Subgroups — #25084446

Order 11008.

784 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145735	C₂	1	1	yes	maximal, characteristic, complemented
2	#19145516	C₂	1	1	yes	maximal, characteristic
3	#19145153	C₂	1	1	yes	maximal, characteristic
4	#19145138	C₂	1	1	yes	maximal, characteristic, complemented
5	#498×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
6	#19145049	C₂	1	1	yes	maximal, characteristic
7	#19134228	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134227	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134216	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134193	C₂	1	1	yes	maximal, characteristic, complemented
11	#19134191	C₂	1	1	yes	maximal, characteristic, complemented
12	#19134181	C₂	1	1	yes	maximal, characteristic, complemented
13	#19134181	C₂	1	1	yes	maximal, characteristic, complemented
14	#19132874	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#1714	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13063354	—	2	2	no	—
17	#14583454	C₂²	1	1	yes	characteristic
18	#14583447	C₂²	1	1	yes	characteristic
19	C₄⋊Q₈×D₄₃	C₂²	1	1	yes	characteristic
20	C₄⋊Q₈×D₄₃	C₂²	1	1	yes	characteristic
21	#14583307	—	2	2	no	—
22	#14583302	C₂²	1	1	yes	characteristic
23	#14583297	C₂²	1	1	yes	characteristic
24	#14583297	C₂²	1	1	yes	characteristic
25	#14583297	C₂²	1	1	yes	characteristic
26	#14583296	—	2	2	no	—
27	#14583295	C₂²	1	1	yes	characteristic
28	#14583295	C₂²	1	1	yes	characteristic
29	#14583295	C₂²	1	1	yes	characteristic
30	#14583295	C₂²	1	1	yes	characteristic
31	#14583295	C₂²	1	1	yes	characteristic
32	#14583290	—	2	2	no	—
33	#14583279	C₂²	1	1	yes	characteristic
34	#14583278	C₂²	1	1	yes	characteristic
35	#14583271	C₂²	1	1	yes	characteristic
36	#14583271	C₂²	1	1	yes	characteristic
37	#14583271	C₂²	1	1	yes	characteristic
38	#14583250	C₂²	1	1	yes	characteristic
39	#14583250	C₂²	1	1	yes	characteristic
40	#14583249	C₂²	1	1	yes	characteristic
41	#14583249	C₂²	1	1	yes	characteristic
42	#14583228	—	2	2	no	—
43	#14583182	—	2	2	no	—
44	#14583127	—	2	2	no	—
45	#14583102	—	2	2	no	—
46	#14583036	—	2	2	no	—
47	#14582990	—	2	2	no	—
48	#14582950	C₂²	1	1	yes	characteristic
49	#14582940	—	2	2	no	—
50	#106×D₄₃	—	2	2	no	—
51	C₄×#10621872	C₂²	1	1	yes	characteristic
52	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
53	#14582621	C₂²	1	1	yes	characteristic
54	C₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
55	C₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
56	C₄₃×#500	C₂²	1	1	yes	characteristic
57	C₄₃×#498	C₂²	1	1	yes	characteristic
58	C₄₃×#492	C₂²	1	1	yes	characteristic
59	C₄₃×#492	C₂²	1	1	yes	characteristic
60	C₄₃×#487	C₂²	1	1	yes	characteristic
61	C₄₃×#486	C₂²	1	1	yes	characteristic
62	C₄₃×#322	C₂²	1	1	yes	characteristic
63	C₂×#10621900	—	2	1	no	—
64	C₂×Q₈×D₄₃	—	2	1	no	—
65	C₂×Q₈×D₄₃	—	2	1	no	—
66	#13063354	—	4	8	no	—
67	C₂×Dic₁₇₂	—	2	2	no	—
68	C₂×#10621885	—	2	2	no	—
69	C₂×#10621883	—	2	2	no	—
70	C₂×#10621883	—	2	2	no	—
71	C₂×#10621883	—	2	2	no	—
72	C₂×#10621872	D₄	1	2	yes	—
73	C₂×C₈×D₄₃	D₄	1	2	yes	—
74	#13063325	C₂³	1	1	yes	characteristic
75	#13063325	C₂³	1	1	yes	characteristic
76	#13063325	C₂³	1	1	yes	characteristic
77	#13063325	C₂³	1	1	yes	characteristic
78	#13063324	—	2	1	no	—
79	#13063324	—	2	1	no	—
80	#13063324	—	2	1	no	—
81	#13063324	—	2	1	no	—
82	#13063323	—	2	1	no	—
83	#13063323	—	2	1	no	—
84	#13063316	—	2	1	no	—
85	#13063312	—	2	1	no	—
86	#13063305	—	2	1	no	—
87	#13063301	—	2	1	no	—
88	#13063296	—	2	1	no	—
89	#13063296	—	2	1	no	—
90	Q₈×Dic₄₃	—	2	1	no	—
91	#13063290	—	2	1	no	—
92	D₄×Dic₄₃	—	2	1	no	—
93	D₄×Dic₄₃	—	2	1	no	—
94	#13063283	—	2	1	no	—
95	C₄⋊C₄×D₄₃	—	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	C₄²×D₄₃	C₂³	1	1	yes	characteristic
100	#13063258	—	2	2	no	—
101	#13063257	—	2	2	no	—
102	#13063257	—	2	2	no	—
103	#13063257	—	2	2	no	—
104	#13063256	—	2	2	no	—
105	#13063256	—	2	2	no	—
106	#13063256	—	2	2	no	—
107	#13063256	—	2	2	no	—
108	#13063256	—	2	2	no	—
109	Dic₄₃⋊C₈	D₄	1	2	yes	—
110	#13063250	—	2	2	no	—
111	#13063250	—	2	2	no	—
112	#13063249	—	2	2	no	—
113	#13063249	—	2	2	no	—
114	(C₂×D₄₃)⋊C₈	D₄	1	2	yes	—
115	#13063235	D₄	1	2	yes	—
116	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
117	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
118	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
119	C₈×Dic₄₃	D₄	1	2	yes	—
120	C₂×SD₁₆×C₄₃	—	2	2	no	—
121	C₂×SD₁₆×C₄₃	—	2	2	no	—
122	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
123	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
124	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
125	#127×C₄₃	C₂³	1	1	yes	characteristic
126	#107×C₄₃	—	2	2	no	—
127	#106×C₄₃	—	2	2	no	—
128	#103×C₄₃	—	2	2	no	—
129	#102×C₄₃	—	2	2	no	—
130	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
131	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
132	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
133	C₂×Q₈×C₄₃	—	2	1	no	—
134	C₂×Q₈×C₄₃	—	2	1	no	—
135	C₂×Q₈×C₄₃	—	2	1	no	—
136	C₂×D₄×C₄₃	—	2	1	no	—
137	C₂×D₄×C₄₃	—	2	1	no	—
138	C₂×D₄×C₄₃	—	2	1	no	—
139	C₂×C₂²⋊D₄₃	—	4	1	no	—
140	C₂²×Dic₄₃	—	4	1	no	—
141	Q₈×D₄₃	—	4	4	no	—
142	Q₈×D₄₃	—	8	2	no	—
143	#10621900	—	4	4	no	—
144	C₂×C₄×D₄₃	—	4	1	no	—
145	C₂×C₄×D₄₃	—	4	1	no	—
146	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
148	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
149	C₂×Dic₈₆	—	2	1	no	—
150	C₂×Dic₈₆	—	2	1	no	—
151	C₂×Dic₈₆	—	2	1	no	—
152	C₂×Dic₈₆	—	2	1	no	—
153	C₂×Dic₈₆	—	4	1	no	—
154	C₂×Dic₈₆	—	4	1	no	—
155	SD₁₆×C₄₃	—	4	4	no	—
156	SD₁₆×C₄₃	—	8	2	no	—
157	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
158	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
159	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
160	C₄⋊C₄×C₄₃	—	2	1	no	—
161	C₄⋊C₄×C₄₃	—	2	1	no	—
162	C₄⋊C₄×C₄₃	—	2	1	no	—
163	C₄⋊C₄×C₄₃	—	2	1	no	—
164	C₄⋊C₄×C₄₃	—	2	1	no	—
165	C₄⋊C₄×C₄₃	—	2	1	no	—
166	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
167	C₂²⋊Dic₄₃	—	4	1	no	—
168	C₂²⋊Dic₄₃	—	4	1	no	—
169	#10621885	—	4	4	no	—
170	#10621883	—	4	4	no	—
171	#10621883	—	4	4	no	—
172	#10621883	—	8	2	no	—
173	(C₂×D₄₃)⋊C₄	—	4	1	no	—
174	C₄⋊Dic₄₃	—	2	1	no	—
175	C₄⋊Dic₄₃	—	2	1	no	—
176	C₄⋊Dic₄₃	—	2	1	no	—
177	C₄⋊Dic₄₃	—	2	1	no	—
178	C₄⋊Dic₄₃	—	2	1	no	—
179	C₄⋊Dic₄₃	—	2	1	no	—
180	C₄⋊Dic₄₃	—	2	1	no	—
181	C₄⋊Dic₄₃	—	2	1	no	—
182	C₄⋊Dic₄₃	—	4	1	no	—
183	Dic₄₃⋊C₄	—	4	1	no	—
184	Dic₄₃⋊C₄	—	4	1	no	—
185	Dic₄₃⋊C₄	—	4	1	no	—
186	Dic₄₃⋊C₄	—	4	1	no	—
187	Dic₄₃⋊C₄	—	4	1	no	—
188	C₄×Dic₄₃	—	4	1	no	—
189	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
190	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
191	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
192	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
193	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
194	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
195	Dic₁₇₂	—	4	4	no	—
196	#10621872	SD₁₆	1	8	yes	complemented
197	C₈×D₄₃	—	2	4	no	—
198	C₂³×C₄₃	—	4	1	no	—
199	C₂²×D₄₃	#127	1	1	yes	characteristic
200	Q₈×C₄₃	—	4	2	no	—
201	Q₈×C₄₃	—	4	2	no	—
202	Q₈×C₄₃	—	4	2	no	—
203	D₄×C₄₃	—	4	2	no	—
204	D₄×C₄₃	—	4	2	no	—
205	D₄×C₄₃	—	4	2	no	—
206	C₂×C₄×C₄₃	—	4	1	no	—
207	C₂×C₄×C₄₃	—	4	1	no	—
208	C₂×C₄×C₄₃	—	4	1	no	—
209	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
210	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
212	C₂²⋊D₄₃	—	8	2	no	—
213	C₂×Dic₄₃	—	4	1	no	—
214	C₂×Dic₄₃	—	4	1	no	—
215	C₂×Dic₄₃	—	4	1	no	—
216	C₂×Dic₄₃	—	4	1	no	—
217	C₂×Dic₄₃	—	8	2	no	—
218	C₂×Dic₄₃	#127	1	1	yes	characteristic
219	C₂×Dic₄₃	#127	1	1	yes	characteristic
220	C₂×Dic₄₃	#127	1	1	yes	characteristic
221	C₄×D₄₃	—	2	2	no	—
222	C₄×D₄₃	—	2	2	no	—
223	C₄×D₄₃	—	8	2	no	—
224	C₄×D₄₃	—	8	2	no	—
225	C₄×D₄₃	C₂×SD₁₆	1	4	yes	—
226	Dic₈₆	—	4	2	no	—
227	Dic₈₆	—	4	2	no	—
228	Dic₈₆	—	4	2	no	—
229	Dic₈₆	—	4	2	no	—
230	Dic₈₆	—	8	2	no	—
231	Dic₈₆	—	8	2	no	—
232	C₈×C₄₃	—	2	2	no	—
233	C₈×C₄₃	—	2	2	no	—
234	C₈×C₄₃	C₂×SD₁₆	1	4	yes	—
235	C₄₃⋊C₈	—	2	2	no	—
236	C₄₃⋊C₈	C₂×SD₁₆	1	4	yes	—
237	C₄₃⋊C₈	#137	1	4	yes	complemented
238	#19622	—	43	1	no	maximal, Sylow
239	C₂²×C₄₃	—	8	1	no	—
240	C₂²×C₄₃	—	8	1	no	—
241	C₂²×C₄₃	—	8	1	no	—
242	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
243	C₂×D₄₃	—	2	1	no	—
244	C₂×D₄₃	—	2	1	no	—
245	C₂×D₄₃	#492	1	2	yes	—
246	C₄×C₄₃	—	8	1	no	—
247	C₄×C₄₃	—	8	1	no	—
248	C₄×C₄₃	—	8	1	no	—
249	C₄×C₄₃	C₂²×SD₁₆	1	2	yes	—
250	C₄×C₄₃	C₂×#137	1	2	yes	—
251	C₄×C₄₃	#577	1	2	yes	—
252	Dic₄₃	—	2	1	no	—
253	Dic₄₃	—	2	1	no	—
254	Dic₄₃	—	8	1	no	—
255	Dic₄₃	—	8	1	no	—
256	Dic₄₃	—	8	1	no	—
257	Dic₄₃	—	8	1	no	—
258	Dic₄₃	#492	1	2	yes	—
259	#3229	—	43	1	no	—
260	#3206	—	43	1	no	—
261	#3167	—	43	1	no	—
262	#3165	—	43	1	no	—
263	C₂×#498	—	43	1	no	—
264	#3152	—	43	1	no	—
265	#1716	—	43	1	no	—
266	#1716	—	43	1	no	—
267	#1714	—	43	1	no	—
268	#1714	D₄₃	1	1	yes	characteristic, complemented
269	#1707	—	43	1	no	—
270	#1707	—	43	1	no	—
271	#1705	—	43	1	no	—
272	#1705	—	43	1	no	—
273	C₈×M₁₆	—	43	1	no	—
274	C₂×C₄₃	—	16	1	no	—
275	C₂×C₄₃	C₂×#492	1	1	yes	characteristic
276	C₂×C₄₃	#3152	1	1	yes	characteristic
277	C₂×C₄₃	#3154	1	1	yes	characteristic
278	D₄₃	—	2	2	no	—
279	C₂×#137	—	86	2	no	—
280	#533	—	43	1	no	—
281	#532	—	43	1	no	—
282	C₂×C₄⋊Q₈	—	43	1	no	—
283	C₂×C₄⋊Q₈	—	43	1	no	—
284	#501	—	86	2	no	—
285	#500	—	43	1	no	—
286	#500	C₂×D₄₃	1	1	yes	characteristic
287	#498	—	43	1	no	—
288	#498	—	43	1	no	—
289	#498	—	43	1	no	—
290	#498	—	43	1	no	—
291	#498	—	43	1	no	—
292	#498	—	43	1	no	—
293	#498	—	43	1	no	—
294	#498	—	43	1	no	—
295	#498	—	86	2	no	—
296	#498	C₂×D₄₃	1	1	yes	characteristic
297	#497	—	86	2	no	—
298	#494	—	43	1	no	—
299	#494	—	43	1	no	—
300	#492	—	43	1	no	—
301	#492	—	43	1	no	—
302	#492	—	43	1	no	—
303	#492	C₂×D₄₃	1	1	yes	characteristic
304	#492	C₂×D₄₃	1	1	yes	characteristic
305	#487	—	43	1	no	—
306	#487	—	43	1	no	—
307	#487	—	43	1	no	—
308	#487	—	43	1	no	—
309	#487	C₂×D₄₃	1	1	yes	characteristic
310	#486	C₂×D₄₃	1	1	yes	characteristic
311	#483	—	86	2	no	—
312	#475	—	86	2	no	—
313	#465	—	86	2	no	—
314	#461	—	86	2	no	—
315	#448	—	86	2	no	—
316	C₄×SD₁₆	—	86	2	no	—
317	#431	—	43	1	no	—
318	#428	—	86	2	no	—
319	C₂×#106	—	86	2	no	—
320	C₄×M₁₆	—	43	1	no	—
321	C₂×C₄×C₈	—	43	1	no	—
322	#322	—	43	1	no	—
323	#322	C₂×D₄₃	1	1	yes	characteristic
324	C₈²	—	43	1	no	—
325	C₈²	—	43	1	no	—
326	C₄₃	#19622	1	1	yes	characteristic, complemented, Sylow
327	C₂×#41	—	86	1	no	—
328	C₂²×Q₈	—	86	1	no	—
329	C₂²×Q₈	—	86	1	no	—
330	#137	—	172	8	no	—
331	C₂×Q₁₆	—	86	2	no	—
332	C₂×Q₁₆	—	86	2	no	—
333	C₂×SD₁₆	—	2	2	no	—
334	C₂×SD₁₆	—	2	2	no	—
335	C₂×SD₁₆	—	86	2	no	—
336	C₂×SD₁₆	—	86	2	no	—
337	C₂×SD₁₆	—	86	2	no	—
338	C₂×M₁₆	—	43	2	no	—
339	C₂²×C₈	—	43	2	no	—
340	C₄⋊Q₈	—	43	1	no	—
341	C₄⋊Q₈	—	43	1	no	—
342	C₄⋊Q₈	—	43	1	no	—
343	C₄⋊Q₈	—	43	1	no	—
344	C₄⋊Q₈	—	86	1	no	—
345	C₄⋊Q₈	—	86	1	no	—
346	C₄⋊Q₈	—	86	1	no	—
347	C₄⋊Q₈	—	86	1	no	—
348	C₄⋊Q₈	—	86	1	no	—
349	C₄⋊Q₈	—	86	1	no	—
350	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
351	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
352	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
353	#127	C₂²×D₄₃	1	1	yes	characteristic
354	#125	—	86	1	no	—
355	#124	—	86	1	no	—
356	C₂²⋊Q₈	—	86	1	no	—
357	C₂²⋊Q₈	—	86	1	no	—
358	#121	—	86	1	no	—
359	#121	—	86	1	no	—
360	C₄×Q₈	—	86	1	no	—
361	C₄×Q₈	—	86	1	no	—
362	C₄×D₄	—	86	1	no	—
363	C₄×D₄	—	86	1	no	—
364	#117	—	86	1	no	—
365	C₂×C₄⋊C₄	—	86	1	no	—
366	C₂×C₄⋊C₄	—	86	1	no	—
367	C₂×C₄⋊C₄	—	86	1	no	—
368	C₂×C₄⋊C₄	—	86	1	no	—
369	C₂×C₄²	—	43	1	no	—
370	#107	—	2	2	no	—
371	#107	—	86	2	no	—
372	#106	—	2	2	no	—
373	#106	—	86	2	no	—
374	#106	—	86	2	no	—
375	#106	—	86	2	no	—
376	#106	—	86	2	no	—
377	#106	—	86	2	no	—
378	#106	—	86	2	no	—
379	#106	—	86	2	no	—
380	#106	—	86	2	no	—
381	C₄⋊C₈	—	43	2	no	—
382	#103	—	2	2	no	—
383	#103	—	86	2	no	—
384	#103	—	86	2	no	—
385	#103	—	86	2	no	—
386	#103	—	86	2	no	—
387	#102	—	2	2	no	—
388	C₂²⋊C₈	—	43	2	no	—
389	#97	—	43	2	no	—
390	C₄×C₈	—	43	2	no	—
391	C₄×C₈	—	43	1	no	—
392	C₄×C₈	—	43	1	no	—
393	C₄×C₈	—	43	1	no	—
394	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
395	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
396	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
397	#41	—	172	4	no	—
398	C₂×Q₈	—	2	1	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	2	1	no	—
401	C₂×Q₈	—	86	1	no	—
402	C₂×Q₈	—	86	1	no	—
403	C₂×Q₈	—	86	1	no	—
404	C₂×Q₈	—	86	1	no	—
405	C₂×Q₈	—	344	2	no	—
406	C₂×Q₈	—	172	1	no	—
407	C₂×Q₈	—	172	1	no	—
408	C₂×Q₈	—	172	4	no	—
409	C₂×D₄	—	2	1	no	—
410	C₂×D₄	—	2	1	no	—
411	C₂×D₄	—	2	1	no	—
412	C₂×D₄	—	172	1	no	—
413	C₂²×C₄	—	43	1	no	—
414	C₂²×C₄	—	43	1	no	—
415	C₂²×C₄	—	43	1	no	—
416	C₂²×C₄	—	172	1	no	—
417	C₂²×C₄	—	172	1	no	—
418	C₂²×C₄	—	172	1	no	—
419	Q₁₆	—	172	4	no	—
420	Q₁₆	—	172	4	no	—
421	SD₁₆	—	4	4	no	—
422	SD₁₆	—	8	2	no	—
423	SD₁₆	—	344	2	no	—
424	SD₁₆	—	172	4	no	—
425	SD₁₆	—	172	4	no	—
426	M₁₆	—	43	8	no	—
427	C₂×C₈	—	43	2	no	—
428	C₂×C₈	—	43	2	no	—
429	C₂×C₈	—	43	2	no	—
430	C₂×C₈	—	86	4	no	—
431	C₂×C₈	D₄×D₄₃	1	2	yes	—
432	C₂×C₈	D₄×D₄₃	1	2	yes	—
433	C₂×C₈	D₄×D₄₃	1	2	yes	—
434	C₄⋊C₄	—	2	1	no	—
435	C₄⋊C₄	—	2	1	no	—
436	C₄⋊C₄	—	2	1	no	—
437	C₄⋊C₄	—	2	1	no	—
438	C₄⋊C₄	—	2	1	no	—
439	C₄⋊C₄	—	2	1	no	—
440	C₄⋊C₄	—	86	1	no	—
441	C₄⋊C₄	—	86	1	no	—
442	C₄⋊C₄	—	86	1	no	—
443	C₄⋊C₄	—	86	1	no	—
444	C₄⋊C₄	—	86	1	no	—
445	C₄⋊C₄	—	86	1	no	—
446	C₄⋊C₄	—	86	1	no	—
447	C₄⋊C₄	—	86	1	no	—
448	C₄⋊C₄	—	172	1	no	—
449	C₄⋊C₄	—	172	1	no	—
450	C₄⋊C₄	—	172	1	no	—
451	C₄⋊C₄	—	172	1	no	—
452	C₄⋊C₄	—	172	1	no	—
453	C₄⋊C₄	—	172	1	no	—
454	C₂²⋊C₄	—	172	1	no	—
455	C₂²⋊C₄	—	172	1	no	—
456	C₂²⋊C₄	—	172	1	no	—
457	C₄²	—	43	1	no	—
458	C₄²	—	43	1	no	—
459	C₄²	—	43	1	no	—
460	C₄²	—	172	1	no	—
461	C₄²	C₂³×D₄₃	1	1	yes	characteristic
462	C₂³	—	4	1	no	—
463	C₂³	—	43	1	no	—
464	Q₈	—	4	2	no	—
465	Q₈	—	4	2	no	—
466	Q₈	—	4	2	no	—
467	Q₈	—	344	2	no	—
468	Q₈	—	344	2	no	—
469	Q₈	—	172	2	no	—
470	Q₈	—	172	2	no	—
471	Q₈	—	172	2	no	—
472	Q₈	—	172	2	no	—
473	D₄	—	4	2	no	—
474	D₄	—	4	2	no	—
475	D₄	—	4	2	no	—
476	D₄	—	344	2	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	43	1	no	—
481	C₂×C₄	—	43	4	no	—
482	C₂×C₄	—	43	1	no	—
483	C₂×C₄	—	43	1	no	—
484	C₂×C₄	—	86	2	no	—
485	C₂×C₄	—	86	2	no	—
486	C₂×C₄	—	344	2	no	—
487	C₂×C₄	—	344	2	no	—
488	C₂×C₄	—	344	2	no	—
489	C₂×C₄	—	172	1	no	—
490	C₂×C₄	—	172	1	no	—
491	C₂×C₄	—	172	1	no	—
492	C₂×C₄	—	172	1	no	—
493	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
494	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
495	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
496	C₈	—	2	2	no	—
497	C₈	—	2	2	no	—
498	C₈	—	43	4	no	—
499	C₈	—	43	4	no	—
500	C₈	—	86	2	no	—
501	C₈	SD₁₆×D₄₃	1	4	yes	—
502	C₂²	—	8	1	no	—
503	C₂²	—	8	1	no	—
504	C₂²	—	8	1	no	—
505	C₂²	—	43	2	no	—
506	C₂²	—	86	1	no	—
507	C₂²	—	86	1	no	—
508	C₂²	#127×D₄₃	1	1	yes	characteristic
509	C₄	—	8	1	no	—
510	C₄	—	8	1	no	—
511	C₄	—	8	1	no	—
512	C₄	—	43	2	no	—
513	C₄	—	86	1	no	—
514	C₄	—	86	1	no	—
515	C₄	—	344	1	no	—
516	C₄	—	344	1	no	—
517	C₄	—	344	1	no	—
518	C₄	—	344	1	no	—
519	C₄	C₂×SD₁₆×D₄₃	1	2	yes	—
520	C₄	#137×D₄₃	1	2	yes	—
521	C₄	#14583709	1	2	yes	—
522	C₂	—	16	1	no	—
523	C₂	—	86	2	no	—
524	C₂	#492×D₄₃	1	1	yes	characteristic
525	C₂	#19145051	1	1	yes	characteristic
526	C₂	#19145068	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	#14583447	C₂²
hypercenter	#1714	D₄₃
hypocenter	C₄₃	#19622
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. #19145735	C₂	semidirect
4. #19145138	C₂	semidirect
5. #498×D₄₃	C₂	semidirect
7. #19134228	C₂	semidirect
8. #19134227	C₂	semidirect
9. #19134216	C₂	semidirect
10. #19134193	C₂	semidirect
11. #19134191	C₂	semidirect
12. #19134181	C₂	semidirect
13. #19134181	C₂	semidirect
14. #19132874	C₂	semidirect
15. C₄₃×#1714	C₂	semidirect
196. #10621872	SD₁₆	semidirect
237. C₄₃⋊C₈	#137	semidirect
268. #1714	D₄₃	semidirect
326. C₄₃	#19622	semidirect

Maximal subgroups

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

subgroup	index
#19145735	2
#19145516	2
#19145153	2
#19145138	2
#498×D₄₃	2
#19145049	2
#19134228	2
#19134227	2
#19134216	2
#19134193	2
#19134191	2
#19134181	2
#19132874	2
C₄₃×#1714	2
#19622	43