Subgroups — C₄₇×#18776 #26058474

Order 12032.

1192 conjugacy classes of subgroups.

The subgroup lattice has 520 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, complemented
2	C₄₇×#3226	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3100	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1649	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1627	C₂	1	4	yes	maximal, complemented
7	C₄₇×#1546	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1486	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1479	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₄₇	—	2	1	no	—
11	C₂×#137×C₄₇	—	2	1	no	—
12	D₄×Q₈×C₄₇	—	2	2	no	—
13	D₄×Q₈×C₄₇	—	2	2	no	—
14	D₄×Q₈×C₄₇	—	2	2	no	—
15	D₄×Q₈×C₄₇	C₂²	1	4	yes	—
16	C₄₇×#532	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₄₇	—	2	1	no	—
18	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
20	C₂×C₂²⋊Q₈×C₄₇	—	2	2	no	—
21	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₄₇	—	2	1	no	—
23	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
24	C₄₇×#500	C₂²	1	2	yes	complemented
25	C₄₇×#486	C₂²	1	2	yes	complemented
26	C₄₇×#480	—	2	1	no	—
27	C₄₇×#480	—	2	2	no	—
28	C₄₇×#474	—	2	2	no	—
29	C₄₇×#474	C₂²	1	2	yes	—
30	C₄₇×#464	—	2	2	no	—
31	C₄₇×#462	C₂²	1	2	yes	complemented
32	C₄₇×#460	C₂²	1	2	yes	complemented
33	C₄₇×#459	C₂²	1	2	yes	—
34	C₄₇×#447	—	2	1	no	—
35	C₄×D₈×C₄₇	—	2	2	no	—
36	C₄₇×#431	C₂²	1	1	yes	characteristic
37	C₄₇×#431	C₂²	1	1	yes	characteristic
38	C₄₇×#423	C₂²	1	1	yes	characteristic
39	C₄₇×#417	—	2	1	no	—
40	C₄₇×#332	C₂²	1	4	yes	complemented
41	C₄₇×Q₈⋊C₈	C₂²	1	4	yes	complemented
42	C₄₇×D₄⋊C₈	C₂²	1	4	yes	—
43	C₂×#41×C₄₇	—	2	1	no	—
44	C₂²×Q₈×C₄₇	—	2	2	no	—
45	C₂²×Q₈×C₄₇	—	2	4	no	—
46	C₂²×Q₈×C₄₇	—	2	4	no	—
47	C₂²×Q₈×C₄₇	—	2	1	no	—
48	C₂²×Q₈×C₄₇	—	4	4	no	—
49	C₂²×Q₈×C₄₇	—	4	4	no	—
50	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
51	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
52	C₂³×C₄×C₄₇	—	2	2	no	—
53	C₂³×C₄×C₄₇	—	2	1	no	—
54	#137×C₄₇	—	4	4	no	—
55	C₂×Q₁₆×C₄₇	—	2	2	no	—
56	C₂×SD₁₆×C₄₇	—	2	2	no	—
57	C₂×D₈×C₄₇	—	2	2	no	—
58	C₂×M₁₆×C₄₇	—	2	1	no	—
59	C₄⋊Q₈×C₄₇	—	2	4	no	—
60	C₄⋊Q₈×C₄₇	—	2	4	no	—
61	C₄⋊Q₈×C₄₇	—	2	1	no	—
62	C₄⋊Q₈×C₄₇	—	2	1	no	—
63	C₄⋊Q₈×C₄₇	D₄	1	2	yes	—
64	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
65	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
66	#127×C₄₇	C₂³	1	1	yes	characteristic
67	#124×C₄₇	—	2	1	no	—
68	C₂²⋊Q₈×C₄₇	—	2	4	no	—
69	C₂²⋊Q₈×C₄₇	—	2	8	no	—
70	C₂²⋊Q₈×C₄₇	—	2	4	no	—
71	C₂²⋊Q₈×C₄₇	—	2	8	no	—
72	#121×C₄₇	—	2	1	no	—
73	#121×C₄₇	—	2	1	no	—
74	C₄×Q₈×C₄₇	—	2	1	no	—
75	C₄×Q₈×C₄₇	—	2	1	no	—
76	C₄×Q₈×C₄₇	D₄	1	2	yes	—
77	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
78	C₄×D₄×C₄₇	—	2	4	no	—
79	C₄×D₄×C₄₇	—	2	4	no	—
80	C₄×D₄×C₄₇	—	2	1	no	—
81	C₄×D₄×C₄₇	—	2	1	no	—
82	C₄×D₄×C₄₇	—	2	1	no	—
83	C₄×D₄×C₄₇	—	2	1	no	—
84	C₄×D₄×C₄₇	D₄	1	2	yes	—
85	C₄×D₄×C₄₇	C₂³	1	2	yes	—
86	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
87	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
88	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
89	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
90	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
91	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
92	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
93	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
94	C₂×C₄²×C₄₇	—	2	1	no	—
95	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
96	#107×C₄₇	—	2	4	no	—
97	#107×C₄₇	—	2	2	no	—
98	C₄⋊C₈×C₄₇	—	2	1	no	—
99	C₄⋊C₈×C₄₇	—	2	1	no	—
100	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
101	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
102	#103×C₄₇	—	2	2	no	—
103	#102×C₄₇	—	2	2	no	—
104	#102×C₄₇	—	2	2	no	—
105	#102×C₄₇	—	2	2	no	—
106	#102×C₄₇	—	2	4	no	—
107	C₂²⋊C₈×C₄₇	—	2	1	no	—
108	C₂²⋊C₈×C₄₇	—	2	1	no	—
109	C₄×C₈×C₄₇	—	2	1	no	—
110	C₄×C₈×C₄₇	C₂³	1	2	yes	—
111	C₂⁴×C₄₇	—	2	1	no	—
112	#41×C₄₇	—	4	2	no	—
113	#41×C₄₇	—	4	2	no	—
114	C₂×Q₈×C₄₇	—	2	8	no	—
115	C₂×Q₈×C₄₇	—	2	1	no	—
116	C₂×Q₈×C₄₇	—	2	2	no	—
117	C₂×Q₈×C₄₇	—	2	2	no	—
118	C₂×Q₈×C₄₇	—	2	2	no	—
119	C₂×Q₈×C₄₇	—	2	1	no	—
120	C₂×Q₈×C₄₇	—	4	8	no	—
121	C₂×Q₈×C₄₇	—	4	8	no	—
122	C₂×Q₈×C₄₇	—	4	16	no	—
123	C₂×Q₈×C₄₇	—	4	8	no	—
124	C₂×Q₈×C₄₇	—	4	2	no	—
125	C₂×Q₈×C₄₇	—	4	2	no	—
126	C₂×Q₈×C₄₇	D₈	1	4	yes	complemented
127	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
128	C₂×D₄×C₄₇	—	2	4	no	—
129	C₂×D₄×C₄₇	—	2	1	no	—
130	C₂×D₄×C₄₇	—	2	1	no	—
131	C₂×D₄×C₄₇	—	2	1	no	—
132	C₂×D₄×C₄₇	—	2	1	no	—
133	C₂×D₄×C₄₇	—	4	1	no	—
134	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₄₇	—	2	1	no	—
136	C₂²×C₄×C₄₇	—	2	8	no	—
137	C₂²×C₄×C₄₇	—	2	1	no	—
138	C₂²×C₄×C₄₇	—	2	2	no	—
139	C₂²×C₄×C₄₇	—	2	1	no	—
140	C₂²×C₄×C₄₇	—	2	2	no	—
141	C₂²×C₄×C₄₇	—	2	2	no	—
142	C₂²×C₄×C₄₇	—	4	8	no	—
143	C₂²×C₄×C₄₇	—	4	2	no	—
144	C₂²×C₄×C₄₇	—	4	2	no	—
145	C₂²×C₄×C₄₇	—	4	1	no	—
146	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
149	Q₁₆×C₄₇	—	4	4	no	—
150	SD₁₆×C₄₇	—	4	4	no	—
151	D₈×C₄₇	—	4	4	no	—
152	M₁₆×C₄₇	—	4	2	no	—
153	C₂×C₈×C₄₇	—	2	2	no	—
154	C₂×C₈×C₄₇	—	2	2	no	—
155	C₂×C₈×C₄₇	—	2	2	no	—
156	C₄⋊C₄×C₄₇	—	2	8	no	—
157	C₄⋊C₄×C₄₇	—	2	2	no	—
158	C₄⋊C₄×C₄₇	—	2	2	no	—
159	C₄⋊C₄×C₄₇	—	2	1	no	—
160	C₄⋊C₄×C₄₇	—	2	1	no	—
161	C₄⋊C₄×C₄₇	—	2	2	no	—
162	C₄⋊C₄×C₄₇	—	2	2	no	—
163	C₄⋊C₄×C₄₇	—	2	2	no	—
164	C₄⋊C₄×C₄₇	—	2	1	no	—
165	C₄⋊C₄×C₄₇	—	2	1	no	—
166	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
167	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
168	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
169	C₂²⋊C₄×C₄₇	—	2	8	no	—
170	C₂²⋊C₄×C₄₇	—	2	2	no	—
171	C₂²⋊C₄×C₄₇	—	2	2	no	—
172	C₂²⋊C₄×C₄₇	—	4	1	no	—
173	C₂²⋊C₄×C₄₇	—	4	1	no	—
174	C₄²×C₄₇	—	2	2	no	—
175	C₄²×C₄₇	—	2	2	no	—
176	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
179	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
180	C₂³×C₄₇	—	2	4	no	—
181	C₂³×C₄₇	—	2	2	no	—
182	C₂³×C₄₇	—	4	2	no	—
183	C₂³×C₄₇	—	4	2	no	—
184	C₂³×C₄₇	—	4	1	no	—
185	C₂³×C₄₇	#120	1	1	yes	characteristic
186	Q₈×C₄₇	—	2	2	no	—
187	Q₈×C₄₇	—	2	4	no	—
188	Q₈×C₄₇	—	4	16	no	—
189	Q₈×C₄₇	—	4	2	no	—
190	Q₈×C₄₇	—	4	2	no	—
191	Q₈×C₄₇	—	4	4	no	—
192	Q₈×C₄₇	—	4	1	no	—
193	Q₈×C₄₇	—	4	1	no	—
194	Q₈×C₄₇	C₂×D₈	1	4	yes	—
195	D₄×C₄₇	—	2	4	no	—
196	D₄×C₄₇	—	2	2	no	—
197	D₄×C₄₇	—	4	2	no	—
198	D₄×C₄₇	—	4	1	no	—
199	D₄×C₄₇	—	4	1	no	—
200	D₄×C₄₇	—	4	2	no	—
201	D₄×C₄₇	—	8	2	no	—
202	D₄×C₄₇	#137	1	4	yes	complemented
203	C₂×C₄×C₄₇	—	2	2	no	—
204	C₂×C₄×C₄₇	—	2	4	no	—
205	C₂×C₄×C₄₇	—	2	2	no	—
206	C₂×C₄×C₄₇	—	2	2	no	—
207	C₂×C₄×C₄₇	—	2	4	no	—
208	C₂×C₄×C₄₇	—	2	2	no	—
209	C₂×C₄×C₄₇	—	4	1	no	—
210	C₂×C₄×C₄₇	—	4	16	no	—
211	C₂×C₄×C₄₇	—	4	2	no	—
212	C₂×C₄×C₄₇	—	4	4	no	—
213	C₂×C₄×C₄₇	—	4	2	no	—
214	C₂×C₄×C₄₇	—	4	2	no	—
215	C₂×C₄×C₄₇	—	4	2	no	—
216	C₂×C₄×C₄₇	—	4	4	no	—
217	C₂×C₄×C₄₇	—	4	1	no	—
218	C₂×C₄×C₄₇	—	8	2	no	—
219	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
220	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
221	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
222	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
223	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
224	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
225	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
227	C₈×C₄₇	—	4	2	no	—
228	C₈×C₄₇	—	4	2	no	—
229	C₈×C₄₇	—	4	2	no	—
230	#18776	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
231	C₂²×C₄₇	—	2	1	no	—
232	C₂²×C₄₇	—	2	1	no	—
233	C₂²×C₄₇	—	2	4	no	—
234	C₂²×C₄₇	—	4	8	no	—
235	C₂²×C₄₇	—	4	2	no	—
236	C₂²×C₄₇	—	4	2	no	—
237	C₂²×C₄₇	—	8	1	no	—
238	C₂²×C₄₇	—	8	1	no	—
239	C₂²×C₄₇	—	8	1	no	—
240	C₂²×C₄₇	#447	1	2	yes	—
241	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
242	C₄×C₄₇	—	2	4	no	—
243	C₄×C₄₇	—	2	1	no	—
244	C₄×C₄₇	—	2	1	no	—
245	C₄×C₄₇	—	2	1	no	—
246	C₄×C₄₇	—	4	4	no	—
247	C₄×C₄₇	—	4	2	no	—
248	C₄×C₄₇	—	4	2	no	—
249	C₄×C₄₇	—	8	1	no	—
250	C₄×C₄₇	#447	1	2	yes	—
251	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
252	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
253	C₄×C₄₇	C₂×#137	1	2	yes	—
254	C₂×D₄×Q₈	C₂×C₄₇	1	1	yes	characteristic, complemented
255	#3226	C₂×C₄₇	1	1	yes	characteristic, complemented
256	#3100	C₂×C₄₇	1	1	yes	characteristic
257	#3037	C₂×C₄₇	1	1	yes	characteristic, complemented
258	#1649	C₂×C₄₇	1	4	yes	complemented
259	#1627	C₂×C₄₇	1	4	yes	complemented
260	#1546	C₂×C₄₇	1	1	yes	characteristic, complemented
261	#1486	C₂×C₄₇	1	1	yes	characteristic, complemented
262	#1479	C₂×C₄₇	1	1	yes	characteristic, complemented
263	C₂×C₄₇	—	2	2	no	—
264	C₂×C₄₇	—	4	4	no	—
265	C₂×C₄₇	—	16	1	no	—
266	C₂×C₄₇	C₂×#447	1	1	yes	characteristic
267	C₂×C₄₇	#3004	1	1	yes	characteristic
268	C₂×C₄₇	#3020	1	1	yes	characteristic
269	C₂³×Q₈	—	2	1	no	—
270	C₂×#137	—	2	1	no	—
271	D₄×Q₈	—	2	2	no	—
272	D₄×Q₈	—	2	2	no	—
273	D₄×Q₈	—	2	2	no	—
274	D₄×Q₈	C₂²×C₄₇	1	4	yes	—
275	#532	C₂²×C₄₇	1	1	yes	characteristic
276	C₂×C₄⋊Q₈	—	2	1	no	—
277	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
278	C₂×C₂²⋊Q₈	—	2	1	no	—
279	C₂×C₂²⋊Q₈	—	2	2	no	—
280	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
281	C₂×C₄×D₄	—	2	1	no	—
282	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
283	#500	C₂²×C₄₇	1	2	yes	complemented
284	#486	C₂²×C₄₇	1	2	yes	complemented
285	#480	—	2	1	no	—
286	#480	—	2	2	no	—
287	#474	—	2	2	no	—
288	#474	C₂²×C₄₇	1	2	yes	—
289	#464	—	2	2	no	—
290	#462	C₂²×C₄₇	1	2	yes	complemented
291	#460	C₂²×C₄₇	1	2	yes	complemented
292	#459	C₂²×C₄₇	1	2	yes	—
293	#447	—	2	1	no	—
294	C₄×D₈	—	2	2	no	—
295	#431	C₂²×C₄₇	1	1	yes	characteristic
296	#431	C₂²×C₄₇	1	1	yes	characteristic
297	#423	C₂²×C₄₇	1	1	yes	characteristic
298	#417	—	2	1	no	—
299	#332	C₂²×C₄₇	1	4	yes	complemented
300	Q₈⋊C₈	C₂²×C₄₇	1	4	yes	complemented
301	D₄⋊C₈	C₂²×C₄₇	1	4	yes	—
302	C₄₇	#18776	1	1	yes	characteristic, direct product factor, Sylow
303	C₂×#41	—	2	1	no	—
304	C₂²×Q₈	—	2	2	no	—
305	C₂²×Q₈	—	2	4	no	—
306	C₂²×Q₈	—	2	4	no	—
307	C₂²×Q₈	—	2	1	no	—
308	C₂²×Q₈	—	4	4	no	—
309	C₂²×Q₈	—	4	4	no	—
310	C₂²×Q₈	D₄×C₄₇	1	1	yes	characteristic
311	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
312	C₂³×C₄	—	2	2	no	—
313	C₂³×C₄	—	2	1	no	—
314	#137	—	4	4	no	—
315	C₂×Q₁₆	—	2	2	no	—
316	C₂×SD₁₆	—	2	2	no	—
317	C₂×D₈	—	2	2	no	—
318	C₂×M₁₆	—	2	1	no	—
319	C₄⋊Q₈	—	2	4	no	—
320	C₄⋊Q₈	—	2	4	no	—
321	C₄⋊Q₈	—	2	1	no	—
322	C₄⋊Q₈	—	2	1	no	—
323	C₄⋊Q₈	D₄×C₄₇	1	2	yes	—
324	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
325	C₄⋊Q₈	C₂³×C₄₇	1	2	yes	—
326	#127	C₂³×C₄₇	1	1	yes	characteristic
327	#124	—	2	1	no	—
328	C₂²⋊Q₈	—	2	4	no	—
329	C₂²⋊Q₈	—	2	8	no	—
330	C₂²⋊Q₈	—	2	4	no	—
331	C₂²⋊Q₈	—	2	8	no	—
332	#121	—	2	1	no	—
333	#121	—	2	1	no	—
334	C₄×Q₈	—	2	1	no	—
335	C₄×Q₈	—	2	1	no	—
336	C₄×Q₈	D₄×C₄₇	1	2	yes	—
337	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
338	C₄×D₄	—	2	4	no	—
339	C₄×D₄	—	2	4	no	—
340	C₄×D₄	—	2	1	no	—
341	C₄×D₄	—	2	1	no	—
342	C₄×D₄	—	2	1	no	—
343	C₄×D₄	—	2	1	no	—
344	C₄×D₄	D₄×C₄₇	1	2	yes	—
345	C₄×D₄	C₂³×C₄₇	1	2	yes	—
346	C₂×C₄⋊C₄	—	2	2	no	—
347	C₂×C₄⋊C₄	—	2	1	no	—
348	C₂×C₄⋊C₄	—	2	1	no	—
349	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
350	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
351	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	2	1	no	—
354	C₂×C₄²	—	2	1	no	—
355	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
356	#107	—	2	2	no	—
357	#107	—	2	4	no	—
358	C₄⋊C₈	—	2	1	no	—
359	C₄⋊C₈	—	2	1	no	—
360	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
361	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
362	#103	—	2	2	no	—
363	#102	—	2	2	no	—
364	#102	—	2	2	no	—
365	#102	—	2	2	no	—
366	#102	—	2	4	no	—
367	C₂²⋊C₈	—	2	1	no	—
368	C₂²⋊C₈	—	2	1	no	—
369	C₄×C₈	—	2	1	no	—
370	C₄×C₈	C₂³×C₄₇	1	2	yes	—
371	C₂⁴	—	2	1	no	—
372	#41	—	4	2	no	—
373	#41	—	4	2	no	—
374	C₂×Q₈	—	2	8	no	—
375	C₂×Q₈	—	2	1	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	2	2	no	—
379	C₂×Q₈	—	2	1	no	—
380	C₂×Q₈	—	4	8	no	—
381	C₂×Q₈	—	4	8	no	—
382	C₂×Q₈	—	4	16	no	—
383	C₂×Q₈	—	4	8	no	—
384	C₂×Q₈	—	4	2	no	—
385	C₂×Q₈	—	4	2	no	—
386	C₂×Q₈	D₈×C₄₇	1	4	yes	complemented
387	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
388	C₂×D₄	—	2	4	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	1	no	—
392	C₂×D₄	—	2	1	no	—
393	C₂×D₄	—	4	1	no	—
394	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	8	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	1	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	4	8	no	—
403	C₂²×C₄	—	4	2	no	—
404	C₂²×C₄	—	4	2	no	—
405	C₂²×C₄	—	4	1	no	—
406	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
407	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
408	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
409	Q₁₆	—	4	4	no	—
410	SD₁₆	—	4	4	no	—
411	D₈	—	4	4	no	—
412	M₁₆	—	4	2	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₄⋊C₄	—	2	8	no	—
417	C₄⋊C₄	—	2	2	no	—
418	C₄⋊C₄	—	2	2	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	2	1	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	1	no	—
426	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
427	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
428	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
429	C₂²⋊C₄	—	2	8	no	—
430	C₂²⋊C₄	—	2	2	no	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	4	1	no	—
433	C₂²⋊C₄	—	4	1	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	2	no	—
436	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
437	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
438	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
439	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
440	C₂³	—	2	4	no	—
441	C₂³	—	2	2	no	—
442	C₂³	—	4	2	no	—
443	C₂³	—	4	2	no	—
444	C₂³	—	4	1	no	—
445	C₂³	#120×C₄₇	1	1	yes	characteristic
446	Q₈	—	2	2	no	—
447	Q₈	—	2	4	no	—
448	Q₈	—	4	16	no	—
449	Q₈	—	4	2	no	—
450	Q₈	—	4	2	no	—
451	Q₈	—	4	4	no	—
452	Q₈	—	4	1	no	—
453	Q₈	—	4	1	no	—
454	Q₈	C₂×D₈×C₄₇	1	4	yes	—
455	D₄	—	2	4	no	—
456	D₄	—	2	2	no	—
457	D₄	—	4	2	no	—
458	D₄	—	4	1	no	—
459	D₄	—	4	1	no	—
460	D₄	—	4	2	no	—
461	D₄	—	8	2	no	—
462	D₄	#137×C₄₇	1	4	yes	complemented
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	4	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	4	1	no	—
470	C₂×C₄	—	4	16	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	4	no	—
473	C₂×C₄	—	4	2	no	—
474	C₂×C₄	—	4	2	no	—
475	C₂×C₄	—	4	2	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	8	2	no	—
479	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
480	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
481	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
482	C₂×C₄	C₂×D₈×C₄₇	1	2	yes	—
483	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
484	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
485	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
486	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
487	C₈	—	4	2	no	—
488	C₈	—	4	2	no	—
489	C₈	—	4	2	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	2	4	no	—
493	C₂²	—	4	8	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	4	2	no	—
496	C₂²	—	8	1	no	—
497	C₂²	—	8	1	no	—
498	C₂²	—	8	1	no	—
499	C₂²	C₄₇×#447	1	2	yes	—
500	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
501	C₄	—	2	4	no	—
502	C₄	—	2	1	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	—	8	1	no	—
509	C₄	C₄₇×#447	1	2	yes	—
510	C₄	C₂²×D₈×C₄₇	1	1	yes	characteristic
511	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
512	C₄	C₂×#137×C₄₇	1	2	yes	—
513	C₂	—	2	2	no	—
514	C₂	—	4	4	no	—
515	C₂	—	16	1	no	—
516	C₂	C₂×C₄₇×#447	1	1	yes	characteristic
517	C₂	C₄₇×#3004	1	1	yes	characteristic
518	C₂	C₄₇×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₇
prime radical	C₄₇×#3100	C₂
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×D₄×Q₈×C₄₇	C₂	semidirect
2. C₄₇×#3226	C₂	semidirect
4. C₄₇×#3037	C₂	semidirect
5. C₄₇×#1649	C₂	semidirect
6. C₄₇×#1627	C₂	semidirect
7. C₄₇×#1546	C₂	semidirect
8. C₄₇×#1486	C₂	semidirect
9. C₄₇×#1479	C₂	semidirect
24. C₄₇×#500	C₂²	semidirect
25. C₄₇×#486	C₂²	semidirect
31. C₄₇×#462	C₂²	semidirect
32. C₄₇×#460	C₂²	semidirect
40. C₄₇×#332	C₂²	semidirect
41. C₄₇×Q₈⋊C₈	C₂²	semidirect
126. C₂×Q₈×C₄₇	D₈	semidirect
202. D₄×C₄₇	#137	semidirect
230. #18776	C₄₇	direct (N × H)
254. C₂×D₄×Q₈	C₂×C₄₇	semidirect
255. #3226	C₂×C₄₇	semidirect
257. #3037	C₂×C₄₇	semidirect
258. #1649	C₂×C₄₇	semidirect
259. #1627	C₂×C₄₇	semidirect
260. #1546	C₂×C₄₇	semidirect
261. #1486	C₂×C₄₇	semidirect
262. #1479	C₂×C₄₇	semidirect
283. #500	C₂²×C₄₇	semidirect
284. #486	C₂²×C₄₇	semidirect
290. #462	C₂²×C₄₇	semidirect
291. #460	C₂²×C₄₇	semidirect
299. #332	C₂²×C₄₇	semidirect
300. Q₈⋊C₈	C₂²×C₄₇	semidirect
302. C₄₇	#18776	direct (N × H)
386. C₂×Q₈	D₈×C₄₇	semidirect
462. D₄	#137×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×#3226	2
C₄₇×#3100	2
C₄₇×#3037	2
C₄₇×#1649	2
C₄₇×#1627	2
C₄₇×#1546	2
C₄₇×#1486	2
C₄₇×#1479	2
#18776	47

Subgroups — C47×#18776 #26058474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18776 #26058474