Subgroups — C₄₇×#18537 #26058235

Order 12032.

1038 conjugacy classes of subgroups.

The subgroup lattice has 688 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3482	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#3138	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3038	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#3038	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1628	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1627	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1626	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1625	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1561	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1489	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1489	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×AGL(1,ℤ/8)×C₄₇	—	2	1	no	—
13	C₂×AGL(1,ℤ/8)×C₄₇	—	2	1	no	—
14	C₄₇×#557	C₂²	1	1	yes	characteristic, complemented
15	C₄₇×#556	—	2	1	no	—
16	C₄₇×#556	C₂²	1	1	yes	characteristic, complemented
17	C₄₇×#552	—	2	2	no	—
18	C₄₇×#552	—	2	1	no	—
19	D₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic, complemented
20	C₄₇×#548	—	2	1	no	—
21	C₄₇×#547	—	2	1	no	—
22	C₄₇×#547	C₂²	1	1	yes	characteristic, complemented
23	C₄₇×#533	—	2	1	no	—
24	C₄₇×#533	C₂²	1	1	yes	characteristic
25	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
26	C₄₇×#529	—	2	1	no	—
27	C₄₇×#529	—	2	2	no	—
28	C₄×#41×C₄₇	—	2	1	no	—
29	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
30	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
32	C₄₇×#490	—	2	2	no	—
33	C₄₇×#486	C₂²	1	2	yes	—
34	C₄₇×#486	C₂²	1	2	yes	—
35	C₄₇×#460	—	2	1	no	—
36	C₄₇×#460	—	2	1	no	—
37	C₄₇×#460	C₂²	1	2	yes	—
38	C₄₇×#460	C₂²	1	2	yes	—
39	C₄₇×#459	—	2	1	no	—
40	C₄₇×#459	—	2	1	no	—
41	C₄₇×#459	C₂²	1	2	yes	—
42	C₄₇×#459	C₂²	1	2	yes	—
43	C₄₇×#423	C₂²	1	1	yes	characteristic
44	C₄₇×#423	C₂²	1	1	yes	characteristic
45	C₄₇×#418	—	2	1	no	—
46	C₄₇×#418	—	2	1	no	—
47	C₄₇×#418	—	2	2	no	—
48	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
49	C₄₇×#332	C₂²	1	2	yes	complemented
50	C₄₇×#332	C₂²	1	2	yes	complemented
51	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
52	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
53	C₄₇×D₄⋊C₈	C₂²	1	2	yes	complemented
54	C₄₇×D₄⋊C₈	C₂²	1	2	yes	complemented
55	C₂×#41×C₄₇	—	2	1	no	—
56	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
57	C₂×#41×C₄₇	D₄	1	1	yes	characteristic
58	C₂²×Q₈×C₄₇	—	2	1	no	—
59	C₂²×D₄×C₄₇	—	2	1	no	—
60	C₂²×D₄×C₄₇	—	2	1	no	—
61	C₂²×D₄×C₄₇	—	2	1	no	—
62	AGL(1,ℤ/8)×C₄₇	—	4	4	no	—
63	AGL(1,ℤ/8)×C₄₇	—	4	4	no	—
64	C₂×SD₁₆×C₄₇	—	2	2	no	—
65	C₂×SD₁₆×C₄₇	—	2	2	no	—
66	C₂×D₈×C₄₇	—	2	2	no	—
67	C₂×D₈×C₄₇	—	2	2	no	—
68	C₂×M₁₆×C₄₇	—	2	1	no	—
69	C₂×M₁₆×C₄₇	—	2	1	no	—
70	C₂×M₁₆×C₄₇	—	2	1	no	—
71	C₄⋊Q₈×C₄₇	—	2	1	no	—
72	C₄⋊Q₈×C₄₇	—	2	1	no	—
73	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
74	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
75	#127×C₄₇	—	2	1	no	—
76	#127×C₄₇	—	2	1	no	—
77	#127×C₄₇	—	2	1	no	—
78	#127×C₄₇	C₂³	1	2	yes	—
79	#126×C₄₇	—	2	2	no	—
80	#126×C₄₇	—	2	2	no	—
81	#126×C₄₇	—	2	2	no	—
82	#125×C₄₇	—	2	2	no	—
83	#125×C₄₇	—	2	2	no	—
84	#125×C₄₇	—	2	1	no	—
85	#125×C₄₇	D₄	1	2	yes	—
86	#124×C₄₇	—	2	2	no	—
87	#124×C₄₇	—	2	1	no	—
88	#123×C₄₇	—	2	2	no	—
89	#123×C₄₇	—	2	2	no	—
90	#123×C₄₇	—	2	2	no	—
91	C₂²⋊Q₈×C₄₇	—	2	2	no	—
92	C₂²⋊Q₈×C₄₇	—	2	1	no	—
93	C₂²⋊Q₈×C₄₇	—	2	1	no	—
94	C₂²⋊Q₈×C₄₇	—	2	1	no	—
95	C₂²⋊Q₈×C₄₇	—	2	1	no	—
96	C₂²⋊Q₈×C₄₇	—	2	2	no	—
97	C₂²⋊Q₈×C₄₇	—	2	1	no	—
98	#121×C₄₇	—	2	2	no	—
99	#121×C₄₇	—	2	1	no	—
100	C₄×Q₈×C₄₇	—	2	2	no	—
101	C₄×Q₈×C₄₇	—	2	2	no	—
102	C₄×Q₈×C₄₇	—	2	1	no	—
103	C₄×Q₈×C₄₇	—	2	1	no	—
104	C₄×Q₈×C₄₇	—	2	1	no	—
105	C₄×Q₈×C₄₇	—	2	1	no	—
106	C₄×Q₈×C₄₇	—	2	1	no	—
107	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
108	C₄×Q₈×C₄₇	D₄	1	1	yes	characteristic
109	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
110	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
111	C₄×D₄×C₄₇	—	2	2	no	—
112	C₄×D₄×C₄₇	—	2	2	no	—
113	C₄×D₄×C₄₇	—	2	1	no	—
114	C₄×D₄×C₄₇	—	2	1	no	—
115	C₄×D₄×C₄₇	—	2	1	no	—
116	C₄×D₄×C₄₇	—	2	1	no	—
117	C₄×D₄×C₄₇	—	2	1	no	—
118	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
119	C₄×D₄×C₄₇	D₄	1	1	yes	characteristic
120	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
121	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
122	#117×C₄₇	—	2	2	no	—
123	#117×C₄₇	—	2	2	no	—
124	#117×C₄₇	—	2	1	no	—
125	#117×C₄₇	—	2	1	no	—
126	#117×C₄₇	—	2	1	no	—
127	#117×C₄₇	D₄	1	1	yes	characteristic
128	#117×C₄₇	D₄	1	1	yes	characteristic
129	#117×C₄₇	D₄	1	2	yes	—
130	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
131	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
132	C₂×C₄²×C₄₇	—	2	2	no	—
133	C₂×C₄²×C₄₇	—	2	1	no	—
134	C₂×C₄²×C₄₇	—	2	1	no	—
135	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
136	C₄⋊C₈×C₄₇	—	2	1	no	—
137	C₄⋊C₈×C₄₇	—	2	1	no	—
138	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
139	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
140	#102×C₄₇	—	2	2	no	—
141	#102×C₄₇	—	2	2	no	—
142	#102×C₄₇	—	2	2	no	—
143	#102×C₄₇	—	2	2	no	—
144	#102×C₄₇	—	2	4	no	—
145	#102×C₄₇	—	2	4	no	—
146	#97×C₄₇	—	2	1	no	—
147	C₄×C₈×C₄₇	C₂³	1	2	yes	—
148	C₂⁴×C₄₇	—	4	1	no	—
149	#41×C₄₇	—	2	2	no	—
150	#41×C₄₇	—	2	2	no	—
151	#41×C₄₇	—	4	1	no	—
152	#41×C₄₇	—	4	1	no	—
153	#41×C₄₇	—	4	2	no	—
154	#41×C₄₇	—	4	2	no	—
155	C₂×Q₈×C₄₇	—	2	2	no	—
156	C₂×Q₈×C₄₇	—	2	1	no	—
157	C₂×Q₈×C₄₇	—	2	1	no	—
158	C₂×Q₈×C₄₇	—	4	2	no	—
159	C₂×Q₈×C₄₇	—	4	2	no	—
160	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
161	C₂×Q₈×C₄₇	C₂×D₄	1	1	yes	characteristic
162	C₂×D₄×C₄₇	—	2	2	no	—
163	C₂×D₄×C₄₇	—	2	1	no	—
164	C₂×D₄×C₄₇	—	2	1	no	—
165	C₂×D₄×C₄₇	—	2	2	no	—
166	C₂×D₄×C₄₇	—	2	2	no	—
167	C₂×D₄×C₄₇	—	2	2	no	—
168	C₂×D₄×C₄₇	—	4	2	no	—
169	C₂×D₄×C₄₇	—	4	2	no	—
170	C₂×D₄×C₄₇	—	4	2	no	—
171	C₂×D₄×C₄₇	—	4	2	no	—
172	C₂×D₄×C₄₇	—	4	4	no	—
173	C₂×D₄×C₄₇	—	4	1	no	—
174	C₂×D₄×C₄₇	—	4	1	no	—
175	C₂×D₄×C₄₇	—	4	1	no	—
176	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
177	C₂×D₄×C₄₇	C₂×D₄	1	1	yes	characteristic
178	C₂²×C₄×C₄₇	—	2	2	no	—
179	C₂²×C₄×C₄₇	—	2	2	no	—
180	C₂²×C₄×C₄₇	—	2	1	no	—
181	C₂²×C₄×C₄₇	—	2	1	no	—
182	C₂²×C₄×C₄₇	—	2	1	no	—
183	C₂²×C₄×C₄₇	—	2	1	no	—
184	C₂²×C₄×C₄₇	—	2	1	no	—
185	C₂²×C₄×C₄₇	—	2	1	no	—
186	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
187	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
188	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
189	SD₁₆×C₄₇	—	4	4	no	—
190	SD₁₆×C₄₇	—	4	4	no	—
191	D₈×C₄₇	—	4	4	no	—
192	D₈×C₄₇	—	4	4	no	—
193	M₁₆×C₄₇	—	4	2	no	—
194	M₁₆×C₄₇	—	4	2	no	—
195	M₁₆×C₄₇	—	4	2	no	—
196	C₂×C₈×C₄₇	—	2	2	no	—
197	C₂×C₈×C₄₇	—	2	2	no	—
198	C₂×C₈×C₄₇	—	2	2	no	—
199	C₄⋊C₄×C₄₇	—	2	2	no	—
200	C₄⋊C₄×C₄₇	—	2	2	no	—
201	C₄⋊C₄×C₄₇	—	2	2	no	—
202	C₄⋊C₄×C₄₇	—	2	2	no	—
203	C₄⋊C₄×C₄₇	—	2	2	no	—
204	C₄⋊C₄×C₄₇	—	2	2	no	—
205	C₄⋊C₄×C₄₇	—	2	1	no	—
206	C₄⋊C₄×C₄₇	—	2	2	no	—
207	C₄⋊C₄×C₄₇	—	2	2	no	—
208	C₄⋊C₄×C₄₇	—	2	1	no	—
209	C₄⋊C₄×C₄₇	—	2	1	no	—
210	C₄⋊C₄×C₄₇	—	2	1	no	—
211	C₄⋊C₄×C₄₇	—	2	1	no	—
212	C₄⋊C₄×C₄₇	—	2	1	no	—
213	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
214	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
215	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
216	C₄⋊C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
217	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
218	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
219	C₂²⋊C₄×C₄₇	—	2	2	no	—
220	C₂²⋊C₄×C₄₇	—	2	2	no	—
221	C₂²⋊C₄×C₄₇	—	2	2	no	—
222	C₂²⋊C₄×C₄₇	—	2	2	no	—
223	C₂²⋊C₄×C₄₇	—	2	1	no	—
224	C₂²⋊C₄×C₄₇	—	2	1	no	—
225	C₂²⋊C₄×C₄₇	—	2	2	no	—
226	C₂²⋊C₄×C₄₇	—	2	1	no	—
227	C₂²⋊C₄×C₄₇	—	2	1	no	—
228	C₂²⋊C₄×C₄₇	—	2	1	no	—
229	C₂²⋊C₄×C₄₇	—	2	1	no	—
230	C₄²×C₄₇	—	2	2	no	—
231	C₄²×C₄₇	—	2	2	no	—
232	C₄²×C₄₇	—	2	1	no	—
233	C₄²×C₄₇	—	2	1	no	—
234	C₄²×C₄₇	—	2	1	no	—
235	C₄²×C₄₇	—	2	2	no	—
236	C₄²×C₄₇	—	2	1	no	—
237	C₄²×C₄₇	—	2	1	no	—
238	C₄²×C₄₇	—	2	1	no	—
239	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
240	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
241	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
242	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
243	C₂³×C₄₇	—	2	1	no	—
244	C₂³×C₄₇	—	2	1	no	—
245	C₂³×C₄₇	—	4	2	no	—
246	C₂³×C₄₇	—	8	2	no	—
247	C₂³×C₄₇	—	8	2	no	—
248	C₂³×C₄₇	—	8	2	no	—
249	C₂³×C₄₇	#120	1	1	yes	characteristic
250	Q₈×C₄₇	—	2	1	no	—
251	Q₈×C₄₇	—	2	1	no	—
252	Q₈×C₄₇	—	2	1	no	—
253	Q₈×C₄₇	—	4	4	no	—
254	Q₈×C₄₇	—	4	1	no	—
255	Q₈×C₄₇	—	4	1	no	—
256	Q₈×C₄₇	—	4	1	no	—
257	Q₈×C₄₇	—	4	1	no	—
258	Q₈×C₄₇	AGL(1,ℤ/8)	1	2	yes	complemented
259	D₄×C₄₇	—	2	1	no	—
260	D₄×C₄₇	—	2	1	no	—
261	D₄×C₄₇	—	2	1	no	—
262	D₄×C₄₇	—	4	2	no	—
263	D₄×C₄₇	—	4	4	no	—
264	D₄×C₄₇	—	4	2	no	—
265	D₄×C₄₇	—	4	4	no	—
266	D₄×C₄₇	—	4	2	no	—
267	D₄×C₄₇	—	4	2	no	—
268	D₄×C₄₇	—	4	2	no	—
269	D₄×C₄₇	—	4	2	no	—
270	D₄×C₄₇	—	8	2	no	—
271	D₄×C₄₇	—	8	2	no	—
272	D₄×C₄₇	—	8	2	no	—
273	D₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	complemented
274	C₂×C₄×C₄₇	—	2	1	no	—
275	C₂×C₄×C₄₇	—	2	1	no	—
276	C₂×C₄×C₄₇	—	2	1	no	—
277	C₂×C₄×C₄₇	—	2	1	no	—
278	C₂×C₄×C₄₇	—	2	1	no	—
279	C₂×C₄×C₄₇	—	2	2	no	—
280	C₂×C₄×C₄₇	—	2	1	no	—
281	C₂×C₄×C₄₇	—	2	1	no	—
282	C₂×C₄×C₄₇	—	2	1	no	—
283	C₂×C₄×C₄₇	—	2	2	no	—
284	C₂×C₄×C₄₇	—	2	1	no	—
285	C₂×C₄×C₄₇	—	2	1	no	—
286	C₂×C₄×C₄₇	—	2	2	no	—
287	C₂×C₄×C₄₇	—	4	2	no	—
288	C₂×C₄×C₄₇	—	4	2	no	—
289	C₂×C₄×C₄₇	—	4	4	no	—
290	C₂×C₄×C₄₇	—	4	4	no	—
291	C₂×C₄×C₄₇	—	4	1	no	—
292	C₂×C₄×C₄₇	—	4	1	no	—
293	C₂×C₄×C₄₇	—	4	1	no	—
294	C₂×C₄×C₄₇	—	4	1	no	—
295	C₂×C₄×C₄₇	—	4	2	no	—
296	C₂×C₄×C₄₇	—	4	2	no	—
297	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
298	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
299	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
300	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
301	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
302	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
303	C₈×C₄₇	—	4	2	no	—
304	C₈×C₄₇	—	4	2	no	—
305	C₈×C₄₇	—	4	2	no	—
306	#18537	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
307	C₂²×C₄₇	—	2	1	no	—
308	C₂²×C₄₇	—	2	1	no	—
309	C₂²×C₄₇	—	2	2	no	—
310	C₂²×C₄₇	—	2	1	no	—
311	C₂²×C₄₇	—	4	1	no	—
312	C₂²×C₄₇	—	4	1	no	—
313	C₂²×C₄₇	—	4	1	no	—
314	C₂²×C₄₇	—	4	1	no	—
315	C₂²×C₄₇	—	4	1	no	—
316	C₂²×C₄₇	—	8	2	no	—
317	C₂²×C₄₇	—	8	2	no	—
318	C₂²×C₄₇	—	8	2	no	—
319	C₂²×C₄₇	—	16	4	no	—
320	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
321	C₄×C₄₇	—	2	1	no	—
322	C₄×C₄₇	—	2	1	no	—
323	C₄×C₄₇	—	2	2	no	—
324	C₄×C₄₇	—	2	1	no	—
325	C₄×C₄₇	—	4	1	no	—
326	C₄×C₄₇	—	4	1	no	—
327	C₄×C₄₇	—	4	2	no	—
328	C₄×C₄₇	—	4	2	no	—
329	C₄×C₄₇	—	4	1	no	—
330	C₄×C₄₇	—	4	1	no	—
331	C₄×C₄₇	—	4	1	no	—
332	C₄×C₄₇	#454	1	2	yes	—
333	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
334	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
335	C₄×C₄₇	#575	1	1	yes	characteristic
336	C₄×C₄₇	#575	1	1	yes	characteristic
337	#3482	C₂×C₄₇	1	1	yes	characteristic, complemented
338	#3138	C₂×C₄₇	1	1	yes	characteristic, complemented
339	#3038	C₂×C₄₇	1	1	yes	characteristic, complemented
340	#3038	C₂×C₄₇	1	1	yes	characteristic, complemented
341	#1628	C₂×C₄₇	1	2	yes	complemented
342	#1627	C₂×C₄₇	1	2	yes	complemented
343	#1626	C₂×C₄₇	1	2	yes	complemented
344	#1625	C₂×C₄₇	1	2	yes	complemented
345	#1561	C₂×C₄₇	1	1	yes	characteristic, complemented
346	#1489	C₂×C₄₇	1	1	yes	characteristic, complemented
347	#1489	C₂×C₄₇	1	1	yes	characteristic, complemented
348	C₂×C₄₇	—	4	1	no	—
349	C₂×C₄₇	—	4	2	no	—
350	C₂×C₄₇	—	8	1	no	—
351	C₂×C₄₇	—	16	2	no	—
352	C₂×C₄₇	#3006	1	1	yes	characteristic
353	C₂×C₄₇	#3006	1	1	yes	characteristic
354	C₂×C₄₇	C₂×#454	1	1	yes	characteristic
355	C₂×AGL(1,ℤ/8)	—	2	1	no	—
356	C₂×AGL(1,ℤ/8)	—	2	1	no	—
357	#557	C₂²×C₄₇	1	1	yes	characteristic, complemented
358	#556	—	2	1	no	—
359	#556	C₂²×C₄₇	1	1	yes	characteristic, complemented
360	#552	—	2	2	no	—
361	#552	—	2	1	no	—
362	D₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic, complemented
363	#548	—	2	1	no	—
364	#547	—	2	1	no	—
365	#547	C₂²×C₄₇	1	1	yes	characteristic, complemented
366	#533	—	2	1	no	—
367	#533	C₂²×C₄₇	1	1	yes	characteristic
368	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
369	#529	—	2	1	no	—
370	#529	—	2	2	no	—
371	C₄×#41	—	2	1	no	—
372	C₄×#41	C₂²×C₄₇	1	1	yes	characteristic
373	C₄×#41	C₂²×C₄₇	1	1	yes	characteristic
374	C₂×C₄×Q₈	—	2	1	no	—
375	#490	—	2	2	no	—
376	#486	C₂²×C₄₇	1	2	yes	—
377	#486	C₂²×C₄₇	1	2	yes	—
378	#460	—	2	1	no	—
379	#460	—	2	1	no	—
380	#460	C₂²×C₄₇	1	2	yes	—
381	#460	C₂²×C₄₇	1	2	yes	—
382	#459	—	2	1	no	—
383	#459	—	2	1	no	—
384	#459	C₂²×C₄₇	1	2	yes	—
385	#459	C₂²×C₄₇	1	2	yes	—
386	#423	C₂²×C₄₇	1	1	yes	characteristic
387	#423	C₂²×C₄₇	1	1	yes	characteristic
388	#418	—	2	2	no	—
389	#418	—	2	1	no	—
390	#418	—	2	1	no	—
391	C₄×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
392	#332	C₂²×C₄₇	1	2	yes	complemented
393	#332	C₂²×C₄₇	1	2	yes	complemented
394	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	complemented
395	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	complemented
396	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
397	D₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
398	C₄₇	#18537	1	1	yes	characteristic, direct product factor, Sylow
399	C₂×#41	—	2	1	no	—
400	C₂×#41	D₄×C₄₇	1	1	yes	characteristic
401	C₂×#41	D₄×C₄₇	1	1	yes	characteristic
402	C₂²×Q₈	—	2	1	no	—
403	C₂²×D₄	—	2	1	no	—
404	C₂²×D₄	—	2	1	no	—
405	C₂²×D₄	—	2	1	no	—
406	AGL(1,ℤ/8)	—	4	4	no	—
407	AGL(1,ℤ/8)	—	4	4	no	—
408	C₂×SD₁₆	—	2	2	no	—
409	C₂×SD₁₆	—	2	2	no	—
410	C₂×D₈	—	2	2	no	—
411	C₂×D₈	—	2	2	no	—
412	C₂×M₁₆	—	2	1	no	—
413	C₂×M₁₆	—	2	1	no	—
414	C₂×M₁₆	—	2	1	no	—
415	C₄⋊Q₈	—	2	1	no	—
416	C₄⋊Q₈	—	2	1	no	—
417	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
418	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
419	#127	—	2	1	no	—
420	#127	—	2	1	no	—
421	#127	—	2	1	no	—
422	#127	C₂³×C₄₇	1	2	yes	—
423	#126	—	2	2	no	—
424	#126	—	2	2	no	—
425	#126	—	2	2	no	—
426	#125	—	2	2	no	—
427	#125	—	2	2	no	—
428	#125	—	2	1	no	—
429	#125	D₄×C₄₇	1	2	yes	—
430	#124	—	2	2	no	—
431	#124	—	2	1	no	—
432	#123	—	2	2	no	—
433	#123	—	2	2	no	—
434	#123	—	2	2	no	—
435	C₂²⋊Q₈	—	2	2	no	—
436	C₂²⋊Q₈	—	2	1	no	—
437	C₂²⋊Q₈	—	2	1	no	—
438	C₂²⋊Q₈	—	2	1	no	—
439	C₂²⋊Q₈	—	2	1	no	—
440	C₂²⋊Q₈	—	2	2	no	—
441	C₂²⋊Q₈	—	2	1	no	—
442	#121	—	2	2	no	—
443	#121	—	2	1	no	—
444	C₄×Q₈	—	2	2	no	—
445	C₄×Q₈	—	2	2	no	—
446	C₄×Q₈	—	2	1	no	—
447	C₄×Q₈	—	2	1	no	—
448	C₄×Q₈	—	2	1	no	—
449	C₄×Q₈	—	2	1	no	—
450	C₄×Q₈	—	2	1	no	—
451	C₄×Q₈	D₄×C₄₇	1	1	yes	characteristic
452	C₄×Q₈	D₄×C₄₇	1	1	yes	characteristic
453	C₄×Q₈	C₂³×C₄₇	1	1	yes	characteristic
454	C₄×Q₈	C₂³×C₄₇	1	1	yes	characteristic
455	C₄×D₄	—	2	2	no	—
456	C₄×D₄	—	2	2	no	—
457	C₄×D₄	—	2	1	no	—
458	C₄×D₄	—	2	1	no	—
459	C₄×D₄	—	2	1	no	—
460	C₄×D₄	—	2	1	no	—
461	C₄×D₄	—	2	1	no	—
462	C₄×D₄	D₄×C₄₇	1	1	yes	characteristic
463	C₄×D₄	D₄×C₄₇	1	1	yes	characteristic
464	C₄×D₄	C₂³×C₄₇	1	1	yes	characteristic
465	C₄×D₄	C₂³×C₄₇	1	1	yes	characteristic
466	#117	—	2	2	no	—
467	#117	—	2	2	no	—
468	#117	—	2	1	no	—
469	#117	—	2	1	no	—
470	#117	—	2	1	no	—
471	#117	D₄×C₄₇	1	1	yes	characteristic
472	#117	D₄×C₄₇	1	1	yes	characteristic
473	#117	D₄×C₄₇	1	2	yes	—
474	C₂×C₄⋊C₄	—	2	2	no	—
475	C₂×C₄⋊C₄	—	2	1	no	—
476	C₂×C₄²	—	2	2	no	—
477	C₂×C₄²	—	2	1	no	—
478	C₂×C₄²	—	2	1	no	—
479	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
480	C₄⋊C₈	—	2	1	no	—
481	C₄⋊C₈	—	2	1	no	—
482	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
483	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
484	#102	—	2	2	no	—
485	#102	—	2	2	no	—
486	#102	—	2	2	no	—
487	#102	—	2	2	no	—
488	#102	—	2	4	no	—
489	#102	—	2	4	no	—
490	#97	—	2	1	no	—
491	C₄×C₈	C₂³×C₄₇	1	2	yes	—
492	C₂⁴	—	4	1	no	—
493	#41	—	2	2	no	—
494	#41	—	2	2	no	—
495	#41	—	4	1	no	—
496	#41	—	4	1	no	—
497	#41	—	4	2	no	—
498	#41	—	4	2	no	—
499	C₂×Q₈	—	2	2	no	—
500	C₂×Q₈	—	2	1	no	—
501	C₂×Q₈	—	2	1	no	—
502	C₂×Q₈	—	4	2	no	—
503	C₂×Q₈	—	4	2	no	—
504	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
505	C₂×Q₈	C₂×D₄×C₄₇	1	1	yes	characteristic
506	C₂×D₄	—	2	2	no	—
507	C₂×D₄	—	2	1	no	—
508	C₂×D₄	—	2	1	no	—
509	C₂×D₄	—	2	2	no	—
510	C₂×D₄	—	2	2	no	—
511	C₂×D₄	—	2	2	no	—
512	C₂×D₄	—	4	2	no	—
513	C₂×D₄	—	4	2	no	—
514	C₂×D₄	—	4	4	no	—
515	C₂×D₄	—	4	2	no	—
516	C₂×D₄	—	4	2	no	—
517	C₂×D₄	—	4	1	no	—
518	C₂×D₄	—	4	1	no	—
519	C₂×D₄	—	4	1	no	—
520	C₂×D₄	C₂×D₄×C₄₇	1	1	yes	characteristic
521	C₂×D₄	C₂×D₄×C₄₇	1	1	yes	characteristic
522	C₂²×C₄	—	2	2	no	—
523	C₂²×C₄	—	2	2	no	—
524	C₂²×C₄	—	2	1	no	—
525	C₂²×C₄	—	2	1	no	—
526	C₂²×C₄	—	2	1	no	—
527	C₂²×C₄	—	2	1	no	—
528	C₂²×C₄	—	2	1	no	—
529	C₂²×C₄	—	2	1	no	—
530	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
531	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
532	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
533	SD₁₆	—	4	4	no	—
534	SD₁₆	—	4	4	no	—
535	D₈	—	4	4	no	—
536	D₈	—	4	4	no	—
537	M₁₆	—	4	2	no	—
538	M₁₆	—	4	2	no	—
539	M₁₆	—	4	2	no	—
540	C₂×C₈	—	2	2	no	—
541	C₂×C₈	—	2	2	no	—
542	C₂×C₈	—	2	2	no	—
543	C₄⋊C₄	—	2	2	no	—
544	C₄⋊C₄	—	2	2	no	—
545	C₄⋊C₄	—	2	2	no	—
546	C₄⋊C₄	—	2	2	no	—
547	C₄⋊C₄	—	2	2	no	—
548	C₄⋊C₄	—	2	2	no	—
549	C₄⋊C₄	—	2	1	no	—
550	C₄⋊C₄	—	2	2	no	—
551	C₄⋊C₄	—	2	2	no	—
552	C₄⋊C₄	—	2	1	no	—
553	C₄⋊C₄	—	2	1	no	—
554	C₄⋊C₄	—	2	1	no	—
555	C₄⋊C₄	—	2	1	no	—
556	C₄⋊C₄	—	2	1	no	—
557	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
558	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
559	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
560	C₄⋊C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
561	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
562	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
563	C₂²⋊C₄	—	2	2	no	—
564	C₂²⋊C₄	—	2	2	no	—
565	C₂²⋊C₄	—	2	2	no	—
566	C₂²⋊C₄	—	2	2	no	—
567	C₂²⋊C₄	—	2	1	no	—
568	C₂²⋊C₄	—	2	1	no	—
569	C₂²⋊C₄	—	2	2	no	—
570	C₂²⋊C₄	—	2	1	no	—
571	C₂²⋊C₄	—	2	1	no	—
572	C₂²⋊C₄	—	2	1	no	—
573	C₂²⋊C₄	—	2	1	no	—
574	C₄²	—	2	2	no	—
575	C₄²	—	2	2	no	—
576	C₄²	—	2	1	no	—
577	C₄²	—	2	1	no	—
578	C₄²	—	2	1	no	—
579	C₄²	—	2	2	no	—
580	C₄²	—	2	1	no	—
581	C₄²	—	2	1	no	—
582	C₄²	—	2	1	no	—
583	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
584	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
585	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
586	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
587	C₂³	—	2	1	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	4	2	no	—
590	C₂³	—	8	2	no	—
591	C₂³	—	8	2	no	—
592	C₂³	—	8	2	no	—
593	C₂³	#120×C₄₇	1	1	yes	characteristic
594	Q₈	—	2	1	no	—
595	Q₈	—	2	1	no	—
596	Q₈	—	2	1	no	—
597	Q₈	—	4	4	no	—
598	Q₈	—	4	1	no	—
599	Q₈	—	4	1	no	—
600	Q₈	—	4	1	no	—
601	Q₈	—	4	1	no	—
602	Q₈	AGL(1,ℤ/8)×C₄₇	1	2	yes	complemented
603	D₄	—	2	1	no	—
604	D₄	—	2	1	no	—
605	D₄	—	2	1	no	—
606	D₄	—	4	2	no	—
607	D₄	—	4	4	no	—
608	D₄	—	4	2	no	—
609	D₄	—	4	4	no	—
610	D₄	—	4	2	no	—
611	D₄	—	4	2	no	—
612	D₄	—	4	2	no	—
613	D₄	—	4	2	no	—
614	D₄	—	8	2	no	—
615	D₄	—	8	2	no	—
616	D₄	—	8	2	no	—
617	D₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	complemented
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	2	no	—
620	C₂×C₄	—	2	1	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	4	2	no	—
632	C₂×C₄	—	4	2	no	—
633	C₂×C₄	—	4	4	no	—
634	C₂×C₄	—	4	4	no	—
635	C₂×C₄	—	4	2	no	—
636	C₂×C₄	—	4	2	no	—
637	C₂×C₄	—	4	1	no	—
638	C₂×C₄	—	4	1	no	—
639	C₂×C₄	—	4	1	no	—
640	C₂×C₄	—	4	1	no	—
641	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
642	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
643	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
644	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
645	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
646	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
647	C₈	—	4	2	no	—
648	C₈	—	4	2	no	—
649	C₈	—	4	2	no	—
650	C₂²	—	2	1	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	1	no	—
654	C₂²	—	4	1	no	—
655	C₂²	—	4	1	no	—
656	C₂²	—	4	1	no	—
657	C₂²	—	4	1	no	—
658	C₂²	—	4	1	no	—
659	C₂²	—	8	2	no	—
660	C₂²	—	8	2	no	—
661	C₂²	—	8	2	no	—
662	C₂²	—	16	4	no	—
663	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
664	C₄	—	2	1	no	—
665	C₄	—	2	1	no	—
666	C₄	—	2	2	no	—
667	C₄	—	2	1	no	—
668	C₄	—	4	1	no	—
669	C₄	—	4	1	no	—
670	C₄	—	4	2	no	—
671	C₄	—	4	2	no	—
672	C₄	—	4	1	no	—
673	C₄	—	4	1	no	—
674	C₄	—	4	1	no	—
675	C₄	C₄₇×#454	1	2	yes	—
676	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
677	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
678	C₄	C₄₇×#575	1	1	yes	characteristic
679	C₄	C₄₇×#575	1	1	yes	characteristic
680	C₂	—	4	1	no	—
681	C₂	—	4	2	no	—
682	C₂	—	8	1	no	—
683	C₂	—	16	2	no	—
684	C₂	C₄₇×#3006	1	1	yes	characteristic
685	C₂	C₄₇×#3006	1	1	yes	characteristic
686	C₂	C₂×C₄₇×#454	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₇
LCS	G ▷ C₄² ▷ C₂² ▷ 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×#3482	C₂	semidirect
2. C₄₇×#3138	C₂	semidirect
3. C₄₇×#3038	C₂	semidirect
4. C₄₇×#3038	C₂	semidirect
5. C₄₇×#1628	C₂	semidirect
6. C₄₇×#1627	C₂	semidirect
7. C₄₇×#1626	C₂	semidirect
8. C₄₇×#1625	C₂	semidirect
9. C₄₇×#1561	C₂	semidirect
10. C₄₇×#1489	C₂	semidirect
11. C₄₇×#1489	C₂	semidirect
14. C₄₇×#557	C₂²	semidirect
16. C₄₇×#556	C₂²	semidirect
19. D₄×Q₈×C₄₇	C₂²	semidirect
22. C₄₇×#547	C₂²	semidirect
49. C₄₇×#332	C₂²	semidirect
50. C₄₇×#332	C₂²	semidirect
51. C₄₇×Q₈⋊C₈	C₂²	semidirect
52. C₄₇×Q₈⋊C₈	C₂²	semidirect
53. C₄₇×D₄⋊C₈	C₂²	semidirect
54. C₄₇×D₄⋊C₈	C₂²	semidirect
258. Q₈×C₄₇	AGL(1,ℤ/8)	semidirect
273. D₄×C₄₇	AGL(1,ℤ/8)	semidirect
306. #18537	C₄₇	direct (N × H)
337. #3482	C₂×C₄₇	semidirect
338. #3138	C₂×C₄₇	semidirect
339. #3038	C₂×C₄₇	semidirect
340. #3038	C₂×C₄₇	semidirect
341. #1628	C₂×C₄₇	semidirect
342. #1627	C₂×C₄₇	semidirect
343. #1626	C₂×C₄₇	semidirect
344. #1625	C₂×C₄₇	semidirect
345. #1561	C₂×C₄₇	semidirect
346. #1489	C₂×C₄₇	semidirect
347. #1489	C₂×C₄₇	semidirect
357. #557	C₂²×C₄₇	semidirect
359. #556	C₂²×C₄₇	semidirect
362. D₄×Q₈	C₂²×C₄₇	semidirect
365. #547	C₂²×C₄₇	semidirect
392. #332	C₂²×C₄₇	semidirect
393. #332	C₂²×C₄₇	semidirect
394. Q₈⋊C₈	C₂²×C₄₇	semidirect
395. Q₈⋊C₈	C₂²×C₄₇	semidirect
396. D₄⋊C₈	C₂²×C₄₇	semidirect
397. D₄⋊C₈	C₂²×C₄₇	semidirect
398. C₄₇	#18537	direct (N × H)
602. Q₈	AGL(1,ℤ/8)×C₄₇	semidirect
617. D₄	AGL(1,ℤ/8)×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#3482	2
C₄₇×#3138	2
C₄₇×#3038	2
C₄₇×#1628	2
C₄₇×#1627	2
C₄₇×#1626	2
C₄₇×#1625	2
C₄₇×#1561	2
C₄₇×#1489	2
#18537	47

Subgroups — C47×#18537 #26058235

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18537 #26058235