Subgroups — D₄₃×#3173 #25966387

Order 11008.

1970 conjugacy classes of subgroups.

The subgroup lattice has 1054 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#542×D₄₃	C₂	1	2	yes	maximal, complemented
2	#19145215	C₂	1	1	yes	maximal, characteristic, complemented
3	#19145214	C₂	1	1	yes	maximal, characteristic, complemented
4	#19145213	C₂	1	1	yes	maximal, characteristic, complemented
5	#19145212	C₂	1	1	yes	maximal, characteristic, complemented
6	#19145211	C₂	1	2	yes	maximal, complemented
7	#19145210	C₂	1	1	yes	maximal, characteristic, complemented
8	#19145209	C₂	1	1	yes	maximal, characteristic, complemented
9	#19145208	C₂	1	2	yes	maximal, complemented
10	#19145207	C₂	1	1	yes	maximal, characteristic, complemented
11	#19145206	C₂	1	2	yes	maximal, complemented
12	#19145205	C₂	1	2	yes	maximal, complemented
13	#498×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#495×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#489×D₄₃	C₂	1	2	yes	maximal, complemented
16	#470×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#469×D₄₃	C₂	1	1	yes	maximal, characteristic
18	#465×D₄₃	C₂	1	2	yes	maximal, complemented
19	#442×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
20	#441×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×SD₁₆×D₄₃	C₂	1	2	yes	maximal, complemented
22	#405×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3173	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₁₆×D₄₃	C₂²	1	1	yes	characteristic
25	C₂×SD₁₆×D₄₃	C₂²	1	2	yes	—
26	C₂×D₈×D₄₃	C₂²	1	1	yes	characteristic
27	C₂×M₁₆×D₄₃	C₂²	1	1	yes	characteristic
28	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
29	#14583523	C₂²	1	2	yes	complemented
30	#14583522	C₂²	1	2	yes	complemented
31	#14583521	C₂²	1	2	yes	complemented
32	#14583520	C₂²	1	2	yes	complemented
33	#14583519	—	2	2	no	—
34	#14583518	C₂²	1	2	yes	complemented
35	#14583517	—	2	2	no	—
36	#14583516	C₂²	1	2	yes	complemented
37	#14583515	—	2	2	no	—
38	#14583514	C₂²	1	2	yes	complemented
39	#14583513	—	2	2	no	—
40	C₄⋊Q₈×D₄₃	C₂²	1	2	yes	—
41	#126×D₄₃	—	2	2	no	—
42	#124×D₄₃	—	2	2	no	—
43	#124×D₄₃	C₂²	1	2	yes	—
44	#123×D₄₃	—	2	2	no	—
45	C₂²⋊Q₈×D₄₃	—	2	2	no	—
46	C₂²⋊Q₈×D₄₃	C₂²	1	2	yes	—
47	#121×D₄₃	C₂²	1	2	yes	—
48	C₄×Q₈×D₄₃	C₂²	1	2	yes	—
49	C₄×D₄×D₄₃	C₂²	1	2	yes	—
50	#117×D₄₃	C₂²	1	1	yes	characteristic
51	#14583297	C₂²	1	1	yes	characteristic, complemented
52	#14583296	C₂²	1	2	yes	complemented
53	#14583296	C₂²	1	1	yes	characteristic, complemented
54	#14583296	C₂²	1	1	yes	characteristic, complemented
55	#14583295	C₂²	1	2	yes	complemented
56	#14583284	C₂²	1	1	yes	characteristic, complemented
57	#14583283	C₂²	1	1	yes	characteristic, complemented
58	#14583282	C₂²	1	1	yes	characteristic, complemented
59	#14583281	C₂²	1	2	yes	complemented
60	#14583280	C₂²	1	2	yes	complemented
61	#14583261	C₂²	1	2	yes	complemented
62	#14583260	C₂²	1	2	yes	complemented
63	#14583260	C₂²	1	2	yes	complemented
64	#14583259	C₂²	1	2	yes	complemented
65	#14583258	C₂²	1	2	yes	complemented
66	#14583257	C₂²	1	2	yes	complemented
67	#14583257	C₂²	1	2	yes	complemented
68	#14583158	C₂²	1	1	yes	characteristic, complemented
69	#14583157	C₂²	1	1	yes	characteristic, complemented
70	#14583156	C₂²	1	2	yes	complemented
71	#14583155	C₂²	1	2	yes	complemented
72	#14583154	C₂²	1	1	yes	characteristic, complemented
73	#14583153	C₂²	1	1	yes	characteristic
74	#14583152	C₂²	1	1	yes	characteristic
75	#14583151	C₂²	1	2	yes	—
76	#14583150	C₂²	1	2	yes	—
77	#14583149	C₂²	1	1	yes	characteristic
78	#14583131	C₂²	1	2	yes	complemented
79	#14583130	C₂²	1	2	yes	complemented
80	#14583129	C₂²	1	2	yes	complemented
81	#14583128	C₂²	1	2	yes	complemented
82	#14583127	C₂²	1	2	yes	complemented
83	#14583126	C₂²	1	2	yes	complemented
84	#14583125	C₂²	1	2	yes	complemented
85	#14583012	C₂²	1	1	yes	characteristic, complemented
86	#14583011	C₂²	1	1	yes	characteristic, complemented
87	#14583010	C₂²	1	1	yes	characteristic, complemented
88	#14583009	C₂²	1	2	yes	complemented
89	#14583008	C₂²	1	2	yes	complemented
90	#14583007	C₂²	1	1	yes	characteristic, complemented
91	#14583006	C₂²	1	1	yes	characteristic, complemented
92	#14583005	C₂²	1	1	yes	characteristic, complemented
93	#14583004	C₂²	1	2	yes	complemented
94	#14583003	C₂²	1	2	yes	complemented
95	#14582990	C₂²	1	2	yes	complemented
96	C₄×#10621873	C₂²	1	2	yes	complemented
97	SD₁₆×Dic₄₃	C₂²	1	2	yes	complemented
98	C₄×#10621884	C₂²	1	2	yes	complemented
99	#14582986	C₂²	1	2	yes	complemented
100	C₄×#10621883	C₂²	1	2	yes	complemented
101	#14582984	C₂²	1	2	yes	complemented
102	#106×D₄₃	C₂²	1	1	yes	characteristic
103	#106×D₄₃	C₂²	1	2	yes	—
104	#106×D₄₃	C₂²	1	1	yes	characteristic
105	#103×D₄₃	C₂²	1	2	yes	—
106	#103×D₄₃	C₂²	1	2	yes	—
107	#102×D₄₃	C₂²	1	2	yes	—
108	#102×D₄₃	C₂²	1	2	yes	—
109	#14582857	C₂²	1	1	yes	characteristic, complemented
110	#14582856	C₂²	1	1	yes	characteristic, complemented
111	#14582856	C₂²	1	1	yes	characteristic, complemented
112	#14582855	C₂²	1	1	yes	characteristic, complemented
113	#14582854	C₂²	1	1	yes	characteristic, complemented
114	#14582853	C₂²	1	1	yes	characteristic, complemented
115	#14582853	C₂²	1	1	yes	characteristic, complemented
116	#97×D₄₃	C₂²	1	1	yes	characteristic
117	#97×D₄₃	C₂²	1	1	yes	characteristic
118	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
120	C₄₃×#542	C₂²	1	2	yes	complemented
121	C₄₃×#498	C₂²	1	1	yes	characteristic, complemented
122	C₄₃×#495	C₂²	1	1	yes	characteristic, complemented
123	C₄₃×#489	C₂²	1	2	yes	complemented
124	C₄₃×#470	C₂²	1	1	yes	characteristic, complemented
125	C₄₃×#469	C₂²	1	1	yes	characteristic
126	C₄₃×#465	C₂²	1	2	yes	complemented
127	C₄₃×#442	C₂²	1	1	yes	characteristic, complemented
128	C₄₃×#441	C₂²	1	1	yes	characteristic, complemented
129	C₄×SD₁₆×C₄₃	C₂²	1	2	yes	complemented
130	C₄₃×#405	C₂²	1	1	yes	characteristic, complemented
131	C₂×Q₈×D₄₃	—	2	2	no	—
132	C₂×Q₈×D₄₃	C₂³	1	2	yes	—
133	C₂×D₄×D₄₃	—	2	2	no	—
134	C₂×D₄×D₄₃	C₂³	1	2	yes	—
135	C₂²×C₄×D₄₃	—	2	2	no	—
136	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
137	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
138	C₂×#10621885	C₂³	1	2	yes	—
139	Q₁₆×D₄₃	—	2	4	no	—
140	C₂×#10621873	C₂³	1	2	yes	—
141	C₂×#10621883	C₂³	1	2	yes	—
142	C₂×#10621884	C₂³	1	2	yes	—
143	SD₁₆×D₄₃	—	2	8	no	—
144	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
145	C₂×#10621882	C₂³	1	2	yes	—
146	D₈×D₄₃	—	2	4	no	—
147	C₂×#10621877	C₂³	1	1	yes	characteristic
148	C₂×#10621872	C₂³	1	1	yes	characteristic
149	C₂×#10621872	C₂³	1	1	yes	characteristic
150	M₁₆×D₄₃	—	2	4	no	—
151	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
152	C₂×C₈×D₄₃	—	2	4	no	—
153	C₂×C₈×D₄₃	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	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
159	#13063325	C₂³	1	2	yes	—
160	#13063324	—	2	2	no	—
161	#13063324	C₂³	1	2	yes	—
162	#13063324	C₂³	1	2	yes	—
163	#13063323	—	2	2	no	—
164	#13063320	—	2	2	no	—
165	#13063320	—	2	2	no	—
166	#13063320	—	2	2	no	—
167	#13063319	—	2	2	no	—
168	#13063318	—	2	2	no	—
169	#13063318	—	2	2	no	—
170	#13063318	—	2	2	no	—
171	#13063314	—	2	2	no	—
172	#13063314	C₂³	1	2	yes	—
173	#13063313	—	2	2	no	—
174	#13063313	C₂³	1	2	yes	—
175	#13063312	—	2	2	no	—
176	#13063312	C₂³	1	2	yes	—
177	#13063311	—	2	2	no	—
178	#13063311	—	2	2	no	—
179	#13063311	—	2	2	no	—
180	#13063311	—	2	2	no	—
181	#13063311	—	2	2	no	—
182	#13063311	—	2	2	no	—
183	#13063310	—	2	2	no	—
184	#13063310	—	2	2	no	—
185	#13063309	—	2	2	no	—
186	#13063308	—	2	2	no	—
187	#13063307	—	2	2	no	—
188	#13063307	—	2	2	no	—
189	#13063306	—	2	2	no	—
190	#13063305	—	2	2	no	—
191	#13063305	C₂³	1	2	yes	—
192	#13063304	—	2	2	no	—
193	#13063304	C₂³	1	2	yes	—
194	#13063303	—	2	2	no	—
195	#13063303	—	2	2	no	—
196	#13063303	—	2	2	no	—
197	#13063302	—	2	2	no	—
198	#13063302	—	2	2	no	—
199	#13063302	—	2	2	no	—
200	#13063301	—	2	2	no	—
201	#13063301	C₂³	1	2	yes	—
202	#13063300	C₂³	1	2	yes	—
203	#13063299	C₂³	1	2	yes	—
204	#13063298	—	2	2	no	—
205	#13063297	—	2	2	no	—
206	#13063296	C₂³	1	2	yes	—
207	Q₈×Dic₄₃	C₂³	1	2	yes	—
208	C₄×Dic₈₆	—	2	2	no	—
209	C₄×Dic₈₆	C₂³	1	2	yes	—
210	#13063290	—	2	2	no	—
211	#13063290	C₂³	1	2	yes	—
212	C₄×D₁₇₂	C₂³	1	2	yes	—
213	D₄×Dic₄₃	C₂³	1	2	yes	—
214	#13063287	C₂³	1	2	yes	—
215	C₄×C₂²⋊D₄₃	—	2	2	no	—
216	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
217	#13063284	C₂³	1	1	yes	characteristic
218	#13063283	D₄	1	2	yes	—
219	#13063282	C₂³	1	1	yes	characteristic
220	#13063282	C₂³	1	1	yes	characteristic
221	#13063281	D₄	1	2	yes	—
222	C₄⋊C₄×D₄₃	—	2	2	no	—
223	C₄⋊C₄×D₄₃	—	2	2	no	—
224	C₄⋊C₄×D₄₃	—	2	2	no	—
225	C₄⋊C₄×D₄₃	D₄	1	2	yes	—
226	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
227	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
228	C₂²⋊C₄×D₄₃	—	2	2	no	—
229	C₂²⋊C₄×D₄₃	—	2	2	no	—
230	C₂²⋊C₄×D₄₃	—	2	2	no	—
231	C₂²⋊C₄×D₄₃	—	2	2	no	—
232	C₂²⋊C₄×D₄₃	—	2	2	no	—
233	C₂²⋊C₄×D₄₃	D₄	1	2	yes	—
234	C₄²×D₄₃	—	2	2	no	—
235	C₄²×D₄₃	C₂³	1	1	yes	characteristic
236	C₄²×D₄₃	C₂³	1	1	yes	characteristic
237	#13063257	C₂³	1	2	yes	—
238	#13063257	C₂³	1	1	yes	characteristic
239	#13063257	C₂³	1	1	yes	characteristic
240	#13063256	C₂³	1	2	yes	—
241	#13063256	C₂³	1	2	yes	—
242	#13063256	C₂³	1	2	yes	—
243	#13063256	C₂³	1	2	yes	—
244	#13063250	C₂³	1	2	yes	—
245	#13063250	C₂³	1	2	yes	—
246	#13063249	C₂³	1	2	yes	—
247	#13063249	C₂³	1	2	yes	—
248	#13063248	C₂³	1	2	yes	—
249	#13063248	C₂³	1	2	yes	—
250	#13063247	C₂³	1	2	yes	—
251	#13063247	C₂³	1	2	yes	—
252	#13063246	C₂³	1	2	yes	—
253	#13063246	C₂³	1	2	yes	—
254	#13063245	C₂³	1	2	yes	—
255	#13063245	C₂³	1	2	yes	—
256	#13063236	C₂³	1	1	yes	characteristic
257	#13063236	C₂³	1	1	yes	characteristic
258	#13063235	C₂³	1	1	yes	characteristic
259	#13063235	C₂³	1	1	yes	characteristic
260	#13063235	C₂³	1	1	yes	characteristic
261	#13063235	C₂³	1	1	yes	characteristic
262	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
263	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
264	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
265	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
266	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
267	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
268	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
269	C₂×SD₁₆×C₄₃	C₂³	1	2	yes	—
270	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
271	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
272	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
273	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
274	#126×C₄₃	—	2	2	no	—
275	#124×C₄₃	—	2	2	no	—
276	#124×C₄₃	C₂³	1	2	yes	—
277	#123×C₄₃	—	2	2	no	—
278	C₂²⋊Q₈×C₄₃	—	2	2	no	—
279	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
280	#121×C₄₃	C₂³	1	2	yes	—
281	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
282	C₄×D₄×C₄₃	C₂³	1	2	yes	—
283	#117×C₄₃	C₂³	1	1	yes	characteristic
284	#106×C₄₃	C₂³	1	2	yes	—
285	#106×C₄₃	C₂³	1	1	yes	characteristic
286	#106×C₄₃	C₂³	1	1	yes	characteristic
287	#103×C₄₃	C₂³	1	2	yes	—
288	#103×C₄₃	C₂³	1	2	yes	—
289	#102×C₄₃	C₂³	1	2	yes	—
290	#102×C₄₃	C₂³	1	2	yes	—
291	#97×C₄₃	C₂³	1	1	yes	characteristic
292	#97×C₄₃	C₂³	1	1	yes	characteristic
293	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
294	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
295	C₂³×D₄₃	—	2	2	no	—
296	C₂³×D₄₃	C₂×D₄	1	1	yes	characteristic
297	C₂×Q₈×C₄₃	—	2	2	no	—
298	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
299	C₂×D₄×C₄₃	—	2	2	no	—
300	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
301	C₂²×C₄×C₄₃	—	2	2	no	—
302	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
303	C₂×C₂²⋊D₄₃	—	2	2	no	—
304	C₂×C₂²⋊D₄₃	—	2	2	no	—
305	C₂×C₂²⋊D₄₃	—	2	2	no	—
306	C₂²×Dic₄₃	—	2	2	no	—
307	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
308	Q₈×D₄₃	—	2	4	no	—
309	Q₈×D₄₃	—	2	4	no	—
310	Q₈×D₄₃	—	8	4	no	—
311	D₄×D₄₃	—	2	4	no	—
312	D₄×D₄₃	—	2	4	no	—
313	D₄×D₄₃	—	8	4	no	—
314	C₂×D₁₇₂	—	2	2	no	—
315	C₂×D₁₇₂	C₂⁴	1	2	yes	—
316	C₂×C₄×D₄₃	—	2	2	no	—
317	C₂×C₄×D₄₃	—	2	2	no	—
318	C₂×C₄×D₄₃	—	2	2	no	—
319	C₂×C₄×D₄₃	—	2	2	no	—
320	C₂×C₄×D₄₃	—	2	2	no	—
321	C₂×C₄×D₄₃	—	2	2	no	—
322	C₂×C₄×D₄₃	—	2	2	no	—
323	C₂×C₄×D₄₃	—	8	4	no	—
324	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
325	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
326	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
327	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
328	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
329	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
330	C₂×Dic₈₆	—	2	2	no	—
331	C₂×Dic₈₆	—	2	2	no	—
332	C₂×Dic₈₆	—	2	2	no	—
333	C₂×Dic₈₆	—	2	2	no	—
334	C₂×Dic₈₆	C₂⁴	1	2	yes	—
335	Q₁₆×C₄₃	—	2	2	no	—
336	SD₁₆×C₄₃	—	2	4	no	—
337	D₈×C₄₃	—	2	2	no	—
338	M₁₆×C₄₃	—	2	2	no	—
339	C₂×C₈×C₄₃	—	2	2	no	—
340	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
341	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
342	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
343	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
344	C₄⋊C₄×C₄₃	—	2	2	no	—
345	C₄⋊C₄×C₄₃	—	2	2	no	—
346	C₄⋊C₄×C₄₃	—	2	2	no	—
347	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
348	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
349	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
350	C₂²⋊C₄×C₄₃	—	2	2	no	—
351	C₂²⋊C₄×C₄₃	—	2	2	no	—
352	C₂²⋊C₄×C₄₃	—	2	2	no	—
353	C₂²⋊C₄×C₄₃	—	2	2	no	—
354	C₂²⋊C₄×C₄₃	—	2	2	no	—
355	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
356	C₄²×C₄₃	—	2	2	no	—
357	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
358	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
359	C₂²⋊Dic₄₃	—	2	2	no	—
360	C₂²⋊Dic₄₃	—	2	2	no	—
361	C₂²⋊Dic₄₃	—	2	2	no	—
362	C₂²⋊Dic₄₃	—	2	2	no	—
363	C₂²⋊Dic₄₃	—	2	2	no	—
364	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
365	#10621885	—	2	4	no	—
366	#10621884	—	2	4	no	—
367	#10621883	—	2	4	no	—
368	#10621882	—	2	4	no	—
369	(C₂×D₄₃)⋊C₄	—	2	2	no	—
370	(C₂×D₄₃)⋊C₄	—	2	2	no	—
371	(C₂×D₄₃)⋊C₄	—	2	2	no	—
372	(C₂×D₄₃)⋊C₄	—	2	2	no	—
373	(C₂×D₄₃)⋊C₄	—	2	2	no	—
374	(C₂×D₄₃)⋊C₄	—	2	2	no	—
375	(C₂×D₄₃)⋊C₄	—	2	2	no	—
376	(C₂×D₄₃)⋊C₄	—	2	2	no	—
377	(C₂×D₄₃)⋊C₄	—	2	2	no	—
378	(C₂×D₄₃)⋊C₄	—	2	2	no	—
379	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
380	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
381	C₄⋊Dic₄₃	—	2	2	no	—
382	C₄⋊Dic₄₃	—	2	2	no	—
383	C₄⋊Dic₄₃	—	2	2	no	—
384	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
385	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
386	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
387	Dic₄₃⋊C₄	—	2	2	no	—
388	Dic₄₃⋊C₄	—	2	2	no	—
389	Dic₄₃⋊C₄	—	2	2	no	—
390	Dic₄₃⋊C₄	—	2	2	no	—
391	Dic₄₃⋊C₄	—	2	2	no	—
392	Dic₄₃⋊C₄	—	2	2	no	—
393	Dic₄₃⋊C₄	—	2	2	no	—
394	Dic₄₃⋊C₄	—	2	2	no	—
395	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
396	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
397	C₄×Dic₄₃	—	2	2	no	—
398	C₄×Dic₄₃	—	2	2	no	—
399	C₄×Dic₄₃	—	2	2	no	—
400	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
401	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
402	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
403	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
404	#10621877	—	2	2	no	—
405	C₂×C₄₃⋊C₈	—	2	2	no	—
406	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
407	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
408	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
409	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
410	Dic₁₇₂	—	2	2	no	—
411	D₃₄₄	—	2	2	no	—
412	#10621873	—	2	4	no	—
413	#10621872	—	2	2	no	—
414	#10621872	—	2	2	no	—
415	C₈×D₄₃	—	2	2	no	—
416	C₈×D₄₃	—	2	2	no	—
417	C₈×D₄₃	—	2	2	no	—
418	C₈×D₄₃	—	2	2	no	—
419	C₈×D₄₃	#41	1	4	yes	—
420	C₈×D₄₃	#41	1	4	yes	—
421	C₂³×C₄₃	—	2	2	no	—
422	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
423	C₂²×D₄₃	—	2	2	no	—
424	C₂²×D₄₃	—	2	4	no	—
425	C₂²×D₄₃	—	2	2	no	—
426	C₂²×D₄₃	—	4	4	no	—
427	C₂²×D₄₃	—	4	4	no	—
428	C₂²×D₄₃	—	4	4	no	—
429	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
430	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
431	Q₈×C₄₃	—	2	2	no	—
432	Q₈×C₄₃	—	2	2	no	—
433	Q₈×C₄₃	—	8	2	no	—
434	D₄×C₄₃	—	2	2	no	—
435	D₄×C₄₃	—	2	2	no	—
436	D₄×C₄₃	—	8	2	no	—
437	C₂×C₄×C₄₃	—	2	1	no	—
438	C₂×C₄×C₄₃	—	2	1	no	—
439	C₂×C₄×C₄₃	—	2	2	no	—
440	C₂×C₄×C₄₃	—	2	2	no	—
441	C₂×C₄×C₄₃	—	2	2	no	—
442	C₂×C₄×C₄₃	—	8	2	no	—
443	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
444	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
445	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
447	C₂²⋊D₄₃	—	4	4	no	—
448	C₂²⋊D₄₃	—	8	2	no	—
449	C₂²⋊D₄₃	—	8	2	no	—
450	C₂×Dic₄₃	—	2	2	no	—
451	C₂×Dic₄₃	—	2	2	no	—
452	C₂×Dic₄₃	—	2	2	no	—
453	C₂×Dic₄₃	—	2	2	no	—
454	C₂×Dic₄₃	—	8	2	no	—
455	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
456	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
457	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
458	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
459	D₁₇₂	—	2	2	no	—
460	D₁₇₂	—	2	2	no	—
461	D₁₇₂	—	8	2	no	—
462	C₄×D₄₃	—	2	2	no	—
463	C₄×D₄₃	—	2	4	no	—
464	C₄×D₄₃	—	2	4	no	—
465	C₄×D₄₃	—	2	1	no	—
466	C₄×D₄₃	—	2	1	no	—
467	C₄×D₄₃	—	2	2	no	—
468	C₄×D₄₃	—	4	4	no	—
469	C₄×D₄₃	—	4	4	no	—
470	C₄×D₄₃	—	4	4	no	—
471	C₄×D₄₃	—	8	2	no	—
472	C₄×D₄₃	—	8	2	no	—
473	C₄×D₄₃	C₂×#41	1	2	yes	—
474	C₄×D₄₃	C₂×#41	1	2	yes	—
475	Dic₈₆	—	2	2	no	—
476	Dic₈₆	—	2	2	no	—
477	Dic₈₆	—	4	4	no	—
478	Dic₈₆	—	8	2	no	—
479	Dic₈₆	—	8	2	no	—
480	Dic₈₆	—	8	2	no	—
481	C₈×C₄₃	—	2	1	no	—
482	C₈×C₄₃	—	2	1	no	—
483	C₈×C₄₃	C₂×#41	1	2	yes	—
484	C₈×C₄₃	C₂×#41	1	2	yes	—
485	C₄₃⋊C₈	—	2	1	no	—
486	C₄₃⋊C₈	—	2	1	no	—
487	C₄₃⋊C₈	C₂×#41	1	2	yes	—
488	C₄₃⋊C₈	C₂×#41	1	2	yes	—
489	C₂×#3173	—	43	1	no	maximal, Sylow
490	C₂²×C₄₃	—	2	1	no	—
491	C₂²×C₄₃	—	2	2	no	—
492	C₂²×C₄₃	—	4	2	no	—
493	C₂²×C₄₃	—	4	2	no	—
494	C₂²×C₄₃	—	4	2	no	—
495	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
496	C₂×D₄₃	—	2	1	no	—
497	C₂×D₄₃	—	2	2	no	—
498	C₂×D₄₃	—	4	4	no	—
499	C₂×D₄₃	—	4	2	no	—
500	C₂×D₄₃	—	4	2	no	—
501	C₂×D₄₃	—	4	2	no	—
502	C₂×D₄₃	—	8	8	no	—
503	C₂×D₄₃	#532	1	2	yes	—
504	C₂×D₄₃	#577	1	4	yes	—
505	C₄×C₄₃	—	2	1	no	—
506	C₄×C₄₃	—	2	2	no	—
507	C₄×C₄₃	—	2	2	no	—
508	C₄×C₄₃	—	4	2	no	—
509	C₄×C₄₃	—	4	2	no	—
510	C₄×C₄₃	—	4	2	no	—
511	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
512	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
513	Dic₄₃	—	2	1	no	—
514	Dic₄₃	—	2	2	no	—
515	Dic₄₃	—	2	2	no	—
516	Dic₄₃	—	4	2	no	—
517	Dic₄₃	—	4	2	no	—
518	Dic₄₃	—	4	2	no	—
519	Dic₄₃	#532	1	2	yes	—
520	C₂×#542	—	43	2	no	—
521	#3173	—	43	1	no	—
522	#3173	—	43	1	no	—
523	#3173	—	43	2	no	—
524	#3173	—	43	1	no	—
525	#3173	—	43	1	no	—
526	#3173	—	43	2	no	—
527	#3173	—	43	1	no	—
528	#3173	—	43	1	no	—
529	#3173	—	43	2	no	—
530	#3173	—	43	1	no	—
531	#3173	—	43	2	no	—
532	#3173	D₄₃	1	1	yes	characteristic, direct product factor
533	C₂×#498	—	43	1	no	—
534	C₂×#495	—	43	1	no	—
535	C₂×#489	—	43	2	no	—
536	C₂×#470	—	43	1	no	—
537	C₂×#469	—	43	1	no	—
538	C₂×#465	—	43	2	no	—
539	C₂×#442	—	43	1	no	—
540	C₂×#441	—	43	1	no	—
541	C₂×C₄×SD₁₆	—	43	2	no	—
542	C₂×#405	—	43	1	no	—
543	C₂×C₄₃	—	4	1	no	—
544	C₂×C₄₃	—	8	2	no	—
545	C₂×C₄₃	C₂×#532	1	1	yes	characteristic
546	C₂×C₄₃	C₂×#577	1	2	yes	—
547	D₄₃	—	4	1	no	—
548	D₄₃	—	8	2	no	—
549	D₄₃	#3173	1	4	yes	direct product factor
550	C₂²×Q₁₆	—	43	1	no	—
551	C₂²×SD₁₆	—	43	2	no	—
552	C₂²×D₈	—	43	1	no	—
553	C₂²×M₁₆	—	43	1	no	—
554	C₂³×C₈	—	43	1	no	—
555	#542	—	43	2	no	—
556	#542	—	43	2	no	—
557	#542	—	43	2	no	—
558	#542	—	43	2	no	—
559	#542	—	43	2	no	—
560	#542	—	43	2	no	—
561	#542	—	43	2	no	—
562	#542	—	86	2	no	—
563	#542	—	86	2	no	—
564	#542	—	86	2	no	—
565	#542	—	86	2	no	—
566	#542	C₂×D₄₃	1	2	yes	complemented
567	C₂×C₄⋊Q₈	—	43	2	no	—
568	C₂×#126	—	86	2	no	—
569	C₂×#124	—	43	2	no	—
570	C₂×#124	—	86	2	no	—
571	C₂×#123	—	86	2	no	—
572	C₂×C₂²⋊Q₈	—	43	2	no	—
573	C₂×C₂²⋊Q₈	—	86	2	no	—
574	C₂×#121	—	43	2	no	—
575	C₂×C₄×Q₈	—	43	2	no	—
576	C₂×C₄×D₄	—	43	2	no	—
577	C₂×#117	—	43	1	no	—
578	#498	—	43	2	no	—
579	#498	—	43	2	no	—
580	#498	—	43	1	no	—
581	#498	—	43	1	no	—
582	#498	—	43	1	no	—
583	#498	C₂×D₄₃	1	1	yes	characteristic, complemented
584	#495	—	43	1	no	—
585	#495	—	43	2	no	—
586	#495	—	43	1	no	—
587	#495	—	43	2	no	—
588	#495	—	43	1	no	—
589	#495	C₂×D₄₃	1	1	yes	characteristic, complemented
590	#489	—	43	2	no	—
591	#489	—	43	2	no	—
592	#489	—	43	2	no	—
593	#489	—	43	2	no	—
594	#489	—	43	2	no	—
595	#489	—	43	2	no	—
596	#489	—	43	2	no	—
597	#489	C₂×D₄₃	1	2	yes	complemented
598	#470	—	43	1	no	—
599	#470	—	43	1	no	—
600	#470	—	43	2	no	—
601	#470	—	43	1	no	—
602	#470	—	43	2	no	—
603	#470	C₂×D₄₃	1	1	yes	characteristic, complemented
604	#469	—	43	1	no	—
605	#469	—	43	1	no	—
606	#469	—	43	2	no	—
607	#469	—	43	1	no	—
608	#469	—	43	2	no	—
609	#469	C₂×D₄₃	1	1	yes	characteristic
610	#465	—	43	2	no	—
611	#465	—	43	2	no	—
612	#465	—	43	2	no	—
613	#465	—	43	2	no	—
614	#465	—	43	2	no	—
615	#465	—	43	2	no	—
616	#465	—	43	2	no	—
617	#465	C₂×D₄₃	1	2	yes	complemented
618	#442	—	43	1	no	—
619	#442	—	43	2	no	—
620	#442	—	43	1	no	—
621	#442	—	43	2	no	—
622	#442	—	43	1	no	—
623	#442	C₂×D₄₃	1	1	yes	characteristic, complemented
624	#441	—	43	1	no	—
625	#441	—	43	2	no	—
626	#441	—	43	1	no	—
627	#441	—	43	2	no	—
628	#441	—	43	1	no	—
629	#441	C₂×D₄₃	1	1	yes	characteristic, complemented
630	C₄×SD₁₆	—	43	2	no	—
631	C₄×SD₁₆	—	43	2	no	—
632	C₄×SD₁₆	—	43	2	no	—
633	C₄×SD₁₆	—	43	2	no	—
634	C₄×SD₁₆	—	43	2	no	—
635	C₄×SD₁₆	—	43	2	no	—
636	C₄×SD₁₆	—	43	2	no	—
637	C₄×SD₁₆	C₂×D₄₃	1	2	yes	complemented
638	C₂×#106	—	43	2	no	—
639	C₂×#106	—	43	1	no	—
640	C₂×#106	—	43	1	no	—
641	C₂×#103	—	43	2	no	—
642	C₂×#103	—	43	2	no	—
643	C₂×#102	—	43	2	no	—
644	C₂×#102	—	43	2	no	—
645	#405	—	43	1	no	—
646	#405	—	43	1	no	—
647	#405	—	43	1	no	—
648	#405	—	43	1	no	—
649	#405	—	43	1	no	—
650	#405	—	43	1	no	—
651	#405	—	43	1	no	—
652	#405	C₂×D₄₃	1	1	yes	characteristic, complemented
653	C₂×#97	—	43	1	no	—
654	C₂×#97	—	43	1	no	—
655	C₂×C₄×C₈	—	43	1	no	—
656	C₂×C₄×C₈	—	43	1	no	—
657	C₄₃	C₂×#3173	1	1	yes	characteristic, complemented, Sylow
658	C₂²×Q₈	—	43	2	no	—
659	C₂²×Q₈	—	86	2	no	—
660	C₂²×D₄	—	43	2	no	—
661	C₂²×D₄	—	86	2	no	—
662	C₂³×C₄	—	43	1	no	—
663	C₂³×C₄	—	86	2	no	—
664	C₂×Q₁₆	—	43	2	no	—
665	C₂×Q₁₆	—	43	1	no	—
666	C₂×Q₁₆	—	86	4	no	—
667	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
668	C₂×SD₁₆	—	43	2	no	—
669	C₂×SD₁₆	—	43	2	no	—
670	C₂×SD₁₆	—	43	2	no	—
671	C₂×SD₁₆	—	86	8	no	—
672	C₂×SD₁₆	C₂²×D₄₃	1	2	yes	—
673	C₂×D₈	—	43	2	no	—
674	C₂×D₈	—	43	1	no	—
675	C₂×D₈	—	86	4	no	—
676	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
677	C₂×M₁₆	—	43	1	no	—
678	C₂×M₁₆	—	43	1	no	—
679	C₂×M₁₆	—	43	1	no	—
680	C₂×M₁₆	—	86	4	no	—
681	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
682	C₂²×C₈	—	43	1	no	—
683	C₂²×C₈	—	43	1	no	—
684	C₂²×C₈	—	43	1	no	—
685	C₂²×C₈	—	43	1	no	—
686	C₂²×C₈	—	43	1	no	—
687	C₂²×C₈	—	43	1	no	—
688	C₂²×C₈	—	43	1	no	—
689	C₂²×C₈	—	86	4	no	—
690	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
691	C₄⋊Q₈	—	43	2	no	—
692	C₄⋊Q₈	—	43	2	no	—
693	C₄⋊Q₈	—	43	2	no	—
694	C₄⋊Q₈	—	86	2	no	—
695	C₄⋊Q₈	—	86	2	no	—
696	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
697	#126	—	2	2	no	—
698	#126	—	86	2	no	—
699	#126	—	86	2	no	—
700	#126	—	86	2	no	—
701	#126	—	86	2	no	—
702	#126	—	86	2	no	—
703	#126	—	86	2	no	—
704	#126	—	86	2	no	—
705	#124	—	2	2	no	—
706	#124	—	43	2	no	—
707	#124	—	43	2	no	—
708	#124	—	43	2	no	—
709	#124	—	86	2	no	—
710	#124	—	86	2	no	—
711	#124	—	86	2	no	—
712	#124	—	86	2	no	—
713	#124	—	86	2	no	—
714	#124	—	86	2	no	—
715	#124	—	86	2	no	—
716	#124	—	86	2	no	—
717	#124	—	86	2	no	—
718	#124	C₂²×D₄₃	1	2	yes	—
719	#123	—	2	2	no	—
720	#123	—	86	2	no	—
721	#123	—	86	2	no	—
722	#123	—	86	2	no	—
723	#123	—	86	2	no	—
724	#123	—	86	2	no	—
725	#123	—	86	2	no	—
726	#123	—	86	2	no	—
727	C₂²⋊Q₈	—	2	2	no	—
728	C₂²⋊Q₈	—	43	2	no	—
729	C₂²⋊Q₈	—	43	2	no	—
730	C₂²⋊Q₈	—	43	2	no	—
731	C₂²⋊Q₈	—	86	2	no	—
732	C₂²⋊Q₈	—	86	2	no	—
733	C₂²⋊Q₈	—	86	2	no	—
734	C₂²⋊Q₈	—	86	2	no	—
735	C₂²⋊Q₈	—	86	2	no	—
736	C₂²⋊Q₈	—	86	2	no	—
737	C₂²⋊Q₈	—	86	2	no	—
738	C₂²⋊Q₈	—	86	2	no	—
739	C₂²⋊Q₈	—	86	2	no	—
740	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
741	#121	—	43	2	no	—
742	#121	—	43	2	no	—
743	#121	—	43	2	no	—
744	#121	—	86	2	no	—
745	#121	—	86	2	no	—
746	#121	C₂²×D₄₃	1	2	yes	—
747	C₄×Q₈	—	43	2	no	—
748	C₄×Q₈	—	43	2	no	—
749	C₄×Q₈	—	43	2	no	—
750	C₄×Q₈	—	86	2	no	—
751	C₄×Q₈	—	86	2	no	—
752	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
753	C₄×D₄	—	43	2	no	—
754	C₄×D₄	—	43	2	no	—
755	C₄×D₄	—	43	2	no	—
756	C₄×D₄	—	86	2	no	—
757	C₄×D₄	—	86	2	no	—
758	C₄×D₄	C₂²×D₄₃	1	2	yes	—
759	#117	—	43	1	no	—
760	#117	—	43	2	no	—
761	#117	—	43	2	no	—
762	#117	—	43	1	no	—
763	#117	—	43	1	no	—
764	#117	C₂²×D₄₃	1	1	yes	characteristic
765	C₂×C₄⋊C₄	—	43	2	no	—
766	C₂×C₄⋊C₄	—	43	2	no	—
767	C₂×C₄⋊C₄	—	43	2	no	—
768	C₂×C₄⋊C₄	—	86	2	no	—
769	C₂×C₄⋊C₄	—	86	2	no	—
770	C₂×C₄⋊C₄	—	86	2	no	—
771	C₂×C₂²⋊C₄	—	43	2	no	—
772	C₂×C₂²⋊C₄	—	86	2	no	—
773	C₂×C₂²⋊C₄	—	86	2	no	—
774	C₂×C₂²⋊C₄	—	86	2	no	—
775	C₂×C₂²⋊C₄	—	86	2	no	—
776	C₂×C₂²⋊C₄	—	86	2	no	—
777	C₂×C₄²	—	43	1	no	—
778	C₂×C₄²	—	43	1	no	—
779	C₂×C₄²	—	86	2	no	—
780	#106	—	43	2	no	—
781	#106	—	43	1	no	—
782	#106	—	43	1	no	—
783	#106	—	43	2	no	—
784	#106	—	43	2	no	—
785	#106	—	43	2	no	—
786	#106	—	43	2	no	—
787	#106	C₂²×D₄₃	1	2	yes	—
788	#106	C₂²×D₄₃	1	1	yes	characteristic
789	#106	C₂²×D₄₃	1	1	yes	characteristic
790	#103	—	43	2	no	—
791	#103	—	43	2	no	—
792	#103	—	43	2	no	—
793	#103	—	43	2	no	—
794	#103	—	43	2	no	—
795	#103	—	43	2	no	—
796	#103	C₂²×D₄₃	1	2	yes	—
797	#103	C₂²×D₄₃	1	2	yes	—
798	#102	—	43	2	no	—
799	#102	—	43	2	no	—
800	#102	—	43	2	no	—
801	#102	—	43	2	no	—
802	#102	—	43	2	no	—
803	#102	—	43	2	no	—
804	#102	C₂²×D₄₃	1	2	yes	—
805	#102	C₂²×D₄₃	1	2	yes	—
806	#97	—	43	1	no	—
807	#97	—	43	1	no	—
808	#97	—	43	1	no	—
809	#97	—	43	1	no	—
810	#97	—	43	1	no	—
811	#97	—	43	1	no	—
812	#97	C₂²×D₄₃	1	1	yes	characteristic
813	#97	C₂²×D₄₃	1	1	yes	characteristic
814	C₄×C₈	—	43	1	no	—
815	C₄×C₈	—	43	1	no	—
816	C₄×C₈	—	43	1	no	—
817	C₄×C₈	—	43	1	no	—
818	C₄×C₈	—	43	1	no	—
819	C₄×C₈	—	43	1	no	—
820	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
821	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
822	C₂⁴	—	43	1	no	—
823	C₂⁴	—	86	2	no	—
824	C₂×Q₈	—	2	2	no	—
825	C₂×Q₈	—	43	2	no	—
826	C₂×Q₈	—	86	2	no	—
827	C₂×Q₈	—	86	2	no	—
828	C₂×Q₈	—	86	2	no	—
829	C₂×Q₈	—	86	4	no	—
830	C₂×Q₈	—	86	4	no	—
831	C₂×Q₈	—	86	2	no	—
832	C₂×Q₈	—	344	4	no	—
833	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
834	C₂×D₄	—	2	2	no	—
835	C₂×D₄	—	43	2	no	—
836	C₂×D₄	—	86	2	no	—
837	C₂×D₄	—	86	4	no	—
838	C₂×D₄	—	86	4	no	—
839	C₂×D₄	—	86	2	no	—
840	C₂×D₄	—	86	2	no	—
841	C₂×D₄	—	86	2	no	—
842	C₂×D₄	—	344	4	no	—
843	C₂×D₄	C₂³×D₄₃	1	2	yes	—
844	C₂²×C₄	—	2	2	no	—
845	C₂²×C₄	—	43	1	no	—
846	C₂²×C₄	—	43	1	no	—
847	C₂²×C₄	—	43	2	no	—
848	C₂²×C₄	—	43	2	no	—
849	C₂²×C₄	—	43	1	no	—
850	C₂²×C₄	—	43	1	no	—
851	C₂²×C₄	—	43	1	no	—
852	C₂²×C₄	—	86	2	no	—
853	C₂²×C₄	—	86	2	no	—
854	C₂²×C₄	—	86	2	no	—
855	C₂²×C₄	—	86	2	no	—
856	C₂²×C₄	—	86	2	no	—
857	C₂²×C₄	—	86	2	no	—
858	C₂²×C₄	—	86	2	no	—
859	C₂²×C₄	—	86	2	no	—
860	C₂²×C₄	—	344	4	no	—
861	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
862	Q₁₆	—	2	2	no	—
863	Q₁₆	—	86	4	no	—
864	Q₁₆	—	86	2	no	—
865	SD₁₆	—	2	4	no	—
866	SD₁₆	—	86	4	no	—
867	SD₁₆	—	86	4	no	—
868	SD₁₆	—	86	4	no	—
869	D₈	—	2	2	no	—
870	D₈	—	86	4	no	—
871	D₈	—	86	2	no	—
872	M₁₆	—	2	2	no	—
873	M₁₆	—	86	2	no	—
874	M₁₆	—	86	2	no	—
875	M₁₆	—	86	2	no	—
876	C₂×C₈	—	2	2	no	—
877	C₂×C₈	—	43	1	no	—
878	C₂×C₈	—	43	1	no	—
879	C₂×C₈	—	43	4	no	—
880	C₂×C₈	—	43	4	no	—
881	C₂×C₈	—	43	1	no	—
882	C₂×C₈	—	43	1	no	—
883	C₂×C₈	—	86	2	no	—
884	C₂×C₈	—	86	2	no	—
885	C₂×C₈	—	86	2	no	—
886	C₂×C₈	—	86	2	no	—
887	C₂×C₈	—	86	2	no	—
888	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
889	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
890	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
891	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	43	2	no	—
896	C₄⋊C₄	—	43	2	no	—
897	C₄⋊C₄	—	43	2	no	—
898	C₄⋊C₄	—	43	2	no	—
899	C₄⋊C₄	—	43	2	no	—
900	C₄⋊C₄	—	86	2	no	—
901	C₄⋊C₄	—	86	2	no	—
902	C₄⋊C₄	—	86	2	no	—
903	C₄⋊C₄	—	86	2	no	—
904	C₄⋊C₄	—	86	2	no	—
905	C₄⋊C₄	—	86	2	no	—
906	C₄⋊C₄	—	86	2	no	—
907	C₄⋊C₄	—	86	2	no	—
908	C₄⋊C₄	—	86	2	no	—
909	C₄⋊C₄	—	86	2	no	—
910	C₄⋊C₄	—	86	2	no	—
911	C₄⋊C₄	D₄×D₄₃	1	2	yes	—
912	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
913	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
914	C₂²⋊C₄	—	2	2	no	—
915	C₂²⋊C₄	—	2	2	no	—
916	C₂²⋊C₄	—	2	2	no	—
917	C₂²⋊C₄	—	2	2	no	—
918	C₂²⋊C₄	—	2	2	no	—
919	C₂²⋊C₄	—	43	2	no	—
920	C₂²⋊C₄	—	43	2	no	—
921	C₂²⋊C₄	—	43	2	no	—
922	C₂²⋊C₄	—	86	2	no	—
923	C₂²⋊C₄	—	86	2	no	—
924	C₂²⋊C₄	—	86	2	no	—
925	C₂²⋊C₄	—	86	2	no	—
926	C₂²⋊C₄	—	86	2	no	—
927	C₂²⋊C₄	—	86	2	no	—
928	C₂²⋊C₄	—	86	2	no	—
929	C₂²⋊C₄	—	86	2	no	—
930	C₂²⋊C₄	—	86	2	no	—
931	C₂²⋊C₄	—	86	2	no	—
932	C₂²⋊C₄	—	86	2	no	—
933	C₂²⋊C₄	—	86	2	no	—
934	C₂²⋊C₄	—	86	2	no	—
935	C₂²⋊C₄	—	86	2	no	—
936	C₂²⋊C₄	—	86	2	no	—
937	C₂²⋊C₄	D₄×D₄₃	1	2	yes	—
938	C₄²	—	2	2	no	—
939	C₄²	—	43	2	no	—
940	C₄²	—	43	2	no	—
941	C₄²	—	43	1	no	—
942	C₄²	—	43	1	no	—
943	C₄²	—	86	2	no	—
944	C₄²	—	86	2	no	—
945	C₄²	—	86	2	no	—
946	C₄²	C₂³×D₄₃	1	1	yes	characteristic
947	C₄²	C₂³×D₄₃	1	1	yes	characteristic
948	C₂³	—	2	2	no	—
949	C₂³	—	43	1	no	—
950	C₂³	—	43	1	no	—
951	C₂³	—	86	2	no	—
952	C₂³	—	86	4	no	—
953	C₂³	—	86	2	no	—
954	C₂³	—	172	4	no	—
955	C₂³	—	172	4	no	—
956	C₂³	—	172	4	no	—
957	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
958	Q₈	—	2	2	no	—
959	Q₈	—	2	2	no	—
960	Q₈	—	8	2	no	—
961	Q₈	—	86	2	no	—
962	Q₈	—	86	2	no	—
963	Q₈	—	344	2	no	—
964	Q₈	—	344	2	no	—
965	Q₈	—	344	2	no	—
966	Q₈	—	172	4	no	—
967	D₄	—	2	2	no	—
968	D₄	—	2	2	no	—
969	D₄	—	8	2	no	—
970	D₄	—	86	2	no	—
971	D₄	—	86	2	no	—
972	D₄	—	344	2	no	—
973	D₄	—	344	2	no	—
974	D₄	—	344	2	no	—
975	D₄	—	172	4	no	—
976	C₂×C₄	—	2	1	no	—
977	C₂×C₄	—	2	1	no	—
978	C₂×C₄	—	2	2	no	—
979	C₂×C₄	—	2	2	no	—
980	C₂×C₄	—	2	2	no	—
981	C₂×C₄	—	8	2	no	—
982	C₂×C₄	—	43	1	no	—
983	C₂×C₄	—	43	2	no	—
984	C₂×C₄	—	43	2	no	—
985	C₂×C₄	—	43	2	no	—
986	C₂×C₄	—	43	2	no	—
987	C₂×C₄	—	43	1	no	—
988	C₂×C₄	—	86	2	no	—
989	C₂×C₄	—	86	2	no	—
990	C₂×C₄	—	86	4	no	—
991	C₂×C₄	—	86	4	no	—
992	C₂×C₄	—	86	2	no	—
993	C₂×C₄	—	86	1	no	—
994	C₂×C₄	—	86	1	no	—
995	C₂×C₄	—	86	2	no	—
996	C₂×C₄	—	86	2	no	—
997	C₂×C₄	—	86	2	no	—
998	C₂×C₄	—	344	2	no	—
999	C₂×C₄	—	344	2	no	—
1000	C₂×C₄	—	344	2	no	—
1001	C₂×C₄	—	172	4	no	—
1002	C₂×C₄	—	172	4	no	—
1003	C₂×C₄	—	172	4	no	—
1004	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
1005	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
1006	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1007	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1008	C₈	—	2	1	no	—
1009	C₈	—	2	1	no	—
1010	C₈	—	43	2	no	—
1011	C₈	—	43	2	no	—
1012	C₈	—	86	1	no	—
1013	C₈	—	86	1	no	—
1014	C₈	#41×D₄₃	1	2	yes	—
1015	C₈	#41×D₄₃	1	2	yes	—
1016	C₂²	—	2	2	no	—
1017	C₂²	—	2	1	no	—
1018	C₂²	—	4	2	no	—
1019	C₂²	—	4	2	no	—
1020	C₂²	—	4	2	no	—
1021	C₂²	—	43	4	no	—
1022	C₂²	—	43	2	no	—
1023	C₂²	—	86	2	no	—
1024	C₂²	—	86	1	no	—
1025	C₂²	—	344	8	no	—
1026	C₂²	—	172	4	no	—
1027	C₂²	—	172	2	no	—
1028	C₂²	—	172	2	no	—
1029	C₂²	—	172	2	no	—
1030	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1031	C₄	—	2	2	no	—
1032	C₄	—	2	2	no	—
1033	C₄	—	2	1	no	—
1034	C₄	—	4	2	no	—
1035	C₄	—	4	2	no	—
1036	C₄	—	4	2	no	—
1037	C₄	—	43	2	no	—
1038	C₄	—	86	2	no	—
1039	C₄	—	86	2	no	—
1040	C₄	—	86	1	no	—
1041	C₄	—	172	2	no	—
1042	C₄	—	172	2	no	—
1043	C₄	—	172	2	no	—
1044	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1045	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1046	C₂	—	4	1	no	—
1047	C₂	—	8	2	no	—
1048	C₂	—	43	4	no	—
1049	C₂	—	344	2	no	—
1050	C₂	—	172	1	no	—
1051	C₂	#532×D₄₃	1	1	yes	characteristic
1052	C₂	#577×D₄₃	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3173	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	#469×D₄₃	C₂
hypercenter	#3173	D₄₃
hypocenter	C₄₃	C₂×#3173
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3173

Complements

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

N	H ≅ G/N	type
1. #542×D₄₃	C₂	semidirect
2. #19145215	C₂	semidirect
3. #19145214	C₂	semidirect
4. #19145213	C₂	semidirect
5. #19145212	C₂	semidirect
6. #19145211	C₂	semidirect
7. #19145210	C₂	semidirect
8. #19145209	C₂	semidirect
9. #19145208	C₂	semidirect
10. #19145207	C₂	semidirect
11. #19145206	C₂	semidirect
12. #19145205	C₂	semidirect
13. #498×D₄₃	C₂	semidirect
14. #495×D₄₃	C₂	semidirect
15. #489×D₄₃	C₂	semidirect
16. #470×D₄₃	C₂	semidirect
18. #465×D₄₃	C₂	semidirect
19. #442×D₄₃	C₂	semidirect
20. #441×D₄₃	C₂	semidirect
21. C₄×SD₁₆×D₄₃	C₂	semidirect
22. #405×D₄₃	C₂	semidirect
23. C₄₃×#3173	C₂	semidirect
29. #14583523	C₂²	semidirect
30. #14583522	C₂²	semidirect
31. #14583521	C₂²	semidirect
32. #14583520	C₂²	semidirect
34. #14583518	C₂²	semidirect
36. #14583516	C₂²	semidirect
38. #14583514	C₂²	semidirect
51. #14583297	C₂²	semidirect
52. #14583296	C₂²	semidirect
53. #14583296	C₂²	semidirect
54. #14583296	C₂²	semidirect
55. #14583295	C₂²	semidirect
56. #14583284	C₂²	semidirect
57. #14583283	C₂²	semidirect
58. #14583282	C₂²	semidirect
59. #14583281	C₂²	semidirect
60. #14583280	C₂²	semidirect
61. #14583261	C₂²	semidirect
62. #14583260	C₂²	semidirect
63. #14583260	C₂²	semidirect
64. #14583259	C₂²	semidirect
65. #14583258	C₂²	semidirect
66. #14583257	C₂²	semidirect
67. #14583257	C₂²	semidirect
68. #14583158	C₂²	semidirect
69. #14583157	C₂²	semidirect
70. #14583156	C₂²	semidirect
71. #14583155	C₂²	semidirect
72. #14583154	C₂²	semidirect
78. #14583131	C₂²	semidirect
79. #14583130	C₂²	semidirect
80. #14583129	C₂²	semidirect
81. #14583128	C₂²	semidirect
82. #14583127	C₂²	semidirect
83. #14583126	C₂²	semidirect
84. #14583125	C₂²	semidirect
85. #14583012	C₂²	semidirect
86. #14583011	C₂²	semidirect
87. #14583010	C₂²	semidirect
88. #14583009	C₂²	semidirect
89. #14583008	C₂²	semidirect
90. #14583007	C₂²	semidirect
91. #14583006	C₂²	semidirect
92. #14583005	C₂²	semidirect
93. #14583004	C₂²	semidirect
94. #14583003	C₂²	semidirect
95. #14582990	C₂²	semidirect
96. C₄×#10621873	C₂²	semidirect
97. SD₁₆×Dic₄₃	C₂²	semidirect
98. C₄×#10621884	C₂²	semidirect
99. #14582986	C₂²	semidirect
100. C₄×#10621883	C₂²	semidirect
101. #14582984	C₂²	semidirect
109. #14582857	C₂²	semidirect
110. #14582856	C₂²	semidirect
111. #14582856	C₂²	semidirect
112. #14582855	C₂²	semidirect
113. #14582854	C₂²	semidirect
114. #14582853	C₂²	semidirect
115. #14582853	C₂²	semidirect
120. C₄₃×#542	C₂²	semidirect
121. C₄₃×#498	C₂²	semidirect
122. C₄₃×#495	C₂²	semidirect
123. C₄₃×#489	C₂²	semidirect
124. C₄₃×#470	C₂²	semidirect
126. C₄₃×#465	C₂²	semidirect
127. C₄₃×#442	C₂²	semidirect
128. C₄₃×#441	C₂²	semidirect
129. C₄×SD₁₆×C₄₃	C₂²	semidirect
130. C₄₃×#405	C₂²	semidirect
532. #3173	D₄₃	direct (N × H)
549. D₄₃	#3173	direct (N × H)
566. #542	C₂×D₄₃	semidirect
583. #498	C₂×D₄₃	semidirect
589. #495	C₂×D₄₃	semidirect
597. #489	C₂×D₄₃	semidirect
603. #470	C₂×D₄₃	semidirect
617. #465	C₂×D₄₃	semidirect
623. #442	C₂×D₄₃	semidirect
629. #441	C₂×D₄₃	semidirect
637. C₄×SD₁₆	C₂×D₄₃	semidirect
652. #405	C₂×D₄₃	semidirect
657. C₄₃	C₂×#3173	semidirect

Maximal subgroups

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

subgroup	index
#542×D₄₃	2
#19145215	2
#19145214	2
#19145213	2
#19145212	2
#19145211	2
#19145210	2
#19145209	2
#19145208	2
#19145207	2
#19145206	2
#19145205	2
#498×D₄₃	2
#495×D₄₃	2
#489×D₄₃	2
#470×D₄₃	2
#469×D₄₃	2
#465×D₄₃	2
#442×D₄₃	2
#441×D₄₃	2
C₄×SD₁₆×D₄₃	2
#405×D₄₃	2
C₄₃×#3173	2
C₂×#3173	43

Subgroups — D43×#3173 #25966387

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×#3173 #25966387