Subgroups — D₄₇×#1580 #26185673

Order 12032.

894 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄×D₈×D₄₇	C₂	1	1	yes	maximal, characteristic
2	C₈×D₄×D₄₇	C₂	1	2	yes	maximal, complemented
3	#20242213	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242212	C₂	1	1	yes	maximal, characteristic, complemented
5	#20242211	C₂	1	1	yes	maximal, characteristic, complemented
6	#20242210	C₂	1	2	yes	maximal, complemented
7	#20242209	C₂	1	2	yes	maximal, complemented
8	#334×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	D₄⋊C₈×D₄₇	C₂	1	2	yes	maximal, complemented
10	#322×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1580	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₄₇	C₄	1	1	yes	characteristic
13	C₂²×C₈×D₄₇	—	2	2	no	—
14	C₄×D₄×D₄₇	C₂²	1	2	yes	—
15	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
16	D₈×Dic₄₇	C₄	1	1	yes	characteristic
17	#15689205	C₄	1	1	yes	characteristic
18	C₄×#10625334	C₂²	1	2	yes	—
19	#15689203	C₄	1	2	yes	—
20	C₈×D₁₈₈	C₂²	1	2	yes	complemented
21	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
22	#15689188	C₂²	1	2	yes	complemented
23	C₈×C₂²⋊D₄₇	—	2	2	no	—
24	(C₂²⋊D₄₇)⋊C₈	—	2	2	no	—
25	#107×D₄₇	C₄	1	1	yes	characteristic
26	C₄⋊C₈×D₄₇	C₂²	1	2	yes	—
27	#102×D₄₇	C₄	1	2	yes	—
28	C₂²⋊C₈×D₄₇	—	2	2	no	—
29	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
32	#15688874	C₂²	1	1	yes	characteristic, complemented
33	#15688873	C₂²	1	2	yes	complemented
34	#15688852	C₂²	1	2	yes	complemented
35	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
36	#15688850	C₂²	1	2	yes	complemented
37	#15688845	C₂²	1	1	yes	characteristic, complemented
38	#15688845	C₂²	1	1	yes	characteristic, complemented
39	#15688844	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₄₇	C₂²	1	2	yes	complemented
42	C₄₇×#334	C₂²	1	1	yes	characteristic, complemented
43	C₄₇×D₄⋊C₈	C₂²	1	2	yes	complemented
44	C₄₇×#322	C₂²	1	1	yes	characteristic, complemented
45	C₂×D₄×D₄₇	C₂×C₄	1	2	yes	—
46	C₂²×C₄×D₄₇	—	2	2	no	—
47	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic
48	C₂×#10625334	C₂×C₄	1	2	yes	—
49	D₈×D₄₇	C₈	1	8	yes	complemented
50	C₂²×C₄₇⋊C₈	—	2	2	no	—
51	C₂×C₈×D₄₇	—	2	2	no	—
52	C₂×C₈×D₄₇	—	2	1	no	—
53	C₂×C₈×D₄₇	—	2	2	no	—
54	C₂×C₈×D₄₇	—	2	2	no	—
55	C₂×C₈×D₄₇	—	4	8	no	—
56	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
58	C₂×C₈×D₄₇	D₄	1	2	yes	—
59	C₄×D₁₈₈	C₂³	1	2	yes	—
60	D₄×Dic₄₇	C₂×C₄	1	2	yes	—
61	#13093986	C₂×C₄	1	2	yes	—
62	C₄×C₂²⋊D₄₇	—	2	2	no	—
63	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
64	C₄⋊C₄×D₄₇	C₂×C₄	1	2	yes	—
65	C₂²⋊C₄×D₄₇	—	2	2	no	—
66	C₄²×D₄₇	C₂³	1	1	yes	characteristic
67	#13093958	C₂×C₄	1	1	yes	characteristic
68	#13093957	C₂×C₄	1	2	yes	—
69	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
70	Dic₄₇⋊C₈	—	2	2	no	—
71	#13093946	C₂×C₄	1	2	yes	—
72	#13093945	C₂×C₄	1	2	yes	—
73	#13093944	C₂×C₄	1	2	yes	—
74	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
75	(C₂×D₄₇)⋊C₈	—	2	2	no	—
76	(C₂×D₄₇)⋊C₈	—	2	2	no	—
77	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
78	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
79	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
80	C₈×Dic₄₇	—	2	1	no	—
81	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₄₇	D₄	1	2	yes	—
84	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic
85	C₂²×C₈×C₄₇	—	2	2	no	—
86	C₄×D₄×C₄₇	C₂³	1	2	yes	—
87	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
89	#102×C₄₇	C₂×C₄	1	2	yes	—
90	C₂²⋊C₈×C₄₇	—	2	2	no	—
91	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
94	C₂³×D₄₇	—	2	2	no	—
95	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂×C₂²⋊D₄₇	—	2	2	no	—
98	C₂²×Dic₄₇	—	2	2	no	—
99	D₄×D₄₇	—	2	4	no	—
100	D₄×D₄₇	C₂×C₈	1	8	yes	complemented
101	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
102	C₂×C₄×D₄₇	—	2	2	no	—
103	C₂×C₄×D₄₇	—	2	2	no	—
104	C₂×C₄×D₄₇	—	2	2	no	—
105	C₂×C₄×D₄₇	—	4	4	no	—
106	C₂×C₄×D₄₇	—	4	4	no	—
107	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
109	C₂×C₄×D₄₇	#41	1	1	yes	characteristic
110	D₈×C₄₇	C₂×C₈	1	4	yes	complemented
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	—	2	1	no	—
113	C₂×C₈×C₄₇	—	4	4	no	—
114	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
117	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
118	C₂²⋊C₄×C₄₇	—	2	2	no	—
119	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
120	C₂²⋊Dic₄₇	—	2	2	no	—
121	#10625334	C₂×C₈	1	8	yes	complemented
122	(C₂×D₄₇)⋊C₄	—	2	2	no	—
123	(C₂×D₄₇)⋊C₄	—	2	2	no	—
124	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
125	Dic₄₇⋊C₄	—	2	2	no	—
126	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
128	C₄×Dic₄₇	#41	1	1	yes	characteristic
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	2	1	no	—
131	C₂×C₄₇⋊C₈	—	4	4	no	—
132	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
135	D₃₇₆	C₂×C₈	1	4	yes	complemented
136	C₈×D₄₇	—	2	2	no	—
137	C₈×D₄₇	—	2	4	no	—
138	C₈×D₄₇	—	4	4	no	—
139	C₈×D₄₇	—	4	4	no	—
140	C₈×D₄₇	—	4	2	no	—
141	C₈×D₄₇	—	4	4	no	—
142	C₈×D₄₇	C₂×C₈	1	4	yes	complemented
143	C₂³×C₄₇	—	2	2	no	—
144	C₂²×D₄₇	—	2	2	no	—
145	C₂²×D₄₇	—	2	8	no	—
146	C₂²×D₄₇	—	4	4	no	—
147	C₂²×D₄₇	—	4	4	no	—
148	C₂²×D₄₇	C₄×D₄	1	1	yes	characteristic
149	D₄×C₄₇	—	2	2	no	—
150	D₄×C₄₇	C₂²×C₈	1	4	yes	complemented
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
157	C₂²⋊D₄₇	—	2	8	no	—
158	C₂×Dic₄₇	—	2	2	no	—
159	C₂×Dic₄₇	—	4	4	no	—
160	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
161	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
162	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
163	D₁₈₈	—	2	2	no	—
164	D₁₈₈	C₂²×C₈	1	4	yes	complemented
165	C₄×D₄₇	—	2	2	no	—
166	C₄×D₄₇	—	4	4	no	—
167	C₄×D₄₇	—	4	2	no	—
168	C₄×D₄₇	—	4	2	no	—
169	C₄×D₄₇	—	4	4	no	—
170	C₄×D₄₇	C₂²×C₈	1	2	yes	—
171	C₄×D₄₇	#131	1	2	yes	—
172	C₄×D₄₇	AGL(1,ℤ/8)	1	4	yes	—
173	C₈×C₄₇	—	2	1	no	—
174	C₈×C₄₇	—	2	2	no	—
175	C₈×C₄₇	—	4	1	no	—
176	C₈×C₄₇	—	4	2	no	—
177	C₈×C₄₇	C₂²×C₈	1	2	yes	complemented
178	C₄₇⋊C₈	—	2	1	no	—
179	C₄₇⋊C₈	—	2	2	no	—
180	C₄₇⋊C₈	—	4	1	no	—
181	C₄₇⋊C₈	—	4	2	no	—
182	C₄₇⋊C₈	C₂²×C₈	1	2	yes	complemented
183	C₂×#1580	—	47	1	no	maximal, Sylow
184	C₂²×C₄₇	—	2	4	no	—
185	C₂²×C₄₇	—	4	2	no	—
186	C₂²×C₄₇	—	4	2	no	—
187	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
188	C₂×D₄₇	—	2	4	no	—
189	C₂×D₄₇	—	4	2	no	—
190	C₂×D₄₇	—	4	2	no	—
191	C₂×D₄₇	—	4	16	no	—
192	C₂×D₄₇	C₈×D₄	1	2	yes	—
193	C₂×D₄₇	#442	1	2	yes	—
194	C₂×D₄₇	#444	1	2	yes	—
195	C₄×C₄₇	—	2	1	no	—
196	C₄×C₄₇	—	4	2	no	—
197	C₄×C₄₇	C₂³×C₈	1	1	yes	characteristic
198	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
199	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
200	Dic₄₇	—	2	1	no	—
201	Dic₄₇	—	4	2	no	—
202	Dic₄₇	C₈×D₄	1	2	yes	—
203	Dic₄₇	#442	1	2	yes	—
204	C₂×C₄×D₈	—	47	1	no	—
205	C₂×C₈×D₄	—	47	2	no	—
206	#1580	—	47	1	no	—
207	#1580	—	47	2	no	—
208	#1580	—	47	1	no	—
209	#1580	—	47	2	no	—
210	#1580	—	47	1	no	—
211	#1580	D₄₇	1	1	yes	characteristic, direct product factor
212	C₂×#334	—	47	1	no	—
213	C₂×D₄⋊C₈	—	47	2	no	—
214	C₂×#322	—	47	1	no	—
215	C₂×C₄₇	—	4	4	no	—
216	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
217	C₂×C₄₇	C₂×#442	1	1	yes	characteristic
218	C₂×C₄₇	C₂×#444	1	1	yes	characteristic
219	D₄₇	—	4	4	no	—
220	D₄₇	#1580	1	4	yes	direct product factor
221	C₂²×D₈	—	47	1	no	—
222	C₂³×C₈	—	94	2	no	—
223	C₂×C₄×D₄	—	47	2	no	—
224	C₄×D₈	—	47	1	no	—
225	C₄×D₈	—	47	2	no	—
226	C₄×D₈	—	47	1	no	—
227	C₄×D₈	—	47	2	no	—
228	C₄×D₈	—	47	1	no	—
229	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
230	C₈×D₄	—	47	2	no	—
231	C₈×D₄	—	47	2	no	—
232	C₈×D₄	—	47	2	no	—
233	C₈×D₄	—	94	2	no	—
234	C₈×D₄	—	94	2	no	—
235	C₈×D₄	C₂×D₄₇	1	2	yes	complemented
236	C₂×#107	—	47	1	no	—
237	C₂×C₄⋊C₈	—	47	2	no	—
238	C₂×#102	—	47	2	no	—
239	C₂×C₂²⋊C₈	—	94	2	no	—
240	C₂×C₄×C₈	—	47	1	no	—
241	C₂×C₄×C₈	—	47	1	no	—
242	C₂×C₄×C₈	—	47	1	no	—
243	#334	—	47	2	no	—
244	#334	—	47	1	no	—
245	#334	C₂×D₄₇	1	1	yes	characteristic, complemented
246	D₄⋊C₈	—	47	2	no	—
247	D₄⋊C₈	—	47	2	no	—
248	D₄⋊C₈	—	47	2	no	—
249	D₄⋊C₈	C₂×D₄₇	1	2	yes	complemented
250	#322	—	47	1	no	—
251	#322	—	47	1	no	—
252	#322	—	47	1	no	—
253	#322	C₂×D₄₇	1	1	yes	characteristic, complemented
254	C₄₇	C₂×#1580	1	1	yes	characteristic, complemented, Sylow
255	C₂²×D₄	—	47	2	no	—
256	C₂³×C₄	—	94	2	no	—
257	C₂×D₈	—	47	2	no	—
258	C₂×D₈	—	47	8	no	—
259	C₂×D₈	—	47	1	no	—
260	C₂×D₈	C₄×D₄₇	1	1	yes	characteristic
261	C₂²×C₈	—	2	2	no	—
262	C₂²×C₈	—	47	1	no	—
263	C₂²×C₈	—	47	1	no	—
264	C₂²×C₈	—	47	2	no	—
265	C₂²×C₈	—	94	2	no	—
266	C₂²×C₈	—	94	2	no	—
267	C₂²×C₈	—	94	1	no	—
268	C₂²×C₈	—	94	2	no	—
269	C₂²×C₈	—	94	2	no	—
270	C₂²×C₈	—	188	8	no	—
271	C₄×D₄	—	47	2	no	—
272	C₄×D₄	—	47	2	no	—
273	C₄×D₄	—	47	2	no	—
274	C₄×D₄	—	94	2	no	—
275	C₄×D₄	—	94	2	no	—
276	C₄×D₄	C₂²×D₄₇	1	2	yes	—
277	C₂×C₄⋊C₄	—	47	2	no	—
278	C₂×C₂²⋊C₄	—	94	2	no	—
279	C₂×C₄²	—	47	1	no	—
280	#107	—	47	1	no	—
281	#107	—	47	2	no	—
282	#107	C₄×D₄₇	1	1	yes	characteristic
283	C₄⋊C₈	—	47	2	no	—
284	C₄⋊C₈	—	94	2	no	—
285	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
286	#102	—	47	2	no	—
287	#102	—	47	2	no	—
288	#102	—	47	2	no	—
289	#102	C₄×D₄₇	1	2	yes	—
290	C₂²⋊C₈	—	2	2	no	—
291	C₂²⋊C₈	—	94	2	no	—
292	C₂²⋊C₈	—	94	2	no	—
293	C₂²⋊C₈	—	94	2	no	—
294	C₄×C₈	—	47	1	no	—
295	C₄×C₈	—	47	1	no	—
296	C₄×C₈	—	47	2	no	—
297	C₄×C₈	—	47	1	no	—
298	C₄×C₈	—	47	1	no	—
299	C₄×C₈	—	47	1	no	—
300	C₄×C₈	—	94	1	no	—
301	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
302	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
303	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
304	C₂⁴	—	94	2	no	—
305	C₂×D₄	—	47	8	no	—
306	C₂×D₄	—	47	2	no	—
307	C₂×D₄	—	94	4	no	—
308	C₂×D₄	—	94	2	no	—
309	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
310	C₂²×C₄	—	2	2	no	—
311	C₂²×C₄	—	47	1	no	—
312	C₂²×C₄	—	47	1	no	—
313	C₂²×C₄	—	47	1	no	—
314	C₂²×C₄	—	94	2	no	—
315	C₂²×C₄	—	94	2	no	—
316	C₂²×C₄	—	94	2	no	—
317	C₂²×C₄	—	94	2	no	—
318	C₂²×C₄	—	188	4	no	—
319	C₂²×C₄	—	188	4	no	—
320	D₈	—	47	8	no	—
321	D₈	—	47	4	no	—
322	D₈	C₈×D₄₇	1	4	yes	complemented
323	C₂×C₈	—	2	2	no	—
324	C₂×C₈	—	2	1	no	—
325	C₂×C₈	—	4	4	no	—
326	C₂×C₈	—	47	1	no	—
327	C₂×C₈	—	47	4	no	—
328	C₂×C₈	—	47	1	no	—
329	C₂×C₈	—	47	2	no	—
330	C₂×C₈	—	94	2	no	—
331	C₂×C₈	—	94	4	no	—
332	C₂×C₈	—	94	2	no	—
333	C₂×C₈	—	94	1	no	—
334	C₂×C₈	—	188	4	no	—
335	C₂×C₈	—	188	4	no	—
336	C₂×C₈	—	188	4	no	—
337	C₂×C₈	—	188	2	no	—
338	C₂×C₈	—	188	4	no	—
339	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
340	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
341	C₂×C₈	D₄×D₄₇	1	2	yes	—
342	C₄⋊C₄	—	47	2	no	—
343	C₄⋊C₄	—	94	2	no	—
344	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
345	C₂²⋊C₄	—	2	2	no	—
346	C₂²⋊C₄	—	94	2	no	—
347	C₂²⋊C₄	—	94	2	no	—
348	C₂²⋊C₄	—	94	2	no	—
349	C₄²	—	47	1	no	—
350	C₄²	—	47	1	no	—
351	C₄²	—	47	1	no	—
352	C₄²	C₂³×D₄₇	1	1	yes	characteristic
353	C₂³	—	2	2	no	—
354	C₂³	—	47	1	no	—
355	C₂³	—	94	8	no	—
356	C₂³	—	94	2	no	—
357	C₂³	—	188	4	no	—
358	C₂³	—	188	4	no	—
359	D₄	—	2	2	no	—
360	D₄	—	47	4	no	—
361	D₄	—	94	8	no	—
362	D₄	—	94	2	no	—
363	D₄	C₂×C₈×D₄₇	1	4	yes	complemented
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	4	2	no	—
367	C₂×C₄	—	47	1	no	—
368	C₂×C₄	—	47	1	no	—
369	C₂×C₄	—	47	2	no	—
370	C₂×C₄	—	47	2	no	—
371	C₂×C₄	—	47	4	no	—
372	C₂×C₄	—	47	1	no	—
373	C₂×C₄	—	94	2	no	—
374	C₂×C₄	—	94	2	no	—
375	C₂×C₄	—	188	4	no	—
376	C₂×C₄	—	188	4	no	—
377	C₂×C₄	—	188	4	no	—
378	C₂×C₄	—	188	2	no	—
379	C₂×C₄	—	188	2	no	—
380	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
381	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
382	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
383	C₈	—	2	1	no	—
384	C₈	—	2	2	no	—
385	C₈	—	4	1	no	—
386	C₈	—	4	2	no	—
387	C₈	—	47	2	no	—
388	C₈	—	94	1	no	—
389	C₈	—	94	2	no	—
390	C₈	—	188	1	no	—
391	C₈	—	188	2	no	—
392	C₈	C₂×C₈×D₄₇	1	2	yes	complemented
393	C₂²	—	2	4	no	—
394	C₂²	—	4	2	no	—
395	C₂²	—	4	2	no	—
396	C₂²	—	47	2	no	—
397	C₂²	—	47	2	no	—
398	C₂²	—	47	2	no	—
399	C₂²	—	94	4	no	—
400	C₂²	—	188	16	no	—
401	C₂²	—	188	2	no	—
402	C₂²	—	188	2	no	—
403	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
404	C₄	—	2	1	no	—
405	C₄	—	4	2	no	—
406	C₄	—	47	2	no	—
407	C₄	—	47	2	no	—
408	C₄	—	94	1	no	—
409	C₄	—	188	2	no	—
410	C₄	C₂²×C₈×D₄₇	1	1	yes	characteristic
411	C₄	#131×D₄₇	1	1	yes	characteristic
412	C₄	AGL(1,ℤ/8)×D₄₇	1	2	yes	—
413	C₂	—	4	4	no	—
414	C₂	—	47	4	no	—
415	C₂	—	188	4	no	—
416	C₂	C₈×D₄×D₄₇	1	1	yes	characteristic
417	C₂	#442×D₄₇	1	1	yes	characteristic
418	C₂	#444×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂³×C₈
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1580	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×D₈×D₄₇	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1580	D₄₇
hypocenter	C₄₇	C₂×#1580
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1580

Complements

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

N	H ≅ G/N	type
2. C₈×D₄×D₄₇	C₂	semidirect
3. #20242213	C₂	semidirect
4. #20242212	C₂	semidirect
5. #20242211	C₂	semidirect
6. #20242210	C₂	semidirect
7. #20242209	C₂	semidirect
8. #334×D₄₇	C₂	semidirect
9. D₄⋊C₈×D₄₇	C₂	semidirect
10. #322×D₄₇	C₂	semidirect
11. C₄₇×#1580	C₂	semidirect
20. C₈×D₁₈₈	C₂²	semidirect
21. D₄×C₄₇⋊C₈	C₂²	semidirect
22. #15689188	C₂²	semidirect
32. #15688874	C₂²	semidirect
33. #15688873	C₂²	semidirect
34. #15688852	C₂²	semidirect
35. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
36. #15688850	C₂²	semidirect
37. #15688845	C₂²	semidirect
38. #15688845	C₂²	semidirect
39. #15688844	C₂²	semidirect
41. C₈×D₄×C₄₇	C₂²	semidirect
42. C₄₇×#334	C₂²	semidirect
43. C₄₇×D₄⋊C₈	C₂²	semidirect
44. C₄₇×#322	C₂²	semidirect
49. D₈×D₄₇	C₈	semidirect
100. D₄×D₄₇	C₂×C₈	semidirect
110. D₈×C₄₇	C₂×C₈	semidirect
121. #10625334	C₂×C₈	semidirect
135. D₃₇₆	C₂×C₈	semidirect
142. C₈×D₄₇	C₂×C₈	semidirect
150. D₄×C₄₇	C₂²×C₈	semidirect
164. D₁₈₈	C₂²×C₈	semidirect
177. C₈×C₄₇	C₂²×C₈	semidirect
182. C₄₇⋊C₈	C₂²×C₈	semidirect
211. #1580	D₄₇	direct (N × H)
220. D₄₇	#1580	direct (N × H)
235. C₈×D₄	C₂×D₄₇	semidirect
245. #334	C₂×D₄₇	semidirect
249. D₄⋊C₈	C₂×D₄₇	semidirect
253. #322	C₂×D₄₇	semidirect
254. C₄₇	C₂×#1580	semidirect
322. D₈	C₈×D₄₇	semidirect
363. D₄	C₂×C₈×D₄₇	semidirect
392. C₈	C₂×C₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₄×D₈×D₄₇	2
C₈×D₄×D₄₇	2
#20242213	2
#20242212	2
#20242211	2
#20242210	2
#20242209	2
#334×D₄₇	2
D₄⋊C₈×D₄₇	2
#322×D₄₇	2
C₄₇×#1580	2
C₂×#1580	47

Subgroups — D47×#1580 #26185673

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — D₄₇×#1580 #26185673