Subgroups — #538×D₄₇ #20256722

Order 6016.

1336 conjugacy classes of subgroups.

The subgroup lattice has 658 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689713	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689712	C₂	1	2	yes	maximal, complemented
3	#15689711	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689710	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689709	C₂	1	2	yes	maximal, complemented
6	#15689708	C₂	1	2	yes	maximal, complemented
7	#15689707	C₂	1	2	yes	maximal, complemented
8	#15689706	C₂	1	2	yes	maximal, complemented
9	#15689705	C₂	1	2	yes	maximal, complemented
10	#126×D₄₇	C₂	1	2	yes	maximal, complemented
11	#124×D₄₇	C₂	1	2	yes	maximal, complemented
12	#123×D₄₇	C₂	1	2	yes	maximal, complemented
13	C₂²⋊Q₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
14	#121×D₄₇	C₂	1	2	yes	maximal, complemented
15	#121×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
16	#120×D₄₇	C₂	1	2	yes	maximal, complemented
17	C₄×D₄×D₄₇	C₂	1	2	yes	maximal, complemented
18	C₂×C₂²⋊C₄×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₇×#538	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂⁴×D₄₇	C₂²	1	1	yes	characteristic
21	C₂×Q₈×D₄₇	C₂²	1	1	yes	characteristic, complemented
22	C₂×D₄×D₄₇	C₂²	1	2	yes	—
23	C₂×D₄×D₄₇	C₂²	1	2	yes	—
24	C₂×D₄×D₄₇	C₂²	1	2	yes	—
25	C₂×D₄×D₄₇	C₂²	1	1	yes	characteristic, complemented
26	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
28	C₂²×C₄×D₄₇	C₂²	1	2	yes	complemented
29	#13094019	C₂²	1	2	yes	complemented
30	#13094019	C₂²	1	2	yes	complemented
31	#13094019	C₂²	1	2	yes	complemented
32	#13094018	C₂²	1	2	yes	complemented
33	#13094017	C₂²	1	2	yes	complemented
34	#13094017	C₂²	1	2	yes	complemented
35	#13094017	C₂²	1	2	yes	complemented
36	#13094013	C₂²	1	2	yes	complemented
37	#13094012	C₂²	1	2	yes	complemented
38	#13094011	C₂²	1	2	yes	complemented
39	#13094010	C₂²	1	2	yes	complemented
40	#13094010	C₂²	1	2	yes	complemented
41	#13094010	C₂²	1	2	yes	complemented
42	#13094010	C₂²	1	2	yes	complemented
43	#13094009	C₂²	1	2	yes	complemented
44	#13094009	C₂²	1	2	yes	complemented
45	#13094008	C₂²	1	2	yes	complemented
46	#13094007	C₂²	1	2	yes	complemented
47	#13094006	C₂²	1	2	yes	complemented
48	#13094006	C₂²	1	2	yes	complemented
49	#13094005	C₂²	1	2	yes	complemented
50	#13094004	C₂²	1	1	yes	characteristic, complemented
51	#13094003	C₂²	1	1	yes	characteristic, complemented
52	#13094002	C₂²	1	2	yes	complemented
53	#13094001	C₂²	1	2	yes	complemented
54	#13094000	C₂²	1	1	yes	characteristic, complemented
55	#13093999	C₂²	1	2	yes	complemented
56	#13093999	C₂²	1	1	yes	characteristic, complemented
57	#13093998	C₂²	1	2	yes	complemented
58	#13093998	C₂²	1	1	yes	characteristic, complemented
59	#13093997	C₂²	1	2	yes	complemented
60	#13093997	C₂²	1	2	yes	complemented
61	#13093997	C₂²	1	2	yes	complemented
62	#13093996	C₂²	1	2	yes	complemented
63	#13093996	C₂²	1	2	yes	complemented
64	#13093996	C₂²	1	2	yes	complemented
65	#13093995	C₂²	1	2	yes	complemented
66	#13093995	C₂²	1	1	yes	characteristic, complemented
67	#13093994	C₂²	1	2	yes	complemented
68	#13093994	C₂²	1	2	yes	complemented
69	#13093994	C₂²	1	2	yes	complemented
70	#13093993	C₂²	1	2	yes	complemented
71	#13093992	C₂²	1	2	yes	complemented
72	#13093992	C₂²	1	2	yes	complemented
73	#13093992	C₂²	1	2	yes	complemented
74	C₄×D₁₈₈	C₂²	1	2	yes	complemented
75	D₄×Dic₄₇	C₂²	1	2	yes	complemented
76	#13093986	C₂²	1	2	yes	complemented
77	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
78	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
79	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
80	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
81	C₄⋊C₄×D₄₇	C₂²	1	2	yes	complemented
82	C₄⋊C₄×D₄₇	C₂²	1	2	yes	complemented
83	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic, complemented
84	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic, complemented
85	C₂×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
86	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
87	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic, complemented
88	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
89	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
90	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
91	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
92	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
93	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	complemented
94	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	complemented
95	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	complemented
96	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	complemented
97	C₄²×D₄₇	C₂²	1	2	yes	complemented
98	#126×C₄₇	C₂²	1	2	yes	complemented
99	#124×C₄₇	C₂²	1	2	yes	complemented
100	#123×C₄₇	C₂²	1	2	yes	complemented
101	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
102	#121×C₄₇	C₂²	1	2	yes	complemented
103	#121×C₄₇	C₂²	1	1	yes	characteristic, complemented
104	#120×C₄₇	C₂²	1	2	yes	complemented
105	C₄×D₄×C₄₇	C₂²	1	2	yes	complemented
106	C₂×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
107	C₂⁴×C₄₇	C₂³	1	1	yes	characteristic
108	C₂³×D₄₇	—	2	4	no	—
109	C₂³×D₄₇	—	4	2	no	—
110	C₂³×D₄₇	—	4	2	no	—
111	C₂³×D₄₇	C₂³	1	2	yes	—
112	C₂³×D₄₇	C₂³	1	2	yes	—
113	C₂³×D₄₇	C₂³	1	1	yes	characteristic
114	C₂³×D₄₇	C₂³	1	2	yes	—
115	C₂³×D₄₇	C₂³	1	1	yes	characteristic
116	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic, complemented
117	C₂×D₄×C₄₇	C₂³	1	2	yes	—
118	C₂×D₄×C₄₇	C₂³	1	2	yes	—
119	C₂×D₄×C₄₇	C₂³	1	2	yes	—
120	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic, complemented
121	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂³	1	2	yes	complemented
124	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
125	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
126	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
127	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
128	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
130	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	complemented
131	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
132	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
133	C₂²×Dic₄₇	C₂³	1	2	yes	complemented
134	Q₈×D₄₇	—	4	2	no	—
135	D₄×D₄₇	—	2	8	no	—
136	D₄×D₄₇	—	4	4	no	—
137	D₄×D₄₇	—	4	4	no	—
138	D₄×D₄₇	—	4	2	no	—
139	C₂×D₁₈₈	C₂³	1	2	yes	—
140	C₂×D₁₈₈	C₂³	1	2	yes	—
141	C₂×D₁₈₈	C₂³	1	2	yes	—
142	C₂×D₁₈₈	C₂³	1	1	yes	characteristic, complemented
143	C₂×C₄×D₄₇	—	4	2	no	—
144	C₂×C₄×D₄₇	—	4	2	no	—
145	C₂×C₄×D₄₇	—	4	4	no	—
146	C₂×C₄×D₄₇	C₂³	1	2	yes	—
147	C₂×C₄×D₄₇	C₂³	1	2	yes	—
148	C₂×C₄×D₄₇	C₂³	1	2	yes	—
149	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
150	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
151	C₂×C₄×D₄₇	C₂³	1	2	yes	—
152	C₂×C₄×D₄₇	C₂³	1	2	yes	—
153	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
154	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
155	C₂×C₄×D₄₇	C₂³	1	2	yes	complemented
156	C₂×C₄×D₄₇	C₂³	1	2	yes	complemented
157	C₂×Dic₉₄	C₂³	1	2	yes	complemented
158	C₂×Dic₉₄	C₂³	1	1	yes	characteristic, complemented
159	C₄⋊C₄×C₄₇	C₂³	1	2	yes	complemented
160	C₄⋊C₄×C₄₇	C₂³	1	2	yes	complemented
161	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic, complemented
162	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic, complemented
163	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
165	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
166	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
167	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	complemented
169	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	complemented
170	C₄²×C₄₇	C₂³	1	2	yes	complemented
171	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
172	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
173	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
174	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
175	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
176	C₂²⋊Dic₄₇	C₂³	1	2	yes	complemented
177	C₂²⋊Dic₄₇	C₂³	1	2	yes	complemented
178	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
179	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
180	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
181	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
182	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
183	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
184	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
186	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	complemented
189	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	complemented
190	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	complemented
191	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	complemented
192	C₄⋊Dic₄₇	C₂³	1	2	yes	complemented
193	C₄⋊Dic₄₇	C₂³	1	2	yes	complemented
194	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic, complemented
195	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic, complemented
196	Dic₄₇⋊C₄	C₂³	1	2	yes	complemented
197	Dic₄₇⋊C₄	C₂³	1	2	yes	complemented
198	Dic₄₇⋊C₄	C₂³	1	2	yes	complemented
199	Dic₄₇⋊C₄	C₂³	1	2	yes	complemented
200	Dic₄₇⋊C₄	C₂³	1	2	yes	complemented
201	Dic₄₇⋊C₄	C₂³	1	2	yes	complemented
202	C₄×Dic₄₇	C₂³	1	2	yes	complemented
203	C₄×Dic₄₇	C₂³	1	2	yes	complemented
204	C₄×Dic₄₇	C₂³	1	2	yes	complemented
205	C₂³×C₄₇	—	2	2	no	—
206	C₂³×C₄₇	—	4	1	no	—
207	C₂³×C₄₇	—	4	1	no	—
208	C₂³×C₄₇	C₂⁴	1	2	yes	—
209	C₂³×C₄₇	C₂⁴	1	2	yes	—
210	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
211	C₂²×D₄₇	—	2	2	no	—
212	C₂²×D₄₇	—	2	2	no	—
213	C₂²×D₄₇	—	2	2	no	—
214	C₂²×D₄₇	—	2	4	no	—
215	C₂²×D₄₇	—	2	4	no	—
216	C₂²×D₄₇	—	2	4	no	—
217	C₂²×D₄₇	—	2	4	no	—
218	C₂²×D₄₇	—	2	4	no	—
219	C₂²×D₄₇	—	2	4	no	—
220	C₂²×D₄₇	—	2	4	no	—
221	C₂²×D₄₇	—	4	2	no	—
222	C₂²×D₄₇	—	4	2	no	—
223	C₂²×D₄₇	—	4	1	no	—
224	C₂²×D₄₇	—	4	1	no	—
225	C₂²×D₄₇	—	4	16	no	—
226	C₂²×D₄₇	#41	1	4	yes	—
227	C₂²×D₄₇	C₂⁴	1	2	yes	—
228	C₂²×D₄₇	C₂⁴	1	2	yes	—
229	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
230	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
231	Q₈×C₄₇	—	4	1	no	—
232	D₄×C₄₇	—	2	4	no	—
233	D₄×C₄₇	—	4	2	no	—
234	D₄×C₄₇	—	4	2	no	—
235	D₄×C₄₇	—	4	1	no	—
236	C₂×C₄×C₄₇	—	4	1	no	—
237	C₂×C₄×C₄₇	—	4	1	no	—
238	C₂×C₄×C₄₇	—	4	2	no	—
239	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
240	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
241	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
242	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
243	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
244	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
245	C₂²⋊D₄₇	—	2	4	no	—
246	C₂²⋊D₄₇	—	2	4	no	—
247	C₂²⋊D₄₇	—	4	2	no	—
248	C₂²⋊D₄₇	—	4	2	no	—
249	C₂²⋊D₄₇	—	4	2	no	—
250	C₂²⋊D₄₇	—	4	2	no	—
251	C₂²⋊D₄₇	—	4	2	no	—
252	C₂×Dic₄₇	—	4	1	no	—
253	C₂×Dic₄₇	—	4	1	no	—
254	C₂×Dic₄₇	—	4	2	no	—
255	C₂×Dic₄₇	C₂⁴	1	2	yes	—
256	C₂×Dic₄₇	C₂⁴	1	2	yes	—
257	C₂×Dic₄₇	C₂⁴	1	2	yes	—
258	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
259	C₂×Dic₄₇	C₂⁴	1	2	yes	—
260	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
261	D₁₈₈	—	2	4	no	—
262	D₁₈₈	—	4	2	no	—
263	D₁₈₈	—	4	2	no	—
264	D₁₈₈	—	4	1	no	—
265	C₄×D₄₇	—	2	4	no	—
266	C₄×D₄₇	—	2	4	no	—
267	C₄×D₄₇	—	2	2	no	—
268	C₄×D₄₇	—	2	4	no	—
269	C₄×D₄₇	—	2	2	no	—
270	C₄×D₄₇	—	2	4	no	—
271	C₄×D₄₇	—	4	1	no	—
272	C₄×D₄₇	—	4	2	no	—
273	C₄×D₄₇	—	4	1	no	—
274	C₄×D₄₇	—	4	2	no	—
275	C₄×D₄₇	—	4	2	no	—
276	Dic₉₄	—	4	2	no	—
277	Dic₉₄	—	4	1	no	—
278	C₂²×C₄₇	—	2	1	no	—
279	C₂²×C₄₇	—	2	1	no	—
280	C₂²×C₄₇	—	2	2	no	—
281	C₂²×C₄₇	—	2	2	no	—
282	C₂²×C₄₇	—	2	2	no	—
283	C₂²×C₄₇	—	2	2	no	—
284	C₂²×C₄₇	—	2	2	no	—
285	C₂²×C₄₇	—	2	2	no	—
286	C₂²×C₄₇	—	4	4	no	—
287	C₂²×C₄₇	C₂×#41	1	2	yes	—
288	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
289	C₂×D₄₇	—	2	1	no	—
290	C₂×D₄₇	—	2	1	no	—
291	C₂×D₄₇	—	2	8	no	—
292	C₂×D₄₇	—	2	2	no	—
293	C₂×D₄₇	—	2	2	no	—
294	C₂×D₄₇	—	2	2	no	—
295	C₂×D₄₇	—	2	2	no	—
296	C₂×D₄₇	—	2	2	no	—
297	C₂×D₄₇	—	2	2	no	—
298	C₂×D₄₇	—	4	8	no	—
299	C₂×D₄₇	—	4	4	no	—
300	C₂×D₄₇	—	4	8	no	—
301	C₂×D₄₇	—	4	8	no	—
302	C₂×D₄₇	C₂×#41	1	2	yes	—
303	C₂×D₄₇	C₂×#41	1	2	yes	—
304	C₂×D₄₇	H(5,𝔽₂)	1	2	yes	—
305	C₂×D₄₇	H(5,𝔽₂)	1	2	yes	—
306	C₄×C₄₇	—	2	2	no	—
307	C₄×C₄₇	—	2	1	no	—
308	C₄×C₄₇	—	2	2	no	—
309	C₄×C₄₇	—	2	2	no	—
310	C₄×C₄₇	—	2	1	no	—
311	C₄×C₄₇	—	2	2	no	—
312	Dic₄₇	—	2	2	no	—
313	Dic₄₇	—	2	1	no	—
314	Dic₄₇	—	2	2	no	—
315	Dic₄₇	—	2	2	no	—
316	Dic₄₇	—	2	1	no	—
317	Dic₄₇	—	2	2	no	—
318	C₂×#538	—	47	1	no	maximal, Sylow
319	C₂×C₄₇	—	2	2	no	—
320	C₂×C₄₇	—	4	2	no	—
321	C₂×C₄₇	—	4	2	no	—
322	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
323	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
324	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
325	D₄₇	—	2	2	no	—
326	D₄₇	—	4	2	no	—
327	D₄₇	—	4	2	no	—
328	D₄₇	#538	1	4	yes	direct product factor
329	#538	—	47	2	no	—
330	#538	—	47	2	no	—
331	#538	—	47	2	no	—
332	#538	—	47	1	no	—
333	#538	—	47	2	no	—
334	#538	—	47	1	no	—
335	#538	—	47	2	no	—
336	#538	—	47	2	no	—
337	#538	—	47	1	no	—
338	#538	D₄₇	1	1	yes	characteristic, direct product factor
339	C₂×#126	—	47	2	no	—
340	C₂×#124	—	47	2	no	—
341	C₂×#123	—	47	2	no	—
342	C₂×C₂²⋊Q₈	—	47	1	no	—
343	C₂×#121	—	47	2	no	—
344	C₂×#121	—	47	1	no	—
345	C₂×#120	—	47	2	no	—
346	C₂×C₄×D₄	—	47	2	no	—
347	C₂²×C₂²⋊C₄	—	47	1	no	—
348	C₄₇	C₂×#538	1	1	yes	characteristic, complemented, Sylow
349	C₂⁵	—	47	1	no	—
350	C₂²×Q₈	—	47	1	no	—
351	C₂²×D₄	—	47	2	no	—
352	C₂²×D₄	—	47	2	no	—
353	C₂²×D₄	—	47	2	no	—
354	C₂²×D₄	—	47	1	no	—
355	C₂³×C₄	—	47	1	no	—
356	C₂³×C₄	—	47	1	no	—
357	C₂³×C₄	—	47	2	no	—
358	#126	—	47	2	no	—
359	#126	—	47	2	no	—
360	#126	—	47	2	no	—
361	#126	—	47	2	no	—
362	#126	—	47	2	no	—
363	#126	—	47	2	no	—
364	#126	—	47	2	no	—
365	#126	C₂×D₄₇	1	2	yes	complemented
366	#124	—	47	2	no	—
367	#124	—	47	2	no	—
368	#124	—	47	2	no	—
369	#124	—	47	2	no	—
370	#124	—	47	2	no	—
371	#124	—	47	2	no	—
372	#124	—	47	2	no	—
373	#124	C₂×D₄₇	1	2	yes	complemented
374	#123	—	47	2	no	—
375	#123	—	47	2	no	—
376	#123	—	47	2	no	—
377	#123	—	47	2	no	—
378	#123	—	47	2	no	—
379	#123	—	47	2	no	—
380	#123	—	47	2	no	—
381	#123	C₂×D₄₇	1	2	yes	complemented
382	C₂²⋊Q₈	—	47	1	no	—
383	C₂²⋊Q₈	—	47	1	no	—
384	C₂²⋊Q₈	—	47	2	no	—
385	C₂²⋊Q₈	—	47	1	no	—
386	C₂²⋊Q₈	—	47	2	no	—
387	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
388	#121	—	47	2	no	—
389	#121	—	47	2	no	—
390	#121	—	47	2	no	—
391	#121	—	47	1	no	—
392	#121	—	47	2	no	—
393	#121	—	47	1	no	—
394	#121	—	47	2	no	—
395	#121	—	47	2	no	—
396	#121	—	47	1	no	—
397	#121	—	47	2	no	—
398	#121	—	47	2	no	—
399	#121	—	47	2	no	—
400	#121	C₂×D₄₇	1	2	yes	complemented
401	#121	C₂×D₄₇	1	1	yes	characteristic, complemented
402	#120	—	47	2	no	—
403	#120	—	47	2	no	—
404	#120	—	47	2	no	—
405	#120	—	47	2	no	—
406	#120	—	47	2	no	—
407	#120	—	47	2	no	—
408	#120	—	47	2	no	—
409	#120	C₂×D₄₇	1	2	yes	complemented
410	C₄×D₄	—	47	2	no	—
411	C₄×D₄	—	47	2	no	—
412	C₄×D₄	—	47	2	no	—
413	C₄×D₄	—	47	2	no	—
414	C₄×D₄	—	47	2	no	—
415	C₄×D₄	—	47	2	no	—
416	C₄×D₄	—	47	2	no	—
417	C₄×D₄	C₂×D₄₇	1	2	yes	complemented
418	C₂×C₄⋊C₄	—	47	2	no	—
419	C₂×C₄⋊C₄	—	47	2	no	—
420	C₂×C₄⋊C₄	—	47	1	no	—
421	C₂×C₄⋊C₄	—	47	1	no	—
422	C₂×C₂²⋊C₄	—	47	1	no	—
423	C₂×C₂²⋊C₄	—	47	1	no	—
424	C₂×C₂²⋊C₄	—	47	1	no	—
425	C₂×C₂²⋊C₄	—	47	2	no	—
426	C₂×C₂²⋊C₄	—	47	2	no	—
427	C₂×C₂²⋊C₄	—	47	2	no	—
428	C₂×C₂²⋊C₄	—	47	2	no	—
429	C₂×C₂²⋊C₄	—	47	2	no	—
430	C₂×C₂²⋊C₄	—	47	2	no	—
431	C₂×C₂²⋊C₄	—	47	2	no	—
432	C₂×C₂²⋊C₄	—	47	2	no	—
433	C₂×C₂²⋊C₄	—	47	2	no	—
434	C₂×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic, complemented
435	C₂×C₄²	—	47	2	no	—
436	C₂⁴	—	47	1	no	—
437	C₂⁴	—	47	2	no	—
438	C₂⁴	—	47	2	no	—
439	C₂⁴	—	47	2	no	—
440	C₂⁴	—	47	1	no	—
441	C₂⁴	—	94	4	no	—
442	C₂⁴	—	188	2	no	—
443	C₂⁴	—	188	2	no	—
444	C₂⁴	C₂²×D₄₇	1	1	yes	characteristic
445	C₂×Q₈	—	47	1	no	—
446	C₂×Q₈	—	47	2	no	—
447	C₂×Q₈	—	188	2	no	—
448	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic, complemented
449	C₂×D₄	—	47	2	no	—
450	C₂×D₄	—	47	2	no	—
451	C₂×D₄	—	47	2	no	—
452	C₂×D₄	—	47	2	no	—
453	C₂×D₄	—	47	2	no	—
454	C₂×D₄	—	47	2	no	—
455	C₂×D₄	—	47	2	no	—
456	C₂×D₄	—	47	2	no	—
457	C₂×D₄	—	47	2	no	—
458	C₂×D₄	—	47	2	no	—
459	C₂×D₄	—	47	1	no	—
460	C₂×D₄	—	94	8	no	—
461	C₂×D₄	—	188	4	no	—
462	C₂×D₄	—	188	2	no	—
463	C₂×D₄	—	188	4	no	—
464	C₂×D₄	C₂²×D₄₇	1	2	yes	—
465	C₂×D₄	C₂²×D₄₇	1	2	yes	—
466	C₂×D₄	C₂²×D₄₇	1	2	yes	—
467	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic, complemented
468	C₂²×C₄	—	47	1	no	—
469	C₂²×C₄	—	47	1	no	—
470	C₂²×C₄	—	47	2	no	—
471	C₂²×C₄	—	47	2	no	—
472	C₂²×C₄	—	47	2	no	—
473	C₂²×C₄	—	47	2	no	—
474	C₂²×C₄	—	47	1	no	—
475	C₂²×C₄	—	47	1	no	—
476	C₂²×C₄	—	47	2	no	—
477	C₂²×C₄	—	47	2	no	—
478	C₂²×C₄	—	47	1	no	—
479	C₂²×C₄	—	47	1	no	—
480	C₂²×C₄	—	47	2	no	—
481	C₂²×C₄	—	47	2	no	—
482	C₂²×C₄	—	188	2	no	—
483	C₂²×C₄	—	188	2	no	—
484	C₂²×C₄	—	188	4	no	—
485	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
486	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
487	C₂²×C₄	C₂²×D₄₇	1	2	yes	complemented
488	C₄⋊C₄	—	47	2	no	—
489	C₄⋊C₄	—	47	2	no	—
490	C₄⋊C₄	—	47	2	no	—
491	C₄⋊C₄	—	47	2	no	—
492	C₄⋊C₄	—	47	2	no	—
493	C₄⋊C₄	—	47	2	no	—
494	C₄⋊C₄	—	47	2	no	—
495	C₄⋊C₄	—	47	2	no	—
496	C₄⋊C₄	—	47	1	no	—
497	C₄⋊C₄	—	47	1	no	—
498	C₄⋊C₄	C₂²×D₄₇	1	2	yes	complemented
499	C₄⋊C₄	C₂²×D₄₇	1	2	yes	complemented
500	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic, complemented
501	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic, complemented
502	C₂²⋊C₄	—	47	2	no	—
503	C₂²⋊C₄	—	47	2	no	—
504	C₂²⋊C₄	—	47	2	no	—
505	C₂²⋊C₄	—	47	2	no	—
506	C₂²⋊C₄	—	47	2	no	—
507	C₂²⋊C₄	—	47	2	no	—
508	C₂²⋊C₄	—	47	2	no	—
509	C₂²⋊C₄	—	47	2	no	—
510	C₂²⋊C₄	—	47	2	no	—
511	C₂²⋊C₄	—	47	2	no	—
512	C₂²⋊C₄	—	47	2	no	—
513	C₂²⋊C₄	—	47	2	no	—
514	C₂²⋊C₄	—	47	2	no	—
515	C₂²⋊C₄	—	47	2	no	—
516	C₂²⋊C₄	—	47	2	no	—
517	C₂²⋊C₄	—	47	2	no	—
518	C₂²⋊C₄	—	47	2	no	—
519	C₂²⋊C₄	—	47	2	no	—
520	C₂²⋊C₄	—	47	2	no	—
521	C₂²⋊C₄	—	47	2	no	—
522	C₂²⋊C₄	—	47	2	no	—
523	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
524	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
525	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
526	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
527	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
528	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	complemented
529	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	complemented
530	C₄²	—	47	2	no	—
531	C₄²	—	47	2	no	—
532	C₄²	—	47	2	no	—
533	C₄²	C₂²×D₄₇	1	2	yes	complemented
534	C₂³	—	2	2	no	—
535	C₂³	—	4	1	no	—
536	C₂³	—	4	1	no	—
537	C₂³	—	47	1	no	—
538	C₂³	—	47	4	no	—
539	C₂³	—	47	1	no	—
540	C₂³	—	47	2	no	—
541	C₂³	—	47	2	no	—
542	C₂³	—	94	2	no	—
543	C₂³	—	94	2	no	—
544	C₂³	—	94	4	no	—
545	C₂³	—	94	4	no	—
546	C₂³	—	94	4	no	—
547	C₂³	—	94	4	no	—
548	C₂³	—	94	4	no	—
549	C₂³	—	94	4	no	—
550	C₂³	—	94	4	no	—
551	C₂³	—	94	2	no	—
552	C₂³	—	188	1	no	—
553	C₂³	—	188	1	no	—
554	C₂³	—	188	2	no	—
555	C₂³	—	188	2	no	—
556	C₂³	—	188	16	no	—
557	C₂³	C₂³×D₄₇	1	2	yes	—
558	C₂³	C₂³×D₄₇	1	2	yes	—
559	C₂³	C₂³×D₄₇	1	1	yes	characteristic
560	Q₈	—	4	1	no	—
561	Q₈	—	188	1	no	—
562	Q₈	—	188	2	no	—
563	D₄	—	2	4	no	—
564	D₄	—	4	2	no	—
565	D₄	—	4	2	no	—
566	D₄	—	4	1	no	—
567	D₄	—	94	4	no	—
568	D₄	—	94	4	no	—
569	D₄	—	94	4	no	—
570	D₄	—	188	2	no	—
571	D₄	—	188	1	no	—
572	D₄	—	188	2	no	—
573	D₄	—	188	2	no	—
574	D₄	—	188	2	no	—
575	D₄	—	188	2	no	—
576	D₄	—	188	2	no	—
577	D₄	—	188	2	no	—
578	C₂×C₄	—	4	1	no	—
579	C₂×C₄	—	4	1	no	—
580	C₂×C₄	—	4	2	no	—
581	C₂×C₄	—	47	2	no	—
582	C₂×C₄	—	47	2	no	—
583	C₂×C₄	—	47	2	no	—
584	C₂×C₄	—	47	1	no	—
585	C₂×C₄	—	47	1	no	—
586	C₂×C₄	—	47	2	no	—
587	C₂×C₄	—	94	4	no	—
588	C₂×C₄	—	94	2	no	—
589	C₂×C₄	—	94	4	no	—
590	C₂×C₄	—	94	2	no	—
591	C₂×C₄	—	94	4	no	—
592	C₂×C₄	—	94	4	no	—
593	C₂×C₄	—	188	2	no	—
594	C₂×C₄	—	188	2	no	—
595	C₂×C₄	—	188	2	no	—
596	C₂×C₄	—	188	1	no	—
597	C₂×C₄	—	188	1	no	—
598	C₂×C₄	—	188	1	no	—
599	C₂×C₄	—	188	2	no	—
600	C₂×C₄	—	188	1	no	—
601	C₂×C₄	C₂³×D₄₇	1	2	yes	—
602	C₂×C₄	C₂³×D₄₇	1	2	yes	—
603	C₂×C₄	C₂³×D₄₇	1	2	yes	—
604	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
605	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
606	C₂×C₄	C₂³×D₄₇	1	2	yes	—
607	C₂²	—	2	1	no	—
608	C₂²	—	2	1	no	—
609	C₂²	—	2	2	no	—
610	C₂²	—	2	2	no	—
611	C₂²	—	2	2	no	—
612	C₂²	—	2	2	no	—
613	C₂²	—	2	2	no	—
614	C₂²	—	2	2	no	—
615	C₂²	—	4	4	no	—
616	C₂²	—	47	2	no	—
617	C₂²	—	47	2	no	—
618	C₂²	—	47	2	no	—
619	C₂²	—	47	2	no	—
620	C₂²	—	94	8	no	—
621	C₂²	—	94	1	no	—
622	C₂²	—	94	1	no	—
623	C₂²	—	94	2	no	—
624	C₂²	—	94	2	no	—
625	C₂²	—	94	2	no	—
626	C₂²	—	94	2	no	—
627	C₂²	—	94	2	no	—
628	C₂²	—	94	2	no	—
629	C₂²	—	188	4	no	—
630	C₂²	—	188	8	no	—
631	C₂²	—	188	8	no	—
632	C₂²	—	188	8	no	—
633	C₂²	#41×D₄₇	1	2	yes	—
634	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
635	C₄	—	2	2	no	—
636	C₄	—	2	2	no	—
637	C₄	—	2	1	no	—
638	C₄	—	2	2	no	—
639	C₄	—	2	1	no	—
640	C₄	—	2	2	no	—
641	C₄	—	94	2	no	—
642	C₄	—	94	2	no	—
643	C₄	—	94	2	no	—
644	C₄	—	94	1	no	—
645	C₄	—	94	1	no	—
646	C₄	—	94	2	no	—
647	C₂	—	2	2	no	—
648	C₂	—	4	2	no	—
649	C₂	—	4	2	no	—
650	C₂	—	47	4	no	—
651	C₂	—	94	2	no	—
652	C₂	—	188	2	no	—
653	C₂	—	188	2	no	—
654	C₂	C₂×#41×D₄₇	1	1	yes	characteristic
655	C₂	H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
656	C₂	H(5,𝔽₂)×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#538	C₂
hypercenter	#538	D₄₇
hypocenter	C₄₇	C₂×#538
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #538

Complements

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

N	H ≅ G/N	type
1. #15689713	C₂	semidirect
2. #15689712	C₂	semidirect
3. #15689711	C₂	semidirect
4. #15689710	C₂	semidirect
5. #15689709	C₂	semidirect
6. #15689708	C₂	semidirect
7. #15689707	C₂	semidirect
8. #15689706	C₂	semidirect
9. #15689705	C₂	semidirect
10. #126×D₄₇	C₂	semidirect
11. #124×D₄₇	C₂	semidirect
12. #123×D₄₇	C₂	semidirect
13. C₂²⋊Q₈×D₄₇	C₂	semidirect
14. #121×D₄₇	C₂	semidirect
15. #121×D₄₇	C₂	semidirect
16. #120×D₄₇	C₂	semidirect
17. C₄×D₄×D₄₇	C₂	semidirect
18. C₂×C₂²⋊C₄×D₄₇	C₂	semidirect
19. C₄₇×#538	C₂	semidirect
21. C₂×Q₈×D₄₇	C₂²	semidirect
25. C₂×D₄×D₄₇	C₂²	semidirect
28. C₂²×C₄×D₄₇	C₂²	semidirect
29. #13094019	C₂²	semidirect
30. #13094019	C₂²	semidirect
31. #13094019	C₂²	semidirect
32. #13094018	C₂²	semidirect
33. #13094017	C₂²	semidirect
34. #13094017	C₂²	semidirect
35. #13094017	C₂²	semidirect
36. #13094013	C₂²	semidirect
37. #13094012	C₂²	semidirect
38. #13094011	C₂²	semidirect
39. #13094010	C₂²	semidirect
40. #13094010	C₂²	semidirect
41. #13094010	C₂²	semidirect
42. #13094010	C₂²	semidirect
43. #13094009	C₂²	semidirect
44. #13094009	C₂²	semidirect
45. #13094008	C₂²	semidirect
46. #13094007	C₂²	semidirect
47. #13094006	C₂²	semidirect
48. #13094006	C₂²	semidirect
49. #13094005	C₂²	semidirect
50. #13094004	C₂²	semidirect
51. #13094003	C₂²	semidirect
52. #13094002	C₂²	semidirect
53. #13094001	C₂²	semidirect
54. #13094000	C₂²	semidirect
55. #13093999	C₂²	semidirect
56. #13093999	C₂²	semidirect
57. #13093998	C₂²	semidirect
58. #13093998	C₂²	semidirect
59. #13093997	C₂²	semidirect
60. #13093997	C₂²	semidirect
61. #13093997	C₂²	semidirect
62. #13093996	C₂²	semidirect
63. #13093996	C₂²	semidirect
64. #13093996	C₂²	semidirect
65. #13093995	C₂²	semidirect
66. #13093995	C₂²	semidirect
67. #13093994	C₂²	semidirect
68. #13093994	C₂²	semidirect
69. #13093994	C₂²	semidirect
70. #13093993	C₂²	semidirect
71. #13093992	C₂²	semidirect
72. #13093992	C₂²	semidirect
73. #13093992	C₂²	semidirect
74. C₄×D₁₈₈	C₂²	semidirect
75. D₄×Dic₄₇	C₂²	semidirect
76. #13093986	C₂²	semidirect
77. C₄×C₂²⋊D₄₇	C₂²	semidirect
78. C₄×C₂²⋊D₄₇	C₂²	semidirect
79. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
80. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
81. C₄⋊C₄×D₄₇	C₂²	semidirect
82. C₄⋊C₄×D₄₇	C₂²	semidirect
83. C₄⋊C₄×D₄₇	C₂²	semidirect
84. C₄⋊C₄×D₄₇	C₂²	semidirect
85. C₂×C₂²⋊Dic₄₇	C₂²	semidirect
86. C₂×(C₂×D₄₇)⋊C₄	C₂²	semidirect
87. C₂×(C₂×D₄₇)⋊C₄	C₂²	semidirect
93. C₂²⋊C₄×D₄₇	C₂²	semidirect
94. C₂²⋊C₄×D₄₇	C₂²	semidirect
95. C₂²⋊C₄×D₄₇	C₂²	semidirect
96. C₂²⋊C₄×D₄₇	C₂²	semidirect
97. C₄²×D₄₇	C₂²	semidirect
98. #126×C₄₇	C₂²	semidirect
99. #124×C₄₇	C₂²	semidirect
100. #123×C₄₇	C₂²	semidirect
101. C₂²⋊Q₈×C₄₇	C₂²	semidirect
102. #121×C₄₇	C₂²	semidirect
103. #121×C₄₇	C₂²	semidirect
104. #120×C₄₇	C₂²	semidirect
105. C₄×D₄×C₄₇	C₂²	semidirect
106. C₂×C₂²⋊C₄×C₄₇	C₂²	semidirect
116. C₂×Q₈×C₄₇	C₂³	semidirect
120. C₂×D₄×C₄₇	C₂³	semidirect
123. C₂²×C₄×C₄₇	C₂³	semidirect
130. C₂×C₂²⋊D₄₇	C₂³	semidirect
133. C₂²×Dic₄₇	C₂³	semidirect
142. C₂×D₁₈₈	C₂³	semidirect
155. C₂×C₄×D₄₇	C₂³	semidirect
156. C₂×C₄×D₄₇	C₂³	semidirect
157. C₂×Dic₉₄	C₂³	semidirect
158. C₂×Dic₉₄	C₂³	semidirect
159. C₄⋊C₄×C₄₇	C₂³	semidirect
160. C₄⋊C₄×C₄₇	C₂³	semidirect
161. C₄⋊C₄×C₄₇	C₂³	semidirect
162. C₄⋊C₄×C₄₇	C₂³	semidirect
168. C₂²⋊C₄×C₄₇	C₂³	semidirect
169. C₂²⋊C₄×C₄₇	C₂³	semidirect
170. C₄²×C₄₇	C₂³	semidirect
176. C₂²⋊Dic₄₇	C₂³	semidirect
177. C₂²⋊Dic₄₇	C₂³	semidirect
188. (C₂×D₄₇)⋊C₄	C₂³	semidirect
189. (C₂×D₄₇)⋊C₄	C₂³	semidirect
190. (C₂×D₄₇)⋊C₄	C₂³	semidirect
191. (C₂×D₄₇)⋊C₄	C₂³	semidirect
192. C₄⋊Dic₄₇	C₂³	semidirect
193. C₄⋊Dic₄₇	C₂³	semidirect
194. C₄⋊Dic₄₇	C₂³	semidirect
195. C₄⋊Dic₄₇	C₂³	semidirect
196. Dic₄₇⋊C₄	C₂³	semidirect
197. Dic₄₇⋊C₄	C₂³	semidirect
198. Dic₄₇⋊C₄	C₂³	semidirect
199. Dic₄₇⋊C₄	C₂³	semidirect
200. Dic₄₇⋊C₄	C₂³	semidirect
201. Dic₄₇⋊C₄	C₂³	semidirect
202. C₄×Dic₄₇	C₂³	semidirect
203. C₄×Dic₄₇	C₂³	semidirect
204. C₄×Dic₄₇	C₂³	semidirect
328. D₄₇	#538	direct (N × H)
338. #538	D₄₇	direct (N × H)
348. C₄₇	C₂×#538	semidirect
365. #126	C₂×D₄₇	semidirect
373. #124	C₂×D₄₇	semidirect
381. #123	C₂×D₄₇	semidirect
387. C₂²⋊Q₈	C₂×D₄₇	semidirect
400. #121	C₂×D₄₇	semidirect
401. #121	C₂×D₄₇	semidirect
409. #120	C₂×D₄₇	semidirect
417. C₄×D₄	C₂×D₄₇	semidirect
434. C₂×C₂²⋊C₄	C₂×D₄₇	semidirect
448. C₂×Q₈	C₂²×D₄₇	semidirect
467. C₂×D₄	C₂²×D₄₇	semidirect
487. C₂²×C₄	C₂²×D₄₇	semidirect
498. C₄⋊C₄	C₂²×D₄₇	semidirect
499. C₄⋊C₄	C₂²×D₄₇	semidirect
500. C₄⋊C₄	C₂²×D₄₇	semidirect
501. C₄⋊C₄	C₂²×D₄₇	semidirect
528. C₂²⋊C₄	C₂²×D₄₇	semidirect
529. C₂²⋊C₄	C₂²×D₄₇	semidirect
533. C₄²	C₂²×D₄₇	semidirect

Subgroups — #538×D47 #20256722

Conjugacy classes of subgroups

Complements

Subgroups — #538×D₄₇ #20256722