Subgroups — C₃×#21419222 #36380945

Order 22599.

332 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃²×C₃₁⋊C₂₇	C₃	1	3	yes	maximal
2	#21419222	C₃	1	9	yes	maximal, direct product factor
3	C₃×C₉²×C₃₁	C₃	1	1	yes	maximal, characteristic
4	C₃×C₃₁⋊C₂₇	C₉	1	27	yes	complemented
5	C₃×C₃₁⋊C₂₇	C₃²	1	9	yes	—
6	C₃²×C₉×C₃₁	C₉	1	3	yes	—
7	C₃²×C₉×C₃₁	C₃²	1	1	yes	characteristic
8	C₉²×C₃₁	C₉	1	6	yes	—
9	C₉²×C₃₁	C₃²	1	3	yes	—
10	C₃³×C₃₁	C₃×C₉	1	1	yes	characteristic
11	C₃×C₉×C₃₁	—	3	9	no	—
12	C₃×C₉×C₃₁	C₃×C₉	1	9	yes	—
13	C₃×C₉×C₃₁	C₃×C₉	1	2	yes	—
14	C₃×C₉×C₃₁	C₃×C₉	1	9	yes	—
15	C₃×C₉×C₃₁	C₃³	1	1	yes	characteristic
16	C₃₁⋊C₂₇	C₃×C₉	1	27	yes	complemented
17	C₃×#6864	—	31	1	no	maximal, Sylow
18	C₃²×C₃₁	C₉²	1	3	yes	—
19	C₃²×C₃₁	C₂₇⋊C₃	1	9	yes	—
20	C₃²×C₃₁	C₃²×C₉	1	1	yes	characteristic
21	C₉×C₃₁	—	3	9	no	—
22	C₉×C₃₁	C₉²	1	6	yes	—
23	C₉×C₃₁	C₃²×C₉	1	3	yes	—
24	C₃²×C₂₇	—	31	3	no	—
25	C₃×C₉²	C₃₁⋊C₃	1	1	yes	characteristic
26	#6864	—	31	9	no	—
27	C₃×C₃₁	#6864	1	9	yes	complemented
28	C₃×C₃₁	C₃×C₉²	1	1	yes	characteristic
29	C₃×C₃₁	C₃×C₂₇⋊C₃	1	3	yes	—
30	C₃²×C₉	C₃₁⋊C₉	1	3	yes	—
31	C₃²×C₉	C₃×C₃₁⋊C₃	1	1	yes	characteristic
32	C₃×C₂₇	—	31	27	no	—
33	C₃×C₂₇	—	31	9	no	—
34	C₉²	C₃₁⋊C₉	1	6	yes	—
35	C₉²	C₃×C₃₁⋊C₃	1	3	yes	—
36	C₃₁	C₃×#6864	1	1	yes	characteristic, complemented, Sylow
37	C₃³	C₃×C₃₁⋊C₉	1	1	yes	characteristic
38	C₃×C₉	—	3	9	no	—
39	C₃×C₉	C₉×C₃₁⋊C₃	1	9	yes	—
40	C₃×C₉	C₃×C₃₁⋊C₉	1	9	yes	—
41	C₃×C₉	C₃×C₃₁⋊C₉	1	2	yes	—
42	C₃×C₉	C₃²×C₃₁⋊C₃	1	1	yes	characteristic
43	C₂₇	—	31	27	no	—
44	C₃²	C₉×C₃₁⋊C₉	1	3	yes	—
45	C₃²	#14578892	1	9	yes	—
46	C₃²	C₃²×C₃₁⋊C₉	1	1	yes	characteristic
47	C₉	—	3	9	no	—
48	C₉	C₉×C₃₁⋊C₉	1	6	yes	—
49	C₉	C₃×C₉×C₃₁⋊C₃	1	3	yes	—
50	C₃	#21419222	1	9	yes	direct product factor
51	C₃	C₃×C₉×C₃₁⋊C₉	1	1	yes	characteristic
52	C₃	C₃×#14578892	1	3	yes	—

	subgroup	G/H
center	C₃²×C₉	C₃×C₃₁⋊C₃
commutator	C₃×C₃₁	C₃×C₉²
Frattini	C₃×C₉	C₃²×C₃₁⋊C₃
Fitting	C₃×C₉²×C₃₁	C₃
socle, prime radical	C₃³×C₃₁	C₃×C₉
cosocle	C₃×C₉×C₃₁	C₃³
hypercenter	C₃×C₉²	C₃₁⋊C₃
hypocenter	C₃₁	C₃×#6864
LCS	G ▷ C₃×C₃₁ ▷ C₃₁
UCS	C₁ ◁ C₃²×C₉ ◁ C₃×C₉²

Complements

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

N	H ≅ G/N	type
2. #21419222	C₃	direct (N × H)
4. C₃×C₃₁⋊C₂₇	C₉	semidirect
16. C₃₁⋊C₂₇	C₃×C₉	semidirect
27. C₃×C₃₁	#6864	semidirect
36. C₃₁	C₃×#6864	semidirect
50. C₃	#21419222	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃²×C₃₁⋊C₂₇	3
#21419222	3
C₃×C₉²×C₃₁	3
C₃×#6864	31

Subgroups — C3×#21419222 #36380945

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#21419222 #36380945