Subgroups — C₂×C₈×Dic₉ #10588779

Order 576.

243 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Dic₉	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₉⋊C₈	C₂	1	1	yes	maximal, characteristic
4	C₈×Dic₉	C₂	1	4	yes	maximal, direct product factor
5	C₂×C₈×Dic₃	—	3	1	no	maximal
6	C₂²×C₄×C₉	C₂²	1	1	yes	characteristic
7	C₂²×Dic₉	C₄	1	2	yes	—
8	C₂×C₈×C₉	C₄	1	4	yes	complemented
9	C₂×C₈×C₉	C₂²	1	2	yes	—
10	C₄×Dic₉	C₄	1	2	yes	—
11	C₄×Dic₉	C₂²	1	2	yes	—
12	C₂×C₉⋊C₈	C₄	1	4	yes	complemented
13	C₂×C₉⋊C₈	C₂²	1	2	yes	—
14	C₂²×C₃×C₈	D₃	1	1	yes	characteristic
15	C₂×C₄×Dic₃	—	3	1	no	—
16	C₂²×C₃⋊C₈	—	3	1	no	—
17	C₈×Dic₃	—	3	4	no	—
18	C₂³×C₉	C₂×C₄	1	1	yes	characteristic
19	C₂×C₄×C₉	C₂×C₄	1	1	yes	characteristic
20	C₂×C₄×C₉	C₂×C₄	1	2	yes	—
21	C₂×C₄×C₉	C₂×C₄	1	2	yes	—
22	C₂×C₄×C₉	C₂³	1	1	yes	characteristic
23	C₂×Dic₉	C₈	1	8	yes	direct product factor
24	C₂×Dic₉	C₂×C₄	1	4	yes	—
25	C₈×C₉	C₂×C₄	1	4	yes	complemented
26	C₉⋊C₈	C₂×C₄	1	4	yes	complemented
27	C₂×C₄×C₈	—	9	1	no	Sylow
28	C₂²×C₃×C₄	C₂×D₃	1	1	yes	characteristic
29	C₂²×Dic₃	—	3	2	no	—
30	C₂×C₃×C₈	Dic₃	1	4	yes	—
31	C₂×C₃×C₈	C₂×D₃	1	2	yes	—
32	C₄×Dic₃	—	3	2	no	—
33	C₄×Dic₃	—	3	2	no	—
34	C₂×C₃⋊C₈	—	3	4	no	—
35	C₂×C₃⋊C₈	—	3	2	no	—
36	C₂²×C₉	C₄²	1	2	yes	—
37	C₂²×C₉	C₂×C₈	1	4	yes	—
38	C₂²×C₉	C₂²×C₄	1	1	yes	characteristic
39	C₄×C₉	C₄²	1	2	yes	—
40	C₄×C₉	C₂²×C₄	1	1	yes	characteristic
41	C₄×C₉	C₂²×C₄	1	1	yes	characteristic
42	Dic₉	C₂×C₈	1	8	yes	direct product factor
43	C₂²×C₈	—	9	1	no	—
44	C₂²×C₈	D₉	1	1	yes	characteristic
45	C₂×C₄²	—	9	1	no	—
46	C₄×C₈	—	9	4	no	—
47	C₂³×C₃	C₄×D₃	1	1	yes	characteristic
48	C₂×C₃×C₄	C₄×D₃	1	1	yes	characteristic
49	C₂×C₃×C₄	C₄×D₃	1	2	yes	—
50	C₂×C₃×C₄	C₂×Dic₃	1	2	yes	—
51	C₂×C₃×C₄	C₂²×D₃	1	1	yes	characteristic
52	C₂×Dic₃	—	3	8	no	—
53	C₂×Dic₃	—	3	4	no	—
54	C₃×C₈	C₂×Dic₃	1	4	yes	—
55	C₃⋊C₈	—	3	4	no	—
56	C₂×C₉	C₄×C₈	1	4	yes	complemented
57	C₂×C₉	C₂×C₄²	1	1	yes	characteristic
58	C₂×C₉	C₂²×C₈	1	2	yes	—
59	C₂²×C₄	—	9	2	no	—
60	C₂²×C₄	C₂×D₉	1	1	yes	characteristic
61	C₂×C₈	—	9	4	no	—
62	C₂×C₈	—	9	2	no	—
63	C₂×C₈	Dic₉	1	4	yes	direct product factor
64	C₂×C₈	C₂×D₉	1	2	yes	—
65	C₄²	—	9	2	no	—
66	C₄²	—	9	2	no	—
67	C₂²×C₃	D₃×C₈	1	4	yes	—
68	C₂²×C₃	C₄×Dic₃	1	2	yes	—
69	C₂²×C₃	C₂×C₄×D₃	1	1	yes	characteristic
70	C₃×C₄	C₄×Dic₃	1	2	yes	—
71	C₃×C₄	C₂×C₄×D₃	1	1	yes	characteristic
72	C₃×C₄	C₂²×Dic₃	1	1	yes	characteristic
73	Dic₃	—	3	8	no	—
74	C₉	C₂×C₄×C₈	1	1	yes	characteristic, complemented, Sylow
75	C₂³	C₄×D₉	1	1	yes	characteristic
76	C₂×C₄	—	9	8	no	—
77	C₂×C₄	—	9	4	no	—
78	C₂×C₄	C₄×D₉	1	1	yes	characteristic
79	C₂×C₄	C₄×D₉	1	2	yes	—
80	C₂×C₄	C₂×Dic₉	1	2	yes	—
81	C₂×C₄	C₂²×D₉	1	1	yes	characteristic
82	C₈	—	9	4	no	—
83	C₈	C₂×Dic₉	1	4	yes	direct product factor
84	C₂×C₃	C₈×Dic₃	1	4	yes	—
85	C₂×C₃	C₂×D₃×C₈	1	2	yes	—
86	C₂×C₃	C₂×C₄×Dic₃	1	1	yes	characteristic
87	C₂²	C₈×D₉	1	4	yes	—
88	C₂²	C₄×Dic₉	1	2	yes	—
89	C₂²	C₂×C₄×D₉	1	1	yes	characteristic
90	C₄	—	9	8	no	—
91	C₄	C₄×Dic₉	1	2	yes	—
92	C₄	C₂×C₄×D₉	1	1	yes	characteristic
93	C₄	C₂²×Dic₉	1	1	yes	characteristic
94	C₃	C₂×C₈×Dic₃	1	1	yes	characteristic
95	C₂	C₈×Dic₉	1	4	yes	direct product factor
96	C₂	C₂×C₈×D₉	1	2	yes	—
97	C₂	C₂×C₄×Dic₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂²×C₈	D₉
commutator, hypocenter	C₉	C₂×C₄×C₈
Frattini	C₂×C₃×C₄	C₂²×D₃
Fitting	C₂²×C₈×C₉	C₂
socle, prime radical	C₂³×C₃	C₄×D₃
cosocle	C₂×C₄×C₉	C₂³
LCS	G ▷ C₉
UCS	C₁ ◁ C₂²×C₈

Complements

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

N	H ≅ G/N	type
4. C₈×Dic₉	C₂	direct (N × H)
8. C₂×C₈×C₉	C₄	semidirect
12. C₂×C₉⋊C₈	C₄	semidirect
23. C₂×Dic₉	C₈	direct (N × H)
25. C₈×C₉	C₂×C₄	semidirect
26. C₉⋊C₈	C₂×C₄	semidirect
42. Dic₉	C₂×C₈	direct (N × H)
56. C₂×C₉	C₄×C₈	semidirect
63. C₂×C₈	Dic₉	direct (N × H)
74. C₉	C₂×C₄×C₈	semidirect
83. C₈	C₂×Dic₉	direct (N × H)
95. C₂	C₈×Dic₉	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×C₈×C₉	2
C₂×C₄×Dic₉	2
C₂²×C₉⋊C₈	2
C₈×Dic₉	2
C₂×C₈×Dic₃	3

Subgroups — C2×C8×Dic9 #10588779

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₈×Dic₉ #10588779