Subgroups — #26220597

Order 12032.

950 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20245853	C₂	1	2	yes	maximal, complemented
2	#20244265	C₂	1	1	yes	maximal, characteristic
3	#20244255	C₂	1	1	yes	maximal, characteristic
4	#20244132	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244117	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244087	C₂	1	2	yes	maximal, complemented
7	#20244073	C₂	1	2	yes	maximal, complemented
8	#20243285	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243213	C₂	1	2	yes	maximal, complemented
10	#97×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#442	C₂	1	1	yes	maximal, characteristic
12	C₂×#13093983	—	2	2	no	—
13	C₂×#13093958	C₂²	1	1	yes	characteristic
14	C₂×#13093956	C₂²	1	1	yes	characteristic
15	C₂×#13093945	C₂²	1	2	yes	—
16	C₂×#13093945	C₂²	1	2	yes	—
17	C₂×#13093935	C₂²	1	1	yes	characteristic
18	C₂×#13093934	C₂²	1	1	yes	characteristic
19	C₂×#13093934	C₂²	1	1	yes	characteristic
20	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
21	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
22	#15689026	C₂²	1	2	yes	—
23	#15689026	C₂²	1	2	yes	—
24	#15689022	C₂²	1	2	yes	—
25	#15689022	C₂²	1	2	yes	—
26	#15689016	—	2	2	no	—
27	#15689016	—	2	2	no	—
28	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
29	C₄×C₂²⋊Dic₄₇	—	2	2	no	—
30	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
31	#15688886	C₂²	1	2	yes	—
32	#15688885	C₂²	1	2	yes	—
33	#15688885	C₂²	1	2	yes	—
34	C₂²×D₈×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₄₇	C₂²	1	2	yes	—
36	C₄₇×#442	C₄	1	8	yes	complemented
37	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#102×C₄₇	C₂²	1	2	yes	—
39	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
40	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
41	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
42	#13093983	—	4	8	no	—
43	C₂×C₄⋊Dic₄₇	—	2	2	no	—
44	C₂×C₄⋊Dic₄₇	—	2	2	no	—
45	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
46	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
47	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
48	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
49	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
50	C₂×C₂²⋊Dic₄₇	—	2	2	no	—
51	C₂×C₄×Dic₄₇	—	2	2	no	—
52	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
53	C₂×C₄×Dic₄₇	D₄	1	2	yes	—
54	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
55	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
56	#13093958	—	2	2	no	—
57	#13093956	—	2	2	no	—
58	#13093945	—	2	4	no	—
59	#13093945	—	2	4	no	—
60	#13093935	—	2	2	no	—
61	#13093934	—	2	2	no	—
62	#13093934	—	2	2	no	—
63	C₈×Dic₄₇	—	2	2	no	—
64	C₈×Dic₄₇	—	2	2	no	—
65	C₄₇⋊#95	—	2	2	no	—
66	C₄₇⋊#95	—	2	2	no	—
67	C₄₇⋊#95	—	2	2	no	—
68	C₂²×D₄×C₄₇	C₂³	1	2	yes	—
69	C₂³×C₄×C₄₇	—	2	2	no	—
70	C₂×D₈×C₄₇	—	2	2	no	—
71	C₂×D₈×C₄₇	—	2	2	no	—
72	C₂×D₈×C₄₇	C₂×C₄	1	4	yes	—
73	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
75	C₄×D₄×C₄₇	—	2	4	no	—
76	C₄×D₄×C₄₇	C₂×C₄	1	8	yes	—
77	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
78	C₂×C₂²⋊C₄×C₄₇	—	2	2	no	—
79	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
80	#106×C₄₇	C₂×C₄	1	4	yes	—
81	#102×C₄₇	C₂×C₄	1	8	yes	—
82	#97×C₄₇	C₂×C₄	1	4	yes	—
83	C₂⁴×C₄₇	—	2	2	no	—
84	C₂×D₄×C₄₇	—	2	2	no	—
85	C₂×D₄×C₄₇	—	2	2	no	—
86	C₂×D₄×C₄₇	—	2	2	no	—
87	C₂×D₄×C₄₇	—	2	2	no	—
88	C₂×D₄×C₄₇	—	2	2	no	—
89	C₂×D₄×C₄₇	C₂²×C₄	1	4	yes	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	—	2	8	no	—
92	C₂²×C₄×C₄₇	—	4	4	no	—
93	C₂²×C₄×C₄₇	—	4	4	no	—
94	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
95	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
96	C₂²×Dic₄₇	—	2	2	no	—
97	C₂²×Dic₄₇	—	2	2	no	—
98	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
99	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
101	D₈×C₄₇	—	2	8	no	—
102	C₂×C₈×C₄₇	—	2	1	no	—
103	C₂×C₈×C₄₇	—	2	1	no	—
104	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
105	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
106	C₂×C₈×C₄₇	#41	1	2	yes	—
107	C₂×C₈×C₄₇	#41	1	2	yes	—
108	C₄⋊C₄×C₄₇	—	2	2	no	—
109	C₄⋊C₄×C₄₇	C₂²×C₄	1	4	yes	—
110	C₂²⋊C₄×C₄₇	—	2	8	no	—
111	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
112	C₄²×C₄₇	#41	1	2	yes	—
113	C₂²⋊Dic₄₇	—	4	4	no	—
114	C₂²⋊Dic₄₇	—	4	4	no	—
115	C₂²⋊Dic₄₇	—	4	4	no	—
116	C₂²⋊Dic₄₇	—	4	4	no	—
117	C₄⋊Dic₄₇	—	2	2	no	—
118	C₄⋊Dic₄₇	—	2	2	no	—
119	C₄⋊Dic₄₇	—	2	2	no	—
120	C₄⋊Dic₄₇	—	2	2	no	—
121	C₄⋊Dic₄₇	—	4	4	no	—
122	C₄⋊Dic₄₇	—	4	4	no	—
123	C₄×Dic₄₇	—	2	1	no	—
124	C₄×Dic₄₇	—	2	1	no	—
125	C₄×Dic₄₇	—	2	1	no	—
126	C₄×Dic₄₇	—	2	1	no	—
127	C₄×Dic₄₇	—	2	4	no	—
128	C₄×Dic₄₇	—	4	2	no	—
129	C₄×Dic₄₇	—	4	4	no	—
130	C₂×C₄₇⋊C₈	—	2	1	no	—
131	C₂×C₄₇⋊C₈	—	2	1	no	—
132	C₂×C₄₇⋊C₈	—	2	1	no	—
133	C₂×C₄₇⋊C₈	—	2	1	no	—
134	C₂×C₄₇⋊C₈	#41	1	2	yes	—
135	C₂×C₄₇⋊C₈	#41	1	2	yes	—
136	C₂³×C₄₇	—	2	4	no	—
137	C₂³×C₄₇	—	4	2	no	—
138	C₂³×C₄₇	—	4	2	no	—
139	C₂³×C₄₇	—	4	2	no	—
140	C₂³×C₄₇	—	4	2	no	—
141	C₂³×C₄₇	—	4	2	no	—
142	C₂³×C₄₇	—	4	2	no	—
143	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
144	D₄×C₄₇	—	2	4	no	—
145	D₄×C₄₇	—	2	4	no	—
146	D₄×C₄₇	—	4	2	no	—
147	D₄×C₄₇	—	4	2	no	—
148	C₂×C₄×C₄₇	—	2	2	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	4	no	—
151	C₂×C₄×C₄₇	—	4	16	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
155	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
161	C₂×Dic₄₇	—	2	2	no	—
162	C₂×Dic₄₇	—	2	2	no	—
163	C₂×Dic₄₇	—	2	1	no	—
164	C₂×Dic₄₇	—	2	1	no	—
165	C₂×Dic₄₇	—	2	2	no	—
166	C₂×Dic₄₇	—	2	2	no	—
167	C₂×Dic₄₇	—	4	2	no	—
168	C₂×Dic₄₇	—	4	2	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	C₂×Dic₄₇	—	4	2	no	—
171	C₂×Dic₄₇	—	4	2	no	—
172	C₂×Dic₄₇	—	4	2	no	—
173	C₂×Dic₄₇	AGL(1,ℤ/8)	1	4	yes	—
174	C₈×C₄₇	—	2	2	no	—
175	C₈×C₄₇	#117	1	4	yes	complemented
176	C₄₇⋊C₈	—	2	2	no	—
177	C₄₇⋊C₈	—	2	2	no	—
178	#21286	—	47	1	no	maximal, Sylow
179	C₂²×C₄₇	—	4	4	no	—
180	C₂²×C₄₇	—	4	4	no	—
181	C₂²×C₄₇	—	4	4	no	—
182	C₂²×C₄₇	—	8	2	no	—
183	C₂²×C₄₇	—	8	2	no	—
184	C₂²×C₄₇	—	8	2	no	—
185	C₂²×C₄₇	—	8	2	no	—
186	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
187	C₂²×C₄₇	#532	1	1	yes	characteristic
188	C₂²×C₄₇	#532	1	1	yes	characteristic
189	C₂²×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
190	C₂²×C₄₇	#575	1	2	yes	—
191	C₄×C₄₇	—	2	4	no	—
192	C₄×C₄₇	—	4	4	no	—
193	C₄×C₄₇	C₂×#117	1	1	yes	characteristic
194	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
195	C₄×C₄₇	#529	1	1	yes	characteristic
196	C₄×C₄₇	#529	1	1	yes	characteristic
197	Dic₄₇	—	2	4	no	—
198	Dic₄₇	—	4	1	no	—
199	Dic₄₇	—	4	1	no	—
200	Dic₄₇	—	8	2	no	—
201	Dic₄₇	—	8	2	no	—
202	C₂×#442	D₄₇	1	1	yes	characteristic
203	#2293	—	47	2	no	—
204	#1972	—	47	1	no	—
205	#1970	—	47	1	no	—
206	#1944	—	47	1	no	—
207	#1941	—	47	1	no	—
208	#1936	—	47	2	no	—
209	#1934	—	47	2	no	—
210	#1776	—	47	1	no	—
211	#1762	—	47	2	no	—
212	C₄×#97	—	47	1	no	—
213	C₂×C₄₇	—	8	4	no	—
214	C₂×C₄₇	#2293	1	1	yes	characteristic
215	C₂×C₄₇	C₄×AGL(1,ℤ/8)	1	2	yes	—
216	C₂×C₄₇	#3180	1	2	yes	—
217	C₂×C₄₇	#3183	1	1	yes	characteristic
218	C₂×C₄₇	#3184	1	1	yes	characteristic
219	C₂²×D₈	C₂×D₄₇	1	1	yes	characteristic
220	C₂×C₄×D₄	C₂×D₄₇	1	2	yes	—
221	C₂×#117	—	94	2	no	—
222	#442	Dic₄₇	1	8	yes	complemented
223	C₂×#107	—	47	1	no	—
224	C₂×#106	—	47	1	no	—
225	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
226	C₂×#102	—	47	2	no	—
227	C₂×#102	—	47	2	no	—
228	C₂×#102	C₂×D₄₇	1	2	yes	—
229	C₂×#97	—	47	1	no	—
230	C₂×#97	—	47	1	no	—
231	C₂×#97	—	47	1	no	—
232	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
233	C₂×C₄×C₈	—	47	1	no	—
234	C₂×C₄×C₈	—	47	1	no	—
235	#390	—	47	2	no	—
236	#390	—	47	2	no	—
237	#389	—	47	2	no	—
238	#389	—	47	2	no	—
239	#388	—	94	2	no	—
240	#388	—	94	2	no	—
241	C₄×C₄⋊C₄	—	47	2	no	—
242	C₄×C₂²⋊C₄	—	94	2	no	—
243	C₄³	—	47	1	no	—
244	#340	—	47	2	no	—
245	#340	—	47	2	no	—
246	#340	—	47	2	no	—
247	C₄₇	#21286	1	1	yes	characteristic, complemented, Sylow
248	C₂²×D₄	C₂²×D₄₇	1	2	yes	—
249	C₂³×C₄	—	2	2	no	—
250	C₂×D₈	—	2	2	no	—
251	C₂×D₈	—	2	2	no	—
252	C₂×D₈	C₂×Dic₄₇	1	4	yes	—
253	C₂²×C₈	—	47	1	no	—
254	C₂²×C₈	—	47	1	no	—
255	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
256	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
257	C₄×D₄	—	2	4	no	—
258	C₄×D₄	C₂×Dic₄₇	1	8	yes	—
259	#117	—	188	8	no	—
260	C₂×C₄⋊C₄	—	47	2	no	—
261	C₂×C₄⋊C₄	—	47	2	no	—
262	C₂×C₄⋊C₄	—	94	2	no	—
263	C₂×C₄⋊C₄	—	94	2	no	—
264	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
265	C₂×C₂²⋊C₄	—	2	2	no	—
266	C₂×C₂²⋊C₄	—	94	2	no	—
267	C₂×C₂²⋊C₄	—	94	2	no	—
268	C₂×C₂²⋊C₄	—	94	2	no	—
269	C₂×C₂²⋊C₄	—	94	2	no	—
270	C₂×C₄²	—	47	2	no	—
271	C₂×C₄²	—	47	1	no	—
272	C₂×C₄²	—	47	1	no	—
273	C₂×C₄²	—	47	2	no	—
274	C₂×C₄²	—	94	2	no	—
275	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
276	#107	—	94	2	no	—
277	#106	—	94	2	no	—
278	#106	C₂×Dic₄₇	1	4	yes	—
279	#102	—	94	4	no	—
280	#102	—	94	4	no	—
281	#102	C₂×Dic₄₇	1	8	yes	—
282	#97	—	94	2	no	—
283	#97	—	94	2	no	—
284	#97	—	94	2	no	—
285	#97	C₂×Dic₄₇	1	4	yes	—
286	C₄×C₈	—	94	2	no	—
287	C₄×C₈	—	94	2	no	—
288	#95	—	94	2	no	—
289	#95	—	94	2	no	—
290	#95	—	94	2	no	—
291	C₂⁴	—	2	2	no	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	—	2	2	no	—
294	C₂×D₄	—	2	2	no	—
295	C₂×D₄	—	2	2	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	C₂²×Dic₄₇	1	4	yes	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	8	no	—
300	C₂²×C₄	—	4	4	no	—
301	C₂²×C₄	—	4	4	no	—
302	C₂²×C₄	—	47	2	no	—
303	C₂²×C₄	—	47	1	no	—
304	C₂²×C₄	—	47	1	no	—
305	C₂²×C₄	—	94	2	no	—
306	C₂²×C₄	—	94	2	no	—
307	C₂²×C₄	D₄×D₄₇	1	2	yes	—
308	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
309	D₈	—	2	8	no	—
310	C₂×C₈	—	2	1	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	47	2	no	—
313	C₂×C₈	—	47	2	no	—
314	C₂×C₈	—	94	1	no	—
315	C₂×C₈	—	94	1	no	—
316	C₂×C₈	—	94	1	no	—
317	C₂×C₈	—	94	1	no	—
318	C₂×C₈	#10625350	1	2	yes	—
319	C₂×C₈	#10625350	1	2	yes	—
320	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
321	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	—	94	2	no	—
324	C₄⋊C₄	—	94	2	no	—
325	C₄⋊C₄	—	94	2	no	—
326	C₄⋊C₄	—	94	2	no	—
327	C₄⋊C₄	—	188	4	no	—
328	C₄⋊C₄	—	188	4	no	—
329	C₄⋊C₄	C₂²×Dic₄₇	1	4	yes	—
330	C₂²⋊C₄	—	2	8	no	—
331	C₂²⋊C₄	—	188	4	no	—
332	C₂²⋊C₄	—	188	4	no	—
333	C₂²⋊C₄	—	188	4	no	—
334	C₂²⋊C₄	—	188	4	no	—
335	C₄²	—	94	4	no	—
336	C₄²	—	94	1	no	—
337	C₄²	—	94	1	no	—
338	C₄²	—	94	1	no	—
339	C₄²	—	94	1	no	—
340	C₄²	—	188	2	no	—
341	C₄²	—	188	4	no	—
342	C₄²	#10625352	1	2	yes	—
343	C₄²	C₂²×Dic₄₇	1	2	yes	—
344	C₂³	—	2	4	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	4	2	no	—
349	C₂³	—	4	2	no	—
350	C₂³	—	4	2	no	—
351	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
352	D₄	—	2	4	no	—
353	D₄	—	2	4	no	—
354	D₄	—	4	2	no	—
355	D₄	—	4	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	4	no	—
359	C₂×C₄	—	4	16	no	—
360	C₂×C₄	—	4	2	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	47	4	no	—
363	C₂×C₄	—	94	2	no	—
364	C₂×C₄	—	94	2	no	—
365	C₂×C₄	—	94	2	no	—
366	C₂×C₄	—	94	2	no	—
367	C₂×C₄	—	94	1	no	—
368	C₂×C₄	—	94	1	no	—
369	C₂×C₄	—	188	2	no	—
370	C₂×C₄	—	188	2	no	—
371	C₂×C₄	—	188	2	no	—
372	C₂×C₄	—	188	2	no	—
373	C₂×C₄	—	188	2	no	—
374	C₂×C₄	—	188	2	no	—
375	C₂×C₄	D₄×Dic₄₇	1	4	yes	—
376	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
377	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
378	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
379	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
380	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
381	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
382	C₈	—	2	2	no	—
383	C₈	—	94	2	no	—
384	C₈	—	94	2	no	—
385	C₈	#13093983	1	4	yes	complemented
386	C₂²	—	4	4	no	—
387	C₂²	—	4	4	no	—
388	C₂²	—	4	4	no	—
389	C₂²	—	8	2	no	—
390	C₂²	—	8	2	no	—
391	C₂²	—	8	2	no	—
392	C₂²	—	8	2	no	—
393	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
394	C₂²	#15689670	1	1	yes	characteristic
395	C₂²	#15689670	1	1	yes	characteristic
396	C₂²	AGL(1,ℤ/8)×D₄₇	1	2	yes	—
397	C₂²	#15689919	1	2	yes	—
398	C₄	—	2	4	no	—
399	C₄	—	4	4	no	—
400	C₄	—	94	4	no	—
401	C₄	—	376	2	no	—
402	C₄	—	376	2	no	—
403	C₄	—	188	1	no	—
404	C₄	—	188	1	no	—
405	C₄	C₂×#13093983	1	1	yes	characteristic
406	C₄	#41×Dic₄₇	1	1	yes	characteristic
407	C₄	#15689655	1	1	yes	characteristic
408	C₄	#15689655	1	1	yes	characteristic
409	C₂	—	8	4	no	—
410	C₂	#20245853	1	1	yes	characteristic
411	C₂	AGL(1,ℤ/8)×Dic₄₇	1	2	yes	—
412	C₂	#20254084	1	2	yes	—
413	C₂	#20254115	1	1	yes	characteristic
414	C₂	#20254123	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#442	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂²×D₈×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#442	D₄₇
hypocenter	C₄₇	#21286
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#442

Complements

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

N	H ≅ G/N	type
1. #20245853	C₂	semidirect
4. #20244132	C₂	semidirect
5. #20244117	C₂	semidirect
6. #20244087	C₂	semidirect
7. #20244073	C₂	semidirect
8. #20243285	C₂	semidirect
9. #20243213	C₂	semidirect
10. #97×Dic₄₇	C₂	semidirect
36. C₄₇×#442	C₄	semidirect
175. C₈×C₄₇	#117	semidirect
222. #442	Dic₄₇	semidirect
247. C₄₇	#21286	semidirect
385. C₈	#13093983	semidirect

Maximal subgroups

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

subgroup	index
#20245853	2
#20244265	2
#20244255	2
#20244132	2
#20244117	2
#20244087	2
#20244073	2
#20243285	2
#20243213	2
#97×Dic₄₇	2
C₂×C₄₇×#442	2
#21286	47