Subgroups — C₄₇×#21887 #26061585

Order 12032.

1194 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#529	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2285	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1989	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1983	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1893	C₂	1	2	yes	maximal
7	C₄₇×#1892	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1803	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1802	C₂	1	2	yes	maximal, complemented
10	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
11	C₄₇×#529	—	2	4	no	—
12	C₄₇×#529	C₄	1	8	yes	complemented
13	C₂×#126×C₄₇	—	2	1	no	—
14	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#123×C₄₇	—	2	1	no	—
17	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₄×C₄₇	—	2	1	no	—
21	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×#117×C₄₇	—	2	1	no	—
23	C₂×#117×C₄₇	—	2	1	no	—
24	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊C₈×C₄₇	—	2	4	no	—
26	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
27	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
28	C₂×#103×C₄₇	C₂²	1	4	yes	—
29	C₂×#102×C₄₇	C₂²	1	4	yes	—
30	C₄₇×#384	C₂²	1	2	yes	—
31	C₄₇×#382	—	2	1	no	—
32	C₄₇×#380	—	2	1	no	—
33	C₄₇×#380	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
35	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
36	C₄₇×#340	C₂²	1	4	yes	—
37	C₄₇×#340	C₂²	1	4	yes	—
38	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
39	C₂²×D₄×C₄₇	—	2	1	no	—
40	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	—	2	1	no	—
42	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
43	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
45	C₂²×C₈×C₄₇	—	2	4	no	—
46	C₂²×C₈×C₄₇	—	4	4	no	—
47	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
48	#126×C₄₇	—	2	8	no	—
49	#125×C₄₇	—	2	2	no	—
50	#125×C₄₇	C₂×C₄	1	4	yes	—
51	#124×C₄₇	—	2	2	no	—
52	#124×C₄₇	C₂×C₄	1	4	yes	—
53	#123×C₄₇	—	2	8	no	—
54	C₂²⋊Q₈×C₄₇	—	2	2	no	—
55	C₂²⋊Q₈×C₄₇	C₂×C₄	1	4	yes	—
56	#121×C₄₇	—	2	2	no	—
57	#121×C₄₇	C₂×C₄	1	4	yes	—
58	C₄×Q₈×C₄₇	—	2	2	no	—
59	C₄×Q₈×C₄₇	C₂×C₄	1	4	yes	—
60	C₄×D₄×C₄₇	—	2	8	no	—
61	C₄×D₄×C₄₇	—	2	2	no	—
62	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
63	#117×C₄₇	—	2	8	no	—
64	#117×C₄₇	—	4	4	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
72	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
75	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
76	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
80	C₂×C₄²×C₄₇	—	2	1	no	—
81	C₂×C₄²×C₄₇	—	2	2	no	—
82	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
83	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
84	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
85	C₂×C₄²×C₄₇	D₄	1	4	yes	—
86	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
87	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
88	C₄⋊C₈×C₄₇	—	2	4	no	—
89	C₄⋊C₈×C₄₇	—	2	4	no	—
90	#103×C₄₇	—	4	4	no	—
91	#102×C₄₇	—	4	4	no	—
92	#95×C₄₇	—	2	2	no	—
93	#95×C₄₇	—	2	2	no	—
94	C₂⁴×C₄₇	—	2	1	no	—
95	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
96	C₂×Q₈×C₄₇	—	2	1	no	—
97	C₂×Q₈×C₄₇	—	2	2	no	—
98	C₂×Q₈×C₄₇	—	2	2	no	—
99	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
100	C₂×D₄×C₄₇	—	2	4	no	—
101	C₂×D₄×C₄₇	—	2	1	no	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	—	2	2	no	—
104	C₂×D₄×C₄₇	—	4	2	no	—
105	C₂×D₄×C₄₇	—	4	2	no	—
106	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	—	2	4	no	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	—	2	2	no	—
112	C₂²×C₄×C₄₇	—	2	1	no	—
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	2	1	no	—
115	C₂²×C₄×C₄₇	—	2	4	no	—
116	C₂²×C₄×C₄₇	—	2	4	no	—
117	C₂²×C₄×C₄₇	—	4	4	no	—
118	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
119	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
120	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
121	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
128	C₂×C₈×C₄₇	—	2	4	no	—
129	C₂×C₈×C₄₇	—	2	4	no	—
130	C₂×C₈×C₄₇	—	2	4	no	—
131	C₂×C₈×C₄₇	—	4	8	no	—
132	C₄⋊C₄×C₄₇	—	2	4	no	—
133	C₄⋊C₄×C₄₇	—	2	4	no	—
134	C₄⋊C₄×C₄₇	—	2	4	no	—
135	C₄⋊C₄×C₄₇	—	2	4	no	—
136	C₄⋊C₄×C₄₇	—	2	1	no	—
137	C₄⋊C₄×C₄₇	—	2	1	no	—
138	C₄⋊C₄×C₄₇	—	2	4	no	—
139	C₄⋊C₄×C₄₇	—	2	4	no	—
140	C₄⋊C₄×C₄₇	—	4	4	no	—
141	C₄⋊C₄×C₄₇	—	4	4	no	—
142	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
143	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
144	C₂²⋊C₄×C₄₇	—	2	4	no	—
145	C₂²⋊C₄×C₄₇	—	2	4	no	—
146	C₂²⋊C₄×C₄₇	—	2	4	no	—
147	C₂²⋊C₄×C₄₇	—	2	4	no	—
148	C₂²⋊C₄×C₄₇	—	2	4	no	—
149	C₂²⋊C₄×C₄₇	—	4	4	no	—
150	C₄²×C₄₇	—	2	4	no	—
151	C₄²×C₄₇	—	4	4	no	—
152	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
153	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
154	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
155	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
156	C₄²×C₄₇	C₂×D₄	1	2	yes	—
157	C₄²×C₄₇	C₂×D₄	1	2	yes	—
158	C₂³×C₄₇	—	2	2	no	—
159	C₂³×C₄₇	—	2	2	no	—
160	C₂³×C₄₇	—	2	2	no	—
161	C₂³×C₄₇	—	4	2	no	—
162	C₂³×C₄₇	—	4	2	no	—
163	C₂³×C₄₇	—	4	1	no	—
164	C₂³×C₄₇	—	4	1	no	—
165	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
167	C₂³×C₄₇	#137	1	2	yes	—
168	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	Q₈×C₄₇	—	2	4	no	—
170	Q₈×C₄₇	—	4	1	no	—
171	Q₈×C₄₇	—	4	1	no	—
172	D₄×C₄₇	—	2	4	no	—
173	D₄×C₄₇	—	4	8	no	—
174	D₄×C₄₇	—	4	1	no	—
175	D₄×C₄₇	—	4	1	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	1	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	1	no	—
181	C₂×C₄×C₄₇	—	2	1	no	—
182	C₂×C₄×C₄₇	—	2	8	no	—
183	C₂×C₄×C₄₇	—	2	4	no	—
184	C₂×C₄×C₄₇	—	2	2	no	—
185	C₂×C₄×C₄₇	—	2	2	no	—
186	C₂×C₄×C₄₇	—	2	8	no	—
187	C₂×C₄×C₄₇	—	2	2	no	—
188	C₂×C₄×C₄₇	—	2	2	no	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	4	2	no	—
191	C₂×C₄×C₄₇	—	4	2	no	—
192	C₂×C₄×C₄₇	—	4	1	no	—
193	C₂×C₄×C₄₇	—	4	1	no	—
194	C₂×C₄×C₄₇	—	4	8	no	—
195	C₂×C₄×C₄₇	—	4	4	no	—
196	C₂×C₄×C₄₇	—	4	4	no	—
197	C₂×C₄×C₄₇	—	4	4	no	—
198	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
199	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
200	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
201	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
202	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
203	C₂×C₄×C₄₇	#135	1	4	yes	—
204	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
205	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
207	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
208	C₈×C₄₇	—	4	4	no	—
209	#21887	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
210	C₂²×C₄₇	—	2	2	no	—
211	C₂²×C₄₇	—	2	2	no	—
212	C₂²×C₄₇	—	2	4	no	—
213	C₂²×C₄₇	—	2	4	no	—
214	C₂²×C₄₇	—	4	2	no	—
215	C₂²×C₄₇	—	4	2	no	—
216	C₂²×C₄₇	—	4	2	no	—
217	C₂²×C₄₇	—	8	2	no	—
218	C₂²×C₄₇	—	8	2	no	—
219	C₂²×C₄₇	#417	1	4	yes	—
220	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
221	C₂²×C₄₇	#537	1	2	yes	—
222	C₂²×C₄₇	C₂×#135	1	2	yes	—
223	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
224	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
225	C₄×C₄₇	—	2	2	no	—
226	C₄×C₄₇	—	2	2	no	—
227	C₄×C₄₇	—	2	2	no	—
228	C₄×C₄₇	—	2	2	no	—
229	C₄×C₄₇	—	4	2	no	—
230	C₄×C₄₇	—	4	2	no	—
231	C₄×C₄₇	—	4	2	no	—
232	C₄×C₄₇	—	8	4	no	—
233	C₄×C₄₇	#416	1	4	yes	—
234	C₄×C₄₇	#520	1	2	yes	—
235	C₄×C₄₇	#535	1	1	yes	characteristic
236	C₄×C₄₇	#536	1	1	yes	characteristic
237	C₂×#529	C₂×C₄₇	1	1	yes	characteristic
238	C₂²×C₄⋊C₈	C₂×C₄₇	1	1	yes	characteristic, complemented
239	#2285	C₂×C₄₇	1	1	yes	characteristic, complemented
240	#1989	C₂×C₄₇	1	2	yes	complemented
241	#1983	C₂×C₄₇	1	2	yes	complemented
242	#1893	C₂×C₄₇	1	2	yes	—
243	#1892	C₂×C₄₇	1	2	yes	complemented
244	#1803	C₂×C₄₇	1	2	yes	complemented
245	#1802	C₂×C₄₇	1	2	yes	complemented
246	C₂×C₄₇	—	2	4	no	—
247	C₂×C₄₇	—	8	2	no	—
248	C₂×C₄₇	#2311	1	1	yes	characteristic
249	C₂×C₄₇	C₂×#416	1	1	yes	characteristic
250	C₂×C₄₇	C₂×#417	1	1	yes	characteristic
251	C₂×C₄₇	#3247	1	2	yes	—
252	C₂×C₄₇	#3248	1	2	yes	—
253	C₂³×C₈	C₂²×C₄₇	1	2	yes	—
254	#529	—	2	4	no	—
255	#529	C₄×C₄₇	1	8	yes	complemented
256	C₂×#126	—	2	1	no	—
257	C₂×#125	C₂²×C₄₇	1	1	yes	characteristic
258	C₂×#124	C₂²×C₄₇	1	1	yes	characteristic
259	C₂×#123	—	2	1	no	—
260	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
261	C₂×#121	C₂²×C₄₇	1	1	yes	characteristic
262	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
263	C₂×C₄×D₄	—	2	1	no	—
264	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
265	C₂×#117	—	2	1	no	—
266	C₂×#117	—	2	1	no	—
267	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
268	C₂×C₄⋊C₈	—	2	4	no	—
269	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
270	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
271	C₂×#103	C₂²×C₄₇	1	4	yes	—
272	C₂×#102	C₂²×C₄₇	1	4	yes	—
273	#384	C₂²×C₄₇	1	2	yes	—
274	#382	—	2	1	no	—
275	#380	—	2	1	no	—
276	#380	C₂²×C₄₇	1	2	yes	—
277	C₄×C₄⋊C₄	—	2	1	no	—
278	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
279	#340	C₂²×C₄₇	1	4	yes	—
280	#340	C₂²×C₄₇	1	4	yes	—
281	C₄₇	#21887	1	1	yes	characteristic, direct product factor, Sylow
282	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
283	C₂²×D₄	—	2	1	no	—
284	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
285	C₂³×C₄	—	2	1	no	—
286	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
287	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
288	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
289	C₂²×C₈	—	2	4	no	—
290	C₂²×C₈	—	4	4	no	—
291	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
292	#126	—	2	8	no	—
293	#125	—	2	2	no	—
294	#125	C₂×C₄×C₄₇	1	4	yes	—
295	#124	—	2	2	no	—
296	#124	C₂×C₄×C₄₇	1	4	yes	—
297	#123	—	2	8	no	—
298	C₂²⋊Q₈	—	2	2	no	—
299	C₂²⋊Q₈	C₂×C₄×C₄₇	1	4	yes	—
300	#121	—	2	2	no	—
301	#121	C₂×C₄×C₄₇	1	4	yes	—
302	C₄×Q₈	—	2	2	no	—
303	C₄×Q₈	C₂×C₄×C₄₇	1	4	yes	—
304	C₄×D₄	—	2	8	no	—
305	C₄×D₄	—	2	2	no	—
306	C₄×D₄	C₂×C₄×C₄₇	1	4	yes	—
307	#117	—	2	8	no	—
308	#117	—	4	4	no	—
309	C₂×C₄⋊C₄	—	2	1	no	—
310	C₂×C₄⋊C₄	—	2	1	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	1	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
316	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
317	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
318	C₂×C₂²⋊C₄	—	2	1	no	—
319	C₂×C₂²⋊C₄	—	2	1	no	—
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	—	2	1	no	—
322	C₂×C₂²⋊C₄	—	2	1	no	—
323	C₂×C₂²⋊C₄	—	2	2	no	—
324	C₂×C₄²	—	2	1	no	—
325	C₂×C₄²	—	2	2	no	—
326	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
327	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
328	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
329	C₂×C₄²	D₄×C₄₇	1	4	yes	—
330	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
331	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
332	C₄⋊C₈	—	2	4	no	—
333	C₄⋊C₈	—	2	4	no	—
334	#103	—	4	4	no	—
335	#102	—	4	4	no	—
336	#95	—	2	2	no	—
337	#95	—	2	2	no	—
338	C₂⁴	—	2	1	no	—
339	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
340	C₂×Q₈	—	2	1	no	—
341	C₂×Q₈	—	2	2	no	—
342	C₂×Q₈	—	2	2	no	—
343	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	—
344	C₂×D₄	—	2	4	no	—
345	C₂×D₄	—	2	1	no	—
346	C₂×D₄	—	2	2	no	—
347	C₂×D₄	—	2	2	no	—
348	C₂×D₄	—	4	2	no	—
349	C₂×D₄	—	4	2	no	—
350	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	4	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	1	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	4	no	—
361	C₂²×C₄	—	4	4	no	—
362	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
363	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
364	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
365	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
366	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
367	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
368	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
369	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
371	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
372	C₂×C₈	—	2	4	no	—
373	C₂×C₈	—	2	4	no	—
374	C₂×C₈	—	2	4	no	—
375	C₂×C₈	—	4	8	no	—
376	C₄⋊C₄	—	2	4	no	—
377	C₄⋊C₄	—	2	4	no	—
378	C₄⋊C₄	—	2	4	no	—
379	C₄⋊C₄	—	2	4	no	—
380	C₄⋊C₄	—	2	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	2	4	no	—
383	C₄⋊C₄	—	2	4	no	—
384	C₄⋊C₄	—	4	4	no	—
385	C₄⋊C₄	—	4	4	no	—
386	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
387	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
388	C₂²⋊C₄	—	2	4	no	—
389	C₂²⋊C₄	—	2	4	no	—
390	C₂²⋊C₄	—	2	4	no	—
391	C₂²⋊C₄	—	2	4	no	—
392	C₂²⋊C₄	—	2	4	no	—
393	C₂²⋊C₄	—	4	4	no	—
394	C₄²	—	2	4	no	—
395	C₄²	—	4	4	no	—
396	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
397	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
398	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
399	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
400	C₄²	C₂×D₄×C₄₇	1	2	yes	—
401	C₄²	C₂×D₄×C₄₇	1	2	yes	—
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	4	2	no	—
406	C₂³	—	4	2	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
410	C₂³	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
411	C₂³	#137×C₄₇	1	2	yes	—
412	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
413	Q₈	—	2	4	no	—
414	Q₈	—	4	1	no	—
415	Q₈	—	4	1	no	—
416	D₄	—	2	4	no	—
417	D₄	—	4	8	no	—
418	D₄	—	4	1	no	—
419	D₄	—	4	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	8	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	1	no	—
437	C₂×C₄	—	4	1	no	—
438	C₂×C₄	—	4	8	no	—
439	C₂×C₄	—	4	4	no	—
440	C₂×C₄	—	4	4	no	—
441	C₂×C₄	—	4	4	no	—
442	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
443	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
444	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
445	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
446	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
447	C₂×C₄	#135×C₄₇	1	4	yes	—
448	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
449	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
450	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
451	C₂×C₄	2₋¹⁺⁴×C₄₇	1	2	yes	—
452	C₈	—	4	4	no	—
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	4	no	—
456	C₂²	—	2	4	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	2	no	—
460	C₂²	—	8	2	no	—
461	C₂²	—	8	2	no	—
462	C₂²	C₄₇×#417	1	4	yes	—
463	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
464	C₂²	C₄₇×#537	1	2	yes	—
465	C₂²	C₂×#135×C₄₇	1	2	yes	—
466	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
467	C₂²	C₂×#137×C₄₇	1	1	yes	characteristic
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	2	no	—
471	C₄	—	2	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	4	2	no	—
475	C₄	—	8	4	no	—
476	C₄	C₄₇×#416	1	4	yes	—
477	C₄	C₄₇×#520	1	2	yes	—
478	C₄	C₄₇×#535	1	1	yes	characteristic
479	C₄	C₄₇×#536	1	1	yes	characteristic
480	C₂	—	2	4	no	—
481	C₂	—	8	2	no	—
482	C₂	C₄₇×#2311	1	1	yes	characteristic
483	C₂	C₂×C₄₇×#416	1	1	yes	characteristic
484	C₂	C₂×C₄₇×#417	1	1	yes	characteristic
485	C₂	C₄₇×#3247	1	2	yes	—
486	C₂	C₄₇×#3248	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×#121×C₄₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂²×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄⋊C₈×C₄₇	C₂	semidirect
3. C₄₇×#2285	C₂	semidirect
4. C₄₇×#1989	C₂	semidirect
5. C₄₇×#1983	C₂	semidirect
7. C₄₇×#1892	C₂	semidirect
8. C₄₇×#1803	C₂	semidirect
9. C₄₇×#1802	C₂	semidirect
12. C₄₇×#529	C₄	semidirect
209. #21887	C₄₇	direct (N × H)
238. C₂²×C₄⋊C₈	C₂×C₄₇	semidirect
239. #2285	C₂×C₄₇	semidirect
240. #1989	C₂×C₄₇	semidirect
241. #1983	C₂×C₄₇	semidirect
243. #1892	C₂×C₄₇	semidirect
244. #1803	C₂×C₄₇	semidirect
245. #1802	C₂×C₄₇	semidirect
255. #529	C₄×C₄₇	semidirect
281. C₄₇	#21887	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#529	2
C₂²×C₄⋊C₈×C₄₇	2
C₄₇×#2285	2
C₄₇×#1989	2
C₄₇×#1983	2
C₄₇×#1893	2
C₄₇×#1892	2
C₄₇×#1803	2
C₄₇×#1802	2
#21887	47

Subgroups — C47×#21887 #26061585

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#21887 #26061585