Subgroups — C₄₇×#25659 #26065357

Order 12032.

1112 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄₇×#559	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄₇×#489	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄₇×#476	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄₇×#2546	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄₇×#2042	C₂	1	2	yes	maximal, complemented
6	C₄₇×#2041	C₂	1	2	yes	maximal
7	C₄₇×#1985	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄₇×#1983	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄₇×#1865	C₂	1	2	yes	maximal, complemented
10	C₄₇×#1864	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1762	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄₇×#559	—	2	4	no	—
13	C₄₇×#559	—	2	4	no	—
14	C₂×C₄⋊Q₈×C₄₇	—	2	1	no	—
15	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
16	C₂×#127×C₄₇	C₂²	1	1	yes	characteristic
17	C₂×#124×C₄₇	—	2	1	no	—
18	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
19	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
20	C₂×#123×C₄₇	—	2	1	no	—
21	C₂×#123×C₄₇	—	2	1	no	—
22	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₄×D₄×C₄₇	—	2	1	no	—
25	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
27	C₄₇×#489	—	2	4	no	—
28	C₄₇×#476	—	2	4	no	—
29	C₂×#106×C₄₇	C₂²	1	2	yes	—
30	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×#103×C₄₇	C₂²	1	2	yes	—
32	C₂×#103×C₄₇	C₂²	1	2	yes	—
33	C₂×#102×C₄₇	C₂²	1	2	yes	—
34	C₂×#102×C₄₇	C₂²	1	2	yes	—
35	C₂×#102×C₄₇	C₂²	1	2	yes	—
36	C₂×#102×C₄₇	C₂²	1	2	yes	—
37	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×#398	—	2	1	no	—
39	C₄₇×#398	—	2	1	no	—
40	C₄₇×#391	—	2	1	no	—
41	C₄₇×#389	C₂²	1	2	yes	—
42	C₄₇×#389	C₂²	1	2	yes	—
43	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
44	C₄₇×#340	C₂²	1	2	yes	—
45	C₄₇×#336	C₂²	1	2	yes	—
46	C₄₇×#336	C₂²	1	2	yes	—
47	C₂²×Q₈×C₄₇	—	2	1	no	—
48	C₂²×Q₈×C₄₇	D₄	1	1	yes	characteristic
49	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
50	C₂²×D₄×C₄₇	—	2	1	no	—
51	C₂²×D₄×C₄₇	—	2	1	no	—
52	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
53	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
54	C₂³×C₄×C₄₇	—	2	1	no	—
55	C₂³×C₄×C₄₇	—	2	1	no	—
56	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
57	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
58	C₄⋊Q₈×C₄₇	—	2	2	no	—
59	C₄⋊Q₈×C₄₇	—	2	2	no	—
60	C₄⋊Q₈×C₄₇	—	4	4	no	—
61	#127×C₄₇	—	2	2	no	—
62	#127×C₄₇	—	2	2	no	—
63	#124×C₄₇	—	2	8	no	—
64	#124×C₄₇	—	2	2	no	—
65	#124×C₄₇	—	2	2	no	—
66	#124×C₄₇	—	2	2	no	—
67	#124×C₄₇	D₄	1	4	yes	—
68	#123×C₄₇	—	2	8	no	—
69	#123×C₄₇	—	2	8	no	—
70	C₄×Q₈×C₄₇	—	2	2	no	—
71	C₄×Q₈×C₄₇	—	2	2	no	—
72	C₄×Q₈×C₄₇	—	2	2	no	—
73	C₄×Q₈×C₄₇	—	2	2	no	—
74	C₄×D₄×C₄₇	—	2	8	no	—
75	C₄×D₄×C₄₇	—	2	2	no	—
76	C₄×D₄×C₄₇	—	2	2	no	—
77	C₄×D₄×C₄₇	—	2	2	no	—
78	C₄×D₄×C₄₇	D₄	1	4	yes	—
79	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
80	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
81	C₂×C₄⋊C₄×C₄₇	—	2	2	no	—
82	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
83	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
84	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
85	C₂×C₄⋊C₄×C₄₇	D₄	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
87	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
88	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
89	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
90	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
91	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
92	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
93	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
94	C₂×C₂²⋊C₄×C₄₇	—	2	1	no	—
95	C₂×C₄²×C₄₇	—	2	1	no	—
96	C₂×C₄²×C₄₇	—	2	1	no	—
97	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
98	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
99	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
100	#106×C₄₇	—	2	4	no	—
101	C₄⋊C₈×C₄₇	—	2	2	no	—
102	#103×C₄₇	—	2	4	no	—
103	#103×C₄₇	—	2	4	no	—
104	#102×C₄₇	—	2	4	no	—
105	#102×C₄₇	—	2	4	no	—
106	#102×C₄₇	—	2	4	no	—
107	#102×C₄₇	—	2	4	no	—
108	#97×C₄₇	—	2	2	no	—
109	#95×C₄₇	—	2	1	no	—
110	#95×C₄₇	—	2	2	no	—
111	#95×C₄₇	—	2	2	no	—
112	C₂⁴×C₄₇	—	2	1	no	—
113	C₂⁴×C₄₇	—	2	1	no	—
114	C₂×Q₈×C₄₇	—	2	2	no	—
115	C₂×Q₈×C₄₇	—	2	2	no	—
116	C₂×Q₈×C₄₇	—	2	1	no	—
117	C₂×Q₈×C₄₇	—	2	2	no	—
118	C₂×Q₈×C₄₇	—	2	2	no	—
119	C₂×Q₈×C₄₇	—	4	1	no	—
120	C₂×Q₈×C₄₇	—	4	2	no	—
121	C₂×Q₈×C₄₇	—	4	2	no	—
122	C₂×Q₈×C₄₇	—	4	2	no	—
123	C₂×Q₈×C₄₇	C₂×D₄	1	2	yes	—
124	C₂×D₄×C₄₇	—	2	4	no	—
125	C₂×D₄×C₄₇	—	2	4	no	—
126	C₂×D₄×C₄₇	—	2	1	no	—
127	C₂×D₄×C₄₇	—	2	1	no	—
128	C₂×D₄×C₄₇	—	2	2	no	—
129	C₂×D₄×C₄₇	—	2	2	no	—
130	C₂×D₄×C₄₇	—	2	2	no	—
131	C₂×D₄×C₄₇	—	2	2	no	—
132	C₂×D₄×C₄₇	—	4	2	no	—
133	C₂×D₄×C₄₇	—	4	2	no	—
134	C₂×D₄×C₄₇	—	8	2	no	—
135	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
136	C₂×D₄×C₄₇	C₂×D₄	1	2	yes	—
137	C₂²×C₄×C₄₇	—	2	1	no	—
138	C₂²×C₄×C₄₇	—	2	1	no	—
139	C₂²×C₄×C₄₇	—	2	2	no	—
140	C₂²×C₄×C₄₇	—	2	4	no	—
141	C₂²×C₄×C₄₇	—	2	4	no	—
142	C₂²×C₄×C₄₇	—	2	2	no	—
143	C₂²×C₄×C₄₇	—	8	2	no	—
144	C₂²×C₄×C₄₇	—	8	2	no	—
145	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
147	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
148	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
152	C₂×C₈×C₄₇	—	2	2	no	—
153	C₂×C₈×C₄₇	—	2	2	no	—
154	C₂×C₈×C₄₇	—	2	2	no	—
155	C₂×C₈×C₄₇	—	2	2	no	—
156	C₂×C₈×C₄₇	—	2	2	no	—
157	C₂×C₈×C₄₇	—	2	2	no	—
158	C₄⋊C₄×C₄₇	—	2	4	no	—
159	C₄⋊C₄×C₄₇	—	2	2	no	—
160	C₄⋊C₄×C₄₇	—	2	2	no	—
161	C₄⋊C₄×C₄₇	—	2	2	no	—
162	C₄⋊C₄×C₄₇	—	2	1	no	—
163	C₄⋊C₄×C₄₇	—	2	2	no	—
164	C₄⋊C₄×C₄₇	—	2	2	no	—
165	C₄⋊C₄×C₄₇	—	2	2	no	—
166	C₄⋊C₄×C₄₇	—	4	4	no	—
167	C₄⋊C₄×C₄₇	—	4	2	no	—
168	C₄⋊C₄×C₄₇	—	4	4	no	—
169	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
170	C₄⋊C₄×C₄₇	#41	1	4	yes	—
171	C₂²⋊C₄×C₄₇	—	2	4	no	—
172	C₂²⋊C₄×C₄₇	—	2	4	no	—
173	C₂²⋊C₄×C₄₇	—	2	4	no	—
174	C₂²⋊C₄×C₄₇	—	2	4	no	—
175	C₂²⋊C₄×C₄₇	—	2	4	no	—
176	C₂²⋊C₄×C₄₇	—	2	4	no	—
177	C₄²×C₄₇	—	2	4	no	—
178	C₄²×C₄₇	—	2	1	no	—
179	C₄²×C₄₇	—	2	1	no	—
180	C₄²×C₄₇	—	2	1	no	—
181	C₄²×C₄₇	—	2	1	no	—
182	C₄²×C₄₇	—	4	2	no	—
183	C₄²×C₄₇	C₂×D₄	1	2	yes	—
184	C₄²×C₄₇	C₂×D₄	1	2	yes	—
185	C₂³×C₄₇	—	2	2	no	—
186	C₂³×C₄₇	—	2	2	no	—
187	C₂³×C₄₇	—	4	2	no	—
188	C₂³×C₄₇	—	4	2	no	—
189	C₂³×C₄₇	—	4	1	no	—
190	C₂³×C₄₇	—	4	1	no	—
191	C₂³×C₄₇	—	4	1	no	—
192	C₂³×C₄₇	—	4	1	no	—
193	C₂³×C₄₇	—	4	2	no	—
194	C₂³×C₄₇	—	4	2	no	—
195	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
196	Q₈×C₄₇	—	2	4	no	—
197	Q₈×C₄₇	—	4	4	no	—
198	Q₈×C₄₇	—	4	1	no	—
199	Q₈×C₄₇	—	4	1	no	—
200	Q₈×C₄₇	—	8	4	no	—
201	D₄×C₄₇	—	2	2	no	—
202	D₄×C₄₇	—	2	2	no	—
203	D₄×C₄₇	—	2	4	no	—
204	D₄×C₄₇	—	4	8	no	—
205	D₄×C₄₇	—	4	1	no	—
206	D₄×C₄₇	—	4	1	no	—
207	D₄×C₄₇	—	4	2	no	—
208	D₄×C₄₇	—	8	4	no	—
209	C₂×C₄×C₄₇	—	2	1	no	—
210	C₂×C₄×C₄₇	—	2	1	no	—
211	C₂×C₄×C₄₇	—	2	1	no	—
212	C₂×C₄×C₄₇	—	2	1	no	—
213	C₂×C₄×C₄₇	—	2	2	no	—
214	C₂×C₄×C₄₇	—	2	2	no	—
215	C₂×C₄×C₄₇	—	2	1	no	—
216	C₂×C₄×C₄₇	—	2	1	no	—
217	C₂×C₄×C₄₇	—	2	2	no	—
218	C₂×C₄×C₄₇	—	2	1	no	—
219	C₂×C₄×C₄₇	—	2	4	no	—
220	C₂×C₄×C₄₇	—	2	1	no	—
221	C₂×C₄×C₄₇	—	2	1	no	—
222	C₂×C₄×C₄₇	—	2	2	no	—
223	C₂×C₄×C₄₇	—	2	2	no	—
224	C₂×C₄×C₄₇	—	4	2	no	—
225	C₂×C₄×C₄₇	—	4	2	no	—
226	C₂×C₄×C₄₇	—	4	2	no	—
227	C₂×C₄×C₄₇	—	4	2	no	—
228	C₂×C₄×C₄₇	—	4	2	no	—
229	C₂×C₄×C₄₇	—	4	2	no	—
230	C₂×C₄×C₄₇	—	4	2	no	—
231	C₂×C₄×C₄₇	—	8	4	no	—
232	C₂×C₄×C₄₇	—	8	4	no	—
233	C₂×C₄×C₄₇	#120	1	2	yes	—
234	C₂×C₄×C₄₇	#120	1	2	yes	—
235	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
236	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
239	C₂×C₄×C₄₇	2₋¹⁺⁴	1	2	yes	—
240	C₈×C₄₇	—	4	2	no	—
241	C₈×C₄₇	—	4	2	no	—
242	#25659	C₄₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
243	C₂²×C₄₇	—	4	2	no	—
244	C₂²×C₄₇	—	4	2	no	—
245	C₂²×C₄₇	—	4	2	no	—
246	C₂²×C₄₇	—	4	2	no	—
247	C₂²×C₄₇	—	4	2	no	—
248	C₂²×C₄₇	—	4	2	no	—
249	C₂²×C₄₇	—	8	2	no	—
250	C₂²×C₄₇	—	8	2	no	—
251	C₂²×C₄₇	—	8	2	no	—
252	C₂²×C₄₇	—	8	2	no	—
253	C₂²×C₄₇	C₂×#120	1	1	yes	characteristic
254	C₂²×C₄₇	#548	1	2	yes	—
255	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
256	C₂²×C₄₇	#575	1	1	yes	characteristic
257	C₂²×C₄₇	#577	1	2	yes	—
258	C₄×C₄₇	—	2	2	no	—
259	C₄×C₄₇	—	2	2	no	—
260	C₄×C₄₇	—	2	2	no	—
261	C₄×C₄₇	—	4	4	no	—
262	C₄×C₄₇	—	4	2	no	—
263	C₄×C₄₇	—	4	1	no	—
264	C₄×C₄₇	—	4	1	no	—
265	C₄×C₄₇	—	4	1	no	—
266	C₄×C₄₇	—	4	2	no	—
267	C₄×C₄₇	—	8	2	no	—
268	C₄×C₄₇	#532	1	1	yes	characteristic
269	C₄×C₄₇	#536	1	1	yes	characteristic
270	C₄×C₄₇	#547	1	2	yes	—
271	C₂×#559	C₂×C₄₇	1	1	yes	characteristic
272	C₂×#489	C₂×C₄₇	1	1	yes	characteristic, complemented
273	C₂×#476	C₂×C₄₇	1	1	yes	characteristic, complemented
274	#2546	C₂×C₄₇	1	1	yes	characteristic, complemented
275	#2042	C₂×C₄₇	1	2	yes	complemented
276	#2041	C₂×C₄₇	1	2	yes	—
277	#1985	C₂×C₄₇	1	1	yes	characteristic, complemented
278	#1983	C₂×C₄₇	1	1	yes	characteristic, complemented
279	#1865	C₂×C₄₇	1	2	yes	complemented
280	#1864	C₂×C₄₇	1	2	yes	complemented
281	#1762	C₂×C₄₇	1	1	yes	characteristic, complemented
282	C₂×C₄₇	—	8	2	no	—
283	C₂×C₄₇	—	8	2	no	—
284	C₂×C₄₇	#2432	1	1	yes	characteristic
285	C₂×C₄₇	#3006	1	1	yes	characteristic
286	C₂×C₄₇	#3009	1	1	yes	characteristic
287	C₂×C₄₇	#3371	1	2	yes	—
288	C₂×C₄₇	#3373	1	2	yes	—
289	#559	—	2	4	no	—
290	#559	—	2	4	no	—
291	C₂×C₄⋊Q₈	—	2	1	no	—
292	C₂×C₄⋊Q₈	C₂²×C₄₇	1	1	yes	characteristic
293	C₂×#127	C₂²×C₄₇	1	1	yes	characteristic
294	C₂×#124	—	2	1	no	—
295	C₂×#124	C₂²×C₄₇	1	1	yes	characteristic
296	C₂×#124	C₂²×C₄₇	1	1	yes	characteristic
297	C₂×#123	—	2	1	no	—
298	C₂×#123	—	2	1	no	—
299	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
300	C₂×C₄×Q₈	C₂²×C₄₇	1	1	yes	characteristic
301	C₂×C₄×D₄	—	2	1	no	—
302	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
303	C₂×C₄×D₄	C₂²×C₄₇	1	1	yes	characteristic
304	#489	—	2	4	no	—
305	#476	—	2	4	no	—
306	C₂×#106	C₂²×C₄₇	1	2	yes	—
307	C₂×C₄⋊C₈	C₂²×C₄₇	1	1	yes	characteristic
308	C₂×#103	C₂²×C₄₇	1	2	yes	—
309	C₂×#103	C₂²×C₄₇	1	2	yes	—
310	C₂×#102	C₂²×C₄₇	1	2	yes	—
311	C₂×#102	C₂²×C₄₇	1	2	yes	—
312	C₂×#102	C₂²×C₄₇	1	2	yes	—
313	C₂×#102	C₂²×C₄₇	1	2	yes	—
314	C₂×#97	C₂²×C₄₇	1	1	yes	characteristic
315	#398	—	2	1	no	—
316	#398	—	2	1	no	—
317	#391	—	2	1	no	—
318	#389	C₂²×C₄₇	1	2	yes	—
319	#389	C₂²×C₄₇	1	2	yes	—
320	C₄×C₄⋊C₄	C₂²×C₄₇	1	1	yes	characteristic
321	#340	C₂²×C₄₇	1	2	yes	—
322	#336	C₂²×C₄₇	1	2	yes	—
323	#336	C₂²×C₄₇	1	2	yes	—
324	C₄₇	#25659	1	1	yes	characteristic, direct product factor, Sylow
325	C₂²×Q₈	—	2	1	no	—
326	C₂²×Q₈	D₄×C₄₇	1	1	yes	characteristic
327	C₂²×Q₈	C₂³×C₄₇	1	1	yes	characteristic
328	C₂²×D₄	—	2	1	no	—
329	C₂²×D₄	—	2	1	no	—
330	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
331	C₂²×D₄	C₂³×C₄₇	1	1	yes	characteristic
332	C₂³×C₄	—	2	1	no	—
333	C₂³×C₄	—	2	1	no	—
334	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
335	C₂²×C₈	C₂³×C₄₇	1	2	yes	—
336	C₄⋊Q₈	—	2	2	no	—
337	C₄⋊Q₈	—	2	2	no	—
338	C₄⋊Q₈	—	4	4	no	—
339	#127	—	2	2	no	—
340	#127	—	2	2	no	—
341	#124	—	2	8	no	—
342	#124	—	2	2	no	—
343	#124	—	2	2	no	—
344	#124	—	2	2	no	—
345	#124	D₄×C₄₇	1	4	yes	—
346	#123	—	2	8	no	—
347	#123	—	2	8	no	—
348	C₄×Q₈	—	2	2	no	—
349	C₄×Q₈	—	2	2	no	—
350	C₄×Q₈	—	2	2	no	—
351	C₄×Q₈	—	2	2	no	—
352	C₄×D₄	—	2	8	no	—
353	C₄×D₄	—	2	2	no	—
354	C₄×D₄	—	2	2	no	—
355	C₄×D₄	—	2	2	no	—
356	C₄×D₄	D₄×C₄₇	1	4	yes	—
357	C₂×C₄⋊C₄	—	2	1	no	—
358	C₂×C₄⋊C₄	—	2	2	no	—
359	C₂×C₄⋊C₄	—	2	2	no	—
360	C₂×C₄⋊C₄	—	2	1	no	—
361	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
362	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
363	C₂×C₄⋊C₄	D₄×C₄₇	1	1	yes	characteristic
364	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
365	C₂×C₄⋊C₄	C₂³×C₄₇	1	1	yes	characteristic
366	C₂×C₄⋊C₄	C₂³×C₄₇	1	2	yes	—
367	C₂×C₂²⋊C₄	—	2	1	no	—
368	C₂×C₂²⋊C₄	—	2	1	no	—
369	C₂×C₂²⋊C₄	—	2	1	no	—
370	C₂×C₂²⋊C₄	—	2	1	no	—
371	C₂×C₂²⋊C₄	—	2	1	no	—
372	C₂×C₂²⋊C₄	—	2	1	no	—
373	C₂×C₄²	—	2	1	no	—
374	C₂×C₄²	—	2	1	no	—
375	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
376	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
377	C₂×C₄²	C₂³×C₄₇	1	1	yes	characteristic
378	#106	—	2	4	no	—
379	C₄⋊C₈	—	2	2	no	—
380	#103	—	2	4	no	—
381	#103	—	2	4	no	—
382	#102	—	2	4	no	—
383	#102	—	2	4	no	—
384	#102	—	2	4	no	—
385	#102	—	2	4	no	—
386	#97	—	2	2	no	—
387	#95	—	2	1	no	—
388	#95	—	2	2	no	—
389	#95	—	2	2	no	—
390	C₂⁴	—	2	1	no	—
391	C₂⁴	—	2	1	no	—
392	C₂×Q₈	—	2	2	no	—
393	C₂×Q₈	—	2	2	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	—	2	2	no	—
396	C₂×Q₈	—	2	2	no	—
397	C₂×Q₈	—	4	1	no	—
398	C₂×Q₈	—	4	2	no	—
399	C₂×Q₈	—	4	2	no	—
400	C₂×Q₈	—	4	2	no	—
401	C₂×Q₈	C₂×D₄×C₄₇	1	2	yes	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	—	2	4	no	—
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	—	2	1	no	—
406	C₂×D₄	—	2	2	no	—
407	C₂×D₄	—	2	2	no	—
408	C₂×D₄	—	2	2	no	—
409	C₂×D₄	—	2	2	no	—
410	C₂×D₄	—	4	2	no	—
411	C₂×D₄	—	4	2	no	—
412	C₂×D₄	—	8	2	no	—
413	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
414	C₂×D₄	C₂×D₄×C₄₇	1	2	yes	—
415	C₂²×C₄	—	2	2	no	—
416	C₂²×C₄	—	2	1	no	—
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	2	4	no	—
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	2	no	—
421	C₂²×C₄	—	8	2	no	—
422	C₂²×C₄	—	8	2	no	—
423	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
424	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
425	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
426	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
427	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
428	C₂²×C₄	C₂×D₄×C₄₇	1	1	yes	characteristic
429	C₂²×C₄	C₂⁴×C₄₇	1	1	yes	characteristic
430	C₂×C₈	—	2	2	no	—
431	C₂×C₈	—	2	2	no	—
432	C₂×C₈	—	2	2	no	—
433	C₂×C₈	—	2	2	no	—
434	C₂×C₈	—	2	2	no	—
435	C₂×C₈	—	2	2	no	—
436	C₄⋊C₄	—	2	4	no	—
437	C₄⋊C₄	—	2	2	no	—
438	C₄⋊C₄	—	2	2	no	—
439	C₄⋊C₄	—	2	2	no	—
440	C₄⋊C₄	—	2	1	no	—
441	C₄⋊C₄	—	2	2	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	4	4	no	—
445	C₄⋊C₄	—	4	2	no	—
446	C₄⋊C₄	—	4	4	no	—
447	C₄⋊C₄	C₂×D₄×C₄₇	1	2	yes	—
448	C₄⋊C₄	#41×C₄₇	1	4	yes	—
449	C₂²⋊C₄	—	2	4	no	—
450	C₂²⋊C₄	—	2	4	no	—
451	C₂²⋊C₄	—	2	4	no	—
452	C₂²⋊C₄	—	2	4	no	—
453	C₂²⋊C₄	—	2	4	no	—
454	C₂²⋊C₄	—	2	4	no	—
455	C₄²	—	2	4	no	—
456	C₄²	—	2	1	no	—
457	C₄²	—	2	1	no	—
458	C₄²	—	2	1	no	—
459	C₄²	—	2	1	no	—
460	C₄²	—	4	2	no	—
461	C₄²	C₂×D₄×C₄₇	1	2	yes	—
462	C₄²	C₂×D₄×C₄₇	1	2	yes	—
463	C₂³	—	2	2	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	4	2	no	—
466	C₂³	—	4	2	no	—
467	C₂³	—	4	1	no	—
468	C₂³	—	4	1	no	—
469	C₂³	—	4	1	no	—
470	C₂³	—	4	1	no	—
471	C₂³	—	4	2	no	—
472	C₂³	—	4	2	no	—
473	C₂³	C₂²×D₄×C₄₇	1	1	yes	characteristic
474	Q₈	—	2	4	no	—
475	Q₈	—	4	4	no	—
476	Q₈	—	4	1	no	—
477	Q₈	—	4	1	no	—
478	Q₈	—	8	4	no	—
479	D₄	—	2	2	no	—
480	D₄	—	2	2	no	—
481	D₄	—	2	4	no	—
482	D₄	—	4	8	no	—
483	D₄	—	4	1	no	—
484	D₄	—	4	1	no	—
485	D₄	—	4	2	no	—
486	D₄	—	8	4	no	—
487	C₂×C₄	—	2	1	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	4	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	—	4	2	no	—
504	C₂×C₄	—	4	2	no	—
505	C₂×C₄	—	4	2	no	—
506	C₂×C₄	—	4	2	no	—
507	C₂×C₄	—	4	2	no	—
508	C₂×C₄	—	4	2	no	—
509	C₂×C₄	—	8	4	no	—
510	C₂×C₄	—	8	4	no	—
511	C₂×C₄	#120×C₄₇	1	2	yes	—
512	C₂×C₄	#120×C₄₇	1	2	yes	—
513	C₂×C₄	AGL(1,ℤ/8)×C₄₇	1	2	yes	—
514	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
515	C₂×C₄	C₂²×D₄×C₄₇	1	1	yes	characteristic
516	C₂×C₄	C₂×#41×C₄₇	1	2	yes	—
517	C₂×C₄	2₋¹⁺⁴×C₄₇	1	2	yes	—
518	C₈	—	4	2	no	—
519	C₈	—	4	2	no	—
520	C₂²	—	4	2	no	—
521	C₂²	—	4	2	no	—
522	C₂²	—	4	2	no	—
523	C₂²	—	4	2	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	8	2	no	—
527	C₂²	—	8	2	no	—
528	C₂²	—	8	2	no	—
529	C₂²	—	8	2	no	—
530	C₂²	C₂×#120×C₄₇	1	1	yes	characteristic
531	C₂²	C₄₇×#548	1	2	yes	—
532	C₂²	C₂×AGL(1,ℤ/8)×C₄₇	1	1	yes	characteristic
533	C₂²	C₄₇×#575	1	1	yes	characteristic
534	C₂²	C₄₇×#577	1	2	yes	—
535	C₄	—	2	2	no	—
536	C₄	—	2	2	no	—
537	C₄	—	2	2	no	—
538	C₄	—	4	4	no	—
539	C₄	—	4	2	no	—
540	C₄	—	4	1	no	—
541	C₄	—	4	1	no	—
542	C₄	—	4	1	no	—
543	C₄	—	4	2	no	—
544	C₄	—	8	2	no	—
545	C₄	C₄₇×#532	1	1	yes	characteristic
546	C₄	C₄₇×#536	1	1	yes	characteristic
547	C₄	C₄₇×#547	1	2	yes	—
548	C₂	—	8	2	no	—
549	C₂	—	8	2	no	—
550	C₂	C₄₇×#2432	1	1	yes	characteristic
551	C₂	C₄₇×#3006	1	1	yes	characteristic
552	C₂	C₄₇×#3009	1	1	yes	characteristic
553	C₂	C₄₇×#3371	1	2	yes	—
554	C₂	C₄₇×#3373	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₄₇	C₂²×D₄
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₄₇
prime radical	C₂×#127×C₄₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₄₇ ◁ C₂×C₄×Q₈×C₄₇ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₄₇×#489	C₂	semidirect
3. C₂×C₄₇×#476	C₂	semidirect
4. C₄₇×#2546	C₂	semidirect
5. C₄₇×#2042	C₂	semidirect
7. C₄₇×#1985	C₂	semidirect
8. C₄₇×#1983	C₂	semidirect
9. C₄₇×#1865	C₂	semidirect
10. C₄₇×#1864	C₂	semidirect
11. C₄₇×#1762	C₂	semidirect
242. #25659	C₄₇	direct (N × H)
272. C₂×#489	C₂×C₄₇	semidirect
273. C₂×#476	C₂×C₄₇	semidirect
274. #2546	C₂×C₄₇	semidirect
275. #2042	C₂×C₄₇	semidirect
277. #1985	C₂×C₄₇	semidirect
278. #1983	C₂×C₄₇	semidirect
279. #1865	C₂×C₄₇	semidirect
280. #1864	C₂×C₄₇	semidirect
281. #1762	C₂×C₄₇	semidirect
324. C₄₇	#25659	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×#559	2
C₂×C₄₇×#489	2
C₂×C₄₇×#476	2
C₄₇×#2546	2
C₄₇×#2042	2
C₄₇×#2041	2
C₄₇×#1985	2
C₄₇×#1983	2
C₄₇×#1865	2
C₄₇×#1864	2
C₄₇×#1762	2
#25659	47

Subgroups — C47×#25659 #26065357

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄₇×#25659 #26065357