Subgroups — #26218373

Order 12032.

914 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄⋊(C₄₇⋊C₈)	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689079	C₂	1	1	yes	maximal, characteristic
3	#20243954	C₂	1	4	yes	maximal, complemented
4	#20243947	C₂	1	4	yes	maximal, complemented
5	#20243085	C₂	1	1	yes	maximal, characteristic
6	#20243085	C₂	1	1	yes	maximal, characteristic
7	#20243085	C₂	1	1	yes	maximal, characteristic
8	#20243082	C₂	1	1	yes	maximal, characteristic
9	C₄₇×#2296	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10625329	C₂²	1	1	yes	characteristic
11	C₂²×#10625329	C₂²	1	1	yes	characteristic
12	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
17	#15689079	—	2	4	no	—
18	C₂×#13093935	C₂²	1	2	yes	—
19	C₂×C₄×C₄₇⋊C₈	C₂²	1	2	yes	—
20	#15688878	C₂²	1	4	yes	—
21	#15688878	C₂²	1	2	yes	—
22	#15688878	C₂²	1	4	yes	—
23	#15688878	C₂²	1	4	yes	—
24	#15688878	C₂²	1	2	yes	—
25	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
26	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
27	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
28	C₄₇×#389	C₄	1	2	yes	—
29	C₄₇×#389	C₄	1	2	yes	—
30	C₄₇×#385	C₄	1	2	yes	—
31	C₄₇×#385	C₄	1	2	yes	—
32	C₄×C₄⋊C₄×C₄₇	C₂²	1	4	yes	—
33	C₂×#10625329	—	2	2	no	—
34	C₂×#10625329	—	2	2	no	—
35	C₂×#10625329	—	2	2	no	—
36	C₂×#10625329	—	2	2	no	—
37	C₂×#10625329	—	2	2	no	—
38	C₂×#10625329	Q₈	1	4	yes	—
39	C₂²×C₄₇⋊C₈	—	2	2	no	—
40	C₂²×C₄₇⋊C₈	—	2	2	no	—
41	C₂²×C₄₇⋊C₈	—	2	2	no	—
42	C₂²×C₄₇⋊C₈	—	2	2	no	—
43	C₂²×C₄₇⋊C₈	—	2	2	no	—
44	C₂²×C₄₇⋊C₈	D₄	1	4	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
46	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
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	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
51	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
52	#13093935	—	2	4	no	—
53	C₄×C₄₇⋊C₈	—	2	4	no	—
54	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
55	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
57	#117×C₄₇	—	2	2	no	—
58	#117×C₄₇	—	2	2	no	—
59	#117×C₄₇	—	2	2	no	—
60	#117×C₄₇	—	2	2	no	—
61	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
62	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
63	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
65	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	4	yes	—
66	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
67	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
68	C₂×C₄²×C₄₇	—	2	2	no	—
69	C₂×C₄²×C₄₇	—	2	2	no	—
70	C₂×C₄²×C₄₇	C₂×C₄	1	2	yes	—
71	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
72	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
73	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
74	#95×C₄₇	C₂×C₄	1	4	yes	—
75	#95×C₄₇	C₂×C₄	1	4	yes	—
76	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
77	C₂²×C₄×C₄₇	—	2	2	no	—
78	C₂²×C₄×C₄₇	—	2	4	no	—
79	C₂²×C₄×C₄₇	—	2	2	no	—
80	C₂²×C₄×C₄₇	—	4	2	no	—
81	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
83	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
84	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
85	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
86	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
88	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
89	C₂²×C₄×C₄₇	#41	1	2	yes	—
90	C₂²×C₄×C₄₇	#41	1	2	yes	—
91	C₂²×C₄×C₄₇	#41	1	2	yes	—
92	C₂²×C₄×C₄₇	#41	1	2	yes	—
93	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
94	C₄⋊C₄×C₄₇	—	2	4	no	—
95	C₄⋊C₄×C₄₇	—	2	2	no	—
96	C₄⋊C₄×C₄₇	—	2	2	no	—
97	C₄⋊C₄×C₄₇	—	2	8	no	—
98	C₄⋊C₄×C₄₇	—	4	4	no	—
99	C₂²⋊C₄×C₄₇	—	2	4	no	—
100	C₂²⋊C₄×C₄₇	—	2	4	no	—
101	C₄²×C₄₇	—	2	4	no	—
102	C₄²×C₄₇	—	2	2	no	—
103	C₄²×C₄₇	—	2	2	no	—
104	C₄²×C₄₇	—	2	2	no	—
105	C₄²×C₄₇	—	2	2	no	—
106	C₄²×C₄₇	—	2	2	no	—
107	C₄²×C₄₇	—	2	2	no	—
108	#10625329	—	2	8	no	—
109	#10625329	—	4	4	no	—
110	C₂×C₄₇⋊C₈	—	2	8	no	—
111	C₂×C₄₇⋊C₈	—	2	2	no	—
112	C₂×C₄₇⋊C₈	—	2	1	no	—
113	C₂×C₄₇⋊C₈	—	2	1	no	—
114	C₂×C₄₇⋊C₈	—	2	1	no	—
115	C₂×C₄₇⋊C₈	—	2	1	no	—
116	C₂×C₄₇⋊C₈	—	2	2	no	—
117	C₂×C₄₇⋊C₈	—	2	2	no	—
118	C₂×C₄₇⋊C₈	—	2	2	no	—
119	C₂×C₄₇⋊C₈	—	2	2	no	—
120	C₂×C₄₇⋊C₈	—	2	2	no	—
121	C₂×C₄₇⋊C₈	—	2	2	no	—
122	C₂×C₄₇⋊C₈	—	2	2	no	—
123	C₂×C₄₇⋊C₈	—	4	4	no	—
124	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
125	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
126	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
127	C₂³×C₄₇	—	2	2	no	—
128	C₂³×C₄₇	—	2	2	no	—
129	C₂³×C₄₇	#117	1	2	yes	—
130	C₂³×C₄₇	C₄×D₄	1	2	yes	—
131	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
132	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
133	C₂×C₄×C₄₇	—	2	8	no	—
134	C₂×C₄×C₄₇	—	2	2	no	—
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	4	no	—
137	C₂×C₄×C₄₇	—	2	2	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	2	2	no	—
140	C₂×C₄×C₄₇	—	2	4	no	—
141	C₂×C₄×C₄₇	—	2	4	no	—
142	C₂×C₄×C₄₇	—	2	2	no	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	2	4	no	—
145	C₂×C₄×C₄₇	—	2	2	no	—
146	C₂×C₄×C₄₇	—	4	4	no	—
147	C₂×C₄×C₄₇	#117	1	2	yes	—
148	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
149	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
150	C₂×C₄×C₄₇	C₂²⋊Q₈	1	4	yes	—
151	C₂×C₄×C₄₇	#123	1	4	yes	—
152	C₂×C₄×C₄₇	#125	1	4	yes	—
153	C₂×C₄×C₄₇	#126	1	4	yes	—
154	C₂×C₄×C₄₇	#131	1	4	yes	—
155	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₂²×Q₈	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	C₄₇⋊C₈	—	2	4	no	—
162	C₄₇⋊C₈	—	2	2	no	—
163	C₄₇⋊C₈	—	2	2	no	—
164	C₄₇⋊C₈	—	4	2	no	—
165	C₄₇⋊C₈	—	4	2	no	—
166	#21024	—	47	1	no	maximal, Sylow
167	C₂²×C₄₇	—	2	4	no	—
168	C₂²×C₄₇	—	2	2	no	—
169	C₂²×C₄₇	—	2	2	no	—
170	C₂²×C₄₇	—	2	4	no	—
171	C₂²×C₄₇	#387	1	4	yes	—
172	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
173	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
174	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
175	C₂²×C₄₇	C₂×#131	1	2	yes	—
176	C₂²×C₄₇	#568	1	2	yes	—
177	C₄×C₄₇	—	2	4	no	—
178	C₄×C₄₇	—	4	4	no	—
179	C₄×C₄₇	—	4	2	no	—
180	C₄×C₄₇	—	4	2	no	—
181	C₄×C₄₇	—	4	2	no	—
182	C₄×C₄₇	#387	1	4	yes	—
183	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
184	C₄×C₄₇	C₂×#123	1	1	yes	characteristic
185	C₄×C₄₇	C₂×#125	1	1	yes	characteristic
186	C₄×C₄₇	C₂×#126	1	1	yes	characteristic
187	C₂²×C₄⋊C₈	—	47	1	no	—
188	C₂×#405	—	47	1	no	—
189	#2296	D₄₇	1	1	yes	characteristic
190	#1917	—	47	4	no	—
191	#1916	—	47	4	no	—
192	#1729	—	47	1	no	—
193	#1729	—	47	1	no	—
194	#1729	—	47	1	no	—
195	#1728	—	47	1	no	—
196	C₂×C₄₇	—	2	4	no	—
197	C₂×C₄₇	C₂×#387	1	1	yes	characteristic
198	C₂×C₄₇	#2925	1	2	yes	—
199	C₂×C₄₇	#2929	1	1	yes	characteristic
200	C₂×C₄₇	#2930	1	1	yes	characteristic
201	C₂×C₄₇	#2962	1	2	yes	—
202	C₂²×M₁₆	—	47	1	no	—
203	C₂²×M₁₆	—	47	1	no	—
204	C₂³×C₈	—	47	1	no	—
205	C₂³×C₈	—	47	1	no	—
206	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
207	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
208	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
209	C₂×C₄⋊C₈	—	47	2	no	—
210	C₂×C₄⋊C₈	—	47	2	no	—
211	C₂×C₄⋊C₈	—	94	4	no	—
212	#405	—	94	4	no	—
213	C₂×#97	—	47	2	no	—
214	C₂×C₄×C₈	—	47	2	no	—
215	#389	Dic₄₇	1	2	yes	—
216	#389	Dic₄₇	1	2	yes	—
217	#385	Dic₄₇	1	2	yes	—
218	#385	Dic₄₇	1	2	yes	—
219	C₄×C₄⋊C₄	C₂×D₄₇	1	4	yes	—
220	#336	—	47	2	no	—
221	#336	—	47	4	no	—
222	#336	—	47	4	no	—
223	#336	—	47	4	no	—
224	#336	—	47	2	no	—
225	C₄₇	#21024	1	1	yes	characteristic, complemented, Sylow
226	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
227	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
228	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
229	C₂×M₁₆	—	47	4	no	—
230	C₂×M₁₆	—	94	2	no	—
231	C₂×M₁₆	—	94	2	no	—
232	C₂×M₁₆	—	94	2	no	—
233	C₂×M₁₆	—	94	2	no	—
234	C₂×M₁₆	—	94	2	no	—
235	C₂²×C₈	—	47	4	no	—
236	C₂²×C₈	—	47	1	no	—
237	C₂²×C₈	—	47	1	no	—
238	C₂²×C₈	—	47	2	no	—
239	C₂²×C₈	—	47	2	no	—
240	C₂²×C₈	—	47	2	no	—
241	C₂²×C₈	—	94	2	no	—
242	C₂²×C₈	—	94	2	no	—
243	C₂²×C₈	—	94	2	no	—
244	C₂²×C₈	—	94	2	no	—
245	C₂²×C₈	—	94	2	no	—
246	#117	—	2	2	no	—
247	#117	—	2	2	no	—
248	#117	—	2	2	no	—
249	#117	—	2	2	no	—
250	C₂×C₄⋊C₄	C₂×Dic₄₇	1	2	yes	—
251	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
252	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
253	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
254	C₂×C₄⋊C₄	C₂×Dic₄₇	1	4	yes	—
255	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
256	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	2	yes	—
257	C₂×C₄²	—	2	2	no	—
258	C₂×C₄²	—	2	2	no	—
259	C₂×C₄²	C₂×Dic₄₇	1	2	yes	—
260	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
261	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
262	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
263	C₄⋊C₈	—	94	4	no	—
264	C₄⋊C₈	—	94	4	no	—
265	#97	—	94	4	no	—
266	C₄×C₈	—	94	4	no	—
267	#95	C₂×Dic₄₇	1	4	yes	—
268	#95	C₂×Dic₄₇	1	4	yes	—
269	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
270	C₂²×C₄	—	2	2	no	—
271	C₂²×C₄	—	2	4	no	—
272	C₂²×C₄	—	2	2	no	—
273	C₂²×C₄	—	4	2	no	—
274	C₂²×C₄	#10625350	1	2	yes	—
275	C₂²×C₄	#10625350	1	2	yes	—
276	C₂²×C₄	D₄×D₄₇	1	2	yes	—
277	C₂²×C₄	#10625352	1	2	yes	—
278	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
279	C₂²×C₄	#10625354	1	2	yes	—
280	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
281	C₂²×C₄	C₂²×Dic₄₇	1	4	yes	—
282	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
283	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
284	C₂²×C₄	C₂²×Dic₄₇	1	2	yes	—
285	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
286	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
287	M₁₆	—	94	8	no	—
288	M₁₆	—	188	4	no	—
289	C₂×C₈	—	47	2	no	—
290	C₂×C₈	—	47	2	no	—
291	C₂×C₈	—	47	4	no	—
292	C₂×C₈	—	94	8	no	—
293	C₂×C₈	—	94	2	no	—
294	C₂×C₈	—	94	1	no	—
295	C₂×C₈	—	94	1	no	—
296	C₂×C₈	—	94	2	no	—
297	C₂×C₈	—	94	1	no	—
298	C₂×C₈	—	94	1	no	—
299	C₂×C₈	—	94	2	no	—
300	C₂×C₈	—	94	2	no	—
301	C₂×C₈	—	94	2	no	—
302	C₂×C₈	—	94	2	no	—
303	C₂×C₈	—	94	2	no	—
304	C₂×C₈	—	94	2	no	—
305	C₂×C₈	—	188	4	no	—
306	C₄⋊C₄	—	2	4	no	—
307	C₄⋊C₄	—	2	2	no	—
308	C₄⋊C₄	—	2	2	no	—
309	C₄⋊C₄	—	2	8	no	—
310	C₄⋊C₄	—	4	4	no	—
311	C₂²⋊C₄	—	2	4	no	—
312	C₂²⋊C₄	—	2	4	no	—
313	C₄²	—	2	4	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	2	2	no	—
316	C₄²	—	2	2	no	—
317	C₄²	—	2	2	no	—
318	C₄²	—	2	2	no	—
319	C₄²	—	2	2	no	—
320	C₂³	—	2	2	no	—
321	C₂³	—	2	2	no	—
322	C₂³	#13093983	1	2	yes	—
323	C₂³	D₄×Dic₄₇	1	2	yes	—
324	C₂³	Q₈×Dic₄₇	1	2	yes	—
325	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
326	C₂×C₄	—	2	8	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	4	no	—
335	C₂×C₄	—	2	2	no	—
336	C₂×C₄	—	2	4	no	—
337	C₂×C₄	—	2	4	no	—
338	C₂×C₄	—	2	2	no	—
339	C₂×C₄	—	4	4	no	—
340	C₂×C₄	#13093983	1	2	yes	—
341	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
342	C₂×C₄	Q₈×Dic₄₇	1	2	yes	—
343	C₂×C₄	#13094002	1	4	yes	—
344	C₂×C₄	#13094009	1	4	yes	—
345	C₂×C₄	#13094014	1	4	yes	—
346	C₂×C₄	#13094019	1	4	yes	—
347	C₂×C₄	#13094031	1	4	yes	—
348	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
349	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
350	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
351	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
352	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
353	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
354	C₈	—	94	4	no	—
355	C₈	—	94	2	no	—
356	C₈	—	94	2	no	—
357	C₈	—	188	2	no	—
358	C₈	—	188	2	no	—
359	C₂²	—	2	4	no	—
360	C₂²	—	2	4	no	—
361	C₂²	—	2	2	no	—
362	C₂²	—	2	2	no	—
363	C₂²	#15689009	1	4	yes	—
364	C₂²	C₂×#13093983	1	1	yes	characteristic
365	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
366	C₂²	C₂×Q₈×Dic₄₇	1	1	yes	characteristic
367	C₂²	C₂×#13094031	1	2	yes	—
368	C₂²	#15689890	1	2	yes	—
369	C₄	—	2	4	no	—
370	C₄	—	4	4	no	—
371	C₄	—	4	2	no	—
372	C₄	—	4	2	no	—
373	C₄	—	4	2	no	—
374	C₄	#15689009	1	4	yes	—
375	C₄	C₂×#13094002	1	1	yes	characteristic
376	C₄	C₂×#13094009	1	1	yes	characteristic
377	C₄	C₂×#13094014	1	1	yes	characteristic
378	C₄	C₂×#13094019	1	1	yes	characteristic
379	C₂	—	2	4	no	—
380	C₂	C₂×#15689009	1	1	yes	characteristic
381	C₂	#20252054	1	2	yes	—
382	C₂	#20252083	1	1	yes	characteristic
383	C₂	#20252092	1	1	yes	characteristic
384	C₂	#20252337	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#2296	C₂
prime radical	C₂⁴×C₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2296	D₄₇
hypocenter	C₄₇	#21024
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #2296

Complements

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

N	H ≅ G/N	type
3. #20243954	C₂	semidirect
4. #20243947	C₂	semidirect
225. C₄₇	#21024	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄⋊(C₄₇⋊C₈)	2
C₂×#15689079	2
#20243954	2
#20243947	2
#20243085	2
#20243082	2
C₄₇×#2296	2
#21024	47