Subgroups — C₂⁴×C₄×C₈×C₄₃ #72199512

Order 22016.

37508 conjugacy classes of subgroups.

The subgroup lattice has 144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁵×C₈×C₄₃	C₂	1	2	yes	maximal
2	C₂⁴×C₄²×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₂³×C₄×C₈×C₄₃	C₂	1	60	yes	maximal, direct product factor
4	C₂⁵×C₄×C₄₃	C₄	1	2	yes	—
5	C₂⁵×C₄×C₄₃	C₂²	1	1	yes	characteristic
6	C₂⁴×C₈×C₄₃	C₄	1	64	yes	direct product factor
7	C₂⁴×C₈×C₄₃	C₂²	1	60	yes	—
8	C₂³×C₄²×C₄₃	C₄	1	30	yes	—
9	C₂³×C₄²×C₄₃	C₂²	1	30	yes	—
10	C₂²×C₄×C₈×C₄₃	C₂²	1	560	yes	direct product factor
11	C₂⁶×C₄₃	C₂×C₄	1	1	yes	characteristic
12	C₂⁴×C₄×C₄₃	C₈	1	64	yes	direct product factor
13	C₂⁴×C₄×C₄₃	C₂×C₄	1	15	yes	—
14	C₂⁴×C₄×C₄₃	C₂×C₄	1	32	yes	—
15	C₂⁴×C₄×C₄₃	C₂×C₄	1	60	yes	—
16	C₂⁴×C₄×C₄₃	C₂³	1	15	yes	—
17	C₂³×C₈×C₄₃	C₂×C₄	1	960	yes	direct product factor
18	C₂³×C₈×C₄₃	C₂³	1	280	yes	—
19	C₂²×C₄²×C₄₃	C₂×C₄	1	420	yes	—
20	C₂²×C₄²×C₄₃	C₂³	1	140	yes	—
21	C₂×C₄×C₈×C₄₃	C₂³	1	960	yes	direct product factor
22	C₂⁵×C₄₃	C₄²	1	16	yes	—
23	C₂⁵×C₄₃	C₂×C₈	1	32	yes	—
24	C₂⁵×C₄₃	C₂²×C₄	1	15	yes	—
25	C₂³×C₄×C₄₃	C₄²	1	240	yes	—
26	C₂³×C₄×C₄₃	C₂×C₈	1	960	yes	direct product factor
27	C₂³×C₄×C₄₃	C₂²×C₄	1	280	yes	—
28	C₂³×C₄×C₄₃	C₂²×C₄	1	105	yes	—
29	C₂³×C₄×C₄₃	C₂²×C₄	1	240	yes	—
30	C₂³×C₄×C₄₃	C₂⁴	1	35	yes	—
31	C₂²×C₈×C₄₃	C₂²×C₄	1	2240	yes	direct product factor
32	C₂²×C₈×C₄₃	C₂⁴	1	240	yes	—
33	C₂×C₄²×C₄₃	C₂²×C₄	1	840	yes	—
34	C₂×C₄²×C₄₃	C₂⁴	1	120	yes	—
35	C₄×C₈×C₄₃	C₂⁴	1	256	yes	direct product factor
36	C₂⁴×C₄₃	C₄×C₈	1	256	yes	direct product factor
37	C₂⁴×C₄₃	C₂×C₄²	1	120	yes	—
38	C₂⁴×C₄₃	C₂²×C₈	1	240	yes	—
39	C₂⁴×C₄₃	C₂³×C₄	1	35	yes	—
40	C₂²×C₄×C₄₃	C₂×C₄²	1	840	yes	—
41	C₂²×C₄×C₄₃	C₂²×C₈	1	2240	yes	direct product factor
42	C₂²×C₄×C₄₃	C₂³×C₄	1	280	yes	—
43	C₂²×C₄×C₄₃	C₂³×C₄	1	105	yes	—
44	C₂²×C₄×C₄₃	C₂³×C₄	1	240	yes	—
45	C₂²×C₄×C₄₃	C₂⁵	1	15	yes	—
46	C₂×C₈×C₄₃	C₂³×C₄	1	960	yes	direct product factor
47	C₂×C₈×C₄₃	C₂⁵	1	32	yes	—
48	C₄²×C₄₃	C₂³×C₄	1	240	yes	—
49	C₄²×C₄₃	C₂⁵	1	16	yes	—
50	C₂⁴×C₄×C₈	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
51	C₂³×C₄₃	C₂×C₄×C₈	1	960	yes	direct product factor
52	C₂³×C₄₃	C₂²×C₄²	1	140	yes	—
53	C₂³×C₄₃	C₂³×C₈	1	280	yes	—
54	C₂³×C₄₃	C₂⁴×C₄	1	15	yes	—
55	C₂×C₄×C₄₃	C₂²×C₄²	1	420	yes	—
56	C₂×C₄×C₄₃	C₂³×C₈	1	960	yes	direct product factor
57	C₂×C₄×C₄₃	C₂⁴×C₄	1	15	yes	—
58	C₂×C₄×C₄₃	C₂⁴×C₄	1	32	yes	—
59	C₂×C₄×C₄₃	C₂⁴×C₄	1	60	yes	—
60	C₂×C₄×C₄₃	C₂⁶	1	1	yes	characteristic
61	C₈×C₄₃	C₂⁴×C₄	1	64	yes	direct product factor
62	C₂⁵×C₈	C₂×C₄₃	1	2	yes	—
63	C₂⁴×C₄²	C₂×C₄₃	1	1	yes	characteristic
64	C₂³×C₄×C₈	C₂×C₄₃	1	60	yes	direct product factor
65	C₂²×C₄₃	C₂²×C₄×C₈	1	560	yes	direct product factor
66	C₂²×C₄₃	C₂³×C₄²	1	30	yes	—
67	C₂²×C₄₃	C₂⁴×C₈	1	60	yes	—
68	C₂²×C₄₃	C₂⁵×C₄	1	1	yes	characteristic
69	C₄×C₄₃	C₂³×C₄²	1	30	yes	—
70	C₄×C₄₃	C₂⁴×C₈	1	64	yes	direct product factor
71	C₄×C₄₃	C₂⁵×C₄	1	2	yes	—
72	C₂⁵×C₄	C₄×C₄₃	1	2	yes	—
73	C₂⁵×C₄	C₂²×C₄₃	1	1	yes	characteristic
74	C₂⁴×C₈	C₄×C₄₃	1	64	yes	direct product factor
75	C₂⁴×C₈	C₂²×C₄₃	1	60	yes	—
76	C₂³×C₄²	C₄×C₄₃	1	30	yes	—
77	C₂³×C₄²	C₂²×C₄₃	1	30	yes	—
78	C₂²×C₄×C₈	C₂²×C₄₃	1	560	yes	direct product factor
79	C₂×C₄₃	C₂³×C₄×C₈	1	60	yes	direct product factor
80	C₂×C₄₃	C₂⁴×C₄²	1	1	yes	characteristic
81	C₂×C₄₃	C₂⁵×C₈	1	2	yes	—
82	C₂⁶	C₂×C₄×C₄₃	1	1	yes	characteristic
83	C₂⁴×C₄	C₈×C₄₃	1	64	yes	direct product factor
84	C₂⁴×C₄	C₂×C₄×C₄₃	1	15	yes	—
85	C₂⁴×C₄	C₂×C₄×C₄₃	1	32	yes	—
86	C₂⁴×C₄	C₂×C₄×C₄₃	1	60	yes	—
87	C₂⁴×C₄	C₂³×C₄₃	1	15	yes	—
88	C₂³×C₈	C₂×C₄×C₄₃	1	960	yes	direct product factor
89	C₂³×C₈	C₂³×C₄₃	1	280	yes	—
90	C₂²×C₄²	C₂×C₄×C₄₃	1	420	yes	—
91	C₂²×C₄²	C₂³×C₄₃	1	140	yes	—
92	C₂×C₄×C₈	C₂³×C₄₃	1	960	yes	direct product factor
93	C₄₃	C₂⁴×C₄×C₈	1	1	yes	characteristic, direct product factor, Sylow
94	C₂⁵	C₄²×C₄₃	1	16	yes	—
95	C₂⁵	C₂×C₈×C₄₃	1	32	yes	—
96	C₂⁵	C₂²×C₄×C₄₃	1	15	yes	—
97	C₂³×C₄	C₄²×C₄₃	1	240	yes	—
98	C₂³×C₄	C₂×C₈×C₄₃	1	960	yes	direct product factor
99	C₂³×C₄	C₂²×C₄×C₄₃	1	280	yes	—
100	C₂³×C₄	C₂²×C₄×C₄₃	1	105	yes	—
101	C₂³×C₄	C₂²×C₄×C₄₃	1	240	yes	—
102	C₂³×C₄	C₂⁴×C₄₃	1	35	yes	—
103	C₂²×C₈	C₂²×C₄×C₄₃	1	2240	yes	direct product factor
104	C₂²×C₈	C₂⁴×C₄₃	1	240	yes	—
105	C₂×C₄²	C₂²×C₄×C₄₃	1	840	yes	—
106	C₂×C₄²	C₂⁴×C₄₃	1	120	yes	—
107	C₄×C₈	C₂⁴×C₄₃	1	256	yes	direct product factor
108	C₂⁴	C₄×C₈×C₄₃	1	256	yes	direct product factor
109	C₂⁴	C₂×C₄²×C₄₃	1	120	yes	—
110	C₂⁴	C₂²×C₈×C₄₃	1	240	yes	—
111	C₂⁴	C₂³×C₄×C₄₃	1	35	yes	—
112	C₂²×C₄	C₂×C₄²×C₄₃	1	840	yes	—
113	C₂²×C₄	C₂²×C₈×C₄₃	1	2240	yes	direct product factor
114	C₂²×C₄	C₂³×C₄×C₄₃	1	280	yes	—
115	C₂²×C₄	C₂³×C₄×C₄₃	1	105	yes	—
116	C₂²×C₄	C₂³×C₄×C₄₃	1	240	yes	—
117	C₂²×C₄	C₂⁵×C₄₃	1	15	yes	—
118	C₂×C₈	C₂³×C₄×C₄₃	1	960	yes	direct product factor
119	C₂×C₈	C₂⁵×C₄₃	1	32	yes	—
120	C₄²	C₂³×C₄×C₄₃	1	240	yes	—
121	C₄²	C₂⁵×C₄₃	1	16	yes	—
122	C₂³	C₂×C₄×C₈×C₄₃	1	960	yes	direct product factor
123	C₂³	C₂²×C₄²×C₄₃	1	140	yes	—
124	C₂³	C₂³×C₈×C₄₃	1	280	yes	—
125	C₂³	C₂⁴×C₄×C₄₃	1	15	yes	—
126	C₂×C₄	C₂²×C₄²×C₄₃	1	420	yes	—
127	C₂×C₄	C₂³×C₈×C₄₃	1	960	yes	direct product factor
128	C₂×C₄	C₂⁴×C₄×C₄₃	1	15	yes	—
129	C₂×C₄	C₂⁴×C₄×C₄₃	1	32	yes	—
130	C₂×C₄	C₂⁴×C₄×C₄₃	1	60	yes	—
131	C₂×C₄	C₂⁶×C₄₃	1	1	yes	characteristic
132	C₈	C₂⁴×C₄×C₄₃	1	64	yes	direct product factor
133	C₂²	C₂²×C₄×C₈×C₄₃	1	560	yes	direct product factor
134	C₂²	C₂³×C₄²×C₄₃	1	30	yes	—
135	C₂²	C₂⁴×C₈×C₄₃	1	60	yes	—
136	C₂²	C₂⁵×C₄×C₄₃	1	1	yes	characteristic
137	C₄	C₂³×C₄²×C₄₃	1	30	yes	—
138	C₄	C₂⁴×C₈×C₄₃	1	64	yes	direct product factor
139	C₄	C₂⁵×C₄×C₄₃	1	2	yes	—
140	C₂	C₂³×C₄×C₈×C₄₃	1	60	yes	direct product factor
141	C₂	C₂⁴×C₄²×C₄₃	1	1	yes	characteristic
142	C₂	C₂⁵×C₈×C₄₃	1	2	yes	—

	subgroup	G/H
center	G	C₁
commutator	C₁	G
Frattini, cosocle	C₂×C₄	C₂⁶×C₄₃
socle, prime radical	C₂⁶×C₄₃	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. C₂³×C₄×C₈×C₄₃	C₂	direct (N × H)
6. C₂⁴×C₈×C₄₃	C₄	direct (N × H)
10. C₂²×C₄×C₈×C₄₃	C₂²	direct (N × H)
12. C₂⁴×C₄×C₄₃	C₈	direct (N × H)
17. C₂³×C₈×C₄₃	C₂×C₄	direct (N × H)
21. C₂×C₄×C₈×C₄₃	C₂³	direct (N × H)
26. C₂³×C₄×C₄₃	C₂×C₈	direct (N × H)
31. C₂²×C₈×C₄₃	C₂²×C₄	direct (N × H)
35. C₄×C₈×C₄₃	C₂⁴	direct (N × H)
36. C₂⁴×C₄₃	C₄×C₈	direct (N × H)
41. C₂²×C₄×C₄₃	C₂²×C₈	direct (N × H)
46. C₂×C₈×C₄₃	C₂³×C₄	direct (N × H)
50. C₂⁴×C₄×C₈	C₄₃	direct (N × H)
51. C₂³×C₄₃	C₂×C₄×C₈	direct (N × H)
56. C₂×C₄×C₄₃	C₂³×C₈	direct (N × H)
61. C₈×C₄₃	C₂⁴×C₄	direct (N × H)
64. C₂³×C₄×C₈	C₂×C₄₃	direct (N × H)
65. C₂²×C₄₃	C₂²×C₄×C₈	direct (N × H)
70. C₄×C₄₃	C₂⁴×C₈	direct (N × H)
74. C₂⁴×C₈	C₄×C₄₃	direct (N × H)
78. C₂²×C₄×C₈	C₂²×C₄₃	direct (N × H)
79. C₂×C₄₃	C₂³×C₄×C₈	direct (N × H)
83. C₂⁴×C₄	C₈×C₄₃	direct (N × H)
88. C₂³×C₈	C₂×C₄×C₄₃	direct (N × H)
92. C₂×C₄×C₈	C₂³×C₄₃	direct (N × H)
93. C₄₃	C₂⁴×C₄×C₈	direct (N × H)
98. C₂³×C₄	C₂×C₈×C₄₃	direct (N × H)
103. C₂²×C₈	C₂²×C₄×C₄₃	direct (N × H)
107. C₄×C₈	C₂⁴×C₄₃	direct (N × H)
108. C₂⁴	C₄×C₈×C₄₃	direct (N × H)
113. C₂²×C₄	C₂²×C₈×C₄₃	direct (N × H)
118. C₂×C₈	C₂³×C₄×C₄₃	direct (N × H)
122. C₂³	C₂×C₄×C₈×C₄₃	direct (N × H)
127. C₂×C₄	C₂³×C₈×C₄₃	direct (N × H)
132. C₈	C₂⁴×C₄×C₄₃	direct (N × H)
133. C₂²	C₂²×C₄×C₈×C₄₃	direct (N × H)
138. C₄	C₂⁴×C₈×C₄₃	direct (N × H)
140. C₂	C₂³×C₄×C₈×C₄₃	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×C₈×C₄₃	2
C₂⁴×C₄²×C₄₃	2
C₂³×C₄×C₈×C₄₃	2
C₂⁴×C₄×C₈	43

Subgroups — C24×C4×C8×C43 #72199512

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂⁴×C₄×C₈×C₄₃ #72199512