Subgroups — D₄₃×#3385 #25977080

Order 11008.

1854 conjugacy classes of subgroups.

The subgroup lattice has 1112 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈²×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
2	#554×D₄₃	C₂	1	1	yes	maximal, characteristic
3	#19147510	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147509	C₂	1	1	yes	maximal, characteristic, complemented
5	#19147508	C₂	1	2	yes	maximal, complemented
6	#19147507	C₂	1	1	yes	maximal, characteristic, complemented
7	#19147506	C₂	1	2	yes	maximal, complemented
8	#19147505	C₂	1	1	yes	maximal, characteristic, complemented
9	#19147504	C₂	1	1	yes	maximal, characteristic, complemented
10	#19147503	C₂	1	1	yes	maximal, characteristic, complemented
11	#19147502	C₂	1	2	yes	maximal, complemented
12	#19147501	C₂	1	1	yes	maximal, characteristic, complemented
13	#19147500	C₂	1	2	yes	maximal, complemented
14	#501×D₄₃	C₂	1	2	yes	maximal, complemented
15	#500×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
16	#479×D₄₃	C₂	1	2	yes	maximal, complemented
17	#477×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
18	#476×D₄₃	C₂	1	1	yes	maximal, characteristic
19	#474×D₄₃	C₂	1	2	yes	maximal
20	#446×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
21	#440×D₄₃	C₂	1	2	yes	maximal
22	C₄×SD₁₆×D₄₃	C₂	1	1	yes	maximal, characteristic
23	C₄₃×#3385	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×SD₁₆×D₄₃	C₂²	1	1	yes	characteristic
25	Q₈×Dic₈₆	—	2	1	no	—
26	Q₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
27	Q₈×Dic₈₆	C₂²	1	2	yes	complemented
28	Q₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
29	#14583629	—	2	2	no	—
30	#14583629	—	2	1	no	—
31	#14583629	C₂²	1	2	yes	complemented
32	#14583629	C₂²	1	1	yes	characteristic, complemented
33	#14583610	C₂²	1	1	yes	characteristic
34	#14583609	C₂²	1	1	yes	characteristic
35	#14583608	C₂²	1	2	yes	—
36	#14583607	—	2	1	no	—
37	#14583606	C₂²	1	1	yes	characteristic
38	#14583605	C₂²	1	2	yes	—
39	#14583604	—	2	1	no	—
40	#14583603	—	2	2	no	—
41	C₄⋊Q₈×D₄₃	—	2	1	no	—
42	C₄⋊Q₈×D₄₃	—	2	2	no	—
43	C₄⋊Q₈×D₄₃	C₂²	1	1	yes	characteristic
44	C₄⋊Q₈×D₄₃	C₂²	1	1	yes	characteristic
45	C₄⋊Q₈×D₄₃	C₂²	1	2	yes	—
46	#125×D₄₃	C₂²	1	2	yes	—
47	C₂²⋊Q₈×D₄₃	—	2	1	no	—
48	C₂²⋊Q₈×D₄₃	—	2	2	no	—
49	C₄×Q₈×D₄₃	—	2	1	no	—
50	C₄×Q₈×D₄₃	C₂²	1	1	yes	characteristic
51	C₄×Q₈×D₄₃	C₂²	1	2	yes	—
52	C₄×Q₈×D₄₃	C₂²	1	1	yes	characteristic
53	C₄×D₄×D₄₃	C₂²	1	2	yes	—
54	C₄×D₄×D₄₃	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊C₄×D₄₃	—	2	1	no	—
56	#14583309	C₂²	1	2	yes	complemented
57	#14583308	C₂²	1	2	yes	complemented
58	#14583307	C₂²	1	2	yes	complemented
59	#14583307	C₂²	1	2	yes	complemented
60	#14583306	C₂²	1	2	yes	complemented
61	#14583306	C₂²	1	2	yes	complemented
62	#14583305	C₂²	1	2	yes	complemented
63	#14583304	C₂²	1	1	yes	characteristic, complemented
64	#14583303	C₂²	1	2	yes	complemented
65	#14583303	C₂²	1	2	yes	complemented
66	#14583302	C₂²	1	1	yes	characteristic, complemented
67	#14583302	C₂²	1	1	yes	characteristic, complemented
68	#14583209	C₂²	1	2	yes	complemented
69	#14583208	C₂²	1	2	yes	complemented
70	#14583207	C₂²	1	2	yes	complemented
71	#14583206	C₂²	1	2	yes	complemented
72	#14583205	C₂²	1	2	yes	complemented
73	#14583204	C₂²	1	2	yes	complemented
74	#14583203	C₂²	1	2	yes	complemented
75	#14583195	C₂²	1	1	yes	characteristic, complemented
76	#14583194	C₂²	1	1	yes	characteristic, complemented
77	#14583193	C₂²	1	2	yes	complemented
78	#14583192	C₂²	1	2	yes	complemented
79	#14583191	C₂²	1	1	yes	characteristic, complemented
80	#14583190	C₂²	1	1	yes	characteristic
81	#14583189	C₂²	1	1	yes	characteristic
82	#14583188	C₂²	1	2	yes	—
83	#14583187	C₂²	1	2	yes	—
84	#14583186	C₂²	1	1	yes	characteristic
85	#14583180	C₂²	1	2	yes	—
86	#14583179	C₂²	1	2	yes	—
87	#14583178	C₂²	1	2	yes	—
88	#14583178	C₂²	1	2	yes	—
89	#14583177	C₂²	1	2	yes	—
90	#14583177	C₂²	1	2	yes	—
91	#14583176	C₂²	1	2	yes	—
92	#14583030	C₂²	1	1	yes	characteristic, complemented
93	#14583029	C₂²	1	1	yes	characteristic, complemented
94	#14583028	C₂²	1	2	yes	complemented
95	#14583027	C₂²	1	2	yes	complemented
96	#14583026	C₂²	1	1	yes	characteristic, complemented
97	#14583002	C₂²	1	2	yes	—
98	#14583001	C₂²	1	2	yes	—
99	#14583000	C₂²	1	2	yes	—
100	#14582999	C₂²	1	2	yes	—
101	#14582998	C₂²	1	2	yes	—
102	#14582997	C₂²	1	2	yes	—
103	#14582996	C₂²	1	2	yes	—
104	#14582990	C₂²	1	1	yes	characteristic
105	C₄×#10621873	C₂²	1	1	yes	characteristic
106	SD₁₆×Dic₄₃	C₂²	1	1	yes	characteristic
107	C₄×#10621884	C₂²	1	1	yes	characteristic
108	#14582986	C₂²	1	1	yes	characteristic
109	C₄×#10621883	C₂²	1	1	yes	characteristic
110	#14582984	C₂²	1	1	yes	characteristic
111	#107×D₄₃	C₂²	1	2	yes	—
112	#107×D₄₃	C₂²	1	2	yes	—
113	#107×D₄₃	C₂²	1	2	yes	—
114	#106×D₄₃	C₂²	1	2	yes	—
115	#106×D₄₃	C₂²	1	1	yes	characteristic
116	C₄⋊C₈×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	1	yes	characteristic
120	#102×D₄₃	C₂²	1	1	yes	characteristic
121	#102×D₄₃	C₂²	1	2	yes	—
122	#97×D₄₃	C₂²	1	2	yes	—
123	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
124	Q₈²×C₄₃	C₂²	1	1	yes	characteristic, complemented
125	C₄₃×#554	C₂²	1	1	yes	characteristic
126	C₄₃×#501	C₂²	1	2	yes	complemented
127	C₄₃×#500	C₂²	1	1	yes	characteristic, complemented
128	C₄₃×#479	C₂²	1	2	yes	complemented
129	C₄₃×#477	C₂²	1	1	yes	characteristic, complemented
130	C₄₃×#476	C₂²	1	1	yes	characteristic
131	C₄₃×#474	C₂²	1	2	yes	—
132	C₄₃×#446	C₂²	1	1	yes	characteristic, complemented
133	C₄₃×#440	C₂²	1	2	yes	—
134	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
135	C₂×Q₈×D₄₃	—	2	1	no	—
136	C₂×Q₈×D₄₃	—	2	1	no	—
137	C₂×Q₈×D₄₃	—	2	2	no	—
138	C₂×Q₈×D₄₃	D₄	1	1	yes	characteristic
139	C₂×Q₈×D₄₃	C₂³	1	1	yes	characteristic
140	C₂×D₄×D₄₃	C₂³	1	1	yes	characteristic
141	C₂²×C₄×D₄₃	—	2	1	no	—
142	C₂²×C₄×D₄₃	—	2	2	no	—
143	C₂×#10621873	C₂³	1	1	yes	characteristic
144	C₂×#10621883	C₂³	1	1	yes	characteristic
145	C₂×#10621884	C₂³	1	1	yes	characteristic
146	SD₁₆×D₄₃	Q₈	1	8	yes	complemented
147	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
148	C₂×C₈×D₄₃	C₂³	1	2	yes	—
149	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
150	#13063325	—	2	1	no	—
151	#13063325	—	2	2	no	—
152	#13063325	C₂³	1	1	yes	characteristic
153	#13063325	C₂³	1	1	yes	characteristic
154	#13063325	C₂³	1	2	yes	—
155	#13063324	—	2	1	no	—
156	#13063324	—	2	2	no	—
157	#13063324	—	2	1	no	—
158	#13063324	—	2	2	no	—
159	#13063324	—	2	2	no	—
160	#13063324	—	2	2	no	—
161	#13063324	—	2	2	no	—
162	#13063324	—	2	1	no	—
163	#13063324	—	2	2	no	—
164	#13063324	—	2	1	no	—
165	#13063324	C₂³	1	2	yes	—
166	#13063324	C₂³	1	2	yes	—
167	#13063324	C₂³	1	2	yes	—
168	#13063324	C₂³	1	2	yes	—
169	#13063323	—	2	2	no	—
170	#13063323	—	2	2	no	—
171	#13063323	—	2	2	no	—
172	#13063323	—	2	1	no	—
173	#13063323	—	2	1	no	—
174	#13063323	—	2	2	no	—
175	#13063317	C₂³	1	2	yes	—
176	#13063316	C₂³	1	2	yes	—
177	#13063316	C₂³	1	2	yes	—
178	#13063315	—	2	2	no	—
179	#13063315	—	2	2	no	—
180	#13063305	—	2	1	no	—
181	#13063305	—	2	2	no	—
182	#13063304	—	2	1	no	—
183	#13063304	—	2	2	no	—
184	#13063303	—	2	2	no	—
185	#13063303	—	2	2	no	—
186	#13063303	—	2	2	no	—
187	#13063302	—	2	2	no	—
188	#13063302	—	2	2	no	—
189	#13063302	—	2	2	no	—
190	#13063301	—	2	1	no	—
191	#13063301	—	2	2	no	—
192	Q₈×Dic₄₃	—	2	1	no	—
193	Q₈×Dic₄₃	D₄	1	1	yes	characteristic
194	Q₈×Dic₄₃	C₂³	1	1	yes	characteristic
195	Q₈×Dic₄₃	C₂³	1	2	yes	—
196	C₄×Dic₈₆	—	2	2	no	—
197	C₄×Dic₈₆	—	2	1	no	—
198	C₄×Dic₈₆	—	2	2	no	—
199	C₄×Dic₈₆	—	2	1	no	—
200	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
201	C₄×Dic₈₆	C₂³	1	2	yes	—
202	C₄×Dic₈₆	C₂³	1	2	yes	—
203	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
204	#13063290	—	2	2	no	—
205	#13063290	—	2	1	no	—
206	#13063290	—	2	1	no	—
207	#13063290	—	2	2	no	—
208	#13063290	D₄	1	2	yes	—
209	#13063290	D₄	1	1	yes	characteristic
210	#13063290	C₂³	1	1	yes	characteristic
211	#13063290	C₂³	1	2	yes	—
212	C₄×D₁₇₂	C₂³	1	2	yes	—
213	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
214	D₄×Dic₄₃	C₂³	1	2	yes	—
215	D₄×Dic₄₃	C₂³	1	1	yes	characteristic
216	#13063287	C₂³	1	1	yes	characteristic
217	#13063287	C₂³	1	2	yes	—
218	C₄×C₂²⋊D₄₃	—	2	2	no	—
219	C₄×C₂²⋊D₄₃	—	2	1	no	—
220	(C₂²⋊D₄₃)⋊C₄	—	2	1	no	—
221	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
222	C₂×C₄⋊Dic₄₃	—	2	1	no	—
223	C₂×Dic₄₃⋊C₄	—	2	2	no	—
224	C₄⋊C₄×D₄₃	—	2	2	no	—
225	C₄⋊C₄×D₄₃	—	2	1	no	—
226	C₄⋊C₄×D₄₃	—	2	2	no	—
227	C₄⋊C₄×D₄₃	—	2	1	no	—
228	C₄⋊C₄×D₄₃	—	2	1	no	—
229	C₄⋊C₄×D₄₃	—	2	2	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	D₄	1	1	yes	characteristic
235	C₄⋊C₄×D₄₃	D₄	1	2	yes	—
236	C₄⋊C₄×D₄₃	C₂³	1	1	yes	characteristic
237	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
238	C₄⋊C₄×D₄₃	C₂³	1	1	yes	characteristic
239	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
240	C₂²⋊C₄×D₄₃	—	2	1	no	—
241	C₂²⋊C₄×D₄₃	—	2	2	no	—
242	C₄²×D₄₃	—	2	2	no	—
243	C₄²×D₄₃	—	2	1	no	—
244	C₄²×D₄₃	C₂³	1	1	yes	characteristic
245	C₄²×D₄₃	C₂³	1	2	yes	—
246	#13063259	C₂³	1	2	yes	—
247	#13063259	C₂³	1	2	yes	—
248	#13063259	C₂³	1	2	yes	—
249	#13063258	C₂³	1	2	yes	—
250	#13063258	C₂³	1	2	yes	—
251	#13063258	C₂³	1	2	yes	—
252	#13063258	C₂³	1	2	yes	—
253	#13063258	C₂³	1	2	yes	—
254	#13063258	C₂³	1	2	yes	—
255	#13063257	C₂³	1	1	yes	characteristic
256	#13063257	C₂³	1	2	yes	—
257	#13063256	C₂³	1	1	yes	characteristic
258	#13063256	C₂³	1	2	yes	—
259	#13063256	C₂³	1	1	yes	characteristic
260	#13063256	C₂³	1	2	yes	—
261	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
262	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
263	Dic₄₃⋊C₈	C₂³	1	2	yes	—
264	Dic₄₃⋊C₈	C₂³	1	2	yes	—
265	Dic₄₃⋊C₈	C₂³	1	2	yes	—
266	#13063250	C₂³	1	2	yes	—
267	#13063250	C₂³	1	1	yes	characteristic
268	#13063249	C₂³	1	2	yes	—
269	#13063249	C₂³	1	1	yes	characteristic
270	#13063248	C₂³	1	2	yes	—
271	#13063248	C₂³	1	1	yes	characteristic
272	#13063247	C₂³	1	1	yes	characteristic
273	#13063247	C₂³	1	2	yes	—
274	#13063246	C₂³	1	1	yes	characteristic
275	#13063246	C₂³	1	2	yes	—
276	#13063245	C₂³	1	1	yes	characteristic
277	#13063245	C₂³	1	2	yes	—
278	#13063236	C₂³	1	2	yes	—
279	#13063235	C₂³	1	2	yes	—
280	#13063235	C₂³	1	2	yes	—
281	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
282	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
283	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
284	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
285	C₄⋊Q₈×C₄₃	—	2	1	no	—
286	C₄⋊Q₈×C₄₃	—	2	2	no	—
287	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
288	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
289	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
290	#125×C₄₃	C₂³	1	2	yes	—
291	C₂²⋊Q₈×C₄₃	—	2	1	no	—
292	C₂²⋊Q₈×C₄₃	—	2	2	no	—
293	C₄×Q₈×C₄₃	—	2	1	no	—
294	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
295	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
296	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
297	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
298	C₄×D₄×C₄₃	C₂³	1	2	yes	—
299	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
300	#107×C₄₃	C₂³	1	2	yes	—
301	#107×C₄₃	C₂³	1	2	yes	—
302	#107×C₄₃	C₂³	1	2	yes	—
303	#106×C₄₃	C₂³	1	1	yes	characteristic
304	#106×C₄₃	C₂³	1	2	yes	—
305	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
306	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
307	#103×C₄₃	C₂³	1	2	yes	—
308	#103×C₄₃	C₂³	1	1	yes	characteristic
309	#102×C₄₃	C₂³	1	1	yes	characteristic
310	#102×C₄₃	C₂³	1	2	yes	—
311	#97×C₄₃	C₂³	1	2	yes	—
312	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
313	C₂³×D₄₃	—	2	1	no	—
314	C₂×Q₈×C₄₃	—	2	1	no	—
315	C₂×Q₈×C₄₃	—	2	2	no	—
316	C₂×Q₈×C₄₃	—	2	1	no	—
317	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
318	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
319	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₄₃	—	2	1	no	—
321	C₂²×C₄×C₄₃	—	2	2	no	—
322	C₂×C₂²⋊D₄₃	—	2	1	no	—
323	C₂²×Dic₄₃	—	2	1	no	—
324	C₂²×Dic₄₃	—	2	2	no	—
325	Q₈×D₄₃	—	2	4	no	—
326	Q₈×D₄₃	—	2	2	no	—
327	Q₈×D₄₃	—	8	4	no	—
328	Q₈×D₄₃	—	8	2	no	—
329	Q₈×D₄₃	—	8	2	no	—
330	Q₈×D₄₃	C₂×Q₈	1	4	yes	—
331	D₄×D₄₃	—	2	2	no	—
332	D₄×D₄₃	C₂×Q₈	1	4	yes	—
333	C₂×D₁₇₂	C₂⁴	1	1	yes	characteristic
334	C₂×C₄×D₄₃	—	2	1	no	—
335	C₂×C₄×D₄₃	—	2	1	no	—
336	C₂×C₄×D₄₃	—	2	2	no	—
337	C₂×C₄×D₄₃	—	2	2	no	—
338	C₂×C₄×D₄₃	—	2	1	no	—
339	C₂×C₄×D₄₃	—	2	2	no	—
340	C₂×C₄×D₄₃	—	2	1	no	—
341	C₂×C₄×D₄₃	—	2	1	no	—
342	C₂×C₄×D₄₃	—	2	2	no	—
343	C₂×C₄×D₄₃	—	4	4	no	—
344	C₂×C₄×D₄₃	—	8	4	no	—
345	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
346	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
347	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
348	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
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	2	no	—
353	C₂×Dic₈₆	—	2	1	no	—
354	C₂×Dic₈₆	—	2	2	no	—
355	C₂×Dic₈₆	—	2	2	no	—
356	C₂×Dic₈₆	—	2	2	no	—
357	C₂×Dic₈₆	—	2	2	no	—
358	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
359	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
360	C₂×Dic₈₆	C₂⁴	1	1	yes	characteristic
361	SD₁₆×C₄₃	C₂×Q₈	1	4	yes	complemented
362	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
364	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₄₃	—	2	2	no	—
366	C₄⋊C₄×C₄₃	—	2	1	no	—
367	C₄⋊C₄×C₄₃	—	2	2	no	—
368	C₄⋊C₄×C₄₃	—	2	1	no	—
369	C₄⋊C₄×C₄₃	—	2	2	no	—
370	C₄⋊C₄×C₄₃	—	2	1	no	—
371	C₄⋊C₄×C₄₃	—	2	2	no	—
372	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
373	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
374	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
375	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
376	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
377	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
378	C₂²⋊C₄×C₄₃	—	2	1	no	—
379	C₂²⋊C₄×C₄₃	—	2	2	no	—
380	C₄²×C₄₃	—	2	2	no	—
381	C₄²×C₄₃	—	2	1	no	—
382	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
383	C₄²×C₄₃	C₂⁴	1	2	yes	—
384	C₂²⋊Dic₄₃	—	2	1	no	—
385	C₂²⋊Dic₄₃	—	2	2	no	—
386	#10621884	C₂×Q₈	1	4	yes	complemented
387	#10621883	C₂×Q₈	1	4	yes	complemented
388	(C₂×D₄₃)⋊C₄	—	2	1	no	—
389	(C₂×D₄₃)⋊C₄	—	2	2	no	—
390	(C₂×D₄₃)⋊C₄	—	2	2	no	—
391	(C₂×D₄₃)⋊C₄	—	2	1	no	—
392	C₄⋊Dic₄₃	—	2	1	no	—
393	C₄⋊Dic₄₃	—	2	2	no	—
394	C₄⋊Dic₄₃	—	2	1	no	—
395	C₄⋊Dic₄₃	—	2	2	no	—
396	C₄⋊Dic₄₃	—	2	2	no	—
397	C₄⋊Dic₄₃	—	2	1	no	—
398	C₄⋊Dic₄₃	—	2	2	no	—
399	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
400	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
401	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
402	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
403	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
404	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
405	Dic₄₃⋊C₄	—	2	2	no	—
406	Dic₄₃⋊C₄	—	2	2	no	—
407	Dic₄₃⋊C₄	—	2	1	no	—
408	Dic₄₃⋊C₄	—	2	2	no	—
409	Dic₄₃⋊C₄	—	2	2	no	—
410	Dic₄₃⋊C₄	—	2	2	no	—
411	Dic₄₃⋊C₄	—	2	2	no	—
412	Dic₄₃⋊C₄	—	2	2	no	—
413	Dic₄₃⋊C₄	—	2	2	no	—
414	Dic₄₃⋊C₄	—	2	2	no	—
415	Dic₄₃⋊C₄	—	2	1	no	—
416	Dic₄₃⋊C₄	—	2	2	no	—
417	Dic₄₃⋊C₄	—	2	1	no	—
418	Dic₄₃⋊C₄	—	2	2	no	—
419	Dic₄₃⋊C₄	—	2	1	no	—
420	Dic₄₃⋊C₄	—	2	2	no	—
421	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
422	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
423	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
424	C₄×Dic₄₃	—	2	2	no	—
425	C₄×Dic₄₃	—	2	1	no	—
426	C₄×Dic₄₃	—	2	2	no	—
427	C₄×Dic₄₃	—	2	1	no	—
428	C₄×Dic₄₃	—	2	2	no	—
429	C₄×Dic₄₃	—	2	1	no	—
430	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
431	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
432	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
433	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
434	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
435	C₄×Dic₄₃	C₂⁴	1	2	yes	—
436	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
437	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
438	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
439	#10621873	C₂×Q₈	1	4	yes	complemented
440	C₈×D₄₃	—	2	2	no	—
441	C₈×D₄₃	—	2	4	no	—
442	C₈×D₄₃	C₂×Q₈	1	4	yes	—
443	C₂³×C₄₃	—	2	1	no	—
444	C₂²×D₄₃	—	2	1	no	—
445	C₂²×D₄₃	—	2	4	no	—
446	C₂²×D₄₃	—	4	2	no	—
447	C₂²×D₄₃	—	4	2	no	—
448	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
449	Q₈×C₄₃	—	2	2	no	—
450	Q₈×C₄₃	—	2	1	no	—
451	Q₈×C₄₃	—	8	1	no	—
452	Q₈×C₄₃	—	8	1	no	—
453	Q₈×C₄₃	—	8	2	no	—
454	Q₈×C₄₃	C₂²×Q₈	1	2	yes	—
455	D₄×C₄₃	—	2	1	no	—
456	D₄×C₄₃	C₂²×Q₈	1	2	yes	—
457	C₂×C₄×C₄₃	—	2	1	no	—
458	C₂×C₄×C₄₃	—	2	2	no	—
459	C₂×C₄×C₄₃	—	2	1	no	—
460	C₂×C₄×C₄₃	—	2	1	no	—
461	C₂×C₄×C₄₃	—	2	2	no	—
462	C₂×C₄×C₄₃	—	4	2	no	—
463	C₂×C₄×C₄₃	—	8	2	no	—
464	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
465	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
466	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
469	C₂²⋊D₄₃	—	2	4	no	—
470	C₂×Dic₄₃	—	2	1	no	—
471	C₂×Dic₄₃	—	2	2	no	—
472	C₂×Dic₄₃	—	2	1	no	—
473	C₂×Dic₄₃	—	2	1	no	—
474	C₂×Dic₄₃	—	2	2	no	—
475	C₂×Dic₄₃	—	4	2	no	—
476	C₂×Dic₄₃	—	8	2	no	—
477	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
478	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
479	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
480	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
481	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
482	D₁₇₂	—	2	1	no	—
483	D₁₇₂	C₂²×Q₈	1	2	yes	—
484	C₄×D₄₃	—	2	4	no	—
485	C₄×D₄₃	—	2	4	no	—
486	C₄×D₄₃	—	2	4	no	—
487	C₄×D₄₃	—	2	2	no	—
488	C₄×D₄₃	—	4	2	no	—
489	C₄×D₄₃	—	4	4	no	—
490	C₄×D₄₃	—	4	2	no	—
491	C₄×D₄₃	—	4	4	no	—
492	C₄×D₄₃	—	4	2	no	—
493	C₄×D₄₃	—	4	2	no	—
494	C₄×D₄₃	—	8	2	no	—
495	C₄×D₄₃	—	8	2	no	—
496	C₄×D₄₃	#137	1	4	yes	—
497	C₄×D₄₃	C₂²×Q₈	1	2	yes	—
498	C₄×D₄₃	2₋¹⁺⁴	1	2	yes	—
499	Dic₈₆	—	2	2	no	—
500	Dic₈₆	—	2	1	no	—
501	Dic₈₆	—	2	4	no	—
502	Dic₈₆	—	2	4	no	—
503	Dic₈₆	—	8	2	no	—
504	Dic₈₆	—	8	2	no	—
505	Dic₈₆	—	8	2	no	—
506	Dic₈₆	—	8	2	no	—
507	Dic₈₆	—	8	1	no	—
508	Dic₈₆	—	8	2	no	—
509	Dic₈₆	—	8	1	no	—
510	Dic₈₆	C₂²×Q₈	1	2	yes	—
511	C₈×C₄₃	—	2	1	no	—
512	C₈×C₄₃	—	2	2	no	—
513	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
514	C₄₃⋊C₈	—	2	1	no	—
515	C₄₃⋊C₈	—	2	2	no	—
516	C₄₃⋊C₈	C₂²×Q₈	1	2	yes	—
517	C₂×#3385	—	43	1	no	maximal, Sylow
518	C₂²×C₄₃	—	2	2	no	—
519	C₂²×C₄₃	—	4	1	no	—
520	C₂²×C₄₃	—	4	1	no	—
521	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
522	C₂×D₄₃	—	2	2	no	—
523	C₂×D₄₃	—	4	1	no	—
524	C₂×D₄₃	—	4	1	no	—
525	C₂×D₄₃	—	4	8	no	—
526	C₂×D₄₃	D₄×Q₈	1	2	yes	—
527	C₂×D₄₃	C₂×#137	1	2	yes	—
528	C₂×D₄₃	#576	1	2	yes	—
529	C₄×C₄₃	—	2	2	no	—
530	C₄×C₄₃	—	2	2	no	—
531	C₄×C₄₃	—	2	1	no	—
532	C₄×C₄₃	—	2	2	no	—
533	C₄×C₄₃	—	4	1	no	—
534	C₄×C₄₃	—	4	2	no	—
535	C₄×C₄₃	—	4	1	no	—
536	C₄×C₄₃	—	4	2	no	—
537	C₄×C₄₃	C₂×#137	1	2	yes	—
538	C₄×C₄₃	C₂³×Q₈	1	1	yes	characteristic
539	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
540	Dic₄₃	—	2	2	no	—
541	Dic₄₃	—	2	2	no	—
542	Dic₄₃	—	2	1	no	—
543	Dic₄₃	—	2	2	no	—
544	Dic₄₃	—	4	1	no	—
545	Dic₄₃	—	4	2	no	—
546	Dic₄₃	—	4	1	no	—
547	Dic₄₃	—	4	2	no	—
548	Dic₄₃	D₄×Q₈	1	2	yes	—
549	Dic₄₃	C₂×#137	1	2	yes	—
550	C₂×Q₈²	—	43	1	no	—
551	C₂×#554	—	43	1	no	—
552	#3385	—	43	2	no	—
553	#3385	—	43	1	no	—
554	#3385	—	43	2	no	—
555	#3385	—	43	1	no	—
556	#3385	—	43	1	no	—
557	#3385	—	43	2	no	—
558	#3385	—	43	1	no	—
559	#3385	—	43	2	no	—
560	#3385	—	43	1	no	—
561	#3385	—	43	1	no	—
562	#3385	—	43	1	no	—
563	#3385	D₄₃	1	1	yes	characteristic, direct product factor
564	C₂×#501	—	43	2	no	—
565	C₂×#500	—	43	1	no	—
566	C₂×#479	—	43	2	no	—
567	C₂×#477	—	43	1	no	—
568	C₂×#476	—	43	1	no	—
569	C₂×#474	—	43	2	no	—
570	C₂×#446	—	43	1	no	—
571	C₂×#440	—	43	2	no	—
572	C₂×C₄×SD₁₆	—	43	1	no	—
573	C₂×C₄₃	—	4	2	no	—
574	C₂×C₄₃	C₂×D₄×Q₈	1	1	yes	characteristic
575	C₂×C₄₃	C₂²×#137	1	1	yes	characteristic
576	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
577	D₄₃	—	4	2	no	—
578	D₄₃	#3385	1	4	yes	direct product factor
579	C₂²×SD₁₆	—	43	1	no	—
580	Q₈²	—	43	2	no	—
581	Q₈²	—	43	1	no	—
582	Q₈²	—	43	2	no	—
583	Q₈²	—	43	1	no	—
584	Q₈²	—	43	1	no	—
585	Q₈²	—	86	1	no	—
586	Q₈²	—	86	2	no	—
587	Q₈²	—	86	1	no	—
588	Q₈²	C₂×D₄₃	1	1	yes	characteristic, complemented
589	#554	—	43	1	no	—
590	#554	—	43	2	no	—
591	#554	—	43	1	no	—
592	#554	—	43	1	no	—
593	#554	—	43	2	no	—
594	#554	—	86	1	no	—
595	#554	—	86	2	no	—
596	#554	—	86	1	no	—
597	#554	C₂×D₄₃	1	1	yes	characteristic
598	C₂×C₄⋊Q₈	—	43	1	no	—
599	C₂×C₄⋊Q₈	—	43	1	no	—
600	C₂×C₄⋊Q₈	—	43	2	no	—
601	C₂×C₄⋊Q₈	—	86	1	no	—
602	C₂×C₄⋊Q₈	—	86	2	no	—
603	C₂×#125	—	43	2	no	—
604	C₂×C₂²⋊Q₈	—	86	2	no	—
605	C₂×C₂²⋊Q₈	—	86	1	no	—
606	C₂×C₄×Q₈	—	43	1	no	—
607	C₂×C₄×Q₈	—	43	1	no	—
608	C₂×C₄×Q₈	—	43	2	no	—
609	C₂×C₄×Q₈	—	86	1	no	—
610	C₂×C₄×D₄	—	43	1	no	—
611	C₂×C₄×D₄	—	43	2	no	—
612	C₂²×C₄⋊C₄	—	86	1	no	—
613	#501	—	43	2	no	—
614	#501	—	43	2	no	—
615	#501	—	43	2	no	—
616	#501	—	43	2	no	—
617	#501	—	43	2	no	—
618	#501	—	43	2	no	—
619	#501	—	43	2	no	—
620	#501	C₂×D₄₃	1	2	yes	complemented
621	#500	—	43	1	no	—
622	#500	—	43	1	no	—
623	#500	—	43	2	no	—
624	#500	—	43	2	no	—
625	#500	—	43	1	no	—
626	#500	C₂×D₄₃	1	1	yes	characteristic, complemented
627	#479	—	43	2	no	—
628	#479	—	43	2	no	—
629	#479	—	43	2	no	—
630	#479	—	43	2	no	—
631	#479	—	43	2	no	—
632	#479	—	43	2	no	—
633	#479	—	43	2	no	—
634	#479	C₂×D₄₃	1	2	yes	complemented
635	#477	—	43	1	no	—
636	#477	—	43	1	no	—
637	#477	—	43	2	no	—
638	#477	—	43	1	no	—
639	#477	—	43	2	no	—
640	#477	C₂×D₄₃	1	1	yes	characteristic, complemented
641	#476	—	43	1	no	—
642	#476	—	43	1	no	—
643	#476	—	43	2	no	—
644	#476	—	43	1	no	—
645	#476	—	43	2	no	—
646	#476	C₂×D₄₃	1	1	yes	characteristic
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	—	43	2	no	—
653	#474	—	43	2	no	—
654	#474	C₂×D₄₃	1	2	yes	—
655	#446	—	43	1	no	—
656	#446	—	43	1	no	—
657	#446	—	43	2	no	—
658	#446	—	43	2	no	—
659	#446	—	43	1	no	—
660	#446	C₂×D₄₃	1	1	yes	characteristic, complemented
661	#440	—	43	2	no	—
662	#440	—	43	2	no	—
663	#440	—	43	2	no	—
664	#440	—	43	2	no	—
665	#440	—	43	2	no	—
666	#440	—	43	2	no	—
667	#440	—	43	2	no	—
668	#440	C₂×D₄₃	1	2	yes	—
669	C₄×SD₁₆	—	43	1	no	—
670	C₄×SD₁₆	—	43	1	no	—
671	C₄×SD₁₆	—	43	1	no	—
672	C₄×SD₁₆	—	43	1	no	—
673	C₄×SD₁₆	—	43	1	no	—
674	C₄×SD₁₆	—	43	1	no	—
675	C₄×SD₁₆	—	43	1	no	—
676	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
677	C₂×#107	—	43	2	no	—
678	C₂×#107	—	43	2	no	—
679	C₂×#107	—	43	2	no	—
680	C₂×#106	—	43	2	no	—
681	C₂×#106	—	43	1	no	—
682	C₂×C₄⋊C₈	—	43	1	no	—
683	C₂×C₄⋊C₈	—	43	2	no	—
684	C₂×#103	—	43	2	no	—
685	C₂×#103	—	43	1	no	—
686	C₂×#102	—	43	1	no	—
687	C₂×#102	—	43	2	no	—
688	C₂×#97	—	43	2	no	—
689	C₂×C₄×C₈	—	43	1	no	—
690	C₄₃	C₂×#3385	1	1	yes	characteristic, complemented, Sylow
691	C₂²×Q₈	—	43	1	no	—
692	C₂²×Q₈	—	43	1	no	—
693	C₂²×Q₈	—	86	1	no	—
694	C₂²×Q₈	—	86	1	no	—
695	C₂²×Q₈	—	86	2	no	—
696	C₂²×D₄	—	43	1	no	—
697	C₂³×C₄	—	86	2	no	—
698	C₂³×C₄	—	86	1	no	—
699	C₂×SD₁₆	—	43	1	no	—
700	C₂×SD₁₆	—	43	1	no	—
701	C₂×SD₁₆	—	43	8	no	—
702	C₂×SD₁₆	—	43	1	no	—
703	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
704	C₂²×C₈	—	43	1	no	—
705	C₂²×C₈	—	43	1	no	—
706	C₂²×C₈	—	43	2	no	—
707	C₄⋊Q₈	—	2	1	no	—
708	C₄⋊Q₈	—	2	2	no	—
709	C₄⋊Q₈	—	43	2	no	—
710	C₄⋊Q₈	—	43	2	no	—
711	C₄⋊Q₈	—	43	2	no	—
712	C₄⋊Q₈	—	43	2	no	—
713	C₄⋊Q₈	—	43	1	no	—
714	C₄⋊Q₈	—	43	2	no	—
715	C₄⋊Q₈	—	43	1	no	—
716	C₄⋊Q₈	—	86	1	no	—
717	C₄⋊Q₈	—	86	2	no	—
718	C₄⋊Q₈	—	86	1	no	—
719	C₄⋊Q₈	—	86	2	no	—
720	C₄⋊Q₈	—	86	1	no	—
721	C₄⋊Q₈	—	86	1	no	—
722	C₄⋊Q₈	—	86	2	no	—
723	C₄⋊Q₈	—	86	1	no	—
724	C₄⋊Q₈	—	86	2	no	—
725	C₄⋊Q₈	—	86	2	no	—
726	C₄⋊Q₈	—	86	2	no	—
727	C₄⋊Q₈	—	86	1	no	—
728	C₄⋊Q₈	—	86	2	no	—
729	C₄⋊Q₈	—	86	2	no	—
730	C₄⋊Q₈	—	86	2	no	—
731	C₄⋊Q₈	—	86	2	no	—
732	C₄⋊Q₈	—	86	1	no	—
733	C₄⋊Q₈	—	86	2	no	—
734	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
735	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
736	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
737	#125	—	43	2	no	—
738	#125	—	43	2	no	—
739	#125	—	43	2	no	—
740	#125	—	86	2	no	—
741	#125	—	86	2	no	—
742	#125	C₂²×D₄₃	1	2	yes	—
743	C₂²⋊Q₈	—	2	1	no	—
744	C₂²⋊Q₈	—	2	2	no	—
745	C₂²⋊Q₈	—	86	2	no	—
746	C₂²⋊Q₈	—	86	2	no	—
747	C₂²⋊Q₈	—	86	2	no	—
748	C₂²⋊Q₈	—	86	2	no	—
749	C₂²⋊Q₈	—	86	2	no	—
750	C₂²⋊Q₈	—	86	2	no	—
751	C₂²⋊Q₈	—	86	1	no	—
752	C₂²⋊Q₈	—	86	2	no	—
753	C₂²⋊Q₈	—	86	2	no	—
754	C₂²⋊Q₈	—	86	1	no	—
755	C₂²⋊Q₈	—	86	1	no	—
756	C₂²⋊Q₈	—	86	2	no	—
757	C₄×Q₈	—	2	1	no	—
758	C₄×Q₈	—	43	1	no	—
759	C₄×Q₈	—	43	2	no	—
760	C₄×Q₈	—	43	1	no	—
761	C₄×Q₈	—	43	2	no	—
762	C₄×Q₈	—	43	1	no	—
763	C₄×Q₈	—	43	1	no	—
764	C₄×Q₈	—	43	2	no	—
765	C₄×Q₈	—	43	1	no	—
766	C₄×Q₈	—	43	2	no	—
767	C₄×Q₈	—	43	1	no	—
768	C₄×Q₈	—	43	2	no	—
769	C₄×Q₈	—	86	2	no	—
770	C₄×Q₈	—	86	1	no	—
771	C₄×Q₈	—	86	2	no	—
772	C₄×Q₈	—	86	1	no	—
773	C₄×Q₈	—	86	2	no	—
774	C₄×Q₈	—	86	1	no	—
775	C₄×Q₈	—	86	2	no	—
776	C₄×Q₈	—	86	1	no	—
777	C₄×Q₈	—	86	1	no	—
778	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
779	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
780	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
781	C₄×D₄	—	43	1	no	—
782	C₄×D₄	—	43	2	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	—	86	2	no	—
788	C₄×D₄	—	86	1	no	—
789	C₄×D₄	—	86	2	no	—
790	C₄×D₄	—	86	1	no	—
791	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
792	C₄×D₄	C₂²×D₄₃	1	2	yes	—
793	C₂×C₄⋊C₄	—	2	1	no	—
794	C₂×C₄⋊C₄	—	43	1	no	—
795	C₂×C₄⋊C₄	—	43	2	no	—
796	C₂×C₄⋊C₄	—	43	1	no	—
797	C₂×C₄⋊C₄	—	43	2	no	—
798	C₂×C₄⋊C₄	—	43	1	no	—
799	C₂×C₄⋊C₄	—	43	2	no	—
800	C₂×C₄⋊C₄	—	86	2	no	—
801	C₂×C₄⋊C₄	—	86	1	no	—
802	C₂×C₄⋊C₄	—	86	2	no	—
803	C₂×C₄⋊C₄	—	86	1	no	—
804	C₂×C₄⋊C₄	—	86	1	no	—
805	C₂×C₄⋊C₄	—	86	2	no	—
806	C₂×C₄⋊C₄	—	86	1	no	—
807	C₂×C₄⋊C₄	—	86	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×C₂²⋊C₄	—	86	2	no	—
813	C₂×C₂²⋊C₄	—	86	1	no	—
814	C₂×C₄²	—	43	2	no	—
815	C₂×C₄²	—	43	1	no	—
816	C₂×C₄²	—	86	1	no	—
817	C₂×C₄²	—	86	2	no	—
818	#107	—	43	2	no	—
819	#107	—	43	2	no	—
820	#107	—	43	2	no	—
821	#107	—	43	2	no	—
822	#107	—	43	2	no	—
823	#107	—	43	2	no	—
824	#107	—	43	2	no	—
825	#107	—	43	2	no	—
826	#107	—	43	2	no	—
827	#107	C₂²×D₄₃	1	2	yes	—
828	#107	C₂²×D₄₃	1	2	yes	—
829	#107	C₂²×D₄₃	1	2	yes	—
830	#106	—	43	1	no	—
831	#106	—	43	2	no	—
832	#106	—	43	1	no	—
833	#106	—	43	1	no	—
834	#106	—	43	2	no	—
835	#106	—	43	2	no	—
836	#106	C₂²×D₄₃	1	1	yes	characteristic
837	#106	C₂²×D₄₃	1	2	yes	—
838	C₄⋊C₈	—	43	2	no	—
839	C₄⋊C₈	—	43	2	no	—
840	C₄⋊C₈	—	43	2	no	—
841	C₄⋊C₈	—	43	2	no	—
842	C₄⋊C₈	—	43	1	no	—
843	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
844	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
845	#103	—	43	1	no	—
846	#103	—	43	2	no	—
847	#103	—	43	1	no	—
848	#103	—	43	2	no	—
849	#103	—	43	1	no	—
850	#103	—	43	2	no	—
851	#103	C₂²×D₄₃	1	1	yes	characteristic
852	#103	C₂²×D₄₃	1	2	yes	—
853	#102	—	43	1	no	—
854	#102	—	43	2	no	—
855	#102	—	43	1	no	—
856	#102	—	43	2	no	—
857	#102	—	43	1	no	—
858	#102	—	43	2	no	—
859	#102	C₂²×D₄₃	1	1	yes	characteristic
860	#102	C₂²×D₄₃	1	2	yes	—
861	#97	—	43	2	no	—
862	#97	—	43	2	no	—
863	#97	—	43	2	no	—
864	#97	C₂²×D₄₃	1	2	yes	—
865	C₄×C₈	—	43	1	no	—
866	C₄×C₈	—	43	1	no	—
867	C₄×C₈	—	43	1	no	—
868	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
869	C₂⁴	—	86	1	no	—
870	C₂×Q₈	—	2	1	no	—
871	C₂×Q₈	—	2	1	no	—
872	C₂×Q₈	—	2	2	no	—
873	C₂×Q₈	—	43	2	no	—
874	C₂×Q₈	—	43	1	no	—
875	C₂×Q₈	—	43	4	no	—
876	C₂×Q₈	—	43	1	no	—
877	C₂×Q₈	—	86	1	no	—
878	C₂×Q₈	—	86	2	no	—
879	C₂×Q₈	—	86	2	no	—
880	C₂×Q₈	—	86	2	no	—
881	C₂×Q₈	—	86	2	no	—
882	C₂×Q₈	—	86	4	no	—
883	C₂×Q₈	—	86	2	no	—
884	C₂×Q₈	—	86	1	no	—
885	C₂×Q₈	—	86	1	no	—
886	C₂×Q₈	—	86	2	no	—
887	C₂×Q₈	—	344	4	no	—
888	C₂×Q₈	—	344	2	no	—
889	C₂×Q₈	—	344	2	no	—
890	C₂×Q₈	D₄×D₄₃	1	1	yes	characteristic
891	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
892	C₂×D₄	—	43	4	no	—
893	C₂×D₄	—	43	1	no	—
894	C₂×D₄	—	86	2	no	—
895	C₂×D₄	—	86	1	no	—
896	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
897	C₂²×C₄	—	2	1	no	—
898	C₂²×C₄	—	2	2	no	—
899	C₂²×C₄	—	43	1	no	—
900	C₂²×C₄	—	43	1	no	—
901	C₂²×C₄	—	43	2	no	—
902	C₂²×C₄	—	43	1	no	—
903	C₂²×C₄	—	43	2	no	—
904	C₂²×C₄	—	86	2	no	—
905	C₂²×C₄	—	86	1	no	—
906	C₂²×C₄	—	86	1	no	—
907	C₂²×C₄	—	86	1	no	—
908	C₂²×C₄	—	86	2	no	—
909	C₂²×C₄	—	86	1	no	—
910	C₂²×C₄	—	86	2	no	—
911	C₂²×C₄	—	86	2	no	—
912	C₂²×C₄	—	86	1	no	—
913	C₂²×C₄	—	86	2	no	—
914	C₂²×C₄	—	86	1	no	—
915	C₂²×C₄	—	344	4	no	—
916	C₂²×C₄	—	172	4	no	—
917	SD₁₆	—	43	4	no	—
918	SD₁₆	—	43	4	no	—
919	SD₁₆	—	43	4	no	—
920	SD₁₆	Q₈×D₄₃	1	4	yes	complemented
921	C₂×C₈	—	43	1	no	—
922	C₂×C₈	—	43	4	no	—
923	C₂×C₈	—	43	1	no	—
924	C₂×C₈	—	43	2	no	—
925	C₂×C₈	—	86	2	no	—
926	C₂×C₈	—	86	4	no	—
927	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
928	C₂×C₈	C₂³×D₄₃	1	2	yes	—
929	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
930	C₄⋊C₄	—	2	2	no	—
931	C₄⋊C₄	—	2	1	no	—
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	1	no	—
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	2	no	—
936	C₄⋊C₄	—	2	2	no	—
937	C₄⋊C₄	—	43	2	no	—
938	C₄⋊C₄	—	43	1	no	—
939	C₄⋊C₄	—	43	2	no	—
940	C₄⋊C₄	—	43	2	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	—	86	1	no	—
947	C₄⋊C₄	—	86	2	no	—
948	C₄⋊C₄	—	86	1	no	—
949	C₄⋊C₄	—	86	2	no	—
950	C₄⋊C₄	—	86	2	no	—
951	C₄⋊C₄	—	86	2	no	—
952	C₄⋊C₄	—	86	2	no	—
953	C₄⋊C₄	—	86	1	no	—
954	C₄⋊C₄	—	86	2	no	—
955	C₄⋊C₄	—	86	1	no	—
956	C₄⋊C₄	—	86	2	no	—
957	C₄⋊C₄	—	86	2	no	—
958	C₄⋊C₄	—	86	2	no	—
959	C₄⋊C₄	—	86	2	no	—
960	C₄⋊C₄	—	86	2	no	—
961	C₄⋊C₄	—	86	2	no	—
962	C₄⋊C₄	—	86	2	no	—
963	C₄⋊C₄	—	86	1	no	—
964	C₄⋊C₄	—	86	1	no	—
965	C₄⋊C₄	—	86	2	no	—
966	C₄⋊C₄	—	86	2	no	—
967	C₄⋊C₄	—	86	1	no	—
968	C₄⋊C₄	—	86	2	no	—
969	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
970	C₄⋊C₄	D₄×D₄₃	1	2	yes	—
971	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
972	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
973	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
974	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	2	no	—
977	C₂²⋊C₄	—	86	1	no	—
978	C₂²⋊C₄	—	86	2	no	—
979	C₂²⋊C₄	—	86	2	no	—
980	C₂²⋊C₄	—	86	1	no	—
981	C₂²⋊C₄	—	86	1	no	—
982	C₂²⋊C₄	—	86	2	no	—
983	C₄²	—	2	2	no	—
984	C₄²	—	2	1	no	—
985	C₄²	—	43	2	no	—
986	C₄²	—	43	2	no	—
987	C₄²	—	43	1	no	—
988	C₄²	—	43	1	no	—
989	C₄²	—	43	1	no	—
990	C₄²	—	43	2	no	—
991	C₄²	—	86	1	no	—
992	C₄²	—	86	2	no	—
993	C₄²	—	86	1	no	—
994	C₄²	—	86	2	no	—
995	C₄²	—	86	2	no	—
996	C₄²	—	86	1	no	—
997	C₄²	C₂³×D₄₃	1	1	yes	characteristic
998	C₄²	C₂³×D₄₃	1	2	yes	—
999	C₂³	—	2	1	no	—
1000	C₂³	—	43	1	no	—
1001	C₂³	—	86	4	no	—
1002	C₂³	—	86	1	no	—
1003	C₂³	—	172	2	no	—
1004	C₂³	—	172	2	no	—
1005	Q₈	—	2	2	no	—
1006	Q₈	—	2	1	no	—
1007	Q₈	—	8	2	no	—
1008	Q₈	—	8	1	no	—
1009	Q₈	—	8	1	no	—
1010	Q₈	—	43	2	no	—
1011	Q₈	—	86	4	no	—
1012	Q₈	—	86	4	no	—
1013	Q₈	—	86	2	no	—
1014	Q₈	—	86	1	no	—
1015	Q₈	—	344	2	no	—
1016	Q₈	—	344	1	no	—
1017	Q₈	—	344	1	no	—
1018	Q₈	—	344	2	no	—
1019	Q₈	—	344	2	no	—
1020	Q₈	—	344	2	no	—
1021	Q₈	—	344	2	no	—
1022	Q₈	C₂×Q₈×D₄₃	1	2	yes	—
1023	D₄	—	2	1	no	—
1024	D₄	—	43	2	no	—
1025	D₄	—	86	4	no	—
1026	D₄	—	86	1	no	—
1027	D₄	C₂×Q₈×D₄₃	1	2	yes	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	2	no	—
1030	C₂×C₄	—	2	1	no	—
1031	C₂×C₄	—	2	1	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	4	2	no	—
1034	C₂×C₄	—	8	2	no	—
1035	C₂×C₄	—	43	1	no	—
1036	C₂×C₄	—	43	1	no	—
1037	C₂×C₄	—	43	4	no	—
1038	C₂×C₄	—	43	2	no	—
1039	C₂×C₄	—	43	2	no	—
1040	C₂×C₄	—	43	2	no	—
1041	C₂×C₄	—	43	1	no	—
1042	C₂×C₄	—	43	2	no	—
1043	C₂×C₄	—	86	4	no	—
1044	C₂×C₄	—	86	4	no	—
1045	C₂×C₄	—	86	2	no	—
1046	C₂×C₄	—	86	4	no	—
1047	C₂×C₄	—	86	1	no	—
1048	C₂×C₄	—	86	1	no	—
1049	C₂×C₄	—	86	2	no	—
1050	C₂×C₄	—	86	1	no	—
1051	C₂×C₄	—	86	2	no	—
1052	C₂×C₄	—	344	2	no	—
1053	C₂×C₄	—	344	2	no	—
1054	C₂×C₄	—	344	2	no	—
1055	C₂×C₄	—	172	2	no	—
1056	C₂×C₄	—	172	4	no	—
1057	C₂×C₄	—	172	2	no	—
1058	C₂×C₄	—	172	2	no	—
1059	C₂×C₄	—	172	4	no	—
1060	C₂×C₄	—	172	2	no	—
1061	C₂×C₄	—	172	2	no	—
1062	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
1063	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1064	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
1065	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1066	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1067	C₈	—	2	1	no	—
1068	C₈	—	2	2	no	—
1069	C₈	—	43	2	no	—
1070	C₈	—	86	1	no	—
1071	C₈	—	86	2	no	—
1072	C₈	C₂×Q₈×D₄₃	1	2	yes	—
1073	C₂²	—	2	2	no	—
1074	C₂²	—	4	1	no	—
1075	C₂²	—	4	1	no	—
1076	C₂²	—	43	2	no	—
1077	C₂²	—	43	2	no	—
1078	C₂²	—	43	2	no	—
1079	C₂²	—	86	2	no	—
1080	C₂²	—	172	8	no	—
1081	C₂²	—	172	1	no	—
1082	C₂²	—	172	1	no	—
1083	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1084	C₄	—	2	2	no	—
1085	C₄	—	2	2	no	—
1086	C₄	—	2	1	no	—
1087	C₄	—	2	2	no	—
1088	C₄	—	4	1	no	—
1089	C₄	—	4	2	no	—
1090	C₄	—	4	1	no	—
1091	C₄	—	4	2	no	—
1092	C₄	—	43	2	no	—
1093	C₄	—	43	2	no	—
1094	C₄	—	86	2	no	—
1095	C₄	—	86	2	no	—
1096	C₄	—	86	1	no	—
1097	C₄	—	86	2	no	—
1098	C₄	—	172	1	no	—
1099	C₄	—	172	2	no	—
1100	C₄	—	172	1	no	—
1101	C₄	—	172	2	no	—
1102	C₄	#137×D₄₃	1	2	yes	—
1103	C₄	C₂²×Q₈×D₄₃	1	1	yes	characteristic
1104	C₄	2₋¹⁺⁴×D₄₃	1	1	yes	characteristic
1105	C₂	—	4	2	no	—
1106	C₂	—	43	4	no	—
1107	C₂	—	172	2	no	—
1108	C₂	D₄×Q₈×D₄₃	1	1	yes	characteristic
1109	C₂	C₂×#137×D₄₃	1	1	yes	characteristic
1110	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×#3385	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	C₂×D₄×D₄₃	C₂³
hypercenter	#3385	D₄₃
hypocenter	C₄₃	C₂×#3385
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #3385

Complements

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

N	H ≅ G/N	type
1. Q₈²×D₄₃	C₂	semidirect
3. #19147510	C₂	semidirect
4. #19147509	C₂	semidirect
5. #19147508	C₂	semidirect
6. #19147507	C₂	semidirect
7. #19147506	C₂	semidirect
8. #19147505	C₂	semidirect
9. #19147504	C₂	semidirect
10. #19147503	C₂	semidirect
11. #19147502	C₂	semidirect
12. #19147501	C₂	semidirect
13. #19147500	C₂	semidirect
14. #501×D₄₃	C₂	semidirect
15. #500×D₄₃	C₂	semidirect
16. #479×D₄₃	C₂	semidirect
17. #477×D₄₃	C₂	semidirect
20. #446×D₄₃	C₂	semidirect
23. C₄₃×#3385	C₂	semidirect
26. Q₈×Dic₈₆	C₂²	semidirect
27. Q₈×Dic₈₆	C₂²	semidirect
28. Q₈×Dic₈₆	C₂²	semidirect
31. #14583629	C₂²	semidirect
32. #14583629	C₂²	semidirect
56. #14583309	C₂²	semidirect
57. #14583308	C₂²	semidirect
58. #14583307	C₂²	semidirect
59. #14583307	C₂²	semidirect
60. #14583306	C₂²	semidirect
61. #14583306	C₂²	semidirect
62. #14583305	C₂²	semidirect
63. #14583304	C₂²	semidirect
64. #14583303	C₂²	semidirect
65. #14583303	C₂²	semidirect
66. #14583302	C₂²	semidirect
67. #14583302	C₂²	semidirect
68. #14583209	C₂²	semidirect
69. #14583208	C₂²	semidirect
70. #14583207	C₂²	semidirect
71. #14583206	C₂²	semidirect
72. #14583205	C₂²	semidirect
73. #14583204	C₂²	semidirect
74. #14583203	C₂²	semidirect
75. #14583195	C₂²	semidirect
76. #14583194	C₂²	semidirect
77. #14583193	C₂²	semidirect
78. #14583192	C₂²	semidirect
79. #14583191	C₂²	semidirect
92. #14583030	C₂²	semidirect
93. #14583029	C₂²	semidirect
94. #14583028	C₂²	semidirect
95. #14583027	C₂²	semidirect
96. #14583026	C₂²	semidirect
124. Q₈²×C₄₃	C₂²	semidirect
126. C₄₃×#501	C₂²	semidirect
127. C₄₃×#500	C₂²	semidirect
128. C₄₃×#479	C₂²	semidirect
129. C₄₃×#477	C₂²	semidirect
132. C₄₃×#446	C₂²	semidirect
146. SD₁₆×D₄₃	Q₈	semidirect
361. SD₁₆×C₄₃	C₂×Q₈	semidirect
386. #10621884	C₂×Q₈	semidirect
387. #10621883	C₂×Q₈	semidirect
439. #10621873	C₂×Q₈	semidirect
563. #3385	D₄₃	direct (N × H)
578. D₄₃	#3385	direct (N × H)
588. Q₈²	C₂×D₄₃	semidirect
620. #501	C₂×D₄₃	semidirect
626. #500	C₂×D₄₃	semidirect
634. #479	C₂×D₄₃	semidirect
640. #477	C₂×D₄₃	semidirect
660. #446	C₂×D₄₃	semidirect
690. C₄₃	C₂×#3385	semidirect
920. SD₁₆	Q₈×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
Q₈²×D₄₃	2
#554×D₄₃	2
#19147510	2
#19147509	2
#19147508	2
#19147507	2
#19147506	2
#19147505	2
#19147504	2
#19147503	2
#19147502	2
#19147501	2
#19147500	2
#501×D₄₃	2
#500×D₄₃	2
#479×D₄₃	2
#477×D₄₃	2
#476×D₄₃	2
#474×D₄₃	2
#446×D₄₃	2
#440×D₄₃	2
C₄×SD₁₆×D₄₃	2
C₄₃×#3385	2
C₂×#3385	43

Subgroups — D43×#3385 #25977080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₃×#3385 #25977080