Subgroups — C₄₇×#32974 #26072672

Order 12032.

1186 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×2₋¹⁺⁴×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#3080	C₂	1	2	yes	maximal, complemented
3	C₄₇×#2565	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1860	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1859	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1857	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1857	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1806	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1801	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1793	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1793	C₂	1	1	yes	maximal, characteristic
12	C₂×2₋¹⁺⁴×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
14	C₄₇×#520	—	2	2	no	—
15	C₄₇×#520	—	2	2	no	—
16	C₄₇×#520	C₂²	1	2	yes	—
17	C₄₇×#519	—	2	2	no	—
18	C₄₇×#519	C₂²	1	1	yes	characteristic
19	C₄×#41×C₄₇	—	2	2	no	—
20	C₄×#41×C₄₇	—	2	2	no	—
21	C₄×#41×C₄₇	C₂²	1	2	yes	—
22	C₂×C₄×Q₈×C₄₇	—	2	2	no	—
23	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₄₇×#479	—	2	2	no	—
25	C₄₇×#479	—	2	2	no	—
26	C₄₇×#478	—	2	2	no	—
27	C₄₇×#478	—	2	2	no	—
28	C₄₇×#428	C₂²	1	2	yes	—
29	C₄₇×#428	C₂²	1	2	yes	—
30	C₄₇×#423	C₂²	1	2	yes	—
31	C₂×#104×C₄₇	C₂²	1	2	yes	—
32	C₂×#104×C₄₇	C₂²	1	2	yes	—
33	C₄₇×#417	C₂²	1	2	yes	—
34	C₄₇×#417	C₂²	1	2	yes	—
35	C₂×#101×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×#101×C₄₇	C₂²	1	1	yes	characteristic
37	C₄₇×#398	—	2	2	no	—
38	C₄₇×#391	C₂²	1	1	yes	characteristic
39	C₄₇×#391	C₂²	1	1	yes	characteristic
40	C₄₇×#387	—	2	2	no	—
41	C₄₇×#384	C₂²	1	1	yes	characteristic
42	C₄₇×#382	C₂²	1	1	yes	characteristic
43	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
44	C₄₇×#343	C₂²	1	2	yes	—
45	C₄₇×#339	C₂²	1	2	yes	—
46	C₄₇×#339	C₂²	1	2	yes	—
47	2₋¹⁺⁴×C₄₇	—	2	4	no	—
48	2₋¹⁺⁴×C₄₇	—	2	2	no	—
49	2₋¹⁺⁴×C₄₇	Q₈	1	4	yes	—
50	C₂×#41×C₄₇	—	2	2	no	—
51	C₂×#41×C₄₇	—	2	2	no	—
52	C₂×#41×C₄₇	C₂³	1	2	yes	—
53	C₂²×Q₈×C₄₇	—	2	2	no	—
54	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
55	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
56	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
57	#125×C₄₇	—	2	2	no	—
58	#125×C₄₇	—	2	2	no	—
59	C₄×Q₈×C₄₇	—	2	2	no	—
60	C₄×Q₈×C₄₇	—	2	4	no	—
61	C₄×Q₈×C₄₇	—	2	2	no	—
62	C₄×Q₈×C₄₇	—	2	2	no	—
63	C₄×Q₈×C₄₇	—	2	2	no	—
64	C₄×Q₈×C₄₇	—	2	2	no	—
65	C₄×Q₈×C₄₇	—	2	2	no	—
66	C₄×Q₈×C₄₇	—	2	2	no	—
67	C₄×Q₈×C₄₇	D₄	1	2	yes	—
68	C₄×Q₈×C₄₇	D₄	1	2	yes	—
69	C₄×D₄×C₄₇	—	2	2	no	—
70	C₄×D₄×C₄₇	—	2	4	no	—
71	C₄×D₄×C₄₇	—	2	2	no	—
72	C₄×D₄×C₄₇	—	2	2	no	—
73	C₄×D₄×C₄₇	—	2	2	no	—
74	C₄×D₄×C₄₇	—	2	4	no	—
75	C₄×D₄×C₄₇	—	2	2	no	—
76	C₄×D₄×C₄₇	D₄	1	2	yes	—
77	C₄×D₄×C₄₇	D₄	1	2	yes	—
78	#117×C₄₇	—	2	4	no	—
79	#117×C₄₇	—	2	4	no	—
80	#117×C₄₇	—	2	2	no	—
81	#117×C₄₇	—	2	2	no	—
82	#117×C₄₇	—	2	2	no	—
83	#117×C₄₇	C₂³	1	2	yes	—
84	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
85	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
86	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
87	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
88	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
89	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
90	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
91	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
92	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
93	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
94	C₂×C₄²×C₄₇	—	2	4	no	—
95	C₂×C₄²×C₄₇	—	2	2	no	—
96	C₂×C₄²×C₄₇	D₄	1	2	yes	—
97	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
100	#107×C₄₇	—	2	2	no	—
101	#107×C₄₇	—	2	2	no	—
102	#106×C₄₇	—	2	2	no	—
103	#106×C₄₇	—	2	2	no	—
104	C₄⋊C₈×C₄₇	—	2	2	no	—
105	C₄⋊C₈×C₄₇	—	2	2	no	—
106	#104×C₄₇	—	2	4	no	—
107	#104×C₄₇	—	2	4	no	—
108	#103×C₄₇	—	2	2	no	—
109	#103×C₄₇	—	2	2	no	—
110	#102×C₄₇	—	2	2	no	—
111	#102×C₄₇	—	2	2	no	—
112	#101×C₄₇	—	2	2	no	—
113	#101×C₄₇	—	2	2	no	—
114	#95×C₄₇	—	2	1	no	—
115	#95×C₄₇	—	2	2	no	—
116	#95×C₄₇	—	2	2	no	—
117	#95×C₄₇	—	2	2	no	—
118	#41×C₄₇	—	2	8	no	—
119	#41×C₄₇	—	2	8	no	—
120	#41×C₄₇	—	2	8	no	—
121	#41×C₄₇	—	2	8	no	—
122	#41×C₄₇	—	2	2	no	—
123	#41×C₄₇	—	2	2	no	—
124	#41×C₄₇	C₂×Q₈	1	4	yes	—
125	#41×C₄₇	#41	1	4	yes	—
126	C₂×Q₈×C₄₇	—	2	2	no	—
127	C₂×Q₈×C₄₇	—	2	8	no	—
128	C₂×Q₈×C₄₇	—	2	8	no	—
129	C₂×Q₈×C₄₇	—	2	2	no	—
130	C₂×Q₈×C₄₇	—	2	2	no	—
131	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
132	C₂×Q₈×C₄₇	C₂×Q₈	1	2	yes	—
133	C₂×Q₈×C₄₇	#41	1	2	yes	—
134	C₂×D₄×C₄₇	—	2	2	no	—
135	C₂×D₄×C₄₇	—	2	2	no	—
136	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₄₇	—	2	4	no	—
138	C₂²×C₄×C₄₇	—	2	2	no	—
139	C₂²×C₄×C₄₇	—	2	1	no	—
140	C₂²×C₄×C₄₇	—	2	4	no	—
141	C₂²×C₄×C₄₇	—	2	2	no	—
142	C₂²×C₄×C₄₇	—	2	2	no	—
143	C₂²×C₄×C₄₇	—	2	1	no	—
144	C₂²×C₄×C₄₇	—	2	1	no	—
145	C₂²×C₄×C₄₇	—	2	1	no	—
146	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
147	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
148	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
151	M₁₆×C₄₇	—	2	2	no	—
152	M₁₆×C₄₇	—	2	2	no	—
153	M₁₆×C₄₇	—	2	2	no	—
154	M₁₆×C₄₇	—	2	2	no	—
155	C₂×C₈×C₄₇	—	2	2	no	—
156	C₂×C₈×C₄₇	—	2	2	no	—
157	C₄⋊C₄×C₄₇	—	2	4	no	—
158	C₄⋊C₄×C₄₇	—	2	2	no	—
159	C₄⋊C₄×C₄₇	—	2	2	no	—
160	C₄⋊C₄×C₄₇	—	2	2	no	—
161	C₄⋊C₄×C₄₇	—	2	4	no	—
162	C₄⋊C₄×C₄₇	—	2	2	no	—
163	C₄⋊C₄×C₄₇	—	2	2	no	—
164	C₄⋊C₄×C₄₇	—	2	2	no	—
165	C₄⋊C₄×C₄₇	—	2	2	no	—
166	C₄⋊C₄×C₄₇	—	4	2	no	—
167	C₄⋊C₄×C₄₇	—	4	4	no	—
168	C₄⋊C₄×C₄₇	—	4	1	no	—
169	C₄⋊C₄×C₄₇	—	4	1	no	—
170	C₄⋊C₄×C₄₇	—	4	2	no	—
171	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
172	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
173	C₂²⋊C₄×C₄₇	—	2	4	no	—
174	C₂²⋊C₄×C₄₇	—	2	2	no	—
175	C₂²⋊C₄×C₄₇	—	2	2	no	—
176	C₂²⋊C₄×C₄₇	—	2	2	no	—
177	C₄²×C₄₇	—	2	4	no	—
178	C₄²×C₄₇	—	2	4	no	—
179	C₄²×C₄₇	—	2	2	no	—
180	C₄²×C₄₇	—	2	2	no	—
181	C₄²×C₄₇	—	2	2	no	—
182	C₄²×C₄₇	—	2	2	no	—
183	C₄²×C₄₇	—	2	2	no	—
184	C₄²×C₄₇	—	2	2	no	—
185	C₄²×C₄₇	—	2	2	no	—
186	C₄²×C₄₇	C₂×D₄	1	2	yes	—
187	C₄²×C₄₇	C₂×D₄	1	2	yes	—
188	C₂³×C₄₇	—	2	2	no	—
189	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
190	Q₈×C₄₇	—	2	8	no	—
191	Q₈×C₄₇	—	2	4	no	—
192	Q₈×C₄₇	—	2	2	no	—
193	Q₈×C₄₇	—	2	4	no	—
194	Q₈×C₄₇	C₂²⋊Q₈	1	4	yes	—
195	D₄×C₄₇	—	2	8	no	—
196	D₄×C₄₇	—	2	4	no	—
197	D₄×C₄₇	—	2	4	no	—
198	D₄×C₄₇	—	2	2	no	—
199	D₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
200	C₂×C₄×C₄₇	—	2	16	no	—
201	C₂×C₄×C₄₇	—	2	2	no	—
202	C₂×C₄×C₄₇	—	2	2	no	—
203	C₂×C₄×C₄₇	—	2	2	no	—
204	C₂×C₄×C₄₇	—	2	4	no	—
205	C₂×C₄×C₄₇	—	2	4	no	—
206	C₂×C₄×C₄₇	—	2	2	no	—
207	C₂×C₄×C₄₇	—	2	2	no	—
208	C₂×C₄×C₄₇	—	2	2	no	—
209	C₂×C₄×C₄₇	—	2	2	no	—
210	C₂×C₄×C₄₇	—	4	1	no	—
211	C₂×C₄×C₄₇	—	4	1	no	—
212	C₂×C₄×C₄₇	—	4	4	no	—
213	C₂×C₄×C₄₇	—	4	1	no	—
214	C₂×C₄×C₄₇	—	4	1	no	—
215	C₂×C₄×C₄₇	—	4	2	no	—
216	C₂×C₄×C₄₇	—	4	1	no	—
217	C₂×C₄×C₄₇	—	4	2	no	—
218	C₂×C₄×C₄₇	—	4	1	no	—
219	C₂×C₄×C₄₇	—	4	2	no	—
220	C₂×C₄×C₄₇	—	4	1	no	—
221	C₂×C₄×C₄₇	—	4	1	no	—
222	C₂×C₄×C₄₇	—	4	1	no	—
223	C₂×C₄×C₄₇	—	8	2	no	—
224	C₂×C₄×C₄₇	—	8	4	no	—
225	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
226	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
227	C₂×C₄×C₄₇	#120	1	2	yes	—
228	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
229	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
230	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
231	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
232	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
233	C₈×C₄₇	—	4	2	no	—
234	C₈×C₄₇	—	4	2	no	—
235	#32974	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
236	C₂²×C₄₇	—	2	1	no	—
237	C₂²×C₄₇	—	2	1	no	—
238	C₂²×C₄₇	—	2	4	no	—
239	C₂²×C₄₇	—	4	2	no	—
240	C₂²×C₄₇	—	4	2	no	—
241	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
242	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
243	C₂²×C₄₇	#525	1	1	yes	characteristic
244	C₄×C₄₇	—	2	4	no	—
245	C₄×C₄₇	—	2	4	no	—
246	C₄×C₄₇	—	2	2	no	—
247	C₄×C₄₇	—	2	1	no	—
248	C₄×C₄₇	—	2	1	no	—
249	C₄×C₄₇	—	4	2	no	—
250	C₄×C₄₇	—	4	2	no	—
251	C₄×C₄₇	—	4	2	no	—
252	C₄×C₄₇	—	4	2	no	—
253	C₄×C₄₇	—	8	1	no	—
254	C₄×C₄₇	—	8	1	no	—
255	C₄×C₄₇	—	8	1	no	—
256	C₄×C₄₇	C₂×C₂²⋊Q₈	1	2	yes	—
257	C₄×C₄₇	#525	1	2	yes	—
258	C₄×2₋¹⁺⁴	C₂×C₄₇	1	1	yes	characteristic
259	#3080	C₂×C₄₇	1	2	yes	complemented
260	#2565	C₂×C₄₇	1	1	yes	characteristic, complemented
261	#1860	C₂×C₄₇	1	2	yes	complemented
262	#1859	C₂×C₄₇	1	2	yes	complemented
263	#1857	C₂×C₄₇	1	1	yes	characteristic, complemented
264	#1857	C₂×C₄₇	1	1	yes	characteristic, complemented
265	#1806	C₂×C₄₇	1	2	yes	complemented
266	#1801	C₂×C₄₇	1	1	yes	characteristic, complemented
267	#1793	C₂×C₄₇	1	1	yes	characteristic
268	#1793	C₂×C₄₇	1	1	yes	characteristic
269	C₂×C₄₇	—	2	1	no	—
270	C₂×C₄₇	—	2	1	no	—
271	C₂×C₄₇	—	4	4	no	—
272	C₂×C₄₇	#2848	1	1	yes	characteristic
273	C₂×C₄₇	#3018	1	1	yes	characteristic
274	C₂×C₄₇	#3020	1	1	yes	characteristic
275	C₂×2₋¹⁺⁴	C₂²×C₄₇	1	1	yes	characteristic
276	C₂×#125	C₂²×C₄₇	1	1	yes	characteristic
277	#520	—	2	2	no	—
278	#520	—	2	2	no	—
279	#520	C₂²×C₄₇	1	2	yes	—
280	#519	—	2	2	no	—
281	#519	C₂²×C₄₇	1	1	yes	characteristic
282	C₄×#41	—	2	2	no	—
283	C₄×#41	—	2	2	no	—
284	C₄×#41	C₂²×C₄₇	1	2	yes	—
285	C₂×C₄×Q₈	—	2	2	no	—
286	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
287	#479	—	2	2	no	—
288	#479	—	2	2	no	—
289	#478	—	2	2	no	—
290	#478	—	2	2	no	—
291	#428	C₂²×C₄₇	1	2	yes	—
292	#428	C₂²×C₄₇	1	2	yes	—
293	#423	C₂²×C₄₇	1	2	yes	—
294	C₂×#104	C₂²×C₄₇	1	2	yes	—
295	C₂×#104	C₂²×C₄₇	1	2	yes	—
296	#417	C₂²×C₄₇	1	2	yes	—
297	#417	C₂²×C₄₇	1	2	yes	—
298	C₂×#101	C₂²×C₄₇	1	1	yes	characteristic
299	C₂×#101	C₂²×C₄₇	1	1	yes	characteristic
300	#398	—	2	2	no	—
301	#391	C₂²×C₄₇	1	1	yes	characteristic
302	#391	C₂²×C₄₇	1	1	yes	characteristic
303	#387	—	2	2	no	—
304	#384	C₂²×C₄₇	1	1	yes	characteristic
305	#382	C₂²×C₄₇	1	1	yes	characteristic
306	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
307	#343	C₂²×C₄₇	1	2	yes	—
308	#339	C₂²×C₄₇	1	2	yes	—
309	#339	C₂²×C₄₇	1	2	yes	—
310	C₄₇	#32974	1	1	yes	characteristic, direct product factor, Sylow
311	2₋¹⁺⁴	—	2	4	no	—
312	2₋¹⁺⁴	—	2	2	no	—
313	2₋¹⁺⁴	Q₈×C₄₇	1	4	yes	—
314	C₂×#41	—	2	2	no	—
315	C₂×#41	—	2	2	no	—
316	C₂×#41	C₂³×C₄₇	1	2	yes	—
317	C₂²×Q₈	—	2	2	no	—
318	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
319	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
320	C₂×M₁₆	C₂³×C₄₇	1	2	yes	—
321	#125	—	2	2	no	—
322	#125	—	2	2	no	—
323	C₄×Q₈	—	2	2	no	—
324	C₄×Q₈	—	2	4	no	—
325	C₄×Q₈	—	2	2	no	—
326	C₄×Q₈	—	2	2	no	—
327	C₄×Q₈	—	2	2	no	—
328	C₄×Q₈	—	2	2	no	—
329	C₄×Q₈	—	2	2	no	—
330	C₄×Q₈	—	2	2	no	—
331	C₄×Q₈	D₄×C₄₇	1	2	yes	—
332	C₄×Q₈	D₄×C₄₇	1	2	yes	—
333	C₄×D₄	—	2	2	no	—
334	C₄×D₄	—	2	4	no	—
335	C₄×D₄	—	2	2	no	—
336	C₄×D₄	—	2	2	no	—
337	C₄×D₄	—	2	2	no	—
338	C₄×D₄	—	2	4	no	—
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	D₄×C₄₇	1	2	yes	—
341	C₄×D₄	D₄×C₄₇	1	2	yes	—
342	#117	—	2	4	no	—
343	#117	—	2	4	no	—
344	#117	—	2	2	no	—
345	#117	—	2	2	no	—
346	#117	—	2	2	no	—
347	#117	C₂³×C₄₇	1	2	yes	—
348	C₂×C₄⋊C₄	—	2	4	no	—
349	C₂×C₄⋊C₄	—	2	2	no	—
350	C₂×C₄⋊C₄	—	2	1	no	—
351	C₂×C₄⋊C₄	—	2	1	no	—
352	C₂×C₄⋊C₄	—	2	1	no	—
353	C₂×C₄⋊C₄	—	2	2	no	—
354	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
355	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
356	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
357	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
358	C₂×C₄²	—	2	4	no	—
359	C₂×C₄²	—	2	2	no	—
360	C₂×C₄²	D₄×C₄₇	1	2	yes	—
361	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
362	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
363	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
364	#107	—	2	2	no	—
365	#107	—	2	2	no	—
366	#106	—	2	2	no	—
367	#106	—	2	2	no	—
368	C₄⋊C₈	—	2	2	no	—
369	C₄⋊C₈	—	2	2	no	—
370	#104	—	2	4	no	—
371	#104	—	2	4	no	—
372	#103	—	2	2	no	—
373	#103	—	2	2	no	—
374	#102	—	2	2	no	—
375	#102	—	2	2	no	—
376	#101	—	2	2	no	—
377	#101	—	2	2	no	—
378	#95	—	2	1	no	—
379	#95	—	2	2	no	—
380	#95	—	2	2	no	—
381	#95	—	2	2	no	—
382	#41	—	2	8	no	—
383	#41	—	2	8	no	—
384	#41	—	2	8	no	—
385	#41	—	2	8	no	—
386	#41	—	2	2	no	—
387	#41	—	2	2	no	—
388	#41	C₂×Q₈×C₄₇	1	4	yes	—
389	#41	#41×C₄₇	1	4	yes	—
390	C₂×Q₈	—	2	2	no	—
391	C₂×Q₈	—	2	8	no	—
392	C₂×Q₈	—	2	8	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	2	no	—
395	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
396	C₂×Q₈	C₂×Q₈×C₄₇	1	2	yes	—
397	C₂×Q₈	#41×C₄₇	1	2	yes	—
398	C₂×D₄	—	2	2	no	—
399	C₂×D₄	—	2	2	no	—
400	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
401	C₂²×C₄	—	2	4	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	—	2	1	no	—
404	C₂²×C₄	—	2	4	no	—
405	C₂²×C₄	—	2	2	no	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	—	2	1	no	—
408	C₂²×C₄	—	2	1	no	—
409	C₂²×C₄	—	2	1	no	—
410	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
411	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
412	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
413	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
414	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
415	M₁₆	—	2	2	no	—
416	M₁₆	—	2	2	no	—
417	M₁₆	—	2	2	no	—
418	M₁₆	—	2	2	no	—
419	C₂×C₈	—	2	2	no	—
420	C₂×C₈	—	2	2	no	—
421	C₄⋊C₄	—	2	4	no	—
422	C₄⋊C₄	—	2	2	no	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	4	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	2	2	no	—
430	C₄⋊C₄	—	4	2	no	—
431	C₄⋊C₄	—	4	4	no	—
432	C₄⋊C₄	—	4	1	no	—
433	C₄⋊C₄	—	4	1	no	—
434	C₄⋊C₄	—	4	2	no	—
435	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
436	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
437	C₂²⋊C₄	—	2	4	no	—
438	C₂²⋊C₄	—	2	2	no	—
439	C₂²⋊C₄	—	2	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₄²	—	2	4	no	—
442	C₄²	—	2	4	no	—
443	C₄²	—	2	2	no	—
444	C₄²	—	2	2	no	—
445	C₄²	—	2	2	no	—
446	C₄²	—	2	2	no	—
447	C₄²	—	2	2	no	—
448	C₄²	—	2	2	no	—
449	C₄²	—	2	2	no	—
450	C₄²	C₂×D₄×C₄₇	1	2	yes	—
451	C₄²	C₂×D₄×C₄₇	1	2	yes	—
452	C₂³	—	2	2	no	—
453	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
454	Q₈	—	2	8	no	—
455	Q₈	—	2	4	no	—
456	Q₈	—	2	2	no	—
457	Q₈	—	2	4	no	—
458	Q₈	C₂²⋊Q₈×C₄₇	1	4	yes	—
459	D₄	—	2	8	no	—
460	D₄	—	2	4	no	—
461	D₄	—	2	4	no	—
462	D₄	—	2	2	no	—
463	D₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
464	C₂×C₄	—	2	16	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	4	no	—
469	C₂×C₄	—	2	4	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	4	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	—	4	2	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	8	2	no	—
488	C₂×C₄	—	8	4	no	—
489	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
490	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
491	C₂×C₄	#120×C₄₇	1	2	yes	—
492	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
493	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
494	C₂×C₄	C₂²×Q₈×C₄₇	1	1	yes	characteristic
495	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
496	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
497	C₈	—	4	2	no	—
498	C₈	—	4	2	no	—
499	C₂²	—	2	1	no	—
500	C₂²	—	2	1	no	—
501	C₂²	—	2	4	no	—
502	C₂²	—	4	2	no	—
503	C₂²	—	4	2	no	—
504	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
505	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
506	C₂²	C₄₇×#525	1	1	yes	characteristic
507	C₄	—	2	4	no	—
508	C₄	—	2	4	no	—
509	C₄	—	2	2	no	—
510	C₄	—	2	1	no	—
511	C₄	—	2	1	no	—
512	C₄	—	4	2	no	—
513	C₄	—	4	2	no	—
514	C₄	—	4	2	no	—
515	C₄	—	4	2	no	—
516	C₄	—	8	1	no	—
517	C₄	—	8	1	no	—
518	C₄	—	8	1	no	—
519	C₄	C₂×C₂²⋊Q₈×C₄₇	1	2	yes	—
520	C₄	C₄₇×#525	1	2	yes	—
521	C₂	—	2	1	no	—
522	C₂	—	2	1	no	—
523	C₂	—	4	4	no	—
524	C₂	C₄₇×#2848	1	1	yes	characteristic
525	C₂	C₄₇×#3018	1	1	yes	characteristic
526	C₂	C₄₇×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×2₋¹⁺⁴×C₄₇	C₂²
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
2. C₄₇×#3080	C₂	semidirect
3. C₄₇×#2565	C₂	semidirect
4. C₄₇×#1860	C₂	semidirect
5. C₄₇×#1859	C₂	semidirect
6. C₄₇×#1857	C₂	semidirect
7. C₄₇×#1857	C₂	semidirect
8. C₄₇×#1806	C₂	semidirect
9. C₄₇×#1801	C₂	semidirect
235. #32974	C₄₇	direct (N × H)
259. #3080	C₂×C₄₇	semidirect
260. #2565	C₂×C₄₇	semidirect
261. #1860	C₂×C₄₇	semidirect
262. #1859	C₂×C₄₇	semidirect
263. #1857	C₂×C₄₇	semidirect
264. #1857	C₂×C₄₇	semidirect
265. #1806	C₂×C₄₇	semidirect
266. #1801	C₂×C₄₇	semidirect
310. C₄₇	#32974	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄×2₋¹⁺⁴×C₄₇	2
C₄₇×#3080	2
C₄₇×#2565	2
C₄₇×#1860	2
C₄₇×#1859	2
C₄₇×#1857	2
C₄₇×#1806	2
C₄₇×#1801	2
C₄₇×#1793	2
#32974	47

Subgroups — C47×#32974 #26072672

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#32974 #26072672