Subgroups — #34063289

Order 19197.

100 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20264238	C₃	1	1	yes	maximal, characteristic, complemented
2	#20264237	C₃	1	1	yes	maximal, characteristic, complemented
3	(C₇₉⋊C₉)⋊C₉	C₃	1	2	yes	maximal, complemented
4	(C₇₉⋊C₉)⋊C₉	C₃	1	2	yes	maximal, complemented
5	(C₇₉⋊C₉)⋊C₉	C₃	1	2	yes	maximal, complemented
6	C₃²⋊(C₇₉⋊C₉)	C₃	1	2	yes	maximal
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	C₃×C₇₉⋊C₉	C₃²	1	2	yes	—
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	C₃³×C₇₉	C₃²	1	1	yes	characteristic
16	C₃×C₉×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	C₃²×C₇₉	—	3	1	no	—
20	C₃²×C₇₉	—	3	1	no	—
21	C₃²×C₇₉	—	3	2	no	—
22	C₃²×C₇₉	C₃³	1	1	yes	characteristic
23	C₉×C₇₉	—	3	1	no	—
24	C₉×C₇₉	—	3	1	no	—
25	C₉×C₇₉	—	3	1	no	—
26	C₇₉⋊C₉	—	3	1	no	—
27	C₇₉⋊C₉	—	3	2	no	—
28	C₇₉⋊C₉	—	3	2	no	—
29	C₇₉⋊C₉	—	3	2	no	—
30	C₇₉⋊C₉	—	3	2	no	—
31	#6898	—	79	1	no	maximal, Sylow
32	C₃×C₇₉	—	9	1	no	—
33	C₃×C₇₉	#737	1	1	yes	characteristic
34	C₃×C₇₉	#737	1	1	yes	characteristic
35	C₃×C₇₉	#737	1	2	yes	—
36	C₉⋊C₉	—	79	2	no	—
37	C₉⋊C₉	—	79	2	no	—
38	C₉⋊C₉	—	79	2	no	—
39	C₉⋊C₉	—	79	1	no	—
40	C₉⋊C₉	—	79	1	no	—
41	C₃²⋊C₉	—	79	1	no	—
42	C₃²⋊C₉	—	79	2	no	—
43	C₃²⋊C₉	C₇₉⋊C₃	1	1	yes	characteristic
44	C₉²	—	79	1	no	—
45	C₇₉	#6898	1	1	yes	characteristic, complemented, Sylow
46	C₃³	C₃×C₇₉⋊C₃	1	1	yes	characteristic
47	C₃×C₉	—	79	1	no	—
48	C₃×C₉	—	79	2	no	—
49	C₃×C₉	—	79	2	no	—
50	C₃×C₉	—	79	2	no	—
51	C₃×C₉	—	79	2	no	—
52	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
53	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
54	C₃×C₉	C₃×C₇₉⋊C₃	1	1	yes	characteristic
55	C₃²	—	3	1	no	—
56	C₃²	—	3	1	no	—
57	C₃²	—	3	2	no	—
58	C₃²	C₃²×C₇₉⋊C₃	1	1	yes	characteristic
59	C₉	—	3	1	no	—
60	C₉	—	3	1	no	—
61	C₉	—	3	1	no	—
62	C₉	—	237	1	no	—
63	C₉	—	237	2	no	—
64	C₉	—	237	2	no	—
65	C₉	—	237	2	no	—
66	C₉	—	237	2	no	—
67	C₃	—	9	1	no	—
68	C₃	#20264262	1	1	yes	characteristic
69	C₃	#20264263	1	1	yes	characteristic
70	C₃	#20264264	1	2	yes	—

	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	#6898
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
1. #20264238	C₃	semidirect
2. #20264237	C₃	semidirect
3. (C₇₉⋊C₉)⋊C₉	C₃	semidirect
4. (C₇₉⋊C₉)⋊C₉	C₃	semidirect
5. (C₇₉⋊C₉)⋊C₉	C₃	semidirect
8. C₉×C₇₉⋊C₉	C₃	semidirect
45. C₇₉	#6898	semidirect

Maximal subgroups

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

subgroup	index
#20264238	3
#20264237	3
(C₇₉⋊C₉)⋊C₉	3
C₃²⋊(C₇₉⋊C₉)	3
C₉×C₇₉⋊C₉	3
C₇₉×C₃²⋊C₉	3
#6898	79