Subgroups — C₄₇×#18674 #26058372

Order 12032.

1176 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3497	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#3245	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3169	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#3037	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1649	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1641	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1627	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1621	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1492	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×2₋¹⁺⁴×C₄₇	—	2	1	no	—
13	C₂×#137×C₄₇	—	2	1	no	—
14	C₄₇×#550	—	2	1	no	—
15	C₄₇×#550	C₂²	1	2	yes	—
16	D₄×Q₈×C₄₇	—	2	1	no	—
17	D₄×Q₈×C₄₇	C₂²	1	2	yes	—
18	C₄₇×#548	—	2	2	no	—
19	C₄₇×#548	—	2	2	no	—
20	C₄₇×#537	—	2	2	no	—
21	C₄₇×#537	—	2	1	no	—
22	C₄₇×#532	—	2	2	no	—
23	C₄₇×#532	C₂²	1	1	yes	characteristic
24	C₄₇×#532	C₂²	1	1	yes	characteristic
25	C₄₇×#532	C₂²	1	1	yes	characteristic
26	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₄₇×#500	C₂²	1	1	yes	characteristic
28	C₄₇×#493	C₂²	1	1	yes	characteristic
29	C₄₇×#486	C₂²	1	1	yes	characteristic
30	C₄₇×#486	C₂²	1	1	yes	characteristic
31	C₄₇×#474	—	2	1	no	—
32	C₄₇×#474	C₂²	1	2	yes	—
33	C₄₇×#466	—	2	2	no	—
34	C₄₇×#466	—	2	2	no	—
35	C₄₇×#464	—	2	2	no	—
36	C₄₇×#462	C₂²	1	2	yes	—
37	C₄₇×#460	C₂²	1	2	yes	—
38	C₄₇×#459	—	2	1	no	—
39	C₄₇×#459	C₂²	1	2	yes	—
40	C₄×D₈×C₄₇	—	2	2	no	—
41	C₄₇×#423	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#417	—	2	1	no	—
44	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
45	C₄₇×#332	C₂²	1	2	yes	—
46	C₄₇×#331	C₂²	1	2	yes	—
47	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
48	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
49	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
50	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
51	2₋¹⁺⁴×C₄₇	—	4	4	no	—
52	2₋¹⁺⁴×C₄₇	—	4	4	no	—
53	C₂×#41×C₄₇	—	2	4	no	—
54	C₂×#41×C₄₇	—	2	2	no	—
55	C₂×#41×C₄₇	—	2	2	no	—
56	C₂×#41×C₄₇	—	2	1	no	—
57	C₂×#41×C₄₇	—	2	1	no	—
58	C₂×#41×C₄₇	—	2	1	no	—
59	C₂²×Q₈×C₄₇	—	2	2	no	—
60	C₂²×Q₈×C₄₇	—	2	2	no	—
61	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
62	#137×C₄₇	—	4	4	no	—
63	C₂×Q₁₆×C₄₇	—	2	2	no	—
64	C₂×SD₁₆×C₄₇	—	2	2	no	—
65	C₂×D₈×C₄₇	—	2	2	no	—
66	C₂×D₈×C₄₇	—	2	2	no	—
67	C₂×M₁₆×C₄₇	—	2	1	no	—
68	C₂²×C₈×C₄₇	—	2	1	no	—
69	C₂²×C₈×C₄₇	—	2	1	no	—
70	C₄⋊Q₈×C₄₇	—	2	2	no	—
71	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
72	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
73	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
74	#127×C₄₇	—	2	2	no	—
75	#127×C₄₇	D₄	1	1	yes	characteristic
76	#127×C₄₇	C₂³	1	1	yes	characteristic
77	#127×C₄₇	C₂³	1	1	yes	characteristic
78	#124×C₄₇	—	2	4	no	—
79	#124×C₄₇	—	2	1	no	—
80	#124×C₄₇	—	2	1	no	—
81	#124×C₄₇	—	2	1	no	—
82	C₂²⋊Q₈×C₄₇	—	2	2	no	—
83	C₂²⋊Q₈×C₄₇	—	2	4	no	—
84	C₂²⋊Q₈×C₄₇	—	2	2	no	—
85	C₂²⋊Q₈×C₄₇	—	2	4	no	—
86	#121×C₄₇	—	2	4	no	—
87	#121×C₄₇	—	2	2	no	—
88	#121×C₄₇	—	2	4	no	—
89	#121×C₄₇	—	2	4	no	—
90	#121×C₄₇	—	2	1	no	—
91	#121×C₄₇	—	2	1	no	—
92	#121×C₄₇	—	2	2	no	—
93	#121×C₄₇	—	2	1	no	—
94	#121×C₄₇	—	2	1	no	—
95	#121×C₄₇	D₄	1	2	yes	—
96	#121×C₄₇	D₄	1	2	yes	—
97	C₄×Q₈×C₄₇	—	2	1	no	—
98	C₄×Q₈×C₄₇	—	2	1	no	—
99	C₄×Q₈×C₄₇	D₄	1	2	yes	—
100	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
101	C₄×D₄×C₄₇	—	2	4	no	—
102	C₄×D₄×C₄₇	—	2	2	no	—
103	C₄×D₄×C₄₇	—	2	2	no	—
104	C₄×D₄×C₄₇	—	2	1	no	—
105	C₄×D₄×C₄₇	—	2	1	no	—
106	C₄×D₄×C₄₇	—	2	1	no	—
107	C₄×D₄×C₄₇	—	2	1	no	—
108	C₄×D₄×C₄₇	D₄	1	2	yes	—
109	C₄×D₄×C₄₇	C₂³	1	2	yes	—
110	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
111	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
112	C₂×C₄²×C₄₇	—	2	1	no	—
113	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
114	#107×C₄₇	—	2	2	no	—
115	#107×C₄₇	—	2	2	no	—
116	C₄⋊C₈×C₄₇	—	2	1	no	—
117	C₄⋊C₈×C₄₇	—	2	1	no	—
118	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
119	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
120	#103×C₄₇	—	2	2	no	—
121	#102×C₄₇	—	2	2	no	—
122	#102×C₄₇	—	2	2	no	—
123	#102×C₄₇	—	2	2	no	—
124	#102×C₄₇	—	2	2	no	—
125	#102×C₄₇	—	2	2	no	—
126	C₄×C₈×C₄₇	—	2	1	no	—
127	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
128	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
129	#41×C₄₇	—	4	16	no	—
130	#41×C₄₇	—	4	4	no	—
131	#41×C₄₇	—	4	8	no	—
132	#41×C₄₇	—	4	4	no	—
133	#41×C₄₇	—	4	2	no	—
134	#41×C₄₇	—	4	2	no	—
135	#41×C₄₇	—	4	2	no	—
136	#41×C₄₇	—	4	2	no	—
137	#41×C₄₇	—	4	2	no	—
138	#41×C₄₇	—	4	2	no	—
139	C₂×Q₈×C₄₇	—	2	4	no	—
140	C₂×Q₈×C₄₇	—	2	1	no	—
141	C₂×Q₈×C₄₇	—	2	1	no	—
142	C₂×Q₈×C₄₇	—	2	2	no	—
143	C₂×Q₈×C₄₇	—	2	1	no	—
144	C₂×Q₈×C₄₇	—	2	1	no	—
145	C₂×Q₈×C₄₇	—	4	4	no	—
146	C₂×Q₈×C₄₇	—	4	8	no	—
147	C₂×Q₈×C₄₇	—	4	4	no	—
148	C₂×Q₈×C₄₇	D₈	1	4	yes	complemented
149	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
150	C₂×D₄×C₄₇	—	2	4	no	—
151	C₂×D₄×C₄₇	—	2	2	no	—
152	C₂×D₄×C₄₇	—	2	2	no	—
153	C₂×D₄×C₄₇	—	2	4	no	—
154	C₂×D₄×C₄₇	—	2	1	no	—
155	C₂×D₄×C₄₇	—	2	1	no	—
156	C₂×D₄×C₄₇	—	2	1	no	—
157	C₂×D₄×C₄₇	—	2	1	no	—
158	C₂×D₄×C₄₇	—	2	1	no	—
159	C₂×D₄×C₄₇	—	2	1	no	—
160	C₂×D₄×C₄₇	—	2	1	no	—
161	C₂×D₄×C₄₇	—	4	1	no	—
162	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
163	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
164	C₂²×C₄×C₄₇	—	2	1	no	—
165	C₂²×C₄×C₄₇	—	2	4	no	—
166	C₂²×C₄×C₄₇	—	2	4	no	—
167	C₂²×C₄×C₄₇	—	2	1	no	—
168	C₂²×C₄×C₄₇	—	2	2	no	—
169	C₂²×C₄×C₄₇	—	2	2	no	—
170	C₂²×C₄×C₄₇	—	4	1	no	—
171	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
172	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
173	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
174	Q₁₆×C₄₇	—	4	4	no	—
175	SD₁₆×C₄₇	—	4	4	no	—
176	D₈×C₄₇	—	4	4	no	—
177	D₈×C₄₇	—	8	2	no	—
178	M₁₆×C₄₇	—	4	2	no	—
179	C₂×C₈×C₄₇	—	2	1	no	—
180	C₂×C₈×C₄₇	—	2	2	no	—
181	C₂×C₈×C₄₇	—	2	2	no	—
182	C₂×C₈×C₄₇	—	2	1	no	—
183	C₂×C₈×C₄₇	—	4	2	no	—
184	C₂×C₈×C₄₇	—	8	1	no	—
185	C₄⋊C₄×C₄₇	—	2	4	no	—
186	C₄⋊C₄×C₄₇	—	2	2	no	—
187	C₄⋊C₄×C₄₇	—	2	1	no	—
188	C₄⋊C₄×C₄₇	—	2	1	no	—
189	C₄⋊C₄×C₄₇	—	2	2	no	—
190	C₄⋊C₄×C₄₇	—	2	1	no	—
191	C₄⋊C₄×C₄₇	—	2	1	no	—
192	C₄⋊C₄×C₄₇	—	2	1	no	—
193	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
194	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
195	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
196	C₂²⋊C₄×C₄₇	—	2	4	no	—
197	C₂²⋊C₄×C₄₇	—	2	4	no	—
198	C₂²⋊C₄×C₄₇	—	2	2	no	—
199	C₂²⋊C₄×C₄₇	—	2	2	no	—
200	C₂²⋊C₄×C₄₇	—	2	2	no	—
201	C₂²⋊C₄×C₄₇	—	2	2	no	—
202	C₂²⋊C₄×C₄₇	—	4	1	no	—
203	C₂²⋊C₄×C₄₇	—	4	1	no	—
204	C₄²×C₄₇	—	2	2	no	—
205	C₄²×C₄₇	—	2	2	no	—
206	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
207	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
208	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
209	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
210	C₂³×C₄₇	—	2	2	no	—
211	C₂³×C₄₇	—	2	2	no	—
212	C₂³×C₄₇	—	4	1	no	—
213	C₂³×C₄₇	#120	1	1	yes	characteristic
214	Q₈×C₄₇	—	2	2	no	—
215	Q₈×C₄₇	—	2	4	no	—
216	Q₈×C₄₇	—	4	8	no	—
217	Q₈×C₄₇	—	4	1	no	—
218	Q₈×C₄₇	—	4	1	no	—
219	Q₈×C₄₇	—	4	2	no	—
220	Q₈×C₄₇	—	4	1	no	—
221	Q₈×C₄₇	—	4	1	no	—
222	Q₈×C₄₇	C₂×D₈	1	4	yes	—
223	D₄×C₄₇	—	2	2	no	—
224	D₄×C₄₇	—	2	2	no	—
225	D₄×C₄₇	—	4	2	no	—
226	D₄×C₄₇	—	4	8	no	—
227	D₄×C₄₇	—	4	2	no	—
228	D₄×C₄₇	—	4	4	no	—
229	D₄×C₄₇	—	4	4	no	—
230	D₄×C₄₇	—	4	1	no	—
231	D₄×C₄₇	—	4	1	no	—
232	D₄×C₄₇	—	4	1	no	—
233	D₄×C₄₇	—	4	1	no	—
234	D₄×C₄₇	—	4	1	no	—
235	D₄×C₄₇	—	4	1	no	—
236	D₄×C₄₇	—	4	1	no	—
237	D₄×C₄₇	—	4	1	no	—
238	D₄×C₄₇	—	4	2	no	—
239	D₄×C₄₇	—	8	1	no	—
240	D₄×C₄₇	—	8	4	no	—
241	D₄×C₄₇	—	8	2	no	—
242	C₂×C₄×C₄₇	—	2	2	no	—
243	C₂×C₄×C₄₇	—	2	4	no	—
244	C₂×C₄×C₄₇	—	2	1	no	—
245	C₂×C₄×C₄₇	—	2	1	no	—
246	C₂×C₄×C₄₇	—	2	2	no	—
247	C₂×C₄×C₄₇	—	2	2	no	—
248	C₂×C₄×C₄₇	—	2	2	no	—
249	C₂×C₄×C₄₇	—	4	1	no	—
250	C₂×C₄×C₄₇	—	4	8	no	—
251	C₂×C₄×C₄₇	—	4	8	no	—
252	C₂×C₄×C₄₇	—	4	2	no	—
253	C₂×C₄×C₄₇	—	4	2	no	—
254	C₂×C₄×C₄₇	—	4	4	no	—
255	C₂×C₄×C₄₇	—	4	1	no	—
256	C₂×C₄×C₄₇	—	8	1	no	—
257	C₂×C₄×C₄₇	—	8	2	no	—
258	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
259	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
260	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
261	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
262	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
263	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
264	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
265	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
266	C₈×C₄₇	—	2	2	no	—
267	C₈×C₄₇	—	4	1	no	—
268	C₈×C₄₇	—	4	2	no	—
269	C₈×C₄₇	—	4	2	no	—
270	#18674	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
271	C₂²×C₄₇	—	2	1	no	—
272	C₂²×C₄₇	—	2	1	no	—
273	C₂²×C₄₇	—	4	2	no	—
274	C₂²×C₄₇	—	4	2	no	—
275	C₂²×C₄₇	—	4	2	no	—
276	C₂²×C₄₇	—	4	2	no	—
277	C₂²×C₄₇	—	4	2	no	—
278	C₂²×C₄₇	—	4	2	no	—
279	C₂²×C₄₇	—	8	1	no	—
280	C₂²×C₄₇	—	8	1	no	—
281	C₂²×C₄₇	—	8	1	no	—
282	C₂²×C₄₇	#447	1	2	yes	—
283	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
284	C₄×C₄₇	—	2	4	no	—
285	C₄×C₄₇	—	2	1	no	—
286	C₄×C₄₇	—	2	1	no	—
287	C₄×C₄₇	—	2	1	no	—
288	C₄×C₄₇	—	4	2	no	—
289	C₄×C₄₇	—	4	2	no	—
290	C₄×C₄₇	—	4	2	no	—
291	C₄×C₄₇	—	8	1	no	—
292	C₄×C₄₇	#447	1	2	yes	—
293	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
294	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
295	C₄×C₄₇	#577	1	1	yes	characteristic
296	C₄×C₄₇	#578	1	1	yes	characteristic
297	#3497	C₂×C₄₇	1	1	yes	characteristic, complemented
298	#3245	C₂×C₄₇	1	1	yes	characteristic, complemented
299	#3169	C₂×C₄₇	1	1	yes	characteristic, complemented
300	#3037	C₂×C₄₇	1	1	yes	characteristic, complemented
301	#1649	C₂×C₄₇	1	2	yes	complemented
302	#1641	C₂×C₄₇	1	2	yes	complemented
303	#1627	C₂×C₄₇	1	2	yes	complemented
304	#1621	C₂×C₄₇	1	2	yes	complemented
305	#1547	C₂×C₄₇	1	1	yes	characteristic, complemented
306	#1492	C₂×C₄₇	1	1	yes	characteristic, complemented
307	C₂×Q₈⋊C₈	C₂×C₄₇	1	1	yes	characteristic, complemented
308	C₂×C₄₇	—	2	2	no	—
309	C₂×C₄₇	—	8	2	no	—
310	C₂×C₄₇	—	8	2	no	—
311	C₂×C₄₇	—	16	1	no	—
312	C₂×C₄₇	C₂×#447	1	1	yes	characteristic
313	C₂×C₄₇	#3013	1	1	yes	characteristic
314	C₂×C₄₇	#3018	1	1	yes	characteristic
315	C₂×2₋¹⁺⁴	—	2	1	no	—
316	C₂×#137	—	2	1	no	—
317	#550	—	2	1	no	—
318	#550	C₂²×C₄₇	1	2	yes	—
319	D₄×Q₈	—	2	1	no	—
320	D₄×Q₈	C₂²×C₄₇	1	2	yes	—
321	#548	—	2	2	no	—
322	#548	—	2	2	no	—
323	#537	—	2	2	no	—
324	#537	—	2	1	no	—
325	#532	—	2	2	no	—
326	#532	C₂²×C₄₇	1	1	yes	characteristic
327	#532	C₂²×C₄₇	1	1	yes	characteristic
328	#532	C₂²×C₄₇	1	1	yes	characteristic
329	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
330	#500	C₂²×C₄₇	1	1	yes	characteristic
331	#493	C₂²×C₄₇	1	1	yes	characteristic
332	#486	C₂²×C₄₇	1	1	yes	characteristic
333	#486	C₂²×C₄₇	1	1	yes	characteristic
334	#474	—	2	1	no	—
335	#474	C₂²×C₄₇	1	2	yes	—
336	#466	—	2	2	no	—
337	#466	—	2	2	no	—
338	#464	—	2	2	no	—
339	#462	C₂²×C₄₇	1	2	yes	—
340	#460	C₂²×C₄₇	1	2	yes	—
341	#459	—	2	1	no	—
342	#459	C₂²×C₄₇	1	2	yes	—
343	C₄×D₈	—	2	2	no	—
344	#423	C₂²×C₄₇	1	1	yes	characteristic
345	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
346	#417	—	2	1	no	—
347	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
348	#332	C₂²×C₄₇	1	2	yes	—
349	#331	C₂²×C₄₇	1	2	yes	—
350	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	—
351	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	—
352	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
353	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
354	C₄₇	#18674	1	1	yes	characteristic, direct product factor, Sylow
355	2₋¹⁺⁴	—	4	4	no	—
356	2₋¹⁺⁴	—	4	4	no	—
357	C₂×#41	—	2	4	no	—
358	C₂×#41	—	2	2	no	—
359	C₂×#41	—	2	2	no	—
360	C₂×#41	—	2	1	no	—
361	C₂×#41	—	2	1	no	—
362	C₂×#41	—	2	1	no	—
363	C₂²×Q₈	—	2	2	no	—
364	C₂²×Q₈	—	2	2	no	—
365	C₂²×Q₈	D₄×C₄₇	1	1	yes	characteristic
366	#137	—	4	4	no	—
367	C₂×Q₁₆	—	2	2	no	—
368	C₂×SD₁₆	—	2	2	no	—
369	C₂×D₈	—	2	2	no	—
370	C₂×D₈	—	2	2	no	—
371	C₂×M₁₆	—	2	1	no	—
372	C₂²×C₈	—	2	1	no	—
373	C₂²×C₈	—	2	1	no	—
374	C₄⋊Q₈	—	2	2	no	—
375	C₄⋊Q₈	D₄×C₄₇	1	1	yes	characteristic
376	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
377	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
378	#127	—	2	2	no	—
379	#127	D₄×C₄₇	1	1	yes	characteristic
380	#127	C₂³×C₄₇	1	1	yes	characteristic
381	#127	C₂³×C₄₇	1	1	yes	characteristic
382	#124	—	2	4	no	—
383	#124	—	2	1	no	—
384	#124	—	2	1	no	—
385	#124	—	2	1	no	—
386	C₂²⋊Q₈	—	2	2	no	—
387	C₂²⋊Q₈	—	2	4	no	—
388	C₂²⋊Q₈	—	2	2	no	—
389	C₂²⋊Q₈	—	2	4	no	—
390	#121	—	2	4	no	—
391	#121	—	2	2	no	—
392	#121	—	2	4	no	—
393	#121	—	2	4	no	—
394	#121	—	2	1	no	—
395	#121	—	2	1	no	—
396	#121	—	2	2	no	—
397	#121	—	2	1	no	—
398	#121	—	2	1	no	—
399	#121	D₄×C₄₇	1	2	yes	—
400	#121	D₄×C₄₇	1	2	yes	—
401	C₄×Q₈	—	2	1	no	—
402	C₄×Q₈	—	2	1	no	—
403	C₄×Q₈	D₄×C₄₇	1	2	yes	—
404	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
405	C₄×D₄	—	2	4	no	—
406	C₄×D₄	—	2	2	no	—
407	C₄×D₄	—	2	2	no	—
408	C₄×D₄	—	2	1	no	—
409	C₄×D₄	—	2	1	no	—
410	C₄×D₄	—	2	1	no	—
411	C₄×D₄	—	2	1	no	—
412	C₄×D₄	D₄×C₄₇	1	2	yes	—
413	C₄×D₄	C₂³×C₄₇	1	2	yes	—
414	C₂×C₄⋊C₄	—	2	1	no	—
415	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
416	C₂×C₄²	—	2	1	no	—
417	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
418	#107	—	2	2	no	—
419	#107	—	2	2	no	—
420	C₄⋊C₈	—	2	1	no	—
421	C₄⋊C₈	—	2	1	no	—
422	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
423	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
424	#103	—	2	2	no	—
425	#102	—	2	2	no	—
426	#102	—	2	2	no	—
427	#102	—	2	2	no	—
428	#102	—	2	2	no	—
429	#102	—	2	2	no	—
430	C₄×C₈	—	2	1	no	—
431	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
432	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
433	#41	—	4	16	no	—
434	#41	—	4	4	no	—
435	#41	—	4	8	no	—
436	#41	—	4	4	no	—
437	#41	—	4	2	no	—
438	#41	—	4	2	no	—
439	#41	—	4	2	no	—
440	#41	—	4	2	no	—
441	#41	—	4	2	no	—
442	#41	—	4	2	no	—
443	C₂×Q₈	—	2	4	no	—
444	C₂×Q₈	—	2	1	no	—
445	C₂×Q₈	—	2	1	no	—
446	C₂×Q₈	—	2	2	no	—
447	C₂×Q₈	—	2	1	no	—
448	C₂×Q₈	—	2	1	no	—
449	C₂×Q₈	—	4	4	no	—
450	C₂×Q₈	—	4	8	no	—
451	C₂×Q₈	—	4	4	no	—
452	C₂×Q₈	D₈×C₄₇	1	4	yes	complemented
453	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
454	C₂×D₄	—	2	4	no	—
455	C₂×D₄	—	2	2	no	—
456	C₂×D₄	—	2	2	no	—
457	C₂×D₄	—	2	4	no	—
458	C₂×D₄	—	2	1	no	—
459	C₂×D₄	—	2	1	no	—
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	2	1	no	—
463	C₂×D₄	—	2	1	no	—
464	C₂×D₄	—	2	1	no	—
465	C₂×D₄	—	4	1	no	—
466	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
467	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
468	C₂²×C₄	—	2	1	no	—
469	C₂²×C₄	—	2	4	no	—
470	C₂²×C₄	—	2	4	no	—
471	C₂²×C₄	—	2	1	no	—
472	C₂²×C₄	—	2	2	no	—
473	C₂²×C₄	—	2	2	no	—
474	C₂²×C₄	—	4	1	no	—
475	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
476	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
477	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
478	Q₁₆	—	4	4	no	—
479	SD₁₆	—	4	4	no	—
480	D₈	—	4	4	no	—
481	D₈	—	8	2	no	—
482	M₁₆	—	4	2	no	—
483	C₂×C₈	—	2	1	no	—
484	C₂×C₈	—	2	1	no	—
485	C₂×C₈	—	2	2	no	—
486	C₂×C₈	—	2	2	no	—
487	C₂×C₈	—	4	2	no	—
488	C₂×C₈	—	8	1	no	—
489	C₄⋊C₄	—	2	4	no	—
490	C₄⋊C₄	—	2	2	no	—
491	C₄⋊C₄	—	2	1	no	—
492	C₄⋊C₄	—	2	1	no	—
493	C₄⋊C₄	—	2	2	no	—
494	C₄⋊C₄	—	2	1	no	—
495	C₄⋊C₄	—	2	1	no	—
496	C₄⋊C₄	—	2	1	no	—
497	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
498	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
499	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	—	2	4	no	—
502	C₂²⋊C₄	—	2	2	no	—
503	C₂²⋊C₄	—	2	2	no	—
504	C₂²⋊C₄	—	2	2	no	—
505	C₂²⋊C₄	—	2	2	no	—
506	C₂²⋊C₄	—	4	1	no	—
507	C₂²⋊C₄	—	4	1	no	—
508	C₄²	—	2	2	no	—
509	C₄²	—	2	2	no	—
510	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
511	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
512	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
513	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
514	C₂³	—	2	2	no	—
515	C₂³	—	2	2	no	—
516	C₂³	—	4	1	no	—
517	C₂³	#120×C₄₇	1	1	yes	characteristic
518	Q₈	—	2	2	no	—
519	Q₈	—	2	4	no	—
520	Q₈	—	4	8	no	—
521	Q₈	—	4	1	no	—
522	Q₈	—	4	1	no	—
523	Q₈	—	4	2	no	—
524	Q₈	—	4	1	no	—
525	Q₈	—	4	1	no	—
526	Q₈	C₂×D₈×C₄₇	1	4	yes	—
527	D₄	—	2	2	no	—
528	D₄	—	2	2	no	—
529	D₄	—	4	2	no	—
530	D₄	—	4	8	no	—
531	D₄	—	4	2	no	—
532	D₄	—	4	4	no	—
533	D₄	—	4	4	no	—
534	D₄	—	4	1	no	—
535	D₄	—	4	1	no	—
536	D₄	—	4	1	no	—
537	D₄	—	4	1	no	—
538	D₄	—	4	1	no	—
539	D₄	—	4	1	no	—
540	D₄	—	4	1	no	—
541	D₄	—	4	1	no	—
542	D₄	—	4	2	no	—
543	D₄	—	8	1	no	—
544	D₄	—	8	4	no	—
545	D₄	—	8	2	no	—
546	C₂×C₄	—	2	2	no	—
547	C₂×C₄	—	2	4	no	—
548	C₂×C₄	—	2	1	no	—
549	C₂×C₄	—	2	1	no	—
550	C₂×C₄	—	2	2	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	2	no	—
553	C₂×C₄	—	4	1	no	—
554	C₂×C₄	—	4	8	no	—
555	C₂×C₄	—	4	8	no	—
556	C₂×C₄	—	4	2	no	—
557	C₂×C₄	—	4	2	no	—
558	C₂×C₄	—	4	4	no	—
559	C₂×C₄	—	4	1	no	—
560	C₂×C₄	—	8	1	no	—
561	C₂×C₄	—	8	2	no	—
562	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
563	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
564	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
565	C₂×C₄	C₂×D₈×C₄₇	1	2	yes	—
566	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
567	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
568	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
569	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
570	C₈	—	2	2	no	—
571	C₈	—	4	1	no	—
572	C₈	—	4	2	no	—
573	C₈	—	4	2	no	—
574	C₂²	—	2	1	no	—
575	C₂²	—	2	1	no	—
576	C₂²	—	4	2	no	—
577	C₂²	—	4	2	no	—
578	C₂²	—	4	2	no	—
579	C₂²	—	4	2	no	—
580	C₂²	—	4	2	no	—
581	C₂²	—	4	2	no	—
582	C₂²	—	8	1	no	—
583	C₂²	—	8	1	no	—
584	C₂²	—	8	1	no	—
585	C₂²	C₄₇×#447	1	2	yes	—
586	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
587	C₄	—	2	4	no	—
588	C₄	—	2	1	no	—
589	C₄	—	2	1	no	—
590	C₄	—	2	1	no	—
591	C₄	—	4	2	no	—
592	C₄	—	4	2	no	—
593	C₄	—	4	2	no	—
594	C₄	—	8	1	no	—
595	C₄	C₄₇×#447	1	2	yes	—
596	C₄	C₂²×D₈×C₄₇	1	1	yes	characteristic
597	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
598	C₄	C₄₇×#577	1	1	yes	characteristic
599	C₄	C₄₇×#578	1	1	yes	characteristic
600	C₂	—	2	2	no	—
601	C₂	—	8	2	no	—
602	C₂	—	8	2	no	—
603	C₂	—	16	1	no	—
604	C₂	C₂×C₄₇×#447	1	1	yes	characteristic
605	C₂	C₄₇×#3013	1	1	yes	characteristic
606	C₂	C₄₇×#3018	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×#3497	C₂	semidirect
2. C₄₇×#3245	C₂	semidirect
3. C₄₇×#3169	C₂	semidirect
4. C₄₇×#3037	C₂	semidirect
5. C₄₇×#1649	C₂	semidirect
6. C₄₇×#1641	C₂	semidirect
7. C₄₇×#1627	C₂	semidirect
8. C₄₇×#1621	C₂	semidirect
9. C₄₇×#1547	C₂	semidirect
10. C₄₇×#1492	C₂	semidirect
11. C₂×C₄₇×Q₈⋊C₈	C₂	semidirect
148. C₂×Q₈×C₄₇	D₈	semidirect
270. #18674	C₄₇	direct (N × H)
297. #3497	C₂×C₄₇	semidirect
298. #3245	C₂×C₄₇	semidirect
299. #3169	C₂×C₄₇	semidirect
300. #3037	C₂×C₄₇	semidirect
301. #1649	C₂×C₄₇	semidirect
302. #1641	C₂×C₄₇	semidirect
303. #1627	C₂×C₄₇	semidirect
304. #1621	C₂×C₄₇	semidirect
305. #1547	C₂×C₄₇	semidirect
306. #1492	C₂×C₄₇	semidirect
307. C₂×Q₈⋊C₈	C₂×C₄₇	semidirect
354. C₄₇	#18674	direct (N × H)
452. C₂×Q₈	D₈×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄₇×#3497	2
C₄₇×#3245	2
C₄₇×#3169	2
C₄₇×#3037	2
C₄₇×#1649	2
C₄₇×#1641	2
C₄₇×#1627	2
C₄₇×#1621	2
C₄₇×#1547	2
C₄₇×#1492	2
C₂×C₄₇×Q₈⋊C₈	2
#18674	47

Subgroups — C47×#18674 #26058372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18674 #26058372