Subgroups — C₄₇×#16229 #26055927

Order 12032.

1142 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#1446	C₂	1	2	yes	maximal
2	C₄₇×#1446	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#1445	C₂	1	2	yes	maximal
4	C₄₇×#1445	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1442	C₂	1	1	yes	maximal, characteristic
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×#1434	C₂	1	2	yes	maximal
10	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
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×C₄²×C₄₇	C₂²	1	2	yes	—
15	C₂×#95×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	2	yes	—
22	C₂×#95×C₄₇	C₂²	1	2	yes	—
23	C₂×#95×C₄₇	C₂²	1	2	yes	—
24	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
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	C₂²×Q₈×C₄₇	—	2	2	no	—
32	C₂²×Q₈×C₄₇	—	2	4	no	—
33	C₂²×Q₈×C₄₇	—	4	2	no	—
34	C₂²×Q₈×C₄₇	—	4	1	no	—
35	C₂²×Q₈×C₄₇	—	4	1	no	—
36	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
37	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
38	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
39	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	C₂³	1	2	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	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
48	C₂×C₄⋊C₄×C₄₇	—	4	1	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	Q₈	1	4	yes	complemented
53	C₂×C₄²×C₄₇	—	2	4	no	—
54	C₂×C₄²×C₄₇	—	4	2	no	—
55	C₂×C₄²×C₄₇	—	4	2	no	—
56	#95×C₄₇	—	2	4	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	—	4	2	no	—
62	#95×C₄₇	—	4	2	no	—
63	#95×C₄₇	—	4	2	no	—
64	#95×C₄₇	—	4	2	no	—
65	#95×C₄₇	—	4	1	no	—
66	#95×C₄₇	—	4	2	no	—
67	#95×C₄₇	—	4	1	no	—
68	#95×C₄₇	—	4	2	no	—
69	#95×C₄₇	—	4	1	no	—
70	#95×C₄₇	—	4	2	no	—
71	#95×C₄₇	Q₈	1	4	yes	complemented
72	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
73	C₂×Q₈×C₄₇	—	4	8	no	—
74	C₂×Q₈×C₄₇	—	4	4	no	—
75	C₂×Q₈×C₄₇	—	4	4	no	—
76	C₂×Q₈×C₄₇	—	4	8	no	—
77	C₂×Q₈×C₄₇	—	4	4	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	2	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	2	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	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	—	2	1	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	1	no	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	—	2	2	no	—
112	C₂²×C₄×C₄₇	—	2	1	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	1	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	C₂×Q₈	1	2	yes	—
128	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
129	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
130	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
131	C₂²×C₄×C₄₇	#41	1	4	yes	—
132	C₂²×C₄×C₄₇	#41	1	4	yes	—
133	C₂²×C₄×C₄₇	#41	1	2	yes	—
134	C₂²×C₄×C₄₇	#41	1	4	yes	—
135	C₄⋊C₄×C₄₇	—	4	4	no	—
136	C₄⋊C₄×C₄₇	—	4	4	no	—
137	C₄⋊C₄×C₄₇	—	4	8	no	—
138	C₄²×C₄₇	—	4	8	no	—
139	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
140	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
141	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
142	C₂³×C₄₇	C₂×#41	1	2	yes	—
143	C₂³×C₄₇	C₂×#41	1	2	yes	—
144	C₂³×C₄₇	C₂×#41	1	2	yes	—
145	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
146	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
147	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
148	C₂³×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
149	C₂³×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
150	Q₈×C₄₇	—	4	16	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	4	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	2	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	—	2	4	no	—
166	C₂×C₄×C₄₇	—	2	4	no	—
167	C₂×C₄×C₄₇	—	2	4	no	—
168	C₂×C₄×C₄₇	—	2	4	no	—
169	C₂×C₄×C₄₇	—	2	4	no	—
170	C₂×C₄×C₄₇	—	2	4	no	—
171	C₂×C₄×C₄₇	—	2	4	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	—	4	2	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	—	4	2	no	—
183	C₂×C₄×C₄₇	—	4	2	no	—
184	C₂×C₄×C₄₇	—	4	1	no	—
185	C₂×C₄×C₄₇	—	4	2	no	—
186	C₂×C₄×C₄₇	—	4	2	no	—
187	C₂×C₄×C₄₇	—	4	1	no	—
188	C₂×C₄×C₄₇	—	4	1	no	—
189	C₂×C₄×C₄₇	—	4	2	no	—
190	C₂×C₄×C₄₇	—	4	1	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	1	no	—
197	C₂×C₄×C₄₇	—	4	2	no	—
198	C₂×C₄×C₄₇	—	4	2	no	—
199	C₂×C₄×C₄₇	—	4	1	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	—	4	2	no	—
204	C₂×C₄×C₄₇	—	4	2	no	—
205	C₂×C₄×C₄₇	—	4	2	no	—
206	C₂×C₄×C₄₇	—	4	2	no	—
207	C₂×C₄×C₄₇	—	4	2	no	—
208	#16229	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
209	C₂²×C₄₇	#529	1	2	yes	—
210	C₂²×C₄₇	#533	1	2	yes	—
211	C₂²×C₄₇	#533	1	2	yes	—
212	C₂²×C₄₇	#538	1	1	yes	characteristic
213	C₂²×C₄₇	#538	1	2	yes	—
214	C₂²×C₄₇	#538	1	2	yes	—
215	C₂²×C₄₇	#542	1	2	yes	—
216	C₂²×C₄₇	#543	1	1	yes	characteristic
217	C₂²×C₄₇	#544	1	1	yes	characteristic
218	C₂²×C₄₇	#551	1	2	yes	—
219	C₂²×C₄₇	#551	1	1	yes	characteristic
220	C₂²×C₄₇	#551	1	2	yes	—
221	C₂²×C₄₇	#551	1	1	yes	characteristic
222	C₂²×C₄₇	#552	1	2	yes	—
223	C₂²×C₄₇	#554	1	2	yes	—
224	C₂²×C₄₇	#554	1	2	yes	—
225	C₂²×C₄₇	#554	1	1	yes	characteristic
226	C₂²×C₄₇	#555	1	1	yes	characteristic
227	C₂²×C₄₇	#557	1	1	yes	characteristic
228	C₂²×C₄₇	Q₈²	1	1	yes	characteristic
229	C₂²×C₄₇	#559	1	2	yes	—
230	C₂²×C₄₇	#560	1	1	yes	characteristic
231	C₂²×C₄₇	#562	1	1	yes	characteristic
232	C₄×C₄₇	—	4	4	no	—
233	C₄×C₄₇	—	4	4	no	—
234	C₄×C₄₇	—	4	2	no	—
235	C₄×C₄₇	—	4	2	no	—
236	C₄×C₄₇	—	4	4	no	—
237	C₄×C₄₇	—	4	2	no	—
238	C₄×C₄₇	—	4	4	no	—
239	C₄×C₄₇	—	4	4	no	—
240	C₄×C₄₇	—	8	2	no	—
241	#1446	C₂×C₄₇	1	2	yes	—
242	#1446	C₂×C₄₇	1	1	yes	characteristic
243	#1445	C₂×C₄₇	1	2	yes	—
244	#1445	C₂×C₄₇	1	1	yes	characteristic
245	#1442	C₂×C₄₇	1	1	yes	characteristic
246	#1441	C₂×C₄₇	1	2	yes	—
247	#1436	C₂×C₄₇	1	2	yes	—
248	#1436	C₂×C₄₇	1	2	yes	—
249	#1434	C₂×C₄₇	1	2	yes	—
250	C₂×C₄₇	#2520	1	2	yes	—
251	C₂×C₄₇	#2572	1	1	yes	characteristic
252	C₂×C₄₇	#2586	1	2	yes	—
253	C₂×C₄₇	#2589	1	2	yes	—
254	C₂×C₄₇	#2607	1	1	yes	characteristic
255	C₂×C₄₇	#2612	1	1	yes	characteristic
256	C₂×C₄₇	#2735	1	1	yes	characteristic
257	C₂×C₄₇	#2742	1	1	yes	characteristic
258	C₂×C₄₇	#2751	1	2	yes	—
259	C₂×C₄₇	#2784	1	1	yes	characteristic
260	C₂×C₄₇	#2806	1	1	yes	characteristic
261	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
262	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
263	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
264	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
265	C₂²×C₄²	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	2	yes	—
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	2	yes	—
277	C₂×#95	C₂²×C₄₇	1	2	yes	—
278	C₂×#95	C₂²×C₄₇	1	2	yes	—
279	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
280	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
281	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
282	C₄₇	#16229	1	1	yes	characteristic, direct product factor, Sylow
283	C₂²×Q₈	—	2	2	no	—
284	C₂²×Q₈	—	2	4	no	—
285	C₂²×Q₈	—	4	2	no	—
286	C₂²×Q₈	—	4	1	no	—
287	C₂²×Q₈	—	4	1	no	—
288	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
289	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
290	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
291	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
292	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
293	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
294	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
295	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
296	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
297	C₂×C₄⋊C₄	—	2	4	no	—
298	C₂×C₄⋊C₄	—	2	4	no	—
299	C₂×C₄⋊C₄	—	2	4	no	—
300	C₂×C₄⋊C₄	—	4	1	no	—
301	C₂×C₄⋊C₄	—	4	1	no	—
302	C₂×C₄⋊C₄	—	4	1	no	—
303	C₂×C₄⋊C₄	—	4	2	no	—
304	C₂×C₄⋊C₄	Q₈×C₄₇	1	4	yes	complemented
305	C₂×C₄²	—	2	4	no	—
306	C₂×C₄²	—	4	2	no	—
307	C₂×C₄²	—	4	2	no	—
308	#95	—	2	4	no	—
309	#95	—	2	4	no	—
310	#95	—	2	4	no	—
311	#95	—	2	4	no	—
312	#95	—	2	4	no	—
313	#95	—	4	2	no	—
314	#95	—	4	2	no	—
315	#95	—	4	2	no	—
316	#95	—	4	2	no	—
317	#95	—	4	2	no	—
318	#95	—	4	1	no	—
319	#95	—	4	2	no	—
320	#95	—	4	1	no	—
321	#95	—	4	2	no	—
322	#95	—	4	1	no	—
323	#95	Q₈×C₄₇	1	4	yes	complemented
324	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
325	C₂×Q₈	—	4	8	no	—
326	C₂×Q₈	—	4	4	no	—
327	C₂×Q₈	—	4	4	no	—
328	C₂×Q₈	—	4	8	no	—
329	C₂×Q₈	—	4	4	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	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	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	2	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	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	1	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	1	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	1	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	—	2	1	no	—
371	C₂²×C₄	—	2	2	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
380	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
381	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
382	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
383	C₂²×C₄	#41×C₄₇	1	2	yes	—
384	C₂²×C₄	#41×C₄₇	1	4	yes	—
385	C₂²×C₄	#41×C₄₇	1	4	yes	—
386	C₂²×C₄	#41×C₄₇	1	4	yes	—
387	C₄⋊C₄	—	4	4	no	—
388	C₄⋊C₄	—	4	4	no	—
389	C₄⋊C₄	—	4	8	no	—
390	C₄²	—	4	8	no	—
391	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
392	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
393	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
394	C₂³	C₂×#41×C₄₇	1	2	yes	—
395	C₂³	C₂×#41×C₄₇	1	2	yes	—
396	C₂³	C₂×#41×C₄₇	1	2	yes	—
397	C₂³	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
398	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
399	C₂³	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
400	C₂³	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
401	C₂³	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
402	Q₈	—	4	16	no	—
403	C₂×C₄	—	2	4	no	—
404	C₂×C₄	—	2	4	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	4	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	4	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	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	1	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	1	no	—
440	C₂×C₄	—	4	1	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	1	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	1	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂²	C₄₇×#529	1	2	yes	—
461	C₂²	C₄₇×#533	1	2	yes	—
462	C₂²	C₄₇×#533	1	2	yes	—
463	C₂²	C₄₇×#538	1	2	yes	—
464	C₂²	C₄₇×#538	1	1	yes	characteristic
465	C₂²	C₄₇×#538	1	2	yes	—
466	C₂²	C₄₇×#542	1	2	yes	—
467	C₂²	C₄₇×#543	1	1	yes	characteristic
468	C₂²	C₄₇×#544	1	1	yes	characteristic
469	C₂²	C₄₇×#551	1	2	yes	—
470	C₂²	C₄₇×#551	1	2	yes	—
471	C₂²	C₄₇×#551	1	1	yes	characteristic
472	C₂²	C₄₇×#551	1	1	yes	characteristic
473	C₂²	C₄₇×#552	1	2	yes	—
474	C₂²	C₄₇×#554	1	2	yes	—
475	C₂²	C₄₇×#554	1	1	yes	characteristic
476	C₂²	C₄₇×#554	1	2	yes	—
477	C₂²	C₄₇×#555	1	1	yes	characteristic
478	C₂²	C₄₇×#557	1	1	yes	characteristic
479	C₂²	Q₈²×C₄₇	1	1	yes	characteristic
480	C₂²	C₄₇×#559	1	2	yes	—
481	C₂²	C₄₇×#560	1	1	yes	characteristic
482	C₂²	C₄₇×#562	1	1	yes	characteristic
483	C₄	—	4	4	no	—
484	C₄	—	4	4	no	—
485	C₄	—	4	4	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	4	no	—
489	C₄	—	4	2	no	—
490	C₄	—	4	4	no	—
491	C₄	—	8	2	no	—
492	C₂	C₄₇×#2520	1	2	yes	—
493	C₂	C₄₇×#2572	1	1	yes	characteristic
494	C₂	C₄₇×#2586	1	2	yes	—
495	C₂	C₄₇×#2589	1	2	yes	—
496	C₂	C₄₇×#2607	1	1	yes	characteristic
497	C₂	C₄₇×#2612	1	1	yes	characteristic
498	C₂	C₄₇×#2735	1	1	yes	characteristic
499	C₂	C₄₇×#2742	1	1	yes	characteristic
500	C₂	C₄₇×#2751	1	2	yes	—
501	C₂	C₄₇×#2784	1	1	yes	characteristic
502	C₂	C₄₇×#2806	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
52. C₂×C₄⋊C₄×C₄₇	Q₈	semidirect
71. #95×C₄₇	Q₈	semidirect
208. #16229	C₄₇	direct (N × H)
282. C₄₇	#16229	direct (N × H)
304. C₂×C₄⋊C₄	Q₈×C₄₇	semidirect
323. #95	Q₈×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#1446	2
C₄₇×#1445	2
C₄₇×#1442	2
C₄₇×#1441	2
C₄₇×#1436	2
C₄₇×#1434	2
#16229	47

Subgroups — C47×#16229 #26055927

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#16229 #26055927