Subgroups — C₄₇×#21113 #26060811

Order 12032.

1054 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic
2	C₄₇×#2293	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄²×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#1925	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1918	C₂	1	2	yes	maximal, complemented
6	C₄₇×#1879	C₂	1	2	yes	maximal
7	C₄₇×#1862	C₂	1	2	yes	maximal, complemented
8	C₄×#107×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#102×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#102×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1744	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
15	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#117×C₄₇	—	2	1	no	—
17	C₂²×C₄²×C₄₇	—	2	1	no	—
18	C₄×D₈×C₄₇	C₄	1	8	yes	complemented
19	C₂×#107×C₄₇	C₂²	1	2	yes	—
20	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×#102×C₄₇	C₂²	1	2	yes	—
22	C₂×#102×C₄₇	C₂²	1	2	yes	—
23	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
25	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
27	C₄₇×#390	C₂²	1	2	yes	—
28	C₄₇×#389	C₂²	1	2	yes	—
29	C₄₇×#388	—	2	2	no	—
30	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
31	C₄×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
32	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
33	C₄×C₂²⋊C₄×C₄₇	—	2	2	no	—
34	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
35	C₄×C₂²⋊C₄×C₄₇	—	2	1	no	—
36	C₄³×C₄₇	C₂²	1	1	yes	characteristic
37	C₄₇×#340	C₂²	1	2	yes	—
38	C₄₇×#340	C₂²	1	2	yes	—
39	C₄₇×#340	C₂²	1	2	yes	—
40	C₄₇×#336	C₂²	1	2	yes	—
41	C₄₇×#336	C₂²	1	2	yes	—
42	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
43	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
44	C₂³×C₄×C₄₇	—	2	2	no	—
45	C₂³×C₄×C₄₇	—	2	1	no	—
46	C₂³×C₄×C₄₇	—	2	1	no	—
47	C₂×D₈×C₄₇	—	2	4	no	—
48	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	—
49	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
50	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
51	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
52	C₄×D₄×C₄₇	—	2	4	no	—
53	C₄×D₄×C₄₇	—	2	4	no	—
54	C₄×D₄×C₄₇	—	2	2	no	—
55	C₄×D₄×C₄₇	—	2	2	no	—
56	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	—
57	C₄×D₄×C₄₇	C₂×C₄	1	4	yes	complemented
58	#117×C₄₇	—	4	4	no	—
59	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
64	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
65	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
66	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
67	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
68	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
69	C₂×C₄²×C₄₇	—	2	2	no	—
70	C₂×C₄²×C₄₇	—	2	1	no	—
71	C₂×C₄²×C₄₇	—	2	1	no	—
72	C₂×C₄²×C₄₇	—	4	4	no	—
73	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	D₄	1	2	yes	—
75	C₂×C₄²×C₄₇	D₄	1	1	yes	characteristic
76	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	#107×C₄₇	—	2	4	no	—
79	#107×C₄₇	C₂×C₄	1	4	yes	complemented
80	#102×C₄₇	—	2	4	no	—
81	#102×C₄₇	—	2	4	no	—
82	#102×C₄₇	C₂×C₄	1	4	yes	—
83	#102×C₄₇	C₂×C₄	1	4	yes	complemented
84	C₄×C₈×C₄₇	—	2	2	no	—
85	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
86	#95×C₄₇	—	2	2	no	—
87	#95×C₄₇	—	2	1	no	—
88	#95×C₄₇	—	2	2	no	—
89	#95×C₄₇	—	2	1	no	—
90	C₂⁴×C₄₇	—	2	1	no	—
91	C₂⁴×C₄₇	—	2	1	no	—
92	C₂×D₄×C₄₇	—	2	2	no	—
93	C₂×D₄×C₄₇	—	2	1	no	—
94	C₂×D₄×C₄₇	—	2	2	no	—
95	C₂×D₄×C₄₇	—	2	2	no	—
96	C₂×D₄×C₄₇	—	2	1	no	—
97	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
99	C₂×D₄×C₄₇	#41	1	4	yes	—
100	C₂²×C₄×C₄₇	—	2	8	no	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	—	2	2	no	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	4	no	—
105	C₂²×C₄×C₄₇	—	2	4	no	—
106	C₂²×C₄×C₄₇	—	2	2	no	—
107	C₂²×C₄×C₄₇	—	4	4	no	—
108	C₂²×C₄×C₄₇	—	4	4	no	—
109	C₂²×C₄×C₄₇	—	4	2	no	—
110	C₂²×C₄×C₄₇	—	4	2	no	—
111	C₂²×C₄×C₄₇	—	4	2	no	—
112	C₂²×C₄×C₄₇	—	4	2	no	—
113	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
114	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
116	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
118	D₈×C₄₇	—	2	8	no	—
119	C₂×C₈×C₄₇	—	2	2	no	—
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
126	C₄⋊C₄×C₄₇	—	2	1	no	—
127	C₄⋊C₄×C₄₇	—	2	1	no	—
128	C₄⋊C₄×C₄₇	—	2	2	no	—
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	—	2	2	no	—
131	C₄⋊C₄×C₄₇	—	4	4	no	—
132	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
133	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
134	C₄⋊C₄×C₄₇	#41	1	4	yes	—
135	C₂²⋊C₄×C₄₇	—	2	8	no	—
136	C₂²⋊C₄×C₄₇	—	2	4	no	—
137	C₂²⋊C₄×C₄₇	—	2	4	no	—
138	C₂²⋊C₄×C₄₇	—	4	4	no	—
139	C₂²⋊C₄×C₄₇	—	4	4	no	—
140	C₄²×C₄₇	—	2	2	no	—
141	C₄²×C₄₇	—	2	2	no	—
142	C₄²×C₄₇	—	2	2	no	—
143	C₄²×C₄₇	—	4	2	no	—
144	C₄²×C₄₇	—	4	4	no	—
145	C₄²×C₄₇	—	4	2	no	—
146	C₄²×C₄₇	—	4	2	no	—
147	C₄²×C₄₇	D₈	1	4	yes	complemented
148	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
149	C₄²×C₄₇	#41	1	2	yes	—
150	C₂³×C₄₇	—	2	2	no	—
151	C₂³×C₄₇	—	2	4	no	—
152	C₂³×C₄₇	—	2	2	no	—
153	C₂³×C₄₇	—	4	1	no	—
154	C₂³×C₄₇	—	4	1	no	—
155	C₂³×C₄₇	—	4	2	no	—
156	C₂³×C₄₇	—	4	2	no	—
157	C₂³×C₄₇	—	4	1	no	—
158	C₂³×C₄₇	—	4	1	no	—
159	C₂³×C₄₇	—	4	2	no	—
160	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
161	D₄×C₄₇	—	2	2	no	—
162	D₄×C₄₇	—	2	2	no	—
163	D₄×C₄₇	—	2	2	no	—
164	D₄×C₄₇	—	2	4	no	—
165	D₄×C₄₇	—	4	2	no	—
166	D₄×C₄₇	#117	1	4	yes	complemented
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	2	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	—	2	4	no	—
174	C₂×C₄×C₄₇	—	2	2	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	4	16	no	—
177	C₂×C₄×C₄₇	—	4	2	no	—
178	C₂×C₄×C₄₇	—	4	1	no	—
179	C₂×C₄×C₄₇	—	4	1	no	—
180	C₂×C₄×C₄₇	—	4	1	no	—
181	C₂×C₄×C₄₇	—	4	1	no	—
182	C₂×C₄×C₄₇	—	4	2	no	—
183	C₂×C₄×C₄₇	—	4	8	no	—
184	C₂×C₄×C₄₇	—	4	8	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	C₄×D₄	1	2	yes	—
189	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
190	C₂×C₄×C₄₇	C₂×D₈	1	4	yes	—
191	C₂×C₄×C₄₇	C₂×D₈	1	2	yes	—
192	C₂×C₄×C₄₇	#135	1	2	yes	—
193	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
194	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
195	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
196	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
197	C₈×C₄₇	—	2	2	no	—
198	C₈×C₄₇	—	2	2	no	—
199	C₈×C₄₇	—	4	2	no	—
200	#21113	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
201	C₂²×C₄₇	—	2	4	no	—
202	C₂²×C₄₇	—	4	4	no	—
203	C₂²×C₄₇	—	4	4	no	—
204	C₂²×C₄₇	—	4	2	no	—
205	C₂²×C₄₇	—	4	2	no	—
206	C₂²×C₄₇	—	4	2	no	—
207	C₂²×C₄₇	—	4	2	no	—
208	C₂²×C₄₇	—	4	2	no	—
209	C₂²×C₄₇	—	8	2	no	—
210	C₂²×C₄₇	—	8	2	no	—
211	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
212	C₂²×C₄₇	#525	1	2	yes	—
213	C₂²×C₄₇	C₂²×D₈	1	1	yes	characteristic
214	C₂²×C₄₇	C₂×#135	1	1	yes	characteristic
215	C₂²×C₄₇	#575	1	2	yes	—
216	C₄×C₄₇	—	2	4	no	—
217	C₄×C₄₇	—	2	2	no	—
218	C₄×C₄₇	—	4	4	no	—
219	C₄×C₄₇	—	4	2	no	—
220	C₄×C₄₇	—	4	2	no	—
221	C₄×C₄₇	—	4	2	no	—
222	C₄×C₄₇	—	8	2	no	—
223	C₄×C₄₇	C₄×D₈	1	4	yes	—
224	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
225	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
226	C₄×C₄₇	#529	1	2	yes	—
227	C₂×C₄×D₈	C₂×C₄₇	1	1	yes	characteristic
228	#2293	C₂×C₄₇	1	1	yes	characteristic, complemented
229	C₄²×D₄	C₂×C₄₇	1	1	yes	characteristic, complemented
230	#1925	C₂×C₄₇	1	2	yes	complemented
231	#1918	C₂×C₄₇	1	2	yes	complemented
232	#1879	C₂×C₄₇	1	2	yes	—
233	#1862	C₂×C₄₇	1	2	yes	complemented
234	C₄×#107	C₂×C₄₇	1	1	yes	characteristic, complemented
235	C₄×#102	C₂×C₄₇	1	1	yes	characteristic, complemented
236	C₄×#102	C₂×C₄₇	1	1	yes	characteristic, complemented
237	#1744	C₂×C₄₇	1	1	yes	characteristic, complemented
238	C₂×C₄₇	—	4	4	no	—
239	C₂×C₄₇	—	8	2	no	—
240	C₂×C₄₇	#2290	1	1	yes	characteristic
241	C₂×C₄₇	C₂×C₄×D₈	1	1	yes	characteristic
242	C₂×C₄₇	#2943	1	1	yes	characteristic
243	C₂×C₄₇	#3100	1	2	yes	—
244	C₂×C₄₇	#3102	1	2	yes	—
245	C₂²×D₈	C₂²×C₄₇	1	1	yes	characteristic
246	C₂×C₄×D₄	C₂²×C₄₇	1	2	yes	—
247	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
248	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
249	C₂×#117	—	2	1	no	—
250	C₂²×C₄²	—	2	1	no	—
251	C₄×D₈	C₄×C₄₇	1	8	yes	complemented
252	C₂×#107	C₂²×C₄₇	1	2	yes	—
253	C₂×#107	C₂²×C₄₇	1	1	yes	characteristic
254	C₂×#102	C₂²×C₄₇	1	2	yes	—
255	C₂×#102	C₂²×C₄₇	1	2	yes	—
256	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic
257	C₂×#102	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	#390	C₂²×C₄₇	1	2	yes	—
261	#389	C₂²×C₄₇	1	2	yes	—
262	#388	—	2	2	no	—
263	C₄×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
264	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
265	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
266	C₄×C₂²⋊C₄	—	2	1	no	—
267	C₄×C₂²⋊C₄	—	2	2	no	—
268	C₄×C₂²⋊C₄	—	2	1	no	—
269	C₄³	C₂²×C₄₇	1	1	yes	characteristic
270	#340	C₂²×C₄₇	1	2	yes	—
271	#340	C₂²×C₄₇	1	2	yes	—
272	#340	C₂²×C₄₇	1	2	yes	—
273	#336	C₂²×C₄₇	1	2	yes	—
274	#336	C₂²×C₄₇	1	2	yes	—
275	C₄₇	#21113	1	1	yes	characteristic, direct product factor, Sylow
276	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
277	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
278	C₂³×C₄	—	2	1	no	—
279	C₂³×C₄	—	2	2	no	—
280	C₂³×C₄	—	2	1	no	—
281	C₂×D₈	—	2	4	no	—
282	C₂×D₈	C₂×C₄×C₄₇	1	4	yes	—
283	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
284	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
285	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
286	C₄×D₄	—	2	4	no	—
287	C₄×D₄	—	2	4	no	—
288	C₄×D₄	—	2	2	no	—
289	C₄×D₄	—	2	2	no	—
290	C₄×D₄	C₂×C₄×C₄₇	1	4	yes	—
291	C₄×D₄	C₂×C₄×C₄₇	1	4	yes	complemented
292	#117	—	4	4	no	—
293	C₂×C₄⋊C₄	—	2	2	no	—
294	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
295	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
296	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
297	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
298	C₂×C₂²⋊C₄	—	2	2	no	—
299	C₂×C₂²⋊C₄	—	2	1	no	—
300	C₂×C₂²⋊C₄	—	2	1	no	—
301	C₂×C₂²⋊C₄	—	2	2	no	—
302	C₂×C₂²⋊C₄	—	2	2	no	—
303	C₂×C₄²	—	2	1	no	—
304	C₂×C₄²	—	2	2	no	—
305	C₂×C₄²	—	2	1	no	—
306	C₂×C₄²	—	4	4	no	—
307	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
308	C₂×C₄²	D₄×C₄₇	1	2	yes	—
309	C₂×C₄²	D₄×C₄₇	1	1	yes	characteristic
310	C₂×C₄²	C₂³×C₄₇	1	2	yes	—
311	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
312	#107	—	2	4	no	—
313	#107	C₂×C₄×C₄₇	1	4	yes	complemented
314	#102	—	2	4	no	—
315	#102	—	2	4	no	—
316	#102	C₂×C₄×C₄₇	1	4	yes	—
317	#102	C₂×C₄×C₄₇	1	4	yes	complemented
318	C₄×C₈	—	2	2	no	—
319	C₄×C₈	C₂×C₄×C₄₇	1	4	yes	complemented
320	#95	—	2	2	no	—
321	#95	—	2	1	no	—
322	#95	—	2	2	no	—
323	#95	—	2	1	no	—
324	C₂⁴	—	2	1	no	—
325	C₂⁴	—	2	1	no	—
326	C₂×D₄	—	2	2	no	—
327	C₂×D₄	—	2	1	no	—
328	C₂×D₄	—	2	2	no	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	1	no	—
331	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
332	C₂×D₄	C₂²×C₄×C₄₇	1	2	yes	—
333	C₂×D₄	#41×C₄₇	1	4	yes	—
334	C₂²×C₄	—	2	8	no	—
335	C₂²×C₄	—	2	1	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	—	2	4	no	—
339	C₂²×C₄	—	2	4	no	—
340	C₂²×C₄	—	2	2	no	—
341	C₂²×C₄	—	4	4	no	—
342	C₂²×C₄	—	4	4	no	—
343	C₂²×C₄	—	4	2	no	—
344	C₂²×C₄	—	4	2	no	—
345	C₂²×C₄	—	4	2	no	—
346	C₂²×C₄	—	4	2	no	—
347	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
348	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
349	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
350	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
351	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
352	D₈	—	2	8	no	—
353	C₂×C₈	—	2	2	no	—
354	C₂×C₈	—	2	2	no	—
355	C₂×C₈	—	2	2	no	—
356	C₂×C₈	—	2	2	no	—
357	C₂×C₈	—	2	2	no	—
358	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
359	C₂×C₈	C₂²×C₄×C₄₇	1	2	yes	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	2	2	no	—
364	C₄⋊C₄	—	2	2	no	—
365	C₄⋊C₄	—	4	4	no	—
366	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
367	C₄⋊C₄	C₂²×C₄×C₄₇	1	2	yes	—
368	C₄⋊C₄	#41×C₄₇	1	4	yes	—
369	C₂²⋊C₄	—	2	8	no	—
370	C₂²⋊C₄	—	2	4	no	—
371	C₂²⋊C₄	—	2	4	no	—
372	C₂²⋊C₄	—	4	4	no	—
373	C₂²⋊C₄	—	4	4	no	—
374	C₄²	—	2	2	no	—
375	C₄²	—	2	2	no	—
376	C₄²	—	2	2	no	—
377	C₄²	—	4	2	no	—
378	C₄²	—	4	4	no	—
379	C₄²	—	4	2	no	—
380	C₄²	—	4	2	no	—
381	C₄²	D₈×C₄₇	1	4	yes	complemented
382	C₄²	C₂²×C₄×C₄₇	1	2	yes	—
383	C₄²	#41×C₄₇	1	2	yes	—
384	C₂³	—	2	2	no	—
385	C₂³	—	2	4	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	4	1	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	4	2	no	—
390	C₂³	—	4	2	no	—
391	C₂³	—	4	1	no	—
392	C₂³	—	4	1	no	—
393	C₂³	—	4	2	no	—
394	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
395	D₄	—	2	2	no	—
396	D₄	—	2	2	no	—
397	D₄	—	2	2	no	—
398	D₄	—	2	4	no	—
399	D₄	—	4	2	no	—
400	D₄	#117×C₄₇	1	4	yes	complemented
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	2	no	—
409	C₂×C₄	—	2	2	no	—
410	C₂×C₄	—	4	16	no	—
411	C₂×C₄	—	4	2	no	—
412	C₂×C₄	—	4	1	no	—
413	C₂×C₄	—	4	1	no	—
414	C₂×C₄	—	4	1	no	—
415	C₂×C₄	—	4	1	no	—
416	C₂×C₄	—	4	2	no	—
417	C₂×C₄	—	4	8	no	—
418	C₂×C₄	—	4	8	no	—
419	C₂×C₄	—	4	2	no	—
420	C₂×C₄	—	4	2	no	—
421	C₂×C₄	—	4	2	no	—
422	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
423	C₂×C₄	C₄×D₄×C₄₇	1	2	yes	—
424	C₂×C₄	C₂×D₈×C₄₇	1	4	yes	—
425	C₂×C₄	C₂×D₈×C₄₇	1	2	yes	—
426	C₂×C₄	#135×C₄₇	1	2	yes	—
427	C₂×C₄	C₂³×C₄×C₄₇	1	1	yes	characteristic
428	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
429	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
430	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	2	2	no	—
433	C₈	—	4	2	no	—
434	C₂²	—	2	4	no	—
435	C₂²	—	4	4	no	—
436	C₂²	—	4	4	no	—
437	C₂²	—	4	2	no	—
438	C₂²	—	4	2	no	—
439	C₂²	—	4	2	no	—
440	C₂²	—	4	2	no	—
441	C₂²	—	4	2	no	—
442	C₂²	—	8	2	no	—
443	C₂²	—	8	2	no	—
444	C₂²	C₂×C₄×D₄×C₄₇	1	1	yes	characteristic
445	C₂²	C₄₇×#525	1	2	yes	—
446	C₂²	C₂²×D₈×C₄₇	1	1	yes	characteristic
447	C₂²	C₂×#135×C₄₇	1	1	yes	characteristic
448	C₂²	C₄₇×#575	1	2	yes	—
449	C₄	—	2	4	no	—
450	C₄	—	2	2	no	—
451	C₄	—	4	4	no	—
452	C₄	—	4	2	no	—
453	C₄	—	4	2	no	—
454	C₄	—	4	2	no	—
455	C₄	—	8	2	no	—
456	C₄	C₄×D₈×C₄₇	1	4	yes	—
457	C₄	C₂×#117×C₄₇	1	1	yes	characteristic
458	C₄	C₄×#41×C₄₇	1	1	yes	characteristic
459	C₄	C₄₇×#529	1	2	yes	—
460	C₂	—	4	4	no	—
461	C₂	—	8	2	no	—
462	C₂	C₄₇×#2290	1	1	yes	characteristic
463	C₂	C₂×C₄×D₈×C₄₇	1	1	yes	characteristic
464	C₂	C₄₇×#2943	1	1	yes	characteristic
465	C₂	C₄₇×#3100	1	2	yes	—
466	C₂	C₄₇×#3102	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₄₇	C₂×D₄
commutator	C₂×C₄	C₂³×C₄×C₄₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₈×C₄₇	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₄₇ ◁ C₄³×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₄₇×#2293	C₂	semidirect
3. C₄²×D₄×C₄₇	C₂	semidirect
4. C₄₇×#1925	C₂	semidirect
5. C₄₇×#1918	C₂	semidirect
7. C₄₇×#1862	C₂	semidirect
8. C₄×#107×C₄₇	C₂	semidirect
9. C₄×#102×C₄₇	C₂	semidirect
10. C₄×#102×C₄₇	C₂	semidirect
11. C₄₇×#1744	C₂	semidirect
18. C₄×D₈×C₄₇	C₄	semidirect
57. C₄×D₄×C₄₇	C₂×C₄	semidirect
79. #107×C₄₇	C₂×C₄	semidirect
83. #102×C₄₇	C₂×C₄	semidirect
85. C₄×C₈×C₄₇	C₂×C₄	semidirect
147. C₄²×C₄₇	D₈	semidirect
166. D₄×C₄₇	#117	semidirect
200. #21113	C₄₇	direct (N × H)
228. #2293	C₂×C₄₇	semidirect
229. C₄²×D₄	C₂×C₄₇	semidirect
230. #1925	C₂×C₄₇	semidirect
231. #1918	C₂×C₄₇	semidirect
233. #1862	C₂×C₄₇	semidirect
234. C₄×#107	C₂×C₄₇	semidirect
235. C₄×#102	C₂×C₄₇	semidirect
236. C₄×#102	C₂×C₄₇	semidirect
237. #1744	C₂×C₄₇	semidirect
251. C₄×D₈	C₄×C₄₇	semidirect
275. C₄₇	#21113	direct (N × H)
291. C₄×D₄	C₂×C₄×C₄₇	semidirect
313. #107	C₂×C₄×C₄₇	semidirect
317. #102	C₂×C₄×C₄₇	semidirect
319. C₄×C₈	C₂×C₄×C₄₇	semidirect
381. C₄²	D₈×C₄₇	semidirect
400. D₄	#117×C₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×D₈×C₄₇	2
C₄₇×#2293	2
C₄²×D₄×C₄₇	2
C₄₇×#1925	2
C₄₇×#1918	2
C₄₇×#1879	2
C₄₇×#1862	2
C₄×#107×C₄₇	2
C₄×#102×C₄₇	2
C₄₇×#1744	2
#21113	47

Subgroups — C47×#21113 #26060811

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#21113 #26060811