Subgroups — C₄₇×#24599 #26064297

Order 12032.

806 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#482	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#428	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2504	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#2346	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2085	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2067	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1949	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1926	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1895	C₂	1	1	yes	maximal, characteristic
10	C₄₇×#1851	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1823	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₄₇×#482	—	2	4	no	—
17	C₄₇×#428	—	2	4	no	—
18	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#107×C₄₇	C₂²	1	2	yes	—
20	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×#106×C₄₇	C₂²	1	2	yes	—
22	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
23	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×#102×C₄₇	C₂²	1	2	yes	—
26	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₄₇×#397	—	2	1	no	—
28	C₄₇×#397	—	2	1	no	—
29	C₄₇×#390	C₂²	1	2	yes	—
30	C₄₇×#389	C₂²	1	2	yes	—
31	C₄₇×#388	—	2	2	no	—
32	C₄₇×#386	—	2	2	no	—
33	C₄₇×#382	—	2	1	no	—
34	C₄₇×#382	C₂²	1	2	yes	—
35	C₄₇×#380	C₂²	1	1	yes	characteristic
36	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
37	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#376	—	2	1	no	—
39	C₄₇×#340	C₂²	1	2	yes	—
40	C₄₇×#340	C₂²	1	2	yes	—
41	C₄₇×#340	C₂²	1	2	yes	—
42	C₄₇×#336	C₂²	1	2	yes	—
43	C₂²×D₄×C₄₇	—	2	1	no	—
44	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	—	2	1	no	—
46	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
47	C₂×M₁₆×C₄₇	—	2	2	no	—
48	C₂×M₁₆×C₄₇	—	2	4	no	—
49	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
52	#121×C₄₇	—	2	2	no	—
53	#121×C₄₇	—	2	2	no	—
54	#117×C₄₇	—	2	2	no	—
55	#117×C₄₇	D₄	1	4	yes	—
56	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
63	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
68	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
71	C₂×C₄²×C₄₇	—	2	1	no	—
72	C₂×C₄²×C₄₇	—	2	2	no	—
73	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
74	#107×C₄₇	—	2	2	no	—
75	#107×C₄₇	—	2	4	no	—
76	#106×C₄₇	—	2	2	no	—
77	#106×C₄₇	—	2	4	no	—
78	C₄⋊C₈×C₄₇	—	2	4	no	—
79	#102×C₄₇	—	2	4	no	—
80	#102×C₄₇	—	2	2	no	—
81	#102×C₄₇	—	2	2	no	—
82	C₂²⋊C₈×C₄₇	—	2	2	no	—
83	#95×C₄₇	—	2	1	no	—
84	#95×C₄₇	—	2	2	no	—
85	#95×C₄₇	—	2	2	no	—
86	#95×C₄₇	—	2	2	no	—
87	#95×C₄₇	—	2	2	no	—
88	#95×C₄₇	D₄	1	1	yes	characteristic
89	#95×C₄₇	D₄	1	1	yes	characteristic
90	C₂⁴×C₄₇	—	2	1	no	—
91	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
92	C₂×D₄×C₄₇	—	2	1	no	—
93	C₂×D₄×C₄₇	—	2	1	no	—
94	C₂×D₄×C₄₇	—	2	2	no	—
95	C₂×D₄×C₄₇	—	2	2	no	—
96	C₂×D₄×C₄₇	—	4	4	no	—
97	C₂×D₄×C₄₇	—	4	2	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	—	4	2	no	—
106	C₂²×C₄×C₄₇	—	8	1	no	—
107	C₂²×C₄×C₄₇	—	8	1	no	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
109	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
112	C₂²×C₄×C₄₇	#41	1	2	yes	—
113	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
114	M₁₆×C₄₇	—	2	8	no	—
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	—	2	1	no	—
118	C₂×C₈×C₄₇	—	2	1	no	—
119	C₂×C₈×C₄₇	—	2	2	no	—
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	#41	1	4	yes	—
122	C₄⋊C₄×C₄₇	—	2	1	no	—
123	C₄⋊C₄×C₄₇	—	2	1	no	—
124	C₄⋊C₄×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	—	2	1	no	—
126	C₄⋊C₄×C₄₇	—	2	2	no	—
127	C₄⋊C₄×C₄₇	—	2	1	no	—
128	C₄⋊C₄×C₄₇	—	2	2	no	—
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	—	4	2	no	—
131	C₄⋊C₄×C₄₇	—	8	2	no	—
132	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
133	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
134	C₂²⋊C₄×C₄₇	—	2	4	no	—
135	C₂²⋊C₄×C₄₇	—	4	2	no	—
136	C₂²⋊C₄×C₄₇	—	4	2	no	—
137	C₂²⋊C₄×C₄₇	—	8	2	no	—
138	C₂²⋊C₄×C₄₇	—	8	2	no	—
139	C₂²⋊C₄×C₄₇	—	8	1	no	—
140	C₄²×C₄₇	—	2	4	no	—
141	C₄²×C₄₇	—	2	2	no	—
142	C₄²×C₄₇	—	2	2	no	—
143	C₄²×C₄₇	—	4	4	no	—
144	C₂³×C₄₇	—	2	2	no	—
145	C₂³×C₄₇	—	2	2	no	—
146	C₂³×C₄₇	—	2	1	no	—
147	C₂³×C₄₇	—	2	1	no	—
148	C₂³×C₄₇	—	4	1	no	—
149	C₂³×C₄₇	—	4	2	no	—
150	C₂³×C₄₇	—	4	2	no	—
151	C₂³×C₄₇	—	4	1	no	—
152	C₂³×C₄₇	—	4	1	no	—
153	C₂³×C₄₇	#121	1	2	yes	—
154	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
155	D₄×C₄₇	—	4	1	no	—
156	D₄×C₄₇	—	4	1	no	—
157	D₄×C₄₇	—	4	2	no	—
158	D₄×C₄₇	—	8	4	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	2	2	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	4	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	4	2	no	—
172	C₂×C₄×C₄₇	—	4	1	no	—
173	C₂×C₄×C₄₇	—	4	1	no	—
174	C₂×C₄×C₄₇	—	4	1	no	—
175	C₂×C₄×C₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	—	4	2	no	—
179	C₂×C₄×C₄₇	—	4	2	no	—
180	C₂×C₄×C₄₇	—	4	2	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	8	4	no	—
183	C₂×C₄×C₄₇	#121	1	2	yes	—
184	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
186	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
187	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
188	C₈×C₄₇	—	2	4	no	—
189	C₈×C₄₇	—	4	1	no	—
190	C₈×C₄₇	—	4	1	no	—
191	#24599	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
192	C₂²×C₄₇	—	2	2	no	—
193	C₂²×C₄₇	—	2	2	no	—
194	C₂²×C₄₇	—	2	2	no	—
195	C₂²×C₄₇	—	4	2	no	—
196	C₂²×C₄₇	—	4	2	no	—
197	C₂²×C₄₇	—	8	2	no	—
198	C₂²×C₄₇	—	8	2	no	—
199	C₂²×C₄₇	—	8	1	no	—
200	C₂²×C₄₇	—	8	1	no	—
201	C₂²×C₄₇	—	8	1	no	—
202	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
203	C₂²×C₄₇	#547	1	2	yes	—
204	C₂²×C₄₇	#575	1	2	yes	—
205	C₂²×C₄₇	#576	1	1	yes	characteristic
206	C₂²×C₄₇	#577	1	1	yes	characteristic
207	C₄×C₄₇	—	2	2	no	—
208	C₄×C₄₇	—	4	2	no	—
209	C₄×C₄₇	—	4	2	no	—
210	C₄×C₄₇	—	4	2	no	—
211	C₄×C₄₇	—	4	2	no	—
212	C₄×C₄₇	—	8	2	no	—
213	C₄×C₄₇	—	8	1	no	—
214	C₄×C₄₇	—	8	2	no	—
215	C₄×C₄₇	#525	1	1	yes	characteristic
216	C₄×C₄₇	#536	1	1	yes	characteristic
217	C₄×C₄₇	#552	1	2	yes	—
218	C₂×#482	C₂×C₄₇	1	1	yes	characteristic
219	C₂×#428	C₂×C₄₇	1	1	yes	characteristic, complemented
220	#2504	C₂×C₄₇	1	1	yes	characteristic
221	#2346	C₂×C₄₇	1	1	yes	characteristic, complemented
222	#2085	C₂×C₄₇	1	2	yes	complemented
223	#2067	C₂×C₄₇	1	2	yes	complemented
224	#1949	C₂×C₄₇	1	2	yes	complemented
225	#1926	C₂×C₄₇	1	2	yes	complemented
226	#1895	C₂×C₄₇	1	1	yes	characteristic
227	#1851	C₂×C₄₇	1	1	yes	characteristic, complemented
228	#1823	C₂×C₄₇	1	1	yes	characteristic, complemented
229	C₂×C₄₇	—	4	2	no	—
230	C₂×C₄₇	—	16	1	no	—
231	C₂×C₄₇	#2413	1	1	yes	characteristic
232	C₂×C₄₇	#3040	1	1	yes	characteristic
233	C₂×C₄₇	#3045	1	1	yes	characteristic
234	C₂×C₄₇	#3347	1	2	yes	—
235	C₂×C₄₇	#3351	1	2	yes	—
236	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
237	C₂×#121	C₂²×C₄₇	1	1	yes	characteristic
238	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
239	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
240	#482	—	2	4	no	—
241	#428	—	2	4	no	—
242	C₂×#107	C₂²×C₄₇	1	1	yes	characteristic
243	C₂×#107	C₂²×C₄₇	1	2	yes	—
244	C₂×#106	C₂²×C₄₇	1	1	yes	characteristic
245	C₂×#106	C₂²×C₄₇	1	2	yes	—
246	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
247	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic
248	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic
249	C₂×#102	C₂²×C₄₇	1	2	yes	—
250	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
251	#397	—	2	1	no	—
252	#397	—	2	1	no	—
253	#390	C₂²×C₄₇	1	2	yes	—
254	#389	C₂²×C₄₇	1	2	yes	—
255	#388	—	2	2	no	—
256	#386	—	2	2	no	—
257	#382	—	2	1	no	—
258	#382	C₂²×C₄₇	1	2	yes	—
259	#380	C₂²×C₄₇	1	1	yes	characteristic
260	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
261	C₄×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
262	#376	—	2	1	no	—
263	#340	C₂²×C₄₇	1	2	yes	—
264	#340	C₂²×C₄₇	1	2	yes	—
265	#340	C₂²×C₄₇	1	2	yes	—
266	#336	C₂²×C₄₇	1	2	yes	—
267	C₄₇	#24599	1	1	yes	characteristic, direct product factor, Sylow
268	C₂²×D₄	—	2	1	no	—
269	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
270	C₂³×C₄	—	2	1	no	—
271	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
272	C₂×M₁₆	—	2	2	no	—
273	C₂×M₁₆	—	2	4	no	—
274	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
275	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
276	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
277	#121	—	2	2	no	—
278	#121	—	2	2	no	—
279	#117	—	2	2	no	—
280	#117	D₄×C₄₇	1	4	yes	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	1	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
287	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
289	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
290	C₂×C₂²⋊C₄	—	2	1	no	—
291	C₂×C₂²⋊C₄	—	2	1	no	—
292	C₂×C₂²⋊C₄	—	2	1	no	—
293	C₂×C₂²⋊C₄	—	2	2	no	—
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
296	C₂×C₄²	—	2	1	no	—
297	C₂×C₄²	—	2	2	no	—
298	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
299	#107	—	2	4	no	—
300	#107	—	2	2	no	—
301	#106	—	2	4	no	—
302	#106	—	2	2	no	—
303	C₄⋊C₈	—	2	4	no	—
304	#102	—	2	4	no	—
305	#102	—	2	2	no	—
306	#102	—	2	2	no	—
307	C₂²⋊C₈	—	2	2	no	—
308	#95	—	2	1	no	—
309	#95	—	2	2	no	—
310	#95	—	2	2	no	—
311	#95	—	2	2	no	—
312	#95	—	2	2	no	—
313	#95	D₄×C₄₇	1	1	yes	characteristic
314	#95	D₄×C₄₇	1	1	yes	characteristic
315	C₂⁴	—	2	1	no	—
316	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
317	C₂×D₄	—	2	1	no	—
318	C₂×D₄	—	2	2	no	—
319	C₂×D₄	—	2	1	no	—
320	C₂×D₄	—	2	2	no	—
321	C₂×D₄	—	4	4	no	—
322	C₂×D₄	—	4	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	1	no	—
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	1	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	—	8	1	no	—
332	C₂²×C₄	—	8	1	no	—
333	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
334	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
335	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
336	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
337	C₂²×C₄	#41×C₄₇	1	2	yes	—
338	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
339	M₁₆	—	2	8	no	—
340	C₂×C₈	—	2	2	no	—
341	C₂×C₈	—	2	2	no	—
342	C₂×C₈	—	2	1	no	—
343	C₂×C₈	—	2	1	no	—
344	C₂×C₈	—	2	2	no	—
345	C₂×C₈	—	2	2	no	—
346	C₂×C₈	#41×C₄₇	1	4	yes	—
347	C₄⋊C₄	—	2	1	no	—
348	C₄⋊C₄	—	2	1	no	—
349	C₄⋊C₄	—	2	2	no	—
350	C₄⋊C₄	—	2	1	no	—
351	C₄⋊C₄	—	2	2	no	—
352	C₄⋊C₄	—	2	2	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	2	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₄⋊C₄	—	8	2	no	—
357	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
358	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
359	C₂²⋊C₄	—	2	4	no	—
360	C₂²⋊C₄	—	4	2	no	—
361	C₂²⋊C₄	—	4	2	no	—
362	C₂²⋊C₄	—	8	2	no	—
363	C₂²⋊C₄	—	8	2	no	—
364	C₂²⋊C₄	—	8	1	no	—
365	C₄²	—	2	4	no	—
366	C₄²	—	2	2	no	—
367	C₄²	—	2	2	no	—
368	C₄²	—	4	4	no	—
369	C₂³	—	2	2	no	—
370	C₂³	—	2	2	no	—
371	C₂³	—	2	1	no	—
372	C₂³	—	2	1	no	—
373	C₂³	—	4	1	no	—
374	C₂³	—	4	2	no	—
375	C₂³	—	4	2	no	—
376	C₂³	—	4	1	no	—
377	C₂³	—	4	1	no	—
378	C₂³	#121×C₄₇	1	2	yes	—
379	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
380	D₄	—	4	1	no	—
381	D₄	—	4	1	no	—
382	D₄	—	4	2	no	—
383	D₄	—	8	4	no	—
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	4	2	no	—
397	C₂×C₄	—	4	1	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	1	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	2	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	8	4	no	—
408	C₂×C₄	#121×C₄₇	1	2	yes	—
409	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
410	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
411	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
412	C₂×C₄	2₋¹⁺⁴×C₄₇	1	2	yes	—
413	C₈	—	2	4	no	—
414	C₈	—	4	1	no	—
415	C₈	—	4	1	no	—
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	4	2	no	—
420	C₂²	—	4	2	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	8	1	no	—
423	C₂²	—	8	2	no	—
424	C₂²	—	8	2	no	—
425	C₂²	—	8	1	no	—
426	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
427	C₂²	C₄₇×#547	1	2	yes	—
428	C₂²	C₄₇×#575	1	2	yes	—
429	C₂²	C₄₇×#576	1	1	yes	characteristic
430	C₂²	C₄₇×#577	1	1	yes	characteristic
431	C₄	—	2	2	no	—
432	C₄	—	4	2	no	—
433	C₄	—	4	2	no	—
434	C₄	—	4	2	no	—
435	C₄	—	4	2	no	—
436	C₄	—	8	1	no	—
437	C₄	—	8	2	no	—
438	C₄	—	8	2	no	—
439	C₄	C₄₇×#525	1	1	yes	characteristic
440	C₄	C₄₇×#536	1	1	yes	characteristic
441	C₄	C₄₇×#552	1	2	yes	—
442	C₂	—	4	2	no	—
443	C₂	—	16	1	no	—
444	C₂	C₄₇×#2413	1	1	yes	characteristic
445	C₂	C₄₇×#3040	1	1	yes	characteristic
446	C₂	C₄₇×#3045	1	1	yes	characteristic
447	C₂	C₄₇×#3347	1	2	yes	—
448	C₂	C₄₇×#3351	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#428	C₂	semidirect
4. C₄₇×#2346	C₂	semidirect
5. C₄₇×#2085	C₂	semidirect
6. C₄₇×#2067	C₂	semidirect
7. C₄₇×#1949	C₂	semidirect
8. C₄₇×#1926	C₂	semidirect
10. C₄₇×#1851	C₂	semidirect
11. C₄₇×#1823	C₂	semidirect
191. #24599	C₄₇	direct (N × H)
219. C₂×#428	C₂×C₄₇	semidirect
221. #2346	C₂×C₄₇	semidirect
222. #2085	C₂×C₄₇	semidirect
223. #2067	C₂×C₄₇	semidirect
224. #1949	C₂×C₄₇	semidirect
225. #1926	C₂×C₄₇	semidirect
227. #1851	C₂×C₄₇	semidirect
228. #1823	C₂×C₄₇	semidirect
267. C₄₇	#24599	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×#482	2
C₂×C₄₇×#428	2
C₄₇×#2504	2
C₄₇×#2346	2
C₄₇×#2085	2
C₄₇×#2067	2
C₄₇×#1949	2
C₄₇×#1926	2
C₄₇×#1895	2
C₄₇×#1851	2
C₄₇×#1823	2
#24599	47

Subgroups — C47×#24599 #26064297

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#24599 #26064297