Subgroups — #25966605

Order 11008.

1978 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148009	C₂	1	2	yes	maximal, complemented
2	#19145285	C₂	1	2	yes	maximal, complemented
3	#19145281	C₂	1	2	yes	maximal, complemented
4	#19145242	C₂	1	1	yes	maximal, characteristic, complemented
5	#19145238	C₂	1	1	yes	maximal, characteristic, complemented
6	#19145237	C₂	1	1	yes	maximal, characteristic, complemented
7	#19145227	C₂	1	1	yes	maximal, characteristic, complemented
8	#19145188	C₂	1	2	yes	maximal, complemented
9	#19145184	C₂	1	2	yes	maximal, complemented
10	#19145171	C₂	1	1	yes	maximal, characteristic, complemented
11	#19145165	C₂	1	1	yes	maximal, characteristic, complemented
12	#19145163	C₂	1	1	yes	maximal, characteristic, complemented
13	#19145128	C₂	1	1	yes	maximal, characteristic, complemented
14	#19145075	C₂	1	1	yes	maximal, characteristic, complemented
15	#19144944	C₂	1	2	yes	maximal, complemented
16	#19144274	C₂	1	2	yes	maximal, complemented
17	#19144260	C₂	1	1	yes	maximal, characteristic, complemented
18	#19144238	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#13063349	C₂	1	2	yes	maximal, complemented
20	C₄×#13063344	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×D₈×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#13063331	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3169	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063349	C₂²	1	2	yes	—
25	C₂×#13063344	C₂²	1	1	yes	characteristic
26	C₂×D₈×D₄₃	C₂²	1	1	yes	characteristic
27	C₂×#13063331	C₂²	1	1	yes	characteristic
28	C₂×#13063331	C₂²	1	1	yes	characteristic
29	#14583526	C₂²	1	2	yes	—
30	#14583523	C₂²	1	2	yes	complemented
31	#14583516	C₂²	1	2	yes	complemented
32	#14583513	—	2	2	no	—
33	#14583503	C₂²	1	2	yes	complemented
34	#14583502	C₂²	1	2	yes	complemented
35	#14583499	—	2	2	no	—
36	#14583483	—	2	2	no	—
37	#14583481	—	2	2	no	—
38	#14583478	C₂²	1	2	yes	—
39	#14583465	C₂²	1	2	yes	—
40	#14583462	C₂²	1	2	yes	—
41	#14583446	C₂²	1	2	yes	complemented
42	#14583445	—	2	2	no	—
43	#14583433	C₂²	1	2	yes	complemented
44	#14583431	C₂²	1	2	yes	complemented
45	#14583429	—	2	2	no	—
46	#14583408	—	2	2	no	—
47	#14583406	—	2	2	no	—
48	C₄×#10621898	C₂²	1	1	yes	characteristic
49	C₄×#10621900	C₂²	1	2	yes	—
50	C₄×D₄×D₄₃	C₂²	1	2	yes	—
51	#14583307	C₂²	1	2	yes	complemented
52	#14583305	C₂²	1	2	yes	complemented
53	#14583303	C₂²	1	1	yes	characteristic, complemented
54	#14583301	C₂²	1	1	yes	characteristic, complemented
55	#14583300	C₂²	1	1	yes	characteristic, complemented
56	#14583287	C₂²	1	2	yes	—
57	#14583286	C₂²	1	2	yes	—
58	#14583283	C₂²	1	1	yes	characteristic
59	#14583282	C₂²	1	1	yes	characteristic
60	#14583274	C₂²	1	1	yes	characteristic
61	#14583263	C₂²	1	2	yes	complemented
62	#14583262	C₂²	1	2	yes	complemented
63	#14583261	C₂²	1	2	yes	complemented
64	#14583257	C₂²	1	2	yes	complemented
65	#14583254	C₂²	1	2	yes	complemented
66	#14583252	C₂²	1	2	yes	complemented
67	#14583244	C₂²	1	2	yes	complemented
68	#14583151	C₂²	1	2	yes	—
69	#14583150	C₂²	1	2	yes	—
70	#14583150	C₂²	1	2	yes	complemented
71	#14583149	C₂²	1	2	yes	complemented
72	#14583146	C₂²	1	2	yes	complemented
73	#14583144	C₂²	1	2	yes	complemented
74	#14583143	C₂²	1	2	yes	complemented
75	#14583143	C₂²	1	2	yes	complemented
76	#14583141	C₂²	1	1	yes	characteristic, complemented
77	#14583140	C₂²	1	1	yes	characteristic, complemented
78	#14583136	C₂²	1	1	yes	characteristic
79	#14583135	C₂²	1	1	yes	characteristic
80	#14583134	C₂²	1	2	yes	complemented
81	#14583132	C₂²	1	1	yes	characteristic
82	#14583132	C₂²	1	1	yes	characteristic, complemented
83	#14583128	C₂²	1	2	yes	complemented
84	#14583127	C₂²	1	2	yes	complemented
85	#14583011	C₂²	1	2	yes	complemented
86	#14583008	C₂²	1	2	yes	complemented
87	#14582998	C₂²	1	2	yes	complemented
88	#14582996	C₂²	1	2	yes	complemented
89	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
90	#14582993	C₂²	1	1	yes	characteristic, complemented
91	#14582990	C₂²	1	2	yes	complemented
92	C₄×#10621873	C₂²	1	2	yes	complemented
93	C₄×#10621883	C₂²	1	2	yes	complemented
94	C₄×#10621883	C₂²	1	2	yes	complemented
95	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
96	D₈×Dic₄₃	C₂²	1	1	yes	characteristic
97	D₈×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
98	#14582981	C₂²	1	1	yes	characteristic
99	C₄×#10621882	C₂²	1	2	yes	—
100	C₄×#10621882	C₂²	1	2	yes	complemented
101	#14582979	C₂²	1	2	yes	—
102	#14582940	C₂²	1	2	yes	—
103	#14582936	C₂²	1	1	yes	characteristic
104	#107×D₄₃	C₂²	1	1	yes	characteristic
105	#14582902	C₂²	1	2	yes	—
106	#14582897	C₂²	1	2	yes	—
107	#14582892	C₂²	1	2	yes	—
108	#102×D₄₃	C₂²	1	2	yes	—
109	#14582854	C₂²	1	1	yes	characteristic, complemented
110	#14582854	C₂²	1	1	yes	characteristic, complemented
111	#14582853	C₂²	1	1	yes	characteristic
112	#14582853	C₂²	1	1	yes	characteristic
113	#14582853	C₂²	1	1	yes	characteristic, complemented
114	#14582853	C₂²	1	1	yes	characteristic, complemented
115	C₄×#10621877	C₂²	1	1	yes	characteristic, complemented
116	C₄×#10621872	C₂²	1	1	yes	characteristic
117	C₄×#10621872	C₂²	1	1	yes	characteristic, complemented
118	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic, complemented
120	C₄₃×#532	C₂²	1	2	yes	complemented
121	C₄₃×#500	C₂²	1	1	yes	characteristic, complemented
122	C₄₃×#493	C₂²	1	1	yes	characteristic
123	C₄₃×#486	C₂²	1	2	yes	complemented
124	C₄₃×#466	C₂²	1	1	yes	characteristic
125	C₄₃×#466	C₂²	1	1	yes	characteristic, complemented
126	C₄₃×#466	C₂²	1	2	yes	complemented
127	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
128	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
129	C₄×D₈×C₄₃	C₂²	1	2	yes	complemented
130	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
131	C₂×#10621898	—	2	2	no	—
132	C₂×#10621898	C₂³	1	1	yes	characteristic
133	C₂×#10621900	C₂³	1	2	yes	—
134	C₂×D₄×D₄₃	C₂³	1	2	yes	—
135	C₂²×C₄×D₄₃	—	2	2	no	—
136	#13063349	—	2	8	no	—
137	#13063344	—	2	4	no	—
138	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
139	C₂×#10621873	C₂³	1	2	yes	—
140	C₂×#10621883	C₂³	1	2	yes	—
141	C₂×#10621883	C₂³	1	2	yes	—
142	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
143	C₂×#10621882	C₂³	1	2	yes	—
144	C₂×#10621882	C₂³	1	2	yes	—
145	D₈×D₄₃	—	2	4	no	—
146	#13063331	—	2	4	no	—
147	#13063331	—	2	4	no	—
148	C₂×#10621877	C₂³	1	1	yes	characteristic
149	C₂×#10621877	C₂³	1	1	yes	characteristic
150	C₂×#10621872	C₂³	1	1	yes	characteristic
151	C₂×#10621872	C₂³	1	1	yes	characteristic
152	C₂×#10621872	C₂³	1	1	yes	characteristic
153	C₂×#10621872	C₂³	1	1	yes	characteristic
154	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
155	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
156	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
157	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
158	#13063324	C₂³	1	2	yes	—
159	#13063323	—	2	2	no	—
160	#13063321	—	2	2	no	—
161	#13063321	C₂³	1	2	yes	—
162	#13063320	—	2	2	no	—
163	#13063319	—	2	2	no	—
164	#13063318	—	2	2	no	—
165	#13063318	—	2	2	no	—
166	#13063317	C₂³	1	2	yes	—
167	#13063316	C₂³	1	2	yes	—
168	#13063315	—	2	2	no	—
169	#13063314	—	2	2	no	—
170	#13063313	C₂³	1	2	yes	—
171	#13063312	—	2	2	no	—
172	#13063312	C₂³	1	2	yes	—
173	#13063311	—	2	2	no	—
174	#13063311	—	2	2	no	—
175	#13063310	—	2	2	no	—
176	#13063309	—	2	2	no	—
177	#13063308	—	2	2	no	—
178	#13063307	—	2	2	no	—
179	#13063307	—	2	2	no	—
180	#13063306	—	2	2	no	—
181	#13063306	—	2	2	no	—
182	#13063306	—	2	2	no	—
183	#13063305	C₂³	1	2	yes	—
184	#13063304	C₂³	1	2	yes	—
185	#13063303	—	2	2	no	—
186	#13063302	—	2	2	no	—
187	#13063302	—	2	2	no	—
188	#13063301	—	2	2	no	—
189	#13063301	—	2	2	no	—
190	#13063300	C₂³	1	2	yes	—
191	#13063299	C₂³	1	2	yes	—
192	#13063298	—	2	2	no	—
193	#13063298	—	2	2	no	—
194	#13063297	—	2	2	no	—
195	#13063297	—	2	2	no	—
196	#13063297	—	2	2	no	—
197	#13063297	—	2	2	no	—
198	#13063297	—	2	2	no	—
199	#13063297	—	2	2	no	—
200	#13063296	—	2	2	no	—
201	#13063296	—	2	2	no	—
202	#13063296	C₂³	1	2	yes	—
203	#13063296	C₂³	1	2	yes	—
204	#13063295	—	2	2	no	—
205	#13063293	—	2	2	no	—
206	#13063293	—	2	2	no	—
207	#13063293	—	2	2	no	—
208	C₄×Dic₈₆	D₄	1	1	yes	characteristic
209	C₄×Dic₈₆	D₄	1	1	yes	characteristic
210	C₄×Dic₈₆	C₂³	1	2	yes	—
211	#13063290	C₂³	1	2	yes	—
212	C₄×D₁₇₂	D₄	1	1	yes	characteristic
213	C₄×D₁₇₂	D₄	1	1	yes	characteristic
214	C₄×D₁₇₂	C₂³	1	2	yes	—
215	D₄×Dic₄₃	C₂³	1	2	yes	—
216	D₄×Dic₄₃	C₂³	1	2	yes	—
217	#13063287	C₂³	1	2	yes	—
218	C₄×C₂²⋊D₄₃	—	2	2	no	—
219	C₄×C₂²⋊D₄₃	—	2	2	no	—
220	C₄×C₂²⋊D₄₃	—	2	2	no	—
221	C₄×C₂²⋊D₄₃	—	2	2	no	—
222	C₄×C₂²⋊D₄₃	—	2	2	no	—
223	C₄×C₂²⋊D₄₃	D₄	1	1	yes	characteristic
224	C₄×C₂²⋊D₄₃	D₄	1	1	yes	characteristic
225	C₄×C₂²⋊D₄₃	D₄	1	1	yes	characteristic
226	C₄×C₂²⋊D₄₃	D₄	1	1	yes	characteristic
227	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
228	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
229	#13063284	—	2	2	no	—
230	#13063284	C₂³	1	1	yes	characteristic
231	#13063283	C₂³	1	2	yes	—
232	#13063282	—	2	2	no	—
233	#13063282	C₂³	1	1	yes	characteristic
234	#13063282	C₂³	1	1	yes	characteristic
235	#13063281	—	2	2	no	—
236	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
237	C₂²⋊C₄×D₄₃	—	2	2	no	—
238	C₂×C₄×Dic₄₃	—	2	2	no	—
239	C₄²×D₄₃	C₂³	1	1	yes	characteristic
240	C₄²×D₄₃	C₂³	1	1	yes	characteristic
241	#13063259	C₂³	1	1	yes	characteristic
242	#13063259	C₂³	1	1	yes	characteristic
243	#13063258	C₂³	1	2	yes	—
244	#13063258	C₂³	1	2	yes	—
245	#13063257	C₂³	1	2	yes	—
246	#13063256	C₂³	1	2	yes	—
247	#13063256	C₂³	1	2	yes	—
248	#13063250	C₂³	1	2	yes	—
249	#13063250	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	#13063246	C₂³	1	2	yes	—
257	#13063246	C₂³	1	2	yes	—
258	#13063245	C₂³	1	2	yes	—
259	#13063245	C₂³	1	2	yes	—
260	#13063236	C₂³	1	1	yes	characteristic
261	#13063236	C₂³	1	1	yes	characteristic
262	#13063235	C₂³	1	1	yes	characteristic
263	#13063235	C₂³	1	1	yes	characteristic
264	#13063235	C₂³	1	1	yes	characteristic
265	#13063235	C₂³	1	1	yes	characteristic
266	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
267	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
268	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
269	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
270	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
271	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
272	C₂×#41×C₄₃	—	2	2	no	—
273	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
274	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
275	C₂×D₈×C₄₃	C₂³	1	2	yes	—
276	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
277	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
278	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
279	#127×C₄₃	C₂³	1	2	yes	—
280	#124×C₄₃	—	2	2	no	—
281	#121×C₄₃	—	2	2	no	—
282	#121×C₄₃	C₂³	1	2	yes	—
283	#121×C₄₃	C₂³	1	2	yes	—
284	C₄×D₄×C₄₃	—	2	2	no	—
285	C₄×D₄×C₄₃	C₂³	1	2	yes	—
286	C₄×D₄×C₄₃	C₂³	1	2	yes	—
287	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
288	#107×C₄₃	C₂³	1	1	yes	characteristic
289	#107×C₄₃	C₂³	1	1	yes	characteristic
290	#107×C₄₃	C₂³	1	2	yes	—
291	#102×C₄₃	C₂³	1	2	yes	—
292	#102×C₄₃	C₂³	1	2	yes	—
293	#102×C₄₃	C₂³	1	2	yes	—
294	#102×C₄₃	C₂³	1	2	yes	—
295	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
297	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
298	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
299	C₂³×D₄₃	—	2	2	no	—
300	#41×C₄₃	—	8	4	no	—
301	C₂×Q₈×C₄₃	—	2	2	no	—
302	C₂×D₄×C₄₃	—	2	2	no	—
303	C₂×D₄×C₄₃	—	2	2	no	—
304	C₂×D₄×C₄₃	—	2	2	no	—
305	C₂×D₄×C₄₃	—	2	2	no	—
306	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
307	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
308	C₂²×C₄×C₄₃	—	2	2	no	—
309	C₂²×C₄×C₄₃	—	2	2	no	—
310	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
311	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
312	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
313	C₂×C₂²⋊D₄₃	—	2	2	no	—
314	C₂×C₂²⋊D₄₃	—	2	2	no	—
315	C₂×C₂²⋊D₄₃	—	2	2	no	—
316	C₂×C₂²⋊D₄₃	—	2	2	no	—
317	C₂×C₂²⋊D₄₃	—	2	2	no	—
318	C₂×C₂²⋊D₄₃	—	2	2	no	—
319	C₂×C₂²⋊D₄₃	—	2	2	no	—
320	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
321	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
322	C₂²×Dic₄₃	—	2	2	no	—
323	C₂²×Dic₄₃	—	2	2	no	—
324	C₂²×Dic₄₃	—	2	2	no	—
325	#10621900	—	2	4	no	—
326	#10621900	—	2	4	no	—
327	D₄×D₄₃	—	2	4	no	—
328	D₄×D₄₃	—	2	4	no	—
329	#10621898	—	2	2	no	—
330	#10621898	—	2	2	no	—
331	#10621898	—	8	4	no	—
332	C₂×D₁₇₂	—	2	2	no	—
333	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
334	C₂×D₁₇₂	C₂⁴	1	2	yes	—
335	C₂×C₄×D₄₃	—	2	2	no	—
336	C₂×C₄×D₄₃	—	2	2	no	—
337	C₂×C₄×D₄₃	—	2	2	no	—
338	C₂×C₄×D₄₃	—	8	4	no	—
339	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
340	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
341	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
342	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
343	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
344	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
345	C₂×Dic₈₆	—	2	2	no	—
346	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
347	C₂×Dic₈₆	C₂⁴	1	2	yes	—
348	D₈×C₄₃	—	2	2	no	—
349	D₈×C₄₃	—	2	2	no	—
350	D₈×C₄₃	—	2	4	no	—
351	C₂×C₈×C₄₃	—	2	2	no	—
352	C₂×C₈×C₄₃	—	2	2	no	—
353	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
354	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
356	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
357	C₄⋊C₄×C₄₃	—	2	2	no	—
358	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
359	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
360	C₂²⋊C₄×C₄₃	—	2	2	no	—
361	C₂²⋊C₄×C₄₃	—	2	2	no	—
362	C₂²⋊C₄×C₄₃	—	2	2	no	—
363	C₂²⋊C₄×C₄₃	—	2	2	no	—
364	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
365	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
366	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
367	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
368	C₂²⋊Dic₄₃	—	2	2	no	—
369	C₂²⋊Dic₄₃	—	2	2	no	—
370	C₂²⋊Dic₄₃	—	2	2	no	—
371	C₂²⋊Dic₄₃	—	2	2	no	—
372	C₂²⋊Dic₄₃	—	2	2	no	—
373	C₂²⋊Dic₄₃	—	2	2	no	—
374	C₂²⋊Dic₄₃	—	2	2	no	—
375	C₂²⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
376	C₂²⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
377	#10621883	—	2	4	no	—
378	#10621883	—	2	4	no	—
379	#10621882	—	2	4	no	—
380	#10621882	—	2	4	no	—
381	(C₂×D₄₃)⋊C₄	—	2	2	no	—
382	(C₂×D₄₃)⋊C₄	—	2	2	no	—
383	(C₂×D₄₃)⋊C₄	—	2	2	no	—
384	(C₂×D₄₃)⋊C₄	—	2	2	no	—
385	(C₂×D₄₃)⋊C₄	—	2	2	no	—
386	(C₂×D₄₃)⋊C₄	—	2	2	no	—
387	(C₂×D₄₃)⋊C₄	—	2	2	no	—
388	(C₂×D₄₃)⋊C₄	—	2	2	no	—
389	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
390	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
391	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
392	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
393	C₄⋊Dic₄₃	—	2	2	no	—
394	C₄⋊Dic₄₃	—	2	2	no	—
395	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
396	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
397	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
398	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
399	Dic₄₃⋊C₄	—	2	2	no	—
400	Dic₄₃⋊C₄	—	2	2	no	—
401	Dic₄₃⋊C₄	—	2	2	no	—
402	Dic₄₃⋊C₄	—	2	2	no	—
403	Dic₄₃⋊C₄	—	2	2	no	—
404	Dic₄₃⋊C₄	—	2	2	no	—
405	Dic₄₃⋊C₄	—	2	2	no	—
406	Dic₄₃⋊C₄	—	2	2	no	—
407	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
408	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
409	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
410	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
411	C₄×Dic₄₃	—	2	2	no	—
412	C₄×Dic₄₃	—	2	2	no	—
413	C₄×Dic₄₃	—	2	2	no	—
414	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
415	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
416	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
417	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
418	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
419	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
420	#10621877	—	2	2	no	—
421	#10621877	—	2	2	no	—
422	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
423	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
424	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
425	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
426	Dic₁₇₂	—	2	2	no	—
427	D₃₄₄	—	2	2	no	—
428	#10621873	—	2	4	no	—
429	#10621872	—	2	2	no	—
430	#10621872	—	2	2	no	—
431	#10621872	—	2	2	no	—
432	#10621872	#41	1	4	yes	complemented
433	C₈×D₄₃	—	2	2	no	—
434	C₈×D₄₃	—	2	2	no	—
435	C₈×D₄₃	—	2	2	no	—
436	C₈×D₄₃	#41	1	4	yes	complemented
437	C₂³×C₄₃	—	2	2	no	—
438	C₂³×C₄₃	—	2	2	no	—
439	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
440	C₂²×D₄₃	—	2	2	no	—
441	C₂²×D₄₃	—	4	4	no	—
442	C₂²×D₄₃	—	8	2	no	—
443	C₂²×D₄₃	—	8	2	no	—
444	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
445	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
446	Q₈×C₄₃	—	8	2	no	—
447	D₄×C₄₃	—	2	2	no	—
448	D₄×C₄₃	—	2	2	no	—
449	D₄×C₄₃	—	2	2	no	—
450	D₄×C₄₃	—	2	2	no	—
451	D₄×C₄₃	—	8	2	no	—
452	D₄×C₄₃	—	8	2	no	—
453	D₄×C₄₃	—	8	2	no	—
454	D₄×C₄₃	—	8	2	no	—
455	C₂×C₄×C₄₃	—	2	2	no	—
456	C₂×C₄×C₄₃	—	2	1	no	—
457	C₂×C₄×C₄₃	—	2	1	no	—
458	C₂×C₄×C₄₃	—	2	2	no	—
459	C₂×C₄×C₄₃	—	2	2	no	—
460	C₂×C₄×C₄₃	—	4	1	no	—
461	C₂×C₄×C₄₃	—	4	4	no	—
462	C₂×C₄×C₄₃	—	4	4	no	—
463	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
469	C₂²⋊D₄₃	—	2	2	no	—
470	C₂²⋊D₄₃	—	2	2	no	—
471	C₂²⋊D₄₃	—	4	4	no	—
472	C₂²⋊D₄₃	—	4	4	no	—
473	C₂²⋊D₄₃	—	8	2	no	—
474	C₂²⋊D₄₃	—	8	2	no	—
475	C₂²⋊D₄₃	—	8	2	no	—
476	C₂²⋊D₄₃	—	8	2	no	—
477	C₂²⋊D₄₃	—	8	2	no	—
478	C₂×Dic₄₃	—	2	2	no	—
479	C₂×Dic₄₃	—	2	2	no	—
480	C₂×Dic₄₃	—	2	2	no	—
481	C₂×Dic₄₃	—	4	4	no	—
482	C₂×Dic₄₃	—	8	2	no	—
483	C₂×Dic₄₃	—	8	2	no	—
484	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
485	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
486	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
487	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
488	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
489	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
490	D₁₇₂	—	2	2	no	—
491	D₁₇₂	—	2	2	no	—
492	D₁₇₂	—	2	2	no	—
493	D₁₇₂	—	8	2	no	—
494	C₄×D₄₃	—	2	2	no	—
495	C₄×D₄₃	—	2	2	no	—
496	C₄×D₄₃	—	2	1	no	—
497	C₄×D₄₃	—	2	1	no	—
498	C₄×D₄₃	—	4	1	no	—
499	C₄×D₄₃	—	4	1	no	—
500	C₄×D₄₃	—	4	4	no	—
501	C₄×D₄₃	—	8	2	no	—
502	C₄×D₄₃	—	8	2	no	—
503	C₄×D₄₃	C₂×#41	1	2	yes	—
504	C₄×D₄₃	C₂×#41	1	2	yes	—
505	Dic₈₆	—	2	2	no	—
506	Dic₈₆	—	2	2	no	—
507	Dic₈₆	—	2	2	no	—
508	Dic₈₆	—	8	2	no	—
509	C₈×C₄₃	—	2	1	no	—
510	C₈×C₄₃	—	2	1	no	—
511	C₈×C₄₃	C₂×#41	1	2	yes	—
512	C₈×C₄₃	C₂×#41	1	2	yes	—
513	C₄₃⋊C₈	—	2	1	no	—
514	C₄₃⋊C₈	—	2	1	no	—
515	C₄₃⋊C₈	C₂×#41	1	2	yes	—
516	C₄₃⋊C₈	C₂×#41	1	2	yes	—
517	#60695	—	43	1	no	maximal, Sylow
518	C₂²×C₄₃	—	2	1	no	—
519	C₂²×C₄₃	—	2	1	no	—
520	C₂²×C₄₃	—	2	1	no	—
521	C₂²×C₄₃	—	4	2	no	—
522	C₂²×C₄₃	—	4	2	no	—
523	C₂²×C₄₃	—	4	2	no	—
524	C₂²×C₄₃	—	4	2	no	—
525	C₂²×C₄₃	—	4	2	no	—
526	C₂²×C₄₃	—	4	2	no	—
527	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
528	C₂×D₄₃	—	2	1	no	—
529	C₂×D₄₃	—	2	1	no	—
530	C₂×D₄₃	—	2	1	no	—
531	C₂×D₄₃	—	2	1	no	—
532	C₂×D₄₃	—	2	1	no	—
533	C₂×D₄₃	—	4	2	no	—
534	C₂×D₄₃	—	4	2	no	—
535	C₂×D₄₃	—	4	2	no	—
536	C₂×D₄₃	—	8	8	no	—
537	C₂×D₄₃	#532	1	2	yes	—
538	C₄×C₄₃	—	2	1	no	—
539	C₄×C₄₃	—	2	1	no	—
540	C₄×C₄₃	—	2	1	no	—
541	C₄×C₄₃	—	2	1	no	—
542	C₄×C₄₃	—	4	2	no	—
543	C₄×C₄₃	—	4	2	no	—
544	C₄×C₄₃	#576	1	2	yes	—
545	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
546	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
547	Dic₄₃	—	2	1	no	—
548	Dic₄₃	—	2	1	no	—
549	Dic₄₃	—	2	1	no	—
550	Dic₄₃	—	2	1	no	—
551	Dic₄₃	—	2	1	no	—
552	Dic₄₃	—	4	2	no	—
553	Dic₄₃	—	4	2	no	—
554	Dic₄₃	—	4	2	no	—
555	Dic₄₃	#532	1	2	yes	—
556	#3460	—	43	2	no	—
557	#3179	—	43	2	no	—
558	#3179	—	43	2	no	—
559	#3176	—	43	1	no	—
560	#3176	—	43	1	no	—
561	#3175	—	43	1	no	—
562	#3175	—	43	1	no	—
563	#3171	—	43	2	no	—
564	#3171	—	43	2	no	—
565	#3169	—	43	1	no	—
566	#3169	D₄₃	1	1	yes	characteristic, complemented
567	#3168	—	43	1	no	—
568	#3168	—	43	1	no	—
569	#3164	—	43	1	no	—
570	#3155	—	43	1	no	—
571	#3136	—	43	2	no	—
572	#3062	—	43	2	no	—
573	#3061	—	43	1	no	—
574	#3058	—	43	1	no	—
575	C₄×AGL(1,ℤ/8)	—	43	2	no	—
576	C₄×#135	—	43	1	no	—
577	C₂×C₄×D₈	—	43	1	no	—
578	C₄×#131	—	43	1	no	—
579	C₂×C₄₃	—	4	1	no	—
580	C₂×C₄₃	—	8	2	no	—
581	C₂×C₄₃	—	8	2	no	—
582	C₂×C₄₃	C₂×#532	1	1	yes	characteristic
583	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
584	C₂×C₄₃	#3584	1	1	yes	characteristic
585	D₄₃	—	2	2	no	—
586	D₄₃	—	4	1	no	—
587	D₄₃	—	8	2	no	—
588	C₂×AGL(1,ℤ/8)	—	43	2	no	—
589	C₂×#135	—	43	1	no	—
590	C₂²×D₈	—	43	1	no	—
591	C₂×#131	—	43	1	no	—
592	C₂×#131	—	43	1	no	—
593	#544	—	43	2	no	—
594	#542	—	43	2	no	—
595	#542	—	43	2	no	—
596	#542	—	86	2	no	—
597	#540	—	43	2	no	—
598	#540	—	43	2	no	—
599	#540	—	86	2	no	—
600	#538	—	86	2	no	—
601	#538	—	86	2	no	—
602	#537	—	43	2	no	—
603	#535	—	43	2	no	—
604	#535	—	43	2	no	—
605	#532	—	43	2	no	—
606	#532	—	86	2	no	—
607	#532	C₂×D₄₃	1	2	yes	complemented
608	#529	—	43	2	no	—
609	#529	—	43	2	no	—
610	#529	—	86	2	no	—
611	#525	—	86	2	no	—
612	#525	—	86	2	no	—
613	C₄×#41	—	43	1	no	—
614	C₄×#41	—	43	2	no	—
615	C₂×C₄×D₄	—	43	2	no	—
616	#501	—	43	2	no	—
617	#501	—	43	2	no	—
618	#500	—	43	1	no	—
619	#500	C₂×D₄₃	1	1	yes	characteristic, complemented
620	#499	—	43	1	no	—
621	#499	—	43	1	no	—
622	#496	—	43	2	no	—
623	#496	—	43	2	no	—
624	#495	—	43	1	no	—
625	#495	—	43	1	no	—
626	#493	—	43	1	no	—
627	#493	C₂×D₄₃	1	1	yes	characteristic
628	#490	—	43	2	no	—
629	#490	—	43	2	no	—
630	#489	—	43	2	no	—
631	#489	—	43	2	no	—
632	#488	—	43	2	no	—
633	#488	—	43	2	no	—
634	#486	—	43	2	no	—
635	#486	C₂×D₄₃	1	2	yes	complemented
636	#469	—	43	2	no	—
637	#469	—	43	2	no	—
638	#469	—	43	2	no	—
639	#469	—	43	2	no	—
640	#468	—	43	2	no	—
641	#468	—	43	2	no	—
642	#468	—	43	2	no	—
643	#468	—	43	2	no	—
644	#467	—	43	1	no	—
645	#467	—	43	1	no	—
646	#466	—	43	1	no	—
647	#466	—	43	1	no	—
648	#466	—	43	1	no	—
649	#466	—	43	1	no	—
650	#466	—	43	2	no	—
651	#466	C₂×D₄₃	1	1	yes	characteristic
652	#466	C₂×D₄₃	1	1	yes	characteristic, complemented
653	#466	C₂×D₄₃	1	2	yes	complemented
654	#465	—	43	2	no	—
655	#465	—	43	2	no	—
656	#442	—	43	2	no	—
657	#442	—	43	2	no	—
658	#440	—	43	2	no	—
659	#440	—	43	2	no	—
660	C₄×Q₁₆	—	43	1	no	—
661	C₄×Q₁₆	—	43	1	no	—
662	C₄×SD₁₆	—	43	2	no	—
663	C₄×SD₁₆	—	43	2	no	—
664	C₄×SD₁₆	—	43	2	no	—
665	C₄×SD₁₆	—	43	2	no	—
666	C₄×D₈	—	43	1	no	—
667	C₄×D₈	—	43	1	no	—
668	C₄×D₈	—	43	2	no	—
669	C₄×D₈	—	43	2	no	—
670	C₄×D₈	—	43	1	no	—
671	C₄×D₈	—	43	2	no	—
672	C₄×D₈	—	43	1	no	—
673	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
674	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic, complemented
675	C₄×D₈	C₂×D₄₃	1	2	yes	complemented
676	#428	—	43	2	no	—
677	#427	—	43	1	no	—
678	C₂×#107	—	43	1	no	—
679	#418	—	43	2	no	—
680	#417	—	43	2	no	—
681	#416	—	43	2	no	—
682	C₂×#102	—	43	2	no	—
683	#405	—	43	1	no	—
684	#405	—	43	1	no	—
685	#405	—	43	1	no	—
686	#405	—	43	1	no	—
687	#405	—	43	1	no	—
688	#405	—	43	1	no	—
689	C₄×M₁₆	—	43	1	no	—
690	C₄×M₁₆	—	43	1	no	—
691	C₄×M₁₆	—	43	1	no	—
692	C₂×C₄×C₈	—	43	1	no	—
693	C₂×C₄×C₈	—	43	1	no	—
694	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
695	C₄₃	#60695	1	1	yes	characteristic, complemented, Sylow
696	C₂×#41	—	2	2	no	—
697	C₂×#41	—	43	1	no	—
698	C₂×#41	—	43	2	no	—
699	C₂×#41	—	86	2	no	—
700	C₂²×D₄	—	43	2	no	—
701	C₂³×C₄	—	86	2	no	—
702	AGL(1,ℤ/8)	—	86	8	no	—
703	#135	—	86	4	no	—
704	C₂×Q₁₆	—	43	1	no	—
705	C₂×SD₁₆	—	43	2	no	—
706	C₂×SD₁₆	—	43	2	no	—
707	C₂×SD₁₆	—	43	2	no	—
708	C₂×D₈	—	43	2	no	—
709	C₂×D₈	—	43	2	no	—
710	C₂×D₈	—	43	1	no	—
711	C₂×D₈	—	86	4	no	—
712	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
713	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
714	C₂×D₈	C₂²×D₄₃	1	2	yes	—
715	#131	—	86	4	no	—
716	#131	—	86	4	no	—
717	C₂×M₁₆	—	43	1	no	—
718	C₂×M₁₆	—	43	1	no	—
719	C₂×M₁₆	—	43	1	no	—
720	C₂×M₁₆	—	43	1	no	—
721	C₂×M₁₆	—	43	1	no	—
722	C₂×M₁₆	—	43	1	no	—
723	C₂²×C₈	—	43	1	no	—
724	C₂²×C₈	—	43	1	no	—
725	C₂²×C₈	—	43	1	no	—
726	C₂²×C₈	—	43	1	no	—
727	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
728	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
729	C₄⋊Q₈	—	43	2	no	—
730	C₄⋊Q₈	—	86	2	no	—
731	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
732	#127	—	43	2	no	—
733	#127	—	86	2	no	—
734	#127	C₂²×D₄₃	1	2	yes	—
735	#126	—	86	2	no	—
736	#126	—	86	2	no	—
737	#126	—	86	2	no	—
738	#126	—	86	2	no	—
739	#125	—	43	2	no	—
740	#125	—	43	2	no	—
741	#125	—	86	2	no	—
742	#124	—	2	2	no	—
743	#124	—	43	2	no	—
744	#124	—	43	2	no	—
745	#124	—	86	2	no	—
746	#124	—	86	2	no	—
747	#124	—	86	2	no	—
748	#124	—	86	2	no	—
749	#123	—	86	2	no	—
750	#123	—	86	2	no	—
751	#123	—	86	2	no	—
752	#123	—	86	2	no	—
753	#123	—	86	2	no	—
754	#123	—	86	2	no	—
755	#123	—	86	2	no	—
756	#123	—	86	2	no	—
757	C₂²⋊Q₈	—	43	2	no	—
758	C₂²⋊Q₈	—	43	2	no	—
759	C₂²⋊Q₈	—	86	2	no	—
760	C₂²⋊Q₈	—	86	2	no	—
761	C₂²⋊Q₈	—	86	2	no	—
762	C₂²⋊Q₈	—	86	2	no	—
763	C₂²⋊Q₈	—	86	2	no	—
764	#121	—	2	2	no	—
765	#121	—	43	2	no	—
766	#121	—	43	2	no	—
767	#121	—	43	2	no	—
768	#121	—	43	2	no	—
769	#121	—	86	2	no	—
770	#121	—	86	2	no	—
771	#121	—	86	2	no	—
772	#121	—	86	2	no	—
773	#121	—	86	2	no	—
774	#121	—	86	2	no	—
775	#121	—	86	2	no	—
776	#121	—	86	2	no	—
777	#121	—	86	2	no	—
778	#121	—	86	2	no	—
779	#121	C₂²×D₄₃	1	2	yes	—
780	#121	C₂²×D₄₃	1	2	yes	—
781	#120	—	86	2	no	—
782	#120	—	86	2	no	—
783	#120	—	86	2	no	—
784	#120	—	86	2	no	—
785	C₄×Q₈	—	43	1	no	—
786	C₄×Q₈	—	43	1	no	—
787	C₄×Q₈	—	43	2	no	—
788	C₄×Q₈	—	43	2	no	—
789	C₄×D₄	—	2	2	no	—
790	C₄×D₄	—	43	1	no	—
791	C₄×D₄	—	43	1	no	—
792	C₄×D₄	—	43	1	no	—
793	C₄×D₄	—	43	1	no	—
794	C₄×D₄	—	43	2	no	—
795	C₄×D₄	—	43	2	no	—
796	C₄×D₄	—	43	2	no	—
797	C₄×D₄	—	43	1	no	—
798	C₄×D₄	—	43	1	no	—
799	C₄×D₄	—	43	2	no	—
800	C₄×D₄	—	86	2	no	—
801	C₄×D₄	—	86	2	no	—
802	C₄×D₄	—	86	2	no	—
803	C₄×D₄	—	86	2	no	—
804	C₄×D₄	—	86	2	no	—
805	C₄×D₄	—	86	2	no	—
806	C₄×D₄	—	86	2	no	—
807	C₄×D₄	C₂²×D₄₃	1	2	yes	—
808	C₄×D₄	C₂²×D₄₃	1	2	yes	—
809	#117	—	43	1	no	—
810	#117	—	43	1	no	—
811	#117	—	43	1	no	—
812	#117	—	43	2	no	—
813	#117	—	86	2	no	—
814	#117	—	86	2	no	—
815	#117	—	86	2	no	—
816	C₂×C₄⋊C₄	—	43	2	no	—
817	C₂×C₂²⋊C₄	—	86	2	no	—
818	C₂×C₄²	—	43	1	no	—
819	C₂×C₄²	—	43	1	no	—
820	C₂×C₄²	—	86	2	no	—
821	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
822	#107	—	43	1	no	—
823	#107	—	43	1	no	—
824	#107	—	43	2	no	—
825	#107	—	43	2	no	—
826	#107	C₂²×D₄₃	1	1	yes	characteristic
827	#107	C₂²×D₄₃	1	1	yes	characteristic
828	#107	C₂²×D₄₃	1	2	yes	—
829	#106	—	43	2	no	—
830	#106	—	43	2	no	—
831	#106	—	43	2	no	—
832	#103	—	43	2	no	—
833	#103	—	43	2	no	—
834	#103	—	43	2	no	—
835	#103	—	43	2	no	—
836	#102	—	43	2	no	—
837	#102	—	43	2	no	—
838	#102	—	43	2	no	—
839	#102	—	43	2	no	—
840	#102	—	43	2	no	—
841	#102	—	43	2	no	—
842	#102	—	43	2	no	—
843	#102	—	43	2	no	—
844	#102	C₂²×D₄₃	1	2	yes	—
845	#102	C₂²×D₄₃	1	2	yes	—
846	#102	C₂²×D₄₃	1	2	yes	—
847	#102	C₂²×D₄₃	1	2	yes	—
848	#97	—	43	1	no	—
849	#97	—	43	1	no	—
850	#97	—	43	1	no	—
851	#97	—	43	1	no	—
852	#97	—	43	1	no	—
853	#97	—	43	1	no	—
854	C₄×C₈	—	43	1	no	—
855	C₄×C₈	—	43	1	no	—
856	C₄×C₈	—	43	1	no	—
857	C₄×C₈	—	43	1	no	—
858	C₄×C₈	—	43	1	no	—
859	C₄×C₈	—	43	1	no	—
860	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
861	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
862	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
863	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
864	C₂⁴	—	86	2	no	—
865	#41	—	8	4	no	—
866	#41	—	86	2	no	—
867	#41	—	86	2	no	—
868	#41	—	86	4	no	—
869	#41	—	86	4	no	—
870	#41	—	344	4	no	—
871	C₂×Q₈	—	2	2	no	—
872	C₂×Q₈	—	43	1	no	—
873	C₂×Q₈	—	43	2	no	—
874	C₂×Q₈	—	86	2	no	—
875	C₂×D₄	—	2	2	no	—
876	C₂×D₄	—	2	2	no	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	2	2	no	—
879	C₂×D₄	—	43	1	no	—
880	C₂×D₄	—	43	1	no	—
881	C₂×D₄	—	43	1	no	—
882	C₂×D₄	—	43	2	no	—
883	C₂×D₄	—	86	2	no	—
884	C₂×D₄	—	86	4	no	—
885	C₂×D₄	—	86	4	no	—
886	C₂×D₄	—	86	2	no	—
887	C₂×D₄	—	86	2	no	—
888	C₂×D₄	—	86	2	no	—
889	C₂×D₄	—	86	2	no	—
890	C₂×D₄	—	86	2	no	—
891	C₂×D₄	—	86	2	no	—
892	C₂×D₄	—	86	2	no	—
893	C₂×D₄	C₂³×D₄₃	1	2	yes	—
894	C₂×D₄	C₂³×D₄₃	1	2	yes	—
895	C₂²×C₄	—	2	2	no	—
896	C₂²×C₄	—	2	2	no	—
897	C₂²×C₄	—	43	1	no	—
898	C₂²×C₄	—	43	1	no	—
899	C₂²×C₄	—	43	1	no	—
900	C₂²×C₄	—	43	1	no	—
901	C₂²×C₄	—	43	1	no	—
902	C₂²×C₄	—	43	1	no	—
903	C₂²×C₄	—	86	2	no	—
904	C₂²×C₄	—	86	2	no	—
905	C₂²×C₄	—	86	2	no	—
906	C₂²×C₄	—	86	2	no	—
907	C₂²×C₄	—	86	2	no	—
908	C₂²×C₄	—	86	2	no	—
909	C₂²×C₄	—	344	4	no	—
910	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
911	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
912	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
913	Q₁₆	—	86	2	no	—
914	SD₁₆	—	86	4	no	—
915	SD₁₆	—	86	4	no	—
916	SD₁₆	—	86	4	no	—
917	D₈	—	2	2	no	—
918	D₈	—	2	2	no	—
919	D₈	—	2	4	no	—
920	D₈	—	86	4	no	—
921	D₈	—	86	4	no	—
922	D₈	—	86	2	no	—
923	M₁₆	—	43	4	no	—
924	M₁₆	—	86	2	no	—
925	M₁₆	—	86	2	no	—
926	M₁₆	—	86	2	no	—
927	M₁₆	—	86	2	no	—
928	M₁₆	—	86	2	no	—
929	C₂×C₈	—	2	2	no	—
930	C₂×C₈	—	2	2	no	—
931	C₂×C₈	—	43	1	no	—
932	C₂×C₈	—	43	1	no	—
933	C₂×C₈	—	43	4	no	—
934	C₂×C₈	—	43	1	no	—
935	C₂×C₈	—	43	1	no	—
936	C₂×C₈	—	86	2	no	—
937	C₂×C₈	—	86	2	no	—
938	C₂×C₈	—	86	2	no	—
939	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
940	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
941	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
942	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	43	1	no	—
945	C₄⋊C₄	—	43	1	no	—
946	C₄⋊C₄	—	43	1	no	—
947	C₄⋊C₄	—	43	1	no	—
948	C₄⋊C₄	—	43	1	no	—
949	C₄⋊C₄	—	43	1	no	—
950	C₄⋊C₄	—	43	2	no	—
951	C₄⋊C₄	—	43	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	C₂³×D₄₃	1	2	yes	—
963	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
964	C₂²⋊C₄	—	2	2	no	—
965	C₂²⋊C₄	—	2	2	no	—
966	C₂²⋊C₄	—	2	2	no	—
967	C₂²⋊C₄	—	2	2	no	—
968	C₂²⋊C₄	—	43	1	no	—
969	C₂²⋊C₄	—	43	1	no	—
970	C₂²⋊C₄	—	43	1	no	—
971	C₂²⋊C₄	—	43	1	no	—
972	C₂²⋊C₄	—	43	1	no	—
973	C₂²⋊C₄	—	43	1	no	—
974	C₂²⋊C₄	—	86	2	no	—
975	C₂²⋊C₄	—	86	2	no	—
976	C₂²⋊C₄	—	86	2	no	—
977	C₂²⋊C₄	—	86	2	no	—
978	C₂²⋊C₄	—	86	2	no	—
979	C₂²⋊C₄	—	86	2	no	—
980	C₂²⋊C₄	—	86	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	C₄²	—	43	1	no	—
990	C₄²	—	43	1	no	—
991	C₄²	—	43	1	no	—
992	C₄²	—	43	1	no	—
993	C₄²	—	43	1	no	—
994	C₄²	—	43	1	no	—
995	C₄²	—	86	2	no	—
996	C₄²	—	86	2	no	—
997	C₄²	—	86	2	no	—
998	C₄²	D₄×D₄₃	1	1	yes	characteristic
999	C₄²	D₄×D₄₃	1	1	yes	characteristic
1000	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1001	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1002	C₂³	—	2	2	no	—
1003	C₂³	—	2	2	no	—
1004	C₂³	—	43	1	no	—
1005	C₂³	—	43	1	no	—
1006	C₂³	—	86	2	no	—
1007	C₂³	—	344	2	no	—
1008	C₂³	—	344	2	no	—
1009	C₂³	—	172	4	no	—
1010	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1011	Q₈	—	8	2	no	—
1012	Q₈	—	86	2	no	—
1013	Q₈	—	86	2	no	—
1014	Q₈	—	86	2	no	—
1015	Q₈	—	344	2	no	—
1016	D₄	—	2	2	no	—
1017	D₄	—	2	2	no	—
1018	D₄	—	2	2	no	—
1019	D₄	—	2	2	no	—
1020	D₄	—	8	2	no	—
1021	D₄	—	8	2	no	—
1022	D₄	—	8	2	no	—
1023	D₄	—	8	2	no	—
1024	D₄	—	86	2	no	—
1025	D₄	—	86	2	no	—
1026	D₄	—	86	2	no	—
1027	D₄	—	86	2	no	—
1028	D₄	—	86	2	no	—
1029	D₄	—	344	2	no	—
1030	D₄	—	344	2	no	—
1031	D₄	—	344	2	no	—
1032	D₄	—	344	2	no	—
1033	D₄	—	344	2	no	—
1034	D₄	—	344	2	no	—
1035	D₄	—	172	4	no	—
1036	D₄	—	172	4	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	2	no	—
1041	C₂×C₄	—	2	2	no	—
1042	C₂×C₄	—	4	1	no	—
1043	C₂×C₄	—	4	4	no	—
1044	C₂×C₄	—	4	4	no	—
1045	C₂×C₄	—	43	1	no	—
1046	C₂×C₄	—	43	2	no	—
1047	C₂×C₄	—	43	2	no	—
1048	C₂×C₄	—	43	1	no	—
1049	C₂×C₄	—	43	1	no	—
1050	C₂×C₄	—	43	1	no	—
1051	C₂×C₄	—	43	1	no	—
1052	C₂×C₄	—	43	1	no	—
1053	C₂×C₄	—	86	2	no	—
1054	C₂×C₄	—	86	2	no	—
1055	C₂×C₄	—	86	1	no	—
1056	C₂×C₄	—	86	1	no	—
1057	C₂×C₄	—	86	2	no	—
1058	C₂×C₄	—	86	2	no	—
1059	C₂×C₄	—	86	2	no	—
1060	C₂×C₄	—	344	2	no	—
1061	C₂×C₄	—	344	2	no	—
1062	C₂×C₄	—	344	2	no	—
1063	C₂×C₄	—	344	2	no	—
1064	C₂×C₄	—	172	1	no	—
1065	C₂×C₄	—	172	1	no	—
1066	C₂×C₄	—	172	4	no	—
1067	C₂×C₄	—	172	4	no	—
1068	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
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	C₂⁴×D₄₃	1	1	yes	characteristic
1074	C₈	—	2	1	no	—
1075	C₈	—	2	1	no	—
1076	C₈	—	43	2	no	—
1077	C₈	—	43	2	no	—
1078	C₈	—	86	1	no	—
1079	C₈	—	86	1	no	—
1080	C₈	#41×D₄₃	1	2	yes	—
1081	C₈	#41×D₄₃	1	2	yes	—
1082	C₂²	—	2	1	no	—
1083	C₂²	—	2	1	no	—
1084	C₂²	—	2	1	no	—
1085	C₂²	—	4	2	no	—
1086	C₂²	—	4	2	no	—
1087	C₂²	—	4	2	no	—
1088	C₂²	—	4	2	no	—
1089	C₂²	—	4	2	no	—
1090	C₂²	—	4	2	no	—
1091	C₂²	—	43	2	no	—
1092	C₂²	—	86	1	no	—
1093	C₂²	—	86	1	no	—
1094	C₂²	—	86	1	no	—
1095	C₂²	—	86	1	no	—
1096	C₂²	—	86	1	no	—
1097	C₂²	—	344	8	no	—
1098	C₂²	—	172	2	no	—
1099	C₂²	—	172	2	no	—
1100	C₂²	—	172	2	no	—
1101	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1102	C₄	—	2	1	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	2	1	no	—
1106	C₄	—	4	2	no	—
1107	C₄	—	4	2	no	—
1108	C₄	—	43	2	no	—
1109	C₄	—	86	1	no	—
1110	C₄	—	86	1	no	—
1111	C₄	—	86	1	no	—
1112	C₄	—	86	1	no	—
1113	C₄	—	86	1	no	—
1114	C₄	—	172	2	no	—
1115	C₄	—	172	2	no	—
1116	C₄	—	172	2	no	—
1117	C₄	#14583700	1	2	yes	—
1118	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1119	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1120	C₂	—	4	1	no	—
1121	C₂	—	8	2	no	—
1122	C₂	—	8	2	no	—
1123	C₂	—	86	2	no	—
1124	C₂	—	344	2	no	—
1125	C₂	—	172	1	no	—
1126	C₂	#532×D₄₃	1	1	yes	characteristic
1127	C₂	C₂×#14583700	1	1	yes	characteristic
1128	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×#3169	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3169	D₄₃
hypocenter	C₄₃	#60695
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3169

Complements

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

N	H ≅ G/N	type
1. #19148009	C₂	semidirect
2. #19145285	C₂	semidirect
3. #19145281	C₂	semidirect
4. #19145242	C₂	semidirect
5. #19145238	C₂	semidirect
6. #19145237	C₂	semidirect
7. #19145227	C₂	semidirect
8. #19145188	C₂	semidirect
9. #19145184	C₂	semidirect
10. #19145171	C₂	semidirect
11. #19145165	C₂	semidirect
12. #19145163	C₂	semidirect
13. #19145128	C₂	semidirect
14. #19145075	C₂	semidirect
15. #19144944	C₂	semidirect
16. #19144274	C₂	semidirect
17. #19144260	C₂	semidirect
18. #19144238	C₂	semidirect
19. C₄×#13063349	C₂	semidirect
20. C₄×#13063344	C₂	semidirect
21. C₄×D₈×D₄₃	C₂	semidirect
22. C₄×#13063331	C₂	semidirect
23. C₄₃×#3169	C₂	semidirect
30. #14583523	C₂²	semidirect
31. #14583516	C₂²	semidirect
33. #14583503	C₂²	semidirect
34. #14583502	C₂²	semidirect
41. #14583446	C₂²	semidirect
43. #14583433	C₂²	semidirect
44. #14583431	C₂²	semidirect
51. #14583307	C₂²	semidirect
52. #14583305	C₂²	semidirect
53. #14583303	C₂²	semidirect
54. #14583301	C₂²	semidirect
55. #14583300	C₂²	semidirect
61. #14583263	C₂²	semidirect
62. #14583262	C₂²	semidirect
63. #14583261	C₂²	semidirect
64. #14583257	C₂²	semidirect
65. #14583254	C₂²	semidirect
66. #14583252	C₂²	semidirect
67. #14583244	C₂²	semidirect
70. #14583150	C₂²	semidirect
71. #14583149	C₂²	semidirect
72. #14583146	C₂²	semidirect
73. #14583144	C₂²	semidirect
74. #14583143	C₂²	semidirect
75. #14583143	C₂²	semidirect
76. #14583141	C₂²	semidirect
77. #14583140	C₂²	semidirect
80. #14583134	C₂²	semidirect
82. #14583132	C₂²	semidirect
83. #14583128	C₂²	semidirect
84. #14583127	C₂²	semidirect
85. #14583011	C₂²	semidirect
86. #14583008	C₂²	semidirect
87. #14582998	C₂²	semidirect
88. #14582996	C₂²	semidirect
89. C₄×Dic₁₇₂	C₂²	semidirect
90. #14582993	C₂²	semidirect
91. #14582990	C₂²	semidirect
92. C₄×#10621873	C₂²	semidirect
93. C₄×#10621883	C₂²	semidirect
94. C₄×#10621883	C₂²	semidirect
97. D₈×Dic₄₃	C₂²	semidirect
100. C₄×#10621882	C₂²	semidirect
109. #14582854	C₂²	semidirect
110. #14582854	C₂²	semidirect
113. #14582853	C₂²	semidirect
114. #14582853	C₂²	semidirect
115. C₄×#10621877	C₂²	semidirect
117. C₄×#10621872	C₂²	semidirect
119. C₄×C₈×D₄₃	C₂²	semidirect
120. C₄₃×#532	C₂²	semidirect
121. C₄₃×#500	C₂²	semidirect
123. C₄₃×#486	C₂²	semidirect
125. C₄₃×#466	C₂²	semidirect
126. C₄₃×#466	C₂²	semidirect
128. C₄×D₈×C₄₃	C₂²	semidirect
129. C₄×D₈×C₄₃	C₂²	semidirect
130. C₂×C₄×C₈×C₄₃	C₂²	semidirect
432. #10621872	#41	semidirect
436. C₈×D₄₃	#41	semidirect
566. #3169	D₄₃	semidirect
607. #532	C₂×D₄₃	semidirect
619. #500	C₂×D₄₃	semidirect
635. #486	C₂×D₄₃	semidirect
652. #466	C₂×D₄₃	semidirect
653. #466	C₂×D₄₃	semidirect
674. C₄×D₈	C₂×D₄₃	semidirect
675. C₄×D₈	C₂×D₄₃	semidirect
694. C₂×C₄×C₈	C₂×D₄₃	semidirect
695. C₄₃	#60695	semidirect

Maximal subgroups

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

subgroup	index
#19148009	2
#19145285	2
#19145281	2
#19145242	2
#19145238	2
#19145237	2
#19145227	2
#19145188	2
#19145184	2
#19145171	2
#19145165	2
#19145163	2
#19145128	2
#19145075	2
#19144944	2
#19144274	2
#19144260	2
#19144238	2
C₄×#13063349	2
C₄×#13063344	2
C₄×D₈×D₄₃	2
C₄×#13063331	2
C₄₃×#3169	2
#60695	43