Subgroups — C₂×C₄₇×#2018 #26063133

Order 12032.

2158 conjugacy classes of subgroups.

The subgroup lattice has 456 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×AGL(1,ℤ/8)×C₄₇	C₂	1	2	yes	maximal, complemented
2	C₂³×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#100×C₄₇	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₇×#408	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2018	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₇×#341	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
8	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
9	C₂×AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
10	C₂×AGL(1,ℤ/8)×C₄₇	—	2	8	no	—
11	C₂×AGL(1,ℤ/8)×C₄₇	—	2	8	no	—
12	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	8	yes	complemented
13	C₂²×SD₁₆×C₄₇	—	2	2	no	—
14	C₂²×D₈×C₄₇	—	2	8	no	—
15	C₂²×D₈×C₄₇	—	2	2	no	—
16	C₂²×D₈×C₄₇	—	2	2	no	—
17	C₂²×D₈×C₄₇	—	2	2	no	—
18	C₂²×D₈×C₄₇	C₂²	1	4	yes	complemented
19	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
20	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
21	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×#100×C₄₇	—	2	8	no	—
23	C₂×#100×C₄₇	C₂²	1	8	yes	complemented
24	C₄₇×#408	—	2	2	no	—
25	C₄₇×#408	C₂²	1	4	yes	complemented
26	C₂×C₂²⋊C₈×C₄₇	—	2	2	no	—
27	C₄₇×#341	C₂²	1	4	yes	complemented
28	C₂⁵×C₄₇	—	2	2	no	—
29	C₂×#41×C₄₇	—	2	1	no	—
30	C₂×#41×C₄₇	—	2	1	no	—
31	C₂×#41×C₄₇	—	2	4	no	—
32	C₂×#41×C₄₇	—	2	4	no	—
33	C₂×#41×C₄₇	D₄	1	2	yes	—
34	C₂×#41×C₄₇	C₂³	1	2	yes	—
35	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
36	C₂²×D₄×C₄₇	—	2	1	no	—
37	C₂²×D₄×C₄₇	—	2	4	no	—
38	C₂²×D₄×C₄₇	—	2	2	no	—
39	C₂²×D₄×C₄₇	—	2	2	no	—
40	C₂²×D₄×C₄₇	—	2	2	no	—
41	C₂²×D₄×C₄₇	—	2	2	no	—
42	C₂²×D₄×C₄₇	—	2	4	no	—
43	C₂²×D₄×C₄₇	—	2	4	no	—
44	C₂²×D₄×C₄₇	—	2	2	no	—
45	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₄₇	D₄	1	8	yes	—
47	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
48	C₂³×C₄×C₄₇	—	2	1	no	—
49	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
50	AGL(1,ℤ/8)×C₄₇	—	2	32	no	—
51	AGL(1,ℤ/8)×C₄₇	—	2	16	no	—
52	AGL(1,ℤ/8)×C₄₇	—	2	16	no	—
53	C₂×SD₁₆×C₄₇	—	2	16	no	—
54	C₂×SD₁₆×C₄₇	—	2	8	no	—
55	C₂×D₈×C₄₇	—	2	16	no	—
56	C₂×D₈×C₄₇	—	2	16	no	—
57	C₂×D₈×C₄₇	—	2	16	no	—
58	C₂×D₈×C₄₇	—	2	16	no	—
59	C₂×D₈×C₄₇	—	2	8	no	—
60	C₂×D₈×C₄₇	—	2	8	no	—
61	C₂×M₁₆×C₄₇	—	2	4	no	—
62	C₂×M₁₆×C₄₇	—	2	2	no	—
63	C₂×M₁₆×C₄₇	—	2	1	no	—
64	C₂×M₁₆×C₄₇	—	2	4	no	—
65	C₂×M₁₆×C₄₇	D₄	1	8	yes	—
66	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
67	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
68	C₂²×C₈×C₄₇	—	2	4	no	—
69	C₂²×C₈×C₄₇	—	2	2	no	—
70	C₂²×C₈×C₄₇	—	2	1	no	—
71	C₂²×C₈×C₄₇	D₄	1	2	yes	—
72	C₂²×C₈×C₄₇	D₄	1	2	yes	—
73	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
74	#100×C₄₇	—	2	16	no	—
75	C₂²⋊C₈×C₄₇	—	2	8	no	—
76	C₂⁴×C₄₇	—	2	1	no	—
77	C₂⁴×C₄₇	—	2	8	no	—
78	C₂⁴×C₄₇	—	2	4	no	—
79	C₂⁴×C₄₇	—	4	2	no	—
80	C₂⁴×C₄₇	—	4	4	no	—
81	C₂⁴×C₄₇	—	4	2	no	—
82	C₂⁴×C₄₇	—	8	8	no	—
83	C₂⁴×C₄₇	#41	1	1	yes	characteristic
84	#41×C₄₇	—	2	8	no	—
85	#41×C₄₇	—	2	4	no	—
86	#41×C₄₇	—	2	4	no	—
87	#41×C₄₇	—	4	2	no	—
88	#41×C₄₇	—	4	4	no	—
89	#41×C₄₇	—	4	2	no	—
90	C₂×Q₈×C₄₇	—	2	1	no	—
91	C₂×Q₈×C₄₇	—	2	4	no	—
92	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
93	C₂×D₄×C₄₇	—	2	2	no	—
94	C₂×D₄×C₄₇	—	2	2	no	—
95	C₂×D₄×C₄₇	—	2	8	no	—
96	C₂×D₄×C₄₇	—	2	8	no	—
97	C₂×D₄×C₄₇	—	2	4	no	—
98	C₂×D₄×C₄₇	—	2	8	no	—
99	C₂×D₄×C₄₇	—	2	8	no	—
100	C₂×D₄×C₄₇	—	2	8	no	—
101	C₂×D₄×C₄₇	—	2	1	no	—
102	C₂×D₄×C₄₇	—	2	4	no	—
103	C₂×D₄×C₄₇	—	2	4	no	—
104	C₂×D₄×C₄₇	—	2	4	no	—
105	C₂×D₄×C₄₇	—	2	4	no	—
106	C₂×D₄×C₄₇	—	2	4	no	—
107	C₂×D₄×C₄₇	—	4	4	no	—
108	C₂×D₄×C₄₇	—	4	4	no	—
109	C₂×D₄×C₄₇	—	4	4	no	—
110	C₂×D₄×C₄₇	—	4	2	no	—
111	C₂×D₄×C₄₇	—	4	4	no	—
112	C₂×D₄×C₄₇	—	4	2	no	—
113	C₂×D₄×C₄₇	—	4	4	no	—
114	C₂×D₄×C₄₇	—	4	4	no	—
115	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
116	C₂×D₄×C₄₇	C₂×D₄	1	8	yes	—
117	C₂²×C₄×C₄₇	—	2	1	no	—
118	C₂²×C₄×C₄₇	—	2	2	no	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	4	2	no	—
121	C₂²×C₄×C₄₇	—	4	2	no	—
122	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
123	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
130	SD₁₆×C₄₇	—	2	32	no	—
131	D₈×C₄₇	—	2	32	no	—
132	D₈×C₄₇	—	2	32	no	—
133	M₁₆×C₄₇	—	2	8	no	—
134	M₁₆×C₄₇	—	2	4	no	—
135	M₁₆×C₄₇	—	2	4	no	—
136	M₁₆×C₄₇	—	4	2	no	—
137	M₁₆×C₄₇	C₂×D₄	1	8	yes	—
138	C₂×C₈×C₄₇	—	2	4	no	—
139	C₂×C₈×C₄₇	—	2	4	no	—
140	C₂×C₈×C₄₇	—	2	8	no	—
141	C₂×C₈×C₄₇	—	2	4	no	—
142	C₂×C₈×C₄₇	—	2	4	no	—
143	C₂×C₈×C₄₇	—	2	2	no	—
144	C₂×C₈×C₄₇	—	4	2	no	—
145	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
146	C₂³×C₄₇	—	2	4	no	—
147	C₂³×C₄₇	—	2	2	no	—
148	C₂³×C₄₇	—	2	8	no	—
149	C₂³×C₄₇	—	4	4	no	—
150	C₂³×C₄₇	—	4	4	no	—
151	C₂³×C₄₇	—	4	2	no	—
152	C₂³×C₄₇	—	4	8	no	—
153	C₂³×C₄₇	—	4	8	no	—
154	C₂³×C₄₇	—	4	4	no	—
155	C₂³×C₄₇	—	8	16	no	—
156	C₂³×C₄₇	—	8	8	no	—
157	C₂³×C₄₇	—	8	16	no	—
158	C₂³×C₄₇	—	8	8	no	—
159	C₂³×C₄₇	—	8	8	no	—
160	C₂³×C₄₇	#121	1	1	yes	characteristic
161	C₂³×C₄₇	#121	1	4	yes	—
162	C₂³×C₄₇	#121	1	1	yes	characteristic
163	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
164	Q₈×C₄₇	—	2	4	no	—
165	Q₈×C₄₇	—	4	2	no	—
166	D₄×C₄₇	—	2	8	no	—
167	D₄×C₄₇	—	2	4	no	—
168	D₄×C₄₇	—	2	8	no	—
169	D₄×C₄₇	—	4	4	no	—
170	D₄×C₄₇	—	4	4	no	—
171	D₄×C₄₇	—	4	4	no	—
172	D₄×C₄₇	—	4	4	no	—
173	D₄×C₄₇	—	4	8	no	—
174	D₄×C₄₇	—	4	8	no	—
175	D₄×C₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	—	4	2	no	—
179	C₂×C₄×C₄₇	—	4	2	no	—
180	C₂×C₄×C₄₇	—	4	4	no	—
181	C₂×C₄×C₄₇	#120	1	2	yes	—
182	C₂×C₄×C₄₇	#120	1	2	yes	—
183	C₂×C₄×C₄₇	#120	1	4	yes	—
184	C₂×C₄×C₄₇	#120	1	4	yes	—
185	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
186	C₂×C₄×C₄₇	#121	1	4	yes	—
187	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
188	C₂×C₄×C₄₇	#127	1	2	yes	—
189	C₂×C₄×C₄₇	#127	1	2	yes	—
190	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
192	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
194	C₈×C₄₇	—	2	4	no	—
195	C₈×C₄₇	—	2	8	no	—
196	C₈×C₄₇	—	4	2	no	—
197	C₂×#2018	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
198	C₂²×C₄₇	—	2	8	no	—
199	C₂²×C₄₇	—	2	2	no	—
200	C₂²×C₄₇	—	2	2	no	—
201	C₂²×C₄₇	—	4	2	no	—
202	C₂²×C₄₇	—	4	8	no	—
203	C₂²×C₄₇	—	4	4	no	—
204	C₂²×C₄₇	—	8	8	no	—
205	C₂²×C₄₇	—	8	8	no	—
206	C₂²×C₄₇	—	8	16	no	—
207	C₂²×C₄₇	—	8	4	no	—
208	C₂²×C₄₇	—	8	16	no	—
209	C₂²×C₄₇	—	8	8	no	—
210	C₂²×C₄₇	#392	1	2	yes	—
211	C₂²×C₄₇	#392	1	2	yes	—
212	C₂²×C₄₇	#472	1	4	yes	—
213	C₂²×C₄₇	C₂×#121	1	2	yes	—
214	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
215	C₄×C₄₇	—	4	2	no	—
216	C₄×C₄₇	#392	1	2	yes	—
217	C₄×C₄₇	#392	1	2	yes	—
218	C₄×C₄₇	C₂×#120	1	1	yes	characteristic
219	C₄×C₄₇	C₂×#120	1	2	yes	—
220	C₄×C₄₇	C₂×#127	1	1	yes	characteristic
221	C₂²×AGL(1,ℤ/8)	C₂×C₄₇	1	2	yes	complemented
222	C₂³×D₈	C₂×C₄₇	1	1	yes	characteristic, complemented
223	C₂²×#100	C₂×C₄₇	1	2	yes	complemented
224	C₂×#408	C₂×C₄₇	1	1	yes	characteristic, complemented
225	#2018	C₂×C₄₇	1	8	yes	direct product factor
226	C₂×#341	C₂×C₄₇	1	1	yes	characteristic, complemented
227	C₂×C₄₇	—	2	2	no	—
228	C₂×C₄₇	—	2	2	no	—
229	C₂×C₄₇	—	8	2	no	—
230	C₂×C₄₇	—	8	8	no	—
231	C₂×C₄₇	#2018	1	4	yes	direct product factor
232	C₂×C₄₇	C₂×#392	1	1	yes	characteristic
233	C₂×C₄₇	C₂×#472	1	2	yes	—
234	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
235	C₂³×D₄	C₂²×C₄₇	1	2	yes	—
236	C₂×AGL(1,ℤ/8)	—	2	4	no	—
237	C₂×AGL(1,ℤ/8)	—	2	8	no	—
238	C₂×AGL(1,ℤ/8)	—	2	8	no	—
239	C₂×AGL(1,ℤ/8)	C₂²×C₄₇	1	8	yes	complemented
240	C₂²×SD₁₆	—	2	2	no	—
241	C₂²×D₈	—	2	8	no	—
242	C₂²×D₈	—	2	2	no	—
243	C₂²×D₈	—	2	2	no	—
244	C₂²×D₈	—	2	2	no	—
245	C₂²×D₈	C₂²×C₄₇	1	4	yes	complemented
246	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
247	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
248	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
249	C₂×#100	—	2	8	no	—
250	C₂×#100	C₂²×C₄₇	1	8	yes	complemented
251	#408	—	2	2	no	—
252	#408	C₂²×C₄₇	1	4	yes	complemented
253	C₂×C₂²⋊C₈	—	2	2	no	—
254	#341	C₂²×C₄₇	1	4	yes	complemented
255	C₄₇	C₂×#2018	1	1	yes	characteristic, direct product factor, Sylow
256	C₂⁵	—	2	2	no	—
257	C₂×#41	—	2	1	no	—
258	C₂×#41	—	2	1	no	—
259	C₂×#41	—	2	4	no	—
260	C₂×#41	—	2	4	no	—
261	C₂×#41	D₄×C₄₇	1	2	yes	—
262	C₂×#41	C₂³×C₄₇	1	2	yes	—
263	C₂²×Q₈	D₄×C₄₇	1	1	yes	characteristic
264	C₂²×D₄	—	2	1	no	—
265	C₂²×D₄	—	2	4	no	—
266	C₂²×D₄	—	2	2	no	—
267	C₂²×D₄	—	2	2	no	—
268	C₂²×D₄	—	2	2	no	—
269	C₂²×D₄	—	2	2	no	—
270	C₂²×D₄	—	2	4	no	—
271	C₂²×D₄	—	2	4	no	—
272	C₂²×D₄	—	2	2	no	—
273	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
274	C₂²×D₄	D₄×C₄₇	1	8	yes	—
275	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
276	C₂³×C₄	—	2	1	no	—
277	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
278	AGL(1,ℤ/8)	—	2	32	no	—
279	AGL(1,ℤ/8)	—	2	16	no	—
280	AGL(1,ℤ/8)	—	2	16	no	—
281	C₂×SD₁₆	—	2	16	no	—
282	C₂×SD₁₆	—	2	8	no	—
283	C₂×D₈	—	2	16	no	—
284	C₂×D₈	—	2	16	no	—
285	C₂×D₈	—	2	16	no	—
286	C₂×D₈	—	2	16	no	—
287	C₂×D₈	—	2	8	no	—
288	C₂×D₈	—	2	8	no	—
289	C₂×M₁₆	—	2	4	no	—
290	C₂×M₁₆	—	2	2	no	—
291	C₂×M₁₆	—	2	1	no	—
292	C₂×M₁₆	—	2	4	no	—
293	C₂×M₁₆	D₄×C₄₇	1	8	yes	—
294	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
295	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
296	C₂²×C₈	—	2	4	no	—
297	C₂²×C₈	—	2	2	no	—
298	C₂²×C₈	—	2	1	no	—
299	C₂²×C₈	D₄×C₄₇	1	2	yes	—
300	C₂²×C₈	D₄×C₄₇	1	2	yes	—
301	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
302	#100	—	2	16	no	—
303	C₂²⋊C₈	—	2	8	no	—
304	C₂⁴	—	2	1	no	—
305	C₂⁴	—	2	8	no	—
306	C₂⁴	—	2	4	no	—
307	C₂⁴	—	4	2	no	—
308	C₂⁴	—	4	4	no	—
309	C₂⁴	—	4	2	no	—
310	C₂⁴	—	8	8	no	—
311	C₂⁴	#41×C₄₇	1	1	yes	characteristic
312	#41	—	2	8	no	—
313	#41	—	2	4	no	—
314	#41	—	2	4	no	—
315	#41	—	4	2	no	—
316	#41	—	4	4	no	—
317	#41	—	4	2	no	—
318	C₂×Q₈	—	2	1	no	—
319	C₂×Q₈	—	2	4	no	—
320	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
321	C₂×D₄	—	2	2	no	—
322	C₂×D₄	—	2	2	no	—
323	C₂×D₄	—	2	8	no	—
324	C₂×D₄	—	2	8	no	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	—	2	8	no	—
327	C₂×D₄	—	2	8	no	—
328	C₂×D₄	—	2	8	no	—
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	4	no	—
331	C₂×D₄	—	2	4	no	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	4	4	no	—
336	C₂×D₄	—	4	4	no	—
337	C₂×D₄	—	4	4	no	—
338	C₂×D₄	—	4	2	no	—
339	C₂×D₄	—	4	4	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	4	4	no	—
342	C₂×D₄	—	4	4	no	—
343	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
344	C₂×D₄	C₂×D₄×C₄₇	1	8	yes	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	4	2	no	—
349	C₂²×C₄	—	4	2	no	—
350	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
351	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
352	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
353	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
354	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
356	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
357	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
358	SD₁₆	—	2	32	no	—
359	D₈	—	2	32	no	—
360	D₈	—	2	32	no	—
361	M₁₆	—	2	8	no	—
362	M₁₆	—	2	4	no	—
363	M₁₆	—	2	4	no	—
364	M₁₆	—	4	2	no	—
365	M₁₆	C₂×D₄×C₄₇	1	8	yes	—
366	C₂×C₈	—	2	4	no	—
367	C₂×C₈	—	2	4	no	—
368	C₂×C₈	—	2	8	no	—
369	C₂×C₈	—	2	4	no	—
370	C₂×C₈	—	2	4	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	4	2	no	—
373	C₂×C₈	C₂×D₄×C₄₇	1	4	yes	—
374	C₂³	—	2	4	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	2	8	no	—
377	C₂³	—	4	4	no	—
378	C₂³	—	4	4	no	—
379	C₂³	—	4	4	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	4	8	no	—
382	C₂³	—	4	8	no	—
383	C₂³	—	8	16	no	—
384	C₂³	—	8	8	no	—
385	C₂³	—	8	16	no	—
386	C₂³	—	8	8	no	—
387	C₂³	—	8	8	no	—
388	C₂³	#121×C₄₇	1	1	yes	characteristic
389	C₂³	#121×C₄₇	1	4	yes	—
390	C₂³	#121×C₄₇	1	1	yes	characteristic
391	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
392	Q₈	—	2	4	no	—
393	Q₈	—	4	2	no	—
394	D₄	—	2	8	no	—
395	D₄	—	2	4	no	—
396	D₄	—	2	8	no	—
397	D₄	—	4	4	no	—
398	D₄	—	4	4	no	—
399	D₄	—	4	4	no	—
400	D₄	—	4	4	no	—
401	D₄	—	4	8	no	—
402	D₄	—	4	8	no	—
403	D₄	—	4	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	4	2	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	4	no	—
409	C₂×C₄	#120×C₄₇	1	2	yes	—
410	C₂×C₄	#120×C₄₇	1	2	yes	—
411	C₂×C₄	#120×C₄₇	1	4	yes	—
412	C₂×C₄	#120×C₄₇	1	4	yes	—
413	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
414	C₂×C₄	#121×C₄₇	1	4	yes	—
415	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
416	C₂×C₄	#127×C₄₇	1	2	yes	—
417	C₂×C₄	#127×C₄₇	1	2	yes	—
418	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
419	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
420	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
421	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
422	C₈	—	2	4	no	—
423	C₈	—	2	8	no	—
424	C₈	—	4	2	no	—
425	C₂²	—	2	8	no	—
426	C₂²	—	2	2	no	—
427	C₂²	—	2	2	no	—
428	C₂²	—	4	4	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	8	no	—
431	C₂²	—	8	8	no	—
432	C₂²	—	8	8	no	—
433	C₂²	—	8	16	no	—
434	C₂²	—	8	4	no	—
435	C₂²	—	8	16	no	—
436	C₂²	—	8	8	no	—
437	C₂²	C₄₇×#392	1	2	yes	—
438	C₂²	C₄₇×#392	1	2	yes	—
439	C₂²	C₄₇×#472	1	4	yes	—
440	C₂²	C₂×#121×C₄₇	1	2	yes	—
441	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
442	C₄	—	4	2	no	—
443	C₄	C₄₇×#392	1	2	yes	—
444	C₄	C₄₇×#392	1	2	yes	—
445	C₄	C₂×#120×C₄₇	1	1	yes	characteristic
446	C₄	C₂×#120×C₄₇	1	2	yes	—
447	C₄	C₂×#127×C₄₇	1	1	yes	characteristic
448	C₂	—	2	2	no	—
449	C₂	—	2	2	no	—
450	C₂	—	8	2	no	—
451	C₂	—	8	8	no	—
452	C₂	C₄₇×#2018	1	4	yes	direct product factor
453	C₂	C₂×C₄₇×#392	1	1	yes	characteristic
454	C₂	C₂×C₄₇×#472	1	2	yes	—

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

Complements

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

N	H ≅ G/N	type
1. C₂²×AGL(1,ℤ/8)×C₄₇	C₂	semidirect
2. C₂³×D₈×C₄₇	C₂	semidirect
3. C₂²×#100×C₄₇	C₂	semidirect
4. C₂×C₄₇×#408	C₂	semidirect
5. C₄₇×#2018	C₂	direct (N × H)
6. C₂×C₄₇×#341	C₂	semidirect
12. C₂×AGL(1,ℤ/8)×C₄₇	C₂²	semidirect
18. C₂²×D₈×C₄₇	C₂²	semidirect
23. C₂×#100×C₄₇	C₂²	semidirect
25. C₄₇×#408	C₂²	semidirect
27. C₄₇×#341	C₂²	semidirect
197. C₂×#2018	C₄₇	direct (N × H)
221. C₂²×AGL(1,ℤ/8)	C₂×C₄₇	semidirect
222. C₂³×D₈	C₂×C₄₇	semidirect
223. C₂²×#100	C₂×C₄₇	semidirect
224. C₂×#408	C₂×C₄₇	semidirect
225. #2018	C₂×C₄₇	direct (N × H)
226. C₂×#341	C₂×C₄₇	semidirect
231. C₂×C₄₇	#2018	direct (N × H)
239. C₂×AGL(1,ℤ/8)	C₂²×C₄₇	semidirect
245. C₂²×D₈	C₂²×C₄₇	semidirect
250. C₂×#100	C₂²×C₄₇	semidirect
252. #408	C₂²×C₄₇	semidirect
254. #341	C₂²×C₄₇	semidirect
255. C₄₇	C₂×#2018	direct (N × H)
452. C₂	C₄₇×#2018	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×AGL(1,ℤ/8)×C₄₇	2
C₂³×D₈×C₄₇	2
C₂²×#100×C₄₇	2
C₂×C₄₇×#408	2
C₄₇×#2018	2
C₂×C₄₇×#341	2
C₂×#2018	47

Subgroups — C2×C47×#2018 #26063133

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#2018 #26063133