Subgroups — #28356851

Order 13851.

512 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₃²⋊#4296	C₃	1	3	yes	maximal
2	(C₃×#4296)⋊C₉	C₃	1	9	yes	maximal, complemented
3	C₃²×C₉×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
4	C₃²×#4296	C₃²	1	9	yes	—
5	C₃²⋊#4296	—	3	9	no	—
6	C₃³×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
7	C₃²×#4294	C₉	1	2	yes	complemented
8	C₃×C₉×C₁₉⋊C₃	—	3	3	no	—
9	C₃×C₉×C₁₉⋊C₃	—	3	6	no	—
10	C₃×C₉×C₁₉⋊C₃	C₉	1	6	yes	complemented
11	C₃×C₉×C₁₉⋊C₃	C₃²	1	3	yes	—
12	C₃²×C₉×C₁₉	C₉	1	1	yes	characteristic, complemented
13	#10624549	—	19	1	no	maximal, Sylow
14	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
15	C₃²×C₁₉⋊C₃	—	3	9	no	—
16	C₃²×C₁₉⋊C₃	C₃×C₉	1	2	yes	—
17	C₃²×C₁₉⋊C₃	H(3,𝔽₃)	1	3	yes	—
18	C₃²×C₁₉⋊C₃	3₋¹⁺²	1	6	yes	—
19	C₃²×C₁₉⋊C₃	C₃³	1	1	yes	characteristic
20	C₃×#4296	—	3	9	no	—
21	C₃×#4296	—	3	27	no	—
22	C₃×C₉×C₁₉	—	3	3	no	—
23	C₃×C₉×C₁₉	C₃×C₉	1	3	yes	—
24	C₃×#4294	—	3	6	no	—
25	C₃×#4294	C₃×C₉	1	6	yes	—
26	C₉×C₁₉⋊C₃	—	3	18	no	—
27	C₉×C₁₉⋊C₃	—	3	3	no	—
28	C₉×C₁₉⋊C₃	—	3	6	no	—
29	C₃³×C₉	—	19	1	no	—
30	C₃×C₃²⋊C₉	—	19	3	no	—
31	#6855	—	19	9	no	—
32	C₃²×C₁₉	—	3	3	no	—
33	C₃²×C₁₉	C₃²⋊C₉	1	3	yes	—
34	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
35	C₃×C₁₉⋊C₃	—	3	6	no	—
36	C₃×C₁₉⋊C₃	—	3	9	no	—
37	C₃×C₁₉⋊C₃	—	3	18	no	—
38	C₃×C₁₉⋊C₃	C₃²⋊C₉	1	6	yes	—
39	C₃×C₁₉⋊C₃	C₃×H(3,𝔽₃)	1	1	yes	characteristic
40	C₃×C₁₉⋊C₃	C₃×3₋¹⁺²	1	2	yes	—
41	C₃×C₁₉⋊C₃	#737	1	9	yes	—
42	#4296	—	9	9	no	—
43	C₉×C₁₉	—	3	3	no	—
44	#4294	—	3	6	no	—
45	C₃⁴	—	19	1	no	—
46	C₃²×C₉	—	19	2	no	—
47	C₃²×C₉	—	19	6	no	—
48	C₃²×C₉	—	19	3	no	—
49	C₃²×C₉	—	19	9	no	—
50	C₃²×C₉	—	57	3	no	—
51	C₃²×C₉	—	57	6	no	—
52	C₃²×C₉	#4296	1	1	yes	characteristic, complemented
53	C₃²⋊C₉	—	57	9	no	—
54	C₃×C₁₉	—	3	3	no	—
55	C₃×C₁₉	C₃×C₃²⋊C₉	1	1	yes	characteristic
56	C₃×C₁₉	#6887	1	3	yes	—
57	C₁₉⋊C₃	—	3	6	no	—
58	C₁₉⋊C₃	#6893	1	3	yes	—
59	C₁₉⋊C₃	#6895	1	6	yes	—
60	C₃³	—	19	1	no	—
61	C₃³	—	19	3	no	—
62	C₃³	—	19	6	no	—
63	C₃³	—	19	2	no	—
64	C₃³	—	57	9	no	—
65	C₃³	C₃×#4296	1	1	yes	characteristic
66	C₃×C₉	—	3	3	no	—
67	C₃×C₉	—	19	6	no	—
68	C₃×C₉	—	57	3	no	—
69	C₃×C₉	—	57	6	no	—
70	C₃×C₉	—	57	18	no	—
71	C₃×C₉	—	57	6	no	—
72	C₃×C₉	—	57	9	no	—
73	C₃×C₉	—	57	27	no	—
74	C₃×C₉	C₃×#4296	1	3	yes	—
75	C₁₉	#10624549	1	1	yes	characteristic, complemented, Sylow
76	C₃²	—	3	3	no	—
77	C₃²	—	19	1	no	—
78	C₃²	—	19	2	no	—
79	C₃²	—	19	9	no	—
80	C₃²	—	19	6	no	—
81	C₃²	—	57	9	no	—
82	C₃²	—	57	18	no	—
83	C₃²	—	57	6	no	—
84	C₃²	C₃²⋊#4296	1	3	yes	—
85	C₃²	C₃²×#4296	1	1	yes	characteristic
86	C₉	—	3	3	no	—
87	C₉	—	57	6	no	—
88	C₉	—	171	9	no	—
89	C₃	—	3	3	no	—
90	C₃	—	19	3	no	—
91	C₃	—	19	6	no	—
92	C₃	—	57	6	no	—
93	C₃	C₃×C₃²⋊#4296	1	1	yes	characteristic
94	C₃	#17987589	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×#4296
commutator, socle	C₃²×C₁₉	C₃²×C₉
Fitting	C₃²×C₉×C₁₉	C₉
prime radical	C₃³×C₁₉⋊C₃	C₃²
cosocle	C₃²×C₁₉⋊C₃	C₃³
hypercenter	C₃²×C₉	#4296
hypocenter	C₁₉	#10624549
LCS	G ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃²×C₉

Complements

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

N	H ≅ G/N	type
2. (C₃×#4296)⋊C₉	C₃	semidirect
7. C₃²×#4294	C₉	semidirect
10. C₃×C₉×C₁₉⋊C₃	C₉	semidirect
12. C₃²×C₉×C₁₉	C₉	semidirect
52. C₃²×C₉	#4296	semidirect
75. C₁₉	#10624549	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₃²⋊#4296	3
(C₃×#4296)⋊C₉	3
C₃²×C₉×C₁₉⋊C₃	3
#10624549	19