Subgroups — C₂×C₄₇×#2040 #26063195

Order 12032.

1498 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#537	C₂	1	1	yes	maximal, characteristic
2	C₂²×#104×C₄₇	C₂	1	2	yes	maximal, complemented
3	C₂×C₄₇×#417	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₇×#382	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2040	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₄₇×#343	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#41×C₄₇	C₂²	1	2	yes	—
8	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
9	C₄₇×#537	—	2	4	no	—
10	C₄₇×#537	—	2	2	no	—
11	C₄₇×#537	C₂²	1	4	yes	—
12	C₂×C₂²⋊Q₈×C₄₇	—	2	2	no	—
13	C₂×#121×C₄₇	—	2	2	no	—
14	C₂×#121×C₄₇	—	2	2	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×#104×C₄₇	—	2	8	no	—
19	C₂×#104×C₄₇	C₂²	1	8	yes	complemented
20	C₄₇×#417	—	2	4	no	—
21	C₄₇×#417	C₂²	1	8	yes	complemented
22	C₂×#103×C₄₇	—	2	2	no	—
23	C₂×#102×C₄₇	—	2	2	no	—
24	C₄₇×#382	—	2	2	no	—
25	C₄₇×#382	C₂²	1	4	yes	complemented
26	C₂×#95×C₄₇	—	2	2	no	—
27	C₄₇×#343	C₂²	1	4	yes	complemented
28	C₂×#41×C₄₇	—	2	2	no	—
29	C₂×#41×C₄₇	—	2	2	no	—
30	C₂×#41×C₄₇	—	2	4	no	—
31	C₂×#41×C₄₇	—	2	4	no	—
32	C₂×#41×C₄₇	—	2	4	no	—
33	C₂×#41×C₄₇	—	2	4	no	—
34	C₂×#41×C₄₇	D₄	1	4	yes	—
35	C₂×#41×C₄₇	C₂³	1	4	yes	—
36	C₂²×Q₈×C₄₇	D₄	1	2	yes	—
37	C₂²×D₄×C₄₇	—	2	2	no	—
38	C₂²×D₄×C₄₇	—	2	2	no	—
39	C₂²×D₄×C₄₇	D₄	1	2	yes	—
40	C₂³×C₄×C₄₇	—	2	1	no	—
41	C₂³×C₄×C₄₇	—	2	2	no	—
42	C₂³×C₄×C₄₇	—	2	1	no	—
43	C₂³×C₄×C₄₇	D₄	1	2	yes	—
44	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
45	C₂×M₁₆×C₄₇	—	2	2	no	—
46	C₂×M₁₆×C₄₇	—	2	4	no	—
47	C₂×M₁₆×C₄₇	—	2	4	no	—
48	C₂×M₁₆×C₄₇	C₂³	1	4	yes	—
49	C₂²×C₈×C₄₇	—	2	2	no	—
50	C₂²⋊Q₈×C₄₇	—	2	8	no	—
51	C₂²⋊Q₈×C₄₇	—	2	8	no	—
52	#121×C₄₇	—	2	8	no	—
53	#121×C₄₇	—	2	8	no	—
54	#121×C₄₇	—	2	8	no	—
55	#121×C₄₇	—	2	8	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
59	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
63	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
65	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
66	C₂×C₄²×C₄₇	—	2	1	no	—
67	C₂×C₄²×C₄₇	—	2	2	no	—
68	C₂×C₄²×C₄₇	D₄	1	4	yes	complemented
69	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
70	#104×C₄₇	—	2	16	no	—
71	#103×C₄₇	—	2	8	no	—
72	#102×C₄₇	—	2	8	no	—
73	#95×C₄₇	—	2	8	no	—
74	C₂⁴×C₄₇	—	2	2	no	—
75	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
76	#41×C₄₇	—	2	8	no	—
77	#41×C₄₇	—	2	8	no	—
78	#41×C₄₇	—	2	4	no	—
79	#41×C₄₇	—	2	4	no	—
80	#41×C₄₇	—	2	4	no	—
81	#41×C₄₇	—	2	4	no	—
82	#41×C₄₇	—	4	4	no	—
83	#41×C₄₇	—	4	4	no	—
84	#41×C₄₇	—	4	4	no	—
85	#41×C₄₇	—	4	4	no	—
86	C₂×Q₈×C₄₇	—	2	2	no	—
87	C₂×Q₈×C₄₇	—	2	4	no	—
88	C₂×Q₈×C₄₇	—	2	4	no	—
89	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
90	C₂×D₄×C₄₇	—	2	4	no	—
91	C₂×D₄×C₄₇	—	2	4	no	—
92	C₂×D₄×C₄₇	—	2	8	no	—
93	C₂×D₄×C₄₇	—	2	2	no	—
94	C₂×D₄×C₄₇	—	2	4	no	—
95	C₂×D₄×C₄₇	—	2	4	no	—
96	C₂×D₄×C₄₇	—	4	4	no	—
97	C₂×D₄×C₄₇	—	4	4	no	—
98	C₂×D₄×C₄₇	—	8	4	no	—
99	C₂×D₄×C₄₇	C₂×D₄	1	4	yes	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	4	no	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	—	2	2	no	—
105	C₂²×C₄×C₄₇	—	2	4	no	—
106	C₂²×C₄×C₄₇	—	2	4	no	—
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	—	4	2	no	—
109	C₂²×C₄×C₄₇	—	4	2	no	—
110	C₂²×C₄×C₄₇	—	4	4	no	—
111	C₂²×C₄×C₄₇	—	4	4	no	—
112	C₂²×C₄×C₄₇	—	4	4	no	—
113	C₂²×C₄×C₄₇	—	4	4	no	—
114	C₂²×C₄×C₄₇	—	4	1	no	—
115	C₂²×C₄×C₄₇	—	4	1	no	—
116	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
117	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₄₇	#41	1	4	yes	—
122	C₂²×C₄×C₄₇	#41	1	2	yes	—
123	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
124	M₁₆×C₄₇	—	2	4	no	—
125	M₁₆×C₄₇	—	2	4	no	—
126	M₁₆×C₄₇	—	4	4	no	—
127	C₂×C₈×C₄₇	—	2	4	no	—
128	C₂×C₈×C₄₇	—	4	4	no	—
129	C₄⋊C₄×C₄₇	—	2	8	no	—
130	C₄⋊C₄×C₄₇	—	2	4	no	—
131	C₄⋊C₄×C₄₇	—	2	4	no	—
132	C₄⋊C₄×C₄₇	—	2	4	no	—
133	C₄⋊C₄×C₄₇	—	4	2	no	—
134	C₂²⋊C₄×C₄₇	—	2	16	no	—
135	C₄²×C₄₇	—	2	4	no	—
136	C₄²×C₄₇	—	2	2	no	—
137	C₄²×C₄₇	C₂×D₄	1	4	yes	complemented
138	C₂³×C₄₇	—	2	2	no	—
139	C₂³×C₄₇	—	2	2	no	—
140	C₂³×C₄₇	—	2	4	no	—
141	C₂³×C₄₇	—	4	4	no	—
142	C₂³×C₄₇	—	4	4	no	—
143	C₂³×C₄₇	—	4	4	no	—
144	C₂³×C₄₇	#120	1	1	yes	characteristic
145	C₂³×C₄₇	#120	1	1	yes	characteristic
146	C₂³×C₄₇	#121	1	2	yes	—
147	C₂³×C₄₇	#124	1	2	yes	—
148	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
149	Q₈×C₄₇	—	2	4	no	—
150	Q₈×C₄₇	—	2	4	no	—
151	Q₈×C₄₇	—	4	4	no	—
152	D₄×C₄₇	—	2	4	no	—
153	D₄×C₄₇	—	2	4	no	—
154	D₄×C₄₇	—	4	4	no	—
155	D₄×C₄₇	—	4	4	no	—
156	D₄×C₄₇	—	4	8	no	—
157	D₄×C₄₇	—	4	4	no	—
158	D₄×C₄₇	—	8	8	no	—
159	C₂×C₄×C₄₇	—	2	4	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	—	4	8	no	—
165	C₂×C₄×C₄₇	—	4	4	no	—
166	C₂×C₄×C₄₇	—	4	4	no	—
167	C₂×C₄×C₄₇	—	4	4	no	—
168	C₂×C₄×C₄₇	—	4	4	no	—
169	C₂×C₄×C₄₇	—	4	8	no	—
170	C₂×C₄×C₄₇	—	4	4	no	—
171	C₂×C₄×C₄₇	—	4	4	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	8	2	no	—
174	C₂×C₄×C₄₇	—	8	2	no	—
175	C₂×C₄×C₄₇	—	8	2	no	—
176	C₂×C₄×C₄₇	#120	1	2	yes	—
177	C₂×C₄×C₄₇	#121	1	4	yes	—
178	C₂×C₄×C₄₇	#121	1	4	yes	—
179	C₂×C₄×C₄₇	#121	1	2	yes	—
180	C₂×C₄×C₄₇	#123	1	4	yes	—
181	C₂×C₄×C₄₇	#123	1	4	yes	—
182	C₂×C₄×C₄₇	#124	1	2	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×#2040	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
189	C₂²×C₄₇	—	2	1	no	—
190	C₂²×C₄₇	—	2	1	no	—
191	C₂²×C₄₇	—	2	1	no	—
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	—	2	4	no	—
194	C₂²×C₄₇	—	2	4	no	—
195	C₂²×C₄₇	—	4	4	no	—
196	C₂²×C₄₇	—	4	4	no	—
197	C₂²×C₄₇	—	4	4	no	—
198	C₂²×C₄₇	—	8	8	no	—
199	C₂²×C₄₇	#394	1	2	yes	—
200	C₂²×C₄₇	#394	1	2	yes	—
201	C₂²×C₄₇	#454	1	2	yes	—
202	C₂²×C₄₇	#455	1	2	yes	—
203	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
204	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
205	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
206	C₄×C₄₇	—	4	4	no	—
207	C₄×C₄₇	—	4	4	no	—
208	C₄×C₄₇	—	4	4	no	—
209	C₄×C₄₇	—	8	2	no	—
210	C₄×C₄₇	#394	1	4	yes	—
211	C₄×C₄₇	C₂×#121	1	2	yes	—
212	C₄×C₄₇	C₂×#123	1	2	yes	—
213	C₂×#537	C₂×C₄₇	1	1	yes	characteristic
214	C₂²×#104	C₂×C₄₇	1	2	yes	complemented
215	C₂×#417	C₂×C₄₇	1	2	yes	complemented
216	C₂×#382	C₂×C₄₇	1	1	yes	characteristic, complemented
217	#2040	C₂×C₄₇	1	8	yes	direct product factor
218	C₂×#343	C₂×C₄₇	1	1	yes	characteristic, complemented
219	C₂×C₄₇	—	2	1	no	—
220	C₂×C₄₇	—	2	1	no	—
221	C₂×C₄₇	—	2	2	no	—
222	C₂×C₄₇	—	8	4	no	—
223	C₂×C₄₇	#2040	1	4	yes	direct product factor
224	C₂×C₄₇	C₂×#394	1	1	yes	characteristic
225	C₂×C₄₇	C₂×#455	1	1	yes	characteristic
226	C₂×C₄₇	C₂×#454	1	1	yes	characteristic
227	C₂²×#41	C₂²×C₄₇	1	2	yes	—
228	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
229	#537	—	2	4	no	—
230	#537	—	2	2	no	—
231	#537	C₂²×C₄₇	1	4	yes	—
232	C₂×C₂²⋊Q₈	—	2	2	no	—
233	C₂×#121	—	2	2	no	—
234	C₂×#121	—	2	2	no	—
235	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
236	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
237	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
238	C₂×#104	—	2	8	no	—
239	C₂×#104	C₂²×C₄₇	1	8	yes	complemented
240	#417	—	2	4	no	—
241	#417	C₂²×C₄₇	1	8	yes	complemented
242	C₂×#103	—	2	2	no	—
243	C₂×#102	—	2	2	no	—
244	#382	—	2	2	no	—
245	#382	C₂²×C₄₇	1	4	yes	complemented
246	C₂×#95	—	2	2	no	—
247	#343	C₂²×C₄₇	1	4	yes	complemented
248	C₄₇	C₂×#2040	1	1	yes	characteristic, direct product factor, Sylow
249	C₂×#41	—	2	2	no	—
250	C₂×#41	—	2	2	no	—
251	C₂×#41	—	2	4	no	—
252	C₂×#41	—	2	4	no	—
253	C₂×#41	—	2	4	no	—
254	C₂×#41	—	2	4	no	—
255	C₂×#41	D₄×C₄₇	1	4	yes	—
256	C₂×#41	C₂³×C₄₇	1	4	yes	—
257	C₂²×Q₈	D₄×C₄₇	1	2	yes	—
258	C₂²×D₄	—	2	2	no	—
259	C₂²×D₄	—	2	2	no	—
260	C₂²×D₄	D₄×C₄₇	1	2	yes	—
261	C₂³×C₄	—	2	1	no	—
262	C₂³×C₄	—	2	2	no	—
263	C₂³×C₄	—	2	1	no	—
264	C₂³×C₄	D₄×C₄₇	1	2	yes	—
265	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
266	C₂×M₁₆	—	2	2	no	—
267	C₂×M₁₆	—	2	4	no	—
268	C₂×M₁₆	—	2	4	no	—
269	C₂×M₁₆	C₂³×C₄₇	1	4	yes	—
270	C₂²×C₈	—	2	2	no	—
271	C₂²⋊Q₈	—	2	8	no	—
272	C₂²⋊Q₈	—	2	8	no	—
273	#121	—	2	8	no	—
274	#121	—	2	8	no	—
275	#121	—	2	8	no	—
276	#121	—	2	8	no	—
277	C₂×C₄⋊C₄	—	2	2	no	—
278	C₂×C₄⋊C₄	—	2	2	no	—
279	C₂×C₄⋊C₄	—	2	2	no	—
280	C₂×C₄⋊C₄	—	2	2	no	—
281	C₂×C₄⋊C₄	—	2	2	no	—
282	C₂×C₄⋊C₄	—	2	1	no	—
283	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
284	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
285	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
286	C₂×C₂²⋊C₄	—	2	4	no	—
287	C₂×C₄²	—	2	1	no	—
288	C₂×C₄²	—	2	2	no	—
289	C₂×C₄²	D₄×C₄₇	1	4	yes	complemented
290	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
291	#104	—	2	16	no	—
292	#103	—	2	8	no	—
293	#102	—	2	8	no	—
294	#95	—	2	8	no	—
295	C₂⁴	—	2	2	no	—
296	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
297	#41	—	2	8	no	—
298	#41	—	2	8	no	—
299	#41	—	2	4	no	—
300	#41	—	2	4	no	—
301	#41	—	2	4	no	—
302	#41	—	2	4	no	—
303	#41	—	4	4	no	—
304	#41	—	4	4	no	—
305	#41	—	4	4	no	—
306	#41	—	4	4	no	—
307	C₂×Q₈	—	2	2	no	—
308	C₂×Q₈	—	2	4	no	—
309	C₂×Q₈	—	2	4	no	—
310	C₂×Q₈	C₂×D₄×C₄₇	1	4	yes	—
311	C₂×D₄	—	2	4	no	—
312	C₂×D₄	—	2	4	no	—
313	C₂×D₄	—	2	8	no	—
314	C₂×D₄	—	2	2	no	—
315	C₂×D₄	—	2	4	no	—
316	C₂×D₄	—	2	4	no	—
317	C₂×D₄	—	4	4	no	—
318	C₂×D₄	—	4	4	no	—
319	C₂×D₄	—	8	4	no	—
320	C₂×D₄	C₂×D₄×C₄₇	1	4	yes	—
321	C₂²×C₄	—	2	2	no	—
322	C₂²×C₄	—	2	2	no	—
323	C₂²×C₄	—	2	4	no	—
324	C₂²×C₄	—	2	2	no	—
325	C₂²×C₄	—	2	2	no	—
326	C₂²×C₄	—	2	4	no	—
327	C₂²×C₄	—	2	4	no	—
328	C₂²×C₄	—	2	2	no	—
329	C₂²×C₄	—	4	2	no	—
330	C₂²×C₄	—	4	2	no	—
331	C₂²×C₄	—	4	4	no	—
332	C₂²×C₄	—	4	4	no	—
333	C₂²×C₄	—	4	4	no	—
334	C₂²×C₄	—	4	4	no	—
335	C₂²×C₄	—	4	1	no	—
336	C₂²×C₄	—	4	1	no	—
337	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
338	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
339	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
340	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
341	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
342	C₂²×C₄	#41×C₄₇	1	4	yes	—
343	C₂²×C₄	#41×C₄₇	1	2	yes	—
344	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
345	M₁₆	—	2	4	no	—
346	M₁₆	—	2	4	no	—
347	M₁₆	—	4	4	no	—
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	—	4	4	no	—
350	C₄⋊C₄	—	2	8	no	—
351	C₄⋊C₄	—	2	4	no	—
352	C₄⋊C₄	—	2	4	no	—
353	C₄⋊C₄	—	2	4	no	—
354	C₄⋊C₄	—	4	2	no	—
355	C₂²⋊C₄	—	2	16	no	—
356	C₄²	—	2	4	no	—
357	C₄²	—	2	2	no	—
358	C₄²	C₂×D₄×C₄₇	1	4	yes	complemented
359	C₂³	—	2	2	no	—
360	C₂³	—	2	2	no	—
361	C₂³	—	2	4	no	—
362	C₂³	—	4	4	no	—
363	C₂³	—	4	4	no	—
364	C₂³	—	4	4	no	—
365	C₂³	#120×C₄₇	1	1	yes	characteristic
366	C₂³	#120×C₄₇	1	1	yes	characteristic
367	C₂³	#121×C₄₇	1	2	yes	—
368	C₂³	#124×C₄₇	1	2	yes	—
369	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
370	Q₈	—	2	4	no	—
371	Q₈	—	2	4	no	—
372	Q₈	—	4	4	no	—
373	D₄	—	2	4	no	—
374	D₄	—	2	4	no	—
375	D₄	—	4	4	no	—
376	D₄	—	4	4	no	—
377	D₄	—	4	8	no	—
378	D₄	—	4	4	no	—
379	D₄	—	8	8	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	4	8	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	4	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	8	no	—
391	C₂×C₄	—	4	4	no	—
392	C₂×C₄	—	4	4	no	—
393	C₂×C₄	—	4	2	no	—
394	C₂×C₄	—	8	2	no	—
395	C₂×C₄	—	8	2	no	—
396	C₂×C₄	—	8	2	no	—
397	C₂×C₄	#120×C₄₇	1	2	yes	—
398	C₂×C₄	#121×C₄₇	1	4	yes	—
399	C₂×C₄	#121×C₄₇	1	4	yes	—
400	C₂×C₄	#121×C₄₇	1	2	yes	—
401	C₂×C₄	#123×C₄₇	1	4	yes	—
402	C₂×C₄	#123×C₄₇	1	4	yes	—
403	C₂×C₄	#124×C₄₇	1	2	yes	—
404	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
405	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
406	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
407	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
408	C₈	—	4	4	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	2	4	no	—
411	C₂²	—	2	1	no	—
412	C₂²	—	2	1	no	—
413	C₂²	—	2	1	no	—
414	C₂²	—	2	1	no	—
415	C₂²	—	4	4	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	4	4	no	—
418	C₂²	—	8	8	no	—
419	C₂²	C₄₇×#394	1	2	yes	—
420	C₂²	C₄₇×#394	1	2	yes	—
421	C₂²	C₄₇×#454	1	2	yes	—
422	C₂²	C₄₇×#455	1	2	yes	—
423	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
424	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
425	C₂²	C₂×#124×C₄₇	1	1	yes	characteristic
426	C₄	—	4	4	no	—
427	C₄	—	4	4	no	—
428	C₄	—	4	4	no	—
429	C₄	—	8	2	no	—
430	C₄	C₄₇×#394	1	4	yes	—
431	C₄	C₂×#121×C₄₇	1	2	yes	—
432	C₄	C₂×#123×C₄₇	1	2	yes	—
433	C₂	—	2	1	no	—
434	C₂	—	2	1	no	—
435	C₂	—	2	2	no	—
436	C₂	—	8	4	no	—
437	C₂	C₄₇×#2040	1	4	yes	direct product factor
438	C₂	C₂×C₄₇×#394	1	1	yes	characteristic
439	C₂	C₂×C₄₇×#455	1	1	yes	characteristic
440	C₂	C₂×C₄₇×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×C₄₇×#537	C₂
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
2. C₂²×#104×C₄₇	C₂	semidirect
3. C₂×C₄₇×#417	C₂	semidirect
4. C₂×C₄₇×#382	C₂	semidirect
5. C₄₇×#2040	C₂	direct (N × H)
6. C₂×C₄₇×#343	C₂	semidirect
19. C₂×#104×C₄₇	C₂²	semidirect
21. C₄₇×#417	C₂²	semidirect
25. C₄₇×#382	C₂²	semidirect
27. C₄₇×#343	C₂²	semidirect
68. C₂×C₄²×C₄₇	D₄	semidirect
137. C₄²×C₄₇	C₂×D₄	semidirect
188. C₂×#2040	C₄₇	direct (N × H)
214. C₂²×#104	C₂×C₄₇	semidirect
215. C₂×#417	C₂×C₄₇	semidirect
216. C₂×#382	C₂×C₄₇	semidirect
217. #2040	C₂×C₄₇	direct (N × H)
218. C₂×#343	C₂×C₄₇	semidirect
223. C₂×C₄₇	#2040	direct (N × H)
239. C₂×#104	C₂²×C₄₇	semidirect
241. #417	C₂²×C₄₇	semidirect
245. #382	C₂²×C₄₇	semidirect
247. #343	C₂²×C₄₇	semidirect
248. C₄₇	C₂×#2040	direct (N × H)
289. C₂×C₄²	D₄×C₄₇	semidirect
358. C₄²	C₂×D₄×C₄₇	semidirect
437. C₂	C₄₇×#2040	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×#537	2
C₂²×#104×C₄₇	2
C₂×C₄₇×#417	2
C₂×C₄₇×#382	2
C₄₇×#2040	2
C₂×C₄₇×#343	2
C₂×#2040	47

Subgroups — C2×C47×#2040 #26063195

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#2040 #26063195