Subgroups — #26223666

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	#20253303	C₂	1	1	yes	maximal, characteristic
2	#20252082	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689078	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244037	C₂	1	2	yes	maximal, complemented
5	#20243988	C₂	1	2	yes	maximal, complemented
6	#20243688	C₂	1	1	yes	maximal, characteristic
7	#20243595	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243488	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243272	C₂	1	2	yes	maximal, complemented
10	#20243232	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1752	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094030	C₂²	1	1	yes	characteristic
13	C₂²×#10625329	C₂²	1	1	yes	characteristic
14	#15689634	C₂²	1	1	yes	characteristic
15	C₂×#13093983	C₂²	1	1	yes	characteristic
16	#15689465	C₄	1	2	yes	complemented
17	#15689459	C₄	1	1	yes	characteristic, complemented
18	#15689454	C₄	1	1	yes	characteristic, complemented
19	#15689448	C₄	1	2	yes	complemented
20	#15689442	C₄	1	1	yes	characteristic, complemented
21	#15689437	C₄	1	1	yes	characteristic, complemented
22	#15689194	—	2	1	no	—
23	#15689194	—	2	1	no	—
24	C₈×C₂²⋊D₄₇	—	2	1	no	—
25	C₈×C₂²⋊D₄₇	—	2	1	no	—
26	C₂×#13093960	C₂²	1	2	yes	—
27	#15689161	C₂²	1	2	yes	—
28	#15689149	C₂²	1	1	yes	characteristic
29	C₂×#13093952	C₂²	1	2	yes	—
30	#15689120	C₂²	1	2	yes	—
31	#15689089	C₂²	1	1	yes	characteristic
32	#15689087	C₂²	1	1	yes	characteristic
33	#15689078	—	2	1	no	—
34	#15689078	—	2	1	no	—
35	#15689078	C₂²	1	2	yes	—
36	#15689078	C₂²	1	2	yes	—
37	#15689078	C₂²	1	1	yes	characteristic
38	C₂×#13093934	—	2	1	no	—
39	C₂×C₈×Dic₄₇	—	2	1	no	—
40	#15688888	C₂²	1	2	yes	—
41	#15688883	C₂²	1	2	yes	—
42	#15688883	C₂²	1	2	yes	—
43	#15688883	C₂²	1	2	yes	—
44	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
45	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
46	C₂×#97×C₄₇	C₂²	1	2	yes	—
47	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
48	C₄₇×#336	C₂²	1	2	yes	—
49	C₂×#10625350	C₂³	1	1	yes	characteristic
50	#13094030	—	2	4	no	—
51	C₂×#10625329	—	2	1	no	—
52	C₂×#10625329	—	2	4	no	—
53	C₂×#10625329	C₂³	1	1	yes	characteristic
54	C₂×#10625329	C₂³	1	1	yes	characteristic
55	C₂×#10625329	C₂³	1	2	yes	—
56	C₂×#10625324	—	2	1	no	—
57	C₂²×C₄₇⋊C₈	—	2	1	no	—
58	C₂×C₈×D₄₇	—	2	1	no	—
59	#13094007	—	2	1	no	—
60	#13094003	C₂×C₄	1	1	yes	characteristic
61	#13094003	C₂×C₄	1	1	yes	characteristic
62	#13093998	C₂×C₄	1	1	yes	characteristic
63	#13093998	C₂×C₄	1	1	yes	characteristic
64	#13093993	—	2	1	no	—
65	C₄×C₂²⋊D₄₇	—	2	1	no	—
66	C₄×C₂²⋊D₄₇	—	2	1	no	—
67	#13093983	—	2	1	no	—
68	#13093983	—	2	1	no	—
69	#13093983	C₂×C₄	1	2	yes	—
70	#13093983	C₂³	1	2	yes	—
71	#13093983	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
74	C₂×C₂²⋊Dic₄₇	—	2	1	no	—
75	C₂×C₄×Dic₄₇	—	2	1	no	—
76	#13093960	—	2	4	no	—
77	#13093958	C₂×C₄	1	2	yes	—
78	#13093958	C₂×C₄	1	2	yes	—
79	#13093956	C₂×C₄	1	2	yes	—
80	#13093956	C₂×C₄	1	2	yes	—
81	Dic₄₇⋊C₈	—	2	1	no	—
82	Dic₄₇⋊C₈	—	2	1	no	—
83	#13093952	—	2	4	no	—
84	#13093949	C₂×C₄	1	2	yes	—
85	#13093949	C₂×C₄	1	2	yes	—
86	#13093946	C₂×C₄	1	2	yes	—
87	#13093946	C₂×C₄	1	2	yes	—
88	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
89	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
90	(C₂×D₄₇)⋊C₈	—	2	1	no	—
91	(C₂×D₄₇)⋊C₈	—	2	1	no	—
92	#13093934	—	2	2	no	—
93	#13093934	—	2	2	no	—
94	#13093934	—	2	1	no	—
95	C₈×Dic₄₇	—	2	2	no	—
96	C₈×Dic₄₇	—	2	2	no	—
97	C₈×Dic₄₇	—	2	1	no	—
98	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
99	C₂²×C₈×C₄₇	—	2	4	no	—
100	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
101	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
102	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
103	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
104	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
105	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
106	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
107	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
108	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
109	C₂²⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
110	C₂²⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
111	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
112	#97×C₄₇	—	2	4	no	—
113	#95×C₄₇	—	2	1	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	2	no	—
118	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
120	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
124	C₂×C₂²⋊D₄₇	—	2	1	no	—
125	C₂×C₂²⋊D₄₇	—	2	1	no	—
126	C₂×C₂²⋊D₄₇	—	2	1	no	—
127	C₂²×Dic₄₇	—	2	1	no	—
128	C₂²×Dic₄₇	—	2	1	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	C₂×C₈×C₄₇	—	2	2	no	—
135	C₂×C₈×C₄₇	—	2	2	no	—
136	C₂×C₈×C₄₇	—	2	2	no	—
137	C₂×C₈×C₄₇	—	2	2	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	C₂²×C₄	1	2	yes	—
142	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
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	#41	1	4	yes	—
148	C₂²⋊C₄×C₄₇	—	4	2	no	—
149	C₄²×C₄₇	—	2	2	no	—
150	C₄²×C₄₇	—	2	2	no	—
151	C₂²⋊Dic₄₇	—	2	2	no	—
152	C₂²⋊Dic₄₇	—	2	1	no	—
153	C₂²⋊Dic₄₇	—	2	1	no	—
154	C₂²⋊Dic₄₇	—	2	2	no	—
155	C₂²⋊Dic₄₇	—	2	1	no	—
156	(C₂×D₄₇)⋊C₄	—	2	1	no	—
157	(C₂×D₄₇)⋊C₄	—	2	1	no	—
158	C₄⋊Dic₄₇	—	2	1	no	—
159	C₄⋊Dic₄₇	—	2	1	no	—
160	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
161	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
162	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
163	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
164	Dic₄₇⋊C₄	—	2	1	no	—
165	Dic₄₇⋊C₄	—	2	1	no	—
166	C₄×Dic₄₇	—	2	2	no	—
167	C₄×Dic₄₇	—	2	2	no	—
168	C₄×Dic₄₇	—	2	1	no	—
169	#10625329	—	2	4	no	—
170	#10625329	—	2	2	no	—
171	#10625329	—	2	2	no	—
172	#10625329	—	2	2	no	—
173	#10625329	#41	1	4	yes	—
174	C₂×C₄₇⋊C₈	—	2	4	no	—
175	C₂×C₄₇⋊C₈	—	2	2	no	—
176	C₂×C₄₇⋊C₈	—	2	1	no	—
177	C₂×C₄₇⋊C₈	—	2	1	no	—
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	—	4	2	no	—
195	C₂×C₄×C₄₇	—	4	2	no	—
196	C₂×C₄×C₄₇	—	4	2	no	—
197	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
199	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
200	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
201	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
202	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
203	C₂²⋊D₄₇	—	4	2	no	—
204	C₂²⋊D₄₇	—	4	2	no	—
205	C₂²⋊D₄₇	—	4	2	no	—
206	C₂×Dic₄₇	—	2	2	no	—
207	C₂×Dic₄₇	—	2	2	no	—
208	C₂×Dic₄₇	—	2	1	no	—
209	C₂×Dic₄₇	—	2	1	no	—
210	C₂×Dic₄₇	—	2	1	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	2	no	—
218	C₈×C₄₇	—	2	2	no	—
219	C₈×C₄₇	—	2	1	no	—
220	C₈×C₄₇	—	2	1	no	—
221	C₈×C₄₇	#123	1	2	yes	—
222	C₈×C₄₇	#123	1	2	yes	—
223	C₄₇⋊C₈	—	2	4	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	—	8	2	no	—
244	C₄×C₄₇	C₄×#41	1	2	yes	—
245	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
246	C₄×C₄₇	#525	1	1	yes	characteristic
247	Dic₄₇	—	4	2	no	—
248	Dic₄₇	—	4	1	no	—
249	Dic₄₇	—	4	2	no	—
250	Dic₄₇	—	4	1	no	—
251	Dic₄₇	—	4	1	no	—
252	#3091	—	47	1	no	—
253	#2929	—	47	1	no	—
254	C₂×#405	—	47	1	no	—
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	D₄₇	1	1	yes	characteristic, complemented
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	—	47	1	no	—
272	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
273	#525	—	47	1	no	—
274	C₂×#117	—	47	1	no	—
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	C₂×D₄₇	1	1	yes	characteristic
293	#405	—	47	2	no	—
294	#405	—	47	2	no	—
295	#405	—	47	1	no	—
296	#405	—	94	1	no	—
297	#405	—	94	1	no	—
298	C₂×#97	—	94	1	no	—
299	C₂×#97	C₂×D₄₇	1	2	yes	—
300	C₂×C₄×C₈	—	94	1	no	—
301	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
302	#341	—	47	2	no	—
303	#339	—	47	2	no	—
304	#339	—	47	2	no	—
305	#339	—	47	2	no	—
306	#336	C₂×D₄₇	1	2	yes	—
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	—	47	2	no	—
312	C₂×M₁₆	—	47	1	no	—
313	C₂×M₁₆	—	47	1	no	—
314	C₂×M₁₆	—	94	4	no	—
315	C₂×M₁₆	—	94	1	no	—
316	C₂×M₁₆	—	94	1	no	—
317	C₂²×C₈	—	2	4	no	—
318	C₂²×C₈	—	94	1	no	—
319	C₂²×C₈	—	94	1	no	—
320	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
321	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
322	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
323	C₂²×C₈	D₁₈₈	1	1	yes	characteristic
324	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
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	—	47	2	no	—
336	#117	—	47	2	no	—
337	#117	—	47	1	no	—
338	#117	—	94	1	no	—
339	#117	—	94	1	no	—
340	C₂×C₄⋊C₄	—	47	1	no	—
341	C₂×C₄⋊C₄	—	47	1	no	—
342	C₂×C₂²⋊C₄	—	2	1	no	—
343	C₂×C₂²⋊C₄	—	94	1	no	—
344	C₂×C₄²	—	94	1	no	—
345	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
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	—	94	1	no	—
359	C₂²⋊C₈	—	94	1	no	—
360	C₂²⋊C₈	—	94	1	no	—
361	C₂²⋊C₈	—	94	1	no	—
362	C₂²⋊C₈	C₄×D₄₇	1	1	yes	characteristic
363	C₂²⋊C₈	C₄×D₄₇	1	1	yes	characteristic
364	C₂²⋊C₈	C₄×D₄₇	1	2	yes	—
365	#97	—	2	4	no	—
366	#97	—	94	2	no	—
367	#97	—	94	2	no	—
368	#97	—	94	1	no	—
369	C₄×C₈	—	94	2	no	—
370	C₄×C₈	—	94	2	no	—
371	C₄×C₈	—	94	1	no	—
372	#95	—	2	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	2	no	—
384	C₂²×C₄	—	94	1	no	—
385	C₂²×C₄	—	94	1	no	—
386	C₂²×C₄	—	94	1	no	—
387	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
388	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
389	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
390	C₂²×C₄	C₂×D₁₈₈	1	1	yes	characteristic
391	C₂²×C₄	#10625350	1	1	yes	characteristic
392	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
393	M₁₆	—	47	4	no	—
394	M₁₆	—	94	4	no	—
395	M₁₆	—	94	2	no	—
396	M₁₆	—	94	2	no	—
397	M₁₆	—	94	2	no	—
398	M₁₆	—	188	2	no	—
399	C₂×C₈	—	2	2	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	—	94	4	no	—
407	C₂×C₈	—	94	2	no	—
408	C₂×C₈	—	94	1	no	—
409	C₂×C₈	—	94	1	no	—
410	C₂×C₈	—	188	2	no	—
411	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
412	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
413	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
414	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
415	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
416	C₂×C₈	C₂×D₁₈₈	1	1	yes	characteristic
417	C₂×C₈	#10625352	1	4	yes	—
418	C₄⋊C₄	—	47	2	no	—
419	C₄⋊C₄	—	47	2	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	—	94	1	no	—
425	C₄⋊C₄	—	94	1	no	—
426	C₂²⋊C₄	—	4	2	no	—
427	C₂²⋊C₄	—	94	2	no	—
428	C₂²⋊C₄	—	94	1	no	—
429	C₂²⋊C₄	—	94	1	no	—
430	C₂²⋊C₄	—	94	2	no	—
431	C₂²⋊C₄	—	94	1	no	—
432	C₂²⋊C₄	—	94	1	no	—
433	C₂²⋊C₄	—	94	1	no	—
434	C₄²	—	2	2	no	—
435	C₄²	—	2	2	no	—
436	C₄²	—	94	2	no	—
437	C₄²	—	94	2	no	—
438	C₄²	—	94	1	no	—
439	C₂³	—	2	2	no	—
440	C₂³	—	2	2	no	—
441	C₂³	—	4	1	no	—
442	C₂³	—	94	1	no	—
443	C₂³	C₄×D₁₈₈	1	1	yes	characteristic
444	C₂³	C₄×D₁₈₈	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	—	4	2	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	94	2	no	—
462	C₂×C₄	—	94	2	no	—
463	C₂×C₄	—	94	1	no	—
464	C₂×C₄	—	94	1	no	—
465	C₂×C₄	—	94	1	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×D₁₈₈	1	1	yes	characteristic
471	C₂×C₄	C₄×D₁₈₈	1	1	yes	characteristic
472	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
473	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
474	C₂×C₄	#41×D₄₇	1	2	yes	—
475	C₂×C₄	C₂×#10625352	1	2	yes	—
476	C₈	—	2	2	no	—
477	C₈	—	2	2	no	—
478	C₈	—	2	1	no	—
479	C₈	—	2	1	no	—
480	C₈	—	94	4	no	—
481	C₈	—	188	1	no	—
482	C₈	—	188	1	no	—
483	C₈	#13094008	1	2	yes	—
484	C₈	#13094008	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	#15689246	1	2	yes	—
497	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
498	C₂²	#15689653	1	2	yes	—
499	C₄	—	2	1	no	—
500	C₄	—	2	1	no	—
501	C₄	—	8	2	no	—
502	C₄	—	188	2	no	—
503	C₄	—	188	1	no	—
504	C₄	—	188	2	no	—
505	C₄	—	188	1	no	—
506	C₄	—	188	1	no	—
507	C₄	C₄×#10625352	1	2	yes	—
508	C₄	C₂×#13094008	1	1	yes	characteristic
509	C₄	#15689635	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×#13094008	1	1	yes	characteristic
515	C₂	C₂×#15689246	1	1	yes	characteristic
516	C₂	#20252292	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₁₈₈
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1752	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#15689634	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1752	D₄₇
hypocenter	C₄₇	#21593
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂³×C₈ ◁ #1752

Complements

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

N	H ≅ G/N	type
3. C₂×#15689078	C₂	semidirect
4. #20244037	C₂	semidirect
5. #20243988	C₂	semidirect
7. #20243595	C₂	semidirect
8. #20243488	C₂	semidirect
9. #20243272	C₂	semidirect
10. #20243232	C₂	semidirect
11. C₄₇×#1752	C₂	semidirect
16. #15689465	C₄	semidirect
17. #15689459	C₄	semidirect
18. #15689454	C₄	semidirect
19. #15689448	C₄	semidirect
20. #15689442	C₄	semidirect
21. #15689437	C₄	semidirect
262. #1752	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
#20253303	2
#20252082	2
C₂×#15689078	2
#20244037	2
#20243988	2
#20243688	2
#20243595	2
#20243488	2
#20243272	2
#20243232	2
C₄₇×#1752	2
#21593	47