Subgroups — C₄₇×#23591 #26063289

Order 12032.

1182 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3460	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×AGL(1,ℤ/8)×C₄₇	C₂	1	2	yes	maximal, complemented
3	C₄₇×#2328	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2061	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2040	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#2037	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2027	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#2006	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#2002	C₂	1	2	yes	maximal, complemented
10	C₄₇×#1759	C₂	1	2	yes	maximal, complemented
11	C₄×#100×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₄₇	C₂²	1	2	yes	—
13	C₄₇×#544	C₂²	1	1	yes	characteristic
14	C₄₇×#542	—	2	2	no	—
15	C₄₇×#540	—	2	2	no	—
16	C₄₇×#538	—	2	2	no	—
17	C₄₇×#537	C₂²	1	1	yes	characteristic
18	C₄₇×#535	C₂²	1	2	yes	—
19	C₄₇×#532	—	2	2	no	—
20	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
21	C₄₇×#529	—	2	2	no	—
22	C₄₇×#525	—	2	2	no	—
23	C₄×#41×C₄₇	C₂²	1	2	yes	—
24	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
26	C₄₇×#442	—	2	2	no	—
27	C₄₇×#440	—	2	2	no	—
28	C₄×SD₁₆×C₄₇	—	2	2	no	—
29	C₄×D₈×C₄₇	—	2	2	no	—
30	C₄₇×#428	C₂²	1	2	yes	—
31	C₂×#104×C₄₇	C₂²	1	2	yes	—
32	C₂×#104×C₄₇	C₂²	1	2	yes	—
33	C₄₇×#418	C₂²	1	2	yes	—
34	C₄₇×#417	C₂²	1	2	yes	—
35	C₂×#100×C₄₇	C₂²	1	2	yes	—
36	C₄×M₁₆×C₄₇	C₂²	1	2	yes	—
37	C₄₇×#390	C₂²	1	1	yes	characteristic
38	C₄₇×#390	C₂²	1	1	yes	characteristic
39	C₄₇×#386	—	2	2	no	—
40	C₄₇×#386	—	2	2	no	—
41	C₄₇×#382	C₂²	1	1	yes	characteristic
42	C₄₇×#376	C₂²	1	1	yes	characteristic
43	C₄₇×#343	C₂²	1	1	yes	characteristic
44	C₄₇×#343	C₂²	1	1	yes	characteristic
45	C₄₇×#339	C₂²	1	2	yes	—
46	C₄₇×#339	C₂²	1	2	yes	—
47	C₂×#41×C₄₇	—	2	2	no	—
48	C₂×#41×C₄₇	C₂³	1	2	yes	—
49	C₂²×D₄×C₄₇	—	2	2	no	—
50	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
51	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₄₇	—	2	1	no	—
53	C₂³×C₄×C₄₇	D₄	1	2	yes	—
54	AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
55	AGL(1,ℤ/8)×C₄₇	—	2	4	no	—
56	C₂×SD₁₆×C₄₇	—	2	2	no	—
57	C₂×D₈×C₄₇	—	2	2	no	—
58	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
59	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
60	C₄⋊Q₈×C₄₇	—	2	2	no	—
61	#127×C₄₇	—	2	2	no	—
62	#127×C₄₇	—	2	2	no	—
63	#127×C₄₇	—	2	2	no	—
64	#126×C₄₇	—	2	4	no	—
65	#125×C₄₇	—	2	2	no	—
66	#124×C₄₇	—	2	4	no	—
67	#124×C₄₇	—	2	2	no	—
68	#123×C₄₇	—	2	4	no	—
69	#123×C₄₇	—	2	4	no	—
70	C₂²⋊Q₈×C₄₇	—	2	2	no	—
71	C₂²⋊Q₈×C₄₇	—	2	2	no	—
72	C₂²⋊Q₈×C₄₇	—	2	2	no	—
73	#121×C₄₇	—	2	2	no	—
74	#121×C₄₇	—	2	4	no	—
75	#121×C₄₇	—	2	2	no	—
76	#121×C₄₇	—	2	2	no	—
77	#121×C₄₇	—	2	2	no	—
78	#121×C₄₇	—	2	2	no	—
79	#120×C₄₇	—	2	4	no	—
80	C₄×Q₈×C₄₇	D₄	1	2	yes	complemented
81	C₄×Q₈×C₄₇	D₄	1	2	yes	complemented
82	C₄×D₄×C₄₇	—	2	4	no	—
83	C₄×D₄×C₄₇	—	2	2	no	—
84	C₄×D₄×C₄₇	—	2	2	no	—
85	C₄×D₄×C₄₇	—	2	2	no	—
86	C₄×D₄×C₄₇	—	2	2	no	—
87	C₄×D₄×C₄₇	—	2	2	no	—
88	C₄×D₄×C₄₇	—	2	2	no	—
89	C₄×D₄×C₄₇	D₄	1	2	yes	complemented
90	C₄×D₄×C₄₇	D₄	1	2	yes	complemented
91	#117×C₄₇	—	2	2	no	—
92	#117×C₄₇	—	2	2	no	—
93	#117×C₄₇	C₂³	1	2	yes	—
94	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
95	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
96	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
97	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
98	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
99	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
100	C₂×C₄²×C₄₇	—	2	2	no	—
101	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
102	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
103	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
104	#107×C₄₇	—	2	2	no	—
105	#106×C₄₇	—	2	2	no	—
106	#104×C₄₇	—	2	4	no	—
107	#104×C₄₇	—	2	4	no	—
108	#103×C₄₇	—	2	2	no	—
109	#102×C₄₇	—	2	2	no	—
110	#102×C₄₇	—	2	2	no	—
111	#102×C₄₇	—	2	2	no	—
112	#100×C₄₇	—	2	4	no	—
113	#97×C₄₇	—	2	2	no	—
114	C₄×C₈×C₄₇	—	2	2	no	—
115	#95×C₄₇	—	2	1	no	—
116	#95×C₄₇	—	2	1	no	—
117	#95×C₄₇	—	2	2	no	—
118	C₂⁴×C₄₇	—	2	1	no	—
119	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
120	#41×C₄₇	—	2	2	no	—
121	#41×C₄₇	—	2	2	no	—
122	#41×C₄₇	—	2	2	no	—
123	#41×C₄₇	—	2	2	no	—
124	#41×C₄₇	—	8	4	no	—
125	C₂×Q₈×C₄₇	—	2	2	no	—
126	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
127	C₂×D₄×C₄₇	—	2	2	no	—
128	C₂×D₄×C₄₇	—	2	4	no	—
129	C₂×D₄×C₄₇	—	2	4	no	—
130	C₂×D₄×C₄₇	—	2	2	no	—
131	C₂×D₄×C₄₇	—	2	8	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	1	no	—
137	C₂×D₄×C₄₇	—	2	1	no	—
138	C₂×D₄×C₄₇	—	2	2	no	—
139	C₂×D₄×C₄₇	—	8	2	no	—
140	C₂×D₄×C₄₇	—	8	2	no	—
141	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
142	C₂×D₄×C₄₇	#41	1	2	yes	complemented
143	C₂²×C₄×C₄₇	—	2	1	no	—
144	C₂²×C₄×C₄₇	—	2	2	no	—
145	C₂²×C₄×C₄₇	—	2	2	no	—
146	C₂²×C₄×C₄₇	—	2	2	no	—
147	C₂²×C₄×C₄₇	—	2	2	no	—
148	C₂²×C₄×C₄₇	—	2	2	no	—
149	C₂²×C₄×C₄₇	—	2	1	no	—
150	C₂²×C₄×C₄₇	—	2	1	no	—
151	C₂²×C₄×C₄₇	—	4	2	no	—
152	C₂²×C₄×C₄₇	—	8	2	no	—
153	C₂²×C₄×C₄₇	—	8	2	no	—
154	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
155	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
158	SD₁₆×C₄₇	—	2	8	no	—
159	D₈×C₄₇	—	2	8	no	—
160	M₁₆×C₄₇	—	2	2	no	—
161	M₁₆×C₄₇	—	2	2	no	—
162	M₁₆×C₄₇	—	2	2	no	—
163	M₁₆×C₄₇	#41	1	4	yes	complemented
164	C₂×C₈×C₄₇	—	2	2	no	—
165	C₂×C₈×C₄₇	—	2	2	no	—
166	C₄⋊C₄×C₄₇	—	2	2	no	—
167	C₄⋊C₄×C₄₇	—	2	2	no	—
168	C₄⋊C₄×C₄₇	—	2	4	no	—
169	C₄⋊C₄×C₄₇	—	2	2	no	—
170	C₄⋊C₄×C₄₇	—	2	2	no	—
171	C₄⋊C₄×C₄₇	—	2	2	no	—
172	C₄⋊C₄×C₄₇	—	2	2	no	—
173	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
174	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
175	C₂²⋊C₄×C₄₇	—	2	4	no	—
176	C₂²⋊C₄×C₄₇	—	2	4	no	—
177	C₂²⋊C₄×C₄₇	—	2	4	no	—
178	C₂²⋊C₄×C₄₇	—	2	2	no	—
179	C₂²⋊C₄×C₄₇	—	2	4	no	—
180	C₂²⋊C₄×C₄₇	—	2	2	no	—
181	C₂²⋊C₄×C₄₇	—	2	2	no	—
182	C₂²⋊C₄×C₄₇	—	4	1	no	—
183	C₂²⋊C₄×C₄₇	—	4	1	no	—
184	C₂²⋊C₄×C₄₇	—	8	2	no	—
185	C₂²⋊C₄×C₄₇	—	8	2	no	—
186	C₄²×C₄₇	—	2	2	no	—
187	C₄²×C₄₇	—	2	2	no	—
188	C₄²×C₄₇	—	2	2	no	—
189	C₄²×C₄₇	—	2	1	no	—
190	C₄²×C₄₇	—	2	2	no	—
191	C₄²×C₄₇	C₂×D₄	1	2	yes	—
192	C₄²×C₄₇	C₂×D₄	1	2	yes	—
193	C₄²×C₄₇	#41	1	2	yes	complemented
194	C₂³×C₄₇	—	2	2	no	—
195	C₂³×C₄₇	—	2	2	no	—
196	C₂³×C₄₇	—	2	2	no	—
197	C₂³×C₄₇	—	2	2	no	—
198	C₂³×C₄₇	—	2	2	no	—
199	C₂³×C₄₇	—	4	2	no	—
200	C₂³×C₄₇	—	4	2	no	—
201	C₂³×C₄₇	—	4	2	no	—
202	C₂³×C₄₇	—	4	2	no	—
203	C₂³×C₄₇	—	4	1	no	—
204	C₂³×C₄₇	—	4	1	no	—
205	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
206	Q₈×C₄₇	—	2	2	no	—
207	Q₈×C₄₇	—	2	2	no	—
208	Q₈×C₄₇	—	8	2	no	—
209	D₄×C₄₇	—	2	2	no	—
210	D₄×C₄₇	—	2	4	no	—
211	D₄×C₄₇	—	2	2	no	—
212	D₄×C₄₇	—	4	2	no	—
213	D₄×C₄₇	—	4	2	no	—
214	D₄×C₄₇	—	4	2	no	—
215	D₄×C₄₇	—	4	2	no	—
216	D₄×C₄₇	—	4	2	no	—
217	D₄×C₄₇	—	8	4	no	—
218	D₄×C₄₇	—	8	8	no	—
219	D₄×C₄₇	—	8	2	no	—
220	D₄×C₄₇	—	8	4	no	—
221	C₂×C₄×C₄₇	—	2	2	no	—
222	C₂×C₄×C₄₇	—	2	2	no	—
223	C₂×C₄×C₄₇	—	2	2	no	—
224	C₂×C₄×C₄₇	—	2	2	no	—
225	C₂×C₄×C₄₇	—	2	2	no	—
226	C₂×C₄×C₄₇	—	4	1	no	—
227	C₂×C₄×C₄₇	—	4	1	no	—
228	C₂×C₄×C₄₇	—	4	4	no	—
229	C₂×C₄×C₄₇	—	4	4	no	—
230	C₂×C₄×C₄₇	—	4	1	no	—
231	C₂×C₄×C₄₇	—	4	1	no	—
232	C₂×C₄×C₄₇	—	4	2	no	—
233	C₂×C₄×C₄₇	—	4	2	no	—
234	C₂×C₄×C₄₇	—	4	2	no	—
235	C₂×C₄×C₄₇	—	4	1	no	—
236	C₂×C₄×C₄₇	—	4	1	no	—
237	C₂×C₄×C₄₇	—	4	2	no	—
238	C₂×C₄×C₄₇	—	4	1	no	—
239	C₂×C₄×C₄₇	—	4	1	no	—
240	C₂×C₄×C₄₇	—	8	2	no	—
241	C₂×C₄×C₄₇	—	8	2	no	—
242	C₂×C₄×C₄₇	—	8	4	no	—
243	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
244	C₂×C₄×C₄₇	#120	1	2	yes	—
245	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
246	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
247	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
248	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
249	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
250	C₈×C₄₇	—	2	4	no	—
251	C₈×C₄₇	—	4	2	no	—
252	#23591	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
253	C₂²×C₄₇	—	2	1	no	—
254	C₂²×C₄₇	—	2	1	no	—
255	C₂²×C₄₇	—	4	4	no	—
256	C₂²×C₄₇	—	4	4	no	—
257	C₂²×C₄₇	—	4	2	no	—
258	C₂²×C₄₇	—	4	2	no	—
259	C₂²×C₄₇	—	4	2	no	—
260	C₂²×C₄₇	—	4	2	no	—
261	C₂²×C₄₇	—	4	2	no	—
262	C₂²×C₄₇	—	4	2	no	—
263	C₂²×C₄₇	—	4	2	no	—
264	C₂²×C₄₇	—	8	2	no	—
265	C₂²×C₄₇	—	8	2	no	—
266	C₂²×C₄₇	—	8	1	no	—
267	C₂²×C₄₇	—	8	1	no	—
268	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
269	C₂²×C₄₇	#525	1	1	yes	characteristic
270	C₂²×C₄₇	#532	1	1	yes	characteristic
271	C₄×C₄₇	—	2	1	no	—
272	C₄×C₄₇	—	2	1	no	—
273	C₄×C₄₇	—	2	2	no	—
274	C₄×C₄₇	—	4	2	no	—
275	C₄×C₄₇	—	4	2	no	—
276	C₄×C₄₇	—	4	2	no	—
277	C₄×C₄₇	—	4	2	no	—
278	C₄×C₄₇	—	4	2	no	—
279	C₄×C₄₇	—	8	1	no	—
280	C₄×C₄₇	—	8	1	no	—
281	C₄×C₄₇	#525	1	2	yes	—
282	C₄×C₄₇	#532	1	2	yes	—
283	#3460	C₂×C₄₇	1	1	yes	characteristic, complemented
284	C₄×AGL(1,ℤ/8)	C₂×C₄₇	1	2	yes	complemented
285	#2328	C₂×C₄₇	1	1	yes	characteristic, complemented
286	#2061	C₂×C₄₇	1	1	yes	characteristic, complemented
287	#2040	C₂×C₄₇	1	1	yes	characteristic, complemented
288	#2037	C₂×C₄₇	1	2	yes	complemented
289	#2027	C₂×C₄₇	1	1	yes	characteristic, complemented
290	#2006	C₂×C₄₇	1	1	yes	characteristic, complemented
291	#2002	C₂×C₄₇	1	2	yes	complemented
292	#1759	C₂×C₄₇	1	2	yes	complemented
293	C₄×#100	C₂×C₄₇	1	1	yes	characteristic, complemented
294	C₂×C₄₇	—	2	1	no	—
295	C₂×C₄₇	—	2	1	no	—
296	C₂×C₄₇	—	8	2	no	—
297	C₂×C₄₇	—	8	2	no	—
298	C₂×C₄₇	—	8	2	no	—
299	C₂×C₄₇	#2388	1	1	yes	characteristic
300	C₂×C₄₇	#3019	1	1	yes	characteristic
301	C₂×C₄₇	#3021	1	1	yes	characteristic
302	C₂×AGL(1,ℤ/8)	C₂²×C₄₇	1	2	yes	—
303	#544	C₂²×C₄₇	1	1	yes	characteristic
304	#542	—	2	2	no	—
305	#540	—	2	2	no	—
306	#538	—	2	2	no	—
307	#537	C₂²×C₄₇	1	1	yes	characteristic
308	#535	C₂²×C₄₇	1	2	yes	—
309	#532	—	2	2	no	—
310	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
311	#529	—	2	2	no	—
312	#525	—	2	2	no	—
313	C₄×#41	C₂²×C₄₇	1	2	yes	—
314	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
315	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
316	#442	—	2	2	no	—
317	#440	—	2	2	no	—
318	C₄×SD₁₆	—	2	2	no	—
319	C₄×D₈	—	2	2	no	—
320	#428	C₂²×C₄₇	1	2	yes	—
321	C₂×#104	C₂²×C₄₇	1	2	yes	—
322	C₂×#104	C₂²×C₄₇	1	2	yes	—
323	#418	C₂²×C₄₇	1	2	yes	—
324	#417	C₂²×C₄₇	1	2	yes	—
325	C₂×#100	C₂²×C₄₇	1	2	yes	—
326	C₄×M₁₆	C₂²×C₄₇	1	2	yes	—
327	#390	C₂²×C₄₇	1	1	yes	characteristic
328	#390	C₂²×C₄₇	1	1	yes	characteristic
329	#386	—	2	2	no	—
330	#386	—	2	2	no	—
331	#382	C₂²×C₄₇	1	1	yes	characteristic
332	#376	C₂²×C₄₇	1	1	yes	characteristic
333	#343	C₂²×C₄₇	1	1	yes	characteristic
334	#343	C₂²×C₄₇	1	1	yes	characteristic
335	#339	C₂²×C₄₇	1	2	yes	—
336	#339	C₂²×C₄₇	1	2	yes	—
337	C₄₇	#23591	1	1	yes	characteristic, direct product factor, Sylow
338	C₂×#41	—	2	2	no	—
339	C₂×#41	C₂³×C₄₇	1	2	yes	—
340	C₂²×D₄	—	2	2	no	—
341	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
342	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
343	C₂³×C₄	—	2	1	no	—
344	C₂³×C₄	D₄×C₄₇	1	2	yes	—
345	AGL(1,ℤ/8)	—	2	4	no	—
346	AGL(1,ℤ/8)	—	2	4	no	—
347	C₂×SD₁₆	—	2	2	no	—
348	C₂×D₈	—	2	2	no	—
349	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
350	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
351	C₄⋊Q₈	—	2	2	no	—
352	#127	—	2	2	no	—
353	#127	—	2	2	no	—
354	#127	—	2	2	no	—
355	#126	—	2	4	no	—
356	#125	—	2	2	no	—
357	#124	—	2	4	no	—
358	#124	—	2	2	no	—
359	#123	—	2	4	no	—
360	#123	—	2	4	no	—
361	C₂²⋊Q₈	—	2	2	no	—
362	C₂²⋊Q₈	—	2	2	no	—
363	C₂²⋊Q₈	—	2	2	no	—
364	#121	—	2	2	no	—
365	#121	—	2	4	no	—
366	#121	—	2	2	no	—
367	#121	—	2	2	no	—
368	#121	—	2	2	no	—
369	#121	—	2	2	no	—
370	#120	—	2	4	no	—
371	C₄×Q₈	D₄×C₄₇	1	2	yes	complemented
372	C₄×Q₈	D₄×C₄₇	1	2	yes	complemented
373	C₄×D₄	—	2	4	no	—
374	C₄×D₄	—	2	2	no	—
375	C₄×D₄	—	2	2	no	—
376	C₄×D₄	—	2	2	no	—
377	C₄×D₄	—	2	2	no	—
378	C₄×D₄	—	2	2	no	—
379	C₄×D₄	—	2	2	no	—
380	C₄×D₄	D₄×C₄₇	1	2	yes	complemented
381	C₄×D₄	D₄×C₄₇	1	2	yes	complemented
382	#117	—	2	2	no	—
383	#117	—	2	2	no	—
384	#117	C₂³×C₄₇	1	2	yes	—
385	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
386	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
387	C₂×C₂²⋊C₄	—	2	1	no	—
388	C₂×C₂²⋊C₄	—	2	2	no	—
389	C₂×C₂²⋊C₄	—	2	2	no	—
390	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
391	C₂×C₄²	—	2	2	no	—
392	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
393	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
394	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
395	#107	—	2	2	no	—
396	#106	—	2	2	no	—
397	#104	—	2	4	no	—
398	#104	—	2	4	no	—
399	#103	—	2	2	no	—
400	#102	—	2	2	no	—
401	#102	—	2	2	no	—
402	#102	—	2	2	no	—
403	#100	—	2	4	no	—
404	#97	—	2	2	no	—
405	C₄×C₈	—	2	2	no	—
406	#95	—	2	1	no	—
407	#95	—	2	1	no	—
408	#95	—	2	2	no	—
409	C₂⁴	—	2	1	no	—
410	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
411	#41	—	2	2	no	—
412	#41	—	2	2	no	—
413	#41	—	2	2	no	—
414	#41	—	2	2	no	—
415	#41	—	8	4	no	—
416	C₂×Q₈	—	2	2	no	—
417	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
418	C₂×D₄	—	2	2	no	—
419	C₂×D₄	—	2	4	no	—
420	C₂×D₄	—	2	4	no	—
421	C₂×D₄	—	2	2	no	—
422	C₂×D₄	—	2	8	no	—
423	C₂×D₄	—	2	2	no	—
424	C₂×D₄	—	2	2	no	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	2	1	no	—
428	C₂×D₄	—	2	1	no	—
429	C₂×D₄	—	2	1	no	—
430	C₂×D₄	—	8	2	no	—
431	C₂×D₄	—	8	2	no	—
432	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
433	C₂×D₄	#41×C₄₇	1	2	yes	complemented
434	C₂²×C₄	—	2	1	no	—
435	C₂²×C₄	—	2	2	no	—
436	C₂²×C₄	—	2	2	no	—
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	2	no	—
440	C₂²×C₄	—	2	1	no	—
441	C₂²×C₄	—	2	1	no	—
442	C₂²×C₄	—	4	2	no	—
443	C₂²×C₄	—	8	2	no	—
444	C₂²×C₄	—	8	2	no	—
445	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
446	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
447	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
448	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
449	SD₁₆	—	2	8	no	—
450	D₈	—	2	8	no	—
451	M₁₆	—	2	2	no	—
452	M₁₆	—	2	2	no	—
453	M₁₆	—	2	2	no	—
454	M₁₆	#41×C₄₇	1	4	yes	complemented
455	C₂×C₈	—	2	2	no	—
456	C₂×C₈	—	2	2	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	2	no	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	2	2	no	—
461	C₄⋊C₄	—	2	2	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
465	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	—	2	4	no	—
468	C₂²⋊C₄	—	2	4	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	—	2	4	no	—
471	C₂²⋊C₄	—	2	2	no	—
472	C₂²⋊C₄	—	2	2	no	—
473	C₂²⋊C₄	—	4	1	no	—
474	C₂²⋊C₄	—	4	1	no	—
475	C₂²⋊C₄	—	8	2	no	—
476	C₂²⋊C₄	—	8	2	no	—
477	C₄²	—	2	2	no	—
478	C₄²	—	2	2	no	—
479	C₄²	—	2	2	no	—
480	C₄²	—	2	1	no	—
481	C₄²	—	2	2	no	—
482	C₄²	C₂×D₄×C₄₇	1	2	yes	—
483	C₄²	C₂×D₄×C₄₇	1	2	yes	—
484	C₄²	#41×C₄₇	1	2	yes	complemented
485	C₂³	—	2	2	no	—
486	C₂³	—	2	2	no	—
487	C₂³	—	2	2	no	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	2	no	—
490	C₂³	—	4	2	no	—
491	C₂³	—	4	2	no	—
492	C₂³	—	4	2	no	—
493	C₂³	—	4	2	no	—
494	C₂³	—	4	1	no	—
495	C₂³	—	4	1	no	—
496	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
497	Q₈	—	2	2	no	—
498	Q₈	—	2	2	no	—
499	Q₈	—	8	2	no	—
500	D₄	—	2	2	no	—
501	D₄	—	2	4	no	—
502	D₄	—	2	2	no	—
503	D₄	—	4	2	no	—
504	D₄	—	4	2	no	—
505	D₄	—	4	2	no	—
506	D₄	—	4	2	no	—
507	D₄	—	4	2	no	—
508	D₄	—	8	4	no	—
509	D₄	—	8	8	no	—
510	D₄	—	8	2	no	—
511	D₄	—	8	4	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	4	1	no	—
518	C₂×C₄	—	4	1	no	—
519	C₂×C₄	—	4	4	no	—
520	C₂×C₄	—	4	4	no	—
521	C₂×C₄	—	4	1	no	—
522	C₂×C₄	—	4	1	no	—
523	C₂×C₄	—	4	2	no	—
524	C₂×C₄	—	4	2	no	—
525	C₂×C₄	—	4	2	no	—
526	C₂×C₄	—	4	1	no	—
527	C₂×C₄	—	4	1	no	—
528	C₂×C₄	—	4	2	no	—
529	C₂×C₄	—	4	1	no	—
530	C₂×C₄	—	4	1	no	—
531	C₂×C₄	—	8	2	no	—
532	C₂×C₄	—	8	2	no	—
533	C₂×C₄	—	8	4	no	—
534	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
535	C₂×C₄	#120×C₄₇	1	2	yes	—
536	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
537	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
538	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
539	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
540	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
541	C₈	—	2	4	no	—
542	C₈	—	4	2	no	—
543	C₂²	—	2	1	no	—
544	C₂²	—	2	1	no	—
545	C₂²	—	4	4	no	—
546	C₂²	—	4	4	no	—
547	C₂²	—	4	2	no	—
548	C₂²	—	4	2	no	—
549	C₂²	—	4	2	no	—
550	C₂²	—	4	2	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	8	2	no	—
555	C₂²	—	8	2	no	—
556	C₂²	—	8	1	no	—
557	C₂²	—	8	1	no	—
558	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
559	C₂²	C₄₇×#525	1	1	yes	characteristic
560	C₂²	C₄₇×#532	1	1	yes	characteristic
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	2	2	no	—
564	C₄	—	4	2	no	—
565	C₄	—	4	2	no	—
566	C₄	—	4	2	no	—
567	C₄	—	4	2	no	—
568	C₄	—	4	2	no	—
569	C₄	—	8	1	no	—
570	C₄	—	8	1	no	—
571	C₄	C₄₇×#525	1	2	yes	—
572	C₄	C₄₇×#532	1	2	yes	—
573	C₂	—	2	1	no	—
574	C₂	—	2	1	no	—
575	C₂	—	8	2	no	—
576	C₂	—	8	2	no	—
577	C₂	—	8	2	no	—
578	C₂	C₄₇×#2388	1	1	yes	characteristic
579	C₂	C₄₇×#3019	1	1	yes	characteristic
580	C₂	C₄₇×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
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. C₄₇×#3460	C₂	semidirect
2. C₄×AGL(1,ℤ/8)×C₄₇	C₂	semidirect
3. C₄₇×#2328	C₂	semidirect
4. C₄₇×#2061	C₂	semidirect
5. C₄₇×#2040	C₂	semidirect
6. C₄₇×#2037	C₂	semidirect
7. C₄₇×#2027	C₂	semidirect
8. C₄₇×#2006	C₂	semidirect
9. C₄₇×#2002	C₂	semidirect
10. C₄₇×#1759	C₂	semidirect
11. C₄×#100×C₄₇	C₂	semidirect
80. C₄×Q₈×C₄₇	D₄	semidirect
81. C₄×Q₈×C₄₇	D₄	semidirect
89. C₄×D₄×C₄₇	D₄	semidirect
90. C₄×D₄×C₄₇	D₄	semidirect
142. C₂×D₄×C₄₇	#41	semidirect
163. M₁₆×C₄₇	#41	semidirect
193. C₄²×C₄₇	#41	semidirect
252. #23591	C₄₇	direct (N × H)
283. #3460	C₂×C₄₇	semidirect
284. C₄×AGL(1,ℤ/8)	C₂×C₄₇	semidirect
285. #2328	C₂×C₄₇	semidirect
286. #2061	C₂×C₄₇	semidirect
287. #2040	C₂×C₄₇	semidirect
288. #2037	C₂×C₄₇	semidirect
289. #2027	C₂×C₄₇	semidirect
290. #2006	C₂×C₄₇	semidirect
291. #2002	C₂×C₄₇	semidirect
292. #1759	C₂×C₄₇	semidirect
293. C₄×#100	C₂×C₄₇	semidirect
337. C₄₇	#23591	direct (N × H)
371. C₄×Q₈	D₄×C₄₇	semidirect
372. C₄×Q₈	D₄×C₄₇	semidirect
380. C₄×D₄	D₄×C₄₇	semidirect
381. C₄×D₄	D₄×C₄₇	semidirect
433. C₂×D₄	#41×C₄₇	semidirect
454. M₁₆	#41×C₄₇	semidirect
484. C₄²	#41×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#3460	2
C₄×AGL(1,ℤ/8)×C₄₇	2
C₄₇×#2328	2
C₄₇×#2061	2
C₄₇×#2040	2
C₄₇×#2037	2
C₄₇×#2027	2
C₄₇×#2006	2
C₄₇×#2002	2
C₄₇×#1759	2
C₄×#100×C₄₇	2
#23591	47

Subgroups — C47×#23591 #26063289

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#23591 #26063289