Subgroups — #25978919

Order 11008.

1908 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148205	C₂	1	1	yes	maximal, characteristic, complemented
2	#19148190	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147605	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147468	C₂	1	1	yes	maximal, characteristic, complemented
5	#19147289	C₂	1	1	yes	maximal, characteristic, complemented
6	#19147253	C₂	1	1	yes	maximal, characteristic, complemented
7	#19147212	C₂	1	1	yes	maximal, characteristic, complemented
8	#19147197	C₂	1	2	yes	maximal, complemented
9	#19146935	C₂	1	1	yes	maximal, characteristic, complemented
10	#19146844	C₂	1	2	yes	maximal, complemented
11	#19146828	C₂	1	1	yes	maximal, characteristic, complemented
12	#19146797	C₂	1	2	yes	maximal, complemented
13	#19146220	C₂	1	2	yes	maximal, complemented
14	#19146216	C₂	1	1	yes	maximal, characteristic, complemented
15	#19145333	C₂	1	1	yes	maximal, characteristic, complemented
16	#19145327	C₂	1	2	yes	maximal, complemented
17	#19144746	C₂	1	1	yes	maximal, characteristic, complemented
18	#19144737	C₂	1	2	yes	maximal, complemented
19	#19144717	C₂	1	1	yes	maximal, characteristic, complemented
20	#19144710	C₂	1	2	yes	maximal, complemented
21	#19143613	C₂	1	1	yes	maximal, characteristic, complemented
22	#19143400	C₂	1	2	yes	maximal, complemented
23	C₄×#137×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063352	C₂²	1	2	yes	—
25	#14583634	—	2	1	no	—
26	#14583634	C₂²	1	1	yes	characteristic
27	#14583634	C₂²	1	1	yes	characteristic, complemented
28	#14583628	C₂²	1	1	yes	characteristic, complemented
29	#14583622	—	2	1	no	—
30	#14583622	C₂²	1	1	yes	characteristic
31	#14583609	C₂²	1	1	yes	characteristic
32	#14583606	C₂²	1	1	yes	characteristic
33	#14583597	—	2	2	no	—
34	#14583597	C₂²	1	2	yes	complemented
35	#14583595	—	2	1	no	—
36	#14583593	C₂²	1	2	yes	—
37	#14583573	—	2	2	no	—
38	#14583571	C₂²	1	1	yes	characteristic
39	#14583560	C₂²	1	2	yes	complemented
40	#14583545	—	2	1	no	—
41	#14583537	C₂²	1	2	yes	—
42	D₄×D₁₇₂	C₂²	1	1	yes	characteristic
43	#14583449	—	2	1	no	—
44	#14583449	C₂²	1	1	yes	characteristic
45	#14583449	C₂²	1	1	yes	characteristic, complemented
46	#14583436	—	2	2	no	—
47	#14583436	C₂²	1	2	yes	—
48	#14583436	C₂²	1	2	yes	complemented
49	#14583433	—	2	1	no	—
50	#14583408	—	2	2	no	—
51	C₄×#10621902	C₂²	1	2	yes	complemented
52	C₄×#10621898	—	2	1	no	—
53	C₄×#10621898	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₁₇₂	—	2	1	no	—
55	C₄×D₄×D₄₃	C₂²	1	2	yes	—
56	#14583299	C₂²	1	2	yes	complemented
57	#14583297	C₂²	1	1	yes	characteristic, complemented
58	#14583284	C₂²	1	2	yes	complemented
59	#14583276	C₂²	1	1	yes	characteristic
60	#14583255	C₂²	1	2	yes	complemented
61	#14583255	C₂²	1	2	yes	complemented
62	#14583246	C₂²	1	1	yes	characteristic
63	#14583246	C₂²	1	1	yes	characteristic, complemented
64	#14583238	C₂²	1	2	yes	complemented
65	#14583228	C₂²	1	2	yes	complemented
66	#14583225	C₂²	1	2	yes	—
67	#14583223	C₂²	1	2	yes	complemented
68	#14583214	C₂²	1	2	yes	complemented
69	#14583212	C₂²	1	2	yes	complemented
70	#14583204	C₂²	1	2	yes	complemented
71	#14583202	C₂²	1	2	yes	complemented
72	#14583201	C₂²	1	2	yes	—
73	#14583198	C₂²	1	2	yes	complemented
74	#14583194	C₂²	1	1	yes	characteristic, complemented
75	#14583194	C₂²	1	1	yes	characteristic, complemented
76	#14583184	C₂²	1	1	yes	characteristic, complemented
77	#14583179	C₂²	1	1	yes	characteristic
78	#14583154	C₂²	1	2	yes	complemented
79	#14583153	C₂²	1	2	yes	—
80	#14583152	C₂²	1	2	yes	complemented
81	#14583152	C₂²	1	2	yes	complemented
82	#14583148	C₂²	1	2	yes	—
83	#14583148	C₂²	1	2	yes	complemented
84	#14583123	C₂²	1	2	yes	complemented
85	#14583117	C₂²	1	2	yes	complemented
86	#14583117	C₂²	1	2	yes	complemented
87	#14583116	C₂²	1	2	yes	—
88	#14583099	C₂²	1	1	yes	characteristic
89	#14583099	C₂²	1	1	yes	characteristic
90	#14583099	C₂²	1	1	yes	characteristic, complemented
91	#14583094	C₂²	1	1	yes	characteristic
92	#14583060	C₂²	1	2	yes	complemented
93	#14583048	C₂²	1	2	yes	—
94	#14583047	C₂²	1	2	yes	—
95	#14583044	C₂²	1	2	yes	—
96	#14583038	C₂²	1	2	yes	complemented
97	#14583034	C₂²	1	2	yes	—
98	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
99	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
100	#14583012	C₂²	1	2	yes	complemented
101	#14583012	C₂²	1	2	yes	complemented
102	#14583009	C₂²	1	2	yes	—
103	#14582997	C₂²	1	2	yes	complemented
104	#14582997	C₂²	1	2	yes	complemented
105	#14582997	C₂²	1	2	yes	complemented
106	SD₁₆×Dic₄₃	C₂²	1	2	yes	—
107	#14582984	C₂²	1	2	yes	complemented
108	#14582981	C₂²	1	2	yes	complemented
109	#14582979	C₂²	1	2	yes	—
110	#14582978	C₂²	1	1	yes	characteristic
111	#14582978	C₂²	1	1	yes	characteristic
112	#14582975	C₂²	1	2	yes	complemented
113	#14582975	C₂²	1	2	yes	complemented
114	#14582956	C₂²	1	1	yes	characteristic, complemented
115	#14582954	C₂²	1	2	yes	complemented
116	#14582940	C₂²	1	2	yes	complemented
117	#14582902	C₂²	1	2	yes	—
118	#14582899	C₂²	1	2	yes	complemented
119	#14582851	C₂²	1	2	yes	complemented
120	C₂×#137×C₄₃	C₂²	1	1	yes	characteristic
121	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
122	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
123	C₄₃×#441	C₂²	1	1	yes	characteristic, complemented
124	C₄₃×#441	C₂²	1	1	yes	characteristic, complemented
125	C₄₃×#440	C₂²	1	1	yes	characteristic
126	C₄₃×#440	C₂²	1	1	yes	characteristic
127	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
128	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
129	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
130	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
131	C₄₃×#428	C₂²	1	1	yes	characteristic, complemented
132	C₄₃×#419	C₂²	1	1	yes	characteristic, complemented
133	C₄₃×#417	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#10621902	C₂³	1	2	yes	—
136	C₂×#10621898	—	2	1	no	—
137	C₂×#10621898	—	2	1	no	—
138	C₂×#10621898	D₄	1	1	yes	characteristic
139	C₂²×D₁₇₂	—	2	1	no	—
140	C₂×D₄×D₄₃	C₂³	1	2	yes	—
141	C₂²×C₄×D₄₃	—	2	2	no	—
142	#13063352	—	2	8	no	—
143	C₂×#10621884	C₂³	1	2	yes	—
144	C₂×#10621884	C₂³	1	2	yes	—
145	C₂×#10621884	C₂³	1	2	yes	—
146	C₂×D₃₄₄	C₂³	1	2	yes	—
147	C₂×D₃₄₄	C₂³	1	2	yes	—
148	C₂×#10621882	C₂³	1	2	yes	—
149	C₂×#10621872	C₂³	1	2	yes	—
150	C₂×#10621872	C₂³	1	2	yes	—
151	#13063325	—	2	1	no	—
152	#13063325	C₂³	1	1	yes	characteristic
153	#13063325	C₂³	1	1	yes	characteristic
154	#13063322	—	2	1	no	—
155	#13063322	C₂³	1	1	yes	characteristic
156	#13063322	C₂³	1	1	yes	characteristic
157	#13063320	—	2	2	no	—
158	#13063320	—	2	2	no	—
159	#13063320	—	2	2	no	—
160	#13063320	—	2	2	no	—
161	#13063319	—	2	2	no	—
162	#13063317	—	2	1	no	—
163	#13063316	—	2	2	no	—
164	#13063316	C₂³	1	2	yes	—
165	#13063316	C₂³	1	2	yes	—
166	#13063314	—	2	2	no	—
167	#13063314	C₂³	1	2	yes	—
168	#13063314	C₂³	1	2	yes	—
169	#13063313	—	2	1	no	—
170	#13063313	—	2	1	no	—
171	#13063313	—	2	1	no	—
172	#13063313	—	2	1	no	—
173	#13063313	—	2	1	no	—
174	#13063310	—	2	2	no	—
175	#13063310	—	2	2	no	—
176	#13063310	—	2	2	no	—
177	#13063310	—	2	2	no	—
178	#13063310	—	2	2	no	—
179	#13063308	—	2	2	no	—
180	#13063307	—	2	2	no	—
181	#13063304	—	2	1	no	—
182	#13063303	—	2	2	no	—
183	#13063302	—	2	2	no	—
184	#13063301	—	2	2	no	—
185	#13063301	C₂³	1	2	yes	—
186	#13063301	C₂³	1	2	yes	—
187	#13063300	—	2	2	no	—
188	#13063300	C₂³	1	2	yes	—
189	#13063300	C₂³	1	2	yes	—
190	#13063299	—	2	1	no	—
191	#13063299	—	2	1	no	—
192	#13063299	—	2	2	no	—
193	#13063299	—	2	2	no	—
194	#13063299	—	2	1	no	—
195	#13063299	C₂³	1	2	yes	—
196	#13063299	C₂³	1	2	yes	—
197	#13063298	—	2	2	no	—
198	#13063297	—	2	2	no	—
199	#13063295	—	2	2	no	—
200	#13063293	—	2	2	no	—
201	Q₈×Dic₄₃	C₂³	1	2	yes	—
202	C₄×Dic₈₆	—	2	1	no	—
203	C₄×Dic₈₆	—	2	1	no	—
204	C₄×Dic₈₆	D₄	1	1	yes	characteristic
205	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
206	C₄×D₁₇₂	—	2	1	no	—
207	C₄×D₁₇₂	—	2	2	no	—
208	C₄×D₁₇₂	—	2	2	no	—
209	C₄×D₁₇₂	—	2	2	no	—
210	C₄×D₁₇₂	—	2	1	no	—
211	C₄×D₁₇₂	—	2	1	no	—
212	C₄×D₁₇₂	—	2	2	no	—
213	C₄×D₁₇₂	—	2	1	no	—
214	C₄×D₁₇₂	—	2	1	no	—
215	C₄×D₁₇₂	—	2	1	no	—
216	C₄×D₁₇₂	D₄	1	1	yes	characteristic
217	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
218	C₄×D₁₇₂	C₂³	1	2	yes	—
219	C₄×D₁₇₂	C₂³	1	2	yes	—
220	D₄×Dic₄₃	C₂³	1	2	yes	—
221	#13063287	—	2	2	no	—
222	#13063287	C₂³	1	2	yes	—
223	#13063287	C₂³	1	2	yes	—
224	C₄×C₂²⋊D₄₃	—	2	2	no	—
225	C₄×C₂²⋊D₄₃	—	2	2	no	—
226	C₄×C₂²⋊D₄₃	—	2	2	no	—
227	C₄×C₂²⋊D₄₃	D₄	1	2	yes	—
228	C₄×C₂²⋊D₄₃	C₂³	1	2	yes	—
229	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
230	#13063284	D₄	1	1	yes	characteristic
231	#13063283	—	2	2	no	—
232	#13063283	C₂³	1	2	yes	—
233	#13063282	—	2	2	no	—
234	#13063282	—	2	2	no	—
235	#13063282	D₄	1	2	yes	—
236	C₂×C₄⋊Dic₄₃	—	2	1	no	—
237	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
238	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
239	C₂²⋊C₄×D₄₃	—	2	2	no	—
240	C₄²×D₄₃	—	2	2	no	—
241	C₄²×D₄₃	C₂³	1	2	yes	—
242	#13063258	C₂³	1	2	yes	—
243	#13063258	C₂³	1	2	yes	—
244	#13063258	C₂³	1	2	yes	—
245	#13063257	C₂³	1	2	yes	—
246	#13063257	C₂³	1	2	yes	—
247	#13063256	C₂³	1	2	yes	—
248	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
249	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
250	Dic₄₃⋊C₈	C₂³	1	2	yes	—
251	Dic₄₃⋊C₈	C₂³	1	2	yes	—
252	#13063249	C₂³	1	2	yes	—
253	#13063249	C₂³	1	2	yes	—
254	#13063249	C₂³	1	2	yes	—
255	#13063247	C₂³	1	2	yes	—
256	#13063247	C₂³	1	2	yes	—
257	#13063247	C₂³	1	2	yes	—
258	#13063247	C₂³	1	2	yes	—
259	#13063246	C₂³	1	2	yes	—
260	#13063245	C₂³	1	2	yes	—
261	#13063245	C₂³	1	2	yes	—
262	#13063245	C₂³	1	2	yes	—
263	#13063245	C₂³	1	2	yes	—
264	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
265	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
266	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
267	#13063236	C₂³	1	2	yes	—
268	C₈×Dic₄₃	C₂³	1	2	yes	—
269	C₈×Dic₄₃	C₂³	1	2	yes	—
270	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
271	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
272	#137×C₄₃	—	2	4	no	—
273	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
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×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
278	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
279	C₄×Q₈×C₄₃	—	2	1	no	—
280	C₄×Q₈×C₄₃	—	2	1	no	—
281	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
282	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
283	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
284	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
285	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
286	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₄₃	—	2	1	no	—
288	C₄×D₄×C₄₃	—	2	1	no	—
289	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
291	#117×C₄₃	—	2	1	no	—
292	#117×C₄₃	C₂³	1	1	yes	characteristic
293	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
294	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₄₃	—	2	1	no	—
296	C₂×C₄²×C₄₃	—	2	1	no	—
297	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
298	#107×C₄₃	C₂³	1	1	yes	characteristic
299	#107×C₄₃	C₂³	1	1	yes	characteristic
300	#106×C₄₃	C₂³	1	1	yes	characteristic
301	#106×C₄₃	C₂³	1	1	yes	characteristic
302	#103×C₄₃	C₂³	1	1	yes	characteristic
303	#103×C₄₃	C₂³	1	1	yes	characteristic
304	#103×C₄₃	C₂³	1	1	yes	characteristic
305	#103×C₄₃	C₂³	1	1	yes	characteristic
306	#103×C₄₃	C₂³	1	1	yes	characteristic
307	#103×C₄₃	C₂³	1	1	yes	characteristic
308	#102×C₄₃	C₂³	1	1	yes	characteristic
309	#102×C₄₃	C₂³	1	1	yes	characteristic
310	#97×C₄₃	C₂³	1	1	yes	characteristic
311	#97×C₄₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
314	C₂³×D₄₃	—	2	2	no	—
315	#41×C₄₃	—	2	2	no	—
316	#41×C₄₃	—	4	1	no	—
317	C₂×Q₈×C₄₃	—	2	1	no	—
318	C₂×Q₈×C₄₃	—	2	2	no	—
319	C₂×Q₈×C₄₃	—	4	1	no	—
320	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
321	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
322	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
323	C₂×D₄×C₄₃	—	2	1	no	—
324	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₄₃	—	2	1	no	—
326	C₂²×C₄×C₄₃	—	2	1	no	—
327	C₂²×C₄×C₄₃	—	2	1	no	—
328	C₂²×C₄×C₄₃	—	2	1	no	—
329	C₂²×C₄×C₄₃	—	2	1	no	—
330	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
332	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
333	C₂×C₂²⋊D₄₃	—	2	2	no	—
334	C₂×C₂²⋊D₄₃	—	2	2	no	—
335	C₂×C₂²⋊D₄₃	—	2	2	no	—
336	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
337	C₂²×Dic₄₃	—	2	2	no	—
338	#10621902	—	2	4	no	—
339	#10621902	—	4	2	no	—
340	D₄×D₄₃	—	2	4	no	—
341	D₄×D₄₃	—	4	2	no	—
342	#10621898	—	4	2	no	—
343	#10621898	—	4	4	no	—
344	#10621898	—	8	2	no	—
345	C₂×D₁₇₂	—	2	1	no	—
346	C₂×D₁₇₂	—	2	1	no	—
347	C₂×D₁₇₂	—	2	1	no	—
348	C₂×D₁₇₂	—	2	1	no	—
349	C₂×D₁₇₂	—	2	2	no	—
350	C₂×D₁₇₂	—	2	2	no	—
351	C₂×D₁₇₂	—	2	2	no	—
352	C₂×D₁₇₂	—	4	4	no	—
353	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
354	C₂×D₁₇₂	C₂⁴	1	2	yes	—
355	C₂×D₁₇₂	C₂⁴	1	2	yes	—
356	C₂×C₄×D₄₃	—	2	2	no	—
357	C₂×C₄×D₄₃	—	2	2	no	—
358	C₂×C₄×D₄₃	—	2	2	no	—
359	C₂×C₄×D₄₃	—	2	2	no	—
360	C₂×C₄×D₄₃	—	2	2	no	—
361	C₂×C₄×D₄₃	—	2	2	no	—
362	C₂×C₄×D₄₃	—	8	4	no	—
363	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
364	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
365	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
366	C₂×Dic₈₆	—	2	1	no	—
367	C₂×Dic₈₆	—	2	1	no	—
368	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
369	Q₁₆×C₄₃	—	2	2	no	—
370	Q₁₆×C₄₃	—	2	2	no	—
371	SD₁₆×C₄₃	—	2	2	no	—
372	SD₁₆×C₄₃	#41	1	4	yes	complemented
373	M₁₆×C₄₃	—	2	2	no	—
374	M₁₆×C₄₃	—	4	1	no	—
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	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
383	C₄⋊C₄×C₄₃	—	2	1	no	—
384	C₄⋊C₄×C₄₃	—	2	1	no	—
385	C₄⋊C₄×C₄₃	—	2	1	no	—
386	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
387	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
388	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
389	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
390	C₂²⋊C₄×C₄₃	—	2	1	no	—
391	C₂²⋊C₄×C₄₃	—	2	1	no	—
392	C₂²⋊C₄×C₄₃	—	2	1	no	—
393	C₄²×C₄₃	—	2	1	no	—
394	C₄²×C₄₃	—	2	1	no	—
395	C₄²×C₄₃	—	2	1	no	—
396	C₄²×C₄₃	—	2	1	no	—
397	C₄²×C₄₃	—	2	1	no	—
398	C₄²×C₄₃	—	2	1	no	—
399	C₄²×C₄₃	—	2	1	no	—
400	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
402	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
403	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
404	C₂²⋊Dic₄₃	—	2	2	no	—
405	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
406	#10621884	—	2	4	no	—
407	#10621884	—	4	2	no	—
408	#10621884	—	4	2	no	—
409	#10621882	—	2	4	no	—
410	(C₂×D₄₃)⋊C₄	—	2	2	no	—
411	(C₂×D₄₃)⋊C₄	—	2	2	no	—
412	(C₂×D₄₃)⋊C₄	—	2	2	no	—
413	(C₂×D₄₃)⋊C₄	—	2	2	no	—
414	(C₂×D₄₃)⋊C₄	—	2	2	no	—
415	(C₂×D₄₃)⋊C₄	—	2	2	no	—
416	(C₂×D₄₃)⋊C₄	—	2	2	no	—
417	(C₂×D₄₃)⋊C₄	—	2	2	no	—
418	(C₂×D₄₃)⋊C₄	—	2	2	no	—
419	(C₂×D₄₃)⋊C₄	—	2	2	no	—
420	(C₂×D₄₃)⋊C₄	—	2	2	no	—
421	(C₂×D₄₃)⋊C₄	—	2	2	no	—
422	(C₂×D₄₃)⋊C₄	—	2	2	no	—
423	(C₂×D₄₃)⋊C₄	—	2	2	no	—
424	(C₂×D₄₃)⋊C₄	—	2	2	no	—
425	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
426	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
427	C₄⋊Dic₄₃	—	2	1	no	—
428	C₄⋊Dic₄₃	—	2	1	no	—
429	C₄⋊Dic₄₃	—	2	2	no	—
430	C₄⋊Dic₄₃	—	2	2	no	—
431	C₄⋊Dic₄₃	—	2	2	no	—
432	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
433	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
434	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
435	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
436	Dic₄₃⋊C₄	—	2	2	no	—
437	Dic₄₃⋊C₄	—	2	2	no	—
438	Dic₄₃⋊C₄	—	2	2	no	—
439	Dic₄₃⋊C₄	—	2	2	no	—
440	Dic₄₃⋊C₄	—	2	2	no	—
441	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
442	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
443	C₄×Dic₄₃	—	2	2	no	—
444	C₄×Dic₄₃	—	2	2	no	—
445	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
446	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
447	C₄×Dic₄₃	C₂⁴	1	2	yes	—
448	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
449	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
450	D₃₄₄	—	2	4	no	—
451	D₃₄₄	—	4	2	no	—
452	#10621872	—	2	4	no	—
453	#10621872	—	4	2	no	—
454	C₂³×C₄₃	—	2	1	no	—
455	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
456	C₂²×D₄₃	—	2	2	no	—
457	C₂²×D₄₃	—	2	2	no	—
458	C₂²×D₄₃	—	4	4	no	—
459	C₂²×D₄₃	—	4	4	no	—
460	C₂²×D₄₃	—	8	2	no	—
461	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
462	Q₈×C₄₃	—	2	1	no	—
463	Q₈×C₄₃	—	2	1	no	—
464	Q₈×C₄₃	—	2	1	no	—
465	Q₈×C₄₃	—	2	1	no	—
466	Q₈×C₄₃	—	2	1	no	—
467	Q₈×C₄₃	—	4	2	no	—
468	Q₈×C₄₃	C₂×#41	1	2	yes	—
469	D₄×C₄₃	—	2	1	no	—
470	D₄×C₄₃	—	4	2	no	—
471	D₄×C₄₃	C₂×#41	1	2	yes	—
472	C₂×C₄×C₄₃	—	2	1	no	—
473	C₂×C₄×C₄₃	—	2	2	no	—
474	C₂×C₄×C₄₃	—	2	1	no	—
475	C₂×C₄×C₄₃	—	2	1	no	—
476	C₂×C₄×C₄₃	—	2	1	no	—
477	C₂×C₄×C₄₃	—	2	1	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	—	4	1	no	—
483	C₂×C₄×C₄₃	—	4	2	no	—
484	C₂×C₄×C₄₃	—	4	2	no	—
485	C₂×C₄×C₄₃	—	4	2	no	—
486	C₂×C₄×C₄₃	—	4	2	no	—
487	C₂×C₄×C₄₃	—	8	1	no	—
488	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
494	C₂²⋊D₄₃	—	4	2	no	—
495	C₂²⋊D₄₃	—	4	4	no	—
496	C₂²⋊D₄₃	—	4	4	no	—
497	C₂²⋊D₄₃	—	8	2	no	—
498	C₂×Dic₄₃	—	2	2	no	—
499	C₂×Dic₄₃	—	2	2	no	—
500	C₂×Dic₄₃	—	8	2	no	—
501	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
502	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
503	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
504	D₁₇₂	—	2	2	no	—
505	D₁₇₂	—	2	2	no	—
506	D₁₇₂	—	2	2	no	—
507	D₁₇₂	—	2	2	no	—
508	D₁₇₂	—	2	2	no	—
509	D₁₇₂	—	4	4	no	—
510	D₁₇₂	—	4	4	no	—
511	D₁₇₂	—	4	2	no	—
512	D₁₇₂	—	4	2	no	—
513	D₁₇₂	—	8	1	no	—
514	D₁₇₂	—	8	1	no	—
515	D₁₇₂	—	8	2	no	—
516	C₄×D₄₃	—	2	2	no	—
517	C₄×D₄₃	—	2	2	no	—
518	C₄×D₄₃	—	4	2	no	—
519	C₄×D₄₃	—	4	2	no	—
520	C₄×D₄₃	—	4	4	no	—
521	C₄×D₄₃	—	4	4	no	—
522	C₄×D₄₃	—	4	4	no	—
523	C₄×D₄₃	—	8	2	no	—
524	C₄×D₄₃	—	8	2	no	—
525	C₄×D₄₃	—	8	2	no	—
526	Dic₈₆	—	2	2	no	—
527	Dic₈₆	—	4	2	no	—
528	Dic₈₆	—	8	1	no	—
529	C₈×C₄₃	—	2	1	no	—
530	C₈×C₄₃	—	2	1	no	—
531	C₈×C₄₃	—	2	1	no	—
532	C₈×C₄₃	C₂×#41	1	2	yes	—
533	C₄₃⋊C₈	—	2	2	no	—
534	C₄₃⋊C₈	—	2	2	no	—
535	#61468	—	43	1	no	maximal, Sylow
536	C₂²×C₄₃	—	2	1	no	—
537	C₂²×C₄₃	—	2	2	no	—
538	C₂²×C₄₃	—	2	1	no	—
539	C₂²×C₄₃	—	2	1	no	—
540	C₂²×C₄₃	—	4	1	no	—
541	C₂²×C₄₃	—	4	1	no	—
542	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
543	C₂×D₄₃	—	2	2	no	—
544	C₂×D₄₃	—	2	2	no	—
545	C₂×D₄₃	—	2	2	no	—
546	C₂×D₄₃	—	4	2	no	—
547	C₂×D₄₃	—	4	2	no	—
548	C₂×D₄₃	—	4	2	no	—
549	C₂×D₄₃	—	4	2	no	—
550	C₂×D₄₃	—	4	2	no	—
551	C₂×D₄₃	—	4	2	no	—
552	C₂×D₄₃	—	8	8	no	—
553	C₄×C₄₃	—	2	1	no	—
554	C₄×C₄₃	—	2	1	no	—
555	C₄×C₄₃	—	2	2	no	—
556	C₄×C₄₃	—	2	1	no	—
557	C₄×C₄₃	—	2	1	no	—
558	C₄×C₄₃	—	4	1	no	—
559	C₄×C₄₃	—	4	1	no	—
560	C₄×C₄₃	—	4	1	no	—
561	C₄×C₄₃	—	4	1	no	—
562	C₄×C₄₃	—	4	1	no	—
563	C₄×C₄₃	—	4	1	no	—
564	C₄×C₄₃	#575	1	2	yes	—
565	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
566	C₄×C₄₃	#585	1	1	yes	characteristic
567	Dic₄₃	—	2	2	no	—
568	Dic₄₃	—	2	2	no	—
569	Dic₄₃	—	2	2	no	—
570	Dic₄₃	—	4	2	no	—
571	Dic₄₃	—	4	2	no	—
572	#3481	—	43	1	no	—
573	#3480	—	43	1	no	—
574	#3396	—	43	1	no	—
575	#3381	—	43	1	no	—
576	#3365	—	43	1	no	—
577	#3361	—	43	1	no	—
578	#3356	—	43	1	no	—
579	#3355	—	43	2	no	—
580	#3333	—	43	1	no	—
581	#3326	—	43	2	no	—
582	#3324	—	43	1	no	—
583	#3322	—	43	2	no	—
584	#3275	—	43	2	no	—
585	#3274	—	43	1	no	—
586	#3184	—	43	1	no	—
587	#3183	—	43	2	no	—
588	#3115	—	43	1	no	—
589	#3114	—	43	2	no	—
590	#3112	—	43	1	no	—
591	#3111	—	43	2	no	—
592	#2971	—	43	1	no	—
593	C₄×#137	D₄₃	1	1	yes	characteristic, complemented
594	C₄×AGL(1,ℤ/8)	—	43	2	no	—
595	C₂×C₄₃	—	4	2	no	—
596	C₂×C₄₃	—	4	1	no	—
597	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
598	C₂×C₄₃	C₂×#575	1	1	yes	characteristic
599	C₂×C₄₃	#3585	1	1	yes	characteristic
600	D₄₃	—	4	2	no	—
601	D₄₃	—	8	2	no	—
602	D₄₃	—	8	2	no	—
603	C₂×#137	C₂×D₄₃	1	1	yes	characteristic
604	C₂×AGL(1,ℤ/8)	—	43	2	no	—
605	#559	—	43	1	no	—
606	#559	—	43	1	no	—
607	#559	—	86	1	no	—
608	#557	—	43	1	no	—
609	#556	—	43	1	no	—
610	#556	—	86	1	no	—
611	#554	—	43	1	no	—
612	#554	—	43	1	no	—
613	#553	—	43	2	no	—
614	#553	—	43	2	no	—
615	#553	—	86	2	no	—
616	#553	—	86	1	no	—
617	#551	—	86	2	no	—
618	#550	—	43	1	no	—
619	#548	—	43	2	no	—
620	#546	—	43	2	no	—
621	#546	—	86	1	no	—
622	D₄²	—	43	1	no	—
623	#532	—	43	1	no	—
624	#532	—	43	1	no	—
625	#532	—	86	1	no	—
626	#529	—	43	2	no	—
627	#529	—	43	2	no	—
628	#529	—	86	1	no	—
629	#529	—	86	2	no	—
630	#525	—	86	2	no	—
631	C₄×#41	—	43	1	no	—
632	C₄×#41	—	43	2	no	—
633	C₄×#41	—	86	1	no	—
634	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
635	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
636	C₂×C₄×D₄	—	43	2	no	—
637	C₂×C₄×D₄	—	86	1	no	—
638	#499	—	43	2	no	—
639	#498	—	43	1	no	—
640	#495	—	43	2	no	—
641	#493	—	43	1	no	—
642	#488	—	43	2	no	—
643	#488	—	43	2	no	—
644	#486	—	43	1	no	—
645	#486	—	43	1	no	—
646	#485	—	43	2	no	—
647	#483	—	43	2	no	—
648	#482	—	43	2	no	—
649	#482	—	43	2	no	—
650	#480	—	43	2	no	—
651	#480	—	43	2	no	—
652	#479	—	43	2	no	—
653	#478	—	43	2	no	—
654	#478	—	43	2	no	—
655	#478	—	43	2	no	—
656	#477	—	43	1	no	—
657	#477	—	43	1	no	—
658	#475	—	43	1	no	—
659	#474	—	43	1	no	—
660	#470	—	43	2	no	—
661	#469	—	43	2	no	—
662	#469	—	43	2	no	—
663	#469	—	43	2	no	—
664	#468	—	43	2	no	—
665	#468	—	43	2	no	—
666	#464	—	43	2	no	—
667	#463	—	43	2	no	—
668	#463	—	43	2	no	—
669	#463	—	43	2	no	—
670	#460	—	43	1	no	—
671	#460	—	43	1	no	—
672	#460	—	43	1	no	—
673	#459	—	43	1	no	—
674	#452	—	43	2	no	—
675	#450	—	43	2	no	—
676	#449	—	43	2	no	—
677	#449	—	43	2	no	—
678	#448	—	43	2	no	—
679	#447	—	43	2	no	—
680	C₈×Q₈	—	43	1	no	—
681	C₈×Q₈	—	43	1	no	—
682	#442	—	43	2	no	—
683	#442	—	43	2	no	—
684	#442	—	43	2	no	—
685	#441	C₂×D₄₃	1	1	yes	characteristic, complemented
686	#441	C₂×D₄₃	1	1	yes	characteristic, complemented
687	#440	—	43	2	no	—
688	#440	—	43	2	no	—
689	#440	—	43	2	no	—
690	#440	C₂×D₄₃	1	1	yes	characteristic
691	#440	C₂×D₄₃	1	1	yes	characteristic
692	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
693	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
694	C₄×SD₁₆	—	43	2	no	—
695	C₄×SD₁₆	—	43	2	no	—
696	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
697	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
698	C₄×D₈	—	43	2	no	—
699	C₄×D₈	—	43	2	no	—
700	#436	—	43	2	no	—
701	#436	—	43	2	no	—
702	#436	—	43	1	no	—
703	#436	—	43	1	no	—
704	#432	—	43	1	no	—
705	#432	—	43	2	no	—
706	#428	—	43	2	no	—
707	#428	C₂×D₄₃	1	1	yes	characteristic, complemented
708	#419	C₂×D₄₃	1	1	yes	characteristic, complemented
709	#418	—	43	2	no	—
710	#417	—	43	2	no	—
711	#417	C₂×D₄₃	1	1	yes	characteristic
712	C₄×M₁₆	—	43	2	no	—
713	C₄×M₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
714	C₄₃	#61468	1	1	yes	characteristic, complemented, Sylow
715	C₂×#41	—	43	1	no	—
716	C₂×#41	—	43	2	no	—
717	C₂×#41	—	86	1	no	—
718	C₂×#41	—	86	1	no	—
719	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
720	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
721	C₂²×D₄	—	43	2	no	—
722	C₂²×D₄	—	86	1	no	—
723	C₂³×C₄	—	86	2	no	—
724	#137	—	2	4	no	—
725	AGL(1,ℤ/8)	—	86	8	no	—
726	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
727	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
728	C₂×SD₁₆	—	43	2	no	—
729	C₂×SD₁₆	—	43	2	no	—
730	C₂×SD₁₆	—	43	2	no	—
731	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
732	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
733	C₂×D₈	—	43	2	no	—
734	C₂×D₈	—	43	2	no	—
735	C₂×D₈	—	43	2	no	—
736	C₂×M₁₆	—	43	2	no	—
737	C₂×M₁₆	—	43	2	no	—
738	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
739	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
740	C₄⋊Q₈	—	43	1	no	—
741	C₄⋊Q₈	—	43	1	no	—
742	C₄⋊Q₈	—	86	1	no	—
743	#127	—	43	1	no	—
744	#127	—	43	1	no	—
745	#127	—	86	1	no	—
746	#126	—	86	2	no	—
747	#126	—	86	2	no	—
748	#126	—	86	2	no	—
749	#126	—	86	2	no	—
750	#126	—	86	2	no	—
751	#125	—	43	2	no	—
752	#125	—	43	2	no	—
753	#125	—	86	1	no	—
754	#125	—	86	2	no	—
755	#124	—	43	2	no	—
756	#124	—	43	2	no	—
757	#124	—	86	1	no	—
758	#124	—	86	1	no	—
759	#124	—	86	1	no	—
760	#124	—	86	2	no	—
761	#124	—	86	1	no	—
762	#124	—	86	1	no	—
763	#123	—	86	2	no	—
764	#123	—	86	2	no	—
765	#123	—	86	2	no	—
766	#123	—	86	2	no	—
767	#123	—	86	2	no	—
768	#123	—	86	2	no	—
769	#123	—	86	2	no	—
770	C₂²⋊Q₈	—	43	2	no	—
771	C₂²⋊Q₈	—	43	2	no	—
772	C₂²⋊Q₈	—	86	2	no	—
773	C₂²⋊Q₈	—	86	2	no	—
774	C₂²⋊Q₈	—	86	2	no	—
775	C₂²⋊Q₈	—	86	1	no	—
776	#121	—	43	2	no	—
777	#121	—	43	2	no	—
778	#121	—	43	2	no	—
779	#121	—	43	2	no	—
780	#121	—	86	2	no	—
781	#121	—	86	2	no	—
782	#121	—	86	2	no	—
783	#121	—	86	1	no	—
784	#121	—	86	2	no	—
785	#121	—	86	2	no	—
786	#121	—	86	1	no	—
787	#121	—	86	1	no	—
788	#120	—	86	2	no	—
789	#120	—	86	2	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	43	1	no	—
793	C₄×Q₈	—	43	1	no	—
794	C₄×Q₈	—	43	2	no	—
795	C₄×Q₈	—	86	1	no	—
796	C₄×Q₈	—	86	1	no	—
797	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
798	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
799	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
800	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
801	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
802	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	43	2	no	—
806	C₄×D₄	—	43	2	no	—
807	C₄×D₄	—	43	2	no	—
808	C₄×D₄	—	43	2	no	—
809	C₄×D₄	—	43	2	no	—
810	C₄×D₄	—	43	1	no	—
811	C₄×D₄	—	43	1	no	—
812	C₄×D₄	—	43	2	no	—
813	C₄×D₄	—	43	2	no	—
814	C₄×D₄	—	86	2	no	—
815	C₄×D₄	—	86	1	no	—
816	C₄×D₄	—	86	1	no	—
817	C₄×D₄	—	86	1	no	—
818	C₄×D₄	—	86	2	no	—
819	C₄×D₄	—	86	2	no	—
820	C₄×D₄	—	86	2	no	—
821	C₄×D₄	—	86	1	no	—
822	C₄×D₄	—	86	2	no	—
823	C₄×D₄	—	86	2	no	—
824	C₄×D₄	—	86	2	no	—
825	C₄×D₄	—	86	2	no	—
826	C₄×D₄	—	86	2	no	—
827	C₄×D₄	—	86	1	no	—
828	C₄×D₄	—	86	1	no	—
829	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
830	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
831	#117	—	2	1	no	—
832	#117	—	43	1	no	—
833	#117	—	43	2	no	—
834	#117	—	43	2	no	—
835	#117	—	86	2	no	—
836	#117	—	86	2	no	—
837	#117	—	86	2	no	—
838	#117	C₂²×D₄₃	1	1	yes	characteristic
839	C₂×C₄⋊C₄	—	2	1	no	—
840	C₂×C₄⋊C₄	—	43	2	no	—
841	C₂×C₄⋊C₄	—	86	1	no	—
842	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
843	C₂×C₂²⋊C₄	—	86	2	no	—
844	C₂×C₂²⋊C₄	—	86	2	no	—
845	C₂×C₄²	—	2	1	no	—
846	C₂×C₄²	—	2	1	no	—
847	C₂×C₄²	—	43	2	no	—
848	C₂×C₄²	—	86	2	no	—
849	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
850	#107	—	43	2	no	—
851	#107	—	43	2	no	—
852	#107	—	43	2	no	—
853	#107	C₂²×D₄₃	1	1	yes	characteristic
854	#107	C₂²×D₄₃	1	1	yes	characteristic
855	#106	—	43	2	no	—
856	#106	—	43	2	no	—
857	#106	—	43	2	no	—
858	#106	C₂²×D₄₃	1	1	yes	characteristic
859	#106	C₂²×D₄₃	1	1	yes	characteristic
860	C₄⋊C₈	—	43	2	no	—
861	C₄⋊C₈	—	43	2	no	—
862	C₄⋊C₈	—	43	1	no	—
863	C₄⋊C₈	—	43	1	no	—
864	#103	—	43	2	no	—
865	#103	—	43	2	no	—
866	#103	—	43	2	no	—
867	#103	C₂²×D₄₃	1	1	yes	characteristic
868	#103	C₂²×D₄₃	1	1	yes	characteristic
869	#103	C₂²×D₄₃	1	1	yes	characteristic
870	#103	C₂²×D₄₃	1	1	yes	characteristic
871	#103	C₂²×D₄₃	1	1	yes	characteristic
872	#103	C₂²×D₄₃	1	1	yes	characteristic
873	#102	—	43	2	no	—
874	#102	—	43	2	no	—
875	#102	—	43	2	no	—
876	#102	—	43	2	no	—
877	#102	—	43	2	no	—
878	#102	—	43	2	no	—
879	#102	—	43	2	no	—
880	#102	—	43	2	no	—
881	#102	—	43	2	no	—
882	#102	C₂²×D₄₃	1	1	yes	characteristic
883	#102	C₂²×D₄₃	1	1	yes	characteristic
884	C₂²⋊C₈	—	43	2	no	—
885	C₂²⋊C₈	—	43	2	no	—
886	C₂²⋊C₈	—	43	2	no	—
887	#97	—	43	2	no	—
888	#97	C₂²×D₄₃	1	1	yes	characteristic
889	#97	C₂²×D₄₃	1	1	yes	characteristic
890	C₄×C₈	—	43	2	no	—
891	C₄×C₈	—	43	2	no	—
892	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
893	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
894	C₂⁴	—	86	2	no	—
895	#41	—	2	2	no	—
896	#41	—	4	1	no	—
897	#41	—	86	4	no	—
898	#41	—	344	2	no	—
899	#41	—	172	2	no	—
900	#41	—	172	4	no	—
901	#41	—	172	2	no	—
902	C₂×Q₈	—	2	1	no	—
903	C₂×Q₈	—	2	2	no	—
904	C₂×Q₈	—	4	1	no	—
905	C₂×Q₈	—	43	1	no	—
906	C₂×Q₈	—	86	1	no	—
907	C₂×Q₈	—	86	1	no	—
908	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
909	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
910	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
911	C₂×D₄	—	2	1	no	—
912	C₂×D₄	—	43	2	no	—
913	C₂×D₄	—	43	1	no	—
914	C₂×D₄	—	43	2	no	—
915	C₂×D₄	—	43	2	no	—
916	C₂×D₄	—	86	2	no	—
917	C₂×D₄	—	86	2	no	—
918	C₂×D₄	—	86	2	no	—
919	C₂×D₄	—	86	2	no	—
920	C₂×D₄	—	86	4	no	—
921	C₂×D₄	—	86	2	no	—
922	C₂×D₄	—	86	2	no	—
923	C₂×D₄	—	86	1	no	—
924	C₂×D₄	—	86	1	no	—
925	C₂×D₄	—	86	1	no	—
926	C₂×D₄	—	86	1	no	—
927	C₂×D₄	—	172	4	no	—
928	C₂×D₄	—	172	2	no	—
929	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	1	no	—
933	C₂²×C₄	—	2	1	no	—
934	C₂²×C₄	—	2	1	no	—
935	C₂²×C₄	—	43	2	no	—
936	C₂²×C₄	—	43	2	no	—
937	C₂²×C₄	—	43	2	no	—
938	C₂²×C₄	—	86	2	no	—
939	C₂²×C₄	—	86	2	no	—
940	C₂²×C₄	—	86	2	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	—	344	4	no	—
946	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
947	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
948	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
949	Q₁₆	—	2	2	no	—
950	Q₁₆	—	2	2	no	—
951	SD₁₆	—	2	2	no	—
952	SD₁₆	—	86	4	no	—
953	SD₁₆	—	172	2	no	—
954	SD₁₆	—	172	2	no	—
955	SD₁₆	#10621898	1	4	yes	complemented
956	D₈	—	86	4	no	—
957	D₈	—	86	4	no	—
958	D₈	—	172	2	no	—
959	M₁₆	—	2	2	no	—
960	M₁₆	—	4	1	no	—
961	M₁₆	—	86	4	no	—
962	M₁₆	—	172	2	no	—
963	C₂×C₈	—	43	2	no	—
964	C₂×C₈	—	43	2	no	—
965	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
966	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
967	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
968	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	1	no	—
972	C₄⋊C₄	—	2	1	no	—
973	C₄⋊C₄	—	2	1	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	43	1	no	—
977	C₄⋊C₄	—	43	1	no	—
978	C₄⋊C₄	—	43	2	no	—
979	C₄⋊C₄	—	43	2	no	—
980	C₄⋊C₄	—	43	2	no	—
981	C₄⋊C₄	—	43	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	2	no	—
987	C₄⋊C₄	—	86	2	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	—	43	2	no	—
1000	C₂²⋊C₄	—	43	2	no	—
1001	C₂²⋊C₄	—	43	2	no	—
1002	C₂²⋊C₄	—	86	2	no	—
1003	C₂²⋊C₄	—	86	2	no	—
1004	C₂²⋊C₄	—	86	2	no	—
1005	C₂²⋊C₄	—	86	2	no	—
1006	C₂²⋊C₄	—	86	2	no	—
1007	C₂²⋊C₄	—	86	2	no	—
1008	C₂²⋊C₄	—	86	2	no	—
1009	C₂²⋊C₄	—	86	2	no	—
1010	C₂²⋊C₄	—	86	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	C₄²	—	2	1	no	—
1019	C₄²	—	2	1	no	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	1	no	—
1025	C₄²	—	43	2	no	—
1026	C₄²	—	43	2	no	—
1027	C₄²	—	43	2	no	—
1028	C₄²	—	86	2	no	—
1029	C₄²	—	86	2	no	—
1030	C₄²	D₄×D₄₃	1	1	yes	characteristic
1031	C₄²	D₄×D₄₃	1	1	yes	characteristic
1032	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1033	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1034	C₂³	—	2	1	no	—
1035	C₂³	—	43	2	no	—
1036	C₂³	—	86	2	no	—
1037	C₂³	—	86	2	no	—
1038	C₂³	—	344	2	no	—
1039	C₂³	—	172	4	no	—
1040	C₂³	—	172	4	no	—
1041	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1042	Q₈	—	2	1	no	—
1043	Q₈	—	2	1	no	—
1044	Q₈	—	2	1	no	—
1045	Q₈	—	2	1	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	4	2	no	—
1048	Q₈	—	86	2	no	—
1049	Q₈	—	344	1	no	—
1050	Q₈	—	172	2	no	—
1051	Q₈	C₂×#10621898	1	2	yes	—
1052	D₄	—	2	1	no	—
1053	D₄	—	4	2	no	—
1054	D₄	—	86	2	no	—
1055	D₄	—	86	2	no	—
1056	D₄	—	86	2	no	—
1057	D₄	—	86	2	no	—
1058	D₄	—	86	2	no	—
1059	D₄	—	344	1	no	—
1060	D₄	—	344	1	no	—
1061	D₄	—	344	2	no	—
1062	D₄	—	344	2	no	—
1063	D₄	—	172	4	no	—
1064	D₄	—	172	4	no	—
1065	D₄	—	172	2	no	—
1066	D₄	—	172	4	no	—
1067	D₄	—	172	4	no	—
1068	D₄	—	172	2	no	—
1069	D₄	—	172	2	no	—
1070	D₄	C₂×#10621898	1	2	yes	—
1071	C₂×C₄	—	2	1	no	—
1072	C₂×C₄	—	2	2	no	—
1073	C₂×C₄	—	2	1	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	1	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	1	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	1	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	4	1	no	—
1082	C₂×C₄	—	4	2	no	—
1083	C₂×C₄	—	4	2	no	—
1084	C₂×C₄	—	4	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	8	1	no	—
1087	C₂×C₄	—	43	2	no	—
1088	C₂×C₄	—	43	2	no	—
1089	C₂×C₄	—	43	2	no	—
1090	C₂×C₄	—	86	2	no	—
1091	C₂×C₄	—	86	2	no	—
1092	C₂×C₄	—	86	2	no	—
1093	C₂×C₄	—	86	2	no	—
1094	C₂×C₄	—	344	2	no	—
1095	C₂×C₄	—	344	2	no	—
1096	C₂×C₄	—	344	2	no	—
1097	C₂×C₄	—	344	2	no	—
1098	C₂×C₄	—	172	2	no	—
1099	C₂×C₄	—	172	2	no	—
1100	C₂×C₄	—	172	4	no	—
1101	C₂×C₄	—	172	4	no	—
1102	C₂×C₄	—	172	4	no	—
1103	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1104	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1105	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1106	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1107	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1108	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1109	C₈	—	2	1	no	—
1110	C₈	—	2	1	no	—
1111	C₈	—	2	1	no	—
1112	C₈	—	86	2	no	—
1113	C₈	—	86	2	no	—
1114	C₈	C₂×#10621898	1	2	yes	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	1	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	1	no	—
1119	C₂²	—	4	1	no	—
1120	C₂²	—	4	1	no	—
1121	C₂²	—	86	2	no	—
1122	C₂²	—	86	2	no	—
1123	C₂²	—	86	2	no	—
1124	C₂²	—	344	8	no	—
1125	C₂²	—	172	2	no	—
1126	C₂²	—	172	2	no	—
1127	C₂²	—	172	2	no	—
1128	C₂²	—	172	2	no	—
1129	C₂²	—	172	2	no	—
1130	C₂²	—	172	2	no	—
1131	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	2	no	—
1135	C₄	—	2	1	no	—
1136	C₄	—	2	1	no	—
1137	C₄	—	4	1	no	—
1138	C₄	—	4	1	no	—
1139	C₄	—	4	1	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	1	no	—
1143	C₄	—	86	2	no	—
1144	C₄	—	86	2	no	—
1145	C₄	—	86	2	no	—
1146	C₄	—	172	2	no	—
1147	C₄	—	172	2	no	—
1148	C₄	#14583698	1	2	yes	—
1149	C₄	C₂²×#10621898	1	1	yes	characteristic
1150	C₄	#14583735	1	1	yes	characteristic
1151	C₂	—	4	1	no	—
1152	C₂	—	4	2	no	—
1153	C₂	—	344	2	no	—
1154	C₂	—	344	2	no	—
1155	C₂	—	172	2	no	—
1156	C₂	D₄×#10621898	1	1	yes	characteristic
1157	C₂	C₂×#14583698	1	1	yes	characteristic
1158	C₂	#19149372	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄×#137×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	C₄×#137	D₄₃
hypocenter	C₄₃	#61468
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#137

Complements

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

N	H ≅ G/N	type
1. #19148205	C₂	semidirect
2. #19148190	C₂	semidirect
3. #19147605	C₂	semidirect
4. #19147468	C₂	semidirect
5. #19147289	C₂	semidirect
6. #19147253	C₂	semidirect
7. #19147212	C₂	semidirect
8. #19147197	C₂	semidirect
9. #19146935	C₂	semidirect
10. #19146844	C₂	semidirect
11. #19146828	C₂	semidirect
12. #19146797	C₂	semidirect
13. #19146220	C₂	semidirect
14. #19146216	C₂	semidirect
15. #19145333	C₂	semidirect
16. #19145327	C₂	semidirect
17. #19144746	C₂	semidirect
18. #19144737	C₂	semidirect
19. #19144717	C₂	semidirect
20. #19144710	C₂	semidirect
21. #19143613	C₂	semidirect
22. #19143400	C₂	semidirect
23. C₄×#137×C₄₃	C₂	semidirect
27. #14583634	C₂²	semidirect
28. #14583628	C₂²	semidirect
34. #14583597	C₂²	semidirect
39. #14583560	C₂²	semidirect
45. #14583449	C₂²	semidirect
48. #14583436	C₂²	semidirect
51. C₄×#10621902	C₂²	semidirect
56. #14583299	C₂²	semidirect
57. #14583297	C₂²	semidirect
58. #14583284	C₂²	semidirect
60. #14583255	C₂²	semidirect
61. #14583255	C₂²	semidirect
63. #14583246	C₂²	semidirect
64. #14583238	C₂²	semidirect
65. #14583228	C₂²	semidirect
67. #14583223	C₂²	semidirect
68. #14583214	C₂²	semidirect
69. #14583212	C₂²	semidirect
70. #14583204	C₂²	semidirect
71. #14583202	C₂²	semidirect
73. #14583198	C₂²	semidirect
74. #14583194	C₂²	semidirect
75. #14583194	C₂²	semidirect
76. #14583184	C₂²	semidirect
78. #14583154	C₂²	semidirect
80. #14583152	C₂²	semidirect
81. #14583152	C₂²	semidirect
83. #14583148	C₂²	semidirect
84. #14583123	C₂²	semidirect
85. #14583117	C₂²	semidirect
86. #14583117	C₂²	semidirect
90. #14583099	C₂²	semidirect
92. #14583060	C₂²	semidirect
96. #14583038	C₂²	semidirect
98. C₈×Dic₈₆	C₂²	semidirect
99. C₈×Dic₈₆	C₂²	semidirect
100. #14583012	C₂²	semidirect
101. #14583012	C₂²	semidirect
103. #14582997	C₂²	semidirect
104. #14582997	C₂²	semidirect
105. #14582997	C₂²	semidirect
107. #14582984	C₂²	semidirect
108. #14582981	C₂²	semidirect
112. #14582975	C₂²	semidirect
113. #14582975	C₂²	semidirect
114. #14582956	C₂²	semidirect
115. #14582954	C₂²	semidirect
116. #14582940	C₂²	semidirect
118. #14582899	C₂²	semidirect
119. #14582851	C₂²	semidirect
122. C₂×C₄×Q₈×C₄₃	C₂²	semidirect
123. C₄₃×#441	C₂²	semidirect
124. C₄₃×#441	C₂²	semidirect
127. C₄×Q₁₆×C₄₃	C₂²	semidirect
128. C₄×Q₁₆×C₄₃	C₂²	semidirect
131. C₄₃×#428	C₂²	semidirect
132. C₄₃×#419	C₂²	semidirect
134. C₄×M₁₆×C₄₃	C₂²	semidirect
372. SD₁₆×C₄₃	#41	semidirect
593. C₄×#137	D₄₃	semidirect
635. C₂×C₄×Q₈	C₂×D₄₃	semidirect
685. #441	C₂×D₄₃	semidirect
686. #441	C₂×D₄₃	semidirect
692. C₄×Q₁₆	C₂×D₄₃	semidirect
693. C₄×Q₁₆	C₂×D₄₃	semidirect
707. #428	C₂×D₄₃	semidirect
708. #419	C₂×D₄₃	semidirect
713. C₄×M₁₆	C₂×D₄₃	semidirect
714. C₄₃	#61468	semidirect
955. SD₁₆	#10621898	semidirect

Maximal subgroups

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

subgroup	index
#19148205	2
#19148190	2
#19147605	2
#19147468	2
#19147289	2
#19147253	2
#19147212	2
#19147197	2
#19146935	2
#19146844	2
#19146828	2
#19146797	2
#19146220	2
#19146216	2
#19145333	2
#19145327	2
#19144746	2
#19144737	2
#19144717	2
#19144710	2
#19143613	2
#19143400	2
C₄×#137×C₄₃	2
#61468	43