Subgroups — #26235100

Order 12032.

732 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689252	C₂	1	2	yes	maximal
2	#20245865	C₂	1	1	yes	maximal, characteristic
3	#20244109	C₂	1	2	yes	maximal
4	#20244108	C₂	1	2	yes	maximal
5	#20244103	C₂	1	2	yes	maximal
6	#20243541	C₂	1	2	yes	maximal
7	#20243247	C₂	1	2	yes	maximal
8	#20243241	C₂	1	1	yes	maximal, characteristic
9	C₄₇×#1842	C₂	1	1	yes	maximal, characteristic
10	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
11	#15689252	—	2	8	no	—
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×Dic₄₇⋊C₈	C₂²	1	2	yes	—
17	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
18	C₂×#13093935	C₂²	1	2	yes	—
19	C₂×#13093934	C₂²	1	2	yes	—
20	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
21	#15689029	C₄	1	1	yes	characteristic
22	#15689029	C₄	1	1	yes	characteristic
23	#15689021	C₄	1	1	yes	characteristic
24	#15689021	C₄	1	1	yes	characteristic
25	#15689007	C₄	1	2	yes	—
26	#15689007	C₄	1	2	yes	—
27	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
28	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
29	#15688969	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	2	yes	—
34	C₂×C₄⋊C₈×C₄₇	C₂²	1	2	yes	—
35	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₄³×C₄₇	C₂²	1	1	yes	characteristic
38	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
39	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
40	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
41	C₄×Dic₉₄	D₄	1	4	yes	—
42	C₄×Dic₉₄	Q₈	1	4	yes	—
43	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
47	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
48	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
49	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
50	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
51	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
52	C₄⋊(C₄₇⋊C₈)	Q₈	1	4	yes	complemented
53	Dic₄₇⋊C₈	—	2	4	no	—
54	Dic₄₇⋊C₈	—	2	4	no	—
55	Dic₄₇⋊C₈	—	4	2	no	—
56	Dic₄₇⋊C₈	—	4	2	no	—
57	#13093935	—	2	4	no	—
58	#13093934	—	2	4	no	—
59	C₈×Dic₄₇	—	2	4	no	—
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	C₄₇⋊#95	C₂×C₄	1	2	yes	—
65	C₄₇⋊#95	C₂×C₄	1	2	yes	—
66	C₄₇⋊#95	C₂×C₄	1	2	yes	—
67	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
68	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
69	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×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	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
76	C₄⋊C₈×C₄₇	—	2	4	no	—
77	C₄⋊C₈×C₄₇	—	2	4	no	—
78	C₄⋊C₈×C₄₇	—	4	1	no	—
79	C₄⋊C₈×C₄₇	—	4	1	no	—
80	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
81	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
82	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
83	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
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	2	yes	—
88	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
89	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
90	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
91	C₂×Dic₉₄	—	4	1	no	—
92	C₂×Dic₉₄	—	4	1	no	—
93	C₂×Dic₉₄	C₄⋊C₄	1	4	yes	—
94	C₂×C₈×C₄₇	—	2	2	no	—
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	C₄²×C₄₇	—	2	2	no	—
101	C₄²×C₄₇	—	2	1	no	—
102	C₄²×C₄₇	—	2	1	no	—
103	C₄²×C₄₇	—	4	1	no	—
104	C₄²×C₄₇	—	4	1	no	—
105	C₄²×C₄₇	—	4	1	no	—
106	C₄²×C₄₇	C₂×D₄	1	2	yes	—
107	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
108	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
109	C₄²×C₄₇	#41	1	2	yes	—
110	C₄⋊Dic₄₇	—	4	1	no	—
111	C₄⋊Dic₄₇	—	4	1	no	—
112	C₄⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
113	Dic₄₇⋊C₄	—	2	4	no	—
114	Dic₄₇⋊C₄	—	4	2	no	—
115	Dic₄₇⋊C₄	C₄⋊C₄	1	8	yes	—
116	C₄×Dic₄₇	—	2	2	no	—
117	C₄×Dic₄₇	—	2	2	no	—
118	C₄×Dic₄₇	C₂×D₄	1	4	yes	—
119	C₄×Dic₄₇	C₂×Q₈	1	4	yes	—
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	—	2	2	no	—
124	C₂×C₄₇⋊C₈	—	2	2	no	—
125	C₂×C₄₇⋊C₈	C₂×Q₈	1	4	yes	—
126	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
127	C₂×C₄×C₄₇	—	2	1	no	—
128	C₂×C₄×C₄₇	—	2	1	no	—
129	C₂×C₄×C₄₇	—	2	1	no	—
130	C₂×C₄×C₄₇	—	2	1	no	—
131	C₂×C₄×C₄₇	—	2	1	no	—
132	C₂×C₄×C₄₇	—	2	1	no	—
133	C₂×C₄×C₄₇	—	2	1	no	—
134	C₂×C₄×C₄₇	—	2	1	no	—
135	C₂×C₄×C₄₇	—	2	1	no	—
136	C₂×C₄×C₄₇	—	2	1	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	C₂×C₄⋊C₄	1	2	yes	—
141	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
142	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
143	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
144	C₂×C₄×C₄₇	#131	1	2	yes	—
145	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
146	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
147	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂×#41	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×Dic₄₇	—	2	2	no	—
152	C₂×Dic₄₇	—	2	2	no	—
153	C₂×Dic₄₇	—	2	2	no	—
154	C₂×Dic₄₇	—	2	2	no	—
155	C₂×Dic₄₇	—	2	2	no	—
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	C₂×C₄⋊C₄	1	4	yes	—
162	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
163	Dic₉₄	—	4	4	no	—
164	C₈×C₄₇	—	4	2	no	—
165	C₈×C₄₇	—	4	2	no	—
166	C₄₇⋊C₈	—	2	4	no	—
167	C₄₇⋊C₈	—	4	2	no	—
168	#22723	—	47	1	no	maximal, Sylow
169	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
170	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
171	C₂²×C₄₇	#520	1	1	yes	characteristic
172	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
173	C₂²×C₄₇	#568	1	1	yes	characteristic
174	C₂²×C₄₇	#568	1	1	yes	characteristic
175	C₂²×C₄₇	#568	1	1	yes	characteristic
176	C₄×C₄₇	—	2	2	no	—
177	C₄×C₄₇	—	2	2	no	—
178	C₄×C₄₇	—	2	2	no	—
179	C₄×C₄₇	—	2	2	no	—
180	C₄×C₄₇	—	2	2	no	—
181	C₄×C₄₇	—	4	1	no	—
182	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
183	C₄×C₄₇	#550	1	1	yes	characteristic
184	C₄×C₄₇	#557	1	1	yes	characteristic
185	C₄×C₄₇	Q₈²	1	1	yes	characteristic
186	Dic₄₇	—	2	4	no	—
187	Dic₄₇	—	2	4	no	—
188	Dic₄₇	—	4	2	no	—
189	Dic₄₇	—	4	2	no	—
190	C₂×#446	—	47	2	no	—
191	#2295	—	47	1	no	—
192	#1940	—	47	2	no	—
193	#1940	—	47	2	no	—
194	#1939	—	47	2	no	—
195	#1843	—	47	2	no	—
196	#1842	D₄₇	1	1	yes	characteristic
197	#1768	—	47	2	no	—
198	#1767	—	47	1	no	—
199	C₂×C₄₇	Q₈×C₄⋊C₄	1	1	yes	characteristic
200	C₂×C₄₇	#2905	1	1	yes	characteristic
201	C₂×C₄₇	#2906	1	1	yes	characteristic
202	C₂×C₄₇	#2961	1	1	yes	characteristic
203	C₂×C₄₇	#2962	1	1	yes	characteristic
204	C₂×C₄₇	#2992	1	1	yes	characteristic
205	C₂×C₄₇	#2995	1	1	yes	characteristic
206	C₂×C₄×Q₈	—	47	1	no	—
207	#446	—	94	8	no	—
208	C₂×C₄⋊C₈	—	47	1	no	—
209	C₂×C₄⋊C₈	—	47	2	no	—
210	C₂×C₄⋊C₈	—	47	2	no	—
211	C₂×C₄⋊C₈	—	47	1	no	—
212	C₂×C₄⋊C₈	—	47	2	no	—
213	C₂×C₄⋊C₈	—	47	2	no	—
214	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
215	C₂×C₄⋊C₈	C₂×D₄₇	1	2	yes	—
216	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
217	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
218	C₂×#97	—	47	2	no	—
219	C₂×#97	—	47	2	no	—
220	C₂×C₄×C₈	—	47	2	no	—
221	#391	—	47	1	no	—
222	#391	—	47	1	no	—
223	#389	—	47	1	no	—
224	#389	—	47	1	no	—
225	#387	—	47	2	no	—
226	#387	—	47	2	no	—
227	C₄×C₄⋊C₄	—	47	1	no	—
228	C₄×C₄⋊C₄	—	47	2	no	—
229	#376	—	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	C₄₇	#22723	1	1	yes	characteristic, complemented, Sylow
235	C₂²×Q₈	—	47	1	no	—
236	C₂²×C₈	—	47	2	no	—
237	C₂²×C₈	—	47	2	no	—
238	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
239	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
240	C₄×Q₈	—	47	4	no	—
241	C₄×Q₈	—	47	4	no	—
242	C₂×C₄⋊C₄	—	47	2	no	—
243	C₂×C₄⋊C₄	—	47	1	no	—
244	C₂×C₄⋊C₄	—	47	2	no	—
245	C₂×C₄⋊C₄	—	47	2	no	—
246	C₂×C₄⋊C₄	—	47	1	no	—
247	C₂×C₄⋊C₄	—	47	1	no	—
248	C₂×C₄²	—	47	2	no	—
249	C₂×C₄²	—	47	2	no	—
250	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
251	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
252	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
253	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
254	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
255	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
256	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
257	C₄⋊C₈	—	2	4	no	—
258	C₄⋊C₈	—	2	4	no	—
259	C₄⋊C₈	—	4	1	no	—
260	C₄⋊C₈	—	4	1	no	—
261	C₄⋊C₈	—	47	4	no	—
262	C₄⋊C₈	—	94	4	no	—
263	C₄⋊C₈	—	94	4	no	—
264	C₄⋊C₈	—	94	2	no	—
265	C₄⋊C₈	—	188	2	no	—
266	C₄⋊C₈	—	188	2	no	—
267	#97	—	94	4	no	—
268	#97	—	94	4	no	—
269	C₄×C₈	—	94	4	no	—
270	#95	—	47	2	no	—
271	#95	—	47	2	no	—
272	#95	—	47	2	no	—
273	#95	—	47	2	no	—
274	#95	—	47	2	no	—
275	#95	—	47	2	no	—
276	#95	—	47	2	no	—
277	C₂×Q₈	—	47	4	no	—
278	C₂×Q₈	—	188	1	no	—
279	C₂×Q₈	—	188	1	no	—
280	C₂²×C₄	—	47	2	no	—
281	C₂²×C₄	—	47	2	no	—
282	C₂²×C₄	—	47	2	no	—
283	C₂²×C₄	—	47	2	no	—
284	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
290	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
291	C₂×C₈	—	2	2	no	—
292	C₂×C₈	—	2	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	2	2	no	—
295	C₂×C₈	—	2	2	no	—
296	C₂×C₈	—	2	2	no	—
297	C₂×C₈	—	47	4	no	—
298	C₂×C₈	—	94	2	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	C₄⋊C₄	—	47	8	no	—
304	C₄⋊C₄	—	47	4	no	—
305	C₄⋊C₄	—	94	4	no	—
306	C₄⋊C₄	—	188	2	no	—
307	C₄⋊C₄	—	188	1	no	—
308	C₄⋊C₄	—	188	1	no	—
309	C₄²	—	2	2	no	—
310	C₄²	—	2	1	no	—
311	C₄²	—	2	1	no	—
312	C₄²	—	4	1	no	—
313	C₄²	—	4	1	no	—
314	C₄²	—	4	1	no	—
315	C₄²	—	47	4	no	—
316	C₄²	—	47	4	no	—
317	C₄²	—	94	2	no	—
318	C₄²	—	94	2	no	—
319	C₄²	D₄×D₄₇	1	2	yes	—
320	C₄²	#10625352	1	2	yes	—
321	C₄²	Q₈×D₄₇	1	2	yes	—
322	C₄²	Q₈×D₄₇	1	2	yes	—
323	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
324	Q₈	—	188	4	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	1	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	2	1	no	—
337	C₂×C₄	—	2	1	no	—
338	C₂×C₄	—	47	4	no	—
339	C₂×C₄	—	47	4	no	—
340	C₂×C₄	—	94	2	no	—
341	C₂×C₄	—	94	2	no	—
342	C₂×C₄	—	94	2	no	—
343	C₂×C₄	—	94	2	no	—
344	C₂×C₄	—	94	2	no	—
345	C₂×C₄	—	94	2	no	—
346	C₂×C₄	—	94	2	no	—
347	C₂×C₄	—	94	2	no	—
348	C₂×C₄	—	94	2	no	—
349	C₂×C₄	—	94	2	no	—
350	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
351	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
352	C₂×C₄	#13093989	1	2	yes	—
353	C₂×C₄	#13093989	1	2	yes	—
354	C₂×C₄	#13094030	1	2	yes	—
355	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
356	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
357	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
358	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
359	C₂×C₄	#13094069	1	1	yes	characteristic
360	C₂×C₄	#13094072	1	1	yes	characteristic
361	C₈	—	4	2	no	—
362	C₈	—	4	2	no	—
363	C₈	—	94	4	no	—
364	C₈	—	188	2	no	—
365	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
366	C₂²	C₂×#13093989	1	1	yes	characteristic
367	C₂²	#15689604	1	1	yes	characteristic
368	C₂²	C₂×#13094030	1	1	yes	characteristic
369	C₂²	#15689889	1	1	yes	characteristic
370	C₂²	#15689889	1	1	yes	characteristic
371	C₂²	#15689889	1	1	yes	characteristic
372	C₄	—	2	2	no	—
373	C₄	—	2	2	no	—
374	C₄	—	2	2	no	—
375	C₄	—	2	2	no	—
376	C₄	—	2	2	no	—
377	C₄	—	4	1	no	—
378	C₄	—	94	4	no	—
379	C₄	—	94	4	no	—
380	C₄	—	188	2	no	—
381	C₄	—	188	2	no	—
382	C₄	#15689788	1	1	yes	characteristic
383	C₄	#15689793	1	1	yes	characteristic
384	C₄	#15689848	1	1	yes	characteristic
385	C₄	#15689853	1	1	yes	characteristic
386	C₂	#20246300	1	1	yes	characteristic
387	C₂	#20251950	1	1	yes	characteristic
388	C₂	#20251953	1	1	yes	characteristic
389	C₂	#20252325	1	1	yes	characteristic
390	C₂	#20252331	1	1	yes	characteristic
391	C₂	#20252524	1	1	yes	characteristic
392	C₂	#20252555	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle, prime radical	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1842	C₂
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1842	D₄₇
hypocenter	C₄₇	#22723
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1842

Complements

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

N	H ≅ G/N	type
52. C₄⋊(C₄₇⋊C₈)	Q₈	semidirect
234. C₄₇	#22723	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689252	2
#20245865	2
#20244109	2
#20244108	2
#20244103	2
#20243541	2
#20243247	2
#20243241	2
C₄₇×#1842	2
#22723	47