Subgroups — #25978979

Order 11008.

1910 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	#19148534	C₂	1	2	yes	maximal, complemented
2	#19147463	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147342	C₂	1	2	yes	maximal, complemented
4	#19146999	C₂	1	1	yes	maximal, characteristic, complemented
5	#19146965	C₂	1	1	yes	maximal, characteristic, complemented
6	#19146944	C₂	1	1	yes	maximal, characteristic, complemented
7	#19146803	C₂	1	2	yes	maximal, complemented
8	#19146623	C₂	1	2	yes	maximal, complemented
9	#19146563	C₂	1	2	yes	maximal, complemented
10	#19146279	C₂	1	1	yes	maximal, characteristic, complemented
11	#19146279	C₂	1	1	yes	maximal, characteristic, complemented
12	#19146270	C₂	1	1	yes	maximal, characteristic, complemented
13	#19145242	C₂	1	1	yes	maximal, characteristic, complemented
14	#19145231	C₂	1	1	yes	maximal, characteristic, complemented
15	#19145162	C₂	1	1	yes	maximal, characteristic, complemented
16	#19144793	C₂	1	2	yes	maximal, complemented
17	#19144778	C₂	1	2	yes	maximal, complemented
18	#19144732	C₂	1	2	yes	maximal, complemented
19	#19143572	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143470	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143442	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₈×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3396	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063348	C₂²	1	1	yes	characteristic
25	C₂×D₈×D₄₃	C₂²	1	1	yes	characteristic
26	C₂×D₈×D₄₃	C₂²	1	1	yes	characteristic
27	#14583609	C₂²	1	2	yes	complemented
28	#14583599	C₂²	1	2	yes	complemented
29	#14583594	—	2	2	no	—
30	#14583590	C₂²	1	2	yes	—
31	#14583579	—	2	2	no	—
32	#14583578	—	2	2	no	—
33	#14583554	C₂²	1	2	yes	complemented
34	#14583542	C₂²	1	2	yes	complemented
35	#14583542	C₂²	1	2	yes	complemented
36	#14583541	—	2	2	no	—
37	#14583534	C₂²	1	2	yes	—
38	#14583518	C₂²	1	2	yes	complemented
39	#14583503	C₂²	1	2	yes	complemented
40	#14583492	—	2	2	no	—
41	#14583483	—	2	2	no	—
42	#14583436	C₂²	1	1	yes	characteristic
43	#14583428	C₂²	1	2	yes	complemented
44	#14583408	—	2	2	no	—
45	#123×D₄₃	—	2	2	no	—
46	#14583381	C₂²	1	2	yes	complemented
47	#14583371	C₂²	1	2	yes	complemented
48	C₄×D₄×D₄₃	C₂²	1	2	yes	complemented
49	#14583304	C₂²	1	1	yes	characteristic, complemented
50	#14583301	C₂²	1	1	yes	characteristic, complemented
51	#14583301	C₂²	1	1	yes	characteristic, complemented
52	#14583263	C₂²	1	2	yes	complemented
53	#14583258	C₂²	1	2	yes	complemented
54	#14583253	C₂²	1	2	yes	complemented
55	#14583238	C₂²	1	2	yes	complemented
56	#14583228	C₂²	1	2	yes	complemented
57	#14583222	C₂²	1	2	yes	complemented
58	#14583216	C₂²	1	2	yes	complemented
59	#14583211	C₂²	1	2	yes	complemented
60	#14583211	C₂²	1	2	yes	complemented
61	#14583206	C₂²	1	2	yes	complemented
62	#14583200	C₂²	1	2	yes	complemented
63	#14583200	C₂²	1	2	yes	complemented
64	#14583199	C₂²	1	2	yes	complemented
65	#14583190	C₂²	1	2	yes	complemented
66	#14583179	C₂²	1	2	yes	complemented
67	#14583149	C₂²	1	2	yes	complemented
68	#14583142	C₂²	1	2	yes	complemented
69	#14583137	C₂²	1	1	yes	characteristic, complemented
70	#14583137	C₂²	1	1	yes	characteristic, complemented
71	#14583132	C₂²	1	1	yes	characteristic
72	#14583132	C₂²	1	1	yes	characteristic
73	#14583132	C₂²	1	1	yes	characteristic, complemented
74	#14583132	C₂²	1	1	yes	characteristic, complemented
75	#14583125	C₂²	1	2	yes	complemented
76	#14583111	C₂²	1	2	yes	complemented
77	#14583111	C₂²	1	2	yes	complemented
78	#14583091	C₂²	1	2	yes	—
79	#14583048	C₂²	1	2	yes	complemented
80	#14583048	C₂²	1	2	yes	complemented
81	#14583043	C₂²	1	2	yes	complemented
82	#14583043	C₂²	1	2	yes	complemented
83	#14583031	C₂²	1	2	yes	—
84	#14583031	C₂²	1	2	yes	—
85	#14583030	C₂²	1	1	yes	characteristic, complemented
86	#14583011	C₂²	1	2	yes	complemented
87	#14583009	C₂²	1	2	yes	complemented
88	#14583008	C₂²	1	2	yes	complemented
89	#14583002	C₂²	1	2	yes	complemented
90	#14583000	C₂²	1	2	yes	complemented
91	#14582997	C₂²	1	2	yes	complemented
92	Q₁₆×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
93	SD₁₆×Dic₄₃	C₂²	1	2	yes	complemented
94	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
95	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
96	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
97	D₈×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
98	D₈×Dic₄₃	C₂²	1	1	yes	characteristic, complemented
99	#14582981	C₂²	1	1	yes	characteristic
100	C₄×#10621882	C₂²	1	2	yes	complemented
101	#14582979	C₂²	1	2	yes	complemented
102	#14582976	C₂²	1	1	yes	characteristic, complemented
103	#14582969	C₂²	1	1	yes	characteristic
104	#14582969	C₂²	1	1	yes	characteristic, complemented
105	C₈×D₁₇₂	C₂²	1	1	yes	characteristic
106	C₈×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
107	C₈×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
108	#14582959	C₂²	1	1	yes	characteristic, complemented
109	#14582959	C₂²	1	1	yes	characteristic, complemented
110	#14582955	C₂²	1	1	yes	characteristic, complemented
111	#14582936	C₂²	1	1	yes	characteristic, complemented
112	#107×D₄₃	C₂²	1	1	yes	characteristic, complemented
113	#107×D₄₃	C₂²	1	1	yes	characteristic, complemented
114	#14582902	C₂²	1	2	yes	complemented
115	#14582899	C₂²	1	2	yes	complemented
116	#102×D₄₃	C₂²	1	2	yes	complemented
117	#14582853	C₂²	1	1	yes	characteristic, complemented
118	#14582853	C₂²	1	1	yes	characteristic, complemented
119	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic, complemented
120	C₄₃×#559	C₂²	1	2	yes	complemented
121	C₄₃×#495	C₂²	1	1	yes	characteristic, complemented
122	C₄₃×#495	C₂²	1	1	yes	characteristic, complemented
123	C₄₃×#493	C₂²	1	1	yes	characteristic
124	C₄₃×#463	C₂²	1	2	yes	complemented
125	C₄₃×#463	C₂²	1	2	yes	complemented
126	C₄₃×#460	C₂²	1	2	yes	complemented
127	C₈×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
128	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
129	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
130	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
131	C₂×#10621902	C₂³	1	2	yes	—
132	C₂×#10621898	—	2	2	no	—
133	C₂×D₄×D₄₃	—	2	2	no	—
134	C₂×D₄×D₄₃	C₂³	1	2	yes	—
135	C₂×D₄×D₄₃	C₂³	1	2	yes	—
136	C₂²×C₄×D₄₃	—	2	2	no	—
137	#13063348	—	2	4	no	—
138	C₂×#10621884	C₂³	1	2	yes	—
139	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
140	C₂×#10621882	C₂³	1	2	yes	—
141	C₂×#10621882	C₂³	1	2	yes	—
142	D₈×D₄₃	—	2	4	no	—
143	D₈×D₄₃	—	2	4	no	—
144	C₂×#10621872	C₂³	1	1	yes	characteristic
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	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
150	#13063325	C₂³	1	2	yes	—
151	#13063320	D₄	1	1	yes	characteristic
152	#13063320	D₄	1	1	yes	characteristic
153	#13063319	—	2	2	no	—
154	#13063318	—	2	2	no	—
155	#13063318	—	2	2	no	—
156	#13063318	—	2	2	no	—
157	#13063317	C₂³	1	2	yes	—
158	#13063317	C₂³	1	2	yes	—
159	#13063316	D₄	1	1	yes	characteristic
160	#13063315	—	2	2	no	—
161	#13063314	D₄	1	1	yes	characteristic
162	#13063311	—	2	2	no	—
163	#13063310	—	2	2	no	—
164	#13063310	D₄	1	1	yes	characteristic
165	#13063310	D₄	1	1	yes	characteristic
166	#13063309	—	2	2	no	—
167	#13063308	—	2	2	no	—
168	#13063307	—	2	2	no	—
169	#13063307	—	2	2	no	—
170	#13063307	—	2	2	no	—
171	#13063307	—	2	2	no	—
172	#13063307	—	2	2	no	—
173	#13063306	—	2	2	no	—
174	#13063306	—	2	2	no	—
175	#13063304	—	2	2	no	—
176	#13063303	—	2	2	no	—
177	#13063303	—	2	2	no	—
178	#13063302	—	2	2	no	—
179	#13063301	—	2	2	no	—
180	#13063301	D₄	1	1	yes	characteristic
181	#13063301	C₂³	1	2	yes	—
182	#13063301	C₂³	1	2	yes	—
183	#13063300	D₄	1	1	yes	characteristic
184	#13063298	—	2	2	no	—
185	#13063298	—	2	2	no	—
186	#13063298	—	2	2	no	—
187	#13063297	—	2	2	no	—
188	#13063297	—	2	2	no	—
189	#13063296	—	2	2	no	—
190	#13063296	C₂³	1	2	yes	—
191	#13063296	C₂³	1	2	yes	—
192	#13063296	C₂³	1	2	yes	—
193	#13063296	C₂³	1	2	yes	—
194	#13063295	—	2	2	no	—
195	#13063295	—	2	2	no	—
196	#13063293	—	2	2	no	—
197	#13063293	—	2	2	no	—
198	Q₈×Dic₄₃	C₂³	1	2	yes	—
199	C₄×D₁₇₂	—	2	2	no	—
200	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
201	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
202	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
203	C₄×D₁₇₂	C₂³	1	2	yes	—
204	C₄×D₁₇₂	C₂³	1	2	yes	—
205	C₄×D₁₇₂	C₂³	1	2	yes	—
206	D₄×Dic₄₃	C₂³	1	2	yes	—
207	D₄×Dic₄₃	C₂³	1	2	yes	—
208	#13063287	—	2	2	no	—
209	#13063287	C₂³	1	2	yes	—
210	C₄×C₂²⋊D₄₃	—	2	2	no	—
211	C₄×C₂²⋊D₄₃	—	2	2	no	—
212	C₄×C₂²⋊D₄₃	—	2	2	no	—
213	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
214	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
215	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
216	#13063283	C₂³	1	2	yes	—
217	#13063282	—	2	2	no	—
218	#13063282	—	2	2	no	—
219	#13063282	C₂³	1	1	yes	characteristic
220	#13063282	C₂³	1	1	yes	characteristic
221	#13063281	—	2	2	no	—
222	C₄⋊C₄×D₄₃	—	2	2	no	—
223	C₄⋊C₄×D₄₃	—	2	2	no	—
224	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
225	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
226	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
227	C₂²⋊C₄×D₄₃	—	2	2	no	—
228	C₂²⋊C₄×D₄₃	—	2	2	no	—
229	C₂²⋊C₄×D₄₃	—	2	2	no	—
230	C₂²⋊C₄×D₄₃	—	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	1	yes	characteristic
235	#13063259	C₂³	1	2	yes	—
236	#13063258	C₂³	1	2	yes	—
237	#13063258	C₂³	1	2	yes	—
238	#13063257	C₂³	1	2	yes	—
239	#13063257	C₂³	1	2	yes	—
240	#13063256	C₂³	1	2	yes	—
241	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
242	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
243	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
244	#13063249	C₂³	1	2	yes	—
245	#13063249	C₂³	1	2	yes	—
246	#13063249	C₂³	1	2	yes	—
247	#13063247	C₂³	1	2	yes	—
248	#13063247	C₂³	1	2	yes	—
249	#13063247	C₂³	1	2	yes	—
250	#13063246	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	#13063246	C₂³	1	2	yes	—
256	#13063245	C₂³	1	2	yes	—
257	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
258	(C₂×D₄₃)⋊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	#13063236	C₂³	1	1	yes	characteristic
265	#13063235	C₂³	1	1	yes	characteristic
266	#13063235	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	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
271	C₂×SD₁₆×C₄₃	C₂³	1	2	yes	—
272	C₂×SD₁₆×C₄₃	C₂³	1	2	yes	—
273	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
274	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
275	C₂×D₈×C₄₃	C₂³	1	2	yes	—
276	#127×C₄₃	C₂³	1	2	yes	—
277	#124×C₄₃	—	2	2	no	—
278	#124×C₄₃	C₂³	1	2	yes	—
279	#124×C₄₃	C₂³	1	2	yes	—
280	#123×C₄₃	—	2	2	no	—
281	#123×C₄₃	—	2	2	no	—
282	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
283	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
284	C₄×D₄×C₄₃	—	2	2	no	—
285	C₄×D₄×C₄₃	C₂³	1	2	yes	—
286	C₄×D₄×C₄₃	C₂³	1	2	yes	—
287	#107×C₄₃	C₂³	1	1	yes	characteristic
288	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
289	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
290	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
291	#103×C₄₃	C₂³	1	2	yes	—
292	#102×C₄₃	C₂³	1	2	yes	—
293	#102×C₄₃	C₂³	1	2	yes	—
294	C₄×C₈×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	C₂³×D₄₃	—	2	2	no	—
298	C₂³×D₄₃	—	2	2	no	—
299	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
300	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
301	C₂×D₄×C₄₃	—	2	2	no	—
302	C₂×D₄×C₄₃	—	2	2	no	—
303	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
304	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
305	C₂²×C₄×C₄₃	—	2	2	no	—
306	C₂²×C₄×C₄₃	—	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	C₂×C₂²⋊D₄₃	—	2	2	no	—
312	C₂×C₂²⋊D₄₃	—	2	2	no	—
313	C₂²×Dic₄₃	—	2	2	no	—
314	C₂²×Dic₄₃	—	2	2	no	—
315	#10621902	—	2	4	no	—
316	#10621902	—	4	2	no	—
317	D₄×D₄₃	—	2	4	no	—
318	D₄×D₄₃	—	2	4	no	—
319	D₄×D₄₃	—	4	2	no	—
320	D₄×D₄₃	—	4	2	no	—
321	D₄×D₄₃	—	8	4	no	—
322	#10621898	—	8	4	no	—
323	C₂×D₁₇₂	—	2	2	no	—
324	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
325	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
326	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
327	C₂×D₁₇₂	C₂⁴	1	2	yes	—
328	C₂×C₄×D₄₃	—	2	2	no	—
329	C₂×C₄×D₄₃	—	2	2	no	—
330	C₂×C₄×D₄₃	—	2	2	no	—
331	C₂×C₄×D₄₃	—	2	2	no	—
332	C₂×C₄×D₄₃	—	2	2	no	—
333	C₂×C₄×D₄₃	—	2	2	no	—
334	C₂×C₄×D₄₃	—	2	2	no	—
335	C₂×C₄×D₄₃	—	8	4	no	—
336	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
337	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
338	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
339	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
340	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
341	C₂×Dic₈₆	—	2	2	no	—
342	Q₁₆×C₄₃	—	2	2	no	—
343	SD₁₆×C₄₃	—	4	2	no	—
344	SD₁₆×C₄₃	—	4	2	no	—
345	D₈×C₄₃	—	2	2	no	—
346	D₈×C₄₃	—	2	2	no	—
347	D₈×C₄₃	—	4	2	no	—
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	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
352	C₄⋊C₄×C₄₃	—	2	2	no	—
353	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
354	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
355	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
356	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
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	—	2	2	no	—
361	C₂²⋊C₄×C₄₃	—	2	2	no	—
362	C₂²⋊C₄×C₄₃	—	2	2	no	—
363	C₄²×C₄₃	—	2	2	no	—
364	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
365	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
366	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
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	—	2	2	no	—
373	#10621884	—	2	4	no	—
374	#10621882	—	2	4	no	—
375	#10621882	—	2	4	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	—	2	2	no	—
382	(C₂×D₄₃)⋊C₄	—	2	2	no	—
383	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
384	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
385	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
386	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
398	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
399	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
400	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
401	Dic₄₃⋊C₄	—	2	2	no	—
402	Dic₄₃⋊C₄	—	2	2	no	—
403	Dic₄₃⋊C₄	—	2	2	no	—
404	Dic₄₃⋊C₄	—	2	2	no	—
405	Dic₄₃⋊C₄	—	2	2	no	—
406	Dic₄₃⋊C₄	—	2	2	no	—
407	Dic₄₃⋊C₄	—	2	2	no	—
408	Dic₄₃⋊C₄	—	2	2	no	—
409	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
410	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
411	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
412	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
413	C₄×Dic₄₃	—	2	2	no	—
414	C₄×Dic₄₃	—	2	2	no	—
415	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
416	C₄×Dic₄₃	C₂×D₄	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	D₃₄₄	#41	1	4	yes	complemented
423	#10621872	—	4	1	no	—
424	#10621872	—	4	1	no	—
425	C₈×D₄₃	—	2	2	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	C₂²×D₄₃	—	2	2	no	—
432	C₂²×D₄₃	—	4	4	no	—
433	C₂²×D₄₃	—	4	4	no	—
434	C₂²×D₄₃	—	4	4	no	—
435	C₂²×D₄₃	—	8	2	no	—
436	C₂²×D₄₃	—	8	2	no	—
437	C₂²×D₄₃	—	8	2	no	—
438	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
439	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
440	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
441	Q₈×C₄₃	—	2	2	no	—
442	Q₈×C₄₃	—	2	2	no	—
443	Q₈×C₄₃	—	4	1	no	—
444	D₄×C₄₃	—	2	2	no	—
445	D₄×C₄₃	—	2	2	no	—
446	D₄×C₄₃	—	2	2	no	—
447	D₄×C₄₃	—	2	2	no	—
448	D₄×C₄₃	—	8	2	no	—
449	D₄×C₄₃	—	8	2	no	—
450	C₂×C₄×C₄₃	—	2	2	no	—
451	C₂×C₄×C₄₃	—	2	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	C₂²×D₄	1	1	yes	characteristic
460	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
461	C₂²⋊D₄₃	—	4	4	no	—
462	C₂²⋊D₄₃	—	4	4	no	—
463	C₂²⋊D₄₃	—	4	4	no	—
464	C₂²⋊D₄₃	—	8	2	no	—
465	C₂²⋊D₄₃	—	8	2	no	—
466	C₂²⋊D₄₃	—	8	2	no	—
467	C₂×Dic₄₃	—	2	2	no	—
468	C₂×Dic₄₃	—	2	2	no	—
469	C₂×Dic₄₃	—	2	2	no	—
470	C₂×Dic₄₃	—	8	2	no	—
471	C₂×Dic₄₃	—	8	2	no	—
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	—	2	2	no	—
480	D₁₇₂	—	4	1	no	—
481	D₁₇₂	—	4	4	no	—
482	D₁₇₂	C₂×#41	1	4	yes	—
483	C₄×D₄₃	—	2	2	no	—
484	C₄×D₄₃	—	2	1	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	1	no	—
490	C₄×D₄₃	—	4	1	no	—
491	C₄×D₄₃	—	4	4	no	—
492	C₄×D₄₃	—	4	4	no	—
493	C₄×D₄₃	—	8	2	no	—
494	C₄×D₄₃	—	8	2	no	—
495	C₄×D₄₃	—	8	2	no	—
496	C₄×D₄₃	—	8	2	no	—
497	C₄×D₄₃	—	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	#61471	—	43	1	no	maximal, Sylow
508	C₂²×C₄₃	—	4	2	no	—
509	C₂²×C₄₃	—	4	2	no	—
510	C₂²×C₄₃	—	4	2	no	—
511	C₂²×C₄₃	—	4	2	no	—
512	C₂²×C₄₃	—	4	2	no	—
513	C₂²×C₄₃	—	4	2	no	—
514	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
515	C₂×D₄₃	—	2	1	no	—
516	C₂×D₄₃	—	2	1	no	—
517	C₂×D₄₃	—	2	1	no	—
518	C₂×D₄₃	—	2	1	no	—
519	C₂×D₄₃	—	2	4	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	—	4	2	no	—
525	C₂×D₄₃	—	4	2	no	—
526	C₂×D₄₃	—	8	8	no	—
527	C₂×D₄₃	—	16	4	no	—
528	C₂×D₄₃	#576	1	2	yes	—
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	—	2	1	no	—
535	C₄×C₄₃	—	4	2	no	—
536	C₄×C₄₃	—	4	2	no	—
537	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
538	C₄×C₄₃	#585	1	1	yes	characteristic
539	Dic₄₃	—	2	1	no	—
540	Dic₄₃	—	2	1	no	—
541	Dic₄₃	—	2	1	no	—
542	Dic₄₃	—	2	1	no	—
543	Dic₄₃	—	2	1	no	—
544	Dic₄₃	—	4	2	no	—
545	Dic₄₃	—	4	2	no	—
546	Dic₄₃	—	4	2	no	—
547	#3513	—	43	2	no	—
548	#3396	D₄₃	1	1	yes	characteristic, complemented
549	#3380	—	43	1	no	—
550	#3370	—	43	2	no	—
551	#3339	—	43	1	no	—
552	#3336	—	43	1	no	—
553	#3334	—	43	1	no	—
554	#3322	—	43	2	no	—
555	#3310	—	43	2	no	—
556	#3306	—	43	2	no	—
557	#3280	—	43	1	no	—
558	#3280	—	43	1	no	—
559	D₄×D₈	—	43	1	no	—
560	#3176	—	43	1	no	—
561	#3175	—	43	1	no	—
562	#3168	—	43	1	no	—
563	#3119	—	43	2	no	—
564	#3118	—	43	2	no	—
565	#3114	—	43	2	no	—
566	#2966	—	43	1	no	—
567	#2951	—	43	1	no	—
568	#2948	—	43	1	no	—
569	C₂×C₄×D₈	—	43	1	no	—
570	C₂×C₄₃	—	8	2	no	—
571	C₂×C₄₃	—	8	2	no	—
572	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
573	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
574	C₂×C₄₃	#3584	1	1	yes	characteristic
575	D₄₃	—	2	2	no	—
576	D₄₃	—	4	1	no	—
577	D₄₃	—	4	1	no	—
578	D₄₃	—	4	4	no	—
579	C₂×#135	—	43	1	no	—
580	C₂²×D₈	—	43	1	no	—
581	C₂²×D₈	—	43	1	no	—
582	#559	C₂×D₄₃	1	2	yes	complemented
583	#554	—	43	2	no	—
584	#553	—	43	2	no	—
585	#553	—	86	2	no	—
586	#552	—	43	2	no	—
587	#551	—	86	2	no	—
588	#551	—	86	2	no	—
589	#547	—	43	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	#540	—	43	2	no	—
596	#539	—	86	2	no	—
597	#538	—	86	2	no	—
598	#529	—	43	1	no	—
599	#529	—	43	2	no	—
600	#525	—	86	2	no	—
601	C₂×#123	—	86	2	no	—
602	#520	—	43	2	no	—
603	#518	—	43	2	no	—
604	C₂×C₄×D₄	—	43	2	no	—
605	#500	—	43	1	no	—
606	#499	—	43	1	no	—
607	#499	—	43	1	no	—
608	#495	C₂×D₄₃	1	1	yes	characteristic, complemented
609	#495	C₂×D₄₃	1	1	yes	characteristic, complemented
610	#493	C₂×D₄₃	1	1	yes	characteristic
611	#490	—	43	2	no	—
612	#489	—	43	2	no	—
613	#488	—	43	2	no	—
614	#485	—	43	2	no	—
615	#483	—	43	2	no	—
616	#482	—	43	2	no	—
617	#481	—	43	2	no	—
618	#480	—	43	2	no	—
619	#480	—	43	2	no	—
620	#479	—	43	2	no	—
621	#478	—	43	2	no	—
622	#478	—	43	2	no	—
623	#478	—	43	2	no	—
624	#476	—	43	2	no	—
625	#474	—	43	2	no	—
626	#469	—	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	#465	—	43	2	no	—
635	#463	—	43	2	no	—
636	#463	—	43	2	no	—
637	#463	C₂×D₄₃	1	2	yes	complemented
638	#463	C₂×D₄₃	1	2	yes	complemented
639	#460	C₂×D₄₃	1	2	yes	complemented
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	C₂×D₄₃	1	1	yes	characteristic, complemented
649	#442	—	43	2	no	—
650	#442	—	43	2	no	—
651	#442	—	43	2	no	—
652	#440	—	43	2	no	—
653	#440	—	43	2	no	—
654	#440	—	43	2	no	—
655	C₄×Q₁₆	—	43	1	no	—
656	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
657	C₄×SD₁₆	—	43	2	no	—
658	C₄×D₈	—	43	1	no	—
659	C₄×D₈	—	43	1	no	—
660	C₄×D₈	—	43	2	no	—
661	C₄×D₈	—	43	1	no	—
662	C₄×D₈	—	43	2	no	—
663	C₄×D₈	—	43	1	no	—
664	C₄×D₈	—	43	1	no	—
665	C₄×D₈	—	43	1	no	—
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	C₂×#107	—	43	1	no	—
679	C₂×#107	—	43	1	no	—
680	#418	—	43	2	no	—
681	#417	—	43	2	no	—
682	C₂×#102	—	43	2	no	—
683	#405	—	43	1	no	—
684	#405	—	43	1	no	—
685	C₂×C₄×C₈	—	43	1	no	—
686	C₄₃	#61471	1	1	yes	characteristic, complemented, Sylow
687	C₂×#41	—	43	2	no	—
688	C₂×#41	—	86	2	no	—
689	C₂²×D₄	—	43	2	no	—
690	C₂²×D₄	—	43	2	no	—
691	C₂²×D₄	—	86	2	no	—
692	C₂³×C₄	—	86	2	no	—
693	#135	—	86	4	no	—
694	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
695	C₂×SD₁₆	—	43	2	no	—
696	C₂×SD₁₆	C₂²×D₄₃	1	2	yes	—
697	C₂×SD₁₆	C₂²×D₄₃	1	2	yes	—
698	C₂×D₈	—	43	2	no	—
699	C₂×D₈	—	43	2	no	—
700	C₂×D₈	—	43	1	no	—
701	C₂×D₈	—	86	4	no	—
702	C₂×D₈	—	86	4	no	—
703	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
704	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
705	C₂×D₈	C₂²×D₄₃	1	2	yes	—
706	C₂×M₁₆	—	43	1	no	—
707	C₂×M₁₆	—	43	1	no	—
708	C₂²×C₈	—	43	1	no	—
709	C₂²×C₈	—	43	1	no	—
710	C₂²×C₈	—	43	1	no	—
711	C₂²×C₈	—	43	1	no	—
712	C₄⋊Q₈	—	43	2	no	—
713	#127	C₂²×D₄₃	1	2	yes	—
714	#126	—	43	1	no	—
715	#126	—	43	1	no	—
716	#126	—	86	2	no	—
717	#126	—	86	2	no	—
718	#126	—	86	2	no	—
719	#126	—	86	2	no	—
720	#125	—	43	1	no	—
721	#125	—	43	2	no	—
722	#125	—	43	2	no	—
723	#125	—	86	2	no	—
724	#124	—	2	2	no	—
725	#124	—	43	1	no	—
726	#124	—	86	2	no	—
727	#124	C₂²×D₄₃	1	2	yes	—
728	#124	C₂²×D₄₃	1	2	yes	—
729	#123	—	2	2	no	—
730	#123	—	2	2	no	—
731	#123	—	43	1	no	—
732	#123	—	43	1	no	—
733	#123	—	86	2	no	—
734	#123	—	86	2	no	—
735	#123	—	86	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	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	2	no	—
767	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
768	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
769	C₄×D₄	—	2	2	no	—
770	C₄×D₄	—	43	2	no	—
771	C₄×D₄	—	43	2	no	—
772	C₄×D₄	—	43	2	no	—
773	C₄×D₄	—	43	1	no	—
774	C₄×D₄	—	43	1	no	—
775	C₄×D₄	—	43	1	no	—
776	C₄×D₄	—	43	2	no	—
777	C₄×D₄	—	43	2	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	—	86	2	no	—
786	C₄×D₄	—	86	2	no	—
787	C₄×D₄	C₂²×D₄₃	1	2	yes	—
788	C₄×D₄	C₂²×D₄₃	1	2	yes	—
789	#117	—	43	1	no	—
790	#117	—	43	1	no	—
791	#117	—	43	2	no	—
792	#117	—	86	2	no	—
793	#117	—	86	2	no	—
794	#117	—	86	2	no	—
795	C₂×C₄⋊C₄	—	43	2	no	—
796	C₂×C₄⋊C₄	—	43	2	no	—
797	C₂×C₄⋊C₄	—	86	2	no	—
798	C₂×C₄⋊C₄	—	86	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×C₂²⋊C₄	—	86	2	no	—
804	C₂×C₄²	—	43	1	no	—
805	#107	—	43	1	no	—
806	#107	—	43	1	no	—
807	#107	—	43	1	no	—
808	#107	—	43	2	no	—
809	#107	—	43	2	no	—
810	#107	—	43	2	no	—
811	#107	C₂²×D₄₃	1	1	yes	characteristic
812	#106	—	43	2	no	—
813	#106	—	43	2	no	—
814	#106	—	43	2	no	—
815	C₄⋊C₈	—	43	1	no	—
816	C₄⋊C₈	—	43	1	no	—
817	C₄⋊C₈	—	43	1	no	—
818	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
819	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
820	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
821	#103	—	43	2	no	—
822	#103	—	43	2	no	—
823	#103	—	43	2	no	—
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	—	43	2	no	—
832	#102	—	43	2	no	—
833	#102	—	43	2	no	—
834	#102	—	43	2	no	—
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	—	43	1	no	—
846	#97	—	43	1	no	—
847	C₄×C₈	—	43	1	no	—
848	C₄×C₈	—	43	1	no	—
849	C₄×C₈	—	43	1	no	—
850	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
851	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
852	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
853	C₂⁴	—	86	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	—	86	2	no	—
859	C₂×Q₈	D₄×D₄₃	1	1	yes	characteristic
860	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
861	C₂×D₄	—	2	2	no	—
862	C₂×D₄	—	2	2	no	—
863	C₂×D₄	—	43	1	no	—
864	C₂×D₄	—	43	1	no	—
865	C₂×D₄	—	43	1	no	—
866	C₂×D₄	—	43	2	no	—
867	C₂×D₄	—	86	2	no	—
868	C₂×D₄	—	86	2	no	—
869	C₂×D₄	—	86	2	no	—
870	C₂×D₄	—	86	4	no	—
871	C₂×D₄	—	86	4	no	—
872	C₂×D₄	—	86	2	no	—
873	C₂×D₄	—	86	2	no	—
874	C₂×D₄	—	86	2	no	—
875	C₂×D₄	—	86	2	no	—
876	C₂×D₄	—	344	4	no	—
877	C₂×D₄	—	172	2	no	—
878	C₂×D₄	—	172	2	no	—
879	C₂×D₄	C₂³×D₄₃	1	2	yes	—
880	C₂×D₄	C₂³×D₄₃	1	2	yes	—
881	C₂²×C₄	—	2	2	no	—
882	C₂²×C₄	—	2	2	no	—
883	C₂²×C₄	—	43	1	no	—
884	C₂²×C₄	—	43	1	no	—
885	C₂²×C₄	—	43	1	no	—
886	C₂²×C₄	—	43	1	no	—
887	C₂²×C₄	—	43	1	no	—
888	C₂²×C₄	—	86	2	no	—
889	C₂²×C₄	—	86	2	no	—
890	C₂²×C₄	—	86	2	no	—
891	C₂²×C₄	—	86	2	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	—	344	4	no	—
898	Q₁₆	—	2	2	no	—
899	SD₁₆	—	4	2	no	—
900	SD₁₆	—	4	2	no	—
901	SD₁₆	—	86	4	no	—
902	D₈	—	2	2	no	—
903	D₈	—	2	2	no	—
904	D₈	—	4	2	no	—
905	D₈	—	43	4	no	—
906	D₈	—	86	4	no	—
907	D₈	—	86	4	no	—
908	M₁₆	—	172	1	no	—
909	M₁₆	—	172	1	no	—
910	C₂×C₈	—	43	1	no	—
911	C₂×C₈	—	43	1	no	—
912	C₂×C₈	—	43	1	no	—
913	C₂×C₈	—	43	1	no	—
914	C₂×C₈	—	86	2	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	—	2	2	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	—	43	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	—	86	2	no	—
941	C₄⋊C₄	—	86	2	no	—
942	C₄⋊C₄	—	86	2	no	—
943	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
944	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
945	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
946	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
947	C₂²⋊C₄	—	2	2	no	—
948	C₂²⋊C₄	—	2	2	no	—
949	C₂²⋊C₄	—	2	2	no	—
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	2	no	—
952	C₂²⋊C₄	—	2	2	no	—
953	C₂²⋊C₄	—	43	1	no	—
954	C₂²⋊C₄	—	43	1	no	—
955	C₂²⋊C₄	—	43	1	no	—
956	C₂²⋊C₄	—	43	1	no	—
957	C₂²⋊C₄	—	43	1	no	—
958	C₂²⋊C₄	—	43	1	no	—
959	C₂²⋊C₄	—	43	1	no	—
960	C₂²⋊C₄	—	43	1	no	—
961	C₂²⋊C₄	—	43	1	no	—
962	C₂²⋊C₄	—	43	1	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	—	86	2	no	—
973	C₂²⋊C₄	—	86	2	no	—
974	C₂²⋊C₄	—	86	2	no	—
975	C₂²⋊C₄	—	86	2	no	—
976	C₄²	—	2	2	no	—
977	C₄²	—	43	1	no	—
978	C₄²	—	43	1	no	—
979	C₄²	—	43	1	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	C₄²	C₂³×D₄₃	1	1	yes	characteristic
985	C₂³	—	2	2	no	—
986	C₂³	—	2	2	no	—
987	C₂³	—	43	1	no	—
988	C₂³	—	43	1	no	—
989	C₂³	—	43	1	no	—
990	C₂³	—	86	2	no	—
991	C₂³	—	344	2	no	—
992	C₂³	—	344	2	no	—
993	C₂³	—	344	2	no	—
994	C₂³	—	172	4	no	—
995	C₂³	—	172	4	no	—
996	C₂³	—	172	4	no	—
997	Q₈	—	2	2	no	—
998	Q₈	—	2	2	no	—
999	Q₈	—	4	1	no	—
1000	Q₈	—	344	2	no	—
1001	D₄	—	2	2	no	—
1002	D₄	—	2	2	no	—
1003	D₄	—	2	2	no	—
1004	D₄	—	2	2	no	—
1005	D₄	—	8	2	no	—
1006	D₄	—	8	2	no	—
1007	D₄	—	43	4	no	—
1008	D₄	—	86	2	no	—
1009	D₄	—	86	2	no	—
1010	D₄	—	86	2	no	—
1011	D₄	—	344	2	no	—
1012	D₄	—	344	2	no	—
1013	D₄	—	344	2	no	—
1014	D₄	—	172	1	no	—
1015	D₄	—	172	4	no	—
1016	D₄	—	172	4	no	—
1017	D₄	—	172	4	no	—
1018	D₄	—	172	4	no	—
1019	C₂×C₄	—	2	2	no	—
1020	C₂×C₄	—	2	2	no	—
1021	C₂×C₄	—	8	2	no	—
1022	C₂×C₄	—	8	2	no	—
1023	C₂×C₄	—	43	1	no	—
1024	C₂×C₄	—	43	1	no	—
1025	C₂×C₄	—	43	1	no	—
1026	C₂×C₄	—	43	1	no	—
1027	C₂×C₄	—	43	1	no	—
1028	C₂×C₄	—	86	2	no	—
1029	C₂×C₄	—	86	1	no	—
1030	C₂×C₄	—	86	1	no	—
1031	C₂×C₄	—	86	1	no	—
1032	C₂×C₄	—	86	1	no	—
1033	C₂×C₄	—	86	1	no	—
1034	C₂×C₄	—	86	1	no	—
1035	C₂×C₄	—	86	2	no	—
1036	C₂×C₄	—	86	2	no	—
1037	C₂×C₄	—	86	2	no	—
1038	C₂×C₄	—	344	2	no	—
1039	C₂×C₄	—	344	2	no	—
1040	C₂×C₄	—	344	2	no	—
1041	C₂×C₄	—	344	2	no	—
1042	C₂×C₄	—	344	2	no	—
1043	C₂×C₄	—	344	2	no	—
1044	C₂×C₄	—	344	2	no	—
1045	C₂×C₄	—	172	1	no	—
1046	C₂×C₄	—	172	4	no	—
1047	C₂×C₄	—	172	4	no	—
1048	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
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	#41×D₄₃	1	2	yes	—
1063	C₂²	—	4	2	no	—
1064	C₂²	—	4	2	no	—
1065	C₂²	—	4	2	no	—
1066	C₂²	—	4	2	no	—
1067	C₂²	—	4	2	no	—
1068	C₂²	—	4	2	no	—
1069	C₂²	—	43	2	no	—
1070	C₂²	—	86	1	no	—
1071	C₂²	—	86	1	no	—
1072	C₂²	—	86	1	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	4	no	—
1079	C₂²	—	344	8	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	—	2	1	no	—
1090	C₄	—	4	2	no	—
1091	C₄	—	4	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	C₂×#41×D₄₃	1	1	yes	characteristic
1101	C₄	#14583734	1	1	yes	characteristic
1102	C₂	—	8	2	no	—
1103	C₂	—	8	2	no	—
1104	C₂	—	86	2	no	—
1105	C₂	—	172	1	no	—
1106	C₂	—	172	1	no	—
1107	C₂	—	172	4	no	—
1108	C₂	#19148085	1	1	yes	characteristic
1109	C₂	#576×D₄₃	1	1	yes	characteristic
1110	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×#3396	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3396	D₄₃
hypocenter	C₄₃	#61471
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #3396

Complements

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

N	H ≅ G/N	type
1. #19148534	C₂	semidirect
2. #19147463	C₂	semidirect
3. #19147342	C₂	semidirect
4. #19146999	C₂	semidirect
5. #19146965	C₂	semidirect
6. #19146944	C₂	semidirect
7. #19146803	C₂	semidirect
8. #19146623	C₂	semidirect
9. #19146563	C₂	semidirect
10. #19146279	C₂	semidirect
11. #19146279	C₂	semidirect
12. #19146270	C₂	semidirect
13. #19145242	C₂	semidirect
14. #19145231	C₂	semidirect
15. #19145162	C₂	semidirect
16. #19144793	C₂	semidirect
17. #19144778	C₂	semidirect
18. #19144732	C₂	semidirect
19. #19143572	C₂	semidirect
20. #19143470	C₂	semidirect
21. #19143442	C₂	semidirect
22. C₄×D₈×D₄₃	C₂	semidirect
23. C₄₃×#3396	C₂	semidirect
27. #14583609	C₂²	semidirect
28. #14583599	C₂²	semidirect
33. #14583554	C₂²	semidirect
34. #14583542	C₂²	semidirect
35. #14583542	C₂²	semidirect
38. #14583518	C₂²	semidirect
39. #14583503	C₂²	semidirect
43. #14583428	C₂²	semidirect
46. #14583381	C₂²	semidirect
47. #14583371	C₂²	semidirect
48. C₄×D₄×D₄₃	C₂²	semidirect
49. #14583304	C₂²	semidirect
50. #14583301	C₂²	semidirect
51. #14583301	C₂²	semidirect
52. #14583263	C₂²	semidirect
53. #14583258	C₂²	semidirect
54. #14583253	C₂²	semidirect
55. #14583238	C₂²	semidirect
56. #14583228	C₂²	semidirect
57. #14583222	C₂²	semidirect
58. #14583216	C₂²	semidirect
59. #14583211	C₂²	semidirect
60. #14583211	C₂²	semidirect
61. #14583206	C₂²	semidirect
62. #14583200	C₂²	semidirect
63. #14583200	C₂²	semidirect
64. #14583199	C₂²	semidirect
65. #14583190	C₂²	semidirect
66. #14583179	C₂²	semidirect
67. #14583149	C₂²	semidirect
68. #14583142	C₂²	semidirect
69. #14583137	C₂²	semidirect
70. #14583137	C₂²	semidirect
73. #14583132	C₂²	semidirect
74. #14583132	C₂²	semidirect
75. #14583125	C₂²	semidirect
76. #14583111	C₂²	semidirect
77. #14583111	C₂²	semidirect
79. #14583048	C₂²	semidirect
80. #14583048	C₂²	semidirect
81. #14583043	C₂²	semidirect
82. #14583043	C₂²	semidirect
85. #14583030	C₂²	semidirect
86. #14583011	C₂²	semidirect
87. #14583009	C₂²	semidirect
88. #14583008	C₂²	semidirect
89. #14583002	C₂²	semidirect
90. #14583000	C₂²	semidirect
91. #14582997	C₂²	semidirect
92. Q₁₆×Dic₄₃	C₂²	semidirect
93. SD₁₆×Dic₄₃	C₂²	semidirect
97. D₈×Dic₄₃	C₂²	semidirect
98. D₈×Dic₄₃	C₂²	semidirect
100. C₄×#10621882	C₂²	semidirect
101. #14582979	C₂²	semidirect
102. #14582976	C₂²	semidirect
104. #14582969	C₂²	semidirect
106. C₈×D₁₇₂	C₂²	semidirect
107. C₈×D₁₇₂	C₂²	semidirect
108. #14582959	C₂²	semidirect
109. #14582959	C₂²	semidirect
110. #14582955	C₂²	semidirect
111. #14582936	C₂²	semidirect
112. #107×D₄₃	C₂²	semidirect
113. #107×D₄₃	C₂²	semidirect
114. #14582902	C₂²	semidirect
115. #14582899	C₂²	semidirect
116. #102×D₄₃	C₂²	semidirect
117. #14582853	C₂²	semidirect
118. #14582853	C₂²	semidirect
119. C₄×C₈×D₄₃	C₂²	semidirect
120. C₄₃×#559	C₂²	semidirect
121. C₄₃×#495	C₂²	semidirect
122. C₄₃×#495	C₂²	semidirect
124. C₄₃×#463	C₂²	semidirect
125. C₄₃×#463	C₂²	semidirect
126. C₄₃×#460	C₂²	semidirect
127. C₈×Q₈×C₄₃	C₂²	semidirect
128. C₄×Q₁₆×C₄₃	C₂²	semidirect
129. C₄×D₈×C₄₃	C₂²	semidirect
130. C₄×D₈×C₄₃	C₂²	semidirect
422. D₃₄₄	#41	semidirect
548. #3396	D₄₃	semidirect
582. #559	C₂×D₄₃	semidirect
608. #495	C₂×D₄₃	semidirect
609. #495	C₂×D₄₃	semidirect
637. #463	C₂×D₄₃	semidirect
638. #463	C₂×D₄₃	semidirect
639. #460	C₂×D₄₃	semidirect
648. C₈×Q₈	C₂×D₄₃	semidirect
656. C₄×Q₁₆	C₂×D₄₃	semidirect
666. C₄×D₈	C₂×D₄₃	semidirect
667. C₄×D₈	C₂×D₄₃	semidirect
686. C₄₃	#61471	semidirect

Maximal subgroups

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

subgroup	index
#19148534	2
#19147463	2
#19147342	2
#19146999	2
#19146965	2
#19146944	2
#19146803	2
#19146623	2
#19146563	2
#19146279	2
#19146270	2
#19145242	2
#19145231	2
#19145162	2
#19144793	2
#19144778	2
#19144732	2
#19143572	2
#19143470	2
#19143442	2
C₄×D₈×D₄₃	2
C₄₃×#3396	2
#61471	43