Subgroups — C₄₇×#18746 #26058444

Order 12032.

1688 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄²×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#3205	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#3036	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1639	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1619	C₂	1	4	yes	maximal, complemented
7	C₄₇×#1545	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1486	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×D₄×C₄₇	—	2	1	no	—
11	C₂³×D₄×C₄₇	—	2	1	no	—
12	C₂×AGL(1,ℤ/8)×C₄₇	—	2	1	no	—
13	D₄²×C₄₇	—	2	2	no	—
14	D₄²×C₄₇	—	2	2	no	—
15	D₄²×C₄₇	—	2	2	no	—
16	D₄²×C₄₇	C₂²	1	4	yes	—
17	C₄₇×#532	C₂²	1	1	yes	characteristic, complemented
18	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#121×C₄₇	—	2	1	no	—
20	C₂×#121×C₄₇	—	2	1	no	—
21	C₂×#120×C₄₇	—	2	2	no	—
22	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
24	C₄₇×#493	C₂²	1	2	yes	complemented
25	C₄₇×#486	C₂²	1	2	yes	complemented
26	C₄₇×#480	—	2	1	no	—
27	C₄₇×#474	C₂²	1	2	yes	complemented
28	C₄₇×#463	—	2	2	no	—
29	C₄₇×#461	C₂²	1	2	yes	complemented
30	C₄₇×#459	—	2	2	no	—
31	C₄₇×#459	C₂²	1	2	yes	complemented
32	C₄₇×#459	C₂²	1	2	yes	complemented
33	C₄₇×#447	—	2	1	no	—
34	C₄₇×#447	—	2	2	no	—
35	C₄×D₈×C₄₇	—	2	2	no	—
36	C₄₇×#431	C₂²	1	1	yes	characteristic, complemented
37	C₄₇×#431	C₂²	1	1	yes	characteristic, complemented
38	C₄₇×#423	C₂²	1	1	yes	characteristic, complemented
39	C₄₇×#417	—	2	1	no	—
40	C₄₇×#331	C₂²	1	4	yes	complemented
41	C₄₇×D₄⋊C₈	C₂²	1	4	yes	complemented
42	C₄₇×D₄⋊C₈	C₂²	1	4	yes	complemented
43	C₂⁵×C₄₇	—	2	2	no	—
44	C₂×#41×C₄₇	—	2	1	no	—
45	C₂²×D₄×C₄₇	—	2	2	no	—
46	C₂²×D₄×C₄₇	—	2	2	no	—
47	C₂²×D₄×C₄₇	—	2	4	no	—
48	C₂²×D₄×C₄₇	—	2	4	no	—
49	C₂²×D₄×C₄₇	—	2	4	no	—
50	C₂²×D₄×C₄₇	—	2	4	no	—
51	C₂²×D₄×C₄₇	—	2	1	no	—
52	C₂²×D₄×C₄₇	—	2	1	no	—
53	C₂²×D₄×C₄₇	—	4	8	no	—
54	C₂²×D₄×C₄₇	—	4	4	no	—
55	C₂²×D₄×C₄₇	—	4	4	no	—
56	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
57	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
58	C₂²×D₄×C₄₇	D₄	1	2	yes	—
59	C₂³×C₄×C₄₇	—	2	1	no	—
60	C₂³×C₄×C₄₇	—	2	1	no	—
61	AGL(1,ℤ/8)×C₄₇	—	4	4	no	—
62	C₂×SD₁₆×C₄₇	—	2	2	no	—
63	C₂×D₈×C₄₇	—	2	2	no	—
64	C₂×D₈×C₄₇	—	2	2	no	—
65	C₂×D₈×C₄₇	—	2	4	no	—
66	C₂×M₁₆×C₄₇	—	2	1	no	—
67	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic, complemented
68	#127×C₄₇	—	2	1	no	—
69	#127×C₄₇	—	2	1	no	—
70	#127×C₄₇	D₄	1	2	yes	—
71	#127×C₄₇	C₂³	1	2	yes	—
72	#127×C₄₇	C₂³	1	1	yes	characteristic, complemented
73	#124×C₄₇	—	2	1	no	—
74	#121×C₄₇	—	2	4	no	—
75	#121×C₄₇	—	2	4	no	—
76	#121×C₄₇	—	2	4	no	—
77	#121×C₄₇	—	2	4	no	—
78	#121×C₄₇	—	2	1	no	—
79	#121×C₄₇	—	2	1	no	—
80	#120×C₄₇	—	2	8	no	—
81	#120×C₄₇	—	2	8	no	—
82	C₄×D₄×C₄₇	—	2	1	no	—
83	C₄×D₄×C₄₇	—	2	1	no	—
84	C₄×D₄×C₄₇	—	2	1	no	—
85	C₄×D₄×C₄₇	—	2	1	no	—
86	C₄×D₄×C₄₇	—	2	1	no	—
87	C₄×D₄×C₄₇	—	2	1	no	—
88	C₄×D₄×C₄₇	D₄	1	2	yes	—
89	C₄×D₄×C₄₇	D₄	1	2	yes	—
90	C₄×D₄×C₄₇	C₂³	1	2	yes	—
91	C₄×D₄×C₄₇	C₂³	1	2	yes	—
92	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
96	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
97	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
98	#107×C₄₇	—	2	2	no	—
99	C₄⋊C₈×C₄₇	—	2	1	no	—
100	C₄⋊C₈×C₄₇	—	2	1	no	—
101	C₄⋊C₈×C₄₇	C₂³	1	2	yes	complemented
102	C₄⋊C₈×C₄₇	C₂³	1	2	yes	complemented
103	#103×C₄₇	—	2	2	no	—
104	#102×C₄₇	—	2	4	no	—
105	#102×C₄₇	—	2	2	no	—
106	#102×C₄₇	—	2	2	no	—
107	#102×C₄₇	—	2	2	no	—
108	C₂²⋊C₈×C₄₇	—	2	1	no	—
109	C₂²⋊C₈×C₄₇	—	2	1	no	—
110	C₄×C₈×C₄₇	—	2	1	no	—
111	C₄×C₈×C₄₇	C₂³	1	2	yes	complemented
112	C₂⁴×C₄₇	—	2	1	no	—
113	C₂⁴×C₄₇	—	2	1	no	—
114	C₂⁴×C₄₇	—	2	8	no	—
115	C₂⁴×C₄₇	—	2	2	no	—
116	C₂⁴×C₄₇	—	4	8	no	—
117	C₂⁴×C₄₇	—	4	8	no	—
118	C₂⁴×C₄₇	—	8	4	no	—
119	#41×C₄₇	—	4	2	no	—
120	#41×C₄₇	—	4	2	no	—
121	C₂×Q₈×C₄₇	—	2	1	no	—
122	C₂×D₄×C₄₇	—	2	4	no	—
123	C₂×D₄×C₄₇	—	2	8	no	—
124	C₂×D₄×C₄₇	—	2	8	no	—
125	C₂×D₄×C₄₇	—	2	1	no	—
126	C₂×D₄×C₄₇	—	2	1	no	—
127	C₂×D₄×C₄₇	—	2	2	no	—
128	C₂×D₄×C₄₇	—	2	2	no	—
129	C₂×D₄×C₄₇	—	2	2	no	—
130	C₂×D₄×C₄₇	—	2	2	no	—
131	C₂×D₄×C₄₇	—	2	2	no	—
132	C₂×D₄×C₄₇	—	2	2	no	—
133	C₂×D₄×C₄₇	—	2	1	no	—
134	C₂×D₄×C₄₇	—	2	1	no	—
135	C₂×D₄×C₄₇	—	2	1	no	—
136	C₂×D₄×C₄₇	—	4	4	no	—
137	C₂×D₄×C₄₇	—	4	16	no	—
138	C₂×D₄×C₄₇	—	4	8	no	—
139	C₂×D₄×C₄₇	—	4	8	no	—
140	C₂×D₄×C₄₇	—	4	16	no	—
141	C₂×D₄×C₄₇	—	4	8	no	—
142	C₂×D₄×C₄₇	—	4	8	no	—
143	C₂×D₄×C₄₇	—	4	8	no	—
144	C₂×D₄×C₄₇	—	4	8	no	—
145	C₂×D₄×C₄₇	—	4	1	no	—
146	C₂×D₄×C₄₇	—	4	2	no	—
147	C₂×D₄×C₄₇	—	4	2	no	—
148	C₂×D₄×C₄₇	—	8	2	no	—
149	C₂×D₄×C₄₇	D₈	1	4	yes	complemented
150	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
151	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
152	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
153	C₂²×C₄×C₄₇	—	2	1	no	—
154	C₂²×C₄×C₄₇	—	2	1	no	—
155	C₂²×C₄×C₄₇	—	2	2	no	—
156	C₂²×C₄×C₄₇	—	2	2	no	—
157	C₂²×C₄×C₄₇	—	2	2	no	—
158	C₂²×C₄×C₄₇	—	2	2	no	—
159	C₂²×C₄×C₄₇	—	4	4	no	—
160	C₂²×C₄×C₄₇	—	4	2	no	—
161	C₂²×C₄×C₄₇	—	4	2	no	—
162	C₂²×C₄×C₄₇	—	4	1	no	—
163	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
164	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
165	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
166	SD₁₆×C₄₇	—	4	4	no	—
167	D₈×C₄₇	—	4	4	no	—
168	D₈×C₄₇	—	4	4	no	—
169	D₈×C₄₇	—	8	4	no	—
170	M₁₆×C₄₇	—	4	2	no	—
171	C₂×C₈×C₄₇	—	2	2	no	—
172	C₂×C₈×C₄₇	—	2	2	no	—
173	C₂×C₈×C₄₇	—	2	2	no	—
174	C₄⋊C₄×C₄₇	—	2	1	no	—
175	C₄⋊C₄×C₄₇	—	2	1	no	—
176	C₄⋊C₄×C₄₇	—	2	1	no	—
177	C₄⋊C₄×C₄₇	—	2	1	no	—
178	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
179	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
180	C₂²⋊C₄×C₄₇	—	2	8	no	—
181	C₂²⋊C₄×C₄₇	—	2	2	no	—
182	C₂²⋊C₄×C₄₇	—	2	2	no	—
183	C₂²⋊C₄×C₄₇	—	2	2	no	—
184	C₂²⋊C₄×C₄₇	—	2	2	no	—
185	C₂²⋊C₄×C₄₇	—	4	1	no	—
186	C₂²⋊C₄×C₄₇	—	4	1	no	—
187	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
188	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
189	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
190	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
191	C₂³×C₄₇	—	2	4	no	—
192	C₂³×C₄₇	—	2	2	no	—
193	C₂³×C₄₇	—	2	2	no	—
194	C₂³×C₄₇	—	2	4	no	—
195	C₂³×C₄₇	—	2	4	no	—
196	C₂³×C₄₇	—	4	2	no	—
197	C₂³×C₄₇	—	4	2	no	—
198	C₂³×C₄₇	—	4	2	no	—
199	C₂³×C₄₇	—	4	4	no	—
200	C₂³×C₄₇	—	4	16	no	—
201	C₂³×C₄₇	—	4	16	no	—
202	C₂³×C₄₇	—	4	4	no	—
203	C₂³×C₄₇	—	4	2	no	—
204	C₂³×C₄₇	—	4	4	no	—
205	C₂³×C₄₇	—	4	1	no	—
206	C₂³×C₄₇	—	8	8	no	—
207	C₂³×C₄₇	—	8	32	no	—
208	C₂³×C₄₇	#120	1	1	yes	characteristic
209	Q₈×C₄₇	—	4	1	no	—
210	Q₈×C₄₇	—	4	1	no	—
211	D₄×C₄₇	—	2	4	no	—
212	D₄×C₄₇	—	2	2	no	—
213	D₄×C₄₇	—	2	2	no	—
214	D₄×C₄₇	—	2	4	no	—
215	D₄×C₄₇	—	4	4	no	—
216	D₄×C₄₇	—	4	4	no	—
217	D₄×C₄₇	—	4	2	no	—
218	D₄×C₄₇	—	4	16	no	—
219	D₄×C₄₇	—	4	16	no	—
220	D₄×C₄₇	—	4	2	no	—
221	D₄×C₄₇	—	4	1	no	—
222	D₄×C₄₇	—	4	2	no	—
223	D₄×C₄₇	—	4	4	no	—
224	D₄×C₄₇	—	4	2	no	—
225	D₄×C₄₇	—	4	1	no	—
226	D₄×C₄₇	—	4	4	no	—
227	D₄×C₄₇	—	8	2	no	—
228	D₄×C₄₇	—	8	2	no	—
229	D₄×C₄₇	C₂×D₈	1	4	yes	—
230	D₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	complemented
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	—	4	1	no	—
235	C₂×C₄×C₄₇	—	4	4	no	—
236	C₂×C₄×C₄₇	—	4	2	no	—
237	C₂×C₄×C₄₇	—	4	2	no	—
238	C₂×C₄×C₄₇	—	4	2	no	—
239	C₂×C₄×C₄₇	—	4	2	no	—
240	C₂×C₄×C₄₇	—	4	4	no	—
241	C₂×C₄×C₄₇	—	4	4	no	—
242	C₂×C₄×C₄₇	—	4	1	no	—
243	C₂×C₄×C₄₇	—	8	2	no	—
244	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
245	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
246	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
247	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
248	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
249	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
252	C₈×C₄₇	—	4	2	no	—
253	C₈×C₄₇	—	4	2	no	—
254	C₈×C₄₇	—	4	2	no	—
255	#18746	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂²×C₄₇	—	2	1	no	—
257	C₂²×C₄₇	—	2	1	no	—
258	C₂²×C₄₇	—	2	4	no	—
259	C₂²×C₄₇	—	2	4	no	—
260	C₂²×C₄₇	—	4	8	no	—
261	C₂²×C₄₇	—	4	8	no	—
262	C₂²×C₄₇	—	4	2	no	—
263	C₂²×C₄₇	—	4	2	no	—
264	C₂²×C₄₇	—	4	2	no	—
265	C₂²×C₄₇	—	4	2	no	—
266	C₂²×C₄₇	—	4	4	no	—
267	C₂²×C₄₇	—	4	4	no	—
268	C₂²×C₄₇	—	4	4	no	—
269	C₂²×C₄₇	—	8	8	no	—
270	C₂²×C₄₇	—	8	32	no	—
271	C₂²×C₄₇	—	8	1	no	—
272	C₂²×C₄₇	—	8	1	no	—
273	C₂²×C₄₇	—	8	1	no	—
274	C₂²×C₄₇	#447	1	2	yes	—
275	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
276	C₄×C₄₇	—	2	1	no	—
277	C₄×C₄₇	—	2	1	no	—
278	C₄×C₄₇	—	2	1	no	—
279	C₄×C₄₇	—	4	2	no	—
280	C₄×C₄₇	—	4	2	no	—
281	C₄×C₄₇	—	8	1	no	—
282	C₄×C₄₇	#447	1	2	yes	—
283	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
284	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
285	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
286	C₂×D₄²	C₂×C₄₇	1	1	yes	characteristic, complemented
287	#3205	C₂×C₄₇	1	1	yes	characteristic, complemented
288	#3100	C₂×C₄₇	1	1	yes	characteristic, complemented
289	#3036	C₂×C₄₇	1	1	yes	characteristic, complemented
290	#1639	C₂×C₄₇	1	4	yes	complemented
291	#1619	C₂×C₄₇	1	4	yes	complemented
292	#1545	C₂×C₄₇	1	1	yes	characteristic, complemented
293	#1486	C₂×C₄₇	1	1	yes	characteristic, complemented
294	#1478	C₂×C₄₇	1	1	yes	characteristic, complemented
295	C₂×C₄₇	—	2	2	no	—
296	C₂×C₄₇	—	4	4	no	—
297	C₂×C₄₇	—	4	4	no	—
298	C₂×C₄₇	—	8	4	no	—
299	C₂×C₄₇	—	16	1	no	—
300	C₂×C₄₇	C₂×#447	1	1	yes	characteristic
301	C₂×C₄₇	#3003	1	1	yes	characteristic
302	C₂×C₄₇	#3019	1	1	yes	characteristic
303	C₂³×D₄	—	2	1	no	—
304	C₂³×D₄	—	2	1	no	—
305	C₂×AGL(1,ℤ/8)	—	2	1	no	—
306	D₄²	—	2	2	no	—
307	D₄²	—	2	2	no	—
308	D₄²	—	2	2	no	—
309	D₄²	C₂²×C₄₇	1	4	yes	—
310	#532	C₂²×C₄₇	1	1	yes	characteristic, complemented
311	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
312	C₂×#121	—	2	1	no	—
313	C₂×#121	—	2	1	no	—
314	C₂×#120	—	2	2	no	—
315	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
316	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
317	#493	C₂²×C₄₇	1	2	yes	complemented
318	#486	C₂²×C₄₇	1	2	yes	complemented
319	#480	—	2	1	no	—
320	#474	C₂²×C₄₇	1	2	yes	complemented
321	#463	—	2	2	no	—
322	#461	C₂²×C₄₇	1	2	yes	complemented
323	#459	—	2	2	no	—
324	#459	C₂²×C₄₇	1	2	yes	complemented
325	#459	C₂²×C₄₇	1	2	yes	complemented
326	#447	—	2	1	no	—
327	#447	—	2	2	no	—
328	C₄×D₈	—	2	2	no	—
329	#431	C₂²×C₄₇	1	1	yes	characteristic, complemented
330	#431	C₂²×C₄₇	1	1	yes	characteristic, complemented
331	#423	C₂²×C₄₇	1	1	yes	characteristic, complemented
332	#417	—	2	1	no	—
333	#331	C₂²×C₄₇	1	4	yes	complemented
334	D₄⋊C₈	C₂²×C₄₇	1	4	yes	complemented
335	D₄⋊C₈	C₂²×C₄₇	1	4	yes	complemented
336	C₄₇	#18746	1	1	yes	characteristic, direct product factor, Sylow
337	C₂⁵	—	2	2	no	—
338	C₂×#41	—	2	1	no	—
339	C₂²×D₄	—	2	2	no	—
340	C₂²×D₄	—	2	2	no	—
341	C₂²×D₄	—	2	4	no	—
342	C₂²×D₄	—	2	4	no	—
343	C₂²×D₄	—	2	4	no	—
344	C₂²×D₄	—	2	4	no	—
345	C₂²×D₄	—	2	1	no	—
346	C₂²×D₄	—	2	1	no	—
347	C₂²×D₄	—	4	8	no	—
348	C₂²×D₄	—	4	4	no	—
349	C₂²×D₄	—	4	4	no	—
350	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
351	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
352	C₂²×D₄	D₄×C₄₇	1	2	yes	—
353	C₂³×C₄	—	2	1	no	—
354	C₂³×C₄	—	2	1	no	—
355	AGL(1,ℤ/8)	—	4	4	no	—
356	C₂×SD₁₆	—	2	2	no	—
357	C₂×D₈	—	2	2	no	—
358	C₂×D₈	—	2	2	no	—
359	C₂×D₈	—	2	4	no	—
360	C₂×M₁₆	—	2	1	no	—
361	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic, complemented
362	#127	—	2	1	no	—
363	#127	—	2	1	no	—
364	#127	D₄×C₄₇	1	2	yes	—
365	#127	C₂³×C₄₇	1	2	yes	—
366	#127	C₂³×C₄₇	1	1	yes	characteristic, complemented
367	#124	—	2	1	no	—
368	#121	—	2	4	no	—
369	#121	—	2	4	no	—
370	#121	—	2	4	no	—
371	#121	—	2	4	no	—
372	#121	—	2	1	no	—
373	#121	—	2	1	no	—
374	#120	—	2	8	no	—
375	#120	—	2	8	no	—
376	C₄×D₄	—	2	1	no	—
377	C₄×D₄	—	2	1	no	—
378	C₄×D₄	—	2	1	no	—
379	C₄×D₄	—	2	1	no	—
380	C₄×D₄	—	2	1	no	—
381	C₄×D₄	—	2	1	no	—
382	C₄×D₄	D₄×C₄₇	1	2	yes	—
383	C₄×D₄	D₄×C₄₇	1	2	yes	—
384	C₄×D₄	C₂³×C₄₇	1	2	yes	—
385	C₄×D₄	C₂³×C₄₇	1	2	yes	—
386	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
387	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
388	C₂×C₂²⋊C₄	—	2	2	no	—
389	C₂×C₂²⋊C₄	—	2	1	no	—
390	C₂×C₂²⋊C₄	—	2	1	no	—
391	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
392	#107	—	2	2	no	—
393	C₄⋊C₈	—	2	1	no	—
394	C₄⋊C₈	—	2	1	no	—
395	C₄⋊C₈	C₂³×C₄₇	1	2	yes	complemented
396	C₄⋊C₈	C₂³×C₄₇	1	2	yes	complemented
397	#103	—	2	2	no	—
398	#102	—	2	2	no	—
399	#102	—	2	4	no	—
400	#102	—	2	2	no	—
401	#102	—	2	2	no	—
402	C₂²⋊C₈	—	2	1	no	—
403	C₂²⋊C₈	—	2	1	no	—
404	C₄×C₈	—	2	1	no	—
405	C₄×C₈	C₂³×C₄₇	1	2	yes	complemented
406	C₂⁴	—	2	1	no	—
407	C₂⁴	—	2	1	no	—
408	C₂⁴	—	2	8	no	—
409	C₂⁴	—	2	2	no	—
410	C₂⁴	—	4	8	no	—
411	C₂⁴	—	4	8	no	—
412	C₂⁴	—	8	4	no	—
413	#41	—	4	2	no	—
414	#41	—	4	2	no	—
415	C₂×Q₈	—	2	1	no	—
416	C₂×D₄	—	2	4	no	—
417	C₂×D₄	—	2	8	no	—
418	C₂×D₄	—	2	8	no	—
419	C₂×D₄	—	2	1	no	—
420	C₂×D₄	—	2	1	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	2	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	4	4	no	—
431	C₂×D₄	—	4	16	no	—
432	C₂×D₄	—	4	8	no	—
433	C₂×D₄	—	4	8	no	—
434	C₂×D₄	—	4	16	no	—
435	C₂×D₄	—	4	8	no	—
436	C₂×D₄	—	4	8	no	—
437	C₂×D₄	—	4	8	no	—
438	C₂×D₄	—	4	8	no	—
439	C₂×D₄	—	4	1	no	—
440	C₂×D₄	—	4	2	no	—
441	C₂×D₄	—	4	2	no	—
442	C₂×D₄	—	8	2	no	—
443	C₂×D₄	D₈×C₄₇	1	4	yes	complemented
444	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
445	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
446	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
447	C₂²×C₄	—	2	1	no	—
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	4	4	no	—
454	C₂²×C₄	—	4	2	no	—
455	C₂²×C₄	—	4	2	no	—
456	C₂²×C₄	—	4	1	no	—
457	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
458	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
459	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
460	SD₁₆	—	4	4	no	—
461	D₈	—	4	4	no	—
462	D₈	—	4	4	no	—
463	D₈	—	8	4	no	—
464	M₁₆	—	4	2	no	—
465	C₂×C₈	—	2	2	no	—
466	C₂×C₈	—	2	2	no	—
467	C₂×C₈	—	2	2	no	—
468	C₄⋊C₄	—	2	1	no	—
469	C₄⋊C₄	—	2	1	no	—
470	C₄⋊C₄	—	2	1	no	—
471	C₄⋊C₄	—	2	1	no	—
472	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
473	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
474	C₂²⋊C₄	—	2	8	no	—
475	C₂²⋊C₄	—	2	2	no	—
476	C₂²⋊C₄	—	2	2	no	—
477	C₂²⋊C₄	—	2	2	no	—
478	C₂²⋊C₄	—	2	2	no	—
479	C₂²⋊C₄	—	4	1	no	—
480	C₂²⋊C₄	—	4	1	no	—
481	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
482	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
483	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
484	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
485	C₂³	—	2	4	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	4	no	—
489	C₂³	—	2	4	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	2	no	—
493	C₂³	—	4	4	no	—
494	C₂³	—	4	16	no	—
495	C₂³	—	4	16	no	—
496	C₂³	—	4	4	no	—
497	C₂³	—	4	2	no	—
498	C₂³	—	4	4	no	—
499	C₂³	—	4	1	no	—
500	C₂³	—	8	8	no	—
501	C₂³	—	8	32	no	—
502	C₂³	#120×C₄₇	1	1	yes	characteristic
503	Q₈	—	4	1	no	—
504	Q₈	—	4	1	no	—
505	D₄	—	2	4	no	—
506	D₄	—	2	2	no	—
507	D₄	—	2	2	no	—
508	D₄	—	2	4	no	—
509	D₄	—	4	4	no	—
510	D₄	—	4	4	no	—
511	D₄	—	4	2	no	—
512	D₄	—	4	16	no	—
513	D₄	—	4	16	no	—
514	D₄	—	4	2	no	—
515	D₄	—	4	1	no	—
516	D₄	—	4	2	no	—
517	D₄	—	4	4	no	—
518	D₄	—	4	2	no	—
519	D₄	—	4	1	no	—
520	D₄	—	4	4	no	—
521	D₄	—	8	2	no	—
522	D₄	—	8	2	no	—
523	D₄	C₂×D₈×C₄₇	1	4	yes	—
524	D₄	AGL(1,ℤ/8)×C₄₇	1	4	yes	complemented
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	4	1	no	—
529	C₂×C₄	—	4	4	no	—
530	C₂×C₄	—	4	2	no	—
531	C₂×C₄	—	4	2	no	—
532	C₂×C₄	—	4	2	no	—
533	C₂×C₄	—	4	2	no	—
534	C₂×C₄	—	4	4	no	—
535	C₂×C₄	—	4	4	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	8	2	no	—
538	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
539	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
540	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
541	C₂×C₄	C₂×D₈×C₄₇	1	2	yes	—
542	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
543	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
544	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
545	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
546	C₈	—	4	2	no	—
547	C₈	—	4	2	no	—
548	C₈	—	4	2	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	2	4	no	—
552	C₂²	—	2	4	no	—
553	C₂²	—	4	8	no	—
554	C₂²	—	4	8	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	4	2	no	—
558	C₂²	—	4	2	no	—
559	C₂²	—	4	4	no	—
560	C₂²	—	4	4	no	—
561	C₂²	—	4	4	no	—
562	C₂²	—	8	8	no	—
563	C₂²	—	8	32	no	—
564	C₂²	—	8	1	no	—
565	C₂²	—	8	1	no	—
566	C₂²	—	8	1	no	—
567	C₂²	C₄₇×#447	1	2	yes	—
568	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
569	C₄	—	2	1	no	—
570	C₄	—	2	1	no	—
571	C₄	—	2	1	no	—
572	C₄	—	4	2	no	—
573	C₄	—	4	2	no	—
574	C₄	—	8	1	no	—
575	C₄	C₄₇×#447	1	2	yes	—
576	C₄	C₂²×D₈×C₄₇	1	1	yes	characteristic
577	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
578	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	2	yes	—
579	C₂	—	2	2	no	—
580	C₂	—	4	4	no	—
581	C₂	—	4	4	no	—
582	C₂	—	8	4	no	—
583	C₂	—	16	1	no	—
584	C₂	C₂×C₄₇×#447	1	1	yes	characteristic
585	C₂	C₄₇×#3003	1	1	yes	characteristic
586	C₂	C₄₇×#3019	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×D₄²×C₄₇	C₂	semidirect
2. C₄₇×#3205	C₂	semidirect
3. C₄₇×#3100	C₂	semidirect
4. C₄₇×#3036	C₂	semidirect
5. C₄₇×#1639	C₂	semidirect
6. C₄₇×#1619	C₂	semidirect
7. C₄₇×#1545	C₂	semidirect
8. C₄₇×#1486	C₂	semidirect
9. C₄₇×#1478	C₂	semidirect
17. C₄₇×#532	C₂²	semidirect
24. C₄₇×#493	C₂²	semidirect
25. C₄₇×#486	C₂²	semidirect
27. C₄₇×#474	C₂²	semidirect
29. C₄₇×#461	C₂²	semidirect
31. C₄₇×#459	C₂²	semidirect
32. C₄₇×#459	C₂²	semidirect
36. C₄₇×#431	C₂²	semidirect
37. C₄₇×#431	C₂²	semidirect
38. C₄₇×#423	C₂²	semidirect
40. C₄₇×#331	C₂²	semidirect
41. C₄₇×D₄⋊C₈	C₂²	semidirect
42. C₄₇×D₄⋊C₈	C₂²	semidirect
67. C₄⋊Q₈×C₄₇	C₂³	semidirect
72. #127×C₄₇	C₂³	semidirect
101. C₄⋊C₈×C₄₇	C₂³	semidirect
102. C₄⋊C₈×C₄₇	C₂³	semidirect
111. C₄×C₈×C₄₇	C₂³	semidirect
149. C₂×D₄×C₄₇	D₈	semidirect
230. D₄×C₄₇	AGL(1,ℤ/8)	semidirect
255. #18746	C₄₇	direct (N × H)
286. C₂×D₄²	C₂×C₄₇	semidirect
287. #3205	C₂×C₄₇	semidirect
288. #3100	C₂×C₄₇	semidirect
289. #3036	C₂×C₄₇	semidirect
290. #1639	C₂×C₄₇	semidirect
291. #1619	C₂×C₄₇	semidirect
292. #1545	C₂×C₄₇	semidirect
293. #1486	C₂×C₄₇	semidirect
294. #1478	C₂×C₄₇	semidirect
310. #532	C₂²×C₄₇	semidirect
317. #493	C₂²×C₄₇	semidirect
318. #486	C₂²×C₄₇	semidirect
320. #474	C₂²×C₄₇	semidirect
322. #461	C₂²×C₄₇	semidirect
324. #459	C₂²×C₄₇	semidirect
325. #459	C₂²×C₄₇	semidirect
329. #431	C₂²×C₄₇	semidirect
330. #431	C₂²×C₄₇	semidirect
331. #423	C₂²×C₄₇	semidirect
333. #331	C₂²×C₄₇	semidirect
334. D₄⋊C₈	C₂²×C₄₇	semidirect
335. D₄⋊C₈	C₂²×C₄₇	semidirect
336. C₄₇	#18746	direct (N × H)
361. C₄⋊Q₈	C₂³×C₄₇	semidirect
366. #127	C₂³×C₄₇	semidirect
395. C₄⋊C₈	C₂³×C₄₇	semidirect
396. C₄⋊C₈	C₂³×C₄₇	semidirect
405. C₄×C₈	C₂³×C₄₇	semidirect
443. C₂×D₄	D₈×C₄₇	semidirect
524. D₄	AGL(1,ℤ/8)×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄²×C₄₇	2
C₄₇×#3205	2
C₄₇×#3100	2
C₄₇×#3036	2
C₄₇×#1639	2
C₄₇×#1619	2
C₄₇×#1545	2
C₄₇×#1486	2
C₄₇×#1478	2
#18746	47

Subgroups — C47×#18746 #26058444

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18746 #26058444