Subgroups — #25975110

Order 11008.

1874 conjugacy classes of subgroups.

The subgroup lattice has 1106 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148149	C₂	1	2	yes	maximal, complemented
2	#19147023	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147015	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147004	C₂	1	2	yes	maximal, complemented
5	#19146997	C₂	1	1	yes	maximal, characteristic, complemented
6	#19146993	C₂	1	1	yes	maximal, characteristic, complemented
7	#19146985	C₂	1	1	yes	maximal, characteristic, complemented
8	#19146975	C₂	1	2	yes	maximal, complemented
9	#19146970	C₂	1	2	yes	maximal, complemented
10	#19146963	C₂	1	1	yes	maximal, characteristic, complemented
11	#19146959	C₂	1	1	yes	maximal, characteristic, complemented
12	#19146948	C₂	1	2	yes	maximal, complemented
13	#19146940	C₂	1	1	yes	maximal, characteristic, complemented
14	#19145107	C₂	1	1	yes	maximal, characteristic, complemented
15	#19144512	C₂	1	2	yes	maximal, complemented
16	#19144508	C₂	1	2	yes	maximal, complemented
17	#19144381	C₂	1	2	yes	maximal, complemented
18	#19144177	C₂	1	1	yes	maximal, characteristic, complemented
19	#19144176	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143366	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×C₈×C₂²⋊D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
22	#427×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×C₄₃×#427	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063347	C₂²	1	1	yes	characteristic
25	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
26	#14583617	C₂²	1	2	yes	—
27	#14583612	C₂²	1	2	yes	—
28	#14583604	C₂²	1	2	yes	—
29	#14583597	C₂²	1	2	yes	—
30	#14583593	C₂²	1	2	yes	—
31	#14583588	C₂²	1	2	yes	—
32	#14583584	C₂²	1	2	yes	—
33	#14583582	—	2	2	no	—
34	#14583575	—	2	2	no	—
35	#14583573	—	2	2	no	—
36	#14583550	C₂²	1	2	yes	—
37	#14583539	—	2	2	no	—
38	#14583452	C₂²	1	2	yes	—
39	#14583433	—	2	2	no	—
40	#14583427	—	2	2	no	—
41	#14583427	—	2	2	no	—
42	#14583411	C₂²	1	2	yes	—
43	#14583410	C₂²	1	2	yes	—
44	C₄×#10621898	—	2	2	no	—
45	#14583367	C₂²	1	2	yes	—
46	C₂×C₄×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
47	#117×D₄₃	C₂²	1	2	yes	—
48	#14583303	C₂²	1	1	yes	characteristic, complemented
49	#14583303	C₂²	1	1	yes	characteristic, complemented
50	#14583300	C₂²	1	1	yes	characteristic, complemented
51	#14583300	C₂²	1	1	yes	characteristic, complemented
52	#14583299	C₂²	1	2	yes	complemented
53	#14583296	C₂²	1	2	yes	complemented
54	#14583243	C₂²	1	2	yes	complemented
55	#14583242	C₂²	1	2	yes	complemented
56	#14583240	C₂²	1	2	yes	complemented
57	#14583240	C₂²	1	2	yes	complemented
58	#14583236	C₂²	1	2	yes	complemented
59	#14583234	C₂²	1	2	yes	complemented
60	#14583231	C₂²	1	2	yes	complemented
61	#14583229	C₂²	1	2	yes	complemented
62	#14583226	C₂²	1	2	yes	complemented
63	#14583225	C₂²	1	2	yes	complemented
64	#14583223	C₂²	1	2	yes	complemented
65	#14583223	C₂²	1	2	yes	complemented
66	#14583219	C₂²	1	2	yes	complemented
67	#14583217	C₂²	1	2	yes	complemented
68	#14583214	C₂²	1	2	yes	complemented
69	#14583212	C₂²	1	2	yes	complemented
70	#14583209	C₂²	1	2	yes	complemented
71	#14583205	C₂²	1	2	yes	complemented
72	#14583202	C₂²	1	2	yes	complemented
73	#14583198	C₂²	1	2	yes	complemented
74	#14583193	C₂²	1	2	yes	complemented
75	#14583188	C₂²	1	2	yes	complemented
76	#14583183	C₂²	1	2	yes	complemented
77	#14583178	C₂²	1	2	yes	complemented
78	#14583141	C₂²	1	1	yes	characteristic, complemented
79	#14583141	C₂²	1	1	yes	characteristic, complemented
80	#14583140	C₂²	1	1	yes	characteristic, complemented
81	#14583140	C₂²	1	1	yes	characteristic, complemented
82	#14583136	C₂²	1	1	yes	characteristic, complemented
83	#14583136	C₂²	1	1	yes	characteristic, complemented
84	#14583135	C₂²	1	1	yes	characteristic, complemented
85	#14583135	C₂²	1	1	yes	characteristic, complemented
86	#14583129	C₂²	1	2	yes	complemented
87	#14583129	C₂²	1	2	yes	complemented
88	#14583128	C₂²	1	2	yes	complemented
89	#14583128	C₂²	1	2	yes	complemented
90	#14582993	C₂²	1	1	yes	characteristic, complemented
91	#14582993	C₂²	1	1	yes	characteristic, complemented
92	#14582986	C₂²	1	2	yes	complemented
93	#14582986	C₂²	1	2	yes	complemented
94	#14582981	C₂²	1	1	yes	characteristic, complemented
95	#14582981	C₂²	1	1	yes	characteristic, complemented
96	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
97	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
98	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
99	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
100	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
101	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
102	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
103	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic
104	#14582937	C₂²	1	1	yes	characteristic
105	#14582936	C₂²	1	1	yes	characteristic, complemented
106	#14582936	C₂²	1	1	yes	characteristic, complemented
107	#14582935	C₂²	1	2	yes	—
108	#14582935	C₂²	1	2	yes	—
109	#14582934	C₂²	1	2	yes	complemented
110	#107×D₄₃	C₂²	1	1	yes	characteristic, complemented
111	#107×D₄₃	C₂²	1	1	yes	characteristic, complemented
112	#106×D₄₃	C₂²	1	2	yes	complemented
113	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
114	#14582896	C₂²	1	2	yes	—
115	#14582893	C₂²	1	2	yes	—
116	#14582893	C₂²	1	2	yes	—
117	C₂×C₂²⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
118	C₂×(C₂×D₄₃)⋊C₈	C₂²	1	1	yes	characteristic
119	C₂×C₈×Dic₄₃	C₂²	1	1	yes	characteristic
120	C₂³×C₈×C₄₃	C₂²	1	1	yes	characteristic
121	C₂×#117×C₄₃	C₂²	1	2	yes	—
122	C₄₃×#427	C₂²	1	1	yes	characteristic
123	C₄₃×#427	C₂²	1	2	yes	—
124	C₄₃×#427	C₂²	1	1	yes	characteristic
125	C₄₃×#427	C₂²	1	1	yes	characteristic, complemented
126	C₄₃×#427	C₂²	1	1	yes	characteristic, complemented
127	C₄₃×#427	C₂²	1	2	yes	complemented
128	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic, complemented
129	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic, complemented
130	C₂×#106×C₄₃	C₂²	1	2	yes	complemented
131	C₂×#10621898	—	2	2	no	—
132	C₂×#10621898	C₂³	1	2	yes	—
133	C₂²×C₂²⋊D₄₃	D₄	1	1	yes	characteristic
134	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
135	#13063347	—	2	4	no	—
136	C₂×Dic₁₇₂	C₂³	1	1	yes	characteristic
137	C₂×#10621873	C₂³	1	2	yes	—
138	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
139	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
140	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
141	C₂×C₈×D₄₃	—	2	4	no	—
142	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
143	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
144	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
145	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
146	#13063324	C₂³	1	2	yes	—
147	#13063324	C₂³	1	2	yes	—
148	#13063320	—	2	2	no	—
149	#13063320	—	2	2	no	—
150	#13063319	—	2	2	no	—
151	#13063319	—	2	2	no	—
152	#13063318	—	2	2	no	—
153	#13063318	—	2	2	no	—
154	#13063317	—	2	2	no	—
155	#13063316	C₂³	1	2	yes	—
156	#13063316	C₂³	1	2	yes	—
157	#13063315	—	2	2	no	—
158	#13063315	—	2	2	no	—
159	#13063313	—	2	2	no	—
160	#13063311	—	2	2	no	—
161	#13063311	—	2	2	no	—
162	#13063310	—	2	2	no	—
163	#13063310	—	2	2	no	—
164	#13063309	—	2	2	no	—
165	#13063308	—	2	2	no	—
166	#13063308	—	2	2	no	—
167	#13063308	—	2	2	no	—
168	#13063307	—	2	2	no	—
169	#13063307	—	2	2	no	—
170	#13063305	C₂³	1	2	yes	—
171	#13063305	C₂³	1	2	yes	—
172	#13063304	—	2	2	no	—
173	#13063304	C₂³	1	2	yes	—
174	#13063304	C₂³	1	2	yes	—
175	#13063303	—	2	2	no	—
176	#13063303	—	2	2	no	—
177	#13063302	—	2	2	no	—
178	#13063302	—	2	2	no	—
179	#13063300	C₂³	1	2	yes	—
180	#13063300	C₂³	1	2	yes	—
181	#13063299	—	2	2	no	—
182	#13063299	C₂³	1	2	yes	—
183	#13063299	C₂³	1	2	yes	—
184	#13063298	—	2	2	no	—
185	#13063298	—	2	2	no	—
186	#13063295	—	2	2	no	—
187	#13063294	—	2	2	no	—
188	C₄×Dic₈₆	—	2	2	no	—
189	C₄×Dic₈₆	—	2	2	no	—
190	C₄×Dic₈₆	—	2	2	no	—
191	#13063290	C₂³	1	2	yes	—
192	#13063290	C₂³	1	2	yes	—
193	C₄×D₁₇₂	—	2	2	no	—
194	C₄×D₁₇₂	—	2	2	no	—
195	C₄×D₁₇₂	—	2	2	no	—
196	#13063287	C₂³	1	2	yes	—
197	#13063287	C₂³	1	2	yes	—
198	C₄×C₂²⋊D₄₃	—	2	2	no	—
199	C₄×C₂²⋊D₄₃	—	2	2	no	—
200	C₄×C₂²⋊D₄₃	—	2	2	no	—
201	C₄×C₂²⋊D₄₃	—	2	2	no	—
202	C₄×C₂²⋊D₄₃	D₄	1	1	yes	characteristic
203	C₄×C₂²⋊D₄₃	D₄	1	1	yes	characteristic
204	C₄×C₂²⋊D₄₃	D₄	1	1	yes	characteristic
205	C₄×C₂²⋊D₄₃	D₄	1	1	yes	characteristic
206	C₄×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
207	C₄×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
208	C₄×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
209	C₄×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
210	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
211	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
212	#13063284	—	2	2	no	—
213	#13063284	C₂³	1	2	yes	—
214	#13063283	C₂³	1	2	yes	—
215	#13063283	C₂³	1	2	yes	—
216	#13063282	—	2	2	no	—
217	#13063282	—	2	2	no	—
218	#13063282	—	2	2	no	—
219	#13063282	—	2	2	no	—
220	#13063281	—	2	2	no	—
221	C₂×Dic₄₃⋊C₄	D₄	1	1	yes	characteristic
222	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
223	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
224	C₂×C₂²⋊Dic₄₃	D₄	1	1	yes	characteristic
225	C₂×(C₂×D₄₃)⋊C₄	D₄	1	1	yes	characteristic
226	C₂²⋊C₄×D₄₃	—	2	2	no	—
227	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
228	C₄²×D₄₃	—	2	2	no	—
229	C₄²×D₄₃	—	2	2	no	—
230	#13063259	C₂³	1	1	yes	characteristic
231	#13063259	C₂³	1	1	yes	characteristic
232	#13063258	C₂³	1	2	yes	—
233	#13063258	C₂³	1	2	yes	—
234	#13063258	C₂³	1	2	yes	—
235	#13063258	C₂³	1	2	yes	—
236	#13063257	C₂³	1	2	yes	—
237	#13063256	C₂³	1	2	yes	—
238	#13063256	C₂³	1	2	yes	—
239	#13063256	C₂³	1	2	yes	—
240	#13063256	C₂³	1	2	yes	—
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	#13063248	C₂³	1	2	yes	—
250	#13063248	C₂³	1	2	yes	—
251	#13063247	C₂³	1	2	yes	—
252	#13063247	C₂³	1	2	yes	—
253	#13063245	C₂³	1	2	yes	—
254	#13063245	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	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
260	C₂²⋊(C₄₃⋊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	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
264	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
265	C₈×Dic₄₃	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	C₂³×C₄×C₄₃	C₂³	1	1	yes	characteristic
270	C₂²×C₈×C₄₃	—	2	4	no	—
271	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
272	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
273	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
274	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
275	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
276	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
277	#117×C₄₃	—	2	2	no	—
278	#117×C₄₃	—	2	2	no	—
279	#117×C₄₃	C₂³	1	2	yes	—
280	#117×C₄₃	C₂³	1	2	yes	—
281	#117×C₄₃	C₂³	1	2	yes	—
282	#117×C₄₃	C₂³	1	2	yes	—
283	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
284	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
285	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
286	C₂×C₄²×C₄₃	—	2	2	no	—
287	#107×C₄₃	C₂³	1	1	yes	characteristic
288	#107×C₄₃	C₂³	1	1	yes	characteristic
289	#107×C₄₃	C₂³	1	2	yes	—
290	#107×C₄₃	C₂³	1	1	yes	characteristic
291	#107×C₄₃	C₂³	1	1	yes	characteristic
292	#107×C₄₃	C₂³	1	2	yes	—
293	#106×C₄₃	C₂³	1	2	yes	—
294	#106×C₄₃	C₂³	1	2	yes	—
295	#106×C₄₃	C₂³	1	2	yes	—
296	#106×C₄₃	C₂³	1	2	yes	—
297	C₂⁴×C₄₃	C₂×D₄	1	1	yes	characteristic
298	C₂³×D₄₃	C₂×D₄	1	1	yes	characteristic
299	C₂²×C₄×C₄₃	—	2	2	no	—
300	C₂²×C₄×C₄₃	—	2	2	no	—
301	C₂²×C₄×C₄₃	—	2	2	no	—
302	C₂²×C₄×C₄₃	—	2	2	no	—
303	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
304	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
305	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
306	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
308	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
309	C₂×C₂²⋊D₄₃	—	2	4	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	C₂×D₄	1	1	yes	characteristic
314	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
315	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
316	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
317	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
318	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
319	C₂²×Dic₄₃	C₂×D₄	1	1	yes	characteristic
320	#10621898	—	2	4	no	—
321	#10621898	—	2	4	no	—
322	#10621898	—	4	8	no	—
323	C₂×D₁₇₂	—	2	2	no	—
324	C₂×D₁₇₂	—	2	2	no	—
325	C₂×D₁₇₂	C₂⁴	1	2	yes	—
326	C₂×C₄×D₄₃	—	2	2	no	—
327	C₂×C₄×D₄₃	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
334	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
335	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
336	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
337	C₂×Dic₈₆	—	2	2	no	—
338	C₂×Dic₈₆	—	2	2	no	—
339	C₂×Dic₈₆	C₂⁴	1	2	yes	—
340	C₂×C₈×C₄₃	—	2	2	no	—
341	C₂×C₈×C₄₃	—	2	2	no	—
342	C₂×C₈×C₄₃	—	2	2	no	—
343	C₂×C₈×C₄₃	—	2	2	no	—
344	C₂×C₈×C₄₃	—	2	2	no	—
345	C₂×C₈×C₄₃	#41	1	4	yes	complemented
346	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
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	C₄⋊C₄×C₄₃	—	2	2	no	—
351	C₄⋊C₄×C₄₃	—	2	2	no	—
352	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
353	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
354	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
355	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
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	C₄²×C₄₃	—	2	2	no	—
361	C₄²×C₄₃	—	2	2	no	—
362	C₄²×C₄₃	—	2	2	no	—
363	C₄²×C₄₃	—	2	2	no	—
364	C₂²⋊Dic₄₃	—	2	2	no	—
365	C₂²⋊Dic₄₃	—	2	2	no	—
366	C₂²⋊Dic₄₃	—	2	2	no	—
367	C₂²⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
368	C₂²⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
369	C₂²⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
370	C₂²⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
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	C₂⁴	1	2	yes	—
390	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
391	Dic₄₃⋊C₄	—	2	2	no	—
392	Dic₄₃⋊C₄	—	2	2	no	—
393	Dic₄₃⋊C₄	—	2	2	no	—
394	Dic₄₃⋊C₄	—	2	2	no	—
395	Dic₄₃⋊C₄	—	2	2	no	—
396	Dic₄₃⋊C₄	—	2	2	no	—
397	Dic₄₃⋊C₄	—	2	2	no	—
398	Dic₄₃⋊C₄	—	2	2	no	—
399	Dic₄₃⋊C₄	—	2	2	no	—
400	Dic₄₃⋊C₄	—	2	2	no	—
401	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
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	C₄×Dic₄₃	—	2	2	no	—
406	C₄×Dic₄₃	—	2	2	no	—
407	C₄×Dic₄₃	—	2	2	no	—
408	C₄×Dic₄₃	—	2	2	no	—
409	C₄×Dic₄₃	—	2	2	no	—
410	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
411	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
412	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
413	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
414	C₂×C₄₃⋊C₈	—	2	2	no	—
415	C₂×C₄₃⋊C₈	—	2	2	no	—
416	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
417	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
418	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
419	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
420	Dic₁₇₂	—	2	2	no	—
421	D₃₄₄	—	2	2	no	—
422	#10621873	—	2	4	no	—
423	C₈×D₄₃	—	2	2	no	—
424	C₈×D₄₃	—	2	2	no	—
425	C₈×D₄₃	—	2	2	no	—
426	C₈×D₄₃	—	2	2	no	—
427	C₂³×C₄₃	—	2	2	no	—
428	C₂³×C₄₃	—	2	2	no	—
429	C₂³×C₄₃	—	4	1	no	—
430	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
431	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
432	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
433	C₂²×D₄₃	—	2	2	no	—
434	C₂²×D₄₃	—	2	2	no	—
435	C₂²×D₄₃	—	2	2	no	—
436	C₂²×D₄₃	—	4	1	no	—
437	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
438	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
439	C₂×C₄×C₄₃	—	2	2	no	—
440	C₂×C₄×C₄₃	—	2	2	no	—
441	C₂×C₄×C₄₃	—	2	2	no	—
442	C₂×C₄×C₄₃	—	2	1	no	—
443	C₂×C₄×C₄₃	—	2	1	no	—
444	C₂×C₄×C₄₃	—	2	1	no	—
445	C₂×C₄×C₄₃	—	2	1	no	—
446	C₂×C₄×C₄₃	—	2	2	no	—
447	C₂×C₄×C₄₃	—	2	2	no	—
448	C₂×C₄×C₄₃	—	2	2	no	—
449	C₂×C₄×C₄₃	—	2	2	no	—
450	C₂×C₄×C₄₃	—	4	4	no	—
451	C₂×C₄×C₄₃	—	8	2	no	—
452	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
456	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
457	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
458	C₂²⋊D₄₃	—	2	2	no	—
459	C₂²⋊D₄₃	—	2	2	no	—
460	C₂²⋊D₄₃	—	2	2	no	—
461	C₂²⋊D₄₃	—	4	4	no	—
462	C₂²⋊D₄₃	—	4	4	no	—
463	C₂²⋊D₄₃	—	8	2	no	—
464	C₂²⋊D₄₃	#135	1	4	yes	complemented
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	—	2	2	no	—
470	C₂×Dic₄₃	—	4	1	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	2	no	—
483	C₄×D₄₃	—	2	1	no	—
484	C₄×D₄₃	—	2	1	no	—
485	C₄×D₄₃	—	2	1	no	—
486	C₄×D₄₃	—	2	1	no	—
487	C₄×D₄₃	—	4	4	no	—
488	C₄×D₄₃	—	4	4	no	—
489	C₄×D₄₃	—	4	4	no	—
490	C₄×D₄₃	—	8	2	no	—
491	C₄×D₄₃	—	8	2	no	—
492	Dic₈₆	—	2	2	no	—
493	Dic₈₆	—	2	2	no	—
494	Dic₈₆	—	4	4	no	—
495	Dic₈₆	—	8	2	no	—
496	C₈×C₄₃	—	2	1	no	—
497	C₈×C₄₃	—	2	1	no	—
498	C₈×C₄₃	C₂×#41	1	2	yes	—
499	C₈×C₄₃	C₂×#41	1	2	yes	—
500	C₄₃⋊C₈	—	2	1	no	—
501	C₄₃⋊C₈	—	2	1	no	—
502	C₄₃⋊C₈	—	2	1	no	—
503	C₄₃⋊C₈	—	2	1	no	—
504	#61234	—	43	1	no	maximal, Sylow
505	C₂²×C₄₃	—	2	1	no	—
506	C₂²×C₄₃	—	2	1	no	—
507	C₂²×C₄₃	—	2	1	no	—
508	C₂²×C₄₃	—	2	1	no	—
509	C₂²×C₄₃	—	2	1	no	—
510	C₂²×C₄₃	—	2	1	no	—
511	C₂²×C₄₃	—	2	1	no	—
512	C₂²×C₄₃	—	4	4	no	—
513	C₂²×C₄₃	#547	1	2	yes	—
514	C₂²×C₄₃	C₂×#135	1	2	yes	—
515	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
516	C₂×D₄₃	—	2	1	no	—
517	C₂×D₄₃	—	2	1	no	—
518	C₂×D₄₃	—	2	1	no	—
519	C₂×D₄₃	—	2	1	no	—
520	C₂×D₄₃	—	2	1	no	—
521	C₂×D₄₃	—	4	4	no	—
522	C₂×D₄₃	—	4	2	no	—
523	C₂×D₄₃	—	4	2	no	—
524	C₂×D₄₃	—	4	2	no	—
525	C₂×D₄₃	C₂×#135	1	2	yes	—
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	—	4	2	no	—
532	C₄×C₄₃	#547	1	2	yes	—
533	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
534	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
535	Dic₄₃	—	2	1	no	—
536	Dic₄₃	—	2	1	no	—
537	Dic₄₃	—	2	1	no	—
538	Dic₄₃	—	2	1	no	—
539	Dic₄₃	—	2	1	no	—
540	Dic₄₃	—	4	2	no	—
541	Dic₄₃	—	4	2	no	—
542	Dic₄₃	—	4	2	no	—
543	Dic₄₃	C₂×#135	1	2	yes	—
544	#3475	—	43	2	no	—
545	#3342	—	43	1	no	—
546	#3341	—	43	1	no	—
547	#3340	—	43	2	no	—
548	#3339	—	43	1	no	—
549	#3339	—	43	1	no	—
550	#3338	—	43	1	no	—
551	#3337	—	43	2	no	—
552	#3337	—	43	2	no	—
553	#3336	—	43	1	no	—
554	#3336	—	43	1	no	—
555	#3335	—	43	2	no	—
556	#3334	—	43	1	no	—
557	#3160	—	43	1	no	—
558	#3091	—	43	2	no	—
559	#3091	—	43	2	no	—
560	#3076	—	43	2	no	—
561	#3050	—	43	1	no	—
562	#3050	—	43	1	no	—
563	C₄×#135	—	43	1	no	—
564	C₂×C₈×D₄	—	43	1	no	—
565	C₂×#427	—	43	1	no	—
566	C₂×#427	D₄₃	1	1	yes	characteristic, complemented
567	C₂×C₄₃	—	2	2	no	—
568	C₂×C₄₃	—	2	2	no	—
569	C₂×C₄₃	—	4	1	no	—
570	C₂×C₄₃	C₂×#547	1	1	yes	characteristic
571	C₂×C₄₃	C₂²×#135	1	1	yes	characteristic
572	C₂×C₄₃	#3584	1	1	yes	characteristic
573	D₄₃	—	2	2	no	—
574	D₄₃	—	4	1	no	—
575	D₄₃	—	8	2	no	—
576	C₂×#135	—	43	1	no	—
577	C₂³×C₈	—	43	1	no	—
578	C₂³×C₈	C₂×D₄₃	1	1	yes	characteristic
579	#556	—	43	2	no	—
580	#555	—	43	2	no	—
581	#554	—	43	2	no	—
582	#553	—	43	2	no	—
583	#553	—	43	2	no	—
584	#552	—	43	2	no	—
585	#552	—	43	2	no	—
586	#552	—	86	2	no	—
587	#551	—	86	2	no	—
588	#551	—	86	2	no	—
589	#547	—	43	2	no	—
590	#546	—	86	2	no	—
591	#533	—	43	2	no	—
592	#529	—	86	2	no	—
593	#529	—	86	2	no	—
594	#529	—	86	2	no	—
595	#525	—	43	2	no	—
596	#525	—	43	2	no	—
597	C₄×#41	—	43	2	no	—
598	C₄×#41	—	86	2	no	—
599	C₂×C₄×D₄	—	43	1	no	—
600	C₂×#117	—	43	2	no	—
601	C₂×#117	C₂×D₄₃	1	2	yes	—
602	#500	—	43	1	no	—
603	#500	—	43	1	no	—
604	#499	—	43	1	no	—
605	#499	—	43	1	no	—
606	#499	—	43	2	no	—
607	#498	—	43	2	no	—
608	#485	—	43	2	no	—
609	#485	—	43	2	no	—
610	#485	—	43	2	no	—
611	#485	—	43	2	no	—
612	#484	—	43	2	no	—
613	#484	—	43	2	no	—
614	#483	—	43	2	no	—
615	#483	—	43	2	no	—
616	#482	—	43	2	no	—
617	#482	—	43	2	no	—
618	#482	—	43	2	no	—
619	#482	—	43	2	no	—
620	#481	—	43	2	no	—
621	#481	—	43	2	no	—
622	#480	—	43	2	no	—
623	#480	—	43	2	no	—
624	#479	—	43	2	no	—
625	#479	—	43	2	no	—
626	#478	—	43	2	no	—
627	#478	—	43	2	no	—
628	#477	—	43	2	no	—
629	#476	—	43	2	no	—
630	#475	—	43	2	no	—
631	#474	—	43	2	no	—
632	#467	—	43	1	no	—
633	#467	—	43	1	no	—
634	#467	—	43	1	no	—
635	#467	—	43	1	no	—
636	#466	—	43	1	no	—
637	#466	—	43	1	no	—
638	#466	—	43	1	no	—
639	#466	—	43	1	no	—
640	#465	—	43	2	no	—
641	#465	—	43	2	no	—
642	#465	—	43	2	no	—
643	#465	—	43	2	no	—
644	C₄×Q₁₆	—	43	1	no	—
645	C₄×Q₁₆	—	43	1	no	—
646	C₄×SD₁₆	—	43	2	no	—
647	C₄×SD₁₆	—	43	2	no	—
648	C₄×D₈	—	43	1	no	—
649	C₄×D₈	—	43	1	no	—
650	C₈×D₄	—	43	1	no	—
651	C₈×D₄	—	43	1	no	—
652	C₈×D₄	—	43	1	no	—
653	C₈×D₄	—	43	1	no	—
654	C₈×D₄	—	43	1	no	—
655	C₈×D₄	—	43	1	no	—
656	C₈×D₄	—	43	1	no	—
657	C₈×D₄	—	43	1	no	—
658	#427	—	43	1	no	—
659	#427	—	43	2	no	—
660	#427	—	43	2	no	—
661	#427	—	43	1	no	—
662	#427	—	43	1	no	—
663	#427	—	43	2	no	—
664	#427	C₂×D₄₃	1	2	yes	—
665	#427	C₂×D₄₃	1	1	yes	characteristic
666	#427	C₂×D₄₃	1	1	yes	characteristic
667	#427	C₂×D₄₃	1	1	yes	characteristic, complemented
668	#427	C₂×D₄₃	1	2	yes	complemented
669	#427	C₂×D₄₃	1	1	yes	characteristic, complemented
670	C₂×#107	—	43	1	no	—
671	C₂×#107	—	43	1	no	—
672	C₂×#107	C₂×D₄₃	1	1	yes	characteristic, complemented
673	C₂×#107	C₂×D₄₃	1	1	yes	characteristic, complemented
674	C₂×#106	—	43	2	no	—
675	C₂×#106	C₂×D₄₃	1	2	yes	complemented
676	C₂×C₄⋊C₈	—	43	1	no	—
677	#416	—	43	2	no	—
678	#416	—	43	2	no	—
679	#416	—	43	2	no	—
680	C₂×C₂²⋊C₈	—	43	1	no	—
681	C₂×C₂²⋊C₈	—	43	1	no	—
682	C₂×C₄×C₈	—	43	1	no	—
683	C₄₃	#61234	1	1	yes	characteristic, complemented, Sylow
684	C₂×#41	—	43	2	no	—
685	C₂×#41	—	86	2	no	—
686	C₂²×D₄	—	43	1	no	—
687	C₂³×C₄	—	43	1	no	—
688	C₂³×C₄	C₂²×D₄₃	1	1	yes	characteristic
689	#135	—	86	4	no	—
690	C₂×Q₁₆	—	43	1	no	—
691	C₂×SD₁₆	—	43	2	no	—
692	C₂×D₈	—	43	1	no	—
693	C₂²×C₈	—	2	4	no	—
694	C₂²×C₈	—	43	1	no	—
695	C₂²×C₈	—	43	1	no	—
696	C₂²×C₈	—	43	1	no	—
697	C₂²×C₈	—	43	1	no	—
698	C₂²×C₈	—	43	1	no	—
699	C₂²×C₈	—	43	1	no	—
700	C₂²×C₈	—	86	4	no	—
701	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
702	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
703	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
704	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
705	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
706	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
707	C₄⋊Q₈	—	43	2	no	—
708	C₄⋊Q₈	—	43	2	no	—
709	#126	—	86	2	no	—
710	#126	—	86	2	no	—
711	#126	—	86	2	no	—
712	#126	—	86	2	no	—
713	#126	—	86	2	no	—
714	#126	—	86	2	no	—
715	#125	—	43	2	no	—
716	#125	—	43	2	no	—
717	#125	—	86	2	no	—
718	#125	—	86	2	no	—
719	#125	—	86	2	no	—
720	#124	—	86	2	no	—
721	#124	—	86	2	no	—
722	#124	—	86	2	no	—
723	#123	—	86	2	no	—
724	#123	—	86	2	no	—
725	#123	—	86	2	no	—
726	#123	—	86	2	no	—
727	#123	—	86	2	no	—
728	#123	—	86	2	no	—
729	#123	—	86	2	no	—
730	#123	—	86	2	no	—
731	C₂²⋊Q₈	—	43	2	no	—
732	C₂²⋊Q₈	—	43	2	no	—
733	C₂²⋊Q₈	—	43	2	no	—
734	C₂²⋊Q₈	—	43	2	no	—
735	C₂²⋊Q₈	—	86	2	no	—
736	C₂²⋊Q₈	—	86	2	no	—
737	C₂²⋊Q₈	—	86	2	no	—
738	C₂²⋊Q₈	—	86	2	no	—
739	C₂²⋊Q₈	—	86	2	no	—
740	#121	—	43	2	no	—
741	#121	—	43	2	no	—
742	#121	—	43	2	no	—
743	#121	—	43	2	no	—
744	#121	—	86	2	no	—
745	#121	—	86	2	no	—
746	#121	—	86	2	no	—
747	#120	—	86	2	no	—
748	#120	—	86	2	no	—
749	C₄×Q₈	—	43	2	no	—
750	C₄×Q₈	—	43	2	no	—
751	C₄×Q₈	—	86	2	no	—
752	C₄×Q₈	—	86	2	no	—
753	C₄×Q₈	—	86	2	no	—
754	C₄×D₄	—	43	1	no	—
755	C₄×D₄	—	43	1	no	—
756	C₄×D₄	—	43	1	no	—
757	C₄×D₄	—	43	1	no	—
758	C₄×D₄	—	43	1	no	—
759	C₄×D₄	—	43	1	no	—
760	C₄×D₄	—	43	1	no	—
761	C₄×D₄	—	43	1	no	—
762	C₄×D₄	—	43	2	no	—
763	C₄×D₄	—	43	2	no	—
764	C₄×D₄	—	86	2	no	—
765	C₄×D₄	—	86	2	no	—
766	C₄×D₄	—	86	2	no	—
767	C₄×D₄	—	86	2	no	—
768	C₄×D₄	—	86	2	no	—
769	C₄×D₄	—	86	2	no	—
770	C₄×D₄	—	86	2	no	—
771	C₄×D₄	—	86	2	no	—
772	C₄×D₄	—	86	2	no	—
773	#117	—	2	2	no	—
774	#117	—	2	2	no	—
775	#117	—	43	2	no	—
776	#117	—	43	2	no	—
777	#117	—	43	2	no	—
778	#117	—	86	2	no	—
779	#117	—	86	2	no	—
780	#117	—	86	2	no	—
781	#117	—	86	2	no	—
782	#117	—	86	2	no	—
783	#117	—	86	2	no	—
784	#117	C₂²×D₄₃	1	2	yes	—
785	#117	C₂²×D₄₃	1	2	yes	—
786	#117	C₂²×D₄₃	1	2	yes	—
787	#117	C₂²×D₄₃	1	2	yes	—
788	C₂×C₄⋊C₄	—	43	1	no	—
789	C₂×C₄⋊C₄	—	43	2	no	—
790	C₂×C₄⋊C₄	—	43	2	no	—
791	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
792	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
793	C₂×C₂²⋊C₄	—	2	2	no	—
794	C₂×C₂²⋊C₄	—	43	1	no	—
795	C₂×C₂²⋊C₄	—	43	1	no	—
796	C₂×C₂²⋊C₄	—	86	2	no	—
797	C₂×C₄²	—	2	2	no	—
798	C₂×C₄²	—	43	1	no	—
799	C₂×C₄²	—	86	2	no	—
800	C₂×C₄²	—	86	2	no	—
801	#107	—	43	1	no	—
802	#107	—	43	1	no	—
803	#107	—	43	2	no	—
804	#107	—	43	2	no	—
805	#107	—	43	2	no	—
806	#107	—	43	2	no	—
807	#107	C₂²×D₄₃	1	1	yes	characteristic
808	#107	C₂²×D₄₃	1	1	yes	characteristic
809	#107	C₂²×D₄₃	1	1	yes	characteristic
810	#107	C₂²×D₄₃	1	1	yes	characteristic
811	#107	C₂²×D₄₃	1	2	yes	—
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	#106	—	43	2	no	—
818	#106	C₂²×D₄₃	1	2	yes	—
819	#106	C₂²×D₄₃	1	2	yes	—
820	#106	C₂²×D₄₃	1	2	yes	—
821	#106	C₂²×D₄₃	1	2	yes	—
822	C₄⋊C₈	—	43	1	no	—
823	C₄⋊C₈	—	43	1	no	—
824	C₄⋊C₈	—	43	1	no	—
825	C₄⋊C₈	—	43	1	no	—
826	#103	—	43	2	no	—
827	#103	—	43	2	no	—
828	#103	—	43	2	no	—
829	#103	—	43	2	no	—
830	#103	—	43	2	no	—
831	#103	—	43	2	no	—
832	#102	—	43	2	no	—
833	#102	—	43	2	no	—
834	#102	—	43	2	no	—
835	#102	—	43	2	no	—
836	#102	—	43	2	no	—
837	#102	—	43	2	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	C₂²⋊C₈	—	43	1	no	—
844	C₂²⋊C₈	—	43	1	no	—
845	C₂²⋊C₈	—	43	1	no	—
846	C₄×C₈	—	43	1	no	—
847	C₄×C₈	—	43	1	no	—
848	C₄×C₈	—	43	1	no	—
849	C₄×C₈	—	43	1	no	—
850	C₂⁴	—	43	1	no	—
851	C₂⁴	D₄×D₄₃	1	1	yes	characteristic
852	#41	—	86	4	no	—
853	#41	—	86	4	no	—
854	#41	—	172	8	no	—
855	C₂×Q₈	—	43	2	no	—
856	C₂×Q₈	—	86	2	no	—
857	C₂×Q₈	—	86	2	no	—
858	C₂×D₄	—	43	1	no	—
859	C₂×D₄	—	43	1	no	—
860	C₂×D₄	—	43	1	no	—
861	C₂×D₄	—	43	1	no	—
862	C₂×D₄	—	43	2	no	—
863	C₂×D₄	—	86	2	no	—
864	C₂×D₄	—	86	2	no	—
865	C₂×D₄	—	86	4	no	—
866	C₂×D₄	—	86	2	no	—
867	C₂×D₄	—	86	2	no	—
868	C₂×D₄	—	86	2	no	—
869	C₂²×C₄	—	2	2	no	—
870	C₂²×C₄	—	2	2	no	—
871	C₂²×C₄	—	2	2	no	—
872	C₂²×C₄	—	2	2	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	—	43	1	no	—
879	C₂²×C₄	—	43	1	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	—	86	2	no	—
886	C₂²×C₄	—	86	2	no	—
887	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
888	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
889	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
890	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
891	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
892	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
893	Q₁₆	—	86	2	no	—
894	SD₁₆	—	86	4	no	—
895	D₈	—	86	2	no	—
896	C₂×C₈	—	2	2	no	—
897	C₂×C₈	—	2	2	no	—
898	C₂×C₈	—	2	2	no	—
899	C₂×C₈	—	2	2	no	—
900	C₂×C₈	—	2	2	no	—
901	C₂×C₈	—	43	1	no	—
902	C₂×C₈	—	43	1	no	—
903	C₂×C₈	—	43	1	no	—
904	C₂×C₈	—	43	1	no	—
905	C₂×C₈	—	86	2	no	—
906	C₂×C₈	—	86	2	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	#10621898	1	4	yes	complemented
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	—	43	1	no	—
919	C₄⋊C₄	—	43	1	no	—
920	C₄⋊C₄	—	43	1	no	—
921	C₄⋊C₄	—	43	1	no	—
922	C₄⋊C₄	—	43	2	no	—
923	C₄⋊C₄	—	43	2	no	—
924	C₄⋊C₄	—	86	2	no	—
925	C₄⋊C₄	—	86	2	no	—
926	C₄⋊C₄	—	86	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	C₂³×D₄₃	1	2	yes	—
939	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
940	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
941	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
942	C₂²⋊C₄	—	2	2	no	—
943	C₂²⋊C₄	—	2	2	no	—
944	C₂²⋊C₄	—	2	2	no	—
945	C₂²⋊C₄	—	2	2	no	—
946	C₂²⋊C₄	—	43	1	no	—
947	C₂²⋊C₄	—	43	1	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	—	86	2	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	C₄²	—	2	2	no	—
968	C₄²	—	2	2	no	—
969	C₄²	—	2	2	no	—
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	—	86	2	no	—
976	C₄²	—	86	2	no	—
977	C₄²	—	86	2	no	—
978	C₄²	—	86	2	no	—
979	C₄²	—	86	2	no	—
980	C₂³	—	2	2	no	—
981	C₂³	—	2	2	no	—
982	C₂³	—	4	1	no	—
983	C₂³	—	43	1	no	—
984	C₂³	—	43	1	no	—
985	C₂³	—	86	2	no	—
986	C₂³	—	86	2	no	—
987	C₂³	—	86	2	no	—
988	C₂³	—	172	1	no	—
989	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
990	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
991	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
992	Q₈	—	86	2	no	—
993	Q₈	—	86	2	no	—
994	Q₈	—	344	2	no	—
995	Q₈	—	172	4	no	—
996	D₄	—	43	4	no	—
997	D₄	—	86	2	no	—
998	D₄	—	86	2	no	—
999	D₄	—	86	2	no	—
1000	D₄	—	86	2	no	—
1001	D₄	—	86	2	no	—
1002	D₄	—	344	2	no	—
1003	D₄	—	344	2	no	—
1004	D₄	—	172	4	no	—
1005	D₄	—	172	4	no	—
1006	D₄	—	172	4	no	—
1007	C₂×C₄	—	2	2	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	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	—	2	2	no	—
1016	C₂×C₄	—	2	2	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	4	4	no	—
1019	C₂×C₄	—	8	2	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	—	43	1	no	—
1025	C₂×C₄	—	43	1	no	—
1026	C₂×C₄	—	86	2	no	—
1027	C₂×C₄	—	86	2	no	—
1028	C₂×C₄	—	86	1	no	—
1029	C₂×C₄	—	86	1	no	—
1030	C₂×C₄	—	86	1	no	—
1031	C₂×C₄	—	86	1	no	—
1032	C₂×C₄	—	86	2	no	—
1033	C₂×C₄	—	86	2	no	—
1034	C₂×C₄	—	86	2	no	—
1035	C₂×C₄	—	86	2	no	—
1036	C₂×C₄	—	86	2	no	—
1037	C₂×C₄	—	344	2	no	—
1038	C₂×C₄	—	344	2	no	—
1039	C₂×C₄	—	172	4	no	—
1040	C₂×C₄	—	172	4	no	—
1041	C₂×C₄	—	172	1	no	—
1042	C₂×C₄	—	172	4	no	—
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	C₂×#10621898	1	2	yes	—
1047	C₂×C₄	#13063373	1	2	yes	—
1048	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1049	C₈	—	2	1	no	—
1050	C₈	—	2	1	no	—
1051	C₈	—	86	1	no	—
1052	C₈	—	86	1	no	—
1053	C₈	—	86	1	no	—
1054	C₈	—	86	1	no	—
1055	C₈	C₂×#10621898	1	2	yes	—
1056	C₈	C₂×#10621898	1	2	yes	—
1057	C₂²	—	2	1	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	2	1	no	—
1061	C₂²	—	2	1	no	—
1062	C₂²	—	2	1	no	—
1063	C₂²	—	2	1	no	—
1064	C₂²	—	4	4	no	—
1065	C₂²	—	43	2	no	—
1066	C₂²	—	86	1	no	—
1067	C₂²	—	86	1	no	—
1068	C₂²	—	86	1	no	—
1069	C₂²	—	86	1	no	—
1070	C₂²	—	86	1	no	—
1071	C₂²	—	172	4	no	—
1072	C₂²	—	172	2	no	—
1073	C₂²	—	172	2	no	—
1074	C₂²	—	172	2	no	—
1075	C₂²	#14583550	1	2	yes	—
1076	C₂²	#135×D₄₃	1	2	yes	—
1077	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1078	C₄	—	2	1	no	—
1079	C₄	—	2	1	no	—
1080	C₄	—	4	2	no	—
1081	C₄	—	4	2	no	—
1082	C₄	—	4	2	no	—
1083	C₄	—	4	2	no	—
1084	C₄	—	43	2	no	—
1085	C₄	—	86	1	no	—
1086	C₄	—	86	1	no	—
1087	C₄	—	86	1	no	—
1088	C₄	—	86	1	no	—
1089	C₄	—	86	1	no	—
1090	C₄	—	172	2	no	—
1091	C₄	—	172	2	no	—
1092	C₄	—	172	2	no	—
1093	C₄	#14583550	1	2	yes	—
1094	C₄	C₂²×#10621898	1	1	yes	characteristic
1095	C₄	C₂×#13063373	1	1	yes	characteristic
1096	C₂	—	2	2	no	—
1097	C₂	—	2	2	no	—
1098	C₂	—	4	1	no	—
1099	C₂	—	86	2	no	—
1100	C₂	—	344	2	no	—
1101	C₂	—	172	1	no	—
1102	C₂	C₂×#14583550	1	1	yes	characteristic
1103	C₂	C₂×#135×D₄₃	1	1	yes	characteristic
1104	C₂	#19149364	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₄₃×#427	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	C₂×#427	D₄₃
hypocenter	C₄₃	#61234
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₄ ◁ C₂×#427

Complements

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

N	H ≅ G/N	type
1. #19148149	C₂	semidirect
2. #19147023	C₂	semidirect
3. #19147015	C₂	semidirect
4. #19147004	C₂	semidirect
5. #19146997	C₂	semidirect
6. #19146993	C₂	semidirect
7. #19146985	C₂	semidirect
8. #19146975	C₂	semidirect
9. #19146970	C₂	semidirect
10. #19146963	C₂	semidirect
11. #19146959	C₂	semidirect
12. #19146948	C₂	semidirect
13. #19146940	C₂	semidirect
14. #19145107	C₂	semidirect
15. #19144512	C₂	semidirect
16. #19144508	C₂	semidirect
17. #19144381	C₂	semidirect
18. #19144177	C₂	semidirect
19. #19144176	C₂	semidirect
20. #19143366	C₂	semidirect
21. C₂×C₈×C₂²⋊D₄₃	C₂	semidirect
22. #427×D₄₃	C₂	semidirect
23. C₂×C₄₃×#427	C₂	semidirect
48. #14583303	C₂²	semidirect
49. #14583303	C₂²	semidirect
50. #14583300	C₂²	semidirect
51. #14583300	C₂²	semidirect
52. #14583299	C₂²	semidirect
53. #14583296	C₂²	semidirect
54. #14583243	C₂²	semidirect
55. #14583242	C₂²	semidirect
56. #14583240	C₂²	semidirect
57. #14583240	C₂²	semidirect
58. #14583236	C₂²	semidirect
59. #14583234	C₂²	semidirect
60. #14583231	C₂²	semidirect
61. #14583229	C₂²	semidirect
62. #14583226	C₂²	semidirect
63. #14583225	C₂²	semidirect
64. #14583223	C₂²	semidirect
65. #14583223	C₂²	semidirect
66. #14583219	C₂²	semidirect
67. #14583217	C₂²	semidirect
68. #14583214	C₂²	semidirect
69. #14583212	C₂²	semidirect
70. #14583209	C₂²	semidirect
71. #14583205	C₂²	semidirect
72. #14583202	C₂²	semidirect
73. #14583198	C₂²	semidirect
74. #14583193	C₂²	semidirect
75. #14583188	C₂²	semidirect
76. #14583183	C₂²	semidirect
77. #14583178	C₂²	semidirect
78. #14583141	C₂²	semidirect
79. #14583141	C₂²	semidirect
80. #14583140	C₂²	semidirect
81. #14583140	C₂²	semidirect
82. #14583136	C₂²	semidirect
83. #14583136	C₂²	semidirect
84. #14583135	C₂²	semidirect
85. #14583135	C₂²	semidirect
86. #14583129	C₂²	semidirect
87. #14583129	C₂²	semidirect
88. #14583128	C₂²	semidirect
89. #14583128	C₂²	semidirect
90. #14582993	C₂²	semidirect
91. #14582993	C₂²	semidirect
92. #14582986	C₂²	semidirect
93. #14582986	C₂²	semidirect
94. #14582981	C₂²	semidirect
95. #14582981	C₂²	semidirect
105. #14582936	C₂²	semidirect
106. #14582936	C₂²	semidirect
109. #14582934	C₂²	semidirect
110. #107×D₄₃	C₂²	semidirect
111. #107×D₄₃	C₂²	semidirect
112. #106×D₄₃	C₂²	semidirect
125. C₄₃×#427	C₂²	semidirect
126. C₄₃×#427	C₂²	semidirect
127. C₄₃×#427	C₂²	semidirect
128. C₂×#107×C₄₃	C₂²	semidirect
129. C₂×#107×C₄₃	C₂²	semidirect
130. C₂×#106×C₄₃	C₂²	semidirect
345. C₂×C₈×C₄₃	#41	semidirect
464. C₂²⋊D₄₃	#135	semidirect
566. C₂×#427	D₄₃	semidirect
667. #427	C₂×D₄₃	semidirect
668. #427	C₂×D₄₃	semidirect
669. #427	C₂×D₄₃	semidirect
672. C₂×#107	C₂×D₄₃	semidirect
673. C₂×#107	C₂×D₄₃	semidirect
675. C₂×#106	C₂×D₄₃	semidirect
683. C₄₃	#61234	semidirect
911. C₂×C₈	#10621898	semidirect

Maximal subgroups

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

subgroup	index
#19148149	2
#19147023	2
#19147015	2
#19147004	2
#19146997	2
#19146993	2
#19146985	2
#19146975	2
#19146970	2
#19146963	2
#19146959	2
#19146948	2
#19146940	2
#19145107	2
#19144512	2
#19144508	2
#19144381	2
#19144177	2
#19144176	2
#19143366	2
C₂×C₈×C₂²⋊D₄₃	2
#427×D₄₃	2
C₂×C₄₃×#427	2
#61234	43