Subgroups — C₄₇×#18318 #26058016

Order 12032.

1172 conjugacy classes of subgroups.

The subgroup lattice has 470 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#543	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#3193	C₂	1	2	yes	maximal, complemented
3	C₄₇×#2539	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1614	C₂	1	4	yes	maximal, complemented
5	C₄₇×#1596	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1508	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1462	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#543	—	2	4	no	—
9	C₄₇×#543	—	2	2	no	—
10	C₄₇×#543	C₂²	1	4	yes	—
11	C₂×#123×C₄₇	—	2	1	no	—
12	C₂×C₂²⋊Q₈×C₄₇	—	2	2	no	—
13	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
14	C₂×C₂²⋊Q₈×C₄₇	—	2	2	no	—
15	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
16	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×#120×C₄₇	—	2	1	no	—
18	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
19	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
20	C₄₇×#484	C₂²	1	4	yes	complemented
21	C₄₇×#480	—	2	2	no	—
22	C₄₇×#468	—	2	4	no	—
23	C₄₇×#450	C₂²	1	4	yes	complemented
24	C₄₇×#448	—	2	2	no	—
25	C₄₇×#407	C₂²	1	2	yes	—
26	C₄₇×#399	C₂²	1	2	yes	—
27	C₄₇×#392	C₂²	1	2	yes	—
28	C₄₇×#390	—	2	2	no	—
29	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
30	C₄₇×#328	C₂²	1	8	yes	complemented
31	C₄₇×#323	C₂²	1	4	yes	—
32	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
33	C₂²×Q₈×C₄₇	—	2	1	no	—
34	C₂²×Q₈×C₄₇	D₄	1	2	yes	complemented
35	C₂²×D₄×C₄₇	—	2	1	no	—
36	C₂²×D₄×C₄₇	—	2	2	no	—
37	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
38	C₂³×C₄×C₄₇	—	2	1	no	—
39	C₂³×C₄×C₄₇	—	2	1	no	—
40	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂×SD₁₆×C₄₇	—	2	4	no	—
43	C₂×M₁₆×C₄₇	—	2	2	no	—
44	#123×C₄₇	—	4	4	no	—
45	C₂²⋊Q₈×C₄₇	—	2	8	no	—
46	C₂²⋊Q₈×C₄₇	—	2	8	no	—
47	C₂²⋊Q₈×C₄₇	—	2	4	no	—
48	C₂²⋊Q₈×C₄₇	—	2	8	no	—
49	C₂²⋊Q₈×C₄₇	—	2	4	no	—
50	C₂²⋊Q₈×C₄₇	—	2	2	no	—
51	C₂²⋊Q₈×C₄₇	—	2	2	no	—
52	C₂²⋊Q₈×C₄₇	—	2	8	no	—
53	C₂²⋊Q₈×C₄₇	D₄	1	4	yes	complemented
54	C₂²⋊Q₈×C₄₇	C₂³	1	4	yes	—
55	#121×C₄₇	—	2	2	no	—
56	#121×C₄₇	—	2	2	no	—
57	#120×C₄₇	—	4	4	no	—
58	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	complemented
63	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
66	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
67	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
68	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
69	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
75	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
76	C₂×C₄²×C₄₇	—	2	1	no	—
77	#107×C₄₇	—	2	4	no	—
78	#103×C₄₇	—	2	4	no	—
79	#102×C₄₇	—	2	4	no	—
80	C₂²⋊C₈×C₄₇	—	2	2	no	—
81	C₂²⋊C₈×C₄₇	C₂³	1	4	yes	—
82	#95×C₄₇	C₂³	1	2	yes	—
83	C₂⁴×C₄₇	—	2	1	no	—
84	C₂⁴×C₄₇	—	2	1	no	—
85	C₂⁴×C₄₇	—	2	4	no	—
86	C₂⁴×C₄₇	—	2	1	no	—
87	C₂⁴×C₄₇	—	4	2	no	—
88	C₂⁴×C₄₇	—	8	1	no	—
89	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
90	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
91	C₂×Q₈×C₄₇	—	2	4	no	—
92	C₂×Q₈×C₄₇	—	2	2	no	—
93	C₂×Q₈×C₄₇	—	8	2	no	—
94	C₂×Q₈×C₄₇	—	8	2	no	—
95	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
96	C₂×D₄×C₄₇	—	2	2	no	—
97	C₂×D₄×C₄₇	—	4	4	no	—
98	C₂×D₄×C₄₇	—	4	2	no	—
99	C₂×D₄×C₄₇	—	4	2	no	—
100	C₂×D₄×C₄₇	—	4	1	no	—
101	C₂×D₄×C₄₇	—	4	1	no	—
102	C₂×D₄×C₄₇	—	4	4	no	—
103	C₂×D₄×C₄₇	—	8	1	no	—
104	C₂×D₄×C₄₇	—	8	2	no	—
105	C₂²×C₄×C₄₇	—	2	2	no	—
106	C₂²×C₄×C₄₇	—	2	1	no	—
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	—	2	4	no	—
110	C₂²×C₄×C₄₇	—	2	4	no	—
111	C₂²×C₄×C₄₇	—	2	1	no	—
112	C₂²×C₄×C₄₇	—	2	1	no	—
113	C₂²×C₄×C₄₇	—	4	2	no	—
114	C₂²×C₄×C₄₇	—	8	1	no	—
115	C₂²×C₄×C₄₇	—	8	2	no	—
116	C₂²×C₄×C₄₇	—	8	2	no	—
117	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
122	SD₁₆×C₄₇	—	8	4	no	—
123	M₁₆×C₄₇	—	8	2	no	—
124	C₂×C₈×C₄₇	—	2	4	no	—
125	C₄⋊C₄×C₄₇	—	2	4	no	—
126	C₄⋊C₄×C₄₇	—	2	8	no	—
127	C₄⋊C₄×C₄₇	—	2	4	no	—
128	C₄⋊C₄×C₄₇	—	2	2	no	—
129	C₄⋊C₄×C₄₇	—	2	4	no	—
130	C₄⋊C₄×C₄₇	—	2	2	no	—
131	C₄⋊C₄×C₄₇	—	4	4	no	—
132	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
133	C₂²⋊C₄×C₄₇	—	2	8	no	—
134	C₂²⋊C₄×C₄₇	—	2	4	no	—
135	C₂²⋊C₄×C₄₇	—	2	4	no	—
136	C₂²⋊C₄×C₄₇	—	2	4	no	—
137	C₂²⋊C₄×C₄₇	—	2	4	no	—
138	C₂²⋊C₄×C₄₇	—	2	4	no	—
139	C₂²⋊C₄×C₄₇	—	4	4	no	—
140	C₂²⋊C₄×C₄₇	—	4	4	no	—
141	C₂²⋊C₄×C₄₇	—	4	2	no	—
142	C₄²×C₄₇	—	8	1	no	—
143	C₂³×C₄₇	—	2	4	no	—
144	C₂³×C₄₇	—	2	4	no	—
145	C₂³×C₄₇	—	2	2	no	—
146	C₂³×C₄₇	—	2	2	no	—
147	C₂³×C₄₇	—	2	2	no	—
148	C₂³×C₄₇	—	2	2	no	—
149	C₂³×C₄₇	—	4	1	no	—
150	C₂³×C₄₇	—	4	2	no	—
151	C₂³×C₄₇	—	4	2	no	—
152	C₂³×C₄₇	—	4	2	no	—
153	C₂³×C₄₇	—	4	1	no	—
154	C₂³×C₄₇	—	4	1	no	—
155	C₂³×C₄₇	—	4	2	no	—
156	C₂³×C₄₇	—	4	2	no	—
157	C₂³×C₄₇	—	4	1	no	—
158	C₂³×C₄₇	—	4	2	no	—
159	C₂³×C₄₇	—	8	1	no	—
160	C₂³×C₄₇	—	8	1	no	—
161	C₂³×C₄₇	—	8	8	no	—
162	C₂³×C₄₇	#120	1	1	yes	characteristic
163	C₂³×C₄₇	#120	1	1	yes	characteristic
164	C₂³×C₄₇	#137	1	4	yes	—
165	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
166	Q₈×C₄₇	—	4	4	no	—
167	Q₈×C₄₇	—	8	2	no	—
168	Q₈×C₄₇	—	8	4	no	—
169	D₄×C₄₇	—	4	4	no	—
170	D₄×C₄₇	—	8	8	no	—
171	D₄×C₄₇	—	8	2	no	—
172	D₄×C₄₇	—	8	2	no	—
173	C₂×C₄×C₄₇	—	2	4	no	—
174	C₂×C₄×C₄₇	—	2	4	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	4	no	—
177	C₂×C₄×C₄₇	—	4	1	no	—
178	C₂×C₄×C₄₇	—	4	2	no	—
179	C₂×C₄×C₄₇	—	4	2	no	—
180	C₂×C₄×C₄₇	—	4	1	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	4	4	no	—
183	C₂×C₄×C₄₇	—	4	2	no	—
184	C₂×C₄×C₄₇	—	4	2	no	—
185	C₂×C₄×C₄₇	—	4	4	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	1	no	—
190	C₂×C₄×C₄₇	—	8	1	no	—
191	C₂×C₄×C₄₇	—	8	4	no	—
192	C₂×C₄×C₄₇	—	8	4	no	—
193	C₂×C₄×C₄₇	#120	1	2	yes	—
194	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
195	C₈×C₄₇	—	4	4	no	—
196	#18318	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
197	C₂²×C₄₇	—	2	1	no	—
198	C₂²×C₄₇	—	2	1	no	—
199	C₂²×C₄₇	—	2	1	no	—
200	C₂²×C₄₇	—	2	1	no	—
201	C₂²×C₄₇	—	2	1	no	—
202	C₂²×C₄₇	—	2	4	no	—
203	C₂²×C₄₇	—	2	1	no	—
204	C₂²×C₄₇	—	2	1	no	—
205	C₂²×C₄₇	—	4	4	no	—
206	C₂²×C₄₇	—	4	4	no	—
207	C₂²×C₄₇	—	4	8	no	—
208	C₂²×C₄₇	—	4	2	no	—
209	C₂²×C₄₇	—	4	2	no	—
210	C₂²×C₄₇	—	8	2	no	—
211	C₂²×C₄₇	—	8	2	no	—
212	C₂²×C₄₇	—	8	2	no	—
213	C₂²×C₄₇	—	8	4	no	—
214	C₂²×C₄₇	—	8	1	no	—
215	C₂²×C₄₇	—	8	1	no	—
216	C₂²×C₄₇	—	8	1	no	—
217	C₂²×C₄₇	#453	1	2	yes	—
218	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
219	C₂²×C₄₇	C₂×#137	1	2	yes	—
220	C₄×C₄₇	—	2	2	no	—
221	C₄×C₄₇	—	2	2	no	—
222	C₄×C₄₇	—	4	4	no	—
223	C₄×C₄₇	—	4	2	no	—
224	C₄×C₄₇	—	4	4	no	—
225	C₄×C₄₇	—	4	4	no	—
226	C₄×C₄₇	—	8	1	no	—
227	C₂×#543	C₂×C₄₇	1	1	yes	characteristic, complemented
228	#3193	C₂×C₄₇	1	2	yes	complemented
229	#2539	C₂×C₄₇	1	1	yes	characteristic
230	#1614	C₂×C₄₇	1	4	yes	complemented
231	#1596	C₂×C₄₇	1	4	yes	complemented
232	#1508	C₂×C₄₇	1	2	yes	complemented
233	#1462	C₂×C₄₇	1	1	yes	characteristic, complemented
234	C₂×C₄₇	—	2	2	no	—
235	C₂×C₄₇	—	2	2	no	—
236	C₂×C₄₇	—	4	1	no	—
237	C₂×C₄₇	—	4	4	no	—
238	C₂×C₄₇	—	16	1	no	—
239	C₂×C₄₇	#3004	1	1	yes	characteristic
240	C₂×C₄₇	C₂×#453	1	1	yes	characteristic
241	C₂×C₄₇	#3026	1	1	yes	characteristic
242	#543	—	2	4	no	—
243	#543	—	2	2	no	—
244	#543	C₂²×C₄₇	1	4	yes	—
245	C₂×#123	—	2	1	no	—
246	C₂×C₂²⋊Q₈	—	2	2	no	—
247	C₂×C₂²⋊Q₈	—	2	1	no	—
248	C₂×C₂²⋊Q₈	—	2	2	no	—
249	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
250	C₂×#121	C₂²×C₄₇	1	1	yes	characteristic
251	C₂×#120	—	2	1	no	—
252	C₂²×C₂²⋊C₄	—	2	1	no	—
253	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
254	#484	C₂²×C₄₇	1	4	yes	complemented
255	#480	—	2	2	no	—
256	#468	—	2	4	no	—
257	#450	C₂²×C₄₇	1	4	yes	complemented
258	#448	—	2	2	no	—
259	#407	C₂²×C₄₇	1	2	yes	—
260	#399	C₂²×C₄₇	1	2	yes	—
261	#392	C₂²×C₄₇	1	2	yes	—
262	#390	—	2	2	no	—
263	C₄×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
264	#328	C₂²×C₄₇	1	8	yes	complemented
265	#323	C₂²×C₄₇	1	4	yes	—
266	C₄₇	#18318	1	1	yes	characteristic, direct product factor, Sylow
267	C₂⁵	D₄×C₄₇	1	1	yes	characteristic
268	C₂²×Q₈	—	2	1	no	—
269	C₂²×Q₈	D₄×C₄₇	1	2	yes	complemented
270	C₂²×D₄	—	2	1	no	—
271	C₂²×D₄	—	2	2	no	—
272	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
273	C₂³×C₄	—	2	1	no	—
274	C₂³×C₄	—	2	1	no	—
275	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
276	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
277	C₂×SD₁₆	—	2	4	no	—
278	C₂×M₁₆	—	2	2	no	—
279	#123	—	4	4	no	—
280	C₂²⋊Q₈	—	2	8	no	—
281	C₂²⋊Q₈	—	2	8	no	—
282	C₂²⋊Q₈	—	2	4	no	—
283	C₂²⋊Q₈	—	2	8	no	—
284	C₂²⋊Q₈	—	2	4	no	—
285	C₂²⋊Q₈	—	2	2	no	—
286	C₂²⋊Q₈	—	2	2	no	—
287	C₂²⋊Q₈	—	2	8	no	—
288	C₂²⋊Q₈	D₄×C₄₇	1	4	yes	complemented
289	C₂²⋊Q₈	C₂³×C₄₇	1	4	yes	—
290	#121	—	2	2	no	—
291	#121	—	2	2	no	—
292	#120	—	4	4	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	—	2	2	no	—
297	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	complemented
298	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
299	C₂×C₂²⋊C₄	—	2	2	no	—
300	C₂×C₂²⋊C₄	—	2	4	no	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	4	no	—
303	C₂×C₂²⋊C₄	—	2	1	no	—
304	C₂×C₂²⋊C₄	—	2	2	no	—
305	C₂×C₂²⋊C₄	—	2	2	no	—
306	C₂×C₂²⋊C₄	—	2	2	no	—
307	C₂×C₂²⋊C₄	—	2	1	no	—
308	C₂×C₂²⋊C₄	—	2	2	no	—
309	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
310	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
311	C₂×C₄²	—	2	1	no	—
312	#107	—	2	4	no	—
313	#103	—	2	4	no	—
314	#102	—	2	4	no	—
315	C₂²⋊C₈	—	2	2	no	—
316	C₂²⋊C₈	C₂³×C₄₇	1	4	yes	—
317	#95	C₂³×C₄₇	1	2	yes	—
318	C₂⁴	—	2	1	no	—
319	C₂⁴	—	2	1	no	—
320	C₂⁴	—	2	4	no	—
321	C₂⁴	—	2	1	no	—
322	C₂⁴	—	4	2	no	—
323	C₂⁴	—	8	1	no	—
324	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
325	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
326	C₂×Q₈	—	2	4	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	8	2	no	—
329	C₂×Q₈	—	8	2	no	—
330	C₂×Q₈	C₂×D₄×C₄₇	1	4	yes	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	4	4	no	—
333	C₂×D₄	—	4	2	no	—
334	C₂×D₄	—	4	2	no	—
335	C₂×D₄	—	4	1	no	—
336	C₂×D₄	—	4	1	no	—
337	C₂×D₄	—	4	4	no	—
338	C₂×D₄	—	8	1	no	—
339	C₂×D₄	—	8	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	4	no	—
345	C₂²×C₄	—	2	4	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	8	1	no	—
350	C₂²×C₄	—	8	2	no	—
351	C₂²×C₄	—	8	2	no	—
352	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
355	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
356	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
357	SD₁₆	—	8	4	no	—
358	M₁₆	—	8	2	no	—
359	C₂×C₈	—	2	4	no	—
360	C₄⋊C₄	—	2	4	no	—
361	C₄⋊C₄	—	2	8	no	—
362	C₄⋊C₄	—	2	4	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	4	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	4	4	no	—
367	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
368	C₂²⋊C₄	—	2	8	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	2	4	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	2	4	no	—
374	C₂²⋊C₄	—	4	4	no	—
375	C₂²⋊C₄	—	4	4	no	—
376	C₂²⋊C₄	—	4	2	no	—
377	C₄²	—	8	1	no	—
378	C₂³	—	2	4	no	—
379	C₂³	—	2	4	no	—
380	C₂³	—	2	2	no	—
381	C₂³	—	2	2	no	—
382	C₂³	—	2	2	no	—
383	C₂³	—	2	2	no	—
384	C₂³	—	4	1	no	—
385	C₂³	—	4	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	2	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	1	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	2	no	—
394	C₂³	—	8	1	no	—
395	C₂³	—	8	1	no	—
396	C₂³	—	8	8	no	—
397	C₂³	#120×C₄₇	1	1	yes	characteristic
398	C₂³	#120×C₄₇	1	1	yes	characteristic
399	C₂³	#137×C₄₇	1	4	yes	—
400	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
401	Q₈	—	4	4	no	—
402	Q₈	—	8	2	no	—
403	Q₈	—	8	4	no	—
404	D₄	—	4	4	no	—
405	D₄	—	8	8	no	—
406	D₄	—	8	2	no	—
407	D₄	—	8	2	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	2	no	—
411	C₂×C₄	—	2	4	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	4	no	—
418	C₂×C₄	—	4	2	no	—
419	C₂×C₄	—	4	4	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	—	8	1	no	—
426	C₂×C₄	—	8	4	no	—
427	C₂×C₄	—	8	4	no	—
428	C₂×C₄	#120×C₄₇	1	2	yes	—
429	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
430	C₈	—	4	4	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	2	1	no	—
434	C₂²	—	2	1	no	—
435	C₂²	—	2	1	no	—
436	C₂²	—	2	4	no	—
437	C₂²	—	2	1	no	—
438	C₂²	—	2	1	no	—
439	C₂²	—	4	4	no	—
440	C₂²	—	4	4	no	—
441	C₂²	—	4	8	no	—
442	C₂²	—	4	2	no	—
443	C₂²	—	4	2	no	—
444	C₂²	—	8	2	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	8	4	no	—
448	C₂²	—	8	1	no	—
449	C₂²	—	8	1	no	—
450	C₂²	—	8	1	no	—
451	C₂²	C₄₇×#453	1	2	yes	—
452	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
453	C₂²	C₂×#137×C₄₇	1	2	yes	—
454	C₄	—	2	2	no	—
455	C₄	—	2	2	no	—
456	C₄	—	4	4	no	—
457	C₄	—	4	2	no	—
458	C₄	—	4	4	no	—
459	C₄	—	4	4	no	—
460	C₄	—	8	1	no	—
461	C₂	—	2	2	no	—
462	C₂	—	2	2	no	—
463	C₂	—	4	1	no	—
464	C₂	—	4	4	no	—
465	C₂	—	16	1	no	—
466	C₂	C₄₇×#3004	1	1	yes	characteristic
467	C₂	C₂×C₄₇×#453	1	1	yes	characteristic
468	C₂	C₄₇×#3026	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₄₇×#2539	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂³×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₇×#543	C₂	semidirect
2. C₄₇×#3193	C₂	semidirect
4. C₄₇×#1614	C₂	semidirect
5. C₄₇×#1596	C₂	semidirect
6. C₄₇×#1508	C₂	semidirect
7. C₄₇×#1462	C₂	semidirect
20. C₄₇×#484	C₂²	semidirect
23. C₄₇×#450	C₂²	semidirect
30. C₄₇×#328	C₂²	semidirect
34. C₂²×Q₈×C₄₇	D₄	semidirect
53. C₂²⋊Q₈×C₄₇	D₄	semidirect
62. C₂×C₄⋊C₄×C₄₇	D₄	semidirect
196. #18318	C₄₇	direct (N × H)
227. C₂×#543	C₂×C₄₇	semidirect
228. #3193	C₂×C₄₇	semidirect
230. #1614	C₂×C₄₇	semidirect
231. #1596	C₂×C₄₇	semidirect
232. #1508	C₂×C₄₇	semidirect
233. #1462	C₂×C₄₇	semidirect
254. #484	C₂²×C₄₇	semidirect
257. #450	C₂²×C₄₇	semidirect
264. #328	C₂²×C₄₇	semidirect
266. C₄₇	#18318	direct (N × H)
269. C₂²×Q₈	D₄×C₄₇	semidirect
288. C₂²⋊Q₈	D₄×C₄₇	semidirect
297. C₂×C₄⋊C₄	D₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#543	2
C₄₇×#3193	2
C₄₇×#2539	2
C₄₇×#1614	2
C₄₇×#1596	2
C₄₇×#1508	2
C₄₇×#1462	2
#18318	47

Subgroups — C47×#18318 #26058016

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18318 #26058016