Subgroups — C₄₇×#17971 #26057669

Order 12032.

600 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	C₄₇×#3167	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#2985	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2981	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#1592	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1590	C₂	1	2	yes	maximal, complemented
6	C₄₇×SD₁₆⋊C₈	C₂	1	2	yes	maximal, complemented
7	C₈×SD₁₆×C₄₇	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1568	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1497	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1496	C₂	1	1	yes	maximal, characteristic
11	C₄₇×#1450	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₇×#533	C₂²	1	1	yes	characteristic
13	C₄₇×#532	C₂²	1	1	yes	characteristic
14	C₄₇×#498	C₄	1	1	yes	characteristic
15	C₄₇×#492	C₄	1	1	yes	characteristic
16	C₄₇×#487	C₄	1	1	yes	characteristic
17	C₄₇×#486	C₄	1	1	yes	characteristic
18	C₄₇×#465	C₄	1	2	yes	—
19	C₄₇×#465	C₄	1	2	yes	—
20	C₄₇×#446	—	2	2	no	—
21	C₄₇×#446	C₂²	1	2	yes	—
22	C₈×Q₈×C₄₇	C₂²	1	2	yes	—
23	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	—
24	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	—
25	C₄₇×#436	C₂²	1	2	yes	—
26	C₄₇×#435	—	2	2	no	—
27	C₈×D₄×C₄₇	C₂²	1	2	yes	—
28	C₄₇×#433	—	2	2	no	—
29	C₄₇×#432	C₂²	1	1	yes	characteristic
30	C₄₇×#432	C₂²	1	1	yes	characteristic
31	C₄₇×#431	C₂²	1	1	yes	characteristic
32	C₄₇×#431	C₂²	1	1	yes	characteristic
33	C₄₇×#408	—	2	2	no	—
34	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
35	C₄₇×#335	C₂²	1	2	yes	—
36	C₄₇×#334	C₂²	1	2	yes	—
37	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
38	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
39	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
40	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
41	C₄₇×#322	C₂²	1	1	yes	characteristic
42	C₄₇×#322	C₂²	1	1	yes	characteristic
43	C₈²×C₄₇	C₂²	1	1	yes	characteristic
44	C₈²×C₄₇	C₂²	1	1	yes	characteristic
45	C₂×#41×C₄₇	—	2	1	no	—
46	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
47	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
48	C₂×M₁₆×C₄₇	—	2	2	no	—
49	C₂²×C₈×C₄₇	—	2	2	no	—
50	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
52	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
53	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
54	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
55	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
56	#125×C₄₇	—	2	1	no	—
57	#124×C₄₇	—	2	1	no	—
58	C₂²⋊Q₈×C₄₇	—	2	1	no	—
59	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
60	#121×C₄₇	—	2	1	no	—
61	#121×C₄₇	C₂×C₄	1	2	yes	—
62	C₄×Q₈×C₄₇	—	2	1	no	—
63	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
64	C₄×D₄×C₄₇	—	2	1	no	—
65	C₄×D₄×C₄₇	C₂³	1	2	yes	—
66	#117×C₄₇	—	2	1	no	—
67	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
68	#106×C₄₇	C₂×C₄	1	2	yes	—
69	#106×C₄₇	C₂×C₄	1	2	yes	—
70	C₄⋊C₈×C₄₇	—	2	2	no	—
71	C₄⋊C₈×C₄₇	—	2	2	no	—
72	C₄⋊C₈×C₄₇	—	2	1	no	—
73	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
74	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
75	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
76	#103×C₄₇	C₂×C₄	1	2	yes	—
77	#103×C₄₇	C₂×C₄	1	2	yes	—
78	#102×C₄₇	C₂×C₄	1	2	yes	—
79	#102×C₄₇	C₂×C₄	1	2	yes	—
80	C₂²⋊C₈×C₄₇	—	2	1	no	—
81	C₂²⋊C₈×C₄₇	—	2	1	no	—
82	C₂²⋊C₈×C₄₇	—	2	1	no	—
83	C₂²⋊C₈×C₄₇	—	2	2	no	—
84	C₂²⋊C₈×C₄₇	—	2	2	no	—
85	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
86	#97×C₄₇	—	2	2	no	—
87	#97×C₄₇	—	2	1	no	—
88	#97×C₄₇	—	2	1	no	—
89	C₄×C₈×C₄₇	—	2	2	no	—
90	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
92	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
95	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
96	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
97	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
98	#41×C₄₇	—	8	2	no	—
99	C₂×Q₈×C₄₇	—	2	1	no	—
100	C₂×Q₈×C₄₇	—	2	1	no	—
101	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	—	2	1	no	—
104	C₂×D₄×C₄₇	—	2	1	no	—
105	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
106	C₂²×C₄×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
110	SD₁₆×C₄₇	—	2	4	no	—
111	SD₁₆×C₄₇	—	2	4	no	—
112	M₁₆×C₄₇	—	8	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	1	no	—
118	C₂×C₈×C₄₇	—	2	1	no	—
119	C₂×C₈×C₄₇	—	8	2	no	—
120	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
126	C₄⋊C₄×C₄₇	—	2	1	no	—
127	C₄⋊C₄×C₄₇	—	2	1	no	—
128	C₄⋊C₄×C₄₇	—	2	1	no	—
129	C₄⋊C₄×C₄₇	—	2	1	no	—
130	C₄⋊C₄×C₄₇	—	2	2	no	—
131	C₄⋊C₄×C₄₇	—	2	2	no	—
132	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
133	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
134	C₂²⋊C₄×C₄₇	—	2	2	no	—
135	C₂²⋊C₄×C₄₇	—	2	2	no	—
136	C₂²⋊C₄×C₄₇	—	2	2	no	—
137	C₄²×C₄₇	—	2	2	no	—
138	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₄₇	#41	1	1	yes	characteristic
141	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
142	C₂³×C₄₇	—	2	2	no	—
143	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
144	Q₈×C₄₇	—	2	2	no	—
145	Q₈×C₄₇	—	2	2	no	—
146	Q₈×C₄₇	—	8	1	no	—
147	Q₈×C₄₇	—	8	1	no	—
148	D₄×C₄₇	—	2	2	no	—
149	D₄×C₄₇	—	2	2	no	—
150	D₄×C₄₇	—	8	1	no	—
151	D₄×C₄₇	—	8	1	no	—
152	D₄×C₄₇	—	8	2	no	—
153	C₂×C₄×C₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	2	2	no	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	2	no	—
158	C₂×C₄×C₄₇	—	2	2	no	—
159	C₂×C₄×C₄₇	—	4	1	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
168	C₈×C₄₇	—	2	1	no	—
169	C₈×C₄₇	—	2	1	no	—
170	C₈×C₄₇	—	2	2	no	—
171	C₈×C₄₇	—	2	2	no	—
172	C₈×C₄₇	—	4	1	no	—
173	C₈×C₄₇	—	4	1	no	—
174	C₈×C₄₇	—	4	2	no	—
175	C₈×C₄₇	—	4	2	no	—
176	C₈×C₄₇	#131	1	2	yes	—
177	C₈×C₄₇	#131	1	2	yes	—
178	#17971	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
179	C₂²×C₄₇	—	2	1	no	—
180	C₂²×C₄₇	—	2	1	no	—
181	C₂²×C₄₇	—	2	1	no	—
182	C₂²×C₄₇	—	4	2	no	—
183	C₂²×C₄₇	—	4	2	no	—
184	C₂²×C₄₇	—	4	2	no	—
185	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
186	C₄×C₄₇	—	2	1	no	—
187	C₄×C₄₇	—	2	1	no	—
188	C₄×C₄₇	—	2	1	no	—
189	C₄×C₄₇	—	2	1	no	—
190	C₄×C₄₇	—	4	2	no	—
191	C₄×C₄₇	—	4	2	no	—
192	C₄×C₄₇	—	4	2	no	—
193	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
194	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
195	C₄×C₄₇	#577	1	2	yes	—
196	#3167	C₂×C₄₇	1	1	yes	characteristic
197	#2985	C₂×C₄₇	1	1	yes	characteristic, complemented
198	#2981	C₂×C₄₇	1	1	yes	characteristic
199	#1592	C₂×C₄₇	1	2	yes	complemented
200	#1590	C₂×C₄₇	1	2	yes	complemented
201	SD₁₆⋊C₈	C₂×C₄₇	1	2	yes	complemented
202	C₈×SD₁₆	C₂×C₄₇	1	2	yes	complemented
203	#1568	C₂×C₄₇	1	1	yes	characteristic, complemented
204	#1497	C₂×C₄₇	1	1	yes	characteristic, complemented
205	#1496	C₂×C₄₇	1	1	yes	characteristic
206	#1450	C₂×C₄₇	1	1	yes	characteristic, complemented
207	C₂×C₄₇	—	4	1	no	—
208	C₂×C₄₇	—	8	2	no	—
209	C₂×C₄₇	#2931	1	1	yes	characteristic
210	C₂×C₄₇	#2949	1	1	yes	characteristic
211	C₂×C₄₇	#2957	1	1	yes	characteristic
212	#533	C₂²×C₄₇	1	1	yes	characteristic
213	#532	C₂²×C₄₇	1	1	yes	characteristic
214	#498	C₄×C₄₇	1	1	yes	characteristic
215	#492	C₄×C₄₇	1	1	yes	characteristic
216	#487	C₄×C₄₇	1	1	yes	characteristic
217	#486	C₄×C₄₇	1	1	yes	characteristic
218	#465	C₄×C₄₇	1	2	yes	—
219	#465	C₄×C₄₇	1	2	yes	—
220	#446	—	2	2	no	—
221	#446	C₂²×C₄₇	1	2	yes	—
222	C₈×Q₈	C₂²×C₄₇	1	2	yes	—
223	C₄×SD₁₆	C₂²×C₄₇	1	2	yes	—
224	C₄×SD₁₆	C₂²×C₄₇	1	2	yes	—
225	#436	C₂²×C₄₇	1	2	yes	—
226	#435	—	2	2	no	—
227	C₈×D₄	C₂²×C₄₇	1	2	yes	—
228	#433	—	2	2	no	—
229	#432	C₂²×C₄₇	1	1	yes	characteristic
230	#432	C₂²×C₄₇	1	1	yes	characteristic
231	#431	C₂²×C₄₇	1	1	yes	characteristic
232	#431	C₂²×C₄₇	1	1	yes	characteristic
233	#408	—	2	2	no	—
234	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
235	#335	C₂²×C₄₇	1	2	yes	—
236	#334	C₂²×C₄₇	1	2	yes	—
237	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	—
238	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	—
239	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
240	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
241	#322	C₂²×C₄₇	1	1	yes	characteristic
242	#322	C₂²×C₄₇	1	1	yes	characteristic
243	C₈²	C₂²×C₄₇	1	1	yes	characteristic
244	C₈²	C₂²×C₄₇	1	1	yes	characteristic
245	C₄₇	#17971	1	1	yes	characteristic, direct product factor, Sylow
246	C₂×#41	—	2	1	no	—
247	C₂×SD₁₆	C₂×C₄×C₄₇	1	2	yes	—
248	C₂×SD₁₆	C₂×C₄×C₄₇	1	2	yes	—
249	C₂×M₁₆	—	2	2	no	—
250	C₂²×C₈	—	2	2	no	—
251	C₂²×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
252	C₂²×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
253	C₄⋊Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
254	C₄⋊Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
255	C₄⋊Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
256	#127	C₂×C₄×C₄₇	1	1	yes	characteristic
257	#125	—	2	1	no	—
258	#124	—	2	1	no	—
259	C₂²⋊Q₈	—	2	1	no	—
260	C₂²⋊Q₈	C₂×C₄×C₄₇	1	2	yes	—
261	#121	—	2	1	no	—
262	#121	C₂×C₄×C₄₇	1	2	yes	—
263	C₄×Q₈	—	2	1	no	—
264	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
265	C₄×D₄	—	2	1	no	—
266	C₄×D₄	C₂³×C₄₇	1	2	yes	—
267	#117	—	2	1	no	—
268	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
269	#106	C₂×C₄×C₄₇	1	2	yes	—
270	#106	C₂×C₄×C₄₇	1	2	yes	—
271	C₄⋊C₈	—	2	2	no	—
272	C₄⋊C₈	—	2	2	no	—
273	C₄⋊C₈	—	2	1	no	—
274	C₄⋊C₈	D₄×C₄₇	1	2	yes	—
275	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
276	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
277	#103	C₂×C₄×C₄₇	1	2	yes	—
278	#103	C₂×C₄×C₄₇	1	2	yes	—
279	#102	C₂×C₄×C₄₇	1	2	yes	—
280	#102	C₂×C₄×C₄₇	1	2	yes	—
281	C₂²⋊C₈	—	2	1	no	—
282	C₂²⋊C₈	—	2	1	no	—
283	C₂²⋊C₈	—	2	1	no	—
284	C₂²⋊C₈	—	2	2	no	—
285	C₂²⋊C₈	—	2	2	no	—
286	C₂²⋊C₈	D₄×C₄₇	1	2	yes	—
287	#97	—	2	2	no	—
288	#97	—	2	1	no	—
289	#97	—	2	1	no	—
290	C₄×C₈	—	2	2	no	—
291	C₄×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
292	C₄×C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
293	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
294	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
295	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
296	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
297	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
298	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
299	#41	—	8	2	no	—
300	C₂×Q₈	—	2	1	no	—
301	C₂×Q₈	—	2	1	no	—
302	C₂×Q₈	C₂²×C₄×C₄₇	1	2	yes	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	—	2	1	no	—
305	C₂×D₄	—	2	1	no	—
306	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
309	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
310	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
311	SD₁₆	—	2	4	no	—
312	SD₁₆	—	2	4	no	—
313	M₁₆	—	8	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	2	2	no	—
317	C₂×C₈	—	2	2	no	—
318	C₂×C₈	—	2	1	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	8	2	no	—
321	C₂×C₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
322	C₂×C₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
323	C₂×C₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
324	C₂×C₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
325	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
326	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
327	C₄⋊C₄	—	2	1	no	—
328	C₄⋊C₄	—	2	1	no	—
329	C₄⋊C₄	—	2	1	no	—
330	C₄⋊C₄	—	2	1	no	—
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	2	2	no	—
333	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
334	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
335	C₂²⋊C₄	—	2	2	no	—
336	C₂²⋊C₄	—	2	2	no	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
340	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
341	C₄²	#41×C₄₇	1	1	yes	characteristic
342	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
343	C₂³	—	2	2	no	—
344	C₂³	C₄×D₄×C₄₇	1	1	yes	characteristic
345	Q₈	—	2	2	no	—
346	Q₈	—	2	2	no	—
347	Q₈	—	8	1	no	—
348	Q₈	—	8	1	no	—
349	D₄	—	2	2	no	—
350	D₄	—	2	2	no	—
351	D₄	—	8	1	no	—
352	D₄	—	8	1	no	—
353	D₄	—	8	2	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	2	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
364	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
365	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
366	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
367	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
368	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
369	C₈	—	2	1	no	—
370	C₈	—	2	1	no	—
371	C₈	—	2	2	no	—
372	C₈	—	2	2	no	—
373	C₈	—	4	1	no	—
374	C₈	—	4	1	no	—
375	C₈	—	4	2	no	—
376	C₈	—	4	2	no	—
377	C₈	#131×C₄₇	1	2	yes	—
378	C₈	#131×C₄₇	1	2	yes	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	4	2	no	—
383	C₂²	—	4	2	no	—
384	C₂²	—	4	2	no	—
385	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
386	C₄	—	2	1	no	—
387	C₄	—	2	1	no	—
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	4	2	no	—
391	C₄	—	4	2	no	—
392	C₄	—	4	2	no	—
393	C₄	C₂×#131×C₄₇	1	1	yes	characteristic
394	C₄	C₂×#131×C₄₇	1	1	yes	characteristic
395	C₄	C₄₇×#577	1	2	yes	—
396	C₂	—	4	1	no	—
397	C₂	—	8	2	no	—
398	C₂	C₄₇×#2931	1	1	yes	characteristic
399	C₂	C₄₇×#2949	1	1	yes	characteristic
400	C₂	C₄₇×#2957	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×#532	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₄₇ ◁ C₄₇×#431 ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#2985	C₂	semidirect
4. C₄₇×#1592	C₂	semidirect
5. C₄₇×#1590	C₂	semidirect
6. C₄₇×SD₁₆⋊C₈	C₂	semidirect
7. C₈×SD₁₆×C₄₇	C₂	semidirect
8. C₄₇×#1568	C₂	semidirect
9. C₄₇×#1497	C₂	semidirect
11. C₄₇×#1450	C₂	semidirect
178. #17971	C₄₇	direct (N × H)
197. #2985	C₂×C₄₇	semidirect
199. #1592	C₂×C₄₇	semidirect
200. #1590	C₂×C₄₇	semidirect
201. SD₁₆⋊C₈	C₂×C₄₇	semidirect
202. C₈×SD₁₆	C₂×C₄₇	semidirect
203. #1568	C₂×C₄₇	semidirect
204. #1497	C₂×C₄₇	semidirect
206. #1450	C₂×C₄₇	semidirect
245. C₄₇	#17971	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×#3167	2
C₄₇×#2985	2
C₄₇×#2981	2
C₄₇×#1592	2
C₄₇×#1590	2
C₄₇×SD₁₆⋊C₈	2
C₈×SD₁₆×C₄₇	2
C₄₇×#1568	2
C₄₇×#1497	2
C₄₇×#1496	2
C₄₇×#1450	2
#17971	47

Subgroups — C47×#17971 #26057669

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#17971 #26057669