Subgroups — #27080603

Order 12032.

2628 conjugacy classes of subgroups.

The subgroup lattice has 908 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689920	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	#20252301	C₂	1	2	yes	maximal, complemented
8	#20252296	C₂	1	4	yes	maximal, complemented
9	#20252293	C₂	1	4	yes	maximal, complemented
10	#20252288	C₂	1	4	yes	maximal, complemented
11	#20252286	C₂	1	4	yes	maximal, complemented
12	C₂×#15689170	C₂	1	1	yes	maximal, characteristic, complemented
13	#421×D₄₇	C₂	1	2	yes	maximal, complemented
14	#20251804	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	#15689920	C₄	1	4	yes	complemented
18	#15689920	C₄	1	4	yes	complemented
19	#15689920	C₂²	1	2	yes	—
20	#15689920	C₂²	1	2	yes	—
21	#15689920	C₂²	1	2	yes	—
22	#15689920	C₂²	1	2	yes	—
23	C₂×#13094056	C₄	1	2	yes	complemented
24	C₂×#13094053	C₄	1	2	yes	complemented
25	C₂×#13094051	C₄	1	2	yes	complemented
26	C₂×#13094048	C₄	1	2	yes	complemented
27	C₂×#13094046	C₂²	1	1	yes	characteristic
28	C₂×#13094044	C₂²	1	2	yes	—
29	#15689890	C₂²	1	2	yes	complemented
30	#15689889	—	2	4	no	—
31	#15689889	C₂²	1	2	yes	complemented
32	#15689889	C₂²	1	2	yes	complemented
33	#15689888	—	2	4	no	—
34	#15689888	C₂²	1	8	yes	complemented
35	#131×D₄₇	—	2	4	no	—
36	#131×D₄₇	C₂²	1	8	yes	complemented
37	C₂²×#10625324	C₂²	1	1	yes	characteristic
38	C₂×M₁₆×D₄₇	—	2	4	no	—
39	C₂×M₁₆×D₄₇	C₂²	1	2	yes	—
40	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
41	#117×D₄₇	C₂²	1	1	yes	characteristic
42	#15689246	C₂²	1	4	yes	complemented
43	#15689245	C₂²	1	4	yes	complemented
44	#15689244	C₂²	1	4	yes	complemented
45	#15689243	C₂²	1	8	yes	complemented
46	#15689242	C₂²	1	8	yes	complemented
47	#15689241	C₂²	1	4	yes	complemented
48	#15689240	C₂²	1	4	yes	complemented
49	#15689239	C₂²	1	4	yes	complemented
50	#15689238	C₂²	1	8	yes	complemented
51	#15689237	C₂²	1	8	yes	complemented
52	#15689170	C₂²	1	2	yes	complemented
53	#15689170	C₂²	1	2	yes	complemented
54	#15689170	C₂²	1	2	yes	complemented
55	#15689170	C₂²	1	2	yes	complemented
56	C₂×#13093960	C₂²	1	1	yes	characteristic, complemented
57	C₂×#13093959	C₂²	1	2	yes	complemented
58	#15689141	C₂²	1	2	yes	complemented
59	#15689140	C₂²	1	2	yes	complemented
60	#15689139	C₂²	1	2	yes	complemented
61	#15689138	C₂²	1	8	yes	complemented
62	#104×D₄₇	C₂²	1	8	yes	complemented
63	#15689081	C₂²	1	1	yes	characteristic, complemented
64	#15689080	C₂²	1	2	yes	complemented
65	#15689079	C₂²	1	1	yes	characteristic, complemented
66	#15689078	C₂²	1	1	yes	characteristic, complemented
67	#15689077	C₂²	1	2	yes	complemented
68	#15689075	C₂²	1	2	yes	complemented
69	C₄×#10625324	C₂²	1	2	yes	complemented
70	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
71	C₄₇×#568	C₂²	1	2	yes	complemented
72	C₄₇×#444	C₂²	1	4	yes	complemented
73	C₄₇×#443	C₂²	1	4	yes	complemented
74	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic, complemented
75	C₄₇×#421	C₂²	1	2	yes	complemented
76	C₄₇×#405	C₂²	1	1	yes	characteristic, complemented
77	C₂×#10625354	C₂×C₄	1	2	yes	—
78	C₂×#10625350	—	2	2	no	—
79	C₂×#10625350	C₂³	1	2	yes	—
80	C₂×#10625352	—	2	2	no	—
81	C₂×#10625352	C₂×C₄	1	2	yes	—
82	#41×D₄₇	—	2	2	no	—
83	#41×D₄₇	—	2	2	no	—
84	#41×D₄₇	—	2	2	no	—
85	#41×D₄₇	—	2	2	no	—
86	#41×D₄₇	C₂×C₄	1	4	yes	—
87	#41×D₄₇	C₂×C₄	1	4	yes	—
88	#41×D₄₇	C₂³	1	4	yes	—
89	#41×D₄₇	C₂³	1	4	yes	—
90	C₂×Q₈×D₄₇	C₂×C₄	1	2	yes	—
91	C₂×D₄×D₄₇	—	2	2	no	—
92	C₂×D₄×D₄₇	C₂×C₄	1	2	yes	—
93	C₂²×C₄×D₄₇	—	2	2	no	—
94	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
95	#13094056	C₂×C₄	1	4	yes	—
96	#13094056	C₂×C₄	1	4	yes	—
97	#13094056	C₂×C₄	1	4	yes	complemented
98	#13094056	C₂×C₄	1	4	yes	complemented
99	#13094053	C₂×C₄	1	4	yes	—
100	#13094053	C₂×C₄	1	4	yes	—
101	#13094053	C₂×C₄	1	4	yes	complemented
102	#13094053	C₂×C₄	1	4	yes	complemented
103	#13094051	C₂×C₄	1	4	yes	—
104	#13094051	C₂×C₄	1	4	yes	—
105	#13094051	C₂×C₄	1	4	yes	complemented
106	#13094051	C₂×C₄	1	4	yes	complemented
107	#13094048	C₂×C₄	1	4	yes	—
108	#13094048	C₂×C₄	1	4	yes	—
109	#13094048	C₂×C₄	1	4	yes	complemented
110	#13094048	C₂×C₄	1	4	yes	complemented
111	#13094046	C₂×C₄	1	2	yes	complemented
112	#13094046	C₂×C₄	1	2	yes	complemented
113	#13094046	C₂³	1	2	yes	—
114	#13094046	C₂³	1	2	yes	—
115	#13094044	C₂×C₄	1	4	yes	complemented
116	#13094044	C₂×C₄	1	4	yes	complemented
117	#13094044	C₂³	1	4	yes	—
118	#13094044	C₂³	1	4	yes	—
119	C₂×Dic₁₈₈	C₂×C₄	1	1	yes	characteristic, complemented
120	C₂×#10625337	C₂×C₄	1	2	yes	complemented
121	C₂×#10625325	C₂×C₄	1	2	yes	complemented
122	C₂×#10625335	C₂×C₄	1	2	yes	complemented
123	C₂×#10625336	C₂×C₄	1	2	yes	complemented
124	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic, complemented
125	C₂×#10625334	C₂×C₄	1	2	yes	complemented
126	#13094032	—	2	4	no	—
127	#13094032	—	2	8	no	—
128	#13094032	—	2	8	no	—
129	#13094032	C₂³	1	8	yes	complemented
130	#13094031	—	2	4	no	—
131	#13094031	C₂³	1	8	yes	complemented
132	#13094030	—	2	4	no	—
133	#13094030	—	2	8	no	—
134	#13094030	—	2	8	no	—
135	#13094030	C₂³	1	8	yes	complemented
136	C₂×#10625329	—	2	4	no	—
137	C₂×#10625329	C₂³	1	2	yes	—
138	C₂×#10625329	C₂³	1	1	yes	characteristic
139	C₂×#10625324	—	2	2	no	—
140	C₂×#10625324	—	2	8	no	—
141	C₂×#10625324	C₂×C₄	1	2	yes	—
142	C₂×#10625324	C₂×C₄	1	2	yes	—
143	C₂×#10625324	C₂×C₄	1	2	yes	—
144	C₂×#10625324	C₂×C₄	1	2	yes	—
145	C₂×#10625324	C₂³	1	1	yes	characteristic
146	C₂×#10625324	C₂³	1	1	yes	characteristic
147	C₂×#10625324	C₂³	1	1	yes	characteristic
148	C₂×#10625324	C₂³	1	1	yes	characteristic
149	C₂×#10625324	C₂³	1	2	yes	—
150	M₁₆×D₄₇	—	2	2	no	—
151	M₁₆×D₄₇	—	2	2	no	—
152	M₁₆×D₄₇	—	2	4	no	—
153	M₁₆×D₄₇	—	2	4	no	—
154	M₁₆×D₄₇	—	2	8	no	—
155	M₁₆×D₄₇	—	2	8	no	—
156	M₁₆×D₄₇	D₄	1	4	yes	—
157	M₁₆×D₄₇	D₄	1	4	yes	—
158	M₁₆×D₄₇	C₂³	1	4	yes	—
159	M₁₆×D₄₇	C₂³	1	4	yes	—
160	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
161	C₂×C₈×D₄₇	—	2	2	no	—
162	C₂×C₈×D₄₇	—	2	8	no	—
163	C₂×C₈×D₄₇	C₂³	1	2	yes	—
164	#13093983	C₂³	1	1	yes	characteristic
165	#13093982	—	2	1	no	—
166	#13093981	C₂³	1	2	yes	—
167	#13093980	—	2	1	no	—
168	C₄⋊C₄×D₄₇	—	2	1	no	—
169	C₂²⋊C₄×D₄₇	—	2	1	no	—
170	C₄²×D₄₇	C₂³	1	2	yes	—
171	#13093960	C₂³	1	2	yes	complemented
172	#13093960	C₂³	1	2	yes	complemented
173	#13093959	C₂³	1	4	yes	complemented
174	#13093959	C₂³	1	4	yes	complemented
175	#13093952	C₂³	1	8	yes	complemented
176	#13093951	C₂³	1	8	yes	complemented
177	#13093950	C₂³	1	8	yes	complemented
178	#13093935	C₂³	1	2	yes	complemented
179	#13093934	C₂³	1	2	yes	complemented
180	#13093934	C₂³	1	2	yes	complemented
181	C₄×C₄₇⋊C₈	C₂³	1	2	yes	complemented
182	C₈×Dic₄₇	C₂³	1	2	yes	complemented
183	C₈×Dic₄₇	C₂³	1	2	yes	complemented
184	C₂×#41×C₄₇	C₂³	1	2	yes	—
185	#135×C₄₇	C₂×C₄	1	2	yes	complemented
186	#135×C₄₇	C₂×C₄	1	2	yes	complemented
187	#135×C₄₇	C₂³	1	2	yes	—
188	#135×C₄₇	C₂³	1	2	yes	—
189	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
190	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	complemented
191	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic, complemented
192	#131×C₄₇	—	2	4	no	—
193	#131×C₄₇	C₂³	1	8	yes	complemented
194	C₂×M₁₆×C₄₇	—	2	4	no	—
195	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
196	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
197	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
198	#117×C₄₇	C₂³	1	1	yes	characteristic
199	#108×C₄₇	C₂³	1	2	yes	complemented
200	#108×C₄₇	C₂³	1	2	yes	complemented
201	#104×C₄₇	C₂³	1	8	yes	complemented
202	#97×C₄₇	C₂³	1	2	yes	complemented
203	C₄×C₈×C₄₇	C₂³	1	2	yes	complemented
204	C₂³×D₄₇	—	2	2	no	—
205	C₂³×D₄₇	#41	1	1	yes	characteristic
206	#41×C₄₇	—	2	2	no	—
207	#41×C₄₇	—	2	2	no	—
208	#41×C₄₇	C₂²×C₄	1	4	yes	—
209	#41×C₄₇	C₂⁴	1	4	yes	—
210	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
211	C₂×D₄×C₄₇	—	2	2	no	—
212	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
213	C₂²×C₄×C₄₇	—	2	2	no	—
214	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
215	C₂×C₂²⋊D₄₇	—	2	2	no	—
216	C₂×C₂²⋊D₄₇	—	2	2	no	—
217	C₂×C₂²⋊D₄₇	—	2	2	no	—
218	C₂²×Dic₄₇	—	2	2	no	—
219	C₂²×Dic₄₇	#41	1	1	yes	characteristic
220	#10625354	—	2	2	no	—
221	#10625354	—	2	2	no	—
222	#10625354	C₂²×C₄	1	4	yes	—
223	#10625354	C₂²×C₄	1	4	yes	—
224	Q₈×D₄₇	—	2	2	no	—
225	Q₈×D₄₇	—	2	2	no	—
226	Q₈×D₄₇	C₂²×C₄	1	4	yes	—
227	Q₈×D₄₇	C₂²×C₄	1	4	yes	—
228	#10625352	—	2	4	no	—
229	#10625352	—	2	4	no	—
230	#10625352	—	2	4	no	—
231	#10625352	—	2	4	no	—
232	#10625352	—	2	2	no	—
233	#10625352	—	2	2	no	—
234	#10625352	C₂²×C₄	1	4	yes	—
235	#10625352	C₂²×C₄	1	4	yes	—
236	D₄×D₄₇	—	2	4	no	—
237	D₄×D₄₇	—	2	4	no	—
238	D₄×D₄₇	—	2	4	no	—
239	D₄×D₄₇	—	2	4	no	—
240	D₄×D₄₇	—	2	2	no	—
241	D₄×D₄₇	—	2	2	no	—
242	D₄×D₄₇	C₂²×C₄	1	4	yes	—
243	D₄×D₄₇	C₂²×C₄	1	4	yes	—
244	#10625350	—	2	2	no	—
245	#10625350	—	2	2	no	—
246	#10625350	—	2	4	no	—
247	#10625350	—	2	4	no	—
248	#10625350	—	2	4	no	—
249	#10625350	—	2	4	no	—
250	#10625350	C₂²×C₄	1	4	yes	—
251	#10625350	C₂⁴	1	4	yes	—
252	C₂×D₁₈₈	—	2	2	no	—
253	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
254	C₂×C₄×D₄₇	—	2	2	no	—
255	C₂×C₄×D₄₇	—	2	2	no	—
256	C₂×C₄×D₄₇	—	2	2	no	—
257	C₂×C₄×D₄₇	—	2	4	no	—
258	C₂×C₄×D₄₇	—	2	4	no	—
259	C₂×C₄×D₄₇	—	2	4	no	—
260	C₂×C₄×D₄₇	—	2	4	no	—
261	C₂×C₄×D₄₇	—	2	2	no	—
262	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
263	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
264	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
265	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
266	C₂×C₄×D₄₇	#41	1	1	yes	characteristic
267	C₂×C₄×D₄₇	#41	1	1	yes	characteristic
268	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
269	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₉₄	—	2	2	no	—
271	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
272	Q₁₆×C₄₇	C₂²×C₄	1	2	yes	—
273	Q₁₆×C₄₇	C₂²×C₄	1	2	yes	—
274	SD₁₆×C₄₇	C₂²×C₄	1	4	yes	—
275	SD₁₆×C₄₇	C₂²×C₄	1	4	yes	—
276	D₈×C₄₇	C₂²×C₄	1	2	yes	—
277	D₈×C₄₇	C₂²×C₄	1	2	yes	—
278	M₁₆×C₄₇	—	2	2	no	—
279	M₁₆×C₄₇	—	2	8	no	—
280	M₁₆×C₄₇	C₂×D₄	1	2	yes	—
281	M₁₆×C₄₇	C₂×D₄	1	2	yes	—
282	M₁₆×C₄₇	C₂⁴	1	4	yes	—
283	C₂×C₈×C₄₇	—	2	2	no	—
284	C₂×C₈×C₄₇	—	2	8	no	—
285	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
286	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
287	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
288	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
289	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
290	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
291	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
292	C₄⋊C₄×C₄₇	—	2	1	no	—
293	C₂²⋊C₄×C₄₇	—	2	1	no	—
294	C₄²×C₄₇	C₂⁴	1	2	yes	—
295	C₂²⋊Dic₄₇	—	2	1	no	—
296	#10625337	C₂²×C₄	1	4	yes	—
297	#10625337	C₂²×C₄	1	4	yes	—
298	#10625336	C₂²×C₄	1	4	yes	—
299	#10625336	C₂²×C₄	1	4	yes	—
300	#10625335	C₂²×C₄	1	4	yes	—
301	#10625335	C₂²×C₄	1	4	yes	—
302	#10625334	C₂²×C₄	1	4	yes	—
303	#10625334	C₂²×C₄	1	4	yes	—
304	(C₂×D₄₇)⋊C₄	—	2	2	no	—
305	C₄⋊Dic₄₇	—	2	1	no	—
306	Dic₄₇⋊C₄	—	2	2	no	—
307	C₄×Dic₄₇	—	2	2	no	—
308	C₄×Dic₄₇	C₂⁴	1	2	yes	—
309	#10625329	—	2	2	no	—
310	#10625329	—	2	8	no	—
311	#10625329	C₂×D₄	1	2	yes	—
312	#10625329	C₂×D₄	1	2	yes	—
313	#10625329	C₂⁴	1	4	yes	—
314	C₂×C₄₇⋊C₈	—	2	2	no	—
315	C₂×C₄₇⋊C₈	—	2	8	no	—
316	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
317	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
318	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
319	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
320	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
321	Dic₁₈₈	C₂²×C₄	1	2	yes	—
322	Dic₁₈₈	C₂²×C₄	1	2	yes	—
323	D₃₇₆	C₂²×C₄	1	2	yes	—
324	D₃₇₆	C₂²×C₄	1	2	yes	—
325	#10625325	C₂²×C₄	1	4	yes	—
326	#10625325	C₂²×C₄	1	4	yes	—
327	#10625324	—	2	4	no	—
328	#10625324	—	2	4	no	—
329	#10625324	—	2	8	no	—
330	#10625324	—	2	8	no	—
331	#10625324	C₂²×C₄	1	2	yes	—
332	#10625324	C₂²×C₄	1	2	yes	—
333	#10625324	C₂²×C₄	1	2	yes	—
334	#10625324	C₂²×C₄	1	2	yes	—
335	#10625324	C₂²×C₄	1	2	yes	—
336	#10625324	C₂²×C₄	1	2	yes	—
337	#10625324	C₂²×C₄	1	2	yes	—
338	#10625324	C₂²×C₄	1	2	yes	—
339	#10625324	C₂×D₄	1	8	yes	—
340	C₈×D₄₇	—	2	4	no	—
341	C₈×D₄₇	—	2	4	no	—
342	C₈×D₄₇	—	2	8	no	—
343	C₈×D₄₇	—	2	8	no	—
344	C₈×D₄₇	C₂×D₄	1	8	yes	—
345	C₂³×C₄₇	—	2	2	no	—
346	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
347	C₂²×D₄₇	—	2	2	no	—
348	C₂²×D₄₇	—	2	4	no	—
349	C₂²×D₄₇	—	2	4	no	—
350	C₂²×D₄₇	—	8	1	no	—
351	C₂²×D₄₇	—	8	4	no	—
352	C₂²×D₄₇	C₄×D₄	1	2	yes	—
353	C₂²×D₄₇	C₄×D₄	1	2	yes	—
354	C₂²×D₄₇	C₂×#41	1	1	yes	characteristic
355	C₂²×D₄₇	C₂×#41	1	1	yes	characteristic
356	Q₈×C₄₇	—	2	2	no	—
357	Q₈×C₄₇	C₂³×C₄	1	4	yes	—
358	D₄×C₄₇	—	2	4	no	—
359	D₄×C₄₇	—	2	4	no	—
360	D₄×C₄₇	—	2	2	no	—
361	D₄×C₄₇	C₂³×C₄	1	4	yes	—
362	C₂×C₄×C₄₇	—	2	2	no	—
363	C₂×C₄×C₄₇	—	2	4	no	—
364	C₂×C₄×C₄₇	—	2	4	no	—
365	C₂×C₄×C₄₇	—	2	2	no	—
366	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
367	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
368	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
369	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
370	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
371	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
372	C₂²⋊D₄₇	—	2	4	no	—
373	C₂²⋊D₄₇	—	2	4	no	—
374	C₂²⋊D₄₇	—	2	4	no	—
375	C₂²⋊D₄₇	—	2	4	no	—
376	C₂²⋊D₄₇	—	2	4	no	—
377	C₂²⋊D₄₇	—	2	4	no	—
378	C₂×Dic₄₇	—	2	2	no	—
379	C₂×Dic₄₇	—	2	4	no	—
380	C₂×Dic₄₇	—	2	4	no	—
381	C₂×Dic₄₇	—	2	2	no	—
382	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
383	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
384	C₂×Dic₄₇	C₂×#41	1	1	yes	characteristic
385	C₂×Dic₄₇	C₂×#41	1	1	yes	characteristic
386	D₁₈₈	—	2	4	no	—
387	D₁₈₈	—	2	4	no	—
388	D₁₈₈	—	2	2	no	—
389	D₁₈₈	C₂³×C₄	1	4	yes	—
390	C₄×D₄₇	—	2	4	no	—
391	C₄×D₄₇	—	2	4	no	—
392	C₄×D₄₇	—	2	4	no	—
393	C₄×D₄₇	—	2	4	no	—
394	C₄×D₄₇	—	2	4	no	—
395	C₄×D₄₇	—	2	4	no	—
396	C₄×D₄₇	—	8	2	no	—
397	C₄×D₄₇	C₄×D₄	1	2	yes	—
398	C₄×D₄₇	C₄×D₄	1	2	yes	—
399	C₄×D₄₇	C₄×D₄	1	2	yes	—
400	C₄×D₄₇	C₄×D₄	1	2	yes	—
401	C₄×D₄₇	C₂³×C₄	1	2	yes	—
402	C₄×D₄₇	C₂³×C₄	1	2	yes	—
403	C₄×D₄₇	C₂²×D₄	1	2	yes	—
404	C₄×D₄₇	C₂²×D₄	1	2	yes	—
405	Dic₉₄	—	2	2	no	—
406	Dic₉₄	—	2	4	no	—
407	Dic₉₄	—	2	4	no	—
408	Dic₉₄	C₂³×C₄	1	4	yes	—
409	C₈×C₄₇	—	2	4	no	—
410	C₈×C₄₇	C₂³×C₄	1	1	yes	characteristic
411	C₈×C₄₇	C₂³×C₄	1	1	yes	characteristic
412	C₈×C₄₇	C₂³×C₄	1	1	yes	characteristic
413	C₈×C₄₇	C₂³×C₄	1	1	yes	characteristic
414	C₈×C₄₇	C₂²×D₄	1	4	yes	—
415	C₄₇⋊C₈	—	2	4	no	—
416	C₄₇⋊C₈	C₂³×C₄	1	2	yes	—
417	C₄₇⋊C₈	C₂³×C₄	1	2	yes	—
418	C₄₇⋊C₈	C₂²×D₄	1	4	yes	—
419	#60182	—	47	1	no	maximal, Sylow
420	C₂²×C₄₇	—	2	4	no	—
421	C₂²×C₄₇	—	4	1	no	—
422	C₂²×C₄₇	—	8	2	no	—
423	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
424	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
425	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
426	C₂×D₄₇	—	2	4	no	—
427	C₂×D₄₇	—	4	1	no	—
428	C₂×D₄₇	—	4	2	no	—
429	C₂×D₄₇	—	4	2	no	—
430	C₂×D₄₇	—	4	1	no	—
431	C₂×D₄₇	—	4	8	no	—
432	C₂×D₄₇	—	8	4	no	—
433	C₂×D₄₇	—	8	2	no	—
434	C₂×D₄₇	C₂×C₄×D₄	1	2	yes	—
435	C₂×D₄₇	C₂×C₄×D₄	1	2	yes	—
436	C₄×C₄₇	—	2	4	no	—
437	C₄×C₄₇	—	4	2	no	—
438	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
439	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
440	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
441	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
442	Dic₄₇	—	2	4	no	—
443	Dic₄₇	—	4	2	no	—
444	Dic₄₇	C₂×C₄×D₄	1	2	yes	—
445	Dic₄₇	C₂×C₄×D₄	1	2	yes	—
446	C₂×#575	—	47	1	no	—
447	C₂×#568	—	47	2	no	—
448	#2957	—	47	1	no	—
449	#2957	—	47	2	no	—
450	#2957	—	47	1	no	—
451	#2957	—	47	1	no	—
452	#2957	—	47	2	no	—
453	#2957	D₄₇	1	1	yes	characteristic, complemented
454	#2956	—	47	4	no	—
455	#2956	—	47	4	no	—
456	#2955	—	47	4	no	—
457	#2955	—	47	4	no	—
458	C₂×#430	—	47	1	no	—
459	C₂×#421	—	47	2	no	—
460	#2873	—	47	1	no	—
461	C₂×C₄₇	—	2	1	no	—
462	C₂×C₄₇	—	2	1	no	—
463	C₂×C₄₇	—	2	1	no	—
464	C₂×C₄₇	—	4	4	no	—
465	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
466	D₄₇	—	2	2	no	—
467	D₄₇	—	2	2	no	—
468	D₄₇	—	4	4	no	—
469	C₂²×#41	—	47	2	no	—
470	#575	—	47	4	no	—
471	#575	—	47	4	no	—
472	#575	—	47	2	no	—
473	#575	—	47	2	no	—
474	#575	—	47	2	no	—
475	#575	—	47	2	no	—
476	C₂×#137	—	47	2	no	—
477	C₂×#137	—	47	2	no	—
478	C₂×AGL(1,ℤ/8)	—	47	2	no	—
479	C₂×AGL(1,ℤ/8)	—	47	2	no	—
480	C₂×#135	—	47	2	no	—
481	C₂×#135	—	47	1	no	—
482	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
483	#568	—	47	2	no	—
484	#568	—	47	8	no	—
485	#568	—	47	2	no	—
486	#568	—	47	2	no	—
487	#568	—	94	4	no	—
488	#568	—	94	4	no	—
489	#568	C₂×D₄₇	1	2	yes	complemented
490	C₂×#131	—	47	8	no	—
491	C₂×#131	—	94	4	no	—
492	C₂²×M₁₆	—	47	1	no	—
493	C₂²×M₁₆	—	47	1	no	—
494	C₂²×M₁₆	—	47	2	no	—
495	C₂²×M₁₆	—	94	4	no	—
496	C₂×#117	—	47	1	no	—
497	#444	—	47	4	no	—
498	#444	—	47	8	no	—
499	#444	—	47	4	no	—
500	#444	—	47	8	no	—
501	#444	—	47	4	no	—
502	#444	C₂×D₄₇	1	4	yes	complemented
503	#443	—	47	4	no	—
504	#443	—	47	8	no	—
505	#443	—	47	4	no	—
506	#443	—	47	8	no	—
507	#443	—	47	4	no	—
508	#443	C₂×D₄₇	1	4	yes	complemented
509	#430	—	47	2	no	—
510	#430	—	47	2	no	—
511	#430	—	47	2	no	—
512	#430	—	47	2	no	—
513	C₂×#108	—	47	2	no	—
514	C₂×#108	—	47	1	no	—
515	C₂×#108	C₂×D₄₇	1	1	yes	characteristic, complemented
516	#421	—	47	2	no	—
517	#421	—	47	2	no	—
518	#421	—	47	2	no	—
519	#421	—	47	8	no	—
520	#421	C₂×D₄₇	1	2	yes	complemented
521	C₂×#104	—	47	8	no	—
522	#405	—	47	1	no	—
523	#405	—	47	1	no	—
524	#405	—	47	1	no	—
525	#405	—	47	2	no	—
526	#405	—	47	2	no	—
527	#405	C₂×D₄₇	1	1	yes	characteristic, complemented
528	C₄×M₁₆	—	47	2	no	—
529	C₄×M₁₆	—	47	2	no	—
530	C₄₇	#60182	1	1	yes	characteristic, complemented, Sylow
531	C₂×#41	—	47	4	no	—
532	C₂×#41	—	47	4	no	—
533	C₂×#41	—	47	4	no	—
534	C₂×#41	—	47	4	no	—
535	C₂×#41	—	47	2	no	—
536	C₂×#41	—	47	2	no	—
537	C₂×#41	—	47	2	no	—
538	C₂×#41	—	94	2	no	—
539	C₂×#41	—	94	2	no	—
540	C₂×#41	—	94	2	no	—
541	C₂×#41	—	94	2	no	—
542	C₂×#41	—	94	2	no	—
543	C₂×#41	—	94	2	no	—
544	C₂×#41	C₂²×D₄₇	1	2	yes	—
545	C₂²×Q₈	—	47	2	no	—
546	C₂²×D₄	—	47	2	no	—
547	C₂²×D₄	—	94	2	no	—
548	C₂³×C₄	—	47	1	no	—
549	C₂³×C₄	—	94	2	no	—
550	#137	—	47	4	no	—
551	#137	—	47	4	no	—
552	#137	—	47	4	no	—
553	#137	—	47	4	no	—
554	#137	—	47	4	no	—
555	#137	—	47	4	no	—
556	#137	—	47	4	no	—
557	#137	—	47	4	no	—
558	AGL(1,ℤ/8)	—	47	4	no	—
559	AGL(1,ℤ/8)	—	47	4	no	—
560	AGL(1,ℤ/8)	—	47	4	no	—
561	AGL(1,ℤ/8)	—	47	4	no	—
562	AGL(1,ℤ/8)	—	47	4	no	—
563	AGL(1,ℤ/8)	—	47	4	no	—
564	AGL(1,ℤ/8)	—	47	4	no	—
565	AGL(1,ℤ/8)	—	47	4	no	—
566	#135	—	47	4	no	—
567	#135	—	47	4	no	—
568	#135	—	47	4	no	—
569	#135	—	47	4	no	—
570	#135	—	47	2	no	—
571	#135	—	47	2	no	—
572	#135	—	47	2	no	—
573	#135	—	47	2	no	—
574	#135	C₄×D₄₇	1	2	yes	complemented
575	#135	C₄×D₄₇	1	2	yes	complemented
576	#135	C₂²×D₄₇	1	2	yes	—
577	#135	C₂²×D₄₇	1	2	yes	—
578	C₂×Q₁₆	—	47	2	no	—
579	C₂×Q₁₆	—	47	1	no	—
580	C₂×Q₁₆	C₄×D₄₇	1	1	yes	characteristic, complemented
581	C₂×SD₁₆	—	47	2	no	—
582	C₂×SD₁₆	—	47	2	no	—
583	C₂×SD₁₆	—	47	2	no	—
584	C₂×SD₁₆	C₄×D₄₇	1	2	yes	complemented
585	C₂×D₈	—	47	2	no	—
586	C₂×D₈	—	47	1	no	—
587	C₂×D₈	C₄×D₄₇	1	1	yes	characteristic, complemented
588	#131	—	2	4	no	—
589	#131	—	47	8	no	—
590	#131	—	47	8	no	—
591	#131	—	47	8	no	—
592	#131	—	94	8	no	—
593	#131	—	94	4	no	—
594	#131	—	94	8	no	—
595	#131	—	94	8	no	—
596	#131	—	94	8	no	—
597	#131	—	94	4	no	—
598	#131	—	94	4	no	—
599	#131	C₂²×D₄₇	1	8	yes	complemented
600	C₂×M₁₆	—	2	4	no	—
601	C₂×M₁₆	—	47	1	no	—
602	C₂×M₁₆	—	47	4	no	—
603	C₂×M₁₆	—	47	4	no	—
604	C₂×M₁₆	—	47	2	no	—
605	C₂×M₁₆	—	47	2	no	—
606	C₂×M₁₆	—	47	2	no	—
607	C₂×M₁₆	—	47	2	no	—
608	C₂×M₁₆	—	47	2	no	—
609	C₂×M₁₆	—	47	1	no	—
610	C₂×M₁₆	—	47	1	no	—
611	C₂×M₁₆	—	47	1	no	—
612	C₂×M₁₆	—	47	1	no	—
613	C₂×M₁₆	—	47	2	no	—
614	C₂×M₁₆	—	47	4	no	—
615	C₂×M₁₆	—	47	4	no	—
616	C₂×M₁₆	—	94	8	no	—
617	C₂×M₁₆	—	94	2	no	—
618	C₂×M₁₆	—	94	8	no	—
619	C₂×M₁₆	—	94	4	no	—
620	C₂×M₁₆	—	94	8	no	—
621	C₂×M₁₆	—	94	2	no	—
622	C₂×M₁₆	—	94	2	no	—
623	C₂×M₁₆	—	94	4	no	—
624	C₂×M₁₆	—	94	4	no	—
625	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
626	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
627	C₂²×C₈	—	47	1	no	—
628	C₂²×C₈	—	47	2	no	—
629	C₂²×C₈	—	94	8	no	—
630	C₂²×C₈	—	94	2	no	—
631	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
632	#117	—	47	1	no	—
633	#117	—	47	2	no	—
634	#117	—	94	1	no	—
635	#117	—	94	1	no	—
636	#117	C₂²×D₄₇	1	1	yes	characteristic
637	C₂×C₄⋊C₄	—	94	1	no	—
638	C₂×C₂²⋊C₄	—	94	1	no	—
639	C₂×C₄²	—	47	2	no	—
640	#108	—	47	4	no	—
641	#108	—	47	4	no	—
642	#108	—	47	2	no	—
643	#108	—	47	2	no	—
644	#108	C₂²×D₄₇	1	2	yes	complemented
645	#108	C₂²×D₄₇	1	2	yes	complemented
646	#104	—	47	8	no	—
647	#104	—	47	8	no	—
648	#104	—	47	8	no	—
649	#104	C₂²×D₄₇	1	8	yes	complemented
650	#97	—	47	2	no	—
651	#97	—	47	2	no	—
652	#97	—	47	2	no	—
653	#97	C₂²×D₄₇	1	2	yes	complemented
654	C₄×C₈	—	47	2	no	—
655	C₄×C₈	—	47	2	no	—
656	C₄×C₈	—	47	2	no	—
657	C₄×C₈	C₂²×D₄₇	1	2	yes	complemented
658	C₂⁴	—	47	1	no	—
659	C₂⁴	—	94	2	no	—
660	#41	—	2	2	no	—
661	#41	—	2	2	no	—
662	#41	—	47	4	no	—
663	#41	—	47	4	no	—
664	#41	—	47	4	no	—
665	#41	—	47	4	no	—
666	#41	—	47	4	no	—
667	#41	—	47	4	no	—
668	#41	—	94	4	no	—
669	#41	—	94	4	no	—
670	#41	—	94	4	no	—
671	#41	—	94	4	no	—
672	#41	—	94	4	no	—
673	#41	—	94	4	no	—
674	#41	—	94	4	no	—
675	#41	—	94	4	no	—
676	#41	—	94	2	no	—
677	#41	—	94	2	no	—
678	#41	—	94	2	no	—
679	#41	—	94	2	no	—
680	#41	—	94	2	no	—
681	#41	—	94	2	no	—
682	#41	C₂×C₄×D₄₇	1	4	yes	—
683	#41	C₂³×D₄₇	1	4	yes	—
684	C₂×Q₈	—	47	4	no	—
685	C₂×Q₈	—	47	4	no	—
686	C₂×Q₈	—	47	2	no	—
687	C₂×Q₈	—	94	2	no	—
688	C₂×Q₈	—	94	2	no	—
689	C₂×Q₈	—	94	2	no	—
690	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
691	C₂×D₄	—	2	2	no	—
692	C₂×D₄	—	47	4	no	—
693	C₂×D₄	—	47	4	no	—
694	C₂×D₄	—	47	2	no	—
695	C₂×D₄	—	94	2	no	—
696	C₂×D₄	—	94	2	no	—
697	C₂×D₄	—	94	2	no	—
698	C₂×D₄	—	94	2	no	—
699	C₂×D₄	—	94	4	no	—
700	C₂×D₄	—	94	4	no	—
701	C₂×D₄	—	94	4	no	—
702	C₂×D₄	—	94	4	no	—
703	C₂×D₄	—	94	2	no	—
704	C₂×D₄	—	94	2	no	—
705	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
706	C₂²×C₄	—	2	2	no	—
707	C₂²×C₄	—	47	1	no	—
708	C₂²×C₄	—	47	2	no	—
709	C₂²×C₄	—	47	2	no	—
710	C₂²×C₄	—	47	2	no	—
711	C₂²×C₄	—	47	2	no	—
712	C₂²×C₄	—	47	1	no	—
713	C₂²×C₄	—	47	1	no	—
714	C₂²×C₄	—	47	1	no	—
715	C₂²×C₄	—	47	1	no	—
716	C₂²×C₄	—	94	4	no	—
717	C₂²×C₄	—	94	4	no	—
718	C₂²×C₄	—	94	2	no	—
719	C₂²×C₄	—	94	4	no	—
720	C₂²×C₄	—	94	4	no	—
721	C₂²×C₄	—	94	2	no	—
722	C₂²×C₄	—	94	2	no	—
723	C₂²×C₄	—	94	2	no	—
724	C₂²×C₄	—	94	2	no	—
725	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
726	Q₁₆	—	47	4	no	—
727	Q₁₆	—	47	4	no	—
728	Q₁₆	—	47	2	no	—
729	Q₁₆	—	47	2	no	—
730	Q₁₆	C₂×C₄×D₄₇	1	2	yes	—
731	Q₁₆	C₂×C₄×D₄₇	1	2	yes	—
732	SD₁₆	—	47	4	no	—
733	SD₁₆	—	47	4	no	—
734	SD₁₆	—	47	4	no	—
735	SD₁₆	—	47	4	no	—
736	SD₁₆	—	47	4	no	—
737	SD₁₆	—	47	4	no	—
738	SD₁₆	C₂×C₄×D₄₇	1	4	yes	—
739	SD₁₆	C₂×C₄×D₄₇	1	4	yes	—
740	D₈	—	47	4	no	—
741	D₈	—	47	4	no	—
742	D₈	—	47	2	no	—
743	D₈	—	47	2	no	—
744	D₈	C₂×C₄×D₄₇	1	2	yes	—
745	D₈	C₂×C₄×D₄₇	1	2	yes	—
746	M₁₆	—	2	2	no	—
747	M₁₆	—	2	8	no	—
748	M₁₆	—	47	2	no	—
749	M₁₆	—	47	2	no	—
750	M₁₆	—	47	2	no	—
751	M₁₆	—	47	2	no	—
752	M₁₆	—	47	2	no	—
753	M₁₆	—	47	2	no	—
754	M₁₆	—	47	2	no	—
755	M₁₆	—	47	2	no	—
756	M₁₆	—	47	2	no	—
757	M₁₆	—	47	2	no	—
758	M₁₆	—	47	8	no	—
759	M₁₆	—	47	4	no	—
760	M₁₆	—	94	8	no	—
761	M₁₆	—	94	4	no	—
762	M₁₆	—	94	4	no	—
763	M₁₆	—	94	8	no	—
764	M₁₆	—	94	2	no	—
765	M₁₆	—	94	8	no	—
766	M₁₆	D₄×D₄₇	1	2	yes	—
767	M₁₆	D₄×D₄₇	1	2	yes	—
768	M₁₆	C₂³×D₄₇	1	4	yes	—
769	C₂×C₈	—	2	2	no	—
770	C₂×C₈	—	2	8	no	—
771	C₂×C₈	—	47	2	no	—
772	C₂×C₈	—	47	2	no	—
773	C₂×C₈	—	47	1	no	—
774	C₂×C₈	—	47	1	no	—
775	C₂×C₈	—	47	2	no	—
776	C₂×C₈	—	47	8	no	—
777	C₂×C₈	—	94	8	no	—
778	C₂×C₈	—	94	4	no	—
779	C₂×C₈	—	94	4	no	—
780	C₂×C₈	—	94	8	no	—
781	C₂×C₈	—	94	2	no	—
782	C₂×C₈	—	94	8	no	—
783	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
784	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
785	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
786	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
787	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
788	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
789	C₂×C₈	C₂³×D₄₇	1	2	yes	—
790	C₄⋊C₄	—	2	1	no	—
791	C₄⋊C₄	—	94	2	no	—
792	C₄⋊C₄	—	94	1	no	—
793	C₂²⋊C₄	—	2	1	no	—
794	C₂²⋊C₄	—	94	2	no	—
795	C₂²⋊C₄	—	94	1	no	—
796	C₄²	—	47	2	no	—
797	C₄²	—	94	2	no	—
798	C₄²	C₂³×D₄₇	1	2	yes	—
799	C₂³	—	2	2	no	—
800	C₂³	—	47	2	no	—
801	C₂³	—	47	2	no	—
802	C₂³	—	47	1	no	—
803	C₂³	—	47	1	no	—
804	C₂³	—	94	4	no	—
805	C₂³	—	94	4	no	—
806	C₂³	—	94	2	no	—
807	C₂³	—	376	1	no	—
808	C₂³	—	376	4	no	—
809	C₂³	#41×D₄₇	1	1	yes	characteristic
810	Q₈	—	2	2	no	—
811	Q₈	—	47	4	no	—
812	Q₈	—	94	4	no	—
813	Q₈	—	94	4	no	—
814	Q₈	—	94	2	no	—
815	Q₈	C₂²×C₄×D₄₇	1	4	yes	—
816	D₄	—	2	4	no	—
817	D₄	—	2	4	no	—
818	D₄	—	2	2	no	—
819	D₄	—	47	4	no	—
820	D₄	—	94	4	no	—
821	D₄	—	94	4	no	—
822	D₄	—	94	4	no	—
823	D₄	—	94	4	no	—
824	D₄	—	94	4	no	—
825	D₄	—	94	4	no	—
826	D₄	—	94	4	no	—
827	D₄	—	94	4	no	—
828	D₄	—	94	2	no	—
829	D₄	C₂²×C₄×D₄₇	1	4	yes	—
830	C₂×C₄	—	2	2	no	—
831	C₂×C₄	—	2	4	no	—
832	C₂×C₄	—	2	4	no	—
833	C₂×C₄	—	2	2	no	—
834	C₂×C₄	—	47	2	no	—
835	C₂×C₄	—	47	2	no	—
836	C₂×C₄	—	47	1	no	—
837	C₂×C₄	—	47	1	no	—
838	C₂×C₄	—	47	2	no	—
839	C₂×C₄	—	47	2	no	—
840	C₂×C₄	—	47	2	no	—
841	C₂×C₄	—	47	2	no	—
842	C₂×C₄	—	47	2	no	—
843	C₂×C₄	—	47	2	no	—
844	C₂×C₄	—	47	2	no	—
845	C₂×C₄	—	47	2	no	—
846	C₂×C₄	—	94	4	no	—
847	C₂×C₄	—	94	4	no	—
848	C₂×C₄	—	94	4	no	—
849	C₂×C₄	—	94	4	no	—
850	C₂×C₄	—	94	4	no	—
851	C₂×C₄	—	94	4	no	—
852	C₂×C₄	—	94	2	no	—
853	C₂×C₄	—	94	4	no	—
854	C₂×C₄	—	94	4	no	—
855	C₂×C₄	—	94	2	no	—
856	C₂×C₄	—	376	2	no	—
857	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
858	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
859	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
860	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
861	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
862	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
863	C₈	—	2	4	no	—
864	C₈	—	47	2	no	—
865	C₈	—	47	2	no	—
866	C₈	—	47	4	no	—
867	C₈	—	94	4	no	—
868	C₈	C₂²×C₄×D₄₇	1	1	yes	characteristic
869	C₈	C₂²×C₄×D₄₇	1	1	yes	characteristic
870	C₈	C₂²×C₄×D₄₇	1	1	yes	characteristic
871	C₈	C₂²×C₄×D₄₇	1	1	yes	characteristic
872	C₈	C₂×D₄×D₄₇	1	4	yes	—
873	C₂²	—	2	4	no	—
874	C₂²	—	4	1	no	—
875	C₂²	—	8	2	no	—
876	C₂²	—	47	2	no	—
877	C₂²	—	47	2	no	—
878	C₂²	—	94	4	no	—
879	C₂²	—	376	2	no	—
880	C₂²	—	376	4	no	—
881	C₂²	—	188	1	no	—
882	C₂²	—	188	2	no	—
883	C₂²	—	188	1	no	—
884	C₂²	—	188	2	no	—
885	C₂²	—	188	8	no	—
886	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
887	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
888	C₂²	C₂×#41×D₄₇	1	1	yes	characteristic
889	C₄	—	2	4	no	—
890	C₄	—	4	2	no	—
891	C₄	—	47	2	no	—
892	C₄	—	47	2	no	—
893	C₄	—	94	4	no	—
894	C₄	—	188	2	no	—
895	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
896	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
897	C₄	C₂³×C₄×D₄₇	1	1	yes	characteristic
898	C₄	C₂²×D₄×D₄₇	1	1	yes	characteristic
899	C₂	—	2	1	no	—
900	C₂	—	2	1	no	—
901	C₂	—	2	1	no	—
902	C₂	—	4	4	no	—
903	C₂	—	94	2	no	—
904	C₂	—	94	2	no	—
905	C₂	—	188	4	no	—
906	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×#15689920	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2957	D₄₇
hypocenter	C₄₇	#60182
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. #20252301	C₂	semidirect
8. #20252296	C₂	semidirect
9. #20252293	C₂	semidirect
10. #20252288	C₂	semidirect
11. #20252286	C₂	semidirect
12. C₂×#15689170	C₂	semidirect
13. #421×D₄₇	C₂	semidirect
14. #20251804	C₂	semidirect
15. C₄₇×#2957	C₂	semidirect
17. #15689920	C₄	semidirect
18. #15689920	C₄	semidirect
23. C₂×#13094056	C₄	semidirect
24. C₂×#13094053	C₄	semidirect
25. C₂×#13094051	C₄	semidirect
26. C₂×#13094048	C₄	semidirect
29. #15689890	C₂²	semidirect
31. #15689889	C₂²	semidirect
32. #15689889	C₂²	semidirect
34. #15689888	C₂²	semidirect
36. #131×D₄₇	C₂²	semidirect
42. #15689246	C₂²	semidirect
43. #15689245	C₂²	semidirect
44. #15689244	C₂²	semidirect
45. #15689243	C₂²	semidirect
46. #15689242	C₂²	semidirect
47. #15689241	C₂²	semidirect
48. #15689240	C₂²	semidirect
49. #15689239	C₂²	semidirect
50. #15689238	C₂²	semidirect
51. #15689237	C₂²	semidirect
52. #15689170	C₂²	semidirect
53. #15689170	C₂²	semidirect
54. #15689170	C₂²	semidirect
55. #15689170	C₂²	semidirect
56. C₂×#13093960	C₂²	semidirect
57. C₂×#13093959	C₂²	semidirect
58. #15689141	C₂²	semidirect
59. #15689140	C₂²	semidirect
60. #15689139	C₂²	semidirect
61. #15689138	C₂²	semidirect
62. #104×D₄₇	C₂²	semidirect
63. #15689081	C₂²	semidirect
64. #15689080	C₂²	semidirect
65. #15689079	C₂²	semidirect
66. #15689078	C₂²	semidirect
67. #15689077	C₂²	semidirect
68. #15689075	C₂²	semidirect
69. C₄×#10625324	C₂²	semidirect
71. C₄₇×#568	C₂²	semidirect
72. C₄₇×#444	C₂²	semidirect
73. C₄₇×#443	C₂²	semidirect
74. C₂×#108×C₄₇	C₂²	semidirect
75. C₄₇×#421	C₂²	semidirect
76. C₄₇×#405	C₂²	semidirect
97. #13094056	C₂×C₄	semidirect
98. #13094056	C₂×C₄	semidirect
101. #13094053	C₂×C₄	semidirect
102. #13094053	C₂×C₄	semidirect
105. #13094051	C₂×C₄	semidirect
106. #13094051	C₂×C₄	semidirect
109. #13094048	C₂×C₄	semidirect
110. #13094048	C₂×C₄	semidirect
111. #13094046	C₂×C₄	semidirect
112. #13094046	C₂×C₄	semidirect
115. #13094044	C₂×C₄	semidirect
116. #13094044	C₂×C₄	semidirect
119. C₂×Dic₁₈₈	C₂×C₄	semidirect
120. C₂×#10625337	C₂×C₄	semidirect
121. C₂×#10625325	C₂×C₄	semidirect
122. C₂×#10625335	C₂×C₄	semidirect
123. C₂×#10625336	C₂×C₄	semidirect
124. C₂×D₃₇₆	C₂×C₄	semidirect
125. C₂×#10625334	C₂×C₄	semidirect
129. #13094032	C₂³	semidirect
131. #13094031	C₂³	semidirect
135. #13094030	C₂³	semidirect
171. #13093960	C₂³	semidirect
172. #13093960	C₂³	semidirect
173. #13093959	C₂³	semidirect
174. #13093959	C₂³	semidirect
175. #13093952	C₂³	semidirect
176. #13093951	C₂³	semidirect
177. #13093950	C₂³	semidirect
178. #13093935	C₂³	semidirect
179. #13093934	C₂³	semidirect
180. #13093934	C₂³	semidirect
181. C₄×C₄₇⋊C₈	C₂³	semidirect
182. C₈×Dic₄₇	C₂³	semidirect
183. C₈×Dic₄₇	C₂³	semidirect
185. #135×C₄₇	C₂×C₄	semidirect
186. #135×C₄₇	C₂×C₄	semidirect
189. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
190. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
191. C₂×D₈×C₄₇	C₂×C₄	semidirect
193. #131×C₄₇	C₂³	semidirect
199. #108×C₄₇	C₂³	semidirect
200. #108×C₄₇	C₂³	semidirect
201. #104×C₄₇	C₂³	semidirect
202. #97×C₄₇	C₂³	semidirect
203. C₄×C₈×C₄₇	C₂³	semidirect
453. #2957	D₄₇	semidirect
489. #568	C₂×D₄₇	semidirect
502. #444	C₂×D₄₇	semidirect
508. #443	C₂×D₄₇	semidirect
515. C₂×#108	C₂×D₄₇	semidirect
520. #421	C₂×D₄₇	semidirect
527. #405	C₂×D₄₇	semidirect
530. C₄₇	#60182	semidirect
574. #135	C₄×D₄₇	semidirect
575. #135	C₄×D₄₇	semidirect
580. C₂×Q₁₆	C₄×D₄₇	semidirect
584. C₂×SD₁₆	C₄×D₄₇	semidirect
587. C₂×D₈	C₄×D₄₇	semidirect
599. #131	C₂²×D₄₇	semidirect
644. #108	C₂²×D₄₇	semidirect
645. #108	C₂²×D₄₇	semidirect
649. #104	C₂²×D₄₇	semidirect
653. #97	C₂²×D₄₇	semidirect
657. 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×#15689920	2
#568×D₄₇	2
#20252306	2
#20252305	2
#20252304	2
#20252303	2
#20252301	2
#20252296	2
#20252293	2
#20252288	2
#20252286	2
C₂×#15689170	2
#421×D₄₇	2
#20251804	2
C₄₇×#2957	2
#60182	47