Subgroups — #26226462

Order 12032.

628 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	#20245886	C₂	1	1	yes	maximal, characteristic
2	#20244004	C₂	1	2	yes	maximal
3	#20243998	C₂	1	2	yes	maximal
4	#20243953	C₂	1	2	yes	maximal, complemented
5	#20243951	C₂	1	2	yes	maximal, complemented
6	#20243541	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243507	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243372	C₂	1	1	yes	maximal, characteristic
9	#20243243	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243243	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1798	C₂	1	1	yes	maximal, characteristic
12	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
13	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
14	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
15	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
16	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×#13093934	C₂²	1	2	yes	—
18	C₂×#13093934	C₂²	1	2	yes	—
19	#15689016	C₄	1	2	yes	—
20	#15689016	C₄	1	2	yes	—
21	#15689009	C₄	1	2	yes	—
22	#15689009	C₄	1	2	yes	—
23	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
24	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
25	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
26	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
27	#15688969	C₂²	1	1	yes	characteristic
28	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
29	#15688878	C₂²	1	2	yes	—
30	#15688877	C₂²	1	2	yes	—
31	#15688877	C₂²	1	2	yes	—
32	#15688877	C₂²	1	2	yes	—
33	#15688877	C₂²	1	2	yes	—
34	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
35	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×C₂²⋊C₈×C₄₇	C₂²	1	2	yes	—
38	C₄₇×#336	C₂²	1	2	yes	—
39	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
40	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
41	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
42	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
43	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
44	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
45	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
46	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
47	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
48	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
49	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
50	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
51	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
52	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
53	Dic₄₇⋊C₈	—	4	2	no	—
54	Dic₄₇⋊C₈	—	4	2	no	—
55	C₂²⋊(C₄₇⋊C₈)	—	4	2	no	—
56	#13093934	—	4	2	no	—
57	#13093934	—	4	2	no	—
58	C₄₇⋊#95	C₂×C₄	1	2	yes	—
59	C₄₇⋊#95	C₂×C₄	1	2	yes	—
60	C₄₇⋊#95	C₂×C₄	1	2	yes	—
61	C₄₇⋊#95	C₂×C₄	1	2	yes	—
62	C₄₇⋊#95	C₂×C₄	1	2	yes	—
63	C₄₇⋊#95	C₂×C₄	1	2	yes	—
64	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
65	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
66	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
67	#117×C₄₇	—	2	2	no	—
68	#117×C₄₇	—	2	2	no	—
69	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
75	C₄⋊C₈×C₄₇	—	2	2	no	—
76	C₄⋊C₈×C₄₇	—	2	2	no	—
77	C₂²⋊C₈×C₄₇	—	4	2	no	—
78	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₄₇	—	2	1	no	—
80	C₂²×C₄×C₄₇	—	2	1	no	—
81	C₂²×C₄×C₄₇	—	2	1	no	—
82	C₂²×C₄×C₄₇	—	2	1	no	—
83	C₂²×C₄×C₄₇	—	2	1	no	—
84	C₂²×C₄×C₄₇	—	2	1	no	—
85	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
91	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
92	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
93	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
94	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
95	C₂×C₈×C₄₇	—	2	2	no	—
96	C₂×C₈×C₄₇	—	2	2	no	—
97	C₂×C₈×C₄₇	—	2	2	no	—
98	C₂×C₈×C₄₇	—	2	2	no	—
99	C₂×C₈×C₄₇	—	2	2	no	—
100	C₂×C₈×C₄₇	—	2	2	no	—
101	C₄⋊C₄×C₄₇	—	2	2	no	—
102	C₄⋊C₄×C₄₇	—	2	2	no	—
103	C₂²⋊C₄×C₄₇	—	2	2	no	—
104	C₂²⋊C₄×C₄₇	—	2	2	no	—
105	C₄²×C₄₇	—	2	1	no	—
106	C₄²×C₄₇	—	2	1	no	—
107	C₄²×C₄₇	#41	1	2	yes	—
108	C₄²×C₄₇	#41	1	2	yes	—
109	C₂²⋊Dic₄₇	—	4	2	no	—
110	C₂²⋊Dic₄₇	—	4	2	no	—
111	C₄⋊Dic₄₇	—	4	2	no	—
112	C₄⋊Dic₄₇	—	4	2	no	—
113	C₄×Dic₄₇	—	2	1	no	—
114	C₄×Dic₄₇	—	2	1	no	—
115	C₄×Dic₄₇	—	2	1	no	—
116	C₄×Dic₄₇	—	2	1	no	—
117	C₄×Dic₄₇	—	2	1	no	—
118	C₄×Dic₄₇	—	2	1	no	—
119	C₄×Dic₄₇	—	2	1	no	—
120	C₄×Dic₄₇	—	2	1	no	—
121	C₄×Dic₄₇	—	4	2	no	—
122	C₄×Dic₄₇	—	4	2	no	—
123	C₂×C₄₇⋊C₈	—	2	2	no	—
124	C₂×C₄₇⋊C₈	—	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	C₂³×C₄₇	—	2	1	no	—
130	C₂³×C₄₇	—	2	1	no	—
131	C₂³×C₄₇	—	2	1	no	—
132	C₂³×C₄₇	—	2	2	no	—
133	C₂³×C₄₇	—	2	2	no	—
134	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	2	no	—
137	C₂×C₄×C₄₇	—	2	1	no	—
138	C₂×C₄×C₄₇	—	2	1	no	—
139	C₂×C₄×C₄₇	—	2	1	no	—
140	C₂×C₄×C₄₇	—	2	1	no	—
141	C₂×C₄×C₄₇	—	2	1	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	2	no	—
144	C₂×C₄×C₄₇	—	4	1	no	—
145	C₂×C₄×C₄₇	—	4	1	no	—
146	C₂×C₄×C₄₇	—	4	1	no	—
147	C₂×C₄×C₄₇	—	4	1	no	—
148	C₂×C₄×C₄₇	#117	1	2	yes	—
149	C₂×C₄×C₄₇	#117	1	2	yes	—
150	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂×#41	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×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
156	C₂×Dic₄₇	—	2	2	no	—
157	C₂×Dic₄₇	—	2	2	no	—
158	C₂×Dic₄₇	—	2	2	no	—
159	C₂×Dic₄₇	—	2	2	no	—
160	C₂×Dic₄₇	—	2	2	no	—
161	C₂×Dic₄₇	—	2	2	no	—
162	C₂×Dic₄₇	—	2	2	no	—
163	C₂×Dic₄₇	—	2	2	no	—
164	C₂×Dic₄₇	—	2	2	no	—
165	C₂×Dic₄₇	—	2	2	no	—
166	C₂×Dic₄₇	—	2	2	no	—
167	C₂×Dic₄₇	—	2	2	no	—
168	C₈×C₄₇	—	4	2	no	—
169	C₈×C₄₇	—	4	2	no	—
170	C₄₇⋊C₈	—	4	2	no	—
171	C₄₇⋊C₈	—	4	2	no	—
172	#21927	—	47	1	no	maximal, Sylow
173	C₂²×C₄₇	—	4	1	no	—
174	C₂²×C₄₇	—	4	1	no	—
175	C₂²×C₄₇	—	4	1	no	—
176	C₂²×C₄₇	—	4	2	no	—
177	C₂²×C₄₇	—	4	2	no	—
178	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
179	C₂²×C₄₇	#520	1	1	yes	characteristic
180	C₂²×C₄₇	#520	1	1	yes	characteristic
181	C₂²×C₄₇	#568	1	2	yes	—
182	C₂²×C₄₇	#568	1	2	yes	—
183	C₄×C₄₇	—	2	2	no	—
184	C₄×C₄₇	—	2	2	no	—
185	C₄×C₄₇	—	4	1	no	—
186	C₄×C₄₇	—	4	1	no	—
187	C₄×C₄₇	—	4	1	no	—
188	C₄×C₄₇	#540	1	1	yes	characteristic
189	C₄×C₄₇	#541	1	1	yes	characteristic
190	C₄×C₄₇	#542	1	1	yes	characteristic
191	C₄×C₄₇	#542	1	1	yes	characteristic
192	Dic₄₇	—	4	2	no	—
193	Dic₄₇	—	4	2	no	—
194	Dic₄₇	—	4	2	no	—
195	Dic₄₇	—	4	2	no	—
196	#2298	—	47	1	no	—
197	#1924	—	47	2	no	—
198	#1924	—	47	2	no	—
199	#1917	—	47	2	no	—
200	#1917	—	47	2	no	—
201	#1843	—	47	1	no	—
202	#1832	—	47	1	no	—
203	#1798	—	47	1	no	—
204	#1798	D₄₇	1	1	yes	characteristic
205	#1767	—	47	1	no	—
206	#1767	—	47	1	no	—
207	C₂×C₄₇	—	8	1	no	—
208	C₂×C₄₇	#2314	1	1	yes	characteristic
209	C₂×C₄₇	#2923	1	1	yes	characteristic
210	C₂×C₄₇	#2923	1	1	yes	characteristic
211	C₂×C₄₇	#2995	1	2	yes	—
212	C₂×C₄₇	#2995	1	2	yes	—
213	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
214	C₂×C₄⋊C₈	—	47	1	no	—
215	C₂×C₄⋊C₈	—	47	1	no	—
216	C₂×C₄⋊C₈	—	47	2	no	—
217	C₂×C₄⋊C₈	—	47	2	no	—
218	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
219	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
220	C₂×C₂²⋊C₈	—	47	2	no	—
221	C₂×C₂²⋊C₈	C₂×D₄₇	1	2	yes	—
222	C₂×#97	—	47	2	no	—
223	C₂×#97	—	47	2	no	—
224	#388	—	47	2	no	—
225	#388	—	47	2	no	—
226	#387	—	47	2	no	—
227	#387	—	47	2	no	—
228	C₄×C₄⋊C₄	—	47	1	no	—
229	C₄×C₄⋊C₄	—	47	1	no	—
230	C₄×C₂²⋊C₄	—	47	1	no	—
231	C₄×C₂²⋊C₄	—	47	1	no	—
232	#376	—	47	1	no	—
233	C₄³	—	47	1	no	—
234	#336	—	47	2	no	—
235	#336	—	47	2	no	—
236	#336	—	47	2	no	—
237	#336	—	47	2	no	—
238	#336	—	47	2	no	—
239	#336	C₂×D₄₇	1	2	yes	—
240	C₄₇	#21927	1	1	yes	characteristic, complemented, Sylow
241	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
242	C₂²×C₈	—	47	2	no	—
243	C₂²×C₈	—	47	2	no	—
244	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
245	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
246	#117	—	2	2	no	—
247	#117	—	2	2	no	—
248	C₂×C₄⋊C₄	—	47	2	no	—
249	C₂×C₄⋊C₄	—	47	2	no	—
250	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
251	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
252	C₂×C₂²⋊C₄	—	47	2	no	—
253	C₂×C₂²⋊C₄	—	47	2	no	—
254	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
255	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
256	C₂×C₄²	—	47	1	no	—
257	C₂×C₄²	—	47	1	no	—
258	C₂×C₄²	—	47	1	no	—
259	C₂×C₄²	—	47	1	no	—
260	C₂×C₄²	—	47	2	no	—
261	C₂×C₄²	—	47	2	no	—
262	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
263	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
264	C₄⋊C₈	—	2	2	no	—
265	C₄⋊C₈	—	2	2	no	—
266	C₄⋊C₈	—	94	2	no	—
267	C₄⋊C₈	—	94	2	no	—
268	C₄⋊C₈	—	188	2	no	—
269	C₄⋊C₈	—	188	2	no	—
270	C₂²⋊C₈	—	4	2	no	—
271	C₂²⋊C₈	—	188	2	no	—
272	#97	—	188	2	no	—
273	#97	—	188	2	no	—
274	#95	—	47	2	no	—
275	#95	—	47	2	no	—
276	#95	—	47	2	no	—
277	#95	—	47	2	no	—
278	#95	—	47	2	no	—
279	#95	—	47	2	no	—
280	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
281	C₂²×C₄	—	2	1	no	—
282	C₂²×C₄	—	2	1	no	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	1	no	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	47	2	no	—
288	C₂²×C₄	—	47	2	no	—
289	C₂²×C₄	—	47	2	no	—
290	C₂²×C₄	—	47	2	no	—
291	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
292	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
293	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
294	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
295	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
296	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	2	2	no	—
303	C₂×C₈	—	94	2	no	—
304	C₂×C₈	—	94	2	no	—
305	C₂×C₈	—	94	2	no	—
306	C₂×C₈	—	94	2	no	—
307	C₂×C₈	—	94	2	no	—
308	C₂×C₈	—	94	2	no	—
309	C₄⋊C₄	—	2	2	no	—
310	C₄⋊C₄	—	2	2	no	—
311	C₄⋊C₄	—	188	2	no	—
312	C₄⋊C₄	—	188	2	no	—
313	C₂²⋊C₄	—	2	2	no	—
314	C₂²⋊C₄	—	2	2	no	—
315	C₂²⋊C₄	—	188	2	no	—
316	C₂²⋊C₄	—	188	2	no	—
317	C₄²	—	2	1	no	—
318	C₄²	—	2	1	no	—
319	C₄²	—	94	1	no	—
320	C₄²	—	94	1	no	—
321	C₄²	—	94	1	no	—
322	C₄²	—	94	1	no	—
323	C₄²	—	94	1	no	—
324	C₄²	—	94	1	no	—
325	C₄²	—	94	1	no	—
326	C₄²	—	94	1	no	—
327	C₄²	—	188	2	no	—
328	C₄²	—	188	2	no	—
329	C₄²	#10625352	1	2	yes	—
330	C₄²	#10625352	1	2	yes	—
331	C₂³	—	2	1	no	—
332	C₂³	—	2	1	no	—
333	C₂³	—	2	1	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
337	C₂×C₄	—	2	2	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	4	1	no	—
347	C₂×C₄	—	4	1	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	94	2	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	2	no	—
358	C₂×C₄	—	94	2	no	—
359	C₂×C₄	—	94	2	no	—
360	C₂×C₄	—	94	2	no	—
361	C₂×C₄	—	94	2	no	—
362	C₂×C₄	#13093980	1	2	yes	—
363	C₂×C₄	#13093980	1	2	yes	—
364	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
365	C₂×C₄	C₂×#10625352	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	2	no	—
371	C₈	—	4	2	no	—
372	C₈	—	188	2	no	—
373	C₈	—	188	2	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	4	2	no	—
378	C₂²	—	4	1	no	—
379	C₂²	C₂×#13093980	1	1	yes	characteristic
380	C₂²	#15689603	1	1	yes	characteristic
381	C₂²	#15689604	1	1	yes	characteristic
382	C₂²	#15689888	1	2	yes	—
383	C₂²	#15689888	1	2	yes	—
384	C₄	—	2	2	no	—
385	C₄	—	2	2	no	—
386	C₄	—	4	1	no	—
387	C₄	—	4	1	no	—
388	C₄	—	4	1	no	—
389	C₄	—	188	2	no	—
390	C₄	—	188	2	no	—
391	C₄	—	188	2	no	—
392	C₄	—	188	2	no	—
393	C₄	#15689726	1	1	yes	characteristic
394	C₄	#15689733	1	1	yes	characteristic
395	C₄	#15689740	1	1	yes	characteristic
396	C₄	#15689746	1	1	yes	characteristic
397	C₂	—	8	1	no	—
398	C₂	#20245995	1	1	yes	characteristic
399	C₂	#20252035	1	1	yes	characteristic
400	C₂	#20252035	1	1	yes	characteristic
401	C₂	#20252553	1	2	yes	—
402	C₂	#20252556	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1798	C₂
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1798	D₄₇
hypocenter	C₄₇	#21927
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1798

Complements

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

N	H ≅ G/N	type
4. #20243953	C₂	semidirect
5. #20243951	C₂	semidirect
6. #20243541	C₂	semidirect
7. #20243507	C₂	semidirect
9. #20243243	C₂	semidirect
10. #20243243	C₂	semidirect
240. C₄₇	#21927	semidirect

Maximal subgroups

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

subgroup	index
#20245886	2
#20244004	2
#20243998	2
#20243953	2
#20243951	2
#20243541	2
#20243507	2
#20243372	2
#20243243	2
C₄₇×#1798	2
#21927	47