Subgroups — D₉×Q₈⋊C₉ #13047039

Order 1296.

110 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₉×Q₈⋊C₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×Q₈×D₉	C₃	1	1	yes	maximal, characteristic
3	D₃×Q₈⋊C₉	—	3	1	no	maximal
4	C₂×C₉×D₉	—	4	1	no	maximal
5	C₃×Q₈×C₉	C₂×C₃	1	1	yes	characteristic
6	C₃×C₄×D₉	—	3	1	no	—
7	C₃×Dic₁₈	—	3	1	no	—
8	C₃×Q₈⋊C₉	—	2	1	no	—
9	C₃×Q₈⋊C₉	D₃	1	1	yes	characteristic
10	C₂×C₉²	—	4	1	no	—
11	C₉×D₉	—	4	2	no	—
12	C₃×D₃×Q₈	—	3	1	no	—
13	Q₈×D₉	C₉	1	1	yes	characteristic, complemented
14	C₂×Q₈⋊C₉	—	9	1	no	—
15	C₂×D₃×C₉	—	12	1	no	—
16	C₂×C₃×D₉	A₄	1	1	yes	characteristic
17	C₃×C₄×C₉	—	3	1	no	—
18	C₃×Dic₉	—	3	1	no	—
19	C₉²	—	4	1	no	Sylow
20	C₃²×Q₈	C₃×D₃	1	1	yes	characteristic
21	C₃×C₄×D₃	—	9	1	no	—
22	C₃×Dic₆	—	9	1	no	—
23	Q₈×C₉	—	2	1	no	—
24	Q₈×C₉	C₂×C₉	1	1	yes	characteristic, complemented
25	C₄×D₉	—	3	1	no	—
26	Dic₁₈	—	3	1	no	—
27	Q₈⋊C₉	—	2	3	no	—
28	Q₈⋊C₉	—	2	1	no	—
29	Q₈⋊C₉	D₉	1	1	yes	characteristic, direct product factor
30	C₂×C₃×C₉	—	4	1	no	—
31	C₂×C₃×C₉	—	8	1	no	—
32	C₂×C₃×C₉	C₂×A₄	1	1	yes	characteristic
33	D₃×C₉	—	12	2	no	—
34	C₃×D₉	SL(2,𝔽₃)	1	2	yes	—
35	C₂×C₃×Q₈	—	9	1	no	—
36	D₃×Q₈	—	3	1	no	—
37	C₂×C₃×D₃	—	3	1	no	—
38	C₃²×C₄	—	3	1	no	—
39	C₃×Dic₃	—	9	1	no	—
40	C₂²×C₉	—	36	1	no	—
41	C₂×D₉	C₂²⋊C₉	1	1	yes	characteristic
42	C₄×C₉	—	3	1	no	—
43	C₄×C₉	—	6	1	no	—
44	Dic₉	—	3	1	no	—
45	C₃×C₉	—	4	1	no	—
46	C₃×C₉	—	8	1	no	—
47	C₃×C₉	C₂×SL(2,𝔽₃)	1	1	yes	characteristic
48	C₃×Q₈	—	2	1	no	—
49	C₃×Q₈	—	27	1	no	—
50	C₃×Q₈	C₃×D₉	1	1	yes	characteristic
51	C₃×Q₈	D₃×C₉	1	1	yes	characteristic
52	C₂×C₃×C₄	—	27	1	no	—
53	C₄×D₃	—	9	1	no	—
54	Dic₆	—	9	1	no	—
55	C₂×C₃²	D₃×A₄	1	1	yes	characteristic
56	C₃×D₃	—	3	2	no	—
57	C₂×C₉	—	2	1	no	—
58	C₂×C₉	—	4	1	no	—
59	C₂×C₉	—	8	3	no	—
60	C₂×C₉	—	8	1	no	—
61	C₂×C₉	—	36	2	no	—
62	C₂×C₉	C₂×C₂²⋊C₉	1	1	yes	characteristic
63	D₉	Q₈⋊C₉	1	2	yes	direct product factor
64	C₂×Q₈	—	9	1	no	Sylow
65	C₂²×C₃	—	9	1	no	—
66	C₂×D₃	—	3	1	no	—
67	C₃×C₄	—	3	1	no	—
68	C₃×C₄	—	3	1	no	—
69	C₃×C₄	—	6	1	no	—
70	C₃×C₄	—	27	1	no	—
71	Dic₃	—	9	1	no	—
72	C₃²	D₃×SL(2,𝔽₃)	1	1	yes	characteristic
73	C₉	—	2	1	no	—
74	C₉	—	4	1	no	—
75	C₉	—	8	3	no	—
76	C₉	—	8	1	no	—
77	C₉	C₂×Q₈⋊C₉	1	1	yes	characteristic, complemented
78	Q₈	—	27	1	no	—
79	Q₈	C₉×D₉	1	1	yes	characteristic, complemented
80	C₂×C₄	—	27	1	no	—
81	C₂×C₃	—	2	1	no	—
82	C₂×C₃	—	9	2	no	—
83	C₂×C₃	A₄×D₉	1	1	yes	characteristic
84	C₂×C₃	D₃×C₂²⋊C₉	1	1	yes	characteristic
85	D₃	—	3	2	no	—
86	C₂²	—	9	1	no	—
87	C₄	—	3	1	no	—
88	C₄	—	27	1	no	—
89	C₃	—	2	1	no	—
90	C₃	D₉×SL(2,𝔽₃)	1	1	yes	characteristic
91	C₃	D₃×Q₈⋊C₉	1	1	yes	characteristic
92	C₂	—	9	2	no	—
93	C₂	D₉×C₂²⋊C₉	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂×C₃	A₄×D₉
commutator, hypocenter	Q₈×C₉	C₂×C₉
Frattini, socle	C₂×C₃²	D₃×A₄
Fitting, cosocle	C₃×Q₈×C₉	C₂×C₃
prime radical	C₂×C₃×D₉	A₄
LCS	G ▷ Q₈×C₉
UCS	C₁ ◁ C₂×C₃

Complements

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

N	H ≅ G/N	type
1. C₉×Q₈⋊C₉	C₂	semidirect
13. Q₈×D₉	C₉	semidirect
24. Q₈×C₉	C₂×C₉	semidirect
29. Q₈⋊C₉	D₉	direct (N × H)
63. D₉	Q₈⋊C₉	direct (N × H)
77. C₉	C₂×Q₈⋊C₉	semidirect
79. Q₈	C₉×D₉	semidirect

Maximal subgroups

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

subgroup	index
C₉×Q₈⋊C₉	2
C₃×Q₈×D₉	3
D₃×Q₈⋊C₉	3
C₂×C₉×D₉	4

Subgroups — D9×Q8⋊C9 #13047039

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₉×Q₈⋊C₉ #13047039