Subgroups — C₂³×Dic₁₂ #87151

Order 384.

1464 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Dic₆	C₂	1	2	yes	maximal
2	C₂³×C₃×C₈	C₂	1	1	yes	maximal, characteristic
3	C₂²×Dic₁₂	C₂	1	28	yes	maximal, direct product factor
4	C₂³×Q₁₆	—	3	1	no	maximal, Sylow
5	C₂³×C₃×C₄	C₂²	1	1	yes	characteristic
6	C₂³×Dic₃	—	2	2	no	—
7	C₂²×Dic₆	—	2	14	no	—
8	C₂²×Dic₆	C₂²	1	28	yes	—
9	C₂²×C₃×C₈	C₂²	1	14	yes	—
10	C₂×Dic₁₂	C₂²	1	112	yes	direct product factor
11	C₂³×Q₈	—	3	2	no	—
12	C₂²×Q₁₆	—	3	28	no	—
13	C₂³×C₈	D₃	1	1	yes	characteristic
14	C₂⁴×C₃	D₄	1	1	yes	characteristic
15	C₂²×C₃×C₄	D₄	1	7	yes	—
16	C₂²×C₃×C₄	C₂³	1	7	yes	—
17	C₂²×Dic₃	—	2	28	no	—
18	C₂×Dic₆	—	2	84	no	—
19	C₂×Dic₆	C₂³	1	56	yes	—
20	C₂×C₃×C₈	C₂³	1	28	yes	—
21	Dic₁₂	C₂³	1	64	yes	direct product factor
22	C₂²×Q₈	—	3	28	no	—
23	C₂²×Q₈	—	6	14	no	—
24	C₂³×C₄	—	6	2	no	—
25	C₂³×C₄	C₂×D₃	1	1	yes	characteristic
26	C₂×Q₁₆	—	3	112	no	—
27	C₂²×C₈	C₂×D₃	1	14	yes	—
28	C₂³×C₃	Q₁₆	1	8	yes	complemented
29	C₂³×C₃	C₂×D₄	1	7	yes	—
30	C₂×C₃×C₄	C₂×D₄	1	21	yes	—
31	C₂×C₃×C₄	C₂⁴	1	7	yes	—
32	C₂×Dic₃	—	2	56	no	—
33	Dic₆	—	2	56	no	—
34	Dic₆	C₂⁴	1	16	yes	—
35	C₃×C₈	C₂⁴	1	8	yes	—
36	C₂⁴	D₁₂	1	1	yes	characteristic
37	C₂×Q₈	—	3	56	no	—
38	C₂×Q₈	—	6	84	no	—
39	C₂²×C₄	—	6	28	no	—
40	C₂²×C₄	D₁₂	1	7	yes	—
41	C₂²×C₄	C₂²×D₃	1	7	yes	—
42	Q₁₆	—	3	64	no	—
43	C₂×C₈	C₂²×D₃	1	28	yes	—
44	C₂²×C₃	C₂×Q₁₆	1	28	yes	complemented
45	C₂²×C₃	C₂²×D₄	1	7	yes	—
46	C₃×C₄	C₂²×D₄	1	7	yes	—
47	C₃×C₄	C₂⁵	1	1	yes	characteristic
48	Dic₃	—	2	16	no	—
49	C₂³	Dic₁₂	1	8	yes	direct product factor
50	C₂³	C₂×D₁₂	1	7	yes	—
51	Q₈	—	3	16	no	—
52	Q₈	—	6	56	no	—
53	C₂×C₄	—	6	56	no	—
54	C₂×C₄	C₂×D₁₂	1	21	yes	—
55	C₂×C₄	C₂³×D₃	1	7	yes	—
56	C₈	C₂³×D₃	1	8	yes	—
57	C₂×C₃	C₂²×Q₁₆	1	14	yes	complemented
58	C₂×C₃	C₂³×D₄	1	1	yes	characteristic
59	C₂²	C₂×Dic₁₂	1	28	yes	direct product factor
60	C₂²	C₂²×D₁₂	1	7	yes	—
61	C₄	—	6	16	no	—
62	C₄	C₂²×D₁₂	1	7	yes	—
63	C₄	C₂⁴×D₃	1	1	yes	characteristic
64	C₃	C₂³×Q₁₆	1	1	yes	characteristic, complemented, Sylow
65	C₂	C₂²×Dic₁₂	1	14	yes	direct product factor
66	C₂	C₂³×D₁₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₁₂
commutator, cosocle	C₃×C₄	C₂⁵
Frattini	C₄	C₂⁴×D₃
Fitting	C₂³×C₃×C₈	C₂
socle, prime radical	C₂⁴×C₃	D₄
hypercenter	C₂³×C₈	D₃
hypocenter	C₃	C₂³×Q₁₆
LCS	G ▷ C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
3. C₂²×Dic₁₂	C₂	direct (N × H)
10. C₂×Dic₁₂	C₂²	direct (N × H)
21. Dic₁₂	C₂³	direct (N × H)
28. C₂³×C₃	Q₁₆	semidirect
44. C₂²×C₃	C₂×Q₁₆	semidirect
49. C₂³	Dic₁₂	direct (N × H)
57. C₂×C₃	C₂²×Q₁₆	semidirect
59. C₂²	C₂×Dic₁₂	direct (N × H)
64. C₃	C₂³×Q₁₆	semidirect
65. C₂	C₂²×Dic₁₂	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×Dic₆	2
C₂³×C₃×C₈	2
C₂²×Dic₁₂	2
C₂³×Q₁₆	3

Subgroups — C23×Dic12 #87151

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×Dic₁₂ #87151