Subgroups — C₄₇×#24784 #26064482

Order 12032.

1040 conjugacy classes of subgroups.

The subgroup lattice has 546 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, complemented
2	C₂×C₄₇×#466	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#435	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄₇×#427	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2414	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2067	C₂	1	2	yes	maximal, complemented
7	C₄₇×#2033	C₂	1	2	yes	maximal, complemented
8	C₄₇×#1972	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1944	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄₇×#1875	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1809	C₂	1	1	yes	maximal, characteristic, 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×#121×C₄₇	C₂²	1	2	yes	—
17	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
18	C₂×#117×C₄₇	C₂²	1	2	yes	—
19	C₄₇×#469	—	2	4	no	—
20	C₄₇×#466	—	2	4	no	—
21	C₄₇×#435	—	2	4	no	—
22	C₄₇×#427	—	2	4	no	—
23	C₂×#107×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×#107×C₄₇	C₂²	1	2	yes	—
25	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
28	C₂×#102×C₄₇	C₂²	1	2	yes	—
29	C₂×#102×C₄₇	C₂²	1	2	yes	—
30	C₂×#102×C₄₇	C₂²	1	2	yes	—
31	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
34	C₄₇×#394	—	2	2	no	—
35	C₄₇×#392	—	2	2	no	—
36	C₄₇×#390	—	2	2	no	—
37	C₄₇×#390	C₂²	1	2	yes	—
38	C₄₇×#389	C₂²	1	2	yes	—
39	C₄₇×#388	—	2	2	no	—
40	C₄₇×#380	C₂²	1	2	yes	—
41	C₄₇×#340	C₂²	1	2	yes	—
42	C₄₇×#340	C₂²	1	2	yes	—
43	C₂²×D₄×C₄₇	—	2	2	no	—
44	C₂²×D₄×C₄₇	—	2	2	no	—
45	C₂²×D₄×C₄₇	D₄	1	1	yes	characteristic
46	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
47	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
48	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
49	C₂×D₈×C₄₇	—	2	2	no	—
50	C₂×D₈×C₄₇	—	2	2	no	—
51	C₂×D₈×C₄₇	—	2	2	no	—
52	C₂×M₁₆×C₄₇	—	2	2	no	—
53	C₂×M₁₆×C₄₇	—	2	2	no	—
54	C₂×M₁₆×C₄₇	—	2	2	no	—
55	C₂²×C₈×C₄₇	—	2	2	no	—
56	C₂²×C₈×C₄₇	—	2	2	no	—
57	C₂²×C₈×C₄₇	D₄	1	4	yes	complemented
58	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
59	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
60	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
61	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
62	#121×C₄₇	—	2	4	no	—
63	#121×C₄₇	—	2	4	no	—
64	#121×C₄₇	—	2	4	no	—
65	#121×C₄₇	—	4	2	no	—
66	C₄×D₄×C₄₇	—	2	2	no	—
67	C₄×D₄×C₄₇	—	2	2	no	—
68	#117×C₄₇	—	2	4	no	—
69	#117×C₄₇	—	4	2	no	—
70	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
71	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
74	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
75	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
76	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
77	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
78	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
79	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
80	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
81	C₂×C₂²⋊C₄×C₄₇	D₄	1	1	yes	characteristic
82	C₂×C₂²⋊C₄×C₄₇	D₄	1	1	yes	characteristic
83	C₂×C₄²×C₄₇	—	2	2	no	—
84	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
85	#107×C₄₇	—	2	2	no	—
86	#107×C₄₇	—	2	4	no	—
87	#106×C₄₇	—	2	2	no	—
88	#106×C₄₇	D₄	1	4	yes	complemented
89	C₄⋊C₈×C₄₇	—	2	2	no	—
90	#102×C₄₇	—	2	4	no	—
91	#102×C₄₇	—	2	4	no	—
92	#102×C₄₇	—	4	2	no	—
93	C₂²⋊C₈×C₄₇	—	2	2	no	—
94	C₂²⋊C₈×C₄₇	—	2	2	no	—
95	#97×C₄₇	—	2	2	no	—
96	#95×C₄₇	—	2	2	no	—
97	#95×C₄₇	—	2	2	no	—
98	C₂⁴×C₄₇	—	2	2	no	—
99	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
101	C₂×D₄×C₄₇	—	2	2	no	—
102	C₂×D₄×C₄₇	—	2	2	no	—
103	C₂×D₄×C₄₇	—	2	2	no	—
104	C₂×D₄×C₄₇	—	2	2	no	—
105	C₂×D₄×C₄₇	—	2	2	no	—
106	C₂×D₄×C₄₇	—	2	2	no	—
107	C₂×D₄×C₄₇	—	2	2	no	—
108	C₂×D₄×C₄₇	—	4	2	no	—
109	C₂×D₄×C₄₇	—	4	4	no	—
110	C₂×D₄×C₄₇	—	4	4	no	—
111	C₂×D₄×C₄₇	—	4	4	no	—
112	C₂×D₄×C₄₇	—	8	2	no	—
113	C₂×D₄×C₄₇	—	8	2	no	—
114	C₂×D₄×C₄₇	—	8	2	no	—
115	C₂²×C₄×C₄₇	—	2	1	no	—
116	C₂²×C₄×C₄₇	—	2	1	no	—
117	C₂²×C₄×C₄₇	—	2	1	no	—
118	C₂²×C₄×C₄₇	—	2	1	no	—
119	C₂²×C₄×C₄₇	—	2	2	no	—
120	C₂²×C₄×C₄₇	—	2	1	no	—
121	C₂²×C₄×C₄₇	—	2	1	no	—
122	C₂²×C₄×C₄₇	—	2	1	no	—
123	C₂²×C₄×C₄₇	—	2	1	no	—
124	C₂²×C₄×C₄₇	—	2	1	no	—
125	C₂²×C₄×C₄₇	—	2	1	no	—
126	C₂²×C₄×C₄₇	—	2	2	no	—
127	C₂²×C₄×C₄₇	—	2	2	no	—
128	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
133	C₂²×C₄×C₄₇	#41	1	2	yes	—
134	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
135	D₈×C₄₇	—	4	4	no	—
136	M₁₆×C₄₇	—	4	4	no	—
137	C₂×C₈×C₄₇	—	2	1	no	—
138	C₂×C₈×C₄₇	—	2	1	no	—
139	C₂×C₈×C₄₇	—	2	8	no	—
140	C₂×C₈×C₄₇	—	2	1	no	—
141	C₂×C₈×C₄₇	—	2	1	no	—
142	C₂×C₈×C₄₇	—	2	1	no	—
143	C₂×C₈×C₄₇	—	2	1	no	—
144	C₂×C₈×C₄₇	—	2	1	no	—
145	C₂×C₈×C₄₇	—	2	1	no	—
146	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
147	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
148	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
149	C₂×C₈×C₄₇	#41	1	2	yes	—
150	C₄⋊C₄×C₄₇	—	2	2	no	—
151	C₄⋊C₄×C₄₇	—	2	2	no	—
152	C₄⋊C₄×C₄₇	—	2	2	no	—
153	C₄⋊C₄×C₄₇	—	2	2	no	—
154	C₄⋊C₄×C₄₇	—	2	2	no	—
155	C₄⋊C₄×C₄₇	—	2	2	no	—
156	C₄⋊C₄×C₄₇	—	8	2	no	—
157	C₄⋊C₄×C₄₇	C₂×D₄	1	4	yes	—
158	C₂²⋊C₄×C₄₇	—	2	2	no	—
159	C₂²⋊C₄×C₄₇	—	2	2	no	—
160	C₂²⋊C₄×C₄₇	—	4	4	no	—
161	C₂²⋊C₄×C₄₇	—	4	4	no	—
162	C₂²⋊C₄×C₄₇	—	4	4	no	—
163	C₂²⋊C₄×C₄₇	—	4	4	no	—
164	C₂²⋊C₄×C₄₇	—	8	2	no	—
165	C₂²⋊C₄×C₄₇	—	8	2	no	—
166	C₄²×C₄₇	—	2	1	no	—
167	C₄²×C₄₇	—	2	1	no	—
168	C₄²×C₄₇	—	4	4	no	—
169	C₂³×C₄₇	—	2	1	no	—
170	C₂³×C₄₇	—	2	1	no	—
171	C₂³×C₄₇	—	2	2	no	—
172	C₂³×C₄₇	—	2	2	no	—
173	C₂³×C₄₇	—	2	1	no	—
174	C₂³×C₄₇	—	2	1	no	—
175	C₂³×C₄₇	—	2	1	no	—
176	C₂³×C₄₇	—	2	2	no	—
177	C₂³×C₄₇	—	2	2	no	—
178	C₂³×C₄₇	—	4	2	no	—
179	C₂³×C₄₇	—	4	2	no	—
180	C₂³×C₄₇	—	4	2	no	—
181	C₂³×C₄₇	—	4	2	no	—
182	C₂³×C₄₇	—	4	2	no	—
183	C₂³×C₄₇	—	4	2	no	—
184	C₂³×C₄₇	—	4	2	no	—
185	C₂³×C₄₇	#121	1	2	yes	—
186	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
187	D₄×C₄₇	—	4	4	no	—
188	D₄×C₄₇	—	4	2	no	—
189	D₄×C₄₇	—	4	2	no	—
190	D₄×C₄₇	—	4	2	no	—
191	D₄×C₄₇	—	4	2	no	—
192	D₄×C₄₇	—	8	8	no	—
193	D₄×C₄₇	—	8	8	no	—
194	C₂×C₄×C₄₇	—	2	1	no	—
195	C₂×C₄×C₄₇	—	2	1	no	—
196	C₂×C₄×C₄₇	—	2	2	no	—
197	C₂×C₄×C₄₇	—	2	2	no	—
198	C₂×C₄×C₄₇	—	2	2	no	—
199	C₂×C₄×C₄₇	—	2	2	no	—
200	C₂×C₄×C₄₇	—	2	1	no	—
201	C₂×C₄×C₄₇	—	2	1	no	—
202	C₂×C₄×C₄₇	—	2	1	no	—
203	C₂×C₄×C₄₇	—	2	4	no	—
204	C₂×C₄×C₄₇	—	2	1	no	—
205	C₂×C₄×C₄₇	—	2	1	no	—
206	C₂×C₄×C₄₇	—	2	2	no	—
207	C₂×C₄×C₄₇	—	2	2	no	—
208	C₂×C₄×C₄₇	—	4	2	no	—
209	C₂×C₄×C₄₇	—	4	2	no	—
210	C₂×C₄×C₄₇	—	4	1	no	—
211	C₂×C₄×C₄₇	—	4	1	no	—
212	C₂×C₄×C₄₇	—	4	1	no	—
213	C₂×C₄×C₄₇	—	4	1	no	—
214	C₂×C₄×C₄₇	—	4	2	no	—
215	C₂×C₄×C₄₇	—	4	2	no	—
216	C₂×C₄×C₄₇	—	4	2	no	—
217	C₂×C₄×C₄₇	—	4	2	no	—
218	C₂×C₄×C₄₇	—	4	2	no	—
219	C₂×C₄×C₄₇	—	4	2	no	—
220	C₂×C₄×C₄₇	#121	1	2	yes	—
221	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
222	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
223	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
224	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
225	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
226	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
227	C₈×C₄₇	—	2	2	no	—
228	C₈×C₄₇	—	4	1	no	—
229	C₈×C₄₇	—	4	1	no	—
230	C₈×C₄₇	#121	1	4	yes	—
231	#24784	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
232	C₂²×C₄₇	—	2	2	no	—
233	C₂²×C₄₇	—	2	2	no	—
234	C₂²×C₄₇	—	2	2	no	—
235	C₂²×C₄₇	—	4	2	no	—
236	C₂²×C₄₇	—	4	2	no	—
237	C₂²×C₄₇	—	4	2	no	—
238	C₂²×C₄₇	—	4	1	no	—
239	C₂²×C₄₇	—	4	2	no	—
240	C₂²×C₄₇	—	4	1	no	—
241	C₂²×C₄₇	—	4	1	no	—
242	C₂²×C₄₇	—	8	2	no	—
243	C₂²×C₄₇	—	8	2	no	—
244	C₂²×C₄₇	—	8	2	no	—
245	C₂²×C₄₇	—	8	2	no	—
246	C₂²×C₄₇	—	8	2	no	—
247	C₂²×C₄₇	—	8	2	no	—
248	C₂²×C₄₇	—	8	2	no	—
249	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
250	C₂²×C₄₇	D₄²	1	1	yes	characteristic
251	C₂²×C₄₇	#547	1	1	yes	characteristic
252	C₂²×C₄₇	#575	1	2	yes	—
253	C₂²×C₄₇	#576	1	2	yes	—
254	C₄×C₄₇	—	2	2	no	—
255	C₄×C₄₇	—	4	1	no	—
256	C₄×C₄₇	—	4	4	no	—
257	C₄×C₄₇	—	4	1	no	—
258	C₄×C₄₇	—	4	1	no	—
259	C₄×C₄₇	—	8	2	no	—
260	C₄×C₄₇	—	8	2	no	—
261	C₄×C₄₇	C₂×#121	1	1	yes	characteristic
262	C₄×C₄₇	#537	1	1	yes	characteristic
263	C₄×C₄₇	#548	1	1	yes	characteristic
264	C₄×C₄₇	#553	1	1	yes	characteristic
265	C₂×#469	C₂×C₄₇	1	1	yes	characteristic, complemented
266	C₂×#466	C₂×C₄₇	1	1	yes	characteristic, complemented
267	C₂×#435	C₂×C₄₇	1	1	yes	characteristic, complemented
268	C₂×#427	C₂×C₄₇	1	1	yes	characteristic, complemented
269	#2414	C₂×C₄₇	1	2	yes	complemented
270	#2067	C₂×C₄₇	1	2	yes	complemented
271	#2033	C₂×C₄₇	1	2	yes	complemented
272	#1972	C₂×C₄₇	1	1	yes	characteristic, complemented
273	#1944	C₂×C₄₇	1	1	yes	characteristic, complemented
274	#1875	C₂×C₄₇	1	2	yes	complemented
275	#1809	C₂×C₄₇	1	1	yes	characteristic, complemented
276	C₂×C₄₇	—	4	2	no	—
277	C₂×C₄₇	—	8	1	no	—
278	C₂×C₄₇	—	16	2	no	—
279	C₂×C₄₇	#2416	1	1	yes	characteristic
280	C₂×C₄₇	#3054	1	1	yes	characteristic
281	C₂×C₄₇	#3058	1	1	yes	characteristic
282	C₂×C₄₇	#3268	1	2	yes	—
283	C₂×C₄₇	#3347	1	2	yes	—
284	C₂²×D₈	C₂²×C₄₇	1	1	yes	characteristic
285	C₂²×M₁₆	C₂²×C₄₇	1	1	yes	characteristic
286	C₂³×C₈	C₂²×C₄₇	1	1	yes	characteristic
287	C₂×#121	C₂²×C₄₇	1	2	yes	—
288	C₂×#121	C₂²×C₄₇	1	2	yes	—
289	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
290	C₂×#117	C₂²×C₄₇	1	2	yes	—
291	#469	—	2	4	no	—
292	#466	—	2	4	no	—
293	#435	—	2	4	no	—
294	#427	—	2	4	no	—
295	C₂×#107	C₂²×C₄₇	1	1	yes	characteristic
296	C₂×#107	C₂²×C₄₇	1	2	yes	—
297	C₂×#106	C₂²×C₄₇	1	1	yes	characteristic
298	C₂×#106	C₂²×C₄₇	1	1	yes	characteristic
299	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
300	C₂×#102	C₂²×C₄₇	1	2	yes	—
301	C₂×#102	C₂²×C₄₇	1	2	yes	—
302	C₂×#102	C₂²×C₄₇	1	2	yes	—
303	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
304	C₂×C₂²⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
305	C₂×#97	C₂²×C₄₇	1	1	yes	characteristic
306	#394	—	2	2	no	—
307	#392	—	2	2	no	—
308	#390	—	2	2	no	—
309	#390	C₂²×C₄₇	1	2	yes	—
310	#389	C₂²×C₄₇	1	2	yes	—
311	#388	—	2	2	no	—
312	#380	C₂²×C₄₇	1	2	yes	—
313	#340	C₂²×C₄₇	1	2	yes	—
314	#340	C₂²×C₄₇	1	2	yes	—
315	C₄₇	#24784	1	1	yes	characteristic, direct product factor, Sylow
316	C₂²×D₄	—	2	2	no	—
317	C₂²×D₄	—	2	2	no	—
318	C₂²×D₄	D₄×C₄₇	1	1	yes	characteristic
319	C₂²×D₄	C₂³×C₄₇	1	2	yes	—
320	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
321	C₂³×C₄	C₂³×C₄₇	1	1	yes	characteristic
322	C₂×D₈	—	2	2	no	—
323	C₂×D₈	—	2	2	no	—
324	C₂×D₈	—	2	2	no	—
325	C₂×M₁₆	—	2	2	no	—
326	C₂×M₁₆	—	2	2	no	—
327	C₂×M₁₆	—	2	2	no	—
328	C₂²×C₈	—	2	2	no	—
329	C₂²×C₈	—	2	2	no	—
330	C₂²×C₈	D₄×C₄₇	1	4	yes	complemented
331	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
332	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
333	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
334	C₂²×C₈	C₂³×C₄₇	1	1	yes	characteristic
335	#121	—	2	4	no	—
336	#121	—	2	4	no	—
337	#121	—	2	4	no	—
338	#121	—	4	2	no	—
339	C₄×D₄	—	2	2	no	—
340	C₄×D₄	—	2	2	no	—
341	#117	—	2	4	no	—
342	#117	—	4	2	no	—
343	C₂×C₄⋊C₄	—	2	2	no	—
344	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
346	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
347	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
348	C₂×C₂²⋊C₄	—	2	2	no	—
349	C₂×C₂²⋊C₄	—	2	2	no	—
350	C₂×C₂²⋊C₄	—	2	2	no	—
351	C₂×C₂²⋊C₄	—	2	2	no	—
352	C₂×C₂²⋊C₄	—	2	2	no	—
353	C₂×C₂²⋊C₄	—	2	2	no	—
354	C₂×C₂²⋊C₄	D₄×C₄₇	1	1	yes	characteristic
355	C₂×C₂²⋊C₄	D₄×C₄₇	1	1	yes	characteristic
356	C₂×C₄²	—	2	2	no	—
357	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
358	#107	—	2	2	no	—
359	#107	—	2	4	no	—
360	#106	—	2	2	no	—
361	#106	D₄×C₄₇	1	4	yes	complemented
362	C₄⋊C₈	—	2	2	no	—
363	#102	—	2	4	no	—
364	#102	—	2	4	no	—
365	#102	—	4	2	no	—
366	C₂²⋊C₈	—	2	2	no	—
367	C₂²⋊C₈	—	2	2	no	—
368	#97	—	2	2	no	—
369	#95	—	2	2	no	—
370	#95	—	2	2	no	—
371	C₂⁴	—	2	2	no	—
372	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
373	C₂⁴	C₂×D₄×C₄₇	1	1	yes	characteristic
374	C₂×D₄	—	2	2	no	—
375	C₂×D₄	—	2	2	no	—
376	C₂×D₄	—	2	2	no	—
377	C₂×D₄	—	2	2	no	—
378	C₂×D₄	—	2	2	no	—
379	C₂×D₄	—	2	2	no	—
380	C₂×D₄	—	2	2	no	—
381	C₂×D₄	—	4	2	no	—
382	C₂×D₄	—	4	4	no	—
383	C₂×D₄	—	4	4	no	—
384	C₂×D₄	—	4	4	no	—
385	C₂×D₄	—	8	2	no	—
386	C₂×D₄	—	8	2	no	—
387	C₂×D₄	—	8	2	no	—
388	C₂²×C₄	—	2	1	no	—
389	C₂²×C₄	—	2	1	no	—
390	C₂²×C₄	—	2	1	no	—
391	C₂²×C₄	—	2	1	no	—
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	1	no	—
394	C₂²×C₄	—	2	1	no	—
395	C₂²×C₄	—	2	1	no	—
396	C₂²×C₄	—	2	1	no	—
397	C₂²×C₄	—	2	1	no	—
398	C₂²×C₄	—	2	1	no	—
399	C₂²×C₄	—	2	2	no	—
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
402	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
403	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
404	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
405	C₂²×C₄	C₂×D₄×C₄₇	1	2	yes	—
406	C₂²×C₄	#41×C₄₇	1	2	yes	—
407	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
408	D₈	—	4	4	no	—
409	M₁₆	—	4	4	no	—
410	C₂×C₈	—	2	1	no	—
411	C₂×C₈	—	2	1	no	—
412	C₂×C₈	—	2	8	no	—
413	C₂×C₈	—	2	1	no	—
414	C₂×C₈	—	2	1	no	—
415	C₂×C₈	—	2	1	no	—
416	C₂×C₈	—	2	1	no	—
417	C₂×C₈	—	2	1	no	—
418	C₂×C₈	—	2	1	no	—
419	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
420	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
421	C₂×C₈	C₂×D₄×C₄₇	1	2	yes	—
422	C₂×C₈	#41×C₄₇	1	2	yes	—
423	C₄⋊C₄	—	2	2	no	—
424	C₄⋊C₄	—	2	2	no	—
425	C₄⋊C₄	—	2	2	no	—
426	C₄⋊C₄	—	2	2	no	—
427	C₄⋊C₄	—	2	2	no	—
428	C₄⋊C₄	—	2	2	no	—
429	C₄⋊C₄	—	8	2	no	—
430	C₄⋊C₄	C₂×D₄×C₄₇	1	4	yes	—
431	C₂²⋊C₄	—	2	2	no	—
432	C₂²⋊C₄	—	2	2	no	—
433	C₂²⋊C₄	—	4	4	no	—
434	C₂²⋊C₄	—	4	4	no	—
435	C₂²⋊C₄	—	4	4	no	—
436	C₂²⋊C₄	—	4	4	no	—
437	C₂²⋊C₄	—	8	2	no	—
438	C₂²⋊C₄	—	8	2	no	—
439	C₄²	—	2	1	no	—
440	C₄²	—	2	1	no	—
441	C₄²	—	4	4	no	—
442	C₂³	—	2	1	no	—
443	C₂³	—	2	1	no	—
444	C₂³	—	2	2	no	—
445	C₂³	—	2	2	no	—
446	C₂³	—	2	1	no	—
447	C₂³	—	2	1	no	—
448	C₂³	—	2	1	no	—
449	C₂³	—	2	2	no	—
450	C₂³	—	2	2	no	—
451	C₂³	—	4	2	no	—
452	C₂³	—	4	2	no	—
453	C₂³	—	4	2	no	—
454	C₂³	—	4	2	no	—
455	C₂³	—	4	2	no	—
456	C₂³	—	4	2	no	—
457	C₂³	—	4	2	no	—
458	C₂³	#121×C₄₇	1	2	yes	—
459	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
460	D₄	—	4	4	no	—
461	D₄	—	4	2	no	—
462	D₄	—	4	2	no	—
463	D₄	—	4	2	no	—
464	D₄	—	4	2	no	—
465	D₄	—	8	8	no	—
466	D₄	—	8	8	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	1	no	—
476	C₂×C₄	—	2	4	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	2	1	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	4	2	no	—
482	C₂×C₄	—	4	2	no	—
483	C₂×C₄	—	4	1	no	—
484	C₂×C₄	—	4	1	no	—
485	C₂×C₄	—	4	1	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	4	2	no	—
492	C₂×C₄	—	4	2	no	—
493	C₂×C₄	#121×C₄₇	1	2	yes	—
494	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
495	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
496	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
497	C₂×C₄	C₂×#41×C₄₇	1	1	yes	characteristic
498	C₂×C₄	H(5,𝔽₂)×C₄₇	1	1	yes	characteristic
499	C₂×C₄	2₋¹⁺⁴×C₄₇	1	1	yes	characteristic
500	C₈	—	2	2	no	—
501	C₈	—	4	1	no	—
502	C₈	—	4	1	no	—
503	C₈	#121×C₄₇	1	4	yes	—
504	C₂²	—	2	2	no	—
505	C₂²	—	2	2	no	—
506	C₂²	—	2	2	no	—
507	C₂²	—	4	2	no	—
508	C₂²	—	4	2	no	—
509	C₂²	—	4	1	no	—
510	C₂²	—	4	1	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	4	1	no	—
513	C₂²	—	4	2	no	—
514	C₂²	—	8	2	no	—
515	C₂²	—	8	2	no	—
516	C₂²	—	8	2	no	—
517	C₂²	—	8	2	no	—
518	C₂²	—	8	2	no	—
519	C₂²	—	8	2	no	—
520	C₂²	—	8	2	no	—
521	C₂²	C₂×#121×C₄₇	1	1	yes	characteristic
522	C₂²	D₄²×C₄₇	1	1	yes	characteristic
523	C₂²	C₄₇×#547	1	1	yes	characteristic
524	C₂²	C₄₇×#575	1	2	yes	—
525	C₂²	C₄₇×#576	1	2	yes	—
526	C₄	—	2	2	no	—
527	C₄	—	4	1	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	1	no	—
530	C₄	—	4	4	no	—
531	C₄	—	8	2	no	—
532	C₄	—	8	2	no	—
533	C₄	C₂×#121×C₄₇	1	1	yes	characteristic
534	C₄	C₄₇×#537	1	1	yes	characteristic
535	C₄	C₄₇×#548	1	1	yes	characteristic
536	C₄	C₄₇×#553	1	1	yes	characteristic
537	C₂	—	4	2	no	—
538	C₂	—	8	1	no	—
539	C₂	—	16	2	no	—
540	C₂	C₄₇×#2416	1	1	yes	characteristic
541	C₂	C₄₇×#3054	1	1	yes	characteristic
542	C₂	C₄₇×#3058	1	1	yes	characteristic
543	C₂	C₄₇×#3268	1	2	yes	—
544	C₂	C₄₇×#3347	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
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
1. C₂×C₄₇×#469	C₂	semidirect
2. C₂×C₄₇×#466	C₂	semidirect
3. C₂×C₄₇×#435	C₂	semidirect
4. C₂×C₄₇×#427	C₂	semidirect
5. C₄₇×#2414	C₂	semidirect
6. C₄₇×#2067	C₂	semidirect
7. C₄₇×#2033	C₂	semidirect
8. C₄₇×#1972	C₂	semidirect
9. C₄₇×#1944	C₂	semidirect
10. C₄₇×#1875	C₂	semidirect
11. C₄₇×#1809	C₂	semidirect
57. C₂²×C₈×C₄₇	D₄	semidirect
88. #106×C₄₇	D₄	semidirect
231. #24784	C₄₇	direct (N × H)
265. C₂×#469	C₂×C₄₇	semidirect
266. C₂×#466	C₂×C₄₇	semidirect
267. C₂×#435	C₂×C₄₇	semidirect
268. C₂×#427	C₂×C₄₇	semidirect
269. #2414	C₂×C₄₇	semidirect
270. #2067	C₂×C₄₇	semidirect
271. #2033	C₂×C₄₇	semidirect
272. #1972	C₂×C₄₇	semidirect
273. #1944	C₂×C₄₇	semidirect
274. #1875	C₂×C₄₇	semidirect
275. #1809	C₂×C₄₇	semidirect
315. C₄₇	#24784	direct (N × H)
330. C₂²×C₈	D₄×C₄₇	semidirect
361. #106	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×#466	2
C₂×C₄₇×#435	2
C₂×C₄₇×#427	2
C₄₇×#2414	2
C₄₇×#2067	2
C₄₇×#2033	2
C₄₇×#1972	2
C₄₇×#1944	2
C₄₇×#1875	2
C₄₇×#1809	2
#24784	47

Subgroups — C47×#24784 #26064482

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#24784 #26064482