Subgroups — D₄₇×#1916 #26218316

Order 12032.

1134 conjugacy classes of subgroups.

The subgroup lattice has 672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄⋊C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄×C₄⋊C₄×D₄₇	C₂	1	1	yes	maximal, characteristic
4	#20243948	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243947	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243946	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243945	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243944	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243943	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243942	C₂	1	1	yes	maximal, characteristic, complemented
11	#336×D₄₇	C₂	1	1	yes	maximal, characteristic
12	#336×D₄₇	C₂	1	1	yes	maximal, characteristic
13	#336×D₄₇	C₂	1	1	yes	maximal, characteristic
14	#336×D₄₇	C₂	1	1	yes	maximal, characteristic
15	C₄₇×#1916	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	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊C₄×D₄₇	C₄	1	1	yes	characteristic
21	C₂×C₄⋊C₄×D₄₇	C₄	1	1	yes	characteristic
22	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
28	C₄⋊C₈×D₄₇	—	2	4	no	—
29	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
32	C₄×C₈×D₄₇	—	2	4	no	—
33	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
34	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
35	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
36	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
37	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
38	#15688974	C₄	1	1	yes	characteristic
39	#15688974	C₄	1	1	yes	characteristic
40	#95×D₄₇	C₄	1	1	yes	characteristic
41	#95×D₄₇	C₄	1	1	yes	characteristic
42	#15688878	C₂²	1	1	yes	characteristic
43	#15688878	C₂²	1	1	yes	characteristic
44	#15688878	C₂²	1	1	yes	characteristic
45	#15688878	C₂²	1	1	yes	characteristic
46	#15688877	C₂²	1	1	yes	characteristic
47	#15688877	C₂²	1	1	yes	characteristic
48	#15688877	C₂²	1	1	yes	characteristic
49	#15688877	C₂²	1	1	yes	characteristic
50	#15688877	C₂²	1	1	yes	characteristic
51	#15688877	C₂²	1	1	yes	characteristic
52	#15688877	C₂²	1	1	yes	characteristic
53	#15688877	C₂²	1	1	yes	characteristic
54	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
55	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
57	C₄₇×#336	C₂²	1	1	yes	characteristic
58	C₄₇×#336	C₂²	1	1	yes	characteristic
59	C₄₇×#336	C₂²	1	1	yes	characteristic
60	C₄₇×#336	C₂²	1	1	yes	characteristic
61	C₂²×C₄×D₄₇	C₂×C₄	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×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
68	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
69	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
72	C₂×C₈×D₄₇	—	2	2	no	—
73	C₂×C₈×D₄₇	—	2	2	no	—
74	C₂×C₈×D₄₇	—	2	2	no	—
75	C₂×C₈×D₄₇	—	2	2	no	—
76	C₂×C₈×D₄₇	—	2	2	no	—
77	C₂×C₈×D₄₇	—	2	2	no	—
78	C₂×C₈×D₄₇	—	2	2	no	—
79	C₂×C₈×D₄₇	—	2	2	no	—
80	C₂×C₈×D₄₇	—	2	2	no	—
81	C₂×C₈×D₄₇	—	2	2	no	—
82	C₂×C₈×D₄₇	D₄	1	4	yes	—
83	C₂×C₈×D₄₇	Q₈	1	4	yes	—
84	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
85	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
86	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₄⋊C₄×D₄₇	—	2	4	no	—
91	C₄⋊C₄×D₄₇	C₈	1	8	yes	complemented
92	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
94	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
96	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
97	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
99	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
100	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
101	C₄²×D₄₇	—	2	2	no	—
102	C₄²×D₄₇	—	2	2	no	—
103	C₄²×D₄₇	—	2	2	no	—
104	C₄²×D₄₇	—	2	2	no	—
105	C₄²×D₄₇	—	2	2	no	—
106	C₄²×D₄₇	—	2	2	no	—
107	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
108	Dic₄₇⋊C₈	—	2	2	no	—
109	Dic₄₇⋊C₈	—	2	2	no	—
110	C₄×C₄₇⋊C₈	—	2	2	no	—
111	C₈×Dic₄₇	—	2	2	no	—
112	C₈×Dic₄₇	—	2	2	no	—
113	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
114	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
115	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
116	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
117	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
118	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
119	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
120	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
121	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
122	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
123	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
124	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
125	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
126	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
128	C₄⋊C₈×C₄₇	—	2	2	no	—
129	C₄×C₈×C₄₇	—	2	2	no	—
130	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
131	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
132	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
133	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
140	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
141	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
142	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
143	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
144	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
146	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
147	C₂×C₄×D₄₇	—	2	2	no	—
148	C₂×C₄×D₄₇	—	2	2	no	—
149	C₂×C₄×D₄₇	—	2	2	no	—
150	C₂×C₄×D₄₇	—	2	2	no	—
151	C₂×C₄×D₄₇	—	2	2	no	—
152	C₂×C₄×D₄₇	—	2	2	no	—
153	C₂×C₄×D₄₇	—	2	2	no	—
154	C₂×C₄×D₄₇	—	2	2	no	—
155	C₂×C₄×D₄₇	—	2	2	no	—
156	C₂×C₄×D₄₇	—	2	2	no	—
157	C₂×C₄×D₄₇	—	2	2	no	—
158	C₂×C₄×D₄₇	—	2	2	no	—
159	C₂×C₄×D₄₇	—	2	2	no	—
160	C₂×C₄×D₄₇	—	2	2	no	—
161	C₂×C₄×D₄₇	C₂×C₈	1	4	yes	—
162	C₂×C₄×D₄₇	C₂×C₈	1	4	yes	—
163	C₂×C₄×D₄₇	C₂×C₈	1	4	yes	—
164	C₂×C₄×D₄₇	M₁₆	1	4	yes	—
165	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
166	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
167	C₂×C₄×D₄₇	#41	1	2	yes	—
168	C₂×C₄×D₄₇	#41	1	2	yes	—
169	C₂×C₄×D₄₇	#41	1	2	yes	—
170	C₂×C₄×D₄₇	#41	1	2	yes	—
171	C₂×C₈×C₄₇	—	2	1	no	—
172	C₂×C₈×C₄₇	—	2	1	no	—
173	C₂×C₈×C₄₇	—	2	1	no	—
174	C₂×C₈×C₄₇	—	2	1	no	—
175	C₂×C₈×C₄₇	—	2	1	no	—
176	C₂×C₈×C₄₇	—	2	1	no	—
177	C₂×C₈×C₄₇	—	2	1	no	—
178	C₂×C₈×C₄₇	—	2	1	no	—
179	C₂×C₈×C₄₇	—	2	1	no	—
180	C₂×C₈×C₄₇	—	2	1	no	—
181	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
182	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
183	C₄⋊C₄×C₄₇	—	2	2	no	—
184	C₄⋊C₄×C₄₇	C₂×C₈	1	4	yes	complemented
185	C₄²×C₄₇	—	2	1	no	—
186	C₄²×C₄₇	—	2	1	no	—
187	C₄²×C₄₇	—	2	1	no	—
188	C₄²×C₄₇	—	2	1	no	—
189	C₄²×C₄₇	—	2	1	no	—
190	C₄²×C₄₇	—	2	1	no	—
191	C₄⋊Dic₄₇	—	2	2	no	—
192	C₄⋊Dic₄₇	C₂×C₈	1	4	yes	complemented
193	Dic₄₇⋊C₄	—	2	2	no	—
194	Dic₄₇⋊C₄	—	2	2	no	—
195	Dic₄₇⋊C₄	C₂×C₈	1	4	yes	complemented
196	Dic₄₇⋊C₄	C₂×C₈	1	4	yes	complemented
197	C₄×Dic₄₇	—	2	1	no	—
198	C₄×Dic₄₇	—	2	1	no	—
199	C₄×Dic₄₇	—	2	1	no	—
200	C₄×Dic₄₇	—	2	1	no	—
201	C₄×Dic₄₇	—	2	1	no	—
202	C₄×Dic₄₇	—	2	1	no	—
203	C₄×Dic₄₇	—	2	2	no	—
204	C₄×Dic₄₇	—	2	2	no	—
205	C₄×Dic₄₇	—	2	2	no	—
206	C₄×Dic₄₇	—	2	2	no	—
207	C₄×Dic₄₇	—	2	2	no	—
208	C₄×Dic₄₇	—	2	2	no	—
209	C₂×C₄₇⋊C₈	—	2	1	no	—
210	C₂×C₄₇⋊C₈	—	2	1	no	—
211	C₂×C₄₇⋊C₈	—	2	1	no	—
212	C₂×C₄₇⋊C₈	—	2	1	no	—
213	C₂×C₄₇⋊C₈	—	2	1	no	—
214	C₂×C₄₇⋊C₈	—	2	1	no	—
215	C₂×C₄₇⋊C₈	—	2	1	no	—
216	C₂×C₄₇⋊C₈	—	2	1	no	—
217	C₂×C₄₇⋊C₈	—	2	1	no	—
218	C₂×C₄₇⋊C₈	—	2	1	no	—
219	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
220	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
221	C₈×D₄₇	—	2	8	no	—
222	C₈×D₄₇	—	2	8	no	—
223	C₈×D₄₇	—	4	4	no	—
224	C₈×D₄₇	—	4	4	no	—
225	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
226	C₂²×D₄₇	#117	1	2	yes	—
227	C₂²×D₄₇	C₄×D₄	1	2	yes	—
228	C₂²×D₄₇	C₄×Q₈	1	2	yes	—
229	C₂²×D₄₇	C₂²×C₈	1	2	yes	—
230	C₂²×D₄₇	C₂×M₁₆	1	2	yes	—
231	C₂²×D₄₇	#131	1	2	yes	—
232	C₂²×D₄₇	#131	1	2	yes	—
233	C₂×C₄×C₄₇	—	2	1	no	—
234	C₂×C₄×C₄₇	—	2	1	no	—
235	C₂×C₄×C₄₇	—	2	1	no	—
236	C₂×C₄×C₄₇	—	2	1	no	—
237	C₂×C₄×C₄₇	—	2	1	no	—
238	C₂×C₄×C₄₇	—	2	1	no	—
239	C₂×C₄×C₄₇	—	2	1	no	—
240	C₂×C₄×C₄₇	—	2	1	no	—
241	C₂×C₄×C₄₇	—	2	1	no	—
242	C₂×C₄×C₄₇	—	2	1	no	—
243	C₂×C₄×C₄₇	—	2	1	no	—
244	C₂×C₄×C₄₇	—	2	1	no	—
245	C₂×C₄×C₄₇	—	2	1	no	—
246	C₂×C₄×C₄₇	—	2	1	no	—
247	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
248	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
249	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
250	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
251	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
252	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
253	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
254	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
255	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
256	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
257	C₂×Dic₄₇	—	2	1	no	—
258	C₂×Dic₄₇	—	2	1	no	—
259	C₂×Dic₄₇	—	2	1	no	—
260	C₂×Dic₄₇	—	2	1	no	—
261	C₂×Dic₄₇	—	2	1	no	—
262	C₂×Dic₄₇	—	2	1	no	—
263	C₂×Dic₄₇	—	2	1	no	—
264	C₂×Dic₄₇	—	2	1	no	—
265	C₂×Dic₄₇	—	2	1	no	—
266	C₂×Dic₄₇	—	2	1	no	—
267	C₂×Dic₄₇	—	2	1	no	—
268	C₂×Dic₄₇	—	2	1	no	—
269	C₂×Dic₄₇	—	2	1	no	—
270	C₂×Dic₄₇	—	2	1	no	—
271	C₂×Dic₄₇	#117	1	2	yes	—
272	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
273	C₂×Dic₄₇	C₄×Q₈	1	2	yes	—
274	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
275	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
276	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
277	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
278	C₄×D₄₇	—	2	8	no	—
279	C₄×D₄₇	—	2	8	no	—
280	C₄×D₄₇	—	2	8	no	—
281	C₄×D₄₇	—	2	8	no	—
282	C₄×D₄₇	—	4	4	no	—
283	C₄×D₄₇	—	4	4	no	—
284	C₄×D₄₇	C₂²⋊Q₈	1	4	yes	—
285	C₄×D₄₇	#123	1	4	yes	—
286	C₄×D₄₇	#125	1	4	yes	—
287	C₄×D₄₇	#126	1	4	yes	—
288	C₈×C₄₇	—	2	2	no	—
289	C₈×C₄₇	—	2	2	no	—
290	C₈×C₄₇	—	4	1	no	—
291	C₈×C₄₇	—	4	1	no	—
292	C₄₇⋊C₈	—	2	2	no	—
293	C₄₇⋊C₈	—	2	2	no	—
294	C₄₇⋊C₈	—	4	1	no	—
295	C₄₇⋊C₈	—	4	1	no	—
296	C₂×#1916	—	47	1	no	maximal, Sylow
297	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
298	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
299	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
300	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
301	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
302	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
303	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
304	C₂×D₄₇	#387	1	4	yes	—
305	C₂×D₄₇	#431	1	4	yes	—
306	C₂×D₄₇	#433	1	4	yes	—
307	C₂×D₄₇	C₈×D₄	1	4	yes	—
308	C₂×D₄₇	#435	1	4	yes	—
309	C₂×D₄₇	C₈×Q₈	1	4	yes	—
310	C₂×D₄₇	#446	1	4	yes	—
311	C₄×C₄₇	—	2	2	no	—
312	C₄×C₄₇	—	2	2	no	—
313	C₄×C₄₇	—	2	2	no	—
314	C₄×C₄₇	—	2	2	no	—
315	C₄×C₄₇	—	4	1	no	—
316	C₄×C₄₇	—	4	1	no	—
317	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
318	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
319	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
320	C₄×C₄₇	C₂×#126	1	1	yes	characteristic
321	Dic₄₇	—	2	2	no	—
322	Dic₄₇	—	2	2	no	—
323	Dic₄₇	—	2	2	no	—
324	Dic₄₇	—	2	2	no	—
325	Dic₄₇	—	4	1	no	—
326	Dic₄₇	—	4	1	no	—
327	Dic₄₇	#387	1	4	yes	—
328	C₂²×C₄⋊C₈	—	47	1	no	—
329	C₂²×C₄×C₈	—	47	1	no	—
330	C₂×C₄×C₄⋊C₄	—	47	1	no	—
331	#1916	—	47	1	no	—
332	#1916	—	47	1	no	—
333	#1916	—	47	1	no	—
334	#1916	—	47	1	no	—
335	#1916	—	47	1	no	—
336	#1916	—	47	1	no	—
337	#1916	—	47	1	no	—
338	#1916	D₄₇	1	1	yes	characteristic, direct product factor
339	C₂×#336	—	47	1	no	—
340	C₂×#336	—	47	1	no	—
341	C₂×#336	—	47	1	no	—
342	C₂×#336	—	47	1	no	—
343	C₂×C₄₇	C₂×#387	1	1	yes	characteristic
344	C₂×C₄₇	C₂×#431	1	1	yes	characteristic
345	C₂×C₄₇	C₂×#433	1	1	yes	characteristic
346	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
347	C₂×C₄₇	C₂×#435	1	1	yes	characteristic
348	C₂×C₄₇	C₂×C₈×Q₈	1	1	yes	characteristic
349	C₂×C₄₇	C₂×#446	1	1	yes	characteristic
350	D₄₇	#1916	1	8	yes	direct product factor
351	C₂³×C₈	—	47	1	no	—
352	C₂³×C₈	—	47	1	no	—
353	C₂³×C₈	—	47	1	no	—
354	C₂³×C₈	—	47	1	no	—
355	C₂²×C₄⋊C₄	—	47	1	no	—
356	C₂²×C₄⋊C₄	—	47	1	no	—
357	C₂²×C₄²	—	47	1	no	—
358	C₂²×C₄²	—	47	1	no	—
359	C₂²×C₄²	—	47	1	no	—
360	C₂×C₄⋊C₈	—	47	1	no	—
361	C₂×C₄⋊C₈	—	47	1	no	—
362	C₂×C₄⋊C₈	—	47	1	no	—
363	C₂×C₄⋊C₈	—	94	4	no	—
364	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
365	C₂×C₄×C₈	—	47	1	no	—
366	C₂×C₄×C₈	—	47	1	no	—
367	C₂×C₄×C₈	—	47	1	no	—
368	C₂×C₄×C₈	—	94	4	no	—
369	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
370	C₄×C₄⋊C₄	—	47	1	no	—
371	C₄×C₄⋊C₄	—	47	1	no	—
372	C₄×C₄⋊C₄	—	47	1	no	—
373	C₄×C₄⋊C₄	—	47	1	no	—
374	C₄×C₄⋊C₄	—	47	1	no	—
375	C₄×C₄⋊C₄	—	47	1	no	—
376	C₄×C₄⋊C₄	—	47	1	no	—
377	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
378	C₂×#95	—	47	1	no	—
379	C₂×#95	—	47	1	no	—
380	#336	—	47	1	no	—
381	#336	—	47	1	no	—
382	#336	—	47	1	no	—
383	#336	—	47	1	no	—
384	#336	—	47	1	no	—
385	#336	—	47	1	no	—
386	#336	—	47	1	no	—
387	#336	—	47	1	no	—
388	#336	—	47	1	no	—
389	#336	—	47	1	no	—
390	#336	—	47	1	no	—
391	#336	—	47	1	no	—
392	#336	C₂×D₄₇	1	1	yes	characteristic
393	#336	C₂×D₄₇	1	1	yes	characteristic
394	#336	C₂×D₄₇	1	1	yes	characteristic
395	#336	C₂×D₄₇	1	1	yes	characteristic
396	C₄₇	C₂×#1916	1	1	yes	characteristic, complemented, Sylow
397	C₂³×C₄	—	47	1	no	—
398	C₂³×C₄	—	47	1	no	—
399	C₂³×C₄	—	47	1	no	—
400	C₂³×C₄	—	47	1	no	—
401	C₂³×C₄	—	47	1	no	—
402	C₂³×C₄	—	47	1	no	—
403	C₂³×C₄	—	47	1	no	—
404	C₂²×C₈	—	47	1	no	—
405	C₂²×C₈	—	47	1	no	—
406	C₂²×C₈	—	47	4	no	—
407	C₂²×C₈	—	47	4	no	—
408	C₂²×C₈	—	47	1	no	—
409	C₂²×C₈	—	47	1	no	—
410	C₂²×C₈	—	94	2	no	—
411	C₂²×C₈	—	94	2	no	—
412	C₂²×C₈	—	94	2	no	—
413	C₂²×C₈	—	94	2	no	—
414	C₂²×C₈	—	94	2	no	—
415	C₂²×C₈	—	94	2	no	—
416	C₂²×C₈	—	94	2	no	—
417	C₂²×C₈	—	94	2	no	—
418	C₂²×C₈	—	94	2	no	—
419	C₂²×C₈	—	94	2	no	—
420	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
421	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
422	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
423	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
424	C₂×C₄⋊C₄	—	47	1	no	—
425	C₂×C₄⋊C₄	—	47	1	no	—
426	C₂×C₄⋊C₄	—	47	1	no	—
427	C₂×C₄⋊C₄	—	47	8	no	—
428	C₂×C₄⋊C₄	—	47	1	no	—
429	C₂×C₄⋊C₄	—	47	1	no	—
430	C₂×C₄⋊C₄	—	47	1	no	—
431	C₂×C₄⋊C₄	—	94	4	no	—
432	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
433	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
434	C₂×C₄²	—	47	1	no	—
435	C₂×C₄²	—	47	1	no	—
436	C₂×C₄²	—	47	1	no	—
437	C₂×C₄²	—	47	1	no	—
438	C₂×C₄²	—	47	1	no	—
439	C₂×C₄²	—	47	1	no	—
440	C₂×C₄²	—	47	1	no	—
441	C₂×C₄²	—	47	1	no	—
442	C₂×C₄²	—	47	1	no	—
443	C₂×C₄²	—	94	2	no	—
444	C₂×C₄²	—	94	2	no	—
445	C₂×C₄²	—	94	2	no	—
446	C₂×C₄²	—	94	2	no	—
447	C₂×C₄²	—	94	2	no	—
448	C₂×C₄²	—	94	2	no	—
449	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
450	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
451	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
452	C₄⋊C₈	—	2	2	no	—
453	C₄⋊C₈	—	94	2	no	—
454	C₄⋊C₈	—	94	2	no	—
455	C₄⋊C₈	—	94	2	no	—
456	C₄×C₈	—	2	2	no	—
457	C₄×C₈	—	94	2	no	—
458	C₄×C₈	—	94	2	no	—
459	C₄×C₈	—	94	2	no	—
460	#95	—	47	1	no	—
461	#95	—	47	1	no	—
462	#95	—	47	1	no	—
463	#95	—	47	1	no	—
464	#95	—	47	1	no	—
465	#95	—	47	1	no	—
466	#95	C₄×D₄₇	1	1	yes	characteristic
467	#95	C₄×D₄₇	1	1	yes	characteristic
468	C₂⁴	—	47	1	no	—
469	C₂²×C₄	—	47	1	no	—
470	C₂²×C₄	—	47	2	no	—
471	C₂²×C₄	—	47	2	no	—
472	C₂²×C₄	—	47	2	no	—
473	C₂²×C₄	—	47	2	no	—
474	C₂²×C₄	—	47	2	no	—
475	C₂²×C₄	—	47	2	no	—
476	C₂²×C₄	—	47	1	no	—
477	C₂²×C₄	—	47	1	no	—
478	C₂²×C₄	—	47	1	no	—
479	C₂²×C₄	—	47	1	no	—
480	C₂²×C₄	—	47	4	no	—
481	C₂²×C₄	—	47	4	no	—
482	C₂²×C₄	—	47	4	no	—
483	C₂²×C₄	—	47	4	no	—
484	C₂²×C₄	—	47	1	no	—
485	C₂²×C₄	—	47	1	no	—
486	C₂²×C₄	—	94	2	no	—
487	C₂²×C₄	—	94	2	no	—
488	C₂²×C₄	—	94	2	no	—
489	C₂²×C₄	—	94	2	no	—
490	C₂²×C₄	—	94	2	no	—
491	C₂²×C₄	—	94	2	no	—
492	C₂²×C₄	—	94	2	no	—
493	C₂²×C₄	—	94	2	no	—
494	C₂²×C₄	—	94	2	no	—
495	C₂²×C₄	—	94	2	no	—
496	C₂²×C₄	—	94	2	no	—
497	C₂²×C₄	—	94	2	no	—
498	C₂²×C₄	—	94	2	no	—
499	C₂²×C₄	—	94	2	no	—
500	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
501	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
502	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
503	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
504	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
505	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
506	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
507	C₂×C₈	—	2	1	no	—
508	C₂×C₈	—	2	1	no	—
509	C₂×C₈	—	2	1	no	—
510	C₂×C₈	—	2	1	no	—
511	C₂×C₈	—	2	1	no	—
512	C₂×C₈	—	2	1	no	—
513	C₂×C₈	—	2	1	no	—
514	C₂×C₈	—	2	1	no	—
515	C₂×C₈	—	2	1	no	—
516	C₂×C₈	—	2	1	no	—
517	C₂×C₈	—	47	2	no	—
518	C₂×C₈	—	47	2	no	—
519	C₂×C₈	—	94	8	no	—
520	C₂×C₈	—	94	8	no	—
521	C₂×C₈	—	94	1	no	—
522	C₂×C₈	—	94	1	no	—
523	C₂×C₈	—	94	1	no	—
524	C₂×C₈	—	94	1	no	—
525	C₂×C₈	—	94	1	no	—
526	C₂×C₈	—	94	1	no	—
527	C₂×C₈	—	94	1	no	—
528	C₂×C₈	—	94	1	no	—
529	C₂×C₈	—	94	1	no	—
530	C₂×C₈	—	94	1	no	—
531	C₂×C₈	—	188	4	no	—
532	C₂×C₈	—	188	4	no	—
533	C₂×C₈	D₄×D₄₇	1	2	yes	—
534	C₂×C₈	Q₈×D₄₇	1	2	yes	—
535	C₄⋊C₄	—	2	2	no	—
536	C₄⋊C₄	—	47	4	no	—
537	C₄⋊C₄	—	47	4	no	—
538	C₄⋊C₄	—	47	4	no	—
539	C₄⋊C₄	—	94	2	no	—
540	C₄⋊C₄	—	94	2	no	—
541	C₄⋊C₄	—	94	2	no	—
542	C₄⋊C₄	C₈×D₄₇	1	4	yes	complemented
543	C₄²	—	2	1	no	—
544	C₄²	—	2	1	no	—
545	C₄²	—	2	1	no	—
546	C₄²	—	2	1	no	—
547	C₄²	—	2	1	no	—
548	C₄²	—	2	1	no	—
549	C₄²	—	94	2	no	—
550	C₄²	—	94	2	no	—
551	C₄²	—	94	2	no	—
552	C₄²	—	94	2	no	—
553	C₄²	—	94	2	no	—
554	C₄²	—	94	2	no	—
555	C₄²	—	94	1	no	—
556	C₄²	—	94	1	no	—
557	C₄²	—	94	1	no	—
558	C₄²	—	94	1	no	—
559	C₄²	—	94	1	no	—
560	C₄²	—	94	1	no	—
561	C₂³	—	47	2	no	—
562	C₂³	—	47	2	no	—
563	C₂³	—	47	2	no	—
564	C₂³	—	47	2	no	—
565	C₂³	—	47	2	no	—
566	C₂³	—	47	2	no	—
567	C₂³	—	47	2	no	—
568	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
569	C₂×C₄	—	2	1	no	—
570	C₂×C₄	—	2	1	no	—
571	C₂×C₄	—	2	1	no	—
572	C₂×C₄	—	2	1	no	—
573	C₂×C₄	—	2	1	no	—
574	C₂×C₄	—	2	1	no	—
575	C₂×C₄	—	2	1	no	—
576	C₂×C₄	—	2	1	no	—
577	C₂×C₄	—	2	1	no	—
578	C₂×C₄	—	2	1	no	—
579	C₂×C₄	—	2	1	no	—
580	C₂×C₄	—	2	1	no	—
581	C₂×C₄	—	2	1	no	—
582	C₂×C₄	—	2	1	no	—
583	C₂×C₄	—	47	2	no	—
584	C₂×C₄	—	47	2	no	—
585	C₂×C₄	—	47	2	no	—
586	C₂×C₄	—	47	4	no	—
587	C₂×C₄	—	47	4	no	—
588	C₂×C₄	—	47	4	no	—
589	C₂×C₄	—	47	4	no	—
590	C₂×C₄	—	47	2	no	—
591	C₂×C₄	—	47	2	no	—
592	C₂×C₄	—	47	2	no	—
593	C₂×C₄	—	47	2	no	—
594	C₂×C₄	—	94	8	no	—
595	C₂×C₄	—	94	8	no	—
596	C₂×C₄	—	94	8	no	—
597	C₂×C₄	—	94	8	no	—
598	C₂×C₄	—	94	1	no	—
599	C₂×C₄	—	94	1	no	—
600	C₂×C₄	—	94	1	no	—
601	C₂×C₄	—	94	1	no	—
602	C₂×C₄	—	94	1	no	—
603	C₂×C₄	—	94	1	no	—
604	C₂×C₄	—	94	1	no	—
605	C₂×C₄	—	94	1	no	—
606	C₂×C₄	—	94	1	no	—
607	C₂×C₄	—	94	1	no	—
608	C₂×C₄	—	94	1	no	—
609	C₂×C₄	—	94	1	no	—
610	C₂×C₄	—	94	1	no	—
611	C₂×C₄	—	94	1	no	—
612	C₂×C₄	—	188	4	no	—
613	C₂×C₄	—	188	4	no	—
614	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
615	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
616	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
617	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
618	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
619	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
620	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
621	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
622	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
623	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
624	C₈	—	2	2	no	—
625	C₈	—	2	2	no	—
626	C₈	—	4	1	no	—
627	C₈	—	4	1	no	—
628	C₈	—	94	2	no	—
629	C₈	—	94	2	no	—
630	C₈	—	188	1	no	—
631	C₈	—	188	1	no	—
632	C₂²	—	47	4	no	—
633	C₂²	—	47	4	no	—
634	C₂²	—	47	4	no	—
635	C₂²	—	47	4	no	—
636	C₂²	—	47	4	no	—
637	C₂²	—	47	4	no	—
638	C₂²	—	47	4	no	—
639	C₂²	#117×D₄₇	1	1	yes	characteristic
640	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
641	C₂²	C₄×Q₈×D₄₇	1	1	yes	characteristic
642	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
643	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
644	C₂²	#131×D₄₇	1	1	yes	characteristic
645	C₂²	#131×D₄₇	1	1	yes	characteristic
646	C₄	—	2	2	no	—
647	C₄	—	2	2	no	—
648	C₄	—	2	2	no	—
649	C₄	—	2	2	no	—
650	C₄	—	4	1	no	—
651	C₄	—	4	1	no	—
652	C₄	—	47	4	no	—
653	C₄	—	94	2	no	—
654	C₄	—	94	2	no	—
655	C₄	—	94	2	no	—
656	C₄	—	94	2	no	—
657	C₄	—	188	1	no	—
658	C₄	—	188	1	no	—
659	C₄	C₂²⋊Q₈×D₄₇	1	1	yes	characteristic
660	C₄	#123×D₄₇	1	1	yes	characteristic
661	C₄	#125×D₄₇	1	1	yes	characteristic
662	C₄	#126×D₄₇	1	1	yes	characteristic
663	C₂	—	47	8	no	—
664	C₂	#387×D₄₇	1	1	yes	characteristic
665	C₂	#431×D₄₇	1	1	yes	characteristic
666	C₂	#433×D₄₇	1	1	yes	characteristic
667	C₂	C₈×D₄×D₄₇	1	1	yes	characteristic
668	C₂	#435×D₄₇	1	1	yes	characteristic
669	C₂	C₈×Q₈×D₄₇	1	1	yes	characteristic
670	C₂	#446×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Fitting	C₄₇×#1916	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1916	D₄₇
hypocenter	C₄₇	C₂×#1916
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1916

Complements

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

N	H ≅ G/N	type
4. #20243948	C₂	semidirect
5. #20243947	C₂	semidirect
6. #20243946	C₂	semidirect
7. #20243945	C₂	semidirect
8. #20243944	C₂	semidirect
9. #20243943	C₂	semidirect
10. #20243942	C₂	semidirect
15. C₄₇×#1916	C₂	semidirect
91. C₄⋊C₄×D₄₇	C₈	semidirect
184. C₄⋊C₄×C₄₇	C₂×C₈	semidirect
192. C₄⋊Dic₄₇	C₂×C₈	semidirect
195. Dic₄₇⋊C₄	C₂×C₈	semidirect
196. Dic₄₇⋊C₄	C₂×C₈	semidirect
338. #1916	D₄₇	direct (N × H)
350. D₄₇	#1916	direct (N × H)
396. C₄₇	C₂×#1916	semidirect
542. C₄⋊C₄	C₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄⋊C₈×D₄₇	2
C₂×C₄×C₈×D₄₇	2
C₄×C₄⋊C₄×D₄₇	2
#20243948	2
#20243947	2
#20243946	2
#20243945	2
#20243944	2
#20243943	2
#20243942	2
#336×D₄₇	2
C₄₇×#1916	2
C₂×#1916	47

Subgroups — D47×#1916 #26218316

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#1916 #26218316