Subgroups — C₄₃×#29664 #24949681

Order 11008.

1132 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#462	C₂	1	2	yes	maximal, complemented
3	C₄₃×#2857	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2024	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2016	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2001	C₂	1	4	yes	maximal
7	C₄₃×#1803	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1797	C₂	1	1	yes	maximal, characteristic
9	C₂²×Q₁₆×C₄₃	C₂²	1	4	yes	—
10	C₄₃×#533	—	2	8	no	—
11	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
12	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×#125×C₄₃	—	2	1	no	—
15	C₂×C₂²⋊Q₈×C₄₃	—	2	1	no	—
16	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
17	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
18	C₂×C₄×Q₈×C₄₃	—	2	1	no	—
19	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
20	C₂×#117×C₄₃	—	2	1	no	—
21	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
22	C₄₃×#462	—	2	8	no	—
23	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
24	C₂×#103×C₄₃	C₂²	1	4	yes	—
25	C₂×#103×C₄₃	C₂²	1	4	yes	—
26	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
27	C₄₃×#391	C₂²	1	2	yes	—
28	C₄₃×#389	—	2	1	no	—
29	C₄₃×#389	—	2	1	no	—
30	C₄₃×#384	C₂²	1	1	yes	characteristic
31	C₄₃×#380	—	2	1	no	—
32	C₄₃×#380	—	2	1	no	—
33	C₄₃×#340	C₂²	1	4	yes	—
34	C₄₃×#336	C₂²	1	2	yes	—
35	C₂²×Q₈×C₄₃	—	2	1	no	—
36	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
37	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
38	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
39	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
41	C₂×Q₁₆×C₄₃	—	2	8	no	—
42	C₂×Q₁₆×C₄₃	—	4	4	no	—
43	C₂×Q₁₆×C₄₃	—	4	4	no	—
44	C₂²×C₈×C₄₃	C₂³	1	4	yes	—
45	C₄⋊Q₈×C₄₃	—	2	4	no	—
46	C₄⋊Q₈×C₄₃	—	2	4	no	—
47	C₄⋊Q₈×C₄₃	—	2	4	no	—
48	#125×C₄₃	—	2	8	no	—
49	C₂²⋊Q₈×C₄₃	—	2	8	no	—
50	C₂²⋊Q₈×C₄₃	—	2	4	no	—
51	C₂²⋊Q₈×C₄₃	—	2	4	no	—
52	C₂²⋊Q₈×C₄₃	—	4	4	no	—
53	C₄×Q₈×C₄₃	—	2	8	no	—
54	C₄×Q₈×C₄₃	—	2	4	no	—
55	C₄×Q₈×C₄₃	D₄	1	8	yes	—
56	#117×C₄₃	—	2	8	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
71	C₂×C₄²×C₄₃	—	2	2	no	—
72	C₂×C₄²×C₄₃	—	2	4	no	—
73	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
77	C₄⋊C₈×C₄₃	—	2	4	no	—
78	#103×C₄₃	—	2	8	no	—
79	#103×C₄₃	—	4	4	no	—
80	C₂²⋊C₈×C₄₃	—	4	2	no	—
81	#95×C₄₃	—	2	2	no	—
82	#95×C₄₃	—	2	2	no	—
83	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
84	C₂×Q₈×C₄₃	—	2	4	no	—
85	C₂×Q₈×C₄₃	—	2	2	no	—
86	C₂×Q₈×C₄₃	—	2	4	no	—
87	C₂×Q₈×C₄₃	—	2	2	no	—
88	C₂×Q₈×C₄₃	—	2	2	no	—
89	C₂×Q₈×C₄₃	—	2	2	no	—
90	C₂×Q₈×C₄₃	—	2	4	no	—
91	C₂×Q₈×C₄₃	—	2	2	no	—
92	C₂×Q₈×C₄₃	—	2	2	no	—
93	C₂×Q₈×C₄₃	—	2	2	no	—
94	C₂×Q₈×C₄₃	—	4	2	no	—
95	C₂×Q₈×C₄₃	—	4	2	no	—
96	C₂×Q₈×C₄₃	C₂×D₄	1	4	yes	—
97	C₂²×C₄×C₄₃	—	2	2	no	—
98	C₂²×C₄×C₄₃	—	2	2	no	—
99	C₂²×C₄×C₄₃	—	2	2	no	—
100	C₂²×C₄×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	—	2	2	no	—
102	C₂²×C₄×C₄₃	—	2	1	no	—
103	C₂²×C₄×C₄₃	—	2	2	no	—
104	C₂²×C₄×C₄₃	—	2	1	no	—
105	C₂²×C₄×C₄₃	—	2	2	no	—
106	C₂²×C₄×C₄₃	—	2	2	no	—
107	C₂²×C₄×C₄₃	—	2	2	no	—
108	C₂²×C₄×C₄₃	—	2	2	no	—
109	C₂²×C₄×C₄₃	—	4	1	no	—
110	C₂²×C₄×C₄₃	Q₁₆	1	4	yes	complemented
111	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
117	Q₁₆×C₄₃	—	4	16	no	—
118	C₂×C₈×C₄₃	—	2	4	no	—
119	C₂×C₈×C₄₃	—	2	4	no	—
120	C₂×C₈×C₄₃	—	2	4	no	—
121	C₄⋊C₄×C₄₃	—	2	4	no	—
122	C₄⋊C₄×C₄₃	—	2	4	no	—
123	C₄⋊C₄×C₄₃	—	2	8	no	—
124	C₄⋊C₄×C₄₃	—	2	4	no	—
125	C₄⋊C₄×C₄₃	—	2	8	no	—
126	C₄⋊C₄×C₄₃	—	2	2	no	—
127	C₄⋊C₄×C₄₃	—	2	4	no	—
128	C₄⋊C₄×C₄₃	—	4	2	no	—
129	C₄⋊C₄×C₄₃	—	4	4	no	—
130	C₄⋊C₄×C₄₃	—	4	2	no	—
131	C₄⋊C₄×C₄₃	—	4	2	no	—
132	C₄⋊C₄×C₄₃	—	4	2	no	—
133	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
134	C₂²⋊C₄×C₄₃	—	2	8	no	—
135	C₂²⋊C₄×C₄₃	—	4	4	no	—
136	C₄²×C₄₃	—	2	2	no	—
137	C₄²×C₄₃	—	2	2	no	—
138	C₄²×C₄₃	—	2	8	no	—
139	C₄²×C₄₃	—	2	2	no	—
140	C₄²×C₄₃	C₂×D₄	1	4	yes	—
141	C₂³×C₄₃	—	2	1	no	—
142	C₂³×C₄₃	—	2	1	no	—
143	C₂³×C₄₃	—	2	1	no	—
144	C₂³×C₄₃	—	2	1	no	—
145	C₂³×C₄₃	—	2	1	no	—
146	C₂³×C₄₃	—	2	1	no	—
147	C₂³×C₄₃	C₂×Q₁₆	1	2	yes	—
148	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
149	Q₈×C₄₃	—	2	4	no	—
150	Q₈×C₄₃	—	2	4	no	—
151	Q₈×C₄₃	—	4	8	no	—
152	Q₈×C₄₃	—	4	2	no	—
153	Q₈×C₄₃	—	4	2	no	—
154	Q₈×C₄₃	—	4	4	no	—
155	Q₈×C₄₃	—	4	4	no	—
156	C₂×C₄×C₄₃	—	2	1	no	—
157	C₂×C₄×C₄₃	—	2	1	no	—
158	C₂×C₄×C₄₃	—	2	1	no	—
159	C₂×C₄×C₄₃	—	2	1	no	—
160	C₂×C₄×C₄₃	—	2	1	no	—
161	C₂×C₄×C₄₃	—	2	1	no	—
162	C₂×C₄×C₄₃	—	2	8	no	—
163	C₂×C₄×C₄₃	—	2	1	no	—
164	C₂×C₄×C₄₃	—	2	4	no	—
165	C₂×C₄×C₄₃	—	2	4	no	—
166	C₂×C₄×C₄₃	—	2	1	no	—
167	C₂×C₄×C₄₃	—	2	1	no	—
168	C₂×C₄×C₄₃	—	4	4	no	—
169	C₂×C₄×C₄₃	—	4	2	no	—
170	C₂×C₄×C₄₃	—	4	2	no	—
171	C₂×C₄×C₄₃	—	4	2	no	—
172	C₂×C₄×C₄₃	—	4	2	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	—	4	2	no	—
175	C₂×C₄×C₄₃	—	4	2	no	—
176	C₂×C₄×C₄₃	—	4	2	no	—
177	C₂×C₄×C₄₃	—	4	2	no	—
178	C₂×C₄×C₄₃	—	4	2	no	—
179	C₂×C₄×C₄₃	—	4	2	no	—
180	C₂×C₄×C₄₃	—	4	2	no	—
181	C₂×C₄×C₄₃	#120	1	2	yes	—
182	C₂×C₄×C₄₃	#120	1	2	yes	—
183	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
184	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
185	C₂×C₄×C₄₃	#137	1	2	yes	—
186	C₂×C₄×C₄₃	#137	1	2	yes	—
187	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
188	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
189	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
190	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
191	C₈×C₄₃	—	4	4	no	—
192	#29664	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂²×C₄₃	—	2	2	no	—
194	C₂²×C₄₃	—	2	2	no	—
195	C₂²×C₄₃	—	2	2	no	—
196	C₂²×C₄₃	—	4	1	no	—
197	C₂²×C₄₃	—	4	1	no	—
198	C₂²×C₄₃	—	4	1	no	—
199	C₂²×C₄₃	—	4	1	no	—
200	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
201	C₂²×C₄₃	#535	1	1	yes	characteristic
202	C₂²×C₄₃	#537	1	1	yes	characteristic
203	C₂²×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
204	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
205	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
206	C₂²×C₄₃	#575	1	1	yes	characteristic
207	C₄×C₄₃	—	2	2	no	—
208	C₄×C₄₃	—	2	2	no	—
209	C₄×C₄₃	—	2	2	no	—
210	C₄×C₄₃	—	4	1	no	—
211	C₄×C₄₃	—	4	4	no	—
212	C₄×C₄₃	—	4	4	no	—
213	C₄×C₄₃	—	8	2	no	—
214	C₄×C₄₃	—	8	2	no	—
215	C₄×C₄₃	#451	1	4	yes	—
216	C₄×C₄₃	#535	1	2	yes	—
217	C₄×C₄₃	#537	1	2	yes	—
218	C₂×#533	C₂×C₄₃	1	1	yes	characteristic
219	C₂×#462	C₂×C₄₃	1	2	yes	complemented
220	#2857	C₂×C₄₃	1	1	yes	characteristic
221	#2024	C₂×C₄₃	1	2	yes	complemented
222	#2016	C₂×C₄₃	1	2	yes	complemented
223	#2001	C₂×C₄₃	1	4	yes	—
224	#1803	C₂×C₄₃	1	2	yes	complemented
225	#1797	C₂×C₄₃	1	1	yes	characteristic
226	C₂×C₄₃	—	4	2	no	—
227	C₂×C₄₃	#2615	1	1	yes	characteristic
228	C₂×C₄₃	C₂×#451	1	1	yes	characteristic
229	C₂×C₄₃	#3007	1	1	yes	characteristic
230	C₂×C₄₃	#3209	1	1	yes	characteristic
231	C₂×C₄₃	#3216	1	1	yes	characteristic
232	C₂×C₄₃	#3249	1	1	yes	characteristic
233	C₂×C₄₃	#3255	1	1	yes	characteristic
234	C₂²×Q₁₆	C₂²×C₄₃	1	4	yes	—
235	#533	—	2	8	no	—
236	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
237	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
238	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
239	C₂×#125	—	2	1	no	—
240	C₂×C₂²⋊Q₈	—	2	1	no	—
241	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
242	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
243	C₂×C₄×Q₈	—	2	1	no	—
244	C₂×C₄×Q₈	C₂²×C₄₃	1	2	yes	—
245	C₂×#117	—	2	1	no	—
246	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
247	#462	—	2	8	no	—
248	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
249	C₂×#103	C₂²×C₄₃	1	4	yes	—
250	C₂×#103	C₂²×C₄₃	1	4	yes	—
251	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
252	#391	C₂²×C₄₃	1	2	yes	—
253	#389	—	2	1	no	—
254	#389	—	2	1	no	—
255	#384	C₂²×C₄₃	1	1	yes	characteristic
256	#380	—	2	1	no	—
257	#380	—	2	1	no	—
258	#340	C₂²×C₄₃	1	4	yes	—
259	#336	C₂²×C₄₃	1	2	yes	—
260	C₄₃	#29664	1	1	yes	characteristic, direct product factor, Sylow
261	C₂²×Q₈	—	2	1	no	—
262	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
263	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
264	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
265	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
266	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
267	C₂×Q₁₆	—	2	8	no	—
268	C₂×Q₁₆	—	4	4	no	—
269	C₂×Q₁₆	—	4	4	no	—
270	C₂²×C₈	C₂³×C₄₃	1	4	yes	—
271	C₄⋊Q₈	—	2	4	no	—
272	C₄⋊Q₈	—	2	4	no	—
273	C₄⋊Q₈	—	2	4	no	—
274	#125	—	2	8	no	—
275	C₂²⋊Q₈	—	2	8	no	—
276	C₂²⋊Q₈	—	2	4	no	—
277	C₂²⋊Q₈	—	2	4	no	—
278	C₂²⋊Q₈	—	4	4	no	—
279	C₄×Q₈	—	2	8	no	—
280	C₄×Q₈	—	2	4	no	—
281	C₄×Q₈	D₄×C₄₃	1	8	yes	—
282	#117	—	2	8	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	1	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	2	2	no	—
287	C₂×C₄⋊C₄	—	2	2	no	—
288	C₂×C₄⋊C₄	—	2	2	no	—
289	C₂×C₄⋊C₄	—	2	1	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	1	no	—
292	C₂×C₄⋊C₄	—	2	1	no	—
293	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
294	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	—	2	4	no	—
299	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
300	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
301	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
302	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
303	C₄⋊C₈	—	2	4	no	—
304	#103	—	2	8	no	—
305	#103	—	4	4	no	—
306	C₂²⋊C₈	—	4	2	no	—
307	#95	—	2	2	no	—
308	#95	—	2	2	no	—
309	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	—	2	2	no	—
312	C₂×Q₈	—	2	4	no	—
313	C₂×Q₈	—	2	2	no	—
314	C₂×Q₈	—	2	2	no	—
315	C₂×Q₈	—	2	2	no	—
316	C₂×Q₈	—	2	4	no	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	4	2	no	—
321	C₂×Q₈	—	4	2	no	—
322	C₂×Q₈	C₂×D₄×C₄₃	1	4	yes	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	1	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	4	1	no	—
336	C₂²×C₄	Q₁₆×C₄₃	1	4	yes	complemented
337	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
338	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
340	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
342	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
343	Q₁₆	—	4	16	no	—
344	C₂×C₈	—	2	4	no	—
345	C₂×C₈	—	2	4	no	—
346	C₂×C₈	—	2	4	no	—
347	C₄⋊C₄	—	2	4	no	—
348	C₄⋊C₄	—	2	4	no	—
349	C₄⋊C₄	—	2	8	no	—
350	C₄⋊C₄	—	2	4	no	—
351	C₄⋊C₄	—	2	8	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	4	no	—
354	C₄⋊C₄	—	4	4	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₄⋊C₄	—	4	2	no	—
357	C₄⋊C₄	—	4	2	no	—
358	C₄⋊C₄	—	4	2	no	—
359	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
360	C₂²⋊C₄	—	2	8	no	—
361	C₂²⋊C₄	—	4	4	no	—
362	C₄²	—	2	2	no	—
363	C₄²	—	2	2	no	—
364	C₄²	—	2	8	no	—
365	C₄²	—	2	2	no	—
366	C₄²	C₂×D₄×C₄₃	1	4	yes	—
367	C₂³	—	2	1	no	—
368	C₂³	—	2	1	no	—
369	C₂³	—	2	1	no	—
370	C₂³	—	2	1	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	C₂×Q₁₆×C₄₃	1	2	yes	—
374	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
375	Q₈	—	2	4	no	—
376	Q₈	—	2	4	no	—
377	Q₈	—	4	8	no	—
378	Q₈	—	4	2	no	—
379	Q₈	—	4	2	no	—
380	Q₈	—	4	4	no	—
381	Q₈	—	4	4	no	—
382	C₂×C₄	—	2	1	no	—
383	C₂×C₄	—	2	1	no	—
384	C₂×C₄	—	2	1	no	—
385	C₂×C₄	—	2	1	no	—
386	C₂×C₄	—	2	1	no	—
387	C₂×C₄	—	2	1	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	1	no	—
390	C₂×C₄	—	2	4	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	4	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	#120×C₄₃	1	2	yes	—
408	C₂×C₄	#120×C₄₃	1	2	yes	—
409	C₂×C₄	C₂×Q₁₆×C₄₃	1	2	yes	—
410	C₂×C₄	C₂×Q₁₆×C₄₃	1	2	yes	—
411	C₂×C₄	#137×C₄₃	1	2	yes	—
412	C₂×C₄	#137×C₄₃	1	2	yes	—
413	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
414	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
415	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
416	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
417	C₈	—	4	4	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	4	1	no	—
422	C₂²	—	4	1	no	—
423	C₂²	—	4	1	no	—
424	C₂²	—	4	1	no	—
425	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
426	C₂²	C₄₃×#535	1	1	yes	characteristic
427	C₂²	C₄₃×#537	1	1	yes	characteristic
428	C₂²	C₂²×Q₁₆×C₄₃	1	1	yes	characteristic
429	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
430	C₂²	C₂×#137×C₄₃	1	1	yes	characteristic
431	C₂²	C₄₃×#575	1	1	yes	characteristic
432	C₄	—	2	2	no	—
433	C₄	—	2	2	no	—
434	C₄	—	2	2	no	—
435	C₄	—	4	1	no	—
436	C₄	—	4	4	no	—
437	C₄	—	4	4	no	—
438	C₄	—	8	2	no	—
439	C₄	—	8	2	no	—
440	C₄	C₄₃×#451	1	4	yes	—
441	C₄	C₄₃×#535	1	2	yes	—
442	C₄	C₄₃×#537	1	2	yes	—
443	C₂	—	4	2	no	—
444	C₂	C₄₃×#2615	1	1	yes	characteristic
445	C₂	C₂×C₄₃×#451	1	1	yes	characteristic
446	C₂	C₄₃×#3007	1	1	yes	characteristic
447	C₂	C₄₃×#3209	1	1	yes	characteristic
448	C₂	C₄₃×#3216	1	1	yes	characteristic
449	C₂	C₄₃×#3249	1	1	yes	characteristic
450	C₂	C₄₃×#3255	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂⁴×C₄₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#462	C₂	semidirect
4. C₄₃×#2024	C₂	semidirect
5. C₄₃×#2016	C₂	semidirect
7. C₄₃×#1803	C₂	semidirect
110. C₂²×C₄×C₄₃	Q₁₆	semidirect
192. #29664	C₄₃	direct (N × H)
219. C₂×#462	C₂×C₄₃	semidirect
221. #2024	C₂×C₄₃	semidirect
222. #2016	C₂×C₄₃	semidirect
224. #1803	C₂×C₄₃	semidirect
260. C₄₃	#29664	direct (N × H)
336. C₂²×C₄	Q₁₆×C₄₃	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#533	2
C₂×C₄₃×#462	2
C₄₃×#2857	2
C₄₃×#2024	2
C₄₃×#2016	2
C₄₃×#2001	2
C₄₃×#1803	2
C₄₃×#1797	2
#29664	43

Subgroups — C43×#29664 #24949681

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29664 #24949681