Subgroups — #26185883

Order 12032.

738 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252344	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#13094052	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689200	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242265	C₂	1	2	yes	maximal, complemented
5	#20242251	C₂	1	2	yes	maximal, complemented
6	#20242230	C₂	1	2	yes	maximal, complemented
7	#20242216	C₂	1	2	yes	maximal, complemented
8	#20241778	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241773	C₂	1	1	yes	maximal, characteristic, complemented
10	#20241675	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1565	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094052	C₄	1	1	yes	characteristic
13	C₂²×#10625324	—	2	1	no	—
14	C₄×#10625350	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
16	#15689247	C₂²	1	1	yes	characteristic, complemented
17	#15689247	C₂²	1	1	yes	characteristic, complemented
18	#15689236	C₄	1	2	yes	—
19	#15689225	C₄	1	2	yes	—
20	C₄×#10625325	C₂²	1	2	yes	—
21	C₄×D₃₇₆	C₂²	1	2	yes	—
22	#15689200	—	2	1	no	—
23	#15689200	—	2	1	no	—
24	#15689200	C₂²	1	2	yes	—
25	#15689200	C₂²	1	2	yes	—
26	#15689188	C₂²	1	1	yes	characteristic, complemented
27	#15689188	C₂²	1	1	yes	characteristic, complemented
28	(C₂²⋊D₄₇)⋊C₈	—	2	1	no	—
29	(C₂²⋊D₄₇)⋊C₈	—	2	1	no	—
30	#15689176	C₂²	1	1	yes	characteristic
31	#15689174	—	2	1	no	—
32	#15689165	C₄	1	1	yes	characteristic
33	#15689129	C₄	1	1	yes	characteristic
34	#15689125	C₄	1	1	yes	characteristic
35	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
36	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
37	C₄×C₈×D₄₇	—	2	1	no	—
38	#15688853	C₂²	1	2	yes	complemented
39	#15688850	C₂²	1	2	yes	—
40	#15688850	C₂²	1	2	yes	—
41	#15688850	C₂²	1	2	yes	complemented
42	#15688845	C₂²	1	2	yes	complemented
43	#15688845	C₂²	1	2	yes	complemented
44	C₄₇×#431	C₂²	1	1	yes	characteristic
45	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
46	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
47	C₄₇×#335	C₂²	1	2	yes	complemented
48	C₄₇×#334	C₂²	1	2	yes	complemented
49	C₂×#10625350	C₂×C₄	1	1	yes	characteristic
50	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₄×D₄₇	—	2	1	no	—
52	#13094052	—	2	4	no	—
53	C₂×#10625325	C₂×C₄	1	2	yes	—
54	C₂×D₃₇₆	C₂×C₄	1	2	yes	—
55	C₂×#10625324	—	2	2	no	—
56	C₂×#10625324	—	2	2	no	—
57	C₂×#10625324	—	4	4	no	—
58	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
59	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
60	C₂×C₈×D₄₇	—	2	1	no	—
61	C₂×C₈×D₄₇	—	2	1	no	—
62	C₄×Dic₉₄	C₂×C₄	1	1	yes	characteristic
63	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
64	C₄×D₁₈₈	—	2	1	no	—
65	C₄×D₁₈₈	—	2	1	no	—
66	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
67	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
68	C₄×D₁₈₈	C₂³	1	2	yes	—
69	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
70	C₄×C₂²⋊D₄₇	—	2	1	no	—
71	C₄×C₂²⋊D₄₇	—	2	1	no	—
72	#13093983	C₂×C₄	1	1	yes	characteristic
73	#13093981	—	2	1	no	—
74	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
76	C₄²×D₄₇	—	2	1	no	—
77	#13093958	C₂×C₄	1	2	yes	—
78	#13093956	C₂×C₄	1	2	yes	—
79	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
80	Dic₄₇⋊C₈	—	2	1	no	—
81	Dic₄₇⋊C₈	—	2	1	no	—
82	#13093949	C₂×C₄	1	2	yes	—
83	#13093946	C₂×C₄	1	2	yes	—
84	#13093946	C₂×C₄	1	2	yes	—
85	#13093946	C₂×C₄	1	2	yes	—
86	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
87	(C₂×D₄₇)⋊C₈	—	2	2	no	—
88	(C₂×D₄₇)⋊C₈	—	2	2	no	—
89	(C₂×D₄₇)⋊C₈	—	2	1	no	—
90	(C₂×D₄₇)⋊C₈	—	2	1	no	—
91	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
92	C₄×C₄₇⋊C₈	D₄	1	1	yes	characteristic
93	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
94	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
95	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
96	C₈×Dic₄₇	—	2	1	no	—
97	C₈×Dic₄₇	—	2	1	no	—
98	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
99	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
100	C₂²×C₈×C₄₇	—	2	1	no	—
101	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
102	C₄⋊C₈×C₄₇	—	2	1	no	—
103	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
104	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
105	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
106	C₂²⋊C₈×C₄₇	—	2	1	no	—
107	#97×C₄₇	C₂×C₄	1	2	yes	—
108	C₄×C₈×C₄₇	—	2	1	no	—
109	C₄×C₈×C₄₇	C₂³	1	2	yes	—
110	C₂³×D₄₇	—	2	1	no	—
111	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
114	C₂×C₂²⋊D₄₇	—	2	1	no	—
115	C₂²×Dic₄₇	—	2	1	no	—
116	#10625350	—	2	2	no	—
117	#10625350	M₁₆	1	4	yes	complemented
118	C₂×D₁₈₈	—	2	2	no	—
119	C₂×D₁₈₈	—	2	2	no	—
120	C₂×D₁₈₈	—	2	1	no	—
121	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
122	C₂×D₁₈₈	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₄×D₄₇	—	2	1	no	—
124	C₂×C₄×D₄₇	—	2	1	no	—
125	C₂×C₄×D₄₇	—	2	2	no	—
126	C₂×C₄×D₄₇	—	2	1	no	—
127	C₂×C₄×D₄₇	—	2	2	no	—
128	C₂×C₄×D₄₇	—	4	2	no	—
129	C₂×C₄×D₄₇	—	4	2	no	—
130	C₂×Dic₉₄	C₂²×C₄	1	1	yes	characteristic
131	M₁₆×C₄₇	—	2	2	no	—
132	M₁₆×C₄₇	—	2	2	no	—
133	C₂×C₈×C₄₇	—	2	2	no	—
134	C₂×C₈×C₄₇	—	2	1	no	—
135	C₂×C₈×C₄₇	—	2	1	no	—
136	C₂×C₈×C₄₇	—	4	2	no	—
137	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
138	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
139	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₄₇	#41	1	1	yes	characteristic
142	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
143	C₂²⋊Dic₄₇	—	2	1	no	—
144	(C₂×D₄₇)⋊C₄	—	2	2	no	—
145	(C₂×D₄₇)⋊C₄	—	2	1	no	—
146	(C₂×D₄₇)⋊C₄	—	2	2	no	—
147	(C₂×D₄₇)⋊C₄	—	2	1	no	—
148	C₄⋊Dic₄₇	—	2	1	no	—
149	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
150	C₄⋊Dic₄₇	C₂²×C₄	1	1	yes	characteristic
151	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
152	Dic₄₇⋊C₄	—	2	1	no	—
153	Dic₄₇⋊C₄	—	2	1	no	—
154	C₄×Dic₄₇	—	2	1	no	—
155	C₄×Dic₄₇	—	2	1	no	—
156	C₄×Dic₄₇	—	2	1	no	—
157	C₂×C₄₇⋊C₈	—	2	2	no	—
158	C₂×C₄₇⋊C₈	—	2	2	no	—
159	C₂×C₄₇⋊C₈	—	4	1	no	—
160	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
161	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
162	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
163	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
164	D₃₇₆	—	2	4	no	—
165	#10625325	—	2	4	no	—
166	#10625324	—	4	4	no	—
167	#10625324	—	4	4	no	—
168	C₈×D₄₇	—	4	2	no	—
169	C₈×D₄₇	—	4	2	no	—
170	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
171	C₂²×D₄₇	—	2	1	no	—
172	C₂²×D₄₇	—	2	2	no	—
173	C₂²×D₄₇	—	4	2	no	—
174	C₂²×D₄₇	—	4	2	no	—
175	C₂²×D₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	1	no	—
178	C₂×C₄×C₄₇	—	4	1	no	—
179	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂×M₁₆	1	2	yes	—
183	C₂×C₄×C₄₇	#131	1	2	yes	—
184	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
187	C₂²⋊D₄₇	—	2	4	no	—
188	C₂×Dic₄₇	—	2	1	no	—
189	C₂×Dic₄₇	—	2	1	no	—
190	C₂×Dic₄₇	—	2	1	no	—
191	C₂×Dic₄₇	—	2	2	no	—
192	C₂×Dic₄₇	—	4	2	no	—
193	D₁₈₈	—	2	2	no	—
194	D₁₈₈	—	2	1	no	—
195	D₁₈₈	—	2	2	no	—
196	D₁₈₈	—	4	2	no	—
197	D₁₈₈	C₂×M₁₆	1	2	yes	complemented
198	C₄×D₄₇	—	2	4	no	—
199	C₄×D₄₇	—	4	2	no	—
200	C₄×D₄₇	—	4	4	no	—
201	C₄×D₄₇	—	4	1	no	—
202	C₄×D₄₇	—	4	2	no	—
203	C₄×D₄₇	—	4	1	no	—
204	C₄×D₄₇	—	4	2	no	—
205	Dic₉₄	—	2	1	no	—
206	Dic₉₄	C₂×M₁₆	1	2	yes	complemented
207	C₈×C₄₇	—	2	2	no	—
208	C₈×C₄₇	—	2	2	no	—
209	C₈×C₄₇	—	4	1	no	—
210	C₈×C₄₇	—	4	2	no	—
211	C₈×C₄₇	—	4	1	no	—
212	C₄₇⋊C₈	—	2	1	no	—
213	C₄₇⋊C₈	—	2	1	no	—
214	C₄₇⋊C₈	—	2	1	no	—
215	C₄₇⋊C₈	—	4	2	no	—
216	C₄₇⋊C₈	AGL(1,ℤ/8)	1	2	yes	complemented
217	#17871	—	47	1	no	maximal, Sylow
218	C₂²×C₄₇	—	2	1	no	—
219	C₂²×C₄₇	—	2	1	no	—
220	C₂²×C₄₇	#435	1	2	yes	—
221	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
222	C₂×D₄₇	—	2	2	no	—
223	C₂×D₄₇	—	4	1	no	—
224	C₂×D₄₇	—	4	1	no	—
225	C₂×D₄₇	—	4	2	no	—
226	C₂×D₄₇	—	4	2	no	—
227	C₂×D₄₇	—	4	2	no	—
228	C₂×D₄₇	—	8	4	no	—
229	C₄×C₄₇	—	2	1	no	—
230	C₄×C₄₇	—	2	1	no	—
231	C₄×C₄₇	—	2	1	no	—
232	C₄×C₄₇	#435	1	2	yes	—
233	C₄×C₄₇	C₂²×M₁₆	1	1	yes	characteristic
234	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
235	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
236	C₄×C₄₇	#575	1	1	yes	characteristic
237	Dic₄₇	—	2	2	no	—
238	Dic₄₇	—	4	2	no	—
239	Dic₄₇	—	4	1	no	—
240	Dic₄₇	—	4	1	no	—
241	C₈×#41	—	47	1	no	—
242	C₄×AGL(1,ℤ/8)	—	47	1	no	—
243	C₂×#436	—	47	1	no	—
244	#1588	—	47	2	no	—
245	#1586	—	47	2	no	—
246	#1583	—	47	2	no	—
247	#1581	—	47	2	no	—
248	#1565	D₄₇	1	1	yes	characteristic, complemented
249	#1478	—	47	1	no	—
250	#1477	—	47	1	no	—
251	#1451	—	47	1	no	—
252	C₂×C₄₇	—	2	2	no	—
253	C₂×C₄₇	C₂×#435	1	1	yes	characteristic
254	C₂×C₄₇	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic
255	C₂×C₄₇	#2955	1	1	yes	characteristic
256	D₄₇	—	4	2	no	—
257	D₄₇	—	8	2	no	—
258	C₂×AGL(1,ℤ/8)	—	47	1	no	—
259	C₂²×M₁₆	—	94	1	no	—
260	C₄×#41	—	47	1	no	—
261	C₂×C₄×D₄	—	47	1	no	—
262	C₈×Q₈	—	47	1	no	—
263	C₈×Q₈	—	47	1	no	—
264	#442	—	47	2	no	—
265	#440	—	47	2	no	—
266	C₄×SD₁₆	—	47	2	no	—
267	C₄×D₈	—	47	2	no	—
268	#436	—	47	2	no	—
269	#436	—	47	2	no	—
270	#436	—	94	1	no	—
271	#436	—	94	1	no	—
272	C₈×D₄	—	47	1	no	—
273	C₈×D₄	—	47	1	no	—
274	C₈×D₄	—	94	1	no	—
275	C₈×D₄	—	94	1	no	—
276	#431	—	47	1	no	—
277	#431	—	94	1	no	—
278	#431	C₂×D₄₇	1	1	yes	characteristic
279	#428	—	47	1	no	—
280	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
281	#418	—	47	1	no	—
282	#417	—	47	1	no	—
283	C₂×C₂²⋊C₈	—	94	1	no	—
284	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
285	C₂×C₄×C₈	—	47	1	no	—
286	C₂×C₄×C₈	—	94	1	no	—
287	#335	C₂×D₄₇	1	2	yes	complemented
288	#334	C₂×D₄₇	1	2	yes	complemented
289	Q₈⋊C₈	—	47	2	no	—
290	D₄⋊C₈	—	47	2	no	—
291	D₄⋊C₈	—	47	2	no	—
292	D₄⋊C₈	—	47	2	no	—
293	#322	—	47	2	no	—
294	#322	—	47	2	no	—
295	C₄₇	#17871	1	1	yes	characteristic, complemented, Sylow
296	C₂×#41	—	47	1	no	—
297	C₂²×D₄	—	47	1	no	—
298	C₂³×C₄	—	94	1	no	—
299	AGL(1,ℤ/8)	—	94	4	no	—
300	C₂×SD₁₆	—	47	2	no	—
301	C₂×D₈	—	47	2	no	—
302	C₂×M₁₆	—	94	2	no	—
303	C₂×M₁₆	—	94	2	no	—
304	C₂×M₁₆	—	188	4	no	—
305	C₂×M₁₆	C₄×D₄₇	1	1	yes	characteristic
306	C₂×M₁₆	C₄×D₄₇	1	1	yes	characteristic
307	C₂²×C₈	—	2	1	no	—
308	C₂²×C₈	—	47	1	no	—
309	C₂²×C₈	—	47	1	no	—
310	C₂²×C₈	—	94	1	no	—
311	C₂²×C₈	—	94	1	no	—
312	C₄×Q₈	—	47	1	no	—
313	C₄×Q₈	—	47	1	no	—
314	C₄×D₄	—	47	2	no	—
315	C₄×D₄	—	47	1	no	—
316	C₄×D₄	—	47	2	no	—
317	C₄×D₄	—	47	1	no	—
318	C₄×D₄	—	94	1	no	—
319	C₄×D₄	—	94	1	no	—
320	C₄×D₄	—	94	1	no	—
321	C₄×D₄	—	94	1	no	—
322	#117	—	47	1	no	—
323	#117	—	94	1	no	—
324	C₂×C₄⋊C₄	—	47	1	no	—
325	C₂×C₂²⋊C₄	—	94	1	no	—
326	C₂×C₄²	—	94	1	no	—
327	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
328	#107	—	47	2	no	—
329	#106	—	47	2	no	—
330	C₄⋊C₈	—	2	1	no	—
331	C₄⋊C₈	—	94	1	no	—
332	C₄⋊C₈	—	94	1	no	—
333	C₄⋊C₈	—	94	1	no	—
334	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
335	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
336	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
337	#103	—	47	2	no	—
338	#102	—	47	2	no	—
339	#102	—	47	2	no	—
340	#102	—	47	2	no	—
341	C₂²⋊C₈	—	2	1	no	—
342	C₂²⋊C₈	—	94	2	no	—
343	C₂²⋊C₈	—	94	2	no	—
344	C₂²⋊C₈	—	94	1	no	—
345	C₂²⋊C₈	—	94	1	no	—
346	C₂²⋊C₈	—	94	1	no	—
347	#97	C₄×D₄₇	1	2	yes	—
348	C₄×C₈	—	2	1	no	—
349	C₄×C₈	—	47	1	no	—
350	C₄×C₈	—	47	1	no	—
351	C₄×C₈	—	47	1	no	—
352	C₄×C₈	—	47	1	no	—
353	C₄×C₈	—	47	2	no	—
354	C₄×C₈	—	94	1	no	—
355	C₄×C₈	—	94	1	no	—
356	C₄×C₈	C₂²×D₄₇	1	2	yes	—
357	C₂⁴	—	94	1	no	—
358	#41	—	47	4	no	—
359	#41	—	94	2	no	—
360	C₂×Q₈	—	47	1	no	—
361	C₂×D₄	—	47	1	no	—
362	C₂×D₄	—	47	2	no	—
363	C₂×D₄	—	94	1	no	—
364	C₂×D₄	—	94	1	no	—
365	C₂×D₄	—	94	2	no	—
366	C₂×D₄	—	94	2	no	—
367	C₂²×C₄	—	94	1	no	—
368	C₂²×C₄	—	94	1	no	—
369	C₂²×C₄	—	94	1	no	—
370	C₂²×C₄	—	94	2	no	—
371	C₂²×C₄	—	94	1	no	—
372	C₂²×C₄	—	94	2	no	—
373	C₂²×C₄	—	188	2	no	—
374	C₂²×C₄	—	188	2	no	—
375	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
376	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
377	C₂²×C₄	#10625354	1	1	yes	characteristic
378	SD₁₆	—	94	4	no	—
379	D₈	—	94	4	no	—
380	M₁₆	—	2	2	no	—
381	M₁₆	—	2	2	no	—
382	M₁₆	—	188	4	no	—
383	M₁₆	—	188	4	no	—
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	2	no	—
387	C₂×C₈	—	4	2	no	—
388	C₂×C₈	—	47	1	no	—
389	C₂×C₈	—	47	1	no	—
390	C₂×C₈	—	47	1	no	—
391	C₂×C₈	—	47	1	no	—
392	C₂×C₈	—	94	2	no	—
393	C₂×C₈	—	94	2	no	—
394	C₂×C₈	—	188	2	no	—
395	C₂×C₈	—	188	2	no	—
396	C₂×C₈	—	188	1	no	—
397	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
398	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
399	C₄⋊C₄	—	47	1	no	—
400	C₄⋊C₄	—	47	1	no	—
401	C₄⋊C₄	—	47	2	no	—
402	C₄⋊C₄	—	94	1	no	—
403	C₄⋊C₄	—	94	1	no	—
404	C₄⋊C₄	—	94	1	no	—
405	C₂²⋊C₄	—	94	1	no	—
406	C₂²⋊C₄	—	94	2	no	—
407	C₂²⋊C₄	—	94	1	no	—
408	C₂²⋊C₄	—	94	2	no	—
409	C₂²⋊C₄	—	94	1	no	—
410	C₄²	—	94	1	no	—
411	C₄²	—	94	1	no	—
412	C₄²	—	94	1	no	—
413	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
414	C₄²	D₄×D₄₇	1	1	yes	characteristic
415	C₄²	#10625354	1	1	yes	characteristic
416	C₄²	C₂³×D₄₇	1	1	yes	characteristic
417	C₂³	—	94	1	no	—
418	C₂³	—	94	2	no	—
419	C₂³	—	188	2	no	—
420	C₂³	—	188	2	no	—
421	C₂³	—	188	2	no	—
422	C₂³	#13093986	1	1	yes	characteristic
423	Q₈	—	47	2	no	—
424	Q₈	—	94	1	no	—
425	D₄	—	47	2	no	—
426	D₄	—	94	4	no	—
427	D₄	—	94	2	no	—
428	D₄	—	94	1	no	—
429	D₄	—	94	2	no	—
430	D₄	—	188	2	no	—
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	4	1	no	—
434	C₂×C₄	—	94	1	no	—
435	C₂×C₄	—	94	4	no	—
436	C₂×C₄	—	94	1	no	—
437	C₂×C₄	—	94	1	no	—
438	C₂×C₄	—	94	2	no	—
439	C₂×C₄	—	188	2	no	—
440	C₂×C₄	—	188	4	no	—
441	C₂×C₄	—	188	2	no	—
442	C₂×C₄	—	188	1	no	—
443	C₂×C₄	—	188	2	no	—
444	C₂×C₄	—	188	1	no	—
445	C₂×C₄	—	188	2	no	—
446	C₂×C₄	#13093986	1	1	yes	characteristic
447	C₂×C₄	#13093986	1	1	yes	characteristic
448	C₂×C₄	#13093986	1	1	yes	characteristic
449	C₂×C₄	M₁₆×D₄₇	1	2	yes	—
450	C₂×C₄	#13094030	1	2	yes	—
451	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
452	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
453	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
454	C₈	—	2	2	no	—
455	C₈	—	2	2	no	—
456	C₈	—	4	2	no	—
457	C₈	—	4	1	no	—
458	C₈	—	4	1	no	—
459	C₈	—	47	2	no	—
460	C₈	—	94	1	no	—
461	C₈	—	94	1	no	—
462	C₈	—	94	1	no	—
463	C₈	—	188	2	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	94	2	no	—
467	C₂²	—	376	4	no	—
468	C₂²	—	188	2	no	—
469	C₂²	—	188	2	no	—
470	C₂²	—	188	2	no	—
471	C₂²	—	188	1	no	—
472	C₂²	—	188	1	no	—
473	C₂²	#15689193	1	2	yes	—
474	C₂²	C₂×#13093986	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	94	2	no	—
479	C₄	—	188	2	no	—
480	C₄	—	188	1	no	—
481	C₄	—	188	1	no	—
482	C₄	#15689193	1	2	yes	—
483	C₄	C₂×M₁₆×D₄₇	1	1	yes	characteristic
484	C₄	C₂×#13094030	1	1	yes	characteristic
485	C₄	AGL(1,ℤ/8)×D₄₇	1	1	yes	characteristic
486	C₄	#15689922	1	1	yes	characteristic
487	C₂	—	2	2	no	—
488	C₂	—	376	2	no	—
489	C₂	—	188	2	no	—
490	C₂	C₂×#15689193	1	1	yes	characteristic
491	C₂	#20252195	1	1	yes	characteristic
492	C₂	#20252290	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1565	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#13094052	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1565	D₄₇
hypocenter	C₄₇	#17871
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #1565

Complements

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

N	H ≅ G/N	type
1. #20252344	C₂	semidirect
3. C₂×#15689200	C₂	semidirect
4. #20242265	C₂	semidirect
5. #20242251	C₂	semidirect
6. #20242230	C₂	semidirect
7. #20242216	C₂	semidirect
8. #20241778	C₂	semidirect
9. #20241773	C₂	semidirect
10. #20241675	C₂	semidirect
11. C₄₇×#1565	C₂	semidirect
16. #15689247	C₂²	semidirect
17. #15689247	C₂²	semidirect
26. #15689188	C₂²	semidirect
27. #15689188	C₂²	semidirect
38. #15688853	C₂²	semidirect
41. #15688850	C₂²	semidirect
42. #15688845	C₂²	semidirect
43. #15688845	C₂²	semidirect
47. C₄₇×#335	C₂²	semidirect
48. C₄₇×#334	C₂²	semidirect
117. #10625350	M₁₆	semidirect
197. D₁₈₈	C₂×M₁₆	semidirect
206. Dic₉₄	C₂×M₁₆	semidirect
216. C₄₇⋊C₈	AGL(1,ℤ/8)	semidirect
248. #1565	D₄₇	semidirect
287. #335	C₂×D₄₇	semidirect
288. #334	C₂×D₄₇	semidirect
295. C₄₇	#17871	semidirect

Maximal subgroups

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

subgroup	index
#20252344	2
C₄×#13094052	2
C₂×#15689200	2
#20242265	2
#20242251	2
#20242230	2
#20242216	2
#20241778	2
#20241773	2
#20241675	2
C₄₇×#1565	2
#17871	47