Subgroups — #26188065

Order 12032.

600 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	#20252393	C₂	1	2	yes	maximal, complemented
2	#20242285	C₂	1	1	yes	maximal, characteristic, complemented
3	#20242273	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242232	C₂	1	2	yes	maximal, complemented
5	#20242225	C₂	1	2	yes	maximal, complemented
6	Q₁₆×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
7	D₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242136	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241796	C₂	1	2	yes	maximal, complemented
10	C₈×#10625329	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3168	C₂	1	1	yes	maximal, characteristic
12	#15689254	C₂²	1	2	yes	—
13	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	—
14	#15689201	—	2	2	no	—
15	#15689201	C₂²	1	2	yes	—
16	#15689195	—	2	2	no	—
17	D₄×C₄₇⋊C₈	C₂²	1	2	yes	—
18	#15689184	—	2	2	no	—
19	#15689176	C₂²	1	2	yes	—
20	#15689176	C₂²	1	1	yes	characteristic
21	#15689079	—	2	2	no	—
22	C₄×#10625329	C₂²	1	1	yes	characteristic
23	#15688876	C₂²	1	1	yes	characteristic
24	#15688876	C₂²	1	1	yes	characteristic
25	#15688874	C₂²	1	2	yes	—
26	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
27	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
28	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
29	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
30	#15688845	C₂²	1	1	yes	characteristic
31	#15688845	C₂²	1	1	yes	characteristic
32	C₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
33	C₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
34	C₄₇×#529	C₂²	1	2	yes	—
35	C₄₇×#499	C₄	1	1	yes	characteristic
36	C₄₇×#495	C₄	1	1	yes	characteristic
37	C₄₇×#488	C₄	1	2	yes	—
38	C₄₇×#467	C₄	1	1	yes	characteristic
39	C₄₇×#466	C₄	1	1	yes	characteristic
40	C₄₇×#465	C₄	1	2	yes	—
41	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
42	C₄×SD₁₆×C₄₇	C₂²	1	2	yes	—
43	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
44	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
45	C₂×#10625329	—	2	2	no	—
46	C₂×#10625329	D₄	1	1	yes	characteristic
47	C₂×#10625329	D₄	1	1	yes	characteristic
48	C₂²×C₄₇⋊C₈	—	2	2	no	—
49	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
50	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
51	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
52	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
53	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
54	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
55	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
56	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
57	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
58	#13093935	—	2	2	no	—
59	#13093935	D₄	1	1	yes	characteristic
60	#13093935	D₄	1	1	yes	characteristic
61	C₄×C₄₇⋊C₈	—	2	2	no	—
62	C₄×C₄₇⋊C₈	—	2	2	no	—
63	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
64	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
65	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
66	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
67	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
69	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic
70	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
71	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
72	#126×C₄₇	—	2	2	no	—
73	#125×C₄₇	C₂×C₄	1	2	yes	—
74	#124×C₄₇	C₂×C₄	1	2	yes	—
75	#123×C₄₇	—	2	2	no	—
76	C₂²⋊Q₈×C₄₇	C₂×C₄	1	2	yes	—
77	#121×C₄₇	C₂×C₄	1	2	yes	—
78	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
79	C₄×D₄×C₄₇	—	2	2	no	—
80	C₄×D₄×C₄₇	C₂³	1	2	yes	—
81	#117×C₄₇	—	2	2	no	—
82	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
83	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
84	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
85	#106×C₄₇	C₂×C₄	1	2	yes	—
86	#103×C₄₇	C₂×C₄	1	2	yes	—
87	#103×C₄₇	C₂×C₄	1	2	yes	—
88	#102×C₄₇	C₂×C₄	1	2	yes	—
89	#102×C₄₇	C₂×C₄	1	2	yes	—
90	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
91	C₄×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
92	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
94	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂×D₄×C₄₇	—	2	2	no	—
96	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
100	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
101	Q₁₆×C₄₇	—	2	2	no	—
102	SD₁₆×C₄₇	—	4	2	no	—
103	D₈×C₄₇	—	2	2	no	—
104	C₂×C₈×C₄₇	—	2	2	no	—
105	C₂×C₈×C₄₇	—	4	1	no	—
106	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₄⋊C₄×C₄₇	—	2	2	no	—
111	C₄⋊C₄×C₄₇	—	2	2	no	—
112	C₄⋊C₄×C₄₇	—	2	2	no	—
113	C₄⋊C₄×C₄₇	—	2	2	no	—
114	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
115	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
116	C₂²⋊C₄×C₄₇	—	2	2	no	—
117	C₂²⋊C₄×C₄₇	—	2	2	no	—
118	C₂²⋊C₄×C₄₇	—	2	2	no	—
119	C₂²⋊C₄×C₄₇	—	2	2	no	—
120	C₂²⋊C₄×C₄₇	—	2	2	no	—
121	C₄²×C₄₇	—	2	2	no	—
122	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
123	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
124	C₄²×C₄₇	#41	1	1	yes	characteristic
125	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
126	#10625329	—	2	2	no	—
127	#10625329	—	2	2	no	—
128	#10625329	—	4	4	no	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	—	2	2	no	—
131	C₂×C₄₇⋊C₈	—	2	1	no	—
132	C₂×C₄₇⋊C₈	—	2	1	no	—
133	C₂×C₄₇⋊C₈	—	4	4	no	—
134	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
135	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
136	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
137	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
138	C₂³×C₄₇	—	2	2	no	—
139	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
140	Q₈×C₄₇	—	2	2	no	—
141	Q₈×C₄₇	—	2	2	no	—
142	D₄×C₄₇	—	2	2	no	—
143	D₄×C₄₇	—	2	2	no	—
144	D₄×C₄₇	—	8	2	no	—
145	C₂×C₄×C₄₇	—	2	1	no	—
146	C₂×C₄×C₄₇	—	2	1	no	—
147	C₂×C₄×C₄₇	—	2	1	no	—
148	C₂×C₄×C₄₇	—	2	1	no	—
149	C₂×C₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	2	2	no	—
152	C₂×C₄×C₄₇	—	4	1	no	—
153	C₂×C₄×C₄₇	—	4	2	no	—
154	C₂×C₄×C₄₇	—	4	2	no	—
155	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
156	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
157	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
158	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
159	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
161	C₈×C₄₇	—	2	1	no	—
162	C₈×C₄₇	—	2	1	no	—
163	C₈×C₄₇	—	2	1	no	—
164	C₈×C₄₇	#131	1	2	yes	—
165	C₄₇⋊C₈	—	2	1	no	—
166	C₄₇⋊C₈	—	2	1	no	—
167	C₄₇⋊C₈	—	4	1	no	—
168	C₄₇⋊C₈	—	4	1	no	—
169	C₄₇⋊C₈	—	4	2	no	—
170	C₄₇⋊C₈	—	4	2	no	—
171	C₄₇⋊C₈	#135	1	2	yes	—
172	C₄₇⋊C₈	#135	1	2	yes	—
173	#18069	—	47	1	no	maximal, Sylow
174	C₂²×C₄₇	—	2	1	no	—
175	C₂²×C₄₇	—	2	1	no	—
176	C₂²×C₄₇	—	2	1	no	—
177	C₂²×C₄₇	—	4	2	no	—
178	C₂²×C₄₇	—	4	2	no	—
179	C₂²×C₄₇	—	4	2	no	—
180	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
181	C₄×C₄₇	—	2	1	no	—
182	C₄×C₄₇	—	2	1	no	—
183	C₄×C₄₇	—	2	1	no	—
184	C₄×C₄₇	—	2	1	no	—
185	C₄×C₄₇	—	4	2	no	—
186	C₄×C₄₇	—	4	2	no	—
187	C₄×C₄₇	—	4	2	no	—
188	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
189	C₄×C₄₇	#568	1	1	yes	characteristic
190	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
191	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
192	#3168	D₄₇	1	1	yes	characteristic
193	#2969	—	47	2	no	—
194	#1591	—	47	1	no	—
195	#1589	—	47	1	no	—
196	#1583	—	47	2	no	—
197	#1582	—	47	2	no	—
198	C₈×Q₁₆	—	47	1	no	—
199	C₈×D₈	—	47	1	no	—
200	#1564	—	47	1	no	—
201	#1482	—	47	2	no	—
202	C₈×M₁₆	—	47	1	no	—
203	C₂×C₄₇	—	4	1	no	—
204	C₂×C₄₇	—	8	2	no	—
205	C₂×C₄₇	#2935	1	1	yes	characteristic
206	C₂×C₄₇	C₄×#135	1	1	yes	characteristic
207	C₂×C₄₇	#2957	1	1	yes	characteristic
208	#529	C₂×D₄₇	1	2	yes	—
209	#499	Dic₄₇	1	1	yes	characteristic
210	#495	Dic₄₇	1	1	yes	characteristic
211	#488	Dic₄₇	1	2	yes	—
212	#467	Dic₄₇	1	1	yes	characteristic
213	#466	Dic₄₇	1	1	yes	characteristic
214	#465	Dic₄₇	1	2	yes	—
215	#446	—	47	2	no	—
216	C₈×Q₈	—	47	2	no	—
217	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
218	C₄×SD₁₆	C₂×D₄₇	1	2	yes	—
219	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
220	#436	—	47	2	no	—
221	#436	—	94	2	no	—
222	#435	—	94	2	no	—
223	C₈×D₄	—	47	2	no	—
224	#433	—	94	2	no	—
225	#431	—	47	1	no	—
226	#431	—	47	2	no	—
227	#405	—	94	2	no	—
228	C₄×M₁₆	—	47	1	no	—
229	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
230	#335	—	47	1	no	—
231	#335	—	47	1	no	—
232	#334	—	47	2	no	—
233	Q₈⋊C₈	—	47	2	no	—
234	Q₈⋊C₈	—	47	2	no	—
235	D₄⋊C₈	—	47	2	no	—
236	D₄⋊C₈	—	47	2	no	—
237	#322	—	47	1	no	—
238	#322	—	47	1	no	—
239	C₈²	—	47	1	no	—
240	C₈²	—	47	1	no	—
241	C₄₇	#18069	1	1	yes	characteristic, complemented, Sylow
242	C₂×Q₁₆	C₂×Dic₄₇	1	1	yes	characteristic
243	C₂×SD₁₆	C₂×Dic₄₇	1	2	yes	—
244	C₂×D₈	C₂×Dic₄₇	1	1	yes	characteristic
245	C₂×M₁₆	—	47	1	no	—
246	C₂×M₁₆	—	47	1	no	—
247	C₂×M₁₆	—	94	2	no	—
248	C₂²×C₈	—	94	2	no	—
249	C₂²×C₈	C₂×Dic₄₇	1	1	yes	characteristic
250	C₂²×C₈	C₂×Dic₄₇	1	1	yes	characteristic
251	#126	—	2	2	no	—
252	#125	C₂×Dic₄₇	1	2	yes	—
253	#124	C₂×Dic₄₇	1	2	yes	—
254	#123	—	2	2	no	—
255	C₂²⋊Q₈	C₂×Dic₄₇	1	2	yes	—
256	#121	C₂×Dic₄₇	1	2	yes	—
257	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
258	C₄×D₄	—	2	2	no	—
259	C₄×D₄	C₂²×D₄₇	1	2	yes	—
260	#117	—	2	2	no	—
261	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
262	#107	C₂×Dic₄₇	1	1	yes	characteristic
263	#107	C₂×Dic₄₇	1	1	yes	characteristic
264	#106	C₂×Dic₄₇	1	2	yes	—
265	C₄⋊C₈	—	47	2	no	—
266	C₄⋊C₈	—	47	2	no	—
267	C₄⋊C₈	—	94	2	no	—
268	C₄⋊C₈	—	94	2	no	—
269	C₄⋊C₈	—	94	1	no	—
270	#103	C₂×Dic₄₇	1	2	yes	—
271	#103	C₂×Dic₄₇	1	2	yes	—
272	#102	C₂×Dic₄₇	1	2	yes	—
273	#102	C₂×Dic₄₇	1	2	yes	—
274	C₂²⋊C₈	—	94	2	no	—
275	C₂²⋊C₈	—	94	2	no	—
276	C₂²⋊C₈	—	94	2	no	—
277	C₂²⋊C₈	—	94	1	no	—
278	#97	—	47	1	no	—
279	#97	—	47	1	no	—
280	#97	—	94	2	no	—
281	C₄×C₈	—	47	1	no	—
282	C₄×C₈	—	47	1	no	—
283	C₄×C₈	—	47	1	no	—
284	C₄×C₈	—	47	1	no	—
285	C₄×C₈	—	94	2	no	—
286	C₄×C₈	—	94	2	no	—
287	C₄×C₈	C₂×Dic₄₇	1	1	yes	characteristic
288	C₄×C₈	C₂×Dic₄₇	1	1	yes	characteristic
289	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
290	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
291	C₂×Q₈	C₂²×Dic₄₇	1	2	yes	—
292	C₂×D₄	—	2	2	no	—
293	C₂×D₄	C₂²×Dic₄₇	1	2	yes	—
294	C₂²×C₄	—	2	2	no	—
295	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
296	C₂²×C₄	#10625352	1	1	yes	characteristic
297	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
298	Q₁₆	—	2	2	no	—
299	SD₁₆	—	4	2	no	—
300	D₈	—	2	2	no	—
301	M₁₆	—	94	2	no	—
302	M₁₆	—	94	2	no	—
303	M₁₆	—	188	4	no	—
304	C₂×C₈	—	2	2	no	—
305	C₂×C₈	—	4	1	no	—
306	C₂×C₈	—	47	1	no	—
307	C₂×C₈	—	47	1	no	—
308	C₂×C₈	—	47	1	no	—
309	C₂×C₈	—	47	1	no	—
310	C₂×C₈	—	94	2	no	—
311	C₂×C₈	—	94	2	no	—
312	C₂×C₈	—	94	1	no	—
313	C₂×C₈	—	94	1	no	—
314	C₂×C₈	—	188	4	no	—
315	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
316	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
317	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
318	C₂×C₈	C₂²×Dic₄₇	1	1	yes	characteristic
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	2	2	no	—
323	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
324	C₄⋊C₄	C₂²×Dic₄₇	1	2	yes	—
325	C₂²⋊C₄	—	2	2	no	—
326	C₂²⋊C₄	—	2	2	no	—
327	C₂²⋊C₄	—	2	2	no	—
328	C₂²⋊C₄	—	2	2	no	—
329	C₂²⋊C₄	—	2	2	no	—
330	C₄²	—	2	2	no	—
331	C₄²	D₄×D₄₇	1	1	yes	characteristic
332	C₄²	#10625352	1	1	yes	characteristic
333	C₄²	C₂²×Dic₄₇	1	1	yes	characteristic
334	C₄²	C₂³×D₄₇	1	1	yes	characteristic
335	C₂³	—	2	2	no	—
336	C₂³	D₄×Dic₄₇	1	1	yes	characteristic
337	Q₈	—	2	2	no	—
338	Q₈	—	2	2	no	—
339	D₄	—	2	2	no	—
340	D₄	—	2	2	no	—
341	D₄	—	8	2	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	1	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	2	2	no	—
349	C₂×C₄	—	4	1	no	—
350	C₂×C₄	—	4	2	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
353	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
354	C₂×C₄	D₄×Dic₄₇	1	1	yes	characteristic
355	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
356	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
357	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
358	C₈	—	2	1	no	—
359	C₈	—	2	1	no	—
360	C₈	—	2	1	no	—
361	C₈	—	47	2	no	—
362	C₈	—	47	2	no	—
363	C₈	—	94	1	no	—
364	C₈	—	94	1	no	—
365	C₈	—	188	1	no	—
366	C₈	—	188	1	no	—
367	C₈	—	188	2	no	—
368	C₈	—	188	2	no	—
369	C₈	#13094031	1	2	yes	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	2	no	—
376	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
377	C₄	—	2	1	no	—
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	4	2	no	—
382	C₄	—	4	2	no	—
383	C₄	—	4	2	no	—
384	C₄	C₂×#13094031	1	1	yes	characteristic
385	C₄	#15689890	1	1	yes	characteristic
386	C₄	#135×D₄₇	1	1	yes	characteristic
387	C₄	#135×D₄₇	1	1	yes	characteristic
388	C₂	—	4	1	no	—
389	C₂	—	8	2	no	—
390	C₂	#20252132	1	1	yes	characteristic
391	C₂	#135×Dic₄₇	1	1	yes	characteristic
392	C₂	#20252305	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3168	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₄₇×#466	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#3168	D₄₇
hypocenter	C₄₇	#18069
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄² ◁ #3168

Complements

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

N	H ≅ G/N	type
1. #20252393	C₂	semidirect
2. #20242285	C₂	semidirect
3. #20242273	C₂	semidirect
4. #20242232	C₂	semidirect
5. #20242225	C₂	semidirect
6. Q₁₆×C₄₇⋊C₈	C₂	semidirect
7. D₈×C₄₇⋊C₈	C₂	semidirect
8. #20242136	C₂	semidirect
9. #20241796	C₂	semidirect
10. C₈×#10625329	C₂	semidirect
241. C₄₇	#18069	semidirect

Maximal subgroups

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

subgroup	index
#20252393	2
#20242285	2
#20242273	2
#20242232	2
#20242225	2
Q₁₆×C₄₇⋊C₈	2
D₈×C₄₇⋊C₈	2
#20242136	2
#20241796	2
C₈×#10625329	2
C₄₇×#3168	2
#18069	47