Subgroups — D₄₇×#3163 #27085895

Order 12032.

1854 conjugacy classes of subgroups.

The subgroup lattice has 690 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#544×D₄₇	C₂	1	2	yes	maximal
2	#20253920	C₂	1	1	yes	maximal, characteristic, complemented
3	#20253919	C₂	1	1	yes	maximal, characteristic, complemented
4	#20253918	C₂	1	2	yes	maximal, complemented
5	#20253917	C₂	1	2	yes	maximal, complemented
6	#20253916	C₂	1	1	yes	maximal, characteristic, complemented
7	#20253915	C₂	1	4	yes	maximal, complemented
8	#20253914	C₂	1	2	yes	maximal, complemented
9	#20253913	C₂	1	2	yes	maximal, complemented
10	#501×D₄₇	C₂	1	4	yes	maximal, complemented
11	#499×D₄₇	C₂	1	2	yes	maximal, complemented
12	#498×D₄₇	C₂	1	2	yes	maximal, complemented
13	#428×D₄₇	C₂	1	2	yes	maximal
14	#427×D₄₇	C₂	1	1	yes	maximal, characteristic
15	C₂×#106×D₄₇	C₂	1	1	yes	maximal, characteristic
16	#405×D₄₇	C₂	1	1	yes	maximal, characteristic
17	C₄₇×#3163	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
20	#15689754	C₂²	1	2	yes	—
21	#15689753	—	2	2	no	—
22	#15689753	C₂²	1	4	yes	—
23	#15689752	—	2	4	no	—
24	#15689751	C₂²	1	2	yes	—
25	#15689751	C₂²	1	2	yes	—
26	#15689750	—	2	2	no	—
27	#15689750	C₂²	1	4	yes	—
28	C₄⋊Q₈×D₄₇	—	2	2	no	—
29	C₄⋊Q₈×D₄₇	C₂²	1	4	yes	—
30	#125×D₄₇	—	2	2	no	—
31	#125×D₄₇	C₂²	1	4	yes	—
32	C₂²⋊Q₈×D₄₇	—	2	4	no	—
33	#117×D₄₇	C₂²	1	2	yes	—
34	#117×D₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
36	#15689533	C₂²	1	4	yes	complemented
37	#15689532	C₂²	1	4	yes	complemented
38	#15689531	C₂²	1	4	yes	complemented
39	#15689531	C₂²	1	4	yes	complemented
40	#15689530	C₂²	1	4	yes	complemented
41	#15689530	C₂²	1	4	yes	complemented
42	#15689529	C₂²	1	4	yes	complemented
43	#15689525	C₂²	1	2	yes	complemented
44	#15689524	C₂²	1	4	yes	complemented
45	#15689523	C₂²	1	2	yes	complemented
46	#15689523	C₂²	1	2	yes	complemented
47	#15689522	C₂²	1	4	yes	complemented
48	#15689521	C₂²	1	2	yes	complemented
49	#15689520	C₂²	1	2	yes	complemented
50	#15689520	C₂²	1	4	yes	complemented
51	#15689520	C₂²	1	2	yes	complemented
52	#15689519	C₂²	1	4	yes	complemented
53	#15689166	C₂²	1	2	yes	—
54	#15689165	C₂²	1	2	yes	—
55	#15689164	C₂²	1	4	yes	—
56	#15689163	C₂²	1	2	yes	—
57	#15689162	C₂²	1	4	yes	—
58	#15689161	C₂²	1	1	yes	characteristic
59	#15689160	C₂²	1	2	yes	—
60	#15689159	C₂²	1	2	yes	—
61	#15689158	C₂²	1	1	yes	characteristic
62	#15689158	C₂²	1	1	yes	characteristic
63	#107×D₄₇	C₂²	1	2	yes	—
64	#107×D₄₇	C₂²	1	4	yes	—
65	C₂×#13093956	C₂²	1	1	yes	characteristic
66	C₂×#13093955	C₂²	1	2	yes	—
67	#106×D₄₇	C₂²	1	2	yes	—
68	#106×D₄₇	C₂²	1	2	yes	—
69	#106×D₄₇	C₂²	1	2	yes	—
70	#106×D₄₇	C₂²	1	2	yes	—
71	#106×D₄₇	C₂²	1	1	yes	characteristic
72	#106×D₄₇	C₂²	1	1	yes	characteristic
73	#106×D₄₇	C₂²	1	4	yes	—
74	#15689081	C₂²	1	1	yes	characteristic
75	#15689080	C₂²	1	2	yes	—
76	#15689079	C₂²	1	1	yes	characteristic
77	#15689078	C₂²	1	1	yes	characteristic
78	#15689077	C₂²	1	2	yes	—
79	#97×D₄₇	C₂²	1	2	yes	—
80	C₄×C₈×D₄₇	C₂²	1	2	yes	—
81	C₄₇×#544	C₂²	1	2	yes	—
82	C₄₇×#501	C₂²	1	4	yes	complemented
83	C₄₇×#499	C₂²	1	2	yes	complemented
84	C₄₇×#498	C₂²	1	2	yes	complemented
85	C₄₇×#428	C₂²	1	2	yes	—
86	C₄₇×#427	C₂²	1	1	yes	characteristic
87	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
88	C₄₇×#405	C₂²	1	1	yes	characteristic
89	C₂×Q₈×D₄₇	—	2	4	no	—
90	C₂²×C₄×D₄₇	—	2	2	no	—
91	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
92	C₂×#10625329	C₂³	1	1	yes	characteristic
93	C₂×#10625324	C₂³	1	2	yes	—
94	M₁₆×D₄₇	Q₈	1	8	yes	complemented
95	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
96	C₂×C₈×D₄₇	Q₈	1	8	yes	complemented
97	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
98	C₂×C₈×D₄₇	C₂³	1	2	yes	—
99	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
100	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
101	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
102	#13094024	—	2	2	no	—
103	#13094024	C₂³	1	4	yes	—
104	#13094023	—	2	2	no	—
105	#13094023	—	2	2	no	—
106	#13094023	—	2	4	no	—
107	#13094023	—	2	4	no	—
108	#13094023	C₂³	1	4	yes	—
109	#13094023	C₂³	1	4	yes	—
110	#13094022	—	2	4	no	—
111	#13094022	—	2	4	no	—
112	#13094016	—	2	2	no	—
113	#13094016	C₂³	1	4	yes	—
114	#13094015	—	2	2	no	—
115	#13094015	—	2	2	no	—
116	#13094015	C₂³	1	4	yes	—
117	#13094015	C₂³	1	4	yes	—
118	#13094014	—	2	4	no	—
119	#13094014	—	2	4	no	—
120	#13094014	—	2	4	no	—
121	#13094014	—	2	4	no	—
122	#13094004	—	2	4	no	—
123	#13094003	—	2	4	no	—
124	#13094002	—	2	4	no	—
125	#13094002	—	2	4	no	—
126	#13094001	—	2	4	no	—
127	#13094001	—	2	4	no	—
128	#13094000	—	2	4	no	—
129	#13093983	C₂³	1	2	yes	—
130	#13093983	C₂³	1	1	yes	characteristic
131	#13093982	D₄	1	2	yes	—
132	#13093982	C₂³	1	2	yes	—
133	#13093982	C₂³	1	2	yes	—
134	#13093981	—	2	2	no	—
135	#13093981	C₂³	1	2	yes	—
136	#13093980	—	2	2	no	—
137	#13093980	D₄	1	2	yes	—
138	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
139	C₂×Dic₄₇⋊C₄	—	2	2	no	—
140	C₄⋊C₄×D₄₇	—	2	2	no	—
141	C₄⋊C₄×D₄₇	—	2	2	no	—
142	C₄⋊C₄×D₄₇	—	2	4	no	—
143	C₄⋊C₄×D₄₇	—	2	4	no	—
144	C₄⋊C₄×D₄₇	—	2	4	no	—
145	C₄⋊C₄×D₄₇	D₄	1	2	yes	—
146	C₄⋊C₄×D₄₇	C₂³	1	4	yes	—
147	C₄⋊C₄×D₄₇	C₂³	1	4	yes	—
148	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
149	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
150	C₂²⋊C₄×D₄₇	—	2	2	no	—
151	C₂²⋊C₄×D₄₇	D₄	1	2	yes	—
152	C₄²×D₄₇	—	2	2	no	—
153	C₄²×D₄₇	C₂³	1	2	yes	—
154	#13093958	C₂³	1	4	yes	—
155	#13093958	C₂³	1	2	yes	—
156	#13093957	C₂³	1	4	yes	—
157	#13093957	C₂³	1	4	yes	—
158	#13093957	C₂³	1	2	yes	—
159	#13093957	C₂³	1	2	yes	—
160	#13093956	C₂³	1	1	yes	characteristic
161	#13093956	C₂³	1	2	yes	—
162	#13093956	C₂³	1	4	yes	—
163	#13093956	C₂³	1	1	yes	characteristic
164	#13093956	C₂³	1	2	yes	—
165	#13093955	C₂³	1	2	yes	—
166	#13093955	C₂³	1	4	yes	—
167	#13093955	C₂³	1	4	yes	—
168	#13093955	C₂³	1	4	yes	—
169	#13093955	C₂³	1	2	yes	—
170	#13093955	C₂³	1	4	yes	—
171	#13093935	C₂³	1	2	yes	—
172	#13093934	C₂³	1	2	yes	—
173	#13093934	C₂³	1	2	yes	—
174	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
175	C₈×Dic₄₇	C₂³	1	2	yes	—
176	C₈×Dic₄₇	C₂³	1	2	yes	—
177	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
178	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
179	C₄⋊Q₈×C₄₇	—	2	2	no	—
180	C₄⋊Q₈×C₄₇	C₂³	1	4	yes	—
181	#125×C₄₇	—	2	2	no	—
182	#125×C₄₇	C₂³	1	4	yes	—
183	C₂²⋊Q₈×C₄₇	—	2	4	no	—
184	#117×C₄₇	C₂³	1	2	yes	—
185	#117×C₄₇	C₂³	1	1	yes	characteristic
186	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
187	#107×C₄₇	C₂³	1	4	yes	—
188	#107×C₄₇	C₂³	1	2	yes	—
189	#106×C₄₇	C₂³	1	1	yes	characteristic
190	#106×C₄₇	C₂³	1	2	yes	—
191	#106×C₄₇	C₂³	1	4	yes	—
192	#106×C₄₇	C₂³	1	1	yes	characteristic
193	#106×C₄₇	C₂³	1	2	yes	—
194	#97×C₄₇	C₂³	1	2	yes	—
195	C₄×C₈×C₄₇	C₂³	1	2	yes	—
196	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
197	C₂×Q₈×C₄₇	—	2	4	no	—
198	C₂²×C₄×C₄₇	—	2	2	no	—
199	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
200	C₂²×Dic₄₇	—	2	2	no	—
201	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
202	Q₈×D₄₇	—	8	8	no	—
203	C₂×C₄×D₄₇	—	2	2	no	—
204	C₂×C₄×D₄₇	—	2	2	no	—
205	C₂×C₄×D₄₇	—	2	4	no	—
206	C₂×C₄×D₄₇	—	2	4	no	—
207	C₂×C₄×D₄₇	—	8	4	no	—
208	C₂×C₄×D₄₇	C₂×D₄	1	4	yes	—
209	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
210	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
211	C₂×C₄×D₄₇	C₂×Q₈	1	4	yes	—
212	C₂×C₄×D₄₇	C₂×Q₈	1	4	yes	—
213	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
214	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
215	C₂×Dic₉₄	—	2	4	no	—
216	C₂×Dic₉₄	—	2	4	no	—
217	C₂×Dic₉₄	—	2	4	no	—
218	M₁₆×C₄₇	C₂×Q₈	1	4	yes	complemented
219	C₂×C₈×C₄₇	C₂×Q₈	1	4	yes	complemented
220	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
221	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
222	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
223	C₄⋊C₄×C₄₇	—	2	2	no	—
224	C₄⋊C₄×C₄₇	—	2	4	no	—
225	C₄⋊C₄×C₄₇	—	2	4	no	—
226	C₄⋊C₄×C₄₇	—	2	4	no	—
227	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
228	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
229	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
230	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
231	C₂²⋊C₄×C₄₇	—	2	2	no	—
232	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
233	C₄²×C₄₇	—	2	2	no	—
234	C₄²×C₄₇	C₂⁴	1	2	yes	—
235	C₂²⋊Dic₄₇	—	2	2	no	—
236	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
237	(C₂×D₄₇)⋊C₄	—	2	2	no	—
238	(C₂×D₄₇)⋊C₄	—	2	2	no	—
239	(C₂×D₄₇)⋊C₄	C₂×D₄	1	4	yes	—
240	C₄⋊Dic₄₇	—	2	2	no	—
241	C₄⋊Dic₄₇	—	2	4	no	—
242	C₄⋊Dic₄₇	—	2	4	no	—
243	C₄⋊Dic₄₇	—	2	4	no	—
244	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
245	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
246	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
247	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
248	Dic₄₇⋊C₄	—	2	4	no	—
249	Dic₄₇⋊C₄	—	2	4	no	—
250	Dic₄₇⋊C₄	—	2	4	no	—
251	Dic₄₇⋊C₄	—	2	4	no	—
252	Dic₄₇⋊C₄	—	2	4	no	—
253	Dic₄₇⋊C₄	—	2	4	no	—
254	Dic₄₇⋊C₄	—	2	4	no	—
255	Dic₄₇⋊C₄	—	2	4	no	—
256	Dic₄₇⋊C₄	—	2	2	no	—
257	Dic₄₇⋊C₄	—	2	2	no	—
258	Dic₄₇⋊C₄	C₂×D₄	1	4	yes	—
259	C₄×Dic₄₇	—	2	2	no	—
260	C₄×Dic₄₇	—	2	2	no	—
261	C₄×Dic₄₇	—	2	2	no	—
262	C₄×Dic₄₇	C₂×D₄	1	4	yes	—
263	C₄×Dic₄₇	C₂⁴	1	2	yes	—
264	#10625329	C₂×Q₈	1	4	yes	complemented
265	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	complemented
266	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
267	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
268	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
269	#10625324	C₂×Q₈	1	8	yes	complemented
270	C₈×D₄₇	C₂×Q₈	1	4	yes	—
271	C₈×D₄₇	C₂×Q₈	1	4	yes	—
272	C₈×D₄₇	C₂×Q₈	1	8	yes	—
273	C₈×D₄₇	C₂×Q₈	1	4	yes	complemented
274	C₈×D₄₇	C₂×Q₈	1	4	yes	complemented
275	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
276	C₂²×D₄₇	—	2	4	no	—
277	C₂²×D₄₇	C₄⋊Q₈	1	4	yes	—
278	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
279	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
280	Q₈×C₄₇	—	8	4	no	—
281	C₂×C₄×C₄₇	—	2	2	no	—
282	C₂×C₄×C₄₇	—	2	2	no	—
283	C₂×C₄×C₄₇	—	2	4	no	—
284	C₂×C₄×C₄₇	—	8	2	no	—
285	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
286	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
287	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
288	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
289	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
290	C₂×Dic₄₇	—	2	2	no	—
291	C₂×Dic₄₇	—	2	2	no	—
292	C₂×Dic₄₇	—	2	4	no	—
293	C₂×Dic₄₇	—	8	2	no	—
294	C₂×Dic₄₇	C₄⋊Q₈	1	4	yes	—
295	C₂×Dic₄₇	C₂²×D₄	1	4	yes	—
296	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
297	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
298	C₄×D₄₇	—	2	8	no	—
299	C₄×D₄₇	—	4	4	no	—
300	C₄×D₄₇	—	4	8	no	—
301	C₄×D₄₇	—	4	4	no	—
302	C₄×D₄₇	—	8	4	no	—
303	C₄×D₄₇	C₄⋊Q₈	1	4	yes	—
304	C₄×D₄₇	C₄⋊Q₈	1	4	yes	—
305	C₄×D₄₇	C₂²×Q₈	1	2	yes	—
306	C₄×D₄₇	C₂²×Q₈	1	2	yes	—
307	C₄×D₄₇	C₂²×Q₈	1	2	yes	—
308	C₄×D₄₇	C₂²×Q₈	1	2	yes	—
309	Dic₉₄	—	8	4	no	—
310	Dic₉₄	—	8	4	no	—
311	Dic₉₄	—	8	4	no	—
312	C₈×C₄₇	C₂²×Q₈	1	2	yes	—
313	C₈×C₄₇	C₂²×Q₈	1	2	yes	—
314	C₈×C₄₇	C₂²×Q₈	1	4	yes	—
315	C₄₇⋊C₈	C₂²×Q₈	1	2	yes	—
316	C₄₇⋊C₈	C₂²×Q₈	1	2	yes	—
317	C₄₇⋊C₈	C₂²×Q₈	1	4	yes	—
318	C₂×#3163	—	47	1	no	maximal, Sylow
319	C₂²×C₄₇	—	2	2	no	—
320	C₂²×C₄₇	C₂×C₄⋊Q₈	1	2	yes	—
321	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
322	C₂×D₄₇	—	2	2	no	—
323	C₂×D₄₇	—	2	8	no	—
324	C₂×D₄₇	C₂×C₄⋊Q₈	1	2	yes	—
325	C₂×D₄₇	C₂×C₄⋊Q₈	1	2	yes	—
326	C₂×D₄₇	#577	1	4	yes	—
327	C₄×C₄₇	—	2	4	no	—
328	C₄×C₄₇	—	4	2	no	—
329	C₄×C₄₇	—	4	4	no	—
330	C₄×C₄₇	—	4	2	no	—
331	C₄×C₄₇	C₂×C₄⋊Q₈	1	2	yes	—
332	C₄×C₄₇	C₂³×Q₈	1	1	yes	characteristic
333	C₄×C₄₇	C₂³×Q₈	1	1	yes	characteristic
334	Dic₄₇	—	2	4	no	—
335	Dic₄₇	—	4	2	no	—
336	Dic₄₇	—	4	4	no	—
337	Dic₄₇	—	4	2	no	—
338	Dic₄₇	C₂×C₄⋊Q₈	1	2	yes	—
339	Dic₄₇	C₂×C₄⋊Q₈	1	2	yes	—
340	C₂×#544	—	47	2	no	—
341	#3163	—	47	4	no	—
342	#3163	—	47	2	no	—
343	#3163	—	47	2	no	—
344	#3163	—	47	2	no	—
345	#3163	—	47	1	no	—
346	#3163	—	47	1	no	—
347	#3163	—	47	1	no	—
348	#3163	—	47	2	no	—
349	#3163	D₄₇	1	1	yes	characteristic, direct product factor
350	C₂×#501	—	47	4	no	—
351	C₂×#499	—	47	2	no	—
352	C₂×#498	—	47	2	no	—
353	C₂×#428	—	47	2	no	—
354	C₂×#427	—	47	1	no	—
355	C₂²×#106	—	47	1	no	—
356	C₂×#405	—	47	1	no	—
357	C₂×C₄₇	—	2	2	no	—
358	C₂×C₄₇	C₂²×C₄⋊Q₈	1	1	yes	characteristic
359	C₂×C₄₇	C₂×#577	1	2	yes	—
360	D₄₇	—	2	2	no	—
361	D₄₇	#3163	1	4	yes	direct product factor
362	C₂²×M₁₆	—	47	1	no	—
363	C₂³×C₈	—	47	1	no	—
364	#544	—	47	4	no	—
365	#544	—	47	4	no	—
366	#544	—	47	2	no	—
367	#544	—	47	2	no	—
368	#544	—	47	2	no	—
369	#544	—	94	4	no	—
370	#544	—	94	2	no	—
371	#544	—	94	2	no	—
372	#544	C₂×D₄₇	1	2	yes	—
373	C₂×C₄⋊Q₈	—	47	4	no	—
374	C₂×C₄⋊Q₈	—	94	2	no	—
375	C₂×#125	—	47	4	no	—
376	C₂×#125	—	94	2	no	—
377	C₂×C₂²⋊Q₈	—	94	4	no	—
378	C₂×#117	—	47	1	no	—
379	C₂×#117	—	47	2	no	—
380	C₂²×C₄⋊C₄	—	47	2	no	—
381	#501	—	47	4	no	—
382	#501	—	47	4	no	—
383	#501	—	47	4	no	—
384	#501	—	47	4	no	—
385	#501	—	47	4	no	—
386	#501	—	47	4	no	—
387	#501	—	47	4	no	—
388	#501	C₂×D₄₇	1	4	yes	complemented
389	#499	—	47	4	no	—
390	#499	—	47	4	no	—
391	#499	—	47	2	no	—
392	#499	—	47	2	no	—
393	#499	—	47	2	no	—
394	#499	C₂×D₄₇	1	2	yes	complemented
395	#498	—	47	4	no	—
396	#498	—	47	2	no	—
397	#498	—	47	2	no	—
398	#498	—	47	4	no	—
399	#498	—	47	2	no	—
400	#498	C₂×D₄₇	1	2	yes	complemented
401	#428	—	47	2	no	—
402	#428	—	47	2	no	—
403	#428	—	47	2	no	—
404	#428	—	47	4	no	—
405	#428	—	47	4	no	—
406	#428	C₂×D₄₇	1	2	yes	—
407	#427	—	47	1	no	—
408	#427	—	47	2	no	—
409	#427	—	47	2	no	—
410	#427	—	47	1	no	—
411	#427	—	47	1	no	—
412	#427	C₂×D₄₇	1	1	yes	characteristic
413	C₂×#107	—	47	4	no	—
414	C₂×#107	—	47	2	no	—
415	C₂×#106	—	47	1	no	—
416	C₂×#106	—	47	2	no	—
417	C₂×#106	—	47	1	no	—
418	C₂×#106	—	47	2	no	—
419	C₂×#106	—	47	4	no	—
420	C₂×#106	—	47	1	no	—
421	C₂×#106	—	47	2	no	—
422	C₂×#106	—	47	2	no	—
423	C₂×#106	—	47	2	no	—
424	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
425	#405	—	47	1	no	—
426	#405	—	47	1	no	—
427	#405	—	47	1	no	—
428	#405	—	47	2	no	—
429	#405	—	47	2	no	—
430	#405	C₂×D₄₇	1	1	yes	characteristic
431	C₂×#97	—	47	2	no	—
432	C₂×C₄×C₈	—	47	2	no	—
433	C₄₇	C₂×#3163	1	1	yes	characteristic, complemented, Sylow
434	C₂²×Q₈	—	94	4	no	—
435	C₂³×C₄	—	47	1	no	—
436	C₂³×C₄	—	94	2	no	—
437	C₂×M₁₆	—	47	1	no	—
438	C₂×M₁₆	—	47	8	no	—
439	C₂×M₁₆	—	47	2	no	—
440	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
441	C₂²×C₈	—	47	1	no	—
442	C₂²×C₈	—	47	8	no	—
443	C₂²×C₈	—	47	1	no	—
444	C₂²×C₈	—	47	1	no	—
445	C₂²×C₈	—	47	1	no	—
446	C₂²×C₈	—	47	1	no	—
447	C₂²×C₈	—	47	2	no	—
448	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
449	C₄⋊Q₈	—	2	2	no	—
450	C₄⋊Q₈	—	47	4	no	—
451	C₄⋊Q₈	—	47	4	no	—
452	C₄⋊Q₈	—	47	4	no	—
453	C₄⋊Q₈	—	94	2	no	—
454	C₄⋊Q₈	—	94	4	no	—
455	C₄⋊Q₈	—	94	4	no	—
456	C₄⋊Q₈	—	94	4	no	—
457	C₄⋊Q₈	—	94	2	no	—
458	C₄⋊Q₈	—	94	4	no	—
459	C₄⋊Q₈	—	94	2	no	—
460	C₄⋊Q₈	C₂²×D₄₇	1	4	yes	—
461	#125	—	2	2	no	—
462	#125	—	47	4	no	—
463	#125	—	47	4	no	—
464	#125	—	47	4	no	—
465	#125	—	94	2	no	—
466	#125	—	94	4	no	—
467	#125	—	94	4	no	—
468	#125	—	94	4	no	—
469	#125	—	94	4	no	—
470	#125	—	94	2	no	—
471	#125	—	94	2	no	—
472	#125	C₂²×D₄₇	1	4	yes	—
473	C₂²⋊Q₈	—	2	4	no	—
474	C₂²⋊Q₈	—	94	4	no	—
475	C₂²⋊Q₈	—	94	4	no	—
476	C₂²⋊Q₈	—	94	4	no	—
477	C₂²⋊Q₈	—	94	4	no	—
478	C₂²⋊Q₈	—	94	4	no	—
479	C₂²⋊Q₈	—	94	4	no	—
480	C₂²⋊Q₈	—	94	4	no	—
481	#117	—	47	1	no	—
482	#117	—	47	2	no	—
483	#117	—	47	2	no	—
484	#117	—	47	2	no	—
485	#117	—	47	2	no	—
486	#117	—	47	2	no	—
487	#117	—	47	2	no	—
488	#117	—	94	2	no	—
489	#117	—	94	2	no	—
490	#117	C₂²×D₄₇	1	2	yes	—
491	#117	C₂²×D₄₇	1	1	yes	characteristic
492	C₂×C₄⋊C₄	—	47	2	no	—
493	C₂×C₄⋊C₄	—	47	2	no	—
494	C₂×C₄⋊C₄	—	47	4	no	—
495	C₂×C₄⋊C₄	—	47	4	no	—
496	C₂×C₄⋊C₄	—	47	2	no	—
497	C₂×C₄⋊C₄	—	47	2	no	—
498	C₂×C₄⋊C₄	—	94	2	no	—
499	C₂×C₄⋊C₄	—	94	2	no	—
500	C₂×C₄⋊C₄	—	94	4	no	—
501	C₂×C₄⋊C₄	—	94	4	no	—
502	C₂×C₄⋊C₄	—	94	4	no	—
503	C₂×C₄⋊C₄	—	94	2	no	—
504	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
505	C₂×C₂²⋊C₄	—	47	2	no	—
506	C₂×C₂²⋊C₄	—	94	2	no	—
507	C₂×C₄²	—	47	2	no	—
508	C₂×C₄²	—	94	2	no	—
509	#107	—	47	2	no	—
510	#107	—	47	4	no	—
511	#107	—	47	2	no	—
512	#107	—	47	2	no	—
513	#107	—	47	4	no	—
514	#107	—	47	4	no	—
515	#107	C₂²×D₄₇	1	2	yes	—
516	#107	C₂²×D₄₇	1	4	yes	—
517	#106	—	47	2	no	—
518	#106	—	47	2	no	—
519	#106	—	47	1	no	—
520	#106	—	47	1	no	—
521	#106	—	47	4	no	—
522	#106	—	47	4	no	—
523	#106	—	47	4	no	—
524	#106	—	47	2	no	—
525	#106	—	47	2	no	—
526	#106	—	47	4	no	—
527	#106	—	47	4	no	—
528	#106	C₂²×D₄₇	1	2	yes	—
529	#106	C₂²×D₄₇	1	2	yes	—
530	#106	C₂²×D₄₇	1	1	yes	characteristic
531	#106	C₂²×D₄₇	1	1	yes	characteristic
532	#106	C₂²×D₄₇	1	4	yes	—
533	#97	—	47	2	no	—
534	#97	—	47	2	no	—
535	#97	—	47	2	no	—
536	#97	C₂²×D₄₇	1	2	yes	—
537	C₄×C₈	—	47	2	no	—
538	C₄×C₈	—	47	2	no	—
539	C₄×C₈	—	47	2	no	—
540	C₄×C₈	C₂²×D₄₇	1	2	yes	—
541	C₂⁴	—	47	1	no	—
542	C₂×Q₈	—	2	4	no	—
543	C₂×Q₈	—	94	4	no	—
544	C₂×Q₈	—	94	4	no	—
545	C₂×Q₈	—	94	4	no	—
546	C₂×Q₈	—	376	8	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	47	1	no	—
549	C₂²×C₄	—	47	1	no	—
550	C₂²×C₄	—	47	1	no	—
551	C₂²×C₄	—	47	4	no	—
552	C₂²×C₄	—	47	4	no	—
553	C₂²×C₄	—	47	1	no	—
554	C₂²×C₄	—	47	1	no	—
555	C₂²×C₄	—	47	4	no	—
556	C₂²×C₄	—	94	4	no	—
557	C₂²×C₄	—	94	2	no	—
558	C₂²×C₄	—	94	2	no	—
559	C₂²×C₄	—	94	4	no	—
560	C₂²×C₄	—	94	2	no	—
561	C₂²×C₄	—	376	4	no	—
562	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
563	M₁₆	—	47	4	no	—
564	M₁₆	—	47	8	no	—
565	M₁₆	Q₈×D₄₇	1	4	yes	complemented
566	C₂×C₈	—	47	4	no	—
567	C₂×C₈	—	47	1	no	—
568	C₂×C₈	—	47	2	no	—
569	C₂×C₈	—	47	1	no	—
570	C₂×C₈	—	47	4	no	—
571	C₂×C₈	—	47	4	no	—
572	C₂×C₈	—	47	8	no	—
573	C₂×C₈	—	47	4	no	—
574	C₂×C₈	—	47	4	no	—
575	C₂×C₈	Q₈×D₄₇	1	4	yes	complemented
576	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
577	C₂×C₈	C₂³×D₄₇	1	2	yes	—
578	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
579	C₄⋊C₄	—	2	2	no	—
580	C₄⋊C₄	—	2	4	no	—
581	C₄⋊C₄	—	2	4	no	—
582	C₄⋊C₄	—	2	4	no	—
583	C₄⋊C₄	—	47	4	no	—
584	C₄⋊C₄	—	47	2	no	—
585	C₄⋊C₄	—	47	4	no	—
586	C₄⋊C₄	—	47	2	no	—
587	C₄⋊C₄	—	47	2	no	—
588	C₄⋊C₄	—	94	4	no	—
589	C₄⋊C₄	—	94	4	no	—
590	C₄⋊C₄	—	94	2	no	—
591	C₄⋊C₄	—	94	2	no	—
592	C₄⋊C₄	—	94	4	no	—
593	C₄⋊C₄	—	94	4	no	—
594	C₄⋊C₄	—	94	4	no	—
595	C₄⋊C₄	—	94	4	no	—
596	C₄⋊C₄	—	94	4	no	—
597	C₄⋊C₄	—	94	4	no	—
598	C₄⋊C₄	—	94	4	no	—
599	C₄⋊C₄	—	94	4	no	—
600	C₄⋊C₄	—	94	2	no	—
601	C₄⋊C₄	—	94	4	no	—
602	C₄⋊C₄	D₄×D₄₇	1	2	yes	—
603	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
604	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
605	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	47	2	no	—
608	C₂²⋊C₄	—	47	4	no	—
609	C₂²⋊C₄	—	94	2	no	—
610	C₂²⋊C₄	—	94	2	no	—
611	C₂²⋊C₄	—	94	2	no	—
612	C₂²⋊C₄	D₄×D₄₇	1	2	yes	—
613	C₄²	—	2	2	no	—
614	C₄²	—	47	4	no	—
615	C₄²	—	47	2	no	—
616	C₄²	—	94	2	no	—
617	C₄²	—	94	2	no	—
618	C₄²	—	94	2	no	—
619	C₄²	C₂³×D₄₇	1	2	yes	—
620	C₂³	—	47	1	no	—
621	C₂³	—	47	4	no	—
622	C₂³	—	47	1	no	—
623	C₂³	—	94	4	no	—
624	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
625	Q₈	—	8	4	no	—
626	Q₈	—	376	4	no	—
627	Q₈	—	376	4	no	—
628	Q₈	—	376	4	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	4	no	—
632	C₂×C₄	—	8	2	no	—
633	C₂×C₄	—	47	4	no	—
634	C₂×C₄	—	47	1	no	—
635	C₂×C₄	—	47	1	no	—
636	C₂×C₄	—	47	4	no	—
637	C₂×C₄	—	47	4	no	—
638	C₂×C₄	—	47	2	no	—
639	C₂×C₄	—	47	2	no	—
640	C₂×C₄	—	47	2	no	—
641	C₂×C₄	—	47	2	no	—
642	C₂×C₄	—	47	4	no	—
643	C₂×C₄	—	94	8	no	—
644	C₂×C₄	—	94	2	no	—
645	C₂×C₄	—	94	2	no	—
646	C₂×C₄	—	94	4	no	—
647	C₂×C₄	—	376	4	no	—
648	C₂×C₄	—	376	2	no	—
649	C₂×C₄	—	188	4	no	—
650	C₂×C₄	—	188	8	no	—
651	C₂×C₄	—	188	4	no	—
652	C₂×C₄	C₂×D₄×D₄₇	1	4	yes	—
653	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
654	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
655	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
656	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
657	C₈	—	47	2	no	—
658	C₈	—	47	2	no	—
659	C₈	—	47	4	no	—
660	C₈	C₂×Q₈×D₄₇	1	2	yes	—
661	C₈	C₂×Q₈×D₄₇	1	2	yes	—
662	C₈	C₂×Q₈×D₄₇	1	4	yes	—
663	C₂²	—	2	2	no	—
664	C₂²	—	47	4	no	—
665	C₂²	—	47	2	no	—
666	C₂²	—	47	2	no	—
667	C₂²	—	94	8	no	—
668	C₂²	—	94	2	no	—
669	C₂²	C₄⋊Q₈×D₄₇	1	2	yes	—
670	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
671	C₄	—	2	4	no	—
672	C₄	—	4	4	no	—
673	C₄	—	4	2	no	—
674	C₄	—	4	2	no	—
675	C₄	—	47	2	no	—
676	C₄	—	47	2	no	—
677	C₄	—	94	4	no	—
678	C₄	—	188	4	no	—
679	C₄	—	188	2	no	—
680	C₄	—	188	2	no	—
681	C₄	C₄⋊Q₈×D₄₇	1	2	yes	—
682	C₄	C₂²×Q₈×D₄₇	1	1	yes	characteristic
683	C₄	C₂²×Q₈×D₄₇	1	1	yes	characteristic
684	C₂	—	2	2	no	—
685	C₂	—	47	4	no	—
686	C₂	—	94	2	no	—
687	C₂	C₂×C₄⋊Q₈×D₄₇	1	1	yes	characteristic
688	C₂	#577×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3163	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	C₂³×D₄₇	C₂×D₄
hypercenter	#3163	D₄₇
hypocenter	C₄₇	C₂×#3163
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3163

Complements

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

N	H ≅ G/N	type
2. #20253920	C₂	semidirect
3. #20253919	C₂	semidirect
4. #20253918	C₂	semidirect
5. #20253917	C₂	semidirect
6. #20253916	C₂	semidirect
7. #20253915	C₂	semidirect
8. #20253914	C₂	semidirect
9. #20253913	C₂	semidirect
10. #501×D₄₇	C₂	semidirect
11. #499×D₄₇	C₂	semidirect
12. #498×D₄₇	C₂	semidirect
17. C₄₇×#3163	C₂	semidirect
36. #15689533	C₂²	semidirect
37. #15689532	C₂²	semidirect
38. #15689531	C₂²	semidirect
39. #15689531	C₂²	semidirect
40. #15689530	C₂²	semidirect
41. #15689530	C₂²	semidirect
42. #15689529	C₂²	semidirect
43. #15689525	C₂²	semidirect
44. #15689524	C₂²	semidirect
45. #15689523	C₂²	semidirect
46. #15689523	C₂²	semidirect
47. #15689522	C₂²	semidirect
48. #15689521	C₂²	semidirect
49. #15689520	C₂²	semidirect
50. #15689520	C₂²	semidirect
51. #15689520	C₂²	semidirect
52. #15689519	C₂²	semidirect
82. C₄₇×#501	C₂²	semidirect
83. C₄₇×#499	C₂²	semidirect
84. C₄₇×#498	C₂²	semidirect
94. M₁₆×D₄₇	Q₈	semidirect
96. C₂×C₈×D₄₇	Q₈	semidirect
218. M₁₆×C₄₇	C₂×Q₈	semidirect
219. C₂×C₈×C₄₇	C₂×Q₈	semidirect
264. #10625329	C₂×Q₈	semidirect
265. C₂×C₄₇⋊C₈	C₂×Q₈	semidirect
269. #10625324	C₂×Q₈	semidirect
273. C₈×D₄₇	C₂×Q₈	semidirect
274. C₈×D₄₇	C₂×Q₈	semidirect
349. #3163	D₄₇	direct (N × H)
361. D₄₇	#3163	direct (N × H)
388. #501	C₂×D₄₇	semidirect
394. #499	C₂×D₄₇	semidirect
400. #498	C₂×D₄₇	semidirect
433. C₄₇	C₂×#3163	semidirect
565. M₁₆	Q₈×D₄₇	semidirect
575. C₂×C₈	Q₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#544×D₄₇	2
#20253920	2
#20253919	2
#20253918	2
#20253917	2
#20253916	2
#20253915	2
#20253914	2
#20253913	2
#501×D₄₇	2
#499×D₄₇	2
#498×D₄₇	2
#428×D₄₇	2
#427×D₄₇	2
C₂×#106×D₄₇	2
#405×D₄₇	2
C₄₇×#3163	2
C₂×#3163	47

Subgroups — D47×#3163 #27085895

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#3163 #27085895