Subgroups — #25084550

Order 11008.

750 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19145747	C₂	1	1	yes	maximal, characteristic
2	#19145742	C₂	1	1	yes	maximal, characteristic
3	#19145180	C₂	1	1	yes	maximal, characteristic
4	#19145138	C₂	1	1	yes	maximal, characteristic
5	#19145136	C₂	1	1	yes	maximal, characteristic
6	#494×D₄₃	C₂	1	1	yes	maximal, characteristic
7	#19134274	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134272	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134270	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134212	C₂	1	1	yes	maximal, characteristic, complemented
11	#19134212	C₂	1	1	yes	maximal, characteristic, complemented
12	#19134191	C₂	1	1	yes	maximal, characteristic, complemented
13	#19134190	C₂	1	1	yes	maximal, characteristic, complemented
14	#19132874	C₂	1	1	yes	maximal, characteristic
15	C₄₃×#1723	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×Q₁₆×D₄₃	—	2	2	no	—
17	#14583454	C₂²	1	1	yes	characteristic
18	#14583454	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	#14583306	—	2	2	no	—
23	#14583304	C₂²	1	1	yes	characteristic
24	#14583304	C₂²	1	1	yes	characteristic
25	#14583302	C₂²	1	1	yes	characteristic
26	#14583302	C₂²	1	1	yes	characteristic
27	#14583302	C₂²	1	1	yes	characteristic
28	#14583302	C₂²	1	1	yes	characteristic
29	#14583302	C₂²	1	1	yes	characteristic
30	#14583297	C₂²	1	1	yes	characteristic
31	#14583295	C₂²	1	1	yes	characteristic
32	#14583295	C₂²	1	1	yes	characteristic
33	#14583279	C₂²	1	1	yes	characteristic
34	#14583278	C₂²	1	1	yes	characteristic
35	#14583278	C₂²	1	1	yes	characteristic
36	#14583278	C₂²	1	1	yes	characteristic
37	#14583277	—	2	2	no	—
38	#14583251	C₂²	1	1	yes	characteristic
39	#14583250	C₂²	1	1	yes	characteristic
40	#14583250	C₂²	1	1	yes	characteristic
41	#14583249	C₂²	1	1	yes	characteristic
42	#14583236	—	2	2	no	—
43	#14583233	—	2	2	no	—
44	#14583193	—	2	2	no	—
45	#14583192	—	2	2	no	—
46	#14583139	—	2	2	no	—
47	#14582991	—	2	2	no	—
48	#14582950	C₂²	1	1	yes	characteristic
49	#14582940	—	2	2	no	—
50	#14582938	—	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×#500	C₂²	1	1	yes	characteristic
58	C₄₃×#498	C₂²	1	1	yes	characteristic
59	C₄₃×#494	C₂²	1	1	yes	characteristic
60	C₄₃×#487	C₂²	1	1	yes	characteristic
61	C₄₃×#487	C₂²	1	1	yes	characteristic
62	C₄₃×#322	C₂²	1	1	yes	characteristic
63	C₂×Q₈×D₄₃	—	2	1	no	—
64	C₂×Q₈×D₄₃	—	2	1	no	—
65	C₂×Dic₁₇₂	—	2	2	no	—
66	C₂×#10621885	—	2	2	no	—
67	C₂×#10621885	—	2	2	no	—
68	C₂×#10621885	—	2	2	no	—
69	Q₁₆×D₄₃	—	4	8	no	—
70	C₂×#10621872	D₄	1	2	yes	—
71	C₂×C₈×D₄₃	D₄	1	2	yes	—
72	#13063325	C₂³	1	1	yes	characteristic
73	#13063325	C₂³	1	1	yes	characteristic
74	#13063325	C₂³	1	1	yes	characteristic
75	#13063325	C₂³	1	1	yes	characteristic
76	#13063324	—	2	1	no	—
77	#13063324	—	2	1	no	—
78	#13063324	—	2	1	no	—
79	#13063324	—	2	1	no	—
80	#13063323	—	2	1	no	—
81	#13063323	—	2	1	no	—
82	#13063316	—	2	1	no	—
83	#13063316	—	2	1	no	—
84	#13063305	—	2	1	no	—
85	#13063305	—	2	1	no	—
86	#13063301	—	2	1	no	—
87	#13063301	—	2	1	no	—
88	Q₈×Dic₄₃	—	2	1	no	—
89	Q₈×Dic₄₃	—	2	1	no	—
90	#13063290	—	2	1	no	—
91	#13063290	—	2	1	no	—
92	#13063283	—	2	1	no	—
93	#13063283	—	2	1	no	—
94	C₄⋊C₄×D₄₃	—	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	C₄²×D₄₃	C₂³	1	1	yes	characteristic
99	#13063259	—	2	2	no	—
100	#13063259	—	2	2	no	—
101	#13063258	—	2	2	no	—
102	#13063258	—	2	2	no	—
103	#13063258	—	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	Dic₄₃⋊C₈	D₄	1	2	yes	—
110	#13063250	—	2	2	no	—
111	#13063250	—	2	2	no	—
112	#13063249	—	2	2	no	—
113	#13063248	—	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×Q₁₆×C₄₃	—	2	2	no	—
121	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
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	#107×C₄₃	—	2	2	no	—
126	#107×C₄₃	—	2	2	no	—
127	#106×C₄₃	—	2	2	no	—
128	#103×C₄₃	—	2	2	no	—
129	#103×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×Q₈×C₄₃	—	2	1	no	—
137	Q₈×D₄₃	—	4	4	no	—
138	Q₈×D₄₃	—	4	4	no	—
139	C₂×C₄×D₄₃	—	4	1	no	—
140	C₂×C₄×D₄₃	—	4	1	no	—
141	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
142	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
143	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
144	C₂×Dic₈₆	—	2	1	no	—
145	C₂×Dic₈₆	—	2	1	no	—
146	C₂×Dic₈₆	—	2	1	no	—
147	C₂×Dic₈₆	—	2	1	no	—
148	C₂×Dic₈₆	—	4	1	no	—
149	C₂×Dic₈₆	—	4	1	no	—
150	Q₁₆×C₄₃	—	4	4	no	—
151	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
152	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
153	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
154	C₄⋊C₄×C₄₃	—	2	1	no	—
155	C₄⋊C₄×C₄₃	—	2	1	no	—
156	C₄⋊C₄×C₄₃	—	2	1	no	—
157	C₄⋊C₄×C₄₃	—	2	1	no	—
158	C₄⋊C₄×C₄₃	—	2	1	no	—
159	C₄⋊C₄×C₄₃	—	2	1	no	—
160	C₄⋊C₄×C₄₃	—	2	1	no	—
161	C₄⋊C₄×C₄₃	—	2	1	no	—
162	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
163	#10621885	—	4	4	no	—
164	#10621885	—	4	4	no	—
165	#10621885	—	4	4	no	—
166	(C₂×D₄₃)⋊C₄	—	4	1	no	—
167	(C₂×D₄₃)⋊C₄	—	4	1	no	—
168	C₄⋊Dic₄₃	—	2	1	no	—
169	C₄⋊Dic₄₃	—	2	1	no	—
170	C₄⋊Dic₄₃	—	2	1	no	—
171	C₄⋊Dic₄₃	—	2	1	no	—
172	C₄⋊Dic₄₃	—	2	1	no	—
173	C₄⋊Dic₄₃	—	2	1	no	—
174	C₄⋊Dic₄₃	—	2	1	no	—
175	C₄⋊Dic₄₃	—	2	1	no	—
176	C₄⋊Dic₄₃	—	4	1	no	—
177	C₄⋊Dic₄₃	—	4	1	no	—
178	Dic₄₃⋊C₄	—	4	1	no	—
179	Dic₄₃⋊C₄	—	4	1	no	—
180	Dic₄₃⋊C₄	—	4	1	no	—
181	Dic₄₃⋊C₄	—	4	1	no	—
182	Dic₄₃⋊C₄	—	4	1	no	—
183	Dic₄₃⋊C₄	—	4	1	no	—
184	C₄×Dic₄₃	—	4	1	no	—
185	C₄×Dic₄₃	—	4	1	no	—
186	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
187	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
188	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
189	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
190	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
191	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
192	Dic₁₇₂	—	4	4	no	—
193	#10621872	Q₁₆	1	8	yes	complemented
194	C₈×D₄₃	—	2	4	no	—
195	C₂²×D₄₃	#127	1	1	yes	characteristic
196	Q₈×C₄₃	—	4	2	no	—
197	Q₈×C₄₃	—	4	2	no	—
198	Q₈×C₄₃	—	4	2	no	—
199	Q₈×C₄₃	—	4	2	no	—
200	C₂×C₄×C₄₃	—	4	1	no	—
201	C₂×C₄×C₄₃	—	4	1	no	—
202	C₂×C₄×C₄₃	—	4	1	no	—
203	C₂×C₄×C₄₃	—	4	1	no	—
204	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
205	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×Dic₄₃	—	4	1	no	—
208	C₂×Dic₄₃	—	4	1	no	—
209	C₂×Dic₄₃	—	4	1	no	—
210	C₂×Dic₄₃	—	4	1	no	—
211	C₂×Dic₄₃	#127	1	1	yes	characteristic
212	C₂×Dic₄₃	#127	1	1	yes	characteristic
213	C₂×Dic₄₃	#127	1	1	yes	characteristic
214	C₄×D₄₃	—	2	2	no	—
215	C₄×D₄₃	—	2	2	no	—
216	C₄×D₄₃	—	8	2	no	—
217	C₄×D₄₃	—	8	2	no	—
218	C₄×D₄₃	C₂×Q₁₆	1	4	yes	—
219	Dic₈₆	—	4	2	no	—
220	Dic₈₆	—	4	2	no	—
221	Dic₈₆	—	4	2	no	—
222	Dic₈₆	—	4	2	no	—
223	Dic₈₆	—	8	2	no	—
224	Dic₈₆	—	8	2	no	—
225	C₈×C₄₃	—	2	2	no	—
226	C₈×C₄₃	—	2	2	no	—
227	C₈×C₄₃	C₂×Q₁₆	1	4	yes	complemented
228	C₄₃⋊C₈	—	2	2	no	—
229	C₄₃⋊C₈	C₂×Q₁₆	1	4	yes	complemented
230	C₄₃⋊C₈	AGL(1,ℤ/8)	1	4	yes	—
231	#19632	—	43	1	no	maximal, Sylow
232	C₂²×C₄₃	C₂×#127	1	1	yes	characteristic
233	C₂×D₄₃	—	2	1	no	—
234	C₂×D₄₃	—	2	1	no	—
235	C₂×D₄₃	#494	1	2	yes	—
236	C₄×C₄₃	—	8	1	no	—
237	C₄×C₄₃	—	8	1	no	—
238	C₄×C₄₃	—	8	1	no	—
239	C₄×C₄₃	—	8	1	no	—
240	C₄×C₄₃	C₂²×Q₁₆	1	2	yes	—
241	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
242	C₄×C₄₃	#578	1	2	yes	—
243	Dic₄₃	—	2	1	no	—
244	Dic₄₃	—	2	1	no	—
245	Dic₄₃	—	8	1	no	—
246	Dic₄₃	—	8	1	no	—
247	Dic₄₃	—	8	1	no	—
248	Dic₄₃	—	8	1	no	—
249	Dic₄₃	#494	1	2	yes	—
250	#3230	—	43	1	no	—
251	#3230	—	43	1	no	—
252	#3170	—	43	1	no	—
253	#3165	—	43	1	no	—
254	#3165	—	43	1	no	—
255	C₂×#494	—	43	1	no	—
256	#1723	—	43	1	no	—
257	#1723	—	43	1	no	—
258	#1723	—	43	1	no	—
259	#1723	D₄₃	1	1	yes	characteristic, complemented
260	#1713	—	43	1	no	—
261	#1713	—	43	1	no	—
262	#1707	—	43	1	no	—
263	#1707	—	43	1	no	—
264	C₈×M₁₆	—	43	1	no	—
265	C₂×C₄₃	C₂×#494	1	1	yes	characteristic
266	C₂×C₄₃	#3151	1	1	yes	characteristic
267	C₂×C₄₃	#3156	1	1	yes	characteristic
268	D₄₃	—	2	2	no	—
269	C₂²×Q₁₆	—	86	2	no	—
270	#533	—	43	1	no	—
271	#533	—	43	1	no	—
272	C₂×C₄⋊Q₈	—	43	1	no	—
273	C₂×C₄⋊Q₈	—	43	1	no	—
274	#501	—	86	2	no	—
275	#501	—	86	2	no	—
276	#500	—	43	1	no	—
277	#500	—	43	1	no	—
278	#500	—	43	1	no	—
279	#500	—	43	1	no	—
280	#500	—	43	1	no	—
281	#500	—	43	1	no	—
282	#500	—	43	1	no	—
283	#500	C₂×D₄₃	1	1	yes	characteristic
284	#500	C₂×D₄₃	1	1	yes	characteristic
285	#498	—	43	1	no	—
286	#498	—	43	1	no	—
287	#498	—	43	1	no	—
288	#498	C₂×D₄₃	1	1	yes	characteristic
289	#494	—	43	1	no	—
290	#494	—	43	1	no	—
291	#494	—	43	1	no	—
292	#494	—	43	1	no	—
293	#494	—	86	2	no	—
294	#494	C₂×D₄₃	1	1	yes	characteristic
295	#487	—	43	1	no	—
296	#487	—	43	1	no	—
297	#487	—	43	1	no	—
298	#487	—	43	1	no	—
299	#487	C₂×D₄₃	1	1	yes	characteristic
300	#487	C₂×D₄₃	1	1	yes	characteristic
301	#484	—	86	2	no	—
302	#484	—	86	2	no	—
303	#477	—	86	2	no	—
304	#477	—	86	2	no	—
305	#467	—	86	2	no	—
306	C₄×Q₁₆	—	86	2	no	—
307	#431	—	43	1	no	—
308	#428	—	86	2	no	—
309	#428	—	86	2	no	—
310	C₄×M₁₆	—	43	1	no	—
311	C₂×C₄×C₈	—	43	1	no	—
312	#322	—	43	1	no	—
313	#322	C₂×D₄₃	1	1	yes	characteristic
314	C₈²	—	43	1	no	—
315	C₈²	—	43	1	no	—
316	C₄₃	#19632	1	1	yes	characteristic, complemented, Sylow
317	C₂²×Q₈	—	86	1	no	—
318	C₂²×Q₈	—	86	1	no	—
319	C₂×Q₁₆	—	2	2	no	—
320	C₂×Q₁₆	—	86	2	no	—
321	C₂×Q₁₆	—	86	2	no	—
322	C₂×Q₁₆	—	86	2	no	—
323	C₂×Q₁₆	—	86	2	no	—
324	C₂×Q₁₆	—	172	8	no	—
325	C₂×M₁₆	—	43	2	no	—
326	C₂²×C₈	—	43	2	no	—
327	C₄⋊Q₈	—	43	1	no	—
328	C₄⋊Q₈	—	43	1	no	—
329	C₄⋊Q₈	—	43	1	no	—
330	C₄⋊Q₈	—	43	1	no	—
331	C₄⋊Q₈	—	86	1	no	—
332	C₄⋊Q₈	—	86	1	no	—
333	C₄⋊Q₈	—	86	1	no	—
334	C₄⋊Q₈	—	86	1	no	—
335	C₄⋊Q₈	—	86	1	no	—
336	C₄⋊Q₈	—	86	1	no	—
337	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
338	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
339	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
340	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
341	#125	—	86	1	no	—
342	#125	—	86	1	no	—
343	C₂²⋊Q₈	—	86	1	no	—
344	C₂²⋊Q₈	—	86	1	no	—
345	C₂²⋊Q₈	—	86	1	no	—
346	C₂²⋊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	—	86	1	no	—
351	#117	—	86	1	no	—
352	#117	—	86	1	no	—
353	C₂×C₄⋊C₄	—	86	1	no	—
354	C₂×C₄⋊C₄	—	86	1	no	—
355	C₂×C₄⋊C₄	—	86	1	no	—
356	C₂×C₄⋊C₄	—	86	1	no	—
357	C₂×C₄²	—	43	1	no	—
358	#107	—	2	2	no	—
359	#107	—	2	2	no	—
360	#107	—	86	2	no	—
361	#107	—	86	2	no	—
362	#107	—	86	2	no	—
363	#107	—	86	2	no	—
364	#107	—	86	2	no	—
365	#107	—	86	2	no	—
366	#107	—	86	2	no	—
367	#106	—	2	2	no	—
368	#106	—	86	2	no	—
369	#106	—	86	2	no	—
370	#106	—	86	2	no	—
371	C₄⋊C₈	—	43	2	no	—
372	#103	—	2	2	no	—
373	#103	—	2	2	no	—
374	#103	—	86	2	no	—
375	#103	—	86	2	no	—
376	#103	—	86	2	no	—
377	#103	—	86	2	no	—
378	C₂²⋊C₈	—	43	2	no	—
379	#97	—	43	2	no	—
380	C₄×C₈	—	43	2	no	—
381	C₄×C₈	—	43	1	no	—
382	C₄×C₈	—	43	1	no	—
383	C₄×C₈	—	43	1	no	—
384	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
385	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
386	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
387	C₂×Q₈	—	2	1	no	—
388	C₂×Q₈	—	2	1	no	—
389	C₂×Q₈	—	2	1	no	—
390	C₂×Q₈	—	2	1	no	—
391	C₂×Q₈	—	86	1	no	—
392	C₂×Q₈	—	86	1	no	—
393	C₂×Q₈	—	86	1	no	—
394	C₂×Q₈	—	86	1	no	—
395	C₂×Q₈	—	172	1	no	—
396	C₂×Q₈	—	172	1	no	—
397	C₂×Q₈	—	172	4	no	—
398	C₂×Q₈	—	172	4	no	—
399	C₂²×C₄	—	43	1	no	—
400	C₂²×C₄	—	43	1	no	—
401	C₂²×C₄	—	43	1	no	—
402	C₂²×C₄	—	172	1	no	—
403	C₂²×C₄	—	172	1	no	—
404	Q₁₆	—	4	4	no	—
405	Q₁₆	—	172	4	no	—
406	Q₁₆	—	172	4	no	—
407	Q₁₆	—	172	4	no	—
408	Q₁₆	—	172	4	no	—
409	M₁₆	—	43	8	no	—
410	C₂×C₈	—	43	2	no	—
411	C₂×C₈	—	43	2	no	—
412	C₂×C₈	—	43	2	no	—
413	C₂×C₈	—	86	4	no	—
414	C₂×C₈	D₄×D₄₃	1	2	yes	—
415	C₂×C₈	D₄×D₄₃	1	2	yes	—
416	C₂×C₈	D₄×D₄₃	1	2	yes	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	1	no	—
422	C₄⋊C₄	—	2	1	no	—
423	C₄⋊C₄	—	2	1	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	86	1	no	—
426	C₄⋊C₄	—	86	1	no	—
427	C₄⋊C₄	—	86	1	no	—
428	C₄⋊C₄	—	86	1	no	—
429	C₄⋊C₄	—	86	1	no	—
430	C₄⋊C₄	—	86	1	no	—
431	C₄⋊C₄	—	86	1	no	—
432	C₄⋊C₄	—	86	1	no	—
433	C₄⋊C₄	—	172	1	no	—
434	C₄⋊C₄	—	172	1	no	—
435	C₄⋊C₄	—	172	1	no	—
436	C₄⋊C₄	—	172	1	no	—
437	C₄⋊C₄	—	172	1	no	—
438	C₄⋊C₄	—	172	1	no	—
439	C₄⋊C₄	—	172	1	no	—
440	C₄⋊C₄	—	172	1	no	—
441	C₂²⋊C₄	—	172	1	no	—
442	C₂²⋊C₄	—	172	1	no	—
443	C₄²	—	43	1	no	—
444	C₄²	—	43	1	no	—
445	C₄²	—	43	1	no	—
446	C₄²	—	172	1	no	—
447	C₄²	—	172	1	no	—
448	C₄²	C₂³×D₄₃	1	1	yes	characteristic
449	C₂³	—	43	1	no	—
450	Q₈	—	4	2	no	—
451	Q₈	—	4	2	no	—
452	Q₈	—	4	2	no	—
453	Q₈	—	4	2	no	—
454	Q₈	—	344	2	no	—
455	Q₈	—	344	2	no	—
456	Q₈	—	172	2	no	—
457	Q₈	—	172	2	no	—
458	Q₈	—	172	2	no	—
459	Q₈	—	172	2	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	43	1	no	—
465	C₂×C₄	—	43	4	no	—
466	C₂×C₄	—	43	1	no	—
467	C₂×C₄	—	43	1	no	—
468	C₂×C₄	—	86	2	no	—
469	C₂×C₄	—	86	2	no	—
470	C₂×C₄	—	344	2	no	—
471	C₂×C₄	—	344	2	no	—
472	C₂×C₄	—	172	1	no	—
473	C₂×C₄	—	172	1	no	—
474	C₂×C₄	—	172	1	no	—
475	C₂×C₄	—	172	1	no	—
476	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
477	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
478	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
479	C₈	—	2	2	no	—
480	C₈	—	2	2	no	—
481	C₈	—	43	4	no	—
482	C₈	—	43	4	no	—
483	C₈	—	86	2	no	—
484	C₈	Q₁₆×D₄₃	1	4	yes	complemented
485	C₂²	—	43	2	no	—
486	C₂²	—	86	1	no	—
487	C₂²	—	86	1	no	—
488	C₂²	#127×D₄₃	1	1	yes	characteristic
489	C₄	—	8	1	no	—
490	C₄	—	8	1	no	—
491	C₄	—	8	1	no	—
492	C₄	—	8	1	no	—
493	C₄	—	43	2	no	—
494	C₄	—	86	1	no	—
495	C₄	—	86	1	no	—
496	C₄	—	344	1	no	—
497	C₄	—	344	1	no	—
498	C₄	—	344	1	no	—
499	C₄	—	344	1	no	—
500	C₄	C₂×Q₁₆×D₄₃	1	2	yes	—
501	C₄	AGL(1,ℤ/8)×D₄₃	1	2	yes	—
502	C₄	#14583715	1	2	yes	—
503	C₂	—	86	2	no	—
504	C₂	#494×D₄₃	1	1	yes	characteristic
505	C₂	#19145044	1	1	yes	characteristic
506	C₂	#19145087	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#127×D₄₃
commutator, cosocle	C₄²×C₄₃	C₂⁴
Frattini	C₄²	C₂³×D₄₃
Fitting	C₄₃×#1723	C₂
socle	C₂²×C₄₃	C₂×#127
prime radical	C₂²×D₄₃	#127
hypercenter	#1723	D₄₃
hypocenter	C₄₃	#19632
LCS	G ▷ C₄²×C₄₃ ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #1723

Complements

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

N	H ≅ G/N	type
7. #19134274	C₂	semidirect
8. #19134272	C₂	semidirect
9. #19134270	C₂	semidirect
10. #19134212	C₂	semidirect
11. #19134212	C₂	semidirect
12. #19134191	C₂	semidirect
13. #19134190	C₂	semidirect
15. C₄₃×#1723	C₂	semidirect
193. #10621872	Q₁₆	semidirect
227. C₈×C₄₃	C₂×Q₁₆	semidirect
229. C₄₃⋊C₈	C₂×Q₁₆	semidirect
259. #1723	D₄₃	semidirect
316. C₄₃	#19632	semidirect
484. C₈	Q₁₆×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19145747	2
#19145742	2
#19145180	2
#19145138	2
#19145136	2
#494×D₄₃	2
#19134274	2
#19134272	2
#19134270	2
#19134212	2
#19134191	2
#19134190	2
#19132874	2
C₄₃×#1723	2
#19632	43