Subgroups — #472×Dic₄₇ #26223159

Order 12032.

946 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	AGL(1,ℤ/8)×Dic₄₇	C₂	1	2	yes	maximal, complemented
2	C₂×D₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	#131×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244299	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244174	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244052	C₂	1	2	yes	maximal, complemented
7	#20243898	C₂	1	2	yes	maximal, complemented
8	#20243452	C₂	1	1	yes	maximal, characteristic, complemented
9	#108×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#100×Dic₄₇	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×#472	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094031	C₂²	1	1	yes	characteristic
13	#41×Dic₄₇	C₂²	1	1	yes	characteristic
14	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
15	#15689235	—	2	2	no	—
16	#15689224	—	2	2	no	—
17	SD₁₆×Dic₄₇	—	2	2	no	—
18	D₈×Dic₄₇	—	2	2	no	—
19	D₈×Dic₄₇	—	2	1	no	—
20	D₈×Dic₄₇	—	2	1	no	—
21	D₈×Dic₄₇	—	2	1	no	—
22	D₈×Dic₄₇	—	2	1	no	—
23	C₂×#13093960	C₂²	1	1	yes	characteristic
24	#15689165	C₂²	1	2	yes	—
25	C₂×#13093958	C₂²	1	1	yes	characteristic
26	#15689128	C₂²	1	2	yes	—
27	#15689124	C₂²	1	2	yes	—
28	C₂×#13093945	C₂²	1	2	yes	—
29	C₂×#13093941	C₂²	1	2	yes	—
30	#15689081	—	2	1	no	—
31	#15689081	C₂²	1	1	yes	characteristic
32	#15689078	—	2	1	no	—
33	#15689078	C₂²	1	1	yes	characteristic
34	M₁₆×Dic₄₇	—	2	1	no	—
35	M₁₆×Dic₄₇	C₂²	1	2	yes	—
36	M₁₆×Dic₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₈×Dic₄₇	—	2	1	no	—
38	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
39	#15688891	C₂²	1	2	yes	—
40	#15688891	C₂²	1	2	yes	—
41	#15688887	C₂²	1	2	yes	—
42	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	2	yes	—
43	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
44	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#472	C₄	1	8	yes	complemented
46	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×#100×C₄₇	C₂²	1	2	yes	—
48	C₂³×Dic₄₇	—	2	2	no	—
49	#13094031	—	2	2	no	—
50	#13094031	—	2	2	no	—
51	C₂×#10625329	—	2	1	no	—
52	C₂×#10625329	C₂³	1	2	yes	—
53	C₂×#10625329	C₂³	1	1	yes	characteristic
54	C₂²×C₄₇⋊C₈	—	2	1	no	—
55	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
56	Q₈×Dic₄₇	D₄	1	1	yes	characteristic
57	Q₈×Dic₄₇	D₄	1	1	yes	characteristic
58	D₄×Dic₄₇	—	2	1	no	—
59	D₄×Dic₄₇	—	2	1	no	—
60	D₄×Dic₄₇	—	2	2	no	—
61	D₄×Dic₄₇	—	2	2	no	—
62	D₄×Dic₄₇	—	2	2	no	—
63	D₄×Dic₄₇	—	2	2	no	—
64	D₄×Dic₄₇	D₄	1	1	yes	characteristic
65	D₄×Dic₄₇	D₄	1	1	yes	characteristic
66	#13093983	—	2	1	no	—
67	#13093983	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
69	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
70	C₂×C₄×Dic₄₇	—	2	1	no	—
71	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
72	#13093960	—	2	2	no	—
73	#13093958	—	2	1	no	—
74	#13093958	—	2	1	no	—
75	#13093958	—	2	2	no	—
76	#13093956	—	2	2	no	—
77	#13093948	—	2	2	no	—
78	#13093945	—	2	2	no	—
79	#13093945	—	2	2	no	—
80	#13093945	—	2	2	no	—
81	#13093945	—	2	2	no	—
82	#13093945	—	2	2	no	—
83	#13093941	—	2	4	no	—
84	#13093934	—	2	1	no	—
85	#13093934	—	2	2	no	—
86	#13093934	—	2	1	no	—
87	#13093934	—	2	1	no	—
88	C₈×Dic₄₇	—	2	1	no	—
89	C₈×Dic₄₇	—	2	1	no	—
90	C₈×Dic₄₇	—	2	2	no	—
91	C₈×Dic₄₇	—	2	1	no	—
92	C₈×Dic₄₇	D₄	1	1	yes	characteristic
93	C₈×Dic₄₇	D₄	1	1	yes	characteristic
94	C₈×Dic₄₇	D₄	1	1	yes	characteristic
95	C₈×Dic₄₇	D₄	1	1	yes	characteristic
96	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
97	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
98	AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
99	AGL(1,ℤ/8)×C₄₇	C₂×C₄	1	8	yes	complemented
100	C₂×SD₁₆×C₄₇	—	2	2	no	—
101	C₂×D₈×C₄₇	—	2	2	no	—
102	C₂×D₈×C₄₇	—	2	1	no	—
103	C₂×D₈×C₄₇	—	2	1	no	—
104	C₂×D₈×C₄₇	—	2	2	no	—
105	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	complemented
106	#131×C₄₇	—	2	2	no	—
107	#131×C₄₇	C₂×C₄	1	4	yes	complemented
108	C₂×M₁₆×C₄₇	—	2	1	no	—
109	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
110	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
111	C₂²×C₈×C₄₇	—	2	1	no	—
112	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
113	#108×C₄₇	C₂×C₄	1	4	yes	complemented
114	#100×C₄₇	C₂×C₄	1	8	yes	complemented
115	C₂⁴×C₄₇	—	2	2	no	—
116	#41×C₄₇	—	2	1	no	—
117	#41×C₄₇	—	2	1	no	—
118	#41×C₄₇	C₂²×C₄	1	2	yes	—
119	#41×C₄₇	#41	1	2	yes	—
120	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂×D₄×C₄₇	—	2	1	no	—
122	C₂×D₄×C₄₇	—	2	2	no	—
123	C₂×D₄×C₄₇	—	2	2	no	—
124	C₂×D₄×C₄₇	—	2	2	no	—
125	C₂×D₄×C₄₇	—	2	2	no	—
126	C₂×D₄×C₄₇	—	2	2	no	—
127	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
128	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	—	2	1	no	—
130	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
131	C₂²×Dic₄₇	—	2	1	no	—
132	C₂²×Dic₄₇	—	2	1	no	—
133	C₂²×Dic₄₇	—	2	2	no	—
134	C₂²×Dic₄₇	—	4	2	no	—
135	C₂²×Dic₄₇	—	4	2	no	—
136	C₂²×Dic₄₇	—	8	4	no	—
137	C₂²×Dic₄₇	#41	1	1	yes	characteristic
138	C₂²×Dic₄₇	#41	1	1	yes	characteristic
139	SD₁₆×C₄₇	—	2	8	no	—
140	D₈×C₄₇	—	2	8	no	—
141	D₈×C₄₇	—	2	4	no	—
142	D₈×C₄₇	—	2	4	no	—
143	M₁₆×C₄₇	—	2	1	no	—
144	M₁₆×C₄₇	—	2	2	no	—
145	M₁₆×C₄₇	—	2	4	no	—
146	M₁₆×C₄₇	C₂²×C₄	1	4	yes	—
147	M₁₆×C₄₇	C₂²×C₄	1	2	yes	—
148	C₂×C₈×C₄₇	—	2	1	no	—
149	C₂×C₈×C₄₇	—	2	2	no	—
150	C₂×C₈×C₄₇	—	2	4	no	—
151	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
152	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
153	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
154	C₂×C₈×C₄₇	#41	1	2	yes	—
155	C₂²⋊Dic₄₇	—	2	1	no	—
156	C₂²⋊Dic₄₇	—	2	1	no	—
157	C₂²⋊Dic₄₇	—	2	1	no	—
158	C₂²⋊Dic₄₇	—	4	2	no	—
159	C₂²⋊Dic₄₇	—	4	2	no	—
160	C₄⋊Dic₄₇	—	2	1	no	—
161	C₄⋊Dic₄₇	—	2	1	no	—
162	C₄⋊Dic₄₇	—	2	2	no	—
163	C₄⋊Dic₄₇	—	2	2	no	—
164	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
165	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
166	C₄×Dic₄₇	—	2	1	no	—
167	C₄×Dic₄₇	—	2	1	no	—
168	C₄×Dic₄₇	—	2	1	no	—
169	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
170	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
171	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
172	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
173	#10625329	—	2	4	no	—
174	#10625329	—	2	1	no	—
175	#10625329	—	2	2	no	—
176	#10625329	—	2	2	no	—
177	#10625329	#41	1	2	yes	—
178	C₂×C₄₇⋊C₈	—	2	4	no	—
179	C₂×C₄₇⋊C₈	—	2	1	no	—
180	C₂×C₄₇⋊C₈	—	2	1	no	—
181	C₂×C₄₇⋊C₈	—	2	1	no	—
182	C₂×C₄₇⋊C₈	—	2	2	no	—
183	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
184	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
185	C₂³×C₄₇	—	2	1	no	—
186	C₂³×C₄₇	—	2	4	no	—
187	C₂³×C₄₇	—	4	2	no	—
188	C₂³×C₄₇	—	4	2	no	—
189	C₂³×C₄₇	—	8	2	no	—
190	C₂³×C₄₇	—	8	2	no	—
191	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
192	Q₈×C₄₇	—	2	1	no	—
193	Q₈×C₄₇	C₄×D₄	1	2	yes	—
194	D₄×C₄₇	—	2	2	no	—
195	D₄×C₄₇	—	2	2	no	—
196	D₄×C₄₇	—	2	4	no	—
197	D₄×C₄₇	—	2	4	no	—
198	D₄×C₄₇	—	2	1	no	—
199	D₄×C₄₇	—	4	2	no	—
200	D₄×C₄₇	—	4	2	no	—
201	D₄×C₄₇	C₄×D₄	1	2	yes	—
202	C₂×C₄×C₄₇	—	2	1	no	—
203	C₂×C₄×C₄₇	—	2	2	no	—
204	C₂×C₄×C₄₇	—	2	2	no	—
205	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
207	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
211	C₂×Dic₄₇	—	2	2	no	—
212	C₂×Dic₄₇	—	2	1	no	—
213	C₂×Dic₄₇	—	2	1	no	—
214	C₂×Dic₄₇	—	4	1	no	—
215	C₂×Dic₄₇	—	4	2	no	—
216	C₂×Dic₄₇	—	4	2	no	—
217	C₂×Dic₄₇	—	4	2	no	—
218	C₂×Dic₄₇	—	8	4	no	—
219	C₂×Dic₄₇	—	8	4	no	—
220	C₂×Dic₄₇	—	8	2	no	—
221	C₂×Dic₄₇	#121	1	1	yes	characteristic
222	C₂×Dic₄₇	#121	1	1	yes	characteristic
223	C₂×Dic₄₇	#121	1	1	yes	characteristic
224	C₂×Dic₄₇	#121	1	1	yes	characteristic
225	C₈×C₄₇	—	2	2	no	—
226	C₈×C₄₇	—	2	4	no	—
227	C₈×C₄₇	C₄×D₄	1	2	yes	—
228	C₈×C₄₇	C₄×D₄	1	2	yes	—
229	C₄₇⋊C₈	—	2	1	no	—
230	C₄₇⋊C₈	—	2	2	no	—
231	C₄₇⋊C₈	—	2	1	no	—
232	C₄₇⋊C₈	—	4	2	no	—
233	C₄×#472	—	47	1	no	maximal, Sylow
234	C₂²×C₄₇	—	2	1	no	—
235	C₂²×C₄₇	—	2	1	no	—
236	C₂²×C₄₇	—	2	2	no	—
237	C₂²×C₄₇	—	4	1	no	—
238	C₂²×C₄₇	—	4	1	no	—
239	C₂²×C₄₇	—	4	4	no	—
240	C₂²×C₄₇	—	8	4	no	—
241	C₂²×C₄₇	—	8	4	no	—
242	C₂²×C₄₇	—	8	2	no	—
243	C₂²×C₄₇	—	8	2	no	—
244	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
245	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
246	C₂²×C₄₇	#529	1	1	yes	characteristic
247	C₄×C₄₇	—	2	2	no	—
248	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
249	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
250	C₄×C₄₇	#525	1	1	yes	characteristic
251	C₄×C₄₇	#532	1	1	yes	characteristic
252	Dic₄₇	—	2	1	no	—
253	Dic₄₇	—	2	1	no	—
254	Dic₄₇	—	2	1	no	—
255	Dic₄₇	—	4	1	no	—
256	Dic₄₇	—	4	1	no	—
257	Dic₄₇	—	8	2	no	—
258	Dic₄₇	#472	1	2	yes	direct product factor
259	C₂×#472	D₄₇	1	1	yes	characteristic
260	C₄×AGL(1,ℤ/8)	—	47	2	no	—
261	C₂×C₄×D₈	—	47	1	no	—
262	C₄×#131	—	47	1	no	—
263	#1978	—	47	1	no	—
264	#1952	—	47	1	no	—
265	#1931	—	47	2	no	—
266	#1907	—	47	2	no	—
267	#1816	—	47	1	no	—
268	C₄×#108	—	47	1	no	—
269	C₄×#100	—	47	2	no	—
270	C₂×C₄₇	—	2	1	no	—
271	C₂×C₄₇	—	2	1	no	—
272	C₂×C₄₇	—	4	2	no	—
273	C₂×C₄₇	—	8	4	no	—
274	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
275	C₂×C₄₇	C₂×#472	1	1	yes	characteristic
276	C₂×C₄₇	#3067	1	1	yes	characteristic
277	C₂×AGL(1,ℤ/8)	C₂×D₄₇	1	2	yes	—
278	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
279	C₂×#131	—	47	1	no	—
280	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
281	C₄×#41	—	47	1	no	—
282	C₂×C₄×D₄	—	47	2	no	—
283	#472	Dic₄₇	1	8	yes	direct product factor
284	#442	—	94	2	no	—
285	#440	—	94	2	no	—
286	C₄×SD₁₆	—	94	2	no	—
287	C₄×D₈	—	94	1	no	—
288	C₄×D₈	—	94	1	no	—
289	C₄×D₈	—	94	1	no	—
290	C₄×D₈	—	94	1	no	—
291	C₄×D₈	—	94	2	no	—
292	C₂×#108	—	47	1	no	—
293	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
294	#428	—	47	2	no	—
295	C₂×#107	—	47	1	no	—
296	#418	—	47	2	no	—
297	#417	—	47	2	no	—
298	C₂×#102	—	47	2	no	—
299	C₂×#100	—	47	2	no	—
300	C₂×#100	C₂×D₄₇	1	2	yes	—
301	#405	—	47	1	no	—
302	#405	—	47	1	no	—
303	#405	—	94	1	no	—
304	#405	—	94	1	no	—
305	C₄×M₁₆	—	47	1	no	—
306	C₄×M₁₆	—	47	2	no	—
307	C₄×M₁₆	—	94	1	no	—
308	C₂×C₄×C₈	—	47	1	no	—
309	C₂×C₄×C₈	—	94	1	no	—
310	#343	—	47	2	no	—
311	#343	—	47	2	no	—
312	#341	—	47	2	no	—
313	C₄₇	C₄×#472	1	1	yes	characteristic, complemented, Sylow
314	C₂×#41	C₂²×D₄₇	1	1	yes	characteristic
315	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
316	C₂³×C₄	—	94	2	no	—
317	AGL(1,ℤ/8)	—	2	4	no	—
318	AGL(1,ℤ/8)	C₂×Dic₄₇	1	8	yes	complemented
319	C₂×SD₁₆	—	2	2	no	—
320	C₂×D₈	—	2	2	no	—
321	C₂×D₈	—	2	1	no	—
322	C₂×D₈	—	2	1	no	—
323	C₂×D₈	—	2	2	no	—
324	C₂×D₈	C₂×Dic₄₇	1	4	yes	complemented
325	#131	—	2	2	no	—
326	#131	—	94	2	no	—
327	#131	—	94	2	no	—
328	#131	C₂×Dic₄₇	1	4	yes	complemented
329	C₂×M₁₆	—	2	1	no	—
330	C₂×M₁₆	—	47	1	no	—
331	C₂×M₁₆	—	47	2	no	—
332	C₂×M₁₆	—	94	1	no	—
333	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
334	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
335	C₂²×C₈	—	2	1	no	—
336	C₂²×C₈	—	47	1	no	—
337	C₂²×C₈	—	94	1	no	—
338	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
339	C₄×Q₈	—	47	1	no	—
340	C₄×Q₈	—	47	1	no	—
341	C₄×D₄	—	47	1	no	—
342	C₄×D₄	—	47	1	no	—
343	C₄×D₄	—	94	2	no	—
344	C₄×D₄	—	94	2	no	—
345	C₄×D₄	—	94	2	no	—
346	C₄×D₄	—	94	2	no	—
347	C₄×D₄	—	94	1	no	—
348	C₄×D₄	—	94	1	no	—
349	#117	—	47	1	no	—
350	#117	—	94	1	no	—
351	C₂×C₄⋊C₄	—	47	2	no	—
352	C₂×C₂²⋊C₄	—	94	2	no	—
353	C₂×C₄²	—	47	1	no	—
354	C₂×C₄²	—	94	1	no	—
355	#108	—	94	2	no	—
356	#108	C₂×Dic₄₇	1	4	yes	complemented
357	#107	—	94	2	no	—
358	#107	—	94	1	no	—
359	#107	—	94	1	no	—
360	#106	—	94	2	no	—
361	#103	—	94	2	no	—
362	#102	—	94	2	no	—
363	#102	—	94	2	no	—
364	#102	—	94	2	no	—
365	#102	—	94	2	no	—
366	#102	—	94	2	no	—
367	#100	—	94	4	no	—
368	#100	C₂×Dic₄₇	1	8	yes	complemented
369	#97	—	94	1	no	—
370	#97	—	94	2	no	—
371	#97	—	94	1	no	—
372	#97	—	94	1	no	—
373	C₄×C₈	—	47	1	no	—
374	C₄×C₈	—	47	1	no	—
375	C₄×C₈	—	47	1	no	—
376	C₄×C₈	—	47	1	no	—
377	C₄×C₈	—	94	1	no	—
378	C₄×C₈	—	94	2	no	—
379	C₄×C₈	—	94	1	no	—
380	C₄×C₈	—	94	1	no	—
381	C₂⁴	—	2	2	no	—
382	#41	—	2	1	no	—
383	#41	—	2	1	no	—
384	#41	#10625352	1	2	yes	—
385	#41	C₂²×Dic₄₇	1	2	yes	—
386	C₂×Q₈	D₄×D₄₇	1	1	yes	characteristic
387	C₂×D₄	—	2	1	no	—
388	C₂×D₄	—	2	2	no	—
389	C₂×D₄	—	2	2	no	—
390	C₂×D₄	—	2	2	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	D₄×D₄₇	1	1	yes	characteristic
394	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	47	1	no	—
397	C₂²×C₄	—	47	1	no	—
398	C₂²×C₄	—	94	1	no	—
399	C₂²×C₄	—	94	1	no	—
400	C₂²×C₄	—	94	2	no	—
401	C₂²×C₄	—	376	4	no	—
402	C₂²×C₄	—	188	2	no	—
403	C₂²×C₄	—	188	2	no	—
404	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
405	SD₁₆	—	2	8	no	—
406	D₈	—	2	8	no	—
407	D₈	—	2	4	no	—
408	D₈	—	2	4	no	—
409	M₁₆	—	2	1	no	—
410	M₁₆	—	2	2	no	—
411	M₁₆	—	2	4	no	—
412	M₁₆	—	47	2	no	—
413	M₁₆	—	94	4	no	—
414	M₁₆	—	94	1	no	—
415	M₁₆	—	94	2	no	—
416	M₁₆	—	94	2	no	—
417	M₁₆	C₂²×Dic₄₇	1	2	yes	—
418	M₁₆	C₂²×Dic₄₇	1	4	yes	—
419	C₂×C₈	—	2	1	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	4	no	—
422	C₂×C₈	—	47	1	no	—
423	C₂×C₈	—	47	1	no	—
424	C₂×C₈	—	94	4	no	—
425	C₂×C₈	—	94	1	no	—
426	C₂×C₈	—	94	1	no	—
427	C₂×C₈	—	94	1	no	—
428	C₂×C₈	—	94	2	no	—
429	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
430	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
431	C₂×C₈	#10625352	1	2	yes	—
432	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
433	C₄⋊C₄	—	47	1	no	—
434	C₄⋊C₄	—	47	1	no	—
435	C₄⋊C₄	—	94	1	no	—
436	C₄⋊C₄	—	94	1	no	—
437	C₄⋊C₄	—	94	2	no	—
438	C₄⋊C₄	—	94	2	no	—
439	C₂²⋊C₄	—	94	1	no	—
440	C₂²⋊C₄	—	94	1	no	—
441	C₂²⋊C₄	—	94	1	no	—
442	C₂²⋊C₄	—	188	2	no	—
443	C₂²⋊C₄	—	188	2	no	—
444	C₄²	—	47	1	no	—
445	C₄²	—	47	1	no	—
446	C₄²	—	47	1	no	—
447	C₄²	—	47	1	no	—
448	C₄²	—	94	1	no	—
449	C₄²	—	94	1	no	—
450	C₄²	—	94	1	no	—
451	C₂³	—	2	1	no	—
452	C₂³	—	2	4	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	8	2	no	—
456	C₂³	—	8	2	no	—
457	C₂³	#41×D₄₇	1	1	yes	characteristic
458	Q₈	—	2	1	no	—
459	Q₈	D₄×Dic₄₇	1	2	yes	—
460	D₄	—	2	2	no	—
461	D₄	—	2	2	no	—
462	D₄	—	2	4	no	—
463	D₄	—	2	4	no	—
464	D₄	—	2	1	no	—
465	D₄	—	4	2	no	—
466	D₄	—	4	2	no	—
467	D₄	D₄×Dic₄₇	1	2	yes	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	47	1	no	—
472	C₂×C₄	—	47	1	no	—
473	C₂×C₄	—	47	1	no	—
474	C₂×C₄	—	47	1	no	—
475	C₂×C₄	—	94	2	no	—
476	C₂×C₄	—	94	1	no	—
477	C₂×C₄	—	94	1	no	—
478	C₂×C₄	—	376	4	no	—
479	C₂×C₄	—	376	4	no	—
480	C₂×C₄	—	376	2	no	—
481	C₂×C₄	—	188	2	no	—
482	C₂×C₄	—	188	1	no	—
483	C₂×C₄	—	188	2	no	—
484	C₂×C₄	—	188	2	no	—
485	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
486	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
487	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
488	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
489	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
490	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
491	C₈	—	2	2	no	—
492	C₈	—	2	4	no	—
493	C₈	—	94	1	no	—
494	C₈	—	94	1	no	—
495	C₈	—	94	2	no	—
496	C₈	—	188	2	no	—
497	C₈	D₄×Dic₄₇	1	2	yes	—
498	C₈	D₄×Dic₄₇	1	2	yes	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	2	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	4	4	no	—
505	C₂²	—	8	4	no	—
506	C₂²	—	8	4	no	—
507	C₂²	—	8	2	no	—
508	C₂²	—	8	2	no	—
509	C₂²	#41×Dic₄₇	1	1	yes	characteristic
510	C₂²	#121×D₄₇	1	1	yes	characteristic
511	C₂²	#15689654	1	1	yes	characteristic
512	C₄	—	2	2	no	—
513	C₄	—	47	2	no	—
514	C₄	—	94	1	no	—
515	C₄	—	94	1	no	—
516	C₄	—	94	1	no	—
517	C₄	—	376	2	no	—
518	C₄	—	188	1	no	—
519	C₄	—	188	1	no	—
520	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
521	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
522	C₄	#15689633	1	1	yes	characteristic
523	C₄	#15689668	1	1	yes	characteristic
524	C₂	—	2	1	no	—
525	C₂	—	2	1	no	—
526	C₂	—	4	2	no	—
527	C₂	—	8	4	no	—
528	C₂	#121×Dic₄₇	1	1	yes	characteristic
529	C₂	#472×D₄₇	1	1	yes	characteristic
530	C₂	#20253106	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#121×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting, prime radical	C₂×C₄₇×#472	C₂
socle	C₂²×C₄₇	C₂×#121
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#472	D₄₇
hypocenter	C₄₇	C₄×#472
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#472

Complements

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

N	H ≅ G/N	type
1. AGL(1,ℤ/8)×Dic₄₇	C₂	semidirect
2. C₂×D₈×Dic₄₇	C₂	semidirect
3. #131×Dic₄₇	C₂	semidirect
4. #20244299	C₂	semidirect
5. #20244174	C₂	semidirect
6. #20244052	C₂	semidirect
7. #20243898	C₂	semidirect
8. #20243452	C₂	semidirect
9. #108×Dic₄₇	C₂	semidirect
10. #100×Dic₄₇	C₂	semidirect
45. C₄₇×#472	C₄	semidirect
99. AGL(1,ℤ/8)×C₄₇	C₂×C₄	semidirect
105. C₂×D₈×C₄₇	C₂×C₄	semidirect
107. #131×C₄₇	C₂×C₄	semidirect
113. #108×C₄₇	C₂×C₄	semidirect
114. #100×C₄₇	C₂×C₄	semidirect
258. Dic₄₇	#472	direct (N × H)
283. #472	Dic₄₇	direct (N × H)
313. C₄₇	C₄×#472	semidirect
318. AGL(1,ℤ/8)	C₂×Dic₄₇	semidirect
324. C₂×D₈	C₂×Dic₄₇	semidirect
328. #131	C₂×Dic₄₇	semidirect
356. #108	C₂×Dic₄₇	semidirect
368. #100	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
AGL(1,ℤ/8)×Dic₄₇	2
C₂×D₈×Dic₄₇	2
#131×Dic₄₇	2
#20244299	2
#20244174	2
#20244052	2
#20243898	2
#20243452	2
#108×Dic₄₇	2
#100×Dic₄₇	2
C₂×C₄₇×#472	2
C₄×#472	47

Subgroups — #472×Dic47 #26223159

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #472×Dic₄₇ #26223159