Subgroups — #26106671

Order 12032.

568 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252018	C₂	1	1	yes	maximal, characteristic
2	#432×D₄₇	C₂	1	1	yes	maximal, characteristic
3	#423×D₄₇	C₂	1	1	yes	maximal, characteristic
4	#20241299	C₂	1	1	yes	maximal, characteristic, complemented
5	#20241298	C₂	1	1	yes	maximal, characteristic, complemented
6	#20241298	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₇×#1307	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×M₁₆×D₄₇	C₄	1	2	yes	—
9	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
10	#15689180	C₂²	1	1	yes	characteristic
11	#15689180	C₂²	1	1	yes	characteristic
12	#15689179	—	2	1	no	—
13	#15689178	—	2	1	no	—
14	#15689178	—	2	1	no	—
15	#15689177	C₄	1	2	yes	—
16	#15689175	—	2	1	no	—
17	#15689173	C₄	1	2	yes	—
18	#15689147	C₂²	1	1	yes	characteristic
19	#15689146	C₄	1	2	yes	—
20	#15689145	—	2	1	no	—
21	#15689145	—	2	1	no	—
22	#15689145	—	2	1	no	—
23	C₄⋊C₈×D₄₇	—	2	1	no	—
24	C₄⋊C₈×D₄₇	—	2	1	no	—
25	C₄⋊C₈×D₄₇	—	2	1	no	—
26	#15689085	C₄	1	2	yes	—
27	C₂²⋊C₈×D₄₇	C₄	1	2	yes	—
28	#15689075	—	2	1	no	—
29	#97×D₄₇	—	2	1	no	—
30	C₄₇×#432	C₂²	1	1	yes	characteristic
31	C₄₇×#432	C₂²	1	1	yes	characteristic
32	C₄₇×#423	C₂²	1	1	yes	characteristic
33	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
36	C₂×#10625329	C₂×C₄	1	2	yes	—
37	C₂×#10625324	—	2	2	no	—
38	C₂×#10625324	—	2	2	no	—
39	M₁₆×D₄₇	—	4	4	no	—
40	C₂×C₈×D₄₇	—	2	2	no	—
41	C₂×C₈×D₄₇	—	2	2	no	—
42	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
44	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
45	C₄²×D₄₇	D₄	1	1	yes	characteristic
46	C₄²×D₄₇	D₄	1	1	yes	characteristic
47	C₄²×D₄₇	D₄	1	1	yes	characteristic
48	C₄²×D₄₇	D₄	1	1	yes	characteristic
49	C₄²×D₄₇	D₄	1	1	yes	characteristic
50	C₄²×D₄₇	D₄	1	1	yes	characteristic
51	C₄²×D₄₇	Q₈	1	1	yes	characteristic
52	C₄²×D₄₇	Q₈	1	1	yes	characteristic
53	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
54	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
55	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
56	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
57	Dic₄₇⋊C₈	—	2	2	no	—
58	Dic₄₇⋊C₈	—	2	2	no	—
59	Dic₄₇⋊C₈	—	2	2	no	—
60	Dic₄₇⋊C₈	—	2	2	no	—
61	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
62	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
63	(C₂×D₄₇)⋊C₈	—	2	2	no	—
64	(C₂×D₄₇)⋊C₈	—	2	2	no	—
65	#13093935	—	2	1	no	—
66	#13093935	—	2	1	no	—
67	#13093934	—	2	2	no	—
68	C₈×Dic₄₇	—	2	2	no	—
69	C₂×M₁₆×C₄₇	C₂×C₄	1	2	yes	—
70	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
71	C₄⋊C₈×C₄₇	—	2	1	no	—
72	C₄⋊C₈×C₄₇	—	2	1	no	—
73	C₄⋊C₈×C₄₇	—	2	1	no	—
74	C₄⋊C₈×C₄₇	—	2	1	no	—
75	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
76	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
77	#97×C₄₇	—	2	1	no	—
78	#97×C₄₇	—	2	1	no	—
79	C₂³×D₄₇	C₄²	1	1	yes	characteristic
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×Dic₄₇	C₄²	1	1	yes	characteristic
84	C₂²×Dic₄₇	C₄²	1	1	yes	characteristic
85	C₂²×Dic₄₇	C₄²	1	1	yes	characteristic
86	C₂×C₄×D₄₇	—	2	2	no	—
87	C₂×C₄×D₄₇	—	2	2	no	—
88	C₂×C₄×D₄₇	—	4	2	no	—
89	C₂×C₄×D₄₇	—	4	2	no	—
90	C₂×C₄×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
91	C₂×C₄×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
93	C₂×C₄×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
95	C₂×C₄×D₄₇	C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
97	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
98	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
99	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
100	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
101	C₂×C₄×D₄₇	C₄⋊C₄	1	1	yes	characteristic
102	M₁₆×C₄₇	—	4	2	no	—
103	C₂×C₈×C₄₇	—	2	2	no	—
104	C₂×C₈×C₄₇	—	2	2	no	—
105	C₂×C₈×C₄₇	—	2	2	no	—
106	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
108	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₄₇	C₂×Q₈	1	1	yes	characteristic
110	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
111	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
112	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
113	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
114	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
115	C₄×Dic₄₇	C₂²⋊C₄	1	1	yes	characteristic
116	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
117	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
118	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
119	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
120	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
121	C₄×Dic₄₇	C₄⋊C₄	1	1	yes	characteristic
122	#10625329	—	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	#10625324	—	4	4	no	—
127	#10625324	—	4	4	no	—
128	C₈×D₄₇	—	4	4	no	—
129	C₈×D₄₇	—	4	4	no	—
130	C₂³×C₄₇	C₂×C₄²	1	1	yes	characteristic
131	C₂²×D₄₇	—	2	2	no	—
132	C₂²×D₄₇	—	2	2	no	—
133	C₂²×D₄₇	—	4	1	no	—
134	C₂²×D₄₇	#95	1	1	yes	characteristic
135	C₂²×D₄₇	#95	1	1	yes	characteristic
136	C₂×C₄×C₄₇	—	2	1	no	—
137	C₂×C₄×C₄₇	—	2	1	no	—
138	C₂×C₄×C₄₇	—	4	1	no	—
139	C₂×C₄×C₄₇	—	4	1	no	—
140	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
141	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×Dic₄₇	—	2	2	no	—
147	C₂×Dic₄₇	—	2	2	no	—
148	C₂×Dic₄₇	—	4	1	no	—
149	C₂×Dic₄₇	#95	1	1	yes	characteristic
150	C₂×Dic₄₇	#95	1	1	yes	characteristic
151	C₂×Dic₄₇	#95	1	1	yes	characteristic
152	C₂×Dic₄₇	#95	1	1	yes	characteristic
153	C₂×Dic₄₇	#95	1	1	yes	characteristic
154	C₂×Dic₄₇	#95	1	1	yes	characteristic
155	C₄×D₄₇	—	2	2	no	—
156	C₄×D₄₇	—	2	2	no	—
157	C₄×D₄₇	—	2	2	no	—
158	C₄×D₄₇	—	2	1	no	—
159	C₄×D₄₇	—	2	1	no	—
160	C₄×D₄₇	—	2	2	no	—
161	C₄×D₄₇	—	2	2	no	—
162	C₄×D₄₇	—	2	2	no	—
163	C₄×D₄₇	—	4	1	no	—
164	C₄×D₄₇	—	4	1	no	—
165	C₄×D₄₇	—	4	1	no	—
166	C₄×D₄₇	—	4	1	no	—
167	C₄×D₄₇	#100	1	2	yes	—
168	C₄×D₄₇	#101	1	2	yes	—
169	C₈×C₄₇	—	4	2	no	—
170	C₈×C₄₇	—	4	2	no	—
171	C₈×C₄₇	—	4	2	no	—
172	C₄₇⋊C₈	—	4	2	no	—
173	C₄₇⋊C₈	—	4	2	no	—
174	C₄₇⋊C₈	—	4	2	no	—
175	#8121	—	47	1	no	maximal, Sylow
176	C₂²×C₄₇	—	2	1	no	—
177	C₂²×C₄₇	—	2	1	no	—
178	C₂²×C₄₇	—	2	1	no	—
179	C₂²×C₄₇	C₂×#95	1	1	yes	characteristic
180	C₂×D₄₇	—	2	1	no	—
181	C₂×D₄₇	—	2	1	no	—
182	C₂×D₄₇	—	2	1	no	—
183	C₂×D₄₇	—	2	1	no	—
184	C₂×D₄₇	—	4	4	no	—
185	C₂×D₄₇	#343	1	2	yes	—
186	C₂×D₄₇	#344	1	2	yes	—
187	C₄×C₄₇	—	2	1	no	—
188	C₄×C₄₇	—	2	1	no	—
189	C₄×C₄₇	—	2	1	no	—
190	C₄×C₄₇	—	2	1	no	—
191	C₄×C₄₇	—	2	1	no	—
192	C₄×C₄₇	C₂×#100	1	1	yes	characteristic
193	C₄×C₄₇	C₂×#101	1	1	yes	characteristic
194	Dic₄₇	—	2	1	no	—
195	Dic₄₇	—	2	1	no	—
196	Dic₄₇	—	2	1	no	—
197	Dic₄₇	—	2	1	no	—
198	Dic₄₇	#343	1	2	yes	—
199	Dic₄₇	#344	1	2	yes	—
200	#2920	—	47	1	no	—
201	C₂×#432	—	47	1	no	—
202	C₂×#423	—	47	1	no	—
203	#1307	—	47	1	no	—
204	#1307	—	47	1	no	—
205	#1307	—	47	1	no	—
206	#1307	D₄₇	1	1	yes	characteristic, complemented
207	C₂×C₄₇	—	4	1	no	—
208	C₂×C₄₇	C₂×#343	1	1	yes	characteristic
209	C₂×C₄₇	C₂×#344	1	1	yes	characteristic
210	C₂×C₄₇	C₂×#344	1	1	yes	characteristic
211	D₄₇	—	2	2	no	—
212	D₄₇	—	2	2	no	—
213	C₂²×M₁₆	—	47	2	no	—
214	C₂²×C₄²	—	47	1	no	—
215	#432	—	47	1	no	—
216	#432	—	47	1	no	—
217	#432	—	47	2	no	—
218	#432	—	94	1	no	—
219	#432	—	94	1	no	—
220	#432	—	94	1	no	—
221	#432	C₂×D₄₇	1	1	yes	characteristic
222	#432	C₂×D₄₇	1	1	yes	characteristic
223	#431	—	47	2	no	—
224	#431	—	94	1	no	—
225	#423	—	47	2	no	—
226	#423	—	47	1	no	—
227	#423	—	94	1	no	—
228	#423	—	94	1	no	—
229	#423	—	94	1	no	—
230	#423	C₂×D₄₇	1	1	yes	characteristic
231	C₂×C₄⋊C₈	—	94	1	no	—
232	C₂×C₄⋊C₈	—	94	1	no	—
233	C₂×C₄⋊C₈	—	94	1	no	—
234	#407	—	47	2	no	—
235	C₂×C₂²⋊C₈	—	47	2	no	—
236	C₄×M₁₆	—	94	1	no	—
237	C₂×#97	—	94	1	no	—
238	C₄₇	#8121	1	1	yes	characteristic, complemented, Sylow
239	C₂³×C₄	—	47	1	no	—
240	C₂³×C₄	—	47	1	no	—
241	C₂³×C₄	—	47	1	no	—
242	C₂×M₁₆	—	47	2	no	—
243	C₂×M₁₆	—	94	2	no	—
244	C₂×M₁₆	—	94	2	no	—
245	C₂×M₁₆	—	188	4	no	—
246	C₂×M₁₆	C₄×D₄₇	1	2	yes	—
247	C₂²×C₈	—	94	2	no	—
248	C₂²×C₈	—	94	2	no	—
249	C₂×C₄²	—	47	1	no	—
250	C₂×C₄²	—	47	1	no	—
251	C₂×C₄²	—	47	1	no	—
252	C₂×C₄²	—	47	1	no	—
253	C₂×C₄²	—	47	1	no	—
254	C₂×C₄²	—	47	1	no	—
255	C₂×C₄²	—	47	1	no	—
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	C₂²×D₄₇	1	1	yes	characteristic
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	2	1	no	—
263	C₄⋊C₈	—	2	1	no	—
264	C₄⋊C₈	—	2	1	no	—
265	C₄⋊C₈	—	94	2	no	—
266	C₄⋊C₈	—	94	2	no	—
267	C₄⋊C₈	—	94	2	no	—
268	C₄⋊C₈	—	94	2	no	—
269	C₄⋊C₈	—	94	1	no	—
270	C₄⋊C₈	—	94	1	no	—
271	C₄⋊C₈	—	94	1	no	—
272	C₄⋊C₈	—	94	1	no	—
273	C₂²⋊C₈	—	47	2	no	—
274	C₂²⋊C₈	—	47	2	no	—
275	C₂²⋊C₈	—	94	2	no	—
276	C₂²⋊C₈	—	94	2	no	—
277	C₂²⋊C₈	C₄×D₄₇	1	2	yes	—
278	C₂²⋊C₈	C₄×D₄₇	1	2	yes	—
279	#97	—	2	1	no	—
280	#97	—	2	1	no	—
281	#97	—	94	2	no	—
282	#97	—	94	1	no	—
283	#97	—	94	1	no	—
284	C₄×C₈	—	94	2	no	—
285	C₂⁴	—	47	1	no	—
286	C₂²×C₄	—	47	1	no	—
287	C₂²×C₄	—	47	1	no	—
288	C₂²×C₄	—	47	1	no	—
289	C₂²×C₄	—	47	1	no	—
290	C₂²×C₄	—	47	1	no	—
291	C₂²×C₄	—	47	1	no	—
292	C₂²×C₄	—	47	1	no	—
293	C₂²×C₄	—	47	1	no	—
294	C₂²×C₄	—	47	1	no	—
295	C₂²×C₄	—	47	1	no	—
296	C₂²×C₄	—	47	1	no	—
297	C₂²×C₄	—	47	1	no	—
298	C₂²×C₄	—	47	1	no	—
299	C₂²×C₄	—	47	1	no	—
300	C₂²×C₄	—	47	1	no	—
301	C₂²×C₄	—	94	2	no	—
302	C₂²×C₄	—	94	2	no	—
303	C₂²×C₄	—	188	2	no	—
304	C₂²×C₄	—	188	2	no	—
305	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
306	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
307	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
308	M₁₆	—	4	2	no	—
309	M₁₆	—	188	4	no	—
310	M₁₆	—	188	4	no	—
311	M₁₆	—	188	2	no	—
312	C₂×C₈	—	2	2	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	2	2	no	—
315	C₂×C₈	—	94	2	no	—
316	C₂×C₈	—	94	2	no	—
317	C₂×C₈	—	94	2	no	—
318	C₂×C₈	—	188	4	no	—
319	C₂×C₈	—	188	4	no	—
320	C₄²	—	47	1	no	—
321	C₄²	—	47	1	no	—
322	C₄²	—	47	1	no	—
323	C₄²	—	47	1	no	—
324	C₄²	—	47	1	no	—
325	C₄²	—	47	1	no	—
326	C₄²	—	47	1	no	—
327	C₄²	—	47	1	no	—
328	C₄²	—	47	1	no	—
329	C₄²	—	47	1	no	—
330	C₄²	—	47	1	no	—
331	C₄²	—	47	1	no	—
332	C₄²	D₄×D₄₇	1	1	yes	characteristic
333	C₄²	D₄×D₄₇	1	1	yes	characteristic
334	C₄²	D₄×D₄₇	1	1	yes	characteristic
335	C₄²	Q₈×D₄₇	1	1	yes	characteristic
336	C₂³	—	47	1	no	—
337	C₂³	—	47	1	no	—
338	C₂³	—	94	2	no	—
339	C₂³	—	94	2	no	—
340	C₂³	—	188	1	no	—
341	C₂³	C₄²×D₄₇	1	1	yes	characteristic
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	1	no	—
346	C₂×C₄	—	47	1	no	—
347	C₂×C₄	—	47	1	no	—
348	C₂×C₄	—	47	2	no	—
349	C₂×C₄	—	47	2	no	—
350	C₂×C₄	—	47	1	no	—
351	C₂×C₄	—	47	1	no	—
352	C₂×C₄	—	47	1	no	—
353	C₂×C₄	—	47	1	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	—	94	1	no	—
363	C₂×C₄	—	94	1	no	—
364	C₂×C₄	—	188	1	no	—
365	C₂×C₄	—	188	1	no	—
366	C₂×C₄	—	188	1	no	—
367	C₂×C₄	—	188	1	no	—
368	C₂×C₄	—	188	1	no	—
369	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
370	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
371	C₂×C₄	C₂²⋊C₄×D₄₇	1	1	yes	characteristic
372	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
373	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
374	C₂×C₄	C₄⋊C₄×D₄₇	1	1	yes	characteristic
375	C₈	—	4	2	no	—
376	C₈	—	4	2	no	—
377	C₈	—	4	2	no	—
378	C₈	—	188	2	no	—
379	C₈	—	188	2	no	—
380	C₈	—	188	2	no	—
381	C₂²	—	2	1	no	—
382	C₂²	—	2	1	no	—
383	C₂²	—	2	1	no	—
384	C₂²	—	47	2	no	—
385	C₂²	—	47	2	no	—
386	C₂²	—	94	1	no	—
387	C₂²	—	94	1	no	—
388	C₂²	—	94	1	no	—
389	C₂²	—	94	1	no	—
390	C₂²	—	188	4	no	—
391	C₂²	#95×D₄₇	1	1	yes	characteristic
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	2	1	no	—
396	C₄	—	2	1	no	—
397	C₄	—	47	2	no	—
398	C₄	—	47	2	no	—
399	C₄	—	94	1	no	—
400	C₄	—	94	1	no	—
401	C₄	—	94	1	no	—
402	C₄	—	94	1	no	—
403	C₄	#100×D₄₇	1	1	yes	characteristic
404	C₄	#101×D₄₇	1	1	yes	characteristic
405	C₂	—	4	1	no	—
406	C₂	—	94	2	no	—
407	C₂	—	94	2	no	—
408	C₂	#343×D₄₇	1	1	yes	characteristic
409	C₂	#344×D₄₇	1	1	yes	characteristic
410	C₂	#344×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#95×D₄₇
commutator	C₂³×C₄₇	C₂×C₄²
Frattini	C₂×C₄²	C₂²×D₄₇
Fitting	C₄₇×#1307	C₂
socle	C₂²×C₄₇	C₂×#95
prime radical	C₂³×D₄₇	C₄²
cosocle	C₂×C₄²×C₄₇	C₂³
hypercenter	#1307	D₄₇
hypocenter	C₄₇	#8121
LCS	G ▷ C₂³×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1307

Complements

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

N	H ≅ G/N	type
4. #20241299	C₂	semidirect
5. #20241298	C₂	semidirect
6. #20241298	C₂	semidirect
7. C₄₇×#1307	C₂	semidirect
206. #1307	D₄₇	semidirect
238. C₄₇	#8121	semidirect

Maximal subgroups

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

subgroup	index
#20252018	2
#432×D₄₇	2
#423×D₄₇	2
#20241299	2
#20241298	2
C₄₇×#1307	2
#8121	47