Subgroups — C₄₃×#18137 #24938154

Order 11008.

1398 conjugacy classes of subgroups.

The subgroup lattice has 466 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#534	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#3094	C₂	1	2	yes	maximal, complemented
3	C₄₃×#2482	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#1613	C₂	1	4	yes	maximal, complemented
5	C₄₃×#1607	C₂	1	4	yes	maximal, complemented
6	C₄₃×#1510	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1462	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₄₃	—	2	1	no	—
9	C₄₃×#534	—	2	4	no	—
10	C₄₃×#534	—	2	2	no	—
11	C₄₃×#534	C₂²	1	4	yes	—
12	C₂×#123×C₄₃	—	2	2	no	—
13	C₂×#121×C₄₃	—	2	1	no	—
14	C₂×#121×C₄₃	C₂²	1	2	yes	—
15	C₂×#120×C₄₃	—	2	2	no	—
16	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
18	C₄₃×#482	—	2	4	no	—
19	C₄₃×#481	C₂²	1	4	yes	complemented
20	C₄₃×#480	C₂²	1	4	yes	complemented
21	C₄₃×#428	—	2	2	no	—
22	C₄₃×#418	—	2	2	no	—
23	C₄₃×#407	C₂²	1	2	yes	complemented
24	C₄₃×#399	C₂²	1	2	yes	complemented
25	C₄₃×#397	C₂²	1	2	yes	complemented
26	C₄₃×#388	—	2	2	no	—
27	C₄₃×#385	—	2	1	no	—
28	C₄₃×#381	C₂²	1	1	yes	characteristic, complemented
29	C₄₃×#379	—	2	1	no	—
30	C₄₃×#327	C₂²	1	8	yes	complemented
31	C₄₃×#323	C₂²	1	4	yes	complemented
32	C₂⁵×C₄₃	—	2	1	no	—
33	C₂⁵×C₄₃	D₄	1	1	yes	characteristic
34	C₂²×D₄×C₄₃	—	2	2	no	—
35	C₂²×D₄×C₄₃	—	2	4	no	—
36	C₂²×D₄×C₄₃	—	2	2	no	—
37	C₂²×D₄×C₄₃	—	2	4	no	—
38	C₂²×D₄×C₄₃	—	2	1	no	—
39	C₂²×D₄×C₄₃	—	4	8	no	—
40	C₂²×D₄×C₄₃	D₄	1	2	yes	—
41	C₂³×C₄×C₄₃	—	2	1	no	—
42	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
44	C₂×M₁₆×C₄₃	—	2	2	no	—
45	#123×C₄₃	—	2	8	no	—
46	#123×C₄₃	—	2	8	no	—
47	#121×C₄₃	—	2	4	no	—
48	#121×C₄₃	—	2	4	no	—
49	#121×C₄₃	—	2	2	no	—
50	#121×C₄₃	—	2	2	no	—
51	#121×C₄₃	D₄	1	4	yes	—
52	#121×C₄₃	C₂³	1	4	yes	—
53	#120×C₄₃	—	2	8	no	—
54	#120×C₄₃	—	2	8	no	—
55	#117×C₄₃	—	2	2	no	—
56	#117×C₄₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
60	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic, complemented
61	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic, complemented
62	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
66	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₃	D₄	1	2	yes	—
71	C₂×C₂²⋊C₄×C₄₃	C₂³	1	2	yes	—
72	C₂×C₄²×C₄₃	—	2	1	no	—
73	#107×C₄₃	—	2	4	no	—
74	#106×C₄₃	—	2	4	no	—
75	#102×C₄₃	—	2	4	no	—
76	#102×C₄₃	—	2	4	no	—
77	C₂²⋊C₈×C₄₃	—	2	2	no	—
78	C₂²⋊C₈×C₄₃	C₂³	1	4	yes	complemented
79	#95×C₄₃	—	2	1	no	—
80	#95×C₄₃	—	2	2	no	—
81	#95×C₄₃	C₂³	1	2	yes	complemented
82	C₂⁴×C₄₃	—	2	1	no	—
83	C₂⁴×C₄₃	—	2	1	no	—
84	C₂⁴×C₄₃	—	2	4	no	—
85	C₂⁴×C₄₃	—	2	4	no	—
86	C₂⁴×C₄₃	—	2	2	no	—
87	C₂⁴×C₄₃	—	4	4	no	—
88	C₂⁴×C₄₃	—	4	2	no	—
89	C₂⁴×C₄₃	—	8	1	no	—
90	C₂⁴×C₄₃	—	8	2	no	—
91	C₂⁴×C₄₃	—	8	2	no	—
92	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
93	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
94	C₂×D₄×C₄₃	—	2	8	no	—
95	C₂×D₄×C₄₃	—	2	4	no	—
96	C₂×D₄×C₄₃	—	2	2	no	—
97	C₂×D₄×C₄₃	—	2	4	no	—
98	C₂×D₄×C₄₃	—	2	4	no	—
99	C₂×D₄×C₄₃	—	4	8	no	—
100	C₂×D₄×C₄₃	—	4	16	no	—
101	C₂×D₄×C₄₃	—	4	8	no	—
102	C₂×D₄×C₄₃	—	4	8	no	—
103	C₂×D₄×C₄₃	—	4	8	no	—
104	C₂×D₄×C₄₃	—	4	4	no	—
105	C₂×D₄×C₄₃	—	8	2	no	—
106	C₂×D₄×C₄₃	C₂×D₄	1	4	yes	—
107	C₂²×C₄×C₄₃	—	2	4	no	—
108	C₂²×C₄×C₄₃	—	2	1	no	—
109	C₂²×C₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	—	2	1	no	—
111	C₂²×C₄×C₄₃	—	2	2	no	—
112	C₂²×C₄×C₄₃	—	2	1	no	—
113	C₂²×C₄×C₄₃	—	2	1	no	—
114	C₂²×C₄×C₄₃	—	4	2	no	—
115	C₂²×C₄×C₄₃	—	4	4	no	—
116	C₂²×C₄×C₄₃	—	8	1	no	—
117	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
122	M₁₆×C₄₃	—	4	4	no	—
123	C₂×C₈×C₄₃	—	2	4	no	—
124	C₄⋊C₄×C₄₃	—	2	4	no	—
125	C₄⋊C₄×C₄₃	—	2	2	no	—
126	C₄⋊C₄×C₄₃	—	2	2	no	—
127	C₄⋊C₄×C₄₃	—	2	2	no	—
128	C₄⋊C₄×C₄₃	—	8	2	no	—
129	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
130	C₂²⋊C₄×C₄₃	—	2	8	no	—
131	C₂²⋊C₄×C₄₃	—	2	4	no	—
132	C₂²⋊C₄×C₄₃	—	2	4	no	—
133	C₂²⋊C₄×C₄₃	—	2	4	no	—
134	C₂²⋊C₄×C₄₃	—	2	4	no	—
135	C₂²⋊C₄×C₄₃	—	4	2	no	—
136	C₂²⋊C₄×C₄₃	—	4	1	no	—
137	C₂²⋊C₄×C₄₃	—	4	1	no	—
138	C₂²⋊C₄×C₄₃	—	4	4	no	—
139	C₂²⋊C₄×C₄₃	—	8	2	no	—
140	C₄²×C₄₃	—	4	2	no	—
141	C₂³×C₄₃	—	2	4	no	—
142	C₂³×C₄₃	—	2	4	no	—
143	C₂³×C₄₃	—	2	2	no	—
144	C₂³×C₄₃	—	2	2	no	—
145	C₂³×C₄₃	—	2	2	no	—
146	C₂³×C₄₃	—	2	2	no	—
147	C₂³×C₄₃	—	2	4	no	—
148	C₂³×C₄₃	—	4	1	no	—
149	C₂³×C₄₃	—	4	2	no	—
150	C₂³×C₄₃	—	4	2	no	—
151	C₂³×C₄₃	—	4	2	no	—
152	C₂³×C₄₃	—	4	4	no	—
153	C₂³×C₄₃	—	4	8	no	—
154	C₂³×C₄₃	—	4	4	no	—
155	C₂³×C₄₃	—	4	2	no	—
156	C₂³×C₄₃	—	4	4	no	—
157	C₂³×C₄₃	—	8	1	no	—
158	C₂³×C₄₃	—	8	1	no	—
159	C₂³×C₄₃	—	8	8	no	—
160	C₂³×C₄₃	—	8	4	no	—
161	C₂³×C₄₃	—	8	4	no	—
162	C₂³×C₄₃	—	8	16	no	—
163	C₂³×C₄₃	#120	1	1	yes	characteristic
164	C₂³×C₄₃	#120	1	1	yes	characteristic
165	C₂³×C₄₃	AGL(1,ℤ/8)	1	4	yes	—
166	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
167	D₄×C₄₃	—	4	4	no	—
168	D₄×C₄₃	—	4	16	no	—
169	D₄×C₄₃	—	4	8	no	—
170	D₄×C₄₃	—	4	8	no	—
171	D₄×C₄₃	—	8	2	no	—
172	D₄×C₄₃	—	8	4	no	—
173	C₂×C₄×C₄₃	—	2	4	no	—
174	C₂×C₄×C₄₃	—	2	2	no	—
175	C₂×C₄×C₄₃	—	2	4	no	—
176	C₂×C₄×C₄₃	—	4	2	no	—
177	C₂×C₄×C₄₃	—	4	1	no	—
178	C₂×C₄×C₄₃	—	4	1	no	—
179	C₂×C₄×C₄₃	—	4	4	no	—
180	C₂×C₄×C₄₃	—	4	8	no	—
181	C₂×C₄×C₄₃	—	4	2	no	—
182	C₂×C₄×C₄₃	—	4	2	no	—
183	C₂×C₄×C₄₃	—	4	2	no	—
184	C₂×C₄×C₄₃	—	4	2	no	—
185	C₂×C₄×C₄₃	—	4	2	no	—
186	C₂×C₄×C₄₃	—	4	1	no	—
187	C₂×C₄×C₄₃	—	4	1	no	—
188	C₂×C₄×C₄₃	—	4	2	no	—
189	C₂×C₄×C₄₃	—	4	2	no	—
190	C₂×C₄×C₄₃	—	8	1	no	—
191	C₂×C₄×C₄₃	#120	1	2	yes	—
192	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
193	C₈×C₄₃	—	4	4	no	—
194	#18137	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂²×C₄₃	—	2	1	no	—
196	C₂²×C₄₃	—	2	1	no	—
197	C₂²×C₄₃	—	2	1	no	—
198	C₂²×C₄₃	—	2	1	no	—
199	C₂²×C₄₃	—	2	4	no	—
200	C₂²×C₄₃	—	2	1	no	—
201	C₂²×C₄₃	—	2	1	no	—
202	C₂²×C₄₃	—	2	1	no	—
203	C₂²×C₄₃	—	4	4	no	—
204	C₂²×C₄₃	—	4	4	no	—
205	C₂²×C₄₃	—	4	8	no	—
206	C₂²×C₄₃	—	4	2	no	—
207	C₂²×C₄₃	—	4	2	no	—
208	C₂²×C₄₃	—	4	4	no	—
209	C₂²×C₄₃	—	4	4	no	—
210	C₂²×C₄₃	—	4	4	no	—
211	C₂²×C₄₃	—	8	2	no	—
212	C₂²×C₄₃	—	8	8	no	—
213	C₂²×C₄₃	—	8	4	no	—
214	C₂²×C₄₃	—	8	16	no	—
215	C₂²×C₄₃	#458	1	2	yes	—
216	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
217	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
218	C₄×C₄₃	—	2	2	no	—
219	C₄×C₄₃	—	2	2	no	—
220	C₄×C₄₃	—	4	4	no	—
221	C₄×C₄₃	—	4	2	no	—
222	C₄×C₄₃	—	8	2	no	—
223	C₄×C₄₃	—	8	1	no	—
224	C₄×C₄₃	—	8	1	no	—
225	C₂×#534	C₂×C₄₃	1	1	yes	characteristic
226	#3094	C₂×C₄₃	1	2	yes	complemented
227	#2482	C₂×C₄₃	1	1	yes	characteristic, complemented
228	#1613	C₂×C₄₃	1	4	yes	complemented
229	#1607	C₂×C₄₃	1	4	yes	complemented
230	#1510	C₂×C₄₃	1	2	yes	complemented
231	#1462	C₂×C₄₃	1	1	yes	characteristic, complemented
232	C₂×C₄₃	—	2	2	no	—
233	C₂×C₄₃	—	2	2	no	—
234	C₂×C₄₃	—	4	1	no	—
235	C₂×C₄₃	—	4	4	no	—
236	C₂×C₄₃	—	8	4	no	—
237	C₂×C₄₃	#3003	1	1	yes	characteristic
238	C₂×C₄₃	#3019	1	1	yes	characteristic
239	C₂×C₄₃	C₂×#458	1	1	yes	characteristic
240	C₂³×D₄	—	2	1	no	—
241	#534	—	2	4	no	—
242	#534	—	2	2	no	—
243	#534	C₂²×C₄₃	1	4	yes	—
244	C₂×#123	—	2	2	no	—
245	C₂×#121	—	2	1	no	—
246	C₂×#121	C₂²×C₄₃	1	2	yes	—
247	C₂×#120	—	2	2	no	—
248	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic, complemented
249	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
250	#482	—	2	4	no	—
251	#481	C₂²×C₄₃	1	4	yes	complemented
252	#480	C₂²×C₄₃	1	4	yes	complemented
253	#428	—	2	2	no	—
254	#418	—	2	2	no	—
255	#407	C₂²×C₄₃	1	2	yes	complemented
256	#399	C₂²×C₄₃	1	2	yes	complemented
257	#397	C₂²×C₄₃	1	2	yes	complemented
258	#388	—	2	2	no	—
259	#385	—	2	1	no	—
260	#381	C₂²×C₄₃	1	1	yes	characteristic, complemented
261	#379	—	2	1	no	—
262	#327	C₂²×C₄₃	1	8	yes	complemented
263	#323	C₂²×C₄₃	1	4	yes	complemented
264	C₄₃	#18137	1	1	yes	characteristic, direct product factor, Sylow
265	C₂⁵	—	2	1	no	—
266	C₂⁵	D₄×C₄₃	1	1	yes	characteristic
267	C₂²×D₄	—	2	2	no	—
268	C₂²×D₄	—	2	4	no	—
269	C₂²×D₄	—	2	2	no	—
270	C₂²×D₄	—	2	4	no	—
271	C₂²×D₄	—	2	1	no	—
272	C₂²×D₄	—	4	8	no	—
273	C₂²×D₄	D₄×C₄₃	1	2	yes	—
274	C₂³×C₄	—	2	1	no	—
275	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
276	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
277	C₂×M₁₆	—	2	2	no	—
278	#123	—	2	8	no	—
279	#123	—	2	8	no	—
280	#121	—	2	4	no	—
281	#121	—	2	4	no	—
282	#121	—	2	2	no	—
283	#121	—	2	2	no	—
284	#121	D₄×C₄₃	1	4	yes	—
285	#121	C₂³×C₄₃	1	4	yes	—
286	#120	—	2	8	no	—
287	#120	—	2	8	no	—
288	#117	—	2	2	no	—
289	#117	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	2	no	—
292	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
293	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic, complemented
294	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic, complemented
295	C₂×C₂²⋊C₄	—	2	2	no	—
296	C₂×C₂²⋊C₄	—	2	2	no	—
297	C₂×C₂²⋊C₄	—	2	2	no	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₂²⋊C₄	D₄×C₄₃	1	2	yes	—
304	C₂×C₂²⋊C₄	C₂³×C₄₃	1	2	yes	—
305	C₂×C₄²	—	2	1	no	—
306	#107	—	2	4	no	—
307	#106	—	2	4	no	—
308	#102	—	2	4	no	—
309	#102	—	2	4	no	—
310	C₂²⋊C₈	—	2	2	no	—
311	C₂²⋊C₈	C₂³×C₄₃	1	4	yes	complemented
312	#95	—	2	1	no	—
313	#95	—	2	2	no	—
314	#95	C₂³×C₄₃	1	2	yes	complemented
315	C₂⁴	—	2	1	no	—
316	C₂⁴	—	2	1	no	—
317	C₂⁴	—	2	4	no	—
318	C₂⁴	—	2	4	no	—
319	C₂⁴	—	2	2	no	—
320	C₂⁴	—	4	4	no	—
321	C₂⁴	—	4	2	no	—
322	C₂⁴	—	8	1	no	—
323	C₂⁴	—	8	2	no	—
324	C₂⁴	—	8	2	no	—
325	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
326	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
327	C₂×D₄	—	2	8	no	—
328	C₂×D₄	—	2	4	no	—
329	C₂×D₄	—	2	4	no	—
330	C₂×D₄	—	2	4	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	4	4	no	—
333	C₂×D₄	—	4	8	no	—
334	C₂×D₄	—	4	16	no	—
335	C₂×D₄	—	4	8	no	—
336	C₂×D₄	—	4	8	no	—
337	C₂×D₄	—	4	8	no	—
338	C₂×D₄	—	8	2	no	—
339	C₂×D₄	C₂×D₄×C₄₃	1	4	yes	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	4	2	no	—
348	C₂²×C₄	—	4	4	no	—
349	C₂²×C₄	—	8	1	no	—
350	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
351	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
352	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
354	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
355	M₁₆	—	4	4	no	—
356	C₂×C₈	—	2	4	no	—
357	C₄⋊C₄	—	2	4	no	—
358	C₄⋊C₄	—	2	2	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	8	2	no	—
362	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
363	C₂²⋊C₄	—	2	8	no	—
364	C₂²⋊C₄	—	2	4	no	—
365	C₂²⋊C₄	—	2	4	no	—
366	C₂²⋊C₄	—	2	4	no	—
367	C₂²⋊C₄	—	2	4	no	—
368	C₂²⋊C₄	—	4	2	no	—
369	C₂²⋊C₄	—	4	1	no	—
370	C₂²⋊C₄	—	4	1	no	—
371	C₂²⋊C₄	—	4	4	no	—
372	C₂²⋊C₄	—	8	2	no	—
373	C₄²	—	4	2	no	—
374	C₂³	—	2	4	no	—
375	C₂³	—	2	4	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	2	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	2	2	no	—
380	C₂³	—	2	4	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	2	no	—
383	C₂³	—	4	2	no	—
384	C₂³	—	4	2	no	—
385	C₂³	—	4	4	no	—
386	C₂³	—	4	8	no	—
387	C₂³	—	4	4	no	—
388	C₂³	—	4	2	no	—
389	C₂³	—	4	4	no	—
390	C₂³	—	8	1	no	—
391	C₂³	—	8	1	no	—
392	C₂³	—	8	8	no	—
393	C₂³	—	8	4	no	—
394	C₂³	—	8	4	no	—
395	C₂³	—	8	16	no	—
396	C₂³	#120×C₄₃	1	1	yes	characteristic
397	C₂³	#120×C₄₃	1	1	yes	characteristic
398	C₂³	AGL(1,ℤ/8)×C₄₃	1	4	yes	—
399	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
400	D₄	—	4	4	no	—
401	D₄	—	4	16	no	—
402	D₄	—	4	8	no	—
403	D₄	—	4	8	no	—
404	D₄	—	8	2	no	—
405	D₄	—	8	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	1	no	—
411	C₂×C₄	—	4	1	no	—
412	C₂×C₄	—	4	4	no	—
413	C₂×C₄	—	4	8	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	1	no	—
420	C₂×C₄	—	4	1	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	8	1	no	—
424	C₂×C₄	#120×C₄₃	1	2	yes	—
425	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
426	C₈	—	4	4	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	8	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	4	4	no	—
442	C₂²	—	4	4	no	—
443	C₂²	—	8	2	no	—
444	C₂²	—	8	8	no	—
445	C₂²	—	8	4	no	—
446	C₂²	—	8	16	no	—
447	C₂²	C₄₃×#458	1	2	yes	—
448	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
449	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	2	yes	—
450	C₄	—	2	2	no	—
451	C₄	—	2	2	no	—
452	C₄	—	4	4	no	—
453	C₄	—	4	2	no	—
454	C₄	—	8	2	no	—
455	C₄	—	8	1	no	—
456	C₄	—	8	1	no	—
457	C₂	—	2	2	no	—
458	C₂	—	2	2	no	—
459	C₂	—	4	1	no	—
460	C₂	—	4	4	no	—
461	C₂	—	8	4	no	—
462	C₂	C₄₃×#3003	1	1	yes	characteristic
463	C₂	C₄₃×#3019	1	1	yes	characteristic
464	C₂	C₂×C₄₃×#458	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₃	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×C₄₃×#534	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₃ ◁ C₂³×C₄×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#3094	C₂	semidirect
3. C₄₃×#2482	C₂	semidirect
4. C₄₃×#1613	C₂	semidirect
5. C₄₃×#1607	C₂	semidirect
6. C₄₃×#1510	C₂	semidirect
7. C₄₃×#1462	C₂	semidirect
16. C₂×#117×C₄₃	C₂²	semidirect
19. C₄₃×#481	C₂²	semidirect
20. C₄₃×#480	C₂²	semidirect
23. C₄₃×#407	C₂²	semidirect
24. C₄₃×#399	C₂²	semidirect
25. C₄₃×#397	C₂²	semidirect
28. C₄₃×#381	C₂²	semidirect
30. C₄₃×#327	C₂²	semidirect
31. C₄₃×#323	C₂²	semidirect
60. C₂×C₄⋊C₄×C₄₃	C₂³	semidirect
61. C₂×C₄⋊C₄×C₄₃	C₂³	semidirect
78. C₂²⋊C₈×C₄₃	C₂³	semidirect
81. #95×C₄₃	C₂³	semidirect
194. #18137	C₄₃	direct (N × H)
226. #3094	C₂×C₄₃	semidirect
227. #2482	C₂×C₄₃	semidirect
228. #1613	C₂×C₄₃	semidirect
229. #1607	C₂×C₄₃	semidirect
230. #1510	C₂×C₄₃	semidirect
231. #1462	C₂×C₄₃	semidirect
248. C₂×#117	C₂²×C₄₃	semidirect
251. #481	C₂²×C₄₃	semidirect
252. #480	C₂²×C₄₃	semidirect
255. #407	C₂²×C₄₃	semidirect
256. #399	C₂²×C₄₃	semidirect
257. #397	C₂²×C₄₃	semidirect
260. #381	C₂²×C₄₃	semidirect
262. #327	C₂²×C₄₃	semidirect
263. #323	C₂²×C₄₃	semidirect
264. C₄₃	#18137	direct (N × H)
293. C₂×C₄⋊C₄	C₂³×C₄₃	semidirect
294. C₂×C₄⋊C₄	C₂³×C₄₃	semidirect
311. C₂²⋊C₈	C₂³×C₄₃	semidirect
314. #95	C₂³×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×#534	2
C₄₃×#3094	2
C₄₃×#2482	2
C₄₃×#1613	2
C₄₃×#1607	2
C₄₃×#1510	2
C₄₃×#1462	2
#18137	43

Subgroups — C43×#18137 #24938154

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#18137 #24938154