Subgroups — C₂⁴×D₃₆ #11919161

Order 1152.

15828 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×D₉	C₂	1	2	yes	maximal, complemented
2	C₂⁴×C₄×C₉	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂³×D₃₆	C₂	1	60	yes	maximal, direct product factor
4	C₂⁴×D₁₂	—	3	1	no	maximal
5	C₂⁵×C₉	C₂²	1	1	yes	characteristic
6	C₂⁴×D₉	—	2	32	no	—
7	C₂⁴×D₉	C₂²	1	60	yes	complemented
8	C₂³×C₄×C₉	C₂²	1	30	yes	complemented
9	C₂²×D₃₆	C₂²	1	560	yes	direct product factor
10	C₂⁵×D₃	—	3	2	no	—
11	C₂⁴×C₃×C₄	D₃	1	1	yes	characteristic
12	C₂³×D₁₂	—	3	60	no	—
13	C₂⁴×C₉	D₄	1	16	yes	complemented
14	C₂⁴×C₉	C₂³	1	15	yes	—
15	C₂³×D₉	—	2	480	no	—
16	C₂³×D₉	C₂³	1	280	yes	complemented
17	C₂²×C₄×C₉	C₂³	1	140	yes	complemented
18	C₂×D₃₆	C₂³	1	960	yes	direct product factor
19	C₂⁴×D₄	—	9	1	no	Sylow
20	C₂⁵×C₃	C₂×D₃	1	1	yes	characteristic
21	C₂⁴×D₃	—	3	60	no	—
22	C₂⁴×D₃	—	6	32	no	—
23	C₂³×C₃×C₄	C₂×D₃	1	30	yes	—
24	C₂²×D₁₂	—	3	560	no	—
25	C₂³×C₉	C₂×D₄	1	120	yes	complemented
26	C₂³×C₉	C₂⁴	1	35	yes	—
27	C₂²×D₉	—	2	1120	no	—
28	C₂²×D₉	C₂⁴	1	240	yes	complemented
29	C₂×C₄×C₉	C₂⁴	1	120	yes	complemented
30	D₃₆	C₂⁴	1	256	yes	direct product factor
31	C₂⁶	—	9	2	no	—
32	C₂³×D₄	—	9	60	no	—
33	C₂⁴×C₄	D₉	1	1	yes	characteristic, complemented
34	C₂⁴×C₃	D₁₂	1	16	yes	—
35	C₂⁴×C₃	C₂²×D₃	1	15	yes	—
36	C₂³×D₃	—	3	280	no	—
37	C₂³×D₃	—	6	480	no	—
38	C₂²×C₃×C₄	C₂²×D₃	1	140	yes	—
39	C₂×D₁₂	—	3	960	no	—
40	C₂²×C₉	C₂²×D₄	1	140	yes	complemented
41	C₂²×C₉	C₂⁵	1	15	yes	—
42	C₂×D₉	—	2	480	no	—
43	C₂×D₉	C₂⁵	1	32	yes	complemented
44	C₄×C₉	C₂⁵	1	16	yes	complemented
45	C₂⁵	—	9	60	no	—
46	C₂⁵	—	18	32	no	—
47	C₂⁵	C₂×D₉	1	1	yes	characteristic
48	C₂²×D₄	—	9	560	no	—
49	C₂³×C₄	C₂×D₉	1	30	yes	complemented
50	C₂³×C₃	C₂×D₁₂	1	120	yes	—
51	C₂³×C₃	C₂³×D₃	1	35	yes	—
52	C₂²×D₃	—	3	240	no	—
53	C₂²×D₃	—	6	1120	no	—
54	C₂×C₃×C₄	C₂³×D₃	1	120	yes	—
55	D₁₂	—	3	256	no	—
56	C₂×C₉	C₂³×D₄	1	30	yes	complemented
57	C₂×C₉	C₂⁶	1	1	yes	characteristic
58	D₉	—	2	32	no	—
59	C₂⁴	—	9	280	no	—
60	C₂⁴	—	18	480	no	—
61	C₂⁴	D₃₆	1	16	yes	direct product factor
62	C₂⁴	C₂²×D₉	1	15	yes	—
63	C₂×D₄	—	9	960	no	—
64	C₂²×C₄	C₂²×D₉	1	140	yes	complemented
65	C₂²×C₃	C₂²×D₁₂	1	140	yes	—
66	C₂²×C₃	C₂⁴×D₃	1	15	yes	—
67	C₂×D₃	—	3	32	no	—
68	C₂×D₃	—	6	480	no	—
69	C₃×C₄	C₂⁴×D₃	1	16	yes	—
70	C₉	C₂⁴×D₄	1	1	yes	characteristic, complemented, Sylow
71	C₂³	—	9	240	no	—
72	C₂³	—	18	1120	no	—
73	C₂³	C₂×D₃₆	1	120	yes	direct product factor
74	C₂³	C₂³×D₉	1	35	yes	—
75	D₄	—	9	256	no	—
76	C₂×C₄	C₂³×D₉	1	120	yes	complemented
77	C₂×C₃	C₂³×D₁₂	1	30	yes	—
78	C₂×C₃	C₂⁵×D₃	1	1	yes	characteristic
79	D₃	—	6	32	no	—
80	C₂²	—	9	32	no	—
81	C₂²	—	18	480	no	—
82	C₂²	C₂²×D₃₆	1	140	yes	direct product factor
83	C₂²	C₂⁴×D₉	1	15	yes	—
84	C₄	C₂⁴×D₉	1	16	yes	complemented
85	C₃	C₂⁴×D₁₂	1	1	yes	characteristic
86	C₂	—	18	32	no	—
87	C₂	C₂³×D₃₆	1	30	yes	direct product factor
88	C₂	C₂⁵×D₉	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁵	C₂×D₉
commutator, cosocle	C₂×C₉	C₂⁶
Frattini	C₂×C₃	C₂⁵×D₃
Fitting	C₂⁴×C₄×C₉	C₂
socle	C₂⁵×C₃	C₂×D₃
hypercenter	C₂⁴×C₄	D₉
hypocenter	C₉	C₂⁴×D₄
LCS	G ▷ C₂×C₉ ▷ C₉
UCS	C₁ ◁ C₂⁵ ◁ C₂⁴×C₄

Complements

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

N	H ≅ G/N	type
1. C₂⁵×D₉	C₂	semidirect
2. C₂⁴×C₄×C₉	C₂	semidirect
3. C₂³×D₃₆	C₂	direct (N × H)
7. C₂⁴×D₉	C₂²	semidirect
8. C₂³×C₄×C₉	C₂²	semidirect
9. C₂²×D₃₆	C₂²	direct (N × H)
13. C₂⁴×C₉	D₄	semidirect
16. C₂³×D₉	C₂³	semidirect
17. C₂²×C₄×C₉	C₂³	semidirect
18. C₂×D₃₆	C₂³	direct (N × H)
25. C₂³×C₉	C₂×D₄	semidirect
28. C₂²×D₉	C₂⁴	semidirect
29. C₂×C₄×C₉	C₂⁴	semidirect
30. D₃₆	C₂⁴	direct (N × H)
33. C₂⁴×C₄	D₉	semidirect
40. C₂²×C₉	C₂²×D₄	semidirect
43. C₂×D₉	C₂⁵	semidirect
44. C₄×C₉	C₂⁵	semidirect
49. C₂³×C₄	C₂×D₉	semidirect
56. C₂×C₉	C₂³×D₄	semidirect
61. C₂⁴	D₃₆	direct (N × H)
64. C₂²×C₄	C₂²×D₉	semidirect
70. C₉	C₂⁴×D₄	semidirect
73. C₂³	C₂×D₃₆	direct (N × H)
76. C₂×C₄	C₂³×D₉	semidirect
82. C₂²	C₂²×D₃₆	direct (N × H)
84. C₄	C₂⁴×D₉	semidirect
87. C₂	C₂³×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
C₂⁵×D₉	2
C₂⁴×C₄×C₉	2
C₂³×D₃₆	2
C₂⁴×D₁₂	3

Subgroups — C24×D36 #11919161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×D₃₆ #11919161