Subgroups — C₄₇×#25049 #26064747

Order 12032.

776 conjugacy classes of subgroups.

The subgroup lattice has 422 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#470	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#441	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2421	C₂	1	2	yes	maximal
4	C₄₇×#2074	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2036	C₂	1	2	yes	maximal
6	C₄₇×#1969	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1943	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1863	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1846	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1809	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1753	C₂	1	1	yes	maximal, characteristic
12	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
15	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
16	C₄₇×#470	—	2	4	no	—
17	C₄₇×#441	—	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	1	yes	characteristic
22	C₂×#103×C₄₇	C₂²	1	2	yes	—
23	C₂×#103×C₄₇	C₂²	1	2	yes	—
24	C₂×#103×C₄₇	C₂²	1	2	yes	—
25	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₄₇×#400	—	2	2	no	—
29	C₄₇×#397	—	2	2	no	—
30	C₄₇×#391	C₂²	1	2	yes	—
31	C₄₇×#389	C₂²	1	2	yes	—
32	C₄₇×#388	—	2	2	no	—
33	C₄₇×#387	—	2	2	no	—
34	C₄₇×#382	C₂²	1	2	yes	—
35	C₄₇×#380	C₂²	1	2	yes	—
36	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
37	C₄₇×#340	C₂²	1	2	yes	—
38	C₄₇×#340	C₂²	1	2	yes	—
39	C₄₇×#336	C₂²	1	1	yes	characteristic
40	C₄₇×#336	C₂²	1	1	yes	characteristic
41	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
42	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
43	C₂×Q₁₆×C₄₇	—	2	2	no	—
44	C₂×Q₁₆×C₄₇	—	2	2	no	—
45	C₂×Q₁₆×C₄₇	D₄	1	4	yes	—
46	C₂×M₁₆×C₄₇	—	2	2	no	—
47	C₂×M₁₆×C₄₇	—	2	2	no	—
48	C₂×M₁₆×C₄₇	—	2	2	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	1	yes	characteristic
52	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
53	C₂²⋊Q₈×C₄₇	—	2	4	no	—
54	C₂²⋊Q₈×C₄₇	—	4	2	no	—
55	C₄×Q₈×C₄₇	—	2	4	no	—
56	C₄×Q₈×C₄₇	—	4	2	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₇	—	2	2	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	2	yes	—
62	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
63	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
64	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
66	C₂×C₄²×C₄₇	—	2	2	no	—
67	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
69	#107×C₄₇	—	2	2	no	—
70	#107×C₄₇	—	4	2	no	—
71	#106×C₄₇	—	2	2	no	—
72	#106×C₄₇	—	2	2	no	—
73	#103×C₄₇	—	2	4	no	—
74	#103×C₄₇	—	2	4	no	—
75	#103×C₄₇	—	2	4	no	—
76	C₂²⋊C₈×C₄₇	—	2	2	no	—
77	#97×C₄₇	—	2	2	no	—
78	C₄×C₈×C₄₇	—	2	2	no	—
79	#95×C₄₇	—	2	2	no	—
80	#95×C₄₇	—	2	2	no	—
81	#95×C₄₇	—	2	2	no	—
82	#95×C₄₇	—	2	2	no	—
83	#95×C₄₇	—	2	2	no	—
84	#95×C₄₇	—	2	2	no	—
85	#95×C₄₇	D₄	1	2	yes	—
86	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
87	C₂×Q₈×C₄₇	—	2	2	no	—
88	C₂×Q₈×C₄₇	—	2	2	no	—
89	C₂×Q₈×C₄₇	—	2	2	no	—
90	C₂×Q₈×C₄₇	—	2	2	no	—
91	C₂×Q₈×C₄₇	—	2	2	no	—
92	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	1	no	—
95	C₂²×C₄×C₄₇	—	2	1	no	—
96	C₂²×C₄×C₄₇	—	2	1	no	—
97	C₂²×C₄×C₄₇	—	2	1	no	—
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
107	Q₁₆×C₄₇	—	2	8	no	—
108	M₁₆×C₄₇	—	4	4	no	—
109	C₂×C₈×C₄₇	—	2	1	no	—
110	C₂×C₈×C₄₇	—	2	1	no	—
111	C₂×C₈×C₄₇	—	2	1	no	—
112	C₂×C₈×C₄₇	—	2	1	no	—
113	C₂×C₈×C₄₇	—	2	1	no	—
114	C₂×C₈×C₄₇	—	2	1	no	—
115	C₂×C₈×C₄₇	—	2	1	no	—
116	C₂×C₈×C₄₇	—	2	1	no	—
117	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₄₇	#41	1	2	yes	—
119	C₂×C₈×C₄₇	#41	1	2	yes	—
120	C₂×C₈×C₄₇	#41	1	2	yes	—
121	C₄⋊C₄×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	—	2	2	no	—
123	C₄⋊C₄×C₄₇	—	2	2	no	—
124	C₄⋊C₄×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	—	2	2	no	—
126	C₄⋊C₄×C₄₇	—	2	2	no	—
127	C₄⋊C₄×C₄₇	—	4	4	no	—
128	C₄⋊C₄×C₄₇	—	4	4	no	—
129	C₄⋊C₄×C₄₇	—	4	4	no	—
130	C₂²⋊C₄×C₄₇	—	4	2	no	—
131	C₂²⋊C₄×C₄₇	—	4	4	no	—
132	C₂²⋊C₄×C₄₇	—	4	4	no	—
133	C₄²×C₄₇	—	2	1	no	—
134	C₄²×C₄₇	—	2	1	no	—
135	C₄²×C₄₇	—	2	1	no	—
136	C₄²×C₄₇	—	2	1	no	—
137	C₄²×C₄₇	—	4	4	no	—
138	C₂³×C₄₇	—	2	1	no	—
139	C₂³×C₄₇	—	2	1	no	—
140	C₂³×C₄₇	—	2	1	no	—
141	C₂³×C₄₇	—	2	2	no	—
142	C₂³×C₄₇	—	2	2	no	—
143	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₄₇	—	2	4	no	—
145	Q₈×C₄₇	—	2	4	no	—
146	Q₈×C₄₇	—	4	2	no	—
147	Q₈×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	2	1	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	4	no	—
151	C₂×C₄×C₄₇	—	2	1	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	4	1	no	—
161	C₂×C₄×C₄₇	—	4	1	no	—
162	C₂×C₄×C₄₇	—	4	1	no	—
163	C₂×C₄×C₄₇	—	4	1	no	—
164	C₂×C₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	4	2	no	—
168	C₂×C₄×C₄₇	—	4	2	no	—
169	C₂×C₄×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	—	4	2	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
175	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
176	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
177	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
178	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
179	C₈×C₄₇	—	2	2	no	—
180	C₈×C₄₇	—	4	1	no	—
181	C₈×C₄₇	—	4	1	no	—
182	C₈×C₄₇	#123	1	4	yes	—
183	#25049	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
184	C₂²×C₄₇	—	4	2	no	—
185	C₂²×C₄₇	—	4	1	no	—
186	C₂²×C₄₇	—	4	1	no	—
187	C₂²×C₄₇	—	4	1	no	—
188	C₂²×C₄₇	—	4	2	no	—
189	C₂²×C₄₇	#532	1	1	yes	characteristic
190	C₂²×C₄₇	D₄²	1	1	yes	characteristic
191	C₂²×C₄₇	#547	1	1	yes	characteristic
192	C₂²×C₄₇	#575	1	2	yes	—
193	C₂²×C₄₇	#578	1	2	yes	—
194	C₄×C₄₇	—	4	2	no	—
195	C₄×C₄₇	—	4	1	no	—
196	C₄×C₄₇	—	4	4	no	—
197	C₄×C₄₇	—	4	2	no	—
198	C₄×C₄₇	—	8	2	no	—
199	C₄×C₄₇	—	8	2	no	—
200	C₄×C₄₇	—	8	2	no	—
201	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
202	C₄×C₄₇	#542	1	1	yes	characteristic
203	C₄×C₄₇	#547	1	1	yes	characteristic
204	C₄×C₄₇	#553	1	1	yes	characteristic
205	C₂×#470	C₂×C₄₇	1	1	yes	characteristic
206	C₂×#441	C₂×C₄₇	1	1	yes	characteristic, complemented
207	#2421	C₂×C₄₇	1	2	yes	—
208	#2074	C₂×C₄₇	1	2	yes	complemented
209	#2036	C₂×C₄₇	1	2	yes	—
210	#1969	C₂×C₄₇	1	1	yes	characteristic, complemented
211	#1943	C₂×C₄₇	1	1	yes	characteristic, complemented
212	#1863	C₂×C₄₇	1	2	yes	complemented
213	#1846	C₂×C₄₇	1	1	yes	characteristic, complemented
214	#1809	C₂×C₄₇	1	1	yes	characteristic
215	#1753	C₂×C₄₇	1	1	yes	characteristic
216	C₂×C₄₇	—	8	1	no	—
217	C₂×C₄₇	#2422	1	1	yes	characteristic
218	C₂×C₄₇	#3177	1	1	yes	characteristic
219	C₂×C₄₇	#3183	1	1	yes	characteristic
220	C₂×C₄₇	#3277	1	2	yes	—
221	C₂×C₄₇	#3349	1	2	yes	—
222	C₂²×Q₁₆	C₂²×C₄₇	1	1	yes	characteristic
223	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
224	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
225	C₂×C₄×Q₈	C₂²×C₄₇	1	2	yes	—
226	#470	—	2	4	no	—
227	#441	—	2	4	no	—
228	C₂×#107	C₂²×C₄₇	1	1	yes	characteristic
229	C₂×#107	C₂²×C₄₇	1	2	yes	—
230	C₂×#106	C₂²×C₄₇	1	1	yes	characteristic
231	C₂×#106	C₂²×C₄₇	1	1	yes	characteristic
232	C₂×#103	C₂²×C₄₇	1	2	yes	—
233	C₂×#103	C₂²×C₄₇	1	2	yes	—
234	C₂×#103	C₂²×C₄₇	1	2	yes	—
235	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
236	C₂×#97	C₂²×C₄₇	1	1	yes	characteristic
237	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
238	#400	—	2	2	no	—
239	#397	—	2	2	no	—
240	#391	C₂²×C₄₇	1	2	yes	—
241	#389	C₂²×C₄₇	1	2	yes	—
242	#388	—	2	2	no	—
243	#387	—	2	2	no	—
244	#382	C₂²×C₄₇	1	2	yes	—
245	#380	C₂²×C₄₇	1	2	yes	—
246	C₄×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
247	#340	C₂²×C₄₇	1	2	yes	—
248	#340	C₂²×C₄₇	1	2	yes	—
249	#336	C₂²×C₄₇	1	1	yes	characteristic
250	#336	C₂²×C₄₇	1	1	yes	characteristic
251	C₄₇	#25049	1	1	yes	characteristic, direct product factor, Sylow
252	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
253	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
254	C₂×Q₁₆	—	2	2	no	—
255	C₂×Q₁₆	—	2	2	no	—
256	C₂×Q₁₆	D₄×C₄₇	1	4	yes	—
257	C₂×M₁₆	—	2	2	no	—
258	C₂×M₁₆	—	2	2	no	—
259	C₂×M₁₆	—	2	2	no	—
260	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
261	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
262	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
263	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
264	C₂²⋊Q₈	—	2	4	no	—
265	C₂²⋊Q₈	—	4	2	no	—
266	C₄×Q₈	—	2	4	no	—
267	C₄×Q₈	—	4	2	no	—
268	C₂×C₄⋊C₄	—	2	2	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
272	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
273	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
274	C₂×C₂²⋊C₄	—	2	2	no	—
275	C₂×C₂²⋊C₄	—	2	2	no	—
276	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
277	C₂×C₄²	—	2	2	no	—
278	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
279	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
280	#107	—	2	2	no	—
281	#107	—	4	2	no	—
282	#106	—	2	2	no	—
283	#106	—	2	2	no	—
284	#103	—	2	4	no	—
285	#103	—	2	4	no	—
286	#103	—	2	4	no	—
287	C₂²⋊C₈	—	2	2	no	—
288	#97	—	2	2	no	—
289	C₄×C₈	—	2	2	no	—
290	#95	—	2	2	no	—
291	#95	—	2	2	no	—
292	#95	—	2	2	no	—
293	#95	—	2	2	no	—
294	#95	—	2	2	no	—
295	#95	—	2	2	no	—
296	#95	D₄×C₄₇	1	2	yes	—
297	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
298	C₂×Q₈	—	2	2	no	—
299	C₂×Q₈	—	2	2	no	—
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	2	no	—
303	C₂×Q₈	C₂×D₄×C₄₇	1	4	yes	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	1	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	2	1	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	2	no	—
313	C₂²×C₄	—	2	2	no	—
314	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
315	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
316	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
317	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
318	Q₁₆	—	2	8	no	—
319	M₁₆	—	4	4	no	—
320	C₂×C₈	—	2	1	no	—
321	C₂×C₈	—	2	1	no	—
322	C₂×C₈	—	2	1	no	—
323	C₂×C₈	—	2	1	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	2	1	no	—
326	C₂×C₈	—	2	1	no	—
327	C₂×C₈	—	2	1	no	—
328	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
329	C₂×C₈	#41×C₄₇	1	2	yes	—
330	C₂×C₈	#41×C₄₇	1	2	yes	—
331	C₂×C₈	#41×C₄₇	1	2	yes	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	2	no	—
336	C₄⋊C₄	—	2	2	no	—
337	C₄⋊C₄	—	2	2	no	—
338	C₄⋊C₄	—	4	4	no	—
339	C₄⋊C₄	—	4	4	no	—
340	C₄⋊C₄	—	4	4	no	—
341	C₂²⋊C₄	—	4	2	no	—
342	C₂²⋊C₄	—	4	4	no	—
343	C₂²⋊C₄	—	4	4	no	—
344	C₄²	—	2	1	no	—
345	C₄²	—	2	1	no	—
346	C₄²	—	2	1	no	—
347	C₄²	—	2	1	no	—
348	C₄²	—	4	4	no	—
349	C₂³	—	2	1	no	—
350	C₂³	—	2	1	no	—
351	C₂³	—	2	1	no	—
352	C₂³	—	2	2	no	—
353	C₂³	—	2	2	no	—
354	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
355	Q₈	—	2	4	no	—
356	Q₈	—	2	4	no	—
357	Q₈	—	4	2	no	—
358	Q₈	—	4	2	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	2	2	no	—
361	C₂×C₄	—	2	4	no	—
362	C₂×C₄	—	2	1	no	—
363	C₂×C₄	—	2	2	no	—
364	C₂×C₄	—	2	1	no	—
365	C₂×C₄	—	2	2	no	—
366	C₂×C₄	—	2	2	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	4	2	no	—
370	C₂×C₄	—	4	2	no	—
371	C₂×C₄	—	4	1	no	—
372	C₂×C₄	—	4	1	no	—
373	C₂×C₄	—	4	1	no	—
374	C₂×C₄	—	4	1	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
385	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
386	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
387	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
388	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
389	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
390	C₈	—	2	2	no	—
391	C₈	—	4	1	no	—
392	C₈	—	4	1	no	—
393	C₈	#123×C₄₇	1	4	yes	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	1	no	—
396	C₂²	—	4	1	no	—
397	C₂²	—	4	1	no	—
398	C₂²	—	4	2	no	—
399	C₂²	C₄₇×#532	1	1	yes	characteristic
400	C₂²	D₄²×C₄₇	1	1	yes	characteristic
401	C₂²	C₄₇×#547	1	1	yes	characteristic
402	C₂²	C₄₇×#575	1	2	yes	—
403	C₂²	C₄₇×#578	1	2	yes	—
404	C₄	—	4	2	no	—
405	C₄	—	4	1	no	—
406	C₄	—	4	4	no	—
407	C₄	—	4	2	no	—
408	C₄	—	8	2	no	—
409	C₄	—	8	2	no	—
410	C₄	—	8	2	no	—
411	C₄	C₂×#123×C₄₇	1	1	yes	characteristic
412	C₄	C₄₇×#542	1	1	yes	characteristic
413	C₄	C₄₇×#547	1	1	yes	characteristic
414	C₄	C₄₇×#553	1	1	yes	characteristic
415	C₂	—	8	1	no	—
416	C₂	C₄₇×#2422	1	1	yes	characteristic
417	C₂	C₄₇×#3177	1	1	yes	characteristic
418	C₂	C₄₇×#3183	1	1	yes	characteristic
419	C₂	C₄₇×#3277	1	2	yes	—
420	C₂	C₄₇×#3349	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂⁴×C₄₇	C₂×D₄
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×#441	C₂	semidirect
4. C₄₇×#2074	C₂	semidirect
6. C₄₇×#1969	C₂	semidirect
7. C₄₇×#1943	C₂	semidirect
8. C₄₇×#1863	C₂	semidirect
9. C₄₇×#1846	C₂	semidirect
183. #25049	C₄₇	direct (N × H)
206. C₂×#441	C₂×C₄₇	semidirect
208. #2074	C₂×C₄₇	semidirect
210. #1969	C₂×C₄₇	semidirect
211. #1943	C₂×C₄₇	semidirect
212. #1863	C₂×C₄₇	semidirect
213. #1846	C₂×C₄₇	semidirect
251. C₄₇	#25049	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×#470	2
C₂×C₄₇×#441	2
C₄₇×#2421	2
C₄₇×#2074	2
C₄₇×#2036	2
C₄₇×#1969	2
C₄₇×#1943	2
C₄₇×#1863	2
C₄₇×#1846	2
C₄₇×#1809	2
C₄₇×#1753	2
#25049	47

Subgroups — C47×#25049 #26064747

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#25049 #26064747