Subgroups — C₉²×Dic₆ #14517275

Order 1944.

396 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₄×C₉²	C₂	1	1	yes	maximal, characteristic
2	C₉²×Dic₃	C₂	1	2	yes	maximal
3	C₃×C₉×Dic₆	C₃	1	4	yes	maximal
4	Q₈×C₉²	—	3	1	no	maximal
5	C₂×C₃×C₉²	C₂²	1	1	yes	characteristic
6	C₃²×C₄×C₉	C₂×C₃	1	4	yes	—
7	C₃×C₉×Dic₃	C₂×C₃	1	8	yes	—
8	C₄×C₉²	—	2	4	no	—
9	C₄×C₉²	—	3	2	no	—
10	C₄×C₉²	D₃	1	1	yes	characteristic
11	C₃×C₉²	Q₈	1	1	yes	characteristic, complemented, Sylow
12	C₃²×Dic₆	C₃²	1	1	yes	characteristic
13	C₃×Q₈×C₉	—	3	4	no	—
14	C₉×Dic₆	C₉	1	12	yes	direct product factor
15	C₂×C₃²×C₉	C₂²×C₃	1	4	yes	—
16	C₂×C₉²	—	2	4	no	—
17	C₂×C₉²	C₂×D₃	1	1	yes	characteristic
18	C₃³×C₄	C₂×C₃²	1	1	yes	characteristic
19	C₃²×Dic₃	C₂×C₃²	1	2	yes	—
20	C₃×C₄×C₉	—	2	4	no	—
21	C₃×C₄×C₉	—	2	12	no	—
22	C₃×C₄×C₉	—	3	8	no	—
23	C₃×C₄×C₉	C₂×C₉	1	12	yes	—
24	C₃×C₄×C₉	C₃×D₃	1	4	yes	—
25	C₉×Dic₃	C₂×C₉	1	24	yes	—
26	C₃²×C₉	C₃×Q₈	1	4	yes	—
27	C₉²	—	2	4	no	—
28	C₉²	Dic₆	1	1	yes	characteristic, direct product factor
29	C₃²×Q₈	—	3	1	no	—
30	C₃×Dic₆	C₃×C₉	1	4	yes	—
31	Q₈×C₉	—	3	12	no	—
32	C₂×C₃³	C₂²×C₃²	1	1	yes	characteristic
33	C₂×C₃×C₉	—	2	4	no	—
34	C₂×C₃×C₉	—	2	12	no	—
35	C₂×C₃×C₉	C₂²×C₉	1	12	yes	—
36	C₂×C₃×C₉	C₂×C₃×D₃	1	4	yes	—
37	C₃²×C₄	—	2	4	no	—
38	C₃²×C₄	—	3	2	no	—
39	C₃²×C₄	C₂×C₃×C₉	1	4	yes	—
40	C₃²×C₄	C₃²×D₃	1	1	yes	characteristic
41	C₃×Dic₃	C₂×C₃×C₉	1	8	yes	—
42	C₄×C₉	—	2	12	no	—
43	C₄×C₉	—	3	24	no	—
44	C₄×C₉	D₃×C₉	1	12	yes	—
45	C₃³	C₃²×Q₈	1	1	yes	characteristic
46	C₃×C₉	—	2	4	no	—
47	C₃×C₉	—	2	12	no	—
48	C₃×C₉	Q₈×C₉	1	12	yes	complemented
49	C₃×C₉	C₃×Dic₆	1	4	yes	—
50	C₃×Q₈	—	3	4	no	—
51	Dic₆	C₉²	1	1	yes	characteristic, direct product factor
52	C₂×C₃²	—	2	4	no	—
53	C₂×C₃²	C₂²×C₃×C₉	1	4	yes	—
54	C₂×C₃²	C₂×C₃²×D₃	1	1	yes	characteristic
55	C₂×C₉	—	2	12	no	—
56	C₂×C₉	C₂×D₃×C₉	1	12	yes	—
57	C₃×C₄	—	2	4	no	—
58	C₃×C₄	—	3	8	no	—
59	C₃×C₄	C₂×C₉²	1	1	yes	characteristic
60	C₃×C₄	C₃×D₃×C₉	1	4	yes	—
61	Dic₃	C₂×C₉²	1	2	yes	—
62	C₃²	—	2	4	no	—
63	C₃²	C₃×Q₈×C₉	1	4	yes	—
64	C₃²	C₃²×Dic₆	1	1	yes	characteristic
65	C₉	—	2	12	no	—
66	C₉	C₉×Dic₆	1	12	yes	direct product factor
67	Q₈	—	3	1	no	Sylow
68	C₂×C₃	—	2	4	no	—
69	C₂×C₃	C₂²×C₉²	1	1	yes	characteristic
70	C₂×C₃	C₂×C₃×D₃×C₉	1	4	yes	—
71	C₄	—	3	2	no	—
72	C₄	D₃×C₉²	1	1	yes	characteristic
73	C₃	—	2	4	no	—
74	C₃	Q₈×C₉²	1	1	yes	characteristic, complemented
75	C₃	C₃×C₉×Dic₆	1	4	yes	—
76	C₂	C₂×D₃×C₉²	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₉²	C₂×D₃
commutator	C₂×C₃	C₂²×C₉²
Frattini	C₂×C₃²	C₂×C₃²×D₃
Fitting	C₃×C₄×C₉²	C₂
socle, prime radical, cosocle	C₂×C₃³	C₂²×C₃²
hypercenter	C₄×C₉²	D₃
hypocenter	C₃	Q₈×C₉²
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₉² ◁ C₄×C₉²

Complements

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

N	H ≅ G/N	type
11. C₃×C₉²	Q₈	semidirect
14. C₉×Dic₆	C₉	direct (N × H)
28. C₉²	Dic₆	direct (N × H)
48. C₃×C₉	Q₈×C₉	semidirect
51. Dic₆	C₉²	direct (N × H)
66. C₉	C₉×Dic₆	direct (N × H)
74. C₃	Q₈×C₉²	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₄×C₉²	2
C₉²×Dic₃	2
C₃×C₉×Dic₆	3
Q₈×C₉²	3

Subgroups — C92×Dic6 #14517275

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₉²×Dic₆ #14517275