Subgroups — D₄₇×#2956 #27080585

Order 12032.

2674 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#575×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#568×D₄₇	C₂	1	2	yes	maximal, complemented
3	#20252299	C₂	1	1	yes	maximal, characteristic, complemented
4	#20252298	C₂	1	1	yes	maximal, characteristic, complemented
5	#20252297	C₂	1	1	yes	maximal, characteristic, complemented
6	#20252296	C₂	1	4	yes	maximal, complemented
7	#20252295	C₂	1	2	yes	maximal, complemented
8	#20252294	C₂	1	2	yes	maximal, complemented
9	#20252293	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	#430×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#104×D₄₇	C₂	1	2	yes	maximal, complemented
14	C₄×M₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#2956	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#41×D₄₇	C₂²	1	2	yes	—
17	#15689923	C₂²	1	1	yes	characteristic
18	#15689922	C₄	1	4	yes	complemented
19	#15689921	C₂²	1	2	yes	—
20	#15689920	C₂²	1	4	yes	—
21	#15689919	C₄	1	4	yes	complemented
22	#137×D₄₇	C₄	1	4	yes	complemented
23	AGL(1,ℤ/8)×D₄₇	C₄	1	4	yes	complemented
24	#135×D₄₇	C₂²	1	4	yes	—
25	#15689890	C₂²	1	2	yes	complemented
26	#15689889	—	2	4	no	—
27	#15689889	C₂²	1	2	yes	complemented
28	#15689889	C₂²	1	2	yes	complemented
29	#15689888	—	2	4	no	—
30	#15689888	C₂²	1	8	yes	complemented
31	#131×D₄₇	—	2	4	no	—
32	#131×D₄₇	C₂²	1	8	yes	complemented
33	C₂×M₁₆×D₄₇	—	2	4	no	—
34	C₂×M₁₆×D₄₇	C₂²	1	2	yes	—
35	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
36	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
38	#15689246	C₂²	1	4	yes	complemented
39	#15689245	C₂²	1	4	yes	complemented
40	#15689244	C₂²	1	4	yes	complemented
41	#15689243	C₂²	1	8	yes	complemented
42	#15689242	C₂²	1	8	yes	complemented
43	#15689241	C₂²	1	4	yes	complemented
44	#15689240	C₂²	1	4	yes	complemented
45	#15689239	C₂²	1	4	yes	complemented
46	#15689238	C₂²	1	8	yes	complemented
47	#15689237	C₂²	1	8	yes	complemented
48	#15689172	C₂²	1	1	yes	characteristic, complemented
49	#15689171	C₂²	1	2	yes	complemented
50	#15689170	C₂²	1	4	yes	complemented
51	#108×D₄₇	C₂²	1	4	yes	complemented
52	C₂×#13093952	C₂²	1	2	yes	complemented
53	C₂×#13093951	C₂²	1	2	yes	complemented
54	C₂×#13093950	C₂²	1	2	yes	complemented
55	#104×D₄₇	C₂²	1	4	yes	complemented
56	#104×D₄₇	C₂²	1	4	yes	complemented
57	#104×D₄₇	C₂²	1	4	yes	complemented
58	#104×D₄₇	C₂²	1	4	yes	complemented
59	C₄×#10625329	C₂²	1	1	yes	characteristic, complemented
60	#15689075	C₂²	1	2	yes	complemented
61	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
62	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
63	C₄×#10625324	C₂²	1	2	yes	complemented
64	#97×D₄₇	C₂²	1	2	yes	complemented
65	C₄×C₈×D₄₇	C₂²	1	2	yes	complemented
66	C₄₇×#575	C₂²	1	1	yes	characteristic
67	C₄₇×#568	C₂²	1	2	yes	complemented
68	C₄₇×#444	C₂²	1	4	yes	complemented
69	C₄₇×#443	C₂²	1	4	yes	complemented
70	C₄₇×#430	C₂²	1	1	yes	characteristic, complemented
71	C₂×#104×C₄₇	C₂²	1	2	yes	complemented
72	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
73	C₂×#10625354	C₂×C₄	1	2	yes	—
74	C₂×#10625350	—	2	2	no	—
75	C₂×#10625350	C₂³	1	2	yes	—
76	C₂×#10625352	—	2	2	no	—
77	C₂×#10625352	C₂×C₄	1	2	yes	—
78	#41×D₄₇	—	2	2	no	—
79	#41×D₄₇	—	2	2	no	—
80	#41×D₄₇	—	2	2	no	—
81	#41×D₄₇	—	2	2	no	—
82	#41×D₄₇	C₂×C₄	1	4	yes	—
83	#41×D₄₇	C₂×C₄	1	4	yes	—
84	#41×D₄₇	C₂³	1	4	yes	—
85	#41×D₄₇	C₂³	1	4	yes	—
86	C₂×Q₈×D₄₇	C₂×C₄	1	2	yes	—
87	C₂×D₄×D₄₇	—	2	2	no	—
88	C₂×D₄×D₄₇	C₂×C₄	1	2	yes	—
89	C₂²×C₄×D₄₇	—	2	2	no	—
90	C₂²×C₄×D₄₇	—	2	1	no	—
91	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
92	#13094057	C₂×C₄	1	4	yes	complemented
93	#13094056	C₂×C₄	1	8	yes	complemented
94	#13094055	C₂×C₄	1	4	yes	complemented
95	#13094054	C₂×C₄	1	4	yes	complemented
96	#13094053	C₂×C₄	1	8	yes	complemented
97	#13094052	C₂×C₄	1	4	yes	complemented
98	#13094051	C₂×C₄	1	8	yes	complemented
99	#13094050	C₂×C₄	1	4	yes	complemented
100	#13094049	C₂×C₄	1	4	yes	complemented
101	#13094048	C₂×C₄	1	8	yes	complemented
102	#13094047	C₂×C₄	1	4	yes	complemented
103	#13094046	C₂³	1	4	yes	—
104	#13094045	C₂×C₄	1	8	yes	complemented
105	#13094044	C₂³	1	8	yes	—
106	#13094043	C₂×C₄	1	4	yes	complemented
107	Q₁₆×D₄₇	C₂×C₄	1	4	yes	complemented
108	SD₁₆×D₄₇	C₂×C₄	1	8	yes	complemented
109	D₈×D₄₇	C₂×C₄	1	4	yes	complemented
110	#13094032	—	2	4	no	—
111	#13094032	—	2	8	no	—
112	#13094032	—	2	8	no	—
113	#13094032	C₂³	1	8	yes	complemented
114	#13094031	—	2	4	no	—
115	#13094031	C₂³	1	8	yes	complemented
116	#13094030	—	2	4	no	—
117	#13094030	—	2	8	no	—
118	#13094030	—	2	8	no	—
119	#13094030	C₂³	1	8	yes	complemented
120	C₂×#10625329	—	2	4	no	—
121	C₂×#10625329	C₂³	1	2	yes	—
122	C₂×#10625329	C₂³	1	1	yes	characteristic
123	C₂×#10625329	C₂³	1	1	yes	characteristic
124	C₂×#10625324	—	2	2	no	—
125	C₂×#10625324	—	2	8	no	—
126	C₂×#10625324	C₂³	1	2	yes	—
127	C₂×#10625324	C₂³	1	2	yes	—
128	M₁₆×D₄₇	—	2	2	no	—
129	M₁₆×D₄₇	—	2	2	no	—
130	M₁₆×D₄₇	—	2	4	no	—
131	M₁₆×D₄₇	—	2	4	no	—
132	M₁₆×D₄₇	—	2	8	no	—
133	M₁₆×D₄₇	—	2	8	no	—
134	M₁₆×D₄₇	C₂×C₄	1	4	yes	—
135	M₁₆×D₄₇	C₂×C₄	1	4	yes	—
136	M₁₆×D₄₇	D₄	1	4	yes	—
137	M₁₆×D₄₇	D₄	1	4	yes	—
138	M₁₆×D₄₇	C₂³	1	4	yes	—
139	M₁₆×D₄₇	C₂³	1	4	yes	—
140	C₂×C₈×D₄₇	—	2	2	no	—
141	C₂×C₈×D₄₇	—	2	8	no	—
142	C₂×C₈×D₄₇	C₂³	1	2	yes	—
143	C₂×C₈×D₄₇	C₂³	1	2	yes	—
144	C₂×C₄×Dic₄₇	—	2	1	no	—
145	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
146	C₄²×D₄₇	—	2	1	no	—
147	C₄²×D₄₇	—	2	1	no	—
148	C₄²×D₄₇	C₂³	1	1	yes	characteristic
149	C₄²×D₄₇	C₂³	1	1	yes	characteristic
150	C₄²×D₄₇	C₂³	1	1	yes	characteristic
151	C₄²×D₄₇	C₂³	1	1	yes	characteristic
152	#13093960	C₂³	1	4	yes	complemented
153	#13093959	C₂³	1	8	yes	complemented
154	#13093952	C₂³	1	4	yes	complemented
155	#13093952	C₂³	1	4	yes	complemented
156	#13093951	C₂³	1	4	yes	complemented
157	#13093951	C₂³	1	4	yes	complemented
158	#13093950	C₂³	1	4	yes	complemented
159	#13093950	C₂³	1	4	yes	complemented
160	#13093935	C₂³	1	2	yes	complemented
161	#13093934	C₂³	1	2	yes	complemented
162	#13093934	C₂³	1	2	yes	complemented
163	C₄×C₄₇⋊C₈	C₂³	1	2	yes	complemented
164	C₈×Dic₄₇	C₂³	1	2	yes	complemented
165	C₈×Dic₄₇	C₂³	1	2	yes	complemented
166	C₂×#41×C₄₇	C₂³	1	2	yes	—
167	#137×C₄₇	C₂×C₄	1	4	yes	complemented
168	AGL(1,ℤ/8)×C₄₇	C₂×C₄	1	4	yes	complemented
169	#135×C₄₇	C₂³	1	4	yes	—
170	#131×C₄₇	—	2	4	no	—
171	#131×C₄₇	C₂³	1	8	yes	complemented
172	C₂×M₁₆×C₄₇	—	2	4	no	—
173	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
174	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
175	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
176	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
177	#108×C₄₇	C₂³	1	4	yes	complemented
178	#104×C₄₇	C₂³	1	4	yes	complemented
179	#104×C₄₇	C₂³	1	4	yes	complemented
180	#97×C₄₇	C₂³	1	2	yes	complemented
181	C₄×C₈×C₄₇	C₂³	1	2	yes	complemented
182	C₂³×D₄₇	—	2	2	no	—
183	C₂³×D₄₇	#41	1	1	yes	characteristic
184	#41×C₄₇	—	2	2	no	—
185	#41×C₄₇	—	2	2	no	—
186	#41×C₄₇	C₂²×C₄	1	4	yes	—
187	#41×C₄₇	C₂⁴	1	4	yes	—
188	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
189	C₂×D₄×C₄₇	—	2	2	no	—
190	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
191	C₂²×C₄×C₄₇	—	2	2	no	—
192	C₂²×C₄×C₄₇	—	2	1	no	—
193	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
194	C₂×C₂²⋊D₄₇	—	2	2	no	—
195	C₂×C₂²⋊D₄₇	—	2	2	no	—
196	C₂×C₂²⋊D₄₇	—	2	2	no	—
197	C₂²×Dic₄₇	—	2	2	no	—
198	C₂²×Dic₄₇	—	2	1	no	—
199	C₂²×Dic₄₇	#41	1	1	yes	characteristic
200	#10625354	—	2	2	no	—
201	#10625354	—	2	2	no	—
202	#10625354	C₂²×C₄	1	4	yes	—
203	#10625354	C₂²×C₄	1	4	yes	—
204	Q₈×D₄₇	—	2	2	no	—
205	Q₈×D₄₇	—	2	2	no	—
206	Q₈×D₄₇	C₂²×C₄	1	4	yes	—
207	Q₈×D₄₇	C₂²×C₄	1	4	yes	—
208	#10625352	—	2	4	no	—
209	#10625352	—	2	4	no	—
210	#10625352	—	2	4	no	—
211	#10625352	—	2	4	no	—
212	#10625352	—	2	2	no	—
213	#10625352	—	2	2	no	—
214	#10625352	C₂²×C₄	1	4	yes	—
215	#10625352	C₂²×C₄	1	4	yes	—
216	D₄×D₄₇	—	2	4	no	—
217	D₄×D₄₇	—	2	4	no	—
218	D₄×D₄₇	—	2	4	no	—
219	D₄×D₄₇	—	2	4	no	—
220	D₄×D₄₇	—	2	2	no	—
221	D₄×D₄₇	—	2	2	no	—
222	D₄×D₄₇	C₂²×C₄	1	4	yes	—
223	D₄×D₄₇	C₂²×C₄	1	4	yes	—
224	#10625350	—	2	2	no	—
225	#10625350	—	2	2	no	—
226	#10625350	—	2	4	no	—
227	#10625350	—	2	4	no	—
228	#10625350	—	2	4	no	—
229	#10625350	—	2	4	no	—
230	#10625350	C₂²×C₄	1	4	yes	—
231	#10625350	C₂⁴	1	4	yes	—
232	C₂×D₁₈₈	—	2	2	no	—
233	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
234	C₂×C₄×D₄₇	—	2	2	no	—
235	C₂×C₄×D₄₇	—	2	1	no	—
236	C₂×C₄×D₄₇	—	2	2	no	—
237	C₂×C₄×D₄₇	—	2	2	no	—
238	C₂×C₄×D₄₇	—	2	4	no	—
239	C₂×C₄×D₄₇	—	2	4	no	—
240	C₂×C₄×D₄₇	—	2	4	no	—
241	C₂×C₄×D₄₇	—	2	4	no	—
242	C₂×C₄×D₄₇	—	2	1	no	—
243	C₂×C₄×D₄₇	—	2	1	no	—
244	C₂×C₄×D₄₇	—	2	1	no	—
245	C₂×C₄×D₄₇	—	4	4	no	—
246	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
247	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
248	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
249	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
250	C₂×C₄×D₄₇	#41	1	1	yes	characteristic
251	C₂×C₄×D₄₇	#41	1	1	yes	characteristic
252	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₉₄	—	2	2	no	—
255	C₂×Dic₉₄	C₂²×C₄	1	2	yes	—
256	Q₁₆×C₄₇	C₂²×C₄	1	4	yes	complemented
257	SD₁₆×C₄₇	C₂²×C₄	1	8	yes	complemented
258	D₈×C₄₇	C₂²×C₄	1	4	yes	complemented
259	M₁₆×C₄₇	—	2	2	no	—
260	M₁₆×C₄₇	—	2	8	no	—
261	M₁₆×C₄₇	C₂²×C₄	1	4	yes	—
262	M₁₆×C₄₇	C₂×D₄	1	4	yes	—
263	M₁₆×C₄₇	C₂⁴	1	4	yes	—
264	C₂×C₈×C₄₇	—	2	2	no	—
265	C₂×C₈×C₄₇	—	2	8	no	—
266	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
267	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
268	C₄²×C₄₇	—	2	1	no	—
269	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
270	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
271	#10625337	C₂²×C₄	1	8	yes	complemented
272	#10625336	C₂²×C₄	1	8	yes	complemented
273	#10625335	C₂²×C₄	1	8	yes	complemented
274	#10625334	C₂²×C₄	1	8	yes	complemented
275	C₄×Dic₄₇	—	2	1	no	—
276	C₄×Dic₄₇	—	2	1	no	—
277	C₄×Dic₄₇	—	2	1	no	—
278	C₄×Dic₄₇	—	2	1	no	—
279	C₄×Dic₄₇	—	2	1	no	—
280	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
281	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
282	#10625329	—	2	2	no	—
283	#10625329	—	2	8	no	—
284	#10625329	C₂²×C₄	1	4	yes	—
285	#10625329	C₂×D₄	1	4	yes	—
286	#10625329	C₂⁴	1	4	yes	—
287	C₂×C₄₇⋊C₈	—	2	2	no	—
288	C₂×C₄₇⋊C₈	—	2	8	no	—
289	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
290	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
291	Dic₁₈₈	C₂²×C₄	1	4	yes	complemented
292	D₃₇₆	C₂²×C₄	1	4	yes	complemented
293	#10625325	C₂²×C₄	1	8	yes	complemented
294	#10625324	—	2	4	no	—
295	#10625324	—	2	4	no	—
296	#10625324	—	2	8	no	—
297	#10625324	—	2	8	no	—
298	#10625324	C₂²×C₄	1	8	yes	—
299	#10625324	C₂×D₄	1	8	yes	—
300	C₈×D₄₇	—	2	4	no	—
301	C₈×D₄₇	—	2	4	no	—
302	C₈×D₄₇	—	2	8	no	—
303	C₈×D₄₇	—	2	8	no	—
304	C₈×D₄₇	C₂²×C₄	1	4	yes	—
305	C₈×D₄₇	C₂²×C₄	1	4	yes	—
306	C₈×D₄₇	C₂×D₄	1	4	yes	—
307	C₈×D₄₇	C₂×D₄	1	4	yes	—
308	C₂³×C₄₇	—	2	2	no	—
309	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
310	C₂²×D₄₇	—	2	2	no	—
311	C₂²×D₄₇	—	2	4	no	—
312	C₂²×D₄₇	—	2	4	no	—
313	C₂²×D₄₇	—	4	2	no	—
314	C₂²×D₄₇	—	8	4	no	—
315	C₂²×D₄₇	C₄×D₄	1	2	yes	—
316	C₂²×D₄₇	C₄×D₄	1	2	yes	—
317	C₂²×D₄₇	C₂×#41	1	1	yes	characteristic
318	C₂²×D₄₇	C₂×#41	1	1	yes	characteristic
319	Q₈×C₄₇	—	2	2	no	—
320	Q₈×C₄₇	C₂³×C₄	1	4	yes	—
321	D₄×C₄₇	—	2	4	no	—
322	D₄×C₄₇	—	2	4	no	—
323	D₄×C₄₇	—	2	2	no	—
324	D₄×C₄₇	C₂³×C₄	1	4	yes	—
325	C₂×C₄×C₄₇	—	2	2	no	—
326	C₂×C₄×C₄₇	—	2	1	no	—
327	C₂×C₄×C₄₇	—	2	4	no	—
328	C₂×C₄×C₄₇	—	2	4	no	—
329	C₂×C₄×C₄₇	—	2	1	no	—
330	C₂×C₄×C₄₇	—	4	2	no	—
331	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
332	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
333	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
334	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
335	C₂²⋊D₄₇	—	2	4	no	—
336	C₂²⋊D₄₇	—	2	4	no	—
337	C₂²⋊D₄₇	—	2	4	no	—
338	C₂²⋊D₄₇	—	2	4	no	—
339	C₂²⋊D₄₇	—	2	4	no	—
340	C₂²⋊D₄₇	—	2	4	no	—
341	C₂×Dic₄₇	—	2	2	no	—
342	C₂×Dic₄₇	—	2	1	no	—
343	C₂×Dic₄₇	—	2	4	no	—
344	C₂×Dic₄₇	—	2	4	no	—
345	C₂×Dic₄₇	—	2	1	no	—
346	C₂×Dic₄₇	—	4	2	no	—
347	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
348	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
349	C₂×Dic₄₇	C₂×#41	1	1	yes	characteristic
350	C₂×Dic₄₇	C₂×#41	1	1	yes	characteristic
351	D₁₈₈	—	2	4	no	—
352	D₁₈₈	—	2	4	no	—
353	D₁₈₈	—	2	2	no	—
354	D₁₈₈	C₂³×C₄	1	4	yes	—
355	C₄×D₄₇	—	2	4	no	—
356	C₄×D₄₇	—	2	4	no	—
357	C₄×D₄₇	—	2	4	no	—
358	C₄×D₄₇	—	2	4	no	—
359	C₄×D₄₇	—	2	4	no	—
360	C₄×D₄₇	—	2	4	no	—
361	C₄×D₄₇	—	2	4	no	—
362	C₄×D₄₇	—	4	2	no	—
363	C₄×D₄₇	—	4	2	no	—
364	C₄×D₄₇	—	4	2	no	—
365	C₄×D₄₇	C₄×D₄	1	2	yes	—
366	C₄×D₄₇	C₄×D₄	1	2	yes	—
367	C₄×D₄₇	C₄×D₄	1	2	yes	—
368	C₄×D₄₇	C₄×D₄	1	2	yes	—
369	C₄×D₄₇	C₂³×C₄	1	1	yes	characteristic
370	C₄×D₄₇	C₂³×C₄	1	1	yes	characteristic
371	C₄×D₄₇	C₂³×C₄	1	2	yes	—
372	C₄×D₄₇	C₂²×D₄	1	1	yes	characteristic
373	C₄×D₄₇	C₂²×D₄	1	2	yes	—
374	C₄×D₄₇	C₂²×D₄	1	1	yes	characteristic
375	Dic₉₄	—	2	2	no	—
376	Dic₉₄	—	2	4	no	—
377	Dic₉₄	—	2	4	no	—
378	Dic₉₄	C₂³×C₄	1	4	yes	—
379	C₈×C₄₇	—	2	4	no	—
380	C₈×C₄₇	C₂³×C₄	1	4	yes	—
381	C₈×C₄₇	C₂²×D₄	1	4	yes	—
382	C₄₇⋊C₈	—	2	4	no	—
383	C₄₇⋊C₈	C₂³×C₄	1	4	yes	—
384	C₄₇⋊C₈	C₂²×D₄	1	4	yes	—
385	C₂×#2956	—	47	1	no	maximal, Sylow
386	C₂²×C₄₇	—	2	4	no	—
387	C₂²×C₄₇	—	4	1	no	—
388	C₂²×C₄₇	—	8	2	no	—
389	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
390	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
391	C₂×D₄₇	—	2	2	no	—
392	C₂×D₄₇	—	2	4	no	—
393	C₂×D₄₇	—	2	4	no	—
394	C₂×D₄₇	—	4	1	no	—
395	C₂×D₄₇	—	4	2	no	—
396	C₂×D₄₇	—	4	8	no	—
397	C₂×D₄₇	—	8	4	no	—
398	C₂×D₄₇	—	8	2	no	—
399	C₂×D₄₇	C₂×C₄×D₄	1	2	yes	—
400	C₂×D₄₇	C₂×C₄×D₄	1	1	yes	characteristic
401	C₂×D₄₇	C₂×C₄×D₄	1	1	yes	characteristic
402	C₄×C₄₇	—	2	2	no	—
403	C₄×C₄₇	—	2	4	no	—
404	C₄×C₄₇	—	4	1	no	—
405	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
406	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
407	C₄×C₄₇	C₂³×D₄	1	1	yes	characteristic
408	Dic₄₇	—	2	2	no	—
409	Dic₄₇	—	2	4	no	—
410	Dic₄₇	—	4	1	no	—
411	Dic₄₇	C₂×C₄×D₄	1	1	yes	characteristic
412	Dic₄₇	C₂×C₄×D₄	1	2	yes	—
413	Dic₄₇	C₂×C₄×D₄	1	1	yes	characteristic
414	C₂×#575	—	47	1	no	—
415	C₂×#568	—	47	2	no	—
416	#2956	—	47	4	no	—
417	#2956	—	47	4	no	—
418	#2956	—	47	1	no	—
419	#2956	—	47	2	no	—
420	#2956	—	47	1	no	—
421	#2956	—	47	1	no	—
422	#2956	—	47	2	no	—
423	#2956	D₄₇	1	1	yes	characteristic, direct product factor
424	C₂×#444	—	47	4	no	—
425	C₂×#443	—	47	4	no	—
426	C₂×#430	—	47	1	no	—
427	C₂²×#104	—	47	2	no	—
428	C₂×C₄×M₁₆	—	47	1	no	—
429	C₂×C₄₇	—	2	1	no	—
430	C₂×C₄₇	—	2	2	no	—
431	C₂×C₄₇	—	4	4	no	—
432	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
433	D₄₇	—	2	2	no	—
434	D₄₇	—	2	1	no	—
435	D₄₇	—	4	4	no	—
436	D₄₇	#2956	1	2	yes	direct product factor
437	C₂²×#41	—	47	2	no	—
438	#575	—	47	2	no	—
439	#575	—	47	4	no	—
440	#575	—	47	4	no	—
441	#575	—	47	4	no	—
442	#575	—	47	1	no	—
443	#575	C₂×D₄₇	1	1	yes	characteristic
444	C₂×#137	—	47	4	no	—
445	C₂×AGL(1,ℤ/8)	—	47	4	no	—
446	C₂×#135	—	47	4	no	—
447	#568	—	47	2	no	—
448	#568	—	47	8	no	—
449	#568	—	47	2	no	—
450	#568	—	47	2	no	—
451	#568	—	94	4	no	—
452	#568	—	94	4	no	—
453	#568	C₂×D₄₇	1	2	yes	complemented
454	C₂×#131	—	47	8	no	—
455	C₂×#131	—	94	4	no	—
456	C₂²×M₁₆	—	47	1	no	—
457	C₂²×M₁₆	—	47	1	no	—
458	C₂²×M₁₆	—	47	2	no	—
459	C₂²×M₁₆	—	94	4	no	—
460	C₂²×C₄²	—	47	1	no	—
461	#444	—	47	4	no	—
462	#444	—	47	8	no	—
463	#444	—	47	4	no	—
464	#444	—	47	8	no	—
465	#444	—	47	4	no	—
466	#444	C₂×D₄₇	1	4	yes	complemented
467	#443	—	47	4	no	—
468	#443	—	47	8	no	—
469	#443	—	47	4	no	—
470	#443	—	47	8	no	—
471	#443	—	47	4	no	—
472	#443	C₂×D₄₇	1	4	yes	complemented
473	#430	—	47	2	no	—
474	#430	—	47	1	no	—
475	#430	—	47	4	no	—
476	#430	C₂×D₄₇	1	1	yes	characteristic, complemented
477	C₂×#108	—	47	4	no	—
478	C₂×#104	—	47	2	no	—
479	C₂×#104	—	47	2	no	—
480	C₂×#104	—	47	2	no	—
481	C₂×#104	—	47	4	no	—
482	C₂×#104	—	47	4	no	—
483	C₂×#104	—	47	4	no	—
484	C₂×#104	—	47	4	no	—
485	C₂×#104	C₂×D₄₇	1	2	yes	complemented
486	C₄×M₁₆	—	47	1	no	—
487	C₄×M₁₆	—	47	1	no	—
488	C₄×M₁₆	—	47	1	no	—
489	C₄×M₁₆	—	47	2	no	—
490	C₄×M₁₆	—	47	2	no	—
491	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
492	C₂×#97	—	47	2	no	—
493	C₂×C₄×C₈	—	47	2	no	—
494	C₄₇	C₂×#2956	1	1	yes	characteristic, complemented, Sylow
495	C₂×#41	—	47	4	no	—
496	C₂×#41	—	47	4	no	—
497	C₂×#41	—	47	4	no	—
498	C₂×#41	—	47	4	no	—
499	C₂×#41	—	47	2	no	—
500	C₂×#41	—	47	2	no	—
501	C₂×#41	—	47	2	no	—
502	C₂×#41	—	94	2	no	—
503	C₂×#41	—	94	2	no	—
504	C₂×#41	—	94	2	no	—
505	C₂×#41	—	94	2	no	—
506	C₂×#41	—	94	2	no	—
507	C₂×#41	—	94	2	no	—
508	C₂×#41	C₂²×D₄₇	1	2	yes	—
509	C₂²×Q₈	—	47	2	no	—
510	C₂²×D₄	—	47	2	no	—
511	C₂²×D₄	—	94	2	no	—
512	C₂³×C₄	—	47	1	no	—
513	C₂³×C₄	—	94	2	no	—
514	C₂³×C₄	—	94	1	no	—
515	#137	—	47	4	no	—
516	#137	—	47	4	no	—
517	#137	—	47	8	no	—
518	#137	—	47	8	no	—
519	#137	—	47	4	no	—
520	#137	C₄×D₄₇	1	4	yes	complemented
521	AGL(1,ℤ/8)	—	47	4	no	—
522	AGL(1,ℤ/8)	—	47	4	no	—
523	AGL(1,ℤ/8)	—	47	8	no	—
524	AGL(1,ℤ/8)	—	47	8	no	—
525	AGL(1,ℤ/8)	—	47	4	no	—
526	AGL(1,ℤ/8)	C₄×D₄₇	1	4	yes	complemented
527	#135	—	47	8	no	—
528	#135	—	47	4	no	—
529	#135	—	47	8	no	—
530	#135	—	47	4	no	—
531	#135	—	47	4	no	—
532	#135	C₂²×D₄₇	1	4	yes	—
533	C₂×Q₁₆	—	47	4	no	—
534	C₂×SD₁₆	—	47	8	no	—
535	C₂×D₈	—	47	4	no	—
536	#131	—	2	4	no	—
537	#131	—	47	8	no	—
538	#131	—	47	8	no	—
539	#131	—	47	8	no	—
540	#131	—	94	8	no	—
541	#131	—	94	4	no	—
542	#131	—	94	8	no	—
543	#131	—	94	8	no	—
544	#131	—	94	8	no	—
545	#131	—	94	4	no	—
546	#131	—	94	4	no	—
547	#131	C₂²×D₄₇	1	8	yes	complemented
548	C₂×M₁₆	—	2	4	no	—
549	C₂×M₁₆	—	47	1	no	—
550	C₂×M₁₆	—	47	1	no	—
551	C₂×M₁₆	—	47	4	no	—
552	C₂×M₁₆	—	47	4	no	—
553	C₂×M₁₆	—	47	4	no	—
554	C₂×M₁₆	—	47	4	no	—
555	C₂×M₁₆	—	47	2	no	—
556	C₂×M₁₆	—	47	2	no	—
557	C₂×M₁₆	—	47	2	no	—
558	C₂×M₁₆	—	47	4	no	—
559	C₂×M₁₆	—	47	4	no	—
560	C₂×M₁₆	—	94	8	no	—
561	C₂×M₁₆	—	94	2	no	—
562	C₂×M₁₆	—	94	8	no	—
563	C₂×M₁₆	—	94	4	no	—
564	C₂×M₁₆	—	94	8	no	—
565	C₂×M₁₆	—	94	2	no	—
566	C₂×M₁₆	—	94	2	no	—
567	C₂×M₁₆	—	94	4	no	—
568	C₂×M₁₆	—	94	4	no	—
569	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
570	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
571	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
572	C₂²×C₈	—	47	2	no	—
573	C₂²×C₈	—	47	2	no	—
574	C₂²×C₈	—	94	8	no	—
575	C₂²×C₈	—	94	2	no	—
576	C₂×C₄²	—	47	1	no	—
577	C₂×C₄²	—	47	1	no	—
578	C₂×C₄²	—	47	1	no	—
579	C₂×C₄²	—	47	1	no	—
580	C₂×C₄²	—	47	1	no	—
581	C₂×C₄²	—	94	1	no	—
582	C₂×C₄²	—	94	1	no	—
583	C₂×C₄²	—	94	1	no	—
584	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
585	#108	—	47	8	no	—
586	#108	—	47	4	no	—
587	#108	C₂²×D₄₇	1	4	yes	complemented
588	#104	—	47	4	no	—
589	#104	—	47	4	no	—
590	#104	—	47	4	no	—
591	#104	—	47	4	no	—
592	#104	—	47	4	no	—
593	#104	—	47	4	no	—
594	#104	C₂²×D₄₇	1	4	yes	complemented
595	#104	C₂²×D₄₇	1	4	yes	complemented
596	#97	—	47	2	no	—
597	#97	—	47	2	no	—
598	#97	—	47	2	no	—
599	#97	C₂²×D₄₇	1	2	yes	complemented
600	C₄×C₈	—	47	2	no	—
601	C₄×C₈	—	47	2	no	—
602	C₄×C₈	—	47	2	no	—
603	C₄×C₈	C₂²×D₄₇	1	2	yes	complemented
604	C₂⁴	—	47	1	no	—
605	C₂⁴	—	94	2	no	—
606	#41	—	2	2	no	—
607	#41	—	2	2	no	—
608	#41	—	47	4	no	—
609	#41	—	47	4	no	—
610	#41	—	47	4	no	—
611	#41	—	47	4	no	—
612	#41	—	47	4	no	—
613	#41	—	47	4	no	—
614	#41	—	94	4	no	—
615	#41	—	94	4	no	—
616	#41	—	94	4	no	—
617	#41	—	94	4	no	—
618	#41	—	94	4	no	—
619	#41	—	94	4	no	—
620	#41	—	94	4	no	—
621	#41	—	94	4	no	—
622	#41	—	94	2	no	—
623	#41	—	94	2	no	—
624	#41	—	94	2	no	—
625	#41	—	94	2	no	—
626	#41	—	94	2	no	—
627	#41	—	94	2	no	—
628	#41	C₂×C₄×D₄₇	1	4	yes	—
629	#41	C₂³×D₄₇	1	4	yes	—
630	C₂×Q₈	—	47	4	no	—
631	C₂×Q₈	—	47	4	no	—
632	C₂×Q₈	—	47	2	no	—
633	C₂×Q₈	—	94	2	no	—
634	C₂×Q₈	—	94	2	no	—
635	C₂×Q₈	—	94	2	no	—
636	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
637	C₂×D₄	—	2	2	no	—
638	C₂×D₄	—	47	4	no	—
639	C₂×D₄	—	47	4	no	—
640	C₂×D₄	—	47	2	no	—
641	C₂×D₄	—	94	2	no	—
642	C₂×D₄	—	94	2	no	—
643	C₂×D₄	—	94	2	no	—
644	C₂×D₄	—	94	2	no	—
645	C₂×D₄	—	94	4	no	—
646	C₂×D₄	—	94	4	no	—
647	C₂×D₄	—	94	4	no	—
648	C₂×D₄	—	94	4	no	—
649	C₂×D₄	—	94	2	no	—
650	C₂×D₄	—	94	2	no	—
651	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
652	C₂²×C₄	—	2	2	no	—
653	C₂²×C₄	—	2	1	no	—
654	C₂²×C₄	—	47	1	no	—
655	C₂²×C₄	—	47	2	no	—
656	C₂²×C₄	—	47	2	no	—
657	C₂²×C₄	—	47	2	no	—
658	C₂²×C₄	—	47	2	no	—
659	C₂²×C₄	—	47	1	no	—
660	C₂²×C₄	—	47	1	no	—
661	C₂²×C₄	—	47	1	no	—
662	C₂²×C₄	—	47	1	no	—
663	C₂²×C₄	—	94	4	no	—
664	C₂²×C₄	—	94	4	no	—
665	C₂²×C₄	—	94	2	no	—
666	C₂²×C₄	—	94	4	no	—
667	C₂²×C₄	—	94	4	no	—
668	C₂²×C₄	—	94	1	no	—
669	C₂²×C₄	—	94	2	no	—
670	C₂²×C₄	—	94	1	no	—
671	C₂²×C₄	—	94	1	no	—
672	C₂²×C₄	—	94	1	no	—
673	C₂²×C₄	—	94	2	no	—
674	C₂²×C₄	—	94	2	no	—
675	C₂²×C₄	—	94	1	no	—
676	C₂²×C₄	—	188	4	no	—
677	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
678	Q₁₆	—	47	8	no	—
679	Q₁₆	—	47	4	no	—
680	Q₁₆	C₂×C₄×D₄₇	1	4	yes	complemented
681	SD₁₆	—	47	8	no	—
682	SD₁₆	—	47	8	no	—
683	SD₁₆	—	47	8	no	—
684	SD₁₆	C₂×C₄×D₄₇	1	8	yes	complemented
685	D₈	—	47	8	no	—
686	D₈	—	47	4	no	—
687	D₈	C₂×C₄×D₄₇	1	4	yes	complemented
688	M₁₆	—	2	2	no	—
689	M₁₆	—	2	8	no	—
690	M₁₆	—	47	4	no	—
691	M₁₆	—	47	4	no	—
692	M₁₆	—	47	8	no	—
693	M₁₆	—	47	8	no	—
694	M₁₆	—	47	4	no	—
695	M₁₆	—	94	8	no	—
696	M₁₆	—	94	4	no	—
697	M₁₆	—	94	4	no	—
698	M₁₆	—	94	8	no	—
699	M₁₆	—	94	2	no	—
700	M₁₆	—	94	8	no	—
701	M₁₆	C₂×C₄×D₄₇	1	4	yes	—
702	M₁₆	D₄×D₄₇	1	4	yes	—
703	M₁₆	C₂³×D₄₇	1	4	yes	—
704	C₂×C₈	—	2	2	no	—
705	C₂×C₈	—	2	8	no	—
706	C₂×C₈	—	47	2	no	—
707	C₂×C₈	—	47	2	no	—
708	C₂×C₈	—	47	4	no	—
709	C₂×C₈	—	47	4	no	—
710	C₂×C₈	—	47	4	no	—
711	C₂×C₈	—	47	4	no	—
712	C₂×C₈	—	94	8	no	—
713	C₂×C₈	—	94	4	no	—
714	C₂×C₈	—	94	4	no	—
715	C₂×C₈	—	94	8	no	—
716	C₂×C₈	—	94	2	no	—
717	C₂×C₈	—	94	8	no	—
718	C₂×C₈	C₂³×D₄₇	1	2	yes	—
719	C₂×C₈	C₂³×D₄₇	1	2	yes	—
720	C₄²	—	2	1	no	—
721	C₄²	—	47	1	no	—
722	C₄²	—	47	1	no	—
723	C₄²	—	94	1	no	—
724	C₄²	—	94	1	no	—
725	C₄²	—	94	1	no	—
726	C₄²	—	94	1	no	—
727	C₄²	—	94	1	no	—
728	C₄²	C₂³×D₄₇	1	1	yes	characteristic
729	C₄²	C₂³×D₄₇	1	1	yes	characteristic
730	C₂³	—	2	2	no	—
731	C₂³	—	47	2	no	—
732	C₂³	—	47	1	no	—
733	C₂³	—	47	2	no	—
734	C₂³	—	47	1	no	—
735	C₂³	—	94	4	no	—
736	C₂³	—	94	4	no	—
737	C₂³	—	94	2	no	—
738	C₂³	—	376	4	no	—
739	C₂³	—	188	2	no	—
740	C₂³	#41×D₄₇	1	1	yes	characteristic
741	Q₈	—	2	2	no	—
742	Q₈	—	47	4	no	—
743	Q₈	—	94	4	no	—
744	Q₈	—	94	4	no	—
745	Q₈	—	94	2	no	—
746	Q₈	C₂²×C₄×D₄₇	1	4	yes	—
747	D₄	—	2	4	no	—
748	D₄	—	2	4	no	—
749	D₄	—	2	2	no	—
750	D₄	—	47	4	no	—
751	D₄	—	94	4	no	—
752	D₄	—	94	4	no	—
753	D₄	—	94	4	no	—
754	D₄	—	94	4	no	—
755	D₄	—	94	4	no	—
756	D₄	—	94	4	no	—
757	D₄	—	94	4	no	—
758	D₄	—	94	4	no	—
759	D₄	—	94	2	no	—
760	D₄	C₂²×C₄×D₄₇	1	4	yes	—
761	C₂×C₄	—	2	2	no	—
762	C₂×C₄	—	2	1	no	—
763	C₂×C₄	—	2	4	no	—
764	C₂×C₄	—	2	4	no	—
765	C₂×C₄	—	2	1	no	—
766	C₂×C₄	—	4	2	no	—
767	C₂×C₄	—	47	2	no	—
768	C₂×C₄	—	47	2	no	—
769	C₂×C₄	—	47	1	no	—
770	C₂×C₄	—	47	1	no	—
771	C₂×C₄	—	47	2	no	—
772	C₂×C₄	—	47	2	no	—
773	C₂×C₄	—	47	2	no	—
774	C₂×C₄	—	47	2	no	—
775	C₂×C₄	—	47	1	no	—
776	C₂×C₄	—	47	1	no	—
777	C₂×C₄	—	47	2	no	—
778	C₂×C₄	—	47	1	no	—
779	C₂×C₄	—	47	1	no	—
780	C₂×C₄	—	47	2	no	—
781	C₂×C₄	—	94	4	no	—
782	C₂×C₄	—	94	4	no	—
783	C₂×C₄	—	94	4	no	—
784	C₂×C₄	—	94	4	no	—
785	C₂×C₄	—	94	4	no	—
786	C₂×C₄	—	94	4	no	—
787	C₂×C₄	—	94	4	no	—
788	C₂×C₄	—	94	2	no	—
789	C₂×C₄	—	94	1	no	—
790	C₂×C₄	—	94	4	no	—
791	C₂×C₄	—	94	4	no	—
792	C₂×C₄	—	94	1	no	—
793	C₂×C₄	—	188	2	no	—
794	C₂×C₄	—	188	2	no	—
795	C₂×C₄	—	188	2	no	—
796	C₂×C₄	—	188	2	no	—
797	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
798	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
799	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
800	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
801	C₈	—	2	4	no	—
802	C₈	—	47	4	no	—
803	C₈	—	47	4	no	—
804	C₈	—	94	4	no	—
805	C₈	C₂²×C₄×D₄₇	1	4	yes	—
806	C₈	C₂×D₄×D₄₇	1	4	yes	—
807	C₂²	—	2	4	no	—
808	C₂²	—	4	1	no	—
809	C₂²	—	8	2	no	—
810	C₂²	—	47	1	no	—
811	C₂²	—	47	2	no	—
812	C₂²	—	47	1	no	—
813	C₂²	—	94	2	no	—
814	C₂²	—	94	4	no	—
815	C₂²	—	94	4	no	—
816	C₂²	—	376	2	no	—
817	C₂²	—	376	4	no	—
818	C₂²	—	188	1	no	—
819	C₂²	—	188	2	no	—
820	C₂²	—	188	8	no	—
821	C₂²	C₄×D₄×D₄₇	1	2	yes	—
822	C₂²	C₂×#41×D₄₇	1	1	yes	characteristic
823	C₄	—	2	2	no	—
824	C₄	—	2	4	no	—
825	C₄	—	4	1	no	—
826	C₄	—	47	1	no	—
827	C₄	—	47	2	no	—
828	C₄	—	47	1	no	—
829	C₄	—	94	2	no	—
830	C₄	—	94	4	no	—
831	C₄	—	188	1	no	—
832	C₄	C₄×D₄×D₄₇	1	2	yes	—
833	C₄	C₂³×C₄×D₄₇	1	1	yes	characteristic
834	C₄	C₂²×D₄×D₄₇	1	1	yes	characteristic
835	C₂	—	2	1	no	—
836	C₂	—	2	2	no	—
837	C₂	—	4	4	no	—
838	C₂	—	47	2	no	—
839	C₂	—	94	2	no	—
840	C₂	—	94	1	no	—
841	C₂	—	188	4	no	—
842	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×#2956	C₂
socle	C₂×C₄₇	C₂²×C₄×D₄
prime radical	#575×D₄₇	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2956	D₄₇
hypocenter	C₄₇	C₂×#2956
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₄ ◁ C₂×M₁₆ ◁ #2956

Complements

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

N	H ≅ G/N	type
2. #568×D₄₇	C₂	semidirect
3. #20252299	C₂	semidirect
4. #20252298	C₂	semidirect
5. #20252297	C₂	semidirect
6. #20252296	C₂	semidirect
7. #20252295	C₂	semidirect
8. #20252294	C₂	semidirect
9. #20252293	C₂	semidirect
10. #444×D₄₇	C₂	semidirect
11. #443×D₄₇	C₂	semidirect
12. #430×D₄₇	C₂	semidirect
13. C₂×#104×D₄₇	C₂	semidirect
14. C₄×M₁₆×D₄₇	C₂	semidirect
15. C₄₇×#2956	C₂	semidirect
18. #15689922	C₄	semidirect
21. #15689919	C₄	semidirect
22. #137×D₄₇	C₄	semidirect
23. AGL(1,ℤ/8)×D₄₇	C₄	semidirect
25. #15689890	C₂²	semidirect
27. #15689889	C₂²	semidirect
28. #15689889	C₂²	semidirect
30. #15689888	C₂²	semidirect
32. #131×D₄₇	C₂²	semidirect
38. #15689246	C₂²	semidirect
39. #15689245	C₂²	semidirect
40. #15689244	C₂²	semidirect
41. #15689243	C₂²	semidirect
42. #15689242	C₂²	semidirect
43. #15689241	C₂²	semidirect
44. #15689240	C₂²	semidirect
45. #15689239	C₂²	semidirect
46. #15689238	C₂²	semidirect
47. #15689237	C₂²	semidirect
48. #15689172	C₂²	semidirect
49. #15689171	C₂²	semidirect
50. #15689170	C₂²	semidirect
51. #108×D₄₇	C₂²	semidirect
52. C₂×#13093952	C₂²	semidirect
53. C₂×#13093951	C₂²	semidirect
54. C₂×#13093950	C₂²	semidirect
55. #104×D₄₇	C₂²	semidirect
56. #104×D₄₇	C₂²	semidirect
57. #104×D₄₇	C₂²	semidirect
58. #104×D₄₇	C₂²	semidirect
59. C₄×#10625329	C₂²	semidirect
60. #15689075	C₂²	semidirect
61. M₁₆×Dic₄₇	C₂²	semidirect
62. M₁₆×Dic₄₇	C₂²	semidirect
63. C₄×#10625324	C₂²	semidirect
64. #97×D₄₇	C₂²	semidirect
65. C₄×C₈×D₄₇	C₂²	semidirect
67. C₄₇×#568	C₂²	semidirect
68. C₄₇×#444	C₂²	semidirect
69. C₄₇×#443	C₂²	semidirect
70. C₄₇×#430	C₂²	semidirect
71. C₂×#104×C₄₇	C₂²	semidirect
72. C₄×M₁₆×C₄₇	C₂²	semidirect
92. #13094057	C₂×C₄	semidirect
93. #13094056	C₂×C₄	semidirect
94. #13094055	C₂×C₄	semidirect
95. #13094054	C₂×C₄	semidirect
96. #13094053	C₂×C₄	semidirect
97. #13094052	C₂×C₄	semidirect
98. #13094051	C₂×C₄	semidirect
99. #13094050	C₂×C₄	semidirect
100. #13094049	C₂×C₄	semidirect
101. #13094048	C₂×C₄	semidirect
102. #13094047	C₂×C₄	semidirect
104. #13094045	C₂×C₄	semidirect
106. #13094043	C₂×C₄	semidirect
107. Q₁₆×D₄₇	C₂×C₄	semidirect
108. SD₁₆×D₄₇	C₂×C₄	semidirect
109. D₈×D₄₇	C₂×C₄	semidirect
113. #13094032	C₂³	semidirect
115. #13094031	C₂³	semidirect
119. #13094030	C₂³	semidirect
152. #13093960	C₂³	semidirect
153. #13093959	C₂³	semidirect
154. #13093952	C₂³	semidirect
155. #13093952	C₂³	semidirect
156. #13093951	C₂³	semidirect
157. #13093951	C₂³	semidirect
158. #13093950	C₂³	semidirect
159. #13093950	C₂³	semidirect
160. #13093935	C₂³	semidirect
161. #13093934	C₂³	semidirect
162. #13093934	C₂³	semidirect
163. C₄×C₄₇⋊C₈	C₂³	semidirect
164. C₈×Dic₄₇	C₂³	semidirect
165. C₈×Dic₄₇	C₂³	semidirect
167. #137×C₄₇	C₂×C₄	semidirect
168. AGL(1,ℤ/8)×C₄₇	C₂×C₄	semidirect
171. #131×C₄₇	C₂³	semidirect
177. #108×C₄₇	C₂³	semidirect
178. #104×C₄₇	C₂³	semidirect
179. #104×C₄₇	C₂³	semidirect
180. #97×C₄₇	C₂³	semidirect
181. C₄×C₈×C₄₇	C₂³	semidirect
256. Q₁₆×C₄₇	C₂²×C₄	semidirect
257. SD₁₆×C₄₇	C₂²×C₄	semidirect
258. D₈×C₄₇	C₂²×C₄	semidirect
271. #10625337	C₂²×C₄	semidirect
272. #10625336	C₂²×C₄	semidirect
273. #10625335	C₂²×C₄	semidirect
274. #10625334	C₂²×C₄	semidirect
291. Dic₁₈₈	C₂²×C₄	semidirect
292. D₃₇₆	C₂²×C₄	semidirect
293. #10625325	C₂²×C₄	semidirect
423. #2956	D₄₇	direct (N × H)
436. D₄₇	#2956	direct (N × H)
453. #568	C₂×D₄₇	semidirect
466. #444	C₂×D₄₇	semidirect
472. #443	C₂×D₄₇	semidirect
476. #430	C₂×D₄₇	semidirect
485. C₂×#104	C₂×D₄₇	semidirect
491. C₄×M₁₆	C₂×D₄₇	semidirect
494. C₄₇	C₂×#2956	semidirect
520. #137	C₄×D₄₇	semidirect
526. AGL(1,ℤ/8)	C₄×D₄₇	semidirect
547. #131	C₂²×D₄₇	semidirect
587. #108	C₂²×D₄₇	semidirect
594. #104	C₂²×D₄₇	semidirect
595. #104	C₂²×D₄₇	semidirect
599. #97	C₂²×D₄₇	semidirect
603. C₄×C₈	C₂²×D₄₇	semidirect
680. Q₁₆	C₂×C₄×D₄₇	semidirect
684. SD₁₆	C₂×C₄×D₄₇	semidirect
687. D₈	C₂×C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#575×D₄₇	2
#568×D₄₇	2
#20252299	2
#20252298	2
#20252297	2
#20252296	2
#20252295	2
#20252294	2
#20252293	2
#444×D₄₇	2
#443×D₄₇	2
#430×D₄₇	2
C₂×#104×D₄₇	2
C₄×M₁₆×D₄₇	2
C₄₇×#2956	2
C₂×#2956	47

Subgroups — D47×#2956 #27080585

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#2956 #27080585