Subgroups — C₄₇×#8447 #26048145

Order 12032.

1016 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#1990	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#1803	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1802	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄₇×#332	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₄₇×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₇×D₄⋊C₈	C₂	1	1	yes	maximal, characteristic
8	C₂³×Q₈×C₄₇	—	2	1	no	—
9	D₄×Q₈×C₄₇	—	2	2	no	—
10	D₄×Q₈×C₄₇	—	2	2	no	—
11	D₄×Q₈×C₄₇	—	2	2	no	—
12	D₄×Q₈×C₄₇	C₄	1	4	yes	complemented
13	C₂×C₄⋊Q₈×C₄₇	—	2	1	no	—
14	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
16	C₂×C₂²⋊Q₈×C₄₇	—	2	2	no	—
17	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₄₇	—	2	1	no	—
19	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×#103×C₄₇	—	2	1	no	—
23	C₂×#102×C₄₇	—	2	1	no	—
24	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
25	C₄₇×#384	C₂²	1	1	yes	characteristic
26	C₄₇×#340	—	2	1	no	—
27	C₄₇×#340	—	2	1	no	—
28	C₄₇×#340	—	2	2	no	—
29	C₄₇×#332	—	2	2	no	—
30	C₄₇×Q₈⋊C₈	—	2	2	no	—
31	C₄₇×D₄⋊C₈	—	2	2	no	—
32	C₂²×Q₈×C₄₇	—	2	2	no	—
33	C₂²×Q₈×C₄₇	—	2	4	no	—
34	C₂²×Q₈×C₄₇	—	2	4	no	—
35	C₂²×Q₈×C₄₇	—	2	1	no	—
36	C₂²×Q₈×C₄₇	—	4	2	no	—
37	C₂²×Q₈×C₄₇	—	4	2	no	—
38	C₂²×Q₈×C₄₇	—	4	2	no	—
39	C₂²×Q₈×C₄₇	—	4	2	no	—
40	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
41	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
42	C₂³×C₄×C₄₇	—	2	2	no	—
43	C₂³×C₄×C₄₇	—	2	1	no	—
44	C₂²×C₈×C₄₇	—	2	1	no	—
45	C₂²×C₈×C₄₇	—	2	1	no	—
46	C₂²×C₈×C₄₇	—	2	1	no	—
47	C₄⋊Q₈×C₄₇	—	2	4	no	—
48	C₄⋊Q₈×C₄₇	—	2	4	no	—
49	C₄⋊Q₈×C₄₇	—	2	1	no	—
50	C₄⋊Q₈×C₄₇	—	2	1	no	—
51	C₄⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
52	C₄⋊Q₈×C₄₇	D₄	1	2	yes	—
53	C₂²⋊Q₈×C₄₇	—	2	4	no	—
54	C₂²⋊Q₈×C₄₇	—	2	8	no	—
55	C₂²⋊Q₈×C₄₇	—	2	4	no	—
56	C₂²⋊Q₈×C₄₇	—	2	8	no	—
57	C₄×Q₈×C₄₇	—	2	1	no	—
58	C₄×Q₈×C₄₇	—	2	1	no	—
59	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
60	C₄×Q₈×C₄₇	D₄	1	2	yes	—
61	C₄×D₄×C₄₇	—	2	4	no	—
62	C₄×D₄×C₄₇	—	2	4	no	—
63	C₄×D₄×C₄₇	—	2	1	no	—
64	C₄×D₄×C₄₇	—	2	1	no	—
65	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
66	C₄×D₄×C₄₇	D₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
72	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
75	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
76	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
78	C₂×C₄²×C₄₇	—	2	1	no	—
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	C₄⋊C₈×C₄₇	—	2	1	no	—
81	C₄⋊C₈×C₄₇	—	2	1	no	—
82	C₄⋊C₈×C₄₇	—	2	1	no	—
83	C₄⋊C₈×C₄₇	—	2	1	no	—
84	#103×C₄₇	—	4	2	no	—
85	#102×C₄₇	—	4	2	no	—
86	C₄×C₈×C₄₇	—	2	1	no	—
87	C₄×C₈×C₄₇	—	2	1	no	—
88	C₂⁴×C₄₇	—	2	1	no	—
89	C₂×Q₈×C₄₇	—	2	8	no	—
90	C₂×Q₈×C₄₇	—	2	2	no	—
91	C₂×Q₈×C₄₇	—	2	1	no	—
92	C₂×Q₈×C₄₇	—	2	2	no	—
93	C₂×Q₈×C₄₇	—	2	1	no	—
94	C₂×Q₈×C₄₇	—	2	1	no	—
95	C₂×Q₈×C₄₇	—	4	4	no	—
96	C₂×Q₈×C₄₇	—	4	4	no	—
97	C₂×Q₈×C₄₇	—	4	8	no	—
98	C₂×Q₈×C₄₇	—	4	8	no	—
99	C₂×Q₈×C₄₇	—	4	8	no	—
100	C₂×Q₈×C₄₇	—	4	8	no	—
101	C₂×Q₈×C₄₇	—	4	1	no	—
102	C₂×Q₈×C₄₇	—	4	1	no	—
103	C₂×Q₈×C₄₇	—	4	1	no	—
104	C₂×Q₈×C₄₇	—	4	1	no	—
105	C₂×Q₈×C₄₇	C₂²⋊C₄	1	2	yes	—
106	C₂×Q₈×C₄₇	D₈	1	2	yes	—
107	C₂×Q₈×C₄₇	SD₁₆	1	2	yes	—
108	C₂×D₄×C₄₇	—	2	1	no	—
109	C₂×D₄×C₄₇	—	2	1	no	—
110	C₂×D₄×C₄₇	—	2	1	no	—
111	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
112	C₂×D₄×C₄₇	SD₁₆	1	2	yes	—
113	C₂×D₄×C₄₇	Q₁₆	1	2	yes	—
114	C₂²×C₄×C₄₇	—	2	1	no	—
115	C₂²×C₄×C₄₇	—	2	8	no	—
116	C₂²×C₄×C₄₇	—	2	1	no	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	—	2	1	no	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	2	2	no	—
121	C₂²×C₄×C₄₇	—	4	4	no	—
122	C₂²×C₄×C₄₇	—	4	4	no	—
123	C₂²×C₄×C₄₇	—	4	1	no	—
124	C₂²×C₄×C₄₇	—	4	1	no	—
125	C₂²×C₄×C₄₇	—	4	1	no	—
126	C₂²×C₄×C₄₇	—	4	1	no	—
127	C₂²×C₄×C₄₇	—	4	1	no	—
128	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₄₇	—	2	2	no	—
132	C₂×C₈×C₄₇	—	4	1	no	—
133	C₂×C₈×C₄₇	—	4	1	no	—
134	C₂×C₈×C₄₇	—	4	1	no	—
135	C₂×C₈×C₄₇	—	4	1	no	—
136	C₂×C₈×C₄₇	—	4	1	no	—
137	C₂×C₈×C₄₇	—	4	1	no	—
138	C₂×C₈×C₄₇	—	4	1	no	—
139	C₂×C₈×C₄₇	—	4	1	no	—
140	C₄⋊C₄×C₄₇	—	2	8	no	—
141	C₄⋊C₄×C₄₇	—	2	2	no	—
142	C₄⋊C₄×C₄₇	—	2	2	no	—
143	C₄⋊C₄×C₄₇	—	2	2	no	—
144	C₄⋊C₄×C₄₇	—	2	2	no	—
145	C₄⋊C₄×C₄₇	—	2	1	no	—
146	C₄⋊C₄×C₄₇	—	2	1	no	—
147	C₄⋊C₄×C₄₇	—	2	2	no	—
148	C₄⋊C₄×C₄₇	—	4	2	no	—
149	C₄⋊C₄×C₄₇	—	4	1	no	—
150	C₄⋊C₄×C₄₇	—	4	1	no	—
151	C₄⋊C₄×C₄₇	—	4	1	no	—
152	C₄⋊C₄×C₄₇	—	4	1	no	—
153	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
154	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
155	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
156	C₂²⋊C₄×C₄₇	—	2	8	no	—
157	C₂²⋊C₄×C₄₇	—	2	2	no	—
158	C₂²⋊C₄×C₄₇	—	2	2	no	—
159	C₄²×C₄₇	—	2	2	no	—
160	C₄²×C₄₇	—	2	2	no	—
161	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
162	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
163	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
164	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
165	C₂³×C₄₇	—	2	2	no	—
166	C₂³×C₄₇	—	2	2	no	—
167	C₂³×C₄₇	—	2	2	no	—
168	C₂³×C₄₇	—	4	1	no	—
169	C₂³×C₄₇	—	4	1	no	—
170	C₂³×C₄₇	—	4	1	no	—
171	C₂³×C₄₇	—	4	1	no	—
172	C₂³×C₄₇	#120	1	1	yes	characteristic
173	Q₈×C₄₇	—	2	2	no	—
174	Q₈×C₄₇	—	2	2	no	—
175	Q₈×C₄₇	—	2	2	no	—
176	Q₈×C₄₇	—	4	16	no	—
177	Q₈×C₄₇	—	4	2	no	—
178	Q₈×C₄₇	—	4	2	no	—
179	Q₈×C₄₇	—	4	2	no	—
180	Q₈×C₄₇	—	4	2	no	—
181	Q₈×C₄₇	#102	1	4	yes	complemented
182	D₄×C₄₇	—	2	2	no	—
183	D₄×C₄₇	—	2	2	no	—
184	D₄×C₄₇	—	2	2	no	—
185	D₄×C₄₇	#103	1	4	yes	complemented
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	1	no	—
190	C₂×C₄×C₄₇	—	2	1	no	—
191	C₂×C₄×C₄₇	—	2	2	no	—
192	C₂×C₄×C₄₇	—	2	4	no	—
193	C₂×C₄×C₄₇	—	2	2	no	—
194	C₂×C₄×C₄₇	—	4	16	no	—
195	C₂×C₄×C₄₇	—	4	2	no	—
196	C₂×C₄×C₄₇	—	4	1	no	—
197	C₂×C₄×C₄₇	—	4	2	no	—
198	C₂×C₄×C₄₇	—	4	1	no	—
199	C₂×C₄×C₄₇	—	4	1	no	—
200	C₂×C₄×C₄₇	—	4	1	no	—
201	C₂×C₄×C₄₇	—	4	2	no	—
202	C₂×C₄×C₄₇	—	4	2	no	—
203	C₂×C₄×C₄₇	—	4	2	no	—
204	C₂×C₄×C₄₇	—	4	2	no	—
205	C₂×C₄×C₄₇	—	8	1	no	—
206	C₂×C₄×C₄₇	—	8	1	no	—
207	C₂×C₄×C₄₇	—	8	1	no	—
208	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
209	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
210	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
211	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
212	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
213	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
215	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
216	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
217	C₂×C₄×C₄₇	C₂×Q₁₆	1	1	yes	characteristic
218	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
219	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
220	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
221	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
222	C₈×C₄₇	—	4	2	no	—
223	C₈×C₄₇	—	8	1	no	—
224	C₈×C₄₇	—	8	1	no	—
225	#8447	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
226	C₂²×C₄₇	—	2	4	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	#379	1	1	yes	characteristic
234	C₂²×C₄₇	#447	1	1	yes	characteristic
235	C₂²×C₄₇	#448	1	1	yes	characteristic
236	C₂²×C₄₇	#450	1	1	yes	characteristic
237	C₂²×C₄₇	#451	1	1	yes	characteristic
238	C₂²×C₄₇	#454	1	1	yes	characteristic
239	C₂²×C₄₇	#456	1	1	yes	characteristic
240	C₄×C₄₇	—	2	1	no	—
241	C₄×C₄₇	—	2	1	no	—
242	C₄×C₄₇	—	2	4	no	—
243	C₄×C₄₇	—	4	2	no	—
244	C₄×C₄₇	—	4	4	no	—
245	C₄×C₄₇	—	4	2	no	—
246	C₄×C₄₇	—	16	1	no	—
247	C₄×C₄₇	C₂×#102	1	1	yes	characteristic
248	C₄×C₄₇	C₂×#103	1	1	yes	characteristic
249	C₄×C₄₇	#418	1	1	yes	characteristic
250	C₄×C₄₇	#419	1	1	yes	characteristic
251	C₄×C₄₇	#447	1	1	yes	characteristic
252	C₄×C₄₇	#448	1	1	yes	characteristic
253	C₄×C₄₇	#450	1	1	yes	characteristic
254	C₄×C₄₇	#451	1	1	yes	characteristic
255	C₂×D₄×Q₈	C₂×C₄₇	1	1	yes	characteristic
256	#1990	C₂×C₄₇	1	1	yes	characteristic, complemented
257	#1803	C₂×C₄₇	1	1	yes	characteristic, complemented
258	#1802	C₂×C₄₇	1	1	yes	characteristic
259	C₂×#332	C₂×C₄₇	1	1	yes	characteristic, complemented
260	C₂×Q₈⋊C₈	C₂×C₄₇	1	1	yes	characteristic, complemented
261	C₂×D₄⋊C₈	C₂×C₄₇	1	1	yes	characteristic
262	C₂×C₄₇	—	4	4	no	—
263	C₂×C₄₇	#1627	1	1	yes	characteristic
264	C₂×C₄₇	#1637	1	1	yes	characteristic
265	C₂×C₄₇	#1649	1	1	yes	characteristic
266	C₂×C₄₇	#1651	1	1	yes	characteristic
267	C₂×C₄₇	#1786	1	1	yes	characteristic
268	C₂×C₄₇	#1787	1	1	yes	characteristic
269	C₂×C₄₇	#1793	1	1	yes	characteristic
270	C₂³×Q₈	—	2	1	no	—
271	D₄×Q₈	—	2	2	no	—
272	D₄×Q₈	—	2	2	no	—
273	D₄×Q₈	—	2	2	no	—
274	D₄×Q₈	C₄×C₄₇	1	4	yes	complemented
275	C₂×C₄⋊Q₈	—	2	1	no	—
276	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
277	C₂×C₂²⋊Q₈	—	2	1	no	—
278	C₂×C₂²⋊Q₈	—	2	2	no	—
279	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
280	C₂×C₄×D₄	—	2	1	no	—
281	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
282	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
283	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
284	C₂×#103	—	2	1	no	—
285	C₂×#102	—	2	1	no	—
286	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
287	#384	C₂²×C₄₇	1	1	yes	characteristic
288	#340	—	2	1	no	—
289	#340	—	2	1	no	—
290	#340	—	2	2	no	—
291	#332	—	2	2	no	—
292	Q₈⋊C₈	—	2	2	no	—
293	D₄⋊C₈	—	2	2	no	—
294	C₄₇	#8447	1	1	yes	characteristic, direct product factor, Sylow
295	C₂²×Q₈	—	2	2	no	—
296	C₂²×Q₈	—	2	4	no	—
297	C₂²×Q₈	—	2	4	no	—
298	C₂²×Q₈	—	2	1	no	—
299	C₂²×Q₈	—	4	2	no	—
300	C₂²×Q₈	—	4	2	no	—
301	C₂²×Q₈	—	4	2	no	—
302	C₂²×Q₈	—	4	2	no	—
303	C₂²×Q₈	D₄×C₄₇	1	1	yes	characteristic
304	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
305	C₂³×C₄	—	2	2	no	—
306	C₂³×C₄	—	2	1	no	—
307	C₂²×C₈	—	2	1	no	—
308	C₂²×C₈	—	2	1	no	—
309	C₂²×C₈	—	2	1	no	—
310	C₄⋊Q₈	—	2	4	no	—
311	C₄⋊Q₈	—	2	4	no	—
312	C₄⋊Q₈	—	2	1	no	—
313	C₄⋊Q₈	—	2	1	no	—
314	C₄⋊Q₈	C₂×C₄×C₄₇	1	2	yes	—
315	C₄⋊Q₈	D₄×C₄₇	1	2	yes	—
316	C₂²⋊Q₈	—	2	4	no	—
317	C₂²⋊Q₈	—	2	8	no	—
318	C₂²⋊Q₈	—	2	4	no	—
319	C₂²⋊Q₈	—	2	8	no	—
320	C₄×Q₈	—	2	1	no	—
321	C₄×Q₈	—	2	1	no	—
322	C₄×Q₈	C₂×C₄×C₄₇	1	2	yes	—
323	C₄×Q₈	D₄×C₄₇	1	2	yes	—
324	C₄×D₄	—	2	4	no	—
325	C₄×D₄	—	2	4	no	—
326	C₄×D₄	—	2	1	no	—
327	C₄×D₄	—	2	1	no	—
328	C₄×D₄	C₂×C₄×C₄₇	1	2	yes	—
329	C₄×D₄	D₄×C₄₇	1	2	yes	—
330	C₂×C₄⋊C₄	—	2	2	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	1	no	—
336	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
337	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
338	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
339	C₂×C₂²⋊C₄	—	2	2	no	—
340	C₂×C₂²⋊C₄	—	2	1	no	—
341	C₂×C₄²	—	2	1	no	—
342	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
343	C₄⋊C₈	—	2	1	no	—
344	C₄⋊C₈	—	2	1	no	—
345	C₄⋊C₈	—	2	1	no	—
346	C₄⋊C₈	—	2	1	no	—
347	#103	—	4	2	no	—
348	#102	—	4	2	no	—
349	C₄×C₈	—	2	1	no	—
350	C₄×C₈	—	2	1	no	—
351	C₂⁴	—	2	1	no	—
352	C₂×Q₈	—	2	8	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	1	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	2	1	no	—
357	C₂×Q₈	—	2	1	no	—
358	C₂×Q₈	—	4	4	no	—
359	C₂×Q₈	—	4	4	no	—
360	C₂×Q₈	—	4	8	no	—
361	C₂×Q₈	—	4	8	no	—
362	C₂×Q₈	—	4	8	no	—
363	C₂×Q₈	—	4	8	no	—
364	C₂×Q₈	—	4	1	no	—
365	C₂×Q₈	—	4	1	no	—
366	C₂×Q₈	—	4	1	no	—
367	C₂×Q₈	—	4	1	no	—
368	C₂×Q₈	C₂²⋊C₄×C₄₇	1	2	yes	—
369	C₂×Q₈	D₈×C₄₇	1	2	yes	—
370	C₂×Q₈	SD₁₆×C₄₇	1	2	yes	—
371	C₂×D₄	—	2	1	no	—
372	C₂×D₄	—	2	1	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	C₂²⋊C₄×C₄₇	1	2	yes	—
375	C₂×D₄	SD₁₆×C₄₇	1	2	yes	—
376	C₂×D₄	Q₁₆×C₄₇	1	2	yes	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	8	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	4	4	no	—
385	C₂²×C₄	—	4	4	no	—
386	C₂²×C₄	—	4	1	no	—
387	C₂²×C₄	—	4	1	no	—
388	C₂²×C₄	—	4	1	no	—
389	C₂²×C₄	—	4	1	no	—
390	C₂²×C₄	—	4	1	no	—
391	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
392	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
393	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
394	C₂×C₈	—	2	2	no	—
395	C₂×C₈	—	4	1	no	—
396	C₂×C₈	—	4	1	no	—
397	C₂×C₈	—	4	1	no	—
398	C₂×C₈	—	4	1	no	—
399	C₂×C₈	—	4	1	no	—
400	C₂×C₈	—	4	1	no	—
401	C₂×C₈	—	4	1	no	—
402	C₂×C₈	—	4	1	no	—
403	C₄⋊C₄	—	2	8	no	—
404	C₄⋊C₄	—	2	2	no	—
405	C₄⋊C₄	—	2	2	no	—
406	C₄⋊C₄	—	2	2	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	1	no	—
409	C₄⋊C₄	—	2	1	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	—	4	1	no	—
413	C₄⋊C₄	—	4	1	no	—
414	C₄⋊C₄	—	4	1	no	—
415	C₄⋊C₄	—	4	1	no	—
416	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
417	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	2	yes	—
418	C₄⋊C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
419	C₂²⋊C₄	—	2	8	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	2	no	—
422	C₄²	—	2	2	no	—
423	C₄²	—	2	2	no	—
424	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
425	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
426	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
427	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
428	C₂³	—	2	2	no	—
429	C₂³	—	2	2	no	—
430	C₂³	—	2	2	no	—
431	C₂³	—	4	1	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	#120×C₄₇	1	1	yes	characteristic
436	Q₈	—	2	2	no	—
437	Q₈	—	2	2	no	—
438	Q₈	—	2	2	no	—
439	Q₈	—	4	16	no	—
440	Q₈	—	4	2	no	—
441	Q₈	—	4	2	no	—
442	Q₈	—	4	2	no	—
443	Q₈	—	4	2	no	—
444	Q₈	#102×C₄₇	1	4	yes	complemented
445	D₄	—	2	2	no	—
446	D₄	—	2	2	no	—
447	D₄	—	2	2	no	—
448	D₄	#103×C₄₇	1	4	yes	complemented
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	4	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	4	16	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	1	no	—
460	C₂×C₄	—	4	1	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	8	1	no	—
469	C₂×C₄	—	8	1	no	—
470	C₂×C₄	—	8	1	no	—
471	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
472	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
473	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
474	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
475	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
476	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
477	C₂×C₄	C₂×D₈×C₄₇	1	1	yes	characteristic
478	C₂×C₄	C₂×SD₁₆×C₄₇	1	1	yes	characteristic
479	C₂×C₄	C₂×SD₁₆×C₄₇	1	1	yes	characteristic
480	C₂×C₄	C₂×Q₁₆×C₄₇	1	1	yes	characteristic
481	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
482	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
483	C₂×C₄	#137×C₄₇	1	1	yes	characteristic
484	C₂×C₄	#137×C₄₇	1	1	yes	characteristic
485	C₈	—	4	2	no	—
486	C₈	—	8	1	no	—
487	C₈	—	8	1	no	—
488	C₂²	—	2	4	no	—
489	C₂²	—	4	2	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	—	4	2	no	—
495	C₂²	C₄₇×#379	1	1	yes	characteristic
496	C₂²	C₄₇×#447	1	1	yes	characteristic
497	C₂²	C₄₇×#448	1	1	yes	characteristic
498	C₂²	C₄₇×#450	1	1	yes	characteristic
499	C₂²	C₄₇×#451	1	1	yes	characteristic
500	C₂²	C₄₇×#454	1	1	yes	characteristic
501	C₂²	C₄₇×#456	1	1	yes	characteristic
502	C₄	—	2	4	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	4	4	no	—
506	C₄	—	4	2	no	—
507	C₄	—	4	2	no	—
508	C₄	—	16	1	no	—
509	C₄	C₂×#102×C₄₇	1	1	yes	characteristic
510	C₄	C₂×#103×C₄₇	1	1	yes	characteristic
511	C₄	C₄₇×#418	1	1	yes	characteristic
512	C₄	C₄₇×#419	1	1	yes	characteristic
513	C₄	C₄₇×#447	1	1	yes	characteristic
514	C₄	C₄₇×#448	1	1	yes	characteristic
515	C₄	C₄₇×#450	1	1	yes	characteristic
516	C₄	C₄₇×#451	1	1	yes	characteristic
517	C₂	—	4	4	no	—
518	C₂	C₄₇×#1627	1	1	yes	characteristic
519	C₂	C₄₇×#1637	1	1	yes	characteristic
520	C₂	C₄₇×#1649	1	1	yes	characteristic
521	C₂	C₄₇×#1651	1	1	yes	characteristic
522	C₂	C₄₇×#1786	1	1	yes	characteristic
523	C₂	C₄₇×#1787	1	1	yes	characteristic
524	C₂	C₄₇×#1793	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	#120
commutator	C₄²	C₂²×C₄×C₄₇
Frattini, cosocle	C₂×C₄²	C₂³×C₄₇
prime radical	C₂²×D₄×C₄₇	D₄
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#1990	C₂	semidirect
3. C₄₇×#1803	C₂	semidirect
5. C₂×C₄₇×#332	C₂	semidirect
6. C₂×C₄₇×Q₈⋊C₈	C₂	semidirect
12. D₄×Q₈×C₄₇	C₄	semidirect
181. Q₈×C₄₇	#102	semidirect
185. D₄×C₄₇	#103	semidirect
225. #8447	C₄₇	direct (N × H)
256. #1990	C₂×C₄₇	semidirect
257. #1803	C₂×C₄₇	semidirect
259. C₂×#332	C₂×C₄₇	semidirect
260. C₂×Q₈⋊C₈	C₂×C₄₇	semidirect
274. D₄×Q₈	C₄×C₄₇	semidirect
294. C₄₇	#8447	direct (N × H)
444. Q₈	#102×C₄₇	semidirect
448. D₄	#103×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₄₇	2
C₄₇×#1990	2
C₄₇×#1803	2
C₄₇×#1802	2
C₂×C₄₇×#332	2
C₂×C₄₇×Q₈⋊C₈	2
C₂×C₄₇×D₄⋊C₈	2
#8447	47

Subgroups — C47×#8447 #26048145

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#8447 #26048145