Subgroups — #20257363

Order 6016.

1014 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689849	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689831	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689829	C₂	1	1	yes	maximal, characteristic, complemented
4	#15689819	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689817	C₂	1	1	yes	maximal, characteristic, complemented
6	#15689811	C₂	1	2	yes	maximal, complemented
7	#15689809	C₂	1	2	yes	maximal, complemented
8	#15689807	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689806	C₂	1	2	yes	maximal, complemented
10	#15689774	C₂	1	1	yes	maximal, characteristic, complemented
11	#15689771	C₂	1	2	yes	maximal, complemented
12	#15689732	C₂	1	2	yes	maximal, complemented
13	#15689717	C₂	1	2	yes	maximal, complemented
14	#15689714	C₂	1	2	yes	maximal, complemented
15	#15689676	C₂	1	1	yes	maximal, characteristic, complemented
16	#15689660	C₂	1	1	yes	maximal, characteristic, complemented
17	#15689659	C₂	1	1	yes	maximal, characteristic, complemented
18	#15689659	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#13094015	C₂	1	1	yes	maximal, characteristic, complemented
20	#125×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
21	#15689603	C₂	1	2	yes	maximal, complemented
22	C₄×#10625352	C₂	1	1	yes	maximal, characteristic, complemented
23	C₄₇×#552	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#10625350	C₂²	1	2	yes	—
25	C₂×#10625352	C₂²	1	1	yes	characteristic
26	#13094023	C₂²	1	2	yes	—
27	#13094023	C₂²	1	1	yes	characteristic
28	#13094023	C₂²	1	1	yes	characteristic
29	#13094019	C₂²	1	2	yes	—
30	#13094019	C₂²	1	2	yes	—
31	#13094019	C₂²	1	2	yes	—
32	#13094019	C₂²	1	2	yes	—
33	#13094018	C₂²	1	2	yes	—
34	#13094017	C₂²	1	2	yes	—
35	#13094016	C₂²	1	2	yes	—
36	#13094016	C₂²	1	1	yes	characteristic
37	#13094015	C₂²	1	2	yes	—
38	#13094015	C₂²	1	1	yes	characteristic
39	#13094015	C₂²	1	2	yes	—
40	#13094015	C₂²	1	2	yes	—
41	#13094015	C₂²	1	1	yes	characteristic
42	#13094015	C₂²	1	1	yes	characteristic
43	#13094015	C₂²	1	1	yes	characteristic
44	#13094015	C₂²	1	1	yes	characteristic
45	#13094014	C₂²	1	2	yes	—
46	#13094014	C₂²	1	2	yes	—
47	#13094014	C₂²	1	2	yes	—
48	#13094014	C₂²	1	2	yes	—
49	#13094013	C₂²	1	1	yes	characteristic
50	#13094009	C₂²	1	2	yes	—
51	#13094009	C₂²	1	2	yes	—
52	#13094008	C₂²	1	2	yes	—
53	#13094008	C₂²	1	2	yes	—
54	#13094007	C₂²	1	2	yes	—
55	#13094006	C₂²	1	2	yes	—
56	#13094006	C₂²	1	2	yes	—
57	#13094006	C₂²	1	2	yes	—
58	#13094004	C₂²	1	2	yes	—
59	#13094004	C₂²	1	2	yes	—
60	#13094002	C₂²	1	2	yes	—
61	#13094002	C₂²	1	2	yes	—
62	#13094002	C₂²	1	2	yes	—
63	#13094001	C₂²	1	2	yes	—
64	#13094001	C₂²	1	2	yes	—
65	#13094001	C₂²	1	2	yes	—
66	#13094000	C₂²	1	1	yes	characteristic
67	#13093999	C₂²	1	1	yes	characteristic
68	#13093998	C₂²	1	1	yes	characteristic
69	#13093998	C₂²	1	1	yes	characteristic
70	#13093997	C₂²	1	2	yes	—
71	#13093996	C₂²	1	2	yes	—
72	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic
73	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic
74	C₄×Dic₉₄	C₂²	1	2	yes	—
75	C₄×Dic₉₄	C₂²	1	2	yes	—
76	C₄×Dic₉₄	C₂²	1	2	yes	—
77	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
78	#13093989	C₂²	1	1	yes	characteristic
79	C₄×D₁₈₈	C₂²	1	2	yes	—
80	C₄×D₁₈₈	C₂²	1	1	yes	characteristic
81	C₄×D₁₈₈	C₂²	1	2	yes	—
82	D₄×Dic₄₇	C₂²	1	1	yes	characteristic
83	#13093986	C₂²	1	1	yes	characteristic
84	#13093986	C₂²	1	1	yes	characteristic
85	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
86	C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
87	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
88	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
89	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
90	(C₂²⋊D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
91	(C₂²⋊D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
92	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
93	#13093983	C₂²	1	1	yes	characteristic
94	#13093982	C₂²	1	2	yes	—
95	#13093982	C₂²	1	2	yes	—
96	#13093982	C₂²	1	2	yes	—
97	#13093982	C₂²	1	1	yes	characteristic
98	#13093981	C₂²	1	2	yes	—
99	#13093980	C₂²	1	1	yes	characteristic
100	#13093980	C₂²	1	1	yes	characteristic
101	C₂×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
102	C₂×C₄⋊Dic₄₇	C₂²	1	2	yes	—
103	C₂×Dic₄₇⋊C₄	C₂²	1	2	yes	—
104	C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
105	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
106	C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
107	C₄⋊C₄×D₄₇	C₂²	1	1	yes	characteristic
108	C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
109	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
110	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
111	C₄²×D₄₇	C₂²	1	1	yes	characteristic
112	#126×C₄₇	C₂²	1	2	yes	—
113	#125×C₄₇	C₂²	1	2	yes	—
114	#125×C₄₇	C₂²	1	1	yes	characteristic
115	#123×C₄₇	C₂²	1	2	yes	—
116	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
117	C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
118	C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
119	C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
120	#117×C₄₇	C₂²	1	2	yes	—
121	#117×C₄₇	C₂²	1	1	yes	characteristic
122	C₂×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
123	C₂×Q₈×C₄₇	C₂³	1	1	yes	characteristic
124	C₂×D₄×C₄₇	C₂³	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂³	1	2	yes	—
126	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
127	C₂²×C₄×C₄₇	C₂³	1	1	yes	characteristic
128	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
129	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
130	C₂×C₂²⋊D₄₇	C₂³	1	2	yes	—
131	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
132	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
133	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
134	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
135	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
136	C₂²×Dic₄₇	C₂³	1	2	yes	—
137	#10625352	—	2	4	no	—
138	#10625350	—	2	8	no	—
139	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
140	C₂×D₁₈₈	C₂³	1	2	yes	—
141	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
142	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₄₇	C₂³	1	2	yes	—
144	C₂×C₄×D₄₇	C₂³	1	2	yes	—
145	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
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×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	1	yes	characteristic
153	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
154	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
155	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
156	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
157	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
158	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
159	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
160	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
161	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
162	C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
163	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
164	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
165	C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
166	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
167	C₄²×C₄₇	C₂³	1	2	yes	—
168	C₄²×C₄₇	C₂³	1	2	yes	—
169	C₄²×C₄₇	C₂³	1	1	yes	characteristic
170	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
171	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
172	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
173	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
174	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
175	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
176	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
177	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
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	C₄⋊Dic₄₇	C₂³	1	2	yes	—
185	C₄⋊Dic₄₇	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	1	yes	characteristic
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	1	yes	characteristic
194	C₄⋊Dic₄₇	C₂³	1	2	yes	—
195	C₄⋊Dic₄₇	C₂³	1	2	yes	—
196	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
197	Dic₄₇⋊C₄	C₂³	1	2	yes	—
198	Dic₄₇⋊C₄	C₂³	1	2	yes	—
199	Dic₄₇⋊C₄	C₂³	1	2	yes	—
200	Dic₄₇⋊C₄	C₂³	1	2	yes	—
201	Dic₄₇⋊C₄	C₂³	1	2	yes	—
202	Dic₄₇⋊C₄	C₂³	1	2	yes	—
203	Dic₄₇⋊C₄	C₂³	1	2	yes	—
204	Dic₄₇⋊C₄	C₂³	1	2	yes	—
205	Dic₄₇⋊C₄	C₂³	1	2	yes	—
206	Dic₄₇⋊C₄	C₂³	1	2	yes	—
207	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
208	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
209	Dic₄₇⋊C₄	C₂³	1	1	yes	characteristic
210	Dic₄₇⋊C₄	C₂³	1	2	yes	—
211	Dic₄₇⋊C₄	C₂³	1	2	yes	—
212	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
213	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
214	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
220	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
221	C₄×Dic₄₇	C₂³	1	2	yes	—
222	C₄×Dic₄₇	C₂³	1	2	yes	—
223	C₄×Dic₄₇	C₂³	1	2	yes	—
224	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
225	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
226	C₂²×D₄₇	C₂⁴	1	2	yes	—
227	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
228	Q₈×C₄₇	—	2	2	no	—
229	D₄×C₄₇	—	2	2	no	—
230	C₂×C₄×C₄₇	—	2	4	no	—
231	C₂×C₄×C₄₇	—	2	2	no	—
232	C₂×C₄×C₄₇	—	2	2	no	—
233	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
235	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
236	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
237	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
238	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
239	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
240	C₂×C₄×C₄₇	C₂⁴	1	2	yes	—
241	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
242	C₂²⋊D₄₇	—	2	4	no	—
243	C₂²⋊D₄₇	—	2	2	no	—
244	C₂²⋊D₄₇	—	4	2	no	—
245	C₂²⋊D₄₇	#41	1	4	yes	—
246	C₂×Dic₄₇	—	2	2	no	—
247	C₂×Dic₄₇	—	2	2	no	—
248	C₂×Dic₄₇	—	4	1	no	—
249	C₂×Dic₄₇	—	4	2	no	—
250	C₂×Dic₄₇	—	4	1	no	—
251	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
252	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
253	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
254	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₄₇	C₂⁴	1	2	yes	—
257	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
258	C₂×Dic₄₇	C₂⁴	1	2	yes	—
259	C₂×Dic₄₇	C₂⁴	1	2	yes	—
260	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
261	D₁₈₈	—	2	4	no	—
262	D₁₈₈	—	2	2	no	—
263	C₄×D₄₇	—	2	4	no	—
264	C₄×D₄₇	—	2	2	no	—
265	C₄×D₄₇	—	2	2	no	—
266	C₄×D₄₇	—	2	4	no	—
267	C₄×D₄₇	—	4	2	no	—
268	C₄×D₄₇	—	4	2	no	—
269	C₄×D₄₇	—	4	1	no	—
270	C₄×D₄₇	—	4	2	no	—
271	Dic₉₄	—	2	4	no	—
272	Dic₉₄	—	2	2	no	—
273	Dic₉₄	—	4	2	no	—
274	C₂²×C₄₇	—	2	1	no	—
275	C₂²×C₄₇	—	2	1	no	—
276	C₂²×C₄₇	—	2	1	no	—
277	C₂²×C₄₇	—	2	1	no	—
278	C₂²×C₄₇	—	2	1	no	—
279	C₂²×C₄₇	C₂×#41	1	2	yes	—
280	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
281	C₂×D₄₇	—	2	1	no	—
282	C₂×D₄₇	—	2	1	no	—
283	C₂×D₄₇	—	2	2	no	—
284	C₂×D₄₇	—	2	2	no	—
285	C₂×D₄₇	—	2	2	no	—
286	C₂×D₄₇	C₂×#41	1	2	yes	—
287	C₄×C₄₇	—	2	1	no	—
288	C₄×C₄₇	—	2	2	no	—
289	C₄×C₄₇	—	2	2	no	—
290	C₄×C₄₇	—	2	1	no	—
291	C₄×C₄₇	—	2	1	no	—
292	C₄×C₄₇	—	2	2	no	—
293	C₄×C₄₇	—	2	2	no	—
294	C₄×C₄₇	—	2	1	no	—
295	C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
296	Dic₄₇	—	2	2	no	—
297	Dic₄₇	—	2	1	no	—
298	Dic₄₇	—	2	1	no	—
299	Dic₄₇	—	2	1	no	—
300	Dic₄₇	—	2	1	no	—
301	Dic₄₇	—	2	2	no	—
302	Dic₄₇	—	2	1	no	—
303	Dic₄₇	—	2	1	no	—
304	Dic₄₇	—	2	2	no	—
305	Dic₄₇	C₂×#41	1	2	yes	—
306	#3515	—	47	1	no	maximal, Sylow
307	C₂×C₄₇	—	2	2	no	—
308	C₂×C₄₇	—	4	1	no	—
309	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
310	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
311	C₂×C₄₇	#585	1	1	yes	characteristic
312	D₄₇	—	2	2	no	—
313	D₄₇	—	4	2	no	—
314	#557	—	47	1	no	—
315	#554	—	47	1	no	—
316	#554	—	47	1	no	—
317	#553	—	47	1	no	—
318	#553	—	47	1	no	—
319	#552	—	47	2	no	—
320	#552	—	47	2	no	—
321	#552	—	47	1	no	—
322	#552	—	47	2	no	—
323	#552	D₄₇	1	1	yes	characteristic, complemented
324	#547	—	47	2	no	—
325	#547	—	47	1	no	—
326	#541	—	47	2	no	—
327	#539	—	47	2	no	—
328	#539	—	47	2	no	—
329	#533	—	47	1	no	—
330	#529	—	47	1	no	—
331	#529	—	47	1	no	—
332	#529	—	47	1	no	—
333	C₂×#125	—	47	1	no	—
334	C₂×#125	—	47	1	no	—
335	#520	—	47	2	no	—
336	C₄×#41	—	47	1	no	—
337	C₄₇	#3515	1	1	yes	characteristic, complemented, Sylow
338	C₂×#41	—	47	1	no	—
339	C₂×#41	—	47	2	no	—
340	C₄⋊Q₈	—	47	1	no	—
341	C₄⋊Q₈	—	47	1	no	—
342	C₄⋊Q₈	—	47	2	no	—
343	#126	—	47	2	no	—
344	#126	—	47	2	no	—
345	#126	—	47	2	no	—
346	#126	—	47	2	no	—
347	#126	—	47	2	no	—
348	#126	—	47	2	no	—
349	#126	C₂×D₄₇	1	2	yes	—
350	#125	—	47	1	no	—
351	#125	—	47	1	no	—
352	#125	—	47	1	no	—
353	#125	—	47	2	no	—
354	#125	—	47	2	no	—
355	#125	—	47	2	no	—
356	#125	—	47	2	no	—
357	#125	—	47	1	no	—
358	#125	—	47	1	no	—
359	#125	—	47	2	no	—
360	#125	—	47	2	no	—
361	#125	—	47	2	no	—
362	#125	—	47	1	no	—
363	#125	—	47	2	no	—
364	#125	C₂×D₄₇	1	1	yes	characteristic
365	#125	C₂×D₄₇	1	2	yes	—
366	#124	—	47	1	no	—
367	#123	—	47	2	no	—
368	#123	—	47	2	no	—
369	#123	—	47	2	no	—
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	C₂×D₄₇	1	2	yes	—
376	C₂²⋊Q₈	—	47	1	no	—
377	C₂²⋊Q₈	—	47	2	no	—
378	C₂²⋊Q₈	—	47	2	no	—
379	C₂²⋊Q₈	—	47	2	no	—
380	C₂²⋊Q₈	—	47	2	no	—
381	C₂²⋊Q₈	—	47	2	no	—
382	C₂²⋊Q₈	—	47	2	no	—
383	C₂²⋊Q₈	—	47	2	no	—
384	C₂²⋊Q₈	—	47	2	no	—
385	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
386	C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
387	#121	—	47	2	no	—
388	#121	—	47	1	no	—
389	#121	—	47	1	no	—
390	#121	—	47	1	no	—
391	#121	—	47	2	no	—
392	C₄×Q₈	—	47	1	no	—
393	C₄×Q₈	—	47	1	no	—
394	C₄×Q₈	—	47	1	no	—
395	C₄×Q₈	—	47	1	no	—
396	C₄×Q₈	—	47	2	no	—
397	C₄×Q₈	—	47	2	no	—
398	C₄×Q₈	—	47	2	no	—
399	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
400	C₄×D₄	—	47	1	no	—
401	C₄×D₄	—	47	1	no	—
402	C₄×D₄	—	47	1	no	—
403	C₄×D₄	—	47	1	no	—
404	C₄×D₄	—	47	1	no	—
405	C₄×D₄	—	47	1	no	—
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	—	47	2	no	—
413	C₄×D₄	—	47	1	no	—
414	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
415	#117	—	47	1	no	—
416	#117	—	47	1	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	2	no	—
423	#117	C₂×D₄₇	1	2	yes	—
424	#117	C₂×D₄₇	1	1	yes	characteristic
425	C₂×C₄⋊C₄	—	47	2	no	—
426	C₂×C₄⋊C₄	—	47	2	no	—
427	C₂×C₄⋊C₄	—	47	1	no	—
428	C₂×C₄⋊C₄	—	47	2	no	—
429	C₂×C₄⋊C₄	—	47	2	no	—
430	C₂×C₄⋊C₄	—	47	2	no	—
431	C₂×C₄⋊C₄	—	47	1	no	—
432	C₂×C₄⋊C₄	—	47	1	no	—
433	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
434	C₂×C₄²	—	47	1	no	—
435	C₂×C₄²	—	47	1	no	—
436	C₂×C₄²	—	47	1	no	—
437	#41	—	94	8	no	—
438	#41	—	94	4	no	—
439	C₂×Q₈	—	47	1	no	—
440	C₂×Q₈	—	47	2	no	—
441	C₂×Q₈	—	47	2	no	—
442	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
443	C₂×D₄	—	47	1	no	—
444	C₂×D₄	—	47	1	no	—
445	C₂×D₄	—	47	2	no	—
446	C₂×D₄	—	47	2	no	—
447	C₂×D₄	—	47	1	no	—
448	C₂×D₄	—	47	2	no	—
449	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
450	C₂²×C₄	—	47	1	no	—
451	C₂²×C₄	—	47	1	no	—
452	C₂²×C₄	—	47	1	no	—
453	C₂²×C₄	—	47	1	no	—
454	C₂²×C₄	—	47	2	no	—
455	C₂²×C₄	—	47	1	no	—
456	C₂²×C₄	—	47	1	no	—
457	C₂²×C₄	—	47	2	no	—
458	C₂²×C₄	—	47	2	no	—
459	C₂²×C₄	—	47	1	no	—
460	C₂²×C₄	—	47	2	no	—
461	C₂²×C₄	—	47	2	no	—
462	C₂²×C₄	—	47	2	no	—
463	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
464	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
465	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
466	C₄⋊C₄	—	47	1	no	—
467	C₄⋊C₄	—	47	2	no	—
468	C₄⋊C₄	—	47	2	no	—
469	C₄⋊C₄	—	47	2	no	—
470	C₄⋊C₄	—	47	2	no	—
471	C₄⋊C₄	—	47	2	no	—
472	C₄⋊C₄	—	47	2	no	—
473	C₄⋊C₄	—	47	2	no	—
474	C₄⋊C₄	—	47	2	no	—
475	C₄⋊C₄	—	47	2	no	—
476	C₄⋊C₄	—	47	2	no	—
477	C₄⋊C₄	—	47	1	no	—
478	C₄⋊C₄	—	47	1	no	—
479	C₄⋊C₄	—	47	1	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	1	no	—
485	C₄⋊C₄	—	47	1	no	—
486	C₄⋊C₄	—	47	1	no	—
487	C₄⋊C₄	—	47	2	no	—
488	C₄⋊C₄	—	47	2	no	—
489	C₄⋊C₄	—	47	2	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	C₂²×D₄₇	1	2	yes	—
495	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
496	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
497	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
498	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
499	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
500	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
501	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
502	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
503	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
504	C₂²⋊C₄	—	47	1	no	—
505	C₂²⋊C₄	—	47	1	no	—
506	C₂²⋊C₄	—	47	2	no	—
507	C₂²⋊C₄	—	47	1	no	—
508	C₂²⋊C₄	—	47	2	no	—
509	C₂²⋊C₄	—	47	2	no	—
510	C₂²⋊C₄	—	47	1	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	C₂²×D₄₇	1	1	yes	characteristic
519	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
520	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
521	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
522	C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
523	C₄²	—	47	1	no	—
524	C₄²	—	47	1	no	—
525	C₄²	—	47	1	no	—
526	C₄²	—	47	1	no	—
527	C₄²	—	47	1	no	—
528	C₄²	—	47	1	no	—
529	C₄²	—	47	1	no	—
530	C₄²	—	47	1	no	—
531	C₄²	—	47	1	no	—
532	C₄²	—	47	2	no	—
533	C₄²	—	47	2	no	—
534	C₄²	—	47	2	no	—
535	C₄²	C₂²×D₄₇	1	1	yes	characteristic
536	C₄²	C₂²×D₄₇	1	2	yes	—
537	C₄²	C₂²×D₄₇	1	2	yes	—
538	C₂³	—	47	1	no	—
539	C₂³	—	47	2	no	—
540	C₂³	C₂³×D₄₇	1	1	yes	characteristic
541	C₂³	C₂³×D₄₇	1	1	yes	characteristic
542	Q₈	—	2	2	no	—
543	Q₈	—	94	4	no	—
544	Q₈	—	94	2	no	—
545	Q₈	—	188	2	no	—
546	D₄	—	2	2	no	—
547	D₄	—	47	4	no	—
548	D₄	—	94	4	no	—
549	D₄	—	94	2	no	—
550	D₄	—	94	4	no	—
551	D₄	—	94	2	no	—
552	D₄	—	188	2	no	—
553	C₂×C₄	—	2	4	no	—
554	C₂×C₄	—	2	2	no	—
555	C₂×C₄	—	2	2	no	—
556	C₂×C₄	—	47	1	no	—
557	C₂×C₄	—	47	1	no	—
558	C₂×C₄	—	47	1	no	—
559	C₂×C₄	—	47	1	no	—
560	C₂×C₄	—	47	1	no	—
561	C₂×C₄	—	47	1	no	—
562	C₂×C₄	—	47	1	no	—
563	C₂×C₄	—	47	2	no	—
564	C₂×C₄	—	47	2	no	—
565	C₂×C₄	—	47	2	no	—
566	C₂×C₄	—	94	4	no	—
567	C₂×C₄	—	94	4	no	—
568	C₂×C₄	—	94	2	no	—
569	C₂×C₄	—	94	2	no	—
570	C₂×C₄	—	94	2	no	—
571	C₂×C₄	—	94	2	no	—
572	C₂×C₄	—	188	1	no	—
573	C₂×C₄	—	188	2	no	—
574	C₂×C₄	—	188	2	no	—
575	C₂×C₄	—	188	2	no	—
576	C₂×C₄	—	188	1	no	—
577	C₂×C₄	—	188	1	no	—
578	C₂×C₄	—	188	2	no	—
579	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
580	C₂×C₄	C₂³×D₄₇	1	2	yes	—
581	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
582	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
583	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
584	C₂×C₄	C₂³×D₄₇	1	2	yes	—
585	C₂×C₄	C₂³×D₄₇	1	2	yes	—
586	C₂×C₄	C₂³×D₄₇	1	2	yes	—
587	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
588	C₂²	—	2	1	no	—
589	C₂²	—	2	1	no	—
590	C₂²	—	2	1	no	—
591	C₂²	—	2	1	no	—
592	C₂²	—	2	1	no	—
593	C₂²	—	47	2	no	—
594	C₂²	—	94	1	no	—
595	C₂²	—	94	1	no	—
596	C₂²	—	94	2	no	—
597	C₂²	—	94	2	no	—
598	C₂²	—	94	2	no	—
599	C₂²	#41×D₄₇	1	2	yes	—
600	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
601	C₄	—	2	2	no	—
602	C₄	—	2	2	no	—
603	C₄	—	2	1	no	—
604	C₄	—	2	1	no	—
605	C₄	—	2	1	no	—
606	C₄	—	2	2	no	—
607	C₄	—	2	1	no	—
608	C₄	—	2	2	no	—
609	C₄	—	47	2	no	—
610	C₄	—	94	1	no	—
611	C₄	—	94	2	no	—
612	C₄	—	94	1	no	—
613	C₄	—	94	1	no	—
614	C₄	—	94	1	no	—
615	C₄	—	94	1	no	—
616	C₄	—	94	2	no	—
617	C₄	—	94	2	no	—
618	C₄	—	94	1	no	—
619	C₄	#13094071	1	2	yes	—
620	C₂	—	2	2	no	—
621	C₂	—	4	1	no	—
622	C₂	—	94	2	no	—
623	C₂	—	188	2	no	—
624	C₂	C₂×#41×D₄₇	1	1	yes	characteristic
625	C₂	C₂×#13094071	1	1	yes	characteristic
626	C₂	#15689960	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₄₇
commutator, socle	C₂²×C₄₇	C₂⁵
Fitting	C₄₇×#552	C₂
hypercenter	#552	D₄₇
hypocenter	C₄₇	#3515
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #552

Complements

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

N	H ≅ G/N	type
1. #15689849	C₂	semidirect
2. #15689831	C₂	semidirect
3. #15689829	C₂	semidirect
4. #15689819	C₂	semidirect
5. #15689817	C₂	semidirect
6. #15689811	C₂	semidirect
7. #15689809	C₂	semidirect
8. #15689807	C₂	semidirect
9. #15689806	C₂	semidirect
10. #15689774	C₂	semidirect
11. #15689771	C₂	semidirect
12. #15689732	C₂	semidirect
13. #15689717	C₂	semidirect
14. #15689714	C₂	semidirect
15. #15689676	C₂	semidirect
16. #15689660	C₂	semidirect
17. #15689659	C₂	semidirect
18. #15689659	C₂	semidirect
19. C₂×#13094015	C₂	semidirect
20. #125×D₄₇	C₂	semidirect
21. #15689603	C₂	semidirect
22. C₄×#10625352	C₂	semidirect
23. C₄₇×#552	C₂	semidirect
323. #552	D₄₇	semidirect
337. C₄₇	#3515	semidirect