Subgroups — C₉×#127⋊C₃ #11721334

Order 864.

108 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×C₄²⋊C₃	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#127⋊C₃	C₃	1	1	yes	maximal, characteristic
3	C₉×#127	C₃	1	1	yes	maximal, characteristic, complemented
4	#127⋊C₉	C₃	1	2	yes	maximal, complemented
5	C₂×C₉×A₄	—	4	1	no	maximal
6	C₃×C₄²⋊C₃	C₂×C₃	1	1	yes	characteristic
7	C₂×D₄×C₉	—	3	1	no	—
8	C₂×D₄×C₉	—	3	1	no	—
9	C₄²×C₉	C₂×C₃	1	1	yes	characteristic, complemented
10	C₄²⋊C₉	C₂×C₃	1	2	yes	complemented
11	C₉×A₄	—	4	1	no	—
12	C₃×#127	C₃²	1	1	yes	characteristic
13	#127⋊C₃	C₉	1	3	yes	direct product factor
14	C₂×C₃×A₄	—	4	1	no	—
15	C₂³×C₉	—	3	1	no	—
16	C₂³×C₉	A₄	1	1	yes	characteristic
17	C₂×C₂²⋊C₉	—	4	2	no	—
18	D₄×C₉	—	6	2	no	—
19	D₄×C₉	—	6	2	no	—
20	C₂×C₄×C₉	—	3	1	no	—
21	C₂×C₃×C₉	—	16	1	no	—
22	C₂×C₃×D₄	—	3	1	no	—
23	C₂×C₃×D₄	—	3	1	no	—
24	C₃×C₄²	C₂×C₃²	1	1	yes	characteristic
25	C₄²⋊C₃	C₂×C₉	1	3	yes	complemented
26	C₃×A₄	—	4	1	no	—
27	C₂²×C₉	—	6	1	no	—
28	C₂²×C₉	—	6	1	no	—
29	C₂²×C₉	—	6	2	no	—
30	C₂²×C₉	C₂×A₄	1	1	yes	characteristic
31	C₂²⋊C₉	—	4	2	no	—
32	C₄×C₉	—	3	2	no	—
33	#127	C₃×C₉	1	1	yes	characteristic, complemented, Sylow
34	C₃×C₉	—	16	1	no	Sylow
35	C₂³×C₃	—	3	1	no	—
36	C₂³×C₃	C₃×A₄	1	1	yes	characteristic
37	C₂×A₄	—	4	3	no	—
38	C₃×D₄	—	6	2	no	—
39	C₃×D₄	—	6	2	no	—
40	C₂×C₃×C₄	—	3	1	no	—
41	C₂×C₃²	—	16	1	no	—
42	C₂×C₉	—	3	1	no	—
43	C₂×C₉	—	4	1	no	—
44	C₂×C₉	—	12	1	no	—
45	C₂×C₉	—	16	2	no	—
46	C₂×D₄	—	3	1	no	—
47	C₂×D₄	—	3	1	no	—
48	C₄²	C₂×C₃×C₉	1	1	yes	characteristic, complemented
49	C₂²×C₃	—	6	1	no	—
50	C₂²×C₃	—	6	1	no	—
51	C₂²×C₃	—	6	2	no	—
52	C₂²×C₃	C₂×C₃×A₄	1	1	yes	characteristic
53	A₄	—	4	3	no	—
54	C₃×C₄	—	3	2	no	—
55	C₃²	—	16	1	no	—
56	C₉	—	16	2	no	—
57	C₉	#127⋊C₃	1	1	yes	characteristic, direct product factor
58	C₂³	—	3	1	no	—
59	C₂³	C₉×A₄	1	1	yes	characteristic
60	D₄	—	6	2	no	—
61	D₄	—	6	2	no	—
62	C₂×C₄	—	3	1	no	—
63	C₂×C₃	—	3	1	no	—
64	C₂×C₃	—	4	1	no	—
65	C₂×C₃	—	12	1	no	—
66	C₂×C₃	—	16	3	no	—
67	C₂²	—	6	1	no	—
68	C₂²	—	6	1	no	—
69	C₂²	—	6	2	no	—
70	C₂²	C₂×C₉×A₄	1	1	yes	characteristic
71	C₄	—	3	2	no	—
72	C₃	—	16	3	no	—
73	C₃	C₃×#127⋊C₃	1	1	yes	characteristic
74	C₂	—	3	1	no	—
75	C₂	—	4	1	no	—
76	C₂	—	12	1	no	—

	subgroup	G/H
center, hypercenter	C₉	#127⋊C₃
commutator, hypocenter	C₄²	C₂×C₃×C₉
Frattini, socle	C₂²×C₃	C₂×C₃×A₄
Fitting	C₉×#127	C₃
prime radical	C₃×#127⋊C₃	C₃
cosocle	C₃×C₄²	C₂×C₃²
LCS	G ▷ C₄²
UCS	C₁ ◁ C₉

Complements

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

N	H ≅ G/N	type
1. C₉×C₄²⋊C₃	C₂	semidirect
3. C₉×#127	C₃	semidirect
4. #127⋊C₉	C₃	semidirect
9. C₄²×C₉	C₂×C₃	semidirect
10. C₄²⋊C₉	C₂×C₃	semidirect
13. #127⋊C₃	C₉	direct (N × H)
25. C₄²⋊C₃	C₂×C₉	semidirect
33. #127	C₃×C₉	semidirect
48. C₄²	C₂×C₃×C₉	semidirect
57. C₉	#127⋊C₃	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×C₄²⋊C₃	2
C₃×#127⋊C₃	3
C₉×#127	3
#127⋊C₉	3
C₂×C₉×A₄	4

Subgroups — C9×#127⋊C3 #11721334

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉×#127⋊C₃ #11721334