Subgroups — #27098851

Order 12032.

2010 conjugacy classes of subgroups.

The subgroup lattice has 1144 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20257416	C₂	1	2	yes	maximal, complemented
2	#20256362	C₂	1	1	yes	maximal, characteristic, complemented
3	#20256252	C₂	1	1	yes	maximal, characteristic, complemented
4	#20256098	C₂	1	2	yes	maximal, complemented
5	#20255808	C₂	1	1	yes	maximal, characteristic, complemented
6	#20255786	C₂	1	1	yes	maximal, characteristic, complemented
7	#20255628	C₂	1	2	yes	maximal, complemented
8	#20255527	C₂	1	2	yes	maximal, complemented
9	#20255523	C₂	1	2	yes	maximal, complemented
10	D₄×D₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
11	#20255062	C₂	1	1	yes	maximal, characteristic, complemented
12	#20255062	C₂	1	1	yes	maximal, characteristic, complemented
13	#20254039	C₂	1	1	yes	maximal, characteristic, complemented
14	#20254031	C₂	1	1	yes	maximal, characteristic, complemented
15	#20253962	C₂	1	1	yes	maximal, characteristic, complemented
16	#20253633	C₂	1	2	yes	maximal, complemented
17	#20253627	C₂	1	2	yes	maximal, complemented
18	#20253476	C₂	1	2	yes	maximal, complemented
19	#20252356	C₂	1	1	yes	maximal, characteristic, complemented
20	#20252239	C₂	1	1	yes	maximal, characteristic, complemented
21	#20252235	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#15689205	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#3339	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
25	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
26	C₂×D₈×D₄₇	C₂²	1	1	yes	characteristic
27	#15689836	C₂²	1	2	yes	complemented
28	#15689829	C₂²	1	2	yes	complemented
29	#15689824	—	2	2	no	—
30	#15689821	C₂²	1	2	yes	complemented
31	#15689794	C₂²	1	2	yes	complemented
32	#15689768	—	2	2	no	—
33	#15689765	—	2	2	no	—
34	#15689762	—	2	2	no	—
35	D₄×D₁₈₈	C₂²	1	2	yes	complemented
36	#15689757	C₂²	1	2	yes	complemented
37	#15689757	C₂²	1	2	yes	complemented
38	#15689729	C₂²	1	2	yes	complemented
39	#15689726	C₂²	1	2	yes	complemented
40	#15689712	—	2	2	no	—
41	#15689709	—	2	2	no	—
42	#15689668	C₂²	1	2	yes	complemented
43	#15689653	C₂²	1	1	yes	characteristic
44	#15689632	—	2	2	no	—
45	#121×D₄₇	—	2	2	no	—
46	#15689597	C₂²	1	2	yes	complemented
47	#15689595	C₂²	1	2	yes	complemented
48	C₂×#13093986	C₂²	1	2	yes	complemented
49	#15689527	C₂²	1	1	yes	characteristic, complemented
50	#15689524	C₂²	1	1	yes	characteristic, complemented
51	#15689500	C₂²	1	1	yes	characteristic, complemented
52	#15689498	C₂²	1	1	yes	characteristic, complemented
53	#15689498	C₂²	1	1	yes	characteristic, complemented
54	#15689489	C₂²	1	2	yes	complemented
55	#15689486	C₂²	1	2	yes	complemented
56	#15689468	C₂²	1	2	yes	complemented
57	#15689450	C₂²	1	2	yes	complemented
58	#15689449	C₂²	1	2	yes	complemented
59	#15689447	C₂²	1	2	yes	complemented
60	#15689441	C₂²	1	2	yes	complemented
61	#15689426	C₂²	1	2	yes	complemented
62	#15689422	C₂²	1	2	yes	complemented
63	#15689420	C₂²	1	2	yes	complemented
64	#15689412	C₂²	1	2	yes	complemented
65	#15689412	C₂²	1	2	yes	complemented
66	#15689377	C₂²	1	2	yes	complemented
67	#15689374	C₂²	1	2	yes	complemented
68	#15689360	C₂²	1	1	yes	characteristic, complemented
69	#15689360	C₂²	1	1	yes	characteristic, complemented
70	#15689359	C₂²	1	1	yes	characteristic, complemented
71	#15689359	C₂²	1	1	yes	characteristic, complemented
72	#15689357	C₂²	1	2	yes	complemented
73	#15689319	C₂²	1	2	yes	complemented
74	#15689318	C₂²	1	2	yes	complemented
75	#15689317	C₂²	1	2	yes	complemented
76	#15689317	C₂²	1	2	yes	complemented
77	#15689317	C₂²	1	2	yes	complemented
78	#15689317	C₂²	1	2	yes	complemented
79	#15689259	C₂²	1	2	yes	complemented
80	#15689259	C₂²	1	2	yes	complemented
81	#15689258	C₂²	1	2	yes	complemented
82	#15689258	C₂²	1	2	yes	complemented
83	#15689256	C₂²	1	2	yes	complemented
84	#15689256	C₂²	1	2	yes	complemented
85	#15689252	C₂²	1	1	yes	characteristic, complemented
86	C₈×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
87	#15689234	C₂²	1	2	yes	complemented
88	#15689234	C₂²	1	2	yes	complemented
89	#15689234	C₂²	1	2	yes	complemented
90	#15689233	C₂²	1	2	yes	complemented
91	#15689232	C₂²	1	2	yes	complemented
92	#15689232	C₂²	1	2	yes	complemented
93	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
94	D₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
95	#15689205	C₂²	1	1	yes	characteristic
96	#15689205	C₂²	1	1	yes	characteristic
97	#15689205	C₂²	1	1	yes	characteristic
98	#15689205	C₂²	1	1	yes	characteristic, complemented
99	#15689205	C₂²	1	1	yes	characteristic, complemented
100	#15689205	C₂²	1	1	yes	characteristic, complemented
101	#15689205	C₂²	1	1	yes	characteristic, complemented
102	#15689205	C₂²	1	2	yes	complemented
103	#15689205	C₂²	1	2	yes	complemented
104	#15689203	C₂²	1	2	yes	complemented
105	#15689198	C₂²	1	1	yes	characteristic, complemented
106	#15689195	C₂²	1	1	yes	characteristic, complemented
107	#15689191	C₂²	1	1	yes	characteristic, complemented
108	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic, complemented
109	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic, complemented
110	#15689183	C₂²	1	1	yes	characteristic, complemented
111	#15689181	C₂²	1	1	yes	characteristic, complemented
112	#15689177	C₂²	1	1	yes	characteristic, complemented
113	#15689160	C₂²	1	1	yes	characteristic, complemented
114	#15689127	C₂²	1	2	yes	complemented
115	#15689126	C₂²	1	2	yes	complemented
116	C₂×#13093944	C₂²	1	2	yes	complemented
117	#15689078	C₂²	1	1	yes	characteristic, complemented
118	#15689077	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
120	C₄₇×#553	C₂²	1	2	yes	complemented
121	C₄₇×#499	C₂²	1	1	yes	characteristic, complemented
122	C₄₇×#482	C₂²	1	2	yes	complemented
123	C₄₇×#481	C₂²	1	2	yes	complemented
124	C₄₇×#478	C₂²	1	2	yes	complemented
125	C₄₇×#466	C₂²	1	1	yes	characteristic, complemented
126	C₄₇×#466	C₂²	1	1	yes	characteristic, complemented
127	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
128	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
129	C₄₇×#427	C₂²	1	1	yes	characteristic, complemented
130	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic, complemented
131	C₂×#10625350	—	2	2	no	—
132	C₂×#10625352	—	2	2	no	—
133	C₂²×D₁₈₈	C₂³	1	2	yes	—
134	C₂²×D₁₈₈	C₂³	1	2	yes	—
135	C₂×D₄×D₄₇	—	2	2	no	—
136	C₂×D₄×D₄₇	—	2	2	no	—
137	C₂×D₄×D₄₇	—	2	2	no	—
138	C₂×D₄×D₄₇	C₂³	1	2	yes	—
139	C₂²×C₄×D₄₇	—	2	2	no	—
140	C₂×D₃₇₆	—	2	4	no	—
141	C₂×D₃₇₆	—	2	4	no	—
142	C₂×D₃₇₆	C₂³	1	2	yes	—
143	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
144	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
145	C₂×D₃₇₆	C₂³	1	2	yes	—
146	C₂×D₃₇₆	C₂³	1	2	yes	—
147	C₂×D₃₇₆	C₂³	1	1	yes	characteristic
148	C₂×#10625334	C₂³	1	2	yes	—
149	C₂×#10625334	C₂³	1	2	yes	—
150	C₂×#10625334	C₂³	1	2	yes	—
151	D₈×D₄₇	—	2	4	no	—
152	C₂×#10625329	C₂³	1	1	yes	characteristic
153	C₂×#10625324	C₂³	1	1	yes	characteristic
154	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
155	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
156	#13094023	C₂³	1	2	yes	—
157	#13094021	C₂³	1	2	yes	—
158	#13094020	C₂³	1	2	yes	—
159	#13094020	C₂³	1	2	yes	—
160	#13094019	—	2	2	no	—
161	#13094019	D₄	1	1	yes	characteristic
162	#13094017	D₄	1	1	yes	characteristic
163	#13094015	C₂³	1	2	yes	—
164	#13094014	D₄	1	1	yes	characteristic
165	#13094012	—	2	2	no	—
166	#13094010	—	2	2	no	—
167	#13094010	—	2	2	no	—
168	#13094010	D₄	1	1	yes	characteristic
169	#13094009	—	2	2	no	—
170	#13094009	—	2	2	no	—
171	#13094009	—	2	2	no	—
172	#13094008	—	2	2	no	—
173	#13094008	D₄	1	1	yes	characteristic
174	#13094006	—	2	2	no	—
175	#13094005	D₄	1	1	yes	characteristic
176	#13094004	—	2	2	no	—
177	#13094002	—	2	2	no	—
178	#13094002	—	2	2	no	—
179	#13094001	D₄	1	1	yes	characteristic
180	#13093999	—	2	2	no	—
181	#13093999	—	2	2	no	—
182	#13093999	—	2	2	no	—
183	#13093999	C₂³	1	2	yes	—
184	#13093999	C₂³	1	2	yes	—
185	#13093998	—	2	2	no	—
186	#13093998	—	2	2	no	—
187	#13093998	C₂³	1	2	yes	—
188	#13093998	C₂³	1	2	yes	—
189	#13093997	—	2	2	no	—
190	#13093997	—	2	2	no	—
191	#13093997	—	2	2	no	—
192	#13093997	—	2	2	no	—
193	#13093997	—	2	2	no	—
194	#13093996	—	2	2	no	—
195	#13093996	—	2	2	no	—
196	#13093996	D₄	1	1	yes	characteristic
197	#13093995	—	2	2	no	—
198	#13093994	—	2	2	no	—
199	#13093994	—	2	2	no	—
200	#13093994	—	2	2	no	—
201	#13093994	—	2	2	no	—
202	#13093992	—	2	2	no	—
203	#13093992	—	2	2	no	—
204	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
205	C₄×D₁₈₈	—	2	2	no	—
206	C₄×D₁₈₈	—	2	2	no	—
207	C₄×D₁₈₈	C₂³	1	2	yes	—
208	D₄×Dic₄₇	C₂³	1	2	yes	—
209	#13093986	—	2	2	no	—
210	#13093986	—	2	2	no	—
211	#13093986	C₂³	1	2	yes	—
212	#13093986	C₂³	1	2	yes	—
213	#13093986	C₂³	1	2	yes	—
214	#13093986	C₂³	1	2	yes	—
215	#13093986	C₂³	1	2	yes	—
216	#13093986	C₂³	1	2	yes	—
217	#13093986	C₂³	1	2	yes	—
218	C₄×C₂²⋊D₄₇	—	2	2	no	—
219	C₄×C₂²⋊D₄₇	—	2	2	no	—
220	C₄×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
221	C₄×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
222	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
223	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
224	#13093983	C₂³	1	1	yes	characteristic
225	#13093982	C₂³	1	2	yes	—
226	#13093981	—	2	2	no	—
227	#13093981	C₂³	1	1	yes	characteristic
228	C₄⋊C₄×D₄₇	—	2	2	no	—
229	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
230	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
231	C₂²⋊C₄×D₄₇	—	2	2	no	—
232	C₂²⋊C₄×D₄₇	—	2	2	no	—
233	C₂²⋊C₄×D₄₇	—	2	2	no	—
234	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
235	#13093958	C₂³	1	1	yes	characteristic
236	#13093957	C₂³	1	2	yes	—
237	#13093955	C₂³	1	2	yes	—
238	#13093955	C₂³	1	2	yes	—
239	C₄⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
240	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
241	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
242	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
243	Dic₄₇⋊C₈	C₂³	1	1	yes	characteristic
244	#13093946	C₂³	1	2	yes	—
245	#13093946	C₂³	1	2	yes	—
246	#13093946	C₂³	1	2	yes	—
247	#13093945	C₂³	1	2	yes	—
248	#13093944	C₂³	1	2	yes	—
249	#13093944	C₂³	1	2	yes	—
250	#13093944	C₂³	1	2	yes	—
251	#13093944	C₂³	1	2	yes	—
252	#13093944	C₂³	1	2	yes	—
253	#13093944	C₂³	1	2	yes	—
254	#13093944	C₂³	1	2	yes	—
255	#13093944	C₂³	1	2	yes	—
256	#13093944	C₂³	1	2	yes	—
257	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
258	C₂²⋊(C₄₇⋊C₈)	C₂³	1	1	yes	characteristic
259	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
260	(C₂×D₄₇)⋊C₈	C₂³	1	1	yes	characteristic
261	#13093935	C₂³	1	1	yes	characteristic
262	#13093934	C₂³	1	1	yes	characteristic
263	#13093934	C₂³	1	1	yes	characteristic
264	#13093934	C₂³	1	1	yes	characteristic
265	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
266	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
267	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
268	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
269	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
270	C₂×D₈×C₄₇	C₂³	1	1	yes	characteristic
271	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
272	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
273	#126×C₄₇	—	2	2	no	—
274	#125×C₄₇	C₂³	1	2	yes	—
275	#123×C₄₇	—	2	2	no	—
276	#121×C₄₇	—	2	2	no	—
277	#121×C₄₇	C₂³	1	2	yes	—
278	#121×C₄₇	C₂³	1	2	yes	—
279	C₄×D₄×C₄₇	—	2	2	no	—
280	C₄×D₄×C₄₇	C₂³	1	2	yes	—
281	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
282	#117×C₄₇	C₂³	1	2	yes	—
283	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
284	#107×C₄₇	C₂³	1	1	yes	characteristic
285	#107×C₄₇	C₂³	1	1	yes	characteristic
286	#107×C₄₇	C₂³	1	2	yes	—
287	#107×C₄₇	C₂³	1	1	yes	characteristic
288	#106×C₄₇	C₂³	1	2	yes	—
289	#106×C₄₇	C₂³	1	2	yes	—
290	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
291	#102×C₄₇	C₂³	1	2	yes	—
292	#102×C₄₇	C₂³	1	2	yes	—
293	#102×C₄₇	C₂³	1	2	yes	—
294	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
295	C₂²⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
296	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
297	C₂³×D₄₇	—	2	2	no	—
298	C₂³×D₄₇	—	2	2	no	—
299	C₂³×D₄₇	—	2	2	no	—
300	C₂×D₄×C₄₇	—	2	2	no	—
301	C₂×D₄×C₄₇	—	2	2	no	—
302	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
303	C₂×D₄×C₄₇	C₂⁴	1	2	yes	—
304	C₂²×C₄×C₄₇	—	2	2	no	—
305	C₂²×C₄×C₄₇	—	2	2	no	—
306	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
307	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
308	C₂×C₂²⋊D₄₇	—	2	2	no	—
309	C₂×C₂²⋊D₄₇	—	2	2	no	—
310	C₂×C₂²⋊D₄₇	—	2	2	no	—
311	C₂×C₂²⋊D₄₇	—	2	2	no	—
312	C₂×C₂²⋊D₄₇	—	2	2	no	—
313	C₂×C₂²⋊D₄₇	—	2	2	no	—
314	C₂×C₂²⋊D₄₇	—	2	2	no	—
315	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
316	C₂×C₂²⋊D₄₇	C₂×D₄	1	1	yes	characteristic
317	C₂²×Dic₄₇	—	2	2	no	—
318	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
319	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
320	#10625352	—	8	4	no	—
321	D₄×D₄₇	—	2	4	no	—
322	D₄×D₄₇	—	4	2	no	—
323	D₄×D₄₇	—	8	4	no	—
324	D₄×D₄₇	—	8	4	no	—
325	D₄×D₄₇	—	8	4	no	—
326	#10625350	—	8	4	no	—
327	C₂×D₁₈₈	—	2	4	no	—
328	C₂×D₁₈₈	—	2	4	no	—
329	C₂×D₁₈₈	—	2	2	no	—
330	C₂×D₁₈₈	—	2	2	no	—
331	C₂×D₁₈₈	—	2	2	no	—
332	C₂×D₁₈₈	—	2	2	no	—
333	C₂×D₁₈₈	—	2	2	no	—
334	C₂×D₁₈₈	—	2	2	no	—
335	C₂×D₁₈₈	—	4	2	no	—
336	C₂×D₁₈₈	—	4	2	no	—
337	C₂×D₁₈₈	C₂⁴	1	2	yes	—
338	C₂×D₁₈₈	C₂⁴	1	2	yes	—
339	C₂×D₁₈₈	C₂⁴	1	2	yes	—
340	C₂×C₄×D₄₇	—	2	2	no	—
341	C₂×C₄×D₄₇	—	2	2	no	—
342	C₂×C₄×D₄₇	—	2	2	no	—
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	—	2	2	no	—
348	C₂×C₄×D₄₇	—	8	4	no	—
349	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
350	C₂×Dic₉₄	—	2	2	no	—
351	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
352	D₈×C₄₇	—	2	2	no	—
353	C₂×C₈×C₄₇	—	2	2	no	—
354	C₂×C₈×C₄₇	—	2	2	no	—
355	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
356	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
357	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
358	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
359	C₄⋊C₄×C₄₇	—	2	2	no	—
360	C₄⋊C₄×C₄₇	—	2	2	no	—
361	C₄⋊C₄×C₄₇	—	2	2	no	—
362	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
363	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
364	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
365	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
366	C₂²⋊C₄×C₄₇	—	2	2	no	—
367	C₂²⋊C₄×C₄₇	—	2	2	no	—
368	C₂²⋊C₄×C₄₇	—	2	2	no	—
369	C₂²⋊C₄×C₄₇	—	2	2	no	—
370	C₂²⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
371	C₂²⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
372	C₄²×C₄₇	—	2	2	no	—
373	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
374	C₂²⋊Dic₄₇	—	2	2	no	—
375	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
376	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
377	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
378	C₂²⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
379	#10625334	—	2	4	no	—
380	#10625334	—	4	2	no	—
381	#10625334	—	4	2	no	—
382	(C₂×D₄₇)⋊C₄	—	2	2	no	—
383	(C₂×D₄₇)⋊C₄	—	2	2	no	—
384	(C₂×D₄₇)⋊C₄	—	2	2	no	—
385	(C₂×D₄₇)⋊C₄	—	2	2	no	—
386	(C₂×D₄₇)⋊C₄	—	2	2	no	—
387	(C₂×D₄₇)⋊C₄	—	2	2	no	—
388	(C₂×D₄₇)⋊C₄	—	2	2	no	—
389	(C₂×D₄₇)⋊C₄	—	2	2	no	—
390	(C₂×D₄₇)⋊C₄	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
396	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
397	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
398	(C₂×D₄₇)⋊C₄	C₂×D₄	1	1	yes	characteristic
399	C₄⋊Dic₄₇	—	2	2	no	—
400	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
401	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
402	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
403	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
404	Dic₄₇⋊C₄	—	2	2	no	—
405	Dic₄₇⋊C₄	—	2	2	no	—
406	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
407	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
408	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
409	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
410	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
411	Dic₄₇⋊C₄	C₂×D₄	1	1	yes	characteristic
412	C₄×Dic₄₇	—	2	2	no	—
413	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
414	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
415	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
416	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
417	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
418	#10625329	—	4	1	no	—
419	C₂×C₄₇⋊C₈	—	4	1	no	—
420	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
421	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
422	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
423	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
424	D₃₇₆	—	2	4	no	—
425	D₃₇₆	—	2	4	no	—
426	D₃₇₆	—	2	2	no	—
427	D₃₇₆	—	2	2	no	—
428	D₃₇₆	—	4	2	no	—
429	D₃₇₆	#41	1	4	yes	complemented
430	#10625324	—	4	1	no	—
431	C₈×D₄₇	—	2	2	no	—
432	C₂³×C₄₇	—	2	2	no	—
433	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
434	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
435	C₂²×D₄₇	—	2	2	no	—
436	C₂²×D₄₇	—	2	2	no	—
437	C₂²×D₄₇	—	2	2	no	—
438	C₂²×D₄₇	—	4	4	no	—
439	C₂²×D₄₇	—	4	4	no	—
440	C₂²×D₄₇	—	4	4	no	—
441	C₂²×D₄₇	—	4	4	no	—
442	C₂²×D₄₇	—	8	2	no	—
443	C₂²×D₄₇	—	8	2	no	—
444	C₂²×D₄₇	—	8	2	no	—
445	C₂²×D₄₇	—	8	2	no	—
446	C₂²×D₄₇	—	8	2	no	—
447	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
448	D₄×C₄₇	—	2	2	no	—
449	D₄×C₄₇	—	2	2	no	—
450	D₄×C₄₇	—	2	2	no	—
451	D₄×C₄₇	—	4	4	no	—
452	D₄×C₄₇	—	8	2	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	2	no	—
458	C₂×C₄×C₄₇	—	2	2	no	—
459	C₂×C₄×C₄₇	—	2	2	no	—
460	C₂×C₄×C₄₇	—	8	2	no	—
461	C₂×C₄×C₄₇	—	8	2	no	—
462	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
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	C₂⁵	1	1	yes	characteristic
467	C₂²⋊D₄₇	—	2	2	no	—
468	C₂²⋊D₄₇	—	2	2	no	—
469	C₂²⋊D₄₇	—	4	4	no	—
470	C₂²⋊D₄₇	—	4	4	no	—
471	C₂²⋊D₄₇	—	4	4	no	—
472	C₂²⋊D₄₇	—	8	2	no	—
473	C₂²⋊D₄₇	—	8	2	no	—
474	C₂²⋊D₄₇	—	8	2	no	—
475	C₂²⋊D₄₇	—	8	2	no	—
476	C₂×Dic₄₇	—	2	2	no	—
477	C₂×Dic₄₇	—	2	2	no	—
478	C₂×Dic₄₇	—	2	2	no	—
479	C₂×Dic₄₇	—	8	2	no	—
480	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
481	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
482	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
483	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
484	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
485	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
486	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
487	D₁₈₈	—	2	2	no	—
488	D₁₈₈	—	2	2	no	—
489	D₁₈₈	—	2	2	no	—
490	D₁₈₈	—	2	2	no	—
491	D₁₈₈	—	2	2	no	—
492	D₁₈₈	—	4	4	no	—
493	D₁₈₈	—	4	4	no	—
494	D₁₈₈	—	8	2	no	—
495	D₁₈₈	—	8	2	no	—
496	D₁₈₈	—	8	2	no	—
497	D₁₈₈	—	8	2	no	—
498	D₁₈₈	C₂×#41	1	4	yes	—
499	C₄×D₄₇	—	2	1	no	—
500	C₄×D₄₇	—	2	1	no	—
501	C₄×D₄₇	—	4	4	no	—
502	C₄×D₄₇	—	4	4	no	—
503	C₄×D₄₇	—	8	2	no	—
504	C₄×D₄₇	—	8	2	no	—
505	C₄×D₄₇	—	8	2	no	—
506	C₄×D₄₇	—	8	2	no	—
507	C₄×D₄₇	—	8	2	no	—
508	C₄×D₄₇	—	8	2	no	—
509	Dic₉₄	—	2	2	no	—
510	Dic₉₄	—	8	2	no	—
511	C₈×C₄₇	—	2	1	no	—
512	C₈×C₄₇	—	2	1	no	—
513	C₈×C₄₇	—	2	1	no	—
514	C₈×C₄₇	C₂×#41	1	2	yes	—
515	C₄₇⋊C₈	—	2	1	no	—
516	C₄₇⋊C₈	—	2	1	no	—
517	C₄₇⋊C₈	—	2	1	no	—
518	C₄₇⋊C₈	—	2	1	no	—
519	#61480	—	47	1	no	maximal, Sylow
520	C₂²×C₄₇	—	2	1	no	—
521	C₂²×C₄₇	—	2	1	no	—
522	C₂²×C₄₇	—	2	1	no	—
523	C₂²×C₄₇	—	2	1	no	—
524	C₂²×C₄₇	—	2	1	no	—
525	C₂²×C₄₇	—	4	2	no	—
526	C₂²×C₄₇	—	4	2	no	—
527	C₂²×C₄₇	—	4	2	no	—
528	C₂²×C₄₇	#576	1	2	yes	—
529	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
530	C₂×D₄₇	—	2	1	no	—
531	C₂×D₄₇	—	2	4	no	—
532	C₂×D₄₇	—	2	1	no	—
533	C₂×D₄₇	—	2	1	no	—
534	C₂×D₄₇	—	4	2	no	—
535	C₂×D₄₇	—	4	2	no	—
536	C₂×D₄₇	—	4	2	no	—
537	C₂×D₄₇	—	4	2	no	—
538	C₂×D₄₇	—	4	2	no	—
539	C₂×D₄₇	—	4	2	no	—
540	C₂×D₄₇	—	4	2	no	—
541	C₂×D₄₇	—	4	2	no	—
542	C₂×D₄₇	—	8	8	no	—
543	C₂×D₄₇	—	16	4	no	—
544	C₂×D₄₇	—	16	4	no	—
545	C₄×C₄₇	—	2	1	no	—
546	C₄×C₄₇	—	2	1	no	—
547	C₄×C₄₇	—	2	1	no	—
548	C₄×C₄₇	—	2	1	no	—
549	C₄×C₄₇	—	4	2	no	—
550	C₄×C₄₇	—	4	2	no	—
551	C₄×C₄₇	—	4	2	no	—
552	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
553	C₄×C₄₇	#585	1	1	yes	characteristic
554	Dic₄₇	—	2	1	no	—
555	Dic₄₇	—	2	1	no	—
556	Dic₄₇	—	2	1	no	—
557	Dic₄₇	—	2	1	no	—
558	Dic₄₇	—	2	1	no	—
559	Dic₄₇	—	2	1	no	—
560	Dic₄₇	—	4	2	no	—
561	Dic₄₇	#576	1	2	yes	—
562	#3519	—	47	2	no	—
563	#3391	—	47	1	no	—
564	#3380	—	47	1	no	—
565	#3366	—	47	2	no	—
566	#3341	—	47	1	no	—
567	#3339	—	47	1	no	—
568	#3339	D₄₇	1	1	yes	characteristic, complemented
569	#3325	—	47	2	no	—
570	#3318	—	47	2	no	—
571	#3318	—	47	2	no	—
572	D₄×D₈	—	47	1	no	—
573	D₄×D₈	—	47	1	no	—
574	D₄×D₈	—	47	1	no	—
575	#3176	—	47	1	no	—
576	#3176	—	47	1	no	—
577	#3169	—	47	1	no	—
578	#3122	—	47	2	no	—
579	#3122	—	47	2	no	—
580	#3109	—	47	2	no	—
581	#2966	—	47	1	no	—
582	#2948	—	47	1	no	—
583	#2948	—	47	1	no	—
584	C₂×C₄×D₈	—	47	1	no	—
585	C₂×C₄₇	—	2	2	no	—
586	C₂×C₄₇	—	4	1	no	—
587	C₂×C₄₇	—	8	2	no	—
588	C₂×C₄₇	D₄×#41	1	1	yes	characteristic
589	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
590	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
591	D₄₇	—	4	1	no	—
592	D₄₇	—	4	4	no	—
593	D₄₇	—	8	2	no	—
594	D₄₇	—	8	2	no	—
595	C₂²×D₈	—	47	1	no	—
596	C₂²×D₈	—	47	1	no	—
597	C₂²×D₈	—	47	1	no	—
598	#555	—	47	2	no	—
599	#554	—	47	2	no	—
600	#553	—	47	2	no	—
601	#553	—	94	2	no	—
602	#553	C₂×D₄₇	1	2	yes	complemented
603	#550	—	47	2	no	—
604	#546	—	94	2	no	—
605	#546	—	94	2	no	—
606	#546	—	94	2	no	—
607	D₄²	—	47	2	no	—
608	D₄²	—	47	2	no	—
609	D₄²	—	47	2	no	—
610	#540	—	47	2	no	—
611	#540	—	47	2	no	—
612	#538	—	94	2	no	—
613	#538	—	94	2	no	—
614	#532	—	47	2	no	—
615	#529	—	47	1	no	—
616	#525	—	94	2	no	—
617	C₂×#121	—	94	2	no	—
618	#518	—	47	2	no	—
619	#518	—	47	2	no	—
620	C₂×C₄×D₄	—	47	2	no	—
621	#500	—	47	1	no	—
622	#499	—	47	1	no	—
623	#499	C₂×D₄₇	1	1	yes	characteristic, complemented
624	#493	—	47	1	no	—
625	#493	—	47	1	no	—
626	#493	—	47	1	no	—
627	#490	—	47	2	no	—
628	#490	—	47	2	no	—
629	#486	—	47	2	no	—
630	#482	—	47	2	no	—
631	#482	—	47	2	no	—
632	#482	—	47	2	no	—
633	#482	C₂×D₄₇	1	2	yes	complemented
634	#481	—	47	2	no	—
635	#481	C₂×D₄₇	1	2	yes	complemented
636	#478	—	47	2	no	—
637	#478	—	47	2	no	—
638	#478	—	47	2	no	—
639	#478	C₂×D₄₇	1	2	yes	complemented
640	#476	—	47	2	no	—
641	#476	—	47	2	no	—
642	#469	—	47	2	no	—
643	#469	—	47	2	no	—
644	#466	—	47	1	no	—
645	#466	—	47	1	no	—
646	#466	—	47	2	no	—
647	#466	—	47	1	no	—
648	#466	—	47	1	no	—
649	#466	C₂×D₄₇	1	1	yes	characteristic, complemented
650	#466	C₂×D₄₇	1	1	yes	characteristic, complemented
651	#459	—	47	2	no	—
652	#459	—	47	2	no	—
653	#459	—	47	2	no	—
654	#459	—	47	2	no	—
655	#459	—	47	2	no	—
656	#459	—	47	2	no	—
657	#447	—	47	2	no	—
658	#447	—	47	2	no	—
659	#447	—	47	2	no	—
660	#447	—	47	2	no	—
661	#447	—	47	2	no	—
662	#447	—	47	2	no	—
663	#446	—	47	1	no	—
664	C₈×Q₈	—	47	1	no	—
665	#442	—	47	2	no	—
666	#442	—	47	2	no	—
667	#442	—	47	2	no	—
668	#442	—	47	2	no	—
669	#442	—	47	2	no	—
670	#442	—	47	2	no	—
671	C₄×D₈	—	47	1	no	—
672	C₄×D₈	—	47	1	no	—
673	C₄×D₈	—	47	1	no	—
674	C₄×D₈	—	47	2	no	—
675	C₄×D₈	—	47	2	no	—
676	C₄×D₈	—	47	1	no	—
677	C₄×D₈	—	47	1	no	—
678	C₄×D₈	—	47	1	no	—
679	C₄×D₈	—	47	1	no	—
680	C₄×D₈	—	47	1	no	—
681	C₄×D₈	—	47	2	no	—
682	C₄×D₈	—	47	1	no	—
683	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic, complemented
684	#436	—	47	1	no	—
685	#435	—	47	1	no	—
686	#435	—	47	1	no	—
687	C₈×D₄	—	47	1	no	—
688	C₈×D₄	—	47	1	no	—
689	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
690	#433	—	47	1	no	—
691	#433	—	47	1	no	—
692	#432	—	47	1	no	—
693	#427	—	47	1	no	—
694	#427	C₂×D₄₇	1	1	yes	characteristic, complemented
695	C₂×#107	C₂×D₄₇	1	1	yes	characteristic, complemented
696	#418	—	47	2	no	—
697	#418	—	47	2	no	—
698	C₂×#102	—	47	2	no	—
699	#405	—	47	1	no	—
700	#405	—	47	1	no	—
701	C₂×C₄×C₈	—	47	1	no	—
702	C₄₇	#61480	1	1	yes	characteristic, complemented, Sylow
703	C₂×#41	—	94	2	no	—
704	C₂×#41	—	94	2	no	—
705	C₂²×D₄	—	47	2	no	—
706	C₂²×D₄	—	47	2	no	—
707	C₂²×D₄	—	47	2	no	—
708	C₂²×D₄	—	94	2	no	—
709	C₂²×D₄	—	94	2	no	—
710	C₂²×D₄	—	94	2	no	—
711	C₂³×C₄	—	94	2	no	—
712	C₂×D₈	—	47	2	no	—
713	C₂×D₈	—	47	2	no	—
714	C₂×D₈	—	47	2	no	—
715	C₂×D₈	—	47	1	no	—
716	C₂×D₈	—	47	2	no	—
717	C₂×D₈	—	47	1	no	—
718	C₂×D₈	—	47	1	no	—
719	C₂×D₈	—	47	2	no	—
720	C₂×D₈	—	47	2	no	—
721	C₂×D₈	—	94	4	no	—
722	C₂×D₈	—	94	4	no	—
723	C₂×D₈	—	94	4	no	—
724	C₂×D₈	C₂²×D₄₇	1	1	yes	characteristic
725	C₂×M₁₆	—	47	1	no	—
726	C₂×M₁₆	—	47	1	no	—
727	C₂²×C₈	—	47	1	no	—
728	C₂²×C₈	—	47	1	no	—
729	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
730	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
731	C₄⋊Q₈	—	47	2	no	—
732	#127	—	47	2	no	—
733	#127	—	47	2	no	—
734	#127	—	47	2	no	—
735	#126	—	2	2	no	—
736	#126	—	47	1	no	—
737	#126	—	47	1	no	—
738	#126	—	94	2	no	—
739	#125	—	47	1	no	—
740	#125	—	47	2	no	—
741	#125	C₂²×D₄₇	1	2	yes	—
742	#124	—	47	1	no	—
743	#124	—	94	2	no	—
744	#124	—	94	2	no	—
745	#124	—	94	2	no	—
746	#123	—	2	2	no	—
747	#123	—	47	1	no	—
748	#123	—	47	1	no	—
749	#123	—	94	2	no	—
750	#123	—	94	2	no	—
751	#123	—	94	2	no	—
752	#123	—	94	2	no	—
753	#123	—	94	2	no	—
754	C₂²⋊Q₈	—	47	1	no	—
755	C₂²⋊Q₈	—	94	2	no	—
756	C₂²⋊Q₈	—	94	2	no	—
757	C₂²⋊Q₈	—	94	2	no	—
758	#121	—	2	2	no	—
759	#121	—	47	1	no	—
760	#121	—	47	2	no	—
761	#121	—	47	2	no	—
762	#121	—	47	2	no	—
763	#121	—	47	2	no	—
764	#121	—	94	2	no	—
765	#121	—	94	2	no	—
766	#121	—	94	2	no	—
767	#121	—	94	2	no	—
768	#121	—	94	2	no	—
769	#121	—	94	2	no	—
770	#121	—	94	2	no	—
771	#121	—	94	2	no	—
772	#121	—	94	2	no	—
773	#121	—	94	2	no	—
774	#121	—	94	2	no	—
775	#121	—	94	2	no	—
776	#121	—	94	2	no	—
777	#121	C₂²×D₄₇	1	2	yes	—
778	#121	C₂²×D₄₇	1	2	yes	—
779	#120	—	94	2	no	—
780	#120	—	94	2	no	—
781	#120	—	94	2	no	—
782	#120	—	94	2	no	—
783	#120	—	94	2	no	—
784	#120	—	94	2	no	—
785	C₄×Q₈	—	47	1	no	—
786	C₄×D₄	—	2	2	no	—
787	C₄×D₄	—	47	1	no	—
788	C₄×D₄	—	47	1	no	—
789	C₄×D₄	—	47	2	no	—
790	C₄×D₄	—	47	2	no	—
791	C₄×D₄	—	47	2	no	—
792	C₄×D₄	—	47	2	no	—
793	C₄×D₄	—	47	2	no	—
794	C₄×D₄	—	47	2	no	—
795	C₄×D₄	—	47	2	no	—
796	C₄×D₄	—	47	2	no	—
797	C₄×D₄	—	47	2	no	—
798	C₄×D₄	—	94	2	no	—
799	C₄×D₄	—	94	2	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	—	94	2	no	—
805	C₄×D₄	—	94	2	no	—
806	C₄×D₄	C₂²×D₄₇	1	2	yes	—
807	C₄×D₄	C₂²×D₄₇	1	1	yes	characteristic
808	#117	—	47	1	no	—
809	#117	—	47	1	no	—
810	#117	—	47	2	no	—
811	#117	—	94	2	no	—
812	#117	C₂²×D₄₇	1	2	yes	—
813	C₂×C₄⋊C₄	—	94	2	no	—
814	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
815	C₂×C₂²⋊C₄	—	94	2	no	—
816	C₂×C₂²⋊C₄	—	94	2	no	—
817	C₂×C₂²⋊C₄	—	94	2	no	—
818	C₂×C₂²⋊C₄	—	94	2	no	—
819	C₂×C₂²⋊C₄	—	94	2	no	—
820	C₂×C₄²	—	47	1	no	—
821	#107	—	47	1	no	—
822	#107	—	47	2	no	—
823	#107	C₂²×D₄₇	1	1	yes	characteristic
824	#107	C₂²×D₄₇	1	1	yes	characteristic
825	#107	C₂²×D₄₇	1	2	yes	—
826	#107	C₂²×D₄₇	1	1	yes	characteristic
827	#106	—	47	2	no	—
828	#106	—	47	2	no	—
829	#106	C₂²×D₄₇	1	2	yes	—
830	#106	C₂²×D₄₇	1	2	yes	—
831	C₄⋊C₈	—	47	1	no	—
832	C₄⋊C₈	—	47	1	no	—
833	C₄⋊C₈	—	47	1	no	—
834	C₄⋊C₈	—	47	1	no	—
835	C₄⋊C₈	—	47	1	no	—
836	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
837	#102	—	47	2	no	—
838	#102	—	47	2	no	—
839	#102	—	47	2	no	—
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	2	yes	—
851	#102	C₂²×D₄₇	1	2	yes	—
852	#102	C₂²×D₄₇	1	2	yes	—
853	C₂²⋊C₈	—	47	1	no	—
854	C₂²⋊C₈	—	47	1	no	—
855	C₂²⋊C₈	—	47	1	no	—
856	C₂²⋊C₈	—	47	1	no	—
857	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
858	C₂²⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
859	#97	—	47	1	no	—
860	#97	—	47	1	no	—
861	#97	—	47	1	no	—
862	#97	—	47	1	no	—
863	C₄×C₈	—	47	1	no	—
864	C₄×C₈	—	47	1	no	—
865	C₄×C₈	—	47	1	no	—
866	C₄×C₈	—	47	1	no	—
867	C₄×C₈	—	47	1	no	—
868	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
869	C₂⁴	—	94	2	no	—
870	C₂⁴	—	94	2	no	—
871	C₂⁴	—	94	2	no	—
872	#41	—	376	4	no	—
873	#41	—	376	4	no	—
874	C₂×Q₈	—	47	1	no	—
875	C₂×Q₈	—	94	2	no	—
876	C₂×D₄	—	2	2	no	—
877	C₂×D₄	—	2	2	no	—
878	C₂×D₄	—	47	1	no	—
879	C₂×D₄	—	47	1	no	—
880	C₂×D₄	—	47	2	no	—
881	C₂×D₄	—	47	2	no	—
882	C₂×D₄	—	47	2	no	—
883	C₂×D₄	—	94	4	no	—
884	C₂×D₄	—	94	4	no	—
885	C₂×D₄	—	94	2	no	—
886	C₂×D₄	—	94	2	no	—
887	C₂×D₄	—	94	2	no	—
888	C₂×D₄	—	94	2	no	—
889	C₂×D₄	—	94	2	no	—
890	C₂×D₄	—	94	2	no	—
891	C₂×D₄	—	94	2	no	—
892	C₂×D₄	—	94	4	no	—
893	C₂×D₄	—	94	2	no	—
894	C₂×D₄	—	94	2	no	—
895	C₂×D₄	—	94	2	no	—
896	C₂×D₄	—	94	2	no	—
897	C₂×D₄	—	94	2	no	—
898	C₂×D₄	—	94	2	no	—
899	C₂×D₄	—	376	4	no	—
900	C₂×D₄	—	376	4	no	—
901	C₂×D₄	—	376	4	no	—
902	C₂×D₄	—	188	2	no	—
903	C₂×D₄	—	188	2	no	—
904	C₂×D₄	—	188	2	no	—
905	C₂×D₄	D₄×D₄₇	1	1	yes	characteristic
906	C₂×D₄	C₂³×D₄₇	1	2	yes	—
907	C₂²×C₄	—	2	2	no	—
908	C₂²×C₄	—	2	2	no	—
909	C₂²×C₄	—	47	1	no	—
910	C₂²×C₄	—	47	1	no	—
911	C₂²×C₄	—	47	1	no	—
912	C₂²×C₄	—	94	2	no	—
913	C₂²×C₄	—	94	2	no	—
914	C₂²×C₄	—	94	2	no	—
915	C₂²×C₄	—	94	2	no	—
916	C₂²×C₄	—	94	2	no	—
917	C₂²×C₄	—	94	2	no	—
918	C₂²×C₄	—	94	2	no	—
919	C₂²×C₄	—	94	2	no	—
920	C₂²×C₄	—	94	2	no	—
921	C₂²×C₄	—	376	4	no	—
922	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
923	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
924	D₈	—	2	2	no	—
925	D₈	—	47	4	no	—
926	D₈	—	94	4	no	—
927	D₈	—	94	4	no	—
928	D₈	—	94	4	no	—
929	D₈	—	94	2	no	—
930	D₈	—	94	2	no	—
931	D₈	—	188	2	no	—
932	D₈	—	188	2	no	—
933	D₈	—	188	2	no	—
934	M₁₆	—	188	1	no	—
935	M₁₆	—	188	1	no	—
936	C₂×C₈	—	2	2	no	—
937	C₂×C₈	—	2	2	no	—
938	C₂×C₈	—	47	1	no	—
939	C₂×C₈	—	47	1	no	—
940	C₂×C₈	—	47	1	no	—
941	C₂×C₈	—	47	1	no	—
942	C₂×C₈	—	94	2	no	—
943	C₂×C₈	—	188	1	no	—
944	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
945	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
946	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
947	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
948	C₄⋊C₄	—	2	2	no	—
949	C₄⋊C₄	—	2	2	no	—
950	C₄⋊C₄	—	2	2	no	—
951	C₄⋊C₄	—	47	1	no	—
952	C₄⋊C₄	—	47	1	no	—
953	C₄⋊C₄	—	47	1	no	—
954	C₄⋊C₄	—	47	1	no	—
955	C₄⋊C₄	—	47	1	no	—
956	C₄⋊C₄	—	47	1	no	—
957	C₄⋊C₄	—	47	1	no	—
958	C₄⋊C₄	—	47	1	no	—
959	C₄⋊C₄	—	47	1	no	—
960	C₄⋊C₄	—	47	2	no	—
961	C₄⋊C₄	—	94	2	no	—
962	C₄⋊C₄	—	94	2	no	—
963	C₄⋊C₄	—	94	2	no	—
964	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
965	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
966	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
967	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
968	C₂²⋊C₄	—	2	2	no	—
969	C₂²⋊C₄	—	2	2	no	—
970	C₂²⋊C₄	—	2	2	no	—
971	C₂²⋊C₄	—	2	2	no	—
972	C₂²⋊C₄	—	47	1	no	—
973	C₂²⋊C₄	—	47	1	no	—
974	C₂²⋊C₄	—	47	1	no	—
975	C₂²⋊C₄	—	47	1	no	—
976	C₂²⋊C₄	—	47	1	no	—
977	C₂²⋊C₄	—	47	1	no	—
978	C₂²⋊C₄	—	47	1	no	—
979	C₂²⋊C₄	—	47	1	no	—
980	C₂²⋊C₄	—	94	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	C₂²⋊C₄	—	94	2	no	—
990	C₂²⋊C₄	—	94	2	no	—
991	C₂²⋊C₄	—	94	2	no	—
992	C₂²⋊C₄	—	94	2	no	—
993	C₂²⋊C₄	—	94	2	no	—
994	C₂²⋊C₄	D₄×D₄₇	1	1	yes	characteristic
995	C₂²⋊C₄	D₄×D₄₇	1	1	yes	characteristic
996	C₄²	—	2	2	no	—
997	C₄²	—	47	1	no	—
998	C₄²	—	47	1	no	—
999	C₄²	—	47	1	no	—
1000	C₄²	—	47	1	no	—
1001	C₄²	—	47	1	no	—
1002	C₄²	—	94	2	no	—
1003	C₄²	C₂³×D₄₇	1	1	yes	characteristic
1004	C₂³	—	2	2	no	—
1005	C₂³	—	47	1	no	—
1006	C₂³	—	94	2	no	—
1007	C₂³	—	94	2	no	—
1008	C₂³	—	94	2	no	—
1009	C₂³	—	376	2	no	—
1010	C₂³	—	376	2	no	—
1011	C₂³	—	376	2	no	—
1012	C₂³	—	376	2	no	—
1013	C₂³	—	376	2	no	—
1014	C₂³	—	188	4	no	—
1015	C₂³	—	188	4	no	—
1016	C₂³	—	188	4	no	—
1017	C₂³	—	188	4	no	—
1018	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1019	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
1020	Q₈	—	94	2	no	—
1021	Q₈	—	376	2	no	—
1022	D₄	—	2	2	no	—
1023	D₄	—	2	2	no	—
1024	D₄	—	2	2	no	—
1025	D₄	—	4	4	no	—
1026	D₄	—	8	2	no	—
1027	D₄	—	47	4	no	—
1028	D₄	—	94	2	no	—
1029	D₄	—	94	2	no	—
1030	D₄	—	94	2	no	—
1031	D₄	—	94	2	no	—
1032	D₄	—	94	2	no	—
1033	D₄	—	94	2	no	—
1034	D₄	—	94	2	no	—
1035	D₄	—	376	2	no	—
1036	D₄	—	376	2	no	—
1037	D₄	—	376	2	no	—
1038	D₄	—	376	2	no	—
1039	D₄	—	376	2	no	—
1040	D₄	—	376	2	no	—
1041	D₄	—	376	2	no	—
1042	D₄	—	376	2	no	—
1043	D₄	—	188	4	no	—
1044	D₄	—	188	4	no	—
1045	D₄	—	188	4	no	—
1046	D₄	—	188	4	no	—
1047	D₄	—	188	4	no	—
1048	C₂×C₄	—	2	1	no	—
1049	C₂×C₄	—	2	1	no	—
1050	C₂×C₄	—	2	1	no	—
1051	C₂×C₄	—	2	1	no	—
1052	C₂×C₄	—	2	2	no	—
1053	C₂×C₄	—	2	2	no	—
1054	C₂×C₄	—	2	2	no	—
1055	C₂×C₄	—	8	2	no	—
1056	C₂×C₄	—	8	2	no	—
1057	C₂×C₄	—	47	1	no	—
1058	C₂×C₄	—	47	1	no	—
1059	C₂×C₄	—	47	1	no	—
1060	C₂×C₄	—	47	1	no	—
1061	C₂×C₄	—	47	1	no	—
1062	C₂×C₄	—	47	1	no	—
1063	C₂×C₄	—	47	1	no	—
1064	C₂×C₄	—	94	2	no	—
1065	C₂×C₄	—	94	2	no	—
1066	C₂×C₄	—	94	1	no	—
1067	C₂×C₄	—	94	1	no	—
1068	C₂×C₄	—	94	2	no	—
1069	C₂×C₄	—	376	2	no	—
1070	C₂×C₄	—	376	2	no	—
1071	C₂×C₄	—	376	2	no	—
1072	C₂×C₄	—	376	2	no	—
1073	C₂×C₄	—	376	2	no	—
1074	C₂×C₄	—	376	2	no	—
1075	C₂×C₄	—	376	2	no	—
1076	C₂×C₄	—	188	4	no	—
1077	C₂×C₄	—	188	4	no	—
1078	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1079	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1080	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1081	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
1082	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
1083	C₈	—	2	1	no	—
1084	C₈	—	2	1	no	—
1085	C₈	—	2	1	no	—
1086	C₈	—	94	1	no	—
1087	C₈	—	94	1	no	—
1088	C₈	—	94	1	no	—
1089	C₈	—	94	1	no	—
1090	C₈	#41×D₄₇	1	2	yes	—
1091	C₂²	—	2	1	no	—
1092	C₂²	—	2	1	no	—
1093	C₂²	—	2	1	no	—
1094	C₂²	—	2	1	no	—
1095	C₂²	—	2	1	no	—
1096	C₂²	—	4	2	no	—
1097	C₂²	—	4	2	no	—
1098	C₂²	—	4	2	no	—
1099	C₂²	—	94	1	no	—
1100	C₂²	—	94	1	no	—
1101	C₂²	—	94	1	no	—
1102	C₂²	—	94	4	no	—
1103	C₂²	—	376	8	no	—
1104	C₂²	—	188	2	no	—
1105	C₂²	—	188	2	no	—
1106	C₂²	—	188	2	no	—
1107	C₂²	—	188	2	no	—
1108	C₂²	—	188	2	no	—
1109	C₂²	—	188	2	no	—
1110	C₂²	—	188	2	no	—
1111	C₂²	—	188	2	no	—
1112	C₂²	—	752	4	no	—
1113	C₂²	—	752	4	no	—
1114	C₂²	#15689925	1	2	yes	—
1115	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
1116	C₄	—	2	1	no	—
1117	C₄	—	2	1	no	—
1118	C₄	—	2	1	no	—
1119	C₄	—	2	1	no	—
1120	C₄	—	4	2	no	—
1121	C₄	—	4	2	no	—
1122	C₄	—	4	2	no	—
1123	C₄	—	47	2	no	—
1124	C₄	—	94	1	no	—
1125	C₄	—	94	1	no	—
1126	C₄	—	94	1	no	—
1127	C₄	—	94	1	no	—
1128	C₄	—	94	1	no	—
1129	C₄	—	94	1	no	—
1130	C₄	—	188	2	no	—
1131	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
1132	C₄	#15689960	1	1	yes	characteristic
1133	C₂	—	2	2	no	—
1134	C₂	—	4	1	no	—
1135	C₂	—	8	2	no	—
1136	C₂	—	376	2	no	—
1137	C₂	—	376	2	no	—
1138	C₂	—	188	1	no	—
1139	C₂	—	188	4	no	—
1140	C₂	#20256875	1	1	yes	characteristic
1141	C₂	#576×D₄₇	1	1	yes	characteristic
1142	C₂	C₂×#15689925	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×#3339	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3339	D₄₇
hypocenter	C₄₇	#61480
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₄×D₄ ◁ #3339

Complements

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

N	H ≅ G/N	type
1. #20257416	C₂	semidirect
2. #20256362	C₂	semidirect
3. #20256252	C₂	semidirect
4. #20256098	C₂	semidirect
5. #20255808	C₂	semidirect
6. #20255786	C₂	semidirect
7. #20255628	C₂	semidirect
8. #20255527	C₂	semidirect
9. #20255523	C₂	semidirect
10. D₄×D₃₇₆	C₂	semidirect
11. #20255062	C₂	semidirect
12. #20255062	C₂	semidirect
13. #20254039	C₂	semidirect
14. #20254031	C₂	semidirect
15. #20253962	C₂	semidirect
16. #20253633	C₂	semidirect
17. #20253627	C₂	semidirect
18. #20253476	C₂	semidirect
19. #20252356	C₂	semidirect
20. #20252239	C₂	semidirect
21. #20252235	C₂	semidirect
22. C₂×#15689205	C₂	semidirect
23. C₄₇×#3339	C₂	semidirect
27. #15689836	C₂²	semidirect
28. #15689829	C₂²	semidirect
30. #15689821	C₂²	semidirect
31. #15689794	C₂²	semidirect
35. D₄×D₁₈₈	C₂²	semidirect
36. #15689757	C₂²	semidirect
37. #15689757	C₂²	semidirect
38. #15689729	C₂²	semidirect
39. #15689726	C₂²	semidirect
42. #15689668	C₂²	semidirect
46. #15689597	C₂²	semidirect
47. #15689595	C₂²	semidirect
48. C₂×#13093986	C₂²	semidirect
49. #15689527	C₂²	semidirect
50. #15689524	C₂²	semidirect
51. #15689500	C₂²	semidirect
52. #15689498	C₂²	semidirect
53. #15689498	C₂²	semidirect
54. #15689489	C₂²	semidirect
55. #15689486	C₂²	semidirect
56. #15689468	C₂²	semidirect
57. #15689450	C₂²	semidirect
58. #15689449	C₂²	semidirect
59. #15689447	C₂²	semidirect
60. #15689441	C₂²	semidirect
61. #15689426	C₂²	semidirect
62. #15689422	C₂²	semidirect
63. #15689420	C₂²	semidirect
64. #15689412	C₂²	semidirect
65. #15689412	C₂²	semidirect
66. #15689377	C₂²	semidirect
67. #15689374	C₂²	semidirect
68. #15689360	C₂²	semidirect
69. #15689360	C₂²	semidirect
70. #15689359	C₂²	semidirect
71. #15689359	C₂²	semidirect
72. #15689357	C₂²	semidirect
73. #15689319	C₂²	semidirect
74. #15689318	C₂²	semidirect
75. #15689317	C₂²	semidirect
76. #15689317	C₂²	semidirect
77. #15689317	C₂²	semidirect
78. #15689317	C₂²	semidirect
79. #15689259	C₂²	semidirect
80. #15689259	C₂²	semidirect
81. #15689258	C₂²	semidirect
82. #15689258	C₂²	semidirect
83. #15689256	C₂²	semidirect
84. #15689256	C₂²	semidirect
85. #15689252	C₂²	semidirect
86. C₈×Dic₉₄	C₂²	semidirect
87. #15689234	C₂²	semidirect
88. #15689234	C₂²	semidirect
89. #15689234	C₂²	semidirect
90. #15689233	C₂²	semidirect
91. #15689232	C₂²	semidirect
92. #15689232	C₂²	semidirect
94. D₈×Dic₄₇	C₂²	semidirect
98. #15689205	C₂²	semidirect
99. #15689205	C₂²	semidirect
100. #15689205	C₂²	semidirect
101. #15689205	C₂²	semidirect
102. #15689205	C₂²	semidirect
103. #15689205	C₂²	semidirect
104. #15689203	C₂²	semidirect
105. #15689198	C₂²	semidirect
106. #15689195	C₂²	semidirect
107. #15689191	C₂²	semidirect
108. C₈×C₂²⋊D₄₇	C₂²	semidirect
109. C₈×C₂²⋊D₄₇	C₂²	semidirect
110. #15689183	C₂²	semidirect
111. #15689181	C₂²	semidirect
112. #15689177	C₂²	semidirect
113. #15689160	C₂²	semidirect
114. #15689127	C₂²	semidirect
115. #15689126	C₂²	semidirect
116. C₂×#13093944	C₂²	semidirect
117. #15689078	C₂²	semidirect
118. #15689077	C₂²	semidirect
119. C₂×C₈×Dic₄₇	C₂²	semidirect
120. C₄₇×#553	C₂²	semidirect
121. C₄₇×#499	C₂²	semidirect
122. C₄₇×#482	C₂²	semidirect
123. C₄₇×#481	C₂²	semidirect
124. C₄₇×#478	C₂²	semidirect
125. C₄₇×#466	C₂²	semidirect
126. C₄₇×#466	C₂²	semidirect
127. C₄×D₈×C₄₇	C₂²	semidirect
128. C₈×D₄×C₄₇	C₂²	semidirect
129. C₄₇×#427	C₂²	semidirect
130. C₂×#107×C₄₇	C₂²	semidirect
429. D₃₇₆	#41	semidirect
568. #3339	D₄₇	semidirect
602. #553	C₂×D₄₇	semidirect
623. #499	C₂×D₄₇	semidirect
633. #482	C₂×D₄₇	semidirect
635. #481	C₂×D₄₇	semidirect
639. #478	C₂×D₄₇	semidirect
649. #466	C₂×D₄₇	semidirect
650. #466	C₂×D₄₇	semidirect
683. C₄×D₈	C₂×D₄₇	semidirect
689. C₈×D₄	C₂×D₄₇	semidirect
694. #427	C₂×D₄₇	semidirect
695. C₂×#107	C₂×D₄₇	semidirect
702. C₄₇	#61480	semidirect

Maximal subgroups

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

subgroup	index
#20257416	2
#20256362	2
#20256252	2
#20256098	2
#20255808	2
#20255786	2
#20255628	2
#20255527	2
#20255523	2
D₄×D₃₇₆	2
#20255062	2
#20254039	2
#20254031	2
#20253962	2
#20253633	2
#20253627	2
#20253476	2
#20252356	2
#20252239	2
#20252235	2
C₂×#15689205	2
C₄₇×#3339	2
#61480	47