Subgroups — C₄₃×#8943 #24928960

Order 11008.

688 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#432	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#121×C₄₃	C₂	1	1	yes	maximal, characteristic
3	C₄×C₂²⋊C₈×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×D₄⋊C₈	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1279	C₂	1	2	yes	maximal, complemented
6	C₂×#121×C₄₃	C₄	1	1	yes	characteristic
7	C₂×C₄×D₄×C₄₃	—	2	1	no	—
8	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
9	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
10	C₄₃×#432	—	2	4	no	—
11	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
12	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
13	C₂×C₂²⋊C₈×C₄₃	—	2	1	no	—
14	C₂×#97×C₄₃	—	2	1	no	—
15	C₂×C₄×C₈×C₄₃	C₂²	1	2	yes	—
16	C₄₃×#390	C₄	1	1	yes	characteristic
17	C₄₃×#389	C₄	1	1	yes	characteristic
18	C₄₃×#388	—	2	1	no	—
19	C₄₃×#386	—	2	1	no	—
20	C₄₃×#380	C₄	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
22	C₄×C₂²⋊C₄×C₄₃	—	2	1	no	—
23	C₄₃×#336	—	2	1	no	—
24	C₄₃×D₄⋊C₈	—	2	4	no	—
25	C₂²×D₄×C₄₃	—	2	1	no	—
26	C₂²×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
27	C₂³×C₄×C₄₃	—	2	1	no	—
28	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
30	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
31	C₂²×C₈×C₄₃	—	2	2	no	—
32	C₂²×C₈×C₄₃	—	2	2	no	—
33	#121×C₄₃	—	2	2	no	—
34	#121×C₄₃	—	2	2	no	—
35	C₄×D₄×C₄₃	—	2	2	no	—
36	C₄×D₄×C₄₃	—	2	2	no	—
37	C₄×D₄×C₄₃	—	4	4	no	—
38	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
39	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
40	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
41	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
43	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
44	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
46	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
47	C₂×C₄²×C₄₃	—	2	2	no	—
48	C₂×C₄²×C₄₃	—	2	2	no	—
49	C₂×C₄²×C₄₃	—	2	1	no	—
50	C₂×C₄²×C₄₃	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
52	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
53	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
54	C₄⋊C₈×C₄₃	—	2	2	no	—
55	C₄⋊C₈×C₄₃	D₄	1	4	yes	complemented
56	C₂²⋊C₈×C₄₃	—	2	4	no	—
57	C₂²⋊C₈×C₄₃	—	2	4	no	—
58	#97×C₄₃	—	2	4	no	—
59	C₄×C₈×C₄₃	—	2	2	no	—
60	C₄×C₈×C₄₃	—	2	2	no	—
61	#95×C₄₃	—	2	1	no	—
62	#95×C₄₃	—	2	1	no	—
63	#95×C₄₃	—	2	1	no	—
64	C₂⁴×C₄₃	—	2	1	no	—
65	C₂⁴×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
66	C₂×D₄×C₄₃	—	2	4	no	—
67	C₂×D₄×C₄₃	—	2	1	no	—
68	C₂×D₄×C₄₃	—	2	2	no	—
69	C₂×D₄×C₄₃	—	2	2	no	—
70	C₂×D₄×C₄₃	—	4	2	no	—
71	C₂×D₄×C₄₃	—	4	2	no	—
72	C₂×D₄×C₄₃	M₁₆	1	2	yes	—
73	C₂²×C₄×C₄₃	—	2	2	no	—
74	C₂²×C₄×C₄₃	—	2	1	no	—
75	C₂²×C₄×C₄₃	—	2	2	no	—
76	C₂²×C₄×C₄₃	—	2	1	no	—
77	C₂²×C₄×C₄₃	—	2	1	no	—
78	C₂²×C₄×C₄₃	—	2	1	no	—
79	C₂²×C₄×C₄₃	—	2	2	no	—
80	C₂²×C₄×C₄₃	—	2	2	no	—
81	C₂²×C₄×C₄₃	—	2	2	no	—
82	C₂²×C₄×C₄₃	—	2	2	no	—
83	C₂²×C₄×C₄₃	—	2	1	no	—
84	C₂²×C₄×C₄₃	—	2	1	no	—
85	C₂²×C₄×C₄₃	—	2	1	no	—
86	C₂²×C₄×C₄₃	—	4	1	no	—
87	C₂²×C₄×C₄₃	—	4	1	no	—
88	C₂²×C₄×C₄₃	—	4	1	no	—
89	C₂²×C₄×C₄₃	—	4	2	no	—
90	C₂²×C₄×C₄₃	—	4	2	no	—
91	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
93	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
94	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
97	C₂×C₈×C₄₃	—	2	4	no	—
98	C₂×C₈×C₄₃	—	2	4	no	—
99	C₂×C₈×C₄₃	—	4	2	no	—
100	C₂×C₈×C₄₃	—	4	2	no	—
101	C₂×C₈×C₄₃	—	4	2	no	—
102	C₂×C₈×C₄₃	—	4	2	no	—
103	C₄⋊C₄×C₄₃	—	2	1	no	—
104	C₄⋊C₄×C₄₃	—	2	2	no	—
105	C₄⋊C₄×C₄₃	—	2	2	no	—
106	C₄⋊C₄×C₄₃	—	4	2	no	—
107	C₄⋊C₄×C₄₃	M₁₆	1	2	yes	—
108	C₂²⋊C₄×C₄₃	—	2	4	no	—
109	C₂²⋊C₄×C₄₃	—	4	2	no	—
110	C₂²⋊C₄×C₄₃	—	4	2	no	—
111	C₂²⋊C₄×C₄₃	—	4	2	no	—
112	C₂²⋊C₄×C₄₃	—	4	2	no	—
113	C₄²×C₄₃	—	2	2	no	—
114	C₄²×C₄₃	—	2	1	no	—
115	C₄²×C₄₃	—	2	2	no	—
116	C₄²×C₄₃	—	2	1	no	—
117	C₄²×C₄₃	—	4	2	no	—
118	C₄²×C₄₃	C₂×D₄	1	2	yes	—
119	C₄²×C₄₃	#41	1	2	yes	—
120	C₂³×C₄₃	—	2	1	no	—
121	C₂³×C₄₃	—	2	1	no	—
122	C₂³×C₄₃	—	2	1	no	—
123	C₂³×C₄₃	—	2	1	no	—
124	C₂³×C₄₃	—	2	1	no	—
125	C₂³×C₄₃	—	2	1	no	—
126	C₂³×C₄₃	—	2	2	no	—
127	C₂³×C₄₃	—	4	1	no	—
128	C₂³×C₄₃	—	4	1	no	—
129	C₂³×C₄₃	—	4	1	no	—
130	C₂³×C₄₃	—	4	1	no	—
131	C₂³×C₄₃	—	4	1	no	—
132	C₂³×C₄₃	—	4	1	no	—
133	C₂³×C₄₃	#104	1	2	yes	—
134	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	D₄×C₄₃	—	2	4	no	—
136	D₄×C₄₃	—	4	8	no	—
137	D₄×C₄₃	—	4	2	no	—
138	C₂×C₄×C₄₃	—	2	1	no	—
139	C₂×C₄×C₄₃	—	2	1	no	—
140	C₂×C₄×C₄₃	—	2	1	no	—
141	C₂×C₄×C₄₃	—	2	1	no	—
142	C₂×C₄×C₄₃	—	2	1	no	—
143	C₂×C₄×C₄₃	—	2	1	no	—
144	C₂×C₄×C₄₃	—	2	2	no	—
145	C₂×C₄×C₄₃	—	2	1	no	—
146	C₂×C₄×C₄₃	—	2	1	no	—
147	C₂×C₄×C₄₃	—	2	1	no	—
148	C₂×C₄×C₄₃	—	2	1	no	—
149	C₂×C₄×C₄₃	—	2	1	no	—
150	C₂×C₄×C₄₃	—	4	4	no	—
151	C₂×C₄×C₄₃	—	4	1	no	—
152	C₂×C₄×C₄₃	—	4	1	no	—
153	C₂×C₄×C₄₃	—	4	2	no	—
154	C₂×C₄×C₄₃	—	4	2	no	—
155	C₂×C₄×C₄₃	—	4	2	no	—
156	C₂×C₄×C₄₃	—	4	2	no	—
157	C₂×C₄×C₄₃	—	4	1	no	—
158	C₂×C₄×C₄₃	—	4	1	no	—
159	C₂×C₄×C₄₃	—	4	1	no	—
160	C₂×C₄×C₄₃	—	4	1	no	—
161	C₂×C₄×C₄₃	—	4	1	no	—
162	C₂×C₄×C₄₃	—	4	1	no	—
163	C₂×C₄×C₄₃	—	8	2	no	—
164	C₂×C₄×C₄₃	—	8	2	no	—
165	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
166	C₂×C₄×C₄₃	#120	1	1	yes	characteristic
167	C₂×C₄×C₄₃	#121	1	2	yes	—
168	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
170	C₂×C₄×C₄₃	C₂×M₁₆	1	1	yes	characteristic
171	C₂×C₄×C₄₃	#131	1	2	yes	—
172	C₂×C₄×C₄₃	#135	1	2	yes	—
173	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
174	C₈×C₄₃	—	4	4	no	—
175	C₈×C₄₃	—	4	4	no	—
176	#8943	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
177	C₂²×C₄₃	—	2	2	no	—
178	C₂²×C₄₃	—	2	2	no	—
179	C₂²×C₄₃	—	2	2	no	—
180	C₂²×C₄₃	—	4	1	no	—
181	C₂²×C₄₃	—	4	1	no	—
182	C₂²×C₄₃	—	4	1	no	—
183	C₂²×C₄₃	—	4	1	no	—
184	C₂²×C₄₃	—	4	2	no	—
185	C₂²×C₄₃	—	4	2	no	—
186	C₂²×C₄₃	—	4	2	no	—
187	C₂²×C₄₃	—	8	1	no	—
188	C₂²×C₄₃	—	8	1	no	—
189	C₂²×C₄₃	—	8	1	no	—
190	C₂²×C₄₃	—	8	1	no	—
191	C₂²×C₄₃	#386	1	1	yes	characteristic
192	C₂²×C₄₃	#407	1	1	yes	characteristic
193	C₂²×C₄₃	#408	1	1	yes	characteristic
194	C₂²×C₄₃	#416	1	1	yes	characteristic
195	C₂²×C₄₃	#418	1	1	yes	characteristic
196	C₂²×C₄₃	C₂×#104	1	1	yes	characteristic
197	C₂²×C₄₃	#421	1	1	yes	characteristic
198	C₄×C₄₃	—	2	2	no	—
199	C₄×C₄₃	—	4	1	no	—
200	C₄×C₄₃	—	4	1	no	—
201	C₄×C₄₃	—	4	1	no	—
202	C₄×C₄₃	—	4	2	no	—
203	C₄×C₄₃	—	8	1	no	—
204	C₄×C₄₃	—	8	1	no	—
205	C₄×C₄₃	#435	1	2	yes	—
206	C₄×C₄₃	#436	1	2	yes	—
207	C₄×C₄₃	#449	1	2	yes	—
208	C₄×C₄₃	#482	1	2	yes	—
209	C₂×#432	C₂×C₄₃	1	1	yes	characteristic, complemented
210	C₄×#121	C₂×C₄₃	1	1	yes	characteristic
211	C₄×C₂²⋊C₈	C₂×C₄₃	1	1	yes	characteristic, complemented
212	C₂×D₄⋊C₈	C₂×C₄₃	1	2	yes	complemented
213	#1279	C₂×C₄₃	1	2	yes	complemented
214	C₂×C₄₃	—	4	2	no	—
215	C₂×C₄₃	—	8	2	no	—
216	C₂×C₄₃	#1488	1	1	yes	characteristic
217	C₂×C₄₃	#1490	1	1	yes	characteristic
218	C₂×C₄₃	#1494	1	1	yes	characteristic
219	C₂×C₄₃	#1496	1	1	yes	characteristic
220	C₂×C₄₃	#1870	1	1	yes	characteristic
221	C₂×C₄₃	#1871	1	1	yes	characteristic
222	C₂×C₄₃	#1875	1	1	yes	characteristic
223	C₂×#121	C₄×C₄₃	1	1	yes	characteristic
224	C₂×C₄×D₄	—	2	1	no	—
225	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
226	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
227	#432	—	2	4	no	—
228	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
229	C₂×C₂²⋊C₈	—	2	1	no	—
230	C₂×C₂²⋊C₈	—	2	1	no	—
231	C₂×#97	—	2	1	no	—
232	C₂×C₄×C₈	C₂²×C₄₃	1	2	yes	—
233	#390	C₄×C₄₃	1	1	yes	characteristic
234	#389	C₄×C₄₃	1	1	yes	characteristic
235	#388	—	2	1	no	—
236	#386	—	2	1	no	—
237	#380	C₄×C₄₃	1	1	yes	characteristic
238	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
239	C₄×C₂²⋊C₄	—	2	1	no	—
240	#336	—	2	1	no	—
241	D₄⋊C₈	—	2	4	no	—
242	C₄₃	#8943	1	1	yes	characteristic, direct product factor, Sylow
243	C₂²×D₄	—	2	1	no	—
244	C₂²×D₄	C₂×C₄×C₄₃	1	1	yes	characteristic
245	C₂³×C₄	—	2	1	no	—
246	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
247	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
248	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
249	C₂²×C₈	—	2	2	no	—
250	C₂²×C₈	—	2	2	no	—
251	#121	—	2	2	no	—
252	#121	—	2	2	no	—
253	C₄×D₄	—	2	2	no	—
254	C₄×D₄	—	2	2	no	—
255	C₄×D₄	—	4	4	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
259	C₂×C₄⋊C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
260	C₂×C₂²⋊C₄	—	2	1	no	—
261	C₂×C₂²⋊C₄	—	2	1	no	—
262	C₂×C₂²⋊C₄	—	2	1	no	—
263	C₂×C₂²⋊C₄	—	2	1	no	—
264	C₂×C₂²⋊C₄	—	2	1	no	—
265	C₂×C₄²	—	2	2	no	—
266	C₂×C₄²	—	2	2	no	—
267	C₂×C₄²	—	2	1	no	—
268	C₂×C₄²	C₂×C₄×C₄₃	1	1	yes	characteristic
269	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
270	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
271	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
272	C₄⋊C₈	—	2	2	no	—
273	C₄⋊C₈	D₄×C₄₃	1	4	yes	complemented
274	C₂²⋊C₈	—	2	4	no	—
275	C₂²⋊C₈	—	2	4	no	—
276	#97	—	2	4	no	—
277	C₄×C₈	—	2	2	no	—
278	C₄×C₈	—	2	2	no	—
279	#95	—	2	1	no	—
280	#95	—	2	1	no	—
281	#95	—	2	1	no	—
282	C₂⁴	—	2	1	no	—
283	C₂⁴	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
284	C₂×D₄	—	2	4	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	2	1	no	—
287	C₂×D₄	—	2	2	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	M₁₆×C₄₃	1	2	yes	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	2	no	—
296	C₂²×C₄	—	2	1	no	—
297	C₂²×C₄	—	2	1	no	—
298	C₂²×C₄	—	2	1	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	—	2	2	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	—	2	1	no	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	4	1	no	—
305	C₂²×C₄	—	4	1	no	—
306	C₂²×C₄	—	4	1	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
310	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
311	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
312	C₂²×C₄	C₂²×C₄×C₄₃	1	1	yes	characteristic
313	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
314	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
315	C₂×C₈	—	2	4	no	—
316	C₂×C₈	—	2	4	no	—
317	C₂×C₈	—	4	2	no	—
318	C₂×C₈	—	4	2	no	—
319	C₂×C₈	—	4	2	no	—
320	C₂×C₈	—	4	2	no	—
321	C₄⋊C₄	—	2	1	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	4	2	no	—
325	C₄⋊C₄	M₁₆×C₄₃	1	2	yes	—
326	C₂²⋊C₄	—	2	4	no	—
327	C₂²⋊C₄	—	4	2	no	—
328	C₂²⋊C₄	—	4	2	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	4	2	no	—
331	C₄²	—	2	2	no	—
332	C₄²	—	2	1	no	—
333	C₄²	—	2	2	no	—
334	C₄²	—	2	1	no	—
335	C₄²	—	4	2	no	—
336	C₄²	C₂×D₄×C₄₃	1	2	yes	—
337	C₄²	#41×C₄₃	1	2	yes	—
338	C₂³	—	2	1	no	—
339	C₂³	—	2	1	no	—
340	C₂³	—	2	1	no	—
341	C₂³	—	2	1	no	—
342	C₂³	—	2	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	4	1	no	—
346	C₂³	—	4	1	no	—
347	C₂³	—	4	1	no	—
348	C₂³	—	4	1	no	—
349	C₂³	—	4	1	no	—
350	C₂³	—	4	1	no	—
351	C₂³	#104×C₄₃	1	2	yes	—
352	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
353	D₄	—	2	4	no	—
354	D₄	—	4	8	no	—
355	D₄	—	4	2	no	—
356	C₂×C₄	—	2	1	no	—
357	C₂×C₄	—	2	1	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	1	no	—
361	C₂×C₄	—	2	1	no	—
362	C₂×C₄	—	2	2	no	—
363	C₂×C₄	—	2	1	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	1	no	—
368	C₂×C₄	—	4	4	no	—
369	C₂×C₄	—	4	1	no	—
370	C₂×C₄	—	4	1	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	1	no	—
376	C₂×C₄	—	4	1	no	—
377	C₂×C₄	—	4	1	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	8	2	no	—
382	C₂×C₄	—	8	2	no	—
383	C₂×C₄	C₄×D₄×C₄₃	1	2	yes	—
384	C₂×C₄	#120×C₄₃	1	1	yes	characteristic
385	C₂×C₄	#121×C₄₃	1	2	yes	—
386	C₂×C₄	#123×C₄₃	1	1	yes	characteristic
387	C₂×C₄	C₂×M₁₆×C₄₃	1	1	yes	characteristic
388	C₂×C₄	C₂×M₁₆×C₄₃	1	1	yes	characteristic
389	C₂×C₄	#131×C₄₃	1	2	yes	—
390	C₂×C₄	#135×C₄₃	1	2	yes	—
391	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
392	C₈	—	4	4	no	—
393	C₈	—	4	4	no	—
394	C₂²	—	2	2	no	—
395	C₂²	—	2	2	no	—
396	C₂²	—	2	2	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	1	no	—
399	C₂²	—	4	1	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	4	2	no	—
403	C₂²	—	4	2	no	—
404	C₂²	—	8	1	no	—
405	C₂²	—	8	1	no	—
406	C₂²	—	8	1	no	—
407	C₂²	—	8	1	no	—
408	C₂²	C₄₃×#386	1	1	yes	characteristic
409	C₂²	C₄₃×#407	1	1	yes	characteristic
410	C₂²	C₄₃×#408	1	1	yes	characteristic
411	C₂²	C₄₃×#416	1	1	yes	characteristic
412	C₂²	C₄₃×#418	1	1	yes	characteristic
413	C₂²	C₂×#104×C₄₃	1	1	yes	characteristic
414	C₂²	C₄₃×#421	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	4	1	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	4	2	no	—
420	C₄	—	8	1	no	—
421	C₄	—	8	1	no	—
422	C₄	C₄₃×#435	1	2	yes	—
423	C₄	C₄₃×#436	1	2	yes	—
424	C₄	C₄₃×#449	1	2	yes	—
425	C₄	C₄₃×#482	1	2	yes	—
426	C₂	—	4	2	no	—
427	C₂	—	8	2	no	—
428	C₂	C₄₃×#1488	1	1	yes	characteristic
429	C₂	C₄₃×#1490	1	1	yes	characteristic
430	C₂	C₄₃×#1494	1	1	yes	characteristic
431	C₂	C₄₃×#1496	1	1	yes	characteristic
432	C₂	C₄₃×#1870	1	1	yes	characteristic
433	C₂	C₄₃×#1871	1	1	yes	characteristic
434	C₂	C₄₃×#1875	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₄₃	C₂×D₄
commutator	C₂²×C₄	C₂²×C₄×C₄₃
Frattini, cosocle	C₂×C₄²	C₂³×C₄₃
socle	C₂³×C₄₃	C₂×C₂²⋊C₄
prime radical	C₂×#121×C₄₃	C₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₃ ◁ C₂²×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₃×#432	C₂	semidirect
3. C₄×C₂²⋊C₈×C₄₃	C₂	semidirect
4. C₂×C₄₃×D₄⋊C₈	C₂	semidirect
5. C₄₃×#1279	C₂	semidirect
55. C₄⋊C₈×C₄₃	D₄	semidirect
176. #8943	C₄₃	direct (N × H)
209. C₂×#432	C₂×C₄₃	semidirect
211. C₄×C₂²⋊C₈	C₂×C₄₃	semidirect
212. C₂×D₄⋊C₈	C₂×C₄₃	semidirect
213. #1279	C₂×C₄₃	semidirect
242. C₄₃	#8943	direct (N × H)
273. C₄⋊C₈	D₄×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×#432	2
C₄×#121×C₄₃	2
C₄×C₂²⋊C₈×C₄₃	2
C₂×C₄₃×D₄⋊C₈	2
C₄₃×#1279	2
#8943	43

Subgroups — C43×#8943 #24928960

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#8943 #24928960