Subgroups — #26223756

Order 12032.

886 conjugacy classes of subgroups.

The subgroup lattice has 644 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689250	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄×#13094001	C₂	1	1	yes	maximal, characteristic
4	#20244326	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244108	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243946	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243942	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243571	C₂	1	1	yes	maximal, characteristic
9	#20243366	C₂	1	1	yes	maximal, characteristic
10	#20243265	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243261	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243249	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243174	C₂	1	1	yes	maximal, characteristic
14	#20243172	C₂	1	1	yes	maximal, characteristic
15	C₄₇×#1851	C₂	1	1	yes	maximal, characteristic
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂×#13094001	C₄	1	1	yes	characteristic
18	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
19	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
20	#15689250	—	2	4	no	—
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×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
26	M₁₆×Dic₄₇	—	2	4	no	—
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×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	#15689027	C₄	1	1	yes	characteristic
36	#15689020	C₄	1	1	yes	characteristic
37	#15689010	C₄	1	1	yes	characteristic
38	#15689006	C₄	1	1	yes	characteristic
39	#15688998	C₄	1	1	yes	characteristic
40	#15688995	C₄	1	1	yes	characteristic
41	#15688981	C₄	1	1	yes	characteristic
42	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
43	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
45	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
46	#15688878	C₂²	1	1	yes	characteristic
47	#15688878	C₂²	1	1	yes	characteristic
48	#15688877	C₂²	1	1	yes	characteristic
49	#15688877	C₂²	1	1	yes	characteristic
50	#15688877	C₂²	1	1	yes	characteristic
51	#15688877	C₂²	1	1	yes	characteristic
52	#15688877	C₂²	1	1	yes	characteristic
53	#15688877	C₂²	1	1	yes	characteristic
54	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
55	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
56	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
57	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
58	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
59	C₄₇×#336	C₂²	1	1	yes	characteristic
60	C₄₇×#336	C₂²	1	1	yes	characteristic
61	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
62	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂³×Dic₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂×#10625329	—	2	2	no	—
65	C₂×#10625329	—	2	2	no	—
66	C₂×#10625329	Q₈	1	4	yes	complemented
67	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
71	#13094001	—	2	4	no	—
72	C₄×Dic₉₄	—	2	2	no	—
73	C₄×Dic₉₄	—	2	2	no	—
74	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
76	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
77	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
78	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
79	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
80	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
81	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
83	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄×Dic₄₇	—	2	2	no	—
86	C₂×C₄×Dic₄₇	—	2	2	no	—
87	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
89	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
90	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
91	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
92	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
93	Dic₄₇⋊C₈	—	2	2	no	—
94	Dic₄₇⋊C₈	—	2	2	no	—
95	Dic₄₇⋊C₈	—	2	2	no	—
96	Dic₄₇⋊C₈	—	2	2	no	—
97	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
98	#13093935	—	2	2	no	—
99	#13093934	—	2	2	no	—
100	#13093934	—	2	2	no	—
101	#13093934	D₄	1	4	yes	—
102	C₄×C₄₇⋊C₈	—	2	2	no	—
103	C₈×Dic₄₇	—	2	2	no	—
104	C₈×Dic₄₇	—	2	2	no	—
105	C₈×Dic₄₇	—	2	2	no	—
106	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
107	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
108	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
109	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
110	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
111	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
112	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
113	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
114	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
115	C₂×M₁₆×C₄₇	—	2	2	no	—
116	C₂×M₁₆×C₄₇	—	2	2	no	—
117	C₂×M₁₆×C₄₇	—	2	2	no	—
118	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
119	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
122	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
123	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
124	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
125	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
126	C₄⋊C₈×C₄₇	—	2	2	no	—
127	C₄⋊C₈×C₄₇	—	2	2	no	—
128	C₂²⋊C₈×C₄₇	—	2	2	no	—
129	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
130	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
131	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	—	2	1	no	—
133	C₂²×C₄×C₄₇	—	2	1	no	—
134	C₂²×C₄×C₄₇	—	2	1	no	—
135	C₂²×C₄×C₄₇	—	2	1	no	—
136	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
142	C₂²×C₄×C₄₇	#41	1	2	yes	—
143	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
144	C₂²×Dic₄₇	—	2	2	no	—
145	C₂²×Dic₄₇	—	2	2	no	—
146	C₂²×Dic₄₇	—	2	2	no	—
147	C₂²×Dic₄₇	—	2	2	no	—
148	C₂²×Dic₄₇	—	4	1	no	—
149	C₂²×Dic₄₇	—	4	1	no	—
150	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
151	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
152	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
153	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
154	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
155	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
156	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
157	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
158	C₂×Dic₉₄	—	2	2	no	—
159	C₂×Dic₉₄	—	2	2	no	—
160	C₂×Dic₉₄	—	4	1	no	—
161	M₁₆×C₄₇	—	2	8	no	—
162	C₂×C₈×C₄₇	—	2	1	no	—
163	C₂×C₈×C₄₇	—	2	1	no	—
164	C₂×C₈×C₄₇	—	2	1	no	—
165	C₂×C₈×C₄₇	—	2	1	no	—
166	C₂×C₈×C₄₇	—	2	1	no	—
167	C₂×C₈×C₄₇	—	2	1	no	—
168	C₂×C₈×C₄₇	—	2	1	no	—
169	C₂×C₈×C₄₇	—	2	1	no	—
170	C₂×C₈×C₄₇	—	2	1	no	—
171	C₂×C₈×C₄₇	—	2	1	no	—
172	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
173	C₂×C₈×C₄₇	#41	1	2	yes	—
174	C₂²⋊C₄×C₄₇	—	2	2	no	—
175	C₂²⋊C₄×C₄₇	—	4	1	no	—
176	C₄²×C₄₇	—	2	1	no	—
177	C₄²×C₄₇	—	2	1	no	—
178	C₄²×C₄₇	—	2	1	no	—
179	C₄²×C₄₇	—	2	1	no	—
180	C₂²⋊Dic₄₇	—	2	2	no	—
181	C₂²⋊Dic₄₇	—	4	1	no	—
182	C₄⋊Dic₄₇	—	2	2	no	—
183	C₄⋊Dic₄₇	—	2	2	no	—
184	C₄⋊Dic₄₇	—	2	2	no	—
185	Dic₄₇⋊C₄	—	2	2	no	—
186	Dic₄₇⋊C₄	—	2	2	no	—
187	Dic₄₇⋊C₄	—	2	2	no	—
188	Dic₄₇⋊C₄	—	2	2	no	—
189	Dic₄₇⋊C₄	—	4	1	no	—
190	Dic₄₇⋊C₄	M₁₆	1	4	yes	complemented
191	C₄×Dic₄₇	—	2	1	no	—
192	C₄×Dic₄₇	—	2	1	no	—
193	C₄×Dic₄₇	—	2	1	no	—
194	C₄×Dic₄₇	—	2	1	no	—
195	C₄×Dic₄₇	—	2	1	no	—
196	C₄×Dic₄₇	—	2	1	no	—
197	C₄×Dic₄₇	—	2	2	no	—
198	C₄×Dic₄₇	—	2	2	no	—
199	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
200	C₄×Dic₄₇	#41	1	2	yes	—
201	#10625329	—	2	8	no	—
202	C₂×C₄₇⋊C₈	—	2	1	no	—
203	C₂×C₄₇⋊C₈	—	2	1	no	—
204	C₂×C₄₇⋊C₈	—	2	1	no	—
205	C₂×C₄₇⋊C₈	—	2	1	no	—
206	C₂×C₄₇⋊C₈	—	2	1	no	—
207	C₂×C₄₇⋊C₈	—	2	1	no	—
208	C₂×C₄₇⋊C₈	—	2	1	no	—
209	C₂×C₄₇⋊C₈	—	2	1	no	—
210	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
211	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
212	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
213	C₂×C₄₇⋊C₈	#41	1	2	yes	—
214	C₂³×C₄₇	—	2	1	no	—
215	C₂³×C₄₇	—	2	1	no	—
216	C₂³×C₄₇	—	2	1	no	—
217	C₂³×C₄₇	—	2	1	no	—
218	C₂³×C₄₇	—	2	1	no	—
219	C₂³×C₄₇	—	2	1	no	—
220	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
221	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
222	C₂×C₄×C₄₇	—	2	1	no	—
223	C₂×C₄×C₄₇	—	2	1	no	—
224	C₂×C₄×C₄₇	—	2	1	no	—
225	C₂×C₄×C₄₇	—	2	1	no	—
226	C₂×C₄×C₄₇	—	2	2	no	—
227	C₂×C₄×C₄₇	—	2	2	no	—
228	C₂×C₄×C₄₇	—	2	2	no	—
229	C₂×C₄×C₄₇	—	2	2	no	—
230	C₂×C₄×C₄₇	—	2	1	no	—
231	C₂×C₄×C₄₇	—	2	1	no	—
232	C₂×C₄×C₄₇	—	2	1	no	—
233	C₂×C₄×C₄₇	—	2	1	no	—
234	C₂×C₄×C₄₇	—	2	1	no	—
235	C₂×C₄×C₄₇	—	2	1	no	—
236	C₂×C₄×C₄₇	—	2	1	no	—
237	C₂×C₄×C₄₇	—	2	1	no	—
238	C₂×C₄×C₄₇	—	2	1	no	—
239	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
240	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
241	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
242	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
243	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
244	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
245	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
246	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
247	C₂×Dic₄₇	—	2	1	no	—
248	C₂×Dic₄₇	—	2	1	no	—
249	C₂×Dic₄₇	—	2	1	no	—
250	C₂×Dic₄₇	—	2	1	no	—
251	C₂×Dic₄₇	—	2	1	no	—
252	C₂×Dic₄₇	—	2	1	no	—
253	C₂×Dic₄₇	—	2	1	no	—
254	C₂×Dic₄₇	—	2	1	no	—
255	C₂×Dic₄₇	—	2	1	no	—
256	C₂×Dic₄₇	—	2	1	no	—
257	C₂×Dic₄₇	—	2	1	no	—
258	C₂×Dic₄₇	—	2	1	no	—
259	C₂×Dic₄₇	—	2	1	no	—
260	C₂×Dic₄₇	—	2	1	no	—
261	C₂×Dic₄₇	—	2	1	no	—
262	C₂×Dic₄₇	—	2	1	no	—
263	C₂×Dic₄₇	—	2	1	no	—
264	C₂×Dic₄₇	—	2	1	no	—
265	C₂×Dic₄₇	—	2	1	no	—
266	C₂×Dic₄₇	—	4	4	no	—
267	C₂×Dic₄₇	—	4	4	no	—
268	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
269	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
270	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
271	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
272	C₂×Dic₄₇	#131	1	2	yes	—
273	Dic₉₄	—	4	4	no	—
274	C₈×C₄₇	—	2	2	no	—
275	C₈×C₄₇	—	2	2	no	—
276	C₈×C₄₇	—	4	1	no	—
277	C₈×C₄₇	—	4	1	no	—
278	C₄₇⋊C₈	—	2	2	no	—
279	C₄₇⋊C₈	—	4	1	no	—
280	C₄₇⋊C₈	—	4	1	no	—
281	C₄₇⋊C₈	C₂²⋊Q₈	1	4	yes	complemented
282	#21600	—	47	1	no	maximal, Sylow
283	C₂²×C₄₇	—	2	2	no	—
284	C₂²×C₄₇	—	2	2	no	—
285	C₂²×C₄₇	—	2	2	no	—
286	C₂²×C₄₇	—	4	1	no	—
287	C₂²×C₄₇	—	4	1	no	—
288	C₂²×C₄₇	—	4	1	no	—
289	C₂²×C₄₇	—	4	1	no	—
290	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
291	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
292	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
293	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
294	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
295	C₂²×C₄₇	#568	1	1	yes	characteristic
296	C₂²×C₄₇	#568	1	1	yes	characteristic
297	C₄×C₄₇	—	2	2	no	—
298	C₄×C₄₇	—	2	2	no	—
299	C₄×C₄₇	—	4	1	no	—
300	C₄×C₄₇	—	4	1	no	—
301	C₄×C₄₇	—	4	1	no	—
302	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
303	C₄×C₄₇	#525	1	1	yes	characteristic
304	C₄×C₄₇	#529	1	1	yes	characteristic
305	C₄×C₄₇	#533	1	1	yes	characteristic
306	Dic₄₇	—	2	2	no	—
307	Dic₄₇	—	2	2	no	—
308	Dic₄₇	—	2	2	no	—
309	Dic₄₇	—	2	2	no	—
310	Dic₄₇	—	2	2	no	—
311	Dic₄₇	—	4	1	no	—
312	Dic₄₇	—	4	1	no	—
313	Dic₄₇	—	4	1	no	—
314	C₂×#446	—	47	1	no	—
315	C₂×C₄×M₁₆	—	47	1	no	—
316	C₄×C₂²⋊Q₈	—	47	1	no	—
317	#1985	—	47	1	no	—
318	#1940	—	47	1	no	—
319	#1916	—	47	1	no	—
320	#1916	—	47	1	no	—
321	#1851	—	47	1	no	—
322	#1851	D₄₇	1	1	yes	characteristic
323	#1797	—	47	1	no	—
324	#1771	—	47	1	no	—
325	#1771	—	47	1	no	—
326	C₈×C₄⋊C₄	—	47	1	no	—
327	#1753	—	47	1	no	—
328	#1753	—	47	1	no	—
329	C₂×C₄₇	—	4	2	no	—
330	C₂×C₄₇	C₄×C₂²⋊Q₈	1	1	yes	characteristic
331	C₂×C₄₇	#2933	1	1	yes	characteristic
332	C₂×C₄₇	D₄×M₁₆	1	1	yes	characteristic
333	C₂×C₄₇	#2962	1	1	yes	characteristic
334	C₂×C₄₇	Q₈×M₁₆	1	1	yes	characteristic
335	C₂×C₄₇	#2965	1	1	yes	characteristic
336	C₂×C₄₇	#2967	1	1	yes	characteristic
337	C₂²×M₁₆	—	47	1	no	—
338	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
339	C₂×C₂²⋊Q₈	—	47	1	no	—
340	C₂×C₄×Q₈	—	47	1	no	—
341	C₂²×C₄²	—	47	1	no	—
342	#446	—	94	4	no	—
343	C₂×C₄⋊C₈	—	47	1	no	—
344	C₂×C₄⋊C₈	—	47	1	no	—
345	C₂×C₄⋊C₈	—	47	1	no	—
346	C₂×C₄⋊C₈	—	47	1	no	—
347	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
348	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
349	C₂×C₂²⋊C₈	—	47	1	no	—
350	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
351	C₄×M₁₆	—	94	4	no	—
352	C₂×#97	—	47	1	no	—
353	C₂×#97	—	47	1	no	—
354	C₂×#97	—	47	1	no	—
355	C₂×#97	—	47	1	no	—
356	C₂×C₄×C₈	—	47	1	no	—
357	C₂×C₄×C₈	—	47	1	no	—
358	C₂×C₄×C₈	—	47	1	no	—
359	C₂×C₄×C₈	—	47	1	no	—
360	#391	—	47	1	no	—
361	#389	—	47	1	no	—
362	#387	—	47	1	no	—
363	#387	—	47	1	no	—
364	#385	—	47	1	no	—
365	#385	—	47	1	no	—
366	#380	—	47	1	no	—
367	C₄×C₄⋊C₄	—	47	1	no	—
368	C₄×C₄⋊C₄	—	47	1	no	—
369	C₄×C₄⋊C₄	—	47	1	no	—
370	C₄×C₂²⋊C₄	—	47	1	no	—
371	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
372	#336	—	47	1	no	—
373	#336	—	47	1	no	—
374	#336	—	47	1	no	—
375	#336	—	47	1	no	—
376	#336	—	47	1	no	—
377	#336	—	47	1	no	—
378	#336	—	47	1	no	—
379	#336	—	47	1	no	—
380	#336	C₂×D₄₇	1	1	yes	characteristic
381	#336	C₂×D₄₇	1	1	yes	characteristic
382	C₄₇	#21600	1	1	yes	characteristic, complemented, Sylow
383	C₂²×Q₈	—	47	1	no	—
384	C₂³×C₄	—	47	1	no	—
385	C₂³×C₄	—	47	1	no	—
386	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
387	C₂×M₁₆	—	2	2	no	—
388	C₂×M₁₆	—	2	2	no	—
389	C₂×M₁₆	—	2	2	no	—
390	C₂×M₁₆	—	47	4	no	—
391	C₂×M₁₆	—	94	2	no	—
392	C₂×M₁₆	—	94	2	no	—
393	C₂²×C₈	—	47	1	no	—
394	C₂²×C₈	—	47	1	no	—
395	C₂²×C₈	—	47	1	no	—
396	C₂²×C₈	—	47	1	no	—
397	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
398	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
399	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
400	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
401	C₂²⋊Q₈	—	94	4	no	—
402	C₄×Q₈	—	94	2	no	—
403	C₄×Q₈	—	94	2	no	—
404	C₂×C₄⋊C₄	—	47	1	no	—
405	C₂×C₄⋊C₄	—	47	1	no	—
406	C₂×C₄⋊C₄	—	47	1	no	—
407	C₂×C₄⋊C₄	—	47	1	no	—
408	C₂×C₄⋊C₄	—	47	1	no	—
409	C₂×C₄⋊C₄	—	47	1	no	—
410	C₂×C₄⋊C₄	—	47	1	no	—
411	C₂×C₄⋊C₄	—	47	1	no	—
412	C₂×C₄⋊C₄	—	47	1	no	—
413	C₂×C₂²⋊C₄	—	47	1	no	—
414	C₂×C₂²⋊C₄	—	47	1	no	—
415	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
416	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
417	C₂×C₄²	—	47	1	no	—
418	C₂×C₄²	—	47	1	no	—
419	C₂×C₄²	—	47	1	no	—
420	C₂×C₄²	—	47	1	no	—
421	C₂×C₄²	—	47	1	no	—
422	C₂×C₄²	—	47	1	no	—
423	C₂×C₄²	—	94	2	no	—
424	C₂×C₄²	—	94	2	no	—
425	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
426	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
427	C₄⋊C₈	—	2	2	no	—
428	C₄⋊C₈	—	2	2	no	—
429	C₄⋊C₈	—	94	2	no	—
430	C₄⋊C₈	—	94	2	no	—
431	C₄⋊C₈	—	94	2	no	—
432	C₄⋊C₈	—	94	2	no	—
433	C₂²⋊C₈	—	2	2	no	—
434	C₂²⋊C₈	—	94	2	no	—
435	#97	—	47	4	no	—
436	#97	—	94	2	no	—
437	#97	—	94	2	no	—
438	#97	—	94	2	no	—
439	C₄×C₈	—	94	2	no	—
440	C₄×C₈	—	94	2	no	—
441	C₄×C₈	—	94	2	no	—
442	C₄×C₈	—	94	2	no	—
443	#95	—	47	1	no	—
444	#95	—	47	1	no	—
445	#95	—	47	1	no	—
446	#95	—	47	1	no	—
447	#95	—	47	1	no	—
448	#95	—	47	1	no	—
449	#95	—	47	1	no	—
450	#95	—	47	1	no	—
451	#95	C₄×D₄₇	1	1	yes	characteristic
452	#95	C₄×D₄₇	1	1	yes	characteristic
453	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
454	C₂×Q₈	—	94	2	no	—
455	C₂×Q₈	—	94	2	no	—
456	C₂×Q₈	—	188	1	no	—
457	C₂²×C₄	—	2	1	no	—
458	C₂²×C₄	—	2	1	no	—
459	C₂²×C₄	—	2	1	no	—
460	C₂²×C₄	—	2	1	no	—
461	C₂²×C₄	—	47	1	no	—
462	C₂²×C₄	—	47	1	no	—
463	C₂²×C₄	—	47	1	no	—
464	C₂²×C₄	—	47	1	no	—
465	C₂²×C₄	—	47	1	no	—
466	C₂²×C₄	—	47	1	no	—
467	C₂²×C₄	—	47	1	no	—
468	C₂²×C₄	—	47	1	no	—
469	C₂²×C₄	—	94	2	no	—
470	C₂²×C₄	—	94	2	no	—
471	C₂²×C₄	—	94	2	no	—
472	C₂²×C₄	—	94	2	no	—
473	C₂²×C₄	—	188	1	no	—
474	C₂²×C₄	—	188	1	no	—
475	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
476	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
477	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
478	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
479	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
480	C₂²×C₄	#10625352	1	2	yes	—
481	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
482	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
483	M₁₆	—	2	8	no	—
484	M₁₆	—	94	8	no	—
485	C₂×C₈	—	2	1	no	—
486	C₂×C₈	—	2	1	no	—
487	C₂×C₈	—	2	1	no	—
488	C₂×C₈	—	2	1	no	—
489	C₂×C₈	—	2	1	no	—
490	C₂×C₈	—	2	1	no	—
491	C₂×C₈	—	2	1	no	—
492	C₂×C₈	—	2	1	no	—
493	C₂×C₈	—	2	1	no	—
494	C₂×C₈	—	2	1	no	—
495	C₂×C₈	—	47	2	no	—
496	C₂×C₈	—	47	2	no	—
497	C₂×C₈	—	47	2	no	—
498	C₂×C₈	—	47	2	no	—
499	C₂×C₈	—	94	1	no	—
500	C₂×C₈	—	94	1	no	—
501	C₂×C₈	—	94	1	no	—
502	C₂×C₈	—	94	1	no	—
503	C₂×C₈	—	94	1	no	—
504	C₂×C₈	—	94	1	no	—
505	C₂×C₈	—	94	1	no	—
506	C₂×C₈	—	94	1	no	—
507	C₂×C₈	D₄×D₄₇	1	2	yes	—
508	C₂×C₈	#10625352	1	2	yes	—
509	C₄⋊C₄	—	47	4	no	—
510	C₄⋊C₄	—	94	2	no	—
511	C₄⋊C₄	—	94	2	no	—
512	C₄⋊C₄	—	94	2	no	—
513	C₄⋊C₄	—	94	2	no	—
514	C₄⋊C₄	—	94	2	no	—
515	C₄⋊C₄	—	94	2	no	—
516	C₄⋊C₄	—	94	2	no	—
517	C₄⋊C₄	—	188	1	no	—
518	C₂²⋊C₄	—	2	2	no	—
519	C₂²⋊C₄	—	4	1	no	—
520	C₂²⋊C₄	—	94	2	no	—
521	C₂²⋊C₄	—	188	1	no	—
522	C₄²	—	2	1	no	—
523	C₄²	—	2	1	no	—
524	C₄²	—	2	1	no	—
525	C₄²	—	2	1	no	—
526	C₄²	—	47	2	no	—
527	C₄²	—	47	2	no	—
528	C₄²	—	94	2	no	—
529	C₄²	—	94	2	no	—
530	C₄²	—	94	1	no	—
531	C₄²	—	94	1	no	—
532	C₄²	—	94	1	no	—
533	C₄²	—	94	1	no	—
534	C₄²	—	94	1	no	—
535	C₄²	—	94	1	no	—
536	C₂³	—	2	1	no	—
537	C₂³	—	2	1	no	—
538	C₂³	—	2	1	no	—
539	C₂³	—	2	1	no	—
540	C₂³	—	2	1	no	—
541	C₂³	—	2	1	no	—
542	C₂³	#13093989	1	2	yes	—
543	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
544	Q₈	—	188	4	no	—
545	C₂×C₄	—	2	1	no	—
546	C₂×C₄	—	2	1	no	—
547	C₂×C₄	—	2	1	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	2	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	2	1	no	—
554	C₂×C₄	—	2	1	no	—
555	C₂×C₄	—	2	1	no	—
556	C₂×C₄	—	2	1	no	—
557	C₂×C₄	—	2	1	no	—
558	C₂×C₄	—	2	1	no	—
559	C₂×C₄	—	2	1	no	—
560	C₂×C₄	—	2	1	no	—
561	C₂×C₄	—	2	1	no	—
562	C₂×C₄	—	47	2	no	—
563	C₂×C₄	—	47	2	no	—
564	C₂×C₄	—	47	2	no	—
565	C₂×C₄	—	47	2	no	—
566	C₂×C₄	—	47	2	no	—
567	C₂×C₄	—	94	1	no	—
568	C₂×C₄	—	94	1	no	—
569	C₂×C₄	—	94	1	no	—
570	C₂×C₄	—	94	1	no	—
571	C₂×C₄	—	94	1	no	—
572	C₂×C₄	—	94	1	no	—
573	C₂×C₄	—	94	1	no	—
574	C₂×C₄	—	94	1	no	—
575	C₂×C₄	—	94	1	no	—
576	C₂×C₄	—	94	1	no	—
577	C₂×C₄	—	94	1	no	—
578	C₂×C₄	—	94	1	no	—
579	C₂×C₄	—	94	1	no	—
580	C₂×C₄	—	94	1	no	—
581	C₂×C₄	—	94	1	no	—
582	C₂×C₄	—	94	1	no	—
583	C₂×C₄	—	94	1	no	—
584	C₂×C₄	—	94	1	no	—
585	C₂×C₄	—	94	1	no	—
586	C₂×C₄	—	188	4	no	—
587	C₂×C₄	—	188	4	no	—
588	C₂×C₄	#13093989	1	2	yes	—
589	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
590	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
591	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
592	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
593	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
594	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
595	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
596	C₈	—	2	2	no	—
597	C₈	—	2	2	no	—
598	C₈	—	4	1	no	—
599	C₈	—	4	1	no	—
600	C₈	—	47	4	no	—
601	C₈	—	94	2	no	—
602	C₈	—	188	1	no	—
603	C₈	—	188	1	no	—
604	C₂²	—	2	2	no	—
605	C₂²	—	2	2	no	—
606	C₂²	—	2	2	no	—
607	C₂²	—	4	1	no	—
608	C₂²	—	4	1	no	—
609	C₂²	—	4	1	no	—
610	C₂²	—	4	1	no	—
611	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
612	C₂²	C₂×#13093989	1	1	yes	characteristic
613	C₂²	C₄×#10625352	1	1	yes	characteristic
614	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
615	C₂²	#131×D₄₇	1	1	yes	characteristic
616	C₂²	#15689888	1	1	yes	characteristic
617	C₂²	#15689889	1	1	yes	characteristic
618	C₄	—	2	2	no	—
619	C₄	—	2	2	no	—
620	C₄	—	4	1	no	—
621	C₄	—	4	1	no	—
622	C₄	—	4	1	no	—
623	C₄	—	94	2	no	—
624	C₄	—	94	2	no	—
625	C₄	—	94	2	no	—
626	C₄	—	94	2	no	—
627	C₄	—	94	2	no	—
628	C₄	—	188	1	no	—
629	C₄	—	188	1	no	—
630	C₄	—	188	1	no	—
631	C₄	C₂²⋊Q₈×D₄₇	1	1	yes	characteristic
632	C₄	#15689629	1	1	yes	characteristic
633	C₄	#15689650	1	1	yes	characteristic
634	C₄	#15689675	1	1	yes	characteristic
635	C₂	—	4	2	no	—
636	C₂	#20245920	1	1	yes	characteristic
637	C₂	#20252117	1	1	yes	characteristic
638	C₂	#20252121	1	1	yes	characteristic
639	C₂	#20252334	1	1	yes	characteristic
640	C₂	#20252339	1	1	yes	characteristic
641	C₂	#20252351	1	1	yes	characteristic
642	C₂	#20252367	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1851	C₂
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1851	D₄₇
hypocenter	C₄₇	#21600
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1851

Complements

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

N	H ≅ G/N	type
1. C₂×#15689250	C₂	semidirect
4. #20244326	C₂	semidirect
5. #20244108	C₂	semidirect
6. #20243946	C₂	semidirect
7. #20243942	C₂	semidirect
10. #20243265	C₂	semidirect
11. #20243261	C₂	semidirect
12. #20243249	C₂	semidirect
66. C₂×#10625329	Q₈	semidirect
190. Dic₄₇⋊C₄	M₁₆	semidirect
281. C₄₇⋊C₈	C₂²⋊Q₈	semidirect
382. C₄₇	#21600	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689250	2
C₂×M₁₆×Dic₄₇	2
C₄×#13094001	2
#20244326	2
#20244108	2
#20243946	2
#20243942	2
#20243571	2
#20243366	2
#20243265	2
#20243261	2
#20243249	2
#20243174	2
#20243172	2
C₄₇×#1851	2
#21600	47