Subgroups — D₄₇×#3160 #27085877

Order 12032.

1942 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#533×D₄₇	C₂	1	2	yes	maximal
2	#20253902	C₂	1	1	yes	maximal, characteristic, complemented
3	#20253901	C₂	1	4	yes	maximal, complemented
4	#20253900	C₂	1	4	yes	maximal, complemented
5	#20253899	C₂	1	2	yes	maximal, complemented
6	#20253898	C₂	1	2	yes	maximal, complemented
7	#20253897	C₂	1	2	yes	maximal, complemented
8	#500×D₄₇	C₂	1	2	yes	maximal, complemented
9	#499×D₄₇	C₂	1	4	yes	maximal, complemented
10	#498×D₄₇	C₂	1	2	yes	maximal, complemented
11	#427×D₄₇	C₂	1	4	yes	maximal
12	C₂×C₄×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
13	C₄₇×#3160	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
15	#15689680	C₂²	1	2	yes	—
16	#15689679	C₂²	1	4	yes	—
17	#15689678	C₂²	1	4	yes	—
18	#15689677	—	2	4	no	—
19	#15689676	C₂²	1	4	yes	—
20	#15689675	—	2	4	no	—
21	C₄⋊Q₈×D₄₇	C₂²	1	4	yes	—
22	#125×D₄₇	C₂²	1	4	yes	—
23	C₂²⋊Q₈×D₄₇	—	2	4	no	—
24	C₄×Q₈×D₄₇	—	2	4	no	—
25	#117×D₄₇	C₂²	1	4	yes	—
26	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
27	#15689528	C₂²	1	2	yes	complemented
28	#15689527	C₂²	1	8	yes	complemented
29	#15689526	C₂²	1	4	yes	complemented
30	#15689525	C₂²	1	4	yes	complemented
31	#15689524	C₂²	1	8	yes	complemented
32	#15689523	C₂²	1	8	yes	complemented
33	#15689522	C₂²	1	8	yes	complemented
34	#15689521	C₂²	1	2	yes	complemented
35	#15689520	C₂²	1	8	yes	complemented
36	#15689519	C₂²	1	4	yes	complemented
37	#15689161	C₂²	1	4	yes	—
38	#15689160	C₂²	1	8	yes	—
39	#15689159	C₂²	1	8	yes	—
40	#15689158	C₂²	1	8	yes	—
41	#107×D₄₇	C₂²	1	8	yes	—
42	#106×D₄₇	C₂²	1	8	yes	—
43	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
44	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
45	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
46	C₄×C₈×D₄₇	C₂²	1	2	yes	—
47	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
48	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
49	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
50	C₄×C₈×D₄₇	C₂²	1	2	yes	—
51	C₄₇×#533	C₂²	1	2	yes	—
52	C₄₇×#500	C₂²	1	2	yes	complemented
53	C₄₇×#499	C₂²	1	4	yes	complemented
54	C₄₇×#498	C₂²	1	2	yes	complemented
55	C₄₇×#427	C₂²	1	4	yes	—
56	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
57	C₂×Q₈×D₄₇	—	2	4	no	—
58	C₂²×C₄×D₄₇	D₄	1	2	yes	—
59	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
60	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
61	C₂×C₈×D₄₇	Q₈	1	16	yes	complemented
62	C₂×C₈×D₄₇	C₂³	1	2	yes	—
63	C₂×C₈×D₄₇	C₂³	1	2	yes	—
64	C₂×C₈×D₄₇	C₂³	1	2	yes	—
65	C₂×C₈×D₄₇	C₂³	1	2	yes	—
66	#13094024	C₂³	1	4	yes	—
67	#13094023	—	2	4	no	—
68	#13094023	C₂³	1	8	yes	—
69	#13094022	—	2	4	no	—
70	#13094016	C₂³	1	4	yes	—
71	#13094015	C₂³	1	8	yes	—
72	#13094014	—	2	8	no	—
73	#13094004	—	2	4	no	—
74	#13094003	—	2	4	no	—
75	#13094002	—	2	8	no	—
76	#13094001	—	2	8	no	—
77	#13094000	—	2	4	no	—
78	Q₈×Dic₄₇	—	2	4	no	—
79	C₄×Dic₉₄	—	2	4	no	—
80	C₄×Dic₉₄	—	2	8	no	—
81	#13093989	—	2	4	no	—
82	#13093989	—	2	8	no	—
83	#13093983	C₂³	1	4	yes	—
84	#13093982	C₂³	1	8	yes	—
85	#13093981	—	2	4	no	—
86	#13093980	—	2	4	no	—
87	C₄⋊C₄×D₄₇	—	2	8	no	—
88	C₄⋊C₄×D₄₇	—	2	4	no	—
89	C₄⋊C₄×D₄₇	C₂³	1	8	yes	—
90	C₂²⋊C₄×D₄₇	—	2	4	no	—
91	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
92	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
93	C₄²×D₄₇	—	2	4	no	—
94	C₄²×D₄₇	D₄	1	2	yes	—
95	C₄²×D₄₇	D₄	1	2	yes	—
96	C₄²×D₄₇	C₂³	1	1	yes	characteristic
97	C₄²×D₄₇	C₂³	1	1	yes	characteristic
98	C₄²×D₄₇	C₂³	1	1	yes	characteristic
99	C₄²×D₄₇	C₂³	1	1	yes	characteristic
100	#13093958	C₂³	1	8	yes	—
101	#13093957	C₂³	1	16	yes	—
102	#13093956	C₂³	1	8	yes	—
103	#13093955	C₂³	1	16	yes	—
104	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
105	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
106	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
107	C₈×Dic₄₇	C₂³	1	2	yes	—
108	C₈×Dic₄₇	C₂³	1	2	yes	—
109	C₈×Dic₄₇	C₂³	1	2	yes	—
110	C₈×Dic₄₇	C₂³	1	2	yes	—
111	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
112	C₄⋊Q₈×C₄₇	C₂³	1	4	yes	—
113	#125×C₄₇	C₂³	1	4	yes	—
114	C₂²⋊Q₈×C₄₇	—	2	4	no	—
115	C₄×Q₈×C₄₇	—	2	4	no	—
116	#117×C₄₇	C₂³	1	4	yes	—
117	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
118	#107×C₄₇	C₂³	1	8	yes	—
119	#106×C₄₇	C₂³	1	8	yes	—
120	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
121	C₄×C₈×C₄₇	C₂³	1	2	yes	—
122	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
123	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
124	C₂×Q₈×C₄₇	—	2	4	no	—
125	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
126	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
127	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
128	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
129	Q₈×D₄₇	—	4	16	no	—
130	C₂×C₄×D₄₇	—	2	8	no	—
131	C₂×C₄×D₄₇	—	2	8	no	—
132	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
133	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
134	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
135	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
136	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
137	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
138	C₂×C₄×D₄₇	C₂×Q₈	1	8	yes	—
139	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
140	C₂×C₄×D₄₇	C₂⁴	1	1	yes	characteristic
141	C₂×Dic₉₄	—	2	4	no	—
142	C₂×Dic₉₄	—	2	8	no	—
143	C₂×C₈×C₄₇	C₂×Q₈	1	8	yes	complemented
144	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
145	C₂×C₈×C₄₇	C₂⁴	1	2	yes	—
146	C₄⋊C₄×C₄₇	—	2	8	no	—
147	C₄⋊C₄×C₄₇	—	2	4	no	—
148	C₄⋊C₄×C₄₇	C₂⁴	1	8	yes	—
149	C₂²⋊C₄×C₄₇	—	2	4	no	—
150	C₄²×C₄₇	—	2	4	no	—
151	C₄²×C₄₇	C₂×D₄	1	2	yes	—
152	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
153	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
154	C₂²⋊Dic₄₇	—	2	4	no	—
155	(C₂×D₄₇)⋊C₄	—	2	8	no	—
156	C₄⋊Dic₄₇	—	2	4	no	—
157	C₄⋊Dic₄₇	—	2	8	no	—
158	C₄⋊Dic₄₇	C₂⁴	1	8	yes	—
159	Dic₄₇⋊C₄	—	2	8	no	—
160	Dic₄₇⋊C₄	—	2	8	no	—
161	Dic₄₇⋊C₄	—	2	8	no	—
162	Dic₄₇⋊C₄	—	2	8	no	—
163	C₄×Dic₄₇	—	2	4	no	—
164	C₄×Dic₄₇	—	2	8	no	—
165	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
166	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
167	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
168	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
169	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
170	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
171	C₄×Dic₄₇	C₂⁴	1	1	yes	characteristic
172	C₂×C₄₇⋊C₈	C₂×Q₈	1	8	yes	complemented
173	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
174	C₂×C₄₇⋊C₈	C₂⁴	1	2	yes	—
175	C₈×D₄₇	C₂×Q₈	1	8	yes	—
176	C₈×D₄₇	C₂×Q₈	1	8	yes	—
177	C₈×D₄₇	C₂×Q₈	1	8	yes	complemented
178	C₈×D₄₇	C₂×Q₈	1	8	yes	complemented
179	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
180	C₂²×D₄₇	—	2	4	no	—
181	C₂²×D₄₇	C₄⋊Q₈	1	4	yes	—
182	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
183	C₂²×D₄₇	C₂²×D₄	1	1	yes	characteristic
184	Q₈×C₄₇	—	4	8	no	—
185	C₂×C₄×C₄₇	—	2	4	no	—
186	C₂×C₄×C₄₇	—	2	8	no	—
187	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
188	C₂×C₄×C₄₇	C₂²×D₄	1	2	yes	—
189	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₂²×Q₈	1	4	yes	—
191	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
192	C₂×Dic₄₇	—	2	4	no	—
193	C₂×Dic₄₇	—	2	8	no	—
194	C₂×Dic₄₇	C₄⋊Q₈	1	4	yes	—
195	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
196	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
197	C₂×Dic₄₇	C₂²×D₄	1	1	yes	characteristic
198	C₂×Dic₄₇	C₂²×D₄	1	2	yes	—
199	C₄×D₄₇	—	2	4	no	—
200	C₄×D₄₇	—	2	4	no	—
201	C₄×D₄₇	—	2	4	no	—
202	C₄×D₄₇	—	4	16	no	—
203	C₄×D₄₇	C₄⋊Q₈	1	4	yes	—
204	C₄×D₄₇	C₄⋊Q₈	1	4	yes	—
205	C₄×D₄₇	#135	1	8	yes	—
206	C₄×D₄₇	C₂²×Q₈	1	4	yes	—
207	C₄×D₄₇	C₂²×Q₈	1	4	yes	—
208	Dic₉₄	—	4	8	no	—
209	Dic₉₄	—	4	16	no	—
210	C₈×C₄₇	C₂²×Q₈	1	4	yes	—
211	C₈×C₄₇	C₂²×Q₈	1	4	yes	—
212	C₄₇⋊C₈	C₂²×Q₈	1	4	yes	—
213	C₄₇⋊C₈	C₂²×Q₈	1	4	yes	—
214	C₂×#3160	—	47	1	no	maximal, Sylow
215	C₂²×C₄₇	—	2	2	no	—
216	C₂²×C₄₇	C₂×C₄⋊Q₈	1	2	yes	—
217	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
218	C₂×D₄₇	—	2	2	no	—
219	C₂×D₄₇	—	2	8	no	—
220	C₂×D₄₇	C₂×C₄⋊Q₈	1	2	yes	—
221	C₂×D₄₇	C₂×C₄⋊Q₈	1	2	yes	—
222	C₂×D₄₇	C₂×#135	1	4	yes	—
223	C₄×C₄₇	—	2	2	no	—
224	C₄×C₄₇	—	4	8	no	—
225	C₄×C₄₇	C₂×C₄⋊Q₈	1	2	yes	—
226	C₄×C₄₇	C₂×#135	1	4	yes	—
227	C₄×C₄₇	C₂³×Q₈	1	2	yes	—
228	Dic₄₇	—	2	2	no	—
229	Dic₄₇	—	4	8	no	—
230	Dic₄₇	C₂×C₄⋊Q₈	1	2	yes	—
231	Dic₄₇	C₂×C₄⋊Q₈	1	2	yes	—
232	Dic₄₇	C₂×#135	1	4	yes	—
233	C₂×#533	—	47	2	no	—
234	#3160	—	47	2	no	—
235	#3160	—	47	4	no	—
236	#3160	—	47	2	no	—
237	#3160	—	47	4	no	—
238	#3160	—	47	1	no	—
239	#3160	—	47	2	no	—
240	#3160	D₄₇	1	1	yes	characteristic, direct product factor
241	C₂×#500	—	47	2	no	—
242	C₂×#499	—	47	4	no	—
243	C₂×#498	—	47	2	no	—
244	C₂×#427	—	47	4	no	—
245	C₂²×C₄×C₈	—	47	1	no	—
246	C₂×C₄₇	—	2	2	no	—
247	C₂×C₄₇	C₂²×C₄⋊Q₈	1	1	yes	characteristic
248	C₂×C₄₇	C₂²×#135	1	2	yes	—
249	D₄₇	—	2	2	no	—
250	D₄₇	#3160	1	4	yes	direct product factor
251	C₂³×C₈	—	47	2	no	—
252	#533	—	47	4	no	—
253	#533	—	47	4	no	—
254	#533	—	47	4	no	—
255	#533	—	47	2	no	—
256	#533	—	94	4	no	—
257	#533	—	94	4	no	—
258	#533	C₂×D₄₇	1	2	yes	—
259	C₂×C₄⋊Q₈	—	47	4	no	—
260	C₂×#125	—	47	4	no	—
261	C₂×C₂²⋊Q₈	—	94	4	no	—
262	C₂×C₄×Q₈	—	94	4	no	—
263	C₂×#117	—	47	4	no	—
264	C₂²×C₄²	—	47	1	no	—
265	#500	—	47	4	no	—
266	#500	—	47	8	no	—
267	#500	—	47	2	no	—
268	#500	C₂×D₄₇	1	2	yes	complemented
269	#499	—	47	8	no	—
270	#499	—	47	8	no	—
271	#499	—	47	8	no	—
272	#499	—	47	4	no	—
273	#499	C₂×D₄₇	1	4	yes	complemented
274	#498	—	47	4	no	—
275	#498	—	47	8	no	—
276	#498	—	47	2	no	—
277	#498	C₂×D₄₇	1	2	yes	complemented
278	#427	—	47	4	no	—
279	#427	—	47	8	no	—
280	#427	—	47	8	no	—
281	#427	—	47	8	no	—
282	#427	C₂×D₄₇	1	4	yes	—
283	C₂×#107	—	47	8	no	—
284	C₂×#106	—	47	8	no	—
285	C₂×C₄×C₈	—	47	2	no	—
286	C₂×C₄×C₈	—	47	1	no	—
287	C₂×C₄×C₈	—	47	1	no	—
288	C₂×C₄×C₈	—	47	2	no	—
289	C₂×C₄×C₈	—	47	1	no	—
290	C₂×C₄×C₈	—	47	2	no	—
291	C₂×C₄×C₈	—	47	1	no	—
292	C₂×C₄×C₈	—	47	1	no	—
293	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
294	C₄₇	C₂×#3160	1	1	yes	characteristic, complemented, Sylow
295	C₂²×Q₈	—	94	4	no	—
296	C₂³×C₄	—	47	1	no	—
297	C₂³×C₄	—	47	2	no	—
298	C₂²×C₈	—	47	2	no	—
299	C₂²×C₈	—	47	16	no	—
300	C₂²×C₈	—	47	2	no	—
301	C₂²×C₈	—	47	2	no	—
302	C₂²×C₈	—	47	2	no	—
303	C₂²×C₈	—	47	2	no	—
304	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
305	C₄⋊Q₈	—	47	8	no	—
306	C₄⋊Q₈	—	47	4	no	—
307	C₄⋊Q₈	—	94	4	no	—
308	C₄⋊Q₈	—	94	4	no	—
309	C₄⋊Q₈	C₂²×D₄₇	1	4	yes	—
310	#125	—	47	8	no	—
311	#125	—	47	4	no	—
312	#125	—	94	8	no	—
313	#125	C₂²×D₄₇	1	4	yes	—
314	C₂²⋊Q₈	—	2	4	no	—
315	C₂²⋊Q₈	—	94	8	no	—
316	C₂²⋊Q₈	—	94	8	no	—
317	C₂²⋊Q₈	—	94	4	no	—
318	C₂²⋊Q₈	—	94	4	no	—
319	C₂²⋊Q₈	—	94	4	no	—
320	C₄×Q₈	—	2	4	no	—
321	C₄×Q₈	—	94	8	no	—
322	C₄×Q₈	—	94	8	no	—
323	C₄×Q₈	—	94	4	no	—
324	C₄×Q₈	—	94	4	no	—
325	C₄×Q₈	—	94	4	no	—
326	#117	—	47	4	no	—
327	#117	—	47	8	no	—
328	#117	—	94	4	no	—
329	#117	—	94	4	no	—
330	#117	C₂²×D₄₇	1	4	yes	—
331	C₂×C₄⋊C₄	—	47	8	no	—
332	C₂×C₄⋊C₄	—	94	8	no	—
333	C₂×C₄⋊C₄	—	94	4	no	—
334	C₂×C₂²⋊C₄	—	94	4	no	—
335	C₂×C₄²	—	47	2	no	—
336	C₂×C₄²	—	47	1	no	—
337	C₂×C₄²	—	47	2	no	—
338	C₂×C₄²	—	47	2	no	—
339	C₂×C₄²	—	47	1	no	—
340	C₂×C₄²	—	47	1	no	—
341	C₂×C₄²	—	47	1	no	—
342	C₂×C₄²	—	47	1	no	—
343	C₂×C₄²	—	94	4	no	—
344	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
345	#107	—	47	8	no	—
346	#107	—	47	16	no	—
347	#107	C₂²×D₄₇	1	8	yes	—
348	#106	—	47	8	no	—
349	#106	—	47	16	no	—
350	#106	C₂²×D₄₇	1	8	yes	—
351	C₄×C₈	—	47	2	no	—
352	C₄×C₈	—	47	2	no	—
353	C₄×C₈	—	47	2	no	—
354	C₄×C₈	—	47	2	no	—
355	C₄×C₈	—	47	1	no	—
356	C₄×C₈	—	47	2	no	—
357	C₄×C₈	—	47	1	no	—
358	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
359	C₄×C₈	C₂²×D₄₇	1	2	yes	—
360	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
361	C₂⁴	—	47	1	no	—
362	C₂×Q₈	—	2	4	no	—
363	C₂×Q₈	—	94	8	no	—
364	C₂×Q₈	—	94	4	no	—
365	C₂×Q₈	—	188	16	no	—
366	C₂²×C₄	—	47	1	no	—
367	C₂²×C₄	—	47	2	no	—
368	C₂²×C₄	—	47	1	no	—
369	C₂²×C₄	—	47	1	no	—
370	C₂²×C₄	—	47	8	no	—
371	C₂²×C₄	—	47	1	no	—
372	C₂²×C₄	—	47	1	no	—
373	C₂²×C₄	—	47	2	no	—
374	C₂²×C₄	—	47	2	no	—
375	C₂²×C₄	—	47	2	no	—
376	C₂²×C₄	—	47	2	no	—
377	C₂²×C₄	—	94	8	no	—
378	C₂²×C₄	—	94	8	no	—
379	C₂²×C₄	D₄×D₄₇	1	2	yes	—
380	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
381	C₂×C₈	—	47	8	no	—
382	C₂×C₈	—	47	2	no	—
383	C₂×C₈	—	47	2	no	—
384	C₂×C₈	—	47	8	no	—
385	C₂×C₈	—	47	8	no	—
386	C₂×C₈	—	47	8	no	—
387	C₂×C₈	—	47	8	no	—
388	C₂×C₈	Q₈×D₄₇	1	8	yes	complemented
389	C₂×C₈	C₂³×D₄₇	1	2	yes	—
390	C₂×C₈	C₂³×D₄₇	1	2	yes	—
391	C₄⋊C₄	—	2	8	no	—
392	C₄⋊C₄	—	2	4	no	—
393	C₄⋊C₄	—	47	8	no	—
394	C₄⋊C₄	—	94	8	no	—
395	C₄⋊C₄	—	94	8	no	—
396	C₄⋊C₄	—	94	8	no	—
397	C₄⋊C₄	—	94	8	no	—
398	C₄⋊C₄	—	94	8	no	—
399	C₄⋊C₄	—	94	4	no	—
400	C₄⋊C₄	C₂³×D₄₇	1	8	yes	—
401	C₂²⋊C₄	—	2	4	no	—
402	C₂²⋊C₄	—	94	8	no	—
403	C₂²⋊C₄	—	94	4	no	—
404	C₄²	—	2	4	no	—
405	C₄²	—	47	2	no	—
406	C₄²	—	47	2	no	—
407	C₄²	—	47	2	no	—
408	C₄²	—	47	2	no	—
409	C₄²	—	47	2	no	—
410	C₄²	—	47	1	no	—
411	C₄²	—	47	1	no	—
412	C₄²	—	94	8	no	—
413	C₄²	—	94	4	no	—
414	C₄²	D₄×D₄₇	1	2	yes	—
415	C₄²	C₂³×D₄₇	1	1	yes	characteristic
416	C₄²	C₂³×D₄₇	1	1	yes	characteristic
417	C₂³	—	47	1	no	—
418	C₂³	—	47	4	no	—
419	C₂³	—	47	1	no	—
420	C₂³	—	94	4	no	—
421	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
422	Q₈	—	4	8	no	—
423	Q₈	—	188	16	no	—
424	Q₈	—	188	8	no	—
425	C₂×C₄	—	2	4	no	—
426	C₂×C₄	—	2	8	no	—
427	C₂×C₄	—	47	4	no	—
428	C₂×C₄	—	47	1	no	—
429	C₂×C₄	—	47	1	no	—
430	C₂×C₄	—	47	2	no	—
431	C₂×C₄	—	47	8	no	—
432	C₂×C₄	—	47	4	no	—
433	C₂×C₄	—	47	4	no	—
434	C₂×C₄	—	47	4	no	—
435	C₂×C₄	—	47	4	no	—
436	C₂×C₄	—	47	2	no	—
437	C₂×C₄	—	94	4	no	—
438	C₂×C₄	—	94	4	no	—
439	C₂×C₄	—	94	4	no	—
440	C₂×C₄	—	94	4	no	—
441	C₂×C₄	—	94	8	no	—
442	C₂×C₄	—	188	16	no	—
443	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
444	C₂×C₄	C₂×D₄×D₄₇	1	2	yes	—
445	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
446	C₂×C₄	C₂×Q₈×D₄₇	1	4	yes	—
447	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
448	C₈	—	47	4	no	—
449	C₈	—	47	4	no	—
450	C₈	C₂×Q₈×D₄₇	1	4	yes	—
451	C₈	C₂×Q₈×D₄₇	1	4	yes	—
452	C₂²	—	2	2	no	—
453	C₂²	—	47	4	no	—
454	C₂²	—	47	2	no	—
455	C₂²	—	47	2	no	—
456	C₂²	—	94	8	no	—
457	C₂²	—	94	2	no	—
458	C₂²	C₄⋊Q₈×D₄₇	1	2	yes	—
459	C₂²	C₂²×D₄×D₄₇	1	1	yes	characteristic
460	C₄	—	2	2	no	—
461	C₄	—	4	8	no	—
462	C₄	—	47	4	no	—
463	C₄	—	47	2	no	—
464	C₄	—	47	2	no	—
465	C₄	—	94	2	no	—
466	C₄	—	188	8	no	—
467	C₄	C₄⋊Q₈×D₄₇	1	2	yes	—
468	C₄	#135×D₄₇	1	4	yes	—
469	C₄	C₂²×Q₈×D₄₇	1	2	yes	—
470	C₂	—	2	2	no	—
471	C₂	—	47	4	no	—
472	C₂	—	94	2	no	—
473	C₂	C₂×C₄⋊Q₈×D₄₇	1	1	yes	characteristic
474	C₂	C₂×#135×D₄₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator, cosocle	C₂×C₄×C₄₇	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₄₇×#3160	C₂
socle	C₂²×C₄₇	C₂³×D₄
prime radical	C₂³×D₄₇	C₂×D₄
hypercenter	#3160	D₄₇
hypocenter	C₄₇	C₂×#3160
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3160

Complements

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

N	H ≅ G/N	type
2. #20253902	C₂	semidirect
3. #20253901	C₂	semidirect
4. #20253900	C₂	semidirect
5. #20253899	C₂	semidirect
6. #20253898	C₂	semidirect
7. #20253897	C₂	semidirect
8. #500×D₄₇	C₂	semidirect
9. #499×D₄₇	C₂	semidirect
10. #498×D₄₇	C₂	semidirect
13. C₄₇×#3160	C₂	semidirect
27. #15689528	C₂²	semidirect
28. #15689527	C₂²	semidirect
29. #15689526	C₂²	semidirect
30. #15689525	C₂²	semidirect
31. #15689524	C₂²	semidirect
32. #15689523	C₂²	semidirect
33. #15689522	C₂²	semidirect
34. #15689521	C₂²	semidirect
35. #15689520	C₂²	semidirect
36. #15689519	C₂²	semidirect
52. C₄₇×#500	C₂²	semidirect
53. C₄₇×#499	C₂²	semidirect
54. C₄₇×#498	C₂²	semidirect
61. C₂×C₈×D₄₇	Q₈	semidirect
143. C₂×C₈×C₄₇	C₂×Q₈	semidirect
172. C₂×C₄₇⋊C₈	C₂×Q₈	semidirect
177. C₈×D₄₇	C₂×Q₈	semidirect
178. C₈×D₄₇	C₂×Q₈	semidirect
240. #3160	D₄₇	direct (N × H)
250. D₄₇	#3160	direct (N × H)
268. #500	C₂×D₄₇	semidirect
273. #499	C₂×D₄₇	semidirect
277. #498	C₂×D₄₇	semidirect
294. C₄₇	C₂×#3160	semidirect
388. C₂×C₈	Q₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#533×D₄₇	2
#20253902	2
#20253901	2
#20253900	2
#20253899	2
#20253898	2
#20253897	2
#500×D₄₇	2
#499×D₄₇	2
#498×D₄₇	2
#427×D₄₇	2
C₂×C₄×C₈×D₄₇	2
C₄₇×#3160	2
C₂×#3160	47

Subgroups — D47×#3160 #27085877

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#3160 #27085877