Subgroups — #25983300

Order 11008.

2090 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148969	C₂	1	1	yes	maximal, characteristic, complemented
2	#19148366	C₂	1	1	yes	maximal, characteristic, complemented
3	#19146924	C₂	1	1	yes	maximal, characteristic, complemented
4	#19146880	C₂	1	1	yes	maximal, characteristic, complemented
5	#19146845	C₂	1	2	yes	maximal, complemented
6	#19146536	C₂	1	1	yes	maximal, characteristic, complemented
7	#19146494	C₂	1	2	yes	maximal, complemented
8	#19146462	C₂	1	1	yes	maximal, characteristic, complemented
9	#19146354	C₂	1	1	yes	maximal, characteristic, complemented
10	#19146297	C₂	1	2	yes	maximal, complemented
11	SD₁₆×D₁₇₂	C₂	1	1	yes	maximal, characteristic, complemented
12	#19146262	C₂	1	1	yes	maximal, characteristic, complemented
13	#19146221	C₂	1	2	yes	maximal, complemented
14	#19146216	C₂	1	1	yes	maximal, characteristic, complemented
15	#19145567	C₂	1	1	yes	maximal, characteristic, complemented
16	#19145530	C₂	1	1	yes	maximal, characteristic, complemented
17	#19145505	C₂	1	2	yes	maximal, complemented
18	#19145454	C₂	1	2	yes	maximal, complemented
19	#19144626	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143911	C₂	1	2	yes	maximal, complemented
21	#19143876	C₂	1	2	yes	maximal, complemented
22	#19143661	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063373	C₂²	1	2	yes	complemented
25	C₂×#13063357	C₂²	1	2	yes	complemented
26	C₂×#13063352	C₂²	1	2	yes	—
27	C₂×#13063348	C₂²	1	2	yes	complemented
28	C₂×SD₁₆×D₄₃	C₂²	1	2	yes	—
29	#14583639	—	2	2	no	—
30	#14583622	C₂²	1	1	yes	characteristic
31	#14583602	C₂²	1	2	yes	—
32	#14583571	—	2	1	no	—
33	#14583571	C₂²	1	1	yes	characteristic
34	#14583571	C₂²	1	1	yes	characteristic
35	#14583571	C₂²	1	1	yes	characteristic, complemented
36	#14583570	—	2	1	no	—
37	Q₈×D₁₇₂	—	2	1	no	—
38	Q₈×D₁₇₂	C₂²	1	1	yes	characteristic
39	Q₈×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
40	#14583561	—	2	2	no	—
41	#14583561	C₂²	1	2	yes	complemented
42	#14583561	C₂²	1	2	yes	complemented
43	#14583554	C₂²	1	1	yes	characteristic
44	#14583545	—	2	1	no	—
45	#14583542	C₂²	1	2	yes	—
46	D₄×D₁₇₂	C₂²	1	1	yes	characteristic
47	#14583520	—	2	1	no	—
48	#14583488	—	2	2	no	—
49	#14583480	—	2	2	no	—
50	#14583480	C₂²	1	2	yes	complemented
51	#14583479	C₂²	1	2	yes	—
52	#14583468	—	2	1	no	—
53	#14583465	C₂²	1	2	yes	—
54	#14583449	—	2	1	no	—
55	#14583449	—	2	1	no	—
56	#14583449	C₂²	1	1	yes	characteristic
57	#14583449	C₂²	1	1	yes	characteristic
58	#14583449	C₂²	1	1	yes	characteristic, complemented
59	#14583281	C₂²	1	2	yes	—
60	#14583276	C₂²	1	1	yes	characteristic
61	#14583272	C₂²	1	1	yes	characteristic
62	#14583256	C₂²	1	2	yes	complemented
63	#14583250	C₂²	1	1	yes	characteristic, complemented
64	#14583246	C₂²	1	1	yes	characteristic, complemented
65	#14583242	C₂²	1	2	yes	complemented
66	#14583231	C₂²	1	2	yes	complemented
67	#14583226	C₂²	1	2	yes	complemented
68	#14583219	C₂²	1	2	yes	complemented
69	#14583217	C₂²	1	2	yes	complemented
70	#14583184	C₂²	1	1	yes	characteristic, complemented
71	#14583184	C₂²	1	1	yes	characteristic, complemented
72	#14583156	C₂²	1	2	yes	complemented
73	#14583153	C₂²	1	2	yes	—
74	#14583151	C₂²	1	2	yes	—
75	#14583146	C₂²	1	2	yes	complemented
76	#14583136	C₂²	1	2	yes	complemented
77	#14583131	C₂²	1	2	yes	complemented
78	#14583129	C₂²	1	2	yes	—
79	#14583127	C₂²	1	2	yes	—
80	#14583115	C₂²	1	2	yes	complemented
81	#14583115	C₂²	1	2	yes	complemented
82	#14583109	C₂²	1	1	yes	characteristic, complemented
83	#14583104	C₂²	1	1	yes	characteristic
84	#14583099	C₂²	1	1	yes	characteristic
85	#14583099	C₂²	1	1	yes	characteristic
86	#14583099	C₂²	1	1	yes	characteristic, complemented
87	#14583094	C₂²	1	1	yes	characteristic
88	#14583064	C₂²	1	2	yes	complemented
89	#14583060	C₂²	1	2	yes	complemented
90	#14583059	C₂²	1	2	yes	complemented
91	#14583053	C₂²	1	2	yes	complemented
92	#14583051	C₂²	1	2	yes	—
93	#14583047	C₂²	1	2	yes	—
94	#14583047	C₂²	1	2	yes	complemented
95	#14583047	C₂²	1	2	yes	complemented
96	#14583046	C₂²	1	2	yes	complemented
97	#14583046	C₂²	1	2	yes	complemented
98	#14583043	C₂²	1	2	yes	—
99	#14583042	C₂²	1	2	yes	—
100	#14583039	C₂²	1	2	yes	—
101	#14583039	C₂²	1	2	yes	complemented
102	#14583038	C₂²	1	2	yes	complemented
103	#14583036	C₂²	1	2	yes	—
104	#14583034	C₂²	1	2	yes	—
105	C₄×#10621884	C₂²	1	2	yes	complemented
106	C₄×#10621884	C₂²	1	2	yes	complemented
107	#14582978	C₂²	1	1	yes	characteristic
108	#14582978	C₂²	1	1	yes	characteristic, complemented
109	#14582976	C₂²	1	2	yes	complemented
110	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
111	C₈×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
112	#14582964	C₂²	1	2	yes	complemented
113	#14582952	C₂²	1	1	yes	characteristic, complemented
114	#14582906	C₂²	1	2	yes	complemented
115	#14582899	C₂²	1	2	yes	complemented
116	#14582894	C₂²	1	2	yes	complemented
117	#103×D₄₃	C₂²	1	2	yes	complemented
118	#14582864	C₂²	1	2	yes	complemented
119	#14582864	C₂²	1	2	yes	complemented
120	C₄₃×#529	C₂²	1	1	yes	characteristic
121	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
122	C₄₃×#483	C₂²	1	1	yes	characteristic, complemented
123	C₄₃×#480	C₂²	1	1	yes	characteristic
124	C₄₃×#479	C₂²	1	1	yes	characteristic, complemented
125	C₄₃×#479	C₂²	1	1	yes	characteristic, complemented
126	C₄₃×#464	C₂²	1	1	yes	characteristic
127	C₄₃×#464	C₂²	1	1	yes	characteristic
128	C₄₃×#451	C₂²	1	1	yes	characteristic, complemented
129	C₄₃×#448	C₂²	1	1	yes	characteristic
130	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
131	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
132	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
133	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
134	C₄₃×#431	C₂²	1	1	yes	characteristic, complemented
135	#13063373	—	4	4	no	—
136	#13063373	—	4	4	no	—
137	C₂×#10621902	—	2	2	no	—
138	C₂×#10621902	C₂³	1	2	yes	—
139	C₂×#10621902	C₂³	1	2	yes	—
140	C₂×#10621902	C₂³	1	2	yes	—
141	C₂×#10621898	—	2	2	no	—
142	C₂×#10621898	—	2	2	no	—
143	C₂×#10621898	—	2	1	no	—
144	C₂×#10621898	—	2	1	no	—
145	C₂×#10621898	C₂³	1	2	yes	—
146	C₂×#10621898	C₂³	1	2	yes	—
147	C₂×Q₈×D₄₃	—	2	2	no	—
148	C₂×Q₈×D₄₃	C₂³	1	2	yes	—
149	C₂×Q₈×D₄₃	C₂³	1	2	yes	—
150	C₂²×D₁₇₂	—	2	1	no	—
151	C₂×D₄×D₄₃	C₂³	1	2	yes	—
152	#13063357	—	4	4	no	—
153	#13063352	—	4	4	no	—
154	#13063348	—	4	4	no	—
155	C₂×#10621885	C₂³	1	2	yes	—
156	C₂×#10621873	C₂³	1	2	yes	—
157	C₂×#10621873	C₂³	1	2	yes	—
158	C₂×#10621883	C₂³	1	2	yes	—
159	C₂×#10621884	C₂³	1	2	yes	—
160	C₂×#10621884	C₂³	1	2	yes	—
161	C₂×#10621884	C₂³	1	2	yes	—
162	SD₁₆×D₄₃	—	4	4	no	—
163	C₂×D₃₄₄	C₂³	1	2	yes	—
164	C₂×D₃₄₄	C₂³	1	2	yes	—
165	C₂×#10621882	C₂³	1	2	yes	—
166	C₂×#10621872	C₂³	1	2	yes	—
167	C₂×#10621872	C₂³	1	2	yes	—
168	C₂×C₈×D₄₃	C₂³	1	2	yes	—
169	C₂×C₈×D₄₃	C₂³	1	2	yes	—
170	#13063325	—	2	1	no	—
171	#13063325	—	2	1	no	—
172	#13063325	D₄	1	1	yes	characteristic
173	#13063325	C₂³	1	1	yes	characteristic
174	#13063325	C₂³	1	1	yes	characteristic
175	#13063322	—	2	1	no	—
176	#13063322	—	2	1	no	—
177	#13063322	—	2	1	no	—
178	#13063322	D₄	1	1	yes	characteristic
179	#13063322	C₂³	1	1	yes	characteristic
180	#13063322	C₂³	1	1	yes	characteristic
181	#13063321	—	2	2	no	—
182	#13063320	—	2	2	no	—
183	#13063320	—	2	2	no	—
184	#13063313	—	2	1	no	—
185	#13063313	—	2	1	no	—
186	#13063313	—	2	2	no	—
187	#13063313	—	2	2	no	—
188	#13063313	D₄	1	2	yes	—
189	#13063313	C₂³	1	2	yes	—
190	#13063311	—	2	2	no	—
191	#13063310	—	2	2	no	—
192	#13063307	—	2	2	no	—
193	#13063307	—	2	2	no	—
194	#13063305	—	2	2	no	—
195	#13063305	—	2	2	no	—
196	#13063305	—	2	2	no	—
197	#13063305	—	2	2	no	—
198	#13063305	—	2	2	no	—
199	#13063305	C₂³	1	2	yes	—
200	#13063305	C₂³	1	2	yes	—
201	#13063304	—	2	1	no	—
202	#13063303	—	2	2	no	—
203	#13063301	C₂³	1	2	yes	—
204	#13063300	—	2	2	no	—
205	#13063300	—	2	2	no	—
206	#13063300	—	2	2	no	—
207	#13063300	—	2	2	no	—
208	#13063300	—	2	2	no	—
209	#13063300	—	2	2	no	—
210	#13063300	—	2	2	no	—
211	#13063300	—	2	2	no	—
212	#13063300	C₂³	1	2	yes	—
213	#13063300	C₂³	1	2	yes	—
214	#13063300	C₂³	1	2	yes	—
215	#13063300	C₂³	1	2	yes	—
216	#13063299	—	2	1	no	—
217	#13063299	—	2	1	no	—
218	#13063299	—	2	1	no	—
219	#13063299	—	2	2	no	—
220	#13063299	—	2	2	no	—
221	#13063299	—	2	1	no	—
222	#13063299	D₄	1	1	yes	characteristic
223	#13063299	D₄	1	2	yes	—
224	#13063299	D₄	1	1	yes	characteristic
225	#13063299	C₂³	1	2	yes	—
226	#13063298	—	2	2	no	—
227	#13063298	—	2	2	no	—
228	#13063298	—	2	2	no	—
229	#13063296	C₂³	1	2	yes	—
230	#13063295	—	2	2	no	—
231	#13063295	—	2	2	no	—
232	#13063295	—	2	2	no	—
233	#13063293	—	2	2	no	—
234	C₄×Dic₈₆	—	2	1	no	—
235	C₄×D₁₇₂	—	2	1	no	—
236	C₄×D₁₇₂	—	2	1	no	—
237	C₄×D₁₇₂	—	2	1	no	—
238	C₄×D₁₇₂	—	2	1	no	—
239	C₄×D₁₇₂	—	2	1	no	—
240	C₄×D₁₇₂	—	2	2	no	—
241	C₄×D₁₇₂	—	2	2	no	—
242	C₄×D₁₇₂	—	2	1	no	—
243	C₄×D₁₇₂	—	2	1	no	—
244	C₄×D₁₇₂	—	2	1	no	—
245	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
246	C₄×D₁₇₂	C₂³	1	2	yes	—
247	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
248	C₄×D₁₇₂	C₂³	1	2	yes	—
249	#13063287	—	2	2	no	—
250	#13063283	C₂³	1	2	yes	—
251	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
252	C₂²⋊C₄×D₄₃	—	2	2	no	—
253	#13063256	C₂³	1	2	yes	—
254	#13063256	C₂³	1	2	yes	—
255	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
256	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
257	#13063250	C₂³	1	2	yes	—
258	#13063250	C₂³	1	2	yes	—
259	#13063249	C₂³	1	2	yes	—
260	#13063249	C₂³	1	2	yes	—
261	#13063248	C₂³	1	2	yes	—
262	#13063248	C₂³	1	2	yes	—
263	#13063247	C₂³	1	2	yes	—
264	#13063247	C₂³	1	2	yes	—
265	#13063245	C₂³	1	2	yes	—
266	#13063245	C₂³	1	2	yes	—
267	#13063245	C₂³	1	2	yes	—
268	#13063245	C₂³	1	2	yes	—
269	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
270	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
271	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
272	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
273	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
274	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
275	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
276	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
277	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
278	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
279	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
280	#126×C₄₃	—	2	1	no	—
281	#125×C₄₃	C₂³	1	1	yes	characteristic
282	#124×C₄₃	C₂³	1	1	yes	characteristic
283	#123×C₄₃	—	2	1	no	—
284	C₂²⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
285	#121×C₄₃	C₂³	1	1	yes	characteristic
286	C₄×Q₈×C₄₃	—	2	1	no	—
287	C₄×Q₈×C₄₃	—	2	1	no	—
288	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
289	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
290	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
291	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
292	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
293	C₄×D₄×C₄₃	—	2	1	no	—
294	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
295	#117×C₄₃	—	2	1	no	—
296	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
297	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
298	C₂×C₄²×C₄₃	—	2	1	no	—
299	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
300	#107×C₄₃	C₂³	1	1	yes	characteristic
301	#107×C₄₃	C₂³	1	1	yes	characteristic
302	#106×C₄₃	C₂³	1	1	yes	characteristic
303	#106×C₄₃	C₂³	1	1	yes	characteristic
304	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
305	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
306	#103×C₄₃	C₂³	1	1	yes	characteristic
307	#103×C₄₃	C₂³	1	1	yes	characteristic
308	#103×C₄₃	C₂³	1	1	yes	characteristic
309	#103×C₄₃	C₂³	1	1	yes	characteristic
310	#103×C₄₃	C₂³	1	1	yes	characteristic
311	#103×C₄₃	C₂³	1	1	yes	characteristic
312	#102×C₄₃	C₂³	1	1	yes	characteristic
313	#102×C₄₃	C₂³	1	1	yes	characteristic
314	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
315	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
316	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
317	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
318	C₂³×D₄₃	—	2	2	no	—
319	C₂×Q₈×C₄₃	—	2	2	no	—
320	C₂×Q₈×C₄₃	—	2	2	no	—
321	C₂×Q₈×C₄₃	—	2	1	no	—
322	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
323	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
324	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₄₃	—	2	1	no	—
326	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
337	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
338	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
339	#10621902	—	2	4	no	—
340	#10621902	—	2	4	no	—
341	#10621902	—	4	2	no	—
342	#10621902	—	4	2	no	—
343	#10621902	—	4	2	no	—
344	#10621902	—	4	2	no	—
345	#10621902	—	4	8	no	—
346	Q₈×D₄₃	—	2	4	no	—
347	Q₈×D₄₃	—	2	4	no	—
348	Q₈×D₄₃	—	4	2	no	—
349	Q₈×D₄₃	—	4	2	no	—
350	Q₈×D₄₃	—	4	8	no	—
351	D₄×D₄₃	—	4	2	no	—
352	D₄×D₄₃	—	4	2	no	—
353	#10621898	—	4	2	no	—
354	#10621898	—	4	2	no	—
355	#10621898	—	4	2	no	—
356	#10621898	—	4	2	no	—
357	#10621898	—	4	8	no	—
358	#10621898	—	4	8	no	—
359	#10621898	—	8	2	no	—
360	#10621898	—	8	2	no	—
361	C₂×D₁₇₂	—	2	1	no	—
362	C₂×D₁₇₂	—	2	1	no	—
363	C₂×D₁₇₂	—	2	1	no	—
364	C₂×D₁₇₂	—	2	1	no	—
365	C₂×D₁₇₂	—	2	2	no	—
366	C₂×D₁₇₂	—	2	2	no	—
367	C₂×D₁₇₂	—	2	2	no	—
368	C₂×D₁₇₂	—	2	2	no	—
369	C₂×D₁₇₂	—	2	2	no	—
370	C₂×D₁₇₂	—	2	2	no	—
371	C₂×D₁₇₂	—	2	2	no	—
372	C₂×D₁₇₂	—	8	2	no	—
373	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
374	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
375	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
376	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
377	C₂×D₁₇₂	C₂⁴	1	2	yes	—
378	C₂×D₁₇₂	C₂⁴	1	2	yes	—
379	C₂×C₄×D₄₃	—	2	2	no	—
380	C₂×C₄×D₄₃	—	2	2	no	—
381	C₂×C₄×D₄₃	—	2	2	no	—
382	C₂×C₄×D₄₃	—	2	2	no	—
383	C₂×C₄×D₄₃	—	2	2	no	—
384	C₂×C₄×D₄₃	—	2	2	no	—
385	C₂×C₄×D₄₃	—	2	2	no	—
386	C₂×C₄×D₄₃	—	2	2	no	—
387	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
388	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
389	C₂×Dic₈₆	—	2	1	no	—
390	C₂×Dic₈₆	—	2	2	no	—
391	C₂×Dic₈₆	—	2	2	no	—
392	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
393	C₂×Dic₈₆	C₂⁴	1	2	yes	—
394	Q₁₆×C₄₃	—	2	2	no	—
395	Q₁₆×C₄₃	—	2	2	no	—
396	SD₁₆×C₄₃	—	2	2	no	—
397	SD₁₆×C₄₃	—	2	2	no	—
398	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
399	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
400	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
401	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
402	C₄⋊C₄×C₄₃	—	2	1	no	—
403	C₄⋊C₄×C₄₃	—	2	1	no	—
404	C₄⋊C₄×C₄₃	—	2	1	no	—
405	C₄⋊C₄×C₄₃	—	2	1	no	—
406	C₄⋊C₄×C₄₃	—	2	1	no	—
407	C₄⋊C₄×C₄₃	—	2	1	no	—
408	C₄⋊C₄×C₄₃	—	2	1	no	—
409	C₄⋊C₄×C₄₃	—	2	1	no	—
410	C₄⋊C₄×C₄₃	—	2	1	no	—
411	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
412	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
413	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
414	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
415	C₂²⋊C₄×C₄₃	—	2	1	no	—
416	C₂²⋊C₄×C₄₃	—	2	1	no	—
417	C₂²⋊C₄×C₄₃	—	2	1	no	—
418	C₂²⋊C₄×C₄₃	—	2	1	no	—
419	C₂²⋊C₄×C₄₃	—	2	1	no	—
420	C₄²×C₄₃	—	2	1	no	—
421	C₄²×C₄₃	—	2	1	no	—
422	C₄²×C₄₃	—	2	1	no	—
423	C₄²×C₄₃	—	2	1	no	—
424	C₄²×C₄₃	—	2	1	no	—
425	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
426	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
427	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
428	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
429	C₂²⋊Dic₄₃	—	2	2	no	—
430	#10621885	—	4	2	no	—
431	#10621884	—	2	4	no	—
432	#10621884	—	2	4	no	—
433	#10621884	—	4	2	no	—
434	#10621883	—	4	2	no	—
435	#10621882	—	4	2	no	—
436	(C₂×D₄₃)⋊C₄	—	2	2	no	—
437	(C₂×D₄₃)⋊C₄	—	2	2	no	—
438	(C₂×D₄₃)⋊C₄	—	2	2	no	—
439	(C₂×D₄₃)⋊C₄	—	2	2	no	—
440	(C₂×D₄₃)⋊C₄	—	2	2	no	—
441	(C₂×D₄₃)⋊C₄	—	2	2	no	—
442	(C₂×D₄₃)⋊C₄	—	2	2	no	—
443	(C₂×D₄₃)⋊C₄	—	2	2	no	—
444	(C₂×D₄₃)⋊C₄	—	2	2	no	—
445	(C₂×D₄₃)⋊C₄	—	2	2	no	—
446	(C₂×D₄₃)⋊C₄	—	2	2	no	—
447	(C₂×D₄₃)⋊C₄	—	2	2	no	—
448	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
449	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
450	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
451	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
452	C₄⋊Dic₄₃	—	2	1	no	—
453	C₄⋊Dic₄₃	—	2	1	no	—
454	C₄⋊Dic₄₃	—	2	1	no	—
455	C₄⋊Dic₄₃	—	2	2	no	—
456	C₄⋊Dic₄₃	—	2	2	no	—
457	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
458	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
459	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
460	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
461	Dic₄₃⋊C₄	—	2	2	no	—
462	Dic₄₃⋊C₄	—	2	2	no	—
463	C₄×Dic₄₃	—	2	2	no	—
464	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
465	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
466	D₃₄₄	—	4	2	no	—
467	D₃₄₄	—	4	2	no	—
468	#10621873	—	4	2	no	—
469	#10621873	—	4	2	no	—
470	#10621872	—	4	2	no	—
471	#10621872	—	4	2	no	—
472	C₈×D₄₃	—	4	2	no	—
473	C₈×D₄₃	—	4	2	no	—
474	C₂³×C₄₃	—	2	1	no	—
475	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
476	C₂²×D₄₃	—	2	2	no	—
477	C₂²×D₄₃	—	2	2	no	—
478	C₂²×D₄₃	—	8	2	no	—
479	C₂²×D₄₃	—	8	2	no	—
480	C₂²×D₄₃	—	8	2	no	—
481	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
482	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
483	Q₈×C₄₃	—	2	4	no	—
484	Q₈×C₄₃	—	2	1	no	—
485	Q₈×C₄₃	—	2	1	no	—
486	Q₈×C₄₃	—	2	1	no	—
487	Q₈×C₄₃	—	2	1	no	—
488	Q₈×C₄₃	H(5,𝔽₂)	1	2	yes	—
489	Q₈×C₄₃	H(5,𝔽₂)	1	2	yes	—
490	D₄×C₄₃	—	2	1	no	—
491	D₄×C₄₃	—	2	1	no	—
492	D₄×C₄₃	—	8	1	no	—
493	C₂×C₄×C₄₃	—	2	4	no	—
494	C₂×C₄×C₄₃	—	2	1	no	—
495	C₂×C₄×C₄₃	—	2	1	no	—
496	C₂×C₄×C₄₃	—	2	2	no	—
497	C₂×C₄×C₄₃	—	2	1	no	—
498	C₂×C₄×C₄₃	—	2	1	no	—
499	C₂×C₄×C₄₃	—	2	1	no	—
500	C₂×C₄×C₄₃	—	2	1	no	—
501	C₂×C₄×C₄₃	—	2	1	no	—
502	C₂×C₄×C₄₃	—	2	1	no	—
503	C₂×C₄×C₄₃	—	2	1	no	—
504	C₂×C₄×C₄₃	—	4	1	no	—
505	C₂×C₄×C₄₃	—	4	2	no	—
506	C₂×C₄×C₄₃	—	8	1	no	—
507	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
512	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
513	C₂²⋊D₄₃	—	4	2	no	—
514	C₂²⋊D₄₃	—	4	2	no	—
515	C₂²⋊D₄₃	—	4	4	no	—
516	C₂²⋊D₄₃	—	8	2	no	—
517	C₂²⋊D₄₃	—	8	2	no	—
518	C₂²⋊D₄₃	—	8	2	no	—
519	C₂×Dic₄₃	—	2	2	no	—
520	C₂×Dic₄₃	—	2	2	no	—
521	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
522	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
523	D₁₇₂	—	2	2	no	—
524	D₁₇₂	—	2	2	no	—
525	D₁₇₂	—	2	2	no	—
526	D₁₇₂	—	2	2	no	—
527	D₁₇₂	—	2	2	no	—
528	D₁₇₂	—	2	2	no	—
529	D₁₇₂	—	4	2	no	—
530	D₁₇₂	—	4	2	no	—
531	D₁₇₂	—	4	4	no	—
532	D₁₇₂	—	4	4	no	—
533	D₁₇₂	—	4	2	no	—
534	D₁₇₂	—	4	2	no	—
535	D₁₇₂	—	8	1	no	—
536	D₁₇₂	—	8	1	no	—
537	D₁₇₂	—	8	2	no	—
538	D₁₇₂	—	8	2	no	—
539	D₁₇₂	—	8	2	no	—
540	D₁₇₂	—	8	2	no	—
541	D₁₇₂	—	8	2	no	—
542	C₄×D₄₃	—	2	2	no	—
543	C₄×D₄₃	—	2	2	no	—
544	C₄×D₄₃	—	2	2	no	—
545	C₄×D₄₃	—	2	2	no	—
546	C₄×D₄₃	—	4	4	no	—
547	C₄×D₄₃	—	4	4	no	—
548	C₄×D₄₃	—	4	4	no	—
549	C₄×D₄₃	—	4	4	no	—
550	C₄×D₄₃	—	4	4	no	—
551	C₄×D₄₃	—	8	2	no	—
552	C₄×D₄₃	—	8	2	no	—
553	C₄×D₄₃	—	8	2	no	—
554	Dic₈₆	—	2	2	no	—
555	Dic₈₆	—	2	2	no	—
556	Dic₈₆	—	4	2	no	—
557	Dic₈₆	—	4	4	no	—
558	Dic₈₆	—	4	4	no	—
559	Dic₈₆	—	4	2	no	—
560	C₈×C₄₃	—	2	1	no	—
561	C₈×C₄₃	—	2	1	no	—
562	C₈×C₄₃	—	2	1	no	—
563	C₈×C₄₃	—	2	1	no	—
564	C₄₃⋊C₈	—	2	2	no	—
565	C₄₃⋊C₈	—	2	2	no	—
566	#61659	—	43	1	no	maximal, Sylow
567	C₂²×C₄₃	—	2	1	no	—
568	C₂²×C₄₃	—	2	1	no	—
569	C₂²×C₄₃	—	2	1	no	—
570	C₂²×C₄₃	—	4	1	no	—
571	C₂²×C₄₃	—	4	1	no	—
572	C₂²×C₄₃	—	4	1	no	—
573	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
574	C₂×D₄₃	—	2	2	no	—
575	C₂×D₄₃	—	2	2	no	—
576	C₂×D₄₃	—	2	2	no	—
577	C₂×D₄₃	—	2	2	no	—
578	C₂×D₄₃	—	2	2	no	—
579	C₂×D₄₃	—	2	2	no	—
580	C₂×D₄₃	—	4	2	no	—
581	C₂×D₄₃	—	4	2	no	—
582	C₂×D₄₃	—	4	2	no	—
583	C₂×D₄₃	—	4	2	no	—
584	C₂×D₄₃	—	4	2	no	—
585	C₂×D₄₃	—	4	2	no	—
586	C₂×D₄₃	—	16	4	no	—
587	C₄×C₄₃	—	2	1	no	—
588	C₄×C₄₃	—	2	1	no	—
589	C₄×C₄₃	—	2	2	no	—
590	C₄×C₄₃	—	2	2	no	—
591	C₄×C₄₃	—	2	1	no	—
592	C₄×C₄₃	—	2	1	no	—
593	C₄×C₄₃	—	4	1	no	—
594	C₄×C₄₃	—	4	1	no	—
595	C₄×C₄₃	—	4	1	no	—
596	C₄×C₄₃	—	4	1	no	—
597	C₄×C₄₃	—	4	1	no	—
598	C₄×C₄₃	#577	1	2	yes	—
599	C₄×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
600	C₄×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
601	Dic₄₃	—	2	2	no	—
602	Dic₄₃	—	2	2	no	—
603	Dic₄₃	—	4	2	no	—
604	Dic₄₃	—	4	2	no	—
605	#3546	—	43	1	no	—
606	#3497	—	43	1	no	—
607	#3332	—	43	1	no	—
608	#3328	—	43	1	no	—
609	#3326	—	43	2	no	—
610	#3304	—	43	1	no	—
611	#3301	—	43	2	no	—
612	#3298	—	43	1	no	—
613	#3287	—	43	1	no	—
614	#3282	—	43	2	no	—
615	D₄×SD₁₆	—	43	1	no	—
616	#3278	—	43	1	no	—
617	#3275	—	43	2	no	—
618	#3274	—	43	1	no	—
619	#3212	—	43	1	no	—
620	#3207	—	43	1	no	—
621	#3204	—	43	2	no	—
622	#3198	—	43	2	no	—
623	#3108	D₄₃	1	1	yes	characteristic, complemented
624	#3103	—	43	1	no	—
625	#3013	—	43	2	no	—
626	#3010	—	43	2	no	—
627	#2979	—	43	1	no	—
628	C₂×C₄₃	—	4	1	no	—
629	C₂×C₄₃	—	8	1	no	—
630	C₂×C₄₃	#3484	1	1	yes	characteristic
631	C₂×C₄₃	C₂×#577	1	1	yes	characteristic
632	C₂×C₄₃	#3584	1	1	yes	characteristic
633	D₄₃	—	4	2	no	—
634	D₄₃	—	4	2	no	—
635	D₄₃	—	8	2	no	—
636	D₄₃	—	8	2	no	—
637	C₂×2₋¹⁺⁴	—	43	2	no	—
638	C₂×#137	—	43	2	no	—
639	C₂×AGL(1,ℤ/8)	—	43	2	no	—
640	C₂×#135	—	43	2	no	—
641	C₂²×SD₁₆	—	43	2	no	—
642	#560	—	86	2	no	—
643	#556	—	43	1	no	—
644	#553	—	43	2	no	—
645	#550	—	43	1	no	—
646	#550	—	43	1	no	—
647	#550	—	43	1	no	—
648	#550	—	86	1	no	—
649	#550	—	86	1	no	—
650	D₄×Q₈	—	43	1	no	—
651	D₄×Q₈	—	43	1	no	—
652	D₄×Q₈	—	86	1	no	—
653	#548	—	43	2	no	—
654	#548	—	43	2	no	—
655	#548	—	86	2	no	—
656	#547	—	43	1	no	—
657	#546	—	43	2	no	—
658	#546	—	86	1	no	—
659	D₄²	—	43	1	no	—
660	#542	—	86	1	no	—
661	#538	—	86	2	no	—
662	#537	—	43	2	no	—
663	#537	—	43	2	no	—
664	#537	—	86	2	no	—
665	#535	—	43	2	no	—
666	#535	—	86	1	no	—
667	#532	—	43	1	no	—
668	#532	—	43	1	no	—
669	#532	—	43	1	no	—
670	#532	—	86	1	no	—
671	#532	—	86	1	no	—
672	#529	C₂×D₄₃	1	1	yes	characteristic
673	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
674	#495	—	43	2	no	—
675	#493	—	43	1	no	—
676	#492	—	43	1	no	—
677	#488	—	43	2	no	—
678	#487	—	43	1	no	—
679	#486	—	43	1	no	—
680	#485	—	43	2	no	—
681	#483	—	43	2	no	—
682	#483	C₂×D₄₃	1	1	yes	characteristic, complemented
683	#482	—	43	2	no	—
684	#481	—	43	2	no	—
685	#481	—	43	2	no	—
686	#480	C₂×D₄₃	1	1	yes	characteristic
687	#479	C₂×D₄₃	1	1	yes	characteristic, complemented
688	#479	C₂×D₄₃	1	1	yes	characteristic, complemented
689	#475	—	43	1	no	—
690	#475	—	43	1	no	—
691	#470	—	43	2	no	—
692	#469	—	43	2	no	—
693	#469	—	43	2	no	—
694	#468	—	43	2	no	—
695	#466	—	43	2	no	—
696	#465	—	43	2	no	—
697	#465	—	43	2	no	—
698	#465	—	43	2	no	—
699	#464	C₂×D₄₃	1	1	yes	characteristic
700	#464	C₂×D₄₃	1	1	yes	characteristic
701	#463	—	43	2	no	—
702	#463	—	43	2	no	—
703	#462	—	43	1	no	—
704	#461	—	43	1	no	—
705	#460	—	43	1	no	—
706	#460	—	43	1	no	—
707	#460	—	43	1	no	—
708	#459	—	43	1	no	—
709	#452	—	43	2	no	—
710	#452	—	43	2	no	—
711	#452	—	43	2	no	—
712	#451	—	43	2	no	—
713	#451	C₂×D₄₃	1	1	yes	characteristic, complemented
714	#450	—	43	2	no	—
715	#449	—	43	2	no	—
716	#449	—	43	2	no	—
717	#449	—	43	2	no	—
718	#449	—	43	2	no	—
719	#449	—	43	2	no	—
720	#449	—	43	2	no	—
721	#449	—	43	2	no	—
722	#448	—	43	2	no	—
723	#448	—	43	2	no	—
724	#448	—	43	2	no	—
725	#448	—	43	2	no	—
726	#448	C₂×D₄₃	1	1	yes	characteristic
727	#447	—	43	2	no	—
728	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
729	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
730	C₄×SD₁₆	—	43	2	no	—
731	C₄×SD₁₆	—	43	2	no	—
732	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
733	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
734	#436	—	43	2	no	—
735	#436	—	43	1	no	—
736	#436	—	43	1	no	—
737	C₈×D₄	—	43	2	no	—
738	C₈×D₄	—	43	1	no	—
739	C₈×D₄	—	43	1	no	—
740	#431	—	43	1	no	—
741	#431	C₂×D₄₃	1	1	yes	characteristic, complemented
742	#419	—	43	2	no	—
743	#417	—	43	2	no	—
744	#416	—	43	2	no	—
745	C₂×#103	—	43	2	no	—
746	#408	—	43	2	no	—
747	#408	—	43	2	no	—
748	C₄₃	#61659	1	1	yes	characteristic, complemented, Sylow
749	2₋¹⁺⁴	—	172	4	no	—
750	2₋¹⁺⁴	—	172	4	no	—
751	C₂×#41	—	43	2	no	—
752	C₂×#41	—	43	2	no	—
753	C₂×#41	—	43	2	no	—
754	C₂×#41	—	43	2	no	—
755	C₂×#41	—	43	2	no	—
756	C₂×#41	—	86	1	no	—
757	C₂×#41	—	86	2	no	—
758	C₂×#41	—	86	2	no	—
759	C₂×#41	—	86	2	no	—
760	C₂×#41	—	86	1	no	—
761	C₂²×Q₈	—	43	2	no	—
762	C₂²×Q₈	—	43	2	no	—
763	C₂²×Q₈	—	86	2	no	—
764	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
765	C₂²×D₄	—	43	2	no	—
766	C₂²×D₄	—	86	1	no	—
767	#137	—	172	4	no	—
768	AGL(1,ℤ/8)	—	172	4	no	—
769	#135	—	172	4	no	—
770	C₂×Q₁₆	—	43	2	no	—
771	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
772	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
773	C₂×SD₁₆	—	43	2	no	—
774	C₂×SD₁₆	—	43	2	no	—
775	C₂×SD₁₆	—	43	2	no	—
776	C₂×SD₁₆	—	43	2	no	—
777	C₂×SD₁₆	—	43	2	no	—
778	C₂×SD₁₆	—	43	2	no	—
779	C₂×SD₁₆	—	172	4	no	—
780	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
781	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
782	C₂×D₈	—	43	2	no	—
783	C₂×D₈	—	43	2	no	—
784	C₂×D₈	—	43	2	no	—
785	C₂×M₁₆	—	43	2	no	—
786	C₂×M₁₆	—	43	2	no	—
787	C₂²×C₈	—	43	2	no	—
788	C₂²×C₈	—	43	2	no	—
789	C₄⋊Q₈	—	43	1	no	—
790	C₄⋊Q₈	—	43	1	no	—
791	C₄⋊Q₈	—	43	1	no	—
792	C₄⋊Q₈	—	86	1	no	—
793	C₄⋊Q₈	—	86	1	no	—
794	#127	—	43	1	no	—
795	#127	—	43	1	no	—
796	#127	—	43	1	no	—
797	#127	—	86	1	no	—
798	#127	—	86	1	no	—
799	#127	—	86	1	no	—
800	#127	—	86	2	no	—
801	#126	—	2	1	no	—
802	#126	—	86	2	no	—
803	#126	—	86	2	no	—
804	#125	C₂²×D₄₃	1	1	yes	characteristic
805	#124	—	43	2	no	—
806	#124	—	43	2	no	—
807	#124	—	86	2	no	—
808	#124	—	86	2	no	—
809	#124	—	86	1	no	—
810	#124	—	86	2	no	—
811	#124	—	86	1	no	—
812	#124	C₂²×D₄₃	1	1	yes	characteristic
813	#123	—	2	1	no	—
814	#123	—	86	2	no	—
815	#123	—	86	2	no	—
816	#123	—	86	2	no	—
817	C₂²⋊Q₈	—	43	2	no	—
818	C₂²⋊Q₈	—	43	2	no	—
819	C₂²⋊Q₈	—	43	2	no	—
820	C₂²⋊Q₈	—	86	2	no	—
821	C₂²⋊Q₈	—	86	2	no	—
822	C₂²⋊Q₈	—	86	2	no	—
823	C₂²⋊Q₈	—	86	2	no	—
824	C₂²⋊Q₈	—	86	2	no	—
825	C₂²⋊Q₈	—	86	2	no	—
826	C₂²⋊Q₈	—	86	1	no	—
827	C₂²⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
828	#121	—	43	1	no	—
829	#121	—	43	1	no	—
830	#121	—	43	2	no	—
831	#121	—	43	2	no	—
832	#121	—	43	2	no	—
833	#121	—	43	2	no	—
834	#121	—	43	2	no	—
835	#121	—	43	2	no	—
836	#121	—	43	2	no	—
837	#121	—	86	2	no	—
838	#121	—	86	2	no	—
839	#121	—	86	2	no	—
840	#121	—	86	2	no	—
841	#121	—	86	2	no	—
842	#121	—	86	2	no	—
843	#121	—	86	2	no	—
844	#121	—	86	2	no	—
845	#121	—	86	2	no	—
846	#121	—	86	2	no	—
847	#121	—	86	2	no	—
848	#121	—	86	1	no	—
849	#121	—	86	2	no	—
850	#121	—	86	2	no	—
851	#121	—	86	1	no	—
852	#121	—	86	1	no	—
853	#121	—	86	1	no	—
854	#121	C₂²×D₄₃	1	1	yes	characteristic
855	#120	—	86	2	no	—
856	#120	—	86	2	no	—
857	#120	—	86	2	no	—
858	#120	—	86	2	no	—
859	C₄×Q₈	—	2	1	no	—
860	C₄×Q₈	—	2	1	no	—
861	C₄×Q₈	—	86	1	no	—
862	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
863	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
864	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
865	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
866	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
867	C₄×D₄	—	2	1	no	—
868	C₄×D₄	—	43	1	no	—
869	C₄×D₄	—	43	2	no	—
870	C₄×D₄	—	43	1	no	—
871	C₄×D₄	—	43	2	no	—
872	C₄×D₄	—	86	2	no	—
873	C₄×D₄	—	86	2	no	—
874	C₄×D₄	—	86	1	no	—
875	C₄×D₄	—	86	1	no	—
876	C₄×D₄	—	86	1	no	—
877	C₄×D₄	—	86	1	no	—
878	C₄×D₄	—	86	1	no	—
879	C₄×D₄	—	86	2	no	—
880	C₄×D₄	—	86	1	no	—
881	C₄×D₄	—	86	1	no	—
882	C₄×D₄	—	86	1	no	—
883	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
884	#117	—	2	1	no	—
885	#117	—	43	2	no	—
886	C₂×C₄⋊C₄	—	2	1	no	—
887	C₂×C₄⋊C₄	—	43	2	no	—
888	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
889	C₂×C₂²⋊C₄	—	86	2	no	—
890	C₂×C₄²	—	2	1	no	—
891	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
892	#107	C₂²×D₄₃	1	1	yes	characteristic
893	#107	C₂²×D₄₃	1	1	yes	characteristic
894	#106	—	43	2	no	—
895	#106	—	43	2	no	—
896	#106	C₂²×D₄₃	1	1	yes	characteristic
897	#106	C₂²×D₄₃	1	1	yes	characteristic
898	C₄⋊C₈	—	43	1	no	—
899	C₄⋊C₈	—	43	1	no	—
900	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
901	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
902	#103	—	43	2	no	—
903	#103	—	43	2	no	—
904	#103	—	43	2	no	—
905	#103	—	43	2	no	—
906	#103	—	43	2	no	—
907	#103	—	43	2	no	—
908	#103	C₂²×D₄₃	1	1	yes	characteristic
909	#103	C₂²×D₄₃	1	1	yes	characteristic
910	#103	C₂²×D₄₃	1	1	yes	characteristic
911	#103	C₂²×D₄₃	1	1	yes	characteristic
912	#103	C₂²×D₄₃	1	1	yes	characteristic
913	#103	C₂²×D₄₃	1	1	yes	characteristic
914	#102	—	43	2	no	—
915	#102	—	43	2	no	—
916	#102	—	43	2	no	—
917	#102	—	43	2	no	—
918	#102	—	43	2	no	—
919	#102	—	43	2	no	—
920	#102	C₂²×D₄₃	1	1	yes	characteristic
921	#102	C₂²×D₄₃	1	1	yes	characteristic
922	C₂²⋊C₈	—	43	2	no	—
923	C₂²⋊C₈	—	43	2	no	—
924	C₂²⋊C₈	—	43	2	no	—
925	C₂²⋊C₈	—	43	2	no	—
926	C₂²⋊C₈	—	43	2	no	—
927	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
928	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
929	C₄×C₈	—	43	2	no	—
930	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
931	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
932	C₂⁴	—	86	2	no	—
933	#41	—	86	4	no	—
934	#41	—	86	4	no	—
935	#41	—	344	2	no	—
936	#41	—	344	2	no	—
937	#41	—	172	2	no	—
938	#41	—	172	2	no	—
939	#41	—	172	2	no	—
940	#41	—	172	2	no	—
941	#41	—	172	8	no	—
942	#41	—	172	8	no	—
943	#41	—	172	2	no	—
944	#41	—	172	2	no	—
945	#41	—	172	2	no	—
946	#41	—	172	2	no	—
947	#41	—	172	8	no	—
948	C₂×Q₈	—	2	2	no	—
949	C₂×Q₈	—	2	2	no	—
950	C₂×Q₈	—	2	1	no	—
951	C₂×Q₈	—	43	2	no	—
952	C₂×Q₈	—	43	2	no	—
953	C₂×Q₈	—	86	2	no	—
954	C₂×Q₈	—	86	2	no	—
955	C₂×Q₈	—	86	1	no	—
956	C₂×Q₈	—	86	4	no	—
957	C₂×Q₈	—	86	4	no	—
958	C₂×Q₈	—	172	2	no	—
959	C₂×Q₈	—	172	2	no	—
960	C₂×Q₈	—	172	8	no	—
961	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
962	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
963	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
964	C₂×D₄	—	2	1	no	—
965	C₂×D₄	—	43	2	no	—
966	C₂×D₄	—	43	2	no	—
967	C₂×D₄	—	43	1	no	—
968	C₂×D₄	—	43	1	no	—
969	C₂×D₄	—	43	2	no	—
970	C₂×D₄	—	43	2	no	—
971	C₂×D₄	—	43	2	no	—
972	C₂×D₄	—	43	2	no	—
973	C₂×D₄	—	86	2	no	—
974	C₂×D₄	—	86	2	no	—
975	C₂×D₄	—	86	2	no	—
976	C₂×D₄	—	86	2	no	—
977	C₂×D₄	—	86	2	no	—
978	C₂×D₄	—	86	2	no	—
979	C₂×D₄	—	86	2	no	—
980	C₂×D₄	—	86	2	no	—
981	C₂×D₄	—	86	2	no	—
982	C₂×D₄	—	86	2	no	—
983	C₂×D₄	—	86	2	no	—
984	C₂×D₄	—	86	1	no	—
985	C₂×D₄	—	86	1	no	—
986	C₂×D₄	—	86	1	no	—
987	C₂×D₄	—	86	1	no	—
988	C₂×D₄	—	344	2	no	—
989	C₂×D₄	—	172	2	no	—
990	C₂×D₄	—	172	2	no	—
991	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
992	C₂²×C₄	—	2	1	no	—
993	C₂²×C₄	—	2	1	no	—
994	C₂²×C₄	—	2	1	no	—
995	C₂²×C₄	—	43	2	no	—
996	C₂²×C₄	—	43	2	no	—
997	C₂²×C₄	—	86	2	no	—
998	C₂²×C₄	—	86	2	no	—
999	C₂²×C₄	—	86	2	no	—
1000	C₂²×C₄	—	86	2	no	—
1001	C₂²×C₄	—	86	2	no	—
1002	C₂²×C₄	—	86	2	no	—
1003	C₂²×C₄	—	86	2	no	—
1004	C₂²×C₄	—	86	2	no	—
1005	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
1006	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
1007	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
1008	Q₁₆	—	2	2	no	—
1009	Q₁₆	—	2	2	no	—
1010	Q₁₆	—	172	2	no	—
1011	SD₁₆	—	2	2	no	—
1012	SD₁₆	—	2	2	no	—
1013	SD₁₆	—	86	4	no	—
1014	SD₁₆	—	86	4	no	—
1015	SD₁₆	—	172	2	no	—
1016	SD₁₆	—	172	2	no	—
1017	SD₁₆	—	172	2	no	—
1018	SD₁₆	—	172	2	no	—
1019	D₈	—	172	2	no	—
1020	D₈	—	172	2	no	—
1021	D₈	—	172	2	no	—
1022	M₁₆	—	172	2	no	—
1023	M₁₆	—	172	2	no	—
1024	C₂×C₈	—	43	2	no	—
1025	C₂×C₈	—	43	2	no	—
1026	C₂×C₈	—	172	2	no	—
1027	C₂×C₈	—	172	2	no	—
1028	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
1029	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
1030	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
1031	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
1032	C₄⋊C₄	—	2	1	no	—
1033	C₄⋊C₄	—	2	1	no	—
1034	C₄⋊C₄	—	2	1	no	—
1035	C₄⋊C₄	—	2	1	no	—
1036	C₄⋊C₄	—	2	1	no	—
1037	C₄⋊C₄	—	2	1	no	—
1038	C₄⋊C₄	—	2	1	no	—
1039	C₄⋊C₄	—	2	1	no	—
1040	C₄⋊C₄	—	2	1	no	—
1041	C₄⋊C₄	—	43	1	no	—
1042	C₄⋊C₄	—	43	1	no	—
1043	C₄⋊C₄	—	43	2	no	—
1044	C₄⋊C₄	—	43	2	no	—
1045	C₄⋊C₄	—	86	2	no	—
1046	C₄⋊C₄	—	86	2	no	—
1047	C₄⋊C₄	—	86	2	no	—
1048	C₄⋊C₄	—	86	2	no	—
1049	C₄⋊C₄	—	86	1	no	—
1050	C₄⋊C₄	—	86	1	no	—
1051	C₄⋊C₄	—	86	1	no	—
1052	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1053	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1054	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1055	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1056	C₂²⋊C₄	—	2	1	no	—
1057	C₂²⋊C₄	—	2	1	no	—
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	2	1	no	—
1060	C₂²⋊C₄	—	2	1	no	—
1061	C₂²⋊C₄	—	43	2	no	—
1062	C₂²⋊C₄	—	43	2	no	—
1063	C₂²⋊C₄	—	43	2	no	—
1064	C₂²⋊C₄	—	43	2	no	—
1065	C₂²⋊C₄	—	86	2	no	—
1066	C₂²⋊C₄	—	86	2	no	—
1067	C₂²⋊C₄	—	86	2	no	—
1068	C₂²⋊C₄	—	86	2	no	—
1069	C₂²⋊C₄	—	86	2	no	—
1070	C₂²⋊C₄	—	86	2	no	—
1071	C₂²⋊C₄	—	86	2	no	—
1072	C₂²⋊C₄	—	86	2	no	—
1073	C₂²⋊C₄	—	86	2	no	—
1074	C₂²⋊C₄	—	86	2	no	—
1075	C₂²⋊C₄	—	86	2	no	—
1076	C₂²⋊C₄	—	86	2	no	—
1077	C₂²⋊C₄	—	86	2	no	—
1078	C₄²	—	2	1	no	—
1079	C₄²	—	2	1	no	—
1080	C₄²	—	2	1	no	—
1081	C₄²	—	2	1	no	—
1082	C₄²	—	2	1	no	—
1083	C₄²	—	86	2	no	—
1084	C₄²	D₄×D₄₃	1	1	yes	characteristic
1085	C₄²	D₄×D₄₃	1	1	yes	characteristic
1086	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1087	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1088	C₂³	—	2	1	no	—
1089	C₂³	—	43	2	no	—
1090	C₂³	—	43	2	no	—
1091	C₂³	—	86	2	no	—
1092	C₂³	—	86	2	no	—
1093	C₂³	—	344	2	no	—
1094	C₂³	—	344	2	no	—
1095	C₂³	—	344	2	no	—
1096	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1097	Q₈	—	2	4	no	—
1098	Q₈	—	2	1	no	—
1099	Q₈	—	2	1	no	—
1100	Q₈	—	2	1	no	—
1101	Q₈	—	2	1	no	—
1102	Q₈	—	86	2	no	—
1103	Q₈	—	86	2	no	—
1104	Q₈	—	172	2	no	—
1105	Q₈	—	172	4	no	—
1106	Q₈	—	172	4	no	—
1107	Q₈	—	172	2	no	—
1108	Q₈	#13063371	1	2	yes	—
1109	Q₈	#13063371	1	2	yes	—
1110	D₄	—	2	1	no	—
1111	D₄	—	2	1	no	—
1112	D₄	—	8	1	no	—
1113	D₄	—	86	2	no	—
1114	D₄	—	86	2	no	—
1115	D₄	—	86	2	no	—
1116	D₄	—	86	2	no	—
1117	D₄	—	86	2	no	—
1118	D₄	—	86	2	no	—
1119	D₄	—	344	1	no	—
1120	D₄	—	344	1	no	—
1121	D₄	—	344	2	no	—
1122	D₄	—	344	2	no	—
1123	D₄	—	344	2	no	—
1124	D₄	—	344	2	no	—
1125	D₄	—	344	2	no	—
1126	D₄	—	344	2	no	—
1127	D₄	—	344	2	no	—
1128	D₄	—	344	2	no	—
1129	D₄	—	172	2	no	—
1130	D₄	—	172	2	no	—
1131	D₄	—	172	4	no	—
1132	D₄	—	172	4	no	—
1133	D₄	—	172	2	no	—
1134	D₄	—	172	2	no	—
1135	D₄	—	172	4	no	—
1136	D₄	—	172	2	no	—
1137	D₄	—	172	2	no	—
1138	C₂×C₄	—	2	4	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	2	1	no	—
1141	C₂×C₄	—	2	2	no	—
1142	C₂×C₄	—	2	1	no	—
1143	C₂×C₄	—	2	1	no	—
1144	C₂×C₄	—	2	1	no	—
1145	C₂×C₄	—	2	1	no	—
1146	C₂×C₄	—	2	1	no	—
1147	C₂×C₄	—	2	1	no	—
1148	C₂×C₄	—	2	1	no	—
1149	C₂×C₄	—	4	1	no	—
1150	C₂×C₄	—	4	2	no	—
1151	C₂×C₄	—	8	1	no	—
1152	C₂×C₄	—	43	2	no	—
1153	C₂×C₄	—	43	2	no	—
1154	C₂×C₄	—	86	2	no	—
1155	C₂×C₄	—	86	2	no	—
1156	C₂×C₄	—	86	2	no	—
1157	C₂×C₄	—	86	2	no	—
1158	C₂×C₄	—	86	2	no	—
1159	C₂×C₄	—	86	2	no	—
1160	C₂×C₄	—	344	2	no	—
1161	C₂×C₄	—	344	2	no	—
1162	C₂×C₄	—	344	2	no	—
1163	C₂×C₄	—	172	4	no	—
1164	C₂×C₄	—	172	4	no	—
1165	C₂×C₄	—	172	4	no	—
1166	C₂×C₄	—	172	4	no	—
1167	C₂×C₄	—	172	4	no	—
1168	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1169	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1170	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1171	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1172	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1173	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1174	C₈	—	2	1	no	—
1175	C₈	—	2	1	no	—
1176	C₈	—	2	1	no	—
1177	C₈	—	2	1	no	—
1178	C₈	—	86	2	no	—
1179	C₈	—	86	2	no	—
1180	C₂²	—	2	1	no	—
1181	C₂²	—	2	1	no	—
1182	C₂²	—	2	1	no	—
1183	C₂²	—	4	1	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	1	no	—
1186	C₂²	—	86	2	no	—
1187	C₂²	—	86	2	no	—
1188	C₂²	—	86	2	no	—
1189	C₂²	—	86	2	no	—
1190	C₂²	—	86	2	no	—
1191	C₂²	—	86	2	no	—
1192	C₂²	—	172	2	no	—
1193	C₂²	—	172	2	no	—
1194	C₂²	—	172	2	no	—
1195	C₂²	—	172	2	no	—
1196	C₂²	—	172	2	no	—
1197	C₂²	—	172	2	no	—
1198	C₂²	—	688	4	no	—
1199	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1200	C₄	—	2	1	no	—
1201	C₄	—	2	1	no	—
1202	C₄	—	2	1	no	—
1203	C₄	—	2	2	no	—
1204	C₄	—	2	2	no	—
1205	C₄	—	2	1	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	4	1	no	—
1210	C₄	—	4	1	no	—
1211	C₄	—	86	2	no	—
1212	C₄	—	86	2	no	—
1213	C₄	—	172	2	no	—
1214	C₄	—	172	2	no	—
1215	C₄	#14583708	1	2	yes	—
1216	C₄	C₂×#13063371	1	1	yes	characteristic
1217	C₄	C₂×#13063371	1	1	yes	characteristic
1218	C₂	—	4	1	no	—
1219	C₂	—	8	1	no	—
1220	C₂	—	344	2	no	—
1221	C₂	—	344	2	no	—
1222	C₂	—	172	2	no	—
1223	C₂	—	172	2	no	—
1224	C₂	#19148228	1	1	yes	characteristic
1225	C₂	C₂×#14583708	1	1	yes	characteristic
1226	C₂	#19149364	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3108	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3108	D₄₃
hypocenter	C₄₃	#61659
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3108

Complements

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

N	H ≅ G/N	type
1. #19148969	C₂	semidirect
2. #19148366	C₂	semidirect
3. #19146924	C₂	semidirect
4. #19146880	C₂	semidirect
5. #19146845	C₂	semidirect
6. #19146536	C₂	semidirect
7. #19146494	C₂	semidirect
8. #19146462	C₂	semidirect
9. #19146354	C₂	semidirect
10. #19146297	C₂	semidirect
11. SD₁₆×D₁₇₂	C₂	semidirect
12. #19146262	C₂	semidirect
13. #19146221	C₂	semidirect
14. #19146216	C₂	semidirect
15. #19145567	C₂	semidirect
16. #19145530	C₂	semidirect
17. #19145505	C₂	semidirect
18. #19145454	C₂	semidirect
19. #19144626	C₂	semidirect
20. #19143911	C₂	semidirect
21. #19143876	C₂	semidirect
22. #19143661	C₂	semidirect
23. C₄₃×#3108	C₂	semidirect
24. C₂×#13063373	C₂²	semidirect
25. C₂×#13063357	C₂²	semidirect
27. C₂×#13063348	C₂²	semidirect
35. #14583571	C₂²	semidirect
39. Q₈×D₁₇₂	C₂²	semidirect
41. #14583561	C₂²	semidirect
42. #14583561	C₂²	semidirect
50. #14583480	C₂²	semidirect
58. #14583449	C₂²	semidirect
62. #14583256	C₂²	semidirect
63. #14583250	C₂²	semidirect
64. #14583246	C₂²	semidirect
65. #14583242	C₂²	semidirect
66. #14583231	C₂²	semidirect
67. #14583226	C₂²	semidirect
68. #14583219	C₂²	semidirect
69. #14583217	C₂²	semidirect
70. #14583184	C₂²	semidirect
71. #14583184	C₂²	semidirect
72. #14583156	C₂²	semidirect
75. #14583146	C₂²	semidirect
76. #14583136	C₂²	semidirect
77. #14583131	C₂²	semidirect
80. #14583115	C₂²	semidirect
81. #14583115	C₂²	semidirect
82. #14583109	C₂²	semidirect
86. #14583099	C₂²	semidirect
88. #14583064	C₂²	semidirect
89. #14583060	C₂²	semidirect
90. #14583059	C₂²	semidirect
91. #14583053	C₂²	semidirect
94. #14583047	C₂²	semidirect
95. #14583047	C₂²	semidirect
96. #14583046	C₂²	semidirect
97. #14583046	C₂²	semidirect
101. #14583039	C₂²	semidirect
102. #14583038	C₂²	semidirect
105. C₄×#10621884	C₂²	semidirect
106. C₄×#10621884	C₂²	semidirect
108. #14582978	C₂²	semidirect
109. #14582976	C₂²	semidirect
111. C₈×D₁₇₂	C₂²	semidirect
112. #14582964	C₂²	semidirect
113. #14582952	C₂²	semidirect
114. #14582906	C₂²	semidirect
115. #14582899	C₂²	semidirect
116. #14582894	C₂²	semidirect
117. #103×D₄₃	C₂²	semidirect
118. #14582864	C₂²	semidirect
119. #14582864	C₂²	semidirect
121. C₂×C₄×Q₈×C₄₃	C₂²	semidirect
122. C₄₃×#483	C₂²	semidirect
124. C₄₃×#479	C₂²	semidirect
125. C₄₃×#479	C₂²	semidirect
128. C₄₃×#451	C₂²	semidirect
130. C₄×Q₁₆×C₄₃	C₂²	semidirect
131. C₄×Q₁₆×C₄₃	C₂²	semidirect
134. C₄₃×#431	C₂²	semidirect
623. #3108	D₄₃	semidirect
673. C₂×C₄×Q₈	C₂×D₄₃	semidirect
682. #483	C₂×D₄₃	semidirect
687. #479	C₂×D₄₃	semidirect
688. #479	C₂×D₄₃	semidirect
713. #451	C₂×D₄₃	semidirect
728. C₄×Q₁₆	C₂×D₄₃	semidirect
729. C₄×Q₁₆	C₂×D₄₃	semidirect
741. #431	C₂×D₄₃	semidirect
748. C₄₃	#61659	semidirect

Maximal subgroups

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

subgroup	index
#19148969	2
#19148366	2
#19146924	2
#19146880	2
#19146845	2
#19146536	2
#19146494	2
#19146462	2
#19146354	2
#19146297	2
SD₁₆×D₁₇₂	2
#19146262	2
#19146221	2
#19146216	2
#19145567	2
#19145530	2
#19145505	2
#19145454	2
#19144626	2
#19143911	2
#19143876	2
#19143661	2
C₄₃×#3108	2
#61659	43