Subgroups — #25978209

Order 11008.

1836 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148159	C₂	1	1	yes	maximal, characteristic
2	#19147622	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147501	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147372	C₂	1	1	yes	maximal, characteristic, complemented
5	#19147335	C₂	1	1	yes	maximal, characteristic, complemented
6	#19147221	C₂	1	1	yes	maximal, characteristic, complemented
7	#19147044	C₂	1	2	yes	maximal, complemented
8	#19146905	C₂	1	1	yes	maximal, characteristic, complemented
9	#19146889	C₂	1	1	yes	maximal, characteristic, complemented
10	#19146670	C₂	1	2	yes	maximal, complemented
11	#19146646	C₂	1	2	yes	maximal, complemented
12	#19146241	C₂	1	1	yes	maximal, characteristic, complemented
13	#19146106	C₂	1	2	yes	maximal, complemented
14	#19145195	C₂	1	2	yes	maximal, complemented
15	#19145177	C₂	1	1	yes	maximal, characteristic, complemented
16	#19144675	C₂	1	2	yes	maximal, complemented
17	#19144660	C₂	1	2	yes	maximal, complemented
18	#19144634	C₂	1	1	yes	maximal, characteristic, complemented
19	#19144599	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143562	C₂	1	1	yes	maximal, characteristic, complemented
21	C₄×#13063356	C₂	1	2	yes	maximal, complemented
22	C₂×C₄×#10621884	C₂	1	1	yes	maximal, characteristic, complemented
23	Q₈×#41×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063356	C₂²	1	2	yes	—
25	C₂²×#10621884	C₂²	1	1	yes	characteristic
26	#14583622	C₂²	1	1	yes	characteristic
27	#14583614	C₂²	1	1	yes	characteristic
28	#14583609	C₂²	1	1	yes	characteristic
29	#14583599	—	2	1	no	—
30	#14583590	—	2	1	no	—
31	#14583589	C₂²	1	2	yes	—
32	#14583578	—	2	2	no	—
33	#14583554	C₂²	1	1	yes	characteristic
34	#14583545	C₂²	1	2	yes	—
35	#14583456	C₂²	1	1	yes	characteristic
36	#14583433	C₂²	1	2	yes	—
37	#14583427	—	2	2	no	—
38	#14583406	—	2	1	no	—
39	C₄×#10621898	C₂²	1	2	yes	—
40	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
41	#117×D₄₃	—	2	1	no	—
42	#14583305	C₂²	1	2	yes	complemented
43	#14583302	C₂²	1	1	yes	characteristic, complemented
44	#14583291	C₂²	1	2	yes	—
45	#14583278	C₂²	1	1	yes	characteristic, complemented
46	#14583267	C₂²	1	2	yes	complemented
47	#14583261	C₂²	1	2	yes	—
48	#14583251	C₂²	1	1	yes	characteristic, complemented
49	#14583249	C₂²	1	1	yes	characteristic, complemented
50	#14583237	C₂²	1	2	yes	complemented
51	#14583237	C₂²	1	2	yes	complemented
52	#14583234	C₂²	1	2	yes	—
53	#14583229	C₂²	1	2	yes	complemented
54	#14583227	C₂²	1	2	yes	—
55	#14583212	C₂²	1	2	yes	—
56	#14583206	C₂²	1	2	yes	complemented
57	#14583206	C₂²	1	2	yes	complemented
58	#14583194	C₂²	1	1	yes	characteristic, complemented
59	#14583194	C₂²	1	1	yes	characteristic, complemented
60	#14583186	C₂²	1	1	yes	characteristic
61	#14583186	C₂²	1	1	yes	characteristic
62	#14583181	C₂²	1	2	yes	complemented
63	#14583176	C₂²	1	2	yes	—
64	#14583155	C₂²	1	2	yes	complemented
65	#14583155	C₂²	1	2	yes	complemented
66	#14583147	C₂²	1	2	yes	—
67	#14583147	C₂²	1	2	yes	—
68	#14583138	C₂²	1	2	yes	—
69	#14583138	C₂²	1	2	yes	—
70	#14583121	C₂²	1	2	yes	—
71	#14583121	C₂²	1	2	yes	—
72	#14583109	C₂²	1	1	yes	characteristic, complemented
73	#14583109	C₂²	1	1	yes	characteristic, complemented
74	#14583106	C₂²	1	2	yes	complemented
75	#14583101	C₂²	1	1	yes	characteristic
76	#14583101	C₂²	1	1	yes	characteristic
77	#14583101	C₂²	1	2	yes	—
78	#14583059	C₂²	1	2	yes	—
79	#14583059	C₂²	1	2	yes	—
80	#14583055	C₂²	1	2	yes	—
81	#14583055	C₂²	1	2	yes	complemented
82	#14583049	C₂²	1	2	yes	—
83	#14583038	C₂²	1	2	yes	—
84	#14583030	C₂²	1	1	yes	characteristic, complemented
85	#14583030	C₂²	1	1	yes	characteristic, complemented
86	#14583004	C₂²	1	2	yes	complemented
87	#14583004	C₂²	1	2	yes	complemented
88	#14582997	C₂²	1	2	yes	—
89	#14582997	C₂²	1	2	yes	—
90	C₄×#10621885	C₂²	1	2	yes	complemented
91	C₄×#10621885	C₂²	1	2	yes	complemented
92	C₄×#10621885	C₂²	1	2	yes	complemented
93	C₄×#10621885	C₂²	1	2	yes	complemented
94	C₄×#10621884	C₂²	1	1	yes	characteristic
95	C₄×#10621884	C₂²	1	1	yes	characteristic
96	C₄×#10621884	C₂²	1	1	yes	characteristic
97	C₄×#10621884	C₂²	1	1	yes	characteristic
98	C₄×#10621884	C₂²	1	2	yes	—
99	C₄×#10621884	C₂²	1	2	yes	—
100	C₄×#10621884	C₂²	1	1	yes	characteristic
101	C₄×#10621884	C₂²	1	1	yes	characteristic
102	C₄×#10621884	C₂²	1	1	yes	characteristic
103	C₄×#10621884	C₂²	1	1	yes	characteristic
104	#14582977	C₂²	1	1	yes	characteristic, complemented
105	#14582977	C₂²	1	1	yes	characteristic, complemented
106	#14582971	C₂²	1	2	yes	—
107	#14582971	C₂²	1	2	yes	—
108	#14582952	C₂²	1	1	yes	characteristic
109	#14582952	C₂²	1	2	yes	complemented
110	#14582939	C₂²	1	2	yes	complemented
111	C₂×#13063256	C₂²	1	1	yes	characteristic
112	#14582908	C₂²	1	2	yes	complemented
113	#14582898	C₂²	1	2	yes	—
114	C₂×#13063249	C₂²	1	1	yes	characteristic
115	C₂×#13063245	C₂²	1	1	yes	characteristic
116	C₄×#10621877	C₂²	1	2	yes	complemented
117	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
118	Q₈²×C₄₃	C₂²	1	1	yes	characteristic, complemented
119	C₄₃×#557	—	2	1	no	—
120	C₄₃×#557	C₂²	1	1	yes	characteristic, complemented
121	C₄₃×#554	—	2	2	no	—
122	C₄₃×#554	—	2	1	no	—
123	C₄₃×#554	C₂²	1	2	yes	—
124	C₄₃×#554	C₂²	1	1	yes	characteristic, complemented
125	D₄×Q₈×C₄₃	C₂²	1	2	yes	—
126	D₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
127	C₄₃×#533	—	2	1	no	—
128	C₄₃×#533	—	2	2	no	—
129	C₄₃×#533	C₂²	1	1	yes	characteristic
130	C₄₃×#533	C₂²	1	2	yes	complemented
131	C₄×#41×C₄₃	—	2	1	no	—
132	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
133	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
134	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	complemented
135	C₂×#10621898	C₂³	1	2	yes	—
136	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
137	C₂²×C₄×D₄₃	—	2	1	no	—
138	#13063356	—	2	8	no	—
139	C₂×#10621885	C₂³	1	2	yes	—
140	C₂×#10621885	C₂³	1	2	yes	—
141	C₂×#10621885	C₂³	1	2	yes	—
142	C₂×#10621885	C₂³	1	2	yes	—
143	C₂×#10621884	—	2	4	no	—
144	C₂×#10621884	C₂³	1	2	yes	—
145	C₂×#10621884	C₂³	1	1	yes	characteristic
146	C₂×#10621884	C₂³	1	1	yes	characteristic
147	C₂×#10621884	C₂³	1	1	yes	characteristic
148	C₂×#10621884	C₂³	1	2	yes	—
149	C₂×#10621884	C₂³	1	1	yes	characteristic
150	C₂×#10621877	C₂³	1	2	yes	—
151	C₂×#10621877	C₂³	1	2	yes	—
152	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
153	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
154	#13063325	C₂³	1	1	yes	characteristic
155	#13063325	C₂³	1	1	yes	characteristic
156	#13063320	—	2	2	no	—
157	#13063319	—	2	2	no	—
158	#13063318	—	2	2	no	—
159	#13063317	—	2	1	no	—
160	#13063317	C₂³	1	2	yes	—
161	#13063315	—	2	2	no	—
162	#13063313	C₂³	1	2	yes	—
163	#13063311	—	2	2	no	—
164	#13063310	—	2	2	no	—
165	#13063308	—	2	2	no	—
166	#13063307	—	2	2	no	—
167	#13063306	—	2	2	no	—
168	#13063304	—	2	1	no	—
169	#13063304	C₂³	1	2	yes	—
170	#13063304	C₂³	1	2	yes	—
171	#13063303	—	2	2	no	—
172	#13063301	—	2	1	no	—
173	#13063301	—	2	1	no	—
174	#13063299	C₂³	1	2	yes	—
175	#13063298	—	2	2	no	—
176	#13063296	—	2	1	no	—
177	#13063296	—	2	1	no	—
178	#13063293	—	2	2	no	—
179	C₄×Dic₈₆	—	2	1	no	—
180	C₄×Dic₈₆	C₂³	1	2	yes	—
181	C₄×Dic₈₆	C₂³	1	2	yes	—
182	C₄×D₁₇₂	—	2	1	no	—
183	C₄×D₁₇₂	—	2	1	no	—
184	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
185	C₄×D₁₇₂	C₂³	1	2	yes	—
186	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
187	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
188	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
189	C₄×C₂²⋊D₄₃	—	2	2	no	—
190	C₄×C₂²⋊D₄₃	—	2	2	no	—
191	C₄×C₂²⋊D₄₃	—	2	2	no	—
192	#13063284	—	2	1	no	—
193	#13063284	C₂³	1	2	yes	—
194	#13063283	—	2	1	no	—
195	#13063283	—	2	1	no	—
196	#13063282	—	2	2	no	—
197	#13063282	—	2	2	no	—
198	#13063281	—	2	2	no	—
199	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
200	C₄⋊C₄×D₄₃	—	2	1	no	—
201	C₄⋊C₄×D₄₃	—	2	1	no	—
202	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
203	C₂²⋊C₄×D₄₃	—	2	2	no	—
204	C₄²×D₄₃	—	2	2	no	—
205	#13063258	C₂³	1	2	yes	—
206	#13063258	C₂³	1	2	yes	—
207	#13063258	C₂³	1	2	yes	—
208	#13063258	C₂³	1	2	yes	—
209	#13063256	C₂³	1	1	yes	characteristic
210	#13063256	C₂³	1	2	yes	—
211	#13063256	C₂³	1	1	yes	characteristic
212	#13063256	C₂³	1	2	yes	—
213	#13063256	C₂³	1	1	yes	characteristic
214	#13063256	C₂³	1	1	yes	characteristic
215	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
216	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
217	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
218	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
219	#13063249	C₂³	1	2	yes	—
220	#13063249	C₂³	1	2	yes	—
221	#13063249	C₂³	1	1	yes	characteristic
222	#13063249	C₂³	1	2	yes	—
223	#13063249	C₂³	1	2	yes	—
224	#13063249	C₂³	1	2	yes	—
225	#13063249	C₂³	1	1	yes	characteristic
226	#13063249	C₂³	1	2	yes	—
227	#13063249	C₂³	1	1	yes	characteristic
228	#13063249	C₂³	1	1	yes	characteristic
229	#13063248	C₂³	1	2	yes	—
230	#13063248	C₂³	1	2	yes	—
231	#13063248	C₂³	1	2	yes	—
232	#13063248	C₂³	1	2	yes	—
233	#13063245	C₂³	1	2	yes	—
234	#13063245	C₂³	1	2	yes	—
235	#13063245	C₂³	1	1	yes	characteristic
236	#13063245	C₂³	1	1	yes	characteristic
237	#13063245	C₂³	1	1	yes	characteristic
238	#13063245	C₂³	1	1	yes	characteristic
239	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
240	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
241	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
242	#13063236	C₂³	1	2	yes	—
243	#13063236	C₂³	1	2	yes	—
244	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
245	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
246	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
247	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
248	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
249	C₂×#41×C₄₃	D₄	1	1	yes	characteristic
250	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
251	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
252	C₄⋊Q₈×C₄₃	—	2	2	no	—
253	C₄⋊Q₈×C₄₃	—	2	1	no	—
254	C₄⋊Q₈×C₄₃	—	2	1	no	—
255	C₄⋊Q₈×C₄₃	—	2	2	no	—
256	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
257	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
258	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
259	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
260	#125×C₄₃	—	2	1	no	—
261	#125×C₄₃	—	2	2	no	—
262	#125×C₄₃	—	2	2	no	—
263	#125×C₄₃	—	2	1	no	—
264	#125×C₄₃	—	2	1	no	—
265	#125×C₄₃	—	2	2	no	—
266	C₂²⋊Q₈×C₄₃	—	2	1	no	—
267	C₂²⋊Q₈×C₄₃	—	2	2	no	—
268	C₂²⋊Q₈×C₄₃	—	2	2	no	—
269	C₂²⋊Q₈×C₄₃	—	2	2	no	—
270	C₂²⋊Q₈×C₄₃	—	2	2	no	—
271	C₂²⋊Q₈×C₄₃	—	2	2	no	—
272	C₂²⋊Q₈×C₄₃	—	2	2	no	—
273	C₂²⋊Q₈×C₄₃	—	2	2	no	—
274	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
275	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
276	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
277	C₄×Q₈×C₄₃	—	2	1	no	—
278	C₄×Q₈×C₄₃	—	2	1	no	—
279	C₄×Q₈×C₄₃	—	2	1	no	—
280	C₄×Q₈×C₄₃	—	2	1	no	—
281	C₄×Q₈×C₄₃	—	2	2	no	—
282	C₄×Q₈×C₄₃	—	2	2	no	—
283	C₄×Q₈×C₄₃	—	2	1	no	—
284	C₄×Q₈×C₄₃	—	2	2	no	—
285	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
286	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
287	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
288	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
289	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
290	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
291	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
292	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
293	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
294	C₄×D₄×C₄₃	—	2	2	no	—
295	C₄×D₄×C₄₃	—	2	1	no	—
296	C₄×D₄×C₄₃	—	2	2	no	—
297	C₄×D₄×C₄₃	—	2	1	no	—
298	C₄×D₄×C₄₃	D₄	1	2	yes	—
299	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
300	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
301	C₄×D₄×C₄₃	C₂³	1	2	yes	—
302	#117×C₄₃	—	2	1	no	—
303	#117×C₄₃	—	2	2	no	—
304	#117×C₄₃	D₄	1	1	yes	characteristic
305	#117×C₄₃	D₄	1	2	yes	—
306	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
307	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
308	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
309	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
310	C₂×C₄²×C₄₃	—	2	1	no	—
311	C₂×C₄²×C₄₃	—	2	2	no	—
312	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
313	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
314	C₂³×D₄₃	—	2	1	no	—
315	#41×C₄₃	—	2	4	no	—
316	C₂×Q₈×C₄₃	—	2	2	no	—
317	C₂×Q₈×C₄₃	—	2	1	no	—
318	C₂×Q₈×C₄₃	—	2	2	no	—
319	C₂×Q₈×C₄₃	—	2	1	no	—
320	C₂×Q₈×C₄₃	—	2	2	no	—
321	C₂×Q₈×C₄₃	—	2	4	no	—
322	C₂×Q₈×C₄₃	—	4	1	no	—
323	C₂×Q₈×C₄₃	—	4	2	no	—
324	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
325	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
327	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
329	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄×C₄₃	—	2	2	no	—
331	C₂²×C₄×C₄₃	—	2	1	no	—
332	C₂²×C₄×C₄₃	—	2	2	no	—
333	C₂²×C₄×C₄₃	—	2	1	no	—
334	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
335	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
337	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
338	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
339	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
340	C₂×C₂²⋊D₄₃	—	2	2	no	—
341	C₂×C₂²⋊D₄₃	—	2	2	no	—
342	C₂²×Dic₄₃	—	2	1	no	—
343	#10621898	—	2	4	no	—
344	#10621898	—	4	2	no	—
345	C₂×D₁₇₂	—	2	1	no	—
346	C₂×D₁₇₂	—	2	2	no	—
347	C₂×D₁₇₂	—	4	1	no	—
348	C₂×D₁₇₂	C₂⁴	1	1	yes	characteristic
349	C₂×D₁₇₂	C₂⁴	1	1	yes	characteristic
350	C₂×C₄×D₄₃	—	2	1	no	—
351	C₂×C₄×D₄₃	—	2	2	no	—
352	C₂×C₄×D₄₃	—	2	1	no	—
353	C₂×C₄×D₄₃	—	2	1	no	—
354	C₂×C₄×D₄₃	—	2	1	no	—
355	C₂×C₄×D₄₃	—	2	2	no	—
356	C₂×C₄×D₄₃	—	4	4	no	—
357	C₂×Dic₈₆	—	2	1	no	—
358	C₂×Dic₈₆	C₂⁴	1	2	yes	—
359	C₄⋊C₄×C₄₃	—	2	1	no	—
360	C₄⋊C₄×C₄₃	—	2	2	no	—
361	C₄⋊C₄×C₄₃	—	2	1	no	—
362	C₄⋊C₄×C₄₃	—	2	1	no	—
363	C₄⋊C₄×C₄₃	—	2	2	no	—
364	C₄⋊C₄×C₄₃	—	2	2	no	—
365	C₄⋊C₄×C₄₃	—	2	1	no	—
366	C₄⋊C₄×C₄₃	—	2	2	no	—
367	C₄⋊C₄×C₄₃	—	2	1	no	—
368	C₄⋊C₄×C₄₃	—	2	2	no	—
369	C₄⋊C₄×C₄₃	—	2	1	no	—
370	C₄⋊C₄×C₄₃	—	2	2	no	—
371	C₄⋊C₄×C₄₃	—	2	1	no	—
372	C₄⋊C₄×C₄₃	—	2	2	no	—
373	C₄⋊C₄×C₄₃	—	2	1	no	—
374	C₄⋊C₄×C₄₃	—	2	2	no	—
375	C₄⋊C₄×C₄₃	—	2	2	no	—
376	C₄⋊C₄×C₄₃	—	2	2	no	—
377	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
378	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
379	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
380	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
381	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
382	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
383	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
384	C₂²⋊C₄×C₄₃	—	2	2	no	—
385	C₂²⋊C₄×C₄₃	—	2	2	no	—
386	C₂²⋊C₄×C₄₃	—	2	2	no	—
387	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
388	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
389	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
390	C₄²×C₄₃	—	2	1	no	—
391	C₄²×C₄₃	—	2	1	no	—
392	C₄²×C₄₃	—	2	2	no	—
393	C₄²×C₄₃	—	2	2	no	—
394	C₄²×C₄₃	—	2	1	no	—
395	C₄²×C₄₃	—	2	2	no	—
396	C₄²×C₄₃	—	2	1	no	—
397	C₄²×C₄₃	C₂×D₄	1	2	yes	—
398	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
399	C₄²×C₄₃	C₂×D₄	1	2	yes	—
400	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
402	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
403	C₄²×C₄₃	C₂⁴	1	2	yes	—
404	C₂²⋊Dic₄₃	—	2	2	no	—
405	C₂²⋊Dic₄₃	—	2	2	no	—
406	C₂²⋊Dic₄₃	—	2	2	no	—
407	#10621885	—	2	4	no	—
408	#10621885	—	2	4	no	—
409	#10621885	—	4	2	no	—
410	#10621885	—	4	2	no	—
411	#10621884	—	2	2	no	—
412	#10621884	—	2	2	no	—
413	#10621884	—	2	4	no	—
414	#10621884	—	2	2	no	—
415	#10621884	—	4	2	no	—
416	#10621884	#41	1	4	yes	complemented
417	(C₂×D₄₃)⋊C₄	—	2	2	no	—
418	(C₂×D₄₃)⋊C₄	—	2	2	no	—
419	(C₂×D₄₃)⋊C₄	—	2	1	no	—
420	(C₂×D₄₃)⋊C₄	—	2	1	no	—
421	(C₂×D₄₃)⋊C₄	—	2	1	no	—
422	(C₂×D₄₃)⋊C₄	—	2	1	no	—
423	(C₂×D₄₃)⋊C₄	—	2	2	no	—
424	(C₂×D₄₃)⋊C₄	—	2	2	no	—
425	C₄⋊Dic₄₃	—	2	1	no	—
426	C₄⋊Dic₄₃	—	2	1	no	—
427	C₄⋊Dic₄₃	—	2	1	no	—
428	C₄⋊Dic₄₃	—	2	1	no	—
429	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
430	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
431	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
432	Dic₄₃⋊C₄	—	2	2	no	—
433	Dic₄₃⋊C₄	—	2	2	no	—
434	Dic₄₃⋊C₄	—	2	2	no	—
435	Dic₄₃⋊C₄	—	2	2	no	—
436	Dic₄₃⋊C₄	—	2	2	no	—
437	Dic₄₃⋊C₄	—	2	2	no	—
438	C₄×Dic₄₃	—	2	2	no	—
439	C₄×Dic₄₃	—	2	2	no	—
440	C₄×Dic₄₃	—	2	2	no	—
441	#10621877	—	2	4	no	—
442	#10621877	—	4	2	no	—
443	C₂×C₄₃⋊C₈	—	2	2	no	—
444	C₂×C₄₃⋊C₈	—	4	1	no	—
445	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
446	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
447	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
448	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
449	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
450	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
451	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
452	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
453	C₂²×D₄₃	—	2	1	no	—
454	C₂²×D₄₃	—	2	1	no	—
455	C₂²×D₄₃	—	4	2	no	—
456	C₂²×D₄₃	—	4	2	no	—
457	C₂²×D₄₃	—	8	1	no	—
458	Q₈×C₄₃	—	2	2	no	—
459	Q₈×C₄₃	—	2	1	no	—
460	Q₈×C₄₃	—	2	1	no	—
461	Q₈×C₄₃	—	2	2	no	—
462	Q₈×C₄₃	—	2	2	no	—
463	Q₈×C₄₃	—	2	1	no	—
464	Q₈×C₄₃	—	4	4	no	—
465	Q₈×C₄₃	—	4	2	no	—
466	Q₈×C₄₃	—	8	1	no	—
467	Q₈×C₄₃	—	8	2	no	—
468	Q₈×C₄₃	C₂×#41	1	2	yes	—
469	D₄×C₄₃	—	2	4	no	—
470	D₄×C₄₃	—	2	2	no	—
471	C₂×C₄×C₄₃	—	2	1	no	—
472	C₂×C₄×C₄₃	—	2	4	no	—
473	C₂×C₄×C₄₃	—	2	1	no	—
474	C₂×C₄×C₄₃	—	2	2	no	—
475	C₂×C₄×C₄₃	—	2	1	no	—
476	C₂×C₄×C₄₃	—	2	2	no	—
477	C₂×C₄×C₄₃	—	2	1	no	—
478	C₂×C₄×C₄₃	—	2	1	no	—
479	C₂×C₄×C₄₃	—	2	2	no	—
480	C₂×C₄×C₄₃	—	2	1	no	—
481	C₂×C₄×C₄₃	—	2	2	no	—
482	C₂×C₄×C₄₃	—	4	1	no	—
483	C₂×C₄×C₄₃	—	4	2	no	—
484	C₂×C₄×C₄₃	—	4	2	no	—
485	C₂×C₄×C₄₃	—	4	4	no	—
486	C₂×C₄×C₄₃	—	8	1	no	—
487	C₂×C₄×C₄₃	—	8	2	no	—
488	C₂×C₄×C₄₃	#137	1	4	yes	complemented
489	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
491	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
498	C₂²⋊D₄₃	—	4	4	no	—
499	C₂²⋊D₄₃	—	8	2	no	—
500	C₂×Dic₄₃	—	2	1	no	—
501	C₂×Dic₄₃	—	2	2	no	—
502	C₂×Dic₄₃	—	2	2	no	—
503	C₂×Dic₄₃	—	2	1	no	—
504	C₂×Dic₄₃	—	4	2	no	—
505	D₁₇₂	—	2	1	no	—
506	D₁₇₂	—	2	1	no	—
507	D₁₇₂	—	2	1	no	—
508	D₁₇₂	—	4	2	no	—
509	D₁₇₂	C₂×#41	1	2	yes	—
510	C₄×D₄₃	—	4	4	no	—
511	C₄×D₄₃	—	4	2	no	—
512	C₄×D₄₃	—	4	2	no	—
513	C₄×D₄₃	—	4	2	no	—
514	C₄×D₄₃	—	4	2	no	—
515	C₄×D₄₃	—	8	2	no	—
516	Dic₈₆	—	2	2	no	—
517	Dic₈₆	—	2	2	no	—
518	Dic₈₆	—	8	1	no	—
519	C₄₃⋊C₈	—	2	1	no	—
520	C₄₃⋊C₈	—	2	2	no	—
521	C₄₃⋊C₈	—	2	1	no	—
522	C₄₃⋊C₈	—	2	1	no	—
523	C₄₃⋊C₈	—	2	2	no	—
524	C₄₃⋊C₈	C₂×#41	1	2	yes	—
525	#61438	—	43	1	no	maximal, Sylow
526	C₂²×C₄₃	—	2	1	no	—
527	C₂²×C₄₃	—	2	1	no	—
528	C₂²×C₄₃	—	2	2	no	—
529	C₂²×C₄₃	—	2	2	no	—
530	C₂²×C₄₃	—	2	2	no	—
531	C₂²×C₄₃	C₂×#137	1	2	yes	—
532	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
533	C₂×D₄₃	—	2	2	no	—
534	C₂×D₄₃	—	4	1	no	—
535	C₂×D₄₃	—	4	1	no	—
536	C₂×D₄₃	—	4	1	no	—
537	C₂×D₄₃	—	4	1	no	—
538	C₂×D₄₃	—	4	1	no	—
539	C₂×D₄₃	—	8	4	no	—
540	C₄×C₄₃	—	2	1	no	—
541	C₄×C₄₃	—	2	2	no	—
542	C₄×C₄₃	—	2	1	no	—
543	C₄×C₄₃	—	2	2	no	—
544	C₄×C₄₃	—	2	1	no	—
545	C₄×C₄₃	—	2	2	no	—
546	C₄×C₄₃	—	2	2	no	—
547	C₄×C₄₃	—	4	1	no	—
548	C₄×C₄₃	—	4	1	no	—
549	C₄×C₄₃	—	4	2	no	—
550	C₄×C₄₃	—	4	1	no	—
551	C₄×C₄₃	—	4	2	no	—
552	C₄×C₄₃	C₂×#137	1	2	yes	—
553	C₄×C₄₃	C₂×#137	1	2	yes	—
554	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
555	C₄×C₄₃	#585	1	1	yes	characteristic
556	Dic₄₃	—	4	2	no	—
557	Dic₄₃	—	4	2	no	—
558	Dic₄₃	—	4	1	no	—
559	Dic₄₃	—	4	1	no	—
560	Q₈×#41	D₄₃	1	1	yes	characteristic, complemented
561	#3475	—	43	1	no	—
562	#3398	—	43	1	no	—
563	#3385	—	43	1	no	—
564	#3372	—	43	1	no	—
565	#3369	—	43	1	no	—
566	#3357	—	43	1	no	—
567	#3344	—	43	2	no	—
568	#3331	—	43	1	no	—
569	#3329	—	43	1	no	—
570	#3314	—	43	2	no	—
571	#3312	—	43	2	no	—
572	#3276	—	43	1	no	—
573	#3266	—	43	2	no	—
574	#3172	—	43	2	no	—
575	#3170	—	43	1	no	—
576	#3108	—	43	2	no	—
577	#3107	—	43	2	no	—
578	#3104	—	43	1	no	—
579	#3101	—	43	1	no	—
580	#2965	—	43	1	no	—
581	C₄×#137	—	43	2	no	—
582	C₂×C₄×SD₁₆	—	43	1	no	—
583	C₂×C₄₃	—	2	2	no	—
584	C₂×C₄₃	—	4	2	no	—
585	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
586	C₂×C₄₃	C₂²×#137	1	1	yes	characteristic
587	C₂×C₄₃	#3584	1	1	yes	characteristic
588	D₄₃	—	4	2	no	—
589	D₄₃	—	8	1	no	—
590	C₂×#137	—	43	2	no	—
591	C₂²×SD₁₆	—	43	1	no	—
592	Q₈²	C₂×D₄₃	1	1	yes	characteristic, complemented
593	#557	—	2	1	no	—
594	#557	C₂×D₄₃	1	1	yes	characteristic, complemented
595	#556	—	43	1	no	—
596	#555	—	43	1	no	—
597	#554	—	2	2	no	—
598	#554	—	2	1	no	—
599	#554	—	43	1	no	—
600	#554	C₂×D₄₃	1	2	yes	—
601	#554	C₂×D₄₃	1	1	yes	characteristic, complemented
602	#553	—	86	1	no	—
603	#552	—	43	2	no	—
604	#552	—	86	1	no	—
605	#551	—	86	2	no	—
606	D₄×Q₈	C₂×D₄₃	1	2	yes	—
607	D₄×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
608	#547	—	43	1	no	—
609	#546	—	43	2	no	—
610	#533	—	2	1	no	—
611	#533	—	2	2	no	—
612	#533	—	43	1	no	—
613	#533	C₂×D₄₃	1	1	yes	characteristic
614	#533	C₂×D₄₃	1	2	yes	complemented
615	#529	—	43	2	no	—
616	#529	—	86	2	no	—
617	#525	—	86	1	no	—
618	C₄×#41	—	2	1	no	—
619	C₄×#41	—	43	2	no	—
620	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
621	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
622	C₂×C₄×Q₈	C₂×D₄₃	1	2	yes	complemented
623	C₂×C₄×D₄	—	43	1	no	—
624	C₂×#117	—	86	1	no	—
625	#501	—	43	2	no	—
626	#500	—	43	1	no	—
627	#497	—	43	2	no	—
628	#494	—	43	1	no	—
629	#491	—	43	2	no	—
630	#489	—	43	2	no	—
631	#487	—	43	1	no	—
632	#487	—	43	1	no	—
633	#485	—	43	2	no	—
634	#485	—	43	2	no	—
635	#484	—	43	2	no	—
636	#483	—	43	2	no	—
637	#483	—	43	2	no	—
638	#480	—	43	2	no	—
639	#479	—	43	2	no	—
640	#479	—	43	2	no	—
641	#477	—	43	1	no	—
642	#477	—	43	1	no	—
643	#476	—	43	1	no	—
644	#476	—	43	1	no	—
645	#475	—	43	2	no	—
646	#474	—	43	2	no	—
647	#470	—	43	2	no	—
648	#470	—	43	2	no	—
649	#468	—	43	2	no	—
650	#468	—	43	2	no	—
651	#467	—	43	2	no	—
652	#467	—	43	2	no	—
653	#464	—	43	2	no	—
654	#464	—	43	2	no	—
655	#462	—	43	2	no	—
656	#462	—	43	1	no	—
657	#462	—	43	1	no	—
658	#461	—	43	1	no	—
659	#461	—	43	1	no	—
660	#461	—	43	2	no	—
661	#452	—	43	2	no	—
662	#452	—	43	2	no	—
663	#451	—	43	2	no	—
664	#451	—	43	2	no	—
665	#450	—	43	2	no	—
666	#448	—	43	2	no	—
667	#446	—	43	1	no	—
668	#446	—	43	1	no	—
669	#441	—	43	2	no	—
670	#441	—	43	2	no	—
671	#440	—	43	2	no	—
672	#440	—	43	2	no	—
673	C₄×Q₁₆	—	43	2	no	—
674	C₄×Q₁₆	—	43	2	no	—
675	C₄×Q₁₆	—	43	2	no	—
676	C₄×Q₁₆	—	43	2	no	—
677	C₄×SD₁₆	—	43	1	no	—
678	C₄×SD₁₆	—	43	1	no	—
679	C₄×SD₁₆	—	43	2	no	—
680	C₄×SD₁₆	—	43	2	no	—
681	C₄×SD₁₆	—	43	1	no	—
682	C₄×SD₁₆	—	43	1	no	—
683	C₄×SD₁₆	—	43	1	no	—
684	C₄×SD₁₆	—	43	1	no	—
685	C₄×SD₁₆	—	43	1	no	—
686	C₄×SD₁₆	—	43	1	no	—
687	#436	—	43	1	no	—
688	#436	—	43	1	no	—
689	#435	—	43	2	no	—
690	#435	—	43	2	no	—
691	#431	—	43	1	no	—
692	#431	—	43	2	no	—
693	#428	—	43	2	no	—
694	C₂×#106	—	43	1	no	—
695	#419	—	43	2	no	—
696	#417	—	43	2	no	—
697	C₂×#103	—	43	1	no	—
698	C₂×#102	—	43	1	no	—
699	C₄×M₁₆	—	43	2	no	—
700	C₂×C₄×C₈	—	43	1	no	—
701	C₄₃	#61438	1	1	yes	characteristic, complemented, Sylow
702	C₂×#41	—	43	2	no	—
703	C₂×#41	C₂²⋊D₄₃	1	1	yes	characteristic
704	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
705	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
706	C₂²×D₄	—	43	1	no	—
707	C₂³×C₄	—	86	1	no	—
708	#137	—	86	8	no	—
709	C₂×Q₁₆	—	43	2	no	—
710	C₂×Q₁₆	—	43	2	no	—
711	C₂×Q₁₆	—	43	2	no	—
712	C₂×Q₁₆	—	43	2	no	—
713	C₂×SD₁₆	—	43	1	no	—
714	C₂×SD₁₆	—	43	1	no	—
715	C₂×SD₁₆	—	43	1	no	—
716	C₂×SD₁₆	—	43	1	no	—
717	C₂×SD₁₆	—	43	2	no	—
718	C₂×SD₁₆	—	43	2	no	—
719	C₂×SD₁₆	—	86	4	no	—
720	C₂×M₁₆	—	43	2	no	—
721	C₂×M₁₆	—	43	2	no	—
722	C₂²×C₈	—	43	1	no	—
723	C₂²×C₈	—	43	1	no	—
724	C₄⋊Q₈	—	2	2	no	—
725	C₄⋊Q₈	—	2	1	no	—
726	C₄⋊Q₈	—	2	1	no	—
727	C₄⋊Q₈	—	2	2	no	—
728	C₄⋊Q₈	—	43	1	no	—
729	C₄⋊Q₈	—	43	1	no	—
730	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
731	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
732	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
733	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
734	#126	—	86	2	no	—
735	#126	—	86	2	no	—
736	#126	—	86	2	no	—
737	#125	—	2	1	no	—
738	#125	—	2	2	no	—
739	#125	—	2	2	no	—
740	#125	—	2	1	no	—
741	#125	—	2	1	no	—
742	#125	—	2	2	no	—
743	#125	—	43	2	no	—
744	#125	—	86	2	no	—
745	#125	—	86	1	no	—
746	#124	—	43	2	no	—
747	#124	—	86	2	no	—
748	#123	—	86	2	no	—
749	#123	—	86	2	no	—
750	#123	—	86	2	no	—
751	#123	—	86	2	no	—
752	C₂²⋊Q₈	—	2	1	no	—
753	C₂²⋊Q₈	—	2	2	no	—
754	C₂²⋊Q₈	—	2	2	no	—
755	C₂²⋊Q₈	—	2	2	no	—
756	C₂²⋊Q₈	—	2	2	no	—
757	C₂²⋊Q₈	—	2	2	no	—
758	C₂²⋊Q₈	—	2	2	no	—
759	C₂²⋊Q₈	—	2	2	no	—
760	C₂²⋊Q₈	—	43	2	no	—
761	C₂²⋊Q₈	—	43	2	no	—
762	C₂²⋊Q₈	—	86	1	no	—
763	C₂²⋊Q₈	—	86	1	no	—
764	C₂²⋊Q₈	—	86	1	no	—
765	C₂²⋊Q₈	—	86	2	no	—
766	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
767	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
768	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
769	#121	—	43	2	no	—
770	#121	—	86	1	no	—
771	#121	—	86	1	no	—
772	#121	—	86	2	no	—
773	#120	—	86	2	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	2	1	no	—
777	C₄×Q₈	—	2	1	no	—
778	C₄×Q₈	—	2	2	no	—
779	C₄×Q₈	—	2	2	no	—
780	C₄×Q₈	—	2	1	no	—
781	C₄×Q₈	—	2	2	no	—
782	C₄×Q₈	—	43	2	no	—
783	C₄×Q₈	—	43	2	no	—
784	C₄×Q₈	—	86	1	no	—
785	C₄×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
786	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
787	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
788	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
789	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
790	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
791	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
792	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
793	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
794	C₄×D₄	—	2	2	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	2	1	no	—
798	C₄×D₄	—	43	1	no	—
799	C₄×D₄	—	43	1	no	—
800	C₄×D₄	—	43	1	no	—
801	C₄×D₄	—	43	1	no	—
802	C₄×D₄	—	43	2	no	—
803	C₄×D₄	—	86	2	no	—
804	C₄×D₄	—	86	2	no	—
805	C₄×D₄	—	86	2	no	—
806	C₄×D₄	—	86	1	no	—
807	C₄×D₄	—	86	1	no	—
808	C₄×D₄	C₂²⋊D₄₃	1	2	yes	—
809	C₄×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
810	C₄×D₄	C₂²×D₄₃	1	2	yes	—
811	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
812	#117	—	2	1	no	—
813	#117	—	2	2	no	—
814	#117	—	43	2	no	—
815	#117	—	86	1	no	—
816	#117	—	86	1	no	—
817	#117	—	86	1	no	—
818	#117	—	86	2	no	—
819	#117	—	86	2	no	—
820	#117	—	86	2	no	—
821	#117	C₂²⋊D₄₃	1	1	yes	characteristic
822	#117	C₂²⋊D₄₃	1	2	yes	—
823	C₂×C₄⋊C₄	—	2	1	no	—
824	C₂×C₄⋊C₄	—	2	2	no	—
825	C₂×C₄⋊C₄	—	43	1	no	—
826	C₂×C₄⋊C₄	—	86	1	no	—
827	C₂×C₄⋊C₄	—	86	1	no	—
828	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
829	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
830	C₂×C₂²⋊C₄	—	86	1	no	—
831	C₂×C₂²⋊C₄	—	86	2	no	—
832	C₂×C₄²	—	2	1	no	—
833	C₂×C₄²	—	2	2	no	—
834	C₂×C₄²	—	86	2	no	—
835	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
836	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
837	#107	—	43	2	no	—
838	#107	—	43	2	no	—
839	#107	—	43	2	no	—
840	#107	—	43	2	no	—
841	#106	—	43	1	no	—
842	#106	—	43	1	no	—
843	#106	—	43	1	no	—
844	#106	—	43	1	no	—
845	#106	—	43	2	no	—
846	#106	—	43	2	no	—
847	C₄⋊C₈	—	43	2	no	—
848	C₄⋊C₈	—	43	2	no	—
849	C₄⋊C₈	—	43	1	no	—
850	C₄⋊C₈	—	43	1	no	—
851	#103	—	43	1	no	—
852	#103	—	43	1	no	—
853	#103	—	43	1	no	—
854	#103	—	43	1	no	—
855	#103	—	43	2	no	—
856	#103	—	43	2	no	—
857	#103	—	43	2	no	—
858	#103	—	43	2	no	—
859	#103	—	43	2	no	—
860	#103	—	43	2	no	—
861	#103	—	43	2	no	—
862	#103	—	43	2	no	—
863	#103	—	43	2	no	—
864	#103	—	43	2	no	—
865	#102	—	43	1	no	—
866	#102	—	43	1	no	—
867	#102	—	43	1	no	—
868	#102	—	43	1	no	—
869	#102	—	43	2	no	—
870	#102	—	43	2	no	—
871	C₂²⋊C₈	—	43	2	no	—
872	C₂²⋊C₈	—	43	2	no	—
873	C₂²⋊C₈	—	43	2	no	—
874	#97	—	43	2	no	—
875	#97	—	43	2	no	—
876	C₄×C₈	—	43	1	no	—
877	C₄×C₈	—	43	1	no	—
878	C₄×C₈	—	43	1	no	—
879	C₄×C₈	—	43	1	no	—
880	C₄×C₈	—	43	2	no	—
881	C₂⁴	—	86	1	no	—
882	#41	—	2	4	no	—
883	#41	—	86	4	no	—
884	#41	—	172	2	no	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	2	1	no	—
887	C₂×Q₈	—	2	2	no	—
888	C₂×Q₈	—	2	1	no	—
889	C₂×Q₈	—	2	2	no	—
890	C₂×Q₈	—	2	4	no	—
891	C₂×Q₈	—	4	1	no	—
892	C₂×Q₈	—	4	2	no	—
893	C₂×Q₈	—	43	2	no	—
894	C₂×Q₈	—	86	1	no	—
895	C₂×Q₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
896	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
897	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
898	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
899	C₂×D₄	—	43	1	no	—
900	C₂×D₄	—	43	1	no	—
901	C₂×D₄	—	86	2	no	—
902	C₂×D₄	—	86	2	no	—
903	C₂×D₄	—	86	2	no	—
904	C₂×D₄	—	86	1	no	—
905	C₂×D₄	—	172	1	no	—
906	C₂×D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
907	C₂×D₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	2	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	86	1	no	—
913	C₂²×C₄	—	86	2	no	—
914	C₂²×C₄	—	86	2	no	—
915	C₂²×C₄	—	86	1	no	—
916	C₂²×C₄	—	86	1	no	—
917	C₂²×C₄	—	86	1	no	—
918	C₂²×C₄	—	86	1	no	—
919	C₂²×C₄	—	172	4	no	—
920	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
921	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
922	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
923	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
924	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
925	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
926	Q₁₆	—	86	4	no	—
927	Q₁₆	—	86	4	no	—
928	Q₁₆	—	172	2	no	—
929	Q₁₆	—	172	2	no	—
930	SD₁₆	—	43	4	no	—
931	SD₁₆	—	86	2	no	—
932	SD₁₆	—	86	2	no	—
933	SD₁₆	—	86	4	no	—
934	SD₁₆	—	86	2	no	—
935	SD₁₆	—	172	2	no	—
936	M₁₆	—	86	4	no	—
937	M₁₆	—	172	2	no	—
938	C₂×C₈	—	43	1	no	—
939	C₂×C₈	—	43	1	no	—
940	C₂×C₈	—	43	1	no	—
941	C₂×C₈	—	43	1	no	—
942	C₂×C₈	—	43	2	no	—
943	C₂×C₈	—	43	2	no	—
944	C₂×C₈	—	86	2	no	—
945	C₂×C₈	—	172	1	no	—
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	2	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	1	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	2	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	1	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	43	1	no	—
965	C₄⋊C₄	—	43	1	no	—
966	C₄⋊C₄	—	43	2	no	—
967	C₄⋊C₄	—	86	1	no	—
968	C₄⋊C₄	—	86	1	no	—
969	C₄⋊C₄	—	86	1	no	—
970	C₄⋊C₄	—	86	2	no	—
971	C₄⋊C₄	—	86	2	no	—
972	C₄⋊C₄	—	86	2	no	—
973	C₄⋊C₄	—	86	2	no	—
974	C₄⋊C₄	—	86	2	no	—
975	C₄⋊C₄	—	86	2	no	—
976	C₄⋊C₄	—	86	1	no	—
977	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
978	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
979	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
980	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
981	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
982	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
983	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	2	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	86	2	no	—
988	C₂²⋊C₄	—	86	2	no	—
989	C₂²⋊C₄	—	86	2	no	—
990	C₂²⋊C₄	—	86	1	no	—
991	C₂²⋊C₄	—	86	2	no	—
992	C₂²⋊C₄	—	86	2	no	—
993	C₂²⋊C₄	—	86	1	no	—
994	C₂²⋊C₄	—	86	1	no	—
995	C₂²⋊C₄	—	86	1	no	—
996	C₂²⋊C₄	—	86	2	no	—
997	C₂²⋊C₄	—	86	2	no	—
998	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
999	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1000	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1001	C₄²	—	2	2	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	2	1	no	—
1006	C₄²	—	2	1	no	—
1007	C₄²	—	2	2	no	—
1008	C₄²	—	86	2	no	—
1009	C₄²	—	86	2	no	—
1010	C₄²	—	86	2	no	—
1011	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
1012	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1013	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
1014	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1015	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1016	C₄²	C₂³×D₄₃	1	2	yes	—
1017	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1018	C₂³	—	86	1	no	—
1019	C₂³	—	86	1	no	—
1020	C₂³	—	344	1	no	—
1021	C₂³	—	172	2	no	—
1022	C₂³	—	172	2	no	—
1023	C₂³	C₂²×C₂²⋊D₄₃	1	2	yes	—
1024	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1025	Q₈	—	2	2	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	2	2	no	—
1029	Q₈	—	2	2	no	—
1030	Q₈	—	2	1	no	—
1031	Q₈	—	4	4	no	—
1032	Q₈	—	4	2	no	—
1033	Q₈	—	8	2	no	—
1034	Q₈	—	8	1	no	—
1035	Q₈	—	86	2	no	—
1036	Q₈	—	86	2	no	—
1037	Q₈	—	344	1	no	—
1038	Q₈	#41×D₄₃	1	2	yes	—
1039	D₄	—	2	4	no	—
1040	D₄	—	2	2	no	—
1041	D₄	—	43	2	no	—
1042	D₄	—	86	1	no	—
1043	D₄	—	86	1	no	—
1044	D₄	—	86	1	no	—
1045	D₄	—	344	2	no	—
1046	D₄	—	172	2	no	—
1047	D₄	—	172	4	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	4	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	2	2	no	—
1057	C₂×C₄	—	2	2	no	—
1058	C₂×C₄	—	2	1	no	—
1059	C₂×C₄	—	4	2	no	—
1060	C₂×C₄	—	4	1	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	4	4	no	—
1063	C₂×C₄	—	8	1	no	—
1064	C₂×C₄	—	8	2	no	—
1065	C₂×C₄	—	86	1	no	—
1066	C₂×C₄	—	86	2	no	—
1067	C₂×C₄	—	86	2	no	—
1068	C₂×C₄	—	86	1	no	—
1069	C₂×C₄	—	344	2	no	—
1070	C₂×C₄	—	172	4	no	—
1071	C₂×C₄	—	172	2	no	—
1072	C₂×C₄	—	172	2	no	—
1073	C₂×C₄	—	172	2	no	—
1074	C₂×C₄	—	172	2	no	—
1075	C₂×C₄	—	172	2	no	—
1076	C₂×C₄	#13063356	1	4	yes	complemented
1077	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1078	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1079	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1080	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1081	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1082	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1083	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1084	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1085	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1086	C₈	—	43	2	no	—
1087	C₈	—	86	1	no	—
1088	C₈	—	86	2	no	—
1089	C₈	—	86	1	no	—
1090	C₈	—	86	1	no	—
1091	C₈	—	86	2	no	—
1092	C₂²	—	2	1	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	2	2	no	—
1096	C₂²	—	2	2	no	—
1097	C₂²	—	86	2	no	—
1098	C₂²	—	344	4	no	—
1099	C₂²	—	172	1	no	—
1100	C₂²	—	172	1	no	—
1101	C₂²	—	172	1	no	—
1102	C₂²	—	172	1	no	—
1103	C₂²	—	172	1	no	—
1104	C₂²	C₂×#13063356	1	2	yes	—
1105	C₂²	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
1106	C₄	—	2	2	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	1	no	—
1109	C₄	—	2	2	no	—
1110	C₄	—	2	1	no	—
1111	C₄	—	2	2	no	—
1112	C₄	—	2	1	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	2	no	—
1115	C₄	—	4	1	no	—
1116	C₄	—	4	1	no	—
1117	C₄	—	4	2	no	—
1118	C₄	—	172	1	no	—
1119	C₄	—	172	1	no	—
1120	C₄	—	172	2	no	—
1121	C₄	—	172	2	no	—
1122	C₄	C₂×#13063356	1	2	yes	—
1123	C₄	C₂×#13063356	1	2	yes	—
1124	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1125	C₄	#14583735	1	1	yes	characteristic
1126	C₂	—	2	2	no	—
1127	C₂	—	4	2	no	—
1128	C₂	—	344	1	no	—
1129	C₂	—	172	2	no	—
1130	C₂	#41×C₂²⋊D₄₃	1	1	yes	characteristic
1131	C₂	C₂²×#13063356	1	1	yes	characteristic
1132	C₂	#19149366	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	Q₈×#41×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	#19148159	C₂
hypercenter	Q₈×#41	D₄₃
hypocenter	C₄₃	#61438
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×#41 ◁ Q₈×#41

Complements

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

N	H ≅ G/N	type
2. #19147622	C₂	semidirect
3. #19147501	C₂	semidirect
4. #19147372	C₂	semidirect
5. #19147335	C₂	semidirect
6. #19147221	C₂	semidirect
7. #19147044	C₂	semidirect
8. #19146905	C₂	semidirect
9. #19146889	C₂	semidirect
10. #19146670	C₂	semidirect
11. #19146646	C₂	semidirect
12. #19146241	C₂	semidirect
13. #19146106	C₂	semidirect
14. #19145195	C₂	semidirect
15. #19145177	C₂	semidirect
16. #19144675	C₂	semidirect
17. #19144660	C₂	semidirect
18. #19144634	C₂	semidirect
19. #19144599	C₂	semidirect
20. #19143562	C₂	semidirect
21. C₄×#13063356	C₂	semidirect
22. C₂×C₄×#10621884	C₂	semidirect
23. Q₈×#41×C₄₃	C₂	semidirect
42. #14583305	C₂²	semidirect
43. #14583302	C₂²	semidirect
45. #14583278	C₂²	semidirect
46. #14583267	C₂²	semidirect
48. #14583251	C₂²	semidirect
49. #14583249	C₂²	semidirect
50. #14583237	C₂²	semidirect
51. #14583237	C₂²	semidirect
53. #14583229	C₂²	semidirect
56. #14583206	C₂²	semidirect
57. #14583206	C₂²	semidirect
58. #14583194	C₂²	semidirect
59. #14583194	C₂²	semidirect
62. #14583181	C₂²	semidirect
64. #14583155	C₂²	semidirect
65. #14583155	C₂²	semidirect
72. #14583109	C₂²	semidirect
73. #14583109	C₂²	semidirect
74. #14583106	C₂²	semidirect
81. #14583055	C₂²	semidirect
84. #14583030	C₂²	semidirect
85. #14583030	C₂²	semidirect
86. #14583004	C₂²	semidirect
87. #14583004	C₂²	semidirect
90. C₄×#10621885	C₂²	semidirect
91. C₄×#10621885	C₂²	semidirect
92. C₄×#10621885	C₂²	semidirect
93. C₄×#10621885	C₂²	semidirect
104. #14582977	C₂²	semidirect
105. #14582977	C₂²	semidirect
109. #14582952	C₂²	semidirect
110. #14582939	C₂²	semidirect
112. #14582908	C₂²	semidirect
116. C₄×#10621877	C₂²	semidirect
118. Q₈²×C₄₃	C₂²	semidirect
120. C₄₃×#557	C₂²	semidirect
124. C₄₃×#554	C₂²	semidirect
126. D₄×Q₈×C₄₃	C₂²	semidirect
130. C₄₃×#533	C₂²	semidirect
134. C₂×C₄×Q₈×C₄₃	C₂²	semidirect
416. #10621884	#41	semidirect
488. C₂×C₄×C₄₃	#137	semidirect
560. Q₈×#41	D₄₃	semidirect
592. Q₈²	C₂×D₄₃	semidirect
594. #557	C₂×D₄₃	semidirect
601. #554	C₂×D₄₃	semidirect
607. D₄×Q₈	C₂×D₄₃	semidirect
614. #533	C₂×D₄₃	semidirect
622. C₂×C₄×Q₈	C₂×D₄₃	semidirect
701. C₄₃	#61438	semidirect
1076. C₂×C₄	#13063356	semidirect

Maximal subgroups

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

subgroup	index
#19148159	2
#19147622	2
#19147501	2
#19147372	2
#19147335	2
#19147221	2
#19147044	2
#19146905	2
#19146889	2
#19146670	2
#19146646	2
#19146241	2
#19146106	2
#19145195	2
#19145177	2
#19144675	2
#19144660	2
#19144634	2
#19144599	2
#19143562	2
C₄×#13063356	2
C₂×C₄×#10621884	2
Q₈×#41×C₄₃	2
#61438	43