Subgroups — #25976004

Order 11008.

1882 conjugacy classes of subgroups.

The subgroup lattice has 1122 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148441	C₂	1	2	yes	maximal, complemented
2	#19147198	C₂	1	2	yes	maximal, complemented
3	#19147195	C₂	1	2	yes	maximal, complemented
4	#19147188	C₂	1	2	yes	maximal, complemented
5	#19147183	C₂	1	2	yes	maximal, complemented
6	#19147015	C₂	1	1	yes	maximal, characteristic, complemented
7	#19147014	C₂	1	1	yes	maximal, characteristic, complemented
8	#19146999	C₂	1	1	yes	maximal, characteristic, complemented
9	#19146998	C₂	1	1	yes	maximal, characteristic, complemented
10	#19146996	C₂	1	1	yes	maximal, characteristic, complemented
11	#19146940	C₂	1	1	yes	maximal, characteristic, complemented
12	#19146939	C₂	1	1	yes	maximal, characteristic, complemented
13	#19145108	C₂	1	1	yes	maximal, characteristic, complemented
14	#19144552	C₂	1	2	yes	maximal, complemented
15	#19144548	C₂	1	2	yes	maximal, complemented
16	#19144390	C₂	1	2	yes	maximal, complemented
17	#19144238	C₂	1	1	yes	maximal, characteristic, complemented
18	#19144238	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄×D₈×D₄₃	C₂	1	1	yes	maximal, characteristic, complemented
20	#19143302	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143192	C₂	1	1	yes	maximal, characteristic, complemented
22	#19143191	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3339	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×D₈×D₄₃	C₂²	1	1	yes	characteristic
25	C₂×#13063331	C₂²	1	1	yes	characteristic
26	C₂×#13063331	C₂²	1	1	yes	characteristic
27	#14583633	—	2	2	no	—
28	#14583632	—	2	2	no	—
29	#14583616	—	2	2	no	—
30	#14583613	C₂²	1	2	yes	complemented
31	#14583612	C₂²	1	2	yes	complemented
32	#14583602	C₂²	1	2	yes	complemented
33	#14583599	C₂²	1	2	yes	complemented
34	#14583595	C₂²	1	2	yes	complemented
35	#14583567	—	2	2	no	—
36	#14583550	C₂²	1	2	yes	complemented
37	#14583549	C₂²	1	2	yes	complemented
38	#14583488	—	2	2	no	—
39	#14583481	—	2	2	no	—
40	#14583465	C₂²	1	2	yes	—
41	#14583465	C₂²	1	2	yes	—
42	#14583455	C₂²	1	2	yes	—
43	#14583446	C₂²	1	1	yes	characteristic
44	#14583408	—	2	2	no	—
45	#14583407	—	2	2	no	—
46	#14583380	C₂²	1	2	yes	—
47	#14583379	C₂²	1	2	yes	—
48	C₄×D₄×D₄₃	C₂²	1	2	yes	—
49	#14583303	C₂²	1	1	yes	characteristic, complemented
50	#14583303	C₂²	1	1	yes	characteristic, complemented
51	#14583301	C₂²	1	1	yes	characteristic, complemented
52	#14583298	C₂²	1	2	yes	complemented
53	#14583296	C₂²	1	2	yes	complemented
54	#14583225	C₂²	1	2	yes	complemented
55	#14583225	C₂²	1	2	yes	complemented
56	#14583224	C₂²	1	2	yes	complemented
57	#14583223	C₂²	1	2	yes	complemented
58	#14583222	C₂²	1	2	yes	complemented
59	#14583222	C₂²	1	2	yes	complemented
60	#14583220	C₂²	1	2	yes	complemented
61	#14583219	C₂²	1	2	yes	complemented
62	#14583218	C₂²	1	2	yes	complemented
63	#14583216	C₂²	1	2	yes	complemented
64	#14583214	C₂²	1	2	yes	complemented
65	#14583212	C₂²	1	2	yes	complemented
66	#14583211	C₂²	1	2	yes	complemented
67	#14583210	C₂²	1	2	yes	complemented
68	#14583200	C₂²	1	2	yes	complemented
69	#14583199	C₂²	1	2	yes	complemented
70	#14583196	C₂²	1	2	yes	complemented
71	#14583188	C₂²	1	2	yes	complemented
72	#14583187	C₂²	1	2	yes	complemented
73	#14583178	C₂²	1	2	yes	complemented
74	#14583177	C₂²	1	2	yes	complemented
75	#14583151	C₂²	1	2	yes	—
76	#14583151	C₂²	1	2	yes	—
77	#14583150	C₂²	1	2	yes	—
78	#14583150	C₂²	1	2	yes	—
79	#14583136	C₂²	1	1	yes	characteristic
80	#14583136	C₂²	1	1	yes	characteristic
81	#14583135	C₂²	1	1	yes	characteristic
82	#14583135	C₂²	1	1	yes	characteristic
83	#14583132	C₂²	1	1	yes	characteristic
84	#14583132	C₂²	1	1	yes	characteristic
85	C₄×D₃₄₄	C₂²	1	1	yes	characteristic
86	D₈×Dic₄₃	C₂²	1	1	yes	characteristic
87	#14582981	C₂²	1	1	yes	characteristic
88	C₄×#10621882	C₂²	1	2	yes	—
89	#14582979	C₂²	1	2	yes	—
90	#14582977	C₂²	1	1	yes	characteristic, complemented
91	#14582976	C₂²	1	1	yes	characteristic, complemented
92	#14582974	C₂²	1	1	yes	characteristic, complemented
93	#14582974	C₂²	1	1	yes	characteristic, complemented
94	C₈×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
95	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic, complemented
96	C₈×C₂²⋊D₄₃	C₂²	1	1	yes	characteristic, complemented
97	#14582942	C₂²	1	2	yes	complemented
98	#14582940	C₂²	1	2	yes	—
99	#14582940	C₂²	1	2	yes	complemented
100	#14582939	C₂²	1	2	yes	complemented
101	#14582938	C₂²	1	2	yes	—
102	#14582938	C₂²	1	2	yes	complemented
103	#14582937	C₂²	1	1	yes	characteristic, complemented
104	#14582936	C₂²	1	1	yes	characteristic
105	#14582936	C₂²	1	1	yes	characteristic
106	#14582936	C₂²	1	1	yes	characteristic, complemented
107	#14582936	C₂²	1	1	yes	characteristic, complemented
108	#14582934	C₂²	1	2	yes	—
109	C₂×#13063259	C₂²	1	1	yes	characteristic, complemented
110	#107×D₄₃	C₂²	1	1	yes	characteristic
111	#107×D₄₃	C₂²	1	1	yes	characteristic, complemented
112	#107×D₄₃	C₂²	1	1	yes	characteristic, complemented
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	#14582864	C₂²	1	1	yes	characteristic
118	#14582864	C₂²	1	1	yes	characteristic
119	C₄×C₈×D₄₃	C₂²	1	1	yes	characteristic
120	C₄₃×#553	C₂²	1	2	yes	complemented
121	C₄₃×#499	C₂²	1	1	yes	characteristic, complemented
122	C₄₃×#482	C₂²	1	2	yes	complemented
123	C₄₃×#481	C₂²	1	2	yes	complemented
124	C₄₃×#478	C₂²	1	2	yes	complemented
125	C₄₃×#466	C₂²	1	1	yes	characteristic
126	C₄₃×#466	C₂²	1	1	yes	characteristic
127	C₄×D₈×C₄₃	C₂²	1	1	yes	characteristic
128	C₈×D₄×C₄₃	C₂²	1	1	yes	characteristic, complemented
129	C₄₃×#427	C₂²	1	1	yes	characteristic, complemented
130	C₂×#107×C₄₃	C₂²	1	1	yes	characteristic, complemented
131	C₂×#10621898	—	2	2	no	—
132	C₂×#10621898	C₂³	1	1	yes	characteristic
133	C₂×#10621898	C₂³	1	1	yes	characteristic
134	C₂×#10621900	—	2	2	no	—
135	C₂×D₄×D₄₃	C₂³	1	2	yes	—
136	C₂²×C₄×D₄₃	—	2	2	no	—
137	C₂×D₃₄₄	C₂³	1	1	yes	characteristic
138	C₂×#10621882	C₂³	1	2	yes	—
139	D₈×D₄₃	—	2	4	no	—
140	#13063331	—	2	4	no	—
141	#13063331	—	2	4	no	—
142	C₂×#10621877	C₂³	1	1	yes	characteristic
143	C₂×#10621877	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	1	yes	characteristic
147	C₂×#10621872	C₂³	1	1	yes	characteristic
148	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
149	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
150	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
151	C₂×C₈×D₄₃	C₂³	1	1	yes	characteristic
152	#13063324	D₄	1	1	yes	characteristic
153	#13063324	C₂³	1	2	yes	—
154	#13063324	C₂³	1	2	yes	—
155	#13063321	—	2	2	no	—
156	#13063321	—	2	2	no	—
157	#13063321	D₄	1	1	yes	characteristic
158	#13063320	—	2	2	no	—
159	#13063320	—	2	2	no	—
160	#13063318	—	2	2	no	—
161	#13063317	C₂³	1	2	yes	—
162	#13063313	—	2	2	no	—
163	#13063312	—	2	2	no	—
164	#13063311	—	2	2	no	—
165	#13063311	—	2	2	no	—
166	#13063311	—	2	2	no	—
167	#13063311	—	2	2	no	—
168	#13063311	D₄	1	1	yes	characteristic
169	#13063311	D₄	1	1	yes	characteristic
170	#13063310	—	2	2	no	—
171	#13063310	—	2	2	no	—
172	#13063308	—	2	2	no	—
173	#13063308	—	2	2	no	—
174	#13063307	—	2	2	no	—
175	#13063307	—	2	2	no	—
176	#13063306	—	2	2	no	—
177	#13063303	—	2	2	no	—
178	#13063303	—	2	2	no	—
179	#13063303	—	2	2	no	—
180	#13063302	—	2	2	no	—
181	#13063300	—	2	2	no	—
182	#13063300	D₄	1	1	yes	characteristic
183	#13063300	C₂³	1	2	yes	—
184	#13063300	C₂³	1	2	yes	—
185	#13063299	C₂³	1	2	yes	—
186	#13063299	C₂³	1	2	yes	—
187	#13063298	—	2	2	no	—
188	#13063298	—	2	2	no	—
189	#13063298	D₄	1	1	yes	characteristic
190	#13063298	D₄	1	1	yes	characteristic
191	#13063297	—	2	2	no	—
192	#13063297	—	2	2	no	—
193	#13063296	D₄	1	1	yes	characteristic
194	#13063296	C₂³	1	2	yes	—
195	#13063296	C₂³	1	2	yes	—
196	#13063295	—	2	2	no	—
197	#13063295	—	2	2	no	—
198	#13063293	—	2	2	no	—
199	#13063293	—	2	2	no	—
200	C₄×Dic₈₆	—	2	2	no	—
201	#13063290	—	2	2	no	—
202	#13063290	—	2	2	no	—
203	#13063290	—	2	2	no	—
204	C₄×D₁₇₂	—	2	2	no	—
205	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
206	C₄×D₁₇₂	C₂³	1	2	yes	—
207	D₄×Dic₄₃	C₂³	1	2	yes	—
208	#13063287	—	2	2	no	—
209	#13063287	—	2	2	no	—
210	#13063287	C₂³	1	2	yes	—
211	C₄×C₂²⋊D₄₃	—	2	2	no	—
212	C₄×C₂²⋊D₄₃	—	2	2	no	—
213	C₄×C₂²⋊D₄₃	—	2	2	no	—
214	C₄×C₂²⋊D₄₃	—	2	2	no	—
215	C₄×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
216	C₄×C₂²⋊D₄₃	C₂³	1	1	yes	characteristic
217	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
218	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
219	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
220	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
221	#13063284	C₂³	1	2	yes	—
222	#13063283	C₂³	1	2	yes	—
223	#13063283	C₂³	1	2	yes	—
224	#13063283	C₂³	1	2	yes	—
225	#13063283	C₂³	1	2	yes	—
226	#13063282	—	2	2	no	—
227	#13063281	—	2	2	no	—
228	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
229	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
230	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
231	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
232	C₂²⋊C₄×D₄₃	—	2	2	no	—
233	C₄²×D₄₃	C₂³	1	1	yes	characteristic
234	#13063259	C₂³	1	1	yes	characteristic
235	#13063259	C₂³	1	1	yes	characteristic
236	#13063259	C₂³	1	2	yes	—
237	#13063259	C₂³	1	1	yes	characteristic
238	#13063258	C₂³	1	2	yes	—
239	#13063258	C₂³	1	2	yes	—
240	#13063258	C₂³	1	2	yes	—
241	#13063258	C₂³	1	2	yes	—
242	#13063258	C₂³	1	2	yes	—
243	#13063257	C₂³	1	2	yes	—
244	#13063257	C₂³	1	2	yes	—
245	#13063256	C₂³	1	2	yes	—
246	#13063256	C₂³	1	2	yes	—
247	#13063256	C₂³	1	2	yes	—
248	#13063256	C₂³	1	2	yes	—
249	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
250	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
251	Dic₄₃⋊C₈	C₂³	1	1	yes	characteristic
252	#13063247	C₂³	1	2	yes	—
253	#13063247	C₂³	1	2	yes	—
254	#13063247	C₂³	1	2	yes	—
255	#13063246	C₂³	1	2	yes	—
256	#13063246	C₂³	1	2	yes	—
257	#13063246	C₂³	1	2	yes	—
258	#13063245	C₂³	1	2	yes	—
259	#13063245	C₂³	1	2	yes	—
260	#13063245	C₂³	1	2	yes	—
261	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
262	C₂²⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
263	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
264	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
265	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
266	(C₂×D₄₃)⋊C₈	C₂³	1	1	yes	characteristic
267	C₄×C₄₃⋊C₈	C₂³	1	1	yes	characteristic
268	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
269	C₈×Dic₄₃	C₂³	1	1	yes	characteristic
270	C₂×D₈×C₄₃	C₂³	1	1	yes	characteristic
271	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
272	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
273	#126×C₄₃	—	2	2	no	—
274	#125×C₄₃	C₂³	1	2	yes	—
275	#123×C₄₃	—	2	2	no	—
276	#121×C₄₃	—	2	2	no	—
277	#121×C₄₃	C₂³	1	2	yes	—
278	#121×C₄₃	C₂³	1	2	yes	—
279	C₄×D₄×C₄₃	—	2	2	no	—
280	C₄×D₄×C₄₃	C₂³	1	2	yes	—
281	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
282	#117×C₄₃	C₂³	1	2	yes	—
283	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
284	#107×C₄₃	C₂³	1	1	yes	characteristic
285	#107×C₄₃	C₂³	1	1	yes	characteristic
286	#107×C₄₃	C₂³	1	2	yes	—
287	#107×C₄₃	C₂³	1	1	yes	characteristic
288	#106×C₄₃	C₂³	1	2	yes	—
289	#106×C₄₃	C₂³	1	2	yes	—
290	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
291	#102×C₄₃	C₂³	1	2	yes	—
292	#102×C₄₃	C₂³	1	2	yes	—
293	#102×C₄₃	C₂³	1	2	yes	—
294	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
295	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
297	C₂³×D₄₃	—	2	2	no	—
298	C₂×D₄×C₄₃	—	2	2	no	—
299	C₂×D₄×C₄₃	—	2	2	no	—
300	C₂×D₄×C₄₃	C₂×D₄	1	1	yes	characteristic
301	C₂×D₄×C₄₃	C₂⁴	1	2	yes	—
302	C₂²×C₄×C₄₃	—	2	2	no	—
303	C₂²×C₄×C₄₃	—	2	2	no	—
304	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
305	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
306	C₂×C₂²⋊D₄₃	—	2	2	no	—
307	C₂×C₂²⋊D₄₃	—	2	2	no	—
308	C₂×C₂²⋊D₄₃	—	2	2	no	—
309	C₂×C₂²⋊D₄₃	—	2	2	no	—
310	C₂×C₂²⋊D₄₃	—	2	2	no	—
311	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
312	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
313	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
314	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
315	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
316	C₂×C₂²⋊D₄₃	C₂×D₄	1	1	yes	characteristic
317	C₂²×Dic₄₃	—	2	2	no	—
318	C₂²×Dic₄₃	—	2	2	no	—
319	#10621900	—	8	4	no	—
320	D₄×D₄₃	—	2	4	no	—
321	D₄×D₄₃	—	2	4	no	—
322	#10621898	—	2	2	no	—
323	#10621898	—	2	2	no	—
324	#10621898	—	2	2	no	—
325	#10621898	—	2	2	no	—
326	#10621898	—	8	4	no	—
327	C₂×D₁₇₂	—	2	2	no	—
328	C₂×D₁₇₂	—	2	2	no	—
329	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
330	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
331	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
332	C₂×D₁₇₂	C₂⁴	1	2	yes	—
333	C₂×C₄×D₄₃	—	2	2	no	—
334	C₂×C₄×D₄₃	—	2	2	no	—
335	C₂×C₄×D₄₃	—	2	2	no	—
336	C₂×C₄×D₄₃	—	2	2	no	—
337	C₂×C₄×D₄₃	—	2	2	no	—
338	C₂×C₄×D₄₃	—	8	4	no	—
339	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
340	C₂×C₄×D₄₃	C₂×D₄	1	1	yes	characteristic
341	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
342	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
343	C₂×C₄×D₄₃	C₂⁴	1	1	yes	characteristic
344	C₂×Dic₈₆	—	2	2	no	—
345	C₂×Dic₈₆	—	2	2	no	—
346	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
347	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
348	D₈×C₄₃	—	2	2	no	—
349	C₂×C₈×C₄₃	—	2	2	no	—
350	C₂×C₈×C₄₃	—	2	2	no	—
351	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
352	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
354	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
355	C₄⋊C₄×C₄₃	—	2	2	no	—
356	C₄⋊C₄×C₄₃	—	2	2	no	—
357	C₄⋊C₄×C₄₃	—	2	2	no	—
358	C₄⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
359	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
360	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
361	C₄⋊C₄×C₄₃	C₂⁴	1	2	yes	—
362	C₂²⋊C₄×C₄₃	—	2	2	no	—
363	C₂²⋊C₄×C₄₃	—	2	2	no	—
364	C₂²⋊C₄×C₄₃	—	2	2	no	—
365	C₂²⋊C₄×C₄₃	—	2	2	no	—
366	C₂²⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
367	C₂²⋊C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
368	C₄²×C₄₃	—	2	2	no	—
369	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
370	C₂²⋊Dic₄₃	—	2	2	no	—
371	C₂²⋊Dic₄₃	—	2	2	no	—
372	C₂²⋊Dic₄₃	—	2	2	no	—
373	C₂²⋊Dic₄₃	—	2	2	no	—
374	C₂²⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
375	C₂²⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
376	#10621882	—	2	4	no	—
377	(C₂×D₄₃)⋊C₄	—	2	2	no	—
378	(C₂×D₄₃)⋊C₄	—	2	2	no	—
379	(C₂×D₄₃)⋊C₄	—	2	2	no	—
380	(C₂×D₄₃)⋊C₄	—	2	2	no	—
381	(C₂×D₄₃)⋊C₄	—	2	2	no	—
382	(C₂×D₄₃)⋊C₄	—	2	2	no	—
383	(C₂×D₄₃)⋊C₄	—	2	2	no	—
384	(C₂×D₄₃)⋊C₄	—	2	2	no	—
385	(C₂×D₄₃)⋊C₄	—	2	2	no	—
386	(C₂×D₄₃)⋊C₄	—	2	2	no	—
387	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
388	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
389	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
390	(C₂×D₄₃)⋊C₄	C₂×D₄	1	1	yes	characteristic
391	C₄⋊Dic₄₃	—	2	2	no	—
392	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
393	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
394	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
395	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
396	Dic₄₃⋊C₄	—	2	2	no	—
397	Dic₄₃⋊C₄	—	2	2	no	—
398	Dic₄₃⋊C₄	—	2	2	no	—
399	Dic₄₃⋊C₄	—	2	2	no	—
400	Dic₄₃⋊C₄	—	2	2	no	—
401	Dic₄₃⋊C₄	—	2	2	no	—
402	Dic₄₃⋊C₄	—	2	2	no	—
403	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
404	Dic₄₃⋊C₄	C₂×D₄	1	1	yes	characteristic
405	C₄×Dic₄₃	—	2	2	no	—
406	C₄×Dic₄₃	—	2	2	no	—
407	C₄×Dic₄₃	—	2	2	no	—
408	C₄×Dic₄₃	—	2	2	no	—
409	C₄×Dic₄₃	—	2	2	no	—
410	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
411	C₄×Dic₄₃	C₂×D₄	1	1	yes	characteristic
412	C₄×Dic₄₃	C₂⁴	1	1	yes	characteristic
413	#10621877	—	2	2	no	—
414	#10621877	—	2	2	no	—
415	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
416	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
417	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
418	C₂×C₄₃⋊C₈	C₂⁴	1	1	yes	characteristic
419	D₃₄₄	—	2	2	no	—
420	#10621872	—	2	2	no	—
421	#10621872	—	2	2	no	—
422	#10621872	—	2	2	no	—
423	#10621872	—	2	2	no	—
424	C₈×D₄₃	—	2	2	no	—
425	C₈×D₄₃	—	2	2	no	—
426	C₈×D₄₃	—	2	2	no	—
427	C₈×D₄₃	#41	1	4	yes	complemented
428	C₂³×C₄₃	—	2	2	no	—
429	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
430	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
431	C₂²×D₄₃	—	2	2	no	—
432	C₂²×D₄₃	—	4	4	no	—
433	C₂²×D₄₃	—	8	2	no	—
434	C₂²×D₄₃	—	8	2	no	—
435	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
436	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
437	C₂²×D₄₃	C₂²×D₄	1	1	yes	characteristic
438	D₄×C₄₃	—	2	2	no	—
439	D₄×C₄₃	—	2	2	no	—
440	D₄×C₄₃	—	4	1	no	—
441	D₄×C₄₃	—	8	2	no	—
442	D₄×C₄₃	—	8	2	no	—
443	C₂×C₄×C₄₃	—	2	1	no	—
444	C₂×C₄×C₄₃	—	2	1	no	—
445	C₂×C₄×C₄₃	—	2	1	no	—
446	C₂×C₄×C₄₃	—	2	1	no	—
447	C₂×C₄×C₄₃	—	2	2	no	—
448	C₂×C₄×C₄₃	—	2	2	no	—
449	C₂×C₄×C₄₃	—	2	2	no	—
450	C₂×C₄×C₄₃	—	8	2	no	—
451	C₂×C₄×C₄₃	—	8	2	no	—
452	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
453	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
454	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
455	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
456	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
457	C₂²⋊D₄₃	—	2	2	no	—
458	C₂²⋊D₄₃	—	2	2	no	—
459	C₂²⋊D₄₃	—	2	2	no	—
460	C₂²⋊D₄₃	—	2	2	no	—
461	C₂²⋊D₄₃	—	2	2	no	—
462	C₂²⋊D₄₃	—	2	2	no	—
463	C₂²⋊D₄₃	—	4	4	no	—
464	C₂²⋊D₄₃	—	8	2	no	—
465	C₂²⋊D₄₃	—	8	2	no	—
466	C₂²⋊D₄₃	—	8	2	no	—
467	C₂²⋊D₄₃	—	8	2	no	—
468	C₂×Dic₄₃	—	2	2	no	—
469	C₂×Dic₄₃	—	2	2	no	—
470	C₂×Dic₄₃	—	2	2	no	—
471	C₂×Dic₄₃	—	4	4	no	—
472	C₂×Dic₄₃	—	8	2	no	—
473	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
474	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
475	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
476	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
477	C₂×Dic₄₃	C₂²×D₄	1	1	yes	characteristic
478	D₁₇₂	—	2	2	no	—
479	D₁₇₂	—	2	2	no	—
480	D₁₇₂	—	2	2	no	—
481	D₁₇₂	—	2	2	no	—
482	D₁₇₂	—	4	1	no	—
483	D₁₇₂	—	8	2	no	—
484	D₁₇₂	—	8	2	no	—
485	C₄×D₄₃	—	2	1	no	—
486	C₄×D₄₃	—	2	1	no	—
487	C₄×D₄₃	—	2	1	no	—
488	C₄×D₄₃	—	2	1	no	—
489	C₄×D₄₃	—	2	2	no	—
490	C₄×D₄₃	—	4	1	no	—
491	C₄×D₄₃	—	4	4	no	—
492	C₄×D₄₃	—	8	2	no	—
493	C₄×D₄₃	—	8	2	no	—
494	C₄×D₄₃	—	8	2	no	—
495	C₄×D₄₃	—	8	2	no	—
496	C₄×D₄₃	C₂×#41	1	2	yes	—
497	C₄×D₄₃	2₋¹⁺⁴	1	2	yes	—
498	Dic₈₆	—	2	2	no	—
499	Dic₈₆	—	2	2	no	—
500	Dic₈₆	—	4	4	no	—
501	Dic₈₆	—	8	2	no	—
502	C₈×C₄₃	—	2	1	no	—
503	C₈×C₄₃	—	2	1	no	—
504	C₈×C₄₃	—	2	1	no	—
505	C₈×C₄₃	C₂×#41	1	2	yes	—
506	C₄₃⋊C₈	—	2	1	no	—
507	C₄₃⋊C₈	—	2	1	no	—
508	C₄₃⋊C₈	—	2	1	no	—
509	C₄₃⋊C₈	C₂×#41	1	2	yes	—
510	#61284	—	43	1	no	maximal, Sylow
511	C₂²×C₄₃	—	2	1	no	—
512	C₂²×C₄₃	—	2	1	no	—
513	C₂²×C₄₃	—	2	1	no	—
514	C₂²×C₄₃	—	2	1	no	—
515	C₂²×C₄₃	—	2	1	no	—
516	C₂²×C₄₃	—	2	1	no	—
517	C₂²×C₄₃	—	4	2	no	—
518	C₂²×C₄₃	—	4	2	no	—
519	C₂²×C₄₃	—	4	2	no	—
520	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
521	C₂×D₄₃	—	2	1	no	—
522	C₂×D₄₃	—	2	1	no	—
523	C₂×D₄₃	—	2	1	no	—
524	C₂×D₄₃	—	2	1	no	—
525	C₂×D₄₃	—	2	1	no	—
526	C₂×D₄₃	—	2	1	no	—
527	C₂×D₄₃	—	2	1	no	—
528	C₂×D₄₃	—	2	1	no	—
529	C₂×D₄₃	—	4	2	no	—
530	C₂×D₄₃	—	4	2	no	—
531	C₂×D₄₃	—	4	2	no	—
532	C₂×D₄₃	—	8	8	no	—
533	C₂×D₄₃	#547	1	2	yes	—
534	C₄×C₄₃	—	2	1	no	—
535	C₄×C₄₃	—	2	1	no	—
536	C₄×C₄₃	—	2	1	no	—
537	C₄×C₄₃	—	2	1	no	—
538	C₄×C₄₃	—	4	2	no	—
539	C₄×C₄₃	—	4	2	no	—
540	C₄×C₄₃	—	4	2	no	—
541	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
542	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
543	Dic₄₃	—	2	1	no	—
544	Dic₄₃	—	2	1	no	—
545	Dic₄₃	—	2	1	no	—
546	Dic₄₃	—	4	2	no	—
547	Dic₄₃	—	4	2	no	—
548	Dic₄₃	—	4	2	no	—
549	Dic₄₃	#547	1	2	yes	—
550	Dic₄₃	#576	1	2	yes	—
551	#3506	—	43	2	no	—
552	#3355	—	43	2	no	—
553	#3355	—	43	2	no	—
554	#3354	—	43	2	no	—
555	#3354	—	43	2	no	—
556	#3341	—	43	1	no	—
557	#3341	—	43	1	no	—
558	#3339	—	43	1	no	—
559	#3339	—	43	1	no	—
560	#3339	—	43	1	no	—
561	#3339	D₄₃	1	1	yes	characteristic, complemented
562	#3334	—	43	1	no	—
563	#3334	—	43	1	no	—
564	#3160	—	43	1	no	—
565	#3096	—	43	2	no	—
566	#3096	—	43	2	no	—
567	#3077	—	43	2	no	—
568	#3058	—	43	1	no	—
569	#3058	—	43	1	no	—
570	C₂×C₄×D₈	—	43	1	no	—
571	#2931	—	43	1	no	—
572	#2913	—	43	1	no	—
573	#2913	—	43	1	no	—
574	C₂×C₄₃	—	4	1	no	—
575	C₂×C₄₃	—	4	1	no	—
576	C₂×C₄₃	—	8	2	no	—
577	C₂×C₄₃	C₂×#547	1	1	yes	characteristic
578	C₂×C₄₃	C₂×#576	1	1	yes	characteristic
579	C₂×C₄₃	#3584	1	1	yes	characteristic
580	D₄₃	—	2	2	no	—
581	D₄₃	—	4	1	no	—
582	D₄₃	—	4	1	no	—
583	D₄₃	—	8	2	no	—
584	C₂²×D₈	—	43	1	no	—
585	C₂×#131	—	43	1	no	—
586	C₂×#131	—	43	1	no	—
587	#559	—	86	2	no	—
588	#559	—	86	2	no	—
589	#556	—	86	2	no	—
590	#555	—	43	2	no	—
591	#555	—	43	2	no	—
592	#553	—	43	2	no	—
593	#553	—	43	2	no	—
594	#553	—	43	2	no	—
595	#553	C₂×D₄₃	1	2	yes	complemented
596	#550	—	86	2	no	—
597	#547	—	43	2	no	—
598	#547	—	43	2	no	—
599	#538	—	86	2	no	—
600	#538	—	86	2	no	—
601	#535	—	43	2	no	—
602	#535	—	43	2	no	—
603	#533	—	43	2	no	—
604	#532	—	43	1	no	—
605	#525	—	86	2	no	—
606	#525	—	86	2	no	—
607	#520	—	43	2	no	—
608	#520	—	43	2	no	—
609	C₂×C₄×D₄	—	43	2	no	—
610	#500	—	43	1	no	—
611	#500	—	43	1	no	—
612	#499	—	43	2	no	—
613	#499	—	43	1	no	—
614	#499	C₂×D₄₃	1	1	yes	characteristic, complemented
615	#498	—	43	2	no	—
616	#482	—	43	2	no	—
617	#482	—	43	2	no	—
618	#482	—	43	2	no	—
619	#482	—	43	2	no	—
620	#482	—	43	2	no	—
621	#482	—	43	2	no	—
622	#482	—	43	2	no	—
623	#482	C₂×D₄₃	1	2	yes	complemented
624	#481	—	43	2	no	—
625	#481	—	43	2	no	—
626	#481	—	43	2	no	—
627	#481	C₂×D₄₃	1	2	yes	complemented
628	#480	—	43	2	no	—
629	#480	—	43	2	no	—
630	#480	—	43	2	no	—
631	#480	—	43	2	no	—
632	#478	—	43	2	no	—
633	#478	—	43	2	no	—
634	#478	—	43	2	no	—
635	#478	C₂×D₄₃	1	2	yes	complemented
636	#476	—	43	2	no	—
637	#476	—	43	2	no	—
638	#474	—	43	2	no	—
639	#474	—	43	2	no	—
640	#469	—	43	2	no	—
641	#469	—	43	2	no	—
642	#469	—	43	2	no	—
643	#469	—	43	2	no	—
644	#466	—	43	1	no	—
645	#466	—	43	1	no	—
646	#466	—	43	1	no	—
647	#466	—	43	1	no	—
648	#466	—	43	1	no	—
649	#466	—	43	1	no	—
650	#466	C₂×D₄₃	1	1	yes	characteristic
651	#466	C₂×D₄₃	1	1	yes	characteristic
652	C₄×D₈	—	43	1	no	—
653	C₄×D₈	—	43	2	no	—
654	C₄×D₈	—	43	1	no	—
655	C₄×D₈	—	43	2	no	—
656	C₄×D₈	—	43	1	no	—
657	C₄×D₈	C₂×D₄₃	1	1	yes	characteristic
658	#436	—	43	1	no	—
659	#436	—	43	1	no	—
660	#436	—	43	1	no	—
661	#436	—	43	1	no	—
662	C₈×D₄	—	43	1	no	—
663	C₈×D₄	—	43	1	no	—
664	C₈×D₄	—	43	1	no	—
665	C₈×D₄	C₂×D₄₃	1	1	yes	characteristic, complemented
666	#428	—	43	2	no	—
667	#428	—	43	2	no	—
668	#428	—	43	2	no	—
669	#428	—	43	2	no	—
670	#428	—	43	2	no	—
671	#428	—	43	2	no	—
672	#427	—	43	1	no	—
673	#427	—	43	1	no	—
674	#427	—	43	1	no	—
675	#427	—	43	1	no	—
676	#427	—	43	1	no	—
677	#427	—	43	2	no	—
678	#427	C₂×D₄₃	1	1	yes	characteristic, complemented
679	C₂×#107	—	43	1	no	—
680	C₂×#107	—	43	1	no	—
681	C₂×#107	—	43	1	no	—
682	C₂×#107	—	43	1	no	—
683	C₂×#107	C₂×D₄₃	1	1	yes	characteristic, complemented
684	#423	—	43	1	no	—
685	#418	—	43	2	no	—
686	#418	—	43	2	no	—
687	C₂×#102	—	43	2	no	—
688	#408	—	43	1	no	—
689	#408	—	43	1	no	—
690	C₂×C₄×C₈	—	43	1	no	—
691	C₄₃	#61284	1	1	yes	characteristic, complemented, Sylow
692	C₂×#41	—	43	1	no	—
693	C₂×#41	—	43	1	no	—
694	C₂×#41	—	86	2	no	—
695	C₂×#41	—	86	2	no	—
696	C₂²×D₄	—	43	2	no	—
697	C₂³×C₄	—	86	2	no	—
698	C₂×D₈	—	43	2	no	—
699	C₂×D₈	—	43	1	no	—
700	C₂×D₈	—	86	4	no	—
701	C₂×D₈	C₂²×D₄₃	1	1	yes	characteristic
702	#131	—	86	4	no	—
703	#131	—	86	4	no	—
704	C₂×M₁₆	—	43	1	no	—
705	C₂×M₁₆	—	43	1	no	—
706	C₂×M₁₆	—	43	1	no	—
707	C₂×M₁₆	—	43	1	no	—
708	C₂×M₁₆	—	43	1	no	—
709	C₂×M₁₆	—	43	1	no	—
710	C₂²×C₈	—	43	1	no	—
711	C₂²×C₈	—	43	1	no	—
712	C₂²×C₈	—	43	1	no	—
713	C₂²×C₈	—	43	1	no	—
714	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
715	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
716	C₄⋊Q₈	—	43	1	no	—
717	C₄⋊Q₈	—	43	2	no	—
718	C₄⋊Q₈	—	43	2	no	—
719	#127	—	43	1	no	—
720	#127	—	86	2	no	—
721	#127	—	86	2	no	—
722	#126	—	2	2	no	—
723	#126	—	86	2	no	—
724	#126	—	86	2	no	—
725	#126	—	86	2	no	—
726	#125	—	43	2	no	—
727	#125	C₂²×D₄₃	1	2	yes	—
728	#124	—	43	1	no	—
729	#124	—	43	1	no	—
730	#124	—	86	2	no	—
731	#124	—	86	2	no	—
732	#124	—	86	2	no	—
733	#124	—	86	2	no	—
734	#124	—	86	2	no	—
735	#124	—	86	2	no	—
736	#123	—	2	2	no	—
737	#123	—	86	2	no	—
738	#123	—	86	2	no	—
739	#123	—	86	2	no	—
740	#123	—	86	2	no	—
741	#123	—	86	2	no	—
742	#123	—	86	2	no	—
743	#123	—	86	2	no	—
744	C₂²⋊Q₈	—	86	2	no	—
745	C₂²⋊Q₈	—	86	2	no	—
746	C₂²⋊Q₈	—	86	2	no	—
747	C₂²⋊Q₈	—	86	2	no	—
748	#121	—	2	2	no	—
749	#121	—	43	1	no	—
750	#121	—	43	1	no	—
751	#121	—	43	1	no	—
752	#121	—	43	1	no	—
753	#121	—	43	2	no	—
754	#121	—	43	2	no	—
755	#121	—	43	2	no	—
756	#121	—	43	2	no	—
757	#121	—	43	2	no	—
758	#121	—	43	2	no	—
759	#121	—	86	2	no	—
760	#121	—	86	2	no	—
761	#121	—	86	2	no	—
762	#121	—	86	2	no	—
763	#121	—	86	2	no	—
764	#121	C₂²×D₄₃	1	2	yes	—
765	#121	C₂²×D₄₃	1	2	yes	—
766	#120	—	86	2	no	—
767	#120	—	86	2	no	—
768	#120	—	86	2	no	—
769	#120	—	86	2	no	—
770	C₄×Q₈	—	86	2	no	—
771	C₄×Q₈	—	86	2	no	—
772	C₄×Q₈	—	86	2	no	—
773	C₄×Q₈	—	86	2	no	—
774	C₄×D₄	—	2	2	no	—
775	C₄×D₄	—	43	1	no	—
776	C₄×D₄	—	43	1	no	—
777	C₄×D₄	—	43	2	no	—
778	C₄×D₄	—	43	2	no	—
779	C₄×D₄	—	43	1	no	—
780	C₄×D₄	—	43	2	no	—
781	C₄×D₄	—	86	2	no	—
782	C₄×D₄	—	86	2	no	—
783	C₄×D₄	—	86	2	no	—
784	C₄×D₄	—	86	2	no	—
785	C₄×D₄	—	86	2	no	—
786	C₄×D₄	—	86	2	no	—
787	C₄×D₄	—	86	2	no	—
788	C₄×D₄	—	86	2	no	—
789	C₄×D₄	—	86	2	no	—
790	C₄×D₄	—	86	2	no	—
791	C₄×D₄	—	86	2	no	—
792	C₄×D₄	C₂²×D₄₃	1	2	yes	—
793	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
794	#117	—	43	2	no	—
795	#117	—	43	2	no	—
796	#117	—	43	2	no	—
797	#117	—	43	2	no	—
798	#117	—	43	2	no	—
799	#117	—	86	2	no	—
800	#117	—	86	2	no	—
801	#117	C₂²×D₄₃	1	2	yes	—
802	C₂×C₄⋊C₄	—	43	2	no	—
803	C₂×C₄⋊C₄	—	43	2	no	—
804	C₂×C₄⋊C₄	—	43	2	no	—
805	C₂×C₄⋊C₄	—	43	2	no	—
806	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
807	C₂×C₂²⋊C₄	—	86	2	no	—
808	C₂×C₄²	—	43	1	no	—
809	#107	—	43	1	no	—
810	#107	—	43	1	no	—
811	#107	—	43	2	no	—
812	#107	—	43	1	no	—
813	#107	—	43	2	no	—
814	#107	—	43	2	no	—
815	#107	—	43	2	no	—
816	#107	—	43	2	no	—
817	#107	—	43	2	no	—
818	#107	C₂²×D₄₃	1	1	yes	characteristic
819	#107	C₂²×D₄₃	1	1	yes	characteristic
820	#107	C₂²×D₄₃	1	2	yes	—
821	#107	C₂²×D₄₃	1	1	yes	characteristic
822	#106	—	43	2	no	—
823	#106	—	43	2	no	—
824	#106	—	43	2	no	—
825	#106	—	43	2	no	—
826	#106	—	43	2	no	—
827	#106	—	43	2	no	—
828	#106	C₂²×D₄₃	1	2	yes	—
829	#106	C₂²×D₄₃	1	2	yes	—
830	C₄⋊C₈	—	43	1	no	—
831	C₄⋊C₈	—	43	1	no	—
832	C₄⋊C₈	—	43	1	no	—
833	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
834	#102	—	43	2	no	—
835	#102	—	43	2	no	—
836	#102	—	43	2	no	—
837	#102	—	43	2	no	—
838	#102	—	43	2	no	—
839	#102	—	43	2	no	—
840	#102	—	43	2	no	—
841	#102	—	43	2	no	—
842	#102	—	43	2	no	—
843	#102	C₂²×D₄₃	1	2	yes	—
844	#102	C₂²×D₄₃	1	2	yes	—
845	#102	C₂²×D₄₃	1	2	yes	—
846	C₂²⋊C₈	—	43	1	no	—
847	C₂²⋊C₈	—	43	1	no	—
848	C₂²⋊C₈	—	43	1	no	—
849	C₂²⋊C₈	—	43	1	no	—
850	C₂²⋊C₈	—	43	1	no	—
851	C₂²⋊C₈	—	43	1	no	—
852	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
853	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
854	C₄×C₈	—	43	1	no	—
855	C₄×C₈	—	43	1	no	—
856	C₄×C₈	—	43	1	no	—
857	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
858	C₂⁴	—	86	2	no	—
859	#41	—	86	2	no	—
860	#41	—	86	2	no	—
861	#41	—	86	2	no	—
862	#41	—	86	2	no	—
863	#41	—	344	4	no	—
864	#41	—	344	4	no	—
865	C₂×Q₈	—	43	1	no	—
866	C₂×Q₈	—	43	1	no	—
867	C₂×Q₈	—	86	2	no	—
868	C₂×Q₈	—	86	2	no	—
869	C₂×D₄	—	2	2	no	—
870	C₂×D₄	—	2	2	no	—
871	C₂×D₄	—	43	1	no	—
872	C₂×D₄	—	43	1	no	—
873	C₂×D₄	—	43	1	no	—
874	C₂×D₄	—	43	1	no	—
875	C₂×D₄	—	43	1	no	—
876	C₂×D₄	—	43	1	no	—
877	C₂×D₄	—	43	1	no	—
878	C₂×D₄	—	43	1	no	—
879	C₂×D₄	—	43	1	no	—
880	C₂×D₄	—	43	2	no	—
881	C₂×D₄	—	86	2	no	—
882	C₂×D₄	—	86	2	no	—
883	C₂×D₄	—	86	4	no	—
884	C₂×D₄	—	86	4	no	—
885	C₂×D₄	—	86	2	no	—
886	C₂×D₄	—	86	2	no	—
887	C₂×D₄	—	86	2	no	—
888	C₂×D₄	—	86	2	no	—
889	C₂×D₄	—	86	2	no	—
890	C₂×D₄	D₄×D₄₃	1	1	yes	characteristic
891	C₂×D₄	C₂³×D₄₃	1	2	yes	—
892	C₂²×C₄	—	2	2	no	—
893	C₂²×C₄	—	2	2	no	—
894	C₂²×C₄	—	43	1	no	—
895	C₂²×C₄	—	43	1	no	—
896	C₂²×C₄	—	43	1	no	—
897	C₂²×C₄	—	43	1	no	—
898	C₂²×C₄	—	43	1	no	—
899	C₂²×C₄	—	86	2	no	—
900	C₂²×C₄	—	86	2	no	—
901	C₂²×C₄	—	86	2	no	—
902	C₂²×C₄	—	86	2	no	—
903	C₂²×C₄	—	86	2	no	—
904	C₂²×C₄	—	86	2	no	—
905	C₂²×C₄	—	86	2	no	—
906	C₂²×C₄	—	344	4	no	—
907	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
908	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
909	D₈	—	2	2	no	—
910	D₈	—	86	4	no	—
911	D₈	—	86	2	no	—
912	M₁₆	—	86	2	no	—
913	M₁₆	—	86	2	no	—
914	M₁₆	—	86	2	no	—
915	M₁₆	—	86	2	no	—
916	M₁₆	—	86	2	no	—
917	M₁₆	—	86	2	no	—
918	C₂×C₈	—	2	2	no	—
919	C₂×C₈	—	2	2	no	—
920	C₂×C₈	—	43	1	no	—
921	C₂×C₈	—	43	4	no	—
922	C₂×C₈	—	43	1	no	—
923	C₂×C₈	—	43	1	no	—
924	C₂×C₈	—	43	1	no	—
925	C₂×C₈	—	86	2	no	—
926	C₂×C₈	—	86	2	no	—
927	C₂×C₈	—	86	2	no	—
928	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
929	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
930	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
931	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
932	C₄⋊C₄	—	2	2	no	—
933	C₄⋊C₄	—	2	2	no	—
934	C₄⋊C₄	—	2	2	no	—
935	C₄⋊C₄	—	43	1	no	—
936	C₄⋊C₄	—	43	1	no	—
937	C₄⋊C₄	—	43	1	no	—
938	C₄⋊C₄	—	43	2	no	—
939	C₄⋊C₄	—	43	2	no	—
940	C₄⋊C₄	—	43	2	no	—
941	C₄⋊C₄	—	86	2	no	—
942	C₄⋊C₄	—	86	2	no	—
943	C₄⋊C₄	—	86	2	no	—
944	C₄⋊C₄	—	86	2	no	—
945	C₄⋊C₄	—	86	2	no	—
946	C₄⋊C₄	—	86	2	no	—
947	C₄⋊C₄	—	86	2	no	—
948	C₄⋊C₄	—	86	2	no	—
949	C₄⋊C₄	D₄×D₄₃	1	1	yes	characteristic
950	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
951	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
952	C₄⋊C₄	C₂³×D₄₃	1	2	yes	—
953	C₂²⋊C₄	—	2	2	no	—
954	C₂²⋊C₄	—	2	2	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	43	1	no	—
958	C₂²⋊C₄	—	43	1	no	—
959	C₂²⋊C₄	—	43	1	no	—
960	C₂²⋊C₄	—	43	1	no	—
961	C₂²⋊C₄	—	43	1	no	—
962	C₂²⋊C₄	—	43	1	no	—
963	C₂²⋊C₄	—	86	2	no	—
964	C₂²⋊C₄	—	86	2	no	—
965	C₂²⋊C₄	—	86	2	no	—
966	C₂²⋊C₄	—	86	2	no	—
967	C₂²⋊C₄	—	86	2	no	—
968	C₂²⋊C₄	—	86	2	no	—
969	C₂²⋊C₄	—	86	2	no	—
970	C₂²⋊C₄	—	86	2	no	—
971	C₂²⋊C₄	—	86	2	no	—
972	C₂²⋊C₄	—	86	2	no	—
973	C₂²⋊C₄	—	86	2	no	—
974	C₂²⋊C₄	—	86	2	no	—
975	C₂²⋊C₄	—	86	2	no	—
976	C₂²⋊C₄	—	86	2	no	—
977	C₂²⋊C₄	D₄×D₄₃	1	1	yes	characteristic
978	C₂²⋊C₄	D₄×D₄₃	1	1	yes	characteristic
979	C₄²	—	2	2	no	—
980	C₄²	—	43	1	no	—
981	C₄²	—	43	1	no	—
982	C₄²	—	43	1	no	—
983	C₄²	—	86	2	no	—
984	C₄²	—	86	2	no	—
985	C₄²	—	86	2	no	—
986	C₄²	—	86	2	no	—
987	C₄²	—	86	2	no	—
988	C₄²	C₂³×D₄₃	1	1	yes	characteristic
989	C₂³	—	2	2	no	—
990	C₂³	—	43	1	no	—
991	C₂³	—	43	1	no	—
992	C₂³	—	43	1	no	—
993	C₂³	—	86	2	no	—
994	C₂³	—	344	2	no	—
995	C₂³	—	344	2	no	—
996	C₂³	—	172	4	no	—
997	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
998	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
999	Q₈	—	86	2	no	—
1000	Q₈	—	86	2	no	—
1001	Q₈	—	344	2	no	—
1002	Q₈	—	172	4	no	—
1003	D₄	—	2	2	no	—
1004	D₄	—	2	2	no	—
1005	D₄	—	4	1	no	—
1006	D₄	—	8	2	no	—
1007	D₄	—	8	2	no	—
1008	D₄	—	86	2	no	—
1009	D₄	—	86	2	no	—
1010	D₄	—	86	2	no	—
1011	D₄	—	86	2	no	—
1012	D₄	—	86	2	no	—
1013	D₄	—	86	2	no	—
1014	D₄	—	86	2	no	—
1015	D₄	—	86	2	no	—
1016	D₄	—	86	2	no	—
1017	D₄	—	86	2	no	—
1018	D₄	—	344	2	no	—
1019	D₄	—	344	2	no	—
1020	D₄	—	344	2	no	—
1021	D₄	—	344	2	no	—
1022	D₄	—	344	2	no	—
1023	D₄	—	344	2	no	—
1024	D₄	—	172	1	no	—
1025	D₄	—	172	4	no	—
1026	C₂×C₄	—	2	1	no	—
1027	C₂×C₄	—	2	1	no	—
1028	C₂×C₄	—	2	1	no	—
1029	C₂×C₄	—	2	1	no	—
1030	C₂×C₄	—	2	2	no	—
1031	C₂×C₄	—	2	2	no	—
1032	C₂×C₄	—	2	2	no	—
1033	C₂×C₄	—	8	2	no	—
1034	C₂×C₄	—	8	2	no	—
1035	C₂×C₄	—	43	1	no	—
1036	C₂×C₄	—	43	1	no	—
1037	C₂×C₄	—	43	2	no	—
1038	C₂×C₄	—	43	2	no	—
1039	C₂×C₄	—	43	1	no	—
1040	C₂×C₄	—	43	1	no	—
1041	C₂×C₄	—	43	1	no	—
1042	C₂×C₄	—	86	2	no	—
1043	C₂×C₄	—	86	1	no	—
1044	C₂×C₄	—	86	1	no	—
1045	C₂×C₄	—	86	1	no	—
1046	C₂×C₄	—	86	1	no	—
1047	C₂×C₄	—	86	2	no	—
1048	C₂×C₄	—	86	2	no	—
1049	C₂×C₄	—	86	2	no	—
1050	C₂×C₄	—	344	2	no	—
1051	C₂×C₄	—	344	2	no	—
1052	C₂×C₄	—	344	2	no	—
1053	C₂×C₄	—	344	2	no	—
1054	C₂×C₄	—	344	2	no	—
1055	C₂×C₄	—	172	1	no	—
1056	C₂×C₄	—	172	4	no	—
1057	C₂×C₄	—	172	4	no	—
1058	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1059	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1060	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1061	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1062	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1063	C₈	—	2	1	no	—
1064	C₈	—	2	1	no	—
1065	C₈	—	2	1	no	—
1066	C₈	—	43	2	no	—
1067	C₈	—	86	1	no	—
1068	C₈	—	86	1	no	—
1069	C₈	—	86	1	no	—
1070	C₈	#41×D₄₃	1	2	yes	—
1071	C₂²	—	2	1	no	—
1072	C₂²	—	2	1	no	—
1073	C₂²	—	2	1	no	—
1074	C₂²	—	2	1	no	—
1075	C₂²	—	2	1	no	—
1076	C₂²	—	2	1	no	—
1077	C₂²	—	4	2	no	—
1078	C₂²	—	4	2	no	—
1079	C₂²	—	4	2	no	—
1080	C₂²	—	43	2	no	—
1081	C₂²	—	86	1	no	—
1082	C₂²	—	86	1	no	—
1083	C₂²	—	86	1	no	—
1084	C₂²	—	86	1	no	—
1085	C₂²	—	86	1	no	—
1086	C₂²	—	86	1	no	—
1087	C₂²	—	86	1	no	—
1088	C₂²	—	86	1	no	—
1089	C₂²	—	344	8	no	—
1090	C₂²	—	172	2	no	—
1091	C₂²	—	172	2	no	—
1092	C₂²	—	172	2	no	—
1093	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1094	C₄	—	2	1	no	—
1095	C₄	—	2	1	no	—
1096	C₄	—	2	1	no	—
1097	C₄	—	2	1	no	—
1098	C₄	—	4	2	no	—
1099	C₄	—	4	2	no	—
1100	C₄	—	4	2	no	—
1101	C₄	—	43	2	no	—
1102	C₄	—	43	2	no	—
1103	C₄	—	86	1	no	—
1104	C₄	—	86	1	no	—
1105	C₄	—	86	1	no	—
1106	C₄	—	172	2	no	—
1107	C₄	—	172	2	no	—
1108	C₄	—	172	2	no	—
1109	C₄	C₂×#41×D₄₃	1	1	yes	characteristic
1110	C₄	2₋¹⁺⁴×D₄₃	1	1	yes	characteristic
1111	C₂	—	4	1	no	—
1112	C₂	—	4	1	no	—
1113	C₂	—	8	2	no	—
1114	C₂	—	86	2	no	—
1115	C₂	—	344	2	no	—
1116	C₂	—	172	1	no	—
1117	C₂	—	172	1	no	—
1118	C₂	#547×D₄₃	1	1	yes	characteristic
1119	C₂	#576×D₄₃	1	1	yes	characteristic
1120	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×#3339	C₂
socle	C₂²×C₄₃	C₂³×D₄
hypercenter	#3339	D₄₃
hypocenter	C₄₃	#61284
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #3339

Complements

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

N	H ≅ G/N	type
1. #19148441	C₂	semidirect
2. #19147198	C₂	semidirect
3. #19147195	C₂	semidirect
4. #19147188	C₂	semidirect
5. #19147183	C₂	semidirect
6. #19147015	C₂	semidirect
7. #19147014	C₂	semidirect
8. #19146999	C₂	semidirect
9. #19146998	C₂	semidirect
10. #19146996	C₂	semidirect
11. #19146940	C₂	semidirect
12. #19146939	C₂	semidirect
13. #19145108	C₂	semidirect
14. #19144552	C₂	semidirect
15. #19144548	C₂	semidirect
16. #19144390	C₂	semidirect
17. #19144238	C₂	semidirect
18. #19144238	C₂	semidirect
19. C₄×D₈×D₄₃	C₂	semidirect
20. #19143302	C₂	semidirect
21. #19143192	C₂	semidirect
22. #19143191	C₂	semidirect
23. C₄₃×#3339	C₂	semidirect
30. #14583613	C₂²	semidirect
31. #14583612	C₂²	semidirect
32. #14583602	C₂²	semidirect
33. #14583599	C₂²	semidirect
34. #14583595	C₂²	semidirect
36. #14583550	C₂²	semidirect
37. #14583549	C₂²	semidirect
49. #14583303	C₂²	semidirect
50. #14583303	C₂²	semidirect
51. #14583301	C₂²	semidirect
52. #14583298	C₂²	semidirect
53. #14583296	C₂²	semidirect
54. #14583225	C₂²	semidirect
55. #14583225	C₂²	semidirect
56. #14583224	C₂²	semidirect
57. #14583223	C₂²	semidirect
58. #14583222	C₂²	semidirect
59. #14583222	C₂²	semidirect
60. #14583220	C₂²	semidirect
61. #14583219	C₂²	semidirect
62. #14583218	C₂²	semidirect
63. #14583216	C₂²	semidirect
64. #14583214	C₂²	semidirect
65. #14583212	C₂²	semidirect
66. #14583211	C₂²	semidirect
67. #14583210	C₂²	semidirect
68. #14583200	C₂²	semidirect
69. #14583199	C₂²	semidirect
70. #14583196	C₂²	semidirect
71. #14583188	C₂²	semidirect
72. #14583187	C₂²	semidirect
73. #14583178	C₂²	semidirect
74. #14583177	C₂²	semidirect
90. #14582977	C₂²	semidirect
91. #14582976	C₂²	semidirect
92. #14582974	C₂²	semidirect
93. #14582974	C₂²	semidirect
94. C₈×D₁₇₂	C₂²	semidirect
95. C₈×C₂²⋊D₄₃	C₂²	semidirect
96. C₈×C₂²⋊D₄₃	C₂²	semidirect
97. #14582942	C₂²	semidirect
99. #14582940	C₂²	semidirect
100. #14582939	C₂²	semidirect
102. #14582938	C₂²	semidirect
103. #14582937	C₂²	semidirect
106. #14582936	C₂²	semidirect
107. #14582936	C₂²	semidirect
109. C₂×#13063259	C₂²	semidirect
111. #107×D₄₃	C₂²	semidirect
112. #107×D₄₃	C₂²	semidirect
120. C₄₃×#553	C₂²	semidirect
121. C₄₃×#499	C₂²	semidirect
122. C₄₃×#482	C₂²	semidirect
123. C₄₃×#481	C₂²	semidirect
124. C₄₃×#478	C₂²	semidirect
128. C₈×D₄×C₄₃	C₂²	semidirect
129. C₄₃×#427	C₂²	semidirect
130. C₂×#107×C₄₃	C₂²	semidirect
427. C₈×D₄₃	#41	semidirect
561. #3339	D₄₃	semidirect
595. #553	C₂×D₄₃	semidirect
614. #499	C₂×D₄₃	semidirect
623. #482	C₂×D₄₃	semidirect
627. #481	C₂×D₄₃	semidirect
635. #478	C₂×D₄₃	semidirect
665. C₈×D₄	C₂×D₄₃	semidirect
678. #427	C₂×D₄₃	semidirect
683. C₂×#107	C₂×D₄₃	semidirect
691. C₄₃	#61284	semidirect

Maximal subgroups

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

subgroup	index
#19148441	2
#19147198	2
#19147195	2
#19147188	2
#19147183	2
#19147015	2
#19147014	2
#19146999	2
#19146998	2
#19146996	2
#19146940	2
#19146939	2
#19145108	2
#19144552	2
#19144548	2
#19144390	2
#19144238	2
C₄×D₈×D₄₃	2
#19143302	2
#19143192	2
#19143191	2
C₄₃×#3339	2
#61284	43