Subgroups — #6895⋊C₈ #14516340

Order 1944.

158 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#6895	C₂	1	1	yes	maximal, characteristic
2	C₉×C₃⋊(C₃⋊C₈)	—	3	1	no	maximal
3	#10619507	C₃	1	1	yes	maximal, characteristic
4	(C₉⋊C₈)⋊C₉	—	3	3	no	maximal
5	C₂×#6895	C₄	1	1	yes	characteristic
6	C₃²×C₄×C₉	D₃	1	1	yes	characteristic
7	C₄×C₉⋊C₉	—	2	3	no	—
8	C₄×C₉⋊C₉	D₃	1	3	yes	—
9	C₄×C₃²⋊C₉	—	2	1	no	—
10	C₄×C₃²⋊C₉	C₂×C₃	1	1	yes	characteristic
11	#6895	C₈	1	1	yes	characteristic, complemented, Sylow
12	C₃×C₃⋊(C₃⋊C₈)	—	3	1	no	—
13	C₉×C₃⋊C₈	—	9	3	no	—
14	C₉×C₃⋊C₈	—	9	1	no	—
15	C₃×C₉⋊C₈	—	3	3	no	—
16	C₂×C₃²×C₉	Dic₃	1	1	yes	characteristic
17	C₂×C₉⋊C₉	—	2	3	no	—
18	C₂×C₉⋊C₉	Dic₃	1	3	yes	—
19	C₂×C₃²⋊C₉	—	2	1	no	—
20	C₂×C₃²⋊C₉	C₃×C₄	1	1	yes	characteristic
21	C₃³×C₄	C₃×D₃	1	1	yes	characteristic
22	C₃×C₄×C₉	—	2	3	no	—
23	C₃×C₄×C₉	—	2	1	no	—
24	C₃×C₄×C₉	—	3	3	no	—
25	C₃×C₄×C₉	C₃×D₃	1	3	yes	—
26	C₃×C₄×C₉	C₃⋊D₃	1	1	yes	characteristic
27	C₃²×C₉	C₃⋊C₈	1	1	yes	characteristic
28	C₉⋊C₉	—	2	3	no	—
29	C₉⋊C₉	C₃⋊C₈	1	3	yes	complemented
30	C₃²⋊C₉	—	2	1	no	—
31	C₃²⋊C₉	C₃×C₈	1	1	yes	characteristic
32	C₃⋊(C₃⋊C₈)	—	3	1	no	—
33	C₃×C₃⋊C₈	—	9	3	no	—
34	C₃×C₃⋊C₈	—	9	1	no	—
35	C₈×C₉	—	27	1	no	—
36	C₉⋊C₈	—	3	3	no	—
37	C₂×C₃³	C₃×Dic₃	1	1	yes	characteristic
38	C₂×C₃×C₉	—	2	3	no	—
39	C₂×C₃×C₉	—	2	1	no	—
40	C₂×C₃×C₉	—	3	3	no	—
41	C₂×C₃×C₉	C₃×Dic₃	1	3	yes	—
42	C₂×C₃×C₉	C₃⋊Dic₃	1	1	yes	characteristic
43	C₃²×C₄	—	3	1	no	—
44	C₃²×C₄	—	6	1	no	—
45	C₃²×C₄	AGL(1,ℤ/9)	1	3	yes	—
46	C₃²×C₄	C₃×C₃⋊D₃	1	1	yes	characteristic
47	C₄×C₉	—	3	1	no	—
48	C₄×C₉	—	3	3	no	—
49	C₄×C₉	—	6	3	no	—
50	C₄×C₉	—	6	1	no	—
51	C₃³	C₃×C₃⋊C₈	1	1	yes	characteristic
52	C₃×C₉	—	2	3	no	—
53	C₃×C₉	—	2	1	no	—
54	C₃×C₉	—	3	3	no	—
55	C₃×C₉	C₃×C₃⋊C₈	1	3	yes	—
56	C₃×C₉	C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
57	C₃×C₈	—	27	1	no	—
58	C₃⋊C₈	—	9	3	no	—
59	C₃⋊C₈	—	9	1	no	—
60	C₂×C₃²	—	3	1	no	—
61	C₂×C₃²	—	6	1	no	—
62	C₂×C₃²	3₋¹⁺²⋊C₄	1	3	yes	—
63	C₂×C₃²	C₃×C₃⋊Dic₃	1	1	yes	characteristic
64	C₂×C₉	—	3	1	no	—
65	C₂×C₉	—	3	3	no	—
66	C₂×C₉	—	6	3	no	—
67	C₂×C₉	—	6	1	no	—
68	C₃×C₄	—	2	1	no	—
69	C₃×C₄	—	3	3	no	—
70	C₃×C₄	C₃⋊AGL(1,ℤ/9)	1	1	yes	characteristic
71	C₃×C₄	#4208	1	1	yes	characteristic
72	C₃²	—	3	1	no	—
73	C₃²	—	6	1	no	—
74	C₃²	3₋¹⁺²⋊C₈	1	3	yes	—
75	C₃²	C₃×C₃⋊(C₃⋊C₈)	1	1	yes	characteristic
76	C₉	—	3	1	no	—
77	C₉	—	3	3	no	—
78	C₉	—	6	3	no	—
79	C₉	—	6	1	no	—
80	C₈	—	27	1	no	Sylow
81	C₂×C₃	—	2	1	no	—
82	C₂×C₃	—	3	3	no	—
83	C₂×C₃	C₃⋊(3₋¹⁺²⋊C₄)	1	1	yes	characteristic
84	C₂×C₃	#66410	1	1	yes	characteristic
85	C₄	#6895⋊C₂	1	1	yes	characteristic
86	C₃	—	2	1	no	—
87	C₃	—	3	3	no	—
88	C₃	C₃⋊(3₋¹⁺²⋊C₈)	1	1	yes	characteristic
89	C₃	#10619725	1	1	yes	characteristic
90	C₂	#6895⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₃×C₄	C₃⋊AGL(1,ℤ/9)
commutator, hypocenter	C₃²⋊C₉	C₃×C₈
Frattini	C₃²×C₄	C₃×C₃⋊D₃
Fitting	C₄×#6895	C₂
socle	C₂×C₃²	C₃×C₃⋊Dic₃
prime radical	C₂×C₃³	C₃×Dic₃
cosocle	C₄×C₃²⋊C₉	C₂×C₃
LCS	G ▷ C₃²⋊C₉
UCS	C₁ ◁ C₃×C₄

Complements

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

N	H ≅ G/N	type
11. #6895	C₈	semidirect
29. C₉⋊C₉	C₃⋊C₈	semidirect

Maximal subgroups

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

subgroup	index
C₄×#6895	2
C₉×C₃⋊(C₃⋊C₈)	3
#10619507	3
(C₉⋊C₈)⋊C₉	3

Subgroups — #6895⋊C8 #14516340

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #6895⋊C₈ #14516340