Subgroups — C₄₇×#20909 #26060607

Order 12032.

2258 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#525	C₂	1	1	yes	maximal, characteristic
2	C₂³×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#417	C₂	1	2	yes	maximal, complemented
4	C₂×C₄₇×#407	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1874	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1872	C₂	1	4	yes	maximal, complemented
7	C₄₇×#1736	C₂	1	2	yes	maximal, complemented
8	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₄₇	—	2	1	no	—
10	C₂⁴×C₄×C₄₇	C₂²	1	1	yes	characteristic
11	C₂²×M₁₆×C₄₇	C₂²	1	2	yes	—
12	C₄₇×#525	—	2	4	no	—
13	C₄₇×#525	C₄	1	8	yes	complemented
14	C₂×#123×C₄₇	—	2	1	no	—
15	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
16	C₂×#121×C₄₇	C₂²	1	2	yes	—
17	C₂×#120×C₄₇	—	2	1	no	—
18	C₂×C₄×D₄×C₄₇	—	2	2	no	—
19	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
20	C₂²×C₄⋊C₄×C₄₇	—	2	2	no	—
21	C₂²×C₄⋊C₄×C₄₇	—	2	1	no	—
22	C₂²×C₄⋊C₄×C₄₇	—	2	8	no	—
23	C₂²×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
24	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
25	C₄₇×#417	—	2	8	no	—
26	C₂×#103×C₄₇	C₂²	1	4	yes	complemented
27	C₂×#102×C₄₇	C₂²	1	4	yes	complemented
28	C₄₇×#407	—	2	4	no	—
29	C₂×C₂²⋊C₈×C₄₇	C₂²	1	4	yes	—
30	C₄₇×#340	C₂²	1	8	yes	complemented
31	C₂⁵×C₄₇	D₄	1	1	yes	characteristic
32	C₂×#41×C₄₇	—	2	2	no	—
33	C₂×#41×C₄₇	—	2	4	no	—
34	C₂×#41×C₄₇	—	2	4	no	—
35	C₂×#41×C₄₇	C₂×C₄	1	4	yes	complemented
36	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
37	C₂²×D₄×C₄₇	—	2	2	no	—
38	C₂²×D₄×C₄₇	—	2	1	no	—
39	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	—	2	4	no	—
41	C₂³×C₄×C₄₇	—	2	4	no	—
42	C₂³×C₄×C₄₇	—	2	8	no	—
43	C₂³×C₄×C₄₇	—	2	4	no	—
44	C₂³×C₄×C₄₇	—	2	2	no	—
45	C₂³×C₄×C₄₇	—	2	1	no	—
46	C₂³×C₄×C₄₇	—	4	8	no	—
47	C₂³×C₄×C₄₇	C₂×C₄	1	4	yes	—
48	C₂³×C₄×C₄₇	D₄	1	2	yes	—
49	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	D₄	1	4	yes	—
51	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
52	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
53	C₂×M₁₆×C₄₇	—	2	4	no	—
54	C₂×M₁₆×C₄₇	—	2	4	no	—
55	C₂×M₁₆×C₄₇	—	2	4	no	—
56	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
57	#123×C₄₇	—	2	8	no	—
58	C₂²⋊Q₈×C₄₇	—	2	4	no	—
59	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
60	#121×C₄₇	—	2	4	no	—
61	#121×C₄₇	C₂×C₄	1	8	yes	complemented
62	#120×C₄₇	—	2	8	no	—
63	C₄×D₄×C₄₇	—	2	16	no	—
64	#117×C₄₇	—	2	2	no	—
65	#117×C₄₇	C₂×C₄	1	4	yes	complemented
66	C₂×C₄⋊C₄×C₄₇	—	2	8	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	16	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
71	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
72	C₂×C₄⋊C₄×C₄₇	—	2	16	no	—
73	C₂×C₄⋊C₄×C₄₇	D₄	1	8	yes	complemented
74	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
76	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
77	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
79	C₂×C₄²×C₄₇	—	2	1	no	—
80	#103×C₄₇	—	2	8	no	—
81	#102×C₄₇	—	2	8	no	—
82	C₂²⋊C₈×C₄₇	—	2	8	no	—
83	C₂⁴×C₄₇	—	2	2	no	—
84	C₂⁴×C₄₇	—	2	2	no	—
85	C₂⁴×C₄₇	—	2	4	no	—
86	C₂⁴×C₄₇	—	2	4	no	—
87	C₂⁴×C₄₇	—	2	1	no	—
88	C₂⁴×C₄₇	C₂²⋊C₄	1	4	yes	—
89	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
90	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
91	#41×C₄₇	—	2	16	no	—
92	#41×C₄₇	—	4	8	no	—
93	C₂×Q₈×C₄₇	—	2	1	no	—
94	C₂×Q₈×C₄₇	—	2	2	no	—
95	C₂×Q₈×C₄₇	—	2	2	no	—
96	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	complemented
97	C₂×D₄×C₄₇	—	2	8	no	—
98	C₂×D₄×C₄₇	—	2	4	no	—
99	C₂×D₄×C₄₇	—	2	2	no	—
100	C₂×D₄×C₄₇	—	2	1	no	—
101	C₂×D₄×C₄₇	—	2	2	no	—
102	C₂×D₄×C₄₇	—	4	2	no	—
103	C₂×D₄×C₄₇	—	4	2	no	—
104	C₂×D₄×C₄₇	—	4	4	no	—
105	C₂×D₄×C₄₇	—	4	4	no	—
106	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	complemented
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	—	2	16	no	—
110	C₂²×C₄×C₄₇	—	2	4	no	—
111	C₂²×C₄×C₄₇	—	2	16	no	—
112	C₂²×C₄×C₄₇	—	2	4	no	—
113	C₂²×C₄×C₄₇	—	2	4	no	—
114	C₂²×C₄×C₄₇	—	2	4	no	—
115	C₂²×C₄×C₄₇	—	2	16	no	—
116	C₂²×C₄×C₄₇	—	2	8	no	—
117	C₂²×C₄×C₄₇	—	2	2	no	—
118	C₂²×C₄×C₄₇	—	2	1	no	—
119	C₂²×C₄×C₄₇	—	2	4	no	—
120	C₂²×C₄×C₄₇	—	2	4	no	—
121	C₂²×C₄×C₄₇	—	4	32	no	—
122	C₂²×C₄×C₄₇	—	4	8	no	—
123	C₂²×C₄×C₄₇	—	4	8	no	—
124	C₂²×C₄×C₄₇	—	4	8	no	—
125	C₂²×C₄×C₄₇	—	4	2	no	—
126	C₂²×C₄×C₄₇	—	4	2	no	—
127	C₂²×C₄×C₄₇	C₂²⋊C₄	1	8	yes	—
128	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
129	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
130	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
131	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
132	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
133	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
135	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
136	C₂²×C₄×C₄₇	#41	1	4	yes	—
137	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
138	M₁₆×C₄₇	—	4	8	no	—
139	C₂×C₈×C₄₇	—	2	4	no	—
140	C₂×C₈×C₄₇	—	2	4	no	—
141	C₂×C₈×C₄₇	—	2	4	no	—
142	C₄⋊C₄×C₄₇	—	2	16	no	—
143	C₄⋊C₄×C₄₇	—	2	8	no	—
144	C₄⋊C₄×C₄₇	—	2	8	no	—
145	C₄⋊C₄×C₄₇	—	2	4	no	—
146	C₄⋊C₄×C₄₇	—	2	2	no	—
147	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	complemented
148	C₄⋊C₄×C₄₇	C₂×D₄	1	8	yes	—
149	C₂²⋊C₄×C₄₇	—	2	4	no	—
150	C₂²⋊C₄×C₄₇	—	2	8	no	—
151	C₂²⋊C₄×C₄₇	—	2	8	no	—
152	C₄²×C₄₇	—	2	4	no	—
153	C₂³×C₄₇	—	2	8	no	—
154	C₂³×C₄₇	—	2	16	no	—
155	C₂³×C₄₇	—	2	8	no	—
156	C₂³×C₄₇	—	2	2	no	—
157	C₂³×C₄₇	—	2	2	no	—
158	C₂³×C₄₇	—	2	2	no	—
159	C₂³×C₄₇	—	2	2	no	—
160	C₂³×C₄₇	—	2	2	no	—
161	C₂³×C₄₇	—	2	2	no	—
162	C₂³×C₄₇	—	2	8	no	—
163	C₂³×C₄₇	—	2	16	no	—
164	C₂³×C₄₇	—	2	2	no	—
165	C₂³×C₄₇	—	4	1	no	—
166	C₂³×C₄₇	—	4	1	no	—
167	C₂³×C₄₇	—	4	2	no	—
168	C₂³×C₄₇	—	4	2	no	—
169	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
170	C₂³×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
171	C₂³×C₄₇	#120	1	2	yes	—
172	C₂³×C₄₇	#123	1	2	yes	—
173	C₂³×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
174	C₂³×C₄₇	#137	1	4	yes	—
175	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
176	Q₈×C₄₇	—	2	4	no	—
177	Q₈×C₄₇	—	4	2	no	—
178	D₄×C₄₇	—	2	4	no	—
179	D₄×C₄₇	—	4	8	no	—
180	D₄×C₄₇	—	4	16	no	—
181	D₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	2	2	no	—
183	C₂×C₄×C₄₇	—	2	2	no	—
184	C₂×C₄×C₄₇	—	2	8	no	—
185	C₂×C₄×C₄₇	—	2	8	no	—
186	C₂×C₄×C₄₇	—	2	8	no	—
187	C₂×C₄×C₄₇	—	2	16	no	—
188	C₂×C₄×C₄₇	—	2	4	no	—
189	C₂×C₄×C₄₇	—	2	2	no	—
190	C₂×C₄×C₄₇	—	2	8	no	—
191	C₂×C₄×C₄₇	—	4	16	no	—
192	C₂×C₄×C₄₇	—	4	32	no	—
193	C₂×C₄×C₄₇	—	4	1	no	—
194	C₂×C₄×C₄₇	—	4	1	no	—
195	C₂×C₄×C₄₇	—	4	8	no	—
196	C₂×C₄×C₄₇	—	4	2	no	—
197	C₂×C₄×C₄₇	—	4	2	no	—
198	C₂×C₄×C₄₇	—	4	8	no	—
199	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	4	yes	—
200	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
201	C₂×C₄×C₄₇	C₄×D₄	1	8	yes	—
202	C₂×C₄×C₄₇	#120	1	2	yes	—
203	C₂×C₄×C₄₇	#121	1	8	yes	—
204	C₂×C₄×C₄₇	#123	1	2	yes	—
205	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
206	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
207	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
208	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
209	C₈×C₄₇	—	4	4	no	—
210	#20909	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
211	C₂²×C₄₇	—	2	32	no	—
212	C₂²×C₄₇	—	2	4	no	—
213	C₂²×C₄₇	—	2	4	no	—
214	C₂²×C₄₇	—	2	4	no	—
215	C₂²×C₄₇	—	2	4	no	—
216	C₂²×C₄₇	—	2	4	no	—
217	C₂²×C₄₇	—	2	2	no	—
218	C₂²×C₄₇	—	2	4	no	—
219	C₂²×C₄₇	—	2	2	no	—
220	C₂²×C₄₇	—	2	4	no	—
221	C₂²×C₄₇	—	2	4	no	—
222	C₂²×C₄₇	—	4	4	no	—
223	C₂²×C₄₇	—	4	2	no	—
224	C₂²×C₄₇	—	8	2	no	—
225	C₂²×C₄₇	—	8	1	no	—
226	C₂²×C₄₇	—	8	1	no	—
227	C₂²×C₄₇	#386	1	4	yes	—
228	C₂²×C₄₇	#417	1	8	yes	complemented
229	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
230	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
231	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
232	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
233	C₂²×C₄₇	C₂×#137	1	2	yes	—
234	C₄×C₄₇	—	2	4	no	—
235	C₄×C₄₇	—	4	4	no	—
236	C₄×C₄₇	—	4	8	no	—
237	C₄×C₄₇	—	4	2	no	—
238	C₄×C₄₇	#386	1	4	yes	—
239	C₄×C₄₇	C₂×C₄×D₄	1	2	yes	—
240	C₄×C₄₇	C₂×#121	1	2	yes	—
241	C₂×#525	C₂×C₄₇	1	1	yes	characteristic
242	C₂³×C₄⋊C₄	C₂×C₄₇	1	1	yes	characteristic, complemented
243	C₂×#417	C₂×C₄₇	1	2	yes	complemented
244	C₂×#407	C₂×C₄₇	1	1	yes	characteristic, complemented
245	#1874	C₂×C₄₇	1	4	yes	complemented
246	#1872	C₂×C₄₇	1	4	yes	complemented
247	#1736	C₂×C₄₇	1	2	yes	complemented
248	C₂×C₄₇	—	2	4	no	—
249	C₂×C₄₇	—	2	8	no	—
250	C₂×C₄₇	—	8	2	no	—
251	C₂×C₄₇	C₂×#386	1	1	yes	characteristic
252	C₂×C₄₇	C₂×#417	1	2	yes	—
253	C₂×C₄₇	#3003	1	1	yes	characteristic
254	C₂×C₄₇	#3004	1	1	yes	characteristic
255	C₂×C₄₇	#3092	1	2	yes	—
256	C₂²×#41	C₂²×C₄₇	1	1	yes	characteristic
257	C₂⁴×C₄	—	2	1	no	—
258	C₂⁴×C₄	C₂²×C₄₇	1	1	yes	characteristic
259	C₂²×M₁₆	C₂²×C₄₇	1	2	yes	—
260	#525	—	2	4	no	—
261	#525	C₄×C₄₇	1	8	yes	complemented
262	C₂×#123	—	2	1	no	—
263	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
264	C₂×#121	C₂²×C₄₇	1	2	yes	—
265	C₂×#120	—	2	1	no	—
266	C₂×C₄×D₄	—	2	2	no	—
267	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
268	C₂²×C₄⋊C₄	—	2	2	no	—
269	C₂²×C₄⋊C₄	—	2	1	no	—
270	C₂²×C₄⋊C₄	—	2	8	no	—
271	C₂²×C₄⋊C₄	C₂²×C₄₇	1	4	yes	—
272	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
273	#417	—	2	8	no	—
274	C₂×#103	C₂²×C₄₇	1	4	yes	complemented
275	C₂×#102	C₂²×C₄₇	1	4	yes	complemented
276	#407	—	2	4	no	—
277	C₂×C₂²⋊C₈	C₂²×C₄₇	1	4	yes	—
278	#340	C₂²×C₄₇	1	8	yes	complemented
279	C₄₇	#20909	1	1	yes	characteristic, direct product factor, Sylow
280	C₂⁵	D₄×C₄₇	1	1	yes	characteristic
281	C₂×#41	—	2	2	no	—
282	C₂×#41	—	2	4	no	—
283	C₂×#41	—	2	4	no	—
284	C₂×#41	C₂×C₄×C₄₇	1	4	yes	complemented
285	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
286	C₂²×D₄	—	2	2	no	—
287	C₂²×D₄	—	2	1	no	—
288	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
289	C₂³×C₄	—	2	4	no	—
290	C₂³×C₄	—	2	4	no	—
291	C₂³×C₄	—	2	8	no	—
292	C₂³×C₄	—	2	4	no	—
293	C₂³×C₄	—	2	2	no	—
294	C₂³×C₄	—	2	1	no	—
295	C₂³×C₄	—	4	8	no	—
296	C₂³×C₄	C₂×C₄×C₄₇	1	4	yes	—
297	C₂³×C₄	D₄×C₄₇	1	2	yes	—
298	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
299	C₂³×C₄	D₄×C₄₇	1	4	yes	—
300	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
301	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
302	C₂×M₁₆	—	2	4	no	—
303	C₂×M₁₆	—	2	4	no	—
304	C₂×M₁₆	—	2	4	no	—
305	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
306	#123	—	2	8	no	—
307	C₂²⋊Q₈	—	2	4	no	—
308	C₂²⋊Q₈	C₂×C₄×C₄₇	1	8	yes	complemented
309	#121	—	2	4	no	—
310	#121	C₂×C₄×C₄₇	1	8	yes	complemented
311	#120	—	2	8	no	—
312	C₄×D₄	—	2	16	no	—
313	#117	—	2	2	no	—
314	#117	C₂×C₄×C₄₇	1	4	yes	complemented
315	C₂×C₄⋊C₄	—	2	8	no	—
316	C₂×C₄⋊C₄	—	2	16	no	—
317	C₂×C₄⋊C₄	—	2	4	no	—
318	C₂×C₄⋊C₄	—	2	2	no	—
319	C₂×C₄⋊C₄	—	2	4	no	—
320	C₂×C₄⋊C₄	—	2	2	no	—
321	C₂×C₄⋊C₄	—	2	16	no	—
322	C₂×C₄⋊C₄	D₄×C₄₇	1	8	yes	complemented
323	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
324	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
325	C₂×C₂²⋊C₄	—	2	1	no	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	2	no	—
328	C₂×C₄²	—	2	1	no	—
329	#103	—	2	8	no	—
330	#102	—	2	8	no	—
331	C₂²⋊C₈	—	2	8	no	—
332	C₂⁴	—	2	2	no	—
333	C₂⁴	—	2	2	no	—
334	C₂⁴	—	2	4	no	—
335	C₂⁴	—	2	4	no	—
336	C₂⁴	—	2	1	no	—
337	C₂⁴	C₂²⋊C₄×C₄₇	1	4	yes	—
338	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
339	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
340	#41	—	2	16	no	—
341	#41	—	4	8	no	—
342	C₂×Q₈	—	2	1	no	—
343	C₂×Q₈	—	2	2	no	—
344	C₂×Q₈	—	2	2	no	—
345	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	complemented
346	C₂×D₄	—	2	8	no	—
347	C₂×D₄	—	2	4	no	—
348	C₂×D₄	—	2	2	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	2	no	—
351	C₂×D₄	—	4	2	no	—
352	C₂×D₄	—	4	2	no	—
353	C₂×D₄	—	4	4	no	—
354	C₂×D₄	—	4	4	no	—
355	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	complemented
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	2	2	no	—
358	C₂²×C₄	—	2	16	no	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	2	16	no	—
361	C₂²×C₄	—	2	4	no	—
362	C₂²×C₄	—	2	4	no	—
363	C₂²×C₄	—	2	4	no	—
364	C₂²×C₄	—	2	16	no	—
365	C₂²×C₄	—	2	8	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	4	no	—
369	C₂²×C₄	—	2	4	no	—
370	C₂²×C₄	—	4	32	no	—
371	C₂²×C₄	—	4	8	no	—
372	C₂²×C₄	—	4	8	no	—
373	C₂²×C₄	—	4	8	no	—
374	C₂²×C₄	—	4	2	no	—
375	C₂²×C₄	—	4	2	no	—
376	C₂²×C₄	C₂²⋊C₄×C₄₇	1	8	yes	—
377	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
378	C₂²×C₄	C₂²×C₄×C₄₇	1	4	yes	—
379	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
380	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
382	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
383	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
384	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
385	C₂²×C₄	#41×C₄₇	1	4	yes	—
386	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
387	M₁₆	—	4	8	no	—
388	C₂×C₈	—	2	4	no	—
389	C₂×C₈	—	2	4	no	—
390	C₂×C₈	—	2	4	no	—
391	C₄⋊C₄	—	2	16	no	—
392	C₄⋊C₄	—	2	8	no	—
393	C₄⋊C₄	—	2	8	no	—
394	C₄⋊C₄	—	2	4	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	complemented
397	C₄⋊C₄	C₂×D₄×C₄₇	1	8	yes	—
398	C₂²⋊C₄	—	2	4	no	—
399	C₂²⋊C₄	—	2	8	no	—
400	C₂²⋊C₄	—	2	8	no	—
401	C₄²	—	2	4	no	—
402	C₂³	—	2	8	no	—
403	C₂³	—	2	16	no	—
404	C₂³	—	2	8	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	2	2	no	—
407	C₂³	—	2	2	no	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	8	no	—
412	C₂³	—	2	16	no	—
413	C₂³	—	2	2	no	—
414	C₂³	—	4	1	no	—
415	C₂³	—	4	1	no	—
416	C₂³	—	4	2	no	—
417	C₂³	—	4	2	no	—
418	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
419	C₂³	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
420	C₂³	#120×C₄₇	1	2	yes	—
421	C₂³	#123×C₄₇	1	2	yes	—
422	C₂³	AGL(1,ℤ/8)×C₄₇	1	4	yes	—
423	C₂³	#137×C₄₇	1	4	yes	—
424	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
425	Q₈	—	2	4	no	—
426	Q₈	—	4	2	no	—
427	D₄	—	2	4	no	—
428	D₄	—	4	8	no	—
429	D₄	—	4	16	no	—
430	D₄	—	4	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	8	no	—
434	C₂×C₄	—	2	8	no	—
435	C₂×C₄	—	2	8	no	—
436	C₂×C₄	—	2	16	no	—
437	C₂×C₄	—	2	4	no	—
438	C₂×C₄	—	2	2	no	—
439	C₂×C₄	—	2	8	no	—
440	C₂×C₄	—	4	16	no	—
441	C₂×C₄	—	4	32	no	—
442	C₂×C₄	—	4	1	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	8	no	—
445	C₂×C₄	—	4	2	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	8	no	—
448	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	4	yes	—
449	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
450	C₂×C₄	C₄×D₄×C₄₇	1	8	yes	—
451	C₂×C₄	#120×C₄₇	1	2	yes	—
452	C₂×C₄	#121×C₄₇	1	8	yes	—
453	C₂×C₄	#123×C₄₇	1	2	yes	—
454	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
455	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
456	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
457	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
458	C₈	—	4	4	no	—
459	C₂²	—	2	32	no	—
460	C₂²	—	2	4	no	—
461	C₂²	—	2	4	no	—
462	C₂²	—	2	4	no	—
463	C₂²	—	2	4	no	—
464	C₂²	—	2	4	no	—
465	C₂²	—	2	4	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	2	2	no	—
469	C₂²	—	2	4	no	—
470	C₂²	—	4	2	no	—
471	C₂²	—	4	4	no	—
472	C₂²	—	8	2	no	—
473	C₂²	—	8	1	no	—
474	C₂²	—	8	1	no	—
475	C₂²	C₄₇×#386	1	4	yes	—
476	C₂²	C₄₇×#417	1	8	yes	complemented
477	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
478	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
479	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
480	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	2	yes	—
481	C₂²	C₂×#137×C₄₇	1	2	yes	—
482	C₄	—	2	4	no	—
483	C₄	—	4	2	no	—
484	C₄	—	4	4	no	—
485	C₄	—	4	8	no	—
486	C₄	C₄₇×#386	1	4	yes	—
487	C₄	C₂×C₄×D₄×C₄₇	1	2	yes	—
488	C₄	C₂×#121×C₄₇	1	2	yes	—
489	C₂	—	2	4	no	—
490	C₂	—	2	8	no	—
491	C₂	—	8	2	no	—
492	C₂	C₂×C₄₇×#386	1	1	yes	characteristic
493	C₂	C₂×C₄₇×#417	1	2	yes	—
494	C₂	C₄₇×#3003	1	1	yes	characteristic
495	C₂	C₄₇×#3004	1	1	yes	characteristic
496	C₂	C₄₇×#3092	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×C₄₇×#525	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂⁴×C₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂³×C₄⋊C₄×C₄₇	C₂	semidirect
3. C₂×C₄₇×#417	C₂	semidirect
4. C₂×C₄₇×#407	C₂	semidirect
5. C₄₇×#1874	C₂	semidirect
6. C₄₇×#1872	C₂	semidirect
7. C₄₇×#1736	C₂	semidirect
13. C₄₇×#525	C₄	semidirect
26. C₂×#103×C₄₇	C₂²	semidirect
27. C₂×#102×C₄₇	C₂²	semidirect
30. C₄₇×#340	C₂²	semidirect
35. C₂×#41×C₄₇	C₂×C₄	semidirect
59. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
61. #121×C₄₇	C₂×C₄	semidirect
65. #117×C₄₇	C₂×C₄	semidirect
73. C₂×C₄⋊C₄×C₄₇	D₄	semidirect
96. C₂×Q₈×C₄₇	C₂²×C₄	semidirect
106. C₂×D₄×C₄₇	C₂²×C₄	semidirect
147. C₄⋊C₄×C₄₇	C₂²×C₄	semidirect
210. #20909	C₄₇	direct (N × H)
228. C₂²×C₄₇	#417	semidirect
242. C₂³×C₄⋊C₄	C₂×C₄₇	semidirect
243. C₂×#417	C₂×C₄₇	semidirect
244. C₂×#407	C₂×C₄₇	semidirect
245. #1874	C₂×C₄₇	semidirect
246. #1872	C₂×C₄₇	semidirect
247. #1736	C₂×C₄₇	semidirect
261. #525	C₄×C₄₇	semidirect
274. C₂×#103	C₂²×C₄₇	semidirect
275. C₂×#102	C₂²×C₄₇	semidirect
278. #340	C₂²×C₄₇	semidirect
279. C₄₇	#20909	direct (N × H)
284. C₂×#41	C₂×C₄×C₄₇	semidirect
308. C₂²⋊Q₈	C₂×C₄×C₄₇	semidirect
310. #121	C₂×C₄×C₄₇	semidirect
314. #117	C₂×C₄×C₄₇	semidirect
322. C₂×C₄⋊C₄	D₄×C₄₇	semidirect
345. C₂×Q₈	C₂²×C₄×C₄₇	semidirect
355. C₂×D₄	C₂²×C₄×C₄₇	semidirect
396. C₄⋊C₄	C₂²×C₄×C₄₇	semidirect
476. C₂²	C₄₇×#417	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#525	2
C₂³×C₄⋊C₄×C₄₇	2
C₂×C₄₇×#417	2
C₂×C₄₇×#407	2
C₄₇×#1874	2
C₄₇×#1872	2
C₄₇×#1736	2
#20909	47

Subgroups — C47×#20909 #26060607

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#20909 #26060607