Subgroups — #26223664

Order 12032.

782 conjugacy classes of subgroups.

The subgroup lattice has 518 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253301	C₂	1	1	yes	maximal, characteristic
2	#20252082	C₂	1	1	yes	maximal, characteristic
3	#20244036	C₂	1	2	yes	maximal, complemented
4	#20243987	C₂	1	2	yes	maximal, complemented
5	#20243690	C₂	1	1	yes	maximal, characteristic
6	#20243593	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243487	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243273	C₂	1	2	yes	maximal, complemented
9	#20243234	C₂	1	2	yes	maximal, complemented
10	#20243164	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094030	C₂²	1	1	yes	characteristic
13	#15689634	C₂²	1	1	yes	characteristic
14	#15689464	C₄	1	2	yes	complemented
15	#15689458	C₄	1	1	yes	characteristic, complemented
16	#15689453	C₄	1	1	yes	characteristic, complemented
17	#15689447	C₄	1	2	yes	complemented
18	#15689441	C₄	1	1	yes	characteristic, complemented
19	#15689436	C₄	1	1	yes	characteristic, complemented
20	#15689194	—	2	1	no	—
21	#15689194	—	2	1	no	—
22	C₈×C₂²⋊D₄₇	—	2	1	no	—
23	C₈×C₂²⋊D₄₇	—	2	1	no	—
24	C₂×#13093959	C₂²	1	2	yes	—
25	#15689159	C₂²	1	2	yes	—
26	#15689149	C₂²	1	1	yes	characteristic
27	C₂×#13093950	C₂²	1	2	yes	—
28	#15689117	C₂²	1	2	yes	—
29	#15689089	C₂²	1	1	yes	characteristic
30	#15689087	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
32	#15689078	C₂²	1	1	yes	characteristic
33	C₂×#13093934	C₂²	1	2	yes	—
34	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
35	#15688887	C₂²	1	2	yes	—
36	#15688884	C₂²	1	2	yes	—
37	#15688882	C₂²	1	2	yes	—
38	#15688882	C₂²	1	2	yes	—
39	#15688877	C₂²	1	2	yes	—
40	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
41	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#405	—	2	1	no	—
44	C₄₇×#405	—	2	1	no	—
45	C₄₇×#405	C₂²	1	2	yes	—
46	C₄₇×#405	C₂²	1	2	yes	—
47	C₂×#97×C₄₇	—	2	1	no	—
48	C₂×C₄×C₈×C₄₇	—	2	1	no	—
49	C₂×#10625350	C₂³	1	1	yes	characteristic
50	#13094030	—	2	4	no	—
51	C₂×#10625329	C₂³	1	1	yes	characteristic
52	C₂×#10625329	C₂³	1	1	yes	characteristic
53	C₂×#10625324	—	2	1	no	—
54	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
55	C₂×C₈×D₄₇	—	2	1	no	—
56	#13094007	—	2	1	no	—
57	#13094003	C₂×C₄	1	1	yes	characteristic
58	#13094003	C₂×C₄	1	1	yes	characteristic
59	#13093998	C₂×C₄	1	1	yes	characteristic
60	#13093998	C₂×C₄	1	1	yes	characteristic
61	#13093993	—	2	1	no	—
62	C₄×C₂²⋊D₄₇	—	2	1	no	—
63	C₄×C₂²⋊D₄₇	—	2	1	no	—
64	#13093983	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
66	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
67	#13093959	—	2	4	no	—
68	#13093957	C₂×C₄	1	2	yes	—
69	#13093957	C₂×C₄	1	2	yes	—
70	#13093955	C₂×C₄	1	2	yes	—
71	#13093955	C₂×C₄	1	2	yes	—
72	Dic₄₇⋊C₈	—	2	1	no	—
73	Dic₄₇⋊C₈	—	2	1	no	—
74	#13093950	—	2	4	no	—
75	#13093947	C₂×C₄	1	2	yes	—
76	#13093947	C₂×C₄	1	2	yes	—
77	#13093944	C₂×C₄	1	2	yes	—
78	#13093944	C₂×C₄	1	2	yes	—
79	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
80	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
81	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
82	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
83	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
84	(C₂×D₄₇)⋊C₈	—	2	1	no	—
85	(C₂×D₄₇)⋊C₈	—	2	1	no	—
86	#13093934	—	2	1	no	—
87	#13093934	—	2	4	no	—
88	C₈×Dic₄₇	—	2	1	no	—
89	C₄₇⋊#95	—	2	1	no	—
90	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
91	C₂×M₁₆×C₄₇	—	2	1	no	—
92	C₂×M₁₆×C₄₇	—	2	4	no	—
93	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
94	C₂²×C₈×C₄₇	—	2	1	no	—
95	C₂²×C₈×C₄₇	—	2	4	no	—
96	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
97	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
98	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
99	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
100	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
101	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	#117×C₄₇	—	2	1	no	—
103	#117×C₄₇	—	2	1	no	—
104	#117×C₄₇	C₂×C₄	1	2	yes	—
105	#117×C₄₇	C₂³	1	2	yes	—
106	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
107	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
108	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
109	C₂×C₄²×C₄₇	—	2	1	no	—
110	#97×C₄₇	—	2	2	no	—
111	#97×C₄₇	—	2	2	no	—
112	C₄×C₈×C₄₇	—	2	2	no	—
113	C₄×C₈×C₄₇	—	2	2	no	—
114	C₂⁴×C₄₇	#41	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	2	1	no	—
118	C₂²×C₄×C₄₇	—	2	1	no	—
119	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
125	C₂×C₂²⋊D₄₇	—	2	1	no	—
126	C₂×C₂²⋊D₄₇	—	2	1	no	—
127	C₂×C₂²⋊D₄₇	—	2	1	no	—
128	C₂²×Dic₄₇	—	2	2	no	—
129	#10625350	—	2	2	no	—
130	#10625350	—	2	2	no	—
131	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×D₄₇	—	2	1	no	—
133	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
134	M₁₆×C₄₇	—	2	4	no	—
135	M₁₆×C₄₇	—	2	2	no	—
136	M₁₆×C₄₇	#41	1	4	yes	—
137	C₂×C₈×C₄₇	—	2	4	no	—
138	C₂×C₈×C₄₇	—	2	2	no	—
139	C₂×C₈×C₄₇	—	2	2	no	—
140	C₂×C₈×C₄₇	—	2	2	no	—
141	C₂×C₈×C₄₇	—	2	2	no	—
142	C₂×C₈×C₄₇	—	2	2	no	—
143	C₂×C₈×C₄₇	—	2	2	no	—
144	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
145	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
146	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
147	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
148	C₂×C₈×C₄₇	#41	1	4	yes	—
149	C₄⋊C₄×C₄₇	—	2	1	no	—
150	C₄⋊C₄×C₄₇	—	2	1	no	—
151	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
152	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
153	C₂²⋊C₄×C₄₇	—	2	2	no	—
154	C₂²⋊C₄×C₄₇	—	2	2	no	—
155	C₄²×C₄₇	—	2	2	no	—
156	C₄²×C₄₇	—	2	2	no	—
157	C₂²⋊Dic₄₇	—	2	1	no	—
158	C₂²⋊Dic₄₇	—	2	1	no	—
159	C₂²⋊Dic₄₇	—	2	1	no	—
160	C₂²⋊Dic₄₇	—	4	2	no	—
161	(C₂×D₄₇)⋊C₄	—	2	1	no	—
162	(C₂×D₄₇)⋊C₄	—	2	1	no	—
163	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
164	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
165	Dic₄₇⋊C₄	—	2	1	no	—
166	Dic₄₇⋊C₄	—	2	1	no	—
167	C₄×Dic₄₇	—	2	1	no	—
168	C₄×Dic₄₇	—	2	2	no	—
169	C₄×Dic₄₇	—	2	2	no	—
170	#10625329	—	2	2	no	—
171	#10625329	—	2	2	no	—
172	C₂×C₄₇⋊C₈	—	2	2	no	—
173	C₂×C₄₇⋊C₈	—	2	2	no	—
174	C₂×C₄₇⋊C₈	—	2	1	no	—
175	C₂×C₄₇⋊C₈	—	2	1	no	—
176	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
177	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
178	#10625324	—	4	2	no	—
179	C₈×D₄₇	—	4	2	no	—
180	C₂³×C₄₇	—	2	2	no	—
181	C₂³×C₄₇	—	2	2	no	—
182	C₂³×C₄₇	—	4	1	no	—
183	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
184	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
185	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
186	C₂²×D₄₇	—	2	1	no	—
187	C₂×C₄×C₄₇	—	2	2	no	—
188	C₂×C₄×C₄₇	—	2	2	no	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	1	no	—
191	C₂×C₄×C₄₇	—	2	1	no	—
192	C₂×C₄×C₄₇	—	2	1	no	—
193	C₂×C₄×C₄₇	—	2	1	no	—
194	C₂×C₄×C₄₇	—	2	2	no	—
195	C₂×C₄×C₄₇	—	2	2	no	—
196	C₂×C₄×C₄₇	—	4	2	no	—
197	C₂×C₄×C₄₇	—	4	2	no	—
198	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
200	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
201	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
203	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
204	C₂²⋊D₄₇	—	4	2	no	—
205	C₂²⋊D₄₇	—	4	2	no	—
206	C₂²⋊D₄₇	—	4	2	no	—
207	C₂×Dic₄₇	—	2	1	no	—
208	C₂×Dic₄₇	—	2	1	no	—
209	C₂×Dic₄₇	—	2	1	no	—
210	C₂×Dic₄₇	—	4	2	no	—
211	C₂×Dic₄₇	—	4	2	no	—
212	C₂×Dic₄₇	—	4	2	no	—
213	D₁₈₈	—	2	2	no	—
214	C₄×D₄₇	—	4	1	no	—
215	C₄×D₄₇	—	4	1	no	—
216	Dic₉₄	—	2	2	no	—
217	C₈×C₄₇	—	2	1	no	—
218	C₈×C₄₇	—	2	1	no	—
219	C₈×C₄₇	—	2	4	no	—
220	C₈×C₄₇	#123	1	2	yes	—
221	C₈×C₄₇	#123	1	2	yes	—
222	C₄₇⋊C₈	—	2	2	no	—
223	C₄₇⋊C₈	—	2	2	no	—
224	C₄₇⋊C₈	—	4	1	no	—
225	C₄₇⋊C₈	—	4	1	no	—
226	#21593	—	47	1	no	maximal, Sylow
227	C₂²×C₄₇	—	2	1	no	—
228	C₂²×C₄₇	—	2	1	no	—
229	C₂²×C₄₇	—	2	1	no	—
230	C₂²×C₄₇	—	2	1	no	—
231	C₂²×C₄₇	—	2	1	no	—
232	C₂²×C₄₇	—	2	1	no	—
233	C₂²×C₄₇	—	2	1	no	—
234	C₂²×C₄₇	—	4	4	no	—
235	C₂²×C₄₇	#444	1	2	yes	—
236	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
237	C₂²×C₄₇	#529	1	2	yes	—
238	C₂×D₄₇	—	4	1	no	—
239	C₂×D₄₇	—	4	1	no	—
240	C₂×D₄₇	—	4	1	no	—
241	C₄×C₄₇	—	2	1	no	—
242	C₄×C₄₇	—	2	1	no	—
243	C₄×C₄₇	—	4	2	no	—
244	C₄×C₄₇	—	4	2	no	—
245	C₄×C₄₇	C₄×#41	1	2	yes	—
246	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
247	C₄×C₄₇	#525	1	1	yes	characteristic
248	Dic₄₇	—	4	1	no	—
249	Dic₄₇	—	4	1	no	—
250	Dic₄₇	—	4	1	no	—
251	Dic₄₇	—	8	2	no	—
252	#3091	—	47	1	no	—
253	#2929	—	47	1	no	—
254	C₂×#405	D₄₇	1	1	yes	characteristic, complemented
255	#1929	—	47	2	no	—
256	#1922	—	47	2	no	—
257	#1871	—	47	1	no	—
258	#1855	—	47	1	no	—
259	#1826	—	47	1	no	—
260	#1773	—	47	2	no	—
261	#1765	—	47	2	no	—
262	#1752	—	47	1	no	—
263	C₂×C₄₇	—	2	2	no	—
264	C₂×C₄₇	—	2	2	no	—
265	C₂×C₄₇	—	4	1	no	—
266	C₂×C₄₇	C₄×#123	1	1	yes	characteristic
267	C₂×C₄₇	C₂×#444	1	1	yes	characteristic
268	C₂×C₄₇	#2955	1	1	yes	characteristic
269	D₄₇	—	8	1	no	—
270	C₂×#131	—	47	1	no	—
271	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
272	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
273	#525	—	47	1	no	—
274	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
275	#485	—	47	2	no	—
276	#484	—	47	1	no	—
277	#483	—	47	1	no	—
278	#482	—	47	2	no	—
279	#481	—	47	1	no	—
280	#480	—	47	1	no	—
281	#435	—	94	1	no	—
282	#435	—	94	1	no	—
283	C₈×D₄	—	94	1	no	—
284	C₈×D₄	—	94	1	no	—
285	C₂×#108	—	47	2	no	—
286	#427	—	47	2	no	—
287	#424	—	47	1	no	—
288	C₂×#104	—	47	2	no	—
289	#416	—	47	2	no	—
290	#408	—	47	1	no	—
291	#407	—	47	1	no	—
292	C₂×C₂²⋊C₈	—	47	1	no	—
293	#405	—	2	1	no	—
294	#405	—	2	1	no	—
295	#405	—	47	1	no	—
296	#405	C₂×D₄₇	1	2	yes	—
297	#405	C₂×D₄₇	1	2	yes	—
298	C₂×#97	—	2	1	no	—
299	C₂×#97	—	47	2	no	—
300	C₂×C₄×C₈	—	2	1	no	—
301	C₄×C₂²⋊C₄	—	47	1	no	—
302	#341	—	47	2	no	—
303	#339	—	47	2	no	—
304	#339	—	47	2	no	—
305	#339	—	47	2	no	—
306	#336	—	47	2	no	—
307	C₄₇	#21593	1	1	yes	characteristic, complemented, Sylow
308	C₂×#41	—	47	1	no	—
309	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
310	#131	—	94	4	no	—
311	C₂×M₁₆	—	2	1	no	—
312	C₂×M₁₆	—	2	4	no	—
313	C₂×M₁₆	—	47	1	no	—
314	C₂×M₁₆	—	47	1	no	—
315	C₂×M₁₆	—	94	1	no	—
316	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
317	C₂²×C₈	—	2	1	no	—
318	C₂²×C₈	—	2	4	no	—
319	C₂²×C₈	—	47	2	no	—
320	C₂²×C₈	—	94	1	no	—
321	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
322	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
323	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
324	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
325	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
326	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
327	#123	—	94	1	no	—
328	C₂²⋊Q₈	—	47	1	no	—
329	C₂²⋊Q₈	—	47	1	no	—
330	#121	—	47	1	no	—
331	#121	—	47	1	no	—
332	#120	—	94	1	no	—
333	C₄×D₄	—	94	1	no	—
334	C₄×D₄	—	94	1	no	—
335	#117	—	2	1	no	—
336	#117	—	2	1	no	—
337	#117	—	47	1	no	—
338	#117	C₄×D₄₇	1	2	yes	—
339	#117	C₂²×D₄₇	1	2	yes	—
340	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
341	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₂²⋊C₄	—	94	1	no	—
344	C₂×C₄²	—	2	1	no	—
345	C₂×C₄²	—	47	2	no	—
346	#108	—	94	4	no	—
347	#107	—	47	2	no	—
348	#107	—	47	2	no	—
349	#106	—	47	2	no	—
350	#106	—	47	2	no	—
351	C₄⋊C₈	—	94	1	no	—
352	C₄⋊C₈	—	94	1	no	—
353	#104	—	94	4	no	—
354	#103	—	47	2	no	—
355	#103	—	47	2	no	—
356	#102	—	47	2	no	—
357	#102	—	47	2	no	—
358	C₂²⋊C₈	—	47	1	no	—
359	C₂²⋊C₈	—	47	1	no	—
360	C₂²⋊C₈	—	47	2	no	—
361	C₂²⋊C₈	—	94	1	no	—
362	C₂²⋊C₈	—	94	1	no	—
363	C₂²⋊C₈	—	94	1	no	—
364	C₂²⋊C₈	—	94	1	no	—
365	#97	—	2	2	no	—
366	#97	—	2	2	no	—
367	#97	—	94	4	no	—
368	#97	—	94	1	no	—
369	C₄×C₈	—	2	2	no	—
370	C₄×C₈	—	2	2	no	—
371	C₄×C₈	—	94	1	no	—
372	#95	—	94	1	no	—
373	C₂⁴	#10625350	1	1	yes	characteristic
374	#41	—	94	2	no	—
375	#41	—	94	2	no	—
376	C₂×Q₈	—	47	1	no	—
377	C₂×D₄	—	47	1	no	—
378	C₂×D₄	—	94	1	no	—
379	C₂×D₄	—	94	1	no	—
380	C₂×D₄	—	94	1	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	1	no	—
384	C₂²×C₄	—	2	1	no	—
385	C₂²×C₄	—	94	1	no	—
386	C₂²×C₄	—	94	2	no	—
387	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
388	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
389	C₂²×C₄	#10625350	1	1	yes	characteristic
390	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
391	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
392	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
393	M₁₆	—	2	4	no	—
394	M₁₆	—	2	2	no	—
395	M₁₆	—	94	2	no	—
396	M₁₆	—	94	2	no	—
397	M₁₆	—	188	2	no	—
398	M₁₆	#10625350	1	4	yes	—
399	C₂×C₈	—	2	4	no	—
400	C₂×C₈	—	2	2	no	—
401	C₂×C₈	—	2	2	no	—
402	C₂×C₈	—	2	2	no	—
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	47	2	no	—
407	C₂×C₈	—	47	2	no	—
408	C₂×C₈	—	94	2	no	—
409	C₂×C₈	—	94	2	no	—
410	C₂×C₈	—	94	1	no	—
411	C₂×C₈	—	94	1	no	—
412	C₂×C₈	—	188	2	no	—
413	C₂×C₈	#10625350	1	4	yes	—
414	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
415	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
416	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
417	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	47	1	no	—
421	C₄⋊C₄	—	47	1	no	—
422	C₄⋊C₄	—	94	1	no	—
423	C₄⋊C₄	—	94	1	no	—
424	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
425	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
426	C₂²⋊C₄	—	2	2	no	—
427	C₂²⋊C₄	—	2	2	no	—
428	C₂²⋊C₄	—	94	1	no	—
429	C₂²⋊C₄	—	94	1	no	—
430	C₂²⋊C₄	—	94	1	no	—
431	C₂²⋊C₄	—	94	1	no	—
432	C₂²⋊C₄	—	94	1	no	—
433	C₂²⋊C₄	—	188	2	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	2	no	—
436	C₄²	—	94	1	no	—
437	C₄²	—	94	2	no	—
438	C₄²	—	94	2	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	94	1	no	—
443	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
444	C₂³	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
445	C₂³	C₂×#10625350	1	1	yes	characteristic
446	Q₈	—	94	2	no	—
447	D₄	—	94	2	no	—
448	D₄	—	188	2	no	—
449	D₄	—	188	2	no	—
450	D₄	—	188	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	2	no	—
453	C₂×C₄	—	2	2	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	2	no	—
462	C₂×C₄	—	94	1	no	—
463	C₂×C₄	—	94	1	no	—
464	C₂×C₄	—	94	1	no	—
465	C₂×C₄	—	188	2	no	—
466	C₂×C₄	—	188	2	no	—
467	C₂×C₄	—	188	2	no	—
468	C₂×C₄	—	188	1	no	—
469	C₂×C₄	—	188	1	no	—
470	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
471	C₂×C₄	C₄×C₂²⋊D₄₇	1	1	yes	characteristic
472	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
473	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
474	C₂×C₄	C₂×#10625350	1	2	yes	—
475	C₂×C₄	C₂×#10625350	1	2	yes	—
476	C₈	—	2	1	no	—
477	C₈	—	2	1	no	—
478	C₈	—	2	4	no	—
479	C₈	—	94	2	no	—
480	C₈	—	94	2	no	—
481	C₈	—	188	1	no	—
482	C₈	—	188	1	no	—
483	C₈	#13094007	1	2	yes	—
484	C₈	#13094007	1	2	yes	—
485	C₂²	—	2	1	no	—
486	C₂²	—	2	1	no	—
487	C₂²	—	2	1	no	—
488	C₂²	—	2	1	no	—
489	C₂²	—	2	1	no	—
490	C₂²	—	2	1	no	—
491	C₂²	—	2	1	no	—
492	C₂²	—	4	4	no	—
493	C₂²	—	188	1	no	—
494	C₂²	—	188	1	no	—
495	C₂²	—	188	1	no	—
496	C₂²	#15689243	1	2	yes	—
497	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
498	C₂²	#15689657	1	2	yes	—
499	C₄	—	2	1	no	—
500	C₄	—	2	1	no	—
501	C₄	—	4	2	no	—
502	C₄	—	4	2	no	—
503	C₄	—	376	2	no	—
504	C₄	—	188	1	no	—
505	C₄	—	188	1	no	—
506	C₄	—	188	1	no	—
507	C₄	C₄×#10625350	1	2	yes	—
508	C₄	C₂×#13094007	1	1	yes	characteristic
509	C₄	#15689634	1	1	yes	characteristic
510	C₂	—	2	2	no	—
511	C₂	—	2	2	no	—
512	C₂	—	4	1	no	—
513	C₂	—	376	1	no	—
514	C₂	C₄×#13094007	1	1	yes	characteristic
515	C₂	C₂×#15689243	1	1	yes	characteristic
516	C₂	#20252289	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×C₂²⋊D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#405	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#15689634	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#405	D₄₇
hypocenter	C₄₇	#21593
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₈ ◁ C₂×#405

Complements

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

N	H ≅ G/N	type
3. #20244036	C₂	semidirect
4. #20243987	C₂	semidirect
6. #20243593	C₂	semidirect
7. #20243487	C₂	semidirect
8. #20243273	C₂	semidirect
9. #20243234	C₂	semidirect
10. #20243164	C₂	semidirect
11. C₂×C₄₇×#405	C₂	semidirect
14. #15689464	C₄	semidirect
15. #15689458	C₄	semidirect
16. #15689453	C₄	semidirect
17. #15689447	C₄	semidirect
18. #15689441	C₄	semidirect
19. #15689436	C₄	semidirect
254. C₂×#405	D₄₇	semidirect
307. C₄₇	#21593	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#20253301	2
#20252082	2
#20244036	2
#20243987	2
#20243690	2
#20243593	2
#20243487	2
#20243273	2
#20243234	2
#20243164	2
C₂×C₄₇×#405	2
#21593	47