Subgroups — C₄₇×#18284 #26057982

Order 12032.

1486 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#534	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#3186	C₂	1	2	yes	maximal, complemented
3	C₄₇×#2617	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1607	C₂	1	4	yes	maximal, complemented
5	C₄₇×#1595	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1519	C₂	1	2	yes	maximal, complemented
7	C₂×C₄₇×#323	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂³×D₄×C₄₇	—	2	1	no	—
9	C₄₇×#534	—	2	4	no	—
10	C₄₇×#534	—	2	2	no	—
11	C₄₇×#534	C₂²	1	4	yes	—
12	C₂×#123×C₄₇	—	2	2	no	—
13	C₂×#121×C₄₇	—	2	1	no	—
14	C₂×#121×C₄₇	C₂²	1	2	yes	—
15	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic, complemented
16	C₂×#120×C₄₇	—	2	2	no	—
17	C₂×#120×C₄₇	—	2	1	no	—
18	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#480	—	2	2	no	—
20	C₄₇×#480	C₂²	1	4	yes	complemented
21	C₄₇×#466	—	2	4	no	—
22	C₄₇×#447	—	2	2	no	—
23	C₄₇×#447	C₂²	1	4	yes	complemented
24	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	complemented
25	C₄₇×#397	C₂²	1	2	yes	complemented
26	C₄₇×#394	—	2	2	no	—
27	C₄₇×#392	C₂²	1	2	yes	complemented
28	C₄₇×#386	—	2	1	no	—
29	C₄₇×#380	C₂²	1	1	yes	characteristic, complemented
30	C₄₇×#327	C₂²	1	8	yes	complemented
31	C₄₇×#323	C₂²	1	4	yes	complemented
32	C₂⁵×C₄₇	—	2	1	no	—
33	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
34	C₂²×D₄×C₄₇	—	2	2	no	—
35	C₂²×D₄×C₄₇	—	2	4	no	—
36	C₂²×D₄×C₄₇	—	2	2	no	—
37	C₂²×D₄×C₄₇	—	2	4	no	—
38	C₂²×D₄×C₄₇	—	2	1	no	—
39	C₂²×D₄×C₄₇	—	2	1	no	—
40	C₂²×D₄×C₄₇	—	2	2	no	—
41	C₂²×D₄×C₄₇	—	4	4	no	—
42	C₂²×D₄×C₄₇	—	4	4	no	—
43	C₂²×D₄×C₄₇	D₄	1	2	yes	complemented
44	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic, complemented
45	C₂³×C₄×C₄₇	—	2	1	no	—
46	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
48	C₂×D₈×C₄₇	—	2	4	no	—
49	C₂²×C₈×C₄₇	—	2	2	no	—
50	#123×C₄₇	—	2	8	no	—
51	#123×C₄₇	—	2	8	no	—
52	#121×C₄₇	—	2	4	no	—
53	#121×C₄₇	—	2	4	no	—
54	#121×C₄₇	—	2	2	no	—
55	#121×C₄₇	—	2	2	no	—
56	#121×C₄₇	—	2	2	no	—
57	#121×C₄₇	—	2	2	no	—
58	#121×C₄₇	D₄	1	4	yes	complemented
59	#121×C₄₇	C₂³	1	4	yes	—
60	#120×C₄₇	—	2	8	no	—
61	#120×C₄₇	—	2	8	no	—
62	#120×C₄₇	—	4	4	no	—
63	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
65	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	complemented
66	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic, complemented
67	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₄₇	—	2	1	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	D₄	1	2	yes	—
76	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
77	#107×C₄₇	—	2	4	no	—
78	#102×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	complemented
82	#95×C₄₇	—	2	2	no	—
83	#95×C₄₇	C₂³	1	2	yes	complemented
84	C₂⁴×C₄₇	—	2	1	no	—
85	C₂⁴×C₄₇	—	2	1	no	—
86	C₂⁴×C₄₇	—	2	2	no	—
87	C₂⁴×C₄₇	—	2	4	no	—
88	C₂⁴×C₄₇	—	2	2	no	—
89	C₂⁴×C₄₇	—	2	1	no	—
90	C₂⁴×C₄₇	—	4	4	no	—
91	C₂⁴×C₄₇	—	8	1	no	—
92	C₂⁴×C₄₇	—	8	1	no	—
93	C₂⁴×C₄₇	—	8	2	no	—
94	C₂⁴×C₄₇	—	8	2	no	—
95	C₂⁴×C₄₇	D₈	1	4	yes	complemented
96	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
97	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂×D₄×C₄₇	—	2	8	no	—
99	C₂×D₄×C₄₇	—	2	4	no	—
100	C₂×D₄×C₄₇	—	2	4	no	—
101	C₂×D₄×C₄₇	—	2	4	no	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	—	2	2	no	—
104	C₂×D₄×C₄₇	—	4	8	no	—
105	C₂×D₄×C₄₇	—	4	16	no	—
106	C₂×D₄×C₄₇	—	4	8	no	—
107	C₂×D₄×C₄₇	—	4	8	no	—
108	C₂×D₄×C₄₇	—	4	4	no	—
109	C₂×D₄×C₄₇	—	4	4	no	—
110	C₂×D₄×C₄₇	—	4	1	no	—
111	C₂×D₄×C₄₇	—	4	1	no	—
112	C₂×D₄×C₄₇	—	4	4	no	—
113	C₂×D₄×C₄₇	—	4	2	no	—
114	C₂×D₄×C₄₇	—	4	2	no	—
115	C₂×D₄×C₄₇	—	8	1	no	—
116	C₂×D₄×C₄₇	—	8	2	no	—
117	C₂×D₄×C₄₇	—	8	2	no	—
118	C₂×D₄×C₄₇	—	8	2	no	—
119	C₂×D₄×C₄₇	—	8	2	no	—
120	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
121	C₂²×C₄×C₄₇	—	2	4	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	—	2	2	no	—
126	C₂²×C₄×C₄₇	—	2	1	no	—
127	C₂²×C₄×C₄₇	—	4	4	no	—
128	C₂²×C₄×C₄₇	—	8	1	no	—
129	C₂²×C₄×C₄₇	—	8	1	no	—
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	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
135	D₈×C₄₇	—	8	4	no	—
136	C₂×C₈×C₄₇	—	2	4	no	—
137	C₂×C₈×C₄₇	—	8	2	no	—
138	C₄⋊C₄×C₄₇	—	2	4	no	—
139	C₄⋊C₄×C₄₇	—	2	2	no	—
140	C₄⋊C₄×C₄₇	—	2	2	no	—
141	C₄⋊C₄×C₄₇	—	8	1	no	—
142	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
143	C₂²⋊C₄×C₄₇	—	2	8	no	—
144	C₂²⋊C₄×C₄₇	—	2	4	no	—
145	C₂²⋊C₄×C₄₇	—	2	4	no	—
146	C₂²⋊C₄×C₄₇	—	2	4	no	—
147	C₂²⋊C₄×C₄₇	—	2	4	no	—
148	C₂²⋊C₄×C₄₇	—	4	4	no	—
149	C₂²⋊C₄×C₄₇	—	4	2	no	—
150	C₂²⋊C₄×C₄₇	—	4	2	no	—
151	C₂²⋊C₄×C₄₇	—	8	2	no	—
152	C₂³×C₄₇	—	2	2	no	—
153	C₂³×C₄₇	—	2	4	no	—
154	C₂³×C₄₇	—	2	2	no	—
155	C₂³×C₄₇	—	2	4	no	—
156	C₂³×C₄₇	—	2	4	no	—
157	C₂³×C₄₇	—	4	1	no	—
158	C₂³×C₄₇	—	4	1	no	—
159	C₂³×C₄₇	—	4	2	no	—
160	C₂³×C₄₇	—	4	2	no	—
161	C₂³×C₄₇	—	4	2	no	—
162	C₂³×C₄₇	—	4	2	no	—
163	C₂³×C₄₇	—	4	8	no	—
164	C₂³×C₄₇	—	4	4	no	—
165	C₂³×C₄₇	—	4	4	no	—
166	C₂³×C₄₇	—	4	2	no	—
167	C₂³×C₄₇	—	4	2	no	—
168	C₂³×C₄₇	—	4	4	no	—
169	C₂³×C₄₇	—	4	1	no	—
170	C₂³×C₄₇	—	4	1	no	—
171	C₂³×C₄₇	—	4	1	no	—
172	C₂³×C₄₇	—	8	1	no	—
173	C₂³×C₄₇	—	8	1	no	—
174	C₂³×C₄₇	—	8	4	no	—
175	C₂³×C₄₇	—	8	4	no	—
176	C₂³×C₄₇	—	8	4	no	—
177	C₂³×C₄₇	—	8	4	no	—
178	C₂³×C₄₇	—	8	16	no	—
179	C₂³×C₄₇	#120	1	1	yes	characteristic
180	C₂³×C₄₇	#120	1	1	yes	characteristic
181	C₂³×C₄₇	C₂×D₈	1	4	yes	—
182	C₂³×C₄₇	C₂×D₈	1	2	yes	—
183	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
184	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
185	D₄×C₄₇	—	4	4	no	—
186	D₄×C₄₇	—	4	4	no	—
187	D₄×C₄₇	—	4	16	no	—
188	D₄×C₄₇	—	4	4	no	—
189	D₄×C₄₇	—	4	4	no	—
190	D₄×C₄₇	—	4	8	no	—
191	D₄×C₄₇	—	8	2	no	—
192	D₄×C₄₇	—	8	4	no	—
193	D₄×C₄₇	—	8	8	no	—
194	D₄×C₄₇	—	8	2	no	—
195	D₄×C₄₇	—	8	2	no	—
196	C₂×C₄×C₄₇	—	2	2	no	—
197	C₂×C₄×C₄₇	—	2	4	no	—
198	C₂×C₄×C₄₇	—	4	1	no	—
199	C₂×C₄×C₄₇	—	4	2	no	—
200	C₂×C₄×C₄₇	—	4	2	no	—
201	C₂×C₄×C₄₇	—	4	1	no	—
202	C₂×C₄×C₄₇	—	4	8	no	—
203	C₂×C₄×C₄₇	—	4	2	no	—
204	C₂×C₄×C₄₇	—	4	4	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	2	no	—
210	C₂×C₄×C₄₇	—	4	1	no	—
211	C₂×C₄×C₄₇	—	4	1	no	—
212	C₂×C₄×C₄₇	—	8	1	no	—
213	C₂×C₄×C₄₇	#120	1	2	yes	—
214	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
215	C₈×C₄₇	—	4	4	no	—
216	#18284	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
217	C₂²×C₄₇	—	2	1	no	—
218	C₂²×C₄₇	—	2	1	no	—
219	C₂²×C₄₇	—	2	1	no	—
220	C₂²×C₄₇	—	2	1	no	—
221	C₂²×C₄₇	—	2	1	no	—
222	C₂²×C₄₇	—	2	1	no	—
223	C₂²×C₄₇	—	2	4	no	—
224	C₂²×C₄₇	—	4	2	no	—
225	C₂²×C₄₇	—	4	2	no	—
226	C₂²×C₄₇	—	4	4	no	—
227	C₂²×C₄₇	—	4	8	no	—
228	C₂²×C₄₇	—	4	2	no	—
229	C₂²×C₄₇	—	4	2	no	—
230	C₂²×C₄₇	—	4	4	no	—
231	C₂²×C₄₇	—	4	4	no	—
232	C₂²×C₄₇	—	4	4	no	—
233	C₂²×C₄₇	—	8	2	no	—
234	C₂²×C₄₇	—	8	4	no	—
235	C₂²×C₄₇	—	8	8	no	—
236	C₂²×C₄₇	—	8	2	no	—
237	C₂²×C₄₇	—	8	2	no	—
238	C₂²×C₄₇	—	8	16	no	—
239	C₂²×C₄₇	—	8	1	no	—
240	C₂²×C₄₇	—	8	1	no	—
241	C₂²×C₄₇	—	8	1	no	—
242	C₂²×C₄₇	#447	1	2	yes	—
243	C₂²×C₄₇	#447	1	2	yes	—
244	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
245	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
246	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
247	C₄×C₄₇	—	2	2	no	—
248	C₄×C₄₇	—	2	2	no	—
249	C₄×C₄₇	—	4	4	no	—
250	C₄×C₄₇	—	4	2	no	—
251	C₄×C₄₇	—	8	2	no	—
252	C₄×C₄₇	—	8	1	no	—
253	C₂×#534	C₂×C₄₇	1	1	yes	characteristic, complemented
254	#3186	C₂×C₄₇	1	2	yes	complemented
255	#2617	C₂×C₄₇	1	1	yes	characteristic, complemented
256	#1607	C₂×C₄₇	1	4	yes	complemented
257	#1595	C₂×C₄₇	1	4	yes	complemented
258	#1519	C₂×C₄₇	1	2	yes	complemented
259	C₂×#323	C₂×C₄₇	1	1	yes	characteristic, complemented
260	C₂×C₄₇	—	2	1	no	—
261	C₂×C₄₇	—	2	2	no	—
262	C₂×C₄₇	—	2	1	no	—
263	C₂×C₄₇	—	2	2	no	—
264	C₂×C₄₇	—	4	4	no	—
265	C₂×C₄₇	—	8	4	no	—
266	C₂×C₄₇	—	16	1	no	—
267	C₂×C₄₇	C₂×#447	1	1	yes	characteristic
268	C₂×C₄₇	#3019	1	1	yes	characteristic
269	C₂×C₄₇	#3026	1	1	yes	characteristic
270	C₂³×D₄	—	2	1	no	—
271	#534	—	2	4	no	—
272	#534	—	2	2	no	—
273	#534	C₂²×C₄₇	1	4	yes	—
274	C₂×#123	—	2	2	no	—
275	C₂×#121	—	2	1	no	—
276	C₂×#121	C₂²×C₄₇	1	2	yes	—
277	C₂×#121	C₂²×C₄₇	1	1	yes	characteristic, complemented
278	C₂×#120	—	2	2	no	—
279	C₂×#120	—	2	1	no	—
280	C₂²×C₂²⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
281	#480	—	2	2	no	—
282	#480	C₂²×C₄₇	1	4	yes	complemented
283	#466	—	2	4	no	—
284	#447	—	2	2	no	—
285	#447	C₂²×C₄₇	1	4	yes	complemented
286	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	complemented
287	#397	C₂²×C₄₇	1	2	yes	complemented
288	#394	—	2	2	no	—
289	#392	C₂²×C₄₇	1	2	yes	complemented
290	#386	—	2	1	no	—
291	#380	C₂²×C₄₇	1	1	yes	characteristic, complemented
292	#327	C₂²×C₄₇	1	8	yes	complemented
293	#323	C₂²×C₄₇	1	4	yes	complemented
294	C₄₇	#18284	1	1	yes	characteristic, direct product factor, Sylow
295	C₂⁵	—	2	1	no	—
296	C₂⁵	D₄×C₄₇	1	1	yes	characteristic
297	C₂²×D₄	—	2	2	no	—
298	C₂²×D₄	—	2	4	no	—
299	C₂²×D₄	—	2	2	no	—
300	C₂²×D₄	—	2	4	no	—
301	C₂²×D₄	—	2	1	no	—
302	C₂²×D₄	—	2	1	no	—
303	C₂²×D₄	—	2	2	no	—
304	C₂²×D₄	—	4	4	no	—
305	C₂²×D₄	—	4	4	no	—
306	C₂²×D₄	D₄×C₄₇	1	2	yes	complemented
307	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic, complemented
308	C₂³×C₄	—	2	1	no	—
309	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
310	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
311	C₂×D₈	—	2	4	no	—
312	C₂²×C₈	—	2	2	no	—
313	#123	—	2	8	no	—
314	#123	—	2	8	no	—
315	#121	—	2	4	no	—
316	#121	—	2	4	no	—
317	#121	—	2	2	no	—
318	#121	—	2	2	no	—
319	#121	—	2	2	no	—
320	#121	—	2	2	no	—
321	#121	D₄×C₄₇	1	4	yes	complemented
322	#121	C₂³×C₄₇	1	4	yes	—
323	#120	—	2	8	no	—
324	#120	—	2	8	no	—
325	#120	—	4	4	no	—
326	C₂×C₄⋊C₄	—	2	1	no	—
327	C₂×C₄⋊C₄	—	2	1	no	—
328	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	complemented
329	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic, complemented
330	C₂×C₂²⋊C₄	—	2	2	no	—
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	2	no	—
334	C₂×C₂²⋊C₄	—	2	1	no	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₂²⋊C₄	—	2	2	no	—
338	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
339	C₂×C₂²⋊C₄	C₂³×C₄₇	1	2	yes	—
340	#107	—	2	4	no	—
341	#102	—	2	4	no	—
342	#102	—	2	4	no	—
343	C₂²⋊C₈	—	2	2	no	—
344	C₂²⋊C₈	C₂³×C₄₇	1	4	yes	complemented
345	#95	—	2	2	no	—
346	#95	C₂³×C₄₇	1	2	yes	complemented
347	C₂⁴	—	2	1	no	—
348	C₂⁴	—	2	1	no	—
349	C₂⁴	—	2	2	no	—
350	C₂⁴	—	2	4	no	—
351	C₂⁴	—	2	2	no	—
352	C₂⁴	—	2	1	no	—
353	C₂⁴	—	4	4	no	—
354	C₂⁴	—	8	1	no	—
355	C₂⁴	—	8	1	no	—
356	C₂⁴	—	8	2	no	—
357	C₂⁴	—	8	2	no	—
358	C₂⁴	D₈×C₄₇	1	4	yes	complemented
359	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
360	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
361	C₂×D₄	—	2	8	no	—
362	C₂×D₄	—	2	4	no	—
363	C₂×D₄	—	2	4	no	—
364	C₂×D₄	—	2	4	no	—
365	C₂×D₄	—	2	2	no	—
366	C₂×D₄	—	2	2	no	—
367	C₂×D₄	—	4	8	no	—
368	C₂×D₄	—	4	16	no	—
369	C₂×D₄	—	4	8	no	—
370	C₂×D₄	—	4	8	no	—
371	C₂×D₄	—	4	4	no	—
372	C₂×D₄	—	4	4	no	—
373	C₂×D₄	—	4	1	no	—
374	C₂×D₄	—	4	1	no	—
375	C₂×D₄	—	4	4	no	—
376	C₂×D₄	—	4	2	no	—
377	C₂×D₄	—	4	2	no	—
378	C₂×D₄	—	8	1	no	—
379	C₂×D₄	—	8	2	no	—
380	C₂×D₄	—	8	2	no	—
381	C₂×D₄	—	8	2	no	—
382	C₂×D₄	—	8	2	no	—
383	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
384	C₂²×C₄	—	2	4	no	—
385	C₂²×C₄	—	2	1	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	4	4	no	—
391	C₂²×C₄	—	8	1	no	—
392	C₂²×C₄	—	8	1	no	—
393	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
394	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
395	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
396	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
397	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
398	D₈	—	8	4	no	—
399	C₂×C₈	—	2	4	no	—
400	C₂×C₈	—	8	2	no	—
401	C₄⋊C₄	—	2	4	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	2	2	no	—
404	C₄⋊C₄	—	8	1	no	—
405	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
406	C₂²⋊C₄	—	2	8	no	—
407	C₂²⋊C₄	—	2	4	no	—
408	C₂²⋊C₄	—	2	4	no	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	2	4	no	—
411	C₂²⋊C₄	—	4	4	no	—
412	C₂²⋊C₄	—	4	2	no	—
413	C₂²⋊C₄	—	4	2	no	—
414	C₂²⋊C₄	—	8	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	4	no	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	4	no	—
419	C₂³	—	2	4	no	—
420	C₂³	—	4	1	no	—
421	C₂³	—	4	1	no	—
422	C₂³	—	4	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	—	4	2	no	—
426	C₂³	—	4	8	no	—
427	C₂³	—	4	4	no	—
428	C₂³	—	4	4	no	—
429	C₂³	—	4	2	no	—
430	C₂³	—	4	2	no	—
431	C₂³	—	4	4	no	—
432	C₂³	—	4	1	no	—
433	C₂³	—	4	1	no	—
434	C₂³	—	4	1	no	—
435	C₂³	—	8	1	no	—
436	C₂³	—	8	1	no	—
437	C₂³	—	8	4	no	—
438	C₂³	—	8	4	no	—
439	C₂³	—	8	4	no	—
440	C₂³	—	8	4	no	—
441	C₂³	—	8	16	no	—
442	C₂³	#120×C₄₇	1	1	yes	characteristic
443	C₂³	#120×C₄₇	1	1	yes	characteristic
444	C₂³	C₂×D₈×C₄₇	1	4	yes	—
445	C₂³	C₂×D₈×C₄₇	1	2	yes	—
446	C₂³	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
447	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
448	D₄	—	4	4	no	—
449	D₄	—	4	4	no	—
450	D₄	—	4	16	no	—
451	D₄	—	4	4	no	—
452	D₄	—	4	4	no	—
453	D₄	—	4	8	no	—
454	D₄	—	8	2	no	—
455	D₄	—	8	4	no	—
456	D₄	—	8	8	no	—
457	D₄	—	8	2	no	—
458	D₄	—	8	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	4	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	4	2	no	—
464	C₂×C₄	—	4	1	no	—
465	C₂×C₄	—	4	8	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	4	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	2	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	8	1	no	—
476	C₂×C₄	#120×C₄₇	1	2	yes	—
477	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
478	C₈	—	4	4	no	—
479	C₂²	—	2	1	no	—
480	C₂²	—	2	1	no	—
481	C₂²	—	2	1	no	—
482	C₂²	—	2	1	no	—
483	C₂²	—	2	1	no	—
484	C₂²	—	2	1	no	—
485	C₂²	—	2	4	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	4	2	no	—
488	C₂²	—	4	4	no	—
489	C₂²	—	4	8	no	—
490	C₂²	—	4	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	4	4	no	—
494	C₂²	—	4	4	no	—
495	C₂²	—	8	2	no	—
496	C₂²	—	8	4	no	—
497	C₂²	—	8	8	no	—
498	C₂²	—	8	2	no	—
499	C₂²	—	8	2	no	—
500	C₂²	—	8	16	no	—
501	C₂²	—	8	1	no	—
502	C₂²	—	8	1	no	—
503	C₂²	—	8	1	no	—
504	C₂²	C₄₇×#447	1	2	yes	—
505	C₂²	C₄₇×#447	1	2	yes	—
506	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
507	C₂²	C₂²×D₈×C₄₇	1	1	yes	characteristic
508	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
509	C₄	—	2	2	no	—
510	C₄	—	2	2	no	—
511	C₄	—	4	4	no	—
512	C₄	—	4	2	no	—
513	C₄	—	8	2	no	—
514	C₄	—	8	1	no	—
515	C₂	—	2	1	no	—
516	C₂	—	2	2	no	—
517	C₂	—	2	1	no	—
518	C₂	—	2	2	no	—
519	C₂	—	4	4	no	—
520	C₂	—	8	4	no	—
521	C₂	—	16	1	no	—
522	C₂	C₂×C₄₇×#447	1	1	yes	characteristic
523	C₂	C₄₇×#3019	1	1	yes	characteristic
524	C₂	C₄₇×#3026	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
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×#534	C₂	semidirect
2. C₄₇×#3186	C₂	semidirect
3. C₄₇×#2617	C₂	semidirect
4. C₄₇×#1607	C₂	semidirect
5. C₄₇×#1595	C₂	semidirect
6. C₄₇×#1519	C₂	semidirect
7. C₂×C₄₇×#323	C₂	semidirect
15. C₂×#121×C₄₇	C₂²	semidirect
20. C₄₇×#480	C₂²	semidirect
23. C₄₇×#447	C₂²	semidirect
24. C₂×C₂²⋊C₈×C₄₇	C₂²	semidirect
25. C₄₇×#397	C₂²	semidirect
27. C₄₇×#392	C₂²	semidirect
29. C₄₇×#380	C₂²	semidirect
30. C₄₇×#327	C₂²	semidirect
31. C₄₇×#323	C₂²	semidirect
43. C₂²×D₄×C₄₇	D₄	semidirect
44. C₂²×D₄×C₄₇	C₂³	semidirect
58. #121×C₄₇	D₄	semidirect
65. C₂×C₄⋊C₄×C₄₇	D₄	semidirect
66. C₂×C₄⋊C₄×C₄₇	C₂³	semidirect
81. C₂²⋊C₈×C₄₇	C₂³	semidirect
83. #95×C₄₇	C₂³	semidirect
95. C₂⁴×C₄₇	D₈	semidirect
216. #18284	C₄₇	direct (N × H)
253. C₂×#534	C₂×C₄₇	semidirect
254. #3186	C₂×C₄₇	semidirect
255. #2617	C₂×C₄₇	semidirect
256. #1607	C₂×C₄₇	semidirect
257. #1595	C₂×C₄₇	semidirect
258. #1519	C₂×C₄₇	semidirect
259. C₂×#323	C₂×C₄₇	semidirect
277. C₂×#121	C₂²×C₄₇	semidirect
282. #480	C₂²×C₄₇	semidirect
285. #447	C₂²×C₄₇	semidirect
286. C₂×C₂²⋊C₈	C₂²×C₄₇	semidirect
287. #397	C₂²×C₄₇	semidirect
289. #392	C₂²×C₄₇	semidirect
291. #380	C₂²×C₄₇	semidirect
292. #327	C₂²×C₄₇	semidirect
293. #323	C₂²×C₄₇	semidirect
294. C₄₇	#18284	direct (N × H)
306. C₂²×D₄	D₄×C₄₇	semidirect
307. C₂²×D₄	C₂³×C₄₇	semidirect
321. #121	D₄×C₄₇	semidirect
328. C₂×C₄⋊C₄	D₄×C₄₇	semidirect
329. C₂×C₄⋊C₄	C₂³×C₄₇	semidirect
344. C₂²⋊C₈	C₂³×C₄₇	semidirect
346. #95	C₂³×C₄₇	semidirect
358. C₂⁴	D₈×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×#534	2
C₄₇×#3186	2
C₄₇×#2617	2
C₄₇×#1607	2
C₄₇×#1595	2
C₄₇×#1519	2
C₂×C₄₇×#323	2
#18284	47

Subgroups — C47×#18284 #26057982

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18284 #26057982