Subgroups — #25100983

Order 11008.

770 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143363	C₂	1	1	yes	maximal, characteristic
2	#19143238	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143235	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135482	C₂	1	1	yes	maximal, characteristic
5	#19135480	C₂	1	1	yes	maximal, characteristic
6	#19135342	C₂	1	1	yes	maximal, characteristic, complemented
7	#19135340	C₂	1	1	yes	maximal, characteristic, complemented
8	#19135301	C₂	1	1	yes	maximal, characteristic, complemented
9	#19135299	C₂	1	1	yes	maximal, characteristic, complemented
10	#19135297	C₂	1	1	yes	maximal, characteristic, complemented
11	#19134496	C₂	1	1	yes	maximal, characteristic, complemented
12	#104×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
13	#19134399	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×C₈×Dic₄₃	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#1937	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13063345	C₂²	1	1	yes	characteristic
17	#41×Dic₄₃	C₂²	1	1	yes	characteristic
18	#14583367	C₂²	1	1	yes	characteristic
19	#14582991	C₄	1	2	yes	complemented
20	#14582990	C₄	1	2	yes	complemented
21	#14582984	C₄	1	2	yes	complemented
22	#14582979	C₄	1	2	yes	complemented
23	#14582959	—	2	2	no	—
24	#14582957	—	2	2	no	—
25	#14582951	—	2	2	no	—
26	#14582949	—	2	2	no	—
27	C₂×#13063260	C₂²	1	1	yes	characteristic
28	C₂×#13063260	C₂²	1	1	yes	characteristic
29	#14582935	C₂²	1	1	yes	characteristic
30	#14582927	C₂²	1	1	yes	characteristic
31	#14582926	C₂²	1	1	yes	characteristic
32	#14582925	C₂²	1	1	yes	characteristic
33	C₂×#13063253	C₂²	1	1	yes	characteristic
34	C₂×#13063252	C₂²	1	1	yes	characteristic
35	C₂×#13063251	C₂²	1	1	yes	characteristic
36	#14582896	C₂²	1	1	yes	characteristic
37	#14582867	C₂²	1	1	yes	characteristic
38	#14582866	C₂²	1	1	yes	characteristic
39	#14582865	C₂²	1	1	yes	characteristic
40	M₁₆×Dic₄₃	C₂²	1	1	yes	characteristic
41	M₁₆×Dic₄₃	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
44	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
45	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
46	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
47	C₄²×Dic₄₃	C₂²	1	1	yes	characteristic
48	#14582664	C₂²	1	1	yes	characteristic
49	#14582660	C₂²	1	1	yes	characteristic
50	#14582659	C₂²	1	1	yes	characteristic
51	#14582658	C₂²	1	1	yes	characteristic
52	C₄₃×#424	C₂²	1	1	yes	characteristic
53	C₂×#104×C₄₃	C₂²	1	1	yes	characteristic
54	C₄₃×#416	C₂²	1	1	yes	characteristic
55	C₄₃×#408	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
57	C₄₃×#341	C₂²	1	1	yes	characteristic
58	C₄₃×#339	C₂²	1	1	yes	characteristic
59	C₂×#10621898	C₂³	1	1	yes	characteristic
60	#13063345	—	2	2	no	—
61	#13063345	—	2	2	no	—
62	C₂×#10621885	C₂×C₄	1	1	yes	characteristic
63	C₂×#10621883	C₂×C₄	1	1	yes	characteristic
64	C₂×#10621884	C₂×C₄	1	1	yes	characteristic
65	C₂×#10621882	C₂×C₄	1	1	yes	characteristic
66	C₂×#10621877	C₂³	1	1	yes	characteristic
67	C₂×#10621877	C₂³	1	1	yes	characteristic
68	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
70	Q₈×Dic₄₃	C₂×C₄	1	2	yes	—
71	#13063290	C₂×C₄	1	2	yes	—
72	D₄×Dic₄₃	—	2	2	no	—
73	D₄×Dic₄₃	C₂×C₄	1	2	yes	—
74	#13063287	C₂×C₄	1	2	yes	—
75	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
76	#13063284	—	2	1	no	—
77	#13063284	C₂³	1	1	yes	characteristic
78	#13063282	—	2	1	no	—
79	C₂×C₄×Dic₄₃	—	2	2	no	—
80	C₂×C₄×Dic₄₃	—	2	1	no	—
81	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
82	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
83	C₄²×D₄₃	—	2	1	no	—
84	#13063260	—	2	2	no	—
85	#13063260	—	2	2	no	—
86	#13063258	C₂×C₄	1	2	yes	—
87	#13063256	C₂×C₄	1	2	yes	—
88	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
89	Dic₄₃⋊C₈	—	2	2	no	—
90	Dic₄₃⋊C₈	—	2	2	no	—
91	#13063253	—	2	2	no	—
92	#13063252	—	2	2	no	—
93	#13063251	—	2	2	no	—
94	#13063250	C₂×C₄	1	2	yes	—
95	#13063247	C₂×C₄	1	2	yes	—
96	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
97	(C₂×D₄₃)⋊C₈	—	2	2	no	—
98	(C₂×D₄₃)⋊C₈	—	2	2	no	—
99	#13063235	—	2	1	no	—
100	#13063235	—	2	1	no	—
101	C₄×C₄₃⋊C₈	—	2	2	no	—
102	C₈×Dic₄₃	—	2	1	no	—
103	C₈×Dic₄₃	—	2	1	no	—
104	C₈×Dic₄₃	—	2	2	no	—
105	C₈×Dic₄₃	—	2	2	no	—
106	C₈×Dic₄₃	C₂×C₄	1	2	yes	—
107	C₈×Dic₄₃	C₂×C₄	1	2	yes	—
108	C₈×Dic₄₃	D₄	1	2	yes	—
109	C₈×Dic₄₃	D₄	1	2	yes	—
110	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
111	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
112	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
115	#117×C₄₃	C₂³	1	1	yes	characteristic
116	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
117	C₄⋊C₈×C₄₃	—	2	2	no	—
118	#104×C₄₃	—	2	2	no	—
119	#103×C₄₃	C₂×C₄	1	2	yes	—
120	#102×C₄₃	C₂×C₄	1	2	yes	—
121	C₂²⋊C₈×C₄₃	—	2	2	no	—
122	C₄×C₈×C₄₃	—	2	2	no	—
123	#41×C₄₃	—	2	1	no	—
124	#41×C₄₃	—	2	1	no	—
125	#41×C₄₃	—	2	1	no	—
126	#41×C₄₃	—	2	1	no	—
127	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
128	C₂×D₄×C₄₃	—	2	1	no	—
129	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₃	—	2	1	no	—
131	C₂²×C₄×C₄₃	—	2	1	no	—
132	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
133	C₂×C₂²⋊D₄₃	—	2	1	no	—
134	C₂²×Dic₄₃	—	2	2	no	—
135	C₂²×Dic₄₃	—	2	1	no	—
136	C₂²×Dic₄₃	#41	1	2	yes	—
137	#10621898	—	2	1	no	—
138	#10621898	—	2	1	no	—
139	#10621898	—	2	1	no	—
140	#10621898	—	2	1	no	—
141	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₄×D₄₃	—	2	1	no	—
143	C₂×C₄×D₄₃	—	2	2	no	—
144	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
145	M₁₆×C₄₃	—	2	1	no	—
146	M₁₆×C₄₃	—	2	1	no	—
147	M₁₆×C₄₃	—	2	1	no	—
148	M₁₆×C₄₃	—	2	1	no	—
149	C₂×C₈×C₄₃	—	2	1	no	—
150	C₂×C₈×C₄₃	—	2	1	no	—
151	C₂×C₈×C₄₃	—	2	1	no	—
152	C₂×C₈×C₄₃	—	2	1	no	—
153	C₂×C₈×C₄₃	—	2	1	no	—
154	C₂×C₈×C₄₃	—	2	1	no	—
155	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
156	C₂×C₈×C₄₃	C₂×D₄	1	2	yes	—
157	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
158	C₂²⋊C₄×C₄₃	—	2	1	no	—
159	C₄²×C₄₃	—	2	1	no	—
160	C₄²×C₄₃	—	2	1	no	—
161	C₄²×C₄₃	#41	1	2	yes	—
162	C₂²⋊Dic₄₃	—	2	2	no	—
163	C₂²⋊Dic₄₃	—	2	1	no	—
164	#10621885	—	2	2	no	—
165	#10621884	—	2	2	no	—
166	#10621883	—	2	2	no	—
167	#10621882	—	2	2	no	—
168	(C₂×D₄₃)⋊C₄	—	2	2	no	—
169	C₄⋊Dic₄₃	—	2	2	no	—
170	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
171	Dic₄₃⋊C₄	—	2	2	no	—
172	C₄×Dic₄₃	—	2	8	no	—
173	C₄×Dic₄₃	—	2	1	no	—
174	C₄×Dic₄₃	—	2	1	no	—
175	C₄×Dic₄₃	—	2	2	no	—
176	C₄×Dic₄₃	—	2	2	no	—
177	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
178	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
179	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
180	C₄×Dic₄₃	#41	1	2	yes	—
181	#10621877	—	2	1	no	—
182	#10621877	—	2	1	no	—
183	#10621877	—	2	1	no	—
184	#10621877	—	2	1	no	—
185	C₂×C₄₃⋊C₈	—	2	1	no	—
186	C₂×C₄₃⋊C₈	—	2	1	no	—
187	C₂×C₄₃⋊C₈	—	2	1	no	—
188	C₂×C₄₃⋊C₈	—	2	1	no	—
189	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
190	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
191	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
192	C₂×C₄₃⋊C₈	#41	1	2	yes	—
193	C₂×C₄₃⋊C₈	#41	1	2	yes	—
194	C₂³×C₄₃	—	2	1	no	—
195	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
196	C₂²×D₄₃	—	2	1	no	—
197	Q₈×C₄₃	—	2	1	no	—
198	Q₈×C₄₃	—	2	1	no	—
199	D₄×C₄₃	—	2	1	no	—
200	D₄×C₄₃	—	2	1	no	—
201	D₄×C₄₃	—	4	1	no	—
202	D₄×C₄₃	—	4	1	no	—
203	C₂×C₄×C₄₃	—	2	4	no	—
204	C₂×C₄×C₄₃	—	2	2	no	—
205	C₂×C₄×C₄₃	—	2	1	no	—
206	C₂×C₄×C₄₃	—	2	2	no	—
207	C₂×C₄×C₄₃	—	4	1	no	—
208	C₂×C₄×C₄₃	—	4	1	no	—
209	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
210	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
215	C₂²⋊D₄₃	—	4	1	no	—
216	C₂²⋊D₄₃	—	4	1	no	—
217	C₂×Dic₄₃	—	2	4	no	—
218	C₂×Dic₄₃	—	2	2	no	—
219	C₂×Dic₄₃	—	2	4	no	—
220	C₂×Dic₄₃	—	2	1	no	—
221	C₂×Dic₄₃	—	2	2	no	—
222	C₂×Dic₄₃	—	4	4	no	—
223	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
224	C₂×Dic₄₃	C₄×D₄	1	2	yes	—
225	D₁₇₂	—	2	1	no	—
226	D₁₇₂	—	2	1	no	—
227	C₄×D₄₃	—	4	1	no	—
228	C₄×D₄₃	—	4	1	no	—
229	C₄×D₄₃	—	4	4	no	—
230	Dic₈₆	—	2	1	no	—
231	Dic₈₆	—	2	1	no	—
232	C₈×C₄₃	—	2	2	no	—
233	C₈×C₄₃	—	2	2	no	—
234	C₈×C₄₃	—	4	1	no	—
235	C₈×C₄₃	—	4	1	no	—
236	C₄₃⋊C₈	—	2	2	no	—
237	C₄₃⋊C₈	—	4	1	no	—
238	C₄₃⋊C₈	—	4	1	no	—
239	C₄₃⋊C₈	#117	1	2	yes	—
240	C₄₃⋊C₈	#117	1	2	yes	—
241	#21292	—	43	1	no	maximal, Sylow
242	C₂²×C₄₃	—	2	2	no	—
243	C₂²×C₄₃	—	4	2	no	—
244	C₂²×C₄₃	—	4	1	no	—
245	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
246	C₂²×C₄₃	#529	1	1	yes	characteristic
247	C₂²×C₄₃	#529	1	1	yes	characteristic
248	C₂×D₄₃	—	4	2	no	—
249	C₂×D₄₃	—	4	1	no	—
250	C₄×C₄₃	—	2	4	no	—
251	C₄×C₄₃	—	4	2	no	—
252	C₄×C₄₃	—	4	1	no	—
253	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
254	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
255	C₄×C₄₃	#532	1	1	yes	characteristic
256	C₄×C₄₃	#532	1	1	yes	characteristic
257	Dic₄₃	—	2	4	no	—
258	Dic₄₃	—	2	2	no	—
259	Dic₄₃	—	4	2	no	—
260	Dic₄₃	—	4	1	no	—
261	Dic₄₃	#443	1	4	yes	—
262	C₄×#135	—	43	1	no	—
263	#2922	—	43	1	no	—
264	#2922	—	43	1	no	—
265	#1974	—	43	1	no	—
266	#1974	—	43	1	no	—
267	#1945	—	43	1	no	—
268	#1945	—	43	1	no	—
269	#1937	—	43	1	no	—
270	#1937	—	43	1	no	—
271	#1937	—	43	1	no	—
272	#1937	D₄₃	1	1	yes	characteristic, complemented
273	C₄×#108	—	43	1	no	—
274	C₄×#104	—	43	1	no	—
275	C₄×#104	—	43	1	no	—
276	C₄²×C₈	—	43	1	no	—
277	C₂×C₄₃	—	2	1	no	—
278	C₂×C₄₃	—	2	1	no	—
279	C₂×C₄₃	—	8	1	no	—
280	C₂×C₄₃	#2293	1	1	yes	characteristic
281	C₂×C₄₃	C₂×#443	1	2	yes	—
282	D₄₃	—	8	1	no	—
283	C₂×#135	—	43	1	no	—
284	C₄×#41	—	43	1	no	—
285	C₄×#41	—	43	1	no	—
286	C₄×Q₁₆	—	43	2	no	—
287	C₄×SD₁₆	—	43	2	no	—
288	C₄×SD₁₆	—	43	2	no	—
289	C₄×D₈	—	43	2	no	—
290	#433	—	86	2	no	—
291	#433	—	86	2	no	—
292	#431	—	86	2	no	—
293	#431	—	86	2	no	—
294	C₂×#108	—	43	1	no	—
295	C₂×#108	—	43	1	no	—
296	#427	—	43	1	no	—
297	#424	—	43	1	no	—
298	#424	—	43	1	no	—
299	#424	—	43	1	no	—
300	#424	C₂×D₄₃	1	1	yes	characteristic
301	C₂×#104	—	43	1	no	—
302	C₂×#104	—	43	1	no	—
303	C₂×#104	—	43	1	no	—
304	C₂×#104	C₂×D₄₃	1	1	yes	characteristic
305	#416	—	43	1	no	—
306	#416	C₂×D₄₃	1	1	yes	characteristic
307	#408	—	43	1	no	—
308	#408	—	43	1	no	—
309	#408	—	43	1	no	—
310	#408	C₂×D₄₃	1	1	yes	characteristic
311	C₄×M₁₆	—	43	1	no	—
312	C₄×M₁₆	—	43	1	no	—
313	C₂×C₄×C₈	—	43	1	no	—
314	C₂×C₄×C₈	—	43	1	no	—
315	C₂×C₄×C₈	—	43	1	no	—
316	C₂×C₄×C₈	—	43	1	no	—
317	C₂×C₄×C₈	—	43	1	no	—
318	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
319	C₄³	—	43	1	no	—
320	#341	—	43	1	no	—
321	#341	C₂×D₄₃	1	1	yes	characteristic
322	#339	—	43	1	no	—
323	#339	—	43	1	no	—
324	#339	—	43	1	no	—
325	#339	C₂×D₄₃	1	1	yes	characteristic
326	C₄₃	#21292	1	1	yes	characteristic, complemented, Sylow
327	C₂×#41	—	43	1	no	—
328	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
329	#135	—	86	2	no	—
330	#135	—	86	2	no	—
331	C₂×Q₁₆	—	43	1	no	—
332	C₂×SD₁₆	—	43	1	no	—
333	C₂×SD₁₆	—	43	1	no	—
334	C₂×D₈	—	43	1	no	—
335	C₂×M₁₆	—	43	1	no	—
336	C₂×M₁₆	—	43	1	no	—
337	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
338	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
339	C₂²×C₈	—	43	1	no	—
340	C₂²×C₈	—	43	1	no	—
341	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
342	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
343	C₄×Q₈	—	43	2	no	—
344	C₄×Q₈	—	43	2	no	—
345	C₄×D₄	—	43	2	no	—
346	C₄×D₄	—	43	2	no	—
347	C₄×D₄	—	86	2	no	—
348	C₄×D₄	—	86	2	no	—
349	#117	—	43	1	no	—
350	#117	—	86	1	no	—
351	#117	—	86	1	no	—
352	#117	C₂²×D₄₃	1	1	yes	characteristic
353	C₂×C₄²	—	43	1	no	—
354	C₂×C₄²	—	43	1	no	—
355	C₂×C₄²	—	86	1	no	—
356	C₂×C₄²	—	86	1	no	—
357	C₂×C₄²	—	86	2	no	—
358	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
359	#108	—	86	2	no	—
360	#108	—	86	2	no	—
361	#107	—	43	2	no	—
362	#106	—	43	2	no	—
363	C₄⋊C₈	—	2	2	no	—
364	C₄⋊C₈	—	86	2	no	—
365	C₄⋊C₈	—	86	2	no	—
366	C₄⋊C₈	—	86	2	no	—
367	#104	—	2	2	no	—
368	#104	—	86	2	no	—
369	#104	—	86	2	no	—
370	#104	—	86	2	no	—
371	#103	—	43	2	no	—
372	#103	C₄×D₄₃	1	2	yes	—
373	#102	—	43	2	no	—
374	#102	C₄×D₄₃	1	2	yes	—
375	C₂²⋊C₈	—	2	2	no	—
376	C₂²⋊C₈	—	86	2	no	—
377	C₂²⋊C₈	—	86	2	no	—
378	C₂²⋊C₈	—	86	2	no	—
379	#97	—	86	1	no	—
380	#97	—	86	1	no	—
381	C₄×C₈	—	2	2	no	—
382	C₄×C₈	—	43	2	no	—
383	C₄×C₈	—	43	2	no	—
384	C₄×C₈	—	43	2	no	—
385	C₄×C₈	—	43	2	no	—
386	C₄×C₈	—	86	2	no	—
387	C₄×C₈	—	86	2	no	—
388	C₄×C₈	—	86	1	no	—
389	C₄×C₈	—	86	1	no	—
390	C₄×C₈	—	86	2	no	—
391	#41	—	2	1	no	—
392	#41	—	2	1	no	—
393	#41	—	2	1	no	—
394	#41	—	2	1	no	—
395	#41	—	86	1	no	—
396	#41	—	86	1	no	—
397	#41	—	86	1	no	—
398	#41	—	86	1	no	—
399	C₂×Q₈	—	43	1	no	—
400	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
401	C₂×D₄	—	2	1	no	—
402	C₂×D₄	—	43	1	no	—
403	C₂×D₄	—	86	1	no	—
404	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
405	C₂²×C₄	—	2	1	no	—
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	—	43	2	no	—
408	C₂²×C₄	—	86	2	no	—
409	C₂²×C₄	—	86	2	no	—
410	C₂²×C₄	—	86	1	no	—
411	C₂²×C₄	—	86	1	no	—
412	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
413	Q₁₆	—	86	2	no	—
414	SD₁₆	—	86	2	no	—
415	SD₁₆	—	86	2	no	—
416	D₈	—	86	2	no	—
417	M₁₆	—	2	1	no	—
418	M₁₆	—	2	1	no	—
419	M₁₆	—	2	1	no	—
420	M₁₆	—	2	1	no	—
421	M₁₆	—	86	1	no	—
422	M₁₆	—	86	1	no	—
423	M₁₆	—	86	1	no	—
424	M₁₆	—	86	1	no	—
425	C₂×C₈	—	2	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	43	1	no	—
432	C₂×C₈	—	43	1	no	—
433	C₂×C₈	—	43	2	no	—
434	C₂×C₈	—	43	2	no	—
435	C₂×C₈	—	43	2	no	—
436	C₂×C₈	—	86	1	no	—
437	C₂×C₈	—	86	1	no	—
438	C₂×C₈	—	86	1	no	—
439	C₂×C₈	—	86	1	no	—
440	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
441	C₂×C₈	D₄×D₄₃	1	2	yes	—
442	C₄⋊C₄	—	43	2	no	—
443	C₄⋊C₄	—	86	2	no	—
444	C₄⋊C₄	—	86	2	no	—
445	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
446	C₂²⋊C₄	—	2	1	no	—
447	C₂²⋊C₄	—	86	2	no	—
448	C₂²⋊C₄	—	86	2	no	—
449	C₂²⋊C₄	—	86	1	no	—
450	C₄²	—	2	1	no	—
451	C₄²	—	2	1	no	—
452	C₄²	—	43	2	no	—
453	C₄²	—	43	1	no	—
454	C₄²	—	43	1	no	—
455	C₄²	—	43	2	no	—
456	C₄²	—	86	2	no	—
457	C₄²	—	86	2	no	—
458	C₄²	—	86	8	no	—
459	C₄²	—	86	1	no	—
460	C₄²	—	86	1	no	—
461	C₄²	#10621900	1	2	yes	—
462	C₂³	—	2	1	no	—
463	C₂³	—	86	1	no	—
464	C₂³	#41×D₄₃	1	1	yes	characteristic
465	Q₈	—	2	1	no	—
466	Q₈	—	2	1	no	—
467	Q₈	—	86	1	no	—
468	Q₈	—	86	1	no	—
469	D₄	—	2	1	no	—
470	D₄	—	2	1	no	—
471	D₄	—	4	1	no	—
472	D₄	—	4	1	no	—
473	D₄	—	86	1	no	—
474	D₄	—	86	1	no	—
475	D₄	—	172	1	no	—
476	D₄	—	172	1	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	43	2	no	—
484	C₂×C₄	—	43	2	no	—
485	C₂×C₄	—	86	4	no	—
486	C₂×C₄	—	86	4	no	—
487	C₂×C₄	—	86	2	no	—
488	C₂×C₄	—	86	2	no	—
489	C₂×C₄	—	86	1	no	—
490	C₂×C₄	—	172	4	no	—
491	C₂×C₄	—	172	4	no	—
492	C₂×C₄	—	172	1	no	—
493	C₂×C₄	—	172	1	no	—
494	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
495	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
496	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
497	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
498	C₂×C₄	#41×D₄₃	1	1	yes	characteristic
499	C₂×C₄	C₂×#10621900	1	1	yes	characteristic
500	C₈	—	2	2	no	—
501	C₈	—	2	2	no	—
502	C₈	—	4	1	no	—
503	C₈	—	4	1	no	—
504	C₈	—	43	2	no	—
505	C₈	—	43	2	no	—
506	C₈	—	86	2	no	—
507	C₈	—	172	1	no	—
508	C₈	—	172	1	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	172	1	no	—
513	C₂²	—	172	2	no	—
514	C₂²	C₄×D₄×D₄₃	1	1	yes	characteristic
515	C₂²	#14583426	1	1	yes	characteristic
516	C₂²	#14583432	1	1	yes	characteristic
517	C₄	—	2	4	no	—
518	C₄	—	4	1	no	—
519	C₄	—	4	2	no	—
520	C₄	—	43	4	no	—
521	C₄	—	86	4	no	—
522	C₄	—	86	2	no	—
523	C₄	—	172	1	no	—
524	C₄	—	172	2	no	—
525	C₄	#117×D₄₃	1	1	yes	characteristic
526	C₄	C₄×#10621900	1	1	yes	characteristic
527	C₄	#14583444	1	1	yes	characteristic
528	C₄	#14583448	1	1	yes	characteristic
529	C₂	—	2	1	no	—
530	C₂	—	2	1	no	—
531	C₂	—	8	1	no	—
532	C₂	—	344	1	no	—
533	C₂	#19137055	1	1	yes	characteristic
534	C₂	#443×D₄₃	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1937	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#13063345	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1937	D₄₃
hypocenter	C₄₃	#21292
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ #1937

Complements

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

N	H ≅ G/N	type
2. #19143238	C₂	semidirect
3. #19143235	C₂	semidirect
6. #19135342	C₂	semidirect
7. #19135340	C₂	semidirect
8. #19135301	C₂	semidirect
9. #19135299	C₂	semidirect
10. #19135297	C₂	semidirect
11. #19134496	C₂	semidirect
12. #104×Dic₄₃	C₂	semidirect
13. #19134399	C₂	semidirect
14. C₄×C₈×Dic₄₃	C₂	semidirect
15. C₄₃×#1937	C₂	semidirect
19. #14582991	C₄	semidirect
20. #14582990	C₄	semidirect
21. #14582984	C₄	semidirect
22. #14582979	C₄	semidirect
272. #1937	D₄₃	semidirect
326. C₄₃	#21292	semidirect

Maximal subgroups

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

subgroup	index
#19143363	2
#19143238	2
#19143235	2
#19135482	2
#19135480	2
#19135342	2
#19135340	2
#19135301	2
#19135299	2
#19135297	2
#19134496	2
#104×Dic₄₃	2
#19134399	2
C₄×C₈×Dic₄₃	2
C₄₃×#1937	2
#21292	43