Subgroups — #25993236

Order 11008.

1696 conjugacy classes of subgroups.

The subgroup lattice has 1088 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19148610	C₂	1	1	yes	maximal, characteristic
2	Q₈×#10621898	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₁₆×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
4	SD₁₆×Dic₈₆	C₂	1	1	yes	maximal, characteristic, complemented
5	#19147271	C₂	1	1	yes	maximal, characteristic, complemented
6	#19147235	C₂	1	1	yes	maximal, characteristic, complemented
7	#19147223	C₂	1	1	yes	maximal, characteristic, complemented
8	#19147214	C₂	1	2	yes	maximal, complemented
9	#19147212	C₂	1	1	yes	maximal, characteristic, complemented
10	#19147203	C₂	1	2	yes	maximal, complemented
11	#19146891	C₂	1	1	yes	maximal, characteristic, complemented
12	#19146882	C₂	1	2	yes	maximal, complemented
13	#19146880	C₂	1	1	yes	maximal, characteristic, complemented
14	#19146871	C₂	1	2	yes	maximal, complemented
15	#19145968	C₂	1	1	yes	maximal, characteristic, complemented
16	#19145965	C₂	1	2	yes	maximal, complemented
17	#19145756	C₂	1	1	yes	maximal, characteristic, complemented
18	#19145753	C₂	1	2	yes	maximal, complemented
19	#19144674	C₂	1	2	yes	maximal, complemented
20	#19144400	C₂	1	1	yes	maximal, characteristic, complemented
21	#19144398	C₂	1	2	yes	maximal, complemented
22	#19143724	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₃×#3108	C₂	1	1	yes	maximal, characteristic, complemented
24	Q₈×Dic₈₆	C₂²	1	1	yes	characteristic
25	Q₈×Dic₈₆	C₂²	1	1	yes	characteristic
26	#14583627	—	2	1	no	—
27	#14583627	C₂²	1	1	yes	characteristic
28	#14583622	C₂²	1	1	yes	characteristic
29	#14583620	C₂²	1	2	yes	—
30	#14583619	—	2	1	no	—
31	#14583616	—	2	2	no	—
32	#14583614	C₂²	1	1	yes	characteristic
33	#14583613	C₂²	1	2	yes	—
34	#14583609	—	2	1	no	—
35	#14583609	C₂²	1	1	yes	characteristic
36	#14583604	—	2	2	no	—
37	#14583604	C₂²	1	2	yes	—
38	Q₈×D₁₇₂	C₂²	1	1	yes	characteristic
39	D₄×Dic₈₆	C₂²	1	1	yes	characteristic
40	Q₈×C₂²⋊D₄₃	C₂²	1	2	yes	—
41	#14583558	—	2	1	no	—
42	#14583520	—	2	1	no	—
43	#14583517	—	2	2	no	—
44	#14583456	—	2	1	no	—
45	#14583456	C₂²	1	1	yes	characteristic
46	#14583456	C₂²	1	1	yes	characteristic
47	#14583455	C₂²	1	2	yes	—
48	#14583453	—	2	2	no	—
49	#14583453	C₂²	1	2	yes	—
50	#14583428	C₂²	1	2	yes	—
51	#14583376	—	2	1	no	—
52	C₄×#10621898	—	2	1	no	—
53	C₄×#10621898	C₂²	1	1	yes	characteristic
54	C₄×Q₈×D₄₃	C₂²	1	2	yes	—
55	#14583304	C₂²	1	1	yes	characteristic
56	#14583303	C₂²	1	2	yes	—
57	#14583297	C₂²	1	1	yes	characteristic
58	#14583296	C₂²	1	2	yes	—
59	#14583250	C₂²	1	1	yes	characteristic
60	#14583250	C₂²	1	1	yes	characteristic
61	#14583248	C₂²	1	2	yes	—
62	#14583248	C₂²	1	2	yes	—
63	#14583243	C₂²	1	2	yes	—
64	#14583242	C₂²	1	2	yes	—
65	#14583241	C₂²	1	2	yes	—
66	#14583241	C₂²	1	2	yes	—
67	#14583239	C₂²	1	2	yes	—
68	#14583238	C₂²	1	2	yes	—
69	#14583228	C₂²	1	2	yes	—
70	#14583211	C₂²	1	2	yes	—
71	#14583207	C₂²	1	2	yes	—
72	#14583207	C₂²	1	2	yes	—
73	#14583206	C₂²	1	2	yes	—
74	#14583206	C₂²	1	2	yes	—
75	#14583203	C₂²	1	2	yes	—
76	#14583194	C₂²	1	1	yes	characteristic
77	#14583194	C₂²	1	1	yes	characteristic
78	#14583194	C₂²	1	1	yes	characteristic
79	#14583193	C₂²	1	2	yes	—
80	#14583192	C₂²	1	2	yes	—
81	#14583192	C₂²	1	2	yes	—
82	#14583189	C₂²	1	1	yes	characteristic
83	#14583187	C₂²	1	2	yes	—
84	#14583184	C₂²	1	1	yes	characteristic
85	#14583184	C₂²	1	1	yes	characteristic
86	#14583183	C₂²	1	2	yes	—
87	#14583182	C₂²	1	2	yes	—
88	#14583156	C₂²	1	2	yes	—
89	#14583155	C₂²	1	2	yes	—
90	#14583154	C₂²	1	2	yes	—
91	#14583144	C₂²	1	2	yes	—
92	#14583143	C₂²	1	2	yes	—
93	#14583142	C₂²	1	2	yes	—
94	#14583118	C₂²	1	2	yes	—
95	#14583109	C₂²	1	1	yes	characteristic
96	#14583107	C₂²	1	2	yes	—
97	#14583104	C₂²	1	1	yes	characteristic
98	#14583102	C₂²	1	2	yes	—
99	#14583053	C₂²	1	2	yes	—
100	#14583036	C₂²	1	2	yes	—
101	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
102	C₈×Dic₈₆	C₂²	1	1	yes	characteristic
103	Q₁₆×Dic₄₃	C₂²	1	2	yes	—
104	#14582991	C₂²	1	2	yes	—
105	#14582990	C₂²	1	2	yes	—
106	SD₁₆×Dic₄₃	C₂²	1	2	yes	—
107	#14582978	C₂²	1	1	yes	characteristic
108	#14582978	C₂²	1	1	yes	characteristic
109	#14582974	C₂²	1	2	yes	—
110	#14582974	C₂²	1	2	yes	—
111	#14582951	C₂²	1	2	yes	—
112	#14582940	C₂²	1	2	yes	—
113	#14582939	C₂²	1	2	yes	—
114	#14582938	C₂²	1	2	yes	—
115	#14582923	C₂²	1	1	yes	characteristic
116	#14582921	C₂²	1	2	yes	—
117	#14582908	C₂²	1	2	yes	—
118	#14582906	C₂²	1	2	yes	—
119	#14582906	C₂²	1	2	yes	—
120	C₄₃×#529	C₂²	1	1	yes	characteristic
121	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
122	C₄₃×#483	C₂²	1	1	yes	characteristic
123	C₄₃×#480	C₂²	1	1	yes	characteristic
124	C₄₃×#479	C₂²	1	1	yes	characteristic
125	C₄₃×#479	C₂²	1	1	yes	characteristic
126	C₄₃×#464	C₂²	1	1	yes	characteristic
127	C₄₃×#464	C₂²	1	1	yes	characteristic
128	C₄₃×#451	C₂²	1	1	yes	characteristic
129	C₄₃×#448	C₂²	1	1	yes	characteristic
130	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
131	C₄×Q₁₆×C₄₃	C₂²	1	1	yes	characteristic
132	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
133	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
134	C₄₃×#431	C₂²	1	1	yes	characteristic
135	C₂×#10621898	D₄	1	1	yes	characteristic
136	C₂²×Dic₈₆	—	2	1	no	—
137	C₂×Q₈×D₄₃	C₂³	1	2	yes	—
138	C₂×#10621885	C₂³	1	2	yes	—
139	C₂×#10621883	C₂³	1	2	yes	—
140	C₂×#10621877	C₂³	1	2	yes	—
141	C₂×#10621872	C₂³	1	2	yes	—
142	C₂×#10621872	C₂³	1	2	yes	—
143	#13063325	—	2	1	no	—
144	#13063325	—	2	1	no	—
145	#13063325	—	2	1	no	—
146	#13063325	C₂³	1	1	yes	characteristic
147	#13063325	C₂³	1	1	yes	characteristic
148	#13063325	C₂³	1	1	yes	characteristic
149	#13063325	C₂³	1	1	yes	characteristic
150	#13063324	—	2	2	no	—
151	#13063324	—	2	2	no	—
152	#13063324	C₂³	1	2	yes	—
153	#13063324	C₂³	1	2	yes	—
154	#13063324	C₂³	1	2	yes	—
155	#13063323	—	2	2	no	—
156	#13063323	C₂³	1	2	yes	—
157	#13063320	—	2	2	no	—
158	#13063320	—	2	2	no	—
159	#13063318	—	2	2	no	—
160	#13063318	—	2	2	no	—
161	#13063317	—	2	1	no	—
162	#13063317	—	2	1	no	—
163	#13063317	—	2	1	no	—
164	#13063317	C₂³	1	2	yes	—
165	#13063315	—	2	2	no	—
166	#13063315	—	2	2	no	—
167	#13063315	—	2	2	no	—
168	#13063313	—	2	1	no	—
169	#13063312	—	2	2	no	—
170	#13063311	—	2	2	no	—
171	#13063311	—	2	2	no	—
172	#13063311	—	2	2	no	—
173	#13063307	—	2	2	no	—
174	#13063305	—	2	2	no	—
175	#13063305	C₂³	1	2	yes	—
176	#13063304	—	2	1	no	—
177	#13063304	—	2	1	no	—
178	#13063304	—	2	1	no	—
179	#13063304	—	2	2	no	—
180	#13063304	—	2	2	no	—
181	#13063304	—	2	1	no	—
182	#13063304	C₂³	1	2	yes	—
183	#13063303	—	2	2	no	—
184	#13063303	—	2	2	no	—
185	#13063303	—	2	2	no	—
186	#13063303	—	2	2	no	—
187	#13063303	—	2	2	no	—
188	#13063302	—	2	2	no	—
189	#13063301	—	2	2	no	—
190	#13063301	C₂³	1	2	yes	—
191	#13063301	C₂³	1	2	yes	—
192	#13063299	—	2	1	no	—
193	#13063297	—	2	2	no	—
194	#13063296	C₂³	1	2	yes	—
195	Q₈×Dic₄₃	C₂³	1	2	yes	—
196	Q₈×Dic₄₃	C₂³	1	2	yes	—
197	C₄×Dic₈₆	—	2	1	no	—
198	C₄×Dic₈₆	—	2	1	no	—
199	C₄×Dic₈₆	—	2	1	no	—
200	C₄×Dic₈₆	—	2	1	no	—
201	C₄×Dic₈₆	—	2	1	no	—
202	C₄×Dic₈₆	—	2	1	no	—
203	C₄×Dic₈₆	—	2	1	no	—
204	C₄×Dic₈₆	—	2	2	no	—
205	C₄×Dic₈₆	—	2	2	no	—
206	C₄×Dic₈₆	D₄	1	1	yes	characteristic
207	C₄×Dic₈₆	C₂³	1	2	yes	—
208	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
209	#13063290	—	2	2	no	—
210	#13063290	—	2	2	no	—
211	#13063290	—	2	2	no	—
212	#13063290	—	2	2	no	—
213	#13063290	C₂³	1	2	yes	—
214	C₄×D₁₇₂	—	2	1	no	—
215	C₄×D₁₇₂	—	2	1	no	—
216	C₄×D₁₇₂	D₄	1	1	yes	characteristic
217	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
218	D₄×Dic₄₃	C₂³	1	2	yes	—
219	C₄×C₂²⋊D₄₃	—	2	2	no	—
220	C₄×C₂²⋊D₄₃	—	2	2	no	—
221	C₄×C₂²⋊D₄₃	D₄	1	2	yes	—
222	C₄×C₂²⋊D₄₃	C₂³	1	2	yes	—
223	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
224	#13063284	—	2	1	no	—
225	#13063284	—	2	1	no	—
226	#13063284	D₄	1	1	yes	characteristic
227	#13063284	C₂³	1	2	yes	—
228	#13063283	C₂³	1	2	yes	—
229	#13063283	C₂³	1	2	yes	—
230	#13063282	—	2	2	no	—
231	#13063282	D₄	1	2	yes	—
232	#13063281	—	2	2	no	—
233	#13063281	—	2	2	no	—
234	C₄⋊C₄×D₄₃	—	2	2	no	—
235	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
236	C₄²×D₄₃	—	2	2	no	—
237	C₄²×D₄₃	C₂³	1	2	yes	—
238	#13063259	C₂³	1	2	yes	—
239	#13063259	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	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
249	C₄⋊(C₄₃⋊C₈)	C₂³	1	1	yes	characteristic
250	C₄⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
251	Dic₄₃⋊C₈	C₂³	1	2	yes	—
252	Dic₄₃⋊C₈	C₂³	1	2	yes	—
253	#13063250	C₂³	1	2	yes	—
254	#13063250	C₂³	1	2	yes	—
255	#13063250	C₂³	1	2	yes	—
256	#13063250	C₂³	1	2	yes	—
257	#13063249	C₂³	1	2	yes	—
258	#13063249	C₂³	1	2	yes	—
259	#13063249	C₂³	1	2	yes	—
260	#13063249	C₂³	1	2	yes	—
261	#13063249	C₂³	1	2	yes	—
262	#13063248	C₂³	1	2	yes	—
263	#13063248	C₂³	1	2	yes	—
264	#13063246	C₂³	1	2	yes	—
265	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
266	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
267	C₈×Dic₄₃	C₂³	1	2	yes	—
268	C₈×Dic₄₃	C₂³	1	2	yes	—
269	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
270	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
271	C₂×Q₁₆×C₄₃	C₂³	1	1	yes	characteristic
272	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
273	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
274	#126×C₄₃	—	2	1	no	—
275	#125×C₄₃	C₂³	1	1	yes	characteristic
276	#124×C₄₃	C₂³	1	1	yes	characteristic
277	#123×C₄₃	—	2	1	no	—
278	C₂²⋊Q₈×C₄₃	C₂³	1	1	yes	characteristic
279	#121×C₄₃	C₂³	1	1	yes	characteristic
280	C₄×Q₈×C₄₃	—	2	1	no	—
281	C₄×Q₈×C₄₃	—	2	1	no	—
282	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
283	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
284	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
285	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
286	C₄×Q₈×C₄₃	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₄₃	—	2	1	no	—
288	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
289	#117×C₄₃	—	2	1	no	—
290	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
291	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
292	C₂×C₄²×C₄₃	—	2	1	no	—
293	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
294	#107×C₄₃	C₂³	1	1	yes	characteristic
295	#107×C₄₃	C₂³	1	1	yes	characteristic
296	#106×C₄₃	C₂³	1	1	yes	characteristic
297	#106×C₄₃	C₂³	1	1	yes	characteristic
298	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
299	C₄⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
300	#103×C₄₃	C₂³	1	1	yes	characteristic
301	#103×C₄₃	C₂³	1	1	yes	characteristic
302	#103×C₄₃	C₂³	1	1	yes	characteristic
303	#103×C₄₃	C₂³	1	1	yes	characteristic
304	#103×C₄₃	C₂³	1	1	yes	characteristic
305	#103×C₄₃	C₂³	1	1	yes	characteristic
306	#102×C₄₃	C₂³	1	1	yes	characteristic
307	#102×C₄₃	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₄₃	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
312	C₂×Q₈×C₄₃	—	2	1	no	—
313	C₂×Q₈×C₄₃	—	2	2	no	—
314	C₂×Q₈×C₄₃	—	4	1	no	—
315	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
316	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
317	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
318	C₂×D₄×C₄₃	—	2	1	no	—
319	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₄₃	—	2	1	no	—
321	C₂²×C₄×C₄₃	—	2	1	no	—
322	C₂²×C₄×C₄₃	—	2	1	no	—
323	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
326	C₂×C₂²⋊D₄₃	—	2	2	no	—
327	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
328	C₂²×Dic₄₃	—	2	2	no	—
329	Q₈×D₄₃	—	2	4	no	—
330	Q₈×D₄₃	—	4	2	no	—
331	#10621898	—	2	4	no	—
332	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
333	C₂×C₄×D₄₃	—	2	2	no	—
334	C₂×C₄×D₄₃	—	2	2	no	—
335	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
336	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
337	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
338	C₂×Dic₈₆	—	2	1	no	—
339	C₂×Dic₈₆	—	2	2	no	—
340	C₂×Dic₈₆	—	2	2	no	—
341	C₂×Dic₈₆	—	2	1	no	—
342	C₂×Dic₈₆	—	2	1	no	—
343	C₂×Dic₈₆	—	2	2	no	—
344	C₂×Dic₈₆	—	2	2	no	—
345	C₂×Dic₈₆	—	4	4	no	—
346	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
347	C₂×Dic₈₆	C₂⁴	1	2	yes	—
348	Q₁₆×C₄₃	—	2	2	no	—
349	Q₁₆×C₄₃	—	4	1	no	—
350	SD₁₆×C₄₃	—	2	2	no	—
351	SD₁₆×C₄₃	—	4	1	no	—
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	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
356	C₄⋊C₄×C₄₃	—	2	1	no	—
357	C₄⋊C₄×C₄₃	—	2	1	no	—
358	C₄⋊C₄×C₄₃	—	2	1	no	—
359	C₄⋊C₄×C₄₃	—	2	1	no	—
360	C₄⋊C₄×C₄₃	—	2	1	no	—
361	C₄⋊C₄×C₄₃	—	2	1	no	—
362	C₄⋊C₄×C₄₃	—	2	1	no	—
363	C₄⋊C₄×C₄₃	—	2	1	no	—
364	C₄⋊C₄×C₄₃	—	2	1	no	—
365	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
367	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
368	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
369	C₂²⋊C₄×C₄₃	—	2	1	no	—
370	C₂²⋊C₄×C₄₃	—	2	1	no	—
371	C₂²⋊C₄×C₄₃	—	2	1	no	—
372	C₂²⋊C₄×C₄₃	—	2	1	no	—
373	C₂²⋊C₄×C₄₃	—	2	1	no	—
374	C₄²×C₄₃	—	2	1	no	—
375	C₄²×C₄₃	—	2	1	no	—
376	C₄²×C₄₃	—	2	1	no	—
377	C₄²×C₄₃	—	2	1	no	—
378	C₄²×C₄₃	—	2	1	no	—
379	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
380	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
381	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
382	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
383	C₂²⋊Dic₄₃	—	2	2	no	—
384	C₂²⋊Dic₄₃	—	2	2	no	—
385	C₂²⋊Dic₄₃	—	2	2	no	—
386	C₂²⋊Dic₄₃	—	2	2	no	—
387	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
388	#10621885	—	4	2	no	—
389	#10621883	—	4	2	no	—
390	(C₂×D₄₃)⋊C₄	—	2	2	no	—
391	(C₂×D₄₃)⋊C₄	—	2	2	no	—
392	(C₂×D₄₃)⋊C₄	—	2	2	no	—
393	(C₂×D₄₃)⋊C₄	—	2	2	no	—
394	(C₂×D₄₃)⋊C₄	—	2	2	no	—
395	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
396	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
397	C₄⋊Dic₄₃	—	2	1	no	—
398	C₄⋊Dic₄₃	—	2	1	no	—
399	C₄⋊Dic₄₃	—	2	1	no	—
400	C₄⋊Dic₄₃	—	2	1	no	—
401	C₄⋊Dic₄₃	—	2	1	no	—
402	C₄⋊Dic₄₃	—	2	2	no	—
403	C₄⋊Dic₄₃	—	2	2	no	—
404	C₄⋊Dic₄₃	—	2	2	no	—
405	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
406	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
407	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
408	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
409	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
410	Dic₄₃⋊C₄	—	2	2	no	—
411	Dic₄₃⋊C₄	—	2	2	no	—
412	Dic₄₃⋊C₄	—	2	2	no	—
413	Dic₄₃⋊C₄	—	2	2	no	—
414	Dic₄₃⋊C₄	—	2	2	no	—
415	Dic₄₃⋊C₄	—	2	2	no	—
416	Dic₄₃⋊C₄	—	2	2	no	—
417	Dic₄₃⋊C₄	—	2	2	no	—
418	Dic₄₃⋊C₄	—	2	2	no	—
419	Dic₄₃⋊C₄	—	2	2	no	—
420	Dic₄₃⋊C₄	—	2	2	no	—
421	Dic₄₃⋊C₄	—	2	2	no	—
422	Dic₄₃⋊C₄	—	2	2	no	—
423	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
424	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
425	C₄×Dic₄₃	—	2	2	no	—
426	C₄×Dic₄₃	—	2	2	no	—
427	C₄×Dic₄₃	—	2	2	no	—
428	C₄×Dic₄₃	—	2	2	no	—
429	C₄×Dic₄₃	—	2	2	no	—
430	C₄×Dic₄₃	—	2	2	no	—
431	C₄×Dic₄₃	—	2	2	no	—
432	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
433	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
434	C₄×Dic₄₃	C₂⁴	1	2	yes	—
435	#10621877	—	4	2	no	—
436	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
437	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
438	#10621872	—	4	2	no	—
439	#10621872	—	4	2	no	—
440	C₂³×C₄₃	—	2	1	no	—
441	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
442	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
443	Q₈×C₄₃	—	2	1	no	—
444	Q₈×C₄₃	—	2	1	no	—
445	Q₈×C₄₃	—	2	1	no	—
446	Q₈×C₄₃	—	2	1	no	—
447	Q₈×C₄₃	—	2	1	no	—
448	Q₈×C₄₃	—	4	2	no	—
449	Q₈×C₄₃	2₋¹⁺⁴	1	2	yes	—
450	D₄×C₄₃	—	2	1	no	—
451	D₄×C₄₃	—	2	1	no	—
452	D₄×C₄₃	—	8	1	no	—
453	C₂×C₄×C₄₃	—	2	1	no	—
454	C₂×C₄×C₄₃	—	2	2	no	—
455	C₂×C₄×C₄₃	—	2	1	no	—
456	C₂×C₄×C₄₃	—	2	1	no	—
457	C₂×C₄×C₄₃	—	2	1	no	—
458	C₂×C₄×C₄₃	—	2	1	no	—
459	C₂×C₄×C₄₃	—	2	1	no	—
460	C₂×C₄×C₄₃	—	2	1	no	—
461	C₂×C₄×C₄₃	—	2	1	no	—
462	C₂×C₄×C₄₃	—	2	1	no	—
463	C₂×C₄×C₄₃	—	4	1	no	—
464	C₂×C₄×C₄₃	—	4	2	no	—
465	C₂×C₄×C₄₃	—	4	2	no	—
466	C₂×C₄×C₄₃	—	8	1	no	—
467	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
473	C₂²⋊D₄₃	—	2	4	no	—
474	C₂²⋊D₄₃	—	8	2	no	—
475	C₂×Dic₄₃	—	2	2	no	—
476	C₂×Dic₄₃	—	2	2	no	—
477	C₂×Dic₄₃	—	2	2	no	—
478	C₂×Dic₄₃	—	2	2	no	—
479	C₂×Dic₄₃	—	4	4	no	—
480	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
481	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
482	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
483	D₁₇₂	—	2	2	no	—
484	C₄×D₄₃	—	2	2	no	—
485	C₄×D₄₃	—	2	2	no	—
486	C₄×D₄₃	—	2	4	no	—
487	C₄×D₄₃	—	4	2	no	—
488	C₄×D₄₃	—	4	4	no	—
489	C₄×D₄₃	—	8	2	no	—
490	Dic₈₆	—	2	2	no	—
491	Dic₈₆	—	2	2	no	—
492	Dic₈₆	—	4	4	no	—
493	Dic₈₆	—	4	2	no	—
494	Dic₈₆	—	4	4	no	—
495	Dic₈₆	—	8	2	no	—
496	Dic₈₆	—	8	2	no	—
497	Dic₈₆	—	8	1	no	—
498	Dic₈₆	—	8	1	no	—
499	Dic₈₆	#137	1	4	yes	—
500	C₈×C₄₃	—	2	1	no	—
501	C₈×C₄₃	—	2	1	no	—
502	C₈×C₄₃	—	2	1	no	—
503	C₈×C₄₃	—	2	1	no	—
504	C₄₃⋊C₈	—	2	2	no	—
505	C₄₃⋊C₈	—	2	2	no	—
506	#62153	—	43	1	no	maximal, Sylow
507	C₂²×C₄₃	—	2	1	no	—
508	C₂²×C₄₃	—	2	1	no	—
509	C₂²×C₄₃	—	2	1	no	—
510	C₂²×C₄₃	—	4	1	no	—
511	C₂²×C₄₃	—	4	1	no	—
512	C₂²×C₄₃	—	4	1	no	—
513	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
514	C₂×D₄₃	—	2	2	no	—
515	C₂×D₄₃	—	2	2	no	—
516	C₂×D₄₃	—	2	2	no	—
517	C₄×C₄₃	—	2	1	no	—
518	C₄×C₄₃	—	2	1	no	—
519	C₄×C₄₃	—	2	2	no	—
520	C₄×C₄₃	—	2	1	no	—
521	C₄×C₄₃	—	2	1	no	—
522	C₄×C₄₃	—	4	1	no	—
523	C₄×C₄₃	—	4	1	no	—
524	C₄×C₄₃	—	4	1	no	—
525	C₄×C₄₃	—	4	1	no	—
526	C₄×C₄₃	—	4	1	no	—
527	C₄×C₄₃	—	4	1	no	—
528	C₄×C₄₃	C₂×#137	1	2	yes	—
529	C₄×C₄₃	C₂×2₋¹⁺⁴	1	1	yes	characteristic
530	C₄×C₄₃	#585	1	1	yes	characteristic
531	Dic₄₃	—	2	2	no	—
532	Dic₄₃	—	2	2	no	—
533	Dic₄₃	—	4	2	no	—
534	Dic₄₃	—	4	2	no	—
535	Dic₄₃	—	4	2	no	—
536	Dic₄₃	—	4	2	no	—
537	Dic₄₃	C₂×#137	1	4	yes	—
538	#3518	—	43	1	no	—
539	Q₈×#41	—	43	1	no	—
540	Q₈×Q₁₆	—	43	1	no	—
541	Q₈×SD₁₆	—	43	1	no	—
542	#3363	—	43	1	no	—
543	#3359	—	43	1	no	—
544	#3357	—	43	2	no	—
545	#3357	—	43	1	no	—
546	#3356	—	43	2	no	—
547	#3356	—	43	1	no	—
548	#3329	—	43	2	no	—
549	#3329	—	43	1	no	—
550	#3328	—	43	2	no	—
551	#3328	—	43	1	no	—
552	#3252	—	43	2	no	—
553	#3252	—	43	1	no	—
554	#3231	—	43	2	no	—
555	#3231	—	43	1	no	—
556	#3108	—	43	2	no	—
557	#3108	D₄₃	1	1	yes	characteristic, complemented
558	#3078	—	43	2	no	—
559	#3078	—	43	1	no	—
560	#2991	—	43	1	no	—
561	C₂×C₄₃	—	4	1	no	—
562	C₂×C₄₃	—	8	1	no	—
563	C₂×C₄₃	#3489	1	1	yes	characteristic
564	C₂×C₄₃	C₂²×#137	1	1	yes	characteristic
565	C₂×C₄₃	#3584	1	1	yes	characteristic
566	D₄₃	—	4	2	no	—
567	Q₈²	—	43	1	no	—
568	Q₈²	—	43	1	no	—
569	#557	—	43	1	no	—
570	#557	—	86	1	no	—
571	#556	—	43	2	no	—
572	#556	—	43	1	no	—
573	#556	—	86	1	no	—
574	#556	—	86	2	no	—
575	#555	—	43	2	no	—
576	#555	—	43	1	no	—
577	#554	—	43	1	no	—
578	#554	—	43	2	no	—
579	#554	—	86	2	no	—
580	#554	—	86	1	no	—
581	D₄×Q₈	—	43	1	no	—
582	D₄×Q₈	—	43	2	no	—
583	D₄×Q₈	—	43	1	no	—
584	#548	—	86	1	no	—
585	#542	—	86	1	no	—
586	#542	—	86	2	no	—
587	#533	—	43	2	no	—
588	#533	—	43	2	no	—
589	#533	—	43	1	no	—
590	#533	—	43	1	no	—
591	#533	—	86	1	no	—
592	#533	—	86	2	no	—
593	#529	—	43	2	no	—
594	#529	C₂×D₄₃	1	1	yes	characteristic
595	#519	—	86	1	no	—
596	C₄×#41	—	43	1	no	—
597	C₄×#41	—	86	1	no	—
598	C₂×C₄×Q₈	—	43	2	no	—
599	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
600	#500	—	43	2	no	—
601	#500	—	43	1	no	—
602	#498	—	43	2	no	—
603	#498	—	43	1	no	—
604	#487	—	43	2	no	—
605	#487	—	43	2	no	—
606	#487	—	43	1	no	—
607	#487	—	43	1	no	—
608	#485	—	43	2	no	—
609	#485	—	43	2	no	—
610	#485	—	43	2	no	—
611	#485	—	43	2	no	—
612	#485	—	43	2	no	—
613	#485	—	43	2	no	—
614	#483	—	43	2	no	—
615	#483	C₂×D₄₃	1	1	yes	characteristic
616	#480	—	43	2	no	—
617	#480	C₂×D₄₃	1	1	yes	characteristic
618	#479	—	43	2	no	—
619	#479	—	43	2	no	—
620	#479	—	43	2	no	—
621	#479	—	43	2	no	—
622	#479	—	43	2	no	—
623	#479	C₂×D₄₃	1	1	yes	characteristic
624	#479	C₂×D₄₃	1	1	yes	characteristic
625	#477	—	43	1	no	—
626	#477	—	43	1	no	—
627	#477	—	43	1	no	—
628	#477	—	43	2	no	—
629	#477	—	43	2	no	—
630	#477	—	43	2	no	—
631	#476	—	43	1	no	—
632	#476	—	43	2	no	—
633	#475	—	43	1	no	—
634	#475	—	43	1	no	—
635	#475	—	43	2	no	—
636	#475	—	43	2	no	—
637	#470	—	43	2	no	—
638	#470	—	43	2	no	—
639	#470	—	43	2	no	—
640	#468	—	43	2	no	—
641	#468	—	43	2	no	—
642	#468	—	43	2	no	—
643	#464	—	43	2	no	—
644	#464	C₂×D₄₃	1	1	yes	characteristic
645	#464	C₂×D₄₃	1	1	yes	characteristic
646	#462	—	43	2	no	—
647	#462	—	43	1	no	—
648	#461	—	43	2	no	—
649	#461	—	43	1	no	—
650	#451	—	43	2	no	—
651	#451	C₂×D₄₃	1	1	yes	characteristic
652	#448	—	43	2	no	—
653	#448	C₂×D₄₃	1	1	yes	characteristic
654	C₈×Q₈	—	43	1	no	—
655	C₈×Q₈	—	43	1	no	—
656	C₄×Q₁₆	—	43	2	no	—
657	C₄×Q₁₆	—	43	2	no	—
658	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
659	C₄×Q₁₆	C₂×D₄₃	1	1	yes	characteristic
660	C₄×SD₁₆	—	43	2	no	—
661	C₄×SD₁₆	—	43	2	no	—
662	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
663	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
664	#436	—	43	2	no	—
665	#436	—	43	2	no	—
666	#436	—	43	1	no	—
667	#436	—	43	1	no	—
668	#431	—	43	2	no	—
669	#431	C₂×D₄₃	1	1	yes	characteristic
670	#428	—	43	2	no	—
671	#428	—	43	2	no	—
672	#428	—	43	2	no	—
673	#423	—	43	1	no	—
674	#423	—	43	2	no	—
675	#419	—	43	2	no	—
676	#419	—	43	2	no	—
677	#419	—	43	2	no	—
678	C₄₃	#62153	1	1	yes	characteristic, complemented, Sylow
679	C₂×#41	—	43	1	no	—
680	C₂²×Q₈	—	43	2	no	—
681	C₂²×Q₈	—	86	1	no	—
682	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
683	C₂×Q₁₆	—	43	2	no	—
684	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
685	C₂×Q₁₆	C₂²×D₄₃	1	1	yes	characteristic
686	C₂×SD₁₆	—	43	2	no	—
687	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
688	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
689	C₂×M₁₆	—	43	2	no	—
690	C₂×M₁₆	—	43	2	no	—
691	C₂×M₁₆	—	43	2	no	—
692	C₄⋊Q₈	—	43	2	no	—
693	C₄⋊Q₈	—	43	2	no	—
694	C₄⋊Q₈	—	43	2	no	—
695	C₄⋊Q₈	—	43	2	no	—
696	C₄⋊Q₈	—	43	1	no	—
697	C₄⋊Q₈	—	43	1	no	—
698	C₄⋊Q₈	—	43	1	no	—
699	C₄⋊Q₈	—	43	1	no	—
700	C₄⋊Q₈	—	86	1	no	—
701	C₄⋊Q₈	—	86	1	no	—
702	C₄⋊Q₈	—	86	1	no	—
703	C₄⋊Q₈	—	86	2	no	—
704	C₄⋊Q₈	—	86	2	no	—
705	C₄⋊Q₈	—	86	2	no	—
706	#126	—	2	1	no	—
707	#126	—	86	2	no	—
708	#126	—	86	2	no	—
709	#126	—	86	2	no	—
710	#126	—	86	2	no	—
711	#125	—	43	2	no	—
712	#125	—	86	1	no	—
713	#125	—	86	1	no	—
714	#125	—	86	2	no	—
715	#125	—	86	2	no	—
716	#125	—	86	2	no	—
717	#125	—	86	1	no	—
718	#125	C₂²×D₄₃	1	1	yes	characteristic
719	#124	—	86	1	no	—
720	#124	—	86	2	no	—
721	#124	—	86	2	no	—
722	#124	—	86	2	no	—
723	#124	—	86	2	no	—
724	#124	C₂²×D₄₃	1	1	yes	characteristic
725	#123	—	2	1	no	—
726	#123	—	86	2	no	—
727	C₂²⋊Q₈	—	43	2	no	—
728	C₂²⋊Q₈	—	43	2	no	—
729	C₂²⋊Q₈	—	43	2	no	—
730	C₂²⋊Q₈	—	43	2	no	—
731	C₂²⋊Q₈	—	86	2	no	—
732	C₂²⋊Q₈	—	86	2	no	—
733	C₂²⋊Q₈	—	86	2	no	—
734	C₂²⋊Q₈	—	86	2	no	—
735	C₂²⋊Q₈	—	86	2	no	—
736	C₂²⋊Q₈	—	86	2	no	—
737	C₂²⋊Q₈	—	86	2	no	—
738	C₂²⋊Q₈	—	86	2	no	—
739	C₂²⋊Q₈	—	86	2	no	—
740	C₂²⋊Q₈	—	86	2	no	—
741	C₂²⋊Q₈	—	86	1	no	—
742	C₂²⋊Q₈	—	86	1	no	—
743	C₂²⋊Q₈	—	86	1	no	—
744	C₂²⋊Q₈	—	86	1	no	—
745	C₂²⋊Q₈	C₂²×D₄₃	1	1	yes	characteristic
746	#121	—	43	2	no	—
747	#121	—	86	1	no	—
748	#121	—	86	2	no	—
749	#121	C₂²×D₄₃	1	1	yes	characteristic
750	C₄×Q₈	—	2	1	no	—
751	C₄×Q₈	—	2	1	no	—
752	C₄×Q₈	—	43	1	no	—
753	C₄×Q₈	—	43	1	no	—
754	C₄×Q₈	—	43	2	no	—
755	C₄×Q₈	—	43	2	no	—
756	C₄×Q₈	—	43	2	no	—
757	C₄×Q₈	—	43	2	no	—
758	C₄×Q₈	—	86	2	no	—
759	C₄×Q₈	—	86	2	no	—
760	C₄×Q₈	—	86	1	no	—
761	C₄×Q₈	—	86	1	no	—
762	C₄×Q₈	—	86	1	no	—
763	C₄×Q₈	—	86	1	no	—
764	C₄×Q₈	—	86	2	no	—
765	C₄×Q₈	—	86	2	no	—
766	C₄×Q₈	—	86	2	no	—
767	C₄×Q₈	—	86	2	no	—
768	C₄×Q₈	—	86	1	no	—
769	C₄×Q₈	—	86	1	no	—
770	C₄×Q₈	—	86	1	no	—
771	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
772	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
773	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
774	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
775	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
776	C₄×D₄	—	2	1	no	—
777	C₄×D₄	—	43	2	no	—
778	C₄×D₄	—	43	2	no	—
779	C₄×D₄	—	43	2	no	—
780	C₄×D₄	—	43	1	no	—
781	C₄×D₄	—	43	1	no	—
782	C₄×D₄	—	86	1	no	—
783	C₄×D₄	—	86	1	no	—
784	C₄×D₄	—	86	2	no	—
785	C₄×D₄	—	86	2	no	—
786	C₄×D₄	—	86	2	no	—
787	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
788	#117	—	2	1	no	—
789	#117	—	43	1	no	—
790	#117	—	43	2	no	—
791	#117	—	43	2	no	—
792	#117	—	43	2	no	—
793	#117	—	43	2	no	—
794	#117	—	86	2	no	—
795	#117	—	86	2	no	—
796	#117	—	86	2	no	—
797	#117	—	86	1	no	—
798	#117	—	86	1	no	—
799	C₂×C₄⋊C₄	—	2	1	no	—
800	C₂×C₄⋊C₄	—	43	2	no	—
801	C₂×C₄⋊C₄	—	86	2	no	—
802	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
803	C₂×C₄²	—	2	1	no	—
804	C₂×C₄²	—	43	2	no	—
805	C₂×C₄²	—	86	2	no	—
806	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
807	#107	—	43	2	no	—
808	#107	—	43	2	no	—
809	#107	—	43	2	no	—
810	#107	—	43	2	no	—
811	#107	—	43	2	no	—
812	#107	C₂²×D₄₃	1	1	yes	characteristic
813	#107	C₂²×D₄₃	1	1	yes	characteristic
814	#106	—	43	2	no	—
815	#106	—	43	2	no	—
816	#106	—	43	2	no	—
817	#106	—	43	2	no	—
818	#106	—	43	2	no	—
819	#106	C₂²×D₄₃	1	1	yes	characteristic
820	#106	C₂²×D₄₃	1	1	yes	characteristic
821	C₄⋊C₈	—	43	2	no	—
822	C₄⋊C₈	—	43	2	no	—
823	C₄⋊C₈	—	43	2	no	—
824	C₄⋊C₈	—	43	1	no	—
825	C₄⋊C₈	—	43	1	no	—
826	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
827	C₄⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
828	#103	—	43	2	no	—
829	#103	—	43	2	no	—
830	#103	—	43	2	no	—
831	#103	—	43	2	no	—
832	#103	—	43	2	no	—
833	#103	—	43	2	no	—
834	#103	—	43	2	no	—
835	#103	—	43	2	no	—
836	#103	—	43	2	no	—
837	#103	—	43	2	no	—
838	#103	—	43	2	no	—
839	#103	C₂²×D₄₃	1	1	yes	characteristic
840	#103	C₂²×D₄₃	1	1	yes	characteristic
841	#103	C₂²×D₄₃	1	1	yes	characteristic
842	#103	C₂²×D₄₃	1	1	yes	characteristic
843	#103	C₂²×D₄₃	1	1	yes	characteristic
844	#103	C₂²×D₄₃	1	1	yes	characteristic
845	#102	—	43	2	no	—
846	#102	C₂²×D₄₃	1	1	yes	characteristic
847	#102	C₂²×D₄₃	1	1	yes	characteristic
848	C₂²⋊C₈	—	43	2	no	—
849	C₂²⋊C₈	—	43	2	no	—
850	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
851	C₂²⋊C₈	C₂²×D₄₃	1	1	yes	characteristic
852	C₄×C₈	—	43	2	no	—
853	C₄×C₈	—	43	2	no	—
854	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
855	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
856	#41	—	86	4	no	—
857	C₂×Q₈	—	2	1	no	—
858	C₂×Q₈	—	2	2	no	—
859	C₂×Q₈	—	4	1	no	—
860	C₂×Q₈	—	43	1	no	—
861	C₂×Q₈	—	43	2	no	—
862	C₂×Q₈	—	86	2	no	—
863	C₂×Q₈	—	86	2	no	—
864	C₂×Q₈	—	86	2	no	—
865	C₂×Q₈	—	86	2	no	—
866	C₂×Q₈	—	86	1	no	—
867	C₂×Q₈	—	86	1	no	—
868	C₂×Q₈	—	86	1	no	—
869	C₂×Q₈	—	86	4	no	—
870	C₂×Q₈	—	172	4	no	—
871	C₂×Q₈	—	172	2	no	—
872	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
873	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
874	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
875	C₂×D₄	—	2	1	no	—
876	C₂×D₄	—	43	2	no	—
877	C₂×D₄	—	43	1	no	—
878	C₂×D₄	—	86	2	no	—
879	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	2	1	no	—
883	C₂²×C₄	—	43	2	no	—
884	C₂²×C₄	—	43	2	no	—
885	C₂²×C₄	—	43	2	no	—
886	C₂²×C₄	—	86	2	no	—
887	C₂²×C₄	—	86	2	no	—
888	C₂²×C₄	—	86	2	no	—
889	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
890	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
891	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
892	Q₁₆	—	2	2	no	—
893	Q₁₆	—	4	1	no	—
894	Q₁₆	—	172	2	no	—
895	SD₁₆	—	2	2	no	—
896	SD₁₆	—	4	1	no	—
897	SD₁₆	—	172	2	no	—
898	M₁₆	—	172	2	no	—
899	M₁₆	—	172	2	no	—
900	M₁₆	—	172	2	no	—
901	C₂×C₈	—	43	2	no	—
902	C₂×C₈	—	43	2	no	—
903	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
904	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
905	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
906	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	1	no	—
914	C₄⋊C₄	—	2	1	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	43	2	no	—
917	C₄⋊C₄	—	43	1	no	—
918	C₄⋊C₄	—	43	2	no	—
919	C₄⋊C₄	—	43	1	no	—
920	C₄⋊C₄	—	43	2	no	—
921	C₄⋊C₄	—	43	2	no	—
922	C₄⋊C₄	—	43	2	no	—
923	C₄⋊C₄	—	86	2	no	—
924	C₄⋊C₄	—	86	2	no	—
925	C₄⋊C₄	—	86	2	no	—
926	C₄⋊C₄	—	86	2	no	—
927	C₄⋊C₄	—	86	2	no	—
928	C₄⋊C₄	—	86	2	no	—
929	C₄⋊C₄	—	86	2	no	—
930	C₄⋊C₄	—	86	2	no	—
931	C₄⋊C₄	—	86	2	no	—
932	C₄⋊C₄	—	86	2	no	—
933	C₄⋊C₄	—	86	2	no	—
934	C₄⋊C₄	—	86	2	no	—
935	C₄⋊C₄	—	86	2	no	—
936	C₄⋊C₄	—	86	1	no	—
937	C₄⋊C₄	—	86	1	no	—
938	C₄⋊C₄	—	86	1	no	—
939	C₄⋊C₄	—	86	2	no	—
940	C₄⋊C₄	—	86	2	no	—
941	C₄⋊C₄	—	86	2	no	—
942	C₄⋊C₄	—	86	1	no	—
943	C₄⋊C₄	—	86	1	no	—
944	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
945	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
946	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
947	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
948	C₂²⋊C₄	—	2	1	no	—
949	C₂²⋊C₄	—	2	1	no	—
950	C₂²⋊C₄	—	2	1	no	—
951	C₂²⋊C₄	—	2	1	no	—
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	43	2	no	—
954	C₂²⋊C₄	—	43	2	no	—
955	C₂²⋊C₄	—	43	2	no	—
956	C₂²⋊C₄	—	86	2	no	—
957	C₂²⋊C₄	—	86	2	no	—
958	C₂²⋊C₄	—	86	2	no	—
959	C₂²⋊C₄	—	86	2	no	—
960	C₂²⋊C₄	—	86	2	no	—
961	C₂²⋊C₄	—	86	2	no	—
962	C₂²⋊C₄	—	86	2	no	—
963	C₂²⋊C₄	—	86	2	no	—
964	C₂²⋊C₄	—	86	2	no	—
965	C₄²	—	2	1	no	—
966	C₄²	—	2	1	no	—
967	C₄²	—	2	1	no	—
968	C₄²	—	2	1	no	—
969	C₄²	—	2	1	no	—
970	C₄²	—	43	2	no	—
971	C₄²	—	43	2	no	—
972	C₄²	—	43	2	no	—
973	C₄²	—	86	2	no	—
974	C₄²	—	86	2	no	—
975	C₄²	—	86	2	no	—
976	C₄²	—	86	2	no	—
977	C₄²	—	86	2	no	—
978	C₄²	—	86	2	no	—
979	C₄²	—	86	2	no	—
980	C₄²	D₄×D₄₃	1	1	yes	characteristic
981	C₄²	D₄×D₄₃	1	1	yes	characteristic
982	C₄²	C₂³×D₄₃	1	1	yes	characteristic
983	C₄²	C₂³×D₄₃	1	1	yes	characteristic
984	C₂³	—	2	1	no	—
985	C₂³	—	43	2	no	—
986	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
987	Q₈	—	2	1	no	—
988	Q₈	—	2	1	no	—
989	Q₈	—	2	1	no	—
990	Q₈	—	2	1	no	—
991	Q₈	—	2	1	no	—
992	Q₈	—	4	2	no	—
993	Q₈	—	43	4	no	—
994	Q₈	—	86	2	no	—
995	Q₈	—	86	2	no	—
996	Q₈	—	344	1	no	—
997	Q₈	—	344	1	no	—
998	Q₈	—	344	2	no	—
999	Q₈	—	344	2	no	—
1000	Q₈	—	172	4	no	—
1001	Q₈	—	172	4	no	—
1002	Q₈	—	172	2	no	—
1003	Q₈	#13063372	1	2	yes	—
1004	D₄	—	2	1	no	—
1005	D₄	—	2	1	no	—
1006	D₄	—	8	1	no	—
1007	D₄	—	86	4	no	—
1008	D₄	—	86	2	no	—
1009	D₄	—	344	2	no	—
1010	C₂×C₄	—	2	1	no	—
1011	C₂×C₄	—	2	2	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	4	1	no	—
1021	C₂×C₄	—	4	2	no	—
1022	C₂×C₄	—	4	2	no	—
1023	C₂×C₄	—	8	1	no	—
1024	C₂×C₄	—	43	2	no	—
1025	C₂×C₄	—	43	2	no	—
1026	C₂×C₄	—	43	2	no	—
1027	C₂×C₄	—	86	4	no	—
1028	C₂×C₄	—	86	2	no	—
1029	C₂×C₄	—	86	2	no	—
1030	C₂×C₄	—	86	2	no	—
1031	C₂×C₄	—	86	2	no	—
1032	C₂×C₄	—	86	2	no	—
1033	C₂×C₄	—	86	2	no	—
1034	C₂×C₄	—	344	2	no	—
1035	C₂×C₄	—	172	2	no	—
1036	C₂×C₄	—	172	4	no	—
1037	C₂×C₄	—	172	4	no	—
1038	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1039	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1040	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1041	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1042	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1043	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1044	C₈	—	2	1	no	—
1045	C₈	—	2	1	no	—
1046	C₈	—	2	1	no	—
1047	C₈	—	2	1	no	—
1048	C₈	—	86	2	no	—
1049	C₈	—	86	2	no	—
1050	C₂²	—	2	1	no	—
1051	C₂²	—	2	1	no	—
1052	C₂²	—	2	1	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	—	86	2	no	—
1057	C₂²	—	86	2	no	—
1058	C₂²	—	86	2	no	—
1059	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1060	C₄	—	2	1	no	—
1061	C₄	—	2	1	no	—
1062	C₄	—	2	1	no	—
1063	C₄	—	2	1	no	—
1064	C₄	—	2	2	no	—
1065	C₄	—	4	1	no	—
1066	C₄	—	4	1	no	—
1067	C₄	—	4	1	no	—
1068	C₄	—	4	1	no	—
1069	C₄	—	4	1	no	—
1070	C₄	—	4	1	no	—
1071	C₄	—	43	4	no	—
1072	C₄	—	86	2	no	—
1073	C₄	—	86	2	no	—
1074	C₄	—	172	2	no	—
1075	C₄	—	172	2	no	—
1076	C₄	—	172	2	no	—
1077	C₄	—	172	2	no	—
1078	C₄	#137×D₄₃	1	2	yes	—
1079	C₄	C₂×#13063372	1	1	yes	characteristic
1080	C₄	#14583735	1	1	yes	characteristic
1081	C₂	—	4	1	no	—
1082	C₂	—	8	1	no	—
1083	C₂	—	172	2	no	—
1084	C₂	#19148267	1	1	yes	characteristic
1085	C₂	C₂×#137×D₄₃	1	1	yes	characteristic
1086	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×#3108	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	#19148610	C₂
hypercenter	#3108	D₄₃
hypocenter	C₄₃	#62153
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3108

Complements

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

N	H ≅ G/N	type
2. Q₈×#10621898	C₂	semidirect
3. Q₁₆×Dic₈₆	C₂	semidirect
4. SD₁₆×Dic₈₆	C₂	semidirect
5. #19147271	C₂	semidirect
6. #19147235	C₂	semidirect
7. #19147223	C₂	semidirect
8. #19147214	C₂	semidirect
9. #19147212	C₂	semidirect
10. #19147203	C₂	semidirect
11. #19146891	C₂	semidirect
12. #19146882	C₂	semidirect
13. #19146880	C₂	semidirect
14. #19146871	C₂	semidirect
15. #19145968	C₂	semidirect
16. #19145965	C₂	semidirect
17. #19145756	C₂	semidirect
18. #19145753	C₂	semidirect
19. #19144674	C₂	semidirect
20. #19144400	C₂	semidirect
21. #19144398	C₂	semidirect
22. #19143724	C₂	semidirect
23. C₄₃×#3108	C₂	semidirect
557. #3108	D₄₃	semidirect
678. C₄₃	#62153	semidirect

Maximal subgroups

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

subgroup	index
#19148610	2
Q₈×#10621898	2
Q₁₆×Dic₈₆	2
SD₁₆×Dic₈₆	2
#19147271	2
#19147235	2
#19147223	2
#19147214	2
#19147212	2
#19147203	2
#19146891	2
#19146882	2
#19146880	2
#19146871	2
#19145968	2
#19145965	2
#19145756	2
#19145753	2
#19144674	2
#19144400	2
#19144398	2
#19143724	2
C₄₃×#3108	2
#62153	43