Subgroups — #25965588

Order 11008.

2098 conjugacy classes of subgroups.

The subgroup lattice has 1184 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×#13063371	C₂	1	1	yes	maximal, characteristic, complemented
2	#19144866	C₂	1	2	yes	maximal, complemented
3	#19144851	C₂	1	2	yes	maximal, complemented
4	#19144773	C₂	1	2	yes	maximal, complemented
5	#19144773	C₂	1	2	yes	maximal, complemented
6	#19144729	C₂	1	2	yes	maximal, complemented
7	#19144698	C₂	1	2	yes	maximal, complemented
8	#19144638	C₂	1	2	yes	maximal, complemented
9	#19144607	C₂	1	2	yes	maximal, complemented
10	#19144558	C₂	1	1	yes	maximal, characteristic, complemented
11	#19144547	C₂	1	1	yes	maximal, characteristic, complemented
12	#19144388	C₂	1	1	yes	maximal, characteristic, complemented
13	#19144377	C₂	1	1	yes	maximal, characteristic, complemented
14	#19144085	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#14583111	C₂	1	1	yes	maximal, characteristic, complemented
16	#19143870	C₂	1	1	yes	maximal, characteristic, complemented
17	#19143861	C₂	1	1	yes	maximal, characteristic
18	#19143454	C₂	1	1	yes	maximal, characteristic, complemented
19	#19143445	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143438	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143427	C₂	1	1	yes	maximal, characteristic, complemented
22	#19143261	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3510	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063371	C₂²	1	1	yes	characteristic
25	C₂×#13063356	C₂²	1	1	yes	characteristic
26	C₂×#13063351	C₂²	1	1	yes	characteristic
27	C₂²×#10621884	C₂²	1	1	yes	characteristic
28	C₂²×#10621882	C₂²	1	1	yes	characteristic
29	#14583382	C₂²	1	1	yes	characteristic
30	#14583381	—	2	1	no	—
31	#14583379	C₂²	1	1	yes	characteristic
32	#14583379	C₂²	1	2	yes	complemented
33	#14583373	C₂²	1	1	yes	characteristic
34	#14583373	C₂²	1	2	yes	complemented
35	#14583371	—	2	2	no	—
36	#14583371	—	2	1	no	—
37	C₄×#10621902	—	2	1	no	—
38	C₄×#10621898	C₂²	1	1	yes	characteristic
39	C₄×#10621898	C₂²	1	2	yes	complemented
40	C₂×C₄×D₁₇₂	C₂²	1	1	yes	characteristic
41	C₂×C₄×D₁₇₂	C₂²	1	2	yes	complemented
42	C₄×D₄×D₄₃	—	2	2	no	—
43	C₄×D₄×D₄₃	—	2	1	no	—
44	#14583237	C₂²	1	2	yes	complemented
45	#14583237	C₂²	1	2	yes	complemented
46	#14583232	C₂²	1	2	yes	complemented
47	#14583227	C₂²	1	2	yes	complemented
48	#14583220	C₂²	1	2	yes	complemented
49	#14583220	C₂²	1	2	yes	complemented
50	#14583215	C₂²	1	2	yes	complemented
51	#14583210	C₂²	1	2	yes	complemented
52	#14583203	C₂²	1	1	yes	characteristic, complemented
53	#14583203	C₂²	1	1	yes	characteristic, complemented
54	#14583196	C₂²	1	1	yes	characteristic, complemented
55	#14583196	C₂²	1	2	yes	complemented
56	#14583196	C₂²	1	1	yes	characteristic, complemented
57	#14583196	C₂²	1	2	yes	complemented
58	#14583191	C₂²	1	1	yes	characteristic, complemented
59	#14583186	C₂²	1	1	yes	characteristic, complemented
60	#14583186	C₂²	1	2	yes	complemented
61	#14583181	C₂²	1	1	yes	characteristic, complemented
62	#14583176	C₂²	1	1	yes	characteristic, complemented
63	#14583176	C₂²	1	2	yes	complemented
64	#14583118	C₂²	1	2	yes	complemented
65	#14583118	C₂²	1	2	yes	complemented
66	#14583111	C₂²	1	2	yes	complemented
67	#14583111	C₂²	1	2	yes	complemented
68	#14583111	C₂²	1	2	yes	complemented
69	#14583111	C₂²	1	2	yes	complemented
70	#14583111	C₂²	1	2	yes	complemented
71	#14583111	C₂²	1	2	yes	complemented
72	#14583059	C₂²	1	2	yes	complemented
73	#14583059	C₂²	1	2	yes	complemented
74	#14583049	C₂²	1	2	yes	complemented
75	#14583049	C₂²	1	2	yes	complemented
76	#14583042	C₂²	1	2	yes	—
77	#14583042	C₂²	1	2	yes	—
78	#14583032	C₂²	1	2	yes	—
79	#14583032	C₂²	1	2	yes	—
80	#14583009	C₂²	1	2	yes	complemented
81	#14583009	C₂²	1	2	yes	complemented
82	#14583009	C₂²	1	2	yes	complemented
83	#14583004	C₂²	1	2	yes	complemented
84	#14582999	C₂²	1	2	yes	complemented
85	#14582997	C₂²	1	2	yes	complemented
86	#14582997	C₂²	1	2	yes	complemented
87	#14582997	C₂²	1	2	yes	complemented
88	C₄×#10621885	C₂²	1	2	yes	complemented
89	C₄×#10621884	C₂²	1	2	yes	complemented
90	C₄×#10621884	C₂²	1	2	yes	complemented
91	C₄×#10621884	C₂²	1	2	yes	complemented
92	C₄×#10621883	C₂²	1	2	yes	complemented
93	C₄×#10621882	C₂²	1	2	yes	complemented
94	C₄×#10621882	C₂²	1	2	yes	complemented
95	C₄×#10621882	C₂²	1	2	yes	complemented
96	#14582960	C₂²	1	2	yes	complemented
97	#14582960	C₂²	1	2	yes	complemented
98	#14582956	C₂²	1	2	yes	complemented
99	#14582952	C₂²	1	2	yes	complemented
100	#14582942	C₂²	1	1	yes	characteristic, complemented
101	#14582942	C₂²	1	1	yes	characteristic, complemented
102	#14582935	C₂²	1	1	yes	characteristic, complemented
103	#14582935	C₂²	1	1	yes	characteristic, complemented
104	#14582923	C₂²	1	1	yes	characteristic, complemented
105	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic, complemented
106	#14582908	C₂²	1	1	yes	characteristic, complemented
107	#14582904	C₂²	1	1	yes	characteristic, complemented
108	#14582903	C₂²	1	1	yes	characteristic
109	#14582903	C₂²	1	1	yes	characteristic
110	#14582893	C₂²	1	1	yes	characteristic
111	#14582893	C₂²	1	1	yes	characteristic
112	C₂×#13063249	C₂²	1	1	yes	characteristic, complemented
113	C₂×#13063246	C₂²	1	1	yes	characteristic, complemented
114	#14582866	C₂²	1	1	yes	characteristic
115	#14582866	C₂²	1	1	yes	characteristic
116	#14582855	C₂²	1	1	yes	characteristic, complemented
117	#14582855	C₂²	1	1	yes	characteristic, complemented
118	C₄₃×#559	—	2	1	no	—
119	C₄₃×#559	—	2	1	no	—
120	C₄₃×#556	—	2	1	no	—
121	C₄₃×#556	—	2	1	no	—
122	C₄₃×#551	—	2	2	no	—
123	C₄₃×#551	—	2	2	no	—
124	C₄₃×#542	C₂²	1	2	yes	complemented
125	C₄₃×#542	C₂²	1	2	yes	complemented
126	C₄₃×#536	C₂²	1	1	yes	characteristic
127	C₄₃×#535	C₂²	1	1	yes	characteristic
128	C₄₃×#533	C₂²	1	1	yes	characteristic, complemented
129	C₄₃×#529	C₂²	1	2	yes	complemented
130	C₄₃×#529	C₂²	1	2	yes	complemented
131	C₂×#124×C₄₃	C₂²	1	1	yes	characteristic, complemented
132	C₄₃×#519	C₂²	1	1	yes	characteristic, complemented
133	C₄₃×#518	C₂²	1	1	yes	characteristic, complemented
134	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
135	#13063371	—	2	4	no	—
136	#13063371	—	2	4	no	—
137	C₂×#10621902	—	2	1	no	—
138	C₂×#10621898	C₂³	1	2	yes	—
139	C₂×#10621898	C₂³	1	1	yes	characteristic
140	C₂²×D₁₇₂	C₂³	1	2	yes	—
141	C₂²×D₁₇₂	C₂³	1	1	yes	characteristic
142	C₂×D₄×D₄₃	—	2	2	no	—
143	C₂×D₄×D₄₃	—	2	1	no	—
144	C₂²×C₄×D₄₃	—	2	1	no	—
145	C₂²×C₄×D₄₃	—	2	2	no	—
146	#13063356	—	2	4	no	—
147	#13063351	—	2	4	no	—
148	C₂×#10621885	C₂³	1	2	yes	—
149	C₂×#10621883	C₂³	1	2	yes	—
150	C₂×#10621884	—	2	4	no	—
151	C₂×#10621884	C₂³	1	2	yes	—
152	C₂×#10621884	C₂³	1	2	yes	—
153	C₂×#10621884	C₂³	1	2	yes	—
154	C₂×#10621882	—	2	4	no	—
155	C₂×#10621882	C₂³	1	2	yes	—
156	C₂×#10621882	C₂³	1	2	yes	—
157	C₂×#10621882	C₂³	1	2	yes	—
158	C₂×#10621877	C₂³	1	1	yes	characteristic
159	C₂×#10621877	C₂³	1	1	yes	characteristic
160	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
161	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
162	Q₈×Dic₄₃	—	2	1	no	—
163	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
164	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
165	C₄×Dic₈₆	C₂³	1	2	yes	—
166	C₄×D₁₇₂	—	2	1	no	—
167	C₄×D₁₇₂	—	2	2	no	—
168	C₄×D₁₇₂	—	2	1	no	—
169	C₄×D₁₇₂	—	2	2	no	—
170	C₄×D₁₇₂	C₂³	1	2	yes	—
171	C₄×D₁₇₂	C₂³	1	2	yes	—
172	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
173	C₄×D₁₇₂	C₂³	1	2	yes	—
174	C₄×D₁₇₂	C₂³	1	2	yes	—
175	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
176	C₄×D₁₇₂	C₂³	1	2	yes	—
177	D₄×Dic₄₃	—	2	2	no	—
178	D₄×Dic₄₃	—	2	1	no	—
179	#13063287	—	2	1	no	—
180	#13063287	—	2	2	no	—
181	#13063287	—	2	1	no	—
182	#13063287	—	2	2	no	—
183	C₄×C₂²⋊D₄₃	—	2	1	no	—
184	C₄×C₂²⋊D₄₃	—	2	2	no	—
185	C₄×C₂²⋊D₄₃	—	2	1	no	—
186	C₄×C₂²⋊D₄₃	—	2	2	no	—
187	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
188	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
189	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
190	#13063284	C₂³	1	1	yes	characteristic
191	#13063284	C₂³	1	2	yes	—
192	#13063283	—	2	1	no	—
193	#13063283	—	2	2	no	—
194	#13063282	—	2	1	no	—
195	#13063282	—	2	2	no	—
196	C₂×C₄⋊Dic₄₃	C₂³	1	1	yes	characteristic
197	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
198	C₄⋊C₄×D₄₃	—	2	1	no	—
199	C₄⋊C₄×D₄₃	—	2	2	no	—
200	C₂×(C₂×D₄₃)⋊C₄	—	2	1	no	—
201	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
202	C₂²⋊C₄×D₄₃	—	2	2	no	—
203	C₂²⋊C₄×D₄₃	—	2	2	no	—
204	C₂²⋊C₄×D₄₃	—	2	2	no	—
205	C₄²×D₄₃	—	2	1	no	—
206	C₄²×D₄₃	—	2	2	no	—
207	#13063258	C₂³	1	1	yes	characteristic
208	#13063258	C₂³	1	1	yes	characteristic
209	#13063258	C₂³	1	2	yes	—
210	#13063258	C₂³	1	2	yes	—
211	#13063258	C₂³	1	1	yes	characteristic
212	#13063258	C₂³	1	1	yes	characteristic
213	#13063256	C₂³	1	1	yes	characteristic
214	#13063256	C₂³	1	1	yes	characteristic
215	#13063256	C₂³	1	1	yes	characteristic
216	#13063256	C₂³	1	1	yes	characteristic
217	#13063256	C₂³	1	2	yes	—
218	#13063256	C₂³	1	2	yes	—
219	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
220	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
221	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
222	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
223	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
224	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
225	#13063249	C₂³	1	2	yes	—
226	#13063249	C₂³	1	2	yes	—
227	#13063249	C₂³	1	2	yes	—
228	#13063249	C₂³	1	2	yes	—
229	#13063248	C₂³	1	1	yes	characteristic
230	#13063248	C₂³	1	1	yes	characteristic
231	#13063248	C₂³	1	1	yes	characteristic
232	#13063248	C₂³	1	1	yes	characteristic
233	#13063246	C₂³	1	2	yes	—
234	#13063246	C₂³	1	2	yes	—
235	#13063246	C₂³	1	2	yes	—
236	#13063246	C₂³	1	2	yes	—
237	#13063245	C₂³	1	2	yes	—
238	#13063245	C₂³	1	2	yes	—
239	#13063245	C₂³	1	1	yes	characteristic
240	#13063245	C₂³	1	1	yes	characteristic
241	#13063245	C₂³	1	2	yes	—
242	#13063245	C₂³	1	2	yes	—
243	#13063245	C₂³	1	1	yes	characteristic
244	#13063245	C₂³	1	1	yes	characteristic
245	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
246	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
247	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
248	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
249	#13063236	C₂³	1	2	yes	—
250	#13063236	C₂³	1	2	yes	—
251	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
252	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
253	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
254	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
255	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
256	C₄⋊Q₈×C₄₃	—	2	1	no	—
257	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
258	C₄⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
259	#127×C₄₃	—	2	1	no	—
260	#126×C₄₃	—	2	2	no	—
261	#126×C₄₃	—	2	2	no	—
262	#126×C₄₃	—	2	2	no	—
263	#126×C₄₃	—	2	2	no	—
264	#125×C₄₃	C₂³	1	1	yes	characteristic
265	#125×C₄₃	C₂³	1	1	yes	characteristic
266	#124×C₄₃	—	2	1	no	—
267	#124×C₄₃	—	2	1	no	—
268	#124×C₄₃	—	2	2	no	—
269	#124×C₄₃	—	2	2	no	—
270	#124×C₄₃	—	2	1	no	—
271	#124×C₄₃	—	2	1	no	—
272	#124×C₄₃	C₂³	1	2	yes	—
273	#124×C₄₃	C₂³	1	2	yes	—
274	#123×C₄₃	—	2	2	no	—
275	#123×C₄₃	—	2	2	no	—
276	#123×C₄₃	—	2	2	no	—
277	#123×C₄₃	—	2	2	no	—
278	#123×C₄₃	—	2	2	no	—
279	C₂²⋊Q₈×C₄₃	—	2	1	no	—
280	C₂²⋊Q₈×C₄₃	—	2	1	no	—
281	C₂²⋊Q₈×C₄₃	—	2	2	no	—
282	C₂²⋊Q₈×C₄₃	—	2	2	no	—
283	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
284	C₂²⋊Q₈×C₄₃	C₂³	1	2	yes	—
285	#121×C₄₃	C₂³	1	2	yes	—
286	#121×C₄₃	C₂³	1	2	yes	—
287	#120×C₄₃	—	2	2	no	—
288	C₄×Q₈×C₄₃	—	2	1	no	—
289	C₄×Q₈×C₄₃	—	2	1	no	—
290	C₄×Q₈×C₄₃	—	2	1	no	—
291	C₄×Q₈×C₄₃	—	2	1	no	—
292	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
293	C₄×Q₈×C₄₃	D₄	1	1	yes	characteristic
294	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
295	C₄×Q₈×C₄₃	C₂³	1	2	yes	—
296	C₄×D₄×C₄₃	—	2	2	no	—
297	C₄×D₄×C₄₃	—	2	2	no	—
298	C₄×D₄×C₄₃	—	2	1	no	—
299	C₄×D₄×C₄₃	—	2	1	no	—
300	C₄×D₄×C₄₃	D₄	1	2	yes	—
301	C₄×D₄×C₄₃	D₄	1	2	yes	—
302	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
303	C₄×D₄×C₄₃	D₄	1	1	yes	characteristic
304	C₄×D₄×C₄₃	C₂³	1	2	yes	—
305	C₄×D₄×C₄₃	C₂³	1	2	yes	—
306	#117×C₄₃	—	2	2	no	—
307	#117×C₄₃	—	2	2	no	—
308	#117×C₄₃	—	2	2	no	—
309	#117×C₄₃	C₂³	1	1	yes	characteristic
310	#117×C₄₃	C₂³	1	1	yes	characteristic
311	#117×C₄₃	C₂³	1	1	yes	characteristic
312	#117×C₄₃	C₂³	1	2	yes	—
313	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
314	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
315	C₂×C₂²⋊C₄×C₄₃	—	2	2	no	—
316	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
317	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
318	C₂⁴×C₄₃	—	2	1	no	—
319	C₂³×D₄₃	—	2	2	no	—
320	C₂³×D₄₃	—	2	1	no	—
321	#41×C₄₃	—	2	2	no	—
322	#41×C₄₃	—	2	2	no	—
323	C₂×Q₈×C₄₃	—	2	1	no	—
324	C₂×Q₈×C₄₃	—	2	1	no	—
325	C₂×Q₈×C₄₃	—	2	1	no	—
326	C₂×Q₈×C₄₃	—	2	2	no	—
327	C₂×Q₈×C₄₃	—	2	2	no	—
328	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
329	C₂×Q₈×C₄₃	C₂⁴	1	2	yes	—
330	C₂×D₄×C₄₃	—	2	1	no	—
331	C₂×D₄×C₄₃	—	2	2	no	—
332	C₂×D₄×C₄₃	—	2	2	no	—
333	C₂×D₄×C₄₃	—	2	2	no	—
334	C₂×D₄×C₄₃	—	2	2	no	—
335	C₂×D₄×C₄₃	C₂×D₄	1	2	yes	—
336	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
337	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
338	C₂²×C₄×C₄₃	—	2	2	no	—
339	C₂²×C₄×C₄₃	—	2	2	no	—
340	C₂²×C₄×C₄₃	—	2	1	no	—
341	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
342	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
343	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
344	C₂²×C₄×C₄₃	C₂×D₄	1	2	yes	—
345	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
346	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
347	C₂×C₂²⋊D₄₃	—	2	2	no	—
348	C₂×C₂²⋊D₄₃	—	2	1	no	—
349	C₂²×Dic₄₃	—	2	2	no	—
350	C₂²×Dic₄₃	—	2	1	no	—
351	#10621902	—	2	8	no	—
352	D₄×D₄₃	—	2	8	no	—
353	D₄×D₄₃	—	2	16	no	—
354	#10621898	—	2	2	no	—
355	#10621898	—	2	4	no	—
356	#10621898	—	2	4	no	—
357	#10621898	#41	1	4	yes	—
358	C₂×D₁₇₂	—	2	2	no	—
359	C₂×D₁₇₂	—	2	1	no	—
360	C₂×D₁₇₂	—	2	2	no	—
361	C₂×D₁₇₂	—	2	4	no	—
362	C₂×D₁₇₂	—	2	4	no	—
363	C₂×D₁₇₂	#41	1	4	yes	—
364	C₂×D₁₇₂	C₂⁴	1	1	yes	characteristic
365	C₂×D₁₇₂	C₂⁴	1	2	yes	—
366	C₂×C₄×D₄₃	—	2	2	no	—
367	C₂×C₄×D₄₃	—	2	1	no	—
368	C₂×C₄×D₄₃	—	2	1	no	—
369	C₂×C₄×D₄₃	—	2	2	no	—
370	C₂×C₄×D₄₃	—	2	2	no	—
371	C₂×C₄×D₄₃	—	2	1	no	—
372	C₂×C₄×D₄₃	—	2	2	no	—
373	C₂×C₄×D₄₃	—	2	2	no	—
374	C₂×C₄×D₄₃	—	2	2	no	—
375	C₂×C₄×D₄₃	—	8	2	no	—
376	C₂×C₄×D₄₃	—	8	4	no	—
377	C₂×Dic₈₆	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄×C₄₃	—	2	1	no	—
379	C₄⋊C₄×C₄₃	—	2	1	no	—
380	C₄⋊C₄×C₄₃	—	2	2	no	—
381	C₄⋊C₄×C₄₃	—	2	2	no	—
382	C₄⋊C₄×C₄₃	—	2	2	no	—
383	C₄⋊C₄×C₄₃	—	2	2	no	—
384	C₄⋊C₄×C₄₃	—	2	1	no	—
385	C₄⋊C₄×C₄₃	—	2	1	no	—
386	C₄⋊C₄×C₄₃	—	2	1	no	—
387	C₄⋊C₄×C₄₃	—	2	1	no	—
388	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
389	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
390	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
391	C₄⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
392	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
393	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
394	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
395	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
396	C₂²⋊C₄×C₄₃	—	2	2	no	—
397	C₂²⋊C₄×C₄₃	—	2	2	no	—
398	C₂²⋊C₄×C₄₃	—	2	2	no	—
399	C₂²⋊C₄×C₄₃	—	2	2	no	—
400	C₂²⋊C₄×C₄₃	—	2	2	no	—
401	C₂²⋊C₄×C₄₃	—	2	2	no	—
402	C₂²⋊C₄×C₄₃	—	2	2	no	—
403	C₂²⋊C₄×C₄₃	—	2	2	no	—
404	C₂²⋊C₄×C₄₃	—	2	1	no	—
405	C₂²⋊C₄×C₄₃	—	2	1	no	—
406	C₂²⋊C₄×C₄₃	—	2	2	no	—
407	C₂²⋊C₄×C₄₃	—	2	2	no	—
408	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
409	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
410	C₂²⋊C₄×C₄₃	C₂×D₄	1	2	yes	—
411	C₄²×C₄₃	—	2	2	no	—
412	C₄²×C₄₃	—	2	2	no	—
413	C₄²×C₄₃	—	2	1	no	—
414	C₄²×C₄₃	—	2	1	no	—
415	C₄²×C₄₃	C₂×D₄	1	2	yes	—
416	C₄²×C₄₃	C₂×D₄	1	2	yes	—
417	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
418	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
419	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
420	C₄²×C₄₃	C₂⁴	1	2	yes	—
421	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
422	C₂²⋊Dic₄₃	—	2	2	no	—
423	C₂²⋊Dic₄₃	—	2	1	no	—
424	#10621885	—	2	4	no	—
425	#10621884	—	2	4	no	—
426	#10621884	—	2	4	no	—
427	#10621884	—	2	4	no	—
428	#10621883	—	2	4	no	—
429	#10621882	—	2	4	no	—
430	#10621882	—	2	4	no	—
431	#10621882	—	2	4	no	—
432	(C₂×D₄₃)⋊C₄	—	2	2	no	—
433	(C₂×D₄₃)⋊C₄	—	2	1	no	—
434	(C₂×D₄₃)⋊C₄	—	2	2	no	—
435	(C₂×D₄₃)⋊C₄	—	2	2	no	—
436	(C₂×D₄₃)⋊C₄	—	2	2	no	—
437	(C₂×D₄₃)⋊C₄	—	2	2	no	—
438	(C₂×D₄₃)⋊C₄	—	2	1	no	—
439	C₄⋊Dic₄₃	—	2	2	no	—
440	C₄⋊Dic₄₃	—	2	1	no	—
441	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
442	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
443	C₄⋊Dic₄₃	C₂⁴	1	1	yes	characteristic
444	Dic₄₃⋊C₄	—	2	2	no	—
445	Dic₄₃⋊C₄	—	2	1	no	—
446	Dic₄₃⋊C₄	—	2	1	no	—
447	C₄×Dic₄₃	—	2	1	no	—
448	C₄×Dic₄₃	—	2	2	no	—
449	C₄×Dic₄₃	—	2	1	no	—
450	C₄×Dic₄₃	—	2	2	no	—
451	C₄×Dic₄₃	—	2	1	no	—
452	#10621877	—	2	2	no	—
453	#10621877	—	2	2	no	—
454	C₂×C₄₃⋊C₈	—	2	2	no	—
455	C₂×C₄₃⋊C₈	—	2	2	no	—
456	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
457	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
458	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
459	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
460	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
461	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
462	C₂³×C₄₃	—	2	2	no	—
463	C₂³×C₄₃	—	4	2	no	—
464	C₂³×C₄₃	—	8	1	no	—
465	C₂³×C₄₃	—	8	1	no	—
466	C₂³×C₄₃	C₂²×D₄	1	2	yes	—
467	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
468	C₂²×D₄₃	—	2	1	no	—
469	C₂²×D₄₃	—	2	2	no	—
470	C₂²×D₄₃	—	2	8	no	—
471	C₂²×D₄₃	—	2	4	no	—
472	C₂²×D₄₃	—	8	1	no	—
473	C₂²×D₄₃	—	8	2	no	—
474	C₂²×D₄₃	—	8	1	no	—
475	C₂²×D₄₃	—	8	2	no	—
476	Q₈×C₄₃	—	2	2	no	—
477	Q₈×C₄₃	—	2	2	no	—
478	Q₈×C₄₃	—	2	2	no	—
479	Q₈×C₄₃	—	4	2	no	—
480	Q₈×C₄₃	—	8	1	no	—
481	Q₈×C₄₃	—	8	1	no	—
482	D₄×C₄₃	—	2	4	no	—
483	D₄×C₄₃	—	2	2	no	—
484	D₄×C₄₃	—	2	2	no	—
485	D₄×C₄₃	—	2	2	no	—
486	D₄×C₄₃	—	4	2	no	—
487	D₄×C₄₃	—	8	2	no	—
488	D₄×C₄₃	—	8	2	no	—
489	C₂×C₄×C₄₃	—	2	2	no	—
490	C₂×C₄×C₄₃	—	2	2	no	—
491	C₂×C₄×C₄₃	—	2	1	no	—
492	C₂×C₄×C₄₃	—	2	1	no	—
493	C₂×C₄×C₄₃	—	2	2	no	—
494	C₂×C₄×C₄₃	—	2	1	no	—
495	C₂×C₄×C₄₃	—	2	1	no	—
496	C₂×C₄×C₄₃	—	4	2	no	—
497	C₂×C₄×C₄₃	—	4	1	no	—
498	C₂×C₄×C₄₃	—	4	2	no	—
499	C₂×C₄×C₄₃	—	4	1	no	—
500	C₂×C₄×C₄₃	—	4	2	no	—
501	C₂×C₄×C₄₃	—	8	2	no	—
502	C₂×C₄×C₄₃	—	8	2	no	—
503	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
504	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
505	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
506	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
507	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
508	C₂×C₄×C₄₃	C₂²×D₄	1	2	yes	—
509	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
510	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
511	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
512	C₂×C₄×C₄₃	C₂×#41	1	2	yes	—
513	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
514	C₂²⋊D₄₃	—	2	8	no	—
515	C₂²⋊D₄₃	—	2	4	no	—
516	C₂×Dic₄₃	—	2	1	no	—
517	C₂×Dic₄₃	—	2	1	no	—
518	C₂×Dic₄₃	—	2	2	no	—
519	C₂×Dic₄₃	—	2	1	no	—
520	C₂×Dic₄₃	—	8	1	no	—
521	C₂×Dic₄₃	—	8	2	no	—
522	D₁₇₂	—	2	8	no	—
523	D₁₇₂	—	2	4	no	—
524	D₁₇₂	—	2	1	no	—
525	D₁₇₂	—	2	2	no	—
526	D₁₇₂	C₂×#41	1	2	yes	—
527	D₁₇₂	C₂×#41	1	4	yes	—
528	C₄×D₄₃	—	2	8	no	—
529	C₄×D₄₃	—	2	4	no	—
530	C₄×D₄₃	—	4	2	no	—
531	C₄×D₄₃	—	4	4	no	—
532	C₄×D₄₃	—	8	2	no	—
533	C₄×D₄₃	—	8	1	no	—
534	C₄×D₄₃	—	8	2	no	—
535	C₄×D₄₃	—	8	2	no	—
536	C₄×D₄₃	—	8	2	no	—
537	Dic₈₆	—	2	1	no	—
538	Dic₈₆	C₂×#41	1	2	yes	—
539	C₄₃⋊C₈	—	2	1	no	—
540	C₄₃⋊C₈	—	2	1	no	—
541	C₄₃⋊C₈	—	2	1	no	—
542	C₄₃⋊C₈	—	2	1	no	—
543	C₄₃⋊C₈	—	2	2	no	—
544	C₄₃⋊C₈	—	2	2	no	—
545	#60592	—	43	1	no	maximal, Sylow
546	C₂²×C₄₃	—	2	1	no	—
547	C₂²×C₄₃	—	2	1	no	—
548	C₂²×C₄₃	—	2	2	no	—
549	C₂²×C₄₃	—	2	2	no	—
550	C₂²×C₄₃	—	2	2	no	—
551	C₂²×C₄₃	—	4	2	no	—
552	C₂²×C₄₃	—	4	2	no	—
553	C₂²×C₄₃	—	4	2	no	—
554	C₂²×C₄₃	—	16	2	no	—
555	C₂²×C₄₃	#525	1	2	yes	—
556	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
557	C₂×D₄₃	—	2	2	no	—
558	C₂×D₄₃	—	2	4	no	—
559	C₂×D₄₃	—	4	2	no	—
560	C₂×D₄₃	—	4	1	no	—
561	C₂×D₄₃	—	4	2	no	—
562	C₂×D₄₃	—	4	1	no	—
563	C₂×D₄₃	—	8	4	no	—
564	C₂×D₄₃	—	8	8	no	—
565	C₄×C₄₃	—	2	2	no	—
566	C₄×C₄₃	—	2	1	no	—
567	C₄×C₄₃	—	2	1	no	—
568	C₄×C₄₃	—	2	1	no	—
569	C₄×C₄₃	—	2	2	no	—
570	C₄×C₄₃	—	2	1	no	—
571	C₄×C₄₃	—	2	2	no	—
572	C₄×C₄₃	—	4	1	no	—
573	C₄×C₄₃	—	4	1	no	—
574	C₄×C₄₃	—	4	1	no	—
575	C₄×C₄₃	—	4	1	no	—
576	C₄×C₄₃	—	4	2	no	—
577	C₄×C₄₃	#525	1	2	yes	—
578	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
579	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
580	Dic₄₃	—	2	2	no	—
581	Dic₄₃	—	4	1	no	—
582	Dic₄₃	—	4	1	no	—
583	Dic₄₃	—	4	2	no	—
584	#3510	D₄₃	1	1	yes	characteristic, complemented
585	C₄×H(5,𝔽₂)	—	43	1	no	—
586	#3125	—	43	2	no	—
587	#3124	—	43	2	no	—
588	#3118	—	43	2	no	—
589	#3118	—	43	2	no	—
590	#3114	—	43	2	no	—
591	#3111	—	43	2	no	—
592	#3105	—	43	2	no	—
593	#3102	—	43	2	no	—
594	#3097	—	43	1	no	—
595	#3096	—	43	1	no	—
596	#3077	—	43	1	no	—
597	#3076	—	43	1	no	—
598	#3040	—	43	1	no	—
599	C₂×#463	—	43	1	no	—
600	#3009	—	43	1	no	—
601	#3008	—	43	1	no	—
602	#2949	—	43	1	no	—
603	#2948	—	43	1	no	—
604	#2947	—	43	1	no	—
605	#2946	—	43	1	no	—
606	#2925	—	43	1	no	—
607	C₂×C₄₃	—	2	2	no	—
608	C₂×C₄₃	—	4	2	no	—
609	C₂×C₄₃	—	8	2	no	—
610	C₂×C₄₃	C₂×#525	1	1	yes	characteristic
611	C₂×C₄₃	#3584	1	1	yes	characteristic
612	C₂×C₄₃	#3585	1	1	yes	characteristic
613	D₄₃	—	4	4	no	—
614	D₄₃	—	4	2	no	—
615	C₂×H(5,𝔽₂)	—	43	1	no	—
616	C₂×#137	—	43	1	no	—
617	C₂×AGL(1,ℤ/8)	—	43	1	no	—
618	C₂²×SD₁₆	—	43	1	no	—
619	C₂²×D₈	—	43	1	no	—
620	#559	—	2	1	no	—
621	#559	—	2	1	no	—
622	#556	—	2	1	no	—
623	#556	—	2	1	no	—
624	#551	—	2	2	no	—
625	#551	—	2	2	no	—
626	#542	C₂×D₄₃	1	2	yes	complemented
627	#542	C₂×D₄₃	1	2	yes	complemented
628	#536	C₂×D₄₃	1	1	yes	characteristic
629	#535	C₂×D₄₃	1	1	yes	characteristic
630	#533	C₂×D₄₃	1	1	yes	characteristic, complemented
631	#529	C₂×D₄₃	1	2	yes	complemented
632	#529	C₂×D₄₃	1	2	yes	complemented
633	C₂×#124	C₂×D₄₃	1	1	yes	characteristic, complemented
634	#520	—	43	1	no	—
635	#520	—	43	2	no	—
636	#520	—	43	1	no	—
637	#520	—	86	1	no	—
638	#519	C₂×D₄₃	1	1	yes	characteristic, complemented
639	#518	—	43	2	no	—
640	#518	—	43	1	no	—
641	#518	—	86	2	no	—
642	#518	—	86	1	no	—
643	#518	C₂×D₄₃	1	1	yes	characteristic, complemented
644	C₄×#41	—	43	1	no	—
645	C₄×#41	—	43	2	no	—
646	C₄×#41	—	86	1	no	—
647	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
648	C₂×C₄×D₄	—	43	1	no	—
649	C₂×C₄×D₄	—	43	2	no	—
650	C₂×C₄×D₄	—	86	2	no	—
651	C₂×C₄×D₄	—	86	1	no	—
652	#485	—	43	2	no	—
653	#485	—	43	2	no	—
654	#484	—	43	2	no	—
655	#483	—	43	2	no	—
656	#482	—	43	2	no	—
657	#482	—	43	2	no	—
658	#481	—	43	2	no	—
659	#480	—	43	2	no	—
660	#479	—	43	1	no	—
661	#479	—	43	1	no	—
662	#478	—	43	1	no	—
663	#478	—	43	1	no	—
664	#478	—	43	2	no	—
665	#478	—	43	2	no	—
666	#477	—	43	1	no	—
667	#476	—	43	1	no	—
668	#476	—	43	2	no	—
669	#475	—	43	1	no	—
670	#474	—	43	1	no	—
671	#474	—	43	2	no	—
672	#464	—	43	2	no	—
673	#464	—	43	2	no	—
674	#463	—	43	2	no	—
675	#463	—	43	2	no	—
676	#463	—	43	2	no	—
677	#463	—	43	2	no	—
678	#463	—	43	2	no	—
679	#463	—	43	2	no	—
680	#452	—	43	2	no	—
681	#452	—	43	2	no	—
682	#450	—	43	2	no	—
683	#450	—	43	2	no	—
684	#449	—	43	2	no	—
685	#449	—	43	2	no	—
686	#447	—	43	2	no	—
687	#447	—	43	2	no	—
688	#442	—	43	2	no	—
689	#442	—	43	2	no	—
690	#442	—	43	2	no	—
691	#441	—	43	2	no	—
692	#440	—	43	2	no	—
693	#440	—	43	2	no	—
694	#440	—	43	2	no	—
695	#440	—	43	2	no	—
696	C₄×Q₁₆	—	43	2	no	—
697	C₄×SD₁₆	—	43	2	no	—
698	C₄×SD₁₆	—	43	2	no	—
699	C₄×SD₁₆	—	43	2	no	—
700	C₄×SD₁₆	—	43	2	no	—
701	C₄×D₈	—	43	2	no	—
702	C₄×D₈	—	43	2	no	—
703	C₄×D₈	—	43	2	no	—
704	#433	—	43	2	no	—
705	#433	—	43	2	no	—
706	#432	—	43	2	no	—
707	#431	—	43	2	no	—
708	#428	—	43	1	no	—
709	#428	—	43	1	no	—
710	#427	—	43	1	no	—
711	#427	—	43	1	no	—
712	#423	—	43	1	no	—
713	C₂×C₄⋊C₈	—	43	1	no	—
714	#419	—	43	1	no	—
715	#418	—	43	1	no	—
716	#418	—	43	1	no	—
717	#418	—	43	1	no	—
718	#416	—	43	1	no	—
719	#416	—	43	1	no	—
720	C₂×#103	—	43	1	no	—
721	C₂×#102	—	43	1	no	—
722	#408	—	43	1	no	—
723	#408	—	43	1	no	—
724	#405	—	43	1	no	—
725	#405	—	43	1	no	—
726	C₄₃	#60592	1	1	yes	characteristic, complemented, Sylow
727	H(5,𝔽₂)	—	86	4	no	—
728	H(5,𝔽₂)	—	86	4	no	—
729	C₂×#41	—	43	1	no	—
730	C₂×#41	—	43	2	no	—
731	C₂×#41	—	86	1	no	—
732	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
733	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
734	C₂²×D₄	—	43	1	no	—
735	C₂²×D₄	—	43	2	no	—
736	C₂²×D₄	—	86	2	no	—
737	C₂²×D₄	—	86	1	no	—
738	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
739	C₂³×C₄	—	86	1	no	—
740	C₂³×C₄	—	86	2	no	—
741	#137	—	86	4	no	—
742	AGL(1,ℤ/8)	—	86	4	no	—
743	C₂×Q₁₆	—	43	2	no	—
744	C₂×SD₁₆	—	43	2	no	—
745	C₂×SD₁₆	—	43	2	no	—
746	C₂×SD₁₆	—	43	2	no	—
747	C₂×SD₁₆	—	43	2	no	—
748	C₂×SD₁₆	—	86	4	no	—
749	C₂×D₈	—	43	2	no	—
750	C₂×D₈	—	43	2	no	—
751	C₂×D₈	—	43	2	no	—
752	C₂×D₈	—	86	4	no	—
753	C₂×M₁₆	—	43	1	no	—
754	C₂×M₁₆	—	43	1	no	—
755	C₂²×C₈	—	43	1	no	—
756	C₂²×C₈	—	43	1	no	—
757	C₄⋊Q₈	—	2	1	no	—
758	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
759	C₄⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
760	#127	—	2	1	no	—
761	#126	—	2	2	no	—
762	#126	—	2	2	no	—
763	#126	—	2	2	no	—
764	#126	—	2	2	no	—
765	#125	C₂²×D₄₃	1	1	yes	characteristic
766	#125	C₂²×D₄₃	1	1	yes	characteristic
767	#124	—	2	1	no	—
768	#124	—	2	1	no	—
769	#124	—	2	2	no	—
770	#124	—	2	2	no	—
771	#124	—	2	1	no	—
772	#124	—	2	1	no	—
773	#124	C₂²×D₄₃	1	2	yes	—
774	#124	C₂²×D₄₃	1	2	yes	—
775	#123	—	2	2	no	—
776	#123	—	2	2	no	—
777	#123	—	2	2	no	—
778	#123	—	2	2	no	—
779	#123	—	2	2	no	—
780	C₂²⋊Q₈	—	2	1	no	—
781	C₂²⋊Q₈	—	2	1	no	—
782	C₂²⋊Q₈	—	2	2	no	—
783	C₂²⋊Q₈	—	2	2	no	—
784	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
785	C₂²⋊Q₈	C₂²×D₄₃	1	2	yes	—
786	#121	C₂²×D₄₃	1	2	yes	—
787	#121	C₂²×D₄₃	1	2	yes	—
788	#120	—	2	2	no	—
789	C₄×Q₈	—	2	1	no	—
790	C₄×Q₈	—	2	1	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	—	43	1	no	—
794	C₄×Q₈	—	43	2	no	—
795	C₄×Q₈	—	43	1	no	—
796	C₄×Q₈	—	86	1	no	—
797	C₄×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
798	C₄×Q₈	C₂²⋊D₄₃	1	1	yes	characteristic
799	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
800	C₄×Q₈	C₂²×D₄₃	1	2	yes	—
801	C₄×D₄	—	2	2	no	—
802	C₄×D₄	—	2	2	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	1	no	—
805	C₄×D₄	—	43	2	no	—
806	C₄×D₄	—	43	1	no	—
807	C₄×D₄	—	43	2	no	—
808	C₄×D₄	—	43	2	no	—
809	C₄×D₄	—	43	2	no	—
810	C₄×D₄	—	43	2	no	—
811	C₄×D₄	—	43	1	no	—
812	C₄×D₄	—	86	2	no	—
813	C₄×D₄	—	86	1	no	—
814	C₄×D₄	—	86	1	no	—
815	C₄×D₄	—	86	2	no	—
816	C₄×D₄	—	86	1	no	—
817	C₄×D₄	—	86	2	no	—
818	C₄×D₄	—	86	1	no	—
819	C₄×D₄	—	86	2	no	—
820	C₄×D₄	—	86	1	no	—
821	C₄×D₄	—	86	2	no	—
822	C₄×D₄	—	86	2	no	—
823	C₄×D₄	—	86	2	no	—
824	C₄×D₄	—	86	2	no	—
825	C₄×D₄	—	86	2	no	—
826	C₄×D₄	—	86	1	no	—
827	C₄×D₄	—	86	2	no	—
828	C₄×D₄	—	86	1	no	—
829	C₄×D₄	C₂²⋊D₄₃	1	2	yes	—
830	C₄×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
831	C₄×D₄	C₂²⋊D₄₃	1	2	yes	—
832	C₄×D₄	C₂²⋊D₄₃	1	1	yes	characteristic
833	C₄×D₄	C₂²×D₄₃	1	2	yes	—
834	C₄×D₄	C₂²×D₄₃	1	2	yes	—
835	#117	—	2	2	no	—
836	#117	—	2	2	no	—
837	#117	—	2	2	no	—
838	#117	—	43	1	no	—
839	#117	—	43	2	no	—
840	#117	—	86	1	no	—
841	#117	—	86	2	no	—
842	#117	—	86	2	no	—
843	#117	—	86	1	no	—
844	#117	C₂²×D₄₃	1	1	yes	characteristic
845	#117	C₂²×D₄₃	1	1	yes	characteristic
846	#117	C₂²×D₄₃	1	1	yes	characteristic
847	#117	C₂²×D₄₃	1	2	yes	—
848	C₂×C₄⋊C₄	—	43	1	no	—
849	C₂×C₄⋊C₄	—	43	2	no	—
850	C₂×C₄⋊C₄	—	86	1	no	—
851	C₂×C₄⋊C₄	—	86	2	no	—
852	C₂×C₂²⋊C₄	—	2	1	no	—
853	C₂×C₂²⋊C₄	—	2	1	no	—
854	C₂×C₂²⋊C₄	—	2	2	no	—
855	C₂×C₂²⋊C₄	—	86	1	no	—
856	C₂×C₂²⋊C₄	—	86	2	no	—
857	C₂×C₂²⋊C₄	—	86	2	no	—
858	C₂×C₂²⋊C₄	—	86	2	no	—
859	C₂×C₂²⋊C₄	—	86	2	no	—
860	C₂×C₄²	—	86	2	no	—
861	C₂×C₄²	—	86	1	no	—
862	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
863	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
864	#107	—	43	1	no	—
865	#107	—	43	1	no	—
866	#107	—	43	1	no	—
867	#107	—	43	1	no	—
868	#107	—	43	2	no	—
869	#107	—	43	2	no	—
870	#106	—	43	1	no	—
871	#106	—	43	1	no	—
872	#106	—	43	1	no	—
873	#106	—	43	1	no	—
874	#106	—	43	2	no	—
875	#106	—	43	2	no	—
876	C₄⋊C₈	—	43	1	no	—
877	C₄⋊C₈	—	43	1	no	—
878	C₄⋊C₈	—	43	1	no	—
879	C₄⋊C₈	—	43	1	no	—
880	C₄⋊C₈	—	43	2	no	—
881	C₄⋊C₈	—	43	2	no	—
882	#103	—	43	2	no	—
883	#103	—	43	2	no	—
884	#103	—	43	2	no	—
885	#103	—	43	2	no	—
886	#103	—	43	1	no	—
887	#103	—	43	1	no	—
888	#103	—	43	1	no	—
889	#103	—	43	1	no	—
890	#102	—	43	2	no	—
891	#102	—	43	2	no	—
892	#102	—	43	2	no	—
893	#102	—	43	2	no	—
894	#102	—	43	1	no	—
895	#102	—	43	1	no	—
896	#102	—	43	1	no	—
897	#102	—	43	1	no	—
898	#102	—	43	2	no	—
899	#102	—	43	2	no	—
900	#102	—	43	2	no	—
901	#102	—	43	2	no	—
902	C₂²⋊C₈	—	43	2	no	—
903	C₂²⋊C₈	—	43	2	no	—
904	C₂²⋊C₈	—	43	2	no	—
905	C₂²⋊C₈	—	43	2	no	—
906	#97	—	43	2	no	—
907	#97	—	43	2	no	—
908	C₄×C₈	—	43	2	no	—
909	C₄×C₈	—	43	2	no	—
910	C₂⁴	—	2	1	no	—
911	C₂⁴	—	86	2	no	—
912	C₂⁴	—	86	1	no	—
913	#41	—	2	2	no	—
914	#41	—	2	2	no	—
915	#41	—	43	4	no	—
916	#41	—	86	4	no	—
917	#41	—	86	4	no	—
918	#41	—	86	8	no	—
919	#41	—	86	2	no	—
920	C₂×Q₈	—	2	1	no	—
921	C₂×Q₈	—	2	1	no	—
922	C₂×Q₈	—	2	1	no	—
923	C₂×Q₈	—	2	2	no	—
924	C₂×Q₈	—	2	2	no	—
925	C₂×Q₈	—	43	1	no	—
926	C₂×Q₈	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
927	C₂×Q₈	C₂³×D₄₃	1	2	yes	—
928	C₂×D₄	—	2	2	no	—
929	C₂×D₄	—	2	2	no	—
930	C₂×D₄	—	2	1	no	—
931	C₂×D₄	—	2	2	no	—
932	C₂×D₄	—	2	2	no	—
933	C₂×D₄	—	43	4	no	—
934	C₂×D₄	—	43	2	no	—
935	C₂×D₄	—	43	1	no	—
936	C₂×D₄	—	86	4	no	—
937	C₂×D₄	—	86	4	no	—
938	C₂×D₄	—	86	16	no	—
939	C₂×D₄	—	86	8	no	—
940	C₂×D₄	—	86	2	no	—
941	C₂×D₄	—	86	1	no	—
942	C₂×D₄	—	86	2	no	—
943	C₂×D₄	—	86	1	no	—
944	C₂×D₄	—	86	2	no	—
945	C₂×D₄	C₂×C₂²⋊D₄₃	1	2	yes	—
946	C₂×D₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
947	C₂×D₄	C₂³×D₄₃	1	2	yes	—
948	C₂²×C₄	—	2	1	no	—
949	C₂²×C₄	—	2	2	no	—
950	C₂²×C₄	—	2	2	no	—
951	C₂²×C₄	—	86	2	no	—
952	C₂²×C₄	—	86	1	no	—
953	C₂²×C₄	—	86	2	no	—
954	C₂²×C₄	—	86	1	no	—
955	C₂²×C₄	—	86	2	no	—
956	C₂²×C₄	—	86	1	no	—
957	C₂²×C₄	—	86	2	no	—
958	C₂²×C₄	—	86	2	no	—
959	C₂²×C₄	—	86	2	no	—
960	C₂²×C₄	—	86	2	no	—
961	C₂²×C₄	—	86	1	no	—
962	C₂²×C₄	—	344	4	no	—
963	C₂²×C₄	—	344	2	no	—
964	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
965	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
966	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
967	C₂²×C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
968	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
969	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
970	Q₁₆	—	86	4	no	—
971	SD₁₆	—	86	4	no	—
972	SD₁₆	—	86	4	no	—
973	SD₁₆	—	86	4	no	—
974	SD₁₆	—	86	4	no	—
975	D₈	—	86	4	no	—
976	D₈	—	86	4	no	—
977	D₈	—	86	4	no	—
978	M₁₆	—	86	2	no	—
979	M₁₆	—	86	2	no	—
980	C₂×C₈	—	43	1	no	—
981	C₂×C₈	—	43	1	no	—
982	C₂×C₈	—	43	2	no	—
983	C₂×C₈	—	43	2	no	—
984	C₂×C₈	—	43	1	no	—
985	C₂×C₈	—	43	1	no	—
986	C₂×C₈	—	86	2	no	—
987	C₂×C₈	—	86	2	no	—
988	C₄⋊C₄	—	2	1	no	—
989	C₄⋊C₄	—	2	1	no	—
990	C₄⋊C₄	—	2	2	no	—
991	C₄⋊C₄	—	2	2	no	—
992	C₄⋊C₄	—	2	2	no	—
993	C₄⋊C₄	—	2	2	no	—
994	C₄⋊C₄	—	2	1	no	—
995	C₄⋊C₄	—	2	1	no	—
996	C₄⋊C₄	—	2	1	no	—
997	C₄⋊C₄	—	2	1	no	—
998	C₄⋊C₄	—	43	2	no	—
999	C₄⋊C₄	—	43	1	no	—
1000	C₄⋊C₄	—	43	1	no	—
1001	C₄⋊C₄	—	86	2	no	—
1002	C₄⋊C₄	—	86	1	no	—
1003	C₄⋊C₄	—	86	2	no	—
1004	C₄⋊C₄	—	86	1	no	—
1005	C₄⋊C₄	—	86	1	no	—
1006	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1007	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1008	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1009	C₄⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1010	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1011	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1012	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1013	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
1014	C₂²⋊C₄	—	2	1	no	—
1015	C₂²⋊C₄	—	2	1	no	—
1016	C₂²⋊C₄	—	2	2	no	—
1017	C₂²⋊C₄	—	2	2	no	—
1018	C₂²⋊C₄	—	2	2	no	—
1019	C₂²⋊C₄	—	2	2	no	—
1020	C₂²⋊C₄	—	2	2	no	—
1021	C₂²⋊C₄	—	2	2	no	—
1022	C₂²⋊C₄	—	2	2	no	—
1023	C₂²⋊C₄	—	2	2	no	—
1024	C₂²⋊C₄	—	2	2	no	—
1025	C₂²⋊C₄	—	2	2	no	—
1026	C₂²⋊C₄	—	86	2	no	—
1027	C₂²⋊C₄	—	86	1	no	—
1028	C₂²⋊C₄	—	86	2	no	—
1029	C₂²⋊C₄	—	86	1	no	—
1030	C₂²⋊C₄	—	86	2	no	—
1031	C₂²⋊C₄	—	86	2	no	—
1032	C₂²⋊C₄	—	86	2	no	—
1033	C₂²⋊C₄	—	86	2	no	—
1034	C₂²⋊C₄	—	86	1	no	—
1035	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1036	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1037	C₂²⋊C₄	C₂×C₂²⋊D₄₃	1	2	yes	—
1038	C₄²	—	2	2	no	—
1039	C₄²	—	2	2	no	—
1040	C₄²	—	2	1	no	—
1041	C₄²	—	2	1	no	—
1042	C₄²	—	86	1	no	—
1043	C₄²	—	86	2	no	—
1044	C₄²	—	86	1	no	—
1045	C₄²	—	86	2	no	—
1046	C₄²	—	86	1	no	—
1047	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
1048	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1049	C₄²	C₂×C₂²⋊D₄₃	1	2	yes	—
1050	C₄²	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
1051	C₄²	C₂³×D₄₃	1	2	yes	—
1052	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1053	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1054	C₂³	—	2	2	no	—
1055	C₂³	—	4	2	no	—
1056	C₂³	—	8	1	no	—
1057	C₂³	—	8	1	no	—
1058	C₂³	—	86	8	no	—
1059	C₂³	—	86	4	no	—
1060	C₂³	—	86	2	no	—
1061	C₂³	—	86	1	no	—
1062	C₂³	—	344	1	no	—
1063	C₂³	—	344	2	no	—
1064	C₂³	—	344	1	no	—
1065	C₂³	—	344	2	no	—
1066	C₂³	C₂²×C₂²⋊D₄₃	1	2	yes	—
1067	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1068	Q₈	—	2	2	no	—
1069	Q₈	—	2	2	no	—
1070	Q₈	—	2	2	no	—
1071	Q₈	—	4	2	no	—
1072	Q₈	—	8	1	no	—
1073	Q₈	—	8	1	no	—
1074	Q₈	—	43	2	no	—
1075	Q₈	—	86	1	no	—
1076	D₄	—	2	4	no	—
1077	D₄	—	2	2	no	—
1078	D₄	—	2	2	no	—
1079	D₄	—	2	2	no	—
1080	D₄	—	4	2	no	—
1081	D₄	—	8	2	no	—
1082	D₄	—	8	2	no	—
1083	D₄	—	43	4	no	—
1084	D₄	—	43	2	no	—
1085	D₄	—	86	8	no	—
1086	D₄	—	86	8	no	—
1087	D₄	—	86	4	no	—
1088	D₄	—	86	4	no	—
1089	D₄	—	86	1	no	—
1090	D₄	—	86	2	no	—
1091	C₂×C₄	—	2	2	no	—
1092	C₂×C₄	—	2	2	no	—
1093	C₂×C₄	—	2	1	no	—
1094	C₂×C₄	—	2	1	no	—
1095	C₂×C₄	—	2	2	no	—
1096	C₂×C₄	—	2	1	no	—
1097	C₂×C₄	—	2	1	no	—
1098	C₂×C₄	—	4	2	no	—
1099	C₂×C₄	—	4	1	no	—
1100	C₂×C₄	—	4	2	no	—
1101	C₂×C₄	—	4	1	no	—
1102	C₂×C₄	—	4	2	no	—
1103	C₂×C₄	—	8	2	no	—
1104	C₂×C₄	—	8	2	no	—
1105	C₂×C₄	—	86	8	no	—
1106	C₂×C₄	—	86	1	no	—
1107	C₂×C₄	—	86	4	no	—
1108	C₂×C₄	—	86	1	no	—
1109	C₂×C₄	—	86	2	no	—
1110	C₂×C₄	—	86	1	no	—
1111	C₂×C₄	—	344	2	no	—
1112	C₂×C₄	—	344	2	no	—
1113	C₂×C₄	—	344	2	no	—
1114	C₂×C₄	—	344	2	no	—
1115	C₂×C₄	—	344	1	no	—
1116	C₂×C₄	—	344	1	no	—
1117	C₂×C₄	—	344	2	no	—
1118	C₂×C₄	—	172	2	no	—
1119	C₂×C₄	—	172	4	no	—
1120	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1121	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1122	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1123	C₂×C₄	C₂²×C₂²⋊D₄₃	1	2	yes	—
1124	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1125	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1126	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1127	C₂×C₄	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
1128	C₂×C₄	#41×D₄₃	1	2	yes	—
1129	C₂×C₄	#41×D₄₃	1	2	yes	—
1130	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1131	C₈	—	86	1	no	—
1132	C₈	—	86	1	no	—
1133	C₈	—	86	1	no	—
1134	C₈	—	86	1	no	—
1135	C₈	—	86	2	no	—
1136	C₈	—	86	2	no	—
1137	C₂²	—	2	1	no	—
1138	C₂²	—	2	1	no	—
1139	C₂²	—	2	2	no	—
1140	C₂²	—	2	2	no	—
1141	C₂²	—	2	2	no	—
1142	C₂²	—	4	2	no	—
1143	C₂²	—	4	2	no	—
1144	C₂²	—	4	2	no	—
1145	C₂²	—	16	2	no	—
1146	C₂²	—	86	4	no	—
1147	C₂²	—	86	2	no	—
1148	C₂²	—	344	4	no	—
1149	C₂²	—	344	8	no	—
1150	C₂²	—	172	2	no	—
1151	C₂²	—	172	1	no	—
1152	C₂²	—	172	2	no	—
1153	C₂²	—	172	1	no	—
1154	C₂²	#14583406	1	2	yes	—
1155	C₂²	C₂³×C₂²⋊D₄₃	1	1	yes	characteristic
1156	C₄	—	2	1	no	—
1157	C₄	—	2	2	no	—
1158	C₄	—	2	1	no	—
1159	C₄	—	2	2	no	—
1160	C₄	—	2	1	no	—
1161	C₄	—	2	2	no	—
1162	C₄	—	2	1	no	—
1163	C₄	—	4	1	no	—
1164	C₄	—	4	1	no	—
1165	C₄	—	4	2	no	—
1166	C₄	—	4	1	no	—
1167	C₄	—	4	1	no	—
1168	C₄	—	86	2	no	—
1169	C₄	—	172	1	no	—
1170	C₄	—	172	1	no	—
1171	C₄	—	172	2	no	—
1172	C₄	#14583406	1	2	yes	—
1173	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1174	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1175	C₂	—	2	2	no	—
1176	C₂	—	4	2	no	—
1177	C₂	—	8	2	no	—
1178	C₂	—	172	4	no	—
1179	C₂	—	172	2	no	—
1180	C₂	C₂×#14583406	1	1	yes	characteristic
1181	C₂	#19149366	1	1	yes	characteristic
1182	C₂	#19149374	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×#3510	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	#19143861	C₂
hypercenter	#3510	D₄₃
hypocenter	C₄₃	#60592
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×#41 ◁ #3510

Complements

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

N	H ≅ G/N	type
1. C₄×#13063371	C₂	semidirect
2. #19144866	C₂	semidirect
3. #19144851	C₂	semidirect
4. #19144773	C₂	semidirect
5. #19144773	C₂	semidirect
6. #19144729	C₂	semidirect
7. #19144698	C₂	semidirect
8. #19144638	C₂	semidirect
9. #19144607	C₂	semidirect
10. #19144558	C₂	semidirect
11. #19144547	C₂	semidirect
12. #19144388	C₂	semidirect
13. #19144377	C₂	semidirect
14. #19144085	C₂	semidirect
15. C₂×#14583111	C₂	semidirect
16. #19143870	C₂	semidirect
18. #19143454	C₂	semidirect
19. #19143445	C₂	semidirect
20. #19143438	C₂	semidirect
21. #19143427	C₂	semidirect
22. #19143261	C₂	semidirect
23. C₄₃×#3510	C₂	semidirect
32. #14583379	C₂²	semidirect
34. #14583373	C₂²	semidirect
39. C₄×#10621898	C₂²	semidirect
41. C₂×C₄×D₁₇₂	C₂²	semidirect
44. #14583237	C₂²	semidirect
45. #14583237	C₂²	semidirect
46. #14583232	C₂²	semidirect
47. #14583227	C₂²	semidirect
48. #14583220	C₂²	semidirect
49. #14583220	C₂²	semidirect
50. #14583215	C₂²	semidirect
51. #14583210	C₂²	semidirect
52. #14583203	C₂²	semidirect
53. #14583203	C₂²	semidirect
54. #14583196	C₂²	semidirect
55. #14583196	C₂²	semidirect
56. #14583196	C₂²	semidirect
57. #14583196	C₂²	semidirect
58. #14583191	C₂²	semidirect
59. #14583186	C₂²	semidirect
60. #14583186	C₂²	semidirect
61. #14583181	C₂²	semidirect
62. #14583176	C₂²	semidirect
63. #14583176	C₂²	semidirect
64. #14583118	C₂²	semidirect
65. #14583118	C₂²	semidirect
66. #14583111	C₂²	semidirect
67. #14583111	C₂²	semidirect
68. #14583111	C₂²	semidirect
69. #14583111	C₂²	semidirect
70. #14583111	C₂²	semidirect
71. #14583111	C₂²	semidirect
72. #14583059	C₂²	semidirect
73. #14583059	C₂²	semidirect
74. #14583049	C₂²	semidirect
75. #14583049	C₂²	semidirect
80. #14583009	C₂²	semidirect
81. #14583009	C₂²	semidirect
82. #14583009	C₂²	semidirect
83. #14583004	C₂²	semidirect
84. #14582999	C₂²	semidirect
85. #14582997	C₂²	semidirect
86. #14582997	C₂²	semidirect
87. #14582997	C₂²	semidirect
88. C₄×#10621885	C₂²	semidirect
89. C₄×#10621884	C₂²	semidirect
90. C₄×#10621884	C₂²	semidirect
91. C₄×#10621884	C₂²	semidirect
92. C₄×#10621883	C₂²	semidirect
93. C₄×#10621882	C₂²	semidirect
94. C₄×#10621882	C₂²	semidirect
95. C₄×#10621882	C₂²	semidirect
96. #14582960	C₂²	semidirect
97. #14582960	C₂²	semidirect
98. #14582956	C₂²	semidirect
99. #14582952	C₂²	semidirect
100. #14582942	C₂²	semidirect
101. #14582942	C₂²	semidirect
102. #14582935	C₂²	semidirect
103. #14582935	C₂²	semidirect
104. #14582923	C₂²	semidirect
105. C₂×C₄⋊(C₄₃⋊C₈)	C₂²	semidirect
106. #14582908	C₂²	semidirect
107. #14582904	C₂²	semidirect
112. C₂×#13063249	C₂²	semidirect
113. C₂×#13063246	C₂²	semidirect
116. #14582855	C₂²	semidirect
117. #14582855	C₂²	semidirect
124. C₄₃×#542	C₂²	semidirect
125. C₄₃×#542	C₂²	semidirect
128. C₄₃×#533	C₂²	semidirect
129. C₄₃×#529	C₂²	semidirect
130. C₄₃×#529	C₂²	semidirect
131. C₂×#124×C₄₃	C₂²	semidirect
132. C₄₃×#519	C₂²	semidirect
133. C₄₃×#518	C₂²	semidirect
584. #3510	D₄₃	semidirect
626. #542	C₂×D₄₃	semidirect
627. #542	C₂×D₄₃	semidirect
630. #533	C₂×D₄₃	semidirect
631. #529	C₂×D₄₃	semidirect
632. #529	C₂×D₄₃	semidirect
633. C₂×#124	C₂×D₄₃	semidirect
638. #519	C₂×D₄₃	semidirect
643. #518	C₂×D₄₃	semidirect
726. C₄₃	#60592	semidirect

Maximal subgroups

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

subgroup	index
C₄×#13063371	2
#19144866	2
#19144851	2
#19144773	2
#19144729	2
#19144698	2
#19144638	2
#19144607	2
#19144558	2
#19144547	2
#19144388	2
#19144377	2
#19144085	2
C₂×#14583111	2
#19143870	2
#19143861	2
#19143454	2
#19143445	2
#19143438	2
#19143427	2
#19143261	2
C₄₃×#3510	2
#60592	43