Subgroups — #26220390

Order 12032.

1046 conjugacy classes of subgroups.

The subgroup lattice has 492 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, complemented
2	C₄×D₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	#20244183	C₂	1	1	yes	maximal, characteristic
4	#20244106	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244104	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243997	C₂	1	2	yes	maximal, complemented
7	#20243991	C₂	1	2	yes	maximal, complemented
8	C₄⋊C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²⋊C₈×Dic₄₇	C₂	1	2	yes	maximal, complemented
10	C₄×C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1954	C₂	1	1	yes	maximal, characteristic
12	C₂×D₄×Dic₄₇	C₄	1	1	yes	characteristic
13	C₂×D₄×Dic₄₇	C₄	1	1	yes	characteristic
14	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
15	#15689173	—	2	8	no	—
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
18	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
19	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
20	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
21	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
22	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
25	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
26	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
27	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
28	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
29	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
30	C₂²⋊C₄×Dic₄₇	C₄	1	2	yes	—
31	C₂²⋊C₄×Dic₄₇	C₄	1	2	yes	—
32	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
33	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
34	#15688877	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	#15688877	C₂²	1	2	yes	—
37	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
40	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
41	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
43	C₂³×Dic₄₇	C₂×C₄	1	2	yes	—
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	D₄×Dic₄₇	—	2	4	no	—
48	D₄×Dic₄₇	C₈	1	8	yes	complemented
49	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
52	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
53	C₂×C₄×Dic₄₇	—	2	4	no	—
54	C₂×C₄×Dic₄₇	—	2	4	no	—
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	2	yes	—
58	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
59	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
62	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
63	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
64	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
65	Dic₄₇⋊C₈	—	2	4	no	—
66	Dic₄₇⋊C₈	—	2	4	no	—
67	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
68	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
69	C₄×C₄₇⋊C₈	—	2	2	no	—
70	C₈×Dic₄₇	—	2	2	no	—
71	C₈×Dic₄₇	—	2	4	no	—
72	C₈×Dic₄₇	—	2	2	no	—
73	C₈×Dic₄₇	—	2	2	no	—
74	C₈×Dic₄₇	D₄	1	4	yes	complemented
75	C₄₇⋊#95	C₂×C₄	1	2	yes	—
76	C₄₇⋊#95	C₂×C₄	1	2	yes	—
77	C₄₇⋊#95	C₂×C₄	1	2	yes	—
78	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
80	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
81	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
83	C₄×D₄×C₄₇	—	2	2	no	—
84	C₄×D₄×C₄₇	—	2	2	no	—
85	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
86	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
87	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₄₇	—	2	2	no	—
89	C₂²⋊C₈×C₄₇	—	2	4	no	—
90	C₂²⋊C₈×C₄₇	—	2	4	no	—
91	C₄×C₈×C₄₇	—	2	2	no	—
92	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
93	C₂×D₄×C₄₇	—	2	2	no	—
94	C₂×D₄×C₄₇	—	2	2	no	—
95	C₂×D₄×C₄₇	C₂×C₈	1	4	yes	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
106	C₂²×Dic₄₇	—	2	4	no	—
107	C₂²×Dic₄₇	—	2	4	no	—
108	C₂²×Dic₄₇	—	2	4	no	—
109	C₂²×Dic₄₇	—	2	4	no	—
110	C₂²×Dic₄₇	—	2	4	no	—
111	C₂²×Dic₄₇	C₂×C₈	1	8	yes	—
112	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
113	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
115	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
117	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₄₇	—	2	1	no	—
119	C₂×C₈×C₄₇	—	2	1	no	—
120	C₂×C₈×C₄₇	—	2	1	no	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₄₇	#41	1	2	yes	—
127	C₄⋊C₄×C₄₇	—	2	2	no	—
128	C₂²⋊C₄×C₄₇	—	2	4	no	—
129	C₄²×C₄₇	#41	1	2	yes	—
130	C₄²×C₄₇	#41	1	2	yes	—
131	C₂²⋊Dic₄₇	—	2	4	no	—
132	C₂²⋊Dic₄₇	C₂×C₈	1	8	yes	—
133	C₄⋊Dic₄₇	—	2	2	no	—
134	C₄⋊Dic₄₇	C₂×C₈	1	4	yes	—
135	C₄×Dic₄₇	—	2	2	no	—
136	C₄×Dic₄₇	—	2	1	no	—
137	C₄×Dic₄₇	—	2	1	no	—
138	C₄×Dic₄₇	—	2	2	no	—
139	C₄×Dic₄₇	—	2	4	no	—
140	C₄×Dic₄₇	—	2	4	no	—
141	C₄×Dic₄₇	—	2	2	no	—
142	C₄×Dic₄₇	—	2	2	no	—
143	C₄×Dic₄₇	C₂×C₈	1	4	yes	—
144	C₄×Dic₄₇	M₁₆	1	4	yes	—
145	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
146	C₄×Dic₄₇	#41	1	2	yes	—
147	C₂×C₄₇⋊C₈	—	2	1	no	—
148	C₂×C₄₇⋊C₈	—	2	1	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	1	no	—
151	C₂×C₄₇⋊C₈	—	2	2	no	—
152	C₂×C₄₇⋊C₈	—	2	2	no	—
153	C₂×C₄₇⋊C₈	—	2	2	no	—
154	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
155	C₂×C₄₇⋊C₈	#41	1	2	yes	—
156	C₂³×C₄₇	—	2	2	no	—
157	C₂³×C₄₇	—	2	2	no	—
158	C₂³×C₄₇	—	2	2	no	—
159	C₂³×C₄₇	—	2	2	no	—
160	C₂³×C₄₇	—	2	2	no	—
161	C₂³×C₄₇	—	2	2	no	—
162	C₂³×C₄₇	C₂²×C₈	1	4	yes	—
163	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
164	D₄×C₄₇	—	2	8	no	—
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	—	4	2	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	#117	1	2	yes	—
175	C₂×C₄×C₄₇	#117	1	2	yes	—
176	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
177	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
178	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
184	C₂×Dic₄₇	—	2	2	no	—
185	C₂×Dic₄₇	—	2	1	no	—
186	C₂×Dic₄₇	—	2	1	no	—
187	C₂×Dic₄₇	—	2	1	no	—
188	C₂×Dic₄₇	—	2	1	no	—
189	C₂×Dic₄₇	—	2	2	no	—
190	C₂×Dic₄₇	—	2	16	no	—
191	C₂×Dic₄₇	—	2	2	no	—
192	C₂×Dic₄₇	—	2	2	no	—
193	C₂×Dic₄₇	—	2	2	no	—
194	C₂×Dic₄₇	—	4	8	no	—
195	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
196	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
197	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
198	C₂×Dic₄₇	C₂²×C₈	1	4	yes	—
199	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
200	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
201	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
202	C₂×Dic₄₇	#131	1	2	yes	—
203	C₂×Dic₄₇	#131	1	2	yes	—
204	C₈×C₄₇	—	2	2	no	—
205	C₈×C₄₇	—	2	2	no	—
206	C₈×C₄₇	—	4	2	no	—
207	C₄₇⋊C₈	—	2	2	no	—
208	C₄₇⋊C₈	—	2	2	no	—
209	C₄₇⋊C₈	—	4	2	no	—
210	#21264	—	47	1	no	maximal, Sylow
211	C₂²×C₄₇	—	2	4	no	—
212	C₂²×C₄₇	—	2	4	no	—
213	C₂²×C₄₇	—	2	4	no	—
214	C₂²×C₄₇	—	4	2	no	—
215	C₂²×C₄₇	—	4	2	no	—
216	C₂²×C₄₇	—	4	2	no	—
217	C₂²×C₄₇	—	4	2	no	—
218	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
219	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
220	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
221	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
222	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
223	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
224	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
225	C₄×C₄₇	—	2	2	no	—
226	C₄×C₄₇	—	4	2	no	—
227	C₄×C₄₇	#431	1	4	yes	complemented
228	C₄×C₄₇	#529	1	1	yes	characteristic
229	C₄×C₄₇	#529	1	1	yes	characteristic
230	C₄×C₄₇	#532	1	1	yes	characteristic
231	C₄×C₄₇	#532	1	1	yes	characteristic
232	Dic₄₇	—	2	4	no	—
233	Dic₄₇	—	2	2	no	—
234	Dic₄₇	—	2	2	no	—
235	Dic₄₇	—	4	2	no	—
236	Dic₄₇	C₈×D₄	1	4	yes	—
237	Dic₄₇	#436	1	4	yes	—
238	C₂×#431	—	47	2	no	—
239	C₄²×D₄	—	47	1	no	—
240	#1954	—	47	1	no	—
241	#1954	D₄₇	1	1	yes	characteristic
242	#1939	—	47	1	no	—
243	#1939	—	47	1	no	—
244	#1923	—	47	2	no	—
245	#1923	—	47	2	no	—
246	C₄×C₄⋊C₈	—	47	1	no	—
247	C₄×C₂²⋊C₈	—	47	2	no	—
248	C₄²×C₈	—	47	1	no	—
249	C₂×C₄₇	—	4	4	no	—
250	C₂×C₄₇	#2293	1	1	yes	characteristic
251	C₂×C₄₇	C₂×#431	1	1	yes	characteristic
252	C₂×C₄₇	#2922	1	1	yes	characteristic
253	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
254	C₂×C₄₇	C₂×#436	1	1	yes	characteristic
255	C₂×C₄₇	C₈×#41	1	1	yes	characteristic
256	C₂×C₄₇	#2965	1	1	yes	characteristic
257	C₂×C₄×D₄	—	47	1	no	—
258	C₂×C₄×D₄	—	47	1	no	—
259	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
260	C₂²×C₄²	—	47	2	no	—
261	#431	—	94	8	no	—
262	C₂×C₄⋊C₈	—	47	2	no	—
263	C₂×C₄⋊C₈	—	47	2	no	—
264	C₂×C₄⋊C₈	—	47	1	no	—
265	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
266	C₂×C₂²⋊C₈	—	47	2	no	—
267	C₂×C₂²⋊C₈	—	47	2	no	—
268	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
269	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
270	C₂×C₄×C₈	—	47	1	no	—
271	C₂×C₄×C₈	—	47	2	no	—
272	C₂×C₄×C₈	—	47	1	no	—
273	C₂×C₄×C₈	—	47	1	no	—
274	C₂×C₄×C₈	—	47	1	no	—
275	C₂×C₄×C₈	—	47	1	no	—
276	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
277	C₄×C₄⋊C₄	—	47	1	no	—
278	C₄×C₄⋊C₄	—	47	1	no	—
279	C₄×C₄⋊C₄	—	47	1	no	—
280	C₄×C₂²⋊C₄	—	47	2	no	—
281	C₄×C₂²⋊C₄	—	47	2	no	—
282	C₄×C₂²⋊C₄	—	47	2	no	—
283	C₄³	—	47	1	no	—
284	#336	—	47	2	no	—
285	#336	—	47	2	no	—
286	#336	—	47	2	no	—
287	C₄₇	#21264	1	1	yes	characteristic, complemented, Sylow
288	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
289	C₂³×C₄	—	47	2	no	—
290	C₂³×C₄	—	47	2	no	—
291	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
292	C₂²×C₈	—	47	1	no	—
293	C₂²×C₈	—	47	1	no	—
294	C₂²×C₈	—	47	2	no	—
295	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
296	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
297	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
298	C₄×D₄	—	2	2	no	—
299	C₄×D₄	—	2	2	no	—
300	C₄×D₄	—	47	8	no	—
301	C₄×D₄	—	94	4	no	—
302	C₂×C₄⋊C₄	—	47	1	no	—
303	C₂×C₄⋊C₄	—	47	1	no	—
304	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
305	C₂×C₂²⋊C₄	—	47	2	no	—
306	C₂×C₂²⋊C₄	—	47	2	no	—
307	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
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	2	no	—
314	C₂×C₄²	—	47	2	no	—
315	C₂×C₄²	—	47	1	no	—
316	C₂×C₄²	—	47	2	no	—
317	C₂×C₄²	—	94	4	no	—
318	C₂×C₄²	—	94	4	no	—
319	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
320	C₄⋊C₈	—	2	2	no	—
321	C₄⋊C₈	—	94	4	no	—
322	C₄⋊C₈	—	94	4	no	—
323	C₄⋊C₈	—	94	2	no	—
324	C₂²⋊C₈	—	2	4	no	—
325	C₂²⋊C₈	—	2	4	no	—
326	C₂²⋊C₈	—	94	4	no	—
327	C₂²⋊C₈	—	94	4	no	—
328	C₄×C₈	—	2	2	no	—
329	C₄×C₈	—	47	4	no	—
330	C₄×C₈	—	94	2	no	—
331	C₄×C₈	—	94	4	no	—
332	C₄×C₈	—	94	2	no	—
333	C₄×C₈	—	94	2	no	—
334	C₄×C₈	—	94	2	no	—
335	#95	—	47	2	no	—
336	#95	—	47	2	no	—
337	#95	—	47	2	no	—
338	C₂⁴	C₂×C₄×D₄₇	1	2	yes	—
339	C₂×D₄	—	2	2	no	—
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	C₈×D₄₇	1	4	yes	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	47	1	no	—
349	C₂²×C₄	—	47	1	no	—
350	C₂²×C₄	—	47	8	no	—
351	C₂²×C₄	—	47	1	no	—
352	C₂²×C₄	—	47	1	no	—
353	C₂²×C₄	—	47	2	no	—
354	C₂²×C₄	—	47	2	no	—
355	C₂²×C₄	—	94	4	no	—
356	C₂²×C₄	—	94	4	no	—
357	C₂²×C₄	—	94	4	no	—
358	C₂²×C₄	—	94	4	no	—
359	C₂²×C₄	—	94	4	no	—
360	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
361	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
362	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
363	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	—	2	1	no	—
368	C₂×C₈	—	2	2	no	—
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	47	2	no	—
372	C₂×C₈	—	47	2	no	—
373	C₂×C₈	—	94	1	no	—
374	C₂×C₈	—	94	1	no	—
375	C₂×C₈	—	94	1	no	—
376	C₂×C₈	—	94	1	no	—
377	C₂×C₈	—	94	2	no	—
378	C₂×C₈	—	94	2	no	—
379	C₂×C₈	—	94	2	no	—
380	C₂×C₈	D₄×D₄₇	1	2	yes	—
381	C₂×C₈	#10625352	1	2	yes	—
382	C₄⋊C₄	—	2	2	no	—
383	C₄⋊C₄	—	47	4	no	—
384	C₄⋊C₄	—	94	2	no	—
385	C₂²⋊C₄	—	2	4	no	—
386	C₂²⋊C₄	—	47	8	no	—
387	C₂²⋊C₄	—	94	4	no	—
388	C₄²	—	47	4	no	—
389	C₄²	—	47	4	no	—
390	C₄²	—	47	2	no	—
391	C₄²	—	47	2	no	—
392	C₄²	—	94	2	no	—
393	C₄²	—	94	2	no	—
394	C₄²	—	94	4	no	—
395	C₄²	—	94	4	no	—
396	C₄²	—	94	2	no	—
397	C₄²	—	94	1	no	—
398	C₄²	—	94	2	no	—
399	C₄²	—	94	1	no	—
400	C₄²	#10625352	1	2	yes	—
401	C₄²	#10625352	1	2	yes	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	C₂×C₈×D₄₇	1	4	yes	—
409	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
410	D₄	—	2	8	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	1	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	47	2	no	—
421	C₂×C₄	—	47	2	no	—
422	C₂×C₄	—	47	2	no	—
423	C₂×C₄	—	47	2	no	—
424	C₂×C₄	—	47	2	no	—
425	C₂×C₄	—	47	2	no	—
426	C₂×C₄	—	47	2	no	—
427	C₂×C₄	—	47	4	no	—
428	C₂×C₄	—	47	2	no	—
429	C₂×C₄	—	94	16	no	—
430	C₂×C₄	—	94	2	no	—
431	C₂×C₄	—	94	1	no	—
432	C₂×C₄	—	94	1	no	—
433	C₂×C₄	—	94	1	no	—
434	C₂×C₄	—	94	1	no	—
435	C₂×C₄	—	94	2	no	—
436	C₂×C₄	—	94	2	no	—
437	C₂×C₄	—	94	2	no	—
438	C₂×C₄	—	94	2	no	—
439	C₂×C₄	—	188	8	no	—
440	C₂×C₄	#13093980	1	2	yes	—
441	C₂×C₄	#13093980	1	2	yes	—
442	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
443	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
444	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
445	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
446	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
447	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
448	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
449	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
450	C₈	—	2	2	no	—
451	C₈	—	2	2	no	—
452	C₈	—	4	2	no	—
453	C₈	—	94	2	no	—
454	C₈	—	94	2	no	—
455	C₈	—	188	2	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	2	4	no	—
458	C₂²	—	2	4	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	4	2	no	—
461	C₂²	—	4	2	no	—
462	C₂²	—	4	2	no	—
463	C₂²	C₂×#13093980	1	1	yes	characteristic
464	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
465	C₂²	C₄×#10625352	1	1	yes	characteristic
466	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
467	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
468	C₂²	#131×D₄₇	1	1	yes	characteristic
469	C₂²	#131×D₄₇	1	1	yes	characteristic
470	C₄	—	2	2	no	—
471	C₄	—	4	2	no	—
472	C₄	—	47	4	no	—
473	C₄	—	47	4	no	—
474	C₄	—	94	4	no	—
475	C₄	—	94	2	no	—
476	C₄	—	94	2	no	—
477	C₄	—	188	2	no	—
478	C₄	#15689173	1	4	yes	complemented
479	C₄	#15689652	1	1	yes	characteristic
480	C₄	#15689654	1	1	yes	characteristic
481	C₄	#15689668	1	1	yes	characteristic
482	C₄	#15689671	1	1	yes	characteristic
483	C₂	—	4	4	no	—
484	C₂	#20245850	1	1	yes	characteristic
485	C₂	C₂×#15689173	1	1	yes	characteristic
486	C₂	#20252028	1	1	yes	characteristic
487	C₂	C₈×D₄×D₄₇	1	1	yes	characteristic
488	C₂	#436×D₄₇	1	1	yes	characteristic
489	C₂	C₈×#10625352	1	1	yes	characteristic
490	C₂	#20252351	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Fitting	C₄₇×#1954	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1954	D₄₇
hypocenter	C₄₇	#21264
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1954

Complements

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

N	H ≅ G/N	type
1. C₂×#15689173	C₂	semidirect
4. #20244106	C₂	semidirect
5. #20244104	C₂	semidirect
6. #20243997	C₂	semidirect
7. #20243991	C₂	semidirect
8. C₄⋊C₈×Dic₄₇	C₂	semidirect
9. C₂²⋊C₈×Dic₄₇	C₂	semidirect
10. C₄×C₈×Dic₄₇	C₂	semidirect
48. D₄×Dic₄₇	C₈	semidirect
74. C₈×Dic₄₇	D₄	semidirect
227. C₄×C₄₇	#431	semidirect
287. C₄₇	#21264	semidirect
478. 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
C₄×D₄×Dic₄₇	2
#20244183	2
#20244106	2
#20244104	2
#20243997	2
#20243991	2
C₄⋊C₈×Dic₄₇	2
C₂²⋊C₈×Dic₄₇	2
C₄×C₈×Dic₄₇	2
C₄₇×#1954	2
#21264	47