Subgroups — #25966447

Order 11008.

1878 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19147982	C₂	1	2	yes	maximal, complemented
2	#19145250	C₂	1	1	yes	maximal, characteristic, complemented
3	#19145247	C₂	1	1	yes	maximal, characteristic, complemented
4	#19145241	C₂	1	1	yes	maximal, characteristic, complemented
5	#19145238	C₂	1	1	yes	maximal, characteristic, complemented
6	#19145237	C₂	1	1	yes	maximal, characteristic, complemented
7	#19145234	C₂	1	1	yes	maximal, characteristic, complemented
8	#19145231	C₂	1	1	yes	maximal, characteristic, complemented
9	#19145221	C₂	1	2	yes	maximal, complemented
10	#19145218	C₂	1	2	yes	maximal, complemented
11	#19145211	C₂	1	2	yes	maximal, complemented
12	#19145206	C₂	1	2	yes	maximal, complemented
13	#19145106	C₂	1	1	yes	maximal, characteristic, complemented
14	#19145020	C₂	1	1	yes	maximal, characteristic, complemented
15	#19144937	C₂	1	2	yes	maximal, complemented
16	#19144199	C₂	1	2	yes	maximal, complemented
17	#19144178	C₂	1	1	yes	maximal, characteristic, complemented
18	#19144174	C₂	1	1	yes	maximal, characteristic, complemented
19	#19143390	C₂	1	2	yes	maximal, complemented
20	C₄×#13063348	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#13063344	C₂	1	1	yes	maximal, characteristic, complemented
22	#405×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3175	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063348	C₂²	1	1	yes	characteristic
25	C₂×#13063346	C₂²	1	2	yes	—
26	C₂×#13063344	C₂²	1	1	yes	characteristic
27	C₂×M₁₆×D₄₃	C₂²	1	1	yes	characteristic
28	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
29	#14583523	C₂²	1	2	yes	—
30	#14583520	C₂²	1	2	yes	—
31	#14583518	C₂²	1	2	yes	—
32	#14583509	C₂²	1	2	yes	—
33	#14583507	C₂²	1	2	yes	—
34	#14583502	C₂²	1	2	yes	—
35	#14583500	C₂²	1	2	yes	—
36	#14583495	—	2	2	no	—
37	#14583490	—	2	2	no	—
38	#14583485	—	2	2	no	—
39	#14583483	—	2	2	no	—
40	#14583454	C₂²	1	2	yes	—
41	#14583448	C₂²	1	2	yes	—
42	#14583435	—	2	2	no	—
43	#14583432	—	2	2	no	—
44	#14583428	—	2	2	no	—
45	#14583426	—	2	2	no	—
46	#14583412	C₂²	1	2	yes	—
47	#14583409	C₂²	1	2	yes	—
48	C₄×#10621902	C₂²	1	2	yes	—
49	C₄×#10621900	C₂²	1	2	yes	—
50	#117×D₄₃	C₂²	1	1	yes	characteristic
51	#14583304	C₂²	1	1	yes	characteristic, complemented
52	#14583300	C₂²	1	2	yes	complemented
53	#14583300	C₂²	1	1	yes	characteristic, complemented
54	#14583300	C₂²	1	1	yes	characteristic, complemented
55	#14583295	C₂²	1	2	yes	complemented
56	#14583283	C₂²	1	1	yes	characteristic, complemented
57	#14583281	C₂²	1	2	yes	complemented
58	#14583277	C₂²	1	1	yes	characteristic, complemented
59	#14583274	C₂²	1	1	yes	characteristic, complemented
60	#14583270	C₂²	1	2	yes	complemented
61	#14583266	C₂²	1	2	yes	complemented
62	#14583266	C₂²	1	2	yes	complemented
63	#14583262	C₂²	1	2	yes	complemented
64	#14583262	C₂²	1	2	yes	complemented
65	#14583261	C₂²	1	2	yes	complemented
66	#14583259	C₂²	1	2	yes	complemented
67	#14583258	C₂²	1	2	yes	complemented
68	#14583156	C₂²	1	2	yes	—
69	#14583155	C₂²	1	2	yes	—
70	#14583151	C₂²	1	2	yes	—
71	#14583150	C₂²	1	2	yes	—
72	#14583146	C₂²	1	2	yes	—
73	#14583145	C₂²	1	2	yes	—
74	#14583142	C₂²	1	2	yes	—
75	#14583141	C₂²	1	1	yes	characteristic
76	#14583140	C₂²	1	1	yes	characteristic
77	#14583137	C₂²	1	1	yes	characteristic
78	#14583136	C₂²	1	1	yes	characteristic
79	#14583135	C₂²	1	1	yes	characteristic
80	#14583132	C₂²	1	1	yes	characteristic
81	#14583131	C₂²	1	2	yes	—
82	#14583130	C₂²	1	2	yes	—
83	#14583127	C₂²	1	2	yes	—
84	#14583126	C₂²	1	2	yes	—
85	#14583009	C₂²	1	2	yes	complemented
86	#14583008	C₂²	1	2	yes	complemented
87	#14583004	C₂²	1	2	yes	complemented
88	#14583003	C₂²	1	2	yes	complemented
89	#14583001	C₂²	1	2	yes	complemented
90	#14583000	C₂²	1	2	yes	complemented
91	#14582998	C₂²	1	2	yes	complemented
92	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
93	Q₁₆×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
94	#14582993	C₂²	1	1	yes	characteristic, complemented
95	#14582990	C₂²	1	2	yes	complemented
96	C₄×#10621884	C₂²	1	2	yes	complemented
97	C₄×#10621883	C₂²	1	2	yes	complemented
98	#14582984	C₂²	1	2	yes	complemented
99	C₄×D₃₄₄	C₂²	1	1	yes	characteristic, complemented
100	D₈×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
101	#14582981	C₂²	1	1	yes	characteristic, complemented
102	#14582936	C₂²	1	2	yes	—
103	#14582936	C₂²	1	1	yes	characteristic
104	#14582936	C₂²	1	1	yes	characteristic
105	#14582894	C₂²	1	2	yes	—
106	#14582894	C₂²	1	2	yes	—
107	#14582892	C₂²	1	2	yes	—
108	#14582892	C₂²	1	2	yes	—
109	#14582857	C₂²	1	1	yes	characteristic
110	#14582856	C₂²	1	1	yes	characteristic
111	#14582856	C₂²	1	1	yes	characteristic
112	#14582855	C₂²	1	1	yes	characteristic
113	#14582854	C₂²	1	1	yes	characteristic
114	#14582853	C₂²	1	1	yes	characteristic
115	#14582853	C₂²	1	1	yes	characteristic
116	#97×D₄₃	C₂²	1	1	yes	characteristic
117	#97×D₄₃	C₂²	1	1	yes	characteristic
118	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
120	C₄₃×#542	C₂²	1	2	yes	—
121	C₄₃×#500	C₂²	1	1	yes	characteristic, complemented
122	C₄₃×#495	C₂²	1	1	yes	characteristic, complemented
123	C₄₃×#489	C₂²	1	2	yes	complemented
124	C₄₃×#468	C₂²	1	2	yes	—
125	C₄₃×#467	C₂²	1	1	yes	characteristic
126	C₄₃×#466	C₂²	1	1	yes	characteristic
127	C₄₃×#440	C₂²	1	2	yes	complemented
128	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
129	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
130	C₄₃×#405	C₂²	1	1	yes	characteristic
131	C₂×#10621902	C₂³	1	2	yes	—
132	C₂×#10621900	C₂³	1	2	yes	—
133	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
134	#13063348	—	2	4	no	—
135	#13063346	—	2	8	no	—
136	#13063344	—	2	4	no	—
137	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
138	C₂×#10621885	C₂³	1	2	yes	—
139	C₂×#10621873	C₂³	1	2	yes	—
140	C₂×#10621883	C₂³	1	2	yes	—
141	C₂×#10621884	C₂³	1	2	yes	—
142	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
143	C₂×#10621882	C₂³	1	2	yes	—
144	C₂×#10621877	C₂³	1	1	yes	characteristic
145	C₂×#10621872	C₂³	1	1	yes	characteristic
146	C₂×#10621872	C₂³	1	1	yes	characteristic
147	M₁₆×D₄₃	—	2	4	no	—
148	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
149	C₂×C₈×D₄₃	—	2	4	no	—
150	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
151	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
152	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
153	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
154	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
155	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
156	#13063325	C₂³	1	2	yes	—
157	#13063323	C₂³	1	2	yes	—
158	#13063321	C₂³	1	2	yes	—
159	#13063320	—	2	2	no	—
160	#13063320	—	2	2	no	—
161	#13063320	—	2	2	no	—
162	#13063319	—	2	2	no	—
163	#13063318	—	2	2	no	—
164	#13063318	—	2	2	no	—
165	#13063318	—	2	2	no	—
166	#13063317	—	2	2	no	—
167	#13063316	—	2	2	no	—
168	#13063316	C₂³	1	2	yes	—
169	#13063316	C₂³	1	2	yes	—
170	#13063315	—	2	2	no	—
171	#13063315	—	2	2	no	—
172	#13063314	—	2	2	no	—
173	#13063313	C₂³	1	2	yes	—
174	#13063311	—	2	2	no	—
175	#13063311	—	2	2	no	—
176	#13063310	—	2	2	no	—
177	#13063310	—	2	2	no	—
178	#13063309	—	2	2	no	—
179	#13063309	—	2	2	no	—
180	#13063308	—	2	2	no	—
181	#13063307	—	2	2	no	—
182	#13063307	—	2	2	no	—
183	#13063307	—	2	2	no	—
184	#13063307	—	2	2	no	—
185	#13063305	—	2	2	no	—
186	#13063305	C₂³	1	2	yes	—
187	#13063304	C₂³	1	2	yes	—
188	#13063303	—	2	2	no	—
189	#13063302	—	2	2	no	—
190	#13063301	—	2	2	no	—
191	#13063301	—	2	2	no	—
192	#13063301	C₂³	1	2	yes	—
193	#13063300	C₂³	1	2	yes	—
194	#13063299	—	2	2	no	—
195	#13063299	C₂³	1	2	yes	—
196	#13063298	—	2	2	no	—
197	#13063298	—	2	2	no	—
198	#13063298	—	2	2	no	—
199	#13063297	—	2	2	no	—
200	#13063296	—	2	2	no	—
201	#13063296	C₂³	1	2	yes	—
202	#13063295	—	2	2	no	—
203	#13063293	—	2	2	no	—
204	Q₈×Dic₄₃	—	2	2	no	—
205	Q₈×Dic₄₃	C₂³	1	2	yes	—
206	C₄×Dic₈₆	C₂³	1	2	yes	—
207	#13063290	—	2	2	no	—
208	#13063290	C₂³	1	2	yes	—
209	C₄×D₁₇₂	—	2	2	no	—
210	C₄×D₁₇₂	C₂³	1	2	yes	—
211	D₄×Dic₄₃	—	2	2	no	—
212	D₄×Dic₄₃	C₂³	1	2	yes	—
213	#13063287	—	2	2	no	—
214	#13063287	—	2	2	no	—
215	#13063287	C₂³	1	2	yes	—
216	C₄×C₂²⋊D₄₃	—	2	2	no	—
217	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
218	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
219	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
220	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
221	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
222	#13063284	C₂³	1	1	yes	characteristic
223	#13063283	—	2	2	no	—
224	#13063283	D₄	1	1	yes	characteristic
225	#13063283	D₄	1	1	yes	characteristic
226	#13063283	C₂³	1	2	yes	—
227	#13063283	C₂³	1	2	yes	—
228	#13063282	C₂³	1	1	yes	characteristic
229	#13063282	C₂³	1	1	yes	characteristic
230	#13063281	—	2	2	no	—
231	#13063281	D₄	1	1	yes	characteristic
232	#13063281	D₄	1	1	yes	characteristic
233	C₄⋊C₄×D₄₃	D₄	1	1	yes	characteristic
234	C₄⋊C₄×D₄₃	D₄	1	1	yes	characteristic
235	C₂²⋊C₄×D₄₃	D₄	1	1	yes	characteristic
236	C₂²⋊C₄×D₄₃	D₄	1	1	yes	characteristic
237	C₂×C₄×Dic₄₃	—	2	2	no	—
238	C₄²×D₄₃	—	2	2	no	—
239	C₄²×D₄₃	C₂³	1	1	yes	characteristic
240	C₄²×D₄₃	C₂³	1	1	yes	characteristic
241	#13063259	C₂³	1	1	yes	characteristic
242	#13063259	C₂³	1	1	yes	characteristic
243	#13063259	C₂³	1	2	yes	—
244	#13063256	C₂³	1	2	yes	—
245	#13063256	C₂³	1	2	yes	—
246	#13063256	C₂³	1	2	yes	—
247	#13063256	C₂³	1	2	yes	—
248	#13063250	C₂³	1	2	yes	—
249	#13063250	C₂³	1	2	yes	—
250	#13063249	C₂³	1	2	yes	—
251	#13063249	C₂³	1	2	yes	—
252	#13063248	C₂³	1	2	yes	—
253	#13063248	C₂³	1	2	yes	—
254	#13063247	C₂³	1	2	yes	—
255	#13063247	C₂³	1	2	yes	—
256	#13063246	C₂³	1	2	yes	—
257	#13063246	C₂³	1	2	yes	—
258	#13063245	C₂³	1	2	yes	—
259	#13063245	C₂³	1	2	yes	—
260	#13063236	C₂³	1	1	yes	characteristic
261	#13063236	C₂³	1	1	yes	characteristic
262	#13063235	C₂³	1	1	yes	characteristic
263	#13063235	C₂³	1	1	yes	characteristic
264	#13063235	C₂³	1	1	yes	characteristic
265	#13063235	C₂³	1	1	yes	characteristic
266	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
267	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
268	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
269	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
270	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
271	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
272	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
273	C₂×SD₁₆×C₄₃	C₂³	1	2	yes	—
274	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
275	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
276	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
277	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
278	#126×C₄₃	—	2	2	no	—
279	#124×C₄₃	—	2	2	no	—
280	#124×C₄₃	C₂³	1	2	yes	—
281	#123×C₄₃	—	2	2	no	—
282	C₂²⋊Q₈×C₄₃	—	2	2	no	—
283	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
284	#121×C₄₃	C₂³	1	2	yes	—
285	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
286	C₄×D₄×C₄₃	C₂³	1	2	yes	—
287	#117×C₄₃	C₂³	1	1	yes	characteristic
288	#107×C₄₃	C₂³	1	1	yes	characteristic
289	#107×C₄₃	C₂³	1	1	yes	characteristic
290	#107×C₄₃	C₂³	1	2	yes	—
291	#103×C₄₃	C₂³	1	2	yes	—
292	#103×C₄₃	C₂³	1	2	yes	—
293	#102×C₄₃	C₂³	1	2	yes	—
294	#102×C₄₃	C₂³	1	2	yes	—
295	#97×C₄₃	C₂³	1	1	yes	characteristic
296	#97×C₄₃	C₂³	1	1	yes	characteristic
297	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
298	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
299	C₂³×D₄₃	C₂×D₄	1	1	yes	characteristic
300	C₂×Q₈×C₄₃	—	2	2	no	—
301	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
302	C₂×D₄×C₄₃	—	2	2	no	—
303	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₄₃	—	2	2	no	—
305	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
306	C₂×C₂²⋊D₄₃	—	2	2	no	—
307	C₂×C₂²⋊D₄₃	—	2	2	no	—
308	C₂×C₂²⋊D₄₃	—	2	2	no	—
309	C₂×C₂²⋊D₄₃	—	2	2	no	—
310	C₂×C₂²⋊D₄₃	—	2	2	no	—
311	C₂²×Dic₄₃	—	2	2	no	—
312	C₂²×Dic₄₃	—	2	2	no	—
313	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
314	#10621902	—	2	4	no	—
315	#10621902	—	2	4	no	—
316	#10621900	—	2	4	no	—
317	#10621900	—	2	4	no	—
318	C₂×D₁₇₂	—	2	2	no	—
319	C₂×D₁₇₂	—	2	2	no	—
320	C₂×D₁₇₂	C₂⁴	1	2	yes	—
321	C₂×C₄×D₄₃	—	2	2	no	—
322	C₂×C₄×D₄₃	—	2	2	no	—
323	C₂×C₄×D₄₃	—	2	2	no	—
324	C₂×C₄×D₄₃	—	2	2	no	—
325	C₂×C₄×D₄₃	—	2	2	no	—
326	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
327	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
328	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
329	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
330	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
331	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
332	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
333	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
334	C₂×Dic₈₆	—	2	2	no	—
335	C₂×Dic₈₆	C₂⁴	1	2	yes	—
336	Q₁₆×C₄₃	—	2	2	no	—
337	SD₁₆×C₄₃	—	2	4	no	—
338	D₈×C₄₃	—	2	2	no	—
339	M₁₆×C₄₃	—	2	2	no	—
340	C₂×C₈×C₄₃	—	2	2	no	—
341	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
342	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
343	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
344	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
345	C₄⋊C₄×C₄₃	—	2	2	no	—
346	C₄⋊C₄×C₄₃	—	2	2	no	—
347	C₄⋊C₄×C₄₃	—	2	2	no	—
348	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
349	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
350	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
351	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
352	C₂²⋊C₄×C₄₃	—	2	2	no	—
353	C₂²⋊C₄×C₄₃	—	2	2	no	—
354	C₂²⋊C₄×C₄₃	—	2	2	no	—
355	C₂²⋊C₄×C₄₃	—	2	2	no	—
356	C₂²⋊C₄×C₄₃	—	2	2	no	—
357	C₂²⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
358	C₂²⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
359	C₄²×C₄₃	—	2	2	no	—
360	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
361	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
362	C₂²⋊Dic₄₃	—	2	2	no	—
363	C₂²⋊Dic₄₃	—	2	2	no	—
364	C₂²⋊Dic₄₃	—	2	2	no	—
365	C₂²⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
366	C₂²⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
367	#10621885	—	2	4	no	—
368	#10621884	—	2	4	no	—
369	#10621883	—	2	4	no	—
370	#10621882	—	2	4	no	—
371	(C₂×D₄₃)⋊C₄	—	2	2	no	—
372	(C₂×D₄₃)⋊C₄	—	2	2	no	—
373	(C₂×D₄₃)⋊C₄	—	2	2	no	—
374	(C₂×D₄₃)⋊C₄	—	2	2	no	—
375	(C₂×D₄₃)⋊C₄	—	2	2	no	—
376	(C₂×D₄₃)⋊C₄	—	2	2	no	—
377	(C₂×D₄₃)⋊C₄	—	2	2	no	—
378	(C₂×D₄₃)⋊C₄	—	2	2	no	—
379	(C₂×D₄₃)⋊C₄	—	2	2	no	—
380	(C₂×D₄₃)⋊C₄	—	2	2	no	—
381	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
382	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
383	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
384	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
385	C₄⋊Dic₄₃	—	2	2	no	—
386	C₄⋊Dic₄₃	—	2	2	no	—
387	C₄⋊Dic₄₃	—	2	2	no	—
388	C₄⋊Dic₄₃	—	2	2	no	—
389	C₄⋊Dic₄₃	—	2	2	no	—
390	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
391	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
392	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
393	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
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	—	2	2	no	—
399	Dic₄₃⋊C₄	—	2	2	no	—
400	Dic₄₃⋊C₄	—	2	2	no	—
401	Dic₄₃⋊C₄	—	2	2	no	—
402	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
403	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
404	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
405	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
406	C₄×Dic₄₃	—	2	2	no	—
407	C₄×Dic₄₃	—	2	2	no	—
408	C₄×Dic₄₃	—	2	2	no	—
409	C₄×Dic₄₃	—	2	2	no	—
410	C₄×Dic₄₃	—	2	2	no	—
411	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
412	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
413	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
414	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
415	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
416	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
417	#10621877	—	2	2	no	—
418	C₂×C₄₃⋊C₈	—	2	2	no	—
419	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
420	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
421	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
422	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
423	Dic₁₇₂	—	2	2	no	—
424	D₃₄₄	—	2	2	no	—
425	#10621873	—	2	4	no	—
426	#10621872	—	2	2	no	—
427	#10621872	—	2	2	no	—
428	C₈×D₄₃	—	2	2	no	—
429	C₈×D₄₃	—	2	2	no	—
430	C₈×D₄₃	—	2	2	no	—
431	C₈×D₄₃	—	2	2	no	—
432	C₈×D₄₃	#41	1	4	yes	—
433	C₈×D₄₃	#41	1	4	yes	—
434	C₂³×C₄₃	—	2	2	no	—
435	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
436	C₂²×D₄₃	—	2	2	no	—
437	C₂²×D₄₃	—	2	2	no	—
438	C₂²×D₄₃	—	4	1	no	—
439	C₂²×D₄₃	—	4	1	no	—
440	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
441	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
442	Q₈×C₄₃	—	2	2	no	—
443	Q₈×C₄₃	—	2	2	no	—
444	Q₈×C₄₃	—	8	2	no	—
445	D₄×C₄₃	—	2	2	no	—
446	D₄×C₄₃	—	2	2	no	—
447	D₄×C₄₃	—	8	2	no	—
448	C₂×C₄×C₄₃	—	2	1	no	—
449	C₂×C₄×C₄₃	—	2	1	no	—
450	C₂×C₄×C₄₃	—	2	2	no	—
451	C₂×C₄×C₄₃	—	2	2	no	—
452	C₂×C₄×C₄₃	—	2	2	no	—
453	C₂×C₄×C₄₃	—	8	2	no	—
454	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
457	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
458	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
459	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
460	C₂²⋊D₄₃	—	4	4	no	—
461	C₂²⋊D₄₃	—	8	2	no	—
462	C₂²⋊D₄₃	—	8	2	no	—
463	C₂²⋊D₄₃	—	8	2	no	—
464	C₂²⋊D₄₃	—	8	2	no	—
465	C₂×Dic₄₃	—	2	2	no	—
466	C₂×Dic₄₃	—	2	2	no	—
467	C₂×Dic₄₃	—	2	2	no	—
468	C₂×Dic₄₃	—	2	2	no	—
469	C₂×Dic₄₃	—	4	4	no	—
470	C₂×Dic₄₃	—	8	2	no	—
471	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
472	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
473	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
474	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
475	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
476	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
477	D₁₇₂	—	2	2	no	—
478	D₁₇₂	—	2	2	no	—
479	D₁₇₂	—	4	4	no	—
480	D₁₇₂	—	8	2	no	—
481	C₄×D₄₃	—	2	2	no	—
482	C₄×D₄₃	—	2	1	no	—
483	C₄×D₄₃	—	2	1	no	—
484	C₄×D₄₃	—	2	2	no	—
485	C₄×D₄₃	—	4	1	no	—
486	C₄×D₄₃	—	4	1	no	—
487	C₄×D₄₃	—	4	1	no	—
488	C₄×D₄₃	—	4	1	no	—
489	C₄×D₄₃	—	4	4	no	—
490	C₄×D₄₃	—	8	2	no	—
491	C₄×D₄₃	—	8	2	no	—
492	C₄×D₄₃	C₂×#41	1	2	yes	—
493	C₄×D₄₃	C₂×#41	1	2	yes	—
494	Dic₈₆	—	2	2	no	—
495	Dic₈₆	—	2	2	no	—
496	Dic₈₆	—	8	2	no	—
497	C₈×C₄₃	—	2	1	no	—
498	C₈×C₄₃	—	2	1	no	—
499	C₈×C₄₃	C₂×#41	1	2	yes	—
500	C₈×C₄₃	C₂×#41	1	2	yes	—
501	C₄₃⋊C₈	—	2	1	no	—
502	C₄₃⋊C₈	—	2	1	no	—
503	C₄₃⋊C₈	C₂×#41	1	2	yes	—
504	C₄₃⋊C₈	C₂×#41	1	2	yes	—
505	#60682	—	43	1	no	maximal, Sylow
506	C₂²×C₄₃	—	2	1	no	—
507	C₂²×C₄₃	—	2	1	no	—
508	C₂²×C₄₃	—	2	1	no	—
509	C₂²×C₄₃	—	4	2	no	—
510	C₂²×C₄₃	—	4	2	no	—
511	C₂²×C₄₃	—	4	2	no	—
512	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
513	C₂×D₄₃	—	2	1	no	—
514	C₂×D₄₃	—	2	1	no	—
515	C₂×D₄₃	—	2	1	no	—
516	C₂×D₄₃	—	2	1	no	—
517	C₂×D₄₃	—	2	1	no	—
518	C₂×D₄₃	—	4	4	no	—
519	C₂×D₄₃	—	4	2	no	—
520	C₂×D₄₃	—	4	2	no	—
521	C₂×D₄₃	—	4	2	no	—
522	C₂×D₄₃	#532	1	2	yes	—
523	C₄×C₄₃	—	2	1	no	—
524	C₄×C₄₃	—	2	1	no	—
525	C₄×C₄₃	—	2	1	no	—
526	C₄×C₄₃	—	2	1	no	—
527	C₄×C₄₃	—	2	1	no	—
528	C₄×C₄₃	—	4	2	no	—
529	C₄×C₄₃	—	4	2	no	—
530	C₄×C₄₃	—	4	2	no	—
531	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
532	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
533	Dic₄₃	—	2	1	no	—
534	Dic₄₃	—	2	1	no	—
535	Dic₄₃	—	2	1	no	—
536	Dic₄₃	—	2	1	no	—
537	Dic₄₃	—	2	1	no	—
538	Dic₄₃	—	4	2	no	—
539	Dic₄₃	—	4	2	no	—
540	Dic₄₃	—	4	2	no	—
541	Dic₄₃	#532	1	2	yes	—
542	#3455	—	43	2	no	—
543	#3177	—	43	1	no	—
544	#3177	—	43	1	no	—
545	#3176	—	43	1	no	—
546	#3176	—	43	1	no	—
547	#3175	—	43	1	no	—
548	#3175	—	43	1	no	—
549	#3175	—	43	1	no	—
550	#3175	D₄₃	1	1	yes	characteristic, complemented
551	#3174	—	43	2	no	—
552	#3174	—	43	2	no	—
553	#3173	—	43	2	no	—
554	#3173	—	43	2	no	—
555	#3160	—	43	1	no	—
556	#3147	—	43	1	no	—
557	#3135	—	43	2	no	—
558	#3054	—	43	2	no	—
559	#3050	—	43	1	no	—
560	#3050	—	43	1	no	—
561	#2943	—	43	2	no	—
562	C₄×#135	—	43	1	no	—
563	C₄×#135	—	43	1	no	—
564	C₂×#405	—	43	1	no	—
565	C₂×C₄₃	—	4	1	no	—
566	C₂×C₄₃	—	8	2	no	—
567	C₂×C₄₃	C₂×#532	1	1	yes	characteristic
568	C₂×C₄₃	#3584	1	1	yes	characteristic
569	C₂×C₄₃	#3584	1	1	yes	characteristic
570	D₄₃	—	2	2	no	—
571	D₄₃	—	4	1	no	—
572	D₄₃	—	8	2	no	—
573	C₂×#135	—	43	1	no	—
574	C₂×#135	—	43	2	no	—
575	C₂×#135	—	43	1	no	—
576	C₂²×M₁₆	—	43	1	no	—
577	C₂³×C₈	—	43	1	no	—
578	#542	—	43	2	no	—
579	#542	—	43	2	no	—
580	#542	—	43	2	no	—
581	#542	C₂×D₄₃	1	2	yes	—
582	#541	—	43	2	no	—
583	#541	—	43	2	no	—
584	#540	—	43	2	no	—
585	#540	—	43	2	no	—
586	#539	—	86	2	no	—
587	#539	—	86	2	no	—
588	#538	—	86	2	no	—
589	#538	—	86	2	no	—
590	#533	—	43	2	no	—
591	#532	—	43	2	no	—
592	#529	—	86	2	no	—
593	#529	—	86	2	no	—
594	#529	—	86	2	no	—
595	#529	—	86	2	no	—
596	#525	—	43	2	no	—
597	#525	—	43	2	no	—
598	C₄×#41	—	43	2	no	—
599	C₄×#41	—	43	2	no	—
600	C₂×#117	—	43	1	no	—
601	#500	—	43	1	no	—
602	#500	C₂×D₄₃	1	1	yes	characteristic, complemented
603	#499	—	43	2	no	—
604	#499	—	43	1	no	—
605	#499	—	43	1	no	—
606	#498	—	43	2	no	—
607	#495	—	43	2	no	—
608	#495	—	43	1	no	—
609	#495	C₂×D₄₃	1	1	yes	characteristic, complemented
610	#494	—	43	1	no	—
611	#493	—	43	1	no	—
612	#492	—	43	2	no	—
613	#491	—	43	2	no	—
614	#491	—	43	2	no	—
615	#490	—	43	2	no	—
616	#490	—	43	2	no	—
617	#489	—	43	2	no	—
618	#489	—	43	2	no	—
619	#489	—	43	2	no	—
620	#489	C₂×D₄₃	1	2	yes	complemented
621	#470	—	43	2	no	—
622	#470	—	43	2	no	—
623	#469	—	43	2	no	—
624	#469	—	43	2	no	—
625	#468	—	43	2	no	—
626	#468	—	43	2	no	—
627	#468	—	43	2	no	—
628	#468	C₂×D₄₃	1	2	yes	—
629	#467	—	43	1	no	—
630	#467	—	43	1	no	—
631	#467	—	43	1	no	—
632	#467	C₂×D₄₃	1	1	yes	characteristic
633	#466	—	43	1	no	—
634	#466	—	43	1	no	—
635	#466	—	43	1	no	—
636	#466	C₂×D₄₃	1	1	yes	characteristic
637	#465	—	43	2	no	—
638	#465	—	43	2	no	—
639	#465	—	43	2	no	—
640	#465	—	43	2	no	—
641	#442	—	43	2	no	—
642	#442	—	43	2	no	—
643	#441	—	43	2	no	—
644	#441	—	43	2	no	—
645	#440	—	43	2	no	—
646	#440	—	43	2	no	—
647	#440	—	43	2	no	—
648	#440	C₂×D₄₃	1	2	yes	complemented
649	C₄×Q₁₆	—	43	1	no	—
650	C₄×Q₁₆	—	43	1	no	—
651	C₄×Q₁₆	—	43	1	no	—
652	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
653	C₄×SD₁₆	—	43	2	no	—
654	C₄×SD₁₆	—	43	2	no	—
655	C₄×SD₁₆	—	43	2	no	—
656	C₄×SD₁₆	—	43	2	no	—
657	C₄×D₈	—	43	1	no	—
658	C₄×D₈	—	43	1	no	—
659	C₄×D₈	—	43	1	no	—
660	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic, complemented
661	#427	—	43	1	no	—
662	#427	—	43	1	no	—
663	#427	—	43	2	no	—
664	#416	—	43	2	no	—
665	#416	—	43	2	no	—
666	#416	—	43	2	no	—
667	#416	—	43	2	no	—
668	#405	—	43	1	no	—
669	#405	—	43	1	no	—
670	#405	—	43	1	no	—
671	#405	—	43	1	no	—
672	#405	—	43	1	no	—
673	#405	—	43	1	no	—
674	#405	—	43	1	no	—
675	#405	C₂×D₄₃	1	1	yes	characteristic
676	C₂×#97	—	43	1	no	—
677	C₂×#97	—	43	1	no	—
678	C₂×C₄×C₈	—	43	1	no	—
679	C₂×C₄×C₈	—	43	1	no	—
680	C₄₃	#60682	1	1	yes	characteristic, complemented, Sylow
681	C₂×#41	—	43	2	no	—
682	C₂×#41	—	43	2	no	—
683	C₂³×C₄	—	43	1	no	—
684	#135	—	86	4	no	—
685	#135	—	86	8	no	—
686	#135	—	86	4	no	—
687	C₂×Q₁₆	—	43	2	no	—
688	C₂×Q₁₆	—	43	1	no	—
689	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
690	C₂×SD₁₆	—	43	2	no	—
691	C₂×SD₁₆	—	43	2	no	—
692	C₂×SD₁₆	—	43	2	no	—
693	C₂×SD₁₆	C₂²×D₄₃	1	2	yes	—
694	C₂×D₈	—	43	2	no	—
695	C₂×D₈	—	43	1	no	—
696	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
697	C₂×M₁₆	—	43	1	no	—
698	C₂×M₁₆	—	43	1	no	—
699	C₂×M₁₆	—	43	1	no	—
700	C₂×M₁₆	—	86	4	no	—
701	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
702	C₂²×C₈	—	43	1	no	—
703	C₂²×C₈	—	43	1	no	—
704	C₂²×C₈	—	43	1	no	—
705	C₂²×C₈	—	43	1	no	—
706	C₂²×C₈	—	43	1	no	—
707	C₂²×C₈	—	43	1	no	—
708	C₂²×C₈	—	43	1	no	—
709	C₂²×C₈	—	86	4	no	—
710	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
711	C₄⋊Q₈	—	43	2	no	—
712	C₄⋊Q₈	—	43	2	no	—
713	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
714	#127	—	43	2	no	—
715	#126	—	2	2	no	—
716	#126	—	86	2	no	—
717	#126	—	86	2	no	—
718	#126	—	86	2	no	—
719	#126	—	86	2	no	—
720	#126	—	86	2	no	—
721	#126	—	86	2	no	—
722	#126	—	86	2	no	—
723	#125	—	43	2	no	—
724	#125	—	43	2	no	—
725	#125	—	86	2	no	—
726	#125	—	86	2	no	—
727	#125	—	86	2	no	—
728	#125	—	86	2	no	—
729	#124	—	2	2	no	—
730	#124	—	43	2	no	—
731	#124	—	86	2	no	—
732	#124	—	86	2	no	—
733	#124	—	86	2	no	—
734	#124	C₂²×D₄₃	1	2	yes	—
735	#123	—	2	2	no	—
736	#123	—	86	2	no	—
737	#123	—	86	2	no	—
738	#123	—	86	2	no	—
739	#123	—	86	2	no	—
740	#123	—	86	2	no	—
741	#123	—	86	2	no	—
742	#123	—	86	2	no	—
743	#123	—	86	2	no	—
744	#123	—	86	2	no	—
745	C₂²⋊Q₈	—	2	2	no	—
746	C₂²⋊Q₈	—	43	2	no	—
747	C₂²⋊Q₈	—	43	2	no	—
748	C₂²⋊Q₈	—	43	2	no	—
749	C₂²⋊Q₈	—	86	2	no	—
750	C₂²⋊Q₈	—	86	2	no	—
751	C₂²⋊Q₈	—	86	2	no	—
752	C₂²⋊Q₈	—	86	2	no	—
753	C₂²⋊Q₈	—	86	2	no	—
754	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
755	#121	—	43	2	no	—
756	#121	—	43	2	no	—
757	#121	—	43	2	no	—
758	#121	—	86	2	no	—
759	#121	—	86	2	no	—
760	#121	—	86	2	no	—
761	#121	—	86	2	no	—
762	#121	—	86	2	no	—
763	#121	—	86	2	no	—
764	#121	C₂²×D₄₃	1	2	yes	—
765	#120	—	86	2	no	—
766	#120	—	86	2	no	—
767	C₄×Q₈	—	43	2	no	—
768	C₄×Q₈	—	43	2	no	—
769	C₄×Q₈	—	43	2	no	—
770	C₄×Q₈	—	86	2	no	—
771	C₄×Q₈	—	86	2	no	—
772	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
773	C₄×D₄	—	43	2	no	—
774	C₄×D₄	—	43	2	no	—
775	C₄×D₄	—	43	2	no	—
776	C₄×D₄	—	86	2	no	—
777	C₄×D₄	—	86	2	no	—
778	C₄×D₄	—	86	2	no	—
779	C₄×D₄	—	86	2	no	—
780	C₄×D₄	—	86	2	no	—
781	C₄×D₄	—	86	2	no	—
782	C₄×D₄	—	86	2	no	—
783	C₄×D₄	—	86	2	no	—
784	C₄×D₄	—	86	2	no	—
785	C₄×D₄	—	86	2	no	—
786	C₄×D₄	C₂²×D₄₃	1	2	yes	—
787	#117	—	43	1	no	—
788	#117	—	43	1	no	—
789	#117	—	43	1	no	—
790	#117	—	43	1	no	—
791	#117	—	43	1	no	—
792	#117	—	43	1	no	—
793	#117	—	43	1	no	—
794	#117	—	43	2	no	—
795	#117	—	43	2	no	—
796	#117	—	86	2	no	—
797	#117	—	86	2	no	—
798	#117	C₂²×D₄₃	1	1	yes	characteristic
799	C₂×C₄⋊C₄	—	43	1	no	—
800	C₂×C₄⋊C₄	—	43	1	no	—
801	C₂×C₂²⋊C₄	—	43	1	no	—
802	C₂×C₂²⋊C₄	—	43	1	no	—
803	C₂×C₄²	—	43	1	no	—
804	C₂×C₄²	—	43	1	no	—
805	C₂×C₄²	—	86	2	no	—
806	C₂×C₄²	—	86	2	no	—
807	#107	—	43	1	no	—
808	#107	—	43	1	no	—
809	#107	—	43	2	no	—
810	#107	C₂²×D₄₃	1	1	yes	characteristic
811	#107	C₂²×D₄₃	1	1	yes	characteristic
812	#107	C₂²×D₄₃	1	2	yes	—
813	#106	—	43	2	no	—
814	#106	—	43	2	no	—
815	#106	—	43	2	no	—
816	#106	—	43	2	no	—
817	#103	—	43	2	no	—
818	#103	—	43	2	no	—
819	#103	—	43	2	no	—
820	#103	—	43	2	no	—
821	#103	—	43	2	no	—
822	#103	—	43	2	no	—
823	#103	C₂²×D₄₃	1	2	yes	—
824	#103	C₂²×D₄₃	1	2	yes	—
825	#102	—	43	2	no	—
826	#102	—	43	2	no	—
827	#102	—	43	2	no	—
828	#102	—	43	2	no	—
829	#102	—	43	2	no	—
830	#102	—	43	2	no	—
831	#102	C₂²×D₄₃	1	2	yes	—
832	#102	C₂²×D₄₃	1	2	yes	—
833	#97	—	43	1	no	—
834	#97	—	43	1	no	—
835	#97	—	43	1	no	—
836	#97	—	43	1	no	—
837	#97	—	43	1	no	—
838	#97	—	43	1	no	—
839	#97	C₂²×D₄₃	1	1	yes	characteristic
840	#97	C₂²×D₄₃	1	1	yes	characteristic
841	C₄×C₈	—	43	1	no	—
842	C₄×C₈	—	43	1	no	—
843	C₄×C₈	—	43	1	no	—
844	C₄×C₈	—	43	1	no	—
845	C₄×C₈	—	43	1	no	—
846	C₄×C₈	—	43	1	no	—
847	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
848	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
849	C₂⁴	—	43	1	no	—
850	#41	—	86	4	no	—
851	#41	—	86	4	no	—
852	#41	—	86	4	no	—
853	#41	—	86	4	no	—
854	C₂×Q₈	—	2	2	no	—
855	C₂×Q₈	—	43	2	no	—
856	C₂×Q₈	—	86	2	no	—
857	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
858	C₂×D₄	—	2	2	no	—
859	C₂×D₄	—	43	2	no	—
860	C₂×D₄	—	86	2	no	—
861	C₂×D₄	—	86	2	no	—
862	C₂×D₄	—	86	2	no	—
863	C₂×D₄	—	86	2	no	—
864	C₂×D₄	—	86	2	no	—
865	C₂×D₄	—	86	2	no	—
866	C₂×D₄	—	86	2	no	—
867	C₂×D₄	C₂³×D₄₃	1	2	yes	—
868	C₂²×C₄	—	2	2	no	—
869	C₂²×C₄	—	43	1	no	—
870	C₂²×C₄	—	43	1	no	—
871	C₂²×C₄	—	43	1	no	—
872	C₂²×C₄	—	43	1	no	—
873	C₂²×C₄	—	43	1	no	—
874	C₂²×C₄	—	43	1	no	—
875	C₂²×C₄	—	43	1	no	—
876	C₂²×C₄	—	43	1	no	—
877	C₂²×C₄	—	43	1	no	—
878	C₂²×C₄	—	86	2	no	—
879	C₂²×C₄	—	86	2	no	—
880	C₂²×C₄	—	86	2	no	—
881	C₂²×C₄	—	86	2	no	—
882	C₂²×C₄	—	86	2	no	—
883	C₂²×C₄	—	86	2	no	—
884	C₂²×C₄	—	86	2	no	—
885	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
886	Q₁₆	—	2	2	no	—
887	Q₁₆	—	86	4	no	—
888	Q₁₆	—	86	2	no	—
889	SD₁₆	—	2	4	no	—
890	SD₁₆	—	86	4	no	—
891	SD₁₆	—	86	4	no	—
892	SD₁₆	—	86	4	no	—
893	D₈	—	2	2	no	—
894	D₈	—	86	4	no	—
895	D₈	—	86	2	no	—
896	M₁₆	—	2	2	no	—
897	M₁₆	—	86	2	no	—
898	M₁₆	—	86	2	no	—
899	M₁₆	—	86	2	no	—
900	C₂×C₈	—	2	2	no	—
901	C₂×C₈	—	43	1	no	—
902	C₂×C₈	—	43	1	no	—
903	C₂×C₈	—	43	4	no	—
904	C₂×C₈	—	43	4	no	—
905	C₂×C₈	—	43	1	no	—
906	C₂×C₈	—	43	1	no	—
907	C₂×C₈	—	86	2	no	—
908	C₂×C₈	—	86	2	no	—
909	C₂×C₈	—	86	2	no	—
910	C₂×C₈	—	86	2	no	—
911	C₂×C₈	—	86	2	no	—
912	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
913	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
914	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
915	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	43	1	no	—
920	C₄⋊C₄	—	43	1	no	—
921	C₄⋊C₄	—	43	1	no	—
922	C₄⋊C₄	—	43	1	no	—
923	C₄⋊C₄	—	43	1	no	—
924	C₄⋊C₄	—	43	1	no	—
925	C₄⋊C₄	—	43	2	no	—
926	C₄⋊C₄	—	43	2	no	—
927	C₄⋊C₄	—	86	2	no	—
928	C₄⋊C₄	—	86	2	no	—
929	C₄⋊C₄	—	86	2	no	—
930	C₄⋊C₄	—	86	2	no	—
931	C₄⋊C₄	—	86	2	no	—
932	C₄⋊C₄	—	86	2	no	—
933	C₄⋊C₄	—	86	2	no	—
934	C₄⋊C₄	—	86	2	no	—
935	C₄⋊C₄	—	86	2	no	—
936	C₄⋊C₄	—	86	2	no	—
937	C₄⋊C₄	—	86	2	no	—
938	C₄⋊C₄	—	86	2	no	—
939	C₄⋊C₄	—	86	2	no	—
940	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
941	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
942	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
943	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	2	2	no	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	43	1	no	—
950	C₂²⋊C₄	—	43	1	no	—
951	C₂²⋊C₄	—	43	1	no	—
952	C₂²⋊C₄	—	43	1	no	—
953	C₂²⋊C₄	—	43	1	no	—
954	C₂²⋊C₄	—	43	1	no	—
955	C₂²⋊C₄	—	86	2	no	—
956	C₂²⋊C₄	—	86	2	no	—
957	C₂²⋊C₄	—	86	2	no	—
958	C₂²⋊C₄	—	86	2	no	—
959	C₂²⋊C₄	—	86	2	no	—
960	C₂²⋊C₄	—	86	2	no	—
961	C₂²⋊C₄	—	86	2	no	—
962	C₂²⋊C₄	—	86	2	no	—
963	C₂²⋊C₄	—	86	2	no	—
964	C₂²⋊C₄	—	86	2	no	—
965	C₂²⋊C₄	—	86	2	no	—
966	C₂²⋊C₄	—	86	2	no	—
967	C₂²⋊C₄	—	86	2	no	—
968	C₂²⋊C₄	D₄×D₄₃	1	1	yes	characteristic
969	C₂²⋊C₄	D₄×D₄₃	1	1	yes	characteristic
970	C₄²	—	2	2	no	—
971	C₄²	—	43	1	no	—
972	C₄²	—	43	1	no	—
973	C₄²	—	43	1	no	—
974	C₄²	—	43	1	no	—
975	C₄²	—	43	1	no	—
976	C₄²	—	43	1	no	—
977	C₄²	—	86	2	no	—
978	C₄²	—	86	2	no	—
979	C₄²	—	86	2	no	—
980	C₄²	—	86	2	no	—
981	C₄²	—	86	2	no	—
982	C₄²	C₂³×D₄₃	1	1	yes	characteristic
983	C₄²	C₂³×D₄₃	1	1	yes	characteristic
984	C₂³	—	2	2	no	—
985	C₂³	—	43	1	no	—
986	C₂³	—	43	1	no	—
987	C₂³	—	86	2	no	—
988	C₂³	—	86	2	no	—
989	C₂³	—	172	1	no	—
990	C₂³	—	172	1	no	—
991	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
992	Q₈	—	2	2	no	—
993	Q₈	—	2	2	no	—
994	Q₈	—	8	2	no	—
995	Q₈	—	86	2	no	—
996	Q₈	—	86	2	no	—
997	Q₈	—	344	2	no	—
998	D₄	—	2	2	no	—
999	D₄	—	2	2	no	—
1000	D₄	—	8	2	no	—
1001	D₄	—	86	2	no	—
1002	D₄	—	86	2	no	—
1003	D₄	—	344	2	no	—
1004	D₄	—	344	2	no	—
1005	D₄	—	344	2	no	—
1006	D₄	—	344	2	no	—
1007	D₄	—	344	2	no	—
1008	D₄	—	172	4	no	—
1009	D₄	—	172	4	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	2	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	2	no	—
1015	C₂×C₄	—	8	2	no	—
1016	C₂×C₄	—	43	1	no	—
1017	C₂×C₄	—	43	2	no	—
1018	C₂×C₄	—	43	2	no	—
1019	C₂×C₄	—	43	1	no	—
1020	C₂×C₄	—	43	1	no	—
1021	C₂×C₄	—	43	1	no	—
1022	C₂×C₄	—	43	1	no	—
1023	C₂×C₄	—	43	1	no	—
1024	C₂×C₄	—	86	2	no	—
1025	C₂×C₄	—	86	2	no	—
1026	C₂×C₄	—	86	2	no	—
1027	C₂×C₄	—	86	1	no	—
1028	C₂×C₄	—	86	1	no	—
1029	C₂×C₄	—	86	2	no	—
1030	C₂×C₄	—	86	2	no	—
1031	C₂×C₄	—	86	2	no	—
1032	C₂×C₄	—	344	2	no	—
1033	C₂×C₄	—	344	2	no	—
1034	C₂×C₄	—	344	2	no	—
1035	C₂×C₄	—	172	1	no	—
1036	C₂×C₄	—	172	1	no	—
1037	C₂×C₄	—	172	1	no	—
1038	C₂×C₄	—	172	1	no	—
1039	C₂×C₄	—	172	4	no	—
1040	C₂×C₄	—	172	4	no	—
1041	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1042	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1043	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1044	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1045	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1046	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1047	C₈	—	2	1	no	—
1048	C₈	—	2	1	no	—
1049	C₈	—	43	2	no	—
1050	C₈	—	43	2	no	—
1051	C₈	—	86	1	no	—
1052	C₈	—	86	1	no	—
1053	C₈	#41×D₄₃	1	2	yes	—
1054	C₈	#41×D₄₃	1	2	yes	—
1055	C₂²	—	2	1	no	—
1056	C₂²	—	2	1	no	—
1057	C₂²	—	2	1	no	—
1058	C₂²	—	4	2	no	—
1059	C₂²	—	4	2	no	—
1060	C₂²	—	4	2	no	—
1061	C₂²	—	43	2	no	—
1062	C₂²	—	86	1	no	—
1063	C₂²	—	86	1	no	—
1064	C₂²	—	86	1	no	—
1065	C₂²	—	86	1	no	—
1066	C₂²	—	86	1	no	—
1067	C₂²	—	172	4	no	—
1068	C₂²	—	172	2	no	—
1069	C₂²	—	172	2	no	—
1070	C₂²	—	172	2	no	—
1071	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1072	C₄	—	2	1	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	1	no	—
1075	C₄	—	2	1	no	—
1076	C₄	—	2	1	no	—
1077	C₄	—	4	2	no	—
1078	C₄	—	4	2	no	—
1079	C₄	—	4	2	no	—
1080	C₄	—	43	2	no	—
1081	C₄	—	86	1	no	—
1082	C₄	—	86	1	no	—
1083	C₄	—	86	1	no	—
1084	C₄	—	86	1	no	—
1085	C₄	—	86	1	no	—
1086	C₄	—	172	2	no	—
1087	C₄	—	172	2	no	—
1088	C₄	—	172	2	no	—
1089	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1090	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1091	C₂	—	4	1	no	—
1092	C₂	—	8	2	no	—
1093	C₂	—	86	2	no	—
1094	C₂	—	344	2	no	—
1095	C₂	—	172	1	no	—
1096	C₂	#532×D₄₃	1	1	yes	characteristic
1097	C₂	#19149363	1	1	yes	characteristic
1098	C₂	#19149365	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×#3175	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3175	D₄₃
hypocenter	C₄₃	#60682
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3175

Complements

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

N	H ≅ G/N	type
1. #19147982	C₂	semidirect
2. #19145250	C₂	semidirect
3. #19145247	C₂	semidirect
4. #19145241	C₂	semidirect
5. #19145238	C₂	semidirect
6. #19145237	C₂	semidirect
7. #19145234	C₂	semidirect
8. #19145231	C₂	semidirect
9. #19145221	C₂	semidirect
10. #19145218	C₂	semidirect
11. #19145211	C₂	semidirect
12. #19145206	C₂	semidirect
13. #19145106	C₂	semidirect
14. #19145020	C₂	semidirect
15. #19144937	C₂	semidirect
16. #19144199	C₂	semidirect
17. #19144178	C₂	semidirect
18. #19144174	C₂	semidirect
19. #19143390	C₂	semidirect
20. C₄×#13063348	C₂	semidirect
21. C₄×#13063344	C₂	semidirect
22. #405×D₄₃	C₂	semidirect
23. C₄₃×#3175	C₂	semidirect
51. #14583304	C₂²	semidirect
52. #14583300	C₂²	semidirect
53. #14583300	C₂²	semidirect
54. #14583300	C₂²	semidirect
55. #14583295	C₂²	semidirect
56. #14583283	C₂²	semidirect
57. #14583281	C₂²	semidirect
58. #14583277	C₂²	semidirect
59. #14583274	C₂²	semidirect
60. #14583270	C₂²	semidirect
61. #14583266	C₂²	semidirect
62. #14583266	C₂²	semidirect
63. #14583262	C₂²	semidirect
64. #14583262	C₂²	semidirect
65. #14583261	C₂²	semidirect
66. #14583259	C₂²	semidirect
67. #14583258	C₂²	semidirect
85. #14583009	C₂²	semidirect
86. #14583008	C₂²	semidirect
87. #14583004	C₂²	semidirect
88. #14583003	C₂²	semidirect
89. #14583001	C₂²	semidirect
90. #14583000	C₂²	semidirect
91. #14582998	C₂²	semidirect
92. C₄×Dic₁₇₂	C₂²	semidirect
93. Q₁₆×Dic₄₃	C₂²	semidirect
94. #14582993	C₂²	semidirect
95. #14582990	C₂²	semidirect
96. C₄×#10621884	C₂²	semidirect
97. C₄×#10621883	C₂²	semidirect
98. #14582984	C₂²	semidirect
99. C₄×D₃₄₄	C₂²	semidirect
100. D₈×Dic₄₃	C₂²	semidirect
101. #14582981	C₂²	semidirect
121. C₄₃×#500	C₂²	semidirect
122. C₄₃×#495	C₂²	semidirect
123. C₄₃×#489	C₂²	semidirect
127. C₄₃×#440	C₂²	semidirect
128. C₄×Q₁₆×C₄₃	C₂²	semidirect
129. C₄×D₈×C₄₃	C₂²	semidirect
550. #3175	D₄₃	semidirect
602. #500	C₂×D₄₃	semidirect
609. #495	C₂×D₄₃	semidirect
620. #489	C₂×D₄₃	semidirect
648. #440	C₂×D₄₃	semidirect
652. C₄×Q₁₆	C₂×D₄₃	semidirect
660. C₄×D₈	C₂×D₄₃	semidirect
680. C₄₃	#60682	semidirect

Maximal subgroups

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

subgroup	index
#19147982	2
#19145250	2
#19145247	2
#19145241	2
#19145238	2
#19145237	2
#19145234	2
#19145231	2
#19145221	2
#19145218	2
#19145211	2
#19145206	2
#19145106	2
#19145020	2
#19144937	2
#19144199	2
#19144178	2
#19144174	2
#19143390	2
C₄×#13063348	2
C₄×#13063344	2
#405×D₄₃	2
C₄₃×#3175	2
#60682	43