Subgroups — #20257128

Order 6016.

1022 conjugacy classes of subgroups.

The subgroup lattice has 634 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689840	C₂	1	2	yes	maximal, complemented
2	#15689832	C₂	1	2	yes	maximal, complemented
3	#15689812	C₂	1	2	yes	maximal, complemented
4	#15689810	C₂	1	2	yes	maximal, complemented
5	#15689809	C₂	1	2	yes	maximal, complemented
6	#15689806	C₂	1	2	yes	maximal, complemented
7	#15689802	C₂	1	2	yes	maximal, complemented
8	#15689796	C₂	1	2	yes	maximal, complemented
9	#15689753	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689742	C₂	1	1	yes	maximal, characteristic, complemented
11	#15689738	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689736	C₂	1	1	yes	maximal, characteristic, complemented
13	#15689731	C₂	1	1	yes	maximal, characteristic, complemented
14	#15689693	C₂	1	1	yes	maximal, characteristic, complemented
15	#15689680	C₂	1	1	yes	maximal, characteristic, complemented
16	#15689675	C₂	1	1	yes	maximal, characteristic, complemented
17	#15689654	C₂	1	1	yes	maximal, characteristic, complemented
18	#15689633	C₂	1	1	yes	maximal, characteristic
19	C₂²⋊Q₈×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
20	#15689602	C₂	1	1	yes	maximal, characteristic, complemented
21	#15689599	C₂	1	1	yes	maximal, characteristic, complemented
22	C₂×#13093981	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#529	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#10625352	C₂²	1	1	yes	characteristic
25	C₂×Q₈×D₄₇	C₂²	1	1	yes	characteristic
26	C₂²×C₄×D₄₇	C₂²	1	1	yes	characteristic
27	#13094024	C₂²	1	1	yes	characteristic, complemented
28	#13094024	C₂²	1	1	yes	characteristic, complemented
29	#13094023	C₂²	1	1	yes	characteristic, complemented
30	#13094023	C₂²	1	2	yes	complemented
31	#13094022	C₂²	1	1	yes	characteristic, complemented
32	#13094019	C₂²	1	2	yes	—
33	#13094019	C₂²	1	2	yes	—
34	#13094019	C₂²	1	2	yes	—
35	#13094018	C₂²	1	2	yes	—
36	#13094017	C₂²	1	2	yes	complemented
37	#13094017	C₂²	1	2	yes	complemented
38	#13094017	C₂²	1	2	yes	complemented
39	#13094016	C₂²	1	2	yes	complemented
40	#13094016	C₂²	1	2	yes	complemented
41	#13094015	C₂²	1	1	yes	characteristic, complemented
42	#13094015	C₂²	1	2	yes	complemented
43	#13094015	C₂²	1	2	yes	complemented
44	#13094014	C₂²	1	2	yes	complemented
45	#13094014	C₂²	1	2	yes	complemented
46	#13094014	C₂²	1	2	yes	complemented
47	#13094011	C₂²	1	1	yes	characteristic, complemented
48	#13094010	C₂²	1	2	yes	—
49	#13094010	C₂²	1	2	yes	—
50	#13094008	C₂²	1	2	yes	—
51	#13094007	C₂²	1	2	yes	—
52	#13094006	C₂²	1	2	yes	—
53	#13094006	C₂²	1	2	yes	—
54	#13094006	C₂²	1	2	yes	—
55	#13094005	C₂²	1	2	yes	—
56	#13094004	C₂²	1	1	yes	characteristic
57	#13094004	C₂²	1	1	yes	characteristic
58	#13094004	C₂²	1	2	yes	—
59	#13094003	C₂²	1	2	yes	—
60	#13094003	C₂²	1	1	yes	characteristic
61	#13094003	C₂²	1	1	yes	characteristic
62	#13094003	C₂²	1	2	yes	complemented
63	#13094002	C₂²	1	2	yes	—
64	#13094002	C₂²	1	2	yes	—
65	#13094001	C₂²	1	2	yes	—
66	#13094001	C₂²	1	2	yes	—
67	#13094001	C₂²	1	2	yes	complemented
68	#13094001	C₂²	1	2	yes	complemented
69	#13094001	C₂²	1	2	yes	complemented
70	#13094000	C₂²	1	1	yes	characteristic
71	#13093995	C₂²	1	1	yes	characteristic
72	#13093992	C₂²	1	2	yes	—
73	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
74	C₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
75	C₄×Dic₉₄	C₂²	1	1	yes	characteristic, complemented
76	C₄×Dic₉₄	C₂²	1	2	yes	complemented
77	C₄×Dic₉₄	C₂²	1	2	yes	complemented
78	#13093989	C₂²	1	1	yes	characteristic, complemented
79	#13093989	C₂²	1	1	yes	characteristic, complemented
80	#13093989	C₂²	1	2	yes	complemented
81	#13093989	C₂²	1	2	yes	complemented
82	D₄×Dic₄₇	C₂²	1	2	yes	—
83	D₄×Dic₄₇	C₂²	1	2	yes	—
84	D₄×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
85	C₄×C₂²⋊D₄₇	C₂²	1	2	yes	—
86	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
87	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
88	#13093983	C₂²	1	2	yes	—
89	#13093982	C₂²	1	1	yes	characteristic
90	#13093982	C₂²	1	2	yes	—
91	#13093981	C₂²	1	1	yes	characteristic
92	#13093981	C₂²	1	1	yes	characteristic
93	#13093981	C₂²	1	1	yes	characteristic
94	#13093981	C₂²	1	2	yes	—
95	#13093981	C₂²	1	1	yes	characteristic
96	#13093981	C₂²	1	1	yes	characteristic
97	#13093981	C₂²	1	1	yes	characteristic
98	#13093981	C₂²	1	1	yes	characteristic
99	#13093981	C₂²	1	1	yes	characteristic
100	#13093980	C₂²	1	2	yes	—
101	#13093980	C₂²	1	2	yes	complemented
102	#13093980	C₂²	1	2	yes	complemented
103	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
104	C₂×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
105	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	complemented
106	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
107	C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
108	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
109	C₂×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
110	C₂²⋊C₄×D₄₇	C₂²	1	2	yes	—
111	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
112	#126×C₄₇	C₂²	1	2	yes	complemented
113	#125×C₄₇	C₂²	1	1	yes	characteristic, complemented
114	#124×C₄₇	C₂²	1	1	yes	characteristic, complemented
115	#123×C₄₇	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
117	#121×C₄₇	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
119	C₄×D₄×C₄₇	C₂²	1	2	yes	—
120	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic, complemented
121	#117×C₄₇	C₂²	1	2	yes	complemented
122	C₂×C₄²×C₄₇	C₂²	1	1	yes	characteristic
123	C₂³×D₄₇	C₂³	1	1	yes	characteristic
124	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
125	C₂×D₄×C₄₇	C₂³	1	2	yes	—
126	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
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	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
132	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
133	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
134	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
135	C₂²×Dic₄₇	C₂³	1	2	yes	—
136	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
137	C₂²×Dic₄₇	C₂³	1	2	yes	—
138	Q₈×D₄₇	—	2	4	no	—
139	#10625352	—	2	4	no	—
140	C₂×C₄×D₄₇	—	2	4	no	—
141	C₂×C₄×D₄₇	C₂³	1	2	yes	—
142	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
144	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
145	C₂×C₄×D₄₇	C₂³	1	2	yes	—
146	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
147	C₂×Dic₉₄	C₂³	1	2	yes	—
148	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
149	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
150	C₂×Dic₉₄	C₂³	1	2	yes	—
151	C₂×Dic₉₄	C₂³	1	2	yes	—
152	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
153	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
154	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
155	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
156	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
157	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
158	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
159	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
160	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
161	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
162	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
163	C₄²×C₄₇	C₂³	1	1	yes	characteristic
164	C₄²×C₄₇	C₂³	1	1	yes	characteristic
165	C₄²×C₄₇	C₂³	1	1	yes	characteristic
166	C₄²×C₄₇	C₂³	1	1	yes	characteristic
167	C₄²×C₄₇	C₂³	1	2	yes	—
168	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
169	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
170	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
171	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
172	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
173	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
174	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
176	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
177	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
178	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
179	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
180	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
181	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
182	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
183	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
184	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
185	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
186	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
187	C₄⋊Dic₄₇	C₂³	1	2	yes	—
188	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
189	C₄⋊Dic₄₇	C₂³	1	2	yes	—
190	C₄⋊Dic₄₇	C₂³	1	2	yes	—
191	C₄⋊Dic₄₇	C₂³	1	2	yes	—
192	C₄⋊Dic₄₇	C₂³	1	2	yes	—
193	C₄⋊Dic₄₇	C₂³	1	2	yes	—
194	C₄⋊Dic₄₇	C₂³	1	2	yes	—
195	Dic₄₇⋊C₄	C₂³	1	2	yes	—
196	Dic₄₇⋊C₄	C₂³	1	2	yes	—
197	Dic₄₇⋊C₄	C₂³	1	2	yes	—
198	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
199	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
200	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
201	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
202	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
203	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
204	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
205	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
206	Dic₄₇⋊C₄	C₂³	1	2	yes	—
207	Dic₄₇⋊C₄	C₂³	1	2	yes	—
208	Dic₄₇⋊C₄	C₂³	1	2	yes	—
209	Dic₄₇⋊C₄	C₂³	1	2	yes	—
210	Dic₄₇⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
215	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
216	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
217	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
218	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
219	C₄×Dic₄₇	C₂³	1	2	yes	—
220	C₄×Dic₄₇	C₂³	1	2	yes	—
221	C₄×Dic₄₇	C₂³	1	2	yes	—
222	C₄×Dic₄₇	C₂³	1	2	yes	—
223	C₄×Dic₄₇	C₂³	1	2	yes	—
224	C₄×Dic₄₇	C₂³	1	2	yes	—
225	C₂³×C₄₇	C₂⁴	1	2	yes	—
226	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
227	C₂²×D₄₇	—	2	2	no	—
228	C₂²×D₄₇	—	2	2	no	—
229	C₂²×D₄₇	—	4	1	no	—
230	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
231	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
232	Q₈×C₄₇	—	2	2	no	—
233	D₄×C₄₇	—	2	4	no	—
234	D₄×C₄₇	—	2	2	no	—
235	C₂×C₄×C₄₇	—	2	2	no	—
236	C₂×C₄×C₄₇	—	2	2	no	—
237	C₂×C₄×C₄₇	—	4	1	no	—
238	C₂×C₄×C₄₇	—	4	2	no	—
239	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
240	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
241	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
242	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
243	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
244	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
245	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
246	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
247	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
248	C₂²⋊D₄₇	—	2	4	no	—
249	C₂²⋊D₄₇	—	4	2	no	—
250	C₂×Dic₄₇	—	2	2	no	—
251	C₂×Dic₄₇	—	2	2	no	—
252	C₂×Dic₄₇	—	2	4	no	—
253	C₂×Dic₄₇	—	4	1	no	—
254	C₂×Dic₄₇	—	4	2	no	—
255	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
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	C₂×Dic₄₇	C₂⁴	1	2	yes	—
262	C₂×Dic₄₇	C₂⁴	1	2	yes	—
263	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
264	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
265	C₄×D₄₇	—	2	2	no	—
266	C₄×D₄₇	—	2	4	no	—
267	C₄×D₄₇	—	2	2	no	—
268	C₄×D₄₇	—	2	2	no	—
269	C₄×D₄₇	—	4	2	no	—
270	C₄×D₄₇	#41	1	4	yes	—
271	Dic₉₄	—	2	2	no	—
272	Dic₉₄	—	2	2	no	—
273	Dic₉₄	—	2	4	no	—
274	Dic₉₄	—	4	2	no	—
275	Dic₉₄	—	4	2	no	—
276	C₂²×C₄₇	—	2	1	no	—
277	C₂²×C₄₇	—	2	1	no	—
278	C₂²×C₄₇	—	2	2	no	—
279	C₂²×C₄₇	—	2	2	no	—
280	C₂²×C₄₇	—	2	2	no	—
281	C₂²×C₄₇	2₋¹⁺⁴	1	2	yes	—
282	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
283	C₂×D₄₇	—	2	1	no	—
284	C₂×D₄₇	—	2	1	no	—
285	C₂×D₄₇	—	2	1	no	—
286	C₂×D₄₇	—	2	1	no	—
287	C₂×D₄₇	—	2	1	no	—
288	C₂×D₄₇	—	4	4	no	—
289	C₂×D₄₇	C₂×#41	1	2	yes	—
290	C₄×C₄₇	—	2	2	no	—
291	C₄×C₄₇	—	2	1	no	—
292	C₄×C₄₇	—	2	1	no	—
293	C₄×C₄₇	—	2	1	no	—
294	C₄×C₄₇	—	2	2	no	—
295	C₄×C₄₇	—	2	1	no	—
296	C₄×C₄₇	—	2	2	no	—
297	C₄×C₄₇	—	2	1	no	—
298	C₄×C₄₇	C₂×#41	1	2	yes	—
299	Dic₄₇	—	2	2	no	—
300	Dic₄₇	—	2	2	no	—
301	Dic₄₇	—	2	1	no	—
302	Dic₄₇	—	2	1	no	—
303	Dic₄₇	—	2	1	no	—
304	Dic₄₇	—	2	1	no	—
305	Dic₄₇	—	2	2	no	—
306	Dic₄₇	—	2	2	no	—
307	Dic₄₇	—	2	1	no	—
308	Dic₄₇	C₂×#41	1	2	yes	—
309	#3495	—	47	1	no	maximal, Sylow
310	C₂×C₄₇	—	2	2	no	—
311	C₂×C₄₇	—	4	2	no	—
312	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
313	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
314	C₂×C₄₇	#585	1	1	yes	characteristic
315	D₄₇	—	2	2	no	—
316	D₄₇	—	4	1	no	—
317	#556	—	47	2	no	—
318	#554	—	47	2	no	—
319	#552	—	47	2	no	—
320	#552	—	47	2	no	—
321	#552	—	47	2	no	—
322	#552	—	47	2	no	—
323	#551	—	47	2	no	—
324	#551	—	47	2	no	—
325	#544	—	47	1	no	—
326	#542	—	47	1	no	—
327	#542	—	47	1	no	—
328	#541	—	47	1	no	—
329	#541	—	47	1	no	—
330	#536	—	47	1	no	—
331	#533	—	47	1	no	—
332	#533	—	47	1	no	—
333	#529	—	47	1	no	—
334	#529	D₄₇	1	1	yes	characteristic, complemented
335	#525	—	47	1	no	—
336	C₂×C₂²⋊Q₈	—	47	1	no	—
337	#520	—	47	1	no	—
338	#519	—	47	1	no	—
339	C₂×#117	—	47	1	no	—
340	C₄₇	#3495	1	1	yes	characteristic, complemented, Sylow
341	C₂×#41	—	47	1	no	—
342	C₂²×Q₈	—	47	1	no	—
343	C₂³×C₄	—	47	1	no	—
344	C₄⋊Q₈	—	47	1	no	—
345	C₄⋊Q₈	—	47	1	no	—
346	C₄⋊Q₈	—	47	2	no	—
347	C₄⋊Q₈	—	47	1	no	—
348	C₄⋊Q₈	—	47	1	no	—
349	#126	—	47	2	no	—
350	#126	—	47	2	no	—
351	#126	—	47	2	no	—
352	#126	—	47	2	no	—
353	#126	—	47	2	no	—
354	#126	—	47	2	no	—
355	#126	—	47	2	no	—
356	#126	C₂×D₄₇	1	2	yes	complemented
357	#125	—	47	1	no	—
358	#125	—	47	2	no	—
359	#125	—	47	2	no	—
360	#125	—	47	2	no	—
361	#125	—	47	2	no	—
362	#125	—	47	2	no	—
363	#125	—	47	2	no	—
364	#125	—	47	2	no	—
365	#125	C₂×D₄₇	1	1	yes	characteristic, complemented
366	#124	—	47	1	no	—
367	#124	—	47	2	no	—
368	#124	—	47	2	no	—
369	#124	C₂×D₄₇	1	1	yes	characteristic, complemented
370	#123	—	47	2	no	—
371	#123	—	47	2	no	—
372	#123	—	47	2	no	—
373	#123	—	47	2	no	—
374	#123	—	47	2	no	—
375	#123	—	47	2	no	—
376	#123	C₂×D₄₇	1	2	yes	—
377	C₂²⋊Q₈	—	47	1	no	—
378	C₂²⋊Q₈	—	47	1	no	—
379	C₂²⋊Q₈	—	47	1	no	—
380	C₂²⋊Q₈	—	47	2	no	—
381	C₂²⋊Q₈	—	47	2	no	—
382	C₂²⋊Q₈	—	47	1	no	—
383	C₂²⋊Q₈	—	47	2	no	—
384	C₂²⋊Q₈	—	47	1	no	—
385	C₂²⋊Q₈	—	47	2	no	—
386	C₂²⋊Q₈	—	47	2	no	—
387	C₂²⋊Q₈	—	47	2	no	—
388	C₂²⋊Q₈	—	47	2	no	—
389	C₂²⋊Q₈	—	47	2	no	—
390	C₂²⋊Q₈	—	47	2	no	—
391	C₂²⋊Q₈	—	47	2	no	—
392	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
393	#121	—	47	1	no	—
394	#121	C₂×D₄₇	1	1	yes	characteristic
395	#120	—	47	2	no	—
396	C₄×Q₈	—	47	1	no	—
397	C₄×Q₈	—	47	1	no	—
398	C₄×Q₈	—	47	2	no	—
399	C₄×Q₈	—	47	1	no	—
400	C₄×Q₈	—	47	2	no	—
401	C₄×Q₈	—	47	1	no	—
402	C₄×Q₈	—	47	2	no	—
403	C₄×Q₈	—	47	1	no	—
404	C₄×Q₈	—	47	2	no	—
405	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic, complemented
406	C₄×D₄	—	47	1	no	—
407	C₄×D₄	—	47	2	no	—
408	C₄×D₄	—	47	2	no	—
409	C₄×D₄	—	47	2	no	—
410	C₄×D₄	—	47	2	no	—
411	C₄×D₄	—	47	2	no	—
412	C₄×D₄	C₂×D₄₇	1	2	yes	—
413	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic, complemented
414	#117	—	47	2	no	—
415	#117	—	47	1	no	—
416	#117	—	47	2	no	—
417	#117	—	47	2	no	—
418	#117	—	47	2	no	—
419	#117	—	47	2	no	—
420	#117	—	47	1	no	—
421	#117	—	47	1	no	—
422	#117	—	47	1	no	—
423	#117	—	47	1	no	—
424	#117	—	47	1	no	—
425	#117	—	47	1	no	—
426	#117	—	47	1	no	—
427	#117	—	47	1	no	—
428	#117	—	47	2	no	—
429	#117	C₂×D₄₇	1	2	yes	complemented
430	C₂×C₄⋊C₄	—	47	1	no	—
431	C₂×C₄⋊C₄	—	47	1	no	—
432	C₂×C₄⋊C₄	—	47	2	no	—
433	C₂×C₄⋊C₄	—	47	1	no	—
434	C₂×C₄⋊C₄	—	47	2	no	—
435	C₂×C₂²⋊C₄	—	47	1	no	—
436	C₂×C₂²⋊C₄	—	47	1	no	—
437	C₂×C₂²⋊C₄	—	47	2	no	—
438	C₂×C₄²	—	47	1	no	—
439	C₂×C₄²	C₂×D₄₇	1	1	yes	characteristic
440	C₂⁴	—	47	1	no	—
441	#41	—	94	4	no	—
442	C₂×Q₈	—	47	2	no	—
443	C₂×Q₈	—	47	1	no	—
444	C₂×Q₈	—	47	1	no	—
445	C₂×Q₈	—	47	2	no	—
446	C₂×Q₈	—	47	2	no	—
447	C₂×Q₈	—	94	4	no	—
448	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
449	C₂×D₄	—	47	2	no	—
450	C₂×D₄	—	47	2	no	—
451	C₂×D₄	C₂²×D₄₇	1	2	yes	—
452	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
453	C₂²×C₄	—	47	1	no	—
454	C₂²×C₄	—	47	1	no	—
455	C₂²×C₄	—	47	1	no	—
456	C₂²×C₄	—	47	2	no	—
457	C₂²×C₄	—	47	1	no	—
458	C₂²×C₄	—	47	2	no	—
459	C₂²×C₄	—	47	2	no	—
460	C₂²×C₄	—	47	1	no	—
461	C₂²×C₄	—	47	1	no	—
462	C₂²×C₄	—	47	1	no	—
463	C₂²×C₄	—	47	2	no	—
464	C₂²×C₄	—	94	4	no	—
465	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
466	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
467	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
468	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
469	C₄⋊C₄	—	47	1	no	—
470	C₄⋊C₄	—	47	2	no	—
471	C₄⋊C₄	—	47	1	no	—
472	C₄⋊C₄	—	47	1	no	—
473	C₄⋊C₄	—	47	1	no	—
474	C₄⋊C₄	—	47	1	no	—
475	C₄⋊C₄	—	47	1	no	—
476	C₄⋊C₄	—	47	1	no	—
477	C₄⋊C₄	—	47	1	no	—
478	C₄⋊C₄	—	47	2	no	—
479	C₄⋊C₄	—	47	2	no	—
480	C₄⋊C₄	—	47	2	no	—
481	C₄⋊C₄	—	47	2	no	—
482	C₄⋊C₄	—	47	2	no	—
483	C₄⋊C₄	—	47	2	no	—
484	C₄⋊C₄	—	47	2	no	—
485	C₄⋊C₄	—	47	2	no	—
486	C₄⋊C₄	—	47	2	no	—
487	C₄⋊C₄	—	47	2	no	—
488	C₄⋊C₄	—	47	2	no	—
489	C₄⋊C₄	—	47	1	no	—
490	C₄⋊C₄	—	47	2	no	—
491	C₄⋊C₄	—	47	1	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	2	no	—
497	C₄⋊C₄	—	47	2	no	—
498	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
499	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
500	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
501	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
502	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
503	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
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	1	no	—
511	C₂²⋊C₄	—	47	1	no	—
512	C₂²⋊C₄	—	47	1	no	—
513	C₂²⋊C₄	—	47	1	no	—
514	C₂²⋊C₄	—	47	1	no	—
515	C₂²⋊C₄	—	47	1	no	—
516	C₂²⋊C₄	—	47	1	no	—
517	C₂²⋊C₄	—	47	1	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	C₂²×D₄₇	1	2	yes	—
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	C₄²	—	47	1	no	—
528	C₄²	—	47	1	no	—
529	C₄²	—	47	1	no	—
530	C₄²	—	47	1	no	—
531	C₄²	—	47	2	no	—
532	C₄²	—	47	2	no	—
533	C₄²	—	47	2	no	—
534	C₄²	—	47	2	no	—
535	C₄²	—	47	2	no	—
536	C₄²	—	47	2	no	—
537	C₄²	C₂²×D₄₇	1	1	yes	characteristic
538	C₄²	C₂²×D₄₇	1	1	yes	characteristic
539	C₄²	C₂²×D₄₇	1	1	yes	characteristic
540	C₄²	C₂²×D₄₇	1	1	yes	characteristic
541	C₄²	C₂²×D₄₇	1	2	yes	—
542	C₂³	—	47	1	no	—
543	C₂³	—	47	1	no	—
544	C₂³	—	94	2	no	—
545	C₂³	—	94	2	no	—
546	C₂³	—	188	1	no	—
547	C₂³	C₂³×D₄₇	1	2	yes	—
548	C₂³	C₂³×D₄₇	1	1	yes	characteristic
549	Q₈	—	2	2	no	—
550	Q₈	—	94	4	no	—
551	Q₈	—	94	2	no	—
552	Q₈	—	94	2	no	—
553	Q₈	—	188	2	no	—
554	Q₈	—	188	2	no	—
555	D₄	—	2	4	no	—
556	D₄	—	2	2	no	—
557	D₄	—	94	4	no	—
558	D₄	—	188	2	no	—
559	C₂×C₄	—	2	2	no	—
560	C₂×C₄	—	2	2	no	—
561	C₂×C₄	—	4	2	no	—
562	C₂×C₄	—	4	1	no	—
563	C₂×C₄	—	47	1	no	—
564	C₂×C₄	—	47	4	no	—
565	C₂×C₄	—	47	1	no	—
566	C₂×C₄	—	47	1	no	—
567	C₂×C₄	—	47	2	no	—
568	C₂×C₄	—	47	1	no	—
569	C₂×C₄	—	47	2	no	—
570	C₂×C₄	—	47	1	no	—
571	C₂×C₄	—	47	2	no	—
572	C₂×C₄	—	47	2	no	—
573	C₂×C₄	—	47	1	no	—
574	C₂×C₄	—	94	2	no	—
575	C₂×C₄	—	94	2	no	—
576	C₂×C₄	—	94	4	no	—
577	C₂×C₄	—	94	2	no	—
578	C₂×C₄	—	94	4	no	—
579	C₂×C₄	—	94	2	no	—
580	C₂×C₄	—	94	2	no	—
581	C₂×C₄	—	188	2	no	—
582	C₂×C₄	—	188	2	no	—
583	C₂×C₄	—	188	1	no	—
584	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
585	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
586	C₂×C₄	C₂³×D₄₇	1	2	yes	—
587	C₂×C₄	C₂³×D₄₇	1	2	yes	—
588	C₂×C₄	C₂³×D₄₇	1	2	yes	—
589	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
590	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
591	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
593	C₂²	—	2	1	no	—
594	C₂²	—	2	1	no	—
595	C₂²	—	2	2	no	—
596	C₂²	—	2	2	no	—
597	C₂²	—	2	2	no	—
598	C₂²	—	47	2	no	—
599	C₂²	—	94	1	no	—
600	C₂²	—	94	1	no	—
601	C₂²	—	94	1	no	—
602	C₂²	—	94	1	no	—
603	C₂²	—	94	1	no	—
604	C₂²	—	188	4	no	—
605	C₂²	#13094071	1	2	yes	—
606	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
607	C₄	—	2	1	no	—
608	C₄	—	2	2	no	—
609	C₄	—	2	1	no	—
610	C₄	—	2	1	no	—
611	C₄	—	2	2	no	—
612	C₄	—	2	1	no	—
613	C₄	—	2	2	no	—
614	C₄	—	2	1	no	—
615	C₄	—	47	2	no	—
616	C₄	—	94	1	no	—
617	C₄	—	94	2	no	—
618	C₄	—	94	2	no	—
619	C₄	—	94	1	no	—
620	C₄	—	94	1	no	—
621	C₄	—	94	1	no	—
622	C₄	—	94	2	no	—
623	C₄	—	94	1	no	—
624	C₄	—	94	2	no	—
625	C₄	#41×D₄₇	1	2	yes	—
626	C₂	—	2	2	no	—
627	C₂	—	4	2	no	—
628	C₂	—	94	2	no	—
629	C₂	—	188	1	no	—
630	C₂	C₂×#41×D₄₇	1	1	yes	characteristic
631	C₂	C₂×#13094071	1	1	yes	characteristic
632	C₂	#15689959	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#529	C₂
hypercenter	#529	D₄₇
hypocenter	C₄₇	#3495
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #529

Complements

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

N	H ≅ G/N	type
1. #15689840	C₂	semidirect
2. #15689832	C₂	semidirect
3. #15689812	C₂	semidirect
4. #15689810	C₂	semidirect
5. #15689809	C₂	semidirect
6. #15689806	C₂	semidirect
7. #15689802	C₂	semidirect
8. #15689796	C₂	semidirect
9. #15689753	C₂	semidirect
10. #15689742	C₂	semidirect
11. #15689738	C₂	semidirect
12. #15689736	C₂	semidirect
13. #15689731	C₂	semidirect
14. #15689693	C₂	semidirect
15. #15689680	C₂	semidirect
16. #15689675	C₂	semidirect
17. #15689654	C₂	semidirect
19. C₂²⋊Q₈×D₄₇	C₂	semidirect
20. #15689602	C₂	semidirect
21. #15689599	C₂	semidirect
22. C₂×#13093981	C₂	semidirect
23. C₄₇×#529	C₂	semidirect
27. #13094024	C₂²	semidirect
28. #13094024	C₂²	semidirect
29. #13094023	C₂²	semidirect
30. #13094023	C₂²	semidirect
31. #13094022	C₂²	semidirect
36. #13094017	C₂²	semidirect
37. #13094017	C₂²	semidirect
38. #13094017	C₂²	semidirect
39. #13094016	C₂²	semidirect
40. #13094016	C₂²	semidirect
41. #13094015	C₂²	semidirect
42. #13094015	C₂²	semidirect
43. #13094015	C₂²	semidirect
44. #13094014	C₂²	semidirect
45. #13094014	C₂²	semidirect
46. #13094014	C₂²	semidirect
47. #13094011	C₂²	semidirect
62. #13094003	C₂²	semidirect
67. #13094001	C₂²	semidirect
68. #13094001	C₂²	semidirect
69. #13094001	C₂²	semidirect
73. Q₈×Dic₄₇	C₂²	semidirect
74. C₄×Dic₉₄	C₂²	semidirect
75. C₄×Dic₉₄	C₂²	semidirect
76. C₄×Dic₉₄	C₂²	semidirect
77. C₄×Dic₉₄	C₂²	semidirect
78. #13093989	C₂²	semidirect
79. #13093989	C₂²	semidirect
80. #13093989	C₂²	semidirect
81. #13093989	C₂²	semidirect
84. D₄×Dic₄₇	C₂²	semidirect
101. #13093980	C₂²	semidirect
102. #13093980	C₂²	semidirect
105. C₂×Dic₄₇⋊C₄	C₂²	semidirect
112. #126×C₄₇	C₂²	semidirect
113. #125×C₄₇	C₂²	semidirect
114. #124×C₄₇	C₂²	semidirect
118. C₄×Q₈×C₄₇	C₂²	semidirect
120. C₄×D₄×C₄₇	C₂²	semidirect
121. #117×C₄₇	C₂²	semidirect
334. #529	D₄₇	semidirect
340. C₄₇	#3495	semidirect
356. #126	C₂×D₄₇	semidirect
365. #125	C₂×D₄₇	semidirect
369. #124	C₂×D₄₇	semidirect
405. C₄×Q₈	C₂×D₄₇	semidirect
413. C₄×D₄	C₂×D₄₇	semidirect
429. #117	C₂×D₄₇	semidirect