Subgroups — C₄₃×#29786 #24949803

Order 11008.

754 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₃×#470	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#424	C₂	1	1	yes	maximal, characteristic
3	C₄₃×#2625	C₂	1	2	yes	maximal
4	C₄₃×#2088	C₂	1	2	yes	maximal, complemented
5	C₄₃×#2068	C₂	1	2	yes	maximal, complemented
6	C₄₃×#2066	C₂	1	2	yes	maximal, complemented
7	C₄₃×#2056	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1892	C₂	1	2	yes	maximal
9	C₄₃×#1809	C₂	1	1	yes	maximal, characteristic
10	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
12	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
14	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
15	C₄₃×#470	—	2	4	no	—
16	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
18	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
19	C₄₃×#424	—	2	4	no	—
20	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	—
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	C₄₃×#400	—	2	2	no	—
26	C₄₃×#398	—	2	2	no	—
27	C₄₃×#397	—	2	2	no	—
28	C₄₃×#397	—	2	2	no	—
29	C₄₃×#391	C₂²	1	2	yes	—
30	C₄₃×#391	C₂²	1	2	yes	—
31	C₄₃×#389	C₂²	1	2	yes	—
32	C₄₃×#389	C₂²	1	2	yes	—
33	C₄₃×#380	C₂²	1	2	yes	—
34	C₄₃×#340	C₂²	1	2	yes	—
35	C₄₃×#340	C₂²	1	2	yes	—
36	C₄₃×#340	C₂²	1	2	yes	—
37	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
38	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
39	C₂×Q₁₆×C₄₃	—	2	2	no	—
40	C₂×Q₁₆×C₄₃	—	4	1	no	—
41	C₂×Q₁₆×C₄₃	—	4	1	no	—
42	C₂×M₁₆×C₄₃	—	4	1	no	—
43	C₂×M₁₆×C₄₃	—	4	1	no	—
44	C₂×M₁₆×C₄₃	D₄	1	4	yes	—
45	C₂²×C₈×C₄₃	—	2	2	no	—
46	C₂²×C₈×C₄₃	—	4	1	no	—
47	C₂²×C₈×C₄₃	—	4	1	no	—
48	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
49	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
51	C₂²⋊Q₈×C₄₃	—	2	4	no	—
52	C₂²⋊Q₈×C₄₃	—	2	4	no	—
53	#117×C₄₃	—	2	2	no	—
54	#117×C₄₃	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
59	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₄₃	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
67	#107×C₄₃	—	4	1	no	—
68	#106×C₄₃	—	2	2	no	—
69	#106×C₄₃	—	4	1	no	—
70	C₄⋊C₈×C₄₃	—	2	4	no	—
71	C₄⋊C₈×C₄₃	—	2	4	no	—
72	#103×C₄₃	—	2	4	no	—
73	#103×C₄₃	—	4	2	no	—
74	#103×C₄₃	—	4	2	no	—
75	#95×C₄₃	—	2	2	no	—
76	#95×C₄₃	—	2	2	no	—
77	#95×C₄₃	—	2	2	no	—
78	#95×C₄₃	—	2	2	no	—
79	#95×C₄₃	—	2	2	no	—
80	#95×C₄₃	—	2	2	no	—
81	#95×C₄₃	—	2	2	no	—
82	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
83	C₂×Q₈×C₄₃	—	2	2	no	—
84	C₂×Q₈×C₄₃	—	2	2	no	—
85	C₂×Q₈×C₄₃	—	2	2	no	—
86	C₂×Q₈×C₄₃	—	2	2	no	—
87	C₂×Q₈×C₄₃	—	2	2	no	—
88	C₂×Q₈×C₄₃	—	2	2	no	—
89	C₂²×C₄×C₄₃	—	2	1	no	—
90	C₂²×C₄×C₄₃	—	2	1	no	—
91	C₂²×C₄×C₄₃	—	2	1	no	—
92	C₂²×C₄×C₄₃	—	2	1	no	—
93	C₂²×C₄×C₄₃	—	2	2	no	—
94	C₂²×C₄×C₄₃	—	2	2	no	—
95	C₂²×C₄×C₄₃	—	2	2	no	—
96	C₂²×C₄×C₄₃	—	2	2	no	—
97	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
98	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
99	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
100	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₃	#41	1	2	yes	—
102	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
103	Q₁₆×C₄₃	—	4	4	no	—
104	M₁₆×C₄₃	—	4	4	no	—
105	C₂×C₈×C₄₃	—	2	1	no	—
106	C₂×C₈×C₄₃	—	2	1	no	—
107	C₂×C₈×C₄₃	—	2	1	no	—
108	C₂×C₈×C₄₃	—	2	1	no	—
109	C₂×C₈×C₄₃	—	2	2	no	—
110	C₂×C₈×C₄₃	—	2	2	no	—
111	C₂×C₈×C₄₃	—	2	2	no	—
112	C₂×C₈×C₄₃	—	4	4	no	—
113	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
114	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
115	C₄⋊C₄×C₄₃	—	2	4	no	—
116	C₄⋊C₄×C₄₃	—	2	2	no	—
117	C₄⋊C₄×C₄₃	—	2	2	no	—
118	C₄⋊C₄×C₄₃	—	2	2	no	—
119	C₄⋊C₄×C₄₃	—	2	2	no	—
120	C₄⋊C₄×C₄₃	—	2	2	no	—
121	C₄⋊C₄×C₄₃	—	2	2	no	—
122	C₄⋊C₄×C₄₃	—	4	4	no	—
123	C₄⋊C₄×C₄₃	—	8	2	no	—
124	C₄⋊C₄×C₄₃	—	8	2	no	—
125	C₂²⋊C₄×C₄₃	—	2	2	no	—
126	C₂²⋊C₄×C₄₃	—	2	2	no	—
127	C₂²⋊C₄×C₄₃	—	4	4	no	—
128	C₂²⋊C₄×C₄₃	—	8	2	no	—
129	C₄²×C₄₃	—	2	2	no	—
130	C₄²×C₄₃	—	2	2	no	—
131	C₂³×C₄₃	—	2	1	no	—
132	C₂³×C₄₃	—	2	1	no	—
133	C₂³×C₄₃	—	2	2	no	—
134	C₂³×C₄₃	—	2	2	no	—
135	C₂³×C₄₃	#121	1	2	yes	—
136	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
137	Q₈×C₄₃	—	4	2	no	—
138	Q₈×C₄₃	—	4	2	no	—
139	Q₈×C₄₃	—	4	2	no	—
140	Q₈×C₄₃	—	4	2	no	—
141	C₂×C₄×C₄₃	—	2	1	no	—
142	C₂×C₄×C₄₃	—	2	1	no	—
143	C₂×C₄×C₄₃	—	2	2	no	—
144	C₂×C₄×C₄₃	—	2	2	no	—
145	C₂×C₄×C₄₃	—	2	2	no	—
146	C₂×C₄×C₄₃	—	2	2	no	—
147	C₂×C₄×C₄₃	—	2	2	no	—
148	C₂×C₄×C₄₃	—	2	2	no	—
149	C₂×C₄×C₄₃	—	2	2	no	—
150	C₂×C₄×C₄₃	—	2	2	no	—
151	C₂×C₄×C₄₃	—	2	2	no	—
152	C₂×C₄×C₄₃	—	2	2	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	2	no	—
158	C₂×C₄×C₄₃	—	4	2	no	—
159	C₂×C₄×C₄₃	—	4	2	no	—
160	C₂×C₄×C₄₃	—	4	2	no	—
161	C₂×C₄×C₄₃	—	4	2	no	—
162	C₂×C₄×C₄₃	—	4	2	no	—
163	C₂×C₄×C₄₃	—	4	2	no	—
164	C₂×C₄×C₄₃	—	4	2	no	—
165	C₂×C₄×C₄₃	#121	1	2	yes	—
166	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
168	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
169	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
171	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
172	C₈×C₄₃	—	2	2	no	—
173	C₈×C₄₃	—	2	2	no	—
174	C₈×C₄₃	—	4	2	no	—
175	#29786	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
176	C₂²×C₄₃	—	2	2	no	—
177	C₂²×C₄₃	—	2	4	no	—
178	C₂²×C₄₃	—	4	2	no	—
179	C₂²×C₄₃	—	4	1	no	—
180	C₂²×C₄₃	—	4	1	no	—
181	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
182	C₂²×C₄₃	#537	1	1	yes	characteristic
183	C₂²×C₄₃	#537	1	1	yes	characteristic
184	C₂²×C₄₃	#577	1	2	yes	—
185	C₂²×C₄₃	#578	1	2	yes	—
186	C₄×C₄₃	—	2	2	no	—
187	C₄×C₄₃	—	4	2	no	—
188	C₄×C₄₃	—	4	2	no	—
189	C₄×C₄₃	—	8	2	no	—
190	C₄×C₄₃	—	8	2	no	—
191	C₄×C₄₃	—	8	2	no	—
192	C₄×C₄₃	—	8	2	no	—
193	C₄×C₄₃	#534	1	1	yes	characteristic
194	C₄×C₄₃	#536	1	1	yes	characteristic
195	C₄×C₄₃	#539	1	1	yes	characteristic
196	C₄×C₄₃	#539	1	1	yes	characteristic
197	C₂×#470	C₂×C₄₃	1	1	yes	characteristic
198	C₂×#424	C₂×C₄₃	1	1	yes	characteristic
199	#2625	C₂×C₄₃	1	2	yes	—
200	#2088	C₂×C₄₃	1	2	yes	complemented
201	#2068	C₂×C₄₃	1	2	yes	complemented
202	#2066	C₂×C₄₃	1	2	yes	complemented
203	#2056	C₂×C₄₃	1	2	yes	complemented
204	#1892	C₂×C₄₃	1	2	yes	—
205	#1809	C₂×C₄₃	1	1	yes	characteristic
206	C₂×C₄₃	—	4	2	no	—
207	C₂×C₄₃	#2618	1	1	yes	characteristic
208	C₂×C₄₃	#3063	1	2	yes	—
209	C₂×C₄₃	#3258	1	2	yes	—
210	C₂×C₄₃	#3261	1	1	yes	characteristic
211	C₂×C₄₃	#3263	1	1	yes	characteristic
212	C₂²×Q₁₆	C₂²×C₄₃	1	1	yes	characteristic
213	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
214	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
215	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
216	C₂×#117	C₂²×C₄₃	1	1	yes	characteristic
217	#470	—	2	4	no	—
218	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
219	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
220	C₂×#106	C₂²×C₄₃	1	1	yes	characteristic
221	#424	—	2	4	no	—
222	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
223	C₂×C₄⋊C₈	C₂²×C₄₃	1	2	yes	—
224	C₂×#103	C₂²×C₄₃	1	2	yes	—
225	C₂×#103	C₂²×C₄₃	1	2	yes	—
226	C₂×#103	C₂²×C₄₃	1	2	yes	—
227	#400	—	2	2	no	—
228	#398	—	2	2	no	—
229	#397	—	2	2	no	—
230	#397	—	2	2	no	—
231	#391	C₂²×C₄₃	1	2	yes	—
232	#391	C₂²×C₄₃	1	2	yes	—
233	#389	C₂²×C₄₃	1	2	yes	—
234	#389	C₂²×C₄₃	1	2	yes	—
235	#380	C₂²×C₄₃	1	2	yes	—
236	#340	C₂²×C₄₃	1	2	yes	—
237	#340	C₂²×C₄₃	1	2	yes	—
238	#340	C₂²×C₄₃	1	2	yes	—
239	C₄₃	#29786	1	1	yes	characteristic, direct product factor, Sylow
240	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
241	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
242	C₂×Q₁₆	—	2	2	no	—
243	C₂×Q₁₆	—	4	1	no	—
244	C₂×Q₁₆	—	4	1	no	—
245	C₂×M₁₆	—	4	1	no	—
246	C₂×M₁₆	—	4	1	no	—
247	C₂×M₁₆	D₄×C₄₃	1	4	yes	—
248	C₂²×C₈	—	2	2	no	—
249	C₂²×C₈	—	4	1	no	—
250	C₂²×C₈	—	4	1	no	—
251	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
252	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
253	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
254	C₂²⋊Q₈	—	2	4	no	—
255	C₂²⋊Q₈	—	2	4	no	—
256	#117	—	2	2	no	—
257	#117	—	2	2	no	—
258	C₂×C₄⋊C₄	—	2	2	no	—
259	C₂×C₄⋊C₄	—	2	2	no	—
260	C₂×C₄⋊C₄	—	2	2	no	—
261	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
262	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
263	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
264	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	2	2	no	—
267	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
268	C₂×C₂²⋊C₄	D₄×C₄₃	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₄₃	1	2	yes	—
270	#107	—	4	1	no	—
271	#106	—	2	2	no	—
272	#106	—	4	1	no	—
273	C₄⋊C₈	—	2	4	no	—
274	C₄⋊C₈	—	2	4	no	—
275	#103	—	2	4	no	—
276	#103	—	4	2	no	—
277	#103	—	4	2	no	—
278	#95	—	2	2	no	—
279	#95	—	2	2	no	—
280	#95	—	2	2	no	—
281	#95	—	2	2	no	—
282	#95	—	2	2	no	—
283	#95	—	2	2	no	—
284	#95	—	2	2	no	—
285	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	2	no	—
288	C₂×Q₈	—	2	2	no	—
289	C₂×Q₈	—	2	2	no	—
290	C₂×Q₈	—	2	2	no	—
291	C₂×Q₈	—	2	2	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	2	1	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	2	no	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
301	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
302	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
303	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
304	C₂²×C₄	#41×C₄₃	1	2	yes	—
305	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
306	Q₁₆	—	4	4	no	—
307	M₁₆	—	4	4	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	4	4	no	—
316	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
317	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	2	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	4	4	no	—
326	C₄⋊C₄	—	8	2	no	—
327	C₄⋊C₄	—	8	2	no	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₂²⋊C₄	—	4	4	no	—
331	C₂²⋊C₄	—	8	2	no	—
332	C₄²	—	2	2	no	—
333	C₄²	—	2	2	no	—
334	C₂³	—	2	1	no	—
335	C₂³	—	2	1	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	2	no	—
338	C₂³	#121×C₄₃	1	2	yes	—
339	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
340	Q₈	—	4	2	no	—
341	Q₈	—	4	2	no	—
342	Q₈	—	4	2	no	—
343	Q₈	—	4	2	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	4	2	no	—
368	C₂×C₄	#121×C₄₃	1	2	yes	—
369	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
370	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
371	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
372	C₂×C₄	H(5,𝔽₂)×C₄₃	1	1	yes	characteristic
373	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
374	C₂×C₄	2₋¹⁺⁴×C₄₃	1	1	yes	characteristic
375	C₈	—	2	2	no	—
376	C₈	—	2	2	no	—
377	C₈	—	4	2	no	—
378	C₂²	—	2	2	no	—
379	C₂²	—	2	4	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	1	no	—
382	C₂²	—	4	1	no	—
383	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
384	C₂²	C₄₃×#537	1	1	yes	characteristic
385	C₂²	C₄₃×#537	1	1	yes	characteristic
386	C₂²	C₄₃×#577	1	2	yes	—
387	C₂²	C₄₃×#578	1	2	yes	—
388	C₄	—	2	2	no	—
389	C₄	—	4	2	no	—
390	C₄	—	4	2	no	—
391	C₄	—	8	2	no	—
392	C₄	—	8	2	no	—
393	C₄	—	8	2	no	—
394	C₄	—	8	2	no	—
395	C₄	C₄₃×#534	1	1	yes	characteristic
396	C₄	C₄₃×#536	1	1	yes	characteristic
397	C₄	C₄₃×#539	1	1	yes	characteristic
398	C₄	C₄₃×#539	1	1	yes	characteristic
399	C₂	—	4	2	no	—
400	C₂	C₄₃×#2618	1	1	yes	characteristic
401	C₂	C₄₃×#3063	1	2	yes	—
402	C₂	C₄₃×#3258	1	2	yes	—
403	C₂	C₄₃×#3261	1	1	yes	characteristic
404	C₂	C₄₃×#3263	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂⁴×C₄₃	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂×#117×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
4. C₄₃×#2088	C₂	semidirect
5. C₄₃×#2068	C₂	semidirect
6. C₄₃×#2066	C₂	semidirect
7. C₄₃×#2056	C₂	semidirect
175. #29786	C₄₃	direct (N × H)
200. #2088	C₂×C₄₃	semidirect
201. #2068	C₂×C₄₃	semidirect
202. #2066	C₂×C₄₃	semidirect
203. #2056	C₂×C₄₃	semidirect
239. C₄₃	#29786	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×#470	2
C₂×C₄₃×#424	2
C₄₃×#2625	2
C₄₃×#2088	2
C₄₃×#2068	2
C₄₃×#2066	2
C₄₃×#2056	2
C₄₃×#1892	2
C₄₃×#1809	2
#29786	43

Subgroups — C43×#29786 #24949803

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#29786 #24949803