Subgroups — C₄₃×#8889 #24928906

Order 11008.

546 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₃×#2354	C₂	1	1	yes	maximal, characteristic
2	C₄₃×#1947	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₃×#1844	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₃×#1802	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₃×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
6	C₄₃×#1296	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#1279	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
9	C₂×#117×C₄₃	—	2	1	no	—
10	C₂×#107×C₄₃	—	2	1	no	—
11	C₂×#106×C₄₃	—	2	2	no	—
12	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
14	C₂×#102×C₄₃	—	2	1	no	—
15	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
16	C₄₃×#390	—	2	1	no	—
17	C₄₃×#388	—	2	2	no	—
18	C₄₃×#384	C₂²	1	1	yes	characteristic
19	C₄₃×#384	C₂²	1	1	yes	characteristic
20	C₄₃×#380	—	2	1	no	—
21	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
22	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
23	C₄₃×#340	—	2	1	no	—
24	C₄₃×#340	—	2	1	no	—
25	C₄₃×D₄⋊C₈	C₄	1	4	yes	complemented
26	C₂²×D₄×C₄₃	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₄₃	—	2	1	no	—
28	C₂²×C₈×C₄₃	—	2	1	no	—
29	C₂²×C₈×C₄₃	—	2	1	no	—
30	C₂²×C₈×C₄₃	—	2	1	no	—
31	C₄×D₄×C₄₃	—	2	1	no	—
32	C₄×D₄×C₄₃	—	2	1	no	—
33	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
34	C₄×D₄×C₄₃	Q₈	1	2	yes	—
35	#117×C₄₃	—	4	2	no	—
36	#117×C₄₃	—	4	2	no	—
37	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
38	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
39	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
40	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
41	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
42	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
43	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₄₃	D₄	1	1	yes	characteristic
45	C₂×C₄⋊C₄×C₄₃	D₄	1	2	yes	—
46	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
47	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
48	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
49	C₂×C₄²×C₄₃	—	2	2	no	—
50	C₂×C₄²×C₄₃	—	2	1	no	—
51	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
52	#107×C₄₃	—	4	2	no	—
53	#106×C₄₃	—	4	4	no	—
54	C₄⋊C₈×C₄₃	—	2	1	no	—
55	C₄⋊C₈×C₄₃	—	2	1	no	—
56	C₄⋊C₈×C₄₃	—	2	1	no	—
57	C₄⋊C₈×C₄₃	C₂×C₄	1	2	yes	—
58	#102×C₄₃	—	4	2	no	—
59	C₄×C₈×C₄₃	—	2	1	no	—
60	C₄×C₈×C₄₃	C₂×C₄	1	2	yes	—
61	#95×C₄₃	—	2	2	no	—
62	#95×C₄₃	—	2	1	no	—
63	C₂⁴×C₄₃	—	2	1	no	—
64	C₂×D₄×C₄₃	—	2	1	no	—
65	C₂×D₄×C₄₃	—	2	1	no	—
66	C₂×D₄×C₄₃	—	2	1	no	—
67	C₂×D₄×C₄₃	—	2	1	no	—
68	C₂×D₄×C₄₃	—	2	1	no	—
69	C₂×D₄×C₄₃	C₄⋊C₄	1	2	yes	—
70	C₂²×C₄×C₄₃	—	2	2	no	—
71	C₂²×C₄×C₄₃	—	2	2	no	—
72	C₂²×C₄×C₄₃	—	2	1	no	—
73	C₂²×C₄×C₄₃	—	2	1	no	—
74	C₂²×C₄×C₄₃	—	2	1	no	—
75	C₂²×C₄×C₄₃	—	2	2	no	—
76	C₂²×C₄×C₄₃	—	4	1	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	1	no	—
81	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
84	C₂×C₈×C₄₃	—	2	2	no	—
85	C₂×C₈×C₄₃	—	2	2	no	—
86	C₂×C₈×C₄₃	—	2	2	no	—
87	C₂×C₈×C₄₃	—	2	2	no	—
88	C₂×C₈×C₄₃	—	4	1	no	—
89	C₂×C₈×C₄₃	—	4	1	no	—
90	C₂×C₈×C₄₃	—	4	1	no	—
91	C₂×C₈×C₄₃	—	4	1	no	—
92	C₂×C₈×C₄₃	—	4	1	no	—
93	C₄⋊C₄×C₄₃	—	2	1	no	—
94	C₄⋊C₄×C₄₃	—	2	1	no	—
95	C₄⋊C₄×C₄₃	—	2	1	no	—
96	C₄⋊C₄×C₄₃	—	2	1	no	—
97	C₄⋊C₄×C₄₃	—	4	2	no	—
98	C₄⋊C₄×C₄₃	—	4	2	no	—
99	C₄⋊C₄×C₄₃	—	4	1	no	—
100	C₄⋊C₄×C₄₃	—	4	1	no	—
101	C₄⋊C₄×C₄₃	—	4	1	no	—
102	C₄⋊C₄×C₄₃	—	4	1	no	—
103	C₄⋊C₄×C₄₃	—	4	1	no	—
104	C₄⋊C₄×C₄₃	—	4	1	no	—
105	C₄⋊C₄×C₄₃	—	4	1	no	—
106	C₄⋊C₄×C₄₃	—	4	1	no	—
107	C₄⋊C₄×C₄₃	C₄⋊C₄	1	2	yes	—
108	C₄⋊C₄×C₄₃	SD₁₆	1	2	yes	—
109	C₂²⋊C₄×C₄₃	—	2	2	no	—
110	C₂²⋊C₄×C₄₃	—	2	2	no	—
111	C₂²⋊C₄×C₄₃	—	4	4	no	—
112	C₂²⋊C₄×C₄₃	—	8	2	no	—
113	C₄²×C₄₃	—	4	4	no	—
114	C₄²×C₄₃	—	4	1	no	—
115	C₄²×C₄₃	—	4	1	no	—
116	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
117	C₄²×C₄₃	C₂×Q₈	1	1	yes	characteristic
118	C₄²×C₄₃	#41	1	1	yes	characteristic
119	C₄²×C₄₃	#41	1	1	yes	characteristic
120	C₂³×C₄₃	—	2	2	no	—
121	C₂³×C₄₃	—	4	1	no	—
122	C₂³×C₄₃	—	4	1	no	—
123	C₂³×C₄₃	—	4	1	no	—
124	C₂³×C₄₃	—	4	1	no	—
125	C₂³×C₄₃	—	4	1	no	—
126	C₂³×C₄₃	—	4	1	no	—
127	C₂³×C₄₃	#120	1	1	yes	characteristic
128	D₄×C₄₃	—	2	2	no	—
129	D₄×C₄₃	—	2	2	no	—
130	D₄×C₄₃	—	4	1	no	—
131	D₄×C₄₃	—	4	1	no	—
132	C₂×C₄×C₄₃	—	2	1	no	—
133	C₂×C₄×C₄₃	—	2	1	no	—
134	C₂×C₄×C₄₃	—	2	2	no	—
135	C₂×C₄×C₄₃	—	2	2	no	—
136	C₂×C₄×C₄₃	—	4	1	no	—
137	C₂×C₄×C₄₃	—	4	1	no	—
138	C₂×C₄×C₄₃	—	4	1	no	—
139	C₂×C₄×C₄₃	—	4	1	no	—
140	C₂×C₄×C₄₃	—	4	2	no	—
141	C₂×C₄×C₄₃	—	4	2	no	—
142	C₂×C₄×C₄₃	—	4	2	no	—
143	C₂×C₄×C₄₃	—	4	2	no	—
144	C₂×C₄×C₄₃	—	4	1	no	—
145	C₂×C₄×C₄₃	—	4	1	no	—
146	C₂×C₄×C₄₃	—	4	2	no	—
147	C₂×C₄×C₄₃	—	4	2	no	—
148	C₂×C₄×C₄₃	—	4	1	no	—
149	C₂×C₄×C₄₃	—	4	2	no	—
150	C₂×C₄×C₄₃	—	8	1	no	—
151	C₂×C₄×C₄₃	—	8	1	no	—
152	C₂×C₄×C₄₃	—	8	1	no	—
153	C₂×C₄×C₄₃	C₂×C₄⋊C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
155	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
157	C₂×C₄×C₄₃	C₂²⋊Q₈	1	1	yes	characteristic
158	C₂×C₄×C₄₃	#123	1	1	yes	characteristic
159	C₂×C₄×C₄₃	C₂×SD₁₆	1	1	yes	characteristic
160	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
161	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
162	C₂×C₄×C₄₃	#135	1	1	yes	characteristic
163	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
164	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
165	C₂×C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
166	C₂×C₄×C₄₃	#137	1	1	yes	characteristic
167	C₈×C₄₃	—	2	4	no	—
168	C₈×C₄₃	—	4	2	no	—
169	C₈×C₄₃	—	8	1	no	—
170	#8889	C₄₃	1	1	yes	maximal, characteristic, direct product factor, Sylow
171	C₂²×C₄₃	—	4	2	no	—
172	C₂²×C₄₃	—	4	2	no	—
173	C₂²×C₄₃	—	4	2	no	—
174	C₂²×C₄₃	—	8	1	no	—
175	C₂²×C₄₃	—	8	1	no	—
176	C₂²×C₄₃	—	8	1	no	—
177	C₂²×C₄₃	—	8	1	no	—
178	C₂²×C₄₃	#385	1	1	yes	characteristic
179	C₂²×C₄₃	#449	1	1	yes	characteristic
180	C₂²×C₄₃	#449	1	1	yes	characteristic
181	C₂²×C₄₃	#450	1	1	yes	characteristic
182	C₂²×C₄₃	#452	1	1	yes	characteristic
183	C₂²×C₄₃	#453	1	1	yes	characteristic
184	C₂²×C₄₃	#456	1	1	yes	characteristic
185	C₄×C₄₃	—	2	1	no	—
186	C₄×C₄₃	—	2	1	no	—
187	C₄×C₄₃	—	4	2	no	—
188	C₄×C₄₃	—	4	2	no	—
189	C₄×C₄₃	—	8	1	no	—
190	C₄×C₄₃	—	8	2	no	—
191	C₄×C₄₃	—	16	1	no	—
192	C₄×C₄₃	#427	1	1	yes	characteristic
193	C₄×C₄₃	#428	1	1	yes	characteristic
194	C₄×C₄₃	C₄×SD₁₆	1	1	yes	characteristic
195	C₄×C₄₃	#442	1	1	yes	characteristic
196	C₄×C₄₃	#476	1	1	yes	characteristic
197	C₄×C₄₃	#478	1	1	yes	characteristic
198	C₄×C₄₃	#482	1	1	yes	characteristic
199	C₄×C₄₃	#485	1	1	yes	characteristic
200	#2354	C₂×C₄₃	1	1	yes	characteristic
201	#1947	C₂×C₄₃	1	1	yes	characteristic, complemented
202	#1844	C₂×C₄₃	1	1	yes	characteristic, complemented
203	#1802	C₂×C₄₃	1	1	yes	characteristic
204	C₂×D₄⋊C₈	C₂×C₄₃	1	1	yes	characteristic
205	#1296	C₂×C₄₃	1	1	yes	characteristic, complemented
206	#1279	C₂×C₄₃	1	1	yes	characteristic, complemented
207	C₂×C₄₃	—	8	2	no	—
208	C₂×C₄₃	#1624	1	1	yes	characteristic
209	C₂×C₄₃	#1631	1	1	yes	characteristic
210	C₂×C₄₃	#1652	1	1	yes	characteristic
211	C₂×C₄₃	#1654	1	1	yes	characteristic
212	C₂×C₄₃	#1854	1	1	yes	characteristic
213	C₂×C₄₃	#1859	1	1	yes	characteristic
214	C₂×C₄₃	#1864	1	1	yes	characteristic
215	C₂×C₄×D₄	C₂²×C₄₃	1	1	yes	characteristic
216	C₂×#117	—	2	1	no	—
217	C₂×#107	—	2	1	no	—
218	C₂×#106	—	2	2	no	—
219	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
220	C₂×C₄⋊C₈	C₂²×C₄₃	1	1	yes	characteristic
221	C₂×#102	—	2	1	no	—
222	C₂×C₄×C₈	C₂²×C₄₃	1	1	yes	characteristic
223	#390	—	2	1	no	—
224	#388	—	2	2	no	—
225	#384	C₂²×C₄₃	1	1	yes	characteristic
226	#384	C₂²×C₄₃	1	1	yes	characteristic
227	#380	—	2	1	no	—
228	C₄×C₄⋊C₄	—	2	1	no	—
229	C₄×C₄⋊C₄	C₂²×C₄₃	1	1	yes	characteristic
230	#340	—	2	1	no	—
231	#340	—	2	1	no	—
232	D₄⋊C₈	C₄×C₄₃	1	4	yes	complemented
233	C₄₃	#8889	1	1	yes	characteristic, direct product factor, Sylow
234	C₂²×D₄	D₄×C₄₃	1	1	yes	characteristic
235	C₂³×C₄	—	2	1	no	—
236	C₂²×C₈	—	2	1	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	2	1	no	—
239	C₄×D₄	—	2	1	no	—
240	C₄×D₄	—	2	1	no	—
241	C₄×D₄	C₂×C₄×C₄₃	1	2	yes	—
242	C₄×D₄	Q₈×C₄₃	1	2	yes	—
243	#117	—	4	2	no	—
244	#117	—	4	2	no	—
245	C₂×C₄⋊C₄	—	2	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	2	1	no	—
249	C₂×C₄⋊C₄	—	2	1	no	—
250	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
251	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
252	C₂×C₄⋊C₄	D₄×C₄₃	1	1	yes	characteristic
253	C₂×C₄⋊C₄	D₄×C₄₃	1	2	yes	—
254	C₂×C₂²⋊C₄	—	2	1	no	—
255	C₂×C₂²⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	C₂³×C₄₃	1	1	yes	characteristic
260	#107	—	4	2	no	—
261	#106	—	4	4	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	C₂×C₄×C₄₃	1	2	yes	—
266	#102	—	4	2	no	—
267	C₄×C₈	—	2	1	no	—
268	C₄×C₈	C₂×C₄×C₄₃	1	2	yes	—
269	#95	—	2	2	no	—
270	#95	—	2	1	no	—
271	C₂⁴	—	2	1	no	—
272	C₂×D₄	—	2	1	no	—
273	C₂×D₄	—	2	1	no	—
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	—	2	1	no	—
276	C₂×D₄	—	2	1	no	—
277	C₂×D₄	C₄⋊C₄×C₄₃	1	2	yes	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	2	1	no	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	2	no	—
284	C₂²×C₄	—	4	1	no	—
285	C₂²×C₄	—	4	1	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	C₂×D₄×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	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	4	1	no	—
297	C₂×C₈	—	4	1	no	—
298	C₂×C₈	—	4	1	no	—
299	C₂×C₈	—	4	1	no	—
300	C₂×C₈	—	4	1	no	—
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	2	1	no	—
303	C₄⋊C₄	—	2	1	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	4	2	no	—
306	C₄⋊C₄	—	4	2	no	—
307	C₄⋊C₄	—	4	1	no	—
308	C₄⋊C₄	—	4	1	no	—
309	C₄⋊C₄	—	4	1	no	—
310	C₄⋊C₄	—	4	1	no	—
311	C₄⋊C₄	—	4	1	no	—
312	C₄⋊C₄	—	4	1	no	—
313	C₄⋊C₄	—	4	1	no	—
314	C₄⋊C₄	—	4	1	no	—
315	C₄⋊C₄	C₄⋊C₄×C₄₃	1	2	yes	—
316	C₄⋊C₄	SD₁₆×C₄₃	1	2	yes	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₂²⋊C₄	—	2	2	no	—
319	C₂²⋊C₄	—	4	4	no	—
320	C₂²⋊C₄	—	8	2	no	—
321	C₄²	—	4	4	no	—
322	C₄²	—	4	1	no	—
323	C₄²	—	4	1	no	—
324	C₄²	C₂²×C₄×C₄₃	1	1	yes	characteristic
325	C₄²	C₂×Q₈×C₄₃	1	1	yes	characteristic
326	C₄²	#41×C₄₃	1	1	yes	characteristic
327	C₄²	#41×C₄₃	1	1	yes	characteristic
328	C₂³	—	2	2	no	—
329	C₂³	—	4	1	no	—
330	C₂³	—	4	1	no	—
331	C₂³	—	4	1	no	—
332	C₂³	—	4	1	no	—
333	C₂³	—	4	1	no	—
334	C₂³	—	4	1	no	—
335	C₂³	#120×C₄₃	1	1	yes	characteristic
336	D₄	—	2	2	no	—
337	D₄	—	2	2	no	—
338	D₄	—	4	1	no	—
339	D₄	—	4	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	2	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	1	no	—
353	C₂×C₄	—	4	1	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	1	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	8	1	no	—
359	C₂×C₄	—	8	1	no	—
360	C₂×C₄	—	8	1	no	—
361	C₂×C₄	C₂×C₄⋊C₄×C₄₃	1	1	yes	characteristic
362	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
363	C₂×C₄	C₄×D₄×C₄₃	1	1	yes	characteristic
364	C₂×C₄	C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
365	C₂×C₄	C₂²⋊Q₈×C₄₃	1	1	yes	characteristic
366	C₂×C₄	#123×C₄₃	1	1	yes	characteristic
367	C₂×C₄	C₂×SD₁₆×C₄₃	1	1	yes	characteristic
368	C₂×C₄	#135×C₄₃	1	1	yes	characteristic
369	C₂×C₄	#135×C₄₃	1	1	yes	characteristic
370	C₂×C₄	#135×C₄₃	1	1	yes	characteristic
371	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
372	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
373	C₂×C₄	AGL(1,ℤ/8)×C₄₃	1	1	yes	characteristic
374	C₂×C₄	#137×C₄₃	1	1	yes	characteristic
375	C₈	—	2	4	no	—
376	C₈	—	4	2	no	—
377	C₈	—	8	1	no	—
378	C₂²	—	4	2	no	—
379	C₂²	—	4	2	no	—
380	C₂²	—	4	2	no	—
381	C₂²	—	8	1	no	—
382	C₂²	—	8	1	no	—
383	C₂²	—	8	1	no	—
384	C₂²	—	8	1	no	—
385	C₂²	C₄₃×#385	1	1	yes	characteristic
386	C₂²	C₄₃×#449	1	1	yes	characteristic
387	C₂²	C₄₃×#449	1	1	yes	characteristic
388	C₂²	C₄₃×#450	1	1	yes	characteristic
389	C₂²	C₄₃×#452	1	1	yes	characteristic
390	C₂²	C₄₃×#453	1	1	yes	characteristic
391	C₂²	C₄₃×#456	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	4	2	no	—
395	C₄	—	4	2	no	—
396	C₄	—	8	1	no	—
397	C₄	—	8	2	no	—
398	C₄	—	16	1	no	—
399	C₄	C₄₃×#427	1	1	yes	characteristic
400	C₄	C₄₃×#428	1	1	yes	characteristic
401	C₄	C₄×SD₁₆×C₄₃	1	1	yes	characteristic
402	C₄	C₄₃×#442	1	1	yes	characteristic
403	C₄	C₄₃×#476	1	1	yes	characteristic
404	C₄	C₄₃×#478	1	1	yes	characteristic
405	C₄	C₄₃×#482	1	1	yes	characteristic
406	C₄	C₄₃×#485	1	1	yes	characteristic
407	C₂	—	8	2	no	—
408	C₂	C₄₃×#1624	1	1	yes	characteristic
409	C₂	C₄₃×#1631	1	1	yes	characteristic
410	C₂	C₄₃×#1652	1	1	yes	characteristic
411	C₂	C₄₃×#1654	1	1	yes	characteristic
412	C₂	C₄₃×#1854	1	1	yes	characteristic
413	C₂	C₄₃×#1859	1	1	yes	characteristic
414	C₂	C₄₃×#1864	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₃	#120
commutator	C₄²	C₂²×C₄×C₄₃
Frattini, cosocle	C₂×C₄²	C₂³×C₄₃
prime radical	C₂²×D₄×C₄₃	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₃ ◁ C₂×C₄²×C₄₃ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₃×#1947	C₂	semidirect
3. C₄₃×#1844	C₂	semidirect
6. C₄₃×#1296	C₂	semidirect
7. C₄₃×#1279	C₂	semidirect
25. C₄₃×D₄⋊C₈	C₄	semidirect
170. #8889	C₄₃	direct (N × H)
201. #1947	C₂×C₄₃	semidirect
202. #1844	C₂×C₄₃	semidirect
205. #1296	C₂×C₄₃	semidirect
206. #1279	C₂×C₄₃	semidirect
232. D₄⋊C₈	C₄×C₄₃	semidirect
233. C₄₃	#8889	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×#2354	2
C₄₃×#1947	2
C₄₃×#1844	2
C₄₃×#1802	2
C₂×C₄₃×D₄⋊C₈	2
C₄₃×#1296	2
C₄₃×#1279	2
#8889	43

Subgroups — C43×#8889 #24928906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₃×#8889 #24928906