Subgroups — C₄₃×#9653 #24929670

Order 11008.

920 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#390	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#1797	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#1749	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₃×#323	C₂	1	4	yes	maximal, complemented
5	C₂³×D₄×C₄₃	C₄	1	1	yes	characteristic
6	C₂²×C₄⋊C₄×C₄₃	C₄	1	1	yes	characteristic
7	C₂²×C₂²⋊C₄×C₄₃	C₄	1	2	yes	—
8	C₂²×C₂²⋊C₄×C₄₃	C₂²	1	2	yes	—
9	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
10	C₂×C₄⋊C₈×C₄₃	—	2	1	no	—
11	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
12	C₂×C₂²⋊C₈×C₄₃	C₂²	1	2	yes	—
13	C₂×#97×C₄₃	—	2	1	no	—
14	C₄₃×#390	—	2	1	no	—
15	C₄₃×#390	—	2	1	no	—
16	C₄₃×#390	—	2	1	no	—
17	C₄₃×#390	—	2	1	no	—
18	C₄₃×#336	—	2	1	no	—
19	C₄₃×#336	—	2	1	no	—
20	C₄₃×#323	—	2	8	no	—
21	C₂⁵×C₄₃	C₂×C₄	1	2	yes	—
22	C₂²×D₄×C₄₃	—	2	4	no	—
23	C₂²×D₄×C₄₃	—	2	1	no	—
24	C₂²×D₄×C₄₃	—	2	1	no	—
25	C₂²×D₄×C₄₃	—	4	2	no	—
26	C₂²×D₄×C₄₃	—	4	2	no	—
27	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
28	C₂³×C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
29	C₂³×C₄×C₄₃	C₂×C₄	1	2	yes	—
30	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
31	C₂²×C₈×C₄₃	—	2	2	no	—
32	C₂²×C₈×C₄₃	—	2	2	no	—
33	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
34	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
35	C₂×C₄⋊C₄×C₄₃	—	4	2	no	—
36	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
37	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
38	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
39	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
40	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
41	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
42	C₂×C₂²⋊C₄×C₄₃	—	4	4	no	—
43	C₂×C₄²×C₄₃	—	4	2	no	—
44	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
45	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
46	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
47	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
48	C₄⋊C₈×C₄₃	—	4	2	no	—
49	C₂²⋊C₈×C₄₃	—	2	2	no	—
50	C₂²⋊C₈×C₄₃	—	2	4	no	—
51	C₂²⋊C₈×C₄₃	D₄	1	4	yes	complemented
52	#97×C₄₃	—	4	2	no	—
53	C₂⁴×C₄₃	—	2	2	no	—
54	C₂⁴×C₄₃	—	2	2	no	—
55	C₂⁴×C₄₃	—	2	4	no	—
56	C₂⁴×C₄₃	—	2	4	no	—
57	C₂⁴×C₄₃	—	4	2	no	—
58	C₂⁴×C₄₃	—	4	2	no	—
59	C₂⁴×C₄₃	—	4	2	no	—
60	C₂⁴×C₄₃	—	4	2	no	—
61	C₂⁴×C₄₃	M₁₆	1	4	yes	—
62	C₂⁴×C₄₃	C₂²×C₄	1	1	yes	characteristic
63	C₂×D₄×C₄₃	—	2	4	no	—
64	C₂×D₄×C₄₃	—	2	4	no	—
65	C₂×D₄×C₄₃	—	4	16	no	—
66	C₂×D₄×C₄₃	—	4	2	no	—
67	C₂×D₄×C₄₃	—	4	2	no	—
68	C₂×D₄×C₄₃	—	4	2	no	—
69	C₂×D₄×C₄₃	—	4	2	no	—
70	C₂²×C₄×C₄₃	—	2	2	no	—
71	C₂²×C₄×C₄₃	—	2	2	no	—
72	C₂²×C₄×C₄₃	—	2	2	no	—
73	C₂²×C₄×C₄₃	—	2	2	no	—
74	C₂²×C₄×C₄₃	—	2	4	no	—
75	C₂²×C₄×C₄₃	—	2	2	no	—
76	C₂²×C₄×C₄₃	—	2	2	no	—
77	C₂²×C₄×C₄₃	—	4	1	no	—
78	C₂²×C₄×C₄₃	—	4	1	no	—
79	C₂²×C₄×C₄₃	—	4	1	no	—
80	C₂²×C₄×C₄₃	—	4	2	no	—
81	C₂²×C₄×C₄₃	—	4	2	no	—
82	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₃	C₂²⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
89	C₂²×C₄×C₄₃	#41	1	2	yes	—
90	C₂×C₈×C₄₃	—	2	4	no	—
91	C₂×C₈×C₄₃	—	4	2	no	—
92	C₂×C₈×C₄₃	—	4	2	no	—
93	C₂×C₈×C₄₃	—	4	2	no	—
94	C₂×C₈×C₄₃	—	4	2	no	—
95	C₂×C₈×C₄₃	—	4	2	no	—
96	C₄⋊C₄×C₄₃	—	4	2	no	—
97	C₄⋊C₄×C₄₃	—	4	2	no	—
98	C₂²⋊C₄×C₄₃	—	4	4	no	—
99	C₂²⋊C₄×C₄₃	—	4	4	no	—
100	C₂²⋊C₄×C₄₃	—	4	4	no	—
101	C₂²⋊C₄×C₄₃	—	4	2	no	—
102	C₂²⋊C₄×C₄₃	—	4	2	no	—
103	C₄²×C₄₃	—	2	2	no	—
104	C₄²×C₄₃	—	2	2	no	—
105	C₄²×C₄₃	—	4	1	no	—
106	C₄²×C₄₃	—	4	1	no	—
107	C₂³×C₄₃	—	2	1	no	—
108	C₂³×C₄₃	—	2	1	no	—
109	C₂³×C₄₃	—	2	1	no	—
110	C₂³×C₄₃	—	2	1	no	—
111	C₂³×C₄₃	—	2	4	no	—
112	C₂³×C₄₃	—	2	8	no	—
113	C₂³×C₄₃	—	4	4	no	—
114	C₂³×C₄₃	—	4	4	no	—
115	C₂³×C₄₃	—	4	4	no	—
116	C₂³×C₄₃	—	4	4	no	—
117	C₂³×C₄₃	—	4	2	no	—
118	C₂³×C₄₃	—	4	2	no	—
119	C₂³×C₄₃	—	4	2	no	—
120	C₂³×C₄₃	—	4	2	no	—
121	C₂³×C₄₃	—	4	2	no	—
122	C₂³×C₄₃	—	4	2	no	—
123	C₂³×C₄₃	—	4	4	no	—
124	C₂³×C₄₃	—	8	4	no	—
125	C₂³×C₄₃	—	8	4	no	—
126	C₂³×C₄₃	—	8	4	no	—
127	C₂³×C₄₃	—	8	4	no	—
128	C₂³×C₄₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
129	C₂³×C₄₃	C₄×D₄	1	2	yes	—
130	C₂³×C₄₃	C₂×M₁₆	1	2	yes	—
131	C₂³×C₄₃	#131	1	2	yes	—
132	D₄×C₄₃	—	4	8	no	—
133	D₄×C₄₃	—	4	8	no	—
134	C₂×C₄×C₄₃	—	2	8	no	—
135	C₂×C₄×C₄₃	—	2	1	no	—
136	C₂×C₄×C₄₃	—	2	1	no	—
137	C₂×C₄×C₄₃	—	2	1	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	1	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	—	4	2	no	—
149	C₂×C₄×C₄₃	—	4	2	no	—
150	C₂×C₄×C₄₃	—	4	4	no	—
151	C₂×C₄×C₄₃	—	4	2	no	—
152	C₂×C₄×C₄₃	—	4	2	no	—
153	C₂×C₄×C₄₃	—	4	2	no	—
154	C₂×C₄×C₄₃	—	8	4	no	—
155	C₂×C₄×C₄₃	#99	1	2	yes	—
156	C₂×C₄×C₄₃	#100	1	2	yes	—
157	C₂×C₄×C₄₃	#100	1	2	yes	—
158	C₂×C₄×C₄₃	#121	1	2	yes	—
159	C₂×C₄×C₄₃	#124	1	1	yes	characteristic
160	C₂×C₄×C₄₃	#127	1	1	yes	characteristic
161	C₈×C₄₃	—	4	4	no	—
162	C₈×C₄₃	—	8	2	no	—
163	#9653	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
164	C₂²×C₄₃	—	2	2	no	—
165	C₂²×C₄₃	—	2	2	no	—
166	C₂²×C₄₃	—	2	2	no	—
167	C₂²×C₄₃	—	2	2	no	—
168	C₂²×C₄₃	—	2	2	no	—
169	C₂²×C₄₃	—	2	2	no	—
170	C₂²×C₄₃	—	4	4	no	—
171	C₂²×C₄₃	—	4	4	no	—
172	C₂²×C₄₃	—	4	4	no	—
173	C₂²×C₄₃	—	8	8	no	—
174	C₂²×C₄₃	—	8	8	no	—
175	C₂²×C₄₃	—	8	2	no	—
176	C₂²×C₄₃	—	8	2	no	—
177	C₂²×C₄₃	—	8	2	no	—
178	C₂²×C₄₃	—	8	2	no	—
179	C₂²×C₄₃	#390	1	1	yes	characteristic
180	C₂²×C₄₃	#407	1	1	yes	characteristic
181	C₂²×C₄₃	#408	1	1	yes	characteristic
182	C₂²×C₄₃	C₂×#99	1	1	yes	characteristic
183	C₂²×C₄₃	#410	1	1	yes	characteristic
184	C₂²×C₄₃	C₂×#100	1	1	yes	characteristic
185	C₂²×C₄₃	C₂×#100	1	1	yes	characteristic
186	C₂²×C₄₃	#435	1	4	yes	—
187	C₄×C₄₃	—	2	2	no	—
188	C₄×C₄₃	—	2	1	no	—
189	C₄×C₄₃	—	2	1	no	—
190	C₄×C₄₃	—	2	2	no	—
191	C₄×C₄₃	—	2	2	no	—
192	C₄×C₄₃	—	2	2	no	—
193	C₄×C₄₃	—	4	1	no	—
194	C₄×C₄₃	—	8	2	no	—
195	C₂×#390	C₂×C₄₃	1	1	yes	characteristic
196	#1797	C₂×C₄₃	1	1	yes	characteristic, complemented
197	#1749	C₂×C₄₃	1	1	yes	characteristic, complemented
198	C₂×#323	C₂×C₄₃	1	4	yes	complemented
199	C₂×C₄₃	—	2	4	no	—
200	C₂×C₄₃	—	8	4	no	—
201	C₂×C₄₃	#1462	1	1	yes	characteristic
202	C₂×C₄₃	#1466	1	1	yes	characteristic
203	C₂×C₄₃	#1469	1	1	yes	characteristic
204	C₂×C₄₃	#1471	1	1	yes	characteristic
205	C₂×C₄₃	#1955	1	1	yes	characteristic
206	C₂×C₄₃	#1964	1	1	yes	characteristic
207	C₂×C₄₃	#1965	1	1	yes	characteristic
208	C₂³×D₄	C₄×C₄₃	1	1	yes	characteristic
209	C₂²×C₄⋊C₄	C₄×C₄₃	1	1	yes	characteristic
210	C₂²×C₂²⋊C₄	C₄×C₄₃	1	2	yes	—
211	C₂²×C₂²⋊C₄	C₂²×C₄₃	1	2	yes	—
212	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
213	C₂×C₄⋊C₈	—	2	1	no	—
214	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
215	C₂×C₂²⋊C₈	C₂²×C₄₃	1	2	yes	—
216	C₂×#97	—	2	1	no	—
217	#390	—	2	1	no	—
218	#390	—	2	1	no	—
219	#390	—	2	1	no	—
220	#390	—	2	1	no	—
221	#336	—	2	1	no	—
222	#336	—	2	1	no	—
223	#323	—	2	8	no	—
224	C₄₃	#9653	1	1	yes	characteristic, direct product factor, Sylow
225	C₂⁵	C₂×C₄×C₄₃	1	2	yes	—
226	C₂²×D₄	—	2	4	no	—
227	C₂²×D₄	—	2	1	no	—
228	C₂²×D₄	—	2	1	no	—
229	C₂²×D₄	—	4	2	no	—
230	C₂²×D₄	—	4	2	no	—
231	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
232	C₂³×C₄	C₂×C₄×C₄₃	1	1	yes	characteristic
233	C₂³×C₄	C₂×C₄×C₄₃	1	2	yes	—
234	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
235	C₂²×C₈	—	2	2	no	—
236	C₂²×C₈	—	2	2	no	—
237	C₂×C₄⋊C₄	—	2	1	no	—
238	C₂×C₄⋊C₄	—	2	1	no	—
239	C₂×C₄⋊C₄	—	4	2	no	—
240	C₂×C₂²⋊C₄	—	2	2	no	—
241	C₂×C₂²⋊C₄	—	2	2	no	—
242	C₂×C₂²⋊C₄	—	2	4	no	—
243	C₂×C₂²⋊C₄	—	2	2	no	—
244	C₂×C₂²⋊C₄	—	2	2	no	—
245	C₂×C₂²⋊C₄	—	2	4	no	—
246	C₂×C₂²⋊C₄	—	4	4	no	—
247	C₂×C₄²	—	4	2	no	—
248	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
249	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
250	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
251	C₂×C₄²	D₄×C₄₃	1	1	yes	characteristic
252	C₄⋊C₈	—	4	2	no	—
253	C₂²⋊C₈	—	2	2	no	—
254	C₂²⋊C₈	—	2	4	no	—
255	C₂²⋊C₈	D₄×C₄₃	1	4	yes	complemented
256	#97	—	4	2	no	—
257	C₂⁴	—	2	2	no	—
258	C₂⁴	—	2	2	no	—
259	C₂⁴	—	2	4	no	—
260	C₂⁴	—	2	4	no	—
261	C₂⁴	—	4	2	no	—
262	C₂⁴	—	4	2	no	—
263	C₂⁴	—	4	2	no	—
264	C₂⁴	—	4	2	no	—
265	C₂⁴	M₁₆×C₄₃	1	4	yes	—
266	C₂⁴	C₂²×C₄×C₄₃	1	1	yes	characteristic
267	C₂×D₄	—	2	4	no	—
268	C₂×D₄	—	2	4	no	—
269	C₂×D₄	—	4	16	no	—
270	C₂×D₄	—	4	2	no	—
271	C₂×D₄	—	4	2	no	—
272	C₂×D₄	—	4	2	no	—
273	C₂×D₄	—	4	2	no	—
274	C₂²×C₄	—	2	2	no	—
275	C₂²×C₄	—	2	2	no	—
276	C₂²×C₄	—	2	2	no	—
277	C₂²×C₄	—	2	2	no	—
278	C₂²×C₄	—	2	2	no	—
279	C₂²×C₄	—	2	2	no	—
280	C₂²×C₄	—	2	4	no	—
281	C₂²×C₄	—	4	1	no	—
282	C₂²×C₄	—	4	1	no	—
283	C₂²×C₄	—	4	1	no	—
284	C₂²×C₄	—	4	2	no	—
285	C₂²×C₄	—	4	2	no	—
286	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
287	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
288	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
289	C₂²×C₄	C₂²⋊C₄×C₄₃	1	1	yes	characteristic
290	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
291	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
293	C₂²×C₄	#41×C₄₃	1	2	yes	—
294	C₂×C₈	—	2	4	no	—
295	C₂×C₈	—	4	2	no	—
296	C₂×C₈	—	4	2	no	—
297	C₂×C₈	—	4	2	no	—
298	C₂×C₈	—	4	2	no	—
299	C₂×C₈	—	4	2	no	—
300	C₄⋊C₄	—	4	2	no	—
301	C₄⋊C₄	—	4	2	no	—
302	C₂²⋊C₄	—	4	4	no	—
303	C₂²⋊C₄	—	4	4	no	—
304	C₂²⋊C₄	—	4	4	no	—
305	C₂²⋊C₄	—	4	2	no	—
306	C₂²⋊C₄	—	4	2	no	—
307	C₄²	—	2	2	no	—
308	C₄²	—	2	2	no	—
309	C₄²	—	4	1	no	—
310	C₄²	—	4	1	no	—
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	2	1	no	—
314	C₂³	—	2	1	no	—
315	C₂³	—	2	4	no	—
316	C₂³	—	2	8	no	—
317	C₂³	—	4	4	no	—
318	C₂³	—	4	4	no	—
319	C₂³	—	4	4	no	—
320	C₂³	—	4	4	no	—
321	C₂³	—	4	2	no	—
322	C₂³	—	4	2	no	—
323	C₂³	—	4	2	no	—
324	C₂³	—	4	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	2	no	—
327	C₂³	—	4	4	no	—
328	C₂³	—	8	4	no	—
329	C₂³	—	8	4	no	—
330	C₂³	—	8	4	no	—
331	C₂³	—	8	4	no	—
332	C₂³	C₂×C₂²⋊C₄×C₄₃	1	1	yes	characteristic
333	C₂³	C₄×D₄×C₄₃	1	2	yes	—
334	C₂³	C₂×M₁₆×C₄₃	1	2	yes	—
335	C₂³	#131×C₄₃	1	2	yes	—
336	D₄	—	4	8	no	—
337	D₄	—	4	8	no	—
338	C₂×C₄	—	2	8	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	1	no	—
347	C₂×C₄	—	2	1	no	—
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	4	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	8	4	no	—
359	C₂×C₄	#99×C₄₃	1	2	yes	—
360	C₂×C₄	#100×C₄₃	1	2	yes	—
361	C₂×C₄	#100×C₄₃	1	2	yes	—
362	C₂×C₄	#121×C₄₃	1	2	yes	—
363	C₂×C₄	#124×C₄₃	1	1	yes	characteristic
364	C₂×C₄	#127×C₄₃	1	1	yes	characteristic
365	C₈	—	4	4	no	—
366	C₈	—	8	2	no	—
367	C₂²	—	2	2	no	—
368	C₂²	—	2	2	no	—
369	C₂²	—	2	2	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	4	4	no	—
374	C₂²	—	4	4	no	—
375	C₂²	—	4	4	no	—
376	C₂²	—	8	8	no	—
377	C₂²	—	8	8	no	—
378	C₂²	—	8	2	no	—
379	C₂²	—	8	2	no	—
380	C₂²	—	8	2	no	—
381	C₂²	—	8	2	no	—
382	C₂²	C₄₃×#390	1	1	yes	characteristic
383	C₂²	C₄₃×#407	1	1	yes	characteristic
384	C₂²	C₄₃×#408	1	1	yes	characteristic
385	C₂²	C₂×#99×C₄₃	1	1	yes	characteristic
386	C₂²	C₄₃×#410	1	1	yes	characteristic
387	C₂²	C₂×#100×C₄₃	1	1	yes	characteristic
388	C₂²	C₂×#100×C₄₃	1	1	yes	characteristic
389	C₂²	C₄₃×#435	1	4	yes	—
390	C₄	—	2	2	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	2	no	—
394	C₄	—	2	2	no	—
395	C₄	—	2	2	no	—
396	C₄	—	4	1	no	—
397	C₄	—	8	2	no	—
398	C₂	—	2	4	no	—
399	C₂	—	8	4	no	—
400	C₂	C₄₃×#1462	1	1	yes	characteristic
401	C₂	C₄₃×#1466	1	1	yes	characteristic
402	C₂	C₄₃×#1469	1	1	yes	characteristic
403	C₂	C₄₃×#1471	1	1	yes	characteristic
404	C₂	C₄₃×#1955	1	1	yes	characteristic
405	C₂	C₄₃×#1964	1	1	yes	characteristic
406	C₂	C₄₃×#1965	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂×C₂²⋊C₄
commutator	C₂⁴	C₂²×C₄×C₄₃
Frattini, cosocle	C₂³×C₄	C₂³×C₄₃
prime radical	C₂³×D₄×C₄₃	C₄
LCS	G ▷ C₂⁴ ▷ 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. C₄₃×#1797	C₂	semidirect
3. C₄₃×#1749	C₂	semidirect
4. C₂×C₄₃×#323	C₂	semidirect
51. C₂²⋊C₈×C₄₃	D₄	semidirect
163. #9653	C₄₃	direct (N × H)
196. #1797	C₂×C₄₃	semidirect
197. #1749	C₂×C₄₃	semidirect
198. C₂×#323	C₂×C₄₃	semidirect
224. C₄₃	#9653	direct (N × H)
255. C₂²⋊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×#390	2
C₄₃×#1797	2
C₄₃×#1749	2
C₂×C₄₃×#323	2
#9653	43

Subgroups — C43×#9653 #24929670

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#9653 #24929670