Subgroups — C₄₇×#16240 #26055938

Order 12032.

1078 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#1445	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#1445	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#1444	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1442	C₂	1	2	yes	maximal
5	C₄₇×#1442	C₂	1	2	yes	maximal
6	C₄₇×#1441	C₂	1	2	yes	maximal
7	C₄₇×#1436	C₂	1	2	yes	maximal
8	C₄₇×#1436	C₂	1	2	yes	maximal
9	C₄₇×C₄⋊#95	C₂	1	2	yes	maximal
10	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
11	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
12	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
16	C₂×#95×C₄₇	C₂²	1	2	yes	—
17	C₂×#95×C₄₇	C₂²	1	2	yes	—
18	C₂×#95×C₄₇	C₂²	1	2	yes	—
19	C₂×#95×C₄₇	C₂²	1	2	yes	—
20	C₂×#95×C₄₇	C₂²	1	2	yes	—
21	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×#95×C₄₇	C₂²	1	2	yes	—
23	C₂×#95×C₄₇	C₂²	1	2	yes	—
24	C₂×#95×C₄₇	C₂²	1	2	yes	—
25	C₂×#95×C₄₇	C₂²	1	2	yes	—
26	C₂×#95×C₄₇	C₂²	1	2	yes	—
27	C₂×#95×C₄₇	C₂²	1	2	yes	—
28	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
31	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
32	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
33	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
34	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
35	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
38	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
39	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
40	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
41	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
42	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
43	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
44	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
45	C₂×C₄⋊C₄×C₄₇	—	4	1	no	—
46	C₂×C₄⋊C₄×C₄₇	—	4	1	no	—
47	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
48	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
49	C₂×C₄⋊C₄×C₄₇	—	4	1	no	—
50	C₂×C₄⋊C₄×C₄₇	—	4	1	no	—
51	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
52	C₂×C₄⋊C₄×C₄₇	—	4	1	no	—
53	C₂×C₄⋊C₄×C₄₇	Q₈	1	4	yes	—
54	C₂×C₄²×C₄₇	—	2	4	no	—
55	C₂×C₄²×C₄₇	—	4	2	no	—
56	C₂×C₄²×C₄₇	—	4	2	no	—
57	#95×C₄₇	—	2	4	no	—
58	#95×C₄₇	—	2	4	no	—
59	#95×C₄₇	—	2	4	no	—
60	#95×C₄₇	—	2	4	no	—
61	#95×C₄₇	—	2	4	no	—
62	#95×C₄₇	—	4	2	no	—
63	#95×C₄₇	—	4	2	no	—
64	#95×C₄₇	—	4	1	no	—
65	#95×C₄₇	—	4	1	no	—
66	#95×C₄₇	—	4	2	no	—
67	#95×C₄₇	—	4	2	no	—
68	#95×C₄₇	—	4	1	no	—
69	#95×C₄₇	—	4	2	no	—
70	#95×C₄₇	—	4	2	no	—
71	#95×C₄₇	Q₈	1	4	yes	—
72	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
73	C₂²×C₄×C₄₇	—	2	2	no	—
74	C₂²×C₄×C₄₇	—	2	2	no	—
75	C₂²×C₄×C₄₇	—	2	2	no	—
76	C₂²×C₄×C₄₇	—	2	2	no	—
77	C₂²×C₄×C₄₇	—	2	2	no	—
78	C₂²×C₄×C₄₇	—	2	2	no	—
79	C₂²×C₄×C₄₇	—	2	2	no	—
80	C₂²×C₄×C₄₇	—	2	2	no	—
81	C₂²×C₄×C₄₇	—	2	2	no	—
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	—	2	2	no	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	2	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	1	no	—
90	C₂²×C₄×C₄₇	—	2	1	no	—
91	C₂²×C₄×C₄₇	—	2	1	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	1	no	—
94	C₂²×C₄×C₄₇	—	2	1	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	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	2	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	—	2	2	no	—
105	C₂²×C₄×C₄₇	—	2	2	no	—
106	C₂²×C₄×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	—	2	2	no	—
112	C₂²×C₄×C₄₇	—	2	2	no	—
113	C₂²×C₄×C₄₇	—	2	2	no	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	—	2	2	no	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	2	2	no	—
121	C₂²×C₄×C₄₇	—	2	2	no	—
122	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
123	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
124	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
125	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
126	C₂²×C₄×C₄₇	#41	1	2	yes	—
127	C₂²×C₄×C₄₇	#41	1	4	yes	—
128	C₂²×C₄×C₄₇	#41	1	4	yes	—
129	C₂²×C₄×C₄₇	#41	1	4	yes	—
130	C₄⋊C₄×C₄₇	—	4	4	no	—
131	C₄⋊C₄×C₄₇	—	4	8	no	—
132	C₄⋊C₄×C₄₇	—	4	8	no	—
133	C₄⋊C₄×C₄₇	—	4	4	no	—
134	C₄⋊C₄×C₄₇	—	4	4	no	—
135	C₄²×C₄₇	—	4	8	no	—
136	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
137	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
138	C₂³×C₄₇	C₂×#41	1	2	yes	—
139	C₂³×C₄₇	C₂×#41	1	2	yes	—
140	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
141	C₂³×C₄₇	C₂×#41	1	2	yes	—
142	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
143	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
144	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
145	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
146	C₂³×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
147	C₂×C₄×C₄₇	—	2	4	no	—
148	C₂×C₄×C₄₇	—	2	4	no	—
149	C₂×C₄×C₄₇	—	2	4	no	—
150	C₂×C₄×C₄₇	—	2	4	no	—
151	C₂×C₄×C₄₇	—	2	4	no	—
152	C₂×C₄×C₄₇	—	2	4	no	—
153	C₂×C₄×C₄₇	—	2	4	no	—
154	C₂×C₄×C₄₇	—	2	2	no	—
155	C₂×C₄×C₄₇	—	2	4	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	4	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	2	4	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	—	2	4	no	—
163	C₂×C₄×C₄₇	—	2	4	no	—
164	C₂×C₄×C₄₇	—	2	4	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	—	4	2	no	—
174	C₂×C₄×C₄₇	—	4	1	no	—
175	C₂×C₄×C₄₇	—	4	1	no	—
176	C₂×C₄×C₄₇	—	4	1	no	—
177	C₂×C₄×C₄₇	—	4	1	no	—
178	C₂×C₄×C₄₇	—	4	1	no	—
179	C₂×C₄×C₄₇	—	4	1	no	—
180	C₂×C₄×C₄₇	—	4	2	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	4	2	no	—
183	C₂×C₄×C₄₇	—	4	2	no	—
184	C₂×C₄×C₄₇	—	4	2	no	—
185	C₂×C₄×C₄₇	—	4	2	no	—
186	C₂×C₄×C₄₇	—	4	2	no	—
187	C₂×C₄×C₄₇	—	4	2	no	—
188	C₂×C₄×C₄₇	—	4	2	no	—
189	C₂×C₄×C₄₇	—	4	2	no	—
190	C₂×C₄×C₄₇	—	4	2	no	—
191	C₂×C₄×C₄₇	—	4	2	no	—
192	C₂×C₄×C₄₇	—	4	2	no	—
193	C₂×C₄×C₄₇	—	4	2	no	—
194	C₂×C₄×C₄₇	—	4	2	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	—	4	2	no	—
203	C₂×C₄×C₄₇	#125	1	8	yes	—
204	#16240	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂²×C₄₇	C₂×#125	1	2	yes	—
206	C₂²×C₄₇	#529	1	2	yes	—
207	C₂²×C₄₇	#533	1	2	yes	—
208	C₂²×C₄₇	#538	1	1	yes	characteristic
209	C₂²×C₄₇	#538	1	2	yes	—
210	C₂²×C₄₇	#539	1	2	yes	—
211	C₂²×C₄₇	#540	1	2	yes	—
212	C₂²×C₄₇	#543	1	1	yes	characteristic
213	C₂²×C₄₇	#544	1	1	yes	characteristic
214	C₂²×C₄₇	#551	1	2	yes	—
215	C₂²×C₄₇	#551	1	2	yes	—
216	C₂²×C₄₇	#553	1	2	yes	—
217	C₂²×C₄₇	#554	1	2	yes	—
218	C₂²×C₄₇	#554	1	1	yes	characteristic
219	C₂²×C₄₇	#554	1	2	yes	—
220	C₂²×C₄₇	#555	1	1	yes	characteristic
221	C₂²×C₄₇	#556	1	2	yes	—
222	C₂²×C₄₇	#557	1	1	yes	characteristic
223	C₂²×C₄₇	Q₈²	1	1	yes	characteristic
224	C₂²×C₄₇	#559	1	1	yes	characteristic
225	C₂²×C₄₇	#559	1	1	yes	characteristic
226	C₂²×C₄₇	#560	1	1	yes	characteristic
227	C₂²×C₄₇	#562	1	1	yes	characteristic
228	C₄×C₄₇	—	2	8	no	—
229	C₄×C₄₇	—	4	2	no	—
230	C₄×C₄₇	—	4	2	no	—
231	C₄×C₄₇	—	4	4	no	—
232	C₄×C₄₇	—	4	4	no	—
233	C₄×C₄₇	—	4	2	no	—
234	C₄×C₄₇	—	8	2	no	—
235	C₄×C₄₇	—	8	2	no	—
236	C₄×C₄₇	—	8	2	no	—
237	#1445	C₂×C₄₇	1	1	yes	characteristic
238	#1445	C₂×C₄₇	1	1	yes	characteristic
239	#1444	C₂×C₄₇	1	1	yes	characteristic
240	#1442	C₂×C₄₇	1	2	yes	—
241	#1442	C₂×C₄₇	1	2	yes	—
242	#1441	C₂×C₄₇	1	2	yes	—
243	#1436	C₂×C₄₇	1	2	yes	—
244	#1436	C₂×C₄₇	1	2	yes	—
245	C₄⋊#95	C₂×C₄₇	1	2	yes	—
246	C₂×C₄₇	#2505	1	2	yes	—
247	C₂×C₄₇	#2507	1	2	yes	—
248	C₂×C₄₇	#2571	1	1	yes	characteristic
249	C₂×C₄₇	#2588	1	2	yes	—
250	C₂×C₄₇	#2593	1	1	yes	characteristic
251	C₂×C₄₇	#2607	1	1	yes	characteristic
252	C₂×C₄₇	#2752	1	1	yes	characteristic
253	C₂×C₄₇	#2784	1	1	yes	characteristic
254	C₂×C₄₇	#2786	1	2	yes	—
255	C₂×C₄₇	#2806	1	1	yes	characteristic
256	C₂×C₄₇	#2807	1	1	yes	characteristic
257	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
258	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
259	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
260	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
261	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
262	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
263	C₂×#95	C₂²×C₄₇	1	2	yes	—
264	C₂×#95	C₂²×C₄₇	1	2	yes	—
265	C₂×#95	C₂²×C₄₇	1	2	yes	—
266	C₂×#95	C₂²×C₄₇	1	2	yes	—
267	C₂×#95	C₂²×C₄₇	1	2	yes	—
268	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
269	C₂×#95	C₂²×C₄₇	1	2	yes	—
270	C₂×#95	C₂²×C₄₇	1	2	yes	—
271	C₂×#95	C₂²×C₄₇	1	2	yes	—
272	C₂×#95	C₂²×C₄₇	1	2	yes	—
273	C₂×#95	C₂²×C₄₇	1	2	yes	—
274	C₂×#95	C₂²×C₄₇	1	2	yes	—
275	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
276	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
277	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
278	C₄₇	#16240	1	1	yes	characteristic, direct product factor, Sylow
279	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
280	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
281	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
282	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
283	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
284	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
285	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
287	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
288	C₂×C₄⋊C₄	—	2	4	no	—
289	C₂×C₄⋊C₄	—	2	4	no	—
290	C₂×C₄⋊C₄	—	2	4	no	—
291	C₂×C₄⋊C₄	—	2	4	no	—
292	C₂×C₄⋊C₄	—	2	2	no	—
293	C₂×C₄⋊C₄	—	4	1	no	—
294	C₂×C₄⋊C₄	—	4	1	no	—
295	C₂×C₄⋊C₄	—	4	2	no	—
296	C₂×C₄⋊C₄	—	4	2	no	—
297	C₂×C₄⋊C₄	—	4	1	no	—
298	C₂×C₄⋊C₄	—	4	1	no	—
299	C₂×C₄⋊C₄	—	4	1	no	—
300	C₂×C₄⋊C₄	—	4	2	no	—
301	C₂×C₄⋊C₄	Q₈×C₄₇	1	4	yes	—
302	C₂×C₄²	—	2	4	no	—
303	C₂×C₄²	—	4	2	no	—
304	C₂×C₄²	—	4	2	no	—
305	#95	—	2	4	no	—
306	#95	—	2	4	no	—
307	#95	—	2	4	no	—
308	#95	—	2	4	no	—
309	#95	—	2	4	no	—
310	#95	—	4	1	no	—
311	#95	—	4	2	no	—
312	#95	—	4	2	no	—
313	#95	—	4	2	no	—
314	#95	—	4	2	no	—
315	#95	—	4	1	no	—
316	#95	—	4	2	no	—
317	#95	—	4	1	no	—
318	#95	—	4	2	no	—
319	#95	Q₈×C₄₇	1	4	yes	—
320	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	2	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	2	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	1	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
371	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
372	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
373	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
374	C₂²×C₄	#41×C₄₇	1	4	yes	—
375	C₂²×C₄	#41×C₄₇	1	2	yes	—
376	C₂²×C₄	#41×C₄₇	1	4	yes	—
377	C₂²×C₄	#41×C₄₇	1	4	yes	—
378	C₄⋊C₄	—	4	4	no	—
379	C₄⋊C₄	—	4	8	no	—
380	C₄⋊C₄	—	4	8	no	—
381	C₄⋊C₄	—	4	4	no	—
382	C₄⋊C₄	—	4	4	no	—
383	C₄²	—	4	8	no	—
384	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
385	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
386	C₂³	C₂×#41×C₄₇	1	2	yes	—
387	C₂³	C₂×#41×C₄₇	1	2	yes	—
388	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
389	C₂³	C₂×#41×C₄₇	1	2	yes	—
390	C₂³	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
391	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
392	C₂³	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
393	C₂³	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
394	C₂³	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	2	4	no	—
398	C₂×C₄	—	2	4	no	—
399	C₂×C₄	—	2	4	no	—
400	C₂×C₄	—	2	4	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	2	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	—	4	1	no	—
423	C₂×C₄	—	4	1	no	—
424	C₂×C₄	—	4	1	no	—
425	C₂×C₄	—	4	1	no	—
426	C₂×C₄	—	4	1	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	1	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	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	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	#125×C₄₇	1	8	yes	—
452	C₂²	C₂×#125×C₄₇	1	2	yes	—
453	C₂²	C₄₇×#529	1	2	yes	—
454	C₂²	C₄₇×#533	1	2	yes	—
455	C₂²	C₄₇×#538	1	2	yes	—
456	C₂²	C₄₇×#538	1	1	yes	characteristic
457	C₂²	C₄₇×#539	1	2	yes	—
458	C₂²	C₄₇×#540	1	2	yes	—
459	C₂²	C₄₇×#543	1	1	yes	characteristic
460	C₂²	C₄₇×#544	1	1	yes	characteristic
461	C₂²	C₄₇×#551	1	2	yes	—
462	C₂²	C₄₇×#551	1	2	yes	—
463	C₂²	C₄₇×#553	1	2	yes	—
464	C₂²	C₄₇×#554	1	2	yes	—
465	C₂²	C₄₇×#554	1	1	yes	characteristic
466	C₂²	C₄₇×#554	1	2	yes	—
467	C₂²	C₄₇×#555	1	1	yes	characteristic
468	C₂²	C₄₇×#556	1	2	yes	—
469	C₂²	C₄₇×#557	1	1	yes	characteristic
470	C₂²	Q₈²×C₄₇	1	1	yes	characteristic
471	C₂²	C₄₇×#559	1	1	yes	characteristic
472	C₂²	C₄₇×#559	1	1	yes	characteristic
473	C₂²	C₄₇×#560	1	1	yes	characteristic
474	C₂²	C₄₇×#562	1	1	yes	characteristic
475	C₄	—	2	8	no	—
476	C₄	—	4	4	no	—
477	C₄	—	4	4	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	4	2	no	—
481	C₄	—	8	2	no	—
482	C₄	—	8	2	no	—
483	C₄	—	8	2	no	—
484	C₂	C₄₇×#2505	1	2	yes	—
485	C₂	C₄₇×#2507	1	2	yes	—
486	C₂	C₄₇×#2571	1	1	yes	characteristic
487	C₂	C₄₇×#2588	1	2	yes	—
488	C₂	C₄₇×#2593	1	1	yes	characteristic
489	C₂	C₄₇×#2607	1	1	yes	characteristic
490	C₂	C₄₇×#2752	1	1	yes	characteristic
491	C₂	C₄₇×#2784	1	1	yes	characteristic
492	C₂	C₄₇×#2786	1	2	yes	—
493	C₂	C₄₇×#2806	1	1	yes	characteristic
494	C₂	C₄₇×#2807	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂⁴×C₄₇	C₂⁴
commutator, Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
LCS	G ▷ C₂⁴ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
204. #16240	C₄₇	direct (N × H)
278. C₄₇	#16240	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×#1445	2
C₄₇×#1444	2
C₄₇×#1442	2
C₄₇×#1441	2
C₄₇×#1436	2
C₄₇×C₄⋊#95	2
#16240	47

Subgroups — C47×#16240 #26055938

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#16240 #26055938