Subgroups — C₂⁴×C₄×D₃ #87553

Order 384.

10552 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂⁴×C₃×C₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂⁴×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂³×C₄×D₃	C₂	1	60	yes	maximal, direct product factor
5	C₂⁵×C₄	—	3	1	no	maximal, Sylow
6	C₂⁵×C₃	C₂²	1	1	yes	characteristic
7	C₂⁴×D₃	C₄	1	32	yes	direct product factor
8	C₂⁴×D₃	C₂²	1	30	yes	—
9	C₂³×C₃×C₄	C₂²	1	30	yes	complemented
10	C₂³×Dic₃	C₂²	1	30	yes	complemented
11	C₂²×C₄×D₃	C₂²	1	560	yes	direct product factor
12	C₂⁶	—	3	1	no	—
13	C₂⁴×C₄	—	3	1	no	—
14	C₂⁴×C₄	—	3	60	no	—
15	C₂⁴×C₄	D₃	1	1	yes	characteristic, direct product factor
16	C₂⁴×C₃	C₂×C₄	1	16	yes	complemented
17	C₂⁴×C₃	C₂³	1	15	yes	—
18	C₂³×D₃	C₂×C₄	1	480	yes	direct product factor
19	C₂³×D₃	C₂³	1	140	yes	—
20	C₂²×C₃×C₄	C₂³	1	140	yes	complemented
21	C₂²×Dic₃	C₂³	1	140	yes	complemented
22	C₂×C₄×D₃	C₂³	1	960	yes	direct product factor
23	C₂⁵	—	3	32	no	—
24	C₂⁵	—	3	30	no	—
25	C₂⁵	C₂×D₃	1	1	yes	characteristic
26	C₂³×C₄	—	3	30	no	—
27	C₂³×C₄	—	3	560	no	—
28	C₂³×C₄	C₂×D₃	1	30	yes	direct product factor
29	C₂³×C₃	C₂²×C₄	1	120	yes	complemented
30	C₂³×C₃	C₂⁴	1	35	yes	—
31	C₂²×D₃	C₂²×C₄	1	1120	yes	direct product factor
32	C₂²×D₃	C₂⁴	1	120	yes	—
33	C₂×C₃×C₄	C₂⁴	1	120	yes	complemented
34	C₂×Dic₃	C₂⁴	1	120	yes	complemented
35	C₄×D₃	C₂⁴	1	256	yes	direct product factor
36	C₂⁴	—	3	480	no	—
37	C₂⁴	—	3	140	no	—
38	C₂⁴	C₄×D₃	1	16	yes	direct product factor
39	C₂⁴	C₂²×D₃	1	15	yes	—
40	C₂²×C₄	—	3	140	no	—
41	C₂²×C₄	—	3	960	no	—
42	C₂²×C₄	C₂²×D₃	1	140	yes	direct product factor
43	C₂²×C₃	C₂³×C₄	1	140	yes	complemented
44	C₂²×C₃	C₂⁵	1	15	yes	—
45	C₂×D₃	C₂³×C₄	1	480	yes	direct product factor
46	C₂×D₃	C₂⁵	1	16	yes	—
47	C₃×C₄	C₂⁵	1	16	yes	complemented
48	Dic₃	C₂⁵	1	16	yes	complemented
49	C₂³	—	3	1120	no	—
50	C₂³	—	3	120	no	—
51	C₂³	C₂×C₄×D₃	1	120	yes	direct product factor
52	C₂³	C₂³×D₃	1	35	yes	—
53	C₂×C₄	—	3	120	no	—
54	C₂×C₄	—	3	256	no	—
55	C₂×C₄	C₂³×D₃	1	120	yes	direct product factor
56	C₂×C₃	C₂⁴×C₄	1	30	yes	complemented
57	C₂×C₃	C₂⁶	1	1	yes	characteristic
58	D₃	C₂⁴×C₄	1	32	yes	direct product factor
59	C₂²	—	3	480	no	—
60	C₂²	—	3	16	no	—
61	C₂²	C₂²×C₄×D₃	1	140	yes	direct product factor
62	C₂²	C₂⁴×D₃	1	15	yes	—
63	C₄	—	3	16	no	—
64	C₄	C₂⁴×D₃	1	16	yes	direct product factor
65	C₃	C₂⁵×C₄	1	1	yes	characteristic, complemented, Sylow
66	C₂	—	3	32	no	—
67	C₂	C₂³×C₄×D₃	1	30	yes	direct product factor
68	C₂	C₂⁵×D₃	1	1	yes	characteristic

	subgroup	G/H
center, hypercenter	C₂⁴×C₄	D₃
commutator, hypocenter	C₃	C₂⁵×C₄
Frattini	C₂	C₂⁵×D₃
Fitting	C₂⁴×C₃×C₄	C₂
socle	C₂⁵×C₃	C₂²
prime radical	C₂⁵×D₃	C₂
cosocle	C₂×C₃	C₂⁶
LCS	G ▷ C₃
UCS	C₁ ◁ C₂⁴×C₄

Complements

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

N	H ≅ G/N	type
2. C₂⁴×C₃×C₄	C₂	semidirect
3. C₂⁴×Dic₃	C₂	semidirect
4. C₂³×C₄×D₃	C₂	direct (N × H)
7. C₂⁴×D₃	C₄	direct (N × H)
9. C₂³×C₃×C₄	C₂²	semidirect
10. C₂³×Dic₃	C₂²	semidirect
11. C₂²×C₄×D₃	C₂²	direct (N × H)
15. C₂⁴×C₄	D₃	direct (N × H)
16. C₂⁴×C₃	C₂×C₄	semidirect
18. C₂³×D₃	C₂×C₄	direct (N × H)
20. C₂²×C₃×C₄	C₂³	semidirect
21. C₂²×Dic₃	C₂³	semidirect
22. C₂×C₄×D₃	C₂³	direct (N × H)
28. C₂³×C₄	C₂×D₃	direct (N × H)
29. C₂³×C₃	C₂²×C₄	semidirect
31. C₂²×D₃	C₂²×C₄	direct (N × H)
33. C₂×C₃×C₄	C₂⁴	semidirect
34. C₂×Dic₃	C₂⁴	semidirect
35. C₄×D₃	C₂⁴	direct (N × H)
38. C₂⁴	C₄×D₃	direct (N × H)
42. C₂²×C₄	C₂²×D₃	direct (N × H)
43. C₂²×C₃	C₂³×C₄	semidirect
45. C₂×D₃	C₂³×C₄	direct (N × H)
47. C₃×C₄	C₂⁵	semidirect
48. Dic₃	C₂⁵	semidirect
51. C₂³	C₂×C₄×D₃	direct (N × H)
55. C₂×C₄	C₂³×D₃	direct (N × H)
56. C₂×C₃	C₂⁴×C₄	semidirect
58. D₃	C₂⁴×C₄	direct (N × H)
61. C₂²	C₂²×C₄×D₃	direct (N × H)
64. C₄	C₂⁴×D₃	direct (N × H)
65. C₃	C₂⁵×C₄	semidirect
67. C₂	C₂³×C₄×D₃	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×D₃	2
C₂⁴×C₃×C₄	2
C₂⁴×Dic₃	2
C₂³×C₄×D₃	2
C₂⁵×C₄	3

Subgroups — C24×C4×D3 #87553

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₄×D₃ #87553