Subgroups — C₄₇×#14000 #26053698

Order 12032.

1534 conjugacy classes of subgroups.

The subgroup lattice has 514 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#391	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#391	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₇×#391	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇×#384	C₂	1	1	yes	maximal, characteristic
5	C₂×C₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic
6	C₄₇×#1442	C₂	1	4	yes	maximal
7	C₄₇×#1436	C₂	1	4	yes	maximal
8	C₄₇×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
9	C₄×#95×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
12	C₂²×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
13	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
16	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄²×C₄₇	C₂²	1	2	yes	—
19	C₄₇×#391	—	2	4	no	—
20	C₄₇×#391	—	2	4	no	—
21	C₄₇×#391	C₄	1	8	yes	complemented
22	C₄₇×#384	—	2	4	no	—
23	C₄×C₄⋊C₄×C₄₇	—	2	4	no	—
24	C₂×#95×C₄₇	C₂²	1	2	yes	—
25	C₂×#95×C₄₇	C₂²	1	2	yes	—
26	C₂×#95×C₄₇	C₂²	1	4	yes	—
27	C₂×#95×C₄₇	C₂²	1	2	yes	—
28	C₂×#95×C₄₇	C₂²	1	2	yes	—
29	C₂×#95×C₄₇	C₂²	1	4	yes	—
30	C₂×#95×C₄₇	C₂²	1	4	yes	—
31	C₂×#95×C₄₇	C₂²	1	2	yes	—
32	C₂²×Q₈×C₄₇	—	2	2	no	—
33	C₂²×Q₈×C₄₇	—	2	2	no	—
34	C₂²×Q₈×C₄₇	—	2	2	no	—
35	C₂²×Q₈×C₄₇	—	2	2	no	—
36	C₂²×Q₈×C₄₇	—	2	2	no	—
37	C₂²×Q₈×C₄₇	—	2	2	no	—
38	C₂²×Q₈×C₄₇	C₂×C₄	1	4	yes	—
39	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
40	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
41	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
42	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
43	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
45	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
46	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
48	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
49	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
53	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
57	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
58	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
59	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
60	C₂×C₄²×C₄₇	—	2	2	no	—
61	C₂×C₄²×C₄₇	—	2	2	no	—
62	C₂×C₄²×C₄₇	—	2	2	no	—
63	C₂×C₄²×C₄₇	—	2	2	no	—
64	C₂×C₄²×C₄₇	—	2	4	no	—
65	C₂×C₄²×C₄₇	—	2	2	no	—
66	C₂×C₄²×C₄₇	—	2	2	no	—
67	C₂×C₄²×C₄₇	—	2	2	no	—
68	C₂×C₄²×C₄₇	—	4	4	no	—
69	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
70	C₂×C₄²×C₄₇	D₄	1	4	yes	—
71	#95×C₄₇	—	2	4	no	—
72	#95×C₄₇	—	2	8	no	—
73	#95×C₄₇	—	2	4	no	—
74	#95×C₄₇	—	2	4	no	—
75	#95×C₄₇	—	2	4	no	—
76	#95×C₄₇	—	4	4	no	—
77	#95×C₄₇	C₂×C₄	1	16	yes	—
78	#95×C₄₇	Q₈	1	8	yes	complemented
79	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
80	C₂×Q₈×C₄₇	—	2	8	no	—
81	C₂×Q₈×C₄₇	—	2	8	no	—
82	C₂×Q₈×C₄₇	—	2	8	no	—
83	C₂×Q₈×C₄₇	—	4	4	no	—
84	C₂×Q₈×C₄₇	—	4	4	no	—
85	C₂×Q₈×C₄₇	—	4	4	no	—
86	C₂×Q₈×C₄₇	—	4	4	no	—
87	C₂²×C₄×C₄₇	—	2	2	no	—
88	C₂²×C₄×C₄₇	—	2	2	no	—
89	C₂²×C₄×C₄₇	—	2	1	no	—
90	C₂²×C₄×C₄₇	—	2	1	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	—	2	2	no	—
105	C₂²×C₄×C₄₇	—	2	4	no	—
106	C₂²×C₄×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	—	2	2	no	—
111	C₂²×C₄×C₄₇	—	2	2	no	—
112	C₂²×C₄×C₄₇	—	2	4	no	—
113	C₂²×C₄×C₄₇	—	2	4	no	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	—	2	4	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
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	4	no	—
122	C₂²×C₄×C₄₇	—	2	4	no	—
123	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
124	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
125	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
126	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
127	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
128	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
129	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
130	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
131	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
133	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
134	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
135	C₂²×C₄×C₄₇	#41	1	4	yes	—
136	C₂²×C₄×C₄₇	#41	1	2	yes	—
137	C₂²×C₄×C₄₇	#41	1	2	yes	—
138	C₂²×C₄×C₄₇	#41	1	2	yes	—
139	C₂²×C₄×C₄₇	#41	1	2	yes	—
140	C₄⋊C₄×C₄₇	—	2	8	no	—
141	C₄⋊C₄×C₄₇	—	2	8	no	—
142	C₄⋊C₄×C₄₇	—	4	16	no	—
143	C₄⋊C₄×C₄₇	—	4	4	no	—
144	C₄²×C₄₇	—	2	8	no	—
145	C₄²×C₄₇	—	2	8	no	—
146	C₄²×C₄₇	—	4	8	no	—
147	C₄²×C₄₇	—	4	4	no	—
148	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
149	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
150	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
151	C₂³×C₄₇	C₂²×Q₈	1	2	yes	—
152	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
153	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
154	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
155	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
156	C₂³×C₄₇	C₂×#41	1	2	yes	—
157	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
158	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
159	Q₈×C₄₇	—	4	16	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	2	4	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	2	no	—
164	C₂×C₄×C₄₇	—	2	4	no	—
165	C₂×C₄×C₄₇	—	2	4	no	—
166	C₂×C₄×C₄₇	—	2	4	no	—
167	C₂×C₄×C₄₇	—	2	4	no	—
168	C₂×C₄×C₄₇	—	2	4	no	—
169	C₂×C₄×C₄₇	—	2	4	no	—
170	C₂×C₄×C₄₇	—	2	4	no	—
171	C₂×C₄×C₄₇	—	2	4	no	—
172	C₂×C₄×C₄₇	—	2	4	no	—
173	C₂×C₄×C₄₇	—	2	4	no	—
174	C₂×C₄×C₄₇	—	2	8	no	—
175	C₂×C₄×C₄₇	—	2	4	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	4	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	2	8	no	—
181	C₂×C₄×C₄₇	—	2	4	no	—
182	C₂×C₄×C₄₇	—	2	4	no	—
183	C₂×C₄×C₄₇	—	4	2	no	—
184	C₂×C₄×C₄₇	—	4	2	no	—
185	C₂×C₄×C₄₇	—	4	2	no	—
186	C₂×C₄×C₄₇	—	4	2	no	—
187	C₂×C₄×C₄₇	—	4	2	no	—
188	C₂×C₄×C₄₇	—	4	2	no	—
189	C₂×C₄×C₄₇	—	4	2	no	—
190	C₂×C₄×C₄₇	—	4	2	no	—
191	C₂×C₄×C₄₇	—	4	2	no	—
192	C₂×C₄×C₄₇	—	4	4	no	—
193	C₂×C₄×C₄₇	—	4	2	no	—
194	C₂×C₄×C₄₇	—	4	2	no	—
195	C₂×C₄×C₄₇	—	4	2	no	—
196	C₂×C₄×C₄₇	—	4	2	no	—
197	C₂×C₄×C₄₇	—	4	2	no	—
198	C₂×C₄×C₄₇	—	4	4	no	—
199	C₂×C₄×C₄₇	—	4	2	no	—
200	C₂×C₄×C₄₇	—	4	2	no	—
201	C₂×C₄×C₄₇	—	4	2	no	—
202	C₂×C₄×C₄₇	—	4	4	no	—
203	C₂×C₄×C₄₇	—	4	4	no	—
204	C₂×C₄×C₄₇	#117	1	4	yes	—
205	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
206	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
207	C₂×C₄×C₄₇	C₄×Q₈	1	8	yes	—
208	C₂×C₄×C₄₇	#121	1	4	yes	—
209	C₂×C₄×C₄₇	#123	1	4	yes	—
210	C₂×C₄×C₄₇	#124	1	4	yes	—
211	C₂×C₄×C₄₇	#126	1	4	yes	—
212	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
213	#14000	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
214	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
215	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
216	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
217	C₂²×C₄₇	C₂×C₄×Q₈	1	2	yes	—
218	C₂²×C₄₇	#520	1	2	yes	—
219	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
220	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
221	C₂²×C₄₇	C₂×#124	1	1	yes	characteristic
222	C₂²×C₄₇	C₂×#126	1	1	yes	characteristic
223	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
224	C₂²×C₄₇	#532	1	1	yes	characteristic
225	C₂²×C₄₇	#533	1	2	yes	—
226	C₂²×C₄₇	#535	1	1	yes	characteristic
227	C₂²×C₄₇	#536	1	1	yes	characteristic
228	C₂²×C₄₇	#542	1	2	yes	—
229	C₂²×C₄₇	#546	1	2	yes	—
230	C₂²×C₄₇	D₄×Q₈	1	2	yes	—
231	C₂²×C₄₇	#552	1	2	yes	—
232	C₂²×C₄₇	#554	1	2	yes	—
233	C₂²×C₄₇	#554	1	2	yes	—
234	C₂²×C₄₇	#556	1	2	yes	—
235	C₂²×C₄₇	#557	1	2	yes	—
236	C₂²×C₄₇	#559	1	2	yes	—
237	C₄×C₄₇	—	2	8	no	—
238	C₄×C₄₇	—	2	4	no	—
239	C₄×C₄₇	—	4	4	no	—
240	C₄×C₄₇	—	4	4	no	—
241	C₄×C₄₇	—	4	2	no	—
242	C₄×C₄₇	—	4	4	no	—
243	C₄×C₄₇	—	4	4	no	—
244	C₄×C₄₇	—	8	2	no	—
245	C₄×C₄₇	#388	1	8	yes	—
246	C₂×#391	C₂×C₄₇	1	1	yes	characteristic
247	C₂×#391	C₂×C₄₇	1	1	yes	characteristic
248	C₂×#391	C₂×C₄₇	1	1	yes	characteristic
249	C₂×#384	C₂×C₄₇	1	1	yes	characteristic
250	C₂×C₄×C₄⋊C₄	C₂×C₄₇	1	1	yes	characteristic
251	#1442	C₂×C₄₇	1	4	yes	—
252	#1436	C₂×C₄₇	1	4	yes	—
253	C₄⋊#95	C₂×C₄₇	1	1	yes	characteristic
254	C₄×#95	C₂×C₄₇	1	1	yes	characteristic
255	C₂×C₄₇	C₂×#388	1	1	yes	characteristic
256	C₂×C₄₇	C₄×C₄⋊Q₈	1	1	yes	characteristic
257	C₂×C₄₇	#2326	1	1	yes	characteristic
258	C₂×C₄₇	#2355	1	2	yes	—
259	C₂×C₄₇	#2360	1	2	yes	—
260	C₂×C₄₇	#2492	1	2	yes	—
261	C₂×C₄₇	#2499	1	1	yes	characteristic
262	C₂×C₄₇	#2502	1	1	yes	characteristic
263	C₂×C₄₇	#2511	1	2	yes	—
264	C₂×C₄₇	#2544	1	1	yes	characteristic
265	C₂×C₄₇	#2546	1	1	yes	characteristic
266	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
267	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
268	C₂²×C₄⋊C₄	C₂²×C₄₇	1	4	yes	—
269	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
270	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
271	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
272	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
273	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
274	C₂²×C₄²	C₂²×C₄₇	1	2	yes	—
275	#391	—	2	4	no	—
276	#391	—	2	4	no	—
277	#391	C₄×C₄₇	1	8	yes	complemented
278	#384	—	2	4	no	—
279	C₄×C₄⋊C₄	—	2	4	no	—
280	C₂×#95	C₂²×C₄₇	1	2	yes	—
281	C₂×#95	C₂²×C₄₇	1	2	yes	—
282	C₂×#95	C₂²×C₄₇	1	4	yes	—
283	C₂×#95	C₂²×C₄₇	1	2	yes	—
284	C₂×#95	C₂²×C₄₇	1	2	yes	—
285	C₂×#95	C₂²×C₄₇	1	4	yes	—
286	C₂×#95	C₂²×C₄₇	1	4	yes	—
287	C₂×#95	C₂²×C₄₇	1	2	yes	—
288	C₄₇	#14000	1	1	yes	characteristic, direct product factor, Sylow
289	C₂²×Q₈	—	2	2	no	—
290	C₂²×Q₈	—	2	2	no	—
291	C₂²×Q₈	—	2	2	no	—
292	C₂²×Q₈	—	2	2	no	—
293	C₂²×Q₈	—	2	2	no	—
294	C₂²×Q₈	—	2	2	no	—
295	C₂²×Q₈	C₂×C₄×C₄₇	1	4	yes	—
296	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
297	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
298	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
299	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
300	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
301	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
302	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
303	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
304	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	2	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	2	no	—
309	C₂×C₄⋊C₄	—	2	8	no	—
310	C₂×C₄⋊C₄	—	2	2	no	—
311	C₂×C₄⋊C₄	—	2	2	no	—
312	C₂×C₄⋊C₄	—	2	8	no	—
313	C₂×C₄⋊C₄	—	2	2	no	—
314	C₂×C₄⋊C₄	—	4	4	no	—
315	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
316	C₂×C₄⋊C₄	D₄×C₄₇	1	4	yes	—
317	C₂×C₄²	—	2	2	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	—	2	2	no	—
321	C₂×C₄²	—	2	4	no	—
322	C₂×C₄²	—	2	2	no	—
323	C₂×C₄²	—	2	2	no	—
324	C₂×C₄²	—	2	2	no	—
325	C₂×C₄²	—	4	4	no	—
326	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
327	C₂×C₄²	D₄×C₄₇	1	4	yes	—
328	#95	—	2	4	no	—
329	#95	—	2	8	no	—
330	#95	—	2	4	no	—
331	#95	—	2	4	no	—
332	#95	—	2	4	no	—
333	#95	—	4	4	no	—
334	#95	C₂×C₄×C₄₇	1	16	yes	—
335	#95	Q₈×C₄₇	1	8	yes	complemented
336	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
337	C₂×Q₈	—	2	8	no	—
338	C₂×Q₈	—	2	8	no	—
339	C₂×Q₈	—	2	8	no	—
340	C₂×Q₈	—	4	4	no	—
341	C₂×Q₈	—	4	4	no	—
342	C₂×Q₈	—	4	4	no	—
343	C₂×Q₈	—	4	4	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	1	no	—
347	C₂²×C₄	—	2	1	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	1	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	4	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	4	no	—
371	C₂²×C₄	—	2	4	no	—
372	C₂²×C₄	—	2	4	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	2	2	no	—
375	C₂²×C₄	—	2	2	no	—
376	C₂²×C₄	—	2	2	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	4	no	—
379	C₂²×C₄	—	2	4	no	—
380	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
381	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
382	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
383	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
384	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
385	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
386	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
387	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
388	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
389	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
390	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
391	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
392	C₂²×C₄	#41×C₄₇	1	4	yes	—
393	C₂²×C₄	#41×C₄₇	1	2	yes	—
394	C₂²×C₄	#41×C₄₇	1	2	yes	—
395	C₂²×C₄	#41×C₄₇	1	2	yes	—
396	C₂²×C₄	#41×C₄₇	1	2	yes	—
397	C₄⋊C₄	—	2	8	no	—
398	C₄⋊C₄	—	2	8	no	—
399	C₄⋊C₄	—	4	16	no	—
400	C₄⋊C₄	—	4	4	no	—
401	C₄²	—	2	8	no	—
402	C₄²	—	2	8	no	—
403	C₄²	—	4	8	no	—
404	C₄²	—	4	4	no	—
405	C₂³	C₂³×C₄×C₄₇	1	1	yes	characteristic
406	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
407	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
408	C₂³	C₂²×Q₈×C₄₇	1	2	yes	—
409	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
410	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
411	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
412	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
413	C₂³	C₂×#41×C₄₇	1	2	yes	—
414	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
415	C₂³	2₋¹⁺⁴×C₄₇	1	2	yes	—
416	Q₈	—	4	16	no	—
417	C₂×C₄	—	2	4	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	4	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	4	no	—
424	C₂×C₄	—	2	4	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	4	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	4	no	—
430	C₂×C₄	—	2	4	no	—
431	C₂×C₄	—	2	8	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	2	no	—
437	C₂×C₄	—	2	8	no	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	4	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	2	no	—
444	C₂×C₄	—	4	2	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	2	no	—
454	C₂×C₄	—	4	2	no	—
455	C₂×C₄	—	4	4	no	—
456	C₂×C₄	—	4	2	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	2	no	—
459	C₂×C₄	—	4	4	no	—
460	C₂×C₄	—	4	4	no	—
461	C₂×C₄	#117×C₄₇	1	4	yes	—
462	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
463	C₂×C₄	C₄×D₄×C₄₇	1	4	yes	—
464	C₂×C₄	C₄×Q₈×C₄₇	1	8	yes	—
465	C₂×C₄	#121×C₄₇	1	4	yes	—
466	C₂×C₄	#123×C₄₇	1	4	yes	—
467	C₂×C₄	#124×C₄₇	1	4	yes	—
468	C₂×C₄	#126×C₄₇	1	4	yes	—
469	C₂×C₄	C₄⋊Q₈×C₄₇	1	4	yes	—
470	C₂²	C₂×#117×C₄₇	1	1	yes	characteristic
471	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
472	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
473	C₂²	C₂×C₄×Q₈×C₄₇	1	2	yes	—
474	C₂²	C₄₇×#520	1	2	yes	—
475	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
476	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
477	C₂²	C₂×#124×C₄₇	1	1	yes	characteristic
478	C₂²	C₂×#126×C₄₇	1	1	yes	characteristic
479	C₂²	C₂×C₄⋊Q₈×C₄₇	1	1	yes	characteristic
480	C₂²	C₄₇×#532	1	1	yes	characteristic
481	C₂²	C₄₇×#533	1	2	yes	—
482	C₂²	C₄₇×#535	1	1	yes	characteristic
483	C₂²	C₄₇×#536	1	1	yes	characteristic
484	C₂²	C₄₇×#542	1	2	yes	—
485	C₂²	C₄₇×#546	1	2	yes	—
486	C₂²	D₄×Q₈×C₄₇	1	2	yes	—
487	C₂²	C₄₇×#552	1	2	yes	—
488	C₂²	C₄₇×#554	1	2	yes	—
489	C₂²	C₄₇×#554	1	2	yes	—
490	C₂²	C₄₇×#556	1	2	yes	—
491	C₂²	C₄₇×#557	1	2	yes	—
492	C₂²	C₄₇×#559	1	2	yes	—
493	C₄	—	2	8	no	—
494	C₄	—	2	4	no	—
495	C₄	—	4	4	no	—
496	C₄	—	4	4	no	—
497	C₄	—	4	4	no	—
498	C₄	—	4	4	no	—
499	C₄	—	4	2	no	—
500	C₄	—	8	2	no	—
501	C₄	C₄₇×#388	1	8	yes	—
502	C₂	C₂×C₄₇×#388	1	1	yes	characteristic
503	C₂	C₄×C₄⋊Q₈×C₄₇	1	1	yes	characteristic
504	C₂	C₄₇×#2326	1	1	yes	characteristic
505	C₂	C₄₇×#2355	1	2	yes	—
506	C₂	C₄₇×#2360	1	2	yes	—
507	C₂	C₄₇×#2492	1	2	yes	—
508	C₂	C₄₇×#2499	1	1	yes	characteristic
509	C₂	C₄₇×#2502	1	1	yes	characteristic
510	C₂	C₄₇×#2511	1	2	yes	—
511	C₂	C₄₇×#2544	1	1	yes	characteristic
512	C₂	C₄₇×#2546	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
21. C₄₇×#391	C₄	semidirect
78. #95×C₄₇	Q₈	semidirect
213. #14000	C₄₇	direct (N × H)
277. #391	C₄×C₄₇	semidirect
288. C₄₇	#14000	direct (N × H)
335. #95	Q₈×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×#391	2
C₂×C₄₇×#384	2
C₂×C₄×C₄⋊C₄×C₄₇	2
C₄₇×#1442	2
C₄₇×#1436	2
C₄₇×C₄⋊#95	2
C₄×#95×C₄₇	2
#14000	47

Subgroups — C47×#14000 #26053698

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#14000 #26053698