Subgroups — C₄₇×#23545 #26063243

Order 12032.

1410 conjugacy classes of subgroups.

The subgroup lattice has 522 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#137×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#424	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#416	C₂	1	1	yes	maximal, characteristic
4	C₂²×#103×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2311	C₂	1	1	yes	maximal, characteristic
6	C₄₇×#2310	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#2056	C₂	1	4	yes	maximal, complemented
8	C₄₇×#2055	C₂	1	4	yes	maximal, complemented
9	C₄₇×#1736	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
11	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
12	C₂×#137×C₄₇	—	2	4	no	—
13	C₂×#137×C₄₇	—	2	4	no	—
14	C₂×#137×C₄₇	—	2	4	no	—
15	C₂²×Q₁₆×C₄₇	C₂²	1	2	yes	—
16	C₂²×SD₁₆×C₄₇	C₂²	1	2	yes	—
17	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
18	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
21	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
22	C₄₇×#424	—	2	4	no	—
23	C₂×C₄⋊C₈×C₄₇	C₂²	1	4	yes	—
24	C₄₇×#416	—	2	4	no	—
25	C₂×#103×C₄₇	—	2	4	no	—
26	C₂×#103×C₄₇	C₂²	1	4	yes	—
27	C₂×#103×C₄₇	C₂²	1	2	yes	—
28	C₂×#102×C₄₇	C₂²	1	2	yes	—
29	C₄₇×#391	—	2	2	no	—
30	C₄₇×#391	C₂²	1	4	yes	—
31	C₄₇×#391	C₂²	1	2	yes	—
32	C₄₇×#390	C₂²	1	2	yes	—
33	C₄₇×#386	—	2	2	no	—
34	C₄₇×#381	—	2	2	no	—
35	C₄₇×#380	—	2	2	no	—
36	C₄₇×#340	C₂²	1	4	yes	—
37	C₂×#41×C₄₇	—	2	2	no	—
38	C₂×#41×C₄₇	—	2	2	no	—
39	C₂×#41×C₄₇	—	2	2	no	—
40	C₂×#41×C₄₇	—	2	2	no	—
41	C₂×#41×C₄₇	—	2	2	no	—
42	C₂×#41×C₄₇	D₄	1	4	yes	—
43	C₂²×Q₈×C₄₇	—	2	1	no	—
44	C₂²×Q₈×C₄₇	—	2	2	no	—
45	C₂²×Q₈×C₄₇	—	2	2	no	—
46	C₂²×Q₈×C₄₇	—	2	2	no	—
47	C₂²×Q₈×C₄₇	—	2	2	no	—
48	C₂²×Q₈×C₄₇	—	2	2	no	—
49	C₂²×Q₈×C₄₇	D₄	1	4	yes	—
50	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
51	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
52	C₂²×D₄×C₄₇	—	2	1	no	—
53	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₄₇	—	2	1	no	—
55	C₂³×C₄×C₄₇	—	2	1	no	—
56	C₂³×C₄×C₄₇	—	2	1	no	—
57	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
58	#137×C₄₇	—	2	32	no	—
59	C₂×Q₁₆×C₄₇	—	2	4	no	—
60	C₂×Q₁₆×C₄₇	—	2	4	no	—
61	C₂×Q₁₆×C₄₇	—	2	4	no	—
62	C₂×SD₁₆×C₄₇	—	2	4	no	—
63	C₂×SD₁₆×C₄₇	—	2	4	no	—
64	C₂×SD₁₆×C₄₇	—	2	4	no	—
65	C₂×M₁₆×C₄₇	—	2	2	no	—
66	C₂×M₁₆×C₄₇	—	2	2	no	—
67	C₂×M₁₆×C₄₇	D₄	1	4	yes	—
68	C₂²×C₈×C₄₇	—	2	2	no	—
69	C₂²×C₈×C₄₇	—	2	2	no	—
70	C₂²×C₈×C₄₇	—	2	2	no	—
71	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
72	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
73	#117×C₄₇	—	2	2	no	—
74	#117×C₄₇	—	2	2	no	—
75	#117×C₄₇	—	2	2	no	—
76	#117×C₄₇	—	2	2	no	—
77	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
78	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
79	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
81	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
83	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
85	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
86	C₂×C₄²×C₄₇	—	2	1	no	—
87	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
88	C₄⋊C₈×C₄₇	—	2	8	no	—
89	#103×C₄₇	—	2	8	no	—
90	#103×C₄₇	—	2	4	no	—
91	#102×C₄₇	—	2	4	no	—
92	#95×C₄₇	—	2	4	no	—
93	#95×C₄₇	—	2	8	no	—
94	C₂⁴×C₄₇	—	2	1	no	—
95	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
96	#41×C₄₇	—	2	8	no	—
97	#41×C₄₇	—	2	8	no	—
98	#41×C₄₇	—	4	4	no	—
99	#41×C₄₇	—	4	4	no	—
100	C₂×Q₈×C₄₇	—	2	4	no	—
101	C₂×Q₈×C₄₇	—	2	2	no	—
102	C₂×Q₈×C₄₇	—	2	1	no	—
103	C₂×Q₈×C₄₇	—	2	8	no	—
104	C₂×Q₈×C₄₇	—	2	8	no	—
105	C₂×Q₈×C₄₇	—	2	2	no	—
106	C₂×Q₈×C₄₇	—	2	2	no	—
107	C₂×Q₈×C₄₇	—	2	1	no	—
108	C₂×Q₈×C₄₇	—	2	1	no	—
109	C₂×Q₈×C₄₇	—	2	2	no	—
110	C₂×Q₈×C₄₇	—	2	2	no	—
111	C₂×Q₈×C₄₇	—	2	1	no	—
112	C₂×Q₈×C₄₇	—	2	1	no	—
113	C₂×Q₈×C₄₇	—	4	2	no	—
114	C₂×Q₈×C₄₇	—	4	2	no	—
115	C₂×Q₈×C₄₇	—	4	4	no	—
116	C₂×Q₈×C₄₇	—	4	4	no	—
117	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
118	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
119	C₂×D₄×C₄₇	—	2	4	no	—
120	C₂×D₄×C₄₇	—	2	1	no	—
121	C₂×D₄×C₄₇	—	2	1	no	—
122	C₂×D₄×C₄₇	—	2	1	no	—
123	C₂×D₄×C₄₇	—	2	1	no	—
124	C₂×D₄×C₄₇	—	2	1	no	—
125	C₂×D₄×C₄₇	—	4	2	no	—
126	C₂×D₄×C₄₇	—	4	2	no	—
127	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₄₇	—	2	4	no	—
129	C₂²×C₄×C₄₇	—	2	1	no	—
130	C₂²×C₄×C₄₇	—	2	2	no	—
131	C₂²×C₄×C₄₇	—	2	4	no	—
132	C₂²×C₄×C₄₇	—	2	2	no	—
133	C₂²×C₄×C₄₇	—	2	2	no	—
134	C₂²×C₄×C₄₇	—	4	2	no	—
135	C₂²×C₄×C₄₇	—	4	2	no	—
136	C₂²×C₄×C₄₇	—	4	2	no	—
137	C₂²×C₄×C₄₇	—	4	2	no	—
138	C₂²×C₄×C₄₇	—	4	2	no	—
139	C₂²×C₄×C₄₇	—	8	2	no	—
140	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
141	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
142	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
145	C₂²×C₄×C₄₇	#41	1	2	yes	—
146	C₂²×C₄×C₄₇	#41	1	2	yes	—
147	C₂²×C₄×C₄₇	#41	1	2	yes	—
148	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
149	Q₁₆×C₄₇	—	2	16	no	—
150	SD₁₆×C₄₇	—	2	16	no	—
151	M₁₆×C₄₇	—	2	8	no	—
152	C₂×C₈×C₄₇	—	2	2	no	—
153	C₂×C₈×C₄₇	—	2	2	no	—
154	C₂×C₈×C₄₇	—	2	2	no	—
155	C₂×C₈×C₄₇	—	2	2	no	—
156	C₂×C₈×C₄₇	—	2	2	no	—
157	C₂×C₈×C₄₇	—	4	4	no	—
158	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
159	C₄⋊C₄×C₄₇	—	2	4	no	—
160	C₄⋊C₄×C₄₇	—	2	2	no	—
161	C₄⋊C₄×C₄₇	—	2	2	no	—
162	C₄⋊C₄×C₄₇	—	2	2	no	—
163	C₄⋊C₄×C₄₇	—	2	2	no	—
164	C₄⋊C₄×C₄₇	—	4	2	no	—
165	C₂²⋊C₄×C₄₇	—	2	4	no	—
166	C₂²⋊C₄×C₄₇	—	4	2	no	—
167	C₂²⋊C₄×C₄₇	—	8	4	no	—
168	C₄²×C₄₇	—	2	2	no	—
169	C₄²×C₄₇	—	2	2	no	—
170	C₄²×C₄₇	—	4	2	no	—
171	C₂³×C₄₇	—	2	2	no	—
172	C₂³×C₄₇	—	2	2	no	—
173	C₂³×C₄₇	—	2	2	no	—
174	C₂³×C₄₇	—	4	1	no	—
175	C₂³×C₄₇	—	4	1	no	—
176	C₂³×C₄₇	—	4	2	no	—
177	C₂³×C₄₇	—	4	2	no	—
178	C₂³×C₄₇	#121	1	2	yes	—
179	C₂³×C₄₇	#121	1	2	yes	—
180	C₂³×C₄₇	#121	1	2	yes	—
181	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
182	Q₈×C₄₇	—	2	4	no	—
183	Q₈×C₄₇	—	2	2	no	—
184	Q₈×C₄₇	—	2	4	no	—
185	Q₈×C₄₇	—	2	2	no	—
186	Q₈×C₄₇	—	4	2	no	—
187	Q₈×C₄₇	—	4	1	no	—
188	Q₈×C₄₇	—	4	2	no	—
189	Q₈×C₄₇	—	4	1	no	—
190	Q₈×C₄₇	—	4	8	no	—
191	D₄×C₄₇	—	2	2	no	—
192	D₄×C₄₇	—	2	2	no	—
193	D₄×C₄₇	—	4	8	no	—
194	D₄×C₄₇	—	4	1	no	—
195	D₄×C₄₇	—	4	1	no	—
196	C₂×C₄×C₄₇	—	2	4	no	—
197	C₂×C₄×C₄₇	—	2	2	no	—
198	C₂×C₄×C₄₇	—	2	4	no	—
199	C₂×C₄×C₄₇	—	2	4	no	—
200	C₂×C₄×C₄₇	—	2	4	no	—
201	C₂×C₄×C₄₇	—	4	1	no	—
202	C₂×C₄×C₄₇	—	4	1	no	—
203	C₂×C₄×C₄₇	—	4	2	no	—
204	C₂×C₄×C₄₇	—	4	2	no	—
205	C₂×C₄×C₄₇	—	4	8	no	—
206	C₂×C₄×C₄₇	—	4	8	no	—
207	C₂×C₄×C₄₇	—	4	2	no	—
208	C₂×C₄×C₄₇	—	4	2	no	—
209	C₂×C₄×C₄₇	—	4	4	no	—
210	C₂×C₄×C₄₇	—	4	2	no	—
211	C₂×C₄×C₄₇	—	4	2	no	—
212	C₂×C₄×C₄₇	—	8	4	no	—
213	C₂×C₄×C₄₇	#120	1	4	yes	—
214	C₂×C₄×C₄₇	#121	1	2	yes	—
215	C₂×C₄×C₄₇	#121	1	2	yes	—
216	C₂×C₄×C₄₇	#121	1	2	yes	—
217	C₂×C₄×C₄₇	#123	1	4	yes	—
218	C₂×C₄×C₄₇	#123	1	4	yes	—
219	C₂×C₄×C₄₇	#124	1	4	yes	—
220	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
226	C₈×C₄₇	—	2	4	no	—
227	C₈×C₄₇	—	4	2	no	—
228	#23545	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂²×C₄₇	—	2	2	no	—
230	C₂²×C₄₇	—	2	2	no	—
231	C₂²×C₄₇	—	2	4	no	—
232	C₂²×C₄₇	—	2	4	no	—
233	C₂²×C₄₇	—	4	2	no	—
234	C₂²×C₄₇	—	4	4	no	—
235	C₂²×C₄₇	—	8	1	no	—
236	C₂²×C₄₇	—	8	1	no	—
237	C₂²×C₄₇	—	8	2	no	—
238	C₂²×C₄₇	#394	1	4	yes	—
239	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
240	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
241	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
242	C₂²×C₄₇	#577	1	2	yes	—
243	C₂²×C₄₇	#578	1	2	yes	—
244	C₄×C₄₇	—	4	2	no	—
245	C₄×C₄₇	—	4	4	no	—
246	C₄×C₄₇	—	4	4	no	—
247	C₄×C₄₇	—	8	2	no	—
248	C₄×C₄₇	—	8	2	no	—
249	C₄×C₄₇	#394	1	4	yes	—
250	C₄×C₄₇	C₂×#120	1	1	yes	characteristic
251	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
252	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
253	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
254	C₂²×#137	C₂×C₄₇	1	1	yes	characteristic
255	C₂×#424	C₂×C₄₇	1	1	yes	characteristic, complemented
256	C₂×#416	C₂×C₄₇	1	1	yes	characteristic
257	C₂²×#103	C₂×C₄₇	1	1	yes	characteristic, complemented
258	#2311	C₂×C₄₇	1	1	yes	characteristic
259	#2310	C₂×C₄₇	1	1	yes	characteristic, complemented
260	#2056	C₂×C₄₇	1	4	yes	complemented
261	#2055	C₂×C₄₇	1	4	yes	complemented
262	#1736	C₂×C₄₇	1	1	yes	characteristic, complemented
263	C₂×C₄₇	—	2	4	no	—
264	C₂×C₄₇	—	8	2	no	—
265	C₂×C₄₇	C₂×#394	1	1	yes	characteristic
266	C₂×C₄₇	#3043	1	1	yes	characteristic
267	C₂×C₄₇	#3044	1	1	yes	characteristic
268	C₂×C₄₇	#3046	1	2	yes	—
269	C₂×C₄₇	#3063	1	2	yes	—
270	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
271	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
272	C₂×#137	—	2	4	no	—
273	C₂×#137	—	2	4	no	—
274	C₂×#137	—	2	4	no	—
275	C₂²×Q₁₆	C₂²×C₄₇	1	2	yes	—
276	C₂²×SD₁₆	C₂²×C₄₇	1	2	yes	—
277	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
278	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
279	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
280	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
281	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
282	#424	—	2	4	no	—
283	C₂×C₄⋊C₈	C₂²×C₄₇	1	4	yes	—
284	#416	—	2	4	no	—
285	C₂×#103	—	2	4	no	—
286	C₂×#103	C₂²×C₄₇	1	4	yes	—
287	C₂×#103	C₂²×C₄₇	1	2	yes	—
288	C₂×#102	C₂²×C₄₇	1	2	yes	—
289	#391	—	2	2	no	—
290	#391	C₂²×C₄₇	1	4	yes	—
291	#391	C₂²×C₄₇	1	2	yes	—
292	#390	C₂²×C₄₇	1	2	yes	—
293	#386	—	2	2	no	—
294	#381	—	2	2	no	—
295	#380	—	2	2	no	—
296	#340	C₂²×C₄₇	1	4	yes	—
297	C₄₇	#23545	1	1	yes	characteristic, direct product factor, Sylow
298	C₂×#41	—	2	2	no	—
299	C₂×#41	—	2	2	no	—
300	C₂×#41	—	2	2	no	—
301	C₂×#41	—	2	2	no	—
302	C₂×#41	—	2	2	no	—
303	C₂×#41	D₄×C₄₇	1	4	yes	—
304	C₂²×Q₈	—	2	1	no	—
305	C₂²×Q₈	—	2	2	no	—
306	C₂²×Q₈	—	2	2	no	—
307	C₂²×Q₈	—	2	2	no	—
308	C₂²×Q₈	—	2	2	no	—
309	C₂²×Q₈	—	2	2	no	—
310	C₂²×Q₈	D₄×C₄₇	1	4	yes	—
311	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
312	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
313	C₂²×D₄	—	2	1	no	—
314	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
315	C₂³×C₄	—	2	1	no	—
316	C₂³×C₄	—	2	1	no	—
317	C₂³×C₄	—	2	1	no	—
318	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
319	#137	—	2	32	no	—
320	C₂×Q₁₆	—	2	4	no	—
321	C₂×Q₁₆	—	2	4	no	—
322	C₂×Q₁₆	—	2	4	no	—
323	C₂×SD₁₆	—	2	4	no	—
324	C₂×SD₁₆	—	2	4	no	—
325	C₂×SD₁₆	—	2	4	no	—
326	C₂×M₁₆	—	2	2	no	—
327	C₂×M₁₆	—	2	2	no	—
328	C₂×M₁₆	D₄×C₄₇	1	4	yes	—
329	C₂²×C₈	—	2	2	no	—
330	C₂²×C₈	—	2	2	no	—
331	C₂²×C₈	—	2	2	no	—
332	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
333	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
334	#117	—	2	2	no	—
335	#117	—	2	2	no	—
336	#117	—	2	2	no	—
337	#117	—	2	2	no	—
338	C₂×C₄⋊C₄	—	2	2	no	—
339	C₂×C₄⋊C₄	—	2	2	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
342	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
343	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
344	C₂×C₂²⋊C₄	—	2	1	no	—
345	C₂×C₂²⋊C₄	—	2	4	no	—
346	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
347	C₂×C₄²	—	2	1	no	—
348	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
349	C₄⋊C₈	—	2	8	no	—
350	#103	—	2	8	no	—
351	#103	—	2	4	no	—
352	#102	—	2	4	no	—
353	#95	—	2	4	no	—
354	#95	—	2	8	no	—
355	C₂⁴	—	2	1	no	—
356	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
357	#41	—	2	8	no	—
358	#41	—	2	8	no	—
359	#41	—	4	4	no	—
360	#41	—	4	4	no	—
361	C₂×Q₈	—	2	4	no	—
362	C₂×Q₈	—	2	2	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	2	8	no	—
365	C₂×Q₈	—	2	8	no	—
366	C₂×Q₈	—	2	2	no	—
367	C₂×Q₈	—	2	2	no	—
368	C₂×Q₈	—	2	1	no	—
369	C₂×Q₈	—	2	1	no	—
370	C₂×Q₈	—	2	2	no	—
371	C₂×Q₈	—	2	2	no	—
372	C₂×Q₈	—	2	1	no	—
373	C₂×Q₈	—	2	1	no	—
374	C₂×Q₈	—	4	2	no	—
375	C₂×Q₈	—	4	2	no	—
376	C₂×Q₈	—	4	4	no	—
377	C₂×Q₈	—	4	4	no	—
378	C₂×Q₈	C₂×D₄×C₄₇	1	4	yes	—
379	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
380	C₂×D₄	—	2	4	no	—
381	C₂×D₄	—	2	1	no	—
382	C₂×D₄	—	2	1	no	—
383	C₂×D₄	—	2	1	no	—
384	C₂×D₄	—	2	1	no	—
385	C₂×D₄	—	2	1	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂×D₄	—	4	2	no	—
388	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
389	C₂²×C₄	—	2	4	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	2	no	—
392	C₂²×C₄	—	2	4	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	—	2	2	no	—
395	C₂²×C₄	—	4	2	no	—
396	C₂²×C₄	—	4	2	no	—
397	C₂²×C₄	—	4	2	no	—
398	C₂²×C₄	—	4	2	no	—
399	C₂²×C₄	—	4	2	no	—
400	C₂²×C₄	—	8	2	no	—
401	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
402	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
403	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
404	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
405	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
406	C₂²×C₄	#41×C₄₇	1	2	yes	—
407	C₂²×C₄	#41×C₄₇	1	2	yes	—
408	C₂²×C₄	#41×C₄₇	1	2	yes	—
409	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
410	Q₁₆	—	2	16	no	—
411	SD₁₆	—	2	16	no	—
412	M₁₆	—	2	8	no	—
413	C₂×C₈	—	2	2	no	—
414	C₂×C₈	—	2	2	no	—
415	C₂×C₈	—	2	2	no	—
416	C₂×C₈	—	2	2	no	—
417	C₂×C₈	—	2	2	no	—
418	C₂×C₈	—	4	4	no	—
419	C₂×C₈	C₂×D₄×C₄₇	1	4	yes	—
420	C₄⋊C₄	—	2	4	no	—
421	C₄⋊C₄	—	2	2	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	4	2	no	—
426	C₂²⋊C₄	—	2	4	no	—
427	C₂²⋊C₄	—	4	2	no	—
428	C₂²⋊C₄	—	8	4	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	4	2	no	—
432	C₂³	—	2	2	no	—
433	C₂³	—	2	2	no	—
434	C₂³	—	2	2	no	—
435	C₂³	—	4	1	no	—
436	C₂³	—	4	1	no	—
437	C₂³	—	4	2	no	—
438	C₂³	—	4	2	no	—
439	C₂³	#121×C₄₇	1	2	yes	—
440	C₂³	#121×C₄₇	1	2	yes	—
441	C₂³	#121×C₄₇	1	2	yes	—
442	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
443	Q₈	—	2	4	no	—
444	Q₈	—	2	2	no	—
445	Q₈	—	2	4	no	—
446	Q₈	—	2	2	no	—
447	Q₈	—	4	2	no	—
448	Q₈	—	4	1	no	—
449	Q₈	—	4	2	no	—
450	Q₈	—	4	1	no	—
451	Q₈	—	4	8	no	—
452	D₄	—	2	2	no	—
453	D₄	—	2	2	no	—
454	D₄	—	4	8	no	—
455	D₄	—	4	1	no	—
456	D₄	—	4	1	no	—
457	C₂×C₄	—	2	4	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	2	4	no	—
462	C₂×C₄	—	4	1	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	2	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	8	no	—
467	C₂×C₄	—	4	8	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	4	no	—
471	C₂×C₄	—	4	2	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	8	4	no	—
474	C₂×C₄	#120×C₄₇	1	4	yes	—
475	C₂×C₄	#121×C₄₇	1	2	yes	—
476	C₂×C₄	#121×C₄₇	1	2	yes	—
477	C₂×C₄	#121×C₄₇	1	2	yes	—
478	C₂×C₄	#123×C₄₇	1	4	yes	—
479	C₂×C₄	#123×C₄₇	1	4	yes	—
480	C₂×C₄	#124×C₄₇	1	4	yes	—
481	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
482	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
483	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
484	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
485	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
486	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
487	C₈	—	2	4	no	—
488	C₈	—	4	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	2	4	no	—
492	C₂²	—	2	4	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	4	2	no	—
495	C₂²	—	8	1	no	—
496	C₂²	—	8	1	no	—
497	C₂²	—	8	2	no	—
498	C₂²	C₄₇×#394	1	4	yes	—
499	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
500	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
501	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
502	C₂²	C₄₇×#577	1	2	yes	—
503	C₂²	C₄₇×#578	1	2	yes	—
504	C₄	—	4	4	no	—
505	C₄	—	4	2	no	—
506	C₄	—	4	4	no	—
507	C₄	—	8	2	no	—
508	C₄	—	8	2	no	—
509	C₄	C₄₇×#394	1	4	yes	—
510	C₄	C₂×#120×C₄₇	1	1	yes	characteristic
511	C₄	C₂×#123×C₄₇	1	1	yes	characteristic
512	C₄	C₂×#123×C₄₇	1	1	yes	characteristic
513	C₄	C₂×#124×C₄₇	1	1	yes	characteristic
514	C₂	—	2	4	no	—
515	C₂	—	8	2	no	—
516	C₂	C₂×C₄₇×#394	1	1	yes	characteristic
517	C₂	C₄₇×#3043	1	1	yes	characteristic
518	C₂	C₄₇×#3044	1	1	yes	characteristic
519	C₂	C₄₇×#3046	1	2	yes	—
520	C₂	C₄₇×#3063	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂²×#41×C₄₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂×#117×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#424	C₂	semidirect
4. C₂²×#103×C₄₇	C₂	semidirect
6. C₄₇×#2310	C₂	semidirect
7. C₄₇×#2056	C₂	semidirect
8. C₄₇×#2055	C₂	semidirect
9. C₄₇×#1736	C₂	semidirect
228. #23545	C₄₇	direct (N × H)
255. C₂×#424	C₂×C₄₇	semidirect
257. C₂²×#103	C₂×C₄₇	semidirect
259. #2310	C₂×C₄₇	semidirect
260. #2056	C₂×C₄₇	semidirect
261. #2055	C₂×C₄₇	semidirect
262. #1736	C₂×C₄₇	semidirect
297. C₄₇	#23545	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#137×C₄₇	2
C₂×C₄₇×#424	2
C₂×C₄₇×#416	2
C₂²×#103×C₄₇	2
C₄₇×#2311	2
C₄₇×#2310	2
C₄₇×#2056	2
C₄₇×#2055	2
C₄₇×#1736	2
#23545	47

Subgroups — C47×#23545 #26063243

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#23545 #26063243