Subgroups — #27106968

Order 12032.

1674 conjugacy classes of subgroups.

The subgroup lattice has 1092 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257189	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256327	C₂	1	2	yes	maximal, complemented
3	#20256294	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256287	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256259	C₂	1	2	yes	maximal, complemented
6	#20256251	C₂	1	1	yes	maximal, characteristic, complemented
7	Q₈×#10625336	C₂	1	1	yes	maximal, characteristic, complemented
8	#20256209	C₂	1	2	yes	maximal, complemented
9	#20256165	C₂	1	1	yes	maximal, characteristic, complemented
10	#20256102	C₂	1	1	yes	maximal, characteristic, complemented
11	#20256033	C₂	1	2	yes	maximal, complemented
12	#20256033	C₂	1	1	yes	maximal, characteristic, complemented
13	#20256026	C₂	1	1	yes	maximal, characteristic, complemented
14	#20254680	C₂	1	2	yes	maximal, complemented
15	#20254650	C₂	1	2	yes	maximal, complemented
16	#20254563	C₂	1	1	yes	maximal, characteristic, complemented
17	#20254543	C₂	1	1	yes	maximal, characteristic, complemented
18	#20253635	C₂	1	2	yes	maximal, complemented
19	#20253566	C₂	1	2	yes	maximal
20	#20253431	C₂	1	1	yes	maximal, characteristic
21	#20253392	C₂	1	1	yes	maximal, characteristic, complemented
22	#20252490	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3555	C₂	1	1	yes	maximal, characteristic, complemented
24	#15689834	—	2	1	no	—
25	#15689833	C₂²	1	2	yes	—
26	#15689833	C₂²	1	1	yes	characteristic
27	#15689833	C₂²	1	2	yes	—
28	#15689833	C₂²	1	1	yes	characteristic
29	#15689829	—	2	2	no	—
30	Q₈×D₁₈₈	C₂²	1	1	yes	characteristic
31	Q₈×D₁₈₈	C₂²	1	1	yes	characteristic
32	#15689788	—	2	1	no	—
33	#15689751	C₂²	1	2	yes	—
34	#15689748	—	2	2	no	—
35	#15689680	C₂²	1	1	yes	characteristic
36	C₂²⋊Q₈×D₄₇	—	2	1	no	—
37	C₂²⋊Q₈×D₄₇	—	2	1	no	—
38	#15689597	C₂²	1	2	yes	—
39	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
40	#15689533	C₂²	1	2	yes	complemented
41	#15689529	C₂²	1	2	yes	complemented
42	#15689526	C₂²	1	1	yes	characteristic, complemented
43	#15689522	C₂²	1	2	yes	complemented
44	#15689522	C₂²	1	2	yes	complemented
45	#15689519	C₂²	1	2	yes	complemented
46	#15689519	C₂²	1	1	yes	characteristic, complemented
47	#15689491	C₂²	1	2	yes	complemented
48	#15689482	C₂²	1	2	yes	complemented
49	#15689477	C₂²	1	2	yes	complemented
50	#15689477	C₂²	1	2	yes	complemented
51	#15689473	C₂²	1	2	yes	complemented
52	#15689473	C₂²	1	1	yes	characteristic, complemented
53	#15689473	C₂²	1	1	yes	characteristic, complemented
54	#15689461	C₂²	1	2	yes	—
55	#15689461	C₂²	1	2	yes	—
56	#15689461	C₂²	1	2	yes	—
57	#15689456	C₂²	1	1	yes	characteristic
58	#15689451	C₂²	1	2	yes	—
59	#15689444	C₂²	1	2	yes	—
60	#15689439	C₂²	1	1	yes	characteristic
61	#15689430	C₂²	1	2	yes	complemented
62	#15689430	C₂²	1	2	yes	complemented
63	#15689430	C₂²	1	2	yes	complemented
64	#15689430	C₂²	1	2	yes	complemented
65	#15689430	C₂²	1	2	yes	complemented
66	#15689423	C₂²	1	2	yes	complemented
67	#15689420	C₂²	1	1	yes	characteristic
68	#15689420	C₂²	1	2	yes	—
69	#15689420	C₂²	1	1	yes	characteristic
70	#15689420	C₂²	1	2	yes	—
71	#15689418	C₂²	1	2	yes	complemented
72	#15689418	C₂²	1	1	yes	characteristic, complemented
73	#15689413	C₂²	1	2	yes	complemented
74	#15689413	C₂²	1	1	yes	characteristic, complemented
75	#15689410	C₂²	1	1	yes	characteristic
76	#15689410	C₂²	1	2	yes	—
77	#15689410	C₂²	1	1	yes	characteristic
78	#15689408	C₂²	1	2	yes	complemented
79	#15689408	C₂²	1	1	yes	characteristic, complemented
80	#15689408	C₂²	1	2	yes	complemented
81	#15689403	C₂²	1	1	yes	characteristic, complemented
82	#15689400	C₂²	1	2	yes	—
83	#15689335	C₂²	1	1	yes	characteristic
84	#15689335	C₂²	1	2	yes	—
85	#15689335	C₂²	1	2	yes	—
86	#15689335	C₂²	1	1	yes	characteristic
87	#15689325	C₂²	1	1	yes	characteristic
88	#15689325	C₂²	1	2	yes	—
89	#15689325	C₂²	1	2	yes	—
90	#15689325	C₂²	1	1	yes	characteristic
91	#15689273	C₂²	1	2	yes	—
92	#15689273	C₂²	1	1	yes	characteristic
93	#15689256	C₂²	1	1	yes	characteristic
94	#15689254	C₂²	1	1	yes	characteristic, complemented
95	#15689254	C₂²	1	1	yes	characteristic, complemented
96	#15689254	C₂²	1	2	yes	complemented
97	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	complemented
98	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
99	Q₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
100	#15689233	C₂²	1	2	yes	—
101	#15689221	C₂²	1	2	yes	—
102	#15689221	C₂²	1	2	yes	—
103	#15689221	C₂²	1	2	yes	—
104	C₄×#10625336	C₂²	1	2	yes	—
105	C₄×#10625336	C₂²	1	2	yes	—
106	C₄×#10625336	C₂²	1	2	yes	—
107	C₄×#10625336	C₂²	1	1	yes	characteristic
108	C₄×#10625336	C₂²	1	2	yes	—
109	C₄×#10625336	C₂²	1	2	yes	—
110	C₄×#10625336	C₂²	1	1	yes	characteristic
111	C₄×#10625334	C₂²	1	1	yes	characteristic
112	C₄×#10625334	C₂²	1	2	yes	—
113	C₄×#10625334	C₂²	1	1	yes	characteristic
114	#15689184	C₂²	1	2	yes	—
115	#15689184	C₂²	1	2	yes	—
116	#15689176	C₂²	1	1	yes	characteristic
117	#15689176	C₂²	1	1	yes	characteristic
118	C₄₇×#563	—	2	2	no	—
119	Q₈²×C₄₇	C₂²	1	1	yes	characteristic, complemented
120	C₄₇×#557	C₂²	1	1	yes	characteristic, complemented
121	C₄₇×#557	C₂²	1	2	yes	complemented
122	C₄₇×#556	—	2	1	no	—
123	C₄₇×#556	C₂²	1	1	yes	characteristic, complemented
124	C₄₇×#556	C₂²	1	2	yes	complemented
125	C₄₇×#554	C₂²	1	1	yes	characteristic, complemented
126	C₄₇×#552	—	2	1	no	—
127	C₄₇×#544	—	2	1	no	—
128	C₄₇×#542	C₂²	1	2	yes	—
129	C₄₇×#541	—	2	1	no	—
130	C₄₇×#541	—	2	2	no	—
131	C₄₇×#541	C₂²	1	2	yes	—
132	C₄₇×#533	C₂²	1	1	yes	characteristic
133	C₄₇×#533	C₂²	1	1	yes	characteristic
134	C₄₇×#529	C₂²	1	1	yes	characteristic
135	C₂×Q₈×D₄₇	—	2	1	no	—
136	C₂×Q₈×D₄₇	—	2	1	no	—
137	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
138	C₂²×C₄×D₄₇	—	2	1	no	—
139	C₂×#10625336	C₂³	1	1	yes	characteristic
140	C₂×#10625336	C₂³	1	2	yes	—
141	C₂×#10625336	C₂³	1	2	yes	—
142	C₂×#10625336	C₂³	1	1	yes	characteristic
143	C₂×#10625334	C₂³	1	1	yes	characteristic
144	C₂×#10625334	C₂³	1	1	yes	characteristic
145	#13094024	C₂³	1	2	yes	—
146	#13094024	C₂³	1	1	yes	characteristic
147	#13094024	C₂³	1	1	yes	characteristic
148	#13094024	C₂³	1	2	yes	—
149	#13094023	—	2	2	no	—
150	#13094016	C₂³	1	2	yes	—
151	#13094016	C₂³	1	2	yes	—
152	#13094016	C₂³	1	2	yes	—
153	#13094015	—	2	2	no	—
154	#13094004	—	2	2	no	—
155	#13094004	—	2	2	no	—
156	#13094004	—	2	1	no	—
157	#13094004	—	2	1	no	—
158	#13094003	—	2	1	no	—
159	#13094003	—	2	1	no	—
160	#13094002	—	2	2	no	—
161	#13094002	—	2	2	no	—
162	#13094002	—	2	2	no	—
163	#13094002	—	2	2	no	—
164	#13094002	—	2	2	no	—
165	#13094002	—	2	2	no	—
166	#13094001	—	2	2	no	—
167	#13094001	—	2	2	no	—
168	#13094000	—	2	2	no	—
169	#13094000	—	2	2	no	—
170	#13094000	—	2	1	no	—
171	#13094000	—	2	1	no	—
172	C₄×Dic₉₄	—	2	1	no	—
173	C₄×Dic₉₄	—	2	1	no	—
174	C₄×D₁₈₈	—	2	1	no	—
175	C₄×D₁₈₈	—	2	1	no	—
176	C₄×D₁₈₈	C₂³	1	2	yes	—
177	C₄×D₁₈₈	C₂³	1	2	yes	—
178	C₄×D₁₈₈	C₂³	1	2	yes	—
179	C₄×D₁₈₈	C₂³	1	2	yes	—
180	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
181	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
182	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
183	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
184	#13093986	—	2	2	no	—
185	#13093986	—	2	2	no	—
186	#13093983	C₂³	1	2	yes	—
187	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
188	C₄⋊C₄×D₄₇	—	2	2	no	—
189	C₄⋊C₄×D₄₇	—	2	2	no	—
190	C₄⋊C₄×D₄₇	—	2	1	no	—
191	C₄⋊C₄×D₄₇	—	2	1	no	—
192	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
193	C₂²⋊C₄×D₄₇	—	2	2	no	—
194	C₂²⋊C₄×D₄₇	—	2	2	no	—
195	#13093957	C₂³	1	2	yes	—
196	#13093957	C₂³	1	2	yes	—
197	#13093957	C₂³	1	2	yes	—
198	#13093957	C₂³	1	1	yes	characteristic
199	#13093957	C₂³	1	2	yes	—
200	#13093957	C₂³	1	1	yes	characteristic
201	#13093955	C₂³	1	2	yes	—
202	#13093955	C₂³	1	2	yes	—
203	#13093955	C₂³	1	1	yes	characteristic
204	#13093955	C₂³	1	2	yes	—
205	#13093955	C₂³	1	2	yes	—
206	#13093955	C₂³	1	2	yes	—
207	#13093955	C₂³	1	1	yes	characteristic
208	#13093955	C₂³	1	2	yes	—
209	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
210	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
211	C₄⋊(C₄₇⋊C₈)	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	1	yes	characteristic
216	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
217	#13093948	C₂³	1	2	yes	—
218	#13093948	C₂³	1	1	yes	characteristic
219	#13093948	C₂³	1	2	yes	—
220	#13093948	C₂³	1	2	yes	—
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	#13093948	C₂³	1	1	yes	characteristic
227	#13093945	C₂³	1	1	yes	characteristic
228	#13093945	C₂³	1	2	yes	—
229	#13093945	C₂³	1	2	yes	—
230	#13093945	C₂³	1	1	yes	characteristic
231	#13093944	C₂³	1	1	yes	characteristic
232	#13093944	C₂³	1	1	yes	characteristic
233	#13093944	C₂³	1	2	yes	—
234	#13093944	C₂³	1	1	yes	characteristic
235	#13093944	C₂³	1	2	yes	—
236	#13093944	C₂³	1	1	yes	characteristic
237	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
238	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
239	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
240	#13093935	C₂³	1	2	yes	—
241	#13093935	C₂³	1	2	yes	—
242	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
243	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
244	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
245	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
246	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
247	C₄⋊Q₈×C₄₇	—	2	2	no	—
248	C₄⋊Q₈×C₄₇	—	2	2	no	—
249	C₄⋊Q₈×C₄₇	—	2	1	no	—
250	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
251	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
252	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
253	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
254	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
255	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
256	#126×C₄₇	—	2	2	no	—
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	—	2	2	no	—
262	#126×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	—	2	1	no	—
270	#125×C₄₇	D₄	1	2	yes	—
271	#125×C₄₇	C₂³	1	1	yes	characteristic
272	#125×C₄₇	C₂³	1	2	yes	—
273	#124×C₄₇	—	2	2	no	—
274	#124×C₄₇	C₂³	1	1	yes	characteristic
275	#124×C₄₇	C₂³	1	2	yes	—
276	#123×C₄₇	—	2	1	no	—
277	#123×C₄₇	—	2	2	no	—
278	C₂²⋊Q₈×C₄₇	—	2	1	no	—
279	C₂²⋊Q₈×C₄₇	—	2	1	no	—
280	C₂²⋊Q₈×C₄₇	—	2	2	no	—
281	C₂²⋊Q₈×C₄₇	—	2	1	no	—
282	C₂²⋊Q₈×C₄₇	—	2	2	no	—
283	C₂²⋊Q₈×C₄₇	—	2	2	no	—
284	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
285	C₂²⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
286	C₂²⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
287	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
288	C₂²⋊Q₈×C₄₇	C₂³	1	2	yes	—
289	#121×C₄₇	C₂³	1	1	yes	characteristic
290	C₄×Q₈×C₄₇	—	2	1	no	—
291	C₄×Q₈×C₄₇	—	2	1	no	—
292	C₄×Q₈×C₄₇	—	2	2	no	—
293	C₄×Q₈×C₄₇	—	2	1	no	—
294	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
295	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
296	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
297	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
298	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
299	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
300	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
301	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
302	C₄×D₄×C₄₇	—	2	1	no	—
303	C₄×D₄×C₄₇	C₂³	1	2	yes	—
304	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
305	#117×C₄₇	—	2	1	no	—
306	#117×C₄₇	—	2	2	no	—
307	#117×C₄₇	—	2	1	no	—
308	#117×C₄₇	—	2	1	no	—
309	#117×C₄₇	C₂³	1	2	yes	—
310	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
311	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
312	C₂³×D₄₇	—	2	1	no	—
313	C₂×Q₈×C₄₇	—	2	1	no	—
314	C₂×Q₈×C₄₇	—	2	2	no	—
315	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
316	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
317	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
318	C₂×Q₈×C₄₇	C₂⁴	1	2	yes	—
319	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
320	C₂×D₄×C₄₇	—	2	1	no	—
321	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
322	C₂²×C₄×C₄₇	—	2	1	no	—
323	C₂²×C₄×C₄₇	—	2	2	no	—
324	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
326	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
327	C₂²×Dic₄₇	—	2	1	no	—
328	Q₈×D₄₇	—	8	2	no	—
329	Q₈×D₄₇	—	8	2	no	—
330	C₂×D₁₈₈	—	2	1	no	—
331	C₂×D₁₈₈	—	2	2	no	—
332	C₂×D₁₈₈	—	2	2	no	—
333	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
334	C₂×D₁₈₈	C₂⁴	1	1	yes	characteristic
335	C₂×C₄×D₄₇	—	2	1	no	—
336	C₂×C₄×D₄₇	—	2	1	no	—
337	C₂×C₄×D₄₇	—	2	2	no	—
338	C₂×C₄×D₄₇	—	2	2	no	—
339	C₂×C₄×D₄₇	—	2	2	no	—
340	C₂×C₄×D₄₇	—	2	2	no	—
341	C₂×C₄×D₄₇	—	2	1	no	—
342	C₂×C₄×D₄₇	—	2	1	no	—
343	C₂×C₄×D₄₇	—	8	2	no	—
344	C₂×Dic₉₄	—	2	1	no	—
345	C₂×Dic₉₄	—	2	1	no	—
346	C₂×Dic₉₄	—	2	2	no	—
347	C₂×Dic₉₄	—	2	2	no	—
348	C₄⋊C₄×C₄₇	—	2	1	no	—
349	C₄⋊C₄×C₄₇	—	2	2	no	—
350	C₄⋊C₄×C₄₇	—	2	1	no	—
351	C₄⋊C₄×C₄₇	—	2	2	no	—
352	C₄⋊C₄×C₄₇	—	2	1	no	—
353	C₄⋊C₄×C₄₇	—	2	1	no	—
354	C₄⋊C₄×C₄₇	—	2	1	no	—
355	C₄⋊C₄×C₄₇	—	2	2	no	—
356	C₄⋊C₄×C₄₇	—	2	2	no	—
357	C₄⋊C₄×C₄₇	—	2	1	no	—
358	C₄⋊C₄×C₄₇	—	2	2	no	—
359	C₄⋊C₄×C₄₇	—	2	2	no	—
360	C₄⋊C₄×C₄₇	—	2	2	no	—
361	C₄⋊C₄×C₄₇	—	2	2	no	—
362	C₄⋊C₄×C₄₇	—	2	2	no	—
363	C₄⋊C₄×C₄₇	—	2	2	no	—
364	C₄⋊C₄×C₄₇	—	2	1	no	—
365	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
366	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
367	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
368	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
369	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
370	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
371	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
372	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
373	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
374	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
375	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
376	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
377	C₂²⋊C₄×C₄₇	—	2	2	no	—
378	C₂²⋊C₄×C₄₇	—	2	1	no	—
379	C₂²⋊C₄×C₄₇	—	2	1	no	—
380	C₂²⋊C₄×C₄₇	—	2	1	no	—
381	C₂²⋊C₄×C₄₇	—	2	1	no	—
382	C₂²⋊C₄×C₄₇	—	2	2	no	—
383	C₂²⋊C₄×C₄₇	—	2	2	no	—
384	C₂²⋊C₄×C₄₇	—	2	1	no	—
385	C₂²⋊C₄×C₄₇	—	2	2	no	—
386	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
387	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
388	C₄²×C₄₇	—	2	2	no	—
389	C₄²×C₄₇	—	2	1	no	—
390	C₄²×C₄₇	—	2	2	no	—
391	C₄²×C₄₇	—	2	2	no	—
392	C₄²×C₄₇	—	2	2	no	—
393	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
394	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
395	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
396	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
397	C₄²×C₄₇	C₂⁴	1	2	yes	—
398	C₄²×C₄₇	C₂⁴	1	2	yes	—
399	C₂²⋊Dic₄₇	—	2	2	no	—
400	#10625336	—	2	2	no	—
401	#10625336	—	2	4	no	—
402	#10625336	—	2	4	no	—
403	#10625336	—	2	2	no	—
404	#10625334	—	2	2	no	—
405	#10625334	—	2	2	no	—
406	(C₂×D₄₇)⋊C₄	—	2	2	no	—
407	(C₂×D₄₇)⋊C₄	—	2	2	no	—
408	(C₂×D₄₇)⋊C₄	—	2	2	no	—
409	(C₂×D₄₇)⋊C₄	—	2	2	no	—
410	(C₂×D₄₇)⋊C₄	—	2	1	no	—
411	(C₂×D₄₇)⋊C₄	—	2	1	no	—
412	(C₂×D₄₇)⋊C₄	—	2	1	no	—
413	(C₂×D₄₇)⋊C₄	—	2	1	no	—
414	C₄⋊Dic₄₇	—	2	1	no	—
415	C₄⋊Dic₄₇	—	2	2	no	—
416	C₄⋊Dic₄₇	—	2	2	no	—
417	C₄⋊Dic₄₇	—	2	1	no	—
418	C₄⋊Dic₄₇	—	2	1	no	—
419	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
420	C₄⋊Dic₄₇	C₂⁴	1	1	yes	characteristic
421	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
422	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
423	Dic₄₇⋊C₄	—	2	2	no	—
424	Dic₄₇⋊C₄	—	2	2	no	—
425	Dic₄₇⋊C₄	—	2	2	no	—
426	Dic₄₇⋊C₄	—	2	2	no	—
427	Dic₄₇⋊C₄	—	2	2	no	—
428	Dic₄₇⋊C₄	—	2	2	no	—
429	C₄×Dic₄₇	—	2	2	no	—
430	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
431	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
432	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
433	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
434	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
435	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
436	C₂³×C₄₇	—	2	1	no	—
437	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
438	C₂²×D₄₇	—	2	1	no	—
439	C₂²×D₄₇	—	2	1	no	—
440	C₂²×D₄₇	—	2	4	no	—
441	C₂²×D₄₇	—	8	1	no	—
442	C₂²×D₄₇	—	8	1	no	—
443	Q₈×C₄₇	—	2	2	no	—
444	Q₈×C₄₇	—	2	2	no	—
445	Q₈×C₄₇	—	2	2	no	—
446	Q₈×C₄₇	—	2	1	no	—
447	Q₈×C₄₇	—	2	2	no	—
448	Q₈×C₄₇	—	2	1	no	—
449	Q₈×C₄₇	—	4	2	no	—
450	Q₈×C₄₇	—	8	1	no	—
451	Q₈×C₄₇	—	8	2	no	—
452	D₄×C₄₇	—	2	1	no	—
453	D₄×C₄₇	—	2	1	no	—
454	D₄×C₄₇	—	8	1	no	—
455	C₂×C₄×C₄₇	—	2	2	no	—
456	C₂×C₄×C₄₇	—	2	1	no	—
457	C₂×C₄×C₄₇	—	2	1	no	—
458	C₂×C₄×C₄₇	—	2	2	no	—
459	C₂×C₄×C₄₇	—	2	1	no	—
460	C₂×C₄×C₄₇	—	2	1	no	—
461	C₂×C₄×C₄₇	—	2	1	no	—
462	C₂×C₄×C₄₇	—	2	2	no	—
463	C₂×C₄×C₄₇	—	4	1	no	—
464	C₂×C₄×C₄₇	—	4	2	no	—
465	C₂×C₄×C₄₇	—	8	2	no	—
466	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
470	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
471	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
472	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
473	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
474	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
475	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
476	C₂×Dic₄₇	—	2	2	no	—
477	C₂×Dic₄₇	—	2	2	no	—
478	C₂×Dic₄₇	—	2	1	no	—
479	C₂×Dic₄₇	—	2	1	no	—
480	C₂×Dic₄₇	—	8	1	no	—
481	D₁₈₈	—	2	4	no	—
482	D₁₈₈	—	2	1	no	—
483	D₁₈₈	—	2	1	no	—
484	D₁₈₈	2₋¹⁺⁴	1	2	yes	—
485	D₁₈₈	2₋¹⁺⁴	1	2	yes	—
486	C₄×D₄₇	—	4	2	no	—
487	C₄×D₄₇	—	4	2	no	—
488	C₄×D₄₇	—	8	2	no	—
489	C₄×D₄₇	—	8	2	no	—
490	C₄×D₄₇	—	8	1	no	—
491	C₄×D₄₇	—	8	1	no	—
492	C₄×D₄₇	—	8	2	no	—
493	C₄×D₄₇	—	8	2	no	—
494	Dic₉₄	—	4	2	no	—
495	Dic₉₄	—	8	1	no	—
496	Dic₉₄	—	8	2	no	—
497	Dic₉₄	—	8	2	no	—
498	C₄₇⋊C₈	—	2	1	no	—
499	C₄₇⋊C₈	—	2	1	no	—
500	C₄₇⋊C₈	—	2	2	no	—
501	C₄₇⋊C₈	—	2	1	no	—
502	C₄₇⋊C₈	—	2	1	no	—
503	C₄₇⋊C₈	—	2	2	no	—
504	#61864	—	47	1	no	maximal, Sylow
505	C₂²×C₄₇	—	2	1	no	—
506	C₂²×C₄₇	—	2	1	no	—
507	C₂²×C₄₇	—	2	1	no	—
508	C₂²×C₄₇	—	4	1	no	—
509	C₂²×C₄₇	—	4	1	no	—
510	C₂²×C₄₇	—	4	1	no	—
511	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
512	C₂×D₄₇	—	2	2	no	—
513	C₂×D₄₇	—	2	2	no	—
514	C₂×D₄₇	—	4	1	no	—
515	C₂×D₄₇	—	4	1	no	—
516	C₂×D₄₇	—	4	1	no	—
517	C₂×D₄₇	—	4	1	no	—
518	C₂×D₄₇	—	8	4	no	—
519	C₄×C₄₇	—	2	1	no	—
520	C₄×C₄₇	—	2	2	no	—
521	C₄×C₄₇	—	2	2	no	—
522	C₄×C₄₇	—	2	1	no	—
523	C₄×C₄₇	—	2	1	no	—
524	C₄×C₄₇	—	2	2	no	—
525	C₄×C₄₇	—	2	2	no	—
526	C₄×C₄₇	—	2	1	no	—
527	C₄×C₄₇	—	4	2	no	—
528	C₄×C₄₇	—	4	1	no	—
529	C₄×C₄₇	—	4	2	no	—
530	C₄×C₄₇	—	4	1	no	—
531	C₄×C₄₇	—	4	1	no	—
532	C₄×C₄₇	#577	1	2	yes	—
533	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
534	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
535	Dic₄₇	—	4	2	no	—
536	Dic₄₇	—	4	2	no	—
537	Dic₄₇	—	4	1	no	—
538	Dic₄₇	—	4	1	no	—
539	#3555	D₄₇	1	1	yes	characteristic, complemented
540	#3501	—	47	1	no	—
541	#3388	—	47	2	no	—
542	#3385	—	47	1	no	—
543	#3384	—	47	1	no	—
544	#3381	—	47	2	no	—
545	#3380	—	47	1	no	—
546	Q₈×SD₁₆	—	47	1	no	—
547	#3376	—	47	2	no	—
548	#3372	—	47	1	no	—
549	#3367	—	47	1	no	—
550	#3360	—	47	1	no	—
551	#3360	—	47	2	no	—
552	#3359	—	47	1	no	—
553	#3244	—	47	2	no	—
554	#3242	—	47	2	no	—
555	#3233	—	47	1	no	—
556	#3231	—	47	1	no	—
557	#3123	—	47	2	no	—
558	#3118	—	47	2	no	—
559	#3105	—	47	1	no	—
560	#3101	—	47	1	no	—
561	#2986	—	47	1	no	—
562	C₂×C₄₇	—	4	1	no	—
563	C₂×C₄₇	—	8	1	no	—
564	C₂×C₄₇	#3486	1	1	yes	characteristic
565	C₂×C₄₇	C₂×#577	1	1	yes	characteristic
566	C₂×C₄₇	#3584	1	1	yes	characteristic
567	D₄₇	—	4	2	no	—
568	D₄₇	—	4	2	no	—
569	#563	—	2	2	no	—
570	Q₈²	C₂×D₄₇	1	1	yes	characteristic, complemented
571	#557	C₂×D₄₇	1	1	yes	characteristic, complemented
572	#557	C₂×D₄₇	1	2	yes	complemented
573	#556	—	2	1	no	—
574	#556	C₂×D₄₇	1	1	yes	characteristic, complemented
575	#556	C₂×D₄₇	1	2	yes	complemented
576	#554	—	47	1	no	—
577	#554	—	47	2	no	—
578	#554	—	47	1	no	—
579	#554	—	47	2	no	—
580	#554	—	94	1	no	—
581	#554	—	94	2	no	—
582	#554	C₂×D₄₇	1	1	yes	characteristic, complemented
583	#552	—	2	1	no	—
584	D₄×Q₈	—	47	1	no	—
585	D₄×Q₈	—	47	1	no	—
586	D₄×Q₈	—	94	1	no	—
587	#544	—	2	1	no	—
588	#544	—	47	2	no	—
589	#543	—	94	2	no	—
590	#542	C₂×D₄₇	1	2	yes	—
591	#541	—	2	1	no	—
592	#541	—	2	2	no	—
593	#541	C₂×D₄₇	1	2	yes	—
594	#533	—	47	1	no	—
595	#533	C₂×D₄₇	1	1	yes	characteristic
596	#533	C₂×D₄₇	1	1	yes	characteristic
597	#529	C₂×D₄₇	1	1	yes	characteristic
598	C₂×C₂²⋊Q₈	—	94	1	no	—
599	C₂×C₂²⋊Q₈	—	94	1	no	—
600	#518	—	47	2	no	—
601	C₂×C₄×D₄	—	47	1	no	—
602	#501	—	47	2	no	—
603	#501	—	47	2	no	—
604	#500	—	47	1	no	—
605	#499	—	47	2	no	—
606	#499	—	47	2	no	—
607	#498	—	47	2	no	—
608	#498	—	47	1	no	—
609	#491	—	47	2	no	—
610	#489	—	47	2	no	—
611	#488	—	47	2	no	—
612	#488	—	47	2	no	—
613	#487	—	47	2	no	—
614	#487	—	47	1	no	—
615	#487	—	47	1	no	—
616	#485	—	47	2	no	—
617	#485	—	47	2	no	—
618	#485	—	47	2	no	—
619	#484	—	47	1	no	—
620	#483	—	47	2	no	—
621	#482	—	47	2	no	—
622	#481	—	47	1	no	—
623	#479	—	47	2	no	—
624	#479	—	47	2	no	—
625	#479	—	47	2	no	—
626	#479	—	47	2	no	—
627	#479	—	47	2	no	—
628	#478	—	47	1	no	—
629	#478	—	47	1	no	—
630	#478	—	47	2	no	—
631	#478	—	47	2	no	—
632	#478	—	47	2	no	—
633	#477	—	47	2	no	—
634	#477	—	47	1	no	—
635	#476	—	47	1	no	—
636	#476	—	47	1	no	—
637	#476	—	47	2	no	—
638	#476	—	47	1	no	—
639	#476	—	47	2	no	—
640	#475	—	47	1	no	—
641	#475	—	47	2	no	—
642	#475	—	47	2	no	—
643	#474	—	47	2	no	—
644	#474	—	47	1	no	—
645	#463	—	47	1	no	—
646	#463	—	47	2	no	—
647	#463	—	47	2	no	—
648	#463	—	47	1	no	—
649	#461	—	47	1	no	—
650	#461	—	47	1	no	—
651	#461	—	47	2	no	—
652	#461	—	47	2	no	—
653	#450	—	47	2	no	—
654	#450	—	47	1	no	—
655	#447	—	47	1	no	—
656	#446	—	47	1	no	—
657	#446	—	47	1	no	—
658	#446	—	47	2	no	—
659	C₈×Q₈	—	47	1	no	—
660	C₈×Q₈	—	47	1	no	—
661	C₈×Q₈	—	47	2	no	—
662	#442	—	47	2	no	—
663	#440	—	47	2	no	—
664	#440	—	47	2	no	—
665	#440	—	47	2	no	—
666	C₄×SD₁₆	—	47	2	no	—
667	C₄×SD₁₆	—	47	2	no	—
668	C₄×SD₁₆	—	47	1	no	—
669	C₄×SD₁₆	—	47	2	no	—
670	C₄×SD₁₆	—	47	2	no	—
671	C₄×SD₁₆	—	47	2	no	—
672	C₄×SD₁₆	—	47	1	no	—
673	C₄×D₈	—	47	1	no	—
674	C₄×D₈	—	47	2	no	—
675	C₄×D₈	—	47	1	no	—
676	#433	—	47	2	no	—
677	#433	—	47	2	no	—
678	#431	—	47	1	no	—
679	#431	—	47	1	no	—
680	C₄₇	#61864	1	1	yes	characteristic, complemented, Sylow
681	C₂²×Q₈	—	94	1	no	—
682	C₂²×Q₈	—	94	1	no	—
683	C₂²×D₄	—	47	1	no	—
684	C₂³×C₄	—	94	1	no	—
685	C₂×SD₁₆	—	47	2	no	—
686	C₂×SD₁₆	—	47	1	no	—
687	C₂×SD₁₆	—	47	2	no	—
688	C₂×SD₁₆	—	47	1	no	—
689	C₂×D₈	—	47	1	no	—
690	C₂×D₈	—	47	1	no	—
691	C₄⋊Q₈	—	2	2	no	—
692	C₄⋊Q₈	—	2	2	no	—
693	C₄⋊Q₈	—	2	1	no	—
694	C₄⋊Q₈	—	47	1	no	—
695	C₄⋊Q₈	—	47	1	no	—
696	C₄⋊Q₈	—	47	2	no	—
697	C₄⋊Q₈	—	47	2	no	—
698	C₄⋊Q₈	—	94	2	no	—
699	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
700	C₄⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
701	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
702	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
703	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
704	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
705	#126	—	2	2	no	—
706	#126	—	2	2	no	—
707	#126	—	2	2	no	—
708	#126	—	2	2	no	—
709	#126	—	2	2	no	—
710	#126	—	2	2	no	—
711	#126	—	2	1	no	—
712	#125	—	2	2	no	—
713	#125	—	2	2	no	—
714	#125	—	2	2	no	—
715	#125	—	2	2	no	—
716	#125	—	2	2	no	—
717	#125	—	2	1	no	—
718	#125	—	2	1	no	—
719	#125	—	47	2	no	—
720	#125	—	47	2	no	—
721	#125	—	47	2	no	—
722	#125	—	94	2	no	—
723	#125	C₂²⋊D₄₇	1	2	yes	—
724	#125	C₂²×D₄₇	1	1	yes	characteristic
725	#125	C₂²×D₄₇	1	2	yes	—
726	#124	—	2	2	no	—
727	#124	C₂²×D₄₇	1	1	yes	characteristic
728	#124	C₂²×D₄₇	1	2	yes	—
729	#123	—	2	1	no	—
730	#123	—	2	2	no	—
731	C₂²⋊Q₈	—	2	1	no	—
732	C₂²⋊Q₈	—	2	1	no	—
733	C₂²⋊Q₈	—	2	2	no	—
734	C₂²⋊Q₈	—	2	1	no	—
735	C₂²⋊Q₈	—	2	2	no	—
736	C₂²⋊Q₈	—	2	2	no	—
737	C₂²⋊Q₈	—	94	1	no	—
738	C₂²⋊Q₈	—	94	1	no	—
739	C₂²⋊Q₈	—	94	2	no	—
740	C₂²⋊Q₈	—	94	2	no	—
741	C₂²⋊Q₈	—	94	1	no	—
742	C₂²⋊Q₈	—	94	1	no	—
743	C₂²⋊Q₈	—	94	1	no	—
744	C₂²⋊Q₈	—	94	1	no	—
745	C₂²⋊Q₈	—	94	2	no	—
746	C₂²⋊Q₈	—	94	2	no	—
747	C₂²⋊Q₈	—	94	2	no	—
748	C₂²⋊Q₈	—	94	2	no	—
749	C₂²⋊Q₈	—	94	2	no	—
750	C₂²⋊Q₈	—	94	2	no	—
751	C₂²⋊Q₈	—	94	2	no	—
752	C₂²⋊Q₈	—	94	2	no	—
753	C₂²⋊Q₈	—	94	2	no	—
754	C₂²⋊Q₈	—	94	2	no	—
755	C₂²⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
756	C₂²⋊Q₈	C₂²⋊D₄₇	1	1	yes	characteristic
757	C₂²⋊Q₈	C₂²⋊D₄₇	1	2	yes	—
758	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
759	C₂²⋊Q₈	C₂²×D₄₇	1	2	yes	—
760	#121	C₂²×D₄₇	1	1	yes	characteristic
761	C₄×Q₈	—	2	1	no	—
762	C₄×Q₈	—	2	1	no	—
763	C₄×Q₈	—	2	2	no	—
764	C₄×Q₈	—	2	1	no	—
765	C₄×Q₈	—	94	1	no	—
766	C₄×Q₈	—	94	1	no	—
767	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
768	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
769	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
770	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
771	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
772	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
773	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
774	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
775	C₄×D₄	—	2	1	no	—
776	C₄×D₄	—	47	1	no	—
777	C₄×D₄	—	47	1	no	—
778	C₄×D₄	—	47	1	no	—
779	C₄×D₄	—	47	1	no	—
780	C₄×D₄	—	47	2	no	—
781	C₄×D₄	—	47	2	no	—
782	C₄×D₄	—	47	2	no	—
783	C₄×D₄	—	47	2	no	—
784	C₄×D₄	—	94	2	no	—
785	C₄×D₄	—	94	2	no	—
786	C₄×D₄	—	94	1	no	—
787	C₄×D₄	—	94	1	no	—
788	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
789	C₄×D₄	C₂²×D₄₇	1	2	yes	—
790	#117	—	2	1	no	—
791	#117	—	2	2	no	—
792	#117	—	2	1	no	—
793	#117	—	2	1	no	—
794	#117	—	47	2	no	—
795	#117	C₂²×D₄₇	1	2	yes	—
796	C₂×C₄⋊C₄	—	2	1	no	—
797	C₂×C₄⋊C₄	—	47	1	no	—
798	C₂×C₄⋊C₄	—	94	2	no	—
799	C₂×C₄⋊C₄	—	94	2	no	—
800	C₂×C₄⋊C₄	—	94	1	no	—
801	C₂×C₄⋊C₄	—	94	1	no	—
802	C₂×C₂²⋊C₄	—	94	1	no	—
803	C₂×C₂²⋊C₄	—	94	2	no	—
804	C₂×C₂²⋊C₄	—	94	2	no	—
805	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
806	#107	—	47	2	no	—
807	#107	—	47	1	no	—
808	#107	—	47	1	no	—
809	#107	—	47	2	no	—
810	#107	—	47	2	no	—
811	#107	—	47	2	no	—
812	#106	—	47	2	no	—
813	#106	—	47	1	no	—
814	#106	—	47	2	no	—
815	#106	—	47	2	no	—
816	#106	—	47	2	no	—
817	#106	—	47	2	no	—
818	#106	—	47	1	no	—
819	#106	—	47	2	no	—
820	C₄⋊C₈	—	47	1	no	—
821	C₄⋊C₈	—	47	1	no	—
822	C₄⋊C₈	—	47	1	no	—
823	C₄⋊C₈	—	47	1	no	—
824	C₄⋊C₈	—	47	2	no	—
825	C₄⋊C₈	—	47	2	no	—
826	C₄⋊C₈	—	47	2	no	—
827	C₄⋊C₈	—	47	2	no	—
828	#103	—	47	2	no	—
829	#103	—	47	2	no	—
830	#103	—	47	2	no	—
831	#103	—	47	2	no	—
832	#103	—	47	1	no	—
833	#103	—	47	2	no	—
834	#103	—	47	1	no	—
835	#103	—	47	2	no	—
836	#103	—	47	2	no	—
837	#103	—	47	2	no	—
838	#102	—	47	1	no	—
839	#102	—	47	2	no	—
840	#102	—	47	1	no	—
841	#102	—	47	2	no	—
842	#102	—	47	2	no	—
843	#102	—	47	1	no	—
844	#102	—	47	1	no	—
845	#102	—	47	1	no	—
846	#102	—	47	1	no	—
847	#102	—	47	2	no	—
848	C₂²⋊C₈	—	47	1	no	—
849	C₂²⋊C₈	—	47	1	no	—
850	C₂²⋊C₈	—	47	2	no	—
851	#97	—	47	2	no	—
852	#97	—	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	C₄×C₈	—	47	2	no	—
858	C₂⁴	—	94	1	no	—
859	C₂×Q₈	—	2	1	no	—
860	C₂×Q₈	—	2	2	no	—
861	C₂×Q₈	—	94	1	no	—
862	C₂×Q₈	—	94	2	no	—
863	C₂×Q₈	—	94	2	no	—
864	C₂×Q₈	—	94	1	no	—
865	C₂×Q₈	—	376	2	no	—
866	C₂×Q₈	—	376	2	no	—
867	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
868	C₂×Q₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
869	C₂×Q₈	C₂×C₂²⋊D₄₇	1	2	yes	—
870	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
871	C₂×Q₈	C₂³×D₄₇	1	2	yes	—
872	C₂×D₄	—	2	1	no	—
873	C₂×D₄	—	47	1	no	—
874	C₂×D₄	—	47	1	no	—
875	C₂×D₄	—	94	2	no	—
876	C₂×D₄	—	94	2	no	—
877	C₂×D₄	—	94	1	no	—
878	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
879	C₂²×C₄	—	2	1	no	—
880	C₂²×C₄	—	2	2	no	—
881	C₂²×C₄	—	94	1	no	—
882	C₂²×C₄	—	94	2	no	—
883	C₂²×C₄	—	94	2	no	—
884	C₂²×C₄	—	94	2	no	—
885	C₂²×C₄	—	94	2	no	—
886	C₂²×C₄	—	94	1	no	—
887	C₂²×C₄	—	94	1	no	—
888	C₂²×C₄	—	94	1	no	—
889	C₂²×C₄	—	94	1	no	—
890	C₂²×C₄	—	376	2	no	—
891	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
892	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
893	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
894	SD₁₆	—	94	4	no	—
895	SD₁₆	—	94	2	no	—
896	SD₁₆	—	94	4	no	—
897	SD₁₆	—	94	2	no	—
898	D₈	—	94	2	no	—
899	D₈	—	94	2	no	—
900	C₂×C₈	—	47	1	no	—
901	C₂×C₈	—	47	2	no	—
902	C₂×C₈	—	47	1	no	—
903	C₂×C₈	—	47	1	no	—
904	C₂×C₈	—	47	2	no	—
905	C₂×C₈	—	47	1	no	—
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	2	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	2	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	2	1	no	—
912	C₄⋊C₄	—	2	1	no	—
913	C₄⋊C₄	—	2	2	no	—
914	C₄⋊C₄	—	2	2	no	—
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	2	no	—
917	C₄⋊C₄	—	2	2	no	—
918	C₄⋊C₄	—	2	2	no	—
919	C₄⋊C₄	—	2	2	no	—
920	C₄⋊C₄	—	2	2	no	—
921	C₄⋊C₄	—	2	2	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	47	1	no	—
924	C₄⋊C₄	—	47	1	no	—
925	C₄⋊C₄	—	47	2	no	—
926	C₄⋊C₄	—	47	2	no	—
927	C₄⋊C₄	—	94	2	no	—
928	C₄⋊C₄	—	94	2	no	—
929	C₄⋊C₄	—	94	2	no	—
930	C₄⋊C₄	—	94	2	no	—
931	C₄⋊C₄	—	94	2	no	—
932	C₄⋊C₄	—	94	2	no	—
933	C₄⋊C₄	—	94	1	no	—
934	C₄⋊C₄	—	94	1	no	—
935	C₄⋊C₄	—	94	2	no	—
936	C₄⋊C₄	—	94	2	no	—
937	C₄⋊C₄	—	94	1	no	—
938	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
939	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
940	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
941	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
942	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
943	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
944	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
945	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
946	C₄⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
947	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
948	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
949	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
950	C₂²⋊C₄	—	2	2	no	—
951	C₂²⋊C₄	—	2	1	no	—
952	C₂²⋊C₄	—	2	1	no	—
953	C₂²⋊C₄	—	2	1	no	—
954	C₂²⋊C₄	—	2	1	no	—
955	C₂²⋊C₄	—	2	2	no	—
956	C₂²⋊C₄	—	2	2	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	2	no	—
959	C₂²⋊C₄	—	94	2	no	—
960	C₂²⋊C₄	—	94	2	no	—
961	C₂²⋊C₄	—	94	2	no	—
962	C₂²⋊C₄	—	94	2	no	—
963	C₂²⋊C₄	—	94	2	no	—
964	C₂²⋊C₄	—	94	1	no	—
965	C₂²⋊C₄	—	94	1	no	—
966	C₂²⋊C₄	—	94	1	no	—
967	C₂²⋊C₄	—	94	1	no	—
968	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
969	C₂²⋊C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
970	C₄²	—	2	2	no	—
971	C₄²	—	2	1	no	—
972	C₄²	—	2	2	no	—
973	C₄²	—	2	2	no	—
974	C₄²	—	2	2	no	—
975	C₄²	—	94	2	no	—
976	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
977	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
978	C₄²	C₂³×D₄₇	1	1	yes	characteristic
979	C₄²	C₂³×D₄₇	1	1	yes	characteristic
980	C₄²	C₂³×D₄₇	1	2	yes	—
981	C₄²	C₂³×D₄₇	1	2	yes	—
982	C₂³	—	2	1	no	—
983	C₂³	—	94	4	no	—
984	C₂³	—	94	1	no	—
985	C₂³	—	94	1	no	—
986	C₂³	—	376	1	no	—
987	C₂³	—	376	1	no	—
988	C₂³	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
989	Q₈	—	2	2	no	—
990	Q₈	—	2	2	no	—
991	Q₈	—	2	1	no	—
992	Q₈	—	2	2	no	—
993	Q₈	—	2	1	no	—
994	Q₈	—	2	2	no	—
995	Q₈	—	4	2	no	—
996	Q₈	—	8	1	no	—
997	Q₈	—	8	2	no	—
998	Q₈	—	376	1	no	—
999	Q₈	—	376	2	no	—
1000	Q₈	—	376	2	no	—
1001	Q₈	—	188	2	no	—
1002	D₄	—	2	1	no	—
1003	D₄	—	2	1	no	—
1004	D₄	—	8	1	no	—
1005	D₄	—	47	2	no	—
1006	D₄	—	47	2	no	—
1007	D₄	—	94	4	no	—
1008	D₄	—	94	1	no	—
1009	D₄	—	94	1	no	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	2	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	2	no	—
1018	C₂×C₄	—	4	1	no	—
1019	C₂×C₄	—	4	2	no	—
1020	C₂×C₄	—	8	2	no	—
1021	C₂×C₄	—	94	2	no	—
1022	C₂×C₄	—	94	2	no	—
1023	C₂×C₄	—	94	1	no	—
1024	C₂×C₄	—	94	1	no	—
1025	C₂×C₄	—	376	2	no	—
1026	C₂×C₄	—	376	2	no	—
1027	C₂×C₄	—	376	1	no	—
1028	C₂×C₄	—	376	1	no	—
1029	C₂×C₄	—	376	2	no	—
1030	C₂×C₄	—	376	2	no	—
1031	C₂×C₄	—	376	1	no	—
1032	C₂×C₄	—	188	2	no	—
1033	C₂×C₄	—	188	2	no	—
1034	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1035	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1036	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1037	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1038	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1039	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1040	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1041	C₂×C₄	C₂²×C₂²⋊D₄₇	1	2	yes	—
1042	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
1043	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1044	C₈	—	94	1	no	—
1045	C₈	—	94	1	no	—
1046	C₈	—	94	1	no	—
1047	C₈	—	94	2	no	—
1048	C₈	—	94	1	no	—
1049	C₈	—	94	2	no	—
1050	C₂²	—	2	1	no	—
1051	C₂²	—	2	1	no	—
1052	C₂²	—	2	1	no	—
1053	C₂²	—	4	1	no	—
1054	C₂²	—	4	1	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	—	94	2	no	—
1057	C₂²	—	94	2	no	—
1058	C₂²	—	376	4	no	—
1059	C₂²	—	188	1	no	—
1060	C₂²	—	188	1	no	—
1061	C₂²	—	188	1	no	—
1062	C₂²	—	188	1	no	—
1063	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
1064	C₄	—	2	1	no	—
1065	C₄	—	2	1	no	—
1066	C₄	—	2	2	no	—
1067	C₄	—	2	2	no	—
1068	C₄	—	2	1	no	—
1069	C₄	—	2	1	no	—
1070	C₄	—	2	2	no	—
1071	C₄	—	2	2	no	—
1072	C₄	—	4	2	no	—
1073	C₄	—	4	1	no	—
1074	C₄	—	4	1	no	—
1075	C₄	—	4	2	no	—
1076	C₄	—	4	1	no	—
1077	C₄	—	188	1	no	—
1078	C₄	—	188	1	no	—
1079	C₄	—	188	2	no	—
1080	C₄	—	188	2	no	—
1081	C₄	#15689931	1	2	yes	—
1082	C₄	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic
1083	C₄	2₋¹⁺⁴×D₄₇	1	1	yes	characteristic
1084	C₂	—	4	1	no	—
1085	C₂	—	8	1	no	—
1086	C₂	—	188	2	no	—
1087	C₂	—	188	2	no	—
1088	C₂	#20257036	1	1	yes	characteristic
1089	C₂	C₂×#15689931	1	1	yes	characteristic
1090	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×#3555	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#15689256	C₂²
hypercenter	#3555	D₄₇
hypocenter	C₄₇	#61864
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #533 ◁ #3555

Complements

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

N	H ≅ G/N	type
1. #20257189	C₂	semidirect
2. #20256327	C₂	semidirect
3. #20256294	C₂	semidirect
4. #20256287	C₂	semidirect
5. #20256259	C₂	semidirect
6. #20256251	C₂	semidirect
7. Q₈×#10625336	C₂	semidirect
8. #20256209	C₂	semidirect
9. #20256165	C₂	semidirect
10. #20256102	C₂	semidirect
11. #20256033	C₂	semidirect
12. #20256033	C₂	semidirect
13. #20256026	C₂	semidirect
14. #20254680	C₂	semidirect
15. #20254650	C₂	semidirect
16. #20254563	C₂	semidirect
17. #20254543	C₂	semidirect
18. #20253635	C₂	semidirect
21. #20253392	C₂	semidirect
22. #20252490	C₂	semidirect
23. C₄₇×#3555	C₂	semidirect
40. #15689533	C₂²	semidirect
41. #15689529	C₂²	semidirect
42. #15689526	C₂²	semidirect
43. #15689522	C₂²	semidirect
44. #15689522	C₂²	semidirect
45. #15689519	C₂²	semidirect
46. #15689519	C₂²	semidirect
47. #15689491	C₂²	semidirect
48. #15689482	C₂²	semidirect
49. #15689477	C₂²	semidirect
50. #15689477	C₂²	semidirect
51. #15689473	C₂²	semidirect
52. #15689473	C₂²	semidirect
53. #15689473	C₂²	semidirect
61. #15689430	C₂²	semidirect
62. #15689430	C₂²	semidirect
63. #15689430	C₂²	semidirect
64. #15689430	C₂²	semidirect
65. #15689430	C₂²	semidirect
66. #15689423	C₂²	semidirect
71. #15689418	C₂²	semidirect
72. #15689418	C₂²	semidirect
73. #15689413	C₂²	semidirect
74. #15689413	C₂²	semidirect
78. #15689408	C₂²	semidirect
79. #15689408	C₂²	semidirect
80. #15689408	C₂²	semidirect
81. #15689403	C₂²	semidirect
94. #15689254	C₂²	semidirect
95. #15689254	C₂²	semidirect
96. #15689254	C₂²	semidirect
97. Q₈×C₄₇⋊C₈	C₂²	semidirect
98. Q₈×C₄₇⋊C₈	C₂²	semidirect
99. Q₈×C₄₇⋊C₈	C₂²	semidirect
119. Q₈²×C₄₇	C₂²	semidirect
120. C₄₇×#557	C₂²	semidirect
121. C₄₇×#557	C₂²	semidirect
123. C₄₇×#556	C₂²	semidirect
124. C₄₇×#556	C₂²	semidirect
125. C₄₇×#554	C₂²	semidirect
539. #3555	D₄₇	semidirect
570. Q₈²	C₂×D₄₇	semidirect
571. #557	C₂×D₄₇	semidirect
572. #557	C₂×D₄₇	semidirect
574. #556	C₂×D₄₇	semidirect
575. #556	C₂×D₄₇	semidirect
582. #554	C₂×D₄₇	semidirect
680. C₄₇	#61864	semidirect

Maximal subgroups

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

subgroup	index
#20257189	2
#20256327	2
#20256294	2
#20256287	2
#20256259	2
#20256251	2
Q₈×#10625336	2
#20256209	2
#20256165	2
#20256102	2
#20256033	2
#20256026	2
#20254680	2
#20254650	2
#20254563	2
#20254543	2
#20253635	2
#20253566	2
#20253431	2
#20253392	2
#20252490	2
C₄₇×#3555	2
#61864	47