Subgroups — #26222403

Order 12032.

1018 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689201	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689195	C₂	1	2	yes	maximal, complemented
3	C₂×#15689079	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244187	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244112	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244003	C₂	1	2	yes	maximal, complemented
7	#20243686	C₂	1	2	yes	maximal, complemented
8	#20243372	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243257	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243172	C₂	1	2	yes	maximal, complemented
11	C₄₇×#2392	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	1	yes	characteristic
13	C₂²×#10625329	C₂²	1	2	yes	—
14	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
15	#15689201	—	2	4	no	—
16	#15689195	—	2	8	no	—
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
21	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
22	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
23	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
24	#15689079	—	2	4	no	—
25	C₂×#13093935	C₂²	1	1	yes	characteristic
26	C₂×#13093935	C₂²	1	2	yes	—
27	C₂×#13093935	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
30	#15688878	C₂²	1	2	yes	—
31	#15688878	C₂²	1	2	yes	—
32	#15688878	C₂²	1	2	yes	—
33	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
34	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#398	C₄	1	1	yes	characteristic
37	C₄₇×#397	C₄	1	1	yes	characteristic
38	C₄₇×#396	C₄	1	2	yes	—
39	C₄₇×#394	C₄	1	2	yes	—
40	C₄₇×#394	C₄	1	1	yes	characteristic
41	C₄₇×#392	C₄	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
44	C₂×#10625329	—	2	2	no	—
45	C₂×#10625329	—	2	2	no	—
46	C₂×#10625329	—	2	4	no	—
47	C₂×#10625329	—	2	4	no	—
48	C₂×#10625329	—	2	2	no	—
49	C₂×#10625329	—	2	4	no	—
50	C₂²×C₄₇⋊C₈	—	2	2	no	—
51	C₂²×C₄₇⋊C₈	—	2	2	no	—
52	C₂²×C₄₇⋊C₈	D₄	1	4	yes	complemented
53	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
54	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
55	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
56	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
57	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
58	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
59	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
60	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
61	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
62	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
63	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
64	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
65	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
66	#13093935	—	2	2	no	—
67	#13093935	—	2	2	no	—
68	#13093935	—	2	4	no	—
69	C₄×C₄₇⋊C₈	—	2	2	no	—
70	C₄×C₄₇⋊C₈	D₄	1	4	yes	complemented
71	C₂²×D₄×C₄₇	C₂×C₄	1	2	yes	—
72	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
74	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
75	C₄×D₄×C₄₇	—	2	4	no	—
76	C₄×D₄×C₄₇	—	2	4	no	—
77	C₄×D₄×C₄₇	—	2	2	no	—
78	C₄×D₄×C₄₇	—	2	2	no	—
79	#117×C₄₇	—	2	2	no	—
80	#117×C₄₇	—	2	2	no	—
81	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
83	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
84	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
86	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
87	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
88	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
89	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
90	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
91	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
92	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
93	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
95	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
96	#95×C₄₇	C₂×C₄	1	2	yes	—
97	#95×C₄₇	C₂×C₄	1	2	yes	—
98	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
99	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
100	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂×D₄×C₄₇	—	2	4	no	—
103	C₂×D₄×C₄₇	—	2	2	no	—
104	C₂×D₄×C₄₇	—	4	2	no	—
105	C₂×D₄×C₄₇	—	4	2	no	—
106	C₂×D₄×C₄₇	—	4	2	no	—
107	C₂²×C₄×C₄₇	—	2	1	no	—
108	C₂²×C₄×C₄₇	—	2	1	no	—
109	C₂²×C₄×C₄₇	—	2	1	no	—
110	C₂²×C₄×C₄₇	—	2	1	no	—
111	C₂²×C₄×C₄₇	—	2	2	no	—
112	C₂²×C₄×C₄₇	—	2	2	no	—
113	C₂²×C₄×C₄₇	—	2	2	no	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
118	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
122	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₄₇	#41	1	2	yes	—
127	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
128	C₄⋊C₄×C₄₇	—	2	2	no	—
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	—	2	4	no	—
131	C₄⋊C₄×C₄₇	—	2	2	no	—
132	C₄⋊C₄×C₄₇	—	4	2	no	—
133	C₂²⋊C₄×C₄₇	—	2	4	no	—
134	C₂²⋊C₄×C₄₇	—	2	2	no	—
135	C₂²⋊C₄×C₄₇	—	2	2	no	—
136	C₂²⋊C₄×C₄₇	—	2	4	no	—
137	C₂²⋊C₄×C₄₇	—	2	4	no	—
138	C₂²⋊C₄×C₄₇	—	4	2	no	—
139	C₂²⋊C₄×C₄₇	—	4	2	no	—
140	C₄²×C₄₇	—	2	1	no	—
141	C₄²×C₄₇	—	2	2	no	—
142	C₄²×C₄₇	—	2	1	no	—
143	C₄²×C₄₇	—	2	2	no	—
144	C₄²×C₄₇	C₂×D₄	1	2	yes	—
145	C₄²×C₄₇	#41	1	2	yes	—
146	#10625329	—	2	8	no	—
147	#10625329	—	4	8	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	1	no	—
152	C₂×C₄₇⋊C₈	—	2	1	no	—
153	C₂×C₄₇⋊C₈	—	2	1	no	—
154	C₂×C₄₇⋊C₈	—	2	8	no	—
155	C₂×C₄₇⋊C₈	—	2	2	no	—
156	C₂×C₄₇⋊C₈	—	2	2	no	—
157	C₂×C₄₇⋊C₈	—	2	2	no	—
158	C₂×C₄₇⋊C₈	—	2	2	no	—
159	C₂×C₄₇⋊C₈	—	2	2	no	—
160	C₂×C₄₇⋊C₈	—	2	2	no	—
161	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
162	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
163	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
164	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
165	C₂×C₄₇⋊C₈	#41	1	2	yes	—
166	C₂×C₄₇⋊C₈	#41	1	2	yes	—
167	C₂³×C₄₇	—	2	1	no	—
168	C₂³×C₄₇	—	2	1	no	—
169	C₂³×C₄₇	—	2	2	no	—
170	C₂³×C₄₇	—	2	2	no	—
171	C₂³×C₄₇	—	2	2	no	—
172	C₂³×C₄₇	—	2	2	no	—
173	C₂³×C₄₇	—	2	2	no	—
174	C₂³×C₄₇	—	2	2	no	—
175	C₂³×C₄₇	—	2	2	no	—
176	C₂³×C₄₇	—	2	2	no	—
177	C₂³×C₄₇	—	2	2	no	—
178	C₂³×C₄₇	C₄×D₄	1	2	yes	—
179	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
180	D₄×C₄₇	—	4	4	no	—
181	D₄×C₄₇	—	4	8	no	—
182	C₂×C₄×C₄₇	—	2	1	no	—
183	C₂×C₄×C₄₇	—	2	1	no	—
184	C₂×C₄×C₄₇	—	2	2	no	—
185	C₂×C₄×C₄₇	—	2	2	no	—
186	C₂×C₄×C₄₇	—	2	2	no	—
187	C₂×C₄×C₄₇	—	2	2	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	1	no	—
192	C₂×C₄×C₄₇	—	2	1	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	—	2	2	no	—
199	C₂×C₄×C₄₇	—	2	2	no	—
200	C₂×C₄×C₄₇	—	2	2	no	—
201	C₂×C₄×C₄₇	—	2	2	no	—
202	C₂×C₄×C₄₇	—	2	2	no	—
203	C₂×C₄×C₄₇	—	4	2	no	—
204	C₂×C₄×C₄₇	—	4	2	no	—
205	C₂×C₄×C₄₇	—	4	2	no	—
206	C₂×C₄×C₄₇	—	4	2	no	—
207	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
208	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
209	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
210	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
215	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
216	C₄₇⋊C₈	—	2	2	no	—
217	C₄₇⋊C₈	—	2	2	no	—
218	C₄₇⋊C₈	—	2	2	no	—
219	C₄₇⋊C₈	—	4	2	no	—
220	C₄₇⋊C₈	—	4	2	no	—
221	C₄₇⋊C₈	#121	1	4	yes	—
222	#21493	—	47	1	no	maximal, Sylow
223	C₂²×C₄₇	—	2	4	no	—
224	C₂²×C₄₇	—	2	2	no	—
225	C₂²×C₄₇	—	4	1	no	—
226	C₂²×C₄₇	—	4	1	no	—
227	C₂²×C₄₇	—	4	2	no	—
228	C₂²×C₄₇	—	4	2	no	—
229	C₂²×C₄₇	—	4	2	no	—
230	C₂²×C₄₇	—	4	2	no	—
231	C₂²×C₄₇	—	4	2	no	—
232	C₂²×C₄₇	—	4	2	no	—
233	C₂²×C₄₇	—	4	2	no	—
234	C₂²×C₄₇	—	4	2	no	—
235	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
236	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
237	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
238	C₂²×C₄₇	#568	1	2	yes	—
239	C₂²×C₄₇	#568	1	2	yes	—
240	C₄×C₄₇	—	2	2	no	—
241	C₄×C₄₇	—	2	2	no	—
242	C₄×C₄₇	—	2	2	no	—
243	C₄×C₄₇	—	4	1	no	—
244	C₄×C₄₇	—	4	2	no	—
245	C₄×C₄₇	—	4	2	no	—
246	C₄×C₄₇	—	4	1	no	—
247	C₄×C₄₇	—	4	2	no	—
248	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
249	C₄×C₄₇	#525	1	1	yes	characteristic
250	C₄×C₄₇	#529	1	1	yes	characteristic
251	C₄×C₄₇	#532	1	1	yes	characteristic
252	C₂×#436	—	47	1	no	—
253	C₂×#435	—	47	2	no	—
254	C₂×#405	—	47	1	no	—
255	#2392	D₄₇	1	1	yes	characteristic
256	#1955	—	47	1	no	—
257	#1940	—	47	1	no	—
258	#1924	—	47	2	no	—
259	#1870	—	47	2	no	—
260	#1798	—	47	1	no	—
261	#1770	—	47	1	no	—
262	#1753	—	47	2	no	—
263	C₂×C₄₇	—	4	2	no	—
264	C₂×C₄₇	—	8	2	no	—
265	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
266	C₂×C₄₇	#2930	1	1	yes	characteristic
267	C₂×C₄₇	#2930	1	2	yes	—
268	C₂×C₄₇	#2932	1	1	yes	characteristic
269	C₂×C₄₇	#2967	1	2	yes	—
270	C₂²×M₁₆	—	47	1	no	—
271	C₂²×M₁₆	—	47	2	no	—
272	C₂³×C₈	—	47	1	no	—
273	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
274	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
275	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
276	#436	—	94	4	no	—
277	#435	—	94	8	no	—
278	C₂×C₄⋊C₈	—	47	1	no	—
279	C₂×C₄⋊C₈	—	47	1	no	—
280	C₂×C₄⋊C₈	—	47	2	no	—
281	C₂×C₂²⋊C₈	—	47	2	no	—
282	C₂×C₂²⋊C₈	—	47	2	no	—
283	C₂×C₂²⋊C₈	—	47	2	no	—
284	C₂×C₂²⋊C₈	—	47	2	no	—
285	#405	—	94	4	no	—
286	C₂×#97	—	47	1	no	—
287	C₂×#97	—	47	1	no	—
288	C₂×#97	—	47	2	no	—
289	C₂×C₄×C₈	—	47	1	no	—
290	C₂×C₄×C₈	—	47	1	no	—
291	#398	Dic₄₇	1	1	yes	characteristic
292	#397	Dic₄₇	1	1	yes	characteristic
293	#396	Dic₄₇	1	2	yes	—
294	#394	Dic₄₇	1	2	yes	—
295	#394	Dic₄₇	1	1	yes	characteristic
296	#392	Dic₄₇	1	1	yes	characteristic
297	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
298	C₄×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
299	#336	—	47	2	no	—
300	#336	—	47	2	no	—
301	#336	—	47	2	no	—
302	C₄₇	#21493	1	1	yes	characteristic, complemented, Sylow
303	C₂²×D₄	C₂×Dic₄₇	1	2	yes	—
304	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
305	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
306	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
307	C₂×M₁₆	—	94	2	no	—
308	C₂×M₁₆	—	94	2	no	—
309	C₂×M₁₆	—	94	4	no	—
310	C₂×M₁₆	—	94	4	no	—
311	C₂×M₁₆	—	94	4	no	—
312	C₂×M₁₆	—	94	2	no	—
313	C₂²×C₈	—	47	1	no	—
314	C₂²×C₈	—	47	4	no	—
315	C₂²×C₈	—	47	1	no	—
316	C₂²×C₈	—	47	1	no	—
317	C₂²×C₈	—	47	1	no	—
318	C₂²×C₈	—	47	2	no	—
319	C₂²×C₈	—	47	2	no	—
320	C₂²×C₈	—	94	2	no	—
321	C₂²×C₈	—	94	2	no	—
322	C₄×D₄	—	2	4	no	—
323	C₄×D₄	—	2	4	no	—
324	C₄×D₄	—	2	2	no	—
325	C₄×D₄	—	2	2	no	—
326	#117	—	2	2	no	—
327	#117	—	2	2	no	—
328	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
331	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
332	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
333	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
334	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
335	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
336	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
337	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
338	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
339	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
340	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
341	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
342	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
343	C₄⋊C₈	—	94	4	no	—
344	C₄⋊C₈	—	94	2	no	—
345	C₄⋊C₈	—	94	2	no	—
346	C₂²⋊C₈	—	94	4	no	—
347	C₂²⋊C₈	—	94	4	no	—
348	C₂²⋊C₈	—	94	4	no	—
349	C₂²⋊C₈	—	94	4	no	—
350	#97	—	94	2	no	—
351	#97	—	94	4	no	—
352	#97	—	94	2	no	—
353	C₄×C₈	—	47	4	no	—
354	C₄×C₈	—	94	2	no	—
355	#95	C₂×Dic₄₇	1	2	yes	—
356	#95	C₂×Dic₄₇	1	2	yes	—
357	#95	C₂×Dic₄₇	1	1	yes	characteristic
358	#95	C₂×Dic₄₇	1	1	yes	characteristic
359	C₂⁴	C₂²×Dic₄₇	1	2	yes	—
360	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
361	C₂×D₄	—	2	4	no	—
362	C₂×D₄	—	2	2	no	—
363	C₂×D₄	—	4	2	no	—
364	C₂×D₄	—	4	2	no	—
365	C₂×D₄	—	4	2	no	—
366	C₂²×C₄	—	2	1	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	2	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	D₄×D₄₇	1	2	yes	—
377	C₂²×C₄	#10625352	1	2	yes	—
378	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
379	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
380	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
381	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
382	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
383	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
384	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
385	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
386	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
387	M₁₆	—	94	8	no	—
388	M₁₆	—	188	8	no	—
389	C₂×C₈	—	47	2	no	—
390	C₂×C₈	—	47	2	no	—
391	C₂×C₈	—	47	2	no	—
392	C₂×C₈	—	47	2	no	—
393	C₂×C₈	—	47	2	no	—
394	C₂×C₈	—	47	2	no	—
395	C₂×C₈	—	94	8	no	—
396	C₂×C₈	—	94	1	no	—
397	C₂×C₈	—	94	1	no	—
398	C₂×C₈	—	94	1	no	—
399	C₂×C₈	—	94	1	no	—
400	C₂×C₈	—	94	1	no	—
401	C₂×C₈	—	94	1	no	—
402	C₂×C₈	—	94	2	no	—
403	C₂×C₈	—	94	2	no	—
404	C₂×C₈	—	94	2	no	—
405	C₂×C₈	—	94	2	no	—
406	C₂×C₈	—	94	2	no	—
407	C₂×C₈	—	94	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	4	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	4	2	no	—
413	C₂²⋊C₄	—	2	4	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	—	2	2	no	—
416	C₂²⋊C₄	—	2	4	no	—
417	C₂²⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	—	4	2	no	—
419	C₂²⋊C₄	—	4	2	no	—
420	C₄²	—	2	1	no	—
421	C₄²	—	2	2	no	—
422	C₄²	—	2	1	no	—
423	C₄²	—	2	2	no	—
424	C₄²	D₄×D₄₇	1	2	yes	—
425	C₄²	#10625352	1	2	yes	—
426	C₂³	—	2	1	no	—
427	C₂³	—	2	1	no	—
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	2	2	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	2	2	no	—
436	C₂³	—	2	2	no	—
437	C₂³	D₄×Dic₄₇	1	2	yes	—
438	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
439	D₄	—	4	4	no	—
440	D₄	—	4	8	no	—
441	C₂×C₄	—	2	1	no	—
442	C₂×C₄	—	2	1	no	—
443	C₂×C₄	—	2	2	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	1	no	—
451	C₂×C₄	—	2	1	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	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
467	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
468	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
469	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
470	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
471	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
472	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
473	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
474	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
475	C₈	—	47	4	no	—
476	C₈	—	94	2	no	—
477	C₈	—	94	2	no	—
478	C₈	—	94	2	no	—
479	C₈	—	188	2	no	—
480	C₈	—	188	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	—	2	4	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	4	1	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	4	2	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
494	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
495	C₂²	#41×Dic₄₇	1	1	yes	characteristic
496	C₂²	#15689890	1	2	yes	—
497	C₂²	#15689890	1	2	yes	—
498	C₄	—	2	2	no	—
499	C₄	—	2	2	no	—
500	C₄	—	2	2	no	—
501	C₄	—	4	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	4	1	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	1	no	—
506	C₄	#121×D₄₇	1	1	yes	characteristic
507	C₄	#15689633	1	1	yes	characteristic
508	C₄	#15689654	1	1	yes	characteristic
509	C₄	#15689668	1	1	yes	characteristic
510	C₂	—	4	2	no	—
511	C₂	—	8	2	no	—
512	C₂	#121×Dic₄₇	1	1	yes	characteristic
513	C₂	#20252092	1	1	yes	characteristic
514	C₂	#20252092	1	2	yes	—
515	C₂	#20252106	1	1	yes	characteristic
516	C₂	#20252375	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#2392	C₂
prime radical	C₄₇×#392	C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2392	D₄₇
hypocenter	C₄₇	#21493
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #2392

Complements

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

N	H ≅ G/N	type
1. C₂×#15689201	C₂	semidirect
2. C₂×#15689195	C₂	semidirect
3. C₂×#15689079	C₂	semidirect
4. #20244187	C₂	semidirect
5. #20244112	C₂	semidirect
6. #20244003	C₂	semidirect
7. #20243686	C₂	semidirect
8. #20243372	C₂	semidirect
9. #20243257	C₂	semidirect
10. #20243172	C₂	semidirect
52. C₂²×C₄₇⋊C₈	D₄	semidirect
70. C₄×C₄₇⋊C₈	D₄	semidirect
302. C₄₇	#21493	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689201	2
C₂×#15689195	2
C₂×#15689079	2
#20244187	2
#20244112	2
#20244003	2
#20243686	2
#20243372	2
#20243257	2
#20243172	2
C₄₇×#2392	2
#21493	47