Subgroups — #27088990

Order 12032.

1700 conjugacy classes of subgroups.

The subgroup lattice has 1100 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257209	C₂	1	1	yes	maximal, characteristic, complemented
2	#20256804	C₂	1	1	yes	maximal, characteristic
3	#20254691	C₂	1	2	yes	maximal, complemented
4	#20254676	C₂	1	2	yes	maximal, complemented
5	#20254648	C₂	1	2	yes	maximal, complemented
6	#20254640	C₂	1	2	yes	maximal, complemented
7	#20254633	C₂	1	2	yes	maximal, complemented
8	#20254576	C₂	1	2	yes	maximal, complemented
9	#20254560	C₂	1	2	yes	maximal, complemented
10	#20254523	C₂	1	2	yes	maximal, complemented
11	#20253928	C₂	1	1	yes	maximal, characteristic, complemented
12	#20253920	C₂	1	1	yes	maximal, characteristic, complemented
13	#20253746	C₂	1	1	yes	maximal, characteristic, complemented
14	#20253746	C₂	1	1	yes	maximal, characteristic, complemented
15	#20253375	C₂	1	1	yes	maximal, characteristic, complemented
16	#20253364	C₂	1	1	yes	maximal, characteristic, complemented
17	#20253349	C₂	1	1	yes	maximal, characteristic, complemented
18	#20253349	C₂	1	1	yes	maximal, characteristic, complemented
19	#20253210	C₂	1	1	yes	maximal, characteristic, complemented
20	#20253181	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#15689424	C₂	1	1	yes	maximal, characteristic, complemented
22	#20252053	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3076	C₂	1	1	yes	maximal, characteristic, complemented
24	#15689851	—	2	1	no	—
25	#15689851	—	2	1	no	—
26	#15689833	—	2	1	no	—
27	#15689833	—	2	1	no	—
28	#15689827	—	2	2	no	—
29	#15689827	—	2	2	no	—
30	#15689751	C₂²	1	1	yes	characteristic
31	#15689751	C₂²	1	1	yes	characteristic
32	#15689751	C₂²	1	1	yes	characteristic
33	#15689750	C₂²	1	2	yes	complemented
34	#15689750	C₂²	1	2	yes	complemented
35	#15689745	C₂²	1	2	yes	—
36	#15689744	—	2	1	no	—
37	#15689728	—	2	1	no	—
38	#15689724	C₂²	1	2	yes	—
39	#15689706	—	2	2	no	—
40	#15689701	C₂²	1	1	yes	characteristic
41	#15689692	C₂²	1	1	yes	characteristic
42	#15689687	C₂²	1	1	yes	characteristic
43	#15689679	C₂²	1	2	yes	complemented
44	#15689673	—	2	1	no	—
45	#15689670	C₂²	1	2	yes	—
46	#15689660	C₂²	1	2	yes	—
47	#15689657	—	2	1	no	—
48	C₂×#13094016	C₂²	1	1	yes	characteristic
49	#125×D₄₇	C₂²	1	2	yes	complemented
50	#15689632	—	2	2	no	—
51	#15689603	C₂²	1	1	yes	characteristic
52	#15689603	C₂²	1	1	yes	characteristic
53	C₄×#10625350	C₂²	1	1	yes	characteristic
54	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
55	#15689531	C₂²	1	2	yes	complemented
56	#15689531	C₂²	1	2	yes	complemented
57	#15689530	C₂²	1	2	yes	complemented
58	#15689530	C₂²	1	2	yes	complemented
59	#15689527	C₂²	1	2	yes	complemented
60	#15689524	C₂²	1	2	yes	complemented
61	#15689523	C₂²	1	2	yes	complemented
62	#15689520	C₂²	1	2	yes	complemented
63	#15689486	C₂²	1	2	yes	—
64	#15689486	C₂²	1	2	yes	—
65	#15689484	C₂²	1	2	yes	—
66	#15689484	C₂²	1	2	yes	—
67	#15689479	C₂²	1	2	yes	—
68	#15689479	C₂²	1	2	yes	—
69	#15689468	C₂²	1	2	yes	—
70	#15689468	C₂²	1	2	yes	—
71	#15689463	C₂²	1	2	yes	complemented
72	#15689462	C₂²	1	2	yes	complemented
73	#15689457	C₂²	1	2	yes	complemented
74	#15689452	C₂²	1	2	yes	complemented
75	#15689450	C₂²	1	2	yes	—
76	#15689450	C₂²	1	2	yes	—
77	#15689449	C₂²	1	2	yes	—
78	#15689449	C₂²	1	2	yes	—
79	#15689446	C₂²	1	2	yes	complemented
80	#15689445	C₂²	1	2	yes	complemented
81	#15689443	C₂²	1	2	yes	—
82	#15689443	C₂²	1	2	yes	—
83	#15689440	C₂²	1	2	yes	complemented
84	#15689438	C₂²	1	2	yes	—
85	#15689438	C₂²	1	2	yes	—
86	#15689435	C₂²	1	2	yes	complemented
87	#15689430	C₂²	1	2	yes	complemented
88	#15689430	C₂²	1	2	yes	complemented
89	#15689424	C₂²	1	2	yes	—
90	#15689424	C₂²	1	2	yes	—
91	#15689424	C₂²	1	2	yes	—
92	#15689424	C₂²	1	2	yes	—
93	#15689423	C₂²	1	2	yes	complemented
94	#15689423	C₂²	1	2	yes	complemented
95	#15689420	C₂²	1	2	yes	—
96	#15689420	C₂²	1	2	yes	—
97	#15689410	C₂²	1	2	yes	—
98	#15689400	C₂²	1	2	yes	—
99	#15689183	C₂²	1	2	yes	complemented
100	#15689183	C₂²	1	2	yes	complemented
101	#15689179	C₂²	1	2	yes	complemented
102	#15689175	C₂²	1	2	yes	complemented
103	#15689166	C₂²	1	1	yes	characteristic
104	#15689166	C₂²	1	1	yes	characteristic
105	#15689166	C₂²	1	1	yes	characteristic
106	#15689166	C₂²	1	1	yes	characteristic
107	C₂×#13093958	C₂²	1	1	yes	characteristic
108	C₂×#13093956	C₂²	1	1	yes	characteristic
109	#15689147	C₂²	1	1	yes	characteristic
110	#15689127	C₂²	1	1	yes	characteristic
111	#15689127	C₂²	1	1	yes	characteristic
112	#15689124	C₂²	1	1	yes	characteristic
113	#15689124	C₂²	1	1	yes	characteristic
114	C₂×#13093946	C₂²	1	1	yes	characteristic
115	C₂×#13093946	C₂²	1	1	yes	characteristic
116	#15689089	C₂²	1	1	yes	characteristic
117	#15689089	C₂²	1	1	yes	characteristic
118	#15689078	C₂²	1	1	yes	characteristic
119	#15689078	C₂²	1	1	yes	characteristic
120	C₄₇×#533	C₂²	1	1	yes	characteristic
121	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
122	C₄₇×#479	C₂²	1	1	yes	characteristic, complemented
123	C₄₇×#479	C₂²	1	1	yes	characteristic, complemented
124	C₄₇×#478	C₂²	1	1	yes	characteristic, complemented
125	C₄₇×#478	C₂²	1	1	yes	characteristic, complemented
126	C₄₇×#477	C₂²	1	1	yes	characteristic, complemented
127	C₄₇×#476	C₂²	1	1	yes	characteristic, complemented
128	C₄₇×#475	C₂²	1	1	yes	characteristic, complemented
129	C₄₇×#474	C₂²	1	1	yes	characteristic, complemented
130	C₄₇×#427	C₂²	1	1	yes	characteristic
131	C₄₇×#427	C₂²	1	1	yes	characteristic
132	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
133	C₄₇×#416	C₂²	1	1	yes	characteristic
134	C₄₇×#416	C₂²	1	1	yes	characteristic
135	C₂×#10625350	—	2	2	no	—
136	C₂×#10625350	C₂³	1	1	yes	characteristic
137	C₂²×D₁₈₈	C₂³	1	1	yes	characteristic
138	C₂²×C₄×D₄₇	—	2	1	no	—
139	C₂×#10625329	C₂³	1	1	yes	characteristic
140	C₂×#10625329	C₂³	1	1	yes	characteristic
141	#13094024	—	2	1	no	—
142	#13094024	—	2	1	no	—
143	#13094024	—	2	1	no	—
144	#13094023	C₂³	1	2	yes	—
145	#13094023	C₂³	1	2	yes	—
146	#13094023	C₂³	1	2	yes	—
147	#13094022	—	2	2	no	—
148	#13094022	—	2	2	no	—
149	#13094021	—	2	1	no	—
150	#13094020	C₂³	1	2	yes	—
151	#13094019	—	2	2	no	—
152	#13094018	—	2	2	no	—
153	#13094016	—	2	1	no	—
154	#13094016	—	2	1	no	—
155	#13094016	—	2	1	no	—
156	#13094016	—	2	1	no	—
157	#13094016	—	2	1	no	—
158	#13094016	C₂³	1	2	yes	—
159	#13094016	C₂³	1	2	yes	—
160	#13094015	C₂³	1	2	yes	—
161	#13094015	C₂³	1	2	yes	—
162	#13094015	C₂³	1	2	yes	—
163	#13094014	—	2	2	no	—
164	#13094014	—	2	2	no	—
165	#13094014	—	2	2	no	—
166	#13094014	—	2	2	no	—
167	#13094013	C₂³	1	2	yes	—
168	#13094012	—	2	1	no	—
169	#13094012	—	2	2	no	—
170	#13094010	—	2	2	no	—
171	#13094009	—	2	2	no	—
172	#13094009	—	2	2	no	—
173	#13094007	—	2	2	no	—
174	#13094006	—	2	2	no	—
175	#13094003	—	2	1	no	—
176	#13094002	—	2	2	no	—
177	#13094002	—	2	2	no	—
178	#13094002	—	2	2	no	—
179	#13094002	—	2	2	no	—
180	#13094002	—	2	2	no	—
181	#13094001	—	2	2	no	—
182	#13094001	—	2	2	no	—
183	#13094001	—	2	2	no	—
184	#13094000	—	2	2	no	—
185	#13094000	—	2	2	no	—
186	#13094000	C₂³	1	2	yes	—
187	#13093999	C₂³	1	2	yes	—
188	#13093999	C₂³	1	2	yes	—
189	#13093998	—	2	1	no	—
190	#13093998	—	2	2	no	—
191	#13093998	—	2	1	no	—
192	#13093998	—	2	1	no	—
193	#13093997	—	2	2	no	—
194	#13093997	—	2	2	no	—
195	#13093996	—	2	2	no	—
196	#13093995	C₂³	1	2	yes	—
197	#13093994	—	2	2	no	—
198	#13093992	—	2	2	no	—
199	C₄×Dic₉₄	—	2	1	no	—
200	C₄×Dic₉₄	—	2	1	no	—
201	C₄×Dic₉₄	D₄	1	1	yes	characteristic
202	C₄×Dic₉₄	D₄	1	1	yes	characteristic
203	#13093989	—	2	2	no	—
204	#13093989	—	2	2	no	—
205	C₄×D₁₈₈	—	2	1	no	—
206	C₄×D₁₈₈	—	2	1	no	—
207	C₄×D₁₈₈	—	2	2	no	—
208	C₄×D₁₈₈	—	2	1	no	—
209	C₄×D₁₈₈	—	2	1	no	—
210	C₄×D₁₈₈	D₄	1	1	yes	characteristic
211	C₄×D₁₈₈	D₄	1	1	yes	characteristic
212	C₄×D₁₈₈	C₂³	1	2	yes	—
213	C₄×D₁₈₈	C₂³	1	2	yes	—
214	C₄×C₂²⋊D₄₇	—	2	2	no	—
215	C₄×C₂²⋊D₄₇	D₄	1	2	yes	—
216	C₄×C₂²⋊D₄₇	D₄	1	2	yes	—
217	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
218	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
219	#13093983	C₂³	1	1	yes	characteristic
220	#13093982	C₂³	1	2	yes	—
221	#13093982	C₂³	1	2	yes	—
222	#13093981	—	2	2	no	—
223	#13093981	C₂³	1	2	yes	—
224	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
225	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
226	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
227	C₂×Dic₄₇⋊C₄	—	2	1	no	—
228	C₂×Dic₄₇⋊C₄	—	2	1	no	—
229	C₄⋊C₄×D₄₇	—	2	2	no	—
230	C₄⋊C₄×D₄₇	—	2	2	no	—
231	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
232	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
233	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
234	C₄²×D₄₇	C₂³	1	2	yes	—
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	#13093957	C₂³	1	2	yes	—
240	#13093957	C₂³	1	2	yes	—
241	#13093956	C₂³	1	2	yes	—
242	#13093956	C₂³	1	2	yes	—
243	#13093955	C₂³	1	2	yes	—
244	#13093955	C₂³	1	2	yes	—
245	#13093955	C₂³	1	2	yes	—
246	#13093955	C₂³	1	2	yes	—
247	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
248	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
249	#13093948	C₂³	1	2	yes	—
250	#13093948	C₂³	1	2	yes	—
251	#13093946	C₂³	1	2	yes	—
252	#13093946	C₂³	1	2	yes	—
253	#13093946	C₂³	1	2	yes	—
254	#13093946	C₂³	1	2	yes	—
255	#13093945	C₂³	1	2	yes	—
256	#13093945	C₂³	1	2	yes	—
257	#13093944	C₂³	1	2	yes	—
258	#13093944	C₂³	1	2	yes	—
259	#13093944	C₂³	1	2	yes	—
260	#13093944	C₂³	1	2	yes	—
261	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
262	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
263	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
264	(C₂×D₄₇)⋊C₈	C₂³	1	2	yes	—
265	#13093934	C₂³	1	2	yes	—
266	#13093934	C₂³	1	2	yes	—
267	C₈×Dic₄₇	C₂³	1	2	yes	—
268	C₈×Dic₄₇	C₂³	1	2	yes	—
269	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
270	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
271	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
272	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
273	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
274	#125×C₄₇	C₂³	1	1	yes	characteristic
275	#125×C₄₇	C₂³	1	1	yes	characteristic
276	C₂²⋊Q₈×C₄₇	—	2	1	no	—
277	C₂²⋊Q₈×C₄₇	—	2	1	no	—
278	C₄×Q₈×C₄₇	—	2	1	no	—
279	C₄×Q₈×C₄₇	—	2	1	no	—
280	C₄×Q₈×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	C₂³	1	1	yes	characteristic
285	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
286	#117×C₄₇	—	2	1	no	—
287	#117×C₄₇	C₂³	1	1	yes	characteristic
288	#117×C₄₇	C₂³	1	1	yes	characteristic
289	#117×C₄₇	C₂³	1	1	yes	characteristic
290	C₂×C₄²×C₄₇	—	2	1	no	—
291	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
292	#107×C₄₇	C₂³	1	1	yes	characteristic
293	#107×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	#106×C₄₇	C₂³	1	1	yes	characteristic
299	#106×C₄₇	C₂³	1	1	yes	characteristic
300	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
301	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
302	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
303	C₄⋊C₈×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	#102×C₄₇	C₂³	1	1	yes	characteristic
311	#102×C₄₇	C₂³	1	1	yes	characteristic
312	C₂³×D₄₇	—	2	1	no	—
313	#41×C₄₇	—	2	2	no	—
314	#41×C₄₇	—	2	2	no	—
315	C₂×Q₈×C₄₇	—	2	1	no	—
316	C₂×Q₈×C₄₇	—	2	1	no	—
317	C₂×Q₈×C₄₇	C₂⁴	1	1	yes	characteristic
318	C₂×D₄×C₄₇	—	2	1	no	—
319	C₂×D₄×C₄₇	C₂⁴	1	1	yes	characteristic
320	C₂²×C₄×C₄₇	—	2	1	no	—
321	C₂²×C₄×C₄₇	—	2	1	no	—
322	C₂²×C₄×C₄₇	—	2	1	no	—
323	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
324	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
325	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
326	C₂×C₂²⋊D₄₇	—	2	2	no	—
327	C₂×C₂²⋊D₄₇	—	2	2	no	—
328	C₂×C₂²⋊D₄₇	—	2	2	no	—
329	C₂×C₂²⋊D₄₇	C₂×D₄	1	2	yes	—
330	C₂²×Dic₄₇	—	2	1	no	—
331	C₂²×Dic₄₇	—	2	1	no	—
332	C₂²×Dic₄₇	—	2	1	no	—
333	#10625350	—	2	2	no	—
334	#10625350	—	2	2	no	—
335	#10625350	—	8	4	no	—
336	C₂×D₁₈₈	—	2	2	no	—
337	C₂×D₁₈₈	—	2	2	no	—
338	C₂×D₁₈₈	—	2	1	no	—
339	C₂×D₁₈₈	—	2	2	no	—
340	C₂×D₁₈₈	—	2	2	no	—
341	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
342	C₂×D₁₈₈	C₂⁴	1	2	yes	—
343	C₂×C₄×D₄₇	—	2	2	no	—
344	C₂×C₄×D₄₇	—	2	2	no	—
345	C₂×C₄×D₄₇	—	2	2	no	—
346	C₂×C₄×D₄₇	—	2	2	no	—
347	C₂×C₄×D₄₇	—	8	2	no	—
348	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
349	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
350	C₂×C₄×D₄₇	C₂⁴	1	2	yes	—
351	C₂×Dic₉₄	—	2	2	no	—
352	C₂×Dic₉₄	—	2	2	no	—
353	C₂×Dic₉₄	—	2	2	no	—
354	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
355	C₂×C₈×C₄₇	—	2	2	no	—
356	C₂×C₈×C₄₇	—	2	2	no	—
357	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
358	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
359	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
360	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
361	C₄⋊C₄×C₄₇	—	2	1	no	—
362	C₄⋊C₄×C₄₇	—	2	1	no	—
363	C₄⋊C₄×C₄₇	—	2	1	no	—
364	C₄⋊C₄×C₄₇	—	2	1	no	—
365	C₄⋊C₄×C₄₇	—	2	1	no	—
366	C₄⋊C₄×C₄₇	—	2	1	no	—
367	C₄⋊C₄×C₄₇	—	2	1	no	—
368	C₄⋊C₄×C₄₇	—	2	1	no	—
369	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
370	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
371	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
372	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
373	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
374	C₄⋊C₄×C₄₇	C₂⁴	1	1	yes	characteristic
375	C₂²⋊C₄×C₄₇	—	2	1	no	—
376	C₂²⋊C₄×C₄₇	—	2	1	no	—
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	C₂×D₄	1	1	yes	characteristic
386	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
387	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
388	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
389	C₂²⋊Dic₄₇	—	2	2	no	—
390	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
391	(C₂×D₄₇)⋊C₄	—	2	2	no	—
392	(C₂×D₄₇)⋊C₄	—	2	2	no	—
393	(C₂×D₄₇)⋊C₄	—	2	2	no	—
394	(C₂×D₄₇)⋊C₄	—	2	2	no	—
395	(C₂×D₄₇)⋊C₄	—	2	2	no	—
396	(C₂×D₄₇)⋊C₄	—	2	2	no	—
397	(C₂×D₄₇)⋊C₄	—	2	2	no	—
398	(C₂×D₄₇)⋊C₄	—	2	2	no	—
399	(C₂×D₄₇)⋊C₄	—	2	2	no	—
400	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
401	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
402	C₄⋊Dic₄₇	—	2	1	no	—
403	C₄⋊Dic₄₇	—	2	1	no	—
404	C₄⋊Dic₄₇	—	2	1	no	—
405	C₄⋊Dic₄₇	—	2	2	no	—
406	C₄⋊Dic₄₇	—	2	2	no	—
407	C₄⋊Dic₄₇	—	2	2	no	—
408	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
409	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
410	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
411	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
412	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
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	—	2	2	no	—
424	Dic₄₇⋊C₄	—	2	2	no	—
425	Dic₄₇⋊C₄	—	2	2	no	—
426	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
427	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
428	C₄×Dic₄₇	—	2	2	no	—
429	C₄×Dic₄₇	—	2	2	no	—
430	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
431	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
432	C₄×Dic₄₇	C₂⁴	1	2	yes	—
433	#10625329	—	2	2	no	—
434	#10625329	—	2	2	no	—
435	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
436	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
437	C₂³×C₄₇	—	2	1	no	—
438	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
439	C₂²×D₄₇	—	2	2	no	—
440	C₂²×D₄₇	—	4	2	no	—
441	C₂²×D₄₇	—	8	1	no	—
442	C₂²×D₄₇	—	8	1	no	—
443	C₂²×D₄₇	C₂²×D₄	1	2	yes	—
444	Q₈×C₄₇	—	2	1	no	—
445	Q₈×C₄₇	—	2	1	no	—
446	Q₈×C₄₇	—	8	1	no	—
447	Q₈×C₄₇	—	8	1	no	—
448	D₄×C₄₇	—	2	1	no	—
449	D₄×C₄₇	—	2	1	no	—
450	D₄×C₄₇	—	4	2	no	—
451	C₂×C₄×C₄₇	—	2	1	no	—
452	C₂×C₄×C₄₇	—	2	1	no	—
453	C₂×C₄×C₄₇	—	2	1	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	—	4	1	no	—
459	C₂×C₄×C₄₇	—	4	1	no	—
460	C₂×C₄×C₄₇	—	4	2	no	—
461	C₂×C₄×C₄₇	—	4	2	no	—
462	C₂×C₄×C₄₇	—	8	1	no	—
463	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
464	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
465	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
466	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
467	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
468	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
469	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
470	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
471	C₂²⋊D₄₇	—	2	4	no	—
472	C₂²⋊D₄₇	—	8	2	no	—
473	C₂²⋊D₄₇	—	8	2	no	—
474	C₂²⋊D₄₇	—	8	2	no	—
475	C₂×Dic₄₇	—	2	2	no	—
476	C₂×Dic₄₇	—	2	2	no	—
477	C₂×Dic₄₇	—	2	2	no	—
478	C₂×Dic₄₇	—	8	1	no	—
479	C₂×Dic₄₇	—	8	1	no	—
480	C₂×Dic₄₇	—	8	1	no	—
481	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
482	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
483	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
484	D₁₈₈	—	2	2	no	—
485	D₁₈₈	—	2	2	no	—
486	D₁₈₈	—	2	2	no	—
487	D₁₈₈	—	4	2	no	—
488	D₁₈₈	—	8	2	no	—
489	D₁₈₈	—	8	2	no	—
490	C₄×D₄₇	—	2	2	no	—
491	C₄×D₄₇	—	2	2	no	—
492	C₄×D₄₇	—	4	2	no	—
493	C₄×D₄₇	—	4	2	no	—
494	C₄×D₄₇	—	4	4	no	—
495	C₄×D₄₇	—	8	2	no	—
496	C₄×D₄₇	—	8	2	no	—
497	C₄×D₄₇	—	8	2	no	—
498	Dic₉₄	—	2	2	no	—
499	Dic₉₄	—	8	2	no	—
500	Dic₉₄	—	8	2	no	—
501	Dic₉₄	—	8	2	no	—
502	C₈×C₄₇	—	2	1	no	—
503	C₈×C₄₇	—	2	1	no	—
504	C₈×C₄₇	—	2	1	no	—
505	C₈×C₄₇	—	2	1	no	—
506	C₄₇⋊C₈	—	2	2	no	—
507	C₄₇⋊C₈	—	2	2	no	—
508	#60890	—	47	1	no	maximal, Sylow
509	C₂²×C₄₇	—	2	1	no	—
510	C₂²×C₄₇	—	2	1	no	—
511	C₂²×C₄₇	—	4	1	no	—
512	C₂²×C₄₇	—	4	1	no	—
513	C₂²×C₄₇	—	4	1	no	—
514	C₂²×C₄₇	#536	1	2	yes	—
515	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
516	C₂×D₄₇	—	2	2	no	—
517	C₂×D₄₇	—	2	2	no	—
518	C₂×D₄₇	—	2	2	no	—
519	C₂×D₄₇	—	4	2	no	—
520	C₂×D₄₇	—	4	2	no	—
521	C₂×D₄₇	—	4	2	no	—
522	C₂×D₄₇	—	8	4	no	—
523	C₄×C₄₇	—	2	1	no	—
524	C₄×C₄₇	—	2	1	no	—
525	C₄×C₄₇	—	2	1	no	—
526	C₄×C₄₇	—	2	1	no	—
527	C₄×C₄₇	—	4	1	no	—
528	C₄×C₄₇	—	4	1	no	—
529	C₄×C₄₇	—	4	1	no	—
530	C₄×C₄₇	—	4	1	no	—
531	C₄×C₄₇	—	4	1	no	—
532	C₄×C₄₇	—	4	1	no	—
533	C₄×C₄₇	—	4	1	no	—
534	C₄×C₄₇	#536	1	2	yes	—
535	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
536	C₄×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
537	Dic₄₇	—	2	2	no	—
538	Dic₄₇	—	2	2	no	—
539	Dic₄₇	—	2	2	no	—
540	Dic₄₇	—	4	2	no	—
541	Dic₄₇	—	4	2	no	—
542	Dic₄₇	—	4	2	no	—
543	#3504	—	47	1	no	—
544	#3460	—	47	1	no	—
545	#3244	—	47	2	no	—
546	#3243	—	47	2	no	—
547	#3241	—	47	2	no	—
548	#3241	—	47	2	no	—
549	#3240	—	47	2	no	—
550	#3234	—	47	2	no	—
551	#3232	—	47	2	no	—
552	#3228	—	47	2	no	—
553	#3164	—	47	1	no	—
554	#3163	—	47	1	no	—
555	#3136	—	47	1	no	—
556	#3136	—	47	1	no	—
557	#3099	—	47	1	no	—
558	#3098	—	47	1	no	—
559	#3096	—	47	1	no	—
560	#3096	—	47	1	no	—
561	#3080	—	47	1	no	—
562	#3077	—	47	1	no	—
563	#3076	D₄₇	1	1	yes	characteristic, complemented
564	C₂×#478	—	47	1	no	—
565	#2925	—	47	1	no	—
566	C₂×C₄₇	—	2	2	no	—
567	C₂×C₄₇	—	8	1	no	—
568	C₂×C₄₇	C₂×#536	1	1	yes	characteristic
569	C₂×C₄₇	#3584	1	1	yes	characteristic
570	C₂×C₄₇	#3585	1	1	yes	characteristic
571	D₄₇	—	4	2	no	—
572	D₄₇	—	8	2	no	—
573	#557	—	94	1	no	—
574	#557	—	94	1	no	—
575	#554	—	94	1	no	—
576	#554	—	94	1	no	—
577	#554	—	94	2	no	—
578	#554	—	94	2	no	—
579	#544	—	47	2	no	—
580	#544	—	47	2	no	—
581	#544	—	47	1	no	—
582	#544	—	47	1	no	—
583	#544	—	47	1	no	—
584	#542	—	47	2	no	—
585	#542	—	94	1	no	—
586	#540	—	47	2	no	—
587	#540	—	94	1	no	—
588	#538	—	94	2	no	—
589	#537	—	47	1	no	—
590	#535	—	47	1	no	—
591	#535	—	47	1	no	—
592	#533	—	47	2	no	—
593	#533	C₂×D₄₇	1	1	yes	characteristic
594	#532	—	47	2	no	—
595	#532	—	94	1	no	—
596	#529	—	47	2	no	—
597	#529	—	94	1	no	—
598	C₂×#125	—	47	2	no	—
599	C₂×#125	—	47	1	no	—
600	#525	—	94	2	no	—
601	#520	—	47	1	no	—
602	#520	—	47	1	no	—
603	C₄×#41	—	47	1	no	—
604	C₄×#41	C₂×D₄₇	1	1	yes	characteristic
605	C₂×C₄×D₄	—	47	1	no	—
606	#501	—	47	2	no	—
607	#501	—	47	2	no	—
608	#501	—	47	2	no	—
609	#501	—	47	2	no	—
610	#500	—	47	2	no	—
611	#499	—	47	2	no	—
612	#499	—	47	2	no	—
613	#498	—	47	2	no	—
614	#490	—	47	2	no	—
615	#490	—	47	2	no	—
616	#489	—	47	2	no	—
617	#489	—	47	2	no	—
618	#488	—	47	2	no	—
619	#488	—	47	2	no	—
620	#486	—	47	2	no	—
621	#486	—	47	2	no	—
622	#485	—	47	2	no	—
623	#485	—	47	2	no	—
624	#484	—	47	2	no	—
625	#483	—	47	2	no	—
626	#482	—	47	2	no	—
627	#482	—	47	2	no	—
628	#482	—	47	2	no	—
629	#482	—	47	2	no	—
630	#482	—	47	2	no	—
631	#482	—	47	2	no	—
632	#481	—	47	2	no	—
633	#481	—	47	2	no	—
634	#481	—	47	2	no	—
635	#480	—	47	2	no	—
636	#480	—	47	2	no	—
637	#480	—	47	2	no	—
638	#479	—	47	2	no	—
639	#479	—	47	2	no	—
640	#479	C₂×D₄₇	1	1	yes	characteristic, complemented
641	#479	C₂×D₄₇	1	1	yes	characteristic, complemented
642	#478	—	47	2	no	—
643	#478	—	47	2	no	—
644	#478	—	47	2	no	—
645	#478	—	47	2	no	—
646	#478	—	47	2	no	—
647	#478	—	47	2	no	—
648	#478	—	47	2	no	—
649	#478	—	47	2	no	—
650	#478	C₂×D₄₇	1	1	yes	characteristic, complemented
651	#478	C₂×D₄₇	1	1	yes	characteristic, complemented
652	#477	C₂×D₄₇	1	1	yes	characteristic, complemented
653	#476	—	47	2	no	—
654	#476	C₂×D₄₇	1	1	yes	characteristic, complemented
655	#475	C₂×D₄₇	1	1	yes	characteristic, complemented
656	#474	—	47	2	no	—
657	#474	C₂×D₄₇	1	1	yes	characteristic, complemented
658	#433	—	47	2	no	—
659	#433	—	47	2	no	—
660	#432	—	47	2	no	—
661	#431	—	47	2	no	—
662	#428	—	47	1	no	—
663	#428	—	47	1	no	—
664	#428	—	47	1	no	—
665	#428	—	47	1	no	—
666	#427	C₂×D₄₇	1	1	yes	characteristic
667	#427	C₂×D₄₇	1	1	yes	characteristic
668	C₂×#107	—	47	1	no	—
669	C₂×#106	—	47	1	no	—
670	#423	—	47	1	no	—
671	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
672	#418	—	47	1	no	—
673	#418	—	47	1	no	—
674	#417	—	47	1	no	—
675	#417	—	47	1	no	—
676	#416	C₂×D₄₇	1	1	yes	characteristic
677	#416	C₂×D₄₇	1	1	yes	characteristic
678	C₂×#102	—	47	1	no	—
679	C₂×#102	—	47	1	no	—
680	#408	—	47	1	no	—
681	#408	—	47	1	no	—
682	#405	—	47	1	no	—
683	#405	—	47	1	no	—
684	C₄₇	#60890	1	1	yes	characteristic, complemented, Sylow
685	C₂×#41	—	47	1	no	—
686	C₂×#41	—	94	2	no	—
687	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
688	C₂²×D₄	—	47	1	no	—
689	C₂³×C₄	—	94	1	no	—
690	C₂×M₁₆	—	47	1	no	—
691	C₂×M₁₆	—	47	1	no	—
692	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
693	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
694	C₄⋊Q₈	—	47	2	no	—
695	C₄⋊Q₈	—	47	2	no	—
696	C₄⋊Q₈	—	47	2	no	—
697	C₄⋊Q₈	—	94	1	no	—
698	C₄⋊Q₈	—	94	1	no	—
699	C₄⋊Q₈	—	94	1	no	—
700	C₄⋊Q₈	—	94	2	no	—
701	C₄⋊Q₈	—	94	2	no	—
702	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
703	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
704	#127	—	47	2	no	—
705	#127	—	94	1	no	—
706	#126	—	94	2	no	—
707	#126	—	94	2	no	—
708	#125	—	47	2	no	—
709	#125	—	47	2	no	—
710	#125	—	47	2	no	—
711	#125	—	47	2	no	—
712	#125	—	47	2	no	—
713	#125	—	94	1	no	—
714	#125	—	94	1	no	—
715	#125	—	94	1	no	—
716	#125	—	94	2	no	—
717	#125	—	94	2	no	—
718	#125	—	94	2	no	—
719	#125	—	94	2	no	—
720	#125	—	94	1	no	—
721	#125	—	94	1	no	—
722	#125	C₂²×D₄₇	1	1	yes	characteristic
723	#125	C₂²×D₄₇	1	1	yes	characteristic
724	#124	—	47	2	no	—
725	#124	—	94	2	no	—
726	#124	—	94	1	no	—
727	#124	—	94	2	no	—
728	#123	—	94	2	no	—
729	#123	—	94	2	no	—
730	#123	—	94	2	no	—
731	#123	—	94	2	no	—
732	C₂²⋊Q₈	—	2	1	no	—
733	C₂²⋊Q₈	—	2	1	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	1	no	—
746	#121	—	47	2	no	—
747	#121	—	47	2	no	—
748	#121	—	47	2	no	—
749	#121	—	94	2	no	—
750	#121	—	94	2	no	—
751	#121	—	94	2	no	—
752	#121	—	94	1	no	—
753	#121	—	94	1	no	—
754	#121	—	94	1	no	—
755	#121	—	94	2	no	—
756	#120	—	94	2	no	—
757	#120	—	94	2	no	—
758	C₄×Q₈	—	2	1	no	—
759	C₄×Q₈	—	2	1	no	—
760	C₄×Q₈	—	47	1	no	—
761	C₄×Q₈	—	47	1	no	—
762	C₄×Q₈	—	94	1	no	—
763	C₄×Q₈	—	94	1	no	—
764	C₄×Q₈	—	94	2	no	—
765	C₄×Q₈	—	94	2	no	—
766	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
767	C₄×Q₈	C₂²×D₄₇	1	1	yes	characteristic
768	C₄×D₄	—	2	1	no	—
769	C₄×D₄	—	2	1	no	—
770	C₄×D₄	—	47	2	no	—
771	C₄×D₄	—	47	2	no	—
772	C₄×D₄	—	47	1	no	—
773	C₄×D₄	—	47	1	no	—
774	C₄×D₄	—	47	2	no	—
775	C₄×D₄	—	47	2	no	—
776	C₄×D₄	—	94	2	no	—
777	C₄×D₄	—	94	1	no	—
778	C₄×D₄	—	94	1	no	—
779	C₄×D₄	—	94	2	no	—
780	C₄×D₄	—	94	2	no	—
781	C₄×D₄	—	94	2	no	—
782	C₄×D₄	—	94	1	no	—
783	C₄×D₄	—	94	1	no	—
784	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
785	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
786	#117	—	2	1	no	—
787	#117	—	47	1	no	—
788	#117	—	47	2	no	—
789	#117	—	47	2	no	—
790	#117	—	47	2	no	—
791	#117	—	94	2	no	—
792	#117	C₂²×D₄₇	1	1	yes	characteristic
793	#117	C₂²×D₄₇	1	1	yes	characteristic
794	#117	C₂²×D₄₇	1	1	yes	characteristic
795	C₂×C₄⋊C₄	—	47	1	no	—
796	C₂×C₄⋊C₄	—	47	1	no	—
797	C₂×C₄⋊C₄	—	47	1	no	—
798	C₂×C₄⋊C₄	—	47	2	no	—
799	C₂×C₄⋊C₄	—	47	2	no	—
800	C₂×C₄⋊C₄	—	94	2	no	—
801	C₂×C₄⋊C₄	—	94	2	no	—
802	C₂×C₄⋊C₄	—	94	1	no	—
803	C₂×C₄⋊C₄	—	94	1	no	—
804	C₂×C₂²⋊C₄	—	94	1	no	—
805	C₂×C₄²	—	2	1	no	—
806	C₂×C₄²	—	47	2	no	—
807	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
808	#107	—	47	2	no	—
809	#107	—	47	2	no	—
810	#107	—	47	2	no	—
811	#107	—	47	2	no	—
812	#107	—	47	2	no	—
813	#107	—	47	2	no	—
814	#107	C₂²×D₄₇	1	1	yes	characteristic
815	#107	C₂²×D₄₇	1	1	yes	characteristic
816	#107	C₂²×D₄₇	1	1	yes	characteristic
817	#107	C₂²×D₄₇	1	1	yes	characteristic
818	#106	—	47	2	no	—
819	#106	—	47	2	no	—
820	#106	—	47	2	no	—
821	#106	—	47	2	no	—
822	#106	—	47	2	no	—
823	#106	—	47	2	no	—
824	#106	C₂²×D₄₇	1	1	yes	characteristic
825	#106	C₂²×D₄₇	1	1	yes	characteristic
826	#106	C₂²×D₄₇	1	1	yes	characteristic
827	#106	C₂²×D₄₇	1	1	yes	characteristic
828	C₄⋊C₈	—	47	2	no	—
829	C₄⋊C₈	—	47	2	no	—
830	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
831	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
832	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
833	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
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	#103	C₂²×D₄₇	1	1	yes	characteristic
839	#103	C₂²×D₄₇	1	1	yes	characteristic
840	#102	—	47	2	no	—
841	#102	—	47	2	no	—
842	#102	—	47	2	no	—
843	#102	—	47	2	no	—
844	#102	—	47	2	no	—
845	#102	—	47	2	no	—
846	#102	—	47	2	no	—
847	#102	—	47	2	no	—
848	#102	—	47	2	no	—
849	#102	—	47	2	no	—
850	#102	C₂²×D₄₇	1	1	yes	characteristic
851	#102	C₂²×D₄₇	1	1	yes	characteristic
852	#102	C₂²×D₄₇	1	1	yes	characteristic
853	#102	C₂²×D₄₇	1	1	yes	characteristic
854	C₂²⋊C₈	—	47	2	no	—
855	C₂²⋊C₈	—	47	2	no	—
856	C₂²⋊C₈	—	47	2	no	—
857	C₂²⋊C₈	—	47	2	no	—
858	#97	—	47	2	no	—
859	#97	—	47	2	no	—
860	C₄×C₈	—	47	2	no	—
861	C₄×C₈	—	47	2	no	—
862	C₂⁴	—	94	1	no	—
863	#41	—	2	2	no	—
864	#41	—	2	2	no	—
865	#41	—	94	2	no	—
866	#41	—	94	2	no	—
867	#41	—	376	4	no	—
868	C₂×Q₈	—	2	1	no	—
869	C₂×Q₈	—	2	1	no	—
870	C₂×Q₈	—	47	1	no	—
871	C₂×Q₈	—	94	2	no	—
872	C₂×Q₈	—	94	2	no	—
873	C₂×Q₈	—	94	2	no	—
874	C₂×Q₈	C₂³×D₄₇	1	1	yes	characteristic
875	C₂×D₄	—	2	1	no	—
876	C₂×D₄	—	47	2	no	—
877	C₂×D₄	—	47	1	no	—
878	C₂×D₄	—	47	2	no	—
879	C₂×D₄	—	94	2	no	—
880	C₂×D₄	—	94	2	no	—
881	C₂×D₄	—	94	2	no	—
882	C₂×D₄	—	94	2	no	—
883	C₂×D₄	—	94	2	no	—
884	C₂×D₄	—	94	1	no	—
885	C₂×D₄	—	94	2	no	—
886	C₂×D₄	—	94	2	no	—
887	C₂×D₄	C₂³×D₄₇	1	1	yes	characteristic
888	C₂²×C₄	—	2	1	no	—
889	C₂²×C₄	—	2	1	no	—
890	C₂²×C₄	—	2	1	no	—
891	C₂²×C₄	—	47	2	no	—
892	C₂²×C₄	—	47	2	no	—
893	C₂²×C₄	—	47	2	no	—
894	C₂²×C₄	—	94	2	no	—
895	C₂²×C₄	—	94	2	no	—
896	C₂²×C₄	—	94	1	no	—
897	C₂²×C₄	—	94	1	no	—
898	C₂²×C₄	—	94	1	no	—
899	C₂²×C₄	—	94	2	no	—
900	C₂²×C₄	—	94	2	no	—
901	C₂²×C₄	—	376	2	no	—
902	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
903	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
904	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
905	M₁₆	—	94	2	no	—
906	M₁₆	—	94	2	no	—
907	C₂×C₈	—	2	2	no	—
908	C₂×C₈	—	2	2	no	—
909	C₂×C₈	—	47	2	no	—
910	C₂×C₈	—	47	2	no	—
911	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
912	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
913	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
914	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
915	C₄⋊C₄	—	2	1	no	—
916	C₄⋊C₄	—	2	1	no	—
917	C₄⋊C₄	—	2	1	no	—
918	C₄⋊C₄	—	2	1	no	—
919	C₄⋊C₄	—	2	1	no	—
920	C₄⋊C₄	—	2	1	no	—
921	C₄⋊C₄	—	2	1	no	—
922	C₄⋊C₄	—	2	1	no	—
923	C₄⋊C₄	—	47	2	no	—
924	C₄⋊C₄	—	47	2	no	—
925	C₄⋊C₄	—	47	1	no	—
926	C₄⋊C₄	—	47	1	no	—
927	C₄⋊C₄	—	47	2	no	—
928	C₄⋊C₄	—	47	2	no	—
929	C₄⋊C₄	—	47	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	2	no	—
942	C₄⋊C₄	—	94	2	no	—
943	C₄⋊C₄	—	94	2	no	—
944	C₄⋊C₄	—	94	2	no	—
945	C₄⋊C₄	—	94	2	no	—
946	C₄⋊C₄	—	94	1	no	—
947	C₄⋊C₄	—	94	1	no	—
948	C₄⋊C₄	—	94	1	no	—
949	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
950	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
951	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
952	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
953	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
954	C₄⋊C₄	C₂³×D₄₇	1	1	yes	characteristic
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	—	2	1	no	—
960	C₂²⋊C₄	—	47	2	no	—
961	C₂²⋊C₄	—	47	2	no	—
962	C₂²⋊C₄	—	47	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	C₂²⋊C₄	—	94	2	no	—
971	C₂²⋊C₄	—	94	2	no	—
972	C₂²⋊C₄	—	94	2	no	—
973	C₄²	—	2	1	no	—
974	C₄²	—	2	1	no	—
975	C₄²	—	2	1	no	—
976	C₄²	—	2	1	no	—
977	C₄²	—	2	1	no	—
978	C₄²	—	47	2	no	—
979	C₄²	—	47	2	no	—
980	C₄²	—	47	2	no	—
981	C₄²	—	94	2	no	—
982	C₄²	—	94	2	no	—
983	C₄²	D₄×D₄₇	1	1	yes	characteristic
984	C₄²	D₄×D₄₇	1	1	yes	characteristic
985	C₄²	C₂³×D₄₇	1	1	yes	characteristic
986	C₄²	C₂³×D₄₇	1	1	yes	characteristic
987	C₂³	—	2	1	no	—
988	C₂³	—	47	2	no	—
989	C₂³	—	94	2	no	—
990	C₂³	—	376	1	no	—
991	C₂³	—	376	1	no	—
992	C₂³	—	188	2	no	—
993	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
994	Q₈	—	2	1	no	—
995	Q₈	—	2	1	no	—
996	Q₈	—	8	1	no	—
997	Q₈	—	8	1	no	—
998	Q₈	—	94	2	no	—
999	Q₈	—	376	2	no	—
1000	Q₈	—	376	2	no	—
1001	Q₈	—	376	2	no	—
1002	D₄	—	2	1	no	—
1003	D₄	—	2	1	no	—
1004	D₄	—	4	2	no	—
1005	D₄	—	94	4	no	—
1006	D₄	—	94	2	no	—
1007	D₄	—	94	2	no	—
1008	D₄	—	94	2	no	—
1009	D₄	—	376	2	no	—
1010	D₄	—	376	2	no	—
1011	D₄	—	376	2	no	—
1012	D₄	—	376	2	no	—
1013	D₄	—	376	2	no	—
1014	D₄	—	188	2	no	—
1015	C₂×C₄	—	2	1	no	—
1016	C₂×C₄	—	2	1	no	—
1017	C₂×C₄	—	2	1	no	—
1018	C₂×C₄	—	2	1	no	—
1019	C₂×C₄	—	2	1	no	—
1020	C₂×C₄	—	2	1	no	—
1021	C₂×C₄	—	2	1	no	—
1022	C₂×C₄	—	4	1	no	—
1023	C₂×C₄	—	4	1	no	—
1024	C₂×C₄	—	4	2	no	—
1025	C₂×C₄	—	4	2	no	—
1026	C₂×C₄	—	8	1	no	—
1027	C₂×C₄	—	47	2	no	—
1028	C₂×C₄	—	47	2	no	—
1029	C₂×C₄	—	47	2	no	—
1030	C₂×C₄	—	94	2	no	—
1031	C₂×C₄	—	94	2	no	—
1032	C₂×C₄	—	94	2	no	—
1033	C₂×C₄	—	94	2	no	—
1034	C₂×C₄	—	94	2	no	—
1035	C₂×C₄	—	376	2	no	—
1036	C₂×C₄	—	376	2	no	—
1037	C₂×C₄	—	376	2	no	—
1038	C₂×C₄	—	376	1	no	—
1039	C₂×C₄	—	376	1	no	—
1040	C₂×C₄	—	376	1	no	—
1041	C₂×C₄	—	188	2	no	—
1042	C₂×C₄	—	188	2	no	—
1043	C₂×C₄	—	188	4	no	—
1044	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1045	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1046	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1047	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1048	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1049	C₂×C₄	#13094071	1	2	yes	—
1050	C₂×C₄	#13094072	1	2	yes	—
1051	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1052	C₈	—	2	1	no	—
1053	C₈	—	2	1	no	—
1054	C₈	—	2	1	no	—
1055	C₈	—	2	1	no	—
1056	C₈	—	94	2	no	—
1057	C₈	—	94	2	no	—
1058	C₂²	—	2	1	no	—
1059	C₂²	—	2	1	no	—
1060	C₂²	—	4	1	no	—
1061	C₂²	—	4	1	no	—
1062	C₂²	—	4	1	no	—
1063	C₂²	—	94	2	no	—
1064	C₂²	—	94	2	no	—
1065	C₂²	—	94	2	no	—
1066	C₂²	—	376	4	no	—
1067	C₂²	—	188	2	no	—
1068	C₂²	—	188	2	no	—
1069	C₂²	—	188	2	no	—
1070	C₂²	#15689696	1	2	yes	—
1071	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1072	C₄	—	2	1	no	—
1073	C₄	—	2	1	no	—
1074	C₄	—	2	1	no	—
1075	C₄	—	2	1	no	—
1076	C₄	—	4	1	no	—
1077	C₄	—	4	1	no	—
1078	C₄	—	4	1	no	—
1079	C₄	—	4	1	no	—
1080	C₄	—	4	1	no	—
1081	C₄	—	4	1	no	—
1082	C₄	—	4	1	no	—
1083	C₄	—	94	2	no	—
1084	C₄	—	94	2	no	—
1085	C₄	—	94	2	no	—
1086	C₄	—	188	2	no	—
1087	C₄	—	188	2	no	—
1088	C₄	—	188	2	no	—
1089	C₄	#15689696	1	2	yes	—
1090	C₄	C₂×#13094071	1	1	yes	characteristic
1091	C₄	C₂×#13094072	1	1	yes	characteristic
1092	C₂	—	2	2	no	—
1093	C₂	—	8	1	no	—
1094	C₂	—	376	2	no	—
1095	C₂	—	188	2	no	—
1096	C₂	C₂×#15689696	1	1	yes	characteristic
1097	C₂	#20258157	1	1	yes	characteristic
1098	C₂	#20258165	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×#3076	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	#20256804	C₂
hypercenter	#3076	D₄₇
hypocenter	C₄₇	#60890
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3076

Complements

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

N	H ≅ G/N	type
1. #20257209	C₂	semidirect
3. #20254691	C₂	semidirect
4. #20254676	C₂	semidirect
5. #20254648	C₂	semidirect
6. #20254640	C₂	semidirect
7. #20254633	C₂	semidirect
8. #20254576	C₂	semidirect
9. #20254560	C₂	semidirect
10. #20254523	C₂	semidirect
11. #20253928	C₂	semidirect
12. #20253920	C₂	semidirect
13. #20253746	C₂	semidirect
14. #20253746	C₂	semidirect
15. #20253375	C₂	semidirect
16. #20253364	C₂	semidirect
17. #20253349	C₂	semidirect
18. #20253349	C₂	semidirect
19. #20253210	C₂	semidirect
20. #20253181	C₂	semidirect
21. C₂×#15689424	C₂	semidirect
22. #20252053	C₂	semidirect
23. C₄₇×#3076	C₂	semidirect
33. #15689750	C₂²	semidirect
34. #15689750	C₂²	semidirect
43. #15689679	C₂²	semidirect
49. #125×D₄₇	C₂²	semidirect
55. #15689531	C₂²	semidirect
56. #15689531	C₂²	semidirect
57. #15689530	C₂²	semidirect
58. #15689530	C₂²	semidirect
59. #15689527	C₂²	semidirect
60. #15689524	C₂²	semidirect
61. #15689523	C₂²	semidirect
62. #15689520	C₂²	semidirect
71. #15689463	C₂²	semidirect
72. #15689462	C₂²	semidirect
73. #15689457	C₂²	semidirect
74. #15689452	C₂²	semidirect
79. #15689446	C₂²	semidirect
80. #15689445	C₂²	semidirect
83. #15689440	C₂²	semidirect
86. #15689435	C₂²	semidirect
87. #15689430	C₂²	semidirect
88. #15689430	C₂²	semidirect
93. #15689423	C₂²	semidirect
94. #15689423	C₂²	semidirect
99. #15689183	C₂²	semidirect
100. #15689183	C₂²	semidirect
101. #15689179	C₂²	semidirect
102. #15689175	C₂²	semidirect
122. C₄₇×#479	C₂²	semidirect
123. C₄₇×#479	C₂²	semidirect
124. C₄₇×#478	C₂²	semidirect
125. C₄₇×#478	C₂²	semidirect
126. C₄₇×#477	C₂²	semidirect
127. C₄₇×#476	C₂²	semidirect
128. C₄₇×#475	C₂²	semidirect
129. C₄₇×#474	C₂²	semidirect
563. #3076	D₄₇	semidirect
640. #479	C₂×D₄₇	semidirect
641. #479	C₂×D₄₇	semidirect
650. #478	C₂×D₄₇	semidirect
651. #478	C₂×D₄₇	semidirect
652. #477	C₂×D₄₇	semidirect
654. #476	C₂×D₄₇	semidirect
655. #475	C₂×D₄₇	semidirect
657. #474	C₂×D₄₇	semidirect
684. C₄₇	#60890	semidirect

Maximal subgroups

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

subgroup	index
#20257209	2
#20256804	2
#20254691	2
#20254676	2
#20254648	2
#20254640	2
#20254633	2
#20254576	2
#20254560	2
#20254523	2
#20253928	2
#20253920	2
#20253746	2
#20253375	2
#20253364	2
#20253349	2
#20253210	2
#20253181	2
C₂×#15689424	2
#20252053	2
C₄₇×#3076	2
#60890	47