Subgroups — C₂³×Dic₄₇₂ #29495171

Order 15104.

2078 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×Dic₂₃₆	C₂	1	2	yes	maximal
2	C₂²×Dic₄₇₂	C₂	1	28	yes	maximal, direct product factor
3	C₂³×C₁₆×C₅₉	C₂	1	1	yes	maximal, characteristic
4	C₂³×Dic₁₁₈	—	2	2	no	—
5	C₂²×Dic₂₃₆	—	2	14	no	—
6	C₂²×Dic₂₃₆	C₂²	1	28	yes	—
7	C₂×Dic₄₇₂	C₂²	1	112	yes	direct product factor
8	C₂³×C₈×C₅₉	C₂²	1	1	yes	characteristic
9	C₂²×C₁₆×C₅₉	C₂²	1	14	yes	—
10	C₂²×Dic₁₁₈	—	2	28	no	—
11	C₂²×Dic₁₁₈	—	4	14	no	—
12	C₂³×Dic₅₉	—	4	2	no	—
13	C₂×Dic₂₃₆	—	2	84	no	—
14	C₂×Dic₂₃₆	C₂³	1	56	yes	—
15	Dic₄₇₂	C₂³	1	64	yes	direct product factor
16	C₂³×C₄×C₅₉	D₄	1	1	yes	characteristic
17	C₂²×C₈×C₅₉	D₄	1	7	yes	—
18	C₂²×C₈×C₅₉	C₂³	1	7	yes	—
19	C₂×C₁₆×C₅₉	C₂³	1	28	yes	—
20	C₂⁴×C₅₉	D₈	1	1	yes	characteristic
21	C₂²×C₄×C₅₉	D₈	1	7	yes	—
22	C₂²×C₄×C₅₉	C₂×D₄	1	7	yes	—
23	C₂²×Dic₅₉	—	4	28	no	—
24	C₂×Dic₁₁₈	—	2	56	no	—
25	C₂×Dic₁₁₈	—	4	84	no	—
26	C₂×C₈×C₅₉	C₂×D₄	1	21	yes	—
27	C₂×C₈×C₅₉	C₂⁴	1	7	yes	—
28	Dic₂₃₆	—	2	56	no	—
29	Dic₂₃₆	C₂⁴	1	16	yes	—
30	C₁₆×C₅₉	C₂⁴	1	8	yes	—
31	C₂³×C₅₉	Q₃₂	1	8	yes	complemented
32	C₂³×C₅₉	C₂×D₈	1	7	yes	—
33	C₂×C₄×C₅₉	C₂×D₈	1	21	yes	—
34	C₂×C₄×C₅₉	C₂²×D₄	1	7	yes	—
35	C₂×Dic₅₉	—	4	56	no	—
36	Dic₁₁₈	—	2	16	no	—
37	Dic₁₁₈	—	4	56	no	—
38	C₈×C₅₉	C₂²×D₄	1	7	yes	—
39	C₈×C₅₉	C₂⁵	1	1	yes	characteristic
40	C₂³×Q₃₂	—	59	1	no	maximal, Sylow
41	C₂²×C₅₉	C₂×Q₃₂	1	28	yes	complemented
42	C₂²×C₅₉	C₂²×D₈	1	7	yes	—
43	C₄×C₅₉	C₂²×D₈	1	7	yes	—
44	C₄×C₅₉	C₂³×D₄	1	1	yes	characteristic
45	Dic₅₉	—	4	16	no	—
46	C₂³×Q₁₆	—	59	2	no	—
47	C₂²×Q₃₂	—	59	28	no	—
48	C₂³×C₁₆	D₅₉	1	1	yes	characteristic
49	C₂×C₅₉	C₂²×Q₃₂	1	14	yes	complemented
50	C₂×C₅₉	C₂³×D₈	1	1	yes	characteristic
51	C₂³×Q₈	—	118	2	no	—
52	C₂²×Q₁₆	—	59	28	no	—
53	C₂²×Q₁₆	—	118	14	no	—
54	C₂³×C₈	C₂×D₅₉	1	1	yes	characteristic
55	C₂×Q₃₂	—	59	112	no	—
56	C₂²×C₁₆	C₂×D₅₉	1	14	yes	—
57	C₅₉	C₂³×Q₃₂	1	1	yes	characteristic, complemented, Sylow
58	C₂²×Q₈	—	118	28	no	—
59	C₂²×Q₈	—	236	14	no	—
60	C₂³×C₄	—	236	2	no	—
61	C₂³×C₄	D₂₃₆	1	1	yes	characteristic
62	C₂×Q₁₆	—	59	56	no	—
63	C₂×Q₁₆	—	118	84	no	—
64	C₂²×C₈	D₂₃₆	1	7	yes	—
65	C₂²×C₈	C₂²×D₅₉	1	7	yes	—
66	Q₃₂	—	59	64	no	—
67	C₂×C₁₆	C₂²×D₅₉	1	28	yes	—
68	C₂⁴	D₄₇₂	1	1	yes	characteristic
69	C₂×Q₈	—	118	56	no	—
70	C₂×Q₈	—	236	84	no	—
71	C₂²×C₄	—	236	28	no	—
72	C₂²×C₄	D₄₇₂	1	7	yes	—
73	C₂²×C₄	C₂×D₂₃₆	1	7	yes	—
74	Q₁₆	—	59	16	no	—
75	Q₁₆	—	118	56	no	—
76	C₂×C₈	C₂×D₂₃₆	1	21	yes	—
77	C₂×C₈	C₂³×D₅₉	1	7	yes	—
78	C₁₆	C₂³×D₅₉	1	8	yes	—
79	C₂³	Dic₄₇₂	1	8	yes	direct product factor
80	C₂³	C₂×D₄₇₂	1	7	yes	—
81	Q₈	—	118	16	no	—
82	Q₈	—	236	56	no	—
83	C₂×C₄	—	236	56	no	—
84	C₂×C₄	C₂×D₄₇₂	1	21	yes	—
85	C₂×C₄	C₂²×D₂₃₆	1	7	yes	—
86	C₈	C₂²×D₂₃₆	1	7	yes	—
87	C₈	C₂⁴×D₅₉	1	1	yes	characteristic
88	C₂²	C₂×Dic₄₇₂	1	28	yes	direct product factor
89	C₂²	C₂²×D₄₇₂	1	7	yes	—
90	C₄	—	236	16	no	—
91	C₄	C₂²×D₄₇₂	1	7	yes	—
92	C₄	C₂³×D₂₃₆	1	1	yes	characteristic
93	C₂	C₂²×Dic₄₇₂	1	14	yes	direct product factor
94	C₂	C₂³×D₄₇₂	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	D₄₇₂
commutator, cosocle	C₈×C₅₉	C₂⁵
Frattini	C₈	C₂⁴×D₅₉
Fitting	C₂³×C₁₆×C₅₉	C₂
socle, prime radical	C₂⁴×C₅₉	D₈
hypercenter	C₂³×C₁₆	D₅₉
hypocenter	C₅₉	C₂³×Q₃₂
LCS	G ▷ C₈×C₅₉ ▷ C₄×C₅₉ ▷ C₂×C₅₉ ▷ C₅₉
UCS	C₁ ◁ C₂⁴ ◁ C₂³×C₄ ◁ C₂³×C₈ ◁ C₂³×C₁₆

Complements

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

N	H ≅ G/N	type
2. C₂²×Dic₄₇₂	C₂	direct (N × H)
7. C₂×Dic₄₇₂	C₂²	direct (N × H)
15. Dic₄₇₂	C₂³	direct (N × H)
31. C₂³×C₅₉	Q₃₂	semidirect
41. C₂²×C₅₉	C₂×Q₃₂	semidirect
49. C₂×C₅₉	C₂²×Q₃₂	semidirect
57. C₅₉	C₂³×Q₃₂	semidirect
79. C₂³	Dic₄₇₂	direct (N × H)
88. C₂²	C₂×Dic₄₇₂	direct (N × H)
93. C₂	C₂²×Dic₄₇₂	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×Dic₂₃₆	2
C₂²×Dic₄₇₂	2
C₂³×C₁₆×C₅₉	2
C₂³×Q₃₂	59

Subgroups — C23×Dic472 #29495171

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×Dic₄₇₂ #29495171