Subgroups — #20257234

Order 6016.

1140 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	#15689857	C₂	1	2	yes	maximal, complemented
2	#15689856	C₂	1	2	yes	maximal, complemented
3	#15689840	C₂	1	2	yes	maximal, complemented
4	#15689837	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689836	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689826	C₂	1	1	yes	maximal, characteristic, complemented
7	#15689823	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689819	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689791	C₂	1	2	yes	maximal, complemented
10	#15689774	C₂	1	1	yes	maximal, characteristic, complemented
11	#15689773	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689712	C₂	1	2	yes	maximal, complemented
13	#15689705	C₂	1	2	yes	maximal, complemented
14	#15689689	C₂	1	1	yes	maximal, characteristic, complemented
15	#15689689	C₂	1	1	yes	maximal, characteristic, complemented
16	#15689679	C₂	1	1	yes	maximal, characteristic, complemented
17	#15689670	C₂	1	1	yes	maximal, characteristic, complemented
18	#15689632	C₂	1	2	yes	maximal, complemented
19	#15689631	C₂	1	2	yes	maximal, complemented
20	#15689604	C₂	1	1	yes	maximal, characteristic, complemented
21	#15689603	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×D₄×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#553	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#10625350	C₂²	1	1	yes	characteristic
25	C₂×#10625350	C₂²	1	1	yes	characteristic
26	C₂×#10625350	C₂²	1	2	yes	complemented
27	C₂×#10625352	C₂²	1	2	yes	complemented
28	C₂×D₄×D₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₄×D₄₇	C₂²	1	2	yes	—
30	#13094023	C₂²	1	1	yes	characteristic, complemented
31	#13094023	C₂²	1	1	yes	characteristic, complemented
32	#13094023	C₂²	1	1	yes	characteristic, complemented
33	#13094020	C₂²	1	2	yes	—
34	#13094020	C₂²	1	2	yes	—
35	#13094020	C₂²	1	1	yes	characteristic, complemented
36	#13094019	C₂²	1	2	yes	complemented
37	#13094019	C₂²	1	2	yes	complemented
38	#13094017	C₂²	1	2	yes	complemented
39	#13094016	C₂²	1	1	yes	characteristic, complemented
40	#13094012	C₂²	1	2	yes	complemented
41	#13094011	C₂²	1	2	yes	complemented
42	#13094010	C₂²	1	2	yes	—
43	#13094010	C₂²	1	2	yes	—
44	#13094010	C₂²	1	2	yes	complemented
45	#13094010	C₂²	1	2	yes	complemented
46	#13094010	C₂²	1	1	yes	characteristic, complemented
47	#13094010	C₂²	1	1	yes	characteristic, complemented
48	#13094009	C₂²	1	2	yes	complemented
49	#13094009	C₂²	1	2	yes	complemented
50	#13094007	C₂²	1	2	yes	complemented
51	#13094007	C₂²	1	2	yes	complemented
52	#13094006	C₂²	1	2	yes	complemented
53	#13094006	C₂²	1	2	yes	complemented
54	#13094005	C₂²	1	2	yes	complemented
55	#13094002	C₂²	1	2	yes	—
56	#13094002	C₂²	1	2	yes	—
57	#13094002	C₂²	1	2	yes	complemented
58	#13094001	C₂²	1	2	yes	complemented
59	#13093999	C₂²	1	1	yes	characteristic
60	#13093999	C₂²	1	1	yes	characteristic
61	#13093999	C₂²	1	1	yes	characteristic
62	#13093999	C₂²	1	2	yes	complemented
63	#13093998	C₂²	1	1	yes	characteristic
64	#13093998	C₂²	1	1	yes	characteristic
65	#13093997	C₂²	1	1	yes	characteristic
66	#13093997	C₂²	1	1	yes	characteristic
67	#13093997	C₂²	1	2	yes	complemented
68	#13093997	C₂²	1	2	yes	complemented
69	#13093996	C₂²	1	2	yes	complemented
70	#13093996	C₂²	1	2	yes	complemented
71	#13093995	C₂²	1	1	yes	characteristic
72	#13093995	C₂²	1	1	yes	characteristic
73	#13093995	C₂²	1	1	yes	characteristic
74	#13093994	C₂²	1	2	yes	—
75	#13093994	C₂²	1	2	yes	—
76	#13093992	C₂²	1	2	yes	—
77	#13093992	C₂²	1	2	yes	—
78	C₄×Dic₉₄	C₂²	1	2	yes	complemented
79	#13093989	C₂²	1	2	yes	complemented
80	#13093989	C₂²	1	2	yes	complemented
81	#13093989	C₂²	1	2	yes	complemented
82	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
83	C₄×D₁₈₈	C₂²	1	2	yes	—
84	C₄×D₁₈₈	C₂²	1	1	yes	characteristic, complemented
85	D₄×Dic₄₇	C₂²	1	1	yes	characteristic
86	#13093986	C₂²	1	1	yes	characteristic
87	#13093986	C₂²	1	2	yes	—
88	#13093986	C₂²	1	2	yes	complemented
89	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
90	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
91	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic, complemented
92	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic, complemented
93	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
94	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	complemented
95	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
96	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
97	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
98	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	complemented
99	#13093983	C₂²	1	1	yes	characteristic, complemented
100	#13093982	C₂²	1	1	yes	characteristic
101	#13093982	C₂²	1	1	yes	characteristic
102	#13093982	C₂²	1	1	yes	characteristic, complemented
103	#13093982	C₂²	1	1	yes	characteristic, complemented
104	#13093981	C₂²	1	2	yes	complemented
105	#13093980	C₂²	1	2	yes	complemented
106	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic, complemented
107	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
108	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic, complemented
109	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic, complemented
110	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
111	C₄²×D₄₇	C₂²	1	1	yes	characteristic
112	#126×C₄₇	C₂²	1	2	yes	complemented
113	#125×C₄₇	C₂²	1	1	yes	characteristic, complemented
114	#123×C₄₇	C₂²	1	2	yes	complemented
115	#121×C₄₇	C₂²	1	1	yes	characteristic
116	#121×C₄₇	C₂²	1	1	yes	characteristic
117	#121×C₄₇	C₂²	1	2	yes	complemented
118	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
120	C₄×D₄×C₄₇	C₂²	1	2	yes	complemented
121	#117×C₄₇	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
123	C₂³×D₄₇	C₂³	1	2	yes	—
124	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₄₇	C₂³	1	2	yes	—
126	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
127	C₂×D₄×C₄₇	C₂³	1	2	yes	—
128	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
131	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
133	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
134	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
135	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
136	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
137	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
138	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
139	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
140	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
141	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
142	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
143	C₂²×Dic₄₇	C₂³	1	2	yes	—
144	C₂²×Dic₄₇	C₂³	1	2	yes	—
145	#10625352	—	4	4	no	—
146	D₄×D₄₇	—	2	4	no	—
147	#10625350	—	2	4	no	—
148	#10625350	—	2	4	no	—
149	#10625350	—	4	4	no	—
150	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
151	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
152	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
153	C₂×D₁₈₈	C₂³	1	2	yes	—
154	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
155	C₂×D₁₈₈	C₂³	1	2	yes	—
156	C₂×C₄×D₄₇	—	4	4	no	—
157	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
158	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
159	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
160	C₂×C₄×D₄₇	C₂³	1	2	yes	—
161	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
162	C₂×C₄×D₄₇	C₂³	1	2	yes	—
163	C₂×C₄×D₄₇	C₂³	1	2	yes	—
164	C₂×C₄×D₄₇	C₂³	1	2	yes	—
165	C₂×C₄×D₄₇	C₂³	1	2	yes	—
166	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
167	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
168	C₂×Dic₉₄	C₂³	1	2	yes	—
169	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
170	C₂×Dic₉₄	C₂³	1	2	yes	—
171	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
172	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
173	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
174	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
175	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
176	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
177	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
178	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
179	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
180	C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
181	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
182	C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
183	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
184	C₄²×C₄₇	C₂³	1	2	yes	—
185	C₄²×C₄₇	C₂³	1	1	yes	characteristic
186	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
187	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
188	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
189	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
190	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
191	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
192	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
193	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
194	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
195	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
196	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
197	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
198	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
199	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
200	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
201	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
202	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
203	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
204	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
205	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
206	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
207	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
208	C₄⋊Dic₄₇	C₂³	1	2	yes	—
209	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
210	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
211	Dic₄₇⋊C₄	C₂³	1	2	yes	—
212	Dic₄₇⋊C₄	C₂³	1	2	yes	—
213	Dic₄₇⋊C₄	C₂³	1	2	yes	—
214	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
215	Dic₄₇⋊C₄	C₂³	1	2	yes	—
216	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
217	Dic₄₇⋊C₄	C₂³	1	2	yes	—
218	Dic₄₇⋊C₄	C₂³	1	2	yes	—
219	Dic₄₇⋊C₄	C₂³	1	2	yes	—
220	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
221	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
222	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
223	C₄×Dic₄₇	C₂³	1	2	yes	—
224	C₄×Dic₄₇	C₂³	1	2	yes	—
225	C₄×Dic₄₇	C₂³	1	2	yes	—
226	C₄×Dic₄₇	C₂³	1	2	yes	—
227	C₄×Dic₄₇	C₂³	1	2	yes	—
228	C₂³×C₄₇	C₂⁴	1	2	yes	—
229	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
230	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
231	C₂²×D₄₇	—	2	4	no	—
232	C₂²×D₄₇	—	4	2	no	—
233	C₂²×D₄₇	—	4	2	no	—
234	C₂²×D₄₇	C₂⁴	1	2	yes	—
235	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
236	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
237	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
238	D₄×C₄₇	—	2	2	no	—
239	D₄×C₄₇	—	4	2	no	—
240	D₄×C₄₇	—	4	2	no	—
241	D₄×C₄₇	—	4	1	no	—
242	C₂×C₄×C₄₇	—	2	2	no	—
243	C₂×C₄×C₄₇	—	2	2	no	—
244	C₂×C₄×C₄₇	—	4	2	no	—
245	C₂×C₄×C₄₇	—	4	2	no	—
246	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
247	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
248	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
249	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
250	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
251	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
252	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
253	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
254	C₂²⋊D₄₇	—	2	2	no	—
255	C₂²⋊D₄₇	—	2	2	no	—
256	C₂²⋊D₄₇	—	2	2	no	—
257	C₂²⋊D₄₇	—	2	2	no	—
258	C₂²⋊D₄₇	—	2	4	no	—
259	C₂²⋊D₄₇	—	2	2	no	—
260	C₂²⋊D₄₇	—	2	2	no	—
261	C₂²⋊D₄₇	—	4	2	no	—
262	C₂²⋊D₄₇	—	4	2	no	—
263	C₂²⋊D₄₇	—	4	2	no	—
264	C₂²⋊D₄₇	—	4	2	no	—
265	C₂×Dic₄₇	—	2	4	no	—
266	C₂×Dic₄₇	—	4	2	no	—
267	C₂×Dic₄₇	C₂⁴	1	2	yes	—
268	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
269	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
270	C₂×Dic₄₇	C₂⁴	1	2	yes	—
271	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
272	C₂×Dic₄₇	C₂⁴	1	2	yes	—
273	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
274	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
275	D₁₈₈	—	2	2	no	—
276	D₁₈₈	—	2	2	no	—
277	D₁₈₈	—	2	2	no	—
278	D₁₈₈	—	4	2	no	—
279	D₁₈₈	—	4	1	no	—
280	D₁₈₈	—	4	2	no	—
281	C₄×D₄₇	—	2	2	no	—
282	C₄×D₄₇	—	2	2	no	—
283	C₄×D₄₇	—	2	2	no	—
284	C₄×D₄₇	—	2	4	no	—
285	C₄×D₄₇	—	4	2	no	—
286	C₄×D₄₇	—	4	2	no	—
287	C₄×D₄₇	—	4	1	no	—
288	C₄×D₄₇	—	4	2	no	—
289	C₄×D₄₇	—	4	2	no	—
290	C₄×D₄₇	#41	1	4	yes	complemented
291	Dic₉₄	—	2	2	no	—
292	Dic₉₄	—	2	2	no	—
293	Dic₉₄	—	2	4	no	—
294	Dic₉₄	—	4	2	no	—
295	C₂²×C₄₇	—	2	1	no	—
296	C₂²×C₄₇	—	2	1	no	—
297	C₂²×C₄₇	—	2	2	no	—
298	C₂²×C₄₇	—	2	2	no	—
299	C₂²×C₄₇	—	2	1	no	—
300	C₂²×C₄₇	—	2	1	no	—
301	C₂²×C₄₇	—	2	1	no	—
302	C₂²×C₄₇	—	2	2	no	—
303	C₂²×C₄₇	—	2	1	no	—
304	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
305	C₂×D₄₇	—	2	1	no	—
306	C₂×D₄₇	—	2	1	no	—
307	C₂×D₄₇	—	2	1	no	—
308	C₂×D₄₇	—	2	1	no	—
309	C₂×D₄₇	—	2	2	no	—
310	C₂×D₄₇	—	2	2	no	—
311	C₂×D₄₇	—	2	1	no	—
312	C₂×D₄₇	—	2	1	no	—
313	C₂×D₄₇	—	2	1	no	—
314	C₂×D₄₇	—	2	1	no	—
315	C₂×D₄₇	—	2	2	no	—
316	C₂×D₄₇	—	4	8	no	—
317	C₂×D₄₇	C₂×#41	1	2	yes	—
318	C₄×C₄₇	—	2	1	no	—
319	C₄×C₄₇	—	2	1	no	—
320	C₄×C₄₇	—	2	2	no	—
321	C₄×C₄₇	—	2	1	no	—
322	C₄×C₄₇	—	2	2	no	—
323	C₄×C₄₇	—	2	2	no	—
324	C₄×C₄₇	—	2	1	no	—
325	C₄×C₄₇	C₂×#41	1	2	yes	—
326	Dic₄₇	—	2	1	no	—
327	Dic₄₇	—	2	1	no	—
328	Dic₄₇	—	2	2	no	—
329	Dic₄₇	—	2	2	no	—
330	Dic₄₇	—	2	1	no	—
331	Dic₄₇	—	2	2	no	—
332	Dic₄₇	C₂×#41	1	2	yes	—
333	Dic₄₇	H(5,𝔽₂)	1	2	yes	—
334	#3506	—	47	1	no	maximal, Sylow
335	C₂×C₄₇	—	4	2	no	—
336	C₂×C₄₇	—	4	1	no	—
337	C₂×C₄₇	—	4	1	no	—
338	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
339	C₂×C₄₇	C₂×H(5,𝔽₂)	1	1	yes	characteristic
340	C₂×C₄₇	#585	1	1	yes	characteristic
341	D₄₇	—	2	2	no	—
342	D₄₇	—	4	1	no	—
343	D₄₇	—	4	1	no	—
344	D₄₇	—	4	2	no	—
345	#559	—	47	2	no	—
346	#559	—	47	2	no	—
347	#556	—	47	2	no	—
348	#555	—	47	1	no	—
349	#555	—	47	1	no	—
350	#553	—	47	1	no	—
351	#553	—	47	1	no	—
352	#553	—	47	1	no	—
353	#553	D₄₇	1	1	yes	characteristic, complemented
354	#550	—	47	2	no	—
355	#547	—	47	1	no	—
356	#547	—	47	1	no	—
357	#538	—	47	2	no	—
358	#538	—	47	2	no	—
359	#535	—	47	1	no	—
360	#535	—	47	1	no	—
361	#533	—	47	1	no	—
362	#532	—	47	1	no	—
363	#525	—	47	2	no	—
364	#525	—	47	2	no	—
365	#520	—	47	1	no	—
366	#520	—	47	1	no	—
367	C₂×C₄×D₄	—	47	1	no	—
368	C₄₇	#3506	1	1	yes	characteristic, complemented, Sylow
369	C₂×#41	—	47	2	no	—
370	C₂×#41	—	47	1	no	—
371	C₂×#41	—	47	1	no	—
372	C₂×#41	—	47	2	no	—
373	C₂²×D₄	—	47	1	no	—
374	C₂³×C₄	—	47	2	no	—
375	C₄⋊Q₈	—	47	1	no	—
376	C₄⋊Q₈	—	47	1	no	—
377	C₄⋊Q₈	—	47	1	no	—
378	#127	—	47	1	no	—
379	#127	—	47	2	no	—
380	#127	—	47	2	no	—
381	#126	—	47	2	no	—
382	#126	—	47	2	no	—
383	#126	—	47	2	no	—
384	#126	C₂×D₄₇	1	2	yes	complemented
385	#125	—	47	1	no	—
386	#125	C₂×D₄₇	1	1	yes	characteristic, complemented
387	#124	—	47	2	no	—
388	#124	—	47	1	no	—
389	#124	—	47	1	no	—
390	#124	—	47	2	no	—
391	#124	—	47	2	no	—
392	#124	—	47	2	no	—
393	#124	—	47	2	no	—
394	#124	—	47	2	no	—
395	#123	—	47	2	no	—
396	#123	—	47	2	no	—
397	#123	—	47	2	no	—
398	#123	—	47	2	no	—
399	#123	—	47	2	no	—
400	#123	—	47	2	no	—
401	#123	—	47	2	no	—
402	#123	C₂×D₄₇	1	2	yes	complemented
403	C₂²⋊Q₈	—	47	2	no	—
404	C₂²⋊Q₈	—	47	2	no	—
405	C₂²⋊Q₈	—	47	2	no	—
406	C₂²⋊Q₈	—	47	2	no	—
407	#121	—	47	2	no	—
408	#121	—	47	1	no	—
409	#121	—	47	1	no	—
410	#121	—	47	1	no	—
411	#121	—	47	2	no	—
412	#121	—	47	1	no	—
413	#121	—	47	1	no	—
414	#121	—	47	1	no	—
415	#121	—	47	1	no	—
416	#121	—	47	1	no	—
417	#121	—	47	2	no	—
418	#121	—	47	1	no	—
419	#121	—	47	1	no	—
420	#121	—	47	2	no	—
421	#121	—	47	2	no	—
422	#121	C₂×D₄₇	1	1	yes	characteristic
423	#121	C₂×D₄₇	1	1	yes	characteristic
424	#121	C₂×D₄₇	1	2	yes	complemented
425	#120	—	47	2	no	—
426	#120	—	47	2	no	—
427	#120	—	47	2	no	—
428	#120	—	47	2	no	—
429	C₄×Q₈	—	47	2	no	—
430	C₄×Q₈	—	47	2	no	—
431	C₄×Q₈	—	47	2	no	—
432	C₄×Q₈	—	47	2	no	—
433	C₄×D₄	—	47	1	no	—
434	C₄×D₄	—	47	2	no	—
435	C₄×D₄	—	47	2	no	—
436	C₄×D₄	—	47	2	no	—
437	C₄×D₄	—	47	2	no	—
438	C₄×D₄	—	47	1	no	—
439	C₄×D₄	—	47	1	no	—
440	C₄×D₄	—	47	1	no	—
441	C₄×D₄	—	47	2	no	—
442	C₄×D₄	—	47	2	no	—
443	C₄×D₄	—	47	2	no	—
444	C₄×D₄	—	47	2	no	—
445	C₄×D₄	—	47	2	no	—
446	C₄×D₄	—	47	2	no	—
447	C₄×D₄	—	47	1	no	—
448	C₄×D₄	—	47	2	no	—
449	C₄×D₄	—	47	1	no	—
450	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
451	C₄×D₄	C₂×D₄₇	1	2	yes	complemented
452	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
453	#117	—	47	1	no	—
454	#117	—	47	1	no	—
455	#117	—	47	1	no	—
456	#117	—	47	1	no	—
457	#117	—	47	1	no	—
458	#117	—	47	2	no	—
459	#117	—	47	2	no	—
460	#117	C₂×D₄₇	1	1	yes	characteristic, complemented
461	C₂×C₄⋊C₄	—	47	1	no	—
462	C₂×C₄⋊C₄	—	47	1	no	—
463	C₂×C₄⋊C₄	—	47	1	no	—
464	C₂×C₄⋊C₄	—	47	1	no	—
465	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic, complemented
466	C₂×C₂²⋊C₄	—	47	2	no	—
467	C₂×C₄²	—	47	1	no	—
468	C₂⁴	—	47	2	no	—
469	#41	—	94	4	no	—
470	#41	—	94	4	no	—
471	#41	—	188	4	no	—
472	#41	—	188	4	no	—
473	C₂×Q₈	—	47	1	no	—
474	C₂×Q₈	—	47	1	no	—
475	C₂×Q₈	—	47	2	no	—
476	C₂×Q₈	—	47	2	no	—
477	C₂×D₄	—	47	1	no	—
478	C₂×D₄	—	47	1	no	—
479	C₂×D₄	—	47	2	no	—
480	C₂×D₄	—	47	1	no	—
481	C₂×D₄	—	47	1	no	—
482	C₂×D₄	—	47	1	no	—
483	C₂×D₄	—	47	1	no	—
484	C₂×D₄	—	47	2	no	—
485	C₂×D₄	—	47	2	no	—
486	C₂×D₄	—	47	2	no	—
487	C₂×D₄	—	47	2	no	—
488	C₂×D₄	—	47	1	no	—
489	C₂×D₄	—	47	1	no	—
490	C₂×D₄	—	47	1	no	—
491	C₂×D₄	—	47	2	no	—
492	C₂×D₄	—	47	1	no	—
493	C₂×D₄	—	47	2	no	—
494	C₂×D₄	—	94	4	no	—
495	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
496	C₂×D₄	C₂²×D₄₇	1	2	yes	—
497	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
498	C₂×D₄	C₂²×D₄₇	1	2	yes	—
499	C₂²×C₄	—	47	1	no	—
500	C₂²×C₄	—	47	2	no	—
501	C₂²×C₄	—	47	2	no	—
502	C₂²×C₄	—	47	1	no	—
503	C₂²×C₄	—	47	1	no	—
504	C₂²×C₄	—	47	1	no	—
505	C₂²×C₄	—	47	2	no	—
506	C₂²×C₄	—	47	1	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	—	188	4	no	—
512	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
513	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
514	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
515	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
516	C₄⋊C₄	—	47	2	no	—
517	C₄⋊C₄	—	47	2	no	—
518	C₄⋊C₄	—	47	2	no	—
519	C₄⋊C₄	—	47	1	no	—
520	C₄⋊C₄	—	47	1	no	—
521	C₄⋊C₄	—	47	2	no	—
522	C₄⋊C₄	—	47	2	no	—
523	C₄⋊C₄	—	47	2	no	—
524	C₄⋊C₄	—	47	2	no	—
525	C₄⋊C₄	—	47	1	no	—
526	C₄⋊C₄	—	47	1	no	—
527	C₄⋊C₄	—	47	2	no	—
528	C₄⋊C₄	—	47	1	no	—
529	C₄⋊C₄	—	47	1	no	—
530	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
531	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
532	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
533	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
534	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
535	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
536	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
537	C₂²⋊C₄	—	47	2	no	—
538	C₂²⋊C₄	—	47	2	no	—
539	C₂²⋊C₄	—	47	2	no	—
540	C₂²⋊C₄	—	47	2	no	—
541	C₂²⋊C₄	—	47	1	no	—
542	C₂²⋊C₄	—	47	1	no	—
543	C₂²⋊C₄	—	47	2	no	—
544	C₂²⋊C₄	—	47	2	no	—
545	C₂²⋊C₄	—	47	2	no	—
546	C₂²⋊C₄	—	47	2	no	—
547	C₂²⋊C₄	—	47	2	no	—
548	C₂²⋊C₄	—	47	2	no	—
549	C₂²⋊C₄	—	47	2	no	—
550	C₂²⋊C₄	—	47	2	no	—
551	C₂²⋊C₄	—	47	1	no	—
552	C₂²⋊C₄	—	47	1	no	—
553	C₂²⋊C₄	—	47	2	no	—
554	C₂²⋊C₄	—	47	2	no	—
555	C₂²⋊C₄	—	47	1	no	—
556	C₂²⋊C₄	—	47	1	no	—
557	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
558	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
559	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
560	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
561	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
562	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
563	C₄²	—	47	1	no	—
564	C₄²	—	47	1	no	—
565	C₄²	—	47	1	no	—
566	C₄²	—	47	2	no	—
567	C₄²	—	47	2	no	—
568	C₄²	—	47	2	no	—
569	C₄²	—	47	2	no	—
570	C₄²	—	47	2	no	—
571	C₄²	C₂²×D₄₇	1	1	yes	characteristic
572	C₄²	C₂²×D₄₇	1	2	yes	—
573	C₂³	—	47	1	no	—
574	C₂³	—	47	2	no	—
575	C₂³	—	47	1	no	—
576	C₂³	—	47	1	no	—
577	C₂³	—	94	4	no	—
578	C₂³	—	188	2	no	—
579	C₂³	—	188	2	no	—
580	C₂³	C₂³×D₄₇	1	2	yes	—
581	C₂³	C₂³×D₄₇	1	1	yes	characteristic
582	C₂³	C₂³×D₄₇	1	1	yes	characteristic
583	Q₈	—	94	2	no	—
584	Q₈	—	94	2	no	—
585	Q₈	—	94	4	no	—
586	Q₈	—	188	2	no	—
587	D₄	—	2	2	no	—
588	D₄	—	4	1	no	—
589	D₄	—	4	2	no	—
590	D₄	—	4	2	no	—
591	D₄	—	94	2	no	—
592	D₄	—	94	2	no	—
593	D₄	—	94	4	no	—
594	D₄	—	94	2	no	—
595	D₄	—	94	2	no	—
596	D₄	—	94	2	no	—
597	D₄	—	94	2	no	—
598	D₄	—	94	2	no	—
599	D₄	—	94	2	no	—
600	D₄	—	94	2	no	—
601	D₄	—	188	1	no	—
602	D₄	—	188	2	no	—
603	D₄	—	188	2	no	—
604	D₄	—	188	2	no	—
605	D₄	—	188	2	no	—
606	D₄	—	188	2	no	—
607	D₄	—	188	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	4	2	no	—
611	C₂×C₄	—	4	2	no	—
612	C₂×C₄	—	47	1	no	—
613	C₂×C₄	—	47	1	no	—
614	C₂×C₄	—	47	4	no	—
615	C₂×C₄	—	47	2	no	—
616	C₂×C₄	—	47	1	no	—
617	C₂×C₄	—	47	1	no	—
618	C₂×C₄	—	47	1	no	—
619	C₂×C₄	—	47	2	no	—
620	C₂×C₄	—	47	2	no	—
621	C₂×C₄	—	94	2	no	—
622	C₂×C₄	—	94	4	no	—
623	C₂×C₄	—	94	4	no	—
624	C₂×C₄	—	94	2	no	—
625	C₂×C₄	—	94	2	no	—
626	C₂×C₄	—	188	1	no	—
627	C₂×C₄	—	188	2	no	—
628	C₂×C₄	—	188	2	no	—
629	C₂×C₄	—	188	2	no	—
630	C₂×C₄	—	188	2	no	—
631	C₂×C₄	—	188	2	no	—
632	C₂×C₄	C₂³×D₄₇	1	2	yes	—
633	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
634	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
635	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
636	C₂×C₄	C₂³×D₄₇	1	2	yes	—
637	C₂×C₄	C₂³×D₄₇	1	2	yes	—
638	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
639	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
640	C₂²	—	2	1	no	—
641	C₂²	—	2	1	no	—
642	C₂²	—	2	2	no	—
643	C₂²	—	2	1	no	—
644	C₂²	—	2	2	no	—
645	C₂²	—	2	1	no	—
646	C₂²	—	2	1	no	—
647	C₂²	—	2	1	no	—
648	C₂²	—	2	2	no	—
649	C₂²	—	47	2	no	—
650	C₂²	—	94	1	no	—
651	C₂²	—	94	1	no	—
652	C₂²	—	94	1	no	—
653	C₂²	—	94	1	no	—
654	C₂²	—	94	2	no	—
655	C₂²	—	94	2	no	—
656	C₂²	—	94	1	no	—
657	C₂²	—	94	1	no	—
658	C₂²	—	94	1	no	—
659	C₂²	—	94	1	no	—
660	C₂²	—	94	2	no	—
661	C₂²	—	188	8	no	—
662	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
663	C₄	—	2	1	no	—
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	2	no	—
668	C₄	—	2	1	no	—
669	C₄	—	2	2	no	—
670	C₄	—	47	2	no	—
671	C₄	—	47	2	no	—
672	C₄	—	94	1	no	—
673	C₄	—	94	1	no	—
674	C₄	—	94	2	no	—
675	C₄	—	94	2	no	—
676	C₄	—	94	1	no	—
677	C₄	—	94	2	no	—
678	C₄	#41×D₄₇	1	2	yes	—
679	C₂	—	4	2	no	—
680	C₂	—	4	1	no	—
681	C₂	—	4	1	no	—
682	C₂	—	94	2	no	—
683	C₂	—	188	2	no	—
684	C₂	—	188	1	no	—
685	C₂	—	188	1	no	—
686	C₂	C₂×#41×D₄₇	1	1	yes	characteristic
687	C₂	H(5,𝔽₂)×D₄₇	1	1	yes	characteristic
688	C₂	#15689959	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#553	C₂
hypercenter	#553	D₄₇
hypocenter	C₄₇	#3506
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #553

Complements

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

N	H ≅ G/N	type
1. #15689857	C₂	semidirect
2. #15689856	C₂	semidirect
3. #15689840	C₂	semidirect
4. #15689837	C₂	semidirect
5. #15689836	C₂	semidirect
6. #15689826	C₂	semidirect
7. #15689823	C₂	semidirect
8. #15689819	C₂	semidirect
9. #15689791	C₂	semidirect
10. #15689774	C₂	semidirect
11. #15689773	C₂	semidirect
12. #15689712	C₂	semidirect
13. #15689705	C₂	semidirect
14. #15689689	C₂	semidirect
15. #15689689	C₂	semidirect
16. #15689679	C₂	semidirect
17. #15689670	C₂	semidirect
18. #15689632	C₂	semidirect
19. #15689631	C₂	semidirect
20. #15689604	C₂	semidirect
21. #15689603	C₂	semidirect
22. C₄×D₄×D₄₇	C₂	semidirect
23. C₄₇×#553	C₂	semidirect
26. C₂×#10625350	C₂²	semidirect
27. C₂×#10625352	C₂²	semidirect
30. #13094023	C₂²	semidirect
31. #13094023	C₂²	semidirect
32. #13094023	C₂²	semidirect
35. #13094020	C₂²	semidirect
36. #13094019	C₂²	semidirect
37. #13094019	C₂²	semidirect
38. #13094017	C₂²	semidirect
39. #13094016	C₂²	semidirect
40. #13094012	C₂²	semidirect
41. #13094011	C₂²	semidirect
44. #13094010	C₂²	semidirect
45. #13094010	C₂²	semidirect
46. #13094010	C₂²	semidirect
47. #13094010	C₂²	semidirect
48. #13094009	C₂²	semidirect
49. #13094009	C₂²	semidirect
50. #13094007	C₂²	semidirect
51. #13094007	C₂²	semidirect
52. #13094006	C₂²	semidirect
53. #13094006	C₂²	semidirect
54. #13094005	C₂²	semidirect
57. #13094002	C₂²	semidirect
58. #13094001	C₂²	semidirect
62. #13093999	C₂²	semidirect
67. #13093997	C₂²	semidirect
68. #13093997	C₂²	semidirect
69. #13093996	C₂²	semidirect
70. #13093996	C₂²	semidirect
78. C₄×Dic₉₄	C₂²	semidirect
79. #13093989	C₂²	semidirect
80. #13093989	C₂²	semidirect
81. #13093989	C₂²	semidirect
84. C₄×D₁₈₈	C₂²	semidirect
88. #13093986	C₂²	semidirect
91. C₄×C₂²⋊D₄₇	C₂²	semidirect
92. C₄×C₂²⋊D₄₇	C₂²	semidirect
93. C₄×C₂²⋊D₄₇	C₂²	semidirect
94. C₄×C₂²⋊D₄₇	C₂²	semidirect
97. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
98. (C₂²⋊D₄₇)⋊C₄	C₂²	semidirect
99. #13093983	C₂²	semidirect
102. #13093982	C₂²	semidirect
103. #13093982	C₂²	semidirect
104. #13093981	C₂²	semidirect
105. #13093980	C₂²	semidirect
106. C₂×C₄⋊Dic₄₇	C₂²	semidirect
108. C₄⋊C₄×D₄₇	C₂²	semidirect
109. C₄⋊C₄×D₄₇	C₂²	semidirect
112. #126×C₄₇	C₂²	semidirect
113. #125×C₄₇	C₂²	semidirect
114. #123×C₄₇	C₂²	semidirect
117. #121×C₄₇	C₂²	semidirect
119. C₄×D₄×C₄₇	C₂²	semidirect
120. C₄×D₄×C₄₇	C₂²	semidirect
121. #117×C₄₇	C₂²	semidirect
122. C₂×C₄⋊C₄×C₄₇	C₂²	semidirect
290. C₄×D₄₇	#41	semidirect
353. #553	D₄₇	semidirect
368. C₄₇	#3506	semidirect
384. #126	C₂×D₄₇	semidirect
386. #125	C₂×D₄₇	semidirect
402. #123	C₂×D₄₇	semidirect
424. #121	C₂×D₄₇	semidirect
451. C₄×D₄	C₂×D₄₇	semidirect
452. C₄×D₄	C₂×D₄₇	semidirect
460. #117	C₂×D₄₇	semidirect
465. C₂×C₄⋊C₄	C₂×D₄₇	semidirect