Subgroups — C₂⁴×C₄²×C₅×C₁₁ #72192249

Order 14080.

48060 conjugacy classes of subgroups.

The subgroup lattice has 120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₄×C₅×C₁₁	C₂	1	3	yes	maximal
2	C₂³×C₄²×C₅×C₁₁	C₂	1	60	yes	maximal, direct product factor
3	C₂⁴×C₄×C₅×C₁₁	C₄	1	96	yes	direct product factor
4	C₂⁴×C₄×C₅×C₁₁	C₂²	1	90	yes	—
5	C₂⁶×C₅×C₁₁	C₂²	1	1	yes	characteristic
6	C₂²×C₄²×C₅×C₁₁	C₂²	1	560	yes	direct product factor
7	C₂⁴×C₄²×C₁₁	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂⁵×C₅×C₁₁	C₂×C₄	1	48	yes	—
9	C₂⁵×C₅×C₁₁	C₂³	1	15	yes	—
10	C₂³×C₄×C₅×C₁₁	C₂×C₄	1	1440	yes	direct product factor
11	C₂³×C₄×C₅×C₁₁	C₂³	1	420	yes	—
12	C₂×C₄²×C₅×C₁₁	C₂³	1	960	yes	direct product factor
13	C₂⁵×C₄×C₁₁	C₂×C₅	1	3	yes	—
14	C₂³×C₄²×C₁₁	C₂×C₅	1	60	yes	direct product factor
15	C₂⁴×C₄²×C₅	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Hall
16	C₂⁴×C₅×C₁₁	C₄²	1	256	yes	direct product factor
17	C₂⁴×C₅×C₁₁	C₂²×C₄	1	360	yes	—
18	C₂⁴×C₅×C₁₁	C₂⁴	1	35	yes	—
19	C₂²×C₄×C₅×C₁₁	C₂²×C₄	1	3360	yes	direct product factor
20	C₂²×C₄×C₅×C₁₁	C₂⁴	1	360	yes	—
21	C₄²×C₅×C₁₁	C₂⁴	1	256	yes	direct product factor
22	C₂⁶×C₁₁	C₂²×C₅	1	1	yes	characteristic
23	C₂⁴×C₄×C₁₁	C₄×C₅	1	96	yes	direct product factor
24	C₂⁴×C₄×C₁₁	C₂²×C₅	1	90	yes	—
25	C₂²×C₄²×C₁₁	C₂²×C₅	1	560	yes	direct product factor
26	C₂⁵×C₄×C₅	C₂×C₁₁	1	3	yes	—
27	C₂³×C₄²×C₅	C₂×C₁₁	1	60	yes	direct product factor
28	C₂³×C₅×C₁₁	C₂×C₄²	1	960	yes	direct product factor
29	C₂³×C₅×C₁₁	C₂³×C₄	1	420	yes	—
30	C₂³×C₅×C₁₁	C₂⁵	1	15	yes	—
31	C₂×C₄×C₅×C₁₁	C₂³×C₄	1	1440	yes	direct product factor
32	C₂×C₄×C₅×C₁₁	C₂⁵	1	48	yes	—
33	C₂⁵×C₁₁	C₂×C₄×C₅	1	48	yes	—
34	C₂⁵×C₁₁	C₂³×C₅	1	15	yes	—
35	C₂³×C₄×C₁₁	C₂×C₄×C₅	1	1440	yes	direct product factor
36	C₂³×C₄×C₁₁	C₂³×C₅	1	420	yes	—
37	C₂×C₄²×C₁₁	C₂³×C₅	1	960	yes	direct product factor
38	C₂⁶×C₅	C₂²×C₁₁	1	1	yes	characteristic
39	C₂⁴×C₄×C₅	C₄×C₁₁	1	96	yes	direct product factor
40	C₂⁴×C₄×C₅	C₂²×C₁₁	1	90	yes	—
41	C₂²×C₄²×C₅	C₂²×C₁₁	1	560	yes	direct product factor
42	C₂⁴×C₄²	C₅×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
43	C₂²×C₅×C₁₁	C₂²×C₄²	1	560	yes	direct product factor
44	C₂²×C₅×C₁₁	C₂⁴×C₄	1	90	yes	—
45	C₂²×C₅×C₁₁	C₂⁶	1	1	yes	characteristic
46	C₄×C₅×C₁₁	C₂⁴×C₄	1	96	yes	direct product factor
47	C₂⁴×C₁₁	C₄²×C₅	1	256	yes	direct product factor
48	C₂⁴×C₁₁	C₂²×C₄×C₅	1	360	yes	—
49	C₂⁴×C₁₁	C₂⁴×C₅	1	35	yes	—
50	C₂²×C₄×C₁₁	C₂²×C₄×C₅	1	3360	yes	direct product factor
51	C₂²×C₄×C₁₁	C₂⁴×C₅	1	360	yes	—
52	C₄²×C₁₁	C₂⁴×C₅	1	256	yes	direct product factor
53	C₂⁵×C₅	C₂×C₄×C₁₁	1	48	yes	—
54	C₂⁵×C₅	C₂³×C₁₁	1	15	yes	—
55	C₂³×C₄×C₅	C₂×C₄×C₁₁	1	1440	yes	direct product factor
56	C₂³×C₄×C₅	C₂³×C₁₁	1	420	yes	—
57	C₂×C₄²×C₅	C₂³×C₁₁	1	960	yes	direct product factor
58	C₂⁵×C₄	C₂×C₅×C₁₁	1	3	yes	—
59	C₂³×C₄²	C₂×C₅×C₁₁	1	60	yes	direct product factor
60	C₂×C₅×C₁₁	C₂³×C₄²	1	60	yes	direct product factor
61	C₂×C₅×C₁₁	C₂⁵×C₄	1	3	yes	—
62	C₂³×C₁₁	C₂×C₄²×C₅	1	960	yes	direct product factor
63	C₂³×C₁₁	C₂³×C₄×C₅	1	420	yes	—
64	C₂³×C₁₁	C₂⁵×C₅	1	15	yes	—
65	C₂×C₄×C₁₁	C₂³×C₄×C₅	1	1440	yes	direct product factor
66	C₂×C₄×C₁₁	C₂⁵×C₅	1	48	yes	—
67	C₂⁴×C₅	C₄²×C₁₁	1	256	yes	direct product factor
68	C₂⁴×C₅	C₂²×C₄×C₁₁	1	360	yes	—
69	C₂⁴×C₅	C₂⁴×C₁₁	1	35	yes	—
70	C₂²×C₄×C₅	C₂²×C₄×C₁₁	1	3360	yes	direct product factor
71	C₂²×C₄×C₅	C₂⁴×C₁₁	1	360	yes	—
72	C₄²×C₅	C₂⁴×C₁₁	1	256	yes	direct product factor
73	C₂⁶	C₂²×C₅×C₁₁	1	1	yes	characteristic
74	C₂⁴×C₄	C₄×C₅×C₁₁	1	96	yes	direct product factor
75	C₂⁴×C₄	C₂²×C₅×C₁₁	1	90	yes	—
76	C₂²×C₄²	C₂²×C₅×C₁₁	1	560	yes	direct product factor
77	C₅×C₁₁	C₂⁴×C₄²	1	1	yes	characteristic, direct product factor, Hall
78	C₂²×C₁₁	C₂²×C₄²×C₅	1	560	yes	direct product factor
79	C₂²×C₁₁	C₂⁴×C₄×C₅	1	90	yes	—
80	C₂²×C₁₁	C₂⁶×C₅	1	1	yes	characteristic
81	C₄×C₁₁	C₂⁴×C₄×C₅	1	96	yes	direct product factor
82	C₂³×C₅	C₂×C₄²×C₁₁	1	960	yes	direct product factor
83	C₂³×C₅	C₂³×C₄×C₁₁	1	420	yes	—
84	C₂³×C₅	C₂⁵×C₁₁	1	15	yes	—
85	C₂×C₄×C₅	C₂³×C₄×C₁₁	1	1440	yes	direct product factor
86	C₂×C₄×C₅	C₂⁵×C₁₁	1	48	yes	—
87	C₂⁵	C₂×C₄×C₅×C₁₁	1	48	yes	—
88	C₂⁵	C₂³×C₅×C₁₁	1	15	yes	—
89	C₂³×C₄	C₂×C₄×C₅×C₁₁	1	1440	yes	direct product factor
90	C₂³×C₄	C₂³×C₅×C₁₁	1	420	yes	—
91	C₂×C₄²	C₂³×C₅×C₁₁	1	960	yes	direct product factor
92	C₂×C₁₁	C₂³×C₄²×C₅	1	60	yes	direct product factor
93	C₂×C₁₁	C₂⁵×C₄×C₅	1	3	yes	—
94	C₂²×C₅	C₂²×C₄²×C₁₁	1	560	yes	direct product factor
95	C₂²×C₅	C₂⁴×C₄×C₁₁	1	90	yes	—
96	C₂²×C₅	C₂⁶×C₁₁	1	1	yes	characteristic
97	C₄×C₅	C₂⁴×C₄×C₁₁	1	96	yes	direct product factor
98	C₂⁴	C₄²×C₅×C₁₁	1	256	yes	direct product factor
99	C₂⁴	C₂²×C₄×C₅×C₁₁	1	360	yes	—
100	C₂⁴	C₂⁴×C₅×C₁₁	1	35	yes	—
101	C₂²×C₄	C₂²×C₄×C₅×C₁₁	1	3360	yes	direct product factor
102	C₂²×C₄	C₂⁴×C₅×C₁₁	1	360	yes	—
103	C₄²	C₂⁴×C₅×C₁₁	1	256	yes	direct product factor
104	C₁₁	C₂⁴×C₄²×C₅	1	1	yes	characteristic, direct product factor, Sylow
105	C₂×C₅	C₂³×C₄²×C₁₁	1	60	yes	direct product factor
106	C₂×C₅	C₂⁵×C₄×C₁₁	1	3	yes	—
107	C₂³	C₂×C₄²×C₅×C₁₁	1	960	yes	direct product factor
108	C₂³	C₂³×C₄×C₅×C₁₁	1	420	yes	—
109	C₂³	C₂⁵×C₅×C₁₁	1	15	yes	—
110	C₂×C₄	C₂³×C₄×C₅×C₁₁	1	1440	yes	direct product factor
111	C₂×C₄	C₂⁵×C₅×C₁₁	1	48	yes	—
112	C₅	C₂⁴×C₄²×C₁₁	1	1	yes	characteristic, direct product factor, Sylow
113	C₂²	C₂²×C₄²×C₅×C₁₁	1	560	yes	direct product factor
114	C₂²	C₂⁶×C₅×C₁₁	1	1	yes	characteristic
115	C₂²	C₂⁴×C₄×C₅×C₁₁	1	90	yes	—
116	C₄	C₂⁴×C₄×C₅×C₁₁	1	96	yes	direct product factor
117	C₂	C₂³×C₄²×C₅×C₁₁	1	60	yes	direct product factor
118	C₂	C₂⁵×C₄×C₅×C₁₁	1	3	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂²	C₂⁶×C₅×C₁₁
socle, prime radical	C₂⁶×C₅×C₁₁	C₂²
LCS	G ▷ C₁
UCS	C₁ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄²×C₅×C₁₁	C₂	direct (N × H)
3. C₂⁴×C₄×C₅×C₁₁	C₄	direct (N × H)
6. C₂²×C₄²×C₅×C₁₁	C₂²	direct (N × H)
7. C₂⁴×C₄²×C₁₁	C₅	direct (N × H)
10. C₂³×C₄×C₅×C₁₁	C₂×C₄	direct (N × H)
12. C₂×C₄²×C₅×C₁₁	C₂³	direct (N × H)
14. C₂³×C₄²×C₁₁	C₂×C₅	direct (N × H)
15. C₂⁴×C₄²×C₅	C₁₁	direct (N × H)
16. C₂⁴×C₅×C₁₁	C₄²	direct (N × H)
19. C₂²×C₄×C₅×C₁₁	C₂²×C₄	direct (N × H)
21. C₄²×C₅×C₁₁	C₂⁴	direct (N × H)
23. C₂⁴×C₄×C₁₁	C₄×C₅	direct (N × H)
25. C₂²×C₄²×C₁₁	C₂²×C₅	direct (N × H)
27. C₂³×C₄²×C₅	C₂×C₁₁	direct (N × H)
28. C₂³×C₅×C₁₁	C₂×C₄²	direct (N × H)
31. C₂×C₄×C₅×C₁₁	C₂³×C₄	direct (N × H)
35. C₂³×C₄×C₁₁	C₂×C₄×C₅	direct (N × H)
37. C₂×C₄²×C₁₁	C₂³×C₅	direct (N × H)
39. C₂⁴×C₄×C₅	C₄×C₁₁	direct (N × H)
41. C₂²×C₄²×C₅	C₂²×C₁₁	direct (N × H)
42. C₂⁴×C₄²	C₅×C₁₁	direct (N × H)
43. C₂²×C₅×C₁₁	C₂²×C₄²	direct (N × H)
46. C₄×C₅×C₁₁	C₂⁴×C₄	direct (N × H)
47. C₂⁴×C₁₁	C₄²×C₅	direct (N × H)
50. C₂²×C₄×C₁₁	C₂²×C₄×C₅	direct (N × H)
52. C₄²×C₁₁	C₂⁴×C₅	direct (N × H)
55. C₂³×C₄×C₅	C₂×C₄×C₁₁	direct (N × H)
57. C₂×C₄²×C₅	C₂³×C₁₁	direct (N × H)
59. C₂³×C₄²	C₂×C₅×C₁₁	direct (N × H)
60. C₂×C₅×C₁₁	C₂³×C₄²	direct (N × H)
62. C₂³×C₁₁	C₂×C₄²×C₅	direct (N × H)
65. C₂×C₄×C₁₁	C₂³×C₄×C₅	direct (N × H)
67. C₂⁴×C₅	C₄²×C₁₁	direct (N × H)
70. C₂²×C₄×C₅	C₂²×C₄×C₁₁	direct (N × H)
72. C₄²×C₅	C₂⁴×C₁₁	direct (N × H)
74. C₂⁴×C₄	C₄×C₅×C₁₁	direct (N × H)
76. C₂²×C₄²	C₂²×C₅×C₁₁	direct (N × H)
77. C₅×C₁₁	C₂⁴×C₄²	direct (N × H)
78. C₂²×C₁₁	C₂²×C₄²×C₅	direct (N × H)
81. C₄×C₁₁	C₂⁴×C₄×C₅	direct (N × H)
82. C₂³×C₅	C₂×C₄²×C₁₁	direct (N × H)
85. C₂×C₄×C₅	C₂³×C₄×C₁₁	direct (N × H)
89. C₂³×C₄	C₂×C₄×C₅×C₁₁	direct (N × H)
91. C₂×C₄²	C₂³×C₅×C₁₁	direct (N × H)
92. C₂×C₁₁	C₂³×C₄²×C₅	direct (N × H)
94. C₂²×C₅	C₂²×C₄²×C₁₁	direct (N × H)
97. C₄×C₅	C₂⁴×C₄×C₁₁	direct (N × H)
98. C₂⁴	C₄²×C₅×C₁₁	direct (N × H)
101. C₂²×C₄	C₂²×C₄×C₅×C₁₁	direct (N × H)
103. C₄²	C₂⁴×C₅×C₁₁	direct (N × H)
104. C₁₁	C₂⁴×C₄²×C₅	direct (N × H)
105. C₂×C₅	C₂³×C₄²×C₁₁	direct (N × H)
107. C₂³	C₂×C₄²×C₅×C₁₁	direct (N × H)
110. C₂×C₄	C₂³×C₄×C₅×C₁₁	direct (N × H)
112. C₅	C₂⁴×C₄²×C₁₁	direct (N × H)
113. C₂²	C₂²×C₄²×C₅×C₁₁	direct (N × H)
116. C₄	C₂⁴×C₄×C₅×C₁₁	direct (N × H)
117. C₂	C₂³×C₄²×C₅×C₁₁	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂⁵×C₄×C₅×C₁₁	2
C₂³×C₄²×C₅×C₁₁	2
C₂⁴×C₄²×C₁₁	5
C₂⁴×C₄²×C₅	11

Subgroups — C24×C42×C5×C11 #72192249

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₄²×C₅×C₁₁ #72192249