Subgroups — C₂×C₄₇×#1786 #26060292

Order 12032.

6086 conjugacy classes of subgroups.

The subgroup lattice has 446 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂⁴×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂²×#102×C₄₇	C₂	1	4	yes	maximal, complemented
3	C₂²×C₂²⋊C₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₇×#380	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1786	C₂	1	8	yes	maximal, direct product factor
6	C₂⁶×C₄₇	—	2	1	no	—
7	C₂³×D₄×C₄₇	—	2	16	no	—
8	C₂³×D₄×C₄₇	—	2	2	no	—
9	C₂³×D₄×C₄₇	—	2	1	no	—
10	C₂³×D₄×C₄₇	—	2	4	no	—
11	C₂³×D₄×C₄₇	C₄	1	8	yes	complemented
12	C₂³×D₄×C₄₇	C₂²	1	4	yes	—
13	C₂³×D₄×C₄₇	C₂²	1	2	yes	—
14	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂³×C₈×C₄₇	C₂²	1	2	yes	complemented
16	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
17	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
18	C₂×#102×C₄₇	—	2	16	no	—
19	C₂×#102×C₄₇	C₂²	1	16	yes	complemented
20	C₂×C₂²⋊C₈×C₄₇	—	2	4	no	—
21	C₂×C₂²⋊C₈×C₄₇	C₂²	1	4	yes	complemented
22	C₄₇×#380	—	2	2	no	—
23	C₄₇×#380	C₂²	1	4	yes	complemented
24	C₂×#95×C₄₇	—	2	1	no	—
25	C₂⁵×C₄₇	—	2	16	no	—
26	C₂⁵×C₄₇	—	2	8	no	—
27	C₂⁵×C₄₇	—	2	4	no	—
28	C₂⁵×C₄₇	—	2	2	no	—
29	C₂⁵×C₄₇	—	4	8	no	—
30	C₂⁵×C₄₇	—	4	4	no	—
31	C₂⁵×C₄₇	—	4	4	no	—
32	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
33	C₂²×D₄×C₄₇	—	2	16	no	—
34	C₂²×D₄×C₄₇	—	2	32	no	—
35	C₂²×D₄×C₄₇	—	2	64	no	—
36	C₂²×D₄×C₄₇	—	2	64	no	—
37	C₂²×D₄×C₄₇	—	2	32	no	—
38	C₂²×D₄×C₄₇	—	2	16	no	—
39	C₂²×D₄×C₄₇	—	2	8	no	—
40	C₂²×D₄×C₄₇	—	2	4	no	—
41	C₂²×D₄×C₄₇	—	2	8	no	—
42	C₂²×D₄×C₄₇	—	2	2	no	—
43	C₂²×D₄×C₄₇	—	2	8	no	—
44	C₂²×D₄×C₄₇	—	2	4	no	—
45	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
46	C₂²×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
47	C₂²×D₄×C₄₇	D₄	1	16	yes	—
48	C₂²×D₄×C₄₇	C₂³	1	4	yes	—
49	C₂³×C₄×C₄₇	—	2	8	no	—
50	C₂³×C₄×C₄₇	—	2	2	no	—
51	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
52	C₂³×C₄×C₄₇	D₄	1	2	yes	—
53	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₄₇	D₄	1	4	yes	—
55	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
56	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₄₇	—	2	4	no	—
58	C₂²×C₈×C₄₇	—	2	8	no	—
59	C₂²×C₈×C₄₇	C₂³	1	4	yes	complemented
60	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
61	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
62	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	complemented
63	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
64	C₂×C₂²⋊C₄×C₄₇	—	4	4	no	—
65	#102×C₄₇	—	2	32	no	—
66	C₂²⋊C₈×C₄₇	—	2	8	no	—
67	#95×C₄₇	—	2	4	no	—
68	C₂⁴×C₄₇	—	2	4	no	—
69	C₂⁴×C₄₇	—	2	4	no	—
70	C₂⁴×C₄₇	—	2	32	no	—
71	C₂⁴×C₄₇	—	2	64	no	—
72	C₂⁴×C₄₇	—	2	8	no	—
73	C₂⁴×C₄₇	—	2	16	no	—
74	C₂⁴×C₄₇	—	2	16	no	—
75	C₂⁴×C₄₇	—	2	4	no	—
76	C₂⁴×C₄₇	—	4	16	no	—
77	C₂⁴×C₄₇	—	4	32	no	—
78	C₂⁴×C₄₇	—	4	64	no	—
79	C₂⁴×C₄₇	—	4	64	no	—
80	C₂⁴×C₄₇	—	4	32	no	—
81	C₂⁴×C₄₇	—	4	8	no	—
82	C₂⁴×C₄₇	—	4	4	no	—
83	C₂⁴×C₄₇	—	4	8	no	—
84	C₂⁴×C₄₇	—	4	4	no	—
85	C₂⁴×C₄₇	—	4	8	no	—
86	C₂⁴×C₄₇	C₂²⋊C₄	1	4	yes	—
87	C₂⁴×C₄₇	D₈	1	4	yes	—
88	C₂⁴×C₄₇	SD₁₆	1	4	yes	—
89	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
90	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
91	C₂×D₄×C₄₇	—	2	32	no	—
92	C₂×D₄×C₄₇	—	2	64	no	—
93	C₂×D₄×C₄₇	—	2	64	no	—
94	C₂×D₄×C₄₇	—	2	128	no	—
95	C₂×D₄×C₄₇	—	2	64	no	—
96	C₂×D₄×C₄₇	—	2	16	no	—
97	C₂×D₄×C₄₇	—	2	8	no	—
98	C₂×D₄×C₄₇	—	2	16	no	—
99	C₂×D₄×C₄₇	—	2	32	no	—
100	C₂×D₄×C₄₇	—	2	16	no	—
101	C₂×D₄×C₄₇	—	2	8	no	—
102	C₂×D₄×C₄₇	—	2	4	no	—
103	C₂×D₄×C₄₇	C₂²⋊C₄	1	32	yes	complemented
104	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
105	C₂×D₄×C₄₇	C₂×D₄	1	16	yes	—
106	C₂²×C₄×C₄₇	—	2	4	no	—
107	C₂²×C₄×C₄₇	—	2	16	no	—
108	C₂²×C₄×C₄₇	—	2	8	no	—
109	C₂²×C₄×C₄₇	—	2	16	no	—
110	C₂²×C₄×C₄₇	—	2	8	no	—
111	C₂²×C₄×C₄₇	—	2	4	no	—
112	C₂²×C₄×C₄₇	—	4	4	no	—
113	C₂²×C₄×C₄₇	—	4	4	no	—
114	C₂²×C₄×C₄₇	—	4	4	no	—
115	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
116	C₂²×C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
117	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
118	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
119	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
121	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂×D₄	1	8	yes	—
123	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
125	C₂×C₈×C₄₇	—	2	4	no	—
126	C₂×C₈×C₄₇	—	2	8	no	—
127	C₂×C₈×C₄₇	—	4	8	no	—
128	C₄⋊C₄×C₄₇	—	2	8	no	—
129	C₄⋊C₄×C₄₇	—	4	4	no	—
130	C₂²⋊C₄×C₄₇	—	4	8	no	—
131	C₂³×C₄₇	—	2	4	no	—
132	C₂³×C₄₇	—	2	4	no	—
133	C₂³×C₄₇	—	2	8	no	—
134	C₂³×C₄₇	—	2	8	no	—
135	C₂³×C₄₇	—	2	16	no	—
136	C₂³×C₄₇	—	2	16	no	—
137	C₂³×C₄₇	—	2	64	no	—
138	C₂³×C₄₇	—	2	8	no	—
139	C₂³×C₄₇	—	2	16	no	—
140	C₂³×C₄₇	—	2	32	no	—
141	C₂³×C₄₇	—	4	32	no	—
142	C₂³×C₄₇	—	4	64	no	—
143	C₂³×C₄₇	—	4	64	no	—
144	C₂³×C₄₇	—	4	256	no	—
145	C₂³×C₄₇	—	4	4	no	—
146	C₂³×C₄₇	—	4	4	no	—
147	C₂³×C₄₇	—	4	8	no	—
148	C₂³×C₄₇	—	4	16	no	—
149	C₂³×C₄₇	—	4	32	no	—
150	C₂³×C₄₇	—	4	16	no	—
151	C₂³×C₄₇	—	4	32	no	—
152	C₂³×C₄₇	—	4	32	no	—
153	C₂³×C₄₇	#102	1	16	yes	complemented
154	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
155	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
156	C₂³×C₄₇	#120	1	4	yes	—
157	C₂³×C₄₇	C₂×D₈	1	4	yes	—
158	C₂³×C₄₇	C₂×D₈	1	2	yes	—
159	C₂³×C₄₇	C₂×SD₁₆	1	4	yes	—
160	C₂³×C₄₇	C₂×SD₁₆	1	2	yes	—
161	C₂³×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
162	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
163	D₄×C₄₇	—	2	64	no	—
164	D₄×C₄₇	—	2	8	no	—
165	D₄×C₄₇	—	2	16	no	—
166	D₄×C₄₇	—	2	32	no	—
167	D₄×C₄₇	C₂×C₂²⋊C₄	1	16	yes	complemented
168	C₂×C₄×C₄₇	—	2	4	no	—
169	C₂×C₄×C₄₇	—	2	8	no	—
170	C₂×C₄×C₄₇	—	2	8	no	—
171	C₂×C₄×C₄₇	—	2	8	no	—
172	C₂×C₄×C₄₇	—	2	16	no	—
173	C₂×C₄×C₄₇	—	4	4	no	—
174	C₂×C₄×C₄₇	—	4	4	no	—
175	C₂×C₄×C₄₇	—	4	4	no	—
176	C₂×C₄×C₄₇	—	8	8	no	—
177	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
178	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	8	yes	—
179	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
180	C₂×C₄×C₄₇	#120	1	8	yes	—
181	C₂×C₄×C₄₇	#120	1	4	yes	—
182	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
184	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
185	C₈×C₄₇	—	4	4	no	—
186	C₂×#1786	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
187	C₂²×C₄₇	—	2	4	no	—
188	C₂²×C₄₇	—	2	8	no	—
189	C₂²×C₄₇	—	2	8	no	—
190	C₂²×C₄₇	—	2	4	no	—
191	C₂²×C₄₇	—	2	32	no	—
192	C₂²×C₄₇	—	2	16	no	—
193	C₂²×C₄₇	—	4	128	no	—
194	C₂²×C₄₇	—	4	8	no	—
195	C₂²×C₄₇	—	4	8	no	—
196	C₂²×C₄₇	—	4	16	no	—
197	C₂²×C₄₇	—	4	16	no	—
198	C₂²×C₄₇	—	4	64	no	—
199	C₂²×C₄₇	#379	1	4	yes	—
200	C₂²×C₄₇	C₂×#102	1	4	yes	—
201	C₂²×C₄₇	C₂×#102	1	8	yes	complemented
202	C₂²×C₄₇	#418	1	4	yes	—
203	C₂²×C₄₇	#447	1	8	yes	—
204	C₂²×C₄₇	#450	1	8	yes	—
205	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
206	C₂²×C₄₇	C₂×#120	1	2	yes	—
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	2	yes	—
210	C₄×C₄₇	—	2	4	no	—
211	C₄×C₄₇	—	8	4	no	—
212	C₄×C₄₇	#379	1	4	yes	—
213	C₄×C₄₇	C₂²×C₂²⋊C₄	1	2	yes	—
214	C₄×C₄₇	C₂×#120	1	2	yes	—
215	C₂⁴×D₄	C₂×C₄₇	1	1	yes	characteristic
216	C₂²×#102	C₂×C₄₇	1	4	yes	complemented
217	C₂²×C₂²⋊C₈	C₂×C₄₇	1	1	yes	characteristic, complemented
218	C₂×#380	C₂×C₄₇	1	1	yes	characteristic, complemented
219	#1786	C₂×C₄₇	1	8	yes	direct product factor
220	C₂×C₄₇	—	2	8	no	—
221	C₂×C₄₇	—	4	16	no	—
222	C₂×C₄₇	#1786	1	8	yes	direct product factor
223	C₂×C₄₇	C₂×#379	1	1	yes	characteristic
224	C₂×C₄₇	C₂²×#102	1	1	yes	characteristic
225	C₂×C₄₇	C₂×#418	1	1	yes	characteristic
226	C₂×C₄₇	C₂×#447	1	2	yes	—
227	C₂×C₄₇	C₂×#450	1	2	yes	—
228	C₂⁶	—	2	1	no	—
229	C₂³×D₄	—	2	16	no	—
230	C₂³×D₄	—	2	1	no	—
231	C₂³×D₄	—	2	2	no	—
232	C₂³×D₄	—	2	4	no	—
233	C₂³×D₄	C₄×C₄₇	1	8	yes	complemented
234	C₂³×D₄	C₂²×C₄₇	1	4	yes	—
235	C₂³×D₄	C₂²×C₄₇	1	2	yes	—
236	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
237	C₂³×C₈	C₂²×C₄₇	1	2	yes	complemented
238	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	complemented
239	C₂²×C₂²⋊C₄	—	2	1	no	—
240	C₂×#102	—	2	16	no	—
241	C₂×#102	C₂²×C₄₇	1	16	yes	complemented
242	C₂×C₂²⋊C₈	—	2	4	no	—
243	C₂×C₂²⋊C₈	C₂²×C₄₇	1	4	yes	complemented
244	#380	—	2	2	no	—
245	#380	C₂²×C₄₇	1	4	yes	complemented
246	C₂×#95	—	2	1	no	—
247	C₄₇	C₂×#1786	1	1	yes	characteristic, direct product factor, Sylow
248	C₂⁵	—	2	16	no	—
249	C₂⁵	—	2	8	no	—
250	C₂⁵	—	2	4	no	—
251	C₂⁵	—	2	2	no	—
252	C₂⁵	—	4	8	no	—
253	C₂⁵	—	4	4	no	—
254	C₂⁵	—	4	4	no	—
255	C₂⁵	D₄×C₄₇	1	1	yes	characteristic
256	C₂²×D₄	—	2	16	no	—
257	C₂²×D₄	—	2	32	no	—
258	C₂²×D₄	—	2	64	no	—
259	C₂²×D₄	—	2	64	no	—
260	C₂²×D₄	—	2	32	no	—
261	C₂²×D₄	—	2	16	no	—
262	C₂²×D₄	—	2	8	no	—
263	C₂²×D₄	—	2	4	no	—
264	C₂²×D₄	—	2	8	no	—
265	C₂²×D₄	—	2	2	no	—
266	C₂²×D₄	—	2	8	no	—
267	C₂²×D₄	—	2	4	no	—
268	C₂²×D₄	C₂×C₄×C₄₇	1	8	yes	—
269	C₂²×D₄	C₂×C₄×C₄₇	1	16	yes	complemented
270	C₂²×D₄	D₄×C₄₇	1	16	yes	—
271	C₂²×D₄	C₂³×C₄₇	1	4	yes	—
272	C₂³×C₄	—	2	8	no	—
273	C₂³×C₄	—	2	2	no	—
274	C₂³×C₄	C₂×C₄×C₄₇	1	4	yes	—
275	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
276	C₂³×C₄	D₄×C₄₇	1	2	yes	—
277	C₂³×C₄	D₄×C₄₇	1	4	yes	—
278	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
279	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
280	C₂²×C₈	—	2	4	no	—
281	C₂²×C₈	—	2	8	no	—
282	C₂²×C₈	C₂³×C₄₇	1	4	yes	complemented
283	C₂×C₄⋊C₄	—	2	8	no	—
284	C₂×C₄⋊C₄	—	2	2	no	—
285	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	complemented
286	C₂×C₂²⋊C₄	—	2	4	no	—
287	C₂×C₂²⋊C₄	—	4	4	no	—
288	#102	—	2	32	no	—
289	C₂²⋊C₈	—	2	8	no	—
290	#95	—	2	4	no	—
291	C₂⁴	—	2	4	no	—
292	C₂⁴	—	2	4	no	—
293	C₂⁴	—	2	32	no	—
294	C₂⁴	—	2	64	no	—
295	C₂⁴	—	2	8	no	—
296	C₂⁴	—	2	16	no	—
297	C₂⁴	—	2	16	no	—
298	C₂⁴	—	2	4	no	—
299	C₂⁴	—	4	64	no	—
300	C₂⁴	—	4	16	no	—
301	C₂⁴	—	4	32	no	—
302	C₂⁴	—	4	64	no	—
303	C₂⁴	—	4	8	no	—
304	C₂⁴	—	4	4	no	—
305	C₂⁴	—	4	8	no	—
306	C₂⁴	—	4	4	no	—
307	C₂⁴	—	4	8	no	—
308	C₂⁴	—	4	32	no	—
309	C₂⁴	C₂²⋊C₄×C₄₇	1	4	yes	—
310	C₂⁴	D₈×C₄₇	1	4	yes	—
311	C₂⁴	SD₁₆×C₄₇	1	4	yes	—
312	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
313	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
314	C₂×D₄	—	2	32	no	—
315	C₂×D₄	—	2	64	no	—
316	C₂×D₄	—	2	64	no	—
317	C₂×D₄	—	2	128	no	—
318	C₂×D₄	—	2	64	no	—
319	C₂×D₄	—	2	16	no	—
320	C₂×D₄	—	2	8	no	—
321	C₂×D₄	—	2	16	no	—
322	C₂×D₄	—	2	32	no	—
323	C₂×D₄	—	2	16	no	—
324	C₂×D₄	—	2	8	no	—
325	C₂×D₄	—	2	4	no	—
326	C₂×D₄	C₂²⋊C₄×C₄₇	1	32	yes	complemented
327	C₂×D₄	C₂²×C₄×C₄₇	1	8	yes	—
328	C₂×D₄	C₂×D₄×C₄₇	1	16	yes	—
329	C₂²×C₄	—	2	4	no	—
330	C₂²×C₄	—	2	16	no	—
331	C₂²×C₄	—	2	8	no	—
332	C₂²×C₄	—	2	16	no	—
333	C₂²×C₄	—	2	8	no	—
334	C₂²×C₄	—	2	4	no	—
335	C₂²×C₄	—	4	4	no	—
336	C₂²×C₄	—	4	4	no	—
337	C₂²×C₄	—	4	4	no	—
338	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
339	C₂²×C₄	C₂²⋊C₄×C₄₇	1	8	yes	—
340	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
341	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
342	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
343	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
344	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₄₇	1	8	yes	—
346	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
347	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
348	C₂×C₈	—	2	4	no	—
349	C₂×C₈	—	2	8	no	—
350	C₂×C₈	—	4	8	no	—
351	C₄⋊C₄	—	2	8	no	—
352	C₄⋊C₄	—	4	4	no	—
353	C₂²⋊C₄	—	4	8	no	—
354	C₂³	—	2	16	no	—
355	C₂³	—	2	4	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	8	no	—
358	C₂³	—	2	8	no	—
359	C₂³	—	2	16	no	—
360	C₂³	—	2	64	no	—
361	C₂³	—	2	8	no	—
362	C₂³	—	2	16	no	—
363	C₂³	—	2	32	no	—
364	C₂³	—	4	256	no	—
365	C₂³	—	4	32	no	—
366	C₂³	—	4	64	no	—
367	C₂³	—	4	64	no	—
368	C₂³	—	4	32	no	—
369	C₂³	—	4	4	no	—
370	C₂³	—	4	4	no	—
371	C₂³	—	4	8	no	—
372	C₂³	—	4	16	no	—
373	C₂³	—	4	32	no	—
374	C₂³	—	4	16	no	—
375	C₂³	—	4	32	no	—
376	C₂³	#102×C₄₇	1	16	yes	complemented
377	C₂³	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
378	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
379	C₂³	#120×C₄₇	1	4	yes	—
380	C₂³	C₂×D₈×C₄₇	1	4	yes	—
381	C₂³	C₂×D₈×C₄₇	1	2	yes	—
382	C₂³	C₂×SD₁₆×C₄₇	1	4	yes	—
383	C₂³	C₂×SD₁₆×C₄₇	1	2	yes	—
384	C₂³	AGL(1,ℤ/8)×C₄₇	1	4	yes	—
385	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
386	D₄	—	2	64	no	—
387	D₄	—	2	8	no	—
388	D₄	—	2	16	no	—
389	D₄	—	2	32	no	—
390	D₄	C₂×C₂²⋊C₄×C₄₇	1	16	yes	complemented
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	2	8	no	—
393	C₂×C₄	—	2	8	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	16	no	—
396	C₂×C₄	—	4	4	no	—
397	C₂×C₄	—	4	4	no	—
398	C₂×C₄	—	4	4	no	—
399	C₂×C₄	—	8	8	no	—
400	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
401	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	8	yes	—
402	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
403	C₂×C₄	#120×C₄₇	1	8	yes	—
404	C₂×C₄	#120×C₄₇	1	4	yes	—
405	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
406	C₂×C₄	C₂²×D₄×C₄₇	1	4	yes	—
407	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
408	C₈	—	4	4	no	—
409	C₂²	—	2	4	no	—
410	C₂²	—	2	32	no	—
411	C₂²	—	2	4	no	—
412	C₂²	—	2	8	no	—
413	C₂²	—	2	8	no	—
414	C₂²	—	2	16	no	—
415	C₂²	—	4	128	no	—
416	C₂²	—	4	64	no	—
417	C₂²	—	4	8	no	—
418	C₂²	—	4	8	no	—
419	C₂²	—	4	16	no	—
420	C₂²	—	4	16	no	—
421	C₂²	C₄₇×#379	1	4	yes	—
422	C₂²	C₂×#102×C₄₇	1	4	yes	—
423	C₂²	C₂×#102×C₄₇	1	8	yes	complemented
424	C₂²	C₄₇×#418	1	4	yes	—
425	C₂²	C₄₇×#447	1	8	yes	—
426	C₂²	C₄₇×#450	1	8	yes	—
427	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
428	C₂²	C₂×#120×C₄₇	1	2	yes	—
429	C₂²	C₂²×D₈×C₄₇	1	1	yes	characteristic
430	C₂²	C₂²×SD₁₆×C₄₇	1	1	yes	characteristic
431	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	2	yes	—
432	C₄	—	2	4	no	—
433	C₄	—	8	4	no	—
434	C₄	C₄₇×#379	1	4	yes	—
435	C₄	C₂²×C₂²⋊C₄×C₄₇	1	2	yes	—
436	C₄	C₂×#120×C₄₇	1	2	yes	—
437	C₂	—	2	8	no	—
438	C₂	—	4	16	no	—
439	C₂	C₄₇×#1786	1	8	yes	direct product factor
440	C₂	C₂×C₄₇×#379	1	1	yes	characteristic
441	C₂	C₂²×#102×C₄₇	1	1	yes	characteristic
442	C₂	C₂×C₄₇×#418	1	1	yes	characteristic
443	C₂	C₂×C₄₇×#447	1	2	yes	—
444	C₂	C₂×C₄₇×#450	1	2	yes	—

	subgroup	G/H
center, socle	C₂⁴×C₄₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂⁴×D₄×C₄₇	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂⁴×C₄₇ ◁ C₂⁴×C₄×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×C₂²⋊C₈×C₄₇	C₂	semidirect
4. C₂×C₄₇×#380	C₂	semidirect
5. C₄₇×#1786	C₂	direct (N × H)
11. C₂³×D₄×C₄₇	C₄	semidirect
15. C₂³×C₈×C₄₇	C₂²	semidirect
16. C₂²×C₄⋊C₄×C₄₇	C₂²	semidirect
19. C₂×#102×C₄₇	C₂²	semidirect
21. C₂×C₂²⋊C₈×C₄₇	C₂²	semidirect
23. C₄₇×#380	C₂²	semidirect
46. C₂²×D₄×C₄₇	C₂×C₄	semidirect
59. C₂²×C₈×C₄₇	C₂³	semidirect
62. C₂×C₄⋊C₄×C₄₇	C₂³	semidirect
103. C₂×D₄×C₄₇	C₂²⋊C₄	semidirect
153. C₂³×C₄₇	#102	semidirect
167. D₄×C₄₇	C₂×C₂²⋊C₄	semidirect
186. C₂×#1786	C₄₇	direct (N × H)
201. C₂²×C₄₇	C₂×#102	semidirect
216. C₂²×#102	C₂×C₄₇	semidirect
217. C₂²×C₂²⋊C₈	C₂×C₄₇	semidirect
218. C₂×#380	C₂×C₄₇	semidirect
219. #1786	C₂×C₄₇	direct (N × H)
222. C₂×C₄₇	#1786	direct (N × H)
233. C₂³×D₄	C₄×C₄₇	semidirect
237. C₂³×C₈	C₂²×C₄₇	semidirect
238. C₂²×C₄⋊C₄	C₂²×C₄₇	semidirect
241. C₂×#102	C₂²×C₄₇	semidirect
243. C₂×C₂²⋊C₈	C₂²×C₄₇	semidirect
245. #380	C₂²×C₄₇	semidirect
247. C₄₇	C₂×#1786	direct (N × H)
269. C₂²×D₄	C₂×C₄×C₄₇	semidirect
282. C₂²×C₈	C₂³×C₄₇	semidirect
285. C₂×C₄⋊C₄	C₂³×C₄₇	semidirect
326. C₂×D₄	C₂²⋊C₄×C₄₇	semidirect
376. C₂³	#102×C₄₇	semidirect
390. D₄	C₂×C₂²⋊C₄×C₄₇	semidirect
423. C₂²	C₂×#102×C₄₇	semidirect
439. C₂	C₄₇×#1786	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂⁴×D₄×C₄₇	2
C₂²×#102×C₄₇	2
C₂²×C₂²⋊C₈×C₄₇	2
C₂×C₄₇×#380	2
C₄₇×#1786	2
C₂×#1786	47

Subgroups — C2×C47×#1786 #26060292

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄₇×#1786 #26060292