Subgroups — #25979322

Order 11008.

1800 conjugacy classes of subgroups.

The subgroup lattice has 1080 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148657	C₂	1	2	yes	maximal, complemented
2	#19147580	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147459	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147428	C₂	1	2	yes	maximal, complemented
5	#19147022	C₂	1	1	yes	maximal, characteristic, complemented
6	#19146992	C₂	1	1	yes	maximal, characteristic, complemented
7	#19146962	C₂	1	1	yes	maximal, characteristic, complemented
8	#19146810	C₂	1	2	yes	maximal, complemented
9	#19146637	C₂	1	2	yes	maximal, complemented
10	#19146577	C₂	1	2	yes	maximal, complemented
11	#19146314	C₂	1	1	yes	maximal, characteristic, complemented
12	#19146283	C₂	1	1	yes	maximal, characteristic, complemented
13	#19146279	C₂	1	1	yes	maximal, characteristic, complemented
14	#19145250	C₂	1	1	yes	maximal, characteristic, complemented
15	#19145230	C₂	1	1	yes	maximal, characteristic, complemented
16	#19144878	C₂	1	2	yes	maximal, complemented
17	#19144844	C₂	1	2	yes	maximal, complemented
18	#19144698	C₂	1	2	yes	maximal, complemented
19	#19143570	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143470	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143442	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#13063347	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3168	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063348	C₂²	1	1	yes	characteristic
25	C₂×#13063347	C₂²	1	1	yes	characteristic
26	C₂×D₈×D₄₃	C₂²	1	1	yes	characteristic
27	#14583620	C₂²	1	2	yes	—
28	#14583618	C₂²	1	2	yes	complemented
29	#14583605	C₂²	1	2	yes	complemented
30	#14583599	—	2	2	no	—
31	#14583596	C₂²	1	2	yes	complemented
32	#14583588	—	2	2	no	—
33	#14583587	C₂²	1	2	yes	—
34	#14583578	—	2	2	no	—
35	#14583573	—	2	2	no	—
36	#14583551	C₂²	1	2	yes	complemented
37	#14583546	C₂²	1	2	yes	—
38	#14583542	C₂²	1	2	yes	—
39	#14583514	C₂²	1	2	yes	complemented
40	#14583507	C₂²	1	2	yes	—
41	#14583492	—	2	2	no	—
42	#14583485	—	2	2	no	—
43	#14583433	C₂²	1	1	yes	characteristic
44	#14583432	—	2	2	no	—
45	#126×D₄₃	—	2	2	no	—
46	#14583381	C₂²	1	2	yes	complemented
47	#14583371	C₂²	1	2	yes	—
48	C₄×#10621898	C₂²	1	2	yes	complemented
49	#14583303	C₂²	1	1	yes	characteristic, complemented
50	#14583300	C₂²	1	1	yes	characteristic, complemented
51	#14583282	C₂²	1	1	yes	characteristic
52	#14583277	C₂²	1	1	yes	characteristic, complemented
53	#14583266	C₂²	1	2	yes	complemented
54	#14583257	C₂²	1	2	yes	complemented
55	#14583243	C₂²	1	2	yes	—
56	#14583238	C₂²	1	2	yes	—
57	#14583237	C₂²	1	2	yes	complemented
58	#14583231	C₂²	1	2	yes	complemented
59	#14583220	C₂²	1	2	yes	complemented
60	#14583216	C₂²	1	2	yes	complemented
61	#14583203	C₂²	1	2	yes	complemented
62	#14583201	C₂²	1	2	yes	complemented
63	#14583198	C₂²	1	2	yes	complemented
64	#14583196	C₂²	1	2	yes	complemented
65	#14583188	C₂²	1	2	yes	complemented
66	#14583182	C₂²	1	2	yes	complemented
67	#14583156	C₂²	1	2	yes	—
68	#14583144	C₂²	1	2	yes	complemented
69	#14583141	C₂²	1	1	yes	characteristic
70	#14583141	C₂²	1	1	yes	characteristic, complemented
71	#14583137	C₂²	1	1	yes	characteristic
72	#14583132	C₂²	1	1	yes	characteristic
73	#14583119	C₂²	1	2	yes	complemented
74	#14583118	C₂²	1	2	yes	complemented
75	#14583113	C₂²	1	2	yes	—
76	#14583111	C₂²	1	2	yes	—
77	#14583103	C₂²	1	2	yes	complemented
78	#14583102	C₂²	1	2	yes	complemented
79	#14583064	C₂²	1	2	yes	complemented
80	#14583059	C₂²	1	2	yes	complemented
81	#14583051	C₂²	1	2	yes	—
82	#14583048	C₂²	1	2	yes	—
83	#14583043	C₂²	1	2	yes	—
84	#14583042	C₂²	1	2	yes	—
85	#14583029	C₂²	1	1	yes	characteristic, complemented
86	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
87	#14583009	C₂²	1	2	yes	—
88	#14583008	C₂²	1	2	yes	—
89	#14583004	C₂²	1	2	yes	complemented
90	#14583002	C₂²	1	2	yes	complemented
91	#14582999	C₂²	1	2	yes	complemented
92	#14582997	C₂²	1	2	yes	complemented
93	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
94	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
95	Q₁₆×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
96	C₄×#10621873	C₂²	1	2	yes	complemented
97	C₄×#10621873	C₂²	1	2	yes	complemented
98	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
99	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
100	D₈×Dic₄₃	C₂²	1	1	yes	characteristic
101	#14582981	C₂²	1	1	yes	characteristic
102	#14582981	C₂²	1	1	yes	characteristic
103	#14582978	C₂²	1	1	yes	characteristic
104	#14582970	C₂²	1	1	yes	characteristic
105	#14582970	C₂²	1	1	yes	characteristic, complemented
106	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
107	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
108	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic, complemented
109	#14582958	C₂²	1	1	yes	characteristic
110	#14582958	C₂²	1	1	yes	characteristic, complemented
111	#14582956	C₂²	1	1	yes	characteristic, complemented
112	#14582937	C₂²	1	1	yes	characteristic, complemented
113	#14582936	C₂²	1	1	yes	characteristic
114	#107×D₄₃	C₂²	1	1	yes	characteristic, complemented
115	#14582902	C₂²	1	2	yes	—
116	#14582899	C₂²	1	2	yes	complemented
117	#14582896	C₂²	1	2	yes	complemented
118	#14582853	C₂²	1	1	yes	characteristic
119	#14582853	C₂²	1	1	yes	characteristic, complemented
120	C₄₃×#529	C₂²	1	2	yes	complemented
121	C₄₃×#499	C₂²	1	1	yes	characteristic, complemented
122	C₄₃×#495	C₂²	1	1	yes	characteristic
123	C₄₃×#488	C₂²	1	2	yes	complemented
124	C₄₃×#467	C₂²	1	1	yes	characteristic, complemented
125	C₄₃×#466	C₂²	1	1	yes	characteristic
126	C₄₃×#465	C₂²	1	2	yes	complemented
127	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
128	C₄×SD₁₆×C₄₃	C₂²	1	2	yes	complemented
129	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
130	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
131	C₂×#10621902	C₂³	1	2	yes	—
132	C₂×#10621898	C₂³	1	2	yes	—
133	C₂×D₄×D₄₃	C₂³	1	2	yes	—
134	#13063348	—	2	4	no	—
135	#13063347	—	2	4	no	—
136	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
137	C₂×#10621885	C₂³	1	2	yes	—
138	C₂×#10621873	C₂³	1	2	yes	—
139	C₂×#10621883	C₂³	1	2	yes	—
140	C₂×#10621884	C₂³	1	2	yes	—
141	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
142	C₂×#10621882	C₂³	1	2	yes	—
143	D₈×D₄₃	—	2	4	no	—
144	C₂×#10621872	C₂³	1	1	yes	characteristic
145	C₂×#10621872	C₂³	1	1	yes	characteristic
146	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
147	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
148	#13063324	C₂³	1	2	yes	—
149	#13063323	C₂³	1	2	yes	—
150	#13063320	—	2	2	no	—
151	#13063320	—	2	2	no	—
152	#13063320	—	2	2	no	—
153	#13063319	—	2	2	no	—
154	#13063319	D₄	1	1	yes	characteristic
155	#13063319	D₄	1	1	yes	characteristic
156	#13063318	—	2	2	no	—
157	#13063318	—	2	2	no	—
158	#13063318	—	2	2	no	—
159	#13063318	—	2	2	no	—
160	#13063318	—	2	2	no	—
161	#13063317	—	2	2	no	—
162	#13063317	D₄	1	1	yes	characteristic
163	#13063316	—	2	2	no	—
164	#13063316	C₂³	1	2	yes	—
165	#13063315	—	2	2	no	—
166	#13063313	D₄	1	1	yes	characteristic
167	#13063312	C₂³	1	2	yes	—
168	#13063311	—	2	2	no	—
169	#13063311	—	2	2	no	—
170	#13063310	—	2	2	no	—
171	#13063310	—	2	2	no	—
172	#13063308	—	2	2	no	—
173	#13063308	D₄	1	1	yes	characteristic
174	#13063308	D₄	1	1	yes	characteristic
175	#13063307	—	2	2	no	—
176	#13063307	—	2	2	no	—
177	#13063307	—	2	2	no	—
178	#13063306	—	2	2	no	—
179	#13063305	—	2	2	no	—
180	#13063305	C₂³	1	2	yes	—
181	#13063305	C₂³	1	2	yes	—
182	#13063304	—	2	2	no	—
183	#13063304	D₄	1	1	yes	characteristic
184	#13063303	—	2	2	no	—
185	#13063303	—	2	2	no	—
186	#13063302	—	2	2	no	—
187	#13063301	C₂³	1	2	yes	—
188	#13063299	D₄	1	1	yes	characteristic
189	#13063298	—	2	2	no	—
190	#13063298	—	2	2	no	—
191	#13063296	—	2	2	no	—
192	#13063296	—	2	2	no	—
193	#13063296	C₂³	1	2	yes	—
194	#13063295	—	2	2	no	—
195	#13063293	—	2	2	no	—
196	Q₈×Dic₄₃	C₂³	1	2	yes	—
197	C₄×Dic₈₆	C₂³	1	2	yes	—
198	C₄×Dic₈₆	C₂³	1	2	yes	—
199	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
200	#13063290	—	2	2	no	—
201	C₄×D₁₇₂	—	2	2	no	—
202	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
203	C₄×D₁₇₂	C₂³	1	2	yes	—
204	C₄×D₁₇₂	C₂³	1	2	yes	—
205	D₄×Dic₄₃	C₂³	1	2	yes	—
206	#13063287	—	2	2	no	—
207	#13063287	C₂³	1	2	yes	—
208	#13063287	C₂³	1	2	yes	—
209	C₄×C₂²⋊D₄₃	—	2	2	no	—
210	C₄×C₂²⋊D₄₃	—	2	2	no	—
211	C₄×C₂²⋊D₄₃	—	2	2	no	—
212	C₄×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
213	C₄×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
214	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
215	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
216	#13063284	C₂³	1	2	yes	—
217	#13063283	—	2	2	no	—
218	#13063283	C₂³	1	2	yes	—
219	#13063282	—	2	2	no	—
220	#13063282	—	2	2	no	—
221	#13063282	C₂³	1	1	yes	characteristic
222	#13063282	C₂³	1	1	yes	characteristic
223	#13063281	—	2	2	no	—
224	C₄⋊C₄×D₄₃	—	2	2	no	—
225	C₄⋊C₄×D₄₃	—	2	2	no	—
226	C₄⋊C₄×D₄₃	—	2	2	no	—
227	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
228	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
229	C₂²⋊C₄×D₄₃	—	2	2	no	—
230	C₂²⋊C₄×D₄₃	—	2	2	no	—
231	C₂²⋊C₄×D₄₃	—	2	2	no	—
232	C₄²×D₄₃	—	2	2	no	—
233	#13063259	C₂³	1	1	yes	characteristic
234	#13063259	C₂³	1	1	yes	characteristic
235	#13063258	C₂³	1	2	yes	—
236	#13063258	C₂³	1	2	yes	—
237	#13063257	C₂³	1	2	yes	—
238	#13063256	C₂³	1	2	yes	—
239	#13063256	C₂³	1	2	yes	—
240	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
241	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
242	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
243	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
244	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
245	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
246	#13063250	C₂³	1	2	yes	—
247	#13063250	C₂³	1	2	yes	—
248	#13063249	C₂³	1	2	yes	—
249	#13063249	C₂³	1	2	yes	—
250	#13063248	C₂³	1	2	yes	—
251	#13063248	C₂³	1	2	yes	—
252	#13063247	C₂³	1	2	yes	—
253	#13063247	C₂³	1	2	yes	—
254	#13063246	C₂³	1	2	yes	—
255	#13063246	C₂³	1	2	yes	—
256	#13063245	C₂³	1	2	yes	—
257	#13063245	C₂³	1	2	yes	—
258	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
259	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
260	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
261	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
262	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
263	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
264	#13063236	C₂³	1	1	yes	characteristic
265	#13063236	C₂³	1	1	yes	characteristic
266	#13063235	C₂³	1	1	yes	characteristic
267	#13063235	C₂³	1	1	yes	characteristic
268	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
269	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
270	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
271	C₂×SD₁₆×C₄₃	C₂³	1	2	yes	—
272	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
273	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
274	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
275	#126×C₄₃	—	2	2	no	—
276	#125×C₄₃	C₂³	1	2	yes	—
277	#124×C₄₃	C₂³	1	2	yes	—
278	#123×C₄₃	—	2	2	no	—
279	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
280	#121×C₄₃	C₂³	1	2	yes	—
281	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
282	C₄×D₄×C₄₃	—	2	2	no	—
283	C₄×D₄×C₄₃	C₂³	1	2	yes	—
284	#117×C₄₃	—	2	2	no	—
285	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
286	#107×C₄₃	C₂³	1	1	yes	characteristic
287	#107×C₄₃	C₂³	1	1	yes	characteristic
288	#106×C₄₃	C₂³	1	2	yes	—
289	#103×C₄₃	C₂³	1	2	yes	—
290	#103×C₄₃	C₂³	1	2	yes	—
291	#102×C₄₃	C₂³	1	2	yes	—
292	#102×C₄₃	C₂³	1	2	yes	—
293	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
294	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
295	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
297	C₂³×D₄₃	—	2	2	no	—
298	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
299	C₂×D₄×C₄₃	—	2	2	no	—
300	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₄₃	—	2	2	no	—
302	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
303	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
305	C₂×C₂²⋊D₄₃	—	2	2	no	—
306	C₂×C₂²⋊D₄₃	—	2	2	no	—
307	C₂×C₂²⋊D₄₃	—	2	2	no	—
308	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
309	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
310	C₂²×Dic₄₃	—	2	2	no	—
311	#10621902	—	2	4	no	—
312	#10621902	—	4	2	no	—
313	D₄×D₄₃	—	2	4	no	—
314	D₄×D₄₃	—	4	2	no	—
315	#10621898	—	2	4	no	—
316	#10621898	—	4	2	no	—
317	C₂×D₁₇₂	—	2	2	no	—
318	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
319	C₂×D₁₇₂	C₂⁴	1	2	yes	—
320	C₂×C₄×D₄₃	—	2	2	no	—
321	C₂×C₄×D₄₃	—	2	2	no	—
322	C₂×C₄×D₄₃	—	2	2	no	—
323	C₂×C₄×D₄₃	—	2	2	no	—
324	C₂×C₄×D₄₃	—	2	2	no	—
325	C₂×C₄×D₄₃	—	2	2	no	—
326	C₂×C₄×D₄₃	—	2	2	no	—
327	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
328	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
329	C₂×Dic₈₆	—	2	2	no	—
330	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
331	C₂×Dic₈₆	C₂⁴	1	2	yes	—
332	Q₁₆×C₄₃	—	2	2	no	—
333	SD₁₆×C₄₃	—	4	2	no	—
334	D₈×C₄₃	—	2	2	no	—
335	C₂×C₈×C₄₃	—	2	2	no	—
336	C₂×C₈×C₄₃	—	4	1	no	—
337	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
338	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
339	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
340	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
341	C₄⋊C₄×C₄₃	—	2	2	no	—
342	C₄⋊C₄×C₄₃	—	2	2	no	—
343	C₄⋊C₄×C₄₃	—	2	2	no	—
344	C₄⋊C₄×C₄₃	—	2	2	no	—
345	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
346	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
347	C₂²⋊C₄×C₄₃	—	2	2	no	—
348	C₂²⋊C₄×C₄₃	—	2	2	no	—
349	C₂²⋊C₄×C₄₃	—	2	2	no	—
350	C₂²⋊C₄×C₄₃	—	2	2	no	—
351	C₂²⋊C₄×C₄₃	—	2	2	no	—
352	C₄²×C₄₃	—	2	2	no	—
353	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
354	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
355	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
356	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
357	C₂²⋊Dic₄₃	—	2	2	no	—
358	C₂²⋊Dic₄₃	—	2	2	no	—
359	C₂²⋊Dic₄₃	—	2	2	no	—
360	C₂²⋊Dic₄₃	—	2	2	no	—
361	C₂²⋊Dic₄₃	—	2	2	no	—
362	C₂²⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
363	C₂²⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
364	#10621885	—	4	2	no	—
365	#10621884	—	2	4	no	—
366	#10621883	—	4	2	no	—
367	#10621882	—	2	4	no	—
368	(C₂×D₄₃)⋊C₄	—	2	2	no	—
369	(C₂×D₄₃)⋊C₄	—	2	2	no	—
370	(C₂×D₄₃)⋊C₄	—	2	2	no	—
371	(C₂×D₄₃)⋊C₄	—	2	2	no	—
372	(C₂×D₄₃)⋊C₄	—	2	2	no	—
373	(C₂×D₄₃)⋊C₄	—	2	2	no	—
374	(C₂×D₄₃)⋊C₄	—	2	2	no	—
375	(C₂×D₄₃)⋊C₄	—	2	2	no	—
376	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
377	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
378	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
379	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
380	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
381	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
382	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
383	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
384	C₄⋊Dic₄₃	—	2	2	no	—
385	C₄⋊Dic₄₃	—	2	2	no	—
386	C₄⋊Dic₄₃	—	2	2	no	—
387	C₄⋊Dic₄₃	—	2	2	no	—
388	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
389	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
390	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
391	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
392	Dic₄₃⋊C₄	—	2	2	no	—
393	Dic₄₃⋊C₄	—	2	2	no	—
394	Dic₄₃⋊C₄	—	2	2	no	—
395	Dic₄₃⋊C₄	—	2	2	no	—
396	Dic₄₃⋊C₄	—	2	2	no	—
397	Dic₄₃⋊C₄	—	2	2	no	—
398	Dic₄₃⋊C₄	—	2	2	no	—
399	Dic₄₃⋊C₄	—	2	2	no	—
400	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
401	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
402	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
403	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
404	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
405	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
406	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
407	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
408	C₄×Dic₄₃	—	2	2	no	—
409	C₄×Dic₄₃	—	2	2	no	—
410	C₄×Dic₄₃	—	2	2	no	—
411	C₄×Dic₄₃	—	2	2	no	—
412	C₄×Dic₄₃	—	2	2	no	—
413	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
414	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
415	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
416	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
417	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
418	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
419	Dic₁₇₂	—	2	2	no	—
420	D₃₄₄	#41	1	4	yes	—
421	#10621873	—	2	4	no	—
422	#10621872	—	4	1	no	—
423	#10621872	—	4	1	no	—
424	C₈×D₄₃	—	2	2	no	—
425	C₈×D₄₃	—	2	2	no	—
426	C₂³×C₄₃	—	2	2	no	—
427	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
428	C₂²×D₄₃	—	2	2	no	—
429	C₂²×D₄₃	—	4	4	no	—
430	C₂²×D₄₃	—	8	2	no	—
431	C₂²×D₄₃	—	8	2	no	—
432	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
433	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
434	Q₈×C₄₃	—	2	2	no	—
435	Q₈×C₄₃	—	2	2	no	—
436	D₄×C₄₃	—	2	2	no	—
437	D₄×C₄₃	—	2	2	no	—
438	D₄×C₄₃	—	8	2	no	—
439	C₂×C₄×C₄₃	—	2	1	no	—
440	C₂×C₄×C₄₃	—	2	1	no	—
441	C₂×C₄×C₄₃	—	2	2	no	—
442	C₂×C₄×C₄₃	—	2	2	no	—
443	C₂×C₄×C₄₃	—	2	2	no	—
444	C₂×C₄×C₄₃	—	4	1	no	—
445	C₂×C₄×C₄₃	—	4	1	no	—
446	C₂×C₄×C₄₃	—	8	2	no	—
447	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
450	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
451	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
452	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
453	C₂²⋊D₄₃	—	4	1	no	—
454	C₂²⋊D₄₃	—	4	1	no	—
455	C₂²⋊D₄₃	—	4	4	no	—
456	C₂²⋊D₄₃	—	4	4	no	—
457	C₂²⋊D₄₃	—	8	2	no	—
458	C₂×Dic₄₃	—	2	2	no	—
459	C₂×Dic₄₃	—	2	2	no	—
460	C₂×Dic₄₃	—	2	2	no	—
461	C₂×Dic₄₃	—	8	2	no	—
462	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
463	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
466	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
467	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
468	D₁₇₂	—	2	2	no	—
469	D₁₇₂	—	4	1	no	—
470	D₁₇₂	—	4	4	no	—
471	D₁₇₂	C₂×#41	1	4	yes	—
472	C₄×D₄₃	—	2	1	no	—
473	C₄×D₄₃	—	2	1	no	—
474	C₄×D₄₃	—	2	1	no	—
475	C₄×D₄₃	—	2	1	no	—
476	C₄×D₄₃	—	4	4	no	—
477	C₄×D₄₃	—	4	4	no	—
478	C₄×D₄₃	—	8	2	no	—
479	C₄×D₄₃	—	8	2	no	—
480	C₄×D₄₃	—	8	2	no	—
481	C₄×D₄₃	—	8	2	no	—
482	C₄×D₄₃	—	8	2	no	—
483	Dic₈₆	—	2	2	no	—
484	Dic₈₆	—	2	2	no	—
485	Dic₈₆	—	4	1	no	—
486	Dic₈₆	—	8	2	no	—
487	C₈×C₄₃	—	2	1	no	—
488	C₈×C₄₃	—	2	1	no	—
489	C₈×C₄₃	—	2	1	no	—
490	C₈×C₄₃	C₂×#41	1	2	yes	—
491	C₄₃⋊C₈	—	2	1	no	—
492	C₄₃⋊C₈	—	2	1	no	—
493	C₄₃⋊C₈	—	2	1	no	—
494	C₄₃⋊C₈	—	2	1	no	—
495	#61487	—	43	1	no	maximal, Sylow
496	C₂²×C₄₃	—	2	1	no	—
497	C₂²×C₄₃	—	2	1	no	—
498	C₂²×C₄₃	—	2	1	no	—
499	C₂²×C₄₃	—	4	2	no	—
500	C₂²×C₄₃	—	4	2	no	—
501	C₂²×C₄₃	—	4	2	no	—
502	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
503	C₂×D₄₃	—	2	1	no	—
504	C₂×D₄₃	—	2	1	no	—
505	C₂×D₄₃	—	2	1	no	—
506	C₂×D₄₃	—	2	1	no	—
507	C₂×D₄₃	—	2	4	no	—
508	C₂×D₄₃	—	2	1	no	—
509	C₂×D₄₃	—	2	1	no	—
510	C₂×D₄₃	—	4	2	no	—
511	C₂×D₄₃	—	4	2	no	—
512	C₂×D₄₃	—	16	4	no	—
513	C₄×C₄₃	—	2	1	no	—
514	C₄×C₄₃	—	2	1	no	—
515	C₄×C₄₃	—	2	1	no	—
516	C₄×C₄₃	—	2	1	no	—
517	C₄×C₄₃	—	2	1	no	—
518	C₄×C₄₃	—	4	2	no	—
519	C₄×C₄₃	—	4	2	no	—
520	C₄×C₄₃	—	4	2	no	—
521	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
522	C₄×C₄₃	#585	1	1	yes	characteristic
523	Dic₄₃	—	2	1	no	—
524	Dic₄₃	—	2	1	no	—
525	Dic₄₃	—	2	1	no	—
526	Dic₄₃	—	2	1	no	—
527	Dic₄₃	—	2	1	no	—
528	Dic₄₃	—	2	1	no	—
529	Dic₄₃	—	4	2	no	—
530	Dic₄₃	—	4	2	no	—
531	Dic₄₃	—	4	2	no	—
532	#3521	—	43	2	no	—
533	#3393	—	43	1	no	—
534	#3380	—	43	1	no	—
535	#3376	—	43	2	no	—
536	#3342	—	43	1	no	—
537	#3339	—	43	1	no	—
538	#3336	—	43	1	no	—
539	#3323	—	43	2	no	—
540	#3311	—	43	2	no	—
541	#3307	—	43	2	no	—
542	#3283	—	43	1	no	—
543	#3280	—	43	1	no	—
544	#3280	—	43	1	no	—
545	#3177	—	43	1	no	—
546	#3175	—	43	1	no	—
547	#3168	D₄₃	1	1	yes	characteristic, complemented
548	#3125	—	43	2	no	—
549	#3123	—	43	2	no	—
550	#3111	—	43	2	no	—
551	#2966	—	43	1	no	—
552	#2951	—	43	1	no	—
553	#2948	—	43	1	no	—
554	C₄×#135	—	43	1	no	—
555	C₂×C₄₃	—	4	1	no	—
556	C₂×C₄₃	—	8	2	no	—
557	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
558	C₂×C₄₃	#3584	1	1	yes	characteristic
559	C₂×C₄₃	#3584	1	1	yes	characteristic
560	D₄₃	—	4	1	no	—
561	D₄₃	—	4	1	no	—
562	D₄₃	—	4	4	no	—
563	C₂×#135	—	43	1	no	—
564	C₂×#135	—	43	1	no	—
565	C₂²×D₈	—	43	1	no	—
566	#556	—	43	2	no	—
567	#556	—	43	2	no	—
568	#554	—	43	2	no	—
569	#553	—	43	2	no	—
570	#553	—	86	2	no	—
571	#552	—	43	2	no	—
572	#552	—	86	2	no	—
573	#551	—	86	2	no	—
574	#551	—	86	2	no	—
575	#547	—	43	2	no	—
576	#546	—	43	2	no	—
577	#546	—	43	2	no	—
578	#542	—	43	2	no	—
579	#541	—	43	2	no	—
580	#539	—	86	2	no	—
581	#538	—	86	2	no	—
582	#529	—	43	1	no	—
583	#529	—	86	2	no	—
584	#529	C₂×D₄₃	1	2	yes	complemented
585	C₂×#126	—	86	2	no	—
586	#520	—	43	2	no	—
587	#518	—	43	2	no	—
588	C₄×#41	—	43	2	no	—
589	#500	—	43	1	no	—
590	#499	—	43	1	no	—
591	#499	C₂×D₄₃	1	1	yes	characteristic, complemented
592	#495	—	43	1	no	—
593	#495	C₂×D₄₃	1	1	yes	characteristic
594	#494	—	43	1	no	—
595	#491	—	43	2	no	—
596	#489	—	43	2	no	—
597	#488	C₂×D₄₃	1	2	yes	complemented
598	#485	—	43	2	no	—
599	#485	—	43	2	no	—
600	#485	—	43	2	no	—
601	#483	—	43	2	no	—
602	#482	—	43	2	no	—
603	#481	—	43	2	no	—
604	#479	—	43	2	no	—
605	#478	—	43	2	no	—
606	#478	—	43	2	no	—
607	#478	—	43	2	no	—
608	#476	—	43	2	no	—
609	#475	—	43	2	no	—
610	#470	—	43	2	no	—
611	#468	—	43	2	no	—
612	#467	—	43	1	no	—
613	#467	—	43	1	no	—
614	#467	—	43	1	no	—
615	#467	C₂×D₄₃	1	1	yes	characteristic, complemented
616	#466	—	43	1	no	—
617	#466	C₂×D₄₃	1	1	yes	characteristic
618	#465	C₂×D₄₃	1	2	yes	complemented
619	#464	—	43	2	no	—
620	#464	—	43	2	no	—
621	#463	—	43	2	no	—
622	#463	—	43	2	no	—
623	#461	—	43	2	no	—
624	#461	—	43	2	no	—
625	#452	—	43	2	no	—
626	#452	—	43	2	no	—
627	#450	—	43	2	no	—
628	#450	—	43	2	no	—
629	#449	—	43	2	no	—
630	#449	—	43	2	no	—
631	#446	—	43	1	no	—
632	C₈×Q₈	—	43	1	no	—
633	#442	—	43	2	no	—
634	#442	—	43	2	no	—
635	#441	—	43	2	no	—
636	#440	—	43	2	no	—
637	#440	—	43	2	no	—
638	#440	—	43	2	no	—
639	C₄×Q₁₆	—	43	1	no	—
640	C₄×Q₁₆	—	43	1	no	—
641	C₄×Q₁₆	—	43	1	no	—
642	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
643	C₄×SD₁₆	—	43	2	no	—
644	C₄×SD₁₆	—	43	2	no	—
645	C₄×SD₁₆	C₂×D₄₃	1	2	yes	complemented
646	C₄×D₈	—	43	1	no	—
647	C₄×D₈	—	43	1	no	—
648	C₄×D₈	—	43	1	no	—
649	C₄×D₈	—	43	1	no	—
650	C₄×D₈	—	43	1	no	—
651	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
652	#436	—	43	1	no	—
653	#435	—	43	1	no	—
654	#435	—	43	1	no	—
655	C₈×D₄	—	43	1	no	—
656	C₈×D₄	—	43	1	no	—
657	C₈×D₄	—	43	1	no	—
658	#433	—	43	1	no	—
659	#433	—	43	1	no	—
660	#432	—	43	1	no	—
661	#427	—	43	1	no	—
662	#427	—	43	1	no	—
663	C₂×#107	—	43	1	no	—
664	#418	—	43	2	no	—
665	#417	—	43	2	no	—
666	#416	—	43	2	no	—
667	#405	—	43	1	no	—
668	#405	—	43	1	no	—
669	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
670	C₄₃	#61487	1	1	yes	characteristic, complemented, Sylow
671	C₂×#41	—	43	2	no	—
672	C₂×#41	—	43	2	no	—
673	C₂²×D₄	—	43	2	no	—
674	#135	—	86	4	no	—
675	#135	—	86	4	no	—
676	C₂×Q₁₆	—	43	2	no	—
677	C₂×Q₁₆	—	43	1	no	—
678	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
679	C₂×SD₁₆	—	43	2	no	—
680	C₂×SD₁₆	—	43	2	no	—
681	C₂×SD₁₆	—	43	2	no	—
682	C₂×SD₁₆	C₂²×D₄₃	1	2	yes	—
683	C₂×D₈	—	43	2	no	—
684	C₂×D₈	—	43	1	no	—
685	C₂×D₈	—	86	4	no	—
686	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
687	C₂×M₁₆	—	43	1	no	—
688	C₂×M₁₆	—	43	1	no	—
689	C₂²×C₈	—	43	1	no	—
690	C₂²×C₈	—	43	1	no	—
691	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
692	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
693	C₄⋊Q₈	—	43	2	no	—
694	C₄⋊Q₈	—	43	2	no	—
695	#126	—	2	2	no	—
696	#126	—	43	1	no	—
697	#126	—	43	1	no	—
698	#126	—	86	2	no	—
699	#126	—	86	2	no	—
700	#126	—	86	2	no	—
701	#126	—	86	2	no	—
702	#126	—	86	2	no	—
703	#126	—	86	2	no	—
704	#126	—	86	2	no	—
705	#126	—	86	2	no	—
706	#126	—	86	2	no	—
707	#125	—	43	2	no	—
708	#125	—	43	1	no	—
709	#125	—	86	2	no	—
710	#125	—	86	2	no	—
711	#125	—	86	2	no	—
712	#125	C₂²×D₄₃	1	2	yes	—
713	#124	—	43	2	no	—
714	#124	—	43	1	no	—
715	#124	—	86	2	no	—
716	#124	—	86	2	no	—
717	#124	C₂²×D₄₃	1	2	yes	—
718	#123	—	2	2	no	—
719	#123	—	43	1	no	—
720	#123	—	43	1	no	—
721	#123	—	86	2	no	—
722	#123	—	86	2	no	—
723	#123	—	86	2	no	—
724	#123	—	86	2	no	—
725	#123	—	86	2	no	—
726	#123	—	86	2	no	—
727	#123	—	86	2	no	—
728	C₂²⋊Q₈	—	43	1	no	—
729	C₂²⋊Q₈	—	43	2	no	—
730	C₂²⋊Q₈	—	43	2	no	—
731	C₂²⋊Q₈	—	43	2	no	—
732	C₂²⋊Q₈	—	86	2	no	—
733	C₂²⋊Q₈	—	86	2	no	—
734	C₂²⋊Q₈	—	86	2	no	—
735	C₂²⋊Q₈	—	86	2	no	—
736	C₂²⋊Q₈	—	86	2	no	—
737	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
738	#121	—	43	1	no	—
739	#121	—	43	2	no	—
740	#121	—	86	2	no	—
741	#121	—	86	2	no	—
742	#121	—	86	2	no	—
743	#121	—	86	2	no	—
744	#121	C₂²×D₄₃	1	2	yes	—
745	#120	—	86	2	no	—
746	#120	—	86	2	no	—
747	C₄×Q₈	—	43	1	no	—
748	C₄×Q₈	—	43	2	no	—
749	C₄×Q₈	—	43	2	no	—
750	C₄×Q₈	—	43	2	no	—
751	C₄×Q₈	—	86	2	no	—
752	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
753	C₄×D₄	—	2	2	no	—
754	C₄×D₄	—	43	1	no	—
755	C₄×D₄	—	43	1	no	—
756	C₄×D₄	—	43	2	no	—
757	C₄×D₄	—	43	2	no	—
758	C₄×D₄	—	43	2	no	—
759	C₄×D₄	—	43	1	no	—
760	C₄×D₄	—	43	2	no	—
761	C₄×D₄	—	43	2	no	—
762	C₄×D₄	—	86	2	no	—
763	C₄×D₄	—	86	2	no	—
764	C₄×D₄	—	86	2	no	—
765	C₄×D₄	—	86	2	no	—
766	C₄×D₄	—	86	2	no	—
767	C₄×D₄	—	86	2	no	—
768	C₄×D₄	—	86	2	no	—
769	C₄×D₄	C₂²×D₄₃	1	2	yes	—
770	#117	—	2	2	no	—
771	#117	—	43	1	no	—
772	#117	—	43	1	no	—
773	#117	—	43	2	no	—
774	#117	—	43	2	no	—
775	#117	—	86	2	no	—
776	#117	—	86	2	no	—
777	#117	—	86	2	no	—
778	#117	—	86	2	no	—
779	C₂×C₄⋊C₄	—	43	2	no	—
780	C₂×C₄⋊C₄	—	86	2	no	—
781	C₂×C₄⋊C₄	—	86	2	no	—
782	C₂×C₄⋊C₄	—	86	2	no	—
783	C₂×C₂²⋊C₄	—	86	2	no	—
784	C₂×C₂²⋊C₄	—	86	2	no	—
785	C₂×C₂²⋊C₄	—	86	2	no	—
786	C₂×C₂²⋊C₄	—	86	2	no	—
787	C₂×C₄²	—	86	2	no	—
788	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
789	#107	—	43	1	no	—
790	#107	—	43	1	no	—
791	#107	—	43	2	no	—
792	#107	—	43	2	no	—
793	#107	C₂²×D₄₃	1	1	yes	characteristic
794	#107	C₂²×D₄₃	1	1	yes	characteristic
795	#106	—	43	2	no	—
796	#106	—	43	2	no	—
797	#106	—	43	2	no	—
798	#106	C₂²×D₄₃	1	2	yes	—
799	C₄⋊C₈	—	43	1	no	—
800	C₄⋊C₈	—	43	1	no	—
801	C₄⋊C₈	—	43	1	no	—
802	C₄⋊C₈	—	43	1	no	—
803	C₄⋊C₈	—	43	1	no	—
804	C₄⋊C₈	—	43	1	no	—
805	#103	—	43	2	no	—
806	#103	—	43	2	no	—
807	#103	—	43	2	no	—
808	#103	—	43	2	no	—
809	#103	—	43	2	no	—
810	#103	—	43	2	no	—
811	#103	C₂²×D₄₃	1	2	yes	—
812	#103	C₂²×D₄₃	1	2	yes	—
813	#102	—	43	2	no	—
814	#102	—	43	2	no	—
815	#102	—	43	2	no	—
816	#102	—	43	2	no	—
817	#102	—	43	2	no	—
818	#102	—	43	2	no	—
819	#102	C₂²×D₄₃	1	2	yes	—
820	#102	C₂²×D₄₃	1	2	yes	—
821	C₂²⋊C₈	—	43	1	no	—
822	C₂²⋊C₈	—	43	1	no	—
823	C₂²⋊C₈	—	43	1	no	—
824	C₂²⋊C₈	—	43	1	no	—
825	C₂²⋊C₈	—	43	1	no	—
826	C₂²⋊C₈	—	43	1	no	—
827	#97	—	43	1	no	—
828	#97	—	43	1	no	—
829	#97	—	43	1	no	—
830	#97	—	43	1	no	—
831	C₄×C₈	—	43	1	no	—
832	C₄×C₈	—	43	1	no	—
833	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
834	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
835	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
836	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
837	C₂⁴	—	86	2	no	—
838	#41	—	86	4	no	—
839	#41	—	86	4	no	—
840	#41	—	172	2	no	—
841	#41	—	172	2	no	—
842	C₂×Q₈	—	43	1	no	—
843	C₂×Q₈	—	43	2	no	—
844	C₂×Q₈	—	86	2	no	—
845	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
846	C₂×D₄	—	2	2	no	—
847	C₂×D₄	—	43	1	no	—
848	C₂×D₄	—	43	1	no	—
849	C₂×D₄	—	43	1	no	—
850	C₂×D₄	—	43	2	no	—
851	C₂×D₄	—	86	2	no	—
852	C₂×D₄	—	86	2	no	—
853	C₂×D₄	—	86	4	no	—
854	C₂×D₄	—	86	2	no	—
855	C₂×D₄	—	86	2	no	—
856	C₂×D₄	—	172	2	no	—
857	C₂×D₄	C₂³×D₄₃	1	2	yes	—
858	C₂²×C₄	—	2	2	no	—
859	C₂²×C₄	—	43	1	no	—
860	C₂²×C₄	—	43	1	no	—
861	C₂²×C₄	—	86	2	no	—
862	C₂²×C₄	—	86	2	no	—
863	C₂²×C₄	—	86	2	no	—
864	C₂²×C₄	—	86	2	no	—
865	C₂²×C₄	—	86	2	no	—
866	C₂²×C₄	—	86	2	no	—
867	C₂²×C₄	—	86	2	no	—
868	C₂²×C₄	—	86	2	no	—
869	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
870	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
871	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
872	Q₁₆	—	2	2	no	—
873	Q₁₆	—	86	2	no	—
874	Q₁₆	—	172	2	no	—
875	SD₁₆	—	4	2	no	—
876	SD₁₆	—	86	4	no	—
877	SD₁₆	—	86	4	no	—
878	SD₁₆	—	172	2	no	—
879	D₈	—	2	2	no	—
880	D₈	—	43	4	no	—
881	D₈	—	86	4	no	—
882	M₁₆	—	172	1	no	—
883	M₁₆	—	172	1	no	—
884	C₂×C₈	—	2	2	no	—
885	C₂×C₈	—	4	1	no	—
886	C₂×C₈	—	43	1	no	—
887	C₂×C₈	—	43	1	no	—
888	C₂×C₈	—	43	1	no	—
889	C₂×C₈	—	43	1	no	—
890	C₂×C₈	—	86	2	no	—
891	C₂×C₈	—	86	2	no	—
892	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
893	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
894	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
895	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
896	C₄⋊C₄	—	2	2	no	—
897	C₄⋊C₄	—	2	2	no	—
898	C₄⋊C₄	—	2	2	no	—
899	C₄⋊C₄	—	2	2	no	—
900	C₄⋊C₄	—	43	1	no	—
901	C₄⋊C₄	—	43	1	no	—
902	C₄⋊C₄	—	43	1	no	—
903	C₄⋊C₄	—	43	1	no	—
904	C₄⋊C₄	—	43	1	no	—
905	C₄⋊C₄	—	43	1	no	—
906	C₄⋊C₄	—	43	1	no	—
907	C₄⋊C₄	—	43	1	no	—
908	C₄⋊C₄	—	43	1	no	—
909	C₄⋊C₄	—	43	1	no	—
910	C₄⋊C₄	—	43	2	no	—
911	C₄⋊C₄	—	43	2	no	—
912	C₄⋊C₄	—	86	2	no	—
913	C₄⋊C₄	—	86	2	no	—
914	C₄⋊C₄	—	86	2	no	—
915	C₄⋊C₄	—	86	2	no	—
916	C₄⋊C₄	—	86	2	no	—
917	C₄⋊C₄	—	86	2	no	—
918	C₄⋊C₄	—	86	2	no	—
919	C₄⋊C₄	—	86	2	no	—
920	C₄⋊C₄	—	86	2	no	—
921	C₄⋊C₄	—	86	2	no	—
922	C₄⋊C₄	—	86	2	no	—
923	C₄⋊C₄	—	86	2	no	—
924	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
925	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
926	C₂²⋊C₄	—	2	2	no	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	43	1	no	—
932	C₂²⋊C₄	—	43	1	no	—
933	C₂²⋊C₄	—	43	1	no	—
934	C₂²⋊C₄	—	43	1	no	—
935	C₂²⋊C₄	—	43	1	no	—
936	C₂²⋊C₄	—	43	1	no	—
937	C₂²⋊C₄	—	43	1	no	—
938	C₂²⋊C₄	—	43	1	no	—
939	C₂²⋊C₄	—	43	1	no	—
940	C₂²⋊C₄	—	43	1	no	—
941	C₂²⋊C₄	—	86	2	no	—
942	C₂²⋊C₄	—	86	2	no	—
943	C₂²⋊C₄	—	86	2	no	—
944	C₂²⋊C₄	—	86	2	no	—
945	C₂²⋊C₄	—	86	2	no	—
946	C₂²⋊C₄	—	86	2	no	—
947	C₂²⋊C₄	—	86	2	no	—
948	C₂²⋊C₄	—	86	2	no	—
949	C₂²⋊C₄	—	86	2	no	—
950	C₂²⋊C₄	—	86	2	no	—
951	C₂²⋊C₄	—	86	2	no	—
952	C₂²⋊C₄	—	86	2	no	—
953	C₂²⋊C₄	—	86	2	no	—
954	C₄²	—	2	2	no	—
955	C₄²	—	43	1	no	—
956	C₄²	—	43	1	no	—
957	C₄²	—	86	2	no	—
958	C₄²	—	86	2	no	—
959	C₄²	—	86	2	no	—
960	C₄²	—	86	2	no	—
961	C₄²	—	86	2	no	—
962	C₄²	D₄×D₄₃	1	1	yes	characteristic
963	C₄²	D₄×D₄₃	1	1	yes	characteristic
964	C₄²	C₂³×D₄₃	1	1	yes	characteristic
965	C₄²	C₂³×D₄₃	1	1	yes	characteristic
966	C₂³	—	2	2	no	—
967	C₂³	—	43	1	no	—
968	C₂³	—	43	1	no	—
969	C₂³	—	86	2	no	—
970	C₂³	—	344	2	no	—
971	C₂³	—	344	2	no	—
972	C₂³	—	172	4	no	—
973	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
974	Q₈	—	2	2	no	—
975	Q₈	—	2	2	no	—
976	Q₈	—	86	2	no	—
977	Q₈	—	86	2	no	—
978	Q₈	—	344	2	no	—
979	Q₈	—	172	1	no	—
980	D₄	—	2	2	no	—
981	D₄	—	2	2	no	—
982	D₄	—	8	2	no	—
983	D₄	—	43	4	no	—
984	D₄	—	86	2	no	—
985	D₄	—	344	2	no	—
986	D₄	—	172	1	no	—
987	D₄	—	172	4	no	—
988	D₄	—	172	1	no	—
989	D₄	—	172	1	no	—
990	D₄	—	172	4	no	—
991	D₄	—	172	4	no	—
992	C₂×C₄	—	2	1	no	—
993	C₂×C₄	—	2	1	no	—
994	C₂×C₄	—	2	2	no	—
995	C₂×C₄	—	2	2	no	—
996	C₂×C₄	—	2	2	no	—
997	C₂×C₄	—	4	1	no	—
998	C₂×C₄	—	4	1	no	—
999	C₂×C₄	—	8	2	no	—
1000	C₂×C₄	—	43	1	no	—
1001	C₂×C₄	—	43	1	no	—
1002	C₂×C₄	—	43	1	no	—
1003	C₂×C₄	—	43	1	no	—
1004	C₂×C₄	—	43	1	no	—
1005	C₂×C₄	—	43	1	no	—
1006	C₂×C₄	—	86	1	no	—
1007	C₂×C₄	—	86	1	no	—
1008	C₂×C₄	—	86	1	no	—
1009	C₂×C₄	—	86	1	no	—
1010	C₂×C₄	—	86	2	no	—
1011	C₂×C₄	—	86	2	no	—
1012	C₂×C₄	—	86	2	no	—
1013	C₂×C₄	—	344	2	no	—
1014	C₂×C₄	—	344	2	no	—
1015	C₂×C₄	—	344	2	no	—
1016	C₂×C₄	—	344	2	no	—
1017	C₂×C₄	—	344	2	no	—
1018	C₂×C₄	—	344	2	no	—
1019	C₂×C₄	—	172	4	no	—
1020	C₂×C₄	—	172	4	no	—
1021	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1022	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1023	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1024	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1025	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1026	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1027	C₈	—	2	1	no	—
1028	C₈	—	2	1	no	—
1029	C₈	—	2	1	no	—
1030	C₈	—	86	1	no	—
1031	C₈	—	86	1	no	—
1032	C₈	—	86	1	no	—
1033	C₈	—	86	1	no	—
1034	C₈	#41×D₄₃	1	2	yes	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	2	1	no	—
1038	C₂²	—	4	2	no	—
1039	C₂²	—	4	2	no	—
1040	C₂²	—	4	2	no	—
1041	C₂²	—	86	1	no	—
1042	C₂²	—	86	1	no	—
1043	C₂²	—	86	4	no	—
1044	C₂²	—	86	1	no	—
1045	C₂²	—	86	1	no	—
1046	C₂²	—	86	1	no	—
1047	C₂²	—	86	1	no	—
1048	C₂²	—	172	2	no	—
1049	C₂²	—	172	2	no	—
1050	C₂²	—	688	4	no	—
1051	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	1	no	—
1057	C₄	—	4	2	no	—
1058	C₄	—	4	2	no	—
1059	C₄	—	4	2	no	—
1060	C₄	—	86	1	no	—
1061	C₄	—	86	1	no	—
1062	C₄	—	86	1	no	—
1063	C₄	—	86	1	no	—
1064	C₄	—	86	1	no	—
1065	C₄	—	86	1	no	—
1066	C₄	—	172	2	no	—
1067	C₄	—	172	2	no	—
1068	C₄	—	172	2	no	—
1069	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1070	C₄	#14583735	1	1	yes	characteristic
1071	C₂	—	4	1	no	—
1072	C₂	—	8	2	no	—
1073	C₂	—	172	1	no	—
1074	C₂	—	172	1	no	—
1075	C₂	—	172	4	no	—
1076	C₂	#19148081	1	1	yes	characteristic
1077	C₂	#19149364	1	1	yes	characteristic
1078	C₂	#19149364	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3168	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3168	D₄₃
hypocenter	C₄₃	#61487
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3168

Complements

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

N	H ≅ G/N	type
1. #19148657	C₂	semidirect
2. #19147580	C₂	semidirect
3. #19147459	C₂	semidirect
4. #19147428	C₂	semidirect
5. #19147022	C₂	semidirect
6. #19146992	C₂	semidirect
7. #19146962	C₂	semidirect
8. #19146810	C₂	semidirect
9. #19146637	C₂	semidirect
10. #19146577	C₂	semidirect
11. #19146314	C₂	semidirect
12. #19146283	C₂	semidirect
13. #19146279	C₂	semidirect
14. #19145250	C₂	semidirect
15. #19145230	C₂	semidirect
16. #19144878	C₂	semidirect
17. #19144844	C₂	semidirect
18. #19144698	C₂	semidirect
19. #19143570	C₂	semidirect
20. #19143470	C₂	semidirect
21. #19143442	C₂	semidirect
22. C₄×#13063347	C₂	semidirect
23. C₄₃×#3168	C₂	semidirect
28. #14583618	C₂²	semidirect
29. #14583605	C₂²	semidirect
31. #14583596	C₂²	semidirect
36. #14583551	C₂²	semidirect
39. #14583514	C₂²	semidirect
46. #14583381	C₂²	semidirect
48. C₄×#10621898	C₂²	semidirect
49. #14583303	C₂²	semidirect
50. #14583300	C₂²	semidirect
52. #14583277	C₂²	semidirect
53. #14583266	C₂²	semidirect
54. #14583257	C₂²	semidirect
57. #14583237	C₂²	semidirect
58. #14583231	C₂²	semidirect
59. #14583220	C₂²	semidirect
60. #14583216	C₂²	semidirect
61. #14583203	C₂²	semidirect
62. #14583201	C₂²	semidirect
63. #14583198	C₂²	semidirect
64. #14583196	C₂²	semidirect
65. #14583188	C₂²	semidirect
66. #14583182	C₂²	semidirect
68. #14583144	C₂²	semidirect
70. #14583141	C₂²	semidirect
73. #14583119	C₂²	semidirect
74. #14583118	C₂²	semidirect
77. #14583103	C₂²	semidirect
78. #14583102	C₂²	semidirect
79. #14583064	C₂²	semidirect
80. #14583059	C₂²	semidirect
85. #14583029	C₂²	semidirect
86. C₈×Dic₈₆	C₂²	semidirect
89. #14583004	C₂²	semidirect
90. #14583002	C₂²	semidirect
91. #14582999	C₂²	semidirect
92. #14582997	C₂²	semidirect
93. C₄×Dic₁₇₂	C₂²	semidirect
94. C₄×Dic₁₇₂	C₂²	semidirect
95. Q₁₆×Dic₄₃	C₂²	semidirect
96. C₄×#10621873	C₂²	semidirect
97. C₄×#10621873	C₂²	semidirect
105. #14582970	C₂²	semidirect
108. C₈×C₂²⋊D₄₃	C₂²	semidirect
110. #14582958	C₂²	semidirect
111. #14582956	C₂²	semidirect
112. #14582937	C₂²	semidirect
114. #107×D₄₃	C₂²	semidirect
116. #14582899	C₂²	semidirect
117. #14582896	C₂²	semidirect
119. #14582853	C₂²	semidirect
120. C₄₃×#529	C₂²	semidirect
121. C₄₃×#499	C₂²	semidirect
123. C₄₃×#488	C₂²	semidirect
124. C₄₃×#467	C₂²	semidirect
126. C₄₃×#465	C₂²	semidirect
127. C₄×Q₁₆×C₄₃	C₂²	semidirect
128. C₄×SD₁₆×C₄₃	C₂²	semidirect
130. C₂×C₄×C₈×C₄₃	C₂²	semidirect
547. #3168	D₄₃	semidirect
584. #529	C₂×D₄₃	semidirect
591. #499	C₂×D₄₃	semidirect
597. #488	C₂×D₄₃	semidirect
615. #467	C₂×D₄₃	semidirect
618. #465	C₂×D₄₃	semidirect
642. C₄×Q₁₆	C₂×D₄₃	semidirect
645. C₄×SD₁₆	C₂×D₄₃	semidirect
669. C₂×C₄×C₈	C₂×D₄₃	semidirect
670. C₄₃	#61487	semidirect

Maximal subgroups

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

subgroup	index
#19148657	2
#19147580	2
#19147459	2
#19147428	2
#19147022	2
#19146992	2
#19146962	2
#19146810	2
#19146637	2
#19146577	2
#19146314	2
#19146283	2
#19146279	2
#19145250	2
#19145230	2
#19144878	2
#19144844	2
#19144698	2
#19143570	2
#19143470	2
#19143442	2
C₄×#13063347	2
C₄₃×#3168	2
#61487	43