Subgroups — C₄₃×#32940 #24952957

Order 11008.

1378 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#131×C₄₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₃×#470	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₃×#467	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#2616	C₂	1	2	yes	maximal
5	C₄₃×#1894	C₂	1	2	yes	maximal, complemented
6	C₄₃×#1892	C₂	1	4	yes	maximal, complemented
7	C₄₃×#1809	C₂	1	2	yes	maximal, complemented
8	C₄₃×#1807	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#41×C₄₃	C₂²	1	1	yes	characteristic
10	C₂²×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
11	C₂×#131×C₄₃	—	2	8	no	—
12	C₂×#131×C₄₃	—	2	4	no	—
13	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
14	C₂²×M₁₆×C₄₃	C₂²	1	2	yes	—
15	C₂³×C₈×C₄₃	C₂²	1	2	yes	—
16	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
17	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	4	yes	—
18	C₂×C₂²⋊Q₈×C₄₃	C₂²	1	2	yes	—
19	C₄₃×#470	—	2	8	no	—
20	C₄₃×#467	—	2	4	no	—
21	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic
22	C₂×#106×C₄₃	C₂²	1	2	yes	—
23	C₂×#103×C₄₃	C₂²	1	2	yes	—
24	C₂×#103×C₄₃	C₂²	1	4	yes	—
25	C₄₃×#395	—	2	2	no	—
26	C₄₃×#394	—	2	2	no	—
27	C₄₃×#394	—	2	4	no	—
28	C₄₃×#380	C₂²	1	2	yes	—
29	C₄₃×#380	C₂²	1	4	yes	—
30	C₄₃×#340	C₂²	1	2	yes	—
31	C₄₃×#340	C₂²	1	4	yes	—
32	C₂×#41×C₄₃	—	2	4	no	—
33	C₂×#41×C₄₃	—	2	2	no	—
34	C₂×#41×C₄₃	—	2	2	no	—
35	C₂×#41×C₄₃	—	2	4	no	—
36	C₂²×Q₈×C₄₃	D₄	1	1	yes	characteristic
37	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
38	C₂²×D₄×C₄₃	D₄	1	2	yes	—
39	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₃	C₂³	1	2	yes	—
41	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
42	C₂×Q₁₆×C₄₃	—	2	2	no	—
43	C₂×Q₁₆×C₄₃	—	2	4	no	—
44	#131×C₄₃	—	2	32	no	—
45	C₂×M₁₆×C₄₃	—	2	2	no	—
46	C₂×M₁₆×C₄₃	—	2	4	no	—
47	C₂×M₁₆×C₄₃	—	2	4	no	—
48	C₂×M₁₆×C₄₃	—	2	4	no	—
49	C₂×M₁₆×C₄₃	D₄	1	8	yes	—
50	C₂²×C₈×C₄₃	—	2	4	no	—
51	C₂²×C₈×C₄₃	—	2	4	no	—
52	C₂²×C₈×C₄₃	—	2	4	no	—
53	C₂²×C₈×C₄₃	—	2	4	no	—
54	C₂²×C₈×C₄₃	D₄	1	4	yes	—
55	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
57	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
58	C₂²⋊Q₈×C₄₃	—	2	4	no	—
59	C₂²⋊Q₈×C₄₃	—	2	8	no	—
60	C₂²⋊Q₈×C₄₃	—	2	8	no	—
61	C₂²⋊Q₈×C₄₃	—	2	4	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	4	no	—
63	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₃	C₂³	1	4	yes	—
65	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
66	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
67	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₄₃	—	2	4	no	—
70	#107×C₄₃	—	2	2	no	—
71	#106×C₄₃	—	2	4	no	—
72	#103×C₄₃	—	2	4	no	—
73	#103×C₄₃	—	2	8	no	—
74	#95×C₄₃	—	2	2	no	—
75	#95×C₄₃	—	2	4	no	—
76	C₂⁴×C₄₃	C₂×D₄	1	2	yes	—
77	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
78	#41×C₄₃	—	2	8	no	—
79	#41×C₄₃	—	2	16	no	—
80	#41×C₄₃	—	2	8	no	—
81	C₂×Q₈×C₄₃	—	2	2	no	—
82	C₂×Q₈×C₄₃	—	2	4	no	—
83	C₂×Q₈×C₄₃	—	2	2	no	—
84	C₂×Q₈×C₄₃	—	2	4	no	—
85	C₂×Q₈×C₄₃	—	2	2	no	—
86	C₂×Q₈×C₄₃	—	2	4	no	—
87	C₂×D₄×C₄₃	—	2	2	no	—
88	C₂×D₄×C₄₃	—	2	4	no	—
89	C₂×D₄×C₄₃	—	2	4	no	—
90	C₂×D₄×C₄₃	—	2	4	no	—
91	C₂×D₄×C₄₃	—	2	4	no	—
92	C₂²×C₄×C₄₃	—	2	2	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	—	2	2	no	—
98	C₂²×C₄×C₄₃	—	2	2	no	—
99	C₂²×C₄×C₄₃	—	2	4	no	—
100	C₂²×C₄×C₄₃	—	2	2	no	—
101	C₂²×C₄×C₄₃	C₂×D₄	1	4	yes	—
102	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₃	#41	1	2	yes	—
106	C₂²×C₄×C₄₃	#41	1	4	yes	—
107	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
108	Q₁₆×C₄₃	—	4	4	no	—
109	M₁₆×C₄₃	—	2	8	no	—
110	M₁₆×C₄₃	—	2	16	no	—
111	C₂×C₈×C₄₃	—	2	16	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	8	no	—
116	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
117	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
118	C₂×C₈×C₄₃	C₂×D₄	1	4	yes	—
119	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
120	C₄⋊C₄×C₄₃	—	2	4	no	—
121	C₄⋊C₄×C₄₃	—	2	2	no	—
122	C₄⋊C₄×C₄₃	—	2	4	no	—
123	C₄⋊C₄×C₄₃	—	2	2	no	—
124	C₄⋊C₄×C₄₃	—	4	4	no	—
125	C₄⋊C₄×C₄₃	—	4	8	no	—
126	C₂²⋊C₄×C₄₃	—	4	4	no	—
127	C₂²⋊C₄×C₄₃	—	4	8	no	—
128	C₂²⋊C₄×C₄₃	—	8	2	no	—
129	C₂²⋊C₄×C₄₃	—	8	4	no	—
130	C₂³×C₄₃	—	2	2	no	—
131	C₂³×C₄₃	—	2	2	no	—
132	C₂³×C₄₃	—	2	2	no	—
133	C₂³×C₄₃	—	2	2	no	—
134	C₂³×C₄₃	—	2	4	no	—
135	C₂³×C₄₃	—	2	2	no	—
136	C₂³×C₄₃	—	2	4	no	—
137	C₂³×C₄₃	#121	1	2	yes	—
138	C₂³×C₄₃	#121	1	4	yes	—
139	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
140	Q₈×C₄₃	—	2	8	no	—
141	Q₈×C₄₃	—	4	2	no	—
142	Q₈×C₄₃	—	4	2	no	—
143	Q₈×C₄₃	—	4	4	no	—
144	D₄×C₄₃	—	2	16	no	—
145	D₄×C₄₃	—	2	8	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	4	no	—
150	C₂×C₄×C₄₃	—	2	2	no	—
151	C₂×C₄×C₄₃	—	2	4	no	—
152	C₂×C₄×C₄₃	—	2	2	no	—
153	C₂×C₄×C₄₃	—	2	4	no	—
154	C₂×C₄×C₄₃	—	2	4	no	—
155	C₂×C₄×C₄₃	—	2	4	no	—
156	C₂×C₄×C₄₃	—	4	2	no	—
157	C₂×C₄×C₄₃	—	4	4	no	—
158	C₂×C₄×C₄₃	—	4	2	no	—
159	C₂×C₄×C₄₃	—	4	4	no	—
160	C₂×C₄×C₄₃	—	4	2	no	—
161	C₂×C₄×C₄₃	—	4	4	no	—
162	C₂×C₄×C₄₃	—	4	2	no	—
163	C₂×C₄×C₄₃	—	4	4	no	—
164	C₂×C₄×C₄₃	#121	1	2	yes	—
165	C₂×C₄×C₄₃	#121	1	4	yes	—
166	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
168	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
169	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
170	C₈×C₄₃	—	2	2	no	—
171	C₈×C₄₃	—	2	4	no	—
172	C₈×C₄₃	#120	1	4	yes	—
173	#32940	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
174	C₂²×C₄₃	—	2	2	no	—
175	C₂²×C₄₃	—	2	4	no	—
176	C₂²×C₄₃	—	2	2	no	—
177	C₂²×C₄₃	—	2	2	no	—
178	C₂²×C₄₃	—	2	8	no	—
179	C₂²×C₄₃	—	4	2	no	—
180	C₂²×C₄₃	—	4	2	no	—
181	C₂²×C₄₃	—	4	4	no	—
182	C₂²×C₄₃	—	4	4	no	—
183	C₂²×C₄₃	C₂×#121	1	1	yes	characteristic
184	C₂²×C₄₃	C₂×#121	1	2	yes	—
185	C₂²×C₄₃	#577	1	2	yes	—
186	C₂²×C₄₃	#578	1	2	yes	—
187	C₄×C₄₃	—	2	4	no	—
188	C₄×C₄₃	—	2	2	no	—
189	C₄×C₄₃	—	8	2	no	—
190	C₄×C₄₃	—	8	2	no	—
191	C₄×C₄₃	—	8	4	no	—
192	C₄×C₄₃	C₂×#120	1	1	yes	characteristic
193	C₄×C₄₃	#525	1	2	yes	—
194	C₄×C₄₃	#525	1	1	yes	characteristic
195	C₂²×#131	C₂×C₄₃	1	1	yes	characteristic
196	C₂×#470	C₂×C₄₃	1	2	yes	complemented
197	C₂×#467	C₂×C₄₃	1	1	yes	characteristic, complemented
198	#2616	C₂×C₄₃	1	2	yes	—
199	#1894	C₂×C₄₃	1	2	yes	complemented
200	#1892	C₂×C₄₃	1	4	yes	complemented
201	#1809	C₂×C₄₃	1	2	yes	complemented
202	#1807	C₂×C₄₃	1	1	yes	characteristic, complemented
203	C₂×C₄₃	—	4	2	no	—
204	C₂×C₄₃	—	4	4	no	—
205	C₂×C₄₃	#2847	1	1	yes	characteristic
206	C₂×C₄₃	#3059	1	1	yes	characteristic
207	C₂×C₄₃	#3060	1	1	yes	characteristic
208	C₂×C₄₃	#3063	1	4	yes	—
209	C₂²×#41	C₂²×C₄₃	1	1	yes	characteristic
210	C₂²×Q₁₆	C₂²×C₄₃	1	1	yes	characteristic
211	C₂×#131	—	2	8	no	—
212	C₂×#131	—	2	4	no	—
213	C₂²×M₁₆	C₂²×C₄₃	1	1	yes	characteristic
214	C₂²×M₁₆	C₂²×C₄₃	1	2	yes	—
215	C₂³×C₈	C₂²×C₄₃	1	2	yes	—
216	C₂³×C₈	C₂²×C₄₃	1	1	yes	characteristic
217	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	4	yes	—
218	C₂×C₂²⋊Q₈	C₂²×C₄₃	1	2	yes	—
219	#470	—	2	8	no	—
220	#467	—	2	4	no	—
221	C₂×#107	C₂²×C₄₃	1	1	yes	characteristic
222	C₂×#106	C₂²×C₄₃	1	2	yes	—
223	C₂×#103	C₂²×C₄₃	1	2	yes	—
224	C₂×#103	C₂²×C₄₃	1	4	yes	—
225	#395	—	2	2	no	—
226	#394	—	2	2	no	—
227	#394	—	2	4	no	—
228	#380	C₂²×C₄₃	1	2	yes	—
229	#380	C₂²×C₄₃	1	4	yes	—
230	#340	C₂²×C₄₃	1	2	yes	—
231	#340	C₂²×C₄₃	1	4	yes	—
232	C₄₃	#32940	1	1	yes	characteristic, direct product factor, Sylow
233	C₂×#41	—	2	4	no	—
234	C₂×#41	—	2	2	no	—
235	C₂×#41	—	2	2	no	—
236	C₂×#41	—	2	4	no	—
237	C₂²×Q₈	D₄×C₄₃	1	1	yes	characteristic
238	C₂²×Q₈	C₂³×C₄₃	1	2	yes	—
239	C₂²×D₄	D₄×C₄₃	1	2	yes	—
240	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
241	C₂³×C₄	C₂³×C₄₃	1	2	yes	—
242	C₂³×C₄	C₂³×C₄₃	1	1	yes	characteristic
243	C₂×Q₁₆	—	2	2	no	—
244	C₂×Q₁₆	—	2	4	no	—
245	#131	—	2	32	no	—
246	C₂×M₁₆	—	2	2	no	—
247	C₂×M₁₆	—	2	4	no	—
248	C₂×M₁₆	—	2	4	no	—
249	C₂×M₁₆	—	2	4	no	—
250	C₂×M₁₆	D₄×C₄₃	1	8	yes	—
251	C₂²×C₈	—	2	4	no	—
252	C₂²×C₈	—	2	4	no	—
253	C₂²×C₈	—	2	4	no	—
254	C₂²×C₈	—	2	4	no	—
255	C₂²×C₈	D₄×C₄₃	1	4	yes	—
256	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
257	C₂²×C₈	C₂³×C₄₃	1	2	yes	—
258	C₂²×C₈	C₂³×C₄₃	1	1	yes	characteristic
259	C₂²⋊Q₈	—	2	4	no	—
260	C₂²⋊Q₈	—	2	8	no	—
261	C₂²⋊Q₈	—	2	8	no	—
262	C₂²⋊Q₈	—	2	4	no	—
263	C₂×C₄⋊C₄	—	2	4	no	—
264	C₂×C₄⋊C₄	—	2	2	no	—
265	C₂×C₄⋊C₄	C₂³×C₄₃	1	4	yes	—
266	C₂×C₄⋊C₄	C₂³×C₄₃	1	2	yes	—
267	C₂×C₂²⋊C₄	—	2	4	no	—
268	C₂×C₂²⋊C₄	—	2	2	no	—
269	C₂×C₂²⋊C₄	—	2	2	no	—
270	C₂×C₂²⋊C₄	—	2	4	no	—
271	#107	—	2	2	no	—
272	#106	—	2	4	no	—
273	#103	—	2	4	no	—
274	#103	—	2	8	no	—
275	#95	—	2	2	no	—
276	#95	—	2	4	no	—
277	C₂⁴	C₂×D₄×C₄₃	1	2	yes	—
278	C₂⁴	C₂×D₄×C₄₃	1	1	yes	characteristic
279	#41	—	2	8	no	—
280	#41	—	2	16	no	—
281	#41	—	2	8	no	—
282	C₂×Q₈	—	2	2	no	—
283	C₂×Q₈	—	2	4	no	—
284	C₂×Q₈	—	2	2	no	—
285	C₂×Q₈	—	2	4	no	—
286	C₂×Q₈	—	2	2	no	—
287	C₂×Q₈	—	2	4	no	—
288	C₂×D₄	—	2	4	no	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	—	2	4	no	—
291	C₂×D₄	—	2	2	no	—
292	C₂×D₄	—	2	4	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	—	2	2	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	—	2	4	no	—
301	C₂²×C₄	—	2	2	no	—
302	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
303	C₂²×C₄	C₂×D₄×C₄₃	1	1	yes	characteristic
304	C₂²×C₄	C₂×D₄×C₄₃	1	4	yes	—
305	C₂²×C₄	C₂×D₄×C₄₃	1	2	yes	—
306	C₂²×C₄	#41×C₄₃	1	2	yes	—
307	C₂²×C₄	#41×C₄₃	1	4	yes	—
308	C₂²×C₄	C₂⁴×C₄₃	1	1	yes	characteristic
309	Q₁₆	—	4	4	no	—
310	M₁₆	—	2	8	no	—
311	M₁₆	—	2	16	no	—
312	C₂×C₈	—	2	16	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	8	no	—
317	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
318	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
319	C₂×C₈	C₂×D₄×C₄₃	1	4	yes	—
320	C₂×C₈	C₂×D₄×C₄₃	1	2	yes	—
321	C₄⋊C₄	—	2	4	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	2	4	no	—
324	C₄⋊C₄	—	2	2	no	—
325	C₄⋊C₄	—	4	4	no	—
326	C₄⋊C₄	—	4	8	no	—
327	C₂²⋊C₄	—	4	4	no	—
328	C₂²⋊C₄	—	4	8	no	—
329	C₂²⋊C₄	—	8	4	no	—
330	C₂²⋊C₄	—	8	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	2	4	no	—
338	C₂³	#121×C₄₃	1	2	yes	—
339	C₂³	#121×C₄₃	1	4	yes	—
340	C₂³	C₂²×D₄×C₄₃	1	1	yes	characteristic
341	Q₈	—	2	8	no	—
342	Q₈	—	4	2	no	—
343	Q₈	—	4	2	no	—
344	Q₈	—	4	4	no	—
345	D₄	—	2	16	no	—
346	D₄	—	2	8	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	4	no	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	4	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	2	4	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	#121×C₄₃	1	2	yes	—
366	C₂×C₄	#121×C₄₃	1	4	yes	—
367	C₂×C₄	C₂²×D₄×C₄₃	1	1	yes	characteristic
368	C₂×C₄	C₂²×D₄×C₄₃	1	2	yes	—
369	C₂×C₄	C₂×#41×C₄₃	1	1	yes	characteristic
370	C₂×C₄	C₂×#41×C₄₃	1	2	yes	—
371	C₈	—	2	2	no	—
372	C₈	—	2	4	no	—
373	C₈	#120×C₄₃	1	4	yes	—
374	C₂²	—	2	2	no	—
375	C₂²	—	2	4	no	—
376	C₂²	—	2	2	no	—
377	C₂²	—	2	2	no	—
378	C₂²	—	2	8	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	4	4	no	—
383	C₂²	C₂×#121×C₄₃	1	1	yes	characteristic
384	C₂²	C₂×#121×C₄₃	1	2	yes	—
385	C₂²	C₄₃×#577	1	2	yes	—
386	C₂²	C₄₃×#578	1	2	yes	—
387	C₄	—	2	4	no	—
388	C₄	—	2	2	no	—
389	C₄	—	8	2	no	—
390	C₄	—	8	2	no	—
391	C₄	—	8	4	no	—
392	C₄	C₂×#120×C₄₃	1	1	yes	characteristic
393	C₄	C₄₃×#525	1	2	yes	—
394	C₄	C₄₃×#525	1	1	yes	characteristic
395	C₂	—	4	2	no	—
396	C₂	—	4	4	no	—
397	C₂	C₄₃×#2847	1	1	yes	characteristic
398	C₂	C₄₃×#3059	1	1	yes	characteristic
399	C₂	C₄₃×#3060	1	1	yes	characteristic
400	C₂	C₄₃×#3063	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₃	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₃
prime radical	C₂²×#41×C₄₃	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂²×#41×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₃×#470	C₂	semidirect
3. C₂×C₄₃×#467	C₂	semidirect
5. C₄₃×#1894	C₂	semidirect
6. C₄₃×#1892	C₂	semidirect
7. C₄₃×#1809	C₂	semidirect
8. C₄₃×#1807	C₂	semidirect
173. #32940	C₄₃	direct (N × H)
196. C₂×#470	C₂×C₄₃	semidirect
197. C₂×#467	C₂×C₄₃	semidirect
199. #1894	C₂×C₄₃	semidirect
200. #1892	C₂×C₄₃	semidirect
201. #1809	C₂×C₄₃	semidirect
202. #1807	C₂×C₄₃	semidirect
232. C₄₃	#32940	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×#131×C₄₃	2
C₂×C₄₃×#470	2
C₂×C₄₃×#467	2
C₄₃×#2616	2
C₄₃×#1894	2
C₄₃×#1892	2
C₄₃×#1809	2
C₄₃×#1807	2
#32940	43

Subgroups — C43×#32940 #24952957

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#32940 #24952957