Subgroups — #25986888

Order 11008.

1688 conjugacy classes of subgroups.

The subgroup lattice has 1080 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	#41×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
3	#19147548	C₂	1	2	yes	maximal, complemented
4	#19147547	C₂	1	2	yes	maximal, complemented
5	#19147525	C₂	1	1	yes	maximal, characteristic, complemented
6	#19147514	C₂	1	1	yes	maximal, characteristic, complemented
7	#19147484	C₂	1	1	yes	maximal, characteristic, complemented
8	#19147468	C₂	1	1	yes	maximal, characteristic, complemented
9	#19147430	C₂	1	2	yes	maximal, complemented
10	#19147415	C₂	1	2	yes	maximal, complemented
11	#19147407	C₂	1	1	yes	maximal, characteristic, complemented
12	#19147385	C₂	1	1	yes	maximal, characteristic, complemented
13	#19147289	C₂	1	1	yes	maximal, characteristic, complemented
14	#19147253	C₂	1	1	yes	maximal, characteristic, complemented
15	#19145839	C₂	1	2	yes	maximal, complemented
16	#19145805	C₂	1	1	yes	maximal, characteristic, complemented
17	#19145777	C₂	1	2	yes	maximal, complemented
18	#19145733	C₂	1	1	yes	maximal, characteristic, complemented
19	#19144746	C₂	1	1	yes	maximal, characteristic
20	#19144705	C₂	1	2	yes	maximal, complemented
21	#19144614	C₂	1	2	yes	maximal, complemented
22	#19143682	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3107	C₂	1	1	yes	maximal, characteristic, complemented
24	#14583634	C₂²	1	1	yes	characteristic
25	#14583634	C₂²	1	1	yes	characteristic
26	Q₈×Dic₈₆	C₂²	1	1	yes	characteristic
27	#14583628	C₂²	1	1	yes	characteristic
28	#14583628	C₂²	1	1	yes	characteristic
29	#14583628	C₂²	1	1	yes	characteristic
30	#14583625	C₂²	1	2	yes	—
31	#14583623	C₂²	1	2	yes	—
32	#14583622	—	2	1	no	—
33	#14583622	—	2	1	no	—
34	#14583610	C₂²	1	2	yes	—
35	#14583608	—	2	2	no	—
36	#14583608	C₂²	1	2	yes	—
37	#14583606	—	2	1	no	—
38	#14583606	C₂²	1	1	yes	characteristic
39	#14583587	—	2	2	no	—
40	D₄×Dic₈₆	—	2	1	no	—
41	D₄×Dic₈₆	C₂²	1	1	yes	characteristic
42	#14583498	—	2	2	no	—
43	#14583475	—	2	1	no	—
44	#14583456	—	2	1	no	—
45	#14583456	C₂²	1	1	yes	characteristic
46	#14583452	—	2	2	no	—
47	#14583452	C₂²	1	2	yes	—
48	#14583449	C₂²	1	1	yes	characteristic
49	#14583435	C₂²	1	2	yes	—
50	#14583435	C₂²	1	2	yes	—
51	#14583379	—	2	1	no	—
52	#41×Dic₄₃	C₂²	1	2	yes	—
53	C₂×C₄×Dic₈₆	—	2	1	no	—
54	C₂×C₄×Dic₈₆	C₂²	1	1	yes	characteristic
55	#14583307	C₂²	1	2	yes	—
56	#14583306	C₂²	1	2	yes	—
57	#14583305	C₂²	1	2	yes	—
58	#14583304	C₂²	1	1	yes	characteristic
59	#14583300	C₂²	1	2	yes	—
60	#14583299	C₂²	1	2	yes	—
61	#14583297	C₂²	1	1	yes	characteristic
62	#14583267	C₂²	1	2	yes	—
63	#14583260	C₂²	1	2	yes	—
64	#14583260	C₂²	1	2	yes	—
65	#14583255	C₂²	1	2	yes	—
66	#14583255	C₂²	1	2	yes	—
67	#14583246	C₂²	1	1	yes	characteristic
68	#14583246	C₂²	1	1	yes	characteristic
69	#14583237	C₂²	1	2	yes	—
70	#14583237	C₂²	1	2	yes	—
71	#14583224	C₂²	1	2	yes	—
72	#14583224	C₂²	1	2	yes	—
73	#14583223	C₂²	1	2	yes	—
74	#14583208	C₂²	1	2	yes	—
75	#14583208	C₂²	1	2	yes	—
76	#14583204	C₂²	1	2	yes	—
77	#14583204	C₂²	1	2	yes	—
78	#14583202	C₂²	1	2	yes	—
79	#14583201	C₂²	1	2	yes	—
80	#14583200	C₂²	1	2	yes	—
81	#14583200	C₂²	1	2	yes	—
82	#14583198	C₂²	1	2	yes	—
83	#14583197	C₂²	1	2	yes	—
84	#14583194	C₂²	1	1	yes	characteristic
85	#14583194	C₂²	1	1	yes	characteristic
86	#14583192	C₂²	1	2	yes	—
87	#14583188	C₂²	1	2	yes	—
88	#14583184	C₂²	1	1	yes	characteristic
89	#14583184	C₂²	1	1	yes	characteristic
90	#14583184	C₂²	1	1	yes	characteristic
91	#14583182	C₂²	1	2	yes	—
92	#14583179	C₂²	1	1	yes	characteristic
93	#14583178	C₂²	1	2	yes	—
94	#14583123	C₂²	1	2	yes	—
95	#14583123	C₂²	1	2	yes	—
96	#14583116	C₂²	1	2	yes	—
97	#14583116	C₂²	1	2	yes	—
98	#14583099	C₂²	1	1	yes	characteristic
99	#14583094	C₂²	1	1	yes	characteristic
100	#14583044	C₂²	1	2	yes	—
101	#14583029	C₂²	1	1	yes	characteristic
102	#14583029	C₂²	1	1	yes	characteristic
103	#14583028	C₂²	1	2	yes	—
104	#14583028	C₂²	1	2	yes	—
105	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
106	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
107	#14583009	C₂²	1	2	yes	—
108	#14583008	C₂²	1	2	yes	—
109	#14583006	C₂²	1	2	yes	—
110	#14583002	C₂²	1	2	yes	—
111	#14583000	C₂²	1	2	yes	—
112	#14582997	C₂²	1	2	yes	—
113	Q₁₆×Dic₄₃	C₂²	1	2	yes	—
114	SD₁₆×Dic₄₃	C₂²	1	2	yes	—
115	#14582984	C₂²	1	2	yes	—
116	#14582979	C₂²	1	2	yes	—
117	#14582956	C₂²	1	1	yes	characteristic
118	#14582953	C₂²	1	2	yes	—
119	#14582949	C₂²	1	2	yes	—
120	C₄₃×#533	C₂²	1	1	yes	characteristic
121	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
122	C₄₃×#485	C₂²	1	1	yes	characteristic
123	C₄₃×#485	C₂²	1	1	yes	characteristic
124	C₄₃×#475	C₂²	1	1	yes	characteristic
125	C₄₃×#474	C₂²	1	1	yes	characteristic
126	C₄₃×#462	C₂²	1	1	yes	characteristic
127	C₄₃×#461	C₂²	1	1	yes	characteristic
128	C₄₃×#452	C₂²	1	1	yes	characteristic
129	C₄₃×#452	C₂²	1	1	yes	characteristic
130	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
131	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
132	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
133	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
134	C₄₃×#431	C₂²	1	1	yes	characteristic
135	C₂×#10621898	—	2	1	no	—
136	C₂²×Dic₈₆	—	2	1	no	—
137	C₂²×Dic₈₆	D₄	1	1	yes	characteristic
138	C₂×#10621884	C₂³	1	2	yes	—
139	C₂×#10621882	C₂³	1	2	yes	—
140	#13063325	—	2	1	no	—
141	#13063325	—	2	1	no	—
142	#13063325	—	2	1	no	—
143	#13063325	—	2	1	no	—
144	#13063325	C₂³	1	1	yes	characteristic
145	#13063325	C₂³	1	1	yes	characteristic
146	#13063325	C₂³	1	1	yes	characteristic
147	#13063324	—	2	2	no	—
148	#13063324	—	2	2	no	—
149	#13063324	C₂³	1	2	yes	—
150	#13063324	C₂³	1	2	yes	—
151	#13063322	C₂³	1	1	yes	characteristic
152	#13063320	—	2	2	no	—
153	#13063320	—	2	2	no	—
154	#13063320	—	2	2	no	—
155	#13063320	—	2	2	no	—
156	#13063317	—	2	2	no	—
157	#13063317	C₂³	1	2	yes	—
158	#13063316	—	2	2	no	—
159	#13063316	—	2	2	no	—
160	#13063316	—	2	2	no	—
161	#13063316	—	2	2	no	—
162	#13063316	C₂³	1	2	yes	—
163	#13063316	C₂³	1	2	yes	—
164	#13063316	C₂³	1	2	yes	—
165	#13063316	C₂³	1	2	yes	—
166	#13063314	C₂³	1	2	yes	—
167	#13063314	C₂³	1	2	yes	—
168	#13063313	—	2	1	no	—
169	#13063313	—	2	1	no	—
170	#13063313	—	2	1	no	—
171	#13063310	—	2	2	no	—
172	#13063310	—	2	2	no	—
173	#13063309	—	2	2	no	—
174	#13063309	—	2	2	no	—
175	#13063305	—	2	2	no	—
176	#13063305	—	2	2	no	—
177	#13063304	—	2	1	no	—
178	#13063304	—	2	1	no	—
179	#13063304	—	2	1	no	—
180	#13063304	—	2	1	no	—
181	#13063304	—	2	2	no	—
182	#13063302	—	2	2	no	—
183	#13063302	—	2	2	no	—
184	#13063302	—	2	2	no	—
185	#13063302	—	2	2	no	—
186	#13063302	—	2	2	no	—
187	#13063302	—	2	2	no	—
188	#13063301	—	2	2	no	—
189	#13063301	—	2	2	no	—
190	#13063299	—	2	1	no	—
191	#13063299	C₂³	1	2	yes	—
192	Q₈×Dic₄₃	C₂³	1	2	yes	—
193	Q₈×Dic₄₃	C₂³	1	2	yes	—
194	Q₈×Dic₄₃	C₂³	1	2	yes	—
195	Q₈×Dic₄₃	C₂³	1	2	yes	—
196	C₄×Dic₈₆	—	2	1	no	—
197	C₄×Dic₈₆	—	2	1	no	—
198	C₄×Dic₈₆	—	2	1	no	—
199	C₄×Dic₈₆	—	2	1	no	—
200	C₄×Dic₈₆	—	2	1	no	—
201	C₄×Dic₈₆	—	2	1	no	—
202	C₄×Dic₈₆	—	2	2	no	—
203	C₄×Dic₈₆	—	2	2	no	—
204	C₄×Dic₈₆	—	2	2	no	—
205	C₄×Dic₈₆	D₄	1	2	yes	—
206	C₄×Dic₈₆	D₄	1	1	yes	characteristic
207	C₄×Dic₈₆	D₄	1	1	yes	characteristic
208	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
209	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
210	C₄×Dic₈₆	C₂³	1	2	yes	—
211	C₄×D₁₇₂	—	2	1	no	—
212	C₄×D₁₇₂	—	2	1	no	—
213	C₄×D₁₇₂	—	2	1	no	—
214	C₄×D₁₇₂	C₂³	1	2	yes	—
215	D₄×Dic₄₃	—	2	2	no	—
216	D₄×Dic₄₃	—	2	2	no	—
217	D₄×Dic₄₃	C₂³	1	2	yes	—
218	D₄×Dic₄₃	C₂³	1	2	yes	—
219	#13063287	C₂³	1	2	yes	—
220	#13063287	C₂³	1	2	yes	—
221	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
222	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
223	#13063284	—	2	2	no	—
224	#13063284	C₂³	1	2	yes	—
225	#13063283	—	2	2	no	—
226	#13063283	—	2	2	no	—
227	#13063283	—	2	2	no	—
228	C₂×C₄⋊Dic₄₃	—	2	1	no	—
229	C₂×C₄⋊Dic₄₃	D₄	1	1	yes	characteristic
230	C₂×Dic₄₃⋊C₄	—	2	2	no	—
231	C₂×Dic₄₃⋊C₄	D₄	1	2	yes	—
232	C₄⋊C₄×D₄₃	—	2	2	no	—
233	C₂×C₄×Dic₄₃	—	2	2	no	—
234	C₂×C₄×Dic₄₃	C₂³	1	2	yes	—
235	#13063259	C₂³	1	2	yes	—
236	#13063259	C₂³	1	2	yes	—
237	#13063258	C₂³	1	2	yes	—
238	#13063258	C₂³	1	2	yes	—
239	#13063258	C₂³	1	2	yes	—
240	#13063257	C₂³	1	2	yes	—
241	#13063257	C₂³	1	2	yes	—
242	#13063256	C₂³	1	2	yes	—
243	#13063256	C₂³	1	2	yes	—
244	#13063256	C₂³	1	2	yes	—
245	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
246	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
247	Dic₄₃⋊C₈	C₂³	1	2	yes	—
248	Dic₄₃⋊C₈	C₂³	1	2	yes	—
249	Dic₄₃⋊C₈	C₂³	1	2	yes	—
250	Dic₄₃⋊C₈	C₂³	1	2	yes	—
251	#13063249	C₂³	1	2	yes	—
252	#13063249	C₂³	1	2	yes	—
253	#13063249	C₂³	1	2	yes	—
254	#13063249	C₂³	1	2	yes	—
255	#13063249	C₂³	1	2	yes	—
256	#13063247	C₂³	1	2	yes	—
257	#13063247	C₂³	1	2	yes	—
258	#13063247	C₂³	1	2	yes	—
259	#13063247	C₂³	1	2	yes	—
260	#13063246	C₂³	1	2	yes	—
261	#13063245	C₂³	1	2	yes	—
262	#13063245	C₂³	1	2	yes	—
263	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
264	#13063236	C₂³	1	2	yes	—
265	#13063235	C₂³	1	2	yes	—
266	#13063235	C₂³	1	2	yes	—
267	C₈×Dic₄₃	C₂³	1	2	yes	—
268	C₈×Dic₄₃	C₂³	1	2	yes	—
269	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
270	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
271	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
272	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
273	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
274	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
275	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
276	#125×C₄₃	—	2	1	no	—
277	C₂²⋊Q₈×C₄₃	—	2	1	no	—
278	C₂²⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
279	C₂²⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
280	C₄×Q₈×C₄₃	—	2	1	no	—
281	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
282	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
283	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
284	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
285	C₄×D₄×C₄₃	—	2	1	no	—
286	C₄×D₄×C₄₃	—	2	1	no	—
287	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
289	#117×C₄₃	—	2	1	no	—
290	#117×C₄₃	—	2	1	no	—
291	#117×C₄₃	C₂³	1	1	yes	characteristic
292	C₂×C₄²×C₄₃	—	2	1	no	—
293	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
294	#107×C₄₃	C₂³	1	1	yes	characteristic
295	#107×C₄₃	C₂³	1	1	yes	characteristic
296	#106×C₄₃	C₂³	1	1	yes	characteristic
297	#106×C₄₃	C₂³	1	1	yes	characteristic
298	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
299	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
300	#103×C₄₃	C₂³	1	1	yes	characteristic
301	#103×C₄₃	C₂³	1	1	yes	characteristic
302	#103×C₄₃	C₂³	1	1	yes	characteristic
303	#103×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	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
309	C₂²⋊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	#41×C₄₃	—	2	2	no	—
313	#41×C₄₃	—	2	2	no	—
314	C₂×Q₈×C₄₃	—	2	1	no	—
315	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
316	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
317	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
318	C₂×D₄×C₄₃	—	2	1	no	—
319	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₄₃	—	2	1	no	—
321	C₂²×C₄×C₄₃	—	2	1	no	—
322	C₂²×C₄×C₄₃	—	2	1	no	—
323	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
326	C₂×C₂²⋊D₄₃	—	2	2	no	—
327	C₂²×Dic₄₃	—	2	2	no	—
328	C₂²×Dic₄₃	—	2	2	no	—
329	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
330	C₂²×Dic₄₃	C₂×D₄	1	2	yes	—
331	#10621898	—	4	4	no	—
332	C₂×D₁₇₂	—	2	1	no	—
333	C₂×D₁₇₂	—	2	1	no	—
334	C₂×D₁₇₂	C₂⁴	1	2	yes	—
335	C₂×C₄×D₄₃	—	2	2	no	—
336	C₂×C₄×D₄₃	—	2	2	no	—
337	C₂×C₄×D₄₃	—	2	2	no	—
338	C₂×Dic₈₆	—	2	1	no	—
339	C₂×Dic₈₆	—	2	1	no	—
340	C₂×Dic₈₆	—	2	2	no	—
341	C₂×Dic₈₆	—	2	1	no	—
342	C₂×Dic₈₆	—	2	2	no	—
343	C₂×Dic₈₆	—	4	2	no	—
344	C₂×Dic₈₆	—	4	4	no	—
345	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
346	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
347	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
348	Q₁₆×C₄₃	—	2	2	no	—
349	Q₁₆×C₄₃	—	2	2	no	—
350	SD₁₆×C₄₃	—	2	2	no	—
351	SD₁₆×C₄₃	—	2	2	no	—
352	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
354	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
356	C₄⋊C₄×C₄₃	—	2	1	no	—
357	C₄⋊C₄×C₄₃	—	2	1	no	—
358	C₄⋊C₄×C₄₃	—	2	1	no	—
359	C₄⋊C₄×C₄₃	—	2	1	no	—
360	C₄⋊C₄×C₄₃	—	2	1	no	—
361	C₄⋊C₄×C₄₃	—	2	1	no	—
362	C₄⋊C₄×C₄₃	—	2	1	no	—
363	C₄⋊C₄×C₄₃	—	2	1	no	—
364	C₄⋊C₄×C₄₃	—	2	1	no	—
365	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
367	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
369	C₂²⋊C₄×C₄₃	—	2	1	no	—
370	C₂²⋊C₄×C₄₃	—	2	1	no	—
371	C₂²⋊C₄×C₄₃	—	2	1	no	—
372	C₂²⋊C₄×C₄₃	—	2	1	no	—
373	C₂²⋊C₄×C₄₃	—	2	1	no	—
374	C₄²×C₄₃	—	2	1	no	—
375	C₄²×C₄₃	—	2	1	no	—
376	C₄²×C₄₃	—	2	1	no	—
377	C₄²×C₄₃	—	2	1	no	—
378	C₄²×C₄₃	—	2	1	no	—
379	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
380	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
381	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
382	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
383	C₂²⋊Dic₄₃	—	2	2	no	—
384	C₂²⋊Dic₄₃	—	2	2	no	—
385	C₂²⋊Dic₄₃	—	2	2	no	—
386	#10621884	—	2	4	no	—
387	#10621882	—	2	4	no	—
388	(C₂×D₄₃)⋊C₄	—	2	2	no	—
389	(C₂×D₄₃)⋊C₄	—	2	2	no	—
390	(C₂×D₄₃)⋊C₄	—	2	2	no	—
391	(C₂×D₄₃)⋊C₄	—	2	2	no	—
392	(C₂×D₄₃)⋊C₄	—	2	2	no	—
393	(C₂×D₄₃)⋊C₄	—	2	2	no	—
394	(C₂×D₄₃)⋊C₄	—	2	2	no	—
395	(C₂×D₄₃)⋊C₄	—	2	2	no	—
396	C₄⋊Dic₄₃	—	2	1	no	—
397	C₄⋊Dic₄₃	—	2	1	no	—
398	C₄⋊Dic₄₃	—	2	1	no	—
399	C₄⋊Dic₄₃	—	2	2	no	—
400	C₄⋊Dic₄₃	—	2	2	no	—
401	C₄⋊Dic₄₃	—	2	2	no	—
402	C₄⋊Dic₄₃	—	2	2	no	—
403	C₄⋊Dic₄₃	—	2	2	no	—
404	C₄⋊Dic₄₃	—	2	2	no	—
405	C₄⋊Dic₄₃	—	2	2	no	—
406	C₄⋊Dic₄₃	—	2	2	no	—
407	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
408	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
409	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
410	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
411	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
412	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
413	Dic₄₃⋊C₄	—	2	2	no	—
414	Dic₄₃⋊C₄	—	2	2	no	—
415	Dic₄₃⋊C₄	—	2	2	no	—
416	Dic₄₃⋊C₄	—	2	2	no	—
417	Dic₄₃⋊C₄	—	2	2	no	—
418	Dic₄₃⋊C₄	—	2	2	no	—
419	Dic₄₃⋊C₄	—	2	2	no	—
420	Dic₄₃⋊C₄	—	2	2	no	—
421	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
422	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
423	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
424	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
425	C₄×Dic₄₃	—	2	2	no	—
426	C₄×Dic₄₃	—	2	2	no	—
427	C₄×Dic₄₃	—	2	2	no	—
428	C₄×Dic₄₃	—	2	2	no	—
429	C₄×Dic₄₃	—	2	2	no	—
430	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
431	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
432	C₄×Dic₄₃	C₂⁴	1	2	yes	—
433	C₄×Dic₄₃	C₂⁴	1	2	yes	—
434	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
435	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
436	C₂³×C₄₃	—	2	1	no	—
437	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
438	C₂²×D₄₃	—	2	2	no	—
439	Q₈×C₄₃	—	2	1	no	—
440	Q₈×C₄₃	—	2	1	no	—
441	Q₈×C₄₃	—	2	1	no	—
442	Q₈×C₄₃	—	2	1	no	—
443	Q₈×C₄₃	—	2	1	no	—
444	Q₈×C₄₃	—	8	1	no	—
445	Q₈×C₄₃	2₋¹⁺⁴	1	2	yes	—
446	D₄×C₄₃	—	2	4	no	—
447	D₄×C₄₃	—	2	1	no	—
448	D₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
449	C₂×C₄×C₄₃	—	2	4	no	—
450	C₂×C₄×C₄₃	—	2	1	no	—
451	C₂×C₄×C₄₃	—	2	2	no	—
452	C₂×C₄×C₄₃	—	2	1	no	—
453	C₂×C₄×C₄₃	—	2	1	no	—
454	C₂×C₄×C₄₃	—	2	1	no	—
455	C₂×C₄×C₄₃	—	2	1	no	—
456	C₂×C₄×C₄₃	—	2	1	no	—
457	C₂×C₄×C₄₃	—	2	1	no	—
458	C₂×C₄×C₄₃	—	2	1	no	—
459	C₂×C₄×C₄₃	—	2	1	no	—
460	C₂×C₄×C₄₃	—	4	1	no	—
461	C₂×C₄×C₄₃	—	4	2	no	—
462	C₂×C₄×C₄₃	—	8	1	no	—
463	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
469	C₂²⋊D₄₃	—	4	4	no	—
470	C₂×Dic₄₃	—	2	2	no	—
471	C₂×Dic₄₃	—	2	2	no	—
472	C₂×Dic₄₃	—	2	2	no	—
473	C₂×Dic₄₃	—	4	2	no	—
474	C₂×Dic₄₃	—	4	2	no	—
475	C₂×Dic₄₃	—	4	4	no	—
476	C₂×Dic₄₃	—	8	2	no	—
477	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
478	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
479	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
480	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
481	D₁₇₂	—	2	2	no	—
482	D₁₇₂	—	2	2	no	—
483	D₁₇₂	—	4	2	no	—
484	D₁₇₂	—	8	1	no	—
485	C₄×D₄₃	—	4	4	no	—
486	C₄×D₄₃	—	8	2	no	—
487	C₄×D₄₃	—	8	2	no	—
488	Dic₈₆	—	2	2	no	—
489	Dic₈₆	—	2	2	no	—
490	Dic₈₆	—	4	2	no	—
491	Dic₈₆	—	4	4	no	—
492	Dic₈₆	—	4	2	no	—
493	Dic₈₆	—	4	2	no	—
494	Dic₈₆	—	8	2	no	—
495	Dic₈₆	—	8	1	no	—
496	C₈×C₄₃	—	2	1	no	—
497	C₈×C₄₃	—	2	1	no	—
498	C₈×C₄₃	—	2	1	no	—
499	C₈×C₄₃	—	2	1	no	—
500	C₄₃⋊C₈	—	2	2	no	—
501	C₄₃⋊C₈	—	2	2	no	—
502	#61845	—	43	1	no	maximal, Sylow
503	C₂²×C₄₃	—	2	1	no	—
504	C₂²×C₄₃	—	2	2	no	—
505	C₂²×C₄₃	—	2	1	no	—
506	C₂²×C₄₃	—	2	1	no	—
507	C₂²×C₄₃	—	4	1	no	—
508	C₂²×C₄₃	—	4	1	no	—
509	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
510	C₂×D₄₃	—	4	2	no	—
511	C₂×D₄₃	—	4	2	no	—
512	C₂×D₄₃	—	4	2	no	—
513	C₄×C₄₃	—	2	1	no	—
514	C₄×C₄₃	—	2	1	no	—
515	C₄×C₄₃	—	2	1	no	—
516	C₄×C₄₃	—	2	2	no	—
517	C₄×C₄₃	—	2	1	no	—
518	C₄×C₄₃	—	4	1	no	—
519	C₄×C₄₃	—	4	1	no	—
520	C₄×C₄₃	—	4	1	no	—
521	C₄×C₄₃	—	4	1	no	—
522	C₄×C₄₃	—	4	1	no	—
523	C₄×C₄₃	—	4	1	no	—
524	C₄×C₄₃	#575	1	2	yes	—
525	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
526	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
527	Dic₄₃	—	2	2	no	—
528	Dic₄₃	—	2	2	no	—
529	Dic₄₃	—	2	2	no	—
530	Dic₄₃	—	2	2	no	—
531	Dic₄₃	—	4	2	no	—
532	Dic₄₃	—	4	2	no	—
533	Dic₄₃	—	4	2	no	—
534	#3507	—	43	1	no	—
535	Q₈×#41	—	43	1	no	—
536	#3389	—	43	2	no	—
537	#3388	—	43	2	no	—
538	#3387	—	43	1	no	—
539	#3386	—	43	1	no	—
540	#3383	—	43	1	no	—
541	#3381	—	43	1	no	—
542	#3377	—	43	2	no	—
543	#3376	—	43	2	no	—
544	#3375	—	43	1	no	—
545	#3373	—	43	1	no	—
546	#3365	—	43	1	no	—
547	#3361	—	43	1	no	—
548	#3240	—	43	2	no	—
549	#3237	—	43	1	no	—
550	#3233	—	43	2	no	—
551	#3228	—	43	1	no	—
552	#3115	—	43	1	no	—
553	#3111	—	43	2	no	—
554	#3107	D₄₃	1	1	yes	characteristic, complemented
555	#3102	—	43	2	no	—
556	#2984	—	43	1	no	—
557	C₂×C₄₃	—	4	1	no	—
558	C₂×C₄₃	—	4	2	no	—
559	C₂×C₄₃	#3486	1	1	yes	characteristic
560	C₂×C₄₃	C₂×#575	1	1	yes	characteristic
561	C₂×C₄₃	#3584	1	1	yes	characteristic
562	D₄₃	—	8	2	no	—
563	#559	—	43	1	no	—
564	#559	—	43	1	no	—
565	Q₈²	—	43	1	no	—
566	#557	—	43	1	no	—
567	#557	—	43	2	no	—
568	#557	—	43	1	no	—
569	#557	—	43	1	no	—
570	#556	—	43	2	no	—
571	#556	—	86	1	no	—
572	#556	—	86	1	no	—
573	#554	—	43	2	no	—
574	#554	—	43	1	no	—
575	#554	—	43	2	no	—
576	#554	—	86	1	no	—
577	#554	—	86	2	no	—
578	#552	—	86	2	no	—
579	D₄×Q₈	—	43	1	no	—
580	D₄×Q₈	—	86	1	no	—
581	#539	—	86	2	no	—
582	#536	—	86	1	no	—
583	#533	—	43	2	no	—
584	#533	—	43	1	no	—
585	#533	—	86	1	no	—
586	#533	—	86	2	no	—
587	#533	C₂×D₄₃	1	1	yes	characteristic
588	#532	—	43	1	no	—
589	#529	—	43	2	no	—
590	#529	—	43	2	no	—
591	#520	—	86	1	no	—
592	C₄×#41	—	43	2	no	—
593	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
594	C₂×C₄×Q₈	—	43	1	no	—
595	C₂×C₄×Q₈	—	86	1	no	—
596	#501	—	43	2	no	—
597	#501	—	43	2	no	—
598	#501	—	43	2	no	—
599	#500	—	43	1	no	—
600	#499	—	43	2	no	—
601	#499	—	43	2	no	—
602	#498	—	43	1	no	—
603	#491	—	43	2	no	—
604	#489	—	43	2	no	—
605	#489	—	43	2	no	—
606	#488	—	43	2	no	—
607	#488	—	43	2	no	—
608	#486	—	43	1	no	—
609	#486	—	43	1	no	—
610	#485	—	43	2	no	—
611	#485	—	43	2	no	—
612	#485	C₂×D₄₃	1	1	yes	characteristic
613	#485	C₂×D₄₃	1	1	yes	characteristic
614	#482	—	43	2	no	—
615	#482	—	43	2	no	—
616	#482	—	43	2	no	—
617	#479	—	43	2	no	—
618	#479	—	43	2	no	—
619	#479	—	43	2	no	—
620	#479	—	43	2	no	—
621	#478	—	43	2	no	—
622	#478	—	43	2	no	—
623	#478	—	43	2	no	—
624	#478	—	43	2	no	—
625	#478	—	43	2	no	—
626	#478	—	43	2	no	—
627	#477	—	43	1	no	—
628	#477	—	43	1	no	—
629	#477	—	43	2	no	—
630	#476	—	43	2	no	—
631	#475	—	43	1	no	—
632	#475	—	43	1	no	—
633	#475	—	43	1	no	—
634	#475	—	43	2	no	—
635	#475	C₂×D₄₃	1	1	yes	characteristic
636	#474	—	43	1	no	—
637	#474	—	43	2	no	—
638	#474	C₂×D₄₃	1	1	yes	characteristic
639	#464	—	43	2	no	—
640	#464	—	43	2	no	—
641	#463	—	43	2	no	—
642	#463	—	43	2	no	—
643	#462	C₂×D₄₃	1	1	yes	characteristic
644	#461	C₂×D₄₃	1	1	yes	characteristic
645	#460	—	43	1	no	—
646	#459	—	43	1	no	—
647	#452	C₂×D₄₃	1	1	yes	characteristic
648	#452	C₂×D₄₃	1	1	yes	characteristic
649	#449	—	43	2	no	—
650	#446	—	43	2	no	—
651	#446	—	43	2	no	—
652	#446	—	43	1	no	—
653	#446	—	43	1	no	—
654	C₈×Q₈	—	43	1	no	—
655	C₈×Q₈	—	43	1	no	—
656	#442	—	43	2	no	—
657	#442	—	43	2	no	—
658	#441	—	43	2	no	—
659	#440	—	43	2	no	—
660	#440	—	43	2	no	—
661	#440	—	43	2	no	—
662	C₄×Q₁₆	—	43	2	no	—
663	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
664	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
665	C₄×SD₁₆	—	43	2	no	—
666	C₄×SD₁₆	—	43	2	no	—
667	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
668	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
669	C₄×D₈	—	43	2	no	—
670	#432	—	43	1	no	—
671	#432	—	43	2	no	—
672	#431	—	43	2	no	—
673	#431	C₂×D₄₃	1	1	yes	characteristic
674	C₄₃	#61845	1	1	yes	characteristic, complemented, Sylow
675	C₂×#41	—	86	1	no	—
676	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
677	C₂²×Q₈	—	43	1	no	—
678	C₂²×Q₈	—	86	1	no	—
679	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
680	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
681	C₂×SD₁₆	—	43	2	no	—
682	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
683	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
684	C₂×D₈	—	43	2	no	—
685	C₄⋊Q₈	—	43	2	no	—
686	C₄⋊Q₈	—	43	2	no	—
687	C₄⋊Q₈	—	43	1	no	—
688	C₄⋊Q₈	—	43	1	no	—
689	C₄⋊Q₈	—	43	1	no	—
690	C₄⋊Q₈	—	86	1	no	—
691	C₄⋊Q₈	—	86	1	no	—
692	C₄⋊Q₈	—	86	1	no	—
693	C₄⋊Q₈	—	86	1	no	—
694	C₄⋊Q₈	—	86	2	no	—
695	C₄⋊Q₈	—	86	2	no	—
696	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
697	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
698	#127	—	43	1	no	—
699	#126	—	86	2	no	—
700	#126	—	86	2	no	—
701	#126	—	86	2	no	—
702	#126	—	86	2	no	—
703	#125	—	2	1	no	—
704	#125	—	43	2	no	—
705	#125	—	43	2	no	—
706	#125	—	43	2	no	—
707	#125	—	43	2	no	—
708	#125	—	43	2	no	—
709	#125	—	86	2	no	—
710	#125	—	86	2	no	—
711	#125	—	86	2	no	—
712	#125	—	86	2	no	—
713	#125	—	86	2	no	—
714	#124	—	43	2	no	—
715	#124	—	43	2	no	—
716	#124	—	86	1	no	—
717	#124	—	86	1	no	—
718	#124	—	86	1	no	—
719	#123	—	86	2	no	—
720	#123	—	86	2	no	—
721	#123	—	86	2	no	—
722	#123	—	86	2	no	—
723	C₂²⋊Q₈	—	2	1	no	—
724	C₂²⋊Q₈	—	86	2	no	—
725	C₂²⋊Q₈	—	86	2	no	—
726	C₂²⋊Q₈	—	86	2	no	—
727	C₂²⋊Q₈	—	86	2	no	—
728	C₂²⋊Q₈	—	86	2	no	—
729	C₂²⋊Q₈	—	86	2	no	—
730	C₂²⋊Q₈	—	86	2	no	—
731	C₂²⋊Q₈	—	86	2	no	—
732	C₂²⋊Q₈	—	86	1	no	—
733	C₂²⋊Q₈	—	86	2	no	—
734	C₂²⋊Q₈	—	86	2	no	—
735	C₂²⋊Q₈	—	86	2	no	—
736	C₂²⋊Q₈	—	86	1	no	—
737	C₂²⋊Q₈	—	86	1	no	—
738	C₂²⋊Q₈	—	86	1	no	—
739	C₂²⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
740	C₂²⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
741	#121	—	43	2	no	—
742	#121	—	86	1	no	—
743	C₄×Q₈	—	2	1	no	—
744	C₄×Q₈	—	43	1	no	—
745	C₄×Q₈	—	43	2	no	—
746	C₄×Q₈	—	43	1	no	—
747	C₄×Q₈	—	43	1	no	—
748	C₄×Q₈	—	43	2	no	—
749	C₄×Q₈	—	43	1	no	—
750	C₄×Q₈	—	43	2	no	—
751	C₄×Q₈	—	43	2	no	—
752	C₄×Q₈	—	43	2	no	—
753	C₄×Q₈	—	43	2	no	—
754	C₄×Q₈	—	86	2	no	—
755	C₄×Q₈	—	86	2	no	—
756	C₄×Q₈	—	86	2	no	—
757	C₄×Q₈	—	86	1	no	—
758	C₄×Q₈	—	86	1	no	—
759	C₄×Q₈	—	86	1	no	—
760	C₄×Q₈	—	86	1	no	—
761	C₄×Q₈	—	86	1	no	—
762	C₄×Q₈	—	86	1	no	—
763	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
764	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
765	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
766	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
767	C₄×D₄	—	2	1	no	—
768	C₄×D₄	—	2	1	no	—
769	C₄×D₄	—	43	2	no	—
770	C₄×D₄	—	43	2	no	—
771	C₄×D₄	—	43	2	no	—
772	C₄×D₄	—	43	2	no	—
773	C₄×D₄	—	43	2	no	—
774	C₄×D₄	—	86	1	no	—
775	C₄×D₄	—	86	1	no	—
776	C₄×D₄	—	86	2	no	—
777	C₄×D₄	—	86	2	no	—
778	C₄×D₄	—	86	2	no	—
779	C₄×D₄	—	86	2	no	—
780	C₄×D₄	—	86	1	no	—
781	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
782	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
783	#117	—	2	1	no	—
784	#117	—	2	1	no	—
785	#117	—	43	2	no	—
786	#117	—	86	2	no	—
787	#117	—	86	2	no	—
788	#117	—	86	2	no	—
789	#117	—	86	2	no	—
790	#117	C₂²×D₄₃	1	1	yes	characteristic
791	C₂×C₄⋊C₄	—	43	1	no	—
792	C₂×C₄⋊C₄	—	43	2	no	—
793	C₂×C₄⋊C₄	—	86	2	no	—
794	C₂×C₄⋊C₄	—	86	2	no	—
795	C₂×C₄⋊C₄	—	86	1	no	—
796	C₂×C₄²	—	2	1	no	—
797	C₂×C₄²	—	43	2	no	—
798	C₂×C₄²	—	86	2	no	—
799	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
800	#107	—	43	2	no	—
801	#107	—	43	2	no	—
802	#107	—	43	2	no	—
803	#107	—	43	2	no	—
804	#107	—	43	2	no	—
805	#107	C₂²×D₄₃	1	1	yes	characteristic
806	#107	C₂²×D₄₃	1	1	yes	characteristic
807	#106	—	43	2	no	—
808	#106	—	43	2	no	—
809	#106	—	43	2	no	—
810	#106	—	43	2	no	—
811	#106	—	43	2	no	—
812	#106	C₂²×D₄₃	1	1	yes	characteristic
813	#106	C₂²×D₄₃	1	1	yes	characteristic
814	C₄⋊C₈	—	43	2	no	—
815	C₄⋊C₈	—	43	2	no	—
816	C₄⋊C₈	—	43	2	no	—
817	C₄⋊C₈	—	43	2	no	—
818	C₄⋊C₈	—	43	1	no	—
819	C₄⋊C₈	—	43	1	no	—
820	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
821	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
822	#103	—	43	2	no	—
823	#103	—	43	2	no	—
824	#103	—	43	2	no	—
825	#103	—	43	2	no	—
826	#103	—	43	2	no	—
827	#103	C₂²×D₄₃	1	1	yes	characteristic
828	#103	C₂²×D₄₃	1	1	yes	characteristic
829	#103	C₂²×D₄₃	1	1	yes	characteristic
830	#103	C₂²×D₄₃	1	1	yes	characteristic
831	#103	C₂²×D₄₃	1	1	yes	characteristic
832	#103	C₂²×D₄₃	1	1	yes	characteristic
833	#102	—	43	2	no	—
834	#102	—	43	2	no	—
835	#102	—	43	2	no	—
836	#102	—	43	2	no	—
837	#102	—	43	2	no	—
838	#102	—	43	2	no	—
839	#102	—	43	2	no	—
840	#102	C₂²×D₄₃	1	1	yes	characteristic
841	#102	C₂²×D₄₃	1	1	yes	characteristic
842	C₂²⋊C₈	—	43	2	no	—
843	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
844	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
845	#97	—	43	2	no	—
846	#97	—	43	2	no	—
847	#97	—	43	2	no	—
848	C₄×C₈	—	43	2	no	—
849	C₄×C₈	—	43	2	no	—
850	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
851	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
852	#41	—	2	2	no	—
853	#41	—	2	2	no	—
854	#41	—	172	4	no	—
855	C₂×Q₈	—	2	1	no	—
856	C₂×Q₈	—	43	1	no	—
857	C₂×Q₈	—	43	1	no	—
858	C₂×Q₈	—	43	2	no	—
859	C₂×Q₈	—	86	2	no	—
860	C₂×Q₈	—	86	2	no	—
861	C₂×Q₈	—	86	1	no	—
862	C₂×Q₈	—	86	1	no	—
863	C₂×Q₈	—	86	1	no	—
864	C₂×Q₈	—	172	2	no	—
865	C₂×Q₈	—	172	4	no	—
866	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
867	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
868	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
869	C₂×D₄	—	2	1	no	—
870	C₂×D₄	—	43	2	no	—
871	C₂×D₄	—	86	2	no	—
872	C₂×D₄	—	86	1	no	—
873	C₂×D₄	—	86	1	no	—
874	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
875	C₂²×C₄	—	2	1	no	—
876	C₂²×C₄	—	2	1	no	—
877	C₂²×C₄	—	2	1	no	—
878	C₂²×C₄	—	43	2	no	—
879	C₂²×C₄	—	43	2	no	—
880	C₂²×C₄	—	86	2	no	—
881	C₂²×C₄	—	86	2	no	—
882	C₂²×C₄	—	86	2	no	—
883	C₂²×C₄	—	86	2	no	—
884	C₂²×C₄	—	86	2	no	—
885	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
886	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
887	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
888	Q₁₆	—	2	2	no	—
889	Q₁₆	—	2	2	no	—
890	SD₁₆	—	2	2	no	—
891	SD₁₆	—	2	2	no	—
892	SD₁₆	—	86	4	no	—
893	D₈	—	86	4	no	—
894	C₂×C₈	—	43	2	no	—
895	C₂×C₈	—	43	2	no	—
896	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
897	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
898	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
899	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
900	C₄⋊C₄	—	2	1	no	—
901	C₄⋊C₄	—	2	1	no	—
902	C₄⋊C₄	—	2	1	no	—
903	C₄⋊C₄	—	2	1	no	—
904	C₄⋊C₄	—	2	1	no	—
905	C₄⋊C₄	—	2	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	43	2	no	—
910	C₄⋊C₄	—	43	1	no	—
911	C₄⋊C₄	—	43	2	no	—
912	C₄⋊C₄	—	43	1	no	—
913	C₄⋊C₄	—	43	2	no	—
914	C₄⋊C₄	—	43	2	no	—
915	C₄⋊C₄	—	43	2	no	—
916	C₄⋊C₄	—	43	2	no	—
917	C₄⋊C₄	—	43	2	no	—
918	C₄⋊C₄	—	43	2	no	—
919	C₄⋊C₄	—	86	2	no	—
920	C₄⋊C₄	—	86	2	no	—
921	C₄⋊C₄	—	86	2	no	—
922	C₄⋊C₄	—	86	2	no	—
923	C₄⋊C₄	—	86	2	no	—
924	C₄⋊C₄	—	86	2	no	—
925	C₄⋊C₄	—	86	2	no	—
926	C₄⋊C₄	—	86	2	no	—
927	C₄⋊C₄	—	86	2	no	—
928	C₄⋊C₄	—	86	2	no	—
929	C₄⋊C₄	—	86	2	no	—
930	C₄⋊C₄	—	86	2	no	—
931	C₄⋊C₄	—	86	2	no	—
932	C₄⋊C₄	—	86	2	no	—
933	C₄⋊C₄	—	86	2	no	—
934	C₄⋊C₄	—	86	1	no	—
935	C₄⋊C₄	—	86	1	no	—
936	C₄⋊C₄	—	86	2	no	—
937	C₄⋊C₄	—	86	1	no	—
938	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
939	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
940	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
941	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
942	C₂²⋊C₄	—	2	1	no	—
943	C₂²⋊C₄	—	2	1	no	—
944	C₂²⋊C₄	—	2	1	no	—
945	C₂²⋊C₄	—	2	1	no	—
946	C₂²⋊C₄	—	2	1	no	—
947	C₂²⋊C₄	—	86	2	no	—
948	C₂²⋊C₄	—	86	2	no	—
949	C₂²⋊C₄	—	86	2	no	—
950	C₂²⋊C₄	—	86	2	no	—
951	C₂²⋊C₄	—	86	2	no	—
952	C₂²⋊C₄	—	86	2	no	—
953	C₂²⋊C₄	—	86	2	no	—
954	C₂²⋊C₄	—	86	2	no	—
955	C₂²⋊C₄	—	86	2	no	—
956	C₂²⋊C₄	—	86	2	no	—
957	C₂²⋊C₄	—	86	2	no	—
958	C₄²	—	2	1	no	—
959	C₄²	—	2	1	no	—
960	C₄²	—	2	1	no	—
961	C₄²	—	2	1	no	—
962	C₄²	—	2	1	no	—
963	C₄²	—	43	2	no	—
964	C₄²	—	43	2	no	—
965	C₄²	—	43	2	no	—
966	C₄²	—	43	2	no	—
967	C₄²	—	86	2	no	—
968	C₄²	—	86	2	no	—
969	C₄²	—	86	2	no	—
970	C₄²	—	86	2	no	—
971	C₄²	—	86	2	no	—
972	C₄²	D₄×D₄₃	1	1	yes	characteristic
973	C₄²	D₄×D₄₃	1	1	yes	characteristic
974	C₄²	C₂³×D₄₃	1	1	yes	characteristic
975	C₄²	C₂³×D₄₃	1	1	yes	characteristic
976	C₂³	—	2	1	no	—
977	C₂³	—	86	2	no	—
978	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
979	Q₈	—	2	1	no	—
980	Q₈	—	2	1	no	—
981	Q₈	—	2	1	no	—
982	Q₈	—	2	1	no	—
983	Q₈	—	2	1	no	—
984	Q₈	—	8	1	no	—
985	Q₈	—	86	2	no	—
986	Q₈	—	86	2	no	—
987	Q₈	—	344	1	no	—
988	Q₈	—	344	2	no	—
989	Q₈	—	172	2	no	—
990	Q₈	—	172	4	no	—
991	Q₈	—	172	2	no	—
992	Q₈	—	172	2	no	—
993	Q₈	#13063372	1	2	yes	—
994	D₄	—	2	4	no	—
995	D₄	—	2	1	no	—
996	D₄	—	86	2	no	—
997	D₄	—	86	2	no	—
998	D₄	—	344	1	no	—
999	D₄	—	172	4	no	—
1000	D₄	—	172	2	no	—
1001	D₄	#13063372	1	2	yes	—
1002	C₂×C₄	—	2	4	no	—
1003	C₂×C₄	—	2	1	no	—
1004	C₂×C₄	—	2	2	no	—
1005	C₂×C₄	—	2	1	no	—
1006	C₂×C₄	—	2	1	no	—
1007	C₂×C₄	—	2	1	no	—
1008	C₂×C₄	—	2	1	no	—
1009	C₂×C₄	—	2	1	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	4	1	no	—
1014	C₂×C₄	—	4	2	no	—
1015	C₂×C₄	—	8	1	no	—
1016	C₂×C₄	—	43	2	no	—
1017	C₂×C₄	—	43	2	no	—
1018	C₂×C₄	—	43	2	no	—
1019	C₂×C₄	—	43	2	no	—
1020	C₂×C₄	—	86	2	no	—
1021	C₂×C₄	—	86	2	no	—
1022	C₂×C₄	—	86	2	no	—
1023	C₂×C₄	—	344	2	no	—
1024	C₂×C₄	—	344	2	no	—
1025	C₂×C₄	—	344	2	no	—
1026	C₂×C₄	—	172	4	no	—
1027	C₂×C₄	—	172	2	no	—
1028	C₂×C₄	—	172	2	no	—
1029	C₂×C₄	—	172	4	no	—
1030	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1031	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1032	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1033	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1034	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1035	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1036	C₈	—	2	1	no	—
1037	C₈	—	2	1	no	—
1038	C₈	—	2	1	no	—
1039	C₈	—	2	1	no	—
1040	C₈	—	86	2	no	—
1041	C₈	—	86	2	no	—
1042	C₂²	—	2	1	no	—
1043	C₂²	—	2	1	no	—
1044	C₂²	—	2	1	no	—
1045	C₂²	—	2	2	no	—
1046	C₂²	—	4	1	no	—
1047	C₂²	—	4	1	no	—
1048	C₂²	—	172	2	no	—
1049	C₂²	—	172	2	no	—
1050	C₂²	—	172	2	no	—
1051	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1052	C₄	—	2	1	no	—
1053	C₄	—	2	1	no	—
1054	C₄	—	2	1	no	—
1055	C₄	—	2	1	no	—
1056	C₄	—	2	2	no	—
1057	C₄	—	4	1	no	—
1058	C₄	—	4	1	no	—
1059	C₄	—	4	1	no	—
1060	C₄	—	4	1	no	—
1061	C₄	—	4	1	no	—
1062	C₄	—	4	1	no	—
1063	C₄	—	86	2	no	—
1064	C₄	—	86	2	no	—
1065	C₄	—	86	2	no	—
1066	C₄	—	86	2	no	—
1067	C₄	—	172	2	no	—
1068	C₄	—	172	2	no	—
1069	C₄	—	172	2	no	—
1070	C₄	#14583698	1	2	yes	—
1071	C₄	C₂×#13063372	1	1	yes	characteristic
1072	C₄	C₂×#13063372	1	1	yes	characteristic
1073	C₂	—	4	1	no	—
1074	C₂	—	4	2	no	—
1075	C₂	—	344	2	no	—
1076	C₂	#19148242	1	1	yes	characteristic
1077	C₂	C₂×#14583698	1	1	yes	characteristic
1078	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×#3107	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	#19144746	C₂
hypercenter	#3107	D₄₃
hypocenter	C₄₃	#61845
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3107

Complements

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

N	H ≅ G/N	type
1. #19148462	C₂	semidirect
2. #41×Dic₈₆	C₂	semidirect
3. #19147548	C₂	semidirect
4. #19147547	C₂	semidirect
5. #19147525	C₂	semidirect
6. #19147514	C₂	semidirect
7. #19147484	C₂	semidirect
8. #19147468	C₂	semidirect
9. #19147430	C₂	semidirect
10. #19147415	C₂	semidirect
11. #19147407	C₂	semidirect
12. #19147385	C₂	semidirect
13. #19147289	C₂	semidirect
14. #19147253	C₂	semidirect
15. #19145839	C₂	semidirect
16. #19145805	C₂	semidirect
17. #19145777	C₂	semidirect
18. #19145733	C₂	semidirect
20. #19144705	C₂	semidirect
21. #19144614	C₂	semidirect
22. #19143682	C₂	semidirect
23. C₄₃×#3107	C₂	semidirect
554. #3107	D₄₃	semidirect
674. C₄₃	#61845	semidirect

Maximal subgroups

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

subgroup	index
#19148462	2
#41×Dic₈₆	2
#19147548	2
#19147547	2
#19147525	2
#19147514	2
#19147484	2
#19147468	2
#19147430	2
#19147415	2
#19147407	2
#19147385	2
#19147289	2
#19147253	2
#19145839	2
#19145805	2
#19145777	2
#19145733	2
#19144746	2
#19144705	2
#19144614	2
#19143682	2
C₄₃×#3107	2
#61845	43