Subgroups — #25979076

Order 11008.

1900 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	#19148546	C₂	1	2	yes	maximal, complemented
2	#19147607	C₂	1	1	yes	maximal, characteristic, complemented
3	D₈×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147388	C₂	1	2	yes	maximal, complemented
5	#19147023	C₂	1	1	yes	maximal, characteristic, complemented
6	#19147019	C₂	1	1	yes	maximal, characteristic, complemented
7	#19147015	C₂	1	1	yes	maximal, characteristic, complemented
8	#19146822	C₂	1	2	yes	maximal, complemented
9	#19146756	C₂	1	2	yes	maximal, complemented
10	#19146752	C₂	1	2	yes	maximal, complemented
11	#19146281	C₂	1	1	yes	maximal, characteristic, complemented
12	#19146280	C₂	1	1	yes	maximal, characteristic, complemented
13	D₈×C₂²⋊D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
14	#19145234	C₂	1	1	yes	maximal, characteristic, complemented
15	#19145230	C₂	1	1	yes	maximal, characteristic, complemented
16	#19145171	C₂	1	1	yes	maximal, characteristic, complemented
17	#19144779	C₂	1	2	yes	maximal, complemented
18	#19144777	C₂	1	2	yes	maximal, complemented
19	#19144742	C₂	1	2	yes	maximal, complemented
20	#19143566	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143442	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#13063344	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#2948	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063344	C₂²	1	1	yes	characteristic
25	C₂×D₈×D₄₃	C₂²	1	1	yes	characteristic
26	#14583632	C₂²	1	2	yes	complemented
27	#14583617	C₂²	1	2	yes	—
28	#14583614	C₂²	1	2	yes	complemented
29	#14583612	C₂²	1	2	yes	complemented
30	#14583578	—	2	2	no	—
31	#14583575	—	2	2	no	—
32	D₄×Dic₈₆	C₂²	1	2	yes	complemented
33	#14583558	—	2	2	no	—
34	#14583544	C₂²	1	2	yes	complemented
35	#14583543	C₂²	1	2	yes	complemented
36	#14583539	—	2	2	no	—
37	D₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
38	#14583520	C₂²	1	2	yes	complemented
39	#14583514	C₂²	1	2	yes	complemented
40	#14583487	—	2	2	no	—
41	#14583482	—	2	2	no	—
42	#14583446	C₂²	1	2	yes	complemented
43	#14583429	—	2	2	no	—
44	#14583427	C₂²	1	1	yes	characteristic
45	C₂×#13063311	—	2	2	no	—
46	#14583371	C₂²	1	2	yes	complemented
47	C₄×#10621900	C₂²	1	2	yes	complemented
48	#14583304	C₂²	1	1	yes	characteristic, complemented
49	#14583303	C₂²	1	1	yes	characteristic, complemented
50	#14583303	C₂²	1	1	yes	characteristic, complemented
51	#14583283	C₂²	1	1	yes	characteristic, complemented
52	#14583282	C₂²	1	1	yes	characteristic, complemented
53	#14583274	C₂²	1	1	yes	characteristic
54	#14583259	C₂²	1	2	yes	complemented
55	#14583257	C₂²	1	2	yes	complemented
56	#14583244	C₂²	1	2	yes	complemented
57	#14583243	C₂²	1	2	yes	complemented
58	#14583240	C₂²	1	2	yes	complemented
59	#14583225	C₂²	1	2	yes	complemented
60	#14583223	C₂²	1	2	yes	complemented
61	#14583221	C₂²	1	2	yes	complemented
62	#14583221	C₂²	1	2	yes	complemented
63	#14583189	C₂²	1	2	yes	complemented
64	#14583188	C₂²	1	2	yes	complemented
65	#14583183	C₂²	1	2	yes	complemented
66	#14583179	C₂²	1	2	yes	complemented
67	#14583177	C₂²	1	2	yes	complemented
68	#14583177	C₂²	1	2	yes	complemented
69	#14583145	C₂²	1	2	yes	complemented
70	#14583144	C₂²	1	2	yes	complemented
71	#14583141	C₂²	1	1	yes	characteristic, complemented
72	#14583140	C₂²	1	1	yes	characteristic, complemented
73	#14583136	C₂²	1	1	yes	characteristic, complemented
74	#14583135	C₂²	1	1	yes	characteristic
75	#14583134	C₂²	1	2	yes	complemented
76	#14583132	C₂²	1	1	yes	characteristic
77	#14583132	C₂²	1	1	yes	characteristic, complemented
78	#14583114	C₂²	1	2	yes	complemented
79	#14583114	C₂²	1	2	yes	complemented
80	#14583113	C₂²	1	2	yes	complemented
81	#14583112	C₂²	1	2	yes	complemented
82	#14583098	C₂²	1	2	yes	complemented
83	#14583092	C₂²	1	2	yes	—
84	#14583051	C₂²	1	2	yes	complemented
85	#14583050	C₂²	1	2	yes	complemented
86	#14583045	C₂²	1	2	yes	complemented
87	#14583041	C₂²	1	2	yes	complemented
88	#14583033	C₂²	1	2	yes	—
89	#14583031	C₂²	1	2	yes	—
90	#14583027	C₂²	1	1	yes	characteristic, complemented
91	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
92	#14583009	C₂²	1	2	yes	complemented
93	#14583008	C₂²	1	2	yes	complemented
94	#14583001	C₂²	1	2	yes	complemented
95	#14582999	C₂²	1	2	yes	complemented
96	C₄×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
97	#14582993	C₂²	1	1	yes	characteristic, complemented
98	#14582990	C₂²	1	2	yes	complemented
99	C₄×#10621883	C₂²	1	2	yes	complemented
100	C₄×D₃₄₄	C₂²	1	1	yes	characteristic, complemented
101	D₈×Dic₄₃	C₂²	1	1	yes	characteristic
102	D₈×Dic₄₃	C₂²	1	1	yes	characteristic
103	#14582981	C₂²	1	1	yes	characteristic, complemented
104	C₄×#10621882	C₂²	1	2	yes	complemented
105	#14582975	C₂²	1	1	yes	characteristic
106	#14582972	C₂²	1	1	yes	characteristic, complemented
107	#14582968	C₂²	1	1	yes	characteristic, complemented
108	C₈×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
109	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
110	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic, complemented
111	#14582961	C₂²	1	1	yes	characteristic, complemented
112	#14582960	C₂²	1	1	yes	characteristic, complemented
113	#14582954	C₂²	1	1	yes	characteristic, complemented
114	#14582936	C₂²	1	1	yes	characteristic, complemented
115	#14582936	C₂²	1	1	yes	characteristic, complemented
116	#14582902	C₂²	1	2	yes	complemented
117	#14582892	C₂²	1	2	yes	complemented
118	#14582853	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic, complemented
120	C₂²×D₈×C₄₃	C₂²	1	1	yes	characteristic
121	C₄₃×#518	C₂²	1	2	yes	complemented
122	C₄₃×#442	C₂²	1	2	yes	complemented
123	C₄₃×#442	C₂²	1	2	yes	complemented
124	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
125	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
126	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
127	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
128	C₄₃×#427	C₂²	1	1	yes	characteristic, complemented
129	C₄₃×#418	C₂²	1	2	yes	complemented
130	C₄₃×#405	C₂²	1	1	yes	characteristic, complemented
131	C₂×#10621898	—	2	2	no	—
132	C₂×#10621900	C₂³	1	2	yes	—
133	C₂²×Dic₈₆	—	2	2	no	—
134	C₂²×C₂²⋊D₄₃	—	2	2	no	—
135	C₂×D₄×D₄₃	C₂³	1	2	yes	—
136	#13063344	—	2	4	no	—
137	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
138	C₂×#10621873	C₂³	1	2	yes	—
139	C₂×#10621883	C₂³	1	2	yes	—
140	C₂×#10621883	C₂³	1	2	yes	—
141	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
142	C₂×#10621882	C₂³	1	2	yes	—
143	C₂×#10621882	C₂³	1	2	yes	—
144	D₈×D₄₃	—	2	4	no	—
145	C₂×#10621872	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	#13063325	C₂³	1	2	yes	—
150	#13063324	C₂³	1	2	yes	—
151	#13063324	C₂³	1	2	yes	—
152	#13063321	C₂³	1	2	yes	—
153	#13063320	—	2	2	no	—
154	#13063320	D₄	1	1	yes	characteristic
155	#13063319	—	2	2	no	—
156	#13063318	—	2	2	no	—
157	#13063318	—	2	2	no	—
158	#13063318	D₄	1	1	yes	characteristic
159	#13063315	D₄	1	1	yes	characteristic
160	#13063313	—	2	2	no	—
161	#13063313	C₂³	1	2	yes	—
162	#13063312	C₂³	1	2	yes	—
163	#13063311	—	2	2	no	—
164	#13063311	—	2	2	no	—
165	#13063311	—	2	2	no	—
166	#13063311	—	2	2	no	—
167	#13063311	—	2	2	no	—
168	#13063311	—	2	2	no	—
169	#13063311	—	2	2	no	—
170	#13063311	—	2	2	no	—
171	#13063311	D₄	1	1	yes	characteristic
172	#13063310	D₄	1	1	yes	characteristic
173	#13063309	—	2	2	no	—
174	#13063308	—	2	2	no	—
175	#13063308	—	2	2	no	—
176	#13063307	—	2	2	no	—
177	#13063307	—	2	2	no	—
178	#13063307	D₄	1	1	yes	characteristic
179	#13063306	—	2	2	no	—
180	#13063305	C₂³	1	2	yes	—
181	#13063304	—	2	2	no	—
182	#13063304	—	2	2	no	—
183	#13063304	C₂³	1	2	yes	—
184	#13063303	—	2	2	no	—
185	#13063303	D₄	1	1	yes	characteristic
186	#13063302	—	2	2	no	—
187	#13063302	—	2	2	no	—
188	#13063300	C₂³	1	2	yes	—
189	#13063299	—	2	2	no	—
190	#13063299	—	2	2	no	—
191	#13063299	C₂³	1	2	yes	—
192	#13063298	—	2	2	no	—
193	#13063298	—	2	2	no	—
194	#13063298	D₄	1	1	yes	characteristic
195	#13063297	—	2	2	no	—
196	#13063297	—	2	2	no	—
197	#13063296	C₂³	1	2	yes	—
198	#13063296	C₂³	1	2	yes	—
199	#13063295	—	2	2	no	—
200	#13063294	—	2	2	no	—
201	#13063294	—	2	2	no	—
202	#13063293	—	2	2	no	—
203	C₄×Dic₈₆	—	2	2	no	—
204	C₄×Dic₈₆	C₂³	1	2	yes	—
205	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
206	#13063290	C₂³	1	2	yes	—
207	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
208	C₄×D₁₇₂	C₂³	1	2	yes	—
209	D₄×Dic₄₃	C₂³	1	2	yes	—
210	D₄×Dic₄₃	C₂³	1	2	yes	—
211	#13063287	C₂³	1	2	yes	—
212	C₄×C₂²⋊D₄₃	—	2	2	no	—
213	C₄×C₂²⋊D₄₃	—	2	2	no	—
214	C₄×C₂²⋊D₄₃	—	2	2	no	—
215	C₄×C₂²⋊D₄₃	—	2	2	no	—
216	C₄×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
217	C₄×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
218	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
219	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
220	#13063284	—	2	2	no	—
221	#13063283	C₂³	1	2	yes	—
222	#13063283	C₂³	1	2	yes	—
223	#13063282	—	2	2	no	—
224	#13063282	C₂³	1	1	yes	characteristic
225	#13063281	—	2	2	no	—
226	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
227	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
228	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
229	C₂²⋊C₄×D₄₃	—	2	2	no	—
230	C₂×C₄×Dic₄₃	—	2	2	no	—
231	C₄²×D₄₃	C₂³	1	1	yes	characteristic
232	#13063259	C₂³	1	1	yes	characteristic
233	#13063259	C₂³	1	1	yes	characteristic
234	#13063259	C₂³	1	2	yes	—
235	#13063258	C₂³	1	2	yes	—
236	#13063258	C₂³	1	2	yes	—
237	#13063256	C₂³	1	2	yes	—
238	#13063256	C₂³	1	2	yes	—
239	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
240	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
241	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
242	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
243	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
244	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
245	#13063250	C₂³	1	2	yes	—
246	#13063250	C₂³	1	2	yes	—
247	#13063248	C₂³	1	2	yes	—
248	#13063248	C₂³	1	2	yes	—
249	#13063247	C₂³	1	2	yes	—
250	#13063247	C₂³	1	2	yes	—
251	#13063246	C₂³	1	2	yes	—
252	#13063246	C₂³	1	2	yes	—
253	#13063246	C₂³	1	2	yes	—
254	#13063246	C₂³	1	2	yes	—
255	#13063245	C₂³	1	2	yes	—
256	#13063245	C₂³	1	2	yes	—
257	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
258	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
259	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
260	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
261	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
262	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
263	#13063236	C₂³	1	1	yes	characteristic
264	#13063235	C₂³	1	1	yes	characteristic
265	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
266	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
267	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
268	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
269	C₂²×D₄×C₄₃	C₂³	1	2	yes	—
270	C₂×D₈×C₄₃	—	2	4	no	—
271	C₂×D₈×C₄₃	C₂³	1	2	yes	—
272	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
273	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
274	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
275	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
276	C₄×D₄×C₄₃	—	2	2	no	—
277	C₄×D₄×C₄₃	—	2	2	no	—
278	C₄×D₄×C₄₃	C₂³	1	2	yes	—
279	C₄×D₄×C₄₃	C₂³	1	2	yes	—
280	C₄×D₄×C₄₃	C₂³	1	2	yes	—
281	C₄×D₄×C₄₃	C₂³	1	2	yes	—
282	#117×C₄₃	C₂³	1	2	yes	—
283	#117×C₄₃	C₂³	1	1	yes	characteristic
284	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
285	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
286	#107×C₄₃	C₂³	1	1	yes	characteristic
287	#107×C₄₃	C₂³	1	1	yes	characteristic
288	#106×C₄₃	C₂³	1	2	yes	—
289	#102×C₄₃	C₂³	1	2	yes	—
290	#102×C₄₃	C₂³	1	2	yes	—
291	#102×C₄₃	C₂³	1	2	yes	—
292	#102×C₄₃	C₂³	1	2	yes	—
293	#97×C₄₃	C₂³	1	1	yes	characteristic
294	#97×C₄₃	C₂³	1	1	yes	characteristic
295	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
297	C₂⁴×C₄₃	—	2	2	no	—
298	C₂³×D₄₃	—	2	2	no	—
299	C₂×D₄×C₄₃	—	2	2	no	—
300	C₂×D₄×C₄₃	—	2	4	no	—
301	C₂×D₄×C₄₃	—	4	2	no	—
302	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
303	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₄₃	—	2	2	no	—
305	C₂²×C₄×C₄₃	—	2	2	no	—
306	C₂²×C₄×C₄₃	—	2	2	no	—
307	C₂²×C₄×C₄₃	—	2	2	no	—
308	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
309	C₂×C₂²⋊D₄₃	—	2	2	no	—
310	C₂×C₂²⋊D₄₃	—	2	2	no	—
311	C₂×C₂²⋊D₄₃	—	2	2	no	—
312	C₂×C₂²⋊D₄₃	—	2	2	no	—
313	C₂×C₂²⋊D₄₃	—	2	2	no	—
314	C₂×C₂²⋊D₄₃	—	2	2	no	—
315	C₂×C₂²⋊D₄₃	—	2	2	no	—
316	C₂×C₂²⋊D₄₃	—	8	4	no	—
317	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
318	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
319	C₂²×Dic₄₃	—	2	2	no	—
320	C₂²×Dic₄₃	—	2	2	no	—
321	C₂²×Dic₄₃	—	2	2	no	—
322	#10621900	—	2	4	no	—
323	#10621900	—	4	2	no	—
324	D₄×D₄₃	—	2	4	no	—
325	D₄×D₄₃	—	4	2	no	—
326	#10621898	—	8	4	no	—
327	C₂×D₁₇₂	—	2	2	no	—
328	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
329	C₂×D₁₇₂	C₂⁴	1	2	yes	—
330	C₂×C₄×D₄₃	—	2	2	no	—
331	C₂×C₄×D₄₃	—	2	2	no	—
332	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
333	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
334	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
335	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
336	C₂×Dic₈₆	—	2	2	no	—
337	C₂×Dic₈₆	—	2	2	no	—
338	C₂×Dic₈₆	—	2	2	no	—
339	C₂×Dic₈₆	—	8	4	no	—
340	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
341	C₂×Dic₈₆	C₂⁴	1	2	yes	—
342	D₈×C₄₃	—	2	4	no	—
343	D₈×C₄₃	—	2	2	no	—
344	D₈×C₄₃	#41	1	4	yes	complemented
345	M₁₆×C₄₃	—	4	1	no	—
346	C₂×C₈×C₄₃	—	2	2	no	—
347	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
348	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
349	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
350	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
351	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
352	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
353	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
354	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
355	C₂²⋊C₄×C₄₃	—	2	2	no	—
356	C₂²⋊C₄×C₄₃	—	2	2	no	—
357	C₂²⋊C₄×C₄₃	—	2	2	no	—
358	C₂²⋊C₄×C₄₃	—	2	2	no	—
359	C₂²⋊C₄×C₄₃	—	2	2	no	—
360	C₂²⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
361	C₂²⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
362	C₄²×C₄₃	—	2	2	no	—
363	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
364	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
365	C₂²⋊Dic₄₃	—	2	2	no	—
366	C₂²⋊Dic₄₃	—	2	2	no	—
367	C₂²⋊Dic₄₃	—	2	2	no	—
368	C₂²⋊Dic₄₃	—	2	2	no	—
369	C₂²⋊Dic₄₃	—	2	2	no	—
370	C₂²⋊Dic₄₃	—	2	2	no	—
371	C₂²⋊Dic₄₃	—	2	2	no	—
372	C₂²⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
373	C₂²⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
374	#10621883	—	2	4	no	—
375	#10621883	—	4	2	no	—
376	#10621882	—	2	4	no	—
377	#10621882	—	4	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	—	2	2	no	—
382	(C₂×D₄₃)⋊C₄	—	2	2	no	—
383	(C₂×D₄₃)⋊C₄	—	2	2	no	—
384	(C₂×D₄₃)⋊C₄	—	2	2	no	—
385	(C₂×D₄₃)⋊C₄	—	2	2	no	—
386	(C₂×D₄₃)⋊C₄	—	2	2	no	—
387	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
388	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
389	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
390	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
391	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
392	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
393	C₄⋊Dic₄₃	—	2	2	no	—
394	C₄⋊Dic₄₃	—	2	2	no	—
395	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
396	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
397	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
398	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
399	Dic₄₃⋊C₄	—	2	2	no	—
400	Dic₄₃⋊C₄	—	2	2	no	—
401	Dic₄₃⋊C₄	—	2	2	no	—
402	Dic₄₃⋊C₄	—	2	2	no	—
403	Dic₄₃⋊C₄	—	2	2	no	—
404	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
405	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
406	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
407	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
408	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
409	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
410	C₄×Dic₄₃	—	2	2	no	—
411	C₄×Dic₄₃	—	2	2	no	—
412	C₄×Dic₄₃	—	2	2	no	—
413	C₄×Dic₄₃	—	2	2	no	—
414	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
415	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
416	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
417	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
418	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
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	Dic₁₇₂	—	2	2	no	—
423	D₃₄₄	—	2	2	no	—
424	#10621873	—	4	2	no	—
425	#10621872	—	4	1	no	—
426	C₈×D₄₃	—	2	2	no	—
427	C₈×D₄₃	—	2	2	no	—
428	C₈×D₄₃	—	4	1	no	—
429	C₂³×C₄₃	—	2	2	no	—
430	C₂³×C₄₃	—	2	2	no	—
431	C₂³×C₄₃	—	4	4	no	—
432	C₂³×C₄₃	—	8	2	no	—
433	C₂³×C₄₃	—	8	2	no	—
434	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
435	C₂²×D₄₃	—	2	2	no	—
436	C₂²×D₄₃	—	4	4	no	—
437	C₂²×D₄₃	—	8	2	no	—
438	C₂²×D₄₃	—	8	2	no	—
439	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
440	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
441	D₄×C₄₃	—	2	2	no	—
442	D₄×C₄₃	—	2	2	no	—
443	D₄×C₄₃	—	2	2	no	—
444	D₄×C₄₃	—	4	4	no	—
445	D₄×C₄₃	C₂×#41	1	4	yes	—
446	C₂×C₄×C₄₃	—	2	1	no	—
447	C₂×C₄×C₄₃	—	2	1	no	—
448	C₂×C₄×C₄₃	—	2	2	no	—
449	C₂×C₄×C₄₃	—	2	2	no	—
450	C₂×C₄×C₄₃	—	8	2	no	—
451	C₂×C₄×C₄₃	—	8	2	no	—
452	C₂×C₄×C₄₃	—	8	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	—	2	2	no	—
461	C₂²⋊D₄₃	—	4	1	no	—
462	C₂²⋊D₄₃	—	4	4	no	—
463	C₂²⋊D₄₃	—	4	4	no	—
464	C₂²⋊D₄₃	—	4	4	no	—
465	C₂²⋊D₄₃	—	8	2	no	—
466	C₂²⋊D₄₃	—	8	2	no	—
467	C₂²⋊D₄₃	—	8	2	no	—
468	C₂²⋊D₄₃	—	8	2	no	—
469	C₂×Dic₄₃	—	2	2	no	—
470	C₂×Dic₄₃	—	2	2	no	—
471	C₂×Dic₄₃	—	2	2	no	—
472	C₂×Dic₄₃	—	4	4	no	—
473	C₂×Dic₄₃	—	4	4	no	—
474	C₂×Dic₄₃	—	8	2	no	—
475	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
476	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
477	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
478	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
479	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
480	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
481	D₁₇₂	—	2	2	no	—
482	D₁₇₂	—	2	2	no	—
483	D₁₇₂	—	4	1	no	—
484	D₁₇₂	—	8	2	no	—
485	C₄×D₄₃	—	2	1	no	—
486	C₄×D₄₃	—	2	1	no	—
487	C₄×D₄₃	—	2	1	no	—
488	C₄×D₄₃	—	2	1	no	—
489	C₄×D₄₃	—	2	2	no	—
490	C₄×D₄₃	—	4	1	no	—
491	C₄×D₄₃	—	8	2	no	—
492	C₄×D₄₃	—	8	2	no	—
493	Dic₈₆	—	2	2	no	—
494	Dic₈₆	—	2	2	no	—
495	Dic₈₆	—	2	2	no	—
496	Dic₈₆	—	4	4	no	—
497	Dic₈₆	—	8	2	no	—
498	Dic₈₆	—	8	2	no	—
499	C₈×C₄₃	—	2	1	no	—
500	C₈×C₄₃	—	2	1	no	—
501	C₈×C₄₃	—	2	1	no	—
502	C₈×C₄₃	C₂×#41	1	2	yes	—
503	C₄₃⋊C₈	—	2	1	no	—
504	C₄₃⋊C₈	—	2	1	no	—
505	C₄₃⋊C₈	—	2	1	no	—
506	C₄₃⋊C₈	—	2	1	no	—
507	#61475	—	43	1	no	maximal, Sylow
508	C₂²×C₄₃	—	2	1	no	—
509	C₂²×C₄₃	—	2	4	no	—
510	C₂²×C₄₃	—	2	1	no	—
511	C₂²×C₄₃	—	2	1	no	—
512	C₂²×C₄₃	—	4	2	no	—
513	C₂²×C₄₃	—	4	2	no	—
514	C₂²×C₄₃	—	4	2	no	—
515	C₂²×C₄₃	—	4	2	no	—
516	C₂²×C₄₃	—	4	2	no	—
517	C₂²×C₄₃	—	16	4	no	—
518	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
519	C₂×D₄₃	—	2	1	no	—
520	C₂×D₄₃	—	2	1	no	—
521	C₂×D₄₃	—	2	1	no	—
522	C₂×D₄₃	—	2	1	no	—
523	C₂×D₄₃	—	2	1	no	—
524	C₂×D₄₃	—	2	1	no	—
525	C₂×D₄₃	—	4	2	no	—
526	C₂×D₄₃	—	4	2	no	—
527	C₂×D₄₃	—	4	2	no	—
528	C₂×D₄₃	—	16	4	no	—
529	C₄×C₄₃	—	2	1	no	—
530	C₄×C₄₃	—	2	1	no	—
531	C₄×C₄₃	—	2	1	no	—
532	C₄×C₄₃	—	2	1	no	—
533	C₄×C₄₃	—	2	1	no	—
534	C₄×C₄₃	—	4	2	no	—
535	C₄×C₄₃	—	4	2	no	—
536	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
537	C₄×C₄₃	#585	1	1	yes	characteristic
538	Dic₄₃	—	2	1	no	—
539	Dic₄₃	—	2	1	no	—
540	Dic₄₃	—	2	1	no	—
541	Dic₄₃	—	2	1	no	—
542	Dic₄₃	—	2	1	no	—
543	Dic₄₃	—	4	2	no	—
544	Dic₄₃	—	4	2	no	—
545	Dic₄₃	—	4	2	no	—
546	Dic₄₃	#576	1	2	yes	—
547	#3514	—	43	2	no	—
548	#3396	—	43	1	no	—
549	Q₈×D₈	—	43	1	no	—
550	#3373	—	43	2	no	—
551	#3342	—	43	1	no	—
552	#3341	—	43	1	no	—
553	#3341	—	43	1	no	—
554	#3324	—	43	2	no	—
555	#3319	—	43	2	no	—
556	#3319	—	43	2	no	—
557	#3280	—	43	1	no	—
558	#3280	—	43	1	no	—
559	D₄×D₈	—	43	1	no	—
560	#3175	—	43	1	no	—
561	#3175	—	43	1	no	—
562	#3169	—	43	1	no	—
563	#3118	—	43	2	no	—
564	#3118	—	43	2	no	—
565	#3115	—	43	2	no	—
566	#2966	—	43	1	no	—
567	#2948	—	43	1	no	—
568	#2948	D₄₃	1	1	yes	characteristic, complemented
569	C₄×#135	—	43	1	no	—
570	C₂×C₄₃	—	4	4	no	—
571	C₂×C₄₃	—	4	1	no	—
572	C₂×C₄₃	—	8	2	no	—
573	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
574	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
575	C₂×C₄₃	#3584	1	1	yes	characteristic
576	D₄₃	—	4	1	no	—
577	D₄₃	—	4	1	no	—
578	D₄₃	—	8	2	no	—
579	C₂×#135	—	43	1	no	—
580	C₂²×D₈	—	43	1	no	—
581	C₂²×D₈	C₂×D₄₃	1	1	yes	characteristic
582	#559	—	43	2	no	—
583	#556	—	43	2	no	—
584	#555	—	43	2	no	—
585	#555	—	43	2	no	—
586	#551	—	86	2	no	—
587	#551	—	86	2	no	—
588	D₄×Q₈	—	43	2	no	—
589	#548	—	86	2	no	—
590	#546	—	43	2	no	—
591	#546	—	43	2	no	—
592	#546	—	86	2	no	—
593	D₄²	—	43	2	no	—
594	#542	—	43	2	no	—
595	#542	—	43	2	no	—
596	#538	—	86	2	no	—
597	#538	—	86	2	no	—
598	#532	—	43	2	no	—
599	#529	—	43	1	no	—
600	#529	—	86	2	no	—
601	C₂×#124	—	86	2	no	—
602	#518	—	43	2	no	—
603	#518	C₂×D₄₃	1	2	yes	complemented
604	C₄×#41	—	43	2	no	—
605	#500	—	43	1	no	—
606	#500	—	43	1	no	—
607	#500	—	43	1	no	—
608	#495	—	43	1	no	—
609	#495	—	43	1	no	—
610	#493	—	43	1	no	—
611	#489	—	43	2	no	—
612	#489	—	43	2	no	—
613	#486	—	43	2	no	—
614	#485	—	43	2	no	—
615	#485	—	43	2	no	—
616	#482	—	43	2	no	—
617	#482	—	43	2	no	—
618	#482	—	43	2	no	—
619	#482	—	43	2	no	—
620	#476	—	43	2	no	—
621	#476	—	43	2	no	—
622	#475	—	43	2	no	—
623	#474	—	43	2	no	—
624	#474	—	43	2	no	—
625	#474	—	43	2	no	—
626	#468	—	43	2	no	—
627	#468	—	43	2	no	—
628	#467	—	43	1	no	—
629	#467	—	43	1	no	—
630	#466	—	43	1	no	—
631	#466	—	43	1	no	—
632	#466	—	43	1	no	—
633	#466	—	43	1	no	—
634	#466	—	43	2	no	—
635	#463	—	43	2	no	—
636	#463	—	43	2	no	—
637	#463	—	43	2	no	—
638	#463	—	43	2	no	—
639	#460	—	43	2	no	—
640	#459	—	43	2	no	—
641	#450	—	43	2	no	—
642	#450	—	43	2	no	—
643	#449	—	43	2	no	—
644	#449	—	43	2	no	—
645	#447	—	43	2	no	—
646	#447	—	43	2	no	—
647	#446	—	43	1	no	—
648	C₈×Q₈	—	43	1	no	—
649	#442	—	43	2	no	—
650	#442	—	43	2	no	—
651	#442	C₂×D₄₃	1	2	yes	complemented
652	#442	C₂×D₄₃	1	2	yes	complemented
653	#440	—	43	2	no	—
654	#440	—	43	2	no	—
655	C₄×Q₁₆	—	43	1	no	—
656	C₄×Q₁₆	—	43	1	no	—
657	C₄×SD₁₆	—	43	2	no	—
658	C₄×SD₁₆	—	43	2	no	—
659	C₄×D₈	—	43	1	no	—
660	C₄×D₈	—	43	1	no	—
661	C₄×D₈	—	43	2	no	—
662	C₄×D₈	—	43	1	no	—
663	C₄×D₈	—	43	1	no	—
664	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
665	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
666	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic, complemented
667	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic, complemented
668	#436	—	43	1	no	—
669	#435	—	43	1	no	—
670	#435	—	43	1	no	—
671	C₈×D₄	—	43	1	no	—
672	C₈×D₄	—	43	1	no	—
673	C₈×D₄	—	43	1	no	—
674	#433	—	43	1	no	—
675	#433	—	43	1	no	—
676	#432	—	43	1	no	—
677	#427	—	43	1	no	—
678	#427	—	43	1	no	—
679	#427	C₂×D₄₃	1	1	yes	characteristic, complemented
680	#418	—	43	2	no	—
681	#418	C₂×D₄₃	1	2	yes	complemented
682	#416	—	43	2	no	—
683	#405	—	43	1	no	—
684	#405	C₂×D₄₃	1	1	yes	characteristic, complemented
685	C₂×C₄×C₈	—	43	1	no	—
686	C₄₃	#61475	1	1	yes	characteristic, complemented, Sylow
687	C₂×#41	—	43	2	no	—
688	C₂×#41	—	86	2	no	—
689	C₂²×Q₈	—	86	2	no	—
690	C₂²×D₄	—	43	2	no	—
691	C₂²×D₄	—	86	2	no	—
692	C₂²×D₄	C₂²×D₄₃	1	2	yes	—
693	#135	—	86	4	no	—
694	C₂×Q₁₆	—	43	1	no	—
695	C₂×SD₁₆	—	43	2	no	—
696	C₂×SD₁₆	—	43	2	no	—
697	C₂×SD₁₆	—	43	2	no	—
698	C₂×D₈	—	2	4	no	—
699	C₂×D₈	—	43	2	no	—
700	C₂×D₈	—	43	2	no	—
701	C₂×D₈	—	43	1	no	—
702	C₂×D₈	—	86	4	no	—
703	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
704	C₂×D₈	C₂²×D₄₃	1	2	yes	—
705	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
706	C₂×M₁₆	—	43	1	no	—
707	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
708	C₂²×C₈	—	43	1	no	—
709	C₂²×C₈	—	43	1	no	—
710	C₂²×C₈	—	43	1	no	—
711	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
712	C₄⋊Q₈	—	43	2	no	—
713	C₄⋊Q₈	—	43	2	no	—
714	C₄⋊Q₈	—	43	2	no	—
715	#127	—	43	2	no	—
716	#126	—	43	1	no	—
717	#126	—	43	1	no	—
718	#126	—	86	2	no	—
719	#126	—	86	2	no	—
720	#126	—	86	2	no	—
721	#126	—	86	2	no	—
722	#125	—	43	1	no	—
723	#124	—	43	1	no	—
724	#124	—	43	2	no	—
725	#124	—	43	2	no	—
726	#124	—	86	2	no	—
727	#124	—	86	2	no	—
728	#124	—	86	2	no	—
729	#124	—	86	2	no	—
730	#124	—	86	2	no	—
731	#124	—	86	2	no	—
732	#124	—	86	2	no	—
733	#124	—	86	2	no	—
734	#124	—	86	2	no	—
735	#123	—	43	1	no	—
736	#123	—	43	1	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	C₂²⋊Q₈	—	43	1	no	—
744	C₂²⋊Q₈	—	43	2	no	—
745	C₂²⋊Q₈	—	43	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	#121	—	43	1	no	—
752	#121	—	43	2	no	—
753	#121	—	43	2	no	—
754	#121	—	43	2	no	—
755	#121	—	43	2	no	—
756	#121	—	86	2	no	—
757	#121	—	86	2	no	—
758	#121	—	86	2	no	—
759	#121	—	86	2	no	—
760	#121	—	86	2	no	—
761	#121	—	86	2	no	—
762	#120	—	86	2	no	—
763	#120	—	86	2	no	—
764	#120	—	86	2	no	—
765	#120	—	86	2	no	—
766	C₄×Q₈	—	43	1	no	—
767	C₄×Q₈	—	43	2	no	—
768	C₄×Q₈	—	43	2	no	—
769	C₄×Q₈	—	86	2	no	—
770	C₄×D₄	—	2	2	no	—
771	C₄×D₄	—	2	2	no	—
772	C₄×D₄	—	43	1	no	—
773	C₄×D₄	—	43	1	no	—
774	C₄×D₄	—	43	2	no	—
775	C₄×D₄	—	43	2	no	—
776	C₄×D₄	—	43	2	no	—
777	C₄×D₄	—	43	1	no	—
778	C₄×D₄	—	43	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	C₂²×D₄₃	1	2	yes	—
786	C₄×D₄	C₂²×D₄₃	1	2	yes	—
787	C₄×D₄	C₂²×D₄₃	1	2	yes	—
788	C₄×D₄	C₂²×D₄₃	1	2	yes	—
789	#117	—	43	1	no	—
790	#117	—	43	2	no	—
791	#117	—	43	2	no	—
792	#117	—	86	2	no	—
793	#117	—	86	2	no	—
794	#117	—	86	2	no	—
795	#117	C₂²×D₄₃	1	2	yes	—
796	#117	C₂²×D₄₃	1	1	yes	characteristic
797	C₂×C₂²⋊C₄	—	2	2	no	—
798	C₂×C₂²⋊C₄	—	2	2	no	—
799	C₂×C₂²⋊C₄	—	86	2	no	—
800	C₂×C₂²⋊C₄	—	86	2	no	—
801	C₂×C₂²⋊C₄	—	86	2	no	—
802	C₂×C₂²⋊C₄	—	86	2	no	—
803	C₂×C₄²	—	43	1	no	—
804	C₂×C₄²	—	86	2	no	—
805	#107	—	43	1	no	—
806	#107	—	43	1	no	—
807	#107	—	43	2	no	—
808	#107	—	43	2	no	—
809	#107	—	43	2	no	—
810	#107	C₂²×D₄₃	1	1	yes	characteristic
811	#107	C₂²×D₄₃	1	1	yes	characteristic
812	#106	—	43	2	no	—
813	#106	—	43	2	no	—
814	#106	C₂²×D₄₃	1	2	yes	—
815	C₄⋊C₈	—	43	1	no	—
816	C₄⋊C₈	—	43	1	no	—
817	C₄⋊C₈	—	43	1	no	—
818	C₄⋊C₈	—	43	1	no	—
819	C₄⋊C₈	—	43	1	no	—
820	C₄⋊C₈	—	43	1	no	—
821	#103	—	43	2	no	—
822	#103	—	43	2	no	—
823	#103	—	43	2	no	—
824	#103	—	43	2	no	—
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	—	43	2	no	—
832	#102	—	43	2	no	—
833	#102	C₂²×D₄₃	1	2	yes	—
834	#102	C₂²×D₄₃	1	2	yes	—
835	#102	C₂²×D₄₃	1	2	yes	—
836	#102	C₂²×D₄₃	1	2	yes	—
837	C₂²⋊C₈	—	43	1	no	—
838	C₂²⋊C₈	—	43	1	no	—
839	C₂²⋊C₈	—	43	1	no	—
840	C₂²⋊C₈	—	43	1	no	—
841	C₂²⋊C₈	—	43	1	no	—
842	C₂²⋊C₈	—	43	1	no	—
843	#97	—	43	1	no	—
844	#97	—	43	1	no	—
845	#97	C₂²×D₄₃	1	1	yes	characteristic
846	#97	C₂²×D₄₃	1	1	yes	characteristic
847	C₄×C₈	—	43	1	no	—
848	C₄×C₈	—	43	1	no	—
849	C₄×C₈	—	43	1	no	—
850	C₄×C₈	—	43	1	no	—
851	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
852	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
853	C₂⁴	—	2	2	no	—
854	C₂⁴	—	86	2	no	—
855	#41	—	86	4	no	—
856	#41	—	344	4	no	—
857	#41	—	172	2	no	—
858	C₂×Q₈	—	43	1	no	—
859	C₂×Q₈	—	43	2	no	—
860	C₂×Q₈	—	86	2	no	—
861	C₂×Q₈	—	86	2	no	—
862	C₂×Q₈	—	86	2	no	—
863	C₂×Q₈	—	344	4	no	—
864	C₂×D₄	—	2	4	no	—
865	C₂×D₄	—	2	2	no	—
866	C₂×D₄	—	4	2	no	—
867	C₂×D₄	—	43	1	no	—
868	C₂×D₄	—	43	1	no	—
869	C₂×D₄	—	43	1	no	—
870	C₂×D₄	—	43	2	no	—
871	C₂×D₄	—	86	2	no	—
872	C₂×D₄	—	86	2	no	—
873	C₂×D₄	—	86	2	no	—
874	C₂×D₄	—	86	2	no	—
875	C₂×D₄	—	86	4	no	—
876	C₂×D₄	—	86	2	no	—
877	C₂×D₄	—	86	2	no	—
878	C₂×D₄	—	86	2	no	—
879	C₂×D₄	—	86	2	no	—
880	C₂×D₄	—	344	4	no	—
881	C₂×D₄	—	172	2	no	—
882	C₂×D₄	C₂³×D₄₃	1	2	yes	—
883	C₂×D₄	C₂³×D₄₃	1	2	yes	—
884	C₂²×C₄	—	2	2	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	2	2	no	—
887	C₂²×C₄	—	2	2	no	—
888	C₂²×C₄	—	43	1	no	—
889	C₂²×C₄	—	43	1	no	—
890	C₂²×C₄	—	43	1	no	—
891	C₂²×C₄	—	43	1	no	—
892	C₂²×C₄	—	86	2	no	—
893	C₂²×C₄	—	86	2	no	—
894	C₂²×C₄	—	86	2	no	—
895	C₂²×C₄	—	86	2	no	—
896	C₂²×C₄	—	86	2	no	—
897	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
898	Q₁₆	—	86	2	no	—
899	SD₁₆	—	86	4	no	—
900	SD₁₆	—	172	2	no	—
901	SD₁₆	—	172	2	no	—
902	D₈	—	2	4	no	—
903	D₈	—	2	2	no	—
904	D₈	—	86	4	no	—
905	D₈	—	86	2	no	—
906	D₈	—	172	2	no	—
907	D₈	#10621898	1	4	yes	complemented
908	M₁₆	—	4	1	no	—
909	M₁₆	—	172	1	no	—
910	C₂×C₈	—	2	2	no	—
911	C₂×C₈	—	43	1	no	—
912	C₂×C₈	—	43	1	no	—
913	C₂×C₈	—	43	1	no	—
914	C₂×C₈	—	43	1	no	—
915	C₂×C₈	—	86	2	no	—
916	C₂×C₈	—	86	2	no	—
917	C₂×C₈	—	172	1	no	—
918	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
919	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
920	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
921	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
922	C₄⋊C₄	—	43	1	no	—
923	C₄⋊C₄	—	43	1	no	—
924	C₄⋊C₄	—	43	1	no	—
925	C₄⋊C₄	—	43	1	no	—
926	C₄⋊C₄	—	43	1	no	—
927	C₄⋊C₄	—	43	1	no	—
928	C₄⋊C₄	—	43	1	no	—
929	C₄⋊C₄	—	43	1	no	—
930	C₄⋊C₄	—	43	2	no	—
931	C₄⋊C₄	—	43	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	D₄×D₄₃	1	1	yes	characteristic
940	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
941	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
942	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
943	C₂²⋊C₄	—	2	2	no	—
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	—	43	1	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	—	43	1	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	—	86	2	no	—
969	C₂²⋊C₄	—	86	2	no	—
970	C₂²⋊C₄	—	86	2	no	—
971	C₂²⋊C₄	—	86	2	no	—
972	C₂²⋊C₄	D₄×D₄₃	1	1	yes	characteristic
973	C₂²⋊C₄	D₄×D₄₃	1	1	yes	characteristic
974	C₄²	—	2	2	no	—
975	C₄²	—	43	1	no	—
976	C₄²	—	43	1	no	—
977	C₄²	—	43	1	no	—
978	C₄²	—	43	1	no	—
979	C₄²	—	86	2	no	—
980	C₄²	—	86	2	no	—
981	C₄²	—	86	2	no	—
982	C₄²	—	86	2	no	—
983	C₄²	C₂³×D₄₃	1	1	yes	characteristic
984	C₄²	C₂³×D₄₃	1	1	yes	characteristic
985	C₂³	—	2	2	no	—
986	C₂³	—	2	2	no	—
987	C₂³	—	4	4	no	—
988	C₂³	—	8	2	no	—
989	C₂³	—	8	2	no	—
990	C₂³	—	43	1	no	—
991	C₂³	—	43	1	no	—
992	C₂³	—	86	2	no	—
993	C₂³	—	344	2	no	—
994	C₂³	—	344	2	no	—
995	C₂³	—	172	4	no	—
996	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
997	Q₈	—	86	2	no	—
998	Q₈	—	86	2	no	—
999	Q₈	—	86	2	no	—
1000	Q₈	—	344	2	no	—
1001	Q₈	—	344	2	no	—
1002	Q₈	—	172	4	no	—
1003	D₄	—	2	2	no	—
1004	D₄	—	2	2	no	—
1005	D₄	—	2	2	no	—
1006	D₄	—	4	4	no	—
1007	D₄	—	86	2	no	—
1008	D₄	—	86	2	no	—
1009	D₄	—	86	2	no	—
1010	D₄	—	344	2	no	—
1011	D₄	—	344	2	no	—
1012	D₄	—	344	2	no	—
1013	D₄	—	344	2	no	—
1014	D₄	—	344	2	no	—
1015	D₄	—	172	1	no	—
1016	D₄	—	172	4	no	—
1017	D₄	—	172	1	no	—
1018	D₄	—	172	4	no	—
1019	D₄	—	172	4	no	—
1020	D₄	C₂×#10621898	1	4	yes	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	2	1	no	—
1023	C₂×C₄	—	2	2	no	—
1024	C₂×C₄	—	2	2	no	—
1025	C₂×C₄	—	8	2	no	—
1026	C₂×C₄	—	8	2	no	—
1027	C₂×C₄	—	8	2	no	—
1028	C₂×C₄	—	8	2	no	—
1029	C₂×C₄	—	43	1	no	—
1030	C₂×C₄	—	43	1	no	—
1031	C₂×C₄	—	43	1	no	—
1032	C₂×C₄	—	43	1	no	—
1033	C₂×C₄	—	43	1	no	—
1034	C₂×C₄	—	43	1	no	—
1035	C₂×C₄	—	86	2	no	—
1036	C₂×C₄	—	86	1	no	—
1037	C₂×C₄	—	86	1	no	—
1038	C₂×C₄	—	86	1	no	—
1039	C₂×C₄	—	86	1	no	—
1040	C₂×C₄	—	86	2	no	—
1041	C₂×C₄	—	86	2	no	—
1042	C₂×C₄	—	86	2	no	—
1043	C₂×C₄	—	344	2	no	—
1044	C₂×C₄	—	344	2	no	—
1045	C₂×C₄	—	344	2	no	—
1046	C₂×C₄	—	172	1	no	—
1047	C₂×C₄	—	172	4	no	—
1048	C₂×C₄	—	172	4	no	—
1049	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1050	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1051	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1052	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1053	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1054	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1055	C₈	—	2	1	no	—
1056	C₈	—	2	1	no	—
1057	C₈	—	2	1	no	—
1058	C₈	—	86	1	no	—
1059	C₈	—	86	1	no	—
1060	C₈	—	86	1	no	—
1061	C₈	—	86	1	no	—
1062	C₈	C₂×#10621898	1	2	yes	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	2	1	no	—
1065	C₂²	—	2	4	no	—
1066	C₂²	—	2	1	no	—
1067	C₂²	—	4	2	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	4	2	no	—
1070	C₂²	—	4	2	no	—
1071	C₂²	—	4	2	no	—
1072	C₂²	—	16	4	no	—
1073	C₂²	—	86	1	no	—
1074	C₂²	—	86	1	no	—
1075	C₂²	—	86	1	no	—
1076	C₂²	—	86	1	no	—
1077	C₂²	—	86	1	no	—
1078	C₂²	—	86	1	no	—
1079	C₂²	—	172	2	no	—
1080	C₂²	—	172	2	no	—
1081	C₂²	—	172	2	no	—
1082	C₂²	—	688	4	no	—
1083	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1084	C₄	—	2	1	no	—
1085	C₄	—	2	1	no	—
1086	C₄	—	2	1	no	—
1087	C₄	—	2	1	no	—
1088	C₄	—	2	1	no	—
1089	C₄	—	4	2	no	—
1090	C₄	—	4	2	no	—
1091	C₄	—	43	2	no	—
1092	C₄	—	86	1	no	—
1093	C₄	—	86	1	no	—
1094	C₄	—	86	1	no	—
1095	C₄	—	86	1	no	—
1096	C₄	—	86	1	no	—
1097	C₄	—	172	2	no	—
1098	C₄	—	172	2	no	—
1099	C₄	—	172	2	no	—
1100	C₄	C₂²×#10621898	1	1	yes	characteristic
1101	C₄	#14583735	1	1	yes	characteristic
1102	C₂	—	4	1	no	—
1103	C₂	—	4	4	no	—
1104	C₂	—	8	2	no	—
1105	C₂	—	344	2	no	—
1106	C₂	—	172	1	no	—
1107	C₂	—	172	1	no	—
1108	C₂	D₄×#10621898	1	1	yes	characteristic
1109	C₂	#576×D₄₃	1	1	yes	characteristic
1110	C₂	#19149363	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×#2948	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#2948	D₄₃
hypocenter	C₄₃	#61475
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #2948

Complements

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

N	H ≅ G/N	type
1. #19148546	C₂	semidirect
2. #19147607	C₂	semidirect
3. D₈×Dic₈₆	C₂	semidirect
4. #19147388	C₂	semidirect
5. #19147023	C₂	semidirect
6. #19147019	C₂	semidirect
7. #19147015	C₂	semidirect
8. #19146822	C₂	semidirect
9. #19146756	C₂	semidirect
10. #19146752	C₂	semidirect
11. #19146281	C₂	semidirect
12. #19146280	C₂	semidirect
13. D₈×C₂²⋊D₄₃	C₂	semidirect
14. #19145234	C₂	semidirect
15. #19145230	C₂	semidirect
16. #19145171	C₂	semidirect
17. #19144779	C₂	semidirect
18. #19144777	C₂	semidirect
19. #19144742	C₂	semidirect
20. #19143566	C₂	semidirect
21. #19143442	C₂	semidirect
22. C₄×#13063344	C₂	semidirect
23. C₄₃×#2948	C₂	semidirect
26. #14583632	C₂²	semidirect
28. #14583614	C₂²	semidirect
29. #14583612	C₂²	semidirect
32. D₄×Dic₈₆	C₂²	semidirect
34. #14583544	C₂²	semidirect
35. #14583543	C₂²	semidirect
38. #14583520	C₂²	semidirect
39. #14583514	C₂²	semidirect
42. #14583446	C₂²	semidirect
46. #14583371	C₂²	semidirect
47. C₄×#10621900	C₂²	semidirect
48. #14583304	C₂²	semidirect
49. #14583303	C₂²	semidirect
50. #14583303	C₂²	semidirect
51. #14583283	C₂²	semidirect
52. #14583282	C₂²	semidirect
54. #14583259	C₂²	semidirect
55. #14583257	C₂²	semidirect
56. #14583244	C₂²	semidirect
57. #14583243	C₂²	semidirect
58. #14583240	C₂²	semidirect
59. #14583225	C₂²	semidirect
60. #14583223	C₂²	semidirect
61. #14583221	C₂²	semidirect
62. #14583221	C₂²	semidirect
63. #14583189	C₂²	semidirect
64. #14583188	C₂²	semidirect
65. #14583183	C₂²	semidirect
66. #14583179	C₂²	semidirect
67. #14583177	C₂²	semidirect
68. #14583177	C₂²	semidirect
69. #14583145	C₂²	semidirect
70. #14583144	C₂²	semidirect
71. #14583141	C₂²	semidirect
72. #14583140	C₂²	semidirect
73. #14583136	C₂²	semidirect
75. #14583134	C₂²	semidirect
77. #14583132	C₂²	semidirect
78. #14583114	C₂²	semidirect
79. #14583114	C₂²	semidirect
80. #14583113	C₂²	semidirect
81. #14583112	C₂²	semidirect
82. #14583098	C₂²	semidirect
84. #14583051	C₂²	semidirect
85. #14583050	C₂²	semidirect
86. #14583045	C₂²	semidirect
87. #14583041	C₂²	semidirect
90. #14583027	C₂²	semidirect
91. C₈×Dic₈₆	C₂²	semidirect
92. #14583009	C₂²	semidirect
93. #14583008	C₂²	semidirect
94. #14583001	C₂²	semidirect
95. #14582999	C₂²	semidirect
96. C₄×Dic₁₇₂	C₂²	semidirect
97. #14582993	C₂²	semidirect
98. #14582990	C₂²	semidirect
99. C₄×#10621883	C₂²	semidirect
100. C₄×D₃₄₄	C₂²	semidirect
103. #14582981	C₂²	semidirect
104. C₄×#10621882	C₂²	semidirect
106. #14582972	C₂²	semidirect
107. #14582968	C₂²	semidirect
108. C₈×D₁₇₂	C₂²	semidirect
110. C₈×C₂²⋊D₄₃	C₂²	semidirect
111. #14582961	C₂²	semidirect
112. #14582960	C₂²	semidirect
113. #14582954	C₂²	semidirect
114. #14582936	C₂²	semidirect
115. #14582936	C₂²	semidirect
116. #14582902	C₂²	semidirect
117. #14582892	C₂²	semidirect
118. #14582853	C₂²	semidirect
119. C₄×C₈×D₄₃	C₂²	semidirect
121. C₄₃×#518	C₂²	semidirect
122. C₄₃×#442	C₂²	semidirect
123. C₄₃×#442	C₂²	semidirect
126. C₄×D₈×C₄₃	C₂²	semidirect
127. C₄×D₈×C₄₃	C₂²	semidirect
128. C₄₃×#427	C₂²	semidirect
129. C₄₃×#418	C₂²	semidirect
130. C₄₃×#405	C₂²	semidirect
344. D₈×C₄₃	#41	semidirect
568. #2948	D₄₃	semidirect
603. #518	C₂×D₄₃	semidirect
651. #442	C₂×D₄₃	semidirect
652. #442	C₂×D₄₃	semidirect
666. C₄×D₈	C₂×D₄₃	semidirect
667. C₄×D₈	C₂×D₄₃	semidirect
679. #427	C₂×D₄₃	semidirect
681. #418	C₂×D₄₃	semidirect
684. #405	C₂×D₄₃	semidirect
686. C₄₃	#61475	semidirect
907. D₈	#10621898	semidirect

Maximal subgroups

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

subgroup	index
#19148546	2
#19147607	2
D₈×Dic₈₆	2
#19147388	2
#19147023	2
#19147019	2
#19147015	2
#19146822	2
#19146756	2
#19146752	2
#19146281	2
#19146280	2
D₈×C₂²⋊D₄₃	2
#19145234	2
#19145230	2
#19145171	2
#19144779	2
#19144777	2
#19144742	2
#19143566	2
#19143442	2
C₄×#13063344	2
C₄₃×#2948	2
#61475	43