Subgroups — #28356890

Order 13851.

428 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095342	C₃	1	3	yes	maximal, complemented
2	#17987557	C₃	1	9	yes	maximal, complemented
3	C₃²×C₉×C₁₉⋊C₃	C₃	1	1	yes	maximal, characteristic
4	#13095342	—	3	9	no	—
5	C₃×#10587020	C₃²	1	9	yes	complemented
6	C₃³×C₁₉⋊C₃	C₉	1	1	yes	characteristic
7	C₃²×#4294	C₉	1	1	yes	characteristic
8	C₃²×#4294	C₃²	1	1	yes	characteristic
9	C₃×C₉×C₁₉⋊C₃	—	3	3	no	—
10	C₃×C₉×C₁₉⋊C₃	—	3	6	no	—
11	C₃×C₉×C₁₉⋊C₃	C₉	1	6	yes	—
12	C₃×C₉×C₁₉⋊C₃	C₃²	1	3	yes	—
13	C₃²×C₉×C₁₉	C₉	1	1	yes	characteristic
14	#10624683	—	19	1	no	maximal, Sylow
15	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
16	C₃²×C₁₉⋊C₃	—	3	3	no	—
17	C₃²×C₁₉⋊C₃	—	3	9	no	—
18	C₃²×C₁₉⋊C₃	C₃×C₉	1	3	yes	—
19	C₃×C₉×C₁₉	—	3	3	no	—
20	C₃×C₉×C₁₉	C₃×C₉	1	3	yes	—
21	C₃×#4294	—	3	3	no	—
22	C₃×#4294	C₃×C₉	1	3	yes	—
23	C₃×#4294	C₃×C₉	1	2	yes	—
24	C₃×#4294	H(3,𝔽₃)	1	3	yes	—
25	C₃×#4294	3₋¹⁺²	1	6	yes	—
26	C₃×#4294	C₃³	1	1	yes	characteristic
27	C₉×C₁₉⋊C₃	—	3	18	no	—
28	C₉×C₁₉⋊C₃	—	3	3	no	—
29	C₉×C₁₉⋊C₃	—	3	6	no	—
30	#10587020	—	3	9	no	—
31	C₃³×C₉	—	19	1	no	—
32	C₃×C₂₇⋊C₃	—	19	3	no	—
33	C₃²⋊C₂₇	—	19	9	no	—
34	C₃²×C₁₉	—	3	3	no	—
35	C₃²×C₁₉	C₃²⋊C₉	1	3	yes	—
36	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
37	C₃×C₁₉⋊C₃	—	3	27	no	—
38	C₃×C₁₉⋊C₃	—	3	3	no	—
39	C₃×C₁₉⋊C₃	—	3	6	no	—
40	C₃×C₁₉⋊C₃	C₂₇⋊C₃	1	9	yes	complemented
41	C₉×C₁₉	—	3	3	no	—
42	#4294	—	3	3	no	—
43	#4294	C₃²⋊C₉	1	6	yes	—
44	#4294	C₃×H(3,𝔽₃)	1	1	yes	characteristic
45	#4294	C₃×3₋¹⁺²	1	2	yes	—
46	C₃⁴	—	19	1	no	—
47	C₃²×C₉	—	19	1	no	—
48	C₃²×C₉	—	19	1	no	—
49	C₃²×C₉	—	19	6	no	—
50	C₃²×C₉	—	19	3	no	—
51	C₃²×C₉	—	57	3	no	—
52	C₃²×C₉	—	57	6	no	—
53	C₃²×C₉	#4296	1	1	yes	characteristic
54	C₂₇⋊C₃	—	57	9	no	—
55	C₃×C₂₇	—	19	9	no	—
56	C₃×C₁₉	—	3	3	no	—
57	C₃×C₁₉	C₃×C₃²⋊C₉	1	1	yes	characteristic
58	C₃×C₁₉	C₃×C₂₇⋊C₃	1	3	yes	—
59	C₁₉⋊C₃	—	3	9	no	—
60	C₃³	—	19	3	no	—
61	C₃³	—	57	9	no	—
62	C₃³	—	57	3	no	—
63	C₃³	C₃×#4296	1	1	yes	characteristic
64	C₃×C₉	—	3	3	no	—
65	C₃×C₉	—	19	3	no	—
66	C₃×C₉	—	19	6	no	—
67	C₃×C₉	—	19	2	no	—
68	C₃×C₉	—	19	1	no	—
69	C₃×C₉	—	19	3	no	—
70	C₃×C₉	—	57	3	no	—
71	C₃×C₉	—	57	18	no	—
72	C₃×C₉	—	57	6	no	—
73	C₃×C₉	—	57	3	no	—
74	C₃×C₉	C₃×#4296	1	3	yes	—
75	C₂₇	—	57	9	no	—
76	C₁₉	#10624683	1	1	yes	characteristic, complemented, Sylow
77	C₃²	—	3	3	no	—
78	C₃²	—	19	9	no	—
79	C₃²	—	57	27	no	—
80	C₃²	—	57	3	no	—
81	C₃²	—	57	6	no	—
82	C₃²	C₃²⋊#4296	1	3	yes	—
83	C₃²	C₃²×#4296	1	1	yes	characteristic
84	C₉	—	3	3	no	—
85	C₉	—	19	1	no	—
86	C₉	—	19	6	no	—
87	C₉	—	19	2	no	—
88	C₉	—	57	3	no	—
89	C₃	—	3	3	no	—
90	C₃	—	57	9	no	—
91	C₃	C₃×C₃²⋊#4296	1	1	yes	characteristic
92	C₃	(C₁₉⋊C₃)⋊(C₂₇⋊C₃)	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	C₉
cosocle	C₃×#4294	C₃³
hypercenter	C₃²×C₉	#4296
hypocenter	C₁₉	#10624683
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
1. C₃×#13095342	C₃	semidirect
2. #17987557	C₃	semidirect
5. C₃×#10587020	C₃²	semidirect
40. C₃×C₁₉⋊C₃	C₂₇⋊C₃	semidirect
76. C₁₉	#10624683	semidirect

Maximal subgroups

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

subgroup	index
C₃×#13095342	3
#17987557	3
C₃²×C₉×C₁₉⋊C₃	3
#10624683	19