃×C₇₉⋊C₃	1	1	yes	characteristic
48	3₋¹⁺²	—	237	6	no	—
49	C₃×C₉	—	79	2	no	—
50	C₃×C₉	—	79	1	no	—
51	C₃×C₉	—	79	2	no	—
52	C₃×C₉	—	79	2	no	—
53	C₃×C₉	—	79	2	no	—
54	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
55	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
56	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
57	C₃²	—	3	2	no	—
58	C₃²	—	3	1	no	—
59	C₃²	—	3	1	no	—
60	C₃²	C₃²×C₇₉⋊C₃	1	1	yes	characteristic
61	C₉	—	3	1	no	—
62	C₉	—	3	1	no	—
63	C₉	—	3	1	no	—
64	C₉	—	79	6	no	—
65	C₉	—	237	2	no	—
66	C₉	—	237	2	no	—
67	C₉	—	237	1	no	—
68	C₉	—	237	2	no	—
69	C₃	—	9	1	no	—
70	C₃	3₋¹⁺²×C₇₉⋊C₃	1	2	yes	—
71	C₃	#20264262	1	1	yes	characteristic
72	C₃	#20264263	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₃²	C₃²×C₇₉⋊C₃
commutator, socle, cosocle	C₃²×C₇₉	C₃³
Fitting	C₇₉×C₃²⋊C₉	C₃
prime radical	C₃³×C₇₉	C₃²
hypercenter	C₃²⋊C₉	C₇₉⋊C₃
hypocenter	C₇₉	#6896
LCS	G ▷ C₃²×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₃² ◁ C₃²⋊C₉

Complements

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

N	H ≅ G/N	type
2. #20264238	C₃	semidirect
3. #20264237	C₃	semidirect
4. (C₇₉⋊C₉)⋊C₉	C₃	semidirect
5. (C₇₉⋊C₉)⋊C₉	C₃	semidirect
6. (C₇₉⋊C₉)⋊C₉	C₃	semidirect
8. C₉×C₇₉⋊C₉	C₃	semidirect
31. C₇₉⋊C₉	3₋¹⁺²	semidirect
46. C₇₉	#6896	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
#20264238	3
#20264237	3
(C₇₉⋊C₉)⋊C₉	3
C₃²⋊(C₇₉⋊C₉)	3
C₉×C₇₉⋊C₉	3
C₇₉×C₃²⋊C₉	3
#6896	79