Subgroups — #26010457

Order 11008.

10894 conjugacy classes of subgroups.

The subgroup lattice has 1034 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19149406	C₂	1	1	yes	maximal, characteristic, complemented
2	#19149405	C₂	1	1	yes	maximal, characteristic, complemented
3	#19149376	C₂	1	1	yes	maximal, characteristic, complemented
4	#19149373	C₂	1	8	yes	maximal, complemented
5	#19149372	C₂	1	6	yes	maximal, complemented
6	#19149371	C₂	1	6	yes	maximal, complemented
7	#19149370	C₂	1	8	yes	maximal, complemented
8	#19149368	C₂	1	6	yes	maximal, complemented
9	#19149367	C₂	1	8	yes	maximal, complemented
10	#19149366	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#14583703	C₂	1	6	yes	maximal, complemented
12	C₂×#14583702	C₂	1	1	yes	maximal, characteristic, complemented
13	#576×D₄₃	C₂	1	8	yes	maximal, complemented
14	#19149308	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₃×#3585	C₂	1	1	yes	maximal, characteristic, complemented
16	#14583736	—	2	2	no	—
17	#14583736	C₂²	1	8	yes	complemented
18	#14583735	—	2	2	no	—
19	#14583735	—	2	4	no	—
20	#14583735	C₂²	1	1	yes	characteristic
21	#14583735	C₂²	1	1	yes	characteristic, complemented
22	#14583735	C₂²	1	6	yes	complemented
23	#14583735	C₂²	1	6	yes	complemented
24	#14583734	—	2	4	no	—
25	#14583734	C₂²	1	8	yes	complemented
26	C₂×#13063371	—	2	4	no	—
27	C₂×#13063371	C₂²	1	1	yes	characteristic, complemented
28	C₂×#13063371	C₂²	1	6	yes	complemented
29	C₂×#13063370	—	2	6	no	—
30	C₂×#13063370	C₂²	1	6	yes	complemented
31	H(5,𝔽₂)×D₄₃	—	2	4	no	—
32	H(5,𝔽₂)×D₄₃	—	2	6	no	—
33	H(5,𝔽₂)×D₄₃	C₂²	1	8	yes	complemented
34	H(5,𝔽₂)×D₄₃	C₂²	1	8	yes	complemented
35	#14583715	C₂²	1	12	yes	complemented
36	#14583715	C₂²	1	4	yes	complemented
37	#14583714	C₂²	1	4	yes	complemented
38	#14583711	C₂²	1	8	yes	complemented
39	#14583710	C₂²	1	4	yes	complemented
40	#14583709	C₂²	1	12	yes	complemented
41	#14583709	C₂²	1	12	yes	complemented
42	#14583708	C₂²	1	12	yes	complemented
43	#14583708	C₂²	1	12	yes	complemented
44	#14583707	C₂²	1	4	yes	complemented
45	#14583706	C₂²	1	24	yes	complemented
46	#14583705	C₂²	1	24	yes	complemented
47	#14583704	C₂²	1	8	yes	complemented
48	#14583703	C₂²	1	12	yes	complemented
49	#14583703	C₂²	1	24	yes	complemented
50	#14583703	C₂²	1	12	yes	complemented
51	#14583703	C₂²	1	24	yes	complemented
52	#14583703	C₂²	1	24	yes	complemented
53	#14583702	C₂²	1	4	yes	complemented
54	#14583702	C₂²	1	8	yes	complemented
55	#14583702	C₂²	1	8	yes	complemented
56	#14583701	C₂²	1	24	yes	complemented
57	#14583700	C₂²	1	24	yes	complemented
58	#14583699	C₂²	1	6	yes	complemented
59	#14583698	C₂²	1	24	yes	complemented
60	#14583697	C₂²	1	6	yes	complemented
61	#14583696	C₂²	1	24	yes	complemented
62	#14583695	C₂²	1	24	yes	complemented
63	C₂×#13063353	C₂²	1	6	yes	complemented
64	C₂×#13063352	C₂²	1	12	yes	complemented
65	C₂×#13063351	C₂²	1	3	yes	complemented
66	C₂×#13063350	C₂²	1	3	yes	complemented
67	C₂×#13063349	C₂²	1	12	yes	complemented
68	AGL(1,ℤ/8)×D₄₃	C₂²	1	24	yes	complemented
69	AGL(1,ℤ/8)×D₄₃	C₂²	1	24	yes	complemented
70	C₂×#13063346	C₂²	1	12	yes	complemented
71	C₂×#13063345	C₂²	1	3	yes	complemented
72	C₂×#13063345	C₂²	1	6	yes	complemented
73	#135×D₄₃	C₂²	1	24	yes	complemented
74	C₂²×#10621882	C₂²	1	3	yes	complemented
75	C₂×D₈×D₄₃	C₂²	1	12	yes	complemented
76	#14583665	C₂²	1	6	yes	complemented
77	#14583664	C₂²	1	8	yes	complemented
78	C₂×#13063333	C₂²	1	6	yes	complemented
79	C₂×#13063332	C₂²	1	1	yes	characteristic, complemented
80	#131×D₄₃	C₂²	1	8	yes	complemented
81	C₄₃×#585	C₂²	1	1	yes	characteristic, complemented
82	C₂×H(5,𝔽₂)×C₄₃	C₂²	1	1	yes	characteristic, complemented
83	C₄₃×#577	C₂²	1	8	yes	complemented
84	C₄₃×#576	C₂²	1	8	yes	complemented
85	C₄₃×#575	C₂²	1	6	yes	complemented
86	C₂×AGL(1,ℤ/8)×C₄₃	C₂²	1	6	yes	complemented
87	C₄₃×#568	C₂²	1	1	yes	characteristic, complemented
88	#13063373	—	2	1	no	—
89	#13063373	—	2	8	no	—
90	#13063373	D₄	1	2	yes	—
91	#13063373	C₂³	1	12	yes	complemented
92	#13063373	C₂³	1	4	yes	complemented
93	#13063372	—	2	8	no	—
94	#13063372	—	2	6	no	—
95	#13063372	—	2	6	no	—
96	#13063372	D₄	1	4	yes	—
97	#13063372	C₂³	1	12	yes	complemented
98	#13063372	C₂³	1	4	yes	complemented
99	#13063372	C₂³	1	4	yes	complemented
100	#13063371	—	2	4	no	—
101	#13063371	—	2	8	no	—
102	#13063371	—	2	8	no	—
103	#13063371	—	2	24	no	—
104	#13063371	—	2	12	no	—
105	#13063371	—	2	12	no	—
106	#13063371	—	2	6	no	—
107	#13063371	—	2	6	no	—
108	#13063371	D₄	1	4	yes	—
109	#13063371	C₂³	1	12	yes	complemented
110	#13063371	C₂³	1	24	yes	complemented
111	#13063371	C₂³	1	12	yes	complemented
112	#13063371	C₂³	1	8	yes	complemented
113	#13063371	C₂³	1	4	yes	complemented
114	#13063370	—	2	3	no	—
115	#13063370	—	2	12	no	—
116	#13063370	—	2	12	no	—
117	#13063370	—	2	24	no	—
118	#13063370	—	2	24	no	—
119	#13063370	—	2	24	no	—
120	#13063370	—	2	12	no	—
121	#13063370	—	2	12	no	—
122	#13063370	D₄	1	6	yes	—
123	#13063370	C₂³	1	12	yes	complemented
124	#13063370	C₂³	1	24	yes	complemented
125	#13063370	C₂³	1	12	yes	complemented
126	C₂×#10621902	—	2	1	no	—
127	C₂×#10621902	—	2	8	no	—
128	C₂×#10621902	C₂³	1	12	yes	complemented
129	C₂×#10621898	—	2	12	no	—
130	C₂×#10621898	—	2	12	no	—
131	C₂×#10621898	—	2	6	no	—
132	C₂×#10621898	C₂³	1	6	yes	—
133	C₂×#10621898	C₂³	1	3	yes	complemented
134	C₂×#10621898	C₂³	1	6	yes	complemented
135	C₂×#10621900	—	2	24	no	—
136	C₂×#10621900	—	2	6	no	—
137	C₂×#10621900	C₂³	1	12	yes	complemented
138	#41×D₄₃	—	2	4	no	—
139	#41×D₄₃	—	2	8	no	—
140	#41×D₄₃	—	2	8	no	—
141	#41×D₄₃	—	2	8	no	—
142	#41×D₄₃	—	2	24	no	—
143	#41×D₄₃	—	2	12	no	—
144	#41×D₄₃	—	2	12	no	—
145	#41×D₄₃	C₂³	1	8	yes	—
146	#41×D₄₃	C₂³	1	24	yes	complemented
147	#41×D₄₃	C₂³	1	24	yes	complemented
148	C₂²×D₁₇₂	—	2	6	no	—
149	C₂²×D₁₇₂	C₂³	1	3	yes	complemented
150	C₂²×C₂²⋊D₄₃	—	2	12	no	—
151	C₂×D₄×D₄₃	—	2	3	no	—
152	C₂×D₄×D₄₃	—	2	12	no	—
153	C₂×D₄×D₄₃	—	2	24	no	—
154	C₂×D₄×D₄₃	—	2	24	no	—
155	C₂×D₄×D₄₃	—	2	6	no	—
156	C₂×D₄×D₄₃	C₂³	1	12	yes	complemented
157	C₂×D₄×D₄₃	C₂³	1	12	yes	complemented
158	#13063358	C₂³	1	12	yes	complemented
159	#13063358	C₂³	1	4	yes	complemented
160	#13063357	C₂³	1	8	yes	complemented
161	#13063357	C₂³	1	24	yes	complemented
162	#13063356	C₂³	1	12	yes	complemented
163	#13063355	C₂³	1	12	yes	complemented
164	#13063354	C₂³	1	24	yes	complemented
165	#13063354	C₂³	1	8	yes	complemented
166	#13063353	C₂³	1	12	yes	complemented
167	#13063353	C₂³	1	24	yes	complemented
168	#13063353	C₂³	1	12	yes	complemented
169	#13063352	C₂³	1	24	yes	complemented
170	#13063352	C₂³	1	48	yes	complemented
171	#13063352	C₂³	1	24	yes	complemented
172	#13063351	C₂³	1	12	yes	complemented
173	#13063351	C₂³	1	24	yes	complemented
174	#13063350	C₂³	1	12	yes	complemented
175	#13063350	C₂³	1	24	yes	complemented
176	#13063349	C₂³	1	24	yes	complemented
177	#13063349	C₂³	1	48	yes	complemented
178	#13063349	C₂³	1	24	yes	complemented
179	#13063348	C₂³	1	24	yes	complemented
180	#13063347	C₂³	1	24	yes	complemented
181	#13063346	C₂³	1	8	yes	complemented
182	#13063346	C₂³	1	24	yes	complemented
183	#13063346	C₂³	1	48	yes	complemented
184	#13063345	C₂³	1	12	yes	complemented
185	#13063345	C₂³	1	12	yes	complemented
186	#13063345	C₂³	1	4	yes	complemented
187	#13063345	C₂³	1	12	yes	complemented
188	#13063345	C₂³	1	12	yes	complemented
189	#13063345	C₂³	1	12	yes	complemented
190	#13063344	C₂³	1	24	yes	complemented
191	C₂×#10621885	C₂³	1	1	yes	characteristic, complemented
192	C₂×#10621885	C₂³	1	6	yes	complemented
193	Q₁₆×D₄₃	C₂³	1	8	yes	complemented
194	C₂×#10621873	C₂³	1	12	yes	complemented
195	C₂×#10621883	C₂³	1	6	yes	complemented
196	C₂×#10621883	C₂³	1	3	yes	complemented
197	C₂×#10621884	C₂³	1	3	yes	complemented
198	C₂×#10621884	C₂³	1	6	yes	complemented
199	SD₁₆×D₄₃	C₂³	1	24	yes	complemented
200	SD₁₆×D₄₃	C₂³	1	24	yes	complemented
201	C₂×D₃₄₄	C₂³	1	12	yes	complemented
202	C₂×#10621882	C₂³	1	6	yes	complemented
203	C₂×#10621882	C₂³	1	12	yes	complemented
204	C₂×#10621882	C₂³	1	3	yes	complemented
205	C₂×#10621882	C₂³	1	12	yes	complemented
206	C₂×#10621882	C₂³	1	6	yes	complemented
207	D₈×D₄₃	C₂³	1	24	yes	complemented
208	D₈×D₄₃	C₂³	1	48	yes	complemented
209	#13063333	C₂³	1	12	yes	complemented
210	#13063333	C₂³	1	4	yes	complemented
211	#13063333	C₂³	1	12	yes	complemented
212	#13063333	C₂³	1	12	yes	complemented
213	#13063332	C₂³	1	4	yes	complemented
214	#13063332	C₂³	1	4	yes	complemented
215	#13063331	C₂³	1	24	yes	complemented
216	C₂×#10621877	C₂³	1	3	yes	complemented
217	C₂×#10621872	C₂³	1	12	yes	complemented
218	M₁₆×D₄₃	C₂³	1	24	yes	complemented
219	C₂²×C₄₃⋊C₈	C₂³	1	3	yes	complemented
220	C₂×C₈×D₄₃	C₂³	1	12	yes	complemented
221	2₋¹⁺⁴×C₄₃	—	2	1	no	—
222	2₋¹⁺⁴×C₄₃	C₂³	1	4	yes	complemented
223	H(5,𝔽₂)×C₄₃	—	2	4	no	—
224	H(5,𝔽₂)×C₄₃	—	2	3	no	—
225	H(5,𝔽₂)×C₄₃	C₂³	1	4	yes	complemented
226	H(5,𝔽₂)×C₄₃	C₂³	1	8	yes	complemented
227	C₂×#41×C₄₃	—	2	4	no	—
228	C₂×#41×C₄₃	—	2	1	no	—
229	C₂×#41×C₄₃	C₂³	1	1	yes	characteristic
230	C₂×#41×C₄₃	C₂³	1	6	yes	complemented
231	C₂×#41×C₄₃	C₂³	1	3	yes	complemented
232	C₂²×D₄×C₄₃	—	2	3	no	—
233	C₂²×D₄×C₄₃	C₂³	1	3	yes	complemented
234	#137×C₄₃	C₂³	1	4	yes	complemented
235	#137×C₄₃	C₂³	1	12	yes	complemented
236	AGL(1,ℤ/8)×C₄₃	C₂³	1	12	yes	complemented
237	AGL(1,ℤ/8)×C₄₃	C₂³	1	24	yes	complemented
238	AGL(1,ℤ/8)×C₄₃	C₂³	1	12	yes	complemented
239	#135×C₄₃	C₂³	1	24	yes	complemented
240	C₂×SD₁₆×C₄₃	C₂³	1	12	yes	complemented
241	C₂×D₈×C₄₃	C₂³	1	12	yes	complemented
242	#131×C₄₃	C₂³	1	8	yes	complemented
243	C₂×M₁₆×C₄₃	C₂³	1	6	yes	complemented
244	C₂⁴×C₄₃	—	2	3	no	—
245	C₂³×D₄₃	—	2	3	no	—
246	C₂³×D₄₃	—	2	12	no	—
247	C₂³×D₄₃	—	2	12	no	—
248	#41×C₄₃	—	2	8	no	—
249	#41×C₄₃	—	2	4	no	—
250	#41×C₄₃	—	2	12	no	—
251	#41×C₄₃	—	2	6	no	—
252	#41×C₄₃	—	2	6	no	—
253	#41×C₄₃	—	2	6	no	—
254	#41×C₄₃	C₂×D₄	1	4	yes	—
255	#41×C₄₃	C₂⁴	1	12	yes	—
256	#41×C₄₃	C₂⁴	1	12	yes	—
257	#41×C₄₃	C₂⁴	1	4	yes	—
258	#41×C₄₃	C₂⁴	1	4	yes	—
259	C₂×Q₈×C₄₃	—	2	4	no	—
260	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
261	C₂×Q₈×C₄₃	C₂⁴	1	6	yes	—
262	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
263	C₂×D₄×C₄₃	—	2	24	no	—
264	C₂×D₄×C₄₃	—	2	12	no	—
265	C₂×D₄×C₄₃	—	2	3	no	—
266	C₂×D₄×C₄₃	—	2	6	no	—
267	C₂×D₄×C₄₃	—	2	3	no	—
268	C₂×D₄×C₄₃	—	2	6	no	—
269	C₂×D₄×C₄₃	C₂×D₄	1	3	yes	—
270	C₂×D₄×C₄₃	C₂⁴	1	6	yes	—
271	C₂×D₄×C₄₃	C₂⁴	1	12	yes	—
272	C₂×D₄×C₄₃	C₂⁴	1	3	yes	—
273	C₂²×C₄×C₄₃	—	2	3	no	—
274	C₂²×C₄×C₄₃	—	2	6	no	—
275	C₂²×C₄×C₄₃	C₂⁴	1	3	yes	—
276	C₂×C₂²⋊D₄₃	—	2	24	no	—
277	C₂×C₂²⋊D₄₃	—	2	48	no	—
278	C₂×C₂²⋊D₄₃	—	2	24	no	—
279	C₂×C₂²⋊D₄₃	—	2	12	no	—
280	C₂×C₂²⋊D₄₃	—	2	12	no	—
281	C₂×C₂²⋊D₄₃	—	2	3	no	—
282	C₂×C₂²⋊D₄₃	—	2	6	no	—
283	C₂×C₂²⋊D₄₃	—	2	12	no	—
284	C₂×C₂²⋊D₄₃	C₂×D₄	1	12	yes	—
285	C₂²×Dic₄₃	—	2	12	no	—
286	#10621902	—	2	4	no	—
287	#10621902	—	2	8	no	—
288	#10621902	—	2	4	no	—
289	#10621902	—	2	12	no	—
290	#10621902	—	2	24	no	—
291	#10621902	C₂×D₄	1	8	yes	—
292	#10621902	C₂⁴	1	24	yes	—
293	#10621902	C₂⁴	1	8	yes	—
294	Q₈×D₄₃	—	2	4	no	—
295	Q₈×D₄₃	—	2	4	no	—
296	Q₈×D₄₃	—	2	12	no	—
297	Q₈×D₄₃	C₂×D₄	1	8	yes	—
298	Q₈×D₄₃	C₂⁴	1	8	yes	—
299	Q₈×D₄₃	C₂⁴	1	8	yes	—
300	#10621900	—	2	12	no	—
301	#10621900	—	2	8	no	—
302	#10621900	—	2	24	no	—
303	#10621900	—	2	24	no	—
304	#10621900	—	2	24	no	—
305	#10621900	—	2	24	no	—
306	#10621900	—	2	12	no	—
307	#10621900	—	2	12	no	—
308	#10621900	—	2	24	no	—
309	#10621900	C₂×D₄	1	24	yes	—
310	#10621900	C₂⁴	1	8	yes	—
311	#10621900	C₂⁴	1	24	yes	—
312	D₄×D₄₃	—	2	12	no	—
313	D₄×D₄₃	—	2	24	no	—
314	D₄×D₄₃	—	2	24	no	—
315	D₄×D₄₃	—	2	24	no	—
316	D₄×D₄₃	—	2	48	no	—
317	D₄×D₄₃	—	2	12	no	—
318	D₄×D₄₃	—	2	24	no	—
319	D₄×D₄₃	—	2	12	no	—
320	D₄×D₄₃	—	2	24	no	—
321	D₄×D₄₃	—	2	24	no	—
322	D₄×D₄₃	—	2	24	no	—
323	D₄×D₄₃	—	2	24	no	—
324	D₄×D₄₃	C₂×D₄	1	24	yes	—
325	D₄×D₄₃	C₂⁴	1	24	yes	—
326	D₄×D₄₃	C₂⁴	1	24	yes	—
327	#10621898	—	2	6	no	—
328	#10621898	—	2	6	no	—
329	#10621898	—	2	6	no	—
330	#10621898	—	2	24	no	—
331	#10621898	—	2	8	no	—
332	#10621898	—	2	12	no	—
333	#10621898	—	2	4	no	—
334	#10621898	—	2	24	no	—
335	#10621898	—	2	24	no	—
336	#10621898	—	2	12	no	—
337	#10621898	—	2	24	no	—
338	#10621898	—	2	12	no	—
339	#10621898	C₂×D₄	1	12	yes	—
340	#10621898	C₂×D₄	1	12	yes	—
341	#10621898	C₂⁴	1	12	yes	—
342	#10621898	C₂⁴	1	4	yes	—
343	#10621898	C₂⁴	1	4	yes	—
344	#10621898	C₂⁴	1	12	yes	—
345	#10621898	C₂⁴	1	12	yes	—
346	C₂×D₁₇₂	—	2	3	no	—
347	C₂×D₁₇₂	—	2	6	no	—
348	C₂×D₁₇₂	—	2	12	no	—
349	C₂×D₁₇₂	—	2	24	no	—
350	C₂×D₁₇₂	—	2	12	no	—
351	C₂×D₁₇₂	—	2	12	no	—
352	C₂×D₁₇₂	C₂×D₄	1	6	yes	—
353	C₂×D₁₇₂	C₂⁴	1	3	yes	—
354	C₂×D₁₇₂	C₂⁴	1	12	yes	—
355	C₂×D₁₇₂	C₂⁴	1	6	yes	—
356	C₂×C₄×D₄₃	—	2	6	no	—
357	C₂×C₄×D₄₃	—	2	3	no	—
358	C₂×C₄×D₄₃	—	2	12	no	—
359	C₂×C₄×D₄₃	—	2	24	no	—
360	C₂×C₄×D₄₃	—	2	24	no	—
361	C₂×C₄×D₄₃	C₂⁴	1	12	yes	—
362	C₂×Dic₈₆	—	2	12	no	—
363	C₂×Dic₈₆	—	2	4	no	—
364	C₂×Dic₈₆	C₂×D₄	1	6	yes	—
365	C₂×Dic₈₆	C₂⁴	1	1	yes	characteristic
366	C₂×Dic₈₆	C₂⁴	1	6	yes	—
367	Q₁₆×C₄₃	C₂⁴	1	8	yes	—
368	SD₁₆×C₄₃	C₂⁴	1	24	yes	—
369	SD₁₆×C₄₃	C₂⁴	1	8	yes	—
370	D₈×C₄₃	C₂⁴	1	24	yes	—
371	M₁₆×C₄₃	C₂⁴	1	4	yes	—
372	M₁₆×C₄₃	C₂⁴	1	12	yes	—
373	C₂×C₈×C₄₃	C₂⁴	1	12	yes	—
374	#10621885	C₂⁴	1	2	yes	—
375	#10621885	C₂⁴	1	4	yes	—
376	#10621885	C₂⁴	1	2	yes	—
377	#10621885	C₂⁴	1	12	yes	—
378	#10621884	C₂⁴	1	12	yes	—
379	#10621884	C₂⁴	1	12	yes	—
380	#10621884	C₂⁴	1	4	yes	—
381	#10621883	C₂⁴	1	12	yes	—
382	#10621883	C₂⁴	1	12	yes	—
383	#10621883	C₂⁴	1	4	yes	—
384	#10621882	C₂⁴	1	4	yes	—
385	#10621882	C₂⁴	1	6	yes	—
386	#10621882	C₂⁴	1	12	yes	—
387	#10621882	C₂⁴	1	24	yes	—
388	#10621882	C₂⁴	1	6	yes	—
389	#10621877	C₂⁴	1	12	yes	—
390	C₂×C₄₃⋊C₈	C₂⁴	1	6	yes	—
391	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
392	C₂×C₄₃⋊C₈	C₂⁴	1	6	yes	—
393	C₂×C₄₃⋊C₈	C₂⁴	1	3	yes	—
394	Dic₁₇₂	C₂⁴	1	8	yes	—
395	D₃₄₄	C₂⁴	1	24	yes	—
396	#10621873	C₂⁴	1	8	yes	—
397	#10621873	C₂⁴	1	24	yes	—
398	#10621872	C₂⁴	1	24	yes	—
399	#10621872	C₂⁴	1	8	yes	—
400	C₈×D₄₃	C₂⁴	1	8	yes	—
401	C₈×D₄₃	C₂⁴	1	24	yes	—
402	C₂³×C₄₃	—	2	12	no	—
403	C₂³×C₄₃	—	2	3	no	—
404	C₂³×C₄₃	—	2	6	no	—
405	C₂³×C₄₃	—	16	3	no	—
406	C₂³×C₄₃	C₂²×D₄	1	3	yes	—
407	C₂²×D₄₃	—	2	12	no	—
408	C₂²×D₄₃	—	2	3	no	—
409	C₂²×D₄₃	—	2	6	no	—
410	C₂²×D₄₃	—	2	24	no	—
411	C₂²×D₄₃	—	2	24	no	—
412	C₂²×D₄₃	—	16	12	no	—
413	C₂²×D₄₃	—	16	12	no	—
414	C₂²×D₄₃	—	16	3	no	—
415	C₂²×D₄₃	C₂²×D₄	1	12	yes	—
416	Q₈×C₄₃	—	2	1	no	—
417	Q₈×C₄₃	—	2	6	no	—
418	Q₈×C₄₃	C₂²×D₄	1	4	yes	—
419	Q₈×C₄₃	C₂⁵	1	2	yes	—
420	Q₈×C₄₃	C₂⁵	1	4	yes	—
421	D₄×C₄₃	—	2	12	no	—
422	D₄×C₄₃	—	2	4	no	—
423	D₄×C₄₃	—	2	12	no	—
424	D₄×C₄₃	—	2	6	no	—
425	D₄×C₄₃	—	2	3	no	—
426	D₄×C₄₃	—	2	12	no	—
427	D₄×C₄₃	C₂²×D₄	1	12	yes	—
428	D₄×C₄₃	C₂⁵	1	6	yes	—
429	D₄×C₄₃	C₂⁵	1	4	yes	—
430	C₂×C₄×C₄₃	—	2	6	no	—
431	C₂×C₄×C₄₃	—	2	1	no	—
432	C₂×C₄×C₄₃	—	2	12	no	—
433	C₂×C₄×C₄₃	—	2	4	no	—
434	C₂×C₄×C₄₃	—	2	12	no	—
435	C₂×C₄×C₄₃	C₂²×D₄	1	6	yes	—
436	C₂×C₄×C₄₃	C₂²×D₄	1	3	yes	—
437	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
438	C₂×C₄×C₄₃	C₂⁵	1	6	yes	—
439	C₂²⋊D₄₃	—	2	4	no	—
440	C₂²⋊D₄₃	—	2	12	no	—
441	C₂²⋊D₄₃	—	2	12	no	—
442	C₂²⋊D₄₃	—	2	8	no	—
443	C₂²⋊D₄₃	—	2	24	no	—
444	C₂²⋊D₄₃	—	2	24	no	—
445	C₂²⋊D₄₃	—	2	24	no	—
446	C₂²⋊D₄₃	C₂²×D₄	1	8	yes	—
447	C₂²⋊D₄₃	C₂²×D₄	1	24	yes	—
448	C₂×Dic₄₃	—	2	1	no	—
449	C₂×Dic₄₃	—	2	6	no	—
450	C₂×Dic₄₃	—	2	8	no	—
451	C₂×Dic₄₃	—	2	24	no	—
452	C₂×Dic₄₃	C₂²×D₄	1	12	yes	—
453	D₁₇₂	—	2	24	no	—
454	D₁₇₂	—	2	8	no	—
455	D₁₇₂	—	2	3	no	—
456	D₁₇₂	—	2	12	no	—
457	D₁₇₂	—	2	6	no	—
458	D₁₇₂	C₂²×D₄	1	4	yes	—
459	D₁₇₂	C₂²×D₄	1	12	yes	—
460	D₁₇₂	C₂⁵	1	6	yes	—
461	D₁₇₂	C₂⁵	1	4	yes	—
462	C₄×D₄₃	—	2	8	no	—
463	C₄×D₄₃	—	2	8	no	—
464	C₄×D₄₃	—	2	4	no	—
465	C₄×D₄₃	—	2	12	no	—
466	C₄×D₄₃	—	2	12	no	—
467	C₄×D₄₃	—	2	8	no	—
468	C₄×D₄₃	—	2	24	no	—
469	C₄×D₄₃	C₂²×D₄	1	24	yes	—
470	C₄×D₄₃	C₂⁵	1	8	yes	—
471	Dic₈₆	—	2	1	no	—
472	Dic₈₆	—	2	6	no	—
473	Dic₈₆	—	2	8	no	—
474	Dic₈₆	—	2	8	no	—
475	Dic₈₆	C₂²×D₄	1	4	yes	—
476	Dic₈₆	C₂²×D₄	1	12	yes	—
477	Dic₈₆	C₂⁵	1	4	yes	—
478	Dic₈₆	C₂⁵	1	2	yes	—
479	C₈×C₄₃	C₂⁵	1	8	yes	—
480	C₄₃⋊C₈	C₂⁵	1	1	yes	characteristic
481	C₄₃⋊C₈	C₂⁵	1	6	yes	—
482	C₄₃⋊C₈	C₂⁵	1	1	yes	characteristic
483	#63091	—	43	1	no	maximal, Sylow
484	C₂²×C₄₃	—	2	4	no	—
485	C₂²×C₄₃	—	2	6	no	—
486	C₂²×C₄₃	—	4	3	no	—
487	C₂²×C₄₃	—	8	6	no	—
488	C₂²×C₄₃	—	8	12	no	—
489	C₂²×C₄₃	—	8	3	no	—
490	C₂²×C₄₃	C₂³×D₄	1	6	yes	—
491	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
492	C₂×D₄₃	—	2	6	no	—
493	C₂×D₄₃	—	2	4	no	—
494	C₂×D₄₃	—	4	12	no	—
495	C₂×D₄₃	—	8	24	no	—
496	C₂×D₄₃	—	8	24	no	—
497	C₂×D₄₃	—	8	12	no	—
498	C₂×D₄₃	—	8	6	no	—
499	C₂×D₄₃	—	8	3	no	—
500	C₂×D₄₃	C₂³×D₄	1	8	yes	—
501	C₄×C₄₃	—	2	2	no	—
502	C₄×C₄₃	—	2	4	no	—
503	C₄×C₄₃	C₂³×D₄	1	1	yes	characteristic
504	C₄×C₄₃	C₂³×D₄	1	6	yes	—
505	C₄×C₄₃	C₂⁶	1	1	yes	characteristic
506	Dic₄₃	—	2	2	no	—
507	Dic₄₃	—	2	4	no	—
508	Dic₄₃	C₂³×D₄	1	8	yes	—
509	H(7,𝔽₂)	—	43	1	no	—
510	H(7,𝔽₂)	—	43	1	no	—
511	#3585	—	43	8	no	—
512	#3585	—	43	8	no	—
513	#3585	—	43	6	no	—
514	#3585	—	43	6	no	—
515	#3585	—	43	1	no	—
516	#3585	D₄₃	1	1	yes	characteristic, complemented
517	#3584	—	43	1	no	—
518	#3584	—	43	8	no	—
519	#3584	—	43	6	no	—
520	C₂×#576	—	43	1	no	—
521	C₂×#576	—	43	8	no	—
522	C₂×#576	—	43	6	no	—
523	#3573	—	43	1	no	—
524	C₂×C₄₃	—	2	6	no	—
525	C₂×C₄₃	—	2	1	no	—
526	C₂×C₄₃	—	4	4	no	—
527	C₂×C₄₃	—	4	6	no	—
528	C₂×C₄₃	C₂⁴×D₄	1	1	yes	characteristic
529	D₄₃	—	2	8	no	—
530	D₄₃	—	4	6	no	—
531	D₄₃	—	4	4	no	—
532	#585	—	43	1	no	—
533	#585	—	43	8	no	—
534	#585	—	43	8	no	—
535	#585	—	43	1	no	—
536	#585	—	43	6	no	—
537	#585	—	43	6	no	—
538	#585	—	86	4	no	—
539	#585	—	86	2	no	—
540	#585	—	86	4	no	—
541	#585	—	86	2	no	—
542	#585	C₂×D₄₃	1	1	yes	characteristic, complemented
543	C₂×H(5,𝔽₂)	—	43	8	no	—
544	C₂×H(5,𝔽₂)	—	43	8	no	—
545	C₂×H(5,𝔽₂)	—	43	1	no	—
546	C₂×H(5,𝔽₂)	—	43	6	no	—
547	C₂×H(5,𝔽₂)	—	43	6	no	—
548	C₂×H(5,𝔽₂)	—	86	6	no	—
549	C₂×H(5,𝔽₂)	—	86	4	no	—
550	C₂×H(5,𝔽₂)	—	86	4	no	—
551	C₂×H(5,𝔽₂)	—	86	6	no	—
552	C₂×H(5,𝔽₂)	C₂×D₄₃	1	1	yes	characteristic, complemented
553	#578	—	43	4	no	—
554	#578	—	43	12	no	—
555	#578	—	43	4	no	—
556	#577	—	43	4	no	—
557	#577	—	43	4	no	—
558	#577	—	43	12	no	—
559	#577	—	43	12	no	—
560	#577	—	43	12	no	—
561	#577	—	43	12	no	—
562	#577	—	43	24	no	—
563	#577	—	43	24	no	—
564	#577	—	43	8	no	—
565	#577	C₂×D₄₃	1	8	yes	complemented
566	#576	—	43	8	no	—
567	#576	—	43	4	no	—
568	#576	—	43	8	no	—
569	#576	—	43	12	no	—
570	#576	—	43	24	no	—
571	#576	—	43	12	no	—
572	#576	—	43	24	no	—
573	#576	—	43	24	no	—
574	#576	—	43	24	no	—
575	#576	—	43	24	no	—
576	#576	—	43	8	no	—
577	#576	C₂×D₄₃	1	8	yes	complemented
578	#575	—	43	6	no	—
579	#575	—	43	24	no	—
580	#575	—	43	24	no	—
581	#575	—	43	24	no	—
582	#575	—	43	6	no	—
583	#575	C₂×D₄₃	1	6	yes	complemented
584	C₂×AGL(1,ℤ/8)	—	43	3	no	—
585	C₂×AGL(1,ℤ/8)	—	43	3	no	—
586	C₂×AGL(1,ℤ/8)	—	43	24	no	—
587	C₂×AGL(1,ℤ/8)	—	43	24	no	—
588	C₂×AGL(1,ℤ/8)	—	43	12	no	—
589	C₂×AGL(1,ℤ/8)	—	43	12	no	—
590	C₂×AGL(1,ℤ/8)	—	43	6	no	—
591	C₂×AGL(1,ℤ/8)	C₂×D₄₃	1	6	yes	complemented
592	C₂×#135	—	43	3	no	—
593	C₂×#135	—	43	6	no	—
594	C₂×#135	—	43	24	no	—
595	C₂×#135	—	43	12	no	—
596	C₂²×D₈	—	43	3	no	—
597	C₂²×D₈	—	43	12	no	—
598	#568	—	43	8	no	—
599	#568	—	43	6	no	—
600	#568	C₂×D₄₃	1	1	yes	characteristic, complemented
601	C₂×#131	—	43	1	no	—
602	C₂×#131	—	43	8	no	—
603	C₂×#131	—	43	6	no	—
604	C₄₃	#63091	1	1	yes	characteristic, complemented, Sylow
605	2₋¹⁺⁴	—	2	1	no	—
606	2₋¹⁺⁴	—	43	4	no	—
607	2₋¹⁺⁴	—	43	2	no	—
608	2₋¹⁺⁴	—	43	4	no	—
609	2₋¹⁺⁴	—	43	12	no	—
610	2₋¹⁺⁴	—	43	4	no	—
611	2₋¹⁺⁴	—	43	4	no	—
612	2₋¹⁺⁴	—	43	12	no	—
613	2₋¹⁺⁴	—	86	8	no	—
614	2₋¹⁺⁴	—	86	8	no	—
615	2₋¹⁺⁴	—	86	6	no	—
616	2₋¹⁺⁴	—	86	6	no	—
617	2₋¹⁺⁴	—	86	1	no	—
618	2₋¹⁺⁴	C₂²×D₄₃	1	4	yes	complemented
619	H(5,𝔽₂)	—	2	4	no	—
620	H(5,𝔽₂)	—	2	3	no	—
621	H(5,𝔽₂)	—	43	4	no	—
622	H(5,𝔽₂)	—	43	6	no	—
623	H(5,𝔽₂)	—	43	12	no	—
624	H(5,𝔽₂)	—	43	12	no	—
625	H(5,𝔽₂)	—	43	24	no	—
626	H(5,𝔽₂)	—	43	8	no	—
627	H(5,𝔽₂)	—	43	4	no	—
628	H(5,𝔽₂)	—	43	12	no	—
629	H(5,𝔽₂)	—	43	24	no	—
630	H(5,𝔽₂)	—	43	12	no	—
631	H(5,𝔽₂)	—	86	12	no	—
632	H(5,𝔽₂)	—	86	12	no	—
633	H(5,𝔽₂)	—	86	24	no	—
634	H(5,𝔽₂)	—	86	24	no	—
635	H(5,𝔽₂)	—	86	24	no	—
636	H(5,𝔽₂)	—	86	12	no	—
637	H(5,𝔽₂)	—	86	12	no	—
638	H(5,𝔽₂)	—	86	24	no	—
639	H(5,𝔽₂)	—	86	6	no	—
640	H(5,𝔽₂)	—	86	6	no	—
641	H(5,𝔽₂)	—	86	8	no	—
642	H(5,𝔽₂)	—	86	8	no	—
643	H(5,𝔽₂)	—	86	12	no	—
644	H(5,𝔽₂)	—	86	12	no	—
645	H(5,𝔽₂)	—	86	4	no	—
646	H(5,𝔽₂)	—	86	3	no	—
647	H(5,𝔽₂)	C₂²×D₄₃	1	8	yes	complemented
648	H(5,𝔽₂)	C₂²×D₄₃	1	4	yes	complemented
649	C₂×#41	—	2	4	no	—
650	C₂×#41	—	2	1	no	—
651	C₂×#41	—	43	8	no	—
652	C₂×#41	—	43	6	no	—
653	C₂×#41	—	43	24	no	—
654	C₂×#41	—	43	24	no	—
655	C₂×#41	—	43	12	no	—
656	C₂×#41	—	43	12	no	—
657	C₂×#41	—	43	3	no	—
658	C₂×#41	—	43	6	no	—
659	C₂×#41	—	86	6	no	—
660	C₂×#41	—	86	12	no	—
661	C₂×#41	—	86	12	no	—
662	C₂×#41	—	86	6	no	—
663	C₂×#41	—	86	24	no	—
664	C₂×#41	—	86	8	no	—
665	C₂×#41	—	86	8	no	—
666	C₂×#41	—	86	8	no	—
667	C₂×#41	—	86	8	no	—
668	C₂×#41	—	86	24	no	—
669	C₂×#41	—	86	12	no	—
670	C₂×#41	—	86	12	no	—
671	C₂×#41	—	86	4	no	—
672	C₂×#41	—	86	1	no	—
673	C₂×#41	C₂²×D₄₃	1	1	yes	characteristic
674	C₂×#41	C₂²×D₄₃	1	3	yes	complemented
675	C₂×#41	C₂²×D₄₃	1	6	yes	complemented
676	C₂²×D₄	—	2	3	no	—
677	C₂²×D₄	—	43	12	no	—
678	C₂²×D₄	—	43	12	no	—
679	C₂²×D₄	—	43	3	no	—
680	C₂²×D₄	—	86	6	no	—
681	C₂²×D₄	—	86	12	no	—
682	C₂²×D₄	—	86	24	no	—
683	C₂²×D₄	—	86	24	no	—
684	C₂²×D₄	—	86	6	no	—
685	C₂²×D₄	—	86	12	no	—
686	C₂²×D₄	—	86	3	no	—
687	C₂²×D₄	C₂²×D₄₃	1	3	yes	complemented
688	#137	—	43	12	no	—
689	#137	—	43	12	no	—
690	#137	—	43	24	no	—
691	#137	—	43	8	no	—
692	#137	—	43	8	no	—
693	#137	—	43	24	no	—
694	#137	—	43	12	no	—
695	#137	—	43	4	no	—
696	#137	C₂²×D₄₃	1	12	yes	complemented
697	#137	C₂²×D₄₃	1	4	yes	complemented
698	AGL(1,ℤ/8)	—	43	24	no	—
699	AGL(1,ℤ/8)	—	43	12	no	—
700	AGL(1,ℤ/8)	—	43	24	no	—
701	AGL(1,ℤ/8)	—	43	12	no	—
702	AGL(1,ℤ/8)	—	43	24	no	—
703	AGL(1,ℤ/8)	—	43	48	no	—
704	AGL(1,ℤ/8)	—	43	24	no	—
705	AGL(1,ℤ/8)	—	43	24	no	—
706	AGL(1,ℤ/8)	—	43	48	no	—
707	AGL(1,ℤ/8)	—	43	24	no	—
708	AGL(1,ℤ/8)	—	43	12	no	—
709	AGL(1,ℤ/8)	—	43	24	no	—
710	AGL(1,ℤ/8)	—	43	12	no	—
711	AGL(1,ℤ/8)	C₂²×D₄₃	1	12	yes	complemented
712	AGL(1,ℤ/8)	C₂²×D₄₃	1	24	yes	complemented
713	AGL(1,ℤ/8)	C₂²×D₄₃	1	12	yes	complemented
714	#135	—	43	4	no	—
715	#135	—	43	12	no	—
716	#135	—	43	12	no	—
717	#135	—	43	12	no	—
718	#135	—	43	12	no	—
719	#135	—	43	12	no	—
720	#135	—	43	24	no	—
721	#135	—	43	8	no	—
722	#135	—	43	24	no	—
723	#135	—	43	48	no	—
724	#135	—	43	24	no	—
725	#135	—	43	24	no	—
726	#135	C₂²×D₄₃	1	24	yes	complemented
727	C₂×Q₁₆	—	43	1	no	—
728	C₂×Q₁₆	—	43	6	no	—
729	C₂×Q₁₆	—	43	8	no	—
730	C₂×SD₁₆	—	43	3	no	—
731	C₂×SD₁₆	—	43	6	no	—
732	C₂×SD₁₆	—	43	3	no	—
733	C₂×SD₁₆	—	43	6	no	—
734	C₂×SD₁₆	—	43	24	no	—
735	C₂×SD₁₆	—	43	24	no	—
736	C₂×SD₁₆	—	43	12	no	—
737	C₂×SD₁₆	C₂²×D₄₃	1	12	yes	complemented
738	C₂×D₈	—	43	3	no	—
739	C₂×D₈	—	43	12	no	—
740	C₂×D₈	—	43	6	no	—
741	C₂×D₈	—	43	6	no	—
742	C₂×D₈	—	43	12	no	—
743	C₂×D₈	—	43	24	no	—
744	C₂×D₈	—	43	48	no	—
745	C₂×D₈	—	43	12	no	—
746	C₂×D₈	C₂²×D₄₃	1	12	yes	complemented
747	#131	—	43	4	no	—
748	#131	—	43	4	no	—
749	#131	—	43	12	no	—
750	#131	—	43	4	no	—
751	#131	—	43	12	no	—
752	#131	—	43	12	no	—
753	#131	—	43	24	no	—
754	#131	C₂²×D₄₃	1	8	yes	complemented
755	C₂×M₁₆	—	43	3	no	—
756	C₂×M₁₆	—	43	24	no	—
757	C₂×M₁₆	—	43	12	no	—
758	C₂×M₁₆	C₂²×D₄₃	1	6	yes	complemented
759	C₂²×C₈	—	43	3	no	—
760	C₂²×C₈	—	43	12	no	—
761	C₂⁴	—	2	3	no	—
762	C₂⁴	—	86	12	no	—
763	C₂⁴	—	86	12	no	—
764	C₂⁴	—	86	3	no	—
765	#41	—	2	8	no	—
766	#41	—	2	4	no	—
767	#41	—	2	12	no	—
768	#41	—	2	6	no	—
769	#41	—	2	6	no	—
770	#41	—	2	6	no	—
771	#41	—	43	8	no	—
772	#41	—	43	24	no	—
773	#41	—	43	12	no	—
774	#41	—	43	12	no	—
775	#41	—	43	4	no	—
776	#41	—	43	12	no	—
777	#41	—	43	8	no	—
778	#41	—	43	24	no	—
779	#41	—	43	24	no	—
780	#41	—	43	8	no	—
781	#41	—	43	4	no	—
782	#41	—	43	12	no	—
783	#41	—	43	12	no	—
784	#41	—	86	24	no	—
785	#41	—	86	24	no	—
786	#41	—	86	8	no	—
787	#41	—	86	24	no	—
788	#41	—	86	4	no	—
789	#41	—	86	12	no	—
790	#41	—	86	12	no	—
791	#41	—	86	12	no	—
792	#41	—	86	24	no	—
793	#41	—	86	24	no	—
794	#41	—	86	24	no	—
795	#41	—	86	24	no	—
796	#41	—	86	24	no	—
797	#41	—	86	24	no	—
798	#41	—	86	8	no	—
799	#41	—	86	12	no	—
800	#41	—	86	24	no	—
801	#41	—	86	12	no	—
802	#41	—	86	12	no	—
803	#41	—	86	4	no	—
804	#41	—	86	8	no	—
805	#41	—	86	4	no	—
806	#41	—	86	12	no	—
807	#41	—	86	6	no	—
808	#41	—	86	6	no	—
809	#41	—	86	6	no	—
810	#41	D₄×D₄₃	1	4	yes	—
811	#41	C₂³×D₄₃	1	4	yes	—
812	#41	C₂³×D₄₃	1	12	yes	—
813	#41	C₂³×D₄₃	1	12	yes	—
814	#41	C₂³×D₄₃	1	4	yes	—
815	C₂×Q₈	—	2	4	no	—
816	C₂×Q₈	—	43	8	no	—
817	C₂×Q₈	—	43	6	no	—
818	C₂×Q₈	—	43	8	no	—
819	C₂×Q₈	—	43	8	no	—
820	C₂×Q₈	—	43	1	no	—
821	C₂×Q₈	—	43	6	no	—
822	C₂×Q₈	—	86	4	no	—
823	C₂×Q₈	—	86	12	no	—
824	C₂×Q₈	—	86	12	no	—
825	C₂×Q₈	—	86	4	no	—
826	C₂×Q₈	—	86	4	no	—
827	C₂×Q₈	D₄×D₄₃	1	1	yes	characteristic
828	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
829	C₂×Q₈	C₂³×D₄₃	1	6	yes	—
830	C₂×D₄	—	2	3	no	—
831	C₂×D₄	—	2	6	no	—
832	C₂×D₄	—	2	24	no	—
833	C₂×D₄	—	2	12	no	—
834	C₂×D₄	—	2	3	no	—
835	C₂×D₄	—	2	6	no	—
836	C₂×D₄	—	43	12	no	—
837	C₂×D₄	—	43	24	no	—
838	C₂×D₄	—	43	24	no	—
839	C₂×D₄	—	43	24	no	—
840	C₂×D₄	—	43	6	no	—
841	C₂×D₄	—	43	3	no	—
842	C₂×D₄	—	43	12	no	—
843	C₂×D₄	—	43	6	no	—
844	C₂×D₄	—	86	12	no	—
845	C₂×D₄	—	86	12	no	—
846	C₂×D₄	—	86	24	no	—
847	C₂×D₄	—	86	12	no	—
848	C₂×D₄	—	86	24	no	—
849	C₂×D₄	—	86	24	no	—
850	C₂×D₄	—	86	12	no	—
851	C₂×D₄	—	86	12	no	—
852	C₂×D₄	—	86	24	no	—
853	C₂×D₄	—	86	24	no	—
854	C₂×D₄	—	86	48	no	—
855	C₂×D₄	—	86	24	no	—
856	C₂×D₄	—	86	12	no	—
857	C₂×D₄	—	86	12	no	—
858	C₂×D₄	—	86	24	no	—
859	C₂×D₄	—	86	24	no	—
860	C₂×D₄	—	86	24	no	—
861	C₂×D₄	—	86	24	no	—
862	C₂×D₄	—	86	48	no	—
863	C₂×D₄	—	86	12	no	—
864	C₂×D₄	—	86	6	no	—
865	C₂×D₄	—	86	3	no	—
866	C₂×D₄	—	86	12	no	—
867	C₂×D₄	—	86	24	no	—
868	C₂×D₄	—	86	6	no	—
869	C₂×D₄	—	86	3	no	—
870	C₂×D₄	D₄×D₄₃	1	3	yes	—
871	C₂×D₄	C₂³×D₄₃	1	3	yes	—
872	C₂×D₄	C₂³×D₄₃	1	12	yes	—
873	C₂×D₄	C₂³×D₄₃	1	6	yes	—
874	C₂²×C₄	—	2	3	no	—
875	C₂²×C₄	—	2	6	no	—
876	C₂²×C₄	—	43	12	no	—
877	C₂²×C₄	—	86	12	no	—
878	C₂²×C₄	—	86	24	no	—
879	C₂²×C₄	—	86	24	no	—
880	C₂²×C₄	—	86	12	no	—
881	C₂²×C₄	—	86	6	no	—
882	C₂²×C₄	—	86	3	no	—
883	C₂²×C₄	C₂³×D₄₃	1	3	yes	—
884	Q₁₆	—	43	2	no	—
885	Q₁₆	—	43	4	no	—
886	Q₁₆	—	43	2	no	—
887	Q₁₆	—	43	12	no	—
888	Q₁₆	—	43	8	no	—
889	Q₁₆	C₂³×D₄₃	1	8	yes	—
890	SD₁₆	—	43	12	no	—
891	SD₁₆	—	43	4	no	—
892	SD₁₆	—	43	12	no	—
893	SD₁₆	—	43	12	no	—
894	SD₁₆	—	43	4	no	—
895	SD₁₆	—	43	12	no	—
896	SD₁₆	—	43	8	no	—
897	SD₁₆	—	43	24	no	—
898	SD₁₆	C₂³×D₄₃	1	8	yes	—
899	SD₁₆	C₂³×D₄₃	1	24	yes	—
900	D₈	—	43	6	no	—
901	D₈	—	43	4	no	—
902	D₈	—	43	6	no	—
903	D₈	—	43	24	no	—
904	D₈	—	43	12	no	—
905	D₈	—	43	24	no	—
906	D₈	C₂³×D₄₃	1	24	yes	—
907	M₁₆	—	43	12	no	—
908	M₁₆	—	43	24	no	—
909	M₁₆	—	43	8	no	—
910	M₁₆	C₂³×D₄₃	1	12	yes	—
911	M₁₆	C₂³×D₄₃	1	4	yes	—
912	C₂×C₈	—	43	1	no	—
913	C₂×C₈	—	43	6	no	—
914	C₂×C₈	—	43	3	no	—
915	C₂×C₈	—	43	6	no	—
916	C₂×C₈	—	43	8	no	—
917	C₂×C₈	—	43	24	no	—
918	C₂×C₈	C₂³×D₄₃	1	12	yes	—
919	C₂³	—	2	6	no	—
920	C₂³	—	2	3	no	—
921	C₂³	—	2	12	no	—
922	C₂³	—	16	3	no	—
923	C₂³	—	43	12	no	—
924	C₂³	—	86	24	no	—
925	C₂³	—	86	24	no	—
926	C₂³	—	86	12	no	—
927	C₂³	—	86	6	no	—
928	C₂³	—	86	3	no	—
929	C₂³	—	688	3	no	—
930	C₂³	—	688	12	no	—
931	C₂³	—	688	12	no	—
932	C₂³	C₂×D₄×D₄₃	1	3	yes	—
933	Q₈	—	2	6	no	—
934	Q₈	—	2	1	no	—
935	Q₈	—	43	12	no	—
936	Q₈	—	43	4	no	—
937	Q₈	—	43	2	no	—
938	Q₈	—	43	4	no	—
939	Q₈	—	86	8	no	—
940	Q₈	—	86	8	no	—
941	Q₈	—	86	6	no	—
942	Q₈	—	86	1	no	—
943	Q₈	C₂×D₄×D₄₃	1	4	yes	—
944	Q₈	C₂⁴×D₄₃	1	2	yes	—
945	Q₈	C₂⁴×D₄₃	1	4	yes	—
946	D₄	—	2	12	no	—
947	D₄	—	2	12	no	—
948	D₄	—	2	4	no	—
949	D₄	—	2	12	no	—
950	D₄	—	2	3	no	—
951	D₄	—	2	6	no	—
952	D₄	—	43	24	no	—
953	D₄	—	43	8	no	—
954	D₄	—	43	12	no	—
955	D₄	—	43	4	no	—
956	D₄	—	43	6	no	—
957	D₄	—	43	4	no	—
958	D₄	—	86	8	no	—
959	D₄	—	86	24	no	—
960	D₄	—	86	24	no	—
961	D₄	—	86	24	no	—
962	D₄	—	86	8	no	—
963	D₄	—	86	24	no	—
964	D₄	—	86	12	no	—
965	D₄	—	86	12	no	—
966	D₄	—	86	4	no	—
967	D₄	—	86	6	no	—
968	D₄	—	86	12	no	—
969	D₄	—	86	3	no	—
970	D₄	C₂×D₄×D₄₃	1	12	yes	—
971	D₄	C₂⁴×D₄₃	1	6	yes	—
972	D₄	C₂⁴×D₄₃	1	4	yes	—
973	C₂×C₄	—	2	1	no	—
974	C₂×C₄	—	2	6	no	—
975	C₂×C₄	—	2	4	no	—
976	C₂×C₄	—	2	12	no	—
977	C₂×C₄	—	2	12	no	—
978	C₂×C₄	—	43	12	no	—
979	C₂×C₄	—	43	24	no	—
980	C₂×C₄	—	43	8	no	—
981	C₂×C₄	—	86	8	no	—
982	C₂×C₄	—	86	24	no	—
983	C₂×C₄	—	86	8	no	—
984	C₂×C₄	—	86	8	no	—
985	C₂×C₄	—	86	8	no	—
986	C₂×C₄	—	86	24	no	—
987	C₂×C₄	—	86	6	no	—
988	C₂×C₄	—	86	1	no	—
989	C₂×C₄	—	86	12	no	—
990	C₂×C₄	—	86	12	no	—
991	C₂×C₄	—	86	4	no	—
992	C₂×C₄	C₂×D₄×D₄₃	1	6	yes	—
993	C₂×C₄	C₂×D₄×D₄₃	1	3	yes	—
994	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
995	C₂×C₄	C₂⁴×D₄₃	1	6	yes	—
996	C₈	—	43	1	no	—
997	C₈	—	43	1	no	—
998	C₈	—	43	6	no	—
999	C₈	C₂⁴×D₄₃	1	8	yes	—
1000	C₂²	—	2	4	no	—
1001	C₂²	—	2	6	no	—
1002	C₂²	—	4	3	no	—
1003	C₂²	—	8	3	no	—
1004	C₂²	—	8	12	no	—
1005	C₂²	—	8	6	no	—
1006	C₂²	—	43	8	no	—
1007	C₂²	—	86	6	no	—
1008	C₂²	—	86	4	no	—
1009	C₂²	—	344	3	no	—
1010	C₂²	—	344	12	no	—
1011	C₂²	—	344	6	no	—
1012	C₂²	—	344	24	no	—
1013	C₂²	—	344	24	no	—
1014	C₂²	—	172	12	no	—
1015	C₂²	C₂²×D₄×D₄₃	1	6	yes	—
1016	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1017	C₄	—	2	2	no	—
1018	C₄	—	2	4	no	—
1019	C₄	—	43	8	no	—
1020	C₄	—	86	2	no	—
1021	C₄	—	86	4	no	—
1022	C₄	C₂²×D₄×D₄₃	1	6	yes	—
1023	C₄	C₂²×D₄×D₄₃	1	1	yes	characteristic
1024	C₄	C₂⁵×D₄₃	1	1	yes	characteristic
1025	C₂	—	2	1	no	—
1026	C₂	—	2	6	no	—
1027	C₂	—	4	6	no	—
1028	C₂	—	4	4	no	—
1029	C₂	—	86	8	no	—
1030	C₂	—	172	6	no	—
1031	C₂	—	172	4	no	—
1032	C₂	C₂³×D₄×D₄₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂³×D₄×D₄₃
commutator, cosocle	C₄×C₄₃	C₂⁶
Frattini	C₄	C₂⁵×D₄₃
Fitting	C₄₃×#3585	C₂
socle	C₂×C₄₃	C₂⁴×D₄
hypercenter	#3585	D₄₃
hypocenter	C₄₃	#63091
LCS	G ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂ ◁ C₂×#41 ◁ #3585

Complements

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

N	H ≅ G/N	type
1. #19149406	C₂	semidirect
2. #19149405	C₂	semidirect
3. #19149376	C₂	semidirect
4. #19149373	C₂	semidirect
5. #19149372	C₂	semidirect
6. #19149371	C₂	semidirect
7. #19149370	C₂	semidirect
8. #19149368	C₂	semidirect
9. #19149367	C₂	semidirect
10. #19149366	C₂	semidirect
11. C₂×#14583703	C₂	semidirect
12. C₂×#14583702	C₂	semidirect
13. #576×D₄₃	C₂	semidirect
14. #19149308	C₂	semidirect
15. C₄₃×#3585	C₂	semidirect
17. #14583736	C₂²	semidirect
21. #14583735	C₂²	semidirect
22. #14583735	C₂²	semidirect
23. #14583735	C₂²	semidirect
25. #14583734	C₂²	semidirect
27. C₂×#13063371	C₂²	semidirect
28. C₂×#13063371	C₂²	semidirect
30. C₂×#13063370	C₂²	semidirect
33. H(5,𝔽₂)×D₄₃	C₂²	semidirect
34. H(5,𝔽₂)×D₄₃	C₂²	semidirect
35. #14583715	C₂²	semidirect
36. #14583715	C₂²	semidirect
37. #14583714	C₂²	semidirect
38. #14583711	C₂²	semidirect
39. #14583710	C₂²	semidirect
40. #14583709	C₂²	semidirect
41. #14583709	C₂²	semidirect
42. #14583708	C₂²	semidirect
43. #14583708	C₂²	semidirect
44. #14583707	C₂²	semidirect
45. #14583706	C₂²	semidirect
46. #14583705	C₂²	semidirect
47. #14583704	C₂²	semidirect
48. #14583703	C₂²	semidirect
49. #14583703	C₂²	semidirect
50. #14583703	C₂²	semidirect
51. #14583703	C₂²	semidirect
52. #14583703	C₂²	semidirect
53. #14583702	C₂²	semidirect
54. #14583702	C₂²	semidirect
55. #14583702	C₂²	semidirect
56. #14583701	C₂²	semidirect
57. #14583700	C₂²	semidirect
58. #14583699	C₂²	semidirect
59. #14583698	C₂²	semidirect
60. #14583697	C₂²	semidirect
61. #14583696	C₂²	semidirect
62. #14583695	C₂²	semidirect
63. C₂×#13063353	C₂²	semidirect
64. C₂×#13063352	C₂²	semidirect
65. C₂×#13063351	C₂²	semidirect
66. C₂×#13063350	C₂²	semidirect
67. C₂×#13063349	C₂²	semidirect
68. AGL(1,ℤ/8)×D₄₃	C₂²	semidirect
69. AGL(1,ℤ/8)×D₄₃	C₂²	semidirect
70. C₂×#13063346	C₂²	semidirect
71. C₂×#13063345	C₂²	semidirect
72. C₂×#13063345	C₂²	semidirect
73. #135×D₄₃	C₂²	semidirect
74. C₂²×#10621882	C₂²	semidirect
75. C₂×D₈×D₄₃	C₂²	semidirect
76. #14583665	C₂²	semidirect
77. #14583664	C₂²	semidirect
78. C₂×#13063333	C₂²	semidirect
79. C₂×#13063332	C₂²	semidirect
80. #131×D₄₃	C₂²	semidirect
81. C₄₃×#585	C₂²	semidirect
82. C₂×H(5,𝔽₂)×C₄₃	C₂²	semidirect
83. C₄₃×#577	C₂²	semidirect
84. C₄₃×#576	C₂²	semidirect
85. C₄₃×#575	C₂²	semidirect
86. C₂×AGL(1,ℤ/8)×C₄₃	C₂²	semidirect
87. C₄₃×#568	C₂²	semidirect
91. #13063373	C₂³	semidirect
92. #13063373	C₂³	semidirect
97. #13063372	C₂³	semidirect
98. #13063372	C₂³	semidirect
99. #13063372	C₂³	semidirect
109. #13063371	C₂³	semidirect
110. #13063371	C₂³	semidirect
111. #13063371	C₂³	semidirect
112. #13063371	C₂³	semidirect
113. #13063371	C₂³	semidirect
123. #13063370	C₂³	semidirect
124. #13063370	C₂³	semidirect
125. #13063370	C₂³	semidirect
128. C₂×#10621902	C₂³	semidirect
133. C₂×#10621898	C₂³	semidirect
134. C₂×#10621898	C₂³	semidirect
137. C₂×#10621900	C₂³	semidirect
146. #41×D₄₃	C₂³	semidirect
147. #41×D₄₃	C₂³	semidirect
149. C₂²×D₁₇₂	C₂³	semidirect
156. C₂×D₄×D₄₃	C₂³	semidirect
157. C₂×D₄×D₄₃	C₂³	semidirect
158. #13063358	C₂³	semidirect
159. #13063358	C₂³	semidirect
160. #13063357	C₂³	semidirect
161. #13063357	C₂³	semidirect
162. #13063356	C₂³	semidirect
163. #13063355	C₂³	semidirect
164. #13063354	C₂³	semidirect
165. #13063354	C₂³	semidirect
166. #13063353	C₂³	semidirect
167. #13063353	C₂³	semidirect
168. #13063353	C₂³	semidirect
169. #13063352	C₂³	semidirect
170. #13063352	C₂³	semidirect
171. #13063352	C₂³	semidirect
172. #13063351	C₂³	semidirect
173. #13063351	C₂³	semidirect
174. #13063350	C₂³	semidirect
175. #13063350	C₂³	semidirect
176. #13063349	C₂³	semidirect
177. #13063349	C₂³	semidirect
178. #13063349	C₂³	semidirect
179. #13063348	C₂³	semidirect
180. #13063347	C₂³	semidirect
181. #13063346	C₂³	semidirect
182. #13063346	C₂³	semidirect
183. #13063346	C₂³	semidirect
184. #13063345	C₂³	semidirect
185. #13063345	C₂³	semidirect
186. #13063345	C₂³	semidirect
187. #13063345	C₂³	semidirect
188. #13063345	C₂³	semidirect
189. #13063345	C₂³	semidirect
190. #13063344	C₂³	semidirect
191. C₂×#10621885	C₂³	semidirect
192. C₂×#10621885	C₂³	semidirect
193. Q₁₆×D₄₃	C₂³	semidirect
194. C₂×#10621873	C₂³	semidirect
195. C₂×#10621883	C₂³	semidirect
196. C₂×#10621883	C₂³	semidirect
197. C₂×#10621884	C₂³	semidirect
198. C₂×#10621884	C₂³	semidirect
199. SD₁₆×D₄₃	C₂³	semidirect
200. SD₁₆×D₄₃	C₂³	semidirect
201. C₂×D₃₄₄	C₂³	semidirect
202. C₂×#10621882	C₂³	semidirect
203. C₂×#10621882	C₂³	semidirect
204. C₂×#10621882	C₂³	semidirect
205. C₂×#10621882	C₂³	semidirect
206. C₂×#10621882	C₂³	semidirect
207. D₈×D₄₃	C₂³	semidirect
208. D₈×D₄₃	C₂³	semidirect
209. #13063333	C₂³	semidirect
210. #13063333	C₂³	semidirect
211. #13063333	C₂³	semidirect
212. #13063333	C₂³	semidirect
213. #13063332	C₂³	semidirect
214. #13063332	C₂³	semidirect
215. #13063331	C₂³	semidirect
216. C₂×#10621877	C₂³	semidirect
217. C₂×#10621872	C₂³	semidirect
218. M₁₆×D₄₃	C₂³	semidirect
219. C₂²×C₄₃⋊C₈	C₂³	semidirect
220. C₂×C₈×D₄₃	C₂³	semidirect
222. 2₋¹⁺⁴×C₄₃	C₂³	semidirect
225. H(5,𝔽₂)×C₄₃	C₂³	semidirect
226. H(5,𝔽₂)×C₄₃	C₂³	semidirect
230. C₂×#41×C₄₃	C₂³	semidirect
231. C₂×#41×C₄₃	C₂³	semidirect
233. C₂²×D₄×C₄₃	C₂³	semidirect
234. #137×C₄₃	C₂³	semidirect
235. #137×C₄₃	C₂³	semidirect
236. AGL(1,ℤ/8)×C₄₃	C₂³	semidirect
237. AGL(1,ℤ/8)×C₄₃	C₂³	semidirect
238. AGL(1,ℤ/8)×C₄₃	C₂³	semidirect
239. #135×C₄₃	C₂³	semidirect
240. C₂×SD₁₆×C₄₃	C₂³	semidirect
241. C₂×D₈×C₄₃	C₂³	semidirect
242. #131×C₄₃	C₂³	semidirect
243. C₂×M₁₆×C₄₃	C₂³	semidirect
516. #3585	D₄₃	semidirect
542. #585	C₂×D₄₃	semidirect
552. C₂×H(5,𝔽₂)	C₂×D₄₃	semidirect
565. #577	C₂×D₄₃	semidirect
577. #576	C₂×D₄₃	semidirect
583. #575	C₂×D₄₃	semidirect
591. C₂×AGL(1,ℤ/8)	C₂×D₄₃	semidirect
600. #568	C₂×D₄₃	semidirect
604. C₄₃	#63091	semidirect
618. 2₋¹⁺⁴	C₂²×D₄₃	semidirect
647. H(5,𝔽₂)	C₂²×D₄₃	semidirect
648. H(5,𝔽₂)	C₂²×D₄₃	semidirect
674. C₂×#41	C₂²×D₄₃	semidirect
675. C₂×#41	C₂²×D₄₃	semidirect
687. C₂²×D₄	C₂²×D₄₃	semidirect
696. #137	C₂²×D₄₃	semidirect
697. #137	C₂²×D₄₃	semidirect
711. AGL(1,ℤ/8)	C₂²×D₄₃	semidirect
712. AGL(1,ℤ/8)	C₂²×D₄₃	semidirect
713. AGL(1,ℤ/8)	C₂²×D₄₃	semidirect
726. #135	C₂²×D₄₃	semidirect
737. C₂×SD₁₆	C₂²×D₄₃	semidirect
746. C₂×D₈	C₂²×D₄₃	semidirect
754. #131	C₂²×D₄₃	semidirect
758. C₂×M₁₆	C₂²×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19149406	2
#19149405	2
#19149376	2
#19149373	2
#19149372	2
#19149371	2
#19149370	2
#19149368	2
#19149367	2
#19149366	2
C₂×#14583703	2
C₂×#14583702	2
#576×D₄₃	2
#19149308	2
C₄₃×#3585	2
#63091	43