Subgroups — C₄₇×#24493 #26064191

Order 12032.

1068 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#485	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₇×#418	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2435	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#2347	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2065	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×#1925	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1894	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1851	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1786	C₂	1	1	yes	maximal, characteristic
12	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×#124×C₄₇	C₂²	1	2	yes	—
15	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
17	C₄₇×#485	—	2	4	no	—
18	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic, complemented
19	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic, complemented
20	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	complemented
21	C₄₇×#418	—	2	4	no	—
22	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic, complemented
23	C₂×#103×C₄₇	C₂²	1	1	yes	characteristic, complemented
24	C₂×#103×C₄₇	C₂²	1	2	yes	complemented
25	C₂×#102×C₄₇	C₂²	1	2	yes	—
26	C₂×#102×C₄₇	C₂²	1	2	yes	—
27	C₂×#102×C₄₇	C₂²	1	2	yes	—
28	C₂×#102×C₄₇	C₂²	1	2	yes	—
29	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
30	C₄₇×#394	—	2	1	no	—
31	C₄₇×#394	—	2	1	no	—
32	C₄₇×#390	C₂²	1	2	yes	—
33	C₄₇×#389	C₂²	1	2	yes	complemented
34	C₄₇×#388	—	2	2	no	—
35	C₄₇×#383	—	2	1	no	—
36	C₄₇×#380	C₂²	1	1	yes	characteristic
37	C₄₇×#379	—	2	2	no	—
38	C₄×C₄⋊C₄×C₄₇	—	2	1	no	—
39	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
40	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
41	C₄₇×#340	C₂²	1	2	yes	complemented
42	C₄₇×#336	C₂²	1	2	yes	complemented
43	C₂⁵×C₄₇	—	2	1	no	—
44	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
45	C₂²×D₄×C₄₇	—	2	4	no	—
46	C₂²×D₄×C₄₇	—	2	2	no	—
47	C₂²×D₄×C₄₇	—	2	1	no	—
48	C₂²×D₄×C₄₇	—	2	2	no	—
49	C₂²×D₄×C₄₇	—	4	2	no	—
50	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
51	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
52	C₂×M₁₆×C₄₇	—	2	2	no	—
53	C₂×M₁₆×C₄₇	—	4	2	no	—
54	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
55	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
57	#124×C₄₇	—	2	4	no	—
58	#124×C₄₇	—	4	2	no	—
59	C₂²⋊Q₈×C₄₇	—	2	2	no	—
60	C₂²⋊Q₈×C₄₇	—	2	2	no	—
61	#117×C₄₇	—	2	2	no	—
62	#117×C₄₇	D₄	1	4	yes	—
63	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
69	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
70	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
71	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₇	—	2	2	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	2	yes	—
77	C₂×C₄²×C₄₇	—	2	1	no	—
78	C₂×C₄²×C₄₇	—	2	2	no	—
79	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
80	#107×C₄₇	—	2	2	no	—
81	#106×C₄₇	—	2	2	no	—
82	C₄⋊C₈×C₄₇	—	4	2	no	—
83	#103×C₄₇	—	2	2	no	—
84	#103×C₄₇	—	2	2	no	—
85	#103×C₄₇	—	4	2	no	—
86	#102×C₄₇	—	2	4	no	—
87	#102×C₄₇	—	2	4	no	—
88	#102×C₄₇	—	2	4	no	—
89	#102×C₄₇	—	4	2	no	—
90	C₂²⋊C₈×C₄₇	—	2	2	no	—
91	#95×C₄₇	—	2	1	no	—
92	#95×C₄₇	—	2	2	no	—
93	#95×C₄₇	—	2	2	no	—
94	#95×C₄₇	D₄	1	1	yes	characteristic
95	#95×C₄₇	D₄	1	1	yes	characteristic
96	C₂⁴×C₄₇	—	2	2	no	—
97	C₂⁴×C₄₇	—	4	4	no	—
98	C₂⁴×C₄₇	—	4	4	no	—
99	C₂⁴×C₄₇	—	4	2	no	—
100	C₂⁴×C₄₇	—	8	1	no	—
101	C₂⁴×C₄₇	—	8	1	no	—
102	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
103	C₂×Q₈×C₄₇	—	2	1	no	—
104	C₂×Q₈×C₄₇	—	2	1	no	—
105	C₂×Q₈×C₄₇	—	2	2	no	—
106	C₂×Q₈×C₄₇	—	2	2	no	—
107	C₂×D₄×C₄₇	—	2	8	no	—
108	C₂×D₄×C₄₇	—	2	2	no	—
109	C₂×D₄×C₄₇	—	2	2	no	—
110	C₂×D₄×C₄₇	—	2	2	no	—
111	C₂×D₄×C₄₇	—	2	2	no	—
112	C₂×D₄×C₄₇	—	2	2	no	—
113	C₂×D₄×C₄₇	—	4	8	no	—
114	C₂×D₄×C₄₇	—	4	4	no	—
115	C₂×D₄×C₄₇	—	4	4	no	—
116	C₂×D₄×C₄₇	—	4	2	no	—
117	C₂×D₄×C₄₇	#41	1	4	yes	—
118	C₂²×C₄×C₄₇	—	2	2	no	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	2	1	no	—
121	C₂²×C₄×C₄₇	—	2	1	no	—
122	C₂²×C₄×C₄₇	—	2	2	no	—
123	C₂²×C₄×C₄₇	—	2	1	no	—
124	C₂²×C₄×C₄₇	—	2	1	no	—
125	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
127	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₄₇	#41	1	2	yes	—
130	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
131	M₁₆×C₄₇	—	4	4	no	—
132	C₂×C₈×C₄₇	—	2	1	no	—
133	C₂×C₈×C₄₇	—	2	1	no	—
134	C₂×C₈×C₄₇	—	2	2	no	—
135	C₂×C₈×C₄₇	—	2	2	no	—
136	C₂×C₈×C₄₇	—	2	2	no	—
137	C₂×C₈×C₄₇	—	2	2	no	—
138	C₂×C₈×C₄₇	—	2	2	no	—
139	C₄⋊C₄×C₄₇	—	2	1	no	—
140	C₄⋊C₄×C₄₇	—	2	1	no	—
141	C₄⋊C₄×C₄₇	—	2	1	no	—
142	C₄⋊C₄×C₄₇	—	2	1	no	—
143	C₄⋊C₄×C₄₇	—	2	2	no	—
144	C₄⋊C₄×C₄₇	—	2	2	no	—
145	C₄⋊C₄×C₄₇	—	4	4	no	—
146	C₄⋊C₄×C₄₇	—	4	2	no	—
147	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
148	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
149	C₂²⋊C₄×C₄₇	—	2	4	no	—
150	C₂²⋊C₄×C₄₇	—	4	2	no	—
151	C₂²⋊C₄×C₄₇	—	4	4	no	—
152	C₂²⋊C₄×C₄₇	—	4	4	no	—
153	C₂²⋊C₄×C₄₇	—	4	2	no	—
154	C₂²⋊C₄×C₄₇	—	8	2	no	—
155	C₂²⋊C₄×C₄₇	—	8	2	no	—
156	C₂²⋊C₄×C₄₇	—	8	1	no	—
157	C₄²×C₄₇	—	2	4	no	—
158	C₄²×C₄₇	—	2	2	no	—
159	C₄²×C₄₇	—	2	2	no	—
160	C₄²×C₄₇	—	8	2	no	—
161	C₂³×C₄₇	—	2	2	no	—
162	C₂³×C₄₇	—	2	2	no	—
163	C₂³×C₄₇	—	2	1	no	—
164	C₂³×C₄₇	—	2	1	no	—
165	C₂³×C₄₇	—	2	4	no	—
166	C₂³×C₄₇	—	4	8	no	—
167	C₂³×C₄₇	—	4	2	no	—
168	C₂³×C₄₇	—	4	2	no	—
169	C₂³×C₄₇	—	4	2	no	—
170	C₂³×C₄₇	—	4	2	no	—
171	C₂³×C₄₇	—	4	2	no	—
172	C₂³×C₄₇	—	4	2	no	—
173	C₂³×C₄₇	—	8	4	no	—
174	C₂³×C₄₇	—	8	4	no	—
175	C₂³×C₄₇	—	8	8	no	—
176	C₂³×C₄₇	—	8	8	no	—
177	C₂³×C₄₇	#121	1	2	yes	—
178	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
179	Q₈×C₄₇	—	4	1	no	—
180	Q₈×C₄₇	—	4	1	no	—
181	Q₈×C₄₇	—	4	2	no	—
182	D₄×C₄₇	—	2	4	no	—
183	D₄×C₄₇	—	2	4	no	—
184	D₄×C₄₇	—	4	8	no	—
185	D₄×C₄₇	—	4	2	no	—
186	D₄×C₄₇	—	4	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	—	2	2	no	—
196	C₂×C₄×C₄₇	—	2	2	no	—
197	C₂×C₄×C₄₇	—	2	2	no	—
198	C₂×C₄×C₄₇	—	2	2	no	—
199	C₂×C₄×C₄₇	—	4	2	no	—
200	C₂×C₄×C₄₇	—	4	1	no	—
201	C₂×C₄×C₄₇	—	4	1	no	—
202	C₂×C₄×C₄₇	—	4	1	no	—
203	C₂×C₄×C₄₇	—	4	1	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	C₂×C₄×C₄₇	—	4	1	no	—
209	C₂×C₄×C₄₇	—	4	1	no	—
210	C₂×C₄×C₄₇	#121	1	2	yes	—
211	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
212	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
213	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
214	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
215	C₈×C₄₇	—	4	1	no	—
216	C₈×C₄₇	—	4	1	no	—
217	C₈×C₄₇	—	4	2	no	—
218	#24493	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
219	C₂²×C₄₇	—	2	2	no	—
220	C₂²×C₄₇	—	2	2	no	—
221	C₂²×C₄₇	—	2	2	no	—
222	C₂²×C₄₇	—	4	2	no	—
223	C₂²×C₄₇	—	4	2	no	—
224	C₂²×C₄₇	—	4	4	no	—
225	C₂²×C₄₇	—	4	4	no	—
226	C₂²×C₄₇	—	4	4	no	—
227	C₂²×C₄₇	—	8	16	no	—
228	C₂²×C₄₇	—	8	2	no	—
229	C₂²×C₄₇	—	8	2	no	—
230	C₂²×C₄₇	—	8	2	no	—
231	C₂²×C₄₇	—	8	2	no	—
232	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
233	C₂²×C₄₇	#546	1	2	yes	—
234	C₂²×C₄₇	#575	1	2	yes	—
235	C₂²×C₄₇	#576	1	1	yes	characteristic
236	C₂²×C₄₇	#577	1	1	yes	characteristic
237	C₄×C₄₇	—	2	2	no	—
238	C₄×C₄₇	—	4	2	no	—
239	C₄×C₄₇	—	4	2	no	—
240	C₄×C₄₇	—	4	2	no	—
241	C₄×C₄₇	—	4	2	no	—
242	C₄×C₄₇	—	8	1	no	—
243	C₄×C₄₇	—	8	1	no	—
244	C₄×C₄₇	—	8	2	no	—
245	C₄×C₄₇	#525	1	1	yes	characteristic
246	C₄×C₄₇	#535	1	1	yes	characteristic
247	C₄×C₄₇	#551	1	2	yes	—
248	C₂×#485	C₂×C₄₇	1	1	yes	characteristic, complemented
249	C₂×#418	C₂×C₄₇	1	1	yes	characteristic
250	#2435	C₂×C₄₇	1	1	yes	characteristic
251	#2347	C₂×C₄₇	1	1	yes	characteristic, complemented
252	#2065	C₂×C₄₇	1	2	yes	complemented
253	#2042	C₂×C₄₇	1	2	yes	complemented
254	#1983	C₂×C₄₇	1	2	yes	complemented
255	#1925	C₂×C₄₇	1	2	yes	complemented
256	#1894	C₂×C₄₇	1	1	yes	characteristic, complemented
257	#1851	C₂×C₄₇	1	1	yes	characteristic, complemented
258	#1786	C₂×C₄₇	1	1	yes	characteristic
259	C₂×C₄₇	—	4	2	no	—
260	C₂×C₄₇	—	8	4	no	—
261	C₂×C₄₇	#2411	1	1	yes	characteristic
262	C₂×C₄₇	#3040	1	1	yes	characteristic
263	C₂×C₄₇	#3045	1	1	yes	characteristic
264	C₂×C₄₇	#3311	1	2	yes	—
265	C₂×C₄₇	#3322	1	2	yes	—
266	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
267	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
268	C₂×#124	C₂²×C₄₇	1	2	yes	—
269	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
270	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
271	#485	—	2	4	no	—
272	C₂×#107	C₂²×C₄₇	1	1	yes	characteristic, complemented
273	C₂×#106	C₂²×C₄₇	1	1	yes	characteristic, complemented
274	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
275	#418	—	2	4	no	—
276	C₂×#103	C₂²×C₄₇	1	1	yes	characteristic, complemented
277	C₂×#103	C₂²×C₄₇	1	1	yes	characteristic, complemented
278	C₂×#103	C₂²×C₄₇	1	2	yes	complemented
279	C₂×#102	C₂²×C₄₇	1	2	yes	—
280	C₂×#102	C₂²×C₄₇	1	2	yes	—
281	C₂×#102	C₂²×C₄₇	1	2	yes	—
282	C₂×#102	C₂²×C₄₇	1	2	yes	—
283	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
284	#394	—	2	1	no	—
285	#394	—	2	1	no	—
286	#390	C₂²×C₄₇	1	2	yes	—
287	#389	C₂²×C₄₇	1	2	yes	complemented
288	#388	—	2	2	no	—
289	#383	—	2	1	no	—
290	#380	C₂²×C₄₇	1	1	yes	characteristic
291	#379	—	2	2	no	—
292	C₄×C₄⋊C₄	—	2	1	no	—
293	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	complemented
294	C₄×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
295	#340	C₂²×C₄₇	1	2	yes	complemented
296	#336	C₂²×C₄₇	1	2	yes	complemented
297	C₄₇	#24493	1	1	yes	characteristic, direct product factor, Sylow
298	C₂⁵	—	2	1	no	—
299	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
300	C₂²×D₄	—	2	4	no	—
301	C₂²×D₄	—	2	2	no	—
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	—	2	2	no	—
304	C₂²×D₄	—	4	2	no	—
305	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
306	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
307	C₂×M₁₆	—	2	2	no	—
308	C₂×M₁₆	—	4	2	no	—
309	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
310	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
311	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
312	#124	—	2	4	no	—
313	#124	—	4	2	no	—
314	C₂²⋊Q₈	—	2	2	no	—
315	C₂²⋊Q₈	—	2	2	no	—
316	#117	—	2	2	no	—
317	#117	D₄×C₄₇	1	4	yes	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
321	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
322	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
324	C₂×C₂²⋊C₄	—	2	1	no	—
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₂²⋊C₄	—	2	2	no	—
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
332	C₂×C₄²	—	2	1	no	—
333	C₂×C₄²	—	2	2	no	—
334	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
335	#107	—	2	2	no	—
336	#106	—	2	2	no	—
337	C₄⋊C₈	—	4	2	no	—
338	#103	—	2	2	no	—
339	#103	—	2	2	no	—
340	#103	—	4	2	no	—
341	#102	—	2	4	no	—
342	#102	—	2	4	no	—
343	#102	—	2	4	no	—
344	#102	—	4	2	no	—
345	C₂²⋊C₈	—	2	2	no	—
346	#95	—	2	1	no	—
347	#95	—	2	2	no	—
348	#95	—	2	2	no	—
349	#95	D₄×C₄₇	1	1	yes	characteristic
350	#95	D₄×C₄₇	1	1	yes	characteristic
351	C₂⁴	—	2	2	no	—
352	C₂⁴	—	4	4	no	—
353	C₂⁴	—	4	4	no	—
354	C₂⁴	—	4	2	no	—
355	C₂⁴	—	8	1	no	—
356	C₂⁴	—	8	1	no	—
357	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	1	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×D₄	—	2	8	no	—
363	C₂×D₄	—	2	2	no	—
364	C₂×D₄	—	2	2	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	2	2	no	—
368	C₂×D₄	—	4	8	no	—
369	C₂×D₄	—	4	4	no	—
370	C₂×D₄	—	4	4	no	—
371	C₂×D₄	—	4	2	no	—
372	C₂×D₄	#41×C₄₇	1	4	yes	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	1	no	—
379	C₂²×C₄	—	2	1	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	M₁₆	—	4	4	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	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	—	2	2	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	2	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	4	4	no	—
401	C₄⋊C₄	—	4	2	no	—
402	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
403	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
404	C₂²⋊C₄	—	2	4	no	—
405	C₂²⋊C₄	—	4	2	no	—
406	C₂²⋊C₄	—	4	4	no	—
407	C₂²⋊C₄	—	4	4	no	—
408	C₂²⋊C₄	—	4	2	no	—
409	C₂²⋊C₄	—	8	2	no	—
410	C₂²⋊C₄	—	8	2	no	—
411	C₂²⋊C₄	—	8	1	no	—
412	C₄²	—	2	4	no	—
413	C₄²	—	2	2	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	8	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	1	no	—
419	C₂³	—	2	1	no	—
420	C₂³	—	2	4	no	—
421	C₂³	—	4	8	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	2	no	—
427	C₂³	—	4	2	no	—
428	C₂³	—	8	4	no	—
429	C₂³	—	8	4	no	—
430	C₂³	—	8	8	no	—
431	C₂³	—	8	8	no	—
432	C₂³	#121×C₄₇	1	2	yes	—
433	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
434	Q₈	—	4	1	no	—
435	Q₈	—	4	1	no	—
436	Q₈	—	4	2	no	—
437	D₄	—	2	4	no	—
438	D₄	—	2	4	no	—
439	D₄	—	4	8	no	—
440	D₄	—	4	2	no	—
441	D₄	—	4	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	2	2	no	—
448	C₂×C₄	—	2	2	no	—
449	C₂×C₄	—	2	2	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	1	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	1	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	1	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	#121×C₄₇	1	2	yes	—
466	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
467	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
468	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
469	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
470	C₈	—	4	1	no	—
471	C₈	—	4	1	no	—
472	C₈	—	4	2	no	—
473	C₂²	—	2	2	no	—
474	C₂²	—	2	2	no	—
475	C₂²	—	2	2	no	—
476	C₂²	—	4	2	no	—
477	C₂²	—	4	2	no	—
478	C₂²	—	4	4	no	—
479	C₂²	—	4	4	no	—
480	C₂²	—	4	4	no	—
481	C₂²	—	8	16	no	—
482	C₂²	—	8	2	no	—
483	C₂²	—	8	2	no	—
484	C₂²	—	8	2	no	—
485	C₂²	—	8	2	no	—
486	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
487	C₂²	C₄₇×#546	1	2	yes	—
488	C₂²	C₄₇×#575	1	2	yes	—
489	C₂²	C₄₇×#576	1	1	yes	characteristic
490	C₂²	C₄₇×#577	1	1	yes	characteristic
491	C₄	—	2	2	no	—
492	C₄	—	4	2	no	—
493	C₄	—	4	2	no	—
494	C₄	—	4	2	no	—
495	C₄	—	4	2	no	—
496	C₄	—	8	1	no	—
497	C₄	—	8	2	no	—
498	C₄	—	8	1	no	—
499	C₄	C₄₇×#525	1	1	yes	characteristic
500	C₄	C₄₇×#535	1	1	yes	characteristic
501	C₄	C₄₇×#551	1	2	yes	—
502	C₂	—	4	2	no	—
503	C₂	—	8	4	no	—
504	C₂	C₄₇×#2411	1	1	yes	characteristic
505	C₂	C₄₇×#3040	1	1	yes	characteristic
506	C₂	C₄₇×#3045	1	1	yes	characteristic
507	C₂	C₄₇×#3311	1	2	yes	—
508	C₂	C₄₇×#3322	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂³×D₄×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
1. C₂×C₄₇×#485	C₂	semidirect
4. C₄₇×#2347	C₂	semidirect
5. C₄₇×#2065	C₂	semidirect
6. C₄₇×#2042	C₂	semidirect
7. C₄₇×#1983	C₂	semidirect
8. C₄₇×#1925	C₂	semidirect
9. C₄₇×#1894	C₂	semidirect
10. C₄₇×#1851	C₂	semidirect
18. C₂×#107×C₄₇	C₂²	semidirect
19. C₂×#106×C₄₇	C₂²	semidirect
20. C₂×C₄⋊C₈×C₄₇	C₂²	semidirect
22. C₂×#103×C₄₇	C₂²	semidirect
23. C₂×#103×C₄₇	C₂²	semidirect
24. C₂×#103×C₄₇	C₂²	semidirect
33. C₄₇×#389	C₂²	semidirect
39. C₄×C₄⋊C₄×C₄₇	C₂²	semidirect
41. C₄₇×#340	C₂²	semidirect
42. C₄₇×#336	C₂²	semidirect
218. #24493	C₄₇	direct (N × H)
248. C₂×#485	C₂×C₄₇	semidirect
251. #2347	C₂×C₄₇	semidirect
252. #2065	C₂×C₄₇	semidirect
253. #2042	C₂×C₄₇	semidirect
254. #1983	C₂×C₄₇	semidirect
255. #1925	C₂×C₄₇	semidirect
256. #1894	C₂×C₄₇	semidirect
257. #1851	C₂×C₄₇	semidirect
272. C₂×#107	C₂²×C₄₇	semidirect
273. C₂×#106	C₂²×C₄₇	semidirect
274. C₂×C₄⋊C₈	C₂²×C₄₇	semidirect
276. C₂×#103	C₂²×C₄₇	semidirect
277. C₂×#103	C₂²×C₄₇	semidirect
278. C₂×#103	C₂²×C₄₇	semidirect
287. #389	C₂²×C₄₇	semidirect
293. C₄×C₄⋊C₄	C₂²×C₄₇	semidirect
295. #340	C₂²×C₄₇	semidirect
296. #336	C₂²×C₄₇	semidirect
297. C₄₇	#24493	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×#485	2
C₂×C₄₇×#418	2
C₄₇×#2435	2
C₄₇×#2347	2
C₄₇×#2065	2
C₄₇×#2042	2
C₄₇×#1983	2
C₄₇×#1925	2
C₄₇×#1894	2
C₄₇×#1851	2
C₄₇×#1786	2
#24493	47

Subgroups — C47×#24493 #26064191

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#24493 #26064191