Subgroups — C₄₇×#29645 #26069343

Order 12032.

1002 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#533	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#485	C₂	1	2	yes	maximal
3	C₄₇×#2855	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#2059	C₂	1	2	yes	maximal, complemented
5	C₄₇×#2058	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#2057	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#2026	C₂	1	2	yes	maximal, complemented
8	C₄₇×#2024	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#2024	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1825	C₂	1	2	yes	maximal
11	C₄₇×#1817	C₂	1	1	yes	maximal, characteristic
12	C₄₇×#533	—	2	8	no	—
13	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×#125×C₄₇	C₂²	1	2	yes	—
16	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
17	C₂×C₂²⋊Q₈×C₄₇	—	2	1	no	—
18	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
20	C₂×C₄×Q₈×C₄₇	—	2	1	no	—
21	C₂×#117×C₄₇	C₂²	1	2	yes	—
22	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
23	C₄₇×#485	—	2	8	no	—
24	C₂×#107×C₄₇	C₂²	1	2	yes	—
25	C₂×#106×C₄₇	C₂²	1	2	yes	—
26	C₂×#103×C₄₇	C₂²	1	2	yes	—
27	C₂×#103×C₄₇	C₂²	1	2	yes	—
28	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
29	C₄₇×#391	C₂²	1	1	yes	characteristic
30	C₄₇×#391	C₂²	1	1	yes	characteristic
31	C₄₇×#389	C₂²	1	1	yes	characteristic
32	C₄₇×#389	C₂²	1	1	yes	characteristic
33	C₄₇×#387	—	2	1	no	—
34	C₄₇×#387	—	2	1	no	—
35	C₄₇×#385	—	2	1	no	—
36	C₄₇×#381	—	2	1	no	—
37	C₄₇×#380	C₂²	1	1	yes	characteristic
38	C₄₇×#340	C₂²	1	2	yes	—
39	C₄₇×#340	C₂²	1	2	yes	—
40	C₄₇×#340	C₂²	1	2	yes	—
41	C₄₇×#340	C₂²	1	2	yes	—
42	C₄₇×#336	C₂²	1	1	yes	characteristic
43	C₄₇×#336	C₂²	1	1	yes	characteristic
44	C₄₇×#336	C₂²	1	2	yes	—
45	C₂²×Q₈×C₄₇	—	2	1	no	—
46	C₂²×Q₈×C₄₇	—	2	1	no	—
47	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
49	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
50	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
52	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
53	C₄⋊Q₈×C₄₇	—	2	4	no	—
54	C₄⋊Q₈×C₄₇	—	2	4	no	—
55	#125×C₄₇	—	2	4	no	—
56	#125×C₄₇	—	2	4	no	—
57	C₂²⋊Q₈×C₄₇	—	2	8	no	—
58	C₂²⋊Q₈×C₄₇	—	2	8	no	—
59	C₂²⋊Q₈×C₄₇	—	2	4	no	—
60	C₄×Q₈×C₄₇	—	2	8	no	—
61	C₄×Q₈×C₄₇	—	2	8	no	—
62	#117×C₄₇	—	2	4	no	—
63	#117×C₄₇	D₄	1	8	yes	—
64	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
68	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
69	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
73	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
74	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
76	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
78	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
79	C₂×C₄²×C₄₇	—	2	4	no	—
80	C₂×C₄²×C₄₇	—	2	2	no	—
81	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
82	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
85	#107×C₄₇	—	2	4	no	—
86	#106×C₄₇	—	2	4	no	—
87	#103×C₄₇	—	2	4	no	—
88	#103×C₄₇	—	2	4	no	—
89	C₂²⋊C₈×C₄₇	—	2	4	no	—
90	#95×C₄₇	—	2	1	no	—
91	#95×C₄₇	—	2	1	no	—
92	#95×C₄₇	—	2	1	no	—
93	#95×C₄₇	—	2	1	no	—
94	#95×C₄₇	—	2	1	no	—
95	#95×C₄₇	—	2	1	no	—
96	#95×C₄₇	—	2	1	no	—
97	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
98	C₂×Q₈×C₄₇	—	2	4	no	—
99	C₂×Q₈×C₄₇	—	2	4	no	—
100	C₂×Q₈×C₄₇	—	2	2	no	—
101	C₂×Q₈×C₄₇	—	2	2	no	—
102	C₂×Q₈×C₄₇	—	2	1	no	—
103	C₂×Q₈×C₄₇	—	2	1	no	—
104	C₂×Q₈×C₄₇	—	4	2	no	—
105	C₂×Q₈×C₄₇	—	4	2	no	—
106	C₂×Q₈×C₄₇	—	4	2	no	—
107	C₂×Q₈×C₄₇	—	4	2	no	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	—	2	1	no	—
110	C₂²×C₄×C₄₇	—	2	1	no	—
111	C₂²×C₄×C₄₇	—	2	2	no	—
112	C₂²×C₄×C₄₇	—	2	2	no	—
113	C₂²×C₄×C₄₇	—	2	2	no	—
114	C₂²×C₄×C₄₇	—	2	2	no	—
115	C₂²×C₄×C₄₇	—	2	2	no	—
116	C₂²×C₄×C₄₇	—	2	2	no	—
117	C₂²×C₄×C₄₇	—	2	1	no	—
118	C₂²×C₄×C₄₇	—	2	1	no	—
119	C₂²×C₄×C₄₇	—	2	1	no	—
120	C₂²×C₄×C₄₇	—	2	1	no	—
121	C₂²×C₄×C₄₇	—	4	1	no	—
122	C₂²×C₄×C₄₇	—	4	1	no	—
123	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
125	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
126	C₂²×C₄×C₄₇	C₂×D₄	1	4	yes	—
127	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
130	C₂×C₈×C₄₇	—	2	2	no	—
131	C₂×C₈×C₄₇	—	2	2	no	—
132	C₂×C₈×C₄₇	—	2	2	no	—
133	C₂×C₈×C₄₇	—	2	2	no	—
134	C₂×C₈×C₄₇	—	2	2	no	—
135	C₂×C₈×C₄₇	—	2	2	no	—
136	C₄⋊C₄×C₄₇	—	2	8	no	—
137	C₄⋊C₄×C₄₇	—	2	8	no	—
138	C₄⋊C₄×C₄₇	—	2	4	no	—
139	C₄⋊C₄×C₄₇	—	2	4	no	—
140	C₄⋊C₄×C₄₇	—	2	2	no	—
141	C₄⋊C₄×C₄₇	—	2	2	no	—
142	C₄⋊C₄×C₄₇	—	2	2	no	—
143	C₄⋊C₄×C₄₇	—	2	1	no	—
144	C₄⋊C₄×C₄₇	—	2	1	no	—
145	C₄⋊C₄×C₄₇	—	2	2	no	—
146	C₄⋊C₄×C₄₇	—	4	2	no	—
147	C₄⋊C₄×C₄₇	—	4	2	no	—
148	C₄⋊C₄×C₄₇	—	4	2	no	—
149	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
150	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
151	C₂²⋊C₄×C₄₇	—	2	8	no	—
152	C₂²⋊C₄×C₄₇	—	4	2	no	—
153	C₂²⋊C₄×C₄₇	—	4	2	no	—
154	C₄²×C₄₇	—	2	2	no	—
155	C₄²×C₄₇	—	2	2	no	—
156	C₄²×C₄₇	—	2	8	no	—
157	C₄²×C₄₇	—	2	2	no	—
158	C₄²×C₄₇	—	2	2	no	—
159	C₂³×C₄₇	—	2	1	no	—
160	C₂³×C₄₇	—	2	1	no	—
161	C₂³×C₄₇	—	2	1	no	—
162	C₂³×C₄₇	—	2	1	no	—
163	C₂³×C₄₇	—	2	1	no	—
164	C₂³×C₄₇	—	2	1	no	—
165	C₂³×C₄₇	#120	1	2	yes	—
166	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
167	Q₈×C₄₇	—	4	8	no	—
168	Q₈×C₄₇	—	4	8	no	—
169	Q₈×C₄₇	—	4	2	no	—
170	Q₈×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	2	4	no	—
178	C₂×C₄×C₄₇	—	2	4	no	—
179	C₂×C₄×C₄₇	—	2	1	no	—
180	C₂×C₄×C₄₇	—	2	1	no	—
181	C₂×C₄×C₄₇	—	2	4	no	—
182	C₂×C₄×C₄₇	—	2	4	no	—
183	C₂×C₄×C₄₇	—	2	1	no	—
184	C₂×C₄×C₄₇	—	2	1	no	—
185	C₂×C₄×C₄₇	—	2	1	no	—
186	C₂×C₄×C₄₇	—	2	1	no	—
187	C₂×C₄×C₄₇	—	4	4	no	—
188	C₂×C₄×C₄₇	—	4	4	no	—
189	C₂×C₄×C₄₇	—	4	2	no	—
190	C₂×C₄×C₄₇	—	4	2	no	—
191	C₂×C₄×C₄₇	—	4	2	no	—
192	C₂×C₄×C₄₇	—	4	2	no	—
193	C₂×C₄×C₄₇	—	4	1	no	—
194	C₂×C₄×C₄₇	—	4	1	no	—
195	C₂×C₄×C₄₇	—	4	1	no	—
196	C₂×C₄×C₄₇	—	4	1	no	—
197	C₂×C₄×C₄₇	—	4	1	no	—
198	C₂×C₄×C₄₇	—	4	1	no	—
199	C₂×C₄×C₄₇	—	4	1	no	—
200	C₂×C₄×C₄₇	—	4	1	no	—
201	C₂×C₄×C₄₇	—	4	1	no	—
202	C₂×C₄×C₄₇	—	4	1	no	—
203	C₂×C₄×C₄₇	—	4	1	no	—
204	C₂×C₄×C₄₇	—	4	1	no	—
205	C₂×C₄×C₄₇	#120	1	2	yes	—
206	C₂×C₄×C₄₇	#135	1	2	yes	—
207	C₂×C₄×C₄₇	#137	1	2	yes	—
208	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
209	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
210	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
211	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
212	C₈×C₄₇	—	4	2	no	—
213	C₈×C₄₇	—	4	2	no	—
214	#29645	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
215	C₂²×C₄₇	—	2	2	no	—
216	C₂²×C₄₇	—	2	2	no	—
217	C₂²×C₄₇	—	2	2	no	—
218	C₂²×C₄₇	—	4	1	no	—
219	C₂²×C₄₇	—	4	1	no	—
220	C₂²×C₄₇	—	4	1	no	—
221	C₂²×C₄₇	—	4	1	no	—
222	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
223	C₂²×C₄₇	#536	1	1	yes	characteristic
224	C₂²×C₄₇	#536	1	1	yes	characteristic
225	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
226	C₂²×C₄₇	C₂×#137	1	1	yes	characteristic
227	C₂²×C₄₇	#575	1	1	yes	characteristic
228	C₂²×C₄₇	#575	1	1	yes	characteristic
229	C₄×C₄₇	—	2	2	no	—
230	C₄×C₄₇	—	2	2	no	—
231	C₄×C₄₇	—	2	2	no	—
232	C₄×C₄₇	—	4	1	no	—
233	C₄×C₄₇	—	4	4	no	—
234	C₄×C₄₇	—	4	1	no	—
235	C₄×C₄₇	—	4	4	no	—
236	C₄×C₄₇	—	8	1	no	—
237	C₄×C₄₇	—	8	1	no	—
238	C₄×C₄₇	—	8	1	no	—
239	C₄×C₄₇	—	8	1	no	—
240	C₄×C₄₇	#536	1	2	yes	—
241	C₄×C₄₇	#536	1	2	yes	—
242	C₂×#533	C₂×C₄₇	1	1	yes	characteristic
243	C₂×#485	C₂×C₄₇	1	2	yes	—
244	#2855	C₂×C₄₇	1	1	yes	characteristic
245	#2059	C₂×C₄₇	1	2	yes	complemented
246	#2058	C₂×C₄₇	1	1	yes	characteristic, complemented
247	#2057	C₂×C₄₇	1	1	yes	characteristic, complemented
248	#2026	C₂×C₄₇	1	2	yes	complemented
249	#2024	C₂×C₄₇	1	1	yes	characteristic, complemented
250	#2024	C₂×C₄₇	1	1	yes	characteristic, complemented
251	#1825	C₂×C₄₇	1	2	yes	—
252	#1817	C₂×C₄₇	1	1	yes	characteristic
253	C₂×C₄₇	—	4	2	no	—
254	C₂×C₄₇	#2614	1	1	yes	characteristic
255	C₂×C₄₇	#3002	1	1	yes	characteristic
256	C₂×C₄₇	#3007	1	1	yes	characteristic
257	C₂×C₄₇	#3231	1	1	yes	characteristic
258	C₂×C₄₇	#3233	1	1	yes	characteristic
259	C₂×C₄₇	#3237	1	1	yes	characteristic
260	C₂×C₄₇	#3240	1	1	yes	characteristic
261	#533	—	2	8	no	—
262	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
263	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
264	C₂×#125	C₂²×C₄₇	1	2	yes	—
265	C₂×C₂²⋊Q₈	—	2	1	no	—
266	C₂×C₂²⋊Q₈	—	2	1	no	—
267	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
268	C₂×C₄×Q₈	—	2	1	no	—
269	C₂×C₄×Q₈	—	2	1	no	—
270	C₂×#117	C₂²×C₄₇	1	2	yes	—
271	C₂²×C₄²	C₂²×C₄₇	1	1	yes	characteristic
272	#485	—	2	8	no	—
273	C₂×#107	C₂²×C₄₇	1	2	yes	—
274	C₂×#106	C₂²×C₄₇	1	2	yes	—
275	C₂×#103	C₂²×C₄₇	1	2	yes	—
276	C₂×#103	C₂²×C₄₇	1	2	yes	—
277	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
278	#391	C₂²×C₄₇	1	1	yes	characteristic
279	#391	C₂²×C₄₇	1	1	yes	characteristic
280	#389	C₂²×C₄₇	1	1	yes	characteristic
281	#389	C₂²×C₄₇	1	1	yes	characteristic
282	#387	—	2	1	no	—
283	#387	—	2	1	no	—
284	#385	—	2	1	no	—
285	#381	—	2	1	no	—
286	#380	C₂²×C₄₇	1	1	yes	characteristic
287	#340	C₂²×C₄₇	1	2	yes	—
288	#340	C₂²×C₄₇	1	2	yes	—
289	#340	C₂²×C₄₇	1	2	yes	—
290	#340	C₂²×C₄₇	1	2	yes	—
291	#336	C₂²×C₄₇	1	1	yes	characteristic
292	#336	C₂²×C₄₇	1	1	yes	characteristic
293	#336	C₂²×C₄₇	1	2	yes	—
294	C₄₇	#29645	1	1	yes	characteristic, direct product factor, Sylow
295	C₂²×Q₈	—	2	1	no	—
296	C₂²×Q₈	—	2	1	no	—
297	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
298	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
299	C₂³×C₄	D₄×C₄₇	1	1	yes	characteristic
300	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
301	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
302	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
303	C₄⋊Q₈	—	2	4	no	—
304	C₄⋊Q₈	—	2	4	no	—
305	#125	—	2	4	no	—
306	#125	—	2	4	no	—
307	C₂²⋊Q₈	—	2	8	no	—
308	C₂²⋊Q₈	—	2	8	no	—
309	C₂²⋊Q₈	—	2	4	no	—
310	C₄×Q₈	—	2	8	no	—
311	C₄×Q₈	—	2	8	no	—
312	#117	—	2	4	no	—
313	#117	D₄×C₄₇	1	8	yes	—
314	C₂×C₄⋊C₄	—	2	2	no	—
315	C₂×C₄⋊C₄	—	2	2	no	—
316	C₂×C₄⋊C₄	—	2	1	no	—
317	C₂×C₄⋊C₄	—	2	1	no	—
318	C₂×C₄⋊C₄	—	2	1	no	—
319	C₂×C₄⋊C₄	—	2	1	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
323	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
324	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
325	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
326	C₂×C₂²⋊C₄	—	2	2	no	—
327	C₂×C₂²⋊C₄	—	2	1	no	—
328	C₂×C₂²⋊C₄	—	2	1	no	—
329	C₂×C₄²	—	2	2	no	—
330	C₂×C₄²	—	2	4	no	—
331	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
332	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
333	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
334	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
335	#107	—	2	4	no	—
336	#106	—	2	4	no	—
337	#103	—	2	4	no	—
338	#103	—	2	4	no	—
339	C₂²⋊C₈	—	2	4	no	—
340	#95	—	2	1	no	—
341	#95	—	2	1	no	—
342	#95	—	2	1	no	—
343	#95	—	2	1	no	—
344	#95	—	2	1	no	—
345	#95	—	2	1	no	—
346	#95	—	2	1	no	—
347	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
348	C₂×Q₈	—	2	4	no	—
349	C₂×Q₈	—	2	4	no	—
350	C₂×Q₈	—	2	2	no	—
351	C₂×Q₈	—	2	2	no	—
352	C₂×Q₈	—	2	1	no	—
353	C₂×Q₈	—	2	1	no	—
354	C₂×Q₈	—	4	2	no	—
355	C₂×Q₈	—	4	2	no	—
356	C₂×Q₈	—	4	2	no	—
357	C₂×Q₈	—	4	2	no	—
358	C₂²×C₄	—	2	2	no	—
359	C₂²×C₄	—	2	1	no	—
360	C₂²×C₄	—	2	1	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	2	2	no	—
363	C₂²×C₄	—	2	2	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	1	no	—
368	C₂²×C₄	—	2	1	no	—
369	C₂²×C₄	—	2	1	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	4	1	no	—
372	C₂²×C₄	—	4	1	no	—
373	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
374	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
375	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
376	C₂²×C₄	C₂×D₄×C₄₇	1	4	yes	—
377	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
378	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
379	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
380	C₂×C₈	—	2	2	no	—
381	C₂×C₈	—	2	2	no	—
382	C₂×C₈	—	2	2	no	—
383	C₂×C₈	—	2	2	no	—
384	C₂×C₈	—	2	2	no	—
385	C₂×C₈	—	2	2	no	—
386	C₄⋊C₄	—	2	8	no	—
387	C₄⋊C₄	—	2	8	no	—
388	C₄⋊C₄	—	2	4	no	—
389	C₄⋊C₄	—	2	4	no	—
390	C₄⋊C₄	—	2	2	no	—
391	C₄⋊C₄	—	2	2	no	—
392	C₄⋊C₄	—	2	2	no	—
393	C₄⋊C₄	—	2	1	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	2	no	—
396	C₄⋊C₄	—	4	2	no	—
397	C₄⋊C₄	—	4	2	no	—
398	C₄⋊C₄	—	4	2	no	—
399	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
400	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
401	C₂²⋊C₄	—	2	8	no	—
402	C₂²⋊C₄	—	4	2	no	—
403	C₂²⋊C₄	—	4	2	no	—
404	C₄²	—	2	2	no	—
405	C₄²	—	2	2	no	—
406	C₄²	—	2	8	no	—
407	C₄²	—	2	2	no	—
408	C₄²	—	2	2	no	—
409	C₂³	—	2	1	no	—
410	C₂³	—	2	1	no	—
411	C₂³	—	2	1	no	—
412	C₂³	—	2	1	no	—
413	C₂³	—	2	1	no	—
414	C₂³	—	2	1	no	—
415	C₂³	#120×C₄₇	1	2	yes	—
416	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
417	Q₈	—	4	8	no	—
418	Q₈	—	4	8	no	—
419	Q₈	—	4	2	no	—
420	Q₈	—	4	2	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	2	4	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	2	1	no	—
431	C₂×C₄	—	2	4	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	1	no	—
434	C₂×C₄	—	2	1	no	—
435	C₂×C₄	—	2	1	no	—
436	C₂×C₄	—	2	1	no	—
437	C₂×C₄	—	4	4	no	—
438	C₂×C₄	—	4	4	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	4	1	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	1	no	—
447	C₂×C₄	—	4	1	no	—
448	C₂×C₄	—	4	1	no	—
449	C₂×C₄	—	4	1	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	1	no	—
452	C₂×C₄	—	4	1	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	#120×C₄₇	1	2	yes	—
456	C₂×C₄	#135×C₄₇	1	2	yes	—
457	C₂×C₄	#137×C₄₇	1	2	yes	—
458	C₂×C₄	C₂²×D₄×C₄₇	1	2	yes	—
459	C₂×C₄	2₋¹⁺⁴×C₄₇	1	2	yes	—
460	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
461	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
462	C₈	—	4	2	no	—
463	C₈	—	4	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	—	2	2	no	—
467	C₂²	—	4	1	no	—
468	C₂²	—	4	1	no	—
469	C₂²	—	4	1	no	—
470	C₂²	—	4	1	no	—
471	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
472	C₂²	C₄₇×#536	1	1	yes	characteristic
473	C₂²	C₄₇×#536	1	1	yes	characteristic
474	C₂²	C₂×#135×C₄₇	1	1	yes	characteristic
475	C₂²	C₂×#137×C₄₇	1	1	yes	characteristic
476	C₂²	C₄₇×#575	1	1	yes	characteristic
477	C₂²	C₄₇×#575	1	1	yes	characteristic
478	C₄	—	2	2	no	—
479	C₄	—	2	2	no	—
480	C₄	—	2	2	no	—
481	C₄	—	4	1	no	—
482	C₄	—	4	4	no	—
483	C₄	—	4	1	no	—
484	C₄	—	4	4	no	—
485	C₄	—	8	1	no	—
486	C₄	—	8	1	no	—
487	C₄	—	8	1	no	—
488	C₄	—	8	1	no	—
489	C₄	C₄₇×#536	1	2	yes	—
490	C₄	C₄₇×#536	1	2	yes	—
491	C₂	—	4	2	no	—
492	C₂	C₄₇×#2614	1	1	yes	characteristic
493	C₂	C₄₇×#3002	1	1	yes	characteristic
494	C₂	C₄₇×#3007	1	1	yes	characteristic
495	C₂	C₄₇×#3231	1	1	yes	characteristic
496	C₂	C₄₇×#3233	1	1	yes	characteristic
497	C₂	C₄₇×#3237	1	1	yes	characteristic
498	C₂	C₄₇×#3240	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
4. C₄₇×#2059	C₂	semidirect
5. C₄₇×#2058	C₂	semidirect
6. C₄₇×#2057	C₂	semidirect
7. C₄₇×#2026	C₂	semidirect
8. C₄₇×#2024	C₂	semidirect
9. C₄₇×#2024	C₂	semidirect
214. #29645	C₄₇	direct (N × H)
245. #2059	C₂×C₄₇	semidirect
246. #2058	C₂×C₄₇	semidirect
247. #2057	C₂×C₄₇	semidirect
248. #2026	C₂×C₄₇	semidirect
249. #2024	C₂×C₄₇	semidirect
250. #2024	C₂×C₄₇	semidirect
294. C₄₇	#29645	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×#533	2
C₂×C₄₇×#485	2
C₄₇×#2855	2
C₄₇×#2059	2
C₄₇×#2058	2
C₄₇×#2057	2
C₄₇×#2026	2
C₄₇×#2024	2
C₄₇×#1825	2
C₄₇×#1817	2
#29645	47

Subgroups — C47×#29645 #26069343

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#29645 #26069343