Subgroups — D₄₃×#1714 #25084306

Order 11008.

914 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#500×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#498×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#492×D₄₃	C₂	1	1	yes	maximal, characteristic
4	#492×D₄₃	C₂	1	1	yes	maximal, characteristic
5	#487×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#486×D₄₃	C₂	1	1	yes	maximal, characteristic
7	#19134220	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134219	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134218	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134217	C₂	1	1	yes	maximal, characteristic, complemented
11	#19134216	C₂	1	1	yes	maximal, characteristic, complemented
12	#19134215	C₂	1	1	yes	maximal, characteristic, complemented
13	#19134214	C₂	1	1	yes	maximal, characteristic, complemented
14	#322×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#1714	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×SD₁₆×D₄₃	—	2	2	no	—
17	C₂×SD₁₆×D₄₃	—	2	2	no	—
18	C₄⋊Q₈×D₄₃	C₂²	1	1	yes	characteristic
19	C₄⋊Q₈×D₄₃	C₂²	1	1	yes	characteristic
20	C₄⋊Q₈×D₄₃	C₂²	1	1	yes	characteristic
21	#127×D₄₃	C₂²	1	1	yes	characteristic
22	#14583304	C₂²	1	1	yes	characteristic, complemented
23	#14583303	—	2	2	no	—
24	#14583302	C₂²	1	1	yes	characteristic, complemented
25	#14583302	C₂²	1	1	yes	characteristic, complemented
26	#14583297	C₂²	1	1	yes	characteristic, complemented
27	#14583296	—	2	2	no	—
28	#14583295	C₂²	1	1	yes	characteristic, complemented
29	#14583295	C₂²	1	1	yes	characteristic, complemented
30	#14583273	C₂²	1	1	yes	characteristic
31	#14583273	C₂²	1	1	yes	characteristic
32	#14583272	C₂²	1	1	yes	characteristic
33	#14583272	C₂²	1	1	yes	characteristic
34	#14583271	C₂²	1	1	yes	characteristic
35	#14583271	C₂²	1	1	yes	characteristic
36	#14583270	—	2	2	no	—
37	#14583270	—	2	2	no	—
38	#14583251	C₂²	1	1	yes	characteristic, complemented
39	#14583250	C₂²	1	1	yes	characteristic, complemented
40	#14583249	C₂²	1	1	yes	characteristic, complemented
41	#14583248	—	2	2	no	—
42	#14583247	C₂²	1	1	yes	characteristic
43	#14583246	C₂²	1	1	yes	characteristic
44	#14583245	C₂²	1	1	yes	characteristic
45	#14583244	—	2	2	no	—
46	#107×D₄₃	—	2	2	no	—
47	#106×D₄₃	—	2	2	no	—
48	#103×D₄₃	—	2	2	no	—
49	#102×D₄₃	—	2	2	no	—
50	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
51	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
52	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
53	#14582621	C₂²	1	1	yes	characteristic, complemented
54	#14582621	C₂²	1	1	yes	characteristic, complemented
55	#14582620	C₂²	1	1	yes	characteristic, complemented
56	C₄₃×#500	C₂²	1	1	yes	characteristic, complemented
57	C₄₃×#498	C₂²	1	1	yes	characteristic, complemented
58	C₄₃×#492	C₂²	1	1	yes	characteristic
59	C₄₃×#492	C₂²	1	1	yes	characteristic
60	C₄₃×#487	C₂²	1	1	yes	characteristic, complemented
61	C₄₃×#486	C₂²	1	1	yes	characteristic
62	C₄₃×#322	C₂²	1	1	yes	characteristic, complemented
63	C₂×Q₈×D₄₃	—	2	1	no	—
64	C₂×Q₈×D₄₃	—	2	1	no	—
65	C₂×Q₈×D₄₃	—	2	1	no	—
66	C₂×D₄×D₄₃	—	2	1	no	—
67	C₂×D₄×D₄₃	—	2	1	no	—
68	C₂×D₄×D₄₃	—	2	1	no	—
69	C₂×#10621873	—	2	2	no	—
70	C₂×#10621873	—	2	2	no	—
71	C₂×#10621883	—	2	2	no	—
72	C₂×#10621883	—	2	2	no	—
73	C₂×#10621884	—	2	2	no	—
74	C₂×#10621884	—	2	2	no	—
75	SD₁₆×D₄₃	—	4	8	no	—
76	SD₁₆×D₄₃	—	4	8	no	—
77	C₂×C₈×D₄₃	D₄	1	2	yes	—
78	C₂×C₈×D₄₃	D₄	1	2	yes	—
79	C₂×C₈×D₄₃	D₄	1	2	yes	—
80	#13063325	C₂³	1	1	yes	characteristic
81	#13063325	C₂³	1	1	yes	characteristic
82	#13063325	C₂³	1	1	yes	characteristic
83	#13063324	—	2	1	no	—
84	#13063324	—	2	1	no	—
85	#13063324	—	2	1	no	—
86	#13063324	—	2	1	no	—
87	#13063324	—	2	1	no	—
88	#13063324	—	2	1	no	—
89	#13063323	—	2	1	no	—
90	#13063323	—	2	1	no	—
91	#13063323	—	2	1	no	—
92	#13063322	C₂³	1	1	yes	characteristic
93	#13063321	—	2	1	no	—
94	#13063321	—	2	1	no	—
95	#13063321	—	2	1	no	—
96	C₄⋊C₄×D₄₃	—	2	1	no	—
97	C₄⋊C₄×D₄₃	—	2	1	no	—
98	C₄⋊C₄×D₄₃	—	2	1	no	—
99	C₄⋊C₄×D₄₃	—	2	1	no	—
100	C₄⋊C₄×D₄₃	—	2	1	no	—
101	C₄⋊C₄×D₄₃	—	2	1	no	—
102	C₄²×D₄₃	C₂³	1	1	yes	characteristic
103	#13063259	—	2	2	no	—
104	#13063258	—	2	2	no	—
105	#13063258	—	2	2	no	—
106	#13063257	—	2	2	no	—
107	#13063256	—	2	2	no	—
108	#13063256	—	2	2	no	—
109	#13063250	—	2	2	no	—
110	#13063249	—	2	2	no	—
111	#13063248	—	2	2	no	—
112	#13063247	—	2	2	no	—
113	#13063246	—	2	2	no	—
114	#13063245	—	2	2	no	—
115	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
116	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
117	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
118	C₈×Dic₄₃	D₄	1	2	yes	—
119	C₈×Dic₄₃	D₄	1	2	yes	—
120	C₈×Dic₄₃	D₄	1	2	yes	—
121	C₂×SD₁₆×C₄₃	—	2	2	no	—
122	C₂×SD₁₆×C₄₃	—	2	2	no	—
123	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
124	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
125	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
126	#127×C₄₃	C₂³	1	1	yes	characteristic
127	#107×C₄₃	—	2	2	no	—
128	#106×C₄₃	—	2	2	no	—
129	#103×C₄₃	—	2	2	no	—
130	#102×C₄₃	—	2	2	no	—
131	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
132	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
133	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
134	C₂³×D₄₃	—	4	1	no	—
135	C₂×Q₈×C₄₃	—	2	1	no	—
136	C₂×Q₈×C₄₃	—	2	1	no	—
137	C₂×Q₈×C₄₃	—	2	1	no	—
138	C₂×D₄×C₄₃	—	2	1	no	—
139	C₂×D₄×C₄₃	—	2	1	no	—
140	C₂×D₄×C₄₃	—	2	1	no	—
141	C₂×C₂²⋊D₄₃	—	4	1	no	—
142	C₂×C₂²⋊D₄₃	—	4	1	no	—
143	C₂×C₂²⋊D₄₃	—	4	1	no	—
144	Q₈×D₄₃	—	4	4	no	—
145	Q₈×D₄₃	—	4	4	no	—
146	Q₈×D₄₃	—	4	4	no	—
147	D₄×D₄₃	—	4	4	no	—
148	D₄×D₄₃	—	4	4	no	—
149	D₄×D₄₃	—	4	4	no	—
150	C₂×D₁₇₂	—	2	1	no	—
151	C₂×D₁₇₂	—	2	1	no	—
152	C₂×D₁₇₂	—	2	1	no	—
153	C₂×C₄×D₄₃	—	4	1	no	—
154	C₂×C₄×D₄₃	—	4	1	no	—
155	C₂×C₄×D₄₃	—	4	1	no	—
156	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
157	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
158	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
159	C₂×Dic₈₆	—	2	1	no	—
160	C₂×Dic₈₆	—	2	1	no	—
161	C₂×Dic₈₆	—	2	1	no	—
162	C₂×Dic₈₆	—	4	1	no	—
163	C₂×Dic₈₆	—	4	1	no	—
164	C₂×Dic₈₆	—	4	1	no	—
165	SD₁₆×C₄₃	—	4	4	no	—
166	SD₁₆×C₄₃	—	4	4	no	—
167	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
168	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
169	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
170	C₄⋊C₄×C₄₃	—	2	1	no	—
171	C₄⋊C₄×C₄₃	—	2	1	no	—
172	C₄⋊C₄×C₄₃	—	2	1	no	—
173	C₄⋊C₄×C₄₃	—	2	1	no	—
174	C₄⋊C₄×C₄₃	—	2	1	no	—
175	C₄⋊C₄×C₄₃	—	2	1	no	—
176	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
177	#10621884	—	4	4	no	—
178	#10621884	—	4	4	no	—
179	#10621883	—	4	4	no	—
180	#10621883	—	4	4	no	—
181	C₄⋊Dic₄₃	—	2	1	no	—
182	C₄⋊Dic₄₃	—	2	1	no	—
183	C₄⋊Dic₄₃	—	2	1	no	—
184	C₄⋊Dic₄₃	—	2	1	no	—
185	C₄⋊Dic₄₃	—	2	1	no	—
186	C₄⋊Dic₄₃	—	2	1	no	—
187	Dic₄₃⋊C₄	—	4	1	no	—
188	Dic₄₃⋊C₄	—	4	1	no	—
189	Dic₄₃⋊C₄	—	4	1	no	—
190	Dic₄₃⋊C₄	—	4	1	no	—
191	Dic₄₃⋊C₄	—	4	1	no	—
192	Dic₄₃⋊C₄	—	4	1	no	—
193	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
194	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
195	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
196	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
197	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
198	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
199	#10621873	—	4	4	no	—
200	#10621873	—	4	4	no	—
201	C₈×D₄₃	—	2	4	no	—
202	C₈×D₄₃	—	2	4	no	—
203	C₈×D₄₃	SD₁₆	1	8	yes	complemented
204	C₂³×C₄₃	—	4	1	no	—
205	C₂²×D₄₃	—	4	1	no	—
206	C₂²×D₄₃	—	8	2	no	—
207	C₂²×D₄₃	—	8	2	no	—
208	C₂²×D₄₃	—	8	2	no	—
209	C₂²×D₄₃	#127	1	1	yes	characteristic
210	Q₈×C₄₃	—	4	2	no	—
211	Q₈×C₄₃	—	4	2	no	—
212	Q₈×C₄₃	—	4	2	no	—
213	D₄×C₄₃	—	4	2	no	—
214	D₄×C₄₃	—	4	2	no	—
215	D₄×C₄₃	—	4	2	no	—
216	C₂×C₄×C₄₃	—	4	1	no	—
217	C₂×C₄×C₄₃	—	4	1	no	—
218	C₂×C₄×C₄₃	—	4	1	no	—
219	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
220	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
222	C₂²⋊D₄₃	—	8	2	no	—
223	C₂²⋊D₄₃	—	8	2	no	—
224	C₂²⋊D₄₃	—	8	2	no	—
225	C₂×Dic₄₃	—	4	1	no	—
226	C₂×Dic₄₃	—	4	1	no	—
227	C₂×Dic₄₃	—	4	1	no	—
228	C₂×Dic₄₃	#127	1	1	yes	characteristic
229	C₂×Dic₄₃	#127	1	1	yes	characteristic
230	C₂×Dic₄₃	#127	1	1	yes	characteristic
231	D₁₇₂	—	4	2	no	—
232	D₁₇₂	—	4	2	no	—
233	D₁₇₂	—	4	2	no	—
234	C₄×D₄₃	—	8	2	no	—
235	C₄×D₄₃	—	8	2	no	—
236	C₄×D₄₃	—	8	2	no	—
237	C₄×D₄₃	C₂×SD₁₆	1	4	yes	—
238	C₄×D₄₃	AGL(1,ℤ/8)	1	4	yes	—
239	C₄×D₄₃	#137	1	4	yes	—
240	Dic₈₆	—	4	2	no	—
241	Dic₈₆	—	4	2	no	—
242	Dic₈₆	—	4	2	no	—
243	Dic₈₆	—	8	2	no	—
244	Dic₈₆	—	8	2	no	—
245	Dic₈₆	—	8	2	no	—
246	C₈×C₄₃	—	2	2	no	—
247	C₈×C₄₃	—	2	2	no	—
248	C₈×C₄₃	C₂×SD₁₆	1	4	yes	complemented
249	C₄₃⋊C₈	—	2	2	no	—
250	C₄₃⋊C₈	—	2	2	no	—
251	C₄₃⋊C₈	C₂×SD₁₆	1	4	yes	complemented
252	C₂×#1714	—	43	1	no	maximal, Sylow
253	C₂²×C₄₃	—	8	1	no	—
254	C₂²×C₄₃	—	8	1	no	—
255	C₂²×C₄₃	—	8	1	no	—
256	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
257	C₂×D₄₃	—	8	1	no	—
258	C₂×D₄₃	—	8	1	no	—
259	C₂×D₄₃	—	8	1	no	—
260	C₂×D₄₃	—	16	4	no	—
261	C₂×D₄₃	#492	1	2	yes	—
262	C₂×D₄₃	#496	1	2	yes	—
263	C₂×D₄₃	#497	1	2	yes	—
264	C₄×C₄₃	—	8	1	no	—
265	C₄×C₄₃	—	8	1	no	—
266	C₄×C₄₃	—	8	1	no	—
267	C₄×C₄₃	C₂²×SD₁₆	1	2	yes	—
268	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
269	C₄×C₄₃	C₂×#137	1	2	yes	—
270	Dic₄₃	—	8	1	no	—
271	Dic₄₃	—	8	1	no	—
272	Dic₄₃	—	8	1	no	—
273	Dic₄₃	#492	1	2	yes	—
274	Dic₄₃	#496	1	2	yes	—
275	Dic₄₃	#497	1	2	yes	—
276	C₂×#500	—	43	1	no	—
277	C₂×#498	—	43	1	no	—
278	C₂×#492	—	43	1	no	—
279	C₂×#492	—	43	1	no	—
280	C₂×#487	—	43	1	no	—
281	C₂×#486	—	43	1	no	—
282	#1714	—	43	1	no	—
283	#1714	—	43	1	no	—
284	#1714	—	43	1	no	—
285	#1714	—	43	1	no	—
286	#1714	—	43	1	no	—
287	#1714	—	43	1	no	—
288	#1714	—	43	1	no	—
289	#1714	D₄₃	1	1	yes	characteristic, direct product factor
290	C₂×#322	—	43	1	no	—
291	C₂×C₄₃	—	16	1	no	—
292	C₂×C₄₃	C₂×#492	1	1	yes	characteristic
293	C₂×C₄₃	C₂×#496	1	1	yes	characteristic
294	C₂×C₄₃	C₂×#497	1	1	yes	characteristic
295	D₄₃	—	16	1	no	—
296	D₄₃	#1714	1	4	yes	direct product factor
297	C₂²×SD₁₆	—	86	2	no	—
298	C₂²×SD₁₆	—	86	2	no	—
299	C₂×C₄⋊Q₈	—	43	1	no	—
300	C₂×C₄⋊Q₈	—	43	1	no	—
301	C₂×C₄⋊Q₈	—	43	1	no	—
302	C₂×#127	—	43	1	no	—
303	#500	—	43	1	no	—
304	#500	—	43	1	no	—
305	#500	—	43	1	no	—
306	#500	—	86	2	no	—
307	#500	C₂×D₄₃	1	1	yes	characteristic, complemented
308	#498	—	43	1	no	—
309	#498	—	43	1	no	—
310	#498	—	43	1	no	—
311	#498	—	86	2	no	—
312	#498	C₂×D₄₃	1	1	yes	characteristic, complemented
313	#492	—	43	1	no	—
314	#492	—	43	1	no	—
315	#492	—	43	1	no	—
316	#492	—	43	1	no	—
317	#492	—	43	1	no	—
318	#492	—	43	1	no	—
319	#492	—	86	2	no	—
320	#492	—	86	2	no	—
321	#492	C₂×D₄₃	1	1	yes	characteristic
322	#492	C₂×D₄₃	1	1	yes	characteristic
323	#487	—	43	1	no	—
324	#487	—	43	1	no	—
325	#487	—	43	1	no	—
326	#487	—	86	2	no	—
327	#487	C₂×D₄₃	1	1	yes	characteristic, complemented
328	#486	—	43	1	no	—
329	#486	—	43	1	no	—
330	#486	—	43	1	no	—
331	#486	—	86	2	no	—
332	#486	C₂×D₄₃	1	1	yes	characteristic
333	C₂×#107	—	86	2	no	—
334	C₂×#106	—	86	2	no	—
335	C₂×#103	—	86	2	no	—
336	C₂×#102	—	86	2	no	—
337	C₂×C₄×C₈	—	43	1	no	—
338	C₂×C₄×C₈	—	43	1	no	—
339	C₂×C₄×C₈	—	43	1	no	—
340	#322	—	43	1	no	—
341	#322	—	43	1	no	—
342	#322	—	43	1	no	—
343	#322	C₂×D₄₃	1	1	yes	characteristic, complemented
344	C₄₃	C₂×#1714	1	1	yes	characteristic, complemented, Sylow
345	C₂²×Q₈	—	86	1	no	—
346	C₂²×Q₈	—	86	1	no	—
347	C₂²×Q₈	—	86	1	no	—
348	C₂²×D₄	—	86	1	no	—
349	C₂²×D₄	—	86	1	no	—
350	C₂²×D₄	—	86	1	no	—
351	C₂×SD₁₆	—	2	2	no	—
352	C₂×SD₁₆	—	2	2	no	—
353	C₂×SD₁₆	—	86	2	no	—
354	C₂×SD₁₆	—	86	2	no	—
355	C₂×SD₁₆	—	86	2	no	—
356	C₂×SD₁₆	—	86	2	no	—
357	C₂×SD₁₆	—	86	2	no	—
358	C₂×SD₁₆	—	86	2	no	—
359	C₂×SD₁₆	—	172	8	no	—
360	C₂×SD₁₆	—	172	8	no	—
361	C₂²×C₈	—	43	2	no	—
362	C₂²×C₈	—	43	2	no	—
363	C₂²×C₈	—	43	2	no	—
364	C₄⋊Q₈	—	43	1	no	—
365	C₄⋊Q₈	—	43	1	no	—
366	C₄⋊Q₈	—	43	1	no	—
367	C₄⋊Q₈	—	86	1	no	—
368	C₄⋊Q₈	—	86	1	no	—
369	C₄⋊Q₈	—	86	1	no	—
370	C₄⋊Q₈	—	86	1	no	—
371	C₄⋊Q₈	—	86	1	no	—
372	C₄⋊Q₈	—	86	1	no	—
373	C₄⋊Q₈	—	86	1	no	—
374	C₄⋊Q₈	—	86	1	no	—
375	C₄⋊Q₈	—	86	1	no	—
376	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
377	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
378	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
379	#127	—	43	1	no	—
380	#127	—	86	1	no	—
381	#127	—	86	1	no	—
382	#127	—	86	1	no	—
383	#127	C₂²×D₄₃	1	1	yes	characteristic
384	C₂×C₄⋊C₄	—	86	1	no	—
385	C₂×C₄⋊C₄	—	86	1	no	—
386	C₂×C₄⋊C₄	—	86	1	no	—
387	C₂×C₄⋊C₄	—	86	1	no	—
388	C₂×C₄⋊C₄	—	86	1	no	—
389	C₂×C₄⋊C₄	—	86	1	no	—
390	C₂×C₄²	—	43	1	no	—
391	#107	—	2	2	no	—
392	#107	—	86	2	no	—
393	#107	—	86	2	no	—
394	#107	—	86	2	no	—
395	#106	—	2	2	no	—
396	#106	—	86	2	no	—
397	#106	—	86	2	no	—
398	#106	—	86	2	no	—
399	#103	—	2	2	no	—
400	#103	—	86	2	no	—
401	#103	—	86	2	no	—
402	#103	—	86	2	no	—
403	#102	—	2	2	no	—
404	#102	—	86	2	no	—
405	#102	—	86	2	no	—
406	#102	—	86	2	no	—
407	C₄×C₈	—	43	2	no	—
408	C₄×C₈	—	43	2	no	—
409	C₄×C₈	—	43	2	no	—
410	C₄×C₈	—	43	1	no	—
411	C₄×C₈	—	43	1	no	—
412	C₄×C₈	—	43	1	no	—
413	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
414	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
415	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
416	C₂⁴	—	172	1	no	—
417	C₂×Q₈	—	2	1	no	—
418	C₂×Q₈	—	2	1	no	—
419	C₂×Q₈	—	2	1	no	—
420	C₂×Q₈	—	86	1	no	—
421	C₂×Q₈	—	86	1	no	—
422	C₂×Q₈	—	86	1	no	—
423	C₂×Q₈	—	172	1	no	—
424	C₂×Q₈	—	172	1	no	—
425	C₂×Q₈	—	172	1	no	—
426	C₂×Q₈	—	172	4	no	—
427	C₂×Q₈	—	172	4	no	—
428	C₂×Q₈	—	172	4	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	1	no	—
432	C₂×D₄	—	86	1	no	—
433	C₂×D₄	—	86	1	no	—
434	C₂×D₄	—	86	1	no	—
435	C₂×D₄	—	172	4	no	—
436	C₂×D₄	—	172	4	no	—
437	C₂×D₄	—	172	4	no	—
438	C₂×D₄	—	172	1	no	—
439	C₂×D₄	—	172	1	no	—
440	C₂×D₄	—	172	1	no	—
441	C₂²×C₄	—	43	1	no	—
442	C₂²×C₄	—	43	1	no	—
443	C₂²×C₄	—	43	1	no	—
444	C₂²×C₄	—	172	1	no	—
445	C₂²×C₄	—	172	1	no	—
446	C₂²×C₄	—	172	1	no	—
447	SD₁₆	—	4	4	no	—
448	SD₁₆	—	4	4	no	—
449	SD₁₆	—	172	4	no	—
450	SD₁₆	—	172	4	no	—
451	SD₁₆	—	172	4	no	—
452	SD₁₆	—	172	4	no	—
453	SD₁₆	—	172	4	no	—
454	SD₁₆	—	172	4	no	—
455	C₂×C₈	—	43	2	no	—
456	C₂×C₈	—	43	8	no	—
457	C₂×C₈	—	43	2	no	—
458	C₂×C₈	—	43	2	no	—
459	C₂×C₈	—	86	4	no	—
460	C₂×C₈	—	86	4	no	—
461	C₂×C₈	D₄×D₄₃	1	2	yes	—
462	C₂×C₈	D₄×D₄₃	1	2	yes	—
463	C₂×C₈	D₄×D₄₃	1	2	yes	—
464	C₄⋊C₄	—	2	1	no	—
465	C₄⋊C₄	—	2	1	no	—
466	C₄⋊C₄	—	2	1	no	—
467	C₄⋊C₄	—	2	1	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	86	1	no	—
471	C₄⋊C₄	—	86	1	no	—
472	C₄⋊C₄	—	86	1	no	—
473	C₄⋊C₄	—	86	1	no	—
474	C₄⋊C₄	—	86	1	no	—
475	C₄⋊C₄	—	86	1	no	—
476	C₄⋊C₄	—	172	1	no	—
477	C₄⋊C₄	—	172	1	no	—
478	C₄⋊C₄	—	172	1	no	—
479	C₄⋊C₄	—	172	1	no	—
480	C₄⋊C₄	—	172	1	no	—
481	C₄⋊C₄	—	172	1	no	—
482	C₄²	—	43	1	no	—
483	C₄²	—	43	1	no	—
484	C₄²	—	43	1	no	—
485	C₄²	C₂³×D₄₃	1	1	yes	characteristic
486	C₂³	—	4	1	no	—
487	C₂³	—	43	1	no	—
488	C₂³	—	344	2	no	—
489	C₂³	—	344	2	no	—
490	C₂³	—	344	2	no	—
491	C₂³	—	172	1	no	—
492	Q₈	—	4	2	no	—
493	Q₈	—	4	2	no	—
494	Q₈	—	4	2	no	—
495	Q₈	—	344	2	no	—
496	Q₈	—	344	2	no	—
497	Q₈	—	344	2	no	—
498	Q₈	—	172	2	no	—
499	Q₈	—	172	2	no	—
500	Q₈	—	172	2	no	—
501	D₄	—	4	2	no	—
502	D₄	—	4	2	no	—
503	D₄	—	4	2	no	—
504	D₄	—	344	2	no	—
505	D₄	—	344	2	no	—
506	D₄	—	344	2	no	—
507	D₄	—	172	2	no	—
508	D₄	—	172	2	no	—
509	D₄	—	172	2	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	4	1	no	—
512	C₂×C₄	—	4	1	no	—
513	C₂×C₄	—	43	1	no	—
514	C₂×C₄	—	43	1	no	—
515	C₂×C₄	—	43	1	no	—
516	C₂×C₄	—	43	4	no	—
517	C₂×C₄	—	43	4	no	—
518	C₂×C₄	—	43	4	no	—
519	C₂×C₄	—	344	2	no	—
520	C₂×C₄	—	344	2	no	—
521	C₂×C₄	—	344	2	no	—
522	C₂×C₄	—	172	1	no	—
523	C₂×C₄	—	172	1	no	—
524	C₂×C₄	—	172	1	no	—
525	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
526	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
527	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
528	C₈	—	2	2	no	—
529	C₈	—	2	2	no	—
530	C₈	—	43	4	no	—
531	C₈	—	86	2	no	—
532	C₈	—	86	2	no	—
533	C₈	SD₁₆×D₄₃	1	4	yes	complemented
534	C₂²	—	8	1	no	—
535	C₂²	—	8	1	no	—
536	C₂²	—	8	1	no	—
537	C₂²	—	43	2	no	—
538	C₂²	—	43	2	no	—
539	C₂²	—	43	2	no	—
540	C₂²	—	344	1	no	—
541	C₂²	—	344	1	no	—
542	C₂²	—	344	1	no	—
543	C₂²	—	688	4	no	—
544	C₂²	#127×D₄₃	1	1	yes	characteristic
545	C₄	—	8	1	no	—
546	C₄	—	8	1	no	—
547	C₄	—	8	1	no	—
548	C₄	—	43	2	no	—
549	C₄	—	43	2	no	—
550	C₄	—	43	2	no	—
551	C₄	—	344	1	no	—
552	C₄	—	344	1	no	—
553	C₄	—	344	1	no	—
554	C₄	C₂×SD₁₆×D₄₃	1	2	yes	—
555	C₄	AGL(1,ℤ/8)×D₄₃	1	2	yes	—
556	C₄	#137×D₄₃	1	2	yes	—
557	C₂	—	16	1	no	—
558	C₂	—	43	4	no	—
559	C₂	—	688	1	no	—
560	C₂	#492×D₄₃	1	1	yes	characteristic
561	C₂	#496×D₄₃	1	1	yes	characteristic
562	C₂	#497×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#127×D₄₃
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1714	C₂
socle	C₂²×C₄₃	C₂×#127
prime radical	#127×D₄₃	C₂²
hypercenter	#1714	D₄₃
hypocenter	C₄₃	C₂×#1714
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1714

Complements

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

N	H ≅ G/N	type
1. #500×D₄₃	C₂	semidirect
2. #498×D₄₃	C₂	semidirect
5. #487×D₄₃	C₂	semidirect
7. #19134220	C₂	semidirect
8. #19134219	C₂	semidirect
9. #19134218	C₂	semidirect
10. #19134217	C₂	semidirect
11. #19134216	C₂	semidirect
12. #19134215	C₂	semidirect
13. #19134214	C₂	semidirect
14. #322×D₄₃	C₂	semidirect
15. C₄₃×#1714	C₂	semidirect
22. #14583304	C₂²	semidirect
24. #14583302	C₂²	semidirect
25. #14583302	C₂²	semidirect
26. #14583297	C₂²	semidirect
28. #14583295	C₂²	semidirect
29. #14583295	C₂²	semidirect
38. #14583251	C₂²	semidirect
39. #14583250	C₂²	semidirect
40. #14583249	C₂²	semidirect
53. #14582621	C₂²	semidirect
54. #14582621	C₂²	semidirect
55. #14582620	C₂²	semidirect
56. C₄₃×#500	C₂²	semidirect
57. C₄₃×#498	C₂²	semidirect
60. C₄₃×#487	C₂²	semidirect
62. C₄₃×#322	C₂²	semidirect
203. C₈×D₄₃	SD₁₆	semidirect
248. C₈×C₄₃	C₂×SD₁₆	semidirect
251. C₄₃⋊C₈	C₂×SD₁₆	semidirect
289. #1714	D₄₃	direct (N × H)
296. D₄₃	#1714	direct (N × H)
307. #500	C₂×D₄₃	semidirect
312. #498	C₂×D₄₃	semidirect
327. #487	C₂×D₄₃	semidirect
343. #322	C₂×D₄₃	semidirect
344. C₄₃	C₂×#1714	semidirect
533. C₈	SD₁₆×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#500×D₄₃	2
#498×D₄₃	2
#492×D₄₃	2
#487×D₄₃	2
#486×D₄₃	2
#19134220	2
#19134219	2
#19134218	2
#19134217	2
#19134216	2
#19134215	2
#19134214	2
#322×D₄₃	2
C₄₃×#1714	2
C₂×#1714	43

Subgroups — D43×#1714 #25084306

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×#1714 #25084306