Subgroups — #27098857

Order 12032.

1880 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257422	C₂	1	1	yes	maximal, characteristic
2	#20256365	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256259	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256165	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256117	C₂	1	1	yes	maximal, characteristic, complemented
6	#20255795	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255767	C₂	1	2	yes	maximal, complemented
8	#20255682	C₂	1	1	yes	maximal, characteristic, complemented
9	#20255613	C₂	1	1	yes	maximal, characteristic, complemented
10	#20255559	C₂	1	2	yes	maximal, complemented
11	#20255403	C₂	1	2	yes	maximal, complemented
12	D₄×#10625336	C₂	1	2	yes	maximal, complemented
13	D₄×#10625336	C₂	1	1	yes	maximal, characteristic, complemented
14	#20254017	C₂	1	2	yes	maximal, complemented
15	#20253948	C₂	1	1	yes	maximal, characteristic, complemented
16	#20253679	C₂	1	2	yes	maximal, complemented
17	#20253635	C₂	1	2	yes	maximal, complemented
18	#20253510	C₂	1	1	yes	maximal, characteristic, complemented
19	#20253483	C₂	1	1	yes	maximal, characteristic, complemented
20	#20252364	C₂	1	1	yes	maximal, characteristic, complemented
21	#20252247	C₂	1	2	yes	maximal, complemented
22	C₂×C₄×#10625336	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3523	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×#10625336	C₂²	1	2	yes	—
25	C₂²×#10625336	C₂²	1	1	yes	characteristic
26	#15689838	C₂²	1	1	yes	characteristic
27	#15689833	C₂²	1	1	yes	characteristic
28	#15689826	—	2	1	no	—
29	#15689819	C₂²	1	2	yes	—
30	#15689795	C₂²	1	1	yes	characteristic
31	#15689766	—	2	1	no	—
32	#15689765	—	2	2	no	—
33	D₄×D₁₈₈	C₂²	1	1	yes	characteristic
34	D₄×D₁₈₈	C₂²	1	2	yes	—
35	#15689728	C₂²	1	2	yes	—
36	#15689712	—	2	2	no	—
37	#15689673	C₂²	1	1	yes	characteristic
38	#15689636	—	2	1	no	—
39	#121×D₄₇	—	2	1	no	—
40	#15689597	C₂²	1	2	yes	—
41	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
42	#15689522	C₂²	1	2	yes	complemented
43	#15689519	C₂²	1	1	yes	characteristic, complemented
44	#15689497	C₂²	1	2	yes	complemented
45	#15689497	C₂²	1	1	yes	characteristic, complemented
46	#15689491	C₂²	1	2	yes	complemented
47	#15689489	C₂²	1	2	yes	complemented
48	#15689473	C₂²	1	1	yes	characteristic, complemented
49	#15689471	C₂²	1	1	yes	characteristic, complemented
50	#15689461	C₂²	1	2	yes	complemented
51	#15689461	C₂²	1	2	yes	complemented
52	#15689456	C₂²	1	2	yes	complemented
53	#15689447	C₂²	1	2	yes	complemented
54	#15689447	C₂²	1	2	yes	complemented
55	#15689436	C₂²	1	2	yes	complemented
56	#15689430	C₂²	1	2	yes	complemented
57	#15689430	C₂²	1	2	yes	complemented
58	#15689420	C₂²	1	2	yes	—
59	#15689420	C₂²	1	2	yes	complemented
60	#15689418	C₂²	1	1	yes	characteristic, complemented
61	#15689418	C₂²	1	1	yes	characteristic, complemented
62	#15689400	C₂²	1	1	yes	characteristic
63	#15689400	C₂²	1	1	yes	characteristic, complemented
64	#15689371	C₂²	1	2	yes	complemented
65	#15689371	C₂²	1	2	yes	complemented
66	#15689354	C₂²	1	2	yes	complemented
67	#15689354	C₂²	1	2	yes	complemented
68	#15689354	C₂²	1	2	yes	complemented
69	#15689354	C₂²	1	2	yes	complemented
70	#15689325	C₂²	1	1	yes	characteristic
71	#15689325	C₂²	1	2	yes	—
72	#15689325	C₂²	1	1	yes	characteristic, complemented
73	#15689325	C₂²	1	2	yes	complemented
74	#15689323	C₂²	1	1	yes	characteristic, complemented
75	#15689323	C₂²	1	1	yes	characteristic, complemented
76	#15689323	C₂²	1	2	yes	complemented
77	#15689323	C₂²	1	2	yes	complemented
78	#15689273	C₂²	1	2	yes	—
79	#15689273	C₂²	1	2	yes	—
80	#15689273	C₂²	1	2	yes	—
81	#15689262	C₂²	1	2	yes	complemented
82	#15689262	C₂²	1	2	yes	complemented
83	#15689262	C₂²	1	2	yes	complemented
84	#15689254	C₂²	1	1	yes	characteristic, complemented
85	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
86	#15689221	C₂²	1	2	yes	—
87	#15689221	C₂²	1	2	yes	—
88	#15689221	C₂²	1	2	yes	complemented
89	#15689221	C₂²	1	2	yes	complemented
90	#15689221	C₂²	1	2	yes	complemented
91	#15689221	C₂²	1	2	yes	complemented
92	C₄×#10625336	C₂²	1	2	yes	—
93	C₄×#10625336	C₂²	1	1	yes	characteristic
94	C₄×#10625336	C₂²	1	1	yes	characteristic
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	1	yes	characteristic, complemented
99	C₄×#10625336	C₂²	1	1	yes	characteristic, complemented
100	C₄×#10625336	C₂²	1	2	yes	complemented
101	C₄×#10625336	C₂²	1	1	yes	characteristic, complemented
102	C₄×#10625336	C₂²	1	2	yes	complemented
103	C₄×#10625336	C₂²	1	1	yes	characteristic, complemented
104	#15689201	C₂²	1	1	yes	characteristic, complemented
105	#15689195	C₂²	1	2	yes	complemented
106	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
107	D₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
108	#15689184	C₂²	1	2	yes	complemented
109	#15689180	C₂²	1	1	yes	characteristic, complemented
110	#15689159	C₂²	1	2	yes	complemented
111	C₂×#13093955	C₂²	1	1	yes	characteristic, complemented
112	#15689132	C₂²	1	2	yes	complemented
113	#15689127	C₂²	1	2	yes	—
114	C₂×#13093948	C₂²	1	1	yes	characteristic, complemented
115	C₂×#13093944	C₂²	1	1	yes	characteristic
116	#15689079	C₂²	1	2	yes	complemented
117	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
118	C₄₇×#557	—	2	1	no	—
119	C₄₇×#557	C₂²	1	1	yes	characteristic, complemented
120	C₄₇×#557	C₂²	1	1	yes	characteristic, complemented
121	C₄₇×#556	—	2	1	no	—
122	C₄₇×#556	C₂²	1	1	yes	characteristic, complemented
123	C₄₇×#552	—	2	2	no	—
124	C₄₇×#552	C₂²	1	2	yes	complemented
125	D₄×Q₈×C₄₇	C₂²	1	2	yes	complemented
126	D₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
127	C₄₇×#541	—	2	2	no	—
128	C₄₇×#541	C₂²	1	2	yes	complemented
129	C₄₇×#533	—	2	1	no	—
130	C₄₇×#533	C₂²	1	1	yes	characteristic, complemented
131	C₄₇×#529	—	2	1	no	—
132	C₄₇×#529	C₂²	1	1	yes	characteristic
133	C₄₇×#519	C₂²	1	2	yes	complemented
134	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
135	C₂×#10625354	—	2	1	no	—
136	C₂×#10625350	—	2	1	no	—
137	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
138	C₂²×D₁₈₈	C₂³	1	2	yes	—
139	C₂×D₄×D₄₇	—	2	2	no	—
140	C₂×D₄×D₄₇	—	2	1	no	—
141	C₂²×C₄×D₄₇	—	2	1	no	—
142	C₂×#10625336	—	2	8	no	—
143	C₂×#10625336	—	2	4	no	—
144	C₂×#10625336	C₂³	1	2	yes	—
145	C₂×#10625336	C₂³	1	2	yes	—
146	C₂×#10625336	C₂³	1	1	yes	characteristic
147	C₂×#10625336	C₂³	1	2	yes	—
148	C₂×#10625336	C₂³	1	1	yes	characteristic
149	C₂×#10625336	C₂³	1	1	yes	characteristic
150	C₂×#10625336	C₂³	1	2	yes	—
151	C₂×#10625336	C₂³	1	2	yes	—
152	C₂×#10625336	C₂³	1	2	yes	—
153	C₂×#10625336	C₂³	1	1	yes	characteristic
154	C₂×#10625329	C₂³	1	2	yes	—
155	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
156	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
157	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
158	#13094024	C₂³	1	1	yes	characteristic
159	#13094021	C₂³	1	2	yes	—
160	#13094021	C₂³	1	1	yes	characteristic
161	#13094019	—	2	2	no	—
162	#13094016	C₂³	1	2	yes	—
163	#13094012	—	2	1	no	—
164	#13094010	—	2	2	no	—
165	#13094009	—	2	2	no	—
166	#13094009	—	2	2	no	—
167	#13094006	—	2	2	no	—
168	#13094002	—	2	2	no	—
169	#13094000	—	2	1	no	—
170	#13093999	—	2	1	no	—
171	#13093999	—	2	2	no	—
172	#13093999	—	2	2	no	—
173	#13093999	—	2	1	no	—
174	#13093998	—	2	1	no	—
175	#13093998	C₂³	1	2	yes	—
176	#13093998	C₂³	1	2	yes	—
177	#13093998	C₂³	1	2	yes	—
178	#13093997	—	2	2	no	—
179	#13093997	—	2	2	no	—
180	#13093996	—	2	2	no	—
181	#13093995	—	2	1	no	—
182	#13093994	—	2	2	no	—
183	#13093994	—	2	2	no	—
184	#13093994	—	2	2	no	—
185	C₄×D₁₈₈	—	2	1	no	—
186	C₄×D₁₈₈	—	2	1	no	—
187	C₄×D₁₈₈	—	2	1	no	—
188	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
189	C₄×D₁₈₈	C₂³	1	2	yes	—
190	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
191	C₄×D₁₈₈	C₂³	1	2	yes	—
192	C₄×D₁₈₈	C₂³	1	2	yes	—
193	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
194	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
195	#13093986	—	2	2	no	—
196	#13093986	—	2	2	no	—
197	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
198	#13093983	C₂³	1	2	yes	—
199	#13093982	—	2	1	no	—
200	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
201	C₄⋊C₄×D₄₇	—	2	1	no	—
202	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
203	C₂²⋊C₄×D₄₇	—	2	2	no	—
204	C₂²⋊C₄×D₄₇	—	2	2	no	—
205	#13093957	C₂³	1	2	yes	—
206	#13093957	C₂³	1	2	yes	—
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	1	yes	characteristic
212	#13093955	C₂³	1	1	yes	characteristic
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	2	yes	—
220	#13093948	C₂³	1	2	yes	—
221	#13093948	C₂³	1	2	yes	—
222	#13093948	C₂³	1	1	yes	characteristic
223	#13093948	C₂³	1	2	yes	—
224	#13093948	C₂³	1	2	yes	—
225	#13093948	C₂³	1	2	yes	—
226	#13093948	C₂³	1	1	yes	characteristic
227	#13093948	C₂³	1	1	yes	characteristic
228	#13093948	C₂³	1	1	yes	characteristic
229	#13093944	C₂³	1	1	yes	characteristic
230	#13093944	C₂³	1	2	yes	—
231	#13093944	C₂³	1	2	yes	—
232	#13093944	C₂³	1	2	yes	—
233	#13093944	C₂³	1	2	yes	—
234	#13093944	C₂³	1	2	yes	—
235	#13093944	C₂³	1	1	yes	characteristic
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	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
250	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
251	C₄⋊Q₈×C₄₇	—	2	1	no	—
252	C₄⋊Q₈×C₄₇	—	2	1	no	—
253	C₄⋊Q₈×C₄₇	—	2	2	no	—
254	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
255	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
256	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
257	#126×C₄₇	—	2	2	no	—
258	#126×C₄₇	—	2	2	no	—
259	#126×C₄₇	—	2	2	no	—
260	#126×C₄₇	—	2	2	no	—
261	#126×C₄₇	D₄	1	2	yes	—
262	#125×C₄₇	—	2	1	no	—
263	#125×C₄₇	—	2	2	no	—
264	#125×C₄₇	—	2	2	no	—
265	#125×C₄₇	—	2	2	no	—
266	#125×C₄₇	—	2	2	no	—
267	#125×C₄₇	—	2	2	no	—
268	#125×C₄₇	—	2	1	no	—
269	#125×C₄₇	D₄	1	1	yes	characteristic
270	#125×C₄₇	C₂³	1	2	yes	—
271	#124×C₄₇	—	2	1	no	—
272	#124×C₄₇	D₄	1	1	yes	characteristic
273	#123×C₄₇	—	2	2	no	—
274	#123×C₄₇	D₄	1	2	yes	—
275	C₂²⋊Q₈×C₄₇	—	2	1	no	—
276	C₂²⋊Q₈×C₄₇	—	2	2	no	—
277	C₂²⋊Q₈×C₄₇	—	2	2	no	—
278	C₂²⋊Q₈×C₄₇	—	2	2	no	—
279	C₂²⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
280	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
281	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
282	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
283	#121×C₄₇	D₄	1	1	yes	characteristic
284	C₄×Q₈×C₄₇	—	2	1	no	—
285	C₄×Q₈×C₄₇	—	2	2	no	—
286	C₄×Q₈×C₄₇	—	2	2	no	—
287	C₄×Q₈×C₄₇	—	2	1	no	—
288	C₄×Q₈×C₄₇	—	2	1	no	—
289	C₄×Q₈×C₄₇	—	2	1	no	—
290	C₄×Q₈×C₄₇	—	2	1	no	—
291	C₄×Q₈×C₄₇	—	2	1	no	—
292	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
293	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
294	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
295	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
296	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
297	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
298	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
299	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
300	C₄×D₄×C₄₇	—	2	2	no	—
301	C₄×D₄×C₄₇	—	2	1	no	—
302	C₄×D₄×C₄₇	C₂³	1	2	yes	—
303	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
304	#117×C₄₇	—	2	1	no	—
305	#117×C₄₇	—	2	2	no	—
306	#117×C₄₇	—	2	2	no	—
307	#117×C₄₇	—	2	2	no	—
308	#117×C₄₇	C₂³	1	2	yes	—
309	#117×C₄₇	C₂³	1	2	yes	—
310	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
311	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
312	C₂×C₄²×C₄₇	—	2	1	no	—
313	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
314	C₂³×D₄₇	—	2	1	no	—
315	C₂³×D₄₇	—	2	2	no	—
316	C₂×Q₈×C₄₇	—	2	1	no	—
317	C₂×Q₈×C₄₇	—	2	2	no	—
318	C₂×Q₈×C₄₇	—	2	1	no	—
319	C₂×Q₈×C₄₇	—	2	2	no	—
320	C₂×Q₈×C₄₇	—	2	4	no	—
321	C₂×Q₈×C₄₇	—	4	1	no	—
322	C₂×Q₈×C₄₇	—	4	2	no	—
323	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
324	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
325	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
326	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
328	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
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	C₂×D₄	1	1	yes	characteristic
333	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
334	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
335	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
336	C₂×C₂²⋊D₄₇	—	2	2	no	—
337	C₂×C₂²⋊D₄₇	—	2	2	no	—
338	C₂×C₂²⋊D₄₇	—	2	2	no	—
339	C₂²×Dic₄₇	—	2	1	no	—
340	#10625354	—	8	2	no	—
341	D₄×D₄₇	—	8	2	no	—
342	D₄×D₄₇	—	8	4	no	—
343	#10625350	—	8	2	no	—
344	C₂×D₁₈₈	—	2	2	no	—
345	C₂×D₁₈₈	—	2	4	no	—
346	C₂×D₁₈₈	—	2	2	no	—
347	C₂×D₁₈₈	—	2	1	no	—
348	C₂×D₁₈₈	—	2	1	no	—
349	C₂×D₁₈₈	—	2	2	no	—
350	C₂×D₁₈₈	—	2	1	no	—
351	C₂×D₁₈₈	—	2	2	no	—
352	C₂×D₁₈₈	—	4	1	no	—
353	C₂×D₁₈₈	—	4	2	no	—
354	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
355	C₂×D₁₈₈	C₂⁴	1	2	yes	—
356	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
357	C₂×C₄×D₄₇	—	2	1	no	—
358	C₂×C₄×D₄₇	—	2	1	no	—
359	C₂×C₄×D₄₇	—	2	1	no	—
360	C₂×C₄×D₄₇	—	2	2	no	—
361	C₂×C₄×D₄₇	—	2	2	no	—
362	C₂×C₄×D₄₇	—	2	2	no	—
363	C₂×C₄×D₄₇	—	2	1	no	—
364	C₂×C₄×D₄₇	—	8	2	no	—
365	C₂×Dic₉₄	—	2	1	no	—
366	C₄⋊C₄×C₄₇	—	2	1	no	—
367	C₄⋊C₄×C₄₇	—	2	1	no	—
368	C₄⋊C₄×C₄₇	—	2	1	no	—
369	C₄⋊C₄×C₄₇	—	2	1	no	—
370	C₄⋊C₄×C₄₇	—	2	1	no	—
371	C₄⋊C₄×C₄₇	—	2	2	no	—
372	C₄⋊C₄×C₄₇	—	2	2	no	—
373	C₄⋊C₄×C₄₇	—	2	2	no	—
374	C₄⋊C₄×C₄₇	—	2	1	no	—
375	C₄⋊C₄×C₄₇	—	2	2	no	—
376	C₄⋊C₄×C₄₇	—	2	1	no	—
377	C₄⋊C₄×C₄₇	—	2	2	no	—
378	C₄⋊C₄×C₄₇	—	2	1	no	—
379	C₄⋊C₄×C₄₇	—	2	2	no	—
380	C₄⋊C₄×C₄₇	—	2	2	no	—
381	C₄⋊C₄×C₄₇	—	2	2	no	—
382	C₄⋊C₄×C₄₇	—	2	2	no	—
383	C₄⋊C₄×C₄₇	—	2	2	no	—
384	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
385	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
386	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
387	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
388	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
389	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
390	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
391	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
392	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
393	C₂²⋊C₄×C₄₇	—	2	2	no	—
394	C₂²⋊C₄×C₄₇	—	2	2	no	—
395	C₂²⋊C₄×C₄₇	—	2	2	no	—
396	C₂²⋊C₄×C₄₇	—	2	2	no	—
397	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
398	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
399	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
400	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
401	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
402	C₄²×C₄₇	—	2	1	no	—
403	C₄²×C₄₇	—	2	1	no	—
404	C₄²×C₄₇	—	2	1	no	—
405	C₄²×C₄₇	—	2	1	no	—
406	C₄²×C₄₇	—	2	2	no	—
407	C₄²×C₄₇	—	2	2	no	—
408	C₄²×C₄₇	—	2	2	no	—
409	C₄²×C₄₇	—	2	2	no	—
410	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
411	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
412	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
413	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
414	C₄²×C₄₇	C₂⁴	1	2	yes	—
415	C₂²⋊Dic₄₇	—	2	2	no	—
416	#10625336	—	2	4	no	—
417	#10625336	—	2	2	no	—
418	#10625336	—	2	4	no	—
419	#10625336	—	2	2	no	—
420	#10625336	—	2	4	no	—
421	#10625336	—	2	2	no	—
422	#10625336	—	4	2	no	—
423	#10625336	—	4	2	no	—
424	#10625336	—	4	2	no	—
425	#10625336	#41	1	4	yes	complemented
426	(C₂×D₄₇)⋊C₄	—	2	1	no	—
427	(C₂×D₄₇)⋊C₄	—	2	2	no	—
428	(C₂×D₄₇)⋊C₄	—	2	2	no	—
429	(C₂×D₄₇)⋊C₄	—	2	2	no	—
430	(C₂×D₄₇)⋊C₄	—	2	1	no	—
431	(C₂×D₄₇)⋊C₄	—	2	1	no	—
432	(C₂×D₄₇)⋊C₄	—	2	1	no	—
433	(C₂×D₄₇)⋊C₄	—	2	2	no	—
434	(C₂×D₄₇)⋊C₄	—	2	2	no	—
435	(C₂×D₄₇)⋊C₄	—	2	2	no	—
436	C₄⋊Dic₄₇	—	2	1	no	—
437	C₄⋊Dic₄₇	—	2	1	no	—
438	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
439	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
440	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
441	Dic₄₇⋊C₄	—	2	2	no	—
442	Dic₄₇⋊C₄	—	2	2	no	—
443	C₄×Dic₄₇	—	2	2	no	—
444	#10625329	—	4	2	no	—
445	C₂×C₄₇⋊C₈	—	2	2	no	—
446	C₂×C₄₇⋊C₈	—	2	4	no	—
447	C₂×C₄₇⋊C₈	—	4	1	no	—
448	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
449	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
450	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
451	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
452	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
453	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
454	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
455	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
456	C₂²×D₄₇	—	2	1	no	—
457	C₂²×D₄₇	—	2	1	no	—
458	C₂²×D₄₇	—	2	2	no	—
459	C₂²×D₄₇	—	4	2	no	—
460	C₂²×D₄₇	—	4	4	no	—
461	C₂²×D₄₇	—	4	2	no	—
462	C₂²×D₄₇	—	8	1	no	—
463	C₂²×D₄₇	—	8	2	no	—
464	C₂²×D₄₇	—	8	2	no	—
465	Q₈×C₄₇	—	2	2	no	—
466	Q₈×C₄₇	—	2	1	no	—
467	Q₈×C₄₇	—	2	2	no	—
468	Q₈×C₄₇	—	2	1	no	—
469	Q₈×C₄₇	—	2	2	no	—
470	Q₈×C₄₇	—	2	1	no	—
471	Q₈×C₄₇	—	4	2	no	—
472	Q₈×C₄₇	—	4	4	no	—
473	Q₈×C₄₇	—	4	2	no	—
474	Q₈×C₄₇	C₂×#41	1	2	yes	—
475	D₄×C₄₇	—	2	4	no	—
476	D₄×C₄₇	—	2	2	no	—
477	C₂×C₄×C₄₇	—	2	2	no	—
478	C₂×C₄×C₄₇	—	2	1	no	—
479	C₂×C₄×C₄₇	—	2	2	no	—
480	C₂×C₄×C₄₇	—	2	1	no	—
481	C₂×C₄×C₄₇	—	2	2	no	—
482	C₂×C₄×C₄₇	—	2	1	no	—
483	C₂×C₄×C₄₇	—	2	2	no	—
484	C₂×C₄×C₄₇	—	2	1	no	—
485	C₂×C₄×C₄₇	—	2	2	no	—
486	C₂×C₄×C₄₇	—	2	1	no	—
487	C₂×C₄×C₄₇	—	2	1	no	—
488	C₂×C₄×C₄₇	—	2	2	no	—
489	C₂×C₄×C₄₇	—	4	2	no	—
490	C₂×C₄×C₄₇	—	4	4	no	—
491	C₂×C₄×C₄₇	—	4	2	no	—
492	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
493	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
494	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
495	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
496	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
497	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
498	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
499	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
500	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
501	C₂²⋊D₄₇	—	4	4	no	—
502	C₂²⋊D₄₇	—	8	2	no	—
503	C₂²⋊D₄₇	—	8	2	no	—
504	C₂×Dic₄₇	—	2	1	no	—
505	C₂×Dic₄₇	—	2	2	no	—
506	C₂×Dic₄₇	—	2	1	no	—
507	C₂×Dic₄₇	—	8	1	no	—
508	D₁₈₈	—	2	1	no	—
509	D₁₈₈	—	2	2	no	—
510	D₁₈₈	—	2	1	no	—
511	D₁₈₈	—	2	1	no	—
512	D₁₈₈	—	2	2	no	—
513	D₁₈₈	—	4	4	no	—
514	D₁₈₈	—	4	2	no	—
515	D₁₈₈	—	4	2	no	—
516	D₁₈₈	—	8	1	no	—
517	D₁₈₈	—	8	2	no	—
518	D₁₈₈	—	8	2	no	—
519	D₁₈₈	C₂×#41	1	2	yes	—
520	C₄×D₄₇	—	4	2	no	—
521	C₄×D₄₇	—	4	2	no	—
522	C₄×D₄₇	—	8	1	no	—
523	C₄×D₄₇	—	8	1	no	—
524	C₄×D₄₇	—	8	2	no	—
525	C₄×D₄₇	—	8	2	no	—
526	C₄×D₄₇	—	8	2	no	—
527	Dic₉₄	—	8	1	no	—
528	C₄₇⋊C₈	—	2	1	no	—
529	C₄₇⋊C₈	—	2	2	no	—
530	C₄₇⋊C₈	—	2	1	no	—
531	C₄₇⋊C₈	—	2	1	no	—
532	C₄₇⋊C₈	—	2	2	no	—
533	C₄₇⋊C₈	C₂×#41	1	2	yes	—
534	#61481	—	47	1	no	maximal, Sylow
535	C₂²×C₄₇	—	2	1	no	—
536	C₂²×C₄₇	—	2	1	no	—
537	C₂²×C₄₇	—	2	2	no	—
538	C₂²×C₄₇	—	2	2	no	—
539	C₂²×C₄₇	—	2	2	no	—
540	C₂²×C₄₇	#577	1	2	yes	—
541	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
542	C₂×D₄₇	—	2	2	no	—
543	C₂×D₄₇	—	4	1	no	—
544	C₂×D₄₇	—	4	1	no	—
545	C₂×D₄₇	—	4	1	no	—
546	C₂×D₄₇	—	4	2	no	—
547	C₂×D₄₇	—	4	1	no	—
548	C₂×D₄₇	—	4	2	no	—
549	C₂×D₄₇	—	4	2	no	—
550	C₂×D₄₇	—	4	1	no	—
551	C₂×D₄₇	—	8	4	no	—
552	C₂×D₄₇	—	16	4	no	—
553	C₄×C₄₇	—	2	1	no	—
554	C₄×C₄₇	—	2	2	no	—
555	C₄×C₄₇	—	2	2	no	—
556	C₄×C₄₇	—	2	1	no	—
557	C₄×C₄₇	—	2	1	no	—
558	C₄×C₄₇	—	2	1	no	—
559	C₄×C₄₇	—	2	2	no	—
560	C₄×C₄₇	—	2	2	no	—
561	C₄×C₄₇	—	4	1	no	—
562	C₄×C₄₇	—	4	2	no	—
563	C₄×C₄₇	—	4	1	no	—
564	C₄×C₄₇	—	4	1	no	—
565	C₄×C₄₇	—	4	2	no	—
566	C₄×C₄₇	#577	1	2	yes	—
567	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
568	C₄×C₄₇	#585	1	1	yes	characteristic
569	Dic₄₇	—	4	2	no	—
570	Dic₄₇	—	4	1	no	—
571	Dic₄₇	—	4	1	no	—
572	#3523	D₄₇	1	1	yes	characteristic, complemented
573	#3519	—	47	1	no	—
574	#3392	—	47	1	no	—
575	#3381	—	47	1	no	—
576	#3372	—	47	1	no	—
577	#3368	—	47	1	no	—
578	#3340	—	47	1	no	—
579	#3337	—	47	2	no	—
580	#3329	—	47	1	no	—
581	#3324	—	47	1	no	—
582	#3320	—	47	2	no	—
583	#3310	—	47	2	no	—
584	D₄×SD₁₆	—	47	2	no	—
585	D₄×SD₁₆	—	47	1	no	—
586	#3174	—	47	2	no	—
587	#3167	—	47	1	no	—
588	#3126	—	47	2	no	—
589	#3123	—	47	2	no	—
590	#3112	—	47	1	no	—
591	#3110	—	47	1	no	—
592	#2966	—	47	1	no	—
593	#2949	—	47	2	no	—
594	C₂×C₄×SD₁₆	—	47	1	no	—
595	C₂×C₄₇	—	2	2	no	—
596	C₂×C₄₇	—	4	2	no	—
597	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
598	C₂×C₄₇	C₂×#577	1	1	yes	characteristic
599	C₂×C₄₇	C₂×#577	1	1	yes	characteristic
600	D₄₇	—	4	2	no	—
601	D₄₇	—	8	1	no	—
602	D₄₇	—	8	2	no	—
603	C₂²×SD₁₆	—	47	1	no	—
604	C₂²×SD₁₆	—	47	2	no	—
605	#557	—	2	1	no	—
606	#557	C₂×D₄₇	1	1	yes	characteristic, complemented
607	#557	C₂×D₄₇	1	1	yes	characteristic, complemented
608	#556	—	2	1	no	—
609	#556	C₂×D₄₇	1	1	yes	characteristic, complemented
610	#555	—	47	1	no	—
611	#554	—	47	1	no	—
612	#553	—	47	2	no	—
613	#553	—	94	1	no	—
614	#552	—	2	2	no	—
615	#552	C₂×D₄₇	1	2	yes	complemented
616	#550	—	47	1	no	—
617	D₄×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
618	D₄×Q₈	C₂×D₄₇	1	2	yes	complemented
619	#546	—	94	1	no	—
620	#546	—	94	2	no	—
621	D₄²	—	47	2	no	—
622	D₄²	—	47	1	no	—
623	#541	—	2	2	no	—
624	#541	C₂×D₄₇	1	2	yes	complemented
625	#540	—	47	2	no	—
626	#538	—	94	2	no	—
627	#533	—	2	1	no	—
628	#533	C₂×D₄₇	1	1	yes	characteristic, complemented
629	#532	—	47	1	no	—
630	#529	—	2	1	no	—
631	#529	C₂×D₄₇	1	1	yes	characteristic
632	#525	—	94	1	no	—
633	C₂×#121	—	94	1	no	—
634	#519	C₂×D₄₇	1	2	yes	complemented
635	#518	—	47	2	no	—
636	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
637	C₂×C₄×D₄	—	47	1	no	—
638	#499	—	47	2	no	—
639	#498	—	47	1	no	—
640	#492	—	47	1	no	—
641	#492	—	47	2	no	—
642	#491	—	47	2	no	—
643	#490	—	47	2	no	—
644	#487	—	47	1	no	—
645	#486	—	47	1	no	—
646	#485	—	47	2	no	—
647	#485	—	47	2	no	—
648	#484	—	47	2	no	—
649	#482	—	47	2	no	—
650	#482	—	47	2	no	—
651	#480	—	47	2	no	—
652	#479	—	47	2	no	—
653	#479	—	47	2	no	—
654	#478	—	47	2	no	—
655	#478	—	47	2	no	—
656	#477	—	47	1	no	—
657	#477	—	47	1	no	—
658	#474	—	47	1	no	—
659	#474	—	47	1	no	—
660	#468	—	47	2	no	—
661	#468	—	47	2	no	—
662	#465	—	47	2	no	—
663	#465	—	47	2	no	—
664	#465	—	47	2	no	—
665	#465	—	47	2	no	—
666	#461	—	47	1	no	—
667	#461	—	47	1	no	—
668	#461	—	47	2	no	—
669	#461	—	47	2	no	—
670	#460	—	47	1	no	—
671	#460	—	47	1	no	—
672	#460	—	47	2	no	—
673	#460	—	47	2	no	—
674	#450	—	47	2	no	—
675	#450	—	47	2	no	—
676	#450	—	47	2	no	—
677	#448	—	47	2	no	—
678	#448	—	47	2	no	—
679	#448	—	47	2	no	—
680	#446	—	47	1	no	—
681	C₈×Q₈	—	47	1	no	—
682	#440	—	47	2	no	—
683	#440	—	47	2	no	—
684	#440	—	47	2	no	—
685	#440	—	47	2	no	—
686	#440	—	47	2	no	—
687	#440	—	47	2	no	—
688	C₄×SD₁₆	—	47	1	no	—
689	C₄×SD₁₆	—	47	2	no	—
690	C₄×SD₁₆	—	47	1	no	—
691	C₄×SD₁₆	—	47	1	no	—
692	C₄×SD₁₆	—	47	1	no	—
693	C₄×SD₁₆	—	47	2	no	—
694	C₄×SD₁₆	—	47	1	no	—
695	C₄×SD₁₆	—	47	2	no	—
696	C₄×SD₁₆	—	47	1	no	—
697	C₄×SD₁₆	—	47	2	no	—
698	C₄×SD₁₆	—	47	1	no	—
699	C₄×SD₁₆	—	47	1	no	—
700	#436	—	47	1	no	—
701	#435	—	47	2	no	—
702	C₈×D₄	—	47	2	no	—
703	C₈×D₄	—	47	1	no	—
704	#433	—	47	2	no	—
705	#432	—	47	1	no	—
706	#427	—	47	2	no	—
707	C₂×#106	—	47	1	no	—
708	#419	—	47	2	no	—
709	#418	—	47	2	no	—
710	C₂×#103	—	47	1	no	—
711	C₂×#102	—	47	1	no	—
712	#405	—	47	2	no	—
713	C₂×C₄×C₈	—	47	1	no	—
714	C₄₇	#61481	1	1	yes	characteristic, complemented, Sylow
715	C₂×#41	—	94	1	no	—
716	C₂×#41	—	94	1	no	—
717	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
718	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
719	C₂²×D₄	—	47	1	no	—
720	C₂²×D₄	—	47	2	no	—
721	C₂²×D₄	—	94	2	no	—
722	C₂²×D₄	—	94	1	no	—
723	C₂³×C₄	—	94	1	no	—
724	C₂×SD₁₆	—	47	1	no	—
725	C₂×SD₁₆	—	47	1	no	—
726	C₂×SD₁₆	—	47	1	no	—
727	C₂×SD₁₆	—	47	1	no	—
728	C₂×SD₁₆	—	47	2	no	—
729	C₂×SD₁₆	—	47	2	no	—
730	C₂×SD₁₆	—	47	2	no	—
731	C₂×SD₁₆	—	47	2	no	—
732	C₂×SD₁₆	—	47	2	no	—
733	C₂×SD₁₆	—	47	2	no	—
734	C₂×SD₁₆	—	94	4	no	—
735	C₂×SD₁₆	—	94	8	no	—
736	C₂×M₁₆	—	47	2	no	—
737	C₂²×C₈	—	47	1	no	—
738	C₂²×C₈	—	47	2	no	—
739	C₂²×C₈	—	47	1	no	—
740	C₄⋊Q₈	—	2	1	no	—
741	C₄⋊Q₈	—	2	1	no	—
742	C₄⋊Q₈	—	2	2	no	—
743	C₄⋊Q₈	—	47	1	no	—
744	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
745	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
746	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
747	#127	—	47	1	no	—
748	#127	—	47	2	no	—
749	#126	—	2	2	no	—
750	#126	—	2	2	no	—
751	#126	—	2	2	no	—
752	#126	—	2	2	no	—
753	#126	—	94	2	no	—
754	#126	C₂²⋊D₄₇	1	2	yes	—
755	#125	—	2	1	no	—
756	#125	—	2	2	no	—
757	#125	—	2	2	no	—
758	#125	—	2	2	no	—
759	#125	—	2	2	no	—
760	#125	—	2	2	no	—
761	#125	—	2	1	no	—
762	#125	—	47	2	no	—
763	#125	C₂²⋊D₄₇	1	1	yes	characteristic
764	#125	C₂²×D₄₇	1	2	yes	—
765	#124	—	2	1	no	—
766	#124	—	94	2	no	—
767	#124	—	94	1	no	—
768	#124	C₂²⋊D₄₇	1	1	yes	characteristic
769	#123	—	2	2	no	—
770	#123	—	94	2	no	—
771	#123	—	94	2	no	—
772	#123	—	94	2	no	—
773	#123	C₂²⋊D₄₇	1	2	yes	—
774	C₂²⋊Q₈	—	2	1	no	—
775	C₂²⋊Q₈	—	2	2	no	—
776	C₂²⋊Q₈	—	2	2	no	—
777	C₂²⋊Q₈	—	2	2	no	—
778	C₂²⋊Q₈	—	94	1	no	—
779	C₂²⋊Q₈	—	94	2	no	—
780	C₂²⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
781	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
782	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
783	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
784	#121	—	47	2	no	—
785	#121	—	47	2	no	—
786	#121	—	47	2	no	—
787	#121	—	94	2	no	—
788	#121	—	94	1	no	—
789	#121	—	94	1	no	—
790	#121	—	94	1	no	—
791	#121	—	94	1	no	—
792	#121	—	94	2	no	—
793	#121	—	94	2	no	—
794	#121	—	94	2	no	—
795	#121	—	94	2	no	—
796	#121	C₂²⋊D₄₇	1	1	yes	characteristic
797	#120	—	94	2	no	—
798	#120	—	94	2	no	—
799	#120	—	94	2	no	—
800	C₄×Q₈	—	2	1	no	—
801	C₄×Q₈	—	2	2	no	—
802	C₄×Q₈	—	2	2	no	—
803	C₄×Q₈	—	2	1	no	—
804	C₄×Q₈	—	2	1	no	—
805	C₄×Q₈	—	2	1	no	—
806	C₄×Q₈	—	2	1	no	—
807	C₄×Q₈	—	2	1	no	—
808	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
809	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
810	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
811	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
812	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
813	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
814	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
815	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
816	C₄×D₄	—	2	2	no	—
817	C₄×D₄	—	2	1	no	—
818	C₄×D₄	—	47	1	no	—
819	C₄×D₄	—	47	1	no	—
820	C₄×D₄	—	47	1	no	—
821	C₄×D₄	—	47	1	no	—
822	C₄×D₄	—	47	2	no	—
823	C₄×D₄	—	47	2	no	—
824	C₄×D₄	—	47	2	no	—
825	C₄×D₄	—	94	2	no	—
826	C₄×D₄	—	94	2	no	—
827	C₄×D₄	—	94	2	no	—
828	C₄×D₄	—	94	1	no	—
829	C₄×D₄	—	94	1	no	—
830	C₄×D₄	—	94	1	no	—
831	C₄×D₄	C₂²×D₄₇	1	2	yes	—
832	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
833	#117	—	2	1	no	—
834	#117	—	2	2	no	—
835	#117	—	2	2	no	—
836	#117	—	2	2	no	—
837	#117	—	47	2	no	—
838	#117	—	94	1	no	—
839	#117	C₂²×D₄₇	1	2	yes	—
840	#117	C₂²×D₄₇	1	2	yes	—
841	C₂×C₄⋊C₄	—	2	1	no	—
842	C₂×C₄⋊C₄	—	47	1	no	—
843	C₂×C₄⋊C₄	—	94	1	no	—
844	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
845	C₂×C₂²⋊C₄	—	94	1	no	—
846	C₂×C₂²⋊C₄	—	94	2	no	—
847	C₂×C₂²⋊C₄	—	94	2	no	—
848	C₂×C₄²	—	2	1	no	—
849	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
850	#107	—	47	2	no	—
851	#107	—	47	2	no	—
852	#107	—	47	2	no	—
853	#107	—	47	2	no	—
854	#106	—	47	1	no	—
855	#106	—	47	1	no	—
856	#106	—	47	1	no	—
857	#106	—	47	1	no	—
858	#106	—	47	2	no	—
859	#106	—	47	2	no	—
860	C₄⋊C₈	—	47	1	no	—
861	C₄⋊C₈	—	47	1	no	—
862	C₄⋊C₈	—	47	2	no	—
863	C₄⋊C₈	—	47	2	no	—
864	#103	—	47	1	no	—
865	#103	—	47	1	no	—
866	#103	—	47	1	no	—
867	#103	—	47	1	no	—
868	#103	—	47	2	no	—
869	#103	—	47	2	no	—
870	#103	—	47	2	no	—
871	#103	—	47	2	no	—
872	#103	—	47	2	no	—
873	#103	—	47	2	no	—
874	#102	—	47	1	no	—
875	#102	—	47	1	no	—
876	#102	—	47	1	no	—
877	#102	—	47	1	no	—
878	#102	—	47	2	no	—
879	#102	—	47	2	no	—
880	#102	—	47	2	no	—
881	#102	—	47	2	no	—
882	#102	—	47	2	no	—
883	#102	—	47	2	no	—
884	C₂²⋊C₈	—	47	2	no	—
885	C₂²⋊C₈	—	47	2	no	—
886	C₂²⋊C₈	—	47	2	no	—
887	#97	—	47	2	no	—
888	#97	—	47	2	no	—
889	C₄×C₈	—	47	1	no	—
890	C₄×C₈	—	47	1	no	—
891	C₄×C₈	—	47	1	no	—
892	C₄×C₈	—	47	1	no	—
893	C₄×C₈	—	47	2	no	—
894	C₂⁴	—	94	2	no	—
895	C₂⁴	—	94	1	no	—
896	#41	—	376	2	no	—
897	#41	—	376	2	no	—
898	C₂×Q₈	—	2	1	no	—
899	C₂×Q₈	—	2	2	no	—
900	C₂×Q₈	—	2	1	no	—
901	C₂×Q₈	—	2	2	no	—
902	C₂×Q₈	—	2	4	no	—
903	C₂×Q₈	—	4	1	no	—
904	C₂×Q₈	—	4	2	no	—
905	C₂×Q₈	—	94	1	no	—
906	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
907	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
908	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
909	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
910	C₂×D₄	—	47	1	no	—
911	C₂×D₄	—	47	1	no	—
912	C₂×D₄	—	47	2	no	—
913	C₂×D₄	—	94	2	no	—
914	C₂×D₄	—	94	4	no	—
915	C₂×D₄	—	94	2	no	—
916	C₂×D₄	—	94	2	no	—
917	C₂×D₄	—	94	2	no	—
918	C₂×D₄	—	94	2	no	—
919	C₂×D₄	—	94	1	no	—
920	C₂×D₄	—	94	2	no	—
921	C₂×D₄	—	94	2	no	—
922	C₂×D₄	—	94	1	no	—
923	C₂×D₄	—	94	1	no	—
924	C₂×D₄	—	376	4	no	—
925	C₂×D₄	—	376	2	no	—
926	C₂×D₄	—	188	1	no	—
927	C₂×D₄	—	188	2	no	—
928	C₂×D₄	C₂×C₂²⋊D₄₇	1	2	yes	—
929	C₂×D₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
930	C₂²×C₄	—	2	1	no	—
931	C₂²×C₄	—	2	1	no	—
932	C₂²×C₄	—	2	2	no	—
933	C₂²×C₄	—	94	1	no	—
934	C₂²×C₄	—	94	1	no	—
935	C₂²×C₄	—	94	2	no	—
936	C₂²×C₄	—	94	2	no	—
937	C₂²×C₄	—	94	2	no	—
938	C₂²×C₄	—	94	1	no	—
939	C₂²×C₄	—	94	1	no	—
940	C₂²×C₄	—	94	1	no	—
941	C₂²×C₄	—	376	2	no	—
942	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
943	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
944	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
945	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
946	SD₁₆	—	47	4	no	—
947	SD₁₆	—	94	2	no	—
948	SD₁₆	—	94	4	no	—
949	SD₁₆	—	94	2	no	—
950	SD₁₆	—	94	4	no	—
951	SD₁₆	—	94	2	no	—
952	SD₁₆	—	94	4	no	—
953	SD₁₆	—	188	2	no	—
954	SD₁₆	—	188	2	no	—
955	SD₁₆	—	188	2	no	—
956	M₁₆	—	188	2	no	—
957	C₂×C₈	—	47	1	no	—
958	C₂×C₈	—	47	1	no	—
959	C₂×C₈	—	47	1	no	—
960	C₂×C₈	—	47	1	no	—
961	C₂×C₈	—	47	2	no	—
962	C₂×C₈	—	47	2	no	—
963	C₂×C₈	—	94	2	no	—
964	C₂×C₈	—	94	4	no	—
965	C₂×C₈	—	188	1	no	—
966	C₄⋊C₄	—	2	1	no	—
967	C₄⋊C₄	—	2	1	no	—
968	C₄⋊C₄	—	2	1	no	—
969	C₄⋊C₄	—	2	1	no	—
970	C₄⋊C₄	—	2	1	no	—
971	C₄⋊C₄	—	2	2	no	—
972	C₄⋊C₄	—	2	2	no	—
973	C₄⋊C₄	—	2	2	no	—
974	C₄⋊C₄	—	2	1	no	—
975	C₄⋊C₄	—	2	2	no	—
976	C₄⋊C₄	—	2	1	no	—
977	C₄⋊C₄	—	2	2	no	—
978	C₄⋊C₄	—	2	1	no	—
979	C₄⋊C₄	—	2	2	no	—
980	C₄⋊C₄	—	2	2	no	—
981	C₄⋊C₄	—	2	2	no	—
982	C₄⋊C₄	—	2	2	no	—
983	C₄⋊C₄	—	2	2	no	—
984	C₄⋊C₄	—	47	1	no	—
985	C₄⋊C₄	—	47	1	no	—
986	C₄⋊C₄	—	47	2	no	—
987	C₄⋊C₄	—	94	2	no	—
988	C₄⋊C₄	—	94	2	no	—
989	C₄⋊C₄	—	94	1	no	—
990	C₄⋊C₄	—	94	1	no	—
991	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
992	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
993	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
994	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
995	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
996	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
997	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
998	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
999	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
1000	C₂²⋊C₄	—	2	2	no	—
1001	C₂²⋊C₄	—	2	2	no	—
1002	C₂²⋊C₄	—	2	2	no	—
1003	C₂²⋊C₄	—	2	2	no	—
1004	C₂²⋊C₄	—	94	2	no	—
1005	C₂²⋊C₄	—	94	1	no	—
1006	C₂²⋊C₄	—	94	2	no	—
1007	C₂²⋊C₄	—	94	1	no	—
1008	C₂²⋊C₄	—	94	2	no	—
1009	C₂²⋊C₄	—	94	1	no	—
1010	C₂²⋊C₄	—	94	2	no	—
1011	C₂²⋊C₄	—	94	1	no	—
1012	C₂²⋊C₄	—	94	2	no	—
1013	C₂²⋊C₄	—	94	2	no	—
1014	C₂²⋊C₄	—	94	2	no	—
1015	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1016	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1017	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1018	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1019	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
1020	C₄²	—	2	1	no	—
1021	C₄²	—	2	1	no	—
1022	C₄²	—	2	1	no	—
1023	C₄²	—	2	1	no	—
1024	C₄²	—	2	2	no	—
1025	C₄²	—	2	2	no	—
1026	C₄²	—	2	2	no	—
1027	C₄²	—	2	2	no	—
1028	C₄²	—	94	2	no	—
1029	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1030	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1031	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1032	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1033	C₄²	C₂³×D₄₇	1	2	yes	—
1034	C₂³	—	94	1	no	—
1035	C₂³	—	94	1	no	—
1036	C₂³	—	94	2	no	—
1037	C₂³	—	376	1	no	—
1038	C₂³	—	376	2	no	—
1039	C₂³	—	376	2	no	—
1040	C₂³	—	188	2	no	—
1041	C₂³	—	188	4	no	—
1042	C₂³	—	188	2	no	—
1043	C₂³	C₂²×C₂²⋊D₄₇	1	2	yes	—
1044	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1045	Q₈	—	2	2	no	—
1046	Q₈	—	2	1	no	—
1047	Q₈	—	2	1	no	—
1048	Q₈	—	2	2	no	—
1049	Q₈	—	2	2	no	—
1050	Q₈	—	2	1	no	—
1051	Q₈	—	4	2	no	—
1052	Q₈	—	4	4	no	—
1053	Q₈	—	4	2	no	—
1054	Q₈	—	376	1	no	—
1055	Q₈	#41×D₄₇	1	2	yes	—
1056	D₄	—	2	4	no	—
1057	D₄	—	2	2	no	—
1058	D₄	—	47	2	no	—
1059	D₄	—	94	1	no	—
1060	D₄	—	94	2	no	—
1061	D₄	—	94	1	no	—
1062	D₄	—	94	1	no	—
1063	D₄	—	94	2	no	—
1064	D₄	—	376	2	no	—
1065	D₄	—	376	1	no	—
1066	D₄	—	376	2	no	—
1067	D₄	—	376	2	no	—
1068	D₄	—	376	2	no	—
1069	D₄	—	188	2	no	—
1070	D₄	—	188	4	no	—
1071	D₄	—	188	4	no	—
1072	D₄	—	188	2	no	—
1073	C₂×C₄	—	2	2	no	—
1074	C₂×C₄	—	2	1	no	—
1075	C₂×C₄	—	2	2	no	—
1076	C₂×C₄	—	2	1	no	—
1077	C₂×C₄	—	2	2	no	—
1078	C₂×C₄	—	2	1	no	—
1079	C₂×C₄	—	2	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	2	no	—
1085	C₂×C₄	—	4	2	no	—
1086	C₂×C₄	—	4	4	no	—
1087	C₂×C₄	—	4	2	no	—
1088	C₂×C₄	—	94	1	no	—
1089	C₂×C₄	—	94	2	no	—
1090	C₂×C₄	—	94	1	no	—
1091	C₂×C₄	—	376	1	no	—
1092	C₂×C₄	—	376	1	no	—
1093	C₂×C₄	—	376	2	no	—
1094	C₂×C₄	—	376	2	no	—
1095	C₂×C₄	—	376	2	no	—
1096	C₂×C₄	—	376	1	no	—
1097	C₂×C₄	—	188	2	no	—
1098	C₂×C₄	—	188	2	no	—
1099	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1100	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1101	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1102	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1103	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1104	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1105	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1106	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1107	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1108	C₈	—	47	2	no	—
1109	C₈	—	94	1	no	—
1110	C₈	—	94	2	no	—
1111	C₈	—	94	1	no	—
1112	C₈	—	94	1	no	—
1113	C₈	—	94	2	no	—
1114	C₂²	—	2	1	no	—
1115	C₂²	—	2	1	no	—
1116	C₂²	—	2	2	no	—
1117	C₂²	—	2	2	no	—
1118	C₂²	—	2	2	no	—
1119	C₂²	—	94	2	no	—
1120	C₂²	—	376	4	no	—
1121	C₂²	—	188	1	no	—
1122	C₂²	—	188	2	no	—
1123	C₂²	—	188	2	no	—
1124	C₂²	—	188	1	no	—
1125	C₂²	—	188	1	no	—
1126	C₂²	—	188	2	no	—
1127	C₂²	—	188	1	no	—
1128	C₂²	—	188	1	no	—
1129	C₂²	—	752	4	no	—
1130	C₂²	#15689931	1	2	yes	—
1131	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1132	C₄	—	2	1	no	—
1133	C₄	—	2	1	no	—
1134	C₄	—	2	1	no	—
1135	C₄	—	2	2	no	—
1136	C₄	—	2	2	no	—
1137	C₄	—	2	1	no	—
1138	C₄	—	2	2	no	—
1139	C₄	—	2	2	no	—
1140	C₄	—	4	1	no	—
1141	C₄	—	4	1	no	—
1142	C₄	—	4	2	no	—
1143	C₄	—	4	1	no	—
1144	C₄	—	4	2	no	—
1145	C₄	—	188	1	no	—
1146	C₄	—	188	1	no	—
1147	C₄	—	188	2	no	—
1148	C₄	#15689931	1	2	yes	—
1149	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1150	C₄	#15689959	1	1	yes	characteristic
1151	C₂	—	2	2	no	—
1152	C₂	—	4	2	no	—
1153	C₂	—	376	1	no	—
1154	C₂	—	376	2	no	—
1155	C₂	—	188	2	no	—
1156	C₂	#41×C₂²⋊D₄₇	1	1	yes	characteristic
1157	C₂	C₂×#15689931	1	1	yes	characteristic
1158	C₂	C₂×#15689931	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×#3523	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#20257422	C₂
hypercenter	#3523	D₄₇
hypocenter	C₄₇	#61481
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #529 ◁ #3523

Complements

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

N	H ≅ G/N	type
2. #20256365	C₂	semidirect
3. #20256259	C₂	semidirect
4. #20256165	C₂	semidirect
5. #20256117	C₂	semidirect
6. #20255795	C₂	semidirect
7. #20255767	C₂	semidirect
8. #20255682	C₂	semidirect
9. #20255613	C₂	semidirect
10. #20255559	C₂	semidirect
11. #20255403	C₂	semidirect
12. D₄×#10625336	C₂	semidirect
13. D₄×#10625336	C₂	semidirect
14. #20254017	C₂	semidirect
15. #20253948	C₂	semidirect
16. #20253679	C₂	semidirect
17. #20253635	C₂	semidirect
18. #20253510	C₂	semidirect
19. #20253483	C₂	semidirect
20. #20252364	C₂	semidirect
21. #20252247	C₂	semidirect
22. C₂×C₄×#10625336	C₂	semidirect
23. C₄₇×#3523	C₂	semidirect
42. #15689522	C₂²	semidirect
43. #15689519	C₂²	semidirect
44. #15689497	C₂²	semidirect
45. #15689497	C₂²	semidirect
46. #15689491	C₂²	semidirect
47. #15689489	C₂²	semidirect
48. #15689473	C₂²	semidirect
49. #15689471	C₂²	semidirect
50. #15689461	C₂²	semidirect
51. #15689461	C₂²	semidirect
52. #15689456	C₂²	semidirect
53. #15689447	C₂²	semidirect
54. #15689447	C₂²	semidirect
55. #15689436	C₂²	semidirect
56. #15689430	C₂²	semidirect
57. #15689430	C₂²	semidirect
59. #15689420	C₂²	semidirect
60. #15689418	C₂²	semidirect
61. #15689418	C₂²	semidirect
63. #15689400	C₂²	semidirect
64. #15689371	C₂²	semidirect
65. #15689371	C₂²	semidirect
66. #15689354	C₂²	semidirect
67. #15689354	C₂²	semidirect
68. #15689354	C₂²	semidirect
69. #15689354	C₂²	semidirect
72. #15689325	C₂²	semidirect
73. #15689325	C₂²	semidirect
74. #15689323	C₂²	semidirect
75. #15689323	C₂²	semidirect
76. #15689323	C₂²	semidirect
77. #15689323	C₂²	semidirect
81. #15689262	C₂²	semidirect
82. #15689262	C₂²	semidirect
83. #15689262	C₂²	semidirect
84. #15689254	C₂²	semidirect
85. Q₈×C₄₇⋊C₈	C₂²	semidirect
88. #15689221	C₂²	semidirect
89. #15689221	C₂²	semidirect
90. #15689221	C₂²	semidirect
91. #15689221	C₂²	semidirect
97. C₄×#10625336	C₂²	semidirect
98. C₄×#10625336	C₂²	semidirect
99. C₄×#10625336	C₂²	semidirect
100. C₄×#10625336	C₂²	semidirect
101. C₄×#10625336	C₂²	semidirect
102. C₄×#10625336	C₂²	semidirect
103. C₄×#10625336	C₂²	semidirect
104. #15689201	C₂²	semidirect
105. #15689195	C₂²	semidirect
106. D₄×C₄₇⋊C₈	C₂²	semidirect
107. D₄×C₄₇⋊C₈	C₂²	semidirect
108. #15689184	C₂²	semidirect
109. #15689180	C₂²	semidirect
110. #15689159	C₂²	semidirect
111. C₂×#13093955	C₂²	semidirect
112. #15689132	C₂²	semidirect
114. C₂×#13093948	C₂²	semidirect
116. #15689079	C₂²	semidirect
117. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
119. C₄₇×#557	C₂²	semidirect
120. C₄₇×#557	C₂²	semidirect
122. C₄₇×#556	C₂²	semidirect
124. C₄₇×#552	C₂²	semidirect
125. D₄×Q₈×C₄₇	C₂²	semidirect
126. D₄×Q₈×C₄₇	C₂²	semidirect
128. C₄₇×#541	C₂²	semidirect
130. C₄₇×#533	C₂²	semidirect
133. C₄₇×#519	C₂²	semidirect
134. C₂×C₄×Q₈×C₄₇	C₂²	semidirect
425. #10625336	#41	semidirect
572. #3523	D₄₇	semidirect
606. #557	C₂×D₄₇	semidirect
607. #557	C₂×D₄₇	semidirect
609. #556	C₂×D₄₇	semidirect
615. #552	C₂×D₄₇	semidirect
617. D₄×Q₈	C₂×D₄₇	semidirect
618. D₄×Q₈	C₂×D₄₇	semidirect
624. #541	C₂×D₄₇	semidirect
628. #533	C₂×D₄₇	semidirect
634. #519	C₂×D₄₇	semidirect
636. C₂×C₄×Q₈	C₂×D₄₇	semidirect
714. C₄₇	#61481	semidirect

Maximal subgroups

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

subgroup	index
#20257422	2
#20256365	2
#20256259	2
#20256165	2
#20256117	2
#20255795	2
#20255767	2
#20255682	2
#20255613	2
#20255559	2
#20255403	2
D₄×#10625336	2
#20254017	2
#20253948	2
#20253679	2
#20253635	2
#20253510	2
#20253483	2
#20252364	2
#20252247	2
C₂×C₄×#10625336	2
C₄₇×#3523	2
#61481	47