Subgroups — C₃×C₉×#95 #11720587

Order 864.

380 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₄×C₉	C₂	1	3	yes	maximal
2	C₃²×#95	C₃	1	1	yes	maximal, characteristic
3	C₉×#95	C₃	1	3	yes	maximal, direct product factor
4	C₂³×C₃×C₉	C₂²	1	1	yes	characteristic
5	C₂×C₃×C₄×C₉	—	2	6	no	—
6	C₂×C₃×C₄×C₉	C₄	1	6	yes	complemented
7	C₂²×C₃²×C₄	C₂×C₃	1	3	yes	—
8	C₂²×C₄×C₉	C₂×C₃	1	9	yes	—
9	C₂²×C₃×C₉	C₂×C₄	1	3	yes	—
10	C₂²×C₃×C₉	D₄	1	3	yes	—
11	C₂²×C₃×C₉	Q₈	1	1	yes	characteristic
12	C₃×C₄×C₉	—	2	6	no	—
13	C₃×#95	C₉	1	3	yes	direct product factor
14	C₃×#95	C₃²	1	1	yes	characteristic
15	C₂³×C₃²	C₂²×C₃	1	1	yes	characteristic
16	C₂×C₃²×C₄	—	2	6	no	—
17	C₂×C₃²×C₄	C₃×C₄	1	6	yes	—
18	C₂³×C₉	C₂²×C₃	1	3	yes	—
19	C₂×C₄×C₉	—	2	18	no	—
20	C₂×C₄×C₉	C₃×C₄	1	18	yes	complemented
21	C₂×C₃×C₉	C₄²	1	1	yes	characteristic
22	C₂×C₃×C₉	C₂²⋊C₄	1	3	yes	—
23	C₂×C₃×C₉	C₄⋊C₄	1	3	yes	—
24	C₂²×C₃×C₄	C₂×C₉	1	9	yes	—
25	C₂²×C₃×C₄	C₂×C₃²	1	3	yes	—
26	C₂²×C₃²	C₂×C₃×C₄	1	3	yes	—
27	C₂²×C₃²	C₃×D₄	1	3	yes	—
28	C₂²×C₃²	C₃×Q₈	1	1	yes	characteristic
29	C₃²×C₄	—	2	6	no	—
30	C₂²×C₉	C₂×C₃×C₄	1	9	yes	—
31	C₂²×C₉	C₃×D₄	1	9	yes	—
32	C₂²×C₉	C₃×Q₈	1	3	yes	—
33	C₄×C₉	—	2	18	no	—
34	#95	C₃×C₉	1	1	yes	characteristic, direct product factor, Sylow
35	C₃×C₉	#95	1	1	yes	characteristic, direct product factor, Sylow
36	C₂³×C₃	C₂²×C₉	1	3	yes	—
37	C₂³×C₃	C₂²×C₃²	1	1	yes	characteristic
38	C₂×C₃×C₄	—	2	18	no	—
39	C₂×C₃×C₄	—	2	6	no	—
40	C₂×C₃×C₄	C₄×C₉	1	18	yes	complemented
41	C₂×C₃×C₄	C₃²×C₄	1	6	yes	—
42	C₂×C₃²	C₃×C₄²	1	1	yes	characteristic
43	C₂×C₃²	C₃×C₂²⋊C₄	1	3	yes	—
44	C₂×C₃²	C₃×C₄⋊C₄	1	3	yes	—
45	C₂×C₉	C₃×C₄²	1	3	yes	—
46	C₂×C₉	C₃×C₂²⋊C₄	1	9	yes	—
47	C₂×C₉	C₃×C₄⋊C₄	1	9	yes	—
48	C₂²×C₄	C₂×C₃×C₉	1	3	yes	—
49	C₂²×C₃	C₂×C₄×C₉	1	9	yes	—
50	C₂²×C₃	D₄×C₉	1	9	yes	—
51	C₂²×C₃	Q₈×C₉	1	3	yes	—
52	C₂²×C₃	C₂×C₃²×C₄	1	3	yes	—
53	C₂²×C₃	C₃²×D₄	1	3	yes	—
54	C₂²×C₃	C₃²×Q₈	1	1	yes	characteristic
55	C₃×C₄	—	2	18	no	—
56	C₃×C₄	—	2	6	no	—
57	C₃²	C₃×#95	1	1	yes	characteristic
58	C₉	C₃×#95	1	3	yes	direct product factor
59	C₂³	C₂²×C₃×C₉	1	1	yes	characteristic
60	C₂×C₄	—	2	6	no	—
61	C₂×C₄	C₃×C₄×C₉	1	6	yes	complemented
62	C₂×C₃	C₄²×C₉	1	3	yes	—
63	C₂×C₃	C₉×C₂²⋊C₄	1	9	yes	—
64	C₂×C₃	C₉×C₄⋊C₄	1	9	yes	—
65	C₂×C₃	C₃²×C₄²	1	1	yes	characteristic
66	C₂×C₃	C₃²×C₂²⋊C₄	1	3	yes	—
67	C₂×C₃	C₃²×C₄⋊C₄	1	3	yes	—
68	C₂²	C₂×C₃×C₄×C₉	1	3	yes	—
69	C₂²	C₃×D₄×C₉	1	3	yes	—
70	C₂²	C₃×Q₈×C₉	1	1	yes	characteristic
71	C₄	—	2	6	no	—
72	C₃	C₉×#95	1	3	yes	direct product factor
73	C₃	C₃²×#95	1	1	yes	characteristic
74	C₂	C₃×C₄²×C₉	1	1	yes	characteristic
75	C₂	C₃×C₉×C₂²⋊C₄	1	3	yes	—
76	C₂	C₃×C₉×C₄⋊C₄	1	3	yes	—

	subgroup	G/H
center	C₂³×C₃×C₉	C₂²
commutator	C₂	C₃×C₄²×C₉
Frattini, cosocle	C₂³×C₃	C₂²×C₃²
socle, prime radical	C₂³×C₃²	C₂²×C₃
LCS	G ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₉ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₉×#95	C₃	direct (N × H)
6. C₂×C₃×C₄×C₉	C₄	semidirect
13. C₃×#95	C₉	direct (N × H)
20. C₂×C₄×C₉	C₃×C₄	semidirect
34. #95	C₃×C₉	direct (N × H)
35. C₃×C₉	#95	direct (N × H)
40. C₂×C₃×C₄	C₄×C₉	semidirect
58. C₉	C₃×#95	direct (N × H)
61. C₂×C₄	C₃×C₄×C₉	semidirect
72. C₃	C₉×#95	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₄×C₉	2
C₃²×#95	3
C₉×#95	3

Subgroups — C3×C9×#95 #11720587

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₉×#95 #11720587