Subgroups — C₂²×C₄×C₈×C₂₃ #15670488

Order 2944.

760 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₈×C₂₃	C₂	1	2	yes	maximal
2	C₂²×C₄²×C₂₃	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₈×C₂₃	C₂	1	12	yes	maximal, direct product factor
4	C₂³×C₄×C₂₃	C₄	1	2	yes	—
5	C₂³×C₄×C₂₃	C₂²	1	1	yes	characteristic
6	C₂²×C₈×C₂₃	C₄	1	16	yes	direct product factor
7	C₂²×C₈×C₂₃	C₂²	1	12	yes	—
8	C₂×C₄²×C₂₃	C₄	1	6	yes	—
9	C₂×C₄²×C₂₃	C₂²	1	6	yes	—
10	C₄×C₈×C₂₃	C₂²	1	16	yes	direct product factor
11	C₂⁴×C₂₃	C₂×C₄	1	1	yes	characteristic
12	C₂²×C₄×C₂₃	C₈	1	16	yes	direct product factor
13	C₂²×C₄×C₂₃	C₂×C₄	1	3	yes	—
14	C₂²×C₄×C₂₃	C₂×C₄	1	8	yes	—
15	C₂²×C₄×C₂₃	C₂×C₄	1	12	yes	—
16	C₂²×C₄×C₂₃	C₂³	1	3	yes	—
17	C₂×C₈×C₂₃	C₂×C₄	1	48	yes	direct product factor
18	C₂×C₈×C₂₃	C₂³	1	8	yes	—
19	C₄²×C₂₃	C₂×C₄	1	12	yes	—
20	C₄²×C₂₃	C₂³	1	4	yes	—
21	C₂³×C₂₃	C₄²	1	4	yes	—
22	C₂³×C₂₃	C₂×C₈	1	8	yes	—
23	C₂³×C₂₃	C₂²×C₄	1	3	yes	—
24	C₂×C₄×C₂₃	C₄²	1	12	yes	—
25	C₂×C₄×C₂₃	C₂×C₈	1	48	yes	direct product factor
26	C₂×C₄×C₂₃	C₂²×C₄	1	3	yes	—
27	C₂×C₄×C₂₃	C₂²×C₄	1	8	yes	—
28	C₂×C₄×C₂₃	C₂²×C₄	1	12	yes	—
29	C₂×C₄×C₂₃	C₂⁴	1	1	yes	characteristic
30	C₈×C₂₃	C₂²×C₄	1	16	yes	direct product factor
31	C₂²×C₄×C₈	C₂₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
32	C₂²×C₂₃	C₄×C₈	1	16	yes	direct product factor
33	C₂²×C₂₃	C₂×C₄²	1	6	yes	—
34	C₂²×C₂₃	C₂²×C₈	1	12	yes	—
35	C₂²×C₂₃	C₂³×C₄	1	1	yes	characteristic
36	C₄×C₂₃	C₂×C₄²	1	6	yes	—
37	C₄×C₂₃	C₂²×C₈	1	16	yes	direct product factor
38	C₄×C₂₃	C₂³×C₄	1	2	yes	—
39	C₂³×C₈	C₂×C₂₃	1	2	yes	—
40	C₂²×C₄²	C₂×C₂₃	1	1	yes	characteristic
41	C₂×C₄×C₈	C₂×C₂₃	1	12	yes	direct product factor
42	C₂×C₂₃	C₂×C₄×C₈	1	12	yes	direct product factor
43	C₂×C₂₃	C₂²×C₄²	1	1	yes	characteristic
44	C₂×C₂₃	C₂³×C₈	1	2	yes	—
45	C₂³×C₄	C₄×C₂₃	1	2	yes	—
46	C₂³×C₄	C₂²×C₂₃	1	1	yes	characteristic
47	C₂²×C₈	C₄×C₂₃	1	16	yes	direct product factor
48	C₂²×C₈	C₂²×C₂₃	1	12	yes	—
49	C₂×C₄²	C₄×C₂₃	1	6	yes	—
50	C₂×C₄²	C₂²×C₂₃	1	6	yes	—
51	C₄×C₈	C₂²×C₂₃	1	16	yes	direct product factor
52	C₂₃	C₂²×C₄×C₈	1	1	yes	characteristic, direct product factor, Sylow
53	C₂⁴	C₂×C₄×C₂₃	1	1	yes	characteristic
54	C₂²×C₄	C₈×C₂₃	1	16	yes	direct product factor
55	C₂²×C₄	C₂×C₄×C₂₃	1	3	yes	—
56	C₂²×C₄	C₂×C₄×C₂₃	1	8	yes	—
57	C₂²×C₄	C₂×C₄×C₂₃	1	12	yes	—
58	C₂²×C₄	C₂³×C₂₃	1	3	yes	—
59	C₂×C₈	C₂×C₄×C₂₃	1	48	yes	direct product factor
60	C₂×C₈	C₂³×C₂₃	1	8	yes	—
61	C₄²	C₂×C₄×C₂₃	1	12	yes	—
62	C₄²	C₂³×C₂₃	1	4	yes	—
63	C₂³	C₄²×C₂₃	1	4	yes	—
64	C₂³	C₂×C₈×C₂₃	1	8	yes	—
65	C₂³	C₂²×C₄×C₂₃	1	3	yes	—
66	C₂×C₄	C₄²×C₂₃	1	12	yes	—
67	C₂×C₄	C₂×C₈×C₂₃	1	48	yes	direct product factor
68	C₂×C₄	C₂²×C₄×C₂₃	1	3	yes	—
69	C₂×C₄	C₂²×C₄×C₂₃	1	8	yes	—
70	C₂×C₄	C₂²×C₄×C₂₃	1	12	yes	—
71	C₂×C₄	C₂⁴×C₂₃	1	1	yes	characteristic
72	C₈	C₂²×C₄×C₂₃	1	16	yes	direct product factor
73	C₂²	C₄×C₈×C₂₃	1	16	yes	direct product factor
74	C₂²	C₂×C₄²×C₂₃	1	6	yes	—
75	C₂²	C₂²×C₈×C₂₃	1	12	yes	—
76	C₂²	C₂³×C₄×C₂₃	1	1	yes	characteristic
77	C₄	C₂×C₄²×C₂₃	1	6	yes	—
78	C₄	C₂²×C₈×C₂₃	1	16	yes	direct product factor
79	C₄	C₂³×C₄×C₂₃	1	2	yes	—
80	C₂	C₂×C₄×C₈×C₂₃	1	12	yes	direct product factor
81	C₂	C₂²×C₄²×C₂₃	1	1	yes	characteristic
82	C₂	C₂³×C₈×C₂₃	1	2	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂⁴×C₂₃
socle, prime radical	C₂⁴×C₂₃	C₂×C₄
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×C₈×C₂₃	C₂	direct (N × H)
6. C₂²×C₈×C₂₃	C₄	direct (N × H)
10. C₄×C₈×C₂₃	C₂²	direct (N × H)
12. C₂²×C₄×C₂₃	C₈	direct (N × H)
17. C₂×C₈×C₂₃	C₂×C₄	direct (N × H)
25. C₂×C₄×C₂₃	C₂×C₈	direct (N × H)
30. C₈×C₂₃	C₂²×C₄	direct (N × H)
31. C₂²×C₄×C₈	C₂₃	direct (N × H)
32. C₂²×C₂₃	C₄×C₈	direct (N × H)
37. C₄×C₂₃	C₂²×C₈	direct (N × H)
41. C₂×C₄×C₈	C₂×C₂₃	direct (N × H)
42. C₂×C₂₃	C₂×C₄×C₈	direct (N × H)
47. C₂²×C₈	C₄×C₂₃	direct (N × H)
51. C₄×C₈	C₂²×C₂₃	direct (N × H)
52. C₂₃	C₂²×C₄×C₈	direct (N × H)
54. C₂²×C₄	C₈×C₂₃	direct (N × H)
59. C₂×C₈	C₂×C₄×C₂₃	direct (N × H)
67. C₂×C₄	C₂×C₈×C₂₃	direct (N × H)
72. C₈	C₂²×C₄×C₂₃	direct (N × H)
73. C₂²	C₄×C₈×C₂₃	direct (N × H)
78. C₄	C₂²×C₈×C₂₃	direct (N × H)
80. C₂	C₂×C₄×C₈×C₂₃	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×C₈×C₂₃	2
C₂²×C₄²×C₂₃	2
C₂×C₄×C₈×C₂₃	2
C₂²×C₄×C₈	23

Subgroups — C22×C4×C8×C23 #15670488

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×C₈×C₂₃ #15670488