Subgroups — C₃×#63438 #11721372

Order 864.

210 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄²×C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×(C₂×D₉)⋊C₄	C₂	1	3	yes	maximal
3	C₃×Dic₉⋊C₄	C₂	1	3	yes	maximal, complemented
4	C₃×#876	—	3	1	no	maximal
5	#63438	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂²×C₃×D₉	C₂²	1	1	yes	characteristic
7	C₂×C₃×C₄×C₉	C₂²	1	3	yes	—
8	C₂×C₃×Dic₉	C₂²	1	3	yes	—
9	C₃²×C₄²	D₃	1	1	yes	characteristic
10	C₃×(C₂×D₃)⋊C₄	—	3	3	no	—
11	C₃×Dic₃⋊C₄	—	3	3	no	—
12	C₄²×C₉	—	2	1	no	—
13	C₄²×C₉	C₂×C₃	1	1	yes	characteristic, complemented
14	(C₂×D₉)⋊C₄	C₂×C₃	1	3	yes	—
15	Dic₉⋊C₄	C₂×C₃	1	3	yes	complemented
16	C₂²×C₃×C₉	C₂³	1	1	yes	characteristic
17	C₂×C₃×D₉	—	2	3	no	—
18	C₃×C₄×C₉	—	2	3	no	—
19	C₃×Dic₉	—	2	3	no	—
20	C₃×#126	—	9	1	no	—
21	#876	—	3	1	no	—
22	C₂²×C₃×D₃	—	3	1	no	—
23	C₂×C₃²×C₄	C₂×D₃	1	3	yes	—
24	C₂×C₃×Dic₃	—	3	3	no	—
25	C₂²×D₉	C₂²×C₃	1	1	yes	characteristic
26	C₂×C₄×C₉	—	2	3	no	—
27	C₂×C₄×C₉	C₂²×C₃	1	3	yes	—
28	C₂×Dic₉	C₂²×C₃	1	3	yes	—
29	C₂×C₃×C₉	#41	1	3	yes	—
30	C₃×D₉	—	4	1	no	—
31	C₃×C₄⋊C₄	—	9	3	no	—
32	C₃×C₂²⋊C₄	—	9	3	no	—
33	C₃×C₄²	—	2	1	no	—
34	C₃×C₄²	D₉	1	1	yes	characteristic, complemented
35	C₃×C₄²	C₃×D₃	1	1	yes	characteristic
36	(C₂×D₃)⋊C₄	—	3	3	no	—
37	Dic₃⋊C₄	—	3	3	no	—
38	C₂²×C₃²	C₂²×D₃	1	1	yes	characteristic
39	C₂×C₃×D₃	—	6	3	no	—
40	C₃²×C₄	—	2	3	no	—
41	C₃×Dic₃	—	6	3	no	—
42	C₂²×C₉	—	2	1	no	—
43	C₂²×C₉	C₂³×C₃	1	1	yes	characteristic
44	C₂×D₉	—	2	3	no	—
45	C₄×C₉	—	2	6	no	—
46	C₄×C₉	—	2	3	no	—
47	Dic₉	—	2	3	no	—
48	#126	—	9	1	no	Sylow
49	C₃×C₉	#126	1	1	yes	characteristic, complemented, Sylow
50	C₂³×C₃	—	9	1	no	—
51	C₂²×D₃	—	3	1	no	—
52	C₂×C₃×C₄	—	2	3	no	—
53	C₂×C₃×C₄	—	9	3	no	—
54	C₂×C₃×C₄	C₂×D₉	1	3	yes	—
55	C₂×C₃×C₄	C₂×C₃×D₃	1	3	yes	—
56	C₂×Dic₃	—	3	3	no	—
57	C₂×C₃²	#235	1	3	yes	—
58	C₃×D₃	—	12	1	no	—
59	C₂×C₉	—	2	3	no	—
60	C₂×C₉	C₃×#41	1	3	yes	—
61	D₉	—	4	1	no	—
62	C₄⋊C₄	—	9	3	no	—
63	C₂²⋊C₄	—	9	3	no	—
64	C₄²	C₃×D₉	1	1	yes	characteristic, complemented
65	C₂²×C₃	—	2	1	no	—
66	C₂²×C₃	—	18	3	no	—
67	C₂²×C₃	C₂²×D₉	1	1	yes	characteristic
68	C₂²×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
69	C₂×D₃	—	6	3	no	—
70	C₃×C₄	—	2	6	no	—
71	C₃×C₄	—	2	3	no	—
72	C₃×C₄	—	2	3	no	—
73	C₃×C₄	—	18	3	no	—
74	Dic₃	—	6	3	no	—
75	C₃²	#876	1	1	yes	characteristic
76	C₉	—	2	1	no	—
77	C₉	C₃×#126	1	1	yes	characteristic, complemented
78	C₂³	—	9	1	no	—
79	C₂×C₄	—	9	3	no	—
80	C₂×C₄	C₂×C₃×D₉	1	3	yes	—
81	C₂×C₃	—	2	3	no	—
82	C₂×C₃	—	36	1	no	—
83	C₂×C₃	#3697	1	3	yes	—
84	C₂×C₃	C₃×#235	1	3	yes	—
85	D₃	—	12	1	no	—
86	C₂²	—	18	3	no	—
87	C₂²	C₂²×C₃×D₉	1	1	yes	characteristic
88	C₄	—	2	3	no	—
89	C₄	—	18	3	no	—
90	C₃	—	2	1	no	—
91	C₃	#63438	1	1	yes	characteristic, direct product factor
92	C₃	C₃×#876	1	1	yes	characteristic
93	C₂	—	36	1	no	—
94	C₂	C₃×#3697	1	3	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂²×D₉
commutator, cosocle	C₂²×C₉	C₂³×C₃
Frattini	C₂²×C₃	C₂²×C₃×D₃
Fitting	C₃×C₄²×C₉	C₂
socle	C₂²×C₃²	C₂²×D₃
prime radical	C₂²×C₃×D₉	C₂²
hypercenter	C₃×C₄²	D₉
hypocenter	C₉	C₃×#126
LCS	G ▷ C₂²×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄²

Complements

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

N	H ≅ G/N	type
1. C₃×C₄²×C₉	C₂	semidirect
3. C₃×Dic₉⋊C₄	C₂	semidirect
5. #63438	C₃	direct (N × H)
13. C₄²×C₉	C₂×C₃	semidirect
15. Dic₉⋊C₄	C₂×C₃	semidirect
34. C₃×C₄²	D₉	semidirect
49. C₃×C₉	#126	semidirect
64. C₄²	C₃×D₉	semidirect
77. C₉	C₃×#126	semidirect
91. C₃	#63438	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×C₄²×C₉	2
C₃×(C₂×D₉)⋊C₄	2
C₃×Dic₉⋊C₄	2
C₃×#876	3
#63438	3

Subgroups — C3×#63438 #11721372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#63438 #11721372