Subgroups — #25099824

Order 11008.

800 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13063345	C₂	1	1	yes	maximal, characteristic
2	#19143239	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×#13063333	C₂	1	1	yes	maximal, characteristic, complemented
4	#19135246	C₂	1	2	yes	maximal, complemented
5	#19135197	C₂	1	2	yes	maximal, complemented
6	#19134919	C₂	1	2	yes	maximal
7	#19134871	C₂	1	2	yes	maximal, complemented
8	C₄×#13063260	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#13063253	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134341	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#104×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13063345	C₂²	1	1	yes	characteristic
13	C₂×#13063333	C₂²	1	2	yes	—
14	C₄×#10621898	C₂²	1	1	yes	characteristic
15	C₄×#10621885	C₄	1	1	yes	characteristic, complemented
16	C₄×#10621885	C₄	1	1	yes	characteristic, complemented
17	C₄×#10621884	C₄	1	1	yes	characteristic, complemented
18	C₄×#10621884	C₄	1	1	yes	characteristic, complemented
19	C₄×#10621883	C₄	1	1	yes	characteristic, complemented
20	C₄×#10621883	C₄	1	1	yes	characteristic, complemented
21	C₄×#10621882	C₄	1	1	yes	characteristic, complemented
22	C₄×#10621882	C₄	1	1	yes	characteristic, complemented
23	#14582960	—	2	2	no	—
24	#14582952	—	2	1	no	—
25	#14582952	—	2	1	no	—
26	C₂×#13063260	C₂²	1	2	yes	—
27	#14582935	C₂²	1	1	yes	characteristic
28	#14582926	C₂²	1	2	yes	—
29	C₂×#13063253	C₂²	1	2	yes	—
30	#14582895	C₂²	1	1	yes	characteristic
31	#14582893	C₂²	1	1	yes	characteristic
32	#14582866	C₂²	1	2	yes	—
33	#14582857	C₂²	1	2	yes	—
34	#14582856	—	2	2	no	—
35	C₄×#10621877	C₂²	1	1	yes	characteristic
36	C₄×#10621872	—	2	1	no	—
37	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
39	C₄×C₈×D₄₃	—	2	1	no	—
40	#14582663	C₂²	1	2	yes	—
41	#14582659	C₂²	1	2	yes	—
42	#14582654	C₂²	1	2	yes	—
43	#14582654	C₂²	1	2	yes	—
44	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
45	C₂×#104×C₄₃	C₂²	1	2	yes	—
46	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
47	C₄³×C₄₃	C₂²	1	1	yes	characteristic
48	C₄₃×#339	C₂²	1	2	yes	—
49	C₂×#10621898	C₂³	1	1	yes	characteristic
50	#13063345	—	2	4	no	—
51	C₂×#10621885	C₂×C₄	1	1	yes	characteristic
52	C₂×#10621883	C₂×C₄	1	1	yes	characteristic
53	C₂×#10621884	C₂×C₄	1	1	yes	characteristic
54	C₂×#10621882	C₂×C₄	1	1	yes	characteristic
55	#13063333	—	2	4	no	—
56	#13063333	—	2	4	no	—
57	C₂×#10621877	C₂³	1	2	yes	—
58	C₂×#10621872	—	2	2	no	—
59	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
60	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
62	C₂×C₈×D₄₃	—	2	2	no	—
63	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
64	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
65	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
66	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
67	C₄×C₂²⋊D₄₃	—	2	1	no	—
68	C₄×C₂²⋊D₄₃	—	2	1	no	—
69	#13063284	C₂³	1	1	yes	characteristic
70	#13063282	—	2	1	no	—
71	C₄²×D₄₃	—	2	1	no	—
72	#13063260	—	2	4	no	—
73	#13063258	C₂×C₄	1	1	yes	characteristic
74	#13063258	C₂×C₄	1	1	yes	characteristic
75	#13063256	C₂×C₄	1	1	yes	characteristic
76	#13063256	C₂×C₄	1	1	yes	characteristic
77	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
78	C₄⋊(C₄₃⋊C₈)	—	2	2	no	—
79	#13063253	—	2	4	no	—
80	#13063249	C₂×C₄	1	1	yes	characteristic
81	#13063249	C₂×C₄	1	1	yes	characteristic
82	#13063248	C₂×C₄	1	1	yes	characteristic
83	#13063248	C₂×C₄	1	1	yes	characteristic
84	#13063246	C₂×C₄	1	1	yes	characteristic
85	#13063246	C₂×C₄	1	1	yes	characteristic
86	#13063245	C₂×C₄	1	1	yes	characteristic
87	#13063245	C₂×C₄	1	1	yes	characteristic
88	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
89	C₂²⋊(C₄₃⋊C₈)	—	2	2	no	—
90	#13063236	—	2	1	no	—
91	#13063235	—	2	2	no	—
92	C₄×C₄₃⋊C₈	—	2	1	no	—
93	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
94	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
95	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
96	C₄×C₄₃⋊C₈	C₂×C₄	1	1	yes	characteristic
97	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
98	C₄×C₄₃⋊C₈	D₄	1	1	yes	characteristic
99	C₄×C₄₃⋊C₈	D₄	1	2	yes	—
100	C₈×Dic₄₃	—	2	2	no	—
101	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
102	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
103	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
104	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
105	C₄×D₄×C₄₃	—	2	1	no	—
106	C₄×D₄×C₄₃	—	2	1	no	—
107	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
108	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
109	#117×C₄₃	—	2	1	no	—
110	#117×C₄₃	C₂³	1	1	yes	characteristic
111	C₂×C₄²×C₄₃	—	2	1	no	—
112	C₂×C₄²×C₄₃	—	2	1	no	—
113	C₂×C₄²×C₄₃	—	2	1	no	—
114	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
115	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
116	#104×C₄₃	—	2	4	no	—
117	#97×C₄₃	—	2	1	no	—
118	C₄×C₈×C₄₃	—	2	1	no	—
119	#41×C₄₃	—	2	2	no	—
120	#41×C₄₃	—	2	2	no	—
121	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
122	C₂×D₄×C₄₃	—	2	1	no	—
123	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₃	—	2	1	no	—
125	C₂²×C₄×C₄₃	—	2	1	no	—
126	C₂²×C₄×C₄₃	—	2	1	no	—
127	C₂²×C₄×C₄₃	—	2	2	no	—
128	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
129	C₂²×C₄×C₄₃	#41	1	1	yes	characteristic
130	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
131	C₂×C₂²⋊D₄₃	—	2	1	no	—
132	#10621898	—	2	2	no	—
133	#10621898	#41	1	4	yes	—
134	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₄×D₄₃	—	2	1	no	—
136	C₂×C₄×D₄₃	—	2	1	no	—
137	C₂×C₄×D₄₃	—	2	1	no	—
138	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
139	M₁₆×C₄₃	—	2	2	no	—
140	M₁₆×C₄₃	#41	1	4	yes	—
141	C₂×C₈×C₄₃	—	2	2	no	—
142	C₄⋊C₄×C₄₃	—	2	1	no	—
143	C₄⋊C₄×C₄₃	—	2	1	no	—
144	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
145	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
146	C₂²⋊C₄×C₄₃	—	2	1	no	—
147	C₂²⋊C₄×C₄₃	—	2	1	no	—
148	C₂²⋊C₄×C₄₃	—	2	1	no	—
149	C₄²×C₄₃	—	2	4	no	—
150	C₄²×C₄₃	—	2	1	no	—
151	C₄²×C₄₃	—	2	1	no	—
152	C₄²×C₄₃	—	2	1	no	—
153	C₄²×C₄₃	—	2	2	no	—
154	C₄²×C₄₃	—	2	2	no	—
155	C₄²×C₄₃	—	4	2	no	—
156	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
157	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
158	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
159	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
160	C₂²⋊Dic₄₃	—	2	1	no	—
161	#10621885	—	2	2	no	—
162	#10621884	—	2	2	no	—
163	#10621883	—	2	2	no	—
164	#10621882	—	2	2	no	—
165	(C₂×D₄₃)⋊C₄	—	2	1	no	—
166	(C₂×D₄₃)⋊C₄	—	2	1	no	—
167	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
168	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
169	Dic₄₃⋊C₄	—	2	1	no	—
170	Dic₄₃⋊C₄	—	2	1	no	—
171	C₄×Dic₄₃	—	2	1	no	—
172	C₄×Dic₄₃	—	2	1	no	—
173	C₄×Dic₄₃	—	2	1	no	—
174	#10621877	—	2	2	no	—
175	#10621877	—	2	2	no	—
176	C₂×C₄₃⋊C₈	—	2	2	no	—
177	C₂×C₄₃⋊C₈	—	2	2	no	—
178	C₂×C₄₃⋊C₈	—	2	2	no	—
179	C₂×C₄₃⋊C₈	—	2	2	no	—
180	C₂×C₄₃⋊C₈	—	2	2	no	—
181	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
182	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
183	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
184	C₂×C₄₃⋊C₈	C₂²×C₄	1	1	yes	characteristic
185	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
186	C₂×C₄₃⋊C₈	C₂×D₄	1	2	yes	—
187	#10621872	—	2	8	no	—
188	C₈×D₄₃	—	2	8	no	—
189	C₂³×C₄₃	—	2	1	no	—
190	C₂³×C₄₃	C₂×#41	1	1	yes	characteristic
191	C₂²×D₄₃	—	2	1	no	—
192	Q₈×C₄₃	—	2	1	no	—
193	Q₈×C₄₃	—	2	1	no	—
194	D₄×C₄₃	—	2	1	no	—
195	D₄×C₄₃	—	2	1	no	—
196	D₄×C₄₃	—	4	2	no	—
197	C₂×C₄×C₄₃	—	2	2	no	—
198	C₂×C₄×C₄₃	—	2	2	no	—
199	C₂×C₄×C₄₃	—	2	4	no	—
200	C₂×C₄×C₄₃	—	2	1	no	—
201	C₂×C₄×C₄₃	—	2	1	no	—
202	C₂×C₄×C₄₃	—	2	1	no	—
203	C₂×C₄×C₄₃	—	4	2	no	—
204	C₂×C₄×C₄₃	—	4	2	no	—
205	C₂×C₄×C₄₃	—	4	2	no	—
206	C₂×C₄×C₄₃	—	4	2	no	—
207	C₂×C₄×C₄₃	—	4	2	no	—
208	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
209	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
210	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₃	C₄×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
213	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
215	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
216	C₂²⋊D₄₃	—	2	4	no	—
217	C₂×Dic₄₃	—	2	1	no	—
218	C₂×Dic₄₃	—	2	1	no	—
219	C₂×Dic₄₃	—	2	1	no	—
220	D₁₇₂	—	2	1	no	—
221	D₁₇₂	#117	1	2	yes	—
222	C₄×D₄₃	—	2	4	no	—
223	C₄×D₄₃	—	4	2	no	—
224	C₄×D₄₃	—	4	2	no	—
225	Dic₈₆	—	2	1	no	—
226	Dic₈₆	#117	1	2	yes	—
227	C₈×C₄₃	—	2	4	no	—
228	C₄₃⋊C₈	—	2	1	no	—
229	C₄₃⋊C₈	—	2	1	no	—
230	C₄₃⋊C₈	—	2	1	no	—
231	C₄₃⋊C₈	—	2	1	no	—
232	C₄₃⋊C₈	—	2	2	no	—
233	C₄₃⋊C₈	—	2	2	no	—
234	C₄₃⋊C₈	—	4	2	no	—
235	#21137	—	43	1	no	maximal, Sylow
236	C₂²×C₄₃	—	2	1	no	—
237	C₂²×C₄₃	—	2	1	no	—
238	C₂²×C₄₃	—	4	1	no	—
239	C₂²×C₄₃	—	4	1	no	—
240	C₂²×C₄₃	—	4	1	no	—
241	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
242	C₂²×C₄₃	#529	1	2	yes	—
243	C₂×D₄₃	—	2	2	no	—
244	C₂×D₄₃	—	4	1	no	—
245	C₂×D₄₃	—	4	1	no	—
246	C₄×C₄₃	—	2	1	no	—
247	C₄×C₄₃	—	2	1	no	—
248	C₄×C₄₃	—	4	4	no	—
249	C₄×C₄₃	—	4	1	no	—
250	C₄×C₄₃	—	4	1	no	—
251	C₄×C₄₃	—	4	1	no	—
252	C₄×C₄₃	#443	1	2	yes	—
253	C₄×C₄₃	#444	1	2	yes	—
254	C₄×C₄₃	C₂×#117	1	1	yes	characteristic
255	C₄×C₄₃	C₄×#41	1	1	yes	characteristic
256	C₄×C₄₃	#525	1	2	yes	—
257	Dic₄₃	—	2	2	no	—
258	Dic₄₃	—	4	1	no	—
259	Dic₄₃	—	4	1	no	—
260	C₄×#135	—	43	1	no	—
261	#2922	—	43	1	no	—
262	C₄×#131	—	43	1	no	—
263	#1929	—	43	2	no	—
264	#1922	—	43	2	no	—
265	#1876	—	43	2	no	—
266	#1866	—	43	2	no	—
267	C₄×#108	—	43	1	no	—
268	C₄×#104	—	43	1	no	—
269	C₄×#104	D₄₃	1	1	yes	characteristic, complemented
270	#1744	—	43	1	no	—
271	C₂×C₄₃	—	2	2	no	—
272	C₂×C₄₃	—	8	1	no	—
273	C₂×C₄₃	#2290	1	1	yes	characteristic
274	C₂×C₄₃	C₂×#443	1	1	yes	characteristic
275	C₂×C₄₃	C₂×#444	1	1	yes	characteristic
276	D₄₃	—	4	2	no	—
277	C₂×#135	—	43	1	no	—
278	C₂×#131	—	43	2	no	—
279	C₄×#41	—	43	1	no	—
280	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
281	C₄×Q₁₆	—	43	1	no	—
282	C₄×Q₁₆	—	43	1	no	—
283	C₄×SD₁₆	—	43	1	no	—
284	C₄×SD₁₆	—	43	1	no	—
285	C₄×SD₁₆	—	43	1	no	—
286	C₄×SD₁₆	—	43	1	no	—
287	C₄×D₈	—	43	1	no	—
288	C₄×D₈	—	43	1	no	—
289	#433	—	86	2	no	—
290	#431	—	86	1	no	—
291	#431	—	86	1	no	—
292	C₂×#108	—	43	2	no	—
293	#427	—	43	1	no	—
294	#424	—	43	2	no	—
295	C₂×#104	—	43	2	no	—
296	C₂×#104	C₂×D₄₃	1	2	yes	—
297	#416	—	43	1	no	—
298	#416	—	43	1	no	—
299	#408	—	43	2	no	—
300	#405	—	43	2	no	—
301	#405	—	86	2	no	—
302	C₄×M₁₆	—	43	1	no	—
303	C₄×M₁₆	—	86	1	no	—
304	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
305	C₂×C₄×C₈	—	43	1	no	—
306	C₂×C₄×C₈	—	43	1	no	—
307	C₂×C₄×C₈	—	86	1	no	—
308	C₄³	C₂×D₄₃	1	1	yes	characteristic
309	#341	—	43	2	no	—
310	#339	—	43	2	no	—
311	#339	C₂×D₄₃	1	2	yes	—
312	#336	—	43	2	no	—
313	#336	—	43	2	no	—
314	C₄₃	#21137	1	1	yes	characteristic, complemented, Sylow
315	C₂×#41	—	43	1	no	—
316	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
317	#135	—	86	4	no	—
318	C₂×Q₁₆	—	43	1	no	—
319	C₂×SD₁₆	—	43	1	no	—
320	C₂×SD₁₆	—	43	1	no	—
321	C₂×D₈	—	43	1	no	—
322	#131	—	86	4	no	—
323	#131	—	86	4	no	—
324	C₂×M₁₆	—	43	2	no	—
325	C₂×M₁₆	—	86	2	no	—
326	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
327	C₂²×C₈	—	43	2	no	—
328	C₂²×C₈	—	43	1	no	—
329	C₂²×C₈	—	43	1	no	—
330	C₂²×C₈	—	86	2	no	—
331	C₄×Q₈	—	43	1	no	—
332	C₄×Q₈	—	43	1	no	—
333	C₄×Q₈	C₄×D₄₃	1	1	yes	characteristic
334	C₄×Q₈	C₄×D₄₃	1	1	yes	characteristic
335	C₄×D₄	—	2	1	no	—
336	C₄×D₄	—	2	1	no	—
337	C₄×D₄	—	43	1	no	—
338	C₄×D₄	—	43	1	no	—
339	C₄×D₄	—	86	1	no	—
340	C₄×D₄	—	86	1	no	—
341	C₄×D₄	C₄×D₄₃	1	1	yes	characteristic
342	C₄×D₄	C₄×D₄₃	1	1	yes	characteristic
343	#117	—	2	1	no	—
344	#117	—	43	1	no	—
345	#117	—	86	1	no	—
346	#117	C₂²×D₄₃	1	1	yes	characteristic
347	C₂×C₄²	—	2	1	no	—
348	C₂×C₄²	—	2	1	no	—
349	C₂×C₄²	—	2	1	no	—
350	C₂×C₄²	—	86	1	no	—
351	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
352	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
353	#108	—	86	4	no	—
354	#107	—	43	1	no	—
355	#107	—	43	1	no	—
356	#106	—	43	1	no	—
357	#106	—	43	1	no	—
358	C₄⋊C₈	—	86	2	no	—
359	C₄⋊C₈	—	86	2	no	—
360	#104	—	2	4	no	—
361	#104	—	86	4	no	—
362	#103	—	43	1	no	—
363	#103	—	43	1	no	—
364	#103	—	43	1	no	—
365	#103	—	43	1	no	—
366	#102	—	43	1	no	—
367	#102	—	43	1	no	—
368	#102	—	43	1	no	—
369	#102	—	43	1	no	—
370	C₂²⋊C₈	—	86	2	no	—
371	C₂²⋊C₈	—	86	2	no	—
372	#97	—	2	1	no	—
373	#97	—	86	2	no	—
374	#97	—	86	1	no	—
375	C₄×C₈	—	2	1	no	—
376	C₄×C₈	—	43	1	no	—
377	C₄×C₈	—	43	1	no	—
378	C₄×C₈	—	43	1	no	—
379	C₄×C₈	—	43	1	no	—
380	C₄×C₈	—	43	2	no	—
381	C₄×C₈	—	43	1	no	—
382	C₄×C₈	—	43	1	no	—
383	C₄×C₈	—	86	2	no	—
384	C₄×C₈	—	86	1	no	—
385	#41	—	2	2	no	—
386	#41	—	2	2	no	—
387	#41	—	43	4	no	—
388	#41	—	86	2	no	—
389	C₂×Q₈	—	43	1	no	—
390	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	43	1	no	—
393	C₂×D₄	—	86	1	no	—
394	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
395	C₂²×C₄	—	2	2	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	86	1	no	—
400	C₂²×C₄	—	86	1	no	—
401	C₂²×C₄	—	86	1	no	—
402	C₂²×C₄	#10621900	1	1	yes	characteristic
403	C₂²×C₄	#10621900	1	1	yes	characteristic
404	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
405	Q₁₆	—	86	2	no	—
406	SD₁₆	—	86	2	no	—
407	SD₁₆	—	86	2	no	—
408	D₈	—	86	2	no	—
409	M₁₆	—	2	2	no	—
410	M₁₆	—	86	8	no	—
411	M₁₆	—	86	2	no	—
412	M₁₆	—	86	2	no	—
413	M₁₆	#10621898	1	4	yes	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	43	1	no	—
416	C₂×C₈	—	43	1	no	—
417	C₂×C₈	—	43	1	no	—
418	C₂×C₈	—	43	1	no	—
419	C₂×C₈	—	43	2	no	—
420	C₂×C₈	—	43	2	no	—
421	C₂×C₈	—	86	8	no	—
422	C₂×C₈	—	86	2	no	—
423	C₂×C₈	—	86	2	no	—
424	C₂×C₈	—	86	2	no	—
425	C₂×C₈	—	86	2	no	—
426	C₂×C₈	—	86	2	no	—
427	C₄⋊C₄	—	2	1	no	—
428	C₄⋊C₄	—	2	1	no	—
429	C₄⋊C₄	—	43	1	no	—
430	C₄⋊C₄	—	43	1	no	—
431	C₄⋊C₄	—	86	1	no	—
432	C₄⋊C₄	—	86	1	no	—
433	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
434	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
435	C₂²⋊C₄	—	2	1	no	—
436	C₂²⋊C₄	—	2	1	no	—
437	C₂²⋊C₄	—	2	1	no	—
438	C₂²⋊C₄	—	86	1	no	—
439	C₂²⋊C₄	—	86	1	no	—
440	C₂²⋊C₄	—	86	1	no	—
441	C₄²	—	2	4	no	—
442	C₄²	—	2	1	no	—
443	C₄²	—	2	1	no	—
444	C₄²	—	2	1	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	4	2	no	—
448	C₄²	—	86	1	no	—
449	C₄²	—	86	1	no	—
450	C₄²	—	86	1	no	—
451	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
452	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
453	C₄²	D₄×D₄₃	1	1	yes	characteristic
454	C₄²	D₄×D₄₃	1	1	yes	characteristic
455	C₂³	—	2	1	no	—
456	C₂³	—	86	1	no	—
457	C₂³	C₂×#10621900	1	1	yes	characteristic
458	Q₈	—	2	1	no	—
459	Q₈	—	2	1	no	—
460	Q₈	—	43	2	no	—
461	Q₈	—	86	1	no	—
462	D₄	—	2	1	no	—
463	D₄	—	2	1	no	—
464	D₄	—	4	2	no	—
465	D₄	—	43	2	no	—
466	D₄	—	86	4	no	—
467	D₄	—	86	1	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	2	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	2	no	—
479	C₂×C₄	—	86	1	no	—
480	C₂×C₄	—	86	4	no	—
481	C₂×C₄	—	86	1	no	—
482	C₂×C₄	—	86	1	no	—
483	C₂×C₄	—	172	2	no	—
484	C₂×C₄	—	172	2	no	—
485	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
486	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
487	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
488	C₂×C₄	(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
489	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
490	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
491	C₂×C₄	#41×D₄₃	1	2	yes	—
492	C₂×C₄	C₂×#10621898	1	2	yes	—
493	C₈	—	2	4	no	—
494	C₈	—	86	1	no	—
495	C₈	—	86	1	no	—
496	C₈	—	86	1	no	—
497	C₈	—	86	1	no	—
498	C₈	—	86	2	no	—
499	C₈	—	86	2	no	—
500	C₈	—	172	2	no	—
501	C₂²	—	2	1	no	—
502	C₂²	—	2	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	1	no	—
505	C₂²	—	4	1	no	—
506	C₂²	—	86	2	no	—
507	C₂²	—	172	1	no	—
508	C₂²	—	172	1	no	—
509	C₂²	C₂×(C₂²⋊D₄₃)⋊C₄	1	1	yes	characteristic
510	C₂²	#14583431	1	2	yes	—
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	4	4	no	—
514	C₄	—	4	1	no	—
515	C₄	—	4	1	no	—
516	C₄	—	4	1	no	—
517	C₄	—	86	2	no	—
518	C₄	—	172	1	no	—
519	C₄	—	172	1	no	—
520	C₄	#14583013	1	2	yes	—
521	C₄	#14583018	1	2	yes	—
522	C₄	#117×D₄₃	1	1	yes	characteristic
523	C₄	C₄×#10621898	1	1	yes	characteristic
524	C₄	#14583408	1	2	yes	—
525	C₂	—	2	2	no	—
526	C₂	—	8	1	no	—
527	C₂	—	172	2	no	—
528	C₂	#19137041	1	1	yes	characteristic
529	C₂	C₂×#14583013	1	1	yes	characteristic
530	C₂	C₂×#14583018	1	1	yes	characteristic

	subgroup	G/H
center	C₄²	D₄×D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄×#104×C₄₃	C₂
socle	C₂²×C₄₃	C₂×C₄×D₄
prime radical	C₂×#13063345	C₂²
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₄×#104	D₄₃
hypocenter	C₄₃	#21137
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₄² ◁ C₂×C₄² ◁ C₄×#104

Complements

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

N	H ≅ G/N	type
2. #19143239	C₂	semidirect
3. C₄×#13063333	C₂	semidirect
4. #19135246	C₂	semidirect
5. #19135197	C₂	semidirect
7. #19134871	C₂	semidirect
8. C₄×#13063260	C₂	semidirect
9. C₄×#13063253	C₂	semidirect
10. #19134341	C₂	semidirect
11. C₄×#104×C₄₃	C₂	semidirect
15. C₄×#10621885	C₄	semidirect
16. C₄×#10621885	C₄	semidirect
17. C₄×#10621884	C₄	semidirect
18. C₄×#10621884	C₄	semidirect
19. C₄×#10621883	C₄	semidirect
20. C₄×#10621883	C₄	semidirect
21. C₄×#10621882	C₄	semidirect
22. C₄×#10621882	C₄	semidirect
269. C₄×#104	D₄₃	semidirect
314. C₄₃	#21137	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13063345	2
#19143239	2
C₄×#13063333	2
#19135246	2
#19135197	2
#19134919	2
#19134871	2
C₄×#13063260	2
C₄×#13063253	2
#19134341	2
C₄×#104×C₄₃	2
#21137	43