Subgroups — #20257002

Order 6016.

1094 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#15689850	C₂	1	1	yes	maximal, characteristic, complemented
2	#15689845	C₂	1	1	yes	maximal, characteristic, complemented
3	#15689840	C₂	1	2	yes	maximal, complemented
4	#15689812	C₂	1	1	yes	maximal, characteristic, complemented
5	#15689806	C₂	1	2	yes	maximal, complemented
6	#15689805	C₂	1	2	yes	maximal, complemented
7	#15689786	C₂	1	1	yes	maximal, characteristic, complemented
8	#15689783	C₂	1	1	yes	maximal, characteristic, complemented
9	#15689782	C₂	1	1	yes	maximal, characteristic, complemented
10	#15689774	C₂	1	1	yes	maximal, characteristic, complemented
11	#15689771	C₂	1	2	yes	maximal, complemented
12	#15689679	C₂	1	2	yes	maximal, complemented
13	#15689675	C₂	1	1	yes	maximal, characteristic, complemented
14	#15689659	C₂	1	1	yes	maximal, characteristic, complemented
15	#15689658	C₂	1	1	yes	maximal, characteristic, complemented
16	#15689656	C₂	1	2	yes	maximal, complemented
17	#15689650	C₂	1	2	yes	maximal, complemented
18	#15689591	C₂	1	2	yes	maximal, complemented
19	#15689591	C₂	1	1	yes	maximal, characteristic, complemented
20	C₄×#10625352	C₂	1	1	yes	maximal, characteristic, complemented
21	C₂×#13093989	C₂	1	1	yes	maximal, characteristic, complemented
22	C₄×Q₈×D₄₇	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×#10625350	C₂²	1	1	yes	characteristic
26	C₂×#10625352	C₂²	1	1	yes	characteristic
27	C₂²×Dic₉₄	C₂²	1	1	yes	characteristic
28	C₂×Q₈×D₄₇	C₂²	1	1	yes	characteristic
29	#13094023	C₂²	1	2	yes	—
30	#13094023	C₂²	1	1	yes	characteristic
31	#13094023	C₂²	1	2	yes	—
32	#13094022	C₂²	1	1	yes	characteristic
33	#13094019	C₂²	1	2	yes	—
34	#13094019	C₂²	1	2	yes	—
35	#13094019	C₂²	1	2	yes	—
36	#13094018	C₂²	1	2	yes	—
37	#13094017	C₂²	1	2	yes	—
38	#13094016	C₂²	1	2	yes	—
39	#13094015	C₂²	1	1	yes	characteristic
40	#13094014	C₂²	1	2	yes	—
41	#13094014	C₂²	1	2	yes	—
42	#13094014	C₂²	1	2	yes	—
43	#13094013	C₂²	1	1	yes	characteristic
44	#13094012	C₂²	1	1	yes	characteristic
45	#13094010	C₂²	1	2	yes	—
46	#13094010	C₂²	1	2	yes	—
47	#13094009	C₂²	1	2	yes	—
48	#13094009	C₂²	1	2	yes	—
49	#13094008	C₂²	1	2	yes	—
50	#13094007	C₂²	1	2	yes	—
51	#13094006	C₂²	1	2	yes	—
52	#13094004	C₂²	1	1	yes	characteristic
53	#13094003	C₂²	1	1	yes	characteristic
54	#13094002	C₂²	1	2	yes	—
55	#13094002	C₂²	1	2	yes	—
56	#13094002	C₂²	1	2	yes	—
57	#13094002	C₂²	1	2	yes	—
58	#13094002	C₂²	1	2	yes	—
59	#13094001	C₂²	1	2	yes	—
60	#13094001	C₂²	1	2	yes	—
61	#13093999	C₂²	1	1	yes	characteristic
62	#13093998	C₂²	1	1	yes	characteristic
63	#13093997	C₂²	1	2	yes	—
64	#13093996	C₂²	1	2	yes	—
65	Q₈×Dic₄₇	C₂²	1	1	yes	characteristic
66	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
67	C₄×Dic₉₄	C₂²	1	2	yes	—
68	C₄×Dic₉₄	C₂²	1	1	yes	characteristic
69	#13093989	C₂²	1	1	yes	characteristic
70	#13093989	C₂²	1	1	yes	characteristic
71	#13093989	C₂²	1	2	yes	—
72	#13093989	C₂²	1	1	yes	characteristic
73	#13093989	C₂²	1	2	yes	—
74	#13093989	C₂²	1	1	yes	characteristic
75	#13093989	C₂²	1	2	yes	—
76	#13093989	C₂²	1	2	yes	—
77	#13093989	C₂²	1	1	yes	characteristic
78	#13093989	C₂²	1	1	yes	characteristic
79	#13093989	C₂²	1	2	yes	—
80	D₄×Dic₄₇	C₂²	1	1	yes	characteristic
81	#13093986	C₂²	1	1	yes	characteristic
82	#13093986	C₂²	1	2	yes	—
83	#13093986	C₂²	1	2	yes	—
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	(C₂²⋊D₄₇)⋊C₄	C₂²	1	2	yes	—
94	#13093982	C₂²	1	1	yes	characteristic
95	#13093982	C₂²	1	2	yes	—
96	#13093982	C₂²	1	2	yes	—
97	#13093981	C₂²	1	2	yes	—
98	#13093981	C₂²	1	2	yes	—
99	#13093981	C₂²	1	2	yes	—
100	#13093980	C₂²	1	1	yes	characteristic
101	#13093980	C₂²	1	1	yes	characteristic
102	#13093980	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	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
107	C₂×C₄×Dic₄₇	C₂²	1	2	yes	—
108	C₂×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
109	C₄²×D₄₇	C₂²	1	1	yes	characteristic
110	C₄²×D₄₇	C₂²	1	2	yes	—
111	C₄²×D₄₇	C₂²	1	2	yes	—
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	2	yes	—
130	C₂×C₂²⋊D₄₇	C₂³	1	1	yes	characteristic
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	2	yes	—
135	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
136	C₂²×Dic₄₇	C₂³	1	1	yes	characteristic
137	Q₈×D₄₇	—	2	4	no	—
138	#10625352	—	2	4	no	—
139	#10625350	—	2	8	no	—
140	#10625350	—	2	4	no	—
141	C₂×D₁₈₈	C₂³	1	2	yes	—
142	C₂×D₁₈₈	C₂³	1	1	yes	characteristic
143	C₂×C₄×D₄₇	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
148	C₂×C₄×D₄₇	C₂³	1	2	yes	—
149	C₂×C₄×D₄₇	C₂³	1	2	yes	—
150	C₂×C₄×D₄₇	C₂³	1	2	yes	—
151	C₂×Dic₉₄	—	2	4	no	—
152	C₂×Dic₉₄	C₂³	1	2	yes	—
153	C₂×Dic₉₄	C₂³	1	2	yes	—
154	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
155	C₂×Dic₉₄	C₂³	1	2	yes	—
156	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
157	C₂×Dic₉₄	C₂³	1	1	yes	characteristic
158	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
159	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
160	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
161	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
162	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
163	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
164	C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
165	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
166	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
167	C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
168	C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
169	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
170	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
171	C₂²⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
172	C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
173	C₄²×C₄₇	C₂³	1	2	yes	—
174	C₄²×C₄₇	C₂³	1	2	yes	—
175	C₄²×C₄₇	C₂³	1	1	yes	characteristic
176	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
177	C₂²⋊Dic₄₇	C₂³	1	1	yes	characteristic
178	C₂²⋊Dic₄₇	C₂³	1	2	yes	—
179	(C₂×D₄₇)⋊C₄	C₂³	1	1	yes	characteristic
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	1	yes	characteristic
186	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
187	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
188	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
189	(C₂×D₄₇)⋊C₄	C₂³	1	2	yes	—
190	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
191	C₄⋊Dic₄₇	C₂³	1	2	yes	—
192	C₄⋊Dic₄₇	C₂³	1	1	yes	characteristic
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	2	yes	—
199	Dic₄₇⋊C₄	C₂³	1	2	yes	—
200	Dic₄₇⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
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	C₄×Dic₄₇	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	2	yes	—
216	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
217	C₄×Dic₄₇	C₂³	1	2	yes	—
218	C₄×Dic₄₇	C₂³	1	2	yes	—
219	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
220	C₄×Dic₄₇	C₂³	1	2	yes	—
221	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
222	C₄×Dic₄₇	C₂³	1	2	yes	—
223	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
224	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
225	C₄×Dic₄₇	C₂³	1	1	yes	characteristic
226	C₄×Dic₄₇	C₂³	1	2	yes	—
227	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
228	C₂³×C₄₇	C₂⁴	1	1	yes	characteristic
229	C₂²×D₄₇	C₂⁴	1	2	yes	—
230	C₂²×D₄₇	C₂⁴	1	1	yes	characteristic
231	Q₈×C₄₇	—	2	2	no	—
232	D₄×C₄₇	—	2	2	no	—
233	C₂×C₄×C₄₇	—	2	4	no	—
234	C₂×C₄×C₄₇	—	2	2	no	—
235	C₂×C₄×C₄₇	—	2	2	no	—
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	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	1	yes	characteristic
244	C₂×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
245	C₂²⋊D₄₇	—	2	4	no	—
246	C₂²⋊D₄₇	—	2	2	no	—
247	C₂²⋊D₄₇	—	2	4	no	—
248	C₂²⋊D₄₇	#41	1	4	yes	complemented
249	C₂×Dic₄₇	—	2	2	no	—
250	C₂×Dic₄₇	—	2	4	no	—
251	C₂×Dic₄₇	—	2	2	no	—
252	C₂×Dic₄₇	—	2	2	no	—
253	C₂×Dic₄₇	—	2	2	no	—
254	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
255	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
256	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
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	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
262	C₂×Dic₄₇	C₂⁴	1	2	yes	—
263	C₂×Dic₄₇	C₂⁴	1	1	yes	characteristic
264	D₁₈₈	—	2	4	no	—
265	D₁₈₈	—	2	2	no	—
266	C₄×D₄₇	—	2	4	no	—
267	C₄×D₄₇	—	2	2	no	—
268	C₄×D₄₇	—	2	2	no	—
269	C₄×D₄₇	—	2	4	no	—
270	C₄×D₄₇	—	2	4	no	—
271	C₄×D₄₇	—	2	4	no	—
272	C₄×D₄₇	—	2	2	no	—
273	C₄×D₄₇	—	2	4	no	—
274	Dic₉₄	—	2	2	no	—
275	Dic₉₄	—	2	4	no	—
276	Dic₉₄	—	2	4	no	—
277	Dic₉₄	—	2	2	no	—
278	Dic₉₄	—	2	4	no	—
279	Dic₉₄	#41	1	4	yes	complemented
280	C₂²×C₄₇	—	2	1	no	—
281	C₂²×C₄₇	—	2	1	no	—
282	C₂²×C₄₇	—	2	1	no	—
283	C₂²×C₄₇	—	2	1	no	—
284	C₂²×C₄₇	—	2	1	no	—
285	C₂²×C₄₇	C₂×#41	1	2	yes	—
286	C₂²×C₄₇	C₂⁵	1	1	yes	characteristic
287	C₂×D₄₇	—	2	1	no	—
288	C₂×D₄₇	—	2	1	no	—
289	C₂×D₄₇	—	2	2	no	—
290	C₂×D₄₇	—	2	2	no	—
291	C₂×D₄₇	—	2	2	no	—
292	C₂×D₄₇	C₂×#41	1	2	yes	—
293	C₄×C₄₇	—	2	1	no	—
294	C₄×C₄₇	—	2	1	no	—
295	C₄×C₄₇	—	2	2	no	—
296	C₄×C₄₇	—	2	2	no	—
297	C₄×C₄₇	—	2	2	no	—
298	C₄×C₄₇	—	2	1	no	—
299	C₄×C₄₇	—	2	1	no	—
300	C₄×C₄₇	—	2	2	no	—
301	C₄×C₄₇	C₂×#41	1	2	yes	—
302	Dic₄₇	—	2	1	no	—
303	Dic₄₇	—	2	2	no	—
304	Dic₄₇	—	2	2	no	—
305	Dic₄₇	—	2	1	no	—
306	Dic₄₇	—	2	1	no	—
307	Dic₄₇	—	2	1	no	—
308	Dic₄₇	—	2	1	no	—
309	Dic₄₇	C₂×#41	1	2	yes	—
310	Dic₄₇	C₂×#41	1	4	yes	—
311	Dic₄₇	2₋¹⁺⁴	1	2	yes	—
312	#3482	—	47	1	no	maximal, Sylow
313	C₂×C₄₇	—	2	2	no	—
314	C₂×C₄₇	—	4	1	no	—
315	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
316	C₂×C₄₇	C₂²×#41	1	1	yes	characteristic
317	C₂×C₄₇	C₂×2₋¹⁺⁴	1	1	yes	characteristic
318	D₄₇	—	2	2	no	—
319	D₄₇	—	4	2	no	—
320	#557	—	47	1	no	—
321	#556	—	47	2	no	—
322	#556	—	47	1	no	—
323	#552	—	47	2	no	—
324	#552	—	47	2	no	—
325	#552	—	47	1	no	—
326	#552	D₄₇	1	1	yes	characteristic, complemented
327	D₄×Q₈	—	47	1	no	—
328	#548	—	47	1	no	—
329	#548	—	47	1	no	—
330	#547	—	47	2	no	—
331	#547	—	47	1	no	—
332	#533	—	47	2	no	—
333	#533	—	47	1	no	—
334	#529	—	47	2	no	—
335	#529	—	47	1	no	—
336	#529	—	47	2	no	—
337	#529	—	47	1	no	—
338	C₄×#41	—	47	1	no	—
339	C₄×#41	—	47	2	no	—
340	C₄×#41	—	47	1	no	—
341	C₂×C₄×Q₈	—	47	1	no	—
342	C₂×C₄×Q₈	—	47	1	no	—
343	C₄₇	#3482	1	1	yes	characteristic, complemented, Sylow
344	C₂×#41	—	47	1	no	—
345	C₂×#41	—	47	2	no	—
346	C₂×#41	—	47	1	no	—
347	C₂²×Q₈	—	47	1	no	—
348	C₂²×Q₈	—	47	1	no	—
349	C₄⋊Q₈	—	47	1	no	—
350	C₄⋊Q₈	—	47	2	no	—
351	C₄⋊Q₈	—	47	1	no	—
352	C₄⋊Q₈	—	47	2	no	—
353	#126	—	47	2	no	—
354	#126	—	47	2	no	—
355	#126	—	47	2	no	—
356	#126	—	47	2	no	—
357	#126	—	47	2	no	—
358	#126	C₂×D₄₇	1	2	yes	—
359	#125	—	47	2	no	—
360	#125	—	47	2	no	—
361	#125	—	47	1	no	—
362	#125	—	47	2	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	#124	—	47	2	no	—
368	#124	—	47	2	no	—
369	#124	—	47	1	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	1	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	2	no	—
391	C₄×Q₈	—	47	1	no	—
392	C₄×Q₈	—	47	1	no	—
393	C₄×Q₈	—	47	2	no	—
394	C₄×Q₈	—	47	2	no	—
395	C₄×Q₈	—	47	1	no	—
396	C₄×Q₈	—	47	1	no	—
397	C₄×Q₈	—	47	2	no	—
398	C₄×Q₈	—	47	1	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	—	47	1	no	—
406	C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
407	C₄×D₄	—	47	1	no	—
408	C₄×D₄	—	47	1	no	—
409	C₄×D₄	—	47	1	no	—
410	C₄×D₄	—	47	1	no	—
411	C₄×D₄	—	47	2	no	—
412	C₄×D₄	—	47	1	no	—
413	C₄×D₄	—	47	2	no	—
414	C₄×D₄	—	47	1	no	—
415	C₄×D₄	—	47	2	no	—
416	C₄×D₄	—	47	1	no	—
417	C₄×D₄	—	47	2	no	—
418	C₄×D₄	—	47	2	no	—
419	C₄×D₄	—	47	2	no	—
420	C₄×D₄	—	47	2	no	—
421	C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
422	#117	—	47	1	no	—
423	#117	—	47	2	no	—
424	#117	—	47	2	no	—
425	#117	—	47	1	no	—
426	#117	—	47	1	no	—
427	#117	—	47	2	no	—
428	#117	—	47	2	no	—
429	#117	—	47	2	no	—
430	#117	—	47	2	no	—
431	#117	C₂×D₄₇	1	1	yes	characteristic
432	#117	C₂×D₄₇	1	2	yes	—
433	C₂×C₄⋊C₄	—	47	2	no	—
434	C₂×C₄⋊C₄	—	47	2	no	—
435	C₂×C₄⋊C₄	—	47	1	no	—
436	C₂×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
437	C₂×C₄²	—	47	1	no	—
438	C₂×C₄²	—	47	2	no	—
439	C₂×C₄²	—	47	1	no	—
440	C₂×C₄²	—	47	1	no	—
441	C₂×C₄²	—	47	2	no	—
442	C₂×C₄²	—	47	2	no	—
443	#41	—	94	8	no	—
444	#41	—	94	4	no	—
445	#41	—	94	4	no	—
446	C₂×Q₈	—	47	1	no	—
447	C₂×Q₈	—	47	2	no	—
448	C₂×Q₈	—	47	2	no	—
449	C₂×Q₈	—	47	1	no	—
450	C₂×Q₈	—	47	2	no	—
451	C₂×Q₈	—	47	1	no	—
452	C₂×Q₈	—	94	4	no	—
453	C₂×Q₈	—	94	4	no	—
454	C₂×Q₈	C₂²×D₄₇	1	1	yes	characteristic
455	C₂×D₄	—	47	1	no	—
456	C₂×D₄	—	47	1	no	—
457	C₂×D₄	—	47	2	no	—
458	C₂×D₄	—	47	2	no	—
459	C₂×D₄	—	47	2	no	—
460	C₂×D₄	—	47	1	no	—
461	C₂×D₄	C₂²×D₄₇	1	1	yes	characteristic
462	C₂²×C₄	—	47	1	no	—
463	C₂²×C₄	—	47	1	no	—
464	C₂²×C₄	—	47	2	no	—
465	C₂²×C₄	—	47	1	no	—
466	C₂²×C₄	—	47	1	no	—
467	C₂²×C₄	—	47	1	no	—
468	C₂²×C₄	—	47	1	no	—
469	C₂²×C₄	—	47	2	no	—
470	C₂²×C₄	—	47	2	no	—
471	C₂²×C₄	—	47	1	no	—
472	C₂²×C₄	—	47	2	no	—
473	C₂²×C₄	—	47	2	no	—
474	C₂²×C₄	—	47	2	no	—
475	C₂²×C₄	C₂²×D₄₇	1	2	yes	—
476	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
477	C₂²×C₄	C₂²×D₄₇	1	1	yes	characteristic
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	1	no	—
485	C₄⋊C₄	—	47	2	no	—
486	C₄⋊C₄	—	47	1	no	—
487	C₄⋊C₄	—	47	2	no	—
488	C₄⋊C₄	—	47	1	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	—	47	1	no	—
495	C₄⋊C₄	—	47	2	no	—
496	C₄⋊C₄	—	47	1	no	—
497	C₄⋊C₄	—	47	2	no	—
498	C₄⋊C₄	—	47	2	no	—
499	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
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	1	yes	characteristic
504	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
505	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
506	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
507	C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
508	C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
509	C₂²⋊C₄	—	47	1	no	—
510	C₂²⋊C₄	—	47	1	no	—
511	C₂²⋊C₄	—	47	2	no	—
512	C₂²⋊C₄	—	47	1	no	—
513	C₂²⋊C₄	—	47	1	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	1	yes	characteristic
524	C₂²⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
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	C₄²	—	47	2	no	—
529	C₄²	—	47	1	no	—
530	C₄²	—	47	1	no	—
531	C₄²	—	47	1	no	—
532	C₄²	—	47	2	no	—
533	C₄²	—	47	1	no	—
534	C₄²	—	47	1	no	—
535	C₄²	—	47	2	no	—
536	C₄²	—	47	1	no	—
537	C₄²	—	47	2	no	—
538	C₄²	—	47	1	no	—
539	C₄²	—	47	2	no	—
540	C₄²	—	47	1	no	—
541	C₄²	—	47	2	no	—
542	C₄²	—	47	2	no	—
543	C₄²	—	47	1	no	—
544	C₄²	C₂²×D₄₇	1	2	yes	—
545	C₄²	C₂²×D₄₇	1	2	yes	—
546	C₄²	C₂²×D₄₇	1	1	yes	characteristic
547	C₂³	—	47	1	no	—
548	C₂³	—	47	2	no	—
549	C₂³	C₂³×D₄₇	1	1	yes	characteristic
550	C₂³	C₂³×D₄₇	1	1	yes	characteristic
551	Q₈	—	2	2	no	—
552	Q₈	—	47	4	no	—
553	Q₈	—	94	4	no	—
554	Q₈	—	94	4	no	—
555	Q₈	—	94	4	no	—
556	Q₈	—	94	2	no	—
557	Q₈	—	94	2	no	—
558	D₄	—	2	2	no	—
559	D₄	—	47	4	no	—
560	D₄	—	94	4	no	—
561	D₄	—	94	4	no	—
562	D₄	—	94	2	no	—
563	D₄	—	94	4	no	—
564	D₄	—	94	2	no	—
565	C₂×C₄	—	2	4	no	—
566	C₂×C₄	—	2	2	no	—
567	C₂×C₄	—	2	2	no	—
568	C₂×C₄	—	47	1	no	—
569	C₂×C₄	—	47	1	no	—
570	C₂×C₄	—	47	2	no	—
571	C₂×C₄	—	47	1	no	—
572	C₂×C₄	—	47	1	no	—
573	C₂×C₄	—	47	1	no	—
574	C₂×C₄	—	47	2	no	—
575	C₂×C₄	—	47	1	no	—
576	C₂×C₄	—	47	1	no	—
577	C₂×C₄	—	47	2	no	—
578	C₂×C₄	—	94	2	no	—
579	C₂×C₄	—	94	4	no	—
580	C₂×C₄	—	94	4	no	—
581	C₂×C₄	—	94	4	no	—
582	C₂×C₄	—	94	4	no	—
583	C₂×C₄	—	94	4	no	—
584	C₂×C₄	—	94	2	no	—
585	C₂×C₄	—	94	2	no	—
586	C₂×C₄	—	94	2	no	—
587	C₂×C₄	—	94	4	no	—
588	C₂×C₄	—	94	2	no	—
589	C₂×C₄	—	94	2	no	—
590	C₂×C₄	—	94	2	no	—
591	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
592	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
593	C₂×C₄	C₂³×D₄₇	1	2	yes	—
594	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
595	C₂×C₄	C₂³×D₄₇	1	2	yes	—
596	C₂×C₄	C₂³×D₄₇	1	2	yes	—
597	C₂×C₄	C₂³×D₄₇	1	2	yes	—
598	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
599	C₂×C₄	C₂³×D₄₇	1	1	yes	characteristic
600	C₂²	—	2	1	no	—
601	C₂²	—	2	1	no	—
602	C₂²	—	2	1	no	—
603	C₂²	—	2	1	no	—
604	C₂²	—	2	1	no	—
605	C₂²	—	47	2	no	—
606	C₂²	—	94	1	no	—
607	C₂²	—	94	1	no	—
608	C₂²	—	94	2	no	—
609	C₂²	—	94	2	no	—
610	C₂²	—	94	2	no	—
611	C₂²	#41×D₄₇	1	2	yes	—
612	C₂²	C₂⁴×D₄₇	1	1	yes	characteristic
613	C₄	—	2	2	no	—
614	C₄	—	2	1	no	—
615	C₄	—	2	2	no	—
616	C₄	—	2	1	no	—
617	C₄	—	2	1	no	—
618	C₄	—	2	2	no	—
619	C₄	—	2	1	no	—
620	C₄	—	2	2	no	—
621	C₄	—	47	2	no	—
622	C₄	—	47	4	no	—
623	C₄	—	47	2	no	—
624	C₄	—	94	1	no	—
625	C₄	—	94	2	no	—
626	C₄	—	94	1	no	—
627	C₄	—	94	2	no	—
628	C₄	—	94	1	no	—
629	C₄	—	94	1	no	—
630	C₄	—	94	1	no	—
631	C₄	#41×D₄₇	1	2	yes	—
632	C₂	—	2	2	no	—
633	C₂	—	4	1	no	—
634	C₂	—	94	2	no	—
635	C₂	—	188	2	no	—
636	C₂	C₂×#41×D₄₇	1	1	yes	characteristic
637	C₂	C₂×#41×D₄₇	1	1	yes	characteristic
638	C₂	2₋¹⁺⁴×D₄₇	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	#3482
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. #15689850	C₂	semidirect
2. #15689845	C₂	semidirect
3. #15689840	C₂	semidirect
4. #15689812	C₂	semidirect
5. #15689806	C₂	semidirect
6. #15689805	C₂	semidirect
7. #15689786	C₂	semidirect
8. #15689783	C₂	semidirect
9. #15689782	C₂	semidirect
10. #15689774	C₂	semidirect
11. #15689771	C₂	semidirect
12. #15689679	C₂	semidirect
13. #15689675	C₂	semidirect
14. #15689659	C₂	semidirect
15. #15689658	C₂	semidirect
16. #15689656	C₂	semidirect
17. #15689650	C₂	semidirect
18. #15689591	C₂	semidirect
19. #15689591	C₂	semidirect
20. C₄×#10625352	C₂	semidirect
21. C₂×#13093989	C₂	semidirect
22. C₄×Q₈×D₄₇	C₂	semidirect
23. C₄₇×#552	C₂	semidirect
248. C₂²⋊D₄₇	#41	semidirect
279. Dic₉₄	#41	semidirect
326. #552	D₄₇	semidirect
343. C₄₇	#3482	semidirect