Subgroups — C₂³×Dic₅₂ #13129559

Order 1664.

1464 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Dic₂₆	C₂	1	2	yes	maximal
2	C₂³×C₈×C₁₃	C₂	1	1	yes	maximal, characteristic
3	C₂²×Dic₅₂	C₂	1	28	yes	maximal, direct product factor
4	C₂³×C₄×C₁₃	C₂²	1	1	yes	characteristic
5	C₂³×Dic₁₃	—	2	2	no	—
6	C₂²×Dic₂₆	—	2	14	no	—
7	C₂²×Dic₂₆	C₂²	1	28	yes	—
8	C₂²×C₈×C₁₃	C₂²	1	14	yes	—
9	C₂×Dic₅₂	C₂²	1	112	yes	direct product factor
10	C₂⁴×C₁₃	D₄	1	1	yes	characteristic
11	C₂²×C₄×C₁₃	D₄	1	7	yes	—
12	C₂²×C₄×C₁₃	C₂³	1	7	yes	—
13	C₂²×Dic₁₃	—	2	28	no	—
14	C₂×Dic₂₆	—	2	84	no	—
15	C₂×Dic₂₆	C₂³	1	56	yes	—
16	C₂×C₈×C₁₃	C₂³	1	28	yes	—
17	Dic₅₂	C₂³	1	64	yes	direct product factor
18	C₂³×Q₁₆	—	13	1	no	maximal, Sylow
19	C₂³×C₁₃	Q₁₆	1	8	yes	complemented
20	C₂³×C₁₃	C₂×D₄	1	7	yes	—
21	C₂×C₄×C₁₃	C₂×D₄	1	21	yes	—
22	C₂×C₄×C₁₃	C₂⁴	1	7	yes	—
23	C₂×Dic₁₃	—	2	56	no	—
24	Dic₂₆	—	2	56	no	—
25	Dic₂₆	C₂⁴	1	16	yes	—
26	C₈×C₁₃	C₂⁴	1	8	yes	—
27	C₂³×Q₈	—	13	2	no	—
28	C₂²×Q₁₆	—	13	28	no	—
29	C₂³×C₈	D₁₃	1	1	yes	characteristic
30	C₂²×C₁₃	C₂×Q₁₆	1	28	yes	complemented
31	C₂²×C₁₃	C₂²×D₄	1	7	yes	—
32	C₄×C₁₃	C₂²×D₄	1	7	yes	—
33	C₄×C₁₃	C₂⁵	1	1	yes	characteristic
34	Dic₁₃	—	2	16	no	—
35	C₂²×Q₈	—	13	28	no	—
36	C₂²×Q₈	—	26	14	no	—
37	C₂³×C₄	—	26	2	no	—
38	C₂³×C₄	C₂×D₁₃	1	1	yes	characteristic
39	C₂×Q₁₆	—	13	112	no	—
40	C₂²×C₈	C₂×D₁₃	1	14	yes	—
41	C₂×C₁₃	C₂²×Q₁₆	1	14	yes	complemented
42	C₂×C₁₃	C₂³×D₄	1	1	yes	characteristic
43	C₂⁴	D₅₂	1	1	yes	characteristic
44	C₂×Q₈	—	13	56	no	—
45	C₂×Q₈	—	26	84	no	—
46	C₂²×C₄	—	26	28	no	—
47	C₂²×C₄	D₅₂	1	7	yes	—
48	C₂²×C₄	C₂²×D₁₃	1	7	yes	—
49	Q₁₆	—	13	64	no	—
50	C₂×C₈	C₂²×D₁₃	1	28	yes	—
51	C₁₃	C₂³×Q₁₆	1	1	yes	characteristic, complemented, Sylow
52	C₂³	Dic₅₂	1	8	yes	direct product factor
53	C₂³	C₂×D₅₂	1	7	yes	—
54	Q₈	—	13	16	no	—
55	Q₈	—	26	56	no	—
56	C₂×C₄	—	26	56	no	—
57	C₂×C₄	C₂×D₅₂	1	21	yes	—
58	C₂×C₄	C₂³×D₁₃	1	7	yes	—
59	C₈	C₂³×D₁₃	1	8	yes	—
60	C₂²	C₂×Dic₅₂	1	28	yes	direct product factor
61	C₂²	C₂²×D₅₂	1	7	yes	—
62	C₄	—	26	16	no	—
63	C₄	C₂²×D₅₂	1	7	yes	—
64	C₄	C₂⁴×D₁₃	1	1	yes	characteristic
65	C₂	C₂²×Dic₅₂	1	14	yes	direct product factor
66	C₂	C₂³×D₅₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₅₂
commutator, cosocle	C₄×C₁₃	C₂⁵
Frattini	C₄	C₂⁴×D₁₃
Fitting	C₂³×C₈×C₁₃	C₂
socle, prime radical	C₂⁴×C₁₃	D₄
hypercenter	C₂³×C₈	D₁₃
hypocenter	C₁₃	C₂³×Q₁₆
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
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×Dic₅₂	C₂	direct (N × H)
9. C₂×Dic₅₂	C₂²	direct (N × H)
17. Dic₅₂	C₂³	direct (N × H)
19. C₂³×C₁₃	Q₁₆	semidirect
30. C₂²×C₁₃	C₂×Q₁₆	semidirect
41. C₂×C₁₃	C₂²×Q₁₆	semidirect
51. C₁₃	C₂³×Q₁₆	semidirect
52. C₂³	Dic₅₂	direct (N × H)
60. C₂²	C₂×Dic₅₂	direct (N × H)
65. C₂	C₂²×Dic₅₂	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×Dic₂₆	2
C₂³×C₈×C₁₃	2
C₂²×Dic₅₂	2
C₂³×Q₁₆	13

Subgroups — C23×Dic52 #13129559

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×Dic₅₂ #13129559