Subgroups — #25979045

Order 11008.

1834 conjugacy classes of subgroups.

The subgroup lattice has 1146 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148558	C₂	1	1	yes	maximal, characteristic, complemented
2	#19147591	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×#10621884	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147409	C₂	1	1	yes	maximal, characteristic, complemented
5	#19147309	C₂	1	1	yes	maximal, characteristic, complemented
6	#19147008	C₂	1	1	yes	maximal, characteristic, complemented
7	#19147002	C₂	1	2	yes	maximal, complemented
8	#19146878	C₂	1	1	yes	maximal, characteristic, complemented
9	#19146831	C₂	1	1	yes	maximal, characteristic, complemented
10	#19146781	C₂	1	2	yes	maximal, complemented
11	#19146625	C₂	1	2	yes	maximal, complemented
12	#19146303	C₂	1	2	yes	maximal, complemented
13	D₄×#10621884	C₂	1	1	yes	maximal, characteristic, complemented
14	#19145206	C₂	1	2	yes	maximal, complemented
15	#19145155	C₂	1	1	yes	maximal, characteristic, complemented
16	#19144824	C₂	1	2	yes	maximal, complemented
17	#19144773	C₂	1	2	yes	maximal, complemented
18	#19144751	C₂	1	1	yes	maximal, characteristic, complemented
19	#19144746	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143571	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143454	C₂	1	2	yes	maximal, complemented
22	C₄×#13063345	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3518	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063345	C₂²	1	1	yes	characteristic
25	C₂²×#10621884	C₂²	1	2	yes	—
26	#14583634	C₂²	1	1	yes	characteristic
27	#14583619	C₂²	1	1	yes	characteristic
28	#14583614	C₂²	1	2	yes	—
29	#14583574	—	2	2	no	—
30	Q₈×D₁₇₂	C₂²	1	1	yes	characteristic
31	#14583559	—	2	1	no	—
32	#14583546	—	2	1	no	—
33	#14583545	C₂²	1	2	yes	—
34	D₄×D₁₇₂	C₂²	1	1	yes	characteristic
35	#14583520	C₂²	1	2	yes	—
36	#14583485	—	2	2	no	—
37	#14583449	C₂²	1	1	yes	characteristic
38	#14583434	—	2	1	no	—
39	#124×D₄₃	—	2	1	no	—
40	#14583373	C₂²	1	2	yes	—
41	C₄×#10621898	C₂²	1	1	yes	characteristic
42	#14583295	C₂²	1	1	yes	characteristic, complemented
43	#14583295	C₂²	1	2	yes	complemented
44	#14583281	C₂²	1	2	yes	complemented
45	#14583273	C₂²	1	1	yes	characteristic
46	#14583261	C₂²	1	2	yes	complemented
47	#14583258	C₂²	1	2	yes	complemented
48	#14583249	C₂²	1	1	yes	characteristic, complemented
49	#14583247	C₂²	1	1	yes	characteristic
50	#14583240	C₂²	1	2	yes	complemented
51	#14583237	C₂²	1	2	yes	complemented
52	#14583237	C₂²	1	2	yes	complemented
53	#14583223	C₂²	1	2	yes	—
54	#14583223	C₂²	1	2	yes	complemented
55	#14583220	C₂²	1	2	yes	complemented
56	#14583194	C₂²	1	2	yes	complemented
57	#14583191	C₂²	1	1	yes	characteristic, complemented
58	#14583186	C₂²	1	1	yes	characteristic
59	#14583186	C₂²	1	2	yes	—
60	#14583184	C₂²	1	2	yes	complemented
61	#14583184	C₂²	1	1	yes	characteristic, complemented
62	#14583179	C₂²	1	1	yes	characteristic, complemented
63	#14583176	C₂²	1	2	yes	complemented
64	#14583155	C₂²	1	2	yes	complemented
65	#14583150	C₂²	1	2	yes	—
66	#14583130	C₂²	1	2	yes	—
67	#14583130	C₂²	1	2	yes	complemented
68	#14583130	C₂²	1	2	yes	complemented
69	#14583126	C₂²	1	2	yes	complemented
70	#14583121	C₂²	1	2	yes	complemented
71	#14583121	C₂²	1	2	yes	complemented
72	#14583111	C₂²	1	2	yes	—
73	#14583111	C₂²	1	2	yes	complemented
74	#14583106	C₂²	1	1	yes	characteristic, complemented
75	#14583101	C₂²	1	1	yes	characteristic
76	#14583099	C₂²	1	1	yes	characteristic
77	#14583094	C₂²	1	1	yes	characteristic
78	#14583059	C₂²	1	2	yes	—
79	#14583055	C₂²	1	2	yes	complemented
80	#14583049	C₂²	1	2	yes	—
81	#14583044	C₂²	1	2	yes	complemented
82	#14583038	C₂²	1	2	yes	—
83	#14583032	C₂²	1	2	yes	—
84	#14583030	C₂²	1	1	yes	characteristic, complemented
85	Q₈×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
86	#14583009	C₂²	1	2	yes	complemented
87	#14583004	C₂²	1	2	yes	complemented
88	#14582997	C₂²	1	2	yes	—
89	#14582997	C₂²	1	2	yes	—
90	#14582997	C₂²	1	2	yes	complemented
91	#14582997	C₂²	1	2	yes	complemented
92	C₄×#10621885	C₂²	1	1	yes	characteristic, complemented
93	C₄×#10621885	C₂²	1	1	yes	characteristic, complemented
94	C₄×#10621884	C₂²	1	1	yes	characteristic
95	C₄×#10621884	C₂²	1	2	yes	—
96	C₄×#10621884	C₂²	1	1	yes	characteristic
97	C₄×#10621884	C₂²	1	2	yes	complemented
98	C₄×#10621884	C₂²	1	2	yes	complemented
99	C₄×#10621884	C₂²	1	2	yes	complemented
100	C₄×#10621883	C₂²	1	1	yes	characteristic, complemented
101	C₄×#10621883	C₂²	1	1	yes	characteristic, complemented
102	C₄×#10621882	C₂²	1	1	yes	characteristic
103	C₄×#10621882	C₂²	1	1	yes	characteristic
104	#14582977	C₂²	1	1	yes	characteristic
105	#14582971	C₂²	1	2	yes	complemented
106	D₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
107	D₄×C₄₃⋊C₈	C₂²	1	2	yes	complemented
108	#14582960	C₂²	1	2	yes	complemented
109	#14582956	C₂²	1	1	yes	characteristic, complemented
110	#14582935	C₂²	1	2	yes	complemented
111	#14582935	C₂²	1	1	yes	characteristic, complemented
112	#14582908	C₂²	1	2	yes	complemented
113	#14582903	C₂²	1	2	yes	—
114	#14582895	C₂²	1	1	yes	characteristic, complemented
115	#14582893	C₂²	1	1	yes	characteristic
116	#14582855	C₂²	1	2	yes	complemented
117	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
118	Q₈²×C₄₃	C₂²	1	1	yes	characteristic, complemented
119	C₄₃×#556	—	2	2	no	—
120	C₄₃×#556	—	2	1	no	—
121	C₄₃×#556	C₂²	1	1	yes	characteristic, complemented
122	C₄₃×#556	C₂²	1	2	yes	complemented
123	C₄₃×#555	—	2	1	no	—
124	C₄₃×#555	C₂²	1	1	yes	characteristic
125	D₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
126	C₄₃×#548	C₂²	1	2	yes	complemented
127	C₄₃×#542	—	2	2	no	—
128	C₄₃×#542	C₂²	1	2	yes	complemented
129	C₄₃×#533	—	2	1	no	—
130	C₄₃×#533	C₂²	1	1	yes	characteristic, complemented
131	C₄₃×#529	—	2	1	no	—
132	C₄₃×#529	C₂²	1	1	yes	characteristic
133	C₄₃×#519	C₂²	1	2	yes	complemented
134	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic, complemented
135	C₂×#10621898	—	2	1	no	—
136	C₂×#10621898	C₂³	1	1	yes	characteristic
137	C₂×Q₈×D₄₃	—	2	1	no	—
138	C₂²×D₁₇₂	C₂³	1	2	yes	—
139	C₂×D₄×D₄₃	—	2	1	no	—
140	#13063345	—	2	4	no	—
141	C₂×#10621885	C₂³	1	1	yes	characteristic
142	C₂×#10621885	C₂³	1	2	yes	—
143	C₂×#10621883	C₂³	1	1	yes	characteristic
144	C₂×#10621884	—	2	8	no	—
145	C₂×#10621884	C₂³	1	2	yes	—
146	C₂×#10621884	C₂³	1	2	yes	—
147	C₂×#10621884	C₂³	1	2	yes	—
148	C₂×#10621884	C₂³	1	2	yes	—
149	C₂×#10621884	C₂³	1	1	yes	characteristic
150	C₂×#10621882	C₂³	1	1	yes	characteristic
151	C₂×#10621882	C₂³	1	2	yes	—
152	C₂×#10621877	C₂³	1	2	yes	—
153	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
154	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
155	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
156	#13063325	C₂³	1	2	yes	—
157	#13063325	C₂³	1	1	yes	characteristic
158	#13063322	C₂³	1	1	yes	characteristic
159	#13063320	—	2	2	no	—
160	#13063318	—	2	2	no	—
161	#13063314	—	2	1	no	—
162	#13063313	—	2	1	no	—
163	#13063313	C₂³	1	2	yes	—
164	#13063312	—	2	1	no	—
165	#13063311	—	2	2	no	—
166	#13063311	—	2	2	no	—
167	#13063311	—	2	2	no	—
168	#13063310	—	2	2	no	—
169	#13063310	—	2	2	no	—
170	#13063307	—	2	2	no	—
171	#13063305	—	2	2	no	—
172	#13063305	—	2	1	no	—
173	#13063304	C₂³	1	2	yes	—
174	#13063303	—	2	2	no	—
175	#13063300	—	2	1	no	—
176	#13063299	—	2	1	no	—
177	#13063299	C₂³	1	2	yes	—
178	#13063299	C₂³	1	2	yes	—
179	#13063298	—	2	2	no	—
180	#13063296	—	2	2	no	—
181	#13063295	—	2	2	no	—
182	#13063293	—	2	2	no	—
183	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
184	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
185	#13063290	—	2	1	no	—
186	C₄×D₁₇₂	—	2	1	no	—
187	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
188	C₄×D₁₇₂	C₂³	1	2	yes	—
189	C₄×D₁₇₂	C₂³	1	2	yes	—
190	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
191	C₄×D₁₇₂	C₂³	1	2	yes	—
192	#13063287	—	2	2	no	—
193	#13063287	—	2	2	no	—
194	#13063287	—	2	1	no	—
195	C₄×C₂²⋊D₄₃	—	2	1	no	—
196	C₄×C₂²⋊D₄₃	—	2	1	no	—
197	#13063284	C₂³	1	1	yes	characteristic
198	#13063284	C₂³	1	2	yes	—
199	#13063283	—	2	2	no	—
200	#13063282	—	2	1	no	—
201	C₂²⋊C₄×D₄₃	—	2	2	no	—
202	C₂²⋊C₄×D₄₃	—	2	2	no	—
203	C₂²⋊C₄×D₄₃	—	2	2	no	—
204	C₄²×D₄₃	—	2	1	no	—
205	#13063258	C₂³	1	1	yes	characteristic
206	#13063258	C₂³	1	2	yes	—
207	#13063258	C₂³	1	2	yes	—
208	#13063258	C₂³	1	1	yes	characteristic
209	#13063256	C₂³	1	2	yes	—
210	#13063256	C₂³	1	1	yes	characteristic
211	#13063256	C₂³	1	2	yes	—
212	#13063256	C₂³	1	2	yes	—
213	#13063256	C₂³	1	2	yes	—
214	#13063256	C₂³	1	1	yes	characteristic
215	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
216	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
217	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
218	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
219	#13063249	C₂³	1	2	yes	—
220	#13063249	C₂³	1	2	yes	—
221	#13063249	C₂³	1	2	yes	—
222	#13063249	C₂³	1	2	yes	—
223	#13063249	C₂³	1	2	yes	—
224	#13063249	C₂³	1	1	yes	characteristic
225	#13063249	C₂³	1	1	yes	characteristic
226	#13063248	C₂³	1	2	yes	—
227	#13063248	C₂³	1	1	yes	characteristic
228	#13063248	C₂³	1	1	yes	characteristic
229	#13063246	C₂³	1	2	yes	—
230	#13063246	C₂³	1	1	yes	characteristic
231	#13063246	C₂³	1	1	yes	characteristic
232	#13063245	C₂³	1	1	yes	characteristic
233	#13063245	C₂³	1	2	yes	—
234	#13063245	C₂³	1	2	yes	—
235	#13063245	C₂³	1	2	yes	—
236	#13063245	C₂³	1	2	yes	—
237	#13063245	C₂³	1	2	yes	—
238	#13063245	C₂³	1	1	yes	characteristic
239	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
240	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
241	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
242	#13063236	C₂³	1	2	yes	—
243	#13063236	C₂³	1	2	yes	—
244	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
245	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
246	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
247	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
248	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
249	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
250	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
251	C₄⋊Q₈×C₄₃	—	2	1	no	—
252	C₄⋊Q₈×C₄₃	—	2	1	no	—
253	C₄⋊Q₈×C₄₃	—	2	2	no	—
254	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
255	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
256	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
257	#126×C₄₃	—	2	2	no	—
258	#126×C₄₃	—	2	2	no	—
259	#126×C₄₃	—	2	2	no	—
260	#126×C₄₃	—	2	2	no	—
261	#126×C₄₃	D₄	1	2	yes	—
262	#125×C₄₃	—	2	1	no	—
263	#125×C₄₃	D₄	1	1	yes	characteristic
264	#124×C₄₃	—	2	2	no	—
265	#124×C₄₃	—	2	2	no	—
266	#124×C₄₃	—	2	2	no	—
267	#124×C₄₃	—	2	2	no	—
268	#124×C₄₃	D₄	1	1	yes	characteristic
269	#124×C₄₃	C₂³	1	2	yes	—
270	#123×C₄₃	—	2	2	no	—
271	#123×C₄₃	D₄	1	2	yes	—
272	C₂²⋊Q₈×C₄₃	—	2	1	no	—
273	C₂²⋊Q₈×C₄₃	—	2	1	no	—
274	C₂²⋊Q₈×C₄₃	—	2	2	no	—
275	C₂²⋊Q₈×C₄₃	—	2	2	no	—
276	C₂²⋊Q₈×C₄₃	—	2	2	no	—
277	C₂²⋊Q₈×C₄₃	D₄	1	1	yes	characteristic
278	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
279	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
280	#121×C₄₃	—	2	1	no	—
281	#121×C₄₃	—	2	2	no	—
282	#121×C₄₃	D₄	1	1	yes	characteristic
283	#121×C₄₃	C₂³	1	2	yes	—
284	C₄×Q₈×C₄₃	—	2	1	no	—
285	C₄×Q₈×C₄₃	—	2	2	no	—
286	C₄×Q₈×C₄₃	—	2	2	no	—
287	C₄×Q₈×C₄₃	—	2	2	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×Q₈×C₄₃	C₂³	1	2	yes	—
292	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
293	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
294	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
295	C₄×D₄×C₄₃	—	2	1	no	—
296	C₄×D₄×C₄₃	—	2	1	no	—
297	C₄×D₄×C₄₃	—	2	1	no	—
298	C₄×D₄×C₄₃	—	2	2	no	—
299	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
300	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
301	C₄×D₄×C₄₃	C₂³	1	2	yes	—
302	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
303	#117×C₄₃	—	2	1	no	—
304	#117×C₄₃	—	2	1	no	—
305	#117×C₄₃	—	2	1	no	—
306	#117×C₄₃	—	2	2	no	—
307	#117×C₄₃	—	2	2	no	—
308	#117×C₄₃	—	2	1	no	—
309	#117×C₄₃	C₂³	1	1	yes	characteristic
310	#117×C₄₃	C₂³	1	2	yes	—
311	#117×C₄₃	C₂³	1	2	yes	—
312	C₂×C₄²×C₄₃	—	2	1	no	—
313	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
314	C₂³×D₄₃	—	2	2	no	—
315	#41×C₄₃	—	2	2	no	—
316	#41×C₄₃	—	4	1	no	—
317	C₂×Q₈×C₄₃	—	2	2	no	—
318	C₂×Q₈×C₄₃	—	2	1	no	—
319	C₂×Q₈×C₄₃	—	2	2	no	—
320	C₂×Q₈×C₄₃	—	2	4	no	—
321	C₂×Q₈×C₄₃	—	4	2	no	—
322	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
323	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
324	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
325	C₂×D₄×C₄₃	—	2	1	no	—
326	C₂×D₄×C₄₃	—	2	2	no	—
327	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
328	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
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	—	2	2	no	—
334	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
338	C₂×C₂²⋊D₄₃	—	2	1	no	—
339	C₂×C₂²⋊D₄₃	—	2	2	no	—
340	C₂×C₂²⋊D₄₃	—	2	2	no	—
341	Q₈×D₄₃	—	8	2	no	—
342	D₄×D₄₃	—	8	2	no	—
343	#10621898	—	2	2	no	—
344	#10621898	—	4	1	no	—
345	#10621898	—	8	2	no	—
346	C₂×D₁₇₂	—	2	2	no	—
347	C₂×D₁₇₂	—	2	1	no	—
348	C₂×D₁₇₂	—	2	1	no	—
349	C₂×D₁₇₂	—	2	4	no	—
350	C₂×D₁₇₂	—	4	2	no	—
351	C₂×D₁₇₂	C₂⁴	1	2	yes	—
352	C₂×D₁₇₂	C₂⁴	1	1	yes	characteristic
353	C₂×C₄×D₄₃	—	2	1	no	—
354	C₂×C₄×D₄₃	—	2	1	no	—
355	C₂×C₄×D₄₃	—	2	1	no	—
356	C₂×C₄×D₄₃	—	2	2	no	—
357	C₂×C₄×D₄₃	—	2	2	no	—
358	C₂×C₄×D₄₃	—	2	2	no	—
359	C₂×Dic₈₆	—	2	1	no	—
360	C₂×Dic₈₆	—	2	2	no	—
361	C₂×Dic₈₆	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
366	C₄⋊C₄×C₄₃	—	2	2	no	—
367	C₄⋊C₄×C₄₃	—	2	2	no	—
368	C₄⋊C₄×C₄₃	—	2	2	no	—
369	C₄⋊C₄×C₄₃	—	2	2	no	—
370	C₄⋊C₄×C₄₃	—	2	1	no	—
371	C₄⋊C₄×C₄₃	—	2	2	no	—
372	C₄⋊C₄×C₄₃	—	2	2	no	—
373	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
374	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
375	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
376	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
377	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
378	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
379	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
380	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
381	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
382	C₂²⋊C₄×C₄₃	—	2	1	no	—
383	C₂²⋊C₄×C₄₃	—	2	1	no	—
384	C₂²⋊C₄×C₄₃	—	2	2	no	—
385	C₂²⋊C₄×C₄₃	—	2	2	no	—
386	C₂²⋊C₄×C₄₃	—	2	2	no	—
387	C₂²⋊C₄×C₄₃	—	2	2	no	—
388	C₂²⋊C₄×C₄₃	—	2	2	no	—
389	C₂²⋊C₄×C₄₃	—	2	1	no	—
390	C₂²⋊C₄×C₄₃	—	2	2	no	—
391	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
392	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
393	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
394	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
395	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
396	C₄²×C₄₃	—	2	1	no	—
397	C₄²×C₄₃	—	2	1	no	—
398	C₄²×C₄₃	—	2	1	no	—
399	C₄²×C₄₃	—	2	2	no	—
400	C₄²×C₄₃	—	2	2	no	—
401	C₄²×C₄₃	—	2	2	no	—
402	C₄²×C₄₃	—	2	2	no	—
403	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
404	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
405	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
406	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
407	C₄²×C₄₃	C₂⁴	1	2	yes	—
408	C₂²⋊Dic₄₃	—	2	2	no	—
409	C₂²⋊Dic₄₃	—	2	2	no	—
410	C₂²⋊Dic₄₃	—	2	1	no	—
411	#10621885	—	2	2	no	—
412	#10621885	—	4	2	no	—
413	#10621884	—	2	4	no	—
414	#10621884	—	2	4	no	—
415	#10621884	—	2	4	no	—
416	#10621884	—	4	2	no	—
417	#10621884	#41	1	4	yes	complemented
418	#10621883	—	2	2	no	—
419	#10621882	—	2	2	no	—
420	#10621882	—	4	2	no	—
421	(C₂×D₄₃)⋊C₄	—	2	1	no	—
422	(C₂×D₄₃)⋊C₄	—	2	2	no	—
423	(C₂×D₄₃)⋊C₄	—	2	2	no	—
424	(C₂×D₄₃)⋊C₄	—	2	2	no	—
425	(C₂×D₄₃)⋊C₄	—	2	2	no	—
426	(C₂×D₄₃)⋊C₄	—	2	2	no	—
427	(C₂×D₄₃)⋊C₄	—	2	1	no	—
428	(C₂×D₄₃)⋊C₄	—	2	2	no	—
429	(C₂×D₄₃)⋊C₄	—	2	2	no	—
430	C₄⋊Dic₄₃	—	2	2	no	—
431	C₄⋊Dic₄₃	—	2	1	no	—
432	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
433	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
434	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
435	Dic₄₃⋊C₄	—	2	1	no	—
436	Dic₄₃⋊C₄	—	2	1	no	—
437	Dic₄₃⋊C₄	—	2	2	no	—
438	C₄×Dic₄₃	—	2	1	no	—
439	C₄×Dic₄₃	—	2	1	no	—
440	C₄×Dic₄₃	—	2	1	no	—
441	C₄×Dic₄₃	—	2	2	no	—
442	#10621877	—	4	2	no	—
443	C₂×C₄₃⋊C₈	—	2	4	no	—
444	C₂×C₄₃⋊C₈	—	2	2	no	—
445	C₂×C₄₃⋊C₈	—	4	1	no	—
446	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
447	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
448	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
449	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
450	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
451	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
452	C₂³×C₄₃	—	2	1	no	—
453	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
454	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
455	C₂²×D₄₃	—	2	1	no	—
456	C₂²×D₄₃	—	2	2	no	—
457	C₂²×D₄₃	—	4	4	no	—
458	C₂²×D₄₃	—	8	2	no	—
459	C₂²×D₄₃	—	8	2	no	—
460	Q₈×C₄₃	—	2	2	no	—
461	Q₈×C₄₃	—	2	1	no	—
462	Q₈×C₄₃	—	2	2	no	—
463	Q₈×C₄₃	—	2	2	no	—
464	Q₈×C₄₃	—	4	4	no	—
465	Q₈×C₄₃	—	8	2	no	—
466	Q₈×C₄₃	—	8	1	no	—
467	Q₈×C₄₃	C₂×#41	1	2	yes	—
468	D₄×C₄₃	—	2	2	no	—
469	D₄×C₄₃	—	2	1	no	—
470	D₄×C₄₃	—	2	1	no	—
471	D₄×C₄₃	—	4	2	no	—
472	D₄×C₄₃	—	4	2	no	—
473	D₄×C₄₃	—	8	2	no	—
474	C₂×C₄×C₄₃	—	2	1	no	—
475	C₂×C₄×C₄₃	—	2	2	no	—
476	C₂×C₄×C₄₃	—	2	2	no	—
477	C₂×C₄×C₄₃	—	2	1	no	—
478	C₂×C₄×C₄₃	—	2	1	no	—
479	C₂×C₄×C₄₃	—	2	2	no	—
480	C₂×C₄×C₄₃	—	2	1	no	—
481	C₂×C₄×C₄₃	—	2	2	no	—
482	C₂×C₄×C₄₃	—	2	2	no	—
483	C₂×C₄×C₄₃	—	2	1	no	—
484	C₂×C₄×C₄₃	—	4	1	no	—
485	C₂×C₄×C₄₃	—	4	2	no	—
486	C₂×C₄×C₄₃	—	4	4	no	—
487	C₂×C₄×C₄₃	—	4	2	no	—
488	C₂×C₄×C₄₃	—	8	1	no	—
489	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
498	C₂²⋊D₄₃	—	4	2	no	—
499	C₂²⋊D₄₃	—	8	2	no	—
500	C₂²⋊D₄₃	—	8	2	no	—
501	C₂×Dic₄₃	—	2	1	no	—
502	C₂×Dic₄₃	—	2	1	no	—
503	C₂×Dic₄₃	—	2	1	no	—
504	C₂×Dic₄₃	—	2	2	no	—
505	D₁₇₂	—	2	2	no	—
506	D₁₇₂	—	2	1	no	—
507	D₁₇₂	—	2	2	no	—
508	D₁₇₂	—	4	4	no	—
509	D₁₇₂	—	4	2	no	—
510	D₁₇₂	—	8	1	no	—
511	D₁₇₂	C₂×#41	1	2	yes	—
512	C₄×D₄₃	—	4	2	no	—
513	C₄×D₄₃	—	4	2	no	—
514	C₄×D₄₃	—	8	1	no	—
515	C₄×D₄₃	—	8	2	no	—
516	C₄×D₄₃	—	8	2	no	—
517	C₄×D₄₃	—	8	2	no	—
518	Dic₈₆	—	2	1	no	—
519	Dic₈₆	—	2	1	no	—
520	Dic₈₆	—	4	2	no	—
521	Dic₈₆	—	8	2	no	—
522	C₄₃⋊C₈	—	2	1	no	—
523	C₄₃⋊C₈	—	2	2	no	—
524	C₄₃⋊C₈	—	2	1	no	—
525	C₄₃⋊C₈	—	2	1	no	—
526	C₄₃⋊C₈	—	2	2	no	—
527	C₄₃⋊C₈	C₂×#41	1	2	yes	—
528	#61474	—	43	1	no	maximal, Sylow
529	C₂²×C₄₃	—	2	2	no	—
530	C₂²×C₄₃	—	2	1	no	—
531	C₂²×C₄₃	—	2	2	no	—
532	C₂²×C₄₃	—	2	1	no	—
533	C₂²×C₄₃	—	2	2	no	—
534	C₂²×C₄₃	—	2	1	no	—
535	C₂²×C₄₃	—	4	1	no	—
536	C₂²×C₄₃	—	4	1	no	—
537	C₂²×C₄₃	—	4	1	no	—
538	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
539	C₂×D₄₃	—	2	2	no	—
540	C₂×D₄₃	—	4	1	no	—
541	C₂×D₄₃	—	4	1	no	—
542	C₂×D₄₃	—	4	2	no	—
543	C₂×D₄₃	—	4	2	no	—
544	C₂×D₄₃	—	4	2	no	—
545	C₂×D₄₃	—	16	4	no	—
546	C₄×C₄₃	—	2	1	no	—
547	C₄×C₄₃	—	2	2	no	—
548	C₄×C₄₃	—	2	1	no	—
549	C₄×C₄₃	—	2	1	no	—
550	C₄×C₄₃	—	2	2	no	—
551	C₄×C₄₃	—	2	2	no	—
552	C₄×C₄₃	—	2	2	no	—
553	C₄×C₄₃	—	2	1	no	—
554	C₄×C₄₃	—	4	1	no	—
555	C₄×C₄₃	—	4	2	no	—
556	C₄×C₄₃	—	4	2	no	—
557	C₄×C₄₃	—	4	1	no	—
558	C₄×C₄₃	#577	1	2	yes	—
559	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
560	C₄×C₄₃	#585	1	1	yes	characteristic
561	Dic₄₃	—	4	1	no	—
562	Dic₄₃	—	4	1	no	—
563	Dic₄₃	—	4	2	no	—
564	Dic₄₃	—	4	1	no	—
565	#3518	D₄₃	1	1	yes	characteristic, complemented
566	#3514	—	43	1	no	—
567	#3394	—	43	1	no	—
568	Q₈×SD₁₆	—	43	1	no	—
569	#3375	—	43	1	no	—
570	#3367	—	43	1	no	—
571	#3340	—	43	2	no	—
572	#3340	—	43	1	no	—
573	#3328	—	43	1	no	—
574	#3325	—	43	1	no	—
575	#3321	—	43	2	no	—
576	#3311	—	43	2	no	—
577	#3282	—	43	2	no	—
578	D₄×SD₁₆	—	43	1	no	—
579	#3173	—	43	2	no	—
580	#3167	—	43	1	no	—
581	#3121	—	43	2	no	—
582	#3118	—	43	2	no	—
583	#3116	—	43	1	no	—
584	#3115	—	43	1	no	—
585	#2966	—	43	1	no	—
586	#2949	—	43	2	no	—
587	C₄×#135	—	43	1	no	—
588	C₂×C₄₃	—	4	2	no	—
589	C₂×C₄₃	—	4	1	no	—
590	C₂×C₄₃	—	8	1	no	—
591	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
592	C₂×C₄₃	C₂×#577	1	1	yes	characteristic
593	C₂×C₄₃	#3584	1	1	yes	characteristic
594	D₄₃	—	4	2	no	—
595	D₄₃	—	8	2	no	—
596	C₂×#135	—	43	1	no	—
597	C₂²×SD₁₆	—	43	2	no	—
598	#559	—	43	1	no	—
599	Q₈²	C₂×D₄₃	1	1	yes	characteristic, complemented
600	#556	—	2	2	no	—
601	#556	—	2	1	no	—
602	#556	—	43	1	no	—
603	#556	C₂×D₄₃	1	1	yes	characteristic, complemented
604	#556	C₂×D₄₃	1	2	yes	complemented
605	#555	—	2	1	no	—
606	#555	—	43	2	no	—
607	#555	C₂×D₄₃	1	1	yes	characteristic
608	#551	—	86	2	no	—
609	D₄×Q₈	—	43	1	no	—
610	D₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
611	#548	—	86	1	no	—
612	#548	C₂×D₄₃	1	2	yes	complemented
613	#546	—	43	2	no	—
614	#546	—	86	1	no	—
615	D₄²	—	43	1	no	—
616	#542	—	2	2	no	—
617	#542	—	43	2	no	—
618	#542	C₂×D₄₃	1	2	yes	complemented
619	#538	—	86	2	no	—
620	#533	—	2	1	no	—
621	#533	C₂×D₄₃	1	1	yes	characteristic, complemented
622	#532	—	43	1	no	—
623	#529	—	2	1	no	—
624	#529	—	86	1	no	—
625	#529	C₂×D₄₃	1	1	yes	characteristic
626	C₂×#124	—	86	1	no	—
627	#519	C₂×D₄₃	1	2	yes	complemented
628	#518	—	43	2	no	—
629	C₄×#41	—	43	1	no	—
630	C₄×#41	C₂×D₄₃	1	1	yes	characteristic, complemented
631	#498	—	43	1	no	—
632	#498	—	43	2	no	—
633	#495	—	43	2	no	—
634	#492	—	43	1	no	—
635	#489	—	43	2	no	—
636	#489	—	43	2	no	—
637	#487	—	43	1	no	—
638	#486	—	43	1	no	—
639	#485	—	43	2	no	—
640	#485	—	43	2	no	—
641	#485	—	43	2	no	—
642	#482	—	43	2	no	—
643	#482	—	43	2	no	—
644	#482	—	43	2	no	—
645	#477	—	43	1	no	—
646	#477	—	43	2	no	—
647	#476	—	43	1	no	—
648	#476	—	43	2	no	—
649	#475	—	43	1	no	—
650	#475	—	43	2	no	—
651	#474	—	43	2	no	—
652	#474	—	43	1	no	—
653	#470	—	43	2	no	—
654	#469	—	43	2	no	—
655	#465	—	43	2	no	—
656	#465	—	43	2	no	—
657	#465	—	43	2	no	—
658	#465	—	43	2	no	—
659	#464	—	43	2	no	—
660	#464	—	43	2	no	—
661	#463	—	43	2	no	—
662	#463	—	43	2	no	—
663	#462	—	43	1	no	—
664	#461	—	43	1	no	—
665	#460	—	43	1	no	—
666	#459	—	43	1	no	—
667	#452	—	43	2	no	—
668	#451	—	43	2	no	—
669	#450	—	43	2	no	—
670	#449	—	43	2	no	—
671	#448	—	43	2	no	—
672	#447	—	43	2	no	—
673	#446	—	43	1	no	—
674	C₈×Q₈	—	43	1	no	—
675	#442	—	43	2	no	—
676	#441	—	43	2	no	—
677	#440	—	43	2	no	—
678	#440	—	43	2	no	—
679	#440	—	43	2	no	—
680	#440	—	43	2	no	—
681	C₄×Q₁₆	—	43	1	no	—
682	C₄×Q₁₆	—	43	1	no	—
683	C₄×SD₁₆	—	43	2	no	—
684	C₄×SD₁₆	—	43	2	no	—
685	C₄×SD₁₆	—	43	1	no	—
686	C₄×SD₁₆	—	43	2	no	—
687	C₄×SD₁₆	—	43	2	no	—
688	C₄×SD₁₆	—	43	1	no	—
689	C₄×SD₁₆	—	43	1	no	—
690	C₄×SD₁₆	—	43	1	no	—
691	C₄×D₈	—	43	1	no	—
692	C₄×D₈	—	43	1	no	—
693	#436	—	43	1	no	—
694	#435	—	43	2	no	—
695	C₈×D₄	—	43	1	no	—
696	C₈×D₄	—	43	2	no	—
697	#433	—	43	2	no	—
698	#432	—	43	1	no	—
699	#427	—	43	1	no	—
700	#427	—	43	2	no	—
701	#419	—	43	2	no	—
702	#418	—	43	2	no	—
703	#416	—	43	1	no	—
704	#416	—	43	1	no	—
705	#405	—	43	2	no	—
706	C₂×C₄×C₈	—	43	1	no	—
707	C₄₃	#61474	1	1	yes	characteristic, complemented, Sylow
708	C₂×#41	—	43	1	no	—
709	C₂×#41	—	86	1	no	—
710	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
711	C₂²×Q₈	—	86	1	no	—
712	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
713	C₂²×D₄	—	43	2	no	—
714	C₂²×D₄	—	86	1	no	—
715	#135	—	86	4	no	—
716	C₂×Q₁₆	—	43	1	no	—
717	C₂×Q₁₆	—	43	2	no	—
718	C₂×SD₁₆	—	43	1	no	—
719	C₂×SD₁₆	—	43	2	no	—
720	C₂×SD₁₆	—	43	2	no	—
721	C₂×SD₁₆	—	43	2	no	—
722	C₂×SD₁₆	—	43	1	no	—
723	C₂×SD₁₆	—	43	2	no	—
724	C₂×SD₁₆	—	86	8	no	—
725	C₂×D₈	—	43	1	no	—
726	C₂×D₈	—	43	2	no	—
727	C₂×M₁₆	—	43	2	no	—
728	C₂²×C₈	—	43	2	no	—
729	C₂²×C₈	—	43	1	no	—
730	C₂²×C₈	—	43	1	no	—
731	C₄⋊Q₈	—	2	1	no	—
732	C₄⋊Q₈	—	2	1	no	—
733	C₄⋊Q₈	—	2	2	no	—
734	C₄⋊Q₈	—	43	1	no	—
735	C₄⋊Q₈	—	43	2	no	—
736	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
737	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
738	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
739	#127	—	43	1	no	—
740	#126	—	2	2	no	—
741	#126	—	2	2	no	—
742	#126	—	2	2	no	—
743	#126	—	2	2	no	—
744	#126	—	86	2	no	—
745	#126	—	86	2	no	—
746	#126	C₂²⋊D₄₃	1	2	yes	—
747	#125	—	2	1	no	—
748	#125	C₂²⋊D₄₃	1	1	yes	characteristic
749	#124	—	2	2	no	—
750	#124	—	2	2	no	—
751	#124	—	2	2	no	—
752	#124	—	2	2	no	—
753	#124	—	43	2	no	—
754	#124	—	86	1	no	—
755	#124	—	86	1	no	—
756	#124	—	86	2	no	—
757	#124	—	86	2	no	—
758	#124	—	86	2	no	—
759	#124	—	86	1	no	—
760	#124	C₂²⋊D₄₃	1	1	yes	characteristic
761	#124	C₂²×D₄₃	1	2	yes	—
762	#123	—	2	2	no	—
763	#123	—	86	2	no	—
764	#123	—	86	2	no	—
765	#123	—	86	2	no	—
766	#123	C₂²⋊D₄₃	1	2	yes	—
767	C₂²⋊Q₈	—	2	1	no	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	43	2	no	—
773	C₂²⋊Q₈	—	86	1	no	—
774	C₂²⋊Q₈	—	86	2	no	—
775	C₂²⋊Q₈	—	86	2	no	—
776	C₂²⋊Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
777	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
778	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
779	#121	—	2	1	no	—
780	#121	—	2	2	no	—
781	#121	—	43	2	no	—
782	#121	—	43	2	no	—
783	#121	—	86	2	no	—
784	#121	—	86	1	no	—
785	#121	—	86	1	no	—
786	#121	—	86	2	no	—
787	#121	C₂²⋊D₄₃	1	1	yes	characteristic
788	#121	C₂²×D₄₃	1	2	yes	—
789	#120	—	86	2	no	—
790	#120	—	86	2	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	2	no	—
793	C₄×Q₈	—	2	2	no	—
794	C₄×Q₈	—	2	2	no	—
795	C₄×Q₈	—	2	1	no	—
796	C₄×Q₈	—	43	1	no	—
797	C₄×Q₈	—	43	1	no	—
798	C₄×Q₈	—	86	1	no	—
799	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
800	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
801	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
802	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
803	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
804	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
805	C₄×D₄	—	2	1	no	—
806	C₄×D₄	—	2	1	no	—
807	C₄×D₄	—	2	1	no	—
808	C₄×D₄	—	2	2	no	—
809	C₄×D₄	—	43	1	no	—
810	C₄×D₄	—	43	1	no	—
811	C₄×D₄	—	43	2	no	—
812	C₄×D₄	—	43	2	no	—
813	C₄×D₄	—	43	2	no	—
814	C₄×D₄	—	86	1	no	—
815	C₄×D₄	—	86	1	no	—
816	C₄×D₄	—	86	2	no	—
817	C₄×D₄	—	86	2	no	—
818	C₄×D₄	—	86	1	no	—
819	C₄×D₄	—	86	1	no	—
820	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
821	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
822	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
823	C₄×D₄	C₂²×D₄₃	1	2	yes	—
824	#117	—	2	1	no	—
825	#117	—	2	1	no	—
826	#117	—	2	1	no	—
827	#117	—	2	2	no	—
828	#117	—	2	2	no	—
829	#117	—	2	1	no	—
830	#117	—	43	1	no	—
831	#117	—	43	2	no	—
832	#117	—	86	2	no	—
833	#117	—	86	1	no	—
834	#117	C₂²×D₄₃	1	1	yes	characteristic
835	#117	C₂²×D₄₃	1	2	yes	—
836	#117	C₂²×D₄₃	1	2	yes	—
837	C₂×C₂²⋊C₄	—	86	2	no	—
838	C₂×C₂²⋊C₄	—	86	2	no	—
839	C₂×C₂²⋊C₄	—	86	2	no	—
840	C₂×C₄²	—	2	1	no	—
841	C₂×C₄²	—	86	1	no	—
842	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
843	#107	—	43	1	no	—
844	#107	—	43	1	no	—
845	#107	—	43	2	no	—
846	#107	—	43	2	no	—
847	#106	—	43	1	no	—
848	#106	—	43	2	no	—
849	#106	—	43	1	no	—
850	#106	—	43	2	no	—
851	#106	—	43	2	no	—
852	#106	—	43	2	no	—
853	C₄⋊C₈	—	43	1	no	—
854	C₄⋊C₈	—	43	1	no	—
855	C₄⋊C₈	—	43	2	no	—
856	C₄⋊C₈	—	43	2	no	—
857	#103	—	43	1	no	—
858	#103	—	43	1	no	—
859	#103	—	43	2	no	—
860	#103	—	43	2	no	—
861	#103	—	43	2	no	—
862	#103	—	43	2	no	—
863	#103	—	43	2	no	—
864	#103	—	43	1	no	—
865	#103	—	43	1	no	—
866	#103	—	43	2	no	—
867	#102	—	43	1	no	—
868	#102	—	43	1	no	—
869	#102	—	43	2	no	—
870	#102	—	43	1	no	—
871	#102	—	43	1	no	—
872	#102	—	43	2	no	—
873	#102	—	43	2	no	—
874	#102	—	43	2	no	—
875	#102	—	43	2	no	—
876	#102	—	43	2	no	—
877	C₂²⋊C₈	—	43	2	no	—
878	C₂²⋊C₈	—	43	2	no	—
879	C₂²⋊C₈	—	43	2	no	—
880	#97	—	43	2	no	—
881	#97	—	43	2	no	—
882	C₄×C₈	—	43	1	no	—
883	C₄×C₈	—	43	1	no	—
884	C₄×C₈	—	43	1	no	—
885	C₄×C₈	—	43	1	no	—
886	C₄×C₈	—	43	2	no	—
887	C₂⁴	—	86	2	no	—
888	#41	—	2	2	no	—
889	#41	—	4	1	no	—
890	#41	—	86	2	no	—
891	#41	—	344	2	no	—
892	#41	—	172	1	no	—
893	C₂×Q₈	—	2	2	no	—
894	C₂×Q₈	—	2	1	no	—
895	C₂×Q₈	—	2	2	no	—
896	C₂×Q₈	—	2	4	no	—
897	C₂×Q₈	—	4	2	no	—
898	C₂×Q₈	—	43	1	no	—
899	C₂×Q₈	—	86	2	no	—
900	C₂×Q₈	—	86	1	no	—
901	C₂×Q₈	—	344	2	no	—
902	C₂×Q₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
903	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
904	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
905	C₂×D₄	—	2	1	no	—
906	C₂×D₄	—	2	2	no	—
907	C₂×D₄	—	43	1	no	—
908	C₂×D₄	—	43	2	no	—
909	C₂×D₄	—	86	4	no	—
910	C₂×D₄	—	86	2	no	—
911	C₂×D₄	—	86	2	no	—
912	C₂×D₄	—	86	1	no	—
913	C₂×D₄	—	86	1	no	—
914	C₂×D₄	—	86	2	no	—
915	C₂×D₄	—	86	1	no	—
916	C₂×D₄	—	344	2	no	—
917	C₂×D₄	—	172	2	no	—
918	C₂×D₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
919	C₂×D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
920	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
921	C₂²×C₄	—	2	2	no	—
922	C₂²×C₄	—	2	1	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	1	no	—
925	C₂²×C₄	—	86	1	no	—
926	C₂²×C₄	—	86	2	no	—
927	C₂²×C₄	—	86	2	no	—
928	C₂²×C₄	—	86	2	no	—
929	C₂²×C₄	—	86	1	no	—
930	C₂²×C₄	—	86	1	no	—
931	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
932	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
933	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
934	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
935	Q₁₆	—	86	2	no	—
936	Q₁₆	—	172	2	no	—
937	SD₁₆	—	43	4	no	—
938	SD₁₆	—	86	2	no	—
939	SD₁₆	—	86	4	no	—
940	SD₁₆	—	86	4	no	—
941	SD₁₆	—	86	4	no	—
942	SD₁₆	—	172	2	no	—
943	D₈	—	86	2	no	—
944	D₈	—	172	2	no	—
945	M₁₆	—	172	2	no	—
946	C₂×C₈	—	43	1	no	—
947	C₂×C₈	—	43	1	no	—
948	C₂×C₈	—	43	1	no	—
949	C₂×C₈	—	43	1	no	—
950	C₂×C₈	—	43	2	no	—
951	C₂×C₈	—	43	2	no	—
952	C₂×C₈	—	86	4	no	—
953	C₂×C₈	—	86	2	no	—
954	C₂×C₈	—	172	1	no	—
955	C₄⋊C₄	—	2	1	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	1	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	1	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	2	no	—
966	C₄⋊C₄	—	43	2	no	—
967	C₄⋊C₄	—	43	1	no	—
968	C₄⋊C₄	—	43	1	no	—
969	C₄⋊C₄	—	86	1	no	—
970	C₄⋊C₄	—	86	1	no	—
971	C₄⋊C₄	—	86	2	no	—
972	C₄⋊C₄	—	86	1	no	—
973	C₄⋊C₄	—	86	2	no	—
974	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
975	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
976	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
977	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
978	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
979	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
980	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
981	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
982	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	2	2	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	2	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	2	1	no	—
989	C₂²⋊C₄	—	2	2	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	2	no	—
992	C₂²⋊C₄	—	86	2	no	—
993	C₂²⋊C₄	—	86	2	no	—
994	C₂²⋊C₄	—	86	1	no	—
995	C₂²⋊C₄	—	86	1	no	—
996	C₂²⋊C₄	—	86	2	no	—
997	C₂²⋊C₄	—	86	2	no	—
998	C₂²⋊C₄	—	86	2	no	—
999	C₂²⋊C₄	—	86	2	no	—
1000	C₂²⋊C₄	—	86	2	no	—
1001	C₂²⋊C₄	—	86	1	no	—
1002	C₂²⋊C₄	—	86	2	no	—
1003	C₂²⋊C₄	—	86	2	no	—
1004	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1005	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1006	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1007	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1008	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1009	C₄²	—	2	1	no	—
1010	C₄²	—	2	1	no	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	2	no	—
1013	C₄²	—	2	2	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	86	1	no	—
1017	C₄²	—	86	1	no	—
1018	C₄²	—	86	1	no	—
1019	C₄²	—	86	2	no	—
1020	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1021	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1022	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1023	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1024	C₄²	C₂³×D₄₃	1	2	yes	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	86	1	no	—
1027	C₂³	—	86	2	no	—
1028	C₂³	—	344	2	no	—
1029	C₂³	—	344	2	no	—
1030	C₂³	—	172	4	no	—
1031	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1032	C₂³	C₂²×C₂²⋊D₄₃	1	2	yes	—
1033	Q₈	—	2	2	no	—
1034	Q₈	—	2	1	no	—
1035	Q₈	—	2	2	no	—
1036	Q₈	—	2	2	no	—
1037	Q₈	—	4	4	no	—
1038	Q₈	—	8	1	no	—
1039	Q₈	—	8	2	no	—
1040	Q₈	—	86	1	no	—
1041	Q₈	—	86	1	no	—
1042	Q₈	—	344	2	no	—
1043	Q₈	—	172	2	no	—
1044	Q₈	#41×D₄₃	1	2	yes	—
1045	D₄	—	2	2	no	—
1046	D₄	—	2	1	no	—
1047	D₄	—	2	1	no	—
1048	D₄	—	4	2	no	—
1049	D₄	—	4	2	no	—
1050	D₄	—	8	2	no	—
1051	D₄	—	43	2	no	—
1052	D₄	—	86	2	no	—
1053	D₄	—	86	1	no	—
1054	D₄	—	86	2	no	—
1055	D₄	—	344	1	no	—
1056	D₄	—	344	2	no	—
1057	D₄	—	344	2	no	—
1058	D₄	—	172	4	no	—
1059	D₄	—	172	2	no	—
1060	D₄	—	172	2	no	—
1061	C₂×C₄	—	2	1	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	2	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	2	no	—
1067	C₂×C₄	—	2	1	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	2	2	no	—
1070	C₂×C₄	—	2	1	no	—
1071	C₂×C₄	—	4	1	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	4	4	no	—
1074	C₂×C₄	—	4	2	no	—
1075	C₂×C₄	—	8	1	no	—
1076	C₂×C₄	—	86	1	no	—
1077	C₂×C₄	—	86	1	no	—
1078	C₂×C₄	—	86	1	no	—
1079	C₂×C₄	—	86	2	no	—
1080	C₂×C₄	—	344	2	no	—
1081	C₂×C₄	—	344	2	no	—
1082	C₂×C₄	—	344	1	no	—
1083	C₂×C₄	—	344	2	no	—
1084	C₂×C₄	—	172	2	no	—
1085	C₂×C₄	—	172	2	no	—
1086	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1087	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1088	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1089	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1090	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1091	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1092	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1093	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1094	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1095	C₈	—	43	2	no	—
1096	C₈	—	86	1	no	—
1097	C₈	—	86	2	no	—
1098	C₈	—	86	1	no	—
1099	C₈	—	86	1	no	—
1100	C₈	—	86	2	no	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	2	2	no	—
1104	C₂²	—	2	1	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	2	2	no	—
1107	C₂²	—	4	1	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	86	2	no	—
1111	C₂²	—	172	2	no	—
1112	C₂²	—	172	2	no	—
1113	C₂²	—	172	2	no	—
1114	C₂²	—	172	1	no	—
1115	C₂²	—	172	1	no	—
1116	C₂²	—	688	4	no	—
1117	C₂²	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
1118	C₄	—	2	1	no	—
1119	C₄	—	2	2	no	—
1120	C₄	—	2	1	no	—
1121	C₄	—	2	2	no	—
1122	C₄	—	2	2	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	1	no	—
1125	C₄	—	2	2	no	—
1126	C₄	—	4	1	no	—
1127	C₄	—	4	2	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	2	no	—
1130	C₄	—	172	2	no	—
1131	C₄	—	172	1	no	—
1132	C₄	—	172	1	no	—
1133	C₄	—	172	1	no	—
1134	C₄	#14583707	1	2	yes	—
1135	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1136	C₄	#14583735	1	1	yes	characteristic
1137	C₂	—	4	2	no	—
1138	C₂	—	4	1	no	—
1139	C₂	—	8	1	no	—
1140	C₂	—	344	2	no	—
1141	C₂	—	172	2	no	—
1142	C₂	#41×C₂²⋊D₄₃	1	1	yes	characteristic
1143	C₂	C₂×#14583707	1	1	yes	characteristic
1144	C₂	#19149366	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3518	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3518	D₄₃
hypocenter	C₄₃	#61474
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ #529 ◁ #3518

Complements

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

N	H ≅ G/N	type
1. #19148558	C₂	semidirect
2. #19147591	C₂	semidirect
3. Q₈×#10621884	C₂	semidirect
4. #19147409	C₂	semidirect
5. #19147309	C₂	semidirect
6. #19147008	C₂	semidirect
7. #19147002	C₂	semidirect
8. #19146878	C₂	semidirect
9. #19146831	C₂	semidirect
10. #19146781	C₂	semidirect
11. #19146625	C₂	semidirect
12. #19146303	C₂	semidirect
13. D₄×#10621884	C₂	semidirect
14. #19145206	C₂	semidirect
15. #19145155	C₂	semidirect
16. #19144824	C₂	semidirect
17. #19144773	C₂	semidirect
18. #19144751	C₂	semidirect
19. #19144746	C₂	semidirect
20. #19143571	C₂	semidirect
21. #19143454	C₂	semidirect
22. C₄×#13063345	C₂	semidirect
23. C₄₃×#3518	C₂	semidirect
42. #14583295	C₂²	semidirect
43. #14583295	C₂²	semidirect
44. #14583281	C₂²	semidirect
46. #14583261	C₂²	semidirect
47. #14583258	C₂²	semidirect
48. #14583249	C₂²	semidirect
50. #14583240	C₂²	semidirect
51. #14583237	C₂²	semidirect
52. #14583237	C₂²	semidirect
54. #14583223	C₂²	semidirect
55. #14583220	C₂²	semidirect
56. #14583194	C₂²	semidirect
57. #14583191	C₂²	semidirect
60. #14583184	C₂²	semidirect
61. #14583184	C₂²	semidirect
62. #14583179	C₂²	semidirect
63. #14583176	C₂²	semidirect
64. #14583155	C₂²	semidirect
67. #14583130	C₂²	semidirect
68. #14583130	C₂²	semidirect
69. #14583126	C₂²	semidirect
70. #14583121	C₂²	semidirect
71. #14583121	C₂²	semidirect
73. #14583111	C₂²	semidirect
74. #14583106	C₂²	semidirect
79. #14583055	C₂²	semidirect
81. #14583044	C₂²	semidirect
84. #14583030	C₂²	semidirect
85. Q₈×C₄₃⋊C₈	C₂²	semidirect
86. #14583009	C₂²	semidirect
87. #14583004	C₂²	semidirect
90. #14582997	C₂²	semidirect
91. #14582997	C₂²	semidirect
92. C₄×#10621885	C₂²	semidirect
93. C₄×#10621885	C₂²	semidirect
97. C₄×#10621884	C₂²	semidirect
98. C₄×#10621884	C₂²	semidirect
99. C₄×#10621884	C₂²	semidirect
100. C₄×#10621883	C₂²	semidirect
101. C₄×#10621883	C₂²	semidirect
105. #14582971	C₂²	semidirect
107. D₄×C₄₃⋊C₈	C₂²	semidirect
108. #14582960	C₂²	semidirect
109. #14582956	C₂²	semidirect
110. #14582935	C₂²	semidirect
111. #14582935	C₂²	semidirect
112. #14582908	C₂²	semidirect
114. #14582895	C₂²	semidirect
116. #14582855	C₂²	semidirect
117. C₂×C₄×C₄₃⋊C₈	C₂²	semidirect
118. Q₈²×C₄₃	C₂²	semidirect
121. C₄₃×#556	C₂²	semidirect
122. C₄₃×#556	C₂²	semidirect
126. C₄₃×#548	C₂²	semidirect
128. C₄₃×#542	C₂²	semidirect
130. C₄₃×#533	C₂²	semidirect
133. C₄₃×#519	C₂²	semidirect
134. C₄×#41×C₄₃	C₂²	semidirect
417. #10621884	#41	semidirect
565. #3518	D₄₃	semidirect
599. Q₈²	C₂×D₄₃	semidirect
603. #556	C₂×D₄₃	semidirect
604. #556	C₂×D₄₃	semidirect
612. #548	C₂×D₄₃	semidirect
618. #542	C₂×D₄₃	semidirect
621. #533	C₂×D₄₃	semidirect
627. #519	C₂×D₄₃	semidirect
630. C₄×#41	C₂×D₄₃	semidirect
707. C₄₃	#61474	semidirect

Maximal subgroups

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

subgroup	index
#19148558	2
#19147591	2
Q₈×#10621884	2
#19147409	2
#19147309	2
#19147008	2
#19147002	2
#19146878	2
#19146831	2
#19146781	2
#19146625	2
#19146303	2
D₄×#10621884	2
#19145206	2
#19145155	2
#19144824	2
#19144773	2
#19144751	2
#19144746	2
#19143571	2
#19143454	2
C₄×#13063345	2
C₄₃×#3518	2
#61474	43