Subgroups — C₄₇×#18018 #26057716

Order 12032.

638 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	C₄₇×#3106	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#2991	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2979	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1589	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1588	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1586	C₂	1	2	yes	maximal, complemented
7	C₈×SD₁₆×C₄₇	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1574	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1492	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1476	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1450	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₇×#532	C₂²	1	1	yes	characteristic
13	C₄×#41×C₄₇	C₂²	1	1	yes	characteristic
14	C₄₇×#482	C₄	1	2	yes	—
15	C₄₇×#477	C₄	1	1	yes	characteristic
16	C₄₇×#476	C₄	1	1	yes	characteristic
17	C₄₇×#460	C₄	1	1	yes	characteristic
18	C₄₇×#459	C₄	1	1	yes	characteristic
19	C₄₇×#449	C₄	1	2	yes	—
20	C₈×Q₈×C₄₇	C₂²	1	2	yes	—
21	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	—
22	C₄×D₈×C₄₇	C₂²	1	2	yes	—
23	C₄₇×#436	—	2	2	no	—
24	C₄₇×#436	—	2	1	no	—
25	C₄₇×#436	C₂²	1	2	yes	—
26	C₄₇×#436	C₂²	1	2	yes	—
27	C₈×D₄×C₄₇	—	2	1	no	—
28	C₈×D₄×C₄₇	C₂²	1	2	yes	—
29	C₄₇×#431	—	2	1	no	—
30	C₄₇×#431	C₂²	1	1	yes	characteristic
31	C₄₇×#431	C₂²	1	1	yes	characteristic
32	C₄₇×#431	C₂²	1	1	yes	characteristic
33	C₄₇×#423	—	2	1	no	—
34	C₄₇×#423	C₂²	1	1	yes	characteristic
35	C₄₇×#408	—	2	2	no	—
36	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₄₇×#335	C₂²	1	2	yes	—
38	C₄₇×#334	C₂²	1	2	yes	—
39	C₄₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
40	C₄₇×Q₈⋊C₈	C₂²	1	1	yes	characteristic
41	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
42	C₄₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
43	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
44	C₄₇×D₄⋊C₈	C₂²	1	1	yes	characteristic
45	C₄₇×#322	C₂²	1	2	yes	—
46	C₈²×C₄₇	C₂²	1	2	yes	—
47	C₂×#41×C₄₇	—	2	1	no	—
48	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
50	C₂×D₈×C₄₇	C₂×C₄	1	2	yes	—
51	C₂×M₁₆×C₄₇	—	2	1	no	—
52	C₂×M₁₆×C₄₇	—	2	2	no	—
53	C₂×M₁₆×C₄₇	—	2	2	no	—
54	C₂²×C₈×C₄₇	—	2	1	no	—
55	C₂²×C₈×C₄₇	—	2	2	no	—
56	C₄⋊Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
57	#127×C₄₇	C₂×C₄	1	1	yes	characteristic
58	#124×C₄₇	—	2	1	no	—
59	#121×C₄₇	—	2	1	no	—
60	#121×C₄₇	C₂×C₄	1	2	yes	—
61	C₄×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
62	C₄×Q₈×C₄₇	C₂³	1	1	yes	characteristic
63	C₄×D₄×C₄₇	—	2	1	no	—
64	C₄×D₄×C₄₇	—	2	1	no	—
65	C₄×D₄×C₄₇	—	2	1	no	—
66	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
67	C₄×D₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₄×D₄×C₄₇	C₂³	1	2	yes	—
69	#117×C₄₇	—	2	1	no	—
70	#117×C₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₇	—	2	1	no	—
72	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
73	#107×C₄₇	C₂×C₄	1	2	yes	—
74	#106×C₄₇	C₂×C₄	1	2	yes	—
75	C₄⋊C₈×C₄₇	—	2	2	no	—
76	C₄⋊C₈×C₄₇	—	2	1	no	—
77	C₄⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
78	C₄⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
79	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
80	C₄⋊C₈×C₄₇	D₄	1	1	yes	characteristic
81	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
82	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
83	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
84	#103×C₄₇	C₂×C₄	1	2	yes	—
85	#102×C₄₇	C₂×C₄	1	2	yes	—
86	#102×C₄₇	C₂×C₄	1	2	yes	—
87	#102×C₄₇	C₂×C₄	1	2	yes	—
88	C₂²⋊C₈×C₄₇	—	2	1	no	—
89	C₂²⋊C₈×C₄₇	—	2	2	no	—
90	C₂²⋊C₈×C₄₇	—	2	2	no	—
91	C₂²⋊C₈×C₄₇	—	2	2	no	—
92	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
93	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
94	C₄×C₈×C₄₇	—	2	2	no	—
95	C₄×C₈×C₄₇	—	2	1	no	—
96	C₄×C₈×C₄₇	—	2	1	no	—
97	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
98	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
99	C₄×C₈×C₄₇	C₂³	1	2	yes	—
100	C₄×C₈×C₄₇	C₂³	1	2	yes	—
101	#41×C₄₇	—	2	2	no	—
102	#41×C₄₇	—	4	1	no	—
103	#41×C₄₇	—	8	1	no	—
104	#41×C₄₇	—	8	1	no	—
105	C₂×Q₈×C₄₇	—	2	1	no	—
106	C₂×Q₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂×D₄×C₄₇	—	2	1	no	—
108	C₂×D₄×C₄₇	—	2	2	no	—
109	C₂×D₄×C₄₇	—	2	1	no	—
110	C₂×D₄×C₄₇	—	2	1	no	—
111	C₂×D₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
112	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
113	C₂²×C₄×C₄₇	—	2	1	no	—
114	C₂²×C₄×C₄₇	—	2	1	no	—
115	C₂²×C₄×C₄₇	—	2	1	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
120	SD₁₆×C₄₇	—	2	4	no	—
121	D₈×C₄₇	—	4	2	no	—
122	M₁₆×C₄₇	—	8	2	no	—
123	M₁₆×C₄₇	—	8	2	no	—
124	M₁₆×C₄₇	—	8	1	no	—
125	C₂×C₈×C₄₇	—	2	4	no	—
126	C₂×C₈×C₄₇	—	2	1	no	—
127	C₂×C₈×C₄₇	—	2	1	no	—
128	C₂×C₈×C₄₇	—	2	2	no	—
129	C₂×C₈×C₄₇	—	2	1	no	—
130	C₂×C₈×C₄₇	—	2	1	no	—
131	C₂×C₈×C₄₇	—	8	2	no	—
132	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
133	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
134	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
135	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
136	C₄⋊C₄×C₄₇	—	2	1	no	—
137	C₄⋊C₄×C₄₇	—	2	1	no	—
138	C₄⋊C₄×C₄₇	—	2	1	no	—
139	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
140	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
141	C₄⋊C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
142	C₂²⋊C₄×C₄₇	—	2	1	no	—
143	C₂²⋊C₄×C₄₇	—	2	1	no	—
144	C₂²⋊C₄×C₄₇	—	2	2	no	—
145	C₂²⋊C₄×C₄₇	—	2	1	no	—
146	C₂²⋊C₄×C₄₇	—	2	2	no	—
147	C₄²×C₄₇	—	2	1	no	—
148	C₄²×C₄₇	—	2	1	no	—
149	C₄²×C₄₇	—	2	1	no	—
150	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
151	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
152	C₄²×C₄₇	#41	1	1	yes	characteristic
153	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
154	C₂³×C₄₇	—	2	1	no	—
155	C₂³×C₄₇	—	2	2	no	—
156	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
157	Q₈×C₄₇	—	2	1	no	—
158	Q₈×C₄₇	—	8	1	no	—
159	Q₈×C₄₇	#131	1	2	yes	—
160	D₄×C₄₇	—	2	2	no	—
161	D₄×C₄₇	—	2	1	no	—
162	D₄×C₄₇	—	2	1	no	—
163	D₄×C₄₇	—	2	2	no	—
164	D₄×C₄₇	—	4	2	no	—
165	D₄×C₄₇	—	4	2	no	—
166	D₄×C₄₇	—	8	1	no	—
167	D₄×C₄₇	—	8	2	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	—	4	1	no	—
179	C₂×C₄×C₄₇	—	4	2	no	—
180	C₂×C₄×C₄₇	—	4	2	no	—
181	C₂×C₄×C₄₇	—	4	1	no	—
182	C₂×C₄×C₄₇	—	4	2	no	—
183	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
184	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
185	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
186	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
187	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
189	C₈×C₄₇	—	2	2	no	—
190	C₈×C₄₇	—	2	2	no	—
191	C₈×C₄₇	—	2	2	no	—
192	C₈×C₄₇	—	2	2	no	—
193	C₈×C₄₇	—	2	2	no	—
194	C₈×C₄₇	—	2	2	no	—
195	C₈×C₄₇	—	4	2	no	—
196	C₈×C₄₇	—	4	1	no	—
197	C₈×C₄₇	—	4	1	no	—
198	#18018	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
199	C₂²×C₄₇	—	2	1	no	—
200	C₂²×C₄₇	—	2	1	no	—
201	C₂²×C₄₇	—	2	1	no	—
202	C₂²×C₄₇	—	4	1	no	—
203	C₂²×C₄₇	—	4	2	no	—
204	C₂²×C₄₇	—	4	2	no	—
205	C₂²×C₄₇	—	4	1	no	—
206	C₂²×C₄₇	—	4	1	no	—
207	C₂²×C₄₇	—	4	2	no	—
208	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
209	C₄×C₄₇	—	2	1	no	—
210	C₄×C₄₇	—	2	2	no	—
211	C₄×C₄₇	—	2	1	no	—
212	C₄×C₄₇	—	2	1	no	—
213	C₄×C₄₇	—	4	1	no	—
214	C₄×C₄₇	—	4	2	no	—
215	C₄×C₄₇	—	4	1	no	—
216	C₄×C₄₇	#443	1	2	yes	—
217	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
218	C₄×C₄₇	#568	1	1	yes	characteristic
219	C₄×C₄₇	#576	1	1	yes	characteristic
220	C₄×C₄₇	#577	1	1	yes	characteristic
221	#3106	C₂×C₄₇	1	1	yes	characteristic
222	#2991	C₂×C₄₇	1	1	yes	characteristic, complemented
223	#2979	C₂×C₄₇	1	1	yes	characteristic, complemented
224	#1589	C₂×C₄₇	1	2	yes	complemented
225	#1588	C₂×C₄₇	1	2	yes	complemented
226	#1586	C₂×C₄₇	1	2	yes	complemented
227	C₈×SD₁₆	C₂×C₄₇	1	2	yes	complemented
228	#1574	C₂×C₄₇	1	1	yes	characteristic, complemented
229	#1492	C₂×C₄₇	1	1	yes	characteristic, complemented
230	#1476	C₂×C₄₇	1	1	yes	characteristic, complemented
231	#1450	C₂×C₄₇	1	1	yes	characteristic, complemented
232	C₂×C₄₇	—	4	1	no	—
233	C₂×C₄₇	—	8	1	no	—
234	C₂×C₄₇	—	8	2	no	—
235	C₂×C₄₇	#2933	1	1	yes	characteristic
236	C₂×C₄₇	#2946	1	1	yes	characteristic
237	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
238	#532	C₂²×C₄₇	1	1	yes	characteristic
239	C₄×#41	C₂²×C₄₇	1	1	yes	characteristic
240	#482	C₄×C₄₇	1	2	yes	—
241	#477	C₄×C₄₇	1	1	yes	characteristic
242	#476	C₄×C₄₇	1	1	yes	characteristic
243	#460	C₄×C₄₇	1	1	yes	characteristic
244	#459	C₄×C₄₇	1	1	yes	characteristic
245	#449	C₄×C₄₇	1	2	yes	—
246	C₈×Q₈	C₂²×C₄₇	1	2	yes	—
247	C₄×SD₁₆	C₂²×C₄₇	1	2	yes	—
248	C₄×D₈	C₂²×C₄₇	1	2	yes	—
249	#436	—	2	1	no	—
250	#436	—	2	2	no	—
251	#436	C₂²×C₄₇	1	2	yes	—
252	#436	C₂²×C₄₇	1	2	yes	—
253	C₈×D₄	—	2	1	no	—
254	C₈×D₄	C₂²×C₄₇	1	2	yes	—
255	#431	—	2	1	no	—
256	#431	C₂²×C₄₇	1	1	yes	characteristic
257	#431	C₂²×C₄₇	1	1	yes	characteristic
258	#431	C₂²×C₄₇	1	1	yes	characteristic
259	#423	—	2	1	no	—
260	#423	C₂²×C₄₇	1	1	yes	characteristic
261	#408	—	2	2	no	—
262	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
263	#335	C₂²×C₄₇	1	2	yes	—
264	#334	C₂²×C₄₇	1	2	yes	—
265	Q₈⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
266	Q₈⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
267	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
268	D₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
269	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
270	D₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
271	#322	C₂²×C₄₇	1	2	yes	—
272	C₈²	C₂²×C₄₇	1	2	yes	—
273	C₄₇	#18018	1	1	yes	characteristic, direct product factor, Sylow
274	C₂×#41	—	2	1	no	—
275	C₂×#41	C₂×C₄×C₄₇	1	1	yes	characteristic
276	C₂×SD₁₆	C₂×C₄×C₄₇	1	2	yes	—
277	C₂×D₈	C₂×C₄×C₄₇	1	2	yes	—
278	C₂×M₁₆	—	2	1	no	—
279	C₂×M₁₆	—	2	2	no	—
280	C₂×M₁₆	—	2	2	no	—
281	C₂²×C₈	—	2	1	no	—
282	C₂²×C₈	—	2	2	no	—
283	C₄⋊Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
284	#127	C₂×C₄×C₄₇	1	1	yes	characteristic
285	#124	—	2	1	no	—
286	#121	—	2	1	no	—
287	#121	C₂×C₄×C₄₇	1	2	yes	—
288	C₄×Q₈	C₂×C₄×C₄₇	1	1	yes	characteristic
289	C₄×Q₈	C₂³×C₄₇	1	1	yes	characteristic
290	C₄×D₄	—	2	1	no	—
291	C₄×D₄	—	2	1	no	—
292	C₄×D₄	—	2	1	no	—
293	C₄×D₄	C₂×C₄×C₄₇	1	1	yes	characteristic
294	C₄×D₄	C₂³×C₄₇	1	1	yes	characteristic
295	C₄×D₄	C₂³×C₄₇	1	2	yes	—
296	#117	—	2	1	no	—
297	#117	C₂×C₄×C₄₇	1	1	yes	characteristic
298	C₂×C₄²	—	2	1	no	—
299	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
300	#107	C₂×C₄×C₄₇	1	2	yes	—
301	#106	C₂×C₄×C₄₇	1	2	yes	—
302	C₄⋊C₈	—	2	2	no	—
303	C₄⋊C₈	—	2	1	no	—
304	C₄⋊C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
305	C₄⋊C₈	C₂×C₄×C₄₇	1	1	yes	characteristic
306	C₄⋊C₈	D₄×C₄₇	1	1	yes	characteristic
307	C₄⋊C₈	D₄×C₄₇	1	1	yes	characteristic
308	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
309	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
310	C₄⋊C₈	C₂³×C₄₇	1	1	yes	characteristic
311	#103	C₂×C₄×C₄₇	1	2	yes	—
312	#102	C₂×C₄×C₄₇	1	2	yes	—
313	#102	C₂×C₄×C₄₇	1	2	yes	—
314	#102	C₂×C₄×C₄₇	1	2	yes	—
315	C₂²⋊C₈	—	2	1	no	—
316	C₂²⋊C₈	—	2	2	no	—
317	C₂²⋊C₈	—	2	2	no	—
318	C₂²⋊C₈	—	2	2	no	—
319	C₂²⋊C₈	C₂×C₄×C₄₇	1	2	yes	—
320	C₂²⋊C₈	D₄×C₄₇	1	2	yes	—
321	C₄×C₈	—	2	2	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	2	1	no	—
324	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
325	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
326	C₄×C₈	C₂³×C₄₇	1	2	yes	—
327	C₄×C₈	C₂³×C₄₇	1	2	yes	—
328	#41	—	2	2	no	—
329	#41	—	4	1	no	—
330	#41	—	8	1	no	—
331	#41	—	8	1	no	—
332	C₂×Q₈	—	2	1	no	—
333	C₂×Q₈	C₂²×C₄×C₄₇	1	1	yes	characteristic
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
339	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
340	C₂²×C₄	—	2	1	no	—
341	C₂²×C₄	—	2	1	no	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	2	no	—
344	C₂²×C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
345	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
346	C₂²×C₄	#41×C₄₇	1	1	yes	characteristic
347	SD₁₆	—	2	4	no	—
348	D₈	—	4	2	no	—
349	M₁₆	—	8	2	no	—
350	M₁₆	—	8	2	no	—
351	M₁₆	—	8	1	no	—
352	C₂×C₈	—	2	4	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	—	2	1	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	—	8	2	no	—
359	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
360	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
361	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
362	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
363	C₄⋊C₄	—	2	1	no	—
364	C₄⋊C₄	—	2	1	no	—
365	C₄⋊C₄	—	2	1	no	—
366	C₄⋊C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
367	C₄⋊C₄	C₂²×C₄×C₄₇	1	1	yes	characteristic
368	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
369	C₂²⋊C₄	—	2	1	no	—
370	C₂²⋊C₄	—	2	1	no	—
371	C₂²⋊C₄	—	2	2	no	—
372	C₂²⋊C₄	—	2	1	no	—
373	C₂²⋊C₄	—	2	2	no	—
374	C₄²	—	2	1	no	—
375	C₄²	—	2	1	no	—
376	C₄²	—	2	1	no	—
377	C₄²	C₂²×C₄×C₄₇	1	1	yes	characteristic
378	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
379	C₄²	#41×C₄₇	1	1	yes	characteristic
380	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
381	C₂³	—	2	1	no	—
382	C₂³	—	2	2	no	—
383	C₂³	C₄×D₄×C₄₇	1	1	yes	characteristic
384	Q₈	—	2	1	no	—
385	Q₈	—	8	1	no	—
386	Q₈	#131×C₄₇	1	2	yes	—
387	D₄	—	2	2	no	—
388	D₄	—	2	1	no	—
389	D₄	—	2	1	no	—
390	D₄	—	2	2	no	—
391	D₄	—	4	2	no	—
392	D₄	—	4	2	no	—
393	D₄	—	8	1	no	—
394	D₄	—	8	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	1	no	—
398	C₂×C₄	—	2	1	no	—
399	C₂×C₄	—	2	1	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	1	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	2	no	—
405	C₂×C₄	—	4	1	no	—
406	C₂×C₄	—	4	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	1	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
411	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
412	C₂×C₄	C₄×D₄×C₄₇	1	1	yes	characteristic
413	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
414	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
415	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
416	C₈	—	2	2	no	—
417	C₈	—	2	2	no	—
418	C₈	—	2	2	no	—
419	C₈	—	2	2	no	—
420	C₈	—	2	2	no	—
421	C₈	—	2	2	no	—
422	C₈	—	4	1	no	—
423	C₈	—	4	2	no	—
424	C₈	—	4	1	no	—
425	C₂²	—	2	1	no	—
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	4	1	no	—
429	C₂²	—	4	2	no	—
430	C₂²	—	4	2	no	—
431	C₂²	—	4	1	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	2	no	—
434	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
435	C₄	—	2	1	no	—
436	C₄	—	2	2	no	—
437	C₄	—	2	1	no	—
438	C₄	—	2	1	no	—
439	C₄	—	4	2	no	—
440	C₄	—	4	1	no	—
441	C₄	—	4	1	no	—
442	C₄	C₄₇×#443	1	2	yes	—
443	C₄	C₂×#131×C₄₇	1	1	yes	characteristic
444	C₄	C₄₇×#568	1	1	yes	characteristic
445	C₄	C₄₇×#576	1	1	yes	characteristic
446	C₄	C₄₇×#577	1	1	yes	characteristic
447	C₂	—	4	1	no	—
448	C₂	—	8	1	no	—
449	C₂	—	8	2	no	—
450	C₂	C₄₇×#2933	1	1	yes	characteristic
451	C₂	C₄₇×#2946	1	1	yes	characteristic
452	C₂	C₂×C₄₇×#443	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×#3106	C₂
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×#2991	C₂	semidirect
3. C₄₇×#2979	C₂	semidirect
4. C₄₇×#1589	C₂	semidirect
5. C₄₇×#1588	C₂	semidirect
6. C₄₇×#1586	C₂	semidirect
7. C₈×SD₁₆×C₄₇	C₂	semidirect
8. C₄₇×#1574	C₂	semidirect
9. C₄₇×#1492	C₂	semidirect
10. C₄₇×#1476	C₂	semidirect
11. C₄₇×#1450	C₂	semidirect
198. #18018	C₄₇	direct (N × H)
222. #2991	C₂×C₄₇	semidirect
223. #2979	C₂×C₄₇	semidirect
224. #1589	C₂×C₄₇	semidirect
225. #1588	C₂×C₄₇	semidirect
226. #1586	C₂×C₄₇	semidirect
227. C₈×SD₁₆	C₂×C₄₇	semidirect
228. #1574	C₂×C₄₇	semidirect
229. #1492	C₂×C₄₇	semidirect
230. #1476	C₂×C₄₇	semidirect
231. #1450	C₂×C₄₇	semidirect
273. C₄₇	#18018	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×#3106	2
C₄₇×#2991	2
C₄₇×#2979	2
C₄₇×#1589	2
C₄₇×#1588	2
C₄₇×#1586	2
C₈×SD₁₆×C₄₇	2
C₄₇×#1574	2
C₄₇×#1492	2
C₄₇×#1476	2
C₄₇×#1450	2
#18018	47

Subgroups — C47×#18018 #26057716

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18018 #26057716