Subgroups — #25975596

Order 11008.

1764 conjugacy classes of subgroups.

The subgroup lattice has 1076 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148340	C₂	1	2	yes	maximal
2	#19147123	C₂	1	2	yes	maximal, complemented
3	#19147119	C₂	1	2	yes	maximal, complemented
4	#19147047	C₂	1	2	yes	maximal, complemented
5	#19147043	C₂	1	2	yes	maximal, complemented
6	#19147023	C₂	1	1	yes	maximal, characteristic, complemented
7	#19146987	C₂	1	1	yes	maximal, characteristic, complemented
8	#19146984	C₂	1	1	yes	maximal, characteristic, complemented
9	#19146965	C₂	1	1	yes	maximal, characteristic, complemented
10	#19146964	C₂	1	1	yes	maximal, characteristic, complemented
11	#19146963	C₂	1	1	yes	maximal, characteristic, complemented
12	#19146958	C₂	1	1	yes	maximal, characteristic, complemented
13	#19145128	C₂	1	1	yes	maximal, characteristic, complemented
14	#19144561	C₂	1	2	yes	maximal, complemented
15	#19144542	C₂	1	2	yes	maximal, complemented
16	#19144430	C₂	1	2	yes	maximal, complemented
17	#19144245	C₂	1	1	yes	maximal, characteristic, complemented
18	#467×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
19	#19143458	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143284	C₂	1	1	yes	maximal, characteristic
21	#19143192	C₂	1	1	yes	maximal, characteristic, complemented
22	#427×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3342	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×Q₁₆×D₄₃	C₂²	1	1	yes	characteristic
25	C₂×#13063331	C₂²	1	1	yes	characteristic
26	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
27	#14583617	C₂²	1	2	yes	—
28	#14583610	C₂²	1	2	yes	—
29	#14583607	C₂²	1	2	yes	—
30	#14583590	—	2	2	no	—
31	#14583590	C₂²	1	2	yes	—
32	#14583589	C₂²	1	2	yes	—
33	#14583588	C₂²	1	2	yes	—
34	#14583585	—	2	2	no	—
35	#14583583	C₂²	1	2	yes	—
36	#14583579	—	2	2	no	—
37	#14583574	—	2	2	no	—
38	#14583526	C₂²	1	2	yes	—
39	#14583513	—	2	2	no	—
40	#14583506	—	2	2	no	—
41	#14583472	C₂²	1	2	yes	—
42	#14583453	—	2	2	no	—
43	#14583432	—	2	2	no	—
44	#14583408	C₂²	1	1	yes	characteristic
45	C₂²⋊Q₈×D₄₃	C₂²	1	2	yes	—
46	#14583379	C₂²	1	2	yes	—
47	#14583375	C₂²	1	2	yes	—
48	#117×D₄₃	C₂²	1	2	yes	—
49	#14583307	C₂²	1	2	yes	complemented
50	#14583305	C₂²	1	2	yes	complemented
51	#14583303	C₂²	1	1	yes	characteristic, complemented
52	#14583301	C₂²	1	1	yes	characteristic, complemented
53	#14583300	C₂²	1	1	yes	characteristic, complemented
54	#14583243	C₂²	1	2	yes	complemented
55	#14583241	C₂²	1	2	yes	—
56	#14583240	C₂²	1	2	yes	—
57	#14583240	C₂²	1	2	yes	complemented
58	#14583238	C₂²	1	2	yes	complemented
59	#14583237	C₂²	1	2	yes	—
60	#14583236	C₂²	1	2	yes	—
61	#14583236	C₂²	1	2	yes	complemented
62	#14583233	C₂²	1	2	yes	—
63	#14583232	C₂²	1	2	yes	complemented
64	#14583231	C₂²	1	2	yes	—
65	#14583230	C₂²	1	2	yes	complemented
66	#14583228	C₂²	1	2	yes	—
67	#14583228	C₂²	1	2	yes	complemented
68	#14583209	C₂²	1	2	yes	complemented
69	#14583207	C₂²	1	2	yes	complemented
70	#14583206	C₂²	1	2	yes	complemented
71	#14583204	C₂²	1	2	yes	complemented
72	#14583192	C₂²	1	2	yes	complemented
73	#14583191	C₂²	1	2	yes	complemented
74	#14583183	C₂²	1	2	yes	complemented
75	#14583156	C₂²	1	2	yes	complemented
76	#14583155	C₂²	1	2	yes	complemented
77	#14583141	C₂²	1	1	yes	characteristic
78	#14583141	C₂²	1	1	yes	characteristic, complemented
79	#14583140	C₂²	1	1	yes	characteristic
80	#14583140	C₂²	1	1	yes	characteristic, complemented
81	#14583139	C₂²	1	2	yes	—
82	#14583138	C₂²	1	2	yes	—
83	#14583137	C₂²	1	1	yes	characteristic
84	#14583137	C₂²	1	1	yes	characteristic, complemented
85	#14583004	C₂²	1	2	yes	complemented
86	#14583003	C₂²	1	2	yes	complemented
87	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
88	Q₁₆×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
89	#14582993	C₂²	1	1	yes	characteristic, complemented
90	#14582973	C₂²	1	1	yes	characteristic
91	#14582971	C₂²	1	1	yes	characteristic
92	#14582969	C₂²	1	1	yes	characteristic
93	#14582967	C₂²	1	1	yes	characteristic
94	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
95	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
96	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
97	#14582942	C₂²	1	2	yes	complemented
98	#14582940	C₂²	1	2	yes	—
99	#14582938	C₂²	1	2	yes	—
100	#14582938	C₂²	1	2	yes	complemented
101	#14582937	C₂²	1	1	yes	characteristic
102	#14582936	C₂²	1	1	yes	characteristic
103	#14582936	C₂²	1	1	yes	characteristic
104	#14582936	C₂²	1	1	yes	characteristic, complemented
105	#14582935	C₂²	1	2	yes	—
106	#14582934	C₂²	1	2	yes	—
107	C₂×#13063259	C₂²	1	1	yes	characteristic, complemented
108	#107×D₄₃	C₂²	1	1	yes	characteristic
109	#107×D₄₃	C₂²	1	1	yes	characteristic
110	#107×D₄₃	C₂²	1	1	yes	characteristic
111	#107×D₄₃	C₂²	1	1	yes	characteristic, complemented
112	#106×D₄₃	C₂²	1	2	yes	—
113	#14582924	C₂²	1	1	yes	characteristic
114	#14582906	C₂²	1	2	yes	—
115	#14582906	C₂²	1	2	yes	—
116	#103×D₄₃	C₂²	1	2	yes	—
117	#14582864	C₂²	1	1	yes	characteristic
118	#14582861	C₂²	1	1	yes	characteristic
119	#14582853	C₂²	1	1	yes	characteristic
120	C₄₃×#556	C₂²	1	2	yes	—
121	C₄₃×#500	C₂²	1	1	yes	characteristic, complemented
122	C₄₃×#485	C₂²	1	2	yes	—
123	C₄₃×#485	C₂²	1	2	yes	complemented
124	C₄₃×#475	C₂²	1	2	yes	complemented
125	C₄₃×#467	C₂²	1	1	yes	characteristic
126	C₄₃×#467	C₂²	1	1	yes	characteristic, complemented
127	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
128	C₈×D₄×C₄₃	C₂²	1	1	yes	characteristic
129	C₄₃×#427	C₂²	1	1	yes	characteristic
130	C₄₃×#427	C₂²	1	1	yes	characteristic, complemented
131	C₂×#10621898	C₂³	1	1	yes	characteristic
132	C₂×Q₈×D₄₃	C₂³	1	2	yes	—
133	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
134	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
135	C₂×#10621885	C₂³	1	2	yes	—
136	Q₁₆×D₄₃	—	2	4	no	—
137	#13063331	—	2	4	no	—
138	C₂×#10621877	C₂³	1	1	yes	characteristic
139	C₂×#10621872	C₂³	1	1	yes	characteristic
140	C₂×#10621872	C₂³	1	1	yes	characteristic
141	C₂×#10621872	C₂³	1	1	yes	characteristic
142	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
143	C₂×C₈×D₄₃	—	2	4	no	—
144	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
145	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
146	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
147	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
148	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
149	#13063324	—	2	2	no	—
150	#13063324	C₂³	1	2	yes	—
151	#13063323	—	2	2	no	—
152	#13063319	—	2	2	no	—
153	#13063319	—	2	2	no	—
154	#13063318	—	2	2	no	—
155	#13063318	—	2	2	no	—
156	#13063318	—	2	2	no	—
157	#13063318	—	2	2	no	—
158	#13063317	—	2	2	no	—
159	#13063317	C₂³	1	2	yes	—
160	#13063316	—	2	2	no	—
161	#13063316	C₂³	1	2	yes	—
162	#13063315	—	2	2	no	—
163	#13063315	—	2	2	no	—
164	#13063315	—	2	2	no	—
165	#13063315	—	2	2	no	—
166	#13063315	—	2	2	no	—
167	#13063311	—	2	2	no	—
168	#13063311	—	2	2	no	—
169	#13063310	—	2	2	no	—
170	#13063310	—	2	2	no	—
171	#13063310	D₄	1	1	yes	characteristic
172	#13063307	—	2	2	no	—
173	#13063307	—	2	2	no	—
174	#13063307	—	2	2	no	—
175	#13063307	D₄	1	1	yes	characteristic
176	#13063306	—	2	2	no	—
177	#13063305	—	2	2	no	—
178	#13063305	C₂³	1	2	yes	—
179	#13063305	C₂³	1	2	yes	—
180	#13063304	C₂³	1	2	yes	—
181	#13063304	C₂³	1	2	yes	—
182	#13063303	—	2	2	no	—
183	#13063303	—	2	2	no	—
184	#13063303	D₄	1	1	yes	characteristic
185	#13063302	—	2	2	no	—
186	#13063302	—	2	2	no	—
187	#13063302	D₄	1	1	yes	characteristic
188	#13063301	—	2	2	no	—
189	#13063301	—	2	2	no	—
190	#13063301	—	2	2	no	—
191	#13063301	C₂³	1	2	yes	—
192	#13063301	C₂³	1	2	yes	—
193	#13063298	D₄	1	1	yes	characteristic
194	#13063297	D₄	1	1	yes	characteristic
195	#13063295	D₄	1	1	yes	characteristic
196	#13063293	D₄	1	1	yes	characteristic
197	Q₈×Dic₄₃	C₂³	1	2	yes	—
198	C₄×Dic₈₆	—	2	2	no	—
199	C₄×Dic₈₆	—	2	2	no	—
200	C₄×Dic₈₆	—	2	2	no	—
201	C₄×Dic₈₆	C₂³	1	2	yes	—
202	#13063290	—	2	2	no	—
203	#13063290	C₂³	1	2	yes	—
204	C₄×D₁₇₂	—	2	2	no	—
205	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
206	#13063287	—	2	2	no	—
207	C₄×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
208	C₄×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
209	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
210	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
211	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
212	#13063284	C₂³	1	2	yes	—
213	#13063283	—	2	2	no	—
214	#13063283	—	2	2	no	—
215	#13063283	C₂³	1	2	yes	—
216	#13063283	C₂³	1	2	yes	—
217	#13063283	C₂³	1	2	yes	—
218	#13063282	—	2	2	no	—
219	#13063282	—	2	2	no	—
220	#13063282	—	2	2	no	—
221	#13063282	—	2	2	no	—
222	#13063282	C₂³	1	1	yes	characteristic
223	#13063281	—	2	2	no	—
224	#13063281	—	2	2	no	—
225	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
226	C₄⋊C₄×D₄₃	—	2	2	no	—
227	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
228	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
229	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
230	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
231	C₂²⋊C₄×D₄₃	—	2	2	no	—
232	C₂²⋊C₄×D₄₃	—	2	2	no	—
233	C₄²×D₄₃	—	2	2	no	—
234	#13063259	C₂³	1	1	yes	characteristic
235	#13063259	C₂³	1	1	yes	characteristic
236	#13063259	C₂³	1	1	yes	characteristic
237	#13063259	C₂³	1	2	yes	—
238	#13063258	C₂³	1	2	yes	—
239	#13063258	C₂³	1	2	yes	—
240	#13063258	C₂³	1	2	yes	—
241	#13063258	C₂³	1	2	yes	—
242	#13063258	C₂³	1	2	yes	—
243	#13063257	C₂³	1	2	yes	—
244	#13063257	C₂³	1	2	yes	—
245	#13063256	C₂³	1	2	yes	—
246	#13063256	C₂³	1	2	yes	—
247	#13063256	C₂³	1	2	yes	—
248	#13063256	C₂³	1	2	yes	—
249	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
250	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
251	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
252	#13063250	C₂³	1	2	yes	—
253	#13063250	C₂³	1	2	yes	—
254	#13063250	C₂³	1	2	yes	—
255	#13063249	C₂³	1	2	yes	—
256	#13063249	C₂³	1	2	yes	—
257	#13063249	C₂³	1	2	yes	—
258	#13063248	C₂³	1	2	yes	—
259	#13063248	C₂³	1	2	yes	—
260	#13063248	C₂³	1	2	yes	—
261	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
262	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
263	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
264	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
265	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
266	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
267	#13063236	C₂³	1	1	yes	characteristic
268	#13063235	C₂³	1	1	yes	characteristic
269	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
270	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
271	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
272	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
273	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
274	#126×C₄₃	—	2	2	no	—
275	#126×C₄₃	—	2	2	no	—
276	#124×C₄₃	—	2	2	no	—
277	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
278	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
279	C₄×Q₈×C₄₃	—	2	2	no	—
280	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
281	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
282	#117×C₄₃	C₂³	1	2	yes	—
283	#117×C₄₃	C₂³	1	2	yes	—
284	#107×C₄₃	C₂³	1	1	yes	characteristic
285	#107×C₄₃	C₂³	1	1	yes	characteristic
286	#107×C₄₃	C₂³	1	2	yes	—
287	#107×C₄₃	C₂³	1	1	yes	characteristic
288	#106×C₄₃	C₂³	1	2	yes	—
289	#106×C₄₃	C₂³	1	2	yes	—
290	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
291	#103×C₄₃	C₂³	1	2	yes	—
292	#103×C₄₃	C₂³	1	2	yes	—
293	#103×C₄₃	C₂³	1	2	yes	—
294	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
295	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
297	C₂³×D₄₃	C₂×D₄	1	1	yes	characteristic
298	C₂×Q₈×C₄₃	—	2	2	no	—
299	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
300	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
301	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
302	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
303	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
304	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
305	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
306	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
307	C₂²×Dic₄₃	—	2	2	no	—
308	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
309	Q₈×D₄₃	—	2	4	no	—
310	Q₈×D₄₃	—	2	4	no	—
311	#10621898	—	2	2	no	—
312	#10621898	—	2	2	no	—
313	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
314	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
315	C₂×C₄×D₄₃	—	2	2	no	—
316	C₂×C₄×D₄₃	—	2	2	no	—
317	C₂×C₄×D₄₃	—	2	2	no	—
318	C₂×C₄×D₄₃	—	2	2	no	—
319	C₂×C₄×D₄₃	—	2	2	no	—
320	C₂×C₄×D₄₃	—	2	2	no	—
321	C₂×C₄×D₄₃	—	2	2	no	—
322	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
323	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
324	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
325	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
326	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
327	C₂×Dic₈₆	—	2	2	no	—
328	C₂×Dic₈₆	—	2	2	no	—
329	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
330	C₂×Dic₈₆	C₂⁴	1	2	yes	—
331	Q₁₆×C₄₃	—	2	2	no	—
332	C₂×C₈×C₄₃	—	2	2	no	—
333	C₂×C₈×C₄₃	—	2	2	no	—
334	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
335	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
336	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
337	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
338	C₄⋊C₄×C₄₃	—	2	2	no	—
339	C₄⋊C₄×C₄₃	—	2	2	no	—
340	C₄⋊C₄×C₄₃	—	2	2	no	—
341	C₄⋊C₄×C₄₃	—	2	2	no	—
342	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
343	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
345	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
346	C₂²⋊C₄×C₄₃	—	2	2	no	—
347	C₂²⋊C₄×C₄₃	—	2	2	no	—
348	C₂²⋊C₄×C₄₃	—	2	2	no	—
349	C₂²⋊C₄×C₄₃	—	2	2	no	—
350	C₂²⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
351	C₂²⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
352	C₄²×C₄₃	—	2	2	no	—
353	C₄²×C₄₃	—	2	2	no	—
354	C₄²×C₄₃	—	2	2	no	—
355	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
356	C₂²⋊Dic₄₃	—	2	2	no	—
357	C₂²⋊Dic₄₃	—	2	2	no	—
358	C₂²⋊Dic₄₃	—	2	2	no	—
359	C₂²⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
360	C₂²⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
361	#10621885	—	2	4	no	—
362	(C₂×D₄₃)⋊C₄	—	2	2	no	—
363	(C₂×D₄₃)⋊C₄	—	2	2	no	—
364	(C₂×D₄₃)⋊C₄	—	2	2	no	—
365	(C₂×D₄₃)⋊C₄	—	2	2	no	—
366	(C₂×D₄₃)⋊C₄	—	2	2	no	—
367	(C₂×D₄₃)⋊C₄	—	2	2	no	—
368	(C₂×D₄₃)⋊C₄	—	2	2	no	—
369	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
370	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
371	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
372	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
373	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
374	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
375	C₄⋊Dic₄₃	—	2	2	no	—
376	C₄⋊Dic₄₃	—	2	2	no	—
377	C₄⋊Dic₄₃	—	2	2	no	—
378	C₄⋊Dic₄₃	—	2	2	no	—
379	C₄⋊Dic₄₃	—	2	2	no	—
380	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
381	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
382	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
383	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
384	Dic₄₃⋊C₄	—	2	2	no	—
385	Dic₄₃⋊C₄	—	2	2	no	—
386	Dic₄₃⋊C₄	—	2	2	no	—
387	Dic₄₃⋊C₄	—	2	2	no	—
388	Dic₄₃⋊C₄	—	2	2	no	—
389	Dic₄₃⋊C₄	—	2	2	no	—
390	Dic₄₃⋊C₄	—	2	2	no	—
391	Dic₄₃⋊C₄	—	2	2	no	—
392	Dic₄₃⋊C₄	—	2	2	no	—
393	Dic₄₃⋊C₄	—	2	2	no	—
394	Dic₄₃⋊C₄	—	2	2	no	—
395	Dic₄₃⋊C₄	—	2	2	no	—
396	Dic₄₃⋊C₄	—	2	2	no	—
397	Dic₄₃⋊C₄	—	2	2	no	—
398	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
399	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
400	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
401	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
402	C₄×Dic₄₃	—	2	2	no	—
403	C₄×Dic₄₃	—	2	2	no	—
404	C₄×Dic₄₃	—	2	2	no	—
405	C₄×Dic₄₃	—	2	2	no	—
406	C₄×Dic₄₃	—	2	2	no	—
407	C₄×Dic₄₃	—	2	2	no	—
408	C₄×Dic₄₃	—	2	2	no	—
409	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
410	#10621877	—	2	2	no	—
411	C₂×C₄₃⋊C₈	—	2	2	no	—
412	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
413	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
414	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
415	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
416	Dic₁₇₂	—	2	2	no	—
417	#10621872	—	2	2	no	—
418	#10621872	—	2	2	no	—
419	#10621872	—	2	2	no	—
420	C₈×D₄₃	—	2	2	no	—
421	C₈×D₄₃	—	2	2	no	—
422	C₈×D₄₃	—	2	2	no	—
423	C₈×D₄₃	—	2	2	no	—
424	C₈×D₄₃	#41	1	4	yes	—
425	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
426	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
427	C₂²×D₄₃	—	2	2	no	—
428	C₂²×D₄₃	—	2	2	no	—
429	C₂²×D₄₃	—	4	1	no	—
430	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
431	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
432	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
433	Q₈×C₄₃	—	2	2	no	—
434	Q₈×C₄₃	—	2	2	no	—
435	Q₈×C₄₃	—	8	2	no	—
436	D₄×C₄₃	—	4	1	no	—
437	C₂×C₄×C₄₃	—	2	1	no	—
438	C₂×C₄×C₄₃	—	2	1	no	—
439	C₂×C₄×C₄₃	—	2	1	no	—
440	C₂×C₄×C₄₃	—	2	1	no	—
441	C₂×C₄×C₄₃	—	2	2	no	—
442	C₂×C₄×C₄₃	—	2	2	no	—
443	C₂×C₄×C₄₃	—	2	2	no	—
444	C₂×C₄×C₄₃	—	2	2	no	—
445	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
446	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
447	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
448	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
449	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
450	C₂²⋊D₄₃	—	2	2	no	—
451	C₂²⋊D₄₃	—	2	2	no	—
452	C₂²⋊D₄₃	—	2	2	no	—
453	C₂²⋊D₄₃	—	4	1	no	—
454	C₂×Dic₄₃	—	2	2	no	—
455	C₂×Dic₄₃	—	2	2	no	—
456	C₂×Dic₄₃	—	2	2	no	—
457	C₂×Dic₄₃	—	2	2	no	—
458	C₂×Dic₄₃	—	2	2	no	—
459	C₂×Dic₄₃	—	8	2	no	—
460	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
461	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
462	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
463	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
465	D₁₇₂	—	2	2	no	—
466	D₁₇₂	—	2	2	no	—
467	C₄×D₄₃	—	2	2	no	—
468	C₄×D₄₃	—	2	1	no	—
469	C₄×D₄₃	—	2	1	no	—
470	C₄×D₄₃	—	2	1	no	—
471	C₄×D₄₃	—	2	1	no	—
472	C₄×D₄₃	—	2	2	no	—
473	C₄×D₄₃	—	4	4	no	—
474	C₄×D₄₃	—	4	4	no	—
475	C₄×D₄₃	—	8	2	no	—
476	C₄×D₄₃	—	8	2	no	—
477	C₄×D₄₃	—	8	2	no	—
478	C₄×D₄₃	C₂×#41	1	2	yes	—
479	C₄×D₄₃	2₋¹⁺⁴	1	2	yes	—
480	Dic₈₆	—	2	2	no	—
481	Dic₈₆	—	2	2	no	—
482	Dic₈₆	—	2	2	no	—
483	Dic₈₆	—	4	4	no	—
484	Dic₈₆	—	8	2	no	—
485	C₈×C₄₃	—	2	1	no	—
486	C₈×C₄₃	—	2	1	no	—
487	C₈×C₄₃	—	2	1	no	—
488	C₈×C₄₃	C₂×#41	1	2	yes	—
489	C₄₃⋊C₈	—	2	1	no	—
490	C₄₃⋊C₈	—	2	1	no	—
491	C₄₃⋊C₈	—	2	1	no	—
492	C₄₃⋊C₈	C₂×#41	1	2	yes	—
493	#61264	—	43	1	no	maximal, Sylow
494	C₂²×C₄₃	—	2	1	no	—
495	C₂²×C₄₃	—	2	1	no	—
496	C₂²×C₄₃	—	2	1	no	—
497	C₂²×C₄₃	—	2	1	no	—
498	C₂²×C₄₃	—	2	1	no	—
499	C₂²×C₄₃	—	2	1	no	—
500	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
501	C₂×D₄₃	—	2	1	no	—
502	C₂×D₄₃	—	2	1	no	—
503	C₂×D₄₃	—	2	1	no	—
504	C₂×D₄₃	—	2	1	no	—
505	C₂×D₄₃	—	2	1	no	—
506	C₂×D₄₃	—	2	1	no	—
507	C₂×D₄₃	—	2	1	no	—
508	C₂×D₄₃	—	4	4	no	—
509	C₂×D₄₃	#547	1	2	yes	—
510	C₂×D₄₃	#578	1	2	yes	—
511	C₄×C₄₃	—	2	1	no	—
512	C₄×C₄₃	—	2	1	no	—
513	C₄×C₄₃	—	2	1	no	—
514	C₄×C₄₃	—	2	1	no	—
515	C₄×C₄₃	—	4	2	no	—
516	C₄×C₄₃	—	4	2	no	—
517	C₄×C₄₃	—	4	2	no	—
518	C₄×C₄₃	—	4	2	no	—
519	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
520	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
521	Dic₄₃	—	2	1	no	—
522	Dic₄₃	—	2	1	no	—
523	Dic₄₃	—	2	1	no	—
524	Dic₄₃	—	2	1	no	—
525	Dic₄₃	—	4	2	no	—
526	Dic₄₃	—	4	2	no	—
527	Dic₄₃	—	4	2	no	—
528	Dic₄₃	—	4	2	no	—
529	Dic₄₃	#547	1	2	yes	—
530	#3495	—	43	2	no	—
531	#3349	—	43	2	no	—
532	#3349	—	43	2	no	—
533	#3344	—	43	2	no	—
534	#3344	—	43	2	no	—
535	#3342	—	43	1	no	—
536	#3342	D₄₃	1	1	yes	characteristic, complemented
537	#3338	—	43	1	no	—
538	#3338	—	43	1	no	—
539	#3336	—	43	1	no	—
540	#3336	—	43	1	no	—
541	#3336	—	43	1	no	—
542	#3336	—	43	1	no	—
543	#3164	—	43	1	no	—
544	#3097	—	43	2	no	—
545	#3095	—	43	2	no	—
546	#3082	—	43	2	no	—
547	#3059	—	43	1	no	—
548	C₂×#467	—	43	1	no	—
549	#2950	—	43	1	no	—
550	#2929	—	43	1	no	—
551	#2913	—	43	1	no	—
552	C₂×#427	—	43	1	no	—
553	C₂×C₄₃	—	4	1	no	—
554	C₂×C₄₃	—	4	1	no	—
555	C₂×C₄₃	C₂×#547	1	1	yes	characteristic
556	C₂×C₄₃	C₂×#578	1	1	yes	characteristic
557	C₂×C₄₃	#3584	1	1	yes	characteristic
558	D₄₃	—	2	2	no	—
559	D₄₃	—	2	2	no	—
560	D₄₃	—	4	1	no	—
561	C₂²×Q₁₆	—	43	1	no	—
562	C₂×#131	—	43	1	no	—
563	C₂³×C₈	—	43	1	no	—
564	#556	—	43	2	no	—
565	#556	C₂×D₄₃	1	2	yes	—
566	#554	—	43	2	no	—
567	#554	—	43	2	no	—
568	#552	—	43	2	no	—
569	#552	—	43	2	no	—
570	#552	—	43	2	no	—
571	#552	—	43	2	no	—
572	#552	—	86	2	no	—
573	#552	—	86	2	no	—
574	#551	—	86	2	no	—
575	#551	—	86	2	no	—
576	#544	—	43	2	no	—
577	#542	—	86	2	no	—
578	#541	—	86	2	no	—
579	#536	—	43	2	no	—
580	#533	—	86	2	no	—
581	#529	—	86	2	no	—
582	#525	—	43	1	no	—
583	C₂×C₂²⋊Q₈	—	43	2	no	—
584	#520	—	43	2	no	—
585	#519	—	43	2	no	—
586	C₂×#117	—	43	2	no	—
587	#501	—	43	2	no	—
588	#501	—	43	2	no	—
589	#500	—	43	1	no	—
590	#500	C₂×D₄₃	1	1	yes	characteristic, complemented
591	#499	—	43	1	no	—
592	#499	—	43	1	no	—
593	#485	—	43	2	no	—
594	#485	—	43	2	no	—
595	#485	—	43	2	no	—
596	#485	—	43	2	no	—
597	#485	—	43	2	no	—
598	#485	—	43	2	no	—
599	#485	C₂×D₄₃	1	2	yes	—
600	#485	C₂×D₄₃	1	2	yes	complemented
601	#484	—	43	2	no	—
602	#484	—	43	2	no	—
603	#484	—	43	2	no	—
604	#484	—	43	2	no	—
605	#483	—	43	2	no	—
606	#483	—	43	2	no	—
607	#483	—	43	2	no	—
608	#483	—	43	2	no	—
609	#479	—	43	2	no	—
610	#479	—	43	2	no	—
611	#479	—	43	2	no	—
612	#479	—	43	2	no	—
613	#477	—	43	2	no	—
614	#477	—	43	2	no	—
615	#475	—	43	2	no	—
616	#475	C₂×D₄₃	1	2	yes	complemented
617	#470	—	43	2	no	—
618	#470	—	43	2	no	—
619	#467	—	43	1	no	—
620	#467	—	43	1	no	—
621	#467	—	43	1	no	—
622	#467	—	43	1	no	—
623	#467	—	43	2	no	—
624	#467	—	43	1	no	—
625	#467	—	43	1	no	—
626	#467	—	43	2	no	—
627	#467	C₂×D₄₃	1	1	yes	characteristic
628	#467	C₂×D₄₃	1	1	yes	characteristic, complemented
629	#441	—	43	2	no	—
630	#441	—	43	2	no	—
631	C₄×Q₁₆	—	43	1	no	—
632	C₄×Q₁₆	—	43	1	no	—
633	C₄×Q₁₆	—	43	1	no	—
634	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
635	#435	—	43	1	no	—
636	#435	—	43	1	no	—
637	#435	—	43	1	no	—
638	#435	—	43	1	no	—
639	C₈×D₄	—	43	1	no	—
640	C₈×D₄	—	43	1	no	—
641	C₈×D₄	—	43	1	no	—
642	C₈×D₄	C₂×D₄₃	1	1	yes	characteristic
643	#428	—	43	2	no	—
644	#428	—	43	2	no	—
645	#428	—	43	2	no	—
646	#428	—	43	2	no	—
647	#427	—	43	1	no	—
648	#427	—	43	2	no	—
649	#427	—	43	1	no	—
650	#427	—	43	1	no	—
651	#427	—	43	1	no	—
652	#427	—	43	2	no	—
653	#427	C₂×D₄₃	1	1	yes	characteristic
654	#427	C₂×D₄₃	1	1	yes	characteristic, complemented
655	C₂×#107	—	43	1	no	—
656	C₂×#107	—	43	1	no	—
657	C₂×#107	—	43	1	no	—
658	C₂×#107	—	43	1	no	—
659	C₂×#107	—	43	1	no	—
660	C₂×#106	—	43	2	no	—
661	#424	—	43	1	no	—
662	#419	—	43	2	no	—
663	#419	—	43	2	no	—
664	C₂×#103	—	43	2	no	—
665	#408	—	43	1	no	—
666	#407	—	43	1	no	—
667	#405	—	43	1	no	—
668	C₄₃	#61264	1	1	yes	characteristic, complemented, Sylow
669	C₂×#41	—	43	1	no	—
670	C₂²×Q₈	—	43	2	no	—
671	C₂³×C₄	—	43	1	no	—
672	C₂×Q₁₆	—	43	2	no	—
673	C₂×Q₁₆	—	43	1	no	—
674	C₂×Q₁₆	—	86	4	no	—
675	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
676	#131	—	86	4	no	—
677	C₂×M₁₆	—	43	1	no	—
678	C₂×M₁₆	—	43	1	no	—
679	C₂×M₁₆	—	43	1	no	—
680	C₂×M₁₆	—	43	1	no	—
681	C₂²×C₈	—	43	1	no	—
682	C₂²×C₈	—	43	1	no	—
683	C₂²×C₈	—	43	1	no	—
684	C₂²×C₈	—	43	1	no	—
685	C₂²×C₈	—	43	1	no	—
686	C₂²×C₈	—	43	1	no	—
687	C₂²×C₈	—	86	4	no	—
688	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
689	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
690	C₄⋊Q₈	—	43	2	no	—
691	C₄⋊Q₈	—	86	2	no	—
692	C₄⋊Q₈	—	86	2	no	—
693	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
694	#126	—	2	2	no	—
695	#126	—	2	2	no	—
696	#126	—	86	2	no	—
697	#126	—	86	2	no	—
698	#126	—	86	2	no	—
699	#126	—	86	2	no	—
700	#126	—	86	2	no	—
701	#126	—	86	2	no	—
702	#125	—	43	2	no	—
703	#125	—	43	2	no	—
704	#125	—	86	2	no	—
705	#125	—	86	2	no	—
706	#125	—	86	2	no	—
707	#125	—	86	2	no	—
708	#125	—	86	2	no	—
709	#125	—	86	2	no	—
710	#125	—	86	2	no	—
711	#124	—	2	2	no	—
712	#124	—	86	2	no	—
713	#124	—	86	2	no	—
714	#123	—	43	1	no	—
715	#123	—	43	1	no	—
716	#123	—	86	2	no	—
717	#123	—	86	2	no	—
718	#123	—	86	2	no	—
719	#123	—	86	2	no	—
720	#123	—	86	2	no	—
721	#123	—	86	2	no	—
722	C₂²⋊Q₈	—	43	1	no	—
723	C₂²⋊Q₈	—	43	1	no	—
724	C₂²⋊Q₈	—	43	2	no	—
725	C₂²⋊Q₈	—	43	2	no	—
726	C₂²⋊Q₈	—	43	2	no	—
727	C₂²⋊Q₈	—	43	2	no	—
728	C₂²⋊Q₈	—	43	2	no	—
729	C₂²⋊Q₈	—	43	2	no	—
730	C₂²⋊Q₈	—	86	2	no	—
731	C₂²⋊Q₈	—	86	2	no	—
732	C₂²⋊Q₈	—	86	2	no	—
733	C₂²⋊Q₈	—	86	2	no	—
734	C₂²⋊Q₈	—	86	2	no	—
735	C₂²⋊Q₈	—	86	2	no	—
736	C₂²⋊Q₈	—	86	2	no	—
737	C₂²⋊Q₈	—	86	2	no	—
738	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
739	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
740	#121	—	43	1	no	—
741	#121	—	43	1	no	—
742	#120	—	43	1	no	—
743	#120	—	43	1	no	—
744	C₄×Q₈	—	2	2	no	—
745	C₄×Q₈	—	43	2	no	—
746	C₄×Q₈	—	43	2	no	—
747	C₄×Q₈	—	43	2	no	—
748	C₄×Q₈	—	86	2	no	—
749	C₄×Q₈	—	86	2	no	—
750	C₄×Q₈	—	86	2	no	—
751	C₄×Q₈	—	86	2	no	—
752	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
753	C₄×D₄	—	43	1	no	—
754	C₄×D₄	—	43	1	no	—
755	C₄×D₄	—	43	1	no	—
756	C₄×D₄	—	86	2	no	—
757	C₄×D₄	—	86	2	no	—
758	C₄×D₄	—	86	2	no	—
759	C₄×D₄	—	86	2	no	—
760	C₄×D₄	—	86	2	no	—
761	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
762	#117	—	43	1	no	—
763	#117	—	43	2	no	—
764	#117	—	43	2	no	—
765	#117	—	43	2	no	—
766	#117	—	43	2	no	—
767	#117	—	86	2	no	—
768	#117	—	86	2	no	—
769	#117	—	86	2	no	—
770	#117	—	86	2	no	—
771	#117	—	86	2	no	—
772	#117	—	86	2	no	—
773	#117	—	86	2	no	—
774	#117	—	86	2	no	—
775	#117	C₂²×D₄₃	1	2	yes	—
776	#117	C₂²×D₄₃	1	2	yes	—
777	C₂×C₄⋊C₄	—	43	2	no	—
778	C₂×C₄⋊C₄	—	43	2	no	—
779	C₂×C₄⋊C₄	—	43	2	no	—
780	C₂×C₄⋊C₄	—	43	2	no	—
781	C₂×C₄⋊C₄	—	43	2	no	—
782	C₂×C₄⋊C₄	—	86	2	no	—
783	C₂×C₂²⋊C₄	—	86	2	no	—
784	C₂×C₂²⋊C₄	—	86	2	no	—
785	C₂×C₄²	—	86	2	no	—
786	#107	—	43	1	no	—
787	#107	—	43	1	no	—
788	#107	—	43	1	no	—
789	#107	—	43	2	no	—
790	#107	—	43	2	no	—
791	#107	—	43	2	no	—
792	#107	—	43	2	no	—
793	#107	—	43	2	no	—
794	#107	—	43	2	no	—
795	#107	C₂²×D₄₃	1	1	yes	characteristic
796	#107	C₂²×D₄₃	1	1	yes	characteristic
797	#107	C₂²×D₄₃	1	1	yes	characteristic
798	#107	C₂²×D₄₃	1	2	yes	—
799	#106	—	43	2	no	—
800	#106	—	43	2	no	—
801	#106	—	43	2	no	—
802	#106	—	43	2	no	—
803	#106	—	43	2	no	—
804	#106	—	43	2	no	—
805	#106	C₂²×D₄₃	1	2	yes	—
806	#106	C₂²×D₄₃	1	2	yes	—
807	C₄⋊C₈	—	43	1	no	—
808	C₄⋊C₈	—	43	1	no	—
809	C₄⋊C₈	—	43	1	no	—
810	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
811	#103	—	43	2	no	—
812	#103	—	43	2	no	—
813	#103	—	43	2	no	—
814	#103	—	43	2	no	—
815	#103	—	43	2	no	—
816	#103	—	43	2	no	—
817	#103	—	43	2	no	—
818	#103	—	43	2	no	—
819	#103	—	43	2	no	—
820	#103	C₂²×D₄₃	1	2	yes	—
821	#103	C₂²×D₄₃	1	2	yes	—
822	#103	C₂²×D₄₃	1	2	yes	—
823	C₂²⋊C₈	—	43	1	no	—
824	C₂²⋊C₈	—	43	1	no	—
825	C₂²⋊C₈	—	43	1	no	—
826	C₂²⋊C₈	—	43	1	no	—
827	C₂²⋊C₈	—	43	1	no	—
828	C₂²⋊C₈	—	43	1	no	—
829	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
830	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
831	#97	—	43	1	no	—
832	#97	—	43	1	no	—
833	C₄×C₈	—	43	1	no	—
834	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
835	C₂⁴	—	43	1	no	—
836	#41	—	86	2	no	—
837	#41	—	86	2	no	—
838	C₂×Q₈	—	2	2	no	—
839	C₂×Q₈	—	43	1	no	—
840	C₂×Q₈	—	43	2	no	—
841	C₂×Q₈	—	86	2	no	—
842	C₂×Q₈	—	86	2	no	—
843	C₂×Q₈	—	86	4	no	—
844	C₂×Q₈	—	86	4	no	—
845	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
846	C₂×D₄	—	43	1	no	—
847	C₂×D₄	—	43	1	no	—
848	C₂×D₄	—	43	1	no	—
849	C₂×D₄	—	43	1	no	—
850	C₂×D₄	—	43	1	no	—
851	C₂×D₄	—	43	1	no	—
852	C₂×D₄	D₄×D₄₃	1	1	yes	characteristic
853	C₂²×C₄	—	43	1	no	—
854	C₂²×C₄	—	43	1	no	—
855	C₂²×C₄	—	43	1	no	—
856	C₂²×C₄	—	43	1	no	—
857	C₂²×C₄	—	43	1	no	—
858	C₂²×C₄	—	43	1	no	—
859	C₂²×C₄	—	86	2	no	—
860	C₂²×C₄	—	86	2	no	—
861	C₂²×C₄	—	86	2	no	—
862	C₂²×C₄	—	86	2	no	—
863	C₂²×C₄	—	86	2	no	—
864	C₂²×C₄	—	86	2	no	—
865	C₂²×C₄	—	86	2	no	—
866	C₂²×C₄	—	86	2	no	—
867	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
868	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
869	Q₁₆	—	2	2	no	—
870	Q₁₆	—	86	4	no	—
871	Q₁₆	—	86	2	no	—
872	M₁₆	—	86	2	no	—
873	M₁₆	—	86	2	no	—
874	M₁₆	—	86	2	no	—
875	M₁₆	—	86	2	no	—
876	C₂×C₈	—	2	2	no	—
877	C₂×C₈	—	2	2	no	—
878	C₂×C₈	—	43	1	no	—
879	C₂×C₈	—	43	4	no	—
880	C₂×C₈	—	43	1	no	—
881	C₂×C₈	—	43	1	no	—
882	C₂×C₈	—	43	1	no	—
883	C₂×C₈	—	86	2	no	—
884	C₂×C₈	—	86	2	no	—
885	C₂×C₈	—	86	2	no	—
886	C₂×C₈	—	86	2	no	—
887	C₂×C₈	—	86	2	no	—
888	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
889	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
890	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
891	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
892	C₄⋊C₄	—	2	2	no	—
893	C₄⋊C₄	—	2	2	no	—
894	C₄⋊C₄	—	2	2	no	—
895	C₄⋊C₄	—	2	2	no	—
896	C₄⋊C₄	—	43	1	no	—
897	C₄⋊C₄	—	43	1	no	—
898	C₄⋊C₄	—	43	1	no	—
899	C₄⋊C₄	—	43	1	no	—
900	C₄⋊C₄	—	43	1	no	—
901	C₄⋊C₄	—	43	2	no	—
902	C₄⋊C₄	—	43	2	no	—
903	C₄⋊C₄	—	43	2	no	—
904	C₄⋊C₄	—	86	2	no	—
905	C₄⋊C₄	—	86	2	no	—
906	C₄⋊C₄	—	86	2	no	—
907	C₄⋊C₄	—	86	2	no	—
908	C₄⋊C₄	—	86	2	no	—
909	C₄⋊C₄	—	86	2	no	—
910	C₄⋊C₄	—	86	2	no	—
911	C₄⋊C₄	—	86	2	no	—
912	C₄⋊C₄	—	86	2	no	—
913	C₄⋊C₄	—	86	2	no	—
914	C₄⋊C₄	—	86	2	no	—
915	C₄⋊C₄	—	86	2	no	—
916	C₄⋊C₄	—	86	2	no	—
917	C₄⋊C₄	—	86	2	no	—
918	C₄⋊C₄	—	86	2	no	—
919	C₄⋊C₄	—	86	2	no	—
920	C₄⋊C₄	—	86	2	no	—
921	C₄⋊C₄	—	86	2	no	—
922	C₄⋊C₄	—	86	2	no	—
923	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
924	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
925	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
926	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
927	C₂²⋊C₄	—	2	2	no	—
928	C₂²⋊C₄	—	2	2	no	—
929	C₂²⋊C₄	—	2	2	no	—
930	C₂²⋊C₄	—	2	2	no	—
931	C₂²⋊C₄	—	43	1	no	—
932	C₂²⋊C₄	—	43	1	no	—
933	C₂²⋊C₄	—	43	1	no	—
934	C₂²⋊C₄	—	43	1	no	—
935	C₂²⋊C₄	—	43	1	no	—
936	C₂²⋊C₄	—	43	1	no	—
937	C₂²⋊C₄	—	43	1	no	—
938	C₂²⋊C₄	—	43	1	no	—
939	C₂²⋊C₄	—	86	2	no	—
940	C₂²⋊C₄	—	86	2	no	—
941	C₂²⋊C₄	—	86	2	no	—
942	C₂²⋊C₄	—	86	2	no	—
943	C₂²⋊C₄	—	86	2	no	—
944	C₂²⋊C₄	—	86	2	no	—
945	C₂²⋊C₄	—	86	2	no	—
946	C₂²⋊C₄	—	86	2	no	—
947	C₂²⋊C₄	—	86	2	no	—
948	C₂²⋊C₄	—	86	2	no	—
949	C₂²⋊C₄	D₄×D₄₃	1	1	yes	characteristic
950	C₂²⋊C₄	D₄×D₄₃	1	1	yes	characteristic
951	C₄²	—	2	2	no	—
952	C₄²	—	2	2	no	—
953	C₄²	—	2	2	no	—
954	C₄²	—	43	1	no	—
955	C₄²	—	86	2	no	—
956	C₄²	—	86	2	no	—
957	C₄²	—	86	2	no	—
958	C₄²	—	86	2	no	—
959	C₄²	—	86	2	no	—
960	C₄²	—	86	2	no	—
961	C₄²	—	86	2	no	—
962	C₄²	C₂³×D₄₃	1	1	yes	characteristic
963	C₂³	—	43	1	no	—
964	C₂³	—	43	1	no	—
965	C₂³	—	43	1	no	—
966	C₂³	—	86	2	no	—
967	C₂³	—	86	2	no	—
968	C₂³	—	172	1	no	—
969	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
970	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
971	Q₈	—	2	2	no	—
972	Q₈	—	2	2	no	—
973	Q₈	—	8	2	no	—
974	Q₈	—	86	2	no	—
975	Q₈	—	86	2	no	—
976	Q₈	—	86	2	no	—
977	Q₈	—	344	2	no	—
978	Q₈	—	172	4	no	—
979	D₄	—	4	1	no	—
980	D₄	—	86	2	no	—
981	D₄	—	86	2	no	—
982	D₄	—	86	2	no	—
983	D₄	—	86	2	no	—
984	D₄	—	86	2	no	—
985	D₄	—	172	1	no	—
986	C₂×C₄	—	2	1	no	—
987	C₂×C₄	—	2	1	no	—
988	C₂×C₄	—	2	1	no	—
989	C₂×C₄	—	2	1	no	—
990	C₂×C₄	—	2	2	no	—
991	C₂×C₄	—	2	2	no	—
992	C₂×C₄	—	2	2	no	—
993	C₂×C₄	—	2	2	no	—
994	C₂×C₄	—	43	1	no	—
995	C₂×C₄	—	43	2	no	—
996	C₂×C₄	—	43	2	no	—
997	C₂×C₄	—	43	1	no	—
998	C₂×C₄	—	43	1	no	—
999	C₂×C₄	—	43	1	no	—
1000	C₂×C₄	—	43	1	no	—
1001	C₂×C₄	—	86	2	no	—
1002	C₂×C₄	—	86	2	no	—
1003	C₂×C₄	—	86	2	no	—
1004	C₂×C₄	—	86	1	no	—
1005	C₂×C₄	—	86	1	no	—
1006	C₂×C₄	—	86	1	no	—
1007	C₂×C₄	—	86	1	no	—
1008	C₂×C₄	—	86	2	no	—
1009	C₂×C₄	—	86	2	no	—
1010	C₂×C₄	—	86	2	no	—
1011	C₂×C₄	—	86	2	no	—
1012	C₂×C₄	—	344	2	no	—
1013	C₂×C₄	—	344	2	no	—
1014	C₂×C₄	—	344	2	no	—
1015	C₂×C₄	—	344	2	no	—
1016	C₂×C₄	—	172	4	no	—
1017	C₂×C₄	—	172	4	no	—
1018	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1019	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1020	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1021	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1022	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1023	C₈	—	2	1	no	—
1024	C₈	—	2	1	no	—
1025	C₈	—	2	1	no	—
1026	C₈	—	43	2	no	—
1027	C₈	—	86	1	no	—
1028	C₈	—	86	1	no	—
1029	C₈	—	86	1	no	—
1030	C₈	#41×D₄₃	1	2	yes	—
1031	C₂²	—	2	1	no	—
1032	C₂²	—	2	1	no	—
1033	C₂²	—	2	1	no	—
1034	C₂²	—	2	1	no	—
1035	C₂²	—	2	1	no	—
1036	C₂²	—	2	1	no	—
1037	C₂²	—	43	2	no	—
1038	C₂²	—	43	2	no	—
1039	C₂²	—	86	1	no	—
1040	C₂²	—	86	1	no	—
1041	C₂²	—	86	1	no	—
1042	C₂²	—	86	1	no	—
1043	C₂²	—	86	1	no	—
1044	C₂²	—	86	1	no	—
1045	C₂²	—	86	1	no	—
1046	C₂²	—	172	4	no	—
1047	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1048	C₄	—	2	1	no	—
1049	C₄	—	2	1	no	—
1050	C₄	—	2	1	no	—
1051	C₄	—	2	1	no	—
1052	C₄	—	4	2	no	—
1053	C₄	—	4	2	no	—
1054	C₄	—	4	2	no	—
1055	C₄	—	4	2	no	—
1056	C₄	—	43	2	no	—
1057	C₄	—	86	1	no	—
1058	C₄	—	86	1	no	—
1059	C₄	—	86	1	no	—
1060	C₄	—	86	1	no	—
1061	C₄	—	172	2	no	—
1062	C₄	—	172	2	no	—
1063	C₄	—	172	2	no	—
1064	C₄	—	172	2	no	—
1065	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1066	C₄	2₋¹⁺⁴×D₄₃	1	1	yes	characteristic
1067	C₂	—	4	1	no	—
1068	C₂	—	4	1	no	—
1069	C₂	—	86	2	no	—
1070	C₂	—	86	2	no	—
1071	C₂	—	172	1	no	—
1072	C₂	#547×D₄₃	1	1	yes	characteristic
1073	C₂	#578×D₄₃	1	1	yes	characteristic
1074	C₂	#19149364	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×#3342	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	#14583408	C₂²
hypercenter	#3342	D₄₃
hypocenter	C₄₃	#61264
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #3342

Complements

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

N	H ≅ G/N	type
2. #19147123	C₂	semidirect
3. #19147119	C₂	semidirect
4. #19147047	C₂	semidirect
5. #19147043	C₂	semidirect
6. #19147023	C₂	semidirect
7. #19146987	C₂	semidirect
8. #19146984	C₂	semidirect
9. #19146965	C₂	semidirect
10. #19146964	C₂	semidirect
11. #19146963	C₂	semidirect
12. #19146958	C₂	semidirect
13. #19145128	C₂	semidirect
14. #19144561	C₂	semidirect
15. #19144542	C₂	semidirect
16. #19144430	C₂	semidirect
17. #19144245	C₂	semidirect
18. #467×D₄₃	C₂	semidirect
19. #19143458	C₂	semidirect
21. #19143192	C₂	semidirect
22. #427×D₄₃	C₂	semidirect
23. C₄₃×#3342	C₂	semidirect
49. #14583307	C₂²	semidirect
50. #14583305	C₂²	semidirect
51. #14583303	C₂²	semidirect
52. #14583301	C₂²	semidirect
53. #14583300	C₂²	semidirect
54. #14583243	C₂²	semidirect
57. #14583240	C₂²	semidirect
58. #14583238	C₂²	semidirect
61. #14583236	C₂²	semidirect
63. #14583232	C₂²	semidirect
65. #14583230	C₂²	semidirect
67. #14583228	C₂²	semidirect
68. #14583209	C₂²	semidirect
69. #14583207	C₂²	semidirect
70. #14583206	C₂²	semidirect
71. #14583204	C₂²	semidirect
72. #14583192	C₂²	semidirect
73. #14583191	C₂²	semidirect
74. #14583183	C₂²	semidirect
75. #14583156	C₂²	semidirect
76. #14583155	C₂²	semidirect
78. #14583141	C₂²	semidirect
80. #14583140	C₂²	semidirect
84. #14583137	C₂²	semidirect
85. #14583004	C₂²	semidirect
86. #14583003	C₂²	semidirect
87. C₄×Dic₁₇₂	C₂²	semidirect
88. Q₁₆×Dic₄₃	C₂²	semidirect
89. #14582993	C₂²	semidirect
97. #14582942	C₂²	semidirect
100. #14582938	C₂²	semidirect
104. #14582936	C₂²	semidirect
107. C₂×#13063259	C₂²	semidirect
111. #107×D₄₃	C₂²	semidirect
121. C₄₃×#500	C₂²	semidirect
123. C₄₃×#485	C₂²	semidirect
124. C₄₃×#475	C₂²	semidirect
126. C₄₃×#467	C₂²	semidirect
127. C₄×Q₁₆×C₄₃	C₂²	semidirect
130. C₄₃×#427	C₂²	semidirect
536. #3342	D₄₃	semidirect
590. #500	C₂×D₄₃	semidirect
600. #485	C₂×D₄₃	semidirect
616. #475	C₂×D₄₃	semidirect
628. #467	C₂×D₄₃	semidirect
634. C₄×Q₁₆	C₂×D₄₃	semidirect
654. #427	C₂×D₄₃	semidirect
668. C₄₃	#61264	semidirect

Maximal subgroups

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

subgroup	index
#19148340	2
#19147123	2
#19147119	2
#19147047	2
#19147043	2
#19147023	2
#19146987	2
#19146984	2
#19146965	2
#19146964	2
#19146963	2
#19146958	2
#19145128	2
#19144561	2
#19144542	2
#19144430	2
#19144245	2
#467×D₄₃	2
#19143458	2
#19143284	2
#19143192	2
#427×D₄₃	2
C₄₃×#3342	2
#61264	43