Subgroups — #460×Dic₄₇ #26222477

Order 12032.

1152 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×SD₁₆×Dic₄₇	C₂	1	2	yes	maximal, complemented
2	#127×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄×Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244316	C₂	1	1	yes	maximal, characteristic
5	#20244152	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244017	C₂	1	2	yes	maximal, complemented
7	#20243745	C₂	1	2	yes	maximal, complemented
8	#20243393	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄⋊C₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#102×Dic₄₇	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×#460	C₂	1	1	yes	maximal, characteristic
12	C₂×Q₈×Dic₄₇	C₂²	1	1	yes	characteristic
13	C₂×Q₈×Dic₄₇	C₂²	1	1	yes	characteristic
14	C₂×D₄×Dic₄₇	—	2	1	no	—
15	C₂×D₄×Dic₄₇	—	2	1	no	—
16	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
17	SD₁₆×Dic₄₇	—	2	8	no	—
18	C₂×#13093956	C₂²	1	2	yes	—
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×#13093948	C₂²	1	2	yes	—
21	C₂×#13093945	C₂²	1	2	yes	—
22	C₂×#13093945	C₂²	1	2	yes	—
23	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
24	#15689026	—	2	1	no	—
25	#15689026	—	2	1	no	—
26	#15689026	C₂²	1	2	yes	—
27	#15688993	C₂²	1	1	yes	characteristic
28	C₄⋊C₄×Dic₄₇	—	2	1	no	—
29	C₄⋊C₄×Dic₄₇	—	2	1	no	—
30	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
31	C₄⋊C₄×Dic₄₇	C₂²	1	1	yes	characteristic
32	C₄×C₄⋊Dic₄₇	—	2	1	no	—
33	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
34	C₄²×Dic₄₇	—	2	1	no	—
35	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
36	#15688886	C₂²	1	2	yes	—
37	#15688885	C₂²	1	2	yes	—
38	#15688877	C₂²	1	2	yes	—
39	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
40	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#460	C₄	1	8	yes	complemented
43	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
44	C₂×#102×C₄₇	C₂²	1	2	yes	—
45	C₂³×Dic₄₇	—	2	2	no	—
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	Q₈×Dic₄₇	—	2	2	no	—
48	Q₈×Dic₄₇	—	2	2	no	—
49	Q₈×Dic₄₇	—	2	2	no	—
50	Q₈×Dic₄₇	D₄	1	4	yes	complemented
51	D₄×Dic₄₇	—	2	4	no	—
52	D₄×Dic₄₇	—	2	4	no	—
53	D₄×Dic₄₇	—	4	4	no	—
54	D₄×Dic₄₇	—	4	4	no	—
55	C₂×C₄⋊Dic₄₇	—	2	1	no	—
56	C₂×C₄⋊Dic₄₇	—	2	1	no	—
57	C₂×C₄⋊Dic₄₇	—	2	1	no	—
58	C₂×C₄⋊Dic₄₇	—	2	1	no	—
59	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
60	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
61	C₂×C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
62	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
63	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
64	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
65	C₂×C₄×Dic₄₇	—	2	1	no	—
66	C₂×C₄×Dic₄₇	—	2	1	no	—
67	C₂×C₄×Dic₄₇	—	2	1	no	—
68	C₂×C₄×Dic₄₇	—	2	1	no	—
69	C₂×C₄×Dic₄₇	—	2	1	no	—
70	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
71	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
72	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
73	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
74	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
75	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
76	#13093956	—	2	4	no	—
77	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
78	#13093948	—	2	4	no	—
79	#13093945	—	2	4	no	—
80	#13093945	—	2	4	no	—
81	C₈×Dic₄₇	—	2	4	no	—
82	C₄₇⋊#95	—	2	1	no	—
83	C₄₇⋊#95	—	2	1	no	—
84	C₄₇⋊#95	—	2	1	no	—
85	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₂²×D₄×C₄₇	—	2	1	no	—
87	C₂²×D₄×C₄₇	—	2	1	no	—
88	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
89	C₂×SD₁₆×C₄₇	—	2	4	no	—
90	C₂×SD₁₆×C₄₇	—	2	4	no	—
91	C₂×SD₁₆×C₄₇	C₂×C₄	1	8	yes	complemented
92	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
93	#127×C₄₇	—	2	2	no	—
94	#127×C₄₇	C₂×C₄	1	4	yes	—
95	C₄×Q₈×C₄₇	—	2	2	no	—
96	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	complemented
97	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
98	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₄₇	—	2	1	no	—
100	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
101	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
102	#102×C₄₇	C₂×C₄	1	8	yes	complemented
103	C₂⁴×C₄₇	—	2	2	no	—
104	C₂×Q₈×C₄₇	—	2	1	no	—
105	C₂×Q₈×C₄₇	—	2	1	no	—
106	C₂×Q₈×C₄₇	—	2	1	no	—
107	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
108	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
109	C₂×Q₈×C₄₇	#41	1	2	yes	—
110	C₂×D₄×C₄₇	—	2	4	no	—
111	C₂×D₄×C₄₇	—	2	4	no	—
112	C₂×D₄×C₄₇	—	2	2	no	—
113	C₂×D₄×C₄₇	—	2	2	no	—
114	C₂×D₄×C₄₇	—	2	2	no	—
115	C₂×D₄×C₄₇	—	2	2	no	—
116	C₂×D₄×C₄₇	—	2	2	no	—
117	C₂×D₄×C₄₇	—	4	2	no	—
118	C₂×D₄×C₄₇	—	4	2	no	—
119	C₂×D₄×C₄₇	—	4	2	no	—
120	C₂×D₄×C₄₇	—	4	2	no	—
121	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
122	C₂²×C₄×C₄₇	—	2	1	no	—
123	C₂²×C₄×C₄₇	—	2	1	no	—
124	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
127	C₂²×Dic₄₇	—	2	1	no	—
128	C₂²×Dic₄₇	—	2	1	no	—
129	C₂²×Dic₄₇	—	2	2	no	—
130	C₂²×Dic₄₇	—	4	4	no	—
131	C₂²×Dic₄₇	—	4	4	no	—
132	C₂²×Dic₄₇	—	4	4	no	—
133	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
135	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
136	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
137	SD₁₆×C₄₇	—	2	16	no	—
138	C₂×C₈×C₄₇	—	2	2	no	—
139	C₂×C₈×C₄₇	—	2	2	no	—
140	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
141	C₄⋊C₄×C₄₇	—	2	4	no	—
142	C₄⋊C₄×C₄₇	—	2	1	no	—
143	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
144	C₄²×C₄₇	—	2	4	no	—
145	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
146	C₄²×C₄₇	#41	1	2	yes	—
147	C₂²⋊Dic₄₇	—	4	4	no	—
148	C₂²⋊Dic₄₇	—	4	4	no	—
149	C₂²⋊Dic₄₇	—	4	4	no	—
150	C₄⋊Dic₄₇	—	2	4	no	—
151	C₄⋊Dic₄₇	—	2	1	no	—
152	C₄⋊Dic₄₇	—	2	1	no	—
153	C₄⋊Dic₄₇	—	2	4	no	—
154	C₄⋊Dic₄₇	—	2	2	no	—
155	C₄⋊Dic₄₇	—	2	2	no	—
156	C₄⋊Dic₄₇	—	4	2	no	—
157	C₄⋊Dic₄₇	—	4	2	no	—
158	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
159	C₄⋊Dic₄₇	#41	1	2	yes	—
160	C₄×Dic₄₇	—	2	4	no	—
161	C₄×Dic₄₇	—	2	2	no	—
162	C₄×Dic₄₇	—	2	1	no	—
163	C₄×Dic₄₇	—	2	1	no	—
164	C₄×Dic₄₇	—	2	4	no	—
165	C₄×Dic₄₇	—	2	2	no	—
166	C₄×Dic₄₇	—	4	1	no	—
167	C₄×Dic₄₇	—	4	2	no	—
168	C₄×Dic₄₇	—	4	2	no	—
169	C₄×Dic₄₇	—	4	2	no	—
170	C₄×Dic₄₇	SD₁₆	1	4	yes	complemented
171	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
172	C₄×Dic₄₇	#41	1	2	yes	—
173	C₂×C₄₇⋊C₈	—	2	2	no	—
174	C₂×C₄₇⋊C₈	—	2	2	no	—
175	C₂×C₄₇⋊C₈	—	2	2	no	—
176	C₂³×C₄₇	—	2	4	no	—
177	C₂³×C₄₇	—	4	2	no	—
178	C₂³×C₄₇	—	4	2	no	—
179	C₂³×C₄₇	—	4	2	no	—
180	C₂³×C₄₇	—	4	2	no	—
181	C₂³×C₄₇	—	4	2	no	—
182	C₂³×C₄₇	—	4	2	no	—
183	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
184	Q₈×C₄₇	—	2	2	no	—
185	Q₈×C₄₇	—	2	2	no	—
186	Q₈×C₄₇	—	2	2	no	—
187	Q₈×C₄₇	C₄×D₄	1	4	yes	complemented
188	D₄×C₄₇	—	2	4	no	—
189	D₄×C₄₇	—	2	4	no	—
190	D₄×C₄₇	—	4	8	no	—
191	D₄×C₄₇	—	4	2	no	—
192	D₄×C₄₇	—	4	2	no	—
193	D₄×C₄₇	—	4	8	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	1	no	—
198	C₂×C₄×C₄₇	—	2	1	no	—
199	C₂×C₄×C₄₇	—	2	2	no	—
200	C₂×C₄×C₄₇	—	4	1	no	—
201	C₂×C₄×C₄₇	—	4	1	no	—
202	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
203	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
204	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
205	C₂×C₄×C₄₇	#135	1	2	yes	—
206	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
207	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
212	C₂×Dic₄₇	—	2	1	no	—
213	C₂×Dic₄₇	—	2	1	no	—
214	C₂×Dic₄₇	—	2	1	no	—
215	C₂×Dic₄₇	—	2	1	no	—
216	C₂×Dic₄₇	—	2	2	no	—
217	C₂×Dic₄₇	—	2	1	no	—
218	C₂×Dic₄₇	—	2	2	no	—
219	C₂×Dic₄₇	—	2	1	no	—
220	C₂×Dic₄₇	—	2	1	no	—
221	C₂×Dic₄₇	—	4	1	no	—
222	C₂×Dic₄₇	—	4	1	no	—
223	C₂×Dic₄₇	—	4	1	no	—
224	C₂×Dic₄₇	—	4	1	no	—
225	C₂×Dic₄₇	—	4	2	no	—
226	C₂×Dic₄₇	—	4	2	no	—
227	C₂×Dic₄₇	—	4	2	no	—
228	C₂×Dic₄₇	—	8	8	no	—
229	C₂×Dic₄₇	#121	1	2	yes	—
230	C₂×Dic₄₇	#121	1	2	yes	—
231	C₂×Dic₄₇	C₂×SD₁₆	1	2	yes	—
232	C₂×Dic₄₇	C₂×SD₁₆	1	2	yes	—
233	C₂×Dic₄₇	AGL(1,ℤ/8)	1	2	yes	—
234	C₈×C₄₇	—	2	4	no	—
235	C₄₇⋊C₈	—	4	2	no	—
236	C₄×#460	—	47	1	no	maximal, Sylow
237	C₂²×C₄₇	—	4	4	no	—
238	C₂²×C₄₇	—	4	4	no	—
239	C₂²×C₄₇	—	4	4	no	—
240	C₂²×C₄₇	—	8	2	no	—
241	C₂²×C₄₇	—	8	2	no	—
242	C₂²×C₄₇	—	8	2	no	—
243	C₂²×C₄₇	—	8	2	no	—
244	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
245	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
246	C₂²×C₄₇	#525	1	1	yes	characteristic
247	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
248	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
249	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
250	C₂²×C₄₇	#575	1	1	yes	characteristic
251	C₄×C₄₇	—	2	2	no	—
252	C₄×C₄₇	—	2	4	no	—
253	C₄×C₄₇	—	4	2	no	—
254	C₄×C₄₇	C₄×SD₁₆	1	4	yes	complemented
255	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
256	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
257	C₄×C₄₇	#529	1	1	yes	characteristic
258	C₄×C₄₇	#532	1	1	yes	characteristic
259	Dic₄₇	—	2	2	no	—
260	Dic₄₇	—	2	2	no	—
261	Dic₄₇	—	4	1	no	—
262	Dic₄₇	—	4	2	no	—
263	Dic₄₇	—	4	2	no	—
264	Dic₄₇	—	8	2	no	—
265	Dic₄₇	#460	1	4	yes	direct product factor
266	C₂×#460	D₄₇	1	1	yes	characteristic
267	C₂×C₄×SD₁₆	—	47	2	no	—
268	C₄×#127	—	47	1	no	—
269	C₄²×Q₈	—	47	1	no	—
270	#1982	—	47	1	no	—
271	#1948	—	47	1	no	—
272	#1926	—	47	2	no	—
273	#1880	—	47	2	no	—
274	#1803	—	47	1	no	—
275	C₄×C₄⋊C₈	—	47	1	no	—
276	C₄×#102	—	47	2	no	—
277	C₂×C₄₇	—	8	4	no	—
278	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
279	C₂×C₄₇	C₂×C₄×SD₁₆	1	1	yes	characteristic
280	C₂×C₄₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
281	C₂×C₄₇	C₂×#460	1	1	yes	characteristic
282	C₂×C₄₇	#3035	1	1	yes	characteristic
283	C₂×C₄₇	#3103	1	1	yes	characteristic
284	C₂×C₄₇	#3106	1	1	yes	characteristic
285	C₂²×SD₁₆	C₂×D₄₇	1	2	yes	—
286	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
287	C₂×C₄×Q₈	—	47	1	no	—
288	C₂×C₄×Q₈	—	47	1	no	—
289	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
290	C₂×C₄×D₄	—	47	2	no	—
291	C₂×C₄×D₄	—	94	1	no	—
292	C₂×C₄×D₄	—	94	1	no	—
293	#460	Dic₄₇	1	8	yes	direct product factor
294	C₄×SD₁₆	—	94	8	no	—
295	C₂×#106	—	47	2	no	—
296	C₂×C₄⋊C₈	—	47	1	no	—
297	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
298	C₂×#103	—	47	2	no	—
299	C₂×#102	—	47	2	no	—
300	C₂×#102	—	47	2	no	—
301	C₂×#102	C₂×D₄₇	1	2	yes	—
302	C₂×C₄×C₈	—	47	2	no	—
303	#390	—	47	2	no	—
304	#390	—	94	1	no	—
305	#390	—	94	1	no	—
306	#384	—	47	1	no	—
307	C₄×C₄⋊C₄	—	47	1	no	—
308	C₄×C₄⋊C₄	—	47	1	no	—
309	C₄×C₄⋊C₄	—	47	1	no	—
310	C₄×C₄⋊C₄	—	94	1	no	—
311	C₄×C₄⋊C₄	—	94	1	no	—
312	C₄×C₄⋊C₄	—	94	1	no	—
313	C₄³	—	47	1	no	—
314	C₄³	—	94	1	no	—
315	#340	—	47	2	no	—
316	#340	—	47	2	no	—
317	#336	—	47	2	no	—
318	C₄₇	C₄×#460	1	1	yes	characteristic, complemented, Sylow
319	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
320	C₂²×D₄	—	2	1	no	—
321	C₂²×D₄	—	2	1	no	—
322	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
323	C₂³×C₄	—	94	2	no	—
324	C₂×SD₁₆	—	2	4	no	—
325	C₂×SD₁₆	—	2	4	no	—
326	C₂×SD₁₆	C₂×Dic₄₇	1	8	yes	complemented
327	C₂²×C₈	—	47	2	no	—
328	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
329	#127	—	2	2	no	—
330	#127	C₂×Dic₄₇	1	4	yes	—
331	C₄×Q₈	—	2	2	no	—
332	C₄×Q₈	—	47	4	no	—
333	C₄×Q₈	—	94	2	no	—
334	C₄×Q₈	—	94	2	no	—
335	C₄×Q₈	—	94	2	no	—
336	C₄×Q₈	C₂×Dic₄₇	1	4	yes	complemented
337	C₄×D₄	—	94	4	no	—
338	C₄×D₄	—	94	4	no	—
339	C₄×D₄	—	188	4	no	—
340	C₄×D₄	—	188	4	no	—
341	C₂×C₄⋊C₄	—	2	1	no	—
342	C₂×C₄⋊C₄	—	47	1	no	—
343	C₂×C₄⋊C₄	—	47	1	no	—
344	C₂×C₄⋊C₄	—	47	2	no	—
345	C₂×C₄⋊C₄	—	94	1	no	—
346	C₂×C₄⋊C₄	—	94	1	no	—
347	C₂×C₄⋊C₄	—	94	1	no	—
348	C₂×C₄⋊C₄	—	94	1	no	—
349	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
350	C₂×C₂²⋊C₄	—	94	2	no	—
351	C₂×C₂²⋊C₄	—	94	2	no	—
352	C₂×C₂²⋊C₄	—	94	2	no	—
353	C₂×C₄²	—	2	1	no	—
354	C₂×C₄²	—	47	1	no	—
355	C₂×C₄²	—	47	1	no	—
356	C₂×C₄²	—	47	1	no	—
357	C₂×C₄²	—	47	1	no	—
358	C₂×C₄²	—	47	1	no	—
359	C₂×C₄²	—	47	1	no	—
360	C₂×C₄²	—	94	1	no	—
361	C₂×C₄²	—	94	1	no	—
362	C₂×C₄²	—	94	1	no	—
363	C₂×C₄²	—	94	1	no	—
364	C₂×C₄²	—	94	1	no	—
365	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
366	#106	—	94	4	no	—
367	C₄⋊C₈	—	94	2	no	—
368	C₄⋊C₈	C₂×Dic₄₇	1	4	yes	complemented
369	#103	—	94	4	no	—
370	#102	—	94	4	no	—
371	#102	—	94	4	no	—
372	#102	C₂×Dic₄₇	1	8	yes	complemented
373	C₄×C₈	—	94	4	no	—
374	#95	—	94	1	no	—
375	#95	—	94	1	no	—
376	#95	—	94	1	no	—
377	C₂⁴	—	2	2	no	—
378	C₂×Q₈	—	2	1	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	2	1	no	—
381	C₂×Q₈	D₄×D₄₇	1	2	yes	—
382	C₂×Q₈	#10625352	1	2	yes	—
383	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
384	C₂×D₄	—	2	4	no	—
385	C₂×D₄	—	2	4	no	—
386	C₂×D₄	—	2	2	no	—
387	C₂×D₄	—	2	2	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	4	2	no	—
392	C₂×D₄	—	4	2	no	—
393	C₂×D₄	—	4	2	no	—
394	C₂×D₄	—	4	2	no	—
395	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	47	1	no	—
399	C₂²×C₄	—	47	1	no	—
400	C₂²×C₄	—	47	1	no	—
401	C₂²×C₄	—	47	1	no	—
402	C₂²×C₄	—	94	1	no	—
403	C₂²×C₄	—	94	1	no	—
404	C₂²×C₄	—	94	2	no	—
405	C₂²×C₄	—	188	4	no	—
406	C₂²×C₄	—	188	4	no	—
407	C₂²×C₄	—	188	4	no	—
408	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
409	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
410	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
411	SD₁₆	—	2	16	no	—
412	C₂×C₈	—	2	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	94	2	no	—
415	C₂×C₈	—	94	2	no	—
416	C₂×C₈	—	94	2	no	—
417	C₂×C₈	C₂²×Dic₄₇	1	4	yes	—
418	C₄⋊C₄	—	2	4	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	47	2	no	—
421	C₄⋊C₄	—	47	2	no	—
422	C₄⋊C₄	—	94	4	no	—
423	C₄⋊C₄	—	94	4	no	—
424	C₄⋊C₄	—	94	1	no	—
425	C₄⋊C₄	—	94	1	no	—
426	C₄⋊C₄	—	94	2	no	—
427	C₄⋊C₄	—	94	2	no	—
428	C₄⋊C₄	—	188	2	no	—
429	C₄⋊C₄	—	188	2	no	—
430	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
431	C₂²⋊C₄	—	188	4	no	—
432	C₂²⋊C₄	—	188	4	no	—
433	C₂²⋊C₄	—	188	4	no	—
434	C₄²	—	2	4	no	—
435	C₄²	—	47	4	no	—
436	C₄²	—	47	2	no	—
437	C₄²	—	47	2	no	—
438	C₄²	—	94	2	no	—
439	C₄²	—	94	4	no	—
440	C₄²	—	94	4	no	—
441	C₄²	—	94	2	no	—
442	C₄²	—	94	1	no	—
443	C₄²	—	94	1	no	—
444	C₄²	—	188	1	no	—
445	C₄²	—	188	2	no	—
446	C₄²	—	188	2	no	—
447	C₄²	—	188	2	no	—
448	C₄²	#10625352	1	2	yes	—
449	C₄²	C₂²×Dic₄₇	1	2	yes	—
450	C₂³	—	2	4	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	2	no	—
457	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
458	Q₈	—	2	2	no	—
459	Q₈	—	2	2	no	—
460	Q₈	—	2	2	no	—
461	Q₈	D₄×Dic₄₇	1	4	yes	complemented
462	D₄	—	2	4	no	—
463	D₄	—	2	4	no	—
464	D₄	—	4	8	no	—
465	D₄	—	4	2	no	—
466	D₄	—	4	2	no	—
467	D₄	—	4	8	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	1	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	47	2	no	—
477	C₂×C₄	—	47	2	no	—
478	C₂×C₄	—	47	2	no	—
479	C₂×C₄	—	47	2	no	—
480	C₂×C₄	—	47	2	no	—
481	C₂×C₄	—	94	1	no	—
482	C₂×C₄	—	94	1	no	—
483	C₂×C₄	—	94	1	no	—
484	C₂×C₄	—	94	1	no	—
485	C₂×C₄	—	94	2	no	—
486	C₂×C₄	—	94	2	no	—
487	C₂×C₄	—	94	1	no	—
488	C₂×C₄	—	94	1	no	—
489	C₂×C₄	—	94	1	no	—
490	C₂×C₄	—	376	8	no	—
491	C₂×C₄	—	188	2	no	—
492	C₂×C₄	—	188	2	no	—
493	C₂×C₄	—	188	2	no	—
494	C₂×C₄	—	188	1	no	—
495	C₂×C₄	—	188	1	no	—
496	C₂×C₄	—	188	1	no	—
497	C₂×C₄	—	188	1	no	—
498	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
499	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
500	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
501	C₂×C₄	#13094045	1	2	yes	—
502	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
503	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
504	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
505	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
506	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
507	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
508	C₈	—	2	4	no	—
509	C₈	—	188	2	no	—
510	C₂²	—	4	4	no	—
511	C₂²	—	4	4	no	—
512	C₂²	—	4	4	no	—
513	C₂²	—	8	2	no	—
514	C₂²	—	8	2	no	—
515	C₂²	—	8	2	no	—
516	C₂²	—	8	2	no	—
517	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
518	C₂²	#121×D₄₇	1	1	yes	characteristic
519	C₂²	#15689633	1	1	yes	characteristic
520	C₂²	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
521	C₂²	C₂×#13094045	1	1	yes	characteristic
522	C₂²	AGL(1,ℤ/8)×D₄₇	1	1	yes	characteristic
523	C₂²	#15689919	1	1	yes	characteristic
524	C₄	—	2	2	no	—
525	C₄	—	2	4	no	—
526	C₄	—	4	2	no	—
527	C₄	—	47	4	no	—
528	C₄	—	94	2	no	—
529	C₄	—	94	2	no	—
530	C₄	—	376	2	no	—
531	C₄	—	188	1	no	—
532	C₄	—	188	2	no	—
533	C₄	—	188	2	no	—
534	C₄	SD₁₆×Dic₄₇	1	4	yes	complemented
535	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
536	C₄	#41×Dic₄₇	1	1	yes	characteristic
537	C₄	#15689654	1	1	yes	characteristic
538	C₄	#15689668	1	1	yes	characteristic
539	C₂	—	8	4	no	—
540	C₂	#121×Dic₄₇	1	1	yes	characteristic
541	C₂	C₂×SD₁₆×Dic₄₇	1	1	yes	characteristic
542	C₂	AGL(1,ℤ/8)×Dic₄₇	1	1	yes	characteristic
543	C₂	#460×D₄₇	1	1	yes	characteristic
544	C₂	#20252838	1	1	yes	characteristic
545	C₂	#20253418	1	1	yes	characteristic
546	C₂	#20253447	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#460	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂×#127×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#460	D₄₇
hypocenter	C₄₇	C₄×#460
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#460

Complements

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

N	H ≅ G/N	type
1. C₂×SD₁₆×Dic₄₇	C₂	semidirect
3. C₄×Q₈×Dic₄₇	C₂	semidirect
5. #20244152	C₂	semidirect
6. #20244017	C₂	semidirect
7. #20243745	C₂	semidirect
8. #20243393	C₂	semidirect
9. C₄⋊C₈×Dic₄₇	C₂	semidirect
10. #102×Dic₄₇	C₂	semidirect
42. C₄₇×#460	C₄	semidirect
50. Q₈×Dic₄₇	D₄	semidirect
91. C₂×SD₁₆×C₄₇	C₂×C₄	semidirect
96. C₄×Q₈×C₄₇	C₂×C₄	semidirect
101. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
102. #102×C₄₇	C₂×C₄	semidirect
170. C₄×Dic₄₇	SD₁₆	semidirect
187. Q₈×C₄₇	C₄×D₄	semidirect
254. C₄×C₄₇	C₄×SD₁₆	semidirect
265. Dic₄₇	#460	direct (N × H)
293. #460	Dic₄₇	direct (N × H)
318. C₄₇	C₄×#460	semidirect
326. C₂×SD₁₆	C₂×Dic₄₇	semidirect
336. C₄×Q₈	C₂×Dic₄₇	semidirect
368. C₄⋊C₈	C₂×Dic₄₇	semidirect
372. #102	C₂×Dic₄₇	semidirect
461. Q₈	D₄×Dic₄₇	semidirect
534. C₄	SD₁₆×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₁₆×Dic₄₇	2
#127×Dic₄₇	2
C₄×Q₈×Dic₄₇	2
#20244316	2
#20244152	2
#20244017	2
#20243745	2
#20243393	2
C₄⋊C₈×Dic₄₇	2
#102×Dic₄₇	2
C₂×C₄₇×#460	2
C₄×#460	47

Subgroups — #460×Dic47 #26222477

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #460×Dic₄₇ #26222477