Subgroups — C₂×C₃×D₃₆ #88696

Order 432.

178 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₉	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×C₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₃₆	C₂	1	4	yes	maximal, direct product factor
4	C₂×C₃×D₁₂	—	3	1	no	maximal
5	C₂×D₃₆	C₃	1	1	yes	maximal, characteristic, direct product factor
6	C₂²×C₃×C₉	C₂²	1	1	yes	characteristic
7	C₂×C₃×D₉	—	2	4	no	—
8	C₂×C₃×D₉	C₂²	1	4	yes	complemented
9	C₃×C₄×C₉	C₂²	1	2	yes	complemented
10	C₂²×C₃×D₃	—	3	2	no	—
11	C₂×C₃²×C₄	D₃	1	1	yes	characteristic
12	C₃×D₁₂	—	3	4	no	—
13	C₂²×D₉	C₂×C₃	1	2	yes	complemented
14	C₂×C₄×C₉	—	2	1	no	—
15	C₂×C₄×C₉	C₂×C₃	1	1	yes	characteristic, complemented
16	D₃₆	C₂×C₃	1	4	yes	direct product factor
17	C₂×C₃×C₉	D₄	1	2	yes	complemented
18	C₂×C₃×C₉	C₂³	1	1	yes	characteristic
19	C₃×D₉	—	2	4	no	—
20	C₂×C₃×D₄	—	9	1	no	—
21	C₂×D₁₂	—	3	1	no	—
22	C₂²×C₃²	C₂×D₃	1	1	yes	characteristic
23	C₂×C₃×D₃	—	3	4	no	—
24	C₂×C₃×D₃	—	6	4	no	—
25	C₃²×C₄	C₂×D₃	1	2	yes	—
26	C₂²×C₉	—	2	1	no	—
27	C₂²×C₉	C₂²×C₃	1	1	yes	characteristic
28	C₂×D₉	—	2	4	no	—
29	C₂×D₉	C₂²×C₃	1	4	yes	complemented
30	C₄×C₉	—	2	2	no	—
31	C₄×C₉	C₂²×C₃	1	2	yes	complemented
32	C₃×C₉	C₂×D₄	1	1	yes	characteristic, complemented, Sylow
33	C₂³×C₃	—	9	2	no	—
34	C₂²×D₃	—	3	2	no	—
35	C₃×D₄	—	9	4	no	—
36	C₂×C₃×C₄	—	2	1	no	—
37	C₂×C₃×C₄	D₉	1	1	yes	characteristic, complemented
38	C₂×C₃×C₄	C₃×D₃	1	1	yes	characteristic
39	D₁₂	—	3	4	no	—
40	C₂×C₃²	D₁₂	1	2	yes	—
41	C₂×C₃²	C₂²×D₃	1	1	yes	characteristic
42	C₃×D₃	—	6	4	no	—
43	C₂×C₉	—	2	2	no	—
44	C₂×C₉	—	2	1	no	—
45	C₂×C₉	C₃×D₄	1	2	yes	complemented
46	C₂×C₉	C₂³×C₃	1	1	yes	characteristic
47	D₉	—	2	4	no	—
48	C₂×D₄	—	9	1	no	Sylow
49	C₂²×C₃	—	2	1	no	—
50	C₂²×C₃	—	9	4	no	—
51	C₂²×C₃	—	18	4	no	—
52	C₂²×C₃	C₂×D₉	1	1	yes	characteristic
53	C₂²×C₃	C₂×C₃×D₃	1	1	yes	characteristic
54	C₂×D₃	—	3	4	no	—
55	C₂×D₃	—	6	4	no	—
56	C₃×C₄	—	2	2	no	—
57	C₃×C₄	C₂×D₉	1	2	yes	complemented
58	C₃×C₄	C₂×C₃×D₃	1	2	yes	—
59	C₃²	C₂×D₁₂	1	1	yes	characteristic
60	C₉	—	2	1	no	—
61	C₉	C₂×C₃×D₄	1	1	yes	characteristic, complemented
62	C₂³	—	9	2	no	—
63	D₄	—	9	4	no	—
64	C₂×C₄	C₃×D₉	1	1	yes	characteristic, complemented
65	C₂×C₃	—	2	2	no	—
66	C₂×C₃	—	2	1	no	—
67	C₂×C₃	—	18	4	no	—
68	C₂×C₃	D₃₆	1	2	yes	direct product factor
69	C₂×C₃	C₂²×D₉	1	1	yes	characteristic
70	C₂×C₃	C₃×D₁₂	1	2	yes	—
71	C₂×C₃	C₂²×C₃×D₃	1	1	yes	characteristic
72	D₃	—	6	4	no	—
73	C₂²	—	9	4	no	—
74	C₂²	—	18	4	no	—
75	C₂²	C₂×C₃×D₉	1	1	yes	characteristic
76	C₄	C₂×C₃×D₉	1	2	yes	complemented
77	C₃	—	2	1	no	—
78	C₃	C₂×D₃₆	1	1	yes	characteristic, direct product factor
79	C₃	C₂×C₃×D₁₂	1	1	yes	characteristic
80	C₂	—	18	4	no	—
81	C₂	C₃×D₃₆	1	2	yes	direct product factor
82	C₂	C₂²×C₃×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₉
commutator, cosocle	C₂×C₉	C₂³×C₃
Frattini	C₂×C₃	C₂²×C₃×D₃
Fitting	C₂×C₃×C₄×C₉	C₂
socle	C₂²×C₃²	C₂×D₃
hypercenter	C₂×C₃×C₄	D₉
hypocenter	C₉	C₂×C₃×D₄
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₉	C₂	semidirect
2. C₂×C₃×C₄×C₉	C₂	semidirect
3. C₃×D₃₆	C₂	direct (N × H)
5. C₂×D₃₆	C₃	direct (N × H)
8. C₂×C₃×D₉	C₂²	semidirect
9. C₃×C₄×C₉	C₂²	semidirect
13. C₂²×D₉	C₂×C₃	semidirect
15. C₂×C₄×C₉	C₂×C₃	semidirect
16. D₃₆	C₂×C₃	direct (N × H)
17. C₂×C₃×C₉	D₄	semidirect
29. C₂×D₉	C₂²×C₃	semidirect
31. C₄×C₉	C₂²×C₃	semidirect
32. C₃×C₉	C₂×D₄	semidirect
37. C₂×C₃×C₄	D₉	semidirect
45. C₂×C₉	C₃×D₄	semidirect
57. C₃×C₄	C₂×D₉	semidirect
61. C₉	C₂×C₃×D₄	semidirect
64. C₂×C₄	C₃×D₉	semidirect
68. C₂×C₃	D₃₆	direct (N × H)
76. C₄	C₂×C₃×D₉	semidirect
78. C₃	C₂×D₃₆	direct (N × H)
81. C₂	C₃×D₃₆	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×C₃×D₉	2
C₂×C₃×C₄×C₉	2
C₃×D₃₆	2
C₂×C₃×D₁₂	3
C₂×D₃₆	3

Subgroups — C2×C3×D36 #88696

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×D₃₆ #88696