Subgroups — #27106984

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	#20257878	C₂	1	1	yes	maximal, characteristic, complemented
2	#20257191	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256337	C₂	1	2	yes	maximal, complemented
4	#20256296	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256285	C₂	1	1	yes	maximal, characteristic, complemented
6	#20256258	C₂	1	2	yes	maximal, complemented
7	#20256253	C₂	1	1	yes	maximal, characteristic, complemented
8	SD₁₆×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
9	#20256219	C₂	1	2	yes	maximal, complemented
10	#20256167	C₂	1	1	yes	maximal, characteristic, complemented
11	#20256104	C₂	1	1	yes	maximal, characteristic, complemented
12	#20256035	C₂	1	1	yes	maximal, characteristic, complemented
13	#20256032	C₂	1	2	yes	maximal, complemented
14	#20256028	C₂	1	1	yes	maximal, characteristic, complemented
15	#20254682	C₂	1	2	yes	maximal, complemented
16	#20254660	C₂	1	2	yes	maximal, complemented
17	#20254563	C₂	1	1	yes	maximal, characteristic, complemented
18	#20254549	C₂	1	1	yes	maximal, characteristic, complemented
19	#20253634	C₂	1	2	yes	maximal, complemented
20	#20253565	C₂	1	2	yes	maximal
21	#20253396	C₂	1	1	yes	maximal, characteristic, complemented
22	#20252489	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3105	C₂	1	1	yes	maximal, characteristic
24	#15689876	—	2	2	no	—
25	Q₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
26	#15689851	C₂²	1	1	yes	characteristic, complemented
27	#15689850	C₂²	1	2	yes	complemented
28	#15689843	—	2	1	no	—
29	#15689843	C₂²	1	1	yes	characteristic, complemented
30	#15689842	C₂²	1	2	yes	complemented
31	#15689832	—	2	2	no	—
32	#15689832	C₂²	1	2	yes	—
33	#15689832	C₂²	1	2	yes	—
34	#15689830	—	2	1	no	—
35	#15689830	C₂²	1	1	yes	characteristic
36	#15689830	C₂²	1	1	yes	characteristic
37	#15689830	C₂²	1	1	yes	characteristic, complemented
38	#15689813	—	2	1	no	—
39	D₄×Dic₉₄	—	2	1	no	—
40	D₄×Dic₉₄	C₂²	1	1	yes	characteristic
41	D₄×Dic₉₄	C₂²	1	1	yes	characteristic
42	#15689754	C₂²	1	2	yes	—
43	#15689751	—	2	1	no	—
44	#15689749	—	2	2	no	—
45	#15689740	C₂²	1	2	yes	—
46	#15689735	—	2	1	no	—
47	#15689733	C₂²	1	2	yes	—
48	#15689730	—	2	2	no	—
49	#15689680	C₂²	1	1	yes	characteristic
50	#15689680	C₂²	1	1	yes	characteristic
51	#15689680	C₂²	1	1	yes	characteristic
52	C₂×#13094003	—	2	1	no	—
53	C₂×#13094003	—	2	1	no	—
54	#15689598	C₂²	1	2	yes	—
55	#15689531	C₂²	1	2	yes	complemented
56	#15689530	C₂²	1	2	yes	complemented
57	#15689528	C₂²	1	1	yes	characteristic, complemented
58	#15689524	C₂²	1	2	yes	complemented
59	#15689522	C₂²	1	2	yes	complemented
60	#15689521	C₂²	1	1	yes	characteristic, complemented
61	#15689520	C₂²	1	2	yes	complemented
62	#15689490	C₂²	1	2	yes	complemented
63	#15689481	C₂²	1	2	yes	complemented
64	#15689477	C₂²	1	2	yes	complemented
65	#15689476	C₂²	1	2	yes	complemented
66	#15689474	C₂²	1	1	yes	characteristic, complemented
67	#15689474	C₂²	1	1	yes	characteristic, complemented
68	#15689472	C₂²	1	2	yes	complemented
69	#15689465	C₂²	1	2	yes	—
70	#15689465	C₂²	1	2	yes	—
71	#15689461	C₂²	1	2	yes	—
72	#15689453	C₂²	1	2	yes	—
73	#15689444	C₂²	1	2	yes	—
74	#15689433	C₂²	1	2	yes	complemented
75	#15689432	C₂²	1	2	yes	complemented
76	#15689431	C₂²	1	2	yes	complemented
77	#15689431	C₂²	1	2	yes	complemented
78	#15689429	C₂²	1	2	yes	complemented
79	#15689425	C₂²	1	2	yes	—
80	#15689421	C₂²	1	2	yes	—
81	#15689421	C₂²	1	2	yes	complemented
82	#15689418	C₂²	1	1	yes	characteristic, complemented
83	#15689417	C₂²	1	2	yes	complemented
84	#15689413	C₂²	1	1	yes	characteristic
85	#15689413	C₂²	1	1	yes	characteristic
86	#15689413	C₂²	1	1	yes	characteristic, complemented
87	#15689411	C₂²	1	2	yes	—
88	#15689411	C₂²	1	2	yes	complemented
89	#15689408	C₂²	1	1	yes	characteristic, complemented
90	#15689407	C₂²	1	2	yes	complemented
91	#15689406	C₂²	1	2	yes	complemented
92	#15689403	C₂²	1	1	yes	characteristic, complemented
93	#15689401	C₂²	1	2	yes	—
94	#15689336	C₂²	1	2	yes	—
95	#15689336	C₂²	1	2	yes	—
96	#15689328	C₂²	1	1	yes	characteristic
97	#15689328	C₂²	1	1	yes	characteristic
98	#15689326	C₂²	1	2	yes	—
99	#15689326	C₂²	1	2	yes	—
100	#15689274	C₂²	1	2	yes	—
101	#15689253	C₂²	1	1	yes	characteristic, complemented
102	#15689253	C₂²	1	1	yes	characteristic, complemented
103	#15689250	C₂²	1	2	yes	complemented
104	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
105	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
106	#15689247	C₂²	1	2	yes	complemented
107	#15689235	C₂²	1	2	yes	—
108	#15689224	C₂²	1	2	yes	—
109	#15689220	C₂²	1	2	yes	—
110	#15689220	C₂²	1	2	yes	—
111	#15689214	C₂²	1	2	yes	—
112	#15689214	C₂²	1	2	yes	—
113	SD₁₆×Dic₄₇	C₂²	1	2	yes	—
114	C₄×#10625335	C₂²	1	2	yes	—
115	C₄×#10625335	C₂²	1	2	yes	—
116	D₈×Dic₄₇	C₂²	1	2	yes	—
117	#15689181	C₂²	1	2	yes	—
118	#15689181	C₂²	1	2	yes	—
119	#15689176	C₂²	1	1	yes	characteristic
120	C₄₇×#529	C₂²	1	1	yes	characteristic
121	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
122	C₄₇×#484	C₂²	1	1	yes	characteristic
123	C₄₇×#481	C₂²	1	1	yes	characteristic
124	C₄₇×#478	C₂²	1	1	yes	characteristic
125	C₄₇×#478	C₂²	1	1	yes	characteristic
126	C₄₇×#463	C₂²	1	1	yes	characteristic
127	C₄₇×#463	C₂²	1	1	yes	characteristic
128	C₄₇×#450	C₂²	1	1	yes	characteristic
129	C₄₇×#447	C₂²	1	1	yes	characteristic
130	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
131	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
132	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
133	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
134	C₄₇×#431	C₂²	1	1	yes	characteristic
135	C₂²×Dic₉₄	—	2	1	no	—
136	C₂²×Dic₉₄	—	2	1	no	—
137	C₂×#10625335	C₂³	1	2	yes	—
138	C₂×#10625335	C₂³	1	2	yes	—
139	#13094024	—	2	1	no	—
140	#13094024	D₄	1	1	yes	characteristic
141	#13094024	D₄	1	1	yes	characteristic
142	#13094024	C₂³	1	1	yes	characteristic
143	#13094024	C₂³	1	1	yes	characteristic
144	#13094024	C₂³	1	1	yes	characteristic
145	#13094024	C₂³	1	1	yes	characteristic
146	#13094023	—	2	2	no	—
147	#13094023	—	2	2	no	—
148	#13094023	—	2	2	no	—
149	#13094023	C₂³	1	2	yes	—
150	#13094023	C₂³	1	2	yes	—
151	#13094023	C₂³	1	2	yes	—
152	#13094022	C₂³	1	2	yes	—
153	#13094017	—	2	2	no	—
154	#13094017	—	2	2	no	—
155	#13094017	—	2	2	no	—
156	#13094017	—	2	2	no	—
157	#13094017	—	2	2	no	—
158	#13094017	—	2	2	no	—
159	#13094016	—	2	1	no	—
160	#13094016	—	2	1	no	—
161	#13094016	D₄	1	2	yes	—
162	#13094016	C₂³	1	2	yes	—
163	#13094015	—	2	2	no	—
164	#13094015	—	2	2	no	—
165	#13094015	C₂³	1	2	yes	—
166	#13094015	C₂³	1	2	yes	—
167	#13094015	C₂³	1	2	yes	—
168	#13094014	—	2	2	no	—
169	#13094014	—	2	2	no	—
170	#13094014	—	2	2	no	—
171	#13094014	—	2	2	no	—
172	#13094011	—	2	2	no	—
173	#13094011	C₂³	1	2	yes	—
174	#13094005	—	2	2	no	—
175	#13094003	—	2	1	no	—
176	#13094003	—	2	1	no	—
177	#13094003	—	2	1	no	—
178	#13094003	—	2	1	no	—
179	#13094003	—	2	1	no	—
180	#13094003	—	2	1	no	—
181	#13094003	—	2	1	no	—
182	#13094003	—	2	2	no	—
183	#13094003	—	2	2	no	—
184	#13094003	—	2	1	no	—
185	#13094003	—	2	1	no	—
186	#13094003	—	2	2	no	—
187	#13094003	—	2	2	no	—
188	#13094003	D₄	1	2	yes	—
189	#13094003	D₄	1	1	yes	characteristic
190	#13094003	D₄	1	1	yes	characteristic
191	#13094003	C₂³	1	2	yes	—
192	#13094001	—	2	2	no	—
193	#13094001	—	2	2	no	—
194	#13094001	—	2	2	no	—
195	#13094001	—	2	2	no	—
196	#13094001	—	2	2	no	—
197	#13094001	—	2	2	no	—
198	#13094001	—	2	2	no	—
199	#13094001	—	2	2	no	—
200	#13094001	—	2	2	no	—
201	#13094001	—	2	2	no	—
202	#13094001	—	2	2	no	—
203	Q₈×Dic₄₇	C₂³	1	2	yes	—
204	C₄×Dic₉₄	—	2	1	no	—
205	C₄×Dic₉₄	—	2	1	no	—
206	C₄×Dic₉₄	—	2	1	no	—
207	C₄×Dic₉₄	—	2	1	no	—
208	C₄×Dic₉₄	—	2	1	no	—
209	C₄×Dic₉₄	C₂³	1	2	yes	—
210	C₄×Dic₉₄	C₂³	1	2	yes	—
211	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
212	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
213	#13093989	—	2	2	no	—
214	#13093989	C₂³	1	2	yes	—
215	#13093989	C₂³	1	2	yes	—
216	D₄×Dic₄₇	—	2	2	no	—
217	D₄×Dic₄₇	—	2	2	no	—
218	D₄×Dic₄₇	C₂³	1	2	yes	—
219	D₄×Dic₄₇	C₂³	1	2	yes	—
220	D₄×Dic₄₇	C₂³	1	2	yes	—
221	D₄×Dic₄₇	C₂³	1	2	yes	—
222	D₄×Dic₄₇	C₂³	1	2	yes	—
223	#13093983	—	2	1	no	—
224	#13093983	—	2	1	no	—
225	#13093983	C₂³	1	2	yes	—
226	#13093983	C₂³	1	2	yes	—
227	#13093980	—	2	2	no	—
228	C₂×C₄⋊Dic₄₇	—	2	1	no	—
229	C₂×C₄⋊Dic₄₇	—	2	1	no	—
230	C₂×C₄⋊Dic₄₇	—	2	1	no	—
231	C₂×Dic₄₇⋊C₄	—	2	2	no	—
232	C₂×Dic₄₇⋊C₄	—	2	2	no	—
233	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
234	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
235	#13093958	C₂³	1	2	yes	—
236	#13093958	C₂³	1	2	yes	—
237	#13093957	C₂³	1	2	yes	—
238	#13093957	C₂³	1	2	yes	—
239	#13093956	C₂³	1	2	yes	—
240	#13093956	C₂³	1	2	yes	—
241	#13093955	C₂³	1	2	yes	—
242	#13093955	C₂³	1	2	yes	—
243	#13093955	C₂³	1	2	yes	—
244	#13093955	C₂³	1	2	yes	—
245	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
246	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
247	Dic₄₇⋊C₈	C₂³	1	2	yes	—
248	Dic₄₇⋊C₈	C₂³	1	2	yes	—
249	Dic₄₇⋊C₈	C₂³	1	2	yes	—
250	Dic₄₇⋊C₈	C₂³	1	2	yes	—
251	#13093949	C₂³	1	2	yes	—
252	#13093949	C₂³	1	2	yes	—
253	#13093949	C₂³	1	2	yes	—
254	#13093949	C₂³	1	2	yes	—
255	#13093948	C₂³	1	2	yes	—
256	#13093948	C₂³	1	2	yes	—
257	#13093947	C₂³	1	2	yes	—
258	#13093947	C₂³	1	2	yes	—
259	#13093945	C₂³	1	2	yes	—
260	#13093945	C₂³	1	2	yes	—
261	#13093945	C₂³	1	2	yes	—
262	#13093945	C₂³	1	2	yes	—
263	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
264	#13093934	C₂³	1	2	yes	—
265	#13093934	C₂³	1	2	yes	—
266	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
267	C₈×Dic₄₇	C₂³	1	2	yes	—
268	C₈×Dic₄₇	C₂³	1	2	yes	—
269	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
270	C₂³×C₄×C₄₇	—	2	1	no	—
271	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
272	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
273	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
274	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
275	#126×C₄₇	—	2	1	no	—
276	#125×C₄₇	C₂³	1	1	yes	characteristic
277	#124×C₄₇	C₂³	1	1	yes	characteristic
278	#123×C₄₇	—	2	1	no	—
279	C₂²⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
280	#121×C₄₇	C₂³	1	1	yes	characteristic
281	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
282	C₄×D₄×C₄₇	—	2	1	no	—
283	C₄×D₄×C₄₇	—	2	1	no	—
284	C₄×D₄×C₄₇	—	2	1	no	—
285	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
286	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
288	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
289	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
290	#117×C₄₇	—	2	1	no	—
291	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
292	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
293	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
294	#107×C₄₇	C₂³	1	1	yes	characteristic
295	#107×C₄₇	C₂³	1	1	yes	characteristic
296	#106×C₄₇	C₂³	1	1	yes	characteristic
297	#106×C₄₇	C₂³	1	1	yes	characteristic
298	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
299	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
300	#103×C₄₇	C₂³	1	1	yes	characteristic
301	#103×C₄₇	C₂³	1	1	yes	characteristic
302	#102×C₄₇	C₂³	1	1	yes	characteristic
303	#102×C₄₇	C₂³	1	1	yes	characteristic
304	#102×C₄₇	C₂³	1	1	yes	characteristic
305	#102×C₄₇	C₂³	1	1	yes	characteristic
306	#102×C₄₇	C₂³	1	1	yes	characteristic
307	#102×C₄₇	C₂³	1	1	yes	characteristic
308	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
309	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
310	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
311	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
312	C₂⁴×C₄₇	—	2	1	no	—
313	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
314	C₂×D₄×C₄₇	—	2	2	no	—
315	C₂×D₄×C₄₇	—	2	2	no	—
316	C₂×D₄×C₄₇	—	2	1	no	—
317	C₂×D₄×C₄₇	—	2	1	no	—
318	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
319	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
320	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
321	C₂²×C₄×C₄₇	—	2	1	no	—
322	C₂²×C₄×C₄₇	—	2	1	no	—
323	C₂²×C₄×C₄₇	—	2	1	no	—
324	C₂²×C₄×C₄₇	—	2	1	no	—
325	C₂²×C₄×C₄₇	—	2	1	no	—
326	C₂²×C₄×C₄₇	—	2	1	no	—
327	C₂²×C₄×C₄₇	—	8	2	no	—
328	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
329	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
331	C₂²×Dic₄₇	—	2	2	no	—
332	C₂²×Dic₄₇	—	2	2	no	—
333	C₂²×Dic₄₇	—	2	2	no	—
334	C₂²×Dic₄₇	—	2	2	no	—
335	C₂²×Dic₄₇	—	2	2	no	—
336	C₂×Dic₉₄	—	2	1	no	—
337	C₂×Dic₉₄	—	2	1	no	—
338	C₂×Dic₉₄	—	2	1	no	—
339	C₂×Dic₉₄	—	2	2	no	—
340	C₂×Dic₉₄	—	2	2	no	—
341	C₂×Dic₉₄	—	2	2	no	—
342	C₂×Dic₉₄	—	8	2	no	—
343	C₂×Dic₉₄	—	8	2	no	—
344	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
345	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
346	C₂×Dic₉₄	C₂×D₄	1	2	yes	—
347	C₂×Dic₉₄	C₂⁴	1	2	yes	—
348	SD₁₆×C₄₇	—	2	2	no	—
349	SD₁₆×C₄₇	—	2	2	no	—
350	D₈×C₄₇	—	2	2	no	—
351	D₈×C₄₇	—	2	2	no	—
352	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
353	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
354	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
355	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
356	C₄⋊C₄×C₄₇	—	2	1	no	—
357	C₄⋊C₄×C₄₇	—	2	1	no	—
358	C₄⋊C₄×C₄₇	—	2	1	no	—
359	C₄⋊C₄×C₄₇	—	2	1	no	—
360	C₄⋊C₄×C₄₇	—	2	1	no	—
361	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
362	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
363	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
364	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
365	C₂²⋊C₄×C₄₇	—	2	1	no	—
366	C₂²⋊C₄×C₄₇	—	2	1	no	—
367	C₂²⋊C₄×C₄₇	—	2	1	no	—
368	C₂²⋊C₄×C₄₇	—	2	1	no	—
369	C₂²⋊C₄×C₄₇	—	2	1	no	—
370	C₂²⋊C₄×C₄₇	—	2	1	no	—
371	C₂²⋊C₄×C₄₇	—	2	1	no	—
372	C₂²⋊C₄×C₄₇	—	2	1	no	—
373	C₂²⋊C₄×C₄₇	—	2	1	no	—
374	C₄²×C₄₇	—	2	1	no	—
375	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
376	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
377	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
378	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
379	C₂²⋊Dic₄₇	—	2	2	no	—
380	C₂²⋊Dic₄₇	—	2	2	no	—
381	C₂²⋊Dic₄₇	—	2	2	no	—
382	C₂²⋊Dic₄₇	—	2	2	no	—
383	C₂²⋊Dic₄₇	—	2	2	no	—
384	C₂²⋊Dic₄₇	—	2	2	no	—
385	C₂²⋊Dic₄₇	—	2	2	no	—
386	C₂²⋊Dic₄₇	—	2	2	no	—
387	C₂²⋊Dic₄₇	—	2	2	no	—
388	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
389	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
390	#10625335	—	2	4	no	—
391	#10625335	—	2	4	no	—
392	C₄⋊Dic₄₇	—	2	1	no	—
393	C₄⋊Dic₄₇	—	2	1	no	—
394	C₄⋊Dic₄₇	—	2	1	no	—
395	C₄⋊Dic₄₇	—	2	1	no	—
396	C₄⋊Dic₄₇	—	2	1	no	—
397	C₄⋊Dic₄₇	—	2	2	no	—
398	C₄⋊Dic₄₇	—	2	2	no	—
399	C₄⋊Dic₄₇	—	2	2	no	—
400	C₄⋊Dic₄₇	—	2	2	no	—
401	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
402	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
403	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
404	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
405	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
406	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
407	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
408	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
409	Dic₄₇⋊C₄	—	2	2	no	—
410	Dic₄₇⋊C₄	—	2	2	no	—
411	Dic₄₇⋊C₄	—	2	2	no	—
412	Dic₄₇⋊C₄	—	2	2	no	—
413	Dic₄₇⋊C₄	—	2	2	no	—
414	Dic₄₇⋊C₄	—	2	2	no	—
415	Dic₄₇⋊C₄	—	2	2	no	—
416	Dic₄₇⋊C₄	—	2	2	no	—
417	Dic₄₇⋊C₄	—	2	2	no	—
418	Dic₄₇⋊C₄	—	2	2	no	—
419	Dic₄₇⋊C₄	—	2	2	no	—
420	Dic₄₇⋊C₄	—	2	2	no	—
421	Dic₄₇⋊C₄	—	2	2	no	—
422	Dic₄₇⋊C₄	—	2	2	no	—
423	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
424	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
425	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
426	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
427	C₄×Dic₄₇	—	2	2	no	—
428	C₄×Dic₄₇	—	2	2	no	—
429	C₄×Dic₄₇	—	2	2	no	—
430	C₄×Dic₄₇	—	2	2	no	—
431	C₄×Dic₄₇	—	2	2	no	—
432	C₄×Dic₄₇	C₂⁴	1	2	yes	—
433	C₄×Dic₄₇	C₂⁴	1	2	yes	—
434	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
435	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
436	C₂³×C₄₇	—	2	4	no	—
437	C₂³×C₄₇	—	2	1	no	—
438	C₂³×C₄₇	—	2	1	no	—
439	C₂³×C₄₇	—	2	1	no	—
440	C₂³×C₄₇	—	8	1	no	—
441	C₂³×C₄₇	—	8	1	no	—
442	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
443	Q₈×C₄₇	—	2	1	no	—
444	Q₈×C₄₇	—	2	1	no	—
445	D₄×C₄₇	—	2	4	no	—
446	D₄×C₄₇	—	2	1	no	—
447	D₄×C₄₇	—	2	1	no	—
448	D₄×C₄₇	—	2	1	no	—
449	D₄×C₄₇	—	2	1	no	—
450	D₄×C₄₇	—	8	1	no	—
451	D₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
452	D₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
453	C₂×C₄×C₄₇	—	2	2	no	—
454	C₂×C₄×C₄₇	—	2	1	no	—
455	C₂×C₄×C₄₇	—	2	1	no	—
456	C₂×C₄×C₄₇	—	2	1	no	—
457	C₂×C₄×C₄₇	—	2	1	no	—
458	C₂×C₄×C₄₇	—	2	1	no	—
459	C₂×C₄×C₄₇	—	2	1	no	—
460	C₂×C₄×C₄₇	—	2	1	no	—
461	C₂×C₄×C₄₇	—	4	1	no	—
462	C₂×C₄×C₄₇	—	4	2	no	—
463	C₂×C₄×C₄₇	—	4	2	no	—
464	C₂×C₄×C₄₇	—	4	2	no	—
465	C₂×C₄×C₄₇	—	8	1	no	—
466	C₂×C₄×C₄₇	—	8	1	no	—
467	C₂×C₄×C₄₇	—	8	1	no	—
468	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
469	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
470	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
471	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
472	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
473	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
474	C₂×Dic₄₇	—	2	2	no	—
475	C₂×Dic₄₇	—	2	2	no	—
476	C₂×Dic₄₇	—	2	2	no	—
477	C₂×Dic₄₇	—	2	2	no	—
478	C₂×Dic₄₇	—	8	2	no	—
479	C₂×Dic₄₇	—	8	2	no	—
480	C₂×Dic₄₇	—	8	2	no	—
481	C₂×Dic₄₇	—	8	2	no	—
482	C₂×Dic₄₇	—	8	2	no	—
483	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
484	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
485	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
486	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
487	Dic₉₄	—	2	2	no	—
488	Dic₉₄	—	2	2	no	—
489	Dic₉₄	—	2	2	no	—
490	Dic₉₄	—	2	2	no	—
491	Dic₉₄	—	4	2	no	—
492	Dic₉₄	—	4	2	no	—
493	Dic₉₄	—	8	2	no	—
494	Dic₉₄	—	8	2	no	—
495	Dic₉₄	—	8	2	no	—
496	Dic₉₄	—	8	1	no	—
497	Dic₉₄	—	8	1	no	—
498	C₈×C₄₇	—	2	1	no	—
499	C₈×C₄₇	—	2	1	no	—
500	C₈×C₄₇	—	2	1	no	—
501	C₈×C₄₇	—	2	1	no	—
502	C₄₇⋊C₈	—	2	2	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	2	no	—
508	C₂²×C₄₇	—	2	2	no	—
509	C₂²×C₄₇	—	2	1	no	—
510	C₂²×C₄₇	—	4	1	no	—
511	C₂²×C₄₇	—	4	1	no	—
512	C₂²×C₄₇	—	4	1	no	—
513	C₂²×C₄₇	—	4	1	no	—
514	C₂²×C₄₇	—	4	1	no	—
515	C₂²×C₄₇	—	4	1	no	—
516	C₂²×C₄₇	—	4	1	no	—
517	C₂²×C₄₇	—	8	4	no	—
518	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
519	C₄×C₄₇	—	2	1	no	—
520	C₄×C₄₇	—	2	1	no	—
521	C₄×C₄₇	—	2	1	no	—
522	C₄×C₄₇	—	2	1	no	—
523	C₄×C₄₇	—	4	1	no	—
524	C₄×C₄₇	—	4	1	no	—
525	C₄×C₄₇	—	4	1	no	—
526	C₄×C₄₇	—	4	1	no	—
527	C₄×C₄₇	—	4	1	no	—
528	C₄×C₄₇	#577	1	2	yes	—
529	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
530	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
531	Dic₄₇	—	2	2	no	—
532	Dic₄₇	—	2	2	no	—
533	Dic₄₇	—	2	2	no	—
534	Dic₄₇	—	2	2	no	—
535	Dic₄₇	—	4	2	no	—
536	Dic₄₇	—	4	2	no	—
537	Dic₄₇	—	4	2	no	—
538	Dic₄₇	—	4	2	no	—
539	#3555	—	47	1	no	—
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	2	no	—
551	#3360	—	47	1	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	D₄₇	1	1	yes	characteristic
560	#3101	—	47	1	no	—
561	#2986	—	47	1	no	—
562	C₂×C₄₇	—	4	1	no	—
563	C₂×C₄₇	—	4	2	no	—
564	C₂×C₄₇	—	4	2	no	—
565	C₂×C₄₇	—	8	1	no	—
566	C₂×C₄₇	#3486	1	1	yes	characteristic
567	C₂×C₄₇	C₂×#577	1	1	yes	characteristic
568	C₂×C₄₇	#3584	1	1	yes	characteristic
569	#563	—	94	2	no	—
570	Q₈²	—	47	1	no	—
571	#557	—	47	2	no	—
572	#557	—	47	1	no	—
573	#556	—	47	2	no	—
574	#556	—	47	1	no	—
575	#556	—	94	1	no	—
576	#554	—	47	1	no	—
577	#554	—	47	2	no	—
578	#554	—	47	1	no	—
579	#554	—	47	2	no	—
580	#554	—	47	1	no	—
581	#554	—	94	2	no	—
582	#554	—	94	1	no	—
583	#552	—	94	1	no	—
584	D₄×Q₈	—	47	1	no	—
585	D₄×Q₈	—	47	1	no	—
586	D₄×Q₈	—	94	1	no	—
587	#544	—	47	2	no	—
588	#544	—	94	1	no	—
589	#543	—	94	2	no	—
590	#542	—	47	2	no	—
591	#541	—	47	2	no	—
592	#541	—	94	1	no	—
593	#541	—	94	2	no	—
594	#533	—	47	1	no	—
595	#533	—	47	1	no	—
596	#533	—	47	1	no	—
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	C₂×D₄₇	1	1	yes	characteristic
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	C₂×D₄₇	1	1	yes	characteristic
620	#483	—	47	2	no	—
621	#482	—	47	2	no	—
622	#481	C₂×D₄₇	1	1	yes	characteristic
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	2	no	—
629	#478	—	47	2	no	—
630	#478	—	47	2	no	—
631	#478	C₂×D₄₇	1	1	yes	characteristic
632	#478	C₂×D₄₇	1	1	yes	characteristic
633	#477	—	47	1	no	—
634	#477	—	47	2	no	—
635	#476	—	47	1	no	—
636	#476	—	47	1	no	—
637	#476	—	47	1	no	—
638	#476	—	47	2	no	—
639	#476	—	47	2	no	—
640	#475	—	47	1	no	—
641	#475	—	47	2	no	—
642	#475	—	47	2	no	—
643	#474	—	47	1	no	—
644	#474	—	47	2	no	—
645	#463	—	47	2	no	—
646	#463	—	47	2	no	—
647	#463	C₂×D₄₇	1	1	yes	characteristic
648	#463	C₂×D₄₇	1	1	yes	characteristic
649	#461	—	47	2	no	—
650	#461	—	47	2	no	—
651	#461	—	47	1	no	—
652	#461	—	47	1	no	—
653	#450	—	47	2	no	—
654	#450	C₂×D₄₇	1	1	yes	characteristic
655	#447	C₂×D₄₇	1	1	yes	characteristic
656	#446	—	47	2	no	—
657	#446	—	47	1	no	—
658	#446	—	47	1	no	—
659	C₈×Q₈	—	47	2	no	—
660	C₈×Q₈	—	47	1	no	—
661	C₈×Q₈	—	47	1	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	2	no	—
669	C₄×SD₁₆	—	47	2	no	—
670	C₄×SD₁₆	—	47	2	no	—
671	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
672	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
673	C₄×D₈	—	47	2	no	—
674	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
675	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
676	#433	—	47	2	no	—
677	#433	—	47	2	no	—
678	#431	—	47	1	no	—
679	#431	C₂×D₄₇	1	1	yes	characteristic
680	C₄₇	#61864	1	1	yes	characteristic, complemented, Sylow
681	C₂²×Q₈	—	94	1	no	—
682	C₂²×Q₈	—	94	1	no	—
683	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
684	C₂³×C₄	—	2	1	no	—
685	C₂×SD₁₆	—	47	2	no	—
686	C₂×SD₁₆	—	47	2	no	—
687	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
688	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
689	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
690	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
691	C₄⋊Q₈	—	47	2	no	—
692	C₄⋊Q₈	—	47	2	no	—
693	C₄⋊Q₈	—	47	2	no	—
694	C₄⋊Q₈	—	47	2	no	—
695	C₄⋊Q₈	—	47	1	no	—
696	C₄⋊Q₈	—	47	1	no	—
697	C₄⋊Q₈	—	47	1	no	—
698	C₄⋊Q₈	—	47	1	no	—
699	C₄⋊Q₈	—	47	1	no	—
700	C₄⋊Q₈	—	47	1	no	—
701	C₄⋊Q₈	—	94	1	no	—
702	C₄⋊Q₈	—	94	2	no	—
703	C₄⋊Q₈	—	94	2	no	—
704	C₄⋊Q₈	—	94	2	no	—
705	#126	—	2	1	no	—
706	#126	—	94	2	no	—
707	#126	—	94	2	no	—
708	#126	—	94	2	no	—
709	#126	—	94	2	no	—
710	#126	—	94	2	no	—
711	#126	—	94	2	no	—
712	#125	—	47	2	no	—
713	#125	—	47	2	no	—
714	#125	—	47	2	no	—
715	#125	—	47	2	no	—
716	#125	—	47	2	no	—
717	#125	—	94	1	no	—
718	#125	—	94	2	no	—
719	#125	—	94	2	no	—
720	#125	—	94	2	no	—
721	#125	—	94	2	no	—
722	#125	—	94	2	no	—
723	#125	—	94	2	no	—
724	#125	—	94	1	no	—
725	#125	C₂²×D₄₇	1	1	yes	characteristic
726	#124	—	47	2	no	—
727	#124	—	94	2	no	—
728	#124	C₂²×D₄₇	1	1	yes	characteristic
729	#123	—	2	1	no	—
730	#123	—	94	2	no	—
731	C₂²⋊Q₈	—	47	1	no	—
732	C₂²⋊Q₈	—	47	1	no	—
733	C₂²⋊Q₈	—	47	2	no	—
734	C₂²⋊Q₈	—	47	2	no	—
735	C₂²⋊Q₈	—	94	2	no	—
736	C₂²⋊Q₈	—	94	2	no	—
737	C₂²⋊Q₈	—	94	2	no	—
738	C₂²⋊Q₈	—	94	2	no	—
739	C₂²⋊Q₈	—	94	2	no	—
740	C₂²⋊Q₈	—	94	2	no	—
741	C₂²⋊Q₈	—	94	2	no	—
742	C₂²⋊Q₈	—	94	2	no	—
743	C₂²⋊Q₈	—	94	2	no	—
744	C₂²⋊Q₈	—	94	2	no	—
745	C₂²⋊Q₈	—	94	2	no	—
746	C₂²⋊Q₈	—	94	2	no	—
747	C₂²⋊Q₈	—	94	2	no	—
748	C₂²⋊Q₈	—	94	1	no	—
749	C₂²⋊Q₈	—	94	1	no	—
750	C₂²⋊Q₈	—	94	2	no	—
751	C₂²⋊Q₈	—	94	2	no	—
752	C₂²⋊Q₈	—	94	1	no	—
753	C₂²⋊Q₈	—	94	1	no	—
754	C₂²⋊Q₈	—	94	1	no	—
755	C₂²⋊Q₈	—	94	1	no	—
756	C₂²⋊Q₈	—	94	1	no	—
757	C₂²⋊Q₈	—	94	1	no	—
758	C₂²⋊Q₈	—	94	1	no	—
759	C₂²⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
760	#121	C₂²×D₄₇	1	1	yes	characteristic
761	C₄×Q₈	—	47	1	no	—
762	C₄×Q₈	—	47	1	no	—
763	C₄×Q₈	—	47	2	no	—
764	C₄×Q₈	—	47	2	no	—
765	C₄×Q₈	—	47	2	no	—
766	C₄×Q₈	—	47	2	no	—
767	C₄×Q₈	—	47	2	no	—
768	C₄×Q₈	—	94	1	no	—
769	C₄×Q₈	—	94	1	no	—
770	C₄×Q₈	—	94	2	no	—
771	C₄×Q₈	—	94	1	no	—
772	C₄×Q₈	—	94	1	no	—
773	C₄×Q₈	—	94	1	no	—
774	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
775	C₄×D₄	—	2	1	no	—
776	C₄×D₄	—	2	1	no	—
777	C₄×D₄	—	2	1	no	—
778	C₄×D₄	—	47	2	no	—
779	C₄×D₄	—	47	2	no	—
780	C₄×D₄	—	47	2	no	—
781	C₄×D₄	—	47	2	no	—
782	C₄×D₄	—	47	2	no	—
783	C₄×D₄	—	94	2	no	—
784	C₄×D₄	—	94	2	no	—
785	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
786	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
787	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
788	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
789	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
790	#117	—	2	1	no	—
791	#117	—	47	2	no	—
792	#117	—	47	2	no	—
793	#117	—	94	2	no	—
794	#117	—	94	1	no	—
795	#117	—	94	1	no	—
796	C₂×C₄⋊C₄	—	94	2	no	—
797	C₂×C₄⋊C₄	—	94	2	no	—
798	C₂×C₄⋊C₄	—	94	1	no	—
799	C₂×C₄⋊C₄	—	94	1	no	—
800	C₂×C₄⋊C₄	—	94	1	no	—
801	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
802	C₂×C₂²⋊C₄	—	2	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	2	no	—
808	#107	—	47	2	no	—
809	#107	—	47	2	no	—
810	#107	C₂²×D₄₇	1	1	yes	characteristic
811	#107	C₂²×D₄₇	1	1	yes	characteristic
812	#106	—	47	2	no	—
813	#106	—	47	2	no	—
814	#106	—	47	2	no	—
815	#106	—	47	2	no	—
816	#106	—	47	2	no	—
817	#106	—	47	2	no	—
818	#106	C₂²×D₄₇	1	1	yes	characteristic
819	#106	C₂²×D₄₇	1	1	yes	characteristic
820	C₄⋊C₈	—	47	2	no	—
821	C₄⋊C₈	—	47	2	no	—
822	C₄⋊C₈	—	47	2	no	—
823	C₄⋊C₈	—	47	2	no	—
824	C₄⋊C₈	—	47	1	no	—
825	C₄⋊C₈	—	47	1	no	—
826	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
827	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
828	#103	—	47	2	no	—
829	#103	—	47	2	no	—
830	#103	—	47	2	no	—
831	#103	—	47	2	no	—
832	#103	—	47	2	no	—
833	#103	—	47	2	no	—
834	#103	—	47	2	no	—
835	#103	—	47	2	no	—
836	#103	C₂²×D₄₇	1	1	yes	characteristic
837	#103	C₂²×D₄₇	1	1	yes	characteristic
838	#102	—	47	2	no	—
839	#102	—	47	2	no	—
840	#102	—	47	2	no	—
841	#102	—	47	2	no	—
842	#102	C₂²×D₄₇	1	1	yes	characteristic
843	#102	C₂²×D₄₇	1	1	yes	characteristic
844	#102	C₂²×D₄₇	1	1	yes	characteristic
845	#102	C₂²×D₄₇	1	1	yes	characteristic
846	#102	C₂²×D₄₇	1	1	yes	characteristic
847	#102	C₂²×D₄₇	1	1	yes	characteristic
848	C₂²⋊C₈	—	47	2	no	—
849	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
850	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
851	#97	—	47	2	no	—
852	#97	—	47	2	no	—
853	C₄×C₈	—	47	2	no	—
854	C₄×C₈	—	47	2	no	—
855	C₄×C₈	—	47	2	no	—
856	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
857	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
858	C₂⁴	—	2	1	no	—
859	C₂×Q₈	—	47	1	no	—
860	C₂×Q₈	—	47	1	no	—
861	C₂×Q₈	—	47	2	no	—
862	C₂×Q₈	—	47	2	no	—
863	C₂×Q₈	—	94	2	no	—
864	C₂×Q₈	—	94	2	no	—
865	C₂×Q₈	—	94	2	no	—
866	C₂×Q₈	—	94	1	no	—
867	C₂×Q₈	—	94	1	no	—
868	C₂×Q₈	—	94	1	no	—
869	C₂×Q₈	—	376	2	no	—
870	C₂×Q₈	—	376	2	no	—
871	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
872	C₂×D₄	—	2	2	no	—
873	C₂×D₄	—	2	2	no	—
874	C₂×D₄	—	2	1	no	—
875	C₂×D₄	—	2	1	no	—
876	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
877	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
878	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
879	C₂²×C₄	—	2	1	no	—
880	C₂²×C₄	—	2	1	no	—
881	C₂²×C₄	—	2	1	no	—
882	C₂²×C₄	—	2	1	no	—
883	C₂²×C₄	—	2	1	no	—
884	C₂²×C₄	—	2	1	no	—
885	C₂²×C₄	—	8	2	no	—
886	C₂²×C₄	—	94	2	no	—
887	C₂²×C₄	—	94	2	no	—
888	C₂²×C₄	—	94	2	no	—
889	C₂²×C₄	—	94	2	no	—
890	C₂²×C₄	—	94	2	no	—
891	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
892	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
893	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
894	SD₁₆	—	2	2	no	—
895	SD₁₆	—	2	2	no	—
896	SD₁₆	—	94	4	no	—
897	SD₁₆	—	94	4	no	—
898	D₈	—	2	2	no	—
899	D₈	—	2	2	no	—
900	C₂×C₈	—	47	2	no	—
901	C₂×C₈	—	47	2	no	—
902	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
903	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
904	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
905	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
906	C₄⋊C₄	—	2	1	no	—
907	C₄⋊C₄	—	2	1	no	—
908	C₄⋊C₄	—	2	1	no	—
909	C₄⋊C₄	—	2	1	no	—
910	C₄⋊C₄	—	2	1	no	—
911	C₄⋊C₄	—	47	2	no	—
912	C₄⋊C₄	—	47	2	no	—
913	C₄⋊C₄	—	47	2	no	—
914	C₄⋊C₄	—	47	2	no	—
915	C₄⋊C₄	—	47	1	no	—
916	C₄⋊C₄	—	47	1	no	—
917	C₄⋊C₄	—	47	2	no	—
918	C₄⋊C₄	—	47	2	no	—
919	C₄⋊C₄	—	47	2	no	—
920	C₄⋊C₄	—	47	2	no	—
921	C₄⋊C₄	—	47	2	no	—
922	C₄⋊C₄	—	47	2	no	—
923	C₄⋊C₄	—	94	2	no	—
924	C₄⋊C₄	—	94	2	no	—
925	C₄⋊C₄	—	94	2	no	—
926	C₄⋊C₄	—	94	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	2	no	—
934	C₄⋊C₄	—	94	2	no	—
935	C₄⋊C₄	—	94	2	no	—
936	C₄⋊C₄	—	94	2	no	—
937	C₄⋊C₄	—	94	2	no	—
938	C₄⋊C₄	—	94	2	no	—
939	C₄⋊C₄	—	94	2	no	—
940	C₄⋊C₄	—	94	2	no	—
941	C₄⋊C₄	—	94	1	no	—
942	C₄⋊C₄	—	94	1	no	—
943	C₄⋊C₄	—	94	1	no	—
944	C₄⋊C₄	—	94	1	no	—
945	C₄⋊C₄	—	94	1	no	—
946	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
947	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
948	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
949	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
950	C₂²⋊C₄	—	2	1	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	1	no	—
956	C₂²⋊C₄	—	2	1	no	—
957	C₂²⋊C₄	—	2	1	no	—
958	C₂²⋊C₄	—	2	1	no	—
959	C₂²⋊C₄	—	47	2	no	—
960	C₂²⋊C₄	—	47	2	no	—
961	C₂²⋊C₄	—	94	2	no	—
962	C₂²⋊C₄	—	94	2	no	—
963	C₂²⋊C₄	—	94	2	no	—
964	C₂²⋊C₄	—	94	2	no	—
965	C₂²⋊C₄	—	94	2	no	—
966	C₂²⋊C₄	—	94	2	no	—
967	C₂²⋊C₄	—	94	2	no	—
968	C₂²⋊C₄	—	94	2	no	—
969	C₂²⋊C₄	—	94	2	no	—
970	C₄²	—	2	1	no	—
971	C₄²	—	47	2	no	—
972	C₄²	—	47	2	no	—
973	C₄²	—	94	2	no	—
974	C₄²	—	94	2	no	—
975	C₄²	—	94	2	no	—
976	C₄²	—	94	2	no	—
977	C₄²	—	94	2	no	—
978	C₄²	D₄×D₄₇	1	1	yes	characteristic
979	C₄²	D₄×D₄₇	1	1	yes	characteristic
980	C₄²	C₂³×D₄₇	1	1	yes	characteristic
981	C₄²	C₂³×D₄₇	1	1	yes	characteristic
982	C₂³	—	2	4	no	—
983	C₂³	—	2	1	no	—
984	C₂³	—	2	1	no	—
985	C₂³	—	2	1	no	—
986	C₂³	—	8	1	no	—
987	C₂³	—	8	1	no	—
988	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
989	Q₈	—	2	1	no	—
990	Q₈	—	2	1	no	—
991	Q₈	—	94	2	no	—
992	Q₈	—	94	2	no	—
993	Q₈	—	94	2	no	—
994	Q₈	—	94	2	no	—
995	Q₈	—	376	1	no	—
996	Q₈	—	376	1	no	—
997	Q₈	—	376	2	no	—
998	Q₈	—	376	2	no	—
999	Q₈	—	376	2	no	—
1000	Q₈	—	188	2	no	—
1001	Q₈	—	188	2	no	—
1002	D₄	—	2	4	no	—
1003	D₄	—	2	1	no	—
1004	D₄	—	2	1	no	—
1005	D₄	—	2	1	no	—
1006	D₄	—	2	1	no	—
1007	D₄	—	8	1	no	—
1008	D₄	#13094071	1	2	yes	—
1009	D₄	#13094071	1	2	yes	—
1010	C₂×C₄	—	2	2	no	—
1011	C₂×C₄	—	2	1	no	—
1012	C₂×C₄	—	2	1	no	—
1013	C₂×C₄	—	2	1	no	—
1014	C₂×C₄	—	2	1	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	4	1	no	—
1019	C₂×C₄	—	4	2	no	—
1020	C₂×C₄	—	4	2	no	—
1021	C₂×C₄	—	4	2	no	—
1022	C₂×C₄	—	8	1	no	—
1023	C₂×C₄	—	8	1	no	—
1024	C₂×C₄	—	8	1	no	—
1025	C₂×C₄	—	47	2	no	—
1026	C₂×C₄	—	47	2	no	—
1027	C₂×C₄	—	47	2	no	—
1028	C₂×C₄	—	47	2	no	—
1029	C₂×C₄	—	94	2	no	—
1030	C₂×C₄	—	94	2	no	—
1031	C₂×C₄	—	94	2	no	—
1032	C₂×C₄	—	94	2	no	—
1033	C₂×C₄	—	376	2	no	—
1034	C₂×C₄	—	376	2	no	—
1035	C₂×C₄	—	376	2	no	—
1036	C₂×C₄	—	376	2	no	—
1037	C₂×C₄	—	376	2	no	—
1038	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1039	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1040	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1041	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1042	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1043	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1044	C₈	—	2	1	no	—
1045	C₈	—	2	1	no	—
1046	C₈	—	2	1	no	—
1047	C₈	—	2	1	no	—
1048	C₈	—	94	2	no	—
1049	C₈	—	94	2	no	—
1050	C₂²	—	2	1	no	—
1051	C₂²	—	2	2	no	—
1052	C₂²	—	2	2	no	—
1053	C₂²	—	2	1	no	—
1054	C₂²	—	2	1	no	—
1055	C₂²	—	4	1	no	—
1056	C₂²	—	4	1	no	—
1057	C₂²	—	4	1	no	—
1058	C₂²	—	4	1	no	—
1059	C₂²	—	4	1	no	—
1060	C₂²	—	4	1	no	—
1061	C₂²	—	4	1	no	—
1062	C₂²	—	8	4	no	—
1063	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1064	C₄	—	2	1	no	—
1065	C₄	—	2	1	no	—
1066	C₄	—	2	1	no	—
1067	C₄	—	2	1	no	—
1068	C₄	—	4	1	no	—
1069	C₄	—	4	1	no	—
1070	C₄	—	4	1	no	—
1071	C₄	—	4	1	no	—
1072	C₄	—	4	1	no	—
1073	C₄	—	94	2	no	—
1074	C₄	—	94	2	no	—
1075	C₄	—	94	2	no	—
1076	C₄	—	94	2	no	—
1077	C₄	—	188	2	no	—
1078	C₄	—	188	2	no	—
1079	C₄	—	188	2	no	—
1080	C₄	—	188	2	no	—
1081	C₄	#15689933	1	2	yes	—
1082	C₄	C₂×#13094071	1	1	yes	characteristic
1083	C₄	C₂×#13094071	1	1	yes	characteristic
1084	C₂	—	4	1	no	—
1085	C₂	—	4	2	no	—
1086	C₂	—	4	2	no	—
1087	C₂	—	8	1	no	—
1088	C₂	#20257035	1	1	yes	characteristic
1089	C₂	C₂×#15689933	1	1	yes	characteristic
1090	C₂	#20258157	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3105	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	C₄₇×#447	C₂²
hypercenter	#3105	D₄₇
hypocenter	C₄₇	#61864
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3105

Complements

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

N	H ≅ G/N	type
1. #20257878	C₂	semidirect
2. #20257191	C₂	semidirect
3. #20256337	C₂	semidirect
4. #20256296	C₂	semidirect
5. #20256285	C₂	semidirect
6. #20256258	C₂	semidirect
7. #20256253	C₂	semidirect
8. SD₁₆×Dic₉₄	C₂	semidirect
9. #20256219	C₂	semidirect
10. #20256167	C₂	semidirect
11. #20256104	C₂	semidirect
12. #20256035	C₂	semidirect
13. #20256032	C₂	semidirect
14. #20256028	C₂	semidirect
15. #20254682	C₂	semidirect
16. #20254660	C₂	semidirect
17. #20254563	C₂	semidirect
18. #20254549	C₂	semidirect
19. #20253634	C₂	semidirect
21. #20253396	C₂	semidirect
22. #20252489	C₂	semidirect
25. Q₈×Dic₉₄	C₂²	semidirect
26. #15689851	C₂²	semidirect
27. #15689850	C₂²	semidirect
29. #15689843	C₂²	semidirect
30. #15689842	C₂²	semidirect
37. #15689830	C₂²	semidirect
55. #15689531	C₂²	semidirect
56. #15689530	C₂²	semidirect
57. #15689528	C₂²	semidirect
58. #15689524	C₂²	semidirect
59. #15689522	C₂²	semidirect
60. #15689521	C₂²	semidirect
61. #15689520	C₂²	semidirect
62. #15689490	C₂²	semidirect
63. #15689481	C₂²	semidirect
64. #15689477	C₂²	semidirect
65. #15689476	C₂²	semidirect
66. #15689474	C₂²	semidirect
67. #15689474	C₂²	semidirect
68. #15689472	C₂²	semidirect
74. #15689433	C₂²	semidirect
75. #15689432	C₂²	semidirect
76. #15689431	C₂²	semidirect
77. #15689431	C₂²	semidirect
78. #15689429	C₂²	semidirect
81. #15689421	C₂²	semidirect
82. #15689418	C₂²	semidirect
83. #15689417	C₂²	semidirect
86. #15689413	C₂²	semidirect
88. #15689411	C₂²	semidirect
89. #15689408	C₂²	semidirect
90. #15689407	C₂²	semidirect
91. #15689406	C₂²	semidirect
92. #15689403	C₂²	semidirect
101. #15689253	C₂²	semidirect
102. #15689253	C₂²	semidirect
103. #15689250	C₂²	semidirect
104. C₈×Dic₉₄	C₂²	semidirect
105. C₈×Dic₉₄	C₂²	semidirect
106. #15689247	C₂²	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
#20257878	2
#20257191	2
#20256337	2
#20256296	2
#20256285	2
#20256258	2
#20256253	2
SD₁₆×Dic₉₄	2
#20256219	2
#20256167	2
#20256104	2
#20256035	2
#20256032	2
#20256028	2
#20254682	2
#20254660	2
#20254563	2
#20254549	2
#20253634	2
#20253565	2
#20253396	2
#20252489	2
C₄₇×#3105	2
#61864	47