Subgroups — C₂₇⋊C₃×C₃₁⋊C₉ #36380948

Order 22599.

320 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#14578892	C₃	1	2	yes	maximal
2	C₃×C₉×C₃₁⋊C₉	C₃	1	1	yes	maximal, characteristic
3	#21419221	C₃	1	3	yes	maximal, complemented
4	#21419220	C₃	1	3	yes	maximal, complemented
5	C₂₇×C₃₁⋊C₉	C₃	1	3	yes	maximal, complemented
6	C₃×C₃₁×C₂₇⋊C₃	C₃	1	1	yes	maximal, characteristic
7	C₃²×C₃₁⋊C₉	C₉	1	3	yes	—
8	#14578892	C₉	1	18	yes	complemented
9	C₃×C₃₁⋊C₂₇	C₃²	1	6	yes	—
10	C₉×C₃₁⋊C₉	C₉	1	6	yes	—
11	C₉×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
12	C₉×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
13	C₉×C₃₁⋊C₉	C₃²	1	1	yes	characteristic
14	C₃²×C₉×C₃₁	C₃²	1	1	yes	characteristic
15	C₃₁×C₂₇⋊C₃	C₉	1	9	yes	complemented
16	C₃×C₂₇×C₃₁	C₃²	1	3	yes	—
17	C₃³×C₃₁	C₃×C₉	1	1	yes	characteristic
18	C₃×C₉×C₃₁	C₃×C₉	1	2	yes	—
19	C₃×C₉×C₃₁	C₃×C₉	1	6	yes	—
20	C₃×C₉×C₃₁	C₃×C₉	1	3	yes	—
21	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
22	C₃×C₃₁⋊C₉	—	3	9	no	—
23	C₃×C₃₁⋊C₉	C₃×C₉	1	3	yes	—
24	C₃×C₃₁⋊C₉	C₃×C₉	1	3	yes	—
25	C₃×C₃₁⋊C₉	C₃×C₉	1	3	yes	—
26	C₂₇×C₃₁	C₃×C₉	1	9	yes	complemented
27	C₃₁⋊C₂₇	C₃×C₉	1	18	yes	complemented
28	C₉×C₂₇⋊C₃	—	31	1	no	maximal, Sylow
29	C₃²×C₃₁	—	3	3	no	—
30	C₃²×C₃₁	C₉²	1	3	yes	—
31	C₃²×C₃₁	C₃²×C₉	1	1	yes	characteristic
32	C₉×C₃₁	C₉²	1	6	yes	—
33	C₉×C₃₁	C₃²×C₉	1	2	yes	—
34	C₉×C₃₁	C₃²×C₉	1	1	yes	characteristic
35	C₃₁⋊C₉	—	3	3	no	—
36	C₃₁⋊C₉	—	3	3	no	—
37	C₃₁⋊C₉	C₂₇⋊C₃	1	9	yes	direct product factor
38	C₃×C₂₇⋊C₃	—	31	2	no	—
39	C₃×C₂₇⋊C₃	C₃₁⋊C₃	1	1	yes	characteristic
40	C₃×C₉²	—	31	1	no	—
41	#6864	—	31	3	no	—
42	#6864	—	31	3	no	—
43	C₉×C₂₇	—	31	3	no	—
44	C₃×C₃₁	—	3	3	no	—
45	C₃×C₃₁	C₃×C₉²	1	1	yes	characteristic
46	C₃×C₃₁	C₃×C₂₇⋊C₃	1	3	yes	—
47	C₃²×C₉	—	31	3	no	—
48	C₃²×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
49	C₂₇⋊C₃	—	31	18	no	—
50	C₂₇⋊C₃	C₃₁⋊C₉	1	9	yes	direct product factor
51	C₃×C₂₇	—	31	6	no	—
52	C₃×C₂₇	C₃×C₃₁⋊C₃	1	3	yes	—
53	C₉²	—	31	6	no	—
54	C₉²	—	31	1	no	—
55	C₉²	—	31	1	no	—
56	C₉²	—	31	1	no	—
57	C₃₁	C₉×C₂₇⋊C₃	1	1	yes	characteristic, complemented, Sylow
58	C₃³	C₉×C₃₁⋊C₃	1	1	yes	characteristic
59	C₃×C₉	—	31	3	no	—
60	C₃×C₉	—	31	3	no	—
61	C₃×C₉	—	31	3	no	—
62	C₃×C₉	—	93	9	no	—
63	C₃×C₉	C₉×C₃₁⋊C₃	1	2	yes	—
64	C₃×C₉	C₉×C₃₁⋊C₃	1	6	yes	—
65	C₃×C₉	C₃×C₃₁⋊C₉	1	3	yes	—
66	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
67	C₂₇	—	31	18	no	—
68	C₂₇	C₃×C₃₁⋊C₉	1	9	yes	complemented
69	C₃²	—	3	3	no	—
70	C₃²	C₉×C₃₁⋊C₉	1	3	yes	—
71	C₃²	C₃×C₉×C₃₁⋊C₃	1	1	yes	characteristic
72	C₉	—	31	9	no	—
73	C₉	—	93	3	no	—
74	C₉	—	93	3	no	—
75	C₉	C₉×C₃₁⋊C₉	1	6	yes	—
76	C₉	C₃×C₉×C₃₁⋊C₃	1	2	yes	—
77	C₉	C₃²×C₃₁⋊C₉	1	1	yes	characteristic
78	C₃	—	3	3	no	—
79	C₃	C₃×C₉×C₃₁⋊C₉	1	1	yes	characteristic
80	C₃	C₂₇⋊C₃×C₃₁⋊C₃	1	3	yes	—

	subgroup	G/H
center, Frattini	C₃×C₉	C₃²×C₃₁⋊C₃
commutator	C₃×C₃₁	C₃×C₉²
Fitting	C₃×C₃₁×C₂₇⋊C₃	C₃
socle	C₃²×C₃₁	C₃²×C₉
prime radical	C₃³×C₃₁	C₃×C₉
cosocle	C₃×C₉×C₃₁	C₃³
hypercenter	C₃×C₂₇⋊C₃	C₃₁⋊C₃
hypocenter	C₃₁	C₉×C₂₇⋊C₃
LCS	G ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃×C₉ ◁ C₃×C₂₇⋊C₃

Complements

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

N	H ≅ G/N	type
3. #21419221	C₃	semidirect
4. #21419220	C₃	semidirect
5. C₂₇×C₃₁⋊C₉	C₃	semidirect
8. #14578892	C₉	semidirect
15. C₃₁×C₂₇⋊C₃	C₉	semidirect
26. C₂₇×C₃₁	C₃×C₉	semidirect
27. C₃₁⋊C₂₇	C₃×C₉	semidirect
37. C₃₁⋊C₉	C₂₇⋊C₃	direct (N × H)
50. C₂₇⋊C₃	C₃₁⋊C₉	direct (N × H)
57. C₃₁	C₉×C₂₇⋊C₃	semidirect
68. C₂₇	C₃×C₃₁⋊C₉	semidirect

Maximal subgroups

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

subgroup	index
C₃×#14578892	3
C₃×C₉×C₃₁⋊C₉	3
#21419221	3
#21419220	3
C₂₇×C₃₁⋊C₉	3
C₃×C₃₁×C₂₇⋊C₃	3
C₉×C₂₇⋊C₃	31

Subgroups — C27⋊C3×C31⋊C9 #36380948

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂₇⋊C₃×C₃₁⋊C₉ #36380948