Subgroups — #25962860

Order 11008.

1744 conjugacy classes of subgroups.

The subgroup lattice has 1098 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148208	C₂	1	1	yes	maximal, characteristic
2	#19143744	C₂	1	1	yes	maximal, characteristic, complemented
3	#19143741	C₂	1	2	yes	maximal, complemented
4	#19143739	C₂	1	1	yes	maximal, characteristic, complemented
5	#19143738	C₂	1	2	yes	maximal, complemented
6	#19143724	C₂	1	1	yes	maximal, characteristic, complemented
7	#19143723	C₂	1	1	yes	maximal, characteristic, complemented
8	#19143723	C₂	1	2	yes	maximal, complemented
9	#19143695	C₂	1	1	yes	maximal, characteristic, complemented
10	#19143694	C₂	1	2	yes	maximal, complemented
11	#19143675	C₂	1	1	yes	maximal, characteristic, complemented
12	#19143674	C₂	1	1	yes	maximal, characteristic, complemented
13	#19143596	C₂	1	1	yes	maximal, characteristic, complemented
14	#19143595	C₂	1	2	yes	maximal, complemented
15	#19143592	C₂	1	2	yes	maximal, complemented
16	#19143557	C₂	1	1	yes	maximal, characteristic, complemented
17	#19143555	C₂	1	2	yes	maximal, complemented
18	C₈×#10621900	C₂	1	1	yes	maximal, characteristic, complemented
19	M₁₆×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143547	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143527	C₂	1	2	yes	maximal, complemented
22	#19143526	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#2969	C₂	1	1	yes	maximal, characteristic, complemented
24	#14583626	C₄	1	1	yes	characteristic
25	#14583618	C₄	1	1	yes	characteristic
26	#14583616	C₄	1	2	yes	—
27	#14583591	C₄	1	1	yes	characteristic
28	#14583587	C₄	1	1	yes	characteristic
29	#14583586	C₄	1	2	yes	—
30	#14583585	C₄	1	2	yes	—
31	#14583562	C₄	1	1	yes	characteristic
32	#14583557	C₄	1	1	yes	characteristic
33	#14583555	C₄	1	1	yes	characteristic
34	#14583549	C₄	1	1	yes	characteristic
35	#14583547	C₄	1	2	yes	—
36	#14583453	C₂²	1	1	yes	characteristic
37	#14583452	C₂²	1	2	yes	—
38	#14583431	C₂²	1	1	yes	characteristic
39	#14583429	C₂²	1	2	yes	—
40	#14583427	C₂²	1	2	yes	—
41	C₄×#10621898	C₂²	1	1	yes	characteristic
42	C₄×#10621900	C₂²	1	1	yes	characteristic
43	C₄×#10621900	C₂²	1	2	yes	—
44	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
45	C₄×Q₈×D₄₃	C₂²	1	1	yes	characteristic
46	#14583030	C₂²	1	1	yes	characteristic
47	#14583029	C₂²	1	1	yes	characteristic
48	#14583029	C₂²	1	1	yes	characteristic
49	#14583028	C₂²	1	2	yes	—
50	#14583028	C₂²	1	2	yes	—
51	#14583027	C₂²	1	1	yes	characteristic
52	#14583027	C₂²	1	2	yes	—
53	#14583027	C₂²	1	2	yes	—
54	#14583027	C₂²	1	1	yes	characteristic
55	#14583027	C₂²	1	2	yes	—
56	#14583027	C₂²	1	2	yes	—
57	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
58	C₈×Dic₈₆	C₂²	1	2	yes	—
59	C₈×Dic₈₆	C₂²	1	2	yes	—
60	C₈×Dic₈₆	C₂²	1	2	yes	—
61	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
62	C₈×Dic₈₆	C₂²	1	2	yes	—
63	C₈×Dic₈₆	C₂²	1	2	yes	—
64	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
65	#14583023	C₂²	1	2	yes	—
66	#14583023	C₂²	1	2	yes	—
67	#14583023	C₂²	1	1	yes	characteristic
68	#14583023	C₂²	1	1	yes	characteristic
69	#14583023	C₂²	1	1	yes	characteristic
70	#14583023	C₂²	1	1	yes	characteristic
71	#14582978	C₂²	1	2	yes	—
72	#14582977	C₂²	1	2	yes	—
73	#14582977	C₂²	1	1	yes	characteristic
74	#14582975	C₂²	1	1	yes	characteristic
75	#14582975	C₂²	1	2	yes	—
76	#14582975	C₂²	1	2	yes	—
77	#14582975	C₂²	1	1	yes	characteristic
78	#14582974	C₂²	1	2	yes	—
79	#14582974	C₂²	1	2	yes	—
80	#14582974	C₂²	1	2	yes	—
81	#14582974	C₂²	1	2	yes	—
82	#14582972	C₂²	1	1	yes	characteristic
83	#14582972	C₂²	1	1	yes	characteristic
84	#14582971	C₂²	1	2	yes	—
85	#14582970	C₂²	1	2	yes	—
86	#14582968	C₂²	1	1	yes	characteristic
87	#14582968	C₂²	1	1	yes	characteristic
88	#14582967	C₂²	1	2	yes	—
89	D₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
90	C₈×C₂²⋊D₄₃	C₂²	1	2	yes	—
91	(C₂²⋊D₄₃)⋊C₈	C₂²	1	2	yes	—
92	#14582960	C₂²	1	2	yes	—
93	#14582959	C₂²	1	2	yes	—
94	#14582958	C₂²	1	2	yes	—
95	#14582957	C₂²	1	2	yes	—
96	#14582957	C₂²	1	2	yes	—
97	#14582952	C₂²	1	1	yes	characteristic
98	#14582951	C₂²	1	1	yes	characteristic
99	#14582951	C₂²	1	1	yes	characteristic
100	#14582951	C₂²	1	2	yes	—
101	#14582950	C₂²	1	1	yes	characteristic
102	#14582950	C₂²	1	2	yes	—
103	#14582950	C₂²	1	1	yes	characteristic
104	#14582949	C₂²	1	2	yes	—
105	#14582949	C₂²	1	2	yes	—
106	#14582949	C₂²	1	2	yes	—
107	#14582949	C₂²	1	2	yes	—
108	#14582927	C₂²	1	2	yes	—
109	#14582926	C₂²	1	2	yes	—
110	#14582924	C₂²	1	2	yes	—
111	#14582923	C₂²	1	1	yes	characteristic
112	#14582922	C₂²	1	2	yes	—
113	#14582922	C₂²	1	2	yes	—
114	#14582921	C₂²	1	1	yes	characteristic
115	#14582921	C₂²	1	2	yes	—
116	#14582921	C₂²	1	1	yes	characteristic
117	#14582856	C₂²	1	2	yes	—
118	#14582854	C₂²	1	2	yes	—
119	#14582851	C₂²	1	2	yes	—
120	M₁₆×Dic₄₃	C₂²	1	2	yes	—
121	C₄×#10621872	C₂²	1	1	yes	characteristic
122	C₂×C₈×Dic₄₃	C₂²	1	2	yes	—
123	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
124	C₄₃×#529	C₂²	1	1	yes	characteristic
125	C₄₃×#446	C₂²	1	1	yes	characteristic
126	C₈×Q₈×C₄₃	C₂²	1	1	yes	characteristic
127	C₄₃×#436	C₂²	1	1	yes	characteristic
128	C₄₃×#436	C₂²	1	2	yes	—
129	C₄₃×#435	C₂²	1	2	yes	—
130	C₈×D₄×C₄₃	C₂²	1	1	yes	characteristic
131	C₄₃×#433	C₂²	1	2	yes	—
132	C₄₃×#431	C₂²	1	1	yes	characteristic
133	C₄₃×#405	C₂²	1	2	yes	—
134	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
135	C₂×#10621898	C₂×C₄	1	1	yes	characteristic
136	C₂×#10621900	C₂×C₄	1	1	yes	characteristic
137	C₂×#10621900	C₂×C₄	1	2	yes	—
138	C₂²×Dic₈₆	C₂×C₄	1	1	yes	characteristic
139	C₂×Q₈×D₄₃	C₂×C₄	1	1	yes	characteristic
140	C₂×#10621877	C₂³	1	2	yes	—
141	C₂×#10621877	C₂³	1	2	yes	—
142	C₂×#10621872	C₂³	1	1	yes	characteristic
143	C₂×#10621872	C₂³	1	1	yes	characteristic
144	C₂×#10621872	C₂³	1	2	yes	—
145	C₂×#10621872	C₂³	1	2	yes	—
146	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
147	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
148	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
149	#13063324	C₂×C₄	1	2	yes	—
150	#13063324	C₂×C₄	1	2	yes	—
151	#13063324	C₂×C₄	1	1	yes	characteristic
152	#13063323	C₂×C₄	1	1	yes	characteristic
153	#13063320	C₂×C₄	1	2	yes	—
154	#13063320	C₂×C₄	1	2	yes	—
155	#13063318	C₂×C₄	1	2	yes	—
156	#13063318	C₂×C₄	1	2	yes	—
157	#13063318	C₂×C₄	1	2	yes	—
158	#13063316	C₂×C₄	1	2	yes	—
159	#13063316	C₂×C₄	1	2	yes	—
160	#13063316	C₂×C₄	1	1	yes	characteristic
161	#13063315	C₂×C₄	1	2	yes	—
162	#13063315	C₂×C₄	1	2	yes	—
163	#13063315	C₂×C₄	1	2	yes	—
164	#13063312	C₂×C₄	1	1	yes	characteristic
165	#13063311	C₂×C₄	1	2	yes	—
166	#13063311	C₂×C₄	1	2	yes	—
167	#13063310	C₂×C₄	1	2	yes	—
168	#13063309	C₂×C₄	1	2	yes	—
169	#13063307	C₂×C₄	1	2	yes	—
170	#13063307	C₂×C₄	1	2	yes	—
171	#13063306	C₂×C₄	1	2	yes	—
172	#13063305	C₂×C₄	1	1	yes	characteristic
173	#13063305	C₂×C₄	1	1	yes	characteristic
174	#13063303	C₂×C₄	1	2	yes	—
175	#13063303	C₂×C₄	1	2	yes	—
176	#13063302	C₂×C₄	1	2	yes	—
177	#13063302	C₂×C₄	1	2	yes	—
178	#13063302	C₂×C₄	1	2	yes	—
179	#13063302	C₂×C₄	1	2	yes	—
180	#13063302	C₂×C₄	1	2	yes	—
181	#13063301	C₂×C₄	1	1	yes	characteristic
182	#13063298	C₂×C₄	1	2	yes	—
183	#13063297	C₂×C₄	1	2	yes	—
184	#13063296	C₂×C₄	1	1	yes	characteristic
185	Q₈×Dic₄₃	C₂×C₄	1	1	yes	characteristic
186	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
187	C₄×Dic₈₆	C₂×C₄	1	2	yes	—
188	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
189	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
190	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
191	C₄×Dic₈₆	C₂³	1	2	yes	—
192	C₄×Dic₈₆	C₂³	1	2	yes	—
193	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
194	C₄×Dic₈₆	C₂³	1	2	yes	—
195	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
196	#13063290	C₂×C₄	1	1	yes	characteristic
197	#13063290	C₂×C₄	1	1	yes	characteristic
198	#13063290	C₂×C₄	1	2	yes	—
199	#13063290	C₂×C₄	1	2	yes	—
200	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
201	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
202	D₄×Dic₄₃	C₂×C₄	1	2	yes	—
203	D₄×Dic₄₃	C₂×C₄	1	1	yes	characteristic
204	C₄×C₂²⋊D₄₃	C₂×C₄	1	1	yes	characteristic
205	C₄×C₂²⋊D₄₃	C₂×C₄	1	1	yes	characteristic
206	C₄×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
207	C₄×C₂²⋊D₄₃	C₂³	1	2	yes	—
208	C₄×C₂²⋊D₄₃	C₂³	1	2	yes	—
209	C₄×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
210	(C₂²⋊D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
211	(C₂²⋊D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
212	(C₂²⋊D₄₃)⋊C₄	C₂×C₄	1	2	yes	—
213	#13063284	C₂×C₄	1	1	yes	characteristic
214	#13063284	C₂³	1	2	yes	—
215	#13063283	C₂×C₄	1	2	yes	—
216	#13063283	C₂×C₄	1	1	yes	characteristic
217	#13063282	C₂×C₄	1	1	yes	characteristic
218	#13063282	C₂×C₄	1	1	yes	characteristic
219	#13063282	C₂³	1	2	yes	—
220	#13063281	C₂×C₄	1	2	yes	—
221	#13063281	C₂×C₄	1	2	yes	—
222	#13063281	C₂×C₄	1	2	yes	—
223	C₂×C₄⋊Dic₄₃	C₂×C₄	1	1	yes	characteristic
224	C₂×Dic₄₃⋊C₄	C₂×C₄	1	2	yes	—
225	C₄⋊C₄×D₄₃	C₂×C₄	1	2	yes	—
226	C₄⋊C₄×D₄₃	C₂×C₄	1	1	yes	characteristic
227	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
228	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
229	C₄²×D₄₃	C₂³	1	1	yes	characteristic
230	C₄²×D₄₃	C₂³	1	1	yes	characteristic
231	C₄²×D₄₃	C₂³	1	2	yes	—
232	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
233	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
234	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
235	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
236	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
237	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
238	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
239	Dic₄₃⋊C₈	C₂³	1	2	yes	—
240	Dic₄₃⋊C₈	C₂³	1	2	yes	—
241	Dic₄₃⋊C₈	C₂³	1	2	yes	—
242	Dic₄₃⋊C₈	C₂³	1	2	yes	—
243	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
244	Dic₄₃⋊C₈	C₂³	1	2	yes	—
245	Dic₄₃⋊C₈	C₂³	1	2	yes	—
246	Dic₄₃⋊C₈	C₂³	1	2	yes	—
247	Dic₄₃⋊C₈	C₂³	1	2	yes	—
248	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
249	Dic₄₃⋊C₈	C₂³	1	2	yes	—
250	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
251	Dic₄₃⋊C₈	C₂³	1	2	yes	—
252	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
253	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
254	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
255	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
256	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
257	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
258	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
259	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
260	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
261	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
262	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
263	#13063236	C₂³	1	2	yes	—
264	#13063235	C₂³	1	1	yes	characteristic
265	#13063235	C₂³	1	1	yes	characteristic
266	#13063235	C₂³	1	2	yes	—
267	#13063235	C₂³	1	2	yes	—
268	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
269	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
270	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
271	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
272	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
273	C₈×Dic₄₃	C₂³	1	2	yes	—
274	C₈×Dic₄₃	C₂³	1	2	yes	—
275	C₈×Dic₄₃	C₂³	1	2	yes	—
276	C₈×Dic₄₃	C₂³	1	2	yes	—
277	C₈×Dic₄₃	C₂³	1	2	yes	—
278	C₈×Dic₄₃	C₂³	1	2	yes	—
279	C₈×Dic₄₃	C₂³	1	2	yes	—
280	C₈×Dic₄₃	C₂³	1	2	yes	—
281	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
282	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
283	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
284	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
285	#126×C₄₃	C₂×C₄	1	2	yes	—
286	#125×C₄₃	C₂×C₄	1	1	yes	characteristic
287	#124×C₄₃	C₂×C₄	1	1	yes	characteristic
288	#123×C₄₃	C₂×C₄	1	2	yes	—
289	C₂²⋊Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
290	#121×C₄₃	C₂×C₄	1	1	yes	characteristic
291	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
292	C₄×D₄×C₄₃	C₂³	1	2	yes	—
293	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
294	#117×C₄₃	C₂³	1	2	yes	—
295	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
296	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
297	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
298	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
299	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
300	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
301	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
302	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
303	#97×C₄₃	C₂³	1	2	yes	—
304	#97×C₄₃	C₂³	1	1	yes	characteristic
305	#97×C₄₃	C₂³	1	1	yes	characteristic
306	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
307	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
308	C₄×C₈×C₄₃	C₂³	1	2	yes	—
309	C₄×C₈×C₄₃	C₂³	1	2	yes	—
310	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
311	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
312	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
313	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
314	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
315	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
316	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
317	C₂×C₂²⋊D₄₃	C₂²×C₄	1	1	yes	characteristic
318	C₂×C₂²⋊D₄₃	C₂²×C₄	1	2	yes	—
319	C₂×C₂²⋊D₄₃	C₂²×C₄	1	2	yes	—
320	C₂×C₂²⋊D₄₃	C₂²×C₄	1	1	yes	characteristic
321	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
322	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
323	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
324	C₂²×Dic₄₃	C₂²×C₄	1	2	yes	—
325	Q₈×D₄₃	—	2	4	no	—
326	#10621900	—	2	4	no	—
327	#10621900	—	4	4	no	—
328	#10621898	—	4	2	no	—
329	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
330	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
331	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
332	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
333	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
334	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
335	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
336	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
337	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
338	C₂×Dic₈₆	—	2	4	no	—
339	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
340	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
341	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
342	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
343	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
344	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
345	M₁₆×C₄₃	—	2	2	no	—
346	M₁₆×C₄₃	—	4	1	no	—
347	M₁₆×C₄₃	—	4	2	no	—
348	C₂×C₈×C₄₃	—	2	4	no	—
349	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
350	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
351	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
353	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
354	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
355	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
356	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
357	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
358	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
359	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
360	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
361	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
362	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
363	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
364	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
365	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
366	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
367	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
368	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
369	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
370	C₄²×C₄₃	C₂⁴	1	2	yes	—
371	C₂²⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
372	C₂²⋊Dic₄₃	C₂²×C₄	1	2	yes	—
373	C₂²⋊Dic₄₃	C₂²×C₄	1	2	yes	—
374	C₂²⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
375	C₂²⋊Dic₄₃	C₂²×C₄	1	2	yes	—
376	C₂²⋊Dic₄₃	C₂²×C₄	1	2	yes	—
377	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	1	yes	characteristic
378	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	1	yes	characteristic
379	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	1	yes	characteristic
380	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	1	yes	characteristic
381	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
382	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
383	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
384	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
385	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
386	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
387	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
388	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
389	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
390	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
391	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
392	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
393	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
394	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
395	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
396	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
397	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
398	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
399	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
400	Dic₄₃⋊C₄	C₂²×C₄	1	1	yes	characteristic
401	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
402	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
403	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
404	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
405	Dic₄₃⋊C₄	C₂²×C₄	1	1	yes	characteristic
406	Dic₄₃⋊C₄	C₂²×C₄	1	1	yes	characteristic
407	Dic₄₃⋊C₄	C₂²×C₄	1	1	yes	characteristic
408	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
409	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
410	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
411	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
412	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
413	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
414	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
415	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
416	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
417	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
418	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
419	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
420	C₄×Dic₄₃	C₂⁴	1	2	yes	—
421	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
422	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
423	C₄×Dic₄₃	C₂⁴	1	2	yes	—
424	#10621877	—	4	2	no	—
425	#10621877	—	4	2	no	—
426	C₂×C₄₃⋊C₈	—	4	2	no	—
427	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
428	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
429	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
430	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
431	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
432	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
433	#10621872	—	2	2	no	—
434	#10621872	—	4	2	no	—
435	#10621872	—	4	1	no	—
436	#10621872	—	4	2	no	—
437	C₈×D₄₃	—	2	2	no	—
438	C₈×D₄₃	—	4	1	no	—
439	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
440	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
441	C₂²×D₄₃	C₂³×C₄	1	1	yes	characteristic
442	C₂²×D₄₃	C₂³×C₄	1	1	yes	characteristic
443	Q₈×C₄₃	—	2	2	no	—
444	D₄×C₄₃	—	2	2	no	—
445	D₄×C₄₃	—	4	2	no	—
446	C₂×C₄×C₄₃	—	2	2	no	—
447	C₂×C₄×C₄₃	—	2	2	no	—
448	C₂×C₄×C₄₃	—	2	1	no	—
449	C₂×C₄×C₄₃	—	2	2	no	—
450	C₂×C₄×C₄₃	—	2	1	no	—
451	C₂×C₄×C₄₃	—	4	1	no	—
452	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
453	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
454	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
455	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
456	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
457	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
458	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
459	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
460	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
461	C₂²⋊D₄₃	—	2	4	no	—
462	C₂²⋊D₄₃	—	2	2	no	—
463	C₂²⋊D₄₃	—	4	1	no	—
464	C₂²⋊D₄₃	—	4	2	no	—
465	C₂×Dic₄₃	—	2	4	no	—
466	C₂×Dic₄₃	—	2	4	no	—
467	C₂×Dic₄₃	—	2	4	no	—
468	C₂×Dic₄₃	—	4	2	no	—
469	C₂×Dic₄₃	C₂³×C₄	1	1	yes	characteristic
470	C₂×Dic₄₃	C₂³×C₄	1	1	yes	characteristic
471	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
472	C₂×Dic₄₃	C₂³×C₄	1	1	yes	characteristic
473	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
474	C₂×Dic₄₃	C₂³×C₄	1	1	yes	characteristic
475	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
476	C₂×Dic₄₃	C₂³×C₄	1	1	yes	characteristic
477	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
478	C₂×Dic₄₃	C₂³×C₄	1	1	yes	characteristic
479	D₁₇₂	—	4	1	no	—
480	C₄×D₄₃	—	2	2	no	—
481	C₄×D₄₃	—	2	2	no	—
482	C₄×D₄₃	—	2	1	no	—
483	C₄×D₄₃	—	2	1	no	—
484	C₄×D₄₃	—	2	1	no	—
485	C₄×D₄₃	—	2	1	no	—
486	C₄×D₄₃	—	2	4	no	—
487	C₄×D₄₃	—	2	2	no	—
488	C₄×D₄₃	—	4	1	no	—
489	C₄×D₄₃	—	4	2	no	—
490	Dic₈₆	—	2	2	no	—
491	Dic₈₆	—	2	4	no	—
492	Dic₈₆	—	2	4	no	—
493	Dic₈₆	—	2	2	no	—
494	Dic₈₆	—	2	4	no	—
495	Dic₈₆	#131	1	4	yes	—
496	C₈×C₄₃	—	2	2	no	—
497	C₈×C₄₃	—	2	1	no	—
498	C₈×C₄₃	—	2	1	no	—
499	C₈×C₄₃	—	2	2	no	—
500	C₈×C₄₃	—	2	1	no	—
501	C₈×C₄₃	2₋¹⁺⁴	1	2	yes	—
502	C₄₃⋊C₈	—	2	1	no	—
503	C₄₃⋊C₈	—	2	1	no	—
504	C₄₃⋊C₈	—	2	1	no	—
505	C₄₃⋊C₈	—	2	2	no	—
506	C₄₃⋊C₈	—	2	1	no	—
507	C₄₃⋊C₈	—	2	2	no	—
508	#60345	—	43	1	no	maximal, Sylow
509	C₂²×C₄₃	—	2	2	no	—
510	C₂²×C₄₃	—	2	1	no	—
511	C₂²×C₄₃	—	2	1	no	—
512	C₂²×C₄₃	—	2	2	no	—
513	C₂²×C₄₃	—	2	2	no	—
514	C₂²×C₄₃	—	2	1	no	—
515	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
516	C₂×D₄₃	—	2	1	no	—
517	C₂×D₄₃	—	2	1	no	—
518	C₂×D₄₃	—	2	1	no	—
519	C₂×D₄₃	—	2	1	no	—
520	C₂×D₄₃	—	2	1	no	—
521	C₂×D₄₃	—	2	1	no	—
522	C₄×C₄₃	—	2	2	no	—
523	C₄×C₄₃	—	2	1	no	—
524	C₄×C₄₃	—	2	1	no	—
525	C₄×C₄₃	—	2	2	no	—
526	C₄×C₄₃	—	2	2	no	—
527	C₄×C₄₃	—	2	1	no	—
528	C₄×C₄₃	—	2	1	no	—
529	C₄×C₄₃	C₂×#131	1	2	yes	—
530	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
531	C₄×C₄₃	#585	1	1	yes	characteristic
532	Dic₄₃	—	2	1	no	—
533	Dic₄₃	—	2	1	no	—
534	Dic₄₃	—	2	1	no	—
535	Dic₄₃	—	2	2	no	—
536	Dic₄₃	—	2	1	no	—
537	Dic₄₃	—	2	1	no	—
538	Dic₄₃	—	2	2	no	—
539	Dic₄₃	—	2	2	no	—
540	Dic₄₃	C₂×#131	1	4	yes	—
541	Dic₄₃	#568	1	2	yes	—
542	#3482	—	43	1	no	—
543	#2993	—	43	1	no	—
544	#2993	—	43	2	no	—
545	#2993	—	43	2	no	—
546	#2993	—	43	1	no	—
547	#2991	—	43	1	no	—
548	#2991	—	43	2	no	—
549	#2991	—	43	1	no	—
550	#2986	—	43	1	no	—
551	#2986	—	43	2	no	—
552	#2982	—	43	1	no	—
553	#2982	—	43	1	no	—
554	#2969	—	43	2	no	—
555	#2969	—	43	1	no	—
556	#2969	—	43	2	no	—
557	#2969	D₄₃	1	1	yes	characteristic, complemented
558	#2965	—	43	2	no	—
559	#2965	—	43	1	no	—
560	C₈×#41	—	43	1	no	—
561	Q₈×M₁₆	—	43	1	no	—
562	Q₈×M₁₆	—	43	1	no	—
563	#2960	—	43	1	no	—
564	#2960	—	43	2	no	—
565	C₂×C₄₃	—	4	1	no	—
566	C₂×C₄₃	—	4	2	no	—
567	C₂×C₄₃	C₄×2₋¹⁺⁴	1	1	yes	characteristic
568	C₂×C₄₃	C₂²×#131	1	1	yes	characteristic
569	C₂×C₄₃	C₂×#568	1	1	yes	characteristic
570	D₄₃	—	4	1	no	—
571	D₄₃	—	4	1	no	—
572	#557	—	43	1	no	—
573	#556	—	43	2	no	—
574	#556	—	43	1	no	—
575	#552	—	43	2	no	—
576	#552	—	43	1	no	—
577	#552	—	43	2	no	—
578	#552	—	43	1	no	—
579	D₄×Q₈	—	43	1	no	—
580	#548	—	43	1	no	—
581	#548	—	43	1	no	—
582	#547	—	43	2	no	—
583	#547	—	43	1	no	—
584	#533	—	43	1	no	—
585	#533	—	43	2	no	—
586	#529	—	43	2	no	—
587	#529	—	43	1	no	—
588	#529	—	43	2	no	—
589	#529	C₂×D₄₃	1	1	yes	characteristic
590	C₄×#41	—	43	1	no	—
591	C₄×#41	—	43	2	no	—
592	C₄×#41	—	43	1	no	—
593	C₂×C₄×Q₈	—	43	1	no	—
594	C₂×C₄×Q₈	—	43	1	no	—
595	#446	—	43	1	no	—
596	#446	—	43	2	no	—
597	#446	—	43	2	no	—
598	#446	—	43	2	no	—
599	#446	—	43	1	no	—
600	#446	—	43	2	no	—
601	#446	—	43	2	no	—
602	#446	—	43	2	no	—
603	#446	—	43	1	no	—
604	#446	—	43	1	no	—
605	#446	—	43	1	no	—
606	#446	C₂×D₄₃	1	1	yes	characteristic
607	C₈×Q₈	—	43	1	no	—
608	C₈×Q₈	—	43	1	no	—
609	C₈×Q₈	—	43	2	no	—
610	C₈×Q₈	—	43	1	no	—
611	C₈×Q₈	—	43	1	no	—
612	C₈×Q₈	—	43	2	no	—
613	C₈×Q₈	—	43	1	no	—
614	C₈×Q₈	—	43	2	no	—
615	C₈×Q₈	—	43	2	no	—
616	C₈×Q₈	—	43	2	no	—
617	C₈×Q₈	—	43	2	no	—
618	C₈×Q₈	—	43	1	no	—
619	C₈×Q₈	—	43	1	no	—
620	C₈×Q₈	—	43	2	no	—
621	C₈×Q₈	C₂×D₄₃	1	1	yes	characteristic
622	#436	—	43	1	no	—
623	#436	—	43	1	no	—
624	#436	—	43	2	no	—
625	#436	—	43	2	no	—
626	#436	—	43	1	no	—
627	#436	—	43	2	no	—
628	#436	—	43	2	no	—
629	#436	—	43	2	no	—
630	#436	—	43	2	no	—
631	#436	—	43	2	no	—
632	#436	—	43	2	no	—
633	#436	C₂×D₄₃	1	1	yes	characteristic
634	#436	C₂×D₄₃	1	2	yes	—
635	#435	—	43	1	no	—
636	#435	—	43	1	no	—
637	#435	—	43	2	no	—
638	#435	—	43	2	no	—
639	#435	—	43	2	no	—
640	#435	—	43	1	no	—
641	#435	—	43	1	no	—
642	#435	C₂×D₄₃	1	2	yes	—
643	C₈×D₄	—	43	2	no	—
644	C₈×D₄	—	43	1	no	—
645	C₈×D₄	—	43	2	no	—
646	C₈×D₄	C₂×D₄₃	1	1	yes	characteristic
647	#433	—	43	2	no	—
648	#433	—	43	2	no	—
649	#433	—	43	2	no	—
650	#433	—	43	2	no	—
651	#433	—	43	2	no	—
652	#433	C₂×D₄₃	1	2	yes	—
653	#431	—	43	1	no	—
654	#431	—	43	1	no	—
655	#431	—	43	2	no	—
656	#431	—	43	1	no	—
657	#431	—	43	2	no	—
658	#431	—	43	2	no	—
659	#431	—	43	2	no	—
660	#431	—	43	2	no	—
661	#431	—	43	1	no	—
662	#431	—	43	1	no	—
663	#431	—	43	2	no	—
664	#431	C₂×D₄₃	1	1	yes	characteristic
665	#424	—	43	2	no	—
666	#424	—	43	2	no	—
667	#424	—	43	2	no	—
668	#423	—	43	2	no	—
669	#423	—	43	2	no	—
670	#423	—	43	1	no	—
671	#423	—	43	1	no	—
672	#423	—	43	2	no	—
673	#423	—	43	1	no	—
674	#405	—	43	2	no	—
675	#405	—	43	2	no	—
676	#405	C₂×D₄₃	1	2	yes	—
677	C₄×M₁₆	—	43	2	no	—
678	C₄×M₁₆	—	43	2	no	—
679	C₄×M₁₆	—	43	1	no	—
680	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic
681	C₂×C₄×C₈	—	43	2	no	—
682	C₂×C₄×C₈	—	43	1	no	—
683	C₄₃	#60345	1	1	yes	characteristic, complemented, Sylow
684	C₂×#41	—	43	1	no	—
685	C₂×#41	—	43	2	no	—
686	C₂×#41	—	43	1	no	—
687	C₂²×Q₈	—	43	1	no	—
688	C₂²×Q₈	—	43	1	no	—
689	C₂×M₁₆	—	43	2	no	—
690	C₂×M₁₆	—	43	2	no	—
691	C₂×M₁₆	—	43	1	no	—
692	C₂×M₁₆	—	43	1	no	—
693	C₂×M₁₆	—	43	2	no	—
694	C₂×M₁₆	—	43	2	no	—
695	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
696	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
697	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
698	C₂²×C₈	—	43	2	no	—
699	C₂²×C₈	—	43	1	no	—
700	C₂²×C₈	—	43	1	no	—
701	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
702	C₄⋊Q₈	—	43	1	no	—
703	C₄⋊Q₈	—	43	2	no	—
704	C₄⋊Q₈	—	43	1	no	—
705	C₄⋊Q₈	—	43	2	no	—
706	#126	—	43	2	no	—
707	#126	—	43	2	no	—
708	#126	—	43	2	no	—
709	#126	—	43	2	no	—
710	#126	—	43	2	no	—
711	#126	C₄×D₄₃	1	2	yes	—
712	#125	—	43	2	no	—
713	#125	—	43	2	no	—
714	#125	—	43	1	no	—
715	#125	—	43	2	no	—
716	#125	—	43	2	no	—
717	#125	—	43	2	no	—
718	#125	C₄×D₄₃	1	1	yes	characteristic
719	#124	—	43	1	no	—
720	#124	—	43	2	no	—
721	#124	—	43	2	no	—
722	#124	C₄×D₄₃	1	1	yes	characteristic
723	#123	—	43	2	no	—
724	#123	—	43	2	no	—
725	#123	—	43	2	no	—
726	#123	—	43	2	no	—
727	#123	—	43	2	no	—
728	#123	C₄×D₄₃	1	2	yes	—
729	C₂²⋊Q₈	—	43	1	no	—
730	C₂²⋊Q₈	—	43	2	no	—
731	C₂²⋊Q₈	—	43	1	no	—
732	C₂²⋊Q₈	—	43	2	no	—
733	C₂²⋊Q₈	—	43	1	no	—
734	C₂²⋊Q₈	—	43	2	no	—
735	C₂²⋊Q₈	—	43	2	no	—
736	C₂²⋊Q₈	—	43	2	no	—
737	C₂²⋊Q₈	—	43	2	no	—
738	C₂²⋊Q₈	—	43	2	no	—
739	C₂²⋊Q₈	C₄×D₄₃	1	1	yes	characteristic
740	#121	—	43	1	no	—
741	#121	—	43	2	no	—
742	#121	—	43	2	no	—
743	#121	C₄×D₄₃	1	1	yes	characteristic
744	C₄×Q₈	—	43	1	no	—
745	C₄×Q₈	—	43	1	no	—
746	C₄×Q₈	—	43	2	no	—
747	C₄×Q₈	—	43	1	no	—
748	C₄×Q₈	—	43	2	no	—
749	C₄×Q₈	—	43	1	no	—
750	C₄×Q₈	—	43	1	no	—
751	C₄×Q₈	—	43	2	no	—
752	C₄×Q₈	—	43	1	no	—
753	C₄×Q₈	—	43	1	no	—
754	C₄×Q₈	—	43	2	no	—
755	C₄×Q₈	—	43	2	no	—
756	C₄×Q₈	—	43	1	no	—
757	C₄×Q₈	—	43	2	no	—
758	C₄×Q₈	—	43	1	no	—
759	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
760	C₄×D₄	—	43	1	no	—
761	C₄×D₄	—	43	2	no	—
762	C₄×D₄	—	43	1	no	—
763	C₄×D₄	—	43	1	no	—
764	C₄×D₄	—	43	1	no	—
765	C₄×D₄	—	43	2	no	—
766	C₄×D₄	—	43	1	no	—
767	C₄×D₄	—	43	2	no	—
768	C₄×D₄	—	43	2	no	—
769	C₄×D₄	—	43	2	no	—
770	C₄×D₄	—	43	2	no	—
771	C₄×D₄	—	43	1	no	—
772	C₄×D₄	—	43	1	no	—
773	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
774	C₄×D₄	C₂²×D₄₃	1	2	yes	—
775	#117	—	43	1	no	—
776	#117	—	43	2	no	—
777	#117	—	43	1	no	—
778	#117	—	43	2	no	—
779	#117	—	43	2	no	—
780	#117	—	43	2	no	—
781	#117	—	43	2	no	—
782	#117	—	43	1	no	—
783	#117	—	43	1	no	—
784	#117	—	43	2	no	—
785	#117	C₂²×D₄₃	1	2	yes	—
786	C₂×C₄⋊C₄	—	43	2	no	—
787	C₂×C₄⋊C₄	—	43	1	no	—
788	C₂×C₄⋊C₄	—	43	2	no	—
789	C₂×C₄⋊C₄	—	43	1	no	—
790	C₂×C₄²	—	43	2	no	—
791	C₂×C₄²	—	43	2	no	—
792	C₂×C₄²	—	43	2	no	—
793	C₂×C₄²	—	43	1	no	—
794	C₂×C₄²	—	43	1	no	—
795	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
796	C₄⋊C₈	—	43	2	no	—
797	C₄⋊C₈	—	43	2	no	—
798	C₄⋊C₈	—	43	2	no	—
799	C₄⋊C₈	—	43	1	no	—
800	C₄⋊C₈	—	43	2	no	—
801	C₄⋊C₈	—	43	2	no	—
802	C₄⋊C₈	—	43	2	no	—
803	C₄⋊C₈	—	43	2	no	—
804	C₄⋊C₈	—	43	2	no	—
805	C₄⋊C₈	—	43	1	no	—
806	C₄⋊C₈	—	43	2	no	—
807	C₄⋊C₈	—	43	1	no	—
808	C₄⋊C₈	—	43	1	no	—
809	C₄⋊C₈	—	43	2	no	—
810	C₄⋊C₈	—	43	1	no	—
811	C₄⋊C₈	—	43	1	no	—
812	C₄⋊C₈	—	43	2	no	—
813	C₄⋊C₈	—	43	2	no	—
814	C₄⋊C₈	—	43	2	no	—
815	C₄⋊C₈	—	43	1	no	—
816	C₄⋊C₈	—	43	1	no	—
817	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
818	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
819	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
820	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
821	C₂²⋊C₈	—	43	1	no	—
822	C₂²⋊C₈	—	43	1	no	—
823	C₂²⋊C₈	—	43	2	no	—
824	C₂²⋊C₈	—	43	2	no	—
825	C₂²⋊C₈	—	43	1	no	—
826	C₂²⋊C₈	—	43	1	no	—
827	C₂²⋊C₈	—	43	2	no	—
828	C₂²⋊C₈	—	43	2	no	—
829	C₂²⋊C₈	—	43	1	no	—
830	C₂²⋊C₈	—	43	1	no	—
831	C₂²⋊C₈	C₂²×D₄₃	1	2	yes	—
832	C₂²⋊C₈	C₂²×D₄₃	1	2	yes	—
833	C₂²⋊C₈	C₂²×D₄₃	1	2	yes	—
834	#97	—	43	1	no	—
835	#97	—	43	2	no	—
836	#97	—	43	1	no	—
837	#97	—	43	2	no	—
838	#97	—	43	2	no	—
839	#97	C₂²×D₄₃	1	2	yes	—
840	#97	C₂²×D₄₃	1	1	yes	characteristic
841	#97	C₂²×D₄₃	1	1	yes	characteristic
842	C₄×C₈	—	43	1	no	—
843	C₄×C₈	—	43	2	no	—
844	C₄×C₈	—	43	2	no	—
845	C₄×C₈	—	43	1	no	—
846	C₄×C₈	—	43	2	no	—
847	C₄×C₈	—	43	2	no	—
848	C₄×C₈	—	43	2	no	—
849	C₄×C₈	—	43	2	no	—
850	C₄×C₈	—	43	2	no	—
851	C₄×C₈	—	43	2	no	—
852	C₄×C₈	—	43	1	no	—
853	C₄×C₈	—	43	1	no	—
854	C₄×C₈	—	43	2	no	—
855	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
856	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
857	C₄×C₈	C₂²×D₄₃	1	2	yes	—
858	C₄×C₈	C₂²×D₄₃	1	2	yes	—
859	#41	—	86	4	no	—
860	#41	—	172	2	no	—
861	#41	—	172	4	no	—
862	C₂×Q₈	—	43	1	no	—
863	C₂×Q₈	—	43	2	no	—
864	C₂×Q₈	—	43	2	no	—
865	C₂×Q₈	—	43	1	no	—
866	C₂×Q₈	—	43	2	no	—
867	C₂×Q₈	—	43	1	no	—
868	C₂×Q₈	—	86	4	no	—
869	C₂×Q₈	—	86	4	no	—
870	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
871	C₂×D₄	—	43	1	no	—
872	C₂×D₄	—	43	2	no	—
873	C₂×D₄	—	43	1	no	—
874	C₂×D₄	—	43	2	no	—
875	C₂×D₄	—	43	1	no	—
876	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
877	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
878	C₂²×C₄	—	43	2	no	—
879	C₂²×C₄	—	43	2	no	—
880	C₂²×C₄	—	43	2	no	—
881	C₂²×C₄	—	43	2	no	—
882	C₂²×C₄	—	43	2	no	—
883	C₂²×C₄	—	43	1	no	—
884	C₂²×C₄	—	43	1	no	—
885	C₂²×C₄	—	43	1	no	—
886	C₂²×C₄	—	43	1	no	—
887	C₂²×C₄	—	43	1	no	—
888	C₂²×C₄	—	43	2	no	—
889	C₂²×C₄	—	43	1	no	—
890	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
891	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
892	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
893	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
894	M₁₆	—	2	2	no	—
895	M₁₆	—	4	1	no	—
896	M₁₆	—	4	2	no	—
897	M₁₆	—	86	2	no	—
898	M₁₆	—	172	1	no	—
899	M₁₆	—	172	2	no	—
900	M₁₆	—	172	2	no	—
901	M₁₆	—	172	2	no	—
902	M₁₆	—	172	2	no	—
903	C₂×C₈	—	2	4	no	—
904	C₂×C₈	—	43	1	no	—
905	C₂×C₈	—	43	1	no	—
906	C₂×C₈	—	43	1	no	—
907	C₂×C₈	—	43	2	no	—
908	C₂×C₈	—	43	1	no	—
909	C₂×C₈	—	43	2	no	—
910	C₂×C₈	—	86	2	no	—
911	C₂×C₈	—	172	1	no	—
912	C₂×C₈	—	172	2	no	—
913	C₂×C₈	C₂³×D₄₃	1	2	yes	—
914	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
915	C₂×C₈	C₂³×D₄₃	1	2	yes	—
916	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
917	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
918	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
919	C₄⋊C₄	—	43	2	no	—
920	C₄⋊C₄	—	43	1	no	—
921	C₄⋊C₄	—	43	2	no	—
922	C₄⋊C₄	—	43	2	no	—
923	C₄⋊C₄	—	43	1	no	—
924	C₄⋊C₄	—	43	2	no	—
925	C₄⋊C₄	—	43	2	no	—
926	C₄⋊C₄	—	43	2	no	—
927	C₄⋊C₄	—	43	2	no	—
928	C₄⋊C₄	—	43	2	no	—
929	C₄⋊C₄	—	43	1	no	—
930	C₄⋊C₄	—	43	2	no	—
931	C₄⋊C₄	—	43	2	no	—
932	C₄⋊C₄	—	43	1	no	—
933	C₄⋊C₄	—	43	2	no	—
934	C₄⋊C₄	—	43	1	no	—
935	C₄⋊C₄	—	43	2	no	—
936	C₄⋊C₄	—	43	1	no	—
937	C₄⋊C₄	—	43	2	no	—
938	C₄⋊C₄	—	43	1	no	—
939	C₄⋊C₄	—	43	1	no	—
940	C₄⋊C₄	—	43	2	no	—
941	C₄⋊C₄	—	43	2	no	—
942	C₄⋊C₄	—	43	2	no	—
943	C₄⋊C₄	—	43	2	no	—
944	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
945	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
946	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
947	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
948	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
949	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
950	C₂²⋊C₄	—	43	1	no	—
951	C₂²⋊C₄	—	43	1	no	—
952	C₂²⋊C₄	—	43	2	no	—
953	C₂²⋊C₄	—	43	2	no	—
954	C₂²⋊C₄	—	43	2	no	—
955	C₂²⋊C₄	—	43	2	no	—
956	C₂²⋊C₄	—	43	1	no	—
957	C₂²⋊C₄	—	43	1	no	—
958	C₂²⋊C₄	—	43	2	no	—
959	C₂²⋊C₄	—	43	2	no	—
960	C₂²⋊C₄	—	43	1	no	—
961	C₂²⋊C₄	—	43	1	no	—
962	C₂²⋊C₄	—	43	2	no	—
963	C₂²⋊C₄	—	43	2	no	—
964	C₂²⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
965	C₂²⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
966	C₂²⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
967	C₂²⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
968	C₂²⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
969	C₄²	—	43	2	no	—
970	C₄²	—	43	1	no	—
971	C₄²	—	43	2	no	—
972	C₄²	—	43	1	no	—
973	C₄²	—	43	2	no	—
974	C₄²	—	43	2	no	—
975	C₄²	—	43	1	no	—
976	C₄²	—	43	2	no	—
977	C₄²	—	43	2	no	—
978	C₄²	—	43	1	no	—
979	C₄²	—	43	1	no	—
980	C₄²	—	43	2	no	—
981	C₄²	—	43	2	no	—
982	C₄²	—	43	1	no	—
983	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
984	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
985	C₄²	C₂³×D₄₃	1	1	yes	characteristic
986	C₄²	C₂³×D₄₃	1	2	yes	—
987	C₄²	C₂³×D₄₃	1	1	yes	characteristic
988	C₂³	—	43	1	no	—
989	C₂³	—	43	1	no	—
990	C₂³	C₂²×C₄×D₄₃	1	2	yes	—
991	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
992	Q₈	—	2	2	no	—
993	Q₈	—	43	4	no	—
994	Q₈	—	86	4	no	—
995	Q₈	—	86	4	no	—
996	Q₈	—	86	2	no	—
997	Q₈	—	86	4	no	—
998	Q₈	—	86	2	no	—
999	D₄	—	2	2	no	—
1000	D₄	—	4	2	no	—
1001	D₄	—	86	4	no	—
1002	D₄	—	86	2	no	—
1003	D₄	—	172	1	no	—
1004	D₄	—	172	1	no	—
1005	D₄	—	172	2	no	—
1006	C₂×C₄	—	2	2	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	2	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	4	1	no	—
1012	C₂×C₄	—	43	2	no	—
1013	C₂×C₄	—	43	1	no	—
1014	C₂×C₄	—	43	1	no	—
1015	C₂×C₄	—	43	1	no	—
1016	C₂×C₄	—	43	2	no	—
1017	C₂×C₄	—	43	1	no	—
1018	C₂×C₄	—	43	1	no	—
1019	C₂×C₄	—	43	2	no	—
1020	C₂×C₄	—	43	1	no	—
1021	C₂×C₄	—	43	2	no	—
1022	C₂×C₄	—	86	4	no	—
1023	C₂×C₄	—	86	2	no	—
1024	C₂×C₄	—	86	4	no	—
1025	C₂×C₄	—	86	4	no	—
1026	C₂×C₄	—	86	4	no	—
1027	C₂×C₄	—	86	2	no	—
1028	C₂×C₄	—	86	2	no	—
1029	C₂×C₄	—	86	1	no	—
1030	C₂×C₄	—	86	1	no	—
1031	C₂×C₄	—	86	1	no	—
1032	C₂×C₄	—	86	1	no	—
1033	C₂×C₄	—	172	1	no	—
1034	C₂×C₄	—	172	2	no	—
1035	C₂×C₄	—	172	2	no	—
1036	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
1037	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
1038	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
1039	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
1040	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
1041	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
1042	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
1043	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
1044	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1045	C₈	—	2	2	no	—
1046	C₈	—	2	1	no	—
1047	C₈	—	2	1	no	—
1048	C₈	—	2	1	no	—
1049	C₈	—	2	2	no	—
1050	C₈	—	86	1	no	—
1051	C₈	—	86	1	no	—
1052	C₈	—	86	1	no	—
1053	C₈	—	86	2	no	—
1054	C₈	—	86	2	no	—
1055	C₈	—	86	1	no	—
1056	C₈	#13063372	1	2	yes	—
1057	C₂²	—	2	2	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	2	no	—
1061	C₂²	—	2	1	no	—
1062	C₂²	—	2	2	no	—
1063	C₂²	—	86	1	no	—
1064	C₂²	—	86	1	no	—
1065	C₂²	—	86	1	no	—
1066	C₂²	—	86	1	no	—
1067	C₂²	—	86	1	no	—
1068	C₂²	—	86	1	no	—
1069	C₂²	C₂³×C₄×D₄₃	1	1	yes	characteristic
1070	C₄	—	2	2	no	—
1071	C₄	—	2	1	no	—
1072	C₄	—	2	1	no	—
1073	C₄	—	2	2	no	—
1074	C₄	—	2	1	no	—
1075	C₄	—	2	1	no	—
1076	C₄	—	2	2	no	—
1077	C₄	—	43	4	no	—
1078	C₄	—	43	2	no	—
1079	C₄	—	86	1	no	—
1080	C₄	—	86	1	no	—
1081	C₄	—	86	1	no	—
1082	C₄	—	86	2	no	—
1083	C₄	—	86	1	no	—
1084	C₄	—	86	2	no	—
1085	C₄	—	86	1	no	—
1086	C₄	—	86	2	no	—
1087	C₄	#131×D₄₃	1	2	yes	—
1088	C₄	C₂×#13063372	1	1	yes	characteristic
1089	C₄	#14583735	1	1	yes	characteristic
1090	C₂	—	4	1	no	—
1091	C₂	—	4	2	no	—
1092	C₂	—	172	1	no	—
1093	C₂	—	172	1	no	—
1094	C₂	C₄×#13063372	1	1	yes	characteristic
1095	C₂	C₂×#131×D₄₃	1	1	yes	characteristic
1096	C₂	#568×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁴×C₄
Fitting	C₄₃×#2969	C₂
prime radical	#19148208	C₂
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	#2969	D₄₃
hypocenter	C₄₃	#60345
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #2969

Complements

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

N	H ≅ G/N	type
2. #19143744	C₂	semidirect
3. #19143741	C₂	semidirect
4. #19143739	C₂	semidirect
5. #19143738	C₂	semidirect
6. #19143724	C₂	semidirect
7. #19143723	C₂	semidirect
8. #19143723	C₂	semidirect
9. #19143695	C₂	semidirect
10. #19143694	C₂	semidirect
11. #19143675	C₂	semidirect
12. #19143674	C₂	semidirect
13. #19143596	C₂	semidirect
14. #19143595	C₂	semidirect
15. #19143592	C₂	semidirect
16. #19143557	C₂	semidirect
17. #19143555	C₂	semidirect
18. C₈×#10621900	C₂	semidirect
19. M₁₆×Dic₈₆	C₂	semidirect
20. #19143547	C₂	semidirect
21. #19143527	C₂	semidirect
22. #19143526	C₂	semidirect
23. C₄₃×#2969	C₂	semidirect
557. #2969	D₄₃	semidirect
683. C₄₃	#60345	semidirect

Maximal subgroups

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

subgroup	index
#19148208	2
#19143744	2
#19143741	2
#19143739	2
#19143738	2
#19143724	2
#19143723	2
#19143695	2
#19143694	2
#19143675	2
#19143674	2
#19143596	2
#19143595	2
#19143592	2
#19143557	2
#19143555	2
C₈×#10621900	2
M₁₆×Dic₈₆	2
#19143547	2
#19143527	2
#19143526	2
C₄₃×#2969	2
#60345	43