Subgroups — C₄₃×#29640 #24949657

Order 11008.

1076 conjugacy classes of subgroups.

The subgroup lattice has 422 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, complemented
2	C₂×C₄₃×#481	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₃×#480	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2854	C₂	1	1	yes	maximal, characteristic
5	C₄₃×#2059	C₂	1	4	yes	maximal, complemented
6	C₄₃×#2025	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1824	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₃×#1823	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₃×#1817	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#125×C₄₃	—	2	4	no	—
11	C₂×#125×C₄₃	—	2	4	no	—
12	C₂×#125×C₄₃	—	2	2	no	—
13	C₂×#125×C₄₃	C₂²	1	4	yes	—
14	C₂×#123×C₄₃	—	2	1	no	—
15	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₄₃	—	2	1	no	—
18	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
21	C₄₃×#481	—	2	4	no	—
22	C₄₃×#480	—	2	4	no	—
23	C₂×#107×C₄₃	C₂²	1	2	yes	—
24	C₂×#106×C₄₃	C₂²	1	2	yes	—
25	C₂×#102×C₄₃	C₂²	1	2	yes	—
26	C₂×#102×C₄₃	C₂²	1	2	yes	—
27	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
29	C₄₃×#390	C₂²	1	2	yes	—
30	C₄₃×#389	C₂²	1	2	yes	—
31	C₄₃×#388	—	2	2	no	—
32	C₄₃×#386	—	2	1	no	—
33	C₄₃×#380	C₂²	1	1	yes	characteristic
34	C₄₃×#340	C₂²	1	4	yes	—
35	C₄₃×#340	C₂²	1	4	yes	—
36	C₄₃×#336	C₂²	1	4	yes	—
37	C₂²×D₄×C₄₃	—	2	1	no	—
38	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₄₃	—	2	1	no	—
40	C₂³×C₄×C₄₃	—	2	1	no	—
41	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₃	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
44	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
45	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
46	#125×C₄₃	—	2	16	no	—
47	#125×C₄₃	—	2	8	no	—
48	#125×C₄₃	—	2	8	no	—
49	#123×C₄₃	—	4	4	no	—
50	#121×C₄₃	—	2	2	no	—
51	#121×C₄₃	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
53	C₂×C₄⋊C₄×C₄₃	—	2	8	no	—
54	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
55	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
56	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₄₃	D₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
66	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
67	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
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	2	no	—
73	C₂×C₄²×C₄₃	D₄	1	2	yes	—
74	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
75	#107×C₄₃	—	2	4	no	—
76	#106×C₄₃	—	2	4	no	—
77	#102×C₄₃	—	2	4	no	—
78	#102×C₄₃	—	2	4	no	—
79	C₂²⋊C₈×C₄₃	—	2	2	no	—
80	C₂²⋊C₈×C₄₃	—	2	2	no	—
81	#95×C₄₃	—	2	1	no	—
82	#95×C₄₃	—	2	2	no	—
83	C₂⁴×C₄₃	—	2	1	no	—
84	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
85	C₂×D₄×C₄₃	—	2	1	no	—
86	C₂×D₄×C₄₃	—	2	1	no	—
87	C₂×D₄×C₄₃	—	2	4	no	—
88	C₂×D₄×C₄₃	—	4	2	no	—
89	C₂×D₄×C₄₃	—	4	2	no	—
90	C₂×D₄×C₄₃	—	4	2	no	—
91	C₂²×C₄×C₄₃	—	2	4	no	—
92	C₂²×C₄×C₄₃	—	2	2	no	—
93	C₂²×C₄×C₄₃	—	2	2	no	—
94	C₂²×C₄×C₄₃	—	2	4	no	—
95	C₂²×C₄×C₄₃	—	2	4	no	—
96	C₂²×C₄×C₄₃	—	2	2	no	—
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	1	no	—
102	C₂²×C₄×C₄₃	—	4	2	no	—
103	C₂²×C₄×C₄₃	—	4	4	no	—
104	C₂²×C₄×C₄₃	—	4	2	no	—
105	C₂²×C₄×C₄₃	—	4	2	no	—
106	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
108	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
112	C₂×C₈×C₄₃	—	2	2	no	—
113	C₂×C₈×C₄₃	—	2	2	no	—
114	C₂×C₈×C₄₃	—	2	4	no	—
115	C₂×C₈×C₄₃	—	2	4	no	—
116	C₄⋊C₄×C₄₃	—	2	16	no	—
117	C₄⋊C₄×C₄₃	—	2	16	no	—
118	C₄⋊C₄×C₄₃	—	2	4	no	—
119	C₄⋊C₄×C₄₃	—	2	4	no	—
120	C₄⋊C₄×C₄₃	—	2	2	no	—
121	C₄⋊C₄×C₄₃	—	2	2	no	—
122	C₄⋊C₄×C₄₃	—	2	1	no	—
123	C₄⋊C₄×C₄₃	—	2	1	no	—
124	C₄⋊C₄×C₄₃	—	2	4	no	—
125	C₄⋊C₄×C₄₃	—	4	4	no	—
126	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
127	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
128	C₂²⋊C₄×C₄₃	—	4	4	no	—
129	C₂²⋊C₄×C₄₃	—	4	4	no	—
130	C₂²⋊C₄×C₄₃	—	4	2	no	—
131	C₂²⋊C₄×C₄₃	—	4	2	no	—
132	C₄²×C₄₃	—	2	4	no	—
133	C₄²×C₄₃	—	2	2	no	—
134	C₄²×C₄₃	—	2	2	no	—
135	C₂³×C₄₃	—	2	2	no	—
136	C₂³×C₄₃	—	2	2	no	—
137	C₂³×C₄₃	—	4	1	no	—
138	C₂³×C₄₃	—	4	2	no	—
139	C₂³×C₄₃	—	4	1	no	—
140	C₂³×C₄₃	—	4	1	no	—
141	C₂³×C₄₃	—	4	2	no	—
142	C₂³×C₄₃	#120	1	2	yes	—
143	C₂³×C₄₃	#135	1	2	yes	—
144	C₂³×C₄₃	AGL(1,ℤ/8)	1	2	yes	—
145	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
146	D₄×C₄₃	—	4	2	no	—
147	D₄×C₄₃	—	4	2	no	—
148	D₄×C₄₃	—	8	4	no	—
149	C₂×C₄×C₄₃	—	2	2	no	—
150	C₂×C₄×C₄₃	—	2	4	no	—
151	C₂×C₄×C₄₃	—	2	4	no	—
152	C₂×C₄×C₄₃	—	2	2	no	—
153	C₂×C₄×C₄₃	—	2	2	no	—
154	C₂×C₄×C₄₃	—	2	4	no	—
155	C₂×C₄×C₄₃	—	2	4	no	—
156	C₂×C₄×C₄₃	—	2	2	no	—
157	C₂×C₄×C₄₃	—	2	2	no	—
158	C₂×C₄×C₄₃	—	2	2	no	—
159	C₂×C₄×C₄₃	—	2	2	no	—
160	C₂×C₄×C₄₃	—	4	4	no	—
161	C₂×C₄×C₄₃	—	4	8	no	—
162	C₂×C₄×C₄₃	—	4	2	no	—
163	C₂×C₄×C₄₃	—	4	2	no	—
164	C₂×C₄×C₄₃	—	4	4	no	—
165	C₂×C₄×C₄₃	—	4	4	no	—
166	C₂×C₄×C₄₃	—	4	8	no	—
167	C₂×C₄×C₄₃	—	4	1	no	—
168	C₂×C₄×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	—	4	1	no	—
170	C₂×C₄×C₄₃	—	4	2	no	—
171	C₂×C₄×C₄₃	—	4	1	no	—
172	C₂×C₄×C₄₃	—	4	2	no	—
173	C₂×C₄×C₄₃	#120	1	2	yes	—
174	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
175	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
176	C₂×C₄×C₄₃	2₋¹⁺⁴	1	4	yes	—
177	C₈×C₄₃	—	4	2	no	—
178	C₈×C₄₃	—	4	2	no	—
179	#29640	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂²×C₄₃	—	2	2	no	—
181	C₂²×C₄₃	—	2	4	no	—
182	C₂²×C₄₃	—	2	4	no	—
183	C₂²×C₄₃	—	2	2	no	—
184	C₂²×C₄₃	—	8	1	no	—
185	C₂²×C₄₃	—	8	2	no	—
186	C₂²×C₄₃	—	8	2	no	—
187	C₂²×C₄₃	—	8	1	no	—
188	C₂²×C₄₃	—	8	1	no	—
189	C₂²×C₄₃	#449	1	4	yes	—
190	C₂²×C₄₃	C₂×#120	1	1	yes	characteristic
191	C₂²×C₄₃	#536	1	2	yes	—
192	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
193	C₂²×C₄₃	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₂²×C₄₃	#575	1	2	yes	—
195	C₄×C₄₃	—	2	2	no	—
196	C₄×C₄₃	—	4	2	no	—
197	C₄×C₄₃	—	4	4	no	—
198	C₄×C₄₃	—	4	2	no	—
199	C₄×C₄₃	—	4	4	no	—
200	C₄×C₄₃	—	8	2	no	—
201	C₄×C₄₃	—	8	1	no	—
202	C₄×C₄₃	#536	1	2	yes	—
203	C₄×C₄₃	#536	1	2	yes	—
204	C₂²×#125	C₂×C₄₃	1	1	yes	characteristic, complemented
205	C₂×#481	C₂×C₄₃	1	1	yes	characteristic
206	C₂×#480	C₂×C₄₃	1	1	yes	characteristic
207	#2854	C₂×C₄₃	1	1	yes	characteristic
208	#2059	C₂×C₄₃	1	4	yes	complemented
209	#2025	C₂×C₄₃	1	4	yes	complemented
210	#1824	C₂×C₄₃	1	1	yes	characteristic, complemented
211	#1823	C₂×C₄₃	1	1	yes	characteristic, complemented
212	#1817	C₂×C₄₃	1	1	yes	characteristic, complemented
213	C₂×C₄₃	—	2	4	no	—
214	C₂×C₄₃	—	16	1	no	—
215	C₂×C₄₃	#2614	1	1	yes	characteristic
216	C₂×C₄₃	C₂×#449	1	1	yes	characteristic
217	C₂×C₄₃	#3005	1	1	yes	characteristic
218	C₂×C₄₃	#3232	1	2	yes	—
219	C₂×C₄₃	#3234	1	2	yes	—
220	C₂×#125	—	2	4	no	—
221	C₂×#125	—	2	4	no	—
222	C₂×#125	—	2	2	no	—
223	C₂×#125	C₂²×C₄₃	1	4	yes	—
224	C₂×#123	—	2	1	no	—
225	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
226	C₂²×C₄⋊C₄	—	2	1	no	—
227	C₂²×C₄⋊C₄	—	2	1	no	—
228	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
229	C₂²×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
230	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
231	#481	—	2	4	no	—
232	#480	—	2	4	no	—
233	C₂×#107	C₂²×C₄₃	1	2	yes	—
234	C₂×#106	C₂²×C₄₃	1	2	yes	—
235	C₂×#102	C₂²×C₄₃	1	2	yes	—
236	C₂×#102	C₂²×C₄₃	1	2	yes	—
237	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
238	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
239	#390	C₂²×C₄₃	1	2	yes	—
240	#389	C₂²×C₄₃	1	2	yes	—
241	#388	—	2	2	no	—
242	#386	—	2	1	no	—
243	#380	C₂²×C₄₃	1	1	yes	characteristic
244	#340	C₂²×C₄₃	1	4	yes	—
245	#340	C₂²×C₄₃	1	4	yes	—
246	#336	C₂²×C₄₃	1	4	yes	—
247	C₄₃	#29640	1	1	yes	characteristic, direct product factor, Sylow
248	C₂²×D₄	—	2	1	no	—
249	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
250	C₂³×C₄	—	2	1	no	—
251	C₂³×C₄	—	2	1	no	—
252	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
253	C₂³×C₄	D₄×C₄₃	1	1	yes	characteristic
254	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
255	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
256	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
257	#125	—	2	16	no	—
258	#125	—	2	8	no	—
259	#125	—	2	8	no	—
260	#123	—	4	4	no	—
261	#121	—	2	2	no	—
262	#121	—	2	2	no	—
263	C₂×C₄⋊C₄	—	2	8	no	—
264	C₂×C₄⋊C₄	—	2	8	no	—
265	C₂×C₄⋊C₄	—	2	4	no	—
266	C₂×C₄⋊C₄	—	2	4	no	—
267	C₂×C₄⋊C₄	—	2	1	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	2	no	—
272	C₂×C₄⋊C₄	D₄×C₄₃	1	4	yes	—
273	C₂×C₄⋊C₄	D₄×C₄₃	1	4	yes	—
274	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
275	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
277	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
278	C₂×C₂²⋊C₄	—	2	1	no	—
279	C₂×C₂²⋊C₄	—	2	1	no	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₄²	—	2	2	no	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	D₄×C₄₃	1	2	yes	—
285	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
286	#107	—	2	4	no	—
287	#106	—	2	4	no	—
288	#102	—	2	4	no	—
289	#102	—	2	4	no	—
290	C₂²⋊C₈	—	2	2	no	—
291	C₂²⋊C₈	—	2	2	no	—
292	#95	—	2	1	no	—
293	#95	—	2	2	no	—
294	C₂⁴	—	2	1	no	—
295	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
296	C₂×D₄	—	2	1	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	4	no	—
299	C₂×D₄	—	4	2	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	—	4	2	no	—
302	C₂²×C₄	—	2	4	no	—
303	C₂²×C₄	—	2	2	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	4	no	—
306	C₂²×C₄	—	2	4	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	4	2	no	—
314	C₂²×C₄	—	4	4	no	—
315	C₂²×C₄	—	4	2	no	—
316	C₂²×C₄	—	4	2	no	—
317	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
318	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
319	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
320	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
321	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
322	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	2	no	—
325	C₂×C₈	—	2	4	no	—
326	C₂×C₈	—	2	4	no	—
327	C₄⋊C₄	—	2	16	no	—
328	C₄⋊C₄	—	2	16	no	—
329	C₄⋊C₄	—	2	4	no	—
330	C₄⋊C₄	—	2	4	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	1	no	—
334	C₄⋊C₄	—	2	1	no	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	4	4	no	—
337	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
338	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
339	C₂²⋊C₄	—	4	4	no	—
340	C₂²⋊C₄	—	4	4	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₂²⋊C₄	—	4	2	no	—
343	C₄²	—	2	4	no	—
344	C₄²	—	2	2	no	—
345	C₄²	—	2	2	no	—
346	C₂³	—	2	2	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	4	1	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	1	no	—
351	C₂³	—	4	1	no	—
352	C₂³	—	4	2	no	—
353	C₂³	#120×C₄₃	1	2	yes	—
354	C₂³	#135×C₄₃	1	2	yes	—
355	C₂³	AGL(1,ℤ/8)×C₄₃	1	2	yes	—
356	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
357	D₄	—	4	2	no	—
358	D₄	—	4	2	no	—
359	D₄	—	8	4	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	2	4	no	—
366	C₂×C₄	—	2	4	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	2	2	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	4	4	no	—
372	C₂×C₄	—	4	8	no	—
373	C₂×C₄	—	4	2	no	—
374	C₂×C₄	—	4	2	no	—
375	C₂×C₄	—	4	4	no	—
376	C₂×C₄	—	4	4	no	—
377	C₂×C₄	—	4	8	no	—
378	C₂×C₄	—	4	1	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	1	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	#120×C₄₃	1	2	yes	—
385	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
386	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
387	C₂×C₄	2₋¹⁺⁴×C₄₃	1	4	yes	—
388	C₈	—	4	2	no	—
389	C₈	—	4	2	no	—
390	C₂²	—	2	2	no	—
391	C₂²	—	2	4	no	—
392	C₂²	—	2	4	no	—
393	C₂²	—	2	2	no	—
394	C₂²	—	8	1	no	—
395	C₂²	—	8	2	no	—
396	C₂²	—	8	2	no	—
397	C₂²	—	8	1	no	—
398	C₂²	—	8	1	no	—
399	C₂²	C₄₃×#449	1	4	yes	—
400	C₂²	C₂×#120×C₄₃	1	1	yes	characteristic
401	C₂²	C₄₃×#536	1	2	yes	—
402	C₂²	C₂×#135×C₄₃	1	1	yes	characteristic
403	C₂²	C₂×AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
404	C₂²	C₄₃×#575	1	2	yes	—
405	C₄	—	2	2	no	—
406	C₄	—	4	2	no	—
407	C₄	—	4	4	no	—
408	C₄	—	4	2	no	—
409	C₄	—	4	4	no	—
410	C₄	—	8	2	no	—
411	C₄	—	8	1	no	—
412	C₄	C₄₃×#536	1	2	yes	—
413	C₄	C₄₃×#536	1	2	yes	—
414	C₂	—	2	4	no	—
415	C₂	—	16	1	no	—
416	C₂	C₄₃×#2614	1	1	yes	characteristic
417	C₂	C₂×C₄₃×#449	1	1	yes	characteristic
418	C₂	C₄₃×#3005	1	1	yes	characteristic
419	C₂	C₄₃×#3232	1	2	yes	—
420	C₂	C₄₃×#3234	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂×#121×C₄₃	C₂²
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
1. C₂²×#125×C₄₃	C₂	semidirect
5. C₄₃×#2059	C₂	semidirect
6. C₄₃×#2025	C₂	semidirect
7. C₄₃×#1824	C₂	semidirect
8. C₄₃×#1823	C₂	semidirect
9. C₄₃×#1817	C₂	semidirect
179. #29640	C₄₃	direct (N × H)
204. C₂²×#125	C₂×C₄₃	semidirect
208. #2059	C₂×C₄₃	semidirect
209. #2025	C₂×C₄₃	semidirect
210. #1824	C₂×C₄₃	semidirect
211. #1823	C₂×C₄₃	semidirect
212. #1817	C₂×C₄₃	semidirect
247. C₄₃	#29640	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×#481	2
C₂×C₄₃×#480	2
C₄₃×#2854	2
C₄₃×#2059	2
C₄₃×#2025	2
C₄₃×#1824	2
C₄₃×#1823	2
C₄₃×#1817	2
#29640	43

Subgroups — C43×#29640 #24949657

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29640 #24949657