Subgroups — C₄₇×#13947 #26053645

Order 12032.

1486 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#1443	C₂	1	2	yes	maximal, complemented
3	C₄₇×#1440	C₂	1	2	yes	maximal
4	C₄₇×#1437	C₂	1	2	yes	maximal
5	C₄₇×#1434	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1434	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1434	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1434	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic
10	C₄₇×C₂²⋊#95	C₂	1	1	yes	maximal, characteristic
11	C₄×#95×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
14	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
15	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
18	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
20	C₄×C₂²⋊C₄×C₄₇	C₄	1	8	yes	complemented
21	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×#95×C₄₇	C₂²	1	2	yes	—
24	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×#95×C₄₇	C₂²	1	2	yes	—
27	C₂×#95×C₄₇	C₂²	1	2	yes	—
28	C₂×#95×C₄₇	C₂²	1	2	yes	—
29	C₂×#95×C₄₇	C₂²	1	2	yes	—
30	C₂×#95×C₄₇	C₂²	1	2	yes	—
31	C₂×#95×C₄₇	C₂²	1	2	yes	—
32	C₂×#95×C₄₇	C₂²	1	2	yes	—
33	C₂×#95×C₄₇	C₂²	1	2	yes	—
34	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
36	C₂⁵×C₄₇	C₂³	1	1	yes	characteristic
37	C₂³×C₄×C₄₇	—	2	2	no	—
38	C₂³×C₄×C₄₇	—	2	2	no	—
39	C₂³×C₄×C₄₇	—	4	2	no	—
40	C₂³×C₄×C₄₇	—	4	2	no	—
41	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
42	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
43	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
44	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
49	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
50	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
52	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
53	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
54	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
55	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
57	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
58	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
59	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
60	C₂×C₂²⋊C₄×C₄₇	—	4	2	no	—
61	C₂×C₂²⋊C₄×C₄₇	—	4	2	no	—
62	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
63	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
64	C₂×C₄²×C₄₇	—	2	4	no	—
65	C₂×C₄²×C₄₇	—	2	4	no	—
66	C₂×C₄²×C₄₇	—	4	2	no	—
67	C₂×C₄²×C₄₇	—	4	2	no	—
68	C₂×C₄²×C₄₇	—	4	2	no	—
69	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
70	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
71	#95×C₄₇	—	2	4	no	—
72	#95×C₄₇	—	2	2	no	—
73	#95×C₄₇	—	2	2	no	—
74	#95×C₄₇	—	2	4	no	—
75	#95×C₄₇	—	2	4	no	—
76	#95×C₄₇	—	2	4	no	—
77	#95×C₄₇	—	2	2	no	—
78	#95×C₄₇	—	2	2	no	—
79	#95×C₄₇	—	4	2	no	—
80	#95×C₄₇	—	4	2	no	—
81	#95×C₄₇	—	4	2	no	—
82	#95×C₄₇	—	4	2	no	—
83	#95×C₄₇	—	4	2	no	—
84	#95×C₄₇	C₂×C₄	1	4	yes	—
85	#95×C₄₇	C₂×C₄	1	4	yes	—
86	C₂⁴×C₄₇	—	2	1	no	—
87	C₂⁴×C₄₇	—	2	1	no	—
88	C₂⁴×C₄₇	—	2	2	no	—
89	C₂⁴×C₄₇	—	2	2	no	—
90	C₂⁴×C₄₇	—	2	1	no	—
91	C₂⁴×C₄₇	—	2	1	no	—
92	C₂⁴×C₄₇	—	2	2	no	—
93	C₂⁴×C₄₇	—	2	2	no	—
94	C₂⁴×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂⁴×C₄₇	#41	1	2	yes	—
96	C₂⁴×C₄₇	#41	1	2	yes	—
97	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	2	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	—	2	2	no	—
104	C₂²×C₄×C₄₇	—	2	2	no	—
105	C₂²×C₄×C₄₇	—	2	1	no	—
106	C₂²×C₄×C₄₇	—	2	1	no	—
107	C₂²×C₄×C₄₇	—	2	1	no	—
108	C₂²×C₄×C₄₇	—	2	1	no	—
109	C₂²×C₄×C₄₇	—	2	1	no	—
110	C₂²×C₄×C₄₇	—	2	1	no	—
111	C₂²×C₄×C₄₇	—	2	2	no	—
112	C₂²×C₄×C₄₇	—	2	2	no	—
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	2	1	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	—	2	2	no	—
123	C₂²×C₄×C₄₇	—	2	2	no	—
124	C₂²×C₄×C₄₇	—	2	2	no	—
125	C₂²×C₄×C₄₇	—	2	2	no	—
126	C₂²×C₄×C₄₇	—	2	2	no	—
127	C₂²×C₄×C₄₇	—	2	2	no	—
128	C₂²×C₄×C₄₇	—	2	2	no	—
129	C₂²×C₄×C₄₇	—	2	2	no	—
130	C₂²×C₄×C₄₇	—	2	8	no	—
131	C₂²×C₄×C₄₇	—	2	2	no	—
132	C₂²×C₄×C₄₇	—	2	2	no	—
133	C₂²×C₄×C₄₇	—	2	2	no	—
134	C₂²×C₄×C₄₇	—	2	2	no	—
135	C₂²×C₄×C₄₇	—	2	2	no	—
136	C₂²×C₄×C₄₇	—	2	2	no	—
137	C₂²×C₄×C₄₇	—	2	2	no	—
138	C₂²×C₄×C₄₇	—	2	2	no	—
139	C₂²×C₄×C₄₇	—	2	2	no	—
140	C₂²×C₄×C₄₇	—	2	2	no	—
141	C₂²×C₄×C₄₇	—	2	2	no	—
142	C₂²×C₄×C₄₇	—	2	2	no	—
143	C₂²×C₄×C₄₇	—	2	2	no	—
144	C₂²×C₄×C₄₇	—	2	2	no	—
145	C₂²×C₄×C₄₇	—	4	4	no	—
146	C₂²×C₄×C₄₇	—	4	4	no	—
147	C₂²×C₄×C₄₇	—	4	8	no	—
148	C₂²×C₄×C₄₇	—	4	8	no	—
149	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
150	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
151	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
152	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
153	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
154	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
155	C₂²×C₄×C₄₇	#41	1	4	yes	—
156	C₂²×C₄×C₄₇	#41	1	4	yes	—
157	C₂²×C₄×C₄₇	#41	1	2	yes	—
158	C₂²×C₄×C₄₇	#41	1	2	yes	—
159	C₂²×C₄×C₄₇	#41	1	2	yes	—
160	C₂²×C₄×C₄₇	#41	1	2	yes	—
161	C₂²⋊C₄×C₄₇	—	2	8	no	—
162	C₂²⋊C₄×C₄₇	—	2	8	no	—
163	C₂²⋊C₄×C₄₇	—	4	8	no	—
164	C₂²⋊C₄×C₄₇	—	4	8	no	—
165	C₄²×C₄₇	—	4	4	no	—
166	C₄²×C₄₇	—	4	4	no	—
167	C₄²×C₄₇	—	4	8	no	—
168	C₂³×C₄₇	—	2	2	no	—
169	C₂³×C₄₇	—	2	2	no	—
170	C₂³×C₄₇	—	2	2	no	—
171	C₂³×C₄₇	—	2	2	no	—
172	C₂³×C₄₇	—	2	2	no	—
173	C₂³×C₄₇	—	2	2	no	—
174	C₂³×C₄₇	—	2	2	no	—
175	C₂³×C₄₇	—	2	2	no	—
176	C₂³×C₄₇	—	2	2	no	—
177	C₂³×C₄₇	—	2	2	no	—
178	C₂³×C₄₇	—	2	4	no	—
179	C₂³×C₄₇	—	2	4	no	—
180	C₂³×C₄₇	—	2	4	no	—
181	C₂³×C₄₇	—	2	4	no	—
182	C₂³×C₄₇	—	4	2	no	—
183	C₂³×C₄₇	—	4	2	no	—
184	C₂³×C₄₇	—	4	2	no	—
185	C₂³×C₄₇	—	4	2	no	—
186	C₂³×C₄₇	—	4	2	no	—
187	C₂³×C₄₇	—	4	2	no	—
188	C₂³×C₄₇	—	4	2	no	—
189	C₂³×C₄₇	—	4	2	no	—
190	C₂³×C₄₇	#117	1	4	yes	—
191	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
192	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
193	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
194	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
195	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
196	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
197	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
198	C₂³×C₄₇	C₂×#41	1	2	yes	—
199	C₂³×C₄₇	C₂×#41	1	2	yes	—
200	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
201	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
202	C₂×C₄×C₄₇	—	2	2	no	—
203	C₂×C₄×C₄₇	—	2	2	no	—
204	C₂×C₄×C₄₇	—	2	2	no	—
205	C₂×C₄×C₄₇	—	2	2	no	—
206	C₂×C₄×C₄₇	—	2	4	no	—
207	C₂×C₄×C₄₇	—	2	4	no	—
208	C₂×C₄×C₄₇	—	2	4	no	—
209	C₂×C₄×C₄₇	—	2	4	no	—
210	C₂×C₄×C₄₇	—	2	2	no	—
211	C₂×C₄×C₄₇	—	2	2	no	—
212	C₂×C₄×C₄₇	—	2	2	no	—
213	C₂×C₄×C₄₇	—	2	2	no	—
214	C₂×C₄×C₄₇	—	2	2	no	—
215	C₂×C₄×C₄₇	—	2	2	no	—
216	C₂×C₄×C₄₇	—	2	2	no	—
217	C₂×C₄×C₄₇	—	2	2	no	—
218	C₂×C₄×C₄₇	—	2	2	no	—
219	C₂×C₄×C₄₇	—	2	2	no	—
220	C₂×C₄×C₄₇	—	2	2	no	—
221	C₂×C₄×C₄₇	—	2	2	no	—
222	C₂×C₄×C₄₇	—	2	4	no	—
223	C₂×C₄×C₄₇	—	2	4	no	—
224	C₂×C₄×C₄₇	—	2	4	no	—
225	C₂×C₄×C₄₇	—	2	4	no	—
226	C₂×C₄×C₄₇	—	2	4	no	—
227	C₂×C₄×C₄₇	—	2	4	no	—
228	C₂×C₄×C₄₇	—	4	16	no	—
229	C₂×C₄×C₄₇	—	4	2	no	—
230	C₂×C₄×C₄₇	—	4	2	no	—
231	C₂×C₄×C₄₇	—	4	2	no	—
232	C₂×C₄×C₄₇	—	4	2	no	—
233	C₂×C₄×C₄₇	—	4	2	no	—
234	C₂×C₄×C₄₇	—	4	2	no	—
235	C₂×C₄×C₄₇	—	4	2	no	—
236	C₂×C₄×C₄₇	—	4	2	no	—
237	C₂×C₄×C₄₇	—	4	2	no	—
238	C₂×C₄×C₄₇	—	4	2	no	—
239	C₂×C₄×C₄₇	—	4	2	no	—
240	C₂×C₄×C₄₇	—	4	2	no	—
241	C₂×C₄×C₄₇	—	4	2	no	—
242	C₂×C₄×C₄₇	—	4	2	no	—
243	C₂×C₄×C₄₇	—	4	2	no	—
244	C₂×C₄×C₄₇	—	4	2	no	—
245	C₂×C₄×C₄₇	—	4	2	no	—
246	C₂×C₄×C₄₇	—	4	2	no	—
247	C₂×C₄×C₄₇	—	4	2	no	—
248	C₂×C₄×C₄₇	—	4	2	no	—
249	C₂×C₄×C₄₇	—	4	2	no	—
250	C₂×C₄×C₄₇	—	4	2	no	—
251	C₂×C₄×C₄₇	—	4	2	no	—
252	C₂×C₄×C₄₇	—	4	2	no	—
253	C₂×C₄×C₄₇	—	4	2	no	—
254	C₂×C₄×C₄₇	—	4	2	no	—
255	C₂×C₄×C₄₇	—	4	2	no	—
256	C₂×C₄×C₄₇	—	4	2	no	—
257	C₂×C₄×C₄₇	—	4	2	no	—
258	C₂×C₄×C₄₇	—	4	2	no	—
259	C₂×C₄×C₄₇	#117	1	4	yes	—
260	C₂×C₄×C₄₇	#117	1	4	yes	—
261	#13947	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
262	C₂²×C₄₇	—	2	4	no	—
263	C₂²×C₄₇	—	2	4	no	—
264	C₂²×C₄₇	—	2	4	no	—
265	C₂²×C₄₇	—	4	2	no	—
266	C₂²×C₄₇	—	4	4	no	—
267	C₂²×C₄₇	—	4	4	no	—
268	C₂²×C₄₇	—	4	4	no	—
269	C₂²×C₄₇	—	4	4	no	—
270	C₂²×C₄₇	—	4	2	no	—
271	C₂²×C₄₇	—	4	2	no	—
272	C₂²×C₄₇	—	4	2	no	—
273	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
274	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
275	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
276	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
277	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
278	C₂²×C₄₇	#518	1	1	yes	characteristic
279	C₂²×C₄₇	#518	1	1	yes	characteristic
280	C₂²×C₄₇	#529	1	1	yes	characteristic
281	C₂²×C₄₇	#529	1	2	yes	—
282	C₂²×C₄₇	#529	1	1	yes	characteristic
283	C₂²×C₄₇	#529	1	2	yes	—
284	C₂²×C₄₇	#529	1	1	yes	characteristic
285	C₂²×C₄₇	#529	1	1	yes	characteristic
286	C₂²×C₄₇	#538	1	2	yes	—
287	C₂²×C₄₇	#538	1	2	yes	—
288	C₂²×C₄₇	#551	1	2	yes	—
289	C₂²×C₄₇	#551	1	2	yes	—
290	C₂²×C₄₇	#551	1	2	yes	—
291	C₂²×C₄₇	#553	1	2	yes	—
292	C₂²×C₄₇	#553	1	2	yes	—
293	C₂²×C₄₇	#553	1	2	yes	—
294	C₂²×C₄₇	#553	1	2	yes	—
295	C₂²×C₄₇	#559	1	2	yes	—
296	C₄×C₄₇	—	2	4	no	—
297	C₄×C₄₇	—	2	4	no	—
298	C₄×C₄₇	—	4	2	no	—
299	C₄×C₄₇	—	4	4	no	—
300	C₄×C₄₇	—	4	4	no	—
301	C₄×C₄₇	—	4	2	no	—
302	C₄×C₄₇	—	4	2	no	—
303	C₄×C₄₇	—	4	2	no	—
304	C₄×C₄₇	—	8	2	no	—
305	C₄×C₄₇	—	8	2	no	—
306	C₂×C₄×C₂²⋊C₄	C₂×C₄₇	1	1	yes	characteristic
307	#1443	C₂×C₄₇	1	2	yes	complemented
308	#1440	C₂×C₄₇	1	2	yes	—
309	#1437	C₂×C₄₇	1	2	yes	—
310	#1434	C₂×C₄₇	1	1	yes	characteristic, complemented
311	#1434	C₂×C₄₇	1	1	yes	characteristic, complemented
312	#1434	C₂×C₄₇	1	1	yes	characteristic, complemented
313	#1434	C₂×C₄₇	1	2	yes	complemented
314	C₂²⋊#95	C₂×C₄₇	1	1	yes	characteristic
315	C₂²⋊#95	C₂×C₄₇	1	1	yes	characteristic
316	C₄×#95	C₂×C₄₇	1	1	yes	characteristic, complemented
317	C₂×C₄₇	—	4	4	no	—
318	C₂×C₄₇	#2283	1	1	yes	characteristic
319	C₂×C₄₇	#2298	1	1	yes	characteristic
320	C₂×C₄₇	#2312	1	1	yes	characteristic
321	C₂×C₄₇	#2353	1	1	yes	characteristic
322	C₂×C₄₇	#2353	1	1	yes	characteristic
323	C₂×C₄₇	#2353	1	1	yes	characteristic
324	C₂×C₄₇	#2357	1	1	yes	characteristic
325	C₂×C₄₇	#2576	1	2	yes	—
326	C₂×C₄₇	#2578	1	2	yes	—
327	C₂×C₄₇	#2595	1	2	yes	—
328	C₂×C₄₇	#2597	1	2	yes	—
329	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
330	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
331	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
332	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
333	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
334	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
335	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
336	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
337	C₄×C₂²⋊C₄	C₄×C₄₇	1	8	yes	complemented
338	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
339	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
340	C₂×#95	C₂²×C₄₇	1	2	yes	—
341	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
342	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
343	C₂×#95	C₂²×C₄₇	1	2	yes	—
344	C₂×#95	C₂²×C₄₇	1	2	yes	—
345	C₂×#95	C₂²×C₄₇	1	2	yes	—
346	C₂×#95	C₂²×C₄₇	1	2	yes	—
347	C₂×#95	C₂²×C₄₇	1	2	yes	—
348	C₂×#95	C₂²×C₄₇	1	2	yes	—
349	C₂×#95	C₂²×C₄₇	1	2	yes	—
350	C₂×#95	C₂²×C₄₇	1	2	yes	—
351	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
352	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
353	C₄₇	#13947	1	1	yes	characteristic, direct product factor, Sylow
354	C₂⁵	C₂³×C₄₇	1	1	yes	characteristic
355	C₂³×C₄	—	2	2	no	—
356	C₂³×C₄	—	2	2	no	—
357	C₂³×C₄	—	4	2	no	—
358	C₂³×C₄	—	4	2	no	—
359	C₂³×C₄	C₂×C₄×C₄₇	1	4	yes	—
360	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
361	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
362	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
363	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
364	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
365	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
366	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
367	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
368	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
369	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
370	C₂×C₂²⋊C₄	—	2	2	no	—
371	C₂×C₂²⋊C₄	—	2	2	no	—
372	C₂×C₂²⋊C₄	—	2	2	no	—
373	C₂×C₂²⋊C₄	—	2	2	no	—
374	C₂×C₂²⋊C₄	—	2	4	no	—
375	C₂×C₂²⋊C₄	—	2	4	no	—
376	C₂×C₂²⋊C₄	—	2	4	no	—
377	C₂×C₂²⋊C₄	—	2	4	no	—
378	C₂×C₂²⋊C₄	—	4	2	no	—
379	C₂×C₂²⋊C₄	—	4	2	no	—
380	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
381	C₂×C₂²⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
382	C₂×C₄²	—	2	4	no	—
383	C₂×C₄²	—	2	4	no	—
384	C₂×C₄²	—	4	2	no	—
385	C₂×C₄²	—	4	2	no	—
386	C₂×C₄²	—	4	2	no	—
387	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
388	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
389	#95	—	2	4	no	—
390	#95	—	2	2	no	—
391	#95	—	2	2	no	—
392	#95	—	2	4	no	—
393	#95	—	2	4	no	—
394	#95	—	2	4	no	—
395	#95	—	2	2	no	—
396	#95	—	2	2	no	—
397	#95	—	4	2	no	—
398	#95	—	4	2	no	—
399	#95	—	4	2	no	—
400	#95	—	4	2	no	—
401	#95	—	4	2	no	—
402	#95	C₂×C₄×C₄₇	1	4	yes	—
403	#95	C₂×C₄×C₄₇	1	4	yes	—
404	C₂⁴	—	2	1	no	—
405	C₂⁴	—	2	1	no	—
406	C₂⁴	—	2	2	no	—
407	C₂⁴	—	2	2	no	—
408	C₂⁴	—	2	1	no	—
409	C₂⁴	—	2	1	no	—
410	C₂⁴	—	2	2	no	—
411	C₂⁴	—	2	2	no	—
412	C₂⁴	C₂²×C₄×C₄₇	1	2	yes	—
413	C₂⁴	#41×C₄₇	1	2	yes	—
414	C₂⁴	#41×C₄₇	1	2	yes	—
415	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	—	2	2	no	—
426	C₂²×C₄	—	2	2	no	—
427	C₂²×C₄	—	2	2	no	—
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	1	no	—
431	C₂²×C₄	—	2	1	no	—
432	C₂²×C₄	—	2	1	no	—
433	C₂²×C₄	—	2	1	no	—
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	1	no	—
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	2	no	—
443	C₂²×C₄	—	2	2	no	—
444	C₂²×C₄	—	2	2	no	—
445	C₂²×C₄	—	2	2	no	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	—	2	8	no	—
449	C₂²×C₄	—	2	2	no	—
450	C₂²×C₄	—	2	2	no	—
451	C₂²×C₄	—	2	2	no	—
452	C₂²×C₄	—	2	2	no	—
453	C₂²×C₄	—	2	2	no	—
454	C₂²×C₄	—	2	2	no	—
455	C₂²×C₄	—	2	2	no	—
456	C₂²×C₄	—	2	2	no	—
457	C₂²×C₄	—	2	2	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	2	2	no	—
461	C₂²×C₄	—	2	2	no	—
462	C₂²×C₄	—	2	2	no	—
463	C₂²×C₄	—	4	4	no	—
464	C₂²×C₄	—	4	4	no	—
465	C₂²×C₄	—	4	8	no	—
466	C₂²×C₄	—	4	8	no	—
467	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
468	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
469	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
470	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
471	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
472	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
473	C₂²×C₄	#41×C₄₇	1	4	yes	—
474	C₂²×C₄	#41×C₄₇	1	4	yes	—
475	C₂²×C₄	#41×C₄₇	1	2	yes	—
476	C₂²×C₄	#41×C₄₇	1	2	yes	—
477	C₂²×C₄	#41×C₄₇	1	2	yes	—
478	C₂²×C₄	#41×C₄₇	1	2	yes	—
479	C₂²⋊C₄	—	2	8	no	—
480	C₂²⋊C₄	—	2	8	no	—
481	C₂²⋊C₄	—	4	8	no	—
482	C₂²⋊C₄	—	4	8	no	—
483	C₄²	—	4	4	no	—
484	C₄²	—	4	4	no	—
485	C₄²	—	4	8	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	2	2	no	—
491	C₂³	—	2	2	no	—
492	C₂³	—	2	2	no	—
493	C₂³	—	2	2	no	—
494	C₂³	—	2	2	no	—
495	C₂³	—	2	2	no	—
496	C₂³	—	2	4	no	—
497	C₂³	—	2	4	no	—
498	C₂³	—	2	4	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	4	2	no	—
501	C₂³	—	4	2	no	—
502	C₂³	—	4	2	no	—
503	C₂³	—	4	2	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	4	2	no	—
507	C₂³	—	4	2	no	—
508	C₂³	#117×C₄₇	1	4	yes	—
509	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
510	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
511	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
512	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
513	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
514	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
515	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
516	C₂³	C₂×#41×C₄₇	1	2	yes	—
517	C₂³	C₂×#41×C₄₇	1	2	yes	—
518	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
519	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	4	no	—
525	C₂×C₄	—	2	4	no	—
526	C₂×C₄	—	2	4	no	—
527	C₂×C₄	—	2	4	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	2	2	no	—
536	C₂×C₄	—	2	2	no	—
537	C₂×C₄	—	2	2	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	4	no	—
541	C₂×C₄	—	2	4	no	—
542	C₂×C₄	—	2	4	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	4	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	4	16	no	—
547	C₂×C₄	—	4	2	no	—
548	C₂×C₄	—	4	2	no	—
549	C₂×C₄	—	4	2	no	—
550	C₂×C₄	—	4	2	no	—
551	C₂×C₄	—	4	2	no	—
552	C₂×C₄	—	4	2	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	2	no	—
559	C₂×C₄	—	4	2	no	—
560	C₂×C₄	—	4	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	2	no	—
563	C₂×C₄	—	4	2	no	—
564	C₂×C₄	—	4	2	no	—
565	C₂×C₄	—	4	2	no	—
566	C₂×C₄	—	4	2	no	—
567	C₂×C₄	—	4	2	no	—
568	C₂×C₄	—	4	2	no	—
569	C₂×C₄	—	4	2	no	—
570	C₂×C₄	—	4	2	no	—
571	C₂×C₄	—	4	2	no	—
572	C₂×C₄	—	4	2	no	—
573	C₂×C₄	—	4	2	no	—
574	C₂×C₄	—	4	2	no	—
575	C₂×C₄	—	4	2	no	—
576	C₂×C₄	—	4	2	no	—
577	C₂×C₄	#117×C₄₇	1	4	yes	—
578	C₂×C₄	#117×C₄₇	1	4	yes	—
579	C₂²	—	2	4	no	—
580	C₂²	—	2	4	no	—
581	C₂²	—	2	4	no	—
582	C₂²	—	4	2	no	—
583	C₂²	—	4	2	no	—
584	C₂²	—	4	4	no	—
585	C₂²	—	4	4	no	—
586	C₂²	—	4	4	no	—
587	C₂²	—	4	4	no	—
588	C₂²	—	4	2	no	—
589	C₂²	—	4	2	no	—
590	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
591	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
592	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
593	C₂²	C₄×#41×C₄₇	1	1	yes	characteristic
594	C₂²	C₄×#41×C₄₇	1	1	yes	characteristic
595	C₂²	C₄₇×#518	1	1	yes	characteristic
596	C₂²	C₄₇×#518	1	1	yes	characteristic
597	C₂²	C₄₇×#529	1	1	yes	characteristic
598	C₂²	C₄₇×#529	1	1	yes	characteristic
599	C₂²	C₄₇×#529	1	1	yes	characteristic
600	C₂²	C₄₇×#529	1	1	yes	characteristic
601	C₂²	C₄₇×#529	1	2	yes	—
602	C₂²	C₄₇×#529	1	2	yes	—
603	C₂²	C₄₇×#538	1	2	yes	—
604	C₂²	C₄₇×#538	1	2	yes	—
605	C₂²	C₄₇×#551	1	2	yes	—
606	C₂²	C₄₇×#551	1	2	yes	—
607	C₂²	C₄₇×#551	1	2	yes	—
608	C₂²	C₄₇×#553	1	2	yes	—
609	C₂²	C₄₇×#553	1	2	yes	—
610	C₂²	C₄₇×#553	1	2	yes	—
611	C₂²	C₄₇×#553	1	2	yes	—
612	C₂²	C₄₇×#559	1	2	yes	—
613	C₄	—	2	4	no	—
614	C₄	—	2	4	no	—
615	C₄	—	4	2	no	—
616	C₄	—	4	4	no	—
617	C₄	—	4	4	no	—
618	C₄	—	4	2	no	—
619	C₄	—	4	2	no	—
620	C₄	—	4	2	no	—
621	C₄	—	8	2	no	—
622	C₄	—	8	2	no	—
623	C₂	—	4	4	no	—
624	C₂	C₄₇×#2283	1	1	yes	characteristic
625	C₂	C₄₇×#2298	1	1	yes	characteristic
626	C₂	C₄₇×#2312	1	1	yes	characteristic
627	C₂	C₄₇×#2353	1	1	yes	characteristic
628	C₂	C₄₇×#2353	1	1	yes	characteristic
629	C₂	C₄₇×#2353	1	1	yes	characteristic
630	C₂	C₄₇×#2357	1	1	yes	characteristic
631	C₂	C₄₇×#2576	1	2	yes	—
632	C₂	C₄₇×#2578	1	2	yes	—
633	C₂	C₄₇×#2595	1	2	yes	—
634	C₂	C₄₇×#2597	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂⁴
commutator	C₂³	C₂³×C₄×C₄₇
Frattini, cosocle	C₂⁴	C₂⁴×C₄₇
prime radical	C₂⁵×C₄₇	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#1443	C₂	semidirect
5. C₄₇×#1434	C₂	semidirect
6. C₄₇×#1434	C₂	semidirect
7. C₄₇×#1434	C₂	semidirect
8. C₄₇×#1434	C₂	semidirect
11. C₄×#95×C₄₇	C₂	semidirect
20. C₄×C₂²⋊C₄×C₄₇	C₄	semidirect
261. #13947	C₄₇	direct (N × H)
307. #1443	C₂×C₄₇	semidirect
310. #1434	C₂×C₄₇	semidirect
311. #1434	C₂×C₄₇	semidirect
312. #1434	C₂×C₄₇	semidirect
313. #1434	C₂×C₄₇	semidirect
316. C₄×#95	C₂×C₄₇	semidirect
337. C₄×C₂²⋊C₄	C₄×C₄₇	semidirect
353. C₄₇	#13947	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×C₄×C₂²⋊C₄×C₄₇	2
C₄₇×#1443	2
C₄₇×#1440	2
C₄₇×#1437	2
C₄₇×#1434	2
C₄₇×C₂²⋊#95	2
C₄×#95×C₄₇	2
#13947	47

Subgroups — C47×#13947 #26053645

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#13947 #26053645