Subgroups — #26111041

Order 12032.

764 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	D₄×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
2	#20244316	C₂	1	1	yes	maximal, characteristic, complemented
3	#20244195	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241272	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241227	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄₇×#459	C₂	1	1	yes	maximal, characteristic
8	C₂×D₄×Dic₄₇	—	2	1	no	—
9	C₂²×C₄⋊Dic₄₇	—	2	1	no	—
10	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
11	C₂×#13093945	—	2	1	no	—
12	C₂×#13093945	—	2	1	no	—
13	C₂×#13093945	—	2	2	no	—
14	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
15	#15689022	—	2	1	no	—
16	#15688998	—	2	2	no	—
17	#15688993	C₂²	1	1	yes	characteristic
18	#15688983	—	2	1	no	—
19	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
20	D₄⋊(C₄₇⋊C₈)	—	2	2	no	—
21	C₂²×D₈×C₄₇	—	2	1	no	—
22	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
24	C₄₇×#459	—	2	2	no	—
25	C₄₇×#459	C₄	1	4	yes	complemented
26	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×#102×C₄₇	—	2	1	no	—
28	C₂³×Dic₄₇	—	2	2	no	—
29	C₂²×C₄₇⋊C₈	—	2	1	no	—
30	C₂²×C₄₇⋊C₈	—	2	1	no	—
31	D₄×Dic₄₇	—	4	2	no	—
32	D₄×Dic₄₇	—	4	2	no	—
33	C₂×C₄⋊Dic₄₇	—	2	2	no	—
34	C₂×C₄⋊Dic₄₇	—	2	1	no	—
35	C₂×C₄⋊Dic₄₇	—	2	1	no	—
36	C₂×C₄⋊Dic₄₇	—	4	2	no	—
37	C₂×C₄⋊Dic₄₇	—	4	2	no	—
38	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
39	C₂×C₄⋊Dic₄₇	D₄	1	1	yes	characteristic
40	C₂×C₄⋊Dic₄₇	D₄	1	2	yes	—
41	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
42	C₂×C₄×Dic₄₇	—	2	1	no	—
43	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
44	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
45	#13093945	—	4	4	no	—
46	#13093945	—	4	2	no	—
47	#13093945	—	4	2	no	—
48	C₄×C₄₇⋊C₈	—	2	1	no	—
49	C₄×C₄₇⋊C₈	—	2	1	no	—
50	C₄₇⋊#95	—	2	2	no	—
51	C₄₇⋊#95	—	2	1	no	—
52	C₂²×D₄×C₄₇	—	2	1	no	—
53	C₂²×D₄×C₄₇	—	2	1	no	—
54	C₂²×D₄×C₄₇	—	2	1	no	—
55	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₇	—	2	1	no	—
57	C₂×D₈×C₄₇	—	2	4	no	—
58	C₂×D₈×C₄₇	—	4	2	no	—
59	C₂×D₈×C₄₇	—	4	2	no	—
60	C₂²×C₈×C₄₇	—	2	1	no	—
61	#127×C₄₇	—	2	1	no	—
62	#127×C₄₇	—	2	1	no	—
63	#127×C₄₇	—	2	1	no	—
64	#127×C₄₇	C₂×C₄	1	2	yes	complemented
65	C₄×D₄×C₄₇	—	2	1	no	—
66	C₄×D₄×C₄₇	—	2	1	no	—
67	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
68	C₄×D₄×C₄₇	D₄	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
70	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
71	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
72	C₄⋊C₈×C₄₇	—	2	1	no	—
73	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	complemented
74	#102×C₄₇	—	2	4	no	—
75	C₂⁴×C₄₇	—	2	1	no	—
76	C₂⁴×C₄₇	—	4	1	no	—
77	C₂×D₄×C₄₇	—	2	2	no	—
78	C₂×D₄×C₄₇	—	2	2	no	—
79	C₂×D₄×C₄₇	—	2	2	no	—
80	C₂×D₄×C₄₇	—	2	1	no	—
81	C₂×D₄×C₄₇	—	2	1	no	—
82	C₂×D₄×C₄₇	—	2	1	no	—
83	C₂×D₄×C₄₇	—	4	2	no	—
84	C₂×D₄×C₄₇	—	4	2	no	—
85	C₂×D₄×C₄₇	—	4	1	no	—
86	C₂×D₄×C₄₇	—	4	1	no	—
87	C₂×D₄×C₄₇	—	4	1	no	—
88	C₂×D₄×C₄₇	—	4	1	no	—
89	C₂×D₄×C₄₇	—	4	1	no	—
90	C₂×D₄×C₄₇	—	4	1	no	—
91	C₂×D₄×C₄₇	—	4	1	no	—
92	C₂×D₄×C₄₇	—	4	1	no	—
93	C₂×D₄×C₄₇	—	4	1	no	—
94	C₂×D₄×C₄₇	—	4	1	no	—
95	C₂×D₄×C₄₇	—	4	1	no	—
96	C₂×D₄×C₄₇	C₂²⋊C₄	1	2	yes	—
97	C₂×D₄×C₄₇	D₈	1	2	yes	—
98	C₂×D₄×C₄₇	SD₁₆	1	2	yes	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	4	1	no	—
103	C₂²×C₄×C₄₇	—	4	1	no	—
104	C₂²×C₄×C₄₇	—	4	1	no	—
105	C₂²×C₄×C₄₇	—	4	1	no	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×Dic₄₇	—	2	1	no	—
110	C₂²×Dic₄₇	—	2	1	no	—
111	C₂²×Dic₄₇	—	2	2	no	—
112	C₂²×Dic₄₇	—	4	4	no	—
113	C₂²×Dic₄₇	—	4	4	no	—
114	C₂²×Dic₄₇	—	8	2	no	—
115	D₈×C₄₇	—	4	8	no	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	—	4	1	no	—
118	C₂×C₈×C₄₇	—	4	1	no	—
119	C₄⋊C₄×C₄₇	—	2	1	no	—
120	C₄⋊C₄×C₄₇	C₂²⋊C₄	1	2	yes	—
121	C₂²⋊C₄×C₄₇	—	2	2	no	—
122	C₂²⋊C₄×C₄₇	—	2	2	no	—
123	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
124	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₄²×C₄₇	#41	1	1	yes	characteristic
126	C₄²×C₄₇	#41	1	1	yes	characteristic
127	C₂²⋊Dic₄₇	—	4	4	no	—
128	C₄⋊Dic₄₇	—	2	1	no	—
129	C₄⋊Dic₄₇	—	2	1	no	—
130	C₄⋊Dic₄₇	—	2	1	no	—
131	C₄⋊Dic₄₇	—	4	4	no	—
132	C₄⋊Dic₄₇	—	4	1	no	—
133	C₄⋊Dic₄₇	—	4	1	no	—
134	C₄⋊Dic₄₇	—	4	1	no	—
135	C₄⋊Dic₄₇	—	4	1	no	—
136	C₄⋊Dic₄₇	—	4	2	no	—
137	C₄⋊Dic₄₇	D₈	1	2	yes	complemented
138	C₄×Dic₄₇	—	4	1	no	—
139	C₄×Dic₄₇	—	4	1	no	—
140	C₂×C₄₇⋊C₈	—	2	2	no	—
141	C₂×C₄₇⋊C₈	—	4	1	no	—
142	C₂×C₄₇⋊C₈	—	4	1	no	—
143	C₂×C₄₇⋊C₈	—	4	1	no	—
144	C₂×C₄₇⋊C₈	—	4	1	no	—
145	C₂×C₄₇⋊C₈	—	4	1	no	—
146	C₂³×C₄₇	—	2	2	no	—
147	C₂³×C₄₇	—	2	2	no	—
148	C₂³×C₄₇	—	2	2	no	—
149	C₂³×C₄₇	—	4	1	no	—
150	C₂³×C₄₇	—	4	1	no	—
151	C₂³×C₄₇	—	4	1	no	—
152	C₂³×C₄₇	—	4	1	no	—
153	C₂³×C₄₇	—	4	2	no	—
154	C₂³×C₄₇	—	8	1	no	—
155	C₂³×C₄₇	—	8	1	no	—
156	C₂³×C₄₇	—	8	1	no	—
157	C₂³×C₄₇	—	8	1	no	—
158	C₂³×C₄₇	—	8	1	no	—
159	C₂³×C₄₇	—	8	1	no	—
160	C₂³×C₄₇	#120	1	1	yes	characteristic
161	D₄×C₄₇	—	2	2	no	—
162	D₄×C₄₇	—	2	2	no	—
163	D₄×C₄₇	—	2	2	no	—
164	D₄×C₄₇	—	4	4	no	—
165	D₄×C₄₇	—	4	2	no	—
166	D₄×C₄₇	—	4	2	no	—
167	D₄×C₄₇	—	4	2	no	—
168	D₄×C₄₇	—	4	2	no	—
169	D₄×C₄₇	—	8	2	no	—
170	D₄×C₄₇	—	8	1	no	—
171	D₄×C₄₇	—	8	1	no	—
172	D₄×C₄₇	—	8	1	no	—
173	D₄×C₄₇	—	8	1	no	—
174	D₄×C₄₇	#102	1	4	yes	complemented
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	4	1	no	—
179	C₂×C₄×C₄₇	—	4	1	no	—
180	C₂×C₄×C₄₇	—	4	2	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	4	2	no	—
183	C₂×C₄×C₄₇	—	4	2	no	—
184	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
187	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
188	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
189	C₂×C₄×C₄₇	#123	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₂×D₈	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂×SD₁₆	1	1	yes	characteristic
193	C₂×C₄×C₄₇	#135	1	1	yes	characteristic
194	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
195	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
196	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	1	yes	characteristic
197	C₂×C₄×C₄₇	#137	1	1	yes	characteristic
198	C₂×Dic₄₇	—	2	2	no	—
199	C₂×Dic₄₇	—	4	1	no	—
200	C₂×Dic₄₇	—	4	1	no	—
201	C₂×Dic₄₇	—	4	1	no	—
202	C₂×Dic₄₇	—	4	2	no	—
203	C₂×Dic₄₇	—	4	2	no	—
204	C₂×Dic₄₇	—	4	1	no	—
205	C₂×Dic₄₇	—	4	2	no	—
206	C₂×Dic₄₇	—	4	1	no	—
207	C₂×Dic₄₇	—	8	8	no	—
208	C₈×C₄₇	—	4	2	no	—
209	C₄₇⋊C₈	—	4	2	no	—
210	C₄₇⋊C₈	—	8	1	no	—
211	#8977	—	47	1	no	maximal, Sylow
212	C₂²×C₄₇	—	2	4	no	—
213	C₂²×C₄₇	—	4	2	no	—
214	C₂²×C₄₇	—	4	2	no	—
215	C₂²×C₄₇	—	4	2	no	—
216	C₂²×C₄₇	—	4	2	no	—
217	C₂²×C₄₇	—	4	2	no	—
218	C₂²×C₄₇	—	4	2	no	—
219	C₂²×C₄₇	—	8	2	no	—
220	C₂²×C₄₇	—	8	2	no	—
221	C₂²×C₄₇	—	8	2	no	—
222	C₂²×C₄₇	—	16	1	no	—
223	C₂²×C₄₇	—	16	1	no	—
224	C₂²×C₄₇	—	16	1	no	—
225	C₂²×C₄₇	—	16	1	no	—
226	C₂²×C₄₇	#386	1	1	yes	characteristic
227	C₂²×C₄₇	#447	1	1	yes	characteristic
228	C₂²×C₄₇	#447	1	1	yes	characteristic
229	C₂²×C₄₇	#448	1	1	yes	characteristic
230	C₂²×C₄₇	#449	1	1	yes	characteristic
231	C₂²×C₄₇	#453	1	1	yes	characteristic
232	C₂²×C₄₇	#454	1	1	yes	characteristic
233	C₄×C₄₇	—	2	1	no	—
234	C₄×C₄₇	—	2	1	no	—
235	C₄×C₄₇	—	4	2	no	—
236	C₄×C₄₇	C₂×#102	1	1	yes	characteristic
237	C₄×C₄₇	#417	1	1	yes	characteristic
238	C₄×C₄₇	C₄×D₈	1	1	yes	characteristic
239	C₄×C₄₇	#442	1	1	yes	characteristic
240	C₄×C₄₇	#459	1	1	yes	characteristic
241	C₄×C₄₇	#463	1	1	yes	characteristic
242	C₄×C₄₇	#480	1	1	yes	characteristic
243	C₄×C₄₇	#481	1	1	yes	characteristic
244	Dic₄₇	—	4	2	no	—
245	Dic₄₇	—	8	2	no	—
246	Dic₄₇	—	8	1	no	—
247	C₂×#459	D₄₇	1	1	yes	characteristic
248	D₄×C₄⋊C₄	—	47	1	no	—
249	#1982	—	47	1	no	—
250	#1957	—	47	1	no	—
251	C₂×D₄⋊C₈	—	47	1	no	—
252	#1296	—	47	1	no	—
253	#1279	—	47	1	no	—
254	C₂×C₄₇	—	4	4	no	—
255	C₂×C₄₇	—	16	2	no	—
256	C₂×C₄₇	#1619	1	1	yes	characteristic
257	C₂×C₄₇	#1622	1	1	yes	characteristic
258	C₂×C₄₇	#1625	1	1	yes	characteristic
259	C₂×C₄₇	#1627	1	1	yes	characteristic
260	C₂×C₄₇	#1874	1	1	yes	characteristic
261	C₂×C₄₇	#1879	1	1	yes	characteristic
262	C₂×C₄₇	#1883	1	1	yes	characteristic
263	C₂²×D₈	—	2	1	no	—
264	C₂×#127	C₂×D₄₇	1	1	yes	characteristic
265	C₂×C₄×D₄	—	94	1	no	—
266	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
267	C₂²×C₄⋊C₄	—	94	1	no	—
268	#459	—	2	2	no	—
269	#459	Dic₄₇	1	4	yes	complemented
270	C₂×C₄⋊C₈	—	47	1	no	—
271	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
272	C₂×#102	—	2	1	no	—
273	C₂×#102	—	94	2	no	—
274	C₂×#102	—	94	1	no	—
275	C₂×#102	—	94	1	no	—
276	C₂×C₄×C₈	—	47	1	no	—
277	#389	—	94	1	no	—
278	#385	—	94	2	no	—
279	#384	—	47	1	no	—
280	#380	—	94	1	no	—
281	C₄×C₄⋊C₄	—	47	1	no	—
282	D₄⋊C₈	—	94	2	no	—
283	C₄₇	#8977	1	1	yes	characteristic, complemented, Sylow
284	C₂²×D₄	—	2	1	no	—
285	C₂²×D₄	—	2	1	no	—
286	C₂²×D₄	—	2	1	no	—
287	C₂²×D₄	C₂²⋊D₄₇	1	1	yes	characteristic
288	C₂³×C₄	—	2	1	no	—
289	C₂³×C₄	—	94	2	no	—
290	C₂×D₈	—	2	4	no	—
291	C₂×D₈	—	4	2	no	—
292	C₂×D₈	—	4	2	no	—
293	C₂²×C₈	—	2	1	no	—
294	C₂²×C₈	—	94	1	no	—
295	C₂²×C₈	—	94	1	no	—
296	#127	—	2	1	no	—
297	#127	—	2	1	no	—
298	#127	—	2	1	no	—
299	#127	C₂×Dic₄₇	1	2	yes	complemented
300	C₄×D₄	—	2	1	no	—
301	C₄×D₄	—	2	1	no	—
302	C₄×D₄	—	188	2	no	—
303	C₄×D₄	—	188	2	no	—
304	C₄×D₄	C₂×Dic₄₇	1	2	yes	—
305	C₄×D₄	C₂²⋊D₄₇	1	2	yes	—
306	C₂×C₄⋊C₄	—	47	1	no	—
307	C₂×C₄⋊C₄	—	47	1	no	—
308	C₂×C₄⋊C₄	—	47	2	no	—
309	C₂×C₄⋊C₄	—	94	2	no	—
310	C₂×C₄⋊C₄	—	94	1	no	—
311	C₂×C₄⋊C₄	—	94	1	no	—
312	C₂×C₄⋊C₄	—	188	2	no	—
313	C₂×C₄⋊C₄	—	188	2	no	—
314	C₂×C₄⋊C₄	C₂²⋊D₄₇	1	1	yes	characteristic
315	C₂×C₂²⋊C₄	—	2	1	no	—
316	C₂×C₂²⋊C₄	—	94	2	no	—
317	C₂×C₄²	—	94	1	no	—
318	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
319	C₄⋊C₈	—	2	1	no	—
320	C₄⋊C₈	—	94	1	no	—
321	C₄⋊C₈	—	94	1	no	—
322	C₄⋊C₈	C₂×Dic₄₇	1	2	yes	complemented
323	#102	—	2	4	no	—
324	#102	—	188	2	no	—
325	#102	—	188	2	no	—
326	#102	—	188	4	no	—
327	C₄×C₈	—	94	1	no	—
328	C₄×C₈	—	94	1	no	—
329	#95	—	94	2	no	—
330	#95	—	94	1	no	—
331	C₂⁴	—	2	1	no	—
332	C₂⁴	—	4	1	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	2	1	no	—
339	C₂×D₄	—	4	2	no	—
340	C₂×D₄	—	4	2	no	—
341	C₂×D₄	—	4	1	no	—
342	C₂×D₄	—	4	1	no	—
343	C₂×D₄	—	4	1	no	—
344	C₂×D₄	—	4	1	no	—
345	C₂×D₄	—	4	1	no	—
346	C₂×D₄	—	4	1	no	—
347	C₂×D₄	—	4	1	no	—
348	C₂×D₄	—	4	1	no	—
349	C₂×D₄	—	4	1	no	—
350	C₂×D₄	—	4	1	no	—
351	C₂×D₄	—	4	1	no	—
352	C₂×D₄	#10625334	1	2	yes	—
353	C₂×D₄	#10625335	1	2	yes	—
354	C₂×D₄	C₂²⋊Dic₄₇	1	2	yes	—
355	C₂²×C₄	—	2	1	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	4	1	no	—
359	C₂²×C₄	—	4	1	no	—
360	C₂²×C₄	—	4	1	no	—
361	C₂²×C₄	—	4	1	no	—
362	C₂²×C₄	—	94	1	no	—
363	C₂²×C₄	—	94	1	no	—
364	C₂²×C₄	—	94	2	no	—
365	C₂²×C₄	—	376	2	no	—
366	C₂²×C₄	—	188	4	no	—
367	C₂²×C₄	—	188	4	no	—
368	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
369	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
370	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
371	D₈	—	4	8	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	4	1	no	—
374	C₂×C₈	—	4	1	no	—
375	C₂×C₈	—	94	2	no	—
376	C₂×C₈	—	188	1	no	—
377	C₂×C₈	—	188	1	no	—
378	C₂×C₈	—	188	1	no	—
379	C₂×C₈	—	188	1	no	—
380	C₂×C₈	—	188	1	no	—
381	C₄⋊C₄	—	2	1	no	—
382	C₄⋊C₄	—	47	2	no	—
383	C₄⋊C₄	—	94	1	no	—
384	C₄⋊C₄	—	94	1	no	—
385	C₄⋊C₄	—	94	1	no	—
386	C₄⋊C₄	—	188	2	no	—
387	C₄⋊C₄	—	188	4	no	—
388	C₄⋊C₄	—	188	1	no	—
389	C₄⋊C₄	—	188	1	no	—
390	C₄⋊C₄	—	188	1	no	—
391	C₄⋊C₄	—	188	1	no	—
392	C₄⋊C₄	C₂²⋊Dic₄₇	1	2	yes	—
393	C₂²⋊C₄	—	2	2	no	—
394	C₂²⋊C₄	—	2	2	no	—
395	C₂²⋊C₄	—	188	4	no	—
396	C₄²	—	188	1	no	—
397	C₄²	—	188	1	no	—
398	C₄²	#10625352	1	1	yes	characteristic
399	C₄²	#10625352	1	1	yes	characteristic
400	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
401	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
402	C₂³	—	2	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	4	1	no	—
406	C₂³	—	4	1	no	—
407	C₂³	—	4	1	no	—
408	C₂³	—	4	1	no	—
409	C₂³	—	4	2	no	—
410	C₂³	—	8	1	no	—
411	C₂³	—	8	1	no	—
412	C₂³	—	8	1	no	—
413	C₂³	—	8	1	no	—
414	C₂³	—	8	1	no	—
415	C₂³	—	8	1	no	—
416	C₂³	#13093992	1	1	yes	characteristic
417	D₄	—	2	2	no	—
418	D₄	—	2	2	no	—
419	D₄	—	2	2	no	—
420	D₄	—	4	4	no	—
421	D₄	—	4	2	no	—
422	D₄	—	4	2	no	—
423	D₄	—	4	2	no	—
424	D₄	—	4	2	no	—
425	D₄	—	8	2	no	—
426	D₄	—	8	1	no	—
427	D₄	—	8	1	no	—
428	D₄	—	8	1	no	—
429	D₄	—	8	1	no	—
430	D₄	#13093945	1	4	yes	complemented
431	C₂×C₄	—	2	1	no	—
432	C₂×C₄	—	2	1	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	4	1	no	—
435	C₂×C₄	—	4	1	no	—
436	C₂×C₄	—	4	2	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	2	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	94	2	no	—
441	C₂×C₄	—	376	8	no	—
442	C₂×C₄	—	188	2	no	—
443	C₂×C₄	—	188	1	no	—
444	C₂×C₄	—	188	2	no	—
445	C₂×C₄	—	188	1	no	—
446	C₂×C₄	—	188	2	no	—
447	C₂×C₄	—	188	1	no	—
448	C₂×C₄	—	188	1	no	—
449	C₂×C₄	—	188	1	no	—
450	C₂×C₄	C₂×C₂²⋊Dic₄₇	1	1	yes	characteristic
451	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
452	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
453	C₂×C₄	#13093996	1	1	yes	characteristic
454	C₂×C₄	#13093996	1	1	yes	characteristic
455	C₂×C₄	#13094005	1	1	yes	characteristic
456	C₂×C₄	D₈×D₄₇	1	1	yes	characteristic
457	C₂×C₄	C₂×#10625334	1	1	yes	characteristic
458	C₂×C₄	C₂×#10625335	1	1	yes	characteristic
459	C₂×C₄	#13094043	1	1	yes	characteristic
460	C₂×C₄	#13094048	1	1	yes	characteristic
461	C₂×C₄	#13094048	1	1	yes	characteristic
462	C₂×C₄	#13094049	1	1	yes	characteristic
463	C₂×C₄	#13094054	1	1	yes	characteristic
464	C₈	—	4	2	no	—
465	C₈	—	376	1	no	—
466	C₈	—	188	2	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	4	2	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	2	no	—
472	C₂²	—	4	2	no	—
473	C₂²	—	4	2	no	—
474	C₂²	—	8	2	no	—
475	C₂²	—	8	2	no	—
476	C₂²	—	8	2	no	—
477	C₂²	—	16	1	no	—
478	C₂²	—	16	1	no	—
479	C₂²	—	16	1	no	—
480	C₂²	—	16	1	no	—
481	C₂²	#15689003	1	1	yes	characteristic
482	C₂²	#15689255	1	1	yes	characteristic
483	C₂²	#15689256	1	1	yes	characteristic
484	C₂²	#15689261	1	1	yes	characteristic
485	C₂²	#15689265	1	1	yes	characteristic
486	C₂²	#15689289	1	1	yes	characteristic
487	C₂²	#15689294	1	1	yes	characteristic
488	C₄	—	2	1	no	—
489	C₄	—	2	1	no	—
490	C₄	—	4	2	no	—
491	C₄	—	376	2	no	—
492	C₄	—	376	1	no	—
493	C₄	—	188	2	no	—
494	C₄	C₂×#13093945	1	1	yes	characteristic
495	C₄	#15689124	1	1	yes	characteristic
496	C₄	D₈×Dic₄₇	1	1	yes	characteristic
497	C₄	#15689235	1	1	yes	characteristic
498	C₄	#15689316	1	1	yes	characteristic
499	C₄	#15689336	1	1	yes	characteristic
500	C₄	#15689434	1	1	yes	characteristic
501	C₄	#15689439	1	1	yes	characteristic
502	C₂	—	4	4	no	—
503	C₂	—	16	2	no	—
504	C₂	#20242441	1	1	yes	characteristic
505	C₂	#20242458	1	1	yes	characteristic
506	C₂	#20242475	1	1	yes	characteristic
507	C₂	#20242490	1	1	yes	characteristic
508	C₂	#20243706	1	1	yes	characteristic
509	C₂	#20243738	1	1	yes	characteristic
510	C₂	#20243766	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#13093992
commutator	C₄²×C₄₇	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting, prime radical	C₂×C₄₇×#459	C₂
socle	C₂³×C₄₇	#120
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	C₂×#459	D₄₇
hypocenter	C₄₇	#8977
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#459

Complements

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

N	H ≅ G/N	type
1. D₄×C₄⋊Dic₄₇	C₂	semidirect
2. #20244316	C₂	semidirect
3. #20244195	C₂	semidirect
4. C₂×D₄⋊(C₄₇⋊C₈)	C₂	semidirect
5. #20241272	C₂	semidirect
6. #20241227	C₂	semidirect
25. C₄₇×#459	C₄	semidirect
64. #127×C₄₇	C₂×C₄	semidirect
73. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
137. C₄⋊Dic₄₇	D₈	semidirect
174. D₄×C₄₇	#102	semidirect
269. #459	Dic₄₇	semidirect
283. C₄₇	#8977	semidirect
299. #127	C₂×Dic₄₇	semidirect
322. C₄⋊C₈	C₂×Dic₄₇	semidirect
430. D₄	#13093945	semidirect

Maximal subgroups

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

subgroup	index
D₄×C₄⋊Dic₄₇	2
#20244316	2
#20244195	2
C₂×D₄⋊(C₄₇⋊C₈)	2
#20241272	2
#20241227	2
C₂×C₄₇×#459	2
#8977	47