Subgroups — C₄₇×#15119 #26054817

Order 12032.

1246 conjugacy classes of subgroups.

The subgroup lattice has 566 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×#376	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#1446	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1446	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1445	C₂	1	2	yes	maximal
6	C₄₇×#1444	C₂	1	1	yes	maximal, characteristic
7	C₄₇×#1443	C₂	1	2	yes	maximal
8	C₄₇×#1442	C₂	1	1	yes	maximal, characteristic
9	C₄₇×#1436	C₂	1	2	yes	maximal
10	C₄₇×#1434	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1434	C₂	1	2	yes	maximal
12	C₂³×Q₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
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	C₄₇×#391	—	2	4	no	—
19	C₄₇×#376	—	2	4	no	—
20	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×#95×C₄₇	C₂²	1	2	yes	—
25	C₂×#95×C₄₇	C₂²	1	2	yes	—
26	C₂×#95×C₄₇	C₂²	1	2	yes	—
27	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×#95×C₄₇	C₂²	1	2	yes	—
29	C₂×#95×C₄₇	C₂²	1	2	yes	—
30	C₂×#95×C₄₇	C₂²	1	2	yes	—
31	C₂×#95×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×#95×C₄₇	C₂²	1	2	yes	—
33	C₂×#95×C₄₇	C₂²	1	2	yes	—
34	C₂×#95×C₄₇	C₂²	1	2	yes	—
35	C₂×#95×C₄₇	C₂²	1	2	yes	—
36	C₂×#95×C₄₇	C₂²	1	2	yes	—
37	C₂²×Q₈×C₄₇	—	2	2	no	—
38	C₂²×Q₈×C₄₇	—	2	4	no	—
39	C₂²×Q₈×C₄₇	—	2	2	no	—
40	C₂²×Q₈×C₄₇	—	2	2	no	—
41	C₂²×Q₈×C₄₇	—	4	2	no	—
42	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
43	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
44	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
46	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
47	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
50	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
51	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
52	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
53	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
56	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
57	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
58	C₂×C₄²×C₄₇	—	2	2	no	—
59	C₂×C₄²×C₄₇	—	2	2	no	—
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	2	no	—
65	C₂×C₄²×C₄₇	D₄	1	4	yes	—
66	C₂×C₄²×C₄₇	Q₈	1	4	yes	complemented
67	#95×C₄₇	—	2	2	no	—
68	#95×C₄₇	—	2	2	no	—
69	#95×C₄₇	—	2	2	no	—
70	#95×C₄₇	—	2	2	no	—
71	#95×C₄₇	—	2	4	no	—
72	#95×C₄₇	—	2	4	no	—
73	#95×C₄₇	—	2	4	no	—
74	#95×C₄₇	—	2	2	no	—
75	#95×C₄₇	—	2	4	no	—
76	#95×C₄₇	—	2	4	no	—
77	#95×C₄₇	—	2	4	no	—
78	#95×C₄₇	—	2	4	no	—
79	#95×C₄₇	—	2	4	no	—
80	#95×C₄₇	—	2	2	no	—
81	#95×C₄₇	—	4	2	no	—
82	#95×C₄₇	—	4	2	no	—
83	#95×C₄₇	—	4	2	no	—
84	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
85	C₂×Q₈×C₄₇	—	2	8	no	—
86	C₂×Q₈×C₄₇	—	4	8	no	—
87	C₂×Q₈×C₄₇	—	4	8	no	—
88	C₂×Q₈×C₄₇	—	4	4	no	—
89	C₂×Q₈×C₄₇	—	4	4	no	—
90	C₂²×C₄×C₄₇	—	2	1	no	—
91	C₂²×C₄×C₄₇	—	2	1	no	—
92	C₂²×C₄×C₄₇	—	2	1	no	—
93	C₂²×C₄×C₄₇	—	2	1	no	—
94	C₂²×C₄×C₄₇	—	2	2	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	1	no	—
97	C₂²×C₄×C₄₇	—	2	1	no	—
98	C₂²×C₄×C₄₇	—	2	1	no	—
99	C₂²×C₄×C₄₇	—	2	1	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	—	2	1	no	—
106	C₂²×C₄×C₄₇	—	2	1	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	2	no	—
113	C₂²×C₄×C₄₇	—	2	2	no	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	—	2	2	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	2	no	—
122	C₂²×C₄×C₄₇	—	2	2	no	—
123	C₂²×C₄×C₄₇	—	2	2	no	—
124	C₂²×C₄×C₄₇	—	2	2	no	—
125	C₂²×C₄×C₄₇	—	2	2	no	—
126	C₂²×C₄×C₄₇	—	2	2	no	—
127	C₂²×C₄×C₄₇	—	2	2	no	—
128	C₂²×C₄×C₄₇	—	2	2	no	—
129	C₂²×C₄×C₄₇	—	2	2	no	—
130	C₂²×C₄×C₄₇	—	2	2	no	—
131	C₂²×C₄×C₄₇	—	2	2	no	—
132	C₂²×C₄×C₄₇	—	2	2	no	—
133	C₂²×C₄×C₄₇	—	2	2	no	—
134	C₂²×C₄×C₄₇	—	2	2	no	—
135	C₂²×C₄×C₄₇	—	2	2	no	—
136	C₂²×C₄×C₄₇	—	2	2	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	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
144	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
145	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
146	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
147	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
148	C₂²×C₄×C₄₇	#41	1	2	yes	—
149	C₂²×C₄×C₄₇	#41	1	2	yes	—
150	C₂²×C₄×C₄₇	#41	1	4	yes	—
151	C₂²×C₄×C₄₇	#41	1	4	yes	—
152	C₂²×C₄×C₄₇	#41	1	2	yes	—
153	C₂²×C₄×C₄₇	#41	1	2	yes	—
154	C₂²×C₄×C₄₇	#41	1	2	yes	—
155	C₄⋊C₄×C₄₇	—	4	8	no	—
156	C₄⋊C₄×C₄₇	—	4	4	no	—
157	C₄²×C₄₇	—	2	8	no	—
158	C₄²×C₄₇	—	2	8	no	—
159	C₄²×C₄₇	—	2	8	no	—
160	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
162	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
163	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
164	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
165	C₂³×C₄₇	C₂×#41	1	2	yes	—
166	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
167	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
168	C₂³×C₄₇	C₂×#41	1	2	yes	—
169	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
170	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
171	Q₈×C₄₇	—	4	16	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	2	no	—
180	C₂×C₄×C₄₇	—	2	4	no	—
181	C₂×C₄×C₄₇	—	2	4	no	—
182	C₂×C₄×C₄₇	—	2	2	no	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	2	2	no	—
185	C₂×C₄×C₄₇	—	2	2	no	—
186	C₂×C₄×C₄₇	—	2	2	no	—
187	C₂×C₄×C₄₇	—	2	4	no	—
188	C₂×C₄×C₄₇	—	2	4	no	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	4	no	—
191	C₂×C₄×C₄₇	—	2	2	no	—
192	C₂×C₄×C₄₇	—	2	4	no	—
193	C₂×C₄×C₄₇	—	2	4	no	—
194	C₂×C₄×C₄₇	—	2	4	no	—
195	C₂×C₄×C₄₇	—	2	4	no	—
196	C₂×C₄×C₄₇	—	2	4	no	—
197	C₂×C₄×C₄₇	—	2	4	no	—
198	C₂×C₄×C₄₇	—	2	4	no	—
199	C₂×C₄×C₄₇	—	4	2	no	—
200	C₂×C₄×C₄₇	—	4	1	no	—
201	C₂×C₄×C₄₇	—	4	1	no	—
202	C₂×C₄×C₄₇	—	4	2	no	—
203	C₂×C₄×C₄₇	—	4	2	no	—
204	C₂×C₄×C₄₇	—	4	1	no	—
205	C₂×C₄×C₄₇	—	4	1	no	—
206	C₂×C₄×C₄₇	—	4	1	no	—
207	C₂×C₄×C₄₇	—	4	1	no	—
208	C₂×C₄×C₄₇	—	4	2	no	—
209	C₂×C₄×C₄₇	—	4	1	no	—
210	C₂×C₄×C₄₇	—	4	1	no	—
211	C₂×C₄×C₄₇	—	4	2	no	—
212	C₂×C₄×C₄₇	—	4	2	no	—
213	C₂×C₄×C₄₇	—	4	2	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	2	no	—
218	C₂×C₄×C₄₇	—	4	2	no	—
219	C₂×C₄×C₄₇	—	4	2	no	—
220	C₂×C₄×C₄₇	—	4	2	no	—
221	C₂×C₄×C₄₇	—	4	2	no	—
222	C₂×C₄×C₄₇	—	4	2	no	—
223	C₂×C₄×C₄₇	—	4	2	no	—
224	C₂×C₄×C₄₇	—	4	2	no	—
225	C₂×C₄×C₄₇	—	4	2	no	—
226	C₂×C₄×C₄₇	—	4	2	no	—
227	C₂×C₄×C₄₇	—	4	2	no	—
228	C₂×C₄×C₄₇	—	4	2	no	—
229	C₂×C₄×C₄₇	—	4	2	no	—
230	C₂×C₄×C₄₇	—	4	2	no	—
231	C₂×C₄×C₄₇	—	4	2	no	—
232	C₂×C₄×C₄₇	—	4	2	no	—
233	C₂×C₄×C₄₇	—	4	2	no	—
234	C₂×C₄×C₄₇	—	4	2	no	—
235	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
236	C₂×C₄×C₄₇	#123	1	4	yes	—
237	#15119	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
238	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
239	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
240	C₂²×C₄₇	#525	1	1	yes	characteristic
241	C₂²×C₄₇	#525	1	1	yes	characteristic
242	C₂²×C₄₇	#529	1	1	yes	characteristic
243	C₂²×C₄₇	#529	1	1	yes	characteristic
244	C₂²×C₄₇	#529	1	2	yes	—
245	C₂²×C₄₇	#532	1	1	yes	characteristic
246	C₂²×C₄₇	#533	1	1	yes	characteristic
247	C₂²×C₄₇	#533	1	1	yes	characteristic
248	C₂²×C₄₇	#533	1	2	yes	—
249	C₂²×C₄₇	#535	1	1	yes	characteristic
250	C₂²×C₄₇	#536	1	1	yes	characteristic
251	C₂²×C₄₇	#542	1	2	yes	—
252	C₂²×C₄₇	#544	1	2	yes	—
253	C₂²×C₄₇	#551	1	2	yes	—
254	C₂²×C₄₇	#551	1	2	yes	—
255	C₂²×C₄₇	#551	1	2	yes	—
256	C₂²×C₄₇	#552	1	2	yes	—
257	C₂²×C₄₇	#552	1	2	yes	—
258	C₂²×C₄₇	#555	1	2	yes	—
259	C₂²×C₄₇	#556	1	2	yes	—
260	C₂²×C₄₇	#556	1	2	yes	—
261	C₄×C₄₇	—	2	4	no	—
262	C₄×C₄₇	—	2	4	no	—
263	C₄×C₄₇	—	4	2	no	—
264	C₄×C₄₇	—	4	2	no	—
265	C₄×C₄₇	—	4	2	no	—
266	C₄×C₄₇	—	4	2	no	—
267	C₄×C₄₇	—	4	4	no	—
268	C₄×C₄₇	—	4	2	no	—
269	C₄×C₄₇	—	4	4	no	—
270	C₄×C₄₇	—	8	2	no	—
271	C₄×C₄₇	—	8	2	no	—
272	C₂×#391	C₂×C₄₇	1	1	yes	characteristic
273	C₂×#376	C₂×C₄₇	1	1	yes	characteristic
274	#1446	C₂×C₄₇	1	1	yes	characteristic
275	#1446	C₂×C₄₇	1	1	yes	characteristic
276	#1445	C₂×C₄₇	1	2	yes	—
277	#1444	C₂×C₄₇	1	1	yes	characteristic
278	#1443	C₂×C₄₇	1	2	yes	—
279	#1442	C₂×C₄₇	1	1	yes	characteristic
280	#1436	C₂×C₄₇	1	2	yes	—
281	#1434	C₂×C₄₇	1	1	yes	characteristic
282	#1434	C₂×C₄₇	1	2	yes	—
283	C₂×C₄₇	#2396	1	1	yes	characteristic
284	C₂×C₄₇	#2482	1	1	yes	characteristic
285	C₂×C₄₇	#2499	1	1	yes	characteristic
286	C₂×C₄₇	#2527	1	2	yes	—
287	C₂×C₄₇	#2532	1	2	yes	—
288	C₂×C₄₇	#2599	1	1	yes	characteristic
289	C₂×C₄₇	#2605	1	2	yes	—
290	C₂×C₄₇	#2610	1	1	yes	characteristic
291	C₂×C₄₇	#2612	1	2	yes	—
292	C₂×C₄₇	#2628	1	1	yes	characteristic
293	C₂×C₄₇	#2855	1	1	yes	characteristic
294	C₂³×Q₈	C₂²×C₄₇	1	1	yes	characteristic
295	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
296	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
297	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
298	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
299	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
300	#391	—	2	4	no	—
301	#376	—	2	4	no	—
302	C₂×#95	C₂²×C₄₇	1	2	yes	—
303	C₂×#95	C₂²×C₄₇	1	2	yes	—
304	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
305	C₂×#95	C₂²×C₄₇	1	2	yes	—
306	C₂×#95	C₂²×C₄₇	1	2	yes	—
307	C₂×#95	C₂²×C₄₇	1	2	yes	—
308	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
309	C₂×#95	C₂²×C₄₇	1	2	yes	—
310	C₂×#95	C₂²×C₄₇	1	2	yes	—
311	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
312	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
313	C₂×#95	C₂²×C₄₇	1	2	yes	—
314	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
315	C₂×#95	C₂²×C₄₇	1	1	yes	characteristic
316	C₂×#95	C₂²×C₄₇	1	2	yes	—
317	C₂×#95	C₂²×C₄₇	1	2	yes	—
318	C₂×#95	C₂²×C₄₇	1	2	yes	—
319	C₄₇	#15119	1	1	yes	characteristic, direct product factor, Sylow
320	C₂²×Q₈	—	2	2	no	—
321	C₂²×Q₈	—	2	4	no	—
322	C₂²×Q₈	—	2	2	no	—
323	C₂²×Q₈	—	2	2	no	—
324	C₂²×Q₈	—	4	2	no	—
325	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
326	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
327	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
328	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
329	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
330	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
331	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
332	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
333	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
334	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
335	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
336	C₂×C₄⋊C₄	—	2	2	no	—
337	C₂×C₄⋊C₄	—	2	4	no	—
338	C₂×C₄⋊C₄	—	2	4	no	—
339	C₂×C₄⋊C₄	—	4	2	no	—
340	C₂×C₄⋊C₄	—	4	2	no	—
341	C₂×C₄²	—	2	2	no	—
342	C₂×C₄²	—	2	2	no	—
343	C₂×C₄²	—	2	2	no	—
344	C₂×C₄²	—	2	2	no	—
345	C₂×C₄²	—	2	2	no	—
346	C₂×C₄²	—	2	2	no	—
347	C₂×C₄²	—	2	2	no	—
348	C₂×C₄²	D₄×C₄₇	1	4	yes	—
349	C₂×C₄²	Q₈×C₄₇	1	4	yes	complemented
350	#95	—	2	2	no	—
351	#95	—	2	2	no	—
352	#95	—	2	2	no	—
353	#95	—	2	2	no	—
354	#95	—	2	4	no	—
355	#95	—	2	4	no	—
356	#95	—	2	4	no	—
357	#95	—	2	2	no	—
358	#95	—	2	4	no	—
359	#95	—	2	4	no	—
360	#95	—	2	4	no	—
361	#95	—	2	4	no	—
362	#95	—	2	4	no	—
363	#95	—	2	2	no	—
364	#95	—	4	2	no	—
365	#95	—	4	2	no	—
366	#95	—	4	2	no	—
367	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
368	C₂×Q₈	—	2	8	no	—
369	C₂×Q₈	—	4	8	no	—
370	C₂×Q₈	—	4	8	no	—
371	C₂×Q₈	—	4	4	no	—
372	C₂×Q₈	—	4	4	no	—
373	C₂²×C₄	—	2	1	no	—
374	C₂²×C₄	—	2	1	no	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	1	no	—
377	C₂²×C₄	—	2	2	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	1	no	—
381	C₂²×C₄	—	2	1	no	—
382	C₂²×C₄	—	2	1	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	2	no	—
388	C₂²×C₄	—	2	2	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	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	2	no	—
398	C₂²×C₄	—	2	2	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	2	no	—
402	C₂²×C₄	—	2	2	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	—	2	2	no	—
409	C₂²×C₄	—	2	2	no	—
410	C₂²×C₄	—	2	2	no	—
411	C₂²×C₄	—	2	2	no	—
412	C₂²×C₄	—	2	2	no	—
413	C₂²×C₄	—	2	2	no	—
414	C₂²×C₄	—	2	2	no	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	2	no	—
417	C₂²×C₄	—	2	2	no	—
418	C₂²×C₄	—	2	2	no	—
419	C₂²×C₄	—	2	2	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	2	2	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	2	2	no	—
425	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
426	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
427	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
428	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
429	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
430	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
431	C₂²×C₄	#41×C₄₇	1	2	yes	—
432	C₂²×C₄	#41×C₄₇	1	4	yes	—
433	C₂²×C₄	#41×C₄₇	1	4	yes	—
434	C₂²×C₄	#41×C₄₇	1	2	yes	—
435	C₂²×C₄	#41×C₄₇	1	2	yes	—
436	C₂²×C₄	#41×C₄₇	1	2	yes	—
437	C₂²×C₄	#41×C₄₇	1	2	yes	—
438	C₄⋊C₄	—	4	8	no	—
439	C₄⋊C₄	—	4	4	no	—
440	C₄²	—	2	8	no	—
441	C₄²	—	2	8	no	—
442	C₄²	—	2	8	no	—
443	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
444	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
445	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
446	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
447	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
448	C₂³	C₂×#41×C₄₇	1	2	yes	—
449	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
450	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
451	C₂³	C₂×#41×C₄₇	1	2	yes	—
452	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
453	C₂³	2₋¹⁺⁴×C₄₇	1	2	yes	—
454	Q₈	—	4	16	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	2	no	—
458	C₂×C₄	—	2	2	no	—
459	C₂×C₄	—	2	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	4	no	—
464	C₂×C₄	—	2	4	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	4	no	—
471	C₂×C₄	—	2	4	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	4	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	4	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	4	no	—
478	C₂×C₄	—	2	4	no	—
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	4	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	2	no	—
486	C₂×C₄	—	4	2	no	—
487	C₂×C₄	—	4	1	no	—
488	C₂×C₄	—	4	1	no	—
489	C₂×C₄	—	4	1	no	—
490	C₂×C₄	—	4	1	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	1	no	—
493	C₂×C₄	—	4	1	no	—
494	C₂×C₄	—	4	2	no	—
495	C₂×C₄	—	4	2	no	—
496	C₂×C₄	—	4	2	no	—
497	C₂×C₄	—	4	2	no	—
498	C₂×C₄	—	4	2	no	—
499	C₂×C₄	—	4	2	no	—
500	C₂×C₄	—	4	2	no	—
501	C₂×C₄	—	4	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	4	2	no	—
510	C₂×C₄	—	4	2	no	—
511	C₂×C₄	—	4	2	no	—
512	C₂×C₄	—	4	2	no	—
513	C₂×C₄	—	4	2	no	—
514	C₂×C₄	—	4	2	no	—
515	C₂×C₄	—	4	2	no	—
516	C₂×C₄	—	4	2	no	—
517	C₂×C₄	—	4	2	no	—
518	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
519	C₂×C₄	#123×C₄₇	1	4	yes	—
520	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
521	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
522	C₂²	C₄₇×#525	1	1	yes	characteristic
523	C₂²	C₄₇×#525	1	1	yes	characteristic
524	C₂²	C₄₇×#529	1	1	yes	characteristic
525	C₂²	C₄₇×#529	1	2	yes	—
526	C₂²	C₄₇×#529	1	1	yes	characteristic
527	C₂²	C₄₇×#532	1	1	yes	characteristic
528	C₂²	C₄₇×#533	1	1	yes	characteristic
529	C₂²	C₄₇×#533	1	1	yes	characteristic
530	C₂²	C₄₇×#533	1	2	yes	—
531	C₂²	C₄₇×#535	1	1	yes	characteristic
532	C₂²	C₄₇×#536	1	1	yes	characteristic
533	C₂²	C₄₇×#542	1	2	yes	—
534	C₂²	C₄₇×#544	1	2	yes	—
535	C₂²	C₄₇×#551	1	2	yes	—
536	C₂²	C₄₇×#551	1	2	yes	—
537	C₂²	C₄₇×#551	1	2	yes	—
538	C₂²	C₄₇×#552	1	2	yes	—
539	C₂²	C₄₇×#552	1	2	yes	—
540	C₂²	C₄₇×#555	1	2	yes	—
541	C₂²	C₄₇×#556	1	2	yes	—
542	C₂²	C₄₇×#556	1	2	yes	—
543	C₄	—	2	4	no	—
544	C₄	—	2	4	no	—
545	C₄	—	4	4	no	—
546	C₄	—	4	2	no	—
547	C₄	—	4	2	no	—
548	C₄	—	4	2	no	—
549	C₄	—	4	2	no	—
550	C₄	—	4	4	no	—
551	C₄	—	4	2	no	—
552	C₄	—	8	2	no	—
553	C₄	—	8	2	no	—
554	C₂	C₄₇×#2396	1	1	yes	characteristic
555	C₂	C₄₇×#2482	1	1	yes	characteristic
556	C₂	C₄₇×#2499	1	1	yes	characteristic
557	C₂	C₄₇×#2527	1	2	yes	—
558	C₂	C₄₇×#2532	1	2	yes	—
559	C₂	C₄₇×#2599	1	1	yes	characteristic
560	C₂	C₄₇×#2605	1	2	yes	—
561	C₂	C₄₇×#2610	1	1	yes	characteristic
562	C₂	C₄₇×#2612	1	2	yes	—
563	C₂	C₄₇×#2628	1	1	yes	characteristic
564	C₂	C₄₇×#2855	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
66. C₂×C₄²×C₄₇	Q₈	semidirect
237. #15119	C₄₇	direct (N × H)
319. C₄₇	#15119	direct (N × H)
349. C₂×C₄²	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×#376	2
C₄₇×#1446	2
C₄₇×#1445	2
C₄₇×#1444	2
C₄₇×#1443	2
C₄₇×#1442	2
C₄₇×#1436	2
C₄₇×#1434	2
#15119	47

Subgroups — C47×#15119 #26054817

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#15119 #26054817