Subgroups — Q₈×C₃⋊Dic₉ #11721855

Order 864.

350 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×Q₈×C₉	C₂	1	1	yes	maximal, characteristic
2	C₄⋊(C₃⋊Dic₉)	C₂	1	3	yes	maximal
3	C₄×C₃⋊Dic₉	C₂	1	3	yes	maximal
4	Q₈×C₃⋊Dic₃	—	3	1	no	maximal
5	Q₈×Dic₉	—	3	3	no	maximal
6	C₃×Q₈×C₉	C₄	1	4	yes	complemented
7	C₂×C₃×C₄×C₉	C₂²	1	3	yes	—
8	C₂×C₃⋊Dic₉	C₂²	1	3	yes	—
9	C₂×C₃⋊Dic₉	C₂²	1	1	yes	characteristic
10	C₂×C₃²×Q₈	D₃	1	1	yes	characteristic
11	C₄⋊(C₃⋊Dic₃)	—	3	3	no	—
12	C₄×C₃⋊Dic₃	—	3	3	no	—
13	C₂×Q₈×C₉	D₃	1	3	yes	—
14	C₄⋊Dic₉	—	3	9	no	—
15	C₄×Dic₉	—	3	9	no	—
16	C₂²×C₃×C₉	C₂³	1	1	yes	characteristic
17	C₃×C₄×C₉	C₂×C₄	1	6	yes	—
18	C₃⋊Dic₉	—	2	3	no	—
19	C₃⋊Dic₉	Q₈	1	2	yes	direct product factor
20	Q₈×Dic₃	—	9	3	no	—
21	Q₈×Dic₃	—	9	1	no	—
22	C₃²×Q₈	Dic₃	1	4	yes	—
23	C₂×C₃²×C₄	C₂×D₃	1	3	yes	—
24	C₂×C₃⋊Dic₃	—	3	1	no	—
25	C₂×C₃⋊Dic₃	—	3	3	no	—
26	Q₈×C₉	Dic₃	1	12	yes	complemented
27	C₂×C₄×C₉	C₂×D₃	1	9	yes	—
28	C₂×Dic₉	—	3	3	no	—
29	C₂×Dic₉	—	3	9	no	—
30	C₂×C₃×C₉	C₂²×C₄	1	1	yes	characteristic
31	C₂×C₃×C₉	C₂×Q₈	1	1	yes	characteristic
32	C₂×C₃×C₉	#41	1	1	yes	characteristic
33	C₂×C₃×Q₈	D₉	1	3	yes	—
34	C₂×C₃×Q₈	C₃⋊D₃	1	1	yes	characteristic
35	C₄⋊Dic₃	—	9	9	no	—
36	C₄⋊Dic₃	—	9	3	no	—
37	C₄×Dic₃	—	9	9	no	—
38	C₄×Dic₃	—	9	3	no	—
39	C₂²×C₃²	C₂²×D₃	1	1	yes	characteristic
40	C₃²×C₄	C₂×Dic₃	1	6	yes	—
41	C₃⋊Dic₃	—	3	2	no	—
42	C₃⋊Dic₃	—	6	3	no	—
43	C₂²×C₉	C₂²×D₃	1	3	yes	—
44	C₄×C₉	C₂×Dic₃	1	18	yes	—
45	Dic₉	—	3	6	no	—
46	Dic₉	—	6	9	no	—
47	C₄×Q₈	—	27	1	no	Sylow
48	C₃×C₉	C₄×Q₈	1	1	yes	characteristic, complemented, Sylow
49	C₃×Q₈	Dic₉	1	12	yes	complemented
50	C₃×Q₈	C₃⋊Dic₃	1	4	yes	—
51	C₂×C₃×C₄	C₂×D₉	1	9	yes	—
52	C₂×C₃×C₄	C₂×C₃⋊D₃	1	3	yes	—
53	C₂×Dic₃	—	9	3	no	—
54	C₂×Dic₃	—	9	1	no	—
55	C₂×Dic₃	—	9	9	no	—
56	C₂×Dic₃	—	9	3	no	—
57	C₂×C₃²	D₃×Q₈	1	1	yes	characteristic
58	C₂×C₃²	#239	1	1	yes	characteristic
59	C₂×C₃²	C₂²×Dic₃	1	1	yes	characteristic
60	C₂×C₉	D₃×Q₈	1	3	yes	—
61	C₂×C₉	#239	1	3	yes	—
62	C₂×C₉	C₂²×Dic₃	1	3	yes	—
63	C₂×Q₈	C₃⋊D₉	1	1	yes	characteristic
64	C₄⋊C₄	—	27	3	no	—
65	C₄²	—	27	3	no	—
66	C₂²×C₃	C₂²×D₉	1	3	yes	—
67	C₂²×C₃	C₂²×C₃⋊D₃	1	1	yes	characteristic
68	C₃×C₄	C₂×Dic₉	1	18	yes	—
69	C₃×C₄	C₂×C₃⋊Dic₃	1	6	yes	—
70	Dic₃	—	9	6	no	—
71	Dic₃	—	9	2	no	—
72	Dic₃	—	18	9	no	—
73	Dic₃	—	18	3	no	—
74	C₃²	Q₈×Dic₃	1	1	yes	characteristic
75	C₉	Q₈×Dic₃	1	3	yes	complemented
76	Q₈	C₃⋊Dic₉	1	4	yes	direct product factor
77	C₂×C₄	—	27	1	no	—
78	C₂×C₄	—	27	3	no	—
79	C₂×C₄	C₂×C₃⋊D₉	1	3	yes	—
80	C₂×C₃	Q₈×D₉	1	3	yes	—
81	C₂×C₃	#3701	1	3	yes	—
82	C₂×C₃	C₂²×Dic₉	1	3	yes	—
83	C₂×C₃	Q₈×C₃⋊D₃	1	1	yes	characteristic
84	C₂×C₃	#3832	1	1	yes	characteristic
85	C₂×C₃	C₂²×C₃⋊Dic₃	1	1	yes	characteristic
86	C₂²	C₂²×C₃⋊D₉	1	1	yes	characteristic
87	C₄	—	27	2	no	—
88	C₄	—	54	3	no	—
89	C₄	C₂×C₃⋊Dic₉	1	6	yes	—
90	C₃	Q₈×Dic₉	1	3	yes	complemented
91	C₃	Q₈×C₃⋊Dic₃	1	1	yes	characteristic
92	C₂	Q₈×C₃⋊D₉	1	1	yes	characteristic
93	C₂	#88746	1	1	yes	characteristic
94	C₂	C₂²×C₃⋊Dic₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×C₃⋊D₉
commutator	C₂×C₃×C₉	C₂²×C₄
Frattini	C₂²×C₃	C₂²×C₃⋊D₃
Fitting	C₂×C₃×Q₈×C₉	C₂
socle, prime radical	C₂²×C₃²	C₂²×D₃
cosocle	C₂²×C₃×C₉	C₂³
hypercenter	C₂×Q₈	C₃⋊D₉
hypocenter	C₃×C₉	C₄×Q₈
LCS	G ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂² ◁ C₂×Q₈

Complements

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

N	H ≅ G/N	type
6. C₃×Q₈×C₉	C₄	semidirect
19. C₃⋊Dic₉	Q₈	direct (N × H)
26. Q₈×C₉	Dic₃	semidirect
48. C₃×C₉	C₄×Q₈	semidirect
49. C₃×Q₈	Dic₉	semidirect
75. C₉	Q₈×Dic₃	semidirect
76. Q₈	C₃⋊Dic₉	direct (N × H)
90. C₃	Q₈×Dic₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₃×Q₈×C₉	2
C₄⋊(C₃⋊Dic₉)	2
C₄×C₃⋊Dic₉	2
Q₈×C₃⋊Dic₃	3
Q₈×Dic₉	3

Subgroups — Q8×C3⋊Dic9 #11721855

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — Q₈×C₃⋊Dic₉ #11721855