Subgroups — C₄₃×#29339 #24949356

Order 11008.

796 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#2850	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#2296	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2101	C₂	1	2	yes	maximal, complemented
4	C₄₃×#2042	C₂	1	2	yes	maximal, complemented
5	C₄₃×#1936	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1935	C₂	1	2	yes	maximal, complemented
7	C₄₃×#1875	C₂	1	1	yes	maximal, characteristic
8	C₄₃×#1875	C₂	1	1	yes	maximal, characteristic
9	C₄₃×#1873	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1873	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₃×#1749	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×#121×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#103×C₄₃	C₂²	1	2	yes	—
19	C₂×#103×C₄₃	C₂²	1	2	yes	—
20	C₂×#102×C₄₃	C₂²	1	2	yes	—
21	C₂×#102×C₄₃	C₂²	1	2	yes	—
22	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
24	C₂×#97×C₄₃	C₂²	1	2	yes	—
25	C₄₃×#391	C₂²	1	1	yes	characteristic
26	C₄₃×#390	C₂²	1	1	yes	characteristic
27	C₄₃×#389	C₂²	1	2	yes	—
28	C₄₃×#389	C₂²	1	2	yes	—
29	C₄₃×#388	—	2	2	no	—
30	C₄₃×#386	—	2	2	no	—
31	C₄₃×#385	—	2	2	no	—
32	C₄₃×#382	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₄₃	—	2	2	no	—
34	C₄₃×#340	C₂²	1	2	yes	—
35	C₄₃×#340	C₂²	1	2	yes	—
36	C₄₃×#340	C₂²	1	2	yes	—
37	C₄₃×#340	C₂²	1	2	yes	—
38	C₄₃×#336	C₂²	1	2	yes	—
39	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
40	C₂²×D₄×C₄₃	—	2	1	no	—
41	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
42	C₂³×C₄×C₄₃	D₄	1	2	yes	—
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	#124×C₄₃	—	4	2	no	—
47	C₂²⋊Q₈×C₄₃	—	2	2	no	—
48	C₂²⋊Q₈×C₄₃	—	2	2	no	—
49	#121×C₄₃	—	2	2	no	—
50	#121×C₄₃	—	2	2	no	—
51	#117×C₄₃	—	2	4	no	—
52	#117×C₄₃	—	4	2	no	—
53	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
54	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
57	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
58	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
59	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
60	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
61	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
64	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
66	C₂×C₄²×C₄₃	—	2	1	no	—
67	C₂×C₄²×C₄₃	—	2	1	no	—
68	C₂×C₄²×C₄₃	—	4	2	no	—
69	C₂×C₄²×C₄₃	D₄	1	2	yes	—
70	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
71	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
72	#103×C₄₃	—	2	4	no	—
73	#103×C₄₃	—	4	2	no	—
74	#102×C₄₃	—	2	4	no	—
75	#102×C₄₃	—	4	2	no	—
76	C₂²⋊C₈×C₄₃	—	2	2	no	—
77	C₂²⋊C₈×C₄₃	—	2	2	no	—
78	#97×C₄₃	—	4	2	no	—
79	#95×C₄₃	—	2	2	no	—
80	#95×C₄₃	—	2	2	no	—
81	#95×C₄₃	—	2	2	no	—
82	#95×C₄₃	—	2	2	no	—
83	C₂⁴×C₄₃	—	2	1	no	—
84	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
85	C₂×Q₈×C₄₃	—	2	2	no	—
86	C₂×Q₈×C₄₃	—	2	1	no	—
87	C₂×Q₈×C₄₃	—	2	1	no	—
88	C₂×Q₈×C₄₃	—	2	2	no	—
89	C₂×D₄×C₄₃	—	2	2	no	—
90	C₂×D₄×C₄₃	—	2	1	no	—
91	C₂×D₄×C₄₃	—	2	1	no	—
92	C₂×D₄×C₄₃	—	2	2	no	—
93	C₂×D₄×C₄₃	—	4	4	no	—
94	C₂×D₄×C₄₃	—	4	2	no	—
95	C₂²×C₄×C₄₃	—	2	2	no	—
96	C₂²×C₄×C₄₃	—	2	2	no	—
97	C₂²×C₄×C₄₃	—	2	2	no	—
98	C₂²×C₄×C₄₃	—	2	1	no	—
99	C₂²×C₄×C₄₃	—	2	2	no	—
100	C₂²×C₄×C₄₃	—	2	1	no	—
101	C₂²×C₄×C₄₃	—	2	1	no	—
102	C₂²×C₄×C₄₃	—	4	2	no	—
103	C₂²×C₄×C₄₃	—	4	2	no	—
104	C₂²×C₄×C₄₃	—	4	2	no	—
105	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
106	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
107	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₃	#41	1	2	yes	—
109	C₂²×C₄×C₄₃	#41	1	2	yes	—
110	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
111	C₂×C₈×C₄₃	—	2	2	no	—
112	C₂×C₈×C₄₃	—	2	2	no	—
113	C₂×C₈×C₄₃	—	2	2	no	—
114	C₂×C₈×C₄₃	—	2	2	no	—
115	C₂×C₈×C₄₃	—	2	2	no	—
116	C₂×C₈×C₄₃	—	2	2	no	—
117	C₄⋊C₄×C₄₃	—	2	2	no	—
118	C₄⋊C₄×C₄₃	—	2	1	no	—
119	C₄⋊C₄×C₄₃	—	2	1	no	—
120	C₄⋊C₄×C₄₃	—	2	1	no	—
121	C₄⋊C₄×C₄₃	—	2	1	no	—
122	C₄⋊C₄×C₄₃	—	2	2	no	—
123	C₄⋊C₄×C₄₃	—	2	2	no	—
124	C₄⋊C₄×C₄₃	—	4	4	no	—
125	C₄⋊C₄×C₄₃	—	4	4	no	—
126	C₄⋊C₄×C₄₃	—	4	2	no	—
127	C₄⋊C₄×C₄₃	#41	1	4	yes	—
128	C₂²⋊C₄×C₄₃	—	2	4	no	—
129	C₂²⋊C₄×C₄₃	—	4	2	no	—
130	C₂²⋊C₄×C₄₃	—	4	4	no	—
131	C₂²⋊C₄×C₄₃	—	4	4	no	—
132	C₂²⋊C₄×C₄₃	—	4	2	no	—
133	C₂²⋊C₄×C₄₃	—	4	2	no	—
134	C₄²×C₄₃	—	2	4	no	—
135	C₄²×C₄₃	—	2	2	no	—
136	C₄²×C₄₃	—	2	2	no	—
137	C₄²×C₄₃	—	4	2	no	—
138	C₄²×C₄₃	—	4	2	no	—
139	C₂³×C₄₃	—	2	1	no	—
140	C₂³×C₄₃	—	2	1	no	—
141	C₂³×C₄₃	—	2	2	no	—
142	C₂³×C₄₃	—	2	2	no	—
143	C₂³×C₄₃	—	4	1	no	—
144	C₂³×C₄₃	—	4	1	no	—
145	C₂³×C₄₃	—	4	1	no	—
146	C₂³×C₄₃	—	4	2	no	—
147	C₂³×C₄₃	—	4	2	no	—
148	C₂³×C₄₃	#124	1	2	yes	—
149	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
150	Q₈×C₄₃	—	4	2	no	—
151	Q₈×C₄₃	—	4	2	no	—
152	D₄×C₄₃	—	4	2	no	—
153	D₄×C₄₃	—	4	2	no	—
154	D₄×C₄₃	—	8	4	no	—
155	C₂×C₄×C₄₃	—	2	1	no	—
156	C₂×C₄×C₄₃	—	2	1	no	—
157	C₂×C₄×C₄₃	—	2	4	no	—
158	C₂×C₄×C₄₃	—	2	4	no	—
159	C₂×C₄×C₄₃	—	2	4	no	—
160	C₂×C₄×C₄₃	—	2	2	no	—
161	C₂×C₄×C₄₃	—	2	2	no	—
162	C₂×C₄×C₄₃	—	2	2	no	—
163	C₂×C₄×C₄₃	—	2	2	no	—
164	C₂×C₄×C₄₃	—	2	2	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	4	8	no	—
167	C₂×C₄×C₄₃	—	4	2	no	—
168	C₂×C₄×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	—	4	1	no	—
170	C₂×C₄×C₄₃	—	4	1	no	—
171	C₂×C₄×C₄₃	—	4	1	no	—
172	C₂×C₄×C₄₃	—	4	1	no	—
173	C₂×C₄×C₄₃	—	4	2	no	—
174	C₂×C₄×C₄₃	—	4	1	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	#124	1	2	yes	—
180	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
181	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
184	C₈×C₄₃	—	4	2	no	—
185	C₈×C₄₃	—	4	2	no	—
186	#29339	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂²×C₄₃	—	2	2	no	—
188	C₂²×C₄₃	—	2	2	no	—
189	C₂²×C₄₃	—	2	2	no	—
190	C₂²×C₄₃	—	4	2	no	—
191	C₂²×C₄₃	—	4	2	no	—
192	C₂²×C₄₃	—	8	1	no	—
193	C₂²×C₄₃	—	8	2	no	—
194	C₂²×C₄₃	—	8	1	no	—
195	C₂²×C₄₃	—	8	1	no	—
196	C₂²×C₄₃	—	8	2	no	—
197	C₂²×C₄₃	#525	1	1	yes	characteristic
198	C₂²×C₄₃	C₂×#124	1	1	yes	characteristic
199	C₂²×C₄₃	#534	1	1	yes	characteristic
200	C₂²×C₄₃	#575	1	2	yes	—
201	C₂²×C₄₃	#575	1	2	yes	—
202	C₄×C₄₃	—	2	2	no	—
203	C₄×C₄₃	—	4	4	no	—
204	C₄×C₄₃	—	4	2	no	—
205	C₄×C₄₃	—	4	2	no	—
206	C₄×C₄₃	—	8	1	no	—
207	C₄×C₄₃	—	8	1	no	—
208	C₄×C₄₃	—	8	1	no	—
209	C₄×C₄₃	—	8	2	no	—
210	C₄×C₄₃	#553	1	2	yes	—
211	C₄×C₄₃	#553	1	2	yes	—
212	#2850	C₂×C₄₃	1	1	yes	characteristic
213	#2296	C₂×C₄₃	1	1	yes	characteristic, complemented
214	#2101	C₂×C₄₃	1	2	yes	complemented
215	#2042	C₂×C₄₃	1	2	yes	complemented
216	#1936	C₂×C₄₃	1	2	yes	complemented
217	#1935	C₂×C₄₃	1	2	yes	complemented
218	#1875	C₂×C₄₃	1	1	yes	characteristic
219	#1875	C₂×C₄₃	1	1	yes	characteristic
220	#1873	C₂×C₄₃	1	1	yes	characteristic, complemented
221	#1873	C₂×C₄₃	1	1	yes	characteristic, complemented
222	#1749	C₂×C₄₃	1	1	yes	characteristic, complemented
223	C₂×C₄₃	—	4	2	no	—
224	C₂×C₄₃	—	16	1	no	—
225	C₂×C₄₃	#2591	1	1	yes	characteristic
226	C₂×C₄₃	#3111	1	2	yes	—
227	C₂×C₄₃	#3135	1	1	yes	characteristic
228	C₂×C₄₃	#3140	1	1	yes	characteristic
229	C₂×C₄₃	#3197	1	2	yes	—
230	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
231	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
232	C₂×#121	C₂²×C₄₃	1	1	yes	characteristic
233	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
234	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
235	C₂²×C₄²	C₂²×C₄₃	1	1	yes	characteristic
236	C₂×#103	C₂²×C₄₃	1	2	yes	—
237	C₂×#103	C₂²×C₄₃	1	2	yes	—
238	C₂×#102	C₂²×C₄₃	1	2	yes	—
239	C₂×#102	C₂²×C₄₃	1	2	yes	—
240	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
241	C₂×C₂²⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
242	C₂×#97	C₂²×C₄₃	1	2	yes	—
243	#391	C₂²×C₄₃	1	1	yes	characteristic
244	#390	C₂²×C₄₃	1	1	yes	characteristic
245	#389	C₂²×C₄₃	1	2	yes	—
246	#389	C₂²×C₄₃	1	2	yes	—
247	#388	—	2	2	no	—
248	#386	—	2	2	no	—
249	#385	—	2	2	no	—
250	#382	C₂²×C₄₃	1	1	yes	characteristic
251	C₄×C₄⋊C₄	—	2	2	no	—
252	#340	C₂²×C₄₃	1	2	yes	—
253	#340	C₂²×C₄₃	1	2	yes	—
254	#340	C₂²×C₄₃	1	2	yes	—
255	#340	C₂²×C₄₃	1	2	yes	—
256	#336	C₂²×C₄₃	1	2	yes	—
257	C₄₃	#29339	1	1	yes	characteristic, direct product factor, Sylow
258	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
259	C₂²×D₄	—	2	1	no	—
260	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
261	C₂³×C₄	D₄×C₄₃	1	2	yes	—
262	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
264	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
265	#124	—	4	2	no	—
266	C₂²⋊Q₈	—	2	2	no	—
267	C₂²⋊Q₈	—	2	2	no	—
268	#121	—	2	2	no	—
269	#121	—	2	2	no	—
270	#117	—	2	4	no	—
271	#117	—	4	2	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	2	no	—
274	C₂×C₄⋊C₄	—	2	2	no	—
275	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
276	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
277	C₂×C₄⋊C₄	C₂³×C₄₃	1	1	yes	characteristic
278	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
279	C₂×C₂²⋊C₄	—	2	1	no	—
280	C₂×C₂²⋊C₄	—	2	1	no	—
281	C₂×C₂²⋊C₄	—	2	1	no	—
282	C₂×C₂²⋊C₄	—	2	1	no	—
283	C₂×C₂²⋊C₄	—	2	2	no	—
284	C₂×C₂²⋊C₄	—	2	2	no	—
285	C₂×C₄²	—	2	1	no	—
286	C₂×C₄²	—	2	1	no	—
287	C₂×C₄²	—	4	2	no	—
288	C₂×C₄²	D₄×C₄₃	1	2	yes	—
289	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
290	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
291	#103	—	2	4	no	—
292	#103	—	4	2	no	—
293	#102	—	2	4	no	—
294	#102	—	4	2	no	—
295	C₂²⋊C₈	—	2	2	no	—
296	C₂²⋊C₈	—	2	2	no	—
297	#97	—	4	2	no	—
298	#95	—	2	2	no	—
299	#95	—	2	2	no	—
300	#95	—	2	2	no	—
301	#95	—	2	2	no	—
302	C₂⁴	—	2	1	no	—
303	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
304	C₂×Q₈	—	2	2	no	—
305	C₂×Q₈	—	2	1	no	—
306	C₂×Q₈	—	2	1	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×D₄	—	2	2	no	—
309	C₂×D₄	—	2	1	no	—
310	C₂×D₄	—	2	1	no	—
311	C₂×D₄	—	2	2	no	—
312	C₂×D₄	—	4	4	no	—
313	C₂×D₄	—	4	2	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	1	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	2	1	no	—
321	C₂²×C₄	—	4	2	no	—
322	C₂²×C₄	—	4	2	no	—
323	C₂²×C₄	—	4	2	no	—
324	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
325	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
326	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
327	C₂²×C₄	#41×C₄₃	1	2	yes	—
328	C₂²×C₄	#41×C₄₃	1	2	yes	—
329	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	1	no	—
338	C₄⋊C₄	—	2	1	no	—
339	C₄⋊C₄	—	2	1	no	—
340	C₄⋊C₄	—	2	1	no	—
341	C₄⋊C₄	—	2	2	no	—
342	C₄⋊C₄	—	2	2	no	—
343	C₄⋊C₄	—	4	4	no	—
344	C₄⋊C₄	—	4	4	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	#41×C₄₃	1	4	yes	—
347	C₂²⋊C₄	—	2	4	no	—
348	C₂²⋊C₄	—	4	4	no	—
349	C₂²⋊C₄	—	4	4	no	—
350	C₂²⋊C₄	—	4	2	no	—
351	C₂²⋊C₄	—	4	2	no	—
352	C₂²⋊C₄	—	4	2	no	—
353	C₄²	—	2	4	no	—
354	C₄²	—	2	2	no	—
355	C₄²	—	2	2	no	—
356	C₄²	—	4	2	no	—
357	C₄²	—	4	2	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	2	no	—
362	C₂³	—	4	1	no	—
363	C₂³	—	4	1	no	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	2	no	—
366	C₂³	—	4	2	no	—
367	C₂³	#124×C₄₃	1	2	yes	—
368	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
369	Q₈	—	4	2	no	—
370	Q₈	—	4	2	no	—
371	D₄	—	4	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	8	4	no	—
374	C₂×C₄	—	2	1	no	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	4	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	2	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	4	8	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	1	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	2	no	—
395	C₂×C₄	—	4	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	#124×C₄₃	1	2	yes	—
399	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
400	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
401	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
402	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
403	C₈	—	4	2	no	—
404	C₈	—	4	2	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	2	no	—
410	C₂²	—	8	1	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	2	no	—
415	C₂²	C₄₃×#525	1	1	yes	characteristic
416	C₂²	C₂×#124×C₄₃	1	1	yes	characteristic
417	C₂²	C₄₃×#534	1	1	yes	characteristic
418	C₂²	C₄₃×#575	1	2	yes	—
419	C₂²	C₄₃×#575	1	2	yes	—
420	C₄	—	2	2	no	—
421	C₄	—	4	4	no	—
422	C₄	—	4	2	no	—
423	C₄	—	4	2	no	—
424	C₄	—	8	1	no	—
425	C₄	—	8	1	no	—
426	C₄	—	8	1	no	—
427	C₄	—	8	2	no	—
428	C₄	C₄₃×#553	1	2	yes	—
429	C₄	C₄₃×#553	1	2	yes	—
430	C₂	—	4	2	no	—
431	C₂	—	16	1	no	—
432	C₂	C₄₃×#2591	1	1	yes	characteristic
433	C₂	C₄₃×#3111	1	2	yes	—
434	C₂	C₄₃×#3135	1	1	yes	characteristic
435	C₂	C₄₃×#3140	1	1	yes	characteristic
436	C₂	C₄₃×#3197	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
2. C₄₃×#2296	C₂	semidirect
3. C₄₃×#2101	C₂	semidirect
4. C₄₃×#2042	C₂	semidirect
5. C₄₃×#1936	C₂	semidirect
6. C₄₃×#1935	C₂	semidirect
9. C₄₃×#1873	C₂	semidirect
10. C₄₃×#1873	C₂	semidirect
11. C₄₃×#1749	C₂	semidirect
186. #29339	C₄₃	direct (N × H)
213. #2296	C₂×C₄₃	semidirect
214. #2101	C₂×C₄₃	semidirect
215. #2042	C₂×C₄₃	semidirect
216. #1936	C₂×C₄₃	semidirect
217. #1935	C₂×C₄₃	semidirect
220. #1873	C₂×C₄₃	semidirect
221. #1873	C₂×C₄₃	semidirect
222. #1749	C₂×C₄₃	semidirect
257. C₄₃	#29339	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₃×#2850	2
C₄₃×#2296	2
C₄₃×#2101	2
C₄₃×#2042	2
C₄₃×#1936	2
C₄₃×#1935	2
C₄₃×#1875	2
C₄₃×#1873	2
C₄₃×#1749	2
#29339	43

Subgroups — C43×#29339 #24949356

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29339 #24949356