Subgroups — C₄₇×#29844 #26069542

Order 12032.

850 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#487	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄₇×#431	C₂	1	1	yes	maximal, characteristic
3	C₄₇×#2857	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#2857	C₂	1	1	yes	maximal, characteristic
5	C₄₇×#2068	C₂	1	4	yes	maximal, complemented
6	C₄₇×#2036	C₂	1	4	yes	maximal
7	C₄₇×#1990	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1956	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1845	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
11	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
12	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
13	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
14	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
15	C₄₇×#487	—	2	4	no	—
16	C₄₇×#431	—	2	4	no	—
17	C₂×#107×C₄₇	C₂²	1	4	yes	—
18	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
19	C₂×#103×C₄₇	C₂²	1	4	yes	—
20	C₂×#103×C₄₇	C₂²	1	4	yes	—
21	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
22	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₄₇×#391	—	2	1	no	—
25	C₄₇×#391	C₂²	1	2	yes	—
26	C₄₇×#389	—	2	1	no	—
27	C₄₇×#389	—	2	1	no	—
28	C₄₇×#389	—	2	1	no	—
29	C₄₇×#389	C₂²	1	2	yes	—
30	C₄₇×#384	C₂²	1	1	yes	characteristic
31	C₄₇×#384	C₂²	1	1	yes	characteristic
32	C₄₇×#380	—	2	1	no	—
33	C₄₇×#380	—	2	1	no	—
34	C₄₇×#380	—	2	1	no	—
35	C₄₇×#380	C₂²	1	2	yes	—
36	C₄₇×#340	C₂²	1	4	yes	—
37	C₂²×Q₈×C₄₇	—	2	1	no	—
38	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
39	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
40	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
41	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
42	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
43	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
44	C₄⋊Q₈×C₄₇	—	2	2	no	—
45	C₄⋊Q₈×C₄₇	—	2	2	no	—
46	C₄⋊Q₈×C₄₇	—	2	2	no	—
47	C₄⋊Q₈×C₄₇	—	2	2	no	—
48	C₂²⋊Q₈×C₄₇	—	4	4	no	—
49	C₂²⋊Q₈×C₄₇	—	4	4	no	—
50	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
51	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
54	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
55	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
56	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
57	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
58	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
59	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
60	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
62	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
63	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
64	C₂×C₄²×C₄₇	—	2	2	no	—
65	C₂×C₄²×C₄₇	—	2	2	no	—
66	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
67	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
68	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
69	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
70	#107×C₄₇	—	4	4	no	—
71	C₄⋊C₈×C₄₇	—	2	4	no	—
72	#103×C₄₇	—	2	8	no	—
73	#103×C₄₇	—	4	4	no	—
74	C₂²⋊C₈×C₄₇	—	2	4	no	—
75	C₄×C₈×C₄₇	—	2	2	no	—
76	C₄×C₈×C₄₇	D₄	1	4	yes	—
77	#95×C₄₇	—	2	2	no	—
78	#95×C₄₇	—	2	2	no	—
79	#95×C₄₇	—	2	2	no	—
80	#95×C₄₇	—	2	2	no	—
81	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
82	C₂×Q₈×C₄₇	—	2	2	no	—
83	C₂×Q₈×C₄₇	—	2	2	no	—
84	C₂×Q₈×C₄₇	—	2	4	no	—
85	C₂×Q₈×C₄₇	—	2	4	no	—
86	C₂×Q₈×C₄₇	—	4	2	no	—
87	C₂×Q₈×C₄₇	—	4	2	no	—
88	C₂×Q₈×C₄₇	—	4	2	no	—
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	2	no	—
92	C₂²×C₄×C₄₇	—	2	2	no	—
93	C₂²×C₄×C₄₇	—	2	2	no	—
94	C₂²×C₄×C₄₇	—	2	1	no	—
95	C₂²×C₄×C₄₇	—	2	1	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	2	no	—
101	C₂²×C₄×C₄₇	—	2	2	no	—
102	C₂²×C₄×C₄₇	Q₁₆	1	4	yes	—
103	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
109	C₂×C₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	—	2	2	no	—
113	C₂×C₈×C₄₇	—	2	2	no	—
114	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
115	C₄⋊C₄×C₄₇	—	2	2	no	—
116	C₄⋊C₄×C₄₇	—	2	2	no	—
117	C₄⋊C₄×C₄₇	—	2	4	no	—
118	C₄⋊C₄×C₄₇	—	2	4	no	—
119	C₄⋊C₄×C₄₇	—	4	4	no	—
120	C₄⋊C₄×C₄₇	—	4	4	no	—
121	C₄⋊C₄×C₄₇	—	4	2	no	—
122	C₄⋊C₄×C₄₇	—	4	2	no	—
123	C₄⋊C₄×C₄₇	—	4	2	no	—
124	C₄⋊C₄×C₄₇	—	4	2	no	—
125	C₄⋊C₄×C₄₇	—	4	2	no	—
126	C₄⋊C₄×C₄₇	—	4	2	no	—
127	C₄⋊C₄×C₄₇	—	4	2	no	—
128	C₂²⋊C₄×C₄₇	—	4	4	no	—
129	C₂²⋊C₄×C₄₇	—	4	4	no	—
130	C₄²×C₄₇	—	2	2	no	—
131	C₄²×C₄₇	—	2	2	no	—
132	C₄²×C₄₇	—	2	1	no	—
133	C₄²×C₄₇	—	2	1	no	—
134	C₄²×C₄₇	C₂×D₄	1	2	yes	—
135	C₄²×C₄₇	#41	1	2	yes	—
136	C₂³×C₄₇	—	2	1	no	—
137	C₂³×C₄₇	—	2	1	no	—
138	C₂³×C₄₇	—	2	1	no	—
139	C₂³×C₄₇	—	2	1	no	—
140	C₂³×C₄₇	—	2	1	no	—
141	C₂³×C₄₇	—	2	1	no	—
142	C₂³×C₄₇	C₂×Q₁₆	1	2	yes	—
143	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
144	Q₈×C₄₇	—	4	4	no	—
145	Q₈×C₄₇	—	4	4	no	—
146	Q₈×C₄₇	—	8	4	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	1	no	—
149	C₂×C₄×C₄₇	—	2	8	no	—
150	C₂×C₄×C₄₇	—	2	1	no	—
151	C₂×C₄×C₄₇	—	2	1	no	—
152	C₂×C₄×C₄₇	—	2	1	no	—
153	C₂×C₄×C₄₇	—	2	1	no	—
154	C₂×C₄×C₄₇	—	2	1	no	—
155	C₂×C₄×C₄₇	—	2	1	no	—
156	C₂×C₄×C₄₇	—	4	2	no	—
157	C₂×C₄×C₄₇	—	4	2	no	—
158	C₂×C₄×C₄₇	—	4	4	no	—
159	C₂×C₄×C₄₇	—	4	2	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	4	2	no	—
164	C₂×C₄×C₄₇	—	4	2	no	—
165	C₂×C₄×C₄₇	—	4	2	no	—
166	C₂×C₄×C₄₇	—	4	2	no	—
167	C₂×C₄×C₄₇	—	4	2	no	—
168	C₂×C₄×C₄₇	—	4	2	no	—
169	C₂×C₄×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	#121	1	2	yes	—
172	C₂×C₄×C₄₇	#121	1	2	yes	—
173	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
174	C₂×C₄×C₄₇	C₂×Q₁₆	1	2	yes	—
175	C₂×C₄×C₄₇	#135	1	2	yes	—
176	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
177	C₂×C₄×C₄₇	#137	1	2	yes	—
178	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
180	C₂×C₄×C₄₇	H(5,𝔽₂)	1	2	yes	—
181	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
182	C₈×C₄₇	—	2	4	no	—
183	C₈×C₄₇	—	4	2	no	—
184	#29844	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
185	C₂²×C₄₇	—	2	2	no	—
186	C₂²×C₄₇	—	2	2	no	—
187	C₂²×C₄₇	—	2	2	no	—
188	C₂²×C₄₇	—	4	1	no	—
189	C₂²×C₄₇	—	4	1	no	—
190	C₂²×C₄₇	—	4	1	no	—
191	C₂²×C₄₇	—	4	1	no	—
192	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
193	C₂²×C₄₇	#535	1	1	yes	characteristic
194	C₂²×C₄₇	#536	1	1	yes	characteristic
195	C₂²×C₄₇	C₂²×Q₁₆	1	1	yes	characteristic
196	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
197	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
198	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
199	C₄×C₄₇	—	2	2	no	—
200	C₄×C₄₇	—	4	1	no	—
201	C₄×C₄₇	—	4	1	no	—
202	C₄×C₄₇	—	8	2	no	—
203	C₄×C₄₇	—	8	2	no	—
204	C₄×C₄₇	—	8	2	no	—
205	C₄×C₄₇	—	8	2	no	—
206	C₄×C₄₇	#467	1	4	yes	—
207	C₄×C₄₇	#468	1	4	yes	—
208	C₄×C₄₇	#537	1	2	yes	—
209	C₄×C₄₇	#542	1	2	yes	—
210	C₂×#487	C₂×C₄₇	1	1	yes	characteristic, complemented
211	C₂×#431	C₂×C₄₇	1	1	yes	characteristic
212	#2857	C₂×C₄₇	1	1	yes	characteristic
213	#2857	C₂×C₄₇	1	1	yes	characteristic
214	#2068	C₂×C₄₇	1	4	yes	complemented
215	#2036	C₂×C₄₇	1	4	yes	—
216	#1990	C₂×C₄₇	1	1	yes	characteristic, complemented
217	#1956	C₂×C₄₇	1	1	yes	characteristic, complemented
218	#1845	C₂×C₄₇	1	1	yes	characteristic, complemented
219	C₂×C₄₇	—	4	2	no	—
220	C₂×C₄₇	#2620	1	1	yes	characteristic
221	C₂×C₄₇	C₂×#467	1	1	yes	characteristic
222	C₂×C₄₇	C₂×#468	1	1	yes	characteristic
223	C₂×C₄₇	#3207	1	1	yes	characteristic
224	C₂×C₄₇	#3209	1	1	yes	characteristic
225	C₂×C₄₇	#3230	1	1	yes	characteristic
226	C₂×C₄₇	#3231	1	1	yes	characteristic
227	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
228	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
229	C₂×C₂²⋊Q₈	—	2	1	no	—
230	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
231	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
232	#487	—	2	4	no	—
233	#431	—	2	4	no	—
234	C₂×#107	C₂²×C₄₇	1	4	yes	—
235	C₂×C₄⋊C₈	C₂²×C₄₇	1	2	yes	—
236	C₂×#103	C₂²×C₄₇	1	4	yes	—
237	C₂×#103	C₂²×C₄₇	1	4	yes	—
238	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
239	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
240	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
241	#391	—	2	1	no	—
242	#391	C₂²×C₄₇	1	2	yes	—
243	#389	—	2	1	no	—
244	#389	—	2	1	no	—
245	#389	—	2	1	no	—
246	#389	C₂²×C₄₇	1	2	yes	—
247	#384	C₂²×C₄₇	1	1	yes	characteristic
248	#384	C₂²×C₄₇	1	1	yes	characteristic
249	#380	—	2	1	no	—
250	#380	—	2	1	no	—
251	#380	—	2	1	no	—
252	#380	C₂²×C₄₇	1	2	yes	—
253	#340	C₂²×C₄₇	1	4	yes	—
254	C₄₇	#29844	1	1	yes	characteristic, direct product factor, Sylow
255	C₂²×Q₈	—	2	1	no	—
256	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
257	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
258	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
259	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
260	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
261	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
262	C₄⋊Q₈	—	2	2	no	—
263	C₄⋊Q₈	—	2	2	no	—
264	C₄⋊Q₈	—	2	2	no	—
265	C₄⋊Q₈	—	2	2	no	—
266	C₂²⋊Q₈	—	4	4	no	—
267	C₂²⋊Q₈	—	4	4	no	—
268	C₂×C₄⋊C₄	—	2	1	no	—
269	C₂×C₄⋊C₄	—	2	2	no	—
270	C₂×C₄⋊C₄	—	2	2	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₄⋊C₄	—	2	1	no	—
273	C₂×C₄⋊C₄	—	2	1	no	—
274	C₂×C₄⋊C₄	—	2	1	no	—
275	C₂×C₄⋊C₄	—	2	1	no	—
276	C₂×C₄⋊C₄	—	2	1	no	—
277	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
278	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
279	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
280	C₂×C₂²⋊C₄	—	2	2	no	—
281	C₂×C₂²⋊C₄	—	2	2	no	—
282	C₂×C₄²	—	2	2	no	—
283	C₂×C₄²	—	2	2	no	—
284	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
285	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
286	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
287	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
288	#107	—	4	4	no	—
289	C₄⋊C₈	—	2	4	no	—
290	#103	—	2	8	no	—
291	#103	—	4	4	no	—
292	C₂²⋊C₈	—	2	4	no	—
293	C₄×C₈	—	2	2	no	—
294	C₄×C₈	D₄×C₄₇	1	4	yes	—
295	#95	—	2	2	no	—
296	#95	—	2	2	no	—
297	#95	—	2	2	no	—
298	#95	—	2	2	no	—
299	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
300	C₂×Q₈	—	2	2	no	—
301	C₂×Q₈	—	2	2	no	—
302	C₂×Q₈	—	2	4	no	—
303	C₂×Q₈	—	2	4	no	—
304	C₂×Q₈	—	4	2	no	—
305	C₂×Q₈	—	4	2	no	—
306	C₂×Q₈	—	4	2	no	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	2	no	—
309	C₂²×C₄	—	2	2	no	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	2	2	no	—
312	C₂²×C₄	—	2	1	no	—
313	C₂²×C₄	—	2	1	no	—
314	C₂²×C₄	—	2	2	no	—
315	C₂²×C₄	—	2	2	no	—
316	C₂²×C₄	—	2	2	no	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	2	2	no	—
319	C₂²×C₄	—	2	2	no	—
320	C₂²×C₄	Q₁₆×C₄₇	1	4	yes	—
321	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
322	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
323	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
324	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
325	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
326	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
327	C₂×C₈	—	2	2	no	—
328	C₂×C₈	—	2	2	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	2	2	no	—
331	C₂×C₈	—	2	2	no	—
332	C₂×C₈	C₂×D₄×C₄₇	1	4	yes	—
333	C₄⋊C₄	—	2	2	no	—
334	C₄⋊C₄	—	2	2	no	—
335	C₄⋊C₄	—	2	4	no	—
336	C₄⋊C₄	—	2	4	no	—
337	C₄⋊C₄	—	4	4	no	—
338	C₄⋊C₄	—	4	4	no	—
339	C₄⋊C₄	—	4	2	no	—
340	C₄⋊C₄	—	4	2	no	—
341	C₄⋊C₄	—	4	2	no	—
342	C₄⋊C₄	—	4	2	no	—
343	C₄⋊C₄	—	4	2	no	—
344	C₄⋊C₄	—	4	2	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₂²⋊C₄	—	4	4	no	—
347	C₂²⋊C₄	—	4	4	no	—
348	C₄²	—	2	2	no	—
349	C₄²	—	2	2	no	—
350	C₄²	—	2	1	no	—
351	C₄²	—	2	1	no	—
352	C₄²	C₂×D₄×C₄₇	1	2	yes	—
353	C₄²	#41×C₄₇	1	2	yes	—
354	C₂³	—	2	1	no	—
355	C₂³	—	2	1	no	—
356	C₂³	—	2	1	no	—
357	C₂³	—	2	1	no	—
358	C₂³	—	2	1	no	—
359	C₂³	—	2	1	no	—
360	C₂³	C₂×Q₁₆×C₄₇	1	2	yes	—
361	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
362	Q₈	—	4	4	no	—
363	Q₈	—	4	4	no	—
364	Q₈	—	8	4	no	—
365	C₂×C₄	—	2	1	no	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	8	no	—
368	C₂×C₄	—	2	1	no	—
369	C₂×C₄	—	2	1	no	—
370	C₂×C₄	—	2	1	no	—
371	C₂×C₄	—	2	1	no	—
372	C₂×C₄	—	2	1	no	—
373	C₂×C₄	—	2	1	no	—
374	C₂×C₄	—	4	4	no	—
375	C₂×C₄	—	4	2	no	—
376	C₂×C₄	—	4	2	no	—
377	C₂×C₄	—	4	2	no	—
378	C₂×C₄	—	4	2	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	4	2	no	—
386	C₂×C₄	—	4	2	no	—
387	C₂×C₄	—	4	2	no	—
388	C₂×C₄	—	4	2	no	—
389	C₂×C₄	#121×C₄₇	1	2	yes	—
390	C₂×C₄	#121×C₄₇	1	2	yes	—
391	C₂×C₄	C₂×Q₁₆×C₄₇	1	2	yes	—
392	C₂×C₄	C₂×Q₁₆×C₄₇	1	2	yes	—
393	C₂×C₄	#135×C₄₇	1	2	yes	—
394	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
395	C₂×C₄	#137×C₄₇	1	2	yes	—
396	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
397	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
398	C₂×C₄	H(5,𝔽₂)×C₄₇	1	2	yes	—
399	C₂×C₄	2₋¹⁺⁴×C₄₇	1	2	yes	—
400	C₈	—	2	4	no	—
401	C₈	—	4	2	no	—
402	C₂²	—	2	2	no	—
403	C₂²	—	2	2	no	—
404	C₂²	—	2	2	no	—
405	C₂²	—	4	1	no	—
406	C₂²	—	4	1	no	—
407	C₂²	—	4	1	no	—
408	C₂²	—	4	1	no	—
409	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
410	C₂²	C₄₇×#535	1	1	yes	characteristic
411	C₂²	C₄₇×#536	1	1	yes	characteristic
412	C₂²	C₂²×Q₁₆×C₄₇	1	1	yes	characteristic
413	C₂²	C₂×#135×C₄₇	1	1	yes	characteristic
414	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
415	C₂²	C₂×#137×C₄₇	1	1	yes	characteristic
416	C₄	—	2	2	no	—
417	C₄	—	4	1	no	—
418	C₄	—	4	1	no	—
419	C₄	—	8	2	no	—
420	C₄	—	8	2	no	—
421	C₄	—	8	2	no	—
422	C₄	—	8	2	no	—
423	C₄	C₄₇×#467	1	4	yes	—
424	C₄	C₄₇×#468	1	4	yes	—
425	C₄	C₄₇×#537	1	2	yes	—
426	C₄	C₄₇×#542	1	2	yes	—
427	C₂	—	4	2	no	—
428	C₂	C₄₇×#2620	1	1	yes	characteristic
429	C₂	C₂×C₄₇×#467	1	1	yes	characteristic
430	C₂	C₂×C₄₇×#468	1	1	yes	characteristic
431	C₂	C₄₇×#3207	1	1	yes	characteristic
432	C₂	C₄₇×#3209	1	1	yes	characteristic
433	C₂	C₄₇×#3230	1	1	yes	characteristic
434	C₂	C₄₇×#3231	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₄₇×#487	C₂	semidirect
5. C₄₇×#2068	C₂	semidirect
7. C₄₇×#1990	C₂	semidirect
8. C₄₇×#1956	C₂	semidirect
9. C₄₇×#1845	C₂	semidirect
184. #29844	C₄₇	direct (N × H)
210. C₂×#487	C₂×C₄₇	semidirect
214. #2068	C₂×C₄₇	semidirect
216. #1990	C₂×C₄₇	semidirect
217. #1956	C₂×C₄₇	semidirect
218. #1845	C₂×C₄₇	semidirect
254. C₄₇	#29844	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#487	2
C₂×C₄₇×#431	2
C₄₇×#2857	2
C₄₇×#2068	2
C₄₇×#2036	2
C₄₇×#1990	2
C₄₇×#1956	2
C₄₇×#1845	2
#29844	47

Subgroups — C47×#29844 #26069542

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#29844 #26069542