Subgroups — C₂₇×#11758608 #41006450

Order 26973.

220 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×#11758608	C₃	1	1	yes	maximal, characteristic
2	#22582488	C₃	1	6	yes	maximal, complemented
3	C₃²⋊#11758601	C₃	1	2	yes	maximal
4	C₂₇×#66524	C₃	1	3	yes	maximal, complemented
5	C₃²×C₂₇×C₃₇	C₃	1	1	yes	maximal, characteristic
6	C₃×#11758608	C₉	1	1	yes	characteristic
7	C₃×#11758601	C₃²	1	6	yes	—
8	#15688504	C₉	1	6	yes	—
9	C₃²⋊#66524	C₉	1	2	yes	—
10	C₉×#66524	C₃²	1	3	yes	—
11	C₃²×C₉×C₃₇	C₃²	1	1	yes	characteristic
12	C₃×C₂₇×C₃₇	—	3	3	no	—
13	C₃×C₂₇×C₃₇	C₃²	1	2	yes	—
14	C₃×C₂₇×C₃₇	C₃²	1	1	yes	characteristic
15	C₃³×C₃₇	C₃×C₉	1	1	yes	characteristic
16	C₃×C₉×C₃₇	—	3	1	no	—
17	C₃×C₉×C₃₇	—	3	2	no	—
18	C₃×C₉×C₃₇	C₃×C₉	1	2	yes	—
19	C₃×C₉×C₃₇	C₃³	1	1	yes	characteristic
20	#11758608	C₂₇	1	9	yes	direct product factor
21	C₃×#66524	C₃×C₉	1	6	yes	—
22	C₃×#66524	C₃×C₉	1	3	yes	—
23	C₂₇×C₃₇	—	3	2	no	—
24	C₂₇×C₃₇	3₋¹⁺²	1	3	yes	complemented
25	#11758601	—	3	6	no	—
26	C₂₇×3₋¹⁺²	—	37	1	no	maximal, Sylow
27	C₃²×C₃₇	—	3	1	no	—
28	C₃²×C₃₇	—	3	2	no	—
29	C₃²×C₃₇	C₃×C₂₇	1	3	yes	—
30	C₃²×C₃₇	C₃²×C₉	1	1	yes	characteristic
31	C₉×C₃₇	—	3	2	no	—
32	C₉×C₃₇	C₃×3₋¹⁺²	1	1	yes	characteristic
33	C₉×C₃₇	#737	1	2	yes	—
34	#66524	—	3	6	no	—
35	#66524	C₃×C₂₇	1	9	yes	complemented
36	C₃²×C₂₇	C₃₇⋊C₃	1	1	yes	characteristic
37	C₉×3₋¹⁺²	—	37	1	no	—
38	C₉⋊C₂₇	—	37	6	no	—
39	C₃²⋊C₂₇	—	37	2	no	—
40	C₉×C₂₇	—	37	3	no	—
41	C₃×C₃₇	—	3	3	no	—
42	C₃×C₃₇	C₉×3₋¹⁺²	1	1	yes	characteristic
43	C₃×C₃₇	C₃²×C₂₇	1	1	yes	characteristic
44	C₃×C₃₇	#6903	1	2	yes	—
45	C₃×3₋¹⁺²	—	37	1	no	—
46	C₃²×C₉	C₃×C₃₇⋊C₃	1	1	yes	characteristic
47	C₃×C₂₇	—	3	3	no	—
48	C₃×C₂₇	—	37	6	no	—
49	C₃×C₂₇	C₃×C₃₇⋊C₃	1	2	yes	—
50	C₃×C₂₇	C₃×C₃₇⋊C₃	1	1	yes	characteristic
51	C₉⋊C₉	—	37	6	no	—
52	C₃²⋊C₉	—	37	2	no	—
53	C₉²	—	37	3	no	—
54	C₃₇	C₂₇×3₋¹⁺²	1	1	yes	characteristic, complemented, Sylow
55	C₃³	C₉×C₃₇⋊C₃	1	1	yes	characteristic
56	3₋¹⁺²	—	37	9	no	—
57	C₃×C₉	—	3	1	no	—
58	C₃×C₉	—	3	2	no	—
59	C₃×C₉	—	37	3	no	—
60	C₃×C₉	—	37	6	no	—
61	C₃×C₉	C₉×C₃₇⋊C₃	1	2	yes	—
62	C₃×C₉	C₃²×C₃₇⋊C₃	1	1	yes	characteristic
63	C₂₇	—	3	2	no	—
64	C₂₇	—	111	6	no	—
65	C₂₇	#11758608	1	3	yes	direct product factor
66	C₃²	—	3	1	no	—
67	C₃²	—	3	2	no	—
68	C₃²	C₂₇×C₃₇⋊C₃	1	3	yes	—
69	C₃²	C₃×C₉×C₃₇⋊C₃	1	1	yes	characteristic
70	C₉	—	3	2	no	—
71	C₉	—	37	9	no	—
72	C₉	—	111	6	no	—
73	C₉	C₃×#11758608	1	1	yes	characteristic
74	C₉	#15688531	1	2	yes	—
75	C₃	—	3	3	no	—
76	C₃	C₉×#11758608	1	1	yes	characteristic
77	C₃	C₃×C₂₇×C₃₇⋊C₃	1	1	yes	characteristic
78	C₃	#22582612	1	2	yes	—

	subgroup	G/H
center	C₃×C₂₇	C₃×C₃₇⋊C₃
commutator	C₃×C₃₇	C₃²×C₂₇
Frattini	C₃×C₉	C₃²×C₃₇⋊C₃
Fitting	C₃²×C₂₇×C₃₇	C₃
socle	C₃²×C₃₇	C₃²×C₉
prime radical	C₃³×C₃₇	C₃×C₉
cosocle	C₃×C₉×C₃₇	C₃³
hypercenter	C₃²×C₂₇	C₃₇⋊C₃
hypocenter	C₃₇	C₂₇×3₋¹⁺²
LCS	G ▷ C₃×C₃₇ ▷ C₃₇
UCS	C₁ ◁ C₃×C₂₇ ◁ C₃²×C₂₇

Complements

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

N	H ≅ G/N	type
2. #22582488	C₃	semidirect
4. C₂₇×#66524	C₃	semidirect
20. #11758608	C₂₇	direct (N × H)
24. C₂₇×C₃₇	3₋¹⁺²	semidirect
35. #66524	C₃×C₂₇	semidirect
54. C₃₇	C₂₇×3₋¹⁺²	semidirect
65. C₂₇	#11758608	direct (N × H)

Maximal subgroups

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

subgroup	index
C₉×#11758608	3
#22582488	3
C₃²⋊#11758601	3
C₂₇×#66524	3
C₃²×C₂₇×C₃₇	3
C₂₇×3₋¹⁺²	37

Subgroups — C27×#11758608 #41006450

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₇×#11758608 #41006450