Subgroups — #25974689

Order 11008.

2046 conjugacy classes of subgroups.

The subgroup lattice has 1208 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148462	C₂	1	1	yes	maximal, characteristic, complemented
2	#19148388	C₂	1	1	yes	maximal, characteristic
3	#19146860	C₂	1	2	yes	maximal, complemented
4	#19146808	C₂	1	2	yes	maximal, complemented
5	#19146703	C₂	1	2	yes	maximal, complemented
6	#19146673	C₂	1	2	yes	maximal, complemented
7	#19146658	C₂	1	2	yes	maximal, complemented
8	#19146628	C₂	1	2	yes	maximal, complemented
9	#19146479	C₂	1	2	yes	maximal, complemented
10	#19146427	C₂	1	2	yes	maximal, complemented
11	#19144984	C₂	1	1	yes	maximal, characteristic, complemented
12	#19144567	C₂	1	1	yes	maximal, characteristic, complemented
13	#19144556	C₂	1	1	yes	maximal, characteristic, complemented
14	#19144251	C₂	1	1	yes	maximal, characteristic, complemented
15	#19144235	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#14583122	C₂	1	1	yes	maximal, characteristic, complemented
17	#19143893	C₂	1	1	yes	maximal, characteristic, complemented
18	#19143875	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×#13063355	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143338	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143124	C₂	1	1	yes	maximal, characteristic, complemented
22	#19143117	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3076	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063372	C₂²	1	1	yes	characteristic
25	C₂×#13063371	C₂²	1	1	yes	characteristic
26	C₂×#13063355	C₂²	1	1	yes	characteristic
27	C₂²×Dic₁₇₂	C₂²	1	1	yes	characteristic, complemented
28	C₂²×#10621873	C₂²	1	1	yes	characteristic
29	C₂×#13063331	C₂²	1	1	yes	characteristic
30	C₂×#13063331	C₂²	1	1	yes	characteristic, complemented
31	#14583634	—	2	1	no	—
32	#14583628	—	2	1	no	—
33	#14583623	C₂²	1	2	yes	complemented
34	#14583622	—	2	1	no	—
35	#14583622	—	2	1	no	—
36	#14583610	C₂²	1	2	yes	complemented
37	#14583587	C₂²	1	2	yes	complemented
38	#14583587	C₂²	1	2	yes	complemented
39	#14583561	C₂²	1	2	yes	—
40	#14583561	C₂²	1	2	yes	—
41	#14583544	—	2	2	no	—
42	#14583544	—	2	2	no	—
43	#14583544	C₂²	1	2	yes	—
44	#14583544	C₂²	1	2	yes	—
45	#14583498	—	2	2	no	—
46	#14583475	—	2	1	no	—
47	#14583475	C₂²	1	1	yes	characteristic
48	#14583475	C₂²	1	1	yes	characteristic
49	#14583475	C₂²	1	1	yes	characteristic, complemented
50	#14583468	—	2	1	no	—
51	#14583468	C₂²	1	1	yes	characteristic
52	#14583449	—	2	1	no	—
53	#14583449	C₂²	1	1	yes	characteristic
54	#14583435	—	2	2	no	—
55	C₂×#13063313	—	2	1	no	—
56	C₂×#13063313	C₂²	1	1	yes	characteristic
57	#14583379	C₂²	1	1	yes	characteristic
58	#14583379	C₂²	1	1	yes	characteristic, complemented
59	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
60	#14583261	C₂²	1	2	yes	complemented
61	#14583261	C₂²	1	2	yes	complemented
62	#14583256	C₂²	1	2	yes	complemented
63	#14583256	C₂²	1	2	yes	complemented
64	#14583243	C₂²	1	2	yes	complemented
65	#14583242	C₂²	1	2	yes	complemented
66	#14583236	C₂²	1	2	yes	complemented
67	#14583231	C₂²	1	2	yes	complemented
68	#14583226	C₂²	1	2	yes	complemented
69	#14583225	C₂²	1	2	yes	complemented
70	#14583219	C₂²	1	2	yes	complemented
71	#14583214	C₂²	1	2	yes	complemented
72	#14583158	C₂²	1	2	yes	complemented
73	#14583158	C₂²	1	2	yes	complemented
74	#14583146	C₂²	1	2	yes	complemented
75	#14583146	C₂²	1	2	yes	complemented
76	#14583141	C₂²	1	2	yes	complemented
77	#14583141	C₂²	1	2	yes	complemented
78	#14583129	C₂²	1	2	yes	complemented
79	#14583129	C₂²	1	2	yes	complemented
80	#14583122	C₂²	1	2	yes	complemented
81	#14583122	C₂²	1	2	yes	complemented
82	#14583122	C₂²	1	2	yes	complemented
83	#14583122	C₂²	1	2	yes	complemented
84	#14583064	C₂²	1	2	yes	—
85	#14583064	C₂²	1	2	yes	—
86	#14583062	C₂²	1	2	yes	complemented
87	#14583062	C₂²	1	2	yes	complemented
88	#14583056	C₂²	1	2	yes	complemented
89	#14583056	C₂²	1	2	yes	complemented
90	#14583051	C₂²	1	2	yes	—
91	#14583051	C₂²	1	2	yes	—
92	#14583004	C₂²	1	2	yes	complemented
93	#14582999	C₂²	1	2	yes	complemented
94	C₄×#10621885	C₂²	1	2	yes	complemented
95	C₄×#10621883	C₂²	1	2	yes	complemented
96	#14582976	C₂²	1	2	yes	complemented
97	#14582969	C₂²	1	2	yes	complemented
98	#14582969	C₂²	1	2	yes	complemented
99	#14582964	C₂²	1	2	yes	complemented
100	#14582942	C₂²	1	1	yes	characteristic, complemented
101	#14582907	C₂²	1	1	yes	characteristic, complemented
102	#14582907	C₂²	1	1	yes	characteristic, complemented
103	#14582907	C₂²	1	1	yes	characteristic, complemented
104	#14582906	C₂²	1	2	yes	complemented
105	#14582903	C₂²	1	1	yes	characteristic
106	#14582903	C₂²	1	1	yes	characteristic
107	#14582902	C₂²	1	2	yes	—
108	#14582900	C₂²	1	1	yes	characteristic
109	#14582899	C₂²	1	2	yes	—
110	#14582897	C₂²	1	2	yes	complemented
111	#14582894	C₂²	1	2	yes	—
112	#14582892	C₂²	1	2	yes	complemented
113	C₂×#13063250	C₂²	1	1	yes	characteristic, complemented
114	#103×D₄₃	C₂²	1	2	yes	complemented
115	C₂×#13063247	C₂²	1	1	yes	characteristic
116	#102×D₄₃	C₂²	1	2	yes	—
117	#14582865	C₂²	1	1	yes	characteristic
118	#14582865	C₂²	1	1	yes	characteristic, complemented
119	C₄×#10621877	C₂²	1	1	yes	characteristic, complemented
120	C₄₃×#533	C₂²	1	1	yes	characteristic, complemented
121	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
122	C₄₃×#479	C₂²	1	1	yes	characteristic, complemented
123	C₄₃×#479	C₂²	1	1	yes	characteristic, complemented
124	C₄₃×#478	C₂²	1	1	yes	characteristic, complemented
125	C₄₃×#478	C₂²	1	1	yes	characteristic, complemented
126	C₄₃×#477	C₂²	1	1	yes	characteristic, complemented
127	C₄₃×#476	C₂²	1	1	yes	characteristic, complemented
128	C₄₃×#475	C₂²	1	1	yes	characteristic, complemented
129	C₄₃×#474	C₂²	1	1	yes	characteristic, complemented
130	C₄₃×#427	C₂²	1	1	yes	characteristic, complemented
131	C₄₃×#427	C₂²	1	1	yes	characteristic, complemented
132	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
133	C₄₃×#416	C₂²	1	1	yes	characteristic
134	C₄₃×#416	C₂²	1	1	yes	characteristic
135	#13063372	—	2	4	no	—
136	#13063372	—	4	2	no	—
137	#13063371	—	2	4	no	—
138	#13063371	—	4	2	no	—
139	C₂×#10621902	C₂³	1	2	yes	—
140	C₂×#10621898	—	2	1	no	—
141	C₂×#10621898	—	2	1	no	—
142	C₂×#10621898	C₂³	1	1	yes	characteristic
143	C₂×#10621898	C₂³	1	1	yes	characteristic
144	C₂×#10621900	—	2	2	no	—
145	C₂×#10621900	C₂³	1	2	yes	—
146	C₂²×Dic₈₆	—	2	1	no	—
147	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
148	C₂²×Dic₈₆	C₂³	1	1	yes	characteristic
149	C₂×Q₈×D₄₃	C₂³	1	2	yes	—
150	C₂²×D₁₇₂	—	2	1	no	—
151	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
152	C₂×D₄×D₄₃	—	2	2	no	—
153	C₂×D₄×D₄₃	C₂³	1	2	yes	—
154	#13063355	—	2	4	no	—
155	C₂×Dic₁₇₂	—	4	2	no	—
156	C₂×Dic₁₇₂	C₂³	1	2	yes	—
157	C₂×Dic₁₇₂	C₂³	1	2	yes	—
158	C₂×#10621885	C₂³	1	2	yes	—
159	C₂×#10621873	—	4	2	no	—
160	C₂×#10621873	C₂³	1	2	yes	—
161	C₂×#10621873	C₂³	1	2	yes	—
162	C₂×#10621883	C₂³	1	2	yes	—
163	#13063331	—	4	2	no	—
164	#13063331	—	4	2	no	—
165	C₂×#10621877	C₂³	1	1	yes	characteristic
166	C₂×#10621877	C₂³	1	1	yes	characteristic
167	C₂×#10621872	C₂³	1	2	yes	—
168	C₂×#10621872	C₂³	1	2	yes	—
169	C₂×C₈×D₄₃	C₂³	1	2	yes	—
170	C₂×C₈×D₄₃	C₂³	1	2	yes	—
171	#13063325	—	2	1	no	—
172	#13063325	—	2	1	no	—
173	#13063325	—	2	1	no	—
174	#13063325	D₄	1	1	yes	characteristic
175	#13063322	—	2	1	no	—
176	#13063322	D₄	1	1	yes	characteristic
177	#13063320	—	2	2	no	—
178	#13063320	—	2	2	no	—
179	#13063320	—	2	2	no	—
180	#13063320	—	2	2	no	—
181	#13063316	—	2	2	no	—
182	#13063316	—	2	2	no	—
183	#13063316	—	2	2	no	—
184	#13063314	—	2	2	no	—
185	#13063313	—	2	1	no	—
186	#13063313	—	2	1	no	—
187	#13063313	—	2	1	no	—
188	#13063313	—	2	1	no	—
189	#13063313	—	2	1	no	—
190	#13063313	—	2	1	no	—
191	#13063313	—	2	2	no	—
192	#13063313	—	2	2	no	—
193	#13063313	D₄	1	1	yes	characteristic
194	#13063313	D₄	1	1	yes	characteristic
195	#13063313	C₂³	1	2	yes	—
196	#13063313	C₂³	1	2	yes	—
197	#13063310	—	2	2	no	—
198	#13063310	—	2	2	no	—
199	#13063309	—	2	2	no	—
200	#13063309	—	2	2	no	—
201	#13063309	—	2	2	no	—
202	#13063309	—	2	2	no	—
203	#13063309	—	2	2	no	—
204	#13063305	—	2	2	no	—
205	#13063305	—	2	2	no	—
206	#13063305	C₂³	1	2	yes	—
207	#13063305	C₂³	1	2	yes	—
208	#13063305	C₂³	1	2	yes	—
209	#13063305	C₂³	1	2	yes	—
210	#13063305	C₂³	1	2	yes	—
211	#13063305	C₂³	1	2	yes	—
212	#13063301	—	2	2	no	—
213	#13063301	—	2	2	no	—
214	#13063300	—	2	2	no	—
215	#13063300	—	2	2	no	—
216	#13063300	C₂³	1	2	yes	—
217	#13063300	C₂³	1	2	yes	—
218	#13063299	—	2	2	no	—
219	#13063299	—	2	2	no	—
220	#13063299	D₄	1	2	yes	—
221	#13063299	D₄	1	2	yes	—
222	#13063295	—	2	2	no	—
223	#13063295	—	2	2	no	—
224	#13063295	—	2	2	no	—
225	Q₈×Dic₄₃	—	2	2	no	—
226	C₄×Dic₈₆	—	2	1	no	—
227	C₄×Dic₈₆	—	2	1	no	—
228	C₄×Dic₈₆	—	2	1	no	—
229	C₄×Dic₈₆	—	2	1	no	—
230	C₄×Dic₈₆	C₂³	1	2	yes	—
231	C₄×Dic₈₆	C₂³	1	2	yes	—
232	C₄×D₁₇₂	—	2	1	no	—
233	C₄×D₁₇₂	—	2	1	no	—
234	C₄×D₁₇₂	—	2	2	no	—
235	C₄×D₁₇₂	—	2	2	no	—
236	C₄×D₁₇₂	C₂³	1	2	yes	—
237	C₄×D₁₇₂	C₂³	1	2	yes	—
238	#13063287	—	2	2	no	—
239	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
240	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
241	#13063283	—	2	2	no	—
242	#13063283	—	2	2	no	—
243	#13063283	C₂³	1	2	yes	—
244	#13063283	C₂³	1	2	yes	—
245	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
246	C₂×Dic₄₃⋊C₄	—	2	1	no	—
247	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
248	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
249	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
250	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
251	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
252	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
253	C₂×C₄×Dic₄₃	—	2	1	no	—
254	#13063258	C₂³	1	2	yes	—
255	#13063256	C₂³	1	2	yes	—
256	#13063250	C₂³	1	2	yes	—
257	#13063250	C₂³	1	2	yes	—
258	#13063249	C₂³	1	2	yes	—
259	#13063248	C₂³	1	2	yes	—
260	#13063248	C₂³	1	2	yes	—
261	#13063248	C₂³	1	2	yes	—
262	#13063248	C₂³	1	2	yes	—
263	#13063248	C₂³	1	2	yes	—
264	#13063248	C₂³	1	2	yes	—
265	#13063247	C₂³	1	2	yes	—
266	#13063247	C₂³	1	2	yes	—
267	#13063246	C₂³	1	2	yes	—
268	#13063245	C₂³	1	2	yes	—
269	#13063245	C₂³	1	2	yes	—
270	#13063245	C₂³	1	2	yes	—
271	#13063245	C₂³	1	2	yes	—
272	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
273	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
274	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
275	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
276	#13063236	C₂³	1	2	yes	—
277	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
278	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
279	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
280	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
281	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
282	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
283	#125×C₄₃	C₂³	1	1	yes	characteristic
284	#125×C₄₃	C₂³	1	1	yes	characteristic
285	C₂²⋊Q₈×C₄₃	—	2	1	no	—
286	C₂²⋊Q₈×C₄₃	—	2	1	no	—
287	C₄×Q₈×C₄₃	—	2	1	no	—
288	C₄×Q₈×C₄₃	—	2	1	no	—
289	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
290	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
291	C₄×D₄×C₄₃	—	2	1	no	—
292	C₄×D₄×C₄₃	—	2	1	no	—
293	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
294	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
295	#117×C₄₃	—	2	1	no	—
296	#117×C₄₃	C₂³	1	1	yes	characteristic
297	#117×C₄₃	C₂³	1	1	yes	characteristic
298	#117×C₄₃	C₂³	1	1	yes	characteristic
299	C₂×C₄²×C₄₃	—	2	1	no	—
300	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
301	#107×C₄₃	C₂³	1	1	yes	characteristic
302	#107×C₄₃	C₂³	1	1	yes	characteristic
303	#107×C₄₃	C₂³	1	1	yes	characteristic
304	#107×C₄₃	C₂³	1	1	yes	characteristic
305	#106×C₄₃	C₂³	1	1	yes	characteristic
306	#106×C₄₃	C₂³	1	1	yes	characteristic
307	#106×C₄₃	C₂³	1	1	yes	characteristic
308	#106×C₄₃	C₂³	1	1	yes	characteristic
309	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
310	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
311	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
312	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
313	#103×C₄₃	C₂³	1	1	yes	characteristic
314	#103×C₄₃	C₂³	1	1	yes	characteristic
315	#103×C₄₃	C₂³	1	1	yes	characteristic
316	#103×C₄₃	C₂³	1	1	yes	characteristic
317	#102×C₄₃	C₂³	1	1	yes	characteristic
318	#102×C₄₃	C₂³	1	1	yes	characteristic
319	#102×C₄₃	C₂³	1	1	yes	characteristic
320	#102×C₄₃	C₂³	1	1	yes	characteristic
321	C₂³×D₄₃	—	2	1	no	—
322	C₂³×D₄₃	—	2	2	no	—
323	#41×C₄₃	—	2	2	no	—
324	#41×C₄₃	#41	1	4	yes	—
325	C₂×Q₈×C₄₃	—	2	1	no	—
326	C₂×Q₈×C₄₃	—	2	1	no	—
327	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
328	C₂×D₄×C₄₃	—	2	1	no	—
329	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
330	C₂²×C₄×C₄₃	—	2	1	no	—
331	C₂²×C₄×C₄₃	—	2	1	no	—
332	C₂²×C₄×C₄₃	—	2	1	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	C₂×D₄	1	2	yes	—
339	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
340	C₂²×Dic₄₃	—	2	2	no	—
341	C₂²×Dic₄₃	—	2	1	no	—
342	C₂²×Dic₄₃	—	2	1	no	—
343	C₂²×Dic₄₃	—	2	1	no	—
344	#10621902	—	2	4	no	—
345	#10621902	—	4	2	no	—
346	Q₈×D₄₃	—	2	4	no	—
347	Q₈×D₄₃	—	4	2	no	—
348	#10621900	—	2	4	no	—
349	#10621900	—	4	2	no	—
350	#10621900	—	4	8	no	—
351	D₄×D₄₃	—	2	4	no	—
352	D₄×D₄₃	—	4	2	no	—
353	D₄×D₄₃	—	4	8	no	—
354	#10621898	—	2	2	no	—
355	#10621898	—	2	2	no	—
356	#10621898	—	2	2	no	—
357	#10621898	—	2	2	no	—
358	#10621898	—	4	4	no	—
359	#10621898	—	4	4	no	—
360	C₂×D₁₇₂	—	2	1	no	—
361	C₂×D₁₇₂	—	2	2	no	—
362	C₂×D₁₇₂	—	2	2	no	—
363	C₂×D₁₇₂	—	2	2	no	—
364	C₂×D₁₇₂	—	2	2	no	—
365	C₂×D₁₇₂	—	2	2	no	—
366	C₂×D₁₇₂	—	4	4	no	—
367	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
368	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
369	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
370	C₂×D₁₇₂	C₂×D₄	1	2	yes	—
371	C₂×D₁₇₂	C₂⁴	1	2	yes	—
372	C₂×C₄×D₄₃	—	2	2	no	—
373	C₂×C₄×D₄₃	—	2	2	no	—
374	C₂×C₄×D₄₃	—	2	2	no	—
375	C₂×C₄×D₄₃	—	2	2	no	—
376	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
377	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
378	C₂×Dic₈₆	—	2	2	no	—
379	C₂×Dic₈₆	—	2	2	no	—
380	C₂×Dic₈₆	—	2	2	no	—
381	C₂×Dic₈₆	—	2	2	no	—
382	C₂×Dic₈₆	—	2	1	no	—
383	C₂×Dic₈₆	—	2	1	no	—
384	C₂×Dic₈₆	—	2	2	no	—
385	C₂×Dic₈₆	—	4	4	no	—
386	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
387	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
388	C₂×Dic₈₆	C₂⁴	1	2	yes	—
389	C₂×Dic₈₆	C₂⁴	1	2	yes	—
390	C₂×C₈×C₄₃	—	2	2	no	—
391	C₂×C₈×C₄₃	—	2	2	no	—
392	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
393	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
394	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
395	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
396	C₄⋊C₄×C₄₃	—	2	1	no	—
397	C₄⋊C₄×C₄₃	—	2	1	no	—
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	—	2	1	no	—
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	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
408	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
409	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
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	C₄²×C₄₃	—	2	1	no	—
416	C₄²×C₄₃	—	2	1	no	—
417	C₄²×C₄₃	—	2	1	no	—
418	C₄²×C₄₃	—	2	1	no	—
419	C₄²×C₄₃	—	2	1	no	—
420	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
421	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
422	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
423	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
424	#10621885	—	2	4	no	—
425	#10621883	—	2	4	no	—
426	(C₂×D₄₃)⋊C₄	—	2	2	no	—
427	(C₂×D₄₃)⋊C₄	—	2	2	no	—
428	(C₂×D₄₃)⋊C₄	—	2	2	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	2	no	—
437	(C₂×D₄₃)⋊C₄	—	2	2	no	—
438	(C₂×D₄₃)⋊C₄	—	2	2	no	—
439	(C₂×D₄₃)⋊C₄	—	2	2	no	—
440	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
441	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
442	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
443	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
444	C₄⋊Dic₄₃	—	2	1	no	—
445	C₄⋊Dic₄₃	—	2	2	no	—
446	C₄⋊Dic₄₃	—	2	2	no	—
447	C₄⋊Dic₄₃	—	2	2	no	—
448	C₄⋊Dic₄₃	—	2	2	no	—
449	C₄⋊Dic₄₃	—	2	2	no	—
450	C₄⋊Dic₄₃	—	2	2	no	—
451	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
452	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
453	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
454	Dic₄₃⋊C₄	—	2	2	no	—
455	Dic₄₃⋊C₄	—	2	2	no	—
456	Dic₄₃⋊C₄	—	2	2	no	—
457	Dic₄₃⋊C₄	—	2	2	no	—
458	C₄×Dic₄₃	—	2	2	no	—
459	C₄×Dic₄₃	—	2	2	no	—
460	C₄×Dic₄₃	—	2	2	no	—
461	C₄×Dic₄₃	—	2	2	no	—
462	#10621877	—	2	2	no	—
463	#10621877	—	2	2	no	—
464	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
465	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
466	Dic₁₇₂	—	4	2	no	—
467	Dic₁₇₂	—	4	2	no	—
468	#10621873	—	4	2	no	—
469	#10621873	—	4	2	no	—
470	#10621872	—	4	2	no	—
471	#10621872	—	4	2	no	—
472	C₈×D₄₃	—	4	2	no	—
473	C₈×D₄₃	—	4	2	no	—
474	C₂³×C₄₃	—	2	1	no	—
475	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
476	C₂²×D₄₃	—	2	2	no	—
477	C₂²×D₄₃	—	4	4	no	—
478	C₂²×D₄₃	—	4	2	no	—
479	C₂²×D₄₃	—	8	2	no	—
480	C₂²×D₄₃	—	8	2	no	—
481	C₂²×D₄₃	—	8	1	no	—
482	C₂²×D₄₃	—	8	1	no	—
483	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
484	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
485	Q₈×C₄₃	—	2	1	no	—
486	Q₈×C₄₃	—	4	2	no	—
487	Q₈×C₄₃	—	8	1	no	—
488	Q₈×C₄₃	C₂×#41	1	2	yes	—
489	D₄×C₄₃	—	2	4	no	—
490	D₄×C₄₃	—	2	1	no	—
491	D₄×C₄₃	C₂×#41	1	2	yes	—
492	C₂×C₄×C₄₃	—	2	1	no	—
493	C₂×C₄×C₄₃	—	2	4	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	—	2	1	no	—
500	C₂×C₄×C₄₃	—	4	1	no	—
501	C₂×C₄×C₄₃	—	4	1	no	—
502	C₂×C₄×C₄₃	—	8	1	no	—
503	C₂×C₄×C₄₃	—	8	1	no	—
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	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	C₂×#41	1	2	yes	—
510	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
511	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
512	C₂²⋊D₄₃	—	2	4	no	—
513	C₂²⋊D₄₃	—	2	4	no	—
514	C₂²⋊D₄₃	—	4	4	no	—
515	C₂²⋊D₄₃	—	4	4	no	—
516	C₂×Dic₄₃	—	2	2	no	—
517	C₂×Dic₄₃	—	2	2	no	—
518	C₂×Dic₄₃	—	2	2	no	—
519	C₂×Dic₄₃	—	4	4	no	—
520	C₂×Dic₄₃	—	4	2	no	—
521	C₂×Dic₄₃	—	4	2	no	—
522	C₂×Dic₄₃	—	8	1	no	—
523	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
524	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
525	D₁₇₂	—	2	2	no	—
526	D₁₇₂	—	2	2	no	—
527	D₁₇₂	—	2	2	no	—
528	D₁₇₂	—	2	2	no	—
529	D₁₇₂	—	4	2	no	—
530	D₁₇₂	—	4	2	no	—
531	D₁₇₂	—	4	4	no	—
532	D₁₇₂	—	4	2	no	—
533	D₁₇₂	—	8	2	no	—
534	D₁₇₂	—	8	2	no	—
535	C₄×D₄₃	—	2	2	no	—
536	C₄×D₄₃	—	2	2	no	—
537	C₄×D₄₃	—	2	2	no	—
538	C₄×D₄₃	—	2	2	no	—
539	C₄×D₄₃	—	4	4	no	—
540	C₄×D₄₃	—	4	4	no	—
541	C₄×D₄₃	—	8	2	no	—
542	C₄×D₄₃	—	8	2	no	—
543	Dic₈₆	—	2	2	no	—
544	Dic₈₆	—	2	2	no	—
545	Dic₈₆	—	2	2	no	—
546	Dic₈₆	—	2	2	no	—
547	Dic₈₆	—	2	2	no	—
548	Dic₈₆	—	2	2	no	—
549	Dic₈₆	—	4	4	no	—
550	Dic₈₆	—	4	2	no	—
551	Dic₈₆	—	4	2	no	—
552	C₈×C₄₃	—	2	1	no	—
553	C₈×C₄₃	—	2	1	no	—
554	C₈×C₄₃	—	2	1	no	—
555	C₈×C₄₃	—	2	1	no	—
556	C₄₃⋊C₈	—	2	2	no	—
557	C₄₃⋊C₈	—	2	2	no	—
558	#61207	—	43	1	no	maximal, Sylow
559	C₂²×C₄₃	—	2	1	no	—
560	C₂²×C₄₃	—	2	1	no	—
561	C₂²×C₄₃	—	2	2	no	—
562	C₂²×C₄₃	—	4	1	no	—
563	C₂²×C₄₃	—	4	1	no	—
564	C₂²×C₄₃	#546	1	2	yes	—
565	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
566	C₂×D₄₃	—	2	2	no	—
567	C₂×D₄₃	—	2	2	no	—
568	C₂×D₄₃	—	2	2	no	—
569	C₂×D₄₃	—	2	2	no	—
570	C₂×D₄₃	—	2	2	no	—
571	C₂×D₄₃	—	2	2	no	—
572	C₂×D₄₃	—	4	2	no	—
573	C₂×D₄₃	—	4	2	no	—
574	C₂×D₄₃	—	4	2	no	—
575	C₂×D₄₃	—	16	4	no	—
576	C₂×D₄₃	—	16	2	no	—
577	C₄×C₄₃	—	2	1	no	—
578	C₄×C₄₃	—	2	1	no	—
579	C₄×C₄₃	—	2	1	no	—
580	C₄×C₄₃	—	2	1	no	—
581	C₄×C₄₃	—	2	2	no	—
582	C₄×C₄₃	—	4	1	no	—
583	C₄×C₄₃	—	4	1	no	—
584	C₄×C₄₃	—	4	1	no	—
585	C₄×C₄₃	—	4	1	no	—
586	C₄×C₄₃	—	4	1	no	—
587	C₄×C₄₃	—	4	1	no	—
588	C₄×C₄₃	#546	1	2	yes	—
589	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
590	C₄×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
591	Dic₄₃	—	2	2	no	—
592	Dic₄₃	—	2	2	no	—
593	Dic₄₃	—	4	2	no	—
594	Dic₄₃	—	4	2	no	—
595	Dic₄₃	—	4	2	no	—
596	#3507	—	43	1	no	—
597	#3500	—	43	1	no	—
598	#3327	—	43	2	no	—
599	#3323	—	43	2	no	—
600	#3316	—	43	2	no	—
601	#3314	—	43	2	no	—
602	#3313	—	43	2	no	—
603	#3311	—	43	2	no	—
604	#3300	—	43	2	no	—
605	#3296	—	43	2	no	—
606	#3140	—	43	1	no	—
607	#3097	—	43	1	no	—
608	#3096	—	43	1	no	—
609	#3076	D₄₃	1	1	yes	characteristic, complemented
610	#3059	—	43	1	no	—
611	#3057	—	43	1	no	—
612	C₂×#464	—	43	1	no	—
613	#3011	—	43	1	no	—
614	#3009	—	43	1	no	—
615	C₄×#137	—	43	1	no	—
616	#2935	—	43	1	no	—
617	#2898	—	43	1	no	—
618	#2897	—	43	1	no	—
619	C₂×C₄₃	—	2	2	no	—
620	C₂×C₄₃	—	4	2	no	—
621	C₂×C₄₃	C₂×#546	1	1	yes	characteristic
622	C₂×C₄₃	#3584	1	1	yes	characteristic
623	C₂×C₄₃	#3586	1	1	yes	characteristic
624	D₄₃	—	4	2	no	—
625	D₄₃	—	4	2	no	—
626	D₄₃	—	8	2	no	—
627	C₂×2₋¹⁺⁴	—	43	1	no	—
628	C₂×H(5,𝔽₂)	—	43	1	no	—
629	C₂×#137	—	43	1	no	—
630	C₂²×Q₁₆	—	43	1	no	—
631	C₂²×SD₁₆	—	43	1	no	—
632	C₂×#131	—	43	1	no	—
633	C₂×#131	—	43	1	no	—
634	#559	—	86	1	no	—
635	#557	—	86	1	no	—
636	#556	—	43	2	no	—
637	#556	—	86	1	no	—
638	#556	—	86	1	no	—
639	#554	—	43	2	no	—
640	#552	—	43	2	no	—
641	#552	—	43	2	no	—
642	#548	—	43	2	no	—
643	#548	—	43	2	no	—
644	#546	—	43	2	no	—
645	#546	—	43	2	no	—
646	#546	—	86	2	no	—
647	#546	—	86	2	no	—
648	#539	—	86	2	no	—
649	#536	—	43	1	no	—
650	#536	—	43	1	no	—
651	#536	—	43	1	no	—
652	#536	—	86	1	no	—
653	#535	—	43	1	no	—
654	#535	—	86	1	no	—
655	#533	C₂×D₄₃	1	1	yes	characteristic, complemented
656	#532	—	43	1	no	—
657	#532	—	86	1	no	—
658	#529	—	86	2	no	—
659	C₂×#124	—	43	1	no	—
660	C₂×#124	—	86	1	no	—
661	#520	—	43	1	no	—
662	#520	—	43	1	no	—
663	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
664	C₂×C₄×Q₈	—	43	1	no	—
665	#489	—	43	2	no	—
666	#489	—	43	2	no	—
667	#488	—	43	2	no	—
668	#488	—	43	2	no	—
669	#485	—	43	2	no	—
670	#485	—	43	2	no	—
671	#484	—	43	2	no	—
672	#483	—	43	2	no	—
673	#482	—	43	2	no	—
674	#482	—	43	2	no	—
675	#481	—	43	2	no	—
676	#480	—	43	2	no	—
677	#479	C₂×D₄₃	1	1	yes	characteristic, complemented
678	#479	C₂×D₄₃	1	1	yes	characteristic, complemented
679	#478	C₂×D₄₃	1	1	yes	characteristic, complemented
680	#478	C₂×D₄₃	1	1	yes	characteristic, complemented
681	#477	C₂×D₄₃	1	1	yes	characteristic, complemented
682	#476	C₂×D₄₃	1	1	yes	characteristic, complemented
683	#475	C₂×D₄₃	1	1	yes	characteristic, complemented
684	#474	C₂×D₄₃	1	1	yes	characteristic, complemented
685	#470	—	43	2	no	—
686	#470	—	43	2	no	—
687	#468	—	43	2	no	—
688	#468	—	43	2	no	—
689	#467	—	43	2	no	—
690	#467	—	43	2	no	—
691	#465	—	43	2	no	—
692	#465	—	43	2	no	—
693	#464	—	43	2	no	—
694	#464	—	43	2	no	—
695	#464	—	43	2	no	—
696	#464	—	43	2	no	—
697	#452	—	43	2	no	—
698	#452	—	43	2	no	—
699	#452	—	43	2	no	—
700	#452	—	43	2	no	—
701	#451	—	43	2	no	—
702	#451	—	43	2	no	—
703	#450	—	43	2	no	—
704	#450	—	43	2	no	—
705	#441	—	43	2	no	—
706	#440	—	43	2	no	—
707	C₄×Q₁₆	—	43	2	no	—
708	C₄×SD₁₆	—	43	2	no	—
709	#436	—	43	2	no	—
710	#435	—	43	2	no	—
711	#435	—	43	2	no	—
712	C₈×D₄	—	43	2	no	—
713	#428	—	43	1	no	—
714	#427	C₂×D₄₃	1	1	yes	characteristic, complemented
715	#427	C₂×D₄₃	1	1	yes	characteristic, complemented
716	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic, complemented
717	#419	—	43	1	no	—
718	#419	—	43	1	no	—
719	#419	—	43	1	no	—
720	#419	—	43	2	no	—
721	#418	—	43	1	no	—
722	#418	—	43	1	no	—
723	#418	—	43	2	no	—
724	#417	—	43	1	no	—
725	#417	—	43	2	no	—
726	#417	—	43	2	no	—
727	#416	—	43	2	no	—
728	#416	—	43	2	no	—
729	#416	C₂×D₄₃	1	1	yes	characteristic
730	#416	C₂×D₄₃	1	1	yes	characteristic
731	C₂×#103	—	43	1	no	—
732	C₂×#103	—	43	2	no	—
733	C₂×#102	—	43	1	no	—
734	C₂×#102	—	43	2	no	—
735	#408	—	43	1	no	—
736	#408	—	43	1	no	—
737	C₄×M₁₆	—	43	1	no	—
738	C₄₃	#61207	1	1	yes	characteristic, complemented, Sylow
739	2₋¹⁺⁴	—	86	4	no	—
740	2₋¹⁺⁴	—	172	2	no	—
741	H(5,𝔽₂)	—	86	4	no	—
742	H(5,𝔽₂)	—	172	2	no	—
743	C₂×#41	—	43	1	no	—
744	C₂×#41	—	43	1	no	—
745	C₂×#41	—	43	2	no	—
746	C₂×#41	—	43	2	no	—
747	C₂×#41	—	86	1	no	—
748	C₂×#41	—	86	1	no	—
749	C₂×#41	—	86	2	no	—
750	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
751	C₂²×Q₈	—	43	2	no	—
752	C₂²×Q₈	—	43	1	no	—
753	C₂²×Q₈	—	43	1	no	—
754	C₂²×Q₈	—	86	1	no	—
755	C₂²×D₄	—	43	2	no	—
756	C₂²×D₄	—	43	1	no	—
757	C₂²×D₄	—	86	1	no	—
758	C₂²×D₄	—	86	2	no	—
759	#137	—	86	4	no	—
760	C₂×Q₁₆	—	43	2	no	—
761	C₂×Q₁₆	—	43	2	no	—
762	C₂×Q₁₆	—	43	2	no	—
763	C₂×Q₁₆	—	172	2	no	—
764	C₂×SD₁₆	—	43	2	no	—
765	C₂×SD₁₆	—	43	2	no	—
766	C₂×SD₁₆	—	43	2	no	—
767	C₂×SD₁₆	—	172	2	no	—
768	#131	—	172	2	no	—
769	#131	—	172	2	no	—
770	C₂×M₁₆	—	43	1	no	—
771	C₂×M₁₆	—	43	1	no	—
772	C₂×M₁₆	—	43	2	no	—
773	C₂×M₁₆	—	43	2	no	—
774	C₂²×C₈	—	43	2	no	—
775	C₂²×C₈	—	43	2	no	—
776	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
777	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
778	C₄⋊Q₈	—	43	1	no	—
779	C₄⋊Q₈	—	86	1	no	—
780	C₄⋊Q₈	—	86	1	no	—
781	C₄⋊Q₈	—	86	1	no	—
782	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
783	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
784	#127	—	43	1	no	—
785	#127	—	86	1	no	—
786	#126	—	86	2	no	—
787	#126	—	86	2	no	—
788	#126	—	86	2	no	—
789	#126	—	86	2	no	—
790	#125	—	86	2	no	—
791	#125	—	86	2	no	—
792	#125	—	86	2	no	—
793	#125	C₂²×D₄₃	1	1	yes	characteristic
794	#125	C₂²×D₄₃	1	1	yes	characteristic
795	#124	—	43	1	no	—
796	#124	—	43	1	no	—
797	#124	—	43	2	no	—
798	#124	—	43	2	no	—
799	#124	—	86	2	no	—
800	#124	—	86	2	no	—
801	#124	—	86	1	no	—
802	#124	—	86	1	no	—
803	#124	—	86	1	no	—
804	#124	—	86	1	no	—
805	#124	—	86	2	no	—
806	#124	—	86	1	no	—
807	#124	—	86	1	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	#123	—	86	2	no	—
815	C₂²⋊Q₈	—	2	1	no	—
816	C₂²⋊Q₈	—	2	1	no	—
817	C₂²⋊Q₈	—	43	2	no	—
818	C₂²⋊Q₈	—	43	2	no	—
819	C₂²⋊Q₈	—	43	2	no	—
820	C₂²⋊Q₈	—	43	2	no	—
821	C₂²⋊Q₈	—	43	2	no	—
822	C₂²⋊Q₈	—	43	2	no	—
823	C₂²⋊Q₈	—	86	2	no	—
824	C₂²⋊Q₈	—	86	2	no	—
825	C₂²⋊Q₈	—	86	2	no	—
826	C₂²⋊Q₈	—	86	2	no	—
827	#121	—	43	2	no	—
828	#121	—	43	2	no	—
829	#121	—	43	2	no	—
830	#121	—	43	2	no	—
831	#121	—	86	2	no	—
832	#121	—	86	2	no	—
833	#121	—	86	2	no	—
834	#121	—	86	2	no	—
835	#120	—	86	2	no	—
836	#120	—	86	2	no	—
837	#120	—	86	2	no	—
838	C₄×Q₈	—	2	1	no	—
839	C₄×Q₈	—	2	1	no	—
840	C₄×Q₈	—	43	2	no	—
841	C₄×Q₈	—	43	2	no	—
842	C₄×Q₈	—	86	1	no	—
843	C₄×Q₈	—	86	1	no	—
844	C₄×Q₈	—	86	2	no	—
845	C₄×Q₈	—	86	1	no	—
846	C₄×Q₈	—	86	1	no	—
847	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
848	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
849	C₄×D₄	—	2	1	no	—
850	C₄×D₄	—	2	1	no	—
851	C₄×D₄	—	43	2	no	—
852	C₄×D₄	—	43	2	no	—
853	C₄×D₄	—	86	2	no	—
854	C₄×D₄	—	86	2	no	—
855	C₄×D₄	—	86	1	no	—
856	C₄×D₄	—	86	1	no	—
857	C₄×D₄	—	86	2	no	—
858	C₄×D₄	—	86	2	no	—
859	C₄×D₄	—	86	2	no	—
860	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
861	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
862	#117	—	2	1	no	—
863	#117	—	43	2	no	—
864	#117	—	43	2	no	—
865	#117	—	86	2	no	—
866	#117	—	86	2	no	—
867	#117	C₂²×D₄₃	1	1	yes	characteristic
868	#117	C₂²×D₄₃	1	1	yes	characteristic
869	#117	C₂²×D₄₃	1	1	yes	characteristic
870	C₂×C₄⋊C₄	—	43	1	no	—
871	C₂×C₄⋊C₄	—	43	2	no	—
872	C₂×C₄⋊C₄	—	43	2	no	—
873	C₂×C₄⋊C₄	—	86	1	no	—
874	C₂×C₂²⋊C₄	—	86	2	no	—
875	C₂×C₂²⋊C₄	—	86	2	no	—
876	C₂×C₂²⋊C₄	—	86	1	no	—
877	C₂×C₂²⋊C₄	—	86	1	no	—
878	C₂×C₄²	—	2	1	no	—
879	C₂×C₄²	—	86	1	no	—
880	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
881	#107	—	43	2	no	—
882	#107	C₂²×D₄₃	1	1	yes	characteristic
883	#107	C₂²×D₄₃	1	1	yes	characteristic
884	#107	C₂²×D₄₃	1	1	yes	characteristic
885	#107	C₂²×D₄₃	1	1	yes	characteristic
886	#106	—	43	2	no	—
887	#106	C₂²×D₄₃	1	1	yes	characteristic
888	#106	C₂²×D₄₃	1	1	yes	characteristic
889	#106	C₂²×D₄₃	1	1	yes	characteristic
890	#106	C₂²×D₄₃	1	1	yes	characteristic
891	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
892	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
893	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
894	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
895	#103	—	43	2	no	—
896	#103	—	43	2	no	—
897	#103	—	43	2	no	—
898	#103	—	43	2	no	—
899	#103	—	43	2	no	—
900	#103	—	43	2	no	—
901	#103	—	43	2	no	—
902	#103	—	43	2	no	—
903	#103	—	43	2	no	—
904	#103	C₂²×D₄₃	1	1	yes	characteristic
905	#103	C₂²×D₄₃	1	1	yes	characteristic
906	#103	C₂²×D₄₃	1	1	yes	characteristic
907	#103	C₂²×D₄₃	1	1	yes	characteristic
908	#102	—	43	2	no	—
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	C₂²×D₄₃	1	1	yes	characteristic
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	C₂²⋊C₈	—	43	2	no	—
920	C₂²⋊C₈	—	43	2	no	—
921	C₂²⋊C₈	—	43	2	no	—
922	C₂²⋊C₈	—	43	2	no	—
923	#97	—	43	2	no	—
924	C₄×C₈	—	43	2	no	—
925	C₂⁴	—	86	2	no	—
926	C₂⁴	—	86	1	no	—
927	#41	—	2	2	no	—
928	#41	—	86	2	no	—
929	#41	—	86	2	no	—
930	#41	—	86	2	no	—
931	#41	—	86	2	no	—
932	#41	—	86	4	no	—
933	#41	—	86	4	no	—
934	#41	—	172	4	no	—
935	#41	—	172	4	no	—
936	#41	—	172	2	no	—
937	#41	—	172	2	no	—
938	#41	—	172	8	no	—
939	#41	#10621902	1	4	yes	—
940	C₂×Q₈	—	2	1	no	—
941	C₂×Q₈	—	2	1	no	—
942	C₂×Q₈	—	43	1	no	—
943	C₂×Q₈	—	43	1	no	—
944	C₂×Q₈	—	43	2	no	—
945	C₂×Q₈	—	43	2	no	—
946	C₂×Q₈	—	86	2	no	—
947	C₂×Q₈	—	86	1	no	—
948	C₂×Q₈	—	86	1	no	—
949	C₂×Q₈	—	86	4	no	—
950	C₂×Q₈	—	86	2	no	—
951	C₂×Q₈	—	86	2	no	—
952	C₂×Q₈	—	86	2	no	—
953	C₂×Q₈	—	86	2	no	—
954	C₂×Q₈	—	172	4	no	—
955	C₂×Q₈	—	172	2	no	—
956	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
957	C₂×D₄	—	2	1	no	—
958	C₂×D₄	—	43	2	no	—
959	C₂×D₄	—	43	2	no	—
960	C₂×D₄	—	43	1	no	—
961	C₂×D₄	—	43	1	no	—
962	C₂×D₄	—	43	2	no	—
963	C₂×D₄	—	43	2	no	—
964	C₂×D₄	—	43	2	no	—
965	C₂×D₄	—	86	2	no	—
966	C₂×D₄	—	86	2	no	—
967	C₂×D₄	—	86	2	no	—
968	C₂×D₄	—	86	2	no	—
969	C₂×D₄	—	86	4	no	—
970	C₂×D₄	—	86	2	no	—
971	C₂×D₄	—	86	1	no	—
972	C₂×D₄	—	86	2	no	—
973	C₂×D₄	—	86	2	no	—
974	C₂×D₄	—	172	4	no	—
975	C₂×D₄	—	172	2	no	—
976	C₂×D₄	—	172	8	no	—
977	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
978	C₂²×C₄	—	2	1	no	—
979	C₂²×C₄	—	2	1	no	—
980	C₂²×C₄	—	2	1	no	—
981	C₂²×C₄	—	43	2	no	—
982	C₂²×C₄	—	43	2	no	—
983	C₂²×C₄	—	86	2	no	—
984	C₂²×C₄	—	86	2	no	—
985	C₂²×C₄	—	86	2	no	—
986	C₂²×C₄	—	86	2	no	—
987	C₂²×C₄	—	86	2	no	—
988	C₂²×C₄	—	86	1	no	—
989	C₂²×C₄	—	86	1	no	—
990	C₂²×C₄	—	86	1	no	—
991	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
992	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
993	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
994	Q₁₆	—	86	4	no	—
995	Q₁₆	—	172	2	no	—
996	Q₁₆	—	172	2	no	—
997	SD₁₆	—	86	4	no	—
998	SD₁₆	—	172	2	no	—
999	SD₁₆	—	172	2	no	—
1000	M₁₆	—	86	2	no	—
1001	M₁₆	—	86	2	no	—
1002	M₁₆	—	172	2	no	—
1003	M₁₆	—	172	2	no	—
1004	C₂×C₈	—	2	2	no	—
1005	C₂×C₈	—	2	2	no	—
1006	C₂×C₈	—	43	2	no	—
1007	C₂×C₈	—	43	2	no	—
1008	C₂×C₈	—	172	2	no	—
1009	C₂×C₈	—	172	2	no	—
1010	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
1011	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
1012	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
1013	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
1014	C₄⋊C₄	—	2	1	no	—
1015	C₄⋊C₄	—	2	1	no	—
1016	C₄⋊C₄	—	2	1	no	—
1017	C₄⋊C₄	—	2	1	no	—
1018	C₄⋊C₄	—	2	1	no	—
1019	C₄⋊C₄	—	2	1	no	—
1020	C₄⋊C₄	—	2	1	no	—
1021	C₄⋊C₄	—	2	1	no	—
1022	C₄⋊C₄	—	43	2	no	—
1023	C₄⋊C₄	—	43	2	no	—
1024	C₄⋊C₄	—	43	2	no	—
1025	C₄⋊C₄	—	86	2	no	—
1026	C₄⋊C₄	—	86	2	no	—
1027	C₄⋊C₄	—	86	2	no	—
1028	C₄⋊C₄	—	86	2	no	—
1029	C₄⋊C₄	—	86	2	no	—
1030	C₄⋊C₄	—	86	2	no	—
1031	C₄⋊C₄	—	86	2	no	—
1032	C₄⋊C₄	—	86	2	no	—
1033	C₄⋊C₄	—	86	1	no	—
1034	C₄⋊C₄	—	86	2	no	—
1035	C₄⋊C₄	—	86	2	no	—
1036	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1037	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1038	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1039	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1040	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1041	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1042	C₂²⋊C₄	—	2	1	no	—
1043	C₂²⋊C₄	—	2	1	no	—
1044	C₂²⋊C₄	—	2	1	no	—
1045	C₂²⋊C₄	—	2	1	no	—
1046	C₂²⋊C₄	—	2	1	no	—
1047	C₂²⋊C₄	—	43	2	no	—
1048	C₂²⋊C₄	—	43	2	no	—
1049	C₂²⋊C₄	—	43	2	no	—
1050	C₂²⋊C₄	—	43	2	no	—
1051	C₂²⋊C₄	—	86	2	no	—
1052	C₂²⋊C₄	—	86	2	no	—
1053	C₂²⋊C₄	—	86	2	no	—
1054	C₂²⋊C₄	—	86	2	no	—
1055	C₂²⋊C₄	—	86	2	no	—
1056	C₂²⋊C₄	—	86	2	no	—
1057	C₂²⋊C₄	—	86	2	no	—
1058	C₂²⋊C₄	—	86	2	no	—
1059	C₂²⋊C₄	—	86	2	no	—
1060	C₂²⋊C₄	—	86	2	no	—
1061	C₂²⋊C₄	—	86	2	no	—
1062	C₂²⋊C₄	—	86	2	no	—
1063	C₂²⋊C₄	—	86	2	no	—
1064	C₂²⋊C₄	—	86	2	no	—
1065	C₄²	—	2	1	no	—
1066	C₄²	—	2	1	no	—
1067	C₄²	—	2	1	no	—
1068	C₄²	—	2	1	no	—
1069	C₄²	—	2	1	no	—
1070	C₄²	—	86	2	no	—
1071	C₄²	—	86	2	no	—
1072	C₄²	—	86	2	no	—
1073	C₄²	—	86	2	no	—
1074	C₄²	D₄×D₄₃	1	1	yes	characteristic
1075	C₄²	D₄×D₄₃	1	1	yes	characteristic
1076	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1077	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1078	C₂³	—	2	1	no	—
1079	C₂³	—	43	2	no	—
1080	C₂³	—	43	2	no	—
1081	C₂³	—	86	2	no	—
1082	C₂³	—	344	1	no	—
1083	C₂³	—	344	1	no	—
1084	C₂³	—	344	2	no	—
1085	C₂³	—	344	2	no	—
1086	C₂³	—	172	4	no	—
1087	C₂³	—	172	2	no	—
1088	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1089	Q₈	—	2	1	no	—
1090	Q₈	—	4	2	no	—
1091	Q₈	—	8	1	no	—
1092	Q₈	—	86	2	no	—
1093	Q₈	—	86	2	no	—
1094	Q₈	—	86	2	no	—
1095	Q₈	—	86	2	no	—
1096	Q₈	—	86	2	no	—
1097	Q₈	—	86	2	no	—
1098	Q₈	—	172	4	no	—
1099	Q₈	—	172	2	no	—
1100	Q₈	—	172	2	no	—
1101	Q₈	C₂×#10621902	1	2	yes	—
1102	D₄	—	2	4	no	—
1103	D₄	—	2	1	no	—
1104	D₄	—	86	4	no	—
1105	D₄	—	86	4	no	—
1106	D₄	—	86	2	no	—
1107	D₄	—	86	2	no	—
1108	D₄	—	86	2	no	—
1109	D₄	—	86	2	no	—
1110	D₄	—	344	2	no	—
1111	D₄	—	344	2	no	—
1112	D₄	—	172	2	no	—
1113	D₄	—	172	2	no	—
1114	D₄	—	172	4	no	—
1115	D₄	—	172	4	no	—
1116	D₄	—	172	4	no	—
1117	D₄	—	172	2	no	—
1118	D₄	C₂×#10621902	1	2	yes	—
1119	C₂×C₄	—	2	1	no	—
1120	C₂×C₄	—	2	4	no	—
1121	C₂×C₄	—	2	1	no	—
1122	C₂×C₄	—	2	1	no	—
1123	C₂×C₄	—	2	1	no	—
1124	C₂×C₄	—	2	1	no	—
1125	C₂×C₄	—	2	1	no	—
1126	C₂×C₄	—	2	1	no	—
1127	C₂×C₄	—	4	1	no	—
1128	C₂×C₄	—	4	1	no	—
1129	C₂×C₄	—	8	1	no	—
1130	C₂×C₄	—	8	1	no	—
1131	C₂×C₄	—	43	2	no	—
1132	C₂×C₄	—	43	2	no	—
1133	C₂×C₄	—	86	2	no	—
1134	C₂×C₄	—	86	2	no	—
1135	C₂×C₄	—	86	2	no	—
1136	C₂×C₄	—	86	2	no	—
1137	C₂×C₄	—	86	2	no	—
1138	C₂×C₄	—	86	2	no	—
1139	C₂×C₄	—	86	2	no	—
1140	C₂×C₄	—	344	2	no	—
1141	C₂×C₄	—	344	2	no	—
1142	C₂×C₄	—	344	1	no	—
1143	C₂×C₄	—	172	4	no	—
1144	C₂×C₄	—	172	4	no	—
1145	C₂×C₄	—	172	4	no	—
1146	C₂×C₄	—	172	2	no	—
1147	C₂×C₄	—	172	2	no	—
1148	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1149	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1150	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1151	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1152	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1153	C₂×C₄	C₂×#10621902	1	2	yes	—
1154	C₂×C₄	#13063371	1	2	yes	—
1155	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1156	C₈	—	2	1	no	—
1157	C₈	—	2	1	no	—
1158	C₈	—	2	1	no	—
1159	C₈	—	2	1	no	—
1160	C₈	—	86	2	no	—
1161	C₈	—	86	2	no	—
1162	C₂²	—	2	1	no	—
1163	C₂²	—	2	1	no	—
1164	C₂²	—	2	2	no	—
1165	C₂²	—	4	1	no	—
1166	C₂²	—	4	1	no	—
1167	C₂²	—	86	2	no	—
1168	C₂²	—	86	2	no	—
1169	C₂²	—	86	2	no	—
1170	C₂²	—	86	2	no	—
1171	C₂²	—	86	2	no	—
1172	C₂²	—	86	2	no	—
1173	C₂²	—	172	2	no	—
1174	C₂²	—	172	2	no	—
1175	C₂²	—	172	2	no	—
1176	C₂²	—	688	2	no	—
1177	C₂²	—	688	4	no	—
1178	C₂²	#14583540	1	2	yes	—
1179	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1180	C₄	—	2	2	no	—
1181	C₄	—	2	1	no	—
1182	C₄	—	2	1	no	—
1183	C₄	—	2	1	no	—
1184	C₄	—	2	1	no	—
1185	C₄	—	4	1	no	—
1186	C₄	—	4	1	no	—
1187	C₄	—	4	1	no	—
1188	C₄	—	4	1	no	—
1189	C₄	—	4	1	no	—
1190	C₄	—	4	1	no	—
1191	C₄	—	86	2	no	—
1192	C₄	—	86	2	no	—
1193	C₄	—	172	2	no	—
1194	C₄	—	172	2	no	—
1195	C₄	—	172	2	no	—
1196	C₄	#14583540	1	2	yes	—
1197	C₄	C₂²×#10621902	1	1	yes	characteristic
1198	C₄	C₂×#13063371	1	1	yes	characteristic
1199	C₂	—	2	2	no	—
1200	C₂	—	4	2	no	—
1201	C₂	—	344	2	no	—
1202	C₂	—	172	2	no	—
1203	C₂	—	172	2	no	—
1204	C₂	C₂×#14583540	1	1	yes	characteristic
1205	C₂	#19149364	1	1	yes	characteristic
1206	C₂	#19149379	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×#3076	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	#19148388	C₂
hypercenter	#3076	D₄₃
hypocenter	C₄₃	#61207
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3076

Complements

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

N	H ≅ G/N	type
1. #19148462	C₂	semidirect
3. #19146860	C₂	semidirect
4. #19146808	C₂	semidirect
5. #19146703	C₂	semidirect
6. #19146673	C₂	semidirect
7. #19146658	C₂	semidirect
8. #19146628	C₂	semidirect
9. #19146479	C₂	semidirect
10. #19146427	C₂	semidirect
11. #19144984	C₂	semidirect
12. #19144567	C₂	semidirect
13. #19144556	C₂	semidirect
14. #19144251	C₂	semidirect
15. #19144235	C₂	semidirect
16. C₂×#14583122	C₂	semidirect
17. #19143893	C₂	semidirect
18. #19143875	C₂	semidirect
19. C₄×#13063355	C₂	semidirect
20. #19143338	C₂	semidirect
21. #19143124	C₂	semidirect
22. #19143117	C₂	semidirect
23. C₄₃×#3076	C₂	semidirect
27. C₂²×Dic₁₇₂	C₂²	semidirect
30. C₂×#13063331	C₂²	semidirect
33. #14583623	C₂²	semidirect
36. #14583610	C₂²	semidirect
37. #14583587	C₂²	semidirect
38. #14583587	C₂²	semidirect
49. #14583475	C₂²	semidirect
58. #14583379	C₂²	semidirect
59. C₂×C₄×Dic₈₆	C₂²	semidirect
60. #14583261	C₂²	semidirect
61. #14583261	C₂²	semidirect
62. #14583256	C₂²	semidirect
63. #14583256	C₂²	semidirect
64. #14583243	C₂²	semidirect
65. #14583242	C₂²	semidirect
66. #14583236	C₂²	semidirect
67. #14583231	C₂²	semidirect
68. #14583226	C₂²	semidirect
69. #14583225	C₂²	semidirect
70. #14583219	C₂²	semidirect
71. #14583214	C₂²	semidirect
72. #14583158	C₂²	semidirect
73. #14583158	C₂²	semidirect
74. #14583146	C₂²	semidirect
75. #14583146	C₂²	semidirect
76. #14583141	C₂²	semidirect
77. #14583141	C₂²	semidirect
78. #14583129	C₂²	semidirect
79. #14583129	C₂²	semidirect
80. #14583122	C₂²	semidirect
81. #14583122	C₂²	semidirect
82. #14583122	C₂²	semidirect
83. #14583122	C₂²	semidirect
86. #14583062	C₂²	semidirect
87. #14583062	C₂²	semidirect
88. #14583056	C₂²	semidirect
89. #14583056	C₂²	semidirect
92. #14583004	C₂²	semidirect
93. #14582999	C₂²	semidirect
94. C₄×#10621885	C₂²	semidirect
95. C₄×#10621883	C₂²	semidirect
96. #14582976	C₂²	semidirect
97. #14582969	C₂²	semidirect
98. #14582969	C₂²	semidirect
99. #14582964	C₂²	semidirect
100. #14582942	C₂²	semidirect
101. #14582907	C₂²	semidirect
102. #14582907	C₂²	semidirect
103. #14582907	C₂²	semidirect
104. #14582906	C₂²	semidirect
110. #14582897	C₂²	semidirect
112. #14582892	C₂²	semidirect
113. C₂×#13063250	C₂²	semidirect
114. #103×D₄₃	C₂²	semidirect
118. #14582865	C₂²	semidirect
119. C₄×#10621877	C₂²	semidirect
120. C₄₃×#533	C₂²	semidirect
122. C₄₃×#479	C₂²	semidirect
123. C₄₃×#479	C₂²	semidirect
124. C₄₃×#478	C₂²	semidirect
125. C₄₃×#478	C₂²	semidirect
126. C₄₃×#477	C₂²	semidirect
127. C₄₃×#476	C₂²	semidirect
128. C₄₃×#475	C₂²	semidirect
129. C₄₃×#474	C₂²	semidirect
130. C₄₃×#427	C₂²	semidirect
131. C₄₃×#427	C₂²	semidirect
132. C₂×C₄⋊C₈×C₄₃	C₂²	semidirect
609. #3076	D₄₃	semidirect
655. #533	C₂×D₄₃	semidirect
677. #479	C₂×D₄₃	semidirect
678. #479	C₂×D₄₃	semidirect
679. #478	C₂×D₄₃	semidirect
680. #478	C₂×D₄₃	semidirect
681. #477	C₂×D₄₃	semidirect
682. #476	C₂×D₄₃	semidirect
683. #475	C₂×D₄₃	semidirect
684. #474	C₂×D₄₃	semidirect
714. #427	C₂×D₄₃	semidirect
715. #427	C₂×D₄₃	semidirect
716. C₂×C₄⋊C₈	C₂×D₄₃	semidirect
738. C₄₃	#61207	semidirect

Maximal subgroups

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

subgroup	index
#19148462	2
#19148388	2
#19146860	2
#19146808	2
#19146703	2
#19146673	2
#19146658	2
#19146628	2
#19146479	2
#19146427	2
#19144984	2
#19144567	2
#19144556	2
#19144251	2
#19144235	2
C₂×#14583122	2
#19143893	2
#19143875	2
C₄×#13063355	2
#19143338	2
#19143124	2
#19143117	2
C₄₃×#3076	2
#61207	43