Subgroups — D₄₃×#3356 #25975327

Order 11008.

1866 conjugacy classes of subgroups.

The subgroup lattice has 1118 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#556×D₄₃	C₂	1	1	yes	maximal, characteristic
2	#554×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#19147213	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147212	C₂	1	1	yes	maximal, characteristic, complemented
5	#19147211	C₂	1	1	yes	maximal, characteristic, complemented
6	#19147210	C₂	1	1	yes	maximal, characteristic, complemented
7	#19147209	C₂	1	1	yes	maximal, characteristic, complemented
8	#19147208	C₂	1	2	yes	maximal, complemented
9	#19147207	C₂	1	1	yes	maximal, characteristic, complemented
10	#19147206	C₂	1	2	yes	maximal, complemented
11	#19147205	C₂	1	2	yes	maximal, complemented
12	#19147204	C₂	1	1	yes	maximal, characteristic, complemented
13	#19147203	C₂	1	2	yes	maximal, complemented
14	#498×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
15	#485×D₄₃	C₂	1	2	yes	maximal, complemented
16	#483×D₄₃	C₂	1	2	yes	maximal, complemented
17	#477×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#475×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
19	#470×D₄₃	C₂	1	2	yes	maximal, complemented
20	C₄×Q₁₆×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#436×D₄₃	C₂	1	1	yes	maximal, characteristic
22	#428×D₄₃	C₂	1	2	yes	maximal, complemented
23	C₄₃×#3356	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₁₆×D₄₃	C₂²	1	1	yes	characteristic
25	C₂×M₁₆×D₄₃	C₂²	1	2	yes	—
26	#14583623	C₂²	1	1	yes	characteristic
27	#14583622	C₂²	1	1	yes	characteristic
28	#14583621	—	2	1	no	—
29	#14583620	C₂²	1	2	yes	—
30	#14583619	C₂²	1	1	yes	characteristic
31	#14583618	—	2	1	no	—
32	#14583617	C₂²	1	2	yes	—
33	#14583616	—	2	2	no	—
34	#14583610	C₂²	1	1	yes	characteristic
35	#14583609	C₂²	1	1	yes	characteristic
36	#14583608	—	2	1	no	—
37	#14583607	C₂²	1	2	yes	—
38	#14583606	C₂²	1	1	yes	characteristic
39	#14583605	—	2	1	no	—
40	#14583604	C₂²	1	2	yes	—
41	#14583603	—	2	2	no	—
42	C₄⋊Q₈×D₄₃	C₂²	1	1	yes	characteristic
43	C₄⋊Q₈×D₄₃	C₂²	1	1	yes	characteristic
44	#126×D₄₃	—	2	2	no	—
45	#125×D₄₃	—	2	1	no	—
46	#124×D₄₃	—	2	1	no	—
47	C₂²⋊Q₈×D₄₃	—	2	2	no	—
48	C₂²⋊Q₈×D₄₃	C₂²	1	2	yes	—
49	C₂²⋊Q₈×D₄₃	C₂²	1	2	yes	—
50	C₄×Q₈×D₄₃	—	2	1	no	—
51	C₄×Q₈×D₄₃	C₂²	1	1	yes	characteristic
52	C₄×Q₈×D₄₃	C₂²	1	1	yes	characteristic
53	C₄×D₄×D₄₃	—	2	1	no	—
54	C₄×D₄×D₄₃	C₂²	1	1	yes	characteristic
55	#117×D₄₃	C₂²	1	2	yes	—
56	C₂×C₄⋊C₄×D₄₃	C₂²	1	2	yes	—
57	#14583297	C₂²	1	1	yes	characteristic, complemented
58	#14583296	C₂²	1	2	yes	complemented
59	#14583296	C₂²	1	2	yes	complemented
60	#14583295	C₂²	1	1	yes	characteristic, complemented
61	#14583295	C₂²	1	1	yes	characteristic, complemented
62	#14583243	C₂²	1	2	yes	complemented
63	#14583242	C₂²	1	2	yes	complemented
64	#14583241	C₂²	1	2	yes	complemented
65	#14583240	C₂²	1	2	yes	complemented
66	#14583239	C₂²	1	2	yes	complemented
67	#14583238	C₂²	1	2	yes	complemented
68	#14583237	C₂²	1	2	yes	complemented
69	#14583231	C₂²	1	2	yes	complemented
70	#14583231	C₂²	1	2	yes	complemented
71	#14583230	C₂²	1	2	yes	complemented
72	#14583229	C₂²	1	2	yes	complemented
73	#14583228	C₂²	1	2	yes	complemented
74	#14583228	C₂²	1	2	yes	complemented
75	#14583227	C₂²	1	2	yes	complemented
76	#14583195	C₂²	1	1	yes	characteristic, complemented
77	#14583194	C₂²	1	1	yes	characteristic, complemented
78	#14583193	C₂²	1	2	yes	complemented
79	#14583192	C₂²	1	2	yes	complemented
80	#14583191	C₂²	1	1	yes	characteristic, complemented
81	#14583185	C₂²	1	1	yes	characteristic, complemented
82	#14583184	C₂²	1	1	yes	characteristic, complemented
83	#14583183	C₂²	1	2	yes	complemented
84	#14583182	C₂²	1	2	yes	complemented
85	#14583181	C₂²	1	1	yes	characteristic, complemented
86	#14583158	C₂²	1	2	yes	complemented
87	#14583157	C₂²	1	2	yes	complemented
88	#14583156	C₂²	1	2	yes	complemented
89	#14583156	C₂²	1	2	yes	complemented
90	#14583155	C₂²	1	2	yes	complemented
91	#14583155	C₂²	1	2	yes	complemented
92	#14583154	C₂²	1	2	yes	complemented
93	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
94	Q₁₆×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
95	#14582993	C₂²	1	1	yes	characteristic, complemented
96	C₄×#10621885	C₂²	1	1	yes	characteristic, complemented
97	C₄×#10621885	C₂²	1	1	yes	characteristic, complemented
98	#14582991	C₂²	1	1	yes	characteristic, complemented
99	#14582991	C₂²	1	1	yes	characteristic, complemented
100	#14582978	C₂²	1	1	yes	characteristic
101	#14582977	C₂²	1	1	yes	characteristic
102	#14582976	C₂²	1	1	yes	characteristic
103	#14582975	C₂²	1	2	yes	—
104	#14582974	C₂²	1	2	yes	—
105	#14582942	C₂²	1	2	yes	complemented
106	#14582941	C₂²	1	2	yes	complemented
107	#14582940	C₂²	1	2	yes	complemented
108	#14582940	C₂²	1	2	yes	complemented
109	#14582939	C₂²	1	2	yes	complemented
110	#14582938	C₂²	1	2	yes	complemented
111	#14582938	C₂²	1	2	yes	complemented
112	#107×D₄₃	C₂²	1	1	yes	characteristic
113	#107×D₄₃	C₂²	1	2	yes	—
114	#106×D₄₃	C₂²	1	2	yes	—
115	#106×D₄₃	C₂²	1	2	yes	—
116	#106×D₄₃	C₂²	1	2	yes	—
117	C₄⋊C₈×D₄₃	C₂²	1	1	yes	characteristic
118	#103×D₄₃	C₂²	1	2	yes	—
119	#103×D₄₃	C₂²	1	2	yes	—
120	#103×D₄₃	C₂²	1	1	yes	characteristic
121	#103×D₄₃	C₂²	1	1	yes	characteristic
122	C₂²⋊C₈×D₄₃	C₂²	1	2	yes	—
123	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
124	C₄₃×#556	C₂²	1	1	yes	characteristic
125	C₄₃×#554	C₂²	1	1	yes	characteristic
126	C₄₃×#498	C₂²	1	1	yes	characteristic, complemented
127	C₄₃×#485	C₂²	1	2	yes	complemented
128	C₄₃×#483	C₂²	1	2	yes	complemented
129	C₄₃×#477	C₂²	1	1	yes	characteristic, complemented
130	C₄₃×#475	C₂²	1	1	yes	characteristic, complemented
131	C₄₃×#470	C₂²	1	2	yes	complemented
132	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
133	C₄₃×#436	C₂²	1	1	yes	characteristic
134	C₄₃×#428	C₂²	1	2	yes	complemented
135	C₂×Q₈×D₄₃	—	2	1	no	—
136	C₂×Q₈×D₄₃	—	2	1	no	—
137	C₂×Q₈×D₄₃	C₂³	1	1	yes	characteristic
138	C₂×Q₈×D₄₃	C₂³	1	1	yes	characteristic
139	C₂×D₄×D₄₃	D₄	1	1	yes	characteristic
140	C₂²×C₄×D₄₃	—	2	2	no	—
141	C₂²×C₄×D₄₃	C₂³	1	2	yes	—
142	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
143	C₂×#10621885	C₂³	1	1	yes	characteristic
144	C₂×#10621885	C₂³	1	1	yes	characteristic
145	Q₁₆×D₄₃	—	2	4	no	—
146	C₂×#10621877	C₂³	1	2	yes	—
147	C₂×#10621872	C₂³	1	2	yes	—
148	C₂×#10621872	C₂³	1	2	yes	—
149	M₁₆×D₄₃	—	2	8	no	—
150	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
151	C₂×C₈×D₄₃	C₂³	1	2	yes	—
152	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
153	#13063325	C₂³	1	1	yes	characteristic
154	#13063325	C₂³	1	1	yes	characteristic
155	#13063324	—	2	1	no	—
156	#13063324	—	2	1	no	—
157	#13063324	C₂³	1	2	yes	—
158	#13063324	C₂³	1	2	yes	—
159	#13063323	—	2	1	no	—
160	#13063323	—	2	1	no	—
161	#13063320	—	2	2	no	—
162	#13063320	—	2	2	no	—
163	#13063320	—	2	2	no	—
164	#13063319	—	2	2	no	—
165	#13063318	—	2	2	no	—
166	#13063318	—	2	2	no	—
167	#13063318	—	2	2	no	—
168	#13063317	—	2	1	no	—
169	#13063316	—	2	1	no	—
170	#13063316	—	2	1	no	—
171	#13063315	—	2	2	no	—
172	#13063315	—	2	2	no	—
173	#13063314	—	2	1	no	—
174	#13063313	—	2	1	no	—
175	#13063312	—	2	1	no	—
176	#13063311	—	2	2	no	—
177	#13063311	—	2	2	no	—
178	#13063305	—	2	2	no	—
179	#13063305	C₂³	1	2	yes	—
180	#13063305	C₂³	1	2	yes	—
181	#13063304	—	2	2	no	—
182	#13063304	C₂³	1	2	yes	—
183	#13063304	C₂³	1	2	yes	—
184	#13063303	—	2	2	no	—
185	#13063303	—	2	2	no	—
186	#13063303	—	2	2	no	—
187	#13063303	—	2	2	no	—
188	#13063302	—	2	2	no	—
189	#13063302	—	2	2	no	—
190	#13063302	—	2	2	no	—
191	#13063302	—	2	2	no	—
192	#13063301	—	2	2	no	—
193	#13063301	C₂³	1	2	yes	—
194	#13063301	C₂³	1	2	yes	—
195	Q₈×Dic₄₃	—	2	1	no	—
196	Q₈×Dic₄₃	C₂³	1	1	yes	characteristic
197	Q₈×Dic₄₃	C₂³	1	1	yes	characteristic
198	C₄×Dic₈₆	—	2	1	no	—
199	C₄×Dic₈₆	—	2	2	no	—
200	C₄×Dic₈₆	—	2	1	no	—
201	C₄×Dic₈₆	—	2	1	no	—
202	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
203	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
204	#13063290	—	2	1	no	—
205	#13063290	—	2	2	no	—
206	#13063290	—	2	1	no	—
207	#13063290	—	2	1	no	—
208	#13063290	C₂³	1	1	yes	characteristic
209	#13063290	C₂³	1	1	yes	characteristic
210	C₄×D₁₇₂	—	2	1	no	—
211	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
212	D₄×Dic₄₃	—	2	1	no	—
213	D₄×Dic₄₃	D₄	1	1	yes	characteristic
214	#13063287	—	2	1	no	—
215	#13063287	D₄	1	1	yes	characteristic
216	C₄×C₂²⋊D₄₃	—	2	2	no	—
217	C₄×C₂²⋊D₄₃	C₂³	1	2	yes	—
218	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
219	(C₂²⋊D₄₃)⋊C₄	D₄	1	2	yes	—
220	#13063284	C₂³	1	2	yes	—
221	#13063283	C₂³	1	2	yes	—
222	#13063283	C₂³	1	2	yes	—
223	#13063282	—	2	2	no	—
224	#13063281	—	2	2	no	—
225	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
226	C₂×Dic₄₃⋊C₄	—	2	2	no	—
227	C₄⋊C₄×D₄₃	—	2	2	no	—
228	C₄⋊C₄×D₄₃	—	2	2	no	—
229	C₄⋊C₄×D₄₃	—	2	1	no	—
230	C₄⋊C₄×D₄₃	—	2	2	no	—
231	C₄⋊C₄×D₄₃	—	2	1	no	—
232	C₄⋊C₄×D₄₃	—	2	1	no	—
233	C₄⋊C₄×D₄₃	—	2	2	no	—
234	C₄⋊C₄×D₄₃	—	2	1	no	—
235	C₄⋊C₄×D₄₃	D₄	1	1	yes	characteristic
236	C₄⋊C₄×D₄₃	C₂³	1	1	yes	characteristic
237	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
238	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
239	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
240	C₄⋊C₄×D₄₃	C₂³	1	1	yes	characteristic
241	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
242	C₂²⋊C₄×D₄₃	—	2	2	no	—
243	C₂²⋊C₄×D₄₃	—	2	2	no	—
244	C₂²⋊C₄×D₄₃	—	2	2	no	—
245	C₂²⋊C₄×D₄₃	D₄	1	2	yes	—
246	C₄²×D₄₃	—	2	2	no	—
247	C₄²×D₄₃	—	2	1	no	—
248	C₄²×D₄₃	—	2	1	no	—
249	C₄²×D₄₃	C₂³	1	1	yes	characteristic
250	#13063259	C₂³	1	2	yes	—
251	#13063259	C₂³	1	1	yes	characteristic
252	#13063258	C₂³	1	2	yes	—
253	#13063258	C₂³	1	2	yes	—
254	#13063258	C₂³	1	1	yes	characteristic
255	#13063258	C₂³	1	1	yes	characteristic
256	#13063257	C₂³	1	2	yes	—
257	#13063257	C₂³	1	2	yes	—
258	#13063257	C₂³	1	2	yes	—
259	#13063256	C₂³	1	2	yes	—
260	#13063256	C₂³	1	2	yes	—
261	#13063256	C₂³	1	2	yes	—
262	#13063256	C₂³	1	2	yes	—
263	#13063256	C₂³	1	2	yes	—
264	#13063256	C₂³	1	2	yes	—
265	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
266	Dic₄₃⋊C₈	C₂³	1	2	yes	—
267	#13063250	C₂³	1	2	yes	—
268	#13063250	C₂³	1	2	yes	—
269	#13063250	C₂³	1	1	yes	characteristic
270	#13063250	C₂³	1	1	yes	characteristic
271	#13063249	C₂³	1	2	yes	—
272	#13063249	C₂³	1	2	yes	—
273	#13063249	C₂³	1	1	yes	characteristic
274	#13063249	C₂³	1	1	yes	characteristic
275	#13063248	C₂³	1	2	yes	—
276	#13063248	C₂³	1	2	yes	—
277	#13063248	C₂³	1	1	yes	characteristic
278	#13063248	C₂³	1	1	yes	characteristic
279	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
280	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
281	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
282	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
283	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
284	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
285	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
286	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
287	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
288	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
289	#126×C₄₃	—	2	2	no	—
290	#125×C₄₃	—	2	1	no	—
291	#124×C₄₃	—	2	1	no	—
292	C₂²⋊Q₈×C₄₃	—	2	2	no	—
293	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
294	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
295	C₄×Q₈×C₄₃	—	2	1	no	—
296	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
297	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
298	C₄×D₄×C₄₃	—	2	1	no	—
299	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
300	#117×C₄₃	C₂³	1	2	yes	—
301	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
302	#107×C₄₃	C₂³	1	2	yes	—
303	#107×C₄₃	C₂³	1	1	yes	characteristic
304	#106×C₄₃	C₂³	1	2	yes	—
305	#106×C₄₃	C₂³	1	2	yes	—
306	#106×C₄₃	C₂³	1	2	yes	—
307	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
308	#103×C₄₃	C₂³	1	2	yes	—
309	#103×C₄₃	C₂³	1	2	yes	—
310	#103×C₄₃	C₂³	1	1	yes	characteristic
311	#103×C₄₃	C₂³	1	1	yes	characteristic
312	C₂²⋊C₈×C₄₃	C₂³	1	2	yes	—
313	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
314	C₂³×D₄₃	C₂×D₄	1	2	yes	—
315	C₂×Q₈×C₄₃	—	2	1	no	—
316	C₂×Q₈×C₄₃	—	2	1	no	—
317	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
318	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
319	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
320	C₂²×C₄×C₄₃	—	2	2	no	—
321	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
322	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
323	C₂²×Dic₄₃	—	2	2	no	—
324	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
325	Q₈×D₄₃	—	2	2	no	—
326	Q₈×D₄₃	—	2	2	no	—
327	Q₈×D₄₃	—	2	2	no	—
328	Q₈×D₄₃	—	2	2	no	—
329	Q₈×D₄₃	—	4	4	no	—
330	Q₈×D₄₃	—	8	2	no	—
331	D₄×D₄₃	—	2	4	no	—
332	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
333	C₂×C₄×D₄₃	—	2	4	no	—
334	C₂×C₄×D₄₃	—	2	4	no	—
335	C₂×C₄×D₄₃	—	2	1	no	—
336	C₂×C₄×D₄₃	—	2	1	no	—
337	C₂×C₄×D₄₃	—	2	1	no	—
338	C₂×C₄×D₄₃	—	2	2	no	—
339	C₂×C₄×D₄₃	—	2	1	no	—
340	C₂×C₄×D₄₃	—	2	2	no	—
341	C₂×C₄×D₄₃	—	2	2	no	—
342	C₂×C₄×D₄₃	—	2	2	no	—
343	C₂×C₄×D₄₃	—	8	4	no	—
344	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
345	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
346	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
347	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
348	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
349	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
350	C₂×Dic₈₆	—	2	1	no	—
351	C₂×Dic₈₆	—	2	1	no	—
352	C₂×Dic₈₆	—	2	1	no	—
353	C₂×Dic₈₆	—	2	2	no	—
354	C₂×Dic₈₆	—	2	1	no	—
355	C₂×Dic₈₆	—	2	2	no	—
356	C₂×Dic₈₆	C₂⁴	1	1	yes	characteristic
357	C₂×Dic₈₆	C₂⁴	1	1	yes	characteristic
358	Q₁₆×C₄₃	—	2	2	no	—
359	M₁₆×C₄₃	—	2	4	no	—
360	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
361	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
362	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
363	C₄⋊C₄×C₄₃	—	2	2	no	—
364	C₄⋊C₄×C₄₃	—	2	1	no	—
365	C₄⋊C₄×C₄₃	—	2	2	no	—
366	C₄⋊C₄×C₄₃	—	2	1	no	—
367	C₄⋊C₄×C₄₃	—	2	1	no	—
368	C₄⋊C₄×C₄₃	—	2	2	no	—
369	C₄⋊C₄×C₄₃	—	2	1	no	—
370	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
371	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
372	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
373	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
374	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
375	C₂²⋊C₄×C₄₃	—	2	2	no	—
376	C₂²⋊C₄×C₄₃	—	2	2	no	—
377	C₂²⋊C₄×C₄₃	—	2	2	no	—
378	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
379	C₄²×C₄₃	—	2	2	no	—
380	C₄²×C₄₃	—	2	1	no	—
381	C₄²×C₄₃	—	2	1	no	—
382	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
383	C₂²⋊Dic₄₃	—	2	2	no	—
384	C₂²⋊Dic₄₃	—	2	2	no	—
385	C₂²⋊Dic₄₃	—	2	2	no	—
386	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
387	#10621885	—	2	2	no	—
388	#10621885	—	2	2	no	—
389	(C₂×D₄₃)⋊C₄	—	2	2	no	—
390	(C₂×D₄₃)⋊C₄	—	2	2	no	—
391	(C₂×D₄₃)⋊C₄	—	2	2	no	—
392	(C₂×D₄₃)⋊C₄	—	2	2	no	—
393	(C₂×D₄₃)⋊C₄	—	2	2	no	—
394	(C₂×D₄₃)⋊C₄	—	2	2	no	—
395	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
396	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
397	C₄⋊Dic₄₃	—	2	2	no	—
398	C₄⋊Dic₄₃	—	2	1	no	—
399	C₄⋊Dic₄₃	—	2	1	no	—
400	C₄⋊Dic₄₃	—	2	2	no	—
401	C₄⋊Dic₄₃	—	2	1	no	—
402	C₄⋊Dic₄₃	—	2	1	no	—
403	C₄⋊Dic₄₃	—	2	2	no	—
404	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
405	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
406	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
407	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
408	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
409	Dic₄₃⋊C₄	—	2	2	no	—
410	Dic₄₃⋊C₄	—	2	1	no	—
411	Dic₄₃⋊C₄	—	2	1	no	—
412	Dic₄₃⋊C₄	—	2	2	no	—
413	Dic₄₃⋊C₄	—	2	1	no	—
414	Dic₄₃⋊C₄	—	2	2	no	—
415	Dic₄₃⋊C₄	—	2	2	no	—
416	Dic₄₃⋊C₄	—	2	2	no	—
417	Dic₄₃⋊C₄	—	2	2	no	—
418	Dic₄₃⋊C₄	—	2	2	no	—
419	Dic₄₃⋊C₄	—	2	1	no	—
420	Dic₄₃⋊C₄	—	2	1	no	—
421	Dic₄₃⋊C₄	—	2	2	no	—
422	Dic₄₃⋊C₄	—	2	2	no	—
423	Dic₄₃⋊C₄	—	2	1	no	—
424	Dic₄₃⋊C₄	—	2	2	no	—
425	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
426	C₄×Dic₄₃	—	2	2	no	—
427	C₄×Dic₄₃	—	2	1	no	—
428	C₄×Dic₄₃	—	2	1	no	—
429	C₄×Dic₄₃	—	2	2	no	—
430	C₄×Dic₄₃	—	2	2	no	—
431	C₄×Dic₄₃	—	2	1	no	—
432	C₄×Dic₄₃	—	2	1	no	—
433	C₄×Dic₄₃	—	2	1	no	—
434	C₄×Dic₄₃	—	2	1	no	—
435	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
436	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
437	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
438	#10621877	—	2	4	no	—
439	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
440	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
441	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
442	Dic₁₇₂	—	2	2	no	—
443	#10621872	—	2	4	no	—
444	#10621872	—	2	4	no	—
445	C₈×D₄₃	—	2	4	no	—
446	C₈×D₄₃	—	2	2	no	—
447	C₈×D₄₃	#41	1	4	yes	—
448	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
449	C₂²×D₄₃	—	2	4	no	—
450	C₂²×D₄₃	—	2	4	no	—
451	C₂²×D₄₃	—	2	4	no	—
452	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
453	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
454	Q₈×C₄₃	—	2	1	no	—
455	Q₈×C₄₃	—	2	1	no	—
456	Q₈×C₄₃	—	2	1	no	—
457	Q₈×C₄₃	—	2	1	no	—
458	Q₈×C₄₃	—	4	2	no	—
459	Q₈×C₄₃	—	8	1	no	—
460	D₄×C₄₃	—	2	2	no	—
461	C₂×C₄×C₄₃	—	2	2	no	—
462	C₂×C₄×C₄₃	—	2	2	no	—
463	C₂×C₄×C₄₃	—	2	1	no	—
464	C₂×C₄×C₄₃	—	2	1	no	—
465	C₂×C₄×C₄₃	—	2	1	no	—
466	C₂×C₄×C₄₃	—	2	1	no	—
467	C₂×C₄×C₄₃	—	2	2	no	—
468	C₂×C₄×C₄₃	—	2	2	no	—
469	C₂×C₄×C₄₃	—	8	2	no	—
470	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
471	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
474	C₂²⋊D₄₃	—	2	4	no	—
475	C₂×Dic₄₃	—	2	4	no	—
476	C₂×Dic₄₃	—	2	1	no	—
477	C₂×Dic₄₃	—	2	1	no	—
478	C₂×Dic₄₃	—	2	1	no	—
479	C₂×Dic₄₃	—	2	1	no	—
480	C₂×Dic₄₃	—	2	2	no	—
481	C₂×Dic₄₃	—	2	2	no	—
482	C₂×Dic₄₃	—	8	2	no	—
483	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
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	D₁₇₂	—	2	2	no	—
488	C₄×D₄₃	—	2	4	no	—
489	C₄×D₄₃	—	2	2	no	—
490	C₄×D₄₃	—	2	2	no	—
491	C₄×D₄₃	—	2	2	no	—
492	C₄×D₄₃	—	2	4	no	—
493	C₄×D₄₃	—	4	2	no	—
494	C₄×D₄₃	—	4	2	no	—
495	C₄×D₄₃	—	4	4	no	—
496	C₄×D₄₃	—	4	2	no	—
497	C₄×D₄₃	—	4	2	no	—
498	C₄×D₄₃	—	4	4	no	—
499	C₄×D₄₃	—	8	2	no	—
500	C₄×D₄₃	—	8	2	no	—
501	C₄×D₄₃	#137	1	4	yes	—
502	C₄×D₄₃	C₂×#41	1	2	yes	—
503	C₄×D₄₃	2₋¹⁺⁴	1	2	yes	—
504	Dic₈₆	—	2	1	no	—
505	Dic₈₆	—	2	1	no	—
506	Dic₈₆	—	2	1	no	—
507	Dic₈₆	—	2	1	no	—
508	Dic₈₆	—	4	2	no	—
509	Dic₈₆	—	4	2	no	—
510	Dic₈₆	—	4	2	no	—
511	Dic₈₆	—	4	4	no	—
512	Dic₈₆	—	8	2	no	—
513	Dic₈₆	—	8	1	no	—
514	C₈×C₄₃	—	2	2	no	—
515	C₈×C₄₃	—	2	1	no	—
516	C₈×C₄₃	C₂×#41	1	2	yes	—
517	C₄₃⋊C₈	—	2	2	no	—
518	C₄₃⋊C₈	—	2	1	no	—
519	C₄₃⋊C₈	C₂×#41	1	2	yes	—
520	C₂×#3356	—	43	1	no	maximal, Sylow
521	C₂²×C₄₃	—	2	2	no	—
522	C₂²×C₄₃	—	2	2	no	—
523	C₂²×C₄₃	—	2	2	no	—
524	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
525	C₂×D₄₃	—	2	2	no	—
526	C₂×D₄₃	—	2	2	no	—
527	C₂×D₄₃	—	2	2	no	—
528	C₂×D₄₃	—	4	8	no	—
529	C₂×D₄₃	#547	1	2	yes	—
530	C₂×D₄₃	C₂×#137	1	2	yes	—
531	C₂×D₄₃	#577	1	2	yes	—
532	C₄×C₄₃	—	2	2	no	—
533	C₄×C₄₃	—	2	1	no	—
534	C₄×C₄₃	—	4	1	no	—
535	C₄×C₄₃	—	4	1	no	—
536	C₄×C₄₃	—	4	2	no	—
537	C₄×C₄₃	—	4	2	no	—
538	C₄×C₄₃	—	4	1	no	—
539	C₄×C₄₃	—	4	1	no	—
540	C₄×C₄₃	C₂×#137	1	2	yes	—
541	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
542	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
543	Dic₄₃	—	2	2	no	—
544	Dic₄₃	—	2	1	no	—
545	Dic₄₃	—	4	1	no	—
546	Dic₄₃	—	4	1	no	—
547	Dic₄₃	—	4	2	no	—
548	Dic₄₃	—	4	2	no	—
549	Dic₄₃	—	4	1	no	—
550	Dic₄₃	—	4	1	no	—
551	Dic₄₃	#547	1	2	yes	—
552	Dic₄₃	C₂×#137	1	2	yes	—
553	C₂×#556	—	43	1	no	—
554	C₂×#554	—	43	1	no	—
555	#3356	—	43	1	no	—
556	#3356	—	43	2	no	—
557	#3356	—	43	2	no	—
558	#3356	—	43	1	no	—
559	#3356	—	43	1	no	—
560	#3356	—	43	2	no	—
561	#3356	—	43	1	no	—
562	#3356	—	43	1	no	—
563	#3356	—	43	2	no	—
564	#3356	—	43	1	no	—
565	#3356	—	43	1	no	—
566	#3356	D₄₃	1	1	yes	characteristic, direct product factor
567	C₂×#498	—	43	1	no	—
568	C₂×#485	—	43	2	no	—
569	C₂×#483	—	43	2	no	—
570	C₂×#477	—	43	1	no	—
571	C₂×#475	—	43	1	no	—
572	C₂×#470	—	43	2	no	—
573	C₂×C₄×Q₁₆	—	43	1	no	—
574	C₂×#436	—	43	1	no	—
575	C₂×#428	—	43	2	no	—
576	C₂×C₄₃	—	4	2	no	—
577	C₂×C₄₃	C₂×#547	1	1	yes	characteristic
578	C₂×C₄₃	C₂²×#137	1	1	yes	characteristic
579	C₂×C₄₃	C₂×#577	1	1	yes	characteristic
580	D₄₃	—	4	2	no	—
581	D₄₃	#3356	1	4	yes	direct product factor
582	C₂²×Q₁₆	—	43	1	no	—
583	C₂²×M₁₆	—	43	2	no	—
584	#556	—	43	1	no	—
585	#556	—	43	2	no	—
586	#556	—	43	1	no	—
587	#556	—	43	1	no	—
588	#556	—	43	2	no	—
589	#556	—	86	1	no	—
590	#556	—	86	1	no	—
591	#556	—	86	2	no	—
592	#556	C₂×D₄₃	1	1	yes	characteristic
593	#554	—	43	1	no	—
594	#554	—	43	2	no	—
595	#554	—	43	1	no	—
596	#554	—	43	1	no	—
597	#554	—	43	2	no	—
598	#554	—	86	1	no	—
599	#554	—	86	2	no	—
600	#554	—	86	1	no	—
601	#554	C₂×D₄₃	1	1	yes	characteristic
602	C₂×C₄⋊Q₈	—	43	1	no	—
603	C₂×C₄⋊Q₈	—	43	1	no	—
604	C₂×#126	—	86	2	no	—
605	C₂×#125	—	86	1	no	—
606	C₂×#124	—	86	1	no	—
607	C₂×C₂²⋊Q₈	—	43	2	no	—
608	C₂×C₂²⋊Q₈	—	43	2	no	—
609	C₂×C₂²⋊Q₈	—	86	2	no	—
610	C₂×C₄×Q₈	—	43	1	no	—
611	C₂×C₄×Q₈	—	43	1	no	—
612	C₂×C₄×Q₈	—	86	1	no	—
613	C₂×C₄×D₄	—	43	1	no	—
614	C₂×C₄×D₄	—	86	1	no	—
615	C₂×#117	—	43	2	no	—
616	C₂²×C₄⋊C₄	—	43	2	no	—
617	#498	—	43	1	no	—
618	#498	—	43	1	no	—
619	#498	—	43	2	no	—
620	#498	—	43	2	no	—
621	#498	—	43	1	no	—
622	#498	C₂×D₄₃	1	1	yes	characteristic, complemented
623	#485	—	43	2	no	—
624	#485	—	43	2	no	—
625	#485	—	43	2	no	—
626	#485	—	43	2	no	—
627	#485	—	43	2	no	—
628	#485	—	43	2	no	—
629	#485	—	43	2	no	—
630	#485	C₂×D₄₃	1	2	yes	complemented
631	#483	—	43	2	no	—
632	#483	—	43	2	no	—
633	#483	—	43	2	no	—
634	#483	—	43	2	no	—
635	#483	—	43	2	no	—
636	#483	—	43	2	no	—
637	#483	—	43	2	no	—
638	#483	C₂×D₄₃	1	2	yes	complemented
639	#477	—	43	1	no	—
640	#477	—	43	1	no	—
641	#477	—	43	2	no	—
642	#477	—	43	1	no	—
643	#477	—	43	2	no	—
644	#477	C₂×D₄₃	1	1	yes	characteristic, complemented
645	#475	—	43	1	no	—
646	#475	—	43	1	no	—
647	#475	—	43	2	no	—
648	#475	—	43	1	no	—
649	#475	—	43	2	no	—
650	#475	C₂×D₄₃	1	1	yes	characteristic, complemented
651	#470	—	43	2	no	—
652	#470	—	43	2	no	—
653	#470	—	43	2	no	—
654	#470	—	43	2	no	—
655	#470	—	43	2	no	—
656	#470	—	43	2	no	—
657	#470	—	43	2	no	—
658	#470	C₂×D₄₃	1	2	yes	complemented
659	C₄×Q₁₆	—	43	1	no	—
660	C₄×Q₁₆	—	43	1	no	—
661	C₄×Q₁₆	—	43	1	no	—
662	C₄×Q₁₆	—	43	1	no	—
663	C₄×Q₁₆	—	43	1	no	—
664	C₄×Q₁₆	—	43	1	no	—
665	C₄×Q₁₆	—	43	1	no	—
666	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
667	#436	—	43	2	no	—
668	#436	—	43	1	no	—
669	#436	—	43	1	no	—
670	#436	—	43	2	no	—
671	#436	—	43	1	no	—
672	#436	C₂×D₄₃	1	1	yes	characteristic
673	#428	—	43	2	no	—
674	#428	—	43	2	no	—
675	#428	—	43	2	no	—
676	#428	—	43	2	no	—
677	#428	—	43	2	no	—
678	#428	—	43	2	no	—
679	#428	—	43	2	no	—
680	#428	C₂×D₄₃	1	2	yes	complemented
681	C₂×#107	—	43	2	no	—
682	C₂×#107	—	43	1	no	—
683	C₂×#106	—	43	2	no	—
684	C₂×#106	—	43	2	no	—
685	C₂×#106	—	43	2	no	—
686	C₂×C₄⋊C₈	—	43	1	no	—
687	C₂×#103	—	43	2	no	—
688	C₂×#103	—	43	2	no	—
689	C₂×#103	—	43	1	no	—
690	C₂×#103	—	43	1	no	—
691	C₂×C₂²⋊C₈	—	43	2	no	—
692	C₂×C₄×C₈	—	43	1	no	—
693	C₄₃	C₂×#3356	1	1	yes	characteristic, complemented, Sylow
694	C₂²×Q₈	—	43	1	no	—
695	C₂²×Q₈	—	43	1	no	—
696	C₂²×Q₈	—	86	1	no	—
697	C₂²×Q₈	—	86	1	no	—
698	C₂²×D₄	—	43	1	no	—
699	C₂³×C₄	—	43	2	no	—
700	C₂³×C₄	—	86	2	no	—
701	C₂×Q₁₆	—	43	1	no	—
702	C₂×Q₁₆	—	43	1	no	—
703	C₂×Q₁₆	—	43	1	no	—
704	C₂×Q₁₆	—	86	4	no	—
705	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
706	C₂×M₁₆	—	43	2	no	—
707	C₂×M₁₆	—	43	2	no	—
708	C₂×M₁₆	—	43	2	no	—
709	C₂×M₁₆	—	86	8	no	—
710	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
711	C₂²×C₈	—	43	1	no	—
712	C₂²×C₈	—	43	2	no	—
713	C₂²×C₈	—	43	1	no	—
714	C₄⋊Q₈	—	43	2	no	—
715	C₄⋊Q₈	—	43	2	no	—
716	C₄⋊Q₈	—	43	1	no	—
717	C₄⋊Q₈	—	43	1	no	—
718	C₄⋊Q₈	—	86	1	no	—
719	C₄⋊Q₈	—	86	1	no	—
720	C₄⋊Q₈	—	86	1	no	—
721	C₄⋊Q₈	—	86	1	no	—
722	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
723	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
724	#126	—	2	2	no	—
725	#126	—	86	2	no	—
726	#126	—	86	2	no	—
727	#126	—	86	2	no	—
728	#126	—	86	2	no	—
729	#126	—	86	2	no	—
730	#126	—	86	2	no	—
731	#126	—	86	2	no	—
732	#125	—	2	1	no	—
733	#125	—	86	1	no	—
734	#125	—	86	2	no	—
735	#125	—	86	2	no	—
736	#125	—	86	1	no	—
737	#125	—	86	1	no	—
738	#124	—	2	1	no	—
739	#124	—	86	1	no	—
740	#124	—	86	2	no	—
741	#124	—	86	2	no	—
742	#124	—	86	1	no	—
743	#124	—	86	1	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	43	2	no	—
746	C₂²⋊Q₈	—	43	2	no	—
747	C₂²⋊Q₈	—	43	2	no	—
748	C₂²⋊Q₈	—	43	2	no	—
749	C₂²⋊Q₈	—	43	2	no	—
750	C₂²⋊Q₈	—	43	2	no	—
751	C₂²⋊Q₈	—	86	2	no	—
752	C₂²⋊Q₈	—	86	2	no	—
753	C₂²⋊Q₈	—	86	2	no	—
754	C₂²⋊Q₈	—	86	2	no	—
755	C₂²⋊Q₈	—	86	2	no	—
756	C₂²⋊Q₈	—	86	2	no	—
757	C₂²⋊Q₈	—	86	2	no	—
758	C₂²⋊Q₈	—	86	2	no	—
759	C₂²⋊Q₈	—	86	2	no	—
760	C₂²⋊Q₈	—	86	2	no	—
761	C₂²⋊Q₈	—	86	2	no	—
762	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
763	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	43	1	no	—
766	C₄×Q₈	—	43	1	no	—
767	C₄×Q₈	—	43	1	no	—
768	C₄×Q₈	—	43	1	no	—
769	C₄×Q₈	—	43	1	no	—
770	C₄×Q₈	—	43	1	no	—
771	C₄×Q₈	—	86	1	no	—
772	C₄×Q₈	—	86	1	no	—
773	C₄×Q₈	—	86	2	no	—
774	C₄×Q₈	—	86	1	no	—
775	C₄×Q₈	—	86	1	no	—
776	C₄×Q₈	—	86	1	no	—
777	C₄×Q₈	—	86	2	no	—
778	C₄×Q₈	—	86	1	no	—
779	C₄×Q₈	—	86	1	no	—
780	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
781	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
782	C₄×D₄	—	2	1	no	—
783	C₄×D₄	—	43	1	no	—
784	C₄×D₄	—	43	2	no	—
785	C₄×D₄	—	43	1	no	—
786	C₄×D₄	—	43	2	no	—
787	C₄×D₄	—	43	1	no	—
788	C₄×D₄	—	86	1	no	—
789	C₄×D₄	—	86	2	no	—
790	C₄×D₄	—	86	1	no	—
791	C₄×D₄	—	86	2	no	—
792	C₄×D₄	—	86	1	no	—
793	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
794	#117	—	43	2	no	—
795	#117	—	43	2	no	—
796	#117	—	43	2	no	—
797	#117	—	86	2	no	—
798	#117	—	86	2	no	—
799	#117	C₂²×D₄₃	1	2	yes	—
800	C₂×C₄⋊C₄	—	43	1	no	—
801	C₂×C₄⋊C₄	—	43	2	no	—
802	C₂×C₄⋊C₄	—	43	1	no	—
803	C₂×C₄⋊C₄	—	43	2	no	—
804	C₂×C₄⋊C₄	—	43	2	no	—
805	C₂×C₄⋊C₄	—	43	2	no	—
806	C₂×C₄⋊C₄	—	43	1	no	—
807	C₂×C₄⋊C₄	—	43	2	no	—
808	C₂×C₄⋊C₄	—	86	2	no	—
809	C₂×C₄⋊C₄	—	86	2	no	—
810	C₂×C₄⋊C₄	—	86	1	no	—
811	C₂×C₄⋊C₄	—	86	1	no	—
812	C₂×C₄⋊C₄	—	86	1	no	—
813	C₂×C₄⋊C₄	—	86	2	no	—
814	C₂×C₄⋊C₄	—	86	2	no	—
815	C₂×C₄⋊C₄	—	86	1	no	—
816	C₂×C₄⋊C₄	—	86	2	no	—
817	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
818	C₂×C₂²⋊C₄	—	43	2	no	—
819	C₂×C₂²⋊C₄	—	86	2	no	—
820	C₂×C₂²⋊C₄	—	86	2	no	—
821	C₂×C₂²⋊C₄	—	86	2	no	—
822	C₂×C₄²	—	43	1	no	—
823	C₂×C₄²	—	86	2	no	—
824	C₂×C₄²	—	86	1	no	—
825	C₂×C₄²	—	86	1	no	—
826	#107	—	43	1	no	—
827	#107	—	43	2	no	—
828	#107	—	43	1	no	—
829	#107	—	43	1	no	—
830	#107	—	43	2	no	—
831	#107	—	43	2	no	—
832	#107	C₂²×D₄₃	1	1	yes	characteristic
833	#107	C₂²×D₄₃	1	2	yes	—
834	#106	—	43	2	no	—
835	#106	—	43	2	no	—
836	#106	—	43	2	no	—
837	#106	—	43	2	no	—
838	#106	—	43	2	no	—
839	#106	—	43	2	no	—
840	#106	—	43	2	no	—
841	#106	—	43	2	no	—
842	#106	—	43	2	no	—
843	#106	C₂²×D₄₃	1	2	yes	—
844	#106	C₂²×D₄₃	1	2	yes	—
845	#106	C₂²×D₄₃	1	2	yes	—
846	C₄⋊C₈	—	43	2	no	—
847	C₄⋊C₈	—	43	1	no	—
848	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
849	#103	—	43	1	no	—
850	#103	—	43	1	no	—
851	#103	—	43	2	no	—
852	#103	—	43	2	no	—
853	#103	—	43	1	no	—
854	#103	—	43	1	no	—
855	#103	—	43	2	no	—
856	#103	—	43	2	no	—
857	#103	—	43	1	no	—
858	#103	—	43	1	no	—
859	#103	—	43	2	no	—
860	#103	—	43	2	no	—
861	#103	C₂²×D₄₃	1	1	yes	characteristic
862	#103	C₂²×D₄₃	1	1	yes	characteristic
863	#103	C₂²×D₄₃	1	2	yes	—
864	#103	C₂²×D₄₃	1	2	yes	—
865	C₂²⋊C₈	—	43	2	no	—
866	C₂²⋊C₈	—	43	2	no	—
867	C₂²⋊C₈	—	43	2	no	—
868	C₂²⋊C₈	C₂²×D₄₃	1	2	yes	—
869	C₄×C₈	—	43	1	no	—
870	C₄×C₈	—	43	1	no	—
871	C₄×C₈	—	43	1	no	—
872	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
873	C₂⁴	—	43	2	no	—
874	C₂×Q₈	—	2	1	no	—
875	C₂×Q₈	—	2	1	no	—
876	C₂×Q₈	—	43	1	no	—
877	C₂×Q₈	—	43	1	no	—
878	C₂×Q₈	—	86	2	no	—
879	C₂×Q₈	—	86	1	no	—
880	C₂×Q₈	—	86	1	no	—
881	C₂×Q₈	—	86	2	no	—
882	C₂×Q₈	—	86	2	no	—
883	C₂×Q₈	—	86	2	no	—
884	C₂×Q₈	—	86	2	no	—
885	C₂×Q₈	—	86	2	no	—
886	C₂×Q₈	—	86	1	no	—
887	C₂×Q₈	—	86	1	no	—
888	C₂×Q₈	—	344	2	no	—
889	C₂×Q₈	—	172	4	no	—
890	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
891	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
892	C₂×D₄	—	43	2	no	—
893	C₂×D₄	—	43	1	no	—
894	C₂×D₄	—	86	4	no	—
895	C₂×D₄	D₄×D₄₃	1	1	yes	characteristic
896	C₂²×C₄	—	2	2	no	—
897	C₂²×C₄	—	43	1	no	—
898	C₂²×C₄	—	43	1	no	—
899	C₂²×C₄	—	43	2	no	—
900	C₂²×C₄	—	43	1	no	—
901	C₂²×C₄	—	43	2	no	—
902	C₂²×C₄	—	43	2	no	—
903	C₂²×C₄	—	43	2	no	—
904	C₂²×C₄	—	86	4	no	—
905	C₂²×C₄	—	86	4	no	—
906	C₂²×C₄	—	86	2	no	—
907	C₂²×C₄	—	86	2	no	—
908	C₂²×C₄	—	86	1	no	—
909	C₂²×C₄	—	86	2	no	—
910	C₂²×C₄	—	86	1	no	—
911	C₂²×C₄	—	86	1	no	—
912	C₂²×C₄	—	86	1	no	—
913	C₂²×C₄	—	86	2	no	—
914	C₂²×C₄	—	86	2	no	—
915	C₂²×C₄	—	344	4	no	—
916	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
917	Q₁₆	—	2	2	no	—
918	Q₁₆	—	86	2	no	—
919	Q₁₆	—	86	2	no	—
920	Q₁₆	—	86	2	no	—
921	M₁₆	—	2	4	no	—
922	M₁₆	—	86	4	no	—
923	M₁₆	—	86	4	no	—
924	M₁₆	—	86	4	no	—
925	C₂×C₈	—	43	1	no	—
926	C₂×C₈	—	43	4	no	—
927	C₂×C₈	—	43	1	no	—
928	C₂×C₈	—	43	2	no	—
929	C₂×C₈	—	86	4	no	—
930	C₂×C₈	—	86	2	no	—
931	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
932	C₂×C₈	C₂³×D₄₃	1	2	yes	—
933	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	2	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	43	2	no	—
942	C₄⋊C₄	—	43	1	no	—
943	C₄⋊C₄	—	43	2	no	—
944	C₄⋊C₄	—	43	1	no	—
945	C₄⋊C₄	—	43	2	no	—
946	C₄⋊C₄	—	43	1	no	—
947	C₄⋊C₄	—	86	1	no	—
948	C₄⋊C₄	—	86	2	no	—
949	C₄⋊C₄	—	86	2	no	—
950	C₄⋊C₄	—	86	2	no	—
951	C₄⋊C₄	—	86	1	no	—
952	C₄⋊C₄	—	86	2	no	—
953	C₄⋊C₄	—	86	2	no	—
954	C₄⋊C₄	—	86	1	no	—
955	C₄⋊C₄	—	86	1	no	—
956	C₄⋊C₄	—	86	1	no	—
957	C₄⋊C₄	—	86	1	no	—
958	C₄⋊C₄	—	86	2	no	—
959	C₄⋊C₄	—	86	2	no	—
960	C₄⋊C₄	—	86	2	no	—
961	C₄⋊C₄	—	86	2	no	—
962	C₄⋊C₄	—	86	2	no	—
963	C₄⋊C₄	—	86	2	no	—
964	C₄⋊C₄	—	86	1	no	—
965	C₄⋊C₄	—	86	1	no	—
966	C₄⋊C₄	—	86	1	no	—
967	C₄⋊C₄	—	86	2	no	—
968	C₄⋊C₄	—	86	2	no	—
969	C₄⋊C₄	—	86	1	no	—
970	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
971	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
972	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
973	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
974	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
975	C₂²⋊C₄	—	2	2	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	2	2	no	—
978	C₂²⋊C₄	—	43	2	no	—
979	C₂²⋊C₄	—	43	2	no	—
980	C₂²⋊C₄	—	43	2	no	—
981	C₂²⋊C₄	—	86	2	no	—
982	C₂²⋊C₄	—	86	2	no	—
983	C₂²⋊C₄	—	86	2	no	—
984	C₂²⋊C₄	—	86	2	no	—
985	C₂²⋊C₄	—	86	2	no	—
986	C₂²⋊C₄	—	86	2	no	—
987	C₂²⋊C₄	—	86	2	no	—
988	C₂²⋊C₄	—	86	2	no	—
989	C₂²⋊C₄	—	86	2	no	—
990	C₂²⋊C₄	D₄×D₄₃	1	2	yes	—
991	C₄²	—	2	2	no	—
992	C₄²	—	2	1	no	—
993	C₄²	—	2	1	no	—
994	C₄²	—	43	1	no	—
995	C₄²	—	43	1	no	—
996	C₄²	—	43	1	no	—
997	C₄²	—	86	2	no	—
998	C₄²	—	86	2	no	—
999	C₄²	—	86	1	no	—
1000	C₄²	—	86	1	no	—
1001	C₄²	—	86	1	no	—
1002	C₄²	—	86	1	no	—
1003	C₄²	—	86	2	no	—
1004	C₄²	—	86	1	no	—
1005	C₄²	—	86	1	no	—
1006	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1007	C₂³	—	43	1	no	—
1008	C₂³	—	43	2	no	—
1009	C₂³	—	86	4	no	—
1010	C₂³	—	86	4	no	—
1011	C₂³	—	86	4	no	—
1012	C₂³	C₂×D₄×D₄₃	1	2	yes	—
1013	Q₈	—	2	1	no	—
1014	Q₈	—	2	1	no	—
1015	Q₈	—	2	1	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	4	2	no	—
1018	Q₈	—	8	1	no	—
1019	Q₈	—	86	1	no	—
1020	Q₈	—	86	1	no	—
1021	Q₈	—	86	1	no	—
1022	Q₈	—	86	1	no	—
1023	Q₈	—	344	1	no	—
1024	Q₈	—	344	2	no	—
1025	Q₈	—	172	2	no	—
1026	Q₈	—	172	2	no	—
1027	Q₈	—	172	4	no	—
1028	Q₈	—	172	2	no	—
1029	D₄	—	2	2	no	—
1030	D₄	—	86	4	no	—
1031	D₄	—	86	2	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	2	2	no	—
1034	C₂×C₄	—	2	1	no	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	1	no	—
1037	C₂×C₄	—	2	2	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	2	no	—
1040	C₂×C₄	—	8	2	no	—
1041	C₂×C₄	—	43	1	no	—
1042	C₂×C₄	—	43	1	no	—
1043	C₂×C₄	—	43	4	no	—
1044	C₂×C₄	—	43	2	no	—
1045	C₂×C₄	—	43	2	no	—
1046	C₂×C₄	—	43	1	no	—
1047	C₂×C₄	—	43	2	no	—
1048	C₂×C₄	—	86	4	no	—
1049	C₂×C₄	—	86	4	no	—
1050	C₂×C₄	—	86	2	no	—
1051	C₂×C₄	—	86	4	no	—
1052	C₂×C₄	—	86	2	no	—
1053	C₂×C₄	—	86	2	no	—
1054	C₂×C₄	—	86	1	no	—
1055	C₂×C₄	—	86	2	no	—
1056	C₂×C₄	—	86	1	no	—
1057	C₂×C₄	—	86	1	no	—
1058	C₂×C₄	—	86	1	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	—	172	2	no	—
1064	C₂×C₄	—	172	4	no	—
1065	C₂×C₄	—	172	2	no	—
1066	C₂×C₄	—	172	2	no	—
1067	C₂×C₄	—	172	4	no	—
1068	C₂×C₄	—	172	2	no	—
1069	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
1070	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1071	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1072	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1073	C₈	—	2	2	no	—
1074	C₈	—	2	1	no	—
1075	C₈	—	43	2	no	—
1076	C₈	—	86	2	no	—
1077	C₈	—	86	1	no	—
1078	C₈	#41×D₄₃	1	2	yes	—
1079	C₂²	—	2	2	no	—
1080	C₂²	—	2	2	no	—
1081	C₂²	—	2	2	no	—
1082	C₂²	—	43	2	no	—
1083	C₂²	—	43	2	no	—
1084	C₂²	—	43	2	no	—
1085	C₂²	—	86	2	no	—
1086	C₂²	—	86	2	no	—
1087	C₂²	—	86	2	no	—
1088	C₂²	—	172	8	no	—
1089	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1090	C₄	—	2	2	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	4	1	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	2	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	2	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	43	2	no	—
1099	C₄	—	43	2	no	—
1100	C₄	—	86	2	no	—
1101	C₄	—	86	1	no	—
1102	C₄	—	172	1	no	—
1103	C₄	—	172	1	no	—
1104	C₄	—	172	2	no	—
1105	C₄	—	172	1	no	—
1106	C₄	—	172	2	no	—
1107	C₄	—	172	1	no	—
1108	C₄	#137×D₄₃	1	2	yes	—
1109	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1110	C₄	2₋¹⁺⁴×D₄₃	1	1	yes	characteristic
1111	C₂	—	4	2	no	—
1112	C₂	—	43	4	no	—
1113	C₂	—	172	2	no	—
1114	C₂	#547×D₄₃	1	1	yes	characteristic
1115	C₂	C₂×#137×D₄₃	1	1	yes	characteristic
1116	C₂	#577×D₄₃	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×#3356	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	C₂×D₄×D₄₃	D₄
hypercenter	#3356	D₄₃
hypocenter	C₄₃	C₂×#3356
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #3356

Complements

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

N	H ≅ G/N	type
3. #19147213	C₂	semidirect
4. #19147212	C₂	semidirect
5. #19147211	C₂	semidirect
6. #19147210	C₂	semidirect
7. #19147209	C₂	semidirect
8. #19147208	C₂	semidirect
9. #19147207	C₂	semidirect
10. #19147206	C₂	semidirect
11. #19147205	C₂	semidirect
12. #19147204	C₂	semidirect
13. #19147203	C₂	semidirect
14. #498×D₄₃	C₂	semidirect
15. #485×D₄₃	C₂	semidirect
16. #483×D₄₃	C₂	semidirect
17. #477×D₄₃	C₂	semidirect
18. #475×D₄₃	C₂	semidirect
19. #470×D₄₃	C₂	semidirect
20. C₄×Q₁₆×D₄₃	C₂	semidirect
22. #428×D₄₃	C₂	semidirect
23. C₄₃×#3356	C₂	semidirect
57. #14583297	C₂²	semidirect
58. #14583296	C₂²	semidirect
59. #14583296	C₂²	semidirect
60. #14583295	C₂²	semidirect
61. #14583295	C₂²	semidirect
62. #14583243	C₂²	semidirect
63. #14583242	C₂²	semidirect
64. #14583241	C₂²	semidirect
65. #14583240	C₂²	semidirect
66. #14583239	C₂²	semidirect
67. #14583238	C₂²	semidirect
68. #14583237	C₂²	semidirect
69. #14583231	C₂²	semidirect
70. #14583231	C₂²	semidirect
71. #14583230	C₂²	semidirect
72. #14583229	C₂²	semidirect
73. #14583228	C₂²	semidirect
74. #14583228	C₂²	semidirect
75. #14583227	C₂²	semidirect
76. #14583195	C₂²	semidirect
77. #14583194	C₂²	semidirect
78. #14583193	C₂²	semidirect
79. #14583192	C₂²	semidirect
80. #14583191	C₂²	semidirect
81. #14583185	C₂²	semidirect
82. #14583184	C₂²	semidirect
83. #14583183	C₂²	semidirect
84. #14583182	C₂²	semidirect
85. #14583181	C₂²	semidirect
86. #14583158	C₂²	semidirect
87. #14583157	C₂²	semidirect
88. #14583156	C₂²	semidirect
89. #14583156	C₂²	semidirect
90. #14583155	C₂²	semidirect
91. #14583155	C₂²	semidirect
92. #14583154	C₂²	semidirect
93. C₄×Dic₁₇₂	C₂²	semidirect
94. Q₁₆×Dic₄₃	C₂²	semidirect
95. #14582993	C₂²	semidirect
96. C₄×#10621885	C₂²	semidirect
97. C₄×#10621885	C₂²	semidirect
98. #14582991	C₂²	semidirect
99. #14582991	C₂²	semidirect
105. #14582942	C₂²	semidirect
106. #14582941	C₂²	semidirect
107. #14582940	C₂²	semidirect
108. #14582940	C₂²	semidirect
109. #14582939	C₂²	semidirect
110. #14582938	C₂²	semidirect
111. #14582938	C₂²	semidirect
126. C₄₃×#498	C₂²	semidirect
127. C₄₃×#485	C₂²	semidirect
128. C₄₃×#483	C₂²	semidirect
129. C₄₃×#477	C₂²	semidirect
130. C₄₃×#475	C₂²	semidirect
131. C₄₃×#470	C₂²	semidirect
132. C₄×Q₁₆×C₄₃	C₂²	semidirect
134. C₄₃×#428	C₂²	semidirect
566. #3356	D₄₃	direct (N × H)
581. D₄₃	#3356	direct (N × H)
622. #498	C₂×D₄₃	semidirect
630. #485	C₂×D₄₃	semidirect
638. #483	C₂×D₄₃	semidirect
644. #477	C₂×D₄₃	semidirect
650. #475	C₂×D₄₃	semidirect
658. #470	C₂×D₄₃	semidirect
666. C₄×Q₁₆	C₂×D₄₃	semidirect
680. #428	C₂×D₄₃	semidirect
693. C₄₃	C₂×#3356	semidirect

Maximal subgroups

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

subgroup	index
#556×D₄₃	2
#554×D₄₃	2
#19147213	2
#19147212	2
#19147211	2
#19147210	2
#19147209	2
#19147208	2
#19147207	2
#19147206	2
#19147205	2
#19147204	2
#19147203	2
#498×D₄₃	2
#485×D₄₃	2
#483×D₄₃	2
#477×D₄₃	2
#475×D₄₃	2
#470×D₄₃	2
C₄×Q₁₆×D₄₃	2
#436×D₄₃	2
#428×D₄₃	2
C₄₃×#3356	2
C₂×#3356	43

Subgroups — D43×#3356 #25975327

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×#3356 #25975327