Subgroups — #25989778

Order 11008.

2126 conjugacy classes of subgroups.

The subgroup lattice has 1228 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148599	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×#10621898	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147574	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147569	C₂	1	1	yes	maximal, characteristic, complemented
5	#19147235	C₂	1	1	yes	maximal, characteristic, complemented
6	#19147228	C₂	1	1	yes	maximal, characteristic, complemented
7	#19146924	C₂	1	1	yes	maximal, characteristic, complemented
8	#19146920	C₂	1	2	yes	maximal, complemented
9	#19146902	C₂	1	1	yes	maximal, characteristic, complemented
10	#19146898	C₂	1	2	yes	maximal, complemented
11	#19146216	C₂	1	1	yes	maximal, characteristic, complemented
12	#19146213	C₂	1	2	yes	maximal, complemented
13	#19146196	C₂	1	1	yes	maximal, characteristic, complemented
14	#19146193	C₂	1	2	yes	maximal, complemented
15	#19145957	C₂	1	1	yes	maximal, characteristic, complemented
16	#19145956	C₂	1	2	yes	maximal, complemented
17	#19145530	C₂	1	1	yes	maximal, characteristic, complemented
18	#19145527	C₂	1	2	yes	maximal, complemented
19	#19144647	C₂	1	2	yes	maximal, complemented
20	#19144059	C₂	1	1	yes	maximal, characteristic, complemented
21	#19144057	C₂	1	2	yes	maximal, complemented
22	#19143724	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3105	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#10621898	—	2	1	no	—
25	C₂×#13063352	C₂²	1	2	yes	—
26	C₂×#13063351	C₂²	1	2	yes	—
27	C₂×#13063349	C₂²	1	2	yes	—
28	#14583627	C₂²	1	1	yes	characteristic, complemented
29	#14583600	—	2	2	no	—
30	#14583595	—	2	1	no	—
31	#14583571	C₂²	1	1	yes	characteristic, complemented
32	#14583570	—	2	1	no	—
33	#14583570	C₂²	1	1	yes	characteristic
34	#14583570	C₂²	1	1	yes	characteristic, complemented
35	#14583567	C₂²	1	2	yes	complemented
36	D₄×Dic₈₆	C₂²	1	1	yes	characteristic
37	#14583558	—	2	1	no	—
38	#14583554	C₂²	1	1	yes	characteristic
39	#14583553	C₂²	1	1	yes	characteristic, complemented
40	#14583551	C₂²	1	2	yes	complemented
41	#14583550	C₂²	1	2	yes	—
42	#14583545	—	2	1	no	—
43	#14583539	—	2	2	no	—
44	D₄×D₁₇₂	C₂²	1	1	yes	characteristic
45	D₄×C₂²⋊D₄₃	C₂²	1	2	yes	—
46	#14583504	—	2	1	no	—
47	#14583501	—	2	2	no	—
48	#14583449	C₂²	1	1	yes	characteristic
49	#14583449	C₂²	1	1	yes	characteristic, complemented
50	#14583448	C₂²	1	2	yes	complemented
51	#14583446	C₂²	1	2	yes	—
52	#14583434	C₂²	1	2	yes	complemented
53	#14583410	—	2	1	no	—
54	#14583408	—	2	2	no	—
55	#14583379	—	2	1	no	—
56	C₄×#10621898	C₂²	1	1	yes	characteristic
57	C₄×D₄×D₄₃	C₂²	1	2	yes	—
58	#14583276	C₂²	1	1	yes	characteristic, complemented
59	#14583274	C₂²	1	2	yes	complemented
60	#14583272	C₂²	1	1	yes	characteristic, complemented
61	#14583270	C₂²	1	2	yes	complemented
62	#14583250	C₂²	1	1	yes	characteristic, complemented
63	#14583248	C₂²	1	2	yes	complemented
64	#14583246	C₂²	1	1	yes	characteristic, complemented
65	#14583244	C₂²	1	2	yes	complemented
66	#14583236	C₂²	1	2	yes	complemented
67	#14583219	C₂²	1	2	yes	complemented
68	#14583196	C₂²	1	2	yes	complemented
69	#14583184	C₂²	1	1	yes	characteristic, complemented
70	#14583183	C₂²	1	2	yes	complemented
71	#14583179	C₂²	1	1	yes	characteristic, complemented
72	#14583178	C₂²	1	2	yes	complemented
73	#14583153	C₂²	1	2	yes	complemented
74	#14583151	C₂²	1	2	yes	complemented
75	#14583150	C₂²	1	2	yes	complemented
76	#14583147	C₂²	1	2	yes	complemented
77	#14583146	C₂²	1	2	yes	complemented
78	#14583144	C₂²	1	2	yes	complemented
79	#14583115	C₂²	1	2	yes	complemented
80	#14583115	C₂²	1	2	yes	complemented
81	#14583114	C₂²	1	2	yes	—
82	#14583114	C₂²	1	2	yes	complemented
83	#14583111	C₂²	1	2	yes	complemented
84	#14583104	C₂²	1	1	yes	characteristic
85	#14583104	C₂²	1	1	yes	characteristic, complemented
86	#14583103	C₂²	1	2	yes	complemented
87	#14583102	C₂²	1	2	yes	—
88	#14583099	C₂²	1	1	yes	characteristic, complemented
89	#14583098	C₂²	1	2	yes	complemented
90	#14583094	C₂²	1	1	yes	characteristic
91	#14583094	C₂²	1	1	yes	characteristic, complemented
92	#14583094	C₂²	1	1	yes	characteristic, complemented
93	#14583093	C₂²	1	2	yes	complemented
94	#14583093	C₂²	1	2	yes	complemented
95	#14583092	C₂²	1	2	yes	—
96	#14583051	C₂²	1	2	yes	—
97	#14583047	C₂²	1	2	yes	complemented
98	#14583046	C₂²	1	2	yes	complemented
99	#14583046	C₂²	1	2	yes	complemented
100	#14583045	C₂²	1	2	yes	complemented
101	#14583043	C₂²	1	2	yes	complemented
102	#14583041	C₂²	1	2	yes	complemented
103	#14583034	C₂²	1	2	yes	—
104	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
105	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
106	#14582990	C₂²	1	2	yes	—
107	#14582986	C₂²	1	2	yes	complemented
108	#14582981	C₂²	1	2	yes	complemented
109	#14582979	C₂²	1	2	yes	—
110	#14582978	C₂²	1	1	yes	characteristic, complemented
111	#14582978	C₂²	1	1	yes	characteristic, complemented
112	#14582974	C₂²	1	2	yes	complemented
113	#14582974	C₂²	1	2	yes	complemented
114	#14582951	C₂²	1	2	yes	complemented
115	#14582923	C₂²	1	1	yes	characteristic, complemented
116	#14582921	C₂²	1	2	yes	complemented
117	#14582899	C₂²	1	2	yes	complemented
118	#14582898	C₂²	1	2	yes	complemented
119	#14582897	C₂²	1	2	yes	complemented
120	C₄₃×#529	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
122	C₄₃×#484	C₂²	1	1	yes	characteristic, complemented
123	C₄₃×#481	C₂²	1	1	yes	characteristic, complemented
124	C₄₃×#478	C₂²	1	1	yes	characteristic
125	C₄₃×#478	C₂²	1	1	yes	characteristic, complemented
126	C₄₃×#463	C₂²	1	1	yes	characteristic
127	C₄₃×#463	C₂²	1	1	yes	characteristic, complemented
128	C₄₃×#450	C₂²	1	1	yes	characteristic
129	C₄₃×#447	C₂²	1	1	yes	characteristic
130	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
131	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic, complemented
132	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
133	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
134	C₄₃×#431	C₂²	1	1	yes	characteristic, complemented
135	C₂×#10621902	C₂³	1	2	yes	—
136	C₂×#10621898	—	2	1	no	—
137	C₂×#10621898	—	2	2	no	—
138	C₂×#10621898	—	2	1	no	—
139	C₂×#10621898	—	2	2	no	—
140	C₂×#10621898	—	2	1	no	—
141	C₂×#10621898	—	2	1	no	—
142	C₂×#10621898	—	4	8	no	—
143	C₂×#10621898	D₄	1	1	yes	characteristic
144	C₂×#10621898	C₂³	1	2	yes	—
145	C₂×#10621900	C₂³	1	2	yes	—
146	C₂²×Dic₈₆	—	2	1	no	—
147	C₂²×D₁₇₂	—	2	1	no	—
148	C₂²×C₂²⋊D₄₃	—	2	2	no	—
149	C₂×D₄×D₄₃	C₂³	1	2	yes	—
150	C₂²×C₄×D₄₃	—	2	2	no	—
151	#13063352	—	4	4	no	—
152	#13063351	—	4	4	no	—
153	#13063349	—	4	4	no	—
154	C₂×#10621873	C₂³	1	2	yes	—
155	C₂×#10621873	C₂³	1	2	yes	—
156	C₂×#10621883	C₂³	1	2	yes	—
157	C₂×#10621883	C₂³	1	2	yes	—
158	C₂×#10621884	C₂³	1	2	yes	—
159	C₂×D₃₄₄	C₂³	1	2	yes	—
160	C₂×D₃₄₄	C₂³	1	2	yes	—
161	C₂×#10621882	C₂³	1	2	yes	—
162	C₂×#10621882	C₂³	1	2	yes	—
163	C₂×#10621882	C₂³	1	2	yes	—
164	C₂×#10621877	C₂³	1	2	yes	—
165	C₂×#10621872	C₂³	1	2	yes	—
166	C₂×#10621872	C₂³	1	2	yes	—
167	#13063325	C₂³	1	1	yes	characteristic
168	#13063325	C₂³	1	1	yes	characteristic
169	#13063324	C₂³	1	2	yes	—
170	#13063323	C₂³	1	2	yes	—
171	#13063322	—	2	1	no	—
172	#13063322	C₂³	1	1	yes	characteristic
173	#13063322	C₂³	1	1	yes	characteristic
174	#13063321	—	2	2	no	—
175	#13063321	C₂³	1	2	yes	—
176	#13063321	C₂³	1	2	yes	—
177	#13063320	—	2	2	no	—
178	#13063317	—	2	1	no	—
179	#13063315	—	2	2	no	—
180	#13063313	—	2	1	no	—
181	#13063313	C₂³	1	2	yes	—
182	#13063311	—	2	2	no	—
183	#13063310	—	2	2	no	—
184	#13063310	—	2	2	no	—
185	#13063310	—	2	2	no	—
186	#13063309	—	2	2	no	—
187	#13063308	—	2	2	no	—
188	#13063307	—	2	2	no	—
189	#13063307	—	2	2	no	—
190	#13063305	C₂³	1	2	yes	—
191	#13063304	—	2	1	no	—
192	#13063304	—	2	1	no	—
193	#13063303	—	2	2	no	—
194	#13063302	—	2	2	no	—
195	#13063300	—	2	2	no	—
196	#13063300	C₂³	1	2	yes	—
197	#13063300	C₂³	1	2	yes	—
198	#13063299	—	2	1	no	—
199	#13063299	—	2	1	no	—
200	#13063299	—	2	1	no	—
201	#13063299	—	2	1	no	—
202	#13063299	—	2	1	no	—
203	#13063299	—	2	1	no	—
204	#13063299	—	2	1	no	—
205	#13063299	C₂³	1	2	yes	—
206	#13063298	—	2	2	no	—
207	#13063298	—	2	2	no	—
208	#13063298	—	2	2	no	—
209	#13063298	—	2	2	no	—
210	#13063298	—	2	2	no	—
211	#13063298	—	2	2	no	—
212	#13063298	—	2	2	no	—
213	#13063297	—	2	2	no	—
214	#13063297	—	2	2	no	—
215	#13063296	C₂³	1	2	yes	—
216	#13063295	—	2	2	no	—
217	#13063294	—	2	2	no	—
218	#13063293	—	2	2	no	—
219	C₄×Dic₈₆	—	2	1	no	—
220	C₄×Dic₈₆	D₄	1	1	yes	characteristic
221	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
222	#13063290	C₂³	1	2	yes	—
223	C₄×D₁₇₂	—	2	1	no	—
224	C₄×D₁₇₂	—	2	1	no	—
225	C₄×D₁₇₂	—	2	1	no	—
226	C₄×D₁₇₂	—	2	1	no	—
227	C₄×D₁₇₂	D₄	1	1	yes	characteristic
228	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
229	C₄×D₁₇₂	C₂³	1	2	yes	—
230	D₄×Dic₄₃	C₂³	1	2	yes	—
231	#13063287	—	2	2	no	—
232	#13063287	C₂³	1	2	yes	—
233	#13063287	C₂³	1	2	yes	—
234	C₄×C₂²⋊D₄₃	—	2	2	no	—
235	C₄×C₂²⋊D₄₃	—	2	2	no	—
236	C₄×C₂²⋊D₄₃	D₄	1	2	yes	—
237	C₄×C₂²⋊D₄₃	C₂³	1	2	yes	—
238	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
239	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
240	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
241	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
242	#13063284	D₄	1	1	yes	characteristic
243	#13063283	—	2	2	no	—
244	#13063282	D₄	1	2	yes	—
245	C₂×C₄⋊Dic₄₃	—	2	1	no	—
246	C₄⋊C₄×D₄₃	—	2	2	no	—
247	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
248	C₂²⋊C₄×D₄₃	—	2	2	no	—
249	C₄²×D₄₃	C₂³	1	2	yes	—
250	#13063258	C₂³	1	2	yes	—
251	#13063256	C₂³	1	2	yes	—
252	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
253	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
254	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
255	Dic₄₃⋊C₈	C₂³	1	2	yes	—
256	Dic₄₃⋊C₈	C₂³	1	2	yes	—
257	#13063250	C₂³	1	2	yes	—
258	#13063250	C₂³	1	2	yes	—
259	#13063249	C₂³	1	2	yes	—
260	#13063248	C₂³	1	2	yes	—
261	#13063248	C₂³	1	2	yes	—
262	#13063247	C₂³	1	2	yes	—
263	#13063247	C₂³	1	2	yes	—
264	#13063246	C₂³	1	2	yes	—
265	#13063245	C₂³	1	2	yes	—
266	#13063245	C₂³	1	2	yes	—
267	#13063245	C₂³	1	2	yes	—
268	#13063245	C₂³	1	2	yes	—
269	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
270	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
271	C₈×Dic₄₃	C₂³	1	2	yes	—
272	C₈×Dic₄₃	C₂³	1	2	yes	—
273	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
274	C₂³×C₄×C₄₃	—	2	1	no	—
275	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
276	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
277	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
278	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
279	#126×C₄₃	—	2	1	no	—
280	#125×C₄₃	C₂³	1	1	yes	characteristic
281	#124×C₄₃	C₂³	1	1	yes	characteristic
282	#123×C₄₃	—	2	1	no	—
283	C₂²⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
284	#121×C₄₃	C₂³	1	1	yes	characteristic
285	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
286	C₄×D₄×C₄₃	—	2	1	no	—
287	C₄×D₄×C₄₃	—	2	1	no	—
288	C₄×D₄×C₄₃	—	2	1	no	—
289	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₄₃	C₂³	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	#117×C₄₃	—	2	1	no	—
295	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
296	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
297	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
298	#107×C₄₃	C₂³	1	1	yes	characteristic
299	#107×C₄₃	C₂³	1	1	yes	characteristic
300	#106×C₄₃	C₂³	1	1	yes	characteristic
301	#106×C₄₃	C₂³	1	1	yes	characteristic
302	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
303	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
304	#103×C₄₃	C₂³	1	1	yes	characteristic
305	#103×C₄₃	C₂³	1	1	yes	characteristic
306	#102×C₄₃	C₂³	1	1	yes	characteristic
307	#102×C₄₃	C₂³	1	1	yes	characteristic
308	#102×C₄₃	C₂³	1	1	yes	characteristic
309	#102×C₄₃	C₂³	1	1	yes	characteristic
310	#102×C₄₃	C₂³	1	1	yes	characteristic
311	#102×C₄₃	C₂³	1	1	yes	characteristic
312	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
313	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
315	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
316	C₂⁴×C₄₃	—	2	1	no	—
317	C₂³×D₄₃	—	2	2	no	—
318	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
319	C₂×D₄×C₄₃	—	2	1	no	—
320	C₂×D₄×C₄₃	—	2	1	no	—
321	C₂×D₄×C₄₃	—	2	2	no	—
322	C₂×D₄×C₄₃	—	4	1	no	—
323	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
324	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
326	C₂²×C₄×C₄₃	—	2	1	no	—
327	C₂²×C₄×C₄₃	—	2	1	no	—
328	C₂²×C₄×C₄₃	—	2	1	no	—
329	C₂²×C₄×C₄₃	—	2	1	no	—
330	C₂²×C₄×C₄₃	—	2	1	no	—
331	C₂²×C₄×C₄₃	—	2	1	no	—
332	C₂²×C₄×C₄₃	—	4	4	no	—
333	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
336	C₂×C₂²⋊D₄₃	—	2	2	no	—
337	C₂×C₂²⋊D₄₃	—	2	2	no	—
338	C₂×C₂²⋊D₄₃	—	2	2	no	—
339	C₂×C₂²⋊D₄₃	—	2	2	no	—
340	C₂×C₂²⋊D₄₃	—	2	2	no	—
341	C₂×C₂²⋊D₄₃	—	2	2	no	—
342	C₂×C₂²⋊D₄₃	—	2	2	no	—
343	C₂×C₂²⋊D₄₃	—	2	2	no	—
344	C₂×C₂²⋊D₄₃	—	2	2	no	—
345	C₂×C₂²⋊D₄₃	—	4	8	no	—
346	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
347	C₂²×Dic₄₃	—	2	2	no	—
348	C₂²×Dic₄₃	—	2	2	no	—
349	#10621902	—	4	2	no	—
350	#10621902	—	4	2	no	—
351	#10621900	—	4	2	no	—
352	#10621900	—	4	2	no	—
353	D₄×D₄₃	—	2	4	no	—
354	D₄×D₄₃	—	4	2	no	—
355	#10621898	—	2	4	no	—
356	#10621898	—	4	2	no	—
357	#10621898	—	4	2	no	—
358	#10621898	—	4	8	no	—
359	#10621898	—	4	4	no	—
360	#10621898	—	4	8	no	—
361	#10621898	—	4	4	no	—
362	#10621898	—	4	4	no	—
363	#10621898	—	4	4	no	—
364	C₂×D₁₇₂	—	2	1	no	—
365	C₂×D₁₇₂	—	2	1	no	—
366	C₂×D₁₇₂	—	2	1	no	—
367	C₂×D₁₇₂	—	2	1	no	—
368	C₂×D₁₇₂	—	2	2	no	—
369	C₂×D₁₇₂	—	2	2	no	—
370	C₂×D₁₇₂	—	2	2	no	—
371	C₂×D₁₇₂	—	4	4	no	—
372	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
373	C₂×D₁₇₂	C₂⁴	1	2	yes	—
374	C₂×D₁₇₂	C₂⁴	1	2	yes	—
375	C₂×C₄×D₄₃	—	2	2	no	—
376	C₂×C₄×D₄₃	—	2	2	no	—
377	C₂×C₄×D₄₃	—	2	2	no	—
378	C₂×C₄×D₄₃	—	2	2	no	—
379	C₂×C₄×D₄₃	—	2	2	no	—
380	C₂×C₄×D₄₃	—	2	2	no	—
381	C₂×C₄×D₄₃	—	4	8	no	—
382	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
383	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
384	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
385	C₂×Dic₈₆	—	2	1	no	—
386	C₂×Dic₈₆	—	2	2	no	—
387	C₂×Dic₈₆	—	4	4	no	—
388	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
389	C₂×Dic₈₆	C₂⁴	1	2	yes	—
390	SD₁₆×C₄₃	—	2	2	no	—
391	SD₁₆×C₄₃	—	4	1	no	—
392	D₈×C₄₃	—	2	2	no	—
393	D₈×C₄₃	—	4	1	no	—
394	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
396	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
397	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
398	C₄⋊C₄×C₄₃	—	2	1	no	—
399	C₄⋊C₄×C₄₃	—	2	1	no	—
400	C₄⋊C₄×C₄₃	—	2	1	no	—
401	C₄⋊C₄×C₄₃	—	2	1	no	—
402	C₄⋊C₄×C₄₃	—	2	1	no	—
403	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
404	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
405	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
406	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
407	C₂²⋊C₄×C₄₃	—	2	1	no	—
408	C₂²⋊C₄×C₄₃	—	2	1	no	—
409	C₂²⋊C₄×C₄₃	—	2	1	no	—
410	C₂²⋊C₄×C₄₃	—	2	1	no	—
411	C₂²⋊C₄×C₄₃	—	2	1	no	—
412	C₂²⋊C₄×C₄₃	—	2	1	no	—
413	C₂²⋊C₄×C₄₃	—	2	1	no	—
414	C₂²⋊C₄×C₄₃	—	2	1	no	—
415	C₂²⋊C₄×C₄₃	—	2	1	no	—
416	C₄²×C₄₃	—	2	1	no	—
417	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
418	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
419	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
420	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
421	C₂²⋊Dic₄₃	—	2	2	no	—
422	C₂²⋊Dic₄₃	—	2	2	no	—
423	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
424	#10621884	—	4	2	no	—
425	#10621883	—	2	4	no	—
426	#10621883	—	4	2	no	—
427	#10621882	—	2	4	no	—
428	#10621882	—	4	2	no	—
429	#10621882	—	4	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	2	no	—
437	(C₂×D₄₃)⋊C₄	—	2	2	no	—
438	(C₂×D₄₃)⋊C₄	—	2	2	no	—
439	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
440	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
441	C₄⋊Dic₄₃	—	2	1	no	—
442	C₄⋊Dic₄₃	—	2	1	no	—
443	C₄⋊Dic₄₃	—	2	1	no	—
444	C₄⋊Dic₄₃	—	2	2	no	—
445	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
446	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
447	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
448	Dic₄₃⋊C₄	—	2	2	no	—
449	Dic₄₃⋊C₄	—	2	2	no	—
450	Dic₄₃⋊C₄	—	2	2	no	—
451	Dic₄₃⋊C₄	—	2	2	no	—
452	Dic₄₃⋊C₄	—	2	2	no	—
453	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
454	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
455	C₄×Dic₄₃	—	2	2	no	—
456	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
457	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
458	C₄×Dic₄₃	C₂⁴	1	2	yes	—
459	#10621877	—	4	2	no	—
460	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
461	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
462	D₃₄₄	—	4	2	no	—
463	D₃₄₄	—	4	2	no	—
464	#10621873	—	4	2	no	—
465	#10621873	—	4	2	no	—
466	#10621872	—	4	2	no	—
467	#10621872	—	4	2	no	—
468	C₂³×C₄₃	—	2	1	no	—
469	C₂³×C₄₃	—	2	1	no	—
470	C₂³×C₄₃	—	2	1	no	—
471	C₂³×C₄₃	—	4	2	no	—
472	C₂³×C₄₃	—	4	2	no	—
473	C₂³×C₄₃	—	8	1	no	—
474	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
475	C₂²×D₄₃	—	2	2	no	—
476	C₂²×D₄₃	—	2	2	no	—
477	C₂²×D₄₃	—	4	4	no	—
478	C₂²×D₄₃	—	4	4	no	—
479	C₂²×D₄₃	—	8	2	no	—
480	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
481	Q₈×C₄₃	—	2	1	no	—
482	Q₈×C₄₃	—	2	1	no	—
483	D₄×C₄₃	—	2	1	no	—
484	D₄×C₄₃	—	2	1	no	—
485	D₄×C₄₃	—	2	1	no	—
486	D₄×C₄₃	—	2	1	no	—
487	D₄×C₄₃	—	2	1	no	—
488	D₄×C₄₃	—	4	2	no	—
489	D₄×C₄₃	—	8	1	no	—
490	D₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
491	C₂×C₄×C₄₃	—	2	2	no	—
492	C₂×C₄×C₄₃	—	2	1	no	—
493	C₂×C₄×C₄₃	—	2	1	no	—
494	C₂×C₄×C₄₃	—	2	1	no	—
495	C₂×C₄×C₄₃	—	2	1	no	—
496	C₂×C₄×C₄₃	—	2	1	no	—
497	C₂×C₄×C₄₃	—	2	1	no	—
498	C₂×C₄×C₄₃	—	2	1	no	—
499	C₂×C₄×C₄₃	—	4	1	no	—
500	C₂×C₄×C₄₃	—	4	2	no	—
501	C₂×C₄×C₄₃	—	4	2	no	—
502	C₂×C₄×C₄₃	—	4	2	no	—
503	C₂×C₄×C₄₃	—	4	2	no	—
504	C₂×C₄×C₄₃	—	4	2	no	—
505	C₂×C₄×C₄₃	—	4	2	no	—
506	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
509	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
512	C₂²⋊D₄₃	—	2	4	no	—
513	C₂²⋊D₄₃	—	4	4	no	—
514	C₂²⋊D₄₃	—	4	4	no	—
515	C₂²⋊D₄₃	—	4	4	no	—
516	C₂²⋊D₄₃	—	4	4	no	—
517	C₂²⋊D₄₃	—	4	4	no	—
518	C₂²⋊D₄₃	—	8	2	no	—
519	C₂²⋊D₄₃	—	8	2	no	—
520	C₂²⋊D₄₃	—	8	2	no	—
521	C₂²⋊D₄₃	—	8	2	no	—
522	C₂×Dic₄₃	—	2	2	no	—
523	C₂×Dic₄₃	—	2	2	no	—
524	C₂×Dic₄₃	—	4	4	no	—
525	C₂×Dic₄₃	—	8	2	no	—
526	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
527	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
528	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
529	D₁₇₂	—	2	2	no	—
530	D₁₇₂	—	2	2	no	—
531	D₁₇₂	—	2	2	no	—
532	D₁₇₂	—	2	2	no	—
533	D₁₇₂	—	2	2	no	—
534	D₁₇₂	—	4	4	no	—
535	D₁₇₂	—	4	2	no	—
536	D₁₇₂	—	4	2	no	—
537	D₁₇₂	—	8	1	no	—
538	D₁₇₂	—	8	1	no	—
539	D₁₇₂	—	8	2	no	—
540	D₁₇₂	—	8	2	no	—
541	C₄×D₄₃	—	2	2	no	—
542	C₄×D₄₃	—	2	2	no	—
543	C₄×D₄₃	—	2	4	no	—
544	C₄×D₄₃	—	4	2	no	—
545	C₄×D₄₃	—	4	4	no	—
546	C₄×D₄₃	—	4	4	no	—
547	C₄×D₄₃	—	4	4	no	—
548	C₄×D₄₃	—	4	4	no	—
549	C₄×D₄₃	—	8	2	no	—
550	C₄×D₄₃	—	8	2	no	—
551	Dic₈₆	—	2	2	no	—
552	Dic₈₆	—	2	2	no	—
553	Dic₈₆	—	4	2	no	—
554	Dic₈₆	—	4	4	no	—
555	Dic₈₆	AGL(1,ℤ/8)	1	4	yes	complemented
556	C₈×C₄₃	—	2	1	no	—
557	C₈×C₄₃	—	2	1	no	—
558	C₈×C₄₃	—	2	1	no	—
559	C₈×C₄₃	—	2	1	no	—
560	C₄₃⋊C₈	—	2	2	no	—
561	C₄₃⋊C₈	—	2	2	no	—
562	#62003	—	43	1	no	maximal, Sylow
563	C₂²×C₄₃	—	2	1	no	—
564	C₂²×C₄₃	—	2	2	no	—
565	C₂²×C₄₃	—	2	1	no	—
566	C₂²×C₄₃	—	2	1	no	—
567	C₂²×C₄₃	—	4	1	no	—
568	C₂²×C₄₃	—	4	1	no	—
569	C₂²×C₄₃	—	4	1	no	—
570	C₂²×C₄₃	—	4	1	no	—
571	C₂²×C₄₃	—	4	1	no	—
572	C₂²×C₄₃	—	4	1	no	—
573	C₂²×C₄₃	—	4	1	no	—
574	C₂²×C₄₃	—	4	1	no	—
575	C₂²×C₄₃	—	8	4	no	—
576	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
577	C₂×D₄₃	—	2	2	no	—
578	C₂×D₄₃	—	2	2	no	—
579	C₂×D₄₃	—	2	2	no	—
580	C₂×D₄₃	—	4	2	no	—
581	C₂×D₄₃	—	4	2	no	—
582	C₂×D₄₃	—	4	2	no	—
583	C₂×D₄₃	—	4	2	no	—
584	C₂×D₄₃	—	4	2	no	—
585	C₂×D₄₃	—	4	2	no	—
586	C₂×D₄₃	—	8	8	no	—
587	C₄×C₄₃	—	2	1	no	—
588	C₄×C₄₃	—	2	1	no	—
589	C₄×C₄₃	—	2	1	no	—
590	C₄×C₄₃	—	2	1	no	—
591	C₄×C₄₃	—	4	1	no	—
592	C₄×C₄₃	—	4	1	no	—
593	C₄×C₄₃	—	4	1	no	—
594	C₄×C₄₃	—	4	1	no	—
595	C₄×C₄₃	—	4	1	no	—
596	C₄×C₄₃	C₂×AGL(1,ℤ/8)	1	2	yes	—
597	C₄×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
598	C₄×C₄₃	#585	1	1	yes	characteristic
599	Dic₄₃	—	2	2	no	—
600	Dic₄₃	—	2	2	no	—
601	Dic₄₃	—	4	2	no	—
602	Dic₄₃	—	4	2	no	—
603	Dic₄₃	C₂×AGL(1,ℤ/8)	1	4	yes	—
604	#3517	—	43	1	no	—
605	D₄×#41	—	43	1	no	—
606	#3392	—	43	1	no	—
607	#3391	—	43	1	no	—
608	#3359	—	43	1	no	—
609	#3358	—	43	1	no	—
610	#3332	—	43	2	no	—
611	#3332	—	43	1	no	—
612	#3330	—	43	2	no	—
613	#3330	—	43	1	no	—
614	#3274	—	43	2	no	—
615	#3274	—	43	1	no	—
616	#3272	—	43	2	no	—
617	#3272	—	43	1	no	—
618	#3251	—	43	2	no	—
619	#3251	—	43	1	no	—
620	#3207	—	43	2	no	—
621	#3207	—	43	1	no	—
622	#3105	—	43	2	no	—
623	#3105	D₄₃	1	1	yes	characteristic, complemented
624	#3036	—	43	2	no	—
625	#3036	—	43	1	no	—
626	#2991	—	43	1	no	—
627	C₂×C₄₃	—	4	2	no	—
628	C₂×C₄₃	—	4	1	no	—
629	C₂×C₄₃	—	8	1	no	—
630	C₂×C₄₃	—	8	1	no	—
631	C₂×C₄₃	#3488	1	1	yes	characteristic
632	C₂×C₄₃	C₂²×AGL(1,ℤ/8)	1	1	yes	characteristic
633	C₂×C₄₃	#3584	1	1	yes	characteristic
634	D₄₃	—	4	2	no	—
635	D₄₃	—	8	2	no	—
636	D₄₃	—	8	2	no	—
637	C₂²×#41	—	86	1	no	—
638	C₂×AGL(1,ℤ/8)	—	43	2	no	—
639	C₂×AGL(1,ℤ/8)	—	43	2	no	—
640	C₂×AGL(1,ℤ/8)	—	43	2	no	—
641	#557	—	43	1	no	—
642	#553	—	86	1	no	—
643	#553	—	86	2	no	—
644	#550	—	43	1	no	—
645	#550	—	43	1	no	—
646	#550	—	43	2	no	—
647	#550	—	43	1	no	—
648	#550	—	86	1	no	—
649	D₄×Q₈	—	43	1	no	—
650	#548	—	86	1	no	—
651	#547	—	43	1	no	—
652	#547	—	43	2	no	—
653	#547	—	43	2	no	—
654	#547	—	43	1	no	—
655	#546	—	86	2	no	—
656	#546	—	86	1	no	—
657	D₄²	—	43	2	no	—
658	D₄²	—	43	1	no	—
659	#540	—	86	1	no	—
660	#540	—	86	2	no	—
661	#532	—	43	2	no	—
662	#532	—	43	2	no	—
663	#532	—	43	1	no	—
664	#532	—	43	1	no	—
665	#529	—	43	2	no	—
666	#529	C₂×D₄₃	1	1	yes	characteristic, complemented
667	#525	—	86	2	no	—
668	#525	—	86	1	no	—
669	#520	—	86	1	no	—
670	C₄×#41	—	43	1	no	—
671	C₂×C₄×D₄	—	43	2	no	—
672	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
673	#493	—	43	2	no	—
674	#493	—	43	1	no	—
675	#492	—	43	2	no	—
676	#492	—	43	1	no	—
677	#487	—	43	2	no	—
678	#487	—	43	1	no	—
679	#486	—	43	2	no	—
680	#486	—	43	1	no	—
681	#484	—	43	2	no	—
682	#484	C₂×D₄₃	1	1	yes	characteristic, complemented
683	#481	—	43	2	no	—
684	#481	C₂×D₄₃	1	1	yes	characteristic, complemented
685	#478	—	43	2	no	—
686	#478	C₂×D₄₃	1	1	yes	characteristic
687	#478	C₂×D₄₃	1	1	yes	characteristic, complemented
688	#475	—	43	1	no	—
689	#475	—	43	2	no	—
690	#474	—	43	1	no	—
691	#474	—	43	2	no	—
692	#469	—	43	2	no	—
693	#469	—	43	2	no	—
694	#469	—	43	2	no	—
695	#468	—	43	2	no	—
696	#468	—	43	2	no	—
697	#468	—	43	2	no	—
698	#463	—	43	2	no	—
699	#463	—	43	2	no	—
700	#463	—	43	2	no	—
701	#463	—	43	2	no	—
702	#463	—	43	2	no	—
703	#463	C₂×D₄₃	1	1	yes	characteristic
704	#463	C₂×D₄₃	1	1	yes	characteristic, complemented
705	#461	—	43	2	no	—
706	#461	—	43	1	no	—
707	#461	—	43	1	no	—
708	#461	—	43	2	no	—
709	#460	—	43	1	no	—
710	#460	—	43	2	no	—
711	#459	—	43	2	no	—
712	#459	—	43	1	no	—
713	#459	—	43	1	no	—
714	#459	—	43	1	no	—
715	#459	—	43	2	no	—
716	#459	—	43	2	no	—
717	#450	—	43	2	no	—
718	#450	C₂×D₄₃	1	1	yes	characteristic
719	#449	—	43	2	no	—
720	#449	—	43	2	no	—
721	#449	—	43	2	no	—
722	#449	—	43	2	no	—
723	#449	—	43	2	no	—
724	#449	—	43	2	no	—
725	#447	—	43	2	no	—
726	#447	C₂×D₄₃	1	1	yes	characteristic
727	C₈×Q₈	—	43	1	no	—
728	C₈×Q₈	—	43	1	no	—
729	C₄×SD₁₆	—	43	2	no	—
730	C₄×SD₁₆	—	43	2	no	—
731	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
732	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic, complemented
733	C₄×D₈	—	43	2	no	—
734	C₄×D₈	—	43	2	no	—
735	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
736	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic, complemented
737	#436	—	43	2	no	—
738	#436	—	43	2	no	—
739	#436	—	43	1	no	—
740	#436	—	43	1	no	—
741	#431	—	43	2	no	—
742	#431	C₂×D₄₃	1	1	yes	characteristic, complemented
743	#423	—	43	1	no	—
744	#423	—	43	2	no	—
745	#417	—	43	2	no	—
746	#417	—	43	2	no	—
747	#417	—	43	2	no	—
748	C₄₃	#62003	1	1	yes	characteristic, complemented, Sylow
749	C₂×#41	—	43	1	no	—
750	C₂×#41	—	43	2	no	—
751	C₂×#41	—	43	2	no	—
752	C₂×#41	—	43	2	no	—
753	C₂×#41	—	86	2	no	—
754	C₂×#41	—	86	2	no	—
755	C₂×#41	—	86	1	no	—
756	C₂×#41	—	86	1	no	—
757	C₂×#41	—	86	1	no	—
758	C₂×#41	—	86	1	no	—
759	C₂×#41	—	172	8	no	—
760	C₂²×Q₈	—	86	1	no	—
761	C₂²×D₄	—	43	2	no	—
762	C₂²×D₄	—	86	1	no	—
763	C₂²×D₄	—	86	2	no	—
764	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
765	C₂³×C₄	—	2	1	no	—
766	C₂³×C₄	—	86	2	no	—
767	AGL(1,ℤ/8)	—	172	4	no	—
768	AGL(1,ℤ/8)	—	172	4	no	—
769	AGL(1,ℤ/8)	—	172	4	no	—
770	C₂×SD₁₆	—	43	2	no	—
771	C₂×SD₁₆	—	43	2	no	—
772	C₂×SD₁₆	—	43	2	no	—
773	C₂×SD₁₆	—	43	2	no	—
774	C₂×SD₁₆	—	43	2	no	—
775	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
776	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
777	C₂×D₈	—	43	2	no	—
778	C₂×D₈	—	43	2	no	—
779	C₂×D₈	—	43	2	no	—
780	C₂×D₈	—	43	2	no	—
781	C₂×D₈	—	43	2	no	—
782	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
783	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
784	C₂×M₁₆	—	43	2	no	—
785	C₂×M₁₆	—	43	2	no	—
786	C₂×M₁₆	—	43	2	no	—
787	C₄⋊Q₈	—	43	2	no	—
788	C₄⋊Q₈	—	43	2	no	—
789	C₄⋊Q₈	—	43	1	no	—
790	C₄⋊Q₈	—	43	1	no	—
791	#127	—	43	2	no	—
792	#127	—	43	2	no	—
793	#127	—	43	1	no	—
794	#127	—	43	1	no	—
795	#127	—	86	1	no	—
796	#127	—	86	2	no	—
797	#126	—	2	1	no	—
798	#126	—	86	2	no	—
799	#125	—	86	1	no	—
800	#125	—	86	2	no	—
801	#125	C₂²×D₄₃	1	1	yes	characteristic
802	#124	—	43	2	no	—
803	#124	—	86	2	no	—
804	#124	—	86	1	no	—
805	#124	C₂²×D₄₃	1	1	yes	characteristic
806	#123	—	2	1	no	—
807	#123	—	86	2	no	—
808	#123	—	86	2	no	—
809	#123	—	86	2	no	—
810	#123	—	86	2	no	—
811	#123	—	86	2	no	—
812	#123	—	86	2	no	—
813	#123	—	86	2	no	—
814	C₂²⋊Q₈	—	43	2	no	—
815	C₂²⋊Q₈	—	86	2	no	—
816	C₂²⋊Q₈	—	86	2	no	—
817	C₂²⋊Q₈	—	86	1	no	—
818	C₂²⋊Q₈	—	86	1	no	—
819	C₂²⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
820	#121	—	43	2	no	—
821	#121	—	43	2	no	—
822	#121	—	43	2	no	—
823	#121	—	43	2	no	—
824	#121	—	86	2	no	—
825	#121	—	86	2	no	—
826	#121	—	86	2	no	—
827	#121	—	86	2	no	—
828	#121	—	86	2	no	—
829	#121	—	86	2	no	—
830	#121	—	86	2	no	—
831	#121	—	86	2	no	—
832	#121	—	86	2	no	—
833	#121	—	86	1	no	—
834	#121	—	86	1	no	—
835	#121	—	86	1	no	—
836	#121	—	86	2	no	—
837	#121	—	86	1	no	—
838	#121	—	86	1	no	—
839	#121	—	86	1	no	—
840	#121	—	86	1	no	—
841	#121	C₂²×D₄₃	1	1	yes	characteristic
842	#120	—	86	2	no	—
843	#120	—	86	2	no	—
844	#120	—	86	2	no	—
845	C₄×Q₈	—	43	1	no	—
846	C₄×Q₈	—	43	1	no	—
847	C₄×Q₈	—	43	2	no	—
848	C₄×Q₈	—	86	1	no	—
849	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
850	C₄×D₄	—	2	1	no	—
851	C₄×D₄	—	2	1	no	—
852	C₄×D₄	—	2	1	no	—
853	C₄×D₄	—	43	2	no	—
854	C₄×D₄	—	43	2	no	—
855	C₄×D₄	—	43	2	no	—
856	C₄×D₄	—	43	2	no	—
857	C₄×D₄	—	43	2	no	—
858	C₄×D₄	—	43	1	no	—
859	C₄×D₄	—	43	1	no	—
860	C₄×D₄	—	43	2	no	—
861	C₄×D₄	—	86	1	no	—
862	C₄×D₄	—	86	2	no	—
863	C₄×D₄	—	86	2	no	—
864	C₄×D₄	—	86	2	no	—
865	C₄×D₄	—	86	2	no	—
866	C₄×D₄	—	86	2	no	—
867	C₄×D₄	—	86	2	no	—
868	C₄×D₄	—	86	2	no	—
869	C₄×D₄	—	86	1	no	—
870	C₄×D₄	—	86	1	no	—
871	C₄×D₄	—	86	1	no	—
872	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
873	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
874	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
875	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
876	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
877	#117	—	2	1	no	—
878	#117	—	43	1	no	—
879	#117	—	43	2	no	—
880	#117	—	86	2	no	—
881	C₂×C₄⋊C₄	—	43	2	no	—
882	C₂×C₄⋊C₄	—	86	2	no	—
883	C₂×C₄⋊C₄	—	86	1	no	—
884	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
885	C₂×C₂²⋊C₄	—	2	1	no	—
886	C₂×C₂²⋊C₄	—	86	2	no	—
887	C₂×C₄²	—	43	2	no	—
888	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
889	#107	—	43	2	no	—
890	#107	C₂²×D₄₃	1	1	yes	characteristic
891	#107	C₂²×D₄₃	1	1	yes	characteristic
892	#106	—	43	2	no	—
893	#106	C₂²×D₄₃	1	1	yes	characteristic
894	#106	C₂²×D₄₃	1	1	yes	characteristic
895	C₄⋊C₈	—	43	2	no	—
896	C₄⋊C₈	—	43	2	no	—
897	C₄⋊C₈	—	43	2	no	—
898	C₄⋊C₈	—	43	1	no	—
899	C₄⋊C₈	—	43	1	no	—
900	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
901	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
902	#103	—	43	2	no	—
903	#103	—	43	2	no	—
904	#103	—	43	2	no	—
905	#103	—	43	2	no	—
906	#103	—	43	2	no	—
907	#103	C₂²×D₄₃	1	1	yes	characteristic
908	#103	C₂²×D₄₃	1	1	yes	characteristic
909	#102	—	43	2	no	—
910	#102	—	43	2	no	—
911	#102	—	43	2	no	—
912	#102	—	43	2	no	—
913	#102	—	43	2	no	—
914	#102	—	43	2	no	—
915	#102	—	43	2	no	—
916	#102	C₂²×D₄₃	1	1	yes	characteristic
917	#102	C₂²×D₄₃	1	1	yes	characteristic
918	#102	C₂²×D₄₃	1	1	yes	characteristic
919	#102	C₂²×D₄₃	1	1	yes	characteristic
920	#102	C₂²×D₄₃	1	1	yes	characteristic
921	#102	C₂²×D₄₃	1	1	yes	characteristic
922	C₂²⋊C₈	—	43	2	no	—
923	C₂²⋊C₈	—	43	2	no	—
924	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
925	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
926	C₄×C₈	—	43	2	no	—
927	C₄×C₈	—	43	2	no	—
928	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
929	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
930	C₂⁴	—	2	1	no	—
931	C₂⁴	—	86	2	no	—
932	#41	—	86	4	no	—
933	#41	—	172	2	no	—
934	#41	—	172	2	no	—
935	#41	—	172	4	no	—
936	#41	—	172	8	no	—
937	#41	—	172	8	no	—
938	#41	—	172	4	no	—
939	#41	—	172	4	no	—
940	#41	—	172	4	no	—
941	#41	—	172	2	no	—
942	#41	—	172	2	no	—
943	#41	—	172	2	no	—
944	#41	—	172	2	no	—
945	C₂×Q₈	—	43	1	no	—
946	C₂×Q₈	—	43	2	no	—
947	C₂×Q₈	—	86	2	no	—
948	C₂×Q₈	—	86	1	no	—
949	C₂×Q₈	—	172	4	no	—
950	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
951	C₂×D₄	—	2	2	no	—
952	C₂×D₄	—	2	1	no	—
953	C₂×D₄	—	2	1	no	—
954	C₂×D₄	—	4	1	no	—
955	C₂×D₄	—	43	2	no	—
956	C₂×D₄	—	43	1	no	—
957	C₂×D₄	—	43	2	no	—
958	C₂×D₄	—	43	2	no	—
959	C₂×D₄	—	86	2	no	—
960	C₂×D₄	—	86	2	no	—
961	C₂×D₄	—	86	2	no	—
962	C₂×D₄	—	86	2	no	—
963	C₂×D₄	—	86	2	no	—
964	C₂×D₄	—	86	2	no	—
965	C₂×D₄	—	86	2	no	—
966	C₂×D₄	—	86	2	no	—
967	C₂×D₄	—	86	4	no	—
968	C₂×D₄	—	86	2	no	—
969	C₂×D₄	—	86	2	no	—
970	C₂×D₄	—	86	2	no	—
971	C₂×D₄	—	86	2	no	—
972	C₂×D₄	—	86	1	no	—
973	C₂×D₄	—	86	1	no	—
974	C₂×D₄	—	86	1	no	—
975	C₂×D₄	—	86	1	no	—
976	C₂×D₄	—	172	4	no	—
977	C₂×D₄	—	172	2	no	—
978	C₂×D₄	—	172	8	no	—
979	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
980	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
981	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
982	C₂²×C₄	—	2	1	no	—
983	C₂²×C₄	—	2	1	no	—
984	C₂²×C₄	—	2	1	no	—
985	C₂²×C₄	—	2	1	no	—
986	C₂²×C₄	—	2	1	no	—
987	C₂²×C₄	—	2	1	no	—
988	C₂²×C₄	—	4	4	no	—
989	C₂²×C₄	—	43	2	no	—
990	C₂²×C₄	—	43	2	no	—
991	C₂²×C₄	—	43	2	no	—
992	C₂²×C₄	—	86	2	no	—
993	C₂²×C₄	—	86	2	no	—
994	C₂²×C₄	—	86	2	no	—
995	C₂²×C₄	—	86	2	no	—
996	C₂²×C₄	—	86	2	no	—
997	C₂²×C₄	—	86	2	no	—
998	C₂²×C₄	—	86	2	no	—
999	C₂²×C₄	—	86	2	no	—
1000	C₂²×C₄	—	172	8	no	—
1001	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
1002	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
1003	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
1004	SD₁₆	—	2	2	no	—
1005	SD₁₆	—	4	1	no	—
1006	SD₁₆	—	86	4	no	—
1007	SD₁₆	—	172	2	no	—
1008	SD₁₆	—	172	2	no	—
1009	SD₁₆	—	172	2	no	—
1010	SD₁₆	—	172	2	no	—
1011	D₈	—	2	2	no	—
1012	D₈	—	4	1	no	—
1013	D₈	—	86	4	no	—
1014	D₈	—	172	2	no	—
1015	D₈	—	172	2	no	—
1016	D₈	—	172	2	no	—
1017	D₈	—	172	2	no	—
1018	M₁₆	—	172	2	no	—
1019	M₁₆	—	172	2	no	—
1020	M₁₆	—	172	2	no	—
1021	C₂×C₈	—	43	2	no	—
1022	C₂×C₈	—	43	2	no	—
1023	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
1024	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
1025	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
1026	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
1027	C₄⋊C₄	—	2	1	no	—
1028	C₄⋊C₄	—	2	1	no	—
1029	C₄⋊C₄	—	2	1	no	—
1030	C₄⋊C₄	—	2	1	no	—
1031	C₄⋊C₄	—	2	1	no	—
1032	C₄⋊C₄	—	43	2	no	—
1033	C₄⋊C₄	—	43	1	no	—
1034	C₄⋊C₄	—	43	2	no	—
1035	C₄⋊C₄	—	43	1	no	—
1036	C₄⋊C₄	—	43	2	no	—
1037	C₄⋊C₄	—	86	2	no	—
1038	C₄⋊C₄	—	86	2	no	—
1039	C₄⋊C₄	—	86	2	no	—
1040	C₄⋊C₄	—	86	2	no	—
1041	C₄⋊C₄	—	86	2	no	—
1042	C₄⋊C₄	—	86	2	no	—
1043	C₄⋊C₄	—	86	1	no	—
1044	C₄⋊C₄	—	86	1	no	—
1045	C₄⋊C₄	—	86	1	no	—
1046	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1047	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1048	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1049	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1050	C₂²⋊C₄	—	2	1	no	—
1051	C₂²⋊C₄	—	2	1	no	—
1052	C₂²⋊C₄	—	2	1	no	—
1053	C₂²⋊C₄	—	2	1	no	—
1054	C₂²⋊C₄	—	2	1	no	—
1055	C₂²⋊C₄	—	2	1	no	—
1056	C₂²⋊C₄	—	2	1	no	—
1057	C₂²⋊C₄	—	2	1	no	—
1058	C₂²⋊C₄	—	2	1	no	—
1059	C₂²⋊C₄	—	43	2	no	—
1060	C₂²⋊C₄	—	43	2	no	—
1061	C₂²⋊C₄	—	43	2	no	—
1062	C₂²⋊C₄	—	86	2	no	—
1063	C₂²⋊C₄	—	86	2	no	—
1064	C₂²⋊C₄	—	86	2	no	—
1065	C₂²⋊C₄	—	86	2	no	—
1066	C₂²⋊C₄	—	86	2	no	—
1067	C₂²⋊C₄	—	86	2	no	—
1068	C₂²⋊C₄	—	86	2	no	—
1069	C₂²⋊C₄	—	86	2	no	—
1070	C₂²⋊C₄	—	86	2	no	—
1071	C₂²⋊C₄	—	86	2	no	—
1072	C₂²⋊C₄	—	86	2	no	—
1073	C₄²	—	2	1	no	—
1074	C₄²	—	43	2	no	—
1075	C₄²	—	43	2	no	—
1076	C₄²	—	43	2	no	—
1077	C₄²	—	86	2	no	—
1078	C₄²	D₄×D₄₃	1	1	yes	characteristic
1079	C₄²	D₄×D₄₃	1	1	yes	characteristic
1080	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1081	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1082	C₂³	—	2	1	no	—
1083	C₂³	—	2	1	no	—
1084	C₂³	—	2	1	no	—
1085	C₂³	—	4	2	no	—
1086	C₂³	—	4	2	no	—
1087	C₂³	—	8	1	no	—
1088	C₂³	—	43	2	no	—
1089	C₂³	—	86	2	no	—
1090	C₂³	—	86	2	no	—
1091	C₂³	—	344	2	no	—
1092	C₂³	—	172	4	no	—
1093	C₂³	—	172	4	no	—
1094	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1095	Q₈	—	2	1	no	—
1096	Q₈	—	2	1	no	—
1097	Q₈	—	43	4	no	—
1098	Q₈	—	86	2	no	—
1099	Q₈	—	86	2	no	—
1100	Q₈	—	172	4	no	—
1101	Q₈	—	172	2	no	—
1102	D₄	—	2	1	no	—
1103	D₄	—	2	1	no	—
1104	D₄	—	2	1	no	—
1105	D₄	—	2	1	no	—
1106	D₄	—	2	1	no	—
1107	D₄	—	4	2	no	—
1108	D₄	—	8	1	no	—
1109	D₄	—	86	4	no	—
1110	D₄	—	86	2	no	—
1111	D₄	—	86	2	no	—
1112	D₄	—	86	2	no	—
1113	D₄	—	86	2	no	—
1114	D₄	—	86	2	no	—
1115	D₄	—	344	1	no	—
1116	D₄	—	344	1	no	—
1117	D₄	—	344	2	no	—
1118	D₄	—	344	2	no	—
1119	D₄	—	344	2	no	—
1120	D₄	—	344	2	no	—
1121	D₄	—	344	2	no	—
1122	D₄	—	344	2	no	—
1123	D₄	—	172	4	no	—
1124	D₄	—	172	4	no	—
1125	D₄	—	172	4	no	—
1126	D₄	—	172	4	no	—
1127	D₄	—	172	4	no	—
1128	D₄	—	172	4	no	—
1129	D₄	—	172	2	no	—
1130	D₄	—	172	2	no	—
1131	D₄	#13063371	1	2	yes	—
1132	C₂×C₄	—	2	2	no	—
1133	C₂×C₄	—	2	1	no	—
1134	C₂×C₄	—	2	1	no	—
1135	C₂×C₄	—	2	1	no	—
1136	C₂×C₄	—	2	1	no	—
1137	C₂×C₄	—	2	1	no	—
1138	C₂×C₄	—	2	1	no	—
1139	C₂×C₄	—	2	1	no	—
1140	C₂×C₄	—	4	1	no	—
1141	C₂×C₄	—	4	2	no	—
1142	C₂×C₄	—	4	2	no	—
1143	C₂×C₄	—	4	2	no	—
1144	C₂×C₄	—	4	2	no	—
1145	C₂×C₄	—	4	2	no	—
1146	C₂×C₄	—	4	2	no	—
1147	C₂×C₄	—	43	2	no	—
1148	C₂×C₄	—	43	2	no	—
1149	C₂×C₄	—	43	2	no	—
1150	C₂×C₄	—	86	4	no	—
1151	C₂×C₄	—	86	2	no	—
1152	C₂×C₄	—	86	2	no	—
1153	C₂×C₄	—	86	2	no	—
1154	C₂×C₄	—	86	2	no	—
1155	C₂×C₄	—	344	2	no	—
1156	C₂×C₄	—	344	2	no	—
1157	C₂×C₄	—	344	2	no	—
1158	C₂×C₄	—	172	2	no	—
1159	C₂×C₄	—	172	4	no	—
1160	C₂×C₄	—	172	4	no	—
1161	C₂×C₄	—	172	4	no	—
1162	C₂×C₄	—	172	4	no	—
1163	C₂×C₄	—	172	4	no	—
1164	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1165	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1166	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1167	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1168	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1169	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1170	C₈	—	2	1	no	—
1171	C₈	—	2	1	no	—
1172	C₈	—	2	1	no	—
1173	C₈	—	2	1	no	—
1174	C₈	—	86	2	no	—
1175	C₈	—	86	2	no	—
1176	C₂²	—	2	1	no	—
1177	C₂²	—	2	1	no	—
1178	C₂²	—	2	1	no	—
1179	C₂²	—	2	2	no	—
1180	C₂²	—	4	1	no	—
1181	C₂²	—	4	1	no	—
1182	C₂²	—	4	1	no	—
1183	C₂²	—	4	1	no	—
1184	C₂²	—	4	1	no	—
1185	C₂²	—	4	1	no	—
1186	C₂²	—	4	1	no	—
1187	C₂²	—	4	1	no	—
1188	C₂²	—	8	4	no	—
1189	C₂²	—	86	2	no	—
1190	C₂²	—	86	2	no	—
1191	C₂²	—	86	2	no	—
1192	C₂²	—	344	8	no	—
1193	C₂²	—	172	2	no	—
1194	C₂²	—	172	2	no	—
1195	C₂²	—	172	2	no	—
1196	C₂²	—	172	2	no	—
1197	C₂²	—	172	2	no	—
1198	C₂²	—	172	2	no	—
1199	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1200	C₄	—	2	1	no	—
1201	C₄	—	2	1	no	—
1202	C₄	—	2	1	no	—
1203	C₄	—	2	1	no	—
1204	C₄	—	4	1	no	—
1205	C₄	—	4	1	no	—
1206	C₄	—	4	1	no	—
1207	C₄	—	4	1	no	—
1208	C₄	—	4	1	no	—
1209	C₄	—	43	4	no	—
1210	C₄	—	86	2	no	—
1211	C₄	—	86	2	no	—
1212	C₄	—	172	2	no	—
1213	C₄	—	172	2	no	—
1214	C₄	AGL(1,ℤ/8)×D₄₃	1	2	yes	—
1215	C₄	C₂×#13063371	1	1	yes	characteristic
1216	C₄	#14583735	1	1	yes	characteristic
1217	C₂	—	4	1	no	—
1218	C₂	—	4	2	no	—
1219	C₂	—	8	1	no	—
1220	C₂	—	8	1	no	—
1221	C₂	—	344	2	no	—
1222	C₂	—	344	2	no	—
1223	C₂	—	172	2	no	—
1224	C₂	#19148256	1	1	yes	characteristic
1225	C₂	C₂×AGL(1,ℤ/8)×D₄₃	1	1	yes	characteristic
1226	C₂	#19149364	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3105	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3105	D₄₃
hypocenter	C₄₃	#62003
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3105

Complements

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

N	H ≅ G/N	type
1. #19148599	C₂	semidirect
2. D₄×#10621898	C₂	semidirect
3. #19147574	C₂	semidirect
4. #19147569	C₂	semidirect
5. #19147235	C₂	semidirect
6. #19147228	C₂	semidirect
7. #19146924	C₂	semidirect
8. #19146920	C₂	semidirect
9. #19146902	C₂	semidirect
10. #19146898	C₂	semidirect
11. #19146216	C₂	semidirect
12. #19146213	C₂	semidirect
13. #19146196	C₂	semidirect
14. #19146193	C₂	semidirect
15. #19145957	C₂	semidirect
16. #19145956	C₂	semidirect
17. #19145530	C₂	semidirect
18. #19145527	C₂	semidirect
19. #19144647	C₂	semidirect
20. #19144059	C₂	semidirect
21. #19144057	C₂	semidirect
22. #19143724	C₂	semidirect
23. C₄₃×#3105	C₂	semidirect
28. #14583627	C₂²	semidirect
31. #14583571	C₂²	semidirect
34. #14583570	C₂²	semidirect
35. #14583567	C₂²	semidirect
39. #14583553	C₂²	semidirect
40. #14583551	C₂²	semidirect
49. #14583449	C₂²	semidirect
50. #14583448	C₂²	semidirect
52. #14583434	C₂²	semidirect
58. #14583276	C₂²	semidirect
59. #14583274	C₂²	semidirect
60. #14583272	C₂²	semidirect
61. #14583270	C₂²	semidirect
62. #14583250	C₂²	semidirect
63. #14583248	C₂²	semidirect
64. #14583246	C₂²	semidirect
65. #14583244	C₂²	semidirect
66. #14583236	C₂²	semidirect
67. #14583219	C₂²	semidirect
68. #14583196	C₂²	semidirect
69. #14583184	C₂²	semidirect
70. #14583183	C₂²	semidirect
71. #14583179	C₂²	semidirect
72. #14583178	C₂²	semidirect
73. #14583153	C₂²	semidirect
74. #14583151	C₂²	semidirect
75. #14583150	C₂²	semidirect
76. #14583147	C₂²	semidirect
77. #14583146	C₂²	semidirect
78. #14583144	C₂²	semidirect
79. #14583115	C₂²	semidirect
80. #14583115	C₂²	semidirect
82. #14583114	C₂²	semidirect
83. #14583111	C₂²	semidirect
85. #14583104	C₂²	semidirect
86. #14583103	C₂²	semidirect
88. #14583099	C₂²	semidirect
89. #14583098	C₂²	semidirect
91. #14583094	C₂²	semidirect
92. #14583094	C₂²	semidirect
93. #14583093	C₂²	semidirect
94. #14583093	C₂²	semidirect
97. #14583047	C₂²	semidirect
98. #14583046	C₂²	semidirect
99. #14583046	C₂²	semidirect
100. #14583045	C₂²	semidirect
101. #14583043	C₂²	semidirect
102. #14583041	C₂²	semidirect
104. C₈×Dic₈₆	C₂²	semidirect
105. C₈×Dic₈₆	C₂²	semidirect
107. #14582986	C₂²	semidirect
108. #14582981	C₂²	semidirect
110. #14582978	C₂²	semidirect
111. #14582978	C₂²	semidirect
112. #14582974	C₂²	semidirect
113. #14582974	C₂²	semidirect
114. #14582951	C₂²	semidirect
115. #14582923	C₂²	semidirect
116. #14582921	C₂²	semidirect
117. #14582899	C₂²	semidirect
118. #14582898	C₂²	semidirect
119. #14582897	C₂²	semidirect
120. C₄₃×#529	C₂²	semidirect
122. C₄₃×#484	C₂²	semidirect
123. C₄₃×#481	C₂²	semidirect
125. C₄₃×#478	C₂²	semidirect
127. C₄₃×#463	C₂²	semidirect
131. C₄×SD₁₆×C₄₃	C₂²	semidirect
133. C₄×D₈×C₄₃	C₂²	semidirect
134. C₄₃×#431	C₂²	semidirect
555. Dic₈₆	AGL(1,ℤ/8)	semidirect
623. #3105	D₄₃	semidirect
666. #529	C₂×D₄₃	semidirect
682. #484	C₂×D₄₃	semidirect
684. #481	C₂×D₄₃	semidirect
687. #478	C₂×D₄₃	semidirect
704. #463	C₂×D₄₃	semidirect
732. C₄×SD₁₆	C₂×D₄₃	semidirect
736. C₄×D₈	C₂×D₄₃	semidirect
742. #431	C₂×D₄₃	semidirect
748. C₄₃	#62003	semidirect

Maximal subgroups

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

subgroup	index
#19148599	2
D₄×#10621898	2
#19147574	2
#19147569	2
#19147235	2
#19147228	2
#19146924	2
#19146920	2
#19146902	2
#19146898	2
#19146216	2
#19146213	2
#19146196	2
#19146193	2
#19145957	2
#19145956	2
#19145530	2
#19145527	2
#19144647	2
#19144059	2
#19144057	2
#19143724	2
C₄₃×#3105	2
#62003	43