Subgroups — (C₃⋊D₉)⋊Q₈ #88636

Order 432.

130 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×C₃⋊D₉	C₂	1	1	yes	maximal, characteristic
2	C₉×Dic₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×Dic₁₈	C₂	1	1	yes	maximal, characteristic, complemented
4	(C₃⋊D₉)⋊C₄	C₂	1	2	yes	maximal
5	#6189	C₂	1	2	yes	maximal, complemented
6	#3797	—	3	1	no	maximal
7	Q₈×D₉	—	3	1	no	maximal
8	C₂×C₃⋊D₉	C₂²	1	1	yes	characteristic
9	C₃×C₄×C₉	C₂²	1	1	yes	characteristic
10	C₃⋊Dic₉	C₂²	1	1	yes	characteristic
11	C₉×Dic₃	C₂²	1	2	yes	—
12	C₃×Dic₉	C₂²	1	2	yes	—
13	C₄×C₃⋊D₃	—	3	1	no	—
14	C₃×Dic₆	—	3	1	no	—
15	C₃×Dic₆	D₃	1	1	yes	characteristic
16	#627	—	3	2	no	—
17	#624	—	3	2	no	—
18	Q₈×C₉	—	3	1	no	—
19	C₄×D₉	—	3	1	no	—
20	C₄×D₉	—	3	2	no	—
21	C₄×D₉	—	6	1	no	—
22	Dic₁₈	—	3	2	no	—
23	Dic₁₈	D₃	1	1	yes	characteristic, complemented
24	C₂×C₃×C₉	C₂³	1	1	yes	characteristic
25	C₃⋊D₉	Q₈	1	2	yes	complemented
26	D₃×Q₈	—	9	1	no	—
27	D₃×Q₈	—	9	1	no	—
28	C₂×C₃⋊D₃	—	3	1	no	—
29	C₃²×C₄	C₂×D₃	1	1	yes	characteristic
30	C₃⋊Dic₃	—	3	1	no	—
31	C₃×Dic₃	—	3	2	no	—
32	C₃×Dic₃	C₂×D₃	1	2	yes	—
33	C₂×D₉	—	3	1	no	—
34	C₂×D₉	—	6	1	no	—
35	C₄×C₉	—	2	1	no	—
36	C₄×C₉	—	3	2	no	—
37	C₄×C₉	C₂×D₃	1	1	yes	characteristic
38	Dic₉	—	3	1	no	—
39	Dic₉	—	6	1	no	—
40	Dic₉	C₂×D₃	1	2	yes	—
41	C₃×C₉	C₂×Q₈	1	1	yes	characteristic, complemented, Sylow
42	C₃×Q₈	—	3	1	no	—
43	C₃×Q₈	—	9	1	no	—
44	C₄×D₃	—	9	2	no	—
45	C₄×D₃	—	9	1	no	—
46	C₄×D₃	—	9	1	no	—
47	C₄×D₃	—	9	2	no	—
48	C₄×D₃	—	18	1	no	—
49	Dic₆	—	3	1	no	—
50	Dic₆	—	9	2	no	—
51	Dic₆	—	9	2	no	—
52	Dic₆	D₉	1	1	yes	characteristic, complemented
53	C₂×C₃²	C₂²×D₃	1	1	yes	characteristic
54	C₃⋊D₃	—	3	2	no	—
55	C₂×C₉	—	2	1	no	—
56	C₂×C₉	C₂²×D₃	1	1	yes	characteristic
57	D₉	—	3	2	no	—
58	D₉	—	6	2	no	—
59	C₂×Q₈	—	27	1	no	Sylow
60	C₂×D₃	—	9	1	no	—
61	C₂×D₃	—	9	1	no	—
62	C₂×D₃	—	18	1	no	—
63	C₃×C₄	—	2	1	no	—
64	C₃×C₄	—	3	2	no	—
65	C₃×C₄	—	9	2	no	—
66	C₃×C₄	C₂×D₉	1	1	yes	characteristic
67	C₃×C₄	D₃²	1	1	yes	characteristic
68	Dic₃	—	3	2	no	—
69	Dic₃	—	9	1	no	—
70	Dic₃	—	9	1	no	—
71	Dic₃	—	18	1	no	—
72	Dic₃	C₂×D₉	1	2	yes	—
73	C₃²	D₃×Q₈	1	1	yes	characteristic
74	C₉	—	2	1	no	—
75	C₉	D₃×Q₈	1	1	yes	characteristic, complemented
76	Q₈	—	3	1	no	—
77	Q₈	—	9	1	no	—
78	Q₈	—	27	2	no	—
79	C₂×C₄	—	27	2	no	—
80	C₂×C₄	—	27	1	no	—
81	C₂×C₃	—	2	1	no	—
82	C₂×C₃	C₂²×D₉	1	1	yes	characteristic
83	C₂×C₃	C₂×D₃²	1	1	yes	characteristic
84	D₃	—	9	2	no	—
85	D₃	—	9	2	no	—
86	D₃	—	18	2	no	—
87	C₂²	—	27	1	no	—
88	C₄	—	3	2	no	—
89	C₄	—	9	2	no	—
90	C₄	—	27	1	no	—
91	C₄	D₃×D₉	1	1	yes	characteristic
92	C₃	—	2	1	no	—
93	C₃	Q₈×D₉	1	1	yes	characteristic, complemented
94	C₃	#3797	1	1	yes	characteristic
95	C₂	—	27	2	no	—
96	C₂	C₂×D₃×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₃×D₉
commutator, cosocle	C₂×C₃×C₉	C₂³
Frattini	C₂×C₃	C₂×D₃²
Fitting	C₃×C₄×C₉	C₂²
socle	C₂×C₃²	C₂²×D₃
prime radical	C₂×C₃⋊D₉	C₂²
hypercenter	C₄	D₃×D₉
hypocenter	C₃×C₉	C₂×Q₈
LCS	G ▷ C₂×C₃×C₉ ▷ C₃×C₉
UCS	C₁ ◁ C₂ ◁ C₄

Complements

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

N	H ≅ G/N	type
2. C₉×Dic₆	C₂	semidirect
3. C₃×Dic₁₈	C₂	semidirect
5. #6189	C₂	semidirect
23. Dic₁₈	D₃	semidirect
25. C₃⋊D₉	Q₈	semidirect
41. C₃×C₉	C₂×Q₈	semidirect
52. Dic₆	D₉	semidirect
75. C₉	D₃×Q₈	semidirect
93. C₃	Q₈×D₉	semidirect

Maximal subgroups

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

subgroup	index
C₄×C₃⋊D₉	2
C₉×Dic₆	2
C₃×Dic₁₈	2
(C₃⋊D₉)⋊C₄	2
#6189	2
#3797	3
Q₈×D₉	3

Subgroups — (C3⋊D9)⋊Q8 #88636

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — (C₃⋊D₉)⋊Q₈ #88636