Subgroups — #26226770

Order 12032.

770 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689178	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689145	C₂	1	1	yes	maximal, characteristic
3	#20245784	C₂	1	1	yes	maximal, characteristic
4	#20244112	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244111	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244109	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243572	C₂	1	2	yes	maximal
8	#20243569	C₂	1	2	yes	maximal
9	#20243541	C₂	1	2	yes	maximal, complemented
10	#20243506	C₂	1	2	yes	maximal, complemented
11	C₄₇×#1940	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	2	yes	—
13	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
14	#15689178	—	2	4	no	—
15	#15689145	—	2	4	no	—
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
18	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
19	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
21	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
22	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
23	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
24	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×#13093935	C₂²	1	1	yes	characteristic
26	#15688990	C₄	1	2	yes	—
27	#15688988	C₄	1	2	yes	—
28	#15688985	C₄	1	2	yes	—
29	#15688980	C₄	1	2	yes	—
30	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
31	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
32	#15688969	C₂²	1	2	yes	—
33	#15688878	C₂²	1	2	yes	—
34	#15688877	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
38	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
39	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#336	C₂²	1	2	yes	—
41	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
43	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
44	C₂×#10625324	—	2	4	no	—
45	C₂×#10625324	—	4	2	no	—
46	C₂×#10625324	—	4	2	no	—
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
50	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
51	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	4	yes	—
52	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
55	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
56	C₄²×D₄₇	D₄	1	4	yes	—
57	C₄²×D₄₇	Q₈	1	4	yes	—
58	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
59	C₄⋊(C₄₇⋊C₈)	—	4	2	no	—
60	Dic₄₇⋊C₈	—	2	4	no	—
61	Dic₄₇⋊C₈	—	2	2	no	—
62	Dic₄₇⋊C₈	—	2	2	no	—
63	Dic₄₇⋊C₈	—	4	2	no	—
64	Dic₄₇⋊C₈	—	4	2	no	—
65	(C₂×D₄₇)⋊C₈	—	2	2	no	—
66	(C₂×D₄₇)⋊C₈	—	2	2	no	—
67	#13093935	—	2	2	no	—
68	C₄₇⋊#95	C₂×C₄	1	4	yes	—
69	C₄₇⋊#95	C₂×C₄	1	4	yes	—
70	C₄₇⋊#95	C₂×C₄	1	4	yes	—
71	C₄₇⋊#95	C₂×C₄	1	2	yes	—
72	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
75	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
76	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
77	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
78	C₄⋊C₈×C₄₇	—	2	2	no	—
79	C₄⋊C₈×C₄₇	—	4	2	no	—
80	#97×C₄₇	—	2	2	no	—
81	#95×C₄₇	C₂×C₄	1	2	yes	—
82	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂²×C₄	1	4	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	1	yes	characteristic
89	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
91	C₂×C₄×D₄₇	—	2	1	no	—
92	C₂×C₄×D₄₇	—	2	1	no	—
93	C₂×C₄×D₄₇	—	2	1	no	—
94	C₂×C₄×D₄₇	—	2	1	no	—
95	C₂×C₄×D₄₇	—	4	2	no	—
96	C₂×C₄×D₄₇	—	4	2	no	—
97	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
98	C₂×C₄×D₄₇	C₄⋊C₄	1	4	yes	—
99	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
100	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
101	C₂×C₈×C₄₇	—	2	2	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	—	2	2	no	—
106	C₂×C₈×C₄₇	—	2	1	no	—
107	C₂×C₈×C₄₇	—	2	2	no	—
108	C₂×C₈×C₄₇	—	2	1	no	—
109	C₂×C₈×C₄₇	—	2	1	no	—
110	C₄⋊C₄×C₄₇	—	4	2	no	—
111	C₄²×C₄₇	—	2	2	no	—
112	C₄²×C₄₇	—	2	2	no	—
113	C₄²×C₄₇	C₂×D₄	1	2	yes	—
114	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
115	(C₂×D₄₇)⋊C₄	—	4	4	no	—
116	C₄⋊Dic₄₇	—	4	2	no	—
117	C₄×Dic₄₇	—	2	2	no	—
118	C₄×Dic₄₇	—	2	2	no	—
119	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
120	C₄×Dic₄₇	C₄⋊C₄	1	4	yes	—
121	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
122	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
123	C₂×C₄₇⋊C₈	—	2	1	no	—
124	C₂×C₄₇⋊C₈	—	2	1	no	—
125	C₂×C₄₇⋊C₈	—	2	2	no	—
126	C₂×C₄₇⋊C₈	—	2	1	no	—
127	C₂×C₄₇⋊C₈	—	2	2	no	—
128	C₂×C₄₇⋊C₈	—	2	1	no	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	2	1	no	—
131	C₂×C₄₇⋊C₈	—	2	1	no	—
132	#10625324	—	4	8	no	—
133	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
134	C₂²×D₄₇	—	2	1	no	—
135	C₂²×D₄₇	—	2	1	no	—
136	C₂²×D₄₇	—	2	2	no	—
137	C₂²×D₄₇	—	2	2	no	—
138	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	2	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	4	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
145	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
146	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
149	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
150	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
151	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
152	C₂×Dic₄₇	—	2	1	no	—
153	C₂×Dic₄₇	—	2	1	no	—
154	C₂×Dic₄₇	—	2	2	no	—
155	C₂×Dic₄₇	—	2	2	no	—
156	C₂×Dic₄₇	—	2	4	no	—
157	C₂×Dic₄₇	—	2	4	no	—
158	C₂×Dic₄₇	—	2	4	no	—
159	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
160	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
161	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
162	C₄×D₄₇	—	2	2	no	—
163	C₄×D₄₇	—	2	2	no	—
164	C₄×D₄₇	—	2	2	no	—
165	C₄×D₄₇	—	2	2	no	—
166	C₄×D₄₇	—	4	4	no	—
167	C₄×D₄₇	—	4	4	no	—
168	C₈×C₄₇	—	4	2	no	—
169	C₈×C₄₇	—	4	1	no	—
170	C₈×C₄₇	—	4	1	no	—
171	C₄₇⋊C₈	—	4	2	no	—
172	C₄₇⋊C₈	—	4	1	no	—
173	C₄₇⋊C₈	—	4	1	no	—
174	#21979	—	47	1	no	maximal, Sylow
175	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
176	C₂²×C₄₇	#520	1	1	yes	characteristic
177	C₂²×C₄₇	#520	1	1	yes	characteristic
178	C₂²×C₄₇	#568	1	2	yes	—
179	C₂²×C₄₇	#568	1	2	yes	—
180	C₂×D₄₇	—	2	2	no	—
181	C₂×D₄₇	—	2	2	no	—
182	C₂×D₄₇	—	2	2	no	—
183	C₂×D₄₇	—	4	2	no	—
184	C₂×D₄₇	—	4	2	no	—
185	C₄×C₄₇	—	2	2	no	—
186	C₄×C₄₇	—	2	2	no	—
187	C₄×C₄₇	—	4	4	no	—
188	C₄×C₄₇	#535	1	1	yes	characteristic
189	C₄×C₄₇	#536	1	1	yes	characteristic
190	C₄×C₄₇	#544	1	1	yes	characteristic
191	C₄×C₄₇	#544	1	1	yes	characteristic
192	Dic₄₇	—	2	2	no	—
193	Dic₄₇	—	2	2	no	—
194	Dic₄₇	—	2	2	no	—
195	Dic₄₇	—	4	4	no	—
196	C₂×#432	—	47	1	no	—
197	C₂×#423	—	47	1	no	—
198	#2283	—	47	1	no	—
199	#1940	—	47	1	no	—
200	#1940	—	47	1	no	—
201	#1940	—	47	1	no	—
202	#1940	D₄₇	1	1	yes	characteristic, complemented
203	#1851	—	47	2	no	—
204	#1851	—	47	2	no	—
205	#1843	—	47	2	no	—
206	#1832	—	47	2	no	—
207	C₂×C₄₇	#2317	1	1	yes	characteristic
208	C₂×C₄₇	#2905	1	1	yes	characteristic
209	C₂×C₄₇	#2905	1	1	yes	characteristic
210	C₂×C₄₇	#2995	1	2	yes	—
211	C₂×C₄₇	#2995	1	2	yes	—
212	D₄₇	—	4	2	no	—
213	C₂²×M₁₆	—	47	2	no	—
214	C₂²×C₄²	—	47	1	no	—
215	#432	—	94	4	no	—
216	#423	—	94	4	no	—
217	C₂×C₄⋊C₈	—	47	1	no	—
218	C₂×C₄⋊C₈	—	47	2	no	—
219	C₂×C₄⋊C₈	—	47	1	no	—
220	C₂×C₄⋊C₈	—	47	1	no	—
221	C₂×C₄⋊C₈	—	47	2	no	—
222	C₂×C₄⋊C₈	—	47	2	no	—
223	C₂×C₄⋊C₈	—	47	2	no	—
224	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
225	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
226	C₂×C₂²⋊C₈	—	47	1	no	—
227	C₂×C₂²⋊C₈	—	47	1	no	—
228	C₂×#97	—	47	1	no	—
229	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
230	#383	—	47	2	no	—
231	#382	—	47	2	no	—
232	#381	—	47	2	no	—
233	#380	—	47	2	no	—
234	C₄×C₄⋊C₄	—	47	1	no	—
235	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
236	C₄×C₂²⋊C₄	—	47	2	no	—
237	#376	—	47	2	no	—
238	#336	—	47	2	no	—
239	#336	—	47	2	no	—
240	#336	—	47	2	no	—
241	#336	C₂×D₄₇	1	2	yes	—
242	C₄₇	#21979	1	1	yes	characteristic, complemented, Sylow
243	C₂³×C₄	—	47	1	no	—
244	C₂³×C₄	—	47	1	no	—
245	C₂³×C₄	—	47	1	no	—
246	C₂×M₁₆	—	94	4	no	—
247	C₂×M₁₆	—	188	2	no	—
248	C₂×M₁₆	—	188	2	no	—
249	C₂²×C₈	—	47	2	no	—
250	C₂²×C₈	—	47	1	no	—
251	C₂²×C₈	—	47	1	no	—
252	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
253	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
254	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
255	C₂×C₄⋊C₄	—	47	2	no	—
256	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
257	C₂×C₂²⋊C₄	—	47	4	no	—
258	C₂×C₄²	—	47	1	no	—
259	C₂×C₄²	—	47	1	no	—
260	C₂×C₄²	—	47	1	no	—
261	C₂×C₄²	—	47	4	no	—
262	C₂×C₄²	—	47	4	no	—
263	C₂×C₄²	—	47	2	no	—
264	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
265	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
266	C₄⋊C₈	—	2	2	no	—
267	C₄⋊C₈	—	4	2	no	—
268	C₄⋊C₈	—	94	4	no	—
269	C₄⋊C₈	—	94	2	no	—
270	C₄⋊C₈	—	94	2	no	—
271	C₄⋊C₈	—	94	2	no	—
272	C₄⋊C₈	—	188	2	no	—
273	C₄⋊C₈	—	188	2	no	—
274	C₄⋊C₈	—	188	2	no	—
275	C₂²⋊C₈	—	94	2	no	—
276	C₂²⋊C₈	—	94	2	no	—
277	#97	—	2	2	no	—
278	#97	—	94	2	no	—
279	#95	—	47	4	no	—
280	#95	—	47	4	no	—
281	#95	—	47	4	no	—
282	#95	—	47	2	no	—
283	#95	C₄×D₄₇	1	2	yes	—
284	C₂⁴	—	47	1	no	—
285	C₂²×C₄	—	47	1	no	—
286	C₂²×C₄	—	47	1	no	—
287	C₂²×C₄	—	47	1	no	—
288	C₂²×C₄	—	47	2	no	—
289	C₂²×C₄	—	47	2	no	—
290	C₂²×C₄	—	47	4	no	—
291	C₂²×C₄	—	47	4	no	—
292	C₂²×C₄	—	47	4	no	—
293	C₂²×C₄	—	94	1	no	—
294	C₂²×C₄	—	94	1	no	—
295	C₂²×C₄	—	94	1	no	—
296	C₂²×C₄	—	94	1	no	—
297	C₂²×C₄	—	188	2	no	—
298	C₂²×C₄	—	188	2	no	—
299	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
300	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
301	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
302	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
303	M₁₆	—	188	8	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	1	no	—
306	C₂×C₈	—	2	2	no	—
307	C₂×C₈	—	2	1	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	1	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	94	1	no	—
314	C₂×C₈	—	94	1	no	—
315	C₂×C₈	—	94	2	no	—
316	C₂×C₈	—	94	1	no	—
317	C₂×C₈	—	94	2	no	—
318	C₂×C₈	—	94	1	no	—
319	C₂×C₈	—	94	2	no	—
320	C₂×C₈	—	94	1	no	—
321	C₂×C₈	—	94	1	no	—
322	C₄⋊C₄	—	4	2	no	—
323	C₄⋊C₄	—	188	2	no	—
324	C₂²⋊C₄	—	188	4	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	47	4	no	—
328	C₄²	—	47	4	no	—
329	C₄²	—	47	2	no	—
330	C₄²	—	47	2	no	—
331	C₄²	—	94	2	no	—
332	C₄²	—	94	2	no	—
333	C₄²	D₄×D₄₇	1	2	yes	—
334	C₄²	Q₈×D₄₇	1	2	yes	—
335	C₂³	—	47	2	no	—
336	C₂³	—	94	1	no	—
337	C₂³	—	94	1	no	—
338	C₂³	—	94	2	no	—
339	C₂³	—	94	2	no	—
340	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
341	C₂×C₄	—	2	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	4	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	47	2	no	—
347	C₂×C₄	—	47	2	no	—
348	C₂×C₄	—	47	2	no	—
349	C₂×C₄	—	94	1	no	—
350	C₂×C₄	—	94	1	no	—
351	C₂×C₄	—	94	2	no	—
352	C₂×C₄	—	94	2	no	—
353	C₂×C₄	—	94	2	no	—
354	C₂×C₄	—	94	2	no	—
355	C₂×C₄	—	94	2	no	—
356	C₂×C₄	—	94	2	no	—
357	C₂×C₄	—	94	4	no	—
358	C₂×C₄	—	94	4	no	—
359	C₂×C₄	—	94	4	no	—
360	C₂×C₄	—	188	4	no	—
361	C₂×C₄	—	188	4	no	—
362	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
363	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
364	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
365	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
366	C₂×C₄	#13094069	1	1	yes	characteristic
367	C₂×C₄	#13094070	1	1	yes	characteristic
368	C₂×C₄	#13094071	1	1	yes	characteristic
369	C₂×C₄	#13094072	1	1	yes	characteristic
370	C₈	—	4	1	no	—
371	C₈	—	4	2	no	—
372	C₈	—	4	1	no	—
373	C₈	—	188	1	no	—
374	C₈	—	188	2	no	—
375	C₈	—	188	1	no	—
376	C₂²	—	94	2	no	—
377	C₂²	—	94	2	no	—
378	C₂²	—	94	2	no	—
379	C₂²	—	188	2	no	—
380	C₂²	—	188	2	no	—
381	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
382	C₂²	#15689602	1	1	yes	characteristic
383	C₂²	#15689605	1	1	yes	characteristic
384	C₂²	#15689888	1	2	yes	—
385	C₂²	#15689889	1	2	yes	—
386	C₄	—	2	2	no	—
387	C₄	—	2	2	no	—
388	C₄	—	4	4	no	—
389	C₄	—	94	2	no	—
390	C₄	—	94	2	no	—
391	C₄	—	94	2	no	—
392	C₄	—	188	4	no	—
393	C₄	#15689689	1	1	yes	characteristic
394	C₄	#15689696	1	1	yes	characteristic
395	C₄	#15689750	1	1	yes	characteristic
396	C₄	#15689753	1	1	yes	characteristic
397	C₂	—	188	2	no	—
398	C₂	#20246010	1	1	yes	characteristic
399	C₂	#20251949	1	1	yes	characteristic
400	C₂	#20251950	1	1	yes	characteristic
401	C₂	#20252554	1	2	yes	—
402	C₂	#20252557	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1940	C₂
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1940	D₄₇
hypocenter	C₄₇	#21979
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1940

Complements

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

N	H ≅ G/N	type
4. #20244112	C₂	semidirect
5. #20244111	C₂	semidirect
6. #20244109	C₂	semidirect
9. #20243541	C₂	semidirect
10. #20243506	C₂	semidirect
11. C₄₇×#1940	C₂	semidirect
202. #1940	D₄₇	semidirect
242. C₄₇	#21979	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689178	2
C₂×#15689145	2
#20245784	2
#20244112	2
#20244111	2
#20244109	2
#20243572	2
#20243569	2
#20243541	2
#20243506	2
C₄₇×#1940	2
#21979	47