Subgroups — C₂³×C₈²×C₄₇ #72201366

Order 24064.

8324 conjugacy classes of subgroups.

The subgroup lattice has 108 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₈×C₄₇	C₂	1	3	yes	maximal
2	C₂²×C₈²×C₄₇	C₂	1	28	yes	maximal, direct product factor
3	C₂⁴×C₈×C₄₇	C₄	1	6	yes	—
4	C₂³×C₄²×C₄₇	C₂²	1	1	yes	characteristic
5	C₂²×C₄×C₈×C₄₇	C₄	1	42	yes	—
6	C₂²×C₄×C₈×C₄₇	C₂²	1	42	yes	—
7	C₂×C₈²×C₄₇	C₂²	1	112	yes	direct product factor
8	C₂⁴×C₄×C₄₇	C₂×C₄	1	3	yes	—
9	C₂³×C₈×C₄₇	C₈	1	96	yes	direct product factor
10	C₂³×C₈×C₄₇	C₂×C₄	1	84	yes	—
11	C₂²×C₄²×C₄₇	C₂×C₄	1	21	yes	—
12	C₂²×C₄²×C₄₇	C₂³	1	7	yes	—
13	C₂×C₄×C₈×C₄₇	C₂×C₄	1	252	yes	—
14	C₂×C₄×C₈×C₄₇	C₂³	1	84	yes	—
15	C₈²×C₄₇	C₂³	1	64	yes	direct product factor
16	C₂⁵×C₄₇	C₄²	1	1	yes	characteristic
17	C₂³×C₄×C₄₇	C₄²	1	21	yes	—
18	C₂³×C₄×C₄₇	C₂×C₈	1	48	yes	—
19	C₂³×C₄×C₄₇	C₂²×C₄	1	21	yes	—
20	C₂²×C₈×C₄₇	C₂×C₈	1	672	yes	direct product factor
21	C₂²×C₈×C₄₇	C₂²×C₄	1	168	yes	—
22	C₂×C₄²×C₄₇	C₄²	1	42	yes	—
23	C₂×C₄²×C₄₇	C₂²×C₄	1	63	yes	—
24	C₂×C₄²×C₄₇	C₂⁴	1	7	yes	—
25	C₄×C₈×C₄₇	C₂²×C₄	1	168	yes	—
26	C₄×C₈×C₄₇	C₂⁴	1	24	yes	—
27	C₂⁴×C₄₇	C₄×C₈	1	24	yes	—
28	C₂⁴×C₄₇	C₂×C₄²	1	7	yes	—
29	C₂²×C₄×C₄₇	C₄×C₈	1	168	yes	—
30	C₂²×C₄×C₄₇	C₂×C₄²	1	63	yes	—
31	C₂²×C₄×C₄₇	C₂²×C₈	1	168	yes	—
32	C₂²×C₄×C₄₇	C₂³×C₄	1	21	yes	—
33	C₂×C₈×C₄₇	C₂²×C₈	1	672	yes	direct product factor
34	C₂×C₈×C₄₇	C₂³×C₄	1	48	yes	—
35	C₄²×C₄₇	C₂×C₄²	1	42	yes	—
36	C₄²×C₄₇	C₂³×C₄	1	21	yes	—
37	C₄²×C₄₇	C₂⁵	1	1	yes	characteristic
38	C₂³×C₈²	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
39	C₂³×C₄₇	C₈²	1	64	yes	direct product factor
40	C₂³×C₄₇	C₂×C₄×C₈	1	84	yes	—
41	C₂³×C₄₇	C₂²×C₄²	1	7	yes	—
42	C₂×C₄×C₄₇	C₂×C₄×C₈	1	252	yes	—
43	C₂×C₄×C₄₇	C₂²×C₄²	1	21	yes	—
44	C₂×C₄×C₄₇	C₂³×C₈	1	84	yes	—
45	C₂×C₄×C₄₇	C₂⁴×C₄	1	3	yes	—
46	C₈×C₄₇	C₂³×C₈	1	96	yes	direct product factor
47	C₂³×C₄×C₈	C₂×C₄₇	1	3	yes	—
48	C₂²×C₈²	C₂×C₄₇	1	28	yes	direct product factor
49	C₂²×C₄₇	C₂×C₈²	1	112	yes	direct product factor
50	C₂²×C₄₇	C₂²×C₄×C₈	1	42	yes	—
51	C₂²×C₄₇	C₂³×C₄²	1	1	yes	characteristic
52	C₄×C₄₇	C₂²×C₄×C₈	1	42	yes	—
53	C₄×C₄₇	C₂⁴×C₈	1	6	yes	—
54	C₂⁴×C₈	C₄×C₄₇	1	6	yes	—
55	C₂³×C₄²	C₂²×C₄₇	1	1	yes	characteristic
56	C₂²×C₄×C₈	C₄×C₄₇	1	42	yes	—
57	C₂²×C₄×C₈	C₂²×C₄₇	1	42	yes	—
58	C₂×C₈²	C₂²×C₄₇	1	112	yes	direct product factor
59	C₂×C₄₇	C₂²×C₈²	1	28	yes	direct product factor
60	C₂×C₄₇	C₂³×C₄×C₈	1	3	yes	—
61	C₂⁴×C₄	C₂×C₄×C₄₇	1	3	yes	—
62	C₂³×C₈	C₈×C₄₇	1	96	yes	direct product factor
63	C₂³×C₈	C₂×C₄×C₄₇	1	84	yes	—
64	C₂²×C₄²	C₂×C₄×C₄₇	1	21	yes	—
65	C₂²×C₄²	C₂³×C₄₇	1	7	yes	—
66	C₂×C₄×C₈	C₂×C₄×C₄₇	1	252	yes	—
67	C₂×C₄×C₈	C₂³×C₄₇	1	84	yes	—
68	C₈²	C₂³×C₄₇	1	64	yes	direct product factor
69	C₄₇	C₂³×C₈²	1	1	yes	characteristic, direct product factor, Sylow
70	C₂⁵	C₄²×C₄₇	1	1	yes	characteristic
71	C₂³×C₄	C₄²×C₄₇	1	21	yes	—
72	C₂³×C₄	C₂×C₈×C₄₇	1	48	yes	—
73	C₂³×C₄	C₂²×C₄×C₄₇	1	21	yes	—
74	C₂²×C₈	C₂×C₈×C₄₇	1	672	yes	direct product factor
75	C₂²×C₈	C₂²×C₄×C₄₇	1	168	yes	—
76	C₂×C₄²	C₄²×C₄₇	1	42	yes	—
77	C₂×C₄²	C₂²×C₄×C₄₇	1	63	yes	—
78	C₂×C₄²	C₂⁴×C₄₇	1	7	yes	—
79	C₄×C₈	C₂²×C₄×C₄₇	1	168	yes	—
80	C₄×C₈	C₂⁴×C₄₇	1	24	yes	—
81	C₂⁴	C₄×C₈×C₄₇	1	24	yes	—
82	C₂⁴	C₂×C₄²×C₄₇	1	7	yes	—
83	C₂²×C₄	C₄×C₈×C₄₇	1	168	yes	—
84	C₂²×C₄	C₂×C₄²×C₄₇	1	63	yes	—
85	C₂²×C₄	C₂²×C₈×C₄₇	1	168	yes	—
86	C₂²×C₄	C₂³×C₄×C₄₇	1	21	yes	—
87	C₂×C₈	C₂²×C₈×C₄₇	1	672	yes	direct product factor
88	C₂×C₈	C₂³×C₄×C₄₇	1	48	yes	—
89	C₄²	C₂×C₄²×C₄₇	1	42	yes	—
90	C₄²	C₂³×C₄×C₄₇	1	21	yes	—
91	C₄²	C₂⁵×C₄₇	1	1	yes	characteristic
92	C₂³	C₈²×C₄₇	1	64	yes	direct product factor
93	C₂³	C₂×C₄×C₈×C₄₇	1	84	yes	—
94	C₂³	C₂²×C₄²×C₄₇	1	7	yes	—
95	C₂×C₄	C₂×C₄×C₈×C₄₇	1	252	yes	—
96	C₂×C₄	C₂²×C₄²×C₄₇	1	21	yes	—
97	C₂×C₄	C₂³×C₈×C₄₇	1	84	yes	—
98	C₂×C₄	C₂⁴×C₄×C₄₇	1	3	yes	—
99	C₈	C₂³×C₈×C₄₇	1	96	yes	direct product factor
100	C₂²	C₂×C₈²×C₄₇	1	112	yes	direct product factor
101	C₂²	C₂²×C₄×C₈×C₄₇	1	42	yes	—
102	C₂²	C₂³×C₄²×C₄₇	1	1	yes	characteristic
103	C₄	C₂²×C₄×C₈×C₄₇	1	42	yes	—
104	C₄	C₂⁴×C₈×C₄₇	1	6	yes	—
105	C₂	C₂²×C₈²×C₄₇	1	28	yes	direct product factor
106	C₂	C₂³×C₄×C₈×C₄₇	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₄²	C₂⁵×C₄₇
socle, prime radical	C₂⁵×C₄₇	C₄²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₈²×C₄₇	C₂	direct (N × H)
7. C₂×C₈²×C₄₇	C₂²	direct (N × H)
9. C₂³×C₈×C₄₇	C₈	direct (N × H)
15. C₈²×C₄₇	C₂³	direct (N × H)
20. C₂²×C₈×C₄₇	C₂×C₈	direct (N × H)
33. C₂×C₈×C₄₇	C₂²×C₈	direct (N × H)
38. C₂³×C₈²	C₄₇	direct (N × H)
39. C₂³×C₄₇	C₈²	direct (N × H)
46. C₈×C₄₇	C₂³×C₈	direct (N × H)
48. C₂²×C₈²	C₂×C₄₇	direct (N × H)
49. C₂²×C₄₇	C₂×C₈²	direct (N × H)
58. C₂×C₈²	C₂²×C₄₇	direct (N × H)
59. C₂×C₄₇	C₂²×C₈²	direct (N × H)
62. C₂³×C₈	C₈×C₄₇	direct (N × H)
68. C₈²	C₂³×C₄₇	direct (N × H)
69. C₄₇	C₂³×C₈²	direct (N × H)
74. C₂²×C₈	C₂×C₈×C₄₇	direct (N × H)
87. C₂×C₈	C₂²×C₈×C₄₇	direct (N × H)
92. C₂³	C₈²×C₄₇	direct (N × H)
99. C₈	C₂³×C₈×C₄₇	direct (N × H)
100. C₂²	C₂×C₈²×C₄₇	direct (N × H)
105. C₂	C₂²×C₈²×C₄₇	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×C₄×C₈×C₄₇	2
C₂²×C₈²×C₄₇	2
C₂³×C₈²	47

Subgroups — C23×C82×C47 #72201366

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂³×C₈²×C₄₇ #72201366