Subgroups — C₂⁴×Dic₁₈ #11919175

Order 1152.

9396 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×C₄×C₉	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×Dic₉	C₂	1	2	yes	maximal
3	C₂³×Dic₁₈	C₂	1	60	yes	maximal, direct product factor
4	C₂⁴×Dic₆	—	3	1	no	maximal
5	C₂⁵×C₉	C₂²	1	1	yes	characteristic
6	C₂³×C₄×C₉	C₂²	1	30	yes	—
7	C₂³×Dic₉	C₂²	1	60	yes	—
8	C₂²×Dic₁₈	C₂²	1	560	yes	direct product factor
9	C₂⁴×C₃×C₄	D₃	1	1	yes	characteristic
10	C₂⁴×Dic₃	—	3	2	no	—
11	C₂³×Dic₆	—	3	60	no	—
12	C₂⁴×C₉	Q₈	1	16	yes	complemented
13	C₂⁴×C₉	C₂³	1	15	yes	—
14	C₂²×C₄×C₉	C₂³	1	140	yes	—
15	C₂²×Dic₉	C₂³	1	280	yes	—
16	C₂×Dic₁₈	C₂³	1	960	yes	direct product factor
17	C₂⁴×Q₈	—	9	1	no	Sylow
18	C₂⁵×C₃	C₂×D₃	1	1	yes	characteristic
19	C₂³×C₃×C₄	C₂×D₃	1	30	yes	—
20	C₂³×Dic₃	—	3	60	no	—
21	C₂²×Dic₆	—	3	560	no	—
22	C₂³×C₉	C₂×Q₈	1	120	yes	complemented
23	C₂³×C₉	C₂⁴	1	35	yes	—
24	C₂×C₄×C₉	C₂⁴	1	120	yes	—
25	C₂×Dic₉	C₂⁴	1	240	yes	—
26	Dic₁₈	C₂⁴	1	256	yes	direct product factor
27	C₂³×Q₈	—	9	60	no	—
28	C₂⁴×C₄	—	9	2	no	—
29	C₂⁴×C₄	D₉	1	1	yes	characteristic
30	C₂⁴×C₃	Dic₆	1	16	yes	—
31	C₂⁴×C₃	C₂²×D₃	1	15	yes	—
32	C₂²×C₃×C₄	C₂²×D₃	1	140	yes	—
33	C₂²×Dic₃	—	3	280	no	—
34	C₂×Dic₆	—	3	960	no	—
35	C₂²×C₉	C₂²×Q₈	1	140	yes	complemented
36	C₂²×C₉	C₂⁵	1	15	yes	—
37	C₄×C₉	C₂⁵	1	16	yes	—
38	Dic₉	C₂⁵	1	32	yes	—
39	C₂⁵	C₂×D₉	1	1	yes	characteristic
40	C₂²×Q₈	—	9	560	no	—
41	C₂³×C₄	—	9	60	no	—
42	C₂³×C₄	C₂×D₉	1	30	yes	—
43	C₂³×C₃	C₂×Dic₆	1	120	yes	—
44	C₂³×C₃	C₂³×D₃	1	35	yes	—
45	C₂×C₃×C₄	C₂³×D₃	1	120	yes	—
46	C₂×Dic₃	—	3	240	no	—
47	Dic₆	—	3	256	no	—
48	C₂×C₉	C₂³×Q₈	1	30	yes	complemented
49	C₂×C₉	C₂⁶	1	1	yes	characteristic
50	C₂⁴	Dic₁₈	1	16	yes	direct product factor
51	C₂⁴	C₂²×D₉	1	15	yes	—
52	C₂×Q₈	—	9	960	no	—
53	C₂²×C₄	—	9	280	no	—
54	C₂²×C₄	C₂²×D₉	1	140	yes	—
55	C₂²×C₃	C₂²×Dic₆	1	140	yes	—
56	C₂²×C₃	C₂⁴×D₃	1	15	yes	—
57	C₃×C₄	C₂⁴×D₃	1	16	yes	—
58	Dic₃	—	3	32	no	—
59	C₉	C₂⁴×Q₈	1	1	yes	characteristic, complemented, Sylow
60	C₂³	C₂×Dic₁₈	1	120	yes	direct product factor
61	C₂³	C₂³×D₉	1	35	yes	—
62	Q₈	—	9	256	no	—
63	C₂×C₄	—	9	240	no	—
64	C₂×C₄	C₂³×D₉	1	120	yes	—
65	C₂×C₃	C₂³×Dic₆	1	30	yes	—
66	C₂×C₃	C₂⁵×D₃	1	1	yes	characteristic
67	C₂²	C₂²×Dic₁₈	1	140	yes	direct product factor
68	C₂²	C₂⁴×D₉	1	15	yes	—
69	C₄	—	9	32	no	—
70	C₄	C₂⁴×D₉	1	16	yes	—
71	C₃	C₂⁴×Dic₆	1	1	yes	characteristic
72	C₂	C₂³×Dic₁₈	1	30	yes	direct product factor
73	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, prime radical	C₂⁵×C₃	C₂×D₃
hypercenter	C₂⁴×C₄	D₉
hypocenter	C₉	C₂⁴×Q₈
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
3. C₂³×Dic₁₈	C₂	direct (N × H)
8. C₂²×Dic₁₈	C₂²	direct (N × H)
12. C₂⁴×C₉	Q₈	semidirect
16. C₂×Dic₁₈	C₂³	direct (N × H)
22. C₂³×C₉	C₂×Q₈	semidirect
26. Dic₁₈	C₂⁴	direct (N × H)
35. C₂²×C₉	C₂²×Q₈	semidirect
48. C₂×C₉	C₂³×Q₈	semidirect
50. C₂⁴	Dic₁₈	direct (N × H)
59. C₉	C₂⁴×Q₈	semidirect
60. C₂³	C₂×Dic₁₈	direct (N × H)
67. C₂²	C₂²×Dic₁₈	direct (N × H)
72. C₂	C₂³×Dic₁₈	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×C₄×C₉	2
C₂⁴×Dic₉	2
C₂³×Dic₁₈	2
C₂⁴×Dic₆	3

Subgroups — C24×Dic18 #11919175

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×Dic₁₈ #11919175