Subgroups — D₄₇×#2948 #27080400

Order 12032.

3086 conjugacy classes of subgroups.

The subgroup lattice has 662 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×D₈×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#518×D₄₇	C₂	1	2	yes	maximal, complemented
3	#20252241	C₂	1	1	yes	maximal, characteristic, complemented
4	#20252240	C₂	1	1	yes	maximal, characteristic, complemented
5	#20252239	C₂	1	1	yes	maximal, characteristic, complemented
6	#20252238	C₂	1	2	yes	maximal, complemented
7	#20252237	C₂	1	4	yes	maximal, complemented
8	#20252236	C₂	1	2	yes	maximal, complemented
9	#20252235	C₂	1	4	yes	maximal, complemented
10	#442×D₄₇	C₂	1	4	yes	maximal, complemented
11	C₄×D₈×D₄₇	C₂	1	4	yes	maximal, complemented
12	#427×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#418×D₄₇	C₂	1	2	yes	maximal, complemented
14	#405×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#2948	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×D₄×D₄₇	C₂²	1	2	yes	—
17	C₂²×D₃₇₆	C₂²	1	1	yes	characteristic
18	C₂²×#10625334	C₂²	1	2	yes	—
19	C₂×D₈×D₄₇	C₄	1	16	yes	complemented
20	C₂×D₈×D₄₇	C₂²	1	2	yes	—
21	C₂×D₈×D₄₇	C₂²	1	2	yes	—
22	C₂×D₈×D₄₇	C₂²	1	2	yes	—
23	C₂×D₈×D₄₇	C₂²	1	2	yes	—
24	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
25	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
26	#15689598	C₂²	1	2	yes	complemented
27	#15689597	C₂²	1	2	yes	complemented
28	#15689597	C₂²	1	2	yes	complemented
29	#15689596	—	2	4	no	—
30	#15689595	—	2	4	no	—
31	#15689595	C₂²	1	8	yes	complemented
32	C₄×D₄×D₄₇	—	2	4	no	—
33	C₄×D₄×D₄₇	C₂²	1	8	yes	complemented
34	#117×D₄₇	C₂²	1	2	yes	—
35	#117×D₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₂²⋊C₄×D₄₇	—	2	4	no	—
37	#15689236	C₂²	1	4	yes	complemented
38	#15689235	C₂²	1	4	yes	complemented
39	#15689234	C₂²	1	4	yes	complemented
40	#15689233	C₂²	1	8	yes	complemented
41	#15689232	C₂²	1	8	yes	complemented
42	C₄×D₃₇₆	C₂²	1	4	yes	complemented
43	D₈×Dic₄₇	C₂²	1	4	yes	complemented
44	#15689205	C₂²	1	4	yes	complemented
45	C₄×#10625334	C₂²	1	8	yes	complemented
46	#15689203	C₂²	1	8	yes	complemented
47	#15689161	C₂²	1	1	yes	characteristic, complemented
48	#15689160	C₂²	1	2	yes	complemented
49	#15689159	C₂²	1	2	yes	complemented
50	#15689158	C₂²	1	2	yes	complemented
51	#107×D₄₇	C₂²	1	2	yes	complemented
52	#106×D₄₇	C₂²	1	2	yes	complemented
53	#15689129	C₂²	1	2	yes	complemented
54	#15689128	C₂²	1	2	yes	complemented
55	#15689127	C₂²	1	2	yes	complemented
56	#15689126	C₂²	1	8	yes	complemented
57	#102×D₄₇	C₂²	1	8	yes	complemented
58	#15689081	C₂²	1	1	yes	characteristic, complemented
59	#15689080	C₂²	1	2	yes	complemented
60	#15689079	C₂²	1	1	yes	characteristic, complemented
61	#15689078	C₂²	1	1	yes	characteristic, complemented
62	#15689077	C₂²	1	2	yes	complemented
63	#97×D₄₇	C₂²	1	2	yes	complemented
64	C₄×C₈×D₄₇	C₂²	1	2	yes	complemented
65	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
66	C₄₇×#518	C₂²	1	2	yes	complemented
67	C₄₇×#442	C₂²	1	4	yes	complemented
68	C₄×D₈×C₄₇	C₂²	1	4	yes	complemented
69	C₄₇×#427	C₂²	1	1	yes	characteristic, complemented
70	C₄₇×#418	C₂²	1	2	yes	complemented
71	C₄₇×#405	C₂²	1	1	yes	characteristic, complemented
72	C₂⁴×D₄₇	—	2	2	no	—
73	C₂²×D₁₈₈	C₂³	1	2	yes	—
74	C₂²×C₂²⋊D₄₇	—	2	2	no	—
75	C₂×D₄×D₄₇	—	2	2	no	—
76	C₂×D₄×D₄₇	—	2	2	no	—
77	C₂×D₄×D₄₇	—	2	8	no	—
78	C₂×D₄×D₄₇	C₂×C₄	1	16	yes	complemented
79	C₂×D₄×D₄₇	C₂³	1	4	yes	—
80	C₂×D₄×D₄₇	C₂³	1	4	yes	—
81	C₂²×C₄×D₄₇	—	2	8	no	—
82	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
83	C₂×D₃₇₆	C₂×C₄	1	8	yes	complemented
84	C₂×D₃₇₆	C₂³	1	2	yes	—
85	C₂×D₃₇₆	C₂³	1	2	yes	—
86	C₂×#10625334	C₂×C₄	1	16	yes	complemented
87	C₂×#10625334	C₂³	1	4	yes	—
88	C₂×#10625334	C₂³	1	4	yes	—
89	D₈×D₄₇	C₂×C₄	1	16	yes	complemented
90	D₈×D₄₇	C₂×C₄	1	16	yes	complemented
91	D₈×D₄₇	C₂×C₄	1	16	yes	complemented
92	D₈×D₄₇	C₂×C₄	1	16	yes	complemented
93	C₂×#10625329	C₂³	1	1	yes	characteristic
94	C₂×#10625324	C₂³	1	2	yes	—
95	M₁₆×D₄₇	—	2	4	no	—
96	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
97	C₂×C₈×D₄₇	C₂×C₄	1	8	yes	complemented
98	C₂×C₈×D₄₇	C₂³	1	2	yes	—
99	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
100	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
101	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
102	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
103	C₄×D₁₈₈	—	2	4	no	—
104	C₄×D₁₈₈	C₂³	1	8	yes	complemented
105	D₄×Dic₄₇	—	2	4	no	—
106	D₄×Dic₄₇	C₂³	1	8	yes	complemented
107	#13093986	—	2	4	no	—
108	#13093986	C₂³	1	8	yes	complemented
109	C₄×C₂²⋊D₄₇	—	2	8	no	—
110	C₄×C₂²⋊D₄₇	—	2	8	no	—
111	(C₂²⋊D₄₇)⋊C₄	—	2	8	no	—
112	(C₂²⋊D₄₇)⋊C₄	—	2	8	no	—
113	#13093983	C₂³	1	2	yes	—
114	#13093983	C₂³	1	1	yes	characteristic
115	#13093982	D₄	1	2	yes	—
116	#13093982	C₂³	1	4	yes	—
117	#13093981	—	2	2	no	—
118	#13093981	C₂³	1	2	yes	—
119	#13093980	—	2	2	no	—
120	#13093980	D₄	1	2	yes	—
121	C₄⋊C₄×D₄₇	D₄	1	2	yes	—
122	C₄⋊C₄×D₄₇	C₂³	1	4	yes	—
123	C₂×C₂²⋊Dic₄₇	—	2	4	no	—
124	C₂×(C₂×D₄₇)⋊C₄	—	2	8	no	—
125	C₂²⋊C₄×D₄₇	—	2	2	no	—
126	C₂²⋊C₄×D₄₇	—	2	8	no	—
127	C₂²⋊C₄×D₄₇	—	2	4	no	—
128	C₂²⋊C₄×D₄₇	—	2	4	no	—
129	C₂²⋊C₄×D₄₇	—	2	8	no	—
130	C₂²⋊C₄×D₄₇	D₄	1	2	yes	—
131	C₄²×D₄₇	—	2	2	no	—
132	C₄²×D₄₇	C₂³	1	2	yes	—
133	#13093958	C₂³	1	2	yes	complemented
134	#13093957	C₂³	1	4	yes	complemented
135	#13093956	C₂³	1	2	yes	complemented
136	#13093955	C₂³	1	4	yes	complemented
137	#13093946	C₂³	1	8	yes	complemented
138	#13093945	C₂³	1	8	yes	complemented
139	#13093944	C₂³	1	8	yes	complemented
140	#13093935	C₂³	1	2	yes	complemented
141	#13093934	C₂³	1	2	yes	complemented
142	#13093934	C₂³	1	2	yes	complemented
143	C₄×C₄₇⋊C₈	C₂³	1	2	yes	complemented
144	C₈×Dic₄₇	C₂³	1	2	yes	complemented
145	C₈×Dic₄₇	C₂³	1	2	yes	complemented
146	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
147	C₂×D₈×C₄₇	C₂×C₄	1	8	yes	complemented
148	C₂×D₈×C₄₇	C₂³	1	2	yes	—
149	C₂×D₈×C₄₇	C₂³	1	2	yes	—
150	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
151	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
152	C₄×D₄×C₄₇	—	2	4	no	—
153	C₄×D₄×C₄₇	C₂³	1	8	yes	complemented
154	#117×C₄₇	C₂³	1	2	yes	—
155	#117×C₄₇	C₂³	1	1	yes	characteristic
156	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
157	#107×C₄₇	C₂³	1	2	yes	complemented
158	#106×C₄₇	C₂³	1	2	yes	complemented
159	#102×C₄₇	C₂³	1	8	yes	complemented
160	#97×C₄₇	C₂³	1	2	yes	complemented
161	C₄×C₈×C₄₇	C₂³	1	2	yes	complemented
162	C₂⁴×C₄₇	—	2	2	no	—
163	C₂³×D₄₇	—	2	2	no	—
164	C₂³×D₄₇	—	2	4	no	—
165	C₂³×D₄₇	—	2	16	no	—
166	C₂³×D₄₇	—	2	4	no	—
167	C₂³×D₄₇	—	8	8	no	—
168	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
169	C₂×D₄×C₄₇	—	2	2	no	—
170	C₂×D₄×C₄₇	—	2	4	no	—
171	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	complemented
172	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
173	C₂²×C₄×C₄₇	—	2	8	no	—
174	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
175	C₂×C₂²⋊D₄₇	—	2	16	no	—
176	C₂×C₂²⋊D₄₇	—	2	4	no	—
177	C₂×C₂²⋊D₄₇	—	2	4	no	—
178	C₂²×Dic₄₇	—	2	8	no	—
179	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
180	D₄×D₄₇	—	2	16	no	—
181	D₄×D₄₇	—	2	16	no	—
182	D₄×D₄₇	—	2	8	no	—
183	D₄×D₄₇	—	2	8	no	—
184	D₄×D₄₇	C₂²×C₄	1	16	yes	—
185	D₄×D₄₇	C₂²×C₄	1	16	yes	complemented
186	C₂×D₁₈₈	—	2	2	no	—
187	C₂×D₁₈₈	—	2	4	no	—
188	C₂×D₁₈₈	C₂²×C₄	1	8	yes	complemented
189	C₂×D₁₈₈	C₂⁴	1	4	yes	—
190	C₂×C₄×D₄₇	—	2	4	no	—
191	C₂×C₄×D₄₇	—	2	8	no	—
192	C₂×C₄×D₄₇	—	2	8	no	—
193	C₂×C₄×D₄₇	—	8	16	no	—
194	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
195	C₂×C₄×D₄₇	C₂×D₄	1	4	yes	—
196	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
197	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
198	C₂×C₄×D₄₇	#41	1	4	yes	—
199	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
200	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
201	D₈×C₄₇	C₂²×C₄	1	8	yes	complemented
202	D₈×C₄₇	C₂²×C₄	1	8	yes	complemented
203	M₁₆×C₄₇	—	2	2	no	—
204	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	complemented
205	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
206	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
207	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
208	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
209	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
210	C₂²⋊C₄×C₄₇	—	2	2	no	—
211	C₂²⋊C₄×C₄₇	—	2	8	no	—
212	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
213	C₄²×C₄₇	—	2	2	no	—
214	C₄²×C₄₇	C₂⁴	1	2	yes	—
215	C₂²⋊Dic₄₇	—	2	2	no	—
216	C₂²⋊Dic₄₇	—	2	8	no	—
217	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
218	#10625334	C₂²×C₄	1	16	yes	complemented
219	#10625334	C₂²×C₄	1	16	yes	complemented
220	(C₂×D₄₇)⋊C₄	—	2	4	no	—
221	(C₂×D₄₇)⋊C₄	—	2	8	no	—
222	(C₂×D₄₇)⋊C₄	—	2	8	no	—
223	(C₂×D₄₇)⋊C₄	C₂×D₄	1	4	yes	—
224	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
225	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
226	Dic₄₇⋊C₄	—	2	4	no	—
227	Dic₄₇⋊C₄	C₂×D₄	1	4	yes	—
228	C₄×Dic₄₇	—	2	2	no	—
229	C₄×Dic₄₇	—	2	4	no	—
230	C₄×Dic₄₇	C₂×D₄	1	4	yes	—
231	C₄×Dic₄₇	C₂⁴	1	2	yes	—
232	#10625329	—	2	2	no	—
233	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	complemented
234	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
235	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
236	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
237	D₃₇₆	C₂²×C₄	1	8	yes	complemented
238	D₃₇₆	C₂²×C₄	1	8	yes	complemented
239	#10625324	—	2	4	no	—
240	C₈×D₄₇	—	2	4	no	—
241	C₈×D₄₇	C₂²×C₄	1	4	yes	—
242	C₈×D₄₇	C₂²×C₄	1	4	yes	—
243	C₈×D₄₇	C₂²×C₄	1	4	yes	complemented
244	C₈×D₄₇	C₂²×C₄	1	4	yes	complemented
245	C₂³×C₄₇	—	2	4	no	—
246	C₂³×C₄₇	—	2	8	no	—
247	C₂³×C₄₇	—	8	4	no	—
248	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
249	C₂²×D₄₇	—	2	4	no	—
250	C₂²×D₄₇	—	2	4	no	—
251	C₂²×D₄₇	—	2	8	no	—
252	C₂²×D₄₇	—	2	16	no	—
253	C₂²×D₄₇	—	2	16	no	—
254	C₂²×D₄₇	—	4	16	no	—
255	C₂²×D₄₇	—	8	32	no	—
256	C₂²×D₄₇	—	8	8	no	—
257	C₂²×D₄₇	—	8	4	no	—
258	C₂²×D₄₇	C₄×D₄	1	4	yes	—
259	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
260	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
261	D₄×C₄₇	—	2	8	no	—
262	D₄×C₄₇	—	2	4	no	—
263	D₄×C₄₇	C₂³×C₄	1	8	yes	—
264	C₂×C₄×C₄₇	—	2	4	no	—
265	C₂×C₄×C₄₇	—	8	8	no	—
266	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
267	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
268	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
270	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
271	C₂²⋊D₄₇	—	2	16	no	—
272	C₂²⋊D₄₇	—	2	16	no	—
273	C₂×Dic₄₇	—	2	4	no	—
274	C₂×Dic₄₇	—	8	8	no	—
275	C₂×Dic₄₇	C₄×D₄	1	4	yes	—
276	C₂×Dic₄₇	C₂²×D₄	1	4	yes	—
277	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
278	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
279	D₁₈₈	—	2	8	no	—
280	D₁₈₈	—	2	4	no	—
281	D₁₈₈	C₂³×C₄	1	8	yes	—
282	C₄×D₄₇	—	2	8	no	—
283	C₄×D₄₇	—	4	8	no	—
284	C₄×D₄₇	—	8	8	no	—
285	C₄×D₄₇	—	8	8	no	—
286	C₄×D₄₇	C₄×D₄	1	4	yes	—
287	C₄×D₄₇	C₄×D₄	1	4	yes	—
288	C₄×D₄₇	C₂³×C₄	1	2	yes	—
289	C₄×D₄₇	C₂³×C₄	1	2	yes	—
290	C₄×D₄₇	C₂×#41	1	2	yes	—
291	C₄×D₄₇	C₂×#41	1	2	yes	—
292	C₈×C₄₇	—	2	2	no	—
293	C₈×C₄₇	C₂³×C₄	1	2	yes	—
294	C₈×C₄₇	C₂³×C₄	1	2	yes	—
295	C₄₇⋊C₈	—	2	2	no	—
296	C₄₇⋊C₈	C₂³×C₄	1	2	yes	—
297	C₄₇⋊C₈	C₂³×C₄	1	2	yes	—
298	C₂×#2948	—	47	1	no	maximal, Sylow
299	C₂²×C₄₇	—	2	2	no	—
300	C₂²×C₄₇	—	2	8	no	—
301	C₂²×C₄₇	—	4	8	no	—
302	C₂²×C₄₇	—	8	8	no	—
303	C₂²×C₄₇	C₂×C₄×D₄	1	2	yes	—
304	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
305	C₂×D₄₇	—	2	2	no	—
306	C₂×D₄₇	—	2	8	no	—
307	C₂×D₄₇	—	2	8	no	—
308	C₂×D₄₇	—	4	8	no	—
309	C₂×D₄₇	—	4	32	no	—
310	C₂×D₄₇	—	8	16	no	—
311	C₂×D₄₇	—	8	8	no	—
312	C₂×D₄₇	C₂×C₄×D₄	1	2	yes	—
313	C₂×D₄₇	C₂×C₄×D₄	1	2	yes	—
314	C₂×D₄₇	#576	1	4	yes	—
315	C₄×C₄₇	—	2	4	no	—
316	C₄×C₄₇	—	4	4	no	—
317	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
318	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
319	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
320	Dic₄₇	—	2	4	no	—
321	Dic₄₇	—	4	4	no	—
322	Dic₄₇	C₂×C₄×D₄	1	2	yes	—
323	Dic₄₇	C₂×C₄×D₄	1	2	yes	—
324	C₂³×D₈	—	47	1	no	—
325	C₂×#518	—	47	2	no	—
326	#2948	—	47	4	no	—
327	#2948	—	47	4	no	—
328	#2948	—	47	1	no	—
329	#2948	—	47	2	no	—
330	#2948	—	47	1	no	—
331	#2948	—	47	1	no	—
332	#2948	—	47	2	no	—
333	#2948	D₄₇	1	1	yes	characteristic, direct product factor
334	C₂×#442	—	47	4	no	—
335	C₂×C₄×D₈	—	47	4	no	—
336	C₂×#427	—	47	1	no	—
337	C₂×#418	—	47	2	no	—
338	C₂×#405	—	47	1	no	—
339	C₂×C₄₇	—	2	2	no	—
340	C₂×C₄₇	—	4	8	no	—
341	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
342	C₂×C₄₇	C₂×#576	1	2	yes	—
343	D₄₇	—	2	2	no	—
344	D₄₇	—	4	8	no	—
345	D₄₇	#2948	1	4	yes	direct product factor
346	C₂³×D₄	—	47	2	no	—
347	C₂²×D₈	—	47	2	no	—
348	C₂²×D₈	—	47	16	no	—
349	C₂²×D₈	—	47	2	no	—
350	C₂²×D₈	—	47	2	no	—
351	C₂²×D₈	—	47	2	no	—
352	C₂²×D₈	—	47	2	no	—
353	C₂²×D₈	—	47	1	no	—
354	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
355	C₂²×M₁₆	—	47	1	no	—
356	C₂³×C₈	—	47	1	no	—
357	#518	—	47	2	no	—
358	#518	—	47	8	no	—
359	#518	—	47	2	no	—
360	#518	—	47	2	no	—
361	#518	—	94	4	no	—
362	#518	—	94	4	no	—
363	#518	C₂×D₄₇	1	2	yes	complemented
364	C₂×C₄×D₄	—	47	8	no	—
365	C₂×C₄×D₄	—	94	4	no	—
366	C₂×#117	—	47	1	no	—
367	C₂×#117	—	47	2	no	—
368	C₂²×C₂²⋊C₄	—	94	4	no	—
369	#442	—	47	4	no	—
370	#442	—	47	8	no	—
371	#442	—	47	4	no	—
372	#442	—	47	8	no	—
373	#442	—	47	4	no	—
374	#442	C₂×D₄₇	1	4	yes	complemented
375	C₄×D₈	—	47	4	no	—
376	C₄×D₈	—	47	8	no	—
377	C₄×D₈	—	47	4	no	—
378	C₄×D₈	—	47	8	no	—
379	C₄×D₈	—	47	4	no	—
380	C₄×D₈	C₂×D₄₇	1	4	yes	complemented
381	#427	—	47	1	no	—
382	#427	—	47	2	no	—
383	#427	—	47	2	no	—
384	#427	—	47	2	no	—
385	#427	C₂×D₄₇	1	1	yes	characteristic, complemented
386	C₂×#107	—	47	2	no	—
387	C₂×#106	—	47	2	no	—
388	#418	—	47	2	no	—
389	#418	—	47	2	no	—
390	#418	—	47	2	no	—
391	#418	—	47	8	no	—
392	#418	C₂×D₄₇	1	2	yes	complemented
393	C₂×#102	—	47	8	no	—
394	#405	—	47	1	no	—
395	#405	—	47	1	no	—
396	#405	—	47	1	no	—
397	#405	—	47	2	no	—
398	#405	—	47	2	no	—
399	#405	C₂×D₄₇	1	1	yes	characteristic, complemented
400	C₂×#97	—	47	2	no	—
401	C₂×C₄×C₈	—	47	2	no	—
402	C₄₇	C₂×#2948	1	1	yes	characteristic, complemented, Sylow
403	C₂⁵	—	94	2	no	—
404	C₂²×D₄	—	47	16	no	—
405	C₂²×D₄	—	47	4	no	—
406	C₂²×D₄	—	47	4	no	—
407	C₂²×D₄	—	47	2	no	—
408	C₂²×D₄	—	94	2	no	—
409	C₂²×D₄	—	94	2	no	—
410	C₂²×D₄	—	94	8	no	—
411	C₂²×D₄	—	94	2	no	—
412	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
413	C₂³×C₄	—	47	1	no	—
414	C₂³×C₄	—	94	8	no	—
415	C₂×D₈	—	47	16	no	—
416	C₂×D₈	—	47	4	no	—
417	C₂×D₈	—	47	4	no	—
418	C₂×D₈	—	47	16	no	—
419	C₂×D₈	—	47	16	no	—
420	C₂×D₈	—	47	16	no	—
421	C₂×D₈	—	47	16	no	—
422	C₂×D₈	—	47	8	no	—
423	C₂×D₈	—	47	2	no	—
424	C₂×D₈	—	47	2	no	—
425	C₂×D₈	C₄×D₄₇	1	8	yes	complemented
426	C₂×D₈	C₂²×D₄₇	1	2	yes	—
427	C₂×D₈	C₂²×D₄₇	1	2	yes	—
428	C₂×M₁₆	—	47	1	no	—
429	C₂×M₁₆	—	47	2	no	—
430	C₂×M₁₆	—	94	4	no	—
431	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
432	C₂²×C₈	—	47	1	no	—
433	C₂²×C₈	—	47	8	no	—
434	C₂²×C₈	—	47	1	no	—
435	C₂²×C₈	—	47	1	no	—
436	C₂²×C₈	—	47	1	no	—
437	C₂²×C₈	—	47	1	no	—
438	C₂²×C₈	—	47	2	no	—
439	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
440	C₄×D₄	—	2	4	no	—
441	C₄×D₄	—	47	8	no	—
442	C₄×D₄	—	47	8	no	—
443	C₄×D₄	—	47	8	no	—
444	C₄×D₄	—	94	4	no	—
445	C₄×D₄	—	94	8	no	—
446	C₄×D₄	—	94	8	no	—
447	C₄×D₄	—	94	8	no	—
448	C₄×D₄	—	94	8	no	—
449	C₄×D₄	—	94	4	no	—
450	C₄×D₄	—	94	4	no	—
451	C₄×D₄	C₂²×D₄₇	1	8	yes	complemented
452	#117	—	47	1	no	—
453	#117	—	47	2	no	—
454	#117	—	47	2	no	—
455	#117	—	47	2	no	—
456	#117	—	47	2	no	—
457	#117	—	47	4	no	—
458	#117	—	94	2	no	—
459	#117	—	94	2	no	—
460	#117	C₂²×D₄₇	1	2	yes	—
461	#117	C₂²×D₄₇	1	1	yes	characteristic
462	C₂×C₄⋊C₄	—	47	2	no	—
463	C₂×C₄⋊C₄	—	47	4	no	—
464	C₂×C₂²⋊C₄	—	2	4	no	—
465	C₂×C₂²⋊C₄	—	47	2	no	—
466	C₂×C₂²⋊C₄	—	94	4	no	—
467	C₂×C₂²⋊C₄	—	94	8	no	—
468	C₂×C₂²⋊C₄	—	94	8	no	—
469	C₂×C₂²⋊C₄	—	94	2	no	—
470	C₂×C₂²⋊C₄	—	94	8	no	—
471	C₂×C₂²⋊C₄	—	94	4	no	—
472	C₂×C₂²⋊C₄	—	94	4	no	—
473	C₂×C₄²	—	47	2	no	—
474	C₂×C₄²	—	94	2	no	—
475	#107	—	47	2	no	—
476	#107	—	47	4	no	—
477	#107	C₂²×D₄₇	1	2	yes	complemented
478	#106	—	47	2	no	—
479	#106	—	47	4	no	—
480	#106	C₂²×D₄₇	1	2	yes	complemented
481	#102	—	47	8	no	—
482	#102	—	47	8	no	—
483	#102	—	47	8	no	—
484	#102	C₂²×D₄₇	1	8	yes	complemented
485	#97	—	47	2	no	—
486	#97	—	47	2	no	—
487	#97	—	47	2	no	—
488	#97	C₂²×D₄₇	1	2	yes	complemented
489	C₄×C₈	—	47	2	no	—
490	C₄×C₈	—	47	2	no	—
491	C₄×C₈	—	47	2	no	—
492	C₄×C₈	C₂²×D₄₇	1	2	yes	complemented
493	C₂⁴	—	2	2	no	—
494	C₂⁴	—	47	1	no	—
495	C₂⁴	—	94	4	no	—
496	C₂⁴	—	94	16	no	—
497	C₂⁴	—	94	4	no	—
498	C₂⁴	—	94	2	no	—
499	C₂⁴	—	376	8	no	—
500	C₂×D₄	—	2	2	no	—
501	C₂×D₄	—	2	4	no	—
502	C₂×D₄	—	47	16	no	—
503	C₂×D₄	—	47	16	no	—
504	C₂×D₄	—	47	8	no	—
505	C₂×D₄	—	47	4	no	—
506	C₂×D₄	—	94	16	no	—
507	C₂×D₄	—	94	16	no	—
508	C₂×D₄	—	94	8	no	—
509	C₂×D₄	—	94	8	no	—
510	C₂×D₄	—	94	4	no	—
511	C₂×D₄	—	94	4	no	—
512	C₂×D₄	—	94	16	no	—
513	C₂×D₄	—	94	2	no	—
514	C₂×D₄	—	94	4	no	—
515	C₂×D₄	C₂×C₄×D₄₇	1	8	yes	complemented
516	C₂×D₄	C₂³×D₄₇	1	4	yes	—
517	C₂²×C₄	—	2	8	no	—
518	C₂²×C₄	—	47	1	no	—
519	C₂²×C₄	—	47	4	no	—
520	C₂²×C₄	—	47	1	no	—
521	C₂²×C₄	—	47	1	no	—
522	C₂²×C₄	—	47	4	no	—
523	C₂²×C₄	—	47	1	no	—
524	C₂²×C₄	—	47	1	no	—
525	C₂²×C₄	—	47	4	no	—
526	C₂²×C₄	—	94	8	no	—
527	C₂²×C₄	—	94	4	no	—
528	C₂²×C₄	—	94	8	no	—
529	C₂²×C₄	—	94	8	no	—
530	C₂²×C₄	—	376	16	no	—
531	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
532	D₈	—	47	16	no	—
533	D₈	—	47	16	no	—
534	D₈	—	47	8	no	—
535	D₈	—	47	8	no	—
536	D₈	C₂×C₄×D₄₇	1	8	yes	complemented
537	D₈	C₂×C₄×D₄₇	1	8	yes	complemented
538	M₁₆	—	2	2	no	—
539	M₁₆	—	94	4	no	—
540	M₁₆	—	94	2	no	—
541	C₂×C₈	—	47	4	no	—
542	C₂×C₈	—	47	1	no	—
543	C₂×C₈	—	47	1	no	—
544	C₂×C₈	—	47	4	no	—
545	C₂×C₈	—	47	4	no	—
546	C₂×C₈	—	47	4	no	—
547	C₂×C₈	—	47	4	no	—
548	C₂×C₈	—	47	2	no	—
549	C₂×C₈	—	94	4	no	—
550	C₂×C₈	C₂×C₄×D₄₇	1	4	yes	complemented
551	C₂×C₈	C₂³×D₄₇	1	2	yes	—
552	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
553	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
554	C₄⋊C₄	—	47	4	no	—
555	C₄⋊C₄	—	47	2	no	—
556	C₄⋊C₄	—	47	4	no	—
557	C₄⋊C₄	—	94	4	no	—
558	C₄⋊C₄	D₄×D₄₇	1	2	yes	—
559	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	2	8	no	—
562	C₂²⋊C₄	—	47	2	no	—
563	C₂²⋊C₄	—	47	4	no	—
564	C₂²⋊C₄	—	94	8	no	—
565	C₂²⋊C₄	—	94	4	no	—
566	C₂²⋊C₄	—	94	8	no	—
567	C₂²⋊C₄	—	94	2	no	—
568	C₂²⋊C₄	—	94	8	no	—
569	C₂²⋊C₄	D₄×D₄₇	1	2	yes	—
570	C₄²	—	2	2	no	—
571	C₄²	—	47	4	no	—
572	C₄²	—	47	2	no	—
573	C₄²	—	94	4	no	—
574	C₄²	—	94	2	no	—
575	C₄²	C₂³×D₄₇	1	2	yes	—
576	C₂³	—	2	4	no	—
577	C₂³	—	2	8	no	—
578	C₂³	—	8	4	no	—
579	C₂³	—	47	1	no	—
580	C₂³	—	47	4	no	—
581	C₂³	—	47	1	no	—
582	C₂³	—	94	4	no	—
583	C₂³	—	94	16	no	—
584	C₂³	—	94	16	no	—
585	C₂³	—	94	8	no	—
586	C₂³	—	94	4	no	—
587	C₂³	—	376	4	no	—
588	C₂³	—	376	8	no	—
589	C₂³	—	376	32	no	—
590	C₂³	—	188	16	no	—
591	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
592	D₄	—	2	8	no	—
593	D₄	—	2	4	no	—
594	D₄	—	47	8	no	—
595	D₄	—	94	16	no	—
596	D₄	—	94	16	no	—
597	D₄	—	94	8	no	—
598	D₄	—	94	4	no	—
599	D₄	C₂²×C₄×D₄₇	1	8	yes	—
600	C₂×C₄	—	2	4	no	—
601	C₂×C₄	—	8	8	no	—
602	C₂×C₄	—	47	4	no	—
603	C₂×C₄	—	47	1	no	—
604	C₂×C₄	—	47	1	no	—
605	C₂×C₄	—	47	4	no	—
606	C₂×C₄	—	47	4	no	—
607	C₂×C₄	—	47	2	no	—
608	C₂×C₄	—	47	2	no	—
609	C₂×C₄	—	47	2	no	—
610	C₂×C₄	—	47	2	no	—
611	C₂×C₄	—	47	4	no	—
612	C₂×C₄	—	94	8	no	—
613	C₂×C₄	—	94	4	no	—
614	C₂×C₄	—	376	8	no	—
615	C₂×C₄	—	376	8	no	—
616	C₂×C₄	—	376	8	no	—
617	C₂×C₄	—	188	8	no	—
618	C₂×C₄	C₂²×C₄×D₄₇	1	2	yes	—
619	C₂×C₄	C₂×D₄×D₄₇	1	4	yes	—
620	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
621	C₂×C₄	#41×D₄₇	1	2	yes	—
622	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
623	C₈	—	2	2	no	—
624	C₈	—	47	2	no	—
625	C₈	—	47	2	no	—
626	C₈	—	94	2	no	—
627	C₈	C₂²×C₄×D₄₇	1	2	yes	—
628	C₈	C₂²×C₄×D₄₇	1	2	yes	—
629	C₂²	—	2	2	no	—
630	C₂²	—	2	8	no	—
631	C₂²	—	4	8	no	—
632	C₂²	—	8	8	no	—
633	C₂²	—	47	2	no	—
634	C₂²	—	47	4	no	—
635	C₂²	—	47	2	no	—
636	C₂²	—	94	8	no	—
637	C₂²	—	94	2	no	—
638	C₂²	—	94	8	no	—
639	C₂²	—	376	8	no	—
640	C₂²	—	376	16	no	—
641	C₂²	—	188	32	no	—
642	C₂²	—	188	8	no	—
643	C₂²	C₄×D₄×D₄₇	1	2	yes	—
644	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
645	C₄	—	2	4	no	—
646	C₄	—	4	4	no	—
647	C₄	—	47	2	no	—
648	C₄	—	47	2	no	—
649	C₄	—	94	4	no	—
650	C₄	—	188	4	no	—
651	C₄	C₄×D₄×D₄₇	1	2	yes	—
652	C₄	C₂³×C₄×D₄₇	1	1	yes	characteristic
653	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
654	C₂	—	2	2	no	—
655	C₂	—	4	8	no	—
656	C₂	—	47	4	no	—
657	C₂	—	94	2	no	—
658	C₂	—	188	8	no	—
659	C₂	C₂×C₄×D₄×D₄₇	1	1	yes	characteristic
660	C₂	#576×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#2948	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	C₂²×D₈×D₄₇	C₂
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	#2948	D₄₇
hypocenter	C₄₇	C₂×#2948
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #117 ◁ #2948

Complements

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

N	H ≅ G/N	type
2. #518×D₄₇	C₂	semidirect
3. #20252241	C₂	semidirect
4. #20252240	C₂	semidirect
5. #20252239	C₂	semidirect
6. #20252238	C₂	semidirect
7. #20252237	C₂	semidirect
8. #20252236	C₂	semidirect
9. #20252235	C₂	semidirect
10. #442×D₄₇	C₂	semidirect
11. C₄×D₈×D₄₇	C₂	semidirect
12. #427×D₄₇	C₂	semidirect
13. #418×D₄₇	C₂	semidirect
14. #405×D₄₇	C₂	semidirect
15. C₄₇×#2948	C₂	semidirect
19. C₂×D₈×D₄₇	C₄	semidirect
26. #15689598	C₂²	semidirect
27. #15689597	C₂²	semidirect
28. #15689597	C₂²	semidirect
31. #15689595	C₂²	semidirect
33. C₄×D₄×D₄₇	C₂²	semidirect
37. #15689236	C₂²	semidirect
38. #15689235	C₂²	semidirect
39. #15689234	C₂²	semidirect
40. #15689233	C₂²	semidirect
41. #15689232	C₂²	semidirect
42. C₄×D₃₇₆	C₂²	semidirect
43. D₈×Dic₄₇	C₂²	semidirect
44. #15689205	C₂²	semidirect
45. C₄×#10625334	C₂²	semidirect
46. #15689203	C₂²	semidirect
47. #15689161	C₂²	semidirect
48. #15689160	C₂²	semidirect
49. #15689159	C₂²	semidirect
50. #15689158	C₂²	semidirect
51. #107×D₄₇	C₂²	semidirect
52. #106×D₄₇	C₂²	semidirect
53. #15689129	C₂²	semidirect
54. #15689128	C₂²	semidirect
55. #15689127	C₂²	semidirect
56. #15689126	C₂²	semidirect
57. #102×D₄₇	C₂²	semidirect
58. #15689081	C₂²	semidirect
59. #15689080	C₂²	semidirect
60. #15689079	C₂²	semidirect
61. #15689078	C₂²	semidirect
62. #15689077	C₂²	semidirect
63. #97×D₄₇	C₂²	semidirect
64. C₄×C₈×D₄₇	C₂²	semidirect
66. C₄₇×#518	C₂²	semidirect
67. C₄₇×#442	C₂²	semidirect
68. C₄×D₈×C₄₇	C₂²	semidirect
69. C₄₇×#427	C₂²	semidirect
70. C₄₇×#418	C₂²	semidirect
71. C₄₇×#405	C₂²	semidirect
78. C₂×D₄×D₄₇	C₂×C₄	semidirect
83. C₂×D₃₇₆	C₂×C₄	semidirect
86. C₂×#10625334	C₂×C₄	semidirect
89. D₈×D₄₇	C₂×C₄	semidirect
90. D₈×D₄₇	C₂×C₄	semidirect
91. D₈×D₄₇	C₂×C₄	semidirect
92. D₈×D₄₇	C₂×C₄	semidirect
97. C₂×C₈×D₄₇	C₂×C₄	semidirect
104. C₄×D₁₈₈	C₂³	semidirect
106. D₄×Dic₄₇	C₂³	semidirect
108. #13093986	C₂³	semidirect
133. #13093958	C₂³	semidirect
134. #13093957	C₂³	semidirect
135. #13093956	C₂³	semidirect
136. #13093955	C₂³	semidirect
137. #13093946	C₂³	semidirect
138. #13093945	C₂³	semidirect
139. #13093944	C₂³	semidirect
140. #13093935	C₂³	semidirect
141. #13093934	C₂³	semidirect
142. #13093934	C₂³	semidirect
143. C₄×C₄₇⋊C₈	C₂³	semidirect
144. C₈×Dic₄₇	C₂³	semidirect
145. C₈×Dic₄₇	C₂³	semidirect
147. C₂×D₈×C₄₇	C₂×C₄	semidirect
153. C₄×D₄×C₄₇	C₂³	semidirect
157. #107×C₄₇	C₂³	semidirect
158. #106×C₄₇	C₂³	semidirect
159. #102×C₄₇	C₂³	semidirect
160. #97×C₄₇	C₂³	semidirect
161. C₄×C₈×C₄₇	C₂³	semidirect
171. C₂×D₄×C₄₇	C₂²×C₄	semidirect
185. D₄×D₄₇	C₂²×C₄	semidirect
188. C₂×D₁₈₈	C₂²×C₄	semidirect
201. D₈×C₄₇	C₂²×C₄	semidirect
202. D₈×C₄₇	C₂²×C₄	semidirect
204. C₂×C₈×C₄₇	C₂²×C₄	semidirect
218. #10625334	C₂²×C₄	semidirect
219. #10625334	C₂²×C₄	semidirect
233. C₂×C₄₇⋊C₈	C₂²×C₄	semidirect
237. D₃₇₆	C₂²×C₄	semidirect
238. D₃₇₆	C₂²×C₄	semidirect
243. C₈×D₄₇	C₂²×C₄	semidirect
244. C₈×D₄₇	C₂²×C₄	semidirect
333. #2948	D₄₇	direct (N × H)
345. D₄₇	#2948	direct (N × H)
363. #518	C₂×D₄₇	semidirect
374. #442	C₂×D₄₇	semidirect
380. C₄×D₈	C₂×D₄₇	semidirect
385. #427	C₂×D₄₇	semidirect
392. #418	C₂×D₄₇	semidirect
399. #405	C₂×D₄₇	semidirect
402. C₄₇	C₂×#2948	semidirect
425. C₂×D₈	C₄×D₄₇	semidirect
451. C₄×D₄	C₂²×D₄₇	semidirect
477. #107	C₂²×D₄₇	semidirect
480. #106	C₂²×D₄₇	semidirect
484. #102	C₂²×D₄₇	semidirect
488. #97	C₂²×D₄₇	semidirect
492. C₄×C₈	C₂²×D₄₇	semidirect
515. C₂×D₄	C₂×C₄×D₄₇	semidirect
536. D₈	C₂×C₄×D₄₇	semidirect
537. D₈	C₂×C₄×D₄₇	semidirect
550. C₂×C₈	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
C₂²×D₈×D₄₇	2
#518×D₄₇	2
#20252241	2
#20252240	2
#20252239	2
#20252238	2
#20252237	2
#20252236	2
#20252235	2
#442×D₄₇	2
C₄×D₈×D₄₇	2
#427×D₄₇	2
#418×D₄₇	2
#405×D₄₇	2
C₄₇×#2948	2
C₂×#2948	47

Subgroups — D47×#2948 #27080400

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#2948 #27080400