Subgroups — C₄₇×#20733 #26060431

Order 12032.

1758 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2283	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1824	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1804	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1786	C₂	1	2	yes	maximal
7	C₄×#102×C₄₇	C₂	1	4	yes	maximal, complemented
8	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
9	C₂⁴×C₄×C₄₇	—	2	1	no	—
10	C₂×C₄×D₄×C₄₇	—	2	1	no	—
11	C₂×C₄×D₄×C₄₇	—	2	1	no	—
12	C₂×C₄×D₄×C₄₇	—	2	4	no	—
13	C₂×C₄×D₄×C₄₇	C₄	1	8	yes	complemented
14	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
15	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
16	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
18	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
19	C₄₇×#431	—	2	4	no	—
20	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	complemented
21	C₂×#102×C₄₇	C₂²	1	8	yes	—
22	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
23	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	complemented
24	C₄₇×#383	—	2	1	no	—
25	C₄₇×#382	C₂²	1	2	yes	complemented
26	C₄₇×#381	—	2	1	no	—
27	C₄₇×#380	C₂²	1	2	yes	—
28	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	complemented
29	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
30	C₄₇×#376	—	2	1	no	—
31	C₄₇×#340	C₂²	1	8	yes	complemented
32	C₂⁵×C₄₇	—	2	1	no	—
33	C₂²×D₄×C₄₇	—	2	8	no	—
34	C₂²×D₄×C₄₇	—	2	1	no	—
35	C₂²×D₄×C₄₇	—	2	2	no	—
36	C₂²×D₄×C₄₇	C₂×C₄	1	4	yes	—
37	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
38	C₂³×C₄×C₄₇	—	2	1	no	—
39	C₂³×C₄×C₄₇	—	2	8	no	—
40	C₂³×C₄×C₄₇	—	2	2	no	—
41	C₂³×C₄×C₄₇	—	2	2	no	—
42	C₂³×C₄×C₄₇	—	4	8	no	—
43	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
44	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
45	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
46	C₂²×C₈×C₄₇	C₂³	1	4	yes	—
47	C₄×D₄×C₄₇	—	2	8	no	—
48	C₄×D₄×C₄₇	—	2	8	no	—
49	C₄×D₄×C₄₇	—	2	4	no	—
50	C₄×D₄×C₄₇	—	2	4	no	—
51	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	—
52	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	—
53	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
55	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
56	C₂×C₄⋊C₄×C₄₇	C₂³	1	4	yes	—
57	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
58	C₂×C₂²⋊C₄×C₄₇	—	2	8	no	—
59	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
60	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
61	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
62	C₂×C₄²×C₄₇	—	2	2	no	—
63	C₂×C₄²×C₄₇	C₂×C₄	1	4	yes	—
64	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
65	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
66	C₂×C₄²×C₄₇	D₄	1	4	yes	—
67	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
69	C₄⋊C₈×C₄₇	—	2	4	no	—
70	#102×C₄₇	—	2	16	no	—
71	C₂²⋊C₈×C₄₇	—	2	4	no	—
72	C₄×C₈×C₄₇	—	2	4	no	—
73	#95×C₄₇	—	2	2	no	—
74	#95×C₄₇	—	2	2	no	—
75	#95×C₄₇	—	2	2	no	—
76	#95×C₄₇	—	2	2	no	—
77	C₂⁴×C₄₇	—	2	8	no	—
78	C₂⁴×C₄₇	—	2	4	no	—
79	C₂⁴×C₄₇	—	2	2	no	—
80	C₂⁴×C₄₇	—	4	4	no	—
81	C₂⁴×C₄₇	—	4	4	no	—
82	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
83	C₂×D₄×C₄₇	—	2	8	no	—
84	C₂×D₄×C₄₇	—	2	16	no	—
85	C₂×D₄×C₄₇	—	2	16	no	—
86	C₂×D₄×C₄₇	—	2	4	no	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	2	4	no	—
89	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
90	C₂×D₄×C₄₇	#41	1	8	yes	—
91	C₂²×C₄×C₄₇	—	2	4	no	—
92	C₂²×C₄×C₄₇	—	2	4	no	—
93	C₂²×C₄×C₄₇	—	2	4	no	—
94	C₂²×C₄×C₄₇	—	2	4	no	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	8	no	—
97	C₂²×C₄×C₄₇	—	2	8	no	—
98	C₂²×C₄×C₄₇	—	2	4	no	—
99	C₂²×C₄×C₄₇	—	4	8	no	—
100	C₂²×C₄×C₄₇	—	4	32	no	—
101	C₂²×C₄×C₄₇	—	4	4	no	—
102	C₂²×C₄×C₄₇	—	4	8	no	—
103	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
104	C₂²×C₄×C₄₇	C₂²⋊C₄	1	4	yes	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
113	C₂×C₈×C₄₇	—	2	4	no	—
114	C₂×C₈×C₄₇	—	2	8	no	—
115	C₄⋊C₄×C₄₇	—	2	4	no	—
116	C₄⋊C₄×C₄₇	—	2	2	no	—
117	C₄⋊C₄×C₄₇	—	2	8	no	—
118	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
119	C₂²⋊C₄×C₄₇	—	2	8	no	—
120	C₂²⋊C₄×C₄₇	—	2	8	no	—
121	C₂²⋊C₄×C₄₇	—	4	4	no	—
122	C₄²×C₄₇	—	4	4	no	—
123	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
124	C₄²×C₄₇	C₂²⋊C₄	1	4	yes	—
125	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
126	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
127	C₄²×C₄₇	C₂×D₄	1	2	yes	—
128	C₄²×C₄₇	C₂×D₄	1	2	yes	—
129	C₂³×C₄₇	—	2	2	no	—
130	C₂³×C₄₇	—	2	2	no	—
131	C₂³×C₄₇	—	2	16	no	—
132	C₂³×C₄₇	—	2	4	no	—
133	C₂³×C₄₇	—	2	8	no	—
134	C₂³×C₄₇	—	4	8	no	—
135	C₂³×C₄₇	—	4	32	no	—
136	C₂³×C₄₇	—	4	4	no	—
137	C₂³×C₄₇	—	4	4	no	—
138	C₂³×C₄₇	—	4	8	no	—
139	C₂³×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
140	C₂³×C₄₇	#135	1	4	yes	—
141	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
142	D₄×C₄₇	—	2	16	no	—
143	D₄×C₄₇	—	2	4	no	—
144	D₄×C₄₇	—	2	8	no	—
145	D₄×C₄₇	#117	1	8	yes	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	8	no	—
151	C₂×C₄×C₄₇	—	2	4	no	—
152	C₂×C₄×C₄₇	—	2	4	no	—
153	C₂×C₄×C₄₇	—	2	8	no	—
154	C₂×C₄×C₄₇	—	2	4	no	—
155	C₂×C₄×C₄₇	—	4	16	no	—
156	C₂×C₄×C₄₇	—	4	8	no	—
157	C₂×C₄×C₄₇	—	4	4	no	—
158	C₂×C₄×C₄₇	—	4	16	no	—
159	C₂×C₄×C₄₇	—	4	4	no	—
160	C₂×C₄×C₄₇	—	4	4	no	—
161	C₂×C₄×C₄₇	—	4	4	no	—
162	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
163	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
164	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
165	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
166	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
167	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	4	yes	—
168	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
169	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
171	C₈×C₄₇	—	4	4	no	—
172	#20733	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
173	C₂²×C₄₇	—	2	8	no	—
174	C₂²×C₄₇	—	2	2	no	—
175	C₂²×C₄₇	—	2	2	no	—
176	C₂²×C₄₇	—	2	8	no	—
177	C₂²×C₄₇	—	4	32	no	—
178	C₂²×C₄₇	—	4	16	no	—
179	C₂²×C₄₇	—	4	4	no	—
180	C₂²×C₄₇	—	4	4	no	—
181	C₂²×C₄₇	#416	1	4	yes	—
182	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
183	C₂²×C₄₇	#525	1	2	yes	—
184	C₂²×C₄₇	C₂×#135	1	2	yes	—
185	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
186	C₄×C₄₇	—	2	2	no	—
187	C₄×C₄₇	—	2	2	no	—
188	C₄×C₄₇	—	2	2	no	—
189	C₄×C₄₇	—	2	2	no	—
190	C₄×C₄₇	—	4	4	no	—
191	C₄×C₄₇	—	8	4	no	—
192	C₄×C₄₇	#418	1	4	yes	—
193	C₄×C₄₇	C₂×#117	1	2	yes	—
194	C₄×C₄₇	#525	1	2	yes	—
195	C₂²×C₄×D₄	C₂×C₄₇	1	1	yes	characteristic
196	C₂×#431	C₂×C₄₇	1	1	yes	characteristic, complemented
197	#2283	C₂×C₄₇	1	1	yes	characteristic, complemented
198	#1824	C₂×C₄₇	1	2	yes	complemented
199	#1804	C₂×C₄₇	1	4	yes	complemented
200	#1786	C₂×C₄₇	1	2	yes	—
201	C₄×#102	C₂×C₄₇	1	4	yes	complemented
202	C₂×C₄₇	—	2	4	no	—
203	C₂×C₄₇	—	4	8	no	—
204	C₂×C₄₇	#2280	1	1	yes	characteristic
205	C₂×C₄₇	C₂×#416	1	1	yes	characteristic
206	C₂×C₄₇	C₂×#418	1	1	yes	characteristic
207	C₂×C₄₇	#3105	1	4	yes	—
208	C₂³×D₄	C₂²×C₄₇	1	1	yes	characteristic
209	C₂⁴×C₄	—	2	1	no	—
210	C₂×C₄×D₄	—	2	1	no	—
211	C₂×C₄×D₄	—	2	1	no	—
212	C₂×C₄×D₄	—	2	4	no	—
213	C₂×C₄×D₄	C₄×C₄₇	1	8	yes	complemented
214	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
215	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
216	C₂²×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
217	C₂²×C₂²⋊C₄	—	2	1	no	—
218	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
219	#431	—	2	4	no	—
220	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	complemented
221	C₂×#102	C₂²×C₄₇	1	8	yes	—
222	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
223	C₂×C₄×C₈	C₂²×C₄₇	1	2	yes	complemented
224	#383	—	2	1	no	—
225	#382	C₂²×C₄₇	1	2	yes	complemented
226	#381	—	2	1	no	—
227	#380	C₂²×C₄₇	1	2	yes	—
228	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	complemented
229	C₄×C₂²⋊C₄	—	2	1	no	—
230	#376	—	2	1	no	—
231	#340	C₂²×C₄₇	1	8	yes	complemented
232	C₄₇	#20733	1	1	yes	characteristic, direct product factor, Sylow
233	C₂⁵	—	2	1	no	—
234	C₂²×D₄	—	2	8	no	—
235	C₂²×D₄	—	2	1	no	—
236	C₂²×D₄	—	2	2	no	—
237	C₂²×D₄	C₂×C₄×C₄₇	1	4	yes	—
238	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
239	C₂³×C₄	—	2	1	no	—
240	C₂³×C₄	—	2	8	no	—
241	C₂³×C₄	—	2	2	no	—
242	C₂³×C₄	—	2	2	no	—
243	C₂³×C₄	—	4	8	no	—
244	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
245	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
246	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
247	C₂²×C₈	C₂³×C₄₇	1	4	yes	—
248	C₄×D₄	—	2	8	no	—
249	C₄×D₄	—	2	8	no	—
250	C₄×D₄	—	2	4	no	—
251	C₄×D₄	—	2	4	no	—
252	C₄×D₄	C₂×C₄×C₄₇	1	8	yes	—
253	C₄×D₄	C₂×C₄×C₄₇	1	8	yes	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	4	yes	—
257	C₂×C₄⋊C₄	C₂³×C₄₇	1	4	yes	—
258	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
259	C₂×C₂²⋊C₄	—	2	8	no	—
260	C₂×C₂²⋊C₄	—	2	2	no	—
261	C₂×C₂²⋊C₄	—	2	2	no	—
262	C₂×C₂²⋊C₄	—	2	2	no	—
263	C₂×C₄²	—	2	2	no	—
264	C₂×C₄²	C₂×C₄×C₄₇	1	4	yes	—
265	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
266	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
267	C₂×C₄²	D₄×C₄₇	1	4	yes	—
268	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
269	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
270	C₄⋊C₈	—	2	4	no	—
271	#102	—	2	16	no	—
272	C₂²⋊C₈	—	2	4	no	—
273	C₄×C₈	—	2	4	no	—
274	#95	—	2	2	no	—
275	#95	—	2	2	no	—
276	#95	—	2	2	no	—
277	#95	—	2	2	no	—
278	C₂⁴	—	2	8	no	—
279	C₂⁴	—	2	4	no	—
280	C₂⁴	—	2	2	no	—
281	C₂⁴	—	4	4	no	—
282	C₂⁴	—	4	4	no	—
283	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
284	C₂×D₄	—	2	8	no	—
285	C₂×D₄	—	2	16	no	—
286	C₂×D₄	—	2	16	no	—
287	C₂×D₄	—	2	4	no	—
288	C₂×D₄	—	2	2	no	—
289	C₂×D₄	—	2	4	no	—
290	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
291	C₂×D₄	#41×C₄₇	1	8	yes	—
292	C₂²×C₄	—	2	4	no	—
293	C₂²×C₄	—	2	4	no	—
294	C₂²×C₄	—	2	4	no	—
295	C₂²×C₄	—	2	4	no	—
296	C₂²×C₄	—	2	2	no	—
297	C₂²×C₄	—	2	8	no	—
298	C₂²×C₄	—	2	8	no	—
299	C₂²×C₄	—	2	4	no	—
300	C₂²×C₄	—	4	8	no	—
301	C₂²×C₄	—	4	32	no	—
302	C₂²×C₄	—	4	4	no	—
303	C₂²×C₄	—	4	8	no	—
304	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
305	C₂²×C₄	C₂²⋊C₄×C₄₇	1	4	yes	—
306	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
307	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
308	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
311	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
312	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
313	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
314	C₂×C₈	—	2	4	no	—
315	C₂×C₈	—	2	8	no	—
316	C₄⋊C₄	—	2	4	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	8	no	—
319	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
320	C₂²⋊C₄	—	2	8	no	—
321	C₂²⋊C₄	—	2	8	no	—
322	C₂²⋊C₄	—	4	4	no	—
323	C₄²	—	4	4	no	—
324	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
325	C₄²	C₂²⋊C₄×C₄₇	1	4	yes	—
326	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
327	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
328	C₄²	C₂×D₄×C₄₇	1	2	yes	—
329	C₄²	C₂×D₄×C₄₇	1	2	yes	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	16	no	—
333	C₂³	—	2	4	no	—
334	C₂³	—	2	8	no	—
335	C₂³	—	4	8	no	—
336	C₂³	—	4	32	no	—
337	C₂³	—	4	4	no	—
338	C₂³	—	4	4	no	—
339	C₂³	—	4	8	no	—
340	C₂³	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
341	C₂³	#135×C₄₇	1	4	yes	—
342	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
343	D₄	—	2	16	no	—
344	D₄	—	2	4	no	—
345	D₄	—	2	8	no	—
346	D₄	#117×C₄₇	1	8	yes	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	2	2	no	—
351	C₂×C₄	—	2	8	no	—
352	C₂×C₄	—	2	4	no	—
353	C₂×C₄	—	2	4	no	—
354	C₂×C₄	—	2	8	no	—
355	C₂×C₄	—	2	4	no	—
356	C₂×C₄	—	4	16	no	—
357	C₂×C₄	—	4	8	no	—
358	C₂×C₄	—	4	4	no	—
359	C₂×C₄	—	4	16	no	—
360	C₂×C₄	—	4	4	no	—
361	C₂×C₄	—	4	4	no	—
362	C₂×C₄	—	4	4	no	—
363	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
364	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
365	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
366	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
367	C₂×C₄	C₂×C₂²⋊C₄×C₄₇	1	2	yes	—
368	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	4	yes	—
369	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
370	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
371	C₂×C₄	C₂×#41×C₄₇	1	4	yes	—
372	C₈	—	4	4	no	—
373	C₂²	—	2	2	no	—
374	C₂²	—	2	8	no	—
375	C₂²	—	2	2	no	—
376	C₂²	—	2	8	no	—
377	C₂²	—	4	32	no	—
378	C₂²	—	4	16	no	—
379	C₂²	—	4	4	no	—
380	C₂²	—	4	4	no	—
381	C₂²	C₄₇×#416	1	4	yes	—
382	C₂²	C₂²×C₂²⋊C₄×C₄₇	1	1	yes	characteristic
383	C₂²	C₄₇×#525	1	2	yes	—
384	C₂²	C₂×#135×C₄₇	1	2	yes	—
385	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	2	yes	—
386	C₄	—	2	2	no	—
387	C₄	—	2	2	no	—
388	C₄	—	2	2	no	—
389	C₄	—	2	2	no	—
390	C₄	—	4	4	no	—
391	C₄	—	8	4	no	—
392	C₄	C₄₇×#418	1	4	yes	—
393	C₄	C₂×#117×C₄₇	1	2	yes	—
394	C₄	C₄₇×#525	1	2	yes	—
395	C₂	—	2	4	no	—
396	C₂	—	4	8	no	—
397	C₂	C₄₇×#2280	1	1	yes	characteristic
398	C₂	C₂×C₄₇×#416	1	1	yes	characteristic
399	C₂	C₂×C₄₇×#418	1	1	yes	characteristic
400	C₂	C₄₇×#3105	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂³×D₄×C₄₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₇ ◁ C₂²×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#431	C₂	semidirect
3. C₄₇×#2283	C₂	semidirect
4. C₄₇×#1824	C₂	semidirect
5. C₄₇×#1804	C₂	semidirect
7. C₄×#102×C₄₇	C₂	semidirect
13. C₂×C₄×D₄×C₄₇	C₄	semidirect
20. C₂×C₄⋊C₈×C₄₇	C₂²	semidirect
23. C₂×C₄×C₈×C₄₇	C₂²	semidirect
25. C₄₇×#382	C₂²	semidirect
28. C₄×C₄⋊C₄×C₄₇	C₂²	semidirect
31. C₄₇×#340	C₂²	semidirect
172. #20733	C₄₇	direct (N × H)
196. C₂×#431	C₂×C₄₇	semidirect
197. #2283	C₂×C₄₇	semidirect
198. #1824	C₂×C₄₇	semidirect
199. #1804	C₂×C₄₇	semidirect
201. C₄×#102	C₂×C₄₇	semidirect
213. C₂×C₄×D₄	C₄×C₄₇	semidirect
220. C₂×C₄⋊C₈	C₂²×C₄₇	semidirect
223. C₂×C₄×C₈	C₂²×C₄₇	semidirect
225. #382	C₂²×C₄₇	semidirect
228. C₄×C₄⋊C₄	C₂²×C₄₇	semidirect
231. #340	C₂²×C₄₇	semidirect
232. C₄₇	#20733	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₄×D₄×C₄₇	2
C₂×C₄₇×#431	2
C₄₇×#2283	2
C₄₇×#1824	2
C₄₇×#1804	2
C₄₇×#1786	2
C₄×#102×C₄₇	2
#20733	47

Subgroups — C47×#20733 #26060431

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#20733 #26060431