Subgroups — #28356690

Order 13851.

132 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#13095342	C₃	1	1	yes	maximal, characteristic, complemented
2	C₃²⋊#10587020	C₃	1	2	yes	maximal, complemented
3	H(3,𝔽₃)×#4294	C₃	1	1	yes	maximal, characteristic
4	#13095342	—	3	3	no	—
5	C₃×#10587020	—	3	1	no	—
6	C₃×#10587020	—	3	2	no	—
7	C₃²×#4294	—	3	1	no	—
8	C₃²×#4294	C₃²	1	1	yes	characteristic
9	C₃²⋊#4294	—	3	2	no	—
10	C₃²⋊#4294	C₉	1	2	yes	—
11	C₃×C₁₉×H(3,𝔽₃)	C₉	1	1	yes	characteristic
12	#10624453	—	19	1	no	maximal, Sylow
13	C₃³×C₁₉	—	3	1	no	—
14	C₃³×C₁₉	C₃×C₉	1	1	yes	characteristic
15	C₁₉×H(3,𝔽₃)	—	3	3	no	—
16	C₃×#4294	—	3	1	no	—
17	C₃×#4294	—	3	1	no	—
18	C₃×#4294	—	3	1	no	—
19	C₃×#4294	—	3	2	no	—
20	C₃×#4294	—	9	1	no	—
21	C₃×#4294	—	9	1	no	—
22	C₃×#4294	—	9	1	no	—
23	C₃×#4294	H(3,𝔽₃)	1	1	yes	characteristic
24	C₃×#4294	3₋¹⁺²	1	2	yes	—
25	#10587020	—	3	3	no	—
26	#10587020	—	9	2	no	—
27	C₃×C₂₇⋊C₃	—	19	1	no	—
28	C₉×H(3,𝔽₃)	—	19	1	no	—
29	C₃²⋊C₂₇	—	19	2	no	—
30	C₃²×C₁₉	—	3	1	no	—
31	C₃²×C₁₉	—	3	3	no	—
32	C₃²×C₁₉	—	3	1	no	—
33	C₃²×C₁₉	—	3	1	no	—
34	C₃²×C₁₉	—	3	1	no	—
35	C₃²×C₁₉	—	9	1	no	—
36	C₃²×C₁₉	—	9	1	no	—
37	C₃²×C₁₉	—	9	1	no	—
38	C₃²×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
39	#4294	—	3	2	no	—
40	#4294	—	9	2	no	—
41	#4294	AΣL(1,𝔽₂₇)	1	1	yes	characteristic
42	#4294	#731	1	1	yes	characteristic
43	#4294	#732	1	1	yes	characteristic
44	C₃×H(3,𝔽₃)	#4296	1	1	yes	characteristic
45	C₃²×C₉	—	19	1	no	—
46	C₃²×C₉	—	57	1	no	—
47	C₂₇⋊C₃	—	57	3	no	—
48	C₃×C₂₇	—	57	1	no	—
49	C₃×C₂₇	—	57	2	no	—
50	C₃²⋊C₉	—	19	2	no	—
51	C₃²⋊C₉	—	57	2	no	—
52	C₃×C₁₉	—	9	1	no	—
53	C₃×C₁₉	—	9	3	no	—
54	C₃×C₁₉	#6869	1	1	yes	characteristic
55	C₃×C₁₉	H(3,𝔽₃)⋊C₉	1	1	yes	characteristic
56	C₃×C₁₉	#6872	1	1	yes	characteristic
57	C₃×C₁₉	#6873	1	1	yes	characteristic
58	C₃³	—	3	1	no	—
59	C₃³	C₃×#4296	1	1	yes	characteristic
60	H(3,𝔽₃)	—	3	3	no	—
61	C₃×C₉	—	19	1	no	—
62	C₃×C₉	—	19	2	no	—
63	C₃×C₉	—	57	1	no	—
64	C₃×C₉	—	57	1	no	—
65	C₃×C₉	—	57	1	no	—
66	C₃×C₉	—	57	2	no	—
67	C₃×C₉	—	171	1	no	—
68	C₃×C₉	—	171	1	no	—
69	C₃×C₉	—	171	1	no	—
70	C₂₇	—	57	3	no	—
71	C₂₇	—	171	2	no	—
72	C₁₉	#10624453	1	1	yes	characteristic, complemented, Sylow
73	C₃²	—	3	1	no	—
74	C₃²	—	3	3	no	—
75	C₃²	—	3	1	no	—
76	C₃²	—	3	1	no	—
77	C₃²	—	3	1	no	—
78	C₃²	—	9	1	no	—
79	C₃²	—	9	1	no	—
80	C₃²	—	9	1	no	—
81	C₃²	C₃²⋊#4296	1	1	yes	characteristic
82	C₉	—	19	1	no	—
83	C₉	—	19	1	no	—
84	C₉	—	19	1	no	—
85	C₉	—	57	2	no	—
86	C₉	—	171	2	no	—
87	C₃	—	9	1	no	—
88	C₃	—	9	3	no	—
89	C₃	#17987561	1	1	yes	characteristic
90	C₃	H(3,𝔽₃)⋊#4296	1	1	yes	characteristic
91	C₃	#17987566	1	1	yes	characteristic
92	C₃	#17987568	1	1	yes	characteristic

	subgroup	G/H
center	C₃²	C₃²⋊#4296
commutator	C₃³×C₁₉	C₃×C₉
Frattini	C₃³	C₃×#4296
Fitting, prime radical	C₃×C₁₉×H(3,𝔽₃)	C₉
socle	C₃²×C₁₉	C₃²⋊C₉
cosocle	C₃²×#4294	C₃²
hypercenter	C₃×H(3,𝔽₃)	#4296
hypocenter	C₁₉	#10624453
LCS	G ▷ C₃³×C₁₉ ▷ C₃²×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₃² ◁ C₃³ ◁ C₃×H(3,𝔽₃)

Complements

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

N	H ≅ G/N	type
1. C₃×#13095342	C₃	semidirect
2. C₃²⋊#10587020	C₃	semidirect
72. C₁₉	#10624453	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
H(3,𝔽₃)×#4294	3
#10624453	19