Subgroups — C₄₇×#24770 #26064468

Order 12032.

924 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#472	C₂	1	2	yes	maximal, complemented
2	C₄₇×#3038	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#459	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×AGL(1,ℤ/8)×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2906	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#2063	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2045	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1965	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1950	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1907	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1800	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	2	yes	—
13	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×D₈×C₄₇	C₂²	1	2	yes	—
15	C₂×#131×C₄₇	C₂²	1	2	yes	—
16	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
17	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#472	—	2	8	no	—
20	C₄₇×#460	—	2	1	no	—
21	C₄₇×#460	—	2	1	no	—
22	C₄₇×#459	—	2	1	no	—
23	C₄₇×#459	—	2	1	no	—
24	C₄₇×#459	—	2	1	no	—
25	C₄₇×#459	—	2	1	no	—
26	C₄₇×#459	—	2	2	no	—
27	C₄₇×#442	—	2	1	no	—
28	C₄₇×#440	—	2	1	no	—
29	C₄×SD₁₆×C₄₇	—	2	1	no	—
30	C₄×D₈×C₄₇	—	2	1	no	—
31	C₂×#108×C₄₇	C₂²	1	2	yes	—
32	C₄₇×#428	C₂²	1	1	yes	characteristic
33	C₄₇×#424	—	2	2	no	—
34	C₄₇×#424	C₂²	1	2	yes	—
35	C₄₇×#423	—	2	1	no	—
36	C₄₇×#423	C₂²	1	1	yes	characteristic
37	C₄₇×#423	C₂²	1	1	yes	characteristic
38	C₂×C₄⋊C₈×C₄₇	—	2	1	no	—
39	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#418	C₂²	1	2	yes	—
41	C₄₇×#418	C₂²	1	1	yes	characteristic
42	C₄₇×#417	C₂²	1	1	yes	characteristic
43	C₂×#102×C₄₇	C₂²	1	2	yes	—
44	C₂×#100×C₄₇	C₂²	1	2	yes	—
45	C₂×#100×C₄₇	C₂²	1	2	yes	—
46	C₂×#100×C₄₇	C₂²	1	2	yes	—
47	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
48	C₄₇×#343	C₂²	1	2	yes	—
49	C₄₇×#341	C₂²	1	2	yes	—
50	C₂×#41×C₄₇	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₄₇	—	2	1	no	—
52	C₂²×D₄×C₄₇	—	2	1	no	—
53	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
54	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
55	C₂³×C₄×C₄₇	—	2	1	no	—
56	AGL(1,ℤ/8)×C₄₇	—	2	2	no	—
57	AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
58	AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
59	AGL(1,ℤ/8)×C₄₇	D₄	1	4	yes	complemented
60	C₂×SD₁₆×C₄₇	—	2	1	no	—
61	C₂×SD₁₆×C₄₇	—	2	2	no	—
62	C₂×D₈×C₄₇	—	2	1	no	—
63	C₂×D₈×C₄₇	—	2	2	no	—
64	C₂×D₈×C₄₇	—	2	4	no	—
65	C₂×D₈×C₄₇	—	2	2	no	—
66	C₂×D₈×C₄₇	—	2	2	no	—
67	C₂×D₈×C₄₇	—	4	2	no	—
68	#131×C₄₇	—	2	4	no	—
69	#131×C₄₇	—	4	2	no	—
70	C₂×M₁₆×C₄₇	—	2	2	no	—
71	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
72	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
73	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
74	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
75	C₂²×C₈×C₄₇	—	2	2	no	—
76	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
77	#127×C₄₇	—	2	1	no	—
78	#127×C₄₇	—	2	1	no	—
79	#127×C₄₇	—	2	1	no	—
80	#127×C₄₇	—	2	1	no	—
81	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
82	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
83	C₄×D₄×C₄₇	—	2	1	no	—
84	C₄×D₄×C₄₇	—	2	1	no	—
85	C₄×D₄×C₄₇	—	2	1	no	—
86	C₄×D₄×C₄₇	—	2	1	no	—
87	C₄×D₄×C₄₇	—	2	1	no	—
88	C₄×D₄×C₄₇	—	2	1	no	—
89	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
90	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
91	#117×C₄₇	—	2	1	no	—
92	#117×C₄₇	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
94	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
95	C₂×C₄²×C₄₇	—	2	1	no	—
96	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
97	#108×C₄₇	—	2	4	no	—
98	#107×C₄₇	—	2	1	no	—
99	#106×C₄₇	—	2	1	no	—
100	C₄⋊C₈×C₄₇	—	2	2	no	—
101	C₄⋊C₈×C₄₇	—	2	2	no	—
102	C₄⋊C₈×C₄₇	—	2	1	no	—
103	C₄⋊C₈×C₄₇	—	2	1	no	—
104	C₄⋊C₈×C₄₇	—	2	1	no	—
105	C₄⋊C₈×C₄₇	—	2	1	no	—
106	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
107	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
108	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
109	#103×C₄₇	—	2	1	no	—
110	#102×C₄₇	—	2	1	no	—
111	#102×C₄₇	—	2	2	no	—
112	#102×C₄₇	—	2	2	no	—
113	#102×C₄₇	—	2	2	no	—
114	#102×C₄₇	—	2	2	no	—
115	#102×C₄₇	—	2	1	no	—
116	#102×C₄₇	—	2	1	no	—
117	#100×C₄₇	—	2	4	no	—
118	#100×C₄₇	—	2	4	no	—
119	#100×C₄₇	—	4	2	no	—
120	#97×C₄₇	—	2	1	no	—
121	C₄×C₈×C₄₇	—	2	1	no	—
122	C₂⁴×C₄₇	—	2	1	no	—
123	C₂⁴×C₄₇	—	2	2	no	—
124	#41×C₄₇	—	2	1	no	—
125	#41×C₄₇	—	2	1	no	—
126	#41×C₄₇	C₂×D₄	1	2	yes	—
127	#41×C₄₇	#41	1	2	yes	—
128	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂×D₄×C₄₇	—	2	1	no	—
130	C₂×D₄×C₄₇	—	2	1	no	—
131	C₂×D₄×C₄₇	—	2	1	no	—
132	C₂×D₄×C₄₇	—	2	2	no	—
133	C₂×D₄×C₄₇	—	2	2	no	—
134	C₂×D₄×C₄₇	—	2	2	no	—
135	C₂×D₄×C₄₇	—	2	1	no	—
136	C₂×D₄×C₄₇	—	2	2	no	—
137	C₂×D₄×C₄₇	—	2	1	no	—
138	C₂×D₄×C₄₇	—	2	2	no	—
139	C₂×D₄×C₄₇	—	2	1	no	—
140	C₂×D₄×C₄₇	—	2	2	no	—
141	C₂×D₄×C₄₇	—	4	1	no	—
142	C₂×D₄×C₄₇	—	4	1	no	—
143	C₂×D₄×C₄₇	—	4	1	no	—
144	C₂×D₄×C₄₇	—	4	1	no	—
145	C₂×D₄×C₄₇	—	8	2	no	—
146	C₂×D₄×C₄₇	—	8	2	no	—
147	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
148	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₇	—	2	1	no	—
150	C₂²×C₄×C₄₇	—	2	1	no	—
151	C₂²×C₄×C₄₇	—	2	1	no	—
152	C₂²×C₄×C₄₇	—	2	1	no	—
153	C₂²×C₄×C₄₇	—	4	1	no	—
154	C₂²×C₄×C₄₇	—	4	1	no	—
155	C₂²×C₄×C₄₇	—	8	2	no	—
156	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
157	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
158	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
159	SD₁₆×C₄₇	—	2	4	no	—
160	SD₁₆×C₄₇	—	4	4	no	—
161	D₈×C₄₇	—	2	4	no	—
162	D₈×C₄₇	—	4	4	no	—
163	D₈×C₄₇	—	4	4	no	—
164	D₈×C₄₇	—	4	4	no	—
165	M₁₆×C₄₇	—	2	1	no	—
166	M₁₆×C₄₇	—	2	2	no	—
167	M₁₆×C₄₇	—	2	2	no	—
168	M₁₆×C₄₇	—	2	2	no	—
169	M₁₆×C₄₇	—	2	2	no	—
170	M₁₆×C₄₇	—	2	1	no	—
171	M₁₆×C₄₇	—	2	1	no	—
172	M₁₆×C₄₇	—	4	4	no	—
173	M₁₆×C₄₇	C₂×D₄	1	2	yes	—
174	C₂×C₈×C₄₇	—	2	1	no	—
175	C₂×C₈×C₄₇	—	2	2	no	—
176	C₂×C₈×C₄₇	—	2	2	no	—
177	C₂×C₈×C₄₇	—	2	1	no	—
178	C₂×C₈×C₄₇	—	2	2	no	—
179	C₂×C₈×C₄₇	—	2	2	no	—
180	C₂×C₈×C₄₇	—	4	4	no	—
181	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
182	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
183	C₄⋊C₄×C₄₇	—	2	1	no	—
184	C₄⋊C₄×C₄₇	—	2	1	no	—
185	C₄⋊C₄×C₄₇	—	2	1	no	—
186	C₄⋊C₄×C₄₇	—	2	1	no	—
187	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
188	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
189	C₂²⋊C₄×C₄₇	—	2	1	no	—
190	C₂²⋊C₄×C₄₇	—	2	1	no	—
191	C₂²⋊C₄×C₄₇	—	2	1	no	—
192	C₂²⋊C₄×C₄₇	—	4	1	no	—
193	C₂²⋊C₄×C₄₇	—	4	1	no	—
194	C₄²×C₄₇	—	2	1	no	—
195	C₄²×C₄₇	—	2	1	no	—
196	C₄²×C₄₇	—	2	1	no	—
197	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
198	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
199	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
200	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
201	C₂³×C₄₇	—	2	1	no	—
202	C₂³×C₄₇	—	2	2	no	—
203	C₂³×C₄₇	—	4	1	no	—
204	C₂³×C₄₇	—	4	1	no	—
205	C₂³×C₄₇	—	4	2	no	—
206	C₂³×C₄₇	—	4	2	no	—
207	C₂³×C₄₇	—	4	2	no	—
208	C₂³×C₄₇	—	8	1	no	—
209	C₂³×C₄₇	—	8	1	no	—
210	C₂³×C₄₇	—	8	2	no	—
211	C₂³×C₄₇	—	8	2	no	—
212	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
213	Q₈×C₄₇	—	2	1	no	—
214	Q₈×C₄₇	#121	1	2	yes	—
215	D₄×C₄₇	—	2	2	no	—
216	D₄×C₄₇	—	2	2	no	—
217	D₄×C₄₇	—	2	2	no	—
218	D₄×C₄₇	—	2	1	no	—
219	D₄×C₄₇	—	2	2	no	—
220	D₄×C₄₇	—	4	2	no	—
221	D₄×C₄₇	—	4	1	no	—
222	D₄×C₄₇	—	4	2	no	—
223	D₄×C₄₇	—	4	2	no	—
224	D₄×C₄₇	—	4	1	no	—
225	D₄×C₄₇	—	4	2	no	—
226	D₄×C₄₇	—	8	2	no	—
227	D₄×C₄₇	—	8	2	no	—
228	D₄×C₄₇	—	8	2	no	—
229	D₄×C₄₇	—	8	2	no	—
230	D₄×C₄₇	#121	1	2	yes	—
231	C₂×C₄×C₄₇	—	2	1	no	—
232	C₂×C₄×C₄₇	—	2	2	no	—
233	C₂×C₄×C₄₇	—	2	2	no	—
234	C₂×C₄×C₄₇	—	2	2	no	—
235	C₂×C₄×C₄₇	—	2	1	no	—
236	C₂×C₄×C₄₇	—	2	1	no	—
237	C₂×C₄×C₄₇	—	4	1	no	—
238	C₂×C₄×C₄₇	—	4	2	no	—
239	C₂×C₄×C₄₇	—	4	1	no	—
240	C₂×C₄×C₄₇	—	8	1	no	—
241	C₂×C₄×C₄₇	—	8	2	no	—
242	C₂×C₄×C₄₇	—	8	2	no	—
243	C₂×C₄×C₄₇	—	8	1	no	—
244	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
245	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
246	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
247	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
248	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
249	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
250	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
251	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
252	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
253	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
254	C₈×C₄₇	—	2	2	no	—
255	C₈×C₄₇	—	2	2	no	—
256	C₈×C₄₇	—	2	2	no	—
257	C₈×C₄₇	—	4	2	no	—
258	C₈×C₄₇	—	4	1	no	—
259	C₈×C₄₇	—	4	2	no	—
260	#24770	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
261	C₂²×C₄₇	—	2	1	no	—
262	C₂²×C₄₇	—	2	1	no	—
263	C₂²×C₄₇	—	2	2	no	—
264	C₂²×C₄₇	—	4	1	no	—
265	C₂²×C₄₇	—	4	1	no	—
266	C₂²×C₄₇	—	4	2	no	—
267	C₂²×C₄₇	—	8	2	no	—
268	C₂²×C₄₇	—	8	2	no	—
269	C₂²×C₄₇	—	8	1	no	—
270	C₂²×C₄₇	—	8	1	no	—
271	C₂²×C₄₇	—	8	2	no	—
272	C₂²×C₄₇	—	8	2	no	—
273	C₂²×C₄₇	—	8	2	no	—
274	C₂²×C₄₇	—	16	2	no	—
275	C₂²×C₄₇	—	16	2	no	—
276	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
277	C₂²×C₄₇	#547	1	1	yes	characteristic
278	C₂²×C₄₇	#553	1	1	yes	characteristic
279	C₄×C₄₇	—	2	2	no	—
280	C₄×C₄₇	—	2	1	no	—
281	C₄×C₄₇	—	2	1	no	—
282	C₄×C₄₇	—	2	1	no	—
283	C₄×C₄₇	—	4	1	no	—
284	C₄×C₄₇	—	4	1	no	—
285	C₄×C₄₇	—	8	1	no	—
286	C₄×C₄₇	#472	1	2	yes	complemented
287	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
288	C₄×C₄₇	#537	1	1	yes	characteristic
289	C₄×C₄₇	D₄²	1	1	yes	characteristic
290	C₄×C₄₇	#548	1	1	yes	characteristic
291	C₂×#472	C₂×C₄₇	1	2	yes	complemented
292	#3038	C₂×C₄₇	1	1	yes	characteristic, complemented
293	C₂×#459	C₂×C₄₇	1	1	yes	characteristic, complemented
294	C₄×AGL(1,ℤ/8)	C₂×C₄₇	1	1	yes	characteristic, complemented
295	#2906	C₂×C₄₇	1	1	yes	characteristic, complemented
296	#2063	C₂×C₄₇	1	2	yes	complemented
297	#2045	C₂×C₄₇	1	2	yes	complemented
298	#1965	C₂×C₄₇	1	1	yes	characteristic, complemented
299	#1950	C₂×C₄₇	1	1	yes	characteristic, complemented
300	#1907	C₂×C₄₇	1	2	yes	complemented
301	#1800	C₂×C₄₇	1	1	yes	characteristic, complemented
302	C₂×C₄₇	—	2	1	no	—
303	C₂×C₄₇	—	2	1	no	—
304	C₂×C₄₇	—	4	2	no	—
305	C₂×C₄₇	—	8	2	no	—
306	C₂×C₄₇	—	16	2	no	—
307	C₂×C₄₇	#2416	1	1	yes	characteristic
308	C₂×C₄₇	C₂×#472	1	1	yes	characteristic
309	C₂×C₄₇	#3068	1	1	yes	characteristic
310	C₂×AGL(1,ℤ/8)	C₂²×C₄₇	1	2	yes	—
311	C₂×AGL(1,ℤ/8)	C₂²×C₄₇	1	1	yes	characteristic
312	C₂²×D₈	C₂²×C₄₇	1	2	yes	—
313	C₂×#131	C₂²×C₄₇	1	2	yes	—
314	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
315	C₄×#41	C₂²×C₄₇	1	1	yes	characteristic
316	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
317	#472	—	2	8	no	—
318	#460	—	2	1	no	—
319	#460	—	2	1	no	—
320	#459	—	2	1	no	—
321	#459	—	2	1	no	—
322	#459	—	2	1	no	—
323	#459	—	2	1	no	—
324	#459	—	2	2	no	—
325	#442	—	2	1	no	—
326	#440	—	2	1	no	—
327	C₄×SD₁₆	—	2	1	no	—
328	C₄×D₈	—	2	1	no	—
329	C₂×#108	C₂²×C₄₇	1	2	yes	—
330	#428	C₂²×C₄₇	1	1	yes	characteristic
331	#424	—	2	2	no	—
332	#424	C₂²×C₄₇	1	2	yes	—
333	#423	—	2	1	no	—
334	#423	C₂²×C₄₇	1	1	yes	characteristic
335	#423	C₂²×C₄₇	1	1	yes	characteristic
336	C₂×C₄⋊C₈	—	2	1	no	—
337	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
338	#418	C₂²×C₄₇	1	2	yes	—
339	#418	C₂²×C₄₇	1	1	yes	characteristic
340	#417	C₂²×C₄₇	1	1	yes	characteristic
341	C₂×#102	C₂²×C₄₇	1	2	yes	—
342	C₂×#100	C₂²×C₄₇	1	2	yes	—
343	C₂×#100	C₂²×C₄₇	1	2	yes	—
344	C₂×#100	C₂²×C₄₇	1	2	yes	—
345	C₄×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
346	#343	C₂²×C₄₇	1	2	yes	—
347	#341	C₂²×C₄₇	1	2	yes	—
348	C₄₇	#24770	1	1	yes	characteristic, direct product factor, Sylow
349	C₂×#41	C₂³×C₄₇	1	1	yes	characteristic
350	C₂²×D₄	—	2	1	no	—
351	C₂²×D₄	—	2	1	no	—
352	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
353	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
354	C₂³×C₄	—	2	1	no	—
355	AGL(1,ℤ/8)	—	2	2	no	—
356	AGL(1,ℤ/8)	—	2	4	no	—
357	AGL(1,ℤ/8)	—	2	4	no	—
358	AGL(1,ℤ/8)	D₄×C₄₇	1	4	yes	complemented
359	C₂×SD₁₆	—	2	1	no	—
360	C₂×SD₁₆	—	2	2	no	—
361	C₂×D₈	—	2	1	no	—
362	C₂×D₈	—	2	4	no	—
363	C₂×D₈	—	2	2	no	—
364	C₂×D₈	—	2	2	no	—
365	C₂×D₈	—	2	2	no	—
366	C₂×D₈	—	4	2	no	—
367	#131	—	2	4	no	—
368	#131	—	4	2	no	—
369	C₂×M₁₆	—	2	2	no	—
370	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
371	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
372	C₂×M₁₆	C₂³×C₄₇	1	1	yes	characteristic
373	C₂×M₁₆	C₂³×C₄₇	1	1	yes	characteristic
374	C₂²×C₈	—	2	2	no	—
375	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
376	#127	—	2	1	no	—
377	#127	—	2	1	no	—
378	#127	—	2	1	no	—
379	#127	—	2	1	no	—
380	C₄×Q₈	D₄×C₄₇	1	1	yes	characteristic
381	C₄×Q₈	D₄×C₄₇	1	1	yes	characteristic
382	C₄×D₄	—	2	1	no	—
383	C₄×D₄	—	2	1	no	—
384	C₄×D₄	—	2	1	no	—
385	C₄×D₄	—	2	1	no	—
386	C₄×D₄	—	2	1	no	—
387	C₄×D₄	—	2	1	no	—
388	C₄×D₄	D₄×C₄₇	1	1	yes	characteristic
389	C₄×D₄	D₄×C₄₇	1	1	yes	characteristic
390	#117	—	2	1	no	—
391	#117	C₂³×C₄₇	1	1	yes	characteristic
392	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
393	C₂×C₂²⋊C₄	—	2	1	no	—
394	C₂×C₄²	—	2	1	no	—
395	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
396	#108	—	2	4	no	—
397	#107	—	2	1	no	—
398	#106	—	2	1	no	—
399	C₄⋊C₈	—	2	2	no	—
400	C₄⋊C₈	—	2	2	no	—
401	C₄⋊C₈	—	2	1	no	—
402	C₄⋊C₈	—	2	1	no	—
403	C₄⋊C₈	—	2	1	no	—
404	C₄⋊C₈	—	2	1	no	—
405	C₄⋊C₈	D₄×C₄₇	1	1	yes	characteristic
406	C₄⋊C₈	D₄×C₄₇	1	1	yes	characteristic
407	C₄⋊C₈	D₄×C₄₇	1	2	yes	—
408	#103	—	2	1	no	—
409	#102	—	2	1	no	—
410	#102	—	2	2	no	—
411	#102	—	2	2	no	—
412	#102	—	2	1	no	—
413	#102	—	2	1	no	—
414	#102	—	2	2	no	—
415	#102	—	2	2	no	—
416	#100	—	2	4	no	—
417	#100	—	2	4	no	—
418	#100	—	4	2	no	—
419	#97	—	2	1	no	—
420	C₄×C₈	—	2	1	no	—
421	C₂⁴	—	2	1	no	—
422	C₂⁴	—	2	2	no	—
423	#41	—	2	1	no	—
424	#41	—	2	1	no	—
425	#41	C₂×D₄×C₄₇	1	2	yes	—
426	#41	#41×C₄₇	1	2	yes	—
427	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	2	1	no	—
431	C₂×D₄	—	2	2	no	—
432	C₂×D₄	—	2	2	no	—
433	C₂×D₄	—	2	2	no	—
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	2	2	no	—
436	C₂×D₄	—	2	1	no	—
437	C₂×D₄	—	2	2	no	—
438	C₂×D₄	—	2	1	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	4	1	no	—
441	C₂×D₄	—	4	1	no	—
442	C₂×D₄	—	4	1	no	—
443	C₂×D₄	—	4	1	no	—
444	C₂×D₄	—	8	2	no	—
445	C₂×D₄	—	8	2	no	—
446	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
447	C₂×D₄	C₂×D₄×C₄₇	1	1	yes	characteristic
448	C₂²×C₄	—	2	1	no	—
449	C₂²×C₄	—	2	1	no	—
450	C₂²×C₄	—	2	1	no	—
451	C₂²×C₄	—	2	1	no	—
452	C₂²×C₄	—	4	1	no	—
453	C₂²×C₄	—	4	1	no	—
454	C₂²×C₄	—	8	2	no	—
455	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
456	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
457	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
458	SD₁₆	—	2	4	no	—
459	SD₁₆	—	4	4	no	—
460	D₈	—	2	4	no	—
461	D₈	—	4	4	no	—
462	D₈	—	4	4	no	—
463	D₈	—	4	4	no	—
464	M₁₆	—	2	1	no	—
465	M₁₆	—	2	2	no	—
466	M₁₆	—	2	2	no	—
467	M₁₆	—	2	2	no	—
468	M₁₆	—	2	1	no	—
469	M₁₆	—	2	2	no	—
470	M₁₆	—	2	1	no	—
471	M₁₆	—	4	4	no	—
472	M₁₆	C₂×D₄×C₄₇	1	2	yes	—
473	C₂×C₈	—	2	1	no	—
474	C₂×C₈	—	2	2	no	—
475	C₂×C₈	—	2	2	no	—
476	C₂×C₈	—	2	1	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	—	2	2	no	—
479	C₂×C₈	—	4	4	no	—
480	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
481	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
482	C₄⋊C₄	—	2	1	no	—
483	C₄⋊C₄	—	2	1	no	—
484	C₄⋊C₄	—	2	1	no	—
485	C₄⋊C₄	—	2	1	no	—
486	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
487	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
488	C₂²⋊C₄	—	2	1	no	—
489	C₂²⋊C₄	—	2	1	no	—
490	C₂²⋊C₄	—	2	1	no	—
491	C₂²⋊C₄	—	4	1	no	—
492	C₂²⋊C₄	—	4	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	2	1	no	—
496	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
497	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
498	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
499	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
500	C₂³	—	2	1	no	—
501	C₂³	—	2	2	no	—
502	C₂³	—	4	1	no	—
503	C₂³	—	4	1	no	—
504	C₂³	—	4	2	no	—
505	C₂³	—	4	2	no	—
506	C₂³	—	4	2	no	—
507	C₂³	—	8	1	no	—
508	C₂³	—	8	1	no	—
509	C₂³	—	8	2	no	—
510	C₂³	—	8	2	no	—
511	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
512	Q₈	—	2	1	no	—
513	Q₈	#121×C₄₇	1	2	yes	—
514	D₄	—	2	2	no	—
515	D₄	—	2	2	no	—
516	D₄	—	2	2	no	—
517	D₄	—	2	1	no	—
518	D₄	—	2	2	no	—
519	D₄	—	4	2	no	—
520	D₄	—	4	1	no	—
521	D₄	—	4	2	no	—
522	D₄	—	4	2	no	—
523	D₄	—	4	1	no	—
524	D₄	—	4	2	no	—
525	D₄	—	8	2	no	—
526	D₄	—	8	2	no	—
527	D₄	—	8	2	no	—
528	D₄	—	8	2	no	—
529	D₄	#121×C₄₇	1	2	yes	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	1	no	—
535	C₂×C₄	—	2	1	no	—
536	C₂×C₄	—	4	1	no	—
537	C₂×C₄	—	4	2	no	—
538	C₂×C₄	—	4	1	no	—
539	C₂×C₄	—	8	1	no	—
540	C₂×C₄	—	8	2	no	—
541	C₂×C₄	—	8	2	no	—
542	C₂×C₄	—	8	1	no	—
543	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
544	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
545	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
546	C₂×C₄	#121×C₄₇	1	1	yes	characteristic
547	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
548	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
549	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
550	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
551	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
552	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
553	C₈	—	2	2	no	—
554	C₈	—	2	2	no	—
555	C₈	—	2	2	no	—
556	C₈	—	4	2	no	—
557	C₈	—	4	1	no	—
558	C₈	—	4	2	no	—
559	C₂²	—	2	1	no	—
560	C₂²	—	2	1	no	—
561	C₂²	—	2	2	no	—
562	C₂²	—	4	1	no	—
563	C₂²	—	4	1	no	—
564	C₂²	—	4	2	no	—
565	C₂²	—	8	2	no	—
566	C₂²	—	8	2	no	—
567	C₂²	—	8	1	no	—
568	C₂²	—	8	1	no	—
569	C₂²	—	8	2	no	—
570	C₂²	—	8	2	no	—
571	C₂²	—	8	2	no	—
572	C₂²	—	16	2	no	—
573	C₂²	—	16	2	no	—
574	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
575	C₂²	C₄₇×#547	1	1	yes	characteristic
576	C₂²	C₄₇×#553	1	1	yes	characteristic
577	C₄	—	2	1	no	—
578	C₄	—	2	1	no	—
579	C₄	—	2	1	no	—
580	C₄	—	2	2	no	—
581	C₄	—	4	1	no	—
582	C₄	—	4	1	no	—
583	C₄	—	8	1	no	—
584	C₄	C₄₇×#472	1	2	yes	complemented
585	C₄	C₂×#121×C₄₇	1	1	yes	characteristic
586	C₄	C₄₇×#537	1	1	yes	characteristic
587	C₄	D₄²×C₄₇	1	1	yes	characteristic
588	C₄	C₄₇×#548	1	1	yes	characteristic
589	C₂	—	2	1	no	—
590	C₂	—	2	1	no	—
591	C₂	—	4	2	no	—
592	C₂	—	8	2	no	—
593	C₂	—	16	2	no	—
594	C₂	C₄₇×#2416	1	1	yes	characteristic
595	C₂	C₂×C₄₇×#472	1	1	yes	characteristic
596	C₂	C₄₇×#3068	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#121
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₇×#472	C₂	semidirect
2. C₄₇×#3038	C₂	semidirect
3. C₂×C₄₇×#459	C₂	semidirect
4. C₄×AGL(1,ℤ/8)×C₄₇	C₂	semidirect
5. C₄₇×#2906	C₂	semidirect
6. C₄₇×#2063	C₂	semidirect
7. C₄₇×#2045	C₂	semidirect
8. C₄₇×#1965	C₂	semidirect
9. C₄₇×#1950	C₂	semidirect
10. C₄₇×#1907	C₂	semidirect
11. C₄₇×#1800	C₂	semidirect
59. AGL(1,ℤ/8)×C₄₇	D₄	semidirect
260. #24770	C₄₇	direct (N × H)
286. C₄×C₄₇	#472	semidirect
291. C₂×#472	C₂×C₄₇	semidirect
292. #3038	C₂×C₄₇	semidirect
293. C₂×#459	C₂×C₄₇	semidirect
294. C₄×AGL(1,ℤ/8)	C₂×C₄₇	semidirect
295. #2906	C₂×C₄₇	semidirect
296. #2063	C₂×C₄₇	semidirect
297. #2045	C₂×C₄₇	semidirect
298. #1965	C₂×C₄₇	semidirect
299. #1950	C₂×C₄₇	semidirect
300. #1907	C₂×C₄₇	semidirect
301. #1800	C₂×C₄₇	semidirect
348. C₄₇	#24770	direct (N × H)
358. AGL(1,ℤ/8)	D₄×C₄₇	semidirect
584. C₄	C₄₇×#472	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#472	2
C₄₇×#3038	2
C₂×C₄₇×#459	2
C₄×AGL(1,ℤ/8)×C₄₇	2
C₄₇×#2906	2
C₄₇×#2063	2
C₄₇×#2045	2
C₄₇×#1965	2
C₄₇×#1950	2
C₄₇×#1907	2
C₄₇×#1800	2
#24770	47

Subgroups — C47×#24770 #26064468

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#24770 #26064468