Subgroups — #28356777

Order 13851.

232 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#17987561	C₃	1	3	yes	maximal, complemented
2	C₃²×#10587025	C₃	1	1	yes	maximal, characteristic
3	#13095342	—	3	3	no	—
4	C₃×#10587025	—	3	9	no	—
5	C₃×#10587025	—	3	1	no	—
6	C₃×#10587025	—	3	2	no	—
7	C₃²×#4294	C₉	1	2	yes	—
8	C₃²×#4294	C₃²	1	1	yes	characteristic
9	C₃⁴×C₁₉	C₉	1	1	yes	characteristic
10	#10624507	—	19	1	no	maximal, Sylow
11	C₃³×C₁₉	—	3	3	no	—
12	C₃³×C₁₉	—	3	1	no	—
13	C₃³×C₁₉	—	9	3	no	—
14	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
15	#10587025	—	3	18	no	—
16	#10587025	—	3	9	no	—
17	C₃×#4294	—	3	2	no	—
18	C₃×#4294	—	3	3	no	—
19	C₃×#4294	—	3	6	no	—
20	C₃×#4294	H(3,𝔽₃)	1	1	yes	characteristic
21	C₃×#4294	3₋¹⁺²	1	2	yes	—
22	#10587020	—	9	3	no	—
23	C₃²×3₋¹⁺²	—	19	1	no	—
24	#6869	—	19	3	no	—
25	C₃²×C₁₉	—	3	3	no	—
26	C₃²×C₁₉	—	3	1	no	—
27	C₃²×C₁₉	—	3	3	no	—
28	C₃²×C₁₉	—	9	9	no	—
29	C₃²×C₁₉	—	9	3	no	—
30	C₃²×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
31	#4294	—	3	2	no	—
32	#4294	—	3	6	no	—
33	#4294	AΣL(1,𝔽₂₇)	1	3	yes	—
34	C₃⁴	#4296	1	1	yes	characteristic
35	C₃×3₋¹⁺²	—	57	1	no	—
36	C₃×3₋¹⁺²	—	57	2	no	—
37	C₃×3₋¹⁺²	—	57	9	no	—
38	C₃²×C₉	—	19	1	no	—
39	C₃²×C₉	—	19	2	no	—
40	C₂₇⋊C₃	—	57	3	no	—
41	C₃×C₁₉	—	3	3	no	—
42	C₃×C₁₉	—	3	1	no	—
43	C₃×C₁₉	—	9	3	no	—
44	C₃×C₁₉	#6866	1	1	yes	characteristic
45	C₃³	—	3	3	no	—
46	C₃³	—	3	1	no	—
47	C₃³	—	9	3	no	—
48	C₃³	C₃×#4296	1	1	yes	characteristic
49	3₋¹⁺²	—	57	9	no	—
50	3₋¹⁺²	—	57	18	no	—
51	C₃×C₉	—	19	1	no	—
52	C₃×C₉	—	19	2	no	—
53	C₃×C₉	—	57	3	no	—
54	C₃×C₉	—	57	2	no	—
55	C₃×C₉	—	57	6	no	—
56	C₂₇	—	171	3	no	—
57	C₁₉	#10624507	1	1	yes	characteristic, complemented, Sylow
58	C₃²	—	3	3	no	—
59	C₃²	—	3	1	no	—
60	C₃²	—	3	3	no	—
61	C₃²	—	9	9	no	—
62	C₃²	—	9	3	no	—
63	C₃²	C₃²⋊#4296	1	1	yes	characteristic
64	C₉	—	19	3	no	—
65	C₉	—	57	2	no	—
66	C₉	—	57	6	no	—
67	C₃	—	3	1	no	—
68	C₃	—	3	3	no	—
69	C₃	—	9	3	no	—
70	C₃	#17987558	1	1	yes	characteristic

	subgroup	G/H
center	C₃	#17987558
commutator	C₃³×C₁₉	C₃×C₉
Frattini	C₃³	C₃×#4296
Fitting, prime radical	C₃⁴×C₁₉	C₉
socle	C₃×C₁₉	#6866
cosocle	C₃²×#4294	C₃²
hypercenter	C₃⁴	#4296
hypocenter	C₁₉	#10624507
LCS	G ▷ C₃³×C₁₉ ▷ C₃²×C₁₉ ▷ C₃×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃ ◁ C₃² ◁ C₃³ ◁ C₃⁴

Complements

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

N	H ≅ G/N	type
1. #17987561	C₃	semidirect
57. C₁₉	#10624507	semidirect

Maximal subgroups

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

subgroup	index
#17987561	3
C₃²×#10587025	3
#10624507	19