Subgroups — #25978026

Order 11008.

1890 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148151	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	#19147241	C₂	1	2	yes	maximal, complemented
5	#19147014	C₂	1	1	yes	maximal, characteristic, complemented
6	#19146962	C₂	1	1	yes	maximal, characteristic, complemented
7	#19146958	C₂	1	1	yes	maximal, characteristic, complemented
8	#19146518	C₂	1	2	yes	maximal, complemented
9	#19146429	C₂	1	2	yes	maximal, complemented
10	#19146425	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	#19145178	C₂	1	1	yes	maximal, characteristic, complemented
15	#19145163	C₂	1	1	yes	maximal, characteristic, complemented
16	#19144611	C₂	1	2	yes	maximal, complemented
17	#19144607	C₂	1	2	yes	maximal, complemented
18	#19144601	C₂	1	2	yes	maximal, complemented
19	C₈×#10621898	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#13063347	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#13063348	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₈×D₄₃	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	#14583618	C₂²	1	2	yes	complemented
28	#14583613	C₂²	1	2	yes	complemented
29	#14583605	C₂²	1	2	yes	complemented
30	#14583594	—	2	2	no	—
31	#14583587	C₂²	1	2	yes	—
32	#14583585	—	2	2	no	—
33	#14583583	C₂²	1	2	yes	—
34	#14583577	—	2	2	no	—
35	#14583574	—	2	2	no	—
36	#14583551	C₂²	1	2	yes	complemented
37	#14583546	C₂²	1	2	yes	—
38	#14583542	C₂²	1	2	yes	—
39	#14583453	C₂²	1	2	yes	—
40	#14583431	—	2	2	no	—
41	#14583431	C₂²	1	2	yes	complemented
42	#14583427	—	2	2	no	—
43	#14583408	—	2	2	no	—
44	C₄×#10621902	C₂²	1	2	yes	complemented
45	C₄×#10621898	C₂²	1	1	yes	characteristic
46	C₄×#10621898	C₂²	1	2	yes	complemented
47	C₄×D₄×D₄₃	C₂²	1	2	yes	—
48	#117×D₄₃	—	2	2	no	—
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	#14583252	C₂²	1	2	yes	complemented
54	#14583248	C₂²	1	2	yes	complemented
55	#14583243	C₂²	1	2	yes	complemented
56	#14583237	C₂²	1	2	yes	complemented
57	#14583231	C₂²	1	2	yes	—
58	#14583228	C₂²	1	2	yes	—
59	#14583222	C₂²	1	2	yes	complemented
60	#14583220	C₂²	1	2	yes	complemented
61	#14583204	C₂²	1	2	yes	complemented
62	#14583203	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	#14583187	C₂²	1	2	yes	complemented
67	#14583141	C₂²	1	1	yes	characteristic
68	#14583141	C₂²	1	1	yes	characteristic, complemented
69	#14583139	C₂²	1	2	yes	—
70	#14583137	C₂²	1	1	yes	characteristic
71	#14583132	C₂²	1	1	yes	characteristic
72	#14583127	C₂²	1	2	yes	complemented
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	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
86	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
87	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
88	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
89	Q₁₆×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
90	C₄×#10621885	C₂²	1	2	yes	complemented
91	C₄×#10621873	C₂²	1	2	yes	complemented
92	C₄×#10621873	C₂²	1	2	yes	complemented
93	C₄×#10621884	C₂²	1	2	yes	complemented
94	C₄×#10621883	C₂²	1	2	yes	complemented
95	#14582984	C₂²	1	2	yes	complemented
96	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
97	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
98	D₈×Dic₄₃	C₂²	1	1	yes	characteristic
99	#14582981	C₂²	1	1	yes	characteristic
100	#14582981	C₂²	1	1	yes	characteristic
101	C₄×#10621882	C₂²	1	2	yes	—
102	#14582979	C₂²	1	2	yes	—
103	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
104	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
105	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
106	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
107	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic, complemented
108	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic, complemented
109	#14582952	C₂²	1	1	yes	characteristic, complemented
110	#14582950	C₂²	1	1	yes	characteristic
111	#14582950	C₂²	1	1	yes	characteristic, complemented
112	#14582937	C₂²	1	1	yes	characteristic, complemented
113	#14582936	C₂²	1	1	yes	characteristic, complemented
114	#107×D₄₃	C₂²	1	1	yes	characteristic
115	#14582896	C₂²	1	2	yes	complemented
116	#14582894	C₂²	1	2	yes	complemented
117	#102×D₄₃	C₂²	1	2	yes	—
118	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₄₃	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	D₄	1	1	yes	characteristic
133	C₂×#10621898	C₂³	1	2	yes	—
134	C₂×D₄×D₄₃	C₂³	1	2	yes	—
135	C₂²×C₄×D₄₃	—	2	2	no	—
136	#13063348	—	2	4	no	—
137	#13063347	—	2	4	no	—
138	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
139	C₂×#10621885	C₂³	1	2	yes	—
140	C₂×#10621873	C₂³	1	2	yes	—
141	C₂×#10621883	C₂³	1	2	yes	—
142	C₂×#10621884	C₂³	1	2	yes	—
143	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
144	C₂×#10621882	C₂³	1	2	yes	—
145	D₈×D₄₃	—	2	4	no	—
146	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
147	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
148	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
149	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
150	#13063324	C₂³	1	2	yes	—
151	#13063323	C₂³	1	2	yes	—
152	#13063320	—	2	2	no	—
153	#13063318	—	2	2	no	—
154	#13063318	—	2	2	no	—
155	#13063318	—	2	2	no	—
156	#13063318	—	2	2	no	—
157	#13063316	—	2	2	no	—
158	#13063316	C₂³	1	2	yes	—
159	#13063315	—	2	2	no	—
160	#13063315	—	2	2	no	—
161	#13063312	—	2	2	no	—
162	#13063312	C₂³	1	2	yes	—
163	#13063311	—	2	2	no	—
164	#13063310	—	2	2	no	—
165	#13063310	—	2	2	no	—
166	#13063307	—	2	2	no	—
167	#13063307	—	2	2	no	—
168	#13063307	—	2	2	no	—
169	#13063307	—	2	2	no	—
170	#13063307	—	2	2	no	—
171	#13063305	—	2	2	no	—
172	#13063305	C₂³	1	2	yes	—
173	#13063305	C₂³	1	2	yes	—
174	#13063303	—	2	2	no	—
175	#13063303	—	2	2	no	—
176	#13063303	—	2	2	no	—
177	#13063302	—	2	2	no	—
178	#13063301	C₂³	1	2	yes	—
179	#13063298	—	2	2	no	—
180	#13063298	—	2	2	no	—
181	#13063297	—	2	2	no	—
182	#13063296	—	2	2	no	—
183	#13063296	C₂³	1	2	yes	—
184	#13063295	—	2	2	no	—
185	#13063293	—	2	2	no	—
186	Q₈×Dic₄₃	C₂³	1	2	yes	—
187	C₄×Dic₈₆	—	2	2	no	—
188	C₄×Dic₈₆	D₄	1	1	yes	characteristic
189	C₄×Dic₈₆	C₂³	1	2	yes	—
190	C₄×Dic₈₆	C₂³	1	2	yes	—
191	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
192	C₄×D₁₇₂	—	2	2	no	—
193	C₄×D₁₇₂	D₄	1	1	yes	characteristic
194	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
195	C₄×D₁₇₂	C₂³	1	2	yes	—
196	C₄×D₁₇₂	C₂³	1	2	yes	—
197	D₄×Dic₄₃	C₂³	1	2	yes	—
198	#13063287	—	2	2	no	—
199	#13063287	C₂³	1	2	yes	—
200	#13063287	C₂³	1	2	yes	—
201	C₄×C₂²⋊D₄₃	—	2	2	no	—
202	C₄×C₂²⋊D₄₃	—	2	2	no	—
203	C₄×C₂²⋊D₄₃	—	2	2	no	—
204	C₄×C₂²⋊D₄₃	—	2	2	no	—
205	C₄×C₂²⋊D₄₃	D₄	1	1	yes	characteristic
206	C₄×C₂²⋊D₄₃	D₄	1	1	yes	characteristic
207	C₄×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
208	C₄×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
209	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
210	#13063284	—	2	2	no	—
211	#13063284	D₄	1	1	yes	characteristic
212	#13063284	C₂³	1	2	yes	—
213	#13063283	—	2	2	no	—
214	#13063283	—	2	2	no	—
215	#13063283	—	2	2	no	—
216	#13063283	C₂³	1	2	yes	—
217	#13063282	—	2	2	no	—
218	#13063282	—	2	2	no	—
219	#13063282	D₄	1	1	yes	characteristic
220	#13063282	D₄	1	1	yes	characteristic
221	#13063281	—	2	2	no	—
222	#13063281	—	2	2	no	—
223	C₄⋊C₄×D₄₃	—	2	2	no	—
224	C₄⋊C₄×D₄₃	—	2	2	no	—
225	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
226	C₂²⋊C₄×D₄₃	—	2	2	no	—
227	C₂²⋊C₄×D₄₃	—	2	2	no	—
228	C₂²⋊C₄×D₄₃	—	2	2	no	—
229	C₄²×D₄₃	—	2	2	no	—
230	C₄²×D₄₃	—	2	2	no	—
231	C₄²×D₄₃	C₂³	1	1	yes	characteristic
232	C₄²×D₄₃	C₂³	1	1	yes	characteristic
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	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
265	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
266	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
267	C₈×Dic₄₃	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	—	2	4	no	—
317	#10621898	—	4	2	no	—
318	C₂×D₁₇₂	—	2	2	no	—
319	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
320	C₂×D₁₇₂	C₂⁴	1	2	yes	—
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	—	2	2	no	—
328	C₂×C₄×D₄₃	—	4	8	no	—
329	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
330	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
331	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
332	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
333	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
334	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
335	C₂×Dic₈₆	—	2	2	no	—
336	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
337	C₂×Dic₈₆	C₂⁴	1	2	yes	—
338	Q₁₆×C₄₃	—	2	2	no	—
339	SD₁₆×C₄₃	—	4	2	no	—
340	D₈×C₄₃	—	2	2	no	—
341	C₂×C₈×C₄₃	—	2	2	no	—
342	C₂×C₈×C₄₃	—	4	1	no	—
343	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
344	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
345	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
346	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
347	C₄⋊C₄×C₄₃	—	2	2	no	—
348	C₄⋊C₄×C₄₃	—	2	2	no	—
349	C₄⋊C₄×C₄₃	—	2	2	no	—
350	C₄⋊C₄×C₄₃	—	2	2	no	—
351	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
352	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
353	C₂²⋊C₄×C₄₃	—	2	2	no	—
354	C₂²⋊C₄×C₄₃	—	2	2	no	—
355	C₂²⋊C₄×C₄₃	—	2	2	no	—
356	C₂²⋊C₄×C₄₃	—	2	2	no	—
357	C₂²⋊C₄×C₄₃	—	2	2	no	—
358	C₄²×C₄₃	—	2	2	no	—
359	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
360	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
361	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
362	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
363	C₂²⋊Dic₄₃	—	2	2	no	—
364	C₂²⋊Dic₄₃	—	2	2	no	—
365	C₂²⋊Dic₄₃	—	2	2	no	—
366	C₂²⋊Dic₄₃	—	2	2	no	—
367	C₂²⋊Dic₄₃	—	2	2	no	—
368	C₂²⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
369	C₂²⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
370	#10621885	—	4	2	no	—
371	#10621884	—	2	4	no	—
372	#10621883	—	4	2	no	—
373	#10621882	—	2	4	no	—
374	(C₂×D₄₃)⋊C₄	—	2	2	no	—
375	(C₂×D₄₃)⋊C₄	—	2	2	no	—
376	(C₂×D₄₃)⋊C₄	—	2	2	no	—
377	(C₂×D₄₃)⋊C₄	—	2	2	no	—
378	(C₂×D₄₃)⋊C₄	—	2	2	no	—
379	(C₂×D₄₃)⋊C₄	—	2	2	no	—
380	(C₂×D₄₃)⋊C₄	—	2	2	no	—
381	(C₂×D₄₃)⋊C₄	—	2	2	no	—
382	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
383	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
384	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
385	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
386	C₄⋊Dic₄₃	—	2	2	no	—
387	C₄⋊Dic₄₃	—	2	2	no	—
388	C₄⋊Dic₄₃	—	2	2	no	—
389	C₄⋊Dic₄₃	—	2	2	no	—
390	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
391	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
392	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
393	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
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	—	2	2	no	—
401	Dic₄₃⋊C₄	—	2	2	no	—
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	C₄×Dic₄₃	—	2	2	no	—
407	C₄×Dic₄₃	—	2	2	no	—
408	C₄×Dic₄₃	—	2	2	no	—
409	C₄×Dic₄₃	—	2	2	no	—
410	C₄×Dic₄₃	—	2	2	no	—
411	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
412	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
413	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
414	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
415	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
416	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
417	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
418	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
419	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
420	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
421	Dic₁₇₂	—	2	2	no	—
422	D₃₄₄	#41	1	4	yes	complemented
423	#10621873	—	2	4	no	—
424	C₈×D₄₃	—	2	2	no	—
425	C₈×D₄₃	—	2	2	no	—
426	C₈×D₄₃	—	4	1	no	—
427	C₈×D₄₃	—	4	1	no	—
428	C₂³×C₄₃	—	2	2	no	—
429	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
430	C₂²×D₄₃	—	2	2	no	—
431	C₂²×D₄₃	—	4	4	no	—
432	C₂²×D₄₃	—	4	4	no	—
433	C₂²×D₄₃	—	8	2	no	—
434	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
435	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
436	Q₈×C₄₃	—	2	2	no	—
437	Q₈×C₄₃	—	2	2	no	—
438	D₄×C₄₃	—	2	2	no	—
439	D₄×C₄₃	—	2	2	no	—
440	D₄×C₄₃	—	8	2	no	—
441	C₂×C₄×C₄₃	—	2	2	no	—
442	C₂×C₄×C₄₃	—	2	1	no	—
443	C₂×C₄×C₄₃	—	2	1	no	—
444	C₂×C₄×C₄₃	—	2	2	no	—
445	C₂×C₄×C₄₃	—	2	2	no	—
446	C₂×C₄×C₄₃	—	2	2	no	—
447	C₂×C₄×C₄₃	—	4	1	no	—
448	C₂×C₄×C₄₃	—	4	4	no	—
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	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
455	C₂²⋊D₄₃	—	2	2	no	—
456	C₂²⋊D₄₃	—	2	2	no	—
457	C₂²⋊D₄₃	—	4	4	no	—
458	C₂²⋊D₄₃	—	4	4	no	—
459	C₂²⋊D₄₃	—	8	2	no	—
460	C₂×Dic₄₃	—	2	2	no	—
461	C₂×Dic₄₃	—	2	2	no	—
462	C₂×Dic₄₃	—	2	2	no	—
463	C₂×Dic₄₃	—	4	4	no	—
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	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
469	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
470	D₁₇₂	—	2	2	no	—
471	D₁₇₂	—	2	2	no	—
472	D₁₇₂	—	4	4	no	—
473	D₁₇₂	C₂×#41	1	4	yes	—
474	C₄×D₄₃	—	2	2	no	—
475	C₄×D₄₃	—	2	1	no	—
476	C₄×D₄₃	—	2	1	no	—
477	C₄×D₄₃	—	2	1	no	—
478	C₄×D₄₃	—	2	1	no	—
479	C₄×D₄₃	—	4	1	no	—
480	C₄×D₄₃	—	4	1	no	—
481	C₄×D₄₃	—	4	4	no	—
482	C₄×D₄₃	—	4	4	no	—
483	C₄×D₄₃	—	4	4	no	—
484	C₄×D₄₃	—	4	4	no	—
485	C₄×D₄₃	—	4	4	no	—
486	C₄×D₄₃	—	8	2	no	—
487	C₄×D₄₃	—	8	2	no	—
488	C₄×D₄₃	#135	1	4	yes	complemented
489	Dic₈₆	—	2	2	no	—
490	Dic₈₆	—	2	2	no	—
491	Dic₈₆	—	2	2	no	—
492	Dic₈₆	—	8	2	no	—
493	C₈×C₄₃	—	2	1	no	—
494	C₈×C₄₃	—	2	1	no	—
495	C₈×C₄₃	—	2	1	no	—
496	C₈×C₄₃	C₂×#41	1	2	yes	—
497	C₄₃⋊C₈	—	2	1	no	—
498	C₄₃⋊C₈	—	2	1	no	—
499	C₄₃⋊C₈	—	2	1	no	—
500	C₄₃⋊C₈	—	2	1	no	—
501	#61427	—	43	1	no	maximal, Sylow
502	C₂²×C₄₃	—	2	1	no	—
503	C₂²×C₄₃	—	2	1	no	—
504	C₂²×C₄₃	—	2	1	no	—
505	C₂²×C₄₃	—	4	2	no	—
506	C₂²×C₄₃	—	4	2	no	—
507	C₂²×C₄₃	—	4	2	no	—
508	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
509	C₂×D₄₃	—	2	1	no	—
510	C₂×D₄₃	—	2	1	no	—
511	C₂×D₄₃	—	2	1	no	—
512	C₂×D₄₃	—	2	4	no	—
513	C₂×D₄₃	—	2	1	no	—
514	C₂×D₄₃	—	2	1	no	—
515	C₂×D₄₃	—	4	2	no	—
516	C₂×D₄₃	—	4	2	no	—
517	C₂×D₄₃	—	8	8	no	—
518	C₂×D₄₃	C₂×#135	1	2	yes	—
519	C₄×C₄₃	—	2	1	no	—
520	C₄×C₄₃	—	2	1	no	—
521	C₄×C₄₃	—	2	1	no	—
522	C₄×C₄₃	—	2	1	no	—
523	C₄×C₄₃	—	4	2	no	—
524	C₄×C₄₃	—	4	2	no	—
525	C₄×C₄₃	—	4	2	no	—
526	C₄×C₄₃	C₂×#135	1	2	yes	—
527	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
528	C₄×C₄₃	#585	1	1	yes	characteristic
529	Dic₄₃	—	2	1	no	—
530	Dic₄₃	—	2	1	no	—
531	Dic₄₃	—	2	1	no	—
532	Dic₄₃	—	2	1	no	—
533	Dic₄₃	—	2	1	no	—
534	Dic₄₃	—	4	2	no	—
535	Dic₄₃	—	4	2	no	—
536	Dic₄₃	—	4	2	no	—
537	Dic₄₃	C₂×#135	1	2	yes	—
538	#3475	—	43	2	no	—
539	#3393	—	43	1	no	—
540	#3380	—	43	1	no	—
541	#3360	—	43	2	no	—
542	#3341	—	43	1	no	—
543	#3336	—	43	1	no	—
544	#3336	—	43	1	no	—
545	#3303	—	43	2	no	—
546	#3296	—	43	2	no	—
547	#3296	—	43	2	no	—
548	#3283	—	43	1	no	—
549	#3280	—	43	1	no	—
550	#3280	—	43	1	no	—
551	#3170	—	43	1	no	—
552	#3168	—	43	1	no	—
553	#3168	D₄₃	1	1	yes	characteristic, complemented
554	#3102	—	43	2	no	—
555	#3102	—	43	2	no	—
556	#3101	—	43	2	no	—
557	C₈×#41	—	43	1	no	—
558	C₄×#135	—	43	1	no	—
559	C₄×#135	—	43	1	no	—
560	C₂×C₄×D₈	—	43	1	no	—
561	C₂×C₄₃	—	4	1	no	—
562	C₂×C₄₃	—	8	2	no	—
563	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
564	C₂×C₄₃	C₂²×#135	1	1	yes	characteristic
565	C₂×C₄₃	#3584	1	1	yes	characteristic
566	D₄₃	—	2	2	no	—
567	D₄₃	—	4	1	no	—
568	D₄₃	—	4	4	no	—
569	C₂×#135	—	43	1	no	—
570	C₂×#135	—	43	1	no	—
571	C₂²×D₈	—	43	1	no	—
572	#556	—	43	2	no	—
573	#555	—	43	2	no	—
574	#554	—	43	2	no	—
575	#553	—	86	2	no	—
576	#552	—	43	2	no	—
577	#552	—	43	2	no	—
578	#552	—	86	2	no	—
579	#551	—	86	2	no	—
580	#551	—	86	2	no	—
581	#547	—	43	2	no	—
582	#546	—	43	2	no	—
583	#546	—	43	2	no	—
584	#533	—	43	2	no	—
585	#529	—	43	2	no	—
586	#529	—	86	2	no	—
587	#529	—	86	2	no	—
588	#529	C₂×D₄₃	1	2	yes	complemented
589	#525	—	86	2	no	—
590	C₄×#41	—	43	1	no	—
591	C₄×#41	—	43	2	no	—
592	C₄×#41	—	43	2	no	—
593	C₂×C₄×D₄	—	43	2	no	—
594	C₂×#117	—	86	2	no	—
595	#500	—	43	1	no	—
596	#499	—	43	1	no	—
597	#499	C₂×D₄₃	1	1	yes	characteristic, complemented
598	#495	—	43	1	no	—
599	#495	C₂×D₄₃	1	1	yes	characteristic
600	#494	—	43	1	no	—
601	#488	—	43	2	no	—
602	#488	C₂×D₄₃	1	2	yes	complemented
603	#487	—	43	2	no	—
604	#485	—	43	2	no	—
605	#485	—	43	2	no	—
606	#483	—	43	2	no	—
607	#483	—	43	2	no	—
608	#482	—	43	2	no	—
609	#482	—	43	2	no	—
610	#479	—	43	2	no	—
611	#479	—	43	2	no	—
612	#478	—	43	2	no	—
613	#478	—	43	2	no	—
614	#476	—	43	2	no	—
615	#476	—	43	2	no	—
616	#467	—	43	1	no	—
617	#467	—	43	1	no	—
618	#467	—	43	1	no	—
619	#467	—	43	2	no	—
620	#467	C₂×D₄₃	1	1	yes	characteristic, complemented
621	#466	—	43	1	no	—
622	#466	C₂×D₄₃	1	1	yes	characteristic
623	#465	—	43	2	no	—
624	#465	C₂×D₄₃	1	2	yes	complemented
625	#464	—	43	2	no	—
626	#464	—	43	2	no	—
627	#463	—	43	2	no	—
628	#463	—	43	2	no	—
629	#461	—	43	2	no	—
630	#461	—	43	2	no	—
631	#452	—	43	2	no	—
632	#452	—	43	2	no	—
633	#450	—	43	2	no	—
634	#450	—	43	2	no	—
635	#449	—	43	2	no	—
636	#449	—	43	2	no	—
637	C₈×Q₈	—	43	1	no	—
638	C₈×Q₈	—	43	1	no	—
639	C₄×Q₁₆	—	43	1	no	—
640	C₄×Q₁₆	—	43	2	no	—
641	C₄×Q₁₆	—	43	1	no	—
642	C₄×Q₁₆	—	43	1	no	—
643	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
644	C₄×SD₁₆	—	43	2	no	—
645	C₄×SD₁₆	—	43	2	no	—
646	C₄×SD₁₆	—	43	2	no	—
647	C₄×SD₁₆	—	43	2	no	—
648	C₄×SD₁₆	—	43	2	no	—
649	C₄×SD₁₆	C₂×D₄₃	1	2	yes	complemented
650	C₄×D₈	—	43	1	no	—
651	C₄×D₈	—	43	2	no	—
652	C₄×D₈	—	43	1	no	—
653	C₄×D₈	—	43	1	no	—
654	C₄×D₈	—	43	2	no	—
655	C₄×D₈	—	43	1	no	—
656	C₄×D₈	—	43	1	no	—
657	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
658	C₈×D₄	—	43	1	no	—
659	C₈×D₄	—	43	1	no	—
660	C₈×D₄	—	43	1	no	—
661	C₈×D₄	—	43	1	no	—
662	C₈×D₄	—	43	1	no	—
663	C₈×D₄	—	43	1	no	—
664	#431	—	43	1	no	—
665	#431	—	43	1	no	—
666	#431	—	43	1	no	—
667	#427	—	43	1	no	—
668	#427	—	43	1	no	—
669	C₂×#107	—	43	1	no	—
670	#416	—	43	2	no	—
671	#416	—	43	2	no	—
672	C₂×#102	—	43	2	no	—
673	C₂×C₄×C₈	—	43	1	no	—
674	C₂×C₄×C₈	—	43	1	no	—
675	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
676	C₄₃	#61427	1	1	yes	characteristic, complemented, Sylow
677	C₂×#41	—	43	1	no	—
678	C₂×#41	—	43	2	no	—
679	C₂×#41	—	43	2	no	—
680	C₂²×D₄	—	43	2	no	—
681	C₂³×C₄	—	86	2	no	—
682	#135	—	86	4	no	—
683	#135	—	86	4	no	—
684	C₂×Q₁₆	—	43	2	no	—
685	C₂×Q₁₆	—	43	1	no	—
686	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
687	C₂×SD₁₆	—	43	2	no	—
688	C₂×SD₁₆	—	43	2	no	—
689	C₂×SD₁₆	—	43	2	no	—
690	C₂×SD₁₆	C₂²×D₄₃	1	2	yes	—
691	C₂×D₈	—	43	2	no	—
692	C₂×D₈	—	43	1	no	—
693	C₂×D₈	—	86	4	no	—
694	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
695	C₂²×C₈	—	43	1	no	—
696	C₂²×C₈	—	43	1	no	—
697	C₂²×C₈	—	43	1	no	—
698	C₂²×C₈	—	43	1	no	—
699	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
700	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
701	C₄⋊Q₈	—	43	2	no	—
702	C₄⋊Q₈	—	43	2	no	—
703	#126	—	2	2	no	—
704	#126	—	86	2	no	—
705	#126	—	86	2	no	—
706	#126	—	86	2	no	—
707	#126	—	86	2	no	—
708	#126	—	86	2	no	—
709	#125	—	43	2	no	—
710	#125	—	86	2	no	—
711	#125	—	86	2	no	—
712	#125	—	86	2	no	—
713	#125	C₂²×D₄₃	1	2	yes	—
714	#124	—	43	2	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	—	86	2	no	—
720	#123	—	86	2	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	C₂²⋊Q₈	—	43	2	no	—
727	C₂²⋊Q₈	—	43	2	no	—
728	C₂²⋊Q₈	—	43	2	no	—
729	C₂²⋊Q₈	—	86	2	no	—
730	C₂²⋊Q₈	—	86	2	no	—
731	C₂²⋊Q₈	—	86	2	no	—
732	C₂²⋊Q₈	—	86	2	no	—
733	C₂²⋊Q₈	—	86	2	no	—
734	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
735	#121	—	43	2	no	—
736	#121	—	86	2	no	—
737	#121	—	86	2	no	—
738	#121	—	86	2	no	—
739	#121	—	86	2	no	—
740	#121	C₂²×D₄₃	1	2	yes	—
741	#120	—	86	2	no	—
742	#120	—	86	2	no	—
743	C₄×Q₈	—	43	1	no	—
744	C₄×Q₈	—	43	1	no	—
745	C₄×Q₈	—	43	2	no	—
746	C₄×Q₈	—	43	2	no	—
747	C₄×Q₈	—	43	2	no	—
748	C₄×Q₈	—	86	2	no	—
749	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
750	C₄×D₄	—	2	2	no	—
751	C₄×D₄	—	43	1	no	—
752	C₄×D₄	—	43	1	no	—
753	C₄×D₄	—	43	1	no	—
754	C₄×D₄	—	43	1	no	—
755	C₄×D₄	—	43	2	no	—
756	C₄×D₄	—	43	2	no	—
757	C₄×D₄	—	43	2	no	—
758	C₄×D₄	—	43	1	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	1	no	—
774	#117	—	43	2	no	—
775	#117	—	43	2	no	—
776	#117	—	86	2	no	—
777	#117	—	86	2	no	—
778	#117	—	86	2	no	—
779	#117	—	86	2	no	—
780	#117	—	86	2	no	—
781	#117	—	86	2	no	—
782	#117	—	86	2	no	—
783	#117	—	86	2	no	—
784	C₂×C₄⋊C₄	—	43	2	no	—
785	C₂×C₄⋊C₄	—	86	2	no	—
786	C₂×C₄⋊C₄	—	86	2	no	—
787	C₂×C₂²⋊C₄	—	86	2	no	—
788	C₂×C₂²⋊C₄	—	86	2	no	—
789	C₂×C₂²⋊C₄	—	86	2	no	—
790	C₂×C₄²	—	43	1	no	—
791	C₂×C₄²	—	43	1	no	—
792	C₂×C₄²	—	86	2	no	—
793	C₂×C₄²	—	86	2	no	—
794	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
795	#107	—	43	1	no	—
796	#107	—	43	1	no	—
797	#107	—	43	2	no	—
798	#107	—	43	2	no	—
799	#107	C₂²×D₄₃	1	1	yes	characteristic
800	#107	C₂²×D₄₃	1	1	yes	characteristic
801	#106	—	43	2	no	—
802	#106	—	43	2	no	—
803	#106	—	43	2	no	—
804	#106	C₂²×D₄₃	1	2	yes	—
805	C₄⋊C₈	—	43	1	no	—
806	C₄⋊C₈	—	43	1	no	—
807	C₄⋊C₈	—	43	1	no	—
808	C₄⋊C₈	—	43	1	no	—
809	C₄⋊C₈	—	43	1	no	—
810	C₄⋊C₈	—	43	1	no	—
811	#103	—	43	2	no	—
812	#103	—	43	2	no	—
813	#103	—	43	2	no	—
814	#103	—	43	2	no	—
815	#103	—	43	2	no	—
816	#103	—	43	2	no	—
817	#103	C₂²×D₄₃	1	2	yes	—
818	#103	C₂²×D₄₃	1	2	yes	—
819	#102	—	43	2	no	—
820	#102	—	43	2	no	—
821	#102	—	43	2	no	—
822	#102	—	43	2	no	—
823	#102	—	43	2	no	—
824	#102	—	43	2	no	—
825	#102	C₂²×D₄₃	1	2	yes	—
826	#102	C₂²×D₄₃	1	2	yes	—
827	C₂²⋊C₈	—	43	1	no	—
828	C₂²⋊C₈	—	43	1	no	—
829	C₂²⋊C₈	—	43	1	no	—
830	C₂²⋊C₈	—	43	1	no	—
831	C₂²⋊C₈	—	43	1	no	—
832	C₂²⋊C₈	—	43	1	no	—
833	C₄×C₈	—	43	1	no	—
834	C₄×C₈	—	43	1	no	—
835	C₄×C₈	—	43	1	no	—
836	C₄×C₈	—	43	1	no	—
837	C₄×C₈	—	43	1	no	—
838	C₄×C₈	—	43	1	no	—
839	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
840	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
841	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
842	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
843	C₂⁴	—	86	2	no	—
844	#41	—	86	4	no	—
845	#41	—	86	4	no	—
846	#41	—	86	4	no	—
847	#41	—	172	2	no	—
848	#41	—	172	2	no	—
849	C₂×Q₈	—	43	1	no	—
850	C₂×Q₈	—	43	2	no	—
851	C₂×Q₈	—	86	2	no	—
852	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
853	C₂×D₄	—	2	2	no	—
854	C₂×D₄	—	43	1	no	—
855	C₂×D₄	—	43	1	no	—
856	C₂×D₄	—	43	1	no	—
857	C₂×D₄	—	43	2	no	—
858	C₂×D₄	—	86	2	no	—
859	C₂×D₄	—	86	2	no	—
860	C₂×D₄	—	86	4	no	—
861	C₂×D₄	—	86	2	no	—
862	C₂×D₄	—	86	2	no	—
863	C₂×D₄	—	172	2	no	—
864	C₂×D₄	C₂³×D₄₃	1	2	yes	—
865	C₂²×C₄	—	2	2	no	—
866	C₂²×C₄	—	43	1	no	—
867	C₂²×C₄	—	43	1	no	—
868	C₂²×C₄	—	43	1	no	—
869	C₂²×C₄	—	43	1	no	—
870	C₂²×C₄	—	43	1	no	—
871	C₂²×C₄	—	43	1	no	—
872	C₂²×C₄	—	86	2	no	—
873	C₂²×C₄	—	86	2	no	—
874	C₂²×C₄	—	86	2	no	—
875	C₂²×C₄	—	86	2	no	—
876	C₂²×C₄	—	86	2	no	—
877	C₂²×C₄	—	86	2	no	—
878	C₂²×C₄	—	86	2	no	—
879	C₂²×C₄	—	86	2	no	—
880	C₂²×C₄	—	172	8	no	—
881	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
882	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
883	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
884	Q₁₆	—	2	2	no	—
885	Q₁₆	—	86	2	no	—
886	Q₁₆	—	172	2	no	—
887	SD₁₆	—	4	2	no	—
888	SD₁₆	—	86	4	no	—
889	SD₁₆	—	86	4	no	—
890	SD₁₆	—	172	2	no	—
891	D₈	—	2	2	no	—
892	D₈	—	43	4	no	—
893	D₈	—	86	4	no	—
894	C₂×C₈	—	2	2	no	—
895	C₂×C₈	—	4	1	no	—
896	C₂×C₈	—	43	1	no	—
897	C₂×C₈	—	43	1	no	—
898	C₂×C₈	—	43	1	no	—
899	C₂×C₈	—	43	1	no	—
900	C₂×C₈	—	86	2	no	—
901	C₂×C₈	—	86	2	no	—
902	C₂×C₈	—	172	1	no	—
903	C₂×C₈	—	172	1	no	—
904	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
905	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
906	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
907	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
908	C₄⋊C₄	—	2	2	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	2	no	—
911	C₄⋊C₄	—	2	2	no	—
912	C₄⋊C₄	—	43	1	no	—
913	C₄⋊C₄	—	43	1	no	—
914	C₄⋊C₄	—	43	1	no	—
915	C₄⋊C₄	—	43	1	no	—
916	C₄⋊C₄	—	43	1	no	—
917	C₄⋊C₄	—	43	1	no	—
918	C₄⋊C₄	—	43	2	no	—
919	C₄⋊C₄	—	43	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	—	86	2	no	—
925	C₄⋊C₄	—	86	2	no	—
926	C₄⋊C₄	—	86	2	no	—
927	C₄⋊C₄	—	86	2	no	—
928	C₄⋊C₄	—	86	2	no	—
929	C₄⋊C₄	—	86	2	no	—
930	C₄⋊C₄	—	86	2	no	—
931	C₄⋊C₄	—	86	2	no	—
932	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
933	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
934	C₂²⋊C₄	—	2	2	no	—
935	C₂²⋊C₄	—	2	2	no	—
936	C₂²⋊C₄	—	2	2	no	—
937	C₂²⋊C₄	—	2	2	no	—
938	C₂²⋊C₄	—	2	2	no	—
939	C₂²⋊C₄	—	43	1	no	—
940	C₂²⋊C₄	—	43	1	no	—
941	C₂²⋊C₄	—	43	1	no	—
942	C₂²⋊C₄	—	43	1	no	—
943	C₂²⋊C₄	—	43	1	no	—
944	C₂²⋊C₄	—	43	1	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	C₂²⋊C₄	—	86	2	no	—
955	C₂²⋊C₄	—	86	2	no	—
956	C₂²⋊C₄	—	86	2	no	—
957	C₂²⋊C₄	—	86	2	no	—
958	C₄²	—	2	2	no	—
959	C₄²	—	43	1	no	—
960	C₄²	—	43	1	no	—
961	C₄²	—	43	1	no	—
962	C₄²	—	43	1	no	—
963	C₄²	—	43	1	no	—
964	C₄²	—	43	1	no	—
965	C₄²	—	86	2	no	—
966	C₄²	—	86	2	no	—
967	C₄²	—	86	2	no	—
968	C₄²	—	86	2	no	—
969	C₄²	—	86	2	no	—
970	C₄²	D₄×D₄₃	1	1	yes	characteristic
971	C₄²	D₄×D₄₃	1	1	yes	characteristic
972	C₄²	C₂³×D₄₃	1	1	yes	characteristic
973	C₄²	C₂³×D₄₃	1	1	yes	characteristic
974	C₂³	—	2	2	no	—
975	C₂³	—	43	1	no	—
976	C₂³	—	43	1	no	—
977	C₂³	—	86	2	no	—
978	C₂³	—	344	2	no	—
979	C₂³	—	172	4	no	—
980	C₂³	—	172	4	no	—
981	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
982	Q₈	—	2	2	no	—
983	Q₈	—	2	2	no	—
984	Q₈	—	86	2	no	—
985	Q₈	—	86	2	no	—
986	Q₈	—	86	2	no	—
987	Q₈	—	344	2	no	—
988	D₄	—	2	2	no	—
989	D₄	—	2	2	no	—
990	D₄	—	8	2	no	—
991	D₄	—	43	4	no	—
992	D₄	—	86	2	no	—
993	D₄	—	86	2	no	—
994	D₄	—	86	2	no	—
995	D₄	—	86	2	no	—
996	D₄	—	344	2	no	—
997	D₄	—	172	4	no	—
998	D₄	—	172	4	no	—
999	D₄	—	172	4	no	—
1000	C₂×C₄	—	2	2	no	—
1001	C₂×C₄	—	2	1	no	—
1002	C₂×C₄	—	2	1	no	—
1003	C₂×C₄	—	2	2	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	2	no	—
1006	C₂×C₄	—	4	1	no	—
1007	C₂×C₄	—	4	4	no	—
1008	C₂×C₄	—	43	1	no	—
1009	C₂×C₄	—	43	4	no	—
1010	C₂×C₄	—	43	1	no	—
1011	C₂×C₄	—	43	1	no	—
1012	C₂×C₄	—	43	1	no	—
1013	C₂×C₄	—	43	1	no	—
1014	C₂×C₄	—	43	1	no	—
1015	C₂×C₄	—	86	2	no	—
1016	C₂×C₄	—	86	1	no	—
1017	C₂×C₄	—	86	1	no	—
1018	C₂×C₄	—	86	1	no	—
1019	C₂×C₄	—	86	1	no	—
1020	C₂×C₄	—	86	2	no	—
1021	C₂×C₄	—	86	2	no	—
1022	C₂×C₄	—	86	2	no	—
1023	C₂×C₄	—	344	2	no	—
1024	C₂×C₄	—	344	2	no	—
1025	C₂×C₄	—	172	1	no	—
1026	C₂×C₄	—	172	1	no	—
1027	C₂×C₄	—	172	4	no	—
1028	C₂×C₄	—	172	4	no	—
1029	C₂×C₄	—	172	4	no	—
1030	C₂×C₄	—	172	4	no	—
1031	C₂×C₄	—	172	4	no	—
1032	C₂×C₄	—	172	4	no	—
1033	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1034	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1035	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1036	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1037	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1038	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1039	C₈	—	2	1	no	—
1040	C₈	—	2	1	no	—
1041	C₈	—	2	1	no	—
1042	C₈	—	86	1	no	—
1043	C₈	—	86	1	no	—
1044	C₈	—	86	1	no	—
1045	C₈	—	86	1	no	—
1046	C₈	#41×D₄₃	1	2	yes	—
1047	C₂²	—	2	1	no	—
1048	C₂²	—	2	1	no	—
1049	C₂²	—	2	1	no	—
1050	C₂²	—	4	2	no	—
1051	C₂²	—	4	2	no	—
1052	C₂²	—	4	2	no	—
1053	C₂²	—	43	2	no	—
1054	C₂²	—	86	1	no	—
1055	C₂²	—	86	1	no	—
1056	C₂²	—	86	1	no	—
1057	C₂²	—	86	1	no	—
1058	C₂²	—	86	4	no	—
1059	C₂²	—	86	1	no	—
1060	C₂²	—	344	8	no	—
1061	C₂²	—	172	2	no	—
1062	C₂²	—	172	2	no	—
1063	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1064	C₄	—	2	1	no	—
1065	C₄	—	2	1	no	—
1066	C₄	—	2	1	no	—
1067	C₄	—	2	1	no	—
1068	C₄	—	4	2	no	—
1069	C₄	—	4	2	no	—
1070	C₄	—	4	2	no	—
1071	C₄	—	43	2	no	—
1072	C₄	—	86	1	no	—
1073	C₄	—	86	1	no	—
1074	C₄	—	86	1	no	—
1075	C₄	—	86	1	no	—
1076	C₄	—	86	1	no	—
1077	C₄	—	172	2	no	—
1078	C₄	—	172	2	no	—
1079	C₄	—	172	2	no	—
1080	C₄	#135×D₄₃	1	2	yes	—
1081	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1082	C₄	#14583735	1	1	yes	characteristic
1083	C₂	—	4	1	no	—
1084	C₂	—	8	2	no	—
1085	C₂	—	86	2	no	—
1086	C₂	—	172	1	no	—
1087	C₂	—	172	4	no	—
1088	C₂	#19148081	1	1	yes	characteristic
1089	C₂	C₂×#135×D₄₃	1	1	yes	characteristic
1090	C₂	#19149364	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×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	#61427
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3168

Complements

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

N	H ≅ G/N	type
1. #19148151	C₂	semidirect
2. #19147580	C₂	semidirect
3. #19147459	C₂	semidirect
4. #19147241	C₂	semidirect
5. #19147014	C₂	semidirect
6. #19146962	C₂	semidirect
7. #19146958	C₂	semidirect
8. #19146518	C₂	semidirect
9. #19146429	C₂	semidirect
10. #19146425	C₂	semidirect
11. #19146314	C₂	semidirect
12. #19146283	C₂	semidirect
13. #19146279	C₂	semidirect
14. #19145178	C₂	semidirect
15. #19145163	C₂	semidirect
16. #19144611	C₂	semidirect
17. #19144607	C₂	semidirect
18. #19144601	C₂	semidirect
19. C₈×#10621898	C₂	semidirect
20. C₄×#13063347	C₂	semidirect
21. C₄×#13063348	C₂	semidirect
22. C₄×D₈×D₄₃	C₂	semidirect
23. C₄₃×#3168	C₂	semidirect
27. #14583618	C₂²	semidirect
28. #14583613	C₂²	semidirect
29. #14583605	C₂²	semidirect
36. #14583551	C₂²	semidirect
41. #14583431	C₂²	semidirect
44. C₄×#10621902	C₂²	semidirect
46. C₄×#10621898	C₂²	semidirect
49. #14583303	C₂²	semidirect
50. #14583300	C₂²	semidirect
52. #14583277	C₂²	semidirect
53. #14583252	C₂²	semidirect
54. #14583248	C₂²	semidirect
55. #14583243	C₂²	semidirect
56. #14583237	C₂²	semidirect
59. #14583222	C₂²	semidirect
60. #14583220	C₂²	semidirect
61. #14583204	C₂²	semidirect
62. #14583203	C₂²	semidirect
63. #14583198	C₂²	semidirect
64. #14583196	C₂²	semidirect
65. #14583188	C₂²	semidirect
66. #14583187	C₂²	semidirect
68. #14583141	C₂²	semidirect
72. #14583127	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. C₈×Dic₈₆	C₂²	semidirect
86. C₈×Dic₈₆	C₂²	semidirect
87. C₄×Dic₁₇₂	C₂²	semidirect
88. C₄×Dic₁₇₂	C₂²	semidirect
89. Q₁₆×Dic₄₃	C₂²	semidirect
90. C₄×#10621885	C₂²	semidirect
91. C₄×#10621873	C₂²	semidirect
92. C₄×#10621873	C₂²	semidirect
93. C₄×#10621884	C₂²	semidirect
94. C₄×#10621883	C₂²	semidirect
95. #14582984	C₂²	semidirect
107. C₈×C₂²⋊D₄₃	C₂²	semidirect
108. C₈×C₂²⋊D₄₃	C₂²	semidirect
109. #14582952	C₂²	semidirect
111. #14582950	C₂²	semidirect
112. #14582937	C₂²	semidirect
113. #14582936	C₂²	semidirect
115. #14582896	C₂²	semidirect
116. #14582894	C₂²	semidirect
119. C₄×C₈×D₄₃	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
422. D₃₄₄	#41	semidirect
488. C₄×D₄₃	#135	semidirect
553. #3168	D₄₃	semidirect
588. #529	C₂×D₄₃	semidirect
597. #499	C₂×D₄₃	semidirect
602. #488	C₂×D₄₃	semidirect
620. #467	C₂×D₄₃	semidirect
624. #465	C₂×D₄₃	semidirect
643. C₄×Q₁₆	C₂×D₄₃	semidirect
649. C₄×SD₁₆	C₂×D₄₃	semidirect
675. C₂×C₄×C₈	C₂×D₄₃	semidirect
676. C₄₃	#61427	semidirect

Maximal subgroups

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

subgroup	index
#19148151	2
#19147580	2
#19147459	2
#19147241	2
#19147014	2
#19146962	2
#19146958	2
#19146518	2
#19146429	2
#19146425	2
#19146314	2
#19146283	2
#19146279	2
#19145178	2
#19145163	2
#19144611	2
#19144607	2
#19144601	2
C₈×#10621898	2
C₄×#13063347	2
C₄×#13063348	2
C₄×D₈×D₄₃	2
C₄₃×#3168	2
#61427	43