Subgroups — C₄₇×#24743 #26064441

Order 12032.

932 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×#464	C₂	1	2	yes	maximal
2	C₂×C₄₇×#462	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#440	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#2547	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#2351	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#2068	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2042	C₂	1	2	yes	maximal
8	C₄₇×#1960	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1940	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1878	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1804	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₄₇	C₂²	1	2	yes	—
13	C₂²×SD₁₆×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×#124×C₄₇	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
17	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#464	—	2	8	no	—
20	C₄₇×#462	—	2	4	no	—
21	C₄₇×#440	—	2	4	no	—
22	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
25	C₂×#103×C₄₇	C₂²	1	2	yes	—
26	C₂×#103×C₄₇	C₂²	1	2	yes	—
27	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×#103×C₄₇	C₂²	1	2	yes	—
29	C₂×#102×C₄₇	C₂²	1	2	yes	—
30	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
32	C₄₇×#397	—	2	1	no	—
33	C₄₇×#397	—	2	1	no	—
34	C₄₇×#391	C₂²	1	2	yes	—
35	C₄₇×#389	—	2	2	no	—
36	C₄₇×#389	C₂²	1	2	yes	—
37	C₄₇×#382	—	2	1	no	—
38	C₄₇×#382	C₂²	1	1	yes	characteristic
39	C₄₇×#380	—	2	2	no	—
40	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
41	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#340	C₂²	1	2	yes	—
43	C₄₇×#336	C₂²	1	2	yes	—
44	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
45	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
46	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₄₇	—	2	1	no	—
48	C₂×Q₁₆×C₄₇	—	2	4	no	—
49	C₂×Q₁₆×C₄₇	—	2	4	no	—
50	C₂×Q₁₆×C₄₇	—	2	4	no	—
51	C₂×SD₁₆×C₄₇	—	2	2	no	—
52	C₂×SD₁₆×C₄₇	—	2	2	no	—
53	C₂×SD₁₆×C₄₇	D₄	1	4	yes	—
54	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
55	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
57	C₄⋊Q₈×C₄₇	—	2	2	no	—
58	C₄⋊Q₈×C₄₇	—	2	2	no	—
59	#124×C₄₇	—	2	4	no	—
60	#124×C₄₇	—	4	2	no	—
61	C₄×Q₈×C₄₇	—	2	2	no	—
62	C₄×Q₈×C₄₇	—	2	4	no	—
63	C₄×Q₈×C₄₇	—	4	2	no	—
64	C₄×Q₈×C₄₇	D₄	1	4	yes	—
65	C₄×D₄×C₄₇	—	2	2	no	—
66	C₄×D₄×C₄₇	—	2	2	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
72	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
76	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
79	C₂×C₄²×C₄₇	—	2	1	no	—
80	C₂×C₄²×C₄₇	—	2	2	no	—
81	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
82	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
83	#107×C₄₇	—	2	2	no	—
84	C₄⋊C₈×C₄₇	—	2	4	no	—
85	C₄⋊C₈×C₄₇	—	2	2	no	—
86	#103×C₄₇	—	2	2	no	—
87	#103×C₄₇	—	2	4	no	—
88	#103×C₄₇	—	2	4	no	—
89	#103×C₄₇	—	4	2	no	—
90	#102×C₄₇	—	2	4	no	—
91	#102×C₄₇	—	2	2	no	—
92	#97×C₄₇	—	2	2	no	—
93	#95×C₄₇	—	2	1	no	—
94	#95×C₄₇	—	2	2	no	—
95	#95×C₄₇	—	2	2	no	—
96	#95×C₄₇	—	2	2	no	—
97	#95×C₄₇	—	2	1	no	—
98	#95×C₄₇	D₄	1	1	yes	characteristic
99	#95×C₄₇	D₄	1	1	yes	characteristic
100	C₂⁴×C₄₇	—	2	1	no	—
101	C₂×Q₈×C₄₇	—	2	1	no	—
102	C₂×Q₈×C₄₇	—	2	1	no	—
103	C₂×Q₈×C₄₇	—	2	1	no	—
104	C₂×Q₈×C₄₇	—	2	2	no	—
105	C₂×Q₈×C₄₇	—	2	2	no	—
106	C₂×Q₈×C₄₇	—	2	2	no	—
107	C₂×Q₈×C₄₇	—	2	2	no	—
108	C₂×Q₈×C₄₇	—	2	2	no	—
109	C₂×Q₈×C₄₇	—	2	2	no	—
110	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
111	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
112	C₂×Q₈×C₄₇	#41	1	2	yes	—
113	C₂×D₄×C₄₇	—	2	1	no	—
114	C₂×D₄×C₄₇	—	2	1	no	—
115	C₂×D₄×C₄₇	—	2	1	no	—
116	C₂×D₄×C₄₇	—	2	1	no	—
117	C₂×D₄×C₄₇	—	2	1	no	—
118	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₄₇	—	2	1	no	—
120	C₂²×C₄×C₄₇	—	2	1	no	—
121	C₂²×C₄×C₄₇	—	2	2	no	—
122	C₂²×C₄×C₄₇	—	2	2	no	—
123	C₂²×C₄×C₄₇	—	2	1	no	—
124	C₂²×C₄×C₄₇	—	4	4	no	—
125	C₂²×C₄×C₄₇	—	4	2	no	—
126	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
131	Q₁₆×C₄₇	—	4	8	no	—
132	SD₁₆×C₄₇	—	2	8	no	—
133	C₂×C₈×C₄₇	—	2	1	no	—
134	C₂×C₈×C₄₇	—	2	1	no	—
135	C₂×C₈×C₄₇	—	2	2	no	—
136	C₂×C₈×C₄₇	—	2	1	no	—
137	C₂×C₈×C₄₇	—	2	2	no	—
138	C₂×C₈×C₄₇	—	2	2	no	—
139	C₂×C₈×C₄₇	—	2	1	no	—
140	C₂×C₈×C₄₇	—	2	1	no	—
141	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
142	C₄⋊C₄×C₄₇	—	2	4	no	—
143	C₄⋊C₄×C₄₇	—	2	1	no	—
144	C₄⋊C₄×C₄₇	—	2	1	no	—
145	C₄⋊C₄×C₄₇	—	2	2	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	4	no	—
150	C₄⋊C₄×C₄₇	—	4	4	no	—
151	C₄⋊C₄×C₄₇	—	4	2	no	—
152	C₄⋊C₄×C₄₇	—	4	2	no	—
153	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
154	C₂²⋊C₄×C₄₇	—	4	4	no	—
155	C₂²⋊C₄×C₄₇	—	4	4	no	—
156	C₂²⋊C₄×C₄₇	—	4	2	no	—
157	C₄²×C₄₇	—	2	4	no	—
158	C₄²×C₄₇	—	2	2	no	—
159	C₄²×C₄₇	—	2	2	no	—
160	C₄²×C₄₇	—	4	4	no	—
161	C₄²×C₄₇	C₂×D₄	1	2	yes	—
162	C₄²×C₄₇	#41	1	2	yes	—
163	C₂³×C₄₇	—	2	2	no	—
164	C₂³×C₄₇	—	4	1	no	—
165	C₂³×C₄₇	—	4	1	no	—
166	C₂³×C₄₇	—	4	2	no	—
167	C₂³×C₄₇	—	4	2	no	—
168	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
169	Q₈×C₄₇	—	2	2	no	—
170	Q₈×C₄₇	—	2	2	no	—
171	Q₈×C₄₇	—	2	2	no	—
172	Q₈×C₄₇	—	4	2	no	—
173	Q₈×C₄₇	—	4	2	no	—
174	Q₈×C₄₇	—	4	2	no	—
175	Q₈×C₄₇	—	4	2	no	—
176	Q₈×C₄₇	#121	1	4	yes	—
177	D₄×C₄₇	—	2	2	no	—
178	D₄×C₄₇	—	2	2	no	—
179	D₄×C₄₇	—	4	1	no	—
180	D₄×C₄₇	—	4	1	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	—	2	2	no	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	2	2	no	—
185	C₂×C₄×C₄₇	—	2	2	no	—
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	2	no	—
190	C₂×C₄×C₄₇	—	2	2	no	—
191	C₂×C₄×C₄₇	—	2	2	no	—
192	C₂×C₄×C₄₇	—	2	2	no	—
193	C₂×C₄×C₄₇	—	4	2	no	—
194	C₂×C₄×C₄₇	—	4	1	no	—
195	C₂×C₄×C₄₇	—	4	2	no	—
196	C₂×C₄×C₄₇	—	4	2	no	—
197	C₂×C₄×C₄₇	—	4	2	no	—
198	C₂×C₄×C₄₇	—	4	2	no	—
199	C₂×C₄×C₄₇	—	4	2	no	—
200	C₂×C₄×C₄₇	—	4	2	no	—
201	C₂×C₄×C₄₇	—	4	2	no	—
202	C₂×C₄×C₄₇	—	8	4	no	—
203	C₂×C₄×C₄₇	#121	1	2	yes	—
204	C₂×C₄×C₄₇	#121	1	2	yes	—
205	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
206	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
208	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
210	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
211	C₈×C₄₇	—	2	2	no	—
212	C₈×C₄₇	—	4	2	no	—
213	C₈×C₄₇	—	4	1	no	—
214	#24743	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂²×C₄₇	—	4	2	no	—
216	C₂²×C₄₇	—	4	4	no	—
217	C₂²×C₄₇	—	8	2	no	—
218	C₂²×C₄₇	—	8	1	no	—
219	C₂²×C₄₇	—	8	1	no	—
220	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
221	C₂²×C₄₇	D₄²	1	1	yes	characteristic
222	C₂²×C₄₇	#548	1	1	yes	characteristic
223	C₂²×C₄₇	#575	1	2	yes	—
224	C₂²×C₄₇	#578	1	2	yes	—
225	C₄×C₄₇	—	2	4	no	—
226	C₄×C₄₇	—	2	2	no	—
227	C₄×C₄₇	—	2	2	no	—
228	C₄×C₄₇	—	4	2	no	—
229	C₄×C₄₇	—	4	2	no	—
230	C₄×C₄₇	—	4	2	no	—
231	C₄×C₄₇	—	8	2	no	—
232	C₄×C₄₇	—	8	2	no	—
233	C₄×C₄₇	—	8	1	no	—
234	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
235	C₄×C₄₇	#537	1	1	yes	characteristic
236	C₄×C₄₇	#547	1	1	yes	characteristic
237	C₄×C₄₇	#553	1	1	yes	characteristic
238	C₂×#464	C₂×C₄₇	1	2	yes	—
239	C₂×#462	C₂×C₄₇	1	1	yes	characteristic, complemented
240	C₂×#440	C₂×C₄₇	1	1	yes	characteristic
241	#2547	C₂×C₄₇	1	1	yes	characteristic
242	#2351	C₂×C₄₇	1	1	yes	characteristic, complemented
243	#2068	C₂×C₄₇	1	2	yes	complemented
244	#2042	C₂×C₄₇	1	2	yes	—
245	#1960	C₂×C₄₇	1	1	yes	characteristic, complemented
246	#1940	C₂×C₄₇	1	1	yes	characteristic, complemented
247	#1878	C₂×C₄₇	1	2	yes	complemented
248	#1804	C₂×C₄₇	1	1	yes	characteristic
249	C₂×C₄₇	—	8	2	no	—
250	C₂×C₄₇	#2416	1	1	yes	characteristic
251	C₂×C₄₇	#3040	1	1	yes	characteristic
252	C₂×C₄₇	#3044	1	1	yes	characteristic
253	C₂×C₄₇	#3269	1	2	yes	—
254	C₂×C₄₇	#3377	1	2	yes	—
255	C₂²×Q₁₆	C₂²×C₄₇	1	2	yes	—
256	C₂²×SD₁₆	C₂²×C₄₇	1	1	yes	characteristic
257	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
258	C₂×#124	C₂²×C₄₇	1	2	yes	—
259	C₂×C₄×Q₈	C₂²×C₄₇	1	2	yes	—
260	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
261	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
262	#464	—	2	8	no	—
263	#462	—	2	4	no	—
264	#440	—	2	4	no	—
265	C₂×#107	C₂²×C₄₇	1	1	yes	characteristic
266	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
267	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
268	C₂×#103	C₂²×C₄₇	1	2	yes	—
269	C₂×#103	C₂²×C₄₇	1	2	yes	—
270	C₂×#103	C₂²×C₄₇	1	1	yes	characteristic
271	C₂×#103	C₂²×C₄₇	1	2	yes	—
272	C₂×#102	C₂²×C₄₇	1	2	yes	—
273	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic
274	C₂×#97	C₂²×C₄₇	1	1	yes	characteristic
275	#397	—	2	1	no	—
276	#397	—	2	1	no	—
277	#391	C₂²×C₄₇	1	2	yes	—
278	#389	—	2	2	no	—
279	#389	C₂²×C₄₇	1	2	yes	—
280	#382	—	2	1	no	—
281	#382	C₂²×C₄₇	1	1	yes	characteristic
282	#380	—	2	2	no	—
283	C₄×C₄⋊C₄	—	2	1	no	—
284	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
285	#340	C₂²×C₄₇	1	2	yes	—
286	#336	C₂²×C₄₇	1	2	yes	—
287	C₄₇	#24743	1	1	yes	characteristic, direct product factor, Sylow
288	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
289	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
290	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
291	C₂³×C₄	—	2	1	no	—
292	C₂×Q₁₆	—	2	4	no	—
293	C₂×Q₁₆	—	2	4	no	—
294	C₂×Q₁₆	—	2	4	no	—
295	C₂×SD₁₆	—	2	2	no	—
296	C₂×SD₁₆	—	2	2	no	—
297	C₂×SD₁₆	D₄×C₄₇	1	4	yes	—
298	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
299	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
300	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
301	C₄⋊Q₈	—	2	2	no	—
302	C₄⋊Q₈	—	2	2	no	—
303	#124	—	2	4	no	—
304	#124	—	4	2	no	—
305	C₄×Q₈	—	2	2	no	—
306	C₄×Q₈	—	2	4	no	—
307	C₄×Q₈	—	4	2	no	—
308	C₄×Q₈	D₄×C₄₇	1	4	yes	—
309	C₄×D₄	—	2	2	no	—
310	C₄×D₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	1	no	—
312	C₂×C₄⋊C₄	—	2	2	no	—
313	C₂×C₄⋊C₄	—	2	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
317	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
318	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
319	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
320	C₂×C₂²⋊C₄	—	2	1	no	—
321	C₂×C₂²⋊C₄	—	2	2	no	—
322	C₂×C₂²⋊C₄	—	2	2	no	—
323	C₂×C₄²	—	2	1	no	—
324	C₂×C₄²	—	2	2	no	—
325	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
326	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
327	#107	—	2	2	no	—
328	C₄⋊C₈	—	2	4	no	—
329	C₄⋊C₈	—	2	2	no	—
330	#103	—	2	2	no	—
331	#103	—	2	4	no	—
332	#103	—	2	4	no	—
333	#103	—	4	2	no	—
334	#102	—	2	4	no	—
335	#102	—	2	2	no	—
336	#97	—	2	2	no	—
337	#95	—	2	1	no	—
338	#95	—	2	2	no	—
339	#95	—	2	2	no	—
340	#95	—	2	2	no	—
341	#95	—	2	1	no	—
342	#95	D₄×C₄₇	1	1	yes	characteristic
343	#95	D₄×C₄₇	1	1	yes	characteristic
344	C₂⁴	—	2	1	no	—
345	C₂×Q₈	—	2	1	no	—
346	C₂×Q₈	—	2	1	no	—
347	C₂×Q₈	—	2	1	no	—
348	C₂×Q₈	—	2	2	no	—
349	C₂×Q₈	—	2	2	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
355	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
356	C₂×Q₈	#41×C₄₇	1	2	yes	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	2	1	no	—
359	C₂×D₄	—	2	1	no	—
360	C₂×D₄	—	2	1	no	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	1	no	—
365	C₂²×C₄	—	2	1	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	4	4	no	—
369	C₂²×C₄	—	4	2	no	—
370	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
371	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
372	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
373	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
374	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
375	Q₁₆	—	4	8	no	—
376	SD₁₆	—	2	8	no	—
377	C₂×C₈	—	2	1	no	—
378	C₂×C₈	—	2	1	no	—
379	C₂×C₈	—	2	1	no	—
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	1	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
386	C₄⋊C₄	—	2	4	no	—
387	C₄⋊C₄	—	2	1	no	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	2	1	no	—
390	C₄⋊C₄	—	2	1	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	4	2	no	—
393	C₄⋊C₄	—	4	4	no	—
394	C₄⋊C₄	—	4	4	no	—
395	C₄⋊C₄	—	4	2	no	—
396	C₄⋊C₄	—	4	2	no	—
397	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
398	C₂²⋊C₄	—	4	4	no	—
399	C₂²⋊C₄	—	4	4	no	—
400	C₂²⋊C₄	—	4	2	no	—
401	C₄²	—	2	4	no	—
402	C₄²	—	2	2	no	—
403	C₄²	—	2	2	no	—
404	C₄²	—	4	4	no	—
405	C₄²	C₂×D₄×C₄₇	1	2	yes	—
406	C₄²	#41×C₄₇	1	2	yes	—
407	C₂³	—	2	2	no	—
408	C₂³	—	4	1	no	—
409	C₂³	—	4	1	no	—
410	C₂³	—	4	2	no	—
411	C₂³	—	4	2	no	—
412	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
413	Q₈	—	2	2	no	—
414	Q₈	—	2	2	no	—
415	Q₈	—	2	2	no	—
416	Q₈	—	4	2	no	—
417	Q₈	—	4	2	no	—
418	Q₈	—	4	2	no	—
419	Q₈	—	4	2	no	—
420	Q₈	#121×C₄₇	1	4	yes	—
421	D₄	—	2	2	no	—
422	D₄	—	2	2	no	—
423	D₄	—	4	1	no	—
424	D₄	—	4	1	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	1	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	8	4	no	—
447	C₂×C₄	#121×C₄₇	1	2	yes	—
448	C₂×C₄	#121×C₄₇	1	2	yes	—
449	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
450	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
451	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
452	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
453	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
454	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
455	C₈	—	2	2	no	—
456	C₈	—	4	2	no	—
457	C₈	—	4	1	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	8	1	no	—
461	C₂²	—	8	1	no	—
462	C₂²	—	8	2	no	—
463	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
464	C₂²	D₄²×C₄₇	1	1	yes	characteristic
465	C₂²	C₄₇×#548	1	1	yes	characteristic
466	C₂²	C₄₇×#575	1	2	yes	—
467	C₂²	C₄₇×#578	1	2	yes	—
468	C₄	—	2	2	no	—
469	C₄	—	2	2	no	—
470	C₄	—	2	4	no	—
471	C₄	—	4	2	no	—
472	C₄	—	4	2	no	—
473	C₄	—	4	2	no	—
474	C₄	—	8	1	no	—
475	C₄	—	8	2	no	—
476	C₄	—	8	2	no	—
477	C₄	C₂×#121×C₄₇	1	1	yes	characteristic
478	C₄	C₄₇×#537	1	1	yes	characteristic
479	C₄	C₄₇×#547	1	1	yes	characteristic
480	C₄	C₄₇×#553	1	1	yes	characteristic
481	C₂	—	8	2	no	—
482	C₂	C₄₇×#2416	1	1	yes	characteristic
483	C₂	C₄₇×#3040	1	1	yes	characteristic
484	C₂	C₄₇×#3044	1	1	yes	characteristic
485	C₂	C₄₇×#3269	1	2	yes	—
486	C₂	C₄₇×#3377	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#462	C₂	semidirect
5. C₄₇×#2351	C₂	semidirect
6. C₄₇×#2068	C₂	semidirect
8. C₄₇×#1960	C₂	semidirect
9. C₄₇×#1940	C₂	semidirect
10. C₄₇×#1878	C₂	semidirect
214. #24743	C₄₇	direct (N × H)
239. C₂×#462	C₂×C₄₇	semidirect
242. #2351	C₂×C₄₇	semidirect
243. #2068	C₂×C₄₇	semidirect
245. #1960	C₂×C₄₇	semidirect
246. #1940	C₂×C₄₇	semidirect
247. #1878	C₂×C₄₇	semidirect
287. C₄₇	#24743	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×#464	2
C₂×C₄₇×#462	2
C₂×C₄₇×#440	2
C₄₇×#2547	2
C₄₇×#2351	2
C₄₇×#2068	2
C₄₇×#2042	2
C₄₇×#1960	2
C₄₇×#1940	2
C₄₇×#1878	2
C₄₇×#1804	2
#24743	47

Subgroups — C47×#24743 #26064441

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#24743 #26064441