Subgroups — C₄₇×#18777 #26058475

Order 12032.

1138 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₄×Q₈×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#3229	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#3101	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#3078	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#1651	C₂	1	4	yes	maximal, complemented
6	C₄₇×#1637	C₂	1	4	yes	maximal, complemented
7	C₄₇×#1546	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1486	C₂	1	1	yes	maximal, characteristic
9	C₄₇×#1479	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Q₈×C₄₇	—	2	1	no	—
11	D₄×Q₈×C₄₇	—	2	2	no	—
12	D₄×Q₈×C₄₇	—	2	2	no	—
13	D₄×Q₈×C₄₇	—	2	2	no	—
14	D₄×Q₈×C₄₇	C₂²	1	4	yes	—
15	C₄₇×#533	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₄₇	—	2	1	no	—
17	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
19	C₂×C₂²⋊Q₈×C₄₇	—	2	2	no	—
20	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×C₄×D₄×C₄₇	—	2	1	no	—
22	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
23	C₄₇×#498	C₂²	1	2	yes	complemented
24	C₄₇×#487	C₂²	1	2	yes	complemented
25	C₄₇×#483	—	2	1	no	—
26	C₄₇×#483	—	2	2	no	—
27	C₄₇×#479	—	2	2	no	—
28	C₄₇×#477	C₂²	1	2	yes	complemented
29	C₄₇×#476	C₂²	1	2	yes	—
30	C₄₇×#475	—	2	2	no	—
31	C₄₇×#475	C₂²	1	2	yes	complemented
32	C₄₇×#461	C₂²	1	2	yes	—
33	C₄₇×#450	—	2	1	no	—
34	C₄×SD₁₆×C₄₇	—	2	2	no	—
35	C₄₇×#431	C₂²	1	1	yes	characteristic
36	C₄₇×#431	C₂²	1	1	yes	characteristic
37	C₄₇×#428	—	2	1	no	—
38	C₄₇×#423	C₂²	1	1	yes	characteristic
39	C₄₇×#419	—	2	1	no	—
40	C₄₇×#332	C₂²	1	4	yes	complemented
41	C₄₇×Q₈⋊C₈	C₂²	1	4	yes	complemented
42	C₄₇×D₄⋊C₈	C₂²	1	4	yes	—
43	C₂²×Q₈×C₄₇	—	2	2	no	—
44	C₂²×Q₈×C₄₇	—	2	4	no	—
45	C₂²×Q₈×C₄₇	—	2	4	no	—
46	C₂²×Q₈×C₄₇	—	2	1	no	—
47	C₂²×Q₈×C₄₇	—	4	4	no	—
48	C₂²×Q₈×C₄₇	—	4	4	no	—
49	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
50	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
51	C₂³×C₄×C₄₇	—	2	2	no	—
52	C₂³×C₄×C₄₇	—	2	1	no	—
53	C₂×SD₁₆×C₄₇	—	2	2	no	—
54	C₂×M₁₆×C₄₇	—	2	1	no	—
55	C₄⋊Q₈×C₄₇	—	2	4	no	—
56	C₄⋊Q₈×C₄₇	—	2	4	no	—
57	C₄⋊Q₈×C₄₇	—	2	1	no	—
58	C₄⋊Q₈×C₄₇	—	2	1	no	—
59	C₄⋊Q₈×C₄₇	D₄	1	2	yes	—
60	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
61	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
62	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
63	#125×C₄₇	—	2	1	no	—
64	C₂²⋊Q₈×C₄₇	—	2	4	no	—
65	C₂²⋊Q₈×C₄₇	—	2	8	no	—
66	C₂²⋊Q₈×C₄₇	—	2	4	no	—
67	C₂²⋊Q₈×C₄₇	—	2	8	no	—
68	C₂²⋊Q₈×C₄₇	—	2	1	no	—
69	C₂²⋊Q₈×C₄₇	—	2	1	no	—
70	C₄×Q₈×C₄₇	—	2	1	no	—
71	C₄×Q₈×C₄₇	—	2	1	no	—
72	C₄×Q₈×C₄₇	—	2	1	no	—
73	C₄×Q₈×C₄₇	—	2	1	no	—
74	C₄×Q₈×C₄₇	D₄	1	2	yes	—
75	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
76	C₄×D₄×C₄₇	—	2	4	no	—
77	C₄×D₄×C₄₇	—	2	4	no	—
78	C₄×D₄×C₄₇	—	2	1	no	—
79	C₄×D₄×C₄₇	—	2	1	no	—
80	C₄×D₄×C₄₇	D₄	1	2	yes	—
81	C₄×D₄×C₄₇	C₂³	1	2	yes	—
82	#117×C₄₇	—	2	1	no	—
83	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
84	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
85	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
86	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
88	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
89	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
90	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
91	C₂×C₄²×C₄₇	—	2	1	no	—
92	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
93	#107×C₄₇	—	2	2	no	—
94	#106×C₄₇	—	2	4	no	—
95	#106×C₄₇	—	2	2	no	—
96	#106×C₄₇	—	2	2	no	—
97	C₄⋊C₈×C₄₇	—	2	1	no	—
98	C₄⋊C₈×C₄₇	—	2	1	no	—
99	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
100	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
101	#103×C₄₇	—	2	2	no	—
102	#103×C₄₇	—	2	2	no	—
103	#103×C₄₇	—	2	2	no	—
104	#103×C₄₇	—	2	4	no	—
105	#102×C₄₇	—	2	2	no	—
106	C₂²⋊C₈×C₄₇	—	2	1	no	—
107	C₂²⋊C₈×C₄₇	—	2	1	no	—
108	C₄×C₈×C₄₇	—	2	1	no	—
109	C₄×C₈×C₄₇	C₂³	1	2	yes	—
110	C₂⁴×C₄₇	—	2	1	no	—
111	C₂×Q₈×C₄₇	—	2	8	no	—
112	C₂×Q₈×C₄₇	—	2	1	no	—
113	C₂×Q₈×C₄₇	—	2	2	no	—
114	C₂×Q₈×C₄₇	—	2	2	no	—
115	C₂×Q₈×C₄₇	—	2	2	no	—
116	C₂×Q₈×C₄₇	—	2	1	no	—
117	C₂×Q₈×C₄₇	—	2	1	no	—
118	C₂×Q₈×C₄₇	—	4	8	no	—
119	C₂×Q₈×C₄₇	—	4	8	no	—
120	C₂×Q₈×C₄₇	—	4	16	no	—
121	C₂×Q₈×C₄₇	—	4	8	no	—
122	C₂×Q₈×C₄₇	—	4	2	no	—
123	C₂×Q₈×C₄₇	—	4	2	no	—
124	C₂×Q₈×C₄₇	SD₁₆	1	4	yes	complemented
125	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
126	C₂×D₄×C₄₇	—	2	4	no	—
127	C₂×D₄×C₄₇	—	2	1	no	—
128	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
129	C₂²×C₄×C₄₇	—	2	1	no	—
130	C₂²×C₄×C₄₇	—	2	8	no	—
131	C₂²×C₄×C₄₇	—	2	1	no	—
132	C₂²×C₄×C₄₇	—	2	2	no	—
133	C₂²×C₄×C₄₇	—	2	1	no	—
134	C₂²×C₄×C₄₇	—	2	2	no	—
135	C₂²×C₄×C₄₇	—	2	2	no	—
136	C₂²×C₄×C₄₇	—	4	8	no	—
137	C₂²×C₄×C₄₇	—	4	2	no	—
138	C₂²×C₄×C₄₇	—	4	2	no	—
139	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
142	SD₁₆×C₄₇	—	4	4	no	—
143	M₁₆×C₄₇	—	4	2	no	—
144	C₂×C₈×C₄₇	—	2	2	no	—
145	C₂×C₈×C₄₇	—	2	2	no	—
146	C₂×C₈×C₄₇	—	2	2	no	—
147	C₄⋊C₄×C₄₇	—	2	8	no	—
148	C₄⋊C₄×C₄₇	—	2	2	no	—
149	C₄⋊C₄×C₄₇	—	2	2	no	—
150	C₄⋊C₄×C₄₇	—	2	1	no	—
151	C₄⋊C₄×C₄₇	—	2	1	no	—
152	C₄⋊C₄×C₄₇	—	2	2	no	—
153	C₄⋊C₄×C₄₇	—	2	2	no	—
154	C₄⋊C₄×C₄₇	—	2	2	no	—
155	C₄⋊C₄×C₄₇	—	2	1	no	—
156	C₄⋊C₄×C₄₇	—	2	1	no	—
157	C₄⋊C₄×C₄₇	—	2	1	no	—
158	C₄⋊C₄×C₄₇	—	2	1	no	—
159	C₄⋊C₄×C₄₇	—	4	1	no	—
160	C₄⋊C₄×C₄₇	—	4	1	no	—
161	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
162	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
163	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
164	C₂²⋊C₄×C₄₇	—	2	8	no	—
165	C₂²⋊C₄×C₄₇	—	2	2	no	—
166	C₂²⋊C₄×C₄₇	—	2	2	no	—
167	C₂²⋊C₄×C₄₇	—	4	1	no	—
168	C₄²×C₄₇	—	2	2	no	—
169	C₄²×C₄₇	—	2	2	no	—
170	C₄²×C₄₇	—	4	1	no	—
171	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
172	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
173	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
174	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
175	C₂³×C₄₇	—	2	4	no	—
176	C₂³×C₄₇	—	2	2	no	—
177	C₂³×C₄₇	—	4	2	no	—
178	C₂³×C₄₇	—	4	2	no	—
179	C₂³×C₄₇	#120	1	1	yes	characteristic
180	Q₈×C₄₇	—	2	2	no	—
181	Q₈×C₄₇	—	2	4	no	—
182	Q₈×C₄₇	—	4	16	no	—
183	Q₈×C₄₇	—	4	2	no	—
184	Q₈×C₄₇	—	4	2	no	—
185	Q₈×C₄₇	—	4	2	no	—
186	Q₈×C₄₇	—	4	4	no	—
187	Q₈×C₄₇	—	4	2	no	—
188	Q₈×C₄₇	C₂×SD₁₆	1	4	yes	—
189	D₄×C₄₇	—	2	4	no	—
190	D₄×C₄₇	—	2	2	no	—
191	D₄×C₄₇	#137	1	4	yes	—
192	C₂×C₄×C₄₇	—	2	2	no	—
193	C₂×C₄×C₄₇	—	2	4	no	—
194	C₂×C₄×C₄₇	—	2	2	no	—
195	C₂×C₄×C₄₇	—	2	2	no	—
196	C₂×C₄×C₄₇	—	2	4	no	—
197	C₂×C₄×C₄₇	—	2	2	no	—
198	C₂×C₄×C₄₇	—	4	1	no	—
199	C₂×C₄×C₄₇	—	4	16	no	—
200	C₂×C₄×C₄₇	—	4	2	no	—
201	C₂×C₄×C₄₇	—	4	4	no	—
202	C₂×C₄×C₄₇	—	4	2	no	—
203	C₂×C₄×C₄₇	—	4	2	no	—
204	C₂×C₄×C₄₇	—	4	2	no	—
205	C₂×C₄×C₄₇	—	4	4	no	—
206	C₂×C₄×C₄₇	—	4	1	no	—
207	C₂×C₄×C₄₇	—	4	1	no	—
208	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
209	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
210	C₂×C₄×C₄₇	#120	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
212	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
213	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
215	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
216	C₈×C₄₇	—	4	2	no	—
217	C₈×C₄₇	—	4	2	no	—
218	C₈×C₄₇	—	4	2	no	—
219	#18777	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
220	C₂²×C₄₇	—	2	1	no	—
221	C₂²×C₄₇	—	2	1	no	—
222	C₂²×C₄₇	—	2	4	no	—
223	C₂²×C₄₇	—	4	8	no	—
224	C₂²×C₄₇	—	4	2	no	—
225	C₂²×C₄₇	—	4	2	no	—
226	C₂²×C₄₇	#450	1	2	yes	—
227	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
228	C₄×C₄₇	—	2	4	no	—
229	C₄×C₄₇	—	2	1	no	—
230	C₄×C₄₇	—	2	1	no	—
231	C₄×C₄₇	—	2	1	no	—
232	C₄×C₄₇	—	4	4	no	—
233	C₄×C₄₇	—	4	2	no	—
234	C₄×C₄₇	—	4	2	no	—
235	C₄×C₄₇	—	8	1	no	—
236	C₄×C₄₇	—	8	1	no	—
237	C₄×C₄₇	#450	1	2	yes	—
238	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
239	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
240	C₄×C₄₇	C₂×#137	1	2	yes	—
241	C₂×D₄×Q₈	C₂×C₄₇	1	1	yes	characteristic
242	#3229	C₂×C₄₇	1	1	yes	characteristic, complemented
243	#3101	C₂×C₄₇	1	1	yes	characteristic
244	#3078	C₂×C₄₇	1	1	yes	characteristic, complemented
245	#1651	C₂×C₄₇	1	4	yes	complemented
246	#1637	C₂×C₄₇	1	4	yes	complemented
247	#1546	C₂×C₄₇	1	1	yes	characteristic, complemented
248	#1486	C₂×C₄₇	1	1	yes	characteristic
249	#1479	C₂×C₄₇	1	1	yes	characteristic, complemented
250	C₂×C₄₇	—	2	2	no	—
251	C₂×C₄₇	—	4	4	no	—
252	C₂×C₄₇	C₂×#450	1	1	yes	characteristic
253	C₂×C₄₇	#3004	1	1	yes	characteristic
254	C₂×C₄₇	#3020	1	1	yes	characteristic
255	C₂³×Q₈	—	2	1	no	—
256	D₄×Q₈	—	2	2	no	—
257	D₄×Q₈	—	2	2	no	—
258	D₄×Q₈	—	2	2	no	—
259	D₄×Q₈	C₂²×C₄₇	1	4	yes	—
260	#533	C₂²×C₄₇	1	1	yes	characteristic
261	C₂×C₄⋊Q₈	—	2	1	no	—
262	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
263	C₂×C₂²⋊Q₈	—	2	1	no	—
264	C₂×C₂²⋊Q₈	—	2	2	no	—
265	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
266	C₂×C₄×D₄	—	2	1	no	—
267	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
268	#498	C₂²×C₄₇	1	2	yes	complemented
269	#487	C₂²×C₄₇	1	2	yes	complemented
270	#483	—	2	1	no	—
271	#483	—	2	2	no	—
272	#479	—	2	2	no	—
273	#477	C₂²×C₄₇	1	2	yes	complemented
274	#476	C₂²×C₄₇	1	2	yes	—
275	#475	—	2	2	no	—
276	#475	C₂²×C₄₇	1	2	yes	complemented
277	#461	C₂²×C₄₇	1	2	yes	—
278	#450	—	2	1	no	—
279	C₄×SD₁₆	—	2	2	no	—
280	#431	C₂²×C₄₇	1	1	yes	characteristic
281	#431	C₂²×C₄₇	1	1	yes	characteristic
282	#428	—	2	1	no	—
283	#423	C₂²×C₄₇	1	1	yes	characteristic
284	#419	—	2	1	no	—
285	#332	C₂²×C₄₇	1	4	yes	complemented
286	Q₈⋊C₈	C₂²×C₄₇	1	4	yes	complemented
287	D₄⋊C₈	C₂²×C₄₇	1	4	yes	—
288	C₄₇	#18777	1	1	yes	characteristic, direct product factor, Sylow
289	C₂²×Q₈	—	2	2	no	—
290	C₂²×Q₈	—	2	4	no	—
291	C₂²×Q₈	—	2	4	no	—
292	C₂²×Q₈	—	2	1	no	—
293	C₂²×Q₈	—	4	4	no	—
294	C₂²×Q₈	—	4	4	no	—
295	C₂²×Q₈	D₄×C₄₇	1	1	yes	characteristic
296	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
297	C₂³×C₄	—	2	2	no	—
298	C₂³×C₄	—	2	1	no	—
299	C₂×SD₁₆	—	2	2	no	—
300	C₂×M₁₆	—	2	1	no	—
301	C₄⋊Q₈	—	2	4	no	—
302	C₄⋊Q₈	—	2	4	no	—
303	C₄⋊Q₈	—	2	1	no	—
304	C₄⋊Q₈	—	2	1	no	—
305	C₄⋊Q₈	D₄×C₄₇	1	2	yes	—
306	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
307	C₄⋊Q₈	C₂³×C₄₇	1	1	yes	characteristic
308	C₄⋊Q₈	C₂³×C₄₇	1	2	yes	—
309	#125	—	2	1	no	—
310	C₂²⋊Q₈	—	2	4	no	—
311	C₂²⋊Q₈	—	2	8	no	—
312	C₂²⋊Q₈	—	2	4	no	—
313	C₂²⋊Q₈	—	2	8	no	—
314	C₂²⋊Q₈	—	2	1	no	—
315	C₂²⋊Q₈	—	2	1	no	—
316	C₄×Q₈	—	2	1	no	—
317	C₄×Q₈	—	2	1	no	—
318	C₄×Q₈	—	2	1	no	—
319	C₄×Q₈	—	2	1	no	—
320	C₄×Q₈	D₄×C₄₇	1	2	yes	—
321	C₄×Q₈	C₂³×C₄₇	1	2	yes	—
322	C₄×D₄	—	2	4	no	—
323	C₄×D₄	—	2	4	no	—
324	C₄×D₄	—	2	1	no	—
325	C₄×D₄	—	2	1	no	—
326	C₄×D₄	D₄×C₄₇	1	2	yes	—
327	C₄×D₄	C₂³×C₄₇	1	2	yes	—
328	#117	—	2	1	no	—
329	C₂×C₄⋊C₄	—	2	2	no	—
330	C₂×C₄⋊C₄	—	2	1	no	—
331	C₂×C₄⋊C₄	—	2	1	no	—
332	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
333	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
334	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
335	C₂×C₂²⋊C₄	—	2	2	no	—
336	C₂×C₂²⋊C₄	—	2	1	no	—
337	C₂×C₄²	—	2	1	no	—
338	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
339	#107	—	2	2	no	—
340	#106	—	2	2	no	—
341	#106	—	2	2	no	—
342	#106	—	2	4	no	—
343	C₄⋊C₈	—	2	1	no	—
344	C₄⋊C₈	—	2	1	no	—
345	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
346	C₄⋊C₈	C₂³×C₄₇	1	2	yes	—
347	#103	—	2	2	no	—
348	#103	—	2	2	no	—
349	#103	—	2	2	no	—
350	#103	—	2	4	no	—
351	#102	—	2	2	no	—
352	C₂²⋊C₈	—	2	1	no	—
353	C₂²⋊C₈	—	2	1	no	—
354	C₄×C₈	—	2	1	no	—
355	C₄×C₈	C₂³×C₄₇	1	2	yes	—
356	C₂⁴	—	2	1	no	—
357	C₂×Q₈	—	2	8	no	—
358	C₂×Q₈	—	2	1	no	—
359	C₂×Q₈	—	2	2	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	2	1	no	—
363	C₂×Q₈	—	2	1	no	—
364	C₂×Q₈	—	4	8	no	—
365	C₂×Q₈	—	4	16	no	—
366	C₂×Q₈	—	4	8	no	—
367	C₂×Q₈	—	4	8	no	—
368	C₂×Q₈	—	4	2	no	—
369	C₂×Q₈	—	4	2	no	—
370	C₂×Q₈	SD₁₆×C₄₇	1	4	yes	complemented
371	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
372	C₂×D₄	—	2	4	no	—
373	C₂×D₄	—	2	1	no	—
374	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	2	8	no	—
377	C₂²×C₄	—	2	1	no	—
378	C₂²×C₄	—	2	2	no	—
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	2	2	no	—
382	C₂²×C₄	—	4	8	no	—
383	C₂²×C₄	—	4	2	no	—
384	C₂²×C₄	—	4	2	no	—
385	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
386	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
387	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
388	SD₁₆	—	4	4	no	—
389	M₁₆	—	4	2	no	—
390	C₂×C₈	—	2	2	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₄⋊C₄	—	2	8	no	—
394	C₄⋊C₄	—	2	2	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	2	1	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	4	1	no	—
406	C₄⋊C₄	—	4	1	no	—
407	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
408	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
409	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
410	C₂²⋊C₄	—	2	8	no	—
411	C₂²⋊C₄	—	2	2	no	—
412	C₂²⋊C₄	—	2	2	no	—
413	C₂²⋊C₄	—	4	1	no	—
414	C₄²	—	2	2	no	—
415	C₄²	—	2	2	no	—
416	C₄²	—	4	1	no	—
417	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
418	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
419	C₄²	C₂×D₄×C₄₇	1	1	yes	characteristic
420	C₄²	C₂⁴×C₄₇	1	1	yes	characteristic
421	C₂³	—	2	4	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	4	2	no	—
424	C₂³	—	4	2	no	—
425	C₂³	#120×C₄₇	1	1	yes	characteristic
426	Q₈	—	2	4	no	—
427	Q₈	—	2	2	no	—
428	Q₈	—	4	16	no	—
429	Q₈	—	4	2	no	—
430	Q₈	—	4	4	no	—
431	Q₈	—	4	2	no	—
432	Q₈	—	4	2	no	—
433	Q₈	—	4	2	no	—
434	Q₈	C₂×SD₁₆×C₄₇	1	4	yes	—
435	D₄	—	2	4	no	—
436	D₄	—	2	2	no	—
437	D₄	#137×C₄₇	1	4	yes	—
438	C₂×C₄	—	2	4	no	—
439	C₂×C₄	—	2	2	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	4	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	16	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	4	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	4	no	—
450	C₂×C₄	—	4	2	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
455	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
456	C₂×C₄	#120×C₄₇	1	1	yes	characteristic
457	C₂×C₄	C₂×SD₁₆×C₄₇	1	2	yes	—
458	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
459	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
460	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
461	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
462	C₈	—	4	2	no	—
463	C₈	—	4	2	no	—
464	C₈	—	4	2	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	2	4	no	—
468	C₂²	—	4	8	no	—
469	C₂²	—	4	2	no	—
470	C₂²	—	4	2	no	—
471	C₂²	C₄₇×#450	1	2	yes	—
472	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
473	C₄	—	2	4	no	—
474	C₄	—	2	1	no	—
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	4	4	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	2	no	—
480	C₄	—	8	1	no	—
481	C₄	—	8	1	no	—
482	C₄	C₄₇×#450	1	2	yes	—
483	C₄	C₂²×SD₁₆×C₄₇	1	1	yes	characteristic
484	C₄	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
485	C₄	C₂×#137×C₄₇	1	2	yes	—
486	C₂	—	2	2	no	—
487	C₂	—	4	4	no	—
488	C₂	C₂×C₄₇×#450	1	1	yes	characteristic
489	C₂	C₄₇×#3004	1	1	yes	characteristic
490	C₂	C₄₇×#3020	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₄₇	C₂×#120
commutator, Frattini, cosocle	C₄²	C₂⁴×C₄₇
prime radical	C₂²×D₄×C₄₇	D₄
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
2. C₄₇×#3229	C₂	semidirect
4. C₄₇×#3078	C₂	semidirect
5. C₄₇×#1651	C₂	semidirect
6. C₄₇×#1637	C₂	semidirect
7. C₄₇×#1546	C₂	semidirect
9. C₄₇×#1479	C₂	semidirect
23. C₄₇×#498	C₂²	semidirect
24. C₄₇×#487	C₂²	semidirect
28. C₄₇×#477	C₂²	semidirect
31. C₄₇×#475	C₂²	semidirect
40. C₄₇×#332	C₂²	semidirect
41. C₄₇×Q₈⋊C₈	C₂²	semidirect
124. C₂×Q₈×C₄₇	SD₁₆	semidirect
219. #18777	C₄₇	direct (N × H)
242. #3229	C₂×C₄₇	semidirect
244. #3078	C₂×C₄₇	semidirect
245. #1651	C₂×C₄₇	semidirect
246. #1637	C₂×C₄₇	semidirect
247. #1546	C₂×C₄₇	semidirect
249. #1479	C₂×C₄₇	semidirect
268. #498	C₂²×C₄₇	semidirect
269. #487	C₂²×C₄₇	semidirect
273. #477	C₂²×C₄₇	semidirect
276. #475	C₂²×C₄₇	semidirect
285. #332	C₂²×C₄₇	semidirect
286. Q₈⋊C₈	C₂²×C₄₇	semidirect
288. C₄₇	#18777	direct (N × H)
370. C₂×Q₈	SD₁₆×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×D₄×Q₈×C₄₇	2
C₄₇×#3229	2
C₄₇×#3101	2
C₄₇×#3078	2
C₄₇×#1651	2
C₄₇×#1637	2
C₄₇×#1546	2
C₄₇×#1486	2
C₄₇×#1479	2
#18777	47

Subgroups — C47×#18777 #26058475

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#18777 #26058475