Subgroups — #25992264

Order 11008.

1804 conjugacy classes of subgroups.

The subgroup lattice has 1126 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148575	C₂	1	1	yes	maximal, characteristic, complemented
2	#19148205	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147468	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147460	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	#19146990	C₂	1	2	yes	maximal, complemented
8	#19146989	C₂	1	1	yes	maximal, characteristic, complemented
9	#19146977	C₂	1	2	yes	maximal, complemented
10	#19146954	C₂	1	1	yes	maximal, characteristic, complemented
11	#19146438	C₂	1	2	yes	maximal, complemented
12	#19146423	C₂	1	2	yes	maximal, complemented
13	#19146421	C₂	1	1	yes	maximal, characteristic, complemented
14	#19146410	C₂	1	1	yes	maximal, characteristic, complemented
15	#19145945	C₂	1	2	yes	maximal, complemented
16	#19145921	C₂	1	1	yes	maximal, characteristic, complemented
17	#19145767	C₂	1	2	yes	maximal, complemented
18	#19145733	C₂	1	1	yes	maximal, characteristic, complemented
19	#19144641	C₂	1	2	yes	maximal, complemented
20	#19144383	C₂	1	1	yes	maximal, characteristic, complemented
21	#478×D₄₃	C₂	1	2	yes	maximal, complemented
22	#19143703	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3102	C₂	1	1	yes	maximal, characteristic, complemented
24	#14583634	C₂²	1	1	yes	characteristic
25	#14583628	C₂²	1	1	yes	characteristic, complemented
26	#14583609	C₂²	1	1	yes	characteristic
27	#14583609	C₂²	1	1	yes	characteristic
28	#14583606	C₂²	1	1	yes	characteristic
29	#14583606	C₂²	1	1	yes	characteristic, complemented
30	#14583596	C₂²	1	2	yes	complemented
31	#14583595	—	2	1	no	—
32	#14583593	C₂²	1	2	yes	—
33	#14583589	—	2	1	no	—
34	#14583585	—	2	2	no	—
35	#14583583	C₂²	1	2	yes	complemented
36	#14583573	—	2	2	no	—
37	#14583554	—	2	1	no	—
38	#14583554	C₂²	1	1	yes	characteristic
39	#14583545	—	2	1	no	—
40	#14583537	C₂²	1	2	yes	—
41	D₄×D₁₇₂	C₂²	1	1	yes	characteristic
42	#14583511	—	2	1	no	—
43	#14583492	—	2	2	no	—
44	#14583456	C₂²	1	1	yes	characteristic, complemented
45	#14583449	C₂²	1	1	yes	characteristic
46	#14583436	C₂²	1	2	yes	—
47	#14583433	—	2	1	no	—
48	#14583428	C₂²	1	2	yes	complemented
49	#125×D₄₃	C₂²	1	2	yes	complemented
50	#14583408	—	2	2	no	—
51	#14583379	—	2	1	no	—
52	C₄×#10621898	C₂²	1	1	yes	characteristic
53	C₂×C₄×D₁₇₂	—	2	1	no	—
54	C₄×D₄×D₄₃	C₂²	1	2	yes	—
55	#14583304	C₂²	1	1	yes	characteristic, complemented
56	#14583300	C₂²	1	2	yes	complemented
57	#14583299	C₂²	1	2	yes	complemented
58	#14583297	C₂²	1	1	yes	characteristic, complemented
59	#14583255	C₂²	1	2	yes	complemented
60	#14583255	C₂²	1	2	yes	complemented
61	#14583246	C₂²	1	1	yes	characteristic
62	#14583246	C₂²	1	1	yes	characteristic
63	#14583233	C₂²	1	2	yes	complemented
64	#14583233	C₂²	1	2	yes	complemented
65	#14583228	C₂²	1	2	yes	complemented
66	#14583224	C₂²	1	2	yes	complemented
67	#14583224	C₂²	1	2	yes	complemented
68	#14583219	C₂²	1	2	yes	—
69	#14583216	C₂²	1	2	yes	complemented
70	#14583214	C₂²	1	2	yes	—
71	#14583206	C₂²	1	2	yes	complemented
72	#14583204	C₂²	1	2	yes	complemented
73	#14583202	C₂²	1	2	yes	complemented
74	#14583201	C₂²	1	2	yes	—
75	#14583200	C₂²	1	2	yes	complemented
76	#14583200	C₂²	1	2	yes	complemented
77	#14583199	C₂²	1	2	yes	—
78	#14583198	C₂²	1	2	yes	complemented
79	#14583197	C₂²	1	2	yes	—
80	#14583197	C₂²	1	2	yes	complemented
81	#14583196	C₂²	1	2	yes	complemented
82	#14583194	C₂²	1	1	yes	characteristic, complemented
83	#14583194	C₂²	1	1	yes	characteristic, complemented
84	#14583189	C₂²	1	1	yes	characteristic
85	#14583189	C₂²	1	1	yes	characteristic, complemented
86	#14583184	C₂²	1	1	yes	characteristic, complemented
87	#14583179	C₂²	1	1	yes	characteristic
88	#14583137	C₂²	1	2	yes	complemented
89	#14583134	C₂²	1	2	yes	—
90	#14583133	C₂²	1	2	yes	complemented
91	#14583131	C₂²	1	2	yes	—
92	#14583130	C₂²	1	2	yes	complemented
93	#14583125	C₂²	1	2	yes	complemented
94	#14583123	C₂²	1	2	yes	complemented
95	#14583116	C₂²	1	2	yes	complemented
96	#14583111	C₂²	1	2	yes	complemented
97	#14583099	C₂²	1	1	yes	characteristic
98	#14583094	C₂²	1	1	yes	characteristic
99	#14583048	C₂²	1	2	yes	—
100	#14583031	C₂²	1	2	yes	—
101	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
102	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
103	SD₁₆×Dic₄₃	C₂²	1	2	yes	—
104	#14582984	C₂²	1	2	yes	complemented
105	D₈×Dic₄₃	C₂²	1	2	yes	—
106	#14582979	C₂²	1	2	yes	complemented
107	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
108	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
109	(C₂²⋊D₄₃)⋊C₈	C₂²	1	2	yes	complemented
110	(C₂²⋊D₄₃)⋊C₈	C₂²	1	2	yes	complemented
111	#14582951	C₂²	1	2	yes	complemented
112	#14582935	C₂²	1	2	yes	complemented
113	#107×D₄₃	C₂²	1	2	yes	complemented
114	#106×D₄₃	C₂²	1	2	yes	complemented
115	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
116	C₄⋊C₈×D₄₃	C₂²	1	2	yes	complemented
117	#14582895	C₂²	1	2	yes	—
118	#102×D₄₃	C₂²	1	2	yes	—
119	#102×D₄₃	C₂²	1	2	yes	—
120	C₄₃×#529	C₂²	1	1	yes	characteristic, complemented
121	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
122	C₄₃×#485	C₂²	1	1	yes	characteristic, complemented
123	C₄₃×#482	C₂²	1	1	yes	characteristic, complemented
124	C₄₃×#479	C₂²	1	1	yes	characteristic, complemented
125	C₄₃×#478	C₂²	1	1	yes	characteristic
126	C₄₃×#464	C₂²	1	1	yes	characteristic, complemented
127	C₄₃×#463	C₂²	1	1	yes	characteristic
128	C₄₃×#452	C₂²	1	1	yes	characteristic
129	C₄₃×#449	C₂²	1	1	yes	characteristic
130	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
131	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
132	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
133	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
134	C₄₃×#431	C₂²	1	1	yes	characteristic, complemented
135	C₂×#10621898	—	2	1	no	—
136	C₂×#10621898	—	2	1	no	—
137	C₂×#10621898	D₄	1	1	yes	characteristic
138	C₂²×D₁₇₂	—	2	1	no	—
139	C₂×D₄×D₄₃	C₂³	1	2	yes	—
140	C₂²×C₄×D₄₃	—	2	2	no	—
141	C₂×#10621884	C₂³	1	2	yes	—
142	C₂×#10621882	C₂³	1	2	yes	—
143	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
144	C₂×C₈×D₄₃	C₂³	1	2	yes	—
145	C₂×C₈×D₄₃	C₂³	1	2	yes	—
146	#13063325	—	2	1	no	—
147	#13063325	C₂³	1	1	yes	characteristic
148	#13063325	C₂³	1	1	yes	characteristic
149	#13063325	C₂³	1	1	yes	characteristic
150	#13063322	C₂³	1	1	yes	characteristic
151	#13063320	—	2	2	no	—
152	#13063319	—	2	2	no	—
153	#13063318	—	2	2	no	—
154	#13063318	—	2	2	no	—
155	#13063318	—	2	2	no	—
156	#13063317	—	2	1	no	—
157	#13063317	—	2	1	no	—
158	#13063317	C₂³	1	2	yes	—
159	#13063316	—	2	2	no	—
160	#13063316	C₂³	1	2	yes	—
161	#13063316	C₂³	1	2	yes	—
162	#13063316	C₂³	1	2	yes	—
163	#13063315	—	2	2	no	—
164	#13063315	—	2	2	no	—
165	#13063315	—	2	2	no	—
166	#13063314	C₂³	1	2	yes	—
167	#13063313	—	2	1	no	—
168	#13063313	—	2	1	no	—
169	#13063310	—	2	2	no	—
170	#13063310	—	2	2	no	—
171	#13063308	—	2	2	no	—
172	#13063307	—	2	2	no	—
173	#13063307	—	2	2	no	—
174	#13063307	—	2	2	no	—
175	#13063307	—	2	2	no	—
176	#13063306	—	2	2	no	—
177	#13063304	—	2	1	no	—
178	#13063304	—	2	1	no	—
179	#13063304	—	2	1	no	—
180	#13063304	—	2	1	no	—
181	#13063304	—	2	1	no	—
182	#13063303	—	2	2	no	—
183	#13063303	—	2	2	no	—
184	#13063302	—	2	2	no	—
185	#13063302	—	2	2	no	—
186	#13063301	C₂³	1	2	yes	—
187	#13063301	C₂³	1	2	yes	—
188	#13063300	C₂³	1	2	yes	—
189	#13063299	—	2	1	no	—
190	#13063299	—	2	1	no	—
191	#13063299	C₂³	1	2	yes	—
192	#13063298	—	2	2	no	—
193	#13063297	—	2	2	no	—
194	#13063296	—	2	2	no	—
195	#13063296	C₂³	1	2	yes	—
196	#13063295	—	2	2	no	—
197	#13063293	—	2	2	no	—
198	Q₈×Dic₄₃	C₂³	1	2	yes	—
199	C₄×Dic₈₆	—	2	1	no	—
200	C₄×Dic₈₆	—	2	1	no	—
201	C₄×Dic₈₆	—	2	1	no	—
202	C₄×Dic₈₆	D₄	1	1	yes	characteristic
203	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
204	C₄×D₁₇₂	—	2	1	no	—
205	C₄×D₁₇₂	—	2	1	no	—
206	C₄×D₁₇₂	—	2	2	no	—
207	C₄×D₁₇₂	—	2	1	no	—
208	C₄×D₁₇₂	—	2	2	no	—
209	C₄×D₁₇₂	—	2	1	no	—
210	C₄×D₁₇₂	D₄	1	1	yes	characteristic
211	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
212	C₄×D₁₇₂	C₂³	1	2	yes	—
213	D₄×Dic₄₃	C₂³	1	2	yes	—
214	D₄×Dic₄₃	C₂³	1	2	yes	—
215	#13063287	C₂³	1	2	yes	—
216	C₄×C₂²⋊D₄₃	—	2	2	no	—
217	C₄×C₂²⋊D₄₃	D₄	1	2	yes	—
218	C₄×C₂²⋊D₄₃	C₂³	1	2	yes	—
219	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
220	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
221	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
222	#13063284	D₄	1	1	yes	characteristic
223	#13063284	C₂³	1	2	yes	—
224	#13063283	—	2	2	no	—
225	#13063282	—	2	2	no	—
226	#13063282	D₄	1	2	yes	—
227	#13063281	—	2	2	no	—
228	C₂×C₄⋊Dic₄₃	—	2	1	no	—
229	C₂×C₄⋊Dic₄₃	—	2	1	no	—
230	C₄⋊C₄×D₄₃	—	2	2	no	—
231	C₄⋊C₄×D₄₃	—	2	2	no	—
232	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
233	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
234	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
235	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
236	C₂²⋊C₄×D₄₃	—	2	2	no	—
237	C₄²×D₄₃	C₂³	1	2	yes	—
238	#13063259	C₂³	1	2	yes	—
239	#13063259	C₂³	1	2	yes	—
240	#13063258	C₂³	1	2	yes	—
241	#13063258	C₂³	1	2	yes	—
242	#13063258	C₂³	1	2	yes	—
243	#13063257	C₂³	1	2	yes	—
244	#13063257	C₂³	1	2	yes	—
245	#13063256	C₂³	1	2	yes	—
246	#13063256	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	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
251	Dic₄₃⋊C₈	C₂³	1	2	yes	—
252	Dic₄₃⋊C₈	C₂³	1	2	yes	—
253	#13063249	C₂³	1	2	yes	—
254	#13063249	C₂³	1	2	yes	—
255	#13063249	C₂³	1	2	yes	—
256	#13063247	C₂³	1	2	yes	—
257	#13063247	C₂³	1	2	yes	—
258	#13063247	C₂³	1	2	yes	—
259	#13063247	C₂³	1	2	yes	—
260	#13063246	C₂³	1	2	yes	—
261	#13063246	C₂³	1	2	yes	—
262	#13063246	C₂³	1	2	yes	—
263	#13063245	C₂³	1	2	yes	—
264	#13063245	C₂³	1	2	yes	—
265	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
266	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
267	C₈×Dic₄₃	C₂³	1	2	yes	—
268	C₈×Dic₄₃	C₂³	1	2	yes	—
269	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
270	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
271	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
272	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
273	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
274	#126×C₄₃	—	2	1	no	—
275	#125×C₄₃	C₂³	1	1	yes	characteristic
276	#124×C₄₃	C₂³	1	1	yes	characteristic
277	#123×C₄₃	—	2	1	no	—
278	C₂²⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
279	#121×C₄₃	C₂³	1	1	yes	characteristic
280	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
281	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
282	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
283	C₄×D₄×C₄₃	—	2	1	no	—
284	C₄×D₄×C₄₃	—	2	1	no	—
285	C₄×D₄×C₄₃	—	2	1	no	—
286	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
289	#117×C₄₃	—	2	1	no	—
290	#117×C₄₃	—	2	1	no	—
291	#117×C₄₃	C₂³	1	1	yes	characteristic
292	C₂×C₄²×C₄₃	—	2	1	no	—
293	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
294	#107×C₄₃	C₂³	1	1	yes	characteristic
295	#107×C₄₃	C₂³	1	1	yes	characteristic
296	#106×C₄₃	C₂³	1	1	yes	characteristic
297	#106×C₄₃	C₂³	1	1	yes	characteristic
298	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
299	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
300	#103×C₄₃	C₂³	1	1	yes	characteristic
301	#103×C₄₃	C₂³	1	1	yes	characteristic
302	#103×C₄₃	C₂³	1	1	yes	characteristic
303	#103×C₄₃	C₂³	1	1	yes	characteristic
304	#102×C₄₃	C₂³	1	1	yes	characteristic
305	#102×C₄₃	C₂³	1	1	yes	characteristic
306	#102×C₄₃	C₂³	1	1	yes	characteristic
307	#102×C₄₃	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
312	C₂³×D₄₃	—	2	2	no	—
313	#41×C₄₃	—	2	2	no	—
314	#41×C₄₃	—	4	1	no	—
315	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
316	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
317	C₂×D₄×C₄₃	—	2	1	no	—
318	C₂×D₄×C₄₃	—	2	1	no	—
319	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
320	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₄₃	—	2	1	no	—
322	C₂²×C₄×C₄₃	—	2	1	no	—
323	C₂²×C₄×C₄₃	—	2	1	no	—
324	C₂²×C₄×C₄₃	—	2	1	no	—
325	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
327	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
328	C₂×C₂²⋊D₄₃	—	2	2	no	—
329	C₂×C₂²⋊D₄₃	—	2	2	no	—
330	C₂×C₂²⋊D₄₃	—	2	2	no	—
331	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
332	C₂²×Dic₄₃	—	2	2	no	—
333	C₂²×Dic₄₃	—	2	2	no	—
334	D₄×D₄₃	—	2	4	no	—
335	D₄×D₄₃	—	4	2	no	—
336	#10621898	—	2	4	no	—
337	#10621898	—	4	4	no	—
338	#10621898	—	8	2	no	—
339	C₂×D₁₇₂	—	2	1	no	—
340	C₂×D₁₇₂	—	2	1	no	—
341	C₂×D₁₇₂	—	2	2	no	—
342	C₂×D₁₇₂	—	4	4	no	—
343	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
344	C₂×D₁₇₂	C₂⁴	1	2	yes	—
345	C₂×C₄×D₄₃	—	2	2	no	—
346	C₂×C₄×D₄₃	—	2	2	no	—
347	C₂×C₄×D₄₃	—	2	2	no	—
348	C₂×C₄×D₄₃	—	2	2	no	—
349	C₂×C₄×D₄₃	—	2	2	no	—
350	C₂×C₄×D₄₃	—	8	4	no	—
351	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
352	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
353	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
354	C₂×Dic₈₆	—	2	1	no	—
355	C₂×Dic₈₆	—	2	1	no	—
356	C₂×Dic₈₆	—	2	1	no	—
357	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
358	Q₁₆×C₄₃	—	4	1	no	—
359	SD₁₆×C₄₃	—	2	2	no	—
360	SD₁₆×C₄₃	—	4	1	no	—
361	D₈×C₄₃	—	2	2	no	—
362	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₄₃	—	2	1	no	—
367	C₄⋊C₄×C₄₃	—	2	1	no	—
368	C₄⋊C₄×C₄₃	—	2	1	no	—
369	C₄⋊C₄×C₄₃	—	2	1	no	—
370	C₄⋊C₄×C₄₃	—	2	1	no	—
371	C₄⋊C₄×C₄₃	—	2	1	no	—
372	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
373	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
374	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
375	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
376	C₂²⋊C₄×C₄₃	—	2	1	no	—
377	C₂²⋊C₄×C₄₃	—	2	1	no	—
378	C₂²⋊C₄×C₄₃	—	2	1	no	—
379	C₂²⋊C₄×C₄₃	—	2	1	no	—
380	C₂²⋊C₄×C₄₃	—	2	1	no	—
381	C₂²⋊C₄×C₄₃	—	2	1	no	—
382	C₂²⋊C₄×C₄₃	—	2	1	no	—
383	C₂²⋊C₄×C₄₃	—	2	1	no	—
384	C₄²×C₄₃	—	2	1	no	—
385	C₄²×C₄₃	—	2	1	no	—
386	C₄²×C₄₃	—	2	1	no	—
387	C₄²×C₄₃	—	2	1	no	—
388	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
389	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
390	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
391	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
392	C₂²⋊Dic₄₃	—	2	2	no	—
393	C₂²⋊Dic₄₃	—	2	2	no	—
394	C₂²⋊Dic₄₃	—	2	2	no	—
395	C₂²⋊Dic₄₃	—	2	2	no	—
396	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
397	#10621884	—	4	2	no	—
398	#10621882	—	4	2	no	—
399	(C₂×D₄₃)⋊C₄	—	2	2	no	—
400	(C₂×D₄₃)⋊C₄	—	2	2	no	—
401	(C₂×D₄₃)⋊C₄	—	2	2	no	—
402	(C₂×D₄₃)⋊C₄	—	2	2	no	—
403	(C₂×D₄₃)⋊C₄	—	2	2	no	—
404	(C₂×D₄₃)⋊C₄	—	2	2	no	—
405	(C₂×D₄₃)⋊C₄	—	2	2	no	—
406	(C₂×D₄₃)⋊C₄	—	2	2	no	—
407	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
408	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
409	C₄⋊Dic₄₃	—	2	1	no	—
410	C₄⋊Dic₄₃	—	2	1	no	—
411	C₄⋊Dic₄₃	—	2	1	no	—
412	C₄⋊Dic₄₃	—	2	2	no	—
413	C₄⋊Dic₄₃	—	2	2	no	—
414	C₄⋊Dic₄₃	—	2	2	no	—
415	C₄⋊Dic₄₃	—	2	2	no	—
416	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
417	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
418	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
419	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
420	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
421	Dic₄₃⋊C₄	—	2	2	no	—
422	Dic₄₃⋊C₄	—	2	2	no	—
423	Dic₄₃⋊C₄	—	2	2	no	—
424	Dic₄₃⋊C₄	—	2	2	no	—
425	Dic₄₃⋊C₄	—	2	2	no	—
426	Dic₄₃⋊C₄	—	2	2	no	—
427	Dic₄₃⋊C₄	—	2	2	no	—
428	Dic₄₃⋊C₄	—	2	2	no	—
429	Dic₄₃⋊C₄	—	2	2	no	—
430	Dic₄₃⋊C₄	—	2	2	no	—
431	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
432	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
433	C₄×Dic₄₃	—	2	2	no	—
434	C₄×Dic₄₃	—	2	2	no	—
435	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
436	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
437	C₄×Dic₄₃	C₂⁴	1	2	yes	—
438	C₂×C₄₃⋊C₈	—	4	2	no	—
439	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
440	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
441	C₈×D₄₃	—	4	2	no	—
442	C₈×D₄₃	—	4	2	no	—
443	C₂³×C₄₃	—	2	1	no	—
444	C₂³×C₄₃	—	2	1	no	—
445	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
446	C₂²×D₄₃	—	2	2	no	—
447	C₂²×D₄₃	—	4	4	no	—
448	C₂²×D₄₃	—	4	4	no	—
449	C₂²×D₄₃	—	8	2	no	—
450	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
451	Q₈×C₄₃	—	2	1	no	—
452	Q₈×C₄₃	—	2	1	no	—
453	Q₈×C₄₃	—	2	1	no	—
454	Q₈×C₄₃	—	2	1	no	—
455	D₄×C₄₃	—	2	1	no	—
456	D₄×C₄₃	—	2	1	no	—
457	D₄×C₄₃	—	2	1	no	—
458	D₄×C₄₃	—	4	2	no	—
459	D₄×C₄₃	—	8	1	no	—
460	D₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
461	C₂×C₄×C₄₃	—	2	2	no	—
462	C₂×C₄×C₄₃	—	2	1	no	—
463	C₂×C₄×C₄₃	—	2	1	no	—
464	C₂×C₄×C₄₃	—	2	1	no	—
465	C₂×C₄×C₄₃	—	2	1	no	—
466	C₂×C₄×C₄₃	—	2	1	no	—
467	C₂×C₄×C₄₃	—	2	1	no	—
468	C₂×C₄×C₄₃	—	2	1	no	—
469	C₂×C₄×C₄₃	—	2	1	no	—
470	C₂×C₄×C₄₃	—	4	1	no	—
471	C₂×C₄×C₄₃	—	4	2	no	—
472	C₂×C₄×C₄₃	—	4	2	no	—
473	C₂×C₄×C₄₃	—	4	2	no	—
474	C₂×C₄×C₄₃	—	4	2	no	—
475	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
476	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
478	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
479	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
480	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
481	C₂²⋊D₄₃	—	2	4	no	—
482	C₂²⋊D₄₃	—	4	4	no	—
483	C₂²⋊D₄₃	—	4	4	no	—
484	C₂²⋊D₄₃	—	8	2	no	—
485	C₂×Dic₄₃	—	2	2	no	—
486	C₂×Dic₄₃	—	2	2	no	—
487	C₂×Dic₄₃	—	2	2	no	—
488	C₂×Dic₄₃	—	8	2	no	—
489	C₂×Dic₄₃	—	8	2	no	—
490	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
491	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
492	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
493	D₁₇₂	—	2	2	no	—
494	D₁₇₂	—	2	2	no	—
495	D₁₇₂	—	4	4	no	—
496	D₁₇₂	—	4	2	no	—
497	D₁₇₂	—	8	1	no	—
498	D₁₇₂	#135	1	4	yes	—
499	C₄×D₄₃	—	2	4	no	—
500	C₄×D₄₃	—	2	2	no	—
501	C₄×D₄₃	—	2	2	no	—
502	C₄×D₄₃	—	4	2	no	—
503	C₄×D₄₃	—	4	4	no	—
504	C₄×D₄₃	—	4	4	no	—
505	C₄×D₄₃	—	8	2	no	—
506	C₄×D₄₃	—	8	2	no	—
507	C₄×D₄₃	—	8	2	no	—
508	Dic₈₆	—	2	2	no	—
509	Dic₈₆	—	4	2	no	—
510	Dic₈₆	—	8	1	no	—
511	Dic₈₆	—	8	1	no	—
512	C₈×C₄₃	—	2	1	no	—
513	C₈×C₄₃	—	2	1	no	—
514	C₈×C₄₃	—	2	1	no	—
515	C₈×C₄₃	—	2	1	no	—
516	C₄₃⋊C₈	—	2	2	no	—
517	C₄₃⋊C₈	—	2	2	no	—
518	#62103	—	43	1	no	maximal, Sylow
519	C₂²×C₄₃	—	2	1	no	—
520	C₂²×C₄₃	—	2	2	no	—
521	C₂²×C₄₃	—	2	1	no	—
522	C₂²×C₄₃	—	2	1	no	—
523	C₂²×C₄₃	—	4	1	no	—
524	C₂²×C₄₃	—	4	1	no	—
525	C₂²×C₄₃	—	4	1	no	—
526	C₂²×C₄₃	—	4	1	no	—
527	C₂²×C₄₃	—	4	1	no	—
528	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
529	C₂×D₄₃	—	2	2	no	—
530	C₂×D₄₃	—	2	2	no	—
531	C₂×D₄₃	—	4	2	no	—
532	C₂×D₄₃	—	4	2	no	—
533	C₂×D₄₃	—	4	2	no	—
534	C₂×D₄₃	—	8	8	no	—
535	C₂×D₄₃	C₂×#135	1	4	yes	—
536	C₄×C₄₃	—	2	1	no	—
537	C₄×C₄₃	—	2	1	no	—
538	C₄×C₄₃	—	2	1	no	—
539	C₄×C₄₃	—	2	1	no	—
540	C₄×C₄₃	—	4	1	no	—
541	C₄×C₄₃	—	4	1	no	—
542	C₄×C₄₃	—	4	1	no	—
543	C₄×C₄₃	—	4	1	no	—
544	C₄×C₄₃	—	4	1	no	—
545	C₄×C₄₃	—	4	1	no	—
546	C₄×C₄₃	C₂×#135	1	2	yes	—
547	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
548	C₄×C₄₃	#585	1	1	yes	characteristic
549	Dic₄₃	—	2	2	no	—
550	Dic₄₃	—	2	2	no	—
551	Dic₄₃	—	2	2	no	—
552	Dic₄₃	—	4	2	no	—
553	Dic₄₃	—	4	2	no	—
554	Dic₄₃	—	4	2	no	—
555	#3515	—	43	1	no	—
556	#3481	—	43	1	no	—
557	#3381	—	43	1	no	—
558	#3380	—	43	1	no	—
559	#3365	—	43	1	no	—
560	#3361	—	43	1	no	—
561	#3339	—	43	2	no	—
562	#3338	—	43	1	no	—
563	#3337	—	43	2	no	—
564	#3335	—	43	1	no	—
565	#3297	—	43	2	no	—
566	#3296	—	43	2	no	—
567	#3295	—	43	1	no	—
568	#3294	—	43	1	no	—
569	#3250	—	43	2	no	—
570	#3247	—	43	1	no	—
571	#3232	—	43	2	no	—
572	#3228	—	43	1	no	—
573	#3105	—	43	2	no	—
574	#3102	D₄₃	1	1	yes	characteristic, complemented
575	#3076	—	43	1	no	—
576	C₂×#478	—	43	2	no	—
577	#2988	—	43	1	no	—
578	C₂×C₄₃	—	4	2	no	—
579	C₂×C₄₃	—	4	1	no	—
580	C₂×C₄₃	—	8	1	no	—
581	C₂×C₄₃	#3489	1	1	yes	characteristic
582	C₂×C₄₃	C₂²×#135	1	1	yes	characteristic
583	C₂×C₄₃	#3585	1	1	yes	characteristic
584	D₄₃	—	2	4	no	—
585	D₄₃	—	8	2	no	—
586	#559	—	43	1	no	—
587	#557	—	43	1	no	—
588	#554	—	43	1	no	—
589	#554	—	43	1	no	—
590	#554	—	43	1	no	—
591	#554	—	43	1	no	—
592	#553	—	43	2	no	—
593	#553	—	43	2	no	—
594	#553	—	86	1	no	—
595	#552	—	43	2	no	—
596	#552	—	86	1	no	—
597	#552	—	86	2	no	—
598	#551	—	86	2	no	—
599	#547	—	43	1	no	—
600	#547	—	86	1	no	—
601	#546	—	43	2	no	—
602	#546	—	86	1	no	—
603	D₄²	—	43	1	no	—
604	#541	—	86	1	no	—
605	#539	—	86	2	no	—
606	#533	—	43	1	no	—
607	#532	—	43	1	no	—
608	#529	—	43	2	no	—
609	#529	—	43	2	no	—
610	#529	—	86	1	no	—
611	#529	C₂×D₄₃	1	1	yes	characteristic, complemented
612	C₂×#125	—	43	2	no	—
613	#525	—	86	2	no	—
614	#520	—	86	1	no	—
615	C₄×#41	—	43	1	no	—
616	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
617	C₂×C₄×D₄	—	43	2	no	—
618	C₂×C₄×D₄	—	86	1	no	—
619	#500	—	43	1	no	—
620	#499	—	43	2	no	—
621	#499	—	43	2	no	—
622	#498	—	43	1	no	—
623	#488	—	43	2	no	—
624	#488	—	43	2	no	—
625	#486	—	43	1	no	—
626	#486	—	43	1	no	—
627	#485	C₂×D₄₃	1	1	yes	characteristic, complemented
628	#484	—	43	2	no	—
629	#484	—	43	2	no	—
630	#483	—	43	2	no	—
631	#482	—	43	2	no	—
632	#482	—	43	2	no	—
633	#482	C₂×D₄₃	1	1	yes	characteristic, complemented
634	#481	—	43	2	no	—
635	#481	—	43	2	no	—
636	#480	—	43	2	no	—
637	#479	—	43	2	no	—
638	#479	—	43	2	no	—
639	#479	C₂×D₄₃	1	1	yes	characteristic, complemented
640	#478	—	43	2	no	—
641	#478	—	43	2	no	—
642	#478	—	43	2	no	—
643	#478	—	43	2	no	—
644	#478	—	43	2	no	—
645	#478	—	43	2	no	—
646	#478	—	43	2	no	—
647	#478	—	43	2	no	—
648	#478	—	43	2	no	—
649	#478	C₂×D₄₃	1	1	yes	characteristic
650	#477	—	43	1	no	—
651	#477	—	43	1	no	—
652	#476	—	43	1	no	—
653	#476	—	43	1	no	—
654	#475	—	43	1	no	—
655	#474	—	43	1	no	—
656	#467	—	43	2	no	—
657	#466	—	43	2	no	—
658	#466	—	43	2	no	—
659	#465	—	43	2	no	—
660	#465	—	43	2	no	—
661	#465	—	43	2	no	—
662	#464	—	43	2	no	—
663	#464	C₂×D₄₃	1	1	yes	characteristic, complemented
664	#463	—	43	2	no	—
665	#463	—	43	2	no	—
666	#463	C₂×D₄₃	1	1	yes	characteristic
667	#460	—	43	1	no	—
668	#459	—	43	1	no	—
669	#452	C₂×D₄₃	1	1	yes	characteristic
670	#450	—	43	2	no	—
671	#449	C₂×D₄₃	1	1	yes	characteristic
672	#447	—	43	2	no	—
673	C₈×Q₈	—	43	1	no	—
674	C₈×Q₈	—	43	1	no	—
675	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
676	C₄×SD₁₆	—	43	2	no	—
677	C₄×SD₁₆	—	43	2	no	—
678	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
679	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
680	C₄×D₈	—	43	2	no	—
681	C₄×D₈	—	43	2	no	—
682	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
683	C₈×D₄	—	43	2	no	—
684	C₈×D₄	—	43	2	no	—
685	C₈×D₄	—	43	1	no	—
686	C₈×D₄	—	43	1	no	—
687	#431	—	43	2	no	—
688	#431	C₂×D₄₃	1	1	yes	characteristic, complemented
689	#427	—	43	2	no	—
690	C₂×#107	—	43	2	no	—
691	C₂×#106	—	43	2	no	—
692	C₂×C₄⋊C₈	—	43	1	no	—
693	C₂×C₄⋊C₈	—	43	2	no	—
694	#416	—	43	2	no	—
695	C₂×#102	—	43	2	no	—
696	C₂×#102	—	43	2	no	—
697	C₄₃	#62103	1	1	yes	characteristic, complemented, Sylow
698	C₂×#41	—	43	1	no	—
699	C₂×#41	—	86	1	no	—
700	C₂×#41	—	86	1	no	—
701	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
702	C₂²×D₄	—	43	2	no	—
703	C₂²×D₄	—	86	1	no	—
704	C₂³×C₄	—	86	2	no	—
705	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
706	C₂×SD₁₆	—	43	2	no	—
707	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
708	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
709	C₂×D₈	—	43	2	no	—
710	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
711	C₂²×C₈	—	43	2	no	—
712	C₂²×C₈	—	43	2	no	—
713	C₂²×C₈	—	43	2	no	—
714	C₄⋊Q₈	—	43	1	no	—
715	C₄⋊Q₈	—	43	1	no	—
716	C₄⋊Q₈	—	43	1	no	—
717	C₄⋊Q₈	—	86	1	no	—
718	#127	—	43	1	no	—
719	#126	—	2	1	no	—
720	#126	—	86	2	no	—
721	#126	—	86	2	no	—
722	#126	—	86	2	no	—
723	#126	—	86	2	no	—
724	#126	—	86	2	no	—
725	#125	—	43	2	no	—
726	#125	—	43	2	no	—
727	#125	—	43	2	no	—
728	#125	—	43	2	no	—
729	#125	—	86	1	no	—
730	#125	—	86	1	no	—
731	#125	—	86	2	no	—
732	#125	—	86	2	no	—
733	#125	—	86	2	no	—
734	#125	—	86	2	no	—
735	#125	C₂²×D₄₃	1	1	yes	characteristic
736	#124	—	43	2	no	—
737	#124	—	86	1	no	—
738	#124	—	86	1	no	—
739	#124	C₂²×D₄₃	1	1	yes	characteristic
740	#123	—	2	1	no	—
741	#123	—	86	2	no	—
742	#123	—	86	2	no	—
743	#123	—	86	2	no	—
744	#123	—	86	2	no	—
745	#123	—	86	2	no	—
746	#123	—	86	2	no	—
747	#123	—	86	2	no	—
748	#123	—	86	2	no	—
749	C₂²⋊Q₈	—	43	2	no	—
750	C₂²⋊Q₈	—	43	2	no	—
751	C₂²⋊Q₈	—	86	2	no	—
752	C₂²⋊Q₈	—	86	2	no	—
753	C₂²⋊Q₈	—	86	2	no	—
754	C₂²⋊Q₈	—	86	2	no	—
755	C₂²⋊Q₈	—	86	1	no	—
756	C₂²⋊Q₈	—	86	1	no	—
757	C₂²⋊Q₈	—	86	1	no	—
758	C₂²⋊Q₈	—	86	1	no	—
759	C₂²⋊Q₈	—	86	1	no	—
760	C₂²⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
761	#121	—	43	2	no	—
762	#121	—	43	2	no	—
763	#121	—	43	2	no	—
764	#121	—	86	2	no	—
765	#121	—	86	2	no	—
766	#121	—	86	1	no	—
767	#121	—	86	2	no	—
768	#121	—	86	1	no	—
769	#121	C₂²×D₄₃	1	1	yes	characteristic
770	#120	—	86	2	no	—
771	#120	—	86	2	no	—
772	C₄×Q₈	—	43	1	no	—
773	C₄×Q₈	—	43	1	no	—
774	C₄×Q₈	—	43	2	no	—
775	C₄×Q₈	—	86	1	no	—
776	C₄×Q₈	—	86	1	no	—
777	C₄×Q₈	—	86	1	no	—
778	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
779	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
780	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
781	C₄×D₄	—	2	1	no	—
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	2	1	no	—
784	C₄×D₄	—	43	2	no	—
785	C₄×D₄	—	43	2	no	—
786	C₄×D₄	—	43	2	no	—
787	C₄×D₄	—	43	2	no	—
788	C₄×D₄	—	43	2	no	—
789	C₄×D₄	—	43	1	no	—
790	C₄×D₄	—	43	1	no	—
791	C₄×D₄	—	43	2	no	—
792	C₄×D₄	—	86	2	no	—
793	C₄×D₄	—	86	1	no	—
794	C₄×D₄	—	86	2	no	—
795	C₄×D₄	—	86	1	no	—
796	C₄×D₄	—	86	1	no	—
797	C₄×D₄	—	86	2	no	—
798	C₄×D₄	—	86	2	no	—
799	C₄×D₄	—	86	2	no	—
800	C₄×D₄	—	86	2	no	—
801	C₄×D₄	—	86	1	no	—
802	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
803	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
804	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
805	#117	—	2	1	no	—
806	#117	—	2	1	no	—
807	#117	—	43	1	no	—
808	#117	—	43	2	no	—
809	#117	—	43	2	no	—
810	#117	—	86	2	no	—
811	#117	—	86	2	no	—
812	#117	—	86	2	no	—
813	#117	C₂²×D₄₃	1	1	yes	characteristic
814	C₂×C₄⋊C₄	—	43	2	no	—
815	C₂×C₄⋊C₄	—	43	2	no	—
816	C₂×C₄⋊C₄	—	43	2	no	—
817	C₂×C₄⋊C₄	—	86	2	no	—
818	C₂×C₄⋊C₄	—	86	2	no	—
819	C₂×C₄⋊C₄	—	86	1	no	—
820	C₂×C₄⋊C₄	—	86	1	no	—
821	C₂×C₂²⋊C₄	—	86	2	no	—
822	C₂×C₂²⋊C₄	—	86	2	no	—
823	C₂×C₄²	—	2	1	no	—
824	C₂×C₄²	—	43	2	no	—
825	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
826	#107	—	43	2	no	—
827	#107	—	43	2	no	—
828	#107	—	43	2	no	—
829	#107	—	43	2	no	—
830	#107	—	43	2	no	—
831	#107	C₂²×D₄₃	1	1	yes	characteristic
832	#107	C₂²×D₄₃	1	1	yes	characteristic
833	#106	—	43	2	no	—
834	#106	—	43	2	no	—
835	#106	—	43	2	no	—
836	#106	—	43	2	no	—
837	#106	—	43	2	no	—
838	#106	C₂²×D₄₃	1	1	yes	characteristic
839	#106	C₂²×D₄₃	1	1	yes	characteristic
840	C₄⋊C₈	—	43	2	no	—
841	C₄⋊C₈	—	43	2	no	—
842	C₄⋊C₈	—	43	2	no	—
843	C₄⋊C₈	—	43	1	no	—
844	C₄⋊C₈	—	43	1	no	—
845	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
846	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
847	#103	—	43	2	no	—
848	#103	—	43	2	no	—
849	#103	—	43	2	no	—
850	#103	C₂²×D₄₃	1	1	yes	characteristic
851	#103	C₂²×D₄₃	1	1	yes	characteristic
852	#103	C₂²×D₄₃	1	1	yes	characteristic
853	#103	C₂²×D₄₃	1	1	yes	characteristic
854	#102	—	43	2	no	—
855	#102	—	43	2	no	—
856	#102	—	43	2	no	—
857	#102	—	43	2	no	—
858	#102	—	43	2	no	—
859	#102	—	43	2	no	—
860	#102	—	43	2	no	—
861	#102	—	43	2	no	—
862	#102	—	43	2	no	—
863	#102	C₂²×D₄₃	1	1	yes	characteristic
864	#102	C₂²×D₄₃	1	1	yes	characteristic
865	#102	C₂²×D₄₃	1	1	yes	characteristic
866	#102	C₂²×D₄₃	1	1	yes	characteristic
867	C₂²⋊C₈	—	43	2	no	—
868	C₂²⋊C₈	—	43	2	no	—
869	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
870	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
871	C₄×C₈	—	43	2	no	—
872	C₄×C₈	—	43	2	no	—
873	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
874	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
875	C₂⁴	—	86	2	no	—
876	#41	—	2	2	no	—
877	#41	—	4	1	no	—
878	#41	—	86	4	no	—
879	#41	—	344	2	no	—
880	#41	—	172	4	no	—
881	C₂×Q₈	—	43	1	no	—
882	C₂×Q₈	—	86	1	no	—
883	C₂×Q₈	—	86	1	no	—
884	C₂×Q₈	—	86	1	no	—
885	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
886	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
887	C₂×D₄	—	2	1	no	—
888	C₂×D₄	—	2	1	no	—
889	C₂×D₄	—	43	2	no	—
890	C₂×D₄	—	43	1	no	—
891	C₂×D₄	—	43	2	no	—
892	C₂×D₄	—	86	2	no	—
893	C₂×D₄	—	86	2	no	—
894	C₂×D₄	—	86	4	no	—
895	C₂×D₄	—	86	2	no	—
896	C₂×D₄	—	86	2	no	—
897	C₂×D₄	—	86	1	no	—
898	C₂×D₄	—	86	1	no	—
899	C₂×D₄	—	172	4	no	—
900	C₂×D₄	—	172	2	no	—
901	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
902	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	2	1	no	—
905	C₂²×C₄	—	2	1	no	—
906	C₂²×C₄	—	2	1	no	—
907	C₂²×C₄	—	43	2	no	—
908	C₂²×C₄	—	43	2	no	—
909	C₂²×C₄	—	43	2	no	—
910	C₂²×C₄	—	86	2	no	—
911	C₂²×C₄	—	86	2	no	—
912	C₂²×C₄	—	86	2	no	—
913	C₂²×C₄	—	86	2	no	—
914	C₂²×C₄	—	86	2	no	—
915	C₂²×C₄	—	86	2	no	—
916	C₂²×C₄	—	86	2	no	—
917	C₂²×C₄	—	344	4	no	—
918	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
919	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
920	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
921	Q₁₆	—	4	1	no	—
922	SD₁₆	—	2	2	no	—
923	SD₁₆	—	4	1	no	—
924	SD₁₆	—	172	2	no	—
925	D₈	—	2	2	no	—
926	D₈	—	172	2	no	—
927	C₂×C₈	—	43	2	no	—
928	C₂×C₈	—	43	2	no	—
929	C₂×C₈	—	172	2	no	—
930	C₂×C₈	—	172	2	no	—
931	C₂×C₈	—	172	2	no	—
932	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
933	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
934	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
935	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	2	1	no	—
942	C₄⋊C₄	—	43	1	no	—
943	C₄⋊C₄	—	43	1	no	—
944	C₄⋊C₄	—	43	2	no	—
945	C₄⋊C₄	—	43	2	no	—
946	C₄⋊C₄	—	43	2	no	—
947	C₄⋊C₄	—	43	2	no	—
948	C₄⋊C₄	—	43	2	no	—
949	C₄⋊C₄	—	86	2	no	—
950	C₄⋊C₄	—	86	2	no	—
951	C₄⋊C₄	—	86	2	no	—
952	C₄⋊C₄	—	86	2	no	—
953	C₄⋊C₄	—	86	2	no	—
954	C₄⋊C₄	—	86	2	no	—
955	C₄⋊C₄	—	86	2	no	—
956	C₄⋊C₄	—	86	2	no	—
957	C₄⋊C₄	—	86	2	no	—
958	C₄⋊C₄	—	86	2	no	—
959	C₄⋊C₄	—	86	2	no	—
960	C₄⋊C₄	—	86	2	no	—
961	C₄⋊C₄	—	86	2	no	—
962	C₄⋊C₄	—	86	1	no	—
963	C₄⋊C₄	—	86	1	no	—
964	C₄⋊C₄	—	86	2	no	—
965	C₄⋊C₄	—	86	1	no	—
966	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
967	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
968	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
969	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
970	C₂²⋊C₄	—	2	1	no	—
971	C₂²⋊C₄	—	2	1	no	—
972	C₂²⋊C₄	—	2	1	no	—
973	C₂²⋊C₄	—	2	1	no	—
974	C₂²⋊C₄	—	2	1	no	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	43	2	no	—
979	C₂²⋊C₄	—	43	2	no	—
980	C₂²⋊C₄	—	43	2	no	—
981	C₂²⋊C₄	—	86	2	no	—
982	C₂²⋊C₄	—	86	2	no	—
983	C₂²⋊C₄	—	86	2	no	—
984	C₂²⋊C₄	—	86	2	no	—
985	C₂²⋊C₄	—	86	2	no	—
986	C₂²⋊C₄	—	86	2	no	—
987	C₂²⋊C₄	—	86	2	no	—
988	C₂²⋊C₄	—	86	2	no	—
989	C₂²⋊C₄	—	86	2	no	—
990	C₂²⋊C₄	—	86	2	no	—
991	C₂²⋊C₄	—	86	2	no	—
992	C₂²⋊C₄	—	86	2	no	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	2	1	no	—
997	C₄²	—	43	2	no	—
998	C₄²	—	43	2	no	—
999	C₄²	—	43	2	no	—
1000	C₄²	—	86	2	no	—
1001	C₄²	—	86	2	no	—
1002	C₄²	D₄×D₄₃	1	1	yes	characteristic
1003	C₄²	D₄×D₄₃	1	1	yes	characteristic
1004	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1005	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1006	C₂³	—	2	1	no	—
1007	C₂³	—	2	1	no	—
1008	C₂³	—	43	2	no	—
1009	C₂³	—	86	2	no	—
1010	C₂³	—	344	2	no	—
1011	C₂³	—	172	4	no	—
1012	C₂³	—	172	4	no	—
1013	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1014	Q₈	—	2	1	no	—
1015	Q₈	—	2	1	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	2	1	no	—
1018	Q₈	—	86	2	no	—
1019	Q₈	—	344	1	no	—
1020	Q₈	—	344	1	no	—
1021	Q₈	—	172	2	no	—
1022	D₄	—	2	1	no	—
1023	D₄	—	2	1	no	—
1024	D₄	—	2	1	no	—
1025	D₄	—	4	2	no	—
1026	D₄	—	8	1	no	—
1027	D₄	—	43	4	no	—
1028	D₄	—	86	4	no	—
1029	D₄	—	86	2	no	—
1030	D₄	—	86	2	no	—
1031	D₄	—	344	1	no	—
1032	D₄	—	344	2	no	—
1033	D₄	—	172	4	no	—
1034	D₄	—	172	4	no	—
1035	D₄	—	172	4	no	—
1036	D₄	—	172	2	no	—
1037	D₄	#13063372	1	2	yes	—
1038	C₂×C₄	—	2	2	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	2	1	no	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	4	1	no	—
1048	C₂×C₄	—	4	2	no	—
1049	C₂×C₄	—	4	2	no	—
1050	C₂×C₄	—	4	2	no	—
1051	C₂×C₄	—	4	2	no	—
1052	C₂×C₄	—	43	2	no	—
1053	C₂×C₄	—	43	2	no	—
1054	C₂×C₄	—	43	2	no	—
1055	C₂×C₄	—	86	4	no	—
1056	C₂×C₄	—	86	2	no	—
1057	C₂×C₄	—	86	2	no	—
1058	C₂×C₄	—	86	2	no	—
1059	C₂×C₄	—	86	2	no	—
1060	C₂×C₄	—	86	2	no	—
1061	C₂×C₄	—	344	2	no	—
1062	C₂×C₄	—	344	2	no	—
1063	C₂×C₄	—	344	2	no	—
1064	C₂×C₄	—	344	2	no	—
1065	C₂×C₄	—	344	2	no	—
1066	C₂×C₄	—	172	2	no	—
1067	C₂×C₄	—	172	4	no	—
1068	C₂×C₄	—	172	4	no	—
1069	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1070	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1071	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1072	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1073	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1074	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1075	C₈	—	2	1	no	—
1076	C₈	—	2	1	no	—
1077	C₈	—	2	1	no	—
1078	C₈	—	2	1	no	—
1079	C₈	—	86	2	no	—
1080	C₈	—	86	2	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	2	no	—
1085	C₂²	—	4	1	no	—
1086	C₂²	—	4	1	no	—
1087	C₂²	—	4	1	no	—
1088	C₂²	—	4	1	no	—
1089	C₂²	—	4	1	no	—
1090	C₂²	—	43	4	no	—
1091	C₂²	—	86	2	no	—
1092	C₂²	—	86	2	no	—
1093	C₂²	—	344	8	no	—
1094	C₂²	—	172	2	no	—
1095	C₂²	—	172	2	no	—
1096	C₂²	—	172	2	no	—
1097	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1098	C₄	—	2	1	no	—
1099	C₄	—	2	1	no	—
1100	C₄	—	2	1	no	—
1101	C₄	—	2	1	no	—
1102	C₄	—	4	1	no	—
1103	C₄	—	4	1	no	—
1104	C₄	—	4	1	no	—
1105	C₄	—	4	1	no	—
1106	C₄	—	4	1	no	—
1107	C₄	—	4	1	no	—
1108	C₄	—	86	2	no	—
1109	C₄	—	86	2	no	—
1110	C₄	—	86	2	no	—
1111	C₄	—	172	2	no	—
1112	C₄	—	172	2	no	—
1113	C₄	—	172	2	no	—
1114	C₄	#135×D₄₃	1	2	yes	—
1115	C₄	C₂×#13063372	1	1	yes	characteristic
1116	C₄	#14583735	1	1	yes	characteristic
1117	C₂	—	4	1	no	—
1118	C₂	—	4	2	no	—
1119	C₂	—	8	1	no	—
1120	C₂	—	86	4	no	—
1121	C₂	—	344	2	no	—
1122	C₂	#19148267	1	1	yes	characteristic
1123	C₂	C₂×#135×D₄₃	1	1	yes	characteristic
1124	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	C₄₃×#3102	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3102	D₄₃
hypocenter	C₄₃	#62103
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3102

Complements

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

N	H ≅ G/N	type
1. #19148575	C₂	semidirect
2. #19148205	C₂	semidirect
3. #19147468	C₂	semidirect
4. #19147460	C₂	semidirect
5. #19147289	C₂	semidirect
6. #19147253	C₂	semidirect
7. #19146990	C₂	semidirect
8. #19146989	C₂	semidirect
9. #19146977	C₂	semidirect
10. #19146954	C₂	semidirect
11. #19146438	C₂	semidirect
12. #19146423	C₂	semidirect
13. #19146421	C₂	semidirect
14. #19146410	C₂	semidirect
15. #19145945	C₂	semidirect
16. #19145921	C₂	semidirect
17. #19145767	C₂	semidirect
18. #19145733	C₂	semidirect
19. #19144641	C₂	semidirect
20. #19144383	C₂	semidirect
21. #478×D₄₃	C₂	semidirect
22. #19143703	C₂	semidirect
23. C₄₃×#3102	C₂	semidirect
25. #14583628	C₂²	semidirect
29. #14583606	C₂²	semidirect
30. #14583596	C₂²	semidirect
35. #14583583	C₂²	semidirect
44. #14583456	C₂²	semidirect
48. #14583428	C₂²	semidirect
49. #125×D₄₃	C₂²	semidirect
55. #14583304	C₂²	semidirect
56. #14583300	C₂²	semidirect
57. #14583299	C₂²	semidirect
58. #14583297	C₂²	semidirect
59. #14583255	C₂²	semidirect
60. #14583255	C₂²	semidirect
63. #14583233	C₂²	semidirect
64. #14583233	C₂²	semidirect
65. #14583228	C₂²	semidirect
66. #14583224	C₂²	semidirect
67. #14583224	C₂²	semidirect
69. #14583216	C₂²	semidirect
71. #14583206	C₂²	semidirect
72. #14583204	C₂²	semidirect
73. #14583202	C₂²	semidirect
75. #14583200	C₂²	semidirect
76. #14583200	C₂²	semidirect
78. #14583198	C₂²	semidirect
80. #14583197	C₂²	semidirect
81. #14583196	C₂²	semidirect
82. #14583194	C₂²	semidirect
83. #14583194	C₂²	semidirect
85. #14583189	C₂²	semidirect
86. #14583184	C₂²	semidirect
88. #14583137	C₂²	semidirect
90. #14583133	C₂²	semidirect
92. #14583130	C₂²	semidirect
93. #14583125	C₂²	semidirect
94. #14583123	C₂²	semidirect
95. #14583116	C₂²	semidirect
96. #14583111	C₂²	semidirect
101. C₈×Dic₈₆	C₂²	semidirect
102. C₈×Dic₈₆	C₂²	semidirect
104. #14582984	C₂²	semidirect
106. #14582979	C₂²	semidirect
109. (C₂²⋊D₄₃)⋊C₈	C₂²	semidirect
110. (C₂²⋊D₄₃)⋊C₈	C₂²	semidirect
111. #14582951	C₂²	semidirect
112. #14582935	C₂²	semidirect
113. #107×D₄₃	C₂²	semidirect
114. #106×D₄₃	C₂²	semidirect
115. C₂×C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
116. C₄⋊C₈×D₄₃	C₂²	semidirect
120. C₄₃×#529	C₂²	semidirect
122. C₄₃×#485	C₂²	semidirect
123. C₄₃×#482	C₂²	semidirect
124. C₄₃×#479	C₂²	semidirect
126. C₄₃×#464	C₂²	semidirect
130. C₄×Q₁₆×C₄₃	C₂²	semidirect
132. C₄×SD₁₆×C₄₃	C₂²	semidirect
134. C₄₃×#431	C₂²	semidirect
574. #3102	D₄₃	semidirect
611. #529	C₂×D₄₃	semidirect
627. #485	C₂×D₄₃	semidirect
633. #482	C₂×D₄₃	semidirect
639. #479	C₂×D₄₃	semidirect
663. #464	C₂×D₄₃	semidirect
675. C₄×Q₁₆	C₂×D₄₃	semidirect
679. C₄×SD₁₆	C₂×D₄₃	semidirect
688. #431	C₂×D₄₃	semidirect
697. C₄₃	#62103	semidirect

Maximal subgroups

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

subgroup	index
#19148575	2
#19148205	2
#19147468	2
#19147460	2
#19147289	2
#19147253	2
#19146990	2
#19146989	2
#19146977	2
#19146954	2
#19146438	2
#19146423	2
#19146421	2
#19146410	2
#19145945	2
#19145921	2
#19145767	2
#19145733	2
#19144641	2
#19144383	2
#478×D₄₃	2
#19143703	2
C₄₃×#3102	2
#62103	43