Subgroups — C₄₇×#25699 #26065397

Order 12032.

1298 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#547	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#498	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2563	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2034	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1988	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1853	C₂	1	4	yes	maximal, complemented
9	C₄×#102×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×#41×C₄₇	—	2	1	no	—
11	C₄₇×#547	—	2	4	no	—
12	C₄₇×#547	—	2	4	no	—
13	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×#123×C₄₇	—	2	2	no	—
16	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
17	C₂×#121×C₄₇	C₂²	1	2	yes	—
18	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
21	C₄₇×#498	—	2	4	no	—
22	C₄₇×#476	—	2	4	no	—
23	C₂×#106×C₄₇	C₂²	1	4	yes	—
24	C₂×#106×C₄₇	C₂²	1	2	yes	—
25	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×#102×C₄₇	C₂²	1	2	yes	—
27	C₂×#102×C₄₇	C₂²	1	2	yes	—
28	C₂×C₂²⋊C₈×C₄₇	C₂²	1	4	yes	—
29	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
30	C₄₇×#393	—	2	2	no	—
31	C₄₇×#390	—	2	1	no	—
32	C₄₇×#382	—	2	1	no	—
33	C₄₇×#380	C₂²	1	4	yes	—
34	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
35	C₄₇×#340	C₂²	1	2	yes	—
36	C₄₇×#340	C₂²	1	4	yes	—
37	C₂×#41×C₄₇	—	2	8	no	—
38	C₂×#41×C₄₇	—	4	4	no	—
39	C₂×#41×C₄₇	—	4	4	no	—
40	C₂²×Q₈×C₄₇	—	2	1	no	—
41	C₂²×Q₈×C₄₇	—	2	1	no	—
42	C₂²×D₄×C₄₇	—	2	2	no	—
43	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
44	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	—	2	2	no	—
46	C₂³×C₄×C₄₇	—	2	1	no	—
47	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
48	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
49	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
50	C₄⋊Q₈×C₄₇	—	2	2	no	—
51	C₄⋊Q₈×C₄₇	—	2	2	no	—
52	C₄⋊Q₈×C₄₇	—	2	2	no	—
53	C₄⋊Q₈×C₄₇	D₄	1	4	yes	—
54	#123×C₄₇	—	2	16	no	—
55	C₂²⋊Q₈×C₄₇	—	2	8	no	—
56	#121×C₄₇	—	2	4	no	—
57	#121×C₄₇	—	2	4	no	—
58	C₄×D₄×C₄₇	—	2	2	no	—
59	C₄×D₄×C₄₇	—	2	2	no	—
60	C₄×D₄×C₄₇	—	2	2	no	—
61	C₄×D₄×C₄₇	D₄	1	4	yes	—
62	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
66	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
71	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
72	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
75	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
76	C₂×C₄²×C₄₇	—	2	1	no	—
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	#106×C₄₇	—	2	4	no	—
79	#106×C₄₇	—	2	8	no	—
80	C₄⋊C₈×C₄₇	—	2	2	no	—
81	#102×C₄₇	—	2	4	no	—
82	#102×C₄₇	—	2	4	no	—
83	C₂²⋊C₈×C₄₇	—	2	8	no	—
84	C₄×C₈×C₄₇	—	2	2	no	—
85	#95×C₄₇	—	2	1	no	—
86	#95×C₄₇	—	2	4	no	—
87	C₂⁴×C₄₇	—	2	1	no	—
88	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
89	#41×C₄₇	—	4	32	no	—
90	C₂×Q₈×C₄₇	—	2	4	no	—
91	C₂×Q₈×C₄₇	—	4	2	no	—
92	C₂×Q₈×C₄₇	—	4	2	no	—
93	C₂×Q₈×C₄₇	—	4	2	no	—
94	C₂×Q₈×C₄₇	—	8	2	no	—
95	C₂×D₄×C₄₇	—	2	8	no	—
96	C₂×D₄×C₄₇	—	2	2	no	—
97	C₂×D₄×C₄₇	—	2	2	no	—
98	C₂×D₄×C₄₇	—	2	1	no	—
99	C₂×D₄×C₄₇	—	2	2	no	—
100	C₂×D₄×C₄₇	—	2	2	no	—
101	C₂×D₄×C₄₇	—	4	4	no	—
102	C₂×D₄×C₄₇	—	4	4	no	—
103	C₂×D₄×C₄₇	SD₁₆	1	4	yes	—
104	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
105	C₂²×C₄×C₄₇	—	2	8	no	—
106	C₂²×C₄×C₄₇	—	2	1	no	—
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	—	2	4	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	4	no	—
113	C₂²×C₄×C₄₇	—	2	2	no	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	—	4	4	no	—
116	C₂²×C₄×C₄₇	—	4	4	no	—
117	C₂²×C₄×C₄₇	—	4	2	no	—
118	C₂²×C₄×C₄₇	—	4	2	no	—
119	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
120	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	—	2	2	no	—
126	C₂×C₈×C₄₇	—	2	4	no	—
127	C₂×C₈×C₄₇	#41	1	4	yes	complemented
128	C₄⋊C₄×C₄₇	—	2	8	no	—
129	C₄⋊C₄×C₄₇	—	2	4	no	—
130	C₄⋊C₄×C₄₇	—	2	2	no	—
131	C₄⋊C₄×C₄₇	—	2	1	no	—
132	C₄⋊C₄×C₄₇	—	2	2	no	—
133	C₄⋊C₄×C₄₇	—	2	2	no	—
134	C₄⋊C₄×C₄₇	—	2	2	no	—
135	C₄⋊C₄×C₄₇	—	2	2	no	—
136	C₄⋊C₄×C₄₇	—	2	2	no	—
137	C₄⋊C₄×C₄₇	—	4	2	no	—
138	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
139	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
140	C₂²⋊C₄×C₄₇	—	2	8	no	—
141	C₂²⋊C₄×C₄₇	—	2	4	no	—
142	C₂²⋊C₄×C₄₇	—	2	4	no	—
143	C₂²⋊C₄×C₄₇	—	8	4	no	—
144	C₄²×C₄₇	—	4	2	no	—
145	C₄²×C₄₇	C₂×D₄	1	2	yes	—
146	C₄²×C₄₇	C₂×D₄	1	2	yes	—
147	C₂³×C₄₇	—	2	2	no	—
148	C₂³×C₄₇	—	2	4	no	—
149	C₂³×C₄₇	—	2	2	no	—
150	C₂³×C₄₇	—	2	4	no	—
151	C₂³×C₄₇	—	2	2	no	—
152	C₂³×C₄₇	—	4	2	no	—
153	C₂³×C₄₇	—	4	1	no	—
154	C₂³×C₄₇	—	4	1	no	—
155	C₂³×C₄₇	—	4	2	no	—
156	C₂³×C₄₇	C₂×SD₁₆	1	4	yes	—
157	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
158	Q₈×C₄₇	—	4	8	no	—
159	Q₈×C₄₇	—	8	4	no	—
160	D₄×C₄₇	—	2	2	no	—
161	D₄×C₄₇	—	2	2	no	—
162	D₄×C₄₇	—	2	8	no	—
163	D₄×C₄₇	—	4	16	no	—
164	D₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	4	no	—
169	C₂×C₄×C₄₇	—	2	4	no	—
170	C₂×C₄×C₄₇	—	4	16	no	—
171	C₂×C₄×C₄₇	—	4	1	no	—
172	C₂×C₄×C₄₇	—	4	2	no	—
173	C₂×C₄×C₄₇	—	4	1	no	—
174	C₂×C₄×C₄₇	—	4	2	no	—
175	C₂×C₄×C₄₇	—	4	2	no	—
176	C₂×C₄×C₄₇	—	4	2	no	—
177	C₂×C₄×C₄₇	—	4	4	no	—
178	C₂×C₄×C₄₇	—	4	8	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	4	no	—
184	C₂×C₄×C₄₇	#120	1	2	yes	—
185	C₂×C₄×C₄₇	#120	1	2	yes	—
186	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
187	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
188	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
191	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
192	C₈×C₄₇	—	2	4	no	—
193	C₈×C₄₇	—	4	2	no	—
194	#25699	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
195	C₂²×C₄₇	—	2	8	no	—
196	C₂²×C₄₇	—	2	4	no	—
197	C₂²×C₄₇	—	4	4	no	—
198	C₂²×C₄₇	—	4	2	no	—
199	C₂²×C₄₇	—	4	2	no	—
200	C₂²×C₄₇	—	4	2	no	—
201	C₂²×C₄₇	—	4	2	no	—
202	C₂²×C₄₇	—	4	2	no	—
203	C₂²×C₄₇	—	8	2	no	—
204	C₂²×C₄₇	—	8	2	no	—
205	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
206	C₂²×C₄₇	#547	1	2	yes	—
207	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
208	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
209	C₂²×C₄₇	#577	1	2	yes	—
210	C₄×C₄₇	—	2	2	no	—
211	C₄×C₄₇	—	4	2	no	—
212	C₄×C₄₇	—	4	2	no	—
213	C₄×C₄₇	—	4	4	no	—
214	C₄×C₄₇	—	8	2	no	—
215	C₄×C₄₇	—	8	2	no	—
216	C₄×C₄₇	#450	1	4	yes	—
217	C₄×C₄₇	#532	1	1	yes	characteristic
218	C₄×C₄₇	#536	1	1	yes	characteristic
219	C₄×C₄₇	#548	1	2	yes	—
220	C₂×#547	C₂×C₄₇	1	1	yes	characteristic
221	C₂×#498	C₂×C₄₇	1	1	yes	characteristic, complemented
222	C₂×#476	C₂×C₄₇	1	1	yes	characteristic, complemented
223	#2563	C₂×C₄₇	1	1	yes	characteristic, complemented
224	#2034	C₂×C₄₇	1	4	yes	complemented
225	#1988	C₂×C₄₇	1	1	yes	characteristic, complemented
226	#1954	C₂×C₄₇	1	1	yes	characteristic, complemented
227	#1853	C₂×C₄₇	1	4	yes	complemented
228	C₄×#102	C₂×C₄₇	1	1	yes	characteristic, complemented
229	C₂×C₄₇	—	4	4	no	—
230	C₂×C₄₇	—	8	2	no	—
231	C₂×C₄₇	#2432	1	1	yes	characteristic
232	C₂×C₄₇	C₂×#450	1	1	yes	characteristic
233	C₂×C₄₇	#3010	1	1	yes	characteristic
234	C₂×C₄₇	#3335	1	2	yes	—
235	C₂×C₄₇	#3354	1	2	yes	—
236	C₂²×#41	—	2	1	no	—
237	#547	—	2	4	no	—
238	#547	—	2	4	no	—
239	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
240	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
241	C₂×#123	—	2	2	no	—
242	C₂×C₂²⋊Q₈	—	2	1	no	—
243	C₂×#121	C₂²×C₄₇	1	2	yes	—
244	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
245	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
246	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
247	#498	—	2	4	no	—
248	#476	—	2	4	no	—
249	C₂×#106	C₂²×C₄₇	1	2	yes	—
250	C₂×#106	C₂²×C₄₇	1	4	yes	—
251	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
252	C₂×#102	C₂²×C₄₇	1	2	yes	—
253	C₂×#102	C₂²×C₄₇	1	2	yes	—
254	C₂×C₂²⋊C₈	C₂²×C₄₇	1	4	yes	—
255	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
256	#393	—	2	2	no	—
257	#390	—	2	1	no	—
258	#382	—	2	1	no	—
259	#380	C₂²×C₄₇	1	4	yes	—
260	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
261	#340	C₂²×C₄₇	1	2	yes	—
262	#340	C₂²×C₄₇	1	4	yes	—
263	C₄₇	#25699	1	1	yes	characteristic, direct product factor, Sylow
264	C₂×#41	—	2	8	no	—
265	C₂×#41	—	4	4	no	—
266	C₂×#41	—	4	4	no	—
267	C₂²×Q₈	—	2	1	no	—
268	C₂²×Q₈	—	2	1	no	—
269	C₂²×D₄	—	2	2	no	—
270	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
271	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
272	C₂³×C₄	—	2	2	no	—
273	C₂³×C₄	—	2	1	no	—
274	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
275	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
276	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
277	C₄⋊Q₈	—	2	2	no	—
278	C₄⋊Q₈	—	2	2	no	—
279	C₄⋊Q₈	—	2	2	no	—
280	C₄⋊Q₈	D₄×C₄₇	1	4	yes	—
281	#123	—	2	16	no	—
282	C₂²⋊Q₈	—	2	8	no	—
283	#121	—	2	4	no	—
284	#121	—	2	4	no	—
285	C₄×D₄	—	2	2	no	—
286	C₄×D₄	—	2	2	no	—
287	C₄×D₄	—	2	2	no	—
288	C₄×D₄	D₄×C₄₇	1	4	yes	—
289	C₂×C₄⋊C₄	—	2	2	no	—
290	C₂×C₄⋊C₄	—	2	1	no	—
291	C₂×C₄⋊C₄	—	2	4	no	—
292	C₂×C₄⋊C₄	—	2	4	no	—
293	C₂×C₄⋊C₄	—	2	1	no	—
294	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
295	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
296	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
297	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₂²⋊C₄	—	2	2	no	—
301	C₂×C₂²⋊C₄	—	2	4	no	—
302	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
305	#106	—	2	4	no	—
306	#106	—	2	8	no	—
307	C₄⋊C₈	—	2	2	no	—
308	#102	—	2	4	no	—
309	#102	—	2	4	no	—
310	C₂²⋊C₈	—	2	8	no	—
311	C₄×C₈	—	2	2	no	—
312	#95	—	2	1	no	—
313	#95	—	2	4	no	—
314	C₂⁴	—	2	1	no	—
315	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
316	#41	—	4	32	no	—
317	C₂×Q₈	—	2	4	no	—
318	C₂×Q₈	—	4	2	no	—
319	C₂×Q₈	—	4	2	no	—
320	C₂×Q₈	—	4	2	no	—
321	C₂×Q₈	—	8	2	no	—
322	C₂×D₄	—	2	8	no	—
323	C₂×D₄	—	2	2	no	—
324	C₂×D₄	—	2	2	no	—
325	C₂×D₄	—	2	1	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	2	no	—
328	C₂×D₄	—	4	4	no	—
329	C₂×D₄	—	4	4	no	—
330	C₂×D₄	SD₁₆×C₄₇	1	4	yes	—
331	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
332	C₂²×C₄	—	2	8	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	2	no	—
335	C₂²×C₄	—	2	4	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	4	4	no	—
343	C₂²×C₄	—	4	4	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
347	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
348	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
349	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
350	C₂×C₈	—	2	2	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	2	2	no	—
353	C₂×C₈	—	2	4	no	—
354	C₂×C₈	#41×C₄₇	1	4	yes	complemented
355	C₄⋊C₄	—	2	8	no	—
356	C₄⋊C₄	—	2	4	no	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	2	no	—
361	C₄⋊C₄	—	2	2	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	4	2	no	—
365	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
366	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
367	C₂²⋊C₄	—	2	8	no	—
368	C₂²⋊C₄	—	2	4	no	—
369	C₂²⋊C₄	—	2	4	no	—
370	C₂²⋊C₄	—	8	4	no	—
371	C₄²	—	4	2	no	—
372	C₄²	C₂×D₄×C₄₇	1	2	yes	—
373	C₄²	C₂×D₄×C₄₇	1	2	yes	—
374	C₂³	—	2	2	no	—
375	C₂³	—	2	4	no	—
376	C₂³	—	2	2	no	—
377	C₂³	—	2	4	no	—
378	C₂³	—	2	2	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	1	no	—
381	C₂³	—	4	1	no	—
382	C₂³	—	4	2	no	—
383	C₂³	C₂×SD₁₆×C₄₇	1	4	yes	—
384	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
385	Q₈	—	4	8	no	—
386	Q₈	—	8	4	no	—
387	D₄	—	2	8	no	—
388	D₄	—	2	2	no	—
389	D₄	—	2	2	no	—
390	D₄	—	4	16	no	—
391	D₄	—	4	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	4	no	—
396	C₂×C₄	—	2	4	no	—
397	C₂×C₄	—	4	16	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	4	1	no	—
401	C₂×C₄	—	4	2	no	—
402	C₂×C₄	—	4	8	no	—
403	C₂×C₄	—	4	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	4	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	4	no	—
411	C₂×C₄	#120×C₄₇	1	2	yes	—
412	C₂×C₄	#120×C₄₇	1	2	yes	—
413	C₂×C₄	C₂×SD₁₆×C₄₇	1	2	yes	—
414	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
415	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
416	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
417	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
418	C₂×C₄	2₋¹⁺⁴×C₄₇	1	2	yes	—
419	C₈	—	2	4	no	—
420	C₈	—	4	2	no	—
421	C₂²	—	2	8	no	—
422	C₂²	—	2	4	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	4	2	no	—
425	C₂²	—	4	2	no	—
426	C₂²	—	4	2	no	—
427	C₂²	—	4	2	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	8	2	no	—
430	C₂²	—	8	2	no	—
431	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
432	C₂²	C₄₇×#547	1	2	yes	—
433	C₂²	C₂²×SD₁₆×C₄₇	1	1	yes	characteristic
434	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
435	C₂²	C₄₇×#577	1	2	yes	—
436	C₄	—	2	2	no	—
437	C₄	—	4	2	no	—
438	C₄	—	4	2	no	—
439	C₄	—	4	4	no	—
440	C₄	—	8	2	no	—
441	C₄	—	8	2	no	—
442	C₄	C₄₇×#450	1	4	yes	—
443	C₄	C₄₇×#532	1	1	yes	characteristic
444	C₄	C₄₇×#536	1	1	yes	characteristic
445	C₄	C₄₇×#548	1	2	yes	—
446	C₂	—	4	4	no	—
447	C₂	—	8	2	no	—
448	C₂	C₄₇×#2432	1	1	yes	characteristic
449	C₂	C₂×C₄₇×#450	1	1	yes	characteristic
450	C₂	C₄₇×#3010	1	1	yes	characteristic
451	C₂	C₄₇×#3335	1	2	yes	—
452	C₂	C₄₇×#3354	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×C₄₇×#547	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂×C₄×D₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#498	C₂	semidirect
3. C₂×C₄₇×#476	C₂	semidirect
4. C₄₇×#2563	C₂	semidirect
5. C₄₇×#2034	C₂	semidirect
6. C₄₇×#1988	C₂	semidirect
7. C₄₇×#1954	C₂	semidirect
8. C₄₇×#1853	C₂	semidirect
9. C₄×#102×C₄₇	C₂	semidirect
127. C₂×C₈×C₄₇	#41	semidirect
194. #25699	C₄₇	direct (N × H)
221. C₂×#498	C₂×C₄₇	semidirect
222. C₂×#476	C₂×C₄₇	semidirect
223. #2563	C₂×C₄₇	semidirect
224. #2034	C₂×C₄₇	semidirect
225. #1988	C₂×C₄₇	semidirect
226. #1954	C₂×C₄₇	semidirect
227. #1853	C₂×C₄₇	semidirect
228. C₄×#102	C₂×C₄₇	semidirect
263. C₄₇	#25699	direct (N × H)
354. C₂×C₈	#41×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×#547	2
C₂×C₄₇×#498	2
C₂×C₄₇×#476	2
C₄₇×#2563	2
C₄₇×#2034	2
C₄₇×#1988	2
C₄₇×#1954	2
C₄₇×#1853	2
C₄×#102×C₄₇	2
#25699	47

Subgroups — C47×#25699 #26065397

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#25699 #26065397