Subgroups — #27098638

Order 12032.

1812 conjugacy classes of subgroups.

The subgroup lattice has 1116 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257003	C₂	1	1	yes	maximal, characteristic
2	Q₈×#10625350	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256393	C₂	1	1	yes	maximal, characteristic, complemented
4	SD₁₆×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
5	#20256064	C₂	1	1	yes	maximal, characteristic, complemented
6	#20256028	C₂	1	1	yes	maximal, characteristic, complemented
7	#20256005	C₂	1	1	yes	maximal, characteristic, complemented
8	#20255999	C₂	1	2	yes	maximal, complemented
9	#20255706	C₂	1	1	yes	maximal, characteristic, complemented
10	#20255700	C₂	1	2	yes	maximal, complemented
11	#20255673	C₂	1	1	yes	maximal, characteristic, complemented
12	#20255667	C₂	1	2	yes	maximal, complemented
13	#20255035	C₂	1	1	yes	maximal, characteristic, complemented
14	#20255028	C₂	1	2	yes	maximal, complemented
15	#20254133	C₂	1	1	yes	maximal, characteristic, complemented
16	#20254130	C₂	1	2	yes	maximal, complemented
17	#20253550	C₂	1	1	yes	maximal, characteristic, complemented
18	#20253546	C₂	1	2	yes	maximal, complemented
19	#20253518	C₂	1	1	yes	maximal, characteristic, complemented
20	#20253516	C₂	1	2	yes	maximal, complemented
21	#20252406	C₂	1	1	yes	maximal, characteristic, complemented
22	#20252210	C₂	1	2	yes	maximal, complemented
23	C₄×#137×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#13094053	C₂²	1	2	yes	—
25	Q₈×Dic₉₄	C₂²	1	1	yes	characteristic
26	#15689851	—	2	1	no	—
27	#15689851	C₂²	1	1	yes	characteristic
28	#15689851	C₂²	1	1	yes	characteristic
29	#15689846	C₂²	1	1	yes	characteristic
30	#15689841	C₂²	1	2	yes	—
31	#15689833	—	2	1	no	—
32	#15689833	C₂²	1	1	yes	characteristic
33	#15689828	—	2	2	no	—
34	#15689828	C₂²	1	2	yes	—
35	#15689813	—	2	1	no	—
36	#15689806	—	2	2	no	—
37	Q₈×D₁₈₈	C₂²	1	1	yes	characteristic
38	D₄×Dic₉₄	C₂²	1	1	yes	characteristic
39	Q₈×C₂²⋊D₄₇	C₂²	1	2	yes	—
40	#15689782	—	2	1	no	—
41	#15689777	C₂²	1	1	yes	characteristic
42	#15689772	C₂²	1	2	yes	—
43	#15689680	—	2	1	no	—
44	#15689680	C₂²	1	1	yes	characteristic
45	#15689680	C₂²	1	1	yes	characteristic
46	#15689677	—	2	2	no	—
47	#15689677	C₂²	1	2	yes	—
48	#15689677	C₂²	1	2	yes	—
49	#15689657	—	2	1	no	—
50	#15689653	—	2	2	no	—
51	C₄×#10625350	—	2	1	no	—
52	C₄×#10625350	C₂²	1	1	yes	characteristic
53	C₄×#10625352	C₂²	1	2	yes	—
54	C₂×C₄×Dic₉₄	—	2	1	no	—
55	C₄×Q₈×D₄₇	C₂²	1	2	yes	—
56	#15689521	C₂²	1	1	yes	characteristic
57	#15689520	C₂²	1	2	yes	—
58	#15689503	C₂²	1	1	yes	characteristic
59	#15689501	C₂²	1	2	yes	—
60	#15689474	C₂²	1	1	yes	characteristic
61	#15689474	C₂²	1	1	yes	characteristic
62	#15689472	C₂²	1	2	yes	—
63	#15689472	C₂²	1	2	yes	—
64	#15689466	C₂²	1	2	yes	—
65	#15689464	C₂²	1	2	yes	—
66	#15689462	C₂²	1	2	yes	—
67	#15689455	C₂²	1	2	yes	—
68	#15689453	C₂²	1	2	yes	—
69	#15689452	C₂²	1	2	yes	—
70	#15689418	C₂²	1	1	yes	characteristic
71	#15689417	C₂²	1	2	yes	—
72	#15689413	C₂²	1	1	yes	characteristic
73	#15689411	C₂²	1	2	yes	—
74	#15689408	C₂²	1	1	yes	characteristic
75	#15689408	C₂²	1	1	yes	characteristic
76	#15689407	C₂²	1	2	yes	—
77	#15689406	C₂²	1	2	yes	—
78	#15689382	C₂²	1	2	yes	—
79	#15689381	C₂²	1	2	yes	—
80	#15689381	C₂²	1	2	yes	—
81	#15689380	C₂²	1	2	yes	—
82	#15689380	C₂²	1	2	yes	—
83	#15689378	C₂²	1	2	yes	—
84	#15689333	C₂²	1	1	yes	characteristic
85	#15689333	C₂²	1	1	yes	characteristic
86	#15689333	C₂²	1	1	yes	characteristic
87	#15689332	C₂²	1	2	yes	—
88	#15689332	C₂²	1	2	yes	—
89	#15689331	C₂²	1	2	yes	—
90	#15689328	C₂²	1	1	yes	characteristic
91	#15689326	C₂²	1	2	yes	—
92	#15689286	C₂²	1	2	yes	—
93	#15689285	C₂²	1	2	yes	—
94	#15689282	C₂²	1	2	yes	—
95	#15689280	C₂²	1	2	yes	—
96	#15689279	C₂²	1	2	yes	—
97	#15689277	C₂²	1	2	yes	—
98	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
99	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
100	#15689231	C₂²	1	2	yes	—
101	#15689231	C₂²	1	2	yes	—
102	#15689228	C₂²	1	2	yes	—
103	#15689228	C₂²	1	2	yes	—
104	#15689228	C₂²	1	2	yes	—
105	#15689223	C₂²	1	2	yes	—
106	#15689217	C₂²	1	2	yes	—
107	#15689215	C₂²	1	2	yes	—
108	#15689214	C₂²	1	2	yes	—
109	SD₁₆×Dic₄₇	C₂²	1	2	yes	—
110	#15689202	C₂²	1	1	yes	characteristic
111	#15689202	C₂²	1	1	yes	characteristic
112	#15689199	C₂²	1	2	yes	—
113	#15689199	C₂²	1	2	yes	—
114	#15689180	C₂²	1	1	yes	characteristic
115	#15689178	C₂²	1	2	yes	—
116	#15689164	C₂²	1	2	yes	—
117	#15689130	C₂²	1	2	yes	—
118	#15689121	C₂²	1	2	yes	—
119	#15689075	C₂²	1	2	yes	—
120	C₂×#137×C₄₇	C₂²	1	1	yes	characteristic
121	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
122	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
123	C₄₇×#441	C₂²	1	1	yes	characteristic
124	C₄₇×#441	C₂²	1	1	yes	characteristic
125	C₄₇×#440	C₂²	1	1	yes	characteristic
126	C₄₇×#440	C₂²	1	1	yes	characteristic
127	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
128	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
129	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
130	C₄×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
131	C₄₇×#428	C₂²	1	1	yes	characteristic
132	C₄₇×#419	C₂²	1	1	yes	characteristic
133	C₄₇×#417	C₂²	1	1	yes	characteristic
134	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
135	C₂×#10625350	D₄	1	1	yes	characteristic
136	C₂×#10625352	C₂³	1	2	yes	—
137	C₂²×Dic₉₄	—	2	1	no	—
138	C₂×Q₈×D₄₇	C₂³	1	2	yes	—
139	#13094053	—	2	8	no	—
140	C₂×Dic₁₈₈	C₂³	1	2	yes	—
141	C₂×Dic₁₈₈	C₂³	1	2	yes	—
142	C₂×#10625337	C₂³	1	2	yes	—
143	C₂×#10625337	C₂³	1	2	yes	—
144	C₂×#10625337	C₂³	1	2	yes	—
145	C₂×#10625335	C₂³	1	2	yes	—
146	C₂×#10625324	C₂³	1	2	yes	—
147	C₂×#10625324	C₂³	1	2	yes	—
148	#13094024	—	2	1	no	—
149	#13094024	—	2	1	no	—
150	#13094024	C₂³	1	1	yes	characteristic
151	#13094024	C₂³	1	1	yes	characteristic
152	#13094024	C₂³	1	1	yes	characteristic
153	#13094024	C₂³	1	1	yes	characteristic
154	#13094023	—	2	2	no	—
155	#13094023	C₂³	1	2	yes	—
156	#13094023	C₂³	1	2	yes	—
157	#13094022	—	2	2	no	—
158	#13094022	C₂³	1	2	yes	—
159	#13094022	C₂³	1	2	yes	—
160	#13094019	—	2	2	no	—
161	#13094018	—	2	2	no	—
162	#13094017	—	2	2	no	—
163	#13094016	—	2	1	no	—
164	#13094016	—	2	1	no	—
165	#13094016	—	2	1	no	—
166	#13094016	—	2	1	no	—
167	#13094016	—	2	1	no	—
168	#13094014	—	2	2	no	—
169	#13094014	—	2	2	no	—
170	#13094014	—	2	2	no	—
171	#13094014	—	2	2	no	—
172	#13094014	—	2	2	no	—
173	#13094012	—	2	1	no	—
174	#13094010	—	2	2	no	—
175	#13094008	—	2	2	no	—
176	#13094007	—	2	2	no	—
177	#13094005	—	2	2	no	—
178	#13094004	—	2	2	no	—
179	#13094004	C₂³	1	2	yes	—
180	#13094004	C₂³	1	2	yes	—
181	#13094003	—	2	1	no	—
182	#13094003	—	2	1	no	—
183	#13094003	—	2	2	no	—
184	#13094003	—	2	2	no	—
185	#13094003	—	2	1	no	—
186	#13094003	C₂³	1	2	yes	—
187	#13094003	C₂³	1	2	yes	—
188	#13094002	—	2	2	no	—
189	#13094002	—	2	2	no	—
190	#13094002	—	2	2	no	—
191	#13094002	—	2	2	no	—
192	#13094001	—	2	2	no	—
193	#13094000	—	2	2	no	—
194	#13094000	C₂³	1	2	yes	—
195	#13094000	C₂³	1	2	yes	—
196	#13093998	—	2	1	no	—
197	#13093996	—	2	2	no	—
198	Q₈×Dic₄₇	C₂³	1	2	yes	—
199	C₄×Dic₉₄	—	2	1	no	—
200	C₄×Dic₉₄	—	2	1	no	—
201	C₄×Dic₉₄	—	2	1	no	—
202	C₄×Dic₉₄	—	2	1	no	—
203	C₄×Dic₉₄	—	2	1	no	—
204	C₄×Dic₉₄	—	2	1	no	—
205	C₄×Dic₉₄	—	2	2	no	—
206	C₄×Dic₉₄	—	2	2	no	—
207	C₄×Dic₉₄	—	2	2	no	—
208	C₄×Dic₉₄	—	2	2	no	—
209	C₄×Dic₉₄	D₄	1	1	yes	characteristic
210	C₄×Dic₉₄	C₂³	1	2	yes	—
211	C₄×Dic₉₄	C₂³	1	2	yes	—
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	C₄×D₁₈₈	—	2	1	no	—
217	C₄×D₁₈₈	—	2	1	no	—
218	C₄×D₁₈₈	D₄	1	1	yes	characteristic
219	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
220	D₄×Dic₄₇	C₂³	1	2	yes	—
221	C₄×C₂²⋊D₄₇	—	2	2	no	—
222	C₄×C₂²⋊D₄₇	—	2	2	no	—
223	C₄×C₂²⋊D₄₇	—	2	2	no	—
224	C₄×C₂²⋊D₄₇	D₄	1	2	yes	—
225	C₄×C₂²⋊D₄₇	C₂³	1	2	yes	—
226	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
227	#13093983	—	2	1	no	—
228	#13093983	—	2	1	no	—
229	#13093983	D₄	1	1	yes	characteristic
230	#13093982	C₂³	1	2	yes	—
231	#13093981	—	2	2	no	—
232	#13093981	—	2	2	no	—
233	#13093981	D₄	1	2	yes	—
234	#13093980	—	2	2	no	—
235	C₂×C₄⋊Dic₄₇	—	2	1	no	—
236	C₂×Dic₄₇⋊C₄	—	2	2	no	—
237	C₄⋊C₄×D₄₇	—	2	2	no	—
238	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
239	C₂×C₄×Dic₄₇	—	2	2	no	—
240	C₄²×D₄₇	—	2	2	no	—
241	C₄²×D₄₇	C₂³	1	2	yes	—
242	#13093957	C₂³	1	2	yes	—
243	#13093956	C₂³	1	2	yes	—
244	#13093956	C₂³	1	2	yes	—
245	#13093955	C₂³	1	2	yes	—
246	#13093955	C₂³	1	2	yes	—
247	#13093955	C₂³	1	2	yes	—
248	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
249	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
250	Dic₄₇⋊C₈	C₂³	1	2	yes	—
251	Dic₄₇⋊C₈	C₂³	1	2	yes	—
252	#13093949	C₂³	1	2	yes	—
253	#13093949	C₂³	1	2	yes	—
254	#13093949	C₂³	1	2	yes	—
255	#13093949	C₂³	1	2	yes	—
256	#13093948	C₂³	1	2	yes	—
257	#13093948	C₂³	1	2	yes	—
258	#13093948	C₂³	1	2	yes	—
259	#13093947	C₂³	1	2	yes	—
260	#13093947	C₂³	1	2	yes	—
261	#13093947	C₂³	1	2	yes	—
262	#13093947	C₂³	1	2	yes	—
263	#13093945	C₂³	1	2	yes	—
264	C₂²⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
265	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
266	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
267	#13093935	C₂³	1	2	yes	—
268	C₈×Dic₄₇	C₂³	1	2	yes	—
269	C₈×Dic₄₇	C₂³	1	2	yes	—
270	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
271	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
272	#137×C₄₇	—	2	4	no	—
273	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
274	C₂×Q₁₆×C₄₇	C₂³	1	1	yes	characteristic
275	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
276	C₂×SD₁₆×C₄₇	C₂³	1	1	yes	characteristic
277	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
278	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
279	C₄×Q₈×C₄₇	—	2	1	no	—
280	C₄×Q₈×C₄₇	—	2	1	no	—
281	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
282	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
283	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
284	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
285	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
286	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
287	C₄×D₄×C₄₇	—	2	1	no	—
288	C₄×D₄×C₄₇	—	2	1	no	—
289	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
290	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
291	#117×C₄₇	—	2	1	no	—
292	#117×C₄₇	C₂³	1	1	yes	characteristic
293	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
294	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
295	C₂×C₄²×C₄₇	—	2	1	no	—
296	C₂×C₄²×C₄₇	—	2	1	no	—
297	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
298	#107×C₄₇	C₂³	1	1	yes	characteristic
299	#107×C₄₇	C₂³	1	1	yes	characteristic
300	#106×C₄₇	C₂³	1	1	yes	characteristic
301	#106×C₄₇	C₂³	1	1	yes	characteristic
302	#103×C₄₇	C₂³	1	1	yes	characteristic
303	#103×C₄₇	C₂³	1	1	yes	characteristic
304	#103×C₄₇	C₂³	1	1	yes	characteristic
305	#103×C₄₇	C₂³	1	1	yes	characteristic
306	#103×C₄₇	C₂³	1	1	yes	characteristic
307	#103×C₄₇	C₂³	1	1	yes	characteristic
308	#102×C₄₇	C₂³	1	1	yes	characteristic
309	#102×C₄₇	C₂³	1	1	yes	characteristic
310	#97×C₄₇	C₂³	1	1	yes	characteristic
311	#97×C₄₇	C₂³	1	1	yes	characteristic
312	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
313	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
314	#41×C₄₇	—	2	2	no	—
315	#41×C₄₇	—	4	1	no	—
316	C₂×Q₈×C₄₇	—	2	1	no	—
317	C₂×Q₈×C₄₇	—	2	2	no	—
318	C₂×Q₈×C₄₇	—	4	1	no	—
319	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
320	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
321	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
322	C₂×D₄×C₄₇	—	2	1	no	—
323	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
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	—	2	1	no	—
328	C₂²×C₄×C₄₇	—	2	1	no	—
329	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
330	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
331	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
332	C₂×C₂²⋊D₄₇	—	2	2	no	—
333	C₂×C₂²⋊D₄₇	C₂×D₄	1	2	yes	—
334	C₂²×Dic₄₇	—	2	2	no	—
335	C₂²×Dic₄₇	—	2	2	no	—
336	Q₈×D₄₇	—	2	4	no	—
337	Q₈×D₄₇	—	4	2	no	—
338	#10625352	—	2	4	no	—
339	#10625352	—	4	2	no	—
340	#10625350	—	2	4	no	—
341	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
342	C₂×C₄×D₄₇	—	2	2	no	—
343	C₂×C₄×D₄₇	—	2	2	no	—
344	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
345	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
346	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
347	C₂×Dic₉₄	—	2	1	no	—
348	C₂×Dic₉₄	—	2	2	no	—
349	C₂×Dic₉₄	—	2	2	no	—
350	C₂×Dic₉₄	—	2	1	no	—
351	C₂×Dic₉₄	—	2	2	no	—
352	C₂×Dic₉₄	—	4	4	no	—
353	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
354	C₂×Dic₉₄	C₂⁴	1	2	yes	—
355	C₂×Dic₉₄	C₂⁴	1	2	yes	—
356	Q₁₆×C₄₇	—	2	2	no	—
357	Q₁₆×C₄₇	—	2	2	no	—
358	SD₁₆×C₄₇	—	2	2	no	—
359	SD₁₆×C₄₇	#41	1	4	yes	complemented
360	M₁₆×C₄₇	—	2	2	no	—
361	M₁₆×C₄₇	—	4	1	no	—
362	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
363	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
364	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
365	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
366	C₄⋊C₄×C₄₇	—	2	1	no	—
367	C₄⋊C₄×C₄₇	—	2	1	no	—
368	C₄⋊C₄×C₄₇	—	2	1	no	—
369	C₄⋊C₄×C₄₇	—	2	1	no	—
370	C₄⋊C₄×C₄₇	—	2	1	no	—
371	C₄⋊C₄×C₄₇	—	2	1	no	—
372	C₄⋊C₄×C₄₇	—	2	1	no	—
373	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
374	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
375	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
376	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
377	C₂²⋊C₄×C₄₇	—	2	1	no	—
378	C₂²⋊C₄×C₄₇	—	2	1	no	—
379	C₂²⋊C₄×C₄₇	—	2	1	no	—
380	C₄²×C₄₇	—	2	1	no	—
381	C₄²×C₄₇	—	2	1	no	—
382	C₄²×C₄₇	—	2	1	no	—
383	C₄²×C₄₇	—	2	1	no	—
384	C₄²×C₄₇	—	2	1	no	—
385	C₄²×C₄₇	—	2	1	no	—
386	C₄²×C₄₇	—	2	1	no	—
387	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
388	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
389	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
390	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
391	C₂²⋊Dic₄₇	—	2	2	no	—
392	C₂²⋊Dic₄₇	—	2	2	no	—
393	C₂²⋊Dic₄₇	—	2	2	no	—
394	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
395	#10625337	—	2	4	no	—
396	#10625337	—	4	2	no	—
397	#10625337	—	4	2	no	—
398	#10625335	—	2	4	no	—
399	(C₂×D₄₇)⋊C₄	—	2	2	no	—
400	(C₂×D₄₇)⋊C₄	—	2	2	no	—
401	(C₂×D₄₇)⋊C₄	—	2	2	no	—
402	(C₂×D₄₇)⋊C₄	—	2	2	no	—
403	(C₂×D₄₇)⋊C₄	—	2	2	no	—
404	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
405	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
406	C₄⋊Dic₄₇	—	2	1	no	—
407	C₄⋊Dic₄₇	—	2	1	no	—
408	C₄⋊Dic₄₇	—	2	1	no	—
409	C₄⋊Dic₄₇	—	2	1	no	—
410	C₄⋊Dic₄₇	—	2	1	no	—
411	C₄⋊Dic₄₇	—	2	1	no	—
412	C₄⋊Dic₄₇	—	2	2	no	—
413	C₄⋊Dic₄₇	—	2	2	no	—
414	C₄⋊Dic₄₇	—	2	2	no	—
415	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
416	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
417	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
418	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
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	—	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	Dic₄₇⋊C₄	—	2	2	no	—
430	Dic₄₇⋊C₄	—	2	2	no	—
431	Dic₄₇⋊C₄	—	2	2	no	—
432	Dic₄₇⋊C₄	—	2	2	no	—
433	Dic₄₇⋊C₄	—	2	2	no	—
434	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
435	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
436	C₄×Dic₄₇	—	2	2	no	—
437	C₄×Dic₄₇	—	2	2	no	—
438	C₄×Dic₄₇	—	2	2	no	—
439	C₄×Dic₄₇	—	2	2	no	—
440	C₄×Dic₄₇	—	2	2	no	—
441	C₄×Dic₄₇	—	2	2	no	—
442	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
443	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
444	C₄×Dic₄₇	C₂⁴	1	2	yes	—
445	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
446	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
447	Dic₁₈₈	—	2	4	no	—
448	Dic₁₈₈	—	4	2	no	—
449	#10625324	—	2	4	no	—
450	#10625324	—	4	2	no	—
451	C₂³×C₄₇	—	2	1	no	—
452	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
453	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
454	Q₈×C₄₇	—	2	1	no	—
455	Q₈×C₄₇	—	2	1	no	—
456	Q₈×C₄₇	—	2	1	no	—
457	Q₈×C₄₇	—	2	1	no	—
458	Q₈×C₄₇	—	2	1	no	—
459	Q₈×C₄₇	—	4	2	no	—
460	Q₈×C₄₇	C₂×#41	1	2	yes	—
461	D₄×C₄₇	—	2	1	no	—
462	D₄×C₄₇	—	4	2	no	—
463	D₄×C₄₇	C₂×#41	1	2	yes	—
464	C₂×C₄×C₄₇	—	2	1	no	—
465	C₂×C₄×C₄₇	—	2	2	no	—
466	C₂×C₄×C₄₇	—	2	1	no	—
467	C₂×C₄×C₄₇	—	2	1	no	—
468	C₂×C₄×C₄₇	—	2	1	no	—
469	C₂×C₄×C₄₇	—	2	1	no	—
470	C₂×C₄×C₄₇	—	2	1	no	—
471	C₂×C₄×C₄₇	—	2	1	no	—
472	C₂×C₄×C₄₇	—	2	1	no	—
473	C₂×C₄×C₄₇	—	2	1	no	—
474	C₂×C₄×C₄₇	—	4	1	no	—
475	C₂×C₄×C₄₇	—	4	2	no	—
476	C₂×C₄×C₄₇	—	4	2	no	—
477	C₂×C₄×C₄₇	—	4	2	no	—
478	C₂×C₄×C₄₇	—	4	2	no	—
479	C₂×C₄×C₄₇	—	8	1	no	—
480	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
481	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
482	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
483	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
484	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
485	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
486	C₂²⋊D₄₇	—	2	4	no	—
487	C₂²⋊D₄₇	—	4	4	no	—
488	C₂×Dic₄₇	—	2	2	no	—
489	C₂×Dic₄₇	—	2	2	no	—
490	C₂×Dic₄₇	—	2	2	no	—
491	C₂×Dic₄₇	—	2	2	no	—
492	C₂×Dic₄₇	—	4	4	no	—
493	C₂×Dic₄₇	—	4	4	no	—
494	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
495	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
496	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
497	D₁₈₈	—	2	2	no	—
498	C₄×D₄₇	—	2	2	no	—
499	C₄×D₄₇	—	2	2	no	—
500	C₄×D₄₇	—	2	4	no	—
501	C₄×D₄₇	—	4	2	no	—
502	C₄×D₄₇	—	4	4	no	—
503	C₄×D₄₇	—	8	2	no	—
504	Dic₉₄	—	2	2	no	—
505	Dic₉₄	—	2	2	no	—
506	Dic₉₄	—	2	2	no	—
507	Dic₉₄	—	2	2	no	—
508	Dic₉₄	—	4	4	no	—
509	Dic₉₄	—	4	2	no	—
510	Dic₉₄	—	4	4	no	—
511	Dic₉₄	—	8	2	no	—
512	Dic₉₄	—	8	1	no	—
513	Dic₉₄	#137	1	4	yes	complemented
514	C₈×C₄₇	—	2	1	no	—
515	C₈×C₄₇	—	2	1	no	—
516	C₈×C₄₇	—	2	1	no	—
517	C₈×C₄₇	C₂×#41	1	2	yes	—
518	C₄₇⋊C₈	—	2	2	no	—
519	C₄₇⋊C₈	—	2	2	no	—
520	#61470	—	47	1	no	maximal, Sylow
521	C₂²×C₄₇	—	2	1	no	—
522	C₂²×C₄₇	—	2	2	no	—
523	C₂²×C₄₇	—	2	1	no	—
524	C₂²×C₄₇	—	2	1	no	—
525	C₂²×C₄₇	—	4	1	no	—
526	C₂²×C₄₇	—	4	1	no	—
527	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
528	C₂×D₄₇	—	2	2	no	—
529	C₂×D₄₇	—	2	2	no	—
530	C₂×D₄₇	—	2	2	no	—
531	C₄×C₄₇	—	2	1	no	—
532	C₄×C₄₇	—	2	1	no	—
533	C₄×C₄₇	—	2	2	no	—
534	C₄×C₄₇	—	2	1	no	—
535	C₄×C₄₇	—	2	1	no	—
536	C₄×C₄₇	—	4	1	no	—
537	C₄×C₄₇	—	4	1	no	—
538	C₄×C₄₇	—	4	1	no	—
539	C₄×C₄₇	—	4	1	no	—
540	C₄×C₄₇	—	4	1	no	—
541	C₄×C₄₇	—	4	1	no	—
542	C₄×C₄₇	C₂×#137	1	2	yes	—
543	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
544	C₄×C₄₇	#585	1	1	yes	characteristic
545	Dic₄₇	—	2	2	no	—
546	Dic₄₇	—	2	2	no	—
547	Dic₄₇	—	4	2	no	—
548	Dic₄₇	—	4	2	no	—
549	Dic₄₇	—	4	2	no	—
550	Dic₄₇	—	4	2	no	—
551	Dic₄₇	C₂×#137	1	4	yes	—
552	#3482	—	47	1	no	—
553	Q₈×#41	—	47	1	no	—
554	#3395	—	47	1	no	—
555	Q₈×SD₁₆	—	47	1	no	—
556	#3363	—	47	1	no	—
557	#3359	—	47	1	no	—
558	#3356	—	47	1	no	—
559	#3356	—	47	2	no	—
560	#3331	—	47	1	no	—
561	#3331	—	47	2	no	—
562	#3328	—	47	1	no	—
563	#3328	—	47	2	no	—
564	#3276	—	47	1	no	—
565	#3276	—	47	2	no	—
566	#3185	—	47	2	no	—
567	#3185	—	47	1	no	—
568	#3116	—	47	2	no	—
569	#3116	—	47	1	no	—
570	#3113	—	47	2	no	—
571	#3113	—	47	1	no	—
572	#2971	—	47	1	no	—
573	C₄×#137	—	47	2	no	—
574	C₄×#137	D₄₇	1	1	yes	characteristic, complemented
575	C₂×C₄₇	—	4	1	no	—
576	C₂×C₄₇	—	4	2	no	—
577	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
578	C₂×C₄₇	C₂²×#137	1	1	yes	characteristic
579	C₂×C₄₇	#3586	1	1	yes	characteristic
580	D₄₇	—	4	2	no	—
581	C₂×#137	—	47	2	no	—
582	C₂×#137	C₂×D₄₇	1	1	yes	characteristic
583	Q₈²	—	47	1	no	—
584	#557	—	47	1	no	—
585	#557	—	47	1	no	—
586	#557	—	94	1	no	—
587	#556	—	47	1	no	—
588	#556	—	47	2	no	—
589	#554	—	47	1	no	—
590	#554	—	47	2	no	—
591	#554	—	94	2	no	—
592	#554	—	94	1	no	—
593	#552	—	94	2	no	—
594	#552	—	94	1	no	—
595	D₄×Q₈	—	47	1	no	—
596	D₄×Q₈	—	47	2	no	—
597	D₄×Q₈	—	47	1	no	—
598	#548	—	94	1	no	—
599	#547	—	47	2	no	—
600	#547	—	47	1	no	—
601	#533	—	47	2	no	—
602	#533	—	47	2	no	—
603	#533	—	47	1	no	—
604	#533	—	47	1	no	—
605	#533	—	94	1	no	—
606	#533	—	94	2	no	—
607	#529	—	94	1	no	—
608	#529	—	94	2	no	—
609	C₄×#41	—	47	1	no	—
610	C₄×#41	—	47	2	no	—
611	C₄×#41	—	94	1	no	—
612	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
613	C₂×C₄×Q₈	—	47	2	no	—
614	C₂×C₄×Q₈	—	94	1	no	—
615	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
616	#498	—	47	2	no	—
617	#498	—	47	1	no	—
618	#494	—	47	2	no	—
619	#494	—	47	1	no	—
620	#487	—	47	2	no	—
621	#487	—	47	2	no	—
622	#487	—	47	1	no	—
623	#487	—	47	1	no	—
624	#485	—	47	2	no	—
625	#485	—	47	2	no	—
626	#485	—	47	2	no	—
627	#483	—	47	2	no	—
628	#483	—	47	2	no	—
629	#483	—	47	2	no	—
630	#477	—	47	1	no	—
631	#477	—	47	2	no	—
632	#476	—	47	1	no	—
633	#476	—	47	2	no	—
634	#475	—	47	1	no	—
635	#475	—	47	1	no	—
636	#475	—	47	2	no	—
637	#475	—	47	2	no	—
638	#470	—	47	2	no	—
639	#470	—	47	2	no	—
640	#470	—	47	2	no	—
641	#470	—	47	2	no	—
642	#470	—	47	2	no	—
643	#470	—	47	2	no	—
644	#462	—	47	2	no	—
645	#462	—	47	1	no	—
646	#462	—	47	1	no	—
647	#462	—	47	1	no	—
648	#462	—	47	2	no	—
649	#462	—	47	2	no	—
650	#461	—	47	2	no	—
651	#461	—	47	1	no	—
652	#452	—	47	2	no	—
653	#452	—	47	2	no	—
654	#452	—	47	2	no	—
655	#451	—	47	2	no	—
656	#451	—	47	2	no	—
657	#451	—	47	2	no	—
658	C₈×Q₈	—	47	1	no	—
659	C₈×Q₈	—	47	1	no	—
660	#441	—	47	2	no	—
661	#441	—	47	2	no	—
662	#441	—	47	2	no	—
663	#441	—	47	2	no	—
664	#441	—	47	2	no	—
665	#441	C₂×D₄₇	1	1	yes	characteristic
666	#441	C₂×D₄₇	1	1	yes	characteristic
667	#440	—	47	2	no	—
668	#440	C₂×D₄₇	1	1	yes	characteristic
669	#440	C₂×D₄₇	1	1	yes	characteristic
670	C₄×Q₁₆	—	47	2	no	—
671	C₄×Q₁₆	—	47	2	no	—
672	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
673	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
674	C₄×SD₁₆	—	47	2	no	—
675	C₄×SD₁₆	—	47	2	no	—
676	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
677	C₄×SD₁₆	C₂×D₄₇	1	1	yes	characteristic
678	#436	—	47	2	no	—
679	#436	—	47	2	no	—
680	#436	—	47	1	no	—
681	#436	—	47	1	no	—
682	#432	—	47	1	no	—
683	#432	—	47	2	no	—
684	#428	—	47	2	no	—
685	#428	C₂×D₄₇	1	1	yes	characteristic
686	#419	—	47	2	no	—
687	#419	C₂×D₄₇	1	1	yes	characteristic
688	#417	—	47	2	no	—
689	#417	C₂×D₄₇	1	1	yes	characteristic
690	C₄×M₁₆	—	47	2	no	—
691	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
692	C₄₇	#61470	1	1	yes	characteristic, complemented, Sylow
693	C₂×#41	—	47	1	no	—
694	C₂×#41	—	47	2	no	—
695	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
696	C₂²×Q₈	—	47	2	no	—
697	C₂²×Q₈	—	94	1	no	—
698	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
699	#137	—	2	4	no	—
700	#137	—	94	8	no	—
701	C₂×Q₁₆	—	47	2	no	—
702	C₂×Q₁₆	—	47	2	no	—
703	C₂×Q₁₆	—	47	2	no	—
704	C₂×Q₁₆	—	47	2	no	—
705	C₂×Q₁₆	—	47	2	no	—
706	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
707	C₂×Q₁₆	C₂²×D₄₇	1	1	yes	characteristic
708	C₂×SD₁₆	—	47	2	no	—
709	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
710	C₂×SD₁₆	C₂²×D₄₇	1	1	yes	characteristic
711	C₂×M₁₆	—	47	2	no	—
712	C₂×M₁₆	—	47	2	no	—
713	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
714	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
715	C₄⋊Q₈	—	47	2	no	—
716	C₄⋊Q₈	—	47	2	no	—
717	C₄⋊Q₈	—	47	2	no	—
718	C₄⋊Q₈	—	47	2	no	—
719	C₄⋊Q₈	—	47	1	no	—
720	C₄⋊Q₈	—	47	1	no	—
721	C₄⋊Q₈	—	47	1	no	—
722	C₄⋊Q₈	—	47	1	no	—
723	C₄⋊Q₈	—	94	1	no	—
724	C₄⋊Q₈	—	94	1	no	—
725	C₄⋊Q₈	—	94	2	no	—
726	C₄⋊Q₈	—	94	2	no	—
727	#126	—	94	2	no	—
728	#126	—	94	2	no	—
729	#126	—	94	2	no	—
730	#125	—	94	1	no	—
731	#125	—	94	1	no	—
732	#125	—	94	1	no	—
733	#125	—	94	2	no	—
734	#125	—	94	2	no	—
735	#125	—	94	2	no	—
736	#125	—	94	2	no	—
737	#125	—	94	2	no	—
738	#125	—	94	1	no	—
739	#125	—	94	1	no	—
740	#124	—	94	1	no	—
741	#124	—	94	2	no	—
742	#123	—	94	2	no	—
743	#123	—	94	2	no	—
744	#123	—	94	2	no	—
745	C₂²⋊Q₈	—	47	2	no	—
746	C₂²⋊Q₈	—	47	2	no	—
747	C₂²⋊Q₈	—	47	2	no	—
748	C₂²⋊Q₈	—	47	2	no	—
749	C₂²⋊Q₈	—	47	2	no	—
750	C₂²⋊Q₈	—	47	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	—	94	2	no	—
756	C₂²⋊Q₈	—	94	2	no	—
757	C₂²⋊Q₈	—	94	2	no	—
758	C₂²⋊Q₈	—	94	2	no	—
759	C₂²⋊Q₈	—	94	2	no	—
760	C₂²⋊Q₈	—	94	1	no	—
761	C₂²⋊Q₈	—	94	1	no	—
762	C₂²⋊Q₈	—	94	1	no	—
763	#121	—	94	1	no	—
764	#121	—	94	2	no	—
765	C₄×Q₈	—	2	1	no	—
766	C₄×Q₈	—	2	1	no	—
767	C₄×Q₈	—	47	1	no	—
768	C₄×Q₈	—	47	1	no	—
769	C₄×Q₈	—	47	2	no	—
770	C₄×Q₈	—	47	2	no	—
771	C₄×Q₈	—	47	2	no	—
772	C₄×Q₈	—	47	2	no	—
773	C₄×Q₈	—	47	2	no	—
774	C₄×Q₈	—	94	2	no	—
775	C₄×Q₈	—	94	2	no	—
776	C₄×Q₈	—	94	2	no	—
777	C₄×Q₈	—	94	2	no	—
778	C₄×Q₈	—	94	1	no	—
779	C₄×Q₈	—	94	1	no	—
780	C₄×Q₈	—	94	1	no	—
781	C₄×Q₈	—	94	1	no	—
782	C₄×Q₈	—	94	2	no	—
783	C₄×Q₈	—	94	1	no	—
784	C₄×Q₈	—	94	1	no	—
785	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
786	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
787	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
788	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
789	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
790	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
791	C₄×D₄	—	2	1	no	—
792	C₄×D₄	—	2	1	no	—
793	C₄×D₄	—	47	2	no	—
794	C₄×D₄	—	47	2	no	—
795	C₄×D₄	—	47	2	no	—
796	C₄×D₄	—	47	1	no	—
797	C₄×D₄	—	47	1	no	—
798	C₄×D₄	—	94	1	no	—
799	C₄×D₄	—	94	1	no	—
800	C₄×D₄	—	94	2	no	—
801	C₄×D₄	—	94	2	no	—
802	C₄×D₄	—	94	2	no	—
803	C₄×D₄	—	94	2	no	—
804	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
805	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
806	#117	—	2	1	no	—
807	#117	—	47	1	no	—
808	#117	—	47	2	no	—
809	#117	—	47	2	no	—
810	#117	—	94	2	no	—
811	#117	—	94	2	no	—
812	#117	—	94	2	no	—
813	#117	—	94	1	no	—
814	#117	—	94	1	no	—
815	#117	C₂²×D₄₇	1	1	yes	characteristic
816	C₂×C₄⋊C₄	—	2	1	no	—
817	C₂×C₄⋊C₄	—	47	2	no	—
818	C₂×C₄⋊C₄	—	94	2	no	—
819	C₂×C₄⋊C₄	—	94	2	no	—
820	C₂×C₄⋊C₄	—	94	1	no	—
821	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
822	C₂×C₄²	—	2	1	no	—
823	C₂×C₄²	—	2	1	no	—
824	C₂×C₄²	—	47	2	no	—
825	C₂×C₄²	—	94	2	no	—
826	C₂×C₄²	—	94	2	no	—
827	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
828	#107	—	47	2	no	—
829	#107	C₂²×D₄₇	1	1	yes	characteristic
830	#107	C₂²×D₄₇	1	1	yes	characteristic
831	#106	—	47	2	no	—
832	#106	—	47	2	no	—
833	#106	—	47	2	no	—
834	#106	—	47	2	no	—
835	#106	—	47	2	no	—
836	#106	C₂²×D₄₇	1	1	yes	characteristic
837	#106	C₂²×D₄₇	1	1	yes	characteristic
838	C₄⋊C₈	—	47	2	no	—
839	C₄⋊C₈	—	47	2	no	—
840	C₄⋊C₈	—	47	1	no	—
841	C₄⋊C₈	—	47	1	no	—
842	#103	—	47	2	no	—
843	#103	—	47	2	no	—
844	#103	—	47	2	no	—
845	#103	—	47	2	no	—
846	#103	—	47	2	no	—
847	#103	—	47	2	no	—
848	#103	—	47	2	no	—
849	#103	—	47	2	no	—
850	#103	—	47	2	no	—
851	#103	—	47	2	no	—
852	#103	—	47	2	no	—
853	#103	C₂²×D₄₇	1	1	yes	characteristic
854	#103	C₂²×D₄₇	1	1	yes	characteristic
855	#103	C₂²×D₄₇	1	1	yes	characteristic
856	#103	C₂²×D₄₇	1	1	yes	characteristic
857	#103	C₂²×D₄₇	1	1	yes	characteristic
858	#103	C₂²×D₄₇	1	1	yes	characteristic
859	#102	—	47	2	no	—
860	#102	C₂²×D₄₇	1	1	yes	characteristic
861	#102	C₂²×D₄₇	1	1	yes	characteristic
862	C₂²⋊C₈	—	47	2	no	—
863	C₂²⋊C₈	—	47	2	no	—
864	C₂²⋊C₈	—	47	2	no	—
865	#97	—	47	2	no	—
866	#97	C₂²×D₄₇	1	1	yes	characteristic
867	#97	C₂²×D₄₇	1	1	yes	characteristic
868	C₄×C₈	—	47	2	no	—
869	C₄×C₈	—	47	2	no	—
870	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
871	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
872	#41	—	2	2	no	—
873	#41	—	4	1	no	—
874	#41	—	94	4	no	—
875	#41	—	94	4	no	—
876	#41	—	188	2	no	—
877	C₂×Q₈	—	2	1	no	—
878	C₂×Q₈	—	2	2	no	—
879	C₂×Q₈	—	4	1	no	—
880	C₂×Q₈	—	47	1	no	—
881	C₂×Q₈	—	47	2	no	—
882	C₂×Q₈	—	47	2	no	—
883	C₂×Q₈	—	94	2	no	—
884	C₂×Q₈	—	94	2	no	—
885	C₂×Q₈	—	94	2	no	—
886	C₂×Q₈	—	94	1	no	—
887	C₂×Q₈	—	94	1	no	—
888	C₂×Q₈	—	94	4	no	—
889	C₂×Q₈	—	188	4	no	—
890	C₂×Q₈	—	188	2	no	—
891	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
892	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
893	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
894	C₂×D₄	—	2	1	no	—
895	C₂×D₄	—	47	2	no	—
896	C₂×D₄	—	47	1	no	—
897	C₂×D₄	—	94	2	no	—
898	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
899	C₂²×C₄	—	2	1	no	—
900	C₂²×C₄	—	2	1	no	—
901	C₂²×C₄	—	2	1	no	—
902	C₂²×C₄	—	2	1	no	—
903	C₂²×C₄	—	2	1	no	—
904	C₂²×C₄	—	47	2	no	—
905	C₂²×C₄	—	47	2	no	—
906	C₂²×C₄	—	47	2	no	—
907	C₂²×C₄	—	94	2	no	—
908	C₂²×C₄	—	94	2	no	—
909	C₂²×C₄	—	94	2	no	—
910	C₂²×C₄	—	94	2	no	—
911	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
912	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
913	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
914	Q₁₆	—	2	2	no	—
915	Q₁₆	—	2	2	no	—
916	Q₁₆	—	94	4	no	—
917	Q₁₆	—	94	4	no	—
918	Q₁₆	—	188	2	no	—
919	Q₁₆	—	188	2	no	—
920	Q₁₆	—	188	2	no	—
921	SD₁₆	—	2	2	no	—
922	SD₁₆	—	94	4	no	—
923	SD₁₆	#10625350	1	4	yes	complemented
924	M₁₆	—	2	2	no	—
925	M₁₆	—	4	1	no	—
926	M₁₆	—	94	4	no	—
927	M₁₆	—	188	2	no	—
928	C₂×C₈	—	47	2	no	—
929	C₂×C₈	—	47	2	no	—
930	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
931	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
932	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
933	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
934	C₄⋊C₄	—	2	1	no	—
935	C₄⋊C₄	—	2	1	no	—
936	C₄⋊C₄	—	2	1	no	—
937	C₄⋊C₄	—	2	1	no	—
938	C₄⋊C₄	—	2	1	no	—
939	C₄⋊C₄	—	2	1	no	—
940	C₄⋊C₄	—	2	1	no	—
941	C₄⋊C₄	—	47	2	no	—
942	C₄⋊C₄	—	47	2	no	—
943	C₄⋊C₄	—	47	1	no	—
944	C₄⋊C₄	—	47	1	no	—
945	C₄⋊C₄	—	47	2	no	—
946	C₄⋊C₄	—	47	2	no	—
947	C₄⋊C₄	—	94	2	no	—
948	C₄⋊C₄	—	94	2	no	—
949	C₄⋊C₄	—	94	2	no	—
950	C₄⋊C₄	—	94	2	no	—
951	C₄⋊C₄	—	94	2	no	—
952	C₄⋊C₄	—	94	2	no	—
953	C₄⋊C₄	—	94	2	no	—
954	C₄⋊C₄	—	94	2	no	—
955	C₄⋊C₄	—	94	2	no	—
956	C₄⋊C₄	—	94	2	no	—
957	C₄⋊C₄	—	94	2	no	—
958	C₄⋊C₄	—	94	2	no	—
959	C₄⋊C₄	—	94	2	no	—
960	C₄⋊C₄	—	94	2	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	—	94	1	no	—
966	C₄⋊C₄	—	94	1	no	—
967	C₄⋊C₄	—	94	1	no	—
968	C₄⋊C₄	—	94	1	no	—
969	C₄⋊C₄	—	94	1	no	—
970	C₄⋊C₄	—	94	1	no	—
971	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
972	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
973	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
974	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
975	C₂²⋊C₄	—	2	1	no	—
976	C₂²⋊C₄	—	2	1	no	—
977	C₂²⋊C₄	—	2	1	no	—
978	C₂²⋊C₄	—	47	2	no	—
979	C₂²⋊C₄	—	47	2	no	—
980	C₂²⋊C₄	—	47	2	no	—
981	C₂²⋊C₄	—	94	2	no	—
982	C₂²⋊C₄	—	94	2	no	—
983	C₂²⋊C₄	—	94	2	no	—
984	C₂²⋊C₄	—	94	2	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	C₄²	—	2	1	no	—
990	C₄²	—	2	1	no	—
991	C₄²	—	2	1	no	—
992	C₄²	—	2	1	no	—
993	C₄²	—	2	1	no	—
994	C₄²	—	2	1	no	—
995	C₄²	—	2	1	no	—
996	C₄²	—	47	2	no	—
997	C₄²	—	47	2	no	—
998	C₄²	—	47	2	no	—
999	C₄²	—	94	2	no	—
1000	C₄²	—	94	2	no	—
1001	C₄²	—	94	2	no	—
1002	C₄²	—	94	2	no	—
1003	C₄²	—	94	2	no	—
1004	C₄²	—	94	2	no	—
1005	C₄²	D₄×D₄₇	1	1	yes	characteristic
1006	C₄²	D₄×D₄₇	1	1	yes	characteristic
1007	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1008	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1009	C₂³	—	2	1	no	—
1010	C₂³	—	47	2	no	—
1011	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1012	Q₈	—	2	1	no	—
1013	Q₈	—	2	1	no	—
1014	Q₈	—	2	1	no	—
1015	Q₈	—	2	1	no	—
1016	Q₈	—	2	1	no	—
1017	Q₈	—	4	2	no	—
1018	Q₈	—	47	4	no	—
1019	Q₈	—	94	2	no	—
1020	Q₈	—	94	2	no	—
1021	Q₈	—	94	2	no	—
1022	Q₈	—	94	2	no	—
1023	Q₈	—	376	1	no	—
1024	Q₈	—	376	2	no	—
1025	Q₈	—	188	4	no	—
1026	Q₈	—	188	4	no	—
1027	Q₈	—	188	2	no	—
1028	Q₈	C₂×#10625350	1	2	yes	—
1029	D₄	—	2	1	no	—
1030	D₄	—	4	2	no	—
1031	D₄	—	94	4	no	—
1032	D₄	—	94	2	no	—
1033	D₄	—	188	4	no	—
1034	D₄	C₂×#10625350	1	2	yes	—
1035	C₂×C₄	—	2	1	no	—
1036	C₂×C₄	—	2	2	no	—
1037	C₂×C₄	—	2	1	no	—
1038	C₂×C₄	—	2	1	no	—
1039	C₂×C₄	—	2	1	no	—
1040	C₂×C₄	—	2	1	no	—
1041	C₂×C₄	—	2	1	no	—
1042	C₂×C₄	—	2	1	no	—
1043	C₂×C₄	—	2	1	no	—
1044	C₂×C₄	—	2	1	no	—
1045	C₂×C₄	—	4	1	no	—
1046	C₂×C₄	—	4	2	no	—
1047	C₂×C₄	—	4	2	no	—
1048	C₂×C₄	—	4	2	no	—
1049	C₂×C₄	—	4	2	no	—
1050	C₂×C₄	—	8	1	no	—
1051	C₂×C₄	—	47	2	no	—
1052	C₂×C₄	—	47	2	no	—
1053	C₂×C₄	—	47	2	no	—
1054	C₂×C₄	—	94	4	no	—
1055	C₂×C₄	—	94	2	no	—
1056	C₂×C₄	—	94	2	no	—
1057	C₂×C₄	—	94	2	no	—
1058	C₂×C₄	—	94	2	no	—
1059	C₂×C₄	—	94	2	no	—
1060	C₂×C₄	—	94	2	no	—
1061	C₂×C₄	—	376	2	no	—
1062	C₂×C₄	—	188	2	no	—
1063	C₂×C₄	—	188	4	no	—
1064	C₂×C₄	—	188	4	no	—
1065	C₂×C₄	—	188	4	no	—
1066	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1067	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1068	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1069	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1070	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1071	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1072	C₈	—	2	1	no	—
1073	C₈	—	2	1	no	—
1074	C₈	—	2	1	no	—
1075	C₈	—	94	2	no	—
1076	C₈	—	94	2	no	—
1077	C₈	C₂×#10625350	1	2	yes	—
1078	C₂²	—	2	1	no	—
1079	C₂²	—	2	1	no	—
1080	C₂²	—	2	2	no	—
1081	C₂²	—	2	1	no	—
1082	C₂²	—	4	1	no	—
1083	C₂²	—	4	1	no	—
1084	C₂²	—	94	2	no	—
1085	C₂²	—	94	2	no	—
1086	C₂²	—	94	2	no	—
1087	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1088	C₄	—	2	1	no	—
1089	C₄	—	2	1	no	—
1090	C₄	—	2	2	no	—
1091	C₄	—	2	1	no	—
1092	C₄	—	2	1	no	—
1093	C₄	—	4	1	no	—
1094	C₄	—	4	1	no	—
1095	C₄	—	4	1	no	—
1096	C₄	—	4	1	no	—
1097	C₄	—	4	1	no	—
1098	C₄	—	4	1	no	—
1099	C₄	—	47	4	no	—
1100	C₄	—	94	2	no	—
1101	C₄	—	94	2	no	—
1102	C₄	—	188	2	no	—
1103	C₄	—	188	2	no	—
1104	C₄	—	188	2	no	—
1105	C₄	—	188	2	no	—
1106	C₄	#137×D₄₇	1	2	yes	—
1107	C₄	C₂²×#10625350	1	1	yes	characteristic
1108	C₄	#15689959	1	1	yes	characteristic
1109	C₂	—	4	1	no	—
1110	C₂	—	4	2	no	—
1111	C₂	—	188	2	no	—
1112	C₂	D₄×#10625350	1	1	yes	characteristic
1113	C₂	C₂×#137×D₄₇	1	1	yes	characteristic
1114	C₂	#20258172	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄×#137×C₄₇	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#20257003	C₂
hypercenter	C₄×#137	D₄₇
hypocenter	C₄₇	#61470
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₄×#137

Complements

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

N	H ≅ G/N	type
2. Q₈×#10625350	C₂	semidirect
3. #20256393	C₂	semidirect
4. SD₁₆×Dic₉₄	C₂	semidirect
5. #20256064	C₂	semidirect
6. #20256028	C₂	semidirect
7. #20256005	C₂	semidirect
8. #20255999	C₂	semidirect
9. #20255706	C₂	semidirect
10. #20255700	C₂	semidirect
11. #20255673	C₂	semidirect
12. #20255667	C₂	semidirect
13. #20255035	C₂	semidirect
14. #20255028	C₂	semidirect
15. #20254133	C₂	semidirect
16. #20254130	C₂	semidirect
17. #20253550	C₂	semidirect
18. #20253546	C₂	semidirect
19. #20253518	C₂	semidirect
20. #20253516	C₂	semidirect
21. #20252406	C₂	semidirect
22. #20252210	C₂	semidirect
23. C₄×#137×C₄₇	C₂	semidirect
359. SD₁₆×C₄₇	#41	semidirect
513. Dic₉₄	#137	semidirect
574. C₄×#137	D₄₇	semidirect
692. C₄₇	#61470	semidirect
923. SD₁₆	#10625350	semidirect

Maximal subgroups

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

subgroup	index
#20257003	2
Q₈×#10625350	2
#20256393	2
SD₁₆×Dic₉₄	2
#20256064	2
#20256028	2
#20256005	2
#20255999	2
#20255706	2
#20255700	2
#20255673	2
#20255667	2
#20255035	2
#20255028	2
#20254133	2
#20254130	2
#20253550	2
#20253546	2
#20253518	2
#20253516	2
#20252406	2
#20252210	2
C₄×#137×C₄₇	2
#61470	47