Subgroups — #26216750

Order 12032.

1174 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×#15689173	C₂	1	2	yes	maximal
2	C₂×C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#20243539	C₂	1	2	yes	maximal, complemented
4	#20243503	C₂	1	2	yes	maximal, complemented
5	#20243368	C₂	1	1	yes	maximal, characteristic
6	#20243366	C₂	1	2	yes	maximal
7	C₄⋊C₈×Dic₄₇	C₂	1	2	yes	maximal, complemented
8	#20243236	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1797	C₂	1	1	yes	maximal, characteristic
10	C₂²×C₄×Dic₄₇	C₄	1	1	yes	characteristic
11	C₂²×C₄×Dic₄₇	C₄	1	1	yes	characteristic
12	C₂²×C₄×Dic₄₇	C₄	1	1	yes	characteristic
13	C₂²×C₄×Dic₄₇	C₄	1	1	yes	characteristic
14	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
16	#15689173	—	2	8	no	—
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
18	C₂×Dic₄₇⋊C₈	C₂²	1	4	yes	—
19	C₂×Dic₄₇⋊C₈	C₂²	1	4	yes	—
20	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
21	C₂×C₈×Dic₄₇	C₂²	1	4	yes	—
22	C₄²×Dic₄₇	C₄	1	1	yes	characteristic
23	C₄²×Dic₄₇	C₄	1	1	yes	characteristic
24	C₄²×Dic₄₇	C₄	1	1	yes	characteristic
25	C₄²×Dic₄₇	C₄	1	1	yes	characteristic
26	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
27	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
28	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
29	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
30	#15688878	C₂²	1	2	yes	—
31	#15688877	C₂²	1	4	yes	—
32	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
34	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
35	C₄₇×#336	C₂²	1	2	yes	—
36	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
37	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
38	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
39	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄₇⋊C₈	C₂³	1	4	yes	—
41	C₂×C₄×Dic₄₇	—	2	4	no	—
42	C₂×C₄×Dic₄₇	—	2	4	no	—
43	C₂×C₄×Dic₄₇	—	2	4	no	—
44	C₂×C₄×Dic₄₇	—	2	4	no	—
45	C₂×C₄×Dic₄₇	C₈	1	8	yes	complemented
46	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×Dic₄₇	D₄	1	4	yes	—
67	C₂×C₄×Dic₄₇	Q₈	1	4	yes	—
68	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
69	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
70	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
71	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
72	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
73	Dic₄₇⋊C₈	—	2	8	no	—
74	Dic₄₇⋊C₈	—	2	8	no	—
75	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
76	C₈×Dic₄₇	—	2	8	no	—
77	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
78	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
81	C₂×C₄²×C₄₇	—	2	4	no	—
82	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
85	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
86	C₄⋊C₈×C₄₇	—	2	4	no	—
87	C₂²⋊C₈×C₄₇	—	2	4	no	—
88	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	C₂×C₈	1	4	yes	—
97	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
105	C₂²×Dic₄₇	—	2	2	no	—
106	C₂²×Dic₄₇	—	2	2	no	—
107	C₂²×Dic₄₇	—	2	2	no	—
108	C₂²×Dic₄₇	—	2	2	no	—
109	C₂²×Dic₄₇	—	2	2	no	—
110	C₂²×Dic₄₇	—	2	2	no	—
111	C₂²×Dic₄₇	—	2	2	no	—
112	C₂²×Dic₄₇	C₄⋊C₄	1	4	yes	—
113	C₂²×Dic₄₇	C₄⋊C₄	1	4	yes	—
114	C₂²×Dic₄₇	C₂×C₈	1	4	yes	—
115	C₂²×Dic₄₇	C₂×C₈	1	4	yes	—
116	C₂²×Dic₄₇	M₁₆	1	4	yes	—
117	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
120	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
124	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₂×C₈×C₄₇	—	2	4	no	—
126	C₂×C₈×C₄₇	—	2	4	no	—
127	C₂×C₈×C₄₇	—	2	4	no	—
128	C₄²×C₄₇	—	2	2	no	—
129	C₄²×C₄₇	—	2	2	no	—
130	C₄²×C₄₇	—	2	2	no	—
131	C₄²×C₄₇	#41	1	4	yes	—
132	C₄×Dic₄₇	—	2	2	no	—
133	C₄×Dic₄₇	—	2	2	no	—
134	C₄×Dic₄₇	—	2	2	no	—
135	C₄×Dic₄₇	—	2	2	no	—
136	C₄×Dic₄₇	—	2	2	no	—
137	C₄×Dic₄₇	—	2	2	no	—
138	C₄×Dic₄₇	—	2	2	no	—
139	C₄×Dic₄₇	—	2	2	no	—
140	C₄×Dic₄₇	—	2	2	no	—
141	C₄×Dic₄₇	—	2	2	no	—
142	C₄×Dic₄₇	—	2	2	no	—
143	C₄×Dic₄₇	—	2	2	no	—
144	C₄×Dic₄₇	—	2	2	no	—
145	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
146	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
147	C₄×Dic₄₇	C₂×C₈	1	4	yes	—
148	C₄×Dic₄₇	C₂×C₈	1	4	yes	—
149	C₄×Dic₄₇	C₂×C₈	1	4	yes	—
150	C₄×Dic₄₇	C₂×C₈	1	4	yes	—
151	C₄×Dic₄₇	M₁₆	1	4	yes	—
152	C₄×Dic₄₇	M₁₆	1	4	yes	—
153	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
154	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
155	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
156	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
157	C₄×Dic₄₇	#41	1	4	yes	—
158	C₂×C₄₇⋊C₈	—	2	4	no	—
159	C₂×C₄₇⋊C₈	—	2	4	no	—
160	C₂×C₄₇⋊C₈	—	2	4	no	—
161	C₂³×C₄₇	—	2	1	no	—
162	C₂³×C₄₇	—	2	1	no	—
163	C₂³×C₄₇	—	2	1	no	—
164	C₂³×C₄₇	—	2	1	no	—
165	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
166	C₂³×C₄₇	C₂²×C₈	1	2	yes	—
167	C₂³×C₄₇	C₂×M₁₆	1	2	yes	—
168	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	—	2	8	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	2	4	no	—
179	C₂×C₄×C₄₇	—	2	4	no	—
180	C₂×C₄×C₄₇	—	2	8	no	—
181	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
182	C₂×C₄×C₄₇	#117	1	2	yes	—
183	C₂×C₄×C₄₇	#117	1	2	yes	—
184	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
185	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
186	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
187	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
188	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
191	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
192	C₂×Dic₄₇	—	2	8	no	—
193	C₂×Dic₄₇	—	2	1	no	—
194	C₂×Dic₄₇	—	2	1	no	—
195	C₂×Dic₄₇	—	2	1	no	—
196	C₂×Dic₄₇	—	2	1	no	—
197	C₂×Dic₄₇	—	2	1	no	—
198	C₂×Dic₄₇	—	2	1	no	—
199	C₂×Dic₄₇	—	2	1	no	—
200	C₂×Dic₄₇	—	2	1	no	—
201	C₂×Dic₄₇	—	2	8	no	—
202	C₂×Dic₄₇	—	2	8	no	—
203	C₂×Dic₄₇	C₄⋊C₈	1	16	yes	complemented
204	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
205	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
206	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
207	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
208	C₂×Dic₄₇	#117	1	2	yes	—
209	C₂×Dic₄₇	#117	1	2	yes	—
210	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
211	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
212	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
213	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
214	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
215	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
216	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
217	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
218	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
219	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
220	C₈×C₄₇	—	4	4	no	—
221	C₄₇⋊C₈	—	4	4	no	—
222	#20808	—	47	1	no	maximal, Sylow
223	C₂²×C₄₇	—	2	2	no	—
224	C₂²×C₄₇	—	2	2	no	—
225	C₂²×C₄₇	—	2	2	no	—
226	C₂²×C₄₇	—	2	2	no	—
227	C₂²×C₄₇	—	2	2	no	—
228	C₂²×C₄₇	—	2	2	no	—
229	C₂²×C₄₇	C₂×C₄⋊C₈	1	4	yes	—
230	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
231	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
232	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
233	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
234	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
235	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
236	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
237	C₄×C₄₇	—	2	2	no	—
238	C₄×C₄₇	—	2	2	no	—
239	C₄×C₄₇	—	2	2	no	—
240	C₄×C₄₇	—	2	2	no	—
241	C₄×C₄₇	#431	1	4	yes	complemented
242	C₄×C₄₇	#532	1	2	yes	—
243	C₄×C₄₇	#533	1	2	yes	—
244	Dic₄₇	—	2	2	no	—
245	Dic₄₇	—	2	2	no	—
246	Dic₄₇	—	2	2	no	—
247	Dic₄₇	—	2	2	no	—
248	Dic₄₇	C₂×C₄⋊C₈	1	4	yes	—
249	Dic₄₇	C₂×C₄⋊C₈	1	4	yes	—
250	Dic₄₇	#423	1	4	yes	—
251	Dic₄₇	#431	1	4	yes	complemented
252	C₂×#431	—	47	2	no	—
253	C₂×C₄³	—	47	1	no	—
254	#1842	—	47	2	no	—
255	#1831	—	47	2	no	—
256	#1797	—	47	1	no	—
257	#1797	—	47	2	no	—
258	#1797	D₄₇	1	1	yes	characteristic
259	C₄×C₄⋊C₈	—	47	2	no	—
260	C₄×C₄⋊C₈	—	47	2	no	—
261	C₂×C₄₇	—	2	4	no	—
262	C₂×C₄₇	#2285	1	1	yes	characteristic
263	C₂×C₄₇	C₂²×C₄⋊C₈	1	1	yes	characteristic
264	C₂×C₄₇	C₂×#423	1	1	yes	characteristic
265	C₂×C₄₇	C₂×#431	1	1	yes	characteristic
266	C₂×C₄₇	C₂×#431	1	1	yes	characteristic
267	C₂×C₄₇	#2920	1	1	yes	characteristic
268	C₂×C₄₇	#2920	1	1	yes	characteristic
269	C₂²×C₄²	—	47	1	no	—
270	C₂²×C₄²	—	47	1	no	—
271	C₂²×C₄²	—	47	1	no	—
272	C₂²×C₄²	—	47	1	no	—
273	C₂²×C₄²	—	47	1	no	—
274	C₂²×C₄²	—	47	1	no	—
275	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
276	#431	—	94	8	no	—
277	C₂×C₄⋊C₈	—	47	4	no	—
278	C₂×C₄⋊C₈	—	47	4	no	—
279	C₂×C₄⋊C₈	—	47	2	no	—
280	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
281	C₂×C₂²⋊C₈	—	47	2	no	—
282	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
283	C₂×C₄×C₈	—	47	4	no	—
284	C₄³	—	47	1	no	—
285	C₄³	—	47	1	no	—
286	C₄³	—	47	1	no	—
287	C₄³	—	47	1	no	—
288	C₄³	—	47	1	no	—
289	C₄³	—	47	1	no	—
290	C₄³	—	47	1	no	—
291	C₄³	—	47	1	no	—
292	#336	—	47	4	no	—
293	#336	—	47	2	no	—
294	#336	C₂×D₄₇	1	2	yes	—
295	C₄₇	#20808	1	1	yes	characteristic, complemented, Sylow
296	C₂³×C₄	—	47	1	no	—
297	C₂³×C₄	—	47	1	no	—
298	C₂³×C₄	—	47	1	no	—
299	C₂³×C₄	—	47	1	no	—
300	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
301	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
302	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
303	C₂²×C₈	—	47	4	no	—
304	C₂²×C₈	C₂²×D₄₇	1	4	yes	—
305	C₂×C₄²	—	2	4	no	—
306	C₂×C₄²	—	47	8	no	—
307	C₂×C₄²	—	47	1	no	—
308	C₂×C₄²	—	47	1	no	—
309	C₂×C₄²	—	47	1	no	—
310	C₂×C₄²	—	47	1	no	—
311	C₂×C₄²	—	47	1	no	—
312	C₂×C₄²	—	47	1	no	—
313	C₂×C₄²	—	47	1	no	—
314	C₂×C₄²	—	47	1	no	—
315	C₂×C₄²	—	47	4	no	—
316	C₂×C₄²	—	47	4	no	—
317	C₂×C₄²	—	47	1	no	—
318	C₂×C₄²	—	47	1	no	—
319	C₂×C₄²	—	47	1	no	—
320	C₂×C₄²	—	47	1	no	—
321	C₂×C₄²	—	47	1	no	—
322	C₂×C₄²	—	47	1	no	—
323	C₂×C₄²	—	47	1	no	—
324	C₂×C₄²	—	47	1	no	—
325	C₂×C₄²	—	47	1	no	—
326	C₂×C₄²	—	47	1	no	—
327	C₂×C₄²	—	47	1	no	—
328	C₂×C₄²	—	47	1	no	—
329	C₂×C₄²	—	47	1	no	—
330	C₂×C₄²	—	47	1	no	—
331	C₂×C₄²	—	47	1	no	—
332	C₂×C₄²	—	47	1	no	—
333	C₂×C₄²	—	94	4	no	—
334	C₂×C₄²	—	94	4	no	—
335	C₂×C₄²	—	94	4	no	—
336	C₂×C₄²	—	94	4	no	—
337	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
338	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
339	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
340	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
341	C₄⋊C₈	—	2	4	no	—
342	C₄⋊C₈	—	94	8	no	—
343	C₄⋊C₈	—	94	8	no	—
344	C₄⋊C₈	—	94	4	no	—
345	C₂²⋊C₈	—	2	4	no	—
346	C₂²⋊C₈	—	94	4	no	—
347	C₄×C₈	—	94	8	no	—
348	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	47	4	no	—
357	C₂²×C₄	—	47	4	no	—
358	C₂²×C₄	—	47	4	no	—
359	C₂²×C₄	—	47	1	no	—
360	C₂²×C₄	—	47	1	no	—
361	C₂²×C₄	—	47	1	no	—
362	C₂²×C₄	—	47	1	no	—
363	C₂²×C₄	—	47	4	no	—
364	C₂²×C₄	—	47	4	no	—
365	C₂²×C₄	—	47	1	no	—
366	C₂²×C₄	—	47	1	no	—
367	C₂²×C₄	—	47	1	no	—
368	C₂²×C₄	—	47	1	no	—
369	C₂²×C₄	—	94	2	no	—
370	C₂²×C₄	—	94	2	no	—
371	C₂²×C₄	—	94	2	no	—
372	C₂²×C₄	—	94	2	no	—
373	C₂²×C₄	—	94	2	no	—
374	C₂²×C₄	—	94	2	no	—
375	C₂²×C₄	—	94	2	no	—
376	C₂²×C₄	C₈×D₄₇	1	4	yes	—
377	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
378	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
379	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
380	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
381	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
382	C₂²×C₄	D₄×D₄₇	1	2	yes	—
383	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
384	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
385	C₂×C₈	—	2	4	no	—
386	C₂×C₈	—	2	4	no	—
387	C₂×C₈	—	2	4	no	—
388	C₂×C₈	—	94	4	no	—
389	C₂×C₈	—	94	4	no	—
390	C₂×C₈	—	94	4	no	—
391	C₄²	—	2	2	no	—
392	C₄²	—	2	2	no	—
393	C₄²	—	2	2	no	—
394	C₄²	—	47	4	no	—
395	C₄²	—	47	4	no	—
396	C₄²	—	47	4	no	—
397	C₄²	—	47	4	no	—
398	C₄²	—	47	4	no	—
399	C₄²	—	47	4	no	—
400	C₄²	—	47	4	no	—
401	C₄²	—	47	4	no	—
402	C₄²	—	47	2	no	—
403	C₄²	—	47	2	no	—
404	C₄²	—	47	2	no	—
405	C₄²	—	47	2	no	—
406	C₄²	—	47	4	no	—
407	C₄²	—	94	2	no	—
408	C₄²	—	94	2	no	—
409	C₄²	—	94	2	no	—
410	C₄²	—	94	2	no	—
411	C₄²	—	94	2	no	—
412	C₄²	—	94	2	no	—
413	C₄²	—	94	2	no	—
414	C₄²	—	94	2	no	—
415	C₄²	—	94	2	no	—
416	C₄²	—	94	2	no	—
417	C₄²	—	94	2	no	—
418	C₄²	—	94	2	no	—
419	C₄²	—	94	2	no	—
420	C₄²	#10625352	1	4	yes	—
421	C₂³	—	2	1	no	—
422	C₂³	—	2	1	no	—
423	C₂³	—	2	1	no	—
424	C₂³	—	2	1	no	—
425	C₂³	C₄⋊C₄×D₄₇	1	2	yes	—
426	C₂³	C₂×C₈×D₄₇	1	2	yes	—
427	C₂³	M₁₆×D₄₇	1	2	yes	—
428	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
429	C₂×C₄	—	2	8	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	2	1	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	2	8	no	—
441	C₂×C₄	—	47	2	no	—
442	C₂×C₄	—	47	2	no	—
443	C₂×C₄	—	47	2	no	—
444	C₂×C₄	—	47	2	no	—
445	C₂×C₄	—	47	2	no	—
446	C₂×C₄	—	47	2	no	—
447	C₂×C₄	—	47	2	no	—
448	C₂×C₄	—	47	2	no	—
449	C₂×C₄	—	47	2	no	—
450	C₂×C₄	—	47	2	no	—
451	C₂×C₄	—	47	2	no	—
452	C₂×C₄	—	47	2	no	—
453	C₂×C₄	—	47	16	no	—
454	C₂×C₄	—	47	2	no	—
455	C₂×C₄	—	47	2	no	—
456	C₂×C₄	—	47	2	no	—
457	C₂×C₄	—	47	2	no	—
458	C₂×C₄	—	94	8	no	—
459	C₂×C₄	—	94	8	no	—
460	C₂×C₄	—	94	8	no	—
461	C₂×C₄	—	94	1	no	—
462	C₂×C₄	—	94	1	no	—
463	C₂×C₄	—	94	1	no	—
464	C₂×C₄	—	94	1	no	—
465	C₂×C₄	—	94	1	no	—
466	C₂×C₄	—	94	1	no	—
467	C₂×C₄	—	94	1	no	—
468	C₂×C₄	—	94	1	no	—
469	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
470	C₂×C₄	#13093980	1	2	yes	—
471	C₂×C₄	#13093980	1	2	yes	—
472	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
473	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
474	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
475	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
476	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
477	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
478	C₂×C₄	#41×D₄₇	1	2	yes	—
479	C₂×C₄	C₂×#10625352	1	2	yes	—
480	C₈	—	4	4	no	—
481	C₈	—	188	4	no	—
482	C₂²	—	2	2	no	—
483	C₂²	—	2	2	no	—
484	C₂²	—	2	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	C₄⋊C₈×D₄₇	1	4	yes	—
489	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
490	C₂²	#117×D₄₇	1	1	yes	characteristic
491	C₂²	C₂×#13093980	1	1	yes	characteristic
492	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
493	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
494	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
495	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
496	C₄	—	2	2	no	—
497	C₄	—	2	2	no	—
498	C₄	—	2	2	no	—
499	C₄	—	2	2	no	—
500	C₄	—	47	4	no	—
501	C₄	—	47	4	no	—
502	C₄	—	47	4	no	—
503	C₄	—	47	4	no	—
504	C₄	—	94	2	no	—
505	C₄	—	94	2	no	—
506	C₄	—	94	2	no	—
507	C₄	—	94	2	no	—
508	C₄	#15689173	1	4	yes	complemented
509	C₄	#15689668	1	2	yes	—
510	C₄	#15689675	1	2	yes	—
511	C₂	—	2	4	no	—
512	C₂	#20245790	1	1	yes	characteristic
513	C₂	C₂×C₄⋊C₈×D₄₇	1	1	yes	characteristic
514	C₂	#423×D₄₇	1	1	yes	characteristic
515	C₂	#431×D₄₇	1	1	yes	characteristic
516	C₂	C₂×#15689173	1	1	yes	characteristic
517	C₂	#20252017	1	1	yes	characteristic
518	C₂	#20252018	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Fitting	C₄₇×#1797	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1797	D₄₇
hypocenter	C₄₇	#20808
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1797

Complements

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

N	H ≅ G/N	type
3. #20243539	C₂	semidirect
4. #20243503	C₂	semidirect
7. C₄⋊C₈×Dic₄₇	C₂	semidirect
8. #20243236	C₂	semidirect
45. C₂×C₄×Dic₄₇	C₈	semidirect
203. C₂×Dic₄₇	C₄⋊C₈	semidirect
241. C₄×C₄₇	#431	semidirect
251. Dic₄₇	#431	semidirect
295. C₄₇	#20808	semidirect
508. C₄	#15689173	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689173	2
C₂×C₄²×Dic₄₇	2
#20243539	2
#20243503	2
#20243368	2
#20243366	2
C₄⋊C₈×Dic₄₇	2
#20243236	2
C₄₇×#1797	2
#20808	47