Subgroups — #25961767

Order 11008.

1790 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19147980	C₂	1	1	yes	maximal, characteristic
2	#19143763	C₂	1	2	yes	maximal, complemented
3	#19143762	C₂	1	2	yes	maximal, complemented
4	#19143753	C₂	1	2	yes	maximal, complemented
5	#19143751	C₂	1	2	yes	maximal, complemented
6	#19143742	C₂	1	2	yes	maximal, complemented
7	#19143740	C₂	1	2	yes	maximal, complemented
8	#19143732	C₂	1	2	yes	maximal, complemented
9	#19143731	C₂	1	2	yes	maximal, complemented
10	#19143541	C₂	1	1	yes	maximal, characteristic, complemented
11	#19143541	C₂	1	1	yes	maximal, characteristic, complemented
12	#19143337	C₂	1	1	yes	maximal, characteristic, complemented
13	#19143337	C₂	1	1	yes	maximal, characteristic, complemented
14	#19143297	C₂	1	1	yes	maximal, characteristic, complemented
15	#19143296	C₂	1	1	yes	maximal, characteristic, complemented
16	#19143288	C₂	1	1	yes	maximal, characteristic, complemented
17	#19143287	C₂	1	1	yes	maximal, characteristic, complemented
18	#19143261	C₂	1	1	yes	maximal, characteristic, complemented
19	#19143260	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143232	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143164	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#14582924	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#2906	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063333	C₂²	1	1	yes	characteristic
25	C₂×#13063333	C₂²	1	1	yes	characteristic
26	C₂²×#10621872	C₂²	1	1	yes	characteristic
27	C₂²×C₈×D₄₃	C₂²	1	1	yes	characteristic
28	#14583521	C₄	1	1	yes	characteristic
29	#14583521	C₄	1	1	yes	characteristic
30	#14583514	C₄	1	1	yes	characteristic
31	#14583514	C₄	1	1	yes	characteristic
32	#14583507	C₄	1	1	yes	characteristic
33	#14583507	C₄	1	1	yes	characteristic
34	#14583500	C₄	1	1	yes	characteristic
35	#14583500	C₄	1	1	yes	characteristic
36	#14583491	C₄	1	2	yes	—
37	#14583491	C₄	1	2	yes	—
38	#14583482	C₄	1	2	yes	—
39	#14583482	C₄	1	2	yes	—
40	#14583452	C₂²	1	1	yes	characteristic
41	#14583445	C₂²	1	1	yes	characteristic
42	#14583433	C₂²	1	2	yes	—
43	#14583433	C₂²	1	2	yes	—
44	#14583427	C₂²	1	2	yes	—
45	#14583427	C₂²	1	2	yes	—
46	#14583411	C₂²	1	1	yes	characteristic
47	#14583406	C₂²	1	1	yes	characteristic
48	C₄×#10621898	C₂²	1	1	yes	characteristic
49	C₂×#13063282	C₂²	1	1	yes	characteristic
50	#14583028	C₂²	1	2	yes	complemented
51	#14583028	C₂²	1	2	yes	complemented
52	#14583028	C₂²	1	2	yes	complemented
53	#14583028	C₂²	1	2	yes	complemented
54	#14583026	C₂²	1	2	yes	complemented
55	#14583026	C₂²	1	2	yes	complemented
56	#14583023	C₂²	1	2	yes	complemented
57	#14583023	C₂²	1	2	yes	complemented
58	#14582976	C₂²	1	2	yes	—
59	#14582976	C₂²	1	2	yes	—
60	#14582975	C₂²	1	2	yes	—
61	#14582975	C₂²	1	2	yes	—
62	#14582975	C₂²	1	2	yes	complemented
63	#14582975	C₂²	1	2	yes	complemented
64	#14582970	C₂²	1	2	yes	—
65	#14582970	C₂²	1	2	yes	—
66	#14582970	C₂²	1	2	yes	complemented
67	#14582970	C₂²	1	2	yes	complemented
68	#14582969	C₂²	1	2	yes	—
69	#14582969	C₂²	1	2	yes	—
70	#14582969	C₂²	1	2	yes	—
71	#14582969	C₂²	1	2	yes	—
72	#14582968	C₂²	1	2	yes	—
73	#14582968	C₂²	1	2	yes	—
74	#14582968	C₂²	1	2	yes	complemented
75	#14582968	C₂²	1	2	yes	complemented
76	#14582964	C₂²	1	2	yes	—
77	#14582964	C₂²	1	2	yes	—
78	C₈×C₂²⋊D₄₃	C₂²	1	2	yes	—
79	C₈×C₂²⋊D₄₃	C₂²	1	2	yes	—
80	C₈×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
81	C₈×C₂²⋊D₄₃	C₂²	1	2	yes	complemented
82	#14582960	C₂²	1	2	yes	complemented
83	#14582960	C₂²	1	2	yes	complemented
84	#14582959	C₂²	1	2	yes	—
85	#14582959	C₂²	1	2	yes	—
86	#14582959	C₂²	1	2	yes	—
87	#14582959	C₂²	1	2	yes	—
88	#14582959	C₂²	1	2	yes	complemented
89	#14582959	C₂²	1	2	yes	complemented
90	#14582956	C₂²	1	2	yes	complemented
91	#14582955	C₂²	1	2	yes	complemented
92	#14582952	C₂²	1	2	yes	complemented
93	#14582951	C₂²	1	2	yes	complemented
94	#14582927	C₂²	1	1	yes	characteristic
95	#14582927	C₂²	1	1	yes	characteristic
96	#14582924	C₂²	1	1	yes	characteristic
97	#14582924	C₂²	1	1	yes	characteristic
98	#14582924	C₂²	1	1	yes	characteristic
99	#14582924	C₂²	1	1	yes	characteristic
100	#14582924	C₂²	1	1	yes	characteristic
101	#14582924	C₂²	1	1	yes	characteristic
102	#14582924	C₂²	1	1	yes	characteristic
103	#14582924	C₂²	1	1	yes	characteristic
104	#14582924	C₂²	1	2	yes	complemented
105	#14582924	C₂²	1	2	yes	complemented
106	#14582923	C₂²	1	1	yes	characteristic
107	#14582921	C₂²	1	2	yes	complemented
108	C₂×C₄⋊(C₄₃⋊C₈)	C₂²	1	1	yes	characteristic
109	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
110	C₂×Dic₄₃⋊C₈	C₂²	1	1	yes	characteristic
111	C₄⋊C₈×D₄₃	C₂²	1	2	yes	complemented
112	#14582866	C₂²	1	1	yes	characteristic
113	#14582866	C₂²	1	1	yes	characteristic
114	#14582865	C₂²	1	1	yes	characteristic
115	#14582865	C₂²	1	1	yes	characteristic
116	#14582862	C₂²	1	1	yes	characteristic
117	#14582862	C₂²	1	1	yes	characteristic
118	#14582855	C₂²	1	1	yes	characteristic
119	#14582855	C₂²	1	1	yes	characteristic
120	#14582854	C₂²	1	1	yes	characteristic
121	#14582854	C₂²	1	1	yes	characteristic
122	M₁₆×Dic₄₃	C₂²	1	1	yes	characteristic
123	M₁₆×Dic₄₃	C₂²	1	1	yes	characteristic
124	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
125	C₂×#131×C₄₃	C₂²	1	1	yes	characteristic
126	C₄×#41×C₄₃	C₂²	1	1	yes	characteristic
127	C₄₃×#424	C₂²	1	1	yes	characteristic
128	C₄₃×#424	C₂²	1	1	yes	characteristic
129	C₄₃×#424	C₂²	1	2	yes	complemented
130	C₄₃×#424	C₂²	1	2	yes	complemented
131	C₄₃×#423	C₂²	1	1	yes	characteristic
132	C₄₃×#423	C₂²	1	2	yes	complemented
133	C₂×C₄⋊C₈×C₄₃	C₂²	1	1	yes	characteristic
134	C₂×C₄⋊C₈×C₄₃	C₂²	1	2	yes	complemented
135	C₂×#10621898	C₂³	1	1	yes	characteristic
136	C₂²×C₄×D₄₃	C₂³	1	1	yes	characteristic
137	#13063333	—	4	2	no	—
138	#13063333	—	4	2	no	—
139	C₂×#10621877	C₂³	1	1	yes	characteristic
140	C₂×#10621877	C₂³	1	1	yes	characteristic
141	C₂×#10621872	—	4	2	no	—
142	C₂×#10621872	C₂³	1	1	yes	characteristic
143	C₂×#10621872	C₂³	1	1	yes	characteristic
144	C₂×#10621872	C₂³	1	1	yes	characteristic
145	C₂×#10621872	C₂³	1	1	yes	characteristic
146	C₂×#10621872	C₂³	1	2	yes	—
147	C₂×#10621872	C₂³	1	2	yes	—
148	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
149	C₂²×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
150	C₂×C₈×D₄₃	—	4	2	no	—
151	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
152	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
153	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
154	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
155	C₂×C₈×D₄₃	C₂³	1	2	yes	—
156	C₂×C₈×D₄₃	C₂³	1	2	yes	—
157	#13063324	C₂×C₄	1	1	yes	characteristic
158	#13063324	C₂×C₄	1	1	yes	characteristic
159	#13063323	C₂×C₄	1	1	yes	characteristic
160	#13063321	C₂×C₄	1	1	yes	characteristic
161	#13063320	C₂×C₄	1	2	yes	—
162	#13063320	C₂×C₄	1	2	yes	—
163	#13063319	C₂×C₄	1	2	yes	—
164	#13063319	C₂×C₄	1	2	yes	—
165	#13063319	C₂×C₄	1	2	yes	—
166	#13063319	C₂×C₄	1	2	yes	—
167	#13063318	C₂×C₄	1	2	yes	—
168	#13063318	C₂×C₄	1	2	yes	—
169	#13063317	C₂×C₄	1	2	yes	—
170	#13063317	C₂×C₄	1	2	yes	—
171	#13063316	C₂×C₄	1	1	yes	characteristic
172	#13063316	C₂×C₄	1	1	yes	characteristic
173	#13063315	C₂×C₄	1	2	yes	—
174	#13063315	C₂×C₄	1	2	yes	—
175	#13063314	C₂×C₄	1	1	yes	characteristic
176	#13063313	C₂×C₄	1	2	yes	—
177	#13063313	C₂×C₄	1	2	yes	—
178	#13063312	C₂×C₄	1	1	yes	characteristic
179	#13063311	C₂×C₄	1	2	yes	—
180	#13063311	C₂×C₄	1	2	yes	—
181	#13063310	C₂×C₄	1	2	yes	—
182	#13063310	C₂×C₄	1	2	yes	—
183	#13063309	C₂×C₄	1	2	yes	—
184	#13063308	C₂×C₄	1	2	yes	—
185	#13063308	C₂×C₄	1	2	yes	—
186	#13063308	C₂×C₄	1	2	yes	—
187	#13063308	C₂×C₄	1	2	yes	—
188	#13063307	C₂×C₄	1	2	yes	—
189	#13063307	C₂×C₄	1	2	yes	—
190	#13063306	C₂×C₄	1	2	yes	—
191	#13063305	C₂×C₄	1	1	yes	characteristic
192	#13063305	C₂×C₄	1	1	yes	characteristic
193	#13063304	C₂×C₄	1	2	yes	—
194	#13063304	C₂×C₄	1	2	yes	—
195	#13063303	C₂×C₄	1	2	yes	—
196	#13063303	C₂×C₄	1	2	yes	—
197	#13063302	C₂×C₄	1	2	yes	—
198	#13063302	C₂×C₄	1	2	yes	—
199	#13063301	C₂×C₄	1	1	yes	characteristic
200	#13063301	C₂×C₄	1	1	yes	characteristic
201	#13063300	C₂×C₄	1	1	yes	characteristic
202	#13063300	C₂×C₄	1	1	yes	characteristic
203	#13063299	C₂×C₄	1	2	yes	—
204	#13063299	C₂×C₄	1	2	yes	—
205	#13063298	C₂×C₄	1	2	yes	—
206	#13063298	C₂×C₄	1	2	yes	—
207	#13063297	C₂×C₄	1	2	yes	—
208	#13063297	C₂×C₄	1	2	yes	—
209	#13063296	C₂×C₄	1	1	yes	characteristic
210	#13063296	C₂×C₄	1	1	yes	characteristic
211	#13063295	C₂×C₄	1	2	yes	—
212	#13063293	C₂×C₄	1	2	yes	—
213	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
214	C₄×Dic₈₆	C₂×C₄	1	1	yes	characteristic
215	C₄×Dic₈₆	C₂³	1	2	yes	—
216	C₄×Dic₈₆	C₂³	1	2	yes	—
217	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
218	C₄×D₁₇₂	C₂×C₄	1	1	yes	characteristic
219	C₄×D₁₇₂	C₂³	1	2	yes	—
220	C₄×D₁₇₂	C₂³	1	2	yes	—
221	C₄×C₂²⋊D₄₃	C₂×C₄	1	2	yes	—
222	C₄×C₂²⋊D₄₃	C₂×C₄	1	2	yes	—
223	C₄×C₂²⋊D₄₃	C₂³	1	2	yes	—
224	C₄×C₂²⋊D₄₃	C₂³	1	2	yes	—
225	C₄×C₂²⋊D₄₃	C₂³	1	2	yes	—
226	C₄×C₂²⋊D₄₃	C₂³	1	2	yes	—
227	#13063284	C₂³	1	1	yes	characteristic
228	#13063282	C₂×C₄	1	1	yes	characteristic
229	#13063282	C₂×C₄	1	1	yes	characteristic
230	#13063282	C₂×C₄	1	1	yes	characteristic
231	#13063282	C₂×C₄	1	1	yes	characteristic
232	#13063282	C₂³	1	1	yes	characteristic
233	#13063282	C₂³	1	1	yes	characteristic
234	#13063282	C₂³	1	1	yes	characteristic
235	#13063282	C₂³	1	1	yes	characteristic
236	#13063282	C₂³	1	2	yes	—
237	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
238	C₂×Dic₄₃⋊C₄	C₂×C₄	1	1	yes	characteristic
239	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
240	C₂×(C₂×D₄₃)⋊C₄	C₂×C₄	1	1	yes	characteristic
241	C₂×C₄×Dic₄₃	C₂³	1	1	yes	characteristic
242	C₄²×D₄₃	C₂³	1	2	yes	—
243	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
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	2	yes	—
248	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
249	Dic₄₃⋊C₈	C₂³	1	2	yes	—
250	Dic₄₃⋊C₈	C₂³	1	2	yes	—
251	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
252	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
253	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
254	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
255	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
256	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
257	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
258	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
259	Dic₄₃⋊C₈	C₂³	1	2	yes	—
260	Dic₄₃⋊C₈	C₂³	1	2	yes	—
261	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
262	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
263	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
264	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
265	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
266	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
267	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
268	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
269	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
270	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
271	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
272	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
273	#13063236	C₂³	1	2	yes	—
274	#13063236	C₂³	1	2	yes	—
275	#13063235	C₂³	1	2	yes	—
276	#13063235	C₂³	1	2	yes	—
277	#13063235	C₂³	1	2	yes	—
278	#13063235	C₂³	1	2	yes	—
279	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
280	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
281	C₈×Dic₄₃	C₂³	1	2	yes	—
282	C₈×Dic₄₃	C₂³	1	2	yes	—
283	C₈×Dic₄₃	C₂³	1	2	yes	—
284	C₈×Dic₄₃	C₂³	1	2	yes	—
285	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
286	#131×C₄₃	—	4	2	no	—
287	#131×C₄₃	—	4	2	no	—
288	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
289	C₂×M₁₆×C₄₃	C₂³	1	1	yes	characteristic
290	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
291	C₂×M₁₆×C₄₃	C₂³	1	2	yes	—
292	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
293	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
294	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
295	C₂²×C₈×C₄₃	C₂³	1	2	yes	—
296	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
297	C₄×Q₈×C₄₃	C₂×C₄	1	1	yes	characteristic
298	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
299	C₄×D₄×C₄₃	C₂×C₄	1	2	yes	—
300	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
301	C₄×D₄×C₄₃	C₂×C₄	1	1	yes	characteristic
302	#117×C₄₃	C₂³	1	1	yes	characteristic
303	#117×C₄₃	C₂³	1	2	yes	—
304	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
305	C₂×C₄²×C₄₃	C₂³	1	2	yes	—
306	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
307	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
308	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
309	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
310	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
311	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
312	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
313	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
314	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
315	C₄⋊C₈×C₄₃	C₂³	1	2	yes	—
316	C₂³×D₄₃	C₂²×C₄	1	1	yes	characteristic
317	#41×C₄₃	—	2	2	no	—
318	#41×C₄₃	—	2	2	no	—
319	C₂×Q₈×C₄₃	C₂²×C₄	1	1	yes	characteristic
320	C₂×D₄×C₄₃	C₂²×C₄	1	2	yes	—
321	C₂×D₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
322	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
323	C₂²×C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
324	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
325	C₂²×C₄×C₄₃	C₂²×C₄	1	2	yes	—
326	C₂²×C₄×C₄₃	C₂⁴	1	2	yes	—
327	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
328	C₂×C₂²⋊D₄₃	C₂²×C₄	1	2	yes	—
329	C₂×C₂²⋊D₄₃	C₂²×C₄	1	2	yes	—
330	C₂×C₂²⋊D₄₃	C₂²×C₄	1	2	yes	—
331	C₂×C₂²⋊D₄₃	C₂²×C₄	1	2	yes	—
332	C₂×C₂²⋊D₄₃	C₂²×C₄	1	2	yes	—
333	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
334	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
335	C₂²×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
336	#10621898	—	2	2	no	—
337	#10621898	—	2	2	no	—
338	C₂×D₁₇₂	C₂²×C₄	1	1	yes	characteristic
339	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
340	C₂×D₁₇₂	C₂²×C₄	1	2	yes	—
341	C₂×C₄×D₄₃	—	2	2	no	—
342	C₂×C₄×D₄₃	—	2	2	no	—
343	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
344	C₂×C₄×D₄₃	C₂²×C₄	1	1	yes	characteristic
345	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
346	C₂×C₄×D₄₃	C₂²×C₄	1	2	yes	—
347	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
348	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
349	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
350	C₂×Dic₈₆	C₂²×C₄	1	1	yes	characteristic
351	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
352	C₂×Dic₈₆	C₂²×C₄	1	2	yes	—
353	M₁₆×C₄₃	—	2	2	no	—
354	M₁₆×C₄₃	—	2	2	no	—
355	M₁₆×C₄₃	—	4	2	no	—
356	M₁₆×C₄₃	—	4	2	no	—
357	C₂×C₈×C₄₃	—	2	2	no	—
358	C₂×C₈×C₄₃	—	2	2	no	—
359	C₂×C₈×C₄₃	—	4	2	no	—
360	C₂×C₈×C₄₃	—	4	2	no	—
361	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
362	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
365	C₂×C₈×C₄₃	C₂⁴	1	2	yes	—
366	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
367	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
368	C₄⋊C₄×C₄₃	C₂²×C₄	1	1	yes	characteristic
369	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
370	C₄⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
371	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
372	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
373	C₂²⋊C₄×C₄₃	C₂²×C₄	1	2	yes	—
374	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
375	C₄²×C₄₃	C₂²×C₄	1	1	yes	characteristic
376	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
377	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
378	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
379	C₄²×C₄₃	C₂⁴	1	2	yes	—
380	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
381	C₂²⋊Dic₄₃	C₂²×C₄	1	2	yes	—
382	C₂²⋊Dic₄₃	C₂²×C₄	1	2	yes	—
383	C₂²⋊Dic₄₃	C₂²×C₄	1	2	yes	—
384	C₂²⋊Dic₄₃	C₂²×C₄	1	2	yes	—
385	C₂²⋊Dic₄₃	C₂²×C₄	1	2	yes	—
386	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	1	yes	characteristic
387	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	1	yes	characteristic
388	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	1	yes	characteristic
389	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	1	yes	characteristic
390	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	1	yes	characteristic
391	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	1	yes	characteristic
392	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	1	yes	characteristic
393	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	1	yes	characteristic
394	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
395	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
396	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
397	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
398	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
399	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
400	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
401	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
402	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
403	(C₂×D₄₃)⋊C₄	C₂²×C₄	1	2	yes	—
404	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
405	C₄⋊Dic₄₃	C₂²×C₄	1	1	yes	characteristic
406	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
407	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
408	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
409	C₄⋊Dic₄₃	C₂²×C₄	1	2	yes	—
410	Dic₄₃⋊C₄	C₂²×C₄	1	1	yes	characteristic
411	Dic₄₃⋊C₄	C₂²×C₄	1	1	yes	characteristic
412	Dic₄₃⋊C₄	C₂²×C₄	1	1	yes	characteristic
413	Dic₄₃⋊C₄	C₂²×C₄	1	1	yes	characteristic
414	Dic₄₃⋊C₄	C₂²×C₄	1	1	yes	characteristic
415	Dic₄₃⋊C₄	C₂²×C₄	1	1	yes	characteristic
416	Dic₄₃⋊C₄	C₂²×C₄	1	1	yes	characteristic
417	Dic₄₃⋊C₄	C₂²×C₄	1	1	yes	characteristic
418	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
419	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
420	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
421	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
422	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
423	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
424	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
425	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
426	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
427	Dic₄₃⋊C₄	C₂²×C₄	1	2	yes	—
428	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
429	C₄×Dic₄₃	C₂²×C₄	1	2	yes	—
430	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
431	C₄×Dic₄₃	C₂²×C₄	1	1	yes	characteristic
432	C₄×Dic₄₃	C₂⁴	1	2	yes	—
433	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
434	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
435	#10621877	—	2	2	no	—
436	#10621877	—	2	2	no	—
437	C₂×C₄₃⋊C₈	—	2	2	no	—
438	C₂×C₄₃⋊C₈	—	2	2	no	—
439	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
440	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
441	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
442	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
443	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
444	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
445	#10621872	—	4	1	no	—
446	#10621872	—	4	1	no	—
447	#10621872	—	4	1	no	—
448	#10621872	—	4	1	no	—
449	#10621872	—	4	2	no	—
450	#10621872	—	4	2	no	—
451	C₈×D₄₃	—	4	1	no	—
452	C₈×D₄₃	—	4	1	no	—
453	C₈×D₄₃	—	4	1	no	—
454	C₈×D₄₃	—	4	1	no	—
455	C₈×D₄₃	—	4	2	no	—
456	C₈×D₄₃	—	4	2	no	—
457	C₂³×C₄₃	C₂³×C₄	1	2	yes	—
458	C₂³×C₄₃	C₂³×C₄	1	1	yes	characteristic
459	C₂²×D₄₃	—	2	2	no	—
460	C₂²×D₄₃	—	4	1	no	—
461	C₂²×D₄₃	—	4	1	no	—
462	C₂²×D₄₃	C₂³×C₄	1	1	yes	characteristic
463	C₂²×D₄₃	C₂³×C₄	1	1	yes	characteristic
464	C₂²×D₄₃	C₂³×C₄	1	2	yes	—
465	Q₈×C₄₃	—	2	2	no	—
466	D₄×C₄₃	—	2	4	no	—
467	D₄×C₄₃	—	2	2	no	—
468	C₂×C₄×C₄₃	—	2	2	no	—
469	C₂×C₄×C₄₃	—	2	2	no	—
470	C₂×C₄×C₄₃	—	4	2	no	—
471	C₂×C₄×C₄₃	—	4	2	no	—
472	C₂×C₄×C₄₃	—	4	1	no	—
473	C₂×C₄×C₄₃	—	4	1	no	—
474	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
475	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
476	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
477	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
478	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
479	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
480	C₂×C₄×C₄₃	C₂³×C₄	1	2	yes	—
481	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
482	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
483	C₂×C₄×C₄₃	2₋¹⁺⁴	1	2	yes	—
484	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
485	C₂²⋊D₄₃	—	2	4	no	—
486	C₂²⋊D₄₃	—	4	2	no	—
487	C₂²⋊D₄₃	—	4	2	no	—
488	C₂²⋊D₄₃	—	4	2	no	—
489	C₂²⋊D₄₃	—	4	2	no	—
490	C₂×Dic₄₃	—	2	2	no	—
491	C₂×Dic₄₃	—	4	1	no	—
492	C₂×Dic₄₃	—	4	1	no	—
493	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
494	C₂×Dic₄₃	C₂³×C₄	1	1	yes	characteristic
495	C₂×Dic₄₃	C₂³×C₄	1	1	yes	characteristic
496	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
497	C₂×Dic₄₃	C₂³×C₄	1	2	yes	—
498	C₂×Dic₄₃	C₂³×C₄	1	1	yes	characteristic
499	C₂×Dic₄₃	C₂³×C₄	1	1	yes	characteristic
500	C₂×Dic₄₃	C₂³×C₄	1	1	yes	characteristic
501	C₂×Dic₄₃	C₂³×C₄	1	1	yes	characteristic
502	D₁₇₂	—	2	2	no	—
503	D₁₇₂	—	4	2	no	—
504	D₁₇₂	—	4	2	no	—
505	C₄×D₄₃	—	2	2	no	—
506	C₄×D₄₃	—	2	2	no	—
507	C₄×D₄₃	—	2	1	no	—
508	C₄×D₄₃	—	2	1	no	—
509	C₄×D₄₃	—	2	2	no	—
510	C₄×D₄₃	—	2	1	no	—
511	C₄×D₄₃	—	2	1	no	—
512	C₄×D₄₃	—	2	2	no	—
513	C₄×D₄₃	—	4	2	no	—
514	C₄×D₄₃	—	4	2	no	—
515	Dic₈₆	—	2	2	no	—
516	Dic₈₆	—	4	2	no	—
517	Dic₈₆	—	4	2	no	—
518	C₈×C₄₃	—	2	1	no	—
519	C₈×C₄₃	—	2	1	no	—
520	C₈×C₄₃	—	2	2	no	—
521	C₈×C₄₃	—	2	2	no	—
522	C₈×C₄₃	—	2	1	no	—
523	C₈×C₄₃	—	2	1	no	—
524	C₄₃⋊C₈	—	2	1	no	—
525	C₄₃⋊C₈	—	2	1	no	—
526	C₄₃⋊C₈	—	2	1	no	—
527	C₄₃⋊C₈	—	2	1	no	—
528	C₄₃⋊C₈	—	2	2	no	—
529	C₄₃⋊C₈	—	2	2	no	—
530	#60267	—	43	1	no	maximal, Sylow
531	C₂²×C₄₃	—	2	1	no	—
532	C₂²×C₄₃	—	2	1	no	—
533	C₂²×C₄₃	—	2	2	no	—
534	C₂²×C₄₃	—	2	2	no	—
535	C₂²×C₄₃	—	2	2	no	—
536	C₂²×C₄₃	#520	1	2	yes	—
537	C₂²×C₄₃	C₂⁴×C₄	1	1	yes	characteristic
538	C₂×D₄₃	—	2	1	no	—
539	C₂×D₄₃	—	2	1	no	—
540	C₂×D₄₃	—	2	2	no	—
541	C₂×D₄₃	—	2	1	no	—
542	C₂×D₄₃	—	2	1	no	—
543	C₂×D₄₃	—	2	1	no	—
544	C₂×D₄₃	—	2	1	no	—
545	C₂×D₄₃	—	2	2	no	—
546	C₂×D₄₃	—	2	2	no	—
547	C₂×D₄₃	—	4	4	no	—
548	C₄×C₄₃	—	2	2	no	—
549	C₄×C₄₃	—	2	2	no	—
550	C₄×C₄₃	—	2	2	no	—
551	C₄×C₄₃	—	2	1	no	—
552	C₄×C₄₃	—	2	1	no	—
553	C₄×C₄₃	—	2	1	no	—
554	C₄×C₄₃	—	2	1	no	—
555	C₄×C₄₃	#520	1	2	yes	—
556	C₄×C₄₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
557	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
558	Dic₄₃	—	2	2	no	—
559	Dic₄₃	—	2	1	no	—
560	Dic₄₃	—	2	1	no	—
561	Dic₄₃	—	2	1	no	—
562	Dic₄₃	—	2	1	no	—
563	Dic₄₃	—	2	2	no	—
564	Dic₄₃	—	2	2	no	—
565	Dic₄₃	—	2	1	no	—
566	Dic₄₃	—	2	1	no	—
567	#3455	—	43	1	no	—
568	#2995	—	43	2	no	—
569	#2995	—	43	2	no	—
570	#2994	—	43	2	no	—
571	#2994	—	43	2	no	—
572	#2993	—	43	2	no	—
573	#2993	—	43	2	no	—
574	#2992	—	43	2	no	—
575	#2992	—	43	2	no	—
576	#2962	—	43	1	no	—
577	#2962	—	43	1	no	—
578	#2935	—	43	1	no	—
579	#2935	—	43	1	no	—
580	#2930	—	43	1	no	—
581	#2930	—	43	1	no	—
582	#2929	—	43	1	no	—
583	#2929	—	43	1	no	—
584	#2925	—	43	1	no	—
585	#2925	—	43	1	no	—
586	#2921	—	43	1	no	—
587	#2906	—	43	1	no	—
588	#2906	D₄₃	1	1	yes	characteristic, complemented
589	C₂×#424	—	43	1	no	—
590	C₂×C₄₃	—	2	2	no	—
591	C₂×C₄₃	—	4	2	no	—
592	C₂×C₄₃	C₂×#520	1	1	yes	characteristic
593	C₂×C₄₃	#3573	1	1	yes	characteristic
594	C₂×C₄₃	#3573	1	1	yes	characteristic
595	D₄₃	—	4	2	no	—
596	D₄₃	—	4	1	no	—
597	D₄₃	—	4	1	no	—
598	C₂×#131	—	43	1	no	—
599	C₂×#131	—	43	1	no	—
600	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
601	C₂×#131	C₂×D₄₃	1	1	yes	characteristic
602	C₂²×M₁₆	—	43	1	no	—
603	C₂³×C₈	—	43	1	no	—
604	#542	—	43	1	no	—
605	#542	—	43	1	no	—
606	#542	—	43	1	no	—
607	#542	—	43	1	no	—
608	#541	—	43	1	no	—
609	#541	—	43	1	no	—
610	#540	—	43	1	no	—
611	#540	—	43	1	no	—
612	#539	—	43	2	no	—
613	#539	—	43	2	no	—
614	#538	—	43	2	no	—
615	#538	—	43	2	no	—
616	#533	—	43	1	no	—
617	#532	—	43	1	no	—
618	#529	—	43	2	no	—
619	#529	—	43	2	no	—
620	#529	—	43	2	no	—
621	#529	—	43	2	no	—
622	#525	—	43	1	no	—
623	#525	—	43	1	no	—
624	C₄×#41	—	43	1	no	—
625	C₄×#41	C₂×D₄₃	1	1	yes	characteristic
626	C₂×#117	—	43	1	no	—
627	#446	—	43	2	no	—
628	#446	—	43	2	no	—
629	#446	—	43	2	no	—
630	#446	—	43	2	no	—
631	#446	—	43	2	no	—
632	#446	—	43	2	no	—
633	C₈×Q₈	—	43	2	no	—
634	C₈×Q₈	—	43	2	no	—
635	#436	—	43	2	no	—
636	#436	—	43	2	no	—
637	#436	—	43	2	no	—
638	#436	—	43	2	no	—
639	#436	—	43	2	no	—
640	#436	—	43	2	no	—
641	#435	—	43	2	no	—
642	#435	—	43	2	no	—
643	#435	—	43	2	no	—
644	#435	—	43	2	no	—
645	#435	—	43	2	no	—
646	#435	—	43	2	no	—
647	#435	—	43	2	no	—
648	#435	—	43	2	no	—
649	#435	—	43	2	no	—
650	#435	—	43	2	no	—
651	#435	—	43	2	no	—
652	#435	—	43	2	no	—
653	C₈×D₄	—	43	2	no	—
654	C₈×D₄	—	43	2	no	—
655	C₈×D₄	—	43	2	no	—
656	C₈×D₄	—	43	2	no	—
657	C₈×D₄	—	43	2	no	—
658	C₈×D₄	—	43	2	no	—
659	#433	—	43	2	no	—
660	#433	—	43	2	no	—
661	#433	—	43	2	no	—
662	#433	—	43	2	no	—
663	#433	—	43	2	no	—
664	#433	—	43	2	no	—
665	#433	—	43	2	no	—
666	#433	—	43	2	no	—
667	#432	—	43	2	no	—
668	#432	—	43	2	no	—
669	#431	—	43	2	no	—
670	#431	—	43	2	no	—
671	#424	—	43	1	no	—
672	#424	—	43	1	no	—
673	#424	—	43	1	no	—
674	#424	—	43	1	no	—
675	#424	—	43	1	no	—
676	#424	—	43	1	no	—
677	#424	—	43	1	no	—
678	#424	—	43	1	no	—
679	#424	—	43	1	no	—
680	#424	—	43	1	no	—
681	#424	—	43	2	no	—
682	#424	—	43	2	no	—
683	#424	C₂×D₄₃	1	1	yes	characteristic
684	#424	C₂×D₄₃	1	1	yes	characteristic
685	#424	C₂×D₄₃	1	2	yes	complemented
686	#424	C₂×D₄₃	1	2	yes	complemented
687	#423	—	43	1	no	—
688	#423	—	43	2	no	—
689	#423	C₂×D₄₃	1	1	yes	characteristic
690	#423	C₂×D₄₃	1	2	yes	complemented
691	C₂×C₄⋊C₈	—	43	1	no	—
692	C₂×C₄⋊C₈	—	43	1	no	—
693	C₂×C₄⋊C₈	—	43	1	no	—
694	C₂×C₄⋊C₈	—	43	2	no	—
695	C₂×C₄⋊C₈	C₂×D₄₃	1	1	yes	characteristic
696	C₂×C₄⋊C₈	C₂×D₄₃	1	2	yes	complemented
697	#408	—	43	1	no	—
698	#408	—	43	1	no	—
699	#408	—	43	1	no	—
700	#408	—	43	1	no	—
701	#407	—	43	1	no	—
702	#407	—	43	1	no	—
703	#405	—	43	1	no	—
704	#405	—	43	1	no	—
705	#405	—	43	1	no	—
706	#405	—	43	1	no	—
707	C₄×M₁₆	—	43	1	no	—
708	C₄×M₁₆	—	43	1	no	—
709	C₄₃	#60267	1	1	yes	characteristic, complemented, Sylow
710	C₂×#41	—	43	1	no	—
711	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
712	C₂³×C₄	—	43	1	no	—
713	#131	—	4	2	no	—
714	#131	—	4	2	no	—
715	#131	—	172	2	no	—
716	#131	—	172	2	no	—
717	C₂×M₁₆	—	43	1	no	—
718	C₂×M₁₆	—	43	1	no	—
719	C₂×M₁₆	—	43	1	no	—
720	C₂×M₁₆	—	43	1	no	—
721	C₂×M₁₆	—	43	1	no	—
722	C₂×M₁₆	—	43	1	no	—
723	C₂×M₁₆	—	43	2	no	—
724	C₂×M₁₆	—	43	2	no	—
725	C₂×M₁₆	—	172	2	no	—
726	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
727	C₂×M₁₆	C₂²×D₄₃	1	1	yes	characteristic
728	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
729	C₂×M₁₆	C₂²×D₄₃	1	2	yes	—
730	C₂²×C₈	—	43	1	no	—
731	C₂²×C₈	—	43	1	no	—
732	C₂²×C₈	—	43	1	no	—
733	C₂²×C₈	—	43	1	no	—
734	C₂²×C₈	—	43	1	no	—
735	C₂²×C₈	—	43	1	no	—
736	C₂²×C₈	—	43	2	no	—
737	C₂²×C₈	—	43	2	no	—
738	C₂²×C₈	—	172	2	no	—
739	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
740	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
741	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
742	C₂²×C₈	C₂²×D₄₃	1	2	yes	—
743	C₄⋊Q₈	—	43	1	no	—
744	C₄⋊Q₈	—	43	1	no	—
745	C₄⋊Q₈	—	43	1	no	—
746	#127	—	43	1	no	—
747	#126	—	43	2	no	—
748	#126	—	43	2	no	—
749	#126	—	43	2	no	—
750	#126	—	43	2	no	—
751	#126	—	43	2	no	—
752	#126	—	43	2	no	—
753	#126	—	43	2	no	—
754	#126	—	43	2	no	—
755	#125	—	43	2	no	—
756	#125	—	43	2	no	—
757	#125	—	43	1	no	—
758	#125	—	43	1	no	—
759	#125	—	43	2	no	—
760	#125	—	43	2	no	—
761	#124	—	43	1	no	—
762	#124	—	43	1	no	—
763	#124	—	43	2	no	—
764	#124	—	43	2	no	—
765	#124	—	43	2	no	—
766	#124	—	43	2	no	—
767	#123	—	43	2	no	—
768	#123	—	43	2	no	—
769	#123	—	43	2	no	—
770	#123	—	43	2	no	—
771	#123	—	43	2	no	—
772	#123	—	43	2	no	—
773	#123	—	43	2	no	—
774	#123	—	43	2	no	—
775	#123	—	43	2	no	—
776	#123	—	43	2	no	—
777	C₂²⋊Q₈	—	43	1	no	—
778	C₂²⋊Q₈	—	43	1	no	—
779	C₂²⋊Q₈	—	43	2	no	—
780	C₂²⋊Q₈	—	43	2	no	—
781	C₂²⋊Q₈	—	43	1	no	—
782	C₂²⋊Q₈	—	43	1	no	—
783	C₂²⋊Q₈	—	43	2	no	—
784	C₂²⋊Q₈	—	43	2	no	—
785	C₂²⋊Q₈	—	43	2	no	—
786	C₂²⋊Q₈	—	43	2	no	—
787	#121	—	43	1	no	—
788	#121	—	43	1	no	—
789	#121	—	43	2	no	—
790	#121	—	43	2	no	—
791	#121	—	43	2	no	—
792	#121	—	43	2	no	—
793	#121	—	43	1	no	—
794	#121	—	43	1	no	—
795	#121	—	43	2	no	—
796	#121	—	43	2	no	—
797	#120	—	43	2	no	—
798	#120	—	43	2	no	—
799	C₄×Q₈	—	43	1	no	—
800	C₄×Q₈	—	43	1	no	—
801	C₄×Q₈	—	43	2	no	—
802	C₄×Q₈	—	43	2	no	—
803	C₄×Q₈	C₄×D₄₃	1	1	yes	characteristic
804	C₄×Q₈	C₄×D₄₃	1	1	yes	characteristic
805	C₄×D₄	—	43	2	no	—
806	C₄×D₄	—	43	2	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	—	43	1	no	—
813	C₄×D₄	—	43	2	no	—
814	C₄×D₄	—	43	2	no	—
815	C₄×D₄	C₄×D₄₃	1	2	yes	—
816	C₄×D₄	C₄×D₄₃	1	2	yes	—
817	C₄×D₄	C₄×D₄₃	1	1	yes	characteristic
818	C₄×D₄	C₄×D₄₃	1	1	yes	characteristic
819	#117	—	43	1	no	—
820	#117	—	43	1	no	—
821	#117	—	43	1	no	—
822	#117	—	43	1	no	—
823	#117	—	43	1	no	—
824	#117	—	43	1	no	—
825	#117	—	43	1	no	—
826	#117	—	43	1	no	—
827	#117	—	43	1	no	—
828	#117	—	43	2	no	—
829	#117	C₂²×D₄₃	1	1	yes	characteristic
830	#117	C₂²×D₄₃	1	2	yes	—
831	C₂×C₄⋊C₄	—	43	1	no	—
832	C₂×C₄⋊C₄	—	43	1	no	—
833	C₂×C₂²⋊C₄	—	43	1	no	—
834	C₂×C₂²⋊C₄	—	43	1	no	—
835	C₂×C₄²	—	43	1	no	—
836	C₂×C₄²	—	43	2	no	—
837	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
838	C₂×C₄²	C₂²×D₄₃	1	2	yes	—
839	C₄⋊C₈	—	43	1	no	—
840	C₄⋊C₈	—	43	1	no	—
841	C₄⋊C₈	—	43	2	no	—
842	C₄⋊C₈	—	43	1	no	—
843	C₄⋊C₈	—	43	1	no	—
844	C₄⋊C₈	—	43	1	no	—
845	C₄⋊C₈	—	43	1	no	—
846	C₄⋊C₈	—	43	2	no	—
847	C₄⋊C₈	—	43	1	no	—
848	C₄⋊C₈	—	43	1	no	—
849	C₄⋊C₈	—	43	2	no	—
850	C₄⋊C₈	—	43	2	no	—
851	C₄⋊C₈	—	43	1	no	—
852	C₄⋊C₈	—	43	1	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	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
858	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
859	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
860	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
861	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
862	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
863	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
864	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
865	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
866	C₄⋊C₈	C₂²×D₄₃	1	2	yes	—
867	C₂²⋊C₈	—	43	2	no	—
868	C₂²⋊C₈	—	43	2	no	—
869	C₂²⋊C₈	—	43	2	no	—
870	C₂²⋊C₈	—	43	2	no	—
871	C₂²⋊C₈	—	43	2	no	—
872	C₂²⋊C₈	—	43	2	no	—
873	C₂²⋊C₈	—	43	2	no	—
874	C₂²⋊C₈	—	43	2	no	—
875	C₂²⋊C₈	—	43	2	no	—
876	C₂²⋊C₈	—	43	2	no	—
877	C₂²⋊C₈	—	43	2	no	—
878	C₂²⋊C₈	—	43	2	no	—
879	#97	—	43	2	no	—
880	#97	—	43	2	no	—
881	#97	—	43	2	no	—
882	#97	—	43	2	no	—
883	#97	—	43	2	no	—
884	#97	—	43	2	no	—
885	C₄×C₈	—	43	2	no	—
886	C₄×C₈	—	43	2	no	—
887	C₄×C₈	—	43	2	no	—
888	C₄×C₈	—	43	2	no	—
889	C₄×C₈	—	43	2	no	—
890	C₄×C₈	—	43	2	no	—
891	C₂⁴	—	43	1	no	—
892	#41	—	2	2	no	—
893	#41	—	2	2	no	—
894	#41	—	86	2	no	—
895	#41	—	86	2	no	—
896	C₂×Q₈	—	43	1	no	—
897	C₂×Q₈	—	43	2	no	—
898	C₂×Q₈	—	43	2	no	—
899	C₂×Q₈	C₂×C₄×D₄₃	1	1	yes	characteristic
900	C₂×D₄	—	43	2	no	—
901	C₂×D₄	—	43	2	no	—
902	C₂×D₄	—	43	2	no	—
903	C₂×D₄	—	43	2	no	—
904	C₂×D₄	—	43	2	no	—
905	C₂×D₄	—	43	1	no	—
906	C₂×D₄	—	43	2	no	—
907	C₂×D₄	—	43	2	no	—
908	C₂×D₄	C₂×C₄×D₄₃	1	2	yes	—
909	C₂×D₄	C₂×C₄×D₄₃	1	1	yes	characteristic
910	C₂²×C₄	—	43	1	no	—
911	C₂²×C₄	—	43	1	no	—
912	C₂²×C₄	—	43	1	no	—
913	C₂²×C₄	—	43	1	no	—
914	C₂²×C₄	—	43	1	no	—
915	C₂²×C₄	—	43	2	no	—
916	C₂²×C₄	—	43	1	no	—
917	C₂²×C₄	—	43	1	no	—
918	C₂²×C₄	—	43	2	no	—
919	C₂²×C₄	—	43	2	no	—
920	C₂²×C₄	—	86	2	no	—
921	C₂²×C₄	—	86	2	no	—
922	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
923	C₂²×C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
924	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
925	C₂²×C₄	C₂×C₄×D₄₃	1	2	yes	—
926	C₂²×C₄	C₂³×D₄₃	1	2	yes	—
927	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
928	M₁₆	—	2	2	no	—
929	M₁₆	—	2	2	no	—
930	M₁₆	—	4	2	no	—
931	M₁₆	—	4	2	no	—
932	M₁₆	—	86	2	no	—
933	M₁₆	—	86	2	no	—
934	M₁₆	—	172	1	no	—
935	M₁₆	—	172	1	no	—
936	M₁₆	—	172	1	no	—
937	M₁₆	—	172	1	no	—
938	M₁₆	—	172	2	no	—
939	M₁₆	—	172	2	no	—
940	C₂×C₈	—	2	2	no	—
941	C₂×C₈	—	2	2	no	—
942	C₂×C₈	—	4	2	no	—
943	C₂×C₈	—	4	2	no	—
944	C₂×C₈	—	43	2	no	—
945	C₂×C₈	—	43	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	—	86	2	no	—
951	C₂×C₈	—	86	2	no	—
952	C₂×C₈	—	172	1	no	—
953	C₂×C₈	—	172	1	no	—
954	C₂×C₈	—	172	1	no	—
955	C₂×C₈	—	172	1	no	—
956	C₂×C₈	—	172	2	no	—
957	C₂×C₈	—	172	2	no	—
958	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
959	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
960	C₂×C₈	C₂³×D₄₃	1	2	yes	—
961	C₂×C₈	C₂³×D₄₃	1	2	yes	—
962	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
963	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
964	C₄⋊C₄	—	43	1	no	—
965	C₄⋊C₄	—	43	1	no	—
966	C₄⋊C₄	—	43	1	no	—
967	C₄⋊C₄	—	43	1	no	—
968	C₄⋊C₄	—	43	1	no	—
969	C₄⋊C₄	—	43	1	no	—
970	C₄⋊C₄	—	43	1	no	—
971	C₄⋊C₄	—	43	1	no	—
972	C₄⋊C₄	—	43	1	no	—
973	C₄⋊C₄	—	43	1	no	—
974	C₄⋊C₄	—	43	2	no	—
975	C₄⋊C₄	—	43	2	no	—
976	C₄⋊C₄	—	43	2	no	—
977	C₄⋊C₄	—	43	2	no	—
978	C₄⋊C₄	—	43	2	no	—
979	C₄⋊C₄	—	43	2	no	—
980	C₄⋊C₄	—	43	2	no	—
981	C₄⋊C₄	—	43	2	no	—
982	C₄⋊C₄	—	43	2	no	—
983	C₄⋊C₄	—	43	2	no	—
984	C₄⋊C₄	—	43	2	no	—
985	C₄⋊C₄	—	43	2	no	—
986	C₄⋊C₄	—	43	2	no	—
987	C₄⋊C₄	—	43	2	no	—
988	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
989	C₄⋊C₄	C₂×C₄×D₄₃	1	1	yes	characteristic
990	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
991	C₄⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
992	C₂²⋊C₄	—	43	2	no	—
993	C₂²⋊C₄	—	43	2	no	—
994	C₂²⋊C₄	—	43	2	no	—
995	C₂²⋊C₄	—	43	2	no	—
996	C₂²⋊C₄	—	43	2	no	—
997	C₂²⋊C₄	—	43	1	no	—
998	C₂²⋊C₄	—	43	1	no	—
999	C₂²⋊C₄	—	43	1	no	—
1000	C₂²⋊C₄	—	43	1	no	—
1001	C₂²⋊C₄	—	43	1	no	—
1002	C₂²⋊C₄	—	43	1	no	—
1003	C₂²⋊C₄	—	43	1	no	—
1004	C₂²⋊C₄	—	43	1	no	—
1005	C₂²⋊C₄	—	43	2	no	—
1006	C₂²⋊C₄	—	43	2	no	—
1007	C₂²⋊C₄	—	43	2	no	—
1008	C₂²⋊C₄	—	43	2	no	—
1009	C₂²⋊C₄	—	43	2	no	—
1010	C₂²⋊C₄	—	43	2	no	—
1011	C₂²⋊C₄	—	43	2	no	—
1012	C₂²⋊C₄	—	43	2	no	—
1013	C₂²⋊C₄	—	43	2	no	—
1014	C₂²⋊C₄	—	43	2	no	—
1015	C₂²⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
1016	C₂²⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
1017	C₂²⋊C₄	C₂×C₄×D₄₃	1	2	yes	—
1018	C₄²	—	43	1	no	—
1019	C₄²	—	43	1	no	—
1020	C₄²	—	43	2	no	—
1021	C₄²	—	43	2	no	—
1022	C₄²	—	43	1	no	—
1023	C₄²	—	43	1	no	—
1024	C₄²	—	43	2	no	—
1025	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
1026	C₄²	C₂×C₄×D₄₃	1	1	yes	characteristic
1027	C₄²	C₂×C₄×D₄₃	1	2	yes	—
1028	C₄²	C₂×C₄×D₄₃	1	2	yes	—
1029	C₄²	C₂³×D₄₃	1	2	yes	—
1030	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1031	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1032	C₂³	—	43	1	no	—
1033	C₂³	—	43	1	no	—
1034	C₂³	—	43	2	no	—
1035	C₂³	—	86	2	no	—
1036	C₂³	—	172	1	no	—
1037	C₂³	—	172	1	no	—
1038	C₂³	C₂²×C₄×D₄₃	1	2	yes	—
1039	C₂³	C₂²×C₄×D₄₃	1	1	yes	characteristic
1040	Q₈	—	2	2	no	—
1041	Q₈	—	86	2	no	—
1042	Q₈	—	172	2	no	—
1043	Q₈	—	172	2	no	—
1044	D₄	—	2	4	no	—
1045	D₄	—	2	2	no	—
1046	D₄	—	86	4	no	—
1047	D₄	—	86	2	no	—
1048	D₄	—	172	2	no	—
1049	D₄	—	172	2	no	—
1050	D₄	—	172	2	no	—
1051	D₄	—	172	2	no	—
1052	D₄	—	172	2	no	—
1053	D₄	—	172	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	2	2	no	—
1056	C₂×C₄	—	4	1	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	4	1	no	—
1059	C₂×C₄	—	4	2	no	—
1060	C₂×C₄	—	43	1	no	—
1061	C₂×C₄	—	43	1	no	—
1062	C₂×C₄	—	43	2	no	—
1063	C₂×C₄	—	43	2	no	—
1064	C₂×C₄	—	43	2	no	—
1065	C₂×C₄	—	43	1	no	—
1066	C₂×C₄	—	43	1	no	—
1067	C₂×C₄	—	43	1	no	—
1068	C₂×C₄	—	43	1	no	—
1069	C₂×C₄	—	86	2	no	—
1070	C₂×C₄	—	86	2	no	—
1071	C₂×C₄	—	86	2	no	—
1072	C₂×C₄	—	86	1	no	—
1073	C₂×C₄	—	86	1	no	—
1074	C₂×C₄	—	86	2	no	—
1075	C₂×C₄	—	86	1	no	—
1076	C₂×C₄	—	86	1	no	—
1077	C₂×C₄	—	86	2	no	—
1078	C₂×C₄	—	172	2	no	—
1079	C₂×C₄	—	172	2	no	—
1080	C₂×C₄	—	172	1	no	—
1081	C₂×C₄	—	172	1	no	—
1082	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
1083	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
1084	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
1085	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
1086	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
1087	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
1088	C₂×C₄	C₂²×C₄×D₄₃	1	2	yes	—
1089	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
1090	C₂×C₄	#13063370	1	2	yes	—
1091	C₂×C₄	#13063373	1	2	yes	—
1092	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1093	C₈	—	2	1	no	—
1094	C₈	—	2	1	no	—
1095	C₈	—	2	1	no	—
1096	C₈	—	2	1	no	—
1097	C₈	—	2	2	no	—
1098	C₈	—	2	2	no	—
1099	C₈	—	86	1	no	—
1100	C₈	—	86	1	no	—
1101	C₈	—	86	1	no	—
1102	C₈	—	86	1	no	—
1103	C₈	—	86	2	no	—
1104	C₈	—	86	2	no	—
1105	C₂²	—	2	1	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	2	2	no	—
1109	C₂²	—	2	2	no	—
1110	C₂²	—	86	1	no	—
1111	C₂²	—	86	1	no	—
1112	C₂²	—	86	2	no	—
1113	C₂²	—	86	2	no	—
1114	C₂²	—	86	1	no	—
1115	C₂²	—	86	1	no	—
1116	C₂²	—	86	2	no	—
1117	C₂²	—	86	1	no	—
1118	C₂²	—	86	1	no	—
1119	C₂²	—	172	4	no	—
1120	C₂²	#14583380	1	2	yes	—
1121	C₂²	C₂³×C₄×D₄₃	1	1	yes	characteristic
1122	C₄	—	2	2	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	1	no	—
1125	C₄	—	2	2	no	—
1126	C₄	—	2	1	no	—
1127	C₄	—	2	1	no	—
1128	C₄	—	2	2	no	—
1129	C₄	—	86	1	no	—
1130	C₄	—	86	1	no	—
1131	C₄	—	86	2	no	—
1132	C₄	—	86	1	no	—
1133	C₄	—	86	2	no	—
1134	C₄	—	86	1	no	—
1135	C₄	—	86	1	no	—
1136	C₄	—	86	2	no	—
1137	C₄	—	86	1	no	—
1138	C₄	#14583380	1	2	yes	—
1139	C₄	C₂×#13063370	1	1	yes	characteristic
1140	C₄	C₂×#13063373	1	1	yes	characteristic
1141	C₂	—	2	2	no	—
1142	C₂	—	4	2	no	—
1143	C₂	—	172	1	no	—
1144	C₂	—	172	1	no	—
1145	C₂	—	172	2	no	—
1146	C₂	C₂×#14583380	1	1	yes	characteristic
1147	C₂	#19149306	1	1	yes	characteristic
1148	C₂	#19149308	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₄	C₂⁴×D₄₃
commutator, socle	C₂²×C₄₃	C₂⁴×C₄
Fitting	C₄₃×#2906	C₂
prime radical	#19147980	C₂
cosocle	C₂×C₄×C₄₃	C₂⁵
hypercenter	#2906	D₄₃
hypocenter	C₄₃	#60267
LCS	G ▷ C₂²×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ #2906

Complements

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

N	H ≅ G/N	type
2. #19143763	C₂	semidirect
3. #19143762	C₂	semidirect
4. #19143753	C₂	semidirect
5. #19143751	C₂	semidirect
6. #19143742	C₂	semidirect
7. #19143740	C₂	semidirect
8. #19143732	C₂	semidirect
9. #19143731	C₂	semidirect
10. #19143541	C₂	semidirect
11. #19143541	C₂	semidirect
12. #19143337	C₂	semidirect
13. #19143337	C₂	semidirect
14. #19143297	C₂	semidirect
15. #19143296	C₂	semidirect
16. #19143288	C₂	semidirect
17. #19143287	C₂	semidirect
18. #19143261	C₂	semidirect
19. #19143260	C₂	semidirect
20. #19143232	C₂	semidirect
21. #19143164	C₂	semidirect
22. C₂×#14582924	C₂	semidirect
23. C₄₃×#2906	C₂	semidirect
50. #14583028	C₂²	semidirect
51. #14583028	C₂²	semidirect
52. #14583028	C₂²	semidirect
53. #14583028	C₂²	semidirect
54. #14583026	C₂²	semidirect
55. #14583026	C₂²	semidirect
56. #14583023	C₂²	semidirect
57. #14583023	C₂²	semidirect
62. #14582975	C₂²	semidirect
63. #14582975	C₂²	semidirect
66. #14582970	C₂²	semidirect
67. #14582970	C₂²	semidirect
74. #14582968	C₂²	semidirect
75. #14582968	C₂²	semidirect
80. C₈×C₂²⋊D₄₃	C₂²	semidirect
81. C₈×C₂²⋊D₄₃	C₂²	semidirect
82. #14582960	C₂²	semidirect
83. #14582960	C₂²	semidirect
88. #14582959	C₂²	semidirect
89. #14582959	C₂²	semidirect
90. #14582956	C₂²	semidirect
91. #14582955	C₂²	semidirect
92. #14582952	C₂²	semidirect
93. #14582951	C₂²	semidirect
104. #14582924	C₂²	semidirect
105. #14582924	C₂²	semidirect
107. #14582921	C₂²	semidirect
111. C₄⋊C₈×D₄₃	C₂²	semidirect
129. C₄₃×#424	C₂²	semidirect
130. C₄₃×#424	C₂²	semidirect
132. C₄₃×#423	C₂²	semidirect
134. C₂×C₄⋊C₈×C₄₃	C₂²	semidirect
588. #2906	D₄₃	semidirect
685. #424	C₂×D₄₃	semidirect
686. #424	C₂×D₄₃	semidirect
690. #423	C₂×D₄₃	semidirect
696. C₂×C₄⋊C₈	C₂×D₄₃	semidirect
709. C₄₃	#60267	semidirect

Maximal subgroups

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

subgroup	index
#19147980	2
#19143763	2
#19143762	2
#19143753	2
#19143751	2
#19143742	2
#19143740	2
#19143732	2
#19143731	2
#19143541	2
#19143337	2
#19143297	2
#19143296	2
#19143288	2
#19143287	2
#19143261	2
#19143260	2
#19143232	2
#19143164	2
C₂×#14582924	2
C₄₃×#2906	2
#60267	43