Subgroups — D₄₇×#2957 #27080593

Order 12032.

2642 conjugacy classes of subgroups.

The subgroup lattice has 1020 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#135×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#568×D₄₇	C₂	1	2	yes	maximal, complemented
3	#20252306	C₂	1	1	yes	maximal, characteristic, complemented
4	#20252305	C₂	1	1	yes	maximal, characteristic, complemented
5	#20252304	C₂	1	1	yes	maximal, characteristic, complemented
6	#20252303	C₂	1	2	yes	maximal, complemented
7	#20252302	C₂	1	4	yes	maximal, complemented
8	#20252301	C₂	1	2	yes	maximal, complemented
9	#20252300	C₂	1	4	yes	maximal, complemented
10	#444×D₄₇	C₂	1	4	yes	maximal, complemented
11	#443×D₄₇	C₂	1	4	yes	maximal, complemented
12	C₂×#108×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#421×D₄₇	C₂	1	2	yes	maximal, complemented
14	#405×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#2957	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×D₄₇	C₂²	1	2	yes	—
17	C₂×#13094047	C₄	1	1	yes	characteristic, complemented
18	C₂×#13094046	C₂²	1	1	yes	characteristic
19	C₂×#13094045	C₄	1	2	yes	complemented
20	C₂×#13094044	C₂²	1	2	yes	—
21	C₂×#13094043	C₄	1	1	yes	characteristic, complemented
22	#135×D₄₇	C₄	1	2	yes	complemented
23	#135×D₄₇	C₄	1	2	yes	complemented
24	#135×D₄₇	C₄	1	2	yes	complemented
25	#135×D₄₇	C₄	1	2	yes	complemented
26	#135×D₄₇	C₂²	1	2	yes	—
27	#135×D₄₇	C₂²	1	2	yes	—
28	#135×D₄₇	C₂²	1	2	yes	—
29	#135×D₄₇	C₂²	1	2	yes	—
30	C₂×Q₁₆×D₄₇	C₄	1	1	yes	characteristic, complemented
31	C₂×SD₁₆×D₄₇	C₄	1	2	yes	complemented
32	C₂×D₈×D₄₇	C₄	1	1	yes	characteristic, complemented
33	#15689890	C₂²	1	2	yes	complemented
34	#15689889	—	2	4	no	—
35	#15689889	C₂²	1	2	yes	complemented
36	#15689889	C₂²	1	2	yes	complemented
37	#15689888	—	2	4	no	—
38	#15689888	C₂²	1	8	yes	complemented
39	#131×D₄₇	—	2	4	no	—
40	#131×D₄₇	C₂²	1	8	yes	complemented
41	C₂×M₁₆×D₄₇	—	2	4	no	—
42	C₂×M₁₆×D₄₇	C₂²	1	2	yes	—
43	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
44	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
45	#117×D₄₇	C₂²	1	1	yes	characteristic
46	#15689246	C₂²	1	4	yes	complemented
47	#15689245	C₂²	1	4	yes	complemented
48	#15689244	C₂²	1	4	yes	complemented
49	#15689243	C₂²	1	8	yes	complemented
50	#15689242	C₂²	1	8	yes	complemented
51	#15689241	C₂²	1	4	yes	complemented
52	#15689240	C₂²	1	4	yes	complemented
53	#15689239	C₂²	1	4	yes	complemented
54	#15689238	C₂²	1	8	yes	complemented
55	#15689237	C₂²	1	8	yes	complemented
56	C₂×#13093960	C₂²	1	1	yes	characteristic, complemented
57	C₂×#13093959	C₂²	1	2	yes	complemented
58	#108×D₄₇	C₂²	1	2	yes	complemented
59	#108×D₄₇	C₂²	1	2	yes	complemented
60	#108×D₄₇	C₂²	1	2	yes	complemented
61	#108×D₄₇	C₂²	1	2	yes	complemented
62	#15689141	C₂²	1	2	yes	complemented
63	#15689140	C₂²	1	2	yes	complemented
64	#15689139	C₂²	1	2	yes	complemented
65	#15689138	C₂²	1	8	yes	complemented
66	#104×D₄₇	C₂²	1	8	yes	complemented
67	#15689081	C₂²	1	1	yes	characteristic, complemented
68	#15689080	C₂²	1	2	yes	complemented
69	#15689079	C₂²	1	1	yes	characteristic, complemented
70	#15689078	C₂²	1	1	yes	characteristic, complemented
71	#15689077	C₂²	1	2	yes	complemented
72	#97×D₄₇	C₂²	1	2	yes	complemented
73	C₄×C₈×D₄₇	C₂²	1	2	yes	complemented
74	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
75	C₄₇×#568	C₂²	1	2	yes	complemented
76	C₄₇×#444	C₂²	1	4	yes	complemented
77	C₄₇×#443	C₂²	1	4	yes	complemented
78	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic, complemented
79	C₄₇×#421	C₂²	1	2	yes	complemented
80	C₄₇×#405	C₂²	1	1	yes	characteristic, complemented
81	C₂×#10625354	C₂×C₄	1	2	yes	—
82	C₂×#10625350	—	2	2	no	—
83	C₂×#10625350	C₂³	1	2	yes	—
84	C₂×#10625352	—	2	2	no	—
85	C₂×#10625352	C₂×C₄	1	2	yes	—
86	#41×D₄₇	—	2	2	no	—
87	#41×D₄₇	—	2	2	no	—
88	#41×D₄₇	—	2	2	no	—
89	#41×D₄₇	—	2	2	no	—
90	#41×D₄₇	C₂×C₄	1	4	yes	—
91	#41×D₄₇	C₂×C₄	1	4	yes	—
92	#41×D₄₇	C₂³	1	4	yes	—
93	#41×D₄₇	C₂³	1	4	yes	—
94	C₂×Q₈×D₄₇	C₂×C₄	1	2	yes	—
95	C₂×D₄×D₄₇	—	2	2	no	—
96	C₂×D₄×D₄₇	C₂×C₄	1	2	yes	—
97	C₂²×C₄×D₄₇	—	2	2	no	—
98	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
99	#13094047	C₂×C₄	1	2	yes	—
100	#13094047	C₂×C₄	1	2	yes	—
101	#13094047	C₂×C₄	1	2	yes	complemented
102	#13094047	C₂×C₄	1	2	yes	complemented
103	#13094046	C₂×C₄	1	2	yes	complemented
104	#13094046	C₂×C₄	1	2	yes	complemented
105	#13094046	C₂³	1	2	yes	—
106	#13094046	C₂³	1	2	yes	—
107	#13094045	C₂×C₄	1	4	yes	—
108	#13094045	C₂×C₄	1	4	yes	—
109	#13094045	C₂×C₄	1	4	yes	complemented
110	#13094045	C₂×C₄	1	4	yes	complemented
111	#13094044	C₂×C₄	1	4	yes	complemented
112	#13094044	C₂×C₄	1	4	yes	complemented
113	#13094044	C₂³	1	4	yes	—
114	#13094044	C₂³	1	4	yes	—
115	#13094043	C₂×C₄	1	2	yes	—
116	#13094043	C₂×C₄	1	2	yes	—
117	#13094043	C₂×C₄	1	2	yes	complemented
118	#13094043	C₂×C₄	1	2	yes	complemented
119	C₂×Dic₁₈₈	C₂×C₄	1	1	yes	characteristic, complemented
120	C₂×#10625337	C₂×C₄	1	2	yes	complemented
121	Q₁₆×D₄₇	C₂×C₄	1	2	yes	—
122	Q₁₆×D₄₇	C₂×C₄	1	2	yes	—
123	Q₁₆×D₄₇	C₂×C₄	1	2	yes	complemented
124	Q₁₆×D₄₇	C₂×C₄	1	2	yes	complemented
125	C₂×#10625325	C₂×C₄	1	2	yes	complemented
126	C₂×#10625335	C₂×C₄	1	2	yes	complemented
127	C₂×#10625336	C₂×C₄	1	2	yes	complemented
128	SD₁₆×D₄₇	C₂×C₄	1	4	yes	—
129	SD₁₆×D₄₇	C₂×C₄	1	4	yes	—
130	SD₁₆×D₄₇	C₂×C₄	1	4	yes	complemented
131	SD₁₆×D₄₇	C₂×C₄	1	4	yes	complemented
132	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic, complemented
133	C₂×#10625334	C₂×C₄	1	2	yes	complemented
134	D₈×D₄₇	C₂×C₄	1	2	yes	—
135	D₈×D₄₇	C₂×C₄	1	2	yes	—
136	D₈×D₄₇	C₂×C₄	1	2	yes	complemented
137	D₈×D₄₇	C₂×C₄	1	2	yes	complemented
138	#13094032	—	2	4	no	—
139	#13094032	—	2	8	no	—
140	#13094032	—	2	8	no	—
141	#13094032	C₂³	1	8	yes	complemented
142	#13094031	—	2	4	no	—
143	#13094031	C₂³	1	8	yes	complemented
144	#13094030	—	2	4	no	—
145	#13094030	—	2	8	no	—
146	#13094030	—	2	8	no	—
147	#13094030	C₂³	1	8	yes	complemented
148	C₂×#10625329	—	2	4	no	—
149	C₂×#10625329	C₂³	1	2	yes	—
150	C₂×#10625329	C₂³	1	1	yes	characteristic
151	C₂×#10625324	—	2	2	no	—
152	C₂×#10625324	—	2	8	no	—
153	C₂×#10625324	C₂³	1	2	yes	—
154	M₁₆×D₄₇	—	2	2	no	—
155	M₁₆×D₄₇	—	2	2	no	—
156	M₁₆×D₄₇	—	2	4	no	—
157	M₁₆×D₄₇	—	2	4	no	—
158	M₁₆×D₄₇	—	2	8	no	—
159	M₁₆×D₄₇	—	2	8	no	—
160	M₁₆×D₄₇	D₄	1	2	yes	—
161	M₁₆×D₄₇	D₄	1	2	yes	—
162	M₁₆×D₄₇	D₄	1	2	yes	—
163	M₁₆×D₄₇	D₄	1	2	yes	—
164	M₁₆×D₄₇	C₂³	1	4	yes	—
165	M₁₆×D₄₇	C₂³	1	4	yes	—
166	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
167	C₂×C₈×D₄₇	—	2	2	no	—
168	C₂×C₈×D₄₇	—	2	8	no	—
169	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
170	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
171	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
172	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
173	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
174	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
175	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
176	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
177	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
178	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
179	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
180	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
181	C₂×C₈×D₄₇	C₂³	1	2	yes	—
182	#13093983	C₂³	1	1	yes	characteristic
183	#13093982	—	2	1	no	—
184	#13093981	C₂³	1	2	yes	—
185	#13093980	—	2	1	no	—
186	C₄⋊C₄×D₄₇	—	2	1	no	—
187	C₂²⋊C₄×D₄₇	—	2	1	no	—
188	C₄²×D₄₇	C₂³	1	2	yes	—
189	#13093960	C₂³	1	2	yes	complemented
190	#13093960	C₂³	1	2	yes	complemented
191	#13093959	C₂³	1	4	yes	complemented
192	#13093959	C₂³	1	4	yes	complemented
193	#13093952	C₂³	1	8	yes	complemented
194	#13093951	C₂³	1	8	yes	complemented
195	#13093950	C₂³	1	8	yes	complemented
196	#13093935	C₂³	1	2	yes	complemented
197	#13093934	C₂³	1	2	yes	complemented
198	#13093934	C₂³	1	2	yes	complemented
199	C₄×C₄₇⋊C₈	C₂³	1	2	yes	complemented
200	C₈×Dic₄₇	C₂³	1	2	yes	complemented
201	C₈×Dic₄₇	C₂³	1	2	yes	complemented
202	C₂×#41×C₄₇	C₂³	1	2	yes	—
203	#135×C₄₇	C₂×C₄	1	2	yes	complemented
204	#135×C₄₇	C₂×C₄	1	2	yes	complemented
205	#135×C₄₇	C₂³	1	2	yes	—
206	#135×C₄₇	C₂³	1	2	yes	—
207	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
208	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
209	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
210	#131×C₄₇	—	2	4	no	—
211	#131×C₄₇	C₂³	1	8	yes	complemented
212	C₂×M₁₆×C₄₇	—	2	4	no	—
213	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
214	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
215	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
216	#117×C₄₇	C₂³	1	1	yes	characteristic
217	#108×C₄₇	C₂³	1	2	yes	complemented
218	#108×C₄₇	C₂³	1	2	yes	complemented
219	#104×C₄₇	C₂³	1	8	yes	complemented
220	#97×C₄₇	C₂³	1	2	yes	complemented
221	C₄×C₈×C₄₇	C₂³	1	2	yes	complemented
222	C₂³×D₄₇	—	2	2	no	—
223	C₂³×D₄₇	#41	1	1	yes	characteristic
224	#41×C₄₇	—	2	2	no	—
225	#41×C₄₇	—	2	2	no	—
226	#41×C₄₇	C₂²×C₄	1	4	yes	—
227	#41×C₄₇	C₂⁴	1	4	yes	—
228	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
229	C₂×D₄×C₄₇	—	2	2	no	—
230	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
231	C₂²×C₄×C₄₇	—	2	2	no	—
232	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
233	C₂×C₂²⋊D₄₇	—	2	2	no	—
234	C₂×C₂²⋊D₄₇	—	2	2	no	—
235	C₂×C₂²⋊D₄₇	—	2	2	no	—
236	C₂²×Dic₄₇	—	2	2	no	—
237	C₂²×Dic₄₇	#41	1	1	yes	characteristic
238	#10625354	—	2	2	no	—
239	#10625354	—	2	2	no	—
240	#10625354	C₂²×C₄	1	4	yes	—
241	#10625354	C₂²×C₄	1	4	yes	—
242	Q₈×D₄₇	—	2	2	no	—
243	Q₈×D₄₇	—	2	2	no	—
244	Q₈×D₄₇	C₂²×C₄	1	4	yes	—
245	Q₈×D₄₇	C₂²×C₄	1	4	yes	—
246	#10625352	—	2	4	no	—
247	#10625352	—	2	4	no	—
248	#10625352	—	2	4	no	—
249	#10625352	—	2	4	no	—
250	#10625352	—	2	2	no	—
251	#10625352	—	2	2	no	—
252	#10625352	C₂²×C₄	1	4	yes	—
253	#10625352	C₂²×C₄	1	4	yes	—
254	D₄×D₄₇	—	2	4	no	—
255	D₄×D₄₇	—	2	4	no	—
256	D₄×D₄₇	—	2	4	no	—
257	D₄×D₄₇	—	2	4	no	—
258	D₄×D₄₇	—	2	2	no	—
259	D₄×D₄₇	—	2	2	no	—
260	D₄×D₄₇	C₂²×C₄	1	4	yes	—
261	D₄×D₄₇	C₂²×C₄	1	4	yes	—
262	#10625350	—	2	2	no	—
263	#10625350	—	2	2	no	—
264	#10625350	—	2	4	no	—
265	#10625350	—	2	4	no	—
266	#10625350	—	2	4	no	—
267	#10625350	—	2	4	no	—
268	#10625350	C₂²×C₄	1	4	yes	—
269	#10625350	C₂⁴	1	4	yes	—
270	C₂×D₁₈₈	—	2	2	no	—
271	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
272	C₂×C₄×D₄₇	—	2	2	no	—
273	C₂×C₄×D₄₇	—	2	2	no	—
274	C₂×C₄×D₄₇	—	2	2	no	—
275	C₂×C₄×D₄₇	—	2	4	no	—
276	C₂×C₄×D₄₇	—	2	4	no	—
277	C₂×C₄×D₄₇	—	2	4	no	—
278	C₂×C₄×D₄₇	—	2	4	no	—
279	C₂×C₄×D₄₇	—	2	2	no	—
280	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
281	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
282	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
283	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
284	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
285	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
286	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
287	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
288	C₂×C₄×D₄₇	#41	1	1	yes	characteristic
289	C₂×C₄×D₄₇	#41	1	1	yes	characteristic
290	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
291	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
292	C₂×Dic₉₄	—	2	2	no	—
293	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
294	Q₁₆×C₄₇	C₂²×C₄	1	2	yes	—
295	Q₁₆×C₄₇	C₂²×C₄	1	2	yes	—
296	SD₁₆×C₄₇	C₂²×C₄	1	4	yes	—
297	SD₁₆×C₄₇	C₂²×C₄	1	4	yes	—
298	D₈×C₄₇	C₂²×C₄	1	2	yes	—
299	D₈×C₄₇	C₂²×C₄	1	2	yes	—
300	M₁₆×C₄₇	—	2	2	no	—
301	M₁₆×C₄₇	—	2	8	no	—
302	M₁₆×C₄₇	C₂×D₄	1	2	yes	—
303	M₁₆×C₄₇	C₂×D₄	1	2	yes	—
304	M₁₆×C₄₇	C₂⁴	1	4	yes	—
305	C₂×C₈×C₄₇	—	2	2	no	—
306	C₂×C₈×C₄₇	—	2	8	no	—
307	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
308	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
309	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
310	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
311	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
312	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
313	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
314	C₄⋊C₄×C₄₇	—	2	1	no	—
315	C₂²⋊C₄×C₄₇	—	2	1	no	—
316	C₄²×C₄₇	C₂⁴	1	2	yes	—
317	C₂²⋊Dic₄₇	—	2	1	no	—
318	#10625337	C₂²×C₄	1	4	yes	—
319	#10625337	C₂²×C₄	1	4	yes	—
320	#10625336	C₂²×C₄	1	4	yes	—
321	#10625336	C₂²×C₄	1	4	yes	—
322	#10625335	C₂²×C₄	1	4	yes	—
323	#10625335	C₂²×C₄	1	4	yes	—
324	#10625334	C₂²×C₄	1	4	yes	—
325	#10625334	C₂²×C₄	1	4	yes	—
326	(C₂×D₄₇)⋊C₄	—	2	2	no	—
327	C₄⋊Dic₄₇	—	2	1	no	—
328	Dic₄₇⋊C₄	—	2	2	no	—
329	C₄×Dic₄₇	—	2	2	no	—
330	C₄×Dic₄₇	C₂⁴	1	2	yes	—
331	#10625329	—	2	2	no	—
332	#10625329	—	2	8	no	—
333	#10625329	C₂×D₄	1	2	yes	—
334	#10625329	C₂×D₄	1	2	yes	—
335	#10625329	C₂⁴	1	4	yes	—
336	C₂×C₄₇⋊C₈	—	2	2	no	—
337	C₂×C₄₇⋊C₈	—	2	8	no	—
338	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
339	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
340	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
341	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
342	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
343	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
344	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
345	Dic₁₈₈	C₂²×C₄	1	2	yes	—
346	Dic₁₈₈	C₂²×C₄	1	2	yes	—
347	D₃₇₆	C₂²×C₄	1	2	yes	—
348	D₃₇₆	C₂²×C₄	1	2	yes	—
349	#10625325	C₂²×C₄	1	4	yes	—
350	#10625325	C₂²×C₄	1	4	yes	—
351	#10625324	—	2	4	no	—
352	#10625324	—	2	4	no	—
353	#10625324	—	2	8	no	—
354	#10625324	—	2	8	no	—
355	#10625324	C₂×D₄	1	4	yes	—
356	#10625324	C₂×D₄	1	4	yes	—
357	C₈×D₄₇	—	2	4	no	—
358	C₈×D₄₇	—	2	4	no	—
359	C₈×D₄₇	—	2	8	no	—
360	C₈×D₄₇	—	2	8	no	—
361	C₈×D₄₇	C₂²×C₄	1	1	yes	characteristic
362	C₈×D₄₇	C₂²×C₄	1	1	yes	characteristic
363	C₈×D₄₇	C₂²×C₄	1	1	yes	characteristic
364	C₈×D₄₇	C₂²×C₄	1	1	yes	characteristic
365	C₈×D₄₇	C₂²×C₄	1	1	yes	characteristic
366	C₈×D₄₇	C₂²×C₄	1	1	yes	characteristic
367	C₈×D₄₇	C₂²×C₄	1	1	yes	characteristic
368	C₈×D₄₇	C₂²×C₄	1	1	yes	characteristic
369	C₈×D₄₇	C₂²×C₄	1	1	yes	characteristic
370	C₈×D₄₇	C₂²×C₄	1	1	yes	characteristic
371	C₈×D₄₇	C₂²×C₄	1	1	yes	characteristic
372	C₈×D₄₇	C₂²×C₄	1	1	yes	characteristic
373	C₈×D₄₇	C₂²×C₄	1	1	yes	characteristic
374	C₈×D₄₇	C₂²×C₄	1	1	yes	characteristic
375	C₈×D₄₇	C₂²×C₄	1	1	yes	characteristic
376	C₈×D₄₇	C₂²×C₄	1	1	yes	characteristic
377	C₈×D₄₇	C₂×D₄	1	4	yes	—
378	C₈×D₄₇	C₂×D₄	1	4	yes	—
379	C₂³×C₄₇	—	2	2	no	—
380	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
381	C₂²×D₄₇	—	2	2	no	—
382	C₂²×D₄₇	—	2	4	no	—
383	C₂²×D₄₇	—	2	4	no	—
384	C₂²×D₄₇	—	4	2	no	—
385	C₂²×D₄₇	—	8	4	no	—
386	C₂²×D₄₇	C₄×D₄	1	1	yes	characteristic
387	C₂²×D₄₇	C₄×D₄	1	1	yes	characteristic
388	C₂²×D₄₇	C₄×D₄	1	1	yes	characteristic
389	C₂²×D₄₇	C₄×D₄	1	1	yes	characteristic
390	C₂²×D₄₇	C₂×#41	1	1	yes	characteristic
391	C₂²×D₄₇	C₂×#41	1	1	yes	characteristic
392	Q₈×C₄₇	—	2	2	no	—
393	Q₈×C₄₇	C₂³×C₄	1	4	yes	—
394	D₄×C₄₇	—	2	4	no	—
395	D₄×C₄₇	—	2	4	no	—
396	D₄×C₄₇	—	2	2	no	—
397	D₄×C₄₇	C₂³×C₄	1	4	yes	—
398	C₂×C₄×C₄₇	—	2	2	no	—
399	C₂×C₄×C₄₇	—	2	4	no	—
400	C₂×C₄×C₄₇	—	2	4	no	—
401	C₂×C₄×C₄₇	—	2	2	no	—
402	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
403	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
404	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
405	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
406	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
407	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
408	C₂²⋊D₄₇	—	2	4	no	—
409	C₂²⋊D₄₇	—	2	4	no	—
410	C₂²⋊D₄₇	—	2	4	no	—
411	C₂²⋊D₄₇	—	2	4	no	—
412	C₂²⋊D₄₇	—	2	4	no	—
413	C₂²⋊D₄₇	—	2	4	no	—
414	C₂×Dic₄₇	—	2	2	no	—
415	C₂×Dic₄₇	—	2	4	no	—
416	C₂×Dic₄₇	—	2	4	no	—
417	C₂×Dic₄₇	—	2	2	no	—
418	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
419	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
420	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
421	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
422	C₂×Dic₄₇	C₂×#41	1	1	yes	characteristic
423	C₂×Dic₄₇	C₂×#41	1	1	yes	characteristic
424	D₁₈₈	—	2	4	no	—
425	D₁₈₈	—	2	4	no	—
426	D₁₈₈	—	2	2	no	—
427	D₁₈₈	C₂³×C₄	1	4	yes	—
428	C₄×D₄₇	—	2	4	no	—
429	C₄×D₄₇	—	2	4	no	—
430	C₄×D₄₇	—	2	4	no	—
431	C₄×D₄₇	—	2	4	no	—
432	C₄×D₄₇	—	2	4	no	—
433	C₄×D₄₇	—	2	4	no	—
434	C₄×D₄₇	—	4	4	no	—
435	C₄×D₄₇	C₄×D₄	1	1	yes	characteristic
436	C₄×D₄₇	C₄×D₄	1	1	yes	characteristic
437	C₄×D₄₇	C₄×D₄	1	1	yes	characteristic
438	C₄×D₄₇	C₄×D₄	1	1	yes	characteristic
439	C₄×D₄₇	C₄×D₄	1	1	yes	characteristic
440	C₄×D₄₇	C₄×D₄	1	1	yes	characteristic
441	C₄×D₄₇	C₄×D₄	1	1	yes	characteristic
442	C₄×D₄₇	C₄×D₄	1	1	yes	characteristic
443	C₄×D₄₇	C₂³×C₄	1	1	yes	characteristic
444	C₄×D₄₇	C₂³×C₄	1	1	yes	characteristic
445	C₄×D₄₇	C₂³×C₄	1	1	yes	characteristic
446	C₄×D₄₇	C₂³×C₄	1	1	yes	characteristic
447	C₄×D₄₇	C₂²×D₄	1	1	yes	characteristic
448	C₄×D₄₇	C₂²×D₄	1	1	yes	characteristic
449	C₄×D₄₇	C₂²×D₄	1	1	yes	characteristic
450	C₄×D₄₇	C₂²×D₄	1	1	yes	characteristic
451	Dic₉₄	—	2	2	no	—
452	Dic₉₄	—	2	4	no	—
453	Dic₉₄	—	2	4	no	—
454	Dic₉₄	C₂³×C₄	1	4	yes	—
455	C₈×C₄₇	—	2	4	no	—
456	C₈×C₄₇	C₂³×C₄	1	1	yes	characteristic
457	C₈×C₄₇	C₂³×C₄	1	1	yes	characteristic
458	C₈×C₄₇	C₂³×C₄	1	1	yes	characteristic
459	C₈×C₄₇	C₂³×C₄	1	1	yes	characteristic
460	C₈×C₄₇	C₂²×D₄	1	4	yes	—
461	C₄₇⋊C₈	—	2	4	no	—
462	C₄₇⋊C₈	C₂³×C₄	1	1	yes	characteristic
463	C₄₇⋊C₈	C₂³×C₄	1	1	yes	characteristic
464	C₄₇⋊C₈	C₂³×C₄	1	1	yes	characteristic
465	C₄₇⋊C₈	C₂³×C₄	1	1	yes	characteristic
466	C₄₇⋊C₈	C₂²×D₄	1	4	yes	—
467	C₂×#2957	—	47	1	no	maximal, Sylow
468	C₂²×C₄₇	—	2	4	no	—
469	C₂²×C₄₇	—	4	1	no	—
470	C₂²×C₄₇	—	8	2	no	—
471	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
472	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
473	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
474	C₂×D₄₇	—	2	2	no	—
475	C₂×D₄₇	—	2	2	no	—
476	C₂×D₄₇	—	2	2	no	—
477	C₂×D₄₇	—	2	4	no	—
478	C₂×D₄₇	—	4	1	no	—
479	C₂×D₄₇	—	4	1	no	—
480	C₂×D₄₇	—	4	1	no	—
481	C₂×D₄₇	—	4	8	no	—
482	C₂×D₄₇	—	8	4	no	—
483	C₂×D₄₇	—	8	2	no	—
484	C₂×D₄₇	C₂×C₄×D₄	1	1	yes	characteristic
485	C₂×D₄₇	C₂×C₄×D₄	1	1	yes	characteristic
486	C₂×D₄₇	C₂×C₄×D₄	1	1	yes	characteristic
487	C₂×D₄₇	C₂×C₄×D₄	1	1	yes	characteristic
488	C₄×C₄₇	—	2	4	no	—
489	C₄×C₄₇	—	4	2	no	—
490	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
491	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
492	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
493	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
494	Dic₄₇	—	2	4	no	—
495	Dic₄₇	—	4	2	no	—
496	Dic₄₇	C₂×C₄×D₄	1	1	yes	characteristic
497	Dic₄₇	C₂×C₄×D₄	1	1	yes	characteristic
498	Dic₄₇	C₂×C₄×D₄	1	1	yes	characteristic
499	Dic₄₇	C₂×C₄×D₄	1	1	yes	characteristic
500	C₂²×#135	—	47	1	no	—
501	C₂×#568	—	47	2	no	—
502	#2957	—	47	4	no	—
503	#2957	—	47	4	no	—
504	#2957	—	47	1	no	—
505	#2957	—	47	2	no	—
506	#2957	—	47	1	no	—
507	#2957	—	47	1	no	—
508	#2957	—	47	2	no	—
509	#2957	D₄₇	1	1	yes	characteristic, direct product factor
510	C₂×#444	—	47	4	no	—
511	C₂×#443	—	47	4	no	—
512	C₂²×#108	—	47	1	no	—
513	C₂×#421	—	47	2	no	—
514	C₂×#405	—	47	1	no	—
515	C₂×C₄₇	—	2	1	no	—
516	C₂×C₄₇	—	2	1	no	—
517	C₂×C₄₇	—	2	1	no	—
518	C₂×C₄₇	—	4	4	no	—
519	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
520	D₄₇	—	2	1	no	—
521	D₄₇	—	2	1	no	—
522	D₄₇	—	2	1	no	—
523	D₄₇	—	4	4	no	—
524	D₄₇	#2957	1	2	yes	direct product factor
525	C₂²×#41	—	47	2	no	—
526	C₂×#135	—	47	2	no	—
527	C₂×#135	—	47	2	no	—
528	C₂×#135	—	47	2	no	—
529	C₂×#135	—	47	2	no	—
530	C₂×#135	—	47	2	no	—
531	C₂×#135	—	47	2	no	—
532	C₂×#135	—	47	2	no	—
533	C₂×#135	—	47	2	no	—
534	C₂×#135	—	47	2	no	—
535	C₂×#135	—	47	1	no	—
536	C₂×#135	—	47	2	no	—
537	C₂×#135	—	47	1	no	—
538	C₂×#135	—	47	1	no	—
539	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
540	C₂²×Q₁₆	—	47	1	no	—
541	C₂²×SD₁₆	—	47	2	no	—
542	C₂²×D₈	—	47	1	no	—
543	#568	—	47	2	no	—
544	#568	—	47	8	no	—
545	#568	—	47	2	no	—
546	#568	—	47	2	no	—
547	#568	—	94	4	no	—
548	#568	—	94	4	no	—
549	#568	C₂×D₄₇	1	2	yes	complemented
550	C₂×#131	—	47	8	no	—
551	C₂×#131	—	94	4	no	—
552	C₂²×M₁₆	—	47	1	no	—
553	C₂²×M₁₆	—	47	2	no	—
554	C₂²×M₁₆	—	94	4	no	—
555	C₂³×C₈	—	47	1	no	—
556	C₂×#117	—	47	1	no	—
557	#444	—	47	4	no	—
558	#444	—	47	8	no	—
559	#444	—	47	4	no	—
560	#444	—	47	8	no	—
561	#444	—	47	4	no	—
562	#444	C₂×D₄₇	1	4	yes	complemented
563	#443	—	47	4	no	—
564	#443	—	47	8	no	—
565	#443	—	47	4	no	—
566	#443	—	47	8	no	—
567	#443	—	47	4	no	—
568	#443	C₂×D₄₇	1	4	yes	complemented
569	C₂×#108	—	47	2	no	—
570	C₂×#108	—	47	1	no	—
571	C₂×#108	—	47	2	no	—
572	C₂×#108	—	47	2	no	—
573	C₂×#108	—	47	2	no	—
574	C₂×#108	—	47	2	no	—
575	C₂×#108	C₂×D₄₇	1	1	yes	characteristic, complemented
576	#421	—	47	2	no	—
577	#421	—	47	2	no	—
578	#421	—	47	2	no	—
579	#421	—	47	8	no	—
580	#421	C₂×D₄₇	1	2	yes	complemented
581	C₂×#104	—	47	8	no	—
582	#405	—	47	1	no	—
583	#405	—	47	1	no	—
584	#405	—	47	1	no	—
585	#405	—	47	2	no	—
586	#405	—	47	2	no	—
587	#405	C₂×D₄₇	1	1	yes	characteristic, complemented
588	C₂×#97	—	47	2	no	—
589	C₂×C₄×C₈	—	47	2	no	—
590	C₄₇	C₂×#2957	1	1	yes	characteristic, complemented, Sylow
591	C₂×#41	—	47	4	no	—
592	C₂×#41	—	47	4	no	—
593	C₂×#41	—	47	4	no	—
594	C₂×#41	—	47	4	no	—
595	C₂×#41	—	47	2	no	—
596	C₂×#41	—	47	2	no	—
597	C₂×#41	—	47	2	no	—
598	C₂×#41	—	94	2	no	—
599	C₂×#41	—	94	2	no	—
600	C₂×#41	—	94	2	no	—
601	C₂×#41	—	94	2	no	—
602	C₂×#41	—	94	2	no	—
603	C₂×#41	—	94	2	no	—
604	C₂×#41	C₂²×D₄₇	1	2	yes	—
605	C₂²×Q₈	—	47	2	no	—
606	C₂²×D₄	—	47	2	no	—
607	C₂²×D₄	—	94	2	no	—
608	C₂³×C₄	—	47	1	no	—
609	C₂³×C₄	—	94	2	no	—
610	#135	—	47	4	no	—
611	#135	—	47	4	no	—
612	#135	—	47	4	no	—
613	#135	—	47	4	no	—
614	#135	—	47	2	no	—
615	#135	—	47	2	no	—
616	#135	—	47	2	no	—
617	#135	—	47	2	no	—
618	#135	—	47	4	no	—
619	#135	—	47	4	no	—
620	#135	—	47	4	no	—
621	#135	—	47	4	no	—
622	#135	—	47	2	no	—
623	#135	—	47	2	no	—
624	#135	—	47	2	no	—
625	#135	—	47	2	no	—
626	#135	—	47	2	no	—
627	#135	—	47	2	no	—
628	#135	—	47	2	no	—
629	#135	—	47	2	no	—
630	#135	C₄×D₄₇	1	2	yes	complemented
631	#135	C₄×D₄₇	1	2	yes	complemented
632	#135	C₂²×D₄₇	1	2	yes	—
633	#135	C₂²×D₄₇	1	2	yes	—
634	C₂×Q₁₆	—	47	2	no	—
635	C₂×Q₁₆	—	47	2	no	—
636	C₂×Q₁₆	—	47	2	no	—
637	C₂×Q₁₆	—	47	2	no	—
638	C₂×Q₁₆	—	47	2	no	—
639	C₂×Q₁₆	—	47	1	no	—
640	C₂×Q₁₆	C₄×D₄₇	1	1	yes	characteristic, complemented
641	C₂×SD₁₆	—	47	2	no	—
642	C₂×SD₁₆	—	47	2	no	—
643	C₂×SD₁₆	—	47	4	no	—
644	C₂×SD₁₆	—	47	4	no	—
645	C₂×SD₁₆	—	47	4	no	—
646	C₂×SD₁₆	—	47	4	no	—
647	C₂×SD₁₆	—	47	2	no	—
648	C₂×SD₁₆	C₄×D₄₇	1	2	yes	complemented
649	C₂×D₈	—	47	2	no	—
650	C₂×D₈	—	47	2	no	—
651	C₂×D₈	—	47	2	no	—
652	C₂×D₈	—	47	2	no	—
653	C₂×D₈	—	47	2	no	—
654	C₂×D₈	—	47	1	no	—
655	C₂×D₈	C₄×D₄₇	1	1	yes	characteristic, complemented
656	#131	—	2	4	no	—
657	#131	—	47	8	no	—
658	#131	—	47	8	no	—
659	#131	—	47	8	no	—
660	#131	—	94	8	no	—
661	#131	—	94	4	no	—
662	#131	—	94	8	no	—
663	#131	—	94	8	no	—
664	#131	—	94	8	no	—
665	#131	—	94	4	no	—
666	#131	—	94	4	no	—
667	#131	C₂²×D₄₇	1	8	yes	complemented
668	C₂×M₁₆	—	2	4	no	—
669	C₂×M₁₆	—	47	1	no	—
670	C₂×M₁₆	—	47	2	no	—
671	C₂×M₁₆	—	47	2	no	—
672	C₂×M₁₆	—	47	2	no	—
673	C₂×M₁₆	—	47	2	no	—
674	C₂×M₁₆	—	47	2	no	—
675	C₂×M₁₆	—	47	2	no	—
676	C₂×M₁₆	—	47	4	no	—
677	C₂×M₁₆	—	47	4	no	—
678	C₂×M₁₆	—	94	8	no	—
679	C₂×M₁₆	—	94	2	no	—
680	C₂×M₁₆	—	94	8	no	—
681	C₂×M₁₆	—	94	4	no	—
682	C₂×M₁₆	—	94	8	no	—
683	C₂×M₁₆	—	94	2	no	—
684	C₂×M₁₆	—	94	2	no	—
685	C₂×M₁₆	—	94	4	no	—
686	C₂×M₁₆	—	94	4	no	—
687	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
688	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
689	C₂²×C₈	—	47	1	no	—
690	C₂²×C₈	—	47	1	no	—
691	C₂²×C₈	—	47	1	no	—
692	C₂²×C₈	—	47	1	no	—
693	C₂²×C₈	—	47	1	no	—
694	C₂²×C₈	—	47	1	no	—
695	C₂²×C₈	—	47	1	no	—
696	C₂²×C₈	—	47	1	no	—
697	C₂²×C₈	—	47	1	no	—
698	C₂²×C₈	—	47	1	no	—
699	C₂²×C₈	—	47	1	no	—
700	C₂²×C₈	—	47	1	no	—
701	C₂²×C₈	—	47	1	no	—
702	C₂²×C₈	—	47	2	no	—
703	C₂²×C₈	—	94	8	no	—
704	C₂²×C₈	—	94	2	no	—
705	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
706	#117	—	47	1	no	—
707	#117	—	47	2	no	—
708	#117	—	94	1	no	—
709	#117	—	94	1	no	—
710	#117	C₂²×D₄₇	1	1	yes	characteristic
711	C₂×C₄⋊C₄	—	94	1	no	—
712	C₂×C₂²⋊C₄	—	94	1	no	—
713	C₂×C₄²	—	47	2	no	—
714	#108	—	47	4	no	—
715	#108	—	47	4	no	—
716	#108	—	47	2	no	—
717	#108	—	47	2	no	—
718	#108	C₂²×D₄₇	1	2	yes	complemented
719	#108	C₂²×D₄₇	1	2	yes	complemented
720	#104	—	47	8	no	—
721	#104	—	47	8	no	—
722	#104	—	47	8	no	—
723	#104	C₂²×D₄₇	1	8	yes	complemented
724	#97	—	47	2	no	—
725	#97	—	47	2	no	—
726	#97	—	47	2	no	—
727	#97	C₂²×D₄₇	1	2	yes	complemented
728	C₄×C₈	—	47	2	no	—
729	C₄×C₈	—	47	2	no	—
730	C₄×C₈	—	47	2	no	—
731	C₄×C₈	C₂²×D₄₇	1	2	yes	complemented
732	C₂⁴	—	47	1	no	—
733	C₂⁴	—	94	2	no	—
734	#41	—	2	2	no	—
735	#41	—	2	2	no	—
736	#41	—	47	4	no	—
737	#41	—	47	4	no	—
738	#41	—	47	4	no	—
739	#41	—	47	4	no	—
740	#41	—	47	4	no	—
741	#41	—	47	4	no	—
742	#41	—	94	4	no	—
743	#41	—	94	4	no	—
744	#41	—	94	4	no	—
745	#41	—	94	4	no	—
746	#41	—	94	4	no	—
747	#41	—	94	4	no	—
748	#41	—	94	4	no	—
749	#41	—	94	4	no	—
750	#41	—	94	2	no	—
751	#41	—	94	2	no	—
752	#41	—	94	2	no	—
753	#41	—	94	2	no	—
754	#41	—	94	2	no	—
755	#41	—	94	2	no	—
756	#41	C₂×C₄×D₄₇	1	4	yes	—
757	#41	C₂³×D₄₇	1	4	yes	—
758	C₂×Q₈	—	47	4	no	—
759	C₂×Q₈	—	47	4	no	—
760	C₂×Q₈	—	47	2	no	—
761	C₂×Q₈	—	94	2	no	—
762	C₂×Q₈	—	94	2	no	—
763	C₂×Q₈	—	94	2	no	—
764	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
765	C₂×D₄	—	2	2	no	—
766	C₂×D₄	—	47	4	no	—
767	C₂×D₄	—	47	4	no	—
768	C₂×D₄	—	47	2	no	—
769	C₂×D₄	—	94	2	no	—
770	C₂×D₄	—	94	2	no	—
771	C₂×D₄	—	94	2	no	—
772	C₂×D₄	—	94	2	no	—
773	C₂×D₄	—	94	4	no	—
774	C₂×D₄	—	94	4	no	—
775	C₂×D₄	—	94	4	no	—
776	C₂×D₄	—	94	4	no	—
777	C₂×D₄	—	94	2	no	—
778	C₂×D₄	—	94	2	no	—
779	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
780	C₂²×C₄	—	2	2	no	—
781	C₂²×C₄	—	47	1	no	—
782	C₂²×C₄	—	47	1	no	—
783	C₂²×C₄	—	47	1	no	—
784	C₂²×C₄	—	47	1	no	—
785	C₂²×C₄	—	47	1	no	—
786	C₂²×C₄	—	47	1	no	—
787	C₂²×C₄	—	47	1	no	—
788	C₂²×C₄	—	47	1	no	—
789	C₂²×C₄	—	47	1	no	—
790	C₂²×C₄	—	47	1	no	—
791	C₂²×C₄	—	47	1	no	—
792	C₂²×C₄	—	47	1	no	—
793	C₂²×C₄	—	47	1	no	—
794	C₂²×C₄	—	94	4	no	—
795	C₂²×C₄	—	94	4	no	—
796	C₂²×C₄	—	94	2	no	—
797	C₂²×C₄	—	94	4	no	—
798	C₂²×C₄	—	94	4	no	—
799	C₂²×C₄	—	94	2	no	—
800	C₂²×C₄	—	94	2	no	—
801	C₂²×C₄	—	94	2	no	—
802	C₂²×C₄	—	94	2	no	—
803	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
804	Q₁₆	—	47	4	no	—
805	Q₁₆	—	47	4	no	—
806	Q₁₆	—	47	2	no	—
807	Q₁₆	—	47	2	no	—
808	Q₁₆	C₂×C₄×D₄₇	1	2	yes	—
809	Q₁₆	C₂×C₄×D₄₇	1	2	yes	—
810	SD₁₆	—	47	4	no	—
811	SD₁₆	—	47	4	no	—
812	SD₁₆	—	47	4	no	—
813	SD₁₆	—	47	4	no	—
814	SD₁₆	—	47	4	no	—
815	SD₁₆	—	47	4	no	—
816	SD₁₆	C₂×C₄×D₄₇	1	4	yes	—
817	SD₁₆	C₂×C₄×D₄₇	1	4	yes	—
818	D₈	—	47	4	no	—
819	D₈	—	47	4	no	—
820	D₈	—	47	2	no	—
821	D₈	—	47	2	no	—
822	D₈	C₂×C₄×D₄₇	1	2	yes	—
823	D₈	C₂×C₄×D₄₇	1	2	yes	—
824	M₁₆	—	2	2	no	—
825	M₁₆	—	2	8	no	—
826	M₁₆	—	47	2	no	—
827	M₁₆	—	47	2	no	—
828	M₁₆	—	47	4	no	—
829	M₁₆	—	47	4	no	—
830	M₁₆	—	47	4	no	—
831	M₁₆	—	94	8	no	—
832	M₁₆	—	94	4	no	—
833	M₁₆	—	94	4	no	—
834	M₁₆	—	94	8	no	—
835	M₁₆	—	94	2	no	—
836	M₁₆	—	94	8	no	—
837	M₁₆	D₄×D₄₇	1	2	yes	—
838	M₁₆	D₄×D₄₇	1	2	yes	—
839	M₁₆	C₂³×D₄₇	1	4	yes	—
840	C₂×C₈	—	2	2	no	—
841	C₂×C₈	—	2	8	no	—
842	C₂×C₈	—	47	1	no	—
843	C₂×C₈	—	47	1	no	—
844	C₂×C₈	—	47	1	no	—
845	C₂×C₈	—	47	1	no	—
846	C₂×C₈	—	47	1	no	—
847	C₂×C₈	—	47	2	no	—
848	C₂×C₈	—	47	1	no	—
849	C₂×C₈	—	47	1	no	—
850	C₂×C₈	—	47	1	no	—
851	C₂×C₈	—	47	1	no	—
852	C₂×C₈	—	47	1	no	—
853	C₂×C₈	—	47	1	no	—
854	C₂×C₈	—	47	1	no	—
855	C₂×C₈	—	47	1	no	—
856	C₂×C₈	—	47	1	no	—
857	C₂×C₈	—	47	1	no	—
858	C₂×C₈	—	47	1	no	—
859	C₂×C₈	—	47	1	no	—
860	C₂×C₈	—	47	1	no	—
861	C₂×C₈	—	47	1	no	—
862	C₂×C₈	—	47	1	no	—
863	C₂×C₈	—	47	1	no	—
864	C₂×C₈	—	47	1	no	—
865	C₂×C₈	—	47	4	no	—
866	C₂×C₈	—	47	4	no	—
867	C₂×C₈	—	94	8	no	—
868	C₂×C₈	—	94	4	no	—
869	C₂×C₈	—	94	4	no	—
870	C₂×C₈	—	94	8	no	—
871	C₂×C₈	—	94	2	no	—
872	C₂×C₈	—	94	8	no	—
873	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
874	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
875	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
876	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
877	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
878	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
879	C₂×C₈	C₂³×D₄₇	1	2	yes	—
880	C₄⋊C₄	—	2	1	no	—
881	C₄⋊C₄	—	94	2	no	—
882	C₄⋊C₄	—	94	1	no	—
883	C₂²⋊C₄	—	2	1	no	—
884	C₂²⋊C₄	—	94	2	no	—
885	C₂²⋊C₄	—	94	1	no	—
886	C₄²	—	47	2	no	—
887	C₄²	—	94	2	no	—
888	C₄²	C₂³×D₄₇	1	2	yes	—
889	C₂³	—	2	2	no	—
890	C₂³	—	47	1	no	—
891	C₂³	—	47	1	no	—
892	C₂³	—	47	1	no	—
893	C₂³	—	47	1	no	—
894	C₂³	—	47	1	no	—
895	C₂³	—	47	1	no	—
896	C₂³	—	94	4	no	—
897	C₂³	—	94	4	no	—
898	C₂³	—	94	2	no	—
899	C₂³	—	376	4	no	—
900	C₂³	—	188	2	no	—
901	C₂³	#41×D₄₇	1	1	yes	characteristic
902	Q₈	—	2	2	no	—
903	Q₈	—	47	4	no	—
904	Q₈	—	94	4	no	—
905	Q₈	—	94	4	no	—
906	Q₈	—	94	2	no	—
907	Q₈	C₂²×C₄×D₄₇	1	4	yes	—
908	D₄	—	2	4	no	—
909	D₄	—	2	4	no	—
910	D₄	—	2	2	no	—
911	D₄	—	47	4	no	—
912	D₄	—	94	4	no	—
913	D₄	—	94	4	no	—
914	D₄	—	94	4	no	—
915	D₄	—	94	4	no	—
916	D₄	—	94	4	no	—
917	D₄	—	94	4	no	—
918	D₄	—	94	4	no	—
919	D₄	—	94	4	no	—
920	D₄	—	94	2	no	—
921	D₄	C₂²×C₄×D₄₇	1	4	yes	—
922	C₂×C₄	—	2	2	no	—
923	C₂×C₄	—	2	4	no	—
924	C₂×C₄	—	2	4	no	—
925	C₂×C₄	—	2	2	no	—
926	C₂×C₄	—	47	1	no	—
927	C₂×C₄	—	47	1	no	—
928	C₂×C₄	—	47	1	no	—
929	C₂×C₄	—	47	1	no	—
930	C₂×C₄	—	47	1	no	—
931	C₂×C₄	—	47	1	no	—
932	C₂×C₄	—	47	1	no	—
933	C₂×C₄	—	47	1	no	—
934	C₂×C₄	—	47	1	no	—
935	C₂×C₄	—	47	1	no	—
936	C₂×C₄	—	47	1	no	—
937	C₂×C₄	—	47	1	no	—
938	C₂×C₄	—	47	1	no	—
939	C₂×C₄	—	47	1	no	—
940	C₂×C₄	—	47	1	no	—
941	C₂×C₄	—	47	1	no	—
942	C₂×C₄	—	47	1	no	—
943	C₂×C₄	—	47	1	no	—
944	C₂×C₄	—	47	1	no	—
945	C₂×C₄	—	47	1	no	—
946	C₂×C₄	—	47	1	no	—
947	C₂×C₄	—	47	1	no	—
948	C₂×C₄	—	94	4	no	—
949	C₂×C₄	—	94	4	no	—
950	C₂×C₄	—	94	4	no	—
951	C₂×C₄	—	94	4	no	—
952	C₂×C₄	—	94	4	no	—
953	C₂×C₄	—	94	4	no	—
954	C₂×C₄	—	94	2	no	—
955	C₂×C₄	—	94	4	no	—
956	C₂×C₄	—	94	4	no	—
957	C₂×C₄	—	94	2	no	—
958	C₂×C₄	—	188	4	no	—
959	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
960	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
961	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
962	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
963	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
964	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
965	C₈	—	2	4	no	—
966	C₈	—	47	1	no	—
967	C₈	—	47	1	no	—
968	C₈	—	47	1	no	—
969	C₈	—	47	1	no	—
970	C₈	—	47	4	no	—
971	C₈	—	94	4	no	—
972	C₈	C₂²×C₄×D₄₇	1	1	yes	characteristic
973	C₈	C₂²×C₄×D₄₇	1	1	yes	characteristic
974	C₈	C₂²×C₄×D₄₇	1	1	yes	characteristic
975	C₈	C₂²×C₄×D₄₇	1	1	yes	characteristic
976	C₈	C₂×D₄×D₄₇	1	4	yes	—
977	C₂²	—	2	4	no	—
978	C₂²	—	4	1	no	—
979	C₂²	—	8	2	no	—
980	C₂²	—	47	1	no	—
981	C₂²	—	47	1	no	—
982	C₂²	—	47	1	no	—
983	C₂²	—	47	1	no	—
984	C₂²	—	94	2	no	—
985	C₂²	—	94	2	no	—
986	C₂²	—	94	2	no	—
987	C₂²	—	94	4	no	—
988	C₂²	—	376	2	no	—
989	C₂²	—	376	4	no	—
990	C₂²	—	188	1	no	—
991	C₂²	—	188	1	no	—
992	C₂²	—	188	1	no	—
993	C₂²	—	188	8	no	—
994	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
995	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
996	C₂²	C₂×#41×D₄₇	1	1	yes	characteristic
997	C₄	—	2	4	no	—
998	C₄	—	4	2	no	—
999	C₄	—	47	1	no	—
1000	C₄	—	47	1	no	—
1001	C₄	—	47	1	no	—
1002	C₄	—	47	1	no	—
1003	C₄	—	94	4	no	—
1004	C₄	—	188	2	no	—
1005	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
1006	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
1007	C₄	C₂³×C₄×D₄₇	1	1	yes	characteristic
1008	C₄	C₂²×D₄×D₄₇	1	1	yes	characteristic
1009	C₂	—	2	1	no	—
1010	C₂	—	2	1	no	—
1011	C₂	—	2	1	no	—
1012	C₂	—	4	4	no	—
1013	C₂	—	47	2	no	—
1014	C₂	—	94	1	no	—
1015	C₂	—	94	1	no	—
1016	C₂	—	94	1	no	—
1017	C₂	—	188	4	no	—
1018	C₂	C₂×C₄×D₄×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₄	C₂²×D₄×D₄₇
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#2957	C₂
socle	C₂×C₄₇	C₂²×C₄×D₄
prime radical	C₂×#135×D₄₇	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2957	D₄₇
hypocenter	C₄₇	C₂×#2957
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #2957

Complements

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

N	H ≅ G/N	type
2. #568×D₄₇	C₂	semidirect
3. #20252306	C₂	semidirect
4. #20252305	C₂	semidirect
5. #20252304	C₂	semidirect
6. #20252303	C₂	semidirect
7. #20252302	C₂	semidirect
8. #20252301	C₂	semidirect
9. #20252300	C₂	semidirect
10. #444×D₄₇	C₂	semidirect
11. #443×D₄₇	C₂	semidirect
12. C₂×#108×D₄₇	C₂	semidirect
13. #421×D₄₇	C₂	semidirect
14. #405×D₄₇	C₂	semidirect
15. C₄₇×#2957	C₂	semidirect
17. C₂×#13094047	C₄	semidirect
19. C₂×#13094045	C₄	semidirect
21. C₂×#13094043	C₄	semidirect
22. #135×D₄₇	C₄	semidirect
23. #135×D₄₇	C₄	semidirect
24. #135×D₄₇	C₄	semidirect
25. #135×D₄₇	C₄	semidirect
30. C₂×Q₁₆×D₄₇	C₄	semidirect
31. C₂×SD₁₆×D₄₇	C₄	semidirect
32. C₂×D₈×D₄₇	C₄	semidirect
33. #15689890	C₂²	semidirect
35. #15689889	C₂²	semidirect
36. #15689889	C₂²	semidirect
38. #15689888	C₂²	semidirect
40. #131×D₄₇	C₂²	semidirect
46. #15689246	C₂²	semidirect
47. #15689245	C₂²	semidirect
48. #15689244	C₂²	semidirect
49. #15689243	C₂²	semidirect
50. #15689242	C₂²	semidirect
51. #15689241	C₂²	semidirect
52. #15689240	C₂²	semidirect
53. #15689239	C₂²	semidirect
54. #15689238	C₂²	semidirect
55. #15689237	C₂²	semidirect
56. C₂×#13093960	C₂²	semidirect
57. C₂×#13093959	C₂²	semidirect
58. #108×D₄₇	C₂²	semidirect
59. #108×D₄₇	C₂²	semidirect
60. #108×D₄₇	C₂²	semidirect
61. #108×D₄₇	C₂²	semidirect
62. #15689141	C₂²	semidirect
63. #15689140	C₂²	semidirect
64. #15689139	C₂²	semidirect
65. #15689138	C₂²	semidirect
66. #104×D₄₇	C₂²	semidirect
67. #15689081	C₂²	semidirect
68. #15689080	C₂²	semidirect
69. #15689079	C₂²	semidirect
70. #15689078	C₂²	semidirect
71. #15689077	C₂²	semidirect
72. #97×D₄₇	C₂²	semidirect
73. C₄×C₈×D₄₇	C₂²	semidirect
75. C₄₇×#568	C₂²	semidirect
76. C₄₇×#444	C₂²	semidirect
77. C₄₇×#443	C₂²	semidirect
78. C₂×#108×C₄₇	C₂²	semidirect
79. C₄₇×#421	C₂²	semidirect
80. C₄₇×#405	C₂²	semidirect
101. #13094047	C₂×C₄	semidirect
102. #13094047	C₂×C₄	semidirect
103. #13094046	C₂×C₄	semidirect
104. #13094046	C₂×C₄	semidirect
109. #13094045	C₂×C₄	semidirect
110. #13094045	C₂×C₄	semidirect
111. #13094044	C₂×C₄	semidirect
112. #13094044	C₂×C₄	semidirect
117. #13094043	C₂×C₄	semidirect
118. #13094043	C₂×C₄	semidirect
119. C₂×Dic₁₈₈	C₂×C₄	semidirect
120. C₂×#10625337	C₂×C₄	semidirect
123. Q₁₆×D₄₇	C₂×C₄	semidirect
124. Q₁₆×D₄₇	C₂×C₄	semidirect
125. C₂×#10625325	C₂×C₄	semidirect
126. C₂×#10625335	C₂×C₄	semidirect
127. C₂×#10625336	C₂×C₄	semidirect
130. SD₁₆×D₄₇	C₂×C₄	semidirect
131. SD₁₆×D₄₇	C₂×C₄	semidirect
132. C₂×D₃₇₆	C₂×C₄	semidirect
133. C₂×#10625334	C₂×C₄	semidirect
136. D₈×D₄₇	C₂×C₄	semidirect
137. D₈×D₄₇	C₂×C₄	semidirect
141. #13094032	C₂³	semidirect
143. #13094031	C₂³	semidirect
147. #13094030	C₂³	semidirect
189. #13093960	C₂³	semidirect
190. #13093960	C₂³	semidirect
191. #13093959	C₂³	semidirect
192. #13093959	C₂³	semidirect
193. #13093952	C₂³	semidirect
194. #13093951	C₂³	semidirect
195. #13093950	C₂³	semidirect
196. #13093935	C₂³	semidirect
197. #13093934	C₂³	semidirect
198. #13093934	C₂³	semidirect
199. C₄×C₄₇⋊C₈	C₂³	semidirect
200. C₈×Dic₄₇	C₂³	semidirect
201. C₈×Dic₄₇	C₂³	semidirect
203. #135×C₄₇	C₂×C₄	semidirect
204. #135×C₄₇	C₂×C₄	semidirect
207. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
208. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
209. C₂×D₈×C₄₇	C₂×C₄	semidirect
211. #131×C₄₇	C₂³	semidirect
217. #108×C₄₇	C₂³	semidirect
218. #108×C₄₇	C₂³	semidirect
219. #104×C₄₇	C₂³	semidirect
220. #97×C₄₇	C₂³	semidirect
221. C₄×C₈×C₄₇	C₂³	semidirect
509. #2957	D₄₇	direct (N × H)
524. D₄₇	#2957	direct (N × H)
549. #568	C₂×D₄₇	semidirect
562. #444	C₂×D₄₇	semidirect
568. #443	C₂×D₄₇	semidirect
575. C₂×#108	C₂×D₄₇	semidirect
580. #421	C₂×D₄₇	semidirect
587. #405	C₂×D₄₇	semidirect
590. C₄₇	C₂×#2957	semidirect
630. #135	C₄×D₄₇	semidirect
631. #135	C₄×D₄₇	semidirect
640. C₂×Q₁₆	C₄×D₄₇	semidirect
648. C₂×SD₁₆	C₄×D₄₇	semidirect
655. C₂×D₈	C₄×D₄₇	semidirect
667. #131	C₂²×D₄₇	semidirect
718. #108	C₂²×D₄₇	semidirect
719. #108	C₂²×D₄₇	semidirect
723. #104	C₂²×D₄₇	semidirect
727. #97	C₂²×D₄₇	semidirect
731. C₄×C₈	C₂²×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#135×D₄₇	2
#568×D₄₇	2
#20252306	2
#20252305	2
#20252304	2
#20252303	2
#20252302	2
#20252301	2
#20252300	2
#444×D₄₇	2
#443×D₄₇	2
C₂×#108×D₄₇	2
#421×D₄₇	2
#405×D₄₇	2
C₄₇×#2957	2
C₂×#2957	47

Subgroups — D47×#2957 #27080593

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#2957 #27080593