Subgroups — #27099131

Order 12032.

1836 conjugacy classes of subgroups.

The subgroup lattice has 1146 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	#20256437	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256287	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256048	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256026	C₂	1	1	yes	maximal, characteristic, complemented
6	#20256003	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255897	C₂	1	2	yes	maximal, complemented
8	#20255316	C₂	1	2	yes	maximal, complemented
9	#20255305	C₂	1	1	yes	maximal, characteristic, complemented
10	#20255217	C₂	1	2	yes	maximal, complemented
11	#20255206	C₂	1	1	yes	maximal, characteristic, complemented
12	#20254988	C₂	1	1	yes	maximal, characteristic, complemented
13	#20254914	C₂	1	2	yes	maximal, complemented
14	#20254058	C₂	1	2	yes	maximal, complemented
15	#20253948	C₂	1	1	yes	maximal, characteristic, complemented
16	#20253665	C₂	1	2	yes	maximal, complemented
17	#20253635	C₂	1	2	yes	maximal, complemented
18	#20253544	C₂	1	1	yes	maximal, characteristic, complemented
19	#20253539	C₂	1	1	yes	maximal, characteristic, complemented
20	#20252364	C₂	1	1	yes	maximal, characteristic, complemented
21	#20252216	C₂	1	2	yes	maximal, complemented
22	C₄×#13094044	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3515	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094049	C₂²	1	2	yes	—
25	C₂×#13094044	C₂²	1	1	yes	characteristic
26	#15689858	C₂²	1	1	yes	characteristic
27	#15689843	C₂²	1	1	yes	characteristic
28	#15689838	C₂²	1	2	yes	—
29	#15689798	—	2	2	no	—
30	Q₈×D₁₈₈	C₂²	1	1	yes	characteristic
31	#15689783	—	2	1	no	—
32	#15689770	—	2	1	no	—
33	#15689769	C₂²	1	2	yes	—
34	D₄×D₁₈₈	C₂²	1	1	yes	characteristic
35	#15689744	C₂²	1	2	yes	—
36	#15689709	—	2	2	no	—
37	#15689673	C₂²	1	1	yes	characteristic
38	#15689658	—	2	1	no	—
39	#124×D₄₇	—	2	1	no	—
40	#15689597	C₂²	1	2	yes	—
41	C₄×#10625350	C₂²	1	1	yes	characteristic
42	#15689533	C₂²	1	2	yes	complemented
43	#15689519	C₂²	1	1	yes	characteristic, complemented
44	#15689515	C₂²	1	2	yes	complemented
45	#15689497	C₂²	1	1	yes	characteristic
46	#15689480	C₂²	1	2	yes	complemented
47	#15689473	C₂²	1	1	yes	characteristic, complemented
48	#15689473	C₂²	1	2	yes	complemented
49	#15689471	C₂²	1	1	yes	characteristic
50	#15689461	C₂²	1	2	yes	complemented
51	#15689461	C₂²	1	2	yes	complemented
52	#15689461	C₂²	1	2	yes	complemented
53	#15689453	C₂²	1	2	yes	complemented
54	#15689447	C₂²	1	2	yes	complemented
55	#15689441	C₂²	1	2	yes	—
56	#15689420	C₂²	1	2	yes	—
57	#15689420	C₂²	1	2	yes	complemented
58	#15689415	C₂²	1	1	yes	characteristic, complemented
59	#15689413	C₂²	1	2	yes	complemented
60	#15689410	C₂²	1	1	yes	characteristic
61	#15689408	C₂²	1	1	yes	characteristic, complemented
62	#15689408	C₂²	1	2	yes	complemented
63	#15689403	C₂²	1	1	yes	characteristic, complemented
64	#15689379	C₂²	1	2	yes	complemented
65	#15689371	C₂²	1	2	yes	—
66	#15689362	C₂²	1	2	yes	complemented
67	#15689354	C₂²	1	2	yes	—
68	#15689354	C₂²	1	2	yes	complemented
69	#15689354	C₂²	1	2	yes	complemented
70	#15689345	C₂²	1	2	yes	complemented
71	#15689338	C₂²	1	2	yes	complemented
72	#15689330	C₂²	1	1	yes	characteristic, complemented
73	#15689325	C₂²	1	1	yes	characteristic
74	#15689325	C₂²	1	2	yes	—
75	#15689325	C₂²	1	2	yes	complemented
76	#15689323	C₂²	1	1	yes	characteristic
77	#15689318	C₂²	1	1	yes	characteristic
78	#15689285	C₂²	1	2	yes	complemented
79	#15689283	C₂²	1	2	yes	—
80	#15689273	C₂²	1	2	yes	—
81	#15689273	C₂²	1	2	yes	—
82	#15689268	C₂²	1	2	yes	—
83	#15689268	C₂²	1	2	yes	complemented
84	#15689254	C₂²	1	1	yes	characteristic, complemented
85	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
86	#15689233	C₂²	1	2	yes	—
87	#15689233	C₂²	1	2	yes	complemented
88	#15689228	C₂²	1	2	yes	complemented
89	#15689221	C₂²	1	2	yes	—
90	#15689221	C₂²	1	2	yes	complemented
91	#15689221	C₂²	1	2	yes	complemented
92	C₄×#10625337	C₂²	1	1	yes	characteristic, complemented
93	C₄×#10625337	C₂²	1	1	yes	characteristic, complemented
94	C₄×#10625336	C₂²	1	2	yes	—
95	C₄×#10625336	C₂²	1	1	yes	characteristic
96	C₄×#10625336	C₂²	1	1	yes	characteristic
97	C₄×#10625336	C₂²	1	2	yes	complemented
98	C₄×#10625336	C₂²	1	2	yes	complemented
99	C₄×#10625335	C₂²	1	1	yes	characteristic, complemented
100	C₄×#10625335	C₂²	1	1	yes	characteristic, complemented
101	C₄×#10625334	C₂²	1	1	yes	characteristic
102	C₄×#10625334	C₂²	1	1	yes	characteristic
103	C₄×#10625334	C₂²	1	2	yes	complemented
104	#15689201	C₂²	1	1	yes	characteristic
105	#15689195	C₂²	1	2	yes	complemented
106	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
107	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
108	#15689184	C₂²	1	2	yes	complemented
109	#15689180	C₂²	1	1	yes	characteristic, complemented
110	#15689163	C₂²	1	2	yes	complemented
111	#15689159	C₂²	1	1	yes	characteristic, complemented
112	#15689119	C₂²	1	2	yes	complemented
113	#15689119	C₂²	1	1	yes	characteristic, complemented
114	#15689117	C₂²	1	1	yes	characteristic
115	C₂×#13093944	C₂²	1	2	yes	—
116	#15689079	C₂²	1	2	yes	complemented
117	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
118	C₄₇×#557	C₂²	1	1	yes	characteristic, complemented
119	C₄₇×#554	C₂²	1	1	yes	characteristic
120	C₄₇×#554	C₂²	1	1	yes	characteristic, complemented
121	C₄₇×#553	—	2	1	no	—
122	C₄₇×#552	—	2	2	no	—
123	C₄₇×#552	—	2	1	no	—
124	C₄₇×#552	C₂²	1	2	yes	complemented
125	C₄₇×#547	C₂²	1	1	yes	characteristic
126	C₄₇×#547	C₂²	1	2	yes	complemented
127	C₄₇×#541	C₂²	1	2	yes	complemented
128	C₄₇×#539	—	2	2	no	—
129	C₄₇×#533	C₂²	1	1	yes	characteristic, complemented
130	C₄₇×#529	—	2	1	no	—
131	C₄₇×#529	C₂²	1	1	yes	characteristic
132	C₂×#125×C₄₇	—	2	1	no	—
133	C₄₇×#520	C₂²	1	2	yes	complemented
134	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic, complemented
135	C₂×#10625350	—	2	1	no	—
136	C₂×#10625350	C₂³	1	1	yes	characteristic
137	C₂×Q₈×D₄₇	—	2	1	no	—
138	C₂²×D₁₈₈	C₂³	1	2	yes	—
139	C₂×D₄×D₄₇	—	2	1	no	—
140	#13094049	—	2	8	no	—
141	#13094044	—	2	4	no	—
142	C₂×#10625337	C₂³	1	1	yes	characteristic
143	C₂×#10625337	C₂³	1	2	yes	—
144	C₂×#10625335	C₂³	1	1	yes	characteristic
145	C₂×#10625336	C₂³	1	2	yes	—
146	C₂×#10625336	C₂³	1	2	yes	—
147	C₂×#10625336	C₂³	1	1	yes	characteristic
148	C₂×#10625336	C₂³	1	2	yes	—
149	C₂×#10625336	C₂³	1	2	yes	—
150	C₂×#10625334	C₂³	1	2	yes	—
151	C₂×#10625334	C₂³	1	1	yes	characteristic
152	C₂×#10625329	C₂³	1	2	yes	—
153	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
154	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
155	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
156	#13094024	C₂³	1	2	yes	—
157	#13094024	C₂³	1	1	yes	characteristic
158	#13094021	C₂³	1	1	yes	characteristic
159	#13094019	—	2	2	no	—
160	#13094017	—	2	2	no	—
161	#13094013	—	2	1	no	—
162	#13094012	—	2	1	no	—
163	#13094012	C₂³	1	2	yes	—
164	#13094011	—	2	1	no	—
165	#13094010	—	2	2	no	—
166	#13094010	—	2	2	no	—
167	#13094010	—	2	2	no	—
168	#13094009	—	2	2	no	—
169	#13094009	—	2	2	no	—
170	#13094006	—	2	2	no	—
171	#13094004	—	2	1	no	—
172	#13094004	—	2	2	no	—
173	#13094003	C₂³	1	2	yes	—
174	#13094002	—	2	2	no	—
175	#13093999	—	2	1	no	—
176	#13093998	—	2	1	no	—
177	#13093998	C₂³	1	2	yes	—
178	#13093998	C₂³	1	2	yes	—
179	#13093997	—	2	2	no	—
180	#13093995	—	2	2	no	—
181	#13093994	—	2	2	no	—
182	#13093992	—	2	2	no	—
183	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
184	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
185	#13093989	—	2	1	no	—
186	C₄×D₁₈₈	—	2	1	no	—
187	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
188	C₄×D₁₈₈	C₂³	1	2	yes	—
189	C₄×D₁₈₈	C₂³	1	2	yes	—
190	C₄×D₁₈₈	C₂³	1	2	yes	—
191	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
192	#13093986	—	2	1	no	—
193	#13093986	—	2	2	no	—
194	#13093986	—	2	2	no	—
195	C₄×C₂²⋊D₄₇	—	2	1	no	—
196	C₄×C₂²⋊D₄₇	—	2	1	no	—
197	#13093983	C₂³	1	1	yes	characteristic
198	#13093983	C₂³	1	2	yes	—
199	#13093982	—	2	2	no	—
200	#13093981	—	2	1	no	—
201	C₂²⋊C₄×D₄₇	—	2	2	no	—
202	C₂²⋊C₄×D₄₇	—	2	2	no	—
203	C₂²⋊C₄×D₄₇	—	2	2	no	—
204	C₄²×D₄₇	—	2	1	no	—
205	#13093957	C₂³	1	1	yes	characteristic
206	#13093957	C₂³	1	1	yes	characteristic
207	#13093957	C₂³	1	2	yes	—
208	#13093957	C₂³	1	2	yes	—
209	#13093955	C₂³	1	2	yes	—
210	#13093955	C₂³	1	2	yes	—
211	#13093955	C₂³	1	2	yes	—
212	#13093955	C₂³	1	2	yes	—
213	#13093955	C₂³	1	1	yes	characteristic
214	#13093955	C₂³	1	1	yes	characteristic
215	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
216	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
217	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
218	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
219	#13093948	C₂³	1	1	yes	characteristic
220	#13093948	C₂³	1	1	yes	characteristic
221	#13093948	C₂³	1	2	yes	—
222	#13093948	C₂³	1	2	yes	—
223	#13093948	C₂³	1	2	yes	—
224	#13093948	C₂³	1	2	yes	—
225	#13093948	C₂³	1	2	yes	—
226	#13093947	C₂³	1	1	yes	characteristic
227	#13093947	C₂³	1	1	yes	characteristic
228	#13093947	C₂³	1	2	yes	—
229	#13093945	C₂³	1	2	yes	—
230	#13093945	C₂³	1	1	yes	characteristic
231	#13093945	C₂³	1	1	yes	characteristic
232	#13093944	C₂³	1	2	yes	—
233	#13093944	C₂³	1	2	yes	—
234	#13093944	C₂³	1	2	yes	—
235	#13093944	C₂³	1	2	yes	—
236	#13093944	C₂³	1	1	yes	characteristic
237	#13093944	C₂³	1	2	yes	—
238	#13093944	C₂³	1	1	yes	characteristic
239	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
240	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
241	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
242	#13093935	C₂³	1	2	yes	—
243	#13093935	C₂³	1	2	yes	—
244	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
245	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
246	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
247	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
248	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
249	C₂×#41×C₄₇	C₂³	1	2	yes	—
250	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
251	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
252	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
253	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
254	#126×C₄₇	—	2	2	no	—
255	#126×C₄₇	—	2	2	no	—
256	#126×C₄₇	—	2	2	no	—
257	#126×C₄₇	D₄	1	2	yes	—
258	#125×C₄₇	—	2	2	no	—
259	#125×C₄₇	—	2	2	no	—
260	#125×C₄₇	—	2	1	no	—
261	#125×C₄₇	—	2	1	no	—
262	#125×C₄₇	—	2	2	no	—
263	#125×C₄₇	—	2	2	no	—
264	#125×C₄₇	—	2	1	no	—
265	#125×C₄₇	D₄	1	1	yes	characteristic
266	#125×C₄₇	C₂³	1	2	yes	—
267	#124×C₄₇	D₄	1	1	yes	characteristic
268	#123×C₄₇	—	2	2	no	—
269	#123×C₄₇	—	2	2	no	—
270	#123×C₄₇	—	2	2	no	—
271	#123×C₄₇	—	2	2	no	—
272	#123×C₄₇	D₄	1	2	yes	—
273	C₂²⋊Q₈×C₄₇	—	2	1	no	—
274	C₂²⋊Q₈×C₄₇	—	2	1	no	—
275	C₂²⋊Q₈×C₄₇	—	2	2	no	—
276	C₂²⋊Q₈×C₄₇	—	2	2	no	—
277	C₂²⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
278	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
279	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
280	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
281	#121×C₄₇	—	2	1	no	—
282	#121×C₄₇	—	2	2	no	—
283	#121×C₄₇	D₄	1	1	yes	characteristic
284	C₄×Q₈×C₄₇	—	2	1	no	—
285	C₄×Q₈×C₄₇	—	2	1	no	—
286	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
287	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
288	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
289	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
290	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
291	C₄×D₄×C₄₇	—	2	1	no	—
292	C₄×D₄×C₄₇	—	2	1	no	—
293	C₄×D₄×C₄₇	—	2	1	no	—
294	C₄×D₄×C₄₇	—	2	2	no	—
295	C₄×D₄×C₄₇	—	2	2	no	—
296	C₄×D₄×C₄₇	C₂³	1	2	yes	—
297	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
298	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
299	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
300	C₄×D₄×C₄₇	C₂³	1	2	yes	—
301	#117×C₄₇	—	2	1	no	—
302	#117×C₄₇	—	2	2	no	—
303	#117×C₄₇	—	2	2	no	—
304	#117×C₄₇	—	2	1	no	—
305	#117×C₄₇	C₂³	1	1	yes	characteristic
306	#117×C₄₇	C₂³	1	2	yes	—
307	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
308	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
309	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
310	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
311	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
312	C₂×C₄²×C₄₇	—	2	1	no	—
313	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
314	C₂³×D₄₇	—	2	2	no	—
315	#41×C₄₇	—	2	2	no	—
316	#41×C₄₇	—	2	4	no	—
317	#41×C₄₇	—	4	2	no	—
318	#41×C₄₇	—	4	1	no	—
319	C₂×Q₈×C₄₇	—	2	1	no	—
320	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
321	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
322	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
323	C₂×D₄×C₄₇	—	2	2	no	—
324	C₂×D₄×C₄₇	—	2	1	no	—
325	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
326	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
327	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
328	C₂²×C₄×C₄₇	—	2	2	no	—
329	C₂²×C₄×C₄₇	—	2	1	no	—
330	C₂²×C₄×C₄₇	—	2	1	no	—
331	C₂²×C₄×C₄₇	—	2	2	no	—
332	C₂²×C₄×C₄₇	—	2	1	no	—
333	C₂²×C₄×C₄₇	—	2	2	no	—
334	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
335	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
336	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
337	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
338	C₂×C₂²⋊D₄₇	—	2	1	no	—
339	C₂×C₂²⋊D₄₇	—	2	2	no	—
340	C₂×C₂²⋊D₄₇	—	2	2	no	—
341	Q₈×D₄₇	—	8	2	no	—
342	D₄×D₄₇	—	8	2	no	—
343	#10625350	—	2	2	no	—
344	#10625350	—	4	1	no	—
345	#10625350	—	8	2	no	—
346	C₂×D₁₈₈	—	2	4	no	—
347	C₂×D₁₈₈	—	2	2	no	—
348	C₂×D₁₈₈	—	2	1	no	—
349	C₂×D₁₈₈	—	2	1	no	—
350	C₂×D₁₈₈	—	4	2	no	—
351	C₂×D₁₈₈	C₂⁴	1	2	yes	—
352	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
353	C₂×C₄×D₄₇	—	2	1	no	—
354	C₂×C₄×D₄₇	—	2	1	no	—
355	C₂×C₄×D₄₇	—	2	1	no	—
356	C₂×C₄×D₄₇	—	2	2	no	—
357	C₂×C₄×D₄₇	—	2	2	no	—
358	C₂×C₄×D₄₇	—	2	2	no	—
359	C₂×Dic₉₄	—	2	1	no	—
360	C₂×Dic₉₄	—	2	2	no	—
361	C₂×Dic₉₄	C₂⁴	1	1	yes	characteristic
362	C₄⋊C₄×C₄₇	—	2	2	no	—
363	C₄⋊C₄×C₄₇	—	2	1	no	—
364	C₄⋊C₄×C₄₇	—	2	1	no	—
365	C₄⋊C₄×C₄₇	—	2	2	no	—
366	C₄⋊C₄×C₄₇	—	2	2	no	—
367	C₄⋊C₄×C₄₇	—	2	2	no	—
368	C₄⋊C₄×C₄₇	—	2	2	no	—
369	C₄⋊C₄×C₄₇	—	2	2	no	—
370	C₄⋊C₄×C₄₇	—	2	2	no	—
371	C₄⋊C₄×C₄₇	—	2	2	no	—
372	C₄⋊C₄×C₄₇	—	2	1	no	—
373	C₄⋊C₄×C₄₇	—	2	1	no	—
374	C₄⋊C₄×C₄₇	—	2	2	no	—
375	C₄⋊C₄×C₄₇	—	2	1	no	—
376	C₄⋊C₄×C₄₇	—	2	2	no	—
377	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
378	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
379	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
380	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
381	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
382	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
383	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
384	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
385	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
386	C₂²⋊C₄×C₄₇	—	2	2	no	—
387	C₂²⋊C₄×C₄₇	—	2	2	no	—
388	C₂²⋊C₄×C₄₇	—	2	1	no	—
389	C₂²⋊C₄×C₄₇	—	2	2	no	—
390	C₂²⋊C₄×C₄₇	—	2	1	no	—
391	C₂²⋊C₄×C₄₇	—	2	1	no	—
392	C₂²⋊C₄×C₄₇	—	2	2	no	—
393	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
394	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
395	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
396	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
397	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
398	C₄²×C₄₇	—	2	1	no	—
399	C₄²×C₄₇	—	2	1	no	—
400	C₄²×C₄₇	—	2	1	no	—
401	C₄²×C₄₇	—	2	2	no	—
402	C₄²×C₄₇	—	2	2	no	—
403	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
404	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
405	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
406	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
407	C₄²×C₄₇	C₂⁴	1	2	yes	—
408	C₂²⋊Dic₄₇	—	2	2	no	—
409	C₂²⋊Dic₄₇	—	2	2	no	—
410	C₂²⋊Dic₄₇	—	2	1	no	—
411	#10625337	—	2	2	no	—
412	#10625337	—	4	2	no	—
413	#10625336	—	2	2	no	—
414	#10625336	—	2	4	no	—
415	#10625336	—	2	4	no	—
416	#10625336	—	4	2	no	—
417	#10625336	—	4	2	no	—
418	#10625335	—	2	2	no	—
419	#10625334	—	2	4	no	—
420	#10625334	#41	1	4	yes	complemented
421	(C₂×D₄₇)⋊C₄	—	2	1	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	—	2	1	no	—
428	(C₂×D₄₇)⋊C₄	—	2	2	no	—
429	(C₂×D₄₇)⋊C₄	—	2	2	no	—
430	C₄⋊Dic₄₇	—	2	2	no	—
431	C₄⋊Dic₄₇	—	2	1	no	—
432	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
433	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
434	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
435	Dic₄₇⋊C₄	—	2	1	no	—
436	Dic₄₇⋊C₄	—	2	1	no	—
437	Dic₄₇⋊C₄	—	2	2	no	—
438	C₄×Dic₄₇	—	2	1	no	—
439	C₄×Dic₄₇	—	2	1	no	—
440	C₄×Dic₄₇	—	2	1	no	—
441	C₄×Dic₄₇	—	2	2	no	—
442	#10625329	—	2	4	no	—
443	C₂×C₄₇⋊C₈	—	2	2	no	—
444	C₂×C₄₇⋊C₈	—	4	1	no	—
445	C₂×C₄₇⋊C₈	—	4	2	no	—
446	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
447	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
448	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
449	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
450	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
451	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
452	C₂³×C₄₇	—	2	1	no	—
453	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
454	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
455	C₂²×D₄₇	—	2	1	no	—
456	C₂²×D₄₇	—	2	2	no	—
457	C₂²×D₄₇	—	4	4	no	—
458	C₂²×D₄₇	—	8	2	no	—
459	C₂²×D₄₇	—	8	2	no	—
460	Q₈×C₄₇	—	2	2	no	—
461	Q₈×C₄₇	—	2	2	no	—
462	Q₈×C₄₇	—	2	1	no	—
463	Q₈×C₄₇	—	2	1	no	—
464	Q₈×C₄₇	—	2	2	no	—
465	Q₈×C₄₇	—	8	1	no	—
466	D₄×C₄₇	—	2	2	no	—
467	D₄×C₄₇	—	2	1	no	—
468	D₄×C₄₇	—	4	2	no	—
469	D₄×C₄₇	—	4	2	no	—
470	D₄×C₄₇	—	4	4	no	—
471	D₄×C₄₇	C₂×#41	1	2	yes	—
472	C₂×C₄×C₄₇	—	2	2	no	—
473	C₂×C₄×C₄₇	—	2	1	no	—
474	C₂×C₄×C₄₇	—	2	2	no	—
475	C₂×C₄×C₄₇	—	2	2	no	—
476	C₂×C₄×C₄₇	—	2	1	no	—
477	C₂×C₄×C₄₇	—	2	1	no	—
478	C₂×C₄×C₄₇	—	2	1	no	—
479	C₂×C₄×C₄₇	—	2	1	no	—
480	C₂×C₄×C₄₇	—	2	2	no	—
481	C₂×C₄×C₄₇	—	2	2	no	—
482	C₂×C₄×C₄₇	—	4	1	no	—
483	C₂×C₄×C₄₇	—	4	2	no	—
484	C₂×C₄×C₄₇	—	4	4	no	—
485	C₂×C₄×C₄₇	—	4	2	no	—
486	C₂×C₄×C₄₇	—	8	1	no	—
487	C₂×C₄×C₄₇	—	8	2	no	—
488	C₂×C₄×C₄₇	—	8	2	no	—
489	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
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	2	yes	—
495	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
496	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
498	C₂²⋊D₄₇	—	4	2	no	—
499	C₂²⋊D₄₇	—	8	2	no	—
500	C₂²⋊D₄₇	—	8	2	no	—
501	C₂×Dic₄₇	—	2	1	no	—
502	C₂×Dic₄₇	—	2	1	no	—
503	C₂×Dic₄₇	—	2	1	no	—
504	C₂×Dic₄₇	—	2	2	no	—
505	D₁₈₈	—	2	2	no	—
506	D₁₈₈	—	2	1	no	—
507	D₁₈₈	—	2	2	no	—
508	D₁₈₈	—	4	4	no	—
509	D₁₈₈	—	4	2	no	—
510	D₁₈₈	—	8	1	no	—
511	D₁₈₈	C₂×#41	1	2	yes	—
512	C₄×D₄₇	—	4	2	no	—
513	C₄×D₄₇	—	4	2	no	—
514	C₄×D₄₇	—	8	1	no	—
515	C₄×D₄₇	—	8	2	no	—
516	C₄×D₄₇	—	8	2	no	—
517	C₄×D₄₇	—	8	2	no	—
518	Dic₉₄	—	2	1	no	—
519	Dic₉₄	—	2	1	no	—
520	Dic₉₄	—	4	2	no	—
521	Dic₉₄	—	8	2	no	—
522	C₄₇⋊C₈	—	2	1	no	—
523	C₄₇⋊C₈	—	2	2	no	—
524	C₄₇⋊C₈	—	2	1	no	—
525	C₄₇⋊C₈	—	2	1	no	—
526	C₄₇⋊C₈	—	2	2	no	—
527	C₄₇⋊C₈	C₂×#41	1	2	yes	—
528	#61493	—	47	1	no	maximal, Sylow
529	C₂²×C₄₇	—	2	1	no	—
530	C₂²×C₄₇	—	2	2	no	—
531	C₂²×C₄₇	—	2	1	no	—
532	C₂²×C₄₇	—	2	2	no	—
533	C₂²×C₄₇	—	2	2	no	—
534	C₂²×C₄₇	—	2	1	no	—
535	C₂²×C₄₇	—	2	2	no	—
536	C₂²×C₄₇	—	4	1	no	—
537	C₂²×C₄₇	—	4	1	no	—
538	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
539	C₂×D₄₇	—	2	2	no	—
540	C₂×D₄₇	—	4	1	no	—
541	C₂×D₄₇	—	4	1	no	—
542	C₂×D₄₇	—	4	2	no	—
543	C₂×D₄₇	—	4	2	no	—
544	C₂×D₄₇	—	4	2	no	—
545	C₂×D₄₇	—	16	4	no	—
546	C₄×C₄₇	—	2	1	no	—
547	C₄×C₄₇	—	2	2	no	—
548	C₄×C₄₇	—	2	1	no	—
549	C₄×C₄₇	—	2	1	no	—
550	C₄×C₄₇	—	2	2	no	—
551	C₄×C₄₇	—	2	2	no	—
552	C₄×C₄₇	—	2	1	no	—
553	C₄×C₄₇	—	4	1	no	—
554	C₄×C₄₇	—	4	2	no	—
555	C₄×C₄₇	—	4	2	no	—
556	C₄×C₄₇	—	4	1	no	—
557	C₄×C₄₇	—	4	1	no	—
558	C₄×C₄₇	#577	1	2	yes	—
559	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
560	C₄×C₄₇	#585	1	1	yes	characteristic
561	Dic₄₇	—	4	1	no	—
562	Dic₄₇	—	4	1	no	—
563	Dic₄₇	—	4	2	no	—
564	Dic₄₇	—	4	1	no	—
565	#3515	D₄₇	1	1	yes	characteristic, complemented
566	#3514	—	47	1	no	—
567	#3400	—	47	1	no	—
568	#3384	—	47	1	no	—
569	#3361	—	47	1	no	—
570	#3359	—	47	1	no	—
571	#3356	—	47	1	no	—
572	#3348	—	47	2	no	—
573	#3303	—	47	2	no	—
574	#3302	—	47	1	no	—
575	#3296	—	47	2	no	—
576	#3295	—	47	1	no	—
577	#3272	—	47	1	no	—
578	#3267	—	47	2	no	—
579	#3178	—	47	2	no	—
580	#3167	—	47	1	no	—
581	#3125	—	47	2	no	—
582	#3123	—	47	2	no	—
583	#3116	—	47	1	no	—
584	#3115	—	47	1	no	—
585	#2966	—	47	1	no	—
586	#2946	—	47	2	no	—
587	C₄×#135	—	47	1	no	—
588	C₂×C₄₇	—	4	2	no	—
589	C₂×C₄₇	—	4	1	no	—
590	C₂×C₄₇	—	4	2	no	—
591	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
592	C₂×C₄₇	C₂×#577	1	1	yes	characteristic
593	C₂×C₄₇	#3584	1	1	yes	characteristic
594	D₄₇	—	4	2	no	—
595	D₄₇	—	8	2	no	—
596	C₂×AGL(1,ℤ/8)	—	47	2	no	—
597	C₂×#135	—	47	1	no	—
598	#559	—	47	1	no	—
599	#557	C₂×D₄₇	1	1	yes	characteristic, complemented
600	#556	—	47	1	no	—
601	#555	—	47	2	no	—
602	#554	C₂×D₄₇	1	1	yes	characteristic
603	#554	C₂×D₄₇	1	1	yes	characteristic, complemented
604	#553	—	2	1	no	—
605	#552	—	2	2	no	—
606	#552	—	2	1	no	—
607	#552	C₂×D₄₇	1	2	yes	complemented
608	#551	—	94	2	no	—
609	D₄×Q₈	—	47	1	no	—
610	#548	—	94	1	no	—
611	#547	C₂×D₄₇	1	1	yes	characteristic
612	#547	C₂×D₄₇	1	2	yes	complemented
613	#546	—	47	2	no	—
614	#546	—	94	1	no	—
615	D₄²	—	47	1	no	—
616	#542	—	47	2	no	—
617	#541	C₂×D₄₇	1	2	yes	complemented
618	#539	—	2	2	no	—
619	#538	—	94	2	no	—
620	#533	C₂×D₄₇	1	1	yes	characteristic, complemented
621	#532	—	47	1	no	—
622	#529	—	2	1	no	—
623	#529	—	94	1	no	—
624	#529	C₂×D₄₇	1	1	yes	characteristic
625	C₂×#125	—	2	1	no	—
626	C₂×#124	—	94	1	no	—
627	#520	C₂×D₄₇	1	2	yes	complemented
628	#518	—	47	2	no	—
629	C₄×#41	—	47	1	no	—
630	C₄×#41	C₂×D₄₇	1	1	yes	characteristic, complemented
631	#501	—	47	2	no	—
632	#498	—	47	1	no	—
633	#497	—	47	2	no	—
634	#492	—	47	1	no	—
635	#488	—	47	2	no	—
636	#487	—	47	1	no	—
637	#487	—	47	2	no	—
638	#486	—	47	1	no	—
639	#485	—	47	2	no	—
640	#485	—	47	2	no	—
641	#485	—	47	2	no	—
642	#483	—	47	2	no	—
643	#482	—	47	2	no	—
644	#481	—	47	2	no	—
645	#478	—	47	2	no	—
646	#478	—	47	2	no	—
647	#477	—	47	1	no	—
648	#476	—	47	1	no	—
649	#476	—	47	2	no	—
650	#475	—	47	2	no	—
651	#475	—	47	1	no	—
652	#474	—	47	1	no	—
653	#470	—	47	2	no	—
654	#468	—	47	2	no	—
655	#467	—	47	2	no	—
656	#465	—	47	2	no	—
657	#465	—	47	2	no	—
658	#465	—	47	2	no	—
659	#464	—	47	2	no	—
660	#463	—	47	2	no	—
661	#462	—	47	1	no	—
662	#461	—	47	1	no	—
663	#461	—	47	2	no	—
664	#461	—	47	2	no	—
665	#460	—	47	1	no	—
666	#459	—	47	1	no	—
667	#452	—	47	2	no	—
668	#452	—	47	2	no	—
669	#450	—	47	2	no	—
670	#450	—	47	2	no	—
671	#449	—	47	2	no	—
672	#449	—	47	2	no	—
673	#446	—	47	1	no	—
674	C₈×Q₈	—	47	1	no	—
675	#442	—	47	2	no	—
676	#442	—	47	2	no	—
677	#441	—	47	2	no	—
678	#440	—	47	2	no	—
679	#440	—	47	2	no	—
680	#440	—	47	2	no	—
681	C₄×Q₁₆	—	47	1	no	—
682	C₄×Q₁₆	—	47	1	no	—
683	C₄×SD₁₆	—	47	1	no	—
684	C₄×SD₁₆	—	47	2	no	—
685	C₄×SD₁₆	—	47	1	no	—
686	C₄×SD₁₆	—	47	2	no	—
687	C₄×SD₁₆	—	47	2	no	—
688	C₄×SD₁₆	—	47	1	no	—
689	C₄×SD₁₆	—	47	1	no	—
690	C₄×D₈	—	47	2	no	—
691	C₄×D₈	—	47	1	no	—
692	C₄×D₈	—	47	1	no	—
693	#436	—	47	1	no	—
694	#435	—	47	2	no	—
695	C₈×D₄	—	47	1	no	—
696	C₈×D₄	—	47	2	no	—
697	#433	—	47	2	no	—
698	#432	—	47	1	no	—
699	#428	—	47	2	no	—
700	#427	—	47	1	no	—
701	#416	—	47	1	no	—
702	#416	—	47	2	no	—
703	#416	—	47	1	no	—
704	C₂×#102	—	47	2	no	—
705	#405	—	47	2	no	—
706	C₂×C₄×C₈	—	47	1	no	—
707	C₄₇	#61493	1	1	yes	characteristic, complemented, Sylow
708	C₂×#41	—	47	1	no	—
709	C₂×#41	—	94	1	no	—
710	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
711	C₂×#41	C₂²×D₄₇	1	2	yes	—
712	C₂²×Q₈	—	94	1	no	—
713	C₂²×D₄	—	47	2	no	—
714	C₂²×D₄	—	94	1	no	—
715	AGL(1,ℤ/8)	—	94	8	no	—
716	#135	—	94	4	no	—
717	C₂×Q₁₆	—	47	1	no	—
718	C₂×Q₁₆	—	47	2	no	—
719	C₂×SD₁₆	—	47	1	no	—
720	C₂×SD₁₆	—	47	2	no	—
721	C₂×SD₁₆	—	47	2	no	—
722	C₂×SD₁₆	—	47	1	no	—
723	C₂×SD₁₆	—	47	2	no	—
724	C₂×SD₁₆	—	47	2	no	—
725	C₂×D₈	—	47	1	no	—
726	C₂×D₈	—	47	2	no	—
727	C₂×M₁₆	—	47	2	no	—
728	C₂²×C₈	—	47	1	no	—
729	C₂²×C₈	—	47	1	no	—
730	C₂²×C₈	—	47	2	no	—
731	C₄⋊Q₈	—	47	1	no	—
732	C₄⋊Q₈	—	47	2	no	—
733	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
734	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
735	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
736	#127	—	47	1	no	—
737	#126	—	2	2	no	—
738	#126	—	2	2	no	—
739	#126	—	2	2	no	—
740	#126	—	94	2	no	—
741	#126	—	94	2	no	—
742	#126	C₂²⋊D₄₇	1	2	yes	—
743	#125	—	2	2	no	—
744	#125	—	2	2	no	—
745	#125	—	2	1	no	—
746	#125	—	2	1	no	—
747	#125	—	2	2	no	—
748	#125	—	2	2	no	—
749	#125	—	2	1	no	—
750	#125	C₂²⋊D₄₇	1	1	yes	characteristic
751	#125	C₂²×D₄₇	1	2	yes	—
752	#124	—	47	2	no	—
753	#124	—	94	1	no	—
754	#124	—	94	1	no	—
755	#124	—	94	2	no	—
756	#124	—	94	2	no	—
757	#124	—	94	2	no	—
758	#124	—	94	1	no	—
759	#124	C₂²⋊D₄₇	1	1	yes	characteristic
760	#123	—	2	2	no	—
761	#123	—	2	2	no	—
762	#123	—	2	2	no	—
763	#123	—	2	2	no	—
764	#123	—	94	2	no	—
765	#123	—	94	2	no	—
766	#123	—	94	2	no	—
767	#123	C₂²⋊D₄₇	1	2	yes	—
768	C₂²⋊Q₈	—	2	1	no	—
769	C₂²⋊Q₈	—	2	1	no	—
770	C₂²⋊Q₈	—	2	2	no	—
771	C₂²⋊Q₈	—	2	2	no	—
772	C₂²⋊Q₈	—	47	2	no	—
773	C₂²⋊Q₈	—	94	1	no	—
774	C₂²⋊Q₈	—	94	2	no	—
775	C₂²⋊Q₈	—	94	2	no	—
776	C₂²⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
777	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
778	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
779	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
780	#121	—	2	1	no	—
781	#121	—	2	2	no	—
782	#121	—	47	2	no	—
783	#121	—	47	2	no	—
784	#121	—	94	2	no	—
785	#121	—	94	1	no	—
786	#121	—	94	1	no	—
787	#121	—	94	2	no	—
788	#121	C₂²⋊D₄₇	1	1	yes	characteristic
789	#120	—	94	2	no	—
790	#120	—	94	2	no	—
791	C₄×Q₈	—	2	1	no	—
792	C₄×Q₈	—	2	1	no	—
793	C₄×Q₈	—	47	1	no	—
794	C₄×Q₈	—	47	1	no	—
795	C₄×Q₈	—	94	1	no	—
796	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
797	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
798	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
799	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
800	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
801	C₄×D₄	—	2	1	no	—
802	C₄×D₄	—	2	1	no	—
803	C₄×D₄	—	2	1	no	—
804	C₄×D₄	—	2	2	no	—
805	C₄×D₄	—	2	2	no	—
806	C₄×D₄	—	47	1	no	—
807	C₄×D₄	—	47	1	no	—
808	C₄×D₄	—	47	2	no	—
809	C₄×D₄	—	47	2	no	—
810	C₄×D₄	—	47	2	no	—
811	C₄×D₄	—	94	1	no	—
812	C₄×D₄	—	94	1	no	—
813	C₄×D₄	—	94	2	no	—
814	C₄×D₄	—	94	2	no	—
815	C₄×D₄	—	94	1	no	—
816	C₄×D₄	—	94	1	no	—
817	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
818	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
819	C₄×D₄	C₂²×D₄₇	1	2	yes	—
820	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
821	C₄×D₄	C₂²×D₄₇	1	2	yes	—
822	#117	—	2	1	no	—
823	#117	—	2	2	no	—
824	#117	—	2	2	no	—
825	#117	—	2	1	no	—
826	#117	—	47	1	no	—
827	#117	—	47	2	no	—
828	#117	—	94	2	no	—
829	#117	—	94	1	no	—
830	#117	C₂²×D₄₇	1	1	yes	characteristic
831	#117	C₂²×D₄₇	1	2	yes	—
832	C₂×C₄⋊C₄	—	2	2	no	—
833	C₂×C₄⋊C₄	—	2	1	no	—
834	C₂×C₄⋊C₄	—	2	2	no	—
835	C₂×C₄⋊C₄	—	2	1	no	—
836	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
837	C₂×C₂²⋊C₄	—	94	2	no	—
838	C₂×C₂²⋊C₄	—	94	2	no	—
839	C₂×C₂²⋊C₄	—	94	2	no	—
840	C₂×C₄²	—	2	1	no	—
841	C₂×C₄²	—	94	1	no	—
842	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
843	#107	—	47	1	no	—
844	#107	—	47	1	no	—
845	#107	—	47	2	no	—
846	#107	—	47	2	no	—
847	#106	—	47	1	no	—
848	#106	—	47	1	no	—
849	#106	—	47	2	no	—
850	#106	—	47	2	no	—
851	#106	—	47	2	no	—
852	#106	—	47	2	no	—
853	C₄⋊C₈	—	47	1	no	—
854	C₄⋊C₈	—	47	1	no	—
855	C₄⋊C₈	—	47	2	no	—
856	C₄⋊C₈	—	47	2	no	—
857	#103	—	47	2	no	—
858	#103	—	47	1	no	—
859	#103	—	47	1	no	—
860	#103	—	47	2	no	—
861	#103	—	47	2	no	—
862	#103	—	47	2	no	—
863	#103	—	47	2	no	—
864	#103	—	47	1	no	—
865	#103	—	47	1	no	—
866	#103	—	47	2	no	—
867	#102	—	47	1	no	—
868	#102	—	47	1	no	—
869	#102	—	47	2	no	—
870	#102	—	47	1	no	—
871	#102	—	47	2	no	—
872	#102	—	47	2	no	—
873	#102	—	47	2	no	—
874	#102	—	47	1	no	—
875	#102	—	47	2	no	—
876	#102	—	47	2	no	—
877	C₂²⋊C₈	—	47	2	no	—
878	C₂²⋊C₈	—	47	2	no	—
879	C₂²⋊C₈	—	47	2	no	—
880	#97	—	47	2	no	—
881	#97	—	47	2	no	—
882	C₄×C₈	—	47	1	no	—
883	C₄×C₈	—	47	1	no	—
884	C₄×C₈	—	47	1	no	—
885	C₄×C₈	—	47	1	no	—
886	C₄×C₈	—	47	2	no	—
887	C₂⁴	—	94	2	no	—
888	#41	—	2	2	no	—
889	#41	—	2	4	no	—
890	#41	—	4	2	no	—
891	#41	—	4	1	no	—
892	#41	—	94	2	no	—
893	#41	—	376	2	no	—
894	#41	—	188	1	no	—
895	C₂×Q₈	—	2	1	no	—
896	C₂×Q₈	—	47	1	no	—
897	C₂×Q₈	—	94	2	no	—
898	C₂×Q₈	—	94	1	no	—
899	C₂×Q₈	—	376	2	no	—
900	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
901	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
902	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
903	C₂×D₄	—	2	1	no	—
904	C₂×D₄	—	2	2	no	—
905	C₂×D₄	—	47	1	no	—
906	C₂×D₄	—	47	2	no	—
907	C₂×D₄	—	94	4	no	—
908	C₂×D₄	—	94	2	no	—
909	C₂×D₄	—	94	2	no	—
910	C₂×D₄	—	94	1	no	—
911	C₂×D₄	—	94	1	no	—
912	C₂×D₄	—	94	2	no	—
913	C₂×D₄	—	94	1	no	—
914	C₂×D₄	—	376	2	no	—
915	C₂×D₄	—	188	2	no	—
916	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
917	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
918	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
919	C₂²×C₄	—	2	2	no	—
920	C₂²×C₄	—	2	1	no	—
921	C₂²×C₄	—	2	1	no	—
922	C₂²×C₄	—	2	2	no	—
923	C₂²×C₄	—	2	1	no	—
924	C₂²×C₄	—	2	2	no	—
925	C₂²×C₄	—	94	1	no	—
926	C₂²×C₄	—	94	2	no	—
927	C₂²×C₄	—	94	2	no	—
928	C₂²×C₄	—	94	2	no	—
929	C₂²×C₄	—	94	1	no	—
930	C₂²×C₄	—	94	1	no	—
931	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
932	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
933	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
934	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
935	Q₁₆	—	94	2	no	—
936	Q₁₆	—	188	2	no	—
937	SD₁₆	—	94	4	no	—
938	SD₁₆	—	94	2	no	—
939	SD₁₆	—	94	4	no	—
940	SD₁₆	—	94	2	no	—
941	SD₁₆	—	188	2	no	—
942	SD₁₆	—	188	2	no	—
943	D₈	—	47	4	no	—
944	D₈	—	94	4	no	—
945	M₁₆	—	94	4	no	—
946	C₂×C₈	—	47	1	no	—
947	C₂×C₈	—	47	1	no	—
948	C₂×C₈	—	47	1	no	—
949	C₂×C₈	—	47	1	no	—
950	C₂×C₈	—	47	2	no	—
951	C₂×C₈	—	47	2	no	—
952	C₂×C₈	—	94	2	no	—
953	C₂×C₈	—	188	1	no	—
954	C₂×C₈	—	188	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	1	no	—
957	C₄⋊C₄	—	2	1	no	—
958	C₄⋊C₄	—	2	2	no	—
959	C₄⋊C₄	—	2	2	no	—
960	C₄⋊C₄	—	2	2	no	—
961	C₄⋊C₄	—	2	2	no	—
962	C₄⋊C₄	—	2	2	no	—
963	C₄⋊C₄	—	2	2	no	—
964	C₄⋊C₄	—	2	2	no	—
965	C₄⋊C₄	—	2	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	2	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	2	no	—
970	C₄⋊C₄	—	47	2	no	—
971	C₄⋊C₄	—	47	1	no	—
972	C₄⋊C₄	—	47	1	no	—
973	C₄⋊C₄	—	94	1	no	—
974	C₄⋊C₄	—	94	1	no	—
975	C₄⋊C₄	—	94	2	no	—
976	C₄⋊C₄	—	94	2	no	—
977	C₄⋊C₄	—	94	1	no	—
978	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
979	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
980	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
981	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
982	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
983	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
984	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
985	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
986	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
987	C₂²⋊C₄	—	2	2	no	—
988	C₂²⋊C₄	—	2	2	no	—
989	C₂²⋊C₄	—	2	1	no	—
990	C₂²⋊C₄	—	2	2	no	—
991	C₂²⋊C₄	—	2	1	no	—
992	C₂²⋊C₄	—	2	1	no	—
993	C₂²⋊C₄	—	2	2	no	—
994	C₂²⋊C₄	—	94	2	no	—
995	C₂²⋊C₄	—	94	2	no	—
996	C₂²⋊C₄	—	94	1	no	—
997	C₂²⋊C₄	—	94	1	no	—
998	C₂²⋊C₄	—	94	2	no	—
999	C₂²⋊C₄	—	94	2	no	—
1000	C₂²⋊C₄	—	94	2	no	—
1001	C₂²⋊C₄	—	94	2	no	—
1002	C₂²⋊C₄	—	94	2	no	—
1003	C₂²⋊C₄	—	94	1	no	—
1004	C₂²⋊C₄	—	94	2	no	—
1005	C₂²⋊C₄	—	94	2	no	—
1006	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1007	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1008	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1009	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1010	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1011	C₄²	—	2	1	no	—
1012	C₄²	—	2	1	no	—
1013	C₄²	—	2	1	no	—
1014	C₄²	—	2	2	no	—
1015	C₄²	—	2	2	no	—
1016	C₄²	—	94	1	no	—
1017	C₄²	—	94	1	no	—
1018	C₄²	—	94	1	no	—
1019	C₄²	—	94	2	no	—
1020	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1021	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1022	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1023	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1024	C₄²	C₂³×D₄₇	1	2	yes	—
1025	C₂³	—	2	1	no	—
1026	C₂³	—	94	1	no	—
1027	C₂³	—	94	2	no	—
1028	C₂³	—	376	2	no	—
1029	C₂³	—	376	2	no	—
1030	C₂³	—	188	4	no	—
1031	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1032	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
1033	Q₈	—	2	2	no	—
1034	Q₈	—	2	2	no	—
1035	Q₈	—	2	1	no	—
1036	Q₈	—	2	1	no	—
1037	Q₈	—	2	2	no	—
1038	Q₈	—	8	1	no	—
1039	Q₈	—	94	1	no	—
1040	Q₈	—	94	1	no	—
1041	Q₈	—	376	2	no	—
1042	Q₈	—	188	2	no	—
1043	D₄	—	2	2	no	—
1044	D₄	—	2	1	no	—
1045	D₄	—	4	2	no	—
1046	D₄	—	4	2	no	—
1047	D₄	—	4	4	no	—
1048	D₄	—	47	2	no	—
1049	D₄	—	94	2	no	—
1050	D₄	—	94	1	no	—
1051	D₄	—	94	2	no	—
1052	D₄	—	376	1	no	—
1053	D₄	—	376	2	no	—
1054	D₄	—	376	2	no	—
1055	D₄	—	188	4	no	—
1056	D₄	—	188	2	no	—
1057	D₄	—	188	2	no	—
1058	D₄	#41×D₄₇	1	2	yes	—
1059	C₂×C₄	—	2	2	no	—
1060	C₂×C₄	—	2	1	no	—
1061	C₂×C₄	—	2	2	no	—
1062	C₂×C₄	—	2	2	no	—
1063	C₂×C₄	—	2	1	no	—
1064	C₂×C₄	—	2	1	no	—
1065	C₂×C₄	—	2	1	no	—
1066	C₂×C₄	—	2	1	no	—
1067	C₂×C₄	—	2	2	no	—
1068	C₂×C₄	—	2	2	no	—
1069	C₂×C₄	—	4	1	no	—
1070	C₂×C₄	—	4	2	no	—
1071	C₂×C₄	—	4	4	no	—
1072	C₂×C₄	—	4	2	no	—
1073	C₂×C₄	—	8	1	no	—
1074	C₂×C₄	—	8	2	no	—
1075	C₂×C₄	—	8	2	no	—
1076	C₂×C₄	—	94	1	no	—
1077	C₂×C₄	—	94	1	no	—
1078	C₂×C₄	—	94	1	no	—
1079	C₂×C₄	—	94	2	no	—
1080	C₂×C₄	—	376	1	no	—
1081	C₂×C₄	—	376	2	no	—
1082	C₂×C₄	—	376	2	no	—
1083	C₂×C₄	—	376	2	no	—
1084	C₂×C₄	—	188	2	no	—
1085	C₂×C₄	—	188	2	no	—
1086	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1087	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1088	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1089	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1090	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1091	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1092	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1093	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1094	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1095	C₈	—	47	2	no	—
1096	C₈	—	94	1	no	—
1097	C₈	—	94	2	no	—
1098	C₈	—	94	1	no	—
1099	C₈	—	94	1	no	—
1100	C₈	—	94	2	no	—
1101	C₂²	—	2	1	no	—
1102	C₂²	—	2	2	no	—
1103	C₂²	—	2	1	no	—
1104	C₂²	—	2	2	no	—
1105	C₂²	—	2	2	no	—
1106	C₂²	—	2	1	no	—
1107	C₂²	—	2	2	no	—
1108	C₂²	—	4	1	no	—
1109	C₂²	—	4	1	no	—
1110	C₂²	—	94	2	no	—
1111	C₂²	—	188	2	no	—
1112	C₂²	—	188	2	no	—
1113	C₂²	—	188	2	no	—
1114	C₂²	—	188	1	no	—
1115	C₂²	—	188	1	no	—
1116	C₂²	—	752	4	no	—
1117	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1118	C₄	—	2	1	no	—
1119	C₄	—	2	2	no	—
1120	C₄	—	2	1	no	—
1121	C₄	—	2	2	no	—
1122	C₄	—	2	1	no	—
1123	C₄	—	2	1	no	—
1124	C₄	—	2	2	no	—
1125	C₄	—	4	1	no	—
1126	C₄	—	4	2	no	—
1127	C₄	—	4	1	no	—
1128	C₄	—	4	1	no	—
1129	C₄	—	4	2	no	—
1130	C₄	—	188	2	no	—
1131	C₄	—	188	1	no	—
1132	C₄	—	188	1	no	—
1133	C₄	—	188	1	no	—
1134	C₄	#15689931	1	2	yes	—
1135	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1136	C₄	#15689959	1	1	yes	characteristic
1137	C₂	—	4	2	no	—
1138	C₂	—	4	1	no	—
1139	C₂	—	4	2	no	—
1140	C₂	—	376	2	no	—
1141	C₂	—	188	2	no	—
1142	C₂	#41×C₂²⋊D₄₇	1	1	yes	characteristic
1143	C₂	C₂×#15689931	1	1	yes	characteristic
1144	C₂	#20258159	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂³×C₂²⋊D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3515	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3515	D₄₇
hypocenter	C₄₇	#61493
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #529 ◁ #3515

Complements

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

N	H ≅ G/N	type
1. #20257351	C₂	semidirect
2. #20256437	C₂	semidirect
3. #20256287	C₂	semidirect
4. #20256048	C₂	semidirect
5. #20256026	C₂	semidirect
6. #20256003	C₂	semidirect
7. #20255897	C₂	semidirect
8. #20255316	C₂	semidirect
9. #20255305	C₂	semidirect
10. #20255217	C₂	semidirect
11. #20255206	C₂	semidirect
12. #20254988	C₂	semidirect
13. #20254914	C₂	semidirect
14. #20254058	C₂	semidirect
15. #20253948	C₂	semidirect
16. #20253665	C₂	semidirect
17. #20253635	C₂	semidirect
18. #20253544	C₂	semidirect
19. #20253539	C₂	semidirect
20. #20252364	C₂	semidirect
21. #20252216	C₂	semidirect
22. C₄×#13094044	C₂	semidirect
23. C₄₇×#3515	C₂	semidirect
42. #15689533	C₂²	semidirect
43. #15689519	C₂²	semidirect
44. #15689515	C₂²	semidirect
46. #15689480	C₂²	semidirect
47. #15689473	C₂²	semidirect
48. #15689473	C₂²	semidirect
50. #15689461	C₂²	semidirect
51. #15689461	C₂²	semidirect
52. #15689461	C₂²	semidirect
53. #15689453	C₂²	semidirect
54. #15689447	C₂²	semidirect
57. #15689420	C₂²	semidirect
58. #15689415	C₂²	semidirect
59. #15689413	C₂²	semidirect
61. #15689408	C₂²	semidirect
62. #15689408	C₂²	semidirect
63. #15689403	C₂²	semidirect
64. #15689379	C₂²	semidirect
66. #15689362	C₂²	semidirect
68. #15689354	C₂²	semidirect
69. #15689354	C₂²	semidirect
70. #15689345	C₂²	semidirect
71. #15689338	C₂²	semidirect
72. #15689330	C₂²	semidirect
75. #15689325	C₂²	semidirect
78. #15689285	C₂²	semidirect
83. #15689268	C₂²	semidirect
84. #15689254	C₂²	semidirect
85. Q₈×C₄₇⋊C₈	C₂²	semidirect
87. #15689233	C₂²	semidirect
88. #15689228	C₂²	semidirect
90. #15689221	C₂²	semidirect
91. #15689221	C₂²	semidirect
92. C₄×#10625337	C₂²	semidirect
93. C₄×#10625337	C₂²	semidirect
97. C₄×#10625336	C₂²	semidirect
98. C₄×#10625336	C₂²	semidirect
99. C₄×#10625335	C₂²	semidirect
100. C₄×#10625335	C₂²	semidirect
103. C₄×#10625334	C₂²	semidirect
105. #15689195	C₂²	semidirect
107. D₄×C₄₇⋊C₈	C₂²	semidirect
108. #15689184	C₂²	semidirect
109. #15689180	C₂²	semidirect
110. #15689163	C₂²	semidirect
111. #15689159	C₂²	semidirect
112. #15689119	C₂²	semidirect
113. #15689119	C₂²	semidirect
116. #15689079	C₂²	semidirect
117. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
118. C₄₇×#557	C₂²	semidirect
120. C₄₇×#554	C₂²	semidirect
124. C₄₇×#552	C₂²	semidirect
126. C₄₇×#547	C₂²	semidirect
127. C₄₇×#541	C₂²	semidirect
129. C₄₇×#533	C₂²	semidirect
133. C₄₇×#520	C₂²	semidirect
134. C₄×#41×C₄₇	C₂²	semidirect
420. #10625334	#41	semidirect
565. #3515	D₄₇	semidirect
599. #557	C₂×D₄₇	semidirect
603. #554	C₂×D₄₇	semidirect
607. #552	C₂×D₄₇	semidirect
612. #547	C₂×D₄₇	semidirect
617. #541	C₂×D₄₇	semidirect
620. #533	C₂×D₄₇	semidirect
627. #520	C₂×D₄₇	semidirect
630. C₄×#41	C₂×D₄₇	semidirect
707. C₄₇	#61493	semidirect

Maximal subgroups

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

subgroup	index
#20257351	2
#20256437	2
#20256287	2
#20256048	2
#20256026	2
#20256003	2
#20255897	2
#20255316	2
#20255305	2
#20255217	2
#20255206	2
#20254988	2
#20254914	2
#20254058	2
#20253948	2
#20253665	2
#20253635	2
#20253544	2
#20253539	2
#20252364	2
#20252216	2
C₄×#13094044	2
C₄₇×#3515	2
#61493	47