Subgroups — #25989807

Order 11008.

1878 conjugacy classes of subgroups.

The subgroup lattice has 1178 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148556	C₂	1	1	yes	maximal, characteristic, complemented
2	#19147591	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147579	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147255	C₂	1	1	yes	maximal, characteristic, complemented
5	#19147244	C₂	1	1	yes	maximal, characteristic, complemented
6	#19146883	C₂	1	1	yes	maximal, characteristic, complemented
7	#19146857	C₂	1	2	yes	maximal, complemented
8	#19146831	C₂	1	1	yes	maximal, characteristic, complemented
9	#19146805	C₂	1	2	yes	maximal, complemented
10	#19146237	C₂	1	1	yes	maximal, characteristic, complemented
11	#19146222	C₂	1	2	yes	maximal, complemented
12	#19146202	C₂	1	2	yes	maximal, complemented
13	#19146195	C₂	1	1	yes	maximal, characteristic, complemented
14	#19145991	C₂	1	2	yes	maximal, complemented
15	#19145962	C₂	1	1	yes	maximal, characteristic, complemented
16	#19145556	C₂	1	2	yes	maximal, complemented
17	#19145547	C₂	1	1	yes	maximal, characteristic, complemented
18	#19144642	C₂	1	1	yes	maximal, characteristic, complemented
19	#19144613	C₂	1	2	yes	maximal, complemented
20	#19144089	C₂	1	2	yes	maximal, complemented
21	#19144059	C₂	1	1	yes	maximal, characteristic, complemented
22	#19143727	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3475	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063355	C₂²	1	2	yes	complemented
25	C₂×#13063351	C₂²	1	2	yes	complemented
26	C₂×#13063350	C₂²	1	2	yes	—
27	#14583634	C₂²	1	1	yes	characteristic, complemented
28	#14583622	C₂²	1	1	yes	characteristic, complemented
29	#14583612	—	2	1	no	—
30	#14583573	—	2	2	no	—
31	D₄×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
32	#14583558	C₂²	1	2	yes	—
33	#14583545	C₂²	1	2	yes	—
34	#14583537	—	2	1	no	—
35	D₄×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
36	#14583521	—	2	1	no	—
37	#14583482	—	2	2	no	—
38	#14583449	C₂²	1	1	yes	characteristic
39	#14583433	C₂²	1	1	yes	characteristic
40	#14583433	C₂²	1	2	yes	complemented
41	C₂×#13063313	C₂²	1	2	yes	complemented
42	#14583371	—	2	1	no	—
43	#14583281	C₂²	1	2	yes	—
44	#14583281	C₂²	1	2	yes	complemented
45	#14583278	C₂²	1	1	yes	characteristic, complemented
46	#14583273	C₂²	1	1	yes	characteristic, complemented
47	#14583256	C₂²	1	2	yes	complemented
48	#14583256	C₂²	1	2	yes	complemented
49	#14583251	C₂²	1	1	yes	characteristic, complemented
50	#14583247	C₂²	1	1	yes	characteristic, complemented
51	#14583240	C₂²	1	2	yes	complemented
52	#14583234	C₂²	1	1	yes	characteristic, complemented
53	#14583223	C₂²	1	2	yes	complemented
54	#14583217	C₂²	1	1	yes	characteristic
55	#14583206	C₂²	1	2	yes	complemented
56	#14583203	C₂²	1	2	yes	complemented
57	#14583199	C₂²	1	1	yes	characteristic, complemented
58	#14583199	C₂²	1	1	yes	characteristic, complemented
59	#14583196	C₂²	1	2	yes	complemented
60	#14583191	C₂²	1	1	yes	characteristic, complemented
61	#14583186	C₂²	1	1	yes	characteristic, complemented
62	#14583155	C₂²	1	2	yes	complemented
63	#14583155	C₂²	1	2	yes	complemented
64	#14583150	C₂²	1	2	yes	—
65	#14583147	C₂²	1	2	yes	—
66	#14583147	C₂²	1	2	yes	complemented
67	#14583143	C₂²	1	2	yes	complemented
68	#14583121	C₂²	1	2	yes	complemented
69	#14583121	C₂²	1	2	yes	complemented
70	#14583121	C₂²	1	2	yes	complemented
71	#14583121	C₂²	1	2	yes	complemented
72	#14583121	C₂²	1	2	yes	complemented
73	#14583118	C₂²	1	2	yes	complemented
74	#14583114	C₂²	1	1	yes	characteristic
75	#14583114	C₂²	1	1	yes	characteristic
76	#14583114	C₂²	1	2	yes	—
77	#14583114	C₂²	1	2	yes	complemented
78	#14583114	C₂²	1	2	yes	complemented
79	#14583114	C₂²	1	2	yes	complemented
80	#14583111	C₂²	1	2	yes	complemented
81	#14583106	C₂²	1	1	yes	characteristic, complemented
82	#14583104	C₂²	1	1	yes	characteristic, complemented
83	#14583104	C₂²	1	1	yes	characteristic, complemented
84	#14583101	C₂²	1	1	yes	characteristic, complemented
85	#14583094	C₂²	1	1	yes	characteristic
86	#14583094	C₂²	1	1	yes	characteristic
87	#14583061	C₂²	1	2	yes	complemented
88	#14583059	C₂²	1	2	yes	complemented
89	#14583059	C₂²	1	2	yes	complemented
90	#14583054	C₂²	1	2	yes	complemented
91	#14583050	C₂²	1	1	yes	characteristic, complemented
92	#14583049	C₂²	1	2	yes	complemented
93	#14583044	C₂²	1	2	yes	—
94	#14583037	C₂²	1	2	yes	complemented
95	#14583033	C₂²	1	1	yes	characteristic
96	#14583032	C₂²	1	2	yes	—
97	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
98	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
99	C₄×#10621885	C₂²	1	2	yes	complemented
100	C₄×#10621884	C₂²	1	2	yes	complemented
101	C₄×#10621883	C₂²	1	1	yes	characteristic, complemented
102	C₄×#10621883	C₂²	1	2	yes	complemented
103	C₄×#10621883	C₂²	1	1	yes	characteristic, complemented
104	C₄×#10621882	C₂²	1	1	yes	characteristic
105	C₄×#10621882	C₂²	1	1	yes	characteristic
106	C₄×#10621882	C₂²	1	2	yes	complemented
107	#14582977	C₂²	1	2	yes	complemented
108	#14582977	C₂²	1	1	yes	characteristic, complemented
109	#14582977	C₂²	1	2	yes	complemented
110	#14582977	C₂²	1	1	yes	characteristic, complemented
111	#14582952	C₂²	1	1	yes	characteristic, complemented
112	#14582952	C₂²	1	2	yes	complemented
113	#14582923	C₂²	1	2	yes	complemented
114	#14582923	C₂²	1	1	yes	characteristic, complemented
115	#14582907	C₂²	1	2	yes	complemented
116	#14582903	C₂²	1	2	yes	complemented
117	#14582898	C₂²	1	2	yes	complemented
118	C₄₃×#556	C₂²	1	1	yes	characteristic, complemented
119	C₄₃×#555	C₂²	1	1	yes	characteristic
120	C₄₃×#554	C₂²	1	1	yes	characteristic, complemented
121	C₄₃×#553	—	2	1	no	—
122	C₄₃×#552	—	2	1	no	—
123	C₄₃×#552	C₂²	1	2	yes	complemented
124	C₄₃×#551	—	2	2	no	—
125	C₄₃×#547	C₂²	1	1	yes	characteristic
126	C₄₃×#546	C₂²	1	2	yes	complemented
127	C₄₃×#533	C₂²	1	1	yes	characteristic, complemented
128	C₄₃×#529	—	2	2	no	—
129	C₄₃×#529	C₂²	1	2	yes	complemented
130	C₄₃×#525	—	2	1	no	—
131	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
132	C₄×#41×C₄₃	C₂²	1	2	yes	complemented
133	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
134	C₂×#117×C₄₃	—	2	1	no	—
135	C₂×#10621898	C₂³	1	2	yes	—
136	C₂²×Dic₈₆	C₂³	1	2	yes	—
137	C₂²×D₁₇₂	C₂³	1	2	yes	—
138	C₂×D₄×D₄₃	—	2	1	no	—
139	#13063355	—	4	4	no	—
140	#13063351	—	4	4	no	—
141	#13063350	—	4	4	no	—
142	C₂×#10621885	C₂³	1	2	yes	—
143	C₂×#10621885	C₂³	1	2	yes	—
144	C₂×#10621885	C₂³	1	2	yes	—
145	C₂×#10621883	C₂³	1	1	yes	characteristic
146	C₂×#10621883	C₂³	1	2	yes	—
147	C₂×#10621883	C₂³	1	1	yes	characteristic
148	C₂×#10621883	C₂³	1	2	yes	—
149	C₂×#10621884	C₂³	1	2	yes	—
150	C₂×#10621884	C₂³	1	2	yes	—
151	C₂×#10621884	C₂³	1	2	yes	—
152	C₂×#10621882	C₂³	1	2	yes	—
153	C₂×#10621882	C₂³	1	1	yes	characteristic
154	C₂×#10621882	C₂³	1	2	yes	—
155	C₂×#10621882	C₂³	1	1	yes	characteristic
156	C₂×#10621877	C₂³	1	2	yes	—
157	C₂×#10621877	C₂³	1	2	yes	—
158	C₂×#10621877	C₂³	1	2	yes	—
159	#13063325	C₂³	1	1	yes	characteristic
160	#13063324	—	2	1	no	—
161	#13063322	C₂³	1	1	yes	characteristic
162	#13063320	—	2	2	no	—
163	#13063319	—	2	1	no	—
164	#13063319	—	2	2	no	—
165	#13063317	C₂³	1	1	yes	characteristic
166	#13063314	—	2	1	no	—
167	#13063313	—	2	2	no	—
168	#13063313	—	2	2	no	—
169	#13063313	C₂³	1	2	yes	—
170	#13063313	C₂³	1	2	yes	—
171	#13063313	C₂³	1	1	yes	characteristic
172	#13063313	C₂³	1	2	yes	—
173	#13063311	—	2	2	no	—
174	#13063310	—	2	2	no	—
175	#13063310	—	2	2	no	—
176	#13063308	—	2	2	no	—
177	#13063308	—	2	1	no	—
178	#13063304	C₂³	1	1	yes	characteristic
179	#13063304	C₂³	1	2	yes	—
180	#13063303	—	2	2	no	—
181	#13063302	—	2	2	no	—
182	#13063301	—	2	1	no	—
183	#13063300	—	2	1	no	—
184	#13063299	—	2	1	no	—
185	#13063299	—	2	1	no	—
186	#13063299	C₂³	1	2	yes	—
187	#13063299	C₂³	1	1	yes	characteristic
188	#13063298	—	2	2	no	—
189	#13063297	—	2	2	no	—
190	#13063295	—	2	2	no	—
191	#13063293	—	2	2	no	—
192	C₄×Dic₈₆	C₂³	1	2	yes	—
193	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
194	C₄×D₁₇₂	—	2	1	no	—
195	C₄×D₁₇₂	—	2	1	no	—
196	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
197	C₄×D₁₇₂	C₂³	1	2	yes	—
198	D₄×Dic₄₃	—	2	1	no	—
199	#13063287	—	2	1	no	—
200	C₄×C₂²⋊D₄₃	—	2	1	no	—
201	C₄×C₂²⋊D₄₃	—	2	2	no	—
202	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
203	#13063283	—	2	1	no	—
204	#13063282	—	2	2	no	—
205	#13063282	—	2	1	no	—
206	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
207	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
208	C₂²⋊C₄×D₄₃	—	2	2	no	—
209	#13063258	C₂³	1	2	yes	—
210	#13063258	C₂³	1	1	yes	characteristic
211	#13063258	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	1	yes	characteristic
219	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
220	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
221	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
222	#13063249	C₂³	1	2	yes	—
223	#13063249	C₂³	1	2	yes	—
224	#13063248	C₂³	1	1	yes	characteristic
225	#13063248	C₂³	1	2	yes	—
226	#13063248	C₂³	1	2	yes	—
227	#13063248	C₂³	1	2	yes	—
228	#13063248	C₂³	1	2	yes	—
229	#13063248	C₂³	1	1	yes	characteristic
230	#13063248	C₂³	1	2	yes	—
231	#13063246	C₂³	1	1	yes	characteristic
232	#13063246	C₂³	1	1	yes	characteristic
233	#13063246	C₂³	1	1	yes	characteristic
234	#13063246	C₂³	1	1	yes	characteristic
235	#13063245	C₂³	1	1	yes	characteristic
236	#13063245	C₂³	1	2	yes	—
237	#13063245	C₂³	1	2	yes	—
238	#13063245	C₂³	1	2	yes	—
239	#13063245	C₂³	1	2	yes	—
240	#13063245	C₂³	1	1	yes	characteristic
241	#13063245	C₂³	1	2	yes	—
242	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
243	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
244	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
245	C₂²⋊(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	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
250	C₂×#41×C₄₃	D₄	1	1	yes	characteristic
251	C₂×#41×C₄₃	C₂³	1	2	yes	—
252	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
253	C₂³×C₄×C₄₃	—	2	1	no	—
254	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
255	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
256	#126×C₄₃	—	2	2	no	—
257	#126×C₄₃	—	2	2	no	—
258	#126×C₄₃	—	2	2	no	—
259	#125×C₄₃	—	2	2	no	—
260	#125×C₄₃	—	2	1	no	—
261	#125×C₄₃	C₂³	1	2	yes	—
262	#124×C₄₃	—	2	2	no	—
263	#124×C₄₃	C₂³	1	2	yes	—
264	#123×C₄₃	—	2	2	no	—
265	#123×C₄₃	—	2	2	no	—
266	#123×C₄₃	—	2	2	no	—
267	#123×C₄₃	—	2	2	no	—
268	C₂²⋊Q₈×C₄₃	—	2	1	no	—
269	C₂²⋊Q₈×C₄₃	—	2	1	no	—
270	C₂²⋊Q₈×C₄₃	—	2	1	no	—
271	C₂²⋊Q₈×C₄₃	—	2	2	no	—
272	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
273	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
274	#121×C₄₃	—	2	1	no	—
275	#121×C₄₃	—	2	1	no	—
276	#121×C₄₃	—	2	2	no	—
277	#121×C₄₃	C₂³	1	2	yes	—
278	#120×C₄₃	—	2	2	no	—
279	C₄×Q₈×C₄₃	—	2	1	no	—
280	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
281	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
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	—	2	2	no	—
286	C₄×D₄×C₄₃	—	2	2	no	—
287	C₄×D₄×C₄₃	—	2	1	no	—
288	C₄×D₄×C₄₃	—	2	1	no	—
289	C₄×D₄×C₄₃	D₄	1	2	yes	—
290	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
291	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
292	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
293	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
294	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
295	C₄×D₄×C₄₃	C₂³	1	2	yes	—
296	C₄×D₄×C₄₃	C₂³	1	2	yes	—
297	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
298	#117×C₄₃	—	2	1	no	—
299	#117×C₄₃	—	2	1	no	—
300	#117×C₄₃	—	2	1	no	—
301	#117×C₄₃	—	2	2	no	—
302	#117×C₄₃	—	2	2	no	—
303	#117×C₄₃	—	2	2	no	—
304	#117×C₄₃	D₄	1	1	yes	characteristic
305	#117×C₄₃	D₄	1	2	yes	—
306	#117×C₄₃	C₂³	1	2	yes	—
307	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
308	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
309	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
310	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
311	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
312	C₂×C₄²×C₄₃	—	2	2	no	—
313	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
314	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
315	C₂⁴×C₄₃	—	2	1	no	—
316	C₂³×D₄₃	—	2	2	no	—
317	#41×C₄₃	—	2	4	no	—
318	#41×C₄₃	—	4	2	no	—
319	#41×C₄₃	—	4	2	no	—
320	C₂×Q₈×C₄₃	—	2	1	no	—
321	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
322	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
323	C₂×D₄×C₄₃	—	2	1	no	—
324	C₂×D₄×C₄₃	—	2	2	no	—
325	C₂×D₄×C₄₃	—	2	2	no	—
326	C₂×D₄×C₄₃	—	2	2	no	—
327	C₂×D₄×C₄₃	—	4	1	no	—
328	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
329	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
330	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
331	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
332	C₂²×C₄×C₄₃	—	2	1	no	—
333	C₂²×C₄×C₄₃	—	2	2	no	—
334	C₂²×C₄×C₄₃	—	2	1	no	—
335	C₂²×C₄×C₄₃	—	2	1	no	—
336	C₂²×C₄×C₄₃	—	2	1	no	—
337	C₂²×C₄×C₄₃	—	2	2	no	—
338	C₂²×C₄×C₄₃	—	2	1	no	—
339	C₂²×C₄×C₄₃	—	4	4	no	—
340	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
341	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
343	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
344	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
345	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
346	C₂×C₂²⋊D₄₃	—	2	2	no	—
347	C₂×C₂²⋊D₄₃	—	2	1	no	—
348	C₂×C₂²⋊D₄₃	—	2	2	no	—
349	C₂²×Dic₄₃	—	2	2	no	—
350	D₄×D₄₃	—	4	4	no	—
351	#10621898	—	4	2	no	—
352	#10621898	—	4	2	no	—
353	C₂×D₁₇₂	—	2	1	no	—
354	C₂×D₁₇₂	—	2	1	no	—
355	C₂×D₁₇₂	—	2	2	no	—
356	C₂×D₁₇₂	—	4	2	no	—
357	C₂×D₁₇₂	—	4	2	no	—
358	C₂×D₁₇₂	C₂⁴	1	1	yes	characteristic
359	C₂×D₁₇₂	C₂⁴	1	2	yes	—
360	C₂×C₄×D₄₃	—	2	1	no	—
361	C₂×C₄×D₄₃	—	2	2	no	—
362	C₂×C₄×D₄₃	—	2	2	no	—
363	C₂×Dic₈₆	—	2	2	no	—
364	C₂×Dic₈₆	—	4	2	no	—
365	C₂×Dic₈₆	—	4	2	no	—
366	C₂×Dic₈₆	C₂⁴	1	1	yes	characteristic
367	C₂×Dic₈₆	C₂⁴	1	2	yes	—
368	C₄⋊C₄×C₄₃	—	2	1	no	—
369	C₄⋊C₄×C₄₃	—	2	1	no	—
370	C₄⋊C₄×C₄₃	—	2	2	no	—
371	C₄⋊C₄×C₄₃	—	2	2	no	—
372	C₄⋊C₄×C₄₃	—	2	1	no	—
373	C₄⋊C₄×C₄₃	—	2	2	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	—	2	1	no	—
378	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
379	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
380	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
381	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
382	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
383	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
385	C₂²⋊C₄×C₄₃	—	2	1	no	—
386	C₂²⋊C₄×C₄₃	—	2	2	no	—
387	C₂²⋊C₄×C₄₃	—	2	2	no	—
388	C₂²⋊C₄×C₄₃	—	2	1	no	—
389	C₂²⋊C₄×C₄₃	—	2	1	no	—
390	C₂²⋊C₄×C₄₃	—	2	1	no	—
391	C₂²⋊C₄×C₄₃	—	2	2	no	—
392	C₂²⋊C₄×C₄₃	—	2	2	no	—
393	C₂²⋊C₄×C₄₃	—	2	2	no	—
394	C₂²⋊C₄×C₄₃	—	2	2	no	—
395	C₂²⋊C₄×C₄₃	—	2	2	no	—
396	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
397	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
398	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
399	C₄²×C₄₃	—	2	2	no	—
400	C₄²×C₄₃	—	2	2	no	—
401	C₄²×C₄₃	—	2	2	no	—
402	C₄²×C₄₃	C₂×D₄	1	2	yes	—
403	C₄²×C₄₃	C₂×D₄	1	2	yes	—
404	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
405	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
406	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
407	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
408	C₄²×C₄₃	C₂⁴	1	2	yes	—
409	C₂²⋊Dic₄₃	—	2	2	no	—
410	C₂²⋊Dic₄₃	—	2	1	no	—
411	#10621885	—	4	2	no	—
412	#10621885	—	4	2	no	—
413	#10621885	—	4	2	no	—
414	#10621884	—	4	2	no	—
415	#10621884	—	4	2	no	—
416	#10621884	—	4	2	no	—
417	#10621883	—	2	4	no	—
418	#10621883	—	2	2	no	—
419	#10621883	—	4	1	no	—
420	#10621883	—	4	2	no	—
421	#10621882	—	2	2	no	—
422	#10621882	—	2	4	no	—
423	#10621882	—	4	1	no	—
424	#10621882	—	4	2	no	—
425	(C₂×D₄₃)⋊C₄	—	2	1	no	—
426	(C₂×D₄₃)⋊C₄	—	2	2	no	—
427	(C₂×D₄₃)⋊C₄	—	2	1	no	—
428	(C₂×D₄₃)⋊C₄	—	2	1	no	—
429	(C₂×D₄₃)⋊C₄	—	2	2	no	—
430	(C₂×D₄₃)⋊C₄	—	2	2	no	—
431	(C₂×D₄₃)⋊C₄	—	2	2	no	—
432	(C₂×D₄₃)⋊C₄	—	2	2	no	—
433	(C₂×D₄₃)⋊C₄	—	2	2	no	—
434	(C₂×D₄₃)⋊C₄	—	2	2	no	—
435	(C₂×D₄₃)⋊C₄	—	2	2	no	—
436	(C₂×D₄₃)⋊C₄	—	2	1	no	—
437	C₄⋊Dic₄₃	—	2	1	no	—
438	C₄⋊Dic₄₃	—	2	1	no	—
439	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
440	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
441	Dic₄₃⋊C₄	—	2	1	no	—
442	Dic₄₃⋊C₄	—	2	1	no	—
443	Dic₄₃⋊C₄	—	2	1	no	—
444	Dic₄₃⋊C₄	—	2	2	no	—
445	Dic₄₃⋊C₄	—	2	2	no	—
446	Dic₄₃⋊C₄	—	2	1	no	—
447	C₄×Dic₄₃	—	2	2	no	—
448	C₄×Dic₄₃	—	2	1	no	—
449	#10621877	—	4	2	no	—
450	#10621877	—	4	2	no	—
451	#10621877	—	4	2	no	—
452	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
453	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
454	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
455	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
456	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
457	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
458	C₂³×C₄₃	—	2	1	no	—
459	C₂³×C₄₃	—	2	1	no	—
460	C₂³×C₄₃	—	4	2	no	—
461	C₂³×C₄₃	—	4	2	no	—
462	C₂³×C₄₃	—	8	1	no	—
463	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
464	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
465	C₂²×D₄₃	—	2	1	no	—
466	C₂²×D₄₃	—	2	2	no	—
467	C₂²×D₄₃	—	4	4	no	—
468	C₂²×D₄₃	—	8	2	no	—
469	C₂²×D₄₃	—	8	2	no	—
470	Q₈×C₄₃	—	2	2	no	—
471	Q₈×C₄₃	—	2	2	no	—
472	Q₈×C₄₃	—	2	2	no	—
473	Q₈×C₄₃	—	8	1	no	—
474	D₄×C₄₃	—	2	2	no	—
475	D₄×C₄₃	—	2	1	no	—
476	D₄×C₄₃	—	2	1	no	—
477	D₄×C₄₃	—	2	1	no	—
478	D₄×C₄₃	—	4	2	no	—
479	D₄×C₄₃	—	4	2	no	—
480	D₄×C₄₃	—	4	4	no	—
481	D₄×C₄₃	—	8	2	no	—
482	D₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
483	C₂×C₄×C₄₃	—	2	2	no	—
484	C₂×C₄×C₄₃	—	2	2	no	—
485	C₂×C₄×C₄₃	—	2	1	no	—
486	C₂×C₄×C₄₃	—	2	2	no	—
487	C₂×C₄×C₄₃	—	2	1	no	—
488	C₂×C₄×C₄₃	—	2	1	no	—
489	C₂×C₄×C₄₃	—	2	2	no	—
490	C₂×C₄×C₄₃	—	2	2	no	—
491	C₂×C₄×C₄₃	—	2	1	no	—
492	C₂×C₄×C₄₃	—	4	2	no	—
493	C₂×C₄×C₄₃	—	4	1	no	—
494	C₂×C₄×C₄₃	—	4	2	no	—
495	C₂×C₄×C₄₃	—	4	4	no	—
496	C₂×C₄×C₄₃	—	4	2	no	—
497	C₂×C₄×C₄₃	—	4	2	no	—
498	C₂×C₄×C₄₃	—	4	2	no	—
499	C₂×C₄×C₄₃	—	4	2	no	—
500	C₂×C₄×C₄₃	—	4	2	no	—
501	C₂×C₄×C₄₃	—	8	2	no	—
502	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
503	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
504	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
505	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
507	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
508	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
511	C₂²⋊D₄₃	—	4	4	no	—
512	C₂²⋊D₄₃	—	8	2	no	—
513	C₂²⋊D₄₃	—	8	1	no	—
514	C₂×Dic₄₃	—	2	1	no	—
515	C₂×Dic₄₃	—	2	1	no	—
516	C₂×Dic₄₃	—	2	2	no	—
517	C₂×Dic₄₃	—	2	1	no	—
518	C₂×Dic₄₃	—	8	2	no	—
519	D₁₇₂	—	2	2	no	—
520	D₁₇₂	—	2	1	no	—
521	D₁₇₂	—	2	1	no	—
522	D₁₇₂	—	2	2	no	—
523	D₁₇₂	—	4	2	no	—
524	D₁₇₂	—	8	1	no	—
525	D₁₇₂	—	8	2	no	—
526	C₄×D₄₃	—	4	2	no	—
527	C₄×D₄₃	—	8	2	no	—
528	C₄×D₄₃	—	8	2	no	—
529	Dic₈₆	—	2	2	no	—
530	Dic₈₆	—	2	1	no	—
531	Dic₈₆	—	2	1	no	—
532	Dic₈₆	—	2	2	no	—
533	Dic₈₆	—	8	2	no	—
534	C₄₃⋊C₈	—	2	2	no	—
535	C₄₃⋊C₈	—	2	1	no	—
536	C₄₃⋊C₈	—	2	2	no	—
537	C₄₃⋊C₈	—	2	1	no	—
538	C₄₃⋊C₈	—	2	1	no	—
539	C₄₃⋊C₈	—	2	1	no	—
540	#62004	—	43	1	no	maximal, Sylow
541	C₂²×C₄₃	—	2	2	no	—
542	C₂²×C₄₃	—	2	1	no	—
543	C₂²×C₄₃	—	2	2	no	—
544	C₂²×C₄₃	—	2	2	no	—
545	C₂²×C₄₃	—	2	1	no	—
546	C₂²×C₄₃	—	2	2	no	—
547	C₂²×C₄₃	—	2	1	no	—
548	C₂²×C₄₃	—	4	1	no	—
549	C₂²×C₄₃	—	4	1	no	—
550	C₂²×C₄₃	—	4	1	no	—
551	C₂²×C₄₃	—	4	1	no	—
552	C₂²×C₄₃	—	4	1	no	—
553	C₂²×C₄₃	—	8	4	no	—
554	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
555	C₂×D₄₃	—	4	1	no	—
556	C₂×D₄₃	—	4	2	no	—
557	C₂×D₄₃	—	4	1	no	—
558	C₂×D₄₃	—	4	2	no	—
559	C₂×D₄₃	—	4	1	no	—
560	C₂×D₄₃	—	4	2	no	—
561	C₂×D₄₃	—	16	4	no	—
562	C₄×C₄₃	—	2	2	no	—
563	C₄×C₄₃	—	2	1	no	—
564	C₄×C₄₃	—	2	1	no	—
565	C₄×C₄₃	—	2	2	no	—
566	C₄×C₄₃	—	2	1	no	—
567	C₄×C₄₃	—	2	1	no	—
568	C₄×C₄₃	—	2	2	no	—
569	C₄×C₄₃	—	4	2	no	—
570	C₄×C₄₃	—	4	2	no	—
571	C₄×C₄₃	—	4	1	no	—
572	C₄×C₄₃	—	4	1	no	—
573	C₄×C₄₃	#575	1	2	yes	—
574	C₄×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
575	C₄×C₄₃	#585	1	1	yes	characteristic
576	Dic₄₃	—	4	1	no	—
577	Dic₄₃	—	4	1	no	—
578	Dic₄₃	—	4	2	no	—
579	Dic₄₃	—	4	1	no	—
580	#3514	—	43	1	no	—
581	#3475	D₄₃	1	1	yes	characteristic, complemented
582	#3394	—	43	1	no	—
583	#3393	—	43	1	no	—
584	#3361	—	43	1	no	—
585	#3360	—	43	1	no	—
586	#3329	—	43	1	no	—
587	#3327	—	43	2	no	—
588	#3325	—	43	1	no	—
589	#3323	—	43	2	no	—
590	#3276	—	43	1	no	—
591	#3275	—	43	2	no	—
592	#3273	—	43	2	no	—
593	#3272	—	43	1	no	—
594	#3256	—	43	2	no	—
595	#3252	—	43	1	no	—
596	#3211	—	43	2	no	—
597	#3210	—	43	1	no	—
598	#3105	—	43	1	no	—
599	#3102	—	43	2	no	—
600	#3040	—	43	2	no	—
601	#3036	—	43	1	no	—
602	#2991	—	43	1	no	—
603	C₂×C₄₃	—	4	2	no	—
604	C₂×C₄₃	—	4	1	no	—
605	C₂×C₄₃	—	4	2	no	—
606	C₂×C₄₃	—	8	1	no	—
607	C₂×C₄₃	#3488	1	1	yes	characteristic
608	C₂×C₄₃	C₂×#575	1	1	yes	characteristic
609	C₂×C₄₃	#3584	1	1	yes	characteristic
610	D₄₃	—	8	2	no	—
611	D₄₃	—	8	1	no	—
612	C₂×#137	—	43	2	no	—
613	C₂×AGL(1,ℤ/8)	—	43	2	no	—
614	C₂×AGL(1,ℤ/8)	—	43	2	no	—
615	#559	—	43	1	no	—
616	#556	—	43	1	no	—
617	#556	C₂×D₄₃	1	1	yes	characteristic, complemented
618	#555	—	86	1	no	—
619	#555	C₂×D₄₃	1	1	yes	characteristic
620	#554	C₂×D₄₃	1	1	yes	characteristic, complemented
621	#553	—	2	1	no	—
622	#552	—	2	1	no	—
623	#552	C₂×D₄₃	1	2	yes	complemented
624	#551	—	2	2	no	—
625	#551	—	86	2	no	—
626	D₄×Q₈	—	43	1	no	—
627	#548	—	43	2	no	—
628	#547	C₂×D₄₃	1	1	yes	characteristic
629	#546	—	43	2	no	—
630	#546	—	86	1	no	—
631	#546	C₂×D₄₃	1	2	yes	complemented
632	D₄²	—	43	1	no	—
633	#542	—	86	1	no	—
634	#538	—	86	2	no	—
635	#533	C₂×D₄₃	1	1	yes	characteristic, complemented
636	#532	—	43	1	no	—
637	#529	—	2	2	no	—
638	#529	—	43	2	no	—
639	#529	—	43	1	no	—
640	#529	C₂×D₄₃	1	2	yes	complemented
641	C₂×#124	—	43	2	no	—
642	#525	—	2	1	no	—
643	#518	—	86	1	no	—
644	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
645	C₄×#41	C₂×D₄₃	1	2	yes	complemented
646	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic, complemented
647	C₂×#117	—	2	1	no	—
648	#495	—	43	2	no	—
649	#495	—	43	2	no	—
650	#494	—	43	1	no	—
651	#492	—	43	1	no	—
652	#488	—	43	2	no	—
653	#488	—	43	2	no	—
654	#487	—	43	1	no	—
655	#486	—	43	1	no	—
656	#485	—	43	2	no	—
657	#484	—	43	1	no	—
658	#482	—	43	2	no	—
659	#481	—	43	1	no	—
660	#479	—	43	2	no	—
661	#479	—	43	2	no	—
662	#478	—	43	2	no	—
663	#478	—	43	1	no	—
664	#478	—	43	1	no	—
665	#477	—	43	1	no	—
666	#476	—	43	1	no	—
667	#470	—	43	2	no	—
668	#470	—	43	2	no	—
669	#469	—	43	2	no	—
670	#468	—	43	2	no	—
671	#468	—	43	2	no	—
672	#468	—	43	2	no	—
673	#464	—	43	2	no	—
674	#464	—	43	2	no	—
675	#464	—	43	2	no	—
676	#464	—	43	2	no	—
677	#464	—	43	2	no	—
678	#464	—	43	2	no	—
679	#463	—	43	2	no	—
680	#463	—	43	2	no	—
681	#463	—	43	2	no	—
682	#463	—	43	1	no	—
683	#463	—	43	1	no	—
684	#463	—	43	2	no	—
685	#463	—	43	2	no	—
686	#462	—	43	1	no	—
687	#461	—	43	1	no	—
688	#461	—	43	1	no	—
689	#461	—	43	1	no	—
690	#459	—	43	1	no	—
691	#459	—	43	1	no	—
692	#452	—	43	2	no	—
693	#452	—	43	2	no	—
694	#452	—	43	2	no	—
695	#451	—	43	2	no	—
696	#450	—	43	1	no	—
697	#450	—	43	2	no	—
698	#449	—	43	2	no	—
699	#448	—	43	2	no	—
700	#447	—	43	1	no	—
701	#447	—	43	2	no	—
702	C₈×Q₈	—	43	1	no	—
703	C₈×Q₈	—	43	1	no	—
704	C₄×Q₁₆	—	43	2	no	—
705	C₄×SD₁₆	—	43	2	no	—
706	C₄×SD₁₆	—	43	1	no	—
707	C₄×SD₁₆	—	43	2	no	—
708	C₄×SD₁₆	—	43	1	no	—
709	C₄×D₈	—	43	2	no	—
710	C₄×D₈	—	43	1	no	—
711	C₄×D₈	—	43	1	no	—
712	#436	—	43	1	no	—
713	#436	—	43	2	no	—
714	#436	—	43	2	no	—
715	#436	—	43	1	no	—
716	#431	—	43	2	no	—
717	#431	—	43	1	no	—
718	#423	—	43	1	no	—
719	#423	—	43	2	no	—
720	#419	—	43	2	no	—
721	#418	—	43	2	no	—
722	#417	—	43	2	no	—
723	C₄₃	#62004	1	1	yes	characteristic, complemented, Sylow
724	C₂×#41	—	43	2	no	—
725	C₂×#41	C₂²⋊D₄₃	1	1	yes	characteristic
726	C₂×#41	C₂²×D₄₃	1	2	yes	—
727	C₂²×Q₈	—	43	2	no	—
728	C₂²×D₄	—	43	2	no	—
729	C₂²×D₄	—	86	1	no	—
730	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
731	C₂³×C₄	—	2	1	no	—
732	#137	—	172	4	no	—
733	AGL(1,ℤ/8)	—	172	4	no	—
734	AGL(1,ℤ/8)	—	172	4	no	—
735	C₂×Q₁₆	—	43	2	no	—
736	C₂×Q₁₆	—	43	2	no	—
737	C₂×Q₁₆	—	43	2	no	—
738	C₂×SD₁₆	—	43	2	no	—
739	C₂×SD₁₆	—	43	1	no	—
740	C₂×SD₁₆	—	43	2	no	—
741	C₂×SD₁₆	—	43	2	no	—
742	C₂×SD₁₆	—	43	2	no	—
743	C₂×SD₁₆	—	43	2	no	—
744	C₂×SD₁₆	—	43	1	no	—
745	C₂×D₈	—	43	1	no	—
746	C₂×D₈	—	43	2	no	—
747	C₂×D₈	—	43	2	no	—
748	C₂×D₈	—	43	1	no	—
749	C₂×M₁₆	—	43	2	no	—
750	C₂×M₁₆	—	43	2	no	—
751	C₂×M₁₆	—	43	2	no	—
752	C₄⋊Q₈	—	43	1	no	—
753	C₄⋊Q₈	—	86	1	no	—
754	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
755	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
756	#127	—	43	1	no	—
757	#126	—	2	2	no	—
758	#126	—	2	2	no	—
759	#126	—	2	2	no	—
760	#126	—	86	2	no	—
761	#126	—	86	2	no	—
762	#126	—	86	1	no	—
763	#125	—	2	2	no	—
764	#125	—	2	1	no	—
765	#125	—	43	1	no	—
766	#125	C₂²×D₄₃	1	2	yes	—
767	#124	—	2	2	no	—
768	#124	—	43	1	no	—
769	#124	—	43	2	no	—
770	#124	—	43	2	no	—
771	#124	—	43	2	no	—
772	#124	—	86	1	no	—
773	#124	—	86	2	no	—
774	#124	—	86	2	no	—
775	#124	—	86	2	no	—
776	#124	C₂²×D₄₃	1	2	yes	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	#123	—	2	2	no	—
781	#123	—	86	1	no	—
782	#123	—	86	2	no	—
783	#123	—	86	2	no	—
784	#123	—	86	2	no	—
785	C₂²⋊Q₈	—	2	1	no	—
786	C₂²⋊Q₈	—	2	1	no	—
787	C₂²⋊Q₈	—	2	1	no	—
788	C₂²⋊Q₈	—	2	2	no	—
789	C₂²⋊Q₈	—	43	2	no	—
790	C₂²⋊Q₈	—	43	1	no	—
791	C₂²⋊Q₈	—	86	1	no	—
792	C₂²⋊Q₈	—	86	2	no	—
793	C₂²⋊Q₈	—	86	2	no	—
794	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
795	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
796	#121	—	2	1	no	—
797	#121	—	2	1	no	—
798	#121	—	2	2	no	—
799	#121	—	43	2	no	—
800	#121	—	43	1	no	—
801	#121	—	86	2	no	—
802	#121	—	86	1	no	—
803	#121	—	86	1	no	—
804	#121	—	86	1	no	—
805	#121	—	86	2	no	—
806	#121	C₂²×D₄₃	1	2	yes	—
807	#120	—	2	2	no	—
808	#120	—	86	2	no	—
809	#120	—	86	2	no	—
810	C₄×Q₈	—	2	1	no	—
811	C₄×Q₈	—	43	2	no	—
812	C₄×Q₈	—	43	1	no	—
813	C₄×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
814	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
815	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
816	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
817	C₄×D₄	—	2	2	no	—
818	C₄×D₄	—	2	2	no	—
819	C₄×D₄	—	2	2	no	—
820	C₄×D₄	—	2	1	no	—
821	C₄×D₄	—	2	1	no	—
822	C₄×D₄	—	43	1	no	—
823	C₄×D₄	—	43	2	no	—
824	C₄×D₄	—	86	1	no	—
825	C₄×D₄	—	86	2	no	—
826	C₄×D₄	—	86	1	no	—
827	C₄×D₄	—	86	1	no	—
828	C₄×D₄	—	86	2	no	—
829	C₄×D₄	—	86	1	no	—
830	C₄×D₄	—	86	1	no	—
831	C₄×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
832	C₄×D₄	C₂²⋊D₄₃	1	2	yes	—
833	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
834	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
835	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
836	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
837	C₄×D₄	C₂²×D₄₃	1	2	yes	—
838	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
839	C₄×D₄	C₂²×D₄₃	1	2	yes	—
840	#117	—	2	1	no	—
841	#117	—	2	1	no	—
842	#117	—	2	1	no	—
843	#117	—	2	2	no	—
844	#117	—	2	2	no	—
845	#117	—	2	2	no	—
846	#117	—	86	1	no	—
847	#117	—	86	1	no	—
848	#117	—	86	2	no	—
849	#117	C₂²⋊D₄₃	1	1	yes	characteristic
850	#117	C₂²⋊D₄₃	1	2	yes	—
851	#117	C₂²×D₄₃	1	2	yes	—
852	C₂×C₄⋊C₄	—	2	1	no	—
853	C₂×C₄⋊C₄	—	2	1	no	—
854	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
855	C₂×C₂²⋊C₄	—	2	1	no	—
856	C₂×C₂²⋊C₄	—	2	2	no	—
857	C₂×C₂²⋊C₄	—	86	2	no	—
858	C₂×C₂²⋊C₄	—	86	2	no	—
859	C₂×C₂²⋊C₄	—	86	2	no	—
860	C₂×C₄²	—	2	2	no	—
861	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
862	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
863	#107	—	43	1	no	—
864	#107	—	43	2	no	—
865	#107	—	43	1	no	—
866	#106	—	43	1	no	—
867	#106	—	43	2	no	—
868	#106	—	43	1	no	—
869	C₄⋊C₈	—	43	2	no	—
870	C₄⋊C₈	—	43	1	no	—
871	C₄⋊C₈	—	43	1	no	—
872	C₄⋊C₈	—	43	1	no	—
873	C₄⋊C₈	—	43	2	no	—
874	C₄⋊C₈	—	43	2	no	—
875	C₄⋊C₈	—	43	1	no	—
876	#103	—	43	2	no	—
877	#103	—	43	2	no	—
878	#103	—	43	2	no	—
879	#103	—	43	2	no	—
880	#103	—	43	1	no	—
881	#103	—	43	2	no	—
882	#103	—	43	2	no	—
883	#103	—	43	2	no	—
884	#103	—	43	1	no	—
885	#102	—	43	1	no	—
886	#102	—	43	1	no	—
887	#102	—	43	1	no	—
888	#102	—	43	1	no	—
889	#102	—	43	2	no	—
890	#102	—	43	2	no	—
891	#102	—	43	1	no	—
892	#102	—	43	2	no	—
893	#102	—	43	2	no	—
894	#102	—	43	2	no	—
895	#102	—	43	1	no	—
896	C₂²⋊C₈	—	43	2	no	—
897	C₂²⋊C₈	—	43	1	no	—
898	C₂²⋊C₈	—	43	2	no	—
899	C₂²⋊C₈	—	43	1	no	—
900	C₄×C₈	—	43	1	no	—
901	C₄×C₈	—	43	1	no	—
902	C₄×C₈	—	43	2	no	—
903	C₄×C₈	—	43	2	no	—
904	C₂⁴	—	2	1	no	—
905	C₂⁴	—	86	2	no	—
906	#41	—	2	4	no	—
907	#41	—	4	2	no	—
908	#41	—	4	2	no	—
909	#41	—	172	2	no	—
910	#41	—	172	2	no	—
911	C₂×Q₈	—	2	1	no	—
912	C₂×Q₈	—	43	1	no	—
913	C₂×Q₈	—	43	2	no	—
914	C₂×Q₈	—	86	2	no	—
915	C₂×Q₈	—	172	2	no	—
916	C₂×Q₈	—	172	2	no	—
917	C₂×Q₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
918	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
919	C₂×D₄	—	2	2	no	—
920	C₂×D₄	—	2	2	no	—
921	C₂×D₄	—	2	2	no	—
922	C₂×D₄	—	2	1	no	—
923	C₂×D₄	—	4	1	no	—
924	C₂×D₄	—	43	1	no	—
925	C₂×D₄	—	43	2	no	—
926	C₂×D₄	—	86	1	no	—
927	C₂×D₄	—	86	2	no	—
928	C₂×D₄	—	86	2	no	—
929	C₂×D₄	—	86	1	no	—
930	C₂×D₄	—	86	2	no	—
931	C₂×D₄	—	86	1	no	—
932	C₂×D₄	—	172	2	no	—
933	C₂×D₄	—	172	2	no	—
934	C₂×D₄	—	172	4	no	—
935	C₂×D₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
936	C₂×D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
937	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
938	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
939	C₂²×C₄	—	2	1	no	—
940	C₂²×C₄	—	2	1	no	—
941	C₂²×C₄	—	2	2	no	—
942	C₂²×C₄	—	2	1	no	—
943	C₂²×C₄	—	2	1	no	—
944	C₂²×C₄	—	2	1	no	—
945	C₂²×C₄	—	2	2	no	—
946	C₂²×C₄	—	4	4	no	—
947	C₂²×C₄	—	86	2	no	—
948	C₂²×C₄	—	86	2	no	—
949	C₂²×C₄	—	86	2	no	—
950	C₂²×C₄	—	86	1	no	—
951	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
952	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
953	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
954	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
955	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
956	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
957	Q₁₆	—	172	2	no	—
958	Q₁₆	—	172	2	no	—
959	Q₁₆	—	172	2	no	—
960	SD₁₆	—	86	4	no	—
961	SD₁₆	—	86	2	no	—
962	SD₁₆	—	172	2	no	—
963	SD₁₆	—	172	1	no	—
964	SD₁₆	—	172	2	no	—
965	SD₁₆	—	172	2	no	—
966	SD₁₆	—	172	2	no	—
967	D₈	—	86	4	no	—
968	D₈	—	86	2	no	—
969	D₈	—	172	2	no	—
970	D₈	—	172	1	no	—
971	M₁₆	—	172	2	no	—
972	M₁₆	—	172	2	no	—
973	M₁₆	—	172	2	no	—
974	C₂×C₈	—	43	1	no	—
975	C₂×C₈	—	43	1	no	—
976	C₂×C₈	—	43	1	no	—
977	C₂×C₈	—	43	2	no	—
978	C₂×C₈	—	43	1	no	—
979	C₂×C₈	—	43	2	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	2	1	no	—
985	C₄⋊C₄	—	2	2	no	—
986	C₄⋊C₄	—	2	2	no	—
987	C₄⋊C₄	—	2	2	no	—
988	C₄⋊C₄	—	2	2	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	43	1	no	—
991	C₄⋊C₄	—	43	1	no	—
992	C₄⋊C₄	—	86	1	no	—
993	C₄⋊C₄	—	86	1	no	—
994	C₄⋊C₄	—	86	1	no	—
995	C₄⋊C₄	—	86	1	no	—
996	C₄⋊C₄	—	86	2	no	—
997	C₄⋊C₄	—	86	1	no	—
998	C₄⋊C₄	—	86	2	no	—
999	C₄⋊C₄	—	86	1	no	—
1000	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1001	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1002	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1003	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1004	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1005	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1006	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
1007	C₂²⋊C₄	—	2	2	no	—
1008	C₂²⋊C₄	—	2	2	no	—
1009	C₂²⋊C₄	—	2	2	no	—
1010	C₂²⋊C₄	—	2	1	no	—
1011	C₂²⋊C₄	—	2	2	no	—
1012	C₂²⋊C₄	—	2	2	no	—
1013	C₂²⋊C₄	—	2	1	no	—
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	86	2	no	—
1019	C₂²⋊C₄	—	86	1	no	—
1020	C₂²⋊C₄	—	86	1	no	—
1021	C₂²⋊C₄	—	86	2	no	—
1022	C₂²⋊C₄	—	86	1	no	—
1023	C₂²⋊C₄	—	86	1	no	—
1024	C₂²⋊C₄	—	86	2	no	—
1025	C₂²⋊C₄	—	86	2	no	—
1026	C₂²⋊C₄	—	86	2	no	—
1027	C₂²⋊C₄	—	86	2	no	—
1028	C₂²⋊C₄	—	86	2	no	—
1029	C₂²⋊C₄	—	86	2	no	—
1030	C₂²⋊C₄	—	86	1	no	—
1031	C₂²⋊C₄	—	86	2	no	—
1032	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1033	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1034	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1035	C₄²	—	2	2	no	—
1036	C₄²	—	2	2	no	—
1037	C₄²	—	2	2	no	—
1038	C₄²	—	86	2	no	—
1039	C₄²	—	86	1	no	—
1040	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
1041	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
1042	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1043	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1044	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1045	C₄²	C₂³×D₄₃	1	2	yes	—
1046	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1047	C₂³	—	2	1	no	—
1048	C₂³	—	2	1	no	—
1049	C₂³	—	4	2	no	—
1050	C₂³	—	4	2	no	—
1051	C₂³	—	8	1	no	—
1052	C₂³	—	86	1	no	—
1053	C₂³	—	86	2	no	—
1054	C₂³	—	344	2	no	—
1055	C₂³	—	344	2	no	—
1056	C₂³	—	172	4	no	—
1057	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1058	C₂³	C₂²×C₂²⋊D₄₃	1	2	yes	—
1059	Q₈	—	2	2	no	—
1060	Q₈	—	2	2	no	—
1061	Q₈	—	2	2	no	—
1062	Q₈	—	8	1	no	—
1063	Q₈	—	86	2	no	—
1064	Q₈	—	86	1	no	—
1065	Q₈	—	86	1	no	—
1066	Q₈	—	86	2	no	—
1067	Q₈	—	344	2	no	—
1068	D₄	—	2	2	no	—
1069	D₄	—	2	1	no	—
1070	D₄	—	2	1	no	—
1071	D₄	—	2	1	no	—
1072	D₄	—	4	2	no	—
1073	D₄	—	4	2	no	—
1074	D₄	—	4	4	no	—
1075	D₄	—	8	2	no	—
1076	D₄	—	86	2	no	—
1077	D₄	—	86	1	no	—
1078	D₄	—	86	1	no	—
1079	D₄	—	86	2	no	—
1080	D₄	—	344	2	no	—
1081	D₄	—	344	1	no	—
1082	D₄	—	344	2	no	—
1083	D₄	—	344	1	no	—
1084	D₄	—	172	4	no	—
1085	D₄	—	172	2	no	—
1086	D₄	#13063371	1	2	yes	—
1087	C₂×C₄	—	2	2	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	2	no	—
1090	C₂×C₄	—	2	1	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	1	no	—
1093	C₂×C₄	—	2	2	no	—
1094	C₂×C₄	—	2	2	no	—
1095	C₂×C₄	—	2	1	no	—
1096	C₂×C₄	—	4	2	no	—
1097	C₂×C₄	—	4	2	no	—
1098	C₂×C₄	—	4	1	no	—
1099	C₂×C₄	—	4	4	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	4	2	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	4	2	no	—
1104	C₂×C₄	—	4	2	no	—
1105	C₂×C₄	—	8	2	no	—
1106	C₂×C₄	—	86	1	no	—
1107	C₂×C₄	—	86	1	no	—
1108	C₂×C₄	—	86	1	no	—
1109	C₂×C₄	—	86	2	no	—
1110	C₂×C₄	—	344	2	no	—
1111	C₂×C₄	—	344	2	no	—
1112	C₂×C₄	—	344	2	no	—
1113	C₂×C₄	—	172	2	no	—
1114	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1115	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1116	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1117	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1118	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1119	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1120	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1121	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1122	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1123	C₈	—	86	2	no	—
1124	C₈	—	86	1	no	—
1125	C₈	—	86	2	no	—
1126	C₈	—	86	1	no	—
1127	C₈	—	86	1	no	—
1128	C₈	—	86	1	no	—
1129	C₂²	—	2	1	no	—
1130	C₂²	—	2	2	no	—
1131	C₂²	—	2	2	no	—
1132	C₂²	—	2	1	no	—
1133	C₂²	—	2	2	no	—
1134	C₂²	—	2	1	no	—
1135	C₂²	—	2	2	no	—
1136	C₂²	—	4	1	no	—
1137	C₂²	—	4	1	no	—
1138	C₂²	—	4	1	no	—
1139	C₂²	—	4	1	no	—
1140	C₂²	—	4	1	no	—
1141	C₂²	—	8	4	no	—
1142	C₂²	—	172	1	no	—
1143	C₂²	—	172	2	no	—
1144	C₂²	—	172	2	no	—
1145	C₂²	—	172	1	no	—
1146	C₂²	—	172	2	no	—
1147	C₂²	—	172	1	no	—
1148	C₂²	—	688	4	no	—
1149	C₂²	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
1150	C₄	—	2	1	no	—
1151	C₄	—	2	2	no	—
1152	C₄	—	2	1	no	—
1153	C₄	—	2	2	no	—
1154	C₄	—	2	1	no	—
1155	C₄	—	2	2	no	—
1156	C₄	—	2	1	no	—
1157	C₄	—	4	1	no	—
1158	C₄	—	4	1	no	—
1159	C₄	—	4	2	no	—
1160	C₄	—	4	2	no	—
1161	C₄	—	172	1	no	—
1162	C₄	—	172	1	no	—
1163	C₄	—	172	2	no	—
1164	C₄	—	172	1	no	—
1165	C₄	#14583697	1	2	yes	—
1166	C₄	C₂×#13063371	1	1	yes	characteristic
1167	C₄	#14583735	1	1	yes	characteristic
1168	C₂	—	4	1	no	—
1169	C₂	—	4	2	no	—
1170	C₂	—	4	2	no	—
1171	C₂	—	8	1	no	—
1172	C₂	—	344	1	no	—
1173	C₂	—	344	2	no	—
1174	C₂	#19148264	1	1	yes	characteristic
1175	C₂	C₂×#14583697	1	1	yes	characteristic
1176	C₂	#19149366	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3475	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3475	D₄₃
hypocenter	C₄₃	#62004
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3475

Complements

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

N	H ≅ G/N	type
1. #19148556	C₂	semidirect
2. #19147591	C₂	semidirect
3. #19147579	C₂	semidirect
4. #19147255	C₂	semidirect
5. #19147244	C₂	semidirect
6. #19146883	C₂	semidirect
7. #19146857	C₂	semidirect
8. #19146831	C₂	semidirect
9. #19146805	C₂	semidirect
10. #19146237	C₂	semidirect
11. #19146222	C₂	semidirect
12. #19146202	C₂	semidirect
13. #19146195	C₂	semidirect
14. #19145991	C₂	semidirect
15. #19145962	C₂	semidirect
16. #19145556	C₂	semidirect
17. #19145547	C₂	semidirect
18. #19144642	C₂	semidirect
19. #19144613	C₂	semidirect
20. #19144089	C₂	semidirect
21. #19144059	C₂	semidirect
22. #19143727	C₂	semidirect
23. C₄₃×#3475	C₂	semidirect
24. C₂×#13063355	C₂²	semidirect
25. C₂×#13063351	C₂²	semidirect
27. #14583634	C₂²	semidirect
28. #14583622	C₂²	semidirect
31. D₄×Dic₈₆	C₂²	semidirect
35. D₄×D₁₇₂	C₂²	semidirect
40. #14583433	C₂²	semidirect
41. C₂×#13063313	C₂²	semidirect
44. #14583281	C₂²	semidirect
45. #14583278	C₂²	semidirect
46. #14583273	C₂²	semidirect
47. #14583256	C₂²	semidirect
48. #14583256	C₂²	semidirect
49. #14583251	C₂²	semidirect
50. #14583247	C₂²	semidirect
51. #14583240	C₂²	semidirect
52. #14583234	C₂²	semidirect
53. #14583223	C₂²	semidirect
55. #14583206	C₂²	semidirect
56. #14583203	C₂²	semidirect
57. #14583199	C₂²	semidirect
58. #14583199	C₂²	semidirect
59. #14583196	C₂²	semidirect
60. #14583191	C₂²	semidirect
61. #14583186	C₂²	semidirect
62. #14583155	C₂²	semidirect
63. #14583155	C₂²	semidirect
66. #14583147	C₂²	semidirect
67. #14583143	C₂²	semidirect
68. #14583121	C₂²	semidirect
69. #14583121	C₂²	semidirect
70. #14583121	C₂²	semidirect
71. #14583121	C₂²	semidirect
72. #14583121	C₂²	semidirect
73. #14583118	C₂²	semidirect
77. #14583114	C₂²	semidirect
78. #14583114	C₂²	semidirect
79. #14583114	C₂²	semidirect
80. #14583111	C₂²	semidirect
81. #14583106	C₂²	semidirect
82. #14583104	C₂²	semidirect
83. #14583104	C₂²	semidirect
84. #14583101	C₂²	semidirect
87. #14583061	C₂²	semidirect
88. #14583059	C₂²	semidirect
89. #14583059	C₂²	semidirect
90. #14583054	C₂²	semidirect
91. #14583050	C₂²	semidirect
92. #14583049	C₂²	semidirect
94. #14583037	C₂²	semidirect
97. Q₈×C₄₃⋊C₈	C₂²	semidirect
98. Q₈×C₄₃⋊C₈	C₂²	semidirect
99. C₄×#10621885	C₂²	semidirect
100. C₄×#10621884	C₂²	semidirect
101. C₄×#10621883	C₂²	semidirect
102. C₄×#10621883	C₂²	semidirect
103. C₄×#10621883	C₂²	semidirect
106. C₄×#10621882	C₂²	semidirect
107. #14582977	C₂²	semidirect
108. #14582977	C₂²	semidirect
109. #14582977	C₂²	semidirect
110. #14582977	C₂²	semidirect
111. #14582952	C₂²	semidirect
112. #14582952	C₂²	semidirect
113. #14582923	C₂²	semidirect
114. #14582923	C₂²	semidirect
115. #14582907	C₂²	semidirect
116. #14582903	C₂²	semidirect
117. #14582898	C₂²	semidirect
118. C₄₃×#556	C₂²	semidirect
120. C₄₃×#554	C₂²	semidirect
123. C₄₃×#552	C₂²	semidirect
126. C₄₃×#546	C₂²	semidirect
127. C₄₃×#533	C₂²	semidirect
129. C₄₃×#529	C₂²	semidirect
132. C₄×#41×C₄₃	C₂²	semidirect
133. C₂×C₄×D₄×C₄₃	C₂²	semidirect
581. #3475	D₄₃	semidirect
617. #556	C₂×D₄₃	semidirect
620. #554	C₂×D₄₃	semidirect
623. #552	C₂×D₄₃	semidirect
631. #546	C₂×D₄₃	semidirect
635. #533	C₂×D₄₃	semidirect
640. #529	C₂×D₄₃	semidirect
645. C₄×#41	C₂×D₄₃	semidirect
646. C₂×C₄×D₄	C₂×D₄₃	semidirect
723. C₄₃	#62004	semidirect

Maximal subgroups

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

subgroup	index
#19148556	2
#19147591	2
#19147579	2
#19147255	2
#19147244	2
#19146883	2
#19146857	2
#19146831	2
#19146805	2
#19146237	2
#19146222	2
#19146202	2
#19146195	2
#19145991	2
#19145962	2
#19145556	2
#19145547	2
#19144642	2
#19144613	2
#19144089	2
#19144059	2
#19143727	2
C₄₃×#3475	2
#62004	43