Subgroups — #25975645

Order 11008.

1810 conjugacy classes of subgroups.

The subgroup lattice has 1156 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148312	C₂	1	1	yes	maximal, characteristic, complemented
2	#19148301	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147205	C₂	1	2	yes	maximal, complemented
4	#19147196	C₂	1	2	yes	maximal, complemented
5	#19147185	C₂	1	2	yes	maximal, complemented
6	#19147165	C₂	1	2	yes	maximal, complemented
7	#19147135	C₂	1	2	yes	maximal, complemented
8	#19147105	C₂	1	2	yes	maximal, complemented
9	#19147075	C₂	1	2	yes	maximal, complemented
10	#19147030	C₂	1	2	yes	maximal, complemented
11	#19145127	C₂	1	1	yes	maximal, characteristic, complemented
12	#19144582	C₂	1	1	yes	maximal, characteristic, complemented
13	#19144571	C₂	1	1	yes	maximal, characteristic, complemented
14	#19144524	C₂	1	1	yes	maximal, characteristic, complemented
15	#19144515	C₂	1	1	yes	maximal, characteristic, complemented
16	#19144455	C₂	1	1	yes	maximal, characteristic, complemented
17	#19144444	C₂	1	1	yes	maximal, characteristic, complemented
18	#19144253	C₂	1	1	yes	maximal, characteristic, complemented
19	#19143471	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143298	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143192	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#14582941	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3054	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063331	C₂²	1	1	yes	characteristic
25	#14583620	C₂²	1	2	yes	—
26	#14583619	—	2	1	no	—
27	#14583614	—	2	1	no	—
28	#14583613	C₂²	1	2	yes	—
29	#14583607	C₂²	1	2	yes	—
30	#14583606	—	2	1	no	—
31	#14583601	C₂²	1	2	yes	—
32	#14583596	C₂²	1	2	yes	—
33	#14583595	—	2	1	no	—
34	#14583595	—	2	1	no	—
35	#14583591	C₂²	1	2	yes	—
36	#14583589	—	2	1	no	—
37	#14583589	—	2	1	no	—
38	#14583583	C₂²	1	2	yes	—
39	#14583553	—	2	1	no	—
40	#14583549	C₂²	1	2	yes	—
41	#14583527	C₂²	1	1	yes	characteristic
42	#14583527	C₂²	1	1	yes	characteristic
43	#14583493	—	2	2	no	—
44	#14583484	—	2	2	no	—
45	#14583477	C₂²	1	1	yes	characteristic
46	#14583477	C₂²	1	1	yes	characteristic
47	#14583426	—	2	2	no	—
48	#14583410	C₂²	1	1	yes	characteristic
49	#14583405	—	2	2	no	—
50	#14583382	C₂²	1	1	yes	characteristic
51	#14583382	C₂²	1	1	yes	characteristic
52	#14583379	C₂²	1	1	yes	characteristic
53	#14583379	C₂²	1	1	yes	characteristic
54	C₂×#13063284	C₂²	1	1	yes	characteristic
55	C₂²×C₄⋊Dic₄₃	C₂²	1	1	yes	characteristic
56	#14583307	C₂²	1	2	yes	complemented
57	#14583307	C₂²	1	2	yes	complemented
58	#14583299	C₂²	1	2	yes	complemented
59	#14583296	C₂²	1	2	yes	complemented
60	#14583239	C₂²	1	2	yes	complemented
61	#14583238	C₂²	1	2	yes	complemented
62	#14583237	C₂²	1	2	yes	—
63	#14583237	C₂²	1	2	yes	—
64	#14583233	C₂²	1	2	yes	complemented
65	#14583232	C₂²	1	2	yes	—
66	#14583228	C₂²	1	2	yes	complemented
67	#14583227	C₂²	1	2	yes	—
68	#14583222	C₂²	1	2	yes	complemented
69	#14583221	C₂²	1	2	yes	complemented
70	#14583220	C₂²	1	2	yes	—
71	#14583220	C₂²	1	2	yes	—
72	#14583216	C₂²	1	2	yes	complemented
73	#14583215	C₂²	1	2	yes	—
74	#14583211	C₂²	1	2	yes	complemented
75	#14583210	C₂²	1	2	yes	—
76	#14583208	C₂²	1	2	yes	complemented
77	#14583204	C₂²	1	2	yes	complemented
78	#14583201	C₂²	1	2	yes	complemented
79	#14583197	C₂²	1	2	yes	complemented
80	#14583192	C₂²	1	2	yes	complemented
81	#14583187	C₂²	1	2	yes	complemented
82	#14583182	C₂²	1	2	yes	complemented
83	#14583177	C₂²	1	2	yes	complemented
84	#14583154	C₂²	1	2	yes	complemented
85	#14583149	C₂²	1	2	yes	complemented
86	#14583125	C₂²	1	2	yes	complemented
87	#14583125	C₂²	1	2	yes	complemented
88	#14583000	C₂²	1	2	yes	complemented
89	#14583000	C₂²	1	2	yes	complemented
90	Q₁₆×Dic₄₃	C₂²	1	2	yes	complemented
91	D₈×Dic₄₃	C₂²	1	2	yes	complemented
92	#14582975	C₂²	1	2	yes	—
93	#14582975	C₂²	1	2	yes	—
94	#14582968	C₂²	1	2	yes	—
95	#14582968	C₂²	1	2	yes	—
96	#14582942	C₂²	1	1	yes	characteristic
97	#14582942	C₂²	1	1	yes	characteristic
98	#14582942	C₂²	1	1	yes	characteristic
99	#14582942	C₂²	1	1	yes	characteristic
100	#14582941	C₂²	1	2	yes	—
101	#14582941	C₂²	1	2	yes	—
102	#14582941	C₂²	1	2	yes	—
103	#14582941	C₂²	1	2	yes	—
104	#14582938	C₂²	1	2	yes	complemented
105	#14582938	C₂²	1	2	yes	complemented
106	#14582936	C₂²	1	2	yes	complemented
107	C₂×#13063259	C₂²	1	1	yes	characteristic
108	C₂×#13063259	C₂²	1	1	yes	characteristic
109	#107×D₄₃	C₂²	1	2	yes	complemented
110	C₂×#13063257	C₂²	1	1	yes	characteristic
111	C₂×#13063257	C₂²	1	1	yes	characteristic
112	#14582925	C₂²	1	1	yes	characteristic
113	#14582900	C₂²	1	1	yes	characteristic
114	#14582900	C₂²	1	1	yes	characteristic
115	#14582900	C₂²	1	1	yes	characteristic
116	#14582900	C₂²	1	1	yes	characteristic
117	#14582865	C₂²	1	1	yes	characteristic
118	#14582863	C₂²	1	1	yes	characteristic
119	#14582854	C₂²	1	1	yes	characteristic
120	C₂×#135×C₄₃	C₂²	1	1	yes	characteristic
121	C₂²×M₁₆×C₄₃	C₂²	1	1	yes	characteristic
122	C₄₃×#525	C₂²	1	1	yes	characteristic
123	C₄₃×#525	C₂²	1	1	yes	characteristic
124	C₄₃×#470	C₂²	1	1	yes	characteristic
125	C₄₃×#470	C₂²	1	1	yes	characteristic
126	C₄₃×#469	C₂²	1	1	yes	characteristic
127	C₄₃×#469	C₂²	1	1	yes	characteristic
128	C₄₃×#468	C₂²	1	1	yes	characteristic
129	C₄₃×#468	C₂²	1	1	yes	characteristic
130	C₄₃×#468	C₂²	1	1	yes	characteristic
131	C₄₃×#468	C₂²	1	1	yes	characteristic
132	C₄₃×#427	C₂²	1	1	yes	characteristic
133	C₄₃×#416	C₂²	1	1	yes	characteristic
134	C₄₃×#416	C₂²	1	1	yes	characteristic
135	C₂×#10621898	C₂³	1	1	yes	characteristic
136	C₂×#10621900	—	2	2	no	—
137	C₂³×Dic₄₃	—	2	1	no	—
138	#13063331	—	2	4	no	—
139	C₂×#10621877	C₂³	1	1	yes	characteristic
140	C₂×#10621877	C₂³	1	1	yes	characteristic
141	C₂×#10621872	C₂³	1	2	yes	—
142	C₂×C₈×D₄₃	C₂³	1	2	yes	—
143	#13063325	—	2	1	no	—
144	#13063325	—	2	1	no	—
145	#13063324	C₂³	1	2	yes	—
146	#13063324	C₂³	1	2	yes	—
147	#13063320	—	2	2	no	—
148	#13063320	—	2	2	no	—
149	#13063318	—	2	2	no	—
150	#13063318	—	2	2	no	—
151	#13063318	—	2	2	no	—
152	#13063318	—	2	2	no	—
153	#13063317	—	2	1	no	—
154	#13063317	—	2	1	no	—
155	#13063316	—	2	2	no	—
156	#13063316	C₂³	1	2	yes	—
157	#13063316	C₂³	1	2	yes	—
158	#13063315	—	2	2	no	—
159	#13063315	—	2	2	no	—
160	#13063312	—	2	2	no	—
161	#13063311	—	2	2	no	—
162	#13063311	—	2	2	no	—
163	#13063309	—	2	2	no	—
164	#13063309	—	2	2	no	—
165	#13063308	D₄	1	2	yes	—
166	#13063307	—	2	2	no	—
167	#13063307	—	2	2	no	—
168	#13063306	—	2	2	no	—
169	#13063306	—	2	2	no	—
170	#13063305	—	2	2	no	—
171	#13063304	—	2	1	no	—
172	#13063304	—	2	1	no	—
173	#13063304	D₄	1	1	yes	characteristic
174	#13063304	D₄	1	1	yes	characteristic
175	#13063302	—	2	2	no	—
176	#13063302	—	2	2	no	—
177	#13063302	—	2	2	no	—
178	#13063302	—	2	2	no	—
179	#13063301	C₂³	1	2	yes	—
180	#13063301	C₂³	1	2	yes	—
181	#13063299	—	2	1	no	—
182	#13063299	—	2	1	no	—
183	#13063299	D₄	1	1	yes	characteristic
184	#13063299	D₄	1	1	yes	characteristic
185	#13063297	—	2	2	no	—
186	#13063297	—	2	2	no	—
187	#13063297	—	2	2	no	—
188	#13063297	—	2	2	no	—
189	#13063296	—	2	2	no	—
190	#13063296	C₂³	1	2	yes	—
191	#13063296	C₂³	1	2	yes	—
192	#13063294	D₄	1	2	yes	—
193	Q₈×Dic₄₃	C₂³	1	2	yes	—
194	Q₈×Dic₄₃	C₂³	1	2	yes	—
195	C₄×Dic₈₆	—	2	1	no	—
196	C₄×Dic₈₆	—	2	1	no	—
197	#13063290	—	2	2	no	—
198	C₄×D₁₇₂	—	2	1	no	—
199	C₄×D₁₇₂	—	2	1	no	—
200	D₄×Dic₄₃	—	2	2	no	—
201	D₄×Dic₄₃	—	2	2	no	—
202	D₄×Dic₄₃	—	2	2	no	—
203	D₄×Dic₄₃	C₂³	1	2	yes	—
204	D₄×Dic₄₃	C₂³	1	2	yes	—
205	C₄×C₂²⋊D₄₃	C₂³	1	2	yes	—
206	C₄×C₂²⋊D₄₃	C₂³	1	2	yes	—
207	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
208	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
209	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
210	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
211	#13063284	—	2	1	no	—
212	#13063284	—	2	1	no	—
213	#13063284	—	2	1	no	—
214	#13063284	—	2	1	no	—
215	#13063284	C₂³	1	2	yes	—
216	#13063284	C₂³	1	2	yes	—
217	#13063284	C₂³	1	1	yes	characteristic
218	#13063283	—	2	2	no	—
219	#13063283	C₂³	1	2	yes	—
220	#13063283	C₂³	1	2	yes	—
221	#13063281	—	2	2	no	—
222	#13063281	—	2	2	no	—
223	C₂×C₄⋊Dic₄₃	—	2	1	no	—
224	C₂×C₄⋊Dic₄₃	—	2	1	no	—
225	C₂×C₄⋊Dic₄₃	—	2	1	no	—
226	C₂×C₄⋊Dic₄₃	—	2	1	no	—
227	C₂×C₄⋊Dic₄₃	—	2	1	no	—
228	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
229	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
230	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
231	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
232	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
233	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
234	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
235	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
236	C₂×C₂²⋊Dic₄₃	—	2	1	no	—
237	C₂×C₄×Dic₄₃	—	2	1	no	—
238	#13063259	C₂³	1	2	yes	—
239	#13063259	C₂³	1	2	yes	—
240	#13063259	C₂³	1	2	yes	—
241	#13063259	C₂³	1	2	yes	—
242	#13063258	C₂³	1	2	yes	—
243	#13063258	C₂³	1	2	yes	—
244	#13063258	C₂³	1	2	yes	—
245	#13063258	C₂³	1	2	yes	—
246	#13063257	C₂³	1	2	yes	—
247	#13063257	C₂³	1	2	yes	—
248	#13063257	C₂³	1	2	yes	—
249	#13063257	C₂³	1	2	yes	—
250	#13063256	C₂³	1	2	yes	—
251	#13063256	C₂³	1	2	yes	—
252	#13063256	C₂³	1	2	yes	—
253	#13063256	C₂³	1	2	yes	—
254	Dic₄₃⋊C₈	C₂³	1	2	yes	—
255	Dic₄₃⋊C₈	C₂³	1	2	yes	—
256	#13063249	C₂³	1	2	yes	—
257	#13063249	C₂³	1	2	yes	—
258	#13063249	C₂³	1	2	yes	—
259	#13063249	C₂³	1	2	yes	—
260	#13063246	C₂³	1	2	yes	—
261	#13063246	C₂³	1	2	yes	—
262	#13063246	C₂³	1	2	yes	—
263	#13063246	C₂³	1	2	yes	—
264	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
265	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
266	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
267	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
268	#13063235	C₂³	1	2	yes	—
269	C₈×Dic₄₃	C₂³	1	2	yes	—
270	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
271	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
272	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
273	#135×C₄₃	—	2	4	no	—
274	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
275	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
276	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
277	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
278	C₂×M₁₆×C₄₃	—	2	4	no	—
279	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
280	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
281	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
282	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
283	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
284	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
285	#123×C₄₃	—	2	1	no	—
286	#123×C₄₃	—	2	1	no	—
287	C₂²⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
288	C₂²⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
289	C₂²⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
290	C₂²⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
291	#121×C₄₃	C₂³	1	1	yes	characteristic
292	#121×C₄₃	C₂³	1	1	yes	characteristic
293	#121×C₄₃	C₂³	1	1	yes	characteristic
294	#121×C₄₃	C₂³	1	1	yes	characteristic
295	#120×C₄₃	—	2	1	no	—
296	#120×C₄₃	—	2	1	no	—
297	C₄×D₄×C₄₃	—	2	1	no	—
298	C₄×D₄×C₄₃	—	2	1	no	—
299	C₄×D₄×C₄₃	—	2	1	no	—
300	C₄×D₄×C₄₃	—	2	1	no	—
301	#117×C₄₃	C₂³	1	1	yes	characteristic
302	#117×C₄₃	C₂³	1	1	yes	characteristic
303	#107×C₄₃	C₂³	1	1	yes	characteristic
304	#107×C₄₃	C₂³	1	1	yes	characteristic
305	#106×C₄₃	C₂³	1	1	yes	characteristic
306	#106×C₄₃	C₂³	1	1	yes	characteristic
307	#103×C₄₃	C₂³	1	1	yes	characteristic
308	#103×C₄₃	C₂³	1	1	yes	characteristic
309	#103×C₄₃	C₂³	1	1	yes	characteristic
310	#103×C₄₃	C₂³	1	1	yes	characteristic
311	#102×C₄₃	C₂³	1	1	yes	characteristic
312	#102×C₄₃	C₂³	1	1	yes	characteristic
313	#102×C₄₃	C₂³	1	1	yes	characteristic
314	#102×C₄₃	C₂³	1	1	yes	characteristic
315	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
316	#41×C₄₃	—	2	2	no	—
317	#41×C₄₃	—	2	2	no	—
318	#41×C₄₃	—	2	2	no	—
319	#41×C₄₃	—	2	2	no	—
320	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
321	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
322	C₂×D₄×C₄₃	—	2	1	no	—
323	C₂×D₄×C₄₃	—	2	1	no	—
324	C₂×D₄×C₄₃	—	2	1	no	—
325	C₂×D₄×C₄₃	—	2	1	no	—
326	C₂×D₄×C₄₃	—	2	1	no	—
327	C₂×D₄×C₄₃	—	2	1	no	—
328	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
329	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₄₃	—	2	2	no	—
331	C₂²×C₄×C₄₃	—	2	2	no	—
332	C₂²×C₄×C₄₃	—	2	1	no	—
333	C₂²×C₄×C₄₃	—	2	1	no	—
334	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
337	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
338	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
340	C₂×C₂²⋊D₄₃	—	2	2	no	—
341	C₂×C₂²⋊D₄₃	—	2	2	no	—
342	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
343	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
344	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
345	C₂²×Dic₄₃	—	2	2	no	—
346	C₂²×Dic₄₃	—	2	2	no	—
347	C₂²×Dic₄₃	—	2	2	no	—
348	C₂²×Dic₄₃	—	2	1	no	—
349	C₂²×Dic₄₃	—	2	1	no	—
350	C₂²×Dic₄₃	—	2	1	no	—
351	C₂²×Dic₄₃	—	2	2	no	—
352	C₂²×Dic₄₃	—	2	1	no	—
353	C₂²×Dic₄₃	—	8	2	no	—
354	#10621900	—	8	4	no	—
355	#10621898	—	2	2	no	—
356	#10621898	—	2	2	no	—
357	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
358	C₂×C₄×D₄₃	—	2	2	no	—
359	C₂×C₄×D₄₃	—	2	2	no	—
360	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
361	C₂×Dic₈₆	—	2	2	no	—
362	C₂×Dic₈₆	—	2	2	no	—
363	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
364	Q₁₆×C₄₃	—	2	2	no	—
365	SD₁₆×C₄₃	—	2	2	no	—
366	SD₁₆×C₄₃	—	2	2	no	—
367	D₈×C₄₃	—	2	2	no	—
368	M₁₆×C₄₃	—	2	2	no	—
369	M₁₆×C₄₃	—	2	2	no	—
370	M₁₆×C₄₃	—	2	2	no	—
371	M₁₆×C₄₃	—	2	2	no	—
372	C₂×C₈×C₄₃	—	2	2	no	—
373	C₂×C₈×C₄₃	#41	1	4	yes	complemented
374	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
376	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
377	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄×C₄₃	—	2	1	no	—
379	C₄⋊C₄×C₄₃	—	2	1	no	—
380	C₄⋊C₄×C₄₃	—	2	1	no	—
381	C₄⋊C₄×C₄₃	—	2	1	no	—
382	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
383	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
385	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
386	C₂²⋊C₄×C₄₃	—	2	1	no	—
387	C₂²⋊C₄×C₄₃	—	2	1	no	—
388	C₂²⋊C₄×C₄₃	—	2	1	no	—
389	C₂²⋊C₄×C₄₃	—	2	1	no	—
390	C₂²⋊C₄×C₄₃	—	2	1	no	—
391	C₂²⋊C₄×C₄₃	—	2	1	no	—
392	C₂²⋊C₄×C₄₃	—	2	1	no	—
393	C₂²⋊C₄×C₄₃	—	2	1	no	—
394	C₂²⋊C₄×C₄₃	—	2	1	no	—
395	C₂²⋊C₄×C₄₃	—	2	1	no	—
396	C₄²×C₄₃	—	2	1	no	—
397	C₄²×C₄₃	—	2	1	no	—
398	C₂²⋊Dic₄₃	—	2	2	no	—
399	C₂²⋊Dic₄₃	—	2	2	no	—
400	C₂²⋊Dic₄₃	—	2	2	no	—
401	C₂²⋊Dic₄₃	—	2	2	no	—
402	C₂²⋊Dic₄₃	—	2	2	no	—
403	C₂²⋊Dic₄₃	—	2	2	no	—
404	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
405	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
406	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
407	(C₂×D₄₃)⋊C₄	—	2	2	no	—
408	(C₂×D₄₃)⋊C₄	—	2	2	no	—
409	(C₂×D₄₃)⋊C₄	—	2	2	no	—
410	(C₂×D₄₃)⋊C₄	—	2	2	no	—
411	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
412	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
413	C₄⋊Dic₄₃	—	2	1	no	—
414	C₄⋊Dic₄₃	—	2	1	no	—
415	C₄⋊Dic₄₃	—	2	2	no	—
416	C₄⋊Dic₄₃	—	2	2	no	—
417	C₄⋊Dic₄₃	—	2	1	no	—
418	C₄⋊Dic₄₃	—	2	1	no	—
419	C₄⋊Dic₄₃	—	2	2	no	—
420	C₄⋊Dic₄₃	—	2	2	no	—
421	C₄⋊Dic₄₃	—	2	2	no	—
422	C₄⋊Dic₄₃	—	2	2	no	—
423	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
424	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
425	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
426	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
427	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
428	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
429	Dic₄₃⋊C₄	—	2	2	no	—
430	Dic₄₃⋊C₄	—	2	2	no	—
431	Dic₄₃⋊C₄	—	2	2	no	—
432	Dic₄₃⋊C₄	—	2	2	no	—
433	Dic₄₃⋊C₄	—	2	2	no	—
434	Dic₄₃⋊C₄	—	2	2	no	—
435	Dic₄₃⋊C₄	—	2	2	no	—
436	Dic₄₃⋊C₄	—	2	2	no	—
437	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
438	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
439	C₄×Dic₄₃	—	2	2	no	—
440	C₄×Dic₄₃	—	2	2	no	—
441	C₄×Dic₄₃	—	2	2	no	—
442	C₄×Dic₄₃	—	2	2	no	—
443	C₄×Dic₄₃	—	2	2	no	—
444	C₄×Dic₄₃	—	2	2	no	—
445	C₄×Dic₄₃	C₂⁴	1	2	yes	—
446	#10621877	—	2	2	no	—
447	#10621877	—	2	2	no	—
448	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
449	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
450	#10621872	—	2	4	no	—
451	C₈×D₄₃	—	2	4	no	—
452	C₂³×C₄₃	—	2	2	no	—
453	C₂³×C₄₃	—	2	1	no	—
454	C₂³×C₄₃	—	2	1	no	—
455	C₂³×C₄₃	—	4	1	no	—
456	C₂³×C₄₃	—	4	1	no	—
457	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
458	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
459	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
460	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
461	Q₈×C₄₃	—	2	1	no	—
462	Q₈×C₄₃	—	2	1	no	—
463	Q₈×C₄₃	—	2	1	no	—
464	Q₈×C₄₃	—	2	1	no	—
465	D₄×C₄₃	—	2	1	no	—
466	D₄×C₄₃	—	2	1	no	—
467	D₄×C₄₃	—	2	1	no	—
468	D₄×C₄₃	—	2	1	no	—
469	D₄×C₄₃	—	4	2	no	—
470	D₄×C₄₃	—	4	2	no	—
471	D₄×C₄₃	—	4	2	no	—
472	D₄×C₄₃	—	4	2	no	—
473	D₄×C₄₃	—	8	1	no	—
474	D₄×C₄₃	—	8	1	no	—
475	C₂×C₄×C₄₃	—	2	2	no	—
476	C₂×C₄×C₄₃	—	2	2	no	—
477	C₂×C₄×C₄₃	—	2	2	no	—
478	C₂×C₄×C₄₃	—	2	1	no	—
479	C₂×C₄×C₄₃	—	2	1	no	—
480	C₂×C₄×C₄₃	—	2	1	no	—
481	C₂×C₄×C₄₃	—	2	1	no	—
482	C₂×C₄×C₄₃	—	2	1	no	—
483	C₂×C₄×C₄₃	—	2	1	no	—
484	C₂×C₄×C₄₃	—	2	1	no	—
485	C₂×C₄×C₄₃	—	2	1	no	—
486	C₂×C₄×C₄₃	—	2	1	no	—
487	C₂×C₄×C₄₃	—	2	1	no	—
488	C₂×C₄×C₄₃	—	4	2	no	—
489	C₂×C₄×C₄₃	—	4	2	no	—
490	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
494	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
495	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
496	C₂²⋊D₄₃	—	2	4	no	—
497	C₂²⋊D₄₃	—	4	2	no	—
498	C₂²⋊D₄₃	—	4	2	no	—
499	C₂²⋊D₄₃	—	8	2	no	—
500	C₂²⋊D₄₃	—	8	2	no	—
501	C₂×Dic₄₃	—	2	2	no	—
502	C₂×Dic₄₃	—	2	2	no	—
503	C₂×Dic₄₃	—	2	2	no	—
504	C₂×Dic₄₃	—	2	2	no	—
505	C₂×Dic₄₃	—	4	4	no	—
506	C₂×Dic₄₃	—	8	2	no	—
507	C₂×Dic₄₃	—	8	2	no	—
508	C₂×Dic₄₃	—	8	1	no	—
509	C₂×Dic₄₃	—	8	1	no	—
510	C₂×Dic₄₃	—	8	1	no	—
511	C₂×Dic₄₃	—	8	2	no	—
512	C₂×Dic₄₃	—	8	1	no	—
513	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
514	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
515	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
516	D₁₇₂	—	2	2	no	—
517	C₄×D₄₃	—	2	2	no	—
518	C₄×D₄₃	—	2	2	no	—
519	C₄×D₄₃	—	8	2	no	—
520	C₄×D₄₃	—	8	2	no	—
521	Dic₈₆	—	2	2	no	—
522	Dic₈₆	—	8	2	no	—
523	Dic₈₆	—	8	2	no	—
524	C₈×C₄₃	—	2	1	no	—
525	C₈×C₄₃	—	2	1	no	—
526	C₈×C₄₃	C₂×#41	1	2	yes	—
527	C₈×C₄₃	C₂×#41	1	2	yes	—
528	C₄₃⋊C₈	—	2	2	no	—
529	C₄₃⋊C₈	—	2	2	no	—
530	#61266	—	43	1	no	maximal, Sylow
531	C₂²×C₄₃	—	2	1	no	—
532	C₂²×C₄₃	—	2	1	no	—
533	C₂²×C₄₃	—	2	1	no	—
534	C₂²×C₄₃	—	2	1	no	—
535	C₂²×C₄₃	—	2	1	no	—
536	C₂²×C₄₃	—	2	1	no	—
537	C₂²×C₄₃	—	2	1	no	—
538	C₂²×C₄₃	—	2	1	no	—
539	C₂²×C₄₃	—	4	4	no	—
540	C₂²×C₄₃	—	4	1	no	—
541	C₂²×C₄₃	—	4	1	no	—
542	C₂²×C₄₃	—	4	1	no	—
543	C₂²×C₄₃	—	4	1	no	—
544	C₂²×C₄₃	—	4	1	no	—
545	C₂²×C₄₃	—	4	1	no	—
546	C₂²×C₄₃	#547	1	2	yes	—
547	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
548	C₂×D₄₃	—	2	2	no	—
549	C₂×D₄₃	—	2	2	no	—
550	C₂×D₄₃	—	2	2	no	—
551	C₄×C₄₃	—	2	1	no	—
552	C₄×C₄₃	—	2	1	no	—
553	C₄×C₄₃	—	4	1	no	—
554	C₄×C₄₃	—	4	1	no	—
555	C₄×C₄₃	—	4	1	no	—
556	C₄×C₄₃	—	4	1	no	—
557	C₄×C₄₃	—	4	1	no	—
558	C₄×C₄₃	—	4	1	no	—
559	C₄×C₄₃	#547	1	2	yes	—
560	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
561	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
562	Dic₄₃	—	2	2	no	—
563	Dic₄₃	—	2	2	no	—
564	Dic₄₃	—	2	2	no	—
565	Dic₄₃	—	4	2	no	—
566	Dic₄₃	—	4	2	no	—
567	Dic₄₃	—	4	2	no	—
568	Dic₄₃	—	4	2	no	—
569	#3493	—	43	1	no	—
570	#3492	—	43	1	no	—
571	#3356	—	43	2	no	—
572	#3355	—	43	2	no	—
573	#3354	—	43	2	no	—
574	#3352	—	43	2	no	—
575	#3350	—	43	2	no	—
576	#3348	—	43	2	no	—
577	#3346	—	43	2	no	—
578	#3343	—	43	2	no	—
579	#3163	—	43	1	no	—
580	#3099	—	43	1	no	—
581	#3098	—	43	1	no	—
582	#3093	—	43	1	no	—
583	#3092	—	43	1	no	—
584	#3084	—	43	1	no	—
585	#3083	—	43	1	no	—
586	#3060	—	43	1	no	—
587	#3054	D₄₃	1	1	yes	characteristic, complemented
588	#2951	—	43	1	no	—
589	#2930	—	43	1	no	—
590	#2913	—	43	1	no	—
591	C₂×#428	—	43	1	no	—
592	C₂×C₄₃	—	2	2	no	—
593	C₂×C₄₃	—	4	1	no	—
594	C₂×C₄₃	—	4	1	no	—
595	C₂×C₄₃	—	8	1	no	—
596	C₂×C₄₃	—	8	1	no	—
597	C₂×C₄₃	C₂×#547	1	1	yes	characteristic
598	C₂×C₄₃	#3585	1	1	yes	characteristic
599	C₂×C₄₃	#3586	1	1	yes	characteristic
600	D₄₃	—	4	2	no	—
601	C₂×#135	C₂×D₄₃	1	1	yes	characteristic
602	C₂×#131	—	43	1	no	—
603	C₂²×M₁₆	C₂×D₄₃	1	1	yes	characteristic
604	#556	—	43	2	no	—
605	#556	—	86	1	no	—
606	#555	—	43	2	no	—
607	#555	—	86	1	no	—
608	#554	—	43	2	no	—
609	#554	—	86	1	no	—
610	#553	—	43	2	no	—
611	#553	—	43	2	no	—
612	#553	—	86	1	no	—
613	#553	—	86	1	no	—
614	#552	—	43	2	no	—
615	#552	—	43	2	no	—
616	#552	—	86	1	no	—
617	#552	—	86	1	no	—
618	#547	—	43	2	no	—
619	#547	—	86	1	no	—
620	#544	—	43	1	no	—
621	#544	—	43	1	no	—
622	#539	—	86	2	no	—
623	#538	—	86	2	no	—
624	#537	—	43	1	no	—
625	#537	—	43	1	no	—
626	#529	—	86	2	no	—
627	#525	—	43	1	no	—
628	#525	—	86	2	no	—
629	#525	C₂×D₄₃	1	1	yes	characteristic
630	#525	C₂×D₄₃	1	1	yes	characteristic
631	#520	—	43	1	no	—
632	#520	—	43	1	no	—
633	#520	—	43	1	no	—
634	#520	—	43	1	no	—
635	C₂×#117	—	43	1	no	—
636	C₂²×C₄⋊C₄	—	43	1	no	—
637	#501	—	43	2	no	—
638	#501	—	43	2	no	—
639	#499	—	43	2	no	—
640	#498	—	43	2	no	—
641	#485	—	43	2	no	—
642	#485	—	43	2	no	—
643	#485	—	43	2	no	—
644	#485	—	43	2	no	—
645	#484	—	43	2	no	—
646	#484	—	43	2	no	—
647	#483	—	43	2	no	—
648	#483	—	43	2	no	—
649	#482	—	43	2	no	—
650	#482	—	43	2	no	—
651	#482	—	43	2	no	—
652	#482	—	43	2	no	—
653	#481	—	43	2	no	—
654	#481	—	43	2	no	—
655	#480	—	43	2	no	—
656	#480	—	43	2	no	—
657	#479	—	43	2	no	—
658	#479	—	43	2	no	—
659	#478	—	43	2	no	—
660	#478	—	43	2	no	—
661	#477	—	43	2	no	—
662	#476	—	43	2	no	—
663	#475	—	43	2	no	—
664	#474	—	43	2	no	—
665	#470	—	43	2	no	—
666	#470	C₂×D₄₃	1	1	yes	characteristic
667	#470	C₂×D₄₃	1	1	yes	characteristic
668	#469	—	43	2	no	—
669	#469	C₂×D₄₃	1	1	yes	characteristic
670	#469	C₂×D₄₃	1	1	yes	characteristic
671	#468	C₂×D₄₃	1	1	yes	characteristic
672	#468	C₂×D₄₃	1	1	yes	characteristic
673	#468	C₂×D₄₃	1	1	yes	characteristic
674	#468	C₂×D₄₃	1	1	yes	characteristic
675	#465	—	43	2	no	—
676	#465	—	43	2	no	—
677	#440	—	43	2	no	—
678	#440	—	43	2	no	—
679	C₄×Q₁₆	—	43	2	no	—
680	C₄×D₈	—	43	2	no	—
681	#436	—	43	2	no	—
682	#436	—	43	2	no	—
683	#435	—	43	2	no	—
684	#435	—	43	2	no	—
685	#428	—	43	2	no	—
686	#428	—	43	2	no	—
687	#428	—	43	2	no	—
688	#428	—	43	2	no	—
689	#428	—	43	1	no	—
690	#428	—	43	1	no	—
691	#428	—	43	1	no	—
692	#428	—	43	1	no	—
693	#428	—	43	2	no	—
694	#428	—	43	2	no	—
695	#427	—	43	2	no	—
696	#427	C₂×D₄₃	1	1	yes	characteristic
697	C₂×#107	—	43	1	no	—
698	C₂×#107	—	43	1	no	—
699	C₂×#107	—	43	2	no	—
700	C₂×#106	—	43	1	no	—
701	C₂×#106	—	43	1	no	—
702	#424	—	43	1	no	—
703	#417	—	43	1	no	—
704	#417	—	43	1	no	—
705	#417	—	43	1	no	—
706	#417	—	43	1	no	—
707	#416	C₂×D₄₃	1	1	yes	characteristic
708	#416	C₂×D₄₃	1	1	yes	characteristic
709	#408	—	43	1	no	—
710	#407	—	43	1	no	—
711	#405	—	43	1	no	—
712	C₄₃	#61266	1	1	yes	characteristic, complemented, Sylow
713	C₂×#41	—	43	1	no	—
714	C₂×#41	—	86	2	no	—
715	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
716	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
717	C₂³×C₄	—	86	1	no	—
718	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
719	#135	—	2	4	no	—
720	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
721	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
722	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
723	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
724	#131	—	86	4	no	—
725	C₂×M₁₆	—	2	4	no	—
726	C₂×M₁₆	—	43	1	no	—
727	C₂×M₁₆	—	43	1	no	—
728	C₂×M₁₆	—	43	2	no	—
729	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
730	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
731	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
732	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
733	C₂²×C₈	—	43	2	no	—
734	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
735	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
736	C₄⋊Q₈	—	43	2	no	—
737	C₄⋊Q₈	—	43	2	no	—
738	C₄⋊Q₈	—	86	1	no	—
739	C₄⋊Q₈	—	86	1	no	—
740	#126	—	86	2	no	—
741	#126	—	86	2	no	—
742	#126	—	86	2	no	—
743	#126	—	86	2	no	—
744	#126	—	86	2	no	—
745	#126	—	86	2	no	—
746	#125	—	43	2	no	—
747	#125	—	43	2	no	—
748	#125	—	86	1	no	—
749	#125	—	86	1	no	—
750	#125	—	86	2	no	—
751	#125	—	86	2	no	—
752	#125	—	86	2	no	—
753	#124	—	86	2	no	—
754	#124	—	86	2	no	—
755	#124	—	86	2	no	—
756	#123	—	2	1	no	—
757	#123	—	2	1	no	—
758	#123	—	43	2	no	—
759	#123	—	86	2	no	—
760	#123	—	86	2	no	—
761	#123	—	86	2	no	—
762	#123	—	86	2	no	—
763	#123	—	86	2	no	—
764	#123	—	86	2	no	—
765	C₂²⋊Q₈	—	43	1	no	—
766	C₂²⋊Q₈	—	43	1	no	—
767	C₂²⋊Q₈	—	43	2	no	—
768	C₂²⋊Q₈	—	43	2	no	—
769	C₂²⋊Q₈	—	86	2	no	—
770	C₂²⋊Q₈	—	86	2	no	—
771	C₂²⋊Q₈	—	86	2	no	—
772	C₂²⋊Q₈	—	86	2	no	—
773	C₂²⋊Q₈	—	86	2	no	—
774	C₂²⋊Q₈	—	86	1	no	—
775	C₂²⋊Q₈	—	86	1	no	—
776	C₂²⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
777	C₂²⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
778	C₂²⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
779	C₂²⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
780	#121	—	43	1	no	—
781	#121	—	43	1	no	—
782	#121	—	43	2	no	—
783	#121	—	43	2	no	—
784	#121	—	86	1	no	—
785	#121	—	86	1	no	—
786	#121	—	86	2	no	—
787	#121	—	86	2	no	—
788	#121	—	86	2	no	—
789	#121	—	86	2	no	—
790	#121	—	86	2	no	—
791	#121	C₂²×D₄₃	1	1	yes	characteristic
792	#121	C₂²×D₄₃	1	1	yes	characteristic
793	#121	C₂²×D₄₃	1	1	yes	characteristic
794	#121	C₂²×D₄₃	1	1	yes	characteristic
795	#120	—	2	1	no	—
796	#120	—	2	1	no	—
797	#120	—	43	2	no	—
798	C₄×Q₈	—	43	2	no	—
799	C₄×Q₈	—	43	2	no	—
800	C₄×Q₈	—	86	1	no	—
801	C₄×Q₈	—	86	1	no	—
802	C₄×Q₈	—	86	2	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	43	2	no	—
808	C₄×D₄	—	43	2	no	—
809	C₄×D₄	—	43	2	no	—
810	C₄×D₄	—	43	2	no	—
811	C₄×D₄	—	86	1	no	—
812	C₄×D₄	—	86	1	no	—
813	C₄×D₄	—	86	2	no	—
814	C₄×D₄	—	86	2	no	—
815	C₄×D₄	—	86	2	no	—
816	C₄×D₄	—	86	2	no	—
817	C₄×D₄	—	86	2	no	—
818	C₄×D₄	—	86	2	no	—
819	C₄×D₄	—	86	2	no	—
820	#117	—	43	1	no	—
821	#117	—	43	2	no	—
822	#117	—	43	2	no	—
823	#117	—	43	2	no	—
824	#117	—	43	2	no	—
825	#117	—	86	2	no	—
826	#117	—	86	2	no	—
827	#117	—	86	2	no	—
828	#117	—	86	1	no	—
829	#117	—	86	1	no	—
830	#117	—	86	1	no	—
831	#117	—	86	1	no	—
832	#117	C₂²×D₄₃	1	1	yes	characteristic
833	#117	C₂²×D₄₃	1	1	yes	characteristic
834	C₂×C₄⋊C₄	—	43	1	no	—
835	C₂×C₄⋊C₄	—	43	1	no	—
836	C₂×C₄⋊C₄	—	43	2	no	—
837	C₂×C₄⋊C₄	—	43	2	no	—
838	C₂×C₄⋊C₄	—	43	1	no	—
839	C₂×C₄⋊C₄	—	43	1	no	—
840	C₂×C₄⋊C₄	—	43	2	no	—
841	C₂×C₄⋊C₄	—	43	2	no	—
842	C₂×C₄⋊C₄	—	86	1	no	—
843	C₂×C₄⋊C₄	—	86	1	no	—
844	C₂×C₄⋊C₄	—	86	1	no	—
845	C₂×C₄⋊C₄	—	86	1	no	—
846	C₂×C₄⋊C₄	—	86	1	no	—
847	C₂×C₂²⋊C₄	—	86	1	no	—
848	C₂×C₄²	—	86	1	no	—
849	#107	—	43	2	no	—
850	#107	—	43	2	no	—
851	#107	—	43	2	no	—
852	#107	—	43	2	no	—
853	#107	—	43	2	no	—
854	#107	—	43	2	no	—
855	#107	—	43	2	no	—
856	#107	—	43	2	no	—
857	#107	C₂²×D₄₃	1	1	yes	characteristic
858	#107	C₂²×D₄₃	1	1	yes	characteristic
859	#106	—	43	2	no	—
860	#106	—	43	2	no	—
861	#106	—	43	2	no	—
862	#106	—	43	2	no	—
863	#106	—	43	2	no	—
864	#106	—	43	2	no	—
865	#106	—	43	2	no	—
866	#106	—	43	2	no	—
867	#106	C₂²×D₄₃	1	1	yes	characteristic
868	#106	C₂²×D₄₃	1	1	yes	characteristic
869	C₄⋊C₈	—	43	2	no	—
870	C₄⋊C₈	—	43	2	no	—
871	#103	—	43	2	no	—
872	#103	—	43	2	no	—
873	#103	—	43	2	no	—
874	#103	—	43	2	no	—
875	#103	C₂²×D₄₃	1	1	yes	characteristic
876	#103	C₂²×D₄₃	1	1	yes	characteristic
877	#103	C₂²×D₄₃	1	1	yes	characteristic
878	#103	C₂²×D₄₃	1	1	yes	characteristic
879	#102	—	43	2	no	—
880	#102	—	43	2	no	—
881	#102	—	43	2	no	—
882	#102	—	43	2	no	—
883	#102	C₂²×D₄₃	1	1	yes	characteristic
884	#102	C₂²×D₄₃	1	1	yes	characteristic
885	#102	C₂²×D₄₃	1	1	yes	characteristic
886	#102	C₂²×D₄₃	1	1	yes	characteristic
887	C₂²⋊C₈	—	43	2	no	—
888	C₂²⋊C₈	—	43	2	no	—
889	C₂²⋊C₈	—	43	2	no	—
890	C₂²⋊C₈	—	43	2	no	—
891	#97	—	43	2	no	—
892	C₄×C₈	—	43	2	no	—
893	C₂⁴	D₄×D₄₃	1	1	yes	characteristic
894	#41	—	2	2	no	—
895	#41	—	2	2	no	—
896	#41	—	2	2	no	—
897	#41	—	2	2	no	—
898	#41	—	86	2	no	—
899	#41	—	86	2	no	—
900	#41	—	344	4	no	—
901	C₂×Q₈	—	43	1	no	—
902	C₂×Q₈	—	86	2	no	—
903	C₂×Q₈	—	86	2	no	—
904	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
905	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	2	1	no	—
908	C₂×D₄	—	2	1	no	—
909	C₂×D₄	—	2	1	no	—
910	C₂×D₄	—	2	1	no	—
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	43	2	no	—
913	C₂×D₄	—	43	2	no	—
914	C₂×D₄	—	43	2	no	—
915	C₂×D₄	—	43	1	no	—
916	C₂×D₄	—	86	2	no	—
917	C₂×D₄	—	86	2	no	—
918	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
919	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
920	C₂²×C₄	—	2	2	no	—
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	43	2	no	—
925	C₂²×C₄	—	86	2	no	—
926	C₂²×C₄	—	86	2	no	—
927	C₂²×C₄	—	86	2	no	—
928	C₂²×C₄	—	86	2	no	—
929	C₂²×C₄	—	86	1	no	—
930	C₂²×C₄	—	86	1	no	—
931	C₂²×C₄	—	86	1	no	—
932	C₂²×C₄	—	86	2	no	—
933	C₂²×C₄	—	86	1	no	—
934	C₂²×C₄	—	86	2	no	—
935	C₂²×C₄	—	344	2	no	—
936	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
937	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
938	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
939	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
940	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
941	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
942	Q₁₆	—	2	2	no	—
943	SD₁₆	—	2	2	no	—
944	SD₁₆	—	2	2	no	—
945	D₈	—	2	2	no	—
946	M₁₆	—	2	2	no	—
947	M₁₆	—	2	2	no	—
948	M₁₆	—	2	2	no	—
949	M₁₆	—	2	2	no	—
950	M₁₆	—	86	2	no	—
951	M₁₆	—	86	2	no	—
952	M₁₆	—	86	4	no	—
953	C₂×C₈	—	2	2	no	—
954	C₂×C₈	—	43	2	no	—
955	C₂×C₈	—	43	2	no	—
956	C₂×C₈	—	86	4	no	—
957	C₂×C₈	#10621900	1	4	yes	complemented
958	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
959	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
960	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
961	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
962	C₄⋊C₄	—	2	1	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	1	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	43	1	no	—
967	C₄⋊C₄	—	43	1	no	—
968	C₄⋊C₄	—	43	2	no	—
969	C₄⋊C₄	—	43	2	no	—
970	C₄⋊C₄	—	43	2	no	—
971	C₄⋊C₄	—	43	2	no	—
972	C₄⋊C₄	—	43	2	no	—
973	C₄⋊C₄	—	43	2	no	—
974	C₄⋊C₄	—	86	2	no	—
975	C₄⋊C₄	—	86	2	no	—
976	C₄⋊C₄	—	86	2	no	—
977	C₄⋊C₄	—	86	2	no	—
978	C₄⋊C₄	—	86	2	no	—
979	C₄⋊C₄	—	86	2	no	—
980	C₄⋊C₄	—	86	2	no	—
981	C₄⋊C₄	—	86	2	no	—
982	C₄⋊C₄	—	86	2	no	—
983	C₄⋊C₄	—	86	2	no	—
984	C₄⋊C₄	—	86	2	no	—
985	C₄⋊C₄	—	86	2	no	—
986	C₄⋊C₄	—	86	1	no	—
987	C₄⋊C₄	—	86	1	no	—
988	C₄⋊C₄	—	86	2	no	—
989	C₄⋊C₄	—	86	2	no	—
990	C₄⋊C₄	—	86	1	no	—
991	C₄⋊C₄	—	86	1	no	—
992	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
993	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
994	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
995	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
996	C₂²⋊C₄	—	2	1	no	—
997	C₂²⋊C₄	—	2	1	no	—
998	C₂²⋊C₄	—	2	1	no	—
999	C₂²⋊C₄	—	2	1	no	—
1000	C₂²⋊C₄	—	2	1	no	—
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	43	2	no	—
1007	C₂²⋊C₄	—	43	2	no	—
1008	C₂²⋊C₄	—	43	2	no	—
1009	C₂²⋊C₄	—	43	2	no	—
1010	C₂²⋊C₄	—	43	2	no	—
1011	C₂²⋊C₄	—	86	2	no	—
1012	C₂²⋊C₄	—	86	2	no	—
1013	C₂²⋊C₄	—	86	2	no	—
1014	C₂²⋊C₄	—	86	2	no	—
1015	C₂²⋊C₄	—	86	2	no	—
1016	C₂²⋊C₄	—	86	2	no	—
1017	C₂²⋊C₄	—	86	2	no	—
1018	C₂²⋊C₄	—	86	2	no	—
1019	C₂²⋊C₄	—	86	2	no	—
1020	C₂²⋊C₄	—	86	2	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	43	2	no	—
1024	C₄²	—	86	2	no	—
1025	C₄²	—	86	2	no	—
1026	C₄²	—	86	2	no	—
1027	C₄²	—	86	2	no	—
1028	C₄²	—	86	2	no	—
1029	C₄²	—	86	2	no	—
1030	C₂³	—	2	2	no	—
1031	C₂³	—	2	1	no	—
1032	C₂³	—	2	1	no	—
1033	C₂³	—	4	1	no	—
1034	C₂³	—	4	1	no	—
1035	C₂³	—	43	2	no	—
1036	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1037	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1038	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1039	Q₈	—	2	1	no	—
1040	Q₈	—	2	1	no	—
1041	Q₈	—	2	1	no	—
1042	Q₈	—	2	1	no	—
1043	Q₈	—	86	2	no	—
1044	Q₈	—	344	2	no	—
1045	Q₈	—	344	2	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	2	1	no	—
1048	D₄	—	2	1	no	—
1049	D₄	—	2	1	no	—
1050	D₄	—	4	2	no	—
1051	D₄	—	4	2	no	—
1052	D₄	—	4	2	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	8	1	no	—
1055	D₄	—	8	1	no	—
1056	D₄	—	86	4	no	—
1057	D₄	—	86	2	no	—
1058	D₄	—	344	2	no	—
1059	D₄	—	344	2	no	—
1060	D₄	—	172	2	no	—
1061	D₄	—	172	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	1	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	1	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	4	2	no	—
1076	C₂×C₄	—	4	2	no	—
1077	C₂×C₄	—	43	2	no	—
1078	C₂×C₄	—	43	2	no	—
1079	C₂×C₄	—	43	2	no	—
1080	C₂×C₄	—	86	2	no	—
1081	C₂×C₄	—	86	2	no	—
1082	C₂×C₄	—	86	2	no	—
1083	C₂×C₄	—	86	2	no	—
1084	C₂×C₄	—	86	2	no	—
1085	C₂×C₄	—	86	2	no	—
1086	C₂×C₄	—	344	2	no	—
1087	C₂×C₄	—	344	2	no	—
1088	C₂×C₄	—	344	2	no	—
1089	C₂×C₄	—	344	2	no	—
1090	C₂×C₄	—	344	1	no	—
1091	C₂×C₄	—	344	2	no	—
1092	C₂×C₄	—	344	1	no	—
1093	C₂×C₄	—	344	1	no	—
1094	C₂×C₄	—	344	1	no	—
1095	C₂×C₄	—	172	4	no	—
1096	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1097	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1098	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1099	C₂×C₄	C₂×#10621900	1	2	yes	—
1100	C₂×C₄	#13063372	1	2	yes	—
1101	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1102	C₈	—	2	1	no	—
1103	C₈	—	2	1	no	—
1104	C₈	—	86	2	no	—
1105	C₈	—	86	2	no	—
1106	C₈	C₂×#10621900	1	2	yes	—
1107	C₈	C₂×#10621900	1	2	yes	—
1108	C₂²	—	2	1	no	—
1109	C₂²	—	2	1	no	—
1110	C₂²	—	2	1	no	—
1111	C₂²	—	2	1	no	—
1112	C₂²	—	2	1	no	—
1113	C₂²	—	2	1	no	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	4	4	no	—
1117	C₂²	—	4	1	no	—
1118	C₂²	—	4	1	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	4	1	no	—
1122	C₂²	—	4	1	no	—
1123	C₂²	—	86	2	no	—
1124	C₂²	—	86	2	no	—
1125	C₂²	—	86	2	no	—
1126	C₂²	#14583549	1	2	yes	—
1127	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1128	C₄	—	2	1	no	—
1129	C₄	—	2	1	no	—
1130	C₄	—	4	1	no	—
1131	C₄	—	4	1	no	—
1132	C₄	—	4	1	no	—
1133	C₄	—	4	1	no	—
1134	C₄	—	4	1	no	—
1135	C₄	—	4	1	no	—
1136	C₄	—	86	2	no	—
1137	C₄	—	86	2	no	—
1138	C₄	—	86	2	no	—
1139	C₄	—	172	2	no	—
1140	C₄	—	172	2	no	—
1141	C₄	—	172	2	no	—
1142	C₄	—	172	2	no	—
1143	C₄	#14583549	1	2	yes	—
1144	C₄	C₂²×#10621900	1	1	yes	characteristic
1145	C₄	C₂×#13063372	1	1	yes	characteristic
1146	C₂	—	2	2	no	—
1147	C₂	—	4	1	no	—
1148	C₂	—	4	1	no	—
1149	C₂	—	8	1	no	—
1150	C₂	—	8	1	no	—
1151	C₂	—	172	2	no	—
1152	C₂	C₂×#14583549	1	1	yes	characteristic
1153	C₂	#19149372	1	1	yes	characteristic
1154	C₂	#19149379	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×#3054	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3054	D₄₃
hypocenter	C₄₃	#61266
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂³×C₄ ◁ #3054

Complements

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

N	H ≅ G/N	type
1. #19148312	C₂	semidirect
2. #19148301	C₂	semidirect
3. #19147205	C₂	semidirect
4. #19147196	C₂	semidirect
5. #19147185	C₂	semidirect
6. #19147165	C₂	semidirect
7. #19147135	C₂	semidirect
8. #19147105	C₂	semidirect
9. #19147075	C₂	semidirect
10. #19147030	C₂	semidirect
11. #19145127	C₂	semidirect
12. #19144582	C₂	semidirect
13. #19144571	C₂	semidirect
14. #19144524	C₂	semidirect
15. #19144515	C₂	semidirect
16. #19144455	C₂	semidirect
17. #19144444	C₂	semidirect
18. #19144253	C₂	semidirect
19. #19143471	C₂	semidirect
20. #19143298	C₂	semidirect
21. #19143192	C₂	semidirect
22. C₂×#14582941	C₂	semidirect
23. C₄₃×#3054	C₂	semidirect
56. #14583307	C₂²	semidirect
57. #14583307	C₂²	semidirect
58. #14583299	C₂²	semidirect
59. #14583296	C₂²	semidirect
60. #14583239	C₂²	semidirect
61. #14583238	C₂²	semidirect
64. #14583233	C₂²	semidirect
66. #14583228	C₂²	semidirect
68. #14583222	C₂²	semidirect
69. #14583221	C₂²	semidirect
72. #14583216	C₂²	semidirect
74. #14583211	C₂²	semidirect
76. #14583208	C₂²	semidirect
77. #14583204	C₂²	semidirect
78. #14583201	C₂²	semidirect
79. #14583197	C₂²	semidirect
80. #14583192	C₂²	semidirect
81. #14583187	C₂²	semidirect
82. #14583182	C₂²	semidirect
83. #14583177	C₂²	semidirect
84. #14583154	C₂²	semidirect
85. #14583149	C₂²	semidirect
86. #14583125	C₂²	semidirect
87. #14583125	C₂²	semidirect
88. #14583000	C₂²	semidirect
89. #14583000	C₂²	semidirect
90. Q₁₆×Dic₄₃	C₂²	semidirect
91. D₈×Dic₄₃	C₂²	semidirect
104. #14582938	C₂²	semidirect
105. #14582938	C₂²	semidirect
106. #14582936	C₂²	semidirect
109. #107×D₄₃	C₂²	semidirect
373. C₂×C₈×C₄₃	#41	semidirect
587. #3054	D₄₃	semidirect
712. C₄₃	#61266	semidirect
957. C₂×C₈	#10621900	semidirect

Maximal subgroups

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

subgroup	index
#19148312	2
#19148301	2
#19147205	2
#19147196	2
#19147185	2
#19147165	2
#19147135	2
#19147105	2
#19147075	2
#19147030	2
#19145127	2
#19144582	2
#19144571	2
#19144524	2
#19144515	2
#19144455	2
#19144444	2
#19144253	2
#19143471	2
#19143298	2
#19143192	2
C₂×#14582941	2
C₄₃×#3054	2
#61266	43