Subgroups — C₄₇×#21537 #26061235

Order 12032.

954 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#470	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#405	C₂	1	1	yes	maximal, characteristic
4	C₄₇×#2323	C₂	1	2	yes	maximal
5	C₄₇×#1971	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#1944	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1933	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1892	C₂	1	2	yes	maximal
9	C₄₇×#1809	C₂	1	1	yes	maximal, characteristic
10	C₄×#106×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1763	C₂	1	2	yes	maximal, complemented
12	C₂²×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
13	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
14	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	2	yes	—
16	C₂×C₄×Q₈×C₄₇	C₂²	1	2	yes	—
17	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#470	C₄	1	8	yes	complemented
19	C₄×Q₁₆×C₄₇	—	2	4	no	—
20	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×#103×C₄₇	C₂²	1	2	yes	—
24	C₂×#103×C₄₇	C₂²	1	2	yes	—
25	C₂×#103×C₄₇	C₂²	1	2	yes	—
26	C₄₇×#405	—	2	4	no	—
27	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₄₇×#391	C₂²	1	2	yes	—
32	C₄₇×#389	—	2	2	no	—
33	C₄₇×#389	C₂²	1	2	yes	—
34	C₄₇×#388	—	2	2	no	—
35	C₄₇×#388	—	2	2	no	—
36	C₄₇×#387	—	2	2	no	—
37	C₄₇×#380	C₂²	1	2	yes	—
38	C₄×C₄⋊C₄×C₄₇	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	C₂²×Q₈×C₄₇	C₂³	1	2	yes	—
43	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂×Q₁₆×C₄₇	—	2	2	no	—
45	C₂×Q₁₆×C₄₇	—	2	2	no	—
46	C₂×Q₁₆×C₄₇	C₂×C₄	1	4	yes	—
47	C₂×M₁₆×C₄₇	—	2	2	no	—
48	C₂×M₁₆×C₄₇	—	2	2	no	—
49	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	—
50	C₂²×C₈×C₄₇	—	2	2	no	—
51	C₂²×C₈×C₄₇	—	2	2	no	—
52	C₂²×C₈×C₄₇	—	2	2	no	—
53	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
54	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
55	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
57	C₂²⋊Q₈×C₄₇	—	2	4	no	—
58	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	—
59	C₄×Q₈×C₄₇	—	2	4	no	—
60	C₄×Q₈×C₄₇	—	2	4	no	—
61	#117×C₄₇	—	2	2	no	—
62	#117×C₄₇	—	2	2	no	—
63	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
64	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
67	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
71	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₇	D₄	1	1	yes	characteristic
74	C₂×C₂²⋊C₄×C₄₇	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₄₇	—	2	2	no	—
76	C₂×C₄²×C₄₇	—	2	2	no	—
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	#107×C₄₇	—	2	2	no	—
80	#106×C₄₇	—	2	2	no	—
81	#106×C₄₇	C₂×C₄	1	4	yes	—
82	#103×C₄₇	—	2	4	no	—
83	#103×C₄₇	—	2	4	no	—
84	#103×C₄₇	C₂×C₄	1	8	yes	—
85	#97×C₄₇	—	2	2	no	—
86	#97×C₄₇	—	2	2	no	—
87	C₄×C₈×C₄₇	—	2	2	no	—
88	C₄×C₈×C₄₇	D₄	1	4	yes	—
89	#95×C₄₇	—	2	2	no	—
90	#95×C₄₇	—	2	2	no	—
91	#95×C₄₇	—	2	2	no	—
92	#95×C₄₇	—	2	2	no	—
93	#95×C₄₇	—	2	2	no	—
94	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
95	C₂×Q₈×C₄₇	—	2	2	no	—
96	C₂×Q₈×C₄₇	—	2	2	no	—
97	C₂×Q₈×C₄₇	—	2	2	no	—
98	C₂×Q₈×C₄₇	—	2	2	no	—
99	C₂×Q₈×C₄₇	—	2	2	no	—
100	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	—	2	2	no	—
106	C₂²×C₄×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
110	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
111	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	#41	1	2	yes	—
116	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
117	Q₁₆×C₄₇	—	2	8	no	—
118	M₁₆×C₄₇	—	2	8	no	—
119	C₂×C₈×C₄₇	—	2	8	no	—
120	C₂×C₈×C₄₇	—	2	1	no	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	—	2	1	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	—	2	1	no	—
126	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
127	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
128	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₄₇	#41	1	2	yes	—
131	C₂×C₈×C₄₇	#41	1	2	yes	—
132	C₄⋊C₄×C₄₇	—	2	8	no	—
133	C₄⋊C₄×C₄₇	—	2	2	no	—
134	C₄⋊C₄×C₄₇	—	2	2	no	—
135	C₄⋊C₄×C₄₇	—	2	2	no	—
136	C₄⋊C₄×C₄₇	—	2	2	no	—
137	C₄⋊C₄×C₄₇	—	2	2	no	—
138	C₄⋊C₄×C₄₇	—	2	2	no	—
139	C₄⋊C₄×C₄₇	—	2	2	no	—
140	C₄⋊C₄×C₄₇	—	4	4	no	—
141	C₄⋊C₄×C₄₇	—	8	2	no	—
142	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
143	C₂²⋊C₄×C₄₇	—	2	8	no	—
144	C₂²⋊C₄×C₄₇	—	2	2	no	—
145	C₂²⋊C₄×C₄₇	—	2	2	no	—
146	C₂²⋊C₄×C₄₇	—	8	2	no	—
147	C₄²×C₄₇	—	2	1	no	—
148	C₄²×C₄₇	—	2	1	no	—
149	C₄²×C₄₇	—	4	4	no	—
150	C₄²×C₄₇	—	8	2	no	—
151	C₄²×C₄₇	C₂×D₄	1	2	yes	—
152	C₄²×C₄₇	#41	1	2	yes	—
153	C₂³×C₄₇	—	2	1	no	—
154	C₂³×C₄₇	—	2	1	no	—
155	C₂³×C₄₇	—	2	2	no	—
156	C₂³×C₄₇	—	2	2	no	—
157	C₂³×C₄₇	C₄×D₄	1	2	yes	—
158	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
159	Q₈×C₄₇	—	2	4	no	—
160	Q₈×C₄₇	—	2	4	no	—
161	Q₈×C₄₇	—	4	2	no	—
162	Q₈×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	2	1	no	—
165	C₂×C₄×C₄₇	—	2	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	2	2	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	4	no	—
172	C₂×C₄×C₄₇	—	2	4	no	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	—	4	2	no	—
179	C₂×C₄×C₄₇	—	4	2	no	—
180	C₂×C₄×C₄₇	—	4	2	no	—
181	C₂×C₄×C₄₇	—	4	2	no	—
182	C₂×C₄×C₄₇	—	4	2	no	—
183	C₂×C₄×C₄₇	—	4	2	no	—
184	C₂×C₄×C₄₇	—	4	2	no	—
185	C₂×C₄×C₄₇	—	4	2	no	—
186	C₂×C₄×C₄₇	—	4	2	no	—
187	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
188	C₂×C₄×C₄₇	#121	1	2	yes	—
189	C₂×C₄×C₄₇	#121	1	2	yes	—
190	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
193	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
196	C₈×C₄₇	—	2	2	no	—
197	C₈×C₄₇	—	2	2	no	—
198	C₈×C₄₇	—	2	2	no	—
199	C₈×C₄₇	C₄×D₄	1	4	yes	—
200	#21537	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂²×C₄₇	—	2	4	no	—
202	C₂²×C₄₇	—	2	2	no	—
203	C₂²×C₄₇	—	4	2	no	—
204	C₂²×C₄₇	—	4	1	no	—
205	C₂²×C₄₇	—	4	1	no	—
206	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
207	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
208	C₂²×C₄₇	#532	1	1	yes	characteristic
209	C₂²×C₄₇	#577	1	2	yes	—
210	C₂²×C₄₇	#578	1	2	yes	—
211	C₄×C₄₇	—	2	2	no	—
212	C₄×C₄₇	—	2	2	no	—
213	C₄×C₄₇	—	2	2	no	—
214	C₄×C₄₇	—	4	4	no	—
215	C₄×C₄₇	—	4	1	no	—
216	C₄×C₄₇	—	4	1	no	—
217	C₄×C₄₇	—	4	4	no	—
218	C₄×C₄₇	—	8	2	no	—
219	C₄×C₄₇	—	8	2	no	—
220	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
221	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
222	C₄×C₄₇	#525	1	1	yes	characteristic
223	C₄×C₄₇	#529	1	1	yes	characteristic
224	C₂×#470	C₂×C₄₇	1	1	yes	characteristic
225	C₂×C₄×Q₁₆	C₂×C₄₇	1	1	yes	characteristic, complemented
226	C₂×#405	C₂×C₄₇	1	1	yes	characteristic
227	#2323	C₂×C₄₇	1	2	yes	—
228	#1971	C₂×C₄₇	1	1	yes	characteristic, complemented
229	#1944	C₂×C₄₇	1	1	yes	characteristic, complemented
230	#1933	C₂×C₄₇	1	2	yes	complemented
231	#1892	C₂×C₄₇	1	2	yes	—
232	#1809	C₂×C₄₇	1	1	yes	characteristic
233	C₄×#106	C₂×C₄₇	1	1	yes	characteristic, complemented
234	#1763	C₂×C₄₇	1	2	yes	complemented
235	C₂×C₄₇	—	4	2	no	—
236	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
237	C₂×C₄₇	#2947	1	2	yes	—
238	C₂×C₄₇	#3059	1	1	yes	characteristic
239	C₂×C₄₇	#3060	1	1	yes	characteristic
240	C₂×C₄₇	#3178	1	2	yes	—
241	C₂²×Q₁₆	C₂²×C₄₇	1	1	yes	characteristic
242	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
243	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
244	C₂×C₂²⋊Q₈	C₂²×C₄₇	1	2	yes	—
245	C₂×C₄×Q₈	C₂²×C₄₇	1	2	yes	—
246	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
247	#470	C₄×C₄₇	1	8	yes	complemented
248	C₄×Q₁₆	—	2	4	no	—
249	C₂×#107	C₂²×C₄₇	1	1	yes	characteristic
250	C₂×#106	C₂²×C₄₇	1	1	yes	characteristic
251	C₂×#106	C₂²×C₄₇	1	1	yes	characteristic
252	C₂×#103	C₂²×C₄₇	1	2	yes	—
253	C₂×#103	C₂²×C₄₇	1	2	yes	—
254	C₂×#103	C₂²×C₄₇	1	2	yes	—
255	#405	—	2	4	no	—
256	C₂×#97	C₂²×C₄₇	1	1	yes	characteristic
257	C₂×#97	C₂²×C₄₇	1	1	yes	characteristic
258	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
259	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
260	#391	C₂²×C₄₇	1	2	yes	—
261	#389	—	2	2	no	—
262	#389	C₂²×C₄₇	1	2	yes	—
263	#388	—	2	2	no	—
264	#388	—	2	2	no	—
265	#387	—	2	2	no	—
266	#380	C₂²×C₄₇	1	2	yes	—
267	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
268	#340	C₂²×C₄₇	1	2	yes	—
269	#340	C₂²×C₄₇	1	2	yes	—
270	#340	C₂²×C₄₇	1	2	yes	—
271	C₄₇	#21537	1	1	yes	characteristic, direct product factor, Sylow
272	C₂²×Q₈	C₂³×C₄₇	1	2	yes	—
273	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
274	C₂×Q₁₆	—	2	2	no	—
275	C₂×Q₁₆	—	2	2	no	—
276	C₂×Q₁₆	C₂×C₄×C₄₇	1	4	yes	—
277	C₂×M₁₆	—	2	2	no	—
278	C₂×M₁₆	—	2	2	no	—
279	C₂×M₁₆	C₂×C₄×C₄₇	1	4	yes	—
280	C₂²×C₈	—	2	2	no	—
281	C₂²×C₈	—	2	2	no	—
282	C₂²×C₈	—	2	2	no	—
283	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
284	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
286	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
287	C₂²⋊Q₈	—	2	4	no	—
288	C₂²⋊Q₈	C₂×C₄×C₄₇	1	8	yes	—
289	C₄×Q₈	—	2	4	no	—
290	C₄×Q₈	—	2	4	no	—
291	#117	—	2	2	no	—
292	#117	—	2	2	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	—	2	2	no	—
295	C₂×C₄⋊C₄	—	2	2	no	—
296	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
297	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
299	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₂²⋊C₄	D₄×C₄₇	1	1	yes	characteristic
304	C₂×C₂²⋊C₄	D₄×C₄₇	1	1	yes	characteristic
305	C₂×C₄²	—	2	2	no	—
306	C₂×C₄²	—	2	2	no	—
307	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
308	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
309	#107	—	2	2	no	—
310	#106	—	2	2	no	—
311	#106	C₂×C₄×C₄₇	1	4	yes	—
312	#103	—	2	4	no	—
313	#103	—	2	4	no	—
314	#103	C₂×C₄×C₄₇	1	8	yes	—
315	#97	—	2	2	no	—
316	#97	—	2	2	no	—
317	C₄×C₈	—	2	2	no	—
318	C₄×C₈	D₄×C₄₇	1	4	yes	—
319	#95	—	2	2	no	—
320	#95	—	2	2	no	—
321	#95	—	2	2	no	—
322	#95	—	2	2	no	—
323	#95	—	2	2	no	—
324	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
325	C₂×Q₈	—	2	2	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	2	no	—
329	C₂×Q₈	—	2	2	no	—
330	C₂×Q₈	C₂²×C₄×C₄₇	1	4	yes	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	1	no	—
333	C₂²×C₄	—	2	1	no	—
334	C₂²×C₄	—	2	1	no	—
335	C₂²×C₄	—	2	2	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	2	2	no	—
339	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
340	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
341	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
342	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
343	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
344	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
345	C₂²×C₄	#41×C₄₇	1	2	yes	—
346	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
347	Q₁₆	—	2	8	no	—
348	M₁₆	—	2	8	no	—
349	C₂×C₈	—	2	8	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	2	1	no	—
353	C₂×C₈	—	2	1	no	—
354	C₂×C₈	—	2	1	no	—
355	C₂×C₈	—	2	1	no	—
356	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
357	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
358	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
359	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
360	C₂×C₈	#41×C₄₇	1	2	yes	—
361	C₂×C₈	#41×C₄₇	1	2	yes	—
362	C₄⋊C₄	—	2	8	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	2	2	no	—
366	C₄⋊C₄	—	2	2	no	—
367	C₄⋊C₄	—	2	2	no	—
368	C₄⋊C₄	—	2	2	no	—
369	C₄⋊C₄	—	2	2	no	—
370	C₄⋊C₄	—	4	4	no	—
371	C₄⋊C₄	—	8	2	no	—
372	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
373	C₂²⋊C₄	—	2	8	no	—
374	C₂²⋊C₄	—	2	2	no	—
375	C₂²⋊C₄	—	2	2	no	—
376	C₂²⋊C₄	—	8	2	no	—
377	C₄²	—	2	1	no	—
378	C₄²	—	2	1	no	—
379	C₄²	—	4	4	no	—
380	C₄²	—	8	2	no	—
381	C₄²	C₂×D₄×C₄₇	1	2	yes	—
382	C₄²	#41×C₄₇	1	2	yes	—
383	C₂³	—	2	1	no	—
384	C₂³	—	2	1	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	C₄×D₄×C₄₇	1	2	yes	—
388	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
389	Q₈	—	2	4	no	—
390	Q₈	—	2	4	no	—
391	Q₈	—	4	2	no	—
392	Q₈	—	4	2	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	1	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	4	no	—
402	C₂×C₄	—	2	4	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	4	2	no	—
408	C₂×C₄	—	4	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	—	4	2	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	2	no	—
413	C₂×C₄	—	4	2	no	—
414	C₂×C₄	—	4	2	no	—
415	C₂×C₄	—	4	2	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
418	C₂×C₄	#121×C₄₇	1	2	yes	—
419	C₂×C₄	#121×C₄₇	1	2	yes	—
420	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
421	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
422	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
423	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
424	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
425	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
426	C₈	—	2	2	no	—
427	C₈	—	2	2	no	—
428	C₈	—	2	2	no	—
429	C₈	C₄×D₄×C₄₇	1	4	yes	—
430	C₂²	—	2	2	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	4	1	no	—
433	C₂²	—	4	1	no	—
434	C₂²	—	4	2	no	—
435	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
436	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
437	C₂²	C₄₇×#532	1	1	yes	characteristic
438	C₂²	C₄₇×#577	1	2	yes	—
439	C₂²	C₄₇×#578	1	2	yes	—
440	C₄	—	2	2	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	2	no	—
443	C₄	—	4	1	no	—
444	C₄	—	4	1	no	—
445	C₄	—	4	4	no	—
446	C₄	—	4	4	no	—
447	C₄	—	8	2	no	—
448	C₄	—	8	2	no	—
449	C₄	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
450	C₄	C₄×#41×C₄₇	1	1	yes	characteristic
451	C₄	C₄₇×#525	1	1	yes	characteristic
452	C₄	C₄₇×#529	1	1	yes	characteristic
453	C₂	—	4	2	no	—
454	C₂	C₄×#121×C₄₇	1	1	yes	characteristic
455	C₂	C₄₇×#2947	1	2	yes	—
456	C₂	C₄₇×#3059	1	1	yes	characteristic
457	C₂	C₄₇×#3060	1	1	yes	characteristic
458	C₂	C₄₇×#3178	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂⁴×C₄₇	C₂×D₄
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂×#117×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄×Q₁₆×C₄₇	C₂	semidirect
5. C₄₇×#1971	C₂	semidirect
6. C₄₇×#1944	C₂	semidirect
7. C₄₇×#1933	C₂	semidirect
10. C₄×#106×C₄₇	C₂	semidirect
11. C₄₇×#1763	C₂	semidirect
18. C₄₇×#470	C₄	semidirect
200. #21537	C₄₇	direct (N × H)
225. C₂×C₄×Q₁₆	C₂×C₄₇	semidirect
228. #1971	C₂×C₄₇	semidirect
229. #1944	C₂×C₄₇	semidirect
230. #1933	C₂×C₄₇	semidirect
233. C₄×#106	C₂×C₄₇	semidirect
234. #1763	C₂×C₄₇	semidirect
247. #470	C₄×C₄₇	semidirect
271. C₄₇	#21537	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×#470	2
C₂×C₄×Q₁₆×C₄₇	2
C₂×C₄₇×#405	2
C₄₇×#2323	2
C₄₇×#1971	2
C₄₇×#1944	2
C₄₇×#1933	2
C₄₇×#1892	2
C₄₇×#1809	2
C₄×#106×C₄₇	2
C₄₇×#1763	2
#21537	47

Subgroups — C47×#21537 #26061235

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#21537 #26061235