Subgroups — #28356702

Order 13851.

94 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²⋊#10587020	C₃	1	3	yes	maximal
2	#17987402	C₃	1	1	yes	maximal, characteristic
3	C₃×#10587020	—	3	3	no	—
4	C₃²×#4294	C₃²	1	1	yes	characteristic
5	#13095305	—	3	2	no	—
6	C₃²⋊#4294	C₉	1	2	yes	—
7	C₉×#4294	—	3	1	no	—
8	C₁₉×C₃²⋊C₉	C₉	1	1	yes	characteristic
9	#10624458	—	19	1	no	maximal, Sylow
10	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
11	C₃×C₉×C₁₉	—	3	1	no	—
12	C₃×#4294	—	3	1	no	—
13	C₃×#4294	—	3	2	no	—
14	C₃×#4294	—	3	2	no	—
15	C₃×#4294	H(3,𝔽₃)	1	1	yes	characteristic
16	C₃×#4294	3₋¹⁺²	1	2	yes	—
17	#10587020	—	9	3	no	—
18	#6887	—	19	1	no	—
19	C₃²⋊C₂₇	—	19	3	no	—
20	C₃²×C₁₉	—	3	1	no	—
21	C₃²×C₁₉	—	3	1	no	—
22	C₃²×C₁₉	—	3	2	no	—
23	C₃²×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
24	C₉×C₁₉	—	9	1	no	—
25	#4294	—	3	2	no	—
26	#4294	—	9	2	no	—
27	#4294	#732	1	1	yes	characteristic
28	#4294	#733	1	2	yes	—
29	C₃²×C₉	—	19	1	no	—
30	C₃×C₂₇	—	57	3	no	—
31	C₉⋊C₉	—	57	2	no	—
32	C₃²⋊C₉	—	19	2	no	—
33	C₃²⋊C₉	#4296	1	1	yes	characteristic
34	C₉²	—	57	1	no	—
35	C₃×C₁₉	—	9	1	no	—
36	C₃×C₁₉	#6868	1	1	yes	characteristic
37	C₃×C₁₉	#6872	1	1	yes	characteristic
38	C₃×C₁₉	#6872	1	2	yes	—
39	C₃³	C₃×#4296	1	1	yes	characteristic
40	C₃×C₉	—	3	1	no	—
41	C₃×C₉	—	19	1	no	—
42	C₃×C₉	—	19	2	no	—
43	C₃×C₉	—	57	1	no	—
44	C₃×C₉	—	57	2	no	—
45	C₃×C₉	—	57	2	no	—
46	C₂₇	—	171	3	no	—
47	C₁₉	#10624458	1	1	yes	characteristic, complemented, Sylow
48	C₃²	—	3	1	no	—
49	C₃²	—	3	1	no	—
50	C₃²	—	3	2	no	—
51	C₃²	C₃²⋊#4296	1	1	yes	characteristic
52	C₉	—	9	1	no	—
53	C₉	—	19	1	no	—
54	C₉	—	19	2	no	—
55	C₉	—	57	2	no	—
56	C₉	—	171	2	no	—
57	C₃	—	9	1	no	—
58	C₃	#17987560	1	1	yes	characteristic
59	C₃	#17987566	1	1	yes	characteristic
60	C₃	#17987567	1	2	yes	—

	subgroup	G/H
center	C₃²	C₃²⋊#4296
commutator, prime radical	C₃³×C₁₉	C₃×C₉
Frattini	C₃³	C₃×#4296
Fitting	C₁₉×C₃²⋊C₉	C₉
socle	C₃²×C₁₉	C₃²⋊C₉
cosocle	C₃²×#4294	C₃²
hypercenter	C₃²⋊C₉	#4296
hypocenter	C₁₉	#10624458
LCS	G ▷ C₃³×C₁₉ ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃²⋊C₉

Complements

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

N	H ≅ G/N	type
47. C₁₉	#10624458	semidirect

Maximal subgroups

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

subgroup	index
C₃²⋊#10587020	3
#17987402	3
#10624458	19