Subgroups — D₄₇×#2168 #26369430

Order 12032.

754 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×M₃₂×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₈×D₄×D₄₇	C₂	1	1	yes	maximal, characteristic
4	#20245216	C₂	1	1	yes	maximal, characteristic, complemented
5	#20245215	C₂	1	1	yes	maximal, characteristic, complemented
6	#20245214	C₂	1	1	yes	maximal, characteristic, complemented
7	#20245213	C₂	1	1	yes	maximal, characteristic, complemented
8	#20245212	C₂	1	1	yes	maximal, characteristic, complemented
9	#20245211	C₂	1	1	yes	maximal, characteristic, complemented
10	#20245210	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄⋊C₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²⋊C₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂²⋊C₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#346×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#2168	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
18	C₄×D₄×D₄₇	C₄	1	1	yes	characteristic
19	C₂×#13093964	C₂²	1	1	yes	characteristic, complemented
20	C₂×#13093963	C₂²	1	1	yes	characteristic, complemented
21	C₂×#13093963	C₂²	1	1	yes	characteristic, complemented
22	M₃₂×D₄₇	—	2	4	no	—
23	C₂²×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
24	C₂×C₁₆×D₄₇	—	2	4	no	—
25	C₂×C₁₆×D₄₇	C₂²	1	1	yes	characteristic
26	C₂×C₁₆×D₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₁₆×D₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₁₆×D₄₇	C₂²	1	1	yes	characteristic
29	C₂×C₁₆×D₄₇	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₁₆×D₄₇	C₂²	1	1	yes	characteristic, complemented
31	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
32	D₄×C₄₇⋊C₈	C₄	1	1	yes	characteristic
33	#15689188	C₄	1	1	yes	characteristic
34	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
35	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
36	(C₂²⋊D₄₇)⋊C₈	C₄	1	1	yes	characteristic
37	(C₂²⋊D₄₇)⋊C₈	C₄	1	1	yes	characteristic
38	C₄⋊C₈×D₄₇	C₄	1	1	yes	characteristic
39	C₂²⋊C₈×D₄₇	C₄	1	1	yes	characteristic
40	C₂²⋊C₈×D₄₇	C₄	1	1	yes	characteristic
41	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
42	C₄⋊(C₄₇⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
43	Dic₄₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
44	Dic₄₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
45	C₂²⋊(C₄₇⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
46	C₂²⋊(C₄₇⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
47	(C₂×D₄₇)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
48	(C₂×D₄₇)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
49	(C₂×D₄₇)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
50	(C₂×D₄₇)⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
51	#15688899	C₂²	1	1	yes	characteristic, complemented
52	#15688898	C₂²	1	1	yes	characteristic, complemented
53	#15688898	C₂²	1	1	yes	characteristic, complemented
54	C₂×M₃₂×C₄₇	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
56	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic
57	C₄₇×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
58	C₄₇×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
59	C₄₇×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
60	C₄₇×#346	C₂²	1	1	yes	characteristic, complemented
61	C₂×D₄×D₄₇	C₈	1	1	yes	characteristic
62	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₄₇	—	2	2	no	—
67	C₂×C₈×D₄₇	—	2	2	no	—
68	C₂×C₈×D₄₇	—	2	2	no	—
69	C₂×C₈×D₄₇	—	2	2	no	—
70	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
76	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
77	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
78	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
79	D₄×Dic₄₇	C₈	1	1	yes	characteristic
80	#13093986	C₈	1	1	yes	characteristic
81	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
82	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
83	(C₂²⋊D₄₇)⋊C₄	C₈	1	1	yes	characteristic
84	(C₂²⋊D₄₇)⋊C₄	C₈	1	1	yes	characteristic
85	C₄⋊C₄×D₄₇	C₈	1	1	yes	characteristic
86	C₂²⋊C₄×D₄₇	C₈	1	1	yes	characteristic
87	C₂²⋊C₄×D₄₇	C₈	1	1	yes	characteristic
88	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
89	#13093964	—	2	2	no	—
90	#13093963	—	2	2	no	—
91	#13093963	—	2	2	no	—
92	C₂×C₄₇⋊C₁₆	—	2	2	no	—
93	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
94	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
95	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
96	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
97	C₁₆×D₄₇	—	2	2	no	—
98	C₁₆×D₄₇	—	2	2	no	—
99	C₁₆×D₄₇	—	2	2	no	—
100	C₁₆×D₄₇	—	2	2	no	—
101	C₁₆×D₄₇	—	2	2	no	—
102	C₁₆×D₄₇	D₄	1	4	yes	complemented
103	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
104	Dic₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
105	Dic₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
106	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
107	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
108	(C₂×D₄₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
109	(C₂×D₄₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
110	(C₂×D₄₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
111	(C₂×D₄₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
112	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
113	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
114	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
117	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
118	M₃₂×C₄₇	—	2	2	no	—
119	C₂×C₁₆×C₄₇	—	2	2	no	—
120	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
121	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
122	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
123	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
124	C₄⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
125	C₂²⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
126	C₂²⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
127	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
128	C₂³×D₄₇	C₂×C₈	1	1	yes	characteristic
129	C₂³×D₄₇	C₂×C₈	1	1	yes	characteristic
130	C₂×D₄×C₄₇	C₂×C₈	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₂²⋊D₄₇	C₂×C₈	1	1	yes	characteristic
134	C₂×C₂²⋊D₄₇	C₂×C₈	1	1	yes	characteristic
135	C₂²×Dic₄₇	C₂×C₈	1	1	yes	characteristic
136	C₂²×Dic₄₇	C₂×C₈	1	1	yes	characteristic
137	D₄×D₄₇	—	2	4	no	—
138	C₂×D₁₈₈	C₂×C₈	1	1	yes	characteristic
139	C₂×C₄×D₄₇	—	2	2	no	—
140	C₂×C₄×D₄₇	—	2	2	no	—
141	C₂×C₄×D₄₇	—	2	2	no	—
142	C₂×C₄×D₄₇	—	2	2	no	—
143	C₂×C₄×D₄₇	C₂×C₈	1	1	yes	characteristic
144	C₂×C₄×D₄₇	C₂×C₈	1	1	yes	characteristic
145	C₂×C₄×D₄₇	C₂×C₈	1	1	yes	characteristic
146	C₂×C₄×D₄₇	C₂×C₈	1	1	yes	characteristic
147	C₂×C₄×D₄₇	C₂×C₈	1	1	yes	characteristic
148	C₂×C₄×D₄₇	C₂×C₈	1	1	yes	characteristic
149	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
152	C₂×C₈×C₄₇	—	2	1	no	—
153	C₂×C₈×C₄₇	—	2	1	no	—
154	C₂×C₈×C₄₇	—	2	1	no	—
155	C₂×C₈×C₄₇	—	2	1	no	—
156	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
157	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
158	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
159	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
160	C₄⋊C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
161	C₂²⋊C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
162	C₂²⋊C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
163	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
164	C₂²⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
165	C₂²⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
166	(C₂×D₄₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
167	(C₂×D₄₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
168	(C₂×D₄₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
169	(C₂×D₄₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
170	C₄⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
171	Dic₄₇⋊C₄	C₂×C₈	1	1	yes	characteristic
172	Dic₄₇⋊C₄	C₂×C₈	1	1	yes	characteristic
173	C₄×Dic₄₇	C₂×C₈	1	1	yes	characteristic
174	C₄×Dic₄₇	C₂×C₈	1	1	yes	characteristic
175	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
176	C₂×C₄₇⋊C₈	—	2	2	no	—
177	C₂×C₄₇⋊C₈	—	2	2	no	—
178	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
180	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
181	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
182	C₈×D₄₇	—	2	2	no	—
183	C₈×D₄₇	—	2	2	no	—
184	C₈×D₄₇	—	2	2	no	—
185	C₈×D₄₇	—	2	1	no	—
186	C₈×D₄₇	—	2	1	no	—
187	C₈×D₄₇	—	2	1	no	—
188	C₈×D₄₇	—	2	1	no	—
189	C₈×D₄₇	—	2	2	no	—
190	C₈×D₄₇	—	2	2	no	—
191	C₈×D₄₇	C₂×D₄	1	2	yes	—
192	C₈×D₄₇	#41	1	2	yes	—
193	C₁₆×C₄₇	—	2	1	no	—
194	C₁₆×C₄₇	—	2	1	no	—
195	C₁₆×C₄₇	—	2	1	no	—
196	C₁₆×C₄₇	C₂×D₄	1	2	yes	complemented
197	C₄₇⋊C₁₆	—	2	1	no	—
198	C₄₇⋊C₁₆	—	2	1	no	—
199	C₄₇⋊C₁₆	—	2	1	no	—
200	C₄₇⋊C₁₆	C₂×D₄	1	2	yes	complemented
201	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
202	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
203	C₂²×D₄₇	—	2	2	no	—
204	C₂²×D₄₇	—	2	2	no	—
205	C₂²×D₄₇	—	2	2	no	—
206	C₂²×D₄₇	—	2	2	no	—
207	C₂²×D₄₇	—	2	2	no	—
208	C₂²×D₄₇	M₃₂	1	4	yes	complemented
209	C₂²×D₄₇	C₂²×C₈	1	1	yes	characteristic
210	C₂²×D₄₇	C₂²×C₈	1	1	yes	characteristic
211	C₂²×D₄₇	C₂²×C₈	1	1	yes	characteristic
212	D₄×C₄₇	—	2	2	no	—
213	C₂×C₄×C₄₇	—	2	1	no	—
214	C₂×C₄×C₄₇	—	2	1	no	—
215	C₂×C₄×C₄₇	—	2	1	no	—
216	C₂×C₄×C₄₇	—	2	1	no	—
217	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
218	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
219	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
220	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
221	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
222	C₂²⋊D₄₇	—	2	2	no	—
223	C₂²⋊D₄₇	—	2	2	no	—
224	C₂×Dic₄₇	—	2	2	no	—
225	C₂×Dic₄₇	—	2	2	no	—
226	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
227	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
228	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
229	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
230	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
231	D₁₈₈	—	2	2	no	—
232	C₄×D₄₇	—	2	2	no	—
233	C₄×D₄₇	—	2	2	no	—
234	C₄×D₄₇	—	2	2	no	—
235	C₄×D₄₇	—	2	2	no	—
236	C₄×D₄₇	—	2	1	no	—
237	C₄×D₄₇	—	2	1	no	—
238	C₄×D₄₇	—	2	1	no	—
239	C₄×D₄₇	—	2	1	no	—
240	C₄×D₄₇	—	2	2	no	—
241	C₄×D₄₇	—	2	2	no	—
242	C₄×D₄₇	C₄×D₄	1	2	yes	—
243	C₄×D₄₇	#131	1	2	yes	—
244	C₈×C₄₇	—	2	1	no	—
245	C₈×C₄₇	—	2	1	no	—
246	C₈×C₄₇	—	2	1	no	—
247	C₈×C₄₇	C₂²×D₄	1	1	yes	characteristic
248	C₈×C₄₇	C₂×#41	1	1	yes	characteristic
249	C₄₇⋊C₈	—	2	1	no	—
250	C₄₇⋊C₈	—	2	1	no	—
251	C₄₇⋊C₈	—	2	1	no	—
252	C₄₇⋊C₈	C₄×D₄	1	2	yes	—
253	C₂×#2168	—	47	1	no	maximal, Sylow
254	C₂²×C₄₇	—	2	1	no	—
255	C₂²×C₄₇	—	2	1	no	—
256	C₂²×C₄₇	—	2	1	no	—
257	C₂²×C₄₇	—	2	1	no	—
258	C₂²×C₄₇	—	2	1	no	—
259	C₂²×C₄₇	C₂×M₃₂	1	2	yes	complemented
260	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
261	C₂×D₄₇	—	2	1	no	—
262	C₂×D₄₇	—	2	1	no	—
263	C₂×D₄₇	—	2	8	no	—
264	C₂×D₄₇	—	2	1	no	—
265	C₂×D₄₇	—	2	1	no	—
266	C₂×D₄₇	—	2	1	no	—
267	C₂×D₄₇	—	4	4	no	—
268	C₂×D₄₇	C₈×D₄	1	2	yes	—
269	C₂×D₄₇	C₂×M₃₂	1	2	yes	—
270	C₂×D₄₇	C₂×M₃₂	1	2	yes	complemented
271	C₂×D₄₇	#504	1	2	yes	—
272	C₄×C₄₇	—	2	1	no	—
273	C₄×C₄₇	—	2	1	no	—
274	C₄×C₄₇	—	2	1	no	—
275	C₄×C₄₇	—	2	1	no	—
276	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
277	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
278	Dic₄₇	—	2	1	no	—
279	Dic₄₇	—	2	1	no	—
280	Dic₄₇	—	2	1	no	—
281	Dic₄₇	—	2	1	no	—
282	Dic₄₇	C₈×D₄	1	2	yes	—
283	C₂²×M₃₂	—	47	1	no	—
284	C₂³×C₁₆	—	47	1	no	—
285	C₂×C₈×D₄	—	47	1	no	—
286	#2168	—	47	1	no	—
287	#2168	—	47	1	no	—
288	#2168	—	47	1	no	—
289	#2168	—	47	1	no	—
290	#2168	—	47	1	no	—
291	#2168	—	47	1	no	—
292	#2168	—	47	1	no	—
293	#2168	D₄₇	1	1	yes	characteristic, direct product factor
294	C₂×C₄⋊C₁₆	—	47	1	no	—
295	C₂×C₂²⋊C₁₆	—	47	1	no	—
296	C₂×C₂²⋊C₁₆	—	47	1	no	—
297	C₂×#346	—	47	1	no	—
298	C₂×C₄₇	—	2	2	no	—
299	C₂×C₄₇	—	4	1	no	—
300	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
301	C₂×C₄₇	C₂²×M₃₂	1	1	yes	characteristic
302	C₂×C₄₇	C₂×#504	1	1	yes	characteristic
303	D₄₇	—	2	2	no	—
304	D₄₇	—	4	1	no	—
305	D₄₇	#2168	1	4	yes	direct product factor
306	C₂³×C₈	—	47	1	no	—
307	C₂³×C₈	—	47	1	no	—
308	C₂×C₄×D₄	—	47	1	no	—
309	C₂×M₃₂	—	47	1	no	—
310	C₂×M₃₂	—	47	1	no	—
311	C₂×M₃₂	—	47	1	no	—
312	C₂×M₃₂	—	94	4	no	—
313	C₂×M₃₂	C₂×D₄₇	1	1	yes	characteristic, complemented
314	C₂²×C₁₆	—	47	1	no	—
315	C₂²×C₁₆	—	47	1	no	—
316	C₂²×C₁₆	—	47	1	no	—
317	C₂²×C₁₆	—	47	1	no	—
318	C₂²×C₁₆	—	47	1	no	—
319	C₂²×C₁₆	—	47	1	no	—
320	C₂²×C₁₆	—	47	1	no	—
321	C₂²×C₁₆	—	94	4	no	—
322	C₂²×C₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
323	C₈×D₄	—	47	1	no	—
324	C₈×D₄	—	47	1	no	—
325	C₈×D₄	—	47	1	no	—
326	C₈×D₄	—	47	1	no	—
327	C₈×D₄	—	47	1	no	—
328	C₈×D₄	—	47	1	no	—
329	C₈×D₄	—	47	1	no	—
330	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic
331	C₂×C₄⋊C₈	—	47	1	no	—
332	C₂×C₂²⋊C₈	—	47	1	no	—
333	C₂×C₂²⋊C₈	—	47	1	no	—
334	C₂×C₄×C₈	—	47	1	no	—
335	C₄⋊C₁₆	—	47	1	no	—
336	C₄⋊C₁₆	—	47	1	no	—
337	C₄⋊C₁₆	—	47	1	no	—
338	C₄⋊C₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
339	C₂²⋊C₁₆	—	47	1	no	—
340	C₂²⋊C₁₆	—	47	1	no	—
341	C₂²⋊C₁₆	—	47	1	no	—
342	C₂²⋊C₁₆	—	47	1	no	—
343	C₂²⋊C₁₆	—	47	1	no	—
344	C₂²⋊C₁₆	—	47	1	no	—
345	C₂²⋊C₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
346	C₂²⋊C₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
347	#346	—	47	1	no	—
348	#346	—	47	1	no	—
349	#346	—	47	1	no	—
350	#346	C₂×D₄₇	1	1	yes	characteristic, complemented
351	C₄₇	C₂×#2168	1	1	yes	characteristic, complemented, Sylow
352	C₂²×D₄	—	47	1	no	—
353	C₂³×C₄	—	47	1	no	—
354	C₂³×C₄	—	47	1	no	—
355	C₂²×C₈	—	47	1	no	—
356	C₂²×C₈	—	47	1	no	—
357	C₂²×C₈	—	47	1	no	—
358	C₂²×C₈	—	47	1	no	—
359	C₂²×C₈	—	47	1	no	—
360	C₂²×C₈	—	47	1	no	—
361	C₂²×C₈	—	47	1	no	—
362	C₂²×C₈	—	47	1	no	—
363	C₂²×C₈	—	47	1	no	—
364	C₂²×C₈	—	47	1	no	—
365	C₂²×C₈	—	94	2	no	—
366	C₂²×C₈	—	94	2	no	—
367	C₂²×C₈	—	94	2	no	—
368	C₂²×C₈	—	94	2	no	—
369	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
370	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
371	C₄×D₄	—	47	1	no	—
372	C₄×D₄	—	47	1	no	—
373	C₄×D₄	—	47	1	no	—
374	C₄×D₄	—	47	1	no	—
375	C₄×D₄	—	47	1	no	—
376	C₄×D₄	—	47	1	no	—
377	C₄×D₄	—	47	1	no	—
378	C₄×D₄	C₄×D₄₇	1	1	yes	characteristic
379	C₂×C₄⋊C₄	—	47	1	no	—
380	C₂×C₂²⋊C₄	—	47	1	no	—
381	C₂×C₂²⋊C₄	—	47	1	no	—
382	C₂×C₄²	—	47	1	no	—
383	M₃₂	—	2	2	no	—
384	M₃₂	—	94	2	no	—
385	M₃₂	—	94	2	no	—
386	M₃₂	—	94	2	no	—
387	C₂×C₁₆	—	2	2	no	—
388	C₂×C₁₆	—	47	1	no	—
389	C₂×C₁₆	—	47	4	no	—
390	C₂×C₁₆	—	47	1	no	—
391	C₂×C₁₆	—	47	1	no	—
392	C₂×C₁₆	—	47	1	no	—
393	C₂×C₁₆	—	94	2	no	—
394	C₂×C₁₆	—	94	2	no	—
395	C₂×C₁₆	—	94	2	no	—
396	C₂×C₁₆	—	94	2	no	—
397	C₂×C₁₆	—	94	2	no	—
398	C₂×C₁₆	—	94	2	no	—
399	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
400	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
401	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
402	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
403	C₄⋊C₈	—	47	1	no	—
404	C₄⋊C₈	—	47	1	no	—
405	C₄⋊C₈	—	47	1	no	—
406	C₄⋊C₈	C₄×D₄₇	1	1	yes	characteristic
407	C₂²⋊C₈	—	47	1	no	—
408	C₂²⋊C₈	—	47	1	no	—
409	C₂²⋊C₈	—	47	1	no	—
410	C₂²⋊C₈	—	47	1	no	—
411	C₂²⋊C₈	—	47	1	no	—
412	C₂²⋊C₈	—	47	1	no	—
413	C₂²⋊C₈	C₄×D₄₇	1	1	yes	characteristic
414	C₂²⋊C₈	C₄×D₄₇	1	1	yes	characteristic
415	C₄×C₈	—	47	1	no	—
416	C₄×C₈	—	47	1	no	—
417	C₄×C₈	—	47	1	no	—
418	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
419	C₂⁴	—	47	1	no	—
420	C₂⁴	—	47	1	no	—
421	C₂×D₄	—	47	1	no	—
422	C₂×D₄	—	47	1	no	—
423	C₂×D₄	—	47	1	no	—
424	C₂×D₄	—	94	4	no	—
425	C₂×D₄	C₈×D₄₇	1	1	yes	characteristic
426	C₂²×C₄	—	47	1	no	—
427	C₂²×C₄	—	47	1	no	—
428	C₂²×C₄	—	47	1	no	—
429	C₂²×C₄	—	47	1	no	—
430	C₂²×C₄	—	47	1	no	—
431	C₂²×C₄	—	47	1	no	—
432	C₂²×C₄	—	47	1	no	—
433	C₂²×C₄	—	47	1	no	—
434	C₂²×C₄	—	47	1	no	—
435	C₂²×C₄	—	47	1	no	—
436	C₂²×C₄	—	47	1	no	—
437	C₂²×C₄	—	94	2	no	—
438	C₂²×C₄	—	94	2	no	—
439	C₂²×C₄	—	94	2	no	—
440	C₂²×C₄	—	94	2	no	—
441	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
442	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
443	C₂×C₈	—	2	1	no	—
444	C₂×C₈	—	2	1	no	—
445	C₂×C₈	—	2	1	no	—
446	C₂×C₈	—	2	1	no	—
447	C₂×C₈	—	47	1	no	—
448	C₂×C₈	—	47	2	no	—
449	C₂×C₈	—	47	2	no	—
450	C₂×C₈	—	47	1	no	—
451	C₂×C₈	—	47	1	no	—
452	C₂×C₈	—	47	1	no	—
453	C₂×C₈	—	94	2	no	—
454	C₂×C₈	—	94	2	no	—
455	C₂×C₈	—	94	2	no	—
456	C₂×C₈	—	94	2	no	—
457	C₂×C₈	—	94	2	no	—
458	C₂×C₈	—	94	2	no	—
459	C₂×C₈	—	94	2	no	—
460	C₂×C₈	—	94	1	no	—
461	C₂×C₈	—	94	1	no	—
462	C₂×C₈	—	94	1	no	—
463	C₂×C₈	—	94	1	no	—
464	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
465	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
466	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
467	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
468	C₄⋊C₄	—	47	1	no	—
469	C₄⋊C₄	—	47	1	no	—
470	C₄⋊C₄	—	47	1	no	—
471	C₄⋊C₄	C₈×D₄₇	1	1	yes	characteristic
472	C₂²⋊C₄	—	47	1	no	—
473	C₂²⋊C₄	—	47	1	no	—
474	C₂²⋊C₄	—	47	1	no	—
475	C₂²⋊C₄	—	47	1	no	—
476	C₂²⋊C₄	—	47	1	no	—
477	C₂²⋊C₄	—	47	1	no	—
478	C₂²⋊C₄	C₈×D₄₇	1	1	yes	characteristic
479	C₂²⋊C₄	C₈×D₄₇	1	1	yes	characteristic
480	C₄²	—	47	1	no	—
481	C₄²	—	47	1	no	—
482	C₄²	—	47	1	no	—
483	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
484	C₁₆	—	2	1	no	—
485	C₁₆	—	2	1	no	—
486	C₁₆	—	2	1	no	—
487	C₁₆	—	47	2	no	—
488	C₁₆	—	94	1	no	—
489	C₁₆	—	94	1	no	—
490	C₁₆	—	94	1	no	—
491	C₁₆	D₄×D₄₇	1	2	yes	complemented
492	C₂³	—	47	1	no	—
493	C₂³	—	47	4	no	—
494	C₂³	—	47	1	no	—
495	C₂³	—	47	1	no	—
496	C₂³	—	94	2	no	—
497	C₂³	—	94	2	no	—
498	C₂³	—	94	2	no	—
499	C₂³	—	94	2	no	—
500	C₂³	—	94	2	no	—
501	C₂³	C₂×C₈×D₄₇	1	1	yes	characteristic
502	C₂³	C₂×C₈×D₄₇	1	1	yes	characteristic
503	D₄	—	2	2	no	—
504	D₄	—	94	2	no	—
505	D₄	—	94	2	no	—
506	D₄	—	94	2	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	47	1	no	—
512	C₂×C₄	—	47	2	no	—
513	C₂×C₄	—	47	2	no	—
514	C₂×C₄	—	47	1	no	—
515	C₂×C₄	—	47	1	no	—
516	C₂×C₄	—	47	1	no	—
517	C₂×C₄	—	47	1	no	—
518	C₂×C₄	—	94	2	no	—
519	C₂×C₄	—	94	2	no	—
520	C₂×C₄	—	94	2	no	—
521	C₂×C₄	—	94	2	no	—
522	C₂×C₄	—	94	2	no	—
523	C₂×C₄	—	94	2	no	—
524	C₂×C₄	—	94	2	no	—
525	C₂×C₄	—	94	2	no	—
526	C₂×C₄	—	94	1	no	—
527	C₂×C₄	—	94	1	no	—
528	C₂×C₄	—	94	1	no	—
529	C₂×C₄	—	94	1	no	—
530	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
531	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
532	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
533	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
534	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
535	C₈	—	2	1	no	—
536	C₈	—	2	1	no	—
537	C₈	—	2	1	no	—
538	C₈	—	47	2	no	—
539	C₈	—	94	1	no	—
540	C₈	—	94	1	no	—
541	C₈	—	94	1	no	—
542	C₈	C₂×D₄×D₄₇	1	1	yes	characteristic
543	C₈	#41×D₄₇	1	1	yes	characteristic
544	C₂²	—	2	1	no	—
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	1	no	—
549	C₂²	—	47	2	no	—
550	C₂²	—	47	2	no	—
551	C₂²	—	47	2	no	—
552	C₂²	—	47	2	no	—
553	C₂²	—	94	8	no	—
554	C₂²	—	94	1	no	—
555	C₂²	—	94	1	no	—
556	C₂²	—	94	1	no	—
557	C₂²	—	94	1	no	—
558	C₂²	—	94	1	no	—
559	C₂²	—	188	4	no	—
560	C₂²	M₃₂×D₄₇	1	2	yes	complemented
561	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
562	C₄	—	2	1	no	—
563	C₄	—	2	1	no	—
564	C₄	—	2	1	no	—
565	C₄	—	2	1	no	—
566	C₄	—	47	2	no	—
567	C₄	—	94	1	no	—
568	C₄	—	94	1	no	—
569	C₄	—	94	1	no	—
570	C₄	—	94	1	no	—
571	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
572	C₄	#131×D₄₇	1	1	yes	characteristic
573	C₂	—	2	2	no	—
574	C₂	—	4	1	no	—
575	C₂	—	47	4	no	—
576	C₂	—	94	2	no	—
577	C₂	—	188	1	no	—
578	C₂	C₈×D₄×D₄₇	1	1	yes	characteristic
579	C₂	C₂×M₃₂×D₄₇	1	1	yes	characteristic
580	C₂	#504×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₄₇
commutator, socle	C₂²×C₄₇	C₂³×C₈
Fitting	C₄₇×#2168	C₂
prime radical	C₂×D₄×D₄₇	C₈
cosocle	C₂×C₈×C₄₇	C₂⁴
hypercenter	#2168	D₄₇
hypocenter	C₄₇	C₂×#2168
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ #2168

Complements

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

N	H ≅ G/N	type
1. C₂×M₃₂×D₄₇	C₂	semidirect
2. C₂²×C₁₆×D₄₇	C₂	semidirect
4. #20245216	C₂	semidirect
5. #20245215	C₂	semidirect
6. #20245214	C₂	semidirect
7. #20245213	C₂	semidirect
8. #20245212	C₂	semidirect
9. #20245211	C₂	semidirect
10. #20245210	C₂	semidirect
11. C₄⋊C₁₆×D₄₇	C₂	semidirect
12. C₂²⋊C₁₆×D₄₇	C₂	semidirect
13. C₂²⋊C₁₆×D₄₇	C₂	semidirect
14. #346×D₄₇	C₂	semidirect
15. C₄₇×#2168	C₂	semidirect
19. C₂×#13093964	C₂²	semidirect
20. C₂×#13093963	C₂²	semidirect
21. C₂×#13093963	C₂²	semidirect
23. C₂²×C₄₇⋊C₁₆	C₂²	semidirect
29. C₂×C₁₆×D₄₇	C₂²	semidirect
30. C₂×C₁₆×D₄₇	C₂²	semidirect
42. C₄⋊(C₄₇⋊C₁₆)	C₂²	semidirect
43. Dic₄₇⋊C₁₆	C₂²	semidirect
44. Dic₄₇⋊C₁₆	C₂²	semidirect
45. C₂²⋊(C₄₇⋊C₁₆)	C₂²	semidirect
46. C₂²⋊(C₄₇⋊C₁₆)	C₂²	semidirect
47. (C₂×D₄₇)⋊C₁₆	C₂²	semidirect
48. (C₂×D₄₇)⋊C₁₆	C₂²	semidirect
49. (C₂×D₄₇)⋊C₁₆	C₂²	semidirect
50. (C₂×D₄₇)⋊C₁₆	C₂²	semidirect
51. #15688899	C₂²	semidirect
52. #15688898	C₂²	semidirect
53. #15688898	C₂²	semidirect
54. C₂×M₃₂×C₄₇	C₂²	semidirect
55. C₂²×C₁₆×C₄₇	C₂²	semidirect
57. C₄₇×C₄⋊C₁₆	C₂²	semidirect
58. C₄₇×C₂²⋊C₁₆	C₂²	semidirect
59. C₄₇×C₂²⋊C₁₆	C₂²	semidirect
60. C₄₇×#346	C₂²	semidirect
102. C₁₆×D₄₇	D₄	semidirect
196. C₁₆×C₄₇	C₂×D₄	semidirect
200. C₄₇⋊C₁₆	C₂×D₄	semidirect
208. C₂²×D₄₇	M₃₂	semidirect
259. C₂²×C₄₇	C₂×M₃₂	semidirect
270. C₂×D₄₇	C₂×M₃₂	semidirect
293. #2168	D₄₇	direct (N × H)
305. D₄₇	#2168	direct (N × H)
313. C₂×M₃₂	C₂×D₄₇	semidirect
322. C₂²×C₁₆	C₂×D₄₇	semidirect
338. C₄⋊C₁₆	C₂×D₄₇	semidirect
345. C₂²⋊C₁₆	C₂×D₄₇	semidirect
346. C₂²⋊C₁₆	C₂×D₄₇	semidirect
350. #346	C₂×D₄₇	semidirect
351. C₄₇	C₂×#2168	semidirect
491. C₁₆	D₄×D₄₇	semidirect
560. C₂²	M₃₂×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×M₃₂×D₄₇	2
C₂²×C₁₆×D₄₇	2
C₈×D₄×D₄₇	2
#20245216	2
#20245215	2
#20245214	2
#20245213	2
#20245212	2
#20245211	2
#20245210	2
C₄⋊C₁₆×D₄₇	2
C₂²⋊C₁₆×D₄₇	2
#346×D₄₇	2
C₄₇×#2168	2
C₂×#2168	47

Subgroups — D47×#2168 #26369430

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#2168 #26369430