Subgroups — C₄₇×#35139 #26074837

Order 12032.

2150 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#529	C₂	1	1	yes	maximal, characteristic
2	C₂²×#125×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2861	C₂	1	2	yes	maximal, complemented
4	C₄₇×#2859	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2664	C₂	1	4	yes	maximal, complemented
6	C₄₇×#2611	C₂	1	4	yes	maximal, complemented
7	C₄₇×#2566	C₂	1	2	yes	maximal, complemented
8	C₄₇×#2565	C₂	1	2	yes	maximal, complemented
9	C₄₇×#2504	C₂	1	1	yes	maximal, characteristic
10	C₄₇×#2503	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#2502	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₇×#2501	C₂	1	1	yes	maximal, characteristic
13	C₄₇×#2413	C₂	1	4	yes	maximal, complemented
14	C₄₇×#2322	C₂	1	4	yes	maximal, complemented
15	C₄×#117×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
16	C₄₇×#529	—	2	8	no	—
17	C₂×#126×C₄₇	C₂²	1	2	yes	—
18	C₂×#125×C₄₇	—	2	8	no	—
19	C₂×#125×C₄₇	C₂²	1	2	yes	—
20	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×#125×C₄₇	C₂²	1	2	yes	—
22	C₂×#125×C₄₇	C₂²	1	2	yes	—
23	C₂×#125×C₄₇	C₂²	1	2	yes	—
24	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×#123×C₄₇	C₂²	1	4	yes	—
26	C₂×#123×C₄₇	C₂²	1	2	yes	—
27	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
32	C₂×#117×C₄₇	C₂²	1	2	yes	—
33	C₂×#117×C₄₇	C₂²	1	2	yes	—
34	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
35	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
36	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
37	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
38	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
39	C₄₇×#400	C₂²	1	4	yes	—
40	C₄₇×#399	C₂²	1	4	yes	—
41	C₄₇×#398	C₂²	1	8	yes	—
42	C₄₇×#398	C₂²	1	4	yes	—
43	C₄₇×#397	C₂²	1	4	yes	—
44	C₄₇×#396	C₂²	1	8	yes	—
45	C₄₇×#391	C₂²	1	2	yes	—
46	C₄₇×#391	C₂²	1	2	yes	—
47	C₄₇×#390	C₂²	1	2	yes	—
48	C₄₇×#390	C₂²	1	2	yes	—
49	C₄₇×#389	C₂²	1	8	yes	—
50	C₄₇×#389	C₂²	1	8	yes	—
51	C₄₇×#388	C₂²	1	8	yes	—
52	C₄₇×#388	C₂²	1	8	yes	—
53	C₄₇×#387	C₂²	1	8	yes	—
54	C₄₇×#386	C₂²	1	4	yes	—
55	C₄₇×#385	C₂²	1	8	yes	—
56	C₄₇×#385	C₂²	1	4	yes	—
57	C₄₇×#384	C₂²	1	2	yes	—
58	C₄₇×#384	C₂²	1	2	yes	—
59	C₄₇×#382	C₂²	1	2	yes	—
60	C₄₇×#382	C₂²	1	2	yes	—
61	C₄₇×#381	C₂²	1	4	yes	—
62	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
63	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
64	C₄×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
65	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
66	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
67	C₄₇×#376	C₂²	1	2	yes	—
68	C₄³×C₄₇	C₂²	1	2	yes	—
69	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
70	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
71	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
73	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
74	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
75	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
76	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
77	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
78	#126×C₄₇	—	2	8	no	—
79	#125×C₄₇	—	2	8	no	—
80	#125×C₄₇	—	2	8	no	—
81	#125×C₄₇	—	2	8	no	—
82	#125×C₄₇	—	2	8	no	—
83	#125×C₄₇	—	2	4	no	—
84	#124×C₄₇	—	2	4	no	—
85	#123×C₄₇	—	2	8	no	—
86	#123×C₄₇	—	2	16	no	—
87	C₂²⋊Q₈×C₄₇	—	2	4	no	—
88	#121×C₄₇	—	2	4	no	—
89	C₄×Q₈×C₄₇	—	2	4	no	—
90	C₄×D₄×C₄₇	—	2	8	no	—
91	C₄×D₄×C₄₇	—	2	4	no	—
92	#117×C₄₇	—	2	8	no	—
93	#117×C₄₇	—	2	8	no	—
94	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
95	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
96	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
97	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
98	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
99	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
100	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
101	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
102	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
103	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
104	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
105	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
107	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
108	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
109	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
110	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
111	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
112	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
113	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
114	C₂×C₄⋊C₄×C₄₇	C₂³	1	8	yes	—
115	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
116	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
117	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
118	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
119	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
120	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
121	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
122	C₂×C₂²⋊C₄×C₄₇	C₂³	1	8	yes	—
123	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
124	C₂×C₄²×C₄₇	D₄	1	8	yes	—
125	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
126	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
127	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
128	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
129	C₂×C₄²×C₄₇	C₂³	1	4	yes	—
130	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
131	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
132	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
133	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
134	#95×C₄₇	C₂³	1	4	yes	—
135	#95×C₄₇	C₂³	1	2	yes	—
136	#95×C₄₇	C₂³	1	2	yes	—
137	#95×C₄₇	C₂³	1	8	yes	—
138	#95×C₄₇	C₂³	1	8	yes	—
139	#95×C₄₇	C₂³	1	8	yes	—
140	#95×C₄₇	C₂³	1	8	yes	—
141	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
142	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
143	C₂×Q₈×C₄₇	—	2	2	no	—
144	C₂×Q₈×C₄₇	—	2	4	no	—
145	C₂×D₄×C₄₇	—	2	4	no	—
146	C₂×D₄×C₄₇	—	2	8	no	—
147	C₂×D₄×C₄₇	—	2	2	no	—
148	C₂×D₄×C₄₇	—	2	4	no	—
149	C₂²×C₄×C₄₇	—	2	4	no	—
150	C₂²×C₄×C₄₇	—	2	4	no	—
151	C₂²×C₄×C₄₇	—	2	4	no	—
152	C₂²×C₄×C₄₇	—	2	4	no	—
153	C₂²×C₄×C₄₇	—	2	8	no	—
154	C₂²×C₄×C₄₇	—	2	4	no	—
155	C₂²×C₄×C₄₇	—	4	2	no	—
156	C₂²×C₄×C₄₇	—	4	4	no	—
157	C₂²×C₄×C₄₇	—	4	4	no	—
158	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
159	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
160	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
161	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
162	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
163	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
164	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
165	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
166	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
167	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
168	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
169	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
170	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
171	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
172	C₂²×C₄×C₄₇	C₂⁴	1	4	yes	—
173	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
174	C₄⋊C₄×C₄₇	—	2	8	no	—
175	C₄⋊C₄×C₄₇	—	2	8	no	—
176	C₄⋊C₄×C₄₇	—	2	8	no	—
177	C₄⋊C₄×C₄₇	—	2	8	no	—
178	C₄⋊C₄×C₄₇	—	2	4	no	—
179	C₄⋊C₄×C₄₇	—	2	4	no	—
180	C₄⋊C₄×C₄₇	—	2	4	no	—
181	C₄⋊C₄×C₄₇	—	2	4	no	—
182	C₄⋊C₄×C₄₇	—	2	4	no	—
183	C₄⋊C₄×C₄₇	—	2	4	no	—
184	C₄⋊C₄×C₄₇	—	2	2	no	—
185	C₄⋊C₄×C₄₇	—	2	4	no	—
186	C₄⋊C₄×C₄₇	—	2	2	no	—
187	C₄⋊C₄×C₄₇	—	2	4	no	—
188	C₄⋊C₄×C₄₇	—	2	8	no	—
189	C₄⋊C₄×C₄₇	—	2	16	no	—
190	C₄⋊C₄×C₄₇	—	4	8	no	—
191	C₂²⋊C₄×C₄₇	—	2	4	no	—
192	C₂²⋊C₄×C₄₇	—	2	4	no	—
193	C₂²⋊C₄×C₄₇	—	2	4	no	—
194	C₂²⋊C₄×C₄₇	—	2	4	no	—
195	C₂²⋊C₄×C₄₇	—	2	4	no	—
196	C₂²⋊C₄×C₄₇	—	2	4	no	—
197	C₂²⋊C₄×C₄₇	—	2	16	no	—
198	C₂²⋊C₄×C₄₇	—	4	8	no	—
199	C₂²⋊C₄×C₄₇	#41	1	8	yes	—
200	C₄²×C₄₇	—	2	4	no	—
201	C₄²×C₄₇	—	2	8	no	—
202	C₄²×C₄₇	—	2	4	no	—
203	C₄²×C₄₇	—	2	4	no	—
204	C₄²×C₄₇	—	4	4	no	—
205	C₄²×C₄₇	C₂×D₄	1	4	yes	—
206	C₄²×C₄₇	C₂×D₄	1	4	yes	—
207	C₄²×C₄₇	C₂×D₄	1	4	yes	—
208	C₄²×C₄₇	C₂×D₄	1	4	yes	—
209	C₂³×C₄₇	—	2	2	no	—
210	C₂³×C₄₇	—	2	2	no	—
211	C₂³×C₄₇	—	2	2	no	—
212	C₂³×C₄₇	—	2	4	no	—
213	C₂³×C₄₇	—	2	4	no	—
214	C₂³×C₄₇	—	2	4	no	—
215	C₂³×C₄₇	C₂²×D₄	1	2	yes	—
216	C₂³×C₄₇	C₂×#41	1	4	yes	—
217	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
218	Q₈×C₄₇	—	4	4	no	—
219	D₄×C₄₇	—	4	8	no	—
220	D₄×C₄₇	—	4	4	no	—
221	C₂×C₄×C₄₇	—	2	8	no	—
222	C₂×C₄×C₄₇	—	2	2	no	—
223	C₂×C₄×C₄₇	—	2	2	no	—
224	C₂×C₄×C₄₇	—	2	4	no	—
225	C₂×C₄×C₄₇	—	2	2	no	—
226	C₂×C₄×C₄₇	—	2	2	no	—
227	C₂×C₄×C₄₇	—	2	4	no	—
228	C₂×C₄×C₄₇	—	2	2	no	—
229	C₂×C₄×C₄₇	—	2	8	no	—
230	C₂×C₄×C₄₇	—	2	2	no	—
231	C₂×C₄×C₄₇	—	2	2	no	—
232	C₂×C₄×C₄₇	—	2	2	no	—
233	C₂×C₄×C₄₇	—	2	4	no	—
234	C₂×C₄×C₄₇	—	2	4	no	—
235	C₂×C₄×C₄₇	—	2	4	no	—
236	C₂×C₄×C₄₇	—	2	8	no	—
237	C₂×C₄×C₄₇	—	2	4	no	—
238	C₂×C₄×C₄₇	—	2	4	no	—
239	C₂×C₄×C₄₇	—	2	4	no	—
240	C₂×C₄×C₄₇	—	2	4	no	—
241	C₂×C₄×C₄₇	—	2	8	no	—
242	C₂×C₄×C₄₇	—	2	4	no	—
243	C₂×C₄×C₄₇	—	4	4	no	—
244	C₂×C₄×C₄₇	—	4	8	no	—
245	C₂×C₄×C₄₇	—	4	8	no	—
246	C₂×C₄×C₄₇	—	4	8	no	—
247	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
248	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
249	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
250	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
251	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
252	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
253	C₂×C₄×C₄₇	C₂×#41	1	8	yes	—
254	C₂×C₄×C₄₇	2₋¹⁺⁴	1	4	yes	—
255	#35139	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
256	C₂²×C₄₇	—	2	2	no	—
257	C₂²×C₄₇	—	2	2	no	—
258	C₂²×C₄₇	—	2	8	no	—
259	C₂²×C₄₇	—	4	2	no	—
260	C₂²×C₄₇	—	4	2	no	—
261	C₂²×C₄₇	—	4	2	no	—
262	C₂²×C₄₇	—	4	8	no	—
263	C₂²×C₄₇	#532	1	4	yes	—
264	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
265	C₂²×C₄₇	C₂²×#41	1	2	yes	—
266	C₂²×C₄₇	C₂×2₋¹⁺⁴	1	2	yes	—
267	C₂²×C₄₇	#585	1	2	yes	—
268	C₄×C₄₇	—	2	2	no	—
269	C₄×C₄₇	—	2	2	no	—
270	C₄×C₄₇	—	2	2	no	—
271	C₄×C₄₇	—	2	2	no	—
272	C₄×C₄₇	—	2	2	no	—
273	C₄×C₄₇	—	2	8	no	—
274	C₄×C₄₇	—	4	4	no	—
275	C₄×C₄₇	—	4	2	no	—
276	C₄×C₄₇	—	4	2	no	—
277	C₄×C₄₇	—	4	2	no	—
278	C₄×C₄₇	—	4	4	no	—
279	C₄×C₄₇	—	4	4	no	—
280	C₄×C₄₇	#536	1	4	yes	—
281	C₂×#529	C₂×C₄₇	1	1	yes	characteristic
282	C₂²×#125	C₂×C₄₇	1	1	yes	characteristic, complemented
283	#2861	C₂×C₄₇	1	2	yes	complemented
284	#2859	C₂×C₄₇	1	2	yes	complemented
285	#2664	C₂×C₄₇	1	4	yes	complemented
286	#2611	C₂×C₄₇	1	4	yes	complemented
287	#2566	C₂×C₄₇	1	2	yes	complemented
288	#2565	C₂×C₄₇	1	2	yes	complemented
289	#2504	C₂×C₄₇	1	1	yes	characteristic
290	#2503	C₂×C₄₇	1	1	yes	characteristic, complemented
291	#2502	C₂×C₄₇	1	1	yes	characteristic, complemented
292	#2501	C₂×C₄₇	1	1	yes	characteristic
293	#2413	C₂×C₄₇	1	4	yes	complemented
294	#2322	C₂×C₄₇	1	4	yes	complemented
295	C₄×#117	C₂×C₄₇	1	1	yes	characteristic, complemented
296	C₂×C₄₇	—	2	4	no	—
297	C₂×C₄₇	—	8	2	no	—
298	C₂×C₄₇	C₂×#532	1	1	yes	characteristic
299	C₂×C₄₇	C₂×#536	1	1	yes	characteristic
300	C₂×C₄₇	#3449	1	1	yes	characteristic
301	C₂×C₄₇	#3515	1	4	yes	—
302	#529	—	2	8	no	—
303	C₂×#126	C₂²×C₄₇	1	2	yes	—
304	C₂×#125	—	2	8	no	—
305	C₂×#125	C₂²×C₄₇	1	2	yes	—
306	C₂×#125	C₂²×C₄₇	1	1	yes	characteristic
307	C₂×#125	C₂²×C₄₇	1	2	yes	—
308	C₂×#125	C₂²×C₄₇	1	2	yes	—
309	C₂×#125	C₂²×C₄₇	1	2	yes	—
310	C₂×#124	C₂²×C₄₇	1	1	yes	characteristic
311	C₂×#123	C₂²×C₄₇	1	4	yes	—
312	C₂×#123	C₂²×C₄₇	1	2	yes	—
313	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
314	C₂×#121	C₂²×C₄₇	1	1	yes	characteristic
315	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
316	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
317	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
318	C₂×#117	C₂²×C₄₇	1	2	yes	—
319	C₂×#117	C₂²×C₄₇	1	2	yes	—
320	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
321	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
322	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
323	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
324	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
325	#400	C₂²×C₄₇	1	4	yes	—
326	#399	C₂²×C₄₇	1	4	yes	—
327	#398	C₂²×C₄₇	1	8	yes	—
328	#398	C₂²×C₄₇	1	4	yes	—
329	#397	C₂²×C₄₇	1	4	yes	—
330	#396	C₂²×C₄₇	1	8	yes	—
331	#391	C₂²×C₄₇	1	2	yes	—
332	#391	C₂²×C₄₇	1	2	yes	—
333	#390	C₂²×C₄₇	1	2	yes	—
334	#390	C₂²×C₄₇	1	2	yes	—
335	#389	C₂²×C₄₇	1	8	yes	—
336	#389	C₂²×C₄₇	1	8	yes	—
337	#388	C₂²×C₄₇	1	8	yes	—
338	#388	C₂²×C₄₇	1	8	yes	—
339	#387	C₂²×C₄₇	1	8	yes	—
340	#386	C₂²×C₄₇	1	4	yes	—
341	#385	C₂²×C₄₇	1	8	yes	—
342	#385	C₂²×C₄₇	1	4	yes	—
343	#384	C₂²×C₄₇	1	2	yes	—
344	#384	C₂²×C₄₇	1	2	yes	—
345	#382	C₂²×C₄₇	1	2	yes	—
346	#382	C₂²×C₄₇	1	2	yes	—
347	#381	C₂²×C₄₇	1	4	yes	—
348	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
349	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
350	C₄×C₂²⋊C₄	C₂²×C₄₇	1	2	yes	—
351	C₄×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
352	C₄×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
353	#376	C₂²×C₄₇	1	2	yes	—
354	C₄³	C₂²×C₄₇	1	2	yes	—
355	C₄₇	#35139	1	1	yes	characteristic, direct product factor, Sylow
356	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
357	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
358	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
359	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
360	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
361	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
362	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
363	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
364	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
365	#126	—	2	8	no	—
366	#125	—	2	8	no	—
367	#125	—	2	8	no	—
368	#125	—	2	8	no	—
369	#125	—	2	8	no	—
370	#125	—	2	4	no	—
371	#124	—	2	4	no	—
372	#123	—	2	8	no	—
373	#123	—	2	16	no	—
374	C₂²⋊Q₈	—	2	4	no	—
375	#121	—	2	4	no	—
376	C₄×Q₈	—	2	4	no	—
377	C₄×D₄	—	2	8	no	—
378	C₄×D₄	—	2	4	no	—
379	#117	—	2	8	no	—
380	#117	—	2	8	no	—
381	C₂×C₄⋊C₄	—	2	4	no	—
382	C₂×C₄⋊C₄	—	2	4	no	—
383	C₂×C₄⋊C₄	—	2	8	no	—
384	C₂×C₄⋊C₄	—	2	8	no	—
385	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
386	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
387	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
388	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
389	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
390	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
391	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
392	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
393	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
394	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
395	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
396	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
397	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
398	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
399	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
400	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
401	C₂×C₄⋊C₄	C₂³×C₄₇	1	8	yes	—
402	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
403	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
404	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
405	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
406	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
407	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
408	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
409	C₂×C₂²⋊C₄	C₂³×C₄₇	1	8	yes	—
410	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
411	C₂×C₄²	D₄×C₄₇	1	8	yes	—
412	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
413	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
414	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
415	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
416	C₂×C₄²	C₂³×C₄₇	1	4	yes	—
417	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
418	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
419	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
420	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
421	#95	C₂³×C₄₇	1	4	yes	—
422	#95	C₂³×C₄₇	1	2	yes	—
423	#95	C₂³×C₄₇	1	2	yes	—
424	#95	C₂³×C₄₇	1	8	yes	—
425	#95	C₂³×C₄₇	1	8	yes	—
426	#95	C₂³×C₄₇	1	8	yes	—
427	#95	C₂³×C₄₇	1	8	yes	—
428	C₂⁴	C₂⁴×C₄₇	1	2	yes	—
429	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
430	C₂×Q₈	—	2	2	no	—
431	C₂×Q₈	—	2	4	no	—
432	C₂×D₄	—	2	4	no	—
433	C₂×D₄	—	2	8	no	—
434	C₂×D₄	—	2	2	no	—
435	C₂×D₄	—	2	4	no	—
436	C₂²×C₄	—	2	4	no	—
437	C₂²×C₄	—	2	4	no	—
438	C₂²×C₄	—	2	4	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	8	no	—
441	C₂²×C₄	—	2	4	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	—	4	4	no	—
444	C₂²×C₄	—	4	4	no	—
445	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
446	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
447	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
448	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
449	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
450	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
451	C₂²×C₄	C₂⁴×C₄₇	1	2	yes	—
452	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
453	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
454	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
455	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
456	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
457	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
458	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
459	C₂²×C₄	C₂⁴×C₄₇	1	4	yes	—
460	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
461	C₄⋊C₄	—	2	8	no	—
462	C₄⋊C₄	—	2	8	no	—
463	C₄⋊C₄	—	2	8	no	—
464	C₄⋊C₄	—	2	8	no	—
465	C₄⋊C₄	—	2	4	no	—
466	C₄⋊C₄	—	2	4	no	—
467	C₄⋊C₄	—	2	4	no	—
468	C₄⋊C₄	—	2	4	no	—
469	C₄⋊C₄	—	2	4	no	—
470	C₄⋊C₄	—	2	4	no	—
471	C₄⋊C₄	—	2	2	no	—
472	C₄⋊C₄	—	2	4	no	—
473	C₄⋊C₄	—	2	2	no	—
474	C₄⋊C₄	—	2	4	no	—
475	C₄⋊C₄	—	2	8	no	—
476	C₄⋊C₄	—	2	16	no	—
477	C₄⋊C₄	—	4	8	no	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	2	4	no	—
480	C₂²⋊C₄	—	2	4	no	—
481	C₂²⋊C₄	—	2	4	no	—
482	C₂²⋊C₄	—	2	4	no	—
483	C₂²⋊C₄	—	2	4	no	—
484	C₂²⋊C₄	—	2	16	no	—
485	C₂²⋊C₄	—	4	8	no	—
486	C₂²⋊C₄	#41×C₄₇	1	8	yes	—
487	C₄²	—	2	4	no	—
488	C₄²	—	2	8	no	—
489	C₄²	—	2	4	no	—
490	C₄²	—	2	4	no	—
491	C₄²	—	4	4	no	—
492	C₄²	C₂×D₄×C₄₇	1	4	yes	—
493	C₄²	C₂×D₄×C₄₇	1	4	yes	—
494	C₄²	C₂×D₄×C₄₇	1	4	yes	—
495	C₄²	C₂×D₄×C₄₇	1	4	yes	—
496	C₂³	—	2	2	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	2	2	no	—
499	C₂³	—	2	4	no	—
500	C₂³	—	2	4	no	—
501	C₂³	—	2	4	no	—
502	C₂³	C₂²×D₄×C₄₇	1	2	yes	—
503	C₂³	C₂×#41×C₄₇	1	4	yes	—
504	C₂³	C₂⁵×C₄₇	1	1	yes	characteristic
505	Q₈	—	4	4	no	—
506	D₄	—	4	8	no	—
507	D₄	—	4	4	no	—
508	C₂×C₄	—	2	8	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	4	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	4	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	8	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	4	no	—
521	C₂×C₄	—	2	4	no	—
522	C₂×C₄	—	2	4	no	—
523	C₂×C₄	—	2	8	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	8	no	—
529	C₂×C₄	—	2	4	no	—
530	C₂×C₄	—	4	4	no	—
531	C₂×C₄	—	4	8	no	—
532	C₂×C₄	—	4	8	no	—
533	C₂×C₄	—	4	8	no	—
534	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
535	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
536	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
537	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
538	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
539	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
540	C₂×C₄	C₂×#41×C₄₇	1	8	yes	—
541	C₂×C₄	2₋¹⁺⁴×C₄₇	1	4	yes	—
542	C₂²	—	2	2	no	—
543	C₂²	—	2	2	no	—
544	C₂²	—	2	8	no	—
545	C₂²	—	4	2	no	—
546	C₂²	—	4	2	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	8	no	—
549	C₂²	C₄₇×#532	1	4	yes	—
550	C₂²	C₂³×D₄×C₄₇	1	1	yes	characteristic
551	C₂²	C₂²×#41×C₄₇	1	2	yes	—
552	C₂²	C₂×2₋¹⁺⁴×C₄₇	1	2	yes	—
553	C₂²	C₄₇×#585	1	2	yes	—
554	C₄	—	2	2	no	—
555	C₄	—	2	2	no	—
556	C₄	—	2	2	no	—
557	C₄	—	2	2	no	—
558	C₄	—	2	2	no	—
559	C₄	—	2	8	no	—
560	C₄	—	4	4	no	—
561	C₄	—	4	2	no	—
562	C₄	—	4	2	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	4	no	—
565	C₄	—	4	4	no	—
566	C₄	C₄₇×#536	1	4	yes	—
567	C₂	—	2	4	no	—
568	C₂	—	8	2	no	—
569	C₂	C₂×C₄₇×#532	1	1	yes	characteristic
570	C₂	C₂×C₄₇×#536	1	1	yes	characteristic
571	C₂	C₄₇×#3449	1	1	yes	characteristic
572	C₂	C₄₇×#3515	1	4	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂⁵
commutator, Frattini, cosocle	C₂³	C₂⁵×C₄₇
prime radical	C₂×#121×C₄₇	C₂²
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#125×C₄₇	C₂	semidirect
3. C₄₇×#2861	C₂	semidirect
4. C₄₇×#2859	C₂	semidirect
5. C₄₇×#2664	C₂	semidirect
6. C₄₇×#2611	C₂	semidirect
7. C₄₇×#2566	C₂	semidirect
8. C₄₇×#2565	C₂	semidirect
10. C₄₇×#2503	C₂	semidirect
11. C₄₇×#2502	C₂	semidirect
13. C₄₇×#2413	C₂	semidirect
14. C₄₇×#2322	C₂	semidirect
15. C₄×#117×C₄₇	C₂	semidirect
255. #35139	C₄₇	direct (N × H)
282. C₂²×#125	C₂×C₄₇	semidirect
283. #2861	C₂×C₄₇	semidirect
284. #2859	C₂×C₄₇	semidirect
285. #2664	C₂×C₄₇	semidirect
286. #2611	C₂×C₄₇	semidirect
287. #2566	C₂×C₄₇	semidirect
288. #2565	C₂×C₄₇	semidirect
290. #2503	C₂×C₄₇	semidirect
291. #2502	C₂×C₄₇	semidirect
293. #2413	C₂×C₄₇	semidirect
294. #2322	C₂×C₄₇	semidirect
295. C₄×#117	C₂×C₄₇	semidirect
355. C₄₇	#35139	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×#529	2
C₂²×#125×C₄₇	2
C₄₇×#2861	2
C₄₇×#2859	2
C₄₇×#2664	2
C₄₇×#2611	2
C₄₇×#2566	2
C₄₇×#2565	2
C₄₇×#2504	2
C₄₇×#2503	2
C₄₇×#2502	2
C₄₇×#2501	2
C₄₇×#2413	2
C₄₇×#2322	2
C₄×#117×C₄₇	2
#35139	47

Subgroups — C47×#35139 #26074837

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#35139 #26074837