Subgroups — #25114195

Order 11008.

692 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19143255	C₂	1	1	yes	maximal, characteristic
2	#19143253	C₂	1	1	yes	maximal, characteristic
3	C₂×#14582935	C₂	1	1	yes	maximal, characteristic
4	#19135347	C₂	1	2	yes	maximal, complemented
5	#19135197	C₂	1	2	yes	maximal, complemented
6	#19135192	C₂	1	2	yes	maximal, complemented
7	#19134695	C₂	1	1	yes	maximal, characteristic
8	#19134631	C₂	1	1	yes	maximal, characteristic
9	#19134478	C₂	1	2	yes	maximal, complemented
10	#19134373	C₂	1	1	yes	maximal, characteristic
11	C₄₃×#1826	C₂	1	1	yes	maximal, characteristic
12	C₂³×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
13	C₂×#13063284	C₂²	1	1	yes	characteristic
14	#14582960	—	2	2	no	—
15	#14582957	—	2	2	no	—
16	#14582956	—	2	1	no	—
17	#14582953	—	2	1	no	—
18	#14582952	—	2	1	no	—
19	#14582949	—	2	1	no	—
20	C₂×#13063260	C₂²	1	2	yes	—
21	#14582935	C₄	1	1	yes	characteristic, complemented
22	#14582935	C₄	1	1	yes	characteristic, complemented
23	#14582935	C₄	1	1	yes	characteristic, complemented
24	#14582935	C₄	1	1	yes	characteristic, complemented
25	#14582935	C₂²	1	1	yes	characteristic
26	#14582935	C₂²	1	1	yes	characteristic
27	#14582935	C₂²	1	1	yes	characteristic
28	#14582935	C₂²	1	1	yes	characteristic
29	C₂×#13063258	C₄	1	1	yes	characteristic, complemented
30	C₂×#13063258	C₄	1	1	yes	characteristic, complemented
31	C₂×#13063256	C₄	1	1	yes	characteristic, complemented
32	C₂×#13063256	C₄	1	1	yes	characteristic, complemented
33	#14582927	C₂²	1	2	yes	—
34	#14582926	C₂²	1	2	yes	—
35	#14582863	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
37	#14582857	C₂²	1	2	yes	—
38	#14582855	C₂²	1	2	yes	—
39	C₂×#13063236	C₂²	1	2	yes	—
40	#14582663	C₂²	1	2	yes	—
41	#14582659	C₂²	1	2	yes	—
42	#14582659	C₂²	1	2	yes	—
43	#14582654	C₂²	1	2	yes	—
44	C₂×#117×C₄₃	C₂²	1	1	yes	characteristic
45	C₄₃×#407	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
47	C₄₃×#339	C₂²	1	2	yes	—
48	C₄₃×#339	C₂²	1	2	yes	—
49	C₂×#10621877	C₂³	1	2	yes	—
50	C₂²×C₄₃⋊C₈	—	2	4	no	—
51	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
53	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
54	C₂²×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
57	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
58	#13063284	—	2	1	no	—
59	#13063284	—	2	1	no	—
60	#13063284	C₂×C₄	1	1	yes	characteristic
61	#13063284	C₂×C₄	1	1	yes	characteristic
62	#13063284	C₂³	1	1	yes	characteristic
63	#13063284	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
66	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
67	C₂×C₄×Dic₄₃	—	2	1	no	—
68	#13063260	—	2	4	no	—
69	#13063258	C₂×C₄	1	1	yes	characteristic
70	#13063258	C₂×C₄	1	1	yes	characteristic
71	#13063258	C₂×C₄	1	1	yes	characteristic
72	#13063258	C₂×C₄	1	1	yes	characteristic
73	#13063258	C₂×C₄	1	1	yes	characteristic
74	#13063258	C₂×C₄	1	1	yes	characteristic
75	#13063258	C₂×C₄	1	1	yes	characteristic
76	#13063258	C₂×C₄	1	1	yes	characteristic
77	#13063256	C₂×C₄	1	1	yes	characteristic
78	#13063256	C₂×C₄	1	1	yes	characteristic
79	#13063256	C₂×C₄	1	1	yes	characteristic
80	#13063256	C₂×C₄	1	1	yes	characteristic
81	#13063256	C₂×C₄	1	1	yes	characteristic
82	#13063256	C₂×C₄	1	1	yes	characteristic
83	#13063256	C₂×C₄	1	1	yes	characteristic
84	#13063256	C₂×C₄	1	1	yes	characteristic
85	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
86	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
87	Dic₄₃⋊C₈	—	2	2	no	—
88	Dic₄₃⋊C₈	—	2	2	no	—
89	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
90	C₂²⋊(C₄₃⋊C₈)	—	2	1	no	—
91	C₂²⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
92	C₂²⋊(C₄₃⋊C₈)	D₄	1	1	yes	characteristic
93	C₂²⋊(C₄₃⋊C₈)	D₄	1	2	yes	—
94	#13063236	—	2	2	no	—
95	#13063236	—	2	4	no	—
96	#13063235	—	2	2	no	—
97	C₄×C₄₃⋊C₈	—	2	2	no	—
98	C₈×Dic₄₃	—	2	2	no	—
99	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
100	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
101	#117×C₄₃	—	2	1	no	—
102	#117×C₄₃	—	2	1	no	—
103	#117×C₄₃	C₂×C₄	1	1	yes	characteristic
104	#117×C₄₃	C₂×C₄	1	1	yes	characteristic
105	#117×C₄₃	C₂³	1	1	yes	characteristic
106	#117×C₄₃	C₂³	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	1	yes	characteristic
109	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
110	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
111	C₂×C₄²×C₄₃	—	2	1	no	—
112	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
113	C₂²⋊C₈×C₄₃	—	2	1	no	—
114	C₂²⋊C₈×C₄₃	—	2	1	no	—
115	#95×C₄₃	—	2	1	no	—
116	C₂⁴×C₄₃	#41	1	1	yes	characteristic
117	C₂²×C₄×C₄₃	—	2	2	no	—
118	C₂²×C₄×C₄₃	—	2	2	no	—
119	C₂²×C₄×C₄₃	—	2	1	no	—
120	C₂²×C₄×C₄₃	—	2	1	no	—
121	C₂²×C₄×C₄₃	—	2	2	no	—
122	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
127	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
128	C₂²×Dic₄₃	—	2	1	no	—
129	C₂²×Dic₄₃	—	2	1	no	—
130	M₁₆×C₄₃	—	2	2	no	—
131	M₁₆×C₄₃	—	2	2	no	—
132	C₂×C₈×C₄₃	—	2	2	no	—
133	C₄⋊C₄×C₄₃	—	2	1	no	—
134	C₄⋊C₄×C₄₃	—	2	1	no	—
135	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
136	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
137	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
138	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
139	C₂²⋊C₄×C₄₃	—	2	1	no	—
140	C₂²⋊C₄×C₄₃	—	2	1	no	—
141	C₂²⋊C₄×C₄₃	—	2	1	no	—
142	C₂²⋊C₄×C₄₃	—	2	1	no	—
143	C₂²⋊C₄×C₄₃	—	4	2	no	—
144	C₄²×C₄₃	—	2	1	no	—
145	C₄²×C₄₃	—	2	1	no	—
146	C₄²×C₄₃	—	2	1	no	—
147	C₄²×C₄₃	—	2	1	no	—
148	C₄²×C₄₃	—	2	2	no	—
149	C₄²×C₄₃	—	2	2	no	—
150	C₂²⋊Dic₄₃	—	2	1	no	—
151	C₂²⋊Dic₄₃	—	2	1	no	—
152	C₂²⋊Dic₄₃	—	2	1	no	—
153	C₂²⋊Dic₄₃	—	2	1	no	—
154	C₄⋊Dic₄₃	—	2	1	no	—
155	C₄⋊Dic₄₃	—	2	1	no	—
156	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
157	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
158	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
159	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
160	C₄×Dic₄₃	—	2	1	no	—
161	C₄×Dic₄₃	—	2	1	no	—
162	C₄×Dic₄₃	—	2	1	no	—
163	C₄×Dic₄₃	—	2	1	no	—
164	#10621877	—	2	2	no	—
165	#10621877	—	2	2	no	—
166	C₂×C₄₃⋊C₈	—	2	2	no	—
167	C₂×C₄₃⋊C₈	—	2	2	no	—
168	C₂×C₄₃⋊C₈	—	2	2	no	—
169	C₂×C₄₃⋊C₈	—	2	2	no	—
170	C₂×C₄₃⋊C₈	—	2	2	no	—
171	C₂×C₄₃⋊C₈	—	2	2	no	—
172	C₂×C₄₃⋊C₈	—	2	2	no	—
173	C₂×C₄₃⋊C₈	—	2	2	no	—
174	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
175	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
179	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
180	C₂×C₄₃⋊C₈	#41	1	4	yes	—
181	C₂³×C₄₃	—	2	2	no	—
182	C₂³×C₄₃	—	2	2	no	—
183	C₂³×C₄₃	—	4	1	no	—
184	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
185	C₂³×C₄₃	C₄×D₄	1	1	yes	characteristic
186	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₄₃	—	2	2	no	—
188	C₂×C₄×C₄₃	—	2	1	no	—
189	C₂×C₄×C₄₃	—	2	1	no	—
190	C₂×C₄×C₄₃	—	2	1	no	—
191	C₂×C₄×C₄₃	—	2	1	no	—
192	C₂×C₄×C₄₃	—	2	2	no	—
193	C₂×C₄×C₄₃	—	2	2	no	—
194	C₂×C₄×C₄₃	—	2	1	no	—
195	C₂×C₄×C₄₃	—	2	1	no	—
196	C₂×C₄×C₄₃	—	2	1	no	—
197	C₂×C₄×C₄₃	—	2	1	no	—
198	C₂×C₄×C₄₃	—	4	2	no	—
199	C₂×C₄×C₄₃	—	4	2	no	—
200	C₂×C₄×C₄₃	—	4	2	no	—
201	C₂×C₄×C₄₃	—	4	2	no	—
202	C₂×C₄×C₄₃	—	8	1	no	—
203	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
204	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
205	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
208	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
209	C₂×Dic₄₃	—	2	1	no	—
210	C₂×Dic₄₃	—	2	1	no	—
211	C₂×Dic₄₃	—	2	1	no	—
212	C₂×Dic₄₃	—	2	1	no	—
213	C₂×Dic₄₃	—	4	2	no	—
214	C₂×Dic₄₃	—	8	1	no	—
215	C₈×C₄₃	—	4	2	no	—
216	C₄₃⋊C₈	—	2	1	no	—
217	C₄₃⋊C₈	—	2	1	no	—
218	C₄₃⋊C₈	—	2	2	no	—
219	C₄₃⋊C₈	—	2	2	no	—
220	C₄₃⋊C₈	—	4	2	no	—
221	C₄₃⋊C₈	#117	1	2	yes	—
222	C₄₃⋊C₈	#117	1	2	yes	—
223	#22607	—	43	1	no	maximal, Sylow
224	C₂²×C₄₃	—	2	1	no	—
225	C₂²×C₄₃	—	2	1	no	—
226	C₂²×C₄₃	—	2	1	no	—
227	C₂²×C₄₃	—	2	1	no	—
228	C₂²×C₄₃	—	2	1	no	—
229	C₂²×C₄₃	—	2	1	no	—
230	C₂²×C₄₃	—	2	1	no	—
231	C₂²×C₄₃	—	4	4	no	—
232	C₂²×C₄₃	#444	1	2	yes	—
233	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
234	C₂²×C₄₃	#552	1	2	yes	—
235	C₄×C₄₃	—	2	1	no	—
236	C₄×C₄₃	—	2	1	no	—
237	C₄×C₄₃	—	4	1	no	—
238	C₄×C₄₃	—	4	1	no	—
239	C₄×C₄₃	—	4	1	no	—
240	C₄×C₄₃	—	4	1	no	—
241	C₄×C₄₃	—	8	2	no	—
242	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
243	C₄×C₄₃	#519	1	1	yes	characteristic
244	C₄×C₄₃	#547	1	2	yes	—
245	Dic₄₃	—	4	1	no	—
246	Dic₄₃	—	4	1	no	—
247	Dic₄₃	—	4	1	no	—
248	Dic₄₃	—	4	1	no	—
249	#2924	—	43	1	no	—
250	#2924	—	43	1	no	—
251	C₂×#427	—	43	1	no	—
252	#1946	—	43	2	no	—
253	#1922	—	43	2	no	—
254	#1922	—	43	2	no	—
255	#1826	—	43	1	no	—
256	#1826	D₄₃	1	1	yes	characteristic
257	#1810	—	43	1	no	—
258	#1773	—	43	2	no	—
259	#1752	—	43	1	no	—
260	C₂×C₄₃	—	2	2	no	—
261	C₂×C₄₃	—	2	2	no	—
262	C₂×C₄₃	—	4	1	no	—
263	C₂×C₄₃	#2344	1	1	yes	characteristic
264	C₂×C₄₃	C₂×#444	1	1	yes	characteristic
265	C₂×C₄₃	#2957	1	1	yes	characteristic
266	C₂³×C₈	—	43	1	no	—
267	C₂×#117	—	43	1	no	—
268	C₂×#117	C₂×D₄₃	1	1	yes	characteristic
269	#433	—	86	2	no	—
270	#433	—	86	2	no	—
271	#432	—	86	1	no	—
272	#432	—	86	1	no	—
273	#431	—	86	1	no	—
274	#431	—	86	1	no	—
275	C₂×#108	—	43	2	no	—
276	#427	—	43	1	no	—
277	#427	—	43	1	no	—
278	#427	—	43	1	no	—
279	#427	—	43	1	no	—
280	#427	—	43	1	no	—
281	#427	—	43	1	no	—
282	#427	—	43	1	no	—
283	#427	—	43	1	no	—
284	C₂×#107	—	43	1	no	—
285	C₂×#107	—	43	1	no	—
286	C₂×#106	—	43	1	no	—
287	C₂×#106	—	43	1	no	—
288	#424	—	43	2	no	—
289	#424	—	43	2	no	—
290	#407	—	43	1	no	—
291	#407	C₂×D₄₃	1	1	yes	characteristic
292	C₂×C₂²⋊C₈	—	43	1	no	—
293	#405	—	43	2	no	—
294	#405	—	43	2	no	—
295	C₂×#97	—	43	2	no	—
296	C₄×C₂²⋊C₄	C₂×D₄₃	1	1	yes	characteristic
297	#341	—	43	2	no	—
298	#339	—	43	2	no	—
299	#339	—	43	2	no	—
300	#339	C₂×D₄₃	1	2	yes	—
301	#339	C₂×D₄₃	1	2	yes	—
302	#336	—	43	2	no	—
303	C₄₃	#22607	1	1	yes	characteristic, complemented, Sylow
304	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
305	C₂×M₁₆	—	43	2	no	—
306	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
307	C₂²×C₈	—	43	1	no	—
308	C₂²×C₈	—	43	1	no	—
309	C₂²×C₈	—	43	1	no	—
310	C₂²×C₈	—	43	1	no	—
311	C₂²×C₈	—	43	1	no	—
312	C₂²×C₈	—	43	1	no	—
313	C₂²×C₈	—	43	2	no	—
314	C₂²×C₈	—	86	4	no	—
315	#117	—	2	1	no	—
316	#117	—	2	1	no	—
317	#117	—	43	1	no	—
318	#117	—	43	1	no	—
319	#117	—	43	1	no	—
320	#117	—	43	1	no	—
321	#117	—	86	1	no	—
322	#117	—	86	1	no	—
323	#117	C₄×D₄₃	1	1	yes	characteristic
324	#117	C₄×D₄₃	1	1	yes	characteristic
325	#117	C₂²×D₄₃	1	1	yes	characteristic
326	#117	C₂²×D₄₃	1	1	yes	characteristic
327	C₂×C₄⋊C₄	—	43	1	no	—
328	C₂×C₄⋊C₄	—	43	1	no	—
329	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₄×D₄₃	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	—	2	1	no	—
332	C₂×C₂²⋊C₄	—	2	1	no	—
333	C₂×C₂²⋊C₄	—	86	1	no	—
334	C₂×C₄²	—	2	1	no	—
335	C₂×C₄²	—	86	1	no	—
336	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
337	#108	—	86	4	no	—
338	#107	—	43	1	no	—
339	#107	—	43	1	no	—
340	#107	—	43	1	no	—
341	#107	—	43	1	no	—
342	#107	—	43	1	no	—
343	#107	—	43	1	no	—
344	#107	—	43	1	no	—
345	#107	—	43	1	no	—
346	#106	—	43	1	no	—
347	#106	—	43	1	no	—
348	#106	—	43	1	no	—
349	#106	—	43	1	no	—
350	#106	—	43	1	no	—
351	#106	—	43	1	no	—
352	#106	—	43	1	no	—
353	#106	—	43	1	no	—
354	C₄⋊C₈	—	86	2	no	—
355	C₄⋊C₈	—	86	2	no	—
356	C₄⋊C₈	—	86	2	no	—
357	C₄⋊C₈	—	86	2	no	—
358	C₂²⋊C₈	—	2	1	no	—
359	C₂²⋊C₈	—	2	1	no	—
360	C₂²⋊C₈	—	43	1	no	—
361	C₂²⋊C₈	—	43	1	no	—
362	C₂²⋊C₈	—	43	2	no	—
363	C₂²⋊C₈	—	86	1	no	—
364	C₂²⋊C₈	—	86	1	no	—
365	#97	—	86	4	no	—
366	#97	—	86	2	no	—
367	#97	—	86	2	no	—
368	C₄×C₈	—	86	2	no	—
369	C₄×C₈	—	86	2	no	—
370	#95	—	2	1	no	—
371	C₂⁴	#10621900	1	1	yes	characteristic
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	86	1	no	—
378	C₂²×C₄	—	86	1	no	—
379	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
380	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
381	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
382	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
383	C₂²×C₄	#10621900	1	1	yes	characteristic
384	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
385	M₁₆	—	2	2	no	—
386	M₁₆	—	2	2	no	—
387	M₁₆	—	86	2	no	—
388	M₁₆	—	86	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	43	1	no	—
391	C₂×C₈	—	43	1	no	—
392	C₂×C₈	—	43	4	no	—
393	C₂×C₈	—	43	1	no	—
394	C₂×C₈	—	43	1	no	—
395	C₂×C₈	—	43	2	no	—
396	C₂×C₈	—	43	2	no	—
397	C₂×C₈	—	86	2	no	—
398	C₂×C₈	—	86	2	no	—
399	C₂×C₈	—	86	2	no	—
400	C₂×C₈	—	86	2	no	—
401	C₂×C₈	—	86	2	no	—
402	C₂×C₈	—	86	2	no	—
403	C₂×C₈	—	86	2	no	—
404	C₂×C₈	—	86	2	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	43	1	no	—
408	C₄⋊C₄	—	43	1	no	—
409	C₄⋊C₄	—	43	1	no	—
410	C₄⋊C₄	—	43	1	no	—
411	C₄⋊C₄	—	86	1	no	—
412	C₄⋊C₄	—	86	1	no	—
413	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
414	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
415	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
416	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
417	C₂²⋊C₄	—	2	1	no	—
418	C₂²⋊C₄	—	2	1	no	—
419	C₂²⋊C₄	—	2	1	no	—
420	C₂²⋊C₄	—	2	1	no	—
421	C₂²⋊C₄	—	4	2	no	—
422	C₂²⋊C₄	—	86	1	no	—
423	C₂²⋊C₄	—	86	1	no	—
424	C₂²⋊C₄	—	86	1	no	—
425	C₂²⋊C₄	—	86	1	no	—
426	C₄²	—	2	1	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	2	1	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	86	1	no	—
433	C₄²	—	86	1	no	—
434	C₄²	—	86	1	no	—
435	C₄²	—	86	1	no	—
436	C₂³	—	2	2	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	4	1	no	—
439	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
440	C₂³	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
441	C₂³	C₂×#10621900	1	1	yes	characteristic
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	2	1	no	—
446	C₂×C₄	—	2	1	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	8	1	no	—
458	C₂×C₄	—	86	1	no	—
459	C₂×C₄	—	86	1	no	—
460	C₂×C₄	—	86	1	no	—
461	C₂×C₄	—	86	1	no	—
462	C₂×C₄	—	344	1	no	—
463	C₂×C₄	—	172	2	no	—
464	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
465	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
466	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
467	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
468	C₂×C₄	#41×D₄₃	1	2	yes	—
469	C₂×C₄	#13063372	1	2	yes	—
470	C₈	—	4	2	no	—
471	C₈	—	43	2	no	—
472	C₈	—	43	2	no	—
473	C₈	—	86	1	no	—
474	C₈	—	86	1	no	—
475	C₈	—	86	2	no	—
476	C₈	—	86	2	no	—
477	C₈	—	172	2	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	4	4	no	—
486	C₂²	#14583018	1	2	yes	—
487	C₂²	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
488	C₂²	#14583586	1	2	yes	—
489	C₄	—	2	1	no	—
490	C₄	—	2	1	no	—
491	C₄	—	4	1	no	—
492	C₄	—	4	1	no	—
493	C₄	—	4	1	no	—
494	C₄	—	4	1	no	—
495	C₄	—	8	2	no	—
496	C₄	—	172	1	no	—
497	C₄	—	172	1	no	—
498	C₄	—	172	1	no	—
499	C₄	—	172	1	no	—
500	C₄	#117×D₄₃	1	1	yes	characteristic
501	C₄	#14583376	1	1	yes	characteristic
502	C₄	#14583547	1	2	yes	—
503	C₂	—	2	2	no	—
504	C₂	—	2	2	no	—
505	C₂	—	4	1	no	—
506	C₂	#19137459	1	1	yes	characteristic
507	C₂	C₂×#14583018	1	1	yes	characteristic
508	C₂	#19143508	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄₃×#1826	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂⁴×C₄₃	#41
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1826	D₄₃
hypocenter	C₄₃	#22607
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ #1826

Complements

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

N	H ≅ G/N	type
4. #19135347	C₂	semidirect
5. #19135197	C₂	semidirect
6. #19135192	C₂	semidirect
9. #19134478	C₂	semidirect
21. #14582935	C₄	semidirect
22. #14582935	C₄	semidirect
23. #14582935	C₄	semidirect
24. #14582935	C₄	semidirect
29. C₂×#13063258	C₄	semidirect
30. C₂×#13063258	C₄	semidirect
31. C₂×#13063256	C₄	semidirect
32. C₂×#13063256	C₄	semidirect
303. C₄₃	#22607	semidirect

Maximal subgroups

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

subgroup	index
#19143255	2
#19143253	2
C₂×#14582935	2
#19135347	2
#19135197	2
#19135192	2
#19134695	2
#19134631	2
#19134478	2
#19134373	2
C₄₃×#1826	2
#22607	43