Subgroups — C₄₃×#28758 #24948775

Order 11008.

812 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	C₂×C₄₃×#489	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#487	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#2658	C₂	1	1	yes	maximal, characteristic
4	C₄₃×#2331	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₃×#2043	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2042	C₂	1	2	yes	maximal
7	C₄₃×#1983	C₂	1	2	yes	maximal
8	C₄₃×#1981	C₂	1	2	yes	maximal, complemented
9	C₄₃×#1960	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₃×#1958	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#1768	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic
19	C₄₃×#489	—	2	4	no	—
20	C₄₃×#487	—	2	4	no	—
21	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
22	C₂×#103×C₄₃	C₂²	1	2	yes	—
23	C₂×#103×C₄₃	C₂²	1	2	yes	—
24	C₂×#103×C₄₃	C₂²	1	2	yes	—
25	C₂×#103×C₄₃	C₂²	1	2	yes	—
26	C₂×#103×C₄₃	C₂²	1	2	yes	—
27	C₂×#103×C₄₃	C₂²	1	2	yes	—
28	C₂×#102×C₄₃	C₂²	1	2	yes	—
29	C₂×#102×C₄₃	C₂²	1	2	yes	—
30	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
32	C₄₃×#399	—	2	2	no	—
33	C₄₃×#399	—	2	2	no	—
34	C₄₃×#391	—	2	2	no	—
35	C₄₃×#389	C₂²	1	2	yes	—
36	C₄₃×#387	—	2	2	no	—
37	C₄₃×#382	C₂²	1	1	yes	characteristic
38	C₄×C₄⋊C₄×C₄₃	C₂²	1	2	yes	—
39	C₄₃×#376	C₂²	1	1	yes	characteristic
40	C₄₃×#336	C₂²	1	2	yes	—
41	C₂²×Q₈×C₄₃	—	2	1	no	—
42	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
43	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
44	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
47	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
48	C₄⋊Q₈×C₄₃	—	2	2	no	—
49	C₄⋊Q₈×C₄₃	—	2	2	no	—
50	C₄⋊Q₈×C₄₃	—	2	2	no	—
51	C₄⋊Q₈×C₄₃	—	2	4	no	—
52	C₄⋊Q₈×C₄₃	—	4	2	no	—
53	C₄⋊Q₈×C₄₃	D₄	1	4	yes	—
54	#124×C₄₃	—	2	2	no	—
55	#124×C₄₃	—	2	2	no	—
56	#124×C₄₃	—	2	4	no	—
57	#124×C₄₃	—	4	2	no	—
58	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
65	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
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×C₄²×C₄₃	—	2	2	no	—
71	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
72	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
73	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₄₃	—	2	4	no	—
75	#103×C₄₃	—	2	4	no	—
76	#103×C₄₃	—	2	4	no	—
77	#103×C₄₃	—	2	4	no	—
78	#103×C₄₃	—	4	2	no	—
79	#103×C₄₃	—	4	2	no	—
80	#103×C₄₃	—	4	2	no	—
81	#102×C₄₃	—	2	4	no	—
82	#102×C₄₃	—	4	2	no	—
83	#97×C₄₃	—	2	2	no	—
84	C₄×C₈×C₄₃	—	2	2	no	—
85	#95×C₄₃	—	2	2	no	—
86	#95×C₄₃	—	2	1	no	—
87	#95×C₄₃	—	2	1	no	—
88	#95×C₄₃	—	2	2	no	—
89	#95×C₄₃	D₄	1	2	yes	—
90	#95×C₄₃	D₄	1	2	yes	—
91	C₂⁴×C₄₃	—	2	1	no	—
92	C₂×Q₈×C₄₃	—	2	4	no	—
93	C₂×Q₈×C₄₃	—	2	1	no	—
94	C₂×Q₈×C₄₃	—	2	1	no	—
95	C₂×Q₈×C₄₃	—	2	1	no	—
96	C₂×Q₈×C₄₃	—	2	1	no	—
97	C₂×Q₈×C₄₃	—	2	2	no	—
98	C₂×Q₈×C₄₃	—	2	1	no	—
99	C₂×Q₈×C₄₃	—	2	1	no	—
100	C₂×Q₈×C₄₃	—	2	2	no	—
101	C₂×Q₈×C₄₃	—	2	2	no	—
102	C₂×Q₈×C₄₃	—	2	2	no	—
103	C₂×Q₈×C₄₃	—	2	2	no	—
104	C₂×Q₈×C₄₃	—	2	2	no	—
105	C₂×Q₈×C₄₃	—	8	2	no	—
106	C₂×D₄×C₄₃	—	2	1	no	—
107	C₂×D₄×C₄₃	—	2	1	no	—
108	C₂×D₄×C₄₃	—	2	2	no	—
109	C₂×D₄×C₄₃	—	2	2	no	—
110	C₂²×C₄×C₄₃	—	2	2	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	—	2	1	no	—
115	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
120	C₂×C₈×C₄₃	—	2	2	no	—
121	C₂×C₈×C₄₃	—	2	2	no	—
122	C₂×C₈×C₄₃	—	2	2	no	—
123	C₂×C₈×C₄₃	—	2	2	no	—
124	C₂×C₈×C₄₃	—	2	2	no	—
125	C₂×C₈×C₄₃	—	2	2	no	—
126	C₄⋊C₄×C₄₃	—	2	4	no	—
127	C₄⋊C₄×C₄₃	—	2	2	no	—
128	C₄⋊C₄×C₄₃	—	2	2	no	—
129	C₄⋊C₄×C₄₃	—	2	2	no	—
130	C₄⋊C₄×C₄₃	—	4	4	no	—
131	C₄⋊C₄×C₄₃	—	4	2	no	—
132	C₄⋊C₄×C₄₃	—	4	2	no	—
133	C₄⋊C₄×C₄₃	—	4	4	no	—
134	C₄⋊C₄×C₄₃	—	8	2	no	—
135	C₄⋊C₄×C₄₃	C₂×D₄	1	4	yes	—
136	C₂²⋊C₄×C₄₃	—	4	4	no	—
137	C₂²⋊C₄×C₄₃	—	4	2	no	—
138	C₂²⋊C₄×C₄₃	—	4	2	no	—
139	C₂²⋊C₄×C₄₃	—	4	4	no	—
140	C₄²×C₄₃	—	2	2	no	—
141	C₄²×C₄₃	—	8	2	no	—
142	C₄²×C₄₃	C₂×D₄	1	2	yes	—
143	C₄²×C₄₃	#41	1	2	yes	—
144	C₄²×C₄₃	#41	1	4	yes	—
145	C₂³×C₄₃	—	4	1	no	—
146	C₂³×C₄₃	—	4	1	no	—
147	C₂³×C₄₃	—	4	1	no	—
148	C₂³×C₄₃	—	4	2	no	—
149	C₂³×C₄₃	—	4	2	no	—
150	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
151	Q₈×C₄₃	—	4	2	no	—
152	Q₈×C₄₃	—	4	2	no	—
153	Q₈×C₄₃	—	4	2	no	—
154	Q₈×C₄₃	—	4	2	no	—
155	Q₈×C₄₃	—	4	2	no	—
156	Q₈×C₄₃	—	4	2	no	—
157	Q₈×C₄₃	—	8	4	no	—
158	D₄×C₄₃	—	4	2	no	—
159	D₄×C₄₃	—	4	2	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	4	no	—
165	C₂×C₄×C₄₃	—	2	2	no	—
166	C₂×C₄×C₄₃	—	2	2	no	—
167	C₂×C₄×C₄₃	—	2	2	no	—
168	C₂×C₄×C₄₃	—	4	2	no	—
169	C₂×C₄×C₄₃	—	4	2	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	1	no	—
174	C₂×C₄×C₄₃	—	4	1	no	—
175	C₂×C₄×C₄₃	—	4	1	no	—
176	C₂×C₄×C₄₃	—	4	1	no	—
177	C₂×C₄×C₄₃	—	4	2	no	—
178	C₂×C₄×C₄₃	—	4	1	no	—
179	C₂×C₄×C₄₃	—	4	1	no	—
180	C₂×C₄×C₄₃	—	4	2	no	—
181	C₂×C₄×C₄₃	—	4	2	no	—
182	C₂×C₄×C₄₃	#121	1	2	yes	—
183	C₂×C₄×C₄₃	#121	1	2	yes	—
184	C₂×C₄×C₄₃	#124	1	4	yes	—
185	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
187	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
188	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
189	C₈×C₄₃	—	4	2	no	—
190	C₈×C₄₃	—	4	2	no	—
191	#28758	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂²×C₄₃	—	8	2	no	—
193	C₂²×C₄₃	—	8	2	no	—
194	C₂²×C₄₃	—	8	1	no	—
195	C₂²×C₄₃	—	8	1	no	—
196	C₂²×C₄₃	—	8	1	no	—
197	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
198	C₂²×C₄₃	C₂×#124	1	1	yes	characteristic
199	C₂²×C₄₃	#535	1	1	yes	characteristic
200	C₂²×C₄₃	#577	1	2	yes	—
201	C₂²×C₄₃	#578	1	2	yes	—
202	C₄×C₄₃	—	2	4	no	—
203	C₄×C₄₃	—	2	2	no	—
204	C₄×C₄₃	—	2	2	no	—
205	C₄×C₄₃	—	4	2	no	—
206	C₄×C₄₃	—	4	4	no	—
207	C₄×C₄₃	—	8	2	no	—
208	C₄×C₄₃	—	8	1	no	—
209	C₄×C₄₃	—	8	1	no	—
210	C₄×C₄₃	—	8	1	no	—
211	C₄×C₄₃	#550	1	2	yes	—
212	C₄×C₄₃	#559	1	2	yes	—
213	C₂×#489	C₂×C₄₃	1	1	yes	characteristic
214	C₂×#487	C₂×C₄₃	1	1	yes	characteristic, complemented
215	#2658	C₂×C₄₃	1	1	yes	characteristic
216	#2331	C₂×C₄₃	1	1	yes	characteristic, complemented
217	#2043	C₂×C₄₃	1	2	yes	complemented
218	#2042	C₂×C₄₃	1	2	yes	—
219	#1983	C₂×C₄₃	1	2	yes	—
220	#1981	C₂×C₄₃	1	2	yes	complemented
221	#1960	C₂×C₄₃	1	1	yes	characteristic, complemented
222	#1958	C₂×C₄₃	1	1	yes	characteristic
223	#1768	C₂×C₄₃	1	1	yes	characteristic, complemented
224	C₂×C₄₃	—	16	1	no	—
225	C₂×C₄₃	#2548	1	1	yes	characteristic
226	C₂×C₄₃	#3042	1	1	yes	characteristic
227	C₂×C₄₃	#3044	1	1	yes	characteristic
228	C₂×C₄₃	#3137	1	2	yes	—
229	C₂×C₄₃	#3225	1	2	yes	—
230	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
231	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
232	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
233	C₂×C₄⋊Q₈	C₂²×C₄₃	1	1	yes	characteristic
234	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
235	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
236	C₂×#124	C₂²×C₄₃	1	1	yes	characteristic
237	#489	—	2	4	no	—
238	#487	—	2	4	no	—
239	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
240	C₂×#103	C₂²×C₄₃	1	2	yes	—
241	C₂×#103	C₂²×C₄₃	1	2	yes	—
242	C₂×#103	C₂²×C₄₃	1	2	yes	—
243	C₂×#103	C₂²×C₄₃	1	2	yes	—
244	C₂×#103	C₂²×C₄₃	1	2	yes	—
245	C₂×#103	C₂²×C₄₃	1	2	yes	—
246	C₂×#102	C₂²×C₄₃	1	2	yes	—
247	C₂×#102	C₂²×C₄₃	1	2	yes	—
248	C₂×#97	C₂²×C₄₃	1	1	yes	characteristic
249	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
250	#399	—	2	2	no	—
251	#399	—	2	2	no	—
252	#391	—	2	2	no	—
253	#389	C₂²×C₄₃	1	2	yes	—
254	#387	—	2	2	no	—
255	#382	C₂²×C₄₃	1	1	yes	characteristic
256	C₄×C₄⋊C₄	C₂²×C₄₃	1	2	yes	—
257	#376	C₂²×C₄₃	1	1	yes	characteristic
258	#336	C₂²×C₄₃	1	2	yes	—
259	C₄₃	#28758	1	1	yes	characteristic, direct product factor, Sylow
260	C₂²×Q₈	—	2	1	no	—
261	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
262	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
263	C₂²×Q₈	C₂³×C₄₃	1	1	yes	characteristic
264	C₂²×D₄	C₂³×C₄₃	1	1	yes	characteristic
265	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
266	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
267	C₄⋊Q₈	—	2	2	no	—
268	C₄⋊Q₈	—	2	2	no	—
269	C₄⋊Q₈	—	2	2	no	—
270	C₄⋊Q₈	—	2	4	no	—
271	C₄⋊Q₈	—	4	2	no	—
272	C₄⋊Q₈	D₄×C₄₃	1	4	yes	—
273	#124	—	2	2	no	—
274	#124	—	2	2	no	—
275	#124	—	2	4	no	—
276	#124	—	4	2	no	—
277	C₂×C₄⋊C₄	—	2	1	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	1	no	—
280	C₂×C₄⋊C₄	—	2	1	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
285	C₂×C₂²⋊C₄	—	2	2	no	—
286	C₂×C₂²⋊C₄	—	2	1	no	—
287	C₂×C₂²⋊C₄	—	2	1	no	—
288	C₂×C₂²⋊C₄	—	2	2	no	—
289	C₂×C₄²	—	2	2	no	—
290	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
291	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
292	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
293	C₄⋊C₈	—	2	4	no	—
294	#103	—	2	4	no	—
295	#103	—	2	4	no	—
296	#103	—	2	4	no	—
297	#103	—	4	2	no	—
298	#103	—	4	2	no	—
299	#103	—	4	2	no	—
300	#102	—	2	4	no	—
301	#102	—	4	2	no	—
302	#97	—	2	2	no	—
303	C₄×C₈	—	2	2	no	—
304	#95	—	2	2	no	—
305	#95	—	2	1	no	—
306	#95	—	2	1	no	—
307	#95	—	2	2	no	—
308	#95	D₄×C₄₃	1	2	yes	—
309	#95	D₄×C₄₃	1	2	yes	—
310	C₂⁴	—	2	1	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	2	1	no	—
313	C₂×Q₈	—	2	1	no	—
314	C₂×Q₈	—	2	1	no	—
315	C₂×Q₈	—	2	1	no	—
316	C₂×Q₈	—	2	2	no	—
317	C₂×Q₈	—	2	1	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	—	2	2	no	—
323	C₂×Q₈	—	2	2	no	—
324	C₂×Q₈	—	8	2	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
337	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
338	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	2	no	—
343	C₂×C₈	—	2	2	no	—
344	C₂×C₈	—	2	2	no	—
345	C₄⋊C₄	—	2	4	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	2	2	no	—
349	C₄⋊C₄	—	4	4	no	—
350	C₄⋊C₄	—	4	2	no	—
351	C₄⋊C₄	—	4	2	no	—
352	C₄⋊C₄	—	4	4	no	—
353	C₄⋊C₄	—	8	2	no	—
354	C₄⋊C₄	C₂×D₄×C₄₃	1	4	yes	—
355	C₂²⋊C₄	—	4	4	no	—
356	C₂²⋊C₄	—	4	2	no	—
357	C₂²⋊C₄	—	4	2	no	—
358	C₂²⋊C₄	—	4	4	no	—
359	C₄²	—	2	2	no	—
360	C₄²	—	8	2	no	—
361	C₄²	C₂×D₄×C₄₃	1	2	yes	—
362	C₄²	#41×C₄₃	1	2	yes	—
363	C₄²	#41×C₄₃	1	4	yes	—
364	C₂³	—	4	1	no	—
365	C₂³	—	4	1	no	—
366	C₂³	—	4	1	no	—
367	C₂³	—	4	2	no	—
368	C₂³	—	4	2	no	—
369	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
370	Q₈	—	4	2	no	—
371	Q₈	—	4	2	no	—
372	Q₈	—	4	2	no	—
373	Q₈	—	4	2	no	—
374	Q₈	—	4	2	no	—
375	Q₈	—	4	2	no	—
376	Q₈	—	8	4	no	—
377	D₄	—	4	2	no	—
378	D₄	—	4	2	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	4	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	—	4	1	no	—
390	C₂×C₄	—	4	1	no	—
391	C₂×C₄	—	4	1	no	—
392	C₂×C₄	—	4	1	no	—
393	C₂×C₄	—	4	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	#121×C₄₃	1	2	yes	—
402	C₂×C₄	#121×C₄₃	1	2	yes	—
403	C₂×C₄	#124×C₄₃	1	4	yes	—
404	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
405	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
406	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
407	C₂×C₄	H(5,𝔽₂)×C₄₃	1	2	yes	—
408	C₈	—	4	2	no	—
409	C₈	—	4	2	no	—
410	C₂²	—	8	2	no	—
411	C₂²	—	8	2	no	—
412	C₂²	—	8	1	no	—
413	C₂²	—	8	1	no	—
414	C₂²	—	8	1	no	—
415	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
416	C₂²	C₂×#124×C₄₃	1	1	yes	characteristic
417	C₂²	C₄₃×#535	1	1	yes	characteristic
418	C₂²	C₄₃×#577	1	2	yes	—
419	C₂²	C₄₃×#578	1	2	yes	—
420	C₄	—	2	4	no	—
421	C₄	—	2	2	no	—
422	C₄	—	2	2	no	—
423	C₄	—	4	2	no	—
424	C₄	—	4	4	no	—
425	C₄	—	8	2	no	—
426	C₄	—	8	1	no	—
427	C₄	—	8	1	no	—
428	C₄	—	8	1	no	—
429	C₄	C₄₃×#550	1	2	yes	—
430	C₄	C₄₃×#559	1	2	yes	—
431	C₂	—	16	1	no	—
432	C₂	C₄₃×#2548	1	1	yes	characteristic
433	C₂	C₄₃×#3042	1	1	yes	characteristic
434	C₂	C₄₃×#3044	1	1	yes	characteristic
435	C₂	C₄₃×#3137	1	2	yes	—
436	C₂	C₄₃×#3225	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×D₄×C₄₃	C₂³
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₄₃×#376 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#487	C₂	semidirect
4. C₄₃×#2331	C₂	semidirect
5. C₄₃×#2043	C₂	semidirect
8. C₄₃×#1981	C₂	semidirect
9. C₄₃×#1960	C₂	semidirect
11. C₄₃×#1768	C₂	semidirect
191. #28758	C₄₃	direct (N × H)
214. C₂×#487	C₂×C₄₃	semidirect
216. #2331	C₂×C₄₃	semidirect
217. #2043	C₂×C₄₃	semidirect
220. #1981	C₂×C₄₃	semidirect
221. #1960	C₂×C₄₃	semidirect
223. #1768	C₂×C₄₃	semidirect
259. C₄₃	#28758	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₃×#489	2
C₂×C₄₃×#487	2
C₄₃×#2658	2
C₄₃×#2331	2
C₄₃×#2043	2
C₄₃×#2042	2
C₄₃×#1983	2
C₄₃×#1981	2
C₄₃×#1960	2
C₄₃×#1958	2
C₄₃×#1768	2
#28758	43

Subgroups — C43×#28758 #24948775

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#28758 #24948775