Subgroups — C₄₇×#17935 #26057633

Order 12032.

726 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3100	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#2931	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#436	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1594	C₂	1	4	yes	maximal, complemented
5	C₄₇×#1586	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1570	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1486	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1480	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1452	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#131×C₄₇	—	2	1	no	—
11	C₂²×M₁₆×C₄₇	—	2	1	no	—
12	C₄₇×#532	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
14	C₄₇×#480	C₄	1	2	yes	—
15	C₄₇×#474	C₄	1	2	yes	—
16	C₄₇×#459	C₄	1	2	yes	—
17	C₄₇×#447	C₄	1	2	yes	—
18	C₄×D₈×C₄₇	C₂²	1	4	yes	—
19	C₄₇×#436	—	2	1	no	—
20	C₄₇×#436	—	2	1	no	—
21	C₄₇×#436	—	2	1	no	—
22	C₄₇×#436	C₂²	1	2	yes	—
23	C₄₇×#436	C₂²	1	2	yes	—
24	C₄₇×#436	C₂²	1	2	yes	complemented
25	C₈×D₄×C₄₇	—	2	1	no	—
26	C₈×D₄×C₄₇	C₂²	1	2	yes	complemented
27	C₄₇×#431	C₂²	1	1	yes	characteristic
28	C₄₇×#431	C₂²	1	1	yes	characteristic
29	C₄₇×#423	C₂²	1	1	yes	characteristic
30	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#408	—	2	1	no	—
32	C₂×C₂²⋊C₈×C₄₇	—	2	1	no	—
33	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₄₇×#334	C₂²	1	4	yes	complemented
35	C₄₇×D₄⋊C₈	C₂²	1	4	yes	—
36	C₄₇×D₄⋊C₈	C₂²	1	4	yes	complemented
37	C₄₇×#322	C₂²	1	2	yes	complemented
38	C₄₇×#322	C₂²	1	2	yes	complemented
39	C₂×#41×C₄₇	—	2	1	no	—
40	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	—	2	1	no	—
42	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	—
43	#131×C₄₇	—	4	4	no	—
44	C₂×M₁₆×C₄₇	—	2	1	no	—
45	C₂×M₁₆×C₄₇	—	2	2	no	—
46	C₂×M₁₆×C₄₇	—	2	2	no	—
47	C₂×M₁₆×C₄₇	—	2	2	no	—
48	C₂×M₁₆×C₄₇	—	4	4	no	—
49	C₂²×C₈×C₄₇	—	2	1	no	—
50	C₂²×C₈×C₄₇	—	2	2	no	—
51	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
53	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
54	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
55	#124×C₄₇	—	2	1	no	—
56	#121×C₄₇	—	2	1	no	—
57	#121×C₄₇	C₂×C₄	1	2	yes	—
58	C₄×D₄×C₄₇	—	2	1	no	—
59	C₄×D₄×C₄₇	—	2	1	no	—
60	C₄×D₄×C₄₇	—	2	1	no	—
61	C₄×D₄×C₄₇	C₂×C₄	1	2	yes	—
62	C₄×D₄×C₄₇	C₂³	1	2	yes	—
63	C₄×D₄×C₄₇	C₂³	1	2	yes	—
64	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
66	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
67	#107×C₄₇	C₂×C₄	1	4	yes	—
68	C₄⋊C₈×C₄₇	—	2	1	no	—
69	C₄⋊C₈×C₄₇	—	2	1	no	—
70	C₄⋊C₈×C₄₇	—	2	1	no	—
71	C₄⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
72	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
73	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
74	#102×C₄₇	C₂×C₄	1	4	yes	—
75	#102×C₄₇	C₂×C₄	1	4	yes	—
76	C₂²⋊C₈×C₄₇	—	2	1	no	—
77	C₂²⋊C₈×C₄₇	—	2	2	no	—
78	C₂²⋊C₈×C₄₇	—	2	2	no	—
79	C₂²⋊C₈×C₄₇	—	2	2	no	—
80	C₂²⋊C₈×C₄₇	—	2	2	no	—
81	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
82	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
83	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
84	C₄×C₈×C₄₇	C₂³	1	2	yes	—
85	C₄×C₈×C₄₇	C₂³	1	2	yes	—
86	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
87	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
88	C₂⁴×C₄₇	—	2	1	no	—
89	#41×C₄₇	—	4	2	no	—
90	#41×C₄₇	—	4	2	no	—
91	C₂×Q₈×C₄₇	—	2	1	no	—
92	C₂×D₄×C₄₇	—	2	2	no	—
93	C₂×D₄×C₄₇	—	2	1	no	—
94	C₂×D₄×C₄₇	—	2	1	no	—
95	C₂×D₄×C₄₇	—	2	1	no	—
96	C₂×D₄×C₄₇	—	4	2	no	—
97	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂²×C₄×C₄₇	—	2	1	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	—	4	2	no	—
104	C₂²×C₄×C₄₇	—	4	2	no	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
108	D₈×C₄₇	—	4	4	no	—
109	M₁₆×C₄₇	—	4	4	no	—
110	M₁₆×C₄₇	—	4	4	no	—
111	M₁₆×C₄₇	—	4	4	no	—
112	M₁₆×C₄₇	—	4	2	no	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₂×C₈×C₄₇	—	2	2	no	—
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	—	2	2	no	—
118	C₂×C₈×C₄₇	—	4	4	no	—
119	C₂×C₈×C₄₇	—	4	2	no	—
120	C₂×C₈×C₄₇	C₂²×C₄	1	4	yes	—
121	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₄⋊C₄×C₄₇	—	2	1	no	—
126	C₄⋊C₄×C₄₇	—	2	1	no	—
127	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
128	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
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	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
134	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₇	#41	1	1	yes	characteristic
136	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
137	C₂³×C₄₇	—	2	2	no	—
138	C₂³×C₄₇	—	2	2	no	—
139	C₂³×C₄₇	—	4	2	no	—
140	C₂³×C₄₇	—	4	2	no	—
141	C₂³×C₄₇	—	4	2	no	—
142	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
143	Q₈×C₄₇	—	4	2	no	—
144	D₄×C₄₇	—	2	2	no	—
145	D₄×C₄₇	—	2	4	no	—
146	D₄×C₄₇	—	2	2	no	—
147	D₄×C₄₇	—	4	2	no	—
148	D₄×C₄₇	—	4	2	no	—
149	D₄×C₄₇	—	4	4	no	—
150	D₄×C₄₇	—	4	2	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	2	2	no	—
153	C₂×C₄×C₄₇	—	2	2	no	—
154	C₂×C₄×C₄₇	—	4	1	no	—
155	C₂×C₄×C₄₇	—	4	2	no	—
156	C₂×C₄×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	4	2	no	—
158	C₂×C₄×C₄₇	—	4	2	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	4	4	no	—
161	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
165	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
166	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
169	C₈×C₄₇	—	2	4	no	—
170	C₈×C₄₇	—	2	1	no	—
171	C₈×C₄₇	—	2	1	no	—
172	C₈×C₄₇	—	2	1	no	—
173	C₈×C₄₇	—	2	1	no	—
174	C₈×C₄₇	—	4	2	no	—
175	C₈×C₄₇	—	4	2	no	—
176	C₈×C₄₇	—	4	2	no	—
177	#17935	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
178	C₂²×C₄₇	—	2	1	no	—
179	C₂²×C₄₇	—	2	1	no	—
180	C₂²×C₄₇	—	4	2	no	—
181	C₂²×C₄₇	—	4	2	no	—
182	C₂²×C₄₇	—	4	2	no	—
183	C₂²×C₄₇	—	4	2	no	—
184	C₂²×C₄₇	—	4	2	no	—
185	C₂²×C₄₇	—	4	2	no	—
186	C₂²×C₄₇	—	8	4	no	—
187	C₂²×C₄₇	#442	1	2	yes	—
188	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
189	C₄×C₄₇	—	2	1	no	—
190	C₄×C₄₇	—	2	1	no	—
191	C₄×C₄₇	—	2	1	no	—
192	C₄×C₄₇	—	4	2	no	—
193	C₄×C₄₇	—	4	2	no	—
194	C₄×C₄₇	#442	1	2	yes	—
195	C₄×C₄₇	#568	1	2	yes	—
196	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
197	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
198	#3100	C₂×C₄₇	1	1	yes	characteristic
199	#2931	C₂×C₄₇	1	1	yes	characteristic, complemented
200	C₂×#436	C₂×C₄₇	1	1	yes	characteristic, complemented
201	#1594	C₂×C₄₇	1	4	yes	complemented
202	#1586	C₂×C₄₇	1	4	yes	complemented
203	#1570	C₂×C₄₇	1	1	yes	characteristic, complemented
204	#1486	C₂×C₄₇	1	1	yes	characteristic, complemented
205	#1480	C₂×C₄₇	1	1	yes	characteristic, complemented
206	#1452	C₂×C₄₇	1	1	yes	characteristic, complemented
207	C₂×C₄₇	—	2	2	no	—
208	C₂×C₄₇	—	8	2	no	—
209	C₂×C₄₇	—	8	2	no	—
210	C₂×C₄₇	#2930	1	1	yes	characteristic
211	C₂×C₄₇	C₂×#442	1	1	yes	characteristic
212	C₂×C₄₇	#2955	1	1	yes	characteristic
213	C₂×#131	—	2	1	no	—
214	C₂²×M₁₆	—	2	1	no	—
215	#532	C₂²×C₄₇	1	1	yes	characteristic
216	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
217	#480	C₄×C₄₇	1	2	yes	—
218	#474	C₄×C₄₇	1	2	yes	—
219	#459	C₄×C₄₇	1	2	yes	—
220	#447	C₄×C₄₇	1	2	yes	—
221	C₄×D₈	C₂²×C₄₇	1	4	yes	—
222	#436	—	2	1	no	—
223	#436	—	2	1	no	—
224	#436	—	2	1	no	—
225	#436	C₂²×C₄₇	1	2	yes	—
226	#436	C₂²×C₄₇	1	2	yes	—
227	#436	C₂²×C₄₇	1	2	yes	complemented
228	C₈×D₄	—	2	1	no	—
229	C₈×D₄	C₂²×C₄₇	1	2	yes	complemented
230	#431	C₂²×C₄₇	1	1	yes	characteristic
231	#431	C₂²×C₄₇	1	1	yes	characteristic
232	#423	C₂²×C₄₇	1	1	yes	characteristic
233	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
234	#408	—	2	1	no	—
235	C₂×C₂²⋊C₈	—	2	1	no	—
236	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
237	#334	C₂²×C₄₇	1	4	yes	complemented
238	D₄⋊C₈	C₂²×C₄₇	1	4	yes	—
239	D₄⋊C₈	C₂²×C₄₇	1	4	yes	complemented
240	#322	C₂²×C₄₇	1	2	yes	complemented
241	#322	C₂²×C₄₇	1	2	yes	complemented
242	C₄₇	#17935	1	1	yes	characteristic, direct product factor, Sylow
243	C₂×#41	—	2	1	no	—
244	C₂²×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
245	C₂³×C₄	—	2	1	no	—
246	C₂×D₈	C₂×C₄×C₄₇	1	4	yes	—
247	#131	—	4	4	no	—
248	C₂×M₁₆	—	2	1	no	—
249	C₂×M₁₆	—	2	2	no	—
250	C₂×M₁₆	—	2	2	no	—
251	C₂×M₁₆	—	2	2	no	—
252	C₂×M₁₆	—	4	4	no	—
253	C₂²×C₈	—	2	1	no	—
254	C₂²×C₈	—	2	2	no	—
255	C₂²×C₈	D₄×C₄₇	1	1	yes	characteristic
256	C₂²×C₈	D₄×C₄₇	1	1	yes	characteristic
257	C₄⋊Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
258	#127	C₂×C₄×C₄₇	1	1	yes	characteristic
259	#124	—	2	1	no	—
260	#121	—	2	1	no	—
261	#121	C₂×C₄×C₄₇	1	2	yes	—
262	C₄×D₄	—	2	1	no	—
263	C₄×D₄	—	2	1	no	—
264	C₄×D₄	—	2	1	no	—
265	C₄×D₄	C₂×C₄×C₄₇	1	2	yes	—
266	C₄×D₄	C₂³×C₄₇	1	2	yes	—
267	C₄×D₄	C₂³×C₄₇	1	2	yes	—
268	C₂×C₄⋊C₄	C₂×C₄×C₄₇	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	—	2	1	no	—
270	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
271	#107	C₂×C₄×C₄₇	1	4	yes	—
272	C₄⋊C₈	—	2	1	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	—	2	1	no	—
275	C₄⋊C₈	C₂×C₄×C₄₇	1	2	yes	—
276	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
277	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
278	#102	C₂×C₄×C₄₇	1	4	yes	—
279	#102	C₂×C₄×C₄₇	1	4	yes	—
280	C₂²⋊C₈	—	2	1	no	—
281	C₂²⋊C₈	—	2	2	no	—
282	C₂²⋊C₈	—	2	2	no	—
283	C₂²⋊C₈	—	2	2	no	—
284	C₂²⋊C₈	—	2	2	no	—
285	C₂²⋊C₈	C₂×C₄×C₄₇	1	2	yes	—
286	C₄×C₈	D₄×C₄₇	1	1	yes	characteristic
287	C₄×C₈	D₄×C₄₇	1	1	yes	characteristic
288	C₄×C₈	C₂³×C₄₇	1	2	yes	—
289	C₄×C₈	C₂³×C₄₇	1	2	yes	—
290	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
291	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
292	C₂⁴	—	2	1	no	—
293	#41	—	4	2	no	—
294	#41	—	4	2	no	—
295	C₂×Q₈	—	2	1	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	2	1	no	—
298	C₂×D₄	—	2	1	no	—
299	C₂×D₄	—	2	1	no	—
300	C₂×D₄	—	4	2	no	—
301	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
302	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
303	C₂²×C₄	—	2	1	no	—
304	C₂²×C₄	—	2	2	no	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	2	no	—
307	C₂²×C₄	—	4	2	no	—
308	C₂²×C₄	—	4	2	no	—
309	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
310	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
311	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
312	D₈	—	4	4	no	—
313	M₁₆	—	4	4	no	—
314	M₁₆	—	4	4	no	—
315	M₁₆	—	4	4	no	—
316	M₁₆	—	4	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	2	no	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	2	no	—
322	C₂×C₈	—	4	4	no	—
323	C₂×C₈	—	4	2	no	—
324	C₂×C₈	C₂²×C₄×C₄₇	1	4	yes	—
325	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
326	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
327	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
328	C₂×C₈	C₂×D₄×C₄₇	1	1	yes	characteristic
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
332	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
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	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
338	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
339	C₄²	#41×C₄₇	1	1	yes	characteristic
340	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
341	C₂³	—	2	2	no	—
342	C₂³	—	2	2	no	—
343	C₂³	—	4	2	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	4	2	no	—
346	C₂³	C₄×D₄×C₄₇	1	1	yes	characteristic
347	Q₈	—	4	2	no	—
348	D₄	—	2	2	no	—
349	D₄	—	2	4	no	—
350	D₄	—	2	2	no	—
351	D₄	—	4	2	no	—
352	D₄	—	4	2	no	—
353	D₄	—	4	4	no	—
354	D₄	—	4	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	4	1	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	4	2	no	—
364	C₂×C₄	—	4	4	no	—
365	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
366	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
367	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
368	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
369	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
370	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
371	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
372	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
373	C₈	—	2	4	no	—
374	C₈	—	2	1	no	—
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	—	4	2	no	—
379	C₈	—	4	2	no	—
380	C₈	—	4	2	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	—	4	2	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	4	2	no	—
389	C₂²	—	8	4	no	—
390	C₂²	C₄₇×#442	1	2	yes	—
391	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	4	2	no	—
396	C₄	—	4	2	no	—
397	C₄	C₄₇×#442	1	2	yes	—
398	C₄	C₄₇×#568	1	2	yes	—
399	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
400	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	8	2	no	—
403	C₂	—	8	2	no	—
404	C₂	C₄₇×#2930	1	1	yes	characteristic
405	C₂	C₂×C₄₇×#442	1	1	yes	characteristic
406	C₂	C₄₇×#2955	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₄₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₄²	C₂⁴×C₄₇
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₄₇×#3100	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₇ ◁ C₂×C₄×C₈×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#2931	C₂	semidirect
3. C₂×C₄₇×#436	C₂	semidirect
4. C₄₇×#1594	C₂	semidirect
5. C₄₇×#1586	C₂	semidirect
6. C₄₇×#1570	C₂	semidirect
7. C₄₇×#1486	C₂	semidirect
8. C₄₇×#1480	C₂	semidirect
9. C₄₇×#1452	C₂	semidirect
24. C₄₇×#436	C₂²	semidirect
26. C₈×D₄×C₄₇	C₂²	semidirect
34. C₄₇×#334	C₂²	semidirect
36. C₄₇×D₄⋊C₈	C₂²	semidirect
37. C₄₇×#322	C₂²	semidirect
38. C₄₇×#322	C₂²	semidirect
177. #17935	C₄₇	direct (N × H)
199. #2931	C₂×C₄₇	semidirect
200. C₂×#436	C₂×C₄₇	semidirect
201. #1594	C₂×C₄₇	semidirect
202. #1586	C₂×C₄₇	semidirect
203. #1570	C₂×C₄₇	semidirect
204. #1486	C₂×C₄₇	semidirect
205. #1480	C₂×C₄₇	semidirect
206. #1452	C₂×C₄₇	semidirect
227. #436	C₂²×C₄₇	semidirect
229. C₈×D₄	C₂²×C₄₇	semidirect
237. #334	C₂²×C₄₇	semidirect
239. D₄⋊C₈	C₂²×C₄₇	semidirect
240. #322	C₂²×C₄₇	semidirect
241. #322	C₂²×C₄₇	semidirect
242. C₄₇	#17935	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×#3100	2
C₄₇×#2931	2
C₂×C₄₇×#436	2
C₄₇×#1594	2
C₄₇×#1586	2
C₄₇×#1570	2
C₄₇×#1486	2
C₄₇×#1480	2
C₄₇×#1452	2
#17935	47

Subgroups — C47×#17935 #26057633

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#17935 #26057633