Subgroups — C₂×C₄₇×#2041 #26063199

Order 12032.

2230 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#127×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#102×C₄₇	C₂	1	2	yes	maximal, complemented
3	C₂²×#102×C₄₇	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₇×#389	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2041	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₇×#336	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂³×D₄×C₄₇	—	2	1	no	—
8	C₂³×D₄×C₄₇	—	2	1	no	—
9	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
10	C₂³×C₈×C₄₇	C₂²	1	2	yes	—
11	C₂×#127×C₄₇	—	2	8	no	—
12	C₂×#127×C₄₇	—	2	2	no	—
13	C₂×#127×C₄₇	C₂²	1	4	yes	—
14	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
15	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×#102×C₄₇	—	2	8	no	—
19	C₂×#102×C₄₇	—	2	8	no	—
20	C₂×#102×C₄₇	C₂²	1	8	yes	complemented
21	C₂×#102×C₄₇	C₂²	1	8	yes	complemented
22	C₄₇×#389	—	2	2	no	—
23	C₄₇×#389	C₂²	1	4	yes	complemented
24	C₂×#95×C₄₇	—	2	1	no	—
25	C₄₇×#336	C₂²	1	4	yes	complemented
26	C₂⁵×C₄₇	—	2	2	no	—
27	C₂²×D₄×C₄₇	—	2	8	no	—
28	C₂²×D₄×C₄₇	—	2	8	no	—
29	C₂²×D₄×C₄₇	—	2	4	no	—
30	C₂²×D₄×C₄₇	—	2	2	no	—
31	C₂²×D₄×C₄₇	—	2	4	no	—
32	C₂²×D₄×C₄₇	—	2	4	no	—
33	C₂²×D₄×C₄₇	—	2	4	no	—
34	C₂²×D₄×C₄₇	—	2	4	no	—
35	C₂²×D₄×C₄₇	—	2	4	no	—
36	C₂²×D₄×C₄₇	—	2	4	no	—
37	C₂²×D₄×C₄₇	—	4	4	no	—
38	C₂²×D₄×C₄₇	—	4	4	no	—
39	C₂²×D₄×C₄₇	—	4	4	no	—
40	C₂²×D₄×C₄₇	—	4	4	no	—
41	C₂²×D₄×C₄₇	D₄	1	8	yes	—
42	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
43	C₂³×C₄×C₄₇	—	2	1	no	—
44	C₂³×C₄×C₄₇	—	2	1	no	—
45	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
46	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
47	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₄₇	—	2	4	no	—
49	C₂²×C₈×C₄₇	—	2	4	no	—
50	C₂²×C₈×C₄₇	—	2	4	no	—
51	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
52	#127×C₄₇	—	2	16	no	—
53	#127×C₄₇	—	2	16	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
58	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
60	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	complemented
61	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
63	C₂×C₄²×C₄₇	—	2	4	no	—
64	C₂×C₄²×C₄₇	D₄	1	2	yes	—
65	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
66	#102×C₄₇	—	2	16	no	—
67	#102×C₄₇	—	2	16	no	—
68	#95×C₄₇	—	2	4	no	—
69	C₂⁴×C₄₇	—	2	8	no	—
70	C₂⁴×C₄₇	—	2	4	no	—
71	C₂⁴×C₄₇	—	4	4	no	—
72	C₂⁴×C₄₇	—	4	4	no	—
73	C₂⁴×C₄₇	—	4	4	no	—
74	C₂⁴×C₄₇	—	4	4	no	—
75	C₂⁴×C₄₇	—	4	4	no	—
76	C₂⁴×C₄₇	—	4	4	no	—
77	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
78	C₂×D₄×C₄₇	—	2	16	no	—
79	C₂×D₄×C₄₇	—	2	16	no	—
80	C₂×D₄×C₄₇	—	2	8	no	—
81	C₂×D₄×C₄₇	—	2	16	no	—
82	C₂×D₄×C₄₇	—	2	16	no	—
83	C₂×D₄×C₄₇	—	2	4	no	—
84	C₂×D₄×C₄₇	—	2	4	no	—
85	C₂×D₄×C₄₇	—	2	4	no	—
86	C₂×D₄×C₄₇	—	2	4	no	—
87	C₂×D₄×C₄₇	—	2	4	no	—
88	C₂×D₄×C₄₇	—	4	8	no	—
89	C₂×D₄×C₄₇	—	4	8	no	—
90	C₂×D₄×C₄₇	—	4	32	no	—
91	C₂×D₄×C₄₇	—	4	32	no	—
92	C₂×D₄×C₄₇	—	4	8	no	—
93	C₂×D₄×C₄₇	—	4	4	no	—
94	C₂×D₄×C₄₇	—	4	8	no	—
95	C₂×D₄×C₄₇	—	4	4	no	—
96	C₂×D₄×C₄₇	—	4	8	no	—
97	C₂×D₄×C₄₇	—	4	8	no	—
98	C₂×D₄×C₄₇	C₂×D₄	1	8	yes	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	—	2	4	no	—
104	C₂²×C₄×C₄₇	—	2	2	no	—
105	C₂²×C₄×C₄₇	—	2	2	no	—
106	C₂²×C₄×C₄₇	—	4	2	no	—
107	C₂²×C₄×C₄₇	—	4	2	no	—
108	C₂²×C₄×C₄₇	—	4	2	no	—
109	C₂²×C₄×C₄₇	—	4	2	no	—
110	C₂²×C₄×C₄₇	—	4	2	no	—
111	C₂²×C₄×C₄₇	D₈	1	4	yes	—
112	C₂²×C₄×C₄₇	SD₁₆	1	4	yes	—
113	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
117	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₇	#41	1	4	yes	—
119	C₂²×C₄×C₄₇	#41	1	2	yes	—
120	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
121	C₂×C₈×C₄₇	—	2	4	no	—
122	C₂×C₈×C₄₇	—	2	4	no	—
123	C₂×C₈×C₄₇	—	2	4	no	—
124	C₂×C₈×C₄₇	—	4	8	no	—
125	C₄⋊C₄×C₄₇	—	2	4	no	—
126	C₄⋊C₄×C₄₇	—	2	2	no	—
127	C₄⋊C₄×C₄₇	—	2	4	no	—
128	C₄⋊C₄×C₄₇	—	4	2	no	—
129	C₄⋊C₄×C₄₇	—	4	8	no	—
130	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	complemented
131	C₄²×C₄₇	—	2	4	no	—
132	C₄²×C₄₇	—	2	4	no	—
133	C₂³×C₄₇	—	2	8	no	—
134	C₂³×C₄₇	—	4	4	no	—
135	C₂³×C₄₇	—	4	4	no	—
136	C₂³×C₄₇	—	4	4	no	—
137	C₂³×C₄₇	—	4	4	no	—
138	C₂³×C₄₇	—	4	4	no	—
139	C₂³×C₄₇	—	4	4	no	—
140	C₂³×C₄₇	—	4	16	no	—
141	C₂³×C₄₇	—	4	16	no	—
142	C₂³×C₄₇	—	4	16	no	—
143	C₂³×C₄₇	—	8	8	no	—
144	C₂³×C₄₇	—	8	8	no	—
145	C₂³×C₄₇	—	8	8	no	—
146	C₂³×C₄₇	—	8	8	no	—
147	C₂³×C₄₇	#120	1	2	yes	—
148	C₂³×C₄₇	#121	1	2	yes	—
149	C₂³×C₄₇	#124	1	2	yes	—
150	C₂³×C₄₇	C₂×D₈	1	2	yes	—
151	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
152	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
153	C₂³×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
154	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
155	D₄×C₄₇	—	2	8	no	—
156	D₄×C₄₇	—	2	8	no	—
157	D₄×C₄₇	—	4	32	no	—
158	D₄×C₄₇	—	4	32	no	—
159	D₄×C₄₇	—	4	4	no	—
160	D₄×C₄₇	—	4	4	no	—
161	D₄×C₄₇	—	4	16	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	2	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	8	no	—
167	C₂×C₄×C₄₇	—	2	8	no	—
168	C₂×C₄×C₄₇	—	2	4	no	—
169	C₂×C₄×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	—	4	8	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	—	4	2	no	—
175	C₂×C₄×C₄₇	—	8	4	no	—
176	C₂×C₄×C₄₇	#120	1	2	yes	—
177	C₂×C₄×C₄₇	#121	1	8	yes	—
178	C₂×C₄×C₄₇	#121	1	2	yes	—
179	C₂×C₄×C₄₇	#123	1	8	yes	—
180	C₂×C₄×C₄₇	#124	1	2	yes	—
181	C₂×C₄×C₄₇	C₂×D₈	1	4	yes	—
182	C₂×C₄×C₄₇	C₂×SD₁₆	1	4	yes	—
183	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
185	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
186	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
187	C₈×C₄₇	—	4	4	no	—
188	C₂×#2041	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂²×C₄₇	—	4	8	no	—
190	C₂²×C₄₇	—	4	8	no	—
191	C₂²×C₄₇	—	4	8	no	—
192	C₂²×C₄₇	—	8	4	no	—
193	C₂²×C₄₇	—	8	4	no	—
194	C₂²×C₄₇	—	8	4	no	—
195	C₂²×C₄₇	—	8	4	no	—
196	C₂²×C₄₇	—	8	32	no	—
197	C₂²×C₄₇	#394	1	4	yes	—
198	C₂²×C₄₇	#447	1	4	yes	—
199	C₂²×C₄₇	#450	1	4	yes	—
200	C₂²×C₄₇	#459	1	4	yes	—
201	C₂²×C₄₇	#460	1	4	yes	—
202	C₂²×C₄₇	#486	1	4	yes	—
203	C₂²×C₄₇	#490	1	4	yes	—
204	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
205	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
206	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
207	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
208	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
209	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
210	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
211	C₄×C₄₇	—	2	4	no	—
212	C₄×C₄₇	—	2	4	no	—
213	C₄×C₄₇	—	4	4	no	—
214	C₄×C₄₇	—	8	2	no	—
215	C₄×C₄₇	#394	1	4	yes	—
216	C₄×C₄₇	C₂×#121	1	2	yes	—
217	C₄×C₄₇	C₂×#123	1	2	yes	—
218	C₂²×#127	C₂×C₄₇	1	1	yes	characteristic
219	C₂²×#102	C₂×C₄₇	1	2	yes	complemented
220	C₂²×#102	C₂×C₄₇	1	2	yes	complemented
221	C₂×#389	C₂×C₄₇	1	1	yes	characteristic, complemented
222	#2041	C₂×C₄₇	1	8	yes	direct product factor
223	C₂×#336	C₂×C₄₇	1	1	yes	characteristic, complemented
224	C₂×C₄₇	—	8	8	no	—
225	C₂×C₄₇	#2041	1	8	yes	direct product factor
226	C₂×C₄₇	C₂×#394	1	1	yes	characteristic
227	C₂×C₄₇	C₂×#447	1	1	yes	characteristic
228	C₂×C₄₇	C₂×#450	1	1	yes	characteristic
229	C₂×C₄₇	C₂×#459	1	1	yes	characteristic
230	C₂×C₄₇	C₂×#460	1	1	yes	characteristic
231	C₂×C₄₇	C₂×#486	1	1	yes	characteristic
232	C₂×C₄₇	C₂×#490	1	1	yes	characteristic
233	C₂³×D₄	—	2	1	no	—
234	C₂³×D₄	—	2	1	no	—
235	C₂³×D₄	C₂²×C₄₇	1	2	yes	—
236	C₂³×C₈	C₂²×C₄₇	1	2	yes	—
237	C₂×#127	—	2	8	no	—
238	C₂×#127	—	2	2	no	—
239	C₂×#127	C₂²×C₄₇	1	4	yes	—
240	C₂²×C₄⋊C₄	—	2	1	no	—
241	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
242	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
243	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
244	C₂×#102	—	2	8	no	—
245	C₂×#102	—	2	8	no	—
246	C₂×#102	C₂²×C₄₇	1	8	yes	complemented
247	C₂×#102	C₂²×C₄₇	1	8	yes	complemented
248	#389	—	2	2	no	—
249	#389	C₂²×C₄₇	1	4	yes	complemented
250	C₂×#95	—	2	1	no	—
251	#336	C₂²×C₄₇	1	4	yes	complemented
252	C₄₇	C₂×#2041	1	1	yes	characteristic, direct product factor, Sylow
253	C₂⁵	—	2	2	no	—
254	C₂²×D₄	—	2	8	no	—
255	C₂²×D₄	—	2	8	no	—
256	C₂²×D₄	—	2	4	no	—
257	C₂²×D₄	—	2	2	no	—
258	C₂²×D₄	—	2	4	no	—
259	C₂²×D₄	—	2	4	no	—
260	C₂²×D₄	—	2	4	no	—
261	C₂²×D₄	—	2	4	no	—
262	C₂²×D₄	—	2	4	no	—
263	C₂²×D₄	—	2	4	no	—
264	C₂²×D₄	—	4	4	no	—
265	C₂²×D₄	—	4	4	no	—
266	C₂²×D₄	—	4	4	no	—
267	C₂²×D₄	—	4	4	no	—
268	C₂²×D₄	D₄×C₄₇	1	8	yes	—
269	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
270	C₂³×C₄	—	2	1	no	—
271	C₂³×C₄	—	2	1	no	—
272	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
273	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
274	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
275	C₂²×C₈	—	2	4	no	—
276	C₂²×C₈	—	2	4	no	—
277	C₂²×C₈	—	2	4	no	—
278	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
279	#127	—	2	16	no	—
280	#127	—	2	16	no	—
281	C₂×C₄⋊C₄	—	2	1	no	—
282	C₂×C₄⋊C₄	—	2	2	no	—
283	C₂×C₄⋊C₄	—	2	4	no	—
284	C₂×C₄⋊C₄	—	2	4	no	—
285	C₂×C₄⋊C₄	—	2	1	no	—
286	C₂×C₄⋊C₄	—	4	4	no	—
287	C₂×C₄⋊C₄	D₄×C₄₇	1	4	yes	complemented
288	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
290	C₂×C₄²	—	2	4	no	—
291	C₂×C₄²	D₄×C₄₇	1	2	yes	—
292	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
293	#102	—	2	16	no	—
294	#102	—	2	16	no	—
295	#95	—	2	4	no	—
296	C₂⁴	—	2	8	no	—
297	C₂⁴	—	2	4	no	—
298	C₂⁴	—	4	4	no	—
299	C₂⁴	—	4	4	no	—
300	C₂⁴	—	4	4	no	—
301	C₂⁴	—	4	4	no	—
302	C₂⁴	—	4	4	no	—
303	C₂⁴	—	4	4	no	—
304	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
305	C₂×D₄	—	2	16	no	—
306	C₂×D₄	—	2	16	no	—
307	C₂×D₄	—	2	8	no	—
308	C₂×D₄	—	2	16	no	—
309	C₂×D₄	—	2	16	no	—
310	C₂×D₄	—	2	4	no	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	2	4	no	—
314	C₂×D₄	—	2	4	no	—
315	C₂×D₄	—	4	32	no	—
316	C₂×D₄	—	4	8	no	—
317	C₂×D₄	—	4	8	no	—
318	C₂×D₄	—	4	32	no	—
319	C₂×D₄	—	4	8	no	—
320	C₂×D₄	—	4	4	no	—
321	C₂×D₄	—	4	8	no	—
322	C₂×D₄	—	4	4	no	—
323	C₂×D₄	—	4	8	no	—
324	C₂×D₄	—	4	8	no	—
325	C₂×D₄	C₂×D₄×C₄₇	1	8	yes	—
326	C₂²×C₄	—	2	2	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	2	2	no	—
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	2	2	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	4	2	no	—
334	C₂²×C₄	—	4	2	no	—
335	C₂²×C₄	—	4	2	no	—
336	C₂²×C₄	—	4	2	no	—
337	C₂²×C₄	—	4	2	no	—
338	C₂²×C₄	D₈×C₄₇	1	4	yes	—
339	C₂²×C₄	SD₁₆×C₄₇	1	4	yes	—
340	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
344	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
345	C₂²×C₄	#41×C₄₇	1	4	yes	—
346	C₂²×C₄	#41×C₄₇	1	2	yes	—
347	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	—	2	4	no	—
350	C₂×C₈	—	2	4	no	—
351	C₂×C₈	—	4	8	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	4	2	no	—
356	C₄⋊C₄	—	4	8	no	—
357	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	complemented
358	C₄²	—	2	4	no	—
359	C₄²	—	2	4	no	—
360	C₂³	—	2	8	no	—
361	C₂³	—	4	16	no	—
362	C₂³	—	4	4	no	—
363	C₂³	—	4	4	no	—
364	C₂³	—	4	4	no	—
365	C₂³	—	4	4	no	—
366	C₂³	—	4	4	no	—
367	C₂³	—	4	4	no	—
368	C₂³	—	4	16	no	—
369	C₂³	—	4	16	no	—
370	C₂³	—	8	8	no	—
371	C₂³	—	8	8	no	—
372	C₂³	—	8	8	no	—
373	C₂³	—	8	8	no	—
374	C₂³	#120×C₄₇	1	2	yes	—
375	C₂³	#121×C₄₇	1	2	yes	—
376	C₂³	#124×C₄₇	1	2	yes	—
377	C₂³	C₂×D₈×C₄₇	1	2	yes	—
378	C₂³	C₂×SD₁₆×C₄₇	1	2	yes	—
379	C₂³	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
380	C₂³	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
381	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
382	D₄	—	2	8	no	—
383	D₄	—	2	8	no	—
384	D₄	—	4	32	no	—
385	D₄	—	4	32	no	—
386	D₄	—	4	4	no	—
387	D₄	—	4	4	no	—
388	D₄	—	4	16	no	—
389	C₂×C₄	—	2	8	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	4	8	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	4	2	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	2	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	8	4	no	—
403	C₂×C₄	#120×C₄₇	1	2	yes	—
404	C₂×C₄	#121×C₄₇	1	8	yes	—
405	C₂×C₄	#121×C₄₇	1	2	yes	—
406	C₂×C₄	#123×C₄₇	1	8	yes	—
407	C₂×C₄	#124×C₄₇	1	2	yes	—
408	C₂×C₄	C₂×D₈×C₄₇	1	4	yes	—
409	C₂×C₄	C₂×SD₁₆×C₄₇	1	4	yes	—
410	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
411	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
412	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
413	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
414	C₈	—	4	4	no	—
415	C₂²	—	4	8	no	—
416	C₂²	—	4	8	no	—
417	C₂²	—	4	8	no	—
418	C₂²	—	8	4	no	—
419	C₂²	—	8	32	no	—
420	C₂²	—	8	4	no	—
421	C₂²	—	8	4	no	—
422	C₂²	—	8	4	no	—
423	C₂²	C₄₇×#394	1	4	yes	—
424	C₂²	C₄₇×#447	1	4	yes	—
425	C₂²	C₄₇×#450	1	4	yes	—
426	C₂²	C₄₇×#459	1	4	yes	—
427	C₂²	C₄₇×#460	1	4	yes	—
428	C₂²	C₄₇×#486	1	4	yes	—
429	C₂²	C₄₇×#490	1	4	yes	—
430	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
431	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
432	C₂²	C₂×#124×C₄₇	1	1	yes	characteristic
433	C₂²	C₂²×D₈×C₄₇	1	1	yes	characteristic
434	C₂²	C₂²×SD₁₆×C₄₇	1	1	yes	characteristic
435	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
436	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
437	C₄	—	2	4	no	—
438	C₄	—	2	4	no	—
439	C₄	—	4	4	no	—
440	C₄	—	8	2	no	—
441	C₄	C₄₇×#394	1	4	yes	—
442	C₄	C₂×#121×C₄₇	1	2	yes	—
443	C₄	C₂×#123×C₄₇	1	2	yes	—
444	C₂	—	8	8	no	—
445	C₂	C₄₇×#2041	1	8	yes	direct product factor
446	C₂	C₂×C₄₇×#394	1	1	yes	characteristic
447	C₂	C₂×C₄₇×#447	1	1	yes	characteristic
448	C₂	C₂×C₄₇×#450	1	1	yes	characteristic
449	C₂	C₂×C₄₇×#459	1	1	yes	characteristic
450	C₂	C₂×C₄₇×#460	1	1	yes	characteristic
451	C₂	C₂×C₄₇×#486	1	1	yes	characteristic
452	C₂	C₂×C₄₇×#490	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂²×#127×C₄₇	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ C₂²×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂²×#102×C₄₇	C₂	semidirect
3. C₂²×#102×C₄₇	C₂	semidirect
4. C₂×C₄₇×#389	C₂	semidirect
5. C₄₇×#2041	C₂	direct (N × H)
6. C₂×C₄₇×#336	C₂	semidirect
20. C₂×#102×C₄₇	C₂²	semidirect
21. C₂×#102×C₄₇	C₂²	semidirect
23. C₄₇×#389	C₂²	semidirect
25. C₄₇×#336	C₂²	semidirect
60. C₂×C₄⋊C₄×C₄₇	D₄	semidirect
130. C₄⋊C₄×C₄₇	C₂×D₄	semidirect
188. C₂×#2041	C₄₇	direct (N × H)
219. C₂²×#102	C₂×C₄₇	semidirect
220. C₂²×#102	C₂×C₄₇	semidirect
221. C₂×#389	C₂×C₄₇	semidirect
222. #2041	C₂×C₄₇	direct (N × H)
223. C₂×#336	C₂×C₄₇	semidirect
225. C₂×C₄₇	#2041	direct (N × H)
246. C₂×#102	C₂²×C₄₇	semidirect
247. C₂×#102	C₂²×C₄₇	semidirect
249. #389	C₂²×C₄₇	semidirect
251. #336	C₂²×C₄₇	semidirect
252. C₄₇	C₂×#2041	direct (N × H)
287. C₂×C₄⋊C₄	D₄×C₄₇	semidirect
357. C₄⋊C₄	C₂×D₄×C₄₇	semidirect
445. C₂	C₄₇×#2041	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×#127×C₄₇	2
C₂²×#102×C₄₇	2
C₂×C₄₇×#389	2
C₄₇×#2041	2
C₂×C₄₇×#336	2
C₂×#2041	47

Subgroups — C2×C47×#2041 #26063199

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#2041 #26063199