Subgroups — #28356720

Order 13851.

156 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	(C₁₉⋊C₃)⋊(C₂₇⋊C₃)	C₃	1	3	yes	maximal
2	#17987403	C₃	1	1	yes	maximal, characteristic
3	#13095344	—	3	3	no	—
4	#13095343	—	3	3	no	—
5	#13095342	—	3	3	no	—
6	(C₁₉⋊C₃)⋊C₂₇	C₉	1	9	yes	complemented
7	C₃×C₉×C₁₉⋊C₃	C₃²	1	1	yes	characteristic
8	#13095305	—	3	1	no	—
9	#13095305	—	3	1	no	—
10	#13095303	—	3	1	no	—
11	C₉×#4294	C₉	1	2	yes	—
12	C₉²×C₁₉	C₉	1	1	yes	characteristic
13	#10624465	—	19	1	no	maximal, Sylow
14	C₃²×C₁₉⋊C₃	3₋¹⁺²	1	1	yes	characteristic
15	C₃×C₉×C₁₉	—	3	1	no	—
16	C₃×C₉×C₁₉	C₃×C₉	1	1	yes	characteristic
17	C₃×#4294	—	3	2	no	—
18	C₃×#4294	H(3,𝔽₃)	1	1	yes	characteristic
19	C₃×#4294	3₋¹⁺²	1	1	yes	characteristic
20	C₉×C₁₉⋊C₃	C₃×C₉	1	3	yes	—
21	C₉×C₁₉⋊C₃	3₋¹⁺²	1	3	yes	—
22	C₉×C₁₉⋊C₃	3₋¹⁺²	1	3	yes	—
23	#10587020	—	3	9	no	—
24	C₃×C₂₇⋊C₃	—	19	3	no	—
25	#6887	—	19	1	no	—
26	C₃²×C₁₉	C₃²⋊C₉	1	1	yes	characteristic
27	C₃×C₁₉⋊C₃	—	9	1	no	—
28	C₃×C₁₉⋊C₃	C₉⋊C₉	1	3	yes	—
29	C₉×C₁₉	—	9	1	no	—
30	C₉×C₁₉	C₉²	1	1	yes	characteristic
31	C₉×C₁₉	C₉⋊C₉	1	1	yes	characteristic
32	C₉×C₁₉	C₉⋊C₉	1	1	yes	characteristic
33	#4294	—	9	2	no	—
34	#4294	C₃²⋊C₉	1	3	yes	—
35	#4294	C₉⋊C₉	1	3	yes	—
36	C₃²×C₉	—	19	1	no	—
37	C₂₇⋊C₃	—	57	3	no	—
38	C₂₇⋊C₃	—	57	3	no	—
39	C₂₇⋊C₃	—	57	3	no	—
40	C₃×C₂₇	—	19	9	no	—
41	C₉⋊C₉	—	57	1	no	—
42	C₉⋊C₉	—	57	1	no	—
43	C₃²⋊C₉	—	57	1	no	—
44	C₉²	—	19	2	no	—
45	C₉²	#4296	1	1	yes	characteristic
46	C₃×C₁₉	—	3	1	no	—
47	C₃×C₁₉	#6855	1	1	yes	characteristic
48	C₁₉⋊C₃	—	3	3	no	—
49	C₃³	—	19	1	no	—
50	C₃×C₉	—	3	1	no	—
51	C₃×C₉	—	19	1	no	—
52	C₃×C₉	—	19	1	no	—
53	C₃×C₉	—	19	3	no	—
54	C₃×C₉	—	19	3	no	—
55	C₃×C₉	—	19	3	no	—
56	C₃×C₉	—	57	2	no	—
57	C₃×C₉	C₃×#4296	1	1	yes	characteristic
58	C₂₇	—	57	9	no	—
59	C₁₉	#10624465	1	1	yes	characteristic, complemented, Sylow
60	C₃²	—	19	3	no	—
61	C₃²	—	171	1	no	—
62	C₃²	C₃²⋊#4296	1	1	yes	characteristic
63	C₉	—	9	1	no	—
64	C₉	—	19	3	no	—
65	C₉	—	19	3	no	—
66	C₉	—	171	2	no	—
67	C₉	C₉×#4296	1	1	yes	characteristic
68	C₉	#13095338	1	1	yes	characteristic
69	C₉	#13095339	1	1	yes	characteristic
70	C₃	—	3	1	no	—
71	C₃	—	57	3	no	—
72	C₃	(C₃×#4296)⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center	C₉	C₉×#4296
commutator	C₉×C₁₉	C₉²
Frattini	C₃×C₉	C₃×#4296
Fitting	C₉²×C₁₉	C₉
socle	C₃×C₁₉	#6855
prime radical	C₃²×C₁₉⋊C₃	3₋¹⁺²
cosocle	C₃×C₉×C₁₉⋊C₃	C₃²
hypercenter	C₉²	#4296
hypocenter	C₁₉	#10624465
LCS	G ▷ C₉×C₁₉ ▷ C₁₉
UCS	C₁ ◁ C₉ ◁ C₉²

Complements

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

N	H ≅ G/N	type
6. (C₁₉⋊C₃)⋊C₂₇	C₉	semidirect
59. C₁₉	#10624465	semidirect

Maximal subgroups

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

subgroup	index
(C₁₉⋊C₃)⋊(C₂₇⋊C₃)	3
#17987403	3
#10624465	19