Subgroups — C₄₇×#24967 #26064665

Order 12032.

926 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄₇×#2537	C₂	1	1	yes	maximal, characteristic
2	D₄×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄₇×#2077	C₂	1	2	yes	maximal, complemented
4	C₄₇×#2034	C₂	1	2	yes	maximal, complemented
5	C₄₇×#1954	C₂	1	1	yes	maximal, characteristic, complemented
6	C₄₇×#1948	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1874	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1834	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1824	C₂	1	2	yes	maximal, complemented
10	C₄₇×#1802	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄×#102×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#121×C₄₇	—	2	1	no	—
13	C₂×#121×C₄₇	C₂²	1	2	yes	—
14	C₂×C₄×D₄×C₄₇	—	2	1	no	—
15	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
17	C₂²×C₄⋊C₄×C₄₇	C₂²	1	2	yes	—
18	C₂×#106×C₄₇	C₂²	1	2	yes	—
19	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
21	C₂×#102×C₄₇	C₂²	1	1	yes	characteristic
22	C₂×#102×C₄₇	C₂²	1	2	yes	—
23	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
24	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
25	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
26	C₄₇×#394	—	2	2	no	—
27	C₄₇×#389	—	2	1	no	—
28	C₄₇×#385	—	2	2	no	—
29	C₄₇×#384	C₂²	1	1	yes	characteristic
30	C₄₇×#384	C₂²	1	1	yes	characteristic
31	C₄₇×#380	—	2	1	no	—
32	C₄₇×#380	C₂²	1	2	yes	—
33	C₄₇×#380	C₂²	1	2	yes	—
34	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
35	C₄₇×#340	C₂²	1	1	yes	characteristic
36	C₄₇×#340	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×#340	C₂²	1	2	yes	—
41	C₂²×D₄×C₄₇	—	2	2	no	—
42	C₂²×D₄×C₄₇	D₄	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	C₂³	1	2	yes	—
47	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
48	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
49	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
50	#121×C₄₇	—	2	4	no	—
51	#121×C₄₇	—	4	2	no	—
52	#121×C₄₇	—	4	4	no	—
53	C₄×D₄×C₄₇	—	2	2	no	—
54	C₄×D₄×C₄₇	—	2	2	no	—
55	C₄×D₄×C₄₇	—	2	2	no	—
56	C₄×D₄×C₄₇	—	2	2	no	—
57	C₄×D₄×C₄₇	—	4	4	no	—
58	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
59	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
60	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
61	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
62	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₇	—	4	2	no	—
65	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
66	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
67	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
69	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
72	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
73	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
74	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
75	C₂×C₂²⋊C₄×C₄₇	D₄	1	2	yes	—
76	C₂×C₄²×C₄₇	—	2	1	no	—
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	#106×C₄₇	—	4	2	no	—
79	C₄⋊C₈×C₄₇	—	2	2	no	—
80	#102×C₄₇	—	2	2	no	—
81	#102×C₄₇	—	2	2	no	—
82	#102×C₄₇	—	4	2	no	—
83	C₂²⋊C₈×C₄₇	—	4	2	no	—
84	C₂²⋊C₈×C₄₇	—	4	2	no	—
85	C₄×C₈×C₄₇	—	2	2	no	—
86	#95×C₄₇	—	2	1	no	—
87	#95×C₄₇	—	2	2	no	—
88	#95×C₄₇	—	2	2	no	—
89	C₂⁴×C₄₇	—	2	1	no	—
90	C₂⁴×C₄₇	C₂×D₄	1	2	yes	—
91	C₂×D₄×C₄₇	—	2	2	no	—
92	C₂×D₄×C₄₇	—	2	2	no	—
93	C₂×D₄×C₄₇	—	2	1	no	—
94	C₂×D₄×C₄₇	—	2	1	no	—
95	C₂×D₄×C₄₇	—	2	1	no	—
96	C₂×D₄×C₄₇	—	2	1	no	—
97	C₂×D₄×C₄₇	—	2	1	no	—
98	C₂×D₄×C₄₇	—	4	4	no	—
99	C₂×D₄×C₄₇	—	4	4	no	—
100	C₂×D₄×C₄₇	—	8	2	no	—
101	C₂×D₄×C₄₇	SD₁₆	1	4	yes	—
102	C₂×D₄×C₄₇	#41	1	2	yes	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	—	2	2	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	—	2	2	no	—
110	C₂²×C₄×C₄₇	—	2	1	no	—
111	C₂²×C₄×C₄₇	—	2	1	no	—
112	C₂²×C₄×C₄₇	—	2	2	no	—
113	C₂²×C₄×C₄₇	—	2	2	no	—
114	C₂²×C₄×C₄₇	—	4	4	no	—
115	C₂²×C₄×C₄₇	—	4	4	no	—
116	C₂²×C₄×C₄₇	—	4	2	no	—
117	C₂²×C₄×C₄₇	—	4	2	no	—
118	C₂²×C₄×C₄₇	—	4	2	no	—
119	C₂²×C₄×C₄₇	—	8	2	no	—
120	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
121	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
122	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
123	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
124	C₂×C₈×C₄₇	—	2	2	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	—	2	1	no	—
129	C₂×C₈×C₄₇	—	2	2	no	—
130	C₂×C₈×C₄₇	—	2	1	no	—
131	C₂×C₈×C₄₇	—	2	1	no	—
132	C₂×C₈×C₄₇	—	2	2	no	—
133	C₄⋊C₄×C₄₇	—	2	2	no	—
134	C₄⋊C₄×C₄₇	—	2	1	no	—
135	C₄⋊C₄×C₄₇	—	2	2	no	—
136	C₄⋊C₄×C₄₇	—	2	1	no	—
137	C₄⋊C₄×C₄₇	—	2	1	no	—
138	C₄⋊C₄×C₄₇	—	2	2	no	—
139	C₄⋊C₄×C₄₇	—	2	1	no	—
140	C₄⋊C₄×C₄₇	—	2	1	no	—
141	C₄⋊C₄×C₄₇	—	2	2	no	—
142	C₄⋊C₄×C₄₇	—	2	2	no	—
143	C₄⋊C₄×C₄₇	—	4	4	no	—
144	C₄⋊C₄×C₄₇	—	4	2	no	—
145	C₄⋊C₄×C₄₇	—	4	2	no	—
146	C₄⋊C₄×C₄₇	—	8	1	no	—
147	C₄⋊C₄×C₄₇	—	8	1	no	—
148	C₄⋊C₄×C₄₇	#41	1	2	yes	—
149	C₂²⋊C₄×C₄₇	—	2	4	no	—
150	C₂²⋊C₄×C₄₇	—	4	4	no	—
151	C₂²⋊C₄×C₄₇	—	4	4	no	—
152	C₂²⋊C₄×C₄₇	—	4	4	no	—
153	C₂²⋊C₄×C₄₇	—	4	2	no	—
154	C₄²×C₄₇	—	4	2	no	—
155	C₄²×C₄₇	#41	1	2	yes	—
156	C₄²×C₄₇	#41	1	2	yes	—
157	C₂³×C₄₇	—	2	2	no	—
158	C₂³×C₄₇	—	2	2	no	—
159	C₂³×C₄₇	—	2	2	no	—
160	C₂³×C₄₇	—	2	2	no	—
161	C₂³×C₄₇	—	2	2	no	—
162	C₂³×C₄₇	—	2	2	no	—
163	C₂³×C₄₇	—	2	2	no	—
164	C₂³×C₄₇	—	4	1	no	—
165	C₂³×C₄₇	—	4	1	no	—
166	C₂³×C₄₇	—	4	1	no	—
167	C₂³×C₄₇	—	4	1	no	—
168	C₂³×C₄₇	—	4	1	no	—
169	C₂³×C₄₇	—	4	1	no	—
170	C₂³×C₄₇	C₂×SD₁₆	1	4	yes	—
171	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
172	D₄×C₄₇	—	2	2	no	—
173	D₄×C₄₇	—	2	2	no	—
174	D₄×C₄₇	—	2	8	no	—
175	D₄×C₄₇	—	4	1	no	—
176	D₄×C₄₇	—	4	1	no	—
177	D₄×C₄₇	—	8	8	no	—
178	C₂×C₄×C₄₇	—	2	1	no	—
179	C₂×C₄×C₄₇	—	2	1	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	—	2	2	no	—
184	C₂×C₄×C₄₇	—	4	1	no	—
185	C₂×C₄×C₄₇	—	4	1	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	1	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	2	no	—
196	C₂×C₄×C₄₇	—	4	1	no	—
197	C₂×C₄×C₄₇	—	4	2	no	—
198	C₂×C₄×C₄₇	—	4	1	no	—
199	C₂×C₄×C₄₇	—	4	2	no	—
200	C₂×C₄×C₄₇	—	4	2	no	—
201	C₂×C₄×C₄₇	—	4	1	no	—
202	C₂×C₄×C₄₇	—	8	8	no	—
203	C₂×C₄×C₄₇	—	8	4	no	—
204	C₂×C₄×C₄₇	#123	1	2	yes	—
205	C₂×C₄×C₄₇	#123	1	2	yes	—
206	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
207	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
208	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
209	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
210	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
211	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
212	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
213	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
214	C₈×C₄₇	—	4	2	no	—
215	C₈×C₄₇	—	4	1	no	—
216	C₈×C₄₇	—	4	1	no	—
217	#24967	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
218	C₂²×C₄₇	—	2	4	no	—
219	C₂²×C₄₇	—	2	4	no	—
220	C₂²×C₄₇	—	2	4	no	—
221	C₂²×C₄₇	—	4	2	no	—
222	C₂²×C₄₇	—	4	2	no	—
223	C₂²×C₄₇	—	4	2	no	—
224	C₂²×C₄₇	—	4	2	no	—
225	C₂²×C₄₇	—	4	2	no	—
226	C₂²×C₄₇	—	4	2	no	—
227	C₂²×C₄₇	—	4	2	no	—
228	C₂²×C₄₇	—	8	1	no	—
229	C₂²×C₄₇	—	8	1	no	—
230	C₂²×C₄₇	—	8	1	no	—
231	C₂²×C₄₇	—	8	1	no	—
232	C₂²×C₄₇	C₂×#123	1	1	yes	characteristic
233	C₂²×C₄₇	#546	1	1	yes	characteristic
234	C₂²×C₄₇	#546	1	1	yes	characteristic
235	C₂²×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
236	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
237	C₂²×C₄₇	#576	1	1	yes	characteristic
238	C₂²×C₄₇	#578	1	1	yes	characteristic
239	C₄×C₄₇	—	2	2	no	—
240	C₄×C₄₇	—	4	2	no	—
241	C₄×C₄₇	—	4	2	no	—
242	C₄×C₄₇	—	8	1	no	—
243	C₄×C₄₇	—	8	1	no	—
244	C₄×C₄₇	—	8	2	no	—
245	C₄×C₄₇	—	8	2	no	—
246	C₄×C₄₇	#481	1	4	yes	—
247	C₄×C₄₇	#529	1	1	yes	characteristic
248	C₄×C₄₇	#540	1	1	yes	characteristic
249	C₄×C₄₇	#553	1	1	yes	characteristic
250	C₄×C₄₇	#555	1	1	yes	characteristic
251	#2537	C₂×C₄₇	1	1	yes	characteristic
252	D₄×C₄⋊C₄	C₂×C₄₇	1	1	yes	characteristic, complemented
253	#2077	C₂×C₄₇	1	2	yes	complemented
254	#2034	C₂×C₄₇	1	2	yes	complemented
255	#1954	C₂×C₄₇	1	1	yes	characteristic, complemented
256	#1948	C₂×C₄₇	1	1	yes	characteristic, complemented
257	#1874	C₂×C₄₇	1	2	yes	complemented
258	#1834	C₂×C₄₇	1	1	yes	characteristic, complemented
259	#1824	C₂×C₄₇	1	2	yes	complemented
260	#1802	C₂×C₄₇	1	1	yes	characteristic, complemented
261	C₄×#102	C₂×C₄₇	1	1	yes	characteristic, complemented
262	C₂×C₄₇	—	4	4	no	—
263	C₂×C₄₇	—	8	2	no	—
264	C₂×C₄₇	#2420	1	1	yes	characteristic
265	C₂×C₄₇	C₂×#481	1	1	yes	characteristic
266	C₂×C₄₇	#3098	1	1	yes	characteristic
267	C₂×C₄₇	#3295	1	1	yes	characteristic
268	C₂×C₄₇	#3298	1	1	yes	characteristic
269	C₂×C₄₇	#3325	1	1	yes	characteristic
270	C₂×C₄₇	#3330	1	1	yes	characteristic
271	C₂×#121	—	2	1	no	—
272	C₂×#121	C₂²×C₄₇	1	2	yes	—
273	C₂×C₄×D₄	—	2	1	no	—
274	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
275	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
276	C₂²×C₄⋊C₄	C₂²×C₄₇	1	2	yes	—
277	C₂×#106	C₂²×C₄₇	1	2	yes	—
278	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
279	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic
280	C₂×#102	C₂²×C₄₇	1	1	yes	characteristic
281	C₂×#102	C₂²×C₄₇	1	2	yes	—
282	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
283	C₂×C₂²⋊C₈	C₂²×C₄₇	1	2	yes	—
284	C₂×C₄×C₈	C₂²×C₄₇	1	1	yes	characteristic
285	#394	—	2	2	no	—
286	#389	—	2	1	no	—
287	#385	—	2	2	no	—
288	#384	C₂²×C₄₇	1	1	yes	characteristic
289	#384	C₂²×C₄₇	1	1	yes	characteristic
290	#380	—	2	1	no	—
291	#380	C₂²×C₄₇	1	2	yes	—
292	#380	C₂²×C₄₇	1	2	yes	—
293	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
294	#340	C₂²×C₄₇	1	2	yes	—
295	#340	C₂²×C₄₇	1	1	yes	characteristic
296	#340	C₂²×C₄₇	1	2	yes	—
297	#340	C₂²×C₄₇	1	1	yes	characteristic
298	#340	C₂²×C₄₇	1	2	yes	—
299	#340	C₂²×C₄₇	1	2	yes	—
300	C₄₇	#24967	1	1	yes	characteristic, direct product factor, Sylow
301	C₂²×D₄	—	2	2	no	—
302	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
303	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
304	C₂³×C₄	—	2	2	no	—
305	C₂³×C₄	—	2	1	no	—
306	C₂³×C₄	C₂³×C₄₇	1	2	yes	—
307	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
308	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
309	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
310	#121	—	2	4	no	—
311	#121	—	4	2	no	—
312	#121	—	4	4	no	—
313	C₄×D₄	—	2	2	no	—
314	C₄×D₄	—	2	2	no	—
315	C₄×D₄	—	2	2	no	—
316	C₄×D₄	—	2	2	no	—
317	C₄×D₄	—	4	4	no	—
318	C₂×C₄⋊C₄	—	2	4	no	—
319	C₂×C₄⋊C₄	—	2	2	no	—
320	C₂×C₄⋊C₄	—	2	1	no	—
321	C₂×C₄⋊C₄	—	2	1	no	—
322	C₂×C₄⋊C₄	—	2	1	no	—
323	C₂×C₄⋊C₄	—	2	1	no	—
324	C₂×C₄⋊C₄	—	4	2	no	—
325	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
327	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
328	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
329	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
330	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	—	2	2	no	—
332	C₂×C₂²⋊C₄	—	2	2	no	—
333	C₂×C₂²⋊C₄	—	2	1	no	—
334	C₂×C₂²⋊C₄	—	2	2	no	—
335	C₂×C₂²⋊C₄	D₄×C₄₇	1	2	yes	—
336	C₂×C₄²	—	2	1	no	—
337	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
338	#106	—	4	2	no	—
339	C₄⋊C₈	—	2	2	no	—
340	#102	—	2	2	no	—
341	#102	—	2	2	no	—
342	#102	—	4	2	no	—
343	C₂²⋊C₈	—	4	2	no	—
344	C₂²⋊C₈	—	4	2	no	—
345	C₄×C₈	—	2	2	no	—
346	#95	—	2	1	no	—
347	#95	—	2	2	no	—
348	#95	—	2	2	no	—
349	C₂⁴	—	2	1	no	—
350	C₂⁴	C₂×D₄×C₄₇	1	2	yes	—
351	C₂×D₄	—	2	2	no	—
352	C₂×D₄	—	2	2	no	—
353	C₂×D₄	—	2	1	no	—
354	C₂×D₄	—	2	1	no	—
355	C₂×D₄	—	2	1	no	—
356	C₂×D₄	—	2	1	no	—
357	C₂×D₄	—	2	1	no	—
358	C₂×D₄	—	4	4	no	—
359	C₂×D₄	—	4	4	no	—
360	C₂×D₄	—	8	2	no	—
361	C₂×D₄	SD₁₆×C₄₇	1	4	yes	—
362	C₂×D₄	#41×C₄₇	1	2	yes	—
363	C₂²×C₄	—	2	1	no	—
364	C₂²×C₄	—	2	2	no	—
365	C₂²×C₄	—	2	2	no	—
366	C₂²×C₄	—	2	2	no	—
367	C₂²×C₄	—	2	2	no	—
368	C₂²×C₄	—	2	2	no	—
369	C₂²×C₄	—	2	2	no	—
370	C₂²×C₄	—	2	1	no	—
371	C₂²×C₄	—	2	1	no	—
372	C₂²×C₄	—	2	2	no	—
373	C₂²×C₄	—	2	2	no	—
374	C₂²×C₄	—	4	4	no	—
375	C₂²×C₄	—	4	4	no	—
376	C₂²×C₄	—	4	2	no	—
377	C₂²×C₄	—	4	2	no	—
378	C₂²×C₄	—	4	2	no	—
379	C₂²×C₄	—	8	2	no	—
380	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
381	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
382	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
383	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
384	C₂×C₈	—	2	1	no	—
385	C₂×C₈	—	2	1	no	—
386	C₂×C₈	—	2	1	no	—
387	C₂×C₈	—	2	1	no	—
388	C₂×C₈	—	2	2	no	—
389	C₂×C₈	—	2	1	no	—
390	C₂×C₈	—	2	1	no	—
391	C₂×C₈	—	2	2	no	—
392	C₂×C₈	—	2	2	no	—
393	C₄⋊C₄	—	2	2	no	—
394	C₄⋊C₄	—	2	1	no	—
395	C₄⋊C₄	—	2	1	no	—
396	C₄⋊C₄	—	2	2	no	—
397	C₄⋊C₄	—	2	1	no	—
398	C₄⋊C₄	—	2	1	no	—
399	C₄⋊C₄	—	2	2	no	—
400	C₄⋊C₄	—	2	2	no	—
401	C₄⋊C₄	—	2	1	no	—
402	C₄⋊C₄	—	2	2	no	—
403	C₄⋊C₄	—	4	4	no	—
404	C₄⋊C₄	—	4	2	no	—
405	C₄⋊C₄	—	4	2	no	—
406	C₄⋊C₄	—	8	1	no	—
407	C₄⋊C₄	—	8	1	no	—
408	C₄⋊C₄	#41×C₄₇	1	2	yes	—
409	C₂²⋊C₄	—	2	4	no	—
410	C₂²⋊C₄	—	4	4	no	—
411	C₂²⋊C₄	—	4	4	no	—
412	C₂²⋊C₄	—	4	4	no	—
413	C₂²⋊C₄	—	4	2	no	—
414	C₄²	—	4	2	no	—
415	C₄²	#41×C₄₇	1	2	yes	—
416	C₄²	#41×C₄₇	1	2	yes	—
417	C₂³	—	2	2	no	—
418	C₂³	—	2	2	no	—
419	C₂³	—	2	2	no	—
420	C₂³	—	2	2	no	—
421	C₂³	—	2	2	no	—
422	C₂³	—	2	2	no	—
423	C₂³	—	2	2	no	—
424	C₂³	—	4	1	no	—
425	C₂³	—	4	1	no	—
426	C₂³	—	4	1	no	—
427	C₂³	—	4	1	no	—
428	C₂³	—	4	1	no	—
429	C₂³	—	4	1	no	—
430	C₂³	C₂×SD₁₆×C₄₇	1	4	yes	—
431	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
432	D₄	—	2	8	no	—
433	D₄	—	2	2	no	—
434	D₄	—	2	2	no	—
435	D₄	—	4	1	no	—
436	D₄	—	4	1	no	—
437	D₄	—	8	8	no	—
438	C₂×C₄	—	2	1	no	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	4	1	no	—
445	C₂×C₄	—	4	1	no	—
446	C₂×C₄	—	4	2	no	—
447	C₂×C₄	—	4	2	no	—
448	C₂×C₄	—	4	2	no	—
449	C₂×C₄	—	4	2	no	—
450	C₂×C₄	—	4	1	no	—
451	C₂×C₄	—	4	2	no	—
452	C₂×C₄	—	4	2	no	—
453	C₂×C₄	—	4	1	no	—
454	C₂×C₄	—	4	1	no	—
455	C₂×C₄	—	4	2	no	—
456	C₂×C₄	—	4	1	no	—
457	C₂×C₄	—	4	2	no	—
458	C₂×C₄	—	4	1	no	—
459	C₂×C₄	—	4	2	no	—
460	C₂×C₄	—	4	2	no	—
461	C₂×C₄	—	4	1	no	—
462	C₂×C₄	—	8	8	no	—
463	C₂×C₄	—	8	4	no	—
464	C₂×C₄	#123×C₄₇	1	2	yes	—
465	C₂×C₄	#123×C₄₇	1	2	yes	—
466	C₂×C₄	C₂×SD₁₆×C₄₇	1	2	yes	—
467	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
468	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
469	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
470	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
471	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
472	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
473	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
474	C₈	—	4	2	no	—
475	C₈	—	4	1	no	—
476	C₈	—	4	1	no	—
477	C₂²	—	2	4	no	—
478	C₂²	—	2	4	no	—
479	C₂²	—	2	4	no	—
480	C₂²	—	4	2	no	—
481	C₂²	—	4	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	2	no	—
484	C₂²	—	4	2	no	—
485	C₂²	—	4	2	no	—
486	C₂²	—	4	2	no	—
487	C₂²	—	8	1	no	—
488	C₂²	—	8	1	no	—
489	C₂²	—	8	1	no	—
490	C₂²	—	8	1	no	—
491	C₂²	C₂×#123×C₄₇	1	1	yes	characteristic
492	C₂²	C₄₇×#546	1	1	yes	characteristic
493	C₂²	C₄₇×#546	1	1	yes	characteristic
494	C₂²	C₂²×SD₁₆×C₄₇	1	1	yes	characteristic
495	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
496	C₂²	C₄₇×#576	1	1	yes	characteristic
497	C₂²	C₄₇×#578	1	1	yes	characteristic
498	C₄	—	2	2	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	2	no	—
501	C₄	—	8	2	no	—
502	C₄	—	8	2	no	—
503	C₄	—	8	1	no	—
504	C₄	—	8	1	no	—
505	C₄	C₄₇×#481	1	4	yes	—
506	C₄	C₄₇×#529	1	1	yes	characteristic
507	C₄	C₄₇×#540	1	1	yes	characteristic
508	C₄	C₄₇×#553	1	1	yes	characteristic
509	C₄	C₄₇×#555	1	1	yes	characteristic
510	C₂	—	4	4	no	—
511	C₂	—	8	2	no	—
512	C₂	C₄₇×#2420	1	1	yes	characteristic
513	C₂	C₂×C₄₇×#481	1	1	yes	characteristic
514	C₂	C₄₇×#3098	1	1	yes	characteristic
515	C₂	C₄₇×#3295	1	1	yes	characteristic
516	C₂	C₄₇×#3298	1	1	yes	characteristic
517	C₂	C₄₇×#3325	1	1	yes	characteristic
518	C₂	C₄₇×#3330	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₄₇×#2537	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂×C₄×D₄×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. D₄×C₄⋊C₄×C₄₇	C₂	semidirect
3. C₄₇×#2077	C₂	semidirect
4. C₄₇×#2034	C₂	semidirect
5. C₄₇×#1954	C₂	semidirect
6. C₄₇×#1948	C₂	semidirect
7. C₄₇×#1874	C₂	semidirect
8. C₄₇×#1834	C₂	semidirect
9. C₄₇×#1824	C₂	semidirect
10. C₄₇×#1802	C₂	semidirect
11. C₄×#102×C₄₇	C₂	semidirect
217. #24967	C₄₇	direct (N × H)
252. D₄×C₄⋊C₄	C₂×C₄₇	semidirect
253. #2077	C₂×C₄₇	semidirect
254. #2034	C₂×C₄₇	semidirect
255. #1954	C₂×C₄₇	semidirect
256. #1948	C₂×C₄₇	semidirect
257. #1874	C₂×C₄₇	semidirect
258. #1834	C₂×C₄₇	semidirect
259. #1824	C₂×C₄₇	semidirect
260. #1802	C₂×C₄₇	semidirect
261. C₄×#102	C₂×C₄₇	semidirect
300. C₄₇	#24967	direct (N × H)

Maximal subgroups

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

subgroup	index
C₄₇×#2537	2
D₄×C₄⋊C₄×C₄₇	2
C₄₇×#2077	2
C₄₇×#2034	2
C₄₇×#1954	2
C₄₇×#1948	2
C₄₇×#1874	2
C₄₇×#1834	2
C₄₇×#1824	2
C₄₇×#1802	2
C₄×#102×C₄₇	2
#24967	47

Subgroups — C47×#24967 #26064665

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#24967 #26064665