Subgroups — #529×Dic₄₇ #26374785

Order 12032.

2670 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#125×Dic₄₇	C₂	1	2	yes	maximal, complemented
2	#126×Dic₄₇	C₂	1	4	yes	maximal, complemented
3	#124×Dic₄₇	C₂	1	2	yes	maximal, complemented
4	C₂²⋊Q₈×Dic₄₇	C₂	1	2	yes	maximal, complemented
5	#123×Dic₄₇	C₂	1	4	yes	maximal, complemented
6	#121×Dic₄₇	C₂	1	2	yes	maximal
7	#20245886	C₂	1	2	yes	maximal, complemented
8	#20245866	C₂	1	1	yes	maximal, characteristic, complemented
9	#20245853	C₂	1	1	yes	maximal, characteristic, complemented
10	#20245833	C₂	1	2	yes	maximal, complemented
11	#20245786	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×Q₈×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	C₄×D₄×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×D₄×Dic₄₇	C₂	1	2	yes	maximal, complemented
15	#117×Dic₄₇	C₂	1	2	yes	maximal, complemented
16	C₂×C₄²×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×C₄₇×#529	C₂	1	1	yes	maximal, characteristic
18	C₂×Q₈×Dic₄₇	C₂²	1	2	yes	—
19	C₂×D₄×Dic₄₇	C₂²	1	4	yes	—
20	C₂×D₄×Dic₄₇	C₂²	1	2	yes	—
21	C₂×#13093983	C₂²	1	2	yes	—
22	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
23	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
24	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
25	C₂²×C₄×Dic₄₇	C₂²	1	1	yes	characteristic
26	C₂²×C₄×Dic₄₇	C₂²	1	2	yes	—
27	#15689030	C₂²	1	2	yes	—
28	#15689026	C₂²	1	2	yes	—
29	#15689022	C₂²	1	2	yes	—
30	#15689022	C₂²	1	2	yes	—
31	#15689016	C₂²	1	4	yes	—
32	#15689016	C₂²	1	4	yes	—
33	#15689016	C₂²	1	4	yes	—
34	#15689016	C₂²	1	4	yes	—
35	#15689009	C₂²	1	4	yes	—
36	#15689009	C₂²	1	4	yes	—
37	#15689009	C₂²	1	4	yes	—
38	#15689009	C₂²	1	4	yes	—
39	#15689003	C₂²	1	4	yes	—
40	#15688998	C₂²	1	4	yes	—
41	#15688991	C₂²	1	2	yes	—
42	#15688989	C₂²	1	2	yes	—
43	#15688986	C₂²	1	2	yes	—
44	#15688983	C₂²	1	2	yes	—
45	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
46	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
47	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
48	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
49	C₄⋊C₄×Dic₄₇	C₂²	1	2	yes	—
50	C₄⋊C₄×Dic₄₇	C₂²	1	4	yes	—
51	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
52	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
53	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
54	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
55	C₂²⋊C₄×Dic₄₇	C₂²	1	4	yes	—
56	C₂²⋊C₄×Dic₄₇	C₂²	1	4	yes	—
57	C₂²⋊C₄×Dic₄₇	C₂²	1	4	yes	—
58	C₂²⋊C₄×Dic₄₇	C₂²	1	4	yes	—
59	C₂²⋊C₄×Dic₄₇	C₂²	1	4	yes	—
60	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
61	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
62	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
63	#15688969	C₂²	1	2	yes	—
64	#15688969	C₂²	1	2	yes	—
65	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
66	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
67	C₄²×Dic₄₇	C₂²	1	2	yes	—
68	C₄²×Dic₄₇	C₂²	1	2	yes	—
69	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
70	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
71	C₄²×Dic₄₇	C₂²	1	2	yes	—
72	C₄₇×#529	C₄	1	16	yes	complemented
73	C₂×#126×C₄₇	C₂²	1	2	yes	—
74	C₂×#125×C₄₇	C₂²	1	1	yes	characteristic
75	C₂×#124×C₄₇	C₂²	1	1	yes	characteristic
76	C₂×#123×C₄₇	C₂²	1	2	yes	—
77	C₂×C₂²⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
78	C₂×#121×C₄₇	C₂²	1	1	yes	characteristic
79	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
80	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
81	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
82	C₂×#117×C₄₇	C₂²	1	2	yes	—
83	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
84	C₂³×Dic₄₇	C₂³	1	4	yes	—
85	C₂³×Dic₄₇	C₂³	1	2	yes	—
86	C₂³×Dic₄₇	C₂³	1	2	yes	—
87	Q₈×Dic₄₇	—	2	8	no	—
88	D₄×Dic₄₇	—	2	16	no	—
89	D₄×Dic₄₇	—	2	8	no	—
90	#13093983	—	2	8	no	—
91	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
92	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
93	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
94	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
95	C₂×C₄⋊Dic₄₇	C₂³	1	4	yes	—
96	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
97	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
98	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
99	C₂×C₂²⋊Dic₄₇	C₂³	1	4	yes	—
100	C₂×C₄×Dic₄₇	—	2	8	no	—
101	C₂×C₄×Dic₄₇	—	2	4	no	—
102	C₂×C₄×Dic₄₇	—	2	8	no	—
103	C₂×C₄×Dic₄₇	—	2	4	no	—
104	C₂×C₄×Dic₄₇	—	2	8	no	—
105	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
106	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
107	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
108	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
109	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
110	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
111	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
112	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
113	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
114	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
115	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
116	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
117	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
118	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
119	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
120	C₂×C₄×Dic₄₇	C₂³	1	4	yes	—
121	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
122	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
123	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
124	C₄₇⋊#95	C₂³	1	4	yes	—
125	C₄₇⋊#95	C₂³	1	4	yes	—
126	C₄₇⋊#95	C₂³	1	4	yes	—
127	C₄₇⋊#95	C₂³	1	4	yes	—
128	C₄₇⋊#95	C₂³	1	4	yes	—
129	C₄₇⋊#95	C₂³	1	4	yes	—
130	C₄₇⋊#95	C₂³	1	4	yes	—
131	C₄₇⋊#95	C₂³	1	2	yes	—
132	C₄₇⋊#95	C₂³	1	4	yes	—
133	C₄₇⋊#95	C₂³	1	2	yes	—
134	C₄₇⋊#95	C₂³	1	4	yes	—
135	C₂²×Q₈×C₄₇	C₂³	1	1	yes	characteristic
136	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
137	C₂²×D₄×C₄₇	C₂³	1	1	yes	characteristic
138	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
139	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
140	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
141	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
142	#126×C₄₇	C₂×C₄	1	16	yes	complemented
143	#125×C₄₇	C₂×C₄	1	8	yes	complemented
144	#124×C₄₇	C₂×C₄	1	8	yes	complemented
145	#123×C₄₇	C₂×C₄	1	16	yes	complemented
146	C₂²⋊Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
147	#121×C₄₇	C₂×C₄	1	8	yes	—
148	C₄×Q₈×C₄₇	C₂×C₄	1	8	yes	complemented
149	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	complemented
150	C₄×D₄×C₄₇	C₂×C₄	1	16	yes	complemented
151	#117×C₄₇	C₂×C₄	1	16	yes	complemented
152	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
153	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
154	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
155	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
156	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
157	C₂×C₄⋊C₄×C₄₇	C₂³	1	1	yes	characteristic
158	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
159	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
160	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
161	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
162	C₂×C₂²⋊C₄×C₄₇	C₂³	1	2	yes	—
163	C₂×C₄²×C₄₇	C₂×C₄	1	8	yes	complemented
164	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
165	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
166	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
167	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
168	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
169	C₂⁴×C₄₇	C₂⁴	1	2	yes	—
170	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
171	C₂×Q₈×C₄₇	—	2	4	no	—
172	C₂×Q₈×C₄₇	C₂²×C₄	1	4	yes	—
173	C₂×D₄×C₄₇	—	2	8	no	—
174	C₂×D₄×C₄₇	—	2	4	no	—
175	C₂×D₄×C₄₇	C₂²×C₄	1	8	yes	—
176	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
177	C₂²×C₄×C₄₇	—	2	4	no	—
178	C₂²×C₄×C₄₇	—	2	2	no	—
179	C₂²×C₄×C₄₇	—	2	2	no	—
180	C₂²×C₄×C₄₇	—	2	4	no	—
181	C₂²×C₄×C₄₇	—	2	4	no	—
182	C₂²×C₄×C₄₇	—	2	4	no	—
183	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
184	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
185	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
186	C₂²×C₄×C₄₇	C₂²×C₄	1	8	yes	—
187	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
188	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
189	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
190	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
191	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
192	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
193	C₂²×C₄×C₄₇	C₂⁴	1	2	yes	—
194	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
195	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
196	C₂²×Dic₄₇	—	2	4	no	—
197	C₂²×Dic₄₇	—	2	4	no	—
198	C₂²×Dic₄₇	—	2	4	no	—
199	C₂²×Dic₄₇	—	2	4	no	—
200	C₂²×Dic₄₇	—	2	4	no	—
201	C₂²×Dic₄₇	—	2	8	no	—
202	C₂²×Dic₄₇	—	2	8	no	—
203	C₂²×Dic₄₇	—	2	8	no	—
204	C₂²×Dic₄₇	#41	1	8	yes	—
205	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
206	C₂²×Dic₄₇	C₂⁴	1	4	yes	—
207	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
208	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
209	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
210	C₂²×Dic₄₇	C₂⁴	1	2	yes	—
211	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
212	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
213	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
214	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
215	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
216	C₄⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
217	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
218	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
219	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
220	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
221	C₂²⋊C₄×C₄₇	C₂²×C₄	1	8	yes	—
222	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
223	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
224	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
225	C₄²×C₄₇	C₂²×C₄	1	4	yes	—
226	C₄²×C₄₇	C₂²×C₄	1	8	yes	—
227	C₂²⋊Dic₄₇	—	2	8	no	—
228	C₂²⋊Dic₄₇	—	2	8	no	—
229	C₂²⋊Dic₄₇	—	2	8	no	—
230	C₂²⋊Dic₄₇	—	2	8	no	—
231	C₄⋊Dic₄₇	—	2	4	no	—
232	C₄⋊Dic₄₇	—	2	4	no	—
233	C₄⋊Dic₄₇	—	2	8	no	—
234	C₄⋊Dic₄₇	—	2	8	no	—
235	C₄⋊Dic₄₇	—	2	8	no	—
236	C₄×Dic₄₇	—	2	2	no	—
237	C₄×Dic₄₇	—	2	2	no	—
238	C₄×Dic₄₇	—	2	4	no	—
239	C₄×Dic₄₇	—	2	4	no	—
240	C₄×Dic₄₇	—	2	4	no	—
241	C₄×Dic₄₇	—	2	4	no	—
242	C₄×Dic₄₇	—	2	4	no	—
243	C₄×Dic₄₇	—	2	4	no	—
244	C₄×Dic₄₇	—	2	4	no	—
245	C₄×Dic₄₇	—	2	4	no	—
246	C₄×Dic₄₇	—	2	4	no	—
247	C₄×Dic₄₇	—	2	4	no	—
248	C₄×Dic₄₇	—	2	4	no	—
249	C₄×Dic₄₇	—	2	8	no	—
250	C₄×Dic₄₇	—	2	8	no	—
251	C₄×Dic₄₇	—	2	8	no	—
252	C₄×Dic₄₇	#41	1	4	yes	—
253	C₄×Dic₄₇	#41	1	4	yes	—
254	C₄×Dic₄₇	#41	1	8	yes	—
255	C₂³×C₄₇	—	2	1	no	—
256	C₂³×C₄₇	—	2	2	no	—
257	C₂³×C₄₇	—	2	1	no	—
258	C₂³×C₄₇	—	2	2	no	—
259	C₂³×C₄₇	—	2	4	no	—
260	C₂³×C₄₇	—	2	4	no	—
261	C₂³×C₄₇	—	2	2	no	—
262	C₂³×C₄₇	C₂³×C₄	1	4	yes	—
263	C₂³×C₄₇	C₂³×C₄	1	2	yes	—
264	C₂³×C₄₇	C₂×#41	1	4	yes	—
265	C₂³×C₄₇	C₂⁵	1	1	yes	characteristic
266	Q₈×C₄₇	—	2	8	no	—
267	D₄×C₄₇	—	2	16	no	—
268	D₄×C₄₇	—	2	8	no	—
269	C₂×C₄×C₄₇	—	2	8	no	—
270	C₂×C₄×C₄₇	—	2	1	no	—
271	C₂×C₄×C₄₇	—	2	2	no	—
272	C₂×C₄×C₄₇	—	2	2	no	—
273	C₂×C₄×C₄₇	—	2	2	no	—
274	C₂×C₄×C₄₇	—	2	2	no	—
275	C₂×C₄×C₄₇	—	2	1	no	—
276	C₂×C₄×C₄₇	—	2	4	no	—
277	C₂×C₄×C₄₇	—	2	4	no	—
278	C₂×C₄×C₄₇	—	2	2	no	—
279	C₂×C₄×C₄₇	—	2	8	no	—
280	C₂×C₄×C₄₇	—	2	16	no	—
281	C₂×C₄×C₄₇	—	2	8	no	—
282	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
283	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
284	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
285	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
286	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
287	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
288	C₂×C₄×C₄₇	C₂³×C₄	1	4	yes	—
289	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
290	C₂×C₄×C₄₇	C₂³×C₄	1	2	yes	—
291	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
292	C₂×C₄×C₄₇	C₂×#41	1	2	yes	—
293	C₂×C₄×C₄₇	C₂×#41	1	4	yes	—
294	C₂×Dic₄₇	—	2	16	no	—
295	C₂×Dic₄₇	—	2	2	no	—
296	C₂×Dic₄₇	—	2	2	no	—
297	C₂×Dic₄₇	—	2	2	no	—
298	C₂×Dic₄₇	—	2	2	no	—
299	C₂×Dic₄₇	—	2	2	no	—
300	C₂×Dic₄₇	—	2	2	no	—
301	C₂×Dic₄₇	—	2	16	no	—
302	C₂×Dic₄₇	—	2	4	no	—
303	C₂×Dic₄₇	—	2	4	no	—
304	C₂×Dic₄₇	—	2	4	no	—
305	C₂×Dic₄₇	—	2	4	no	—
306	C₂×Dic₄₇	—	2	4	no	—
307	C₂×Dic₄₇	—	2	4	no	—
308	C₂×Dic₄₇	—	4	16	no	—
309	C₂×Dic₄₇	C₂×#41	1	4	yes	—
310	C₂×Dic₄₇	C₂×#41	1	4	yes	—
311	C₂×Dic₄₇	C₂×#41	1	4	yes	—
312	C₂×Dic₄₇	C₂×#41	1	4	yes	—
313	C₂×Dic₄₇	C₂×#41	1	4	yes	—
314	C₂×Dic₄₇	C₂×#41	1	4	yes	—
315	C₄×#529	—	47	1	no	maximal, Sylow
316	C₂²×C₄₇	—	2	2	no	—
317	C₂²×C₄₇	—	2	2	no	—
318	C₂²×C₄₇	—	2	4	no	—
319	C₂²×C₄₇	—	2	4	no	—
320	C₂²×C₄₇	—	2	4	no	—
321	C₂²×C₄₇	—	2	4	no	—
322	C₂²×C₄₇	—	2	4	no	—
323	C₂²×C₄₇	—	4	4	no	—
324	C₂²×C₄₇	—	4	4	no	—
325	C₂²×C₄₇	C₄×#41	1	4	yes	—
326	C₂²×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
327	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
328	C₂²×C₄₇	C₂²×#41	1	2	yes	—
329	C₂²×C₄₇	C₂²×#41	1	2	yes	—
330	C₂²×C₄₇	C₂²×#41	1	1	yes	characteristic
331	C₄×C₄₇	—	2	2	no	—
332	C₄×C₄₇	—	2	2	no	—
333	C₄×C₄₇	—	2	2	no	—
334	C₄×C₄₇	—	2	2	no	—
335	C₄×C₄₇	—	2	4	no	—
336	C₄×C₄₇	—	2	4	no	—
337	C₄×C₄₇	—	2	4	no	—
338	C₄×C₄₇	C₄×#41	1	4	yes	—
339	C₄×C₄₇	C₄×#41	1	4	yes	—
340	Dic₄₇	—	2	4	no	—
341	Dic₄₇	—	2	4	no	—
342	Dic₄₇	—	2	4	no	—
343	Dic₄₇	—	4	4	no	—
344	Dic₄₇	—	4	4	no	—
345	Dic₄₇	#529	1	8	yes	direct product factor
346	C₂×#529	D₄₇	1	1	yes	characteristic
347	C₄×#125	—	47	2	no	—
348	C₄×#126	—	47	4	no	—
349	C₄×#124	—	47	2	no	—
350	C₄×C₂²⋊Q₈	—	47	2	no	—
351	C₄×#123	—	47	4	no	—
352	C₄×#121	—	47	2	no	—
353	#2298	—	47	2	no	—
354	#2295	—	47	1	no	—
355	#2293	—	47	1	no	—
356	#2290	—	47	2	no	—
357	#2283	—	47	1	no	—
358	C₄²×Q₈	—	47	1	no	—
359	C₄²×D₄	—	47	2	no	—
360	C₄²×D₄	—	47	1	no	—
361	C₄×#117	—	47	2	no	—
362	C₂×C₄³	—	47	1	no	—
363	C₂×C₄₇	—	2	4	no	—
364	C₂×C₄₇	—	4	4	no	—
365	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
366	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
367	C₂×C₄₇	C₂×C₄×#41	1	1	yes	characteristic
368	C₂×C₄₇	C₂×#529	1	2	yes	—
369	C₂×C₄₇	#3444	1	2	yes	—
370	#529	Dic₄₇	1	16	yes	direct product factor
371	C₂×#126	C₂×D₄₇	1	2	yes	—
372	C₂×#125	C₂×D₄₇	1	1	yes	characteristic
373	C₂×#124	C₂×D₄₇	1	1	yes	characteristic
374	C₂×#123	C₂×D₄₇	1	2	yes	—
375	C₂×C₂²⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
376	C₂×#121	C₂×D₄₇	1	1	yes	characteristic
377	C₂×C₄×Q₈	—	47	2	no	—
378	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
379	C₂×C₄×D₄	—	47	4	no	—
380	C₂×C₄×D₄	—	47	2	no	—
381	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
382	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
383	C₂×#117	—	47	2	no	—
384	C₂×#117	C₂×D₄₇	1	2	yes	—
385	C₂²×C₄²	—	47	1	no	—
386	C₂²×C₄²	—	47	1	no	—
387	C₂²×C₄²	—	47	2	no	—
388	C₂²×C₄²	—	47	2	no	—
389	C₂²×C₄²	—	47	2	no	—
390	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
391	#391	—	47	2	no	—
392	#390	—	47	2	no	—
393	#389	—	47	2	no	—
394	#389	—	47	2	no	—
395	#388	—	47	4	no	—
396	#388	—	47	4	no	—
397	#388	—	47	4	no	—
398	#388	—	47	4	no	—
399	#387	—	47	4	no	—
400	#387	—	47	4	no	—
401	#387	—	47	4	no	—
402	#387	—	47	4	no	—
403	#386	—	47	4	no	—
404	#385	—	47	4	no	—
405	#383	—	47	2	no	—
406	#382	—	47	2	no	—
407	#381	—	47	2	no	—
408	#380	—	47	2	no	—
409	C₄×C₄⋊C₄	—	47	4	no	—
410	C₄×C₄⋊C₄	—	47	4	no	—
411	C₄×C₄⋊C₄	—	47	4	no	—
412	C₄×C₄⋊C₄	—	47	4	no	—
413	C₄×C₄⋊C₄	—	47	2	no	—
414	C₄×C₄⋊C₄	—	47	2	no	—
415	C₄×C₄⋊C₄	—	47	1	no	—
416	C₄×C₄⋊C₄	—	47	2	no	—
417	C₄×C₄⋊C₄	—	47	1	no	—
418	C₄×C₄⋊C₄	—	47	2	no	—
419	C₄×C₂²⋊C₄	—	47	2	no	—
420	C₄×C₂²⋊C₄	—	47	2	no	—
421	C₄×C₂²⋊C₄	—	47	2	no	—
422	C₄×C₂²⋊C₄	—	47	4	no	—
423	C₄×C₂²⋊C₄	—	47	4	no	—
424	C₄×C₂²⋊C₄	—	47	4	no	—
425	C₄×C₂²⋊C₄	—	47	4	no	—
426	C₄×C₂²⋊C₄	—	47	4	no	—
427	#376	—	47	2	no	—
428	#376	—	47	2	no	—
429	C₄³	—	47	2	no	—
430	C₄³	—	47	2	no	—
431	C₄³	—	47	1	no	—
432	C₄³	—	47	1	no	—
433	C₄³	—	47	1	no	—
434	C₄³	—	47	1	no	—
435	C₄³	—	47	2	no	—
436	C₄₇	C₄×#529	1	1	yes	characteristic, complemented, Sylow
437	C₂²×Q₈	C₂²×D₄₇	1	1	yes	characteristic
438	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
439	C₂²×D₄	C₂²×D₄₇	1	1	yes	characteristic
440	C₂³×C₄	—	47	2	no	—
441	C₂³×C₄	—	47	4	no	—
442	C₂³×C₄	—	47	2	no	—
443	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
444	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
445	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
446	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
447	#126	C₂×Dic₄₇	1	16	yes	complemented
448	#125	C₂×Dic₄₇	1	8	yes	complemented
449	#124	C₂×Dic₄₇	1	8	yes	complemented
450	#123	C₂×Dic₄₇	1	16	yes	complemented
451	C₂²⋊Q₈	C₂×Dic₄₇	1	8	yes	complemented
452	#121	C₂×Dic₄₇	1	8	yes	—
453	C₄×Q₈	—	94	8	no	—
454	C₄×Q₈	C₂×Dic₄₇	1	8	yes	complemented
455	C₄×D₄	—	94	8	no	—
456	C₄×D₄	—	94	16	no	—
457	C₄×D₄	C₂×Dic₄₇	1	8	yes	complemented
458	C₄×D₄	C₂×Dic₄₇	1	16	yes	complemented
459	#117	—	94	8	no	—
460	#117	C₂×Dic₄₇	1	16	yes	complemented
461	C₂×C₄⋊C₄	—	47	4	no	—
462	C₂×C₄⋊C₄	—	47	2	no	—
463	C₂×C₄⋊C₄	—	47	4	no	—
464	C₂×C₄⋊C₄	—	47	2	no	—
465	C₂×C₄⋊C₄	—	47	4	no	—
466	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
467	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
468	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
469	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
470	C₂×C₄⋊C₄	C₂²×D₄₇	1	1	yes	characteristic
471	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
472	C₂×C₂²⋊C₄	—	47	4	no	—
473	C₂×C₂²⋊C₄	—	47	4	no	—
474	C₂×C₂²⋊C₄	—	47	4	no	—
475	C₂×C₂²⋊C₄	—	47	4	no	—
476	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
477	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
478	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
479	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
480	C₂×C₂²⋊C₄	C₂²×D₄₇	1	2	yes	—
481	C₂×C₄²	—	47	2	no	—
482	C₂×C₄²	—	47	1	no	—
483	C₂×C₄²	—	47	1	no	—
484	C₂×C₄²	—	47	4	no	—
485	C₂×C₄²	—	47	4	no	—
486	C₂×C₄²	—	47	2	no	—
487	C₂×C₄²	—	47	2	no	—
488	C₂×C₄²	—	47	2	no	—
489	C₂×C₄²	—	47	2	no	—
490	C₂×C₄²	—	47	2	no	—
491	C₂×C₄²	—	47	2	no	—
492	C₂×C₄²	—	47	2	no	—
493	C₂×C₄²	—	47	2	no	—
494	C₂×C₄²	—	47	2	no	—
495	C₂×C₄²	—	47	4	no	—
496	C₂×C₄²	—	47	2	no	—
497	C₂×C₄²	—	47	1	no	—
498	C₂×C₄²	—	47	1	no	—
499	C₂×C₄²	—	47	2	no	—
500	C₂×C₄²	—	94	4	no	—
501	C₂×C₄²	—	94	8	no	—
502	C₂×C₄²	—	94	4	no	—
503	C₂×C₄²	—	94	8	no	—
504	C₂×C₄²	—	94	8	no	—
505	C₂×C₄²	C₂×Dic₄₇	1	8	yes	complemented
506	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
507	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
508	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
509	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
510	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
511	#95	—	47	4	no	—
512	#95	—	47	4	no	—
513	#95	—	47	4	no	—
514	#95	—	47	4	no	—
515	#95	—	47	2	no	—
516	#95	—	47	4	no	—
517	#95	—	47	4	no	—
518	#95	—	47	4	no	—
519	#95	—	47	4	no	—
520	#95	—	47	2	no	—
521	#95	—	47	4	no	—
522	C₂⁴	C₂³×D₄₇	1	2	yes	—
523	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
524	C₂×Q₈	—	2	4	no	—
525	C₂×Q₈	C₂²×Dic₄₇	1	4	yes	—
526	C₂×D₄	—	2	8	no	—
527	C₂×D₄	—	2	4	no	—
528	C₂×D₄	C₂²×Dic₄₇	1	8	yes	—
529	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
530	C₂²×C₄	—	2	4	no	—
531	C₂²×C₄	—	2	2	no	—
532	C₂²×C₄	—	2	2	no	—
533	C₂²×C₄	—	2	4	no	—
534	C₂²×C₄	—	2	4	no	—
535	C₂²×C₄	—	2	4	no	—
536	C₂²×C₄	—	47	2	no	—
537	C₂²×C₄	—	47	8	no	—
538	C₂²×C₄	—	47	2	no	—
539	C₂²×C₄	—	47	2	no	—
540	C₂²×C₄	—	47	2	no	—
541	C₂²×C₄	—	47	4	no	—
542	C₂²×C₄	—	47	4	no	—
543	C₂²×C₄	—	94	4	no	—
544	C₂²×C₄	—	94	4	no	—
545	C₂²×C₄	—	94	4	no	—
546	C₂²×C₄	—	94	4	no	—
547	C₂²×C₄	—	94	8	no	—
548	C₂²×C₄	—	94	8	no	—
549	C₂²×C₄	—	94	8	no	—
550	C₂²×C₄	—	94	4	no	—
551	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
552	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
553	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
554	C₂²×C₄	C₂²×Dic₄₇	1	8	yes	—
555	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
556	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
557	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
558	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
559	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
560	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
561	C₂²×C₄	C₂³×D₄₇	1	2	yes	—
562	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
563	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
564	C₄⋊C₄	—	94	8	no	—
565	C₄⋊C₄	—	94	8	no	—
566	C₄⋊C₄	—	94	8	no	—
567	C₄⋊C₄	—	94	4	no	—
568	C₄⋊C₄	—	94	4	no	—
569	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
570	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
571	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
572	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
573	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
574	C₄⋊C₄	C₂²×Dic₄₇	1	8	yes	—
575	C₂²⋊C₄	—	94	8	no	—
576	C₂²⋊C₄	—	94	8	no	—
577	C₂²⋊C₄	—	94	8	no	—
578	C₂²⋊C₄	—	94	8	no	—
579	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
580	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
581	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
582	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
583	C₂²⋊C₄	C₂²×Dic₄₇	1	8	yes	—
584	C₄²	—	47	4	no	—
585	C₄²	—	47	4	no	—
586	C₄²	—	47	8	no	—
587	C₄²	—	94	4	no	—
588	C₄²	—	94	4	no	—
589	C₄²	—	94	8	no	—
590	C₄²	—	94	4	no	—
591	C₄²	—	94	4	no	—
592	C₄²	—	94	4	no	—
593	C₄²	—	94	4	no	—
594	C₄²	—	94	4	no	—
595	C₄²	—	94	4	no	—
596	C₄²	—	94	8	no	—
597	C₄²	—	94	8	no	—
598	C₄²	—	94	2	no	—
599	C₄²	—	94	2	no	—
600	C₄²	—	94	4	no	—
601	C₄²	—	94	4	no	—
602	C₄²	—	94	4	no	—
603	C₄²	C₂²×Dic₄₇	1	4	yes	—
604	C₄²	C₂²×Dic₄₇	1	4	yes	—
605	C₄²	C₂²×Dic₄₇	1	4	yes	—
606	C₄²	C₂²×Dic₄₇	1	4	yes	—
607	C₄²	C₂²×Dic₄₇	1	8	yes	—
608	C₂³	—	2	1	no	—
609	C₂³	—	2	2	no	—
610	C₂³	—	2	1	no	—
611	C₂³	—	2	2	no	—
612	C₂³	—	2	4	no	—
613	C₂³	—	2	4	no	—
614	C₂³	—	2	2	no	—
615	C₂³	C₂³×Dic₄₇	1	4	yes	—
616	C₂³	C₂³×Dic₄₇	1	2	yes	—
617	C₂³	#41×D₄₇	1	4	yes	—
618	C₂³	C₂⁴×D₄₇	1	1	yes	characteristic
619	Q₈	—	2	8	no	—
620	D₄	—	2	16	no	—
621	D₄	—	2	8	no	—
622	C₂×C₄	—	2	8	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	2	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	2	no	—
627	C₂×C₄	—	2	2	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	4	no	—
630	C₂×C₄	—	2	4	no	—
631	C₂×C₄	—	2	2	no	—
632	C₂×C₄	—	2	8	no	—
633	C₂×C₄	—	2	16	no	—
634	C₂×C₄	—	2	8	no	—
635	C₂×C₄	—	47	4	no	—
636	C₂×C₄	—	47	4	no	—
637	C₂×C₄	—	47	4	no	—
638	C₂×C₄	—	47	4	no	—
639	C₂×C₄	—	47	4	no	—
640	C₂×C₄	—	47	4	no	—
641	C₂×C₄	—	94	16	no	—
642	C₂×C₄	—	94	16	no	—
643	C₂×C₄	—	94	2	no	—
644	C₂×C₄	—	94	2	no	—
645	C₂×C₄	—	94	2	no	—
646	C₂×C₄	—	94	2	no	—
647	C₂×C₄	—	94	2	no	—
648	C₂×C₄	—	94	2	no	—
649	C₂×C₄	—	94	4	no	—
650	C₂×C₄	—	94	4	no	—
651	C₂×C₄	—	94	4	no	—
652	C₂×C₄	—	94	4	no	—
653	C₂×C₄	—	94	4	no	—
654	C₂×C₄	—	94	4	no	—
655	C₂×C₄	—	188	16	no	—
656	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
657	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
658	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
659	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
660	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
661	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
662	C₂×C₄	C₂³×Dic₄₇	1	4	yes	—
663	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
664	C₂×C₄	C₂³×Dic₄₇	1	2	yes	—
665	C₂×C₄	#41×D₄₇	1	2	yes	—
666	C₂×C₄	#41×D₄₇	1	2	yes	—
667	C₂×C₄	#41×D₄₇	1	4	yes	—
668	C₂²	—	2	2	no	—
669	C₂²	—	2	2	no	—
670	C₂²	—	2	4	no	—
671	C₂²	—	2	4	no	—
672	C₂²	—	2	4	no	—
673	C₂²	—	2	4	no	—
674	C₂²	—	2	4	no	—
675	C₂²	—	4	4	no	—
676	C₂²	—	4	4	no	—
677	C₂²	#41×Dic₄₇	1	4	yes	—
678	C₂²	C₂⁴×Dic₄₇	1	1	yes	characteristic
679	C₂²	C₂×#41×D₄₇	1	1	yes	characteristic
680	C₂²	C₂×#41×D₄₇	1	2	yes	—
681	C₂²	C₂×#41×D₄₇	1	2	yes	—
682	C₂²	C₂×#41×D₄₇	1	1	yes	characteristic
683	C₄	—	2	2	no	—
684	C₄	—	2	2	no	—
685	C₄	—	2	2	no	—
686	C₄	—	2	2	no	—
687	C₄	—	2	4	no	—
688	C₄	—	2	4	no	—
689	C₄	—	2	4	no	—
690	C₄	—	47	8	no	—
691	C₄	—	94	4	no	—
692	C₄	—	94	4	no	—
693	C₄	—	94	4	no	—
694	C₄	—	188	4	no	—
695	C₄	—	188	4	no	—
696	C₄	#41×Dic₄₇	1	4	yes	—
697	C₄	#41×Dic₄₇	1	4	yes	—
698	C₂	—	2	4	no	—
699	C₂	—	4	4	no	—
700	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
701	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
702	C₂	C₂×#41×Dic₄₇	1	1	yes	characteristic
703	C₂	#529×D₄₇	1	2	yes	—
704	C₂	#20256682	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂⁴×C₄
Frattini	C₂³	C₂⁴×D₄₇
Fitting	C₂×C₄₇×#529	C₂
socle, cosocle	C₂³×C₄₇	C₂⁵
prime radical	C₂×#121×C₄₇	C₂²
hypercenter	C₂×#529	D₄₇
hypocenter	C₄₇	C₄×#529
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#529

Complements

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

N	H ≅ G/N	type
1. #125×Dic₄₇	C₂	semidirect
2. #126×Dic₄₇	C₂	semidirect
3. #124×Dic₄₇	C₂	semidirect
4. C₂²⋊Q₈×Dic₄₇	C₂	semidirect
5. #123×Dic₄₇	C₂	semidirect
7. #20245886	C₂	semidirect
8. #20245866	C₂	semidirect
9. #20245853	C₂	semidirect
10. #20245833	C₂	semidirect
11. #20245786	C₂	semidirect
12. C₄×Q₈×Dic₄₇	C₂	semidirect
13. C₄×D₄×Dic₄₇	C₂	semidirect
14. C₄×D₄×Dic₄₇	C₂	semidirect
15. #117×Dic₄₇	C₂	semidirect
16. C₂×C₄²×Dic₄₇	C₂	semidirect
72. C₄₇×#529	C₄	semidirect
142. #126×C₄₇	C₂×C₄	semidirect
143. #125×C₄₇	C₂×C₄	semidirect
144. #124×C₄₇	C₂×C₄	semidirect
145. #123×C₄₇	C₂×C₄	semidirect
146. C₂²⋊Q₈×C₄₇	C₂×C₄	semidirect
148. C₄×Q₈×C₄₇	C₂×C₄	semidirect
149. C₄×D₄×C₄₇	C₂×C₄	semidirect
150. C₄×D₄×C₄₇	C₂×C₄	semidirect
151. #117×C₄₇	C₂×C₄	semidirect
163. C₂×C₄²×C₄₇	C₂×C₄	semidirect
345. Dic₄₇	#529	direct (N × H)
370. #529	Dic₄₇	direct (N × H)
436. C₄₇	C₄×#529	semidirect
447. #126	C₂×Dic₄₇	semidirect
448. #125	C₂×Dic₄₇	semidirect
449. #124	C₂×Dic₄₇	semidirect
450. #123	C₂×Dic₄₇	semidirect
451. C₂²⋊Q₈	C₂×Dic₄₇	semidirect
454. C₄×Q₈	C₂×Dic₄₇	semidirect
457. C₄×D₄	C₂×Dic₄₇	semidirect
458. C₄×D₄	C₂×Dic₄₇	semidirect
460. #117	C₂×Dic₄₇	semidirect
505. C₂×C₄²	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
#125×Dic₄₇	2
#126×Dic₄₇	2
#124×Dic₄₇	2
C₂²⋊Q₈×Dic₄₇	2
#123×Dic₄₇	2
#121×Dic₄₇	2
#20245886	2
#20245866	2
#20245853	2
#20245833	2
#20245786	2
C₄×Q₈×Dic₄₇	2
C₄×D₄×Dic₄₇	2
#117×Dic₄₇	2
C₂×C₄²×Dic₄₇	2
C₂×C₄₇×#529	2
C₄×#529	47

Subgroups — #529×Dic47 #26374785

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #529×Dic₄₇ #26374785