Subgroups — #26214639

Order 12032.

1118 conjugacy classes of subgroups.

The subgroup lattice has 586 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
2	C₂×#15689195	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689079	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243263	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243257	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243245	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243172	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243172	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243172	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243166	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243154	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243150	C₂	1	1	yes	maximal, characteristic, complemented
14	#20243075	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#2290	C₂	1	1	yes	maximal, characteristic
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂²×#10625329	C₂²	1	1	yes	characteristic
18	C₂²×#10625329	C₂²	1	1	yes	characteristic
19	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
20	#15689201	C₄	1	8	yes	complemented
21	#15689195	C₄	1	8	yes	complemented
22	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊(C₄₇⋊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×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
28	#15689079	—	2	4	no	—
29	C₄×#10625329	—	2	4	no	—
30	C₂×#13093935	C₂²	1	1	yes	characteristic
31	C₂×#13093935	C₂²	1	1	yes	characteristic
32	C₂×#13093935	C₂²	1	1	yes	characteristic
33	C₂×#13093935	C₂²	1	1	yes	characteristic
34	C₂×#13093935	C₂²	1	1	yes	characteristic
35	C₂×#13093935	C₂²	1	1	yes	characteristic
36	C₂×#13093935	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
42	#15688878	C₂²	1	1	yes	characteristic
43	#15688878	C₂²	1	1	yes	characteristic
44	#15688878	C₂²	1	1	yes	characteristic
45	#15688878	C₂²	1	1	yes	characteristic
46	#15688878	C₂²	1	1	yes	characteristic
47	#15688878	C₂²	1	1	yes	characteristic
48	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
49	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
50	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
51	C₄₇×#388	C₄	1	2	yes	—
52	C₄₇×#387	C₄	1	2	yes	—
53	C₄₇×#386	C₄	1	2	yes	—
54	C₄₇×#385	C₄	1	2	yes	—
55	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
57	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
58	C₄₇×#376	C₂²	1	1	yes	characteristic
59	C₂×#10625329	—	2	2	no	—
60	C₂×#10625329	—	2	2	no	—
61	C₂×#10625329	—	2	2	no	—
62	C₂×#10625329	—	2	2	no	—
63	C₂×#10625329	—	2	2	no	—
64	C₂×#10625329	—	2	2	no	—
65	C₂×#10625329	C₂×C₄	1	4	yes	—
66	C₂×#10625329	C₂×C₄	1	4	yes	—
67	C₂×#10625329	C₂×C₄	1	4	yes	complemented
68	C₂²×C₄₇⋊C₈	—	2	2	no	—
69	C₂²×C₄₇⋊C₈	—	2	2	no	—
70	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
71	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
73	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
75	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
79	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
80	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
81	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
82	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
83	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
84	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
85	#13093935	—	2	2	no	—
86	#13093935	—	2	2	no	—
87	#13093935	—	2	2	no	—
88	#13093935	—	2	2	no	—
89	#13093935	—	2	2	no	—
90	#13093935	—	2	2	no	—
91	#13093935	C₂×C₄	1	4	yes	complemented
92	C₄×C₄₇⋊C₈	—	2	2	no	—
93	C₄×C₄₇⋊C₈	—	2	2	no	—
94	C₄×C₄₇⋊C₈	—	2	2	no	—
95	C₄×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
96	C₄×C₄₇⋊C₈	D₄	1	4	yes	complemented
97	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
98	C₂³×C₄×C₄₇	C₂×C₄	1	2	yes	—
99	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
100	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
101	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
102	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
103	#117×C₄₇	—	2	2	no	—
104	#117×C₄₇	—	2	2	no	—
105	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
106	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
107	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
109	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
110	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
111	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
112	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
113	C₂×C₄²×C₄₇	—	2	2	no	—
114	C₂×C₄²×C₄₇	—	2	2	no	—
115	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
116	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
117	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
118	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
119	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
121	#95×C₄₇	C₂×C₄	1	2	yes	—
122	#95×C₄₇	C₂×C₄	1	2	yes	—
123	#95×C₄₇	C₂×C₄	1	2	yes	—
124	#95×C₄₇	C₂×C₄	1	2	yes	—
125	#95×C₄₇	C₂×C₄	1	2	yes	—
126	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂×D₄×C₄₇	—	4	2	no	—
129	C₂×D₄×C₄₇	C₄²	1	4	yes	—
130	C₂²×C₄×C₄₇	—	2	1	no	—
131	C₂²×C₄×C₄₇	—	2	1	no	—
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	—	2	1	no	—
137	C₂²×C₄×C₄₇	—	2	1	no	—
138	C₂²×C₄×C₄₇	—	2	4	no	—
139	C₂²×C₄×C₄₇	—	4	2	no	—
140	C₂²×C₄×C₄₇	—	4	2	no	—
141	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
142	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
143	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
144	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
149	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
150	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
151	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
152	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
153	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
154	C₄⋊C₄×C₄₇	—	2	4	no	—
155	C₄⋊C₄×C₄₇	—	4	2	no	—
156	C₄⋊C₄×C₄₇	C₄²	1	4	yes	—
157	C₂²⋊C₄×C₄₇	—	2	4	no	—
158	C₂²⋊C₄×C₄₇	—	4	2	no	—
159	C₂²⋊C₄×C₄₇	—	4	2	no	—
160	C₂²⋊C₄×C₄₇	C₄²	1	4	yes	—
161	C₂²⋊C₄×C₄₇	C₄²	1	4	yes	—
162	C₄²×C₄₇	—	2	4	no	—
163	C₄²×C₄₇	—	2	1	no	—
164	C₄²×C₄₇	—	2	1	no	—
165	C₄²×C₄₇	—	2	1	no	—
166	C₄²×C₄₇	—	2	1	no	—
167	C₄²×C₄₇	—	2	1	no	—
168	C₄²×C₄₇	—	2	1	no	—
169	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
170	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
171	C₄²×C₄₇	C₂×D₄	1	2	yes	—
172	C₄²×C₄₇	#41	1	2	yes	—
173	#10625329	—	2	8	no	—
174	#10625329	—	2	8	no	—
175	#10625329	—	2	8	no	—
176	C₂×C₄₇⋊C₈	—	2	1	no	—
177	C₂×C₄₇⋊C₈	—	2	1	no	—
178	C₂×C₄₇⋊C₈	—	2	1	no	—
179	C₂×C₄₇⋊C₈	—	2	1	no	—
180	C₂×C₄₇⋊C₈	—	2	1	no	—
181	C₂×C₄₇⋊C₈	—	2	1	no	—
182	C₂×C₄₇⋊C₈	—	2	1	no	—
183	C₂×C₄₇⋊C₈	—	2	1	no	—
184	C₂×C₄₇⋊C₈	—	2	1	no	—
185	C₂×C₄₇⋊C₈	—	2	1	no	—
186	C₂×C₄₇⋊C₈	—	2	1	no	—
187	C₂×C₄₇⋊C₈	—	2	1	no	—
188	C₂×C₄₇⋊C₈	—	2	8	no	—
189	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
190	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
191	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
192	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
193	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
194	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
195	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
196	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
197	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
198	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
199	C₂×C₄₇⋊C₈	#41	1	2	yes	—
200	C₂×C₄₇⋊C₈	#41	1	2	yes	—
201	C₂³×C₄₇	—	2	1	no	—
202	C₂³×C₄₇	—	2	1	no	—
203	C₂³×C₄₇	—	2	1	no	—
204	C₂³×C₄₇	—	2	1	no	—
205	C₂³×C₄₇	—	2	2	no	—
206	C₂³×C₄₇	—	2	2	no	—
207	C₂³×C₄₇	—	2	2	no	—
208	C₂³×C₄₇	—	2	2	no	—
209	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
210	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
211	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
212	D₄×C₄₇	—	4	4	no	—
213	C₂×C₄×C₄₇	—	2	1	no	—
214	C₂×C₄×C₄₇	—	2	1	no	—
215	C₂×C₄×C₄₇	—	2	1	no	—
216	C₂×C₄×C₄₇	—	2	1	no	—
217	C₂×C₄×C₄₇	—	2	2	no	—
218	C₂×C₄×C₄₇	—	2	2	no	—
219	C₂×C₄×C₄₇	—	2	2	no	—
220	C₂×C₄×C₄₇	—	2	2	no	—
221	C₂×C₄×C₄₇	—	2	2	no	—
222	C₂×C₄×C₄₇	—	2	2	no	—
223	C₂×C₄×C₄₇	—	2	2	no	—
224	C₂×C₄×C₄₇	—	2	2	no	—
225	C₂×C₄×C₄₇	—	2	2	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	2	no	—
231	C₂×C₄×C₄₇	—	2	2	no	—
232	C₂×C₄×C₄₇	—	2	2	no	—
233	C₂×C₄×C₄₇	—	2	2	no	—
234	C₂×C₄×C₄₇	—	2	2	no	—
235	C₂×C₄×C₄₇	—	2	2	no	—
236	C₂×C₄×C₄₇	—	2	2	no	—
237	C₂×C₄×C₄₇	—	2	2	no	—
238	C₂×C₄×C₄₇	—	4	8	no	—
239	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
240	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
241	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
242	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
243	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
244	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
245	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
246	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
249	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
250	C₄₇⋊C₈	—	2	2	no	—
251	C₄₇⋊C₈	—	2	2	no	—
252	C₄₇⋊C₈	—	2	2	no	—
253	C₄₇⋊C₈	—	2	2	no	—
254	C₄₇⋊C₈	—	2	2	no	—
255	C₄₇⋊C₈	—	2	2	no	—
256	C₄₇⋊C₈	C₄×D₄	1	4	yes	—
257	C₄₇⋊C₈	C₄×D₄	1	4	yes	—
258	#20487	—	47	1	no	maximal, Sylow
259	C₂²×C₄₇	—	2	2	no	—
260	C₂²×C₄₇	—	2	2	no	—
261	C₂²×C₄₇	—	2	2	no	—
262	C₂²×C₄₇	—	2	2	no	—
263	C₂²×C₄₇	—	2	2	no	—
264	C₂²×C₄₇	—	2	2	no	—
265	C₂²×C₄₇	—	4	2	no	—
266	C₂²×C₄₇	—	4	2	no	—
267	C₂²×C₄₇	—	4	2	no	—
268	C₂²×C₄₇	—	4	2	no	—
269	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
270	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
271	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
272	C₂²×C₄₇	#568	1	2	yes	—
273	C₂²×C₄₇	#568	1	2	yes	—
274	C₄×C₄₇	—	2	2	no	—
275	C₄×C₄₇	—	2	2	no	—
276	C₄×C₄₇	—	2	4	no	—
277	C₄×C₄₇	—	2	2	no	—
278	C₄×C₄₇	—	2	2	no	—
279	C₄×C₄₇	—	4	2	no	—
280	C₄×C₄₇	—	4	2	no	—
281	C₄×C₄₇	—	4	2	no	—
282	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
283	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
284	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
285	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
286	C₂×#436	—	47	1	no	—
287	C₂×#435	—	47	1	no	—
288	C₂×#405	—	47	1	no	—
289	C₂×C₄×M₁₆	—	47	1	no	—
290	#2290	D₄₇	1	1	yes	characteristic
291	#1771	—	47	1	no	—
292	#1770	—	47	1	no	—
293	#1768	—	47	1	no	—
294	#1753	—	47	1	no	—
295	#1753	—	47	1	no	—
296	#1753	—	47	1	no	—
297	#1752	—	47	1	no	—
298	#1750	—	47	1	no	—
299	#1749	—	47	1	no	—
300	#1726	—	47	1	no	—
301	C₂×C₄₇	—	4	2	no	—
302	C₂×C₄₇	—	4	2	no	—
303	C₂×C₄₇	C₄²×D₄	1	1	yes	characteristic
304	C₂×C₄₇	#2873	1	1	yes	characteristic
305	C₂×C₄₇	#2875	1	1	yes	characteristic
306	C₂×C₄₇	#2930	1	2	yes	—
307	C₂×C₄₇	#2967	1	2	yes	—
308	C₂²×M₁₆	—	47	1	no	—
309	C₂²×M₁₆	—	47	1	no	—
310	C₂²×M₁₆	—	47	1	no	—
311	C₂³×C₈	—	47	1	no	—
312	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
313	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
314	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
315	#436	—	47	8	no	—
316	#435	—	47	8	no	—
317	C₂×C₄⋊C₈	—	47	1	no	—
318	C₂×C₄⋊C₈	—	47	1	no	—
319	C₂×C₂²⋊C₈	—	47	1	no	—
320	C₂×C₂²⋊C₈	—	47	1	no	—
321	C₂×C₂²⋊C₈	—	47	1	no	—
322	C₂×C₂²⋊C₈	—	47	1	no	—
323	#405	—	94	4	no	—
324	C₄×M₁₆	—	94	4	no	—
325	C₂×#97	—	47	1	no	—
326	C₂×#97	—	47	1	no	—
327	C₂×#97	—	47	1	no	—
328	C₂×#97	—	47	1	no	—
329	C₂×#97	—	47	1	no	—
330	C₂×#97	—	47	1	no	—
331	C₂×#97	—	47	1	no	—
332	C₂×C₄×C₈	—	47	1	no	—
333	C₂×C₄×C₈	—	47	1	no	—
334	C₂×C₄×C₈	—	47	1	no	—
335	C₂×C₄×C₈	—	47	1	no	—
336	C₂×C₄×C₈	—	47	1	no	—
337	#388	Dic₄₇	1	2	yes	—
338	#387	Dic₄₇	1	2	yes	—
339	#386	Dic₄₇	1	2	yes	—
340	#385	Dic₄₇	1	2	yes	—
341	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
342	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
343	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
344	#376	C₂×D₄₇	1	1	yes	characteristic
345	#336	—	47	1	no	—
346	#336	—	47	1	no	—
347	#336	—	47	1	no	—
348	#336	—	47	1	no	—
349	#336	—	47	1	no	—
350	#336	—	47	1	no	—
351	C₄₇	#20487	1	1	yes	characteristic, complemented, Sylow
352	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
353	C₂³×C₄	C₂×Dic₄₇	1	2	yes	—
354	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
355	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
356	C₂×M₁₆	—	47	4	no	—
357	C₂×M₁₆	—	47	4	no	—
358	C₂×M₁₆	—	47	4	no	—
359	C₂×M₁₆	—	94	2	no	—
360	C₂×M₁₆	—	94	2	no	—
361	C₂×M₁₆	—	94	2	no	—
362	C₂×M₁₆	—	94	2	no	—
363	C₂×M₁₆	—	94	2	no	—
364	C₂×M₁₆	—	94	2	no	—
365	C₂²×C₈	—	47	1	no	—
366	C₂²×C₈	—	47	1	no	—
367	C₂²×C₈	—	47	4	no	—
368	C₂²×C₈	—	47	1	no	—
369	C₂²×C₈	—	47	1	no	—
370	C₂²×C₈	—	47	1	no	—
371	C₂²×C₈	—	47	1	no	—
372	C₂²×C₈	—	47	1	no	—
373	C₂²×C₈	—	47	1	no	—
374	C₂²×C₈	—	94	2	no	—
375	C₂²×C₈	—	94	2	no	—
376	C₄×D₄	C₄×D₄₇	1	4	yes	—
377	C₄×D₄	C₄×D₄₇	1	4	yes	—
378	#117	—	2	2	no	—
379	#117	—	2	2	no	—
380	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
381	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
382	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
383	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
384	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
385	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
386	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
388	C₂×C₄²	—	2	2	no	—
389	C₂×C₄²	—	2	2	no	—
390	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
391	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
392	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
393	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
394	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
395	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
396	C₄⋊C₈	—	47	4	no	—
397	C₄⋊C₈	—	47	4	no	—
398	C₂²⋊C₈	—	47	4	no	—
399	C₂²⋊C₈	—	47	4	no	—
400	C₂²⋊C₈	—	47	4	no	—
401	C₂²⋊C₈	—	47	4	no	—
402	#97	—	47	4	no	—
403	#97	—	94	2	no	—
404	#97	—	94	2	no	—
405	#97	—	94	2	no	—
406	#97	—	94	2	no	—
407	#97	—	94	2	no	—
408	#97	—	94	2	no	—
409	C₄×C₈	—	47	4	no	—
410	C₄×C₈	—	47	4	no	—
411	C₄×C₈	—	94	2	no	—
412	C₄×C₈	—	94	2	no	—
413	C₄×C₈	—	94	2	no	—
414	#95	C₂×Dic₄₇	1	2	yes	—
415	#95	C₂×Dic₄₇	1	2	yes	—
416	#95	C₂×Dic₄₇	1	2	yes	—
417	#95	C₂×Dic₄₇	1	2	yes	—
418	#95	C₂×Dic₄₇	1	2	yes	—
419	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
420	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
421	C₂×D₄	—	4	2	no	—
422	C₂×D₄	C₄×Dic₄₇	1	4	yes	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	2	1	no	—
428	C₂²×C₄	—	2	1	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	4	no	—
432	C₂²×C₄	—	4	2	no	—
433	C₂²×C₄	—	4	2	no	—
434	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
435	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
436	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
437	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
438	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
439	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
440	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
441	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
442	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
443	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
444	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
445	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
446	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
447	M₁₆	—	94	8	no	—
448	M₁₆	—	94	8	no	—
449	M₁₆	—	94	8	no	—
450	C₂×C₈	—	47	2	no	—
451	C₂×C₈	—	47	2	no	—
452	C₂×C₈	—	47	2	no	—
453	C₂×C₈	—	47	2	no	—
454	C₂×C₈	—	47	2	no	—
455	C₂×C₈	—	47	2	no	—
456	C₂×C₈	—	47	2	no	—
457	C₂×C₈	—	47	2	no	—
458	C₂×C₈	—	47	2	no	—
459	C₂×C₈	—	47	2	no	—
460	C₂×C₈	—	47	2	no	—
461	C₂×C₈	—	47	2	no	—
462	C₂×C₈	—	94	8	no	—
463	C₂×C₈	—	94	1	no	—
464	C₂×C₈	—	94	1	no	—
465	C₂×C₈	—	94	1	no	—
466	C₂×C₈	—	94	1	no	—
467	C₂×C₈	—	94	1	no	—
468	C₂×C₈	—	94	1	no	—
469	C₂×C₈	—	94	1	no	—
470	C₂×C₈	—	94	1	no	—
471	C₂×C₈	—	94	1	no	—
472	C₂×C₈	—	94	1	no	—
473	C₂×C₈	—	94	1	no	—
474	C₂×C₈	—	94	1	no	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	4	2	no	—
477	C₄⋊C₄	C₄×Dic₄₇	1	4	yes	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	4	2	no	—
480	C₂²⋊C₄	—	4	2	no	—
481	C₂²⋊C₄	C₄×Dic₄₇	1	4	yes	—
482	C₂²⋊C₄	C₄×Dic₄₇	1	4	yes	—
483	C₄²	—	2	4	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	2	1	no	—
486	C₄²	—	2	1	no	—
487	C₄²	—	2	1	no	—
488	C₄²	—	2	1	no	—
489	C₄²	—	2	1	no	—
490	C₄²	C₂×C₄×D₄₇	1	2	yes	—
491	C₄²	C₂×C₄×D₄₇	1	2	yes	—
492	C₄²	D₄×D₄₇	1	2	yes	—
493	C₄²	#10625352	1	2	yes	—
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	1	no	—
497	C₂³	—	2	1	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	2	no	—
500	C₂³	—	2	2	no	—
501	C₂³	—	2	2	no	—
502	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
503	C₂³	C₂×C₄×Dic₄₇	1	2	yes	—
504	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
505	D₄	—	4	4	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	4	8	no	—
532	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
533	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
534	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
535	C₂×C₄	C₂×C₄×Dic₄₇	1	2	yes	—
536	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
537	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
538	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
539	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
540	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
541	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
542	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
543	C₈	—	47	4	no	—
544	C₈	—	47	4	no	—
545	C₈	—	94	2	no	—
546	C₈	—	94	2	no	—
547	C₈	—	94	2	no	—
548	C₈	—	94	2	no	—
549	C₈	—	94	2	no	—
550	C₈	—	94	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	2	no	—
560	C₂²	—	4	2	no	—
561	C₂²	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
562	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
563	C₂²	#41×Dic₄₇	1	1	yes	characteristic
564	C₂²	#15689890	1	2	yes	—
565	C₂²	#15689890	1	2	yes	—
566	C₄	—	2	2	no	—
567	C₄	—	2	2	no	—
568	C₄	—	2	4	no	—
569	C₄	—	2	2	no	—
570	C₄	—	2	2	no	—
571	C₄	—	4	2	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	2	no	—
574	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
575	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
576	C₄	C₄×#10625352	1	1	yes	characteristic
577	C₄	C₄×#10625352	1	1	yes	characteristic
578	C₂	—	4	2	no	—
579	C₂	—	4	2	no	—
580	C₂	C₄×D₄×Dic₄₇	1	1	yes	characteristic
581	C₂	#20251807	1	1	yes	characteristic
582	C₂	#20251816	1	1	yes	characteristic
583	C₂	#20252092	1	2	yes	—
584	C₂	#20252375	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₄₇×#2290	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2290	D₄₇
hypocenter	C₄₇	#20487
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #2290

Complements

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

N	H ≅ G/N	type
3. C₂×#15689079	C₂	semidirect
4. C₂×C₄×#10625329	C₂	semidirect
5. #20243263	C₂	semidirect
6. #20243257	C₂	semidirect
7. #20243245	C₂	semidirect
8. #20243172	C₂	semidirect
9. #20243172	C₂	semidirect
10. #20243172	C₂	semidirect
11. #20243166	C₂	semidirect
12. #20243154	C₂	semidirect
13. #20243150	C₂	semidirect
14. #20243075	C₂	semidirect
20. #15689201	C₄	semidirect
21. #15689195	C₄	semidirect
67. C₂×#10625329	C₂×C₄	semidirect
70. C₂²×C₄₇⋊C₈	C₂×C₄	semidirect
79. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
80. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
83. C₂²⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
84. C₂²⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
91. #13093935	C₂×C₄	semidirect
95. C₄×C₄₇⋊C₈	C₂×C₄	semidirect
96. C₄×C₄₇⋊C₈	D₄	semidirect
351. C₄₇	#20487	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
C₂×C₄×#10625329	2
#20243263	2
#20243257	2
#20243245	2
#20243172	2
#20243166	2
#20243154	2
#20243150	2
#20243075	2
C₄₇×#2290	2
#20487	47