Subgroups — C₄₇×#21541 #26061239

Order 12032.

1066 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#469	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#442	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#405	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2324	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1970	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#1941	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1936	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1893	C₂	1	2	yes	maximal, complemented
9	C₄₇×#1809	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1776	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#102×C₄₇	C₂	1	2	yes	maximal, complemented
12	C₂²×D₈×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×#121×C₄₇	C₂²	1	2	yes	—
16	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
17	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
18	C₄₇×#469	C₄	1	8	yes	complemented
19	C₄₇×#442	—	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×#102×C₄₇	C₂²	1	2	yes	—
24	C₂×#102×C₄₇	C₂²	1	2	yes	—
25	C₂×#102×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×#390	—	2	2	no	—
32	C₄₇×#390	C₂²	1	2	yes	—
33	C₄₇×#389	C₂²	1	2	yes	—
34	C₄₇×#388	—	2	2	no	—
35	C₄₇×#386	—	2	2	no	—
36	C₄₇×#385	—	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×D₄×C₄₇	—	2	2	no	—
43	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
44	C₂³×C₄×C₄₇	—	2	2	no	—
45	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
46	C₂×D₈×C₄₇	—	2	2	no	—
47	C₂×D₈×C₄₇	—	2	2	no	—
48	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	—
49	C₂×M₁₆×C₄₇	—	2	2	no	—
50	C₂×M₁₆×C₄₇	—	2	2	no	—
51	C₂×M₁₆×C₄₇	C₂×C₄	1	4	yes	complemented
52	C₂²×C₈×C₄₇	—	2	2	no	—
53	C₂²×C₈×C₄₇	—	2	2	no	—
54	C₂²×C₈×C₄₇	—	2	2	no	—
55	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
56	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
57	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
58	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
59	#121×C₄₇	—	2	4	no	—
60	#121×C₄₇	C₂×C₄	1	8	yes	complemented
61	C₄×D₄×C₄₇	—	2	4	no	—
62	C₄×D₄×C₄₇	—	2	4	no	—
63	#117×C₄₇	—	2	2	no	—
64	#117×C₄₇	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
66	C₂×C₄⋊C₄×C₄₇	D₄	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
68	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
70	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
71	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
74	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
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	complemented
82	#102×C₄₇	—	2	4	no	—
83	#102×C₄₇	—	2	4	no	—
84	#102×C₄₇	C₂×C₄	1	8	yes	complemented
85	#97×C₄₇	—	2	2	no	—
86	#97×C₄₇	D₄	1	4	yes	complemented
87	C₄×C₈×C₄₇	—	2	2	no	—
88	C₄×C₈×C₄₇	—	2	2	no	—
89	#95×C₄₇	—	2	2	no	—
90	#95×C₄₇	—	2	2	no	—
91	#95×C₄₇	—	2	2	no	—
92	C₂⁴×C₄₇	—	2	2	no	—
93	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
94	C₂×D₄×C₄₇	—	2	8	no	—
95	C₂×D₄×C₄₇	—	2	2	no	—
96	C₂×D₄×C₄₇	—	2	2	no	—
97	C₂×D₄×C₄₇	—	2	2	no	—
98	C₂×D₄×C₄₇	—	2	2	no	—
99	C₂×D₄×C₄₇	—	2	2	no	—
100	C₂×D₄×C₄₇	—	8	2	no	—
101	C₂×D₄×C₄₇	—	8	2	no	—
102	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	—	2	1	no	—
106	C₂²×C₄×C₄₇	—	2	1	no	—
107	C₂²×C₄×C₄₇	—	2	2	no	—
108	C₂²×C₄×C₄₇	—	2	2	no	—
109	C₂²×C₄×C₄₇	—	2	2	no	—
110	C₂²×C₄×C₄₇	—	4	4	no	—
111	C₂²×C₄×C₄₇	—	8	2	no	—
112	C₂²×C₄×C₄₇	—	8	2	no	—
113	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
114	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
117	C₂²×C₄×C₄₇	#41	1	2	yes	—
118	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
119	D₈×C₄₇	—	2	8	no	—
120	M₁₆×C₄₇	—	2	8	no	—
121	C₂×C₈×C₄₇	—	2	8	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	—	2	1	no	—
127	C₂×C₈×C₄₇	—	2	1	no	—
128	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
129	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
130	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
131	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₄₇	#41	1	2	yes	—
133	C₂×C₈×C₄₇	#41	1	2	yes	—
134	C₄⋊C₄×C₄₇	—	2	4	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	—	8	2	no	—
141	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
142	C₂²⋊C₄×C₄₇	—	2	8	no	—
143	C₂²⋊C₄×C₄₇	—	2	4	no	—
144	C₂²⋊C₄×C₄₇	—	4	4	no	—
145	C₂²⋊C₄×C₄₇	—	8	2	no	—
146	C₂²⋊C₄×C₄₇	—	8	2	no	—
147	C₂²⋊C₄×C₄₇	—	8	2	no	—
148	C₄²×C₄₇	—	2	1	no	—
149	C₄²×C₄₇	—	2	1	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	—	2	4	no	—
158	C₂³×C₄₇	—	4	2	no	—
159	C₂³×C₄₇	—	4	2	no	—
160	C₂³×C₄₇	—	4	2	no	—
161	C₂³×C₄₇	—	4	2	no	—
162	C₂³×C₄₇	—	4	2	no	—
163	C₂³×C₄₇	—	4	2	no	—
164	C₂³×C₄₇	C₄×D₄	1	2	yes	—
165	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
166	D₄×C₄₇	—	2	4	no	—
167	D₄×C₄₇	—	2	4	no	—
168	D₄×C₄₇	—	4	2	no	—
169	D₄×C₄₇	—	4	2	no	—
170	D₄×C₄₇	—	8	8	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	2	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	4	no	—
180	C₂×C₄×C₄₇	—	2	2	no	—
181	C₂×C₄×C₄₇	—	2	2	no	—
182	C₂×C₄×C₄₇	—	2	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	—	4	2	no	—
188	C₂×C₄×C₄₇	—	4	2	no	—
189	C₂×C₄×C₄₇	—	4	2	no	—
190	C₂×C₄×C₄₇	—	4	2	no	—
191	C₂×C₄×C₄₇	—	8	8	no	—
192	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
193	C₂×C₄×C₄₇	#121	1	4	yes	—
194	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
195	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
196	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
197	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
198	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
199	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
200	C₈×C₄₇	—	2	2	no	—
201	C₈×C₄₇	—	2	2	no	—
202	C₈×C₄₇	—	2	2	no	—
203	C₈×C₄₇	C₄×D₄	1	4	yes	—
204	#21541	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
205	C₂²×C₄₇	—	2	4	no	—
206	C₂²×C₄₇	—	2	2	no	—
207	C₂²×C₄₇	—	4	1	no	—
208	C₂²×C₄₇	—	4	1	no	—
209	C₂²×C₄₇	—	4	2	no	—
210	C₂²×C₄₇	—	4	4	no	—
211	C₂²×C₄₇	—	4	4	no	—
212	C₂²×C₄₇	—	4	4	no	—
213	C₂²×C₄₇	—	8	2	no	—
214	C₂²×C₄₇	—	8	2	no	—
215	C₂²×C₄₇	—	8	2	no	—
216	C₂²×C₄₇	—	8	2	no	—
217	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
218	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
219	C₂²×C₄₇	#532	1	1	yes	characteristic
220	C₂²×C₄₇	#576	1	2	yes	—
221	C₂²×C₄₇	#577	1	2	yes	—
222	C₄×C₄₇	—	2	4	no	—
223	C₄×C₄₇	—	2	2	no	—
224	C₄×C₄₇	—	4	4	no	—
225	C₄×C₄₇	—	4	2	no	—
226	C₄×C₄₇	—	8	2	no	—
227	C₄×C₄₇	—	8	2	no	—
228	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
229	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
230	C₄×C₄₇	#525	1	1	yes	characteristic
231	C₄×C₄₇	#529	1	1	yes	characteristic
232	C₂×#469	C₂×C₄₇	1	1	yes	characteristic
233	C₂×#442	C₂×C₄₇	1	1	yes	characteristic, complemented
234	C₂×#405	C₂×C₄₇	1	1	yes	characteristic, complemented
235	#2324	C₂×C₄₇	1	2	yes	complemented
236	#1970	C₂×C₄₇	1	1	yes	characteristic, complemented
237	#1941	C₂×C₄₇	1	1	yes	characteristic, complemented
238	#1936	C₂×C₄₇	1	2	yes	complemented
239	#1893	C₂×C₄₇	1	2	yes	complemented
240	#1809	C₂×C₄₇	1	1	yes	characteristic, complemented
241	#1776	C₂×C₄₇	1	1	yes	characteristic, complemented
242	C₄×#102	C₂×C₄₇	1	2	yes	complemented
243	C₂×C₄₇	—	4	2	no	—
244	C₂×C₄₇	—	8	4	no	—
245	C₂×C₄₇	C₄×#121	1	1	yes	characteristic
246	C₂×C₄₇	#2946	1	2	yes	—
247	C₂×C₄₇	#3062	1	2	yes	—
248	C₂×C₄₇	#3173	1	1	yes	characteristic
249	C₂×C₄₇	#3176	1	1	yes	characteristic
250	C₂²×D₈	C₂²×C₄₇	1	1	yes	characteristic
251	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
252	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
253	C₂×#121	C₂²×C₄₇	1	2	yes	—
254	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
255	C₂×#117	C₂²×C₄₇	1	1	yes	characteristic
256	#469	C₄×C₄₇	1	8	yes	complemented
257	#442	—	2	4	no	—
258	C₂×#107	C₂²×C₄₇	1	1	yes	characteristic
259	C₂×#106	C₂²×C₄₇	1	1	yes	characteristic
260	C₂×#106	C₂²×C₄₇	1	1	yes	characteristic
261	C₂×#102	C₂²×C₄₇	1	2	yes	—
262	C₂×#102	C₂²×C₄₇	1	2	yes	—
263	C₂×#102	C₂²×C₄₇	1	2	yes	—
264	#405	—	2	4	no	—
265	C₂×#97	C₂²×C₄₇	1	1	yes	characteristic
266	C₂×#97	C₂²×C₄₇	1	1	yes	characteristic
267	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
268	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
269	#390	—	2	2	no	—
270	#390	C₂²×C₄₇	1	2	yes	—
271	#389	C₂²×C₄₇	1	2	yes	—
272	#388	—	2	2	no	—
273	#386	—	2	2	no	—
274	#385	—	2	2	no	—
275	#380	C₂²×C₄₇	1	2	yes	—
276	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
277	#340	C₂²×C₄₇	1	2	yes	—
278	#340	C₂²×C₄₇	1	2	yes	—
279	#340	C₂²×C₄₇	1	2	yes	—
280	C₄₇	#21541	1	1	yes	characteristic, direct product factor, Sylow
281	C₂²×D₄	—	2	2	no	—
282	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
283	C₂³×C₄	—	2	2	no	—
284	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
285	C₂×D₈	—	2	2	no	—
286	C₂×D₈	—	2	2	no	—
287	C₂×D₈	C₂×C₄×C₄₇	1	4	yes	—
288	C₂×M₁₆	—	2	2	no	—
289	C₂×M₁₆	—	2	2	no	—
290	C₂×M₁₆	C₂×C₄×C₄₇	1	4	yes	complemented
291	C₂²×C₈	—	2	2	no	—
292	C₂²×C₈	—	2	2	no	—
293	C₂²×C₈	—	2	2	no	—
294	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
295	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
296	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
297	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
298	#121	—	2	4	no	—
299	#121	C₂×C₄×C₄₇	1	8	yes	complemented
300	C₄×D₄	—	2	4	no	—
301	C₄×D₄	—	2	4	no	—
302	#117	—	2	2	no	—
303	#117	—	2	2	no	—
304	C₂×C₄⋊C₄	—	2	2	no	—
305	C₂×C₄⋊C₄	D₄×C₄₇	1	2	yes	—
306	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
307	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
308	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
309	C₂×C₂²⋊C₄	—	2	2	no	—
310	C₂×C₂²⋊C₄	—	2	2	no	—
311	C₂×C₂²⋊C₄	—	2	2	no	—
312	C₂×C₂²⋊C₄	—	2	2	no	—
313	C₂×C₂²⋊C₄	—	2	2	no	—
314	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
315	C₂×C₄²	—	2	2	no	—
316	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
317	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
318	#107	—	2	2	no	—
319	#106	—	2	2	no	—
320	#106	C₂×C₄×C₄₇	1	4	yes	complemented
321	#102	—	2	4	no	—
322	#102	—	2	4	no	—
323	#102	C₂×C₄×C₄₇	1	8	yes	complemented
324	#97	—	2	2	no	—
325	#97	D₄×C₄₇	1	4	yes	complemented
326	C₄×C₈	—	2	2	no	—
327	C₄×C₈	—	2	2	no	—
328	#95	—	2	2	no	—
329	#95	—	2	2	no	—
330	#95	—	2	2	no	—
331	C₂⁴	—	2	2	no	—
332	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
333	C₂×D₄	—	2	8	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	—	2	2	no	—
338	C₂×D₄	—	2	2	no	—
339	C₂×D₄	—	8	2	no	—
340	C₂×D₄	—	8	2	no	—
341	C₂×D₄	C₂²×C₄×C₄₇	1	4	yes	—
342	C₂²×C₄	—	2	1	no	—
343	C₂²×C₄	—	2	1	no	—
344	C₂²×C₄	—	2	1	no	—
345	C₂²×C₄	—	2	1	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	4	4	no	—
350	C₂²×C₄	—	8	2	no	—
351	C₂²×C₄	—	8	2	no	—
352	C₂²×C₄	C₂²×C₄×C₄₇	1	2	yes	—
353	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
354	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
355	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
356	C₂²×C₄	#41×C₄₇	1	2	yes	—
357	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
358	D₈	—	2	8	no	—
359	M₁₆	—	2	8	no	—
360	C₂×C₈	—	2	8	no	—
361	C₂×C₈	—	2	1	no	—
362	C₂×C₈	—	2	1	no	—
363	C₂×C₈	—	2	1	no	—
364	C₂×C₈	—	2	1	no	—
365	C₂×C₈	—	2	1	no	—
366	C₂×C₈	—	2	1	no	—
367	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
368	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
369	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
370	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
371	C₂×C₈	#41×C₄₇	1	2	yes	—
372	C₂×C₈	#41×C₄₇	1	2	yes	—
373	C₄⋊C₄	—	2	4	no	—
374	C₄⋊C₄	—	2	2	no	—
375	C₄⋊C₄	—	2	2	no	—
376	C₄⋊C₄	—	2	2	no	—
377	C₄⋊C₄	—	2	2	no	—
378	C₄⋊C₄	—	2	2	no	—
379	C₄⋊C₄	—	8	2	no	—
380	C₄⋊C₄	C₂²×C₄×C₄₇	1	4	yes	—
381	C₂²⋊C₄	—	2	8	no	—
382	C₂²⋊C₄	—	2	4	no	—
383	C₂²⋊C₄	—	4	4	no	—
384	C₂²⋊C₄	—	8	2	no	—
385	C₂²⋊C₄	—	8	2	no	—
386	C₂²⋊C₄	—	8	2	no	—
387	C₄²	—	2	1	no	—
388	C₄²	—	2	1	no	—
389	C₄²	—	8	2	no	—
390	C₄²	C₂×D₄×C₄₇	1	2	yes	—
391	C₄²	#41×C₄₇	1	2	yes	—
392	C₂³	—	2	1	no	—
393	C₂³	—	2	1	no	—
394	C₂³	—	2	2	no	—
395	C₂³	—	2	2	no	—
396	C₂³	—	2	4	no	—
397	C₂³	—	4	2	no	—
398	C₂³	—	4	2	no	—
399	C₂³	—	4	2	no	—
400	C₂³	—	4	2	no	—
401	C₂³	—	4	2	no	—
402	C₂³	—	4	2	no	—
403	C₂³	C₄×D₄×C₄₇	1	2	yes	—
404	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
405	D₄	—	2	4	no	—
406	D₄	—	2	4	no	—
407	D₄	—	4	2	no	—
408	D₄	—	4	2	no	—
409	D₄	—	8	8	no	—
410	C₂×C₄	—	2	1	no	—
411	C₂×C₄	—	2	1	no	—
412	C₂×C₄	—	2	2	no	—
413	C₂×C₄	—	2	2	no	—
414	C₂×C₄	—	2	2	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	2	no	—
418	C₂×C₄	—	2	4	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	4	2	no	—
423	C₂×C₄	—	4	2	no	—
424	C₂×C₄	—	4	2	no	—
425	C₂×C₄	—	4	2	no	—
426	C₂×C₄	—	4	2	no	—
427	C₂×C₄	—	4	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	4	2	no	—
430	C₂×C₄	—	8	8	no	—
431	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
432	C₂×C₄	#121×C₄₇	1	4	yes	—
433	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
434	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
435	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
436	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
437	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
438	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
439	C₈	—	2	2	no	—
440	C₈	—	2	2	no	—
441	C₈	—	2	2	no	—
442	C₈	C₄×D₄×C₄₇	1	4	yes	—
443	C₂²	—	2	2	no	—
444	C₂²	—	2	4	no	—
445	C₂²	—	4	2	no	—
446	C₂²	—	4	1	no	—
447	C₂²	—	4	1	no	—
448	C₂²	—	4	4	no	—
449	C₂²	—	4	4	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	8	2	no	—
452	C₂²	—	8	2	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	8	2	no	—
455	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
456	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
457	C₂²	C₄₇×#532	1	1	yes	characteristic
458	C₂²	C₄₇×#576	1	2	yes	—
459	C₂²	C₄₇×#577	1	2	yes	—
460	C₄	—	2	4	no	—
461	C₄	—	2	2	no	—
462	C₄	—	4	2	no	—
463	C₄	—	4	4	no	—
464	C₄	—	8	2	no	—
465	C₄	—	8	2	no	—
466	C₄	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
467	C₄	C₄×#41×C₄₇	1	1	yes	characteristic
468	C₄	C₄₇×#525	1	1	yes	characteristic
469	C₄	C₄₇×#529	1	1	yes	characteristic
470	C₂	—	4	2	no	—
471	C₂	—	8	4	no	—
472	C₂	C₄×#121×C₄₇	1	1	yes	characteristic
473	C₂	C₄₇×#2946	1	2	yes	—
474	C₂	C₄₇×#3062	1	2	yes	—
475	C₂	C₄₇×#3173	1	1	yes	characteristic
476	C₂	C₄₇×#3176	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×C₄₇×#469	C₂
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×C₄₇×#442	C₂	semidirect
3. C₂×C₄₇×#405	C₂	semidirect
4. C₄₇×#2324	C₂	semidirect
5. C₄₇×#1970	C₂	semidirect
6. C₄₇×#1941	C₂	semidirect
7. C₄₇×#1936	C₂	semidirect
8. C₄₇×#1893	C₂	semidirect
9. C₄₇×#1809	C₂	semidirect
10. C₄₇×#1776	C₂	semidirect
11. C₄×#102×C₄₇	C₂	semidirect
18. C₄₇×#469	C₄	semidirect
51. C₂×M₁₆×C₄₇	C₂×C₄	semidirect
60. #121×C₄₇	C₂×C₄	semidirect
81. #106×C₄₇	C₂×C₄	semidirect
84. #102×C₄₇	C₂×C₄	semidirect
86. #97×C₄₇	D₄	semidirect
204. #21541	C₄₇	direct (N × H)
233. C₂×#442	C₂×C₄₇	semidirect
234. C₂×#405	C₂×C₄₇	semidirect
235. #2324	C₂×C₄₇	semidirect
236. #1970	C₂×C₄₇	semidirect
237. #1941	C₂×C₄₇	semidirect
238. #1936	C₂×C₄₇	semidirect
239. #1893	C₂×C₄₇	semidirect
240. #1809	C₂×C₄₇	semidirect
241. #1776	C₂×C₄₇	semidirect
242. C₄×#102	C₂×C₄₇	semidirect
256. #469	C₄×C₄₇	semidirect
280. C₄₇	#21541	direct (N × H)
290. C₂×M₁₆	C₂×C₄×C₄₇	semidirect
299. #121	C₂×C₄×C₄₇	semidirect
320. #106	C₂×C₄×C₄₇	semidirect
323. #102	C₂×C₄×C₄₇	semidirect
325. #97	D₄×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄₇×#469	2
C₂×C₄₇×#442	2
C₂×C₄₇×#405	2
C₄₇×#2324	2
C₄₇×#1970	2
C₄₇×#1941	2
C₄₇×#1936	2
C₄₇×#1893	2
C₄₇×#1809	2
C₄₇×#1776	2
C₄×#102×C₄₇	2
#21541	47

Subgroups — C47×#21541 #26061239

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#21541 #26061239