Subgroups — C₄₃×#14664 #24934681

Order 11008.

1334 conjugacy classes of subgroups.

The subgroup lattice has 198 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#125×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#382	C₂	1	2	yes	maximal
3	C₄₃×#1445	C₂	1	4	yes	maximal
4	C₄₃×#1441	C₂	1	8	yes	maximal
5	C₂×#125×C₄₃	—	2	8	no	—
6	C₂×#125×C₄₃	C₄	1	8	yes	complemented
7	C₂²×C₄⋊C₄×C₄₃	C₂²	1	4	yes	—
8	C₂²×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
9	C₂²×C₄⋊C₄×C₄₃	C₂²	1	4	yes	—
10	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
11	C₄₃×#382	—	2	8	no	—
12	C₂×#95×C₄₃	C₂²	1	4	yes	—
13	C₂×#95×C₄₃	C₂²	1	4	yes	—
14	C₂×#95×C₄₃	C₂²	1	16	yes	—
15	C₂³×C₄×C₄₃	C₂³	1	8	yes	—
16	C₂³×C₄×C₄₃	C₂³	1	4	yes	—
17	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
18	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
19	#125×C₄₃	—	2	32	no	—
20	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
21	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
22	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
23	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
24	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
25	C₂×C₄⋊C₄×C₄₃	—	4	8	no	—
26	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	16	yes	—
27	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	8	yes	—
28	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
29	C₂×C₄²×C₄₃	D₄	1	8	yes	—
30	#95×C₄₃	—	2	8	no	—
31	#95×C₄₃	—	2	8	no	—
32	#95×C₄₃	—	4	16	no	—
33	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
34	C₂²×C₄×C₄₃	—	2	4	no	—
35	C₂²×C₄×C₄₃	—	2	4	no	—
36	C₂²×C₄×C₄₃	—	2	8	no	—
37	C₂²×C₄×C₄₃	—	2	4	no	—
38	C₂²×C₄×C₄₃	—	2	8	no	—
39	C₂²×C₄×C₄₃	—	2	8	no	—
40	C₂²×C₄×C₄₃	—	2	16	no	—
41	C₂²×C₄×C₄₃	—	2	4	no	—
42	C₂²×C₄×C₄₃	—	2	4	no	—
43	C₂²×C₄×C₄₃	—	2	8	no	—
44	C₂²×C₄×C₄₃	—	2	16	no	—
45	C₂²×C₄×C₄₃	—	2	8	no	—
46	C₂²×C₄×C₄₃	C₂²×C₄	1	8	yes	—
47	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
48	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
49	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
50	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
51	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
52	C₄⋊C₄×C₄₃	—	2	16	no	—
53	C₄⋊C₄×C₄₃	—	2	32	no	—
54	C₄⋊C₄×C₄₃	—	4	16	no	—
55	C₄²×C₄₃	C₂²⋊C₄	1	16	yes	—
56	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
57	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
58	C₂³×C₄₃	H(5,𝔽₂)	1	4	yes	—
59	C₂³×C₄₃	2₋¹⁺⁴	1	4	yes	—
60	C₂³×C₄₃	2₋¹⁺⁴	1	4	yes	—
61	C₂×C₄×C₄₃	—	2	4	no	—
62	C₂×C₄×C₄₃	—	2	8	no	—
63	C₂×C₄×C₄₃	—	2	4	no	—
64	C₂×C₄×C₄₃	—	2	8	no	—
65	C₂×C₄×C₄₃	—	2	4	no	—
66	C₂×C₄×C₄₃	—	2	8	no	—
67	C₂×C₄×C₄₃	—	2	8	no	—
68	C₂×C₄×C₄₃	—	2	16	no	—
69	C₂×C₄×C₄₃	—	4	4	no	—
70	C₂×C₄×C₄₃	—	4	4	no	—
71	C₂×C₄×C₄₃	—	4	8	no	—
72	C₂×C₄×C₄₃	—	4	8	no	—
73	C₂×C₄×C₄₃	—	4	8	no	—
74	C₂×C₄×C₄₃	—	4	8	no	—
75	C₂×C₄×C₄₃	—	4	16	no	—
76	C₂×C₄×C₄₃	—	4	16	no	—
77	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
78	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	8	yes	—
79	#14664	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
80	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄₃	#519	1	2	yes	—
82	C₂²×C₄₃	#520	1	4	yes	—
83	C₂²×C₄₃	#535	1	2	yes	—
84	C₂²×C₄₃	#536	1	4	yes	—
85	C₂²×C₄₃	#536	1	2	yes	—
86	C₂²×C₄₃	#537	1	4	yes	—
87	C₂²×C₄₃	#562	1	4	yes	—
88	C₂²×C₄₃	#563	1	8	yes	—
89	C₂²×C₄₃	#564	1	4	yes	—
90	C₄×C₄₃	—	2	4	no	—
91	C₄×C₄₃	—	2	8	no	—
92	C₄×C₄₃	—	4	8	no	—
93	C₄×C₄₃	—	8	8	no	—
94	C₂²×#125	C₂×C₄₃	1	1	yes	characteristic
95	C₂×#382	C₂×C₄₃	1	2	yes	—
96	#1445	C₂×C₄₃	1	4	yes	—
97	#1441	C₂×C₄₃	1	8	yes	—
98	C₂×C₄₃	#2310	1	1	yes	characteristic
99	C₂×C₄₃	#2311	1	2	yes	—
100	C₂×C₄₃	#2382	1	4	yes	—
101	C₂×C₄₃	#2820	1	4	yes	—
102	C₂×C₄₃	#2822	1	4	yes	—
103	C₂×#125	—	2	8	no	—
104	C₂×#125	C₄×C₄₃	1	8	yes	complemented
105	C₂²×C₄⋊C₄	C₂²×C₄₃	1	4	yes	—
106	C₂²×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
107	C₂²×C₄⋊C₄	C₂²×C₄₃	1	4	yes	—
108	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
109	#382	—	2	8	no	—
110	C₂×#95	C₂²×C₄₃	1	4	yes	—
111	C₂×#95	C₂²×C₄₃	1	4	yes	—
112	C₂×#95	C₂²×C₄₃	1	16	yes	—
113	C₄₃	#14664	1	1	yes	characteristic, direct product factor, Sylow
114	C₂³×C₄	C₂³×C₄₃	1	8	yes	—
115	C₂³×C₄	C₂³×C₄₃	1	4	yes	—
116	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
117	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
118	#125	—	2	32	no	—
119	C₂×C₄⋊C₄	—	2	8	no	—
120	C₂×C₄⋊C₄	—	2	4	no	—
121	C₂×C₄⋊C₄	—	2	4	no	—
122	C₂×C₄⋊C₄	—	2	8	no	—
123	C₂×C₄⋊C₄	—	2	8	no	—
124	C₂×C₄⋊C₄	—	4	8	no	—
125	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	16	yes	—
126	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	8	yes	—
127	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
128	C₂×C₄²	D₄×C₄₃	1	8	yes	—
129	#95	—	2	8	no	—
130	#95	—	2	8	no	—
131	#95	—	4	16	no	—
132	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
133	C₂²×C₄	—	2	4	no	—
134	C₂²×C₄	—	2	4	no	—
135	C₂²×C₄	—	2	4	no	—
136	C₂²×C₄	—	2	4	no	—
137	C₂²×C₄	—	2	4	no	—
138	C₂²×C₄	—	2	8	no	—
139	C₂²×C₄	—	2	8	no	—
140	C₂²×C₄	—	2	8	no	—
141	C₂²×C₄	—	2	8	no	—
142	C₂²×C₄	—	2	16	no	—
143	C₂²×C₄	—	2	16	no	—
144	C₂²×C₄	—	2	8	no	—
145	C₂²×C₄	C₂²×C₄×C₄₃	1	8	yes	—
146	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
147	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
148	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
149	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
150	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
151	C₄⋊C₄	—	2	16	no	—
152	C₄⋊C₄	—	2	32	no	—
153	C₄⋊C₄	—	4	16	no	—
154	C₄²	C₂²⋊C₄×C₄₃	1	16	yes	—
155	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
156	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
157	C₂³	H(5,𝔽₂)×C₄₃	1	4	yes	—
158	C₂³	2₋¹⁺⁴×C₄₃	1	4	yes	—
159	C₂³	2₋¹⁺⁴×C₄₃	1	4	yes	—
160	C₂×C₄	—	2	4	no	—
161	C₂×C₄	—	2	8	no	—
162	C₂×C₄	—	2	4	no	—
163	C₂×C₄	—	2	8	no	—
164	C₂×C₄	—	2	4	no	—
165	C₂×C₄	—	2	8	no	—
166	C₂×C₄	—	2	8	no	—
167	C₂×C₄	—	2	16	no	—
168	C₂×C₄	—	4	4	no	—
169	C₂×C₄	—	4	4	no	—
170	C₂×C₄	—	4	8	no	—
171	C₂×C₄	—	4	8	no	—
172	C₂×C₄	—	4	8	no	—
173	C₂×C₄	—	4	8	no	—
174	C₂×C₄	—	4	16	no	—
175	C₂×C₄	—	4	16	no	—
176	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
177	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	8	yes	—
178	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
179	C₂²	C₄₃×#519	1	2	yes	—
180	C₂²	C₄₃×#520	1	4	yes	—
181	C₂²	C₄₃×#535	1	2	yes	—
182	C₂²	C₄₃×#536	1	4	yes	—
183	C₂²	C₄₃×#536	1	2	yes	—
184	C₂²	C₄₃×#537	1	4	yes	—
185	C₂²	C₄₃×#562	1	4	yes	—
186	C₂²	C₄₃×#563	1	8	yes	—
187	C₂²	C₄₃×#564	1	4	yes	—
188	C₄	—	2	4	no	—
189	C₄	—	2	8	no	—
190	C₄	—	4	8	no	—
191	C₄	—	8	8	no	—
192	C₂	C₄₃×#2310	1	1	yes	characteristic
193	C₂	C₄₃×#2311	1	2	yes	—
194	C₂	C₄₃×#2382	1	4	yes	—
195	C₂	C₄₃×#2820	1	4	yes	—
196	C₂	C₄₃×#2822	1	4	yes	—

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₃
Frattini, cosocle	C₂⁴	C₂⁴×C₄₃
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
6. C₂×#125×C₄₃	C₄	semidirect
79. #14664	C₄₃	direct (N × H)
104. C₂×#125	C₄×C₄₃	semidirect
113. C₄₃	#14664	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#125×C₄₃	2
C₂×C₄₃×#382	2
C₄₃×#1445	2
C₄₃×#1441	2
#14664	43

Subgroups — C43×#14664 #24934681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#14664 #24934681