Subgroups — C₄₇×#18782 #26058480

Order 12032.

1224 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#547	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#3227	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3100	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#3036	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1654	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1625	C₂	1	4	yes	maximal, complemented
7	C₄₇×#1549	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1486	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1478	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₇	—	2	1	no	—
11	C₂×AGL(1,ℤ/8)×C₄₇	—	2	1	no	—
12	C₄₇×#547	—	2	2	no	—
13	C₄₇×#547	—	2	2	no	—
14	C₄₇×#547	—	2	2	no	—
15	C₄₇×#547	C₂²	1	4	yes	—
16	C₄₇×#532	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×#123×C₄₇	—	2	2	no	—
19	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
20	C₂×#121×C₄₇	—	2	1	no	—
21	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
24	C₄₇×#498	C₂²	1	2	yes	complemented
25	C₄₇×#486	C₂²	1	2	yes	complemented
26	C₄₇×#481	—	2	2	no	—
27	C₄₇×#480	—	2	1	no	—
28	C₄₇×#476	—	2	2	no	—
29	C₄₇×#474	C₂²	1	2	yes	complemented
30	C₄₇×#463	—	2	2	no	—
31	C₄₇×#461	C₂²	1	2	yes	complemented
32	C₄₇×#459	C₂²	1	2	yes	complemented
33	C₄₇×#459	C₂²	1	2	yes	complemented
34	C₄₇×#447	—	2	1	no	—
35	C₄×D₈×C₄₇	—	2	2	no	—
36	C₄₇×#431	C₂²	1	1	yes	characteristic
37	C₄₇×#431	C₂²	1	1	yes	characteristic
38	C₄₇×#423	C₂²	1	1	yes	characteristic
39	C₄₇×#417	—	2	1	no	—
40	C₄₇×#332	C₂²	1	4	yes	complemented
41	C₄₇×D₄⋊C₈	C₂²	1	4	yes	complemented
42	C₄₇×D₄⋊C₈	C₂²	1	4	yes	complemented
43	C₂×#41×C₄₇	—	2	4	no	—
44	C₂×#41×C₄₇	—	2	4	no	—
45	C₂×#41×C₄₇	—	2	1	no	—
46	C₂×#41×C₄₇	—	4	8	no	—
47	C₂²×Q₈×C₄₇	—	2	1	no	—
48	C₂²×D₄×C₄₇	—	2	2	no	—
49	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	—	2	2	no	—
52	C₂³×C₄×C₄₇	—	2	1	no	—
53	C₂³×C₄×C₄₇	—	2	1	no	—
54	AGL(1,ℤ/8)×C₄₇	—	4	4	no	—
55	C₂×SD₁₆×C₄₇	—	2	2	no	—
56	C₂×D₈×C₄₇	—	2	2	no	—
57	C₂×D₈×C₄₇	—	2	2	no	—
58	C₂×M₁₆×C₄₇	—	2	1	no	—
59	C₄⋊Q₈×C₄₇	—	2	1	no	—
60	C₄⋊Q₈×C₄₇	—	2	1	no	—
61	C₄⋊Q₈×C₄₇	D₄	1	2	yes	—
62	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
63	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
64	#127×C₄₇	C₂³	1	1	yes	characteristic
65	#124×C₄₇	—	2	1	no	—
66	#123×C₄₇	—	2	8	no	—
67	#123×C₄₇	—	2	8	no	—
68	C₂²⋊Q₈×C₄₇	—	2	4	no	—
69	C₂²⋊Q₈×C₄₇	—	2	4	no	—
70	#121×C₄₇	—	2	4	no	—
71	#121×C₄₇	—	2	4	no	—
72	#121×C₄₇	—	2	1	no	—
73	#121×C₄₇	—	2	1	no	—
74	C₄×D₄×C₄₇	—	2	1	no	—
75	C₄×D₄×C₄₇	—	2	1	no	—
76	C₄×D₄×C₄₇	—	2	1	no	—
77	C₄×D₄×C₄₇	—	2	1	no	—
78	C₄×D₄×C₄₇	—	2	1	no	—
79	C₄×D₄×C₄₇	—	2	1	no	—
80	C₄×D₄×C₄₇	D₄	1	2	yes	—
81	C₄×D₄×C₄₇	D₄	1	2	yes	—
82	C₄×D₄×C₄₇	C₂³	1	2	yes	—
83	C₄×D₄×C₄₇	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
85	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
86	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
87	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
88	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
89	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
90	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
91	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
92	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
94	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
95	#107×C₄₇	—	2	2	no	—
96	#106×C₄₇	—	2	4	no	—
97	C₄⋊C₈×C₄₇	—	2	1	no	—
98	C₄⋊C₈×C₄₇	—	2	1	no	—
99	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
100	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
101	#103×C₄₇	—	2	2	no	—
102	#102×C₄₇	—	2	2	no	—
103	#102×C₄₇	—	2	2	no	—
104	#102×C₄₇	—	2	2	no	—
105	#102×C₄₇	—	2	4	no	—
106	C₂²⋊C₈×C₄₇	—	2	1	no	—
107	C₂²⋊C₈×C₄₇	—	2	1	no	—
108	C₄×C₈×C₄₇	—	2	1	no	—
109	C₄×C₈×C₄₇	C₂³	1	2	yes	—
110	C₂⁴×C₄₇	—	2	1	no	—
111	C₂⁴×C₄₇	—	2	1	no	—
112	#41×C₄₇	—	4	16	no	—
113	#41×C₄₇	—	4	8	no	—
114	#41×C₄₇	—	4	8	no	—
115	#41×C₄₇	—	4	2	no	—
116	#41×C₄₇	—	4	2	no	—
117	C₂×Q₈×C₄₇	—	2	2	no	—
118	C₂×Q₈×C₄₇	—	2	2	no	—
119	C₂×Q₈×C₄₇	—	2	1	no	—
120	C₂×Q₈×C₄₇	—	4	4	no	—
121	C₂×D₄×C₄₇	—	2	4	no	—
122	C₂×D₄×C₄₇	—	2	8	no	—
123	C₂×D₄×C₄₇	—	2	1	no	—
124	C₂×D₄×C₄₇	—	2	1	no	—
125	C₂×D₄×C₄₇	—	2	2	no	—
126	C₂×D₄×C₄₇	—	2	2	no	—
127	C₂×D₄×C₄₇	—	2	1	no	—
128	C₂×D₄×C₄₇	—	2	1	no	—
129	C₂×D₄×C₄₇	—	2	1	no	—
130	C₂×D₄×C₄₇	—	4	8	no	—
131	C₂×D₄×C₄₇	—	4	1	no	—
132	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
133	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
134	C₂²×C₄×C₄₇	—	2	8	no	—
135	C₂²×C₄×C₄₇	—	2	1	no	—
136	C₂²×C₄×C₄₇	—	2	1	no	—
137	C₂²×C₄×C₄₇	—	2	2	no	—
138	C₂²×C₄×C₄₇	—	2	2	no	—
139	C₂²×C₄×C₄₇	—	2	2	no	—
140	C₂²×C₄×C₄₇	—	2	2	no	—
141	C₂²×C₄×C₄₇	—	2	2	no	—
142	C₂²×C₄×C₄₇	—	4	4	no	—
143	C₂²×C₄×C₄₇	—	4	8	no	—
144	C₂²×C₄×C₄₇	—	4	2	no	—
145	C₂²×C₄×C₄₇	—	4	2	no	—
146	C₂²×C₄×C₄₇	—	4	1	no	—
147	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
150	SD₁₆×C₄₇	—	4	4	no	—
151	D₈×C₄₇	—	4	4	no	—
152	D₈×C₄₇	—	4	4	no	—
153	M₁₆×C₄₇	—	4	2	no	—
154	C₂×C₈×C₄₇	—	2	2	no	—
155	C₂×C₈×C₄₇	—	2	2	no	—
156	C₂×C₈×C₄₇	—	2	2	no	—
157	C₄⋊C₄×C₄₇	—	2	8	no	—
158	C₄⋊C₄×C₄₇	—	2	1	no	—
159	C₄⋊C₄×C₄₇	—	2	2	no	—
160	C₄⋊C₄×C₄₇	—	2	1	no	—
161	C₄⋊C₄×C₄₇	—	2	2	no	—
162	C₄⋊C₄×C₄₇	—	2	2	no	—
163	C₄⋊C₄×C₄₇	—	2	1	no	—
164	C₄⋊C₄×C₄₇	—	2	1	no	—
165	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
166	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
167	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
168	C₂²⋊C₄×C₄₇	—	2	8	no	—
169	C₂²⋊C₄×C₄₇	—	2	2	no	—
170	C₂²⋊C₄×C₄₇	—	2	2	no	—
171	C₂²⋊C₄×C₄₇	—	2	2	no	—
172	C₂²⋊C₄×C₄₇	—	2	2	no	—
173	C₂²⋊C₄×C₄₇	—	4	1	no	—
174	C₂²⋊C₄×C₄₇	—	4	1	no	—
175	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
176	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
177	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
178	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
179	C₂³×C₄₇	—	2	4	no	—
180	C₂³×C₄₇	—	2	2	no	—
181	C₂³×C₄₇	—	2	2	no	—
182	C₂³×C₄₇	—	4	2	no	—
183	C₂³×C₄₇	—	4	2	no	—
184	C₂³×C₄₇	—	4	2	no	—
185	C₂³×C₄₇	—	4	2	no	—
186	C₂³×C₄₇	—	4	2	no	—
187	C₂³×C₄₇	—	4	1	no	—
188	C₂³×C₄₇	#120	1	1	yes	characteristic
189	Q₈×C₄₇	—	4	4	no	—
190	Q₈×C₄₇	—	4	4	no	—
191	Q₈×C₄₇	—	4	1	no	—
192	Q₈×C₄₇	—	4	1	no	—
193	D₄×C₄₇	—	2	4	no	—
194	D₄×C₄₇	—	2	2	no	—
195	D₄×C₄₇	—	2	2	no	—
196	D₄×C₄₇	—	2	2	no	—
197	D₄×C₄₇	—	4	2	no	—
198	D₄×C₄₇	—	4	16	no	—
199	D₄×C₄₇	—	4	1	no	—
200	D₄×C₄₇	—	4	1	no	—
201	D₄×C₄₇	—	4	2	no	—
202	D₄×C₄₇	—	4	2	no	—
203	D₄×C₄₇	—	8	2	no	—
204	D₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	complemented
205	C₂×C₄×C₄₇	—	2	2	no	—
206	C₂×C₄×C₄₇	—	2	2	no	—
207	C₂×C₄×C₄₇	—	2	2	no	—
208	C₂×C₄×C₄₇	—	2	4	no	—
209	C₂×C₄×C₄₇	—	4	1	no	—
210	C₂×C₄×C₄₇	—	4	4	no	—
211	C₂×C₄×C₄₇	—	4	2	no	—
212	C₂×C₄×C₄₇	—	4	4	no	—
213	C₂×C₄×C₄₇	—	4	16	no	—
214	C₂×C₄×C₄₇	—	4	2	no	—
215	C₂×C₄×C₄₇	—	4	2	no	—
216	C₂×C₄×C₄₇	—	4	2	no	—
217	C₂×C₄×C₄₇	—	4	4	no	—
218	C₂×C₄×C₄₇	—	4	4	no	—
219	C₂×C₄×C₄₇	—	4	1	no	—
220	C₂×C₄×C₄₇	—	8	2	no	—
221	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
222	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
223	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
224	C₂×C₄×C₄₇	#135	1	2	yes	—
225	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
226	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
229	C₈×C₄₇	—	4	2	no	—
230	C₈×C₄₇	—	4	2	no	—
231	C₈×C₄₇	—	4	2	no	—
232	#18782	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
233	C₂²×C₄₇	—	2	1	no	—
234	C₂²×C₄₇	—	2	1	no	—
235	C₂²×C₄₇	—	2	4	no	—
236	C₂²×C₄₇	—	4	8	no	—
237	C₂²×C₄₇	—	4	2	no	—
238	C₂²×C₄₇	—	4	2	no	—
239	C₂²×C₄₇	—	4	2	no	—
240	C₂²×C₄₇	—	4	2	no	—
241	C₂²×C₄₇	—	4	2	no	—
242	C₂²×C₄₇	—	8	4	no	—
243	C₂²×C₄₇	—	8	1	no	—
244	C₂²×C₄₇	—	8	1	no	—
245	C₂²×C₄₇	—	8	1	no	—
246	C₂²×C₄₇	#449	1	2	yes	—
247	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
248	C₄×C₄₇	—	2	1	no	—
249	C₄×C₄₇	—	2	1	no	—
250	C₄×C₄₇	—	2	1	no	—
251	C₄×C₄₇	—	4	2	no	—
252	C₄×C₄₇	—	4	2	no	—
253	C₄×C₄₇	—	4	4	no	—
254	C₄×C₄₇	—	8	1	no	—
255	C₄×C₄₇	#449	1	2	yes	—
256	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
257	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
258	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
259	C₂×#547	C₂×C₄₇	1	1	yes	characteristic, complemented
260	#3227	C₂×C₄₇	1	1	yes	characteristic, complemented
261	#3100	C₂×C₄₇	1	1	yes	characteristic, complemented
262	#3036	C₂×C₄₇	1	1	yes	characteristic, complemented
263	#1654	C₂×C₄₇	1	4	yes	complemented
264	#1625	C₂×C₄₇	1	4	yes	complemented
265	#1549	C₂×C₄₇	1	1	yes	characteristic, complemented
266	#1486	C₂×C₄₇	1	1	yes	characteristic, complemented
267	#1478	C₂×C₄₇	1	1	yes	characteristic, complemented
268	C₂×C₄₇	—	2	2	no	—
269	C₂×C₄₇	—	4	4	no	—
270	C₂×C₄₇	—	8	2	no	—
271	C₂×C₄₇	—	16	1	no	—
272	C₂×C₄₇	C₂×#449	1	1	yes	characteristic
273	C₂×C₄₇	#3003	1	1	yes	characteristic
274	C₂×C₄₇	#3020	1	1	yes	characteristic
275	C₂²×#41	—	2	1	no	—
276	C₂×AGL(1,ℤ/8)	—	2	1	no	—
277	#547	—	2	2	no	—
278	#547	—	2	2	no	—
279	#547	—	2	2	no	—
280	#547	C₂²×C₄₇	1	4	yes	—
281	#532	C₂²×C₄₇	1	1	yes	characteristic
282	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
283	C₂×#123	—	2	2	no	—
284	C₂×C₂²⋊Q₈	—	2	1	no	—
285	C₂×#121	—	2	1	no	—
286	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
287	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
288	C₂²×C₄⋊C₄	—	2	1	no	—
289	#498	C₂²×C₄₇	1	2	yes	complemented
290	#486	C₂²×C₄₇	1	2	yes	complemented
291	#481	—	2	2	no	—
292	#480	—	2	1	no	—
293	#476	—	2	2	no	—
294	#474	C₂²×C₄₇	1	2	yes	complemented
295	#463	—	2	2	no	—
296	#461	C₂²×C₄₇	1	2	yes	complemented
297	#459	C₂²×C₄₇	1	2	yes	complemented
298	#459	C₂²×C₄₇	1	2	yes	complemented
299	#447	—	2	1	no	—
300	C₄×D₈	—	2	2	no	—
301	#431	C₂²×C₄₇	1	1	yes	characteristic
302	#431	C₂²×C₄₇	1	1	yes	characteristic
303	#423	C₂²×C₄₇	1	1	yes	characteristic
304	#417	—	2	1	no	—
305	#332	C₂²×C₄₇	1	4	yes	complemented
306	D₄⋊C₈	C₂²×C₄₇	1	4	yes	complemented
307	D₄⋊C₈	C₂²×C₄₇	1	4	yes	complemented
308	C₄₇	#18782	1	1	yes	characteristic, direct product factor, Sylow
309	C₂×#41	—	2	4	no	—
310	C₂×#41	—	2	4	no	—
311	C₂×#41	—	2	1	no	—
312	C₂×#41	—	4	8	no	—
313	C₂²×Q₈	—	2	1	no	—
314	C₂²×D₄	—	2	2	no	—
315	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
316	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
317	C₂³×C₄	—	2	2	no	—
318	C₂³×C₄	—	2	1	no	—
319	C₂³×C₄	—	2	1	no	—
320	AGL(1,ℤ/8)	—	4	4	no	—
321	C₂×SD₁₆	—	2	2	no	—
322	C₂×D₈	—	2	2	no	—
323	C₂×D₈	—	2	2	no	—
324	C₂×M₁₆	—	2	1	no	—
325	C₄⋊Q₈	—	2	1	no	—
326	C₄⋊Q₈	—	2	1	no	—
327	C₄⋊Q₈	D₄×C₄₇	1	2	yes	—
328	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
329	C₄⋊Q₈	C₂³×C₄₇	1	2	yes	—
330	#127	C₂³×C₄₇	1	1	yes	characteristic
331	#124	—	2	1	no	—
332	#123	—	2	8	no	—
333	#123	—	2	8	no	—
334	C₂²⋊Q₈	—	2	4	no	—
335	C₂²⋊Q₈	—	2	4	no	—
336	#121	—	2	4	no	—
337	#121	—	2	4	no	—
338	#121	—	2	1	no	—
339	#121	—	2	1	no	—
340	C₄×D₄	—	2	1	no	—
341	C₄×D₄	—	2	1	no	—
342	C₄×D₄	—	2	1	no	—
343	C₄×D₄	—	2	1	no	—
344	C₄×D₄	—	2	1	no	—
345	C₄×D₄	—	2	1	no	—
346	C₄×D₄	D₄×C₄₇	1	2	yes	—
347	C₄×D₄	D₄×C₄₇	1	2	yes	—
348	C₄×D₄	C₂³×C₄₇	1	2	yes	—
349	C₄×D₄	C₂³×C₄₇	1	2	yes	—
350	C₂×C₄⋊C₄	—	2	2	no	—
351	C₂×C₄⋊C₄	—	2	4	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	4	no	—
354	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
355	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
356	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
357	C₂×C₂²⋊C₄	—	2	2	no	—
358	C₂×C₂²⋊C₄	—	2	1	no	—
359	C₂×C₂²⋊C₄	—	2	1	no	—
360	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
361	#107	—	2	2	no	—
362	#106	—	2	4	no	—
363	C₄⋊C₈	—	2	1	no	—
364	C₄⋊C₈	—	2	1	no	—
365	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
366	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
367	#103	—	2	2	no	—
368	#102	—	2	2	no	—
369	#102	—	2	2	no	—
370	#102	—	2	2	no	—
371	#102	—	2	4	no	—
372	C₂²⋊C₈	—	2	1	no	—
373	C₂²⋊C₈	—	2	1	no	—
374	C₄×C₈	—	2	1	no	—
375	C₄×C₈	C₂³×C₄₇	1	2	yes	—
376	C₂⁴	—	2	1	no	—
377	C₂⁴	—	2	1	no	—
378	#41	—	4	16	no	—
379	#41	—	4	8	no	—
380	#41	—	4	8	no	—
381	#41	—	4	2	no	—
382	#41	—	4	2	no	—
383	C₂×Q₈	—	2	2	no	—
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	4	4	no	—
387	C₂×D₄	—	2	4	no	—
388	C₂×D₄	—	2	8	no	—
389	C₂×D₄	—	2	1	no	—
390	C₂×D₄	—	2	1	no	—
391	C₂×D₄	—	2	2	no	—
392	C₂×D₄	—	2	2	no	—
393	C₂×D₄	—	2	1	no	—
394	C₂×D₄	—	2	1	no	—
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	4	8	no	—
397	C₂×D₄	—	4	1	no	—
398	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
399	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
400	C₂²×C₄	—	2	8	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	1	no	—
403	C₂²×C₄	—	2	2	no	—
404	C₂²×C₄	—	2	2	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	2	no	—
408	C₂²×C₄	—	4	4	no	—
409	C₂²×C₄	—	4	8	no	—
410	C₂²×C₄	—	4	2	no	—
411	C₂²×C₄	—	4	2	no	—
412	C₂²×C₄	—	4	1	no	—
413	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
414	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
415	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
416	SD₁₆	—	4	4	no	—
417	D₈	—	4	4	no	—
418	D₈	—	4	4	no	—
419	M₁₆	—	4	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₂×C₈	—	2	2	no	—
422	C₂×C₈	—	2	2	no	—
423	C₄⋊C₄	—	2	8	no	—
424	C₄⋊C₄	—	2	1	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	1	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	1	no	—
430	C₄⋊C₄	—	2	1	no	—
431	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
432	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
433	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
434	C₂²⋊C₄	—	2	8	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	—	4	1	no	—
440	C₂²⋊C₄	—	4	1	no	—
441	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
442	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
443	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
444	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
445	C₂³	—	2	4	no	—
446	C₂³	—	2	2	no	—
447	C₂³	—	2	2	no	—
448	C₂³	—	4	2	no	—
449	C₂³	—	4	2	no	—
450	C₂³	—	4	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	1	no	—
454	C₂³	#120×C₄₇	1	1	yes	characteristic
455	Q₈	—	4	4	no	—
456	Q₈	—	4	4	no	—
457	Q₈	—	4	1	no	—
458	Q₈	—	4	1	no	—
459	D₄	—	2	4	no	—
460	D₄	—	2	2	no	—
461	D₄	—	2	2	no	—
462	D₄	—	2	2	no	—
463	D₄	—	4	2	no	—
464	D₄	—	4	16	no	—
465	D₄	—	4	2	no	—
466	D₄	—	4	1	no	—
467	D₄	—	4	1	no	—
468	D₄	—	4	2	no	—
469	D₄	—	8	2	no	—
470	D₄	AGL(1,ℤ/8)×C₄₇	1	4	yes	complemented
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	4	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	2	no	—
478	C₂×C₄	—	4	4	no	—
479	C₂×C₄	—	4	16	no	—
480	C₂×C₄	—	4	2	no	—
481	C₂×C₄	—	4	4	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	4	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	8	2	no	—
487	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
488	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
489	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
490	C₂×C₄	#135×C₄₇	1	2	yes	—
491	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
492	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
493	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
494	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
495	C₈	—	4	2	no	—
496	C₈	—	4	2	no	—
497	C₈	—	4	2	no	—
498	C₂²	—	2	1	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	4	no	—
501	C₂²	—	4	8	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	—	4	2	no	—
505	C₂²	—	4	2	no	—
506	C₂²	—	4	2	no	—
507	C₂²	—	8	4	no	—
508	C₂²	—	8	1	no	—
509	C₂²	—	8	1	no	—
510	C₂²	—	8	1	no	—
511	C₂²	C₄₇×#449	1	2	yes	—
512	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	2	1	no	—
516	C₄	—	4	2	no	—
517	C₄	—	4	2	no	—
518	C₄	—	4	4	no	—
519	C₄	—	8	1	no	—
520	C₄	C₄₇×#449	1	2	yes	—
521	C₄	C₂×#135×C₄₇	1	1	yes	characteristic
522	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
523	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	2	yes	—
524	C₂	—	2	2	no	—
525	C₂	—	4	4	no	—
526	C₂	—	8	2	no	—
527	C₂	—	16	1	no	—
528	C₂	C₂×C₄₇×#449	1	1	yes	characteristic
529	C₂	C₄₇×#3003	1	1	yes	characteristic
530	C₂	C₄₇×#3020	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. C₂×C₄₇×#547	C₂	semidirect
2. C₄₇×#3227	C₂	semidirect
3. C₄₇×#3100	C₂	semidirect
4. C₄₇×#3036	C₂	semidirect
5. C₄₇×#1654	C₂	semidirect
6. C₄₇×#1625	C₂	semidirect
7. C₄₇×#1549	C₂	semidirect
8. C₄₇×#1486	C₂	semidirect
9. C₄₇×#1478	C₂	semidirect
24. C₄₇×#498	C₂²	semidirect
25. C₄₇×#486	C₂²	semidirect
29. C₄₇×#474	C₂²	semidirect
31. C₄₇×#461	C₂²	semidirect
32. C₄₇×#459	C₂²	semidirect
33. C₄₇×#459	C₂²	semidirect
40. C₄₇×#332	C₂²	semidirect
41. C₄₇×D₄⋊C₈	C₂²	semidirect
42. C₄₇×D₄⋊C₈	C₂²	semidirect
204. D₄×C₄₇	AGL(1,ℤ/8)	semidirect
232. #18782	C₄₇	direct (N × H)
259. C₂×#547	C₂×C₄₇	semidirect
260. #3227	C₂×C₄₇	semidirect
261. #3100	C₂×C₄₇	semidirect
262. #3036	C₂×C₄₇	semidirect
263. #1654	C₂×C₄₇	semidirect
264. #1625	C₂×C₄₇	semidirect
265. #1549	C₂×C₄₇	semidirect
266. #1486	C₂×C₄₇	semidirect
267. #1478	C₂×C₄₇	semidirect
289. #498	C₂²×C₄₇	semidirect
290. #486	C₂²×C₄₇	semidirect
294. #474	C₂²×C₄₇	semidirect
296. #461	C₂²×C₄₇	semidirect
297. #459	C₂²×C₄₇	semidirect
298. #459	C₂²×C₄₇	semidirect
305. #332	C₂²×C₄₇	semidirect
306. D₄⋊C₈	C₂²×C₄₇	semidirect
307. D₄⋊C₈	C₂²×C₄₇	semidirect
308. C₄₇	#18782	direct (N × H)
470. 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
C₂×C₄₇×#547	2
C₄₇×#3227	2
C₄₇×#3100	2
C₄₇×#3036	2
C₄₇×#1654	2
C₄₇×#1625	2
C₄₇×#1549	2
C₄₇×#1486	2
C₄₇×#1478	2
#18782	47

Subgroups — C47×#18782 #26058480

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18782 #26058480