Subgroups — C₄₇×#24481 #26064179

Order 12032.

1012 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#480	C₂	1	1	yes	maximal, characteristic
2	C₂²×#103×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2436	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#2344	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2068	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2042	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1983	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1928	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1893	C₂	1	1	yes	maximal, characteristic
10	C₄₇×#1850	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1787	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×#124×C₄₇	C₂²	1	2	yes	—
15	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#117×C₄₇	—	2	1	no	—
17	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#480	—	2	4	no	—
19	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
22	C₂×#103×C₄₇	—	2	4	no	—
23	C₂×#103×C₄₇	C₂²	1	2	yes	—
24	C₂×#103×C₄₇	C₂²	1	2	yes	—
25	C₂×#103×C₄₇	C₂²	1	2	yes	—
26	C₂×#103×C₄₇	C₂²	1	2	yes	—
27	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×#102×C₄₇	C₂²	1	2	yes	—
30	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#393	—	2	2	no	—
32	C₄₇×#391	C₂²	1	2	yes	—
33	C₄₇×#389	C₂²	1	2	yes	—
34	C₄₇×#387	—	2	2	no	—
35	C₄₇×#386	—	2	1	no	—
36	C₄₇×#386	—	2	1	no	—
37	C₄₇×#381	—	2	1	no	—
38	C₄₇×#380	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
40	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#340	C₂²	1	2	yes	—
42	C₄₇×#336	C₂²	1	2	yes	—
43	C₂²×Q₈×C₄₇	—	2	1	no	—
44	C₂²×Q₈×C₄₇	—	2	4	no	—
45	C₂²×Q₈×C₄₇	—	2	2	no	—
46	C₂²×Q₈×C₄₇	—	2	2	no	—
47	C₂²×Q₈×C₄₇	—	4	2	no	—
48	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
49	C₂²×D₄×C₄₇	—	2	1	no	—
50	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	—	2	1	no	—
52	C₂³×C₄×C₄₇	—	2	1	no	—
53	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₄₇	—	2	2	no	—
55	C₂²×C₈×C₄₇	—	4	2	no	—
56	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
57	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
59	#124×C₄₇	—	2	4	no	—
60	#124×C₄₇	—	4	2	no	—
61	#121×C₄₇	—	2	2	no	—
62	#121×C₄₇	—	2	2	no	—
63	#117×C₄₇	—	4	4	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
67	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
68	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
69	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₇	D₄	1	1	yes	characteristic
77	C₂×C₂²⋊C₄×C₄₇	D₄	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	—	2	2	no	—
79	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
80	#107×C₄₇	—	2	2	no	—
81	#107×C₄₇	—	2	2	no	—
82	C₄⋊C₈×C₄₇	—	4	2	no	—
83	#103×C₄₇	—	2	4	no	—
84	#103×C₄₇	—	2	4	no	—
85	#103×C₄₇	—	2	4	no	—
86	#103×C₄₇	—	4	2	no	—
87	#102×C₄₇	—	2	2	no	—
88	#102×C₄₇	—	2	2	no	—
89	#102×C₄₇	—	4	2	no	—
90	C₂²⋊C₈×C₄₇	—	2	2	no	—
91	#95×C₄₇	—	2	2	no	—
92	#95×C₄₇	—	2	1	no	—
93	#95×C₄₇	—	2	2	no	—
94	#95×C₄₇	—	2	2	no	—
95	#95×C₄₇	—	2	2	no	—
96	#95×C₄₇	D₄	1	2	yes	—
97	C₂⁴×C₄₇	—	2	1	no	—
98	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂×Q₈×C₄₇	—	2	2	no	—
100	C₂×Q₈×C₄₇	—	2	8	no	—
101	C₂×Q₈×C₄₇	—	2	2	no	—
102	C₂×Q₈×C₄₇	—	2	2	no	—
103	C₂×Q₈×C₄₇	—	2	2	no	—
104	C₂×Q₈×C₄₇	—	2	2	no	—
105	C₂×Q₈×C₄₇	—	4	4	no	—
106	C₂×Q₈×C₄₇	—	4	8	no	—
107	C₂×Q₈×C₄₇	—	4	4	no	—
108	C₂×Q₈×C₄₇	—	4	2	no	—
109	C₂×Q₈×C₄₇	#41	1	4	yes	—
110	C₂×D₄×C₄₇	—	2	1	no	—
111	C₂×D₄×C₄₇	—	2	1	no	—
112	C₂×D₄×C₄₇	—	2	2	no	—
113	C₂×D₄×C₄₇	—	2	2	no	—
114	C₂×D₄×C₄₇	—	4	2	no	—
115	C₂×D₄×C₄₇	—	4	2	no	—
116	C₂×D₄×C₄₇	—	4	2	no	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	—	2	2	no	—
119	C₂²×C₄×C₄₇	—	2	4	no	—
120	C₂²×C₄×C₄₇	—	2	1	no	—
121	C₂²×C₄×C₄₇	—	2	2	no	—
122	C₂²×C₄×C₄₇	—	2	1	no	—
123	C₂²×C₄×C₄₇	—	2	2	no	—
124	C₂²×C₄×C₄₇	—	2	1	no	—
125	C₂²×C₄×C₄₇	—	4	4	no	—
126	C₂²×C₄×C₄₇	—	4	2	no	—
127	C₂²×C₄×C₄₇	—	4	2	no	—
128	C₂²×C₄×C₄₇	—	4	2	no	—
129	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₄₇	#41	1	2	yes	—
134	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
135	C₂×C₈×C₄₇	—	2	2	no	—
136	C₂×C₈×C₄₇	—	2	1	no	—
137	C₂×C₈×C₄₇	—	2	1	no	—
138	C₂×C₈×C₄₇	—	2	2	no	—
139	C₂×C₈×C₄₇	—	2	2	no	—
140	C₂×C₈×C₄₇	—	2	2	no	—
141	C₂×C₈×C₄₇	—	2	2	no	—
142	C₂×C₈×C₄₇	—	4	4	no	—
143	C₄⋊C₄×C₄₇	—	2	4	no	—
144	C₄⋊C₄×C₄₇	—	2	1	no	—
145	C₄⋊C₄×C₄₇	—	2	1	no	—
146	C₄⋊C₄×C₄₇	—	2	1	no	—
147	C₄⋊C₄×C₄₇	—	2	2	no	—
148	C₄⋊C₄×C₄₇	—	2	1	no	—
149	C₄⋊C₄×C₄₇	—	2	2	no	—
150	C₄⋊C₄×C₄₇	—	4	4	no	—
151	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
152	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
153	C₂²⋊C₄×C₄₇	—	2	2	no	—
154	C₂²⋊C₄×C₄₇	—	2	2	no	—
155	C₂²⋊C₄×C₄₇	—	4	4	no	—
156	C₂²⋊C₄×C₄₇	—	4	4	no	—
157	C₂²⋊C₄×C₄₇	—	4	2	no	—
158	C₂²⋊C₄×C₄₇	—	4	2	no	—
159	C₄²×C₄₇	—	2	2	no	—
160	C₄²×C₄₇	—	2	2	no	—
161	C₄²×C₄₇	—	4	4	no	—
162	C₂³×C₄₇	—	2	2	no	—
163	C₂³×C₄₇	—	2	2	no	—
164	C₂³×C₄₇	—	4	1	no	—
165	C₂³×C₄₇	—	4	2	no	—
166	C₂³×C₄₇	—	4	1	no	—
167	C₂³×C₄₇	—	4	1	no	—
168	C₂³×C₄₇	—	4	2	no	—
169	C₂³×C₄₇	#121	1	2	yes	—
170	C₂³×C₄₇	#135	1	2	yes	—
171	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
172	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
173	Q₈×C₄₇	—	2	4	no	—
174	Q₈×C₄₇	—	2	4	no	—
175	Q₈×C₄₇	—	4	8	no	—
176	Q₈×C₄₇	—	4	2	no	—
177	Q₈×C₄₇	—	4	2	no	—
178	D₄×C₄₇	—	4	1	no	—
179	D₄×C₄₇	—	4	1	no	—
180	D₄×C₄₇	—	4	2	no	—
181	D₄×C₄₇	—	8	4	no	—
182	C₂×C₄×C₄₇	—	2	2	no	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	2	2	no	—
185	C₂×C₄×C₄₇	—	2	4	no	—
186	C₂×C₄×C₄₇	—	2	2	no	—
187	C₂×C₄×C₄₇	—	2	2	no	—
188	C₂×C₄×C₄₇	—	2	2	no	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	4	no	—
191	C₂×C₄×C₄₇	—	2	2	no	—
192	C₂×C₄×C₄₇	—	2	2	no	—
193	C₂×C₄×C₄₇	—	2	2	no	—
194	C₂×C₄×C₄₇	—	2	2	no	—
195	C₂×C₄×C₄₇	—	4	8	no	—
196	C₂×C₄×C₄₇	—	4	2	no	—
197	C₂×C₄×C₄₇	—	4	2	no	—
198	C₂×C₄×C₄₇	—	4	1	no	—
199	C₂×C₄×C₄₇	—	4	1	no	—
200	C₂×C₄×C₄₇	—	4	1	no	—
201	C₂×C₄×C₄₇	—	4	1	no	—
202	C₂×C₄×C₄₇	—	4	8	no	—
203	C₂×C₄×C₄₇	—	4	1	no	—
204	C₂×C₄×C₄₇	—	4	2	no	—
205	C₂×C₄×C₄₇	—	4	1	no	—
206	C₂×C₄×C₄₇	—	4	2	no	—
207	C₂×C₄×C₄₇	—	4	1	no	—
208	C₂×C₄×C₄₇	—	4	2	no	—
209	C₂×C₄×C₄₇	#121	1	2	yes	—
210	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
212	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
213	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
214	C₈×C₄₇	—	4	1	no	—
215	C₈×C₄₇	—	4	1	no	—
216	C₈×C₄₇	—	4	2	no	—
217	#24481	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂²×C₄₇	—	2	2	no	—
219	C₂²×C₄₇	—	2	2	no	—
220	C₂²×C₄₇	—	2	4	no	—
221	C₂²×C₄₇	—	2	4	no	—
222	C₂²×C₄₇	—	8	1	no	—
223	C₂²×C₄₇	—	8	1	no	—
224	C₂²×C₄₇	—	8	1	no	—
225	C₂²×C₄₇	—	8	2	no	—
226	C₂²×C₄₇	—	8	2	no	—
227	C₂²×C₄₇	#463	1	4	yes	—
228	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
229	C₂²×C₄₇	#546	1	2	yes	—
230	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
231	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
232	C₂²×C₄₇	#578	1	2	yes	—
233	C₄×C₄₇	—	2	2	no	—
234	C₄×C₄₇	—	4	4	no	—
235	C₄×C₄₇	—	4	2	no	—
236	C₄×C₄₇	—	4	2	no	—
237	C₄×C₄₇	—	4	2	no	—
238	C₄×C₄₇	—	4	2	no	—
239	C₄×C₄₇	—	8	1	no	—
240	C₄×C₄₇	—	8	2	no	—
241	C₄×C₄₇	#525	1	1	yes	characteristic
242	C₄×C₄₇	#535	1	1	yes	characteristic
243	C₄×C₄₇	#551	1	2	yes	—
244	C₂×#480	C₂×C₄₇	1	1	yes	characteristic
245	C₂²×#103	C₂×C₄₇	1	1	yes	characteristic, complemented
246	#2436	C₂×C₄₇	1	1	yes	characteristic
247	#2344	C₂×C₄₇	1	1	yes	characteristic, complemented
248	#2068	C₂×C₄₇	1	2	yes	complemented
249	#2042	C₂×C₄₇	1	2	yes	complemented
250	#1983	C₂×C₄₇	1	2	yes	complemented
251	#1928	C₂×C₄₇	1	2	yes	complemented
252	#1893	C₂×C₄₇	1	1	yes	characteristic
253	#1850	C₂×C₄₇	1	1	yes	characteristic, complemented
254	#1787	C₂×C₄₇	1	1	yes	characteristic, complemented
255	C₂×C₄₇	—	2	4	no	—
256	C₂×C₄₇	—	16	1	no	—
257	C₂×C₄₇	#2411	1	1	yes	characteristic
258	C₂×C₄₇	C₂×#463	1	1	yes	characteristic
259	C₂×C₄₇	#3044	1	1	yes	characteristic
260	C₂×C₄₇	#3300	1	2	yes	—
261	C₂×C₄₇	#3308	1	2	yes	—
262	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
263	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
264	C₂×#124	C₂²×C₄₇	1	2	yes	—
265	C₂×#121	C₂²×C₄₇	1	1	yes	characteristic
266	C₂×#117	—	2	1	no	—
267	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
268	#480	—	2	4	no	—
269	C₂×#107	C₂²×C₄₇	1	1	yes	characteristic
270	C₂×#107	C₂²×C₄₇	1	1	yes	characteristic
271	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
272	C₂×#103	—	2	4	no	—
273	C₂×#103	C₂²×C₄₇	1	2	yes	—
274	C₂×#103	C₂²×C₄₇	1	2	yes	—
275	C₂×#103	C₂²×C₄₇	1	2	yes	—
276	C₂×#103	C₂²×C₄₇	1	2	yes	—
277	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic
278	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic
279	C₂×#102	C₂²×C₄₇	1	2	yes	—
280	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
281	#393	—	2	2	no	—
282	#391	C₂²×C₄₇	1	2	yes	—
283	#389	C₂²×C₄₇	1	2	yes	—
284	#387	—	2	2	no	—
285	#386	—	2	1	no	—
286	#386	—	2	1	no	—
287	#381	—	2	1	no	—
288	#380	C₂²×C₄₇	1	1	yes	characteristic
289	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
290	C₄×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
291	#340	C₂²×C₄₇	1	2	yes	—
292	#336	C₂²×C₄₇	1	2	yes	—
293	C₄₇	#24481	1	1	yes	characteristic, direct product factor, Sylow
294	C₂²×Q₈	—	2	1	no	—
295	C₂²×Q₈	—	2	4	no	—
296	C₂²×Q₈	—	2	2	no	—
297	C₂²×Q₈	—	2	2	no	—
298	C₂²×Q₈	—	4	2	no	—
299	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
300	C₂²×D₄	—	2	1	no	—
301	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
302	C₂³×C₄	—	2	1	no	—
303	C₂³×C₄	—	2	1	no	—
304	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
305	C₂²×C₈	—	2	2	no	—
306	C₂²×C₈	—	4	2	no	—
307	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
308	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
309	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
310	#124	—	2	4	no	—
311	#124	—	4	2	no	—
312	#121	—	2	2	no	—
313	#121	—	2	2	no	—
314	#117	—	4	4	no	—
315	C₂×C₄⋊C₄	—	2	1	no	—
316	C₂×C₄⋊C₄	—	2	2	no	—
317	C₂×C₄⋊C₄	—	2	2	no	—
318	C₂×C₄⋊C₄	D₄×C₄₇	1	4	yes	—
319	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
320	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
321	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
323	C₂×C₂²⋊C₄	—	2	1	no	—
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₂²⋊C₄	—	2	2	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	D₄×C₄₇	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	D₄×C₄₇	1	1	yes	characteristic
329	C₂×C₄²	—	2	2	no	—
330	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
331	#107	—	2	2	no	—
332	#107	—	2	2	no	—
333	C₄⋊C₈	—	4	2	no	—
334	#103	—	2	4	no	—
335	#103	—	2	4	no	—
336	#103	—	2	4	no	—
337	#103	—	4	2	no	—
338	#102	—	2	2	no	—
339	#102	—	2	2	no	—
340	#102	—	4	2	no	—
341	C₂²⋊C₈	—	2	2	no	—
342	#95	—	2	2	no	—
343	#95	—	2	1	no	—
344	#95	—	2	2	no	—
345	#95	—	2	2	no	—
346	#95	—	2	2	no	—
347	#95	D₄×C₄₇	1	2	yes	—
348	C₂⁴	—	2	1	no	—
349	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	8	no	—
352	C₂×Q₈	—	2	2	no	—
353	C₂×Q₈	—	2	2	no	—
354	C₂×Q₈	—	2	2	no	—
355	C₂×Q₈	—	2	2	no	—
356	C₂×Q₈	—	4	4	no	—
357	C₂×Q₈	—	4	8	no	—
358	C₂×Q₈	—	4	4	no	—
359	C₂×Q₈	—	4	2	no	—
360	C₂×Q₈	#41×C₄₇	1	4	yes	—
361	C₂×D₄	—	2	1	no	—
362	C₂×D₄	—	2	1	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	4	2	no	—
366	C₂×D₄	—	4	2	no	—
367	C₂×D₄	—	4	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	4	4	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	—	4	2	no	—
380	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
382	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
384	C₂²×C₄	#41×C₄₇	1	2	yes	—
385	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	4	4	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	1	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	4	4	no	—
402	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
403	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
404	C₂²⋊C₄	—	2	2	no	—
405	C₂²⋊C₄	—	2	2	no	—
406	C₂²⋊C₄	—	4	4	no	—
407	C₂²⋊C₄	—	4	4	no	—
408	C₂²⋊C₄	—	4	2	no	—
409	C₂²⋊C₄	—	4	2	no	—
410	C₄²	—	2	2	no	—
411	C₄²	—	2	2	no	—
412	C₄²	—	4	4	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	4	1	no	—
418	C₂³	—	4	1	no	—
419	C₂³	—	4	2	no	—
420	C₂³	#121×C₄₇	1	2	yes	—
421	C₂³	#135×C₄₇	1	2	yes	—
422	C₂³	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
423	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
424	Q₈	—	2	4	no	—
425	Q₈	—	2	4	no	—
426	Q₈	—	4	8	no	—
427	Q₈	—	4	2	no	—
428	Q₈	—	4	2	no	—
429	D₄	—	4	1	no	—
430	D₄	—	4	1	no	—
431	D₄	—	4	2	no	—
432	D₄	—	8	4	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	2	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	4	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	2	no	—
446	C₂×C₄	—	4	8	no	—
447	C₂×C₄	—	4	8	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	#121×C₄₇	1	2	yes	—
461	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
462	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
463	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
464	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
465	C₈	—	4	1	no	—
466	C₈	—	4	1	no	—
467	C₈	—	4	2	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	4	no	—
470	C₂²	—	2	4	no	—
471	C₂²	—	2	2	no	—
472	C₂²	—	8	1	no	—
473	C₂²	—	8	1	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	1	no	—
477	C₂²	C₄₇×#463	1	4	yes	—
478	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
479	C₂²	C₄₇×#546	1	2	yes	—
480	C₂²	C₂×#135×C₄₇	1	1	yes	characteristic
481	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
482	C₂²	C₄₇×#578	1	2	yes	—
483	C₄	—	2	2	no	—
484	C₄	—	4	2	no	—
485	C₄	—	4	2	no	—
486	C₄	—	4	2	no	—
487	C₄	—	4	2	no	—
488	C₄	—	4	4	no	—
489	C₄	—	8	1	no	—
490	C₄	—	8	2	no	—
491	C₄	C₄₇×#525	1	1	yes	characteristic
492	C₄	C₄₇×#535	1	1	yes	characteristic
493	C₄	C₄₇×#551	1	2	yes	—
494	C₂	—	2	4	no	—
495	C₂	—	16	1	no	—
496	C₂	C₄₇×#2411	1	1	yes	characteristic
497	C₂	C₂×C₄₇×#463	1	1	yes	characteristic
498	C₂	C₄₇×#3044	1	1	yes	characteristic
499	C₂	C₄₇×#3300	1	2	yes	—
500	C₂	C₄₇×#3308	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×#121×C₄₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₄×C₂²⋊C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#103×C₄₇	C₂	semidirect
4. C₄₇×#2344	C₂	semidirect
5. C₄₇×#2068	C₂	semidirect
6. C₄₇×#2042	C₂	semidirect
7. C₄₇×#1983	C₂	semidirect
8. C₄₇×#1928	C₂	semidirect
10. C₄₇×#1850	C₂	semidirect
11. C₄₇×#1787	C₂	semidirect
217. #24481	C₄₇	direct (N × H)
245. C₂²×#103	C₂×C₄₇	semidirect
247. #2344	C₂×C₄₇	semidirect
248. #2068	C₂×C₄₇	semidirect
249. #2042	C₂×C₄₇	semidirect
250. #1983	C₂×C₄₇	semidirect
251. #1928	C₂×C₄₇	semidirect
253. #1850	C₂×C₄₇	semidirect
254. #1787	C₂×C₄₇	semidirect
293. C₄₇	#24481	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×#480	2
C₂²×#103×C₄₇	2
C₄₇×#2436	2
C₄₇×#2344	2
C₄₇×#2068	2
C₄₇×#2042	2
C₄₇×#1983	2
C₄₇×#1928	2
C₄₇×#1893	2
C₄₇×#1850	2
C₄₇×#1787	2
#24481	47

Subgroups — C47×#24481 #26064179

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#24481 #26064179