Subgroups — #25961602

Order 11008.

1626 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19147998	C₂	1	1	yes	maximal, characteristic
2	#19143698	C₂	1	4	yes	maximal, complemented
3	#19143695	C₂	1	4	yes	maximal, complemented
4	#19143688	C₂	1	4	yes	maximal, complemented
5	#19143686	C₂	1	4	yes	maximal, complemented
6	#19143541	C₂	1	2	yes	maximal, complemented
7	#19143539	C₂	1	2	yes	maximal, complemented
8	#19143536	C₂	1	1	yes	maximal, characteristic, complemented
9	#19143532	C₂	1	1	yes	maximal, characteristic, complemented
10	#19143529	C₂	1	1	yes	maximal, characteristic, complemented
11	#19143252	C₂	1	2	yes	maximal
12	#19143250	C₂	1	2	yes	maximal
13	#19143232	C₂	1	1	yes	maximal, characteristic
14	C₂×#14582958	C₂	1	1	yes	maximal, characteristic
15	C₄₃×#2960	C₂	1	1	yes	maximal, characteristic, complemented
16	#14583529	C₄	1	2	yes	—
17	#14583529	C₄	1	2	yes	—
18	#14583528	C₄	1	2	yes	—
19	#14583528	C₄	1	2	yes	—
20	#14583526	C₄	1	2	yes	—
21	#14583526	C₄	1	2	yes	—
22	#14583524	C₄	1	2	yes	—
23	#14583524	C₄	1	2	yes	—
24	#14583456	C₂²	1	1	yes	characteristic
25	#14583453	C₂²	1	4	yes	—
26	#14583453	C₂²	1	4	yes	—
27	#14583452	C₂²	1	2	yes	—
28	C₂×#13063282	C₂²	1	1	yes	characteristic
29	#117×D₄₃	C₂²	1	2	yes	—
30	#14583030	C₂²	1	4	yes	complemented
31	#14583030	C₂²	1	4	yes	complemented
32	#14583029	C₂²	1	2	yes	complemented
33	#14583029	C₂²	1	4	yes	complemented
34	#14583029	C₂²	1	2	yes	complemented
35	#14583028	C₂²	1	4	yes	complemented
36	#14583028	C₂²	1	4	yes	complemented
37	#14583028	C₂²	1	4	yes	complemented
38	#14583028	C₂²	1	4	yes	complemented
39	#14583027	C₂²	1	4	yes	complemented
40	#14583027	C₂²	1	4	yes	complemented
41	#14583026	C₂²	1	4	yes	complemented
42	C₈×Dic₈₆	C₂²	1	4	yes	complemented
43	C₈×Dic₈₆	C₂²	1	2	yes	complemented
44	C₈×Dic₈₆	C₂²	1	2	yes	complemented
45	#14583023	C₂²	1	4	yes	complemented
46	#14582961	C₂²	1	4	yes	—
47	#14582959	C₂²	1	4	yes	—
48	#14582959	C₂²	1	4	yes	—
49	#14582959	C₂²	1	4	yes	—
50	#14582959	C₂²	1	4	yes	—
51	#14582958	C₂²	1	2	yes	—
52	#14582958	C₂²	1	4	yes	—
53	#14582958	C₂²	1	2	yes	—
54	#14582958	C₂²	1	2	yes	—
55	#14582958	C₂²	1	2	yes	—
56	#14582955	C₂²	1	4	yes	—
57	#14582954	C₂²	1	4	yes	—
58	#14582951	C₂²	1	4	yes	—
59	#14582950	C₂²	1	4	yes	—
60	#14582927	C₂²	1	2	yes	—
61	#14582926	C₂²	1	2	yes	—
62	#14582925	C₂²	1	2	yes	—
63	#14582923	C₂²	1	1	yes	characteristic
64	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
65	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
66	#14582862	C₂²	1	2	yes	—
67	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
68	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
69	#14582857	C₂²	1	2	yes	—
70	#14582855	C₂²	1	2	yes	—
71	#14582854	C₂²	1	2	yes	—
72	M₁₆×Dic₄₃	C₂²	1	2	yes	—
73	C₂×#13063236	C₂²	1	1	yes	characteristic
74	C₄₃×#533	C₂²	1	1	yes	characteristic
75	C₄₃×#446	C₂²	1	2	yes	complemented
76	C₄₃×#446	C₂²	1	2	yes	complemented
77	C₈×Q₈×C₄₃	C₂²	1	2	yes	complemented
78	C₈×Q₈×C₄₃	C₂²	1	2	yes	complemented
79	C₄₃×#424	C₂²	1	2	yes	—
80	C₄₃×#423	C₂²	1	1	yes	characteristic
81	C₄₃×#405	C₂²	1	2	yes	—
82	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
83	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
84	C₂×#10621877	C₂³	1	2	yes	—
85	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
86	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
87	#13063325	C₂×C₄	1	1	yes	characteristic
88	#13063325	C₂×C₄	1	1	yes	characteristic
89	#13063324	C₂×C₄	1	2	yes	—
90	#13063324	C₂×C₄	1	2	yes	—
91	#13063324	C₂×C₄	1	4	yes	—
92	#13063324	C₂×C₄	1	4	yes	—
93	#13063323	C₂×C₄	1	4	yes	—
94	#13063323	C₂×C₄	1	4	yes	—
95	#13063317	C₂×C₄	1	2	yes	—
96	#13063316	C₂×C₄	1	2	yes	—
97	#13063316	C₂×C₄	1	2	yes	—
98	#13063315	C₂×C₄	1	4	yes	—
99	#13063315	C₂×C₄	1	4	yes	—
100	#13063315	C₂×C₄	1	4	yes	—
101	#13063315	C₂×C₄	1	4	yes	—
102	#13063305	C₂×C₄	1	4	yes	—
103	#13063305	C₂×C₄	1	4	yes	—
104	#13063304	C₂×C₄	1	2	yes	—
105	#13063304	C₂×C₄	1	2	yes	—
106	#13063303	C₂×C₄	1	4	yes	—
107	#13063303	C₂×C₄	1	4	yes	—
108	#13063303	C₂×C₄	1	4	yes	—
109	#13063303	C₂×C₄	1	4	yes	—
110	#13063302	C₂×C₄	1	4	yes	—
111	#13063302	C₂×C₄	1	4	yes	—
112	#13063301	C₂×C₄	1	4	yes	—
113	#13063301	C₂×C₄	1	4	yes	—
114	C₄×Dic₈₆	C₂³	1	4	yes	—
115	C₄×Dic₈₆	C₂³	1	4	yes	—
116	C₄×Dic₈₆	C₂³	1	2	yes	—
117	C₄×Dic₈₆	C₂³	1	2	yes	—
118	#13063284	C₂³	1	2	yes	—
119	#13063283	C₂×C₄	1	2	yes	—
120	#13063283	C₂×C₄	1	2	yes	—
121	#13063282	C₂×C₄	1	2	yes	—
122	#13063282	C₂×C₄	1	2	yes	—
123	#13063282	C₂³	1	4	yes	—
124	#13063282	C₂³	1	2	yes	—
125	#13063282	C₂³	1	2	yes	—
126	#13063281	C₂×C₄	1	4	yes	—
127	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
128	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
129	C₄⋊C₄×D₄₃	C₂×C₄	1	2	yes	—
130	C₄⋊C₄×D₄₃	C₂×C₄	1	2	yes	—
131	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
132	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
133	C₂²⋊C₄×D₄₃	C₂×C₄	1	4	yes	—
134	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
135	C₄²×D₄₃	C₂³	1	4	yes	—
136	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
137	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
138	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
139	C₄⋊(C₄₃⋊C₈)	C₂³	1	4	yes	—
140	Dic₄₃⋊C₈	C₂³	1	2	yes	—
141	Dic₄₃⋊C₈	C₂³	1	2	yes	—
142	Dic₄₃⋊C₈	C₂³	1	2	yes	—
143	Dic₄₃⋊C₈	C₂³	1	2	yes	—
144	Dic₄₃⋊C₈	C₂³	1	4	yes	—
145	Dic₄₃⋊C₈	C₂³	1	4	yes	—
146	Dic₄₃⋊C₈	C₂³	1	4	yes	—
147	Dic₄₃⋊C₈	C₂³	1	4	yes	—
148	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
149	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
150	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
151	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
152	(C₂×D₄₃)⋊C₈	C₂³	1	4	yes	—
153	(C₂×D₄₃)⋊C₈	C₂³	1	4	yes	—
154	#13063236	C₂³	1	2	yes	—
155	#13063236	C₂³	1	2	yes	—
156	#13063236	C₂³	1	4	yes	—
157	#13063235	C₂³	1	4	yes	—
158	#13063235	C₂³	1	4	yes	—
159	#13063235	C₂³	1	4	yes	—
160	C₄×C₄₃⋊C₈	C₂³	1	4	yes	—
161	C₈×Dic₄₃	C₂³	1	4	yes	—
162	C₈×Dic₄₃	C₂³	1	4	yes	—
163	C₈×Dic₄₃	C₂³	1	4	yes	—
164	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
165	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
166	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
167	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
168	C₄⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
169	#125×C₄₃	C₂×C₄	1	2	yes	—
170	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
171	C₂²⋊Q₈×C₄₃	C₂×C₄	1	2	yes	—
172	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
173	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
174	#117×C₄₃	C₂³	1	2	yes	—
175	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
176	C₄⋊C₈×C₄₃	C₂³	1	4	yes	—
177	C₄⋊C₈×C₄₃	C₂³	1	4	yes	—
178	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
179	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
180	#97×C₄₃	C₂³	1	4	yes	—
181	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
182	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
183	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
184	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
185	C₄×C₈×C₄₃	C₂³	1	4	yes	—
186	C₂³×D₄₃	C₂²×C₄	1	1	yes	characteristic
187	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
188	C₂×Q₈×C₄₃	C₂²×C₄	1	2	yes	—
189	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
190	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
191	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
192	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
193	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
194	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
195	C₂×C₄×D₄₃	—	2	2	no	—
196	C₂×C₄×D₄₃	—	2	2	no	—
197	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
198	C₂×C₄×D₄₃	C₂²×C₄	1	4	yes	—
199	C₂×C₄×D₄₃	C₂²×C₄	1	4	yes	—
200	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
201	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
202	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
203	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
204	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
205	M₁₆×C₄₃	—	2	4	no	—
206	C₂×C₈×C₄₃	—	2	2	no	—
207	C₂×C₈×C₄₃	—	2	2	no	—
208	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
209	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
210	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
211	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
212	C₂×C₈×C₄₃	C₂⁴	1	4	yes	—
213	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
214	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
215	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
216	C₄⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
217	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
218	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
219	C₂²⋊C₄×C₄₃	C₂²×C₄	1	4	yes	—
220	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
221	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
222	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
223	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
224	C₄²×C₄₃	C₂⁴	1	4	yes	—
225	C₂²⋊Dic₄₃	C₂²×C₄	1	4	yes	—
226	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	4	yes	—
227	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	4	yes	—
228	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
229	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
230	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
231	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
232	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
233	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
234	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
235	C₄⋊Dic₄₃	C₂²×C₄	1	4	yes	—
236	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
237	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
238	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
239	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
240	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
241	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
242	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
243	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
244	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
245	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
246	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
247	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
248	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
249	Dic₄₃⋊C₄	C₂²×C₄	1	4	yes	—
250	C₄×Dic₄₃	C₂²×C₄	1	4	yes	—
251	C₄×Dic₄₃	C₂²×C₄	1	4	yes	—
252	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
253	C₄×Dic₄₃	C₂⁴	1	4	yes	—
254	C₄×Dic₄₃	C₂⁴	1	2	yes	—
255	#10621877	—	2	4	no	—
256	C₂×C₄₃⋊C₈	—	2	2	no	—
257	C₂×C₄₃⋊C₈	—	2	2	no	—
258	C₂×C₄₃⋊C₈	C₂⁴	1	4	yes	—
259	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
260	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
261	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
262	C₂²×D₄₃	—	2	2	no	—
263	C₂²×D₄₃	—	4	1	no	—
264	C₂²×D₄₃	—	4	1	no	—
265	C₂²×D₄₃	C₂³×C₄	1	2	yes	—
266	Q₈×C₄₃	—	4	2	no	—
267	Q₈×C₄₃	—	4	2	no	—
268	C₂×C₄×C₄₃	—	4	1	no	—
269	C₂×C₄×C₄₃	—	4	1	no	—
270	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
271	C₂×C₄×C₄₃	C₂³×C₄	1	4	yes	—
272	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
273	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
274	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
275	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
276	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
277	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
278	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
279	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
280	C₂×Dic₄₃	—	2	2	no	—
281	C₂×Dic₄₃	—	4	1	no	—
282	C₂×Dic₄₃	—	4	1	no	—
283	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
284	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
285	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
286	C₂×Dic₄₃	C₂³×C₄	1	4	yes	—
287	C₂×Dic₄₃	C₂³×C₄	1	4	yes	—
288	C₄×D₄₃	—	2	4	no	—
289	C₄×D₄₃	—	2	2	no	—
290	C₄×D₄₃	—	2	2	no	—
291	C₄×D₄₃	—	4	4	no	—
292	C₄×D₄₃	—	4	4	no	—
293	Dic₈₆	—	4	2	no	—
294	Dic₈₆	—	4	2	no	—
295	Dic₈₆	—	4	4	no	—
296	Dic₈₆	—	4	4	no	—
297	C₈×C₄₃	—	2	1	no	—
298	C₈×C₄₃	—	2	1	no	—
299	C₈×C₄₃	—	2	1	no	—
300	C₈×C₄₃	—	2	1	no	—
301	C₈×C₄₃	—	2	4	no	—
302	C₄₃⋊C₈	—	2	2	no	—
303	C₄₃⋊C₈	—	2	2	no	—
304	C₄₃⋊C₈	—	2	4	no	—
305	#60252	—	43	1	no	maximal, Sylow
306	C₂²×C₄₃	—	2	1	no	—
307	C₂²×C₄₃	—	2	1	no	—
308	C₂²×C₄₃	#519	1	2	yes	—
309	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
310	C₂×D₄₃	—	2	2	no	—
311	C₂×D₄₃	—	2	2	no	—
312	C₂×D₄₃	—	2	2	no	—
313	C₂×D₄₃	—	8	2	no	—
314	C₄×C₄₃	—	2	1	no	—
315	C₄×C₄₃	—	2	1	no	—
316	C₄×C₄₃	—	2	4	no	—
317	C₄×C₄₃	—	2	4	no	—
318	C₄×C₄₃	—	2	1	no	—
319	C₄×C₄₃	—	2	1	no	—
320	C₄×C₄₃	#519	1	2	yes	—
321	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
322	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
323	Dic₄₃	—	2	2	no	—
324	Dic₄₃	—	2	4	no	—
325	Dic₄₃	—	2	4	no	—
326	Dic₄₃	—	2	2	no	—
327	Dic₄₃	—	2	2	no	—
328	#3458	—	43	1	no	—
329	#2987	—	43	4	no	—
330	#2986	—	43	4	no	—
331	#2985	—	43	4	no	—
332	#2985	—	43	4	no	—
333	#2962	—	43	2	no	—
334	#2962	—	43	2	no	—
335	#2961	—	43	1	no	—
336	#2961	—	43	1	no	—
337	#2960	—	43	1	no	—
338	#2960	D₄₃	1	1	yes	characteristic, complemented
339	#2924	—	43	2	no	—
340	#2924	—	43	2	no	—
341	#2921	—	43	1	no	—
342	C₂×#433	—	43	1	no	—
343	C₂×C₄₃	—	2	2	no	—
344	C₂×C₄₃	C₂×#519	1	1	yes	characteristic
345	C₂×C₄₃	#3573	1	1	yes	characteristic
346	C₂×C₄₃	#3573	1	1	yes	characteristic
347	D₄₃	—	4	2	no	—
348	#544	—	43	2	no	—
349	#544	—	43	2	no	—
350	#544	—	43	2	no	—
351	#544	—	43	2	no	—
352	#544	—	43	2	no	—
353	#544	—	43	2	no	—
354	#543	—	43	2	no	—
355	#543	—	43	2	no	—
356	#533	—	43	4	no	—
357	#533	—	43	4	no	—
358	#533	—	43	2	no	—
359	#533	—	43	1	no	—
360	#533	C₂×D₄₃	1	1	yes	characteristic
361	C₂×#117	—	43	2	no	—
362	C₂×#117	—	43	1	no	—
363	#446	—	43	4	no	—
364	#446	—	43	4	no	—
365	#446	—	43	4	no	—
366	#446	—	43	4	no	—
367	#446	—	43	4	no	—
368	#446	—	43	4	no	—
369	#446	—	43	4	no	—
370	#446	—	43	4	no	—
371	#446	—	43	4	no	—
372	#446	—	43	2	no	—
373	#446	—	43	2	no	—
374	#446	—	43	4	no	—
375	#446	C₂×D₄₃	1	2	yes	complemented
376	#446	C₂×D₄₃	1	2	yes	complemented
377	C₈×Q₈	—	43	4	no	—
378	C₈×Q₈	—	43	2	no	—
379	C₈×Q₈	—	43	2	no	—
380	C₈×Q₈	—	43	4	no	—
381	C₈×Q₈	C₂×D₄₃	1	2	yes	complemented
382	C₈×Q₈	C₂×D₄₃	1	2	yes	complemented
383	#433	—	43	4	no	—
384	#433	—	43	4	no	—
385	#433	—	43	4	no	—
386	#433	—	43	4	no	—
387	#433	—	43	4	no	—
388	#433	—	43	2	no	—
389	#433	—	43	2	no	—
390	#433	—	43	2	no	—
391	#433	—	43	2	no	—
392	#433	—	43	4	no	—
393	#432	—	43	4	no	—
394	#432	—	43	4	no	—
395	#431	—	43	4	no	—
396	#431	—	43	4	no	—
397	#424	—	43	2	no	—
398	#424	—	43	2	no	—
399	#424	—	43	2	no	—
400	#424	C₂×D₄₃	1	2	yes	—
401	#423	—	43	1	no	—
402	#423	C₂×D₄₃	1	1	yes	characteristic
403	C₂×C₄⋊C₈	—	43	1	no	—
404	C₂×C₄⋊C₈	—	43	1	no	—
405	#407	—	43	2	no	—
406	C₂×C₂²⋊C₈	—	43	1	no	—
407	C₂×C₂²⋊C₈	—	43	1	no	—
408	#405	—	43	2	no	—
409	#405	—	43	2	no	—
410	#405	—	43	2	no	—
411	#405	C₂×D₄₃	1	2	yes	—
412	C₄×M₁₆	—	43	2	no	—
413	C₂×#97	—	43	1	no	—
414	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
415	C₄₃	#60252	1	1	yes	characteristic, complemented, Sylow
416	C₂³×C₄	—	43	1	no	—
417	C₂×M₁₆	—	43	2	no	—
418	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
419	C₂²×C₈	—	43	1	no	—
420	C₂²×C₈	—	43	1	no	—
421	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
422	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
423	C₄⋊Q₈	—	43	4	no	—
424	C₄⋊Q₈	—	43	4	no	—
425	C₄⋊Q₈	—	43	4	no	—
426	C₄⋊Q₈	—	43	4	no	—
427	C₄⋊Q₈	—	43	2	no	—
428	C₄⋊Q₈	—	43	2	no	—
429	C₄⋊Q₈	—	43	1	no	—
430	C₄⋊Q₈	—	43	1	no	—
431	C₄⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
432	C₄⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
433	#125	—	43	4	no	—
434	#125	—	43	4	no	—
435	#125	—	43	4	no	—
436	#125	—	43	4	no	—
437	#125	—	43	2	no	—
438	#125	—	43	2	no	—
439	#125	—	43	2	no	—
440	#125	C₄×D₄₃	1	2	yes	—
441	C₂²⋊Q₈	—	43	4	no	—
442	C₂²⋊Q₈	—	43	4	no	—
443	C₂²⋊Q₈	—	43	2	no	—
444	C₂²⋊Q₈	—	43	2	no	—
445	C₂²⋊Q₈	—	43	4	no	—
446	C₂²⋊Q₈	—	43	4	no	—
447	C₂²⋊Q₈	—	43	4	no	—
448	C₂²⋊Q₈	—	43	4	no	—
449	C₂²⋊Q₈	—	43	4	no	—
450	C₂²⋊Q₈	—	43	4	no	—
451	C₂²⋊Q₈	—	43	4	no	—
452	C₂²⋊Q₈	—	43	4	no	—
453	C₂²⋊Q₈	C₄×D₄₃	1	2	yes	—
454	C₂²⋊Q₈	C₄×D₄₃	1	2	yes	—
455	C₄×Q₈	—	43	4	no	—
456	C₄×Q₈	—	43	4	no	—
457	C₄×Q₈	—	43	2	no	—
458	C₄×Q₈	—	43	2	no	—
459	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
460	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
461	#117	—	43	2	no	—
462	#117	—	43	2	no	—
463	#117	—	43	2	no	—
464	#117	—	43	4	no	—
465	#117	—	43	2	no	—
466	#117	—	43	2	no	—
467	#117	—	43	4	no	—
468	#117	—	43	2	no	—
469	#117	—	43	2	no	—
470	#117	C₂²×D₄₃	1	2	yes	—
471	C₂×C₄⋊C₄	—	43	1	no	—
472	C₂×C₄⋊C₄	—	43	1	no	—
473	C₂×C₄⋊C₄	—	43	2	no	—
474	C₂×C₄⋊C₄	—	43	2	no	—
475	C₂×C₂²⋊C₄	—	43	1	no	—
476	C₂×C₂²⋊C₄	—	43	1	no	—
477	C₂×C₂²⋊C₄	—	43	4	no	—
478	C₂×C₄²	—	43	1	no	—
479	C₂×C₄²	—	43	4	no	—
480	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
481	C₄⋊C₈	—	43	2	no	—
482	C₄⋊C₈	—	43	2	no	—
483	C₄⋊C₈	—	43	2	no	—
484	C₄⋊C₈	—	43	2	no	—
485	C₄⋊C₈	—	43	4	no	—
486	C₄⋊C₈	—	43	4	no	—
487	C₄⋊C₈	—	43	4	no	—
488	C₄⋊C₈	—	43	4	no	—
489	C₄⋊C₈	—	43	2	no	—
490	C₄⋊C₈	—	43	2	no	—
491	C₄⋊C₈	—	43	4	no	—
492	C₄⋊C₈	—	43	4	no	—
493	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
494	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
495	C₄⋊C₈	C₂²×D₄₃	1	4	yes	—
496	C₄⋊C₈	C₂²×D₄₃	1	4	yes	—
497	C₂²⋊C₈	—	43	2	no	—
498	C₂²⋊C₈	—	43	2	no	—
499	C₂²⋊C₈	—	43	2	no	—
500	C₂²⋊C₈	—	43	2	no	—
501	C₂²⋊C₈	—	43	4	no	—
502	C₂²⋊C₈	—	43	4	no	—
503	#97	—	43	4	no	—
504	#97	—	43	4	no	—
505	#97	—	43	4	no	—
506	#97	—	43	2	no	—
507	#97	—	43	2	no	—
508	#97	—	43	4	no	—
509	#97	C₂²×D₄₃	1	4	yes	—
510	C₄×C₈	—	43	4	no	—
511	C₄×C₈	—	43	4	no	—
512	C₄×C₈	—	43	4	no	—
513	C₄×C₈	—	43	4	no	—
514	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
515	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
516	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
517	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
518	C₄×C₈	C₂²×D₄₃	1	4	yes	—
519	C₂⁴	—	43	1	no	—
520	C₂×Q₈	—	43	4	no	—
521	C₂×Q₈	—	43	4	no	—
522	C₂×Q₈	—	43	2	no	—
523	C₂×Q₈	—	43	2	no	—
524	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
525	C₂×Q₈	C₂×C₄×D₄₃	1	2	yes	—
526	C₂²×C₄	—	43	1	no	—
527	C₂²×C₄	—	43	1	no	—
528	C₂²×C₄	—	43	1	no	—
529	C₂²×C₄	—	43	2	no	—
530	C₂²×C₄	—	43	2	no	—
531	C₂²×C₄	—	43	4	no	—
532	C₂²×C₄	—	43	4	no	—
533	C₂²×C₄	—	86	2	no	—
534	C₂²×C₄	—	86	2	no	—
535	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
536	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
537	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
538	M₁₆	—	2	4	no	—
539	M₁₆	—	86	4	no	—
540	C₂×C₈	—	2	2	no	—
541	C₂×C₈	—	2	2	no	—
542	C₂×C₈	—	43	4	no	—
543	C₂×C₈	—	43	2	no	—
544	C₂×C₈	—	43	2	no	—
545	C₂×C₈	—	86	2	no	—
546	C₂×C₈	—	86	2	no	—
547	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
548	C₂×C₈	C₂³×D₄₃	1	4	yes	—
549	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
550	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
551	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
552	C₄⋊C₄	—	43	4	no	—
553	C₄⋊C₄	—	43	4	no	—
554	C₄⋊C₄	—	43	2	no	—
555	C₄⋊C₄	—	43	2	no	—
556	C₄⋊C₄	—	43	2	no	—
557	C₄⋊C₄	—	43	2	no	—
558	C₄⋊C₄	—	43	2	no	—
559	C₄⋊C₄	—	43	2	no	—
560	C₄⋊C₄	—	43	4	no	—
561	C₄⋊C₄	—	43	4	no	—
562	C₄⋊C₄	—	43	4	no	—
563	C₄⋊C₄	—	43	4	no	—
564	C₄⋊C₄	—	43	4	no	—
565	C₄⋊C₄	—	43	4	no	—
566	C₄⋊C₄	—	43	4	no	—
567	C₄⋊C₄	—	43	4	no	—
568	C₄⋊C₄	—	43	2	no	—
569	C₄⋊C₄	—	43	2	no	—
570	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
571	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
572	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
573	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
574	C₄⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
575	C₄⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
576	C₂²⋊C₄	—	43	4	no	—
577	C₂²⋊C₄	—	43	4	no	—
578	C₂²⋊C₄	—	43	4	no	—
579	C₂²⋊C₄	—	43	2	no	—
580	C₂²⋊C₄	—	43	2	no	—
581	C₂²⋊C₄	—	43	2	no	—
582	C₂²⋊C₄	—	43	2	no	—
583	C₂²⋊C₄	C₂×C₄×D₄₃	1	4	yes	—
584	C₄²	—	43	4	no	—
585	C₄²	—	43	4	no	—
586	C₄²	—	43	2	no	—
587	C₄²	—	43	2	no	—
588	C₄²	—	43	4	no	—
589	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
590	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
591	C₄²	C₂³×D₄₃	1	4	yes	—
592	C₄²	C₂³×D₄₃	1	1	yes	characteristic
593	C₄²	C₂³×D₄₃	1	1	yes	characteristic
594	C₂³	—	43	2	no	—
595	C₂³	—	86	2	no	—
596	C₂³	—	172	1	no	—
597	C₂³	—	172	1	no	—
598	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
599	Q₈	—	4	2	no	—
600	Q₈	—	4	2	no	—
601	Q₈	—	172	2	no	—
602	Q₈	—	172	2	no	—
603	Q₈	—	172	4	no	—
604	Q₈	—	172	4	no	—
605	C₂×C₄	—	4	1	no	—
606	C₂×C₄	—	4	1	no	—
607	C₂×C₄	—	43	2	no	—
608	C₂×C₄	—	43	4	no	—
609	C₂×C₄	—	43	4	no	—
610	C₂×C₄	—	43	2	no	—
611	C₂×C₄	—	43	2	no	—
612	C₂×C₄	—	86	2	no	—
613	C₂×C₄	—	86	4	no	—
614	C₂×C₄	—	86	2	no	—
615	C₂×C₄	—	86	2	no	—
616	C₂×C₄	—	172	4	no	—
617	C₂×C₄	—	172	4	no	—
618	C₂×C₄	—	172	1	no	—
619	C₂×C₄	—	172	1	no	—
620	C₂×C₄	C₂²×C₄×D₄₃	1	4	yes	—
621	C₂×C₄	C₂²×C₄×D₄₃	1	4	yes	—
622	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
623	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
624	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
625	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
626	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
627	C₂×C₄	#13063372	1	2	yes	—
628	C₂×C₄	#13063373	1	2	yes	—
629	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
630	C₈	—	2	1	no	—
631	C₈	—	2	1	no	—
632	C₈	—	2	4	no	—
633	C₈	—	2	1	no	—
634	C₈	—	2	1	no	—
635	C₈	—	86	2	no	—
636	C₈	—	86	2	no	—
637	C₈	—	86	4	no	—
638	C₂²	—	2	1	no	—
639	C₂²	—	2	1	no	—
640	C₂²	—	86	2	no	—
641	C₂²	—	86	2	no	—
642	C₂²	—	86	2	no	—
643	C₂²	—	344	2	no	—
644	C₂²	#14583375	1	2	yes	—
645	C₂²	C₂³×C₄×D₄₃	1	1	yes	characteristic
646	C₄	—	2	1	no	—
647	C₄	—	2	1	no	—
648	C₄	—	2	1	no	—
649	C₄	—	2	1	no	—
650	C₄	—	2	4	no	—
651	C₄	—	2	4	no	—
652	C₄	—	86	2	no	—
653	C₄	—	86	4	no	—
654	C₄	—	86	4	no	—
655	C₄	—	86	2	no	—
656	C₄	—	86	2	no	—
657	C₄	#14583375	1	2	yes	—
658	C₄	C₂×#13063372	1	1	yes	characteristic
659	C₄	C₂×#13063373	1	1	yes	characteristic
660	C₂	—	2	2	no	—
661	C₂	—	172	2	no	—
662	C₂	C₂×#14583375	1	1	yes	characteristic
663	C₂	#19149306	1	1	yes	characteristic
664	C₂	#19149306	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁴×C₄
Fitting	C₄₃×#2960	C₂
prime radical	C₂³×D₄₃	C₂²×C₄
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	#2960	D₄₃
hypocenter	C₄₃	#60252
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #2960

Complements

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

N	H ≅ G/N	type
2. #19143698	C₂	semidirect
3. #19143695	C₂	semidirect
4. #19143688	C₂	semidirect
5. #19143686	C₂	semidirect
6. #19143541	C₂	semidirect
7. #19143539	C₂	semidirect
8. #19143536	C₂	semidirect
9. #19143532	C₂	semidirect
10. #19143529	C₂	semidirect
15. C₄₃×#2960	C₂	semidirect
30. #14583030	C₂²	semidirect
31. #14583030	C₂²	semidirect
32. #14583029	C₂²	semidirect
33. #14583029	C₂²	semidirect
34. #14583029	C₂²	semidirect
35. #14583028	C₂²	semidirect
36. #14583028	C₂²	semidirect
37. #14583028	C₂²	semidirect
38. #14583028	C₂²	semidirect
39. #14583027	C₂²	semidirect
40. #14583027	C₂²	semidirect
41. #14583026	C₂²	semidirect
42. C₈×Dic₈₆	C₂²	semidirect
43. C₈×Dic₈₆	C₂²	semidirect
44. C₈×Dic₈₆	C₂²	semidirect
45. #14583023	C₂²	semidirect
75. C₄₃×#446	C₂²	semidirect
76. C₄₃×#446	C₂²	semidirect
77. C₈×Q₈×C₄₃	C₂²	semidirect
78. C₈×Q₈×C₄₃	C₂²	semidirect
338. #2960	D₄₃	semidirect
375. #446	C₂×D₄₃	semidirect
376. #446	C₂×D₄₃	semidirect
381. C₈×Q₈	C₂×D₄₃	semidirect
382. C₈×Q₈	C₂×D₄₃	semidirect
415. C₄₃	#60252	semidirect

Maximal subgroups

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

subgroup	index
#19147998	2
#19143698	2
#19143695	2
#19143688	2
#19143686	2
#19143541	2
#19143539	2
#19143536	2
#19143532	2
#19143529	2
#19143252	2
#19143250	2
#19143232	2
C₂×#14582958	2
C₄₃×#2960	2
#60252	43