Subgroups — D₄₃×#3375 #25976326

Order 11008.

1906 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#559×D₄₃	C₂	1	1	yes	maximal, characteristic
2	Q₈²×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147414	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147413	C₂	1	1	yes	maximal, characteristic, complemented
5	#19147412	C₂	1	2	yes	maximal, complemented
6	#19147411	C₂	1	1	yes	maximal, characteristic, complemented
7	#19147410	C₂	1	2	yes	maximal, complemented
8	#19147409	C₂	1	1	yes	maximal, characteristic, complemented
9	#19147408	C₂	1	1	yes	maximal, characteristic, complemented
10	#19147407	C₂	1	1	yes	maximal, characteristic, complemented
11	#19147406	C₂	1	2	yes	maximal, complemented
12	#19147405	C₂	1	1	yes	maximal, characteristic, complemented
13	#19147404	C₂	1	2	yes	maximal, complemented
14	#489×D₄₃	C₂	1	2	yes	maximal, complemented
15	#486×D₄₃	C₂	1	1	yes	maximal, characteristic
16	#477×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
17	#474×D₄₃	C₂	1	2	yes	maximal, complemented
18	#464×D₄₃	C₂	1	2	yes	maximal, complemented
19	#460×D₄₃	C₂	1	1	yes	maximal, characteristic
20	#446×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#440×D₄₃	C₂	1	2	yes	maximal, complemented
22	C₄×Q₁₆×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3375	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	#14583635	C₂²	1	1	yes	characteristic
27	#14583634	C₂²	1	1	yes	characteristic
28	#14583634	C₂²	1	1	yes	characteristic
29	#14583633	—	2	2	no	—
30	#14583632	—	2	1	no	—
31	#14583632	C₂²	1	2	yes	—
32	#14583631	—	2	1	no	—
33	#14583631	C₂²	1	2	yes	—
34	Q₈×Dic₈₆	—	2	1	no	—
35	Q₈×Dic₈₆	C₂²	1	2	yes	complemented
36	Q₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
37	Q₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
38	#14583629	—	2	1	no	—
39	#14583629	—	2	2	no	—
40	#14583629	C₂²	1	2	yes	complemented
41	#14583629	C₂²	1	1	yes	characteristic, complemented
42	C₄⋊Q₈×D₄₃	—	2	1	no	—
43	C₄⋊Q₈×D₄₃	—	2	2	no	—
44	C₄⋊Q₈×D₄₃	C₂²	1	2	yes	—
45	C₄⋊Q₈×D₄₃	C₂²	1	1	yes	characteristic
46	#127×D₄₃	C₂²	1	1	yes	characteristic
47	#124×D₄₃	—	2	1	no	—
48	#124×D₄₃	C₂²	1	2	yes	—
49	#123×D₄₃	—	2	2	no	—
50	C₄×Q₈×D₄₃	—	2	1	no	—
51	C₄×Q₈×D₄₃	C₂²	1	1	yes	characteristic
52	C₄×Q₈×D₄₃	C₂²	1	2	yes	—
53	C₄×Q₈×D₄₃	C₂²	1	1	yes	characteristic
54	C₄×Q₈×D₄₃	C₂²	1	1	yes	characteristic
55	C₄×D₄×D₄₃	—	2	1	no	—
56	C₄×D₄×D₄₃	C₂²	1	2	yes	—
57	#14583261	C₂²	1	2	yes	complemented
58	#14583260	C₂²	1	2	yes	complemented
59	#14583260	C₂²	1	2	yes	complemented
60	#14583259	C₂²	1	2	yes	complemented
61	#14583258	C₂²	1	2	yes	complemented
62	#14583257	C₂²	1	2	yes	complemented
63	#14583257	C₂²	1	2	yes	complemented
64	#14583247	C₂²	1	1	yes	characteristic
65	#14583246	C₂²	1	1	yes	characteristic
66	#14583245	C₂²	1	1	yes	characteristic
67	#14583244	C₂²	1	2	yes	—
68	#14583244	C₂²	1	2	yes	—
69	#14583195	C₂²	1	1	yes	characteristic, complemented
70	#14583194	C₂²	1	1	yes	characteristic, complemented
71	#14583193	C₂²	1	2	yes	complemented
72	#14583192	C₂²	1	2	yes	complemented
73	#14583191	C₂²	1	1	yes	characteristic, complemented
74	#14583180	C₂²	1	2	yes	complemented
75	#14583179	C₂²	1	2	yes	complemented
76	#14583178	C₂²	1	2	yes	complemented
77	#14583178	C₂²	1	2	yes	complemented
78	#14583177	C₂²	1	2	yes	complemented
79	#14583177	C₂²	1	2	yes	complemented
80	#14583176	C₂²	1	2	yes	complemented
81	#14583124	C₂²	1	2	yes	complemented
82	#14583123	C₂²	1	2	yes	complemented
83	#14583122	C₂²	1	2	yes	complemented
84	#14583121	C₂²	1	2	yes	complemented
85	#14583120	C₂²	1	2	yes	complemented
86	#14583119	C₂²	1	2	yes	complemented
87	#14583118	C₂²	1	2	yes	complemented
88	#14583100	C₂²	1	1	yes	characteristic
89	#14583099	C₂²	1	1	yes	characteristic
90	#14583098	C₂²	1	2	yes	—
91	#14583097	C₂²	1	2	yes	—
92	#14583096	C₂²	1	1	yes	characteristic
93	#14583030	C₂²	1	1	yes	characteristic, complemented
94	#14583029	C₂²	1	1	yes	characteristic, complemented
95	#14583028	C₂²	1	2	yes	complemented
96	#14583027	C₂²	1	2	yes	complemented
97	#14583026	C₂²	1	1	yes	characteristic, complemented
98	#14583002	C₂²	1	2	yes	complemented
99	#14583001	C₂²	1	2	yes	complemented
100	#14583000	C₂²	1	2	yes	complemented
101	#14582999	C₂²	1	2	yes	complemented
102	#14582998	C₂²	1	2	yes	complemented
103	#14582997	C₂²	1	2	yes	complemented
104	#14582996	C₂²	1	2	yes	complemented
105	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
106	Q₁₆×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
107	#14582993	C₂²	1	1	yes	characteristic, complemented
108	C₄×#10621885	C₂²	1	1	yes	characteristic, complemented
109	C₄×#10621885	C₂²	1	1	yes	characteristic, complemented
110	#14582991	C₂²	1	1	yes	characteristic, complemented
111	#14582991	C₂²	1	1	yes	characteristic, complemented
112	#107×D₄₃	C₂²	1	1	yes	characteristic
113	#107×D₄₃	C₂²	1	2	yes	—
114	C₄⋊C₈×D₄₃	C₂²	1	1	yes	characteristic
115	C₄⋊C₈×D₄₃	C₂²	1	2	yes	—
116	#103×D₄₃	C₂²	1	2	yes	—
117	#103×D₄₃	C₂²	1	1	yes	characteristic
118	#103×D₄₃	C₂²	1	1	yes	characteristic
119	#102×D₄₃	C₂²	1	2	yes	—
120	#102×D₄₃	C₂²	1	2	yes	—
121	#102×D₄₃	C₂²	1	2	yes	—
122	#97×D₄₃	C₂²	1	2	yes	—
123	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
124	C₄₃×#559	C₂²	1	1	yes	characteristic
125	Q₈²×C₄₃	C₂²	1	1	yes	characteristic, complemented
126	C₄₃×#489	C₂²	1	2	yes	complemented
127	C₄₃×#486	C₂²	1	1	yes	characteristic
128	C₄₃×#477	C₂²	1	1	yes	characteristic, complemented
129	C₄₃×#474	C₂²	1	2	yes	complemented
130	C₄₃×#464	C₂²	1	2	yes	complemented
131	C₄₃×#460	C₂²	1	1	yes	characteristic
132	C₄₃×#446	C₂²	1	1	yes	characteristic, complemented
133	C₄₃×#440	C₂²	1	2	yes	complemented
134	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×Q₈×D₄₃	—	2	2	no	—
136	C₂×Q₈×D₄₃	—	2	1	no	—
137	C₂×Q₈×D₄₃	D₄	1	1	yes	characteristic
138	C₂×Q₈×D₄₃	C₂³	1	1	yes	characteristic
139	C₂×Q₈×D₄₃	C₂³	1	1	yes	characteristic
140	C₂×D₄×D₄₃	—	2	1	no	—
141	C₂×D₄×D₄₃	—	2	1	no	—
142	C₂×D₄×D₄₃	C₂³	1	2	yes	—
143	C₂²×C₄×D₄₃	—	2	2	no	—
144	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
145	C₂×#10621885	C₂³	1	1	yes	characteristic
146	C₂×#10621885	C₂³	1	1	yes	characteristic
147	Q₁₆×D₄₃	—	2	4	no	—
148	C₂×#10621873	C₂³	1	2	yes	—
149	C₂×#10621883	C₂³	1	2	yes	—
150	C₂×#10621884	C₂³	1	2	yes	—
151	SD₁₆×D₄₃	—	2	8	no	—
152	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
153	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
154	C₂×C₈×D₄₃	C₂³	1	2	yes	—
155	#13063325	—	2	1	no	—
156	#13063325	—	2	2	no	—
157	#13063325	C₂³	1	2	yes	—
158	#13063325	C₂³	1	1	yes	characteristic
159	#13063324	—	2	1	no	—
160	#13063324	—	2	2	no	—
161	#13063324	—	2	1	no	—
162	#13063324	—	2	2	no	—
163	#13063324	—	2	2	no	—
164	#13063324	—	2	2	no	—
165	#13063324	—	2	2	no	—
166	#13063324	—	2	2	no	—
167	#13063324	—	2	1	no	—
168	#13063324	C₂³	1	2	yes	—
169	#13063324	C₂³	1	2	yes	—
170	#13063324	C₂³	1	2	yes	—
171	#13063323	—	2	2	no	—
172	#13063323	—	2	2	no	—
173	#13063323	—	2	2	no	—
174	#13063323	—	2	2	no	—
175	#13063323	—	2	1	no	—
176	#13063322	C₂³	1	1	yes	characteristic
177	#13063321	—	2	1	no	—
178	#13063321	—	2	1	no	—
179	#13063321	C₂³	1	2	yes	—
180	#13063314	—	2	1	no	—
181	#13063314	C₂³	1	2	yes	—
182	#13063313	—	2	1	no	—
183	#13063313	C₂³	1	2	yes	—
184	#13063312	—	2	1	no	—
185	#13063312	C₂³	1	2	yes	—
186	#13063311	—	2	2	no	—
187	#13063311	—	2	2	no	—
188	#13063311	—	2	2	no	—
189	#13063311	—	2	2	no	—
190	#13063310	—	2	2	no	—
191	#13063310	—	2	2	no	—
192	#13063309	—	2	2	no	—
193	#13063308	—	2	2	no	—
194	#13063307	—	2	2	no	—
195	#13063307	—	2	2	no	—
196	#13063306	—	2	2	no	—
197	Q₈×Dic₄₃	—	2	1	no	—
198	Q₈×Dic₄₃	D₄	1	1	yes	characteristic
199	Q₈×Dic₄₃	C₂³	1	1	yes	characteristic
200	Q₈×Dic₄₃	C₂³	1	2	yes	—
201	Q₈×Dic₄₃	C₂³	1	1	yes	characteristic
202	C₄×Dic₈₆	—	2	2	no	—
203	C₄×Dic₈₆	—	2	1	no	—
204	C₄×Dic₈₆	—	2	2	no	—
205	C₄×Dic₈₆	—	2	1	no	—
206	C₄×Dic₈₆	—	2	1	no	—
207	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
208	C₄×Dic₈₆	C₂³	1	2	yes	—
209	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
210	C₄×Dic₈₆	C₂³	1	2	yes	—
211	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
212	#13063290	—	2	2	no	—
213	#13063290	—	2	1	no	—
214	#13063290	—	2	2	no	—
215	#13063290	—	2	1	no	—
216	#13063290	—	2	1	no	—
217	#13063290	D₄	1	1	yes	characteristic
218	#13063290	D₄	1	2	yes	—
219	#13063290	C₂³	1	1	yes	characteristic
220	#13063290	C₂³	1	2	yes	—
221	#13063290	C₂³	1	1	yes	characteristic
222	C₄×D₁₇₂	—	2	1	no	—
223	C₄×D₁₇₂	C₂³	1	2	yes	—
224	D₄×Dic₄₃	—	2	1	no	—
225	D₄×Dic₄₃	C₂³	1	2	yes	—
226	#13063287	—	2	1	no	—
227	#13063287	C₂³	1	2	yes	—
228	C₄×C₂²⋊D₄₃	—	2	2	no	—
229	C₄×C₂²⋊D₄₃	—	2	2	no	—
230	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
231	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
232	C₄⋊C₄×D₄₃	—	2	2	no	—
233	C₄⋊C₄×D₄₃	—	2	1	no	—
234	C₄⋊C₄×D₄₃	—	2	1	no	—
235	C₄⋊C₄×D₄₃	—	2	2	no	—
236	C₄⋊C₄×D₄₃	—	2	1	no	—
237	C₄⋊C₄×D₄₃	D₄	1	1	yes	characteristic
238	C₄⋊C₄×D₄₃	D₄	1	2	yes	—
239	C₄⋊C₄×D₄₃	C₂³	1	1	yes	characteristic
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	C₄²×D₄₃	—	2	1	no	—
246	C₄²×D₄₃	—	2	2	no	—
247	C₄²×D₄₃	—	2	1	no	—
248	C₄²×D₄₃	C₂³	1	1	yes	characteristic
249	C₄²×D₄₃	C₂³	1	2	yes	—
250	#13063259	C₂³	1	1	yes	characteristic
251	#13063259	C₂³	1	2	yes	—
252	#13063258	C₂³	1	1	yes	characteristic
253	#13063258	C₂³	1	2	yes	—
254	#13063258	C₂³	1	1	yes	characteristic
255	#13063258	C₂³	1	2	yes	—
256	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
257	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
258	Dic₄₃⋊C₈	C₂³	1	2	yes	—
259	Dic₄₃⋊C₈	C₂³	1	2	yes	—
260	Dic₄₃⋊C₈	C₂³	1	2	yes	—
261	#13063250	C₂³	1	2	yes	—
262	#13063250	C₂³	1	1	yes	characteristic
263	#13063250	C₂³	1	1	yes	characteristic
264	#13063249	C₂³	1	2	yes	—
265	#13063249	C₂³	1	1	yes	characteristic
266	#13063249	C₂³	1	1	yes	characteristic
267	#13063248	C₂³	1	2	yes	—
268	#13063248	C₂³	1	1	yes	characteristic
269	#13063248	C₂³	1	1	yes	characteristic
270	#13063247	C₂³	1	2	yes	—
271	#13063247	C₂³	1	2	yes	—
272	#13063247	C₂³	1	2	yes	—
273	#13063246	C₂³	1	2	yes	—
274	#13063246	C₂³	1	2	yes	—
275	#13063246	C₂³	1	2	yes	—
276	#13063245	C₂³	1	2	yes	—
277	#13063245	C₂³	1	2	yes	—
278	#13063245	C₂³	1	2	yes	—
279	#13063236	C₂³	1	2	yes	—
280	#13063235	C₂³	1	2	yes	—
281	#13063235	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×SD₁₆×C₄₃	C₂³	1	2	yes	—
287	C₄⋊Q₈×C₄₃	—	2	1	no	—
288	C₄⋊Q₈×C₄₃	—	2	2	no	—
289	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
290	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
291	#127×C₄₃	C₂³	1	1	yes	characteristic
292	#124×C₄₃	—	2	1	no	—
293	#124×C₄₃	C₂³	1	2	yes	—
294	#123×C₄₃	—	2	2	no	—
295	C₄×Q₈×C₄₃	—	2	1	no	—
296	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
297	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
298	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
299	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
300	C₄×D₄×C₄₃	—	2	1	no	—
301	C₄×D₄×C₄₃	C₂³	1	2	yes	—
302	#107×C₄₃	C₂³	1	1	yes	characteristic
303	#107×C₄₃	C₂³	1	2	yes	—
304	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
305	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
306	#103×C₄₃	C₂³	1	2	yes	—
307	#103×C₄₃	C₂³	1	1	yes	characteristic
308	#103×C₄₃	C₂³	1	1	yes	characteristic
309	#102×C₄₃	C₂³	1	2	yes	—
310	#102×C₄₃	C₂³	1	2	yes	—
311	#102×C₄₃	C₂³	1	2	yes	—
312	#97×C₄₃	C₂³	1	2	yes	—
313	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
314	C₂³×D₄₃	—	2	2	no	—
315	C₂×Q₈×C₄₃	—	2	1	no	—
316	C₂×Q₈×C₄₃	—	2	2	no	—
317	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
318	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
319	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
320	C₂×D₄×C₄₃	—	2	1	no	—
321	C₂×D₄×C₄₃	—	2	1	no	—
322	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
323	C₂²×C₄×C₄₃	—	2	2	no	—
324	C₂×C₂²⋊D₄₃	—	2	2	no	—
325	C₂×C₂²⋊D₄₃	—	2	2	no	—
326	C₂×C₂²⋊D₄₃	—	2	2	no	—
327	C₂²×Dic₄₃	—	2	2	no	—
328	Q₈×D₄₃	—	2	4	no	—
329	Q₈×D₄₃	—	2	2	no	—
330	Q₈×D₄₃	—	2	2	no	—
331	Q₈×D₄₃	—	2	2	no	—
332	Q₈×D₄₃	—	8	4	no	—
333	Q₈×D₄₃	—	8	2	no	—
334	Q₈×D₄₃	#41	1	4	yes	—
335	D₄×D₄₃	—	2	4	no	—
336	D₄×D₄₃	—	2	4	no	—
337	D₄×D₄₃	—	4	4	no	—
338	D₄×D₄₃	—	8	2	no	—
339	C₂×D₁₇₂	—	2	1	no	—
340	C₂×D₁₇₂	—	2	1	no	—
341	C₂×D₁₇₂	C₂⁴	1	2	yes	—
342	C₂×C₄×D₄₃	—	2	2	no	—
343	C₂×C₄×D₄₃	—	2	2	no	—
344	C₂×C₄×D₄₃	—	2	1	no	—
345	C₂×C₄×D₄₃	—	2	1	no	—
346	C₂×C₄×D₄₃	—	2	1	no	—
347	C₂×C₄×D₄₃	—	2	2	no	—
348	C₂×C₄×D₄₃	—	2	1	no	—
349	C₂×C₄×D₄₃	—	8	4	no	—
350	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
351	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
352	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
353	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
354	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
355	C₂×Dic₈₆	—	2	1	no	—
356	C₂×Dic₈₆	—	2	1	no	—
357	C₂×Dic₈₆	—	2	1	no	—
358	C₂×Dic₈₆	—	2	2	no	—
359	C₂×Dic₈₆	—	2	2	no	—
360	C₂×Dic₈₆	—	2	2	no	—
361	C₂×Dic₈₆	—	2	2	no	—
362	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
363	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
364	C₂×Dic₈₆	C₂⁴	1	1	yes	characteristic
365	C₂×Dic₈₆	C₂⁴	1	1	yes	characteristic
366	Q₁₆×C₄₃	—	2	2	no	—
367	SD₁₆×C₄₃	—	2	4	no	—
368	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
369	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
370	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
371	C₄⋊C₄×C₄₃	—	2	2	no	—
372	C₄⋊C₄×C₄₃	—	2	1	no	—
373	C₄⋊C₄×C₄₃	—	2	1	no	—
374	C₄⋊C₄×C₄₃	—	2	1	no	—
375	C₄⋊C₄×C₄₃	—	2	2	no	—
376	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
377	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
378	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
379	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
380	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
381	C₂²⋊C₄×C₄₃	—	2	2	no	—
382	C₂²⋊C₄×C₄₃	—	2	2	no	—
383	C₂²⋊C₄×C₄₃	—	2	2	no	—
384	C₄²×C₄₃	—	2	1	no	—
385	C₄²×C₄₃	—	2	2	no	—
386	C₄²×C₄₃	—	2	1	no	—
387	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
388	C₄²×C₄₃	C₂⁴	1	2	yes	—
389	C₂²⋊Dic₄₃	—	2	2	no	—
390	C₂²⋊Dic₄₃	—	2	2	no	—
391	C₂²⋊Dic₄₃	—	2	2	no	—
392	#10621885	—	2	2	no	—
393	#10621885	—	2	2	no	—
394	#10621884	—	2	4	no	—
395	#10621883	—	2	4	no	—
396	(C₂×D₄₃)⋊C₄	—	2	2	no	—
397	(C₂×D₄₃)⋊C₄	—	2	2	no	—
398	(C₂×D₄₃)⋊C₄	—	2	2	no	—
399	(C₂×D₄₃)⋊C₄	—	2	2	no	—
400	(C₂×D₄₃)⋊C₄	—	2	2	no	—
401	(C₂×D₄₃)⋊C₄	—	2	2	no	—
402	C₄⋊Dic₄₃	—	2	2	no	—
403	C₄⋊Dic₄₃	—	2	1	no	—
404	C₄⋊Dic₄₃	—	2	1	no	—
405	C₄⋊Dic₄₃	—	2	1	no	—
406	C₄⋊Dic₄₃	—	2	2	no	—
407	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
408	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
409	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
410	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
411	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
412	Dic₄₃⋊C₄	—	2	1	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	1	no	—
419	Dic₄₃⋊C₄	—	2	1	no	—
420	Dic₄₃⋊C₄	—	2	2	no	—
421	Dic₄₃⋊C₄	—	2	1	no	—
422	Dic₄₃⋊C₄	—	2	1	no	—
423	Dic₄₃⋊C₄	—	2	2	no	—
424	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
425	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
426	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
427	C₄×Dic₄₃	—	2	1	no	—
428	C₄×Dic₄₃	—	2	2	no	—
429	C₄×Dic₄₃	—	2	1	no	—
430	C₄×Dic₄₃	—	2	1	no	—
431	C₄×Dic₄₃	—	2	1	no	—
432	C₄×Dic₄₃	—	2	2	no	—
433	C₄×Dic₄₃	—	2	1	no	—
434	C₄×Dic₄₃	—	2	2	no	—
435	C₄×Dic₄₃	—	2	1	no	—
436	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
437	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
438	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
439	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
440	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
441	C₄×Dic₄₃	C₂⁴	1	2	yes	—
442	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
443	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
444	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
445	Dic₁₇₂	—	2	2	no	—
446	#10621873	—	2	4	no	—
447	C₈×D₄₃	—	2	4	no	—
448	C₈×D₄₃	—	2	2	no	—
449	C₈×D₄₃	—	2	2	no	—
450	C₂³×C₄₃	—	2	2	no	—
451	C₂²×D₄₃	—	2	2	no	—
452	C₂²×D₄₃	—	4	4	no	—
453	C₂²×D₄₃	—	4	4	no	—
454	C₂²×D₄₃	—	4	4	no	—
455	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
456	Q₈×C₄₃	—	2	2	no	—
457	Q₈×C₄₃	—	2	1	no	—
458	Q₈×C₄₃	—	2	1	no	—
459	Q₈×C₄₃	—	2	1	no	—
460	Q₈×C₄₃	—	8	2	no	—
461	Q₈×C₄₃	—	8	1	no	—
462	Q₈×C₄₃	C₂×#41	1	2	yes	—
463	D₄×C₄₃	—	2	2	no	—
464	D₄×C₄₃	—	2	2	no	—
465	D₄×C₄₃	—	4	2	no	—
466	D₄×C₄₃	—	8	1	no	—
467	C₂×C₄×C₄₃	—	2	1	no	—
468	C₂×C₄×C₄₃	—	2	2	no	—
469	C₂×C₄×C₄₃	—	2	1	no	—
470	C₂×C₄×C₄₃	—	2	1	no	—
471	C₂×C₄×C₄₃	—	2	1	no	—
472	C₂×C₄×C₄₃	—	8	2	no	—
473	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
474	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
476	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
477	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
478	C₂²⋊D₄₃	—	4	4	no	—
479	C₂²⋊D₄₃	—	4	4	no	—
480	C₂²⋊D₄₃	—	8	2	no	—
481	C₂×Dic₄₃	—	2	1	no	—
482	C₂×Dic₄₃	—	2	2	no	—
483	C₂×Dic₄₃	—	2	1	no	—
484	C₂×Dic₄₃	—	2	1	no	—
485	C₂×Dic₄₃	—	2	1	no	—
486	C₂×Dic₄₃	—	8	2	no	—
487	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
488	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
489	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
490	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
491	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
492	D₁₇₂	—	2	2	no	—
493	D₁₇₂	—	2	2	no	—
494	D₁₇₂	—	4	2	no	—
495	D₁₇₂	—	8	1	no	—
496	C₄×D₄₃	—	2	4	no	—
497	C₄×D₄₃	—	2	4	no	—
498	C₄×D₄₃	—	2	4	no	—
499	C₄×D₄₃	—	2	2	no	—
500	C₄×D₄₃	—	4	2	no	—
501	C₄×D₄₃	—	4	2	no	—
502	C₄×D₄₃	—	4	2	no	—
503	C₄×D₄₃	—	4	4	no	—
504	C₄×D₄₃	—	8	2	no	—
505	C₄×D₄₃	—	8	2	no	—
506	C₄×D₄₃	#137	1	4	yes	—
507	C₄×D₄₃	C₂×#41	1	2	yes	—
508	C₄×D₄₃	2₋¹⁺⁴	1	2	yes	—
509	Dic₈₆	—	2	2	no	—
510	Dic₈₆	—	2	1	no	—
511	Dic₈₆	—	2	4	no	—
512	Dic₈₆	—	2	4	no	—
513	Dic₈₆	—	2	1	no	—
514	Dic₈₆	—	2	1	no	—
515	Dic₈₆	—	4	2	no	—
516	Dic₈₆	—	8	2	no	—
517	Dic₈₆	—	8	2	no	—
518	Dic₈₆	—	8	2	no	—
519	Dic₈₆	—	8	2	no	—
520	Dic₈₆	—	8	1	no	—
521	Dic₈₆	C₂×#41	1	2	yes	—
522	C₈×C₄₃	—	2	2	no	—
523	C₈×C₄₃	—	2	1	no	—
524	C₈×C₄₃	—	2	1	no	—
525	C₄₃⋊C₈	—	2	2	no	—
526	C₄₃⋊C₈	—	2	1	no	—
527	C₄₃⋊C₈	—	2	1	no	—
528	C₂×#3375	—	43	1	no	maximal, Sylow
529	C₂²×C₄₃	—	4	2	no	—
530	C₂²×C₄₃	—	4	2	no	—
531	C₂²×C₄₃	—	4	2	no	—
532	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
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	#548	1	2	yes	—
538	C₂×D₄₃	C₂×#137	1	2	yes	—
539	C₂×D₄₃	#576	1	2	yes	—
540	C₄×C₄₃	—	2	2	no	—
541	C₄×C₄₃	—	2	2	no	—
542	C₄×C₄₃	—	2	2	no	—
543	C₄×C₄₃	—	2	1	no	—
544	C₄×C₄₃	—	4	1	no	—
545	C₄×C₄₃	—	4	1	no	—
546	C₄×C₄₃	—	4	2	no	—
547	C₄×C₄₃	—	4	1	no	—
548	C₄×C₄₃	C₂×#137	1	2	yes	—
549	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
550	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
551	Dic₄₃	—	2	2	no	—
552	Dic₄₃	—	2	2	no	—
553	Dic₄₃	—	2	2	no	—
554	Dic₄₃	—	2	1	no	—
555	Dic₄₃	—	4	1	no	—
556	Dic₄₃	—	4	1	no	—
557	Dic₄₃	—	4	2	no	—
558	Dic₄₃	—	4	1	no	—
559	Dic₄₃	#548	1	2	yes	—
560	Dic₄₃	C₂×#137	1	2	yes	—
561	C₂×#559	—	43	1	no	—
562	C₂×Q₈²	—	43	1	no	—
563	#3375	—	43	2	no	—
564	#3375	—	43	1	no	—
565	#3375	—	43	1	no	—
566	#3375	—	43	2	no	—
567	#3375	—	43	2	no	—
568	#3375	—	43	1	no	—
569	#3375	—	43	1	no	—
570	#3375	—	43	2	no	—
571	#3375	—	43	1	no	—
572	#3375	—	43	1	no	—
573	#3375	—	43	1	no	—
574	#3375	D₄₃	1	1	yes	characteristic, direct product factor
575	C₂×#489	—	43	2	no	—
576	C₂×#486	—	43	1	no	—
577	C₂×#477	—	43	1	no	—
578	C₂×#474	—	43	2	no	—
579	C₂×#464	—	43	2	no	—
580	C₂×#460	—	43	1	no	—
581	C₂×#446	—	43	1	no	—
582	C₂×#440	—	43	2	no	—
583	C₂×C₄×Q₁₆	—	43	1	no	—
584	C₂×C₄₃	—	8	2	no	—
585	C₂×C₄₃	C₂×#548	1	1	yes	characteristic
586	C₂×C₄₃	C₂²×#137	1	1	yes	characteristic
587	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
588	D₄₃	—	8	2	no	—
589	D₄₃	#3375	1	4	yes	direct product factor
590	C₂²×Q₁₆	—	43	1	no	—
591	C₂²×SD₁₆	—	43	2	no	—
592	#559	—	43	1	no	—
593	#559	—	43	2	no	—
594	#559	—	43	1	no	—
595	#559	—	43	1	no	—
596	#559	—	43	2	no	—
597	#559	—	86	1	no	—
598	#559	—	86	2	no	—
599	#559	—	86	1	no	—
600	#559	C₂×D₄₃	1	1	yes	characteristic
601	Q₈²	—	43	2	no	—
602	Q₈²	—	43	1	no	—
603	Q₈²	—	43	2	no	—
604	Q₈²	—	43	1	no	—
605	Q₈²	—	43	1	no	—
606	Q₈²	—	86	1	no	—
607	Q₈²	—	86	2	no	—
608	Q₈²	—	86	1	no	—
609	Q₈²	C₂×D₄₃	1	1	yes	characteristic, complemented
610	C₂×C₄⋊Q₈	—	43	1	no	—
611	C₂×C₄⋊Q₈	—	43	2	no	—
612	C₂×C₄⋊Q₈	—	86	1	no	—
613	C₂×C₄⋊Q₈	—	86	2	no	—
614	C₂×#127	—	43	1	no	—
615	C₂×#124	—	43	2	no	—
616	C₂×#124	—	86	1	no	—
617	C₂×#123	—	86	2	no	—
618	C₂×C₄×Q₈	—	43	1	no	—
619	C₂×C₄×Q₈	—	43	1	no	—
620	C₂×C₄×Q₈	—	43	1	no	—
621	C₂×C₄×Q₈	—	43	2	no	—
622	C₂×C₄×Q₈	—	86	1	no	—
623	C₂×C₄×D₄	—	43	2	no	—
624	C₂×C₄×D₄	—	86	1	no	—
625	#489	—	43	2	no	—
626	#489	—	43	2	no	—
627	#489	—	43	2	no	—
628	#489	—	43	2	no	—
629	#489	—	43	2	no	—
630	#489	—	43	2	no	—
631	#489	—	43	2	no	—
632	#489	C₂×D₄₃	1	2	yes	complemented
633	#486	—	43	1	no	—
634	#486	—	43	1	no	—
635	#486	—	43	2	no	—
636	#486	—	43	2	no	—
637	#486	—	43	1	no	—
638	#486	C₂×D₄₃	1	1	yes	characteristic
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	#474	—	43	2	no	—
646	#474	—	43	2	no	—
647	#474	—	43	2	no	—
648	#474	—	43	2	no	—
649	#474	—	43	2	no	—
650	#474	—	43	2	no	—
651	#474	—	43	2	no	—
652	#474	C₂×D₄₃	1	2	yes	complemented
653	#464	—	43	2	no	—
654	#464	—	43	2	no	—
655	#464	—	43	2	no	—
656	#464	—	43	2	no	—
657	#464	—	43	2	no	—
658	#464	—	43	2	no	—
659	#464	—	43	2	no	—
660	#464	C₂×D₄₃	1	2	yes	complemented
661	#460	—	43	2	no	—
662	#460	—	43	1	no	—
663	#460	—	43	1	no	—
664	#460	—	43	1	no	—
665	#460	—	43	2	no	—
666	#460	C₂×D₄₃	1	1	yes	characteristic
667	#446	—	43	1	no	—
668	#446	—	43	1	no	—
669	#446	—	43	2	no	—
670	#446	—	43	2	no	—
671	#446	—	43	1	no	—
672	#446	C₂×D₄₃	1	1	yes	characteristic, complemented
673	#440	—	43	2	no	—
674	#440	—	43	2	no	—
675	#440	—	43	2	no	—
676	#440	—	43	2	no	—
677	#440	—	43	2	no	—
678	#440	—	43	2	no	—
679	#440	—	43	2	no	—
680	#440	C₂×D₄₃	1	2	yes	complemented
681	C₄×Q₁₆	—	43	1	no	—
682	C₄×Q₁₆	—	43	1	no	—
683	C₄×Q₁₆	—	43	1	no	—
684	C₄×Q₁₆	—	43	1	no	—
685	C₄×Q₁₆	—	43	1	no	—
686	C₄×Q₁₆	—	43	1	no	—
687	C₄×Q₁₆	—	43	1	no	—
688	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
689	C₂×#107	—	43	2	no	—
690	C₂×#107	—	43	1	no	—
691	C₂×C₄⋊C₈	—	43	1	no	—
692	C₂×C₄⋊C₈	—	43	2	no	—
693	C₂×#103	—	43	2	no	—
694	C₂×#103	—	43	1	no	—
695	C₂×#103	—	43	1	no	—
696	C₂×#102	—	43	2	no	—
697	C₂×#102	—	43	2	no	—
698	C₂×#102	—	43	2	no	—
699	C₂×#97	—	43	2	no	—
700	C₂×C₄×C₈	—	43	1	no	—
701	C₄₃	C₂×#3375	1	1	yes	characteristic, complemented, Sylow
702	C₂²×Q₈	—	43	1	no	—
703	C₂²×Q₈	—	43	1	no	—
704	C₂²×Q₈	—	43	1	no	—
705	C₂²×Q₈	—	86	2	no	—
706	C₂²×Q₈	—	86	1	no	—
707	C₂²×D₄	—	43	2	no	—
708	C₂²×D₄	—	86	1	no	—
709	C₂²×D₄	—	86	1	no	—
710	C₂³×C₄	—	86	2	no	—
711	C₂×Q₁₆	—	43	1	no	—
712	C₂×Q₁₆	—	43	1	no	—
713	C₂×Q₁₆	—	43	1	no	—
714	C₂×Q₁₆	—	86	4	no	—
715	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
716	C₂×SD₁₆	—	43	2	no	—
717	C₂×SD₁₆	—	43	2	no	—
718	C₂×SD₁₆	—	43	2	no	—
719	C₂×SD₁₆	—	86	8	no	—
720	C₂×SD₁₆	C₂²×D₄₃	1	2	yes	—
721	C₂²×C₈	—	43	2	no	—
722	C₂²×C₈	—	43	1	no	—
723	C₂²×C₈	—	43	1	no	—
724	C₄⋊Q₈	—	2	1	no	—
725	C₄⋊Q₈	—	2	2	no	—
726	C₄⋊Q₈	—	43	2	no	—
727	C₄⋊Q₈	—	43	2	no	—
728	C₄⋊Q₈	—	43	2	no	—
729	C₄⋊Q₈	—	43	2	no	—
730	C₄⋊Q₈	—	43	1	no	—
731	C₄⋊Q₈	—	86	1	no	—
732	C₄⋊Q₈	—	86	2	no	—
733	C₄⋊Q₈	—	86	2	no	—
734	C₄⋊Q₈	—	86	1	no	—
735	C₄⋊Q₈	—	86	2	no	—
736	C₄⋊Q₈	—	86	1	no	—
737	C₄⋊Q₈	—	86	2	no	—
738	C₄⋊Q₈	—	86	2	no	—
739	C₄⋊Q₈	—	86	2	no	—
740	C₄⋊Q₈	—	86	1	no	—
741	C₄⋊Q₈	—	86	2	no	—
742	C₄⋊Q₈	—	86	2	no	—
743	C₄⋊Q₈	—	86	2	no	—
744	C₄⋊Q₈	—	86	2	no	—
745	C₄⋊Q₈	—	86	1	no	—
746	C₄⋊Q₈	—	86	2	no	—
747	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
748	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
749	#127	—	43	2	no	—
750	#127	—	43	1	no	—
751	#127	—	86	1	no	—
752	#127	—	86	1	no	—
753	#127	C₂²×D₄₃	1	1	yes	characteristic
754	#124	—	2	1	no	—
755	#124	—	43	2	no	—
756	#124	—	43	2	no	—
757	#124	—	43	2	no	—
758	#124	—	86	1	no	—
759	#124	—	86	2	no	—
760	#124	—	86	2	no	—
761	#124	—	86	2	no	—
762	#124	—	86	2	no	—
763	#124	—	86	1	no	—
764	#124	—	86	1	no	—
765	#124	C₂²×D₄₃	1	2	yes	—
766	#123	—	2	2	no	—
767	#123	—	86	2	no	—
768	#123	—	86	2	no	—
769	#123	—	86	2	no	—
770	#123	—	86	2	no	—
771	#123	—	86	2	no	—
772	#123	—	86	2	no	—
773	#123	—	86	2	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	43	1	no	—
776	C₄×Q₈	—	43	2	no	—
777	C₄×Q₈	—	43	1	no	—
778	C₄×Q₈	—	43	2	no	—
779	C₄×Q₈	—	43	1	no	—
780	C₄×Q₈	—	43	1	no	—
781	C₄×Q₈	—	43	2	no	—
782	C₄×Q₈	—	43	1	no	—
783	C₄×Q₈	—	43	1	no	—
784	C₄×Q₈	—	43	2	no	—
785	C₄×Q₈	—	43	1	no	—
786	C₄×Q₈	—	43	1	no	—
787	C₄×Q₈	—	43	2	no	—
788	C₄×Q₈	—	43	1	no	—
789	C₄×Q₈	—	86	2	no	—
790	C₄×Q₈	—	86	1	no	—
791	C₄×Q₈	—	86	1	no	—
792	C₄×Q₈	—	86	2	no	—
793	C₄×Q₈	—	86	1	no	—
794	C₄×Q₈	—	86	2	no	—
795	C₄×Q₈	—	86	1	no	—
796	C₄×Q₈	—	86	1	no	—
797	C₄×Q₈	—	86	2	no	—
798	C₄×Q₈	—	86	1	no	—
799	C₄×Q₈	—	86	1	no	—
800	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
801	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
802	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
803	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	43	2	no	—
806	C₄×D₄	—	43	2	no	—
807	C₄×D₄	—	43	2	no	—
808	C₄×D₄	—	86	1	no	—
809	C₄×D₄	—	86	2	no	—
810	C₄×D₄	—	86	2	no	—
811	C₄×D₄	—	86	2	no	—
812	C₄×D₄	—	86	2	no	—
813	C₄×D₄	—	86	1	no	—
814	C₄×D₄	—	86	1	no	—
815	C₄×D₄	C₂²×D₄₃	1	2	yes	—
816	C₂×C₄⋊C₄	—	43	1	no	—
817	C₂×C₄⋊C₄	—	43	2	no	—
818	C₂×C₄⋊C₄	—	43	1	no	—
819	C₂×C₄⋊C₄	—	43	1	no	—
820	C₂×C₄⋊C₄	—	43	2	no	—
821	C₂×C₄⋊C₄	—	86	1	no	—
822	C₂×C₄⋊C₄	—	86	2	no	—
823	C₂×C₄⋊C₄	—	86	1	no	—
824	C₂×C₄⋊C₄	—	86	1	no	—
825	C₂×C₄⋊C₄	—	86	2	no	—
826	C₂×C₂²⋊C₄	—	86	2	no	—
827	C₂×C₂²⋊C₄	—	86	2	no	—
828	C₂×C₂²⋊C₄	—	86	2	no	—
829	C₂×C₄²	—	43	2	no	—
830	C₂×C₄²	—	43	1	no	—
831	C₂×C₄²	—	86	1	no	—
832	C₂×C₄²	—	86	1	no	—
833	C₂×C₄²	—	86	2	no	—
834	#107	—	43	1	no	—
835	#107	—	43	2	no	—
836	#107	—	43	1	no	—
837	#107	—	43	1	no	—
838	#107	—	43	2	no	—
839	#107	—	43	2	no	—
840	#107	C₂²×D₄₃	1	1	yes	characteristic
841	#107	C₂²×D₄₃	1	2	yes	—
842	C₄⋊C₈	—	43	2	no	—
843	C₄⋊C₈	—	43	2	no	—
844	C₄⋊C₈	—	43	2	no	—
845	C₄⋊C₈	—	43	1	no	—
846	C₄⋊C₈	—	43	2	no	—
847	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
848	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
849	#103	—	43	1	no	—
850	#103	—	43	1	no	—
851	#103	—	43	2	no	—
852	#103	—	43	1	no	—
853	#103	—	43	1	no	—
854	#103	—	43	2	no	—
855	#103	—	43	1	no	—
856	#103	—	43	1	no	—
857	#103	—	43	2	no	—
858	#103	C₂²×D₄₃	1	1	yes	characteristic
859	#103	C₂²×D₄₃	1	1	yes	characteristic
860	#103	C₂²×D₄₃	1	2	yes	—
861	#102	—	43	2	no	—
862	#102	—	43	2	no	—
863	#102	—	43	2	no	—
864	#102	—	43	2	no	—
865	#102	—	43	2	no	—
866	#102	—	43	2	no	—
867	#102	—	43	2	no	—
868	#102	—	43	2	no	—
869	#102	—	43	2	no	—
870	#102	C₂²×D₄₃	1	2	yes	—
871	#102	C₂²×D₄₃	1	2	yes	—
872	#102	C₂²×D₄₃	1	2	yes	—
873	#97	—	43	2	no	—
874	#97	—	43	2	no	—
875	#97	—	43	2	no	—
876	#97	C₂²×D₄₃	1	2	yes	—
877	C₄×C₈	—	43	1	no	—
878	C₄×C₈	—	43	1	no	—
879	C₄×C₈	—	43	1	no	—
880	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
881	C₂⁴	—	86	2	no	—
882	C₂×Q₈	—	2	2	no	—
883	C₂×Q₈	—	2	1	no	—
884	C₂×Q₈	—	43	2	no	—
885	C₂×Q₈	—	43	1	no	—
886	C₂×Q₈	—	43	4	no	—
887	C₂×Q₈	—	43	1	no	—
888	C₂×Q₈	—	43	1	no	—
889	C₂×Q₈	—	86	1	no	—
890	C₂×Q₈	—	86	2	no	—
891	C₂×Q₈	—	86	2	no	—
892	C₂×Q₈	—	86	2	no	—
893	C₂×Q₈	—	86	1	no	—
894	C₂×Q₈	—	86	4	no	—
895	C₂×Q₈	—	86	2	no	—
896	C₂×Q₈	—	86	2	no	—
897	C₂×Q₈	—	86	2	no	—
898	C₂×Q₈	—	86	2	no	—
899	C₂×Q₈	—	86	1	no	—
900	C₂×Q₈	—	344	4	no	—
901	C₂×Q₈	—	344	2	no	—
902	C₂×Q₈	D₄×D₄₃	1	1	yes	characteristic
903	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
904	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	1	no	—
907	C₂×D₄	—	43	2	no	—
908	C₂×D₄	—	86	4	no	—
909	C₂×D₄	—	86	4	no	—
910	C₂×D₄	—	86	2	no	—
911	C₂×D₄	—	86	2	no	—
912	C₂×D₄	—	86	2	no	—
913	C₂×D₄	—	86	1	no	—
914	C₂×D₄	—	86	1	no	—
915	C₂×D₄	—	344	2	no	—
916	C₂×D₄	—	172	4	no	—
917	C₂×D₄	C₂³×D₄₃	1	2	yes	—
918	C₂²×C₄	—	2	2	no	—
919	C₂²×C₄	—	43	1	no	—
920	C₂²×C₄	—	43	1	no	—
921	C₂²×C₄	—	43	2	no	—
922	C₂²×C₄	—	43	2	no	—
923	C₂²×C₄	—	43	1	no	—
924	C₂²×C₄	—	86	2	no	—
925	C₂²×C₄	—	86	1	no	—
926	C₂²×C₄	—	86	1	no	—
927	C₂²×C₄	—	86	1	no	—
928	C₂²×C₄	—	86	1	no	—
929	C₂²×C₄	—	86	2	no	—
930	C₂²×C₄	—	86	2	no	—
931	C₂²×C₄	—	86	2	no	—
932	C₂²×C₄	—	344	4	no	—
933	Q₁₆	—	2	2	no	—
934	Q₁₆	—	86	2	no	—
935	Q₁₆	—	86	2	no	—
936	Q₁₆	—	86	2	no	—
937	SD₁₆	—	2	4	no	—
938	SD₁₆	—	86	4	no	—
939	SD₁₆	—	86	4	no	—
940	SD₁₆	—	86	4	no	—
941	C₂×C₈	—	43	1	no	—
942	C₂×C₈	—	43	1	no	—
943	C₂×C₈	—	43	2	no	—
944	C₂×C₈	—	86	4	no	—
945	C₂×C₈	—	86	2	no	—
946	C₂×C₈	—	86	2	no	—
947	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
948	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
949	C₂×C₈	C₂³×D₄₃	1	2	yes	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	43	2	no	—
956	C₄⋊C₄	—	43	1	no	—
957	C₄⋊C₄	—	43	2	no	—
958	C₄⋊C₄	—	43	2	no	—
959	C₄⋊C₄	—	43	2	no	—
960	C₄⋊C₄	—	43	2	no	—
961	C₄⋊C₄	—	43	1	no	—
962	C₄⋊C₄	—	43	1	no	—
963	C₄⋊C₄	—	86	1	no	—
964	C₄⋊C₄	—	86	1	no	—
965	C₄⋊C₄	—	86	2	no	—
966	C₄⋊C₄	—	86	1	no	—
967	C₄⋊C₄	—	86	1	no	—
968	C₄⋊C₄	—	86	2	no	—
969	C₄⋊C₄	—	86	1	no	—
970	C₄⋊C₄	—	86	2	no	—
971	C₄⋊C₄	—	86	1	no	—
972	C₄⋊C₄	—	86	2	no	—
973	C₄⋊C₄	—	86	2	no	—
974	C₄⋊C₄	—	86	2	no	—
975	C₄⋊C₄	—	86	1	no	—
976	C₄⋊C₄	—	86	2	no	—
977	C₄⋊C₄	—	86	1	no	—
978	C₄⋊C₄	—	86	2	no	—
979	C₄⋊C₄	—	86	1	no	—
980	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
981	C₄⋊C₄	D₄×D₄₃	1	2	yes	—
982	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
983	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
984	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	86	2	no	—
989	C₂²⋊C₄	—	86	2	no	—
990	C₂²⋊C₄	—	86	2	no	—
991	C₂²⋊C₄	—	86	2	no	—
992	C₂²⋊C₄	—	86	2	no	—
993	C₂²⋊C₄	—	86	2	no	—
994	C₂²⋊C₄	—	86	2	no	—
995	C₂²⋊C₄	—	86	2	no	—
996	C₂²⋊C₄	—	86	2	no	—
997	C₄²	—	2	1	no	—
998	C₄²	—	2	2	no	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	43	2	no	—
1001	C₄²	—	43	2	no	—
1002	C₄²	—	43	1	no	—
1003	C₄²	—	43	1	no	—
1004	C₄²	—	43	1	no	—
1005	C₄²	—	43	2	no	—
1006	C₄²	—	86	1	no	—
1007	C₄²	—	86	1	no	—
1008	C₄²	—	86	1	no	—
1009	C₄²	—	86	2	no	—
1010	C₄²	—	86	1	no	—
1011	C₄²	—	86	2	no	—
1012	C₄²	—	86	1	no	—
1013	C₄²	—	86	2	no	—
1014	C₄²	—	86	1	no	—
1015	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1016	C₄²	C₂³×D₄₃	1	2	yes	—
1017	C₂³	—	2	2	no	—
1018	C₂³	—	43	1	no	—
1019	C₂³	—	86	2	no	—
1020	C₂³	—	172	4	no	—
1021	C₂³	—	172	4	no	—
1022	C₂³	—	172	4	no	—
1023	Q₈	—	2	2	no	—
1024	Q₈	—	2	1	no	—
1025	Q₈	—	2	1	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	8	2	no	—
1028	Q₈	—	8	1	no	—
1029	Q₈	—	43	2	no	—
1030	Q₈	—	86	4	no	—
1031	Q₈	—	86	4	no	—
1032	Q₈	—	86	2	no	—
1033	Q₈	—	86	1	no	—
1034	Q₈	—	86	1	no	—
1035	Q₈	—	86	1	no	—
1036	Q₈	—	344	2	no	—
1037	Q₈	—	344	1	no	—
1038	Q₈	—	344	2	no	—
1039	Q₈	—	344	2	no	—
1040	Q₈	—	344	2	no	—
1041	Q₈	—	172	2	no	—
1042	Q₈	#41×D₄₃	1	2	yes	—
1043	D₄	—	2	2	no	—
1044	D₄	—	2	2	no	—
1045	D₄	—	4	2	no	—
1046	D₄	—	8	1	no	—
1047	D₄	—	86	2	no	—
1048	D₄	—	86	2	no	—
1049	D₄	—	344	1	no	—
1050	D₄	—	344	2	no	—
1051	D₄	—	172	4	no	—
1052	D₄	—	172	4	no	—
1053	D₄	—	172	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	1	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	8	2	no	—
1060	C₂×C₄	—	43	1	no	—
1061	C₂×C₄	—	43	1	no	—
1062	C₂×C₄	—	43	4	no	—
1063	C₂×C₄	—	43	2	no	—
1064	C₂×C₄	—	43	2	no	—
1065	C₂×C₄	—	43	2	no	—
1066	C₂×C₄	—	43	2	no	—
1067	C₂×C₄	—	43	1	no	—
1068	C₂×C₄	—	86	4	no	—
1069	C₂×C₄	—	86	2	no	—
1070	C₂×C₄	—	86	4	no	—
1071	C₂×C₄	—	86	4	no	—
1072	C₂×C₄	—	86	1	no	—
1073	C₂×C₄	—	86	1	no	—
1074	C₂×C₄	—	86	1	no	—
1075	C₂×C₄	—	86	1	no	—
1076	C₂×C₄	—	86	2	no	—
1077	C₂×C₄	—	344	2	no	—
1078	C₂×C₄	—	344	2	no	—
1079	C₂×C₄	—	344	2	no	—
1080	C₂×C₄	—	172	2	no	—
1081	C₂×C₄	—	172	2	no	—
1082	C₂×C₄	—	172	2	no	—
1083	C₂×C₄	—	172	4	no	—
1084	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
1085	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
1086	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1087	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1088	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1089	C₈	—	2	2	no	—
1090	C₈	—	2	1	no	—
1091	C₈	—	2	1	no	—
1092	C₈	—	86	2	no	—
1093	C₈	—	86	1	no	—
1094	C₈	—	86	1	no	—
1095	C₂²	—	4	2	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	2	no	—
1098	C₂²	—	43	2	no	—
1099	C₂²	—	43	2	no	—
1100	C₂²	—	43	2	no	—
1101	C₂²	—	344	8	no	—
1102	C₂²	—	172	2	no	—
1103	C₂²	—	172	2	no	—
1104	C₂²	—	172	2	no	—
1105	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1106	C₄	—	2	2	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	2	no	—
1109	C₄	—	2	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	2	no	—
1114	C₄	—	43	2	no	—
1115	C₄	—	43	2	no	—
1116	C₄	—	86	2	no	—
1117	C₄	—	86	2	no	—
1118	C₄	—	86	2	no	—
1119	C₄	—	86	1	no	—
1120	C₄	—	172	1	no	—
1121	C₄	—	172	1	no	—
1122	C₄	—	172	1	no	—
1123	C₄	—	172	2	no	—
1124	C₄	#137×D₄₃	1	2	yes	—
1125	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1126	C₄	2₋¹⁺⁴×D₄₃	1	1	yes	characteristic
1127	C₂	—	8	2	no	—
1128	C₂	—	43	4	no	—
1129	C₂	—	344	2	no	—
1130	C₂	#548×D₄₃	1	1	yes	characteristic
1131	C₂	C₂×#137×D₄₃	1	1	yes	characteristic
1132	C₂	#576×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×#3375	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	#127×D₄₃	C₂²
hypercenter	#3375	D₄₃
hypocenter	C₄₃	C₂×#3375
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #3375

Complements

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

N	H ≅ G/N	type
2. Q₈²×D₄₃	C₂	semidirect
3. #19147414	C₂	semidirect
4. #19147413	C₂	semidirect
5. #19147412	C₂	semidirect
6. #19147411	C₂	semidirect
7. #19147410	C₂	semidirect
8. #19147409	C₂	semidirect
9. #19147408	C₂	semidirect
10. #19147407	C₂	semidirect
11. #19147406	C₂	semidirect
12. #19147405	C₂	semidirect
13. #19147404	C₂	semidirect
14. #489×D₄₃	C₂	semidirect
16. #477×D₄₃	C₂	semidirect
17. #474×D₄₃	C₂	semidirect
18. #464×D₄₃	C₂	semidirect
20. #446×D₄₃	C₂	semidirect
21. #440×D₄₃	C₂	semidirect
22. C₄×Q₁₆×D₄₃	C₂	semidirect
23. C₄₃×#3375	C₂	semidirect
35. Q₈×Dic₈₆	C₂²	semidirect
36. Q₈×Dic₈₆	C₂²	semidirect
37. Q₈×Dic₈₆	C₂²	semidirect
40. #14583629	C₂²	semidirect
41. #14583629	C₂²	semidirect
57. #14583261	C₂²	semidirect
58. #14583260	C₂²	semidirect
59. #14583260	C₂²	semidirect
60. #14583259	C₂²	semidirect
61. #14583258	C₂²	semidirect
62. #14583257	C₂²	semidirect
63. #14583257	C₂²	semidirect
69. #14583195	C₂²	semidirect
70. #14583194	C₂²	semidirect
71. #14583193	C₂²	semidirect
72. #14583192	C₂²	semidirect
73. #14583191	C₂²	semidirect
74. #14583180	C₂²	semidirect
75. #14583179	C₂²	semidirect
76. #14583178	C₂²	semidirect
77. #14583178	C₂²	semidirect
78. #14583177	C₂²	semidirect
79. #14583177	C₂²	semidirect
80. #14583176	C₂²	semidirect
81. #14583124	C₂²	semidirect
82. #14583123	C₂²	semidirect
83. #14583122	C₂²	semidirect
84. #14583121	C₂²	semidirect
85. #14583120	C₂²	semidirect
86. #14583119	C₂²	semidirect
87. #14583118	C₂²	semidirect
93. #14583030	C₂²	semidirect
94. #14583029	C₂²	semidirect
95. #14583028	C₂²	semidirect
96. #14583027	C₂²	semidirect
97. #14583026	C₂²	semidirect
98. #14583002	C₂²	semidirect
99. #14583001	C₂²	semidirect
100. #14583000	C₂²	semidirect
101. #14582999	C₂²	semidirect
102. #14582998	C₂²	semidirect
103. #14582997	C₂²	semidirect
104. #14582996	C₂²	semidirect
105. C₄×Dic₁₇₂	C₂²	semidirect
106. Q₁₆×Dic₄₃	C₂²	semidirect
107. #14582993	C₂²	semidirect
108. C₄×#10621885	C₂²	semidirect
109. C₄×#10621885	C₂²	semidirect
110. #14582991	C₂²	semidirect
111. #14582991	C₂²	semidirect
125. Q₈²×C₄₃	C₂²	semidirect
126. C₄₃×#489	C₂²	semidirect
128. C₄₃×#477	C₂²	semidirect
129. C₄₃×#474	C₂²	semidirect
130. C₄₃×#464	C₂²	semidirect
132. C₄₃×#446	C₂²	semidirect
133. C₄₃×#440	C₂²	semidirect
134. C₄×Q₁₆×C₄₃	C₂²	semidirect
574. #3375	D₄₃	direct (N × H)
589. D₄₃	#3375	direct (N × H)
609. Q₈²	C₂×D₄₃	semidirect
632. #489	C₂×D₄₃	semidirect
644. #477	C₂×D₄₃	semidirect
652. #474	C₂×D₄₃	semidirect
660. #464	C₂×D₄₃	semidirect
672. #446	C₂×D₄₃	semidirect
680. #440	C₂×D₄₃	semidirect
688. C₄×Q₁₆	C₂×D₄₃	semidirect
701. C₄₃	C₂×#3375	semidirect

Maximal subgroups

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

subgroup	index
#559×D₄₃	2
Q₈²×D₄₃	2
#19147414	2
#19147413	2
#19147412	2
#19147411	2
#19147410	2
#19147409	2
#19147408	2
#19147407	2
#19147406	2
#19147405	2
#19147404	2
#489×D₄₃	2
#486×D₄₃	2
#477×D₄₃	2
#474×D₄₃	2
#464×D₄₃	2
#460×D₄₃	2
#446×D₄₃	2
#440×D₄₃	2
C₄×Q₁₆×D₄₃	2
C₄₃×#3375	2
C₂×#3375	43

Subgroups — D43×#3375 #25976326

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×#3375 #25976326