Subgroups — #25977236

Order 11008.

1750 conjugacy classes of subgroups.

The subgroup lattice has 1094 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148404	C₂	1	1	yes	maximal, characteristic, complemented
2	#19148390	C₂	1	1	yes	maximal, characteristic
3	#19147547	C₂	1	2	yes	maximal, complemented
4	#19147533	C₂	1	2	yes	maximal, complemented
5	#19147516	C₂	1	1	yes	maximal, characteristic, complemented
6	#19147515	C₂	1	1	yes	maximal, characteristic, complemented
7	#19147509	C₂	1	1	yes	maximal, characteristic, complemented
8	#19147501	C₂	1	1	yes	maximal, characteristic, complemented
9	#19147475	C₂	1	2	yes	maximal, complemented
10	#19147472	C₂	1	1	yes	maximal, characteristic, complemented
11	#19147471	C₂	1	2	yes	maximal, complemented
12	#19147468	C₂	1	1	yes	maximal, characteristic, complemented
13	#19147452	C₂	1	1	yes	maximal, characteristic, complemented
14	#19145120	C₂	1	2	yes	maximal, complemented
15	#19145104	C₂	1	1	yes	maximal, characteristic, complemented
16	#19144430	C₂	1	2	yes	maximal, complemented
17	#19144421	C₂	1	2	yes	maximal
18	#19144395	C₂	1	1	yes	maximal, characteristic, complemented
19	#19144393	C₂	1	1	yes	maximal, characteristic
20	#19143524	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143449	C₂	1	2	yes	maximal
22	C₄×SD₁₆×D₄₃	C₂	1	1	yes	maximal, characteristic
23	Q₈×SD₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×SD₁₆×D₄₃	C₂²	1	1	yes	characteristic
25	#14583629	—	2	1	no	—
26	#14583629	C₂²	1	1	yes	characteristic, complemented
27	#14583628	C₂²	1	1	yes	characteristic, complemented
28	#14583627	—	2	1	no	—
29	#14583627	C₂²	1	1	yes	characteristic, complemented
30	#14583625	C₂²	1	2	yes	complemented
31	#14583624	—	2	2	no	—
32	#14583624	C₂²	1	2	yes	complemented
33	#14583610	C₂²	1	2	yes	—
34	#14583609	C₂²	1	1	yes	characteristic
35	#14583608	C₂²	1	2	yes	—
36	#14583607	—	2	1	no	—
37	#14583606	C₂²	1	1	yes	characteristic
38	#14583603	—	2	2	no	—
39	#14583564	C₂²	1	1	yes	characteristic
40	Q₈×C₂²⋊D₄₃	—	2	1	no	—
41	#14583526	—	2	2	no	—
42	#14583526	C₂²	1	2	yes	—
43	#14583526	C₂²	1	2	yes	—
44	#14583524	—	2	2	no	—
45	#14583454	—	2	1	no	—
46	#14583454	C₂²	1	1	yes	characteristic
47	#14583454	C₂²	1	1	yes	characteristic
48	#14583453	—	2	1	no	—
49	#14583453	C₂²	1	1	yes	characteristic
50	C₂×#13063301	—	2	1	no	—
51	C₂²⋊Q₈×D₄₃	—	2	1	no	—
52	#14583375	C₂²	1	2	yes	—
53	#14583371	C₂²	1	2	yes	—
54	C₄×Q₈×D₄₃	C₂²	1	1	yes	characteristic
55	C₄×D₄×D₄₃	C₂²	1	1	yes	characteristic
56	#14583306	C₂²	1	2	yes	complemented
57	#14583306	C₂²	1	2	yes	complemented
58	#14583305	C₂²	1	2	yes	complemented
59	#14583305	C₂²	1	2	yes	complemented
60	#14583302	C₂²	1	1	yes	characteristic, complemented
61	#14583302	C₂²	1	1	yes	characteristic, complemented
62	#14583301	C₂²	1	2	yes	complemented
63	#14583299	C₂²	1	2	yes	complemented
64	#14583299	C₂²	1	2	yes	complemented
65	#14583299	C₂²	1	2	yes	complemented
66	#14583297	C₂²	1	1	yes	characteristic, complemented
67	#14583296	C₂²	1	2	yes	complemented
68	#14583209	C₂²	1	2	yes	complemented
69	#14583209	C₂²	1	2	yes	complemented
70	#14583208	C₂²	1	2	yes	complemented
71	#14583207	C₂²	1	2	yes	complemented
72	#14583206	C₂²	1	2	yes	complemented
73	#14583204	C₂²	1	2	yes	complemented
74	#14583201	C₂²	1	2	yes	—
75	#14583200	C₂²	1	2	yes	—
76	#14583199	C₂²	1	2	yes	—
77	#14583198	C₂²	1	2	yes	—
78	#14583198	C₂²	1	2	yes	—
79	#14583197	C₂²	1	2	yes	—
80	#14583195	C₂²	1	1	yes	characteristic, complemented
81	#14583194	C₂²	1	1	yes	characteristic, complemented
82	#14583192	C₂²	1	2	yes	complemented
83	#14583191	C₂²	1	2	yes	complemented
84	#14583188	C₂²	1	2	yes	—
85	#14583186	C₂²	1	1	yes	characteristic
86	#14583183	C₂²	1	2	yes	complemented
87	#14583181	C₂²	1	1	yes	characteristic, complemented
88	#14583180	C₂²	1	1	yes	characteristic
89	#14583179	C₂²	1	1	yes	characteristic
90	#14583177	C₂²	1	2	yes	—
91	#14583176	C₂²	1	2	yes	—
92	#14583030	C₂²	1	1	yes	characteristic, complemented
93	#14583028	C₂²	1	2	yes	complemented
94	#14583026	C₂²	1	1	yes	characteristic, complemented
95	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
96	C₈×Dic₈₆	C₂²	1	2	yes	complemented
97	#14583002	C₂²	1	2	yes	—
98	#14582999	C₂²	1	2	yes	—
99	#14582997	C₂²	1	2	yes	—
100	#14582996	C₂²	1	2	yes	—
101	#14582990	C₂²	1	1	yes	characteristic
102	C₄×#10621873	C₂²	1	2	yes	—
103	C₄×#10621873	C₂²	1	1	yes	characteristic
104	SD₁₆×Dic₄₃	C₂²	1	2	yes	—
105	SD₁₆×Dic₄₃	C₂²	1	1	yes	characteristic
106	C₄×#10621884	C₂²	1	1	yes	characteristic
107	#14582986	C₂²	1	2	yes	—
108	#14582986	C₂²	1	1	yes	characteristic
109	C₄×#10621883	C₂²	1	1	yes	characteristic
110	#14582984	C₂²	1	1	yes	characteristic
111	#14582938	C₂²	1	2	yes	—
112	#14582938	C₂²	1	2	yes	—
113	#14582934	C₂²	1	2	yes	—
114	#14582934	C₂²	1	2	yes	—
115	#106×D₄₃	C₂²	1	1	yes	characteristic
116	#14582924	C₂²	1	2	yes	—
117	#14582921	C₂²	1	1	yes	characteristic
118	#14582906	C₂²	1	2	yes	—
119	#14582902	C₂²	1	2	yes	—
120	#103×D₄₃	C₂²	1	1	yes	characteristic
121	#102×D₄₃	C₂²	1	1	yes	characteristic
122	#14582853	C₂²	1	2	yes	—
123	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
124	Q₈²×C₄₃	C₂²	1	1	yes	characteristic, complemented
125	D₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
126	C₄₃×#498	C₂²	1	1	yes	characteristic, complemented
127	C₄₃×#498	C₂²	1	2	yes	complemented
128	C₄₃×#476	C₂²	1	2	yes	—
129	C₄₃×#476	C₂²	1	1	yes	characteristic
130	C₄₃×#475	C₂²	1	2	yes	complemented
131	C₄₃×#475	C₂²	1	1	yes	characteristic, complemented
132	C₈×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
133	C₄×SD₁₆×C₄₃	C₂²	1	2	yes	—
134	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
135	C₂×Q₈×D₄₃	—	2	1	no	—
136	C₂×Q₈×D₄₃	C₂³	1	1	yes	characteristic
137	C₂×D₄×D₄₃	C₂³	1	1	yes	characteristic
138	C₂²×C₄×D₄₃	—	2	1	no	—
139	C₂×#10621873	C₂³	1	1	yes	characteristic
140	C₂×#10621883	C₂³	1	1	yes	characteristic
141	C₂×#10621884	C₂³	1	1	yes	characteristic
142	SD₁₆×D₄₃	Q₈	1	8	yes	complemented
143	C₂×#10621872	C₂³	1	2	yes	—
144	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
145	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
146	#13063325	—	2	1	no	—
147	#13063325	C₂³	1	1	yes	characteristic
148	#13063325	C₂³	1	1	yes	characteristic
149	#13063324	—	2	2	no	—
150	#13063324	—	2	1	no	—
151	#13063324	D₄	1	1	yes	characteristic
152	#13063324	C₂³	1	2	yes	—
153	#13063324	C₂³	1	2	yes	—
154	#13063323	—	2	1	no	—
155	#13063323	—	2	2	no	—
156	#13063323	—	2	2	no	—
157	#13063323	—	2	2	no	—
158	#13063323	—	2	2	no	—
159	#13063323	D₄	1	1	yes	characteristic
160	#13063317	—	2	2	no	—
161	#13063317	C₂³	1	2	yes	—
162	#13063317	C₂³	1	2	yes	—
163	#13063316	—	2	2	no	—
164	#13063316	—	2	2	no	—
165	#13063316	C₂³	1	2	yes	—
166	#13063316	C₂³	1	2	yes	—
167	#13063316	C₂³	1	2	yes	—
168	#13063316	C₂³	1	2	yes	—
169	#13063315	—	2	2	no	—
170	#13063315	—	2	2	no	—
171	#13063315	—	2	2	no	—
172	#13063315	—	2	2	no	—
173	#13063315	—	2	2	no	—
174	#13063315	D₄	1	2	yes	—
175	#13063305	—	2	1	no	—
176	#13063305	—	2	1	no	—
177	#13063305	—	2	2	no	—
178	#13063305	D₄	1	1	yes	characteristic
179	#13063304	—	2	1	no	—
180	#13063304	—	2	2	no	—
181	#13063303	—	2	2	no	—
182	#13063303	—	2	2	no	—
183	#13063303	—	2	2	no	—
184	#13063303	—	2	2	no	—
185	#13063303	D₄	1	2	yes	—
186	#13063302	—	2	2	no	—
187	#13063302	—	2	2	no	—
188	#13063302	—	2	2	no	—
189	#13063301	—	2	1	no	—
190	#13063301	—	2	1	no	—
191	#13063301	—	2	1	no	—
192	#13063301	—	2	2	no	—
193	#13063301	—	2	2	no	—
194	#13063301	—	2	1	no	—
195	#13063301	—	2	2	no	—
196	#13063301	—	2	2	no	—
197	#13063301	D₄	1	1	yes	characteristic
198	Q₈×Dic₄₃	—	2	2	no	—
199	Q₈×Dic₄₃	—	2	1	no	—
200	Q₈×Dic₄₃	—	2	1	no	—
201	Q₈×Dic₄₃	C₂³	1	1	yes	characteristic
202	Q₈×Dic₄₃	C₂³	1	2	yes	—
203	C₄×Dic₈₆	—	2	1	no	—
204	C₄×Dic₈₆	—	2	2	no	—
205	C₄×Dic₈₆	—	2	2	no	—
206	C₄×Dic₈₆	—	2	1	no	—
207	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
208	C₄×Dic₈₆	C₂³	1	2	yes	—
209	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
210	C₄×Dic₈₆	C₂³	1	2	yes	—
211	#13063290	—	2	1	no	—
212	#13063290	—	2	1	no	—
213	#13063290	—	2	2	no	—
214	#13063290	—	2	1	no	—
215	#13063290	—	2	1	no	—
216	#13063290	—	2	1	no	—
217	#13063290	C₂³	1	1	yes	characteristic
218	#13063290	C₂³	1	2	yes	—
219	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
220	C₄×D₁₇₂	C₂³	1	2	yes	—
221	D₄×Dic₄₃	C₂³	1	2	yes	—
222	D₄×Dic₄₃	C₂³	1	1	yes	characteristic
223	#13063287	C₂³	1	2	yes	—
224	#13063287	C₂³	1	1	yes	characteristic
225	C₄×C₂²⋊D₄₃	—	2	2	no	—
226	C₄×C₂²⋊D₄₃	—	2	1	no	—
227	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
228	(C₂²⋊D₄₃)⋊C₄	—	2	1	no	—
229	#13063283	—	2	2	no	—
230	#13063283	C₂³	1	2	yes	—
231	#13063283	C₂³	1	2	yes	—
232	#13063282	—	2	2	no	—
233	#13063282	C₂³	1	2	yes	—
234	C₂×C₄⋊Dic₄₃	—	2	1	no	—
235	C₂×Dic₄₃⋊C₄	—	2	2	no	—
236	C₄⋊C₄×D₄₃	—	2	1	no	—
237	C₄⋊C₄×D₄₃	—	2	1	no	—
238	C₄⋊C₄×D₄₃	—	2	2	no	—
239	C₄⋊C₄×D₄₃	C₂³	1	1	yes	characteristic
240	C₄⋊C₄×D₄₃	C₂³	1	1	yes	characteristic
241	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
242	C₂²⋊C₄×D₄₃	—	2	1	no	—
243	C₂²⋊C₄×D₄₃	—	2	2	no	—
244	C₄²×D₄₃	—	2	1	no	—
245	C₄²×D₄₃	C₂³	1	1	yes	characteristic
246	#13063259	C₂³	1	2	yes	—
247	#13063259	C₂³	1	2	yes	—
248	#13063258	C₂³	1	2	yes	—
249	#13063258	C₂³	1	2	yes	—
250	#13063258	C₂³	1	2	yes	—
251	#13063258	C₂³	1	2	yes	—
252	#13063258	C₂³	1	2	yes	—
253	#13063258	C₂³	1	2	yes	—
254	#13063257	C₂³	1	1	yes	characteristic
255	#13063257	C₂³	1	2	yes	—
256	#13063257	C₂³	1	2	yes	—
257	#13063256	C₂³	1	2	yes	—
258	#13063256	C₂³	1	2	yes	—
259	#13063256	C₂³	1	1	yes	characteristic
260	#13063256	C₂³	1	1	yes	characteristic
261	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
262	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
263	Dic₄₃⋊C₈	C₂³	1	2	yes	—
264	Dic₄₃⋊C₈	C₂³	1	2	yes	—
265	Dic₄₃⋊C₈	C₂³	1	2	yes	—
266	#13063250	C₂³	1	1	yes	characteristic
267	#13063250	C₂³	1	2	yes	—
268	#13063249	C₂³	1	1	yes	characteristic
269	#13063249	C₂³	1	2	yes	—
270	#13063248	C₂³	1	1	yes	characteristic
271	#13063248	C₂³	1	2	yes	—
272	#13063247	C₂³	1	1	yes	characteristic
273	#13063247	C₂³	1	2	yes	—
274	#13063246	C₂³	1	1	yes	characteristic
275	#13063246	C₂³	1	2	yes	—
276	#13063245	C₂³	1	1	yes	characteristic
277	#13063245	C₂³	1	2	yes	—
278	#13063236	C₂³	1	2	yes	—
279	#13063235	C₂³	1	2	yes	—
280	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
281	C₈×Dic₄₃	C₂³	1	2	yes	—
282	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
283	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
284	C₂²×Q₈×C₄₃	—	2	1	no	—
285	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
286	C₄⋊Q₈×C₄₃	—	2	2	no	—
287	C₄⋊Q₈×C₄₃	—	2	1	no	—
288	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
289	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
290	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
291	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
292	C₂²⋊Q₈×C₄₃	—	2	2	no	—
293	C₂²⋊Q₈×C₄₃	—	2	1	no	—
294	C₄×Q₈×C₄₃	—	2	1	no	—
295	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
296	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
297	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
298	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
299	C₄×D₄×C₄₃	C₂³	1	2	yes	—
300	#106×C₄₃	C₂³	1	2	yes	—
301	#106×C₄₃	C₂³	1	1	yes	characteristic
302	#106×C₄₃	C₂³	1	2	yes	—
303	#106×C₄₃	C₂³	1	2	yes	—
304	#106×C₄₃	C₂³	1	2	yes	—
305	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
306	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
307	#103×C₄₃	C₂³	1	1	yes	characteristic
308	#103×C₄₃	C₂³	1	2	yes	—
309	#102×C₄₃	C₂³	1	1	yes	characteristic
310	#102×C₄₃	C₂³	1	2	yes	—
311	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₄₃	C₂³	1	2	yes	—
313	C₂³×D₄₃	—	2	1	no	—
314	C₂×Q₈×C₄₃	—	2	1	no	—
315	C₂×Q₈×C₄₃	—	2	2	no	—
316	C₂×Q₈×C₄₃	—	2	1	no	—
317	C₂×Q₈×C₄₃	—	2	2	no	—
318	C₂×Q₈×C₄₃	—	8	2	no	—
319	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
320	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
321	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₄₃	—	2	1	no	—
323	C₂²×C₄×C₄₃	—	2	2	no	—
324	C₂×C₂²⋊D₄₃	—	2	1	no	—
325	C₂²×Dic₄₃	—	2	2	no	—
326	C₂²×Dic₄₃	—	2	1	no	—
327	Q₈×D₄₃	—	2	2	no	—
328	Q₈×D₄₃	—	8	2	no	—
329	Q₈×D₄₃	C₂×Q₈	1	4	yes	complemented
330	D₄×D₄₃	—	2	2	no	—
331	D₄×D₄₃	C₂×Q₈	1	4	yes	—
332	C₂×D₁₇₂	C₂⁴	1	1	yes	characteristic
333	C₂×C₄×D₄₃	—	2	1	no	—
334	C₂×C₄×D₄₃	—	2	2	no	—
335	C₂×C₄×D₄₃	—	2	2	no	—
336	C₂×C₄×D₄₃	—	2	1	no	—
337	C₂×C₄×D₄₃	—	2	1	no	—
338	C₂×C₄×D₄₃	—	2	1	no	—
339	C₂×C₄×D₄₃	—	2	1	no	—
340	C₂×C₄×D₄₃	—	8	2	no	—
341	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
342	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
343	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
344	C₂×Dic₈₆	—	2	1	no	—
345	C₂×Dic₈₆	—	2	1	no	—
346	C₂×Dic₈₆	—	2	1	no	—
347	C₂×Dic₈₆	—	2	2	no	—
348	C₂×Dic₈₆	—	2	2	no	—
349	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
350	C₂×Dic₈₆	C₂×D₄	1	2	yes	—
351	C₂×Dic₈₆	C₂⁴	1	1	yes	characteristic
352	SD₁₆×C₄₃	C₂×Q₈	1	4	yes	complemented
353	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
354	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
355	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
356	C₄⋊C₄×C₄₃	—	2	1	no	—
357	C₄⋊C₄×C₄₃	—	2	2	no	—
358	C₄⋊C₄×C₄₃	—	2	1	no	—
359	C₄⋊C₄×C₄₃	—	2	2	no	—
360	C₄⋊C₄×C₄₃	—	2	2	no	—
361	C₄⋊C₄×C₄₃	—	2	1	no	—
362	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
363	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
364	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
365	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
366	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
367	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
368	C₂²⋊C₄×C₄₃	—	2	2	no	—
369	C₂²⋊C₄×C₄₃	—	2	1	no	—
370	C₄²×C₄₃	—	2	1	no	—
371	C₄²×C₄₃	—	2	2	no	—
372	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
373	C₄²×C₄₃	C₂⁴	1	2	yes	—
374	C₂²⋊Dic₄₃	—	2	2	no	—
375	C₂²⋊Dic₄₃	—	2	1	no	—
376	#10621884	C₂×Q₈	1	4	yes	complemented
377	#10621883	C₂×Q₈	1	4	yes	complemented
378	(C₂×D₄₃)⋊C₄	—	2	1	no	—
379	(C₂×D₄₃)⋊C₄	—	2	2	no	—
380	(C₂×D₄₃)⋊C₄	—	2	1	no	—
381	(C₂×D₄₃)⋊C₄	—	2	2	no	—
382	(C₂×D₄₃)⋊C₄	—	2	2	no	—
383	(C₂×D₄₃)⋊C₄	—	2	2	no	—
384	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
385	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
386	C₄⋊Dic₄₃	—	2	1	no	—
387	C₄⋊Dic₄₃	—	2	1	no	—
388	C₄⋊Dic₄₃	—	2	1	no	—
389	C₄⋊Dic₄₃	—	2	2	no	—
390	C₄⋊Dic₄₃	—	2	2	no	—
391	C₄⋊Dic₄₃	—	2	2	no	—
392	C₄⋊Dic₄₃	—	2	2	no	—
393	C₄⋊Dic₄₃	—	2	2	no	—
394	C₄⋊Dic₄₃	C₂×D₄	1	2	yes	—
395	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
396	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
397	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
398	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
399	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
400	Dic₄₃⋊C₄	—	2	1	no	—
401	Dic₄₃⋊C₄	—	2	2	no	—
402	Dic₄₃⋊C₄	—	2	2	no	—
403	Dic₄₃⋊C₄	—	2	2	no	—
404	Dic₄₃⋊C₄	—	2	2	no	—
405	Dic₄₃⋊C₄	—	2	2	no	—
406	Dic₄₃⋊C₄	—	2	2	no	—
407	Dic₄₃⋊C₄	—	2	1	no	—
408	Dic₄₃⋊C₄	—	2	2	no	—
409	Dic₄₃⋊C₄	—	2	1	no	—
410	Dic₄₃⋊C₄	—	2	1	no	—
411	Dic₄₃⋊C₄	—	2	2	no	—
412	Dic₄₃⋊C₄	—	2	2	no	—
413	Dic₄₃⋊C₄	—	2	2	no	—
414	Dic₄₃⋊C₄	—	2	2	no	—
415	Dic₄₃⋊C₄	—	2	2	no	—
416	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
417	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
418	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
419	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
420	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
421	C₄×Dic₄₃	—	2	1	no	—
422	C₄×Dic₄₃	—	2	2	no	—
423	C₄×Dic₄₃	—	2	1	no	—
424	C₄×Dic₄₃	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
430	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
431	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
432	C₄×Dic₄₃	C₂⁴	1	2	yes	—
433	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
434	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
435	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
436	#10621873	C₂×Q₈	1	4	yes	complemented
437	#10621872	—	2	4	no	—
438	C₈×D₄₃	—	2	2	no	—
439	C₈×D₄₃	C₂×Q₈	1	4	yes	complemented
440	C₂³×C₄₃	—	2	1	no	—
441	C₂²×D₄₃	—	2	1	no	—
442	C₂²×D₄₃	—	2	4	no	—
443	C₂²×D₄₃	—	8	1	no	—
444	C₂²×D₄₃	—	8	1	no	—
445	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
446	Q₈×C₄₃	—	2	2	no	—
447	Q₈×C₄₃	—	2	1	no	—
448	Q₈×C₄₃	—	4	2	no	—
449	Q₈×C₄₃	—	8	2	no	—
450	Q₈×C₄₃	—	8	1	no	—
451	Q₈×C₄₃	—	8	2	no	—
452	Q₈×C₄₃	C₂²×Q₈	1	2	yes	—
453	D₄×C₄₃	—	2	1	no	—
454	D₄×C₄₃	C₂²×Q₈	1	2	yes	—
455	C₂×C₄×C₄₃	—	2	1	no	—
456	C₂×C₄×C₄₃	—	2	2	no	—
457	C₂×C₄×C₄₃	—	2	1	no	—
458	C₂×C₄×C₄₃	—	2	2	no	—
459	C₂×C₄×C₄₃	—	2	1	no	—
460	C₂×C₄×C₄₃	—	4	2	no	—
461	C₂×C₄×C₄₃	—	8	2	no	—
462	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
463	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
465	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
467	C₂²⋊D₄₃	—	2	4	no	—
468	C₂×Dic₄₃	—	2	1	no	—
469	C₂×Dic₄₃	—	2	2	no	—
470	C₂×Dic₄₃	—	2	1	no	—
471	C₂×Dic₄₃	—	2	2	no	—
472	C₂×Dic₄₃	—	2	1	no	—
473	C₂×Dic₄₃	—	8	1	no	—
474	C₂×Dic₄₃	—	8	2	no	—
475	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
476	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
477	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
478	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
479	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
480	D₁₇₂	—	2	1	no	—
481	D₁₇₂	C₂²×Q₈	1	2	yes	—
482	C₄×D₄₃	—	2	4	no	—
483	C₄×D₄₃	—	2	2	no	—
484	C₄×D₄₃	—	4	1	no	—
485	C₄×D₄₃	—	4	2	no	—
486	C₄×D₄₃	—	8	1	no	—
487	C₄×D₄₃	—	8	2	no	—
488	C₄×D₄₃	—	8	2	no	—
489	C₄×D₄₃	—	8	1	no	—
490	C₄×D₄₃	—	8	1	no	—
491	C₄×D₄₃	C₂²×Q₈	1	2	yes	—
492	C₄×D₄₃	2₋¹⁺⁴	1	2	yes	—
493	Dic₈₆	—	2	2	no	—
494	Dic₈₆	—	2	1	no	—
495	Dic₈₆	—	2	4	no	—
496	Dic₈₆	—	4	2	no	—
497	Dic₈₆	—	4	2	no	—
498	Dic₈₆	—	8	2	no	—
499	Dic₈₆	—	8	2	no	—
500	Dic₈₆	—	8	1	no	—
501	Dic₈₆	C₂²×Q₈	1	2	yes	—
502	C₈×C₄₃	—	2	1	no	—
503	C₈×C₄₃	—	2	2	no	—
504	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
505	C₄₃⋊C₈	—	2	1	no	—
506	C₄₃⋊C₈	—	2	2	no	—
507	C₄₃⋊C₈	C₂²×Q₈	1	2	yes	—
508	#61371	—	43	1	no	maximal, Sylow
509	C₂²×C₄₃	—	2	2	no	—
510	C₂²×C₄₃	—	4	1	no	—
511	C₂²×C₄₃	—	4	1	no	—
512	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
513	C₂×D₄₃	—	2	1	no	—
514	C₂×D₄₃	—	2	1	no	—
515	C₂×D₄₃	—	2	2	no	—
516	C₂×D₄₃	—	4	1	no	—
517	C₂×D₄₃	—	4	1	no	—
518	C₂×D₄₃	—	8	4	no	—
519	C₂×D₄₃	D₄×Q₈	1	2	yes	—
520	C₄×C₄₃	—	2	2	no	—
521	C₄×C₄₃	—	2	1	no	—
522	C₄×C₄₃	—	2	2	no	—
523	C₄×C₄₃	—	2	2	no	—
524	C₄×C₄₃	—	4	2	no	—
525	C₄×C₄₃	—	4	1	no	—
526	C₄×C₄₃	—	4	2	no	—
527	C₄×C₄₃	—	4	1	no	—
528	C₄×C₄₃	#577	1	2	yes	—
529	C₄×C₄₃	C₂³×Q₈	1	1	yes	characteristic
530	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
531	Dic₄₃	—	2	1	no	—
532	Dic₄₃	—	2	2	no	—
533	Dic₄₃	—	2	2	no	—
534	Dic₄₃	—	2	2	no	—
535	Dic₄₃	—	2	1	no	—
536	Dic₄₃	—	4	1	no	—
537	Dic₄₃	—	4	2	no	—
538	Dic₄₃	—	4	2	no	—
539	Dic₄₃	—	4	1	no	—
540	Dic₄₃	D₄×Q₈	1	2	yes	—
541	#3502	—	43	1	no	—
542	#3501	—	43	1	no	—
543	#3388	—	43	2	no	—
544	#3388	—	43	2	no	—
545	#3386	—	43	1	no	—
546	#3386	—	43	1	no	—
547	#3385	—	43	1	no	—
548	#3385	—	43	1	no	—
549	#3381	—	43	2	no	—
550	#3381	—	43	1	no	—
551	#3381	—	43	1	no	—
552	#3381	—	43	2	no	—
553	Q₈×SD₁₆	—	43	1	no	—
554	Q₈×SD₁₆	D₄₃	1	1	yes	characteristic, complemented
555	#3163	—	43	2	no	—
556	#3160	—	43	1	no	—
557	#3082	—	43	2	no	—
558	#3081	—	43	2	no	—
559	#3078	—	43	1	no	—
560	#3077	—	43	1	no	—
561	#2960	—	43	1	no	—
562	#2949	—	43	2	no	—
563	C₂×C₄×SD₁₆	—	43	1	no	—
564	C₂×C₄₃	—	4	2	no	—
565	C₂×C₄₃	C₂×D₄×Q₈	1	1	yes	characteristic
566	C₂×C₄₃	C₂×#577	1	1	yes	characteristic
567	C₂×C₄₃	#3584	1	1	yes	characteristic
568	D₄₃	—	2	2	no	—
569	D₄₃	—	4	2	no	—
570	C₂²×SD₁₆	—	43	1	no	—
571	Q₈²	—	43	1	no	—
572	Q₈²	—	86	1	no	—
573	Q₈²	C₂×D₄₃	1	1	yes	characteristic, complemented
574	#557	—	43	2	no	—
575	#557	—	43	1	no	—
576	#557	—	43	2	no	—
577	#557	—	43	1	no	—
578	#557	—	86	1	no	—
579	#557	—	86	2	no	—
580	#554	—	43	2	no	—
581	#554	—	43	1	no	—
582	#554	—	43	1	no	—
583	#554	—	43	2	no	—
584	#554	—	86	2	no	—
585	#554	—	86	1	no	—
586	D₄×Q₈	—	43	1	no	—
587	D₄×Q₈	—	86	1	no	—
588	D₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
589	#544	—	43	2	no	—
590	#544	—	43	2	no	—
591	#544	—	86	2	no	—
592	#543	—	86	2	no	—
593	#533	—	43	1	no	—
594	#533	—	43	1	no	—
595	#533	—	43	1	no	—
596	#533	—	86	1	no	—
597	#533	—	86	1	no	—
598	C₂×C₂²⋊Q₈	—	86	1	no	—
599	C₂×C₂²⋊Q₈	—	86	1	no	—
600	#519	—	43	2	no	—
601	#518	—	43	2	no	—
602	C₂×C₄×Q₈	—	43	1	no	—
603	C₂×C₄×D₄	—	43	1	no	—
604	#501	—	43	2	no	—
605	#501	—	43	2	no	—
606	#501	—	43	2	no	—
607	#501	—	43	2	no	—
608	#500	—	43	1	no	—
609	#500	—	43	1	no	—
610	#499	—	43	2	no	—
611	#499	—	43	2	no	—
612	#499	—	43	2	no	—
613	#499	—	43	2	no	—
614	#498	—	43	2	no	—
615	#498	—	43	1	no	—
616	#498	C₂×D₄₃	1	1	yes	characteristic, complemented
617	#498	C₂×D₄₃	1	2	yes	complemented
618	#479	—	43	2	no	—
619	#479	—	43	2	no	—
620	#479	—	43	2	no	—
621	#479	—	43	2	no	—
622	#479	—	43	2	no	—
623	#479	—	43	2	no	—
624	#478	—	43	2	no	—
625	#478	—	43	2	no	—
626	#478	—	43	2	no	—
627	#478	—	43	2	no	—
628	#478	—	43	2	no	—
629	#478	—	43	2	no	—
630	#477	—	43	2	no	—
631	#477	—	43	1	no	—
632	#477	—	43	1	no	—
633	#477	—	43	2	no	—
634	#476	—	43	1	no	—
635	#476	—	43	2	no	—
636	#476	C₂×D₄₃	1	1	yes	characteristic
637	#476	C₂×D₄₃	1	2	yes	—
638	#475	—	43	1	no	—
639	#475	—	43	2	no	—
640	#475	C₂×D₄₃	1	1	yes	characteristic, complemented
641	#475	C₂×D₄₃	1	2	yes	complemented
642	#474	—	43	2	no	—
643	#474	—	43	1	no	—
644	#474	—	43	1	no	—
645	#474	—	43	2	no	—
646	#446	—	43	1	no	—
647	#446	—	43	1	no	—
648	#446	—	43	2	no	—
649	C₈×Q₈	—	43	1	no	—
650	C₈×Q₈	—	43	2	no	—
651	C₈×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
652	#440	—	43	2	no	—
653	#440	—	43	2	no	—
654	#440	—	43	2	no	—
655	#440	—	43	2	no	—
656	C₄×SD₁₆	—	43	1	no	—
657	C₄×SD₁₆	—	43	2	no	—
658	C₄×SD₁₆	—	43	1	no	—
659	C₄×SD₁₆	—	43	1	no	—
660	C₄×SD₁₆	—	43	2	no	—
661	C₄×SD₁₆	—	43	1	no	—
662	C₄×SD₁₆	—	43	1	no	—
663	C₄×SD₁₆	—	43	1	no	—
664	C₄×SD₁₆	—	43	1	no	—
665	C₄×SD₁₆	—	43	2	no	—
666	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
667	C₄×SD₁₆	C₂×D₄₃	1	2	yes	—
668	#428	—	43	2	no	—
669	#428	—	43	2	no	—
670	#427	—	43	2	no	—
671	#427	—	43	2	no	—
672	C₂×#106	—	43	1	no	—
673	#424	—	43	2	no	—
674	#423	—	43	1	no	—
675	#419	—	43	2	no	—
676	#418	—	43	2	no	—
677	C₂×#103	—	43	1	no	—
678	C₂×#102	—	43	1	no	—
679	#405	—	43	2	no	—
680	C₂×C₄×C₈	—	43	1	no	—
681	C₄₃	#61371	1	1	yes	characteristic, complemented, Sylow
682	C₂²×Q₈	—	2	1	no	—
683	C₂²×Q₈	—	43	1	no	—
684	C₂²×Q₈	—	86	1	no	—
685	C₂²×D₄	—	43	1	no	—
686	C₂³×C₄	—	86	1	no	—
687	C₂×SD₁₆	—	43	1	no	—
688	C₂×SD₁₆	—	43	1	no	—
689	C₂×SD₁₆	—	43	8	no	—
690	C₂×SD₁₆	—	43	1	no	—
691	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
692	C₂×M₁₆	—	43	2	no	—
693	C₂²×C₈	—	43	1	no	—
694	C₂²×C₈	—	43	1	no	—
695	C₄⋊Q₈	—	2	1	no	—
696	C₄⋊Q₈	—	2	2	no	—
697	C₄⋊Q₈	—	43	1	no	—
698	C₄⋊Q₈	—	43	1	no	—
699	C₄⋊Q₈	—	43	2	no	—
700	C₄⋊Q₈	—	43	2	no	—
701	C₄⋊Q₈	—	43	1	no	—
702	C₄⋊Q₈	—	43	1	no	—
703	C₄⋊Q₈	—	86	1	no	—
704	C₄⋊Q₈	—	86	1	no	—
705	C₄⋊Q₈	—	86	2	no	—
706	C₄⋊Q₈	—	86	2	no	—
707	C₄⋊Q₈	—	86	2	no	—
708	C₄⋊Q₈	—	86	2	no	—
709	C₄⋊Q₈	—	86	2	no	—
710	C₄⋊Q₈	—	86	1	no	—
711	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
712	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
713	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
714	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
715	#125	—	43	2	no	—
716	#125	—	43	2	no	—
717	#125	—	43	2	no	—
718	#125	—	43	2	no	—
719	#125	—	43	2	no	—
720	#125	—	43	2	no	—
721	#125	—	43	2	no	—
722	#125	—	86	2	no	—
723	#125	—	86	2	no	—
724	#125	—	86	2	no	—
725	#125	—	86	2	no	—
726	#125	—	86	2	no	—
727	#125	—	86	2	no	—
728	#125	—	86	2	no	—
729	#125	—	86	2	no	—
730	C₂²⋊Q₈	—	2	1	no	—
731	C₂²⋊Q₈	—	2	2	no	—
732	C₂²⋊Q₈	—	43	1	no	—
733	C₂²⋊Q₈	—	43	1	no	—
734	C₂²⋊Q₈	—	43	2	no	—
735	C₂²⋊Q₈	—	86	2	no	—
736	C₂²⋊Q₈	—	86	2	no	—
737	C₂²⋊Q₈	—	86	2	no	—
738	C₂²⋊Q₈	—	86	2	no	—
739	C₂²⋊Q₈	—	86	2	no	—
740	C₂²⋊Q₈	—	86	2	no	—
741	C₂²⋊Q₈	—	86	2	no	—
742	C₂²⋊Q₈	—	86	2	no	—
743	C₂²⋊Q₈	—	86	1	no	—
744	C₂²⋊Q₈	—	86	1	no	—
745	C₂²⋊Q₈	—	86	2	no	—
746	C₂²⋊Q₈	—	86	2	no	—
747	C₂²⋊Q₈	—	86	1	no	—
748	C₂²⋊Q₈	—	86	2	no	—
749	C₂²⋊Q₈	—	86	2	no	—
750	C₂²⋊Q₈	—	86	1	no	—
751	C₂²⋊Q₈	—	86	1	no	—
752	C₂²⋊Q₈	—	86	1	no	—
753	C₂²⋊Q₈	—	86	1	no	—
754	C₂²⋊Q₈	—	86	2	no	—
755	C₄×Q₈	—	2	1	no	—
756	C₄×Q₈	—	43	1	no	—
757	C₄×Q₈	—	43	2	no	—
758	C₄×Q₈	—	43	1	no	—
759	C₄×Q₈	—	43	2	no	—
760	C₄×Q₈	—	43	1	no	—
761	C₄×Q₈	—	43	2	no	—
762	C₄×Q₈	—	43	1	no	—
763	C₄×Q₈	—	43	2	no	—
764	C₄×Q₈	—	86	1	no	—
765	C₄×Q₈	—	86	2	no	—
766	C₄×Q₈	—	86	2	no	—
767	C₄×Q₈	—	86	1	no	—
768	C₄×Q₈	—	86	1	no	—
769	C₄×Q₈	—	86	1	no	—
770	C₄×Q₈	—	86	1	no	—
771	C₄×Q₈	—	86	1	no	—
772	C₄×Q₈	—	86	1	no	—
773	C₄×Q₈	—	86	2	no	—
774	C₄×Q₈	—	86	1	no	—
775	C₄×Q₈	—	86	2	no	—
776	C₄×Q₈	—	86	1	no	—
777	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
778	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
779	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
780	C₄×D₄	—	43	1	no	—
781	C₄×D₄	—	43	2	no	—
782	C₄×D₄	—	43	1	no	—
783	C₄×D₄	—	43	2	no	—
784	C₄×D₄	—	43	1	no	—
785	C₄×D₄	—	43	2	no	—
786	C₄×D₄	—	86	1	no	—
787	C₄×D₄	—	86	1	no	—
788	C₄×D₄	—	86	2	no	—
789	C₄×D₄	—	86	2	no	—
790	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
791	C₄×D₄	C₂²×D₄₃	1	2	yes	—
792	#117	—	43	2	no	—
793	#117	—	43	2	no	—
794	#117	—	43	2	no	—
795	#117	—	86	2	no	—
796	#117	—	86	2	no	—
797	C₂×C₄⋊C₄	—	43	1	no	—
798	C₂×C₄⋊C₄	—	43	1	no	—
799	C₂×C₄⋊C₄	—	86	2	no	—
800	C₂×C₄⋊C₄	—	86	1	no	—
801	C₂×C₄⋊C₄	—	86	2	no	—
802	C₂×C₄⋊C₄	—	86	1	no	—
803	C₂×C₄⋊C₄	—	86	1	no	—
804	C₂×C₂²⋊C₄	—	86	2	no	—
805	C₂×C₂²⋊C₄	—	86	1	no	—
806	C₂×C₂²⋊C₄	—	86	2	no	—
807	C₂×C₄²	—	43	1	no	—
808	C₂×C₄²	—	86	1	no	—
809	#107	—	43	2	no	—
810	#107	—	43	2	no	—
811	#107	—	43	2	no	—
812	#107	—	43	2	no	—
813	#107	—	43	2	no	—
814	#107	—	43	2	no	—
815	#107	—	43	2	no	—
816	#107	—	43	2	no	—
817	#106	—	43	1	no	—
818	#106	—	43	2	no	—
819	#106	—	43	2	no	—
820	#106	—	43	1	no	—
821	#106	—	43	1	no	—
822	#106	—	43	2	no	—
823	#106	—	43	2	no	—
824	#106	C₂²×D₄₃	1	1	yes	characteristic
825	#106	C₂²×D₄₃	1	2	yes	—
826	#106	C₂²×D₄₃	1	2	yes	—
827	#106	C₂²×D₄₃	1	2	yes	—
828	#106	C₂²×D₄₃	1	2	yes	—
829	C₄⋊C₈	—	43	2	no	—
830	C₄⋊C₈	—	43	2	no	—
831	C₄⋊C₈	—	43	2	no	—
832	C₄⋊C₈	—	43	1	no	—
833	C₄⋊C₈	—	43	2	no	—
834	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
835	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
836	#103	—	43	1	no	—
837	#103	—	43	2	no	—
838	#103	—	43	1	no	—
839	#103	—	43	2	no	—
840	#103	—	43	1	no	—
841	#103	—	43	2	no	—
842	#103	C₂²×D₄₃	1	1	yes	characteristic
843	#103	C₂²×D₄₃	1	2	yes	—
844	#102	—	43	1	no	—
845	#102	—	43	2	no	—
846	#102	—	43	1	no	—
847	#102	—	43	2	no	—
848	#102	—	43	1	no	—
849	#102	—	43	2	no	—
850	#102	C₂²×D₄₃	1	1	yes	characteristic
851	#102	C₂²×D₄₃	1	2	yes	—
852	#97	—	43	2	no	—
853	#97	—	43	2	no	—
854	C₄×C₈	—	43	1	no	—
855	C₄×C₈	—	43	1	no	—
856	C₄×C₈	—	43	2	no	—
857	C₄×C₈	—	43	1	no	—
858	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
859	C₄×C₈	C₂²×D₄₃	1	2	yes	—
860	C₂⁴	—	86	1	no	—
861	C₂×Q₈	—	2	1	no	—
862	C₂×Q₈	—	2	1	no	—
863	C₂×Q₈	—	2	2	no	—
864	C₂×Q₈	—	2	2	no	—
865	C₂×Q₈	—	8	2	no	—
866	C₂×Q₈	—	43	1	no	—
867	C₂×Q₈	—	43	2	no	—
868	C₂×Q₈	—	43	4	no	—
869	C₂×Q₈	—	43	1	no	—
870	C₂×Q₈	—	86	1	no	—
871	C₂×Q₈	—	86	2	no	—
872	C₂×Q₈	—	86	2	no	—
873	C₂×Q₈	—	86	2	no	—
874	C₂×Q₈	—	86	1	no	—
875	C₂×Q₈	—	86	1	no	—
876	C₂×Q₈	—	344	2	no	—
877	C₂×Q₈	D₄×D₄₃	1	1	yes	characteristic
878	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
879	C₂×D₄	—	43	4	no	—
880	C₂×D₄	—	43	1	no	—
881	C₂×D₄	—	86	2	no	—
882	C₂×D₄	—	86	1	no	—
883	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
884	C₂²×C₄	—	2	1	no	—
885	C₂²×C₄	—	2	2	no	—
886	C₂²×C₄	—	43	1	no	—
887	C₂²×C₄	—	43	1	no	—
888	C₂²×C₄	—	43	1	no	—
889	C₂²×C₄	—	86	2	no	—
890	C₂²×C₄	—	86	1	no	—
891	C₂²×C₄	—	86	1	no	—
892	C₂²×C₄	—	86	1	no	—
893	C₂²×C₄	—	86	1	no	—
894	C₂²×C₄	—	86	2	no	—
895	C₂²×C₄	—	86	1	no	—
896	C₂²×C₄	—	86	2	no	—
897	C₂²×C₄	—	86	1	no	—
898	C₂²×C₄	—	344	2	no	—
899	SD₁₆	—	43	4	no	—
900	SD₁₆	—	43	4	no	—
901	SD₁₆	—	43	4	no	—
902	SD₁₆	Q₈×D₄₃	1	4	yes	complemented
903	M₁₆	—	86	4	no	—
904	C₂×C₈	—	43	1	no	—
905	C₂×C₈	—	43	4	no	—
906	C₂×C₈	—	43	1	no	—
907	C₂×C₈	—	43	2	no	—
908	C₂×C₈	—	86	2	no	—
909	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
910	C₂×C₈	C₂³×D₄₃	1	2	yes	—
911	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	43	2	no	—
919	C₄⋊C₄	—	43	2	no	—
920	C₄⋊C₄	—	43	1	no	—
921	C₄⋊C₄	—	43	2	no	—
922	C₄⋊C₄	—	43	2	no	—
923	C₄⋊C₄	—	43	2	no	—
924	C₄⋊C₄	—	43	2	no	—
925	C₄⋊C₄	—	43	1	no	—
926	C₄⋊C₄	—	43	2	no	—
927	C₄⋊C₄	—	43	1	no	—
928	C₄⋊C₄	—	43	2	no	—
929	C₄⋊C₄	—	86	1	no	—
930	C₄⋊C₄	—	86	1	no	—
931	C₄⋊C₄	—	86	2	no	—
932	C₄⋊C₄	—	86	1	no	—
933	C₄⋊C₄	—	86	1	no	—
934	C₄⋊C₄	—	86	2	no	—
935	C₄⋊C₄	—	86	2	no	—
936	C₄⋊C₄	—	86	2	no	—
937	C₄⋊C₄	—	86	2	no	—
938	C₄⋊C₄	—	86	2	no	—
939	C₄⋊C₄	—	86	2	no	—
940	C₄⋊C₄	—	86	2	no	—
941	C₄⋊C₄	—	86	2	no	—
942	C₄⋊C₄	—	86	2	no	—
943	C₄⋊C₄	—	86	2	no	—
944	C₄⋊C₄	—	86	2	no	—
945	C₄⋊C₄	—	86	1	no	—
946	C₄⋊C₄	—	86	1	no	—
947	C₄⋊C₄	—	86	2	no	—
948	C₄⋊C₄	—	86	2	no	—
949	C₄⋊C₄	—	86	2	no	—
950	C₄⋊C₄	—	86	2	no	—
951	C₄⋊C₄	—	86	2	no	—
952	C₄⋊C₄	—	86	1	no	—
953	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
954	C₄⋊C₄	D₄×D₄₃	1	2	yes	—
955	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
956	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
957	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
958	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
959	C₂²⋊C₄	—	2	2	no	—
960	C₂²⋊C₄	—	2	1	no	—
961	C₂²⋊C₄	—	43	2	no	—
962	C₂²⋊C₄	—	43	2	no	—
963	C₂²⋊C₄	—	86	2	no	—
964	C₂²⋊C₄	—	86	1	no	—
965	C₂²⋊C₄	—	86	2	no	—
966	C₂²⋊C₄	—	86	2	no	—
967	C₂²⋊C₄	—	86	1	no	—
968	C₂²⋊C₄	—	86	2	no	—
969	C₂²⋊C₄	—	86	2	no	—
970	C₂²⋊C₄	—	86	1	no	—
971	C₄²	—	2	1	no	—
972	C₄²	—	2	2	no	—
973	C₄²	—	43	1	no	—
974	C₄²	—	43	1	no	—
975	C₄²	—	43	1	no	—
976	C₄²	—	43	2	no	—
977	C₄²	—	86	1	no	—
978	C₄²	—	86	1	no	—
979	C₄²	—	86	2	no	—
980	C₄²	—	86	2	no	—
981	C₄²	—	86	2	no	—
982	C₄²	—	86	2	no	—
983	C₄²	—	86	1	no	—
984	C₄²	—	86	2	no	—
985	C₄²	C₂³×D₄₃	1	1	yes	characteristic
986	C₄²	C₂³×D₄₃	1	2	yes	—
987	C₂³	—	2	1	no	—
988	C₂³	—	43	1	no	—
989	C₂³	—	86	4	no	—
990	C₂³	—	86	1	no	—
991	C₂³	—	344	1	no	—
992	C₂³	—	344	1	no	—
993	Q₈	—	2	2	no	—
994	Q₈	—	2	1	no	—
995	Q₈	—	4	2	no	—
996	Q₈	—	8	2	no	—
997	Q₈	—	8	2	no	—
998	Q₈	—	8	1	no	—
999	Q₈	—	43	2	no	—
1000	Q₈	—	86	4	no	—
1001	Q₈	—	86	2	no	—
1002	Q₈	—	86	1	no	—
1003	Q₈	—	344	1	no	—
1004	Q₈	—	344	2	no	—
1005	Q₈	—	344	2	no	—
1006	Q₈	—	172	2	no	—
1007	Q₈	—	172	2	no	—
1008	Q₈	C₂×Q₈×D₄₃	1	2	yes	—
1009	D₄	—	2	1	no	—
1010	D₄	—	43	2	no	—
1011	D₄	—	86	4	no	—
1012	D₄	—	86	1	no	—
1013	D₄	C₂×Q₈×D₄₃	1	2	yes	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	2	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	4	2	no	—
1020	C₂×C₄	—	8	2	no	—
1021	C₂×C₄	—	43	1	no	—
1022	C₂×C₄	—	43	2	no	—
1023	C₂×C₄	—	43	2	no	—
1024	C₂×C₄	—	43	1	no	—
1025	C₂×C₄	—	43	1	no	—
1026	C₂×C₄	—	43	2	no	—
1027	C₂×C₄	—	43	2	no	—
1028	C₂×C₄	—	86	4	no	—
1029	C₂×C₄	—	86	1	no	—
1030	C₂×C₄	—	86	2	no	—
1031	C₂×C₄	—	86	2	no	—
1032	C₂×C₄	—	86	1	no	—
1033	C₂×C₄	—	86	2	no	—
1034	C₂×C₄	—	86	1	no	—
1035	C₂×C₄	—	344	2	no	—
1036	C₂×C₄	—	344	1	no	—
1037	C₂×C₄	—	344	2	no	—
1038	C₂×C₄	—	344	1	no	—
1039	C₂×C₄	—	344	1	no	—
1040	C₂×C₄	—	344	1	no	—
1041	C₂×C₄	—	344	2	no	—
1042	C₂×C₄	—	172	1	no	—
1043	C₂×C₄	—	172	2	no	—
1044	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
1045	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1046	C₂×C₄	C₂×D₄×D₄₃	1	2	yes	—
1047	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1048	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1049	C₈	—	2	1	no	—
1050	C₈	—	2	2	no	—
1051	C₈	—	43	2	no	—
1052	C₈	—	86	1	no	—
1053	C₈	—	86	2	no	—
1054	C₈	C₂×Q₈×D₄₃	1	2	yes	—
1055	C₂²	—	2	2	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	1	no	—
1058	C₂²	—	43	2	no	—
1059	C₂²	—	86	1	no	—
1060	C₂²	—	86	1	no	—
1061	C₂²	—	86	2	no	—
1062	C₂²	—	344	4	no	—
1063	C₂²	—	172	1	no	—
1064	C₂²	—	172	1	no	—
1065	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1066	C₄	—	2	2	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	2	2	no	—
1069	C₄	—	2	1	no	—
1070	C₄	—	4	1	no	—
1071	C₄	—	4	2	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	4	2	no	—
1074	C₄	—	43	2	no	—
1075	C₄	—	86	2	no	—
1076	C₄	—	86	1	no	—
1077	C₄	—	86	2	no	—
1078	C₄	—	86	2	no	—
1079	C₄	—	86	1	no	—
1080	C₄	—	172	1	no	—
1081	C₄	—	172	2	no	—
1082	C₄	—	172	2	no	—
1083	C₄	—	172	1	no	—
1084	C₄	#14583705	1	2	yes	—
1085	C₄	C₂²×Q₈×D₄₃	1	1	yes	characteristic
1086	C₄	2₋¹⁺⁴×D₄₃	1	1	yes	characteristic
1087	C₂	—	4	2	no	—
1088	C₂	—	86	2	no	—
1089	C₂	—	172	2	no	—
1090	C₂	D₄×Q₈×D₄₃	1	1	yes	characteristic
1091	C₂	C₂×#14583705	1	1	yes	characteristic
1092	C₂	#19149367	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	Q₈×SD₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	C₂×D₄×D₄₃	C₂³
hypercenter	Q₈×SD₁₆	D₄₃
hypocenter	C₄₃	#61371
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ Q₈×SD₁₆

Complements

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

N	H ≅ G/N	type
1. #19148404	C₂	semidirect
3. #19147547	C₂	semidirect
4. #19147533	C₂	semidirect
5. #19147516	C₂	semidirect
6. #19147515	C₂	semidirect
7. #19147509	C₂	semidirect
8. #19147501	C₂	semidirect
9. #19147475	C₂	semidirect
10. #19147472	C₂	semidirect
11. #19147471	C₂	semidirect
12. #19147468	C₂	semidirect
13. #19147452	C₂	semidirect
14. #19145120	C₂	semidirect
15. #19145104	C₂	semidirect
16. #19144430	C₂	semidirect
18. #19144395	C₂	semidirect
20. #19143524	C₂	semidirect
23. Q₈×SD₁₆×C₄₃	C₂	semidirect
26. #14583629	C₂²	semidirect
27. #14583628	C₂²	semidirect
29. #14583627	C₂²	semidirect
30. #14583625	C₂²	semidirect
32. #14583624	C₂²	semidirect
56. #14583306	C₂²	semidirect
57. #14583306	C₂²	semidirect
58. #14583305	C₂²	semidirect
59. #14583305	C₂²	semidirect
60. #14583302	C₂²	semidirect
61. #14583302	C₂²	semidirect
62. #14583301	C₂²	semidirect
63. #14583299	C₂²	semidirect
64. #14583299	C₂²	semidirect
65. #14583299	C₂²	semidirect
66. #14583297	C₂²	semidirect
67. #14583296	C₂²	semidirect
68. #14583209	C₂²	semidirect
69. #14583209	C₂²	semidirect
70. #14583208	C₂²	semidirect
71. #14583207	C₂²	semidirect
72. #14583206	C₂²	semidirect
73. #14583204	C₂²	semidirect
80. #14583195	C₂²	semidirect
81. #14583194	C₂²	semidirect
82. #14583192	C₂²	semidirect
83. #14583191	C₂²	semidirect
86. #14583183	C₂²	semidirect
87. #14583181	C₂²	semidirect
92. #14583030	C₂²	semidirect
93. #14583028	C₂²	semidirect
94. #14583026	C₂²	semidirect
95. C₈×Dic₈₆	C₂²	semidirect
96. C₈×Dic₈₆	C₂²	semidirect
124. Q₈²×C₄₃	C₂²	semidirect
126. C₄₃×#498	C₂²	semidirect
127. C₄₃×#498	C₂²	semidirect
130. C₄₃×#475	C₂²	semidirect
131. C₄₃×#475	C₂²	semidirect
132. C₈×Q₈×C₄₃	C₂²	semidirect
142. SD₁₆×D₄₃	Q₈	semidirect
329. Q₈×D₄₃	C₂×Q₈	semidirect
352. SD₁₆×C₄₃	C₂×Q₈	semidirect
376. #10621884	C₂×Q₈	semidirect
377. #10621883	C₂×Q₈	semidirect
436. #10621873	C₂×Q₈	semidirect
439. C₈×D₄₃	C₂×Q₈	semidirect
554. Q₈×SD₁₆	D₄₃	semidirect
573. Q₈²	C₂×D₄₃	semidirect
616. #498	C₂×D₄₃	semidirect
617. #498	C₂×D₄₃	semidirect
640. #475	C₂×D₄₃	semidirect
641. #475	C₂×D₄₃	semidirect
651. C₈×Q₈	C₂×D₄₃	semidirect
681. C₄₃	#61371	semidirect
902. SD₁₆	Q₈×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19148404	2
#19148390	2
#19147547	2
#19147533	2
#19147516	2
#19147515	2
#19147509	2
#19147501	2
#19147475	2
#19147472	2
#19147471	2
#19147468	2
#19147452	2
#19145120	2
#19145104	2
#19144430	2
#19144421	2
#19144395	2
#19144393	2
#19143524	2
#19143449	2
C₄×SD₁₆×D₄₃	2
Q₈×SD₁₆×C₄₃	2
#61371	43