Subgroups — D₄₇×#3164 #27085904

Order 12032.

1854 conjugacy classes of subgroups.

The subgroup lattice has 726 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	#20253928	C₂	1	1	yes	maximal, characteristic, complemented
3	#20253927	C₂	1	1	yes	maximal, characteristic, complemented
4	#20253926	C₂	1	2	yes	maximal, complemented
5	#20253925	C₂	1	2	yes	maximal, complemented
6	#20253924	C₂	1	1	yes	maximal, characteristic, complemented
7	#20253923	C₂	1	4	yes	maximal, complemented
8	#20253922	C₂	1	2	yes	maximal, complemented
9	#20253921	C₂	1	2	yes	maximal, complemented
10	#501×D₄₇	C₂	1	4	yes	maximal, complemented
11	#500×D₄₇	C₂	1	2	yes	maximal, complemented
12	#499×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×#107×D₄₇	C₂	1	1	yes	maximal, characteristic
16	#405×D₄₇	C₂	1	1	yes	maximal, characteristic
17	C₄₇×#3164	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	#15689528	C₂²	1	2	yes	complemented
44	#15689527	C₂²	1	2	yes	complemented
45	#15689527	C₂²	1	4	yes	complemented
46	#15689527	C₂²	1	2	yes	complemented
47	#15689526	C₂²	1	4	yes	complemented
48	#15689525	C₂²	1	2	yes	complemented
49	#15689524	C₂²	1	2	yes	complemented
50	#15689524	C₂²	1	2	yes	complemented
51	#15689523	C₂²	1	4	yes	complemented
52	#15689522	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	1	yes	characteristic
60	#15689160	C₂²	1	1	yes	characteristic
61	#15689159	C₂²	1	2	yes	—
62	#15689158	C₂²	1	2	yes	—
63	C₂×#13093958	C₂²	1	1	yes	characteristic
64	C₂×#13093957	C₂²	1	2	yes	—
65	#107×D₄₇	C₂²	1	2	yes	—
66	#107×D₄₇	C₂²	1	2	yes	—
67	#107×D₄₇	C₂²	1	2	yes	—
68	#107×D₄₇	C₂²	1	2	yes	—
69	#107×D₄₇	C₂²	1	1	yes	characteristic
70	#107×D₄₇	C₂²	1	1	yes	characteristic
71	#107×D₄₇	C₂²	1	4	yes	—
72	#106×D₄₇	C₂²	1	2	yes	—
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×#500	C₂²	1	2	yes	complemented
84	C₄₇×#499	C₂²	1	2	yes	complemented
85	C₄₇×#428	C₂²	1	2	yes	—
86	C₄₇×#427	C₂²	1	1	yes	characteristic
87	C₂×#107×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	1	yes	characteristic
132	#13093982	D₄	1	1	yes	characteristic
133	#13093982	C₂³	1	2	yes	—
134	#13093982	C₂³	1	2	yes	—
135	#13093981	—	2	2	no	—
136	#13093981	C₂³	1	2	yes	—
137	#13093980	—	2	2	no	—
138	#13093980	D₄	1	2	yes	—
139	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
140	C₂×Dic₄₇⋊C₄	—	2	2	no	—
141	C₄⋊C₄×D₄₇	—	2	2	no	—
142	C₄⋊C₄×D₄₇	—	2	2	no	—
143	C₄⋊C₄×D₄₇	—	2	4	no	—
144	C₄⋊C₄×D₄₇	—	2	4	no	—
145	C₄⋊C₄×D₄₇	—	2	4	no	—
146	C₄⋊C₄×D₄₇	D₄	1	1	yes	characteristic
147	C₄⋊C₄×D₄₇	D₄	1	1	yes	characteristic
148	C₄⋊C₄×D₄₇	C₂³	1	4	yes	—
149	C₄⋊C₄×D₄₇	C₂³	1	4	yes	—
150	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
151	C₄⋊C₄×D₄₇	C₂³	1	2	yes	—
152	C₂²⋊C₄×D₄₇	—	2	2	no	—
153	C₂²⋊C₄×D₄₇	D₄	1	2	yes	—
154	C₄²×D₄₇	—	2	2	no	—
155	C₄²×D₄₇	C₂³	1	2	yes	—
156	#13093958	C₂³	1	1	yes	characteristic
157	#13093958	C₂³	1	2	yes	—
158	#13093958	C₂³	1	1	yes	characteristic
159	#13093958	C₂³	1	4	yes	—
160	#13093958	C₂³	1	2	yes	—
161	#13093957	C₂³	1	2	yes	—
162	#13093957	C₂³	1	4	yes	—
163	#13093957	C₂³	1	2	yes	—
164	#13093957	C₂³	1	4	yes	—
165	#13093957	C₂³	1	4	yes	—
166	#13093957	C₂³	1	4	yes	—
167	#13093956	C₂³	1	4	yes	—
168	#13093956	C₂³	1	2	yes	—
169	#13093955	C₂³	1	4	yes	—
170	#13093955	C₂³	1	4	yes	—
171	#13093955	C₂³	1	2	yes	—
172	#13093955	C₂³	1	2	yes	—
173	#13093935	C₂³	1	2	yes	—
174	#13093934	C₂³	1	2	yes	—
175	#13093934	C₂³	1	2	yes	—
176	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
177	C₈×Dic₄₇	C₂³	1	2	yes	—
178	C₈×Dic₄₇	C₂³	1	2	yes	—
179	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
180	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
181	C₄⋊Q₈×C₄₇	—	2	2	no	—
182	C₄⋊Q₈×C₄₇	C₂³	1	4	yes	—
183	#125×C₄₇	—	2	2	no	—
184	#125×C₄₇	C₂³	1	4	yes	—
185	C₂²⋊Q₈×C₄₇	—	2	4	no	—
186	#117×C₄₇	C₂³	1	2	yes	—
187	#117×C₄₇	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
189	#107×C₄₇	C₂³	1	1	yes	characteristic
190	#107×C₄₇	C₂³	1	2	yes	—
191	#107×C₄₇	C₂³	1	1	yes	characteristic
192	#107×C₄₇	C₂³	1	4	yes	—
193	#107×C₄₇	C₂³	1	2	yes	—
194	#106×C₄₇	C₂³	1	4	yes	—
195	#106×C₄₇	C₂³	1	2	yes	—
196	#97×C₄₇	C₂³	1	2	yes	—
197	C₄×C₈×C₄₇	C₂³	1	2	yes	—
198	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
199	C₂×Q₈×C₄₇	—	2	4	no	—
200	C₂²×C₄×C₄₇	—	2	2	no	—
201	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
202	C₂²×Dic₄₇	—	2	2	no	—
203	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
204	Q₈×D₄₇	—	8	8	no	—
205	C₂×C₄×D₄₇	—	2	2	no	—
206	C₂×C₄×D₄₇	—	2	2	no	—
207	C₂×C₄×D₄₇	—	2	4	no	—
208	C₂×C₄×D₄₇	—	2	4	no	—
209	C₂×C₄×D₄₇	—	8	4	no	—
210	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
211	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
212	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
213	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
214	C₂×C₄×D₄₇	C₂×Q₈	1	4	yes	—
215	C₂×C₄×D₄₇	C₂×Q₈	1	4	yes	—
216	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
217	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
218	C₂×Dic₉₄	—	2	4	no	—
219	C₂×Dic₉₄	—	2	4	no	—
220	C₂×Dic₉₄	—	2	4	no	—
221	M₁₆×C₄₇	C₂×Q₈	1	4	yes	complemented
222	C₂×C₈×C₄₇	C₂×Q₈	1	4	yes	complemented
223	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
224	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
225	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
226	C₄⋊C₄×C₄₇	—	2	2	no	—
227	C₄⋊C₄×C₄₇	—	2	4	no	—
228	C₄⋊C₄×C₄₇	—	2	4	no	—
229	C₄⋊C₄×C₄₇	—	2	4	no	—
230	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
231	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
232	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
233	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
234	C₄⋊C₄×C₄₇	C₂⁴	1	2	yes	—
235	C₂²⋊C₄×C₄₇	—	2	2	no	—
236	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
237	C₄²×C₄₇	—	2	2	no	—
238	C₄²×C₄₇	C₂⁴	1	2	yes	—
239	C₂²⋊Dic₄₇	—	2	2	no	—
240	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
241	(C₂×D₄₇)⋊C₄	—	2	2	no	—
242	(C₂×D₄₇)⋊C₄	—	2	2	no	—
243	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
244	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
245	C₄⋊Dic₄₇	—	2	2	no	—
246	C₄⋊Dic₄₇	—	2	4	no	—
247	C₄⋊Dic₄₇	—	2	4	no	—
248	C₄⋊Dic₄₇	—	2	4	no	—
249	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
250	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
251	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
252	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
253	C₄⋊Dic₄₇	C₂⁴	1	2	yes	—
254	Dic₄₇⋊C₄	—	2	4	no	—
255	Dic₄₇⋊C₄	—	2	4	no	—
256	Dic₄₇⋊C₄	—	2	4	no	—
257	Dic₄₇⋊C₄	—	2	4	no	—
258	Dic₄₇⋊C₄	—	2	4	no	—
259	Dic₄₇⋊C₄	—	2	4	no	—
260	Dic₄₇⋊C₄	—	2	4	no	—
261	Dic₄₇⋊C₄	—	2	4	no	—
262	Dic₄₇⋊C₄	—	2	2	no	—
263	Dic₄₇⋊C₄	—	2	2	no	—
264	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
265	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
266	C₄×Dic₄₇	—	2	2	no	—
267	C₄×Dic₄₇	—	2	2	no	—
268	C₄×Dic₄₇	—	2	2	no	—
269	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
270	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
271	C₄×Dic₄₇	C₂⁴	1	2	yes	—
272	#10625329	C₂×Q₈	1	4	yes	complemented
273	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	complemented
274	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
275	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
276	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
277	#10625324	C₂×Q₈	1	8	yes	complemented
278	C₈×D₄₇	C₂×Q₈	1	4	yes	—
279	C₈×D₄₇	C₂×Q₈	1	4	yes	—
280	C₈×D₄₇	C₂×Q₈	1	8	yes	—
281	C₈×D₄₇	C₂×Q₈	1	4	yes	complemented
282	C₈×D₄₇	C₂×Q₈	1	4	yes	complemented
283	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
284	C₂²×D₄₇	—	2	2	no	—
285	C₂²×D₄₇	—	2	2	no	—
286	C₂²×D₄₇	C₄⋊Q₈	1	4	yes	—
287	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
288	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
289	Q₈×C₄₇	—	8	4	no	—
290	C₂×C₄×C₄₇	—	2	2	no	—
291	C₂×C₄×C₄₇	—	2	2	no	—
292	C₂×C₄×C₄₇	—	2	4	no	—
293	C₂×C₄×C₄₇	—	8	2	no	—
294	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
295	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
296	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
297	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
298	C₂×C₄×C₄₇	C₂²×Q₈	1	2	yes	—
299	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
300	C₂×Dic₄₇	—	2	2	no	—
301	C₂×Dic₄₇	—	2	2	no	—
302	C₂×Dic₄₇	—	2	4	no	—
303	C₂×Dic₄₇	—	8	2	no	—
304	C₂×Dic₄₇	C₄⋊Q₈	1	4	yes	—
305	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
306	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
307	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
308	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
309	C₄×D₄₇	—	2	4	no	—
310	C₄×D₄₇	—	2	4	no	—
311	C₄×D₄₇	—	4	8	no	—
312	C₄×D₄₇	—	4	4	no	—
313	C₄×D₄₇	—	4	4	no	—
314	C₄×D₄₇	—	8	4	no	—
315	C₄×D₄₇	C₄⋊Q₈	1	4	yes	—
316	C₄×D₄₇	C₄⋊Q₈	1	4	yes	—
317	C₄×D₄₇	C₂²×Q₈	1	2	yes	—
318	C₄×D₄₇	C₂²×Q₈	1	2	yes	—
319	C₄×D₄₇	C₂²×Q₈	1	2	yes	—
320	C₄×D₄₇	C₂²×Q₈	1	2	yes	—
321	Dic₉₄	—	8	4	no	—
322	Dic₉₄	—	8	4	no	—
323	Dic₉₄	—	8	4	no	—
324	C₈×C₄₇	C₂²×Q₈	1	2	yes	—
325	C₈×C₄₇	C₂²×Q₈	1	2	yes	—
326	C₈×C₄₇	C₂²×Q₈	1	4	yes	—
327	C₄₇⋊C₈	C₂²×Q₈	1	2	yes	—
328	C₄₇⋊C₈	C₂²×Q₈	1	2	yes	—
329	C₄₇⋊C₈	C₂²×Q₈	1	4	yes	—
330	C₂×#3164	—	47	1	no	maximal, Sylow
331	C₂²×C₄₇	—	2	1	no	—
332	C₂²×C₄₇	—	2	1	no	—
333	C₂²×C₄₇	C₂×C₄⋊Q₈	1	2	yes	—
334	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
335	C₂×D₄₇	—	2	1	no	—
336	C₂×D₄₇	—	2	1	no	—
337	C₂×D₄₇	—	2	8	no	—
338	C₂×D₄₇	C₂×C₄⋊Q₈	1	2	yes	—
339	C₂×D₄₇	C₂×C₄⋊Q₈	1	2	yes	—
340	C₂×D₄₇	#576	1	2	yes	—
341	C₂×D₄₇	#578	1	2	yes	—
342	C₄×C₄₇	—	2	2	no	—
343	C₄×C₄₇	—	2	2	no	—
344	C₄×C₄₇	—	4	2	no	—
345	C₄×C₄₇	—	4	4	no	—
346	C₄×C₄₇	—	4	2	no	—
347	C₄×C₄₇	C₂×C₄⋊Q₈	1	2	yes	—
348	C₄×C₄₇	C₂³×Q₈	1	1	yes	characteristic
349	C₄×C₄₇	C₂³×Q₈	1	1	yes	characteristic
350	Dic₄₇	—	2	2	no	—
351	Dic₄₇	—	2	2	no	—
352	Dic₄₇	—	4	2	no	—
353	Dic₄₇	—	4	4	no	—
354	Dic₄₇	—	4	2	no	—
355	Dic₄₇	C₂×C₄⋊Q₈	1	2	yes	—
356	Dic₄₇	C₂×C₄⋊Q₈	1	2	yes	—
357	C₂×#544	—	47	2	no	—
358	#3164	—	47	4	no	—
359	#3164	—	47	2	no	—
360	#3164	—	47	2	no	—
361	#3164	—	47	2	no	—
362	#3164	—	47	1	no	—
363	#3164	—	47	1	no	—
364	#3164	—	47	1	no	—
365	#3164	—	47	2	no	—
366	#3164	D₄₇	1	1	yes	characteristic, direct product factor
367	C₂×#501	—	47	4	no	—
368	C₂×#500	—	47	2	no	—
369	C₂×#499	—	47	2	no	—
370	C₂×#428	—	47	2	no	—
371	C₂×#427	—	47	1	no	—
372	C₂²×#107	—	47	1	no	—
373	C₂×#405	—	47	1	no	—
374	C₂×C₄₇	—	2	2	no	—
375	C₂×C₄₇	C₂²×C₄⋊Q₈	1	1	yes	characteristic
376	C₂×C₄₇	C₂×#576	1	1	yes	characteristic
377	C₂×C₄₇	C₂×#578	1	1	yes	characteristic
378	D₄₇	—	2	2	no	—
379	D₄₇	#3164	1	4	yes	direct product factor
380	C₂²×M₁₆	—	47	1	no	—
381	C₂³×C₈	—	47	1	no	—
382	#544	—	47	4	no	—
383	#544	—	47	4	no	—
384	#544	—	47	2	no	—
385	#544	—	47	2	no	—
386	#544	—	47	2	no	—
387	#544	—	94	4	no	—
388	#544	—	94	2	no	—
389	#544	—	94	2	no	—
390	#544	C₂×D₄₇	1	2	yes	—
391	C₂×C₄⋊Q₈	—	47	4	no	—
392	C₂×C₄⋊Q₈	—	94	2	no	—
393	C₂×#125	—	47	4	no	—
394	C₂×#125	—	94	2	no	—
395	C₂×C₂²⋊Q₈	—	94	4	no	—
396	C₂×#117	—	47	1	no	—
397	C₂×#117	—	47	2	no	—
398	C₂²×C₄⋊C₄	—	47	2	no	—
399	#501	—	47	4	no	—
400	#501	—	47	4	no	—
401	#501	—	47	4	no	—
402	#501	—	47	4	no	—
403	#501	—	47	4	no	—
404	#501	—	47	4	no	—
405	#501	—	47	4	no	—
406	#501	C₂×D₄₇	1	4	yes	complemented
407	#500	—	47	4	no	—
408	#500	—	47	2	no	—
409	#500	—	47	2	no	—
410	#500	—	47	4	no	—
411	#500	—	47	2	no	—
412	#500	C₂×D₄₇	1	2	yes	complemented
413	#499	—	47	4	no	—
414	#499	—	47	2	no	—
415	#499	—	47	2	no	—
416	#499	—	47	4	no	—
417	#499	—	47	2	no	—
418	#499	C₂×D₄₇	1	2	yes	complemented
419	#428	—	47	2	no	—
420	#428	—	47	2	no	—
421	#428	—	47	2	no	—
422	#428	—	47	4	no	—
423	#428	—	47	4	no	—
424	#428	C₂×D₄₇	1	2	yes	—
425	#427	—	47	1	no	—
426	#427	—	47	2	no	—
427	#427	—	47	1	no	—
428	#427	—	47	1	no	—
429	#427	—	47	2	no	—
430	#427	C₂×D₄₇	1	1	yes	characteristic
431	C₂×#107	—	47	1	no	—
432	C₂×#107	—	47	2	no	—
433	C₂×#107	—	47	1	no	—
434	C₂×#107	—	47	2	no	—
435	C₂×#107	—	47	1	no	—
436	C₂×#107	—	47	4	no	—
437	C₂×#107	—	47	2	no	—
438	C₂×#107	—	47	2	no	—
439	C₂×#107	—	47	2	no	—
440	C₂×#107	C₂×D₄₇	1	1	yes	characteristic
441	C₂×#106	—	47	4	no	—
442	C₂×#106	—	47	2	no	—
443	#405	—	47	1	no	—
444	#405	—	47	1	no	—
445	#405	—	47	1	no	—
446	#405	—	47	2	no	—
447	#405	—	47	2	no	—
448	#405	C₂×D₄₇	1	1	yes	characteristic
449	C₂×#97	—	47	2	no	—
450	C₂×C₄×C₈	—	47	2	no	—
451	C₄₇	C₂×#3164	1	1	yes	characteristic, complemented, Sylow
452	C₂²×Q₈	—	94	4	no	—
453	C₂³×C₄	—	47	1	no	—
454	C₂³×C₄	—	94	2	no	—
455	C₂×M₁₆	—	47	1	no	—
456	C₂×M₁₆	—	47	8	no	—
457	C₂×M₁₆	—	47	2	no	—
458	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
459	C₂²×C₈	—	47	1	no	—
460	C₂²×C₈	—	47	8	no	—
461	C₂²×C₈	—	47	1	no	—
462	C₂²×C₈	—	47	1	no	—
463	C₂²×C₈	—	47	1	no	—
464	C₂²×C₈	—	47	1	no	—
465	C₂²×C₈	—	47	2	no	—
466	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
467	C₄⋊Q₈	—	2	2	no	—
468	C₄⋊Q₈	—	47	4	no	—
469	C₄⋊Q₈	—	47	4	no	—
470	C₄⋊Q₈	—	47	4	no	—
471	C₄⋊Q₈	—	94	2	no	—
472	C₄⋊Q₈	—	94	4	no	—
473	C₄⋊Q₈	—	94	4	no	—
474	C₄⋊Q₈	—	94	4	no	—
475	C₄⋊Q₈	—	94	2	no	—
476	C₄⋊Q₈	—	94	4	no	—
477	C₄⋊Q₈	—	94	2	no	—
478	C₄⋊Q₈	C₂²×D₄₇	1	4	yes	—
479	#125	—	2	2	no	—
480	#125	—	47	4	no	—
481	#125	—	47	4	no	—
482	#125	—	47	4	no	—
483	#125	—	94	2	no	—
484	#125	—	94	4	no	—
485	#125	—	94	4	no	—
486	#125	—	94	4	no	—
487	#125	—	94	4	no	—
488	#125	—	94	2	no	—
489	#125	—	94	2	no	—
490	#125	C₂²×D₄₇	1	4	yes	—
491	C₂²⋊Q₈	—	2	4	no	—
492	C₂²⋊Q₈	—	94	4	no	—
493	C₂²⋊Q₈	—	94	4	no	—
494	C₂²⋊Q₈	—	94	4	no	—
495	C₂²⋊Q₈	—	94	4	no	—
496	C₂²⋊Q₈	—	94	4	no	—
497	C₂²⋊Q₈	—	94	4	no	—
498	C₂²⋊Q₈	—	94	4	no	—
499	#117	—	47	1	no	—
500	#117	—	47	1	no	—
501	#117	—	47	1	no	—
502	#117	—	47	2	no	—
503	#117	—	47	2	no	—
504	#117	—	47	2	no	—
505	#117	—	47	2	no	—
506	#117	—	47	2	no	—
507	#117	—	94	2	no	—
508	#117	—	94	2	no	—
509	#117	C₂²×D₄₇	1	2	yes	—
510	#117	C₂²×D₄₇	1	1	yes	characteristic
511	C₂×C₄⋊C₄	—	47	1	no	—
512	C₂×C₄⋊C₄	—	47	1	no	—
513	C₂×C₄⋊C₄	—	47	2	no	—
514	C₂×C₄⋊C₄	—	47	4	no	—
515	C₂×C₄⋊C₄	—	47	4	no	—
516	C₂×C₄⋊C₄	—	47	2	no	—
517	C₂×C₄⋊C₄	—	47	2	no	—
518	C₂×C₄⋊C₄	—	94	2	no	—
519	C₂×C₄⋊C₄	—	94	2	no	—
520	C₂×C₄⋊C₄	—	94	4	no	—
521	C₂×C₄⋊C₄	—	94	4	no	—
522	C₂×C₄⋊C₄	—	94	4	no	—
523	C₂×C₄⋊C₄	—	94	2	no	—
524	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
525	C₂×C₂²⋊C₄	—	47	2	no	—
526	C₂×C₂²⋊C₄	—	94	2	no	—
527	C₂×C₄²	—	47	2	no	—
528	C₂×C₄²	—	94	2	no	—
529	#107	—	47	2	no	—
530	#107	—	47	2	no	—
531	#107	—	47	1	no	—
532	#107	—	47	1	no	—
533	#107	—	47	4	no	—
534	#107	—	47	4	no	—
535	#107	—	47	4	no	—
536	#107	—	47	2	no	—
537	#107	—	47	2	no	—
538	#107	—	47	4	no	—
539	#107	—	47	4	no	—
540	#107	C₂²×D₄₇	1	2	yes	—
541	#107	C₂²×D₄₇	1	2	yes	—
542	#107	C₂²×D₄₇	1	1	yes	characteristic
543	#107	C₂²×D₄₇	1	1	yes	characteristic
544	#107	C₂²×D₄₇	1	4	yes	—
545	#106	—	47	2	no	—
546	#106	—	47	4	no	—
547	#106	—	47	2	no	—
548	#106	—	47	2	no	—
549	#106	—	47	4	no	—
550	#106	—	47	4	no	—
551	#106	C₂²×D₄₇	1	2	yes	—
552	#106	C₂²×D₄₇	1	4	yes	—
553	#97	—	47	2	no	—
554	#97	—	47	2	no	—
555	#97	—	47	2	no	—
556	#97	C₂²×D₄₇	1	2	yes	—
557	C₄×C₈	—	47	2	no	—
558	C₄×C₈	—	47	2	no	—
559	C₄×C₈	—	47	2	no	—
560	C₄×C₈	C₂²×D₄₇	1	2	yes	—
561	C₂⁴	—	47	1	no	—
562	C₂×Q₈	—	2	4	no	—
563	C₂×Q₈	—	94	4	no	—
564	C₂×Q₈	—	94	4	no	—
565	C₂×Q₈	—	94	4	no	—
566	C₂×Q₈	—	376	8	no	—
567	C₂²×C₄	—	2	2	no	—
568	C₂²×C₄	—	47	1	no	—
569	C₂²×C₄	—	47	1	no	—
570	C₂²×C₄	—	47	1	no	—
571	C₂²×C₄	—	47	4	no	—
572	C₂²×C₄	—	47	4	no	—
573	C₂²×C₄	—	47	1	no	—
574	C₂²×C₄	—	47	1	no	—
575	C₂²×C₄	—	47	2	no	—
576	C₂²×C₄	—	47	2	no	—
577	C₂²×C₄	—	94	4	no	—
578	C₂²×C₄	—	94	2	no	—
579	C₂²×C₄	—	94	2	no	—
580	C₂²×C₄	—	94	4	no	—
581	C₂²×C₄	—	94	2	no	—
582	C₂²×C₄	—	376	4	no	—
583	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
584	M₁₆	—	47	4	no	—
585	M₁₆	—	47	8	no	—
586	M₁₆	Q₈×D₄₇	1	4	yes	complemented
587	C₂×C₈	—	47	4	no	—
588	C₂×C₈	—	47	1	no	—
589	C₂×C₈	—	47	2	no	—
590	C₂×C₈	—	47	1	no	—
591	C₂×C₈	—	47	4	no	—
592	C₂×C₈	—	47	4	no	—
593	C₂×C₈	—	47	8	no	—
594	C₂×C₈	—	47	4	no	—
595	C₂×C₈	—	47	4	no	—
596	C₂×C₈	Q₈×D₄₇	1	4	yes	complemented
597	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
598	C₂×C₈	C₂³×D₄₇	1	2	yes	—
599	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
600	C₄⋊C₄	—	2	2	no	—
601	C₄⋊C₄	—	2	4	no	—
602	C₄⋊C₄	—	2	4	no	—
603	C₄⋊C₄	—	2	4	no	—
604	C₄⋊C₄	—	47	2	no	—
605	C₄⋊C₄	—	47	2	no	—
606	C₄⋊C₄	—	47	1	no	—
607	C₄⋊C₄	—	47	1	no	—
608	C₄⋊C₄	—	47	2	no	—
609	C₄⋊C₄	—	47	4	no	—
610	C₄⋊C₄	—	47	2	no	—
611	C₄⋊C₄	—	94	4	no	—
612	C₄⋊C₄	—	94	4	no	—
613	C₄⋊C₄	—	94	2	no	—
614	C₄⋊C₄	—	94	2	no	—
615	C₄⋊C₄	—	94	4	no	—
616	C₄⋊C₄	—	94	4	no	—
617	C₄⋊C₄	—	94	4	no	—
618	C₄⋊C₄	—	94	4	no	—
619	C₄⋊C₄	—	94	4	no	—
620	C₄⋊C₄	—	94	4	no	—
621	C₄⋊C₄	—	94	4	no	—
622	C₄⋊C₄	—	94	4	no	—
623	C₄⋊C₄	—	94	2	no	—
624	C₄⋊C₄	—	94	4	no	—
625	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
626	C₄⋊C₄	D₄×D₄₇	1	1	yes	characteristic
627	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
628	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
629	C₄⋊C₄	C₂³×D₄₇	1	2	yes	—
630	C₂²⋊C₄	—	2	2	no	—
631	C₂²⋊C₄	—	47	2	no	—
632	C₂²⋊C₄	—	47	2	no	—
633	C₂²⋊C₄	—	47	2	no	—
634	C₂²⋊C₄	—	94	2	no	—
635	C₂²⋊C₄	—	94	2	no	—
636	C₂²⋊C₄	—	94	2	no	—
637	C₂²⋊C₄	D₄×D₄₇	1	2	yes	—
638	C₄²	—	2	2	no	—
639	C₄²	—	47	2	no	—
640	C₄²	—	47	2	no	—
641	C₄²	—	47	2	no	—
642	C₄²	—	94	2	no	—
643	C₄²	—	94	2	no	—
644	C₄²	—	94	2	no	—
645	C₄²	C₂³×D₄₇	1	2	yes	—
646	C₂³	—	47	1	no	—
647	C₂³	—	47	4	no	—
648	C₂³	—	47	1	no	—
649	C₂³	—	94	2	no	—
650	C₂³	—	94	2	no	—
651	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
652	Q₈	—	8	4	no	—
653	Q₈	—	376	4	no	—
654	Q₈	—	376	4	no	—
655	Q₈	—	376	4	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	4	no	—
659	C₂×C₄	—	8	2	no	—
660	C₂×C₄	—	47	4	no	—
661	C₂×C₄	—	47	1	no	—
662	C₂×C₄	—	47	1	no	—
663	C₂×C₄	—	47	4	no	—
664	C₂×C₄	—	47	4	no	—
665	C₂×C₄	—	47	2	no	—
666	C₂×C₄	—	47	2	no	—
667	C₂×C₄	—	47	2	no	—
668	C₂×C₄	—	47	2	no	—
669	C₂×C₄	—	47	2	no	—
670	C₂×C₄	—	47	2	no	—
671	C₂×C₄	—	94	4	no	—
672	C₂×C₄	—	94	4	no	—
673	C₂×C₄	—	94	2	no	—
674	C₂×C₄	—	94	2	no	—
675	C₂×C₄	—	94	4	no	—
676	C₂×C₄	—	376	4	no	—
677	C₂×C₄	—	376	2	no	—
678	C₂×C₄	—	188	4	no	—
679	C₂×C₄	—	188	8	no	—
680	C₂×C₄	—	188	4	no	—
681	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
682	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
683	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
684	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
685	C₂×C₄	C₂×Q₈×D₄₇	1	2	yes	—
686	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
687	C₈	—	47	2	no	—
688	C₈	—	47	2	no	—
689	C₈	—	47	4	no	—
690	C₈	C₂×Q₈×D₄₇	1	2	yes	—
691	C₈	C₂×Q₈×D₄₇	1	2	yes	—
692	C₈	C₂×Q₈×D₄₇	1	4	yes	—
693	C₂²	—	2	1	no	—
694	C₂²	—	2	1	no	—
695	C₂²	—	47	2	no	—
696	C₂²	—	47	2	no	—
697	C₂²	—	47	2	no	—
698	C₂²	—	47	2	no	—
699	C₂²	—	94	8	no	—
700	C₂²	—	94	1	no	—
701	C₂²	—	94	1	no	—
702	C₂²	C₄⋊Q₈×D₄₇	1	2	yes	—
703	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
704	C₄	—	2	2	no	—
705	C₄	—	2	2	no	—
706	C₄	—	4	4	no	—
707	C₄	—	4	2	no	—
708	C₄	—	4	2	no	—
709	C₄	—	47	2	no	—
710	C₄	—	47	2	no	—
711	C₄	—	94	2	no	—
712	C₄	—	94	2	no	—
713	C₄	—	188	4	no	—
714	C₄	—	188	2	no	—
715	C₄	—	188	2	no	—
716	C₄	C₄⋊Q₈×D₄₇	1	2	yes	—
717	C₄	C₂²×Q₈×D₄₇	1	1	yes	characteristic
718	C₄	C₂²×Q₈×D₄₇	1	1	yes	characteristic
719	C₂	—	2	2	no	—
720	C₂	—	47	4	no	—
721	C₂	—	94	2	no	—
722	C₂	C₂×C₄⋊Q₈×D₄₇	1	1	yes	characteristic
723	C₂	#576×D₄₇	1	1	yes	characteristic
724	C₂	#578×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3164	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	C₂³×D₄₇	C₂×D₄
hypercenter	#3164	D₄₇
hypocenter	C₄₇	C₂×#3164
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3164

Complements

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

N	H ≅ G/N	type
2. #20253928	C₂	semidirect
3. #20253927	C₂	semidirect
4. #20253926	C₂	semidirect
5. #20253925	C₂	semidirect
6. #20253924	C₂	semidirect
7. #20253923	C₂	semidirect
8. #20253922	C₂	semidirect
9. #20253921	C₂	semidirect
10. #501×D₄₇	C₂	semidirect
11. #500×D₄₇	C₂	semidirect
12. #499×D₄₇	C₂	semidirect
17. C₄₇×#3164	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. #15689528	C₂²	semidirect
44. #15689527	C₂²	semidirect
45. #15689527	C₂²	semidirect
46. #15689527	C₂²	semidirect
47. #15689526	C₂²	semidirect
48. #15689525	C₂²	semidirect
49. #15689524	C₂²	semidirect
50. #15689524	C₂²	semidirect
51. #15689523	C₂²	semidirect
52. #15689522	C₂²	semidirect
82. C₄₇×#501	C₂²	semidirect
83. C₄₇×#500	C₂²	semidirect
84. C₄₇×#499	C₂²	semidirect
94. M₁₆×D₄₇	Q₈	semidirect
96. C₂×C₈×D₄₇	Q₈	semidirect
221. M₁₆×C₄₇	C₂×Q₈	semidirect
222. C₂×C₈×C₄₇	C₂×Q₈	semidirect
272. #10625329	C₂×Q₈	semidirect
273. C₂×C₄₇⋊C₈	C₂×Q₈	semidirect
277. #10625324	C₂×Q₈	semidirect
281. C₈×D₄₇	C₂×Q₈	semidirect
282. C₈×D₄₇	C₂×Q₈	semidirect
366. #3164	D₄₇	direct (N × H)
379. D₄₇	#3164	direct (N × H)
406. #501	C₂×D₄₇	semidirect
412. #500	C₂×D₄₇	semidirect
418. #499	C₂×D₄₇	semidirect
451. C₄₇	C₂×#3164	semidirect
586. M₁₆	Q₈×D₄₇	semidirect
596. 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
#20253928	2
#20253927	2
#20253926	2
#20253925	2
#20253924	2
#20253923	2
#20253922	2
#20253921	2
#501×D₄₇	2
#500×D₄₇	2
#499×D₄₇	2
#428×D₄₇	2
#427×D₄₇	2
C₂×#107×D₄₇	2
#405×D₄₇	2
C₄₇×#3164	2
C₂×#3164	47

Subgroups — D47×#3164 #27085904

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#3164 #27085904