Subgroups — C₄₇×#24354 #26064052

Order 12032.

1872 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₇×#459	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₇×#447	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2433	C₂	1	1	yes	maximal, characteristic, complemented
5	D₄×C₂²⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#2054	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2011	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1893	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1879	C₂	1	2	yes	maximal, complemented
10	C₄₇×#1850	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1786	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
13	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×D₈×C₄₇	—	2	4	no	—
15	C₂²×D₈×C₄₇	—	2	8	no	—
16	C₂²×D₈×C₄₇	C₂²	1	2	yes	—
17	C₂²×D₈×C₄₇	C₂²	1	2	yes	—
18	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
20	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×#127×C₄₇	C₂²	1	2	yes	complemented
22	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×#120×C₄₇	—	2	1	no	—
24	C₂×#120×C₄₇	—	2	1	no	—
25	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	complemented
26	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
27	C₄₇×#459	—	2	8	no	—
28	C₄₇×#447	—	2	4	no	—
29	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	complemented
30	C₂×#102×C₄₇	C₂²	1	2	yes	complemented
31	C₂×#102×C₄₇	C₂²	1	2	yes	complemented
32	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic, complemented
33	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic, complemented
34	C₂×#102×C₄₇	C₂²	1	2	yes	complemented
35	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#392	—	2	2	no	—
37	C₄₇×#390	C₂²	1	2	yes	complemented
38	C₄₇×#390	C₂²	1	2	yes	complemented
39	C₄₇×#386	—	2	2	no	—
40	C₄₇×#380	C₂²	1	1	yes	characteristic
41	C₄₇×#379	—	2	1	no	—
42	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#340	C₂²	1	2	yes	complemented
44	C₄₇×#336	C₂²	1	2	yes	complemented
45	C₂⁵×C₄₇	—	2	1	no	—
46	C₂⁵×C₄₇	—	2	1	no	—
47	C₂²×D₄×C₄₇	—	2	4	no	—
48	C₂²×D₄×C₄₇	—	2	4	no	—
49	C₂²×D₄×C₄₇	—	2	1	no	—
50	C₂²×D₄×C₄₇	—	2	2	no	—
51	C₂²×D₄×C₄₇	—	2	1	no	—
52	C₂²×D₄×C₄₇	—	2	1	no	—
53	C₂²×D₄×C₄₇	—	2	2	no	—
54	C₂²×D₄×C₄₇	—	2	2	no	—
55	C₂²×D₄×C₄₇	—	2	2	no	—
56	C₂²×D₄×C₄₇	—	2	2	no	—
57	C₂²×D₄×C₄₇	—	4	2	no	—
58	C₂²×D₄×C₄₇	—	4	2	no	—
59	C₂²×D₄×C₄₇	D₄	1	4	yes	complemented
60	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
61	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
62	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
63	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
64	C₂³×C₄×C₄₇	—	2	2	no	—
65	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
66	C₂×D₈×C₄₇	—	2	32	no	—
67	C₂×D₈×C₄₇	—	2	4	no	—
68	C₂×D₈×C₄₇	—	2	4	no	—
69	C₂×D₈×C₄₇	—	2	4	no	—
70	C₂×D₈×C₄₇	—	2	4	no	—
71	C₂×D₈×C₄₇	—	2	4	no	—
72	C₂×D₈×C₄₇	—	2	2	no	—
73	C₂×D₈×C₄₇	—	2	2	no	—
74	C₂×D₈×C₄₇	—	2	4	no	—
75	C₂×D₈×C₄₇	—	4	2	no	—
76	C₂×D₈×C₄₇	D₄	1	8	yes	complemented
77	C₂²×C₈×C₄₇	—	2	2	no	—
78	C₂²×C₈×C₄₇	—	2	4	no	—
79	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
82	#127×C₄₇	—	2	4	no	—
83	#127×C₄₇	—	4	2	no	—
84	#121×C₄₇	—	2	2	no	—
85	#121×C₄₇	—	2	2	no	—
86	#120×C₄₇	—	4	4	no	—
87	#120×C₄₇	—	4	4	no	—
88	C₄×D₄×C₄₇	—	2	4	no	—
89	C₄×D₄×C₄₇	—	4	2	no	—
90	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
91	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
92	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
94	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
95	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
96	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
97	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
98	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₄₇	—	4	4	no	—
100	C₂×C₂²⋊C₄×C₄₇	D₄	1	1	yes	characteristic
101	C₂×C₂²⋊C₄×C₄₇	D₄	1	1	yes	characteristic
102	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
103	C₄⋊C₈×C₄₇	—	2	4	no	—
104	#102×C₄₇	—	2	4	no	—
105	#102×C₄₇	—	2	2	no	—
106	#102×C₄₇	—	2	2	no	—
107	#102×C₄₇	—	2	4	no	—
108	#102×C₄₇	—	4	2	no	—
109	C₂²⋊C₈×C₄₇	—	2	2	no	—
110	#95×C₄₇	—	2	1	no	—
111	#95×C₄₇	D₄	1	2	yes	—
112	C₂⁴×C₄₇	—	2	1	no	—
113	C₂⁴×C₄₇	—	2	1	no	—
114	C₂⁴×C₄₇	—	2	2	no	—
115	C₂⁴×C₄₇	—	2	4	no	—
116	C₂⁴×C₄₇	—	2	1	no	—
117	C₂⁴×C₄₇	—	4	4	no	—
118	C₂⁴×C₄₇	—	4	4	no	—
119	C₂⁴×C₄₇	—	4	2	no	—
120	C₂⁴×C₄₇	—	4	2	no	—
121	C₂⁴×C₄₇	—	4	2	no	—
122	C₂⁴×C₄₇	—	4	2	no	—
123	C₂⁴×C₄₇	—	4	2	no	—
124	C₂⁴×C₄₇	—	8	2	no	—
125	C₂⁴×C₄₇	—	8	2	no	—
126	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
127	C₂×D₄×C₄₇	—	2	8	no	—
128	C₂×D₄×C₄₇	—	2	8	no	—
129	C₂×D₄×C₄₇	—	2	4	no	—
130	C₂×D₄×C₄₇	—	2	2	no	—
131	C₂×D₄×C₄₇	—	2	2	no	—
132	C₂×D₄×C₄₇	—	2	2	no	—
133	C₂×D₄×C₄₇	—	2	1	no	—
134	C₂×D₄×C₄₇	—	2	2	no	—
135	C₂×D₄×C₄₇	—	2	1	no	—
136	C₂×D₄×C₄₇	—	2	2	no	—
137	C₂×D₄×C₄₇	—	2	1	no	—
138	C₂×D₄×C₄₇	—	2	1	no	—
139	C₂×D₄×C₄₇	—	2	2	no	—
140	C₂×D₄×C₄₇	—	2	2	no	—
141	C₂×D₄×C₄₇	—	2	2	no	—
142	C₂×D₄×C₄₇	—	2	2	no	—
143	C₂×D₄×C₄₇	—	2	2	no	—
144	C₂×D₄×C₄₇	—	4	4	no	—
145	C₂×D₄×C₄₇	—	4	8	no	—
146	C₂×D₄×C₄₇	—	4	8	no	—
147	C₂×D₄×C₄₇	—	4	4	no	—
148	C₂×D₄×C₄₇	—	4	4	no	—
149	C₂×D₄×C₄₇	—	4	4	no	—
150	C₂×D₄×C₄₇	—	4	4	no	—
151	C₂×D₄×C₄₇	—	4	4	no	—
152	C₂×D₄×C₄₇	—	4	4	no	—
153	C₂×D₄×C₄₇	—	4	2	no	—
154	C₂×D₄×C₄₇	—	4	2	no	—
155	C₂×D₄×C₄₇	—	4	2	no	—
156	C₂×D₄×C₄₇	—	4	2	no	—
157	C₂×D₄×C₄₇	—	4	4	no	—
158	C₂×D₄×C₄₇	—	8	2	no	—
159	C₂×D₄×C₄₇	—	8	2	no	—
160	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
161	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
162	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
163	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₄₇	—	2	2	no	—
165	C₂²×C₄×C₄₇	—	2	2	no	—
166	C₂²×C₄×C₄₇	—	2	1	no	—
167	C₂²×C₄×C₄₇	—	2	2	no	—
168	C₂²×C₄×C₄₇	—	4	4	no	—
169	C₂²×C₄×C₄₇	—	4	4	no	—
170	C₂²×C₄×C₄₇	—	8	2	no	—
171	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
172	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
174	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
175	C₂²×C₄×C₄₇	#41	1	2	yes	—
176	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
177	D₈×C₄₇	—	2	16	no	—
178	D₈×C₄₇	—	2	16	no	—
179	D₈×C₄₇	—	4	4	no	—
180	D₈×C₄₇	—	4	4	no	—
181	C₂×C₈×C₄₇	—	2	8	no	—
182	C₂×C₈×C₄₇	—	2	2	no	—
183	C₂×C₈×C₄₇	—	2	2	no	—
184	C₂×C₈×C₄₇	—	2	2	no	—
185	C₂×C₈×C₄₇	—	2	1	no	—
186	C₂×C₈×C₄₇	—	2	1	no	—
187	C₂×C₈×C₄₇	—	2	2	no	—
188	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
189	C₄⋊C₄×C₄₇	—	2	2	no	—
190	C₄⋊C₄×C₄₇	—	2	1	no	—
191	C₄⋊C₄×C₄₇	—	2	1	no	—
192	C₄⋊C₄×C₄₇	—	2	2	no	—
193	C₂²⋊C₄×C₄₇	—	2	2	no	—
194	C₂²⋊C₄×C₄₇	—	4	4	no	—
195	C₂²⋊C₄×C₄₇	—	4	4	no	—
196	C₂²⋊C₄×C₄₇	—	4	2	no	—
197	C₂²⋊C₄×C₄₇	—	4	2	no	—
198	C₂²⋊C₄×C₄₇	—	4	4	no	—
199	C₂²⋊C₄×C₄₇	—	4	4	no	—
200	C₂²⋊C₄×C₄₇	—	8	2	no	—
201	C₂²⋊C₄×C₄₇	D₈	1	4	yes	complemented
202	C₄²×C₄₇	—	2	2	no	—
203	C₄²×C₄₇	—	2	2	no	—
204	C₂³×C₄₇	—	2	2	no	—
205	C₂³×C₄₇	—	2	2	no	—
206	C₂³×C₄₇	—	2	2	no	—
207	C₂³×C₄₇	—	2	4	no	—
208	C₂³×C₄₇	—	2	2	no	—
209	C₂³×C₄₇	—	2	4	no	—
210	C₂³×C₄₇	—	4	8	no	—
211	C₂³×C₄₇	—	4	8	no	—
212	C₂³×C₄₇	—	4	1	no	—
213	C₂³×C₄₇	—	4	1	no	—
214	C₂³×C₄₇	—	4	2	no	—
215	C₂³×C₄₇	—	4	2	no	—
216	C₂³×C₄₇	—	4	2	no	—
217	C₂³×C₄₇	—	4	2	no	—
218	C₂³×C₄₇	—	4	1	no	—
219	C₂³×C₄₇	—	4	2	no	—
220	C₂³×C₄₇	—	4	2	no	—
221	C₂³×C₄₇	—	4	1	no	—
222	C₂³×C₄₇	—	4	2	no	—
223	C₂³×C₄₇	—	4	2	no	—
224	C₂³×C₄₇	—	4	2	no	—
225	C₂³×C₄₇	—	4	8	no	—
226	C₂³×C₄₇	—	4	1	no	—
227	C₂³×C₄₇	—	4	2	no	—
228	C₂³×C₄₇	—	4	1	no	—
229	C₂³×C₄₇	—	4	1	no	—
230	C₂³×C₄₇	—	4	2	no	—
231	C₂³×C₄₇	—	8	4	no	—
232	C₂³×C₄₇	—	8	8	no	—
233	C₂³×C₄₇	—	8	8	no	—
234	C₂³×C₄₇	—	8	8	no	—
235	C₂³×C₄₇	—	8	8	no	—
236	C₂³×C₄₇	—	8	4	no	—
237	C₂³×C₄₇	—	8	4	no	—
238	C₂³×C₄₇	#121	1	2	yes	—
239	C₂³×C₄₇	C₂×D₈	1	2	yes	—
240	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
241	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
242	D₄×C₄₇	—	2	2	no	—
243	D₄×C₄₇	—	2	4	no	—
244	D₄×C₄₇	—	2	2	no	—
245	D₄×C₄₇	—	2	2	no	—
246	D₄×C₄₇	—	2	4	no	—
247	D₄×C₄₇	—	2	4	no	—
248	D₄×C₄₇	—	4	8	no	—
249	D₄×C₄₇	—	4	8	no	—
250	D₄×C₄₇	—	4	1	no	—
251	D₄×C₄₇	—	4	2	no	—
252	D₄×C₄₇	—	4	1	no	—
253	D₄×C₄₇	—	4	2	no	—
254	D₄×C₄₇	—	4	2	no	—
255	D₄×C₄₇	—	4	2	no	—
256	D₄×C₄₇	—	8	8	no	—
257	D₄×C₄₇	—	8	8	no	—
258	D₄×C₄₇	—	8	4	no	—
259	D₄×C₄₇	#120	1	4	yes	complemented
260	C₂×C₄×C₄₇	—	2	2	no	—
261	C₂×C₄×C₄₇	—	2	2	no	—
262	C₂×C₄×C₄₇	—	2	2	no	—
263	C₂×C₄×C₄₇	—	2	2	no	—
264	C₂×C₄×C₄₇	—	2	2	no	—
265	C₂×C₄×C₄₇	—	2	4	no	—
266	C₂×C₄×C₄₇	—	2	2	no	—
267	C₂×C₄×C₄₇	—	2	2	no	—
268	C₂×C₄×C₄₇	—	2	2	no	—
269	C₂×C₄×C₄₇	—	4	1	no	—
270	C₂×C₄×C₄₇	—	4	2	no	—
271	C₂×C₄×C₄₇	—	4	2	no	—
272	C₂×C₄×C₄₇	—	4	1	no	—
273	C₂×C₄×C₄₇	—	4	1	no	—
274	C₂×C₄×C₄₇	—	4	2	no	—
275	C₂×C₄×C₄₇	—	8	8	no	—
276	C₂×C₄×C₄₇	#121	1	2	yes	—
277	C₂×C₄×C₄₇	C₂×D₈	1	4	yes	complemented
278	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
279	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
280	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
281	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
282	C₈×C₄₇	—	2	4	no	—
283	C₈×C₄₇	—	4	1	no	—
284	C₈×C₄₇	—	4	1	no	—
285	#24354	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
286	C₂²×C₄₇	—	2	2	no	—
287	C₂²×C₄₇	—	2	4	no	—
288	C₂²×C₄₇	—	2	4	no	—
289	C₂²×C₄₇	—	2	2	no	—
290	C₂²×C₄₇	—	2	4	no	—
291	C₂²×C₄₇	—	4	4	no	—
292	C₂²×C₄₇	—	4	4	no	—
293	C₂²×C₄₇	—	4	2	no	—
294	C₂²×C₄₇	—	4	2	no	—
295	C₂²×C₄₇	—	4	2	no	—
296	C₂²×C₄₇	—	4	4	no	—
297	C₂²×C₄₇	—	4	4	no	—
298	C₂²×C₄₇	—	4	4	no	—
299	C₂²×C₄₇	—	4	2	no	—
300	C₂²×C₄₇	—	4	2	no	—
301	C₂²×C₄₇	—	8	16	no	—
302	C₂²×C₄₇	—	8	16	no	—
303	C₂²×C₄₇	—	8	2	no	—
304	C₂²×C₄₇	—	8	2	no	—
305	C₂²×C₄₇	—	8	2	no	—
306	C₂²×C₄₇	—	8	2	no	—
307	C₂²×C₄₇	—	8	2	no	—
308	C₂²×C₄₇	—	8	2	no	—
309	C₂²×C₄₇	—	8	1	no	—
310	C₂²×C₄₇	—	8	2	no	—
311	C₂²×C₄₇	—	8	2	no	—
312	C₂²×C₄₇	—	8	1	no	—
313	C₂²×C₄₇	—	8	1	no	—
314	C₂²×C₄₇	#459	1	4	yes	complemented
315	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
316	C₂²×C₄₇	D₄²	1	2	yes	—
317	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
318	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
319	C₂²×C₄₇	#576	1	2	yes	—
320	C₄×C₄₇	—	2	2	no	—
321	C₄×C₄₇	—	2	4	no	—
322	C₄×C₄₇	—	4	2	no	—
323	C₄×C₄₇	—	8	2	no	—
324	C₄×C₄₇	—	8	1	no	—
325	C₄×C₄₇	C₂×#120	1	1	yes	characteristic
326	C₄×C₄₇	#534	1	1	yes	characteristic
327	C₄×C₄₇	#546	1	2	yes	—
328	C₂³×D₈	C₂×C₄₇	1	1	yes	characteristic, complemented
329	C₂×#459	C₂×C₄₇	1	2	yes	complemented
330	C₂×#447	C₂×C₄₇	1	1	yes	characteristic, complemented
331	#2433	C₂×C₄₇	1	1	yes	characteristic, complemented
332	D₄×C₂²⋊C₄	C₂×C₄₇	1	1	yes	characteristic, complemented
333	#2054	C₂×C₄₇	1	2	yes	complemented
334	#2011	C₂×C₄₇	1	2	yes	complemented
335	#1893	C₂×C₄₇	1	1	yes	characteristic, complemented
336	#1879	C₂×C₄₇	1	2	yes	complemented
337	#1850	C₂×C₄₇	1	1	yes	characteristic, complemented
338	#1786	C₂×C₄₇	1	1	yes	characteristic, complemented
339	C₂×C₄₇	—	2	4	no	—
340	C₂×C₄₇	—	4	4	no	—
341	C₂×C₄₇	—	8	4	no	—
342	C₂×C₄₇	—	8	2	no	—
343	C₂×C₄₇	—	16	1	no	—
344	C₂×C₄₇	#2410	1	1	yes	characteristic
345	C₂×C₄₇	C₂×#459	1	1	yes	characteristic
346	C₂×C₄₇	#3041	1	1	yes	characteristic
347	C₂×C₄₇	#3264	1	2	yes	—
348	C₂×C₄₇	D₄×D₈	1	2	yes	—
349	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
350	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
351	C₂²×D₈	—	2	4	no	—
352	C₂²×D₈	—	2	8	no	—
353	C₂²×D₈	C₂²×C₄₇	1	2	yes	—
354	C₂²×D₈	C₂²×C₄₇	1	2	yes	—
355	C₂²×D₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
356	C₂²×D₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
357	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
358	C₂×#127	C₂²×C₄₇	1	2	yes	complemented
359	C₂×#121	C₂²×C₄₇	1	1	yes	characteristic
360	C₂×#120	—	2	1	no	—
361	C₂×#120	—	2	1	no	—
362	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	complemented
363	C₂²×C₂²⋊C₄	—	2	1	no	—
364	#459	—	2	8	no	—
365	#447	—	2	4	no	—
366	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
367	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic, complemented
368	C₂×#102	C₂²×C₄₇	1	2	yes	complemented
369	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic, complemented
370	C₂×#102	C₂²×C₄₇	1	2	yes	complemented
371	C₂×#102	C₂²×C₄₇	1	2	yes	complemented
372	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
373	#392	—	2	2	no	—
374	#390	C₂²×C₄₇	1	2	yes	complemented
375	#390	C₂²×C₄₇	1	2	yes	complemented
376	#386	—	2	2	no	—
377	#380	C₂²×C₄₇	1	1	yes	characteristic
378	#379	—	2	1	no	—
379	C₄×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
380	#340	C₂²×C₄₇	1	2	yes	complemented
381	#336	C₂²×C₄₇	1	2	yes	complemented
382	C₄₇	#24354	1	1	yes	characteristic, direct product factor, Sylow
383	C₂⁵	—	2	1	no	—
384	C₂⁵	—	2	1	no	—
385	C₂²×D₄	—	2	4	no	—
386	C₂²×D₄	—	2	4	no	—
387	C₂²×D₄	—	2	1	no	—
388	C₂²×D₄	—	2	2	no	—
389	C₂²×D₄	—	2	1	no	—
390	C₂²×D₄	—	2	1	no	—
391	C₂²×D₄	—	2	2	no	—
392	C₂²×D₄	—	2	2	no	—
393	C₂²×D₄	—	2	2	no	—
394	C₂²×D₄	—	2	2	no	—
395	C₂²×D₄	—	4	2	no	—
396	C₂²×D₄	—	4	2	no	—
397	C₂²×D₄	D₄×C₄₇	1	4	yes	complemented
398	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
399	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
400	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
401	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
402	C₂³×C₄	—	2	2	no	—
403	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
404	C₂×D₈	—	2	32	no	—
405	C₂×D₈	—	2	4	no	—
406	C₂×D₈	—	2	4	no	—
407	C₂×D₈	—	2	4	no	—
408	C₂×D₈	—	2	4	no	—
409	C₂×D₈	—	2	2	no	—
410	C₂×D₈	—	2	2	no	—
411	C₂×D₈	—	2	4	no	—
412	C₂×D₈	—	2	4	no	—
413	C₂×D₈	—	4	2	no	—
414	C₂×D₈	D₄×C₄₇	1	8	yes	complemented
415	C₂²×C₈	—	2	2	no	—
416	C₂²×C₈	—	2	4	no	—
417	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
418	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
419	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
420	#127	—	2	4	no	—
421	#127	—	4	2	no	—
422	#121	—	2	2	no	—
423	#121	—	2	2	no	—
424	#120	—	4	4	no	—
425	#120	—	4	4	no	—
426	C₄×D₄	—	2	4	no	—
427	C₄×D₄	—	4	2	no	—
428	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
429	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
430	C₂×C₂²⋊C₄	—	2	1	no	—
431	C₂×C₂²⋊C₄	—	2	2	no	—
432	C₂×C₂²⋊C₄	—	2	2	no	—
433	C₂×C₂²⋊C₄	—	2	2	no	—
434	C₂×C₂²⋊C₄	—	2	2	no	—
435	C₂×C₂²⋊C₄	—	2	1	no	—
436	C₂×C₂²⋊C₄	—	2	2	no	—
437	C₂×C₂²⋊C₄	—	4	4	no	—
438	C₂×C₂²⋊C₄	D₄×C₄₇	1	1	yes	characteristic
439	C₂×C₂²⋊C₄	D₄×C₄₇	1	1	yes	characteristic
440	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
441	C₄⋊C₈	—	2	4	no	—
442	#102	—	2	2	no	—
443	#102	—	2	2	no	—
444	#102	—	2	4	no	—
445	#102	—	2	4	no	—
446	#102	—	4	2	no	—
447	C₂²⋊C₈	—	2	2	no	—
448	#95	—	2	1	no	—
449	#95	D₄×C₄₇	1	2	yes	—
450	C₂⁴	—	2	1	no	—
451	C₂⁴	—	2	1	no	—
452	C₂⁴	—	2	2	no	—
453	C₂⁴	—	2	4	no	—
454	C₂⁴	—	2	1	no	—
455	C₂⁴	—	4	4	no	—
456	C₂⁴	—	4	4	no	—
457	C₂⁴	—	4	2	no	—
458	C₂⁴	—	4	2	no	—
459	C₂⁴	—	4	2	no	—
460	C₂⁴	—	4	2	no	—
461	C₂⁴	—	4	2	no	—
462	C₂⁴	—	8	2	no	—
463	C₂⁴	—	8	2	no	—
464	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
465	C₂×D₄	—	2	8	no	—
466	C₂×D₄	—	2	8	no	—
467	C₂×D₄	—	2	4	no	—
468	C₂×D₄	—	2	2	no	—
469	C₂×D₄	—	2	2	no	—
470	C₂×D₄	—	2	2	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	2	1	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	2	2	no	—
475	C₂×D₄	—	2	1	no	—
476	C₂×D₄	—	2	1	no	—
477	C₂×D₄	—	2	2	no	—
478	C₂×D₄	—	2	2	no	—
479	C₂×D₄	—	2	2	no	—
480	C₂×D₄	—	2	2	no	—
481	C₂×D₄	—	2	2	no	—
482	C₂×D₄	—	4	4	no	—
483	C₂×D₄	—	4	8	no	—
484	C₂×D₄	—	4	8	no	—
485	C₂×D₄	—	4	4	no	—
486	C₂×D₄	—	4	4	no	—
487	C₂×D₄	—	4	4	no	—
488	C₂×D₄	—	4	4	no	—
489	C₂×D₄	—	4	4	no	—
490	C₂×D₄	—	4	4	no	—
491	C₂×D₄	—	4	2	no	—
492	C₂×D₄	—	4	2	no	—
493	C₂×D₄	—	4	2	no	—
494	C₂×D₄	—	4	2	no	—
495	C₂×D₄	—	4	4	no	—
496	C₂×D₄	—	8	2	no	—
497	C₂×D₄	—	8	2	no	—
498	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
499	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
500	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
501	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
502	C₂²×C₄	—	2	2	no	—
503	C₂²×C₄	—	2	2	no	—
504	C₂²×C₄	—	2	2	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	4	4	no	—
507	C₂²×C₄	—	4	4	no	—
508	C₂²×C₄	—	8	2	no	—
509	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
510	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
511	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
512	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
513	C₂²×C₄	#41×C₄₇	1	2	yes	—
514	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
515	D₈	—	2	16	no	—
516	D₈	—	2	16	no	—
517	D₈	—	4	4	no	—
518	D₈	—	4	4	no	—
519	C₂×C₈	—	2	8	no	—
520	C₂×C₈	—	2	2	no	—
521	C₂×C₈	—	2	2	no	—
522	C₂×C₈	—	2	1	no	—
523	C₂×C₈	—	2	1	no	—
524	C₂×C₈	—	2	2	no	—
525	C₂×C₈	—	2	2	no	—
526	C₂×C₈	C₂×D₄×C₄₇	1	4	yes	—
527	C₄⋊C₄	—	2	2	no	—
528	C₄⋊C₄	—	2	1	no	—
529	C₄⋊C₄	—	2	1	no	—
530	C₄⋊C₄	—	2	2	no	—
531	C₂²⋊C₄	—	2	2	no	—
532	C₂²⋊C₄	—	4	4	no	—
533	C₂²⋊C₄	—	4	4	no	—
534	C₂²⋊C₄	—	4	2	no	—
535	C₂²⋊C₄	—	4	2	no	—
536	C₂²⋊C₄	—	4	4	no	—
537	C₂²⋊C₄	—	4	4	no	—
538	C₂²⋊C₄	—	8	2	no	—
539	C₂²⋊C₄	D₈×C₄₇	1	4	yes	complemented
540	C₄²	—	2	2	no	—
541	C₄²	—	2	2	no	—
542	C₂³	—	2	2	no	—
543	C₂³	—	2	2	no	—
544	C₂³	—	2	2	no	—
545	C₂³	—	2	4	no	—
546	C₂³	—	2	2	no	—
547	C₂³	—	2	4	no	—
548	C₂³	—	4	8	no	—
549	C₂³	—	4	8	no	—
550	C₂³	—	4	1	no	—
551	C₂³	—	4	1	no	—
552	C₂³	—	4	2	no	—
553	C₂³	—	4	8	no	—
554	C₂³	—	4	2	no	—
555	C₂³	—	4	2	no	—
556	C₂³	—	4	2	no	—
557	C₂³	—	4	1	no	—
558	C₂³	—	4	2	no	—
559	C₂³	—	4	2	no	—
560	C₂³	—	4	1	no	—
561	C₂³	—	4	2	no	—
562	C₂³	—	4	2	no	—
563	C₂³	—	4	2	no	—
564	C₂³	—	4	1	no	—
565	C₂³	—	4	2	no	—
566	C₂³	—	4	1	no	—
567	C₂³	—	4	1	no	—
568	C₂³	—	4	2	no	—
569	C₂³	—	8	4	no	—
570	C₂³	—	8	8	no	—
571	C₂³	—	8	8	no	—
572	C₂³	—	8	8	no	—
573	C₂³	—	8	8	no	—
574	C₂³	—	8	4	no	—
575	C₂³	—	8	4	no	—
576	C₂³	#121×C₄₇	1	2	yes	—
577	C₂³	C₂×D₈×C₄₇	1	2	yes	—
578	C₂³	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
579	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
580	D₄	—	2	2	no	—
581	D₄	—	2	4	no	—
582	D₄	—	2	2	no	—
583	D₄	—	2	2	no	—
584	D₄	—	2	4	no	—
585	D₄	—	2	4	no	—
586	D₄	—	4	8	no	—
587	D₄	—	4	8	no	—
588	D₄	—	4	1	no	—
589	D₄	—	4	2	no	—
590	D₄	—	4	1	no	—
591	D₄	—	4	2	no	—
592	D₄	—	4	2	no	—
593	D₄	—	4	2	no	—
594	D₄	—	8	8	no	—
595	D₄	—	8	8	no	—
596	D₄	—	8	4	no	—
597	D₄	#120×C₄₇	1	4	yes	complemented
598	C₂×C₄	—	2	2	no	—
599	C₂×C₄	—	2	2	no	—
600	C₂×C₄	—	2	2	no	—
601	C₂×C₄	—	2	2	no	—
602	C₂×C₄	—	2	2	no	—
603	C₂×C₄	—	2	4	no	—
604	C₂×C₄	—	2	2	no	—
605	C₂×C₄	—	2	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	4	1	no	—
608	C₂×C₄	—	4	2	no	—
609	C₂×C₄	—	4	2	no	—
610	C₂×C₄	—	4	1	no	—
611	C₂×C₄	—	4	1	no	—
612	C₂×C₄	—	4	2	no	—
613	C₂×C₄	—	8	8	no	—
614	C₂×C₄	#121×C₄₇	1	2	yes	—
615	C₂×C₄	C₂×D₈×C₄₇	1	4	yes	complemented
616	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
617	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
618	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
619	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
620	C₈	—	2	4	no	—
621	C₈	—	4	1	no	—
622	C₈	—	4	1	no	—
623	C₂²	—	2	2	no	—
624	C₂²	—	2	2	no	—
625	C₂²	—	2	4	no	—
626	C₂²	—	2	4	no	—
627	C₂²	—	2	4	no	—
628	C₂²	—	4	2	no	—
629	C₂²	—	4	4	no	—
630	C₂²	—	4	4	no	—
631	C₂²	—	4	2	no	—
632	C₂²	—	4	2	no	—
633	C₂²	—	4	2	no	—
634	C₂²	—	4	4	no	—
635	C₂²	—	4	4	no	—
636	C₂²	—	4	4	no	—
637	C₂²	—	4	2	no	—
638	C₂²	—	8	16	no	—
639	C₂²	—	8	16	no	—
640	C₂²	—	8	2	no	—
641	C₂²	—	8	2	no	—
642	C₂²	—	8	2	no	—
643	C₂²	—	8	2	no	—
644	C₂²	—	8	2	no	—
645	C₂²	—	8	2	no	—
646	C₂²	—	8	1	no	—
647	C₂²	—	8	1	no	—
648	C₂²	—	8	2	no	—
649	C₂²	—	8	2	no	—
650	C₂²	—	8	1	no	—
651	C₂²	C₄₇×#459	1	4	yes	complemented
652	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
653	C₂²	D₄²×C₄₇	1	2	yes	—
654	C₂²	C₂²×D₈×C₄₇	1	1	yes	characteristic
655	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
656	C₂²	C₄₇×#576	1	2	yes	—
657	C₄	—	2	2	no	—
658	C₄	—	2	4	no	—
659	C₄	—	4	2	no	—
660	C₄	—	8	2	no	—
661	C₄	—	8	1	no	—
662	C₄	C₂×#120×C₄₇	1	1	yes	characteristic
663	C₄	C₄₇×#534	1	1	yes	characteristic
664	C₄	C₄₇×#546	1	2	yes	—
665	C₂	—	2	4	no	—
666	C₂	—	4	4	no	—
667	C₂	—	8	2	no	—
668	C₂	—	8	4	no	—
669	C₂	—	16	1	no	—
670	C₂	C₄₇×#2410	1	1	yes	characteristic
671	C₂	C₂×C₄₇×#459	1	1	yes	characteristic
672	C₂	C₄₇×#3041	1	1	yes	characteristic
673	C₂	C₄₇×#3264	1	2	yes	—
674	C₂	D₄×D₈×C₄₇	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
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. C₂³×D₈×C₄₇	C₂	semidirect
2. C₂×C₄₇×#459	C₂	semidirect
3. C₂×C₄₇×#447	C₂	semidirect
4. C₄₇×#2433	C₂	semidirect
5. D₄×C₂²⋊C₄×C₄₇	C₂	semidirect
6. C₄₇×#2054	C₂	semidirect
7. C₄₇×#2011	C₂	semidirect
8. C₄₇×#1893	C₂	semidirect
9. C₄₇×#1879	C₂	semidirect
10. C₄₇×#1850	C₂	semidirect
11. C₄₇×#1786	C₂	semidirect
18. C₂²×D₈×C₄₇	C₂²	semidirect
19. C₂²×D₈×C₄₇	C₂²	semidirect
21. C₂×#127×C₄₇	C₂²	semidirect
25. C₂×C₄×D₄×C₄₇	C₂²	semidirect
29. C₂×C₄⋊C₈×C₄₇	C₂²	semidirect
30. C₂×#102×C₄₇	C₂²	semidirect
31. C₂×#102×C₄₇	C₂²	semidirect
32. C₂×#102×C₄₇	C₂²	semidirect
33. C₂×#102×C₄₇	C₂²	semidirect
34. C₂×#102×C₄₇	C₂²	semidirect
37. C₄₇×#390	C₂²	semidirect
38. C₄₇×#390	C₂²	semidirect
43. C₄₇×#340	C₂²	semidirect
44. C₄₇×#336	C₂²	semidirect
59. C₂²×D₄×C₄₇	D₄	semidirect
76. C₂×D₈×C₄₇	D₄	semidirect
201. C₂²⋊C₄×C₄₇	D₈	semidirect
259. D₄×C₄₇	#120	semidirect
277. C₂×C₄×C₄₇	C₂×D₈	semidirect
285. #24354	C₄₇	direct (N × H)
314. C₂²×C₄₇	#459	semidirect
328. C₂³×D₈	C₂×C₄₇	semidirect
329. C₂×#459	C₂×C₄₇	semidirect
330. C₂×#447	C₂×C₄₇	semidirect
331. #2433	C₂×C₄₇	semidirect
332. D₄×C₂²⋊C₄	C₂×C₄₇	semidirect
333. #2054	C₂×C₄₇	semidirect
334. #2011	C₂×C₄₇	semidirect
335. #1893	C₂×C₄₇	semidirect
336. #1879	C₂×C₄₇	semidirect
337. #1850	C₂×C₄₇	semidirect
338. #1786	C₂×C₄₇	semidirect
355. C₂²×D₈	C₂²×C₄₇	semidirect
356. C₂²×D₈	C₂²×C₄₇	semidirect
358. C₂×#127	C₂²×C₄₇	semidirect
362. C₂×C₄×D₄	C₂²×C₄₇	semidirect
366. C₂×C₄⋊C₈	C₂²×C₄₇	semidirect
367. C₂×#102	C₂²×C₄₇	semidirect
368. C₂×#102	C₂²×C₄₇	semidirect
369. C₂×#102	C₂²×C₄₇	semidirect
370. C₂×#102	C₂²×C₄₇	semidirect
371. C₂×#102	C₂²×C₄₇	semidirect
374. #390	C₂²×C₄₇	semidirect
375. #390	C₂²×C₄₇	semidirect
380. #340	C₂²×C₄₇	semidirect
381. #336	C₂²×C₄₇	semidirect
382. C₄₇	#24354	direct (N × H)
397. C₂²×D₄	D₄×C₄₇	semidirect
414. C₂×D₈	D₄×C₄₇	semidirect
539. C₂²⋊C₄	D₈×C₄₇	semidirect
597. D₄	#120×C₄₇	semidirect
615. C₂×C₄	C₂×D₈×C₄₇	semidirect
651. C₂²	C₄₇×#459	semidirect

Maximal subgroups

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

subgroup	index
C₂³×D₈×C₄₇	2
C₂×C₄₇×#459	2
C₂×C₄₇×#447	2
C₄₇×#2433	2
D₄×C₂²⋊C₄×C₄₇	2
C₄₇×#2054	2
C₄₇×#2011	2
C₄₇×#1893	2
C₄₇×#1879	2
C₄₇×#1850	2
C₄₇×#1786	2
#24354	47

Subgroups — C47×#24354 #26064052

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#24354 #26064052