Subgroups — #470×Dic₄₇ #26222934

Order 12032.

1002 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×M₁₆×Dic₄₇	C₂	1	1	yes	maximal, characteristic
3	C₂²⋊Q₈×Dic₄₇	C₂	1	2	yes	maximal
4	#20244260	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244132	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244080	C₂	1	2	yes	maximal, complemented
7	#20243822	C₂	1	2	yes	maximal
8	#20243421	C₂	1	1	yes	maximal, characteristic
9	#106×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	#103×Dic₄₇	C₂	1	2	yes	maximal, complemented
11	C₂×C₄₇×#470	C₂	1	1	yes	maximal, characteristic
12	C₂²×#10625329	C₂²	1	1	yes	characteristic
13	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
14	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
15	Q₁₆×Dic₄₇	—	2	4	no	—
16	C₂×#13093958	C₂²	1	1	yes	characteristic
17	C₂×#13093956	C₂²	1	1	yes	characteristic
18	C₂×#13093948	C₂²	1	2	yes	—
19	C₂×#13093948	C₂²	1	2	yes	—
20	M₁₆×Dic₄₇	—	2	4	no	—
21	C₂×#13093934	C₂²	1	1	yes	characteristic
22	C₂×#13093934	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
25	#15689030	C₂²	1	2	yes	—
26	#15689022	C₂²	1	2	yes	—
27	#15689009	—	2	2	no	—
28	#15688998	—	2	2	no	—
29	#15688983	C₂²	1	2	yes	—
30	C₄⋊C₄×Dic₄₇	—	2	2	no	—
31	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
32	C₂²⋊C₄×Dic₄₇	—	2	2	no	—
33	#15688886	C₂²	1	2	yes	—
34	#15688885	C₂²	1	2	yes	—
35	#15688885	C₂²	1	2	yes	—
36	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
37	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
39	C₄₇×#470	C₄	1	8	yes	complemented
40	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×#103×C₄₇	C₂²	1	2	yes	—
42	C₂³×Dic₄₇	D₄	1	1	yes	characteristic
43	C₂³×Dic₄₇	D₄	1	1	yes	characteristic
44	C₂×#10625329	—	2	2	no	—
45	C₂×#10625329	—	2	2	no	—
46	C₂×#10625329	—	2	2	no	—
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	Q₈×Dic₄₇	—	2	4	no	—
50	Q₈×Dic₄₇	—	2	4	no	—
51	C₂×C₄⋊Dic₄₇	—	2	2	no	—
52	C₂×C₄⋊Dic₄₇	—	2	2	no	—
53	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
54	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
55	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
56	C₂×C₄×Dic₄₇	—	2	2	no	—
57	C₂×C₄×Dic₄₇	—	2	2	no	—
58	C₂×C₄×Dic₄₇	—	2	2	no	—
59	C₂×C₄×Dic₄₇	—	2	2	no	—
60	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
61	C₂×C₄×Dic₄₇	D₄	1	1	yes	characteristic
62	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
63	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
64	#13093958	—	2	2	no	—
65	#13093956	—	2	2	no	—
66	#13093948	—	2	4	no	—
67	#13093948	—	2	4	no	—
68	#13093934	—	2	2	no	—
69	#13093934	—	2	2	no	—
70	C₈×Dic₄₇	—	2	2	no	—
71	C₈×Dic₄₇	D₄	1	4	yes	—
72	C₄₇⋊#95	—	2	2	no	—
73	C₄₇⋊#95	—	2	2	no	—
74	C₄₇⋊#95	—	2	2	no	—
75	C₄₇⋊#95	—	2	2	no	—
76	C₄₇⋊#95	—	2	2	no	—
77	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
78	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×Q₁₆×C₄₇	—	2	2	no	—
80	C₂×Q₁₆×C₄₇	—	2	2	no	—
81	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
82	C₂×M₁₆×C₄₇	—	2	2	no	—
83	C₂×M₁₆×C₄₇	—	2	2	no	—
84	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
85	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
87	C₂²⋊Q₈×C₄₇	—	2	4	no	—
88	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	—
89	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
90	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
91	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
92	#106×C₄₇	C₂×C₄	1	4	yes	complemented
93	#103×C₄₇	C₂×C₄	1	8	yes	complemented
94	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₄₇	—	2	2	no	—
96	C₂×Q₈×C₄₇	—	2	2	no	—
97	C₂×Q₈×C₄₇	—	2	2	no	—
98	C₂×Q₈×C₄₇	—	2	2	no	—
99	C₂×Q₈×C₄₇	—	2	2	no	—
100	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	—	2	2	no	—
106	C₂²×C₄×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	#41	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
111	C₂²×Dic₄₇	—	2	2	no	—
112	C₂²×Dic₄₇	—	2	2	no	—
113	C₂²×Dic₄₇	—	2	4	no	—
114	C₂²×Dic₄₇	—	2	2	no	—
115	C₂²×Dic₄₇	—	2	2	no	—
116	C₂²×Dic₄₇	—	4	2	no	—
117	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
121	Q₁₆×C₄₇	—	2	8	no	—
122	M₁₆×C₄₇	—	2	8	no	—
123	C₂×C₈×C₄₇	—	2	1	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
126	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
128	C₂×C₈×C₄₇	#41	1	2	yes	—
129	C₄⋊C₄×C₄₇	—	2	8	no	—
130	C₄⋊C₄×C₄₇	—	2	2	no	—
131	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
132	C₂²⋊C₄×C₄₇	—	2	8	no	—
133	C₂²⋊Dic₄₇	—	4	4	no	—
134	C₄⋊Dic₄₇	—	2	2	no	—
135	C₄⋊Dic₄₇	—	2	2	no	—
136	C₄⋊Dic₄₇	—	2	2	no	—
137	C₄⋊Dic₄₇	—	2	2	no	—
138	C₄⋊Dic₄₇	—	4	4	no	—
139	C₄⋊Dic₄₇	—	4	4	no	—
140	C₄×Dic₄₇	—	2	1	no	—
141	C₄×Dic₄₇	—	2	1	no	—
142	C₄×Dic₄₇	—	2	2	no	—
143	C₄×Dic₄₇	—	2	2	no	—
144	C₄×Dic₄₇	—	4	4	no	—
145	C₄×Dic₄₇	—	4	4	no	—
146	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
147	C₄×Dic₄₇	#41	1	2	yes	—
148	#10625329	—	2	8	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	1	no	—
151	C₂×C₄₇⋊C₈	—	2	1	no	—
152	C₂×C₄₇⋊C₈	—	2	1	no	—
153	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
154	C₂×C₄₇⋊C₈	#41	1	2	yes	—
155	C₂³×C₄₇	—	2	1	no	—
156	C₂³×C₄₇	—	2	1	no	—
157	C₂³×C₄₇	—	2	2	no	—
158	C₂³×C₄₇	—	2	2	no	—
159	C₂³×C₄₇	C₄×D₄	1	2	yes	—
160	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	Q₈×C₄₇	—	2	4	no	—
162	Q₈×C₄₇	—	2	4	no	—
163	Q₈×C₄₇	—	4	2	no	—
164	Q₈×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	—	2	1	no	—
166	C₂×C₄×C₄₇	—	2	1	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	4	no	—
172	C₂×C₄×C₄₇	—	2	4	no	—
173	C₂×C₄×C₄₇	—	4	2	no	—
174	C₂×C₄×C₄₇	—	4	2	no	—
175	C₂×C₄×C₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
178	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
184	C₂×Dic₄₇	—	2	2	no	—
185	C₂×Dic₄₇	—	2	1	no	—
186	C₂×Dic₄₇	—	2	1	no	—
187	C₂×Dic₄₇	—	2	2	no	—
188	C₂×Dic₄₇	—	2	2	no	—
189	C₂×Dic₄₇	—	4	4	no	—
190	C₂×Dic₄₇	—	4	4	no	—
191	C₂×Dic₄₇	—	4	2	no	—
192	C₂×Dic₄₇	—	4	2	no	—
193	C₂×Dic₄₇	—	4	2	no	—
194	C₂×Dic₄₇	—	4	2	no	—
195	C₂×Dic₄₇	—	4	2	no	—
196	C₂×Dic₄₇	—	4	2	no	—
197	C₂×Dic₄₇	#121	1	2	yes	—
198	C₂×Dic₄₇	#121	1	2	yes	—
199	C₂×Dic₄₇	#137	1	4	yes	—
200	C₈×C₄₇	—	2	2	no	—
201	C₈×C₄₇	C₄×D₄	1	4	yes	—
202	C₄₇⋊C₈	—	2	2	no	—
203	C₄₇⋊C₈	—	2	2	no	—
204	C₄×#470	—	47	1	no	maximal, Sylow
205	C₂²×C₄₇	—	2	4	no	—
206	C₂²×C₄₇	—	2	2	no	—
207	C₂²×C₄₇	—	4	2	no	—
208	C₂²×C₄₇	—	4	1	no	—
209	C₂²×C₄₇	—	4	1	no	—
210	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
211	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
212	C₂²×C₄₇	#532	1	1	yes	characteristic
213	C₂²×C₄₇	C₂×#137	1	2	yes	—
214	C₂²×C₄₇	#575	1	2	yes	—
215	C₄×C₄₇	—	2	2	no	—
216	C₄×C₄₇	—	4	4	no	—
217	C₄×C₄₇	—	4	4	no	—
218	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
219	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
220	C₄×C₄₇	#525	1	1	yes	characteristic
221	C₄×C₄₇	#529	1	1	yes	characteristic
222	Dic₄₇	—	2	2	no	—
223	Dic₄₇	—	4	1	no	—
224	Dic₄₇	—	4	1	no	—
225	Dic₄₇	—	8	2	no	—
226	Dic₄₇	—	8	2	no	—
227	Dic₄₇	#470	1	4	yes	direct product factor
228	C₂×#470	D₄₇	1	1	yes	characteristic
229	C₂×C₄×Q₁₆	—	47	1	no	—
230	C₂×C₄×M₁₆	—	47	1	no	—
231	C₄×C₂²⋊Q₈	—	47	2	no	—
232	#1971	—	47	1	no	—
233	#1944	—	47	1	no	—
234	#1935	—	47	2	no	—
235	#1894	—	47	2	no	—
236	#1809	—	47	1	no	—
237	C₄×#106	—	47	1	no	—
238	C₄×#103	—	47	2	no	—
239	C₂×C₄₇	—	4	2	no	—
240	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
241	C₂×C₄₇	C₄×#137	1	2	yes	—
242	C₂×C₄₇	C₂×#470	1	1	yes	characteristic
243	C₂×C₄₇	#3054	1	1	yes	characteristic
244	C₂×C₄₇	#3172	1	2	yes	—
245	C₂²×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
246	C₂²×M₁₆	—	47	1	no	—
247	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
248	C₂×C₂²⋊Q₈	C₂×D₄₇	1	2	yes	—
249	C₂×C₄×Q₈	—	47	2	no	—
250	C₂²×C₄²	—	47	1	no	—
251	#470	Dic₄₇	1	8	yes	direct product factor
252	C₄×Q₁₆	—	94	4	no	—
253	C₂×#107	—	47	1	no	—
254	C₂×#106	—	47	1	no	—
255	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
256	C₂×#103	—	47	2	no	—
257	C₂×#103	—	47	2	no	—
258	C₂×#103	C₂×D₄₇	1	2	yes	—
259	C₄×M₁₆	—	94	4	no	—
260	C₂×#97	—	47	1	no	—
261	C₂×#97	—	47	1	no	—
262	C₂×C₄×C₈	—	47	1	no	—
263	C₂×C₄×C₈	—	47	1	no	—
264	#391	—	47	2	no	—
265	#389	—	47	2	no	—
266	#387	—	94	2	no	—
267	#385	—	94	2	no	—
268	#380	—	47	2	no	—
269	C₄×C₄⋊C₄	—	47	2	no	—
270	C₄×C₄⋊C₄	—	94	2	no	—
271	C₄×C₂²⋊C₄	—	94	2	no	—
272	#340	—	47	2	no	—
273	#340	—	47	2	no	—
274	#340	—	47	2	no	—
275	C₄₇	C₄×#470	1	1	yes	characteristic, complemented, Sylow
276	C₂²×Q₈	C₂²×D₄₇	1	2	yes	—
277	C₂³×C₄	—	47	1	no	—
278	C₂³×C₄	—	47	1	no	—
279	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
280	C₂×Q₁₆	—	2	2	no	—
281	C₂×Q₁₆	—	2	2	no	—
282	C₂×Q₁₆	C₂×Dic₄₇	1	4	yes	complemented
283	C₂×M₁₆	—	2	2	no	—
284	C₂×M₁₆	—	2	2	no	—
285	C₂×M₁₆	—	94	2	no	—
286	C₂×M₁₆	—	94	2	no	—
287	C₂×M₁₆	—	94	2	no	—
288	C₂×M₁₆	C₂×Dic₄₇	1	4	yes	—
289	C₂²×C₈	—	47	1	no	—
290	C₂²×C₈	—	47	1	no	—
291	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
292	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
293	C₂²⋊Q₈	—	2	4	no	—
294	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	—
295	C₄×Q₈	—	94	4	no	—
296	C₄×Q₈	—	94	4	no	—
297	C₂×C₄⋊C₄	—	2	2	no	—
298	C₂×C₄⋊C₄	—	47	2	no	—
299	C₂×C₄⋊C₄	—	47	2	no	—
300	C₂×C₄⋊C₄	—	94	2	no	—
301	C₂×C₄⋊C₄	—	94	2	no	—
302	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
303	C₂×C₂²⋊C₄	—	2	2	no	—
304	C₂×C₂²⋊C₄	—	94	2	no	—
305	C₂×C₄²	—	47	1	no	—
306	C₂×C₄²	—	47	1	no	—
307	C₂×C₄²	—	47	1	no	—
308	C₂×C₄²	—	47	1	no	—
309	C₂×C₄²	—	94	2	no	—
310	C₂×C₄²	—	94	2	no	—
311	C₂×C₄²	—	94	2	no	—
312	C₂×C₄²	—	94	2	no	—
313	#107	—	94	2	no	—
314	#106	—	94	2	no	—
315	#106	C₂×Dic₄₇	1	4	yes	complemented
316	#103	—	94	4	no	—
317	#103	—	94	4	no	—
318	#103	C₂×Dic₄₇	1	8	yes	complemented
319	#97	—	94	2	no	—
320	#97	—	94	2	no	—
321	C₄×C₈	—	47	4	no	—
322	C₄×C₈	—	94	2	no	—
323	#95	—	94	2	no	—
324	#95	—	94	2	no	—
325	#95	—	94	2	no	—
326	#95	—	94	2	no	—
327	#95	—	94	2	no	—
328	C₂⁴	D₄×D₄₇	1	1	yes	characteristic
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	—	2	2	no	—
333	C₂×Q₈	—	2	2	no	—
334	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	1	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	2	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	47	1	no	—
342	C₂²×C₄	—	47	1	no	—
343	C₂²×C₄	—	47	1	no	—
344	C₂²×C₄	—	47	1	no	—
345	C₂²×C₄	—	94	2	no	—
346	C₂²×C₄	—	94	2	no	—
347	C₂²×C₄	—	94	4	no	—
348	C₂²×C₄	—	94	2	no	—
349	C₂²×C₄	—	94	2	no	—
350	C₂²×C₄	—	188	2	no	—
351	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
352	C₂²×C₄	#10625352	1	2	yes	—
353	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
354	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
355	Q₁₆	—	2	8	no	—
356	M₁₆	—	2	8	no	—
357	M₁₆	—	94	8	no	—
358	C₂×C₈	—	2	1	no	—
359	C₂×C₈	—	2	1	no	—
360	C₂×C₈	—	47	2	no	—
361	C₂×C₈	—	47	2	no	—
362	C₂×C₈	—	94	1	no	—
363	C₂×C₈	—	94	1	no	—
364	C₂×C₈	—	94	1	no	—
365	C₂×C₈	—	94	1	no	—
366	C₂×C₈	D₄×D₄₇	1	2	yes	—
367	C₂×C₈	#10625352	1	2	yes	—
368	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
369	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
370	C₄⋊C₄	—	2	8	no	—
371	C₄⋊C₄	—	2	2	no	—
372	C₄⋊C₄	—	94	2	no	—
373	C₄⋊C₄	—	94	2	no	—
374	C₄⋊C₄	—	94	2	no	—
375	C₄⋊C₄	—	94	2	no	—
376	C₄⋊C₄	—	188	4	no	—
377	C₄⋊C₄	—	188	4	no	—
378	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
379	C₂²⋊C₄	—	2	8	no	—
380	C₂²⋊C₄	—	188	4	no	—
381	C₄²	—	47	2	no	—
382	C₄²	—	47	2	no	—
383	C₄²	—	94	2	no	—
384	C₄²	—	94	2	no	—
385	C₄²	—	94	1	no	—
386	C₄²	—	94	1	no	—
387	C₄²	—	188	4	no	—
388	C₄²	—	188	4	no	—
389	C₂³	—	2	1	no	—
390	C₂³	—	2	2	no	—
391	C₂³	—	2	2	no	—
392	C₂³	—	2	1	no	—
393	C₂³	D₄×Dic₄₇	1	2	yes	—
394	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
395	Q₈	—	2	4	no	—
396	Q₈	—	2	4	no	—
397	Q₈	—	4	2	no	—
398	Q₈	—	4	2	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	47	2	no	—
412	C₂×C₄	—	47	4	no	—
413	C₂×C₄	—	47	2	no	—
414	C₂×C₄	—	94	2	no	—
415	C₂×C₄	—	94	1	no	—
416	C₂×C₄	—	94	1	no	—
417	C₂×C₄	—	94	2	no	—
418	C₂×C₄	—	94	2	no	—
419	C₂×C₄	—	188	4	no	—
420	C₂×C₄	—	188	4	no	—
421	C₂×C₄	—	188	2	no	—
422	C₂×C₄	—	188	2	no	—
423	C₂×C₄	—	188	2	no	—
424	C₂×C₄	—	188	2	no	—
425	C₂×C₄	—	188	2	no	—
426	C₂×C₄	—	188	2	no	—
427	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
428	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
429	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
430	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
431	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
432	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
433	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
434	C₈	—	2	2	no	—
435	C₈	—	94	2	no	—
436	C₈	—	94	2	no	—
437	C₈	D₄×Dic₄₇	1	4	yes	—
438	C₂²	—	2	4	no	—
439	C₂²	—	2	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	1	no	—
442	C₂²	—	4	1	no	—
443	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
444	C₂²	#121×D₄₇	1	1	yes	characteristic
445	C₂²	#15689668	1	1	yes	characteristic
446	C₂²	#137×D₄₇	1	2	yes	—
447	C₂²	#15689922	1	2	yes	—
448	C₄	—	2	2	no	—
449	C₄	—	4	4	no	—
450	C₄	—	4	4	no	—
451	C₄	—	47	4	no	—
452	C₄	—	94	2	no	—
453	C₄	—	376	2	no	—
454	C₄	—	376	2	no	—
455	C₄	—	188	1	no	—
456	C₄	—	188	1	no	—
457	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
458	C₄	#41×Dic₄₇	1	1	yes	characteristic
459	C₄	#15689633	1	1	yes	characteristic
460	C₄	#15689654	1	1	yes	characteristic
461	C₂	—	4	2	no	—
462	C₂	#121×Dic₄₇	1	1	yes	characteristic
463	C₂	#137×Dic₄₇	1	2	yes	—
464	C₂	#470×D₄₇	1	1	yes	characteristic
465	C₂	#20252999	1	1	yes	characteristic
466	C₂	#20253989	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#470	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂⁴×C₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#470	D₄₇
hypocenter	C₄₇	C₄×#470
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂³×C₄ ◁ C₂×#470

Complements

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

N	H ≅ G/N	type
1. C₂×Q₁₆×Dic₄₇	C₂	semidirect
4. #20244260	C₂	semidirect
5. #20244132	C₂	semidirect
6. #20244080	C₂	semidirect
9. #106×Dic₄₇	C₂	semidirect
10. #103×Dic₄₇	C₂	semidirect
39. C₄₇×#470	C₄	semidirect
81. C₂×Q₁₆×C₄₇	C₂×C₄	semidirect
92. #106×C₄₇	C₂×C₄	semidirect
93. #103×C₄₇	C₂×C₄	semidirect
227. Dic₄₇	#470	direct (N × H)
251. #470	Dic₄₇	direct (N × H)
275. C₄₇	C₄×#470	semidirect
282. C₂×Q₁₆	C₂×Dic₄₇	semidirect
315. #106	C₂×Dic₄₇	semidirect
318. #103	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×Q₁₆×Dic₄₇	2
C₂×M₁₆×Dic₄₇	2
C₂²⋊Q₈×Dic₄₇	2
#20244260	2
#20244132	2
#20244080	2
#20243822	2
#20243421	2
#106×Dic₄₇	2
#103×Dic₄₇	2
C₂×C₄₇×#470	2
C₄×#470	47

Subgroups — #470×Dic47 #26222934

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #470×Dic₄₇ #26222934