Subgroups — #27109530

Order 12032.

1868 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257351	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256983	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256398	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256382	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256082	C₂	1	1	yes	maximal, characteristic, complemented
6	#20256071	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255673	C₂	1	1	yes	maximal, characteristic, complemented
8	#20255644	C₂	1	2	yes	maximal, complemented
9	#20255621	C₂	1	1	yes	maximal, characteristic, complemented
10	#20255592	C₂	1	2	yes	maximal, complemented
11	#20255055	C₂	1	1	yes	maximal, characteristic, complemented
12	#20255045	C₂	1	2	yes	maximal, complemented
13	#20255022	C₂	1	2	yes	maximal, complemented
14	#20255009	C₂	1	1	yes	maximal, characteristic, complemented
15	#20254791	C₂	1	2	yes	maximal, complemented
16	#20254750	C₂	1	1	yes	maximal, characteristic, complemented
17	#20254357	C₂	1	2	yes	maximal, complemented
18	#20254323	C₂	1	1	yes	maximal, characteristic, complemented
19	#20253413	C₂	1	2	yes	maximal, complemented
20	#20252879	C₂	1	2	yes	maximal, complemented
21	#20252860	C₂	1	1	yes	maximal, characteristic, complemented
22	#20252517	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3108	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094056	C₂²	1	2	yes	complemented
25	C₂×#13094055	C₂²	1	2	yes	complemented
26	C₂×#13094051	C₂²	1	2	yes	—
27	#15689858	—	2	1	no	—
28	#15689858	C₂²	1	1	yes	characteristic
29	#15689858	C₂²	1	1	yes	characteristic, complemented
30	#15689852	C₂²	1	1	yes	characteristic, complemented
31	#15689846	—	2	1	no	—
32	#15689846	C₂²	1	1	yes	characteristic
33	#15689843	C₂²	1	1	yes	characteristic
34	#15689838	—	2	1	no	—
35	#15689821	—	2	2	no	—
36	#15689821	C₂²	1	2	yes	complemented
37	#15689798	—	2	2	no	—
38	#15689795	C₂²	1	1	yes	characteristic
39	Q₈×D₁₈₈	C₂²	1	1	yes	characteristic
40	#15689784	C₂²	1	2	yes	complemented
41	#15689783	C₂²	1	2	yes	—
42	#15689770	C₂²	1	2	yes	—
43	#15689769	—	2	1	no	—
44	D₄×D₁₈₈	C₂²	1	1	yes	characteristic
45	#15689744	—	2	1	no	—
46	#15689709	—	2	2	no	—
47	#15689673	—	2	1	no	—
48	#15689673	C₂²	1	1	yes	characteristic
49	#15689673	C₂²	1	1	yes	characteristic, complemented
50	#15689660	—	2	2	no	—
51	#15689660	C₂²	1	2	yes	complemented
52	#15689658	C₂²	1	2	yes	—
53	#124×D₄₇	C₂²	1	2	yes	—
54	#15689597	—	2	1	no	—
55	C₄×#10625354	C₂²	1	2	yes	complemented
56	C₄×#10625350	—	2	1	no	—
57	C₄×#10625350	C₂²	1	1	yes	characteristic
58	#15689508	C₂²	1	2	yes	complemented
59	#15689504	C₂²	1	2	yes	—
60	#15689500	C₂²	1	1	yes	characteristic
61	#15689496	C₂²	1	1	yes	characteristic, complemented
62	#15689479	C₂²	1	2	yes	complemented
63	#15689476	C₂²	1	2	yes	—
64	#15689474	C₂²	1	1	yes	characteristic, complemented
65	#15689470	C₂²	1	1	yes	characteristic
66	#15689466	C₂²	1	2	yes	complemented
67	#15689449	C₂²	1	2	yes	—
68	#15689433	C₂²	1	2	yes	complemented
69	#15689426	C₂²	1	2	yes	complemented
70	#15689420	C₂²	1	2	yes	complemented
71	#15689408	C₂²	1	1	yes	characteristic, complemented
72	#15689403	C₂²	1	1	yes	characteristic
73	#15689380	C₂²	1	2	yes	complemented
74	#15689377	C₂²	1	2	yes	—
75	#15689374	C₂²	1	2	yes	—
76	#15689372	C₂²	1	2	yes	—
77	#15689371	C₂²	1	2	yes	complemented
78	#15689370	C₂²	1	2	yes	complemented
79	#15689348	C₂²	1	2	yes	complemented
80	#15689347	C₂²	1	2	yes	complemented
81	#15689345	C₂²	1	2	yes	complemented
82	#15689345	C₂²	1	2	yes	complemented
83	#15689343	C₂²	1	2	yes	—
84	#15689341	C₂²	1	2	yes	complemented
85	#15689341	C₂²	1	2	yes	complemented
86	#15689339	C₂²	1	2	yes	complemented
87	#15689339	C₂²	1	2	yes	complemented
88	#15689337	C₂²	1	2	yes	—
89	#15689335	C₂²	1	2	yes	—
90	#15689333	C₂²	1	1	yes	characteristic, complemented
91	#15689333	C₂²	1	1	yes	characteristic, complemented
92	#15689323	C₂²	1	1	yes	characteristic
93	#15689323	C₂²	1	1	yes	characteristic
94	#15689323	C₂²	1	1	yes	characteristic, complemented
95	#15689318	C₂²	1	1	yes	characteristic
96	#15689288	C₂²	1	2	yes	complemented
97	#15689277	C₂²	1	2	yes	complemented
98	#15689272	C₂²	1	2	yes	—
99	#15689271	C₂²	1	2	yes	—
100	#15689270	C₂²	1	2	yes	complemented
101	#15689270	C₂²	1	2	yes	complemented
102	#15689263	C₂²	1	2	yes	complemented
103	#15689258	C₂²	1	2	yes	—
104	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
105	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
106	#15689215	C₂²	1	2	yes	complemented
107	#15689210	C₂²	1	2	yes	complemented
108	#15689208	C₂²	1	2	yes	complemented
109	#15689205	C₂²	1	2	yes	complemented
110	#15689202	C₂²	1	1	yes	characteristic
111	#15689202	C₂²	1	1	yes	characteristic
112	#15689198	C₂²	1	2	yes	complemented
113	#15689198	C₂²	1	2	yes	complemented
114	#15689175	C₂²	1	2	yes	complemented
115	#15689147	C₂²	1	1	yes	characteristic, complemented
116	#15689145	C₂²	1	2	yes	complemented
117	#15689130	C₂²	1	2	yes	complemented
118	#15689126	C₂²	1	2	yes	—
119	#15689122	C₂²	1	2	yes	complemented
120	C₄₇×#529	C₂²	1	1	yes	characteristic
121	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
122	C₄₇×#483	C₂²	1	1	yes	characteristic, complemented
123	C₄₇×#480	C₂²	1	1	yes	characteristic
124	C₄₇×#479	C₂²	1	1	yes	characteristic, complemented
125	C₄₇×#479	C₂²	1	1	yes	characteristic, complemented
126	C₄₇×#464	C₂²	1	1	yes	characteristic
127	C₄₇×#464	C₂²	1	1	yes	characteristic
128	C₄₇×#451	C₂²	1	1	yes	characteristic, complemented
129	C₄₇×#448	C₂²	1	1	yes	characteristic
130	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
131	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
132	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
133	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
134	C₄₇×#431	C₂²	1	1	yes	characteristic, complemented
135	C₂×#10625354	C₂³	1	2	yes	—
136	C₂×#10625350	—	2	1	no	—
137	C₂×#10625350	D₄	1	1	yes	characteristic
138	C₂×#10625350	C₂³	1	2	yes	—
139	C₂×Q₈×D₄₇	C₂³	1	2	yes	—
140	C₂²×D₁₈₈	—	2	1	no	—
141	C₂×D₄×D₄₇	C₂³	1	2	yes	—
142	#13094056	—	4	4	no	—
143	#13094055	—	4	4	no	—
144	#13094051	—	4	4	no	—
145	C₂×#10625337	C₂³	1	2	yes	—
146	C₂×#10625337	C₂³	1	2	yes	—
147	C₂×#10625325	C₂³	1	2	yes	—
148	C₂×#10625325	C₂³	1	2	yes	—
149	C₂×#10625336	C₂³	1	2	yes	—
150	C₂×#10625336	C₂³	1	2	yes	—
151	C₂×#10625336	C₂³	1	2	yes	—
152	C₂×D₃₇₆	C₂³	1	2	yes	—
153	C₂×D₃₇₆	C₂³	1	2	yes	—
154	C₂×#10625334	C₂³	1	2	yes	—
155	C₂×#10625329	C₂³	1	2	yes	—
156	C₂×#10625324	C₂³	1	2	yes	—
157	C₂×#10625324	C₂³	1	2	yes	—
158	#13094024	—	2	1	no	—
159	#13094024	—	2	1	no	—
160	#13094024	C₂³	1	1	yes	characteristic
161	#13094024	C₂³	1	1	yes	characteristic
162	#13094021	—	2	1	no	—
163	#13094021	C₂³	1	1	yes	characteristic
164	#13094021	C₂³	1	1	yes	characteristic
165	#13094019	—	2	2	no	—
166	#13094019	—	2	2	no	—
167	#13094019	—	2	2	no	—
168	#13094019	—	2	2	no	—
169	#13094017	—	2	2	no	—
170	#13094015	—	2	2	no	—
171	#13094015	C₂³	1	2	yes	—
172	#13094013	—	2	2	no	—
173	#13094013	C₂³	1	2	yes	—
174	#13094013	C₂³	1	2	yes	—
175	#13094012	—	2	1	no	—
176	#13094012	—	2	1	no	—
177	#13094012	—	2	1	no	—
178	#13094012	—	2	1	no	—
179	#13094012	C₂³	1	2	yes	—
180	#13094011	C₂³	1	2	yes	—
181	#13094010	—	2	2	no	—
182	#13094010	—	2	2	no	—
183	#13094010	—	2	2	no	—
184	#13094009	—	2	2	no	—
185	#13094009	—	2	2	no	—
186	#13094009	—	2	2	no	—
187	#13094009	—	2	2	no	—
188	#13094009	—	2	2	no	—
189	#13094006	—	2	2	no	—
190	#13094004	—	2	2	no	—
191	#13094004	C₂³	1	2	yes	—
192	#13094003	—	2	1	no	—
193	#13094002	—	2	2	no	—
194	#13094000	—	2	2	no	—
195	#13094000	C₂³	1	2	yes	—
196	#13093999	—	2	2	no	—
197	#13093999	C₂³	1	2	yes	—
198	#13093999	C₂³	1	2	yes	—
199	#13093998	—	2	1	no	—
200	#13093998	—	2	1	no	—
201	#13093998	—	2	1	no	—
202	#13093998	—	2	2	no	—
203	#13093998	—	2	2	no	—
204	#13093998	—	2	1	no	—
205	#13093998	C₂³	1	2	yes	—
206	#13093997	—	2	2	no	—
207	#13093995	—	2	2	no	—
208	#13093994	—	2	2	no	—
209	#13093992	—	2	2	no	—
210	Q₈×Dic₄₇	C₂³	1	2	yes	—
211	C₄×Dic₉₄	—	2	1	no	—
212	C₄×Dic₉₄	—	2	1	no	—
213	C₄×Dic₉₄	D₄	1	1	yes	characteristic
214	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
215	#13093989	C₂³	1	2	yes	—
216	C₄×D₁₈₈	—	2	1	no	—
217	C₄×D₁₈₈	—	2	2	no	—
218	C₄×D₁₈₈	—	2	2	no	—
219	C₄×D₁₈₈	—	2	1	no	—
220	C₄×D₁₈₈	—	2	1	no	—
221	C₄×D₁₈₈	—	2	1	no	—
222	C₄×D₁₈₈	—	2	1	no	—
223	C₄×D₁₈₈	—	2	1	no	—
224	C₄×D₁₈₈	—	2	1	no	—
225	C₄×D₁₈₈	D₄	1	1	yes	characteristic
226	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
227	C₄×D₁₈₈	C₂³	1	2	yes	—
228	#13093986	—	2	2	no	—
229	#13093986	—	2	2	no	—
230	#13093986	—	2	2	no	—
231	#13093986	C₂³	1	2	yes	—
232	#13093986	C₂³	1	2	yes	—
233	C₄×C₂²⋊D₄₇	—	2	2	no	—
234	C₄×C₂²⋊D₄₇	—	2	2	no	—
235	C₄×C₂²⋊D₄₇	D₄	1	2	yes	—
236	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
237	#13093983	—	2	1	no	—
238	#13093983	D₄	1	1	yes	characteristic
239	#13093982	—	2	2	no	—
240	#13093982	—	2	2	no	—
241	#13093982	C₂³	1	2	yes	—
242	#13093981	—	2	2	no	—
243	#13093981	D₄	1	2	yes	—
244	C₂²⋊C₄×D₄₇	—	2	2	no	—
245	C₂²⋊C₄×D₄₇	—	2	2	no	—
246	C₂²⋊C₄×D₄₇	—	2	2	no	—
247	C₄²×D₄₇	—	2	2	no	—
248	C₄²×D₄₇	C₂³	1	2	yes	—
249	#13093957	C₂³	1	2	yes	—
250	#13093955	C₂³	1	2	yes	—
251	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
252	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
253	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
254	Dic₄₇⋊C₈	C₂³	1	2	yes	—
255	Dic₄₇⋊C₈	C₂³	1	2	yes	—
256	#13093949	C₂³	1	2	yes	—
257	#13093949	C₂³	1	2	yes	—
258	#13093948	C₂³	1	2	yes	—
259	#13093947	C₂³	1	2	yes	—
260	#13093947	C₂³	1	2	yes	—
261	#13093946	C₂³	1	2	yes	—
262	#13093946	C₂³	1	2	yes	—
263	#13093945	C₂³	1	2	yes	—
264	#13093944	C₂³	1	2	yes	—
265	#13093944	C₂³	1	2	yes	—
266	#13093944	C₂³	1	2	yes	—
267	#13093944	C₂³	1	2	yes	—
268	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
269	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
270	C₈×Dic₄₇	C₂³	1	2	yes	—
271	C₈×Dic₄₇	C₂³	1	2	yes	—
272	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
273	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
274	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
275	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
276	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
277	#126×C₄₇	—	2	1	no	—
278	#125×C₄₇	C₂³	1	1	yes	characteristic
279	#124×C₄₇	C₂³	1	1	yes	characteristic
280	#123×C₄₇	—	2	1	no	—
281	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
282	#121×C₄₇	C₂³	1	1	yes	characteristic
283	C₄×Q₈×C₄₇	—	2	1	no	—
284	C₄×Q₈×C₄₇	—	2	1	no	—
285	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
286	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
287	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
288	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
289	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₄₇	—	2	1	no	—
291	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
292	#117×C₄₇	—	2	1	no	—
293	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
294	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₄₇	—	2	1	no	—
296	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
297	#107×C₄₇	C₂³	1	1	yes	characteristic
298	#107×C₄₇	C₂³	1	1	yes	characteristic
299	#106×C₄₇	C₂³	1	1	yes	characteristic
300	#106×C₄₇	C₂³	1	1	yes	characteristic
301	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
302	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
303	#103×C₄₇	C₂³	1	1	yes	characteristic
304	#103×C₄₇	C₂³	1	1	yes	characteristic
305	#103×C₄₇	C₂³	1	1	yes	characteristic
306	#103×C₄₇	C₂³	1	1	yes	characteristic
307	#103×C₄₇	C₂³	1	1	yes	characteristic
308	#103×C₄₇	C₂³	1	1	yes	characteristic
309	#102×C₄₇	C₂³	1	1	yes	characteristic
310	#102×C₄₇	C₂³	1	1	yes	characteristic
311	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
312	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
314	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
315	C₂³×D₄₇	—	2	2	no	—
316	C₂×Q₈×C₄₇	—	2	1	no	—
317	C₂×Q₈×C₄₇	—	2	2	no	—
318	C₂×Q₈×C₄₇	—	4	1	no	—
319	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
320	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
321	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
322	C₂×D₄×C₄₇	—	2	1	no	—
323	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
324	C₂²×C₄×C₄₇	—	2	1	no	—
325	C₂²×C₄×C₄₇	—	2	1	no	—
326	C₂²×C₄×C₄₇	—	2	1	no	—
327	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
328	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
329	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
330	C₂×C₂²⋊D₄₇	—	2	2	no	—
331	C₂×C₂²⋊D₄₇	—	2	2	no	—
332	C₂×C₂²⋊D₄₇	—	2	2	no	—
333	C₂×C₂²⋊D₄₇	C₂×D₄	1	2	yes	—
334	#10625354	—	2	4	no	—
335	#10625354	—	4	2	no	—
336	Q₈×D₄₇	—	4	2	no	—
337	Q₈×D₄₇	—	4	2	no	—
338	D₄×D₄₇	—	4	2	no	—
339	D₄×D₄₇	—	4	2	no	—
340	#10625350	—	4	2	no	—
341	#10625350	—	4	2	no	—
342	#10625350	—	4	2	no	—
343	#10625350	—	4	4	no	—
344	C₂×D₁₈₈	—	2	2	no	—
345	C₂×D₁₈₈	—	2	2	no	—
346	C₂×D₁₈₈	—	2	1	no	—
347	C₂×D₁₈₈	—	2	1	no	—
348	C₂×D₁₈₈	—	2	2	no	—
349	C₂×D₁₈₈	—	2	1	no	—
350	C₂×D₁₈₈	—	2	1	no	—
351	C₂×D₁₈₈	—	4	4	no	—
352	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
353	C₂×D₁₈₈	C₂⁴	1	2	yes	—
354	C₂×D₁₈₈	C₂⁴	1	2	yes	—
355	C₂×C₄×D₄₇	—	2	2	no	—
356	C₂×C₄×D₄₇	—	2	2	no	—
357	C₂×C₄×D₄₇	—	2	2	no	—
358	C₂×C₄×D₄₇	—	2	2	no	—
359	C₂×C₄×D₄₇	—	2	2	no	—
360	C₂×C₄×D₄₇	—	2	2	no	—
361	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
362	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
363	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
364	C₂×Dic₉₄	—	2	1	no	—
365	C₂×Dic₉₄	—	2	2	no	—
366	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
367	C₂×Dic₉₄	C₂⁴	1	2	yes	—
368	Q₁₆×C₄₇	—	2	2	no	—
369	Q₁₆×C₄₇	—	4	1	no	—
370	SD₁₆×C₄₇	—	2	2	no	—
371	SD₁₆×C₄₇	—	4	1	no	—
372	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
373	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
374	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
375	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
376	C₄⋊C₄×C₄₇	—	2	1	no	—
377	C₄⋊C₄×C₄₇	—	2	1	no	—
378	C₄⋊C₄×C₄₇	—	2	1	no	—
379	C₄⋊C₄×C₄₇	—	2	1	no	—
380	C₄⋊C₄×C₄₇	—	2	1	no	—
381	C₄⋊C₄×C₄₇	—	2	1	no	—
382	C₄⋊C₄×C₄₇	—	2	1	no	—
383	C₄⋊C₄×C₄₇	—	2	1	no	—
384	C₄⋊C₄×C₄₇	—	2	1	no	—
385	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
386	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
387	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
388	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
389	C₂²⋊C₄×C₄₇	—	2	1	no	—
390	C₂²⋊C₄×C₄₇	—	2	1	no	—
391	C₂²⋊C₄×C₄₇	—	2	1	no	—
392	C₂²⋊C₄×C₄₇	—	2	1	no	—
393	C₂²⋊C₄×C₄₇	—	2	1	no	—
394	C₄²×C₄₇	—	2	1	no	—
395	C₄²×C₄₇	—	2	1	no	—
396	C₄²×C₄₇	—	2	1	no	—
397	C₄²×C₄₇	—	2	1	no	—
398	C₄²×C₄₇	—	2	1	no	—
399	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
400	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
402	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
403	C₂²⋊Dic₄₇	—	2	2	no	—
404	C₂²⋊Dic₄₇	—	2	2	no	—
405	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
406	#10625337	—	2	4	no	—
407	#10625337	—	4	2	no	—
408	#10625336	—	2	4	no	—
409	#10625336	—	4	2	no	—
410	#10625336	—	4	2	no	—
411	#10625334	—	4	2	no	—
412	(C₂×D₄₇)⋊C₄	—	2	2	no	—
413	(C₂×D₄₇)⋊C₄	—	2	2	no	—
414	(C₂×D₄₇)⋊C₄	—	2	2	no	—
415	(C₂×D₄₇)⋊C₄	—	2	2	no	—
416	(C₂×D₄₇)⋊C₄	—	2	2	no	—
417	(C₂×D₄₇)⋊C₄	—	2	2	no	—
418	(C₂×D₄₇)⋊C₄	—	2	2	no	—
419	(C₂×D₄₇)⋊C₄	—	2	2	no	—
420	(C₂×D₄₇)⋊C₄	—	2	2	no	—
421	(C₂×D₄₇)⋊C₄	—	2	2	no	—
422	(C₂×D₄₇)⋊C₄	—	2	2	no	—
423	(C₂×D₄₇)⋊C₄	—	2	2	no	—
424	(C₂×D₄₇)⋊C₄	—	2	2	no	—
425	(C₂×D₄₇)⋊C₄	—	2	2	no	—
426	(C₂×D₄₇)⋊C₄	—	2	2	no	—
427	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
428	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
429	C₄⋊Dic₄₇	—	2	1	no	—
430	C₄⋊Dic₄₇	—	2	1	no	—
431	C₄⋊Dic₄₇	—	2	1	no	—
432	C₄⋊Dic₄₇	—	2	2	no	—
433	C₄⋊Dic₄₇	—	2	2	no	—
434	C₄⋊Dic₄₇	—	2	2	no	—
435	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
436	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
437	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
438	Dic₄₇⋊C₄	—	2	2	no	—
439	Dic₄₇⋊C₄	—	2	2	no	—
440	Dic₄₇⋊C₄	—	2	2	no	—
441	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
442	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
443	C₄×Dic₄₇	—	2	2	no	—
444	C₄×Dic₄₇	—	2	2	no	—
445	C₄×Dic₄₇	—	2	2	no	—
446	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
447	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
448	C₄×Dic₄₇	C₂⁴	1	2	yes	—
449	#10625329	—	4	2	no	—
450	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
451	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
452	D₃₇₆	—	4	2	no	—
453	D₃₇₆	—	4	2	no	—
454	#10625325	—	4	2	no	—
455	#10625325	—	4	2	no	—
456	#10625324	—	4	2	no	—
457	#10625324	—	4	2	no	—
458	C₂³×C₄₇	—	2	1	no	—
459	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
460	C₂²×D₄₇	—	2	2	no	—
461	C₂²×D₄₇	—	2	2	no	—
462	C₂²×D₄₇	—	4	4	no	—
463	C₂²×D₄₇	—	8	2	no	—
464	C₂²×D₄₇	—	8	2	no	—
465	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
466	Q₈×C₄₇	—	2	1	no	—
467	Q₈×C₄₇	—	2	1	no	—
468	Q₈×C₄₇	—	2	1	no	—
469	Q₈×C₄₇	—	2	1	no	—
470	Q₈×C₄₇	—	2	1	no	—
471	Q₈×C₄₇	—	4	2	no	—
472	Q₈×C₄₇	H(5,𝔽₂)	1	2	yes	—
473	D₄×C₄₇	—	2	1	no	—
474	D₄×C₄₇	—	2	1	no	—
475	D₄×C₄₇	—	8	1	no	—
476	C₂×C₄×C₄₇	—	2	1	no	—
477	C₂×C₄×C₄₇	—	2	2	no	—
478	C₂×C₄×C₄₇	—	2	1	no	—
479	C₂×C₄×C₄₇	—	2	1	no	—
480	C₂×C₄×C₄₇	—	2	1	no	—
481	C₂×C₄×C₄₇	—	2	1	no	—
482	C₂×C₄×C₄₇	—	2	1	no	—
483	C₂×C₄×C₄₇	—	2	1	no	—
484	C₂×C₄×C₄₇	—	2	1	no	—
485	C₂×C₄×C₄₇	—	2	1	no	—
486	C₂×C₄×C₄₇	—	4	1	no	—
487	C₂×C₄×C₄₇	—	4	2	no	—
488	C₂×C₄×C₄₇	—	4	2	no	—
489	C₂×C₄×C₄₇	—	8	1	no	—
490	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
492	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
493	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
494	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
495	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
496	C₂²⋊D₄₇	—	4	2	no	—
497	C₂²⋊D₄₇	—	4	4	no	—
498	C₂²⋊D₄₇	—	8	2	no	—
499	C₂²⋊D₄₇	—	8	2	no	—
500	C₂×Dic₄₇	—	2	2	no	—
501	C₂×Dic₄₇	—	2	2	no	—
502	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
503	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
504	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
505	D₁₈₈	—	2	2	no	—
506	D₁₈₈	—	2	2	no	—
507	D₁₈₈	—	2	2	no	—
508	D₁₈₈	—	2	2	no	—
509	D₁₈₈	—	2	2	no	—
510	D₁₈₈	—	4	4	no	—
511	D₁₈₈	—	4	4	no	—
512	D₁₈₈	—	4	2	no	—
513	D₁₈₈	—	4	2	no	—
514	D₁₈₈	—	8	1	no	—
515	D₁₈₈	—	8	1	no	—
516	D₁₈₈	—	8	2	no	—
517	C₄×D₄₇	—	2	2	no	—
518	C₄×D₄₇	—	2	2	no	—
519	C₄×D₄₇	—	4	2	no	—
520	C₄×D₄₇	—	4	2	no	—
521	C₄×D₄₇	—	4	4	no	—
522	C₄×D₄₇	—	4	4	no	—
523	C₄×D₄₇	—	8	2	no	—
524	C₄×D₄₇	—	8	2	no	—
525	C₄×D₄₇	—	8	2	no	—
526	C₄×D₄₇	—	8	2	no	—
527	Dic₉₄	—	2	2	no	—
528	Dic₉₄	—	2	2	no	—
529	Dic₉₄	—	2	2	no	—
530	Dic₉₄	—	4	2	no	—
531	Dic₉₄	—	8	2	no	—
532	C₈×C₄₇	—	2	1	no	—
533	C₈×C₄₇	—	2	1	no	—
534	C₈×C₄₇	—	2	1	no	—
535	C₈×C₄₇	—	2	1	no	—
536	C₄₇⋊C₈	—	2	2	no	—
537	C₄₇⋊C₈	—	2	2	no	—
538	#62006	—	47	1	no	maximal, Sylow
539	C₂²×C₄₇	—	2	1	no	—
540	C₂²×C₄₇	—	2	1	no	—
541	C₂²×C₄₇	—	2	1	no	—
542	C₂²×C₄₇	—	4	1	no	—
543	C₂²×C₄₇	—	4	1	no	—
544	C₂²×C₄₇	—	4	1	no	—
545	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
546	C₂×D₄₇	—	2	2	no	—
547	C₂×D₄₇	—	2	2	no	—
548	C₂×D₄₇	—	2	2	no	—
549	C₂×D₄₇	—	4	2	no	—
550	C₂×D₄₇	—	4	2	no	—
551	C₂×D₄₇	—	4	2	no	—
552	C₂×D₄₇	—	4	2	no	—
553	C₂×D₄₇	—	4	2	no	—
554	C₂×D₄₇	—	4	2	no	—
555	C₂×D₄₇	—	16	4	no	—
556	C₄×C₄₇	—	2	1	no	—
557	C₄×C₄₇	—	2	1	no	—
558	C₄×C₄₇	—	2	2	no	—
559	C₄×C₄₇	—	2	1	no	—
560	C₄×C₄₇	—	2	1	no	—
561	C₄×C₄₇	—	4	1	no	—
562	C₄×C₄₇	—	4	1	no	—
563	C₄×C₄₇	—	4	1	no	—
564	C₄×C₄₇	—	4	1	no	—
565	C₄×C₄₇	—	4	1	no	—
566	C₄×C₄₇	—	4	1	no	—
567	C₄×C₄₇	#575	1	2	yes	—
568	C₄×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
569	C₄×C₄₇	#585	1	1	yes	characteristic
570	Dic₄₇	—	2	2	no	—
571	Dic₄₇	—	2	2	no	—
572	Dic₄₇	—	2	2	no	—
573	Dic₄₇	—	4	2	no	—
574	Dic₄₇	—	4	2	no	—
575	#3514	—	47	1	no	—
576	#3480	—	47	1	no	—
577	#3396	—	47	1	no	—
578	#3394	—	47	1	no	—
579	#3365	—	47	1	no	—
580	#3364	—	47	1	no	—
581	#3328	—	47	1	no	—
582	#3326	—	47	2	no	—
583	#3324	—	47	1	no	—
584	#3322	—	47	2	no	—
585	#3278	—	47	1	no	—
586	#3277	—	47	2	no	—
587	#3275	—	47	2	no	—
588	#3274	—	47	1	no	—
589	#3256	—	47	2	no	—
590	#3251	—	47	1	no	—
591	#3211	—	47	2	no	—
592	#3207	—	47	1	no	—
593	#3108	D₄₇	1	1	yes	characteristic, complemented
594	#3102	—	47	2	no	—
595	#3040	—	47	2	no	—
596	#3037	—	47	1	no	—
597	#2991	—	47	1	no	—
598	C₂×C₄₇	—	4	1	no	—
599	C₂×C₄₇	—	8	1	no	—
600	C₂×C₄₇	#3488	1	1	yes	characteristic
601	C₂×C₄₇	C₂×#575	1	1	yes	characteristic
602	C₂×C₄₇	#3584	1	1	yes	characteristic
603	D₄₇	—	4	2	no	—
604	D₄₇	—	8	2	no	—
605	D₄₇	—	8	2	no	—
606	C₂×#137	—	47	2	no	—
607	C₂×#137	—	47	2	no	—
608	C₂×AGL(1,ℤ/8)	—	47	2	no	—
609	#559	—	47	1	no	—
610	#559	—	47	1	no	—
611	#559	—	94	1	no	—
612	#557	—	47	1	no	—
613	#556	—	47	1	no	—
614	#556	—	47	1	no	—
615	#556	—	94	1	no	—
616	#555	—	94	1	no	—
617	#553	—	47	2	no	—
618	#553	—	94	2	no	—
619	#551	—	94	2	no	—
620	#550	—	47	1	no	—
621	D₄×Q₈	—	47	1	no	—
622	#548	—	47	2	no	—
623	#548	—	47	2	no	—
624	#546	—	47	2	no	—
625	#546	—	94	1	no	—
626	D₄²	—	47	1	no	—
627	#542	—	94	1	no	—
628	#538	—	94	2	no	—
629	#532	—	47	1	no	—
630	#532	—	47	1	no	—
631	#532	—	94	1	no	—
632	#529	—	47	2	no	—
633	#529	—	47	2	no	—
634	#529	—	94	2	no	—
635	#529	C₂×D₄₇	1	1	yes	characteristic
636	C₂×#124	—	47	2	no	—
637	#518	—	94	1	no	—
638	C₄×#41	—	47	1	no	—
639	C₄×#41	—	47	2	no	—
640	C₄×#41	—	94	1	no	—
641	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
642	#495	—	47	2	no	—
643	#495	—	47	2	no	—
644	#493	—	47	1	no	—
645	#492	—	47	1	no	—
646	#488	—	47	2	no	—
647	#488	—	47	2	no	—
648	#487	—	47	1	no	—
649	#486	—	47	1	no	—
650	#485	—	47	2	no	—
651	#483	C₂×D₄₇	1	1	yes	characteristic, complemented
652	#482	—	47	2	no	—
653	#480	C₂×D₄₇	1	1	yes	characteristic
654	#479	—	47	2	no	—
655	#479	C₂×D₄₇	1	1	yes	characteristic, complemented
656	#479	C₂×D₄₇	1	1	yes	characteristic, complemented
657	#478	—	47	2	no	—
658	#478	—	47	2	no	—
659	#475	—	47	1	no	—
660	#474	—	47	1	no	—
661	#470	—	47	2	no	—
662	#469	—	47	2	no	—
663	#469	—	47	2	no	—
664	#468	—	47	2	no	—
665	#468	—	47	2	no	—
666	#468	—	47	2	no	—
667	#464	—	47	2	no	—
668	#464	—	47	2	no	—
669	#464	—	47	2	no	—
670	#464	—	47	2	no	—
671	#464	—	47	2	no	—
672	#464	C₂×D₄₇	1	1	yes	characteristic
673	#464	C₂×D₄₇	1	1	yes	characteristic
674	#463	—	47	2	no	—
675	#463	—	47	2	no	—
676	#463	—	47	2	no	—
677	#463	—	47	2	no	—
678	#463	—	47	2	no	—
679	#463	—	47	2	no	—
680	#462	—	47	1	no	—
681	#462	—	47	1	no	—
682	#460	—	47	1	no	—
683	#460	—	47	1	no	—
684	#460	—	47	1	no	—
685	#459	—	47	1	no	—
686	#452	—	47	2	no	—
687	#451	—	47	2	no	—
688	#451	C₂×D₄₇	1	1	yes	characteristic, complemented
689	#450	—	47	2	no	—
690	#449	—	47	2	no	—
691	#449	—	47	2	no	—
692	#449	—	47	2	no	—
693	#448	—	47	2	no	—
694	#448	C₂×D₄₇	1	1	yes	characteristic
695	#447	—	47	2	no	—
696	C₈×Q₈	—	47	1	no	—
697	C₈×Q₈	—	47	1	no	—
698	C₄×Q₁₆	—	47	2	no	—
699	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
700	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
701	C₄×SD₁₆	—	47	2	no	—
702	C₄×SD₁₆	—	47	2	no	—
703	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
704	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
705	C₄×D₈	—	47	2	no	—
706	#436	—	47	2	no	—
707	#436	—	47	2	no	—
708	#436	—	47	1	no	—
709	#436	—	47	1	no	—
710	#431	—	47	2	no	—
711	#431	C₂×D₄₇	1	1	yes	characteristic, complemented
712	#423	—	47	1	no	—
713	#423	—	47	2	no	—
714	#419	—	47	2	no	—
715	#418	—	47	2	no	—
716	#417	—	47	2	no	—
717	C₄₇	#62006	1	1	yes	characteristic, complemented, Sylow
718	C₂×#41	—	47	1	no	—
719	C₂×#41	—	47	2	no	—
720	C₂×#41	—	47	2	no	—
721	C₂×#41	—	94	1	no	—
722	C₂²×Q₈	—	47	2	no	—
723	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
724	C₂²×D₄	—	47	2	no	—
725	C₂²×D₄	—	94	1	no	—
726	#137	—	188	4	no	—
727	#137	—	188	4	no	—
728	AGL(1,ℤ/8)	—	188	4	no	—
729	C₂×Q₁₆	—	47	2	no	—
730	C₂×Q₁₆	—	47	2	no	—
731	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
732	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
733	C₂×SD₁₆	—	47	2	no	—
734	C₂×SD₁₆	—	47	2	no	—
735	C₂×SD₁₆	—	47	2	no	—
736	C₂×SD₁₆	—	47	2	no	—
737	C₂×SD₁₆	—	47	2	no	—
738	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
739	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
740	C₂×D₈	—	47	2	no	—
741	C₂×D₈	—	47	2	no	—
742	C₂×D₈	—	47	2	no	—
743	C₂×M₁₆	—	47	2	no	—
744	C₂×M₁₆	—	47	2	no	—
745	C₂×M₁₆	—	47	2	no	—
746	C₄⋊Q₈	—	47	1	no	—
747	C₄⋊Q₈	—	47	1	no	—
748	C₄⋊Q₈	—	94	1	no	—
749	C₄⋊Q₈	—	94	1	no	—
750	#127	—	47	1	no	—
751	#127	—	47	1	no	—
752	#127	—	94	1	no	—
753	#126	—	2	1	no	—
754	#126	—	94	2	no	—
755	#126	—	94	2	no	—
756	#126	—	94	2	no	—
757	#126	—	94	2	no	—
758	#126	—	94	2	no	—
759	#125	—	47	2	no	—
760	#125	—	94	2	no	—
761	#125	C₂²×D₄₇	1	1	yes	characteristic
762	#124	—	47	2	no	—
763	#124	—	47	2	no	—
764	#124	—	47	2	no	—
765	#124	—	47	2	no	—
766	#124	—	94	1	no	—
767	#124	—	94	1	no	—
768	#124	—	94	1	no	—
769	#124	—	94	2	no	—
770	#124	—	94	2	no	—
771	#124	—	94	2	no	—
772	#124	—	94	2	no	—
773	#124	—	94	1	no	—
774	#124	C₂²×D₄₇	1	1	yes	characteristic
775	#123	—	2	1	no	—
776	#123	—	94	2	no	—
777	#123	—	94	2	no	—
778	#123	—	94	2	no	—
779	#123	—	94	2	no	—
780	#123	—	94	2	no	—
781	#123	—	94	2	no	—
782	C₂²⋊Q₈	—	47	2	no	—
783	C₂²⋊Q₈	—	47	2	no	—
784	C₂²⋊Q₈	—	94	2	no	—
785	C₂²⋊Q₈	—	94	2	no	—
786	C₂²⋊Q₈	—	94	2	no	—
787	C₂²⋊Q₈	—	94	1	no	—
788	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
789	#121	—	47	2	no	—
790	#121	—	47	2	no	—
791	#121	—	47	2	no	—
792	#121	—	94	2	no	—
793	#121	—	94	2	no	—
794	#121	—	94	2	no	—
795	#121	—	94	1	no	—
796	#121	—	94	2	no	—
797	#121	—	94	2	no	—
798	#121	—	94	1	no	—
799	#121	—	94	1	no	—
800	#121	—	94	1	no	—
801	#121	C₂²×D₄₇	1	1	yes	characteristic
802	#120	—	94	2	no	—
803	#120	—	94	2	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	—	2	1	no	—
806	C₄×Q₈	—	47	1	no	—
807	C₄×Q₈	—	47	1	no	—
808	C₄×Q₈	—	47	2	no	—
809	C₄×Q₈	—	47	2	no	—
810	C₄×Q₈	—	94	1	no	—
811	C₄×Q₈	—	94	1	no	—
812	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
813	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
814	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
815	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
816	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	47	2	no	—
819	C₄×D₄	—	47	2	no	—
820	C₄×D₄	—	47	2	no	—
821	C₄×D₄	—	47	2	no	—
822	C₄×D₄	—	47	1	no	—
823	C₄×D₄	—	47	1	no	—
824	C₄×D₄	—	47	2	no	—
825	C₄×D₄	—	94	1	no	—
826	C₄×D₄	—	94	1	no	—
827	C₄×D₄	—	94	1	no	—
828	C₄×D₄	—	94	2	no	—
829	C₄×D₄	—	94	2	no	—
830	C₄×D₄	—	94	1	no	—
831	C₄×D₄	—	94	2	no	—
832	C₄×D₄	—	94	2	no	—
833	C₄×D₄	—	94	2	no	—
834	C₄×D₄	—	94	2	no	—
835	C₄×D₄	—	94	2	no	—
836	C₄×D₄	—	94	1	no	—
837	C₄×D₄	—	94	1	no	—
838	C₄×D₄	—	94	1	no	—
839	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
840	#117	—	2	1	no	—
841	#117	—	47	1	no	—
842	#117	—	47	2	no	—
843	#117	—	47	2	no	—
844	#117	—	94	2	no	—
845	#117	—	94	2	no	—
846	#117	—	94	2	no	—
847	#117	—	94	1	no	—
848	C₂×C₄⋊C₄	—	2	1	no	—
849	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
850	C₂×C₂²⋊C₄	—	94	2	no	—
851	C₂×C₂²⋊C₄	—	94	2	no	—
852	C₂×C₂²⋊C₄	—	94	2	no	—
853	C₂×C₄²	—	2	1	no	—
854	C₂×C₄²	—	47	2	no	—
855	C₂×C₄²	—	94	2	no	—
856	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
857	#107	—	47	2	no	—
858	#107	C₂²×D₄₇	1	1	yes	characteristic
859	#107	C₂²×D₄₇	1	1	yes	characteristic
860	#106	—	47	2	no	—
861	#106	C₂²×D₄₇	1	1	yes	characteristic
862	#106	C₂²×D₄₇	1	1	yes	characteristic
863	C₄⋊C₈	—	47	2	no	—
864	C₄⋊C₈	—	47	2	no	—
865	C₄⋊C₈	—	47	2	no	—
866	C₄⋊C₈	—	47	1	no	—
867	C₄⋊C₈	—	47	1	no	—
868	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
869	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
870	#103	—	47	2	no	—
871	#103	—	47	2	no	—
872	#103	—	47	2	no	—
873	#103	—	47	2	no	—
874	#103	—	47	2	no	—
875	#103	C₂²×D₄₇	1	1	yes	characteristic
876	#103	C₂²×D₄₇	1	1	yes	characteristic
877	#103	C₂²×D₄₇	1	1	yes	characteristic
878	#103	C₂²×D₄₇	1	1	yes	characteristic
879	#103	C₂²×D₄₇	1	1	yes	characteristic
880	#103	C₂²×D₄₇	1	1	yes	characteristic
881	#102	—	47	2	no	—
882	#102	—	47	2	no	—
883	#102	—	47	2	no	—
884	#102	—	47	2	no	—
885	#102	—	47	2	no	—
886	#102	—	47	2	no	—
887	#102	—	47	2	no	—
888	#102	C₂²×D₄₇	1	1	yes	characteristic
889	#102	C₂²×D₄₇	1	1	yes	characteristic
890	C₂²⋊C₈	—	47	2	no	—
891	C₂²⋊C₈	—	47	2	no	—
892	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
893	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
894	C₄×C₈	—	47	2	no	—
895	C₄×C₈	—	47	2	no	—
896	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
897	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
898	C₂⁴	—	94	2	no	—
899	#41	—	94	4	no	—
900	#41	—	188	2	no	—
901	#41	—	188	2	no	—
902	#41	—	188	2	no	—
903	#41	—	188	4	no	—
904	#41	—	188	2	no	—
905	C₂×Q₈	—	2	1	no	—
906	C₂×Q₈	—	2	2	no	—
907	C₂×Q₈	—	4	1	no	—
908	C₂×Q₈	—	47	1	no	—
909	C₂×Q₈	—	47	2	no	—
910	C₂×Q₈	—	94	2	no	—
911	C₂×Q₈	—	94	1	no	—
912	C₂×Q₈	—	188	2	no	—
913	C₂×Q₈	—	188	2	no	—
914	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
915	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
916	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
917	C₂×D₄	—	2	1	no	—
918	C₂×D₄	—	47	2	no	—
919	C₂×D₄	—	47	1	no	—
920	C₂×D₄	—	47	2	no	—
921	C₂×D₄	—	47	2	no	—
922	C₂×D₄	—	94	2	no	—
923	C₂×D₄	—	94	2	no	—
924	C₂×D₄	—	94	2	no	—
925	C₂×D₄	—	94	2	no	—
926	C₂×D₄	—	94	2	no	—
927	C₂×D₄	—	94	2	no	—
928	C₂×D₄	—	94	1	no	—
929	C₂×D₄	—	94	1	no	—
930	C₂×D₄	—	94	1	no	—
931	C₂×D₄	—	94	1	no	—
932	C₂×D₄	—	188	4	no	—
933	C₂×D₄	—	188	2	no	—
934	C₂×D₄	—	188	2	no	—
935	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
936	C₂²×C₄	—	2	1	no	—
937	C₂²×C₄	—	2	1	no	—
938	C₂²×C₄	—	2	1	no	—
939	C₂²×C₄	—	47	2	no	—
940	C₂²×C₄	—	47	2	no	—
941	C₂²×C₄	—	47	2	no	—
942	C₂²×C₄	—	94	2	no	—
943	C₂²×C₄	—	94	2	no	—
944	C₂²×C₄	—	94	2	no	—
945	C₂²×C₄	—	94	2	no	—
946	C₂²×C₄	—	94	2	no	—
947	C₂²×C₄	—	94	2	no	—
948	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
949	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
950	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
951	Q₁₆	—	2	2	no	—
952	Q₁₆	—	4	1	no	—
953	Q₁₆	—	94	4	no	—
954	Q₁₆	—	188	2	no	—
955	SD₁₆	—	2	2	no	—
956	SD₁₆	—	4	1	no	—
957	SD₁₆	—	94	4	no	—
958	SD₁₆	—	188	2	no	—
959	SD₁₆	—	188	2	no	—
960	SD₁₆	—	188	2	no	—
961	SD₁₆	—	188	2	no	—
962	D₈	—	188	2	no	—
963	D₈	—	188	2	no	—
964	D₈	—	188	2	no	—
965	M₁₆	—	188	2	no	—
966	M₁₆	—	188	2	no	—
967	M₁₆	—	188	2	no	—
968	C₂×C₈	—	47	2	no	—
969	C₂×C₈	—	47	2	no	—
970	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
971	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
972	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
973	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	1	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	1	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	1	no	—
980	C₄⋊C₄	—	2	1	no	—
981	C₄⋊C₄	—	2	1	no	—
982	C₄⋊C₄	—	2	1	no	—
983	C₄⋊C₄	—	47	2	no	—
984	C₄⋊C₄	—	47	2	no	—
985	C₄⋊C₄	—	47	1	no	—
986	C₄⋊C₄	—	47	1	no	—
987	C₄⋊C₄	—	47	2	no	—
988	C₄⋊C₄	—	94	2	no	—
989	C₄⋊C₄	—	94	2	no	—
990	C₄⋊C₄	—	94	2	no	—
991	C₄⋊C₄	—	94	2	no	—
992	C₄⋊C₄	—	94	2	no	—
993	C₄⋊C₄	—	94	2	no	—
994	C₄⋊C₄	—	94	1	no	—
995	C₄⋊C₄	—	94	1	no	—
996	C₄⋊C₄	—	94	1	no	—
997	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
998	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
999	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1000	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
1001	C₂²⋊C₄	—	2	1	no	—
1002	C₂²⋊C₄	—	2	1	no	—
1003	C₂²⋊C₄	—	2	1	no	—
1004	C₂²⋊C₄	—	2	1	no	—
1005	C₂²⋊C₄	—	2	1	no	—
1006	C₂²⋊C₄	—	47	2	no	—
1007	C₂²⋊C₄	—	47	2	no	—
1008	C₂²⋊C₄	—	47	2	no	—
1009	C₂²⋊C₄	—	94	2	no	—
1010	C₂²⋊C₄	—	94	2	no	—
1011	C₂²⋊C₄	—	94	2	no	—
1012	C₂²⋊C₄	—	94	2	no	—
1013	C₂²⋊C₄	—	94	2	no	—
1014	C₂²⋊C₄	—	94	2	no	—
1015	C₂²⋊C₄	—	94	2	no	—
1016	C₂²⋊C₄	—	94	2	no	—
1017	C₂²⋊C₄	—	94	2	no	—
1018	C₂²⋊C₄	—	94	2	no	—
1019	C₂²⋊C₄	—	94	2	no	—
1020	C₂²⋊C₄	—	94	2	no	—
1021	C₂²⋊C₄	—	94	2	no	—
1022	C₂²⋊C₄	—	94	2	no	—
1023	C₂²⋊C₄	—	94	2	no	—
1024	C₂²⋊C₄	—	94	2	no	—
1025	C₂²⋊C₄	—	94	2	no	—
1026	C₄²	—	2	1	no	—
1027	C₄²	—	2	1	no	—
1028	C₄²	—	2	1	no	—
1029	C₄²	—	2	1	no	—
1030	C₄²	—	2	1	no	—
1031	C₄²	—	47	2	no	—
1032	C₄²	—	47	2	no	—
1033	C₄²	—	47	2	no	—
1034	C₄²	—	94	2	no	—
1035	C₄²	—	94	2	no	—
1036	C₄²	—	94	2	no	—
1037	C₄²	D₄×D₄₇	1	1	yes	characteristic
1038	C₄²	D₄×D₄₇	1	1	yes	characteristic
1039	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1040	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1041	C₂³	—	2	1	no	—
1042	C₂³	—	47	2	no	—
1043	C₂³	—	94	2	no	—
1044	C₂³	—	94	2	no	—
1045	C₂³	—	376	2	no	—
1046	C₂³	—	376	2	no	—
1047	C₂³	—	188	4	no	—
1048	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1049	Q₈	—	2	1	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	2	1	no	—
1052	Q₈	—	2	1	no	—
1053	Q₈	—	2	1	no	—
1054	Q₈	—	4	2	no	—
1055	Q₈	—	94	2	no	—
1056	Q₈	—	94	2	no	—
1057	Q₈	—	94	2	no	—
1058	Q₈	—	376	2	no	—
1059	Q₈	—	188	2	no	—
1060	Q₈	#13094070	1	2	yes	—
1061	D₄	—	2	1	no	—
1062	D₄	—	2	1	no	—
1063	D₄	—	8	1	no	—
1064	D₄	—	94	2	no	—
1065	D₄	—	94	2	no	—
1066	D₄	—	94	2	no	—
1067	D₄	—	94	2	no	—
1068	D₄	—	94	2	no	—
1069	D₄	—	376	1	no	—
1070	D₄	—	376	1	no	—
1071	D₄	—	376	2	no	—
1072	D₄	—	376	2	no	—
1073	D₄	—	376	2	no	—
1074	D₄	—	188	4	no	—
1075	D₄	—	188	4	no	—
1076	D₄	—	188	2	no	—
1077	D₄	—	188	4	no	—
1078	D₄	—	188	2	no	—
1079	D₄	—	188	2	no	—
1080	C₂×C₄	—	2	1	no	—
1081	C₂×C₄	—	2	2	no	—
1082	C₂×C₄	—	2	1	no	—
1083	C₂×C₄	—	2	1	no	—
1084	C₂×C₄	—	2	1	no	—
1085	C₂×C₄	—	2	1	no	—
1086	C₂×C₄	—	2	1	no	—
1087	C₂×C₄	—	2	1	no	—
1088	C₂×C₄	—	2	1	no	—
1089	C₂×C₄	—	2	1	no	—
1090	C₂×C₄	—	4	1	no	—
1091	C₂×C₄	—	4	2	no	—
1092	C₂×C₄	—	4	2	no	—
1093	C₂×C₄	—	8	1	no	—
1094	C₂×C₄	—	47	2	no	—
1095	C₂×C₄	—	47	2	no	—
1096	C₂×C₄	—	47	2	no	—
1097	C₂×C₄	—	94	2	no	—
1098	C₂×C₄	—	94	2	no	—
1099	C₂×C₄	—	94	2	no	—
1100	C₂×C₄	—	94	2	no	—
1101	C₂×C₄	—	376	2	no	—
1102	C₂×C₄	—	376	2	no	—
1103	C₂×C₄	—	376	2	no	—
1104	C₂×C₄	—	376	2	no	—
1105	C₂×C₄	—	188	2	no	—
1106	C₂×C₄	—	188	2	no	—
1107	C₂×C₄	—	188	4	no	—
1108	C₂×C₄	—	188	4	no	—
1109	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1110	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1111	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1112	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1113	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1114	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1115	C₈	—	2	1	no	—
1116	C₈	—	2	1	no	—
1117	C₈	—	2	1	no	—
1118	C₈	—	2	1	no	—
1119	C₈	—	94	2	no	—
1120	C₈	—	94	2	no	—
1121	C₂²	—	2	1	no	—
1122	C₂²	—	2	1	no	—
1123	C₂²	—	2	1	no	—
1124	C₂²	—	4	1	no	—
1125	C₂²	—	4	1	no	—
1126	C₂²	—	4	1	no	—
1127	C₂²	—	94	2	no	—
1128	C₂²	—	94	2	no	—
1129	C₂²	—	94	2	no	—
1130	C₂²	—	188	2	no	—
1131	C₂²	—	188	2	no	—
1132	C₂²	—	188	2	no	—
1133	C₂²	—	188	2	no	—
1134	C₂²	—	188	2	no	—
1135	C₂²	—	188	2	no	—
1136	C₂²	—	752	4	no	—
1137	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1138	C₄	—	2	1	no	—
1139	C₄	—	2	2	no	—
1140	C₄	—	2	1	no	—
1141	C₄	—	2	1	no	—
1142	C₄	—	2	1	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	1	no	—
1145	C₄	—	4	1	no	—
1146	C₄	—	4	1	no	—
1147	C₄	—	4	1	no	—
1148	C₄	—	4	1	no	—
1149	C₄	—	94	2	no	—
1150	C₄	—	94	2	no	—
1151	C₄	—	94	2	no	—
1152	C₄	—	188	2	no	—
1153	C₄	—	188	2	no	—
1154	C₄	#15689922	1	2	yes	—
1155	C₄	C₂×#13094070	1	1	yes	characteristic
1156	C₄	#15689959	1	1	yes	characteristic
1157	C₂	—	4	1	no	—
1158	C₂	—	8	1	no	—
1159	C₂	—	376	2	no	—
1160	C₂	—	376	2	no	—
1161	C₂	—	188	2	no	—
1162	C₂	#20257049	1	1	yes	characteristic
1163	C₂	C₂×#15689922	1	1	yes	characteristic
1164	C₂	#20258157	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3108	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3108	D₄₇
hypocenter	C₄₇	#62006
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3108

Complements

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

N	H ≅ G/N	type
1. #20257351	C₂	semidirect
2. #20256983	C₂	semidirect
3. #20256398	C₂	semidirect
4. #20256382	C₂	semidirect
5. #20256082	C₂	semidirect
6. #20256071	C₂	semidirect
7. #20255673	C₂	semidirect
8. #20255644	C₂	semidirect
9. #20255621	C₂	semidirect
10. #20255592	C₂	semidirect
11. #20255055	C₂	semidirect
12. #20255045	C₂	semidirect
13. #20255022	C₂	semidirect
14. #20255009	C₂	semidirect
15. #20254791	C₂	semidirect
16. #20254750	C₂	semidirect
17. #20254357	C₂	semidirect
18. #20254323	C₂	semidirect
19. #20253413	C₂	semidirect
20. #20252879	C₂	semidirect
21. #20252860	C₂	semidirect
22. #20252517	C₂	semidirect
23. C₄₇×#3108	C₂	semidirect
24. C₂×#13094056	C₂²	semidirect
25. C₂×#13094055	C₂²	semidirect
29. #15689858	C₂²	semidirect
30. #15689852	C₂²	semidirect
36. #15689821	C₂²	semidirect
40. #15689784	C₂²	semidirect
49. #15689673	C₂²	semidirect
51. #15689660	C₂²	semidirect
55. C₄×#10625354	C₂²	semidirect
58. #15689508	C₂²	semidirect
61. #15689496	C₂²	semidirect
62. #15689479	C₂²	semidirect
64. #15689474	C₂²	semidirect
66. #15689466	C₂²	semidirect
68. #15689433	C₂²	semidirect
69. #15689426	C₂²	semidirect
70. #15689420	C₂²	semidirect
71. #15689408	C₂²	semidirect
73. #15689380	C₂²	semidirect
77. #15689371	C₂²	semidirect
78. #15689370	C₂²	semidirect
79. #15689348	C₂²	semidirect
80. #15689347	C₂²	semidirect
81. #15689345	C₂²	semidirect
82. #15689345	C₂²	semidirect
84. #15689341	C₂²	semidirect
85. #15689341	C₂²	semidirect
86. #15689339	C₂²	semidirect
87. #15689339	C₂²	semidirect
90. #15689333	C₂²	semidirect
91. #15689333	C₂²	semidirect
94. #15689323	C₂²	semidirect
96. #15689288	C₂²	semidirect
97. #15689277	C₂²	semidirect
100. #15689270	C₂²	semidirect
101. #15689270	C₂²	semidirect
102. #15689263	C₂²	semidirect
104. C₈×Dic₉₄	C₂²	semidirect
105. C₈×Dic₉₄	C₂²	semidirect
106. #15689215	C₂²	semidirect
107. #15689210	C₂²	semidirect
108. #15689208	C₂²	semidirect
109. #15689205	C₂²	semidirect
112. #15689198	C₂²	semidirect
113. #15689198	C₂²	semidirect
114. #15689175	C₂²	semidirect
115. #15689147	C₂²	semidirect
116. #15689145	C₂²	semidirect
117. #15689130	C₂²	semidirect
119. #15689122	C₂²	semidirect
121. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
122. C₄₇×#483	C₂²	semidirect
124. C₄₇×#479	C₂²	semidirect
125. C₄₇×#479	C₂²	semidirect
128. C₄₇×#451	C₂²	semidirect
130. C₄×Q₁₆×C₄₇	C₂²	semidirect
131. C₄×Q₁₆×C₄₇	C₂²	semidirect
134. C₄₇×#431	C₂²	semidirect
593. #3108	D₄₇	semidirect
641. C₂×C₄×Q₈	C₂×D₄₇	semidirect
651. #483	C₂×D₄₇	semidirect
655. #479	C₂×D₄₇	semidirect
656. #479	C₂×D₄₇	semidirect
688. #451	C₂×D₄₇	semidirect
699. C₄×Q₁₆	C₂×D₄₇	semidirect
700. C₄×Q₁₆	C₂×D₄₇	semidirect
711. #431	C₂×D₄₇	semidirect
717. C₄₇	#62006	semidirect

Maximal subgroups

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

subgroup	index
#20257351	2
#20256983	2
#20256398	2
#20256382	2
#20256082	2
#20256071	2
#20255673	2
#20255644	2
#20255621	2
#20255592	2
#20255055	2
#20255045	2
#20255022	2
#20255009	2
#20254791	2
#20254750	2
#20254357	2
#20254323	2
#20253413	2
#20252879	2
#20252860	2
#20252517	2
C₄₇×#3108	2
#62006	47