Subgroups — C₂³×D₄₇₂ #21438812

Order 7552.

1976 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₂₃₆	C₂	1	2	yes	maximal, complemented
2	C₂²×D₄₇₂	C₂	1	28	yes	maximal, direct product factor
3	C₂³×C₈×C₅₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂⁴×D₅₉	—	2	2	no	—
5	C₂²×D₂₃₆	—	2	14	no	—
6	C₂²×D₂₃₆	C₂²	1	28	yes	complemented
7	C₂×D₄₇₂	C₂²	1	112	yes	direct product factor
8	C₂³×C₄×C₅₉	C₂²	1	1	yes	characteristic
9	C₂²×C₈×C₅₉	C₂²	1	14	yes	complemented
10	C₂⁴×C₅₉	D₄	1	1	yes	characteristic
11	C₂³×D₅₉	—	2	28	no	—
12	C₂³×D₅₉	—	4	16	no	—
13	C₂²×C₄×C₅₉	D₄	1	7	yes	—
14	C₂²×C₄×C₅₉	C₂³	1	7	yes	—
15	C₂×D₂₃₆	—	2	84	no	—
16	C₂×D₂₃₆	C₂³	1	56	yes	complemented
17	C₂×C₈×C₅₉	C₂³	1	28	yes	complemented
18	D₄₇₂	C₂³	1	64	yes	direct product factor
19	C₂³×C₅₉	D₈	1	8	yes	complemented
20	C₂³×C₅₉	C₂×D₄	1	7	yes	—
21	C₂²×D₅₉	—	2	56	no	—
22	C₂²×D₅₉	—	4	112	no	—
23	C₂×C₄×C₅₉	C₂×D₄	1	21	yes	—
24	C₂×C₄×C₅₉	C₂⁴	1	7	yes	—
25	D₂₃₆	—	2	56	no	—
26	D₂₃₆	C₂⁴	1	16	yes	complemented
27	C₈×C₅₉	C₂⁴	1	8	yes	complemented
28	C₂²×C₅₉	C₂×D₈	1	28	yes	complemented
29	C₂²×C₅₉	C₂²×D₄	1	7	yes	—
30	C₂×D₅₉	—	2	16	no	—
31	C₂×D₅₉	—	4	112	no	—
32	C₄×C₅₉	C₂²×D₄	1	7	yes	—
33	C₄×C₅₉	C₂⁵	1	1	yes	characteristic
34	C₂³×D₈	—	59	1	no	maximal, Sylow
35	C₂×C₅₉	C₂²×D₈	1	14	yes	complemented
36	C₂×C₅₉	C₂³×D₄	1	1	yes	characteristic
37	D₅₉	—	4	16	no	—
38	C₂³×D₄	—	59	2	no	—
39	C₂²×D₈	—	59	28	no	—
40	C₂³×C₈	D₅₉	1	1	yes	characteristic, complemented
41	C₅₉	C₂³×D₈	1	1	yes	characteristic, complemented, Sylow
42	C₂⁵	—	118	2	no	—
43	C₂²×D₄	—	59	28	no	—
44	C₂²×D₄	—	118	14	no	—
45	C₂³×C₄	C₂×D₅₉	1	1	yes	characteristic
46	C₂×D₈	—	59	112	no	—
47	C₂²×C₈	C₂×D₅₉	1	14	yes	complemented
48	C₂⁴	—	118	28	no	—
49	C₂⁴	—	236	16	no	—
50	C₂⁴	D₂₃₆	1	1	yes	characteristic
51	C₂×D₄	—	59	56	no	—
52	C₂×D₄	—	118	84	no	—
53	C₂²×C₄	D₂₃₆	1	7	yes	—
54	C₂²×C₄	C₂²×D₅₉	1	7	yes	—
55	D₈	—	59	64	no	—
56	C₂×C₈	C₂²×D₅₉	1	28	yes	complemented
57	C₂³	—	118	56	no	—
58	C₂³	—	236	112	no	—
59	C₂³	D₄₇₂	1	8	yes	direct product factor
60	C₂³	C₂×D₂₃₆	1	7	yes	—
61	D₄	—	59	16	no	—
62	D₄	—	118	56	no	—
63	C₂×C₄	C₂×D₂₃₆	1	21	yes	—
64	C₂×C₄	C₂³×D₅₉	1	7	yes	—
65	C₈	C₂³×D₅₉	1	8	yes	complemented
66	C₂²	—	118	16	no	—
67	C₂²	—	236	112	no	—
68	C₂²	C₂×D₄₇₂	1	28	yes	direct product factor
69	C₂²	C₂²×D₂₃₆	1	7	yes	—
70	C₄	C₂²×D₂₃₆	1	7	yes	—
71	C₄	C₂⁴×D₅₉	1	1	yes	characteristic
72	C₂	—	236	16	no	—
73	C₂	C₂²×D₄₇₂	1	14	yes	direct product factor
74	C₂	C₂³×D₂₃₆	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₂₃₆
commutator	C₄×C₅₉	C₂⁵
Frattini	C₄	C₂⁴×D₅₉
Fitting	C₂³×C₈×C₅₉	C₂
socle	C₂⁴×C₅₉	D₄
hypercenter	C₂³×C₈	D₅₉
hypocenter	C₅₉	C₂³×D₈
LCS	G ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×C₈

Complements

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

N	H ≅ G/N	type
1. C₂³×D₂₃₆	C₂	semidirect
2. C₂²×D₄₇₂	C₂	direct (N × H)
3. C₂³×C₈×C₅₉	C₂	semidirect
6. C₂²×D₂₃₆	C₂²	semidirect
7. C₂×D₄₇₂	C₂²	direct (N × H)
9. C₂²×C₈×C₅₉	C₂²	semidirect
16. C₂×D₂₃₆	C₂³	semidirect
17. C₂×C₈×C₅₉	C₂³	semidirect
18. D₄₇₂	C₂³	direct (N × H)
19. C₂³×C₅₉	D₈	semidirect
26. D₂₃₆	C₂⁴	semidirect
27. C₈×C₅₉	C₂⁴	semidirect
28. C₂²×C₅₉	C₂×D₈	semidirect
35. C₂×C₅₉	C₂²×D₈	semidirect
40. C₂³×C₈	D₅₉	semidirect
41. C₅₉	C₂³×D₈	semidirect
47. C₂²×C₈	C₂×D₅₉	semidirect
56. C₂×C₈	C₂²×D₅₉	semidirect
59. C₂³	D₄₇₂	direct (N × H)
65. C₈	C₂³×D₅₉	semidirect
68. C₂²	C₂×D₄₇₂	direct (N × H)
73. C₂	C₂²×D₄₇₂	direct (N × H)

Subgroups — C23×D472 #21438812

Conjugacy classes of subgroups

Complements

Subgroups — C₂³×D₄₇₂ #21438812