Subgroups — D₄₇×#3176 #27086104

Order 12032.

2098 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#540×D₄₇	C₂	1	2	yes	maximal, complemented
2	#20254039	C₂	1	1	yes	maximal, characteristic, complemented
3	#20254038	C₂	1	1	yes	maximal, characteristic, complemented
4	#20254037	C₂	1	2	yes	maximal, complemented
5	#20254036	C₂	1	2	yes	maximal, complemented
6	#20254035	C₂	1	1	yes	maximal, characteristic, complemented
7	#20254034	C₂	1	2	yes	maximal, complemented
8	#20254033	C₂	1	2	yes	maximal, complemented
9	#20254032	C₂	1	2	yes	maximal, complemented
10	#20254031	C₂	1	2	yes	maximal, complemented
11	#499×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	#493×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
13	#490×D₄₇	C₂	1	2	yes	maximal, complemented
14	#469×D₄₇	C₂	1	2	yes	maximal, complemented
15	#466×D₄₇	C₂	1	2	yes	maximal, complemented
16	#442×D₄₇	C₂	1	2	yes	maximal, complemented
17	C₄×D₈×D₄₇	C₂	1	2	yes	maximal, complemented
18	#405×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
19	C₄₇×#3176	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×D₈×D₄₇	C₂²	1	2	yes	—
21	C₂×D₈×D₄₇	C₂²	1	2	yes	—
22	C₂×M₁₆×D₄₇	C₂²	1	1	yes	characteristic
23	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
24	#15689729	C₂²	1	2	yes	complemented
25	#15689728	C₂²	1	2	yes	complemented
26	#15689727	C₂²	1	2	yes	complemented
27	#15689726	C₂²	1	4	yes	complemented
28	#15689725	—	2	4	no	—
29	#15689724	C₂²	1	4	yes	complemented
30	#15689723	—	2	4	no	—
31	#127×D₄₇	C₂²	1	2	yes	—
32	#125×D₄₇	C₂²	1	2	yes	—
33	#123×D₄₇	—	2	4	no	—
34	#121×D₄₇	—	2	4	no	—
35	#121×D₄₇	C₂²	1	4	yes	—
36	C₄×D₄×D₄₇	C₂²	1	4	yes	—
37	#117×D₄₇	C₂²	1	1	yes	characteristic
38	#15689525	C₂²	1	1	yes	characteristic, complemented
39	#15689524	C₂²	1	2	yes	complemented
40	#15689523	C₂²	1	2	yes	complemented
41	#15689522	C₂²	1	2	yes	complemented
42	#15689500	C₂²	1	1	yes	characteristic, complemented
43	#15689499	C₂²	1	2	yes	complemented
44	#15689498	C₂²	1	2	yes	complemented
45	#15689498	C₂²	1	2	yes	complemented
46	#15689489	C₂²	1	2	yes	complemented
47	#15689488	C₂²	1	2	yes	complemented
48	#15689487	C₂²	1	2	yes	complemented
49	#15689486	C₂²	1	4	yes	complemented
50	#15689486	C₂²	1	4	yes	complemented
51	#15689377	C₂²	1	2	yes	complemented
52	#15689376	C₂²	1	2	yes	complemented
53	#15689375	C₂²	1	4	yes	complemented
54	#15689374	C₂²	1	4	yes	complemented
55	#15689373	C₂²	1	2	yes	complemented
56	#15689360	C₂²	1	2	yes	complemented
57	#15689359	C₂²	1	2	yes	complemented
58	#15689358	C₂²	1	4	yes	complemented
59	#15689357	C₂²	1	4	yes	complemented
60	#15689356	C₂²	1	2	yes	complemented
61	#15689236	C₂²	1	2	yes	complemented
62	#15689235	C₂²	1	2	yes	complemented
63	#15689234	C₂²	1	2	yes	complemented
64	#15689233	C₂²	1	4	yes	complemented
65	#15689232	C₂²	1	4	yes	complemented
66	C₄×D₃₇₆	C₂²	1	2	yes	complemented
67	D₈×Dic₄₇	C₂²	1	2	yes	complemented
68	#15689205	C₂²	1	2	yes	complemented
69	C₄×#10625334	C₂²	1	4	yes	complemented
70	#15689203	C₂²	1	4	yes	complemented
71	#107×D₄₇	C₂²	1	2	yes	—
72	#106×D₄₇	C₂²	1	2	yes	—
73	#102×D₄₇	C₂²	1	4	yes	—
74	#102×D₄₇	C₂²	1	4	yes	—
75	#15689081	C₂²	1	1	yes	characteristic, complemented
76	#15689080	C₂²	1	1	yes	characteristic, complemented
77	#15689080	C₂²	1	1	yes	characteristic, complemented
78	#15689079	C₂²	1	1	yes	characteristic, complemented
79	#15689078	C₂²	1	1	yes	characteristic, complemented
80	#15689077	C₂²	1	1	yes	characteristic, complemented
81	#15689077	C₂²	1	1	yes	characteristic, complemented
82	#97×D₄₇	C₂²	1	1	yes	characteristic
83	#97×D₄₇	C₂²	1	1	yes	characteristic
84	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
85	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
86	C₄₇×#540	C₂²	1	2	yes	complemented
87	C₄₇×#499	C₂²	1	1	yes	characteristic, complemented
88	C₄₇×#493	C₂²	1	1	yes	characteristic, complemented
89	C₄₇×#490	C₂²	1	2	yes	complemented
90	C₄₇×#469	C₂²	1	2	yes	complemented
91	C₄₇×#466	C₂²	1	2	yes	complemented
92	C₄₇×#442	C₂²	1	2	yes	complemented
93	C₄×D₈×C₄₇	C₂²	1	2	yes	complemented
94	C₄₇×#405	C₂²	1	1	yes	characteristic, complemented
95	C₂×D₄×D₄₇	—	2	4	no	—
96	C₂×D₄×D₄₇	—	2	4	no	—
97	C₂×D₄×D₄₇	C₂³	1	4	yes	—
98	C₂²×C₄×D₄₇	—	2	4	no	—
99	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
100	C₂×D₃₇₆	C₂³	1	2	yes	—
101	C₂×D₃₇₆	C₂³	1	2	yes	—
102	C₂×#10625334	C₂³	1	4	yes	—
103	C₂×#10625334	C₂³	1	4	yes	—
104	D₈×D₄₇	—	2	8	no	—
105	D₈×D₄₇	—	2	8	no	—
106	C₂×#10625329	C₂³	1	1	yes	characteristic
107	C₂×#10625324	C₂³	1	1	yes	characteristic
108	C₂×#10625324	C₂³	1	1	yes	characteristic
109	M₁₆×D₄₇	—	2	4	no	—
110	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
111	C₂×C₈×D₄₇	—	2	4	no	—
112	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
113	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
114	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
115	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
116	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
117	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
118	#13094021	C₂³	1	2	yes	—
119	#13094020	—	2	4	no	—
120	#13094020	C₂³	1	4	yes	—
121	#13094016	C₂³	1	2	yes	—
122	#13094015	C₂³	1	4	yes	—
123	#13094014	—	2	4	no	—
124	#13094009	—	2	4	no	—
125	#13094009	—	2	4	no	—
126	#13094008	—	2	4	no	—
127	#13094007	—	2	4	no	—
128	#13094006	—	2	4	no	—
129	#13094006	—	2	4	no	—
130	#13094005	—	2	4	no	—
131	#13093999	—	2	4	no	—
132	#13093999	C₂³	1	4	yes	—
133	#13093998	—	2	4	no	—
134	#13093998	C₂³	1	4	yes	—
135	#13093997	—	2	4	no	—
136	#13093997	—	2	4	no	—
137	#13093997	—	2	4	no	—
138	#13093996	—	2	4	no	—
139	#13093996	—	2	4	no	—
140	#13093996	—	2	4	no	—
141	#13093995	—	2	4	no	—
142	#13093995	C₂³	1	4	yes	—
143	C₄×D₁₈₈	C₂³	1	4	yes	—
144	D₄×Dic₄₇	C₂³	1	4	yes	—
145	#13093986	C₂³	1	4	yes	—
146	C₄×C₂²⋊D₄₇	—	2	4	no	—
147	(C₂²⋊D₄₇)⋊C₄	—	2	4	no	—
148	#13093983	C₂³	1	1	yes	characteristic
149	#13093982	D₄	1	2	yes	—
150	#13093981	C₂³	1	1	yes	characteristic
151	#13093981	C₂³	1	1	yes	characteristic
152	#13093980	D₄	1	2	yes	—
153	C₄⋊C₄×D₄₇	—	2	4	no	—
154	C₄⋊C₄×D₄₇	D₄	1	2	yes	—
155	C₄⋊C₄×D₄₇	C₂³	1	4	yes	—
156	C₂²⋊C₄×D₄₇	—	2	4	no	—
157	C₂²⋊C₄×D₄₇	—	2	4	no	—
158	C₂²⋊C₄×D₄₇	D₄	1	2	yes	—
159	C₄²×D₄₇	C₂³	1	1	yes	characteristic
160	C₄²×D₄₇	C₂³	1	1	yes	characteristic
161	#13093958	C₂³	1	2	yes	—
162	#13093957	C₂³	1	4	yes	—
163	#13093956	C₂³	1	2	yes	—
164	#13093955	C₂³	1	4	yes	—
165	#13093946	C₂³	1	4	yes	—
166	#13093946	C₂³	1	4	yes	—
167	#13093945	C₂³	1	4	yes	—
168	#13093945	C₂³	1	4	yes	—
169	#13093944	C₂³	1	4	yes	—
170	#13093944	C₂³	1	4	yes	—
171	#13093935	C₂³	1	1	yes	characteristic
172	#13093935	C₂³	1	1	yes	characteristic
173	#13093934	C₂³	1	1	yes	characteristic
174	#13093934	C₂³	1	1	yes	characteristic
175	#13093934	C₂³	1	1	yes	characteristic
176	#13093934	C₂³	1	1	yes	characteristic
177	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
178	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
179	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
180	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
181	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
182	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
183	C₂×D₈×C₄₇	C₂³	1	2	yes	—
184	C₂×D₈×C₄₇	C₂³	1	2	yes	—
185	C₂×M₁₆×C₄₇	C₂³	1	1	yes	characteristic
186	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
187	#127×C₄₇	C₂³	1	2	yes	—
188	#125×C₄₇	C₂³	1	2	yes	—
189	#123×C₄₇	—	2	4	no	—
190	#121×C₄₇	—	2	4	no	—
191	#121×C₄₇	C₂³	1	4	yes	—
192	C₄×D₄×C₄₇	C₂³	1	4	yes	—
193	#117×C₄₇	C₂³	1	1	yes	characteristic
194	#107×C₄₇	C₂³	1	2	yes	—
195	#106×C₄₇	C₂³	1	2	yes	—
196	#102×C₄₇	C₂³	1	4	yes	—
197	#102×C₄₇	C₂³	1	4	yes	—
198	#97×C₄₇	C₂³	1	1	yes	characteristic
199	#97×C₄₇	C₂³	1	1	yes	characteristic
200	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
201	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
202	C₂³×D₄₇	—	2	4	no	—
203	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
204	C₂×D₄×C₄₇	—	2	4	no	—
205	C₂×D₄×C₄₇	—	2	4	no	—
206	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
207	C₂²×C₄×C₄₇	—	2	4	no	—
208	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
209	C₂×C₂²⋊D₄₇	—	2	4	no	—
210	C₂×C₂²⋊D₄₇	—	2	4	no	—
211	C₂×C₂²⋊D₄₇	—	2	4	no	—
212	C₂×C₂²⋊D₄₇	—	2	4	no	—
213	C₂×C₂²⋊D₄₇	—	2	4	no	—
214	C₂²×Dic₄₇	—	2	4	no	—
215	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
216	D₄×D₄₇	—	2	8	no	—
217	D₄×D₄₇	—	2	8	no	—
218	D₄×D₄₇	—	8	8	no	—
219	D₄×D₄₇	—	8	8	no	—
220	C₂×D₁₈₈	—	2	4	no	—
221	C₂×D₁₈₈	—	2	4	no	—
222	C₂×D₁₈₈	C₂⁴	1	4	yes	—
223	C₂×C₄×D₄₇	—	2	2	no	—
224	C₂×C₄×D₄₇	—	2	2	no	—
225	C₂×C₄×D₄₇	—	2	4	no	—
226	C₂×C₄×D₄₇	—	2	4	no	—
227	C₂×C₄×D₄₇	—	2	4	no	—
228	C₂×C₄×D₄₇	—	8	8	no	—
229	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
230	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
231	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
232	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
233	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
234	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
235	D₈×C₄₇	—	2	4	no	—
236	D₈×C₄₇	—	2	4	no	—
237	M₁₆×C₄₇	—	2	2	no	—
238	C₂×C₈×C₄₇	—	2	2	no	—
239	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
240	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
241	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
242	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
243	C₄⋊C₄×C₄₇	—	2	4	no	—
244	C₄⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
245	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
246	C₂²⋊C₄×C₄₇	—	2	4	no	—
247	C₂²⋊C₄×C₄₇	—	2	4	no	—
248	C₂²⋊C₄×C₄₇	C₂×D₄	1	2	yes	—
249	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
250	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
251	C₂²⋊Dic₄₇	—	2	4	no	—
252	C₂²⋊Dic₄₇	—	2	4	no	—
253	C₂²⋊Dic₄₇	C₂×D₄	1	2	yes	—
254	#10625334	—	2	8	no	—
255	#10625334	—	2	8	no	—
256	(C₂×D₄₇)⋊C₄	—	2	4	no	—
257	(C₂×D₄₇)⋊C₄	—	2	4	no	—
258	(C₂×D₄₇)⋊C₄	—	2	4	no	—
259	(C₂×D₄₇)⋊C₄	—	2	4	no	—
260	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
261	(C₂×D₄₇)⋊C₄	C₂×D₄	1	2	yes	—
262	C₄⋊Dic₄₇	—	2	4	no	—
263	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
264	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
265	Dic₄₇⋊C₄	—	2	4	no	—
266	Dic₄₇⋊C₄	—	2	4	no	—
267	Dic₄₇⋊C₄	—	2	4	no	—
268	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
269	Dic₄₇⋊C₄	C₂×D₄	1	2	yes	—
270	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
271	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
272	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
273	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
274	#10625329	—	2	2	no	—
275	C₂×C₄₇⋊C₈	—	2	2	no	—
276	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
277	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
278	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
279	C₂×C₄₇⋊C₈	C₂⁴	1	1	yes	characteristic
280	D₃₇₆	—	2	4	no	—
281	D₃₇₆	—	2	4	no	—
282	#10625324	—	2	2	no	—
283	#10625324	—	2	2	no	—
284	C₈×D₄₇	—	2	2	no	—
285	C₈×D₄₇	—	2	2	no	—
286	C₈×D₄₇	—	2	2	no	—
287	C₈×D₄₇	—	2	2	no	—
288	C₈×D₄₇	#41	1	4	yes	—
289	C₈×D₄₇	#41	1	4	yes	—
290	C₂³×C₄₇	—	2	4	no	—
291	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
292	C₂²×D₄₇	—	2	2	no	—
293	C₂²×D₄₇	—	2	4	no	—
294	C₂²×D₄₇	—	2	4	no	—
295	C₂²×D₄₇	—	4	8	no	—
296	C₂²×D₄₇	—	4	8	no	—
297	C₂²×D₄₇	—	4	8	no	—
298	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
299	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
300	D₄×C₄₇	—	2	4	no	—
301	D₄×C₄₇	—	2	4	no	—
302	D₄×C₄₇	—	8	4	no	—
303	D₄×C₄₇	—	8	4	no	—
304	C₂×C₄×C₄₇	—	2	1	no	—
305	C₂×C₄×C₄₇	—	2	1	no	—
306	C₂×C₄×C₄₇	—	2	4	no	—
307	C₂×C₄×C₄₇	—	8	4	no	—
308	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
309	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
310	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
311	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
312	C₂²⋊D₄₇	—	4	8	no	—
313	C₂²⋊D₄₇	—	8	4	no	—
314	C₂²⋊D₄₇	—	8	4	no	—
315	C₂²⋊D₄₇	—	8	4	no	—
316	C₂²⋊D₄₇	—	8	4	no	—
317	C₂×Dic₄₇	—	2	2	no	—
318	C₂×Dic₄₇	—	2	4	no	—
319	C₂×Dic₄₇	—	8	4	no	—
320	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
321	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
322	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
323	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
324	D₁₈₈	—	2	4	no	—
325	D₁₈₈	—	2	4	no	—
326	D₁₈₈	—	8	4	no	—
327	D₁₈₈	—	8	4	no	—
328	C₄×D₄₇	—	2	2	no	—
329	C₄×D₄₇	—	2	4	no	—
330	C₄×D₄₇	—	2	4	no	—
331	C₄×D₄₇	—	2	1	no	—
332	C₄×D₄₇	—	2	1	no	—
333	C₄×D₄₇	—	2	2	no	—
334	C₄×D₄₇	—	4	8	no	—
335	C₄×D₄₇	—	8	4	no	—
336	C₄×D₄₇	—	8	4	no	—
337	C₄×D₄₇	C₂×#41	1	2	yes	—
338	C₄×D₄₇	C₂×#41	1	2	yes	—
339	C₈×C₄₇	—	2	1	no	—
340	C₈×C₄₇	—	2	1	no	—
341	C₈×C₄₇	C₂×#41	1	2	yes	—
342	C₈×C₄₇	C₂×#41	1	2	yes	—
343	C₄₇⋊C₈	—	2	1	no	—
344	C₄₇⋊C₈	—	2	1	no	—
345	C₄₇⋊C₈	C₂×#41	1	2	yes	—
346	C₄₇⋊C₈	C₂×#41	1	2	yes	—
347	C₂×#3176	—	47	1	no	maximal, Sylow
348	C₂²×C₄₇	—	2	1	no	—
349	C₂²×C₄₇	—	2	2	no	—
350	C₂²×C₄₇	—	4	4	no	—
351	C₂²×C₄₇	—	4	4	no	—
352	C₂²×C₄₇	—	4	4	no	—
353	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
354	C₂×D₄₇	—	2	1	no	—
355	C₂×D₄₇	—	2	2	no	—
356	C₂×D₄₇	—	4	4	no	—
357	C₂×D₄₇	—	4	4	no	—
358	C₂×D₄₇	—	4	4	no	—
359	C₂×D₄₇	—	4	4	no	—
360	C₂×D₄₇	—	8	16	no	—
361	C₂×D₄₇	#532	1	2	yes	—
362	C₂×D₄₇	#576	1	4	yes	—
363	C₄×C₄₇	—	2	1	no	—
364	C₄×C₄₇	—	2	2	no	—
365	C₄×C₄₇	—	2	2	no	—
366	C₄×C₄₇	—	4	4	no	—
367	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
368	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
369	Dic₄₇	—	2	1	no	—
370	Dic₄₇	—	2	2	no	—
371	Dic₄₇	—	2	2	no	—
372	Dic₄₇	—	4	4	no	—
373	Dic₄₇	#532	1	2	yes	—
374	C₂×#540	—	47	2	no	—
375	#3176	—	47	1	no	—
376	#3176	—	47	1	no	—
377	#3176	—	47	2	no	—
378	#3176	—	47	2	no	—
379	#3176	—	47	2	no	—
380	#3176	—	47	2	no	—
381	#3176	—	47	2	no	—
382	#3176	—	47	1	no	—
383	#3176	—	47	2	no	—
384	#3176	D₄₇	1	1	yes	characteristic, direct product factor
385	C₂×#499	—	47	1	no	—
386	C₂×#493	—	47	1	no	—
387	C₂×#490	—	47	2	no	—
388	C₂×#469	—	47	2	no	—
389	C₂×#466	—	47	2	no	—
390	C₂×#442	—	47	2	no	—
391	C₂×C₄×D₈	—	47	2	no	—
392	C₂×#405	—	47	1	no	—
393	C₂×C₄₇	—	4	1	no	—
394	C₂×C₄₇	—	8	4	no	—
395	C₂×C₄₇	C₂×#532	1	1	yes	characteristic
396	C₂×C₄₇	C₂×#576	1	2	yes	—
397	D₄₇	—	4	1	no	—
398	D₄₇	—	8	4	no	—
399	D₄₇	#3176	1	4	yes	direct product factor
400	C₂²×D₈	—	47	2	no	—
401	C₂²×D₈	—	47	2	no	—
402	C₂²×M₁₆	—	47	1	no	—
403	C₂³×C₈	—	47	1	no	—
404	#540	—	47	2	no	—
405	#540	—	47	2	no	—
406	#540	—	47	4	no	—
407	#540	—	47	4	no	—
408	#540	—	47	2	no	—
409	#540	—	94	4	no	—
410	#540	—	94	4	no	—
411	#540	C₂×D₄₇	1	2	yes	complemented
412	C₂×#127	—	47	2	no	—
413	C₂×#125	—	47	2	no	—
414	C₂×#123	—	94	4	no	—
415	C₂×#121	—	47	4	no	—
416	C₂×#121	—	94	4	no	—
417	C₂×C₄×D₄	—	47	4	no	—
418	C₂×#117	—	47	1	no	—
419	#499	—	47	2	no	—
420	#499	—	47	2	no	—
421	#499	—	47	2	no	—
422	#499	—	47	1	no	—
423	#499	C₂×D₄₇	1	1	yes	characteristic, complemented
424	#493	—	47	2	no	—
425	#493	—	47	2	no	—
426	#493	—	47	2	no	—
427	#493	—	47	1	no	—
428	#493	C₂×D₄₇	1	1	yes	characteristic, complemented
429	#490	—	47	2	no	—
430	#490	—	47	2	no	—
431	#490	—	47	4	no	—
432	#490	—	47	4	no	—
433	#490	—	47	2	no	—
434	#490	C₂×D₄₇	1	2	yes	complemented
435	#469	—	47	2	no	—
436	#469	—	47	2	no	—
437	#469	—	47	4	no	—
438	#469	—	47	2	no	—
439	#469	—	47	4	no	—
440	#469	C₂×D₄₇	1	2	yes	complemented
441	#466	—	47	2	no	—
442	#466	—	47	2	no	—
443	#466	—	47	4	no	—
444	#466	—	47	2	no	—
445	#466	—	47	4	no	—
446	#466	C₂×D₄₇	1	2	yes	complemented
447	#442	—	47	2	no	—
448	#442	—	47	4	no	—
449	#442	—	47	2	no	—
450	#442	—	47	4	no	—
451	#442	—	47	2	no	—
452	#442	C₂×D₄₇	1	2	yes	complemented
453	C₄×D₈	—	47	2	no	—
454	C₄×D₈	—	47	4	no	—
455	C₄×D₈	—	47	2	no	—
456	C₄×D₈	—	47	4	no	—
457	C₄×D₈	—	47	2	no	—
458	C₄×D₈	C₂×D₄₇	1	2	yes	complemented
459	C₂×#107	—	47	2	no	—
460	C₂×#106	—	47	2	no	—
461	C₂×#102	—	47	4	no	—
462	C₂×#102	—	47	4	no	—
463	#405	—	47	1	no	—
464	#405	—	47	1	no	—
465	#405	—	47	1	no	—
466	#405	—	47	1	no	—
467	#405	—	47	1	no	—
468	#405	—	47	1	no	—
469	#405	—	47	1	no	—
470	#405	C₂×D₄₇	1	1	yes	characteristic, complemented
471	C₂×#97	—	47	1	no	—
472	C₂×#97	—	47	1	no	—
473	C₂×C₄×C₈	—	47	1	no	—
474	C₂×C₄×C₈	—	47	1	no	—
475	C₄₇	C₂×#3176	1	1	yes	characteristic, complemented, Sylow
476	C₂²×D₄	—	47	4	no	—
477	C₂²×D₄	—	94	4	no	—
478	C₂²×D₄	—	94	4	no	—
479	C₂³×C₄	—	47	1	no	—
480	C₂³×C₄	—	94	4	no	—
481	C₂×D₈	—	47	4	no	—
482	C₂×D₈	—	47	4	no	—
483	C₂×D₈	—	47	2	no	—
484	C₂×D₈	—	47	2	no	—
485	C₂×D₈	—	94	8	no	—
486	C₂×D₈	—	94	8	no	—
487	C₂×D₈	C₂²×D₄₇	1	2	yes	—
488	C₂×D₈	C₂²×D₄₇	1	2	yes	—
489	C₂×M₁₆	—	47	1	no	—
490	C₂×M₁₆	—	47	1	no	—
491	C₂×M₁₆	—	47	1	no	—
492	C₂×M₁₆	—	94	4	no	—
493	C₂×M₁₆	C₂²×D₄₇	1	1	yes	characteristic
494	C₂²×C₈	—	47	1	no	—
495	C₂²×C₈	—	47	1	no	—
496	C₂²×C₈	—	47	1	no	—
497	C₂²×C₈	—	47	1	no	—
498	C₂²×C₈	—	47	1	no	—
499	C₂²×C₈	—	47	1	no	—
500	C₂²×C₈	—	47	1	no	—
501	C₂²×C₈	—	94	4	no	—
502	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
503	#127	—	47	4	no	—
504	#127	—	47	2	no	—
505	#127	—	94	4	no	—
506	#127	C₂²×D₄₇	1	2	yes	—
507	#125	—	47	4	no	—
508	#125	—	47	2	no	—
509	#125	—	94	4	no	—
510	#125	C₂²×D₄₇	1	2	yes	—
511	#123	—	2	4	no	—
512	#123	—	94	4	no	—
513	#123	—	94	4	no	—
514	#123	—	94	4	no	—
515	#123	—	94	4	no	—
516	#123	—	94	4	no	—
517	#123	—	94	4	no	—
518	#123	—	94	4	no	—
519	#121	—	2	4	no	—
520	#121	—	47	4	no	—
521	#121	—	47	4	no	—
522	#121	—	47	4	no	—
523	#121	—	94	4	no	—
524	#121	—	94	4	no	—
525	#121	—	94	4	no	—
526	#121	—	94	4	no	—
527	#121	—	94	4	no	—
528	#121	—	94	4	no	—
529	#121	—	94	4	no	—
530	#121	—	94	4	no	—
531	#121	—	94	4	no	—
532	#121	C₂²×D₄₇	1	4	yes	—
533	C₄×D₄	—	47	4	no	—
534	C₄×D₄	—	47	4	no	—
535	C₄×D₄	—	47	4	no	—
536	C₄×D₄	—	94	4	no	—
537	C₄×D₄	—	94	4	no	—
538	C₄×D₄	C₂²×D₄₇	1	4	yes	—
539	#117	—	47	1	no	—
540	#117	—	47	2	no	—
541	#117	—	47	2	no	—
542	#117	—	47	1	no	—
543	#117	—	47	1	no	—
544	#117	C₂²×D₄₇	1	1	yes	characteristic
545	C₂×C₄⋊C₄	—	47	2	no	—
546	C₂×C₄⋊C₄	—	47	4	no	—
547	C₂×C₄⋊C₄	—	94	4	no	—
548	C₂×C₂²⋊C₄	—	47	2	no	—
549	C₂×C₂²⋊C₄	—	94	4	no	—
550	C₂×C₂²⋊C₄	—	94	4	no	—
551	C₂×C₄²	—	47	1	no	—
552	C₂×C₄²	—	47	1	no	—
553	#107	—	47	2	no	—
554	#107	—	47	4	no	—
555	#107	C₂²×D₄₇	1	2	yes	—
556	#106	—	47	2	no	—
557	#106	—	47	4	no	—
558	#106	C₂²×D₄₇	1	2	yes	—
559	#102	—	47	4	no	—
560	#102	—	47	4	no	—
561	#102	—	47	4	no	—
562	#102	—	47	4	no	—
563	#102	—	47	4	no	—
564	#102	—	47	4	no	—
565	#102	C₂²×D₄₇	1	4	yes	—
566	#102	C₂²×D₄₇	1	4	yes	—
567	#97	—	47	1	no	—
568	#97	—	47	1	no	—
569	#97	—	47	1	no	—
570	#97	—	47	1	no	—
571	#97	—	47	1	no	—
572	#97	—	47	1	no	—
573	#97	C₂²×D₄₇	1	1	yes	characteristic
574	#97	C₂²×D₄₇	1	1	yes	characteristic
575	C₄×C₈	—	47	1	no	—
576	C₄×C₈	—	47	1	no	—
577	C₄×C₈	—	47	1	no	—
578	C₄×C₈	—	47	1	no	—
579	C₄×C₈	—	47	1	no	—
580	C₄×C₈	—	47	1	no	—
581	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
582	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
583	C₂⁴	—	47	1	no	—
584	C₂⁴	—	94	4	no	—
585	C₂×D₄	—	2	4	no	—
586	C₂×D₄	—	2	4	no	—
587	C₂×D₄	—	47	4	no	—
588	C₂×D₄	—	94	4	no	—
589	C₂×D₄	—	94	8	no	—
590	C₂×D₄	—	94	8	no	—
591	C₂×D₄	—	94	4	no	—
592	C₂×D₄	—	94	4	no	—
593	C₂×D₄	—	94	4	no	—
594	C₂×D₄	—	94	4	no	—
595	C₂×D₄	—	94	4	no	—
596	C₂×D₄	—	94	4	no	—
597	C₂×D₄	—	376	8	no	—
598	C₂×D₄	—	376	8	no	—
599	C₂×D₄	C₂³×D₄₇	1	4	yes	—
600	C₂²×C₄	—	2	4	no	—
601	C₂²×C₄	—	47	1	no	—
602	C₂²×C₄	—	47	1	no	—
603	C₂²×C₄	—	47	2	no	—
604	C₂²×C₄	—	47	2	no	—
605	C₂²×C₄	—	47	1	no	—
606	C₂²×C₄	—	47	1	no	—
607	C₂²×C₄	—	47	1	no	—
608	C₂²×C₄	—	94	2	no	—
609	C₂²×C₄	—	94	2	no	—
610	C₂²×C₄	—	94	4	no	—
611	C₂²×C₄	—	94	4	no	—
612	C₂²×C₄	—	94	4	no	—
613	C₂²×C₄	—	94	4	no	—
614	C₂²×C₄	—	376	8	no	—
615	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
616	D₈	—	2	4	no	—
617	D₈	—	2	4	no	—
618	D₈	—	94	8	no	—
619	D₈	—	94	8	no	—
620	D₈	—	94	4	no	—
621	D₈	—	94	4	no	—
622	M₁₆	—	2	2	no	—
623	M₁₆	—	94	2	no	—
624	M₁₆	—	94	2	no	—
625	M₁₆	—	94	2	no	—
626	C₂×C₈	—	2	2	no	—
627	C₂×C₈	—	47	1	no	—
628	C₂×C₈	—	47	1	no	—
629	C₂×C₈	—	47	4	no	—
630	C₂×C₈	—	47	4	no	—
631	C₂×C₈	—	47	1	no	—
632	C₂×C₈	—	47	1	no	—
633	C₂×C₈	—	94	2	no	—
634	C₂×C₈	—	94	2	no	—
635	C₂×C₈	—	94	2	no	—
636	C₂×C₈	—	94	2	no	—
637	C₂×C₈	—	94	2	no	—
638	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
639	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
640	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
641	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
642	C₄⋊C₄	—	2	4	no	—
643	C₄⋊C₄	—	47	2	no	—
644	C₄⋊C₄	—	47	2	no	—
645	C₄⋊C₄	—	47	2	no	—
646	C₄⋊C₄	—	47	4	no	—
647	C₄⋊C₄	—	94	4	no	—
648	C₄⋊C₄	—	94	4	no	—
649	C₄⋊C₄	—	94	4	no	—
650	C₄⋊C₄	—	94	4	no	—
651	C₄⋊C₄	D₄×D₄₇	1	2	yes	—
652	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
653	C₂²⋊C₄	—	2	4	no	—
654	C₂²⋊C₄	—	2	4	no	—
655	C₂²⋊C₄	—	47	2	no	—
656	C₂²⋊C₄	—	47	2	no	—
657	C₂²⋊C₄	—	47	2	no	—
658	C₂²⋊C₄	—	94	4	no	—
659	C₂²⋊C₄	—	94	4	no	—
660	C₂²⋊C₄	—	94	4	no	—
661	C₂²⋊C₄	—	94	4	no	—
662	C₂²⋊C₄	—	94	4	no	—
663	C₂²⋊C₄	—	94	4	no	—
664	C₂²⋊C₄	D₄×D₄₇	1	2	yes	—
665	C₄²	—	47	2	no	—
666	C₄²	—	47	2	no	—
667	C₄²	—	47	1	no	—
668	C₄²	—	47	1	no	—
669	C₄²	C₂³×D₄₇	1	1	yes	characteristic
670	C₄²	C₂³×D₄₇	1	1	yes	characteristic
671	C₂³	—	2	4	no	—
672	C₂³	—	47	1	no	—
673	C₂³	—	47	1	no	—
674	C₂³	—	94	2	no	—
675	C₂³	—	94	4	no	—
676	C₂³	—	94	4	no	—
677	C₂³	—	188	8	no	—
678	C₂³	—	188	8	no	—
679	C₂³	—	188	8	no	—
680	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
681	D₄	—	2	4	no	—
682	D₄	—	2	4	no	—
683	D₄	—	8	4	no	—
684	D₄	—	8	4	no	—
685	D₄	—	94	4	no	—
686	D₄	—	94	4	no	—
687	D₄	—	376	4	no	—
688	D₄	—	376	4	no	—
689	D₄	—	376	4	no	—
690	D₄	—	376	4	no	—
691	D₄	—	376	4	no	—
692	D₄	—	376	4	no	—
693	D₄	—	188	8	no	—
694	C₂×C₄	—	2	1	no	—
695	C₂×C₄	—	2	1	no	—
696	C₂×C₄	—	2	4	no	—
697	C₂×C₄	—	8	4	no	—
698	C₂×C₄	—	47	1	no	—
699	C₂×C₄	—	47	2	no	—
700	C₂×C₄	—	47	2	no	—
701	C₂×C₄	—	47	2	no	—
702	C₂×C₄	—	47	2	no	—
703	C₂×C₄	—	47	1	no	—
704	C₂×C₄	—	94	2	no	—
705	C₂×C₄	—	94	2	no	—
706	C₂×C₄	—	94	4	no	—
707	C₂×C₄	—	94	4	no	—
708	C₂×C₄	—	94	2	no	—
709	C₂×C₄	—	94	1	no	—
710	C₂×C₄	—	94	1	no	—
711	C₂×C₄	—	94	4	no	—
712	C₂×C₄	—	376	4	no	—
713	C₂×C₄	—	376	4	no	—
714	C₂×C₄	—	376	4	no	—
715	C₂×C₄	—	188	8	no	—
716	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
717	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
718	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
719	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
720	C₈	—	2	1	no	—
721	C₈	—	2	1	no	—
722	C₈	—	47	2	no	—
723	C₈	—	47	2	no	—
724	C₈	—	94	1	no	—
725	C₈	—	94	1	no	—
726	C₈	#41×D₄₇	1	2	yes	—
727	C₈	#41×D₄₇	1	2	yes	—
728	C₂²	—	2	2	no	—
729	C₂²	—	2	1	no	—
730	C₂²	—	4	4	no	—
731	C₂²	—	4	4	no	—
732	C₂²	—	4	4	no	—
733	C₂²	—	47	4	no	—
734	C₂²	—	47	2	no	—
735	C₂²	—	94	2	no	—
736	C₂²	—	94	1	no	—
737	C₂²	—	376	16	no	—
738	C₂²	—	188	4	no	—
739	C₂²	—	188	4	no	—
740	C₂²	—	188	4	no	—
741	C₂²	—	188	4	no	—
742	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
743	C₄	—	2	2	no	—
744	C₄	—	2	2	no	—
745	C₄	—	2	1	no	—
746	C₄	—	4	4	no	—
747	C₄	—	47	2	no	—
748	C₄	—	94	2	no	—
749	C₄	—	94	2	no	—
750	C₄	—	94	1	no	—
751	C₄	—	188	4	no	—
752	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
753	C₄	C₂×#41×D₄₇	1	1	yes	characteristic
754	C₂	—	4	1	no	—
755	C₂	—	8	4	no	—
756	C₂	—	47	4	no	—
757	C₂	—	376	4	no	—
758	C₂	—	188	1	no	—
759	C₂	#532×D₄₇	1	1	yes	characteristic
760	C₂	#576×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3176	C₂
socle	C₂²×C₄₇	C₂³×D₄
hypercenter	#3176	D₄₇
hypocenter	C₄₇	C₂×#3176
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ #117 ◁ #3176

Complements

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

N	H ≅ G/N	type
1. #540×D₄₇	C₂	semidirect
2. #20254039	C₂	semidirect
3. #20254038	C₂	semidirect
4. #20254037	C₂	semidirect
5. #20254036	C₂	semidirect
6. #20254035	C₂	semidirect
7. #20254034	C₂	semidirect
8. #20254033	C₂	semidirect
9. #20254032	C₂	semidirect
10. #20254031	C₂	semidirect
11. #499×D₄₇	C₂	semidirect
12. #493×D₄₇	C₂	semidirect
13. #490×D₄₇	C₂	semidirect
14. #469×D₄₇	C₂	semidirect
15. #466×D₄₇	C₂	semidirect
16. #442×D₄₇	C₂	semidirect
17. C₄×D₈×D₄₇	C₂	semidirect
18. #405×D₄₇	C₂	semidirect
19. C₄₇×#3176	C₂	semidirect
24. #15689729	C₂²	semidirect
25. #15689728	C₂²	semidirect
26. #15689727	C₂²	semidirect
27. #15689726	C₂²	semidirect
29. #15689724	C₂²	semidirect
38. #15689525	C₂²	semidirect
39. #15689524	C₂²	semidirect
40. #15689523	C₂²	semidirect
41. #15689522	C₂²	semidirect
42. #15689500	C₂²	semidirect
43. #15689499	C₂²	semidirect
44. #15689498	C₂²	semidirect
45. #15689498	C₂²	semidirect
46. #15689489	C₂²	semidirect
47. #15689488	C₂²	semidirect
48. #15689487	C₂²	semidirect
49. #15689486	C₂²	semidirect
50. #15689486	C₂²	semidirect
51. #15689377	C₂²	semidirect
52. #15689376	C₂²	semidirect
53. #15689375	C₂²	semidirect
54. #15689374	C₂²	semidirect
55. #15689373	C₂²	semidirect
56. #15689360	C₂²	semidirect
57. #15689359	C₂²	semidirect
58. #15689358	C₂²	semidirect
59. #15689357	C₂²	semidirect
60. #15689356	C₂²	semidirect
61. #15689236	C₂²	semidirect
62. #15689235	C₂²	semidirect
63. #15689234	C₂²	semidirect
64. #15689233	C₂²	semidirect
65. #15689232	C₂²	semidirect
66. C₄×D₃₇₆	C₂²	semidirect
67. D₈×Dic₄₇	C₂²	semidirect
68. #15689205	C₂²	semidirect
69. C₄×#10625334	C₂²	semidirect
70. #15689203	C₂²	semidirect
75. #15689081	C₂²	semidirect
76. #15689080	C₂²	semidirect
77. #15689080	C₂²	semidirect
78. #15689079	C₂²	semidirect
79. #15689078	C₂²	semidirect
80. #15689077	C₂²	semidirect
81. #15689077	C₂²	semidirect
86. C₄₇×#540	C₂²	semidirect
87. C₄₇×#499	C₂²	semidirect
88. C₄₇×#493	C₂²	semidirect
89. C₄₇×#490	C₂²	semidirect
90. C₄₇×#469	C₂²	semidirect
91. C₄₇×#466	C₂²	semidirect
92. C₄₇×#442	C₂²	semidirect
93. C₄×D₈×C₄₇	C₂²	semidirect
94. C₄₇×#405	C₂²	semidirect
384. #3176	D₄₇	direct (N × H)
399. D₄₇	#3176	direct (N × H)
411. #540	C₂×D₄₇	semidirect
423. #499	C₂×D₄₇	semidirect
428. #493	C₂×D₄₇	semidirect
434. #490	C₂×D₄₇	semidirect
440. #469	C₂×D₄₇	semidirect
446. #466	C₂×D₄₇	semidirect
452. #442	C₂×D₄₇	semidirect
458. C₄×D₈	C₂×D₄₇	semidirect
470. #405	C₂×D₄₇	semidirect
475. C₄₇	C₂×#3176	semidirect

Maximal subgroups

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

subgroup	index
#540×D₄₇	2
#20254039	2
#20254038	2
#20254037	2
#20254036	2
#20254035	2
#20254034	2
#20254033	2
#20254032	2
#20254031	2
#499×D₄₇	2
#493×D₄₇	2
#490×D₄₇	2
#469×D₄₇	2
#466×D₄₇	2
#442×D₄₇	2
C₄×D₈×D₄₇	2
#405×D₄₇	2
C₄₇×#3176	2
C₂×#3176	47

Subgroups — D47×#3176 #27086104

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#3176 #27086104