Subgroups — C₄₇×#18839 #26058537

Order 12032.

936 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#3501	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄₇×#3254	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3210	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#3109	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#1637	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1632	C₂	1	2	yes	maximal, complemented
7	C₄₇×#1627	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1622	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1559	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1497	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1486	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₇×#554	—	2	1	no	—
13	C₄₇×#554	—	2	2	no	—
14	C₄₇×#554	—	2	2	no	—
15	C₄₇×#554	C₂²	1	2	yes	—
16	D₄×Q₈×C₄₇	—	2	1	no	—
17	D₄×Q₈×C₄₇	C₂²	1	2	yes	—
18	C₄₇×#544	—	2	1	no	—
19	C₄₇×#543	—	2	2	no	—
20	C₄₇×#533	C₂²	1	1	yes	characteristic
21	C₄₇×#533	C₂²	1	1	yes	characteristic
22	C₄₇×#532	C₂²	1	1	yes	characteristic
23	C₂×C₂²⋊Q₈×C₄₇	—	2	2	no	—
24	C₄₇×#518	—	2	1	no	—
25	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
26	C₄₇×#494	C₂²	1	1	yes	characteristic, complemented
27	C₄₇×#492	C₂²	1	1	yes	characteristic, complemented
28	C₄₇×#487	C₂²	1	1	yes	characteristic, complemented
29	C₄₇×#486	C₂²	1	1	yes	characteristic, complemented
30	C₄₇×#481	—	2	1	no	—
31	C₄₇×#477	C₂²	1	2	yes	complemented
32	C₄₇×#476	C₂²	1	2	yes	—
33	C₄₇×#474	—	2	1	no	—
34	C₄₇×#468	—	2	2	no	—
35	C₄₇×#464	—	2	2	no	—
36	C₄₇×#461	—	2	1	no	—
37	C₄₇×#460	C₂²	1	2	yes	complemented
38	C₄₇×#459	C₂²	1	2	yes	—
39	C₄₇×#452	—	2	2	no	—
40	C₄₇×#447	—	2	1	no	—
41	C₄₇×#442	—	2	2	no	—
42	C₄₇×#432	C₂²	1	1	yes	characteristic
43	C₄₇×#431	C₂²	1	1	yes	characteristic
44	C₄₇×#423	C₂²	1	1	yes	characteristic
45	C₄₇×#333	C₂²	1	2	yes	complemented
46	C₄₇×#332	C₂²	1	2	yes	complemented
47	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
48	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	complemented
49	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
50	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
51	C₂×#41×C₄₇	—	2	1	no	—
52	C₂²×Q₈×C₄₇	—	2	2	no	—
53	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
54	C₂³×C₄×C₄₇	—	2	1	no	—
55	C₂×Q₁₆×C₄₇	—	2	2	no	—
56	C₂×SD₁₆×C₄₇	—	2	2	no	—
57	C₂×SD₁₆×C₄₇	—	2	2	no	—
58	C₂×D₈×C₄₇	—	2	2	no	—
59	C₂×M₁₆×C₄₇	—	2	1	no	—
60	C₄⋊Q₈×C₄₇	—	2	2	no	—
61	C₄⋊Q₈×C₄₇	—	2	2	no	—
62	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
63	C₄⋊Q₈×C₄₇	D₄	1	1	yes	characteristic
64	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
65	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
66	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
67	#127×C₄₇	C₂³	1	1	yes	characteristic
68	#125×C₄₇	—	2	2	no	—
69	#125×C₄₇	—	2	2	no	—
70	#125×C₄₇	—	2	1	no	—
71	#125×C₄₇	—	2	1	no	—
72	#124×C₄₇	—	2	1	no	—
73	C₂²⋊Q₈×C₄₇	—	2	4	no	—
74	C₂²⋊Q₈×C₄₇	—	2	4	no	—
75	C₂²⋊Q₈×C₄₇	—	2	4	no	—
76	C₂²⋊Q₈×C₄₇	—	2	4	no	—
77	C₂²⋊Q₈×C₄₇	—	2	2	no	—
78	C₂²⋊Q₈×C₄₇	—	2	4	no	—
79	C₂²⋊Q₈×C₄₇	—	2	1	no	—
80	C₂²⋊Q₈×C₄₇	—	2	1	no	—
81	C₂²⋊Q₈×C₄₇	—	2	2	no	—
82	C₂²⋊Q₈×C₄₇	—	2	4	no	—
83	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
84	C₂²⋊Q₈×C₄₇	D₄	1	2	yes	—
85	#121×C₄₇	—	2	1	no	—
86	#121×C₄₇	—	2	1	no	—
87	C₄×Q₈×C₄₇	—	2	1	no	—
88	C₄×Q₈×C₄₇	—	2	1	no	—
89	C₄×Q₈×C₄₇	D₄	1	2	yes	—
90	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
91	C₄×D₄×C₄₇	—	2	2	no	—
92	C₄×D₄×C₄₇	—	2	2	no	—
93	C₄×D₄×C₄₇	—	2	2	no	—
94	C₄×D₄×C₄₇	—	2	2	no	—
95	C₄×D₄×C₄₇	—	2	1	no	—
96	C₄×D₄×C₄₇	—	2	1	no	—
97	C₄×D₄×C₄₇	—	2	1	no	—
98	C₄×D₄×C₄₇	—	2	1	no	—
99	C₄×D₄×C₄₇	D₄	1	2	yes	—
100	C₄×D₄×C₄₇	C₂³	1	2	yes	—
101	#117×C₄₇	—	2	1	no	—
102	#117×C₄₇	—	2	1	no	—
103	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
104	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
105	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
106	C₂×C₂²⋊C₄×C₄₇	—	2	4	no	—
107	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
108	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
109	#107×C₄₇	—	2	2	no	—
110	#106×C₄₇	—	2	2	no	—
111	C₄⋊C₈×C₄₇	—	2	1	no	—
112	C₄⋊C₈×C₄₇	—	2	1	no	—
113	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
114	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
115	#103×C₄₇	—	2	2	no	—
116	#103×C₄₇	—	2	2	no	—
117	#102×C₄₇	—	2	2	no	—
118	#102×C₄₇	—	2	2	no	—
119	#102×C₄₇	—	2	2	no	—
120	#102×C₄₇	—	2	2	no	—
121	C₂²⋊C₈×C₄₇	—	2	1	no	—
122	C₂²⋊C₈×C₄₇	—	2	1	no	—
123	#97×C₄₇	—	2	1	no	—
124	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
125	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
126	C₂⁴×C₄₇	—	2	1	no	—
127	#41×C₄₇	—	8	2	no	—
128	C₂×Q₈×C₄₇	—	2	4	no	—
129	C₂×Q₈×C₄₇	—	2	1	no	—
130	C₂×Q₈×C₄₇	—	2	1	no	—
131	C₂×Q₈×C₄₇	—	2	1	no	—
132	C₂×Q₈×C₄₇	—	8	2	no	—
133	C₂×Q₈×C₄₇	—	8	2	no	—
134	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
135	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
136	C₂×D₄×C₄₇	—	2	4	no	—
137	C₂×D₄×C₄₇	—	2	1	no	—
138	C₂×D₄×C₄₇	—	2	1	no	—
139	C₂×D₄×C₄₇	—	2	1	no	—
140	C₂×D₄×C₄₇	—	2	1	no	—
141	C₂×D₄×C₄₇	—	4	1	no	—
142	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
143	C₂²×C₄×C₄₇	—	2	4	no	—
144	C₂²×C₄×C₄₇	—	2	4	no	—
145	C₂²×C₄×C₄₇	—	2	1	no	—
146	C₂²×C₄×C₄₇	—	2	2	no	—
147	C₂²×C₄×C₄₇	—	2	2	no	—
148	C₂²×C₄×C₄₇	—	4	1	no	—
149	C₂²×C₄×C₄₇	—	8	1	no	—
150	C₂²×C₄×C₄₇	—	8	1	no	—
151	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
154	Q₁₆×C₄₇	—	8	2	no	—
155	SD₁₆×C₄₇	—	8	2	no	—
156	SD₁₆×C₄₇	—	8	2	no	—
157	D₈×C₄₇	—	4	4	no	—
158	M₁₆×C₄₇	—	8	1	no	—
159	C₂×C₈×C₄₇	—	2	1	no	—
160	C₂×C₈×C₄₇	—	2	2	no	—
161	C₂×C₈×C₄₇	—	2	1	no	—
162	C₂×C₈×C₄₇	—	2	2	no	—
163	C₄⋊C₄×C₄₇	—	2	4	no	—
164	C₄⋊C₄×C₄₇	—	2	4	no	—
165	C₄⋊C₄×C₄₇	—	2	4	no	—
166	C₄⋊C₄×C₄₇	—	2	2	no	—
167	C₄⋊C₄×C₄₇	—	2	2	no	—
168	C₄⋊C₄×C₄₇	—	2	1	no	—
169	C₄⋊C₄×C₄₇	—	2	1	no	—
170	C₄⋊C₄×C₄₇	—	2	1	no	—
171	C₄⋊C₄×C₄₇	—	2	1	no	—
172	C₄⋊C₄×C₄₇	—	2	2	no	—
173	C₄⋊C₄×C₄₇	—	2	1	no	—
174	C₄⋊C₄×C₄₇	—	2	1	no	—
175	C₄⋊C₄×C₄₇	—	2	1	no	—
176	C₄⋊C₄×C₄₇	—	2	2	no	—
177	C₄⋊C₄×C₄₇	—	2	1	no	—
178	C₄⋊C₄×C₄₇	—	2	1	no	—
179	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
180	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
181	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
182	C₂²⋊C₄×C₄₇	—	2	4	no	—
183	C₂²⋊C₄×C₄₇	—	2	4	no	—
184	C₂²⋊C₄×C₄₇	—	2	2	no	—
185	C₂²⋊C₄×C₄₇	—	2	2	no	—
186	C₂²⋊C₄×C₄₇	—	2	2	no	—
187	C₂²⋊C₄×C₄₇	—	2	2	no	—
188	C₂²⋊C₄×C₄₇	—	4	1	no	—
189	C₂²⋊C₄×C₄₇	—	4	1	no	—
190	C₄²×C₄₇	—	2	2	no	—
191	C₄²×C₄₇	—	2	2	no	—
192	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
193	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
194	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
195	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
196	C₂³×C₄₇	—	2	4	no	—
197	C₂³×C₄₇	—	2	2	no	—
198	C₂³×C₄₇	—	4	1	no	—
199	C₂³×C₄₇	—	8	1	no	—
200	C₂³×C₄₇	—	8	1	no	—
201	C₂³×C₄₇	#120	1	1	yes	characteristic
202	Q₈×C₄₇	—	2	2	no	—
203	Q₈×C₄₇	—	2	2	no	—
204	Q₈×C₄₇	—	4	2	no	—
205	Q₈×C₄₇	—	4	2	no	—
206	Q₈×C₄₇	—	4	1	no	—
207	Q₈×C₄₇	—	4	1	no	—
208	Q₈×C₄₇	—	8	1	no	—
209	Q₈×C₄₇	—	8	4	no	—
210	D₄×C₄₇	—	2	4	no	—
211	D₄×C₄₇	—	2	2	no	—
212	D₄×C₄₇	—	4	2	no	—
213	D₄×C₄₇	—	4	2	no	—
214	D₄×C₄₇	—	4	1	no	—
215	D₄×C₄₇	—	4	1	no	—
216	D₄×C₄₇	—	8	2	no	—
217	D₄×C₄₇	#137	1	4	yes	—
218	C₂×C₄×C₄₇	—	2	2	no	—
219	C₂×C₄×C₄₇	—	2	1	no	—
220	C₂×C₄×C₄₇	—	2	1	no	—
221	C₂×C₄×C₄₇	—	2	2	no	—
222	C₂×C₄×C₄₇	—	2	2	no	—
223	C₂×C₄×C₄₇	—	2	2	no	—
224	C₂×C₄×C₄₇	—	2	2	no	—
225	C₂×C₄×C₄₇	—	2	2	no	—
226	C₂×C₄×C₄₇	—	4	1	no	—
227	C₂×C₄×C₄₇	—	4	2	no	—
228	C₂×C₄×C₄₇	—	4	2	no	—
229	C₂×C₄×C₄₇	—	4	1	no	—
230	C₂×C₄×C₄₇	—	8	2	no	—
231	C₂×C₄×C₄₇	—	8	2	no	—
232	C₂×C₄×C₄₇	—	8	1	no	—
233	C₂×C₄×C₄₇	—	8	4	no	—
234	C₂×C₄×C₄₇	—	8	4	no	—
235	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
236	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
237	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
238	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
239	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
240	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
241	C₈×C₄₇	—	4	1	no	—
242	C₈×C₄₇	—	4	1	no	—
243	C₈×C₄₇	—	4	2	no	—
244	C₈×C₄₇	—	4	2	no	—
245	#18839	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
246	C₂²×C₄₇	—	2	1	no	—
247	C₂²×C₄₇	—	2	4	no	—
248	C₂²×C₄₇	—	2	1	no	—
249	C₂²×C₄₇	—	2	1	no	—
250	C₂²×C₄₇	—	4	2	no	—
251	C₂²×C₄₇	—	4	2	no	—
252	C₂²×C₄₇	—	8	4	no	—
253	C₂²×C₄₇	—	8	1	no	—
254	C₂²×C₄₇	—	8	1	no	—
255	C₂²×C₄₇	—	8	1	no	—
256	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
257	C₄×C₄₇	—	2	1	no	—
258	C₄×C₄₇	—	2	1	no	—
259	C₄×C₄₇	—	2	1	no	—
260	C₄×C₄₇	—	2	1	no	—
261	C₄×C₄₇	—	4	2	no	—
262	C₄×C₄₇	—	4	2	no	—
263	C₄×C₄₇	—	4	2	no	—
264	C₄×C₄₇	—	4	2	no	—
265	C₄×C₄₇	—	4	2	no	—
266	C₄×C₄₇	—	8	1	no	—
267	C₄×C₄₇	C₂×#137	1	2	yes	—
268	C₄×C₄₇	#576	1	1	yes	characteristic
269	C₄×C₄₇	#577	1	1	yes	characteristic
270	#3501	C₂×C₄₇	1	1	yes	characteristic, complemented
271	#3254	C₂×C₄₇	1	1	yes	characteristic, complemented
272	#3210	C₂×C₄₇	1	1	yes	characteristic, complemented
273	#3109	C₂×C₄₇	1	1	yes	characteristic
274	#1637	C₂×C₄₇	1	2	yes	complemented
275	#1632	C₂×C₄₇	1	2	yes	complemented
276	#1627	C₂×C₄₇	1	2	yes	complemented
277	#1622	C₂×C₄₇	1	2	yes	complemented
278	#1559	C₂×C₄₇	1	1	yes	characteristic, complemented
279	#1497	C₂×C₄₇	1	1	yes	characteristic, complemented
280	#1486	C₂×C₄₇	1	1	yes	characteristic, complemented
281	C₂×C₄₇	—	4	1	no	—
282	C₂×C₄₇	—	4	4	no	—
283	C₂×C₄₇	—	16	1	no	—
284	C₂×C₄₇	#3004	1	1	yes	characteristic
285	C₂×C₄₇	#3012	1	1	yes	characteristic
286	C₂×C₄₇	#3021	1	1	yes	characteristic
287	#554	—	2	1	no	—
288	#554	—	2	2	no	—
289	#554	—	2	2	no	—
290	#554	C₂²×C₄₇	1	2	yes	—
291	D₄×Q₈	—	2	1	no	—
292	D₄×Q₈	C₂²×C₄₇	1	2	yes	—
293	#544	—	2	1	no	—
294	#543	—	2	2	no	—
295	#533	C₂²×C₄₇	1	1	yes	characteristic
296	#533	C₂²×C₄₇	1	1	yes	characteristic
297	#532	C₂²×C₄₇	1	1	yes	characteristic
298	C₂×C₂²⋊Q₈	—	2	2	no	—
299	#518	—	2	1	no	—
300	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
301	#494	C₂²×C₄₇	1	1	yes	characteristic, complemented
302	#492	C₂²×C₄₇	1	1	yes	characteristic, complemented
303	#487	C₂²×C₄₇	1	1	yes	characteristic, complemented
304	#486	C₂²×C₄₇	1	1	yes	characteristic, complemented
305	#481	—	2	1	no	—
306	#477	C₂²×C₄₇	1	2	yes	complemented
307	#476	C₂²×C₄₇	1	2	yes	—
308	#474	—	2	1	no	—
309	#468	—	2	2	no	—
310	#464	—	2	2	no	—
311	#461	—	2	1	no	—
312	#460	C₂²×C₄₇	1	2	yes	complemented
313	#459	C₂²×C₄₇	1	2	yes	—
314	#452	—	2	2	no	—
315	#447	—	2	1	no	—
316	#442	—	2	2	no	—
317	#432	C₂²×C₄₇	1	1	yes	characteristic
318	#431	C₂²×C₄₇	1	1	yes	characteristic
319	#423	C₂²×C₄₇	1	1	yes	characteristic
320	#333	C₂²×C₄₇	1	2	yes	complemented
321	#332	C₂²×C₄₇	1	2	yes	complemented
322	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	complemented
323	Q₈⋊C₈	C₂²×C₄₇	1	2	yes	complemented
324	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
325	D₄⋊C₈	C₂²×C₄₇	1	2	yes	—
326	C₄₇	#18839	1	1	yes	characteristic, direct product factor, Sylow
327	C₂×#41	—	2	1	no	—
328	C₂²×Q₈	—	2	2	no	—
329	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
330	C₂³×C₄	—	2	1	no	—
331	C₂×Q₁₆	—	2	2	no	—
332	C₂×SD₁₆	—	2	2	no	—
333	C₂×SD₁₆	—	2	2	no	—
334	C₂×D₈	—	2	2	no	—
335	C₂×M₁₆	—	2	1	no	—
336	C₄⋊Q₈	—	2	2	no	—
337	C₄⋊Q₈	—	2	2	no	—
338	C₄⋊Q₈	D₄×C₄₇	1	1	yes	characteristic
339	C₄⋊Q₈	D₄×C₄₇	1	1	yes	characteristic
340	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
341	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
342	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
343	#127	C₂³×C₄₇	1	1	yes	characteristic
344	#125	—	2	2	no	—
345	#125	—	2	2	no	—
346	#125	—	2	1	no	—
347	#125	—	2	1	no	—
348	#124	—	2	1	no	—
349	C₂²⋊Q₈	—	2	4	no	—
350	C₂²⋊Q₈	—	2	4	no	—
351	C₂²⋊Q₈	—	2	4	no	—
352	C₂²⋊Q₈	—	2	4	no	—
353	C₂²⋊Q₈	—	2	2	no	—
354	C₂²⋊Q₈	—	2	4	no	—
355	C₂²⋊Q₈	—	2	1	no	—
356	C₂²⋊Q₈	—	2	1	no	—
357	C₂²⋊Q₈	—	2	2	no	—
358	C₂²⋊Q₈	—	2	4	no	—
359	C₂²⋊Q₈	D₄×C₄₇	1	2	yes	—
360	C₂²⋊Q₈	D₄×C₄₇	1	2	yes	—
361	#121	—	2	1	no	—
362	#121	—	2	1	no	—
363	C₄×Q₈	—	2	1	no	—
364	C₄×Q₈	—	2	1	no	—
365	C₄×Q₈	D₄×C₄₇	1	2	yes	—
366	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
367	C₄×D₄	—	2	2	no	—
368	C₄×D₄	—	2	2	no	—
369	C₄×D₄	—	2	2	no	—
370	C₄×D₄	—	2	2	no	—
371	C₄×D₄	—	2	1	no	—
372	C₄×D₄	—	2	1	no	—
373	C₄×D₄	—	2	1	no	—
374	C₄×D₄	—	2	1	no	—
375	C₄×D₄	D₄×C₄₇	1	2	yes	—
376	C₄×D₄	C₂³×C₄₇	1	2	yes	—
377	#117	—	2	1	no	—
378	#117	—	2	1	no	—
379	C₂×C₄⋊C₄	—	2	4	no	—
380	C₂×C₄⋊C₄	—	2	2	no	—
381	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
382	C₂×C₂²⋊C₄	—	2	4	no	—
383	C₂×C₂²⋊C₄	—	2	1	no	—
384	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
385	#107	—	2	2	no	—
386	#106	—	2	2	no	—
387	C₄⋊C₈	—	2	1	no	—
388	C₄⋊C₈	—	2	1	no	—
389	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
390	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
391	#103	—	2	2	no	—
392	#103	—	2	2	no	—
393	#102	—	2	2	no	—
394	#102	—	2	2	no	—
395	#102	—	2	2	no	—
396	#102	—	2	2	no	—
397	C₂²⋊C₈	—	2	1	no	—
398	C₂²⋊C₈	—	2	1	no	—
399	#97	—	2	1	no	—
400	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
401	C₄×C₈	C₂³×C₄₇	1	1	yes	characteristic
402	C₂⁴	—	2	1	no	—
403	#41	—	8	2	no	—
404	C₂×Q₈	—	2	4	no	—
405	C₂×Q₈	—	2	1	no	—
406	C₂×Q₈	—	2	1	no	—
407	C₂×Q₈	—	2	1	no	—
408	C₂×Q₈	—	8	2	no	—
409	C₂×Q₈	—	8	2	no	—
410	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
411	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
412	C₂×D₄	—	2	4	no	—
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	2	1	no	—
415	C₂×D₄	—	2	1	no	—
416	C₂×D₄	—	2	1	no	—
417	C₂×D₄	—	4	1	no	—
418	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	2	1	no	—
422	C₂²×C₄	—	2	2	no	—
423	C₂²×C₄	—	2	2	no	—
424	C₂²×C₄	—	4	1	no	—
425	C₂²×C₄	—	8	1	no	—
426	C₂²×C₄	—	8	1	no	—
427	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
429	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
430	Q₁₆	—	8	2	no	—
431	SD₁₆	—	8	2	no	—
432	SD₁₆	—	8	2	no	—
433	D₈	—	4	4	no	—
434	M₁₆	—	8	1	no	—
435	C₂×C₈	—	2	1	no	—
436	C₂×C₈	—	2	1	no	—
437	C₂×C₈	—	2	2	no	—
438	C₂×C₈	—	2	2	no	—
439	C₄⋊C₄	—	2	4	no	—
440	C₄⋊C₄	—	2	4	no	—
441	C₄⋊C₄	—	2	4	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	1	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	—	2	2	no	—
449	C₄⋊C₄	—	2	1	no	—
450	C₄⋊C₄	—	2	1	no	—
451	C₄⋊C₄	—	2	1	no	—
452	C₄⋊C₄	—	2	2	no	—
453	C₄⋊C₄	—	2	1	no	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
456	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
457	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
458	C₂²⋊C₄	—	2	4	no	—
459	C₂²⋊C₄	—	2	4	no	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	—	2	2	no	—
462	C₂²⋊C₄	—	2	2	no	—
463	C₂²⋊C₄	—	2	2	no	—
464	C₂²⋊C₄	—	4	1	no	—
465	C₂²⋊C₄	—	4	1	no	—
466	C₄²	—	2	2	no	—
467	C₄²	—	2	2	no	—
468	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
469	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
470	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
471	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
472	C₂³	—	2	4	no	—
473	C₂³	—	2	2	no	—
474	C₂³	—	4	1	no	—
475	C₂³	—	8	1	no	—
476	C₂³	—	8	1	no	—
477	C₂³	#120×C₄₇	1	1	yes	characteristic
478	Q₈	—	2	2	no	—
479	Q₈	—	2	2	no	—
480	Q₈	—	4	2	no	—
481	Q₈	—	4	2	no	—
482	Q₈	—	4	1	no	—
483	Q₈	—	4	1	no	—
484	Q₈	—	8	1	no	—
485	Q₈	—	8	4	no	—
486	D₄	—	2	4	no	—
487	D₄	—	2	2	no	—
488	D₄	—	4	2	no	—
489	D₄	—	4	2	no	—
490	D₄	—	4	1	no	—
491	D₄	—	4	1	no	—
492	D₄	—	8	2	no	—
493	D₄	#137×C₄₇	1	4	yes	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	4	1	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	1	no	—
506	C₂×C₄	—	8	2	no	—
507	C₂×C₄	—	8	2	no	—
508	C₂×C₄	—	8	1	no	—
509	C₂×C₄	—	8	4	no	—
510	C₂×C₄	—	8	4	no	—
511	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
512	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
513	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
514	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
516	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
517	C₈	—	4	1	no	—
518	C₈	—	4	1	no	—
519	C₈	—	4	2	no	—
520	C₈	—	4	2	no	—
521	C₂²	—	2	1	no	—
522	C₂²	—	2	4	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	8	4	no	—
528	C₂²	—	8	1	no	—
529	C₂²	—	8	1	no	—
530	C₂²	—	8	1	no	—
531	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
532	C₄	—	2	1	no	—
533	C₄	—	2	1	no	—
534	C₄	—	2	1	no	—
535	C₄	—	2	1	no	—
536	C₄	—	4	2	no	—
537	C₄	—	4	2	no	—
538	C₄	—	4	2	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	2	no	—
541	C₄	—	8	1	no	—
542	C₄	C₂×#137×C₄₇	1	2	yes	—
543	C₄	C₄₇×#576	1	1	yes	characteristic
544	C₄	C₄₇×#577	1	1	yes	characteristic
545	C₂	—	4	1	no	—
546	C₂	—	4	4	no	—
547	C₂	—	16	1	no	—
548	C₂	C₄₇×#3004	1	1	yes	characteristic
549	C₂	C₄₇×#3012	1	1	yes	characteristic
550	C₂	C₄₇×#3021	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₇
prime radical	C₄₇×#3109	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄₇ ◁ C₂×C₄²×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₄₇×#3501	C₂	semidirect
2. C₄₇×#3254	C₂	semidirect
3. C₄₇×#3210	C₂	semidirect
5. C₄₇×#1637	C₂	semidirect
6. C₄₇×#1632	C₂	semidirect
7. C₄₇×#1627	C₂	semidirect
8. C₄₇×#1622	C₂	semidirect
9. C₄₇×#1559	C₂	semidirect
10. C₄₇×#1497	C₂	semidirect
11. C₄₇×#1486	C₂	semidirect
26. C₄₇×#494	C₂²	semidirect
27. C₄₇×#492	C₂²	semidirect
28. C₄₇×#487	C₂²	semidirect
29. C₄₇×#486	C₂²	semidirect
31. C₄₇×#477	C₂²	semidirect
37. C₄₇×#460	C₂²	semidirect
45. C₄₇×#333	C₂²	semidirect
46. C₄₇×#332	C₂²	semidirect
47. C₄₇×Q₈⋊C₈	C₂²	semidirect
48. C₄₇×Q₈⋊C₈	C₂²	semidirect
245. #18839	C₄₇	direct (N × H)
270. #3501	C₂×C₄₇	semidirect
271. #3254	C₂×C₄₇	semidirect
272. #3210	C₂×C₄₇	semidirect
274. #1637	C₂×C₄₇	semidirect
275. #1632	C₂×C₄₇	semidirect
276. #1627	C₂×C₄₇	semidirect
277. #1622	C₂×C₄₇	semidirect
278. #1559	C₂×C₄₇	semidirect
279. #1497	C₂×C₄₇	semidirect
280. #1486	C₂×C₄₇	semidirect
301. #494	C₂²×C₄₇	semidirect
302. #492	C₂²×C₄₇	semidirect
303. #487	C₂²×C₄₇	semidirect
304. #486	C₂²×C₄₇	semidirect
306. #477	C₂²×C₄₇	semidirect
312. #460	C₂²×C₄₇	semidirect
320. #333	C₂²×C₄₇	semidirect
321. #332	C₂²×C₄₇	semidirect
322. Q₈⋊C₈	C₂²×C₄₇	semidirect
323. Q₈⋊C₈	C₂²×C₄₇	semidirect
326. C₄₇	#18839	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×#3501	2
C₄₇×#3254	2
C₄₇×#3210	2
C₄₇×#3109	2
C₄₇×#1637	2
C₄₇×#1632	2
C₄₇×#1627	2
C₄₇×#1622	2
C₄₇×#1559	2
C₄₇×#1497	2
C₄₇×#1486	2
#18839	47

Subgroups — C47×#18839 #26058537

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18839 #26058537