Subgroups — #28356881

Order 13851.

290 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095342	C₃	1	2	yes	maximal
2	C₃²×#10587020	C₃	1	1	yes	maximal, characteristic
3	#17987555	C₃	1	6	yes	maximal, complemented
4	C₉×#10587020	C₃	1	3	yes	maximal, complemented
5	#17987402	C₃	1	1	yes	maximal, characteristic
6	#13095342	C₉	1	18	yes	complemented
7	C₃×#10587020	C₉	1	9	yes	complemented
8	C₃×#10587020	C₃²	1	1	yes	characteristic
9	C₃×#10587020	C₃²	1	2	yes	—
10	C₃×#10587020	C₃²	1	6	yes	—
11	C₃²×#4294	C₃²	1	1	yes	characteristic
12	#13095305	C₉	1	6	yes	—
13	C₃²⋊#4294	C₉	1	2	yes	—
14	C₉×#4294	C₃²	1	3	yes	—
15	C₁₉×C₃²⋊C₉	C₉	1	1	yes	characteristic
16	#10624681	—	19	1	no	maximal, Sylow
17	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
18	C₃×C₉×C₁₉	C₃×C₉	1	3	yes	—
19	C₃×#4294	C₃×C₉	1	6	yes	—
20	C₃×#4294	C₃×C₉	1	2	yes	—
21	C₃×#4294	C₃×C₉	1	3	yes	—
22	C₃×#4294	C₃×C₉	1	6	yes	—
23	C₃×#4294	C₃³	1	1	yes	characteristic
24	#10587020	C₃×C₉	1	3	yes	—
25	#10587020	C₃×C₉	1	6	yes	—
26	#10587020	C₃×C₉	1	18	yes	—
27	C₃×C₂₇⋊C₃	—	19	2	no	—
28	C₃²×C₂₇	—	19	1	no	—
29	#6887	—	19	1	no	—
30	#6864	—	19	6	no	—
31	C₉×C₂₇	—	19	3	no	—
32	C₃²×C₁₉	—	3	1	no	—
33	C₃²×C₁₉	—	3	2	no	—
34	C₃²×C₁₉	C₉²	1	3	yes	—
35	C₃²×C₁₉	C₃²×C₉	1	1	yes	characteristic
36	C₉×C₁₉	—	3	3	no	—
37	#4294	—	3	6	no	—
38	#4294	C₉²	1	6	yes	—
39	#4294	C₃²×C₉	1	1	yes	characteristic
40	#4294	C₃²×C₉	1	2	yes	—
41	C₃²×C₉	—	19	1	no	—
42	C₂₇⋊C₃	—	19	18	no	—
43	C₃×C₂₇	—	19	9	no	—
44	C₃×C₂₇	—	19	1	no	—
45	C₃×C₂₇	—	19	6	no	—
46	C₃×C₂₇	—	19	2	no	—
47	C₉⋊C₉	—	19	6	no	—
48	C₃²⋊C₉	—	19	2	no	—
49	C₃²⋊C₉	#4296	1	1	yes	characteristic
50	C₉²	—	19	3	no	—
51	C₃×C₁₉	—	3	3	no	—
52	C₃×C₁₉	C₃×C₉²	1	1	yes	characteristic
53	C₃×C₁₉	#6903	1	1	yes	characteristic
54	C₃×C₁₉	#6903	1	2	yes	—
55	C₃³	C₃×#4296	1	1	yes	characteristic
56	C₃×C₉	—	19	3	no	—
57	C₃×C₉	—	19	6	no	—
58	C₃×C₉	—	19	2	no	—
59	C₃×C₉	—	19	1	no	—
60	C₃×C₉	—	19	6	no	—
61	C₃×C₉	C₃×#4296	1	3	yes	—
62	C₂₇	—	19	3	no	—
63	C₂₇	—	19	6	no	—
64	C₂₇	—	19	18	no	—
65	C₁₉	#10624681	1	1	yes	characteristic, complemented, Sylow
66	C₃²	—	3	1	no	—
67	C₃²	—	3	2	no	—
68	C₃²	C₉×#4296	1	3	yes	—
69	C₃²	C₃²×#4296	1	1	yes	characteristic
70	C₉	—	3	3	no	—
71	C₉	—	19	1	no	—
72	C₉	—	19	2	no	—
73	C₉	—	19	6	no	—
74	C₉	—	57	6	no	—
75	C₃	—	3	3	no	—
76	C₃	C₃×C₉×#4296	1	1	yes	characteristic
77	C₃	#17987598	1	1	yes	characteristic
78	C₃	#17987599	1	2	yes	—

	subgroup	G/H
center, Frattini	C₃²	C₃²×#4296
commutator	C₃×C₁₉	C₃×C₉²
Fitting	C₁₉×C₃²⋊C₉	C₉
socle	C₃²×C₁₉	C₃²×C₉
prime radical	C₃³×C₁₉	C₃×C₉
cosocle	C₃×#4294	C₃³
hypercenter	C₃²⋊C₉	#4296
hypocenter	C₁₉	#10624681
LCS	G ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃²⋊C₉

Complements

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

N	H ≅ G/N	type
3. #17987555	C₃	semidirect
4. C₉×#10587020	C₃	semidirect
6. #13095342	C₉	semidirect
7. C₃×#10587020	C₉	semidirect
65. C₁₉	#10624681	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
C₃²×#10587020	3
#17987555	3
C₉×#10587020	3
#17987402	3
#10624681	19