Subgroups — C₄₃×#14662 #24934679

Order 11008.

1854 conjugacy classes of subgroups.

The subgroup lattice has 266 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#124×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#382	C₂	1	2	yes	maximal, complemented
3	C₄₃×#1446	C₂	1	2	yes	maximal, complemented
4	C₄₃×#1439	C₂	1	8	yes	maximal, complemented
5	C₄₃×#1438	C₂	1	2	yes	maximal
6	C₂³×Q₈×C₄₃	C₂²	1	1	yes	characteristic
7	C₂³×D₄×C₄₃	C₂²	1	1	yes	characteristic
8	C₂×#124×C₄₃	—	2	8	no	—
9	C₂×#124×C₄₃	C₄	1	8	yes	complemented
10	C₂²×C₄⋊C₄×C₄₃	C₂²	1	4	yes	—
11	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	4	yes	—
12	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	8	yes	—
13	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
14	C₄₃×#382	—	2	8	no	—
15	C₂×#95×C₄₃	C₂²	1	4	yes	—
16	C₂×#95×C₄₃	C₂²	1	4	yes	—
17	C₂×#95×C₄₃	C₂²	1	8	yes	—
18	C₂⁵×C₄₃	C₂³	1	2	yes	—
19	C₂²×Q₈×C₄₃	—	2	4	no	—
20	C₂²×Q₈×C₄₃	—	4	4	no	—
21	C₂²×Q₈×C₄₃	C₂×C₄	1	4	yes	—
22	C₂²×D₄×C₄₃	—	2	4	no	—
23	C₂²×D₄×C₄₃	—	4	4	no	—
24	C₂²×D₄×C₄₃	C₂×C₄	1	4	yes	—
25	C₂³×C₄×C₄₃	C₂³	1	8	yes	—
26	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
27	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
28	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
29	#124×C₄₃	—	2	32	no	—
30	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
31	C₂×C₄⋊C₄×C₄₃	—	4	8	no	—
32	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
33	C₂×C₂²⋊C₄×C₄₃	—	2	8	no	—
34	C₂×C₂²⋊C₄×C₄₃	—	4	8	no	—
35	C₂×C₂²⋊C₄×C₄₃	—	4	16	no	—
36	C₂×C₂²⋊C₄×C₄₃	C₂×C₄	1	16	yes	—
37	C₂×C₄²×C₄₃	C₂×C₄	1	4	yes	—
38	C₂×C₄²×C₄₃	D₄	1	8	yes	—
39	#95×C₄₃	—	2	8	no	—
40	#95×C₄₃	—	2	8	no	—
41	#95×C₄₃	—	4	8	no	—
42	C₂⁴×C₄₃	—	2	4	no	—
43	C₂⁴×C₄₃	—	2	8	no	—
44	C₂⁴×C₄₃	—	2	8	no	—
45	C₂⁴×C₄₃	—	2	8	no	—
46	C₂⁴×C₄₃	C₂²×C₄	1	4	yes	—
47	C₂⁴×C₄₃	C₂⁴	1	1	yes	characteristic
48	C₂×Q₈×C₄₃	—	2	8	no	—
49	C₂×Q₈×C₄₃	—	4	8	no	—
50	C₂×Q₈×C₄₃	—	4	16	no	—
51	C₂×D₄×C₄₃	—	2	8	no	—
52	C₂×D₄×C₄₃	—	4	8	no	—
53	C₂×D₄×C₄₃	—	4	16	no	—
54	C₂²×C₄×C₄₃	—	2	4	no	—
55	C₂²×C₄×C₄₃	—	2	8	no	—
56	C₂²×C₄×C₄₃	—	2	4	no	—
57	C₂²×C₄×C₄₃	—	2	4	no	—
58	C₂²×C₄×C₄₃	—	2	8	no	—
59	C₂²×C₄×C₄₃	—	2	16	no	—
60	C₂²×C₄×C₄₃	—	2	8	no	—
61	C₂²×C₄×C₄₃	—	2	16	no	—
62	C₂²×C₄×C₄₃	—	2	4	no	—
63	C₂²×C₄×C₄₃	—	2	8	no	—
64	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
65	C₂²×C₄×C₄₃	C₂²×C₄	1	4	yes	—
66	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
67	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
68	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
69	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
70	C₄⋊C₄×C₄₃	—	4	16	no	—
71	C₂²⋊C₄×C₄₃	—	2	32	no	—
72	C₂²⋊C₄×C₄₃	—	4	32	no	—
73	C₄²×C₄₃	C₂²⋊C₄	1	16	yes	complemented
74	C₂³×C₄₃	—	2	4	no	—
75	C₂³×C₄₃	—	2	8	no	—
76	C₂³×C₄₃	—	2	16	no	—
77	C₂³×C₄₃	—	4	8	no	—
78	C₂³×C₄₃	—	4	4	no	—
79	C₂³×C₄₃	—	4	4	no	—
80	C₂³×C₄₃	—	4	8	no	—
81	C₂³×C₄₃	—	4	8	no	—
82	C₂³×C₄₃	—	4	16	no	—
83	C₂³×C₄₃	—	4	8	no	—
84	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
85	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
86	C₂³×C₄₃	H(5,𝔽₂)	1	4	yes	—
87	C₂³×C₄₃	H(5,𝔽₂)	1	4	yes	—
88	C₂³×C₄₃	2₋¹⁺⁴	1	4	yes	—
89	Q₈×C₄₃	—	4	16	no	—
90	D₄×C₄₃	—	4	16	no	—
91	C₂×C₄×C₄₃	—	2	4	no	—
92	C₂×C₄×C₄₃	—	2	8	no	—
93	C₂×C₄×C₄₃	—	2	4	no	—
94	C₂×C₄×C₄₃	—	2	8	no	—
95	C₂×C₄×C₄₃	—	2	4	no	—
96	C₂×C₄×C₄₃	—	2	8	no	—
97	C₂×C₄×C₄₃	—	2	4	no	—
98	C₂×C₄×C₄₃	—	2	8	no	—
99	C₂×C₄×C₄₃	—	4	8	no	—
100	C₂×C₄×C₄₃	—	4	8	no	—
101	C₂×C₄×C₄₃	—	4	8	no	—
102	C₂×C₄×C₄₃	—	4	8	no	—
103	C₂×C₄×C₄₃	—	4	16	no	—
104	C₂×C₄×C₄₃	—	4	16	no	—
105	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	8	yes	—
106	C₂×C₄×C₄₃	C₂×C₂²⋊C₄	1	4	yes	—
107	#14662	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
108	C₂²×C₄₃	—	4	4	no	—
109	C₂²×C₄₃	—	4	8	no	—
110	C₂²×C₄₃	—	4	16	no	—
111	C₂²×C₄₃	—	8	8	no	—
112	C₂²×C₄₃	—	8	8	no	—
113	C₂²×C₄₃	C₂²×C₂²⋊C₄	1	1	yes	characteristic
114	C₂²×C₄₃	#518	1	2	yes	—
115	C₂²×C₄₃	#520	1	4	yes	—
116	C₂²×C₄₃	#535	1	2	yes	—
117	C₂²×C₄₃	#535	1	4	yes	—
118	C₂²×C₄₃	#536	1	2	yes	—
119	C₂²×C₄₃	#537	1	4	yes	—
120	C₂²×C₄₃	H(3,𝔽₄)	1	4	yes	—
121	C₂²×C₄₃	#562	1	8	yes	—
122	C₂²×C₄₃	#563	1	4	yes	—
123	C₄×C₄₃	—	2	4	no	—
124	C₄×C₄₃	—	2	8	no	—
125	C₄×C₄₃	—	4	4	no	—
126	C₄×C₄₃	—	8	8	no	—
127	C₂²×#124	C₂×C₄₃	1	1	yes	characteristic
128	C₂×#382	C₂×C₄₃	1	2	yes	complemented
129	#1446	C₂×C₄₃	1	2	yes	complemented
130	#1439	C₂×C₄₃	1	8	yes	complemented
131	#1438	C₂×C₄₃	1	2	yes	—
132	C₂×C₄₃	—	8	4	no	—
133	C₂×C₄₃	#2309	1	1	yes	characteristic
134	C₂×C₄₃	#2311	1	2	yes	—
135	C₂×C₄₃	#2379	1	4	yes	—
136	C₂×C₄₃	#2819	1	4	yes	—
137	C₂×C₄₃	#2820	1	4	yes	—
138	C₂³×Q₈	C₂²×C₄₃	1	1	yes	characteristic
139	C₂³×D₄	C₂²×C₄₃	1	1	yes	characteristic
140	C₂×#124	—	2	8	no	—
141	C₂×#124	C₄×C₄₃	1	8	yes	complemented
142	C₂²×C₄⋊C₄	C₂²×C₄₃	1	4	yes	—
143	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	4	yes	—
144	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	8	yes	—
145	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
146	#382	—	2	8	no	—
147	C₂×#95	C₂²×C₄₃	1	4	yes	—
148	C₂×#95	C₂²×C₄₃	1	4	yes	—
149	C₂×#95	C₂²×C₄₃	1	8	yes	—
150	C₄₃	#14662	1	1	yes	characteristic, direct product factor, Sylow
151	C₂⁵	C₂³×C₄₃	1	2	yes	—
152	C₂²×Q₈	—	2	4	no	—
153	C₂²×Q₈	—	4	4	no	—
154	C₂²×Q₈	C₂×C₄×C₄₃	1	4	yes	—
155	C₂²×D₄	—	2	4	no	—
156	C₂²×D₄	—	4	4	no	—
157	C₂²×D₄	C₂×C₄×C₄₃	1	4	yes	—
158	C₂³×C₄	C₂³×C₄₃	1	8	yes	—
159	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
160	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
161	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
162	#124	—	2	32	no	—
163	C₂×C₄⋊C₄	—	2	8	no	—
164	C₂×C₄⋊C₄	—	4	8	no	—
165	C₂×C₂²⋊C₄	—	2	8	no	—
166	C₂×C₂²⋊C₄	—	2	8	no	—
167	C₂×C₂²⋊C₄	—	4	8	no	—
168	C₂×C₂²⋊C₄	—	4	16	no	—
169	C₂×C₂²⋊C₄	C₂×C₄×C₄₃	1	16	yes	—
170	C₂×C₄²	C₂×C₄×C₄₃	1	4	yes	—
171	C₂×C₄²	D₄×C₄₃	1	8	yes	—
172	#95	—	2	8	no	—
173	#95	—	2	8	no	—
174	#95	—	4	8	no	—
175	C₂⁴	—	2	4	no	—
176	C₂⁴	—	2	8	no	—
177	C₂⁴	—	2	8	no	—
178	C₂⁴	—	2	8	no	—
179	C₂⁴	C₂²×C₄×C₄₃	1	4	yes	—
180	C₂⁴	C₂⁴×C₄₃	1	1	yes	characteristic
181	C₂×Q₈	—	2	8	no	—
182	C₂×Q₈	—	4	8	no	—
183	C₂×Q₈	—	4	16	no	—
184	C₂×D₄	—	2	8	no	—
185	C₂×D₄	—	4	8	no	—
186	C₂×D₄	—	4	16	no	—
187	C₂²×C₄	—	2	4	no	—
188	C₂²×C₄	—	2	4	no	—
189	C₂²×C₄	—	2	4	no	—
190	C₂²×C₄	—	2	4	no	—
191	C₂²×C₄	—	2	8	no	—
192	C₂²×C₄	—	2	8	no	—
193	C₂²×C₄	—	2	16	no	—
194	C₂²×C₄	—	2	8	no	—
195	C₂²×C₄	—	2	16	no	—
196	C₂²×C₄	—	2	8	no	—
197	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
198	C₂²×C₄	C₂²×C₄×C₄₃	1	4	yes	—
199	C₂²×C₄	C₂²×C₄×C₄₃	1	2	yes	—
200	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
201	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
202	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
203	C₄⋊C₄	—	4	16	no	—
204	C₂²⋊C₄	—	2	32	no	—
205	C₂²⋊C₄	—	4	32	no	—
206	C₄²	C₂²⋊C₄×C₄₃	1	16	yes	complemented
207	C₂³	—	2	4	no	—
208	C₂³	—	2	8	no	—
209	C₂³	—	2	16	no	—
210	C₂³	—	4	8	no	—
211	C₂³	—	4	4	no	—
212	C₂³	—	4	4	no	—
213	C₂³	—	4	8	no	—
214	C₂³	—	4	8	no	—
215	C₂³	—	4	16	no	—
216	C₂³	—	4	8	no	—
217	C₂³	C₂³×C₄×C₄₃	1	1	yes	characteristic
218	C₂³	C₂²×D₄×C₄₃	1	2	yes	—
219	C₂³	H(5,𝔽₂)×C₄₃	1	4	yes	—
220	C₂³	H(5,𝔽₂)×C₄₃	1	4	yes	—
221	C₂³	2₋¹⁺⁴×C₄₃	1	4	yes	—
222	Q₈	—	4	16	no	—
223	D₄	—	4	16	no	—
224	C₂×C₄	—	2	4	no	—
225	C₂×C₄	—	2	8	no	—
226	C₂×C₄	—	2	4	no	—
227	C₂×C₄	—	2	8	no	—
228	C₂×C₄	—	2	4	no	—
229	C₂×C₄	—	2	8	no	—
230	C₂×C₄	—	2	4	no	—
231	C₂×C₄	—	2	8	no	—
232	C₂×C₄	—	4	8	no	—
233	C₂×C₄	—	4	8	no	—
234	C₂×C₄	—	4	8	no	—
235	C₂×C₄	—	4	8	no	—
236	C₂×C₄	—	4	16	no	—
237	C₂×C₄	—	4	16	no	—
238	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	8	yes	—
239	C₂×C₄	C₂×C₂²⋊C₄×C₄₃	1	4	yes	—
240	C₂²	—	4	16	no	—
241	C₂²	—	4	4	no	—
242	C₂²	—	4	8	no	—
243	C₂²	—	8	8	no	—
244	C₂²	—	8	8	no	—
245	C₂²	C₂²×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
246	C₂²	C₄₃×#518	1	2	yes	—
247	C₂²	C₄₃×#520	1	4	yes	—
248	C₂²	C₄₃×#535	1	2	yes	—
249	C₂²	C₄₃×#535	1	4	yes	—
250	C₂²	C₄₃×#536	1	2	yes	—
251	C₂²	C₄₃×#537	1	4	yes	—
252	C₂²	C₄₃×H(3,𝔽₄)	1	4	yes	—
253	C₂²	C₄₃×#562	1	8	yes	—
254	C₂²	C₄₃×#563	1	4	yes	—
255	C₄	—	2	4	no	—
256	C₄	—	2	8	no	—
257	C₄	—	4	4	no	—
258	C₄	—	8	8	no	—
259	C₂	—	8	4	no	—
260	C₂	C₄₃×#2309	1	1	yes	characteristic
261	C₂	C₄₃×#2311	1	2	yes	—
262	C₂	C₄₃×#2379	1	4	yes	—
263	C₂	C₄₃×#2819	1	4	yes	—
264	C₂	C₄₃×#2820	1	4	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₄₃	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₃
Frattini, cosocle	C₂⁴	C₂⁴×C₄₃
prime radical	C₂³×D₄×C₄₃	C₂²
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
2. C₂×C₄₃×#382	C₂	semidirect
3. C₄₃×#1446	C₂	semidirect
4. C₄₃×#1439	C₂	semidirect
9. C₂×#124×C₄₃	C₄	semidirect
73. C₄²×C₄₃	C₂²⋊C₄	semidirect
107. #14662	C₄₃	direct (N × H)
128. C₂×#382	C₂×C₄₃	semidirect
129. #1446	C₂×C₄₃	semidirect
130. #1439	C₂×C₄₃	semidirect
141. C₂×#124	C₄×C₄₃	semidirect
150. C₄₃	#14662	direct (N × H)
206. C₄²	C₂²⋊C₄×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#124×C₄₃	2
C₂×C₄₃×#382	2
C₄₃×#1446	2
C₄₃×#1439	2
C₄₃×#1438	2
#14662	43

Subgroups — C43×#14662 #24934679

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#14662 #24934679