Subgroups — #25978213

Order 11008.

1836 conjugacy classes of subgroups.

The subgroup lattice has 1134 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	Q₈×#10621898	C₂	1	1	yes	maximal, characteristic, complemented
2	#19148153	C₂	1	1	yes	maximal, characteristic
3	#19147624	C₂	1	1	yes	maximal, characteristic, complemented
4	#19147503	C₂	1	1	yes	maximal, characteristic, complemented
5	#19147374	C₂	1	1	yes	maximal, characteristic, complemented
6	#19147333	C₂	1	1	yes	maximal, characteristic, complemented
7	#19147223	C₂	1	1	yes	maximal, characteristic, complemented
8	#19147046	C₂	1	2	yes	maximal, complemented
9	#19146913	C₂	1	1	yes	maximal, characteristic, complemented
10	#19146891	C₂	1	1	yes	maximal, characteristic, complemented
11	#19146672	C₂	1	2	yes	maximal, complemented
12	#19146642	C₂	1	2	yes	maximal, complemented
13	#19146242	C₂	1	1	yes	maximal, characteristic, complemented
14	#19146105	C₂	1	2	yes	maximal, complemented
15	#19145197	C₂	1	2	yes	maximal, complemented
16	#19145181	C₂	1	1	yes	maximal, characteristic, complemented
17	#19144673	C₂	1	2	yes	maximal, complemented
18	#19144662	C₂	1	2	yes	maximal, complemented
19	#19144634	C₂	1	1	yes	maximal, characteristic, complemented
20	#19144603	C₂	1	1	yes	maximal, characteristic, complemented
21	#19143561	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×#13063354	C₂	1	2	yes	maximal, complemented
23	C₂×C₄×SD₁₆×C₄₃	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13063354	C₂²	1	2	yes	—
25	Q₈×Dic₈₆	C₂²	1	1	yes	characteristic, complemented
26	#14583627	—	2	1	no	—
27	#14583627	C₂²	1	1	yes	characteristic, complemented
28	#14583619	C₂²	1	1	yes	characteristic
29	#14583614	C₂²	1	1	yes	characteristic
30	#14583609	—	2	1	no	—
31	#14583609	C₂²	1	1	yes	characteristic, complemented
32	#14583606	C₂²	1	1	yes	characteristic
33	#14583604	—	2	2	no	—
34	#14583604	C₂²	1	2	yes	—
35	#14583595	—	2	1	no	—
36	#14583589	—	2	1	no	—
37	#14583584	C₂²	1	2	yes	—
38	#14583575	—	2	2	no	—
39	Q₈×D₁₇₂	C₂²	1	1	yes	characteristic, complemented
40	Q₈×C₂²⋊D₄₃	C₂²	1	2	yes	—
41	#14583553	C₂²	1	1	yes	characteristic
42	#14583543	C₂²	1	2	yes	—
43	#14583456	—	2	1	no	—
44	#14583456	C₂²	1	1	yes	characteristic
45	#14583456	C₂²	1	1	yes	characteristic
46	#14583453	—	2	2	no	—
47	#14583453	C₂²	1	2	yes	complemented
48	#14583431	C₂²	1	2	yes	—
49	#14583429	—	2	2	no	—
50	#14583410	—	2	1	no	—
51	C₄×#10621898	—	2	1	no	—
52	C₄×#10621898	C₂²	1	1	yes	characteristic
53	C₄×#10621900	C₂²	1	2	yes	—
54	C₄×Q₈×D₄₃	C₂²	1	2	yes	complemented
55	C₂×#13063284	—	2	1	no	—
56	#14583306	C₂²	1	2	yes	complemented
57	#14583304	C₂²	1	1	yes	characteristic, complemented
58	#14583290	C₂²	1	2	yes	—
59	#14583279	C₂²	1	1	yes	characteristic, complemented
60	#14583266	C₂²	1	2	yes	complemented
61	#14583257	C₂²	1	2	yes	—
62	#14583250	C₂²	1	1	yes	characteristic, complemented
63	#14583250	C₂²	1	1	yes	characteristic, complemented
64	#14583243	C₂²	1	2	yes	complemented
65	#14583239	C₂²	1	2	yes	complemented
66	#14583234	C₂²	1	2	yes	—
67	#14583231	C₂²	1	2	yes	complemented
68	#14583229	C₂²	1	2	yes	—
69	#14583211	C₂²	1	2	yes	—
70	#14583209	C₂²	1	2	yes	complemented
71	#14583208	C₂²	1	2	yes	complemented
72	#14583194	C₂²	1	1	yes	characteristic, complemented
73	#14583194	C₂²	1	1	yes	characteristic, complemented
74	#14583189	C₂²	1	1	yes	characteristic
75	#14583189	C₂²	1	1	yes	characteristic
76	#14583183	C₂²	1	2	yes	complemented
77	#14583177	C₂²	1	2	yes	—
78	#14583158	C₂²	1	2	yes	complemented
79	#14583156	C₂²	1	2	yes	complemented
80	#14583144	C₂²	1	2	yes	—
81	#14583142	C₂²	1	2	yes	—
82	#14583140	C₂²	1	2	yes	—
83	#14583140	C₂²	1	2	yes	—
84	#14583120	C₂²	1	2	yes	—
85	#14583119	C₂²	1	2	yes	—
86	#14583109	C₂²	1	1	yes	characteristic, complemented
87	#14583109	C₂²	1	1	yes	characteristic, complemented
88	#14583108	C₂²	1	2	yes	complemented
89	#14583104	C₂²	1	1	yes	characteristic
90	#14583104	C₂²	1	1	yes	characteristic
91	#14583102	C₂²	1	2	yes	—
92	#14583062	C₂²	1	2	yes	—
93	#14583058	C₂²	1	2	yes	—
94	#14583056	C₂²	1	2	yes	complemented
95	#14583055	C₂²	1	2	yes	—
96	#14583050	C₂²	1	2	yes	—
97	#14583036	C₂²	1	2	yes	—
98	#14583029	C₂²	1	1	yes	characteristic, complemented
99	#14583029	C₂²	1	1	yes	characteristic, complemented
100	#14583005	C₂²	1	2	yes	complemented
101	#14583003	C₂²	1	2	yes	complemented
102	#14583000	C₂²	1	2	yes	—
103	#14582996	C₂²	1	2	yes	—
104	C₄×Dic₁₇₂	C₂²	1	2	yes	complemented
105	C₄×Dic₁₇₂	C₂²	1	2	yes	complemented
106	C₄×#10621885	C₂²	1	2	yes	complemented
107	C₄×#10621885	C₂²	1	2	yes	complemented
108	C₄×#10621883	C₂²	1	2	yes	—
109	C₄×#10621883	C₂²	1	2	yes	—
110	#14582978	C₂²	1	1	yes	characteristic, complemented
111	#14582978	C₂²	1	1	yes	characteristic, complemented
112	#14582970	C₂²	1	2	yes	—
113	#14582970	C₂²	1	2	yes	—
114	#14582952	C₂²	1	1	yes	characteristic
115	#14582950	C₂²	1	2	yes	complemented
116	#14582938	C₂²	1	2	yes	complemented
117	#14582906	C₂²	1	2	yes	complemented
118	#14582897	C₂²	1	2	yes	—
119	C₄×#10621872	C₂²	1	2	yes	complemented
120	C₂²×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
121	C₂×C₄×Q₈×C₄₃	C₂²	1	1	yes	characteristic
122	C₂×C₄×D₄×C₄₃	C₂²	1	1	yes	characteristic
123	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
124	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
125	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
126	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
127	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
128	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
129	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
130	C₄×SD₁₆×C₄₃	C₂²	1	1	yes	characteristic
131	C₂×#106×C₄₃	C₂²	1	1	yes	characteristic
132	C₂×#103×C₄₃	C₂²	1	1	yes	characteristic
133	C₂×#102×C₄₃	C₂²	1	1	yes	characteristic
134	C₂×C₄×C₈×C₄₃	C₂²	1	1	yes	characteristic
135	C₂×#10621898	D₄	1	1	yes	characteristic
136	C₂×#10621900	C₂³	1	2	yes	—
137	C₂×Q₈×D₄₃	C₂³	1	2	yes	—
138	#13063354	—	2	8	no	—
139	C₂×Dic₁₇₂	C₂³	1	2	yes	—
140	C₂×Dic₁₇₂	C₂³	1	2	yes	—
141	C₂×#10621885	C₂³	1	2	yes	—
142	C₂×#10621885	C₂³	1	2	yes	—
143	C₂×#10621883	C₂³	1	2	yes	—
144	C₂×#10621883	C₂³	1	2	yes	—
145	C₂×#10621872	C₂³	1	2	yes	—
146	C₂×#10621872	C₂³	1	2	yes	—
147	#13063325	—	2	1	no	—
148	#13063325	—	2	1	no	—
149	#13063325	C₂³	1	1	yes	characteristic
150	#13063325	C₂³	1	1	yes	characteristic
151	#13063325	C₂³	1	1	yes	characteristic
152	#13063325	C₂³	1	1	yes	characteristic
153	#13063324	—	2	2	no	—
154	#13063324	C₂³	1	2	yes	—
155	#13063323	—	2	2	no	—
156	#13063323	C₂³	1	2	yes	—
157	#13063320	—	2	2	no	—
158	#13063318	—	2	2	no	—
159	#13063318	—	2	2	no	—
160	#13063317	—	2	1	no	—
161	#13063317	—	2	1	no	—
162	#13063317	—	2	1	no	—
163	#13063317	—	2	1	no	—
164	#13063316	C₂³	1	2	yes	—
165	#13063315	—	2	2	no	—
166	#13063315	—	2	2	no	—
167	#13063315	—	2	2	no	—
168	#13063315	—	2	2	no	—
169	#13063312	C₂³	1	2	yes	—
170	#13063311	—	2	2	no	—
171	#13063309	—	2	2	no	—
172	#13063308	—	2	2	no	—
173	#13063307	—	2	2	no	—
174	#13063306	—	2	2	no	—
175	#13063305	—	2	2	no	—
176	#13063305	C₂³	1	2	yes	—
177	#13063305	C₂³	1	2	yes	—
178	#13063304	—	2	1	no	—
179	#13063304	—	2	1	no	—
180	#13063304	—	2	1	no	—
181	#13063304	—	2	1	no	—
182	#13063304	—	2	2	no	—
183	#13063304	—	2	2	no	—
184	#13063304	C₂³	1	2	yes	—
185	#13063304	C₂³	1	2	yes	—
186	#13063303	—	2	2	no	—
187	#13063303	—	2	2	no	—
188	#13063303	—	2	2	no	—
189	#13063302	—	2	2	no	—
190	#13063301	—	2	2	no	—
191	#13063301	C₂³	1	2	yes	—
192	#13063299	—	2	1	no	—
193	#13063299	—	2	1	no	—
194	#13063297	—	2	2	no	—
195	#13063296	C₂³	1	2	yes	—
196	#13063294	—	2	2	no	—
197	Q₈×Dic₄₃	C₂³	1	2	yes	—
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	2	no	—
203	C₄×Dic₈₆	—	2	2	no	—
204	C₄×Dic₈₆	D₄	1	1	yes	characteristic
205	C₄×Dic₈₆	C₂³	1	2	yes	—
206	C₄×Dic₈₆	C₂³	1	2	yes	—
207	C₄×Dic₈₆	C₂³	1	1	yes	characteristic
208	#13063290	—	2	2	no	—
209	#13063290	C₂³	1	2	yes	—
210	#13063290	C₂³	1	2	yes	—
211	C₄×D₁₇₂	—	2	1	no	—
212	C₄×D₁₇₂	—	2	1	no	—
213	C₄×D₁₇₂	D₄	1	1	yes	characteristic
214	C₄×D₁₇₂	C₂³	1	1	yes	characteristic
215	D₄×Dic₄₃	C₂³	1	2	yes	—
216	C₄×C₂²⋊D₄₃	—	2	2	no	—
217	C₄×C₂²⋊D₄₃	—	2	2	no	—
218	C₄×C₂²⋊D₄₃	—	2	2	no	—
219	C₄×C₂²⋊D₄₃	—	2	2	no	—
220	C₄×C₂²⋊D₄₃	D₄	1	2	yes	—
221	C₄×C₂²⋊D₄₃	C₂³	1	2	yes	—
222	(C₂²⋊D₄₃)⋊C₄	—	2	2	no	—
223	#13063284	—	2	1	no	—
224	#13063284	—	2	1	no	—
225	#13063284	—	2	2	no	—
226	#13063284	—	2	1	no	—
227	#13063284	—	2	1	no	—
228	#13063284	—	2	2	no	—
229	#13063284	D₄	1	1	yes	characteristic
230	#13063283	C₂³	1	2	yes	—
231	#13063282	—	2	2	no	—
232	#13063282	D₄	1	2	yes	—
233	#13063281	—	2	2	no	—
234	C₂×C₄⋊Dic₄₃	—	2	1	no	—
235	C₂×C₄⋊Dic₄₃	—	2	1	no	—
236	C₄⋊C₄×D₄₃	—	2	2	no	—
237	C₄⋊C₄×D₄₃	C₂³	1	2	yes	—
238	C₂×C₂²⋊Dic₄₃	—	2	2	no	—
239	C₂×C₄×Dic₄₃	—	2	2	no	—
240	C₄²×D₄₃	—	2	2	no	—
241	C₄²×D₄₃	C₂³	1	2	yes	—
242	#13063259	C₂³	1	2	yes	—
243	#13063259	C₂³	1	2	yes	—
244	#13063258	C₂³	1	2	yes	—
245	#13063258	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	Dic₄₃⋊C₈	C₂³	1	2	yes	—
251	Dic₄₃⋊C₈	C₂³	1	2	yes	—
252	#13063250	C₂³	1	2	yes	—
253	#13063250	C₂³	1	2	yes	—
254	#13063250	C₂³	1	2	yes	—
255	#13063250	C₂³	1	2	yes	—
256	#13063249	C₂³	1	2	yes	—
257	#13063249	C₂³	1	2	yes	—
258	#13063248	C₂³	1	2	yes	—
259	#13063248	C₂³	1	2	yes	—
260	#13063248	C₂³	1	2	yes	—
261	#13063248	C₂³	1	2	yes	—
262	#13063246	C₂³	1	2	yes	—
263	#13063246	C₂³	1	2	yes	—
264	C₂²⋊(C₄₃⋊C₈)	C₂³	1	2	yes	—
265	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
266	(C₂×D₄₃)⋊C₈	C₂³	1	2	yes	—
267	#13063235	C₂³	1	2	yes	—
268	#13063235	C₂³	1	2	yes	—
269	C₄×C₄₃⋊C₈	C₂³	1	2	yes	—
270	C₂²×Q₈×C₄₃	C₂³	1	1	yes	characteristic
271	C₂²×D₄×C₄₃	C₂³	1	1	yes	characteristic
272	C₂³×C₄×C₄₃	—	2	1	no	—
273	C₂×SD₁₆×C₄₃	—	2	4	no	—
274	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
275	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
276	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
277	C₂×SD₁₆×C₄₃	C₂³	1	1	yes	characteristic
278	C₂²×C₈×C₄₃	C₂³	1	1	yes	characteristic
279	C₂²×C₈×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×D₄×C₄₃	—	2	1	no	—
287	C₄×D₄×C₄₃	—	2	1	no	—
288	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
289	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
291	C₄×D₄×C₄₃	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
293	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄×C₄₃	C₂³	1	1	yes	characteristic
295	C₂×C₂²⋊C₄×C₄₃	—	2	1	no	—
296	C₂×C₄²×C₄₃	—	2	1	no	—
297	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
298	#106×C₄₃	C₂³	1	1	yes	characteristic
299	#106×C₄₃	C₂³	1	1	yes	characteristic
300	#106×C₄₃	C₂³	1	1	yes	characteristic
301	#106×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	#102×C₄₃	C₂³	1	1	yes	characteristic
309	#102×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	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₄₃	C₂³	1	1	yes	characteristic
314	C₂⁴×C₄₃	—	2	1	no	—
315	C₂×Q₈×C₄₃	—	2	1	no	—
316	C₂×Q₈×C₄₃	—	2	2	no	—
317	C₂×Q₈×C₄₃	—	4	1	no	—
318	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
319	C₂×Q₈×C₄₃	C₂⁴	1	1	yes	characteristic
320	C₂×D₄×C₄₃	—	2	1	no	—
321	C₂×D₄×C₄₃	—	2	2	no	—
322	C₂×D₄×C₄₃	—	4	1	no	—
323	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
324	C₂×D₄×C₄₃	C₂⁴	1	1	yes	characteristic
325	C₂²×C₄×C₄₃	—	2	1	no	—
326	C₂²×C₄×C₄₃	—	2	1	no	—
327	C₂²×C₄×C₄₃	—	2	1	no	—
328	C₂²×C₄×C₄₃	—	2	1	no	—
329	C₂²×C₄×C₄₃	—	2	1	no	—
330	C₂²×C₄×C₄₃	—	2	1	no	—
331	C₂²×C₄×C₄₃	—	2	1	no	—
332	C₂²×C₄×C₄₃	—	4	4	no	—
333	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
336	C₂×C₂²⋊D₄₃	—	2	2	no	—
337	C₂×C₂²⋊D₄₃	—	2	2	no	—
338	C₂×C₂²⋊D₄₃	C₂×D₄	1	2	yes	—
339	C₂²×Dic₄₃	—	2	2	no	—
340	C₂²×Dic₄₃	—	2	2	no	—
341	Q₈×D₄₃	—	2	4	no	—
342	Q₈×D₄₃	—	4	2	no	—
343	#10621900	—	2	4	no	—
344	#10621900	—	4	2	no	—
345	#10621898	—	2	4	no	—
346	C₂×D₁₇₂	C₂×D₄	1	1	yes	characteristic
347	C₂×C₄×D₄₃	—	2	2	no	—
348	C₂×C₄×D₄₃	—	2	2	no	—
349	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
350	C₂×C₄×D₄₃	C₂×D₄	1	2	yes	—
351	C₂×C₄×D₄₃	C₂⁴	1	2	yes	—
352	C₂×Dic₈₆	—	2	2	no	—
353	C₂×Dic₈₆	—	2	1	no	—
354	C₂×Dic₈₆	—	2	1	no	—
355	C₂×Dic₈₆	—	2	2	no	—
356	C₂×Dic₈₆	C₂×D₄	1	1	yes	characteristic
357	C₂×Dic₈₆	C₂⁴	1	2	yes	—
358	C₂×Dic₈₆	C₂⁴	1	2	yes	—
359	SD₁₆×C₄₃	—	2	2	no	—
360	SD₁₆×C₄₃	—	2	2	no	—
361	SD₁₆×C₄₃	—	2	2	no	—
362	SD₁₆×C₄₃	#41	1	4	yes	complemented
363	C₂×C₈×C₄₃	—	2	2	no	—
364	C₂×C₈×C₄₃	—	4	1	no	—
365	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
366	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
367	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
368	C₂×C₈×C₄₃	C₂⁴	1	1	yes	characteristic
369	C₄⋊C₄×C₄₃	—	2	1	no	—
370	C₄⋊C₄×C₄₃	—	2	1	no	—
371	C₄⋊C₄×C₄₃	—	2	1	no	—
372	C₄⋊C₄×C₄₃	—	2	1	no	—
373	C₄⋊C₄×C₄₃	—	2	1	no	—
374	C₄⋊C₄×C₄₃	—	2	1	no	—
375	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
376	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
377	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
378	C₄⋊C₄×C₄₃	C₂⁴	1	1	yes	characteristic
379	C₂²⋊C₄×C₄₃	—	2	1	no	—
380	C₂²⋊C₄×C₄₃	—	2	1	no	—
381	C₂²⋊C₄×C₄₃	—	2	1	no	—
382	C₂²⋊C₄×C₄₃	—	2	1	no	—
383	C₄²×C₄₃	—	2	1	no	—
384	C₄²×C₄₃	—	2	1	no	—
385	C₄²×C₄₃	—	2	1	no	—
386	C₄²×C₄₃	—	2	1	no	—
387	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
388	C₄²×C₄₃	C₂×D₄	1	1	yes	characteristic
389	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
390	C₄²×C₄₃	C₂⁴	1	1	yes	characteristic
391	C₂²⋊Dic₄₃	—	2	2	no	—
392	C₂²⋊Dic₄₃	—	2	2	no	—
393	C₂²⋊Dic₄₃	—	2	2	no	—
394	C₂²⋊Dic₄₃	—	2	2	no	—
395	C₂²⋊Dic₄₃	—	2	2	no	—
396	C₂²⋊Dic₄₃	—	2	2	no	—
397	C₂²⋊Dic₄₃	C₂×D₄	1	2	yes	—
398	#10621885	—	2	4	no	—
399	#10621885	—	4	2	no	—
400	#10621883	—	2	4	no	—
401	#10621883	—	4	2	no	—
402	(C₂×D₄₃)⋊C₄	—	2	2	no	—
403	(C₂×D₄₃)⋊C₄	—	2	2	no	—
404	(C₂×D₄₃)⋊C₄	—	2	2	no	—
405	(C₂×D₄₃)⋊C₄	—	2	2	no	—
406	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
407	(C₂×D₄₃)⋊C₄	C₂×D₄	1	2	yes	—
408	C₄⋊Dic₄₃	—	2	1	no	—
409	C₄⋊Dic₄₃	—	2	1	no	—
410	C₄⋊Dic₄₃	—	2	1	no	—
411	C₄⋊Dic₄₃	—	2	1	no	—
412	C₄⋊Dic₄₃	—	2	1	no	—
413	C₄⋊Dic₄₃	—	2	1	no	—
414	C₄⋊Dic₄₃	—	2	2	no	—
415	C₄⋊Dic₄₃	—	2	2	no	—
416	C₄⋊Dic₄₃	—	2	2	no	—
417	C₄⋊Dic₄₃	—	2	2	no	—
418	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
419	C₄⋊Dic₄₃	C₂×D₄	1	1	yes	characteristic
420	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
421	C₄⋊Dic₄₃	C₂⁴	1	2	yes	—
422	Dic₄₃⋊C₄	—	2	2	no	—
423	Dic₄₃⋊C₄	—	2	2	no	—
424	Dic₄₃⋊C₄	—	2	2	no	—
425	Dic₄₃⋊C₄	—	2	2	no	—
426	Dic₄₃⋊C₄	—	2	2	no	—
427	Dic₄₃⋊C₄	—	2	2	no	—
428	Dic₄₃⋊C₄	—	2	2	no	—
429	Dic₄₃⋊C₄	—	2	2	no	—
430	Dic₄₃⋊C₄	—	2	2	no	—
431	Dic₄₃⋊C₄	—	2	2	no	—
432	Dic₄₃⋊C₄	—	2	2	no	—
433	Dic₄₃⋊C₄	—	2	2	no	—
434	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
435	Dic₄₃⋊C₄	C₂×D₄	1	2	yes	—
436	C₄×Dic₄₃	—	2	2	no	—
437	C₄×Dic₄₃	—	2	2	no	—
438	C₄×Dic₄₃	—	2	2	no	—
439	C₄×Dic₄₃	—	2	2	no	—
440	C₄×Dic₄₃	—	2	2	no	—
441	C₄×Dic₄₃	—	2	2	no	—
442	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
443	C₄×Dic₄₃	C₂×D₄	1	2	yes	—
444	C₄×Dic₄₃	C₂⁴	1	2	yes	—
445	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
446	C₂×C₄₃⋊C₈	C₂⁴	1	2	yes	—
447	Dic₁₇₂	—	2	4	no	—
448	Dic₁₇₂	—	4	2	no	—
449	#10621872	—	2	4	no	—
450	#10621872	—	4	2	no	—
451	C₂³×C₄₃	—	2	1	no	—
452	C₂³×C₄₃	—	2	1	no	—
453	C₂³×C₄₃	—	4	2	no	—
454	C₂³×C₄₃	—	4	2	no	—
455	C₂³×C₄₃	—	8	1	no	—
456	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
457	C₂²×D₄₃	C₂²×D₄	1	2	yes	—
458	Q₈×C₄₃	—	2	1	no	—
459	Q₈×C₄₃	—	2	1	no	—
460	Q₈×C₄₃	—	2	1	no	—
461	Q₈×C₄₃	—	4	2	no	—
462	Q₈×C₄₃	C₂×#41	1	2	yes	—
463	D₄×C₄₃	—	2	1	no	—
464	D₄×C₄₃	—	2	1	no	—
465	D₄×C₄₃	—	2	1	no	—
466	D₄×C₄₃	—	4	2	no	—
467	D₄×C₄₃	C₂×#41	1	2	yes	—
468	C₂×C₄×C₄₃	—	2	1	no	—
469	C₂×C₄×C₄₃	—	2	1	no	—
470	C₂×C₄×C₄₃	—	2	1	no	—
471	C₂×C₄×C₄₃	—	2	1	no	—
472	C₂×C₄×C₄₃	—	2	1	no	—
473	C₂×C₄×C₄₃	—	2	1	no	—
474	C₂×C₄×C₄₃	—	2	1	no	—
475	C₂×C₄×C₄₃	—	2	1	no	—
476	C₂×C₄×C₄₃	—	4	1	no	—
477	C₂×C₄×C₄₃	—	4	2	no	—
478	C₂×C₄×C₄₃	—	4	2	no	—
479	C₂×C₄×C₄₃	—	4	2	no	—
480	C₂×C₄×C₄₃	—	4	2	no	—
481	C₂×C₄×C₄₃	—	4	2	no	—
482	C₂×C₄×C₄₃	—	4	2	no	—
483	C₂×C₄×C₄₃	—	8	1	no	—
484	C₂×C₄×C₄₃	#137	1	4	yes	complemented
485	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
489	C₂×C₄×C₄₃	C₂²×D₄	1	1	yes	characteristic
490	C₂×C₄×C₄₃	C₂⁵	1	1	yes	characteristic
491	C₂²⋊D₄₃	—	2	4	no	—
492	C₂²⋊D₄₃	—	4	4	no	—
493	C₂²⋊D₄₃	—	8	2	no	—
494	C₂×Dic₄₃	—	2	2	no	—
495	C₂×Dic₄₃	—	2	2	no	—
496	C₂×Dic₄₃	—	2	2	no	—
497	C₂×Dic₄₃	—	2	2	no	—
498	C₂×Dic₄₃	—	4	4	no	—
499	C₂×Dic₄₃	—	8	2	no	—
500	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
501	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
502	C₂×Dic₄₃	C₂²×D₄	1	2	yes	—
503	D₁₇₂	—	2	2	no	—
504	C₄×D₄₃	—	2	4	no	—
505	C₄×D₄₃	—	2	2	no	—
506	C₄×D₄₃	—	2	2	no	—
507	C₄×D₄₃	—	4	2	no	—
508	C₄×D₄₃	—	4	4	no	—
509	C₄×D₄₃	—	8	2	no	—
510	Dic₈₆	—	2	2	no	—
511	Dic₈₆	—	2	2	no	—
512	Dic₈₆	—	2	2	no	—
513	Dic₈₆	—	2	2	no	—
514	Dic₈₆	—	2	2	no	—
515	Dic₈₆	—	4	4	no	—
516	Dic₈₆	—	8	2	no	—
517	Dic₈₆	—	8	1	no	—
518	Dic₈₆	—	8	1	no	—
519	C₈×C₄₃	—	2	1	no	—
520	C₈×C₄₃	—	2	1	no	—
521	C₈×C₄₃	—	2	1	no	—
522	C₈×C₄₃	C₂×#41	1	2	yes	—
523	C₄₃⋊C₈	—	2	2	no	—
524	C₄₃⋊C₈	—	2	2	no	—
525	#61438	—	43	1	no	maximal, Sylow
526	C₂²×C₄₃	—	2	1	no	—
527	C₂²×C₄₃	—	2	1	no	—
528	C₂²×C₄₃	—	2	2	no	—
529	C₂²×C₄₃	—	4	1	no	—
530	C₂²×C₄₃	—	4	1	no	—
531	C₂²×C₄₃	—	4	1	no	—
532	C₂²×C₄₃	—	4	1	no	—
533	C₂²×C₄₃	—	4	1	no	—
534	C₂²×C₄₃	—	8	4	no	—
535	C₂²×C₄₃	C₂×#137	1	2	yes	—
536	C₂²×C₄₃	C₂³×D₄	1	1	yes	characteristic
537	C₂×D₄₃	—	2	2	no	—
538	C₂×D₄₃	—	2	2	no	—
539	C₂×D₄₃	—	2	2	no	—
540	C₄×C₄₃	—	2	1	no	—
541	C₄×C₄₃	—	2	1	no	—
542	C₄×C₄₃	—	2	2	no	—
543	C₄×C₄₃	—	2	1	no	—
544	C₄×C₄₃	—	4	1	no	—
545	C₄×C₄₃	—	4	1	no	—
546	C₄×C₄₃	—	4	1	no	—
547	C₄×C₄₃	—	4	1	no	—
548	C₄×C₄₃	—	4	1	no	—
549	C₄×C₄₃	C₂×#137	1	2	yes	—
550	C₄×C₄₃	C₂×#137	1	2	yes	—
551	C₄×C₄₃	C₂²×#41	1	1	yes	characteristic
552	C₄×C₄₃	#585	1	1	yes	characteristic
553	Dic₄₃	—	2	2	no	—
554	Dic₄₃	—	2	2	no	—
555	Dic₄₃	—	2	2	no	—
556	Dic₄₃	—	4	2	no	—
557	Dic₄₃	—	4	2	no	—
558	Dic₄₃	—	4	2	no	—
559	Dic₄₃	—	4	2	no	—
560	Q₈×#41	—	43	1	no	—
561	#3475	—	43	1	no	—
562	#3398	—	43	1	no	—
563	#3385	—	43	1	no	—
564	#3372	—	43	1	no	—
565	#3369	—	43	1	no	—
566	#3357	—	43	1	no	—
567	#3344	—	43	2	no	—
568	#3331	—	43	1	no	—
569	#3329	—	43	1	no	—
570	#3314	—	43	2	no	—
571	#3312	—	43	2	no	—
572	#3276	—	43	1	no	—
573	#3266	—	43	2	no	—
574	#3172	—	43	2	no	—
575	#3170	—	43	1	no	—
576	#3108	—	43	2	no	—
577	#3107	—	43	2	no	—
578	#3104	—	43	1	no	—
579	#3101	—	43	1	no	—
580	#2965	—	43	1	no	—
581	C₄×#137	—	43	2	no	—
582	C₂×C₄×SD₁₆	D₄₃	1	1	yes	characteristic, complemented
583	C₂×C₄₃	—	2	2	no	—
584	C₂×C₄₃	—	4	2	no	—
585	C₂×C₄₃	—	8	1	no	—
586	C₂×C₄₃	D₄×#41	1	1	yes	characteristic
587	C₂×C₄₃	C₂²×#137	1	1	yes	characteristic
588	C₂×C₄₃	#3584	1	1	yes	characteristic
589	D₄₃	—	4	2	no	—
590	C₂×#137	—	43	2	no	—
591	C₂²×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
592	Q₈²	—	43	1	no	—
593	#557	—	43	1	no	—
594	#557	—	86	1	no	—
595	#556	—	43	1	no	—
596	#555	—	43	1	no	—
597	#554	—	43	1	no	—
598	#554	—	43	2	no	—
599	#554	—	43	1	no	—
600	#554	—	86	2	no	—
601	#554	—	86	1	no	—
602	#553	—	86	1	no	—
603	#552	—	43	2	no	—
604	#552	—	86	1	no	—
605	#551	—	86	2	no	—
606	D₄×Q₈	—	43	2	no	—
607	D₄×Q₈	—	43	1	no	—
608	#547	—	43	1	no	—
609	#546	—	43	2	no	—
610	#533	—	43	2	no	—
611	#533	—	43	1	no	—
612	#533	—	43	1	no	—
613	#533	—	86	1	no	—
614	#533	—	86	2	no	—
615	#529	—	43	2	no	—
616	#529	—	86	2	no	—
617	#525	—	86	1	no	—
618	C₄×#41	—	43	1	no	—
619	C₄×#41	—	43	2	no	—
620	C₄×#41	—	86	1	no	—
621	C₂×C₄×Q₈	—	43	2	no	—
622	C₂×C₄×Q₈	C₂×D₄₃	1	1	yes	characteristic
623	C₂×C₄×D₄	C₂×D₄₃	1	1	yes	characteristic
624	C₂×#117	—	86	1	no	—
625	#501	—	43	2	no	—
626	#500	—	43	1	no	—
627	#497	—	43	2	no	—
628	#494	—	43	1	no	—
629	#491	—	43	2	no	—
630	#489	—	43	2	no	—
631	#487	—	43	1	no	—
632	#487	—	43	1	no	—
633	#485	—	43	2	no	—
634	#485	—	43	2	no	—
635	#484	—	43	2	no	—
636	#483	—	43	2	no	—
637	#483	—	43	2	no	—
638	#480	—	43	2	no	—
639	#479	—	43	2	no	—
640	#479	—	43	2	no	—
641	#477	—	43	1	no	—
642	#477	—	43	1	no	—
643	#476	—	43	1	no	—
644	#476	—	43	1	no	—
645	#475	—	43	2	no	—
646	#474	—	43	2	no	—
647	#470	—	43	2	no	—
648	#470	—	43	2	no	—
649	#468	—	43	2	no	—
650	#468	—	43	2	no	—
651	#467	—	43	2	no	—
652	#467	—	43	2	no	—
653	#464	—	43	2	no	—
654	#464	—	43	2	no	—
655	#462	—	43	1	no	—
656	#462	—	43	1	no	—
657	#462	—	43	2	no	—
658	#461	—	43	2	no	—
659	#461	—	43	1	no	—
660	#461	—	43	1	no	—
661	#452	—	43	2	no	—
662	#452	—	43	2	no	—
663	#451	—	43	2	no	—
664	#451	—	43	2	no	—
665	#450	—	43	2	no	—
666	#448	—	43	2	no	—
667	#446	—	43	1	no	—
668	#446	—	43	1	no	—
669	#441	—	43	2	no	—
670	#441	—	43	2	no	—
671	#440	—	43	2	no	—
672	#440	—	43	2	no	—
673	C₄×Q₁₆	—	43	2	no	—
674	C₄×Q₁₆	—	43	2	no	—
675	C₄×Q₁₆	—	43	2	no	—
676	C₄×Q₁₆	—	43	2	no	—
677	C₄×SD₁₆	—	43	2	no	—
678	C₄×SD₁₆	—	43	2	no	—
679	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
680	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
681	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
682	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
683	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
684	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
685	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
686	C₄×SD₁₆	C₂×D₄₃	1	1	yes	characteristic
687	#436	—	43	1	no	—
688	#436	—	43	1	no	—
689	#435	—	43	2	no	—
690	#435	—	43	2	no	—
691	#431	—	43	1	no	—
692	#431	—	43	2	no	—
693	#428	—	43	2	no	—
694	C₂×#106	C₂×D₄₃	1	1	yes	characteristic
695	#419	—	43	2	no	—
696	#417	—	43	2	no	—
697	C₂×#103	C₂×D₄₃	1	1	yes	characteristic
698	C₂×#102	C₂×D₄₃	1	1	yes	characteristic
699	C₄×M₁₆	—	43	2	no	—
700	C₂×C₄×C₈	C₂×D₄₃	1	1	yes	characteristic
701	C₄₃	#61438	1	1	yes	characteristic, complemented, Sylow
702	C₂×#41	—	43	1	no	—
703	C₂×#41	—	43	2	no	—
704	C₂²×Q₈	—	43	2	no	—
705	C₂²×Q₈	C₂²×D₄₃	1	1	yes	characteristic
706	C₂²×D₄	C₂²×D₄₃	1	1	yes	characteristic
707	C₂³×C₄	—	2	1	no	—
708	#137	—	86	8	no	—
709	C₂×Q₁₆	—	43	2	no	—
710	C₂×Q₁₆	—	43	2	no	—
711	C₂×Q₁₆	—	43	2	no	—
712	C₂×Q₁₆	—	43	2	no	—
713	C₂×SD₁₆	—	2	4	no	—
714	C₂×SD₁₆	—	43	2	no	—
715	C₂×SD₁₆	—	43	2	no	—
716	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
717	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
718	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
719	C₂×SD₁₆	C₂²×D₄₃	1	1	yes	characteristic
720	C₂×M₁₆	—	43	2	no	—
721	C₂×M₁₆	—	43	2	no	—
722	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
723	C₂²×C₈	C₂²×D₄₃	1	1	yes	characteristic
724	C₄⋊Q₈	—	43	2	no	—
725	C₄⋊Q₈	—	43	2	no	—
726	C₄⋊Q₈	—	43	1	no	—
727	C₄⋊Q₈	—	43	1	no	—
728	C₄⋊Q₈	—	43	1	no	—
729	C₄⋊Q₈	—	43	1	no	—
730	C₄⋊Q₈	—	86	1	no	—
731	C₄⋊Q₈	—	86	1	no	—
732	C₄⋊Q₈	—	86	2	no	—
733	C₄⋊Q₈	—	86	2	no	—
734	#126	—	86	2	no	—
735	#126	—	86	2	no	—
736	#126	—	86	2	no	—
737	#125	—	43	2	no	—
738	#125	—	86	1	no	—
739	#125	—	86	1	no	—
740	#125	—	86	2	no	—
741	#125	—	86	2	no	—
742	#125	—	86	2	no	—
743	#125	—	86	2	no	—
744	#125	—	86	1	no	—
745	#125	—	86	1	no	—
746	#124	—	43	2	no	—
747	#124	—	86	2	no	—
748	#123	—	86	2	no	—
749	#123	—	86	2	no	—
750	#123	—	86	2	no	—
751	#123	—	86	2	no	—
752	C₂²⋊Q₈	—	43	2	no	—
753	C₂²⋊Q₈	—	43	2	no	—
754	C₂²⋊Q₈	—	43	2	no	—
755	C₂²⋊Q₈	—	43	2	no	—
756	C₂²⋊Q₈	—	43	2	no	—
757	C₂²⋊Q₈	—	86	2	no	—
758	C₂²⋊Q₈	—	86	2	no	—
759	C₂²⋊Q₈	—	86	2	no	—
760	C₂²⋊Q₈	—	86	2	no	—
761	C₂²⋊Q₈	—	86	2	no	—
762	C₂²⋊Q₈	—	86	2	no	—
763	C₂²⋊Q₈	—	86	2	no	—
764	C₂²⋊Q₈	—	86	2	no	—
765	C₂²⋊Q₈	—	86	1	no	—
766	C₂²⋊Q₈	—	86	1	no	—
767	C₂²⋊Q₈	—	86	1	no	—
768	C₂²⋊Q₈	—	86	1	no	—
769	#121	—	43	2	no	—
770	#121	—	86	2	no	—
771	#121	—	86	1	no	—
772	#121	—	86	1	no	—
773	#120	—	86	2	no	—
774	C₄×Q₈	—	2	1	no	—
775	C₄×Q₈	—	2	1	no	—
776	C₄×Q₈	—	43	1	no	—
777	C₄×Q₈	—	43	1	no	—
778	C₄×Q₈	—	43	2	no	—
779	C₄×Q₈	—	43	2	no	—
780	C₄×Q₈	—	43	2	no	—
781	C₄×Q₈	—	43	2	no	—
782	C₄×Q₈	—	43	2	no	—
783	C₄×Q₈	—	86	2	no	—
784	C₄×Q₈	—	86	2	no	—
785	C₄×Q₈	—	86	1	no	—
786	C₄×Q₈	—	86	1	no	—
787	C₄×Q₈	—	86	2	no	—
788	C₄×Q₈	—	86	1	no	—
789	C₄×Q₈	—	86	1	no	—
790	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
791	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
792	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
793	C₄×Q₈	C₂²×D₄₃	1	1	yes	characteristic
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	1	no	—
796	C₄×D₄	—	43	2	no	—
797	C₄×D₄	—	43	2	no	—
798	C₄×D₄	—	43	2	no	—
799	C₄×D₄	—	43	1	no	—
800	C₄×D₄	—	43	1	no	—
801	C₄×D₄	—	86	1	no	—
802	C₄×D₄	—	86	1	no	—
803	C₄×D₄	—	86	2	no	—
804	C₄×D₄	—	86	2	no	—
805	C₄×D₄	—	86	2	no	—
806	C₄×D₄	—	86	2	no	—
807	C₄×D₄	—	86	2	no	—
808	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
809	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
810	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
811	C₄×D₄	C₂²×D₄₃	1	1	yes	characteristic
812	#117	—	43	1	no	—
813	#117	—	43	2	no	—
814	#117	—	43	2	no	—
815	#117	—	86	2	no	—
816	#117	—	86	2	no	—
817	#117	—	86	2	no	—
818	#117	—	86	2	no	—
819	#117	—	86	1	no	—
820	#117	—	86	1	no	—
821	#117	—	86	1	no	—
822	#117	—	86	1	no	—
823	C₂×C₄⋊C₄	—	2	1	no	—
824	C₂×C₄⋊C₄	—	43	2	no	—
825	C₂×C₄⋊C₄	—	86	2	no	—
826	C₂×C₄⋊C₄	—	86	1	no	—
827	C₂×C₄⋊C₄	—	86	1	no	—
828	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
829	C₂×C₄⋊C₄	C₂²×D₄₃	1	1	yes	characteristic
830	C₂×C₂²⋊C₄	—	2	1	no	—
831	C₂×C₂²⋊C₄	—	86	2	no	—
832	C₂×C₄²	—	2	1	no	—
833	C₂×C₄²	—	43	2	no	—
834	C₂×C₄²	—	86	2	no	—
835	C₂×C₄²	—	86	2	no	—
836	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
837	#107	—	43	2	no	—
838	#107	—	43	2	no	—
839	#107	—	43	2	no	—
840	#107	—	43	2	no	—
841	#106	—	43	2	no	—
842	#106	—	43	2	no	—
843	#106	C₂²×D₄₃	1	1	yes	characteristic
844	#106	C₂²×D₄₃	1	1	yes	characteristic
845	#106	C₂²×D₄₃	1	1	yes	characteristic
846	#106	C₂²×D₄₃	1	1	yes	characteristic
847	C₄⋊C₈	—	43	2	no	—
848	C₄⋊C₈	—	43	2	no	—
849	C₄⋊C₈	—	43	1	no	—
850	C₄⋊C₈	—	43	1	no	—
851	#103	—	43	2	no	—
852	#103	—	43	2	no	—
853	#103	—	43	2	no	—
854	#103	—	43	2	no	—
855	#103	—	43	2	no	—
856	#103	—	43	2	no	—
857	#103	—	43	2	no	—
858	#103	—	43	2	no	—
859	#103	—	43	2	no	—
860	#103	—	43	2	no	—
861	#103	C₂²×D₄₃	1	1	yes	characteristic
862	#103	C₂²×D₄₃	1	1	yes	characteristic
863	#103	C₂²×D₄₃	1	1	yes	characteristic
864	#103	C₂²×D₄₃	1	1	yes	characteristic
865	#102	—	43	2	no	—
866	#102	—	43	2	no	—
867	#102	C₂²×D₄₃	1	1	yes	characteristic
868	#102	C₂²×D₄₃	1	1	yes	characteristic
869	#102	C₂²×D₄₃	1	1	yes	characteristic
870	#102	C₂²×D₄₃	1	1	yes	characteristic
871	C₂²⋊C₈	—	43	2	no	—
872	C₂²⋊C₈	—	43	2	no	—
873	C₂²⋊C₈	—	43	2	no	—
874	#97	—	43	2	no	—
875	#97	—	43	2	no	—
876	C₄×C₈	—	43	2	no	—
877	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
878	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
879	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
880	C₄×C₈	C₂²×D₄₃	1	1	yes	characteristic
881	C₂⁴	—	2	1	no	—
882	#41	—	86	4	no	—
883	#41	—	86	4	no	—
884	#41	—	172	2	no	—
885	C₂×Q₈	—	2	1	no	—
886	C₂×Q₈	—	2	2	no	—
887	C₂×Q₈	—	4	1	no	—
888	C₂×Q₈	—	43	1	no	—
889	C₂×Q₈	—	43	2	no	—
890	C₂×Q₈	—	43	2	no	—
891	C₂×Q₈	—	86	2	no	—
892	C₂×Q₈	—	86	2	no	—
893	C₂×Q₈	—	86	1	no	—
894	C₂×Q₈	—	86	1	no	—
895	C₂×Q₈	—	86	4	no	—
896	C₂×Q₈	—	172	2	no	—
897	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
898	C₂×Q₈	C₂³×D₄₃	1	1	yes	characteristic
899	C₂×D₄	—	2	2	no	—
900	C₂×D₄	—	2	1	no	—
901	C₂×D₄	—	4	1	no	—
902	C₂×D₄	—	43	2	no	—
903	C₂×D₄	—	43	1	no	—
904	C₂×D₄	—	86	2	no	—
905	C₂×D₄	—	86	2	no	—
906	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
907	C₂×D₄	C₂³×D₄₃	1	1	yes	characteristic
908	C₂²×C₄	—	2	1	no	—
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	1	no	—
915	C₂²×C₄	—	4	4	no	—
916	C₂²×C₄	—	43	2	no	—
917	C₂²×C₄	—	43	2	no	—
918	C₂²×C₄	—	43	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	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
924	C₂²×C₄	D₄×D₄₃	1	1	yes	characteristic
925	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
926	Q₁₆	—	86	4	no	—
927	Q₁₆	—	86	4	no	—
928	Q₁₆	—	172	2	no	—
929	Q₁₆	—	172	2	no	—
930	SD₁₆	—	2	2	no	—
931	SD₁₆	—	2	2	no	—
932	SD₁₆	—	2	2	no	—
933	SD₁₆	—	86	4	no	—
934	SD₁₆	—	172	2	no	—
935	SD₁₆	#10621898	1	4	yes	complemented
936	M₁₆	—	86	4	no	—
937	M₁₆	—	172	2	no	—
938	C₂×C₈	—	2	2	no	—
939	C₂×C₈	—	4	1	no	—
940	C₂×C₈	—	43	2	no	—
941	C₂×C₈	—	43	2	no	—
942	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
943	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
944	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
945	C₂×C₈	C₂³×D₄₃	1	1	yes	characteristic
946	C₄⋊C₄	—	2	1	no	—
947	C₄⋊C₄	—	2	1	no	—
948	C₄⋊C₄	—	2	1	no	—
949	C₄⋊C₄	—	2	1	no	—
950	C₄⋊C₄	—	2	1	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	43	1	no	—
953	C₄⋊C₄	—	43	1	no	—
954	C₄⋊C₄	—	43	2	no	—
955	C₄⋊C₄	—	43	2	no	—
956	C₄⋊C₄	—	43	2	no	—
957	C₄⋊C₄	—	43	2	no	—
958	C₄⋊C₄	—	86	2	no	—
959	C₄⋊C₄	—	86	2	no	—
960	C₄⋊C₄	—	86	2	no	—
961	C₄⋊C₄	—	86	2	no	—
962	C₄⋊C₄	—	86	2	no	—
963	C₄⋊C₄	—	86	2	no	—
964	C₄⋊C₄	—	86	2	no	—
965	C₄⋊C₄	—	86	2	no	—
966	C₄⋊C₄	—	86	2	no	—
967	C₄⋊C₄	—	86	2	no	—
968	C₄⋊C₄	—	86	2	no	—
969	C₄⋊C₄	—	86	2	no	—
970	C₄⋊C₄	—	86	1	no	—
971	C₄⋊C₄	—	86	1	no	—
972	C₄⋊C₄	—	86	2	no	—
973	C₄⋊C₄	—	86	2	no	—
974	C₄⋊C₄	—	86	1	no	—
975	C₄⋊C₄	—	86	1	no	—
976	C₄⋊C₄	—	86	2	no	—
977	C₄⋊C₄	—	86	2	no	—
978	C₄⋊C₄	—	86	1	no	—
979	C₄⋊C₄	—	86	1	no	—
980	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
981	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
982	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
983	C₄⋊C₄	C₂³×D₄₃	1	1	yes	characteristic
984	C₂²⋊C₄	—	2	1	no	—
985	C₂²⋊C₄	—	2	1	no	—
986	C₂²⋊C₄	—	2	1	no	—
987	C₂²⋊C₄	—	2	1	no	—
988	C₂²⋊C₄	—	43	2	no	—
989	C₂²⋊C₄	—	43	2	no	—
990	C₂²⋊C₄	—	43	2	no	—
991	C₂²⋊C₄	—	86	2	no	—
992	C₂²⋊C₄	—	86	2	no	—
993	C₂²⋊C₄	—	86	2	no	—
994	C₂²⋊C₄	—	86	2	no	—
995	C₂²⋊C₄	—	86	2	no	—
996	C₂²⋊C₄	—	86	2	no	—
997	C₂²⋊C₄	—	86	2	no	—
998	C₂²⋊C₄	—	86	2	no	—
999	C₂²⋊C₄	—	86	2	no	—
1000	C₂²⋊C₄	—	86	2	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	1	no	—
1003	C₄²	—	2	1	no	—
1004	C₄²	—	2	1	no	—
1005	C₄²	—	43	2	no	—
1006	C₄²	—	43	2	no	—
1007	C₄²	—	43	2	no	—
1008	C₄²	—	86	2	no	—
1009	C₄²	—	86	2	no	—
1010	C₄²	—	86	2	no	—
1011	C₄²	—	86	2	no	—
1012	C₄²	—	86	2	no	—
1013	C₄²	—	86	2	no	—
1014	C₄²	D₄×D₄₃	1	1	yes	characteristic
1015	C₄²	D₄×D₄₃	1	1	yes	characteristic
1016	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1017	C₄²	C₂³×D₄₃	1	1	yes	characteristic
1018	C₂³	—	2	1	no	—
1019	C₂³	—	2	1	no	—
1020	C₂³	—	4	2	no	—
1021	C₂³	—	4	2	no	—
1022	C₂³	—	8	1	no	—
1023	C₂³	—	43	2	no	—
1024	C₂³	C₂×D₄×D₄₃	1	1	yes	characteristic
1025	Q₈	—	2	1	no	—
1026	Q₈	—	2	1	no	—
1027	Q₈	—	2	1	no	—
1028	Q₈	—	4	2	no	—
1029	Q₈	—	86	2	no	—
1030	Q₈	—	86	2	no	—
1031	Q₈	—	86	2	no	—
1032	Q₈	—	86	2	no	—
1033	Q₈	—	86	2	no	—
1034	Q₈	—	344	1	no	—
1035	Q₈	—	344	1	no	—
1036	Q₈	—	344	2	no	—
1037	Q₈	—	172	4	no	—
1038	Q₈	C₂×#10621898	1	2	yes	—
1039	D₄	—	2	1	no	—
1040	D₄	—	2	1	no	—
1041	D₄	—	2	1	no	—
1042	D₄	—	4	2	no	—
1043	D₄	—	86	4	no	—
1044	D₄	—	86	2	no	—
1045	D₄	—	344	2	no	—
1046	D₄	—	172	4	no	—
1047	D₄	C₂×#10621898	1	2	yes	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	1	no	—
1053	C₂×C₄	—	2	1	no	—
1054	C₂×C₄	—	2	1	no	—
1055	C₂×C₄	—	2	1	no	—
1056	C₂×C₄	—	4	1	no	—
1057	C₂×C₄	—	4	2	no	—
1058	C₂×C₄	—	4	2	no	—
1059	C₂×C₄	—	4	2	no	—
1060	C₂×C₄	—	4	2	no	—
1061	C₂×C₄	—	4	2	no	—
1062	C₂×C₄	—	4	2	no	—
1063	C₂×C₄	—	8	1	no	—
1064	C₂×C₄	—	43	2	no	—
1065	C₂×C₄	—	43	2	no	—
1066	C₂×C₄	—	43	2	no	—
1067	C₂×C₄	—	86	4	no	—
1068	C₂×C₄	—	86	2	no	—
1069	C₂×C₄	—	86	2	no	—
1070	C₂×C₄	—	86	2	no	—
1071	C₂×C₄	—	86	2	no	—
1072	C₂×C₄	—	86	2	no	—
1073	C₂×C₄	—	86	2	no	—
1074	C₂×C₄	—	344	2	no	—
1075	C₂×C₄	—	344	2	no	—
1076	C₂×C₄	—	172	2	no	—
1077	C₂×C₄	—	172	4	no	—
1078	C₂×C₄	—	172	4	no	—
1079	C₂×C₄	#13063354	1	4	yes	complemented
1080	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1081	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1082	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1083	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1084	C₂×C₄	C₂×D₄×D₄₃	1	1	yes	characteristic
1085	C₂×C₄	C₂⁴×D₄₃	1	1	yes	characteristic
1086	C₈	—	2	1	no	—
1087	C₈	—	2	1	no	—
1088	C₈	—	2	1	no	—
1089	C₈	—	86	2	no	—
1090	C₈	—	86	2	no	—
1091	C₈	C₂×#10621898	1	2	yes	—
1092	C₂²	—	2	1	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	2	no	—
1095	C₂²	—	4	1	no	—
1096	C₂²	—	4	1	no	—
1097	C₂²	—	4	1	no	—
1098	C₂²	—	4	1	no	—
1099	C₂²	—	4	1	no	—
1100	C₂²	—	8	4	no	—
1101	C₂²	—	86	2	no	—
1102	C₂²	—	86	2	no	—
1103	C₂²	—	86	2	no	—
1104	C₂²	C₂×#13063354	1	2	yes	—
1105	C₂²	C₂²×D₄×D₄₃	1	1	yes	characteristic
1106	C₄	—	2	1	no	—
1107	C₄	—	2	2	no	—
1108	C₄	—	2	1	no	—
1109	C₄	—	2	1	no	—
1110	C₄	—	4	1	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	1	no	—
1113	C₄	—	4	1	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	86	2	no	—
1116	C₄	—	86	2	no	—
1117	C₄	—	86	2	no	—
1118	C₄	—	172	2	no	—
1119	C₄	—	172	2	no	—
1120	C₄	—	172	2	no	—
1121	C₄	—	172	2	no	—
1122	C₄	C₂×#13063354	1	2	yes	—
1123	C₄	C₂×#13063354	1	2	yes	—
1124	C₄	C₂²×#10621898	1	1	yes	characteristic
1125	C₄	#14583735	1	1	yes	characteristic
1126	C₂	—	2	2	no	—
1127	C₂	—	4	2	no	—
1128	C₂	—	8	1	no	—
1129	C₂	—	172	2	no	—
1130	C₂	D₄×#10621898	1	1	yes	characteristic
1131	C₂	C₂²×#13063354	1	1	yes	characteristic
1132	C₂	#19149364	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₃
commutator, cosocle	C₂×C₄×C₄₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₃
Fitting	C₂×C₄×SD₁₆×C₄₃	C₂
socle	C₂²×C₄₃	C₂³×D₄
prime radical	#19148153	C₂
hypercenter	C₂×C₄×SD₁₆	D₄₃
hypocenter	C₄₃	#61438
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ C₂×C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
1. Q₈×#10621898	C₂	semidirect
3. #19147624	C₂	semidirect
4. #19147503	C₂	semidirect
5. #19147374	C₂	semidirect
6. #19147333	C₂	semidirect
7. #19147223	C₂	semidirect
8. #19147046	C₂	semidirect
9. #19146913	C₂	semidirect
10. #19146891	C₂	semidirect
11. #19146672	C₂	semidirect
12. #19146642	C₂	semidirect
13. #19146242	C₂	semidirect
14. #19146105	C₂	semidirect
15. #19145197	C₂	semidirect
16. #19145181	C₂	semidirect
17. #19144673	C₂	semidirect
18. #19144662	C₂	semidirect
19. #19144634	C₂	semidirect
20. #19144603	C₂	semidirect
21. #19143561	C₂	semidirect
22. C₄×#13063354	C₂	semidirect
23. C₂×C₄×SD₁₆×C₄₃	C₂	semidirect
25. Q₈×Dic₈₆	C₂²	semidirect
27. #14583627	C₂²	semidirect
31. #14583609	C₂²	semidirect
39. Q₈×D₁₇₂	C₂²	semidirect
47. #14583453	C₂²	semidirect
54. C₄×Q₈×D₄₃	C₂²	semidirect
56. #14583306	C₂²	semidirect
57. #14583304	C₂²	semidirect
59. #14583279	C₂²	semidirect
60. #14583266	C₂²	semidirect
62. #14583250	C₂²	semidirect
63. #14583250	C₂²	semidirect
64. #14583243	C₂²	semidirect
65. #14583239	C₂²	semidirect
67. #14583231	C₂²	semidirect
70. #14583209	C₂²	semidirect
71. #14583208	C₂²	semidirect
72. #14583194	C₂²	semidirect
73. #14583194	C₂²	semidirect
76. #14583183	C₂²	semidirect
78. #14583158	C₂²	semidirect
79. #14583156	C₂²	semidirect
86. #14583109	C₂²	semidirect
87. #14583109	C₂²	semidirect
88. #14583108	C₂²	semidirect
94. #14583056	C₂²	semidirect
98. #14583029	C₂²	semidirect
99. #14583029	C₂²	semidirect
100. #14583005	C₂²	semidirect
101. #14583003	C₂²	semidirect
104. C₄×Dic₁₇₂	C₂²	semidirect
105. C₄×Dic₁₇₂	C₂²	semidirect
106. C₄×#10621885	C₂²	semidirect
107. C₄×#10621885	C₂²	semidirect
110. #14582978	C₂²	semidirect
111. #14582978	C₂²	semidirect
115. #14582950	C₂²	semidirect
116. #14582938	C₂²	semidirect
117. #14582906	C₂²	semidirect
119. C₄×#10621872	C₂²	semidirect
362. SD₁₆×C₄₃	#41	semidirect
484. C₂×C₄×C₄₃	#137	semidirect
582. C₂×C₄×SD₁₆	D₄₃	semidirect
701. C₄₃	#61438	semidirect
935. SD₁₆	#10621898	semidirect
1079. C₂×C₄	#13063354	semidirect

Maximal subgroups

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

subgroup	index
Q₈×#10621898	2
#19148153	2
#19147624	2
#19147503	2
#19147374	2
#19147333	2
#19147223	2
#19147046	2
#19146913	2
#19146891	2
#19146672	2
#19146642	2
#19146242	2
#19146105	2
#19145197	2
#19145181	2
#19144673	2
#19144662	2
#19144634	2
#19144603	2
#19143561	2
C₄×#13063354	2
C₂×C₄×SD₁₆×C₄₃	2
#61438	43