Subgroups — D₄₇×#1939 #26219539

Order 12032.

1246 conjugacy classes of subgroups.

The subgroup lattice has 516 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	2	yes	maximal
2	C₂×C₄⋊C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
4	C₄×C₄⋊C₄×D₄₇	C₂	1	1	yes	maximal, characteristic
5	#20244107	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244106	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244105	C₂	1	2	yes	maximal, complemented
8	#20244104	C₂	1	1	yes	maximal, characteristic, complemented
9	#20244103	C₂	1	2	yes	maximal, complemented
10	#336×D₄₇	C₂	1	2	yes	maximal
11	C₄₇×#1939	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
13	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
14	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊C₄×D₄₇	C₄	1	1	yes	characteristic
16	C₂×C₄⋊C₄×D₄₇	C₄	1	1	yes	characteristic
17	C₂×C₄²×D₄₇	C₂²	1	2	yes	—
18	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
20	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
22	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
23	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
24	C₄⋊C₈×D₄₇	—	2	8	no	—
25	C₄⋊C₈×D₄₇	—	2	4	no	—
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
28	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
29	C₄×C₈×D₄₇	—	2	4	no	—
30	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
31	C₄⋊C₄×Dic₄₇	C₄	1	1	yes	characteristic
32	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
33	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
34	#15688974	C₄	1	2	yes	—
35	#95×D₄₇	C₄	1	2	yes	—
36	#15688878	C₂²	1	2	yes	—
37	#15688877	C₂²	1	2	yes	—
38	#15688877	C₂²	1	2	yes	—
39	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
40	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#336	C₂²	1	2	yes	—
44	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
45	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
47	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
51	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
52	C₂×C₈×D₄₇	—	2	2	no	—
53	C₂×C₈×D₄₇	—	2	2	no	—
54	C₂×C₈×D₄₇	—	2	2	no	—
55	C₂×C₈×D₄₇	—	2	2	no	—
56	C₂×C₈×D₄₇	—	2	4	no	—
57	C₂×C₈×D₄₇	—	2	4	no	—
58	C₂×C₈×D₄₇	—	2	4	no	—
59	C₂×C₈×D₄₇	D₄	1	4	yes	—
60	C₂×C₈×D₄₇	Q₈	1	4	yes	—
61	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
62	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
65	C₄⋊C₄×D₄₇	—	2	4	no	—
66	C₄⋊C₄×D₄₇	C₈	1	8	yes	complemented
67	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
68	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
69	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
72	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
73	C₄²×D₄₇	—	2	4	no	—
74	C₄²×D₄₇	—	2	4	no	—
75	C₄²×D₄₇	D₄	1	4	yes	—
76	C₄²×D₄₇	Q₈	1	4	yes	—
77	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
78	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
79	Dic₄₇⋊C₈	—	2	4	no	—
80	Dic₄₇⋊C₈	—	2	4	no	—
81	Dic₄₇⋊C₈	—	2	4	no	—
82	C₄×C₄₇⋊C₈	—	2	2	no	—
83	C₈×Dic₄₇	—	2	2	no	—
84	C₈×Dic₄₇	—	2	2	no	—
85	C₄₇⋊#95	C₂×C₄	1	2	yes	—
86	C₄₇⋊#95	C₂×C₄	1	2	yes	—
87	C₄₇⋊#95	C₂×C₄	1	2	yes	—
88	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
89	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
90	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
91	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
94	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
95	C₄⋊C₈×C₄₇	—	2	4	no	—
96	C₄⋊C₈×C₄₇	—	2	2	no	—
97	C₄×C₈×C₄₇	—	2	2	no	—
98	#95×C₄₇	C₂×C₄	1	2	yes	—
99	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
105	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
106	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
108	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₄×D₄₇	—	2	4	no	—
111	C₂×C₄×D₄₇	—	2	2	no	—
112	C₂×C₄×D₄₇	—	2	2	no	—
113	C₂×C₄×D₄₇	—	2	4	no	—
114	C₂×C₄×D₄₇	—	2	4	no	—
115	C₂×C₄×D₄₇	—	2	4	no	—
116	C₂×C₄×D₄₇	—	2	4	no	—
117	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
118	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
119	C₂×C₄×D₄₇	C₂×C₈	1	8	yes	—
120	C₂×C₄×D₄₇	C₂×C₈	1	4	yes	—
121	C₂×C₄×D₄₇	M₁₆	1	4	yes	—
122	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
123	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
124	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
125	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
126	C₂×C₄×D₄₇	#41	1	2	yes	—
127	C₂×C₄×D₄₇	#41	1	2	yes	—
128	C₂×C₈×C₄₇	—	2	1	no	—
129	C₂×C₈×C₄₇	—	2	1	no	—
130	C₂×C₈×C₄₇	—	2	1	no	—
131	C₂×C₈×C₄₇	—	2	1	no	—
132	C₂×C₈×C₄₇	—	2	2	no	—
133	C₂×C₈×C₄₇	—	2	2	no	—
134	C₂×C₈×C₄₇	—	2	2	no	—
135	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
136	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
137	C₄⋊C₄×C₄₇	—	2	2	no	—
138	C₄⋊C₄×C₄₇	C₂×C₈	1	4	yes	complemented
139	C₄²×C₄₇	—	2	2	no	—
140	C₄²×C₄₇	—	2	2	no	—
141	C₄²×C₄₇	C₂×D₄	1	2	yes	—
142	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
143	C₄⋊Dic₄₇	—	2	2	no	—
144	C₄⋊Dic₄₇	C₂×C₈	1	4	yes	complemented
145	Dic₄₇⋊C₄	—	2	4	no	—
146	Dic₄₇⋊C₄	C₂×C₈	1	8	yes	complemented
147	C₄×Dic₄₇	—	2	2	no	—
148	C₄×Dic₄₇	—	2	2	no	—
149	C₄×Dic₄₇	—	2	4	no	—
150	C₄×Dic₄₇	—	2	4	no	—
151	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
152	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
153	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
154	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
155	C₂×C₄₇⋊C₈	—	2	1	no	—
156	C₂×C₄₇⋊C₈	—	2	1	no	—
157	C₂×C₄₇⋊C₈	—	2	1	no	—
158	C₂×C₄₇⋊C₈	—	2	1	no	—
159	C₂×C₄₇⋊C₈	—	2	2	no	—
160	C₂×C₄₇⋊C₈	—	2	2	no	—
161	C₂×C₄₇⋊C₈	—	2	2	no	—
162	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
163	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
164	C₈×D₄₇	—	2	8	no	—
165	C₈×D₄₇	—	2	8	no	—
166	C₈×D₄₇	—	4	8	no	—
167	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
168	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
169	C₂²×D₄₇	C₄×D₄	1	2	yes	—
170	C₂²×D₄₇	C₄×Q₈	1	2	yes	—
171	C₂²×D₄₇	C₂²×C₈	1	2	yes	—
172	C₂²×D₄₇	C₂×M₁₆	1	2	yes	—
173	C₂²×D₄₇	#131	1	2	yes	—
174	C₂²×D₄₇	#131	1	2	yes	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
183	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
184	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
185	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
186	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
187	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
193	C₂×Dic₄₇	—	2	2	no	—
194	C₂×Dic₄₇	—	2	1	no	—
195	C₂×Dic₄₇	—	2	1	no	—
196	C₂×Dic₄₇	—	2	2	no	—
197	C₂×Dic₄₇	—	2	2	no	—
198	C₂×Dic₄₇	—	2	2	no	—
199	C₂×Dic₄₇	—	2	2	no	—
200	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
201	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
202	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
203	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
204	C₂×Dic₄₇	C₄×Q₈	1	2	yes	—
205	C₂×Dic₄₇	C₂²×C₈	1	4	yes	—
206	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
207	C₂×Dic₄₇	C₂×M₁₆	1	2	yes	—
208	C₄×D₄₇	—	2	8	no	—
209	C₄×D₄₇	—	2	16	no	—
210	C₄×D₄₇	—	4	8	no	—
211	C₄×D₄₇	C₄⋊C₈	1	16	yes	complemented
212	C₄×D₄₇	#121	1	4	yes	—
213	C₄×D₄₇	C₂²⋊Q₈	1	4	yes	—
214	C₄×D₄₇	#125	1	4	yes	—
215	C₄×D₄₇	C₄⋊Q₈	1	4	yes	—
216	C₈×C₄₇	—	2	2	no	—
217	C₈×C₄₇	—	2	2	no	—
218	C₈×C₄₇	—	4	2	no	—
219	C₄₇⋊C₈	—	2	2	no	—
220	C₄₇⋊C₈	—	2	2	no	—
221	C₄₇⋊C₈	—	4	2	no	—
222	C₂×#1939	—	47	1	no	maximal, Sylow
223	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
224	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
225	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
226	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
227	C₂²×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
228	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
229	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
230	C₂×D₄₇	#389	1	4	yes	—
231	C₂×D₄₇	C₂×C₄⋊C₈	1	4	yes	—
232	C₂×D₄₇	#424	1	4	yes	—
233	C₂×D₄₇	C₈×D₄	1	4	yes	—
234	C₂×D₄₇	#436	1	4	yes	—
235	C₂×D₄₇	C₈×Q₈	1	4	yes	—
236	C₂×D₄₇	#446	1	4	yes	—
237	C₄×C₄₇	—	2	2	no	—
238	C₄×C₄₇	—	2	4	no	—
239	C₄×C₄₇	—	4	2	no	—
240	C₄×C₄₇	C₂×C₄⋊C₈	1	4	yes	complemented
241	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
242	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
243	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
244	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
245	Dic₄₇	—	2	2	no	—
246	Dic₄₇	—	2	4	no	—
247	Dic₄₇	—	4	2	no	—
248	Dic₄₇	#389	1	4	yes	—
249	Dic₄₇	C₂×C₄⋊C₈	1	4	yes	complemented
250	C₂²×C₄⋊C₈	—	47	2	no	—
251	C₂²×C₄⋊C₈	—	47	1	no	—
252	C₂²×C₄×C₈	—	47	1	no	—
253	C₂×C₄×C₄⋊C₄	—	47	1	no	—
254	#1939	—	47	2	no	—
255	#1939	—	47	1	no	—
256	#1939	—	47	1	no	—
257	#1939	—	47	1	no	—
258	#1939	—	47	2	no	—
259	#1939	D₄₇	1	1	yes	characteristic, direct product factor
260	C₂×#336	—	47	2	no	—
261	C₂×C₄₇	C₂×#389	1	1	yes	characteristic
262	C₂×C₄₇	C₂²×C₄⋊C₈	1	1	yes	characteristic
263	C₂×C₄₇	C₂×#424	1	1	yes	characteristic
264	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
265	C₂×C₄₇	C₂×#436	1	1	yes	characteristic
266	C₂×C₄₇	C₂×C₈×Q₈	1	1	yes	characteristic
267	C₂×C₄₇	C₂×#446	1	1	yes	characteristic
268	D₄₇	#1939	1	8	yes	direct product factor
269	C₂³×C₈	—	47	1	no	—
270	C₂³×C₈	—	47	1	no	—
271	C₂³×C₈	—	47	2	no	—
272	C₂²×C₄⋊C₄	—	47	1	no	—
273	C₂²×C₄⋊C₄	—	47	1	no	—
274	C₂²×C₄²	—	47	1	no	—
275	C₂²×C₄²	—	47	2	no	—
276	C₂×C₄⋊C₈	—	47	2	no	—
277	C₂×C₄⋊C₈	—	47	2	no	—
278	C₂×C₄⋊C₈	—	47	2	no	—
279	C₂×C₄⋊C₈	—	47	2	no	—
280	C₂×C₄⋊C₈	—	47	1	no	—
281	C₂×C₄⋊C₈	—	94	4	no	—
282	C₂×C₄⋊C₈	—	94	8	no	—
283	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
284	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
285	C₂×C₄×C₈	—	47	1	no	—
286	C₂×C₄×C₈	—	47	1	no	—
287	C₂×C₄×C₈	—	47	1	no	—
288	C₂×C₄×C₈	—	94	4	no	—
289	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
290	C₄×C₄⋊C₄	—	47	1	no	—
291	C₄×C₄⋊C₄	—	47	1	no	—
292	C₄×C₄⋊C₄	—	47	1	no	—
293	C₄×C₄⋊C₄	—	47	2	no	—
294	C₄×C₄⋊C₄	—	47	2	no	—
295	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
296	C₂×#95	—	47	2	no	—
297	#336	—	47	2	no	—
298	#336	—	47	2	no	—
299	#336	—	47	2	no	—
300	#336	C₂×D₄₇	1	2	yes	—
301	C₄₇	C₂×#1939	1	1	yes	characteristic, complemented, Sylow
302	C₂³×C₄	—	47	1	no	—
303	C₂³×C₄	—	47	1	no	—
304	C₂³×C₄	—	47	2	no	—
305	C₂³×C₄	—	47	1	no	—
306	C₂³×C₄	—	47	2	no	—
307	C₂²×C₈	—	47	1	no	—
308	C₂²×C₈	—	47	1	no	—
309	C₂²×C₈	—	47	4	no	—
310	C₂²×C₈	—	47	4	no	—
311	C₂²×C₈	—	47	2	no	—
312	C₂²×C₈	—	94	2	no	—
313	C₂²×C₈	—	94	2	no	—
314	C₂²×C₈	—	94	2	no	—
315	C₂²×C₈	—	94	2	no	—
316	C₂²×C₈	—	94	4	no	—
317	C₂²×C₈	—	94	4	no	—
318	C₂²×C₈	—	94	4	no	—
319	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
320	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
321	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
322	C₂×C₄⋊C₄	—	47	2	no	—
323	C₂×C₄⋊C₄	—	47	1	no	—
324	C₂×C₄⋊C₄	—	47	8	no	—
325	C₂×C₄⋊C₄	—	47	2	no	—
326	C₂×C₄⋊C₄	—	47	1	no	—
327	C₂×C₄⋊C₄	—	94	4	no	—
328	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
329	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
330	C₂×C₄²	—	47	1	no	—
331	C₂×C₄²	—	47	1	no	—
332	C₂×C₄²	—	47	1	no	—
333	C₂×C₄²	—	47	4	no	—
334	C₂×C₄²	—	47	4	no	—
335	C₂×C₄²	—	47	2	no	—
336	C₂×C₄²	—	47	2	no	—
337	C₂×C₄²	—	47	2	no	—
338	C₂×C₄²	—	94	4	no	—
339	C₂×C₄²	—	94	4	no	—
340	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
341	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
342	C₄⋊C₈	—	2	4	no	—
343	C₄⋊C₈	—	2	2	no	—
344	C₄⋊C₈	—	94	4	no	—
345	C₄⋊C₈	—	94	4	no	—
346	C₄⋊C₈	—	94	4	no	—
347	C₄⋊C₈	—	94	4	no	—
348	C₄⋊C₈	—	94	2	no	—
349	C₄×C₈	—	2	2	no	—
350	C₄×C₈	—	94	2	no	—
351	C₄×C₈	—	94	2	no	—
352	C₄×C₈	—	94	2	no	—
353	#95	—	47	2	no	—
354	#95	—	47	2	no	—
355	#95	—	47	2	no	—
356	#95	C₄×D₄₇	1	2	yes	—
357	C₂⁴	—	47	1	no	—
358	C₂²×C₄	—	47	1	no	—
359	C₂²×C₄	—	47	1	no	—
360	C₂²×C₄	—	47	4	no	—
361	C₂²×C₄	—	47	4	no	—
362	C₂²×C₄	—	47	4	no	—
363	C₂²×C₄	—	47	2	no	—
364	C₂²×C₄	—	47	2	no	—
365	C₂²×C₄	—	47	2	no	—
366	C₂²×C₄	—	47	2	no	—
367	C₂²×C₄	—	47	2	no	—
368	C₂²×C₄	—	47	2	no	—
369	C₂²×C₄	—	47	1	no	—
370	C₂²×C₄	—	47	2	no	—
371	C₂²×C₄	—	47	4	no	—
372	C₂²×C₄	—	47	8	no	—
373	C₂²×C₄	—	47	2	no	—
374	C₂²×C₄	—	94	4	no	—
375	C₂²×C₄	—	94	4	no	—
376	C₂²×C₄	—	94	2	no	—
377	C₂²×C₄	—	94	2	no	—
378	C₂²×C₄	—	94	4	no	—
379	C₂²×C₄	—	94	4	no	—
380	C₂²×C₄	—	94	4	no	—
381	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
382	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
383	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
384	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
385	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	1	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₂×C₈	—	47	2	no	—
394	C₂×C₈	—	47	2	no	—
395	C₂×C₈	—	94	8	no	—
396	C₂×C₈	—	94	8	no	—
397	C₂×C₈	—	94	1	no	—
398	C₂×C₈	—	94	1	no	—
399	C₂×C₈	—	94	1	no	—
400	C₂×C₈	—	94	1	no	—
401	C₂×C₈	—	94	2	no	—
402	C₂×C₈	—	94	2	no	—
403	C₂×C₈	—	94	2	no	—
404	C₂×C₈	—	188	8	no	—
405	C₂×C₈	D₄×D₄₇	1	2	yes	—
406	C₂×C₈	Q₈×D₄₇	1	2	yes	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	47	8	no	—
409	C₄⋊C₄	—	47	4	no	—
410	C₄⋊C₄	—	94	4	no	—
411	C₄⋊C₄	—	94	2	no	—
412	C₄⋊C₄	C₈×D₄₇	1	4	yes	complemented
413	C₄²	—	2	2	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	47	4	no	—
416	C₄²	—	47	4	no	—
417	C₄²	—	47	2	no	—
418	C₄²	—	47	2	no	—
419	C₄²	—	94	4	no	—
420	C₄²	—	94	4	no	—
421	C₄²	—	94	2	no	—
422	C₄²	—	94	2	no	—
423	C₄²	D₄×D₄₇	1	2	yes	—
424	C₄²	Q₈×D₄₇	1	2	yes	—
425	C₂³	—	47	2	no	—
426	C₂³	—	47	2	no	—
427	C₂³	—	47	2	no	—
428	C₂³	—	47	2	no	—
429	C₂³	—	47	2	no	—
430	C₂³	—	47	2	no	—
431	C₂³	—	47	2	no	—
432	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	2	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	47	2	no	—
441	C₂×C₄	—	47	2	no	—
442	C₂×C₄	—	47	2	no	—
443	C₂×C₄	—	47	2	no	—
444	C₂×C₄	—	47	2	no	—
445	C₂×C₄	—	47	2	no	—
446	C₂×C₄	—	47	4	no	—
447	C₂×C₄	—	47	4	no	—
448	C₂×C₄	—	47	4	no	—
449	C₂×C₄	—	47	16	no	—
450	C₂×C₄	—	47	4	no	—
451	C₂×C₄	—	47	2	no	—
452	C₂×C₄	—	47	4	no	—
453	C₂×C₄	—	94	8	no	—
454	C₂×C₄	—	94	16	no	—
455	C₂×C₄	—	94	2	no	—
456	C₂×C₄	—	94	1	no	—
457	C₂×C₄	—	94	1	no	—
458	C₂×C₄	—	94	2	no	—
459	C₂×C₄	—	94	2	no	—
460	C₂×C₄	—	94	2	no	—
461	C₂×C₄	—	94	2	no	—
462	C₂×C₄	—	188	8	no	—
463	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
464	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
465	C₂×C₄	C₂×C₈×D₄₇	1	4	yes	—
466	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
467	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
468	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
469	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
470	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
471	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
472	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
473	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
474	C₈	—	2	2	no	—
475	C₈	—	2	2	no	—
476	C₈	—	4	2	no	—
477	C₈	—	94	2	no	—
478	C₈	—	94	2	no	—
479	C₈	—	188	2	no	—
480	C₂²	—	47	4	no	—
481	C₂²	—	47	4	no	—
482	C₂²	—	47	4	no	—
483	C₂²	—	47	4	no	—
484	C₂²	—	47	4	no	—
485	C₂²	—	47	4	no	—
486	C₂²	—	47	4	no	—
487	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
488	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
489	C₂²	C₄×Q₈×D₄₇	1	1	yes	characteristic
490	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
491	C₂²	C₂×M₁₆×D₄₇	1	1	yes	characteristic
492	C₂²	#131×D₄₇	1	1	yes	characteristic
493	C₂²	#131×D₄₇	1	1	yes	characteristic
494	C₄	—	2	2	no	—
495	C₄	—	2	4	no	—
496	C₄	—	4	2	no	—
497	C₄	—	47	4	no	—
498	C₄	—	47	4	no	—
499	C₄	—	94	2	no	—
500	C₄	—	94	4	no	—
501	C₄	—	188	2	no	—
502	C₄	C₄⋊C₈×D₄₇	1	4	yes	complemented
503	C₄	#121×D₄₇	1	1	yes	characteristic
504	C₄	C₂²⋊Q₈×D₄₇	1	1	yes	characteristic
505	C₄	#125×D₄₇	1	1	yes	characteristic
506	C₄	C₄⋊Q₈×D₄₇	1	1	yes	characteristic
507	C₂	—	47	8	no	—
508	C₂	#389×D₄₇	1	1	yes	characteristic
509	C₂	C₂×C₄⋊C₈×D₄₇	1	1	yes	characteristic
510	C₂	#424×D₄₇	1	1	yes	characteristic
511	C₂	C₈×D₄×D₄₇	1	1	yes	characteristic
512	C₂	#436×D₄₇	1	1	yes	characteristic
513	C₂	C₈×Q₈×D₄₇	1	1	yes	characteristic
514	C₂	#446×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂³×C₈
Fitting	C₄₇×#1939	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1939	D₄₇
hypocenter	C₄₇	C₂×#1939
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1939

Complements

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

N	H ≅ G/N	type
5. #20244107	C₂	semidirect
6. #20244106	C₂	semidirect
7. #20244105	C₂	semidirect
8. #20244104	C₂	semidirect
9. #20244103	C₂	semidirect
11. C₄₇×#1939	C₂	semidirect
66. C₄⋊C₄×D₄₇	C₈	semidirect
138. C₄⋊C₄×C₄₇	C₂×C₈	semidirect
144. C₄⋊Dic₄₇	C₂×C₈	semidirect
146. Dic₄₇⋊C₄	C₂×C₈	semidirect
211. C₄×D₄₇	C₄⋊C₈	semidirect
240. C₄×C₄₇	C₂×C₄⋊C₈	semidirect
249. Dic₄₇	C₂×C₄⋊C₈	semidirect
259. #1939	D₄₇	direct (N × H)
268. D₄₇	#1939	direct (N × H)
301. C₄₇	C₂×#1939	semidirect
412. C₄⋊C₄	C₈×D₄₇	semidirect
502. 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
#20244107	2
#20244106	2
#20244105	2
#20244104	2
#20244103	2
#336×D₄₇	2
C₄₇×#1939	2
C₂×#1939	47

Subgroups — D47×#1939 #26219539

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#1939 #26219539