Subgroups — #25977229

Order 11008.

1818 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148394	C₂	1	2	yes	maximal, complemented
2	#19147553	C₂	1	2	yes	maximal, complemented
3	#19147549	C₂	1	2	yes	maximal, complemented
4	#19147497	C₂	1	2	yes	maximal, complemented
5	#19147489	C₂	1	2	yes	maximal, complemented
6	#19147463	C₂	1	1	yes	maximal, characteristic, complemented
7	#19147462	C₂	1	1	yes	maximal, characteristic, complemented
8	#19147462	C₂	1	1	yes	maximal, characteristic, complemented
9	#19147459	C₂	1	1	yes	maximal, characteristic, complemented
10	#19147459	C₂	1	1	yes	maximal, characteristic, complemented
11	D₈×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
12	#19147447	C₂	1	1	yes	maximal, characteristic, complemented
13	#19145132	C₂	1	1	yes	maximal, characteristic, complemented
14	#19145128	C₂	1	1	yes	maximal, characteristic, complemented
15	#19145108	C₂	1	1	yes	maximal, characteristic, complemented
16	#19144425	C₂	1	2	yes	maximal, complemented
17	#19144421	C₂	1	2	yes	maximal, complemented
18	#19144390	C₂	1	2	yes	maximal, complemented
19	#19143524	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143442	C₂	1	1	yes	maximal, characteristic
21	#19143442	C₂	1	1	yes	maximal, characteristic
22	C₄×D₈×D₄₃	C₂	1	1	yes	maximal, characteristic
23	C₄₃×#3380	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×D₈×D₄₃	C₂²	1	1	yes	characteristic
25	#14583609	C₂²	1	2	yes	complemented
26	#14583608	C₂²	1	2	yes	complemented
27	#14583608	C₂²	1	2	yes	complemented
28	#14583605	C₂²	1	2	yes	complemented
29	#14583605	C₂²	1	2	yes	complemented
30	#14583604	—	2	2	no	—
31	#14583603	—	2	2	no	—
32	#14583603	—	2	2	no	—
33	D₄×Dic₈₆	C₂²	1	2	yes	complemented
34	#14583564	C₂²	1	2	yes	complemented
35	#14583562	—	2	2	no	—
36	#14583529	C₂²	1	2	yes	—
37	#14583526	C₂²	1	2	yes	—
38	#14583524	—	2	2	no	—
39	#14583524	—	2	2	no	—
40	#14583455	C₂²	1	2	yes	—
41	#14583453	C₂²	1	1	yes	characteristic
42	C₂×#13063303	—	2	2	no	—
43	C₂²⋊Q₈×D₄₃	—	2	2	no	—
44	#14583371	C₂²	1	2	yes	—
45	#14583371	C₂²	1	2	yes	—
46	C₄×D₄×D₄₃	C₂²	1	2	yes	—
47	#14583309	C₂²	1	2	yes	complemented
48	#14583307	C₂²	1	2	yes	complemented
49	#14583306	C₂²	1	2	yes	complemented
50	#14583305	C₂²	1	2	yes	complemented
51	#14583304	C₂²	1	1	yes	characteristic, complemented
52	#14583303	C₂²	1	1	yes	characteristic, complemented
53	#14583303	C₂²	1	1	yes	characteristic, complemented
54	#14583303	C₂²	1	1	yes	characteristic, complemented
55	#14583303	C₂²	1	1	yes	characteristic, complemented
56	#14583301	C₂²	1	1	yes	characteristic, complemented
57	#14583301	C₂²	1	1	yes	characteristic, complemented
58	#14583300	C₂²	1	1	yes	characteristic, complemented
59	#14583300	C₂²	1	1	yes	characteristic, complemented
60	#14583298	C₂²	1	2	yes	complemented
61	#14583296	C₂²	1	2	yes	complemented
62	#14583201	C₂²	1	2	yes	complemented
63	#14583201	C₂²	1	2	yes	complemented
64	#14583200	C₂²	1	2	yes	complemented
65	#14583200	C₂²	1	2	yes	complemented
66	#14583199	C₂²	1	2	yes	complemented
67	#14583199	C₂²	1	2	yes	complemented
68	#14583198	C₂²	1	2	yes	complemented
69	#14583198	C₂²	1	2	yes	complemented
70	#14583196	C₂²	1	2	yes	complemented
71	#14583196	C₂²	1	2	yes	complemented
72	#14583190	C₂²	1	2	yes	complemented
73	#14583188	C₂²	1	2	yes	complemented
74	#14583188	C₂²	1	2	yes	complemented
75	#14583187	C₂²	1	2	yes	complemented
76	#14583187	C₂²	1	2	yes	complemented
77	#14583179	C₂²	1	2	yes	complemented
78	#14583178	C₂²	1	2	yes	complemented
79	#14583178	C₂²	1	2	yes	complemented
80	#14583177	C₂²	1	2	yes	complemented
81	#14583177	C₂²	1	2	yes	complemented
82	#14583176	C₂²	1	2	yes	complemented
83	#14583030	C₂²	1	1	yes	characteristic, complemented
84	#14583028	C₂²	1	1	yes	characteristic, complemented
85	#14583028	C₂²	1	1	yes	characteristic, complemented
86	#14583026	C₂²	1	1	yes	characteristic, complemented
87	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
88	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
89	C₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
90	#14583009	C₂²	1	2	yes	—
91	#14583009	C₂²	1	2	yes	—
92	#14583008	C₂²	1	2	yes	—
93	#14583008	C₂²	1	2	yes	—
94	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
95	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
96	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
97	D₈×Dic₄₃	C₂²	1	1	yes	characteristic
98	D₈×Dic₄₃	C₂²	1	1	yes	characteristic
99	D₈×Dic₄₃	C₂²	1	1	yes	characteristic
100	#14582981	C₂²	1	1	yes	characteristic
101	#14582981	C₂²	1	1	yes	characteristic
102	#14582981	C₂²	1	1	yes	characteristic
103	C₄×#10621882	C₂²	1	2	yes	—
104	#14582979	C₂²	1	2	yes	—
105	#14582940	C₂²	1	2	yes	—
106	#14582938	C₂²	1	2	yes	—
107	#14582936	C₂²	1	1	yes	characteristic
108	#14582936	C₂²	1	1	yes	characteristic
109	#14582934	C₂²	1	2	yes	—
110	#107×D₄₃	C₂²	1	1	yes	characteristic
111	#14582924	C₂²	1	1	yes	characteristic
112	#14582924	C₂²	1	1	yes	characteristic
113	#14582921	C₂²	1	1	yes	characteristic
114	#14582902	C₂²	1	2	yes	—
115	#14582902	C₂²	1	2	yes	—
116	#102×D₄₃	C₂²	1	2	yes	—
117	#14582853	C₂²	1	1	yes	characteristic
118	#14582853	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
120	C₄₃×#554	C₂²	1	2	yes	complemented
121	C₄₃×#500	C₂²	1	1	yes	characteristic, complemented
122	C₄₃×#499	C₂²	1	1	yes	characteristic, complemented
123	C₄₃×#499	C₂²	1	1	yes	characteristic, complemented
124	C₄₃×#478	C₂²	1	2	yes	complemented
125	C₄₃×#478	C₂²	1	2	yes	complemented
126	C₄₃×#476	C₂²	1	2	yes	complemented
127	C₈×Q₈×C₄₃	C₂²	1	1	yes	characteristic, complemented
128	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
129	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
130	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
131	C₂²×Dic₈₆	—	2	2	no	—
132	C₂×Q₈×D₄₃	—	2	2	no	—
133	C₂×D₄×D₄₃	C₂³	1	2	yes	—
134	C₂²×C₄×D₄₃	—	2	2	no	—
135	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
136	C₂×#10621882	C₂³	1	2	yes	—
137	D₈×D₄₃	Q₈	1	8	yes	complemented
138	C₂×#10621872	C₂³	1	1	yes	characteristic
139	C₂×#10621872	C₂³	1	1	yes	characteristic
140	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
141	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
142	#13063325	C₂³	1	2	yes	—
143	#13063324	—	2	2	no	—
144	#13063324	D₄	1	1	yes	characteristic
145	#13063324	C₂³	1	2	yes	—
146	#13063324	C₂³	1	2	yes	—
147	#13063324	C₂³	1	2	yes	—
148	#13063324	C₂³	1	2	yes	—
149	#13063323	—	2	2	no	—
150	#13063323	D₄	1	1	yes	characteristic
151	#13063317	C₂³	1	2	yes	—
152	#13063317	C₂³	1	2	yes	—
153	#13063316	C₂³	1	2	yes	—
154	#13063316	C₂³	1	2	yes	—
155	#13063315	—	2	2	no	—
156	#13063315	—	2	2	no	—
157	#13063315	D₄	1	1	yes	characteristic
158	#13063315	D₄	1	1	yes	characteristic
159	#13063305	—	2	2	no	—
160	#13063305	—	2	2	no	—
161	#13063305	—	2	2	no	—
162	#13063305	D₄	1	1	yes	characteristic
163	#13063304	—	2	2	no	—
164	#13063304	—	2	2	no	—
165	#13063304	—	2	2	no	—
166	#13063303	—	2	2	no	—
167	#13063303	—	2	2	no	—
168	#13063303	—	2	2	no	—
169	#13063303	—	2	2	no	—
170	#13063303	—	2	2	no	—
171	#13063303	—	2	2	no	—
172	#13063303	—	2	2	no	—
173	#13063303	—	2	2	no	—
174	#13063303	—	2	2	no	—
175	#13063303	—	2	2	no	—
176	#13063303	—	2	2	no	—
177	#13063303	—	2	2	no	—
178	#13063303	D₄	1	1	yes	characteristic
179	#13063303	D₄	1	1	yes	characteristic
180	#13063302	—	2	2	no	—
181	#13063302	—	2	2	no	—
182	#13063302	—	2	2	no	—
183	#13063302	—	2	2	no	—
184	#13063302	—	2	2	no	—
185	#13063302	—	2	2	no	—
186	#13063301	—	2	2	no	—
187	#13063301	—	2	2	no	—
188	#13063301	—	2	2	no	—
189	#13063301	D₄	1	1	yes	characteristic
190	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
191	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
192	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
193	#13063290	—	2	2	no	—
194	#13063290	—	2	2	no	—
195	C₄×D₁₇₂	C₂³	1	2	yes	—
196	C₄×D₁₇₂	C₂³	1	2	yes	—
197	C₄×D₁₇₂	C₂³	1	2	yes	—
198	D₄×Dic₄₃	C₂³	1	2	yes	—
199	D₄×Dic₄₃	C₂³	1	2	yes	—
200	D₄×Dic₄₃	C₂³	1	2	yes	—
201	#13063287	C₂³	1	2	yes	—
202	#13063287	C₂³	1	2	yes	—
203	#13063287	C₂³	1	2	yes	—
204	C₄×C₂²⋊D₄₃	—	2	2	no	—
205	C₄×C₂²⋊D₄₃	—	2	2	no	—
206	C₄×C₂²⋊D₄₃	—	2	2	no	—
207	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
208	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
209	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
210	#13063283	C₂³	1	2	yes	—
211	#13063283	C₂³	1	2	yes	—
212	#13063282	C₂³	1	1	yes	characteristic
213	#13063282	C₂³	1	1	yes	characteristic
214	C₂×Dic₄₃⋊C₄	—	2	2	no	—
215	C₂×Dic₄₃⋊C₄	—	2	2	no	—
216	C₄⋊C₄×D₄₃	—	2	2	no	—
217	C₄⋊C₄×D₄₃	—	2	2	no	—
218	C₄⋊C₄×D₄₃	—	2	2	no	—
219	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
220	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
221	C₂×(C₂×D₄₃)⋊C₄	—	2	2	no	—
222	C₂²⋊C₄×D₄₃	—	2	2	no	—
223	C₂²⋊C₄×D₄₃	—	2	2	no	—
224	C₂²⋊C₄×D₄₃	—	2	2	no	—
225	C₄²×D₄₃	C₂³	1	1	yes	characteristic
226	#13063259	C₂³	1	1	yes	characteristic
227	#13063259	C₂³	1	1	yes	characteristic
228	#13063259	C₂³	1	1	yes	characteristic
229	#13063259	C₂³	1	2	yes	—
230	#13063258	C₂³	1	2	yes	—
231	#13063258	C₂³	1	2	yes	—
232	#13063258	C₂³	1	2	yes	—
233	#13063258	C₂³	1	2	yes	—
234	#13063258	C₂³	1	2	yes	—
235	#13063257	C₂³	1	2	yes	—
236	#13063257	C₂³	1	2	yes	—
237	#13063256	C₂³	1	2	yes	—
238	#13063256	C₂³	1	2	yes	—
239	#13063256	C₂³	1	2	yes	—
240	#13063256	C₂³	1	2	yes	—
241	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
242	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
243	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
244	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
245	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
246	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
247	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
248	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
249	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
250	#13063247	C₂³	1	2	yes	—
251	#13063247	C₂³	1	2	yes	—
252	#13063247	C₂³	1	2	yes	—
253	#13063246	C₂³	1	2	yes	—
254	#13063246	C₂³	1	2	yes	—
255	#13063246	C₂³	1	2	yes	—
256	#13063245	C₂³	1	2	yes	—
257	#13063245	C₂³	1	2	yes	—
258	#13063245	C₂³	1	2	yes	—
259	#13063236	C₂³	1	1	yes	characteristic
260	#13063236	C₂³	1	1	yes	characteristic
261	#13063235	C₂³	1	1	yes	characteristic
262	#13063235	C₂³	1	1	yes	characteristic
263	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
264	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
265	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
266	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
267	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
268	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
269	C₄⋊Q₈×C₄₃	C₂³	1	2	yes	—
270	#125×C₄₃	C₂³	1	2	yes	—
271	#125×C₄₃	C₂³	1	2	yes	—
272	C₂²⋊Q₈×C₄₃	—	2	2	no	—
273	C₂²⋊Q₈×C₄₃	—	2	2	no	—
274	C₂²⋊Q₈×C₄₃	—	2	2	no	—
275	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
276	C₄×D₄×C₄₃	C₂³	1	2	yes	—
277	C₄×D₄×C₄₃	C₂³	1	2	yes	—
278	C₄×D₄×C₄₃	C₂³	1	2	yes	—
279	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
280	#107×C₄₃	C₂³	1	1	yes	characteristic
281	#107×C₄₃	C₂³	1	1	yes	characteristic
282	#107×C₄₃	C₂³	1	1	yes	characteristic
283	#107×C₄₃	C₂³	1	2	yes	—
284	#106×C₄₃	C₂³	1	2	yes	—
285	#106×C₄₃	C₂³	1	2	yes	—
286	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
287	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
288	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
289	#102×C₄₃	C₂³	1	2	yes	—
290	#102×C₄₃	C₂³	1	2	yes	—
291	#102×C₄₃	C₂³	1	2	yes	—
292	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
293	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
294	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
295	C₂³×D₄₃	—	2	2	no	—
296	C₂×Q₈×C₄₃	—	2	2	no	—
297	C₂×Q₈×C₄₃	C₂×D₄	1	1	yes	characteristic
298	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
299	C₂²×C₄×C₄₃	—	2	2	no	—
300	C₂²×C₄×C₄₃	—	2	2	no	—
301	C₂²×C₄×C₄₃	—	2	2	no	—
302	C₂×C₂²⋊D₄₃	—	2	2	no	—
303	C₂²×Dic₄₃	—	2	2	no	—
304	C₂²×Dic₄₃	—	2	2	no	—
305	C₂²×Dic₄₃	—	2	2	no	—
306	Q₈×D₄₃	—	8	4	no	—
307	D₄×D₄₃	—	2	4	no	—
308	D₄×D₄₃	C₂×Q₈	1	8	yes	complemented
309	C₂×D₁₇₂	C₂⁴	1	2	yes	—
310	C₂×C₄×D₄₃	—	2	2	no	—
311	C₂×C₄×D₄₃	—	2	2	no	—
312	C₂×C₄×D₄₃	—	2	2	no	—
313	C₂×C₄×D₄₃	—	2	2	no	—
314	C₂×C₄×D₄₃	—	2	2	no	—
315	C₂×C₄×D₄₃	—	2	2	no	—
316	C₂×C₄×D₄₃	—	2	2	no	—
317	C₂×C₄×D₄₃	—	8	4	no	—
318	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
319	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
320	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
321	C₂×Dic₈₆	—	2	2	no	—
322	C₂×Dic₈₆	—	2	2	no	—
323	C₂×Dic₈₆	—	2	2	no	—
324	C₂×Dic₈₆	—	2	2	no	—
325	C₂×Dic₈₆	—	2	2	no	—
326	C₂×Dic₈₆	—	8	4	no	—
327	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
328	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
329	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
330	D₈×C₄₃	C₂×Q₈	1	4	yes	complemented
331	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
332	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
333	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
334	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
335	C₄⋊C₄×C₄₃	—	2	2	no	—
336	C₄⋊C₄×C₄₃	—	2	2	no	—
337	C₄⋊C₄×C₄₃	—	2	2	no	—
338	C₄⋊C₄×C₄₃	—	2	2	no	—
339	C₄⋊C₄×C₄₃	—	2	2	no	—
340	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
341	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
342	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
343	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
344	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
345	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
346	C₂²⋊C₄×C₄₃	—	2	2	no	—
347	C₂²⋊C₄×C₄₃	—	2	2	no	—
348	C₂²⋊C₄×C₄₃	—	2	2	no	—
349	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
350	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
351	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
352	C₂²⋊Dic₄₃	—	2	2	no	—
353	C₂²⋊Dic₄₃	—	2	2	no	—
354	C₂²⋊Dic₄₃	—	2	2	no	—
355	#10621882	C₂×Q₈	1	8	yes	complemented
356	(C₂×D₄₃)⋊C₄	—	2	2	no	—
357	(C₂×D₄₃)⋊C₄	—	2	2	no	—
358	(C₂×D₄₃)⋊C₄	—	2	2	no	—
359	(C₂×D₄₃)⋊C₄	—	2	2	no	—
360	(C₂×D₄₃)⋊C₄	—	2	2	no	—
361	(C₂×D₄₃)⋊C₄	—	2	2	no	—
362	(C₂×D₄₃)⋊C₄	—	2	2	no	—
363	(C₂×D₄₃)⋊C₄	—	2	2	no	—
364	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
365	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
366	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
367	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
368	C₄⋊Dic₄₃	—	2	2	no	—
369	C₄⋊Dic₄₃	—	2	2	no	—
370	C₄⋊Dic₄₃	—	2	2	no	—
371	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
372	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
373	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
374	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
375	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
376	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
377	Dic₄₃⋊C₄	—	2	2	no	—
378	Dic₄₃⋊C₄	—	2	2	no	—
379	Dic₄₃⋊C₄	—	2	2	no	—
380	Dic₄₃⋊C₄	—	2	2	no	—
381	Dic₄₃⋊C₄	—	2	2	no	—
382	Dic₄₃⋊C₄	—	2	2	no	—
383	Dic₄₃⋊C₄	—	2	2	no	—
384	Dic₄₃⋊C₄	—	2	2	no	—
385	Dic₄₃⋊C₄	—	2	2	no	—
386	Dic₄₃⋊C₄	—	2	2	no	—
387	Dic₄₃⋊C₄	—	2	2	no	—
388	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
389	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
390	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
391	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
392	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
393	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
394	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
395	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
396	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
397	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
398	C₄×Dic₄₃	—	2	2	no	—
399	C₄×Dic₄₃	—	2	2	no	—
400	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
401	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
402	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
403	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
404	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
405	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
406	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
407	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
408	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
409	D₃₄₄	C₂×Q₈	1	4	yes	complemented
410	#10621872	—	2	2	no	—
411	#10621872	—	2	2	no	—
412	C₈×D₄₃	—	2	2	no	—
413	C₈×D₄₃	C₂×Q₈	1	4	yes	complemented
414	C₂³×C₄₃	—	2	2	no	—
415	C₂²×D₄₃	—	2	2	no	—
416	C₂²×D₄₃	—	2	8	no	—
417	C₂²×D₄₃	—	8	2	no	—
418	C₂²×D₄₃	—	8	2	no	—
419	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
420	Q₈×C₄₃	—	4	1	no	—
421	Q₈×C₄₃	—	8	2	no	—
422	D₄×C₄₃	—	2	2	no	—
423	D₄×C₄₃	C₂²×Q₈	1	4	yes	—
424	C₂×C₄×C₄₃	—	2	2	no	—
425	C₂×C₄×C₄₃	—	2	2	no	—
426	C₂×C₄×C₄₃	—	2	2	no	—
427	C₂×C₄×C₄₃	—	8	2	no	—
428	C₂×C₄×C₄₃	—	8	2	no	—
429	C₂×C₄×C₄₃	—	8	2	no	—
430	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
431	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
432	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
433	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
434	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
435	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
436	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
437	C₂²⋊D₄₃	—	2	8	no	—
438	C₂×Dic₄₃	—	2	2	no	—
439	C₂×Dic₄₃	—	2	2	no	—
440	C₂×Dic₄₃	—	2	2	no	—
441	C₂×Dic₄₃	—	4	4	no	—
442	C₂×Dic₄₃	—	8	2	no	—
443	C₂×Dic₄₃	—	8	2	no	—
444	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
445	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
446	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
447	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
448	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
449	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
450	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
451	D₁₇₂	—	2	2	no	—
452	D₁₇₂	C₂²×Q₈	1	4	yes	—
453	C₄×D₄₃	—	2	2	no	—
454	C₄×D₄₃	—	4	1	no	—
455	C₄×D₄₃	—	4	4	no	—
456	C₄×D₄₃	—	8	2	no	—
457	C₄×D₄₃	—	8	2	no	—
458	C₄×D₄₃	—	8	2	no	—
459	C₄×D₄₃	—	8	2	no	—
460	C₄×D₄₃	—	8	2	no	—
461	C₄×D₄₃	—	8	2	no	—
462	C₄×D₄₃	C₂²×Q₈	1	2	yes	—
463	C₄×D₄₃	2₋¹⁺⁴	1	2	yes	—
464	Dic₈₆	—	2	2	no	—
465	Dic₈₆	—	2	2	no	—
466	Dic₈₆	—	4	1	no	—
467	Dic₈₆	—	4	4	no	—
468	Dic₈₆	—	8	2	no	—
469	Dic₈₆	—	8	2	no	—
470	Dic₈₆	—	8	2	no	—
471	Dic₈₆	—	8	2	no	—
472	C₈×C₄₃	—	2	1	no	—
473	C₈×C₄₃	—	2	1	no	—
474	C₈×C₄₃	—	2	1	no	—
475	C₈×C₄₃	C₂²×Q₈	1	2	yes	—
476	C₄₃⋊C₈	—	2	1	no	—
477	C₄₃⋊C₈	—	2	1	no	—
478	C₄₃⋊C₈	—	2	1	no	—
479	C₄₃⋊C₈	C₂²×Q₈	1	2	yes	—
480	#61370	—	43	1	no	maximal, Sylow
481	C₂²×C₄₃	—	2	4	no	—
482	C₂²×C₄₃	—	4	2	no	—
483	C₂²×C₄₃	—	4	2	no	—
484	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
485	C₂×D₄₃	—	2	1	no	—
486	C₂×D₄₃	—	2	1	no	—
487	C₂×D₄₃	—	2	4	no	—
488	C₂×D₄₃	—	4	2	no	—
489	C₂×D₄₃	—	4	2	no	—
490	C₂×D₄₃	—	8	8	no	—
491	C₂×D₄₃	D₄×Q₈	1	2	yes	—
492	C₄×C₄₃	—	2	1	no	—
493	C₄×C₄₃	—	2	1	no	—
494	C₄×C₄₃	—	2	1	no	—
495	C₄×C₄₃	—	2	1	no	—
496	C₄×C₄₃	—	2	1	no	—
497	C₄×C₄₃	—	2	1	no	—
498	C₄×C₄₃	—	4	2	no	—
499	C₄×C₄₃	—	4	2	no	—
500	C₄×C₄₃	—	4	2	no	—
501	C₄×C₄₃	C₂³×Q₈	1	1	yes	characteristic
502	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
503	Dic₄₃	—	2	1	no	—
504	Dic₄₃	—	2	1	no	—
505	Dic₄₃	—	2	1	no	—
506	Dic₄₃	—	2	1	no	—
507	Dic₄₃	—	2	1	no	—
508	Dic₄₃	—	4	2	no	—
509	Dic₄₃	—	4	2	no	—
510	Dic₄₃	—	4	2	no	—
511	Dic₄₃	D₄×Q₈	1	2	yes	—
512	Dic₄₃	#576	1	2	yes	—
513	#3501	—	43	2	no	—
514	#3389	—	43	2	no	—
515	#3389	—	43	2	no	—
516	#3384	—	43	2	no	—
517	#3384	—	43	2	no	—
518	#3380	—	43	1	no	—
519	#3380	—	43	1	no	—
520	#3380	—	43	1	no	—
521	#3380	—	43	1	no	—
522	#3380	—	43	1	no	—
523	#3380	D₄₃	1	1	yes	characteristic, complemented
524	Q₈×D₈	—	43	1	no	—
525	Q₈×D₈	—	43	1	no	—
526	#3164	—	43	1	no	—
527	#3164	—	43	1	no	—
528	#3160	—	43	1	no	—
529	#3081	—	43	2	no	—
530	#3081	—	43	2	no	—
531	#3077	—	43	2	no	—
532	#2960	—	43	1	no	—
533	#2948	—	43	1	no	—
534	#2948	—	43	1	no	—
535	C₂×C₄×D₈	—	43	1	no	—
536	C₂×C₄₃	—	4	4	no	—
537	C₂×C₄₃	C₂×D₄×Q₈	1	1	yes	characteristic
538	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
539	C₂×C₄₃	#3584	1	1	yes	characteristic
540	D₄₃	—	2	2	no	—
541	D₄₃	—	4	4	no	—
542	C₂²×D₈	—	43	1	no	—
543	#554	—	43	2	no	—
544	#554	—	43	2	no	—
545	#554	—	43	2	no	—
546	#554	—	43	2	no	—
547	#554	—	43	2	no	—
548	#554	—	86	2	no	—
549	#554	—	86	2	no	—
550	#554	—	86	2	no	—
551	#554	C₂×D₄₃	1	2	yes	complemented
552	D₄×Q₈	—	43	2	no	—
553	D₄×Q₈	—	43	2	no	—
554	D₄×Q₈	—	86	2	no	—
555	#544	—	43	2	no	—
556	#544	—	43	2	no	—
557	#543	—	86	2	no	—
558	#543	—	86	2	no	—
559	#533	—	43	1	no	—
560	#533	—	43	2	no	—
561	C₂×C₂²⋊Q₈	—	86	2	no	—
562	C₂×C₂²⋊Q₈	—	86	2	no	—
563	#518	—	43	2	no	—
564	#518	—	43	2	no	—
565	C₂×C₄×D₄	—	43	2	no	—
566	#501	—	43	2	no	—
567	#501	—	43	2	no	—
568	#501	—	43	2	no	—
569	#501	—	43	2	no	—
570	#500	—	43	1	no	—
571	#500	—	43	1	no	—
572	#500	—	43	1	no	—
573	#500	—	43	1	no	—
574	#500	—	43	1	no	—
575	#500	C₂×D₄₃	1	1	yes	characteristic, complemented
576	#499	—	43	2	no	—
577	#499	—	43	1	no	—
578	#499	—	43	1	no	—
579	#499	—	43	1	no	—
580	#499	—	43	1	no	—
581	#499	C₂×D₄₃	1	1	yes	characteristic, complemented
582	#499	C₂×D₄₃	1	1	yes	characteristic, complemented
583	#498	—	43	2	no	—
584	#478	—	43	2	no	—
585	#478	—	43	2	no	—
586	#478	—	43	2	no	—
587	#478	—	43	2	no	—
588	#478	—	43	2	no	—
589	#478	—	43	2	no	—
590	#478	—	43	2	no	—
591	#478	—	43	2	no	—
592	#478	—	43	2	no	—
593	#478	—	43	2	no	—
594	#478	C₂×D₄₃	1	2	yes	complemented
595	#478	C₂×D₄₃	1	2	yes	complemented
596	#476	—	43	2	no	—
597	#476	—	43	2	no	—
598	#476	—	43	2	no	—
599	#476	—	43	2	no	—
600	#476	—	43	2	no	—
601	#476	C₂×D₄₃	1	2	yes	complemented
602	#474	—	43	2	no	—
603	#474	—	43	2	no	—
604	#474	—	43	2	no	—
605	#474	—	43	2	no	—
606	#474	—	43	2	no	—
607	#474	—	43	2	no	—
608	#446	—	43	1	no	—
609	#446	—	43	1	no	—
610	#446	—	43	1	no	—
611	#446	—	43	1	no	—
612	C₈×Q₈	—	43	1	no	—
613	C₈×Q₈	—	43	1	no	—
614	C₈×Q₈	—	43	1	no	—
615	C₈×Q₈	C₂×D₄₃	1	1	yes	characteristic, complemented
616	#442	—	43	2	no	—
617	#442	—	43	2	no	—
618	#442	—	43	2	no	—
619	#442	—	43	2	no	—
620	C₄×D₈	—	43	1	no	—
621	C₄×D₈	—	43	1	no	—
622	C₄×D₈	—	43	1	no	—
623	C₄×D₈	—	43	2	no	—
624	C₄×D₈	—	43	1	no	—
625	C₄×D₈	—	43	1	no	—
626	C₄×D₈	—	43	1	no	—
627	C₄×D₈	—	43	2	no	—
628	C₄×D₈	—	43	1	no	—
629	C₄×D₈	—	43	1	no	—
630	C₄×D₈	—	43	1	no	—
631	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
632	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
633	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
634	#428	—	43	2	no	—
635	#428	—	43	2	no	—
636	#427	—	43	1	no	—
637	#427	—	43	1	no	—
638	#427	—	43	2	no	—
639	C₂×#107	—	43	1	no	—
640	#424	—	43	1	no	—
641	#424	—	43	1	no	—
642	#423	—	43	1	no	—
643	#418	—	43	2	no	—
644	#418	—	43	2	no	—
645	C₂×#102	—	43	2	no	—
646	#405	—	43	1	no	—
647	#405	—	43	1	no	—
648	C₂×C₄×C₈	—	43	1	no	—
649	C₄₃	#61370	1	1	yes	characteristic, complemented, Sylow
650	C₂²×Q₈	—	86	2	no	—
651	C₂²×Q₈	—	86	2	no	—
652	C₂²×D₄	—	43	2	no	—
653	C₂³×C₄	—	86	2	no	—
654	C₂×D₈	—	43	2	no	—
655	C₂×D₈	—	43	8	no	—
656	C₂×D₈	—	43	1	no	—
657	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
658	C₂×M₁₆	—	43	1	no	—
659	C₂×M₁₆	—	43	1	no	—
660	C₂²×C₈	—	43	1	no	—
661	C₂²×C₈	—	43	1	no	—
662	C₄⋊Q₈	—	43	1	no	—
663	C₄⋊Q₈	—	43	1	no	—
664	C₄⋊Q₈	—	43	2	no	—
665	C₄⋊Q₈	—	43	2	no	—
666	C₄⋊Q₈	—	43	2	no	—
667	C₄⋊Q₈	—	43	2	no	—
668	C₄⋊Q₈	—	43	2	no	—
669	C₄⋊Q₈	—	86	2	no	—
670	C₄⋊Q₈	—	86	2	no	—
671	C₄⋊Q₈	C₂²×D₄₃	1	2	yes	—
672	#125	—	43	1	no	—
673	#125	—	43	1	no	—
674	#125	—	43	2	no	—
675	#125	—	43	2	no	—
676	#125	—	43	2	no	—
677	#125	—	43	2	no	—
678	#125	—	86	2	no	—
679	#125	—	86	2	no	—
680	#125	C₂²×D₄₃	1	2	yes	—
681	#125	C₂²×D₄₃	1	2	yes	—
682	C₂²⋊Q₈	—	2	2	no	—
683	C₂²⋊Q₈	—	2	2	no	—
684	C₂²⋊Q₈	—	2	2	no	—
685	C₂²⋊Q₈	—	43	1	no	—
686	C₂²⋊Q₈	—	43	1	no	—
687	C₂²⋊Q₈	—	43	1	no	—
688	C₂²⋊Q₈	—	43	1	no	—
689	C₂²⋊Q₈	—	86	2	no	—
690	C₂²⋊Q₈	—	86	2	no	—
691	C₂²⋊Q₈	—	86	2	no	—
692	C₂²⋊Q₈	—	86	2	no	—
693	C₂²⋊Q₈	—	86	2	no	—
694	C₂²⋊Q₈	—	86	2	no	—
695	C₂²⋊Q₈	—	86	2	no	—
696	C₂²⋊Q₈	—	86	2	no	—
697	C₂²⋊Q₈	—	86	2	no	—
698	C₂²⋊Q₈	—	86	2	no	—
699	C₂²⋊Q₈	—	86	2	no	—
700	C₂²⋊Q₈	—	86	2	no	—
701	C₂²⋊Q₈	—	86	2	no	—
702	C₂²⋊Q₈	—	86	2	no	—
703	C₂²⋊Q₈	—	86	2	no	—
704	C₂²⋊Q₈	—	86	2	no	—
705	C₂²⋊Q₈	—	86	2	no	—
706	C₂²⋊Q₈	—	86	2	no	—
707	C₂²⋊Q₈	—	86	2	no	—
708	C₂²⋊Q₈	—	86	2	no	—
709	C₂²⋊Q₈	—	86	2	no	—
710	C₂²⋊Q₈	—	86	2	no	—
711	C₂²⋊Q₈	—	86	2	no	—
712	C₂²⋊Q₈	—	86	2	no	—
713	C₂²⋊Q₈	—	86	2	no	—
714	C₂²⋊Q₈	—	86	2	no	—
715	C₂²⋊Q₈	—	86	2	no	—
716	C₄×Q₈	—	43	1	no	—
717	C₄×Q₈	—	43	1	no	—
718	C₄×Q₈	—	43	1	no	—
719	C₄×Q₈	—	86	2	no	—
720	C₄×Q₈	—	86	2	no	—
721	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
722	C₄×D₄	—	43	2	no	—
723	C₄×D₄	—	43	2	no	—
724	C₄×D₄	—	43	2	no	—
725	C₄×D₄	—	43	2	no	—
726	C₄×D₄	—	43	2	no	—
727	C₄×D₄	—	43	2	no	—
728	C₄×D₄	—	43	2	no	—
729	C₄×D₄	—	43	2	no	—
730	C₄×D₄	—	43	2	no	—
731	C₄×D₄	—	86	2	no	—
732	C₄×D₄	—	86	2	no	—
733	C₄×D₄	—	86	2	no	—
734	C₄×D₄	—	86	2	no	—
735	C₄×D₄	—	86	2	no	—
736	C₄×D₄	—	86	2	no	—
737	C₄×D₄	C₂²×D₄₃	1	2	yes	—
738	C₄×D₄	C₂²×D₄₃	1	2	yes	—
739	C₄×D₄	C₂²×D₄₃	1	2	yes	—
740	#117	—	43	1	no	—
741	#117	—	43	1	no	—
742	#117	—	43	2	no	—
743	#117	—	43	2	no	—
744	C₂×C₄⋊C₄	—	2	2	no	—
745	C₂×C₄⋊C₄	—	43	2	no	—
746	C₂×C₄⋊C₄	—	86	2	no	—
747	C₂×C₄⋊C₄	—	86	2	no	—
748	C₂×C₄⋊C₄	—	86	2	no	—
749	C₂×C₄⋊C₄	—	86	2	no	—
750	C₂×C₄⋊C₄	—	86	2	no	—
751	C₂×C₂²⋊C₄	—	86	2	no	—
752	C₂×C₂²⋊C₄	—	86	2	no	—
753	C₂×C₂²⋊C₄	—	86	2	no	—
754	C₂×C₂²⋊C₄	—	86	2	no	—
755	C₂×C₂²⋊C₄	—	86	2	no	—
756	C₂×C₄²	—	43	1	no	—
757	#107	—	43	1	no	—
758	#107	—	43	1	no	—
759	#107	—	43	1	no	—
760	#107	—	43	2	no	—
761	#107	—	43	2	no	—
762	#107	—	43	2	no	—
763	#107	—	43	2	no	—
764	#107	—	43	2	no	—
765	#107	—	43	2	no	—
766	#107	C₂²×D₄₃	1	1	yes	characteristic
767	#107	C₂²×D₄₃	1	1	yes	characteristic
768	#107	C₂²×D₄₃	1	1	yes	characteristic
769	#107	C₂²×D₄₃	1	2	yes	—
770	#106	—	43	2	no	—
771	#106	—	43	2	no	—
772	#106	—	43	2	no	—
773	#106	—	43	2	no	—
774	#106	—	43	2	no	—
775	#106	—	43	2	no	—
776	#106	C₂²×D₄₃	1	2	yes	—
777	#106	C₂²×D₄₃	1	2	yes	—
778	C₄⋊C₈	—	43	1	no	—
779	C₄⋊C₈	—	43	1	no	—
780	C₄⋊C₈	—	43	1	no	—
781	C₄⋊C₈	—	43	1	no	—
782	C₄⋊C₈	—	43	1	no	—
783	C₄⋊C₈	—	43	1	no	—
784	C₄⋊C₈	—	43	1	no	—
785	C₄⋊C₈	—	43	1	no	—
786	C₄⋊C₈	—	43	1	no	—
787	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
788	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
789	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
790	#102	—	43	2	no	—
791	#102	—	43	2	no	—
792	#102	—	43	2	no	—
793	#102	—	43	2	no	—
794	#102	—	43	2	no	—
795	#102	—	43	2	no	—
796	#102	—	43	2	no	—
797	#102	—	43	2	no	—
798	#102	—	43	2	no	—
799	#102	C₂²×D₄₃	1	2	yes	—
800	#102	C₂²×D₄₃	1	2	yes	—
801	#102	C₂²×D₄₃	1	2	yes	—
802	#97	—	43	1	no	—
803	#97	—	43	1	no	—
804	#97	—	43	1	no	—
805	#97	—	43	1	no	—
806	C₄×C₈	—	43	1	no	—
807	C₄×C₈	—	43	1	no	—
808	C₄×C₈	—	43	1	no	—
809	C₄×C₈	—	43	1	no	—
810	C₄×C₈	—	43	1	no	—
811	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
812	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
813	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
814	C₂⁴	—	86	2	no	—
815	C₂×Q₈	—	2	2	no	—
816	C₂×Q₈	—	43	1	no	—
817	C₂×Q₈	—	43	1	no	—
818	C₂×Q₈	—	43	1	no	—
819	C₂×Q₈	—	86	2	no	—
820	C₂×Q₈	—	86	2	no	—
821	C₂×Q₈	—	86	2	no	—
822	C₂×Q₈	—	86	2	no	—
823	C₂×Q₈	—	86	2	no	—
824	C₂×Q₈	—	344	4	no	—
825	C₂×Q₈	—	344	4	no	—
826	C₂×Q₈	D₄×D₄₃	1	1	yes	characteristic
827	C₂×D₄	—	43	8	no	—
828	C₂×D₄	—	43	2	no	—
829	C₂×D₄	—	86	4	no	—
830	C₂×D₄	—	86	2	no	—
831	C₂×D₄	C₂³×D₄₃	1	2	yes	—
832	C₂²×C₄	—	2	2	no	—
833	C₂²×C₄	—	2	2	no	—
834	C₂²×C₄	—	2	2	no	—
835	C₂²×C₄	—	43	1	no	—
836	C₂²×C₄	—	43	1	no	—
837	C₂²×C₄	—	43	1	no	—
838	C₂²×C₄	—	86	2	no	—
839	C₂²×C₄	—	86	2	no	—
840	C₂²×C₄	—	86	2	no	—
841	C₂²×C₄	—	86	2	no	—
842	C₂²×C₄	—	86	2	no	—
843	C₂²×C₄	—	86	2	no	—
844	C₂²×C₄	—	86	2	no	—
845	C₂²×C₄	—	86	2	no	—
846	C₂²×C₄	—	86	2	no	—
847	C₂²×C₄	—	86	2	no	—
848	C₂²×C₄	—	344	4	no	—
849	D₈	—	43	8	no	—
850	D₈	—	43	4	no	—
851	D₈	Q₈×D₄₃	1	4	yes	complemented
852	M₁₆	—	86	2	no	—
853	M₁₆	—	86	2	no	—
854	C₂×C₈	—	43	1	no	—
855	C₂×C₈	—	43	4	no	—
856	C₂×C₈	—	43	1	no	—
857	C₂×C₈	—	43	1	no	—
858	C₂×C₈	—	43	1	no	—
859	C₂×C₈	—	86	2	no	—
860	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
861	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
862	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
863	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
864	C₄⋊C₄	—	2	2	no	—
865	C₄⋊C₄	—	2	2	no	—
866	C₄⋊C₄	—	2	2	no	—
867	C₄⋊C₄	—	2	2	no	—
868	C₄⋊C₄	—	2	2	no	—
869	C₄⋊C₄	—	43	1	no	—
870	C₄⋊C₄	—	43	1	no	—
871	C₄⋊C₄	—	43	1	no	—
872	C₄⋊C₄	—	43	1	no	—
873	C₄⋊C₄	—	43	1	no	—
874	C₄⋊C₄	—	43	1	no	—
875	C₄⋊C₄	—	43	1	no	—
876	C₄⋊C₄	—	43	1	no	—
877	C₄⋊C₄	—	43	1	no	—
878	C₄⋊C₄	—	43	1	no	—
879	C₄⋊C₄	—	43	1	no	—
880	C₄⋊C₄	—	43	1	no	—
881	C₄⋊C₄	—	43	1	no	—
882	C₄⋊C₄	—	43	2	no	—
883	C₄⋊C₄	—	43	2	no	—
884	C₄⋊C₄	—	43	2	no	—
885	C₄⋊C₄	—	86	2	no	—
886	C₄⋊C₄	—	86	2	no	—
887	C₄⋊C₄	—	86	2	no	—
888	C₄⋊C₄	—	86	2	no	—
889	C₄⋊C₄	—	86	2	no	—
890	C₄⋊C₄	—	86	2	no	—
891	C₄⋊C₄	—	86	2	no	—
892	C₄⋊C₄	—	86	2	no	—
893	C₄⋊C₄	—	86	2	no	—
894	C₄⋊C₄	—	86	2	no	—
895	C₄⋊C₄	—	86	2	no	—
896	C₄⋊C₄	—	86	2	no	—
897	C₄⋊C₄	—	86	2	no	—
898	C₄⋊C₄	—	86	2	no	—
899	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
900	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
901	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
902	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
903	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
904	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
905	C₂²⋊C₄	—	2	2	no	—
906	C₂²⋊C₄	—	2	2	no	—
907	C₂²⋊C₄	—	2	2	no	—
908	C₂²⋊C₄	—	43	1	no	—
909	C₂²⋊C₄	—	43	1	no	—
910	C₂²⋊C₄	—	43	1	no	—
911	C₂²⋊C₄	—	43	1	no	—
912	C₂²⋊C₄	—	86	2	no	—
913	C₂²⋊C₄	—	86	2	no	—
914	C₂²⋊C₄	—	86	2	no	—
915	C₂²⋊C₄	—	86	2	no	—
916	C₂²⋊C₄	—	86	2	no	—
917	C₂²⋊C₄	—	86	2	no	—
918	C₂²⋊C₄	—	86	2	no	—
919	C₂²⋊C₄	—	86	2	no	—
920	C₂²⋊C₄	—	86	2	no	—
921	C₂²⋊C₄	—	86	2	no	—
922	C₂²⋊C₄	—	86	2	no	—
923	C₄²	—	43	1	no	—
924	C₄²	—	43	1	no	—
925	C₄²	—	43	1	no	—
926	C₄²	—	43	1	no	—
927	C₄²	—	43	1	no	—
928	C₄²	—	86	2	no	—
929	C₄²	—	86	2	no	—
930	C₄²	C₂³×D₄₃	1	1	yes	characteristic
931	C₄²	C₂³×D₄₃	1	1	yes	characteristic
932	C₄²	C₂³×D₄₃	1	1	yes	characteristic
933	C₂³	—	2	2	no	—
934	C₂³	—	43	1	no	—
935	C₂³	—	86	8	no	—
936	C₂³	—	86	2	no	—
937	C₂³	—	344	2	no	—
938	C₂³	—	344	2	no	—
939	Q₈	—	4	1	no	—
940	Q₈	—	8	2	no	—
941	Q₈	—	86	2	no	—
942	Q₈	—	86	2	no	—
943	Q₈	—	344	2	no	—
944	Q₈	—	344	2	no	—
945	Q₈	—	344	2	no	—
946	Q₈	—	344	2	no	—
947	Q₈	—	172	1	no	—
948	Q₈	—	172	4	no	—
949	D₄	—	2	2	no	—
950	D₄	—	43	4	no	—
951	D₄	—	86	8	no	—
952	D₄	—	86	2	no	—
953	D₄	C₂×Q₈×D₄₃	1	4	yes	—
954	C₂×C₄	—	2	2	no	—
955	C₂×C₄	—	2	2	no	—
956	C₂×C₄	—	2	2	no	—
957	C₂×C₄	—	8	2	no	—
958	C₂×C₄	—	8	2	no	—
959	C₂×C₄	—	8	2	no	—
960	C₂×C₄	—	43	1	no	—
961	C₂×C₄	—	43	1	no	—
962	C₂×C₄	—	43	2	no	—
963	C₂×C₄	—	43	2	no	—
964	C₂×C₄	—	43	1	no	—
965	C₂×C₄	—	43	1	no	—
966	C₂×C₄	—	43	1	no	—
967	C₂×C₄	—	43	1	no	—
968	C₂×C₄	—	43	1	no	—
969	C₂×C₄	—	86	2	no	—
970	C₂×C₄	—	86	2	no	—
971	C₂×C₄	—	86	2	no	—
972	C₂×C₄	—	86	2	no	—
973	C₂×C₄	—	344	2	no	—
974	C₂×C₄	—	344	2	no	—
975	C₂×C₄	—	344	2	no	—
976	C₂×C₄	—	344	2	no	—
977	C₂×C₄	—	344	2	no	—
978	C₂×C₄	—	344	2	no	—
979	C₂×C₄	—	344	2	no	—
980	C₂×C₄	—	344	2	no	—
981	C₂×C₄	—	172	1	no	—
982	C₂×C₄	—	172	4	no	—
983	C₂×C₄	—	172	4	no	—
984	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
985	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
986	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
987	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
988	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
989	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
990	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
991	C₈	—	2	1	no	—
992	C₈	—	2	1	no	—
993	C₈	—	2	1	no	—
994	C₈	—	43	2	no	—
995	C₈	—	86	1	no	—
996	C₈	—	86	1	no	—
997	C₈	—	86	1	no	—
998	C₈	C₂×Q₈×D₄₃	1	2	yes	—
999	C₂²	—	2	4	no	—
1000	C₂²	—	4	2	no	—
1001	C₂²	—	4	2	no	—
1002	C₂²	—	43	2	no	—
1003	C₂²	—	86	1	no	—
1004	C₂²	—	86	1	no	—
1005	C₂²	—	86	4	no	—
1006	C₂²	—	344	8	no	—
1007	C₂²	—	172	2	no	—
1008	C₂²	—	172	2	no	—
1009	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1010	C₄	—	2	1	no	—
1011	C₄	—	2	1	no	—
1012	C₄	—	2	1	no	—
1013	C₄	—	2	1	no	—
1014	C₄	—	2	1	no	—
1015	C₄	—	2	1	no	—
1016	C₄	—	4	2	no	—
1017	C₄	—	4	2	no	—
1018	C₄	—	4	2	no	—
1019	C₄	—	43	2	no	—
1020	C₄	—	43	2	no	—
1021	C₄	—	86	1	no	—
1022	C₄	—	86	1	no	—
1023	C₄	—	86	1	no	—
1024	C₄	—	86	1	no	—
1025	C₄	—	86	1	no	—
1026	C₄	—	172	2	no	—
1027	C₄	—	172	2	no	—
1028	C₄	—	172	2	no	—
1029	C₄	C₂²×Q₈×D₄₃	1	1	yes	characteristic
1030	C₄	2₋¹⁺⁴×D₄₃	1	1	yes	characteristic
1031	C₂	—	4	4	no	—
1032	C₂	—	86	2	no	—
1033	C₂	—	172	4	no	—
1034	C₂	D₄×Q₈×D₄₃	1	1	yes	characteristic
1035	C₂	#576×D₄₃	1	1	yes	characteristic
1036	C₂	#19149364	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₄₃×#3380	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	C₂×D₈×D₄₃	C₂²
hypercenter	#3380	D₄₃
hypocenter	C₄₃	#61370
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×Q₈ ◁ #3380

Complements

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

N	H ≅ G/N	type
1. #19148394	C₂	semidirect
2. #19147553	C₂	semidirect
3. #19147549	C₂	semidirect
4. #19147497	C₂	semidirect
5. #19147489	C₂	semidirect
6. #19147463	C₂	semidirect
7. #19147462	C₂	semidirect
8. #19147462	C₂	semidirect
9. #19147459	C₂	semidirect
10. #19147459	C₂	semidirect
11. D₈×Dic₈₆	C₂	semidirect
12. #19147447	C₂	semidirect
13. #19145132	C₂	semidirect
14. #19145128	C₂	semidirect
15. #19145108	C₂	semidirect
16. #19144425	C₂	semidirect
17. #19144421	C₂	semidirect
18. #19144390	C₂	semidirect
19. #19143524	C₂	semidirect
23. C₄₃×#3380	C₂	semidirect
25. #14583609	C₂²	semidirect
26. #14583608	C₂²	semidirect
27. #14583608	C₂²	semidirect
28. #14583605	C₂²	semidirect
29. #14583605	C₂²	semidirect
33. D₄×Dic₈₆	C₂²	semidirect
34. #14583564	C₂²	semidirect
47. #14583309	C₂²	semidirect
48. #14583307	C₂²	semidirect
49. #14583306	C₂²	semidirect
50. #14583305	C₂²	semidirect
51. #14583304	C₂²	semidirect
52. #14583303	C₂²	semidirect
53. #14583303	C₂²	semidirect
54. #14583303	C₂²	semidirect
55. #14583303	C₂²	semidirect
56. #14583301	C₂²	semidirect
57. #14583301	C₂²	semidirect
58. #14583300	C₂²	semidirect
59. #14583300	C₂²	semidirect
60. #14583298	C₂²	semidirect
61. #14583296	C₂²	semidirect
62. #14583201	C₂²	semidirect
63. #14583201	C₂²	semidirect
64. #14583200	C₂²	semidirect
65. #14583200	C₂²	semidirect
66. #14583199	C₂²	semidirect
67. #14583199	C₂²	semidirect
68. #14583198	C₂²	semidirect
69. #14583198	C₂²	semidirect
70. #14583196	C₂²	semidirect
71. #14583196	C₂²	semidirect
72. #14583190	C₂²	semidirect
73. #14583188	C₂²	semidirect
74. #14583188	C₂²	semidirect
75. #14583187	C₂²	semidirect
76. #14583187	C₂²	semidirect
77. #14583179	C₂²	semidirect
78. #14583178	C₂²	semidirect
79. #14583178	C₂²	semidirect
80. #14583177	C₂²	semidirect
81. #14583177	C₂²	semidirect
82. #14583176	C₂²	semidirect
83. #14583030	C₂²	semidirect
84. #14583028	C₂²	semidirect
85. #14583028	C₂²	semidirect
86. #14583026	C₂²	semidirect
87. C₈×Dic₈₆	C₂²	semidirect
88. C₈×Dic₈₆	C₂²	semidirect
89. C₈×Dic₈₆	C₂²	semidirect
120. C₄₃×#554	C₂²	semidirect
121. C₄₃×#500	C₂²	semidirect
122. C₄₃×#499	C₂²	semidirect
123. C₄₃×#499	C₂²	semidirect
124. C₄₃×#478	C₂²	semidirect
125. C₄₃×#478	C₂²	semidirect
126. C₄₃×#476	C₂²	semidirect
127. C₈×Q₈×C₄₃	C₂²	semidirect
137. D₈×D₄₃	Q₈	semidirect
308. D₄×D₄₃	C₂×Q₈	semidirect
330. D₈×C₄₃	C₂×Q₈	semidirect
355. #10621882	C₂×Q₈	semidirect
409. D₃₄₄	C₂×Q₈	semidirect
413. C₈×D₄₃	C₂×Q₈	semidirect
523. #3380	D₄₃	semidirect
551. #554	C₂×D₄₃	semidirect
575. #500	C₂×D₄₃	semidirect
581. #499	C₂×D₄₃	semidirect
582. #499	C₂×D₄₃	semidirect
594. #478	C₂×D₄₃	semidirect
595. #478	C₂×D₄₃	semidirect
601. #476	C₂×D₄₃	semidirect
615. C₈×Q₈	C₂×D₄₃	semidirect
649. C₄₃	#61370	semidirect
851. D₈	Q₈×D₄₃	semidirect

Maximal subgroups

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

subgroup	index
#19148394	2
#19147553	2
#19147549	2
#19147497	2
#19147489	2
#19147463	2
#19147462	2
#19147459	2
D₈×Dic₈₆	2
#19147447	2
#19145132	2
#19145128	2
#19145108	2
#19144425	2
#19144421	2
#19144390	2
#19143524	2
#19143442	2
C₄×D₈×D₄₃	2
C₄₃×#3380	2
#61370	43