Subgroups — #25095358

Order 11008.

866 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14582955	C₂	1	1	yes	maximal, characteristic
2	C₂×#14582954	C₂	1	1	yes	maximal, characteristic
3	#19136999	C₂	1	1	yes	maximal, characteristic
4	#19134472	C₂	1	1	yes	maximal, characteristic, complemented
5	#19134471	C₂	1	1	yes	maximal, characteristic, complemented
6	#19134470	C₂	1	1	yes	maximal, characteristic, complemented
7	#19134469	C₂	1	1	yes	maximal, characteristic, complemented
8	#19134468	C₂	1	1	yes	maximal, characteristic, complemented
9	#19134467	C₂	1	1	yes	maximal, characteristic, complemented
10	#19134466	C₂	1	1	yes	maximal, characteristic, complemented
11	#19134364	C₂	1	1	yes	maximal, characteristic
12	#19134362	C₂	1	1	yes	maximal, characteristic
13	#19134360	C₂	1	1	yes	maximal, characteristic
14	#19134360	C₂	1	1	yes	maximal, characteristic
15	C₄₃×#1771	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13063282	C₂²	1	1	yes	characteristic
17	C₂×#13063282	C₂²	1	1	yes	characteristic
18	C₂×C₄²×D₄₃	C₂²	1	1	yes	characteristic
19	#14582955	C₄	1	8	yes	complemented
20	#14582954	C₄	1	8	yes	complemented
21	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×#13063236	C₂²	1	1	yes	characteristic
29	C₂×#13063236	C₂²	1	1	yes	characteristic
30	C₂×#13063235	C₂²	1	1	yes	characteristic
31	C₂×#13063235	C₂²	1	1	yes	characteristic
32	C₂×#13063235	C₂²	1	1	yes	characteristic
33	C₂×#13063235	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
36	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
37	#14582768	C₄	1	2	yes	—
38	#14582763	C₄	1	2	yes	—
39	#14582758	C₄	1	2	yes	—
40	#14582756	C₄	1	2	yes	—
41	C₄×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
42	C₄×Dic₄₃⋊C₄	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
44	#14582654	C₂²	1	1	yes	characteristic
45	#14582654	C₂²	1	1	yes	characteristic
46	#14582653	C₂²	1	1	yes	characteristic
47	#14582653	C₂²	1	1	yes	characteristic
48	#14582653	C₂²	1	1	yes	characteristic
49	#14582653	C₂²	1	1	yes	characteristic
50	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
51	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
52	C₂×#97×C₄₃	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
54	C₄×C₄⋊C₄×C₄₃	C₂²	1	1	yes	characteristic
55	C₄₃×#336	C₂²	1	1	yes	characteristic
56	C₄₃×#336	C₂²	1	1	yes	characteristic
57	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
58	C₂²×C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
60	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
64	#13063282	—	4	1	no	—
65	#13063282	—	4	1	no	—
66	#13063282	—	4	1	no	—
67	#13063282	—	4	1	no	—
68	C₂×C₄⋊Dic₄₃	C₂×C₄	1	2	yes	—
69	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
70	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
71	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
72	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
73	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
74	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
75	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
77	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
78	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
79	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
80	C₄²×D₄₃	C₂×C₄	1	4	yes	—
81	C₄²×D₄₃	C₂×C₄	1	4	yes	—
82	C₄⋊(C₄₃⋊C₈)	C₂×C₄	1	4	yes	—
83	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
84	Dic₄₃⋊C₈	C₂×C₄	1	4	yes	—
85	(C₂×D₄₃)⋊C₈	C₂×C₄	1	4	yes	—
86	(C₂×D₄₃)⋊C₈	C₂×C₄	1	4	yes	—
87	(C₂×D₄₃)⋊C₈	C₂×C₄	1	4	yes	—
88	(C₂×D₄₃)⋊C₈	C₂×C₄	1	4	yes	—
89	#13063236	—	4	1	no	—
90	#13063236	C₂×C₄	1	4	yes	—
91	#13063235	—	4	1	no	—
92	#13063235	—	4	1	no	—
93	#13063235	C₂×C₄	1	4	yes	—
94	#13063235	C₂×C₄	1	4	yes	—
95	C₄×C₄₃⋊C₈	—	4	1	no	—
96	C₈×Dic₄₃	—	4	1	no	—
97	C₈×Dic₄₃	—	4	1	no	—
98	C₄₃⋊#95	C₂×C₄	1	2	yes	—
99	C₄₃⋊#95	C₂×C₄	1	2	yes	—
100	C₄₃⋊#95	C₂×C₄	1	2	yes	—
101	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
105	C₂×C₄⋊C₄×C₄₃	C₂×C₄	1	2	yes	—
106	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
107	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
109	C₄⋊C₈×C₄₃	C₂×C₄	1	4	yes	—
110	#97×C₄₃	—	4	1	no	—
111	#97×C₄₃	C₂×C₄	1	4	yes	—
112	C₄×C₈×C₄₃	—	4	1	no	—
113	#95×C₄₃	C₂×C₄	1	2	yes	—
114	C₂³×D₄₃	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
116	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
117	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
120	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
121	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
122	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
123	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
124	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₄×D₄₃	—	2	1	no	—
126	C₂×C₄×D₄₃	—	2	1	no	—
127	C₂×C₄×D₄₃	—	2	1	no	—
128	C₂×C₄×D₄₃	—	2	1	no	—
129	C₂×C₄×D₄₃	—	4	2	no	—
130	C₂×C₄×D₄₃	—	4	2	no	—
131	C₂×C₄×D₄₃	C₄²	1	4	yes	—
132	C₂×C₄×D₄₃	C₄²	1	4	yes	—
133	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
134	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
135	C₂×C₈×C₄₃	—	2	1	no	—
136	C₂×C₈×C₄₃	—	2	1	no	—
137	C₂×C₈×C₄₃	—	2	1	no	—
138	C₂×C₈×C₄₃	—	2	1	no	—
139	C₂×C₈×C₄₃	—	2	1	no	—
140	C₂×C₈×C₄₃	—	2	1	no	—
141	C₂×C₈×C₄₃	—	2	1	no	—
142	C₂×C₈×C₄₃	—	2	1	no	—
143	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₄₃	C₂²×C₄	1	2	yes	—
147	C₄⋊C₄×C₄₃	—	4	2	no	—
148	C₄²×C₄₃	—	2	1	no	—
149	C₄²×C₄₃	—	2	1	no	—
150	C₄²×C₄₃	—	2	1	no	—
151	C₄²×C₄₃	—	2	1	no	—
152	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
153	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
154	(C₂×D₄₃)⋊C₄	—	4	2	no	—
155	(C₂×D₄₃)⋊C₄	—	4	2	no	—
156	C₄⋊Dic₄₃	—	4	2	no	—
157	Dic₄₃⋊C₄	—	4	2	no	—
158	Dic₄₃⋊C₄	—	4	2	no	—
159	Dic₄₃⋊C₄	—	4	2	no	—
160	Dic₄₃⋊C₄	—	4	2	no	—
161	C₄×Dic₄₃	—	2	1	no	—
162	C₄×Dic₄₃	—	2	1	no	—
163	C₄×Dic₄₃	—	2	1	no	—
164	C₄×Dic₄₃	—	2	1	no	—
165	C₄×Dic₄₃	C₄²	1	4	yes	—
166	C₄×Dic₄₃	C₄²	1	4	yes	—
167	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
168	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
169	C₂×C₄₃⋊C₈	—	2	1	no	—
170	C₂×C₄₃⋊C₈	—	2	1	no	—
171	C₂×C₄₃⋊C₈	—	2	1	no	—
172	C₂×C₄₃⋊C₈	—	2	1	no	—
173	C₂×C₄₃⋊C₈	—	2	1	no	—
174	C₂×C₄₃⋊C₈	—	2	1	no	—
175	C₂×C₄₃⋊C₈	—	2	1	no	—
176	C₂×C₄₃⋊C₈	—	2	1	no	—
177	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
178	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
179	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
180	C₂×C₄₃⋊C₈	C₂²×C₄	1	2	yes	—
181	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
182	C₂²×D₄₃	—	2	1	no	—
183	C₂²×D₄₃	—	2	1	no	—
184	C₂²×D₄₃	—	2	2	no	—
185	C₂²×D₄₃	—	2	2	no	—
186	C₂²×D₄₃	C₂×C₄²	1	2	yes	—
187	C₂×C₄×C₄₃	—	2	2	no	—
188	C₂×C₄×C₄₃	—	2	2	no	—
189	C₂×C₄×C₄₃	—	2	2	no	—
190	C₂×C₄×C₄₃	—	2	2	no	—
191	C₂×C₄×C₄₃	—	2	2	no	—
192	C₂×C₄×C₄₃	—	2	2	no	—
193	C₂×C₄×C₄₃	—	2	2	no	—
194	C₂×C₄×C₄₃	—	2	2	no	—
195	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
196	C₂×C₄×C₄₃	C₂×C₄²	1	2	yes	—
197	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
198	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
200	C₂×C₄×C₄₃	H(5,𝔽₂)	1	1	yes	characteristic
201	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
202	C₂×C₄×C₄₃	2₋¹⁺⁴	1	1	yes	characteristic
203	C₂×Dic₄₃	—	2	1	no	—
204	C₂×Dic₄₃	—	2	1	no	—
205	C₂×Dic₄₃	—	2	2	no	—
206	C₂×Dic₄₃	—	2	2	no	—
207	C₂×Dic₄₃	—	2	2	no	—
208	C₂×Dic₄₃	—	2	2	no	—
209	C₂×Dic₄₃	—	2	2	no	—
210	C₂×Dic₄₃	—	2	2	no	—
211	C₂×Dic₄₃	—	2	2	no	—
212	C₂×Dic₄₃	—	2	2	no	—
213	C₂×Dic₄₃	C₂×C₄²	1	2	yes	—
214	C₂×Dic₄₃	C₂×C₄²	1	2	yes	—
215	C₂×Dic₄₃	C₂×C₄²	1	2	yes	—
216	C₄×D₄₃	—	2	2	no	—
217	C₄×D₄₃	—	2	2	no	—
218	C₄×D₄₃	—	2	2	no	—
219	C₄×D₄₃	—	2	2	no	—
220	C₄×D₄₃	—	4	4	no	—
221	C₄×D₄₃	—	4	4	no	—
222	C₈×C₄₃	—	2	2	no	—
223	C₈×C₄₃	—	2	2	no	—
224	C₈×C₄₃	—	2	2	no	—
225	C₈×C₄₃	—	2	2	no	—
226	C₄₃⋊C₈	—	2	2	no	—
227	C₄₃⋊C₈	—	2	2	no	—
228	C₄₃⋊C₈	—	2	2	no	—
229	C₄₃⋊C₈	—	2	2	no	—
230	#20539	—	43	1	no	maximal, Sylow
231	C₂²×C₄₃	C₂²×C₄²	1	1	yes	characteristic
232	C₂²×C₄₃	#518	1	1	yes	characteristic
233	C₂²×C₄₃	#519	1	1	yes	characteristic
234	C₂²×C₄₃	#568	1	2	yes	—
235	C₂²×C₄₃	#568	1	2	yes	—
236	C₂×D₄₃	—	2	2	no	—
237	C₂×D₄₃	—	2	2	no	—
238	C₂×D₄₃	—	2	2	no	—
239	C₂×D₄₃	—	4	2	no	—
240	C₂×D₄₃	—	4	2	no	—
241	C₄×C₄₃	—	2	2	no	—
242	C₄×C₄₃	—	2	2	no	—
243	C₄×C₄₃	—	4	2	no	—
244	C₄×C₄₃	—	4	2	no	—
245	C₄×C₄₃	#520	1	1	yes	characteristic
246	C₄×C₄₃	#520	1	1	yes	characteristic
247	C₄×C₄₃	#520	1	1	yes	characteristic
248	C₄×C₄₃	#520	1	1	yes	characteristic
249	Dic₄₃	—	2	2	no	—
250	Dic₄₃	—	2	2	no	—
251	Dic₄₃	—	2	2	no	—
252	Dic₄₃	—	4	2	no	—
253	Dic₄₃	—	4	2	no	—
254	C₂×#432	—	43	1	no	—
255	C₂×#432	—	43	1	no	—
256	#2285	—	43	1	no	—
257	#1771	—	43	1	no	—
258	#1771	—	43	1	no	—
259	#1771	—	43	1	no	—
260	#1771	—	43	1	no	—
261	#1771	—	43	1	no	—
262	#1771	—	43	1	no	—
263	#1771	—	43	1	no	—
264	#1771	D₄₃	1	1	yes	characteristic, complemented
265	#1750	—	43	1	no	—
266	#1750	—	43	1	no	—
267	#1750	—	43	1	no	—
268	#1750	—	43	1	no	—
269	C₂×C₄₃	#2274	1	1	yes	characteristic
270	C₂×C₄₃	#2873	1	1	yes	characteristic
271	C₂×C₄₃	#2873	1	1	yes	characteristic
272	C₂×C₄₃	#2980	1	2	yes	—
273	C₂×C₄₃	#2987	1	2	yes	—
274	D₄₃	—	4	2	no	—
275	C₂×#117	—	43	1	no	—
276	C₂×#117	—	43	1	no	—
277	C₂²×C₄²	—	43	1	no	—
278	#432	—	43	8	no	—
279	#432	—	43	8	no	—
280	C₂×C₄⋊C₈	—	43	1	no	—
281	C₂×C₄⋊C₈	—	43	1	no	—
282	C₂×C₄⋊C₈	—	43	1	no	—
283	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
284	C₂×C₂²⋊C₈	—	43	1	no	—
285	C₂×C₂²⋊C₈	—	43	1	no	—
286	C₂×C₂²⋊C₈	—	43	1	no	—
287	C₂×C₂²⋊C₈	—	43	1	no	—
288	C₂×#97	—	43	1	no	—
289	C₂×#97	—	43	1	no	—
290	C₂×#97	—	43	1	no	—
291	C₂×#97	—	43	1	no	—
292	C₂×#97	—	43	1	no	—
293	C₂×#97	—	43	1	no	—
294	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
295	C₂×#97	C₂×D₄₃	1	1	yes	characteristic
296	C₂×C₄×C₈	—	43	1	no	—
297	C₂×C₄×C₈	—	43	1	no	—
298	C₂×C₄×C₈	—	43	1	no	—
299	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
300	#384	—	43	2	no	—
301	#382	—	43	2	no	—
302	#380	—	43	2	no	—
303	#380	—	43	2	no	—
304	C₄×C₄⋊C₄	—	43	1	no	—
305	C₄×C₄⋊C₄	—	43	1	no	—
306	C₄×C₄⋊C₄	—	43	1	no	—
307	C₄×C₄⋊C₄	C₂×D₄₃	1	1	yes	characteristic
308	#336	—	43	1	no	—
309	#336	—	43	1	no	—
310	#336	—	43	1	no	—
311	#336	—	43	1	no	—
312	#336	—	43	1	no	—
313	#336	—	43	1	no	—
314	#336	C₂×D₄₃	1	1	yes	characteristic
315	#336	C₂×D₄₃	1	1	yes	characteristic
316	C₄₃	#20539	1	1	yes	characteristic, complemented, Sylow
317	C₂³×C₄	—	43	1	no	—
318	C₂³×C₄	—	43	1	no	—
319	C₂³×C₄	—	43	1	no	—
320	C₂²×C₈	—	43	1	no	—
321	C₂²×C₈	—	43	1	no	—
322	C₂²×C₈	—	43	1	no	—
323	C₂²×C₈	—	43	1	no	—
324	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
325	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
326	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
327	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
328	#117	—	172	1	no	—
329	#117	—	172	1	no	—
330	#117	—	172	1	no	—
331	#117	—	172	1	no	—
332	C₂×C₄⋊C₄	—	43	2	no	—
333	C₂×C₄⋊C₄	—	43	2	no	—
334	C₂×C₄⋊C₄	—	43	2	no	—
335	C₂×C₄⋊C₄	—	43	2	no	—
336	C₂×C₄⋊C₄	—	43	2	no	—
337	C₂×C₄⋊C₄	C₄×D₄₃	1	2	yes	—
338	C₂×C₂²⋊C₄	—	43	2	no	—
339	C₂×C₂²⋊C₄	—	43	2	no	—
340	C₂×C₄²	—	43	1	no	—
341	C₂×C₄²	—	43	1	no	—
342	C₂×C₄²	—	43	1	no	—
343	C₂×C₄²	—	43	4	no	—
344	C₂×C₄²	—	43	4	no	—
345	C₂×C₄²	—	43	1	no	—
346	C₂×C₄²	—	43	1	no	—
347	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
348	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
349	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
350	C₄⋊C₈	—	43	4	no	—
351	C₄⋊C₈	—	43	4	no	—
352	C₄⋊C₈	—	43	4	no	—
353	C₄⋊C₈	C₄×D₄₃	1	4	yes	—
354	C₂²⋊C₈	—	43	4	no	—
355	C₂²⋊C₈	—	43	4	no	—
356	C₂²⋊C₈	—	43	4	no	—
357	C₂²⋊C₈	—	43	4	no	—
358	#97	—	4	1	no	—
359	#97	—	43	4	no	—
360	#97	—	43	4	no	—
361	#97	—	43	4	no	—
362	#97	—	172	1	no	—
363	#97	—	172	1	no	—
364	#97	—	172	1	no	—
365	#97	C₄×D₄₃	1	4	yes	—
366	C₄×C₈	—	4	1	no	—
367	C₄×C₈	—	172	1	no	—
368	C₄×C₈	—	172	1	no	—
369	C₄×C₈	—	172	1	no	—
370	#95	—	43	2	no	—
371	#95	—	43	2	no	—
372	#95	—	43	2	no	—
373	#95	C₄×D₄₃	1	2	yes	—
374	C₂⁴	—	43	1	no	—
375	C₂²×C₄	—	43	1	no	—
376	C₂²×C₄	—	43	1	no	—
377	C₂²×C₄	—	43	1	no	—
378	C₂²×C₄	—	43	2	no	—
379	C₂²×C₄	—	43	2	no	—
380	C₂²×C₄	—	43	4	no	—
381	C₂²×C₄	—	43	4	no	—
382	C₂²×C₄	—	43	2	no	—
383	C₂²×C₄	—	43	2	no	—
384	C₂²×C₄	—	86	1	no	—
385	C₂²×C₄	—	86	1	no	—
386	C₂²×C₄	—	86	1	no	—
387	C₂²×C₄	—	86	1	no	—
388	C₂²×C₄	—	172	2	no	—
389	C₂²×C₄	—	172	2	no	—
390	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
391	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
392	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
393	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
394	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	43	2	no	—
404	C₂×C₈	—	43	2	no	—
405	C₂×C₈	—	43	2	no	—
406	C₂×C₈	—	43	2	no	—
407	C₂×C₈	—	86	1	no	—
408	C₂×C₈	—	86	1	no	—
409	C₂×C₈	—	86	1	no	—
410	C₂×C₈	—	86	1	no	—
411	C₂×C₈	—	86	1	no	—
412	C₂×C₈	—	86	1	no	—
413	C₂×C₈	—	86	1	no	—
414	C₂×C₈	—	86	1	no	—
415	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
416	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
417	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
418	C₂×C₈	C₂×C₄×D₄₃	1	2	yes	—
419	C₄⋊C₄	—	4	2	no	—
420	C₄⋊C₄	—	172	2	no	—
421	C₄⋊C₄	—	172	2	no	—
422	C₄⋊C₄	—	172	2	no	—
423	C₄⋊C₄	—	172	2	no	—
424	C₄⋊C₄	—	172	2	no	—
425	C₂²⋊C₄	—	172	2	no	—
426	C₂²⋊C₄	—	172	2	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	2	1	no	—
429	C₄²	—	2	1	no	—
430	C₄²	—	2	1	no	—
431	C₄²	—	43	4	no	—
432	C₄²	—	43	4	no	—
433	C₄²	—	43	2	no	—
434	C₄²	—	43	2	no	—
435	C₄²	—	86	1	no	—
436	C₄²	—	86	1	no	—
437	C₄²	—	86	1	no	—
438	C₄²	—	86	1	no	—
439	C₄²	C₂×C₄×D₄₃	1	2	yes	—
440	C₄²	C₂×C₄×D₄₃	1	2	yes	—
441	C₂³	—	43	2	no	—
442	C₂³	—	86	1	no	—
443	C₂³	—	86	1	no	—
444	C₂³	—	86	2	no	—
445	C₂³	—	86	2	no	—
446	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	43	2	no	—
456	C₂×C₄	—	43	2	no	—
457	C₂×C₄	—	43	2	no	—
458	C₂×C₄	—	86	1	no	—
459	C₂×C₄	—	86	1	no	—
460	C₂×C₄	—	86	2	no	—
461	C₂×C₄	—	86	2	no	—
462	C₂×C₄	—	86	2	no	—
463	C₂×C₄	—	86	2	no	—
464	C₂×C₄	—	86	2	no	—
465	C₂×C₄	—	86	2	no	—
466	C₂×C₄	—	86	2	no	—
467	C₂×C₄	—	86	2	no	—
468	C₂×C₄	—	86	2	no	—
469	C₂×C₄	—	86	2	no	—
470	C₂×C₄	—	86	2	no	—
471	C₂×C₄	—	86	2	no	—
472	C₂×C₄	—	172	4	no	—
473	C₂×C₄	—	172	4	no	—
474	C₂×C₄	C₄²×D₄₃	1	2	yes	—
475	C₂×C₄	C₄²×D₄₃	1	2	yes	—
476	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
477	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
478	C₂×C₄	#13063370	1	1	yes	characteristic
479	C₂×C₄	#13063371	1	1	yes	characteristic
480	C₂×C₄	#13063372	1	1	yes	characteristic
481	C₂×C₄	#13063373	1	1	yes	characteristic
482	C₈	—	2	2	no	—
483	C₈	—	2	2	no	—
484	C₈	—	2	2	no	—
485	C₈	—	2	2	no	—
486	C₈	—	86	2	no	—
487	C₈	—	86	2	no	—
488	C₈	—	86	2	no	—
489	C₈	—	86	2	no	—
490	C₂²	—	86	2	no	—
491	C₂²	—	86	2	no	—
492	C₂²	—	86	2	no	—
493	C₂²	—	172	2	no	—
494	C₂²	—	172	2	no	—
495	C₂²	C₂×C₄²×D₄₃	1	1	yes	characteristic
496	C₂²	#14583371	1	1	yes	characteristic
497	C₂²	#14583375	1	1	yes	characteristic
498	C₂²	#14583664	1	2	yes	—
499	C₂²	#14583665	1	2	yes	—
500	C₄	—	2	2	no	—
501	C₄	—	2	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	2	no	—
504	C₄	—	86	2	no	—
505	C₄	—	86	2	no	—
506	C₄	—	86	2	no	—
507	C₄	—	172	2	no	—
508	C₄	—	172	2	no	—
509	C₄	#14583378	1	1	yes	characteristic
510	C₄	#14583379	1	1	yes	characteristic
511	C₄	#14583380	1	1	yes	characteristic
512	C₄	#14583381	1	1	yes	characteristic
513	C₂	—	172	2	no	—
514	C₂	#19136949	1	1	yes	characteristic
515	C₂	#19143011	1	1	yes	characteristic
516	C₂	#19143012	1	1	yes	characteristic
517	C₂	#19143663	1	2	yes	—
518	C₂	#19143698	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₃
commutator	C₂²×C₄₃	C₂²×C₄²
Fitting	C₄₃×#1771	C₂
socle	C₂³×C₄₃	C₂³×C₄
prime radical	C₂³×D₄₃	C₂²×C₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	#1771	D₄₃
hypocenter	C₄₃	#20539
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂²×C₄ ◁ #1771

Complements

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

N	H ≅ G/N	type
4. #19134472	C₂	semidirect
5. #19134471	C₂	semidirect
6. #19134470	C₂	semidirect
7. #19134469	C₂	semidirect
8. #19134468	C₂	semidirect
9. #19134467	C₂	semidirect
10. #19134466	C₂	semidirect
15. C₄₃×#1771	C₂	semidirect
19. #14582955	C₄	semidirect
20. #14582954	C₄	semidirect
264. #1771	D₄₃	semidirect
316. C₄₃	#20539	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14582955	2
C₂×#14582954	2
#19136999	2
#19134472	2
#19134471	2
#19134470	2
#19134469	2
#19134468	2
#19134467	2
#19134466	2
#19134364	2
#19134362	2
#19134360	2
C₄₃×#1771	2
#20539	43