Subgroups — C₄₇×#25677 #26065375

Order 12032.

1038 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	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#501	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#491	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2851	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#2036	C₂	1	2	yes	maximal
6	C₄₇×#2035	C₂	1	2	yes	maximal
7	C₄₇×#1993	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1960	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1865	C₂	1	2	yes	maximal, complemented
10	C₄₇×#1863	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1749	C₂	1	1	yes	maximal, characteristic
12	C₄₇×#533	—	2	4	no	—
13	C₄₇×#533	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#125×C₄₇	—	2	1	no	—
17	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
19	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
20	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
21	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
22	C₂×#117×C₄₇	—	2	1	no	—
23	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
24	C₄₇×#501	—	2	4	no	—
25	C₄₇×#491	—	2	4	no	—
26	C₂×#107×C₄₇	C₂²	1	2	yes	—
27	C₂×#106×C₄₇	C₂²	1	2	yes	—
28	C₂×#103×C₄₇	C₂²	1	2	yes	—
29	C₂×#103×C₄₇	C₂²	1	2	yes	—
30	C₂×#103×C₄₇	C₂²	1	2	yes	—
31	C₂×#103×C₄₇	C₂²	1	2	yes	—
32	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
33	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
35	C₄₇×#389	C₂²	1	1	yes	characteristic
36	C₄₇×#389	C₂²	1	1	yes	characteristic
37	C₄₇×#387	—	2	1	no	—
38	C₄₇×#387	—	2	1	no	—
39	C₄₇×#385	—	2	1	no	—
40	C₄₇×#385	—	2	1	no	—
41	C₄₇×#382	C₂²	1	1	yes	characteristic
42	C₄₇×#380	C₂²	1	1	yes	characteristic
43	C₄₇×#380	C₂²	1	1	yes	characteristic
44	C₄₇×#340	C₂²	1	2	yes	—
45	C₄₇×#340	C₂²	1	2	yes	—
46	C₄₇×#336	C₂²	1	2	yes	—
47	C₂²×Q₈×C₄₇	—	2	1	no	—
48	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
49	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
52	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
53	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
54	C₄⋊Q₈×C₄₇	—	2	2	no	—
55	C₄⋊Q₈×C₄₇	—	2	2	no	—
56	C₄⋊Q₈×C₄₇	D₄	1	4	yes	—
57	C₄⋊Q₈×C₄₇	D₄	1	4	yes	—
58	#125×C₄₇	—	2	8	no	—
59	#125×C₄₇	—	2	2	no	—
60	#125×C₄₇	—	2	2	no	—
61	C₂²⋊Q₈×C₄₇	—	2	8	no	—
62	C₂²⋊Q₈×C₄₇	—	2	4	no	—
63	C₂²⋊Q₈×C₄₇	—	2	4	no	—
64	C₄×Q₈×C₄₇	—	2	8	no	—
65	C₄×Q₈×C₄₇	—	2	4	no	—
66	C₄×Q₈×C₄₇	—	2	4	no	—
67	#117×C₄₇	—	2	8	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
72	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
73	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
74	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
75	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
76	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
77	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
79	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
81	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
82	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
83	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
84	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
85	C₂×C₄²×C₄₇	—	2	2	no	—
86	C₂×C₄²×C₄₇	—	2	2	no	—
87	C₂×C₄²×C₄₇	—	2	2	no	—
88	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
89	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
90	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	#107×C₄₇	—	2	4	no	—
93	#106×C₄₇	—	2	4	no	—
94	#103×C₄₇	—	2	4	no	—
95	#103×C₄₇	—	2	4	no	—
96	#103×C₄₇	—	2	4	no	—
97	#103×C₄₇	—	2	4	no	—
98	C₂²⋊C₈×C₄₇	—	2	4	no	—
99	#97×C₄₇	—	2	2	no	—
100	#97×C₄₇	—	2	2	no	—
101	#95×C₄₇	—	2	1	no	—
102	#95×C₄₇	—	2	1	no	—
103	#95×C₄₇	—	2	1	no	—
104	#95×C₄₇	—	2	1	no	—
105	#95×C₄₇	—	2	1	no	—
106	#95×C₄₇	—	2	1	no	—
107	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂×Q₈×C₄₇	—	2	4	no	—
109	C₂×Q₈×C₄₇	—	2	2	no	—
110	C₂×Q₈×C₄₇	—	2	2	no	—
111	C₂×Q₈×C₄₇	—	2	2	no	—
112	C₂×Q₈×C₄₇	—	2	2	no	—
113	C₂×Q₈×C₄₇	—	2	2	no	—
114	C₂×Q₈×C₄₇	—	4	2	no	—
115	C₂×Q₈×C₄₇	—	4	2	no	—
116	C₂×Q₈×C₄₇	C₂×D₄	1	4	yes	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	—	2	2	no	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	2	2	no	—
121	C₂²×C₄×C₄₇	—	2	2	no	—
122	C₂²×C₄×C₄₇	—	2	2	no	—
123	C₂²×C₄×C₄₇	—	2	1	no	—
124	C₂²×C₄×C₄₇	—	2	1	no	—
125	C₂²×C₄×C₄₇	—	2	2	no	—
126	C₂²×C₄×C₄₇	—	2	2	no	—
127	C₂²×C₄×C₄₇	—	2	1	no	—
128	C₂²×C₄×C₄₇	—	2	1	no	—
129	C₂²×C₄×C₄₇	—	2	1	no	—
130	C₂²×C₄×C₄₇	—	2	1	no	—
131	C₂²×C₄×C₄₇	—	4	1	no	—
132	C₂²×C₄×C₄₇	—	4	1	no	—
133	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
137	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
139	C₂×C₈×C₄₇	—	2	2	no	—
140	C₂×C₈×C₄₇	—	2	2	no	—
141	C₂×C₈×C₄₇	—	2	2	no	—
142	C₂×C₈×C₄₇	—	2	2	no	—
143	C₂×C₈×C₄₇	—	2	2	no	—
144	C₂×C₈×C₄₇	#41	1	4	yes	—
145	C₄⋊C₄×C₄₇	—	2	8	no	—
146	C₄⋊C₄×C₄₇	—	2	8	no	—
147	C₄⋊C₄×C₄₇	—	2	4	no	—
148	C₄⋊C₄×C₄₇	—	2	4	no	—
149	C₄⋊C₄×C₄₇	—	2	4	no	—
150	C₄⋊C₄×C₄₇	—	2	2	no	—
151	C₄⋊C₄×C₄₇	—	2	1	no	—
152	C₄⋊C₄×C₄₇	—	2	1	no	—
153	C₄⋊C₄×C₄₇	—	2	1	no	—
154	C₄⋊C₄×C₄₇	—	2	1	no	—
155	C₄⋊C₄×C₄₇	—	2	2	no	—
156	C₄⋊C₄×C₄₇	—	2	2	no	—
157	C₄⋊C₄×C₄₇	—	4	2	no	—
158	C₄⋊C₄×C₄₇	—	4	2	no	—
159	C₄⋊C₄×C₄₇	—	4	2	no	—
160	C₄⋊C₄×C₄₇	—	4	2	no	—
161	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
162	C₂²⋊C₄×C₄₇	—	2	8	no	—
163	C₂²⋊C₄×C₄₇	—	4	2	no	—
164	C₂²⋊C₄×C₄₇	—	4	2	no	—
165	C₄²×C₄₇	—	2	8	no	—
166	C₄²×C₄₇	—	2	2	no	—
167	C₄²×C₄₇	—	2	2	no	—
168	C₄²×C₄₇	—	2	1	no	—
169	C₄²×C₄₇	—	2	1	no	—
170	C₄²×C₄₇	C₂×D₄	1	2	yes	—
171	C₄²×C₄₇	C₂×D₄	1	2	yes	—
172	C₂³×C₄₇	—	2	1	no	—
173	C₂³×C₄₇	—	2	1	no	—
174	C₂³×C₄₇	—	2	1	no	—
175	C₂³×C₄₇	—	2	1	no	—
176	C₂³×C₄₇	—	2	1	no	—
177	C₂³×C₄₇	—	2	1	no	—
178	C₂³×C₄₇	#137	1	2	yes	—
179	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
180	Q₈×C₄₇	—	2	4	no	—
181	Q₈×C₄₇	—	2	4	no	—
182	Q₈×C₄₇	—	4	8	no	—
183	Q₈×C₄₇	—	4	2	no	—
184	Q₈×C₄₇	—	4	2	no	—
185	C₂×C₄×C₄₇	—	2	8	no	—
186	C₂×C₄×C₄₇	—	2	1	no	—
187	C₂×C₄×C₄₇	—	2	1	no	—
188	C₂×C₄×C₄₇	—	2	1	no	—
189	C₂×C₄×C₄₇	—	2	1	no	—
190	C₂×C₄×C₄₇	—	2	1	no	—
191	C₂×C₄×C₄₇	—	2	1	no	—
192	C₂×C₄×C₄₇	—	2	1	no	—
193	C₂×C₄×C₄₇	—	2	1	no	—
194	C₂×C₄×C₄₇	—	2	4	no	—
195	C₂×C₄×C₄₇	—	2	4	no	—
196	C₂×C₄×C₄₇	—	2	1	no	—
197	C₂×C₄×C₄₇	—	2	1	no	—
198	C₂×C₄×C₄₇	—	2	1	no	—
199	C₂×C₄×C₄₇	—	2	1	no	—
200	C₂×C₄×C₄₇	—	4	4	no	—
201	C₂×C₄×C₄₇	—	4	2	no	—
202	C₂×C₄×C₄₇	—	4	2	no	—
203	C₂×C₄×C₄₇	—	4	2	no	—
204	C₂×C₄×C₄₇	—	4	2	no	—
205	C₂×C₄×C₄₇	—	4	2	no	—
206	C₂×C₄×C₄₇	—	4	2	no	—
207	C₂×C₄×C₄₇	—	4	1	no	—
208	C₂×C₄×C₄₇	—	4	1	no	—
209	C₂×C₄×C₄₇	—	4	1	no	—
210	C₂×C₄×C₄₇	—	4	1	no	—
211	C₂×C₄×C₄₇	—	4	1	no	—
212	C₂×C₄×C₄₇	—	4	1	no	—
213	C₂×C₄×C₄₇	—	4	1	no	—
214	C₂×C₄×C₄₇	—	4	1	no	—
215	C₂×C₄×C₄₇	—	4	1	no	—
216	C₂×C₄×C₄₇	—	4	1	no	—
217	C₂×C₄×C₄₇	—	4	1	no	—
218	C₂×C₄×C₄₇	—	4	1	no	—
219	C₂×C₄×C₄₇	#120	1	2	yes	—
220	C₂×C₄×C₄₇	#120	1	2	yes	—
221	C₂×C₄×C₄₇	#137	1	2	yes	—
222	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
224	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
225	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
226	C₈×C₄₇	—	2	4	no	—
227	C₈×C₄₇	—	4	2	no	—
228	#25677	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
229	C₂²×C₄₇	—	2	2	no	—
230	C₂²×C₄₇	—	2	2	no	—
231	C₂²×C₄₇	—	2	2	no	—
232	C₂²×C₄₇	—	4	1	no	—
233	C₂²×C₄₇	—	4	1	no	—
234	C₂²×C₄₇	—	4	1	no	—
235	C₂²×C₄₇	—	4	1	no	—
236	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
237	C₂²×C₄₇	#532	1	1	yes	characteristic
238	C₂²×C₄₇	#536	1	1	yes	characteristic
239	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
240	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
241	C₂²×C₄₇	#575	1	1	yes	characteristic
242	C₂²×C₄₇	#575	1	1	yes	characteristic
243	C₄×C₄₇	—	2	2	no	—
244	C₄×C₄₇	—	2	2	no	—
245	C₄×C₄₇	—	2	2	no	—
246	C₄×C₄₇	—	4	1	no	—
247	C₄×C₄₇	—	4	4	no	—
248	C₄×C₄₇	—	4	1	no	—
249	C₄×C₄₇	—	4	4	no	—
250	C₄×C₄₇	—	8	1	no	—
251	C₄×C₄₇	—	8	1	no	—
252	C₄×C₄₇	—	8	1	no	—
253	C₄×C₄₇	—	8	1	no	—
254	C₄×C₄₇	#547	1	2	yes	—
255	C₄×C₄₇	#548	1	2	yes	—
256	C₂×#533	C₂×C₄₇	1	1	yes	characteristic
257	C₂×#501	C₂×C₄₇	1	1	yes	characteristic, complemented
258	C₂×#491	C₂×C₄₇	1	1	yes	characteristic, complemented
259	#2851	C₂×C₄₇	1	1	yes	characteristic
260	#2036	C₂×C₄₇	1	2	yes	—
261	#2035	C₂×C₄₇	1	2	yes	—
262	#1993	C₂×C₄₇	1	1	yes	characteristic, complemented
263	#1960	C₂×C₄₇	1	1	yes	characteristic, complemented
264	#1865	C₂×C₄₇	1	2	yes	complemented
265	#1863	C₂×C₄₇	1	2	yes	complemented
266	#1749	C₂×C₄₇	1	1	yes	characteristic
267	C₂×C₄₇	—	4	2	no	—
268	C₂×C₄₇	#2432	1	1	yes	characteristic
269	C₂×C₄₇	#3004	1	1	yes	characteristic
270	C₂×C₄₇	#3005	1	1	yes	characteristic
271	C₂×C₄₇	#3172	1	1	yes	characteristic
272	C₂×C₄₇	#3181	1	1	yes	characteristic
273	C₂×C₄₇	#3236	1	1	yes	characteristic
274	C₂×C₄₇	#3237	1	1	yes	characteristic
275	#533	—	2	4	no	—
276	#533	—	2	4	no	—
277	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
278	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
279	C₂×#125	—	2	1	no	—
280	C₂×#125	C₂²×C₄₇	1	1	yes	characteristic
281	C₂×C₂²⋊Q₈	—	2	1	no	—
282	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
283	C₂×C₄×Q₈	—	2	1	no	—
284	C₂×C₄×Q₈	C₂²×C₄₇	1	2	yes	—
285	C₂×#117	—	2	1	no	—
286	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
287	#501	—	2	4	no	—
288	#491	—	2	4	no	—
289	C₂×#107	C₂²×C₄₇	1	2	yes	—
290	C₂×#106	C₂²×C₄₇	1	2	yes	—
291	C₂×#103	C₂²×C₄₇	1	2	yes	—
292	C₂×#103	C₂²×C₄₇	1	2	yes	—
293	C₂×#103	C₂²×C₄₇	1	2	yes	—
294	C₂×#103	C₂²×C₄₇	1	2	yes	—
295	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
296	C₂×#97	C₂²×C₄₇	1	1	yes	characteristic
297	C₂×#97	C₂²×C₄₇	1	1	yes	characteristic
298	#389	C₂²×C₄₇	1	1	yes	characteristic
299	#389	C₂²×C₄₇	1	1	yes	characteristic
300	#387	—	2	1	no	—
301	#387	—	2	1	no	—
302	#385	—	2	1	no	—
303	#385	—	2	1	no	—
304	#382	C₂²×C₄₇	1	1	yes	characteristic
305	#380	C₂²×C₄₇	1	1	yes	characteristic
306	#380	C₂²×C₄₇	1	1	yes	characteristic
307	#340	C₂²×C₄₇	1	2	yes	—
308	#340	C₂²×C₄₇	1	2	yes	—
309	#336	C₂²×C₄₇	1	2	yes	—
310	C₄₇	#25677	1	1	yes	characteristic, direct product factor, Sylow
311	C₂²×Q₈	—	2	1	no	—
312	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
313	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
314	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
315	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
316	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
317	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
318	C₄⋊Q₈	—	2	2	no	—
319	C₄⋊Q₈	—	2	2	no	—
320	C₄⋊Q₈	D₄×C₄₇	1	4	yes	—
321	C₄⋊Q₈	D₄×C₄₇	1	4	yes	—
322	#125	—	2	8	no	—
323	#125	—	2	2	no	—
324	#125	—	2	2	no	—
325	C₂²⋊Q₈	—	2	8	no	—
326	C₂²⋊Q₈	—	2	4	no	—
327	C₂²⋊Q₈	—	2	4	no	—
328	C₄×Q₈	—	2	8	no	—
329	C₄×Q₈	—	2	4	no	—
330	C₄×Q₈	—	2	4	no	—
331	#117	—	2	8	no	—
332	C₂×C₄⋊C₄	—	2	1	no	—
333	C₂×C₄⋊C₄	—	2	1	no	—
334	C₂×C₄⋊C₄	—	2	1	no	—
335	C₂×C₄⋊C₄	—	2	2	no	—
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	1	no	—
338	C₂×C₄⋊C₄	—	2	1	no	—
339	C₂×C₄⋊C₄	—	2	1	no	—
340	C₂×C₄⋊C₄	—	2	1	no	—
341	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
346	C₂×C₂²⋊C₄	—	2	2	no	—
347	C₂×C₂²⋊C₄	—	2	1	no	—
348	C₂×C₂²⋊C₄	—	2	1	no	—
349	C₂×C₄²	—	2	2	no	—
350	C₂×C₄²	—	2	2	no	—
351	C₂×C₄²	—	2	2	no	—
352	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
353	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
354	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
355	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
356	#107	—	2	4	no	—
357	#106	—	2	4	no	—
358	#103	—	2	4	no	—
359	#103	—	2	4	no	—
360	#103	—	2	4	no	—
361	#103	—	2	4	no	—
362	C₂²⋊C₈	—	2	4	no	—
363	#97	—	2	2	no	—
364	#97	—	2	2	no	—
365	#95	—	2	1	no	—
366	#95	—	2	1	no	—
367	#95	—	2	1	no	—
368	#95	—	2	1	no	—
369	#95	—	2	1	no	—
370	#95	—	2	1	no	—
371	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
372	C₂×Q₈	—	2	4	no	—
373	C₂×Q₈	—	2	2	no	—
374	C₂×Q₈	—	2	2	no	—
375	C₂×Q₈	—	2	2	no	—
376	C₂×Q₈	—	2	2	no	—
377	C₂×Q₈	—	2	2	no	—
378	C₂×Q₈	—	4	2	no	—
379	C₂×Q₈	—	4	2	no	—
380	C₂×Q₈	C₂×D₄×C₄₇	1	4	yes	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	2	2	no	—
383	C₂²×C₄	—	2	2	no	—
384	C₂²×C₄	—	2	2	no	—
385	C₂²×C₄	—	2	2	no	—
386	C₂²×C₄	—	2	2	no	—
387	C₂²×C₄	—	2	1	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	2	no	—
390	C₂²×C₄	—	2	2	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	1	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	4	1	no	—
396	C₂²×C₄	—	4	1	no	—
397	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
398	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
399	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
400	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
401	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
402	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
403	C₂×C₈	—	2	2	no	—
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	2	2	no	—
406	C₂×C₈	—	2	2	no	—
407	C₂×C₈	—	2	2	no	—
408	C₂×C₈	#41×C₄₇	1	4	yes	—
409	C₄⋊C₄	—	2	8	no	—
410	C₄⋊C₄	—	2	8	no	—
411	C₄⋊C₄	—	2	4	no	—
412	C₄⋊C₄	—	2	4	no	—
413	C₄⋊C₄	—	2	4	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	2	no	—
420	C₄⋊C₄	—	2	2	no	—
421	C₄⋊C₄	—	4	2	no	—
422	C₄⋊C₄	—	4	2	no	—
423	C₄⋊C₄	—	4	2	no	—
424	C₄⋊C₄	—	4	2	no	—
425	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
426	C₂²⋊C₄	—	2	8	no	—
427	C₂²⋊C₄	—	4	2	no	—
428	C₂²⋊C₄	—	4	2	no	—
429	C₄²	—	2	8	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	2	2	no	—
432	C₄²	—	2	1	no	—
433	C₄²	—	2	1	no	—
434	C₄²	C₂×D₄×C₄₇	1	2	yes	—
435	C₄²	C₂×D₄×C₄₇	1	2	yes	—
436	C₂³	—	2	1	no	—
437	C₂³	—	2	1	no	—
438	C₂³	—	2	1	no	—
439	C₂³	—	2	1	no	—
440	C₂³	—	2	1	no	—
441	C₂³	—	2	1	no	—
442	C₂³	#137×C₄₇	1	2	yes	—
443	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
444	Q₈	—	2	4	no	—
445	Q₈	—	2	4	no	—
446	Q₈	—	4	8	no	—
447	Q₈	—	4	2	no	—
448	Q₈	—	4	2	no	—
449	C₂×C₄	—	2	8	no	—
450	C₂×C₄	—	2	1	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	1	no	—
456	C₂×C₄	—	2	1	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	4	no	—
459	C₂×C₄	—	2	4	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	4	4	no	—
465	C₂×C₄	—	4	2	no	—
466	C₂×C₄	—	4	2	no	—
467	C₂×C₄	—	4	2	no	—
468	C₂×C₄	—	4	2	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	4	2	no	—
471	C₂×C₄	—	4	1	no	—
472	C₂×C₄	—	4	1	no	—
473	C₂×C₄	—	4	1	no	—
474	C₂×C₄	—	4	1	no	—
475	C₂×C₄	—	4	1	no	—
476	C₂×C₄	—	4	1	no	—
477	C₂×C₄	—	4	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	1	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	4	1	no	—
482	C₂×C₄	—	4	1	no	—
483	C₂×C₄	#120×C₄₇	1	2	yes	—
484	C₂×C₄	#120×C₄₇	1	2	yes	—
485	C₂×C₄	#137×C₄₇	1	2	yes	—
486	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
487	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
488	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
489	C₂×C₄	2₋¹⁺⁴×C₄₇	1	2	yes	—
490	C₈	—	2	4	no	—
491	C₈	—	4	2	no	—
492	C₂²	—	2	2	no	—
493	C₂²	—	2	2	no	—
494	C₂²	—	2	2	no	—
495	C₂²	—	4	1	no	—
496	C₂²	—	4	1	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
500	C₂²	C₄₇×#532	1	1	yes	characteristic
501	C₂²	C₄₇×#536	1	1	yes	characteristic
502	C₂²	C₂×#137×C₄₇	1	1	yes	characteristic
503	C₂²	C₂×#137×C₄₇	1	1	yes	characteristic
504	C₂²	C₄₇×#575	1	1	yes	characteristic
505	C₂²	C₄₇×#575	1	1	yes	characteristic
506	C₄	—	2	2	no	—
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	4	1	no	—
510	C₄	—	4	4	no	—
511	C₄	—	4	1	no	—
512	C₄	—	4	4	no	—
513	C₄	—	8	1	no	—
514	C₄	—	8	1	no	—
515	C₄	—	8	1	no	—
516	C₄	—	8	1	no	—
517	C₄	C₄₇×#547	1	2	yes	—
518	C₄	C₄₇×#548	1	2	yes	—
519	C₂	—	4	2	no	—
520	C₂	C₄₇×#2432	1	1	yes	characteristic
521	C₂	C₄₇×#3004	1	1	yes	characteristic
522	C₂	C₄₇×#3005	1	1	yes	characteristic
523	C₂	C₄₇×#3172	1	1	yes	characteristic
524	C₂	C₄₇×#3181	1	1	yes	characteristic
525	C₂	C₄₇×#3236	1	1	yes	characteristic
526	C₂	C₄₇×#3237	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂⁴×C₄₇	C₂×D₄
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂²×C₄²×C₄₇ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
2. C₂×C₄₇×#501	C₂	semidirect
3. C₂×C₄₇×#491	C₂	semidirect
7. C₄₇×#1993	C₂	semidirect
8. C₄₇×#1960	C₂	semidirect
9. C₄₇×#1865	C₂	semidirect
10. C₄₇×#1863	C₂	semidirect
228. #25677	C₄₇	direct (N × H)
257. C₂×#501	C₂×C₄₇	semidirect
258. C₂×#491	C₂×C₄₇	semidirect
262. #1993	C₂×C₄₇	semidirect
263. #1960	C₂×C₄₇	semidirect
264. #1865	C₂×C₄₇	semidirect
265. #1863	C₂×C₄₇	semidirect
310. C₄₇	#25677	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#533	2
C₂×C₄₇×#501	2
C₂×C₄₇×#491	2
C₄₇×#2851	2
C₄₇×#2036	2
C₄₇×#2035	2
C₄₇×#1993	2
C₄₇×#1960	2
C₄₇×#1865	2
C₄₇×#1863	2
C₄₇×#1749	2
#25677	47

Subgroups — C47×#25677 #26065375

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#25677 #26065375