Subgroups — C₄₇×#15228 #26054926

Order 12032.

1550 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#125×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#389	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄₇×#384	C₂	1	1	yes	maximal, characteristic
4	C₂×C₄₇×#382	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1444	C₂	1	4	yes	maximal
6	C₄₇×#1441	C₂	1	4	yes	maximal
7	C₄₇×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
8	C₄₇×C₄⋊#95	C₂	1	1	yes	maximal, characteristic
9	C₄×#95×C₄₇	C₂	1	1	yes	maximal, characteristic
10	C₂×#125×C₄₇	—	2	4	no	—
11	C₂×#125×C₄₇	—	2	4	no	—
12	C₂×#125×C₄₇	—	2	4	no	—
13	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
15	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
17	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
21	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
22	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
24	C₄₇×#389	—	2	4	no	—
25	C₄₇×#384	—	2	4	no	—
26	C₄₇×#382	—	2	4	no	—
27	C₂×#95×C₄₇	C₂²	1	4	yes	—
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	4	yes	—
32	C₂×#95×C₄₇	C₂²	1	4	yes	—
33	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
34	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
35	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
36	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
37	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
38	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
39	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
40	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
41	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	#125×C₄₇	—	2	32	no	—
43	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
44	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
45	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
46	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
47	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
48	C₂×C₄⋊C₄×C₄₇	—	2	4	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	2	no	—
53	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
58	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
59	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
61	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
62	C₂×C₄⋊C₄×C₄₇	—	4	4	no	—
63	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
64	C₂×C₄⋊C₄×C₄₇	D₄	1	4	yes	—
65	C₂×C₄⋊C₄×C₄₇	Q₈	1	4	yes	—
66	C₂×C₄²×C₄₇	—	2	2	no	—
67	C₂×C₄²×C₄₇	—	2	2	no	—
68	C₂×C₄²×C₄₇	—	2	2	no	—
69	C₂×C₄²×C₄₇	—	2	2	no	—
70	C₂×C₄²×C₄₇	—	2	2	no	—
71	C₂×C₄²×C₄₇	—	2	2	no	—
72	C₂×C₄²×C₄₇	D₄	1	4	yes	—
73	C₂×C₄²×C₄₇	Q₈	1	4	yes	—
74	C₂×C₄²×C₄₇	Q₈	1	4	yes	—
75	#95×C₄₇	—	2	8	no	—
76	#95×C₄₇	—	2	4	no	—
77	#95×C₄₇	—	2	4	no	—
78	#95×C₄₇	—	2	4	no	—
79	#95×C₄₇	—	2	8	no	—
80	#95×C₄₇	—	4	4	no	—
81	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	—	2	2	no	—
83	C₂²×C₄×C₄₇	—	2	2	no	—
84	C₂²×C₄×C₄₇	—	2	2	no	—
85	C₂²×C₄×C₄₇	—	2	2	no	—
86	C₂²×C₄×C₄₇	—	2	1	no	—
87	C₂²×C₄×C₄₇	—	2	1	no	—
88	C₂²×C₄×C₄₇	—	2	1	no	—
89	C₂²×C₄×C₄₇	—	2	1	no	—
90	C₂²×C₄×C₄₇	—	2	2	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	4	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	—	2	4	no	—
104	C₂²×C₄×C₄₇	—	2	4	no	—
105	C₂²×C₄×C₄₇	—	2	2	no	—
106	C₂²×C₄×C₄₇	—	2	4	no	—
107	C₂²×C₄×C₄₇	—	2	4	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	4	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	4	no	—
116	C₂²×C₄×C₄₇	—	2	4	no	—
117	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
118	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
119	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
120	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
121	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
122	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
123	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
124	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
125	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
126	C₂²×C₄×C₄₇	C₂×Q₈	1	4	yes	—
127	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
128	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
129	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
130	C₂²×C₄×C₄₇	#41	1	4	yes	—
131	C₂²×C₄×C₄₇	#41	1	4	yes	—
132	C₂²×C₄×C₄₇	#41	1	2	yes	—
133	C₄⋊C₄×C₄₇	—	2	16	no	—
134	C₄⋊C₄×C₄₇	—	2	16	no	—
135	C₄⋊C₄×C₄₇	—	2	8	no	—
136	C₄⋊C₄×C₄₇	—	2	8	no	—
137	C₄⋊C₄×C₄₇	—	2	8	no	—
138	C₄⋊C₄×C₄₇	—	4	16	no	—
139	C₄⋊C₄×C₄₇	—	4	8	no	—
140	C₄⋊C₄×C₄₇	—	4	4	no	—
141	C₄²×C₄₇	—	2	8	no	—
142	C₄²×C₄₇	—	2	8	no	—
143	C₄²×C₄₇	—	2	8	no	—
144	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
145	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
146	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
147	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
148	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
149	C₂³×C₄₇	C₂²×Q₈	1	1	yes	characteristic
150	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
151	C₂³×C₄₇	C₂×#41	1	2	yes	—
152	C₂³×C₄₇	C₂×#41	1	2	yes	—
153	C₂³×C₄₇	H(5,𝔽₂)	1	2	yes	—
154	C₂³×C₄₇	2₋¹⁺⁴	1	2	yes	—
155	C₂×C₄×C₄₇	—	2	4	no	—
156	C₂×C₄×C₄₇	—	2	4	no	—
157	C₂×C₄×C₄₇	—	2	4	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	4	no	—
160	C₂×C₄×C₄₇	—	2	4	no	—
161	C₂×C₄×C₄₇	—	2	2	no	—
162	C₂×C₄×C₄₇	—	2	2	no	—
163	C₂×C₄×C₄₇	—	2	4	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	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	4	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	4	no	—
173	C₂×C₄×C₄₇	—	2	8	no	—
174	C₂×C₄×C₄₇	—	2	8	no	—
175	C₂×C₄×C₄₇	—	2	8	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	—	4	2	no	—
179	C₂×C₄×C₄₇	—	4	2	no	—
180	C₂×C₄×C₄₇	—	4	2	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	4	2	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	4	no	—
187	C₂×C₄×C₄₇	—	4	2	no	—
188	C₂×C₄×C₄₇	—	4	4	no	—
189	C₂×C₄×C₄₇	—	4	2	no	—
190	C₂×C₄×C₄₇	—	4	2	no	—
191	C₂×C₄×C₄₇	—	4	4	no	—
192	C₂×C₄×C₄₇	—	4	2	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	4	no	—
197	C₂×C₄×C₄₇	—	4	4	no	—
198	C₂×C₄×C₄₇	#120	1	4	yes	—
199	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
200	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
201	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
202	C₂×C₄×C₄₇	#125	1	8	yes	complemented
203	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
204	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
205	C₂×C₄×C₄₇	C₄⋊Q₈	1	4	yes	—
206	#15228	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
207	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
208	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
209	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
210	C₂²×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
211	C₂²×C₄₇	C₂×#125	1	2	yes	—
212	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
213	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
214	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
215	C₂²×C₄₇	#532	1	1	yes	characteristic
216	C₂²×C₄₇	#532	1	1	yes	characteristic
217	C₂²×C₄₇	#533	1	2	yes	—
218	C₂²×C₄₇	#535	1	1	yes	characteristic
219	C₂²×C₄₇	#536	1	1	yes	characteristic
220	C₂²×C₄₇	#544	1	2	yes	—
221	C₂²×C₄₇	#544	1	2	yes	—
222	C₂²×C₄₇	#546	1	2	yes	—
223	C₂²×C₄₇	#547	1	2	yes	—
224	C₂²×C₄₇	#548	1	2	yes	—
225	C₂²×C₄₇	#550	1	2	yes	—
226	C₂²×C₄₇	#552	1	2	yes	—
227	C₂²×C₄₇	#553	1	2	yes	—
228	C₂²×C₄₇	#554	1	2	yes	—
229	C₂²×C₄₇	#557	1	2	yes	—
230	C₄×C₄₇	—	2	8	no	—
231	C₄×C₄₇	—	4	4	no	—
232	C₄×C₄₇	—	4	2	no	—
233	C₄×C₄₇	—	4	4	no	—
234	C₄×C₄₇	—	4	2	no	—
235	C₄×C₄₇	—	4	4	no	—
236	C₄×C₄₇	—	4	4	no	—
237	C₄×C₄₇	—	8	2	no	—
238	C₄×C₄₇	#395	1	8	yes	—
239	C₂²×#125	C₂×C₄₇	1	1	yes	characteristic
240	C₂×#389	C₂×C₄₇	1	1	yes	characteristic
241	C₂×#384	C₂×C₄₇	1	1	yes	characteristic
242	C₂×#382	C₂×C₄₇	1	1	yes	characteristic
243	#1444	C₂×C₄₇	1	4	yes	—
244	#1441	C₂×C₄₇	1	4	yes	—
245	C₄⋊#95	C₂×C₄₇	1	1	yes	characteristic
246	C₄⋊#95	C₂×C₄₇	1	1	yes	characteristic
247	C₄×#95	C₂×C₄₇	1	1	yes	characteristic
248	C₂×C₄₇	C₂×#395	1	1	yes	characteristic
249	C₂×C₄₇	#2431	1	1	yes	characteristic
250	C₂×C₄₇	#2432	1	1	yes	characteristic
251	C₂×C₄₇	#2441	1	2	yes	—
252	C₂×C₄₇	#2442	1	2	yes	—
253	C₂×C₄₇	#2550	1	2	yes	—
254	C₂×C₄₇	#2552	1	2	yes	—
255	C₂×C₄₇	#2565	1	1	yes	characteristic
256	C₂×C₄₇	#2566	1	1	yes	characteristic
257	C₂×C₄₇	#2660	1	1	yes	characteristic
258	C₂×C₄₇	#2859	1	1	yes	characteristic
259	C₂×#125	—	2	4	no	—
260	C₂×#125	—	2	4	no	—
261	C₂×#125	—	2	4	no	—
262	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
263	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
264	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
265	C₂²×C₄⋊C₄	C₂²×C₄₇	1	4	yes	—
266	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
267	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
268	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
269	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
270	C₂²×C₄²	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	#389	—	2	4	no	—
274	#384	—	2	4	no	—
275	#382	—	2	4	no	—
276	C₂×#95	C₂²×C₄₇	1	2	yes	—
277	C₂×#95	C₂²×C₄₇	1	2	yes	—
278	C₂×#95	C₂²×C₄₇	1	4	yes	—
279	C₂×#95	C₂²×C₄₇	1	2	yes	—
280	C₂×#95	C₂²×C₄₇	1	4	yes	—
281	C₂×#95	C₂²×C₄₇	1	4	yes	—
282	C₄₇	#15228	1	1	yes	characteristic, direct product factor, Sylow
283	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
284	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
285	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
286	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
287	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
288	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
289	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
290	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
291	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
292	#125	—	2	32	no	—
293	C₂×C₄⋊C₄	—	2	4	no	—
294	C₂×C₄⋊C₄	—	2	4	no	—
295	C₂×C₄⋊C₄	—	2	4	no	—
296	C₂×C₄⋊C₄	—	2	4	no	—
297	C₂×C₄⋊C₄	—	2	4	no	—
298	C₂×C₄⋊C₄	—	2	4	no	—
299	C₂×C₄⋊C₄	—	2	2	no	—
300	C₂×C₄⋊C₄	—	2	2	no	—
301	C₂×C₄⋊C₄	—	2	2	no	—
302	C₂×C₄⋊C₄	—	2	2	no	—
303	C₂×C₄⋊C₄	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	—	2	2	no	—
306	C₂×C₄⋊C₄	—	2	8	no	—
307	C₂×C₄⋊C₄	—	2	2	no	—
308	C₂×C₄⋊C₄	—	2	4	no	—
309	C₂×C₄⋊C₄	—	2	2	no	—
310	C₂×C₄⋊C₄	—	2	8	no	—
311	C₂×C₄⋊C₄	—	4	4	no	—
312	C₂×C₄⋊C₄	—	4	4	no	—
313	C₂×C₄⋊C₄	D₄×C₄₇	1	4	yes	—
314	C₂×C₄⋊C₄	D₄×C₄₇	1	4	yes	—
315	C₂×C₄⋊C₄	Q₈×C₄₇	1	4	yes	—
316	C₂×C₄²	—	2	2	no	—
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	2	no	—
322	C₂×C₄²	D₄×C₄₇	1	4	yes	—
323	C₂×C₄²	Q₈×C₄₇	1	4	yes	—
324	C₂×C₄²	Q₈×C₄₇	1	4	yes	—
325	#95	—	2	8	no	—
326	#95	—	2	4	no	—
327	#95	—	2	4	no	—
328	#95	—	2	8	no	—
329	#95	—	2	4	no	—
330	#95	—	4	4	no	—
331	C₂⁴	C₂⁴×C₄₇	1	1	yes	characteristic
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	2	2	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	2	1	no	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	—	2	2	no	—
345	C₂²×C₄	—	2	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	4	no	—
351	C₂²×C₄	—	2	4	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	4	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	4	no	—
357	C₂²×C₄	—	2	4	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	2	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	4	no	—
366	C₂²×C₄	—	2	4	no	—
367	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
368	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
369	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
370	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
371	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
372	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
373	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
374	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
375	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
376	C₂²×C₄	C₂×Q₈×C₄₇	1	4	yes	—
377	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
378	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
379	C₂²×C₄	C₂×Q₈×C₄₇	1	2	yes	—
380	C₂²×C₄	#41×C₄₇	1	4	yes	—
381	C₂²×C₄	#41×C₄₇	1	4	yes	—
382	C₂²×C₄	#41×C₄₇	1	2	yes	—
383	C₄⋊C₄	—	2	16	no	—
384	C₄⋊C₄	—	2	16	no	—
385	C₄⋊C₄	—	2	8	no	—
386	C₄⋊C₄	—	2	8	no	—
387	C₄⋊C₄	—	2	8	no	—
388	C₄⋊C₄	—	4	16	no	—
389	C₄⋊C₄	—	4	8	no	—
390	C₄⋊C₄	—	4	4	no	—
391	C₄²	—	2	8	no	—
392	C₄²	—	2	8	no	—
393	C₄²	—	2	8	no	—
394	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
395	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
396	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
397	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
398	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
399	C₂³	C₂²×Q₈×C₄₇	1	1	yes	characteristic
400	C₂³	C₂×#41×C₄₇	1	1	yes	characteristic
401	C₂³	C₂×#41×C₄₇	1	2	yes	—
402	C₂³	C₂×#41×C₄₇	1	2	yes	—
403	C₂³	H(5,𝔽₂)×C₄₇	1	2	yes	—
404	C₂³	2₋¹⁺⁴×C₄₇	1	2	yes	—
405	C₂×C₄	—	2	4	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	2	4	no	—
410	C₂×C₄	—	2	4	no	—
411	C₂×C₄	—	2	2	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	4	no	—
414	C₂×C₄	—	2	4	no	—
415	C₂×C₄	—	2	4	no	—
416	C₂×C₄	—	2	4	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	4	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	4	no	—
423	C₂×C₄	—	2	8	no	—
424	C₂×C₄	—	2	8	no	—
425	C₂×C₄	—	2	8	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	4	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	4	2	no	—
433	C₂×C₄	—	4	2	no	—
434	C₂×C₄	—	4	2	no	—
435	C₂×C₄	—	4	2	no	—
436	C₂×C₄	—	4	4	no	—
437	C₂×C₄	—	4	2	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	4	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	4	no	—
447	C₂×C₄	—	4	4	no	—
448	C₂×C₄	#120×C₄₇	1	4	yes	—
449	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
450	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
451	C₂×C₄	C₂²⋊Q₈×C₄₇	1	4	yes	—
452	C₂×C₄	#125×C₄₇	1	8	yes	complemented
453	C₂×C₄	C₄⋊Q₈×C₄₇	1	4	yes	—
454	C₂×C₄	C₄⋊Q₈×C₄₇	1	4	yes	—
455	C₂×C₄	C₄⋊Q₈×C₄₇	1	4	yes	—
456	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
457	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
458	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
459	C₂²	C₂×C₂²⋊Q₈×C₄₇	1	1	yes	characteristic
460	C₂²	C₂×#125×C₄₇	1	2	yes	—
461	C₂²	C₂×C₄⋊Q₈×C₄₇	1	1	yes	characteristic
462	C₂²	C₂×C₄⋊Q₈×C₄₇	1	1	yes	characteristic
463	C₂²	C₂×C₄⋊Q₈×C₄₇	1	1	yes	characteristic
464	C₂²	C₄₇×#532	1	1	yes	characteristic
465	C₂²	C₄₇×#532	1	1	yes	characteristic
466	C₂²	C₄₇×#533	1	2	yes	—
467	C₂²	C₄₇×#535	1	1	yes	characteristic
468	C₂²	C₄₇×#536	1	1	yes	characteristic
469	C₂²	C₄₇×#544	1	2	yes	—
470	C₂²	C₄₇×#544	1	2	yes	—
471	C₂²	C₄₇×#546	1	2	yes	—
472	C₂²	C₄₇×#547	1	2	yes	—
473	C₂²	C₄₇×#548	1	2	yes	—
474	C₂²	C₄₇×#550	1	2	yes	—
475	C₂²	C₄₇×#552	1	2	yes	—
476	C₂²	C₄₇×#553	1	2	yes	—
477	C₂²	C₄₇×#554	1	2	yes	—
478	C₂²	C₄₇×#557	1	2	yes	—
479	C₄	—	2	8	no	—
480	C₄	—	4	4	no	—
481	C₄	—	4	2	no	—
482	C₄	—	4	4	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	4	no	—
485	C₄	—	4	4	no	—
486	C₄	—	8	2	no	—
487	C₄	C₄₇×#395	1	8	yes	—
488	C₂	C₂×C₄₇×#395	1	1	yes	characteristic
489	C₂	C₄₇×#2431	1	1	yes	characteristic
490	C₂	C₄₇×#2432	1	1	yes	characteristic
491	C₂	C₄₇×#2441	1	2	yes	—
492	C₂	C₄₇×#2442	1	2	yes	—
493	C₂	C₄₇×#2550	1	2	yes	—
494	C₂	C₄₇×#2552	1	2	yes	—
495	C₂	C₄₇×#2565	1	1	yes	characteristic
496	C₂	C₄₇×#2566	1	1	yes	characteristic
497	C₂	C₄₇×#2660	1	1	yes	characteristic
498	C₂	C₄₇×#2859	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
202. C₂×C₄×C₄₇	#125	semidirect
206. #15228	C₄₇	direct (N × H)
282. C₄₇	#15228	direct (N × H)
452. C₂×C₄	#125×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#125×C₄₇	2
C₂×C₄₇×#389	2
C₂×C₄₇×#384	2
C₂×C₄₇×#382	2
C₄₇×#1444	2
C₄₇×#1441	2
C₄₇×C₄⋊#95	2
C₄×#95×C₄₇	2
#15228	47

Subgroups — C47×#15228 #26054926

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#15228 #26054926