Subgroups — #27096418

Order 12032.

1792 conjugacy classes of subgroups.

The subgroup lattice has 1130 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257286	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256230	C₂	1	2	yes	maximal, complemented
3	#20256215	C₂	1	2	yes	maximal, complemented
4	#20256202	C₂	1	2	yes	maximal, complemented
5	#20256180	C₂	1	2	yes	maximal, complemented
6	#20256156	C₂	1	2	yes	maximal, complemented
7	#20256141	C₂	1	2	yes	maximal, complemented
8	#20256128	C₂	1	2	yes	maximal, complemented
9	#20256106	C₂	1	2	yes	maximal, complemented
10	#20253758	C₂	1	1	yes	maximal, characteristic, complemented
11	#20253747	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15689485	C₂	1	1	yes	maximal, characteristic, complemented
13	#20253224	C₂	1	1	yes	maximal, characteristic, complemented
14	#20253213	C₂	1	1	yes	maximal, characteristic, complemented
15	#20253197	C₂	1	1	yes	maximal, characteristic, complemented
16	#20252938	C₂	1	1	yes	maximal, characteristic, complemented
17	#20252927	C₂	1	1	yes	maximal, characteristic
18	#20252882	C₂	1	1	yes	maximal, characteristic, complemented
19	#20252329	C₂	1	1	yes	maximal, characteristic, complemented
20	#20252227	C₂	1	1	yes	maximal, characteristic, complemented
21	#20252216	C₂	1	1	yes	maximal, characteristic, complemented
22	#20252186	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3503	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094054	C₂²	1	1	yes	characteristic
25	C₂×#13094049	C₂²	1	1	yes	characteristic
26	C₂×#13094044	C₂²	1	1	yes	characteristic
27	#15689858	C₂²	1	2	yes	—
28	#15689858	C₂²	1	2	yes	—
29	#15689846	C₂²	1	2	yes	—
30	#15689846	C₂²	1	2	yes	—
31	#15689800	—	2	2	no	—
32	#15689800	—	2	2	no	—
33	#15689747	—	2	1	no	—
34	#15689747	—	2	1	no	—
35	#15689699	C₂²	1	1	yes	characteristic
36	#15689692	C₂²	1	1	yes	characteristic
37	#15689658	—	2	1	no	—
38	#15689658	—	2	1	no	—
39	C₂×#13094012	C₂²	1	1	yes	characteristic
40	#15689600	C₂²	1	1	yes	characteristic
41	#15689597	C₂²	1	1	yes	characteristic
42	C₄×#10625350	C₂²	1	1	yes	characteristic
43	#15689493	C₂²	1	2	yes	complemented
44	#15689489	C₂²	1	2	yes	—
45	#15689485	C₂²	1	2	yes	—
46	#15689485	C₂²	1	2	yes	—
47	#15689485	C₂²	1	2	yes	—
48	#15689485	C₂²	1	2	yes	—
49	#15689485	C₂²	1	2	yes	—
50	#15689485	C₂²	1	2	yes	complemented
51	#15689480	C₂²	1	2	yes	—
52	#15689480	C₂²	1	2	yes	complemented
53	#15689475	C₂²	1	2	yes	complemented
54	#15689471	C₂²	1	2	yes	—
55	#15689427	C₂²	1	2	yes	complemented
56	#15689427	C₂²	1	2	yes	complemented
57	#15689420	C₂²	1	2	yes	—
58	#15689420	C₂²	1	2	yes	—
59	#15689415	C₂²	1	2	yes	complemented
60	#15689415	C₂²	1	2	yes	complemented
61	#15689410	C₂²	1	2	yes	—
62	#15689410	C₂²	1	2	yes	complemented
63	#15689405	C₂²	1	2	yes	complemented
64	#15689405	C₂²	1	2	yes	complemented
65	#15689400	C₂²	1	2	yes	—
66	#15689400	C₂²	1	2	yes	complemented
67	#15689345	C₂²	1	2	yes	—
68	#15689345	C₂²	1	2	yes	—
69	#15689345	C₂²	1	2	yes	—
70	#15689345	C₂²	1	2	yes	complemented
71	#15689338	C₂²	1	2	yes	—
72	#15689338	C₂²	1	2	yes	—
73	#15689338	C₂²	1	2	yes	—
74	#15689338	C₂²	1	2	yes	complemented
75	#15689333	C₂²	1	2	yes	complemented
76	#15689328	C₂²	1	2	yes	complemented
77	#15689323	C₂²	1	2	yes	—
78	#15689318	C₂²	1	2	yes	—
79	#15689254	C₂²	1	2	yes	complemented
80	#15689254	C₂²	1	2	yes	complemented
81	#15689254	C₂²	1	2	yes	complemented
82	#15689254	C₂²	1	2	yes	complemented
83	#15689233	C₂²	1	2	yes	—
84	#15689233	C₂²	1	1	yes	characteristic, complemented
85	#15689233	C₂²	1	1	yes	characteristic, complemented
86	#15689228	C₂²	1	1	yes	characteristic, complemented
87	#15689228	C₂²	1	1	yes	characteristic, complemented
88	#15689228	C₂²	1	2	yes	complemented
89	#15689223	C₂²	1	1	yes	characteristic, complemented
90	#15689223	C₂²	1	1	yes	characteristic, complemented
91	#15689223	C₂²	1	2	yes	complemented
92	#15689221	C₂²	1	2	yes	—
93	#15689221	C₂²	1	1	yes	characteristic, complemented
94	#15689221	C₂²	1	1	yes	characteristic, complemented
95	C₄×#10625337	C₂²	1	2	yes	complemented
96	C₄×#10625336	C₂²	1	2	yes	—
97	C₄×#10625335	C₂²	1	2	yes	complemented
98	C₄×#10625334	C₂²	1	2	yes	—
99	#15689163	C₂²	1	1	yes	characteristic
100	#15689163	C₂²	1	1	yes	characteristic
101	#15689159	C₂²	1	1	yes	characteristic
102	#15689150	C₂²	1	1	yes	characteristic
103	#15689150	C₂²	1	1	yes	characteristic
104	#15689147	C₂²	1	1	yes	characteristic
105	#15689131	C₂²	1	1	yes	characteristic
106	#15689127	C₂²	1	1	yes	characteristic
107	#15689122	C₂²	1	1	yes	characteristic
108	#15689122	C₂²	1	1	yes	characteristic
109	#15689119	C₂²	1	1	yes	characteristic
110	#15689117	C₂²	1	1	yes	characteristic
111	C₂×#13093947	C₂²	1	1	yes	characteristic
112	C₂×#13093947	C₂²	1	1	yes	characteristic
113	C₂×#13093944	C₂²	1	1	yes	characteristic
114	C₂×#13093944	C₂²	1	1	yes	characteristic
115	#15689079	C₂²	1	1	yes	characteristic
116	#15689079	C₂²	1	1	yes	characteristic
117	C₂×#13093935	C₂²	1	1	yes	characteristic
118	Q₈²×C₄₇	C₂²	1	2	yes	complemented
119	C₄₇×#557	C₂²	1	2	yes	complemented
120	C₄₇×#554	—	2	2	no	—
121	C₄₇×#554	C₂²	1	2	yes	complemented
122	D₄×Q₈×C₄₇	—	2	2	no	—
123	D₄×Q₈×C₄₇	C₂²	1	2	yes	complemented
124	C₄₇×#544	—	2	1	no	—
125	C₄₇×#544	—	2	1	no	—
126	C₄₇×#544	C₂²	1	1	yes	characteristic
127	C₄₇×#544	C₂²	1	1	yes	characteristic
128	C₄₇×#533	—	2	1	no	—
129	C₄₇×#533	C₂²	1	1	yes	characteristic
130	C₂×C₄⋊Q₈×C₄₇	—	2	1	no	—
131	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
132	C₄₇×#520	C₂²	1	1	yes	characteristic
133	C₄₇×#520	C₂²	1	1	yes	characteristic
134	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
135	C₂×#10625350	C₂³	1	1	yes	characteristic
136	C₂²×Dic₉₄	C₂³	1	1	yes	characteristic
137	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
138	#13094054	—	2	4	no	—
139	#13094049	—	2	4	no	—
140	#13094044	—	2	4	no	—
141	C₂×#10625337	C₂³	1	2	yes	—
142	C₂×#10625337	C₂³	1	1	yes	characteristic
143	C₂×#10625335	C₂³	1	1	yes	characteristic
144	C₂×#10625335	C₂³	1	2	yes	—
145	C₂×#10625336	C₂³	1	2	yes	—
146	C₂×#10625336	C₂³	1	1	yes	characteristic
147	C₂×#10625334	C₂³	1	2	yes	—
148	C₂×#10625334	C₂³	1	1	yes	characteristic
149	C₂×#10625329	C₂³	1	1	yes	characteristic
150	C₂×#10625329	C₂³	1	1	yes	characteristic
151	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
152	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
153	#13094024	C₂³	1	2	yes	—
154	#13094021	C₂³	1	2	yes	—
155	#13094019	—	2	2	no	—
156	#13094019	—	2	2	no	—
157	#13094019	—	2	2	no	—
158	#13094019	—	2	2	no	—
159	#13094013	—	2	2	no	—
160	#13094013	—	2	2	no	—
161	#13094012	—	2	1	no	—
162	#13094012	—	2	1	no	—
163	#13094012	C₂³	1	2	yes	—
164	#13094012	C₂³	1	2	yes	—
165	#13094012	C₂³	1	2	yes	—
166	#13094012	C₂³	1	2	yes	—
167	#13094009	—	2	2	no	—
168	#13094009	—	2	2	no	—
169	#13094009	—	2	2	no	—
170	#13094009	—	2	2	no	—
171	#13094008	—	2	2	no	—
172	#13094004	—	2	1	no	—
173	#13094004	—	2	1	no	—
174	#13094000	—	2	2	no	—
175	#13094000	—	2	2	no	—
176	#13093999	—	2	1	no	—
177	#13093999	—	2	1	no	—
178	#13093994	—	2	2	no	—
179	C₄×Dic₉₄	C₂³	1	2	yes	—
180	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
181	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
182	C₄×Dic₉₄	C₂³	1	2	yes	—
183	#13093989	—	2	1	no	—
184	#13093989	—	2	1	no	—
185	C₄×D₁₈₈	C₂³	1	2	yes	—
186	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
187	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
188	C₄×D₁₈₈	C₂³	1	2	yes	—
189	#13093986	—	2	1	no	—
190	#13093986	—	2	1	no	—
191	#13093986	—	2	2	no	—
192	#13093986	—	2	2	no	—
193	C₄×C₂²⋊D₄₇	—	2	1	no	—
194	C₄×C₂²⋊D₄₇	—	2	1	no	—
195	#13093983	C₂³	1	1	yes	characteristic
196	#13093982	—	2	2	no	—
197	#13093982	—	2	2	no	—
198	#13093981	—	2	1	no	—
199	#13093980	—	2	2	no	—
200	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
201	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
202	C₂²⋊C₄×D₄₇	—	2	2	no	—
203	C₄²×D₄₇	—	2	1	no	—
204	#13093957	C₂³	1	2	yes	—
205	#13093957	C₂³	1	2	yes	—
206	#13093957	C₂³	1	1	yes	characteristic
207	#13093957	C₂³	1	1	yes	characteristic
208	#13093955	C₂³	1	1	yes	characteristic
209	#13093955	C₂³	1	1	yes	characteristic
210	#13093955	C₂³	1	2	yes	—
211	#13093955	C₂³	1	2	yes	—
212	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
213	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
214	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
215	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
216	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
217	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
218	#13093948	C₂³	1	1	yes	characteristic
219	#13093948	C₂³	1	1	yes	characteristic
220	#13093947	C₂³	1	2	yes	—
221	#13093947	C₂³	1	1	yes	characteristic
222	#13093947	C₂³	1	2	yes	—
223	#13093947	C₂³	1	2	yes	—
224	#13093947	C₂³	1	2	yes	—
225	#13093947	C₂³	1	1	yes	characteristic
226	#13093947	C₂³	1	2	yes	—
227	#13093947	C₂³	1	2	yes	—
228	#13093947	C₂³	1	2	yes	—
229	#13093947	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	1	yes	characteristic
234	#13093944	C₂³	1	1	yes	characteristic
235	#13093944	C₂³	1	2	yes	—
236	#13093944	C₂³	1	2	yes	—
237	#13093944	C₂³	1	2	yes	—
238	#13093944	C₂³	1	2	yes	—
239	#13093944	C₂³	1	2	yes	—
240	#13093944	C₂³	1	2	yes	—
241	#13093944	C₂³	1	2	yes	—
242	#13093935	C₂³	1	2	yes	—
243	#13093935	C₂³	1	1	yes	characteristic
244	#13093935	C₂³	1	1	yes	characteristic
245	#13093935	C₂³	1	2	yes	—
246	#13093935	C₂³	1	1	yes	characteristic
247	#13093935	C₂³	1	1	yes	characteristic
248	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
249	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
250	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
251	C₂²×Q₈×C₄₇	—	2	2	no	—
252	C₂²×Q₈×C₄₇	—	2	1	no	—
253	C₄⋊Q₈×C₄₇	—	2	2	no	—
254	C₄⋊Q₈×C₄₇	—	2	1	no	—
255	C₄⋊Q₈×C₄₇	—	2	1	no	—
256	C₄⋊Q₈×C₄₇	—	2	2	no	—
257	C₄⋊Q₈×C₄₇	—	2	2	no	—
258	C₄⋊Q₈×C₄₇	—	2	2	no	—
259	C₄⋊Q₈×C₄₇	—	2	1	no	—
260	C₄⋊Q₈×C₄₇	—	2	1	no	—
261	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
262	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
263	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
264	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
265	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
266	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
267	#125×C₄₇	—	2	1	no	—
268	#125×C₄₇	—	2	1	no	—
269	#125×C₄₇	—	2	2	no	—
270	#125×C₄₇	—	2	2	no	—
271	#125×C₄₇	D₄	1	1	yes	characteristic
272	#125×C₄₇	D₄	1	1	yes	characteristic
273	#125×C₄₇	C₂³	1	2	yes	—
274	#125×C₄₇	C₂³	1	2	yes	—
275	C₂²⋊Q₈×C₄₇	—	2	2	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	—	2	2	no	—
280	C₂²⋊Q₈×C₄₇	—	2	2	no	—
281	C₂²⋊Q₈×C₄₇	—	2	2	no	—
282	C₂²⋊Q₈×C₄₇	—	2	2	no	—
283	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
284	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
285	C₄×Q₈×C₄₇	—	2	2	no	—
286	C₄×Q₈×C₄₇	—	2	2	no	—
287	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
288	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
289	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
290	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
291	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
292	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
293	C₄×D₄×C₄₇	—	2	1	no	—
294	C₄×D₄×C₄₇	—	2	1	no	—
295	C₄×D₄×C₄₇	—	2	2	no	—
296	C₄×D₄×C₄₇	—	2	2	no	—
297	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
298	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
299	C₄×D₄×C₄₇	C₂³	1	2	yes	—
300	C₄×D₄×C₄₇	C₂³	1	2	yes	—
301	#117×C₄₇	—	2	1	no	—
302	#117×C₄₇	—	2	1	no	—
303	#117×C₄₇	—	2	1	no	—
304	#117×C₄₇	C₂³	1	1	yes	characteristic
305	#117×C₄₇	C₂³	1	1	yes	characteristic
306	#117×C₄₇	C₂³	1	1	yes	characteristic
307	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
308	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
309	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
310	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
311	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
312	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
313	C₂×C₄²×C₄₇	—	2	1	no	—
314	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
315	C₂³×D₄₇	—	2	1	no	—
316	#41×C₄₇	—	2	2	no	—
317	#41×C₄₇	#41	1	4	yes	—
318	C₂×Q₈×C₄₇	—	2	2	no	—
319	C₂×Q₈×C₄₇	—	2	2	no	—
320	C₂×Q₈×C₄₇	—	2	2	no	—
321	C₂×Q₈×C₄₇	—	2	2	no	—
322	C₂×Q₈×C₄₇	—	8	2	no	—
323	C₂×Q₈×C₄₇	—	8	4	no	—
324	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
325	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
326	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
327	C₂×D₄×C₄₇	—	2	1	no	—
328	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
329	C₂²×C₄×C₄₇	—	2	1	no	—
330	C₂²×C₄×C₄₇	—	2	1	no	—
331	C₂²×C₄×C₄₇	—	2	1	no	—
332	C₂²×C₄×C₄₇	—	2	1	no	—
333	C₂²×C₄×C₄₇	—	2	1	no	—
334	C₂²×C₄×C₄₇	—	2	2	no	—
335	C₂²×C₄×C₄₇	—	2	2	no	—
336	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
337	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
338	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
339	C₂×C₂²⋊D₄₇	—	2	1	no	—
340	C₂²×Dic₄₇	—	2	1	no	—
341	#10625350	—	2	2	no	—
342	#10625350	—	2	2	no	—
343	C₂×D₁₈₈	—	2	2	no	—
344	C₂×D₁₈₈	—	2	2	no	—
345	C₂×D₁₈₈	—	2	1	no	—
346	C₂×D₁₈₈	—	2	2	no	—
347	C₂×D₁₈₈	—	2	2	no	—
348	C₂×D₁₈₈	C₂⁴	1	2	yes	—
349	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
350	C₂×C₄×D₄₇	—	2	1	no	—
351	C₂×C₄×D₄₇	—	2	1	no	—
352	C₂×C₄×D₄₇	—	2	1	no	—
353	C₂×C₄×D₄₇	—	2	2	no	—
354	C₂×C₄×D₄₇	—	2	2	no	—
355	C₂×Dic₉₄	—	2	2	no	—
356	C₂×Dic₉₄	—	2	2	no	—
357	C₂×Dic₉₄	—	2	1	no	—
358	C₂×Dic₉₄	C₂⁴	1	2	yes	—
359	C₂×Dic₉₄	C₂⁴	1	1	yes	characteristic
360	C₄⋊C₄×C₄₇	—	2	2	no	—
361	C₄⋊C₄×C₄₇	—	2	1	no	—
362	C₄⋊C₄×C₄₇	—	2	1	no	—
363	C₄⋊C₄×C₄₇	—	2	2	no	—
364	C₄⋊C₄×C₄₇	—	2	2	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	1	no	—
369	C₄⋊C₄×C₄₇	—	2	1	no	—
370	C₄⋊C₄×C₄₇	—	2	2	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	C₂×D₄	1	1	yes	characteristic
375	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
376	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
377	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
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	2	yes	—
381	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
382	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
383	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
384	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
385	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
386	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
387	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
388	C₂²⋊C₄×C₄₇	—	2	1	no	—
389	C₂²⋊C₄×C₄₇	—	2	1	no	—
390	C₂²⋊C₄×C₄₇	—	2	1	no	—
391	C₂²⋊C₄×C₄₇	—	2	2	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	C₄²×C₄₇	—	2	1	no	—
396	C₄²×C₄₇	—	2	1	no	—
397	C₄²×C₄₇	—	2	1	no	—
398	C₄²×C₄₇	—	2	2	no	—
399	C₄²×C₄₇	—	2	2	no	—
400	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
401	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
402	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
403	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
404	C₄²×C₄₇	C₂⁴	1	2	yes	—
405	C₄²×C₄₇	C₂⁴	1	2	yes	—
406	C₂²⋊Dic₄₇	—	2	1	no	—
407	#10625337	—	2	2	no	—
408	#10625337	—	2	4	no	—
409	#10625336	—	2	2	no	—
410	#10625336	—	2	4	no	—
411	#10625335	—	2	2	no	—
412	#10625335	—	2	4	no	—
413	#10625334	—	2	2	no	—
414	#10625334	—	2	4	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	1	no	—
422	(C₂×D₄₇)⋊C₄	—	2	1	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	C₄⋊Dic₄₇	—	2	2	no	—
428	C₄⋊Dic₄₇	—	2	2	no	—
429	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
430	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
431	Dic₄₇⋊C₄	—	2	2	no	—
432	Dic₄₇⋊C₄	—	2	2	no	—
433	Dic₄₇⋊C₄	—	2	1	no	—
434	Dic₄₇⋊C₄	—	2	1	no	—
435	C₄×Dic₄₇	—	2	1	no	—
436	C₄×Dic₄₇	—	2	1	no	—
437	C₄×Dic₄₇	—	2	1	no	—
438	C₄×Dic₄₇	—	2	2	no	—
439	C₄×Dic₄₇	—	2	2	no	—
440	#10625329	—	2	2	no	—
441	#10625329	—	2	2	no	—
442	C₂×C₄₇⋊C₈	—	2	2	no	—
443	C₂×C₄₇⋊C₈	—	2	2	no	—
444	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
445	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
446	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
447	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
448	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
449	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
450	C₂³×C₄₇	—	2	1	no	—
451	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
452	C₂²×D₄₇	—	2	2	no	—
453	C₂²×D₄₇	—	2	1	no	—
454	C₂²×D₄₇	—	4	2	no	—
455	C₂²×D₄₇	—	8	1	no	—
456	C₂²×D₄₇	—	8	1	no	—
457	Q₈×C₄₇	—	2	1	no	—
458	Q₈×C₄₇	—	4	2	no	—
459	Q₈×C₄₇	—	4	2	no	—
460	Q₈×C₄₇	—	4	4	no	—
461	Q₈×C₄₇	—	8	2	no	—
462	Q₈×C₄₇	—	8	2	no	—
463	Q₈×C₄₇	—	8	2	no	—
464	Q₈×C₄₇	C₂×#41	1	2	yes	—
465	D₄×C₄₇	—	2	4	no	—
466	D₄×C₄₇	—	2	1	no	—
467	D₄×C₄₇	C₂×#41	1	2	yes	—
468	C₂×C₄×C₄₇	—	2	1	no	—
469	C₂×C₄×C₄₇	—	2	4	no	—
470	C₂×C₄×C₄₇	—	2	1	no	—
471	C₂×C₄×C₄₇	—	2	1	no	—
472	C₂×C₄×C₄₇	—	2	2	no	—
473	C₂×C₄×C₄₇	—	2	2	no	—
474	C₂×C₄×C₄₇	—	4	1	no	—
475	C₂×C₄×C₄₇	—	4	1	no	—
476	C₂×C₄×C₄₇	—	4	2	no	—
477	C₂×C₄×C₄₇	—	4	2	no	—
478	C₂×C₄×C₄₇	—	8	2	no	—
479	C₂×C₄×C₄₇	—	8	2	no	—
480	C₂×C₄×C₄₇	—	8	1	no	—
481	C₂×C₄×C₄₇	—	8	1	no	—
482	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
483	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
484	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
486	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
487	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
488	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
489	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
490	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
491	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
492	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
493	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
494	C₂²⋊D₄₇	—	4	2	no	—
495	C₂×Dic₄₇	—	2	1	no	—
496	C₂×Dic₄₇	—	2	1	no	—
497	C₂×Dic₄₇	—	2	1	no	—
498	C₂×Dic₄₇	—	2	2	no	—
499	C₂×Dic₄₇	—	4	2	no	—
500	D₁₈₈	—	2	2	no	—
501	D₁₈₈	—	2	1	no	—
502	D₁₈₈	—	2	2	no	—
503	D₁₈₈	—	2	1	no	—
504	D₁₈₈	—	4	2	no	—
505	D₁₈₈	—	8	2	no	—
506	D₁₈₈	—	8	2	no	—
507	C₄×D₄₇	—	4	2	no	—
508	C₄×D₄₇	—	8	1	no	—
509	C₄×D₄₇	—	8	2	no	—
510	C₄×D₄₇	—	8	1	no	—
511	C₄×D₄₇	—	8	2	no	—
512	Dic₉₄	—	2	2	no	—
513	Dic₉₄	—	2	1	no	—
514	Dic₉₄	—	2	2	no	—
515	Dic₉₄	—	2	1	no	—
516	Dic₉₄	—	4	2	no	—
517	C₄₇⋊C₈	—	2	1	no	—
518	C₄₇⋊C₈	—	2	1	no	—
519	C₄₇⋊C₈	—	2	2	no	—
520	C₄₇⋊C₈	—	2	2	no	—
521	C₄₇⋊C₈	—	2	1	no	—
522	C₄₇⋊C₈	—	2	1	no	—
523	#61336	—	47	1	no	maximal, Sylow
524	C₂²×C₄₇	—	2	1	no	—
525	C₂²×C₄₇	—	2	1	no	—
526	C₂²×C₄₇	—	2	2	no	—
527	C₂²×C₄₇	—	4	1	no	—
528	C₂²×C₄₇	—	4	1	no	—
529	C₂²×C₄₇	#548	1	2	yes	—
530	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
531	C₂×D₄₇	—	4	1	no	—
532	C₂×D₄₇	—	4	2	no	—
533	C₂×D₄₇	—	4	1	no	—
534	C₂×D₄₇	—	4	2	no	—
535	C₂×D₄₇	—	4	1	no	—
536	C₂×D₄₇	—	4	2	no	—
537	C₂×D₄₇	—	16	2	no	—
538	C₄×C₄₇	—	2	1	no	—
539	C₄×C₄₇	—	2	2	no	—
540	C₄×C₄₇	—	2	2	no	—
541	C₄×C₄₇	—	2	1	no	—
542	C₄×C₄₇	—	2	1	no	—
543	C₄×C₄₇	—	2	2	no	—
544	C₄×C₄₇	—	2	2	no	—
545	C₄×C₄₇	—	2	1	no	—
546	C₄×C₄₇	—	2	2	no	—
547	C₄×C₄₇	—	4	1	no	—
548	C₄×C₄₇	—	4	2	no	—
549	C₄×C₄₇	—	4	2	no	—
550	C₄×C₄₇	—	4	1	no	—
551	C₄×C₄₇	#548	1	2	yes	—
552	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
553	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
554	Dic₄₇	—	4	1	no	—
555	Dic₄₇	—	4	1	no	—
556	Dic₄₇	—	4	2	no	—
557	Dic₄₇	—	4	1	no	—
558	#3510	—	47	1	no	—
559	#3503	D₄₇	1	1	yes	characteristic, complemented
560	#3377	—	47	2	no	—
561	#3376	—	47	2	no	—
562	#3375	—	47	2	no	—
563	#3373	—	47	2	no	—
564	#3371	—	47	2	no	—
565	#3370	—	47	2	no	—
566	#3369	—	47	2	no	—
567	#3367	—	47	2	no	—
568	#3137	—	47	1	no	—
569	#3136	—	47	1	no	—
570	C₂×#489	—	47	1	no	—
571	#3082	—	47	1	no	—
572	#3081	—	47	1	no	—
573	#3079	—	47	1	no	—
574	#3046	—	47	1	no	—
575	#3045	—	47	1	no	—
576	#3040	—	47	1	no	—
577	#2961	—	47	1	no	—
578	#2947	—	47	1	no	—
579	#2946	—	47	1	no	—
580	#2943	—	47	1	no	—
581	C₂×C₄₇	—	2	2	no	—
582	C₂×C₄₇	—	4	2	no	—
583	C₂×C₄₇	C₂×#548	1	1	yes	characteristic
584	C₂×C₄₇	#3585	1	1	yes	characteristic
585	C₂×C₄₇	#3586	1	1	yes	characteristic
586	D₄₇	—	8	1	no	—
587	D₄₇	—	8	2	no	—
588	C₂×#137	—	47	1	no	—
589	C₂×AGL(1,ℤ/8)	—	47	1	no	—
590	C₂×#135	—	47	1	no	—
591	#559	—	47	2	no	—
592	#559	—	47	2	no	—
593	Q₈²	C₂×D₄₇	1	2	yes	complemented
594	#557	C₂×D₄₇	1	2	yes	complemented
595	#556	—	47	2	no	—
596	#556	—	47	2	no	—
597	#554	—	2	2	no	—
598	#554	C₂×D₄₇	1	2	yes	complemented
599	#551	—	94	2	no	—
600	#551	—	94	2	no	—
601	D₄×Q₈	—	2	2	no	—
602	D₄×Q₈	C₂×D₄₇	1	2	yes	complemented
603	#544	—	2	1	no	—
604	#544	—	2	1	no	—
605	#544	C₂×D₄₇	1	1	yes	characteristic
606	#544	C₂×D₄₇	1	1	yes	characteristic
607	#542	—	94	1	no	—
608	#542	—	94	1	no	—
609	#536	—	47	1	no	—
610	#535	—	47	1	no	—
611	#533	—	2	1	no	—
612	#533	C₂×D₄₇	1	1	yes	characteristic
613	C₂×C₄⋊Q₈	—	2	1	no	—
614	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
615	#529	—	94	1	no	—
616	#529	—	94	1	no	—
617	C₂×#124	—	47	1	no	—
618	#520	C₂×D₄₇	1	1	yes	characteristic
619	#520	C₂×D₄₇	1	1	yes	characteristic
620	#519	—	47	1	no	—
621	#518	—	47	1	no	—
622	C₄×#41	—	47	1	no	—
623	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
624	#491	—	47	2	no	—
625	#490	—	47	2	no	—
626	#489	—	47	2	no	—
627	#489	—	47	2	no	—
628	#489	—	47	2	no	—
629	#489	—	47	2	no	—
630	#489	—	47	2	no	—
631	#489	—	47	2	no	—
632	#488	—	47	2	no	—
633	#488	—	47	2	no	—
634	#487	—	47	2	no	—
635	#486	—	47	2	no	—
636	#479	—	47	2	no	—
637	#479	—	47	2	no	—
638	#478	—	47	2	no	—
639	#478	—	47	2	no	—
640	#477	—	47	2	no	—
641	#477	—	47	2	no	—
642	#476	—	47	2	no	—
643	#476	—	47	2	no	—
644	#475	—	47	2	no	—
645	#475	—	47	2	no	—
646	#474	—	47	2	no	—
647	#474	—	47	2	no	—
648	#464	—	47	2	no	—
649	#464	—	47	2	no	—
650	#464	—	47	2	no	—
651	#464	—	47	2	no	—
652	#463	—	47	2	no	—
653	#463	—	47	2	no	—
654	#463	—	47	2	no	—
655	#463	—	47	2	no	—
656	#462	—	47	2	no	—
657	#461	—	47	2	no	—
658	#460	—	47	2	no	—
659	#459	—	47	2	no	—
660	#446	—	47	2	no	—
661	#446	—	47	2	no	—
662	#446	—	47	2	no	—
663	#446	—	47	2	no	—
664	#442	—	47	2	no	—
665	#442	—	47	1	no	—
666	#442	—	47	1	no	—
667	#441	—	47	1	no	—
668	#441	—	47	2	no	—
669	#441	—	47	1	no	—
670	#440	—	47	2	no	—
671	#440	—	47	1	no	—
672	#440	—	47	1	no	—
673	#440	—	47	1	no	—
674	#440	—	47	2	no	—
675	#440	—	47	1	no	—
676	C₄×Q₁₆	—	47	2	no	—
677	C₄×SD₁₆	—	47	2	no	—
678	C₄×SD₁₆	—	47	2	no	—
679	C₄×D₈	—	47	2	no	—
680	#428	—	47	1	no	—
681	#428	—	47	1	no	—
682	#427	—	47	1	no	—
683	#424	—	47	1	no	—
684	#424	—	47	1	no	—
685	#423	—	47	1	no	—
686	#419	—	47	1	no	—
687	#418	—	47	1	no	—
688	#417	—	47	1	no	—
689	#417	—	47	1	no	—
690	#416	—	47	1	no	—
691	#416	—	47	1	no	—
692	C₂×#103	—	47	1	no	—
693	C₂×#103	—	47	1	no	—
694	C₂×#102	—	47	1	no	—
695	C₂×#102	—	47	1	no	—
696	#405	—	47	1	no	—
697	#405	—	47	1	no	—
698	C₂×#97	—	47	1	no	—
699	C₄₇	#61336	1	1	yes	characteristic, complemented, Sylow
700	C₂×#41	—	47	1	no	—
701	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
702	C₂²×Q₈	—	2	2	no	—
703	C₂²×Q₈	—	2	1	no	—
704	C₂²×Q₈	—	47	1	no	—
705	C₂²×D₄	—	47	1	no	—
706	#137	—	94	4	no	—
707	AGL(1,ℤ/8)	—	94	4	no	—
708	#135	—	94	4	no	—
709	C₂×Q₁₆	—	47	1	no	—
710	C₂×Q₁₆	—	47	2	no	—
711	C₂×SD₁₆	—	47	1	no	—
712	C₂×SD₁₆	—	47	2	no	—
713	C₂×SD₁₆	—	47	1	no	—
714	C₂×SD₁₆	—	47	2	no	—
715	C₂×D₈	—	47	1	no	—
716	C₂×D₈	—	47	2	no	—
717	C₂×M₁₆	—	47	1	no	—
718	C₂×M₁₆	—	47	1	no	—
719	C₂²×C₈	—	47	1	no	—
720	C₂²×C₈	—	47	1	no	—
721	C₄⋊Q₈	—	2	2	no	—
722	C₄⋊Q₈	—	2	1	no	—
723	C₄⋊Q₈	—	2	1	no	—
724	C₄⋊Q₈	—	2	2	no	—
725	C₄⋊Q₈	—	2	2	no	—
726	C₄⋊Q₈	—	2	2	no	—
727	C₄⋊Q₈	—	2	1	no	—
728	C₄⋊Q₈	—	2	1	no	—
729	C₄⋊Q₈	—	47	2	no	—
730	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
731	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
732	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
733	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
734	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
735	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
736	#127	—	47	2	no	—
737	#126	—	94	2	no	—
738	#126	—	94	2	no	—
739	#126	—	94	2	no	—
740	#126	—	94	2	no	—
741	#125	—	2	1	no	—
742	#125	—	2	1	no	—
743	#125	—	2	2	no	—
744	#125	—	2	2	no	—
745	#125	C₂²⋊D₄₇	1	1	yes	characteristic
746	#125	C₂²⋊D₄₇	1	1	yes	characteristic
747	#125	C₂²×D₄₇	1	2	yes	—
748	#125	C₂²×D₄₇	1	2	yes	—
749	#124	—	47	2	no	—
750	#124	—	47	2	no	—
751	#124	—	47	2	no	—
752	#124	—	47	2	no	—
753	#124	—	94	2	no	—
754	#124	—	94	2	no	—
755	#124	—	94	1	no	—
756	#124	—	94	1	no	—
757	#123	—	94	2	no	—
758	#123	—	94	2	no	—
759	#123	—	94	2	no	—
760	#123	—	94	2	no	—
761	#123	—	94	2	no	—
762	C₂²⋊Q₈	—	2	2	no	—
763	C₂²⋊Q₈	—	2	2	no	—
764	C₂²⋊Q₈	—	2	2	no	—
765	C₂²⋊Q₈	—	2	2	no	—
766	C₂²⋊Q₈	—	2	2	no	—
767	C₂²⋊Q₈	—	2	2	no	—
768	C₂²⋊Q₈	—	2	2	no	—
769	C₂²⋊Q₈	—	2	2	no	—
770	C₂²⋊Q₈	—	94	2	no	—
771	C₂²⋊Q₈	—	94	2	no	—
772	C₂²⋊Q₈	—	94	1	no	—
773	C₂²⋊Q₈	—	94	1	no	—
774	C₂²⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
775	C₂²⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
776	#121	—	94	1	no	—
777	#121	—	94	1	no	—
778	#120	—	94	2	no	—
779	C₄×Q₈	—	2	2	no	—
780	C₄×Q₈	—	2	2	no	—
781	C₄×Q₈	—	47	1	no	—
782	C₄×Q₈	—	47	1	no	—
783	C₄×Q₈	—	47	2	no	—
784	C₄×Q₈	—	47	2	no	—
785	C₄×Q₈	—	94	1	no	—
786	C₄×Q₈	—	94	1	no	—
787	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
788	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
789	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
790	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
791	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
792	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
793	C₄×D₄	—	2	1	no	—
794	C₄×D₄	—	2	1	no	—
795	C₄×D₄	—	2	2	no	—
796	C₄×D₄	—	2	2	no	—
797	C₄×D₄	—	47	1	no	—
798	C₄×D₄	—	47	1	no	—
799	C₄×D₄	—	47	2	no	—
800	C₄×D₄	—	47	2	no	—
801	C₄×D₄	—	94	1	no	—
802	C₄×D₄	—	94	1	no	—
803	C₄×D₄	—	94	1	no	—
804	C₄×D₄	—	94	1	no	—
805	C₄×D₄	—	94	2	no	—
806	C₄×D₄	—	94	2	no	—
807	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
808	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
809	C₄×D₄	C₂²×D₄₇	1	2	yes	—
810	C₄×D₄	C₂²×D₄₇	1	2	yes	—
811	#117	—	2	1	no	—
812	#117	—	2	1	no	—
813	#117	—	2	1	no	—
814	#117	—	47	1	no	—
815	#117	—	94	2	no	—
816	#117	—	94	2	no	—
817	#117	—	94	2	no	—
818	#117	—	94	1	no	—
819	#117	C₂²×D₄₇	1	1	yes	characteristic
820	#117	C₂²×D₄₇	1	1	yes	characteristic
821	#117	C₂²×D₄₇	1	1	yes	characteristic
822	C₂×C₄⋊C₄	—	2	1	no	—
823	C₂×C₄⋊C₄	—	2	1	no	—
824	C₂×C₄⋊C₄	—	2	1	no	—
825	C₂×C₄⋊C₄	—	2	2	no	—
826	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
827	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
828	C₂×C₂²⋊C₄	—	94	1	no	—
829	C₂×C₂²⋊C₄	—	94	1	no	—
830	C₂×C₂²⋊C₄	—	94	2	no	—
831	C₂×C₄²	—	2	1	no	—
832	C₂×C₄²	—	94	1	no	—
833	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
834	#107	—	47	1	no	—
835	#107	—	47	1	no	—
836	#107	—	47	2	no	—
837	#107	—	47	2	no	—
838	#106	—	47	1	no	—
839	#106	—	47	1	no	—
840	#106	—	47	2	no	—
841	#106	—	47	2	no	—
842	C₄⋊C₈	—	47	2	no	—
843	C₄⋊C₈	—	47	2	no	—
844	C₄⋊C₈	—	47	2	no	—
845	C₄⋊C₈	—	47	2	no	—
846	C₄⋊C₈	—	47	2	no	—
847	C₄⋊C₈	—	47	2	no	—
848	#103	—	47	1	no	—
849	#103	—	47	1	no	—
850	#103	—	47	2	no	—
851	#103	—	47	2	no	—
852	#103	—	47	2	no	—
853	#103	—	47	2	no	—
854	#103	—	47	1	no	—
855	#103	—	47	1	no	—
856	#103	—	47	2	no	—
857	#103	—	47	2	no	—
858	#103	—	47	2	no	—
859	#103	—	47	2	no	—
860	#102	—	47	1	no	—
861	#102	—	47	1	no	—
862	#102	—	47	2	no	—
863	#102	—	47	2	no	—
864	#102	—	47	2	no	—
865	#102	—	47	2	no	—
866	#102	—	47	1	no	—
867	#102	—	47	1	no	—
868	#102	—	47	2	no	—
869	#102	—	47	2	no	—
870	#102	—	47	2	no	—
871	#102	—	47	2	no	—
872	#97	—	47	1	no	—
873	#97	—	47	1	no	—
874	#97	—	47	1	no	—
875	#97	—	47	1	no	—
876	#97	—	47	2	no	—
877	#97	—	47	2	no	—
878	C₄×C₈	—	47	2	no	—
879	C₄×C₈	—	47	2	no	—
880	C₂⁴	—	94	1	no	—
881	#41	—	2	2	no	—
882	#41	—	94	2	no	—
883	#41	—	94	2	no	—
884	#41	#10625354	1	4	yes	—
885	C₂×Q₈	—	2	2	no	—
886	C₂×Q₈	—	2	2	no	—
887	C₂×Q₈	—	2	2	no	—
888	C₂×Q₈	—	2	2	no	—
889	C₂×Q₈	—	8	2	no	—
890	C₂×Q₈	—	8	4	no	—
891	C₂×Q₈	—	47	2	no	—
892	C₂×Q₈	—	47	1	no	—
893	C₂×Q₈	—	94	1	no	—
894	C₂×Q₈	—	94	2	no	—
895	C₂×Q₈	—	94	2	no	—
896	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
897	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
898	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
899	C₂×D₄	—	2	1	no	—
900	C₂×D₄	—	47	2	no	—
901	C₂×D₄	—	47	1	no	—
902	C₂×D₄	—	94	1	no	—
903	C₂×D₄	—	94	2	no	—
904	C₂×D₄	—	94	2	no	—
905	C₂×D₄	—	94	1	no	—
906	C₂×D₄	—	94	2	no	—
907	C₂×D₄	—	94	2	no	—
908	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
909	C₂²×C₄	—	2	1	no	—
910	C₂²×C₄	—	2	1	no	—
911	C₂²×C₄	—	2	1	no	—
912	C₂²×C₄	—	2	1	no	—
913	C₂²×C₄	—	2	1	no	—
914	C₂²×C₄	—	2	2	no	—
915	C₂²×C₄	—	2	2	no	—
916	C₂²×C₄	—	94	1	no	—
917	C₂²×C₄	—	94	1	no	—
918	C₂²×C₄	—	94	1	no	—
919	C₂²×C₄	—	94	2	no	—
920	C₂²×C₄	—	94	2	no	—
921	C₂²×C₄	—	94	1	no	—
922	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
923	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
924	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
925	Q₁₆	—	94	2	no	—
926	Q₁₆	—	94	4	no	—
927	SD₁₆	—	94	2	no	—
928	SD₁₆	—	94	4	no	—
929	SD₁₆	—	94	2	no	—
930	SD₁₆	—	94	4	no	—
931	D₈	—	94	2	no	—
932	D₈	—	94	4	no	—
933	M₁₆	—	94	2	no	—
934	M₁₆	—	94	2	no	—
935	C₂×C₈	—	47	1	no	—
936	C₂×C₈	—	47	1	no	—
937	C₂×C₈	—	47	2	no	—
938	C₂×C₈	—	47	2	no	—
939	C₂×C₈	—	47	1	no	—
940	C₂×C₈	—	47	1	no	—
941	C₂×C₈	—	94	2	no	—
942	C₂×C₈	—	94	2	no	—
943	C₄⋊C₄	—	2	2	no	—
944	C₄⋊C₄	—	2	1	no	—
945	C₄⋊C₄	—	2	1	no	—
946	C₄⋊C₄	—	2	2	no	—
947	C₄⋊C₄	—	2	2	no	—
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	2	1	no	—
952	C₄⋊C₄	—	2	1	no	—
953	C₄⋊C₄	—	2	2	no	—
954	C₄⋊C₄	—	2	2	no	—
955	C₄⋊C₄	—	2	2	no	—
956	C₄⋊C₄	—	2	2	no	—
957	C₄⋊C₄	—	47	1	no	—
958	C₄⋊C₄	—	47	1	no	—
959	C₄⋊C₄	—	94	1	no	—
960	C₄⋊C₄	—	94	1	no	—
961	C₄⋊C₄	—	94	2	no	—
962	C₄⋊C₄	—	94	2	no	—
963	C₄⋊C₄	—	94	2	no	—
964	C₄⋊C₄	—	94	2	no	—
965	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
966	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
967	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
968	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
969	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
970	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
971	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
972	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
973	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
974	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
975	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
976	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
977	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
978	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
979	C₂²⋊C₄	—	2	1	no	—
980	C₂²⋊C₄	—	2	1	no	—
981	C₂²⋊C₄	—	2	1	no	—
982	C₂²⋊C₄	—	2	2	no	—
983	C₂²⋊C₄	—	2	2	no	—
984	C₂²⋊C₄	—	94	1	no	—
985	C₂²⋊C₄	—	94	2	no	—
986	C₂²⋊C₄	—	94	2	no	—
987	C₂²⋊C₄	—	94	2	no	—
988	C₂²⋊C₄	—	94	2	no	—
989	C₂²⋊C₄	—	94	2	no	—
990	C₂²⋊C₄	—	94	2	no	—
991	C₂²⋊C₄	—	94	1	no	—
992	C₂²⋊C₄	—	94	1	no	—
993	C₂²⋊C₄	—	94	2	no	—
994	C₂²⋊C₄	—	94	2	no	—
995	C₂²⋊C₄	—	94	2	no	—
996	C₂²⋊C₄	—	94	2	no	—
997	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
998	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
999	C₄²	—	2	1	no	—
1000	C₄²	—	2	1	no	—
1001	C₄²	—	2	1	no	—
1002	C₄²	—	2	2	no	—
1003	C₄²	—	2	2	no	—
1004	C₄²	—	94	1	no	—
1005	C₄²	—	94	1	no	—
1006	C₄²	—	94	1	no	—
1007	C₄²	—	94	2	no	—
1008	C₄²	—	94	2	no	—
1009	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1010	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
1011	C₄²	C₂³×D₄₇	1	2	yes	—
1012	C₄²	C₂³×D₄₇	1	2	yes	—
1013	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1014	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1015	C₂³	—	2	1	no	—
1016	C₂³	—	94	2	no	—
1017	C₂³	—	94	1	no	—
1018	C₂³	—	376	1	no	—
1019	C₂³	—	376	1	no	—
1020	C₂³	—	188	2	no	—
1021	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1022	Q₈	—	2	1	no	—
1023	Q₈	—	4	2	no	—
1024	Q₈	—	4	2	no	—
1025	Q₈	—	4	4	no	—
1026	Q₈	—	8	2	no	—
1027	Q₈	—	8	2	no	—
1028	Q₈	—	8	2	no	—
1029	Q₈	—	94	2	no	—
1030	Q₈	—	94	1	no	—
1031	Q₈	—	94	2	no	—
1032	Q₈	—	94	1	no	—
1033	Q₈	—	188	2	no	—
1034	Q₈	C₂×#10625354	1	2	yes	—
1035	D₄	—	2	4	no	—
1036	D₄	—	2	1	no	—
1037	D₄	—	94	2	no	—
1038	D₄	—	94	1	no	—
1039	D₄	—	94	2	no	—
1040	D₄	—	94	1	no	—
1041	D₄	—	376	2	no	—
1042	D₄	—	376	2	no	—
1043	D₄	—	188	2	no	—
1044	D₄	—	188	2	no	—
1045	D₄	C₂×#10625354	1	2	yes	—
1046	C₂×C₄	—	2	1	no	—
1047	C₂×C₄	—	2	4	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	2	no	—
1051	C₂×C₄	—	2	2	no	—
1052	C₂×C₄	—	4	1	no	—
1053	C₂×C₄	—	4	1	no	—
1054	C₂×C₄	—	4	2	no	—
1055	C₂×C₄	—	4	2	no	—
1056	C₂×C₄	—	8	2	no	—
1057	C₂×C₄	—	8	2	no	—
1058	C₂×C₄	—	8	1	no	—
1059	C₂×C₄	—	8	1	no	—
1060	C₂×C₄	—	94	1	no	—
1061	C₂×C₄	—	94	1	no	—
1062	C₂×C₄	—	94	2	no	—
1063	C₂×C₄	—	94	1	no	—
1064	C₂×C₄	—	376	1	no	—
1065	C₂×C₄	—	376	2	no	—
1066	C₂×C₄	—	376	1	no	—
1067	C₂×C₄	—	376	2	no	—
1068	C₂×C₄	—	188	2	no	—
1069	C₂×C₄	—	188	2	no	—
1070	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1071	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1072	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1073	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1074	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1075	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1076	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1077	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1078	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1079	C₂×C₄	C₂×#10625354	1	2	yes	—
1080	C₂×C₄	#13094072	1	2	yes	—
1081	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1082	C₈	—	94	1	no	—
1083	C₈	—	94	1	no	—
1084	C₈	—	94	2	no	—
1085	C₈	—	94	2	no	—
1086	C₈	—	94	1	no	—
1087	C₈	—	94	1	no	—
1088	C₂²	—	2	1	no	—
1089	C₂²	—	2	1	no	—
1090	C₂²	—	2	2	no	—
1091	C₂²	—	4	1	no	—
1092	C₂²	—	4	1	no	—
1093	C₂²	—	188	1	no	—
1094	C₂²	—	188	2	no	—
1095	C₂²	—	188	1	no	—
1096	C₂²	—	188	2	no	—
1097	C₂²	—	188	1	no	—
1098	C₂²	—	188	2	no	—
1099	C₂²	—	752	2	no	—
1100	C₂²	#15689784	1	2	yes	—
1101	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1102	C₄	—	2	2	no	—
1103	C₄	—	2	1	no	—
1104	C₄	—	2	1	no	—
1105	C₄	—	2	2	no	—
1106	C₄	—	2	2	no	—
1107	C₄	—	2	1	no	—
1108	C₄	—	2	1	no	—
1109	C₄	—	2	2	no	—
1110	C₄	—	2	2	no	—
1111	C₄	—	4	1	no	—
1112	C₄	—	4	2	no	—
1113	C₄	—	4	2	no	—
1114	C₄	—	4	1	no	—
1115	C₄	—	188	1	no	—
1116	C₄	—	188	2	no	—
1117	C₄	—	188	1	no	—
1118	C₄	—	188	1	no	—
1119	C₄	#15689784	1	2	yes	—
1120	C₄	C₂²×#10625354	1	1	yes	characteristic
1121	C₄	C₂×#13094072	1	1	yes	characteristic
1122	C₂	—	2	2	no	—
1123	C₂	—	4	2	no	—
1124	C₂	—	376	2	no	—
1125	C₂	—	376	1	no	—
1126	C₂	C₂×#15689784	1	1	yes	characteristic
1127	C₂	#20258168	1	1	yes	characteristic
1128	C₂	#20258175	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×#3503	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#20252927	C₂
hypercenter	#3503	D₄₇
hypocenter	C₄₇	#61336
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #533 ◁ #3503

Complements

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

N	H ≅ G/N	type
1. #20257286	C₂	semidirect
2. #20256230	C₂	semidirect
3. #20256215	C₂	semidirect
4. #20256202	C₂	semidirect
5. #20256180	C₂	semidirect
6. #20256156	C₂	semidirect
7. #20256141	C₂	semidirect
8. #20256128	C₂	semidirect
9. #20256106	C₂	semidirect
10. #20253758	C₂	semidirect
11. #20253747	C₂	semidirect
12. C₂×#15689485	C₂	semidirect
13. #20253224	C₂	semidirect
14. #20253213	C₂	semidirect
15. #20253197	C₂	semidirect
16. #20252938	C₂	semidirect
18. #20252882	C₂	semidirect
19. #20252329	C₂	semidirect
20. #20252227	C₂	semidirect
21. #20252216	C₂	semidirect
22. #20252186	C₂	semidirect
23. C₄₇×#3503	C₂	semidirect
43. #15689493	C₂²	semidirect
50. #15689485	C₂²	semidirect
52. #15689480	C₂²	semidirect
53. #15689475	C₂²	semidirect
55. #15689427	C₂²	semidirect
56. #15689427	C₂²	semidirect
59. #15689415	C₂²	semidirect
60. #15689415	C₂²	semidirect
62. #15689410	C₂²	semidirect
63. #15689405	C₂²	semidirect
64. #15689405	C₂²	semidirect
66. #15689400	C₂²	semidirect
70. #15689345	C₂²	semidirect
74. #15689338	C₂²	semidirect
75. #15689333	C₂²	semidirect
76. #15689328	C₂²	semidirect
79. #15689254	C₂²	semidirect
80. #15689254	C₂²	semidirect
81. #15689254	C₂²	semidirect
82. #15689254	C₂²	semidirect
84. #15689233	C₂²	semidirect
85. #15689233	C₂²	semidirect
86. #15689228	C₂²	semidirect
87. #15689228	C₂²	semidirect
88. #15689228	C₂²	semidirect
89. #15689223	C₂²	semidirect
90. #15689223	C₂²	semidirect
91. #15689223	C₂²	semidirect
93. #15689221	C₂²	semidirect
94. #15689221	C₂²	semidirect
95. C₄×#10625337	C₂²	semidirect
97. C₄×#10625335	C₂²	semidirect
118. Q₈²×C₄₇	C₂²	semidirect
119. C₄₇×#557	C₂²	semidirect
121. C₄₇×#554	C₂²	semidirect
123. D₄×Q₈×C₄₇	C₂²	semidirect
559. #3503	D₄₇	semidirect
593. Q₈²	C₂×D₄₇	semidirect
594. #557	C₂×D₄₇	semidirect
598. #554	C₂×D₄₇	semidirect
602. D₄×Q₈	C₂×D₄₇	semidirect
699. C₄₇	#61336	semidirect

Maximal subgroups

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

subgroup	index
#20257286	2
#20256230	2
#20256215	2
#20256202	2
#20256180	2
#20256156	2
#20256141	2
#20256128	2
#20256106	2
#20253758	2
#20253747	2
C₂×#15689485	2
#20253224	2
#20253213	2
#20253197	2
#20252938	2
#20252927	2
#20252882	2
#20252329	2
#20252227	2
#20252216	2
#20252186	2
C₄₇×#3503	2
#61336	47