Subgroups — #26214470

Order 12032.

958 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689177	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689173	C₂	1	1	yes	maximal, characteristic
3	#117×Dic₄₇	C₂	1	1	yes	maximal, characteristic
4	#20243242	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243240	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄×Dic₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243236	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243156	C₂	1	1	yes	maximal, characteristic
9	#20243156	C₂	1	1	yes	maximal, characteristic
10	#20243154	C₂	1	1	yes	maximal, characteristic
11	#20243138	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243138	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243076	C₂	1	1	yes	maximal, characteristic, complemented
14	#20243074	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#1750	C₂	1	1	yes	maximal, characteristic
16	C₂×#13093983	C₂²	1	1	yes	characteristic
17	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
18	#15689177	C₄	1	8	yes	complemented
19	#15689173	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×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×#13093935	C₂²	1	1	yes	characteristic
27	C₂×#13093934	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×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
34	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
36	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
37	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
38	C₂²⋊C₄×Dic₄₇	C₄	1	2	yes	—
39	C₂²⋊C₄×Dic₄₇	C₄	1	2	yes	—
40	#15688969	C₂²	1	1	yes	characteristic
41	#15688969	C₂²	1	1	yes	characteristic
42	C₄²×Dic₄₇	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	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
52	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
53	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
54	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
55	C₄₇×#336	C₂²	1	1	yes	characteristic
56	C₄₇×#336	C₂²	1	1	yes	characteristic
57	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
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	#13093983	—	2	2	no	—
64	#13093983	—	2	2	no	—
65	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
66	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
67	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
68	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
69	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
70	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
71	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄×Dic₄₇	C₂×C₄	1	4	yes	—
74	C₂×C₄×Dic₄₇	C₂×C₄	1	4	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	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
84	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
85	#13093935	—	2	2	no	—
86	#13093934	—	2	2	no	—
87	#13093934	—	2	2	no	—
88	#13093934	C₂×C₄	1	4	yes	—
89	#13093934	C₂×C₄	1	4	yes	—
90	C₄×C₄₇⋊C₈	—	2	2	no	—
91	C₈×Dic₄₇	—	2	2	no	—
92	C₈×Dic₄₇	—	2	2	no	—
93	C₈×Dic₄₇	C₂×C₄	1	4	yes	—
94	C₈×Dic₄₇	C₂×C₄	1	4	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	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
103	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
104	#117×C₄₇	—	2	2	no	—
105	#117×C₄₇	—	2	2	no	—
106	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
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	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	—
112	#97×C₄₇	—	2	2	no	—
113	C₄×C₈×C₄₇	—	2	2	no	—
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	—	2	4	no	—
126	C₂²×Dic₄₇	—	4	2	no	—
127	C₂²×Dic₄₇	C₄²	1	4	yes	—
128	C₂²×Dic₄₇	C₄²	1	4	yes	—
129	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
130	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
131	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
132	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
133	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
134	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
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	—	2	1	no	—
140	C₂×C₈×C₄₇	—	2	1	no	—
141	C₂×C₈×C₄₇	—	2	1	no	—
142	C₂×C₈×C₄₇	—	2	1	no	—
143	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
146	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
147	C₄⋊C₄×C₄₇	—	2	4	no	—
148	C₂²⋊C₄×C₄₇	—	2	4	no	—
149	C₄²×C₄₇	—	2	1	no	—
150	C₄²×C₄₇	—	2	1	no	—
151	C₄²×C₄₇	#41	1	2	yes	—
152	C₄²×C₄₇	#41	1	2	yes	—
153	C₂²⋊Dic₄₇	—	2	4	no	—
154	C₄⋊Dic₄₇	—	2	4	no	—
155	C₄×Dic₄₇	—	2	1	no	—
156	C₄×Dic₄₇	—	2	1	no	—
157	C₄×Dic₄₇	—	2	4	no	—
158	C₄×Dic₄₇	—	2	4	no	—
159	C₄×Dic₄₇	—	4	2	no	—
160	C₄×Dic₄₇	—	4	2	no	—
161	C₄×Dic₄₇	C₄²	1	4	yes	—
162	C₄×Dic₄₇	C₄²	1	4	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	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
167	C₄×Dic₄₇	#41	1	2	yes	—
168	C₄×Dic₄₇	#41	1	2	yes	—
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	—	2	1	no	—
176	C₂×C₄₇⋊C₈	—	2	1	no	—
177	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
178	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
179	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
180	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
181	C₂³×C₄₇	—	2	1	no	—
182	C₂³×C₄₇	—	2	1	no	—
183	C₂³×C₄₇	—	2	2	no	—
184	C₂³×C₄₇	—	2	2	no	—
185	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
186	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₄₇	—	2	1	no	—
188	C₂×C₄×C₄₇	—	2	1	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	—	2	2	no	—
197	C₂×C₄×C₄₇	—	2	2	no	—
198	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
199	C₂×C₄×C₄₇	#117	1	4	yes	—
200	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
202	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
203	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
204	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
205	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
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	8	no	—
212	C₂×Dic₄₇	—	2	2	no	—
213	C₂×Dic₄₇	—	2	2	no	—
214	C₂×Dic₄₇	—	2	2	no	—
215	C₂×Dic₄₇	—	4	4	no	—
216	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
217	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
218	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
219	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
220	C₂×Dic₄₇	#117	1	4	yes	—
221	C₂×Dic₄₇	#131	1	4	yes	—
222	C₈×C₄₇	—	2	2	no	—
223	C₈×C₄₇	—	2	2	no	—
224	C₈×C₄₇	—	2	2	no	—
225	C₈×C₄₇	—	2	2	no	—
226	C₄₇⋊C₈	—	2	2	no	—
227	C₄₇⋊C₈	—	2	2	no	—
228	C₄₇⋊C₈	—	2	2	no	—
229	C₄₇⋊C₈	—	2	2	no	—
230	#20470	—	47	1	no	maximal, Sylow
231	C₂²×C₄₇	—	2	2	no	—
232	C₂²×C₄₇	—	2	2	no	—
233	C₂²×C₄₇	—	2	2	no	—
234	C₂²×C₄₇	—	4	2	no	—
235	C₂²×C₄₇	—	4	2	no	—
236	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
237	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
238	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
239	C₂²×C₄₇	C₂×#131	1	2	yes	—
240	C₂²×C₄₇	#568	1	2	yes	—
241	C₄×C₄₇	—	2	4	no	—
242	C₄×C₄₇	—	2	2	no	—
243	C₄×C₄₇	—	4	2	no	—
244	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
245	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
246	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
247	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
248	Dic₄₇	—	2	2	no	—
249	Dic₄₇	—	2	2	no	—
250	Dic₄₇	—	2	2	no	—
251	Dic₄₇	—	2	4	no	—
252	Dic₄₇	—	4	2	no	—
253	Dic₄₇	#405	1	4	yes	—
254	C₂×#432	—	47	1	no	—
255	C₂×#431	—	47	1	no	—
256	C₄×#117	—	47	1	no	—
257	#1767	—	47	1	no	—
258	#1767	—	47	1	no	—
259	C₄×C₄⋊C₈	—	47	1	no	—
260	C₄×C₄⋊C₈	—	47	1	no	—
261	#1750	—	47	1	no	—
262	#1750	—	47	1	no	—
263	#1750	—	47	1	no	—
264	#1750	D₄₇	1	1	yes	characteristic
265	#1746	—	47	1	no	—
266	#1746	—	47	1	no	—
267	#1726	—	47	1	no	—
268	#1726	—	47	1	no	—
269	C₂×C₄₇	—	4	2	no	—
270	C₂×C₄₇	C₄×#117	1	1	yes	characteristic
271	C₂×C₄₇	C₂×#405	1	1	yes	characteristic
272	C₂×C₄₇	#2873	1	1	yes	characteristic
273	C₂×C₄₇	#2925	1	2	yes	—
274	C₂×C₄₇	#2925	1	2	yes	—
275	C₂×#117	—	47	1	no	—
276	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
277	C₂²×C₄²	—	47	1	no	—
278	#432	—	47	8	no	—
279	#431	—	47	8	no	—
280	C₂×C₄⋊C₈	—	47	1	no	—
281	C₂×C₄⋊C₈	—	47	1	no	—
282	C₂×C₄⋊C₈	—	47	1	no	—
283	C₂×C₄⋊C₈	—	47	1	no	—
284	C₂×C₂²⋊C₈	—	47	1	no	—
285	C₂×C₂²⋊C₈	—	47	1	no	—
286	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
287	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
288	C₂×#97	—	47	1	no	—
289	C₂×#97	—	47	1	no	—
290	C₂×#97	—	47	1	no	—
291	C₂×#97	—	47	1	no	—
292	C₂×#97	—	47	1	no	—
293	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
294	C₂×C₄×C₈	—	47	1	no	—
295	C₂×C₄×C₈	—	47	1	no	—
296	C₂×C₄×C₈	—	47	1	no	—
297	C₂×C₄×C₈	—	47	1	no	—
298	C₂×C₄×C₈	—	47	1	no	—
299	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
300	C₄×C₄⋊C₄	—	47	2	no	—
301	C₄×C₄⋊C₄	—	47	2	no	—
302	C₄×C₂²⋊C₄	—	47	2	no	—
303	C₄×C₂²⋊C₄	—	47	2	no	—
304	#376	—	47	1	no	—
305	#376	—	47	1	no	—
306	C₄³	—	47	1	no	—
307	C₄³	—	47	1	no	—
308	#336	—	47	1	no	—
309	#336	—	47	1	no	—
310	#336	—	47	1	no	—
311	#336	—	47	1	no	—
312	#336	—	47	1	no	—
313	#336	—	47	1	no	—
314	#336	C₂×D₄₇	1	1	yes	characteristic
315	#336	C₂×D₄₇	1	1	yes	characteristic
316	C₄₇	#20470	1	1	yes	characteristic, complemented, Sylow
317	C₂³×C₄	—	47	1	no	—
318	C₂³×C₄	—	47	1	no	—
319	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
320	C₂²×C₈	—	47	1	no	—
321	C₂²×C₈	—	47	1	no	—
322	C₂²×C₈	—	47	1	no	—
323	C₂²×C₈	—	47	1	no	—
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	—	2	2	no	—
329	#117	—	2	2	no	—
330	#117	—	94	2	no	—
331	#117	—	94	2	no	—
332	C₂×C₄⋊C₄	—	47	2	no	—
333	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
334	C₂×C₂²⋊C₄	—	47	2	no	—
335	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
336	C₂×C₄²	—	47	1	no	—
337	C₂×C₄²	—	47	1	no	—
338	C₂×C₄²	—	47	4	no	—
339	C₂×C₄²	—	47	4	no	—
340	C₂×C₄²	—	47	1	no	—
341	C₂×C₄²	—	47	1	no	—
342	C₂×C₄²	—	47	1	no	—
343	C₂×C₄²	—	47	2	no	—
344	C₂×C₄²	—	47	2	no	—
345	C₂×C₄²	—	47	1	no	—
346	C₂×C₄²	—	47	2	no	—
347	C₂×C₄²	—	47	2	no	—
348	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
349	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
350	C₄⋊C₈	—	47	4	no	—
351	C₄⋊C₈	—	47	4	no	—
352	C₄⋊C₈	—	47	4	no	—
353	C₄⋊C₈	—	47	4	no	—
354	C₂²⋊C₈	—	47	4	no	—
355	C₂²⋊C₈	—	47	4	no	—
356	C₂²⋊C₈	C₄×D₄₇	1	4	yes	—
357	C₂²⋊C₈	C₄×D₄₇	1	4	yes	—
358	#97	—	2	2	no	—
359	#97	—	47	4	no	—
360	#97	—	47	4	no	—
361	#97	—	94	2	no	—
362	#97	—	94	2	no	—
363	#97	—	94	2	no	—
364	C₄×C₈	—	2	2	no	—
365	C₄×C₈	—	47	4	no	—
366	C₄×C₈	—	47	4	no	—
367	C₄×C₈	—	94	2	no	—
368	C₄×C₈	—	94	2	no	—
369	C₄×C₈	—	94	2	no	—
370	#95	—	47	2	no	—
371	#95	—	47	2	no	—
372	#95	—	47	2	no	—
373	#95	—	47	2	no	—
374	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	47	1	no	—
380	C₂²×C₄	—	47	4	no	—
381	C₂²×C₄	—	47	1	no	—
382	C₂²×C₄	—	47	1	no	—
383	C₂²×C₄	—	47	2	no	—
384	C₂²×C₄	—	47	1	no	—
385	C₂²×C₄	—	47	4	no	—
386	C₂²×C₄	—	47	2	no	—
387	C₂²×C₄	—	94	4	no	—
388	C₂²×C₄	—	188	2	no	—
389	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
390	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
391	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
392	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
393	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
394	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
395	C₂×C₈	—	2	1	no	—
396	C₂×C₈	—	2	1	no	—
397	C₂×C₈	—	2	1	no	—
398	C₂×C₈	—	2	1	no	—
399	C₂×C₈	—	2	1	no	—
400	C₂×C₈	—	2	1	no	—
401	C₂×C₈	—	2	1	no	—
402	C₂×C₈	—	2	1	no	—
403	C₂×C₈	—	47	2	no	—
404	C₂×C₈	—	47	2	no	—
405	C₂×C₈	—	47	2	no	—
406	C₂×C₈	—	47	2	no	—
407	C₂×C₈	—	94	1	no	—
408	C₂×C₈	—	94	1	no	—
409	C₂×C₈	—	94	1	no	—
410	C₂×C₈	—	94	1	no	—
411	C₂×C₈	—	94	1	no	—
412	C₂×C₈	—	94	1	no	—
413	C₂×C₈	—	94	1	no	—
414	C₂×C₈	—	94	1	no	—
415	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
416	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
417	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
418	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	94	4	no	—
421	C₂²⋊C₄	—	2	4	no	—
422	C₂²⋊C₄	—	94	4	no	—
423	C₄²	—	2	1	no	—
424	C₄²	—	2	1	no	—
425	C₄²	—	47	4	no	—
426	C₄²	—	47	4	no	—
427	C₄²	—	47	2	no	—
428	C₄²	—	47	2	no	—
429	C₄²	—	47	2	no	—
430	C₄²	—	47	2	no	—
431	C₄²	—	47	2	no	—
432	C₄²	—	47	2	no	—
433	C₄²	—	94	4	no	—
434	C₄²	—	94	4	no	—
435	C₄²	—	94	1	no	—
436	C₄²	—	94	1	no	—
437	C₄²	—	188	2	no	—
438	C₄²	—	188	2	no	—
439	C₄²	#10625352	1	2	yes	—
440	C₄²	#10625352	1	2	yes	—
441	C₂³	—	2	1	no	—
442	C₂³	—	2	1	no	—
443	C₂³	—	2	2	no	—
444	C₂³	—	2	2	no	—
445	C₂³	C₄²×D₄₇	1	2	yes	—
446	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
447	C₂×C₄	—	2	1	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	47	2	no	—
459	C₂×C₄	—	47	4	no	—
460	C₂×C₄	—	47	2	no	—
461	C₂×C₄	—	47	2	no	—
462	C₂×C₄	—	47	2	no	—
463	C₂×C₄	—	47	4	no	—
464	C₂×C₄	—	94	8	no	—
465	C₂×C₄	—	94	2	no	—
466	C₂×C₄	—	94	2	no	—
467	C₂×C₄	—	94	2	no	—
468	C₂×C₄	—	94	2	no	—
469	C₂×C₄	—	94	2	no	—
470	C₂×C₄	—	94	2	no	—
471	C₂×C₄	—	94	2	no	—
472	C₂×C₄	—	94	2	no	—
473	C₂×C₄	—	188	4	no	—
474	C₂×C₄	C₄²×D₄₇	1	2	yes	—
475	C₂×C₄	#13093980	1	4	yes	—
476	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
477	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
478	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
479	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
480	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
481	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
482	C₈	—	2	2	no	—
483	C₈	—	2	2	no	—
484	C₈	—	2	2	no	—
485	C₈	—	2	2	no	—
486	C₈	—	94	2	no	—
487	C₈	—	94	2	no	—
488	C₈	—	94	2	no	—
489	C₈	—	94	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	2	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
496	C₂²	#117×D₄₇	1	1	yes	characteristic
497	C₂²	C₂×#13093980	1	1	yes	characteristic
498	C₂²	#131×D₄₇	1	2	yes	—
499	C₂²	#15689888	1	2	yes	—
500	C₄	—	2	4	no	—
501	C₄	—	2	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	47	4	no	—
504	C₄	—	94	4	no	—
505	C₄	—	94	2	no	—
506	C₄	—	94	2	no	—
507	C₄	—	94	2	no	—
508	C₄	—	188	2	no	—
509	C₄	C₄×#10625352	1	1	yes	characteristic
510	C₄	C₄×#10625352	1	1	yes	characteristic
511	C₄	C₄×#10625352	1	1	yes	characteristic
512	C₄	C₄×#10625352	1	1	yes	characteristic
513	C₂	—	4	2	no	—
514	C₂	C₄×#13093980	1	1	yes	characteristic
515	C₂	#405×D₄₇	1	1	yes	characteristic
516	C₂	#20251804	1	1	yes	characteristic
517	C₂	#20252050	1	2	yes	—
518	C₂	#20252051	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₄₇×#1750	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1750	D₄₇
hypocenter	C₄₇	#20470
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1750

Complements

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

N	H ≅ G/N	type
4. #20243242	C₂	semidirect
5. #20243240	C₂	semidirect
6. C₄×Dic₄₇⋊C₈	C₂	semidirect
7. #20243236	C₂	semidirect
11. #20243138	C₂	semidirect
12. #20243138	C₂	semidirect
13. #20243076	C₂	semidirect
14. #20243074	C₂	semidirect
18. #15689177	C₄	semidirect
19. #15689173	C₄	semidirect
316. C₄₇	#20470	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689177	2
C₂×#15689173	2
#117×Dic₄₇	2
#20243242	2
#20243240	2
C₄×Dic₄₇⋊C₈	2
#20243236	2
#20243156	2
#20243154	2
#20243138	2
#20243076	2
#20243074	2
C₄₇×#1750	2
#20470	47