Subgroups — #26215285

Order 12032.

982 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689202	C₂	1	1	yes	maximal, characteristic
2	C₂×C₈×D₁₈₈	C₂	1	1	yes	maximal, characteristic
3	#20245852	C₂	1	1	yes	maximal, characteristic
4	#20243255	C₂	1	1	yes	maximal, characteristic, complemented
5	C₈×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243241	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243170	C₂	1	2	yes	maximal, complemented
8	#20243163	C₂	1	2	yes	maximal, complemented
9	#20243153	C₂	1	2	yes	maximal, complemented
10	#20243083	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1744	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	2	yes	—
13	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
14	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
15	C₂×#13093981	C₂²	1	2	yes	—
16	#15689202	C₄	1	8	yes	complemented
17	C₈×D₁₈₈	C₄	1	8	yes	complemented
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
21	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
22	C₂×#13093935	C₂²	1	2	yes	—
23	C₂×#13093934	C₂²	1	2	yes	—
24	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
25	#15689025	C₄	1	2	yes	—
26	#15689021	C₄	1	2	yes	—
27	#15689014	C₄	1	4	yes	—
28	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
29	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
30	#15688878	C₂²	1	2	yes	—
31	#15688877	C₂²	1	2	yes	—
32	#15688877	C₂²	1	2	yes	—
33	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
35	C₄³×C₄₇	C₂²	1	1	yes	characteristic
36	C₄₇×#336	C₂²	1	1	yes	characteristic
37	C₄₇×#336	C₂²	1	1	yes	characteristic
38	C₄₇×#336	C₂²	1	1	yes	characteristic
39	C₄₇×#336	C₂²	1	1	yes	characteristic
40	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₄×D₄₇	C₂³	1	2	yes	—
42	C₂×#10625324	—	4	2	no	—
43	C₂×#10625324	—	4	2	no	—
44	C₂×#10625324	C₂×C₄	1	8	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
47	C₂×C₈×D₄₇	—	4	2	no	—
48	C₂×C₈×D₄₇	—	4	2	no	—
49	C₂×C₈×D₄₇	C₂×C₄	1	8	yes	—
50	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
51	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
52	#13093981	—	4	2	no	—
53	#13093981	—	4	2	no	—
54	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
55	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂×Dic₄₇⋊C₄	C₂×C₄	1	4	yes	—
57	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	4	yes	—
58	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	4	yes	—
59	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
60	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
61	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
62	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	—
63	(C₂×D₄₇)⋊C₈	C₂×C₄	1	8	yes	—
64	(C₂×D₄₇)⋊C₈	C₂×C₄	1	8	yes	—
65	#13093935	—	4	2	no	—
66	#13093934	—	4	2	no	—
67	C₈×Dic₄₇	—	4	2	no	—
68	C₄₇⋊#95	C₂×C₄	1	4	yes	—
69	C₄₇⋊#95	C₂×C₄	1	2	yes	—
70	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
71	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
72	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
75	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
76	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
79	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	—
80	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	—
81	C₂³×D₄₇	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
87	C₂²×Dic₄₇	C₂²×C₄	1	4	yes	—
88	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
89	C₂×D₁₈₈	—	2	4	no	—
90	C₂×D₁₈₈	C₄²	1	4	yes	—
91	C₂×C₄×D₄₇	—	2	2	no	—
92	C₂×C₄×D₄₇	—	2	2	no	—
93	C₂×C₄×D₄₇	—	2	2	no	—
94	C₂×C₄×D₄₇	—	2	2	no	—
95	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
96	C₂×C₄×D₄₇	C₂²×C₄	1	4	yes	—
97	C₂×C₈×C₄₇	—	2	1	no	—
98	C₂×C₈×C₄₇	—	2	1	no	—
99	C₂×C₈×C₄₇	—	2	1	no	—
100	C₂×C₈×C₄₇	—	2	1	no	—
101	C₂×C₈×C₄₇	—	2	1	no	—
102	C₂×C₈×C₄₇	—	2	1	no	—
103	C₂×C₈×C₄₇	—	2	1	no	—
104	C₂×C₈×C₄₇	—	2	1	no	—
105	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
106	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
107	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
108	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
109	C₄²×C₄₇	—	2	4	no	—
110	C₄²×C₄₇	—	2	1	no	—
111	C₄²×C₄₇	—	2	1	no	—
112	C₄²×C₄₇	—	2	1	no	—
113	C₄²×C₄₇	—	2	1	no	—
114	C₄²×C₄₇	—	4	2	no	—
115	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
116	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
117	(C₂×D₄₇)⋊C₄	—	4	4	no	—
118	(C₂×D₄₇)⋊C₄	—	4	4	no	—
119	(C₂×D₄₇)⋊C₄	C₄²	1	8	yes	—
120	C₄⋊Dic₄₇	—	2	4	no	—
121	C₄⋊Dic₄₇	C₄²	1	4	yes	—
122	Dic₄₇⋊C₄	—	4	4	no	—
123	C₄×Dic₄₇	—	2	2	no	—
124	C₄×Dic₄₇	—	2	2	no	—
125	C₂×C₄₇⋊C₈	—	2	2	no	—
126	C₂×C₄₇⋊C₈	—	2	2	no	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	—	2	2	no	—
129	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
130	C₂×C₄₇⋊C₈	C₂²×C₄	1	4	yes	—
131	#10625324	—	4	8	no	—
132	C₈×D₄₇	—	4	8	no	—
133	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
134	C₂²×D₄₇	—	2	2	no	—
135	C₂²×D₄₇	—	2	2	no	—
136	C₂²×D₄₇	—	2	4	no	—
137	C₂²×D₄₇	—	2	4	no	—
138	C₂²×D₄₇	C₂×C₄²	1	4	yes	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	2	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	2	2	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
147	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
148	C₂×C₄×C₄₇	#131	1	4	yes	—
149	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
152	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
153	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
154	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
155	C₂×Dic₄₇	—	2	2	no	—
156	C₂×Dic₄₇	—	2	2	no	—
157	C₂×Dic₄₇	—	2	4	no	—
158	C₂×Dic₄₇	—	2	4	no	—
159	C₂×Dic₄₇	—	2	4	no	—
160	C₂×Dic₄₇	C₂×C₄²	1	4	yes	—
161	D₁₈₈	—	2	8	no	—
162	C₄×D₄₇	—	2	4	no	—
163	C₄×D₄₇	—	2	4	no	—
164	C₄×D₄₇	—	2	4	no	—
165	C₄×D₄₇	—	2	4	no	—
166	C₈×C₄₇	—	2	2	no	—
167	C₈×C₄₇	—	2	2	no	—
168	C₈×C₄₇	—	2	2	no	—
169	C₈×C₄₇	—	2	2	no	—
170	C₄₇⋊C₈	—	2	4	no	—
171	C₄₇⋊C₈	—	2	4	no	—
172	#20565	—	47	1	no	maximal, Sylow
173	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
174	C₂²×C₄₇	#518	1	1	yes	characteristic
175	C₂²×C₄₇	#520	1	1	yes	characteristic
176	C₂²×C₄₇	C₂×#131	1	2	yes	—
177	C₂²×C₄₇	#568	1	2	yes	—
178	C₂×D₄₇	—	2	4	no	—
179	C₂×D₄₇	—	2	4	no	—
180	C₂×D₄₇	—	2	4	no	—
181	C₂×D₄₇	—	4	4	no	—
182	C₂×D₄₇	—	4	4	no	—
183	C₄×C₄₇	—	2	2	no	—
184	C₄×C₄₇	—	4	2	no	—
185	C₄×C₄₇	—	4	2	no	—
186	C₄×C₄₇	#405	1	4	yes	—
187	C₄×C₄₇	#518	1	1	yes	characteristic
188	C₄×C₄₇	#518	1	1	yes	characteristic
189	C₄×C₄₇	#520	1	1	yes	characteristic
190	C₄×C₄₇	#520	1	1	yes	characteristic
191	Dic₄₇	—	2	4	no	—
192	Dic₄₇	—	4	4	no	—
193	C₂×#436	—	47	1	no	—
194	C₂×C₈×D₄	—	47	1	no	—
195	#2293	—	47	1	no	—
196	#1770	—	47	1	no	—
197	C₈×C₄⋊C₄	—	47	1	no	—
198	#1767	—	47	1	no	—
199	#1753	—	47	2	no	—
200	#1752	—	47	2	no	—
201	#1750	—	47	2	no	—
202	#1744	D₄₇	1	1	yes	characteristic, complemented
203	#1729	—	47	2	no	—
204	C₂×C₄₇	#2275	1	1	yes	characteristic
205	C₂×C₄₇	C₂×#405	1	1	yes	characteristic
206	C₂×C₄₇	#2875	1	1	yes	characteristic
207	C₂×C₄₇	#2981	1	2	yes	—
208	C₂×C₄₇	#2993	1	2	yes	—
209	D₄₇	—	4	4	no	—
210	C₂²×M₁₆	—	47	2	no	—
211	C₂³×C₈	—	47	2	no	—
212	C₂×C₄×D₄	—	47	1	no	—
213	C₂×#117	—	47	2	no	—
214	#436	—	47	8	no	—
215	C₈×D₄	—	47	8	no	—
216	C₂×C₄⋊C₈	—	47	1	no	—
217	C₂×C₄⋊C₈	—	47	1	no	—
218	C₂×C₂²⋊C₈	—	47	2	no	—
219	C₂×C₂²⋊C₈	—	47	2	no	—
220	C₂×#97	—	47	2	no	—
221	C₂×#97	—	47	2	no	—
222	C₂×C₄×C₈	—	47	2	no	—
223	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
224	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
225	#390	—	47	2	no	—
226	#389	—	47	2	no	—
227	#388	—	47	4	no	—
228	C₄×C₄⋊C₄	—	47	1	no	—
229	C₄×C₂²⋊C₄	—	47	2	no	—
230	C₄³	C₂×D₄₇	1	1	yes	characteristic
231	#336	—	47	2	no	—
232	#336	—	47	2	no	—
233	#336	—	47	2	no	—
234	#336	C₂×D₄₇	1	1	yes	characteristic
235	#336	C₂×D₄₇	1	1	yes	characteristic
236	#336	C₂×D₄₇	1	1	yes	characteristic
237	#336	C₂×D₄₇	1	1	yes	characteristic
238	C₄₇	#20565	1	1	yes	characteristic, complemented, Sylow
239	C₂²×D₄	—	47	1	no	—
240	C₂³×C₄	—	47	2	no	—
241	C₂×M₁₆	—	47	8	no	—
242	C₂×M₁₆	—	188	2	no	—
243	C₂×M₁₆	—	188	2	no	—
244	C₂²×C₈	—	47	2	no	—
245	C₂²×C₈	—	47	2	no	—
246	C₂²×C₈	—	47	8	no	—
247	C₂²×C₈	—	188	2	no	—
248	C₂²×C₈	—	188	2	no	—
249	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
250	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
251	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
252	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
253	C₄×D₄	—	47	4	no	—
254	C₄×D₄	—	47	4	no	—
255	#117	—	188	2	no	—
256	#117	—	188	2	no	—
257	C₂×C₄⋊C₄	—	47	1	no	—
258	C₂×C₄⋊C₄	—	47	2	no	—
259	C₂×C₄⋊C₄	—	47	4	no	—
260	C₂×C₂²⋊C₄	—	47	2	no	—
261	C₂×C₂²⋊C₄	—	47	4	no	—
262	C₂×C₂²⋊C₄	—	47	4	no	—
263	C₂×C₄²	—	47	2	no	—
264	C₂×C₄²	C₄×D₄₇	1	2	yes	—
265	C₂×C₄²	C₄×D₄₇	1	2	yes	—
266	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
267	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
268	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
269	C₄⋊C₈	—	47	4	no	—
270	C₄⋊C₈	—	47	4	no	—
271	C₂²⋊C₈	—	47	8	no	—
272	C₂²⋊C₈	—	47	8	no	—
273	#97	—	188	2	no	—
274	#97	—	188	2	no	—
275	C₄×C₈	—	188	2	no	—
276	C₄×C₈	C₄×D₄₇	1	4	yes	—
277	C₄×C₈	C₄×D₄₇	1	4	yes	—
278	#95	—	47	4	no	—
279	#95	—	47	2	no	—
280	C₂⁴	—	47	2	no	—
281	C₂×D₄	—	47	4	no	—
282	C₂×D₄	—	94	4	no	—
283	C₂²×C₄	—	47	2	no	—
284	C₂²×C₄	—	47	4	no	—
285	C₂²×C₄	—	47	4	no	—
286	C₂²×C₄	—	47	4	no	—
287	C₂²×C₄	—	94	2	no	—
288	C₂²×C₄	—	94	2	no	—
289	C₂²×C₄	—	94	2	no	—
290	C₂²×C₄	—	94	2	no	—
291	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
292	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
293	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
295	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
296	M₁₆	—	188	8	no	—
297	C₂×C₈	—	2	1	no	—
298	C₂×C₈	—	2	1	no	—
299	C₂×C₈	—	2	1	no	—
300	C₂×C₈	—	2	1	no	—
301	C₂×C₈	—	2	1	no	—
302	C₂×C₈	—	2	1	no	—
303	C₂×C₈	—	2	1	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	47	4	no	—
306	C₂×C₈	—	47	4	no	—
307	C₂×C₈	—	94	2	no	—
308	C₂×C₈	—	94	2	no	—
309	C₂×C₈	—	94	2	no	—
310	C₂×C₈	—	94	2	no	—
311	C₂×C₈	—	188	8	no	—
312	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
313	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
314	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
315	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
316	C₄⋊C₄	—	47	4	no	—
317	C₄⋊C₄	—	94	4	no	—
318	C₄⋊C₄	—	188	4	no	—
319	C₂²⋊C₄	—	47	8	no	—
320	C₂²⋊C₄	—	188	4	no	—
321	C₂²⋊C₄	—	188	4	no	—
322	C₄²	—	2	4	no	—
323	C₄²	—	2	1	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	2	1	no	—
327	C₄²	—	4	2	no	—
328	C₄²	—	94	2	no	—
329	C₄²	—	94	2	no	—
330	C₄²	C₂×C₄×D₄₇	1	2	yes	—
331	C₄²	C₂×C₄×D₄₇	1	2	yes	—
332	C₂³	—	47	4	no	—
333	C₂³	—	94	2	no	—
334	C₂³	—	94	2	no	—
335	C₂³	—	94	4	no	—
336	C₂³	—	94	4	no	—
337	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
338	D₄	—	94	8	no	—
339	C₂×C₄	—	2	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	2	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	47	4	no	—
347	C₂×C₄	—	94	2	no	—
348	C₂×C₄	—	94	2	no	—
349	C₂×C₄	—	94	4	no	—
350	C₂×C₄	—	94	4	no	—
351	C₂×C₄	—	94	4	no	—
352	C₂×C₄	—	94	4	no	—
353	C₂×C₄	—	94	4	no	—
354	C₂×C₄	—	94	4	no	—
355	C₂×C₄	—	94	4	no	—
356	C₂×C₄	C₄²×D₄₇	1	2	yes	—
357	C₂×C₄	C₄²×D₄₇	1	2	yes	—
358	C₂×C₄	#13094030	1	4	yes	—
359	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
360	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
361	C₂×C₄	#13094070	1	1	yes	characteristic
362	C₂×C₄	#13094070	1	1	yes	characteristic
363	C₂×C₄	#13094070	1	1	yes	characteristic
364	C₂×C₄	#13094071	1	1	yes	characteristic
365	C₈	—	2	2	no	—
366	C₈	—	2	2	no	—
367	C₈	—	2	2	no	—
368	C₈	—	2	2	no	—
369	C₈	—	94	4	no	—
370	C₈	—	94	4	no	—
371	C₂²	—	94	4	no	—
372	C₂²	—	94	4	no	—
373	C₂²	—	94	4	no	—
374	C₂²	—	188	4	no	—
375	C₂²	—	188	4	no	—
376	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
377	C₂²	#15689597	1	1	yes	characteristic
378	C₂²	#15689603	1	1	yes	characteristic
379	C₂²	C₂×#13094030	1	2	yes	—
380	C₂²	#15689889	1	2	yes	—
381	C₄	—	2	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	—	94	4	no	—
385	C₄	—	188	4	no	—
386	C₄	#15689077	1	4	yes	—
387	C₄	#15689597	1	1	yes	characteristic
388	C₄	#15689597	1	1	yes	characteristic
389	C₄	#15689603	1	1	yes	characteristic
390	C₄	#15689603	1	1	yes	characteristic
391	C₂	—	188	4	no	—
392	C₂	#20245750	1	1	yes	characteristic
393	C₂	C₂×#15689077	1	1	yes	characteristic
394	C₂	#20251813	1	1	yes	characteristic
395	C₂	#20252463	1	2	yes	—
396	C₂	#20252539	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₄₇×#1744	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×D₁₈₈	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1744	D₄₇
hypocenter	C₄₇	#20565
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1744

Complements

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

N	H ≅ G/N	type
4. #20243255	C₂	semidirect
5. C₈×C₄⋊Dic₄₇	C₂	semidirect
6. #20243241	C₂	semidirect
7. #20243170	C₂	semidirect
8. #20243163	C₂	semidirect
9. #20243153	C₂	semidirect
10. #20243083	C₂	semidirect
11. C₄₇×#1744	C₂	semidirect
16. #15689202	C₄	semidirect
17. C₈×D₁₈₈	C₄	semidirect
202. #1744	D₄₇	semidirect
238. C₄₇	#20565	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689202	2
C₂×C₈×D₁₈₈	2
#20245852	2
#20243255	2
C₈×C₄⋊Dic₄₇	2
#20243241	2
#20243170	2
#20243163	2
#20243153	2
#20243083	2
C₄₇×#1744	2
#20565	47