Subgroups — #26215137

Order 12032.

870 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689181	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689149	C₂	1	1	yes	maximal, characteristic
3	#20245884	C₂	1	1	yes	maximal, characteristic
4	#20243262	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243259	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243254	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×Dic₄₇⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243246	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243244	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243240	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×Dic₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243174	C₂	1	1	yes	maximal, characteristic
13	#20243172	C₂	1	1	yes	maximal, characteristic
14	#20243164	C₂	1	1	yes	maximal, characteristic
15	C₈×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂×#13093983	C₂²	1	1	yes	characteristic
18	#15689181	C₄	1	8	yes	complemented
19	#15689149	C₄	1	8	yes	complemented
20	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×#13093935	C₂²	1	1	yes	characteristic
28	C₂×#13093934	C₂²	1	1	yes	characteristic
29	C₂×#13093934	C₂²	1	1	yes	characteristic
30	C₂×#13093934	C₂²	1	1	yes	characteristic
31	C₂×#13093934	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
35	#15689017	C₄	1	2	yes	—
36	#15689011	C₄	1	2	yes	—
37	#15689008	C₄	1	2	yes	—
38	#15689006	C₄	1	2	yes	—
39	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
40	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
41	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
42	#15688969	C₂²	1	1	yes	characteristic
43	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
44	#15688878	C₂²	1	1	yes	characteristic
45	#15688878	C₂²	1	1	yes	characteristic
46	#15688877	C₂²	1	1	yes	characteristic
47	#15688877	C₂²	1	1	yes	characteristic
48	#15688877	C₂²	1	1	yes	characteristic
49	#15688877	C₂²	1	1	yes	characteristic
50	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
52	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
53	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
54	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
55	C₄₇×#336	C₂²	1	1	yes	characteristic
56	C₄₇×#336	C₂²	1	1	yes	characteristic
57	C₂×#10625329	—	4	1	no	—
58	C₂×#10625329	—	4	1	no	—
59	C₂×#10625329	C₂×C₄	1	4	yes	—
60	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
61	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
62	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
63	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
64	#13093983	C₂×C₄	1	4	yes	—
65	#13093983	C₂×C₄	1	4	yes	—
66	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
69	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
70	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
71	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
74	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
75	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
76	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
77	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
79	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
80	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
81	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
82	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
83	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
84	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	—
85	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
86	#13093935	—	4	1	no	—
87	#13093934	—	4	1	no	—
88	#13093934	—	4	1	no	—
89	#13093934	—	4	1	no	—
90	#13093934	C₂×C₄	1	4	yes	—
91	C₄×C₄₇⋊C₈	—	4	1	no	—
92	C₈×Dic₄₇	—	4	1	no	—
93	C₈×Dic₄₇	C₂×C₄	1	4	yes	—
94	C₄₇⋊#95	C₂×C₄	1	2	yes	—
95	C₄₇⋊#95	C₂×C₄	1	2	yes	—
96	C₄₇⋊#95	C₂×C₄	1	2	yes	—
97	C₄₇⋊#95	C₂×C₄	1	2	yes	—
98	C₄₇⋊#95	C₂×C₄	1	2	yes	—
99	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
100	C₂²×C₈×C₄₇	—	4	1	no	—
101	C₂²×C₈×C₄₇	—	4	1	no	—
102	C₂²×C₈×C₄₇	C₂×C₄	1	4	yes	—
103	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
104	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
105	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
108	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
109	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
110	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
111	C₄×C₈×C₄₇	—	4	1	no	—
112	C₄×C₈×C₄₇	—	4	1	no	—
113	#95×C₄₇	C₂×C₄	1	2	yes	—
114	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	—	2	1	no	—
116	C₂²×C₄×C₄₇	—	2	1	no	—
117	C₂²×C₄×C₄₇	—	2	1	no	—
118	C₂²×C₄×C₄₇	—	2	1	no	—
119	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
120	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
123	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
124	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
125	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
126	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
127	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₈×C₄₇	—	2	1	no	—
132	C₂×C₈×C₄₇	—	2	1	no	—
133	C₂×C₈×C₄₇	—	2	1	no	—
134	C₂×C₈×C₄₇	—	2	1	no	—
135	C₂×C₈×C₄₇	—	2	1	no	—
136	C₂×C₈×C₄₇	—	2	1	no	—
137	C₂×C₈×C₄₇	—	2	1	no	—
138	C₂×C₈×C₄₇	—	2	1	no	—
139	C₂×C₈×C₄₇	—	4	4	no	—
140	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
141	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
142	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
144	C₂²⋊C₄×C₄₇	—	2	4	no	—
145	C₄²×C₄₇	—	2	1	no	—
146	C₄²×C₄₇	—	2	1	no	—
147	C₄²×C₄₇	—	2	1	no	—
148	C₄²×C₄₇	—	2	1	no	—
149	C₂²⋊Dic₄₇	—	4	2	no	—
150	C₂²⋊Dic₄₇	C₄²	1	4	yes	—
151	C₂²⋊Dic₄₇	C₄²	1	4	yes	—
152	C₄⋊Dic₄₇	C₄²	1	4	yes	—
153	C₄⋊Dic₄₇	C₄²	1	4	yes	—
154	Dic₄₇⋊C₄	—	2	4	no	—
155	Dic₄₇⋊C₄	—	4	2	no	—
156	C₄×Dic₄₇	—	2	4	no	—
157	C₄×Dic₄₇	—	2	1	no	—
158	C₄×Dic₄₇	—	2	1	no	—
159	C₄×Dic₄₇	—	2	1	no	—
160	C₄×Dic₄₇	—	2	1	no	—
161	C₄×Dic₄₇	—	4	2	no	—
162	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
163	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
164	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
165	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
166	#10625329	—	4	4	no	—
167	C₂×C₄₇⋊C₈	—	2	1	no	—
168	C₂×C₄₇⋊C₈	—	2	1	no	—
169	C₂×C₄₇⋊C₈	—	2	1	no	—
170	C₂×C₄₇⋊C₈	—	2	1	no	—
171	C₂×C₄₇⋊C₈	—	2	1	no	—
172	C₂×C₄₇⋊C₈	—	2	1	no	—
173	C₂×C₄₇⋊C₈	—	2	1	no	—
174	C₂×C₄₇⋊C₈	—	2	1	no	—
175	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
176	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
177	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
178	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
179	C₂³×C₄₇	—	2	1	no	—
180	C₂³×C₄₇	—	2	1	no	—
181	C₂³×C₄₇	—	2	2	no	—
182	C₂³×C₄₇	—	2	2	no	—
183	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
184	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	—	2	2	no	—
186	C₂×C₄×C₄₇	—	2	1	no	—
187	C₂×C₄×C₄₇	—	2	1	no	—
188	C₂×C₄×C₄₇	—	2	2	no	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	2	no	—
191	C₂×C₄×C₄₇	—	2	2	no	—
192	C₂×C₄×C₄₇	—	2	2	no	—
193	C₂×C₄×C₄₇	—	2	2	no	—
194	C₂×C₄×C₄₇	—	2	2	no	—
195	C₂×C₄×C₄₇	—	2	2	no	—
196	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
197	C₂×C₄×C₄₇	#131	1	4	yes	—
198	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
199	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
201	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
202	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
203	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
204	C₂×Dic₄₇	—	2	2	no	—
205	C₂×Dic₄₇	—	2	2	no	—
206	C₂×Dic₄₇	—	2	2	no	—
207	C₂×Dic₄₇	—	2	2	no	—
208	C₂×Dic₄₇	—	2	2	no	—
209	C₂×Dic₄₇	—	2	2	no	—
210	C₂×Dic₄₇	—	2	2	no	—
211	C₂×Dic₄₇	—	2	2	no	—
212	C₂×Dic₄₇	—	2	2	no	—
213	C₂×Dic₄₇	—	2	2	no	—
214	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
215	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
216	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
217	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
218	C₈×C₄₇	—	2	2	no	—
219	C₈×C₄₇	—	2	2	no	—
220	C₈×C₄₇	—	2	2	no	—
221	C₈×C₄₇	—	2	2	no	—
222	C₄₇⋊C₈	—	2	2	no	—
223	C₄₇⋊C₈	—	2	2	no	—
224	C₄₇⋊C₈	—	2	2	no	—
225	C₄₇⋊C₈	—	2	2	no	—
226	#20553	—	47	1	no	maximal, Sylow
227	C₂²×C₄₇	—	2	2	no	—
228	C₂²×C₄₇	—	2	2	no	—
229	C₂²×C₄₇	—	2	2	no	—
230	C₂²×C₄₇	—	4	2	no	—
231	C₂²×C₄₇	—	4	2	no	—
232	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
233	C₂²×C₄₇	#520	1	1	yes	characteristic
234	C₂²×C₄₇	#520	1	1	yes	characteristic
235	C₂²×C₄₇	C₂×#131	1	2	yes	—
236	C₂²×C₄₇	#568	1	2	yes	—
237	C₄×C₄₇	—	2	4	no	—
238	C₄×C₄₇	—	2	2	no	—
239	C₄×C₄₇	—	4	2	no	—
240	C₄×C₄₇	#518	1	1	yes	characteristic
241	C₄×C₄₇	#519	1	1	yes	characteristic
242	C₄×C₄₇	#520	1	1	yes	characteristic
243	C₄×C₄₇	#520	1	1	yes	characteristic
244	Dic₄₇	—	2	2	no	—
245	Dic₄₇	—	2	2	no	—
246	Dic₄₇	—	2	2	no	—
247	Dic₄₇	—	2	2	no	—
248	Dic₄₇	—	4	2	no	—
249	Dic₄₇	—	4	2	no	—
250	C₂×#433	—	47	1	no	—
251	C₂×#424	—	47	1	no	—
252	#2298	—	47	1	no	—
253	#1771	—	47	1	no	—
254	#1771	—	47	1	no	—
255	#1770	—	47	1	no	—
256	C₈×C₄⋊C₄	—	47	1	no	—
257	#1768	—	47	1	no	—
258	#1768	—	47	1	no	—
259	#1767	—	47	1	no	—
260	C₄×C₄⋊C₈	—	47	1	no	—
261	#1753	—	47	1	no	—
262	#1753	—	47	1	no	—
263	#1752	—	47	1	no	—
264	C₈×C₂²⋊C₄	D₄₇	1	1	yes	characteristic
265	C₂×C₄₇	—	4	2	no	—
266	C₂×C₄₇	#2274	1	1	yes	characteristic
267	C₂×C₄₇	C₄×#131	1	1	yes	characteristic
268	C₂×C₄₇	#2875	1	1	yes	characteristic
269	C₂×C₄₇	#2992	1	2	yes	—
270	C₂×C₄₇	#2993	1	2	yes	—
271	C₂²×M₁₆	—	47	1	no	—
272	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
273	C₂×#117	—	47	1	no	—
274	#433	—	47	8	no	—
275	#424	—	47	8	no	—
276	C₂×C₄⋊C₈	—	47	1	no	—
277	C₂×C₄⋊C₈	—	47	1	no	—
278	C₂×C₄⋊C₈	—	47	1	no	—
279	C₂×C₄⋊C₈	—	47	1	no	—
280	C₂×C₄⋊C₈	—	47	1	no	—
281	C₂×C₄⋊C₈	—	47	1	no	—
282	C₂×C₂²⋊C₈	—	47	1	no	—
283	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
284	C₂×#97	—	47	1	no	—
285	C₂×#97	—	47	1	no	—
286	C₂×#97	—	47	1	no	—
287	C₂×#97	—	47	1	no	—
288	C₂×#97	—	47	1	no	—
289	C₂×C₄×C₈	—	47	1	no	—
290	C₂×C₄×C₈	—	47	1	no	—
291	C₂×C₄×C₈	—	47	1	no	—
292	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
293	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
294	#388	—	47	2	no	—
295	#388	—	47	2	no	—
296	#387	—	47	2	no	—
297	#387	—	47	2	no	—
298	C₄×C₄⋊C₄	—	47	1	no	—
299	C₄×C₄⋊C₄	—	47	1	no	—
300	C₄×C₂²⋊C₄	—	47	1	no	—
301	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
302	#376	—	47	1	no	—
303	C₄³	—	47	1	no	—
304	#336	—	47	1	no	—
305	#336	—	47	1	no	—
306	#336	—	47	1	no	—
307	#336	—	47	1	no	—
308	#336	—	47	1	no	—
309	#336	—	47	1	no	—
310	#336	C₂×D₄₇	1	1	yes	characteristic
311	#336	C₂×D₄₇	1	1	yes	characteristic
312	C₄₇	#20553	1	1	yes	characteristic, complemented, Sylow
313	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
314	C₂×M₁₆	—	47	4	no	—
315	C₂×M₁₆	—	188	1	no	—
316	C₂×M₁₆	—	188	1	no	—
317	C₂²×C₈	—	4	1	no	—
318	C₂²×C₈	—	4	1	no	—
319	C₂²×C₈	—	47	1	no	—
320	C₂²×C₈	—	47	1	no	—
321	C₂²×C₈	—	47	1	no	—
322	C₂²×C₈	—	47	1	no	—
323	C₂²×C₈	C₄×D₄₇	1	4	yes	—
324	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
325	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
326	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
327	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
328	#117	—	47	4	no	—
329	#117	—	47	4	no	—
330	C₂×C₄⋊C₄	—	47	1	no	—
331	C₂×C₄⋊C₄	—	47	1	no	—
332	C₂×C₄⋊C₄	—	47	2	no	—
333	C₂×C₄⋊C₄	—	47	2	no	—
334	C₂×C₂²⋊C₄	—	47	1	no	—
335	C₂×C₂²⋊C₄	—	47	1	no	—
336	C₂×C₂²⋊C₄	—	47	2	no	—
337	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
338	C₂×C₄²	—	47	1	no	—
339	C₂×C₄²	—	47	1	no	—
340	C₂×C₄²	—	47	2	no	—
341	C₂×C₄²	—	47	1	no	—
342	C₂×C₄²	—	47	1	no	—
343	C₂×C₄²	—	47	2	no	—
344	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
345	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
346	C₄⋊C₈	—	47	4	no	—
347	C₄⋊C₈	—	47	4	no	—
348	C₄⋊C₈	—	47	4	no	—
349	C₄⋊C₈	—	47	4	no	—
350	C₄⋊C₈	—	47	4	no	—
351	C₄⋊C₈	—	47	4	no	—
352	C₂²⋊C₈	—	47	4	no	—
353	C₂²⋊C₈	C₄×D₄₇	1	4	yes	—
354	#97	—	47	4	no	—
355	#97	—	188	1	no	—
356	#97	—	188	1	no	—
357	#97	—	188	1	no	—
358	#97	—	188	1	no	—
359	C₄×C₈	—	4	1	no	—
360	C₄×C₈	—	4	1	no	—
361	C₄×C₈	—	47	4	no	—
362	C₄×C₈	—	188	1	no	—
363	C₄×C₈	—	188	1	no	—
364	#95	—	47	2	no	—
365	#95	—	47	2	no	—
366	#95	—	47	2	no	—
367	#95	—	47	2	no	—
368	#95	—	47	2	no	—
369	#95	C₄×D₄₇	1	2	yes	—
370	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	1	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	47	1	no	—
376	C₂²×C₄	—	47	1	no	—
377	C₂²×C₄	—	47	1	no	—
378	C₂²×C₄	—	47	1	no	—
379	C₂²×C₄	—	47	2	no	—
380	C₂²×C₄	—	47	2	no	—
381	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
382	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
384	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
385	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
386	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
387	M₁₆	—	188	4	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	1	no	—
392	C₂×C₈	—	2	1	no	—
393	C₂×C₈	—	2	1	no	—
394	C₂×C₈	—	2	1	no	—
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	4	4	no	—
397	C₂×C₈	—	47	2	no	—
398	C₂×C₈	—	47	2	no	—
399	C₂×C₈	—	47	2	no	—
400	C₂×C₈	—	47	2	no	—
401	C₂×C₈	—	94	1	no	—
402	C₂×C₈	—	94	1	no	—
403	C₂×C₈	—	94	1	no	—
404	C₂×C₈	—	94	1	no	—
405	C₂×C₈	—	94	1	no	—
406	C₂×C₈	—	94	1	no	—
407	C₂×C₈	—	94	1	no	—
408	C₂×C₈	—	94	1	no	—
409	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
410	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
411	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
412	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
413	C₄⋊C₄	—	47	4	no	—
414	C₄⋊C₄	—	47	4	no	—
415	C₄⋊C₄	—	94	4	no	—
416	C₄⋊C₄	—	188	2	no	—
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	—	47	4	no	—
419	C₂²⋊C₄	—	47	4	no	—
420	C₂²⋊C₄	—	188	2	no	—
421	C₄²	—	2	1	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	47	2	no	—
426	C₄²	—	47	2	no	—
427	C₄²	—	47	2	no	—
428	C₄²	—	47	2	no	—
429	C₄²	—	94	4	no	—
430	C₄²	—	94	1	no	—
431	C₄²	—	94	1	no	—
432	C₄²	—	94	1	no	—
433	C₄²	—	94	1	no	—
434	C₄²	—	188	2	no	—
435	C₂³	—	2	1	no	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	2	no	—
438	C₂³	—	2	2	no	—
439	C₂³	C₄²×D₄₇	1	2	yes	—
440	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	47	2	no	—
453	C₂×C₄	—	47	2	no	—
454	C₂×C₄	—	47	2	no	—
455	C₂×C₄	—	47	2	no	—
456	C₂×C₄	—	94	2	no	—
457	C₂×C₄	—	94	2	no	—
458	C₂×C₄	—	94	2	no	—
459	C₂×C₄	—	94	2	no	—
460	C₂×C₄	—	94	2	no	—
461	C₂×C₄	—	94	2	no	—
462	C₂×C₄	—	94	2	no	—
463	C₂×C₄	—	94	2	no	—
464	C₂×C₄	—	94	2	no	—
465	C₂×C₄	—	94	2	no	—
466	C₂×C₄	C₄²×D₄₇	1	2	yes	—
467	C₂×C₄	#13094030	1	4	yes	—
468	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
469	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
470	C₂×C₄	#13094069	1	1	yes	characteristic
471	C₂×C₄	#13094069	1	1	yes	characteristic
472	C₂×C₄	#13094071	1	1	yes	characteristic
473	C₂×C₄	#13094071	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	—	2	2	no	—
476	C₈	—	2	2	no	—
477	C₈	—	2	2	no	—
478	C₈	—	94	2	no	—
479	C₈	—	94	2	no	—
480	C₈	—	94	2	no	—
481	C₈	—	94	2	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
488	C₂²	#15689602	1	1	yes	characteristic
489	C₂²	#15689602	1	1	yes	characteristic
490	C₂²	C₂×#13094030	1	2	yes	—
491	C₂²	#15689888	1	2	yes	—
492	C₄	—	2	4	no	—
493	C₄	—	2	2	no	—
494	C₄	—	4	2	no	—
495	C₄	—	94	2	no	—
496	C₄	—	94	2	no	—
497	C₄	—	94	2	no	—
498	C₄	—	94	2	no	—
499	C₄	—	188	2	no	—
500	C₄	—	188	2	no	—
501	C₄	#15689596	1	1	yes	characteristic
502	C₄	#15689600	1	1	yes	characteristic
503	C₄	#15689602	1	1	yes	characteristic
504	C₄	#15689602	1	1	yes	characteristic
505	C₂	—	4	2	no	—
506	C₂	#20245743	1	1	yes	characteristic
507	C₂	C₄×#13094030	1	1	yes	characteristic
508	C₂	#20251815	1	1	yes	characteristic
509	C₂	#20252521	1	2	yes	—
510	C₂	#20252538	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₈×C₂²⋊C₄×C₄₇	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₈×C₂²⋊C₄	D₄₇
hypocenter	C₄₇	#20553
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₈×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
4. #20243262	C₂	semidirect
5. #20243259	C₂	semidirect
6. #20243254	C₂	semidirect
7. C₈×Dic₄₇⋊C₄	C₂	semidirect
8. #20243246	C₂	semidirect
9. #20243244	C₂	semidirect
10. #20243240	C₂	semidirect
11. C₄×Dic₄₇⋊C₈	C₂	semidirect
18. #15689181	C₄	semidirect
19. #15689149	C₄	semidirect
312. C₄₇	#20553	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689181	2
C₂×#15689149	2
#20245884	2
#20243262	2
#20243259	2
#20243254	2
C₈×Dic₄₇⋊C₄	2
#20243246	2
#20243244	2
#20243240	2
C₄×Dic₄₇⋊C₈	2
#20243174	2
#20243172	2
#20243164	2
C₈×C₂²⋊C₄×C₄₇	2
#20553	47