Subgroups — #26204292

Order 12032.

794 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20254516	C₂	1	1	yes	maximal, characteristic, complemented
2	#20254513	C₂	1	1	yes	maximal, characteristic, complemented
3	#20253963	C₂	1	1	yes	maximal, characteristic
4	C₂×#15689502	C₂	1	1	yes	maximal, characteristic, complemented
5	#20253782	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243049	C₂	1	2	yes	maximal, complemented
7	#20243045	C₂	1	2	yes	maximal, complemented
8	#20242992	C₂	1	2	yes	maximal, complemented
9	#20242984	C₂	1	2	yes	maximal, complemented
10	M₁₆×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3141	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625337	—	2	2	no	—
13	#15689673	C₂²	1	1	yes	characteristic
14	C₂×#13094024	C₂²	1	1	yes	characteristic
15	#15689526	C₂²	1	1	yes	characteristic
16	#15689519	C₂²	1	2	yes	—
17	#15689519	C₂²	1	2	yes	—
18	#15689502	—	2	2	no	—
19	#15689502	C₂²	1	2	yes	—
20	#15689502	C₂²	1	2	yes	—
21	#15689499	C₂²	1	1	yes	characteristic
22	#15689483	—	2	2	no	—
23	#15689474	C₂²	1	2	yes	—
24	#15689471	C₂²	1	1	yes	characteristic
25	#15689471	C₂²	1	2	yes	—
26	#15689470	C₂²	1	2	yes	—
27	#15689469	C₂²	1	1	yes	characteristic
28	#15689469	C₂²	1	2	yes	—
29	#15689441	—	2	2	no	—
30	#15689439	—	2	2	no	—
31	#15689413	—	2	2	no	—
32	#15689410	—	2	2	no	—
33	#15689357	—	2	2	no	—
34	C₄×#10625334	—	2	2	no	—
35	#15689176	C₂²	1	1	yes	characteristic
36	#15689125	—	2	2	no	—
37	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
38	#15688844	C₂²	1	2	yes	—
39	C₈×C₄₇⋊C₈	C₂²	1	2	yes	—
40	C₄₇×#532	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Q₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#489	—	2	2	no	—
43	C₄₇×#487	C₂²	1	2	yes	—
44	C₄₇×#486	C₂²	1	2	yes	—
45	C₄₇×#417	—	2	2	no	—
46	C₄×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×#10625350	—	2	1	no	—
48	C₂²×Dic₉₄	—	2	1	no	—
49	C₂×#10625337	—	2	4	no	—
50	C₂×#10625337	—	2	4	no	—
51	C₂×#10625337	—	4	8	no	—
52	C₂×#10625334	—	2	2	no	—
53	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
54	#13094024	—	2	1	no	—
55	#13094024	—	2	1	no	—
56	#13094024	—	2	1	no	—
57	#13094024	C₂³	1	1	yes	characteristic
58	#13094024	C₂³	1	2	yes	—
59	#13094021	C₂³	1	1	yes	characteristic
60	#13094012	—	2	1	no	—
61	#13093998	—	2	1	no	—
62	#13093998	—	2	1	no	—
63	C₄×D₁₈₈	—	2	1	no	—
64	C₄×D₁₈₈	—	2	1	no	—
65	C₂×C₄⋊Dic₄₇	—	2	1	no	—
66	C₂×C₄⋊Dic₄₇	—	2	1	no	—
67	#13093957	—	2	2	no	—
68	#13093955	—	2	4	no	—
69	#13093955	—	2	4	no	—
70	C₄⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
71	#13093949	—	2	4	no	—
72	#13093946	—	2	4	no	—
73	#13093945	—	2	2	no	—
74	#13093945	—	2	4	no	—
75	#13093944	—	2	2	no	—
76	#13093944	—	2	4	no	—
77	C₂²⋊(C₄₇⋊C₈)	D₄	1	2	yes	—
78	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
79	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
80	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
81	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
82	C₂×#41×C₄₇	—	2	1	no	—
83	C₂²×Q₈×C₄₇	—	2	1	no	—
84	C₂×M₁₆×C₄₇	D₄	1	2	yes	—
85	C₄⋊Q₈×C₄₇	—	2	1	no	—
86	C₄⋊Q₈×C₄₇	—	2	1	no	—
87	C₄⋊Q₈×C₄₇	—	2	1	no	—
88	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
89	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
90	#127×C₄₇	C₂³	1	1	yes	characteristic
91	#124×C₄₇	—	2	1	no	—
92	#121×C₄₇	—	2	1	no	—
93	#121×C₄₇	—	2	1	no	—
94	C₄×D₄×C₄₇	—	2	1	no	—
95	C₄×D₄×C₄₇	—	2	1	no	—
96	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
97	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
98	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
99	#103×C₄₇	—	2	4	no	—
100	#102×C₄₇	—	2	4	no	—
101	#97×C₄₇	D₄	1	2	yes	—
102	C₄×C₈×C₄₇	C₂³	1	2	yes	—
103	#41×C₄₇	—	4	4	no	—
104	C₂×Q₈×C₄₇	—	2	1	no	—
105	C₂×Q₈×C₄₇	—	2	2	no	—
106	C₂×Q₈×C₄₇	—	4	4	no	—
107	C₂×Q₈×C₄₇	—	4	1	no	—
108	C₂×D₄×C₄₇	—	2	1	no	—
109	C₂×D₄×C₄₇	—	2	1	no	—
110	C₂×D₄×C₄₇	—	2	1	no	—
111	C₂×D₄×C₄₇	—	4	1	no	—
112	C₂²×C₄×C₄₇	—	4	1	no	—
113	C₂²×C₄×C₄₇	—	4	1	no	—
114	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₂×C₂²⋊D₄₇	—	4	1	no	—
118	C₂²×Dic₄₇	—	4	1	no	—
119	#10625350	—	4	4	no	—
120	C₂×D₁₈₈	—	2	1	no	—
121	C₂×D₁₈₈	—	2	1	no	—
122	C₂×D₁₈₈	—	2	1	no	—
123	C₂×C₄×D₄₇	—	4	1	no	—
124	C₂×Dic₉₄	—	2	1	no	—
125	C₂×Dic₉₄	—	2	2	no	—
126	C₂×Dic₉₄	—	4	4	no	—
127	C₂×Dic₉₄	—	4	1	no	—
128	M₁₆×C₄₇	—	2	4	no	—
129	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
130	C₄⋊C₄×C₄₇	—	2	2	no	—
131	C₄⋊C₄×C₄₇	—	2	2	no	—
132	C₄⋊C₄×C₄₇	—	2	1	no	—
133	C₄⋊C₄×C₄₇	—	2	1	no	—
134	C₄⋊C₄×C₄₇	—	4	1	no	—
135	C₄⋊C₄×C₄₇	—	4	1	no	—
136	C₂²⋊C₄×C₄₇	—	4	1	no	—
137	C₂²⋊C₄×C₄₇	—	4	1	no	—
138	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
141	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
142	#10625337	—	4	8	no	—
143	#10625337	—	4	8	no	—
144	#10625334	—	4	4	no	—
145	(C₂×D₄₇)⋊C₄	—	4	1	no	—
146	(C₂×D₄₇)⋊C₄	—	4	1	no	—
147	C₄⋊Dic₄₇	—	2	2	no	—
148	C₄⋊Dic₄₇	—	2	1	no	—
149	C₄⋊Dic₄₇	—	2	2	no	—
150	C₄⋊Dic₄₇	—	2	1	no	—
151	C₄⋊Dic₄₇	—	4	1	no	—
152	C₄⋊Dic₄₇	—	4	1	no	—
153	C₂×C₄₇⋊C₈	—	2	4	no	—
154	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
155	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
156	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
157	C₂³×C₄₇	—	4	1	no	—
158	C₂³×C₄₇	#127	1	1	yes	characteristic
159	C₂²×D₄₇	—	4	1	no	—
160	Q₈×C₄₇	—	4	2	no	—
161	Q₈×C₄₇	—	4	4	no	—
162	Q₈×C₄₇	—	8	2	no	—
163	D₄×C₄₇	—	4	2	no	—
164	D₄×C₄₇	—	4	2	no	—
165	D₄×C₄₇	—	4	2	no	—
166	D₄×C₄₇	—	8	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	2	no	—
169	C₂×C₄×C₄₇	—	4	1	no	—
170	C₂×C₄×C₄₇	—	4	2	no	—
171	C₂×C₄×C₄₇	—	8	2	no	—
172	C₂×C₄×C₄₇	—	8	2	no	—
173	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
174	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
175	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
176	C₂×C₄×C₄₇	#135	1	4	yes	—
177	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
180	C₂²⋊D₄₇	—	8	2	no	—
181	C₂×Dic₄₇	—	4	2	no	—
182	C₂×Dic₄₇	—	4	1	no	—
183	C₂×Dic₄₇	—	8	2	no	—
184	D₁₈₈	—	4	2	no	—
185	D₁₈₈	—	4	2	no	—
186	D₁₈₈	—	4	2	no	—
187	C₄×D₄₇	—	8	2	no	—
188	Dic₉₄	—	4	2	no	—
189	Dic₉₄	—	4	4	no	—
190	Dic₉₄	—	8	2	no	—
191	C₈×C₄₇	—	2	4	no	—
192	C₄₇⋊C₈	—	2	2	no	—
193	C₄₇⋊C₈	—	2	4	no	—
194	C₄₇⋊C₈	AGL(1,ℤ/8)	1	4	yes	—
195	#19639	—	47	1	no	maximal, Sylow
196	C₂²×C₄₇	—	2	1	no	—
197	C₂²×C₄₇	—	2	1	no	—
198	C₂²×C₄₇	—	8	1	no	—
199	C₂²×C₄₇	—	8	1	no	—
200	C₂²×C₄₇	—	8	1	no	—
201	C₂²×C₄₇	#495	1	2	yes	—
202	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
203	C₂×D₄₇	—	8	1	no	—
204	C₂×D₄₇	—	8	1	no	—
205	C₂×D₄₇	—	8	1	no	—
206	C₄×C₄₇	—	2	1	no	—
207	C₄×C₄₇	—	2	1	no	—
208	C₄×C₄₇	—	8	1	no	—
209	C₄×C₄₇	—	8	2	no	—
210	C₄×C₄₇	#495	1	2	yes	—
211	C₄×C₄₇	C₂×#135	1	2	yes	—
212	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
213	C₄×C₄₇	#578	1	2	yes	—
214	Dic₄₇	—	8	1	no	—
215	Dic₄₇	—	8	2	no	—
216	#3227	—	47	1	no	—
217	#3227	—	47	1	no	—
218	#3169	—	47	1	no	—
219	C₂×#494	—	47	1	no	—
220	#3141	—	47	1	no	—
221	#3141	D₄₇	1	1	yes	characteristic, complemented
222	#1720	—	47	2	no	—
223	#1720	—	47	2	no	—
224	#1709	—	47	2	no	—
225	#1707	—	47	2	no	—
226	C₈×M₁₆	—	47	1	no	—
227	C₂×C₄₇	—	2	2	no	—
228	C₂×C₄₇	—	16	1	no	—
229	C₂×C₄₇	C₂×#495	1	1	yes	characteristic
230	C₂×C₄₇	#3151	1	1	yes	characteristic
231	C₂×C₄₇	#3156	1	1	yes	characteristic
232	D₄₇	—	16	1	no	—
233	C₂²×Q₁₆	—	94	2	no	—
234	#532	—	47	1	no	—
235	#532	C₂×D₄₇	1	1	yes	characteristic
236	C₂×C₄⋊Q₈	—	47	1	no	—
237	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
238	#500	—	47	1	no	—
239	#498	—	47	2	no	—
240	#498	—	47	2	no	—
241	#494	—	47	2	no	—
242	#494	—	47	2	no	—
243	#494	—	94	2	no	—
244	#493	—	47	1	no	—
245	#489	—	2	2	no	—
246	#489	—	94	2	no	—
247	#487	—	47	2	no	—
248	#487	C₂×D₄₇	1	2	yes	—
249	#486	—	47	1	no	—
250	#486	—	47	2	no	—
251	#486	—	47	1	no	—
252	#486	—	47	2	no	—
253	#486	—	47	2	no	—
254	#486	C₂×D₄₇	1	2	yes	—
255	#481	—	94	2	no	—
256	#481	—	94	2	no	—
257	#476	—	94	2	no	—
258	#476	—	94	2	no	—
259	#466	—	94	2	no	—
260	C₄×D₈	—	94	2	no	—
261	#431	—	47	1	no	—
262	#417	—	2	2	no	—
263	#417	—	94	2	no	—
264	C₄×M₁₆	C₂×D₄₇	1	1	yes	characteristic
265	C₂×C₄×C₈	—	47	1	no	—
266	#322	—	47	2	no	—
267	C₈²	—	47	2	no	—
268	C₄₇	#19639	1	1	yes	characteristic, complemented, Sylow
269	C₂×#41	—	2	1	no	—
270	C₂×#41	—	94	1	no	—
271	C₂²×Q₈	—	2	1	no	—
272	C₂²×Q₈	—	94	1	no	—
273	C₂×Q₁₆	—	94	4	no	—
274	C₂×Q₁₆	—	94	4	no	—
275	C₂×Q₁₆	—	188	8	no	—
276	C₂×D₈	—	94	2	no	—
277	C₂×M₁₆	C₂²⋊D₄₇	1	2	yes	—
278	C₂²×C₈	—	47	2	no	—
279	C₄⋊Q₈	—	2	1	no	—
280	C₄⋊Q₈	—	2	1	no	—
281	C₄⋊Q₈	—	2	1	no	—
282	C₄⋊Q₈	—	47	2	no	—
283	C₄⋊Q₈	—	47	1	no	—
284	C₄⋊Q₈	—	94	1	no	—
285	C₄⋊Q₈	—	94	1	no	—
286	C₄⋊Q₈	—	94	1	no	—
287	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
288	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
289	#127	—	47	1	no	—
290	#127	C₂²×D₄₇	1	1	yes	characteristic
291	#124	—	2	1	no	—
292	#124	—	94	1	no	—
293	#121	—	2	1	no	—
294	#121	—	2	1	no	—
295	#121	—	94	1	no	—
296	#121	—	94	1	no	—
297	C₄×D₄	—	2	1	no	—
298	C₄×D₄	—	2	1	no	—
299	C₄×D₄	—	94	1	no	—
300	C₄×D₄	—	94	1	no	—
301	C₂×C₄⋊C₄	—	2	1	no	—
302	C₂×C₄⋊C₄	—	2	1	no	—
303	C₂×C₄⋊C₄	—	94	1	no	—
304	C₂×C₄⋊C₄	—	94	1	no	—
305	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
306	#107	—	94	2	no	—
307	#106	—	94	4	no	—
308	#106	—	94	4	no	—
309	C₄⋊C₈	—	47	2	no	—
310	#103	—	2	4	no	—
311	#103	—	94	4	no	—
312	#102	—	2	4	no	—
313	#102	—	94	2	no	—
314	#102	—	94	4	no	—
315	#102	—	94	2	no	—
316	#102	—	94	4	no	—
317	#102	—	94	4	no	—
318	C₂²⋊C₈	—	47	2	no	—
319	#97	C₂²⋊D₄₇	1	2	yes	—
320	C₄×C₈	—	47	2	no	—
321	C₄×C₈	—	47	1	no	—
322	C₄×C₈	—	47	2	no	—
323	C₄×C₈	—	47	1	no	—
324	C₄×C₈	C₂²×D₄₇	1	2	yes	—
325	#41	—	4	4	no	—
326	#41	—	188	4	no	—
327	C₂×Q₈	—	2	2	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	4	4	no	—
330	C₂×Q₈	—	4	1	no	—
331	C₂×Q₈	—	94	2	no	—
332	C₂×Q₈	—	94	1	no	—
333	C₂×Q₈	—	188	4	no	—
334	C₂×Q₈	—	188	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	2	1	no	—
337	C₂×D₄	—	2	1	no	—
338	C₂×D₄	—	4	1	no	—
339	C₂×D₄	—	94	1	no	—
340	C₂×D₄	—	94	1	no	—
341	C₂×D₄	—	94	1	no	—
342	C₂×D₄	—	188	1	no	—
343	C₂²×C₄	—	4	1	no	—
344	C₂²×C₄	—	4	1	no	—
345	C₂²×C₄	—	188	1	no	—
346	C₂²×C₄	—	188	1	no	—
347	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
348	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
349	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
350	Q₁₆	—	188	8	no	—
351	Q₁₆	—	188	8	no	—
352	D₈	—	188	4	no	—
353	M₁₆	—	2	4	no	—
354	C₂×C₈	—	47	2	no	—
355	C₂×C₈	—	47	2	no	—
356	C₂×C₈	—	47	4	no	—
357	C₂×C₈	—	94	4	no	—
358	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	2	2	no	—
363	C₄⋊C₄	—	4	1	no	—
364	C₄⋊C₄	—	4	1	no	—
365	C₄⋊C₄	—	94	2	no	—
366	C₄⋊C₄	—	94	1	no	—
367	C₄⋊C₄	—	94	1	no	—
368	C₄⋊C₄	—	94	2	no	—
369	C₄⋊C₄	—	188	1	no	—
370	C₄⋊C₄	—	188	1	no	—
371	C₂²⋊C₄	—	4	1	no	—
372	C₂²⋊C₄	—	4	1	no	—
373	C₂²⋊C₄	—	188	1	no	—
374	C₂²⋊C₄	—	188	1	no	—
375	C₄²	D₄×D₄₇	1	1	yes	characteristic
376	C₄²	D₄×D₄₇	1	1	yes	characteristic
377	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
378	C₄²	C₂³×D₄₇	1	1	yes	characteristic
379	C₂³	—	4	1	no	—
380	C₂³	—	188	1	no	—
381	C₂³	#13094020	1	1	yes	characteristic
382	Q₈	—	4	2	no	—
383	Q₈	—	4	4	no	—
384	Q₈	—	8	2	no	—
385	Q₈	—	376	2	no	—
386	Q₈	—	188	2	no	—
387	Q₈	—	188	4	no	—
388	D₄	—	4	2	no	—
389	D₄	—	4	2	no	—
390	D₄	—	4	2	no	—
391	D₄	—	8	2	no	—
392	D₄	—	376	2	no	—
393	D₄	—	188	2	no	—
394	D₄	—	188	2	no	—
395	D₄	—	188	2	no	—
396	C₂×C₄	—	2	2	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	4	1	no	—
399	C₂×C₄	—	4	2	no	—
400	C₂×C₄	—	8	2	no	—
401	C₂×C₄	—	8	2	no	—
402	C₂×C₄	—	376	2	no	—
403	C₂×C₄	—	376	2	no	—
404	C₂×C₄	—	188	1	no	—
405	C₂×C₄	—	188	2	no	—
406	C₂×C₄	#13094020	1	1	yes	characteristic
407	C₂×C₄	#13094020	1	1	yes	characteristic
408	C₂×C₄	#13094020	1	1	yes	characteristic
409	C₂×C₄	#13094044	1	4	yes	—
410	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
411	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
412	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
413	C₈	—	2	4	no	—
414	C₈	—	47	4	no	—
415	C₈	—	94	2	no	—
416	C₈	—	94	4	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	8	1	no	—
421	C₂²	—	8	1	no	—
422	C₂²	—	376	1	no	—
423	C₂²	—	376	1	no	—
424	C₂²	—	376	1	no	—
425	C₂²	#15689505	1	2	yes	—
426	C₂²	C₂×#13094020	1	1	yes	characteristic
427	C₄	—	2	1	no	—
428	C₄	—	2	1	no	—
429	C₄	—	8	1	no	—
430	C₄	—	8	2	no	—
431	C₄	—	376	1	no	—
432	C₄	—	376	2	no	—
433	C₄	#15689505	1	2	yes	—
434	C₄	C₂×#13094044	1	2	yes	—
435	C₄	AGL(1,ℤ/8)×D₄₇	1	2	yes	—
436	C₄	#15689939	1	2	yes	—
437	C₂	—	2	2	no	—
438	C₂	—	16	1	no	—
439	C₂	—	752	1	no	—
440	C₂	C₂×#15689505	1	1	yes	characteristic
441	C₂	#20253836	1	1	yes	characteristic
442	C₂	#20253881	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13094020
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3141	C₂
socle	C₂²×C₄₇	C₂×#127
prime radical	#20253963	C₂
hypercenter	#3141	D₄₇
hypocenter	C₄₇	#19639
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3141

Complements

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

N	H ≅ G/N	type
1. #20254516	C₂	semidirect
2. #20254513	C₂	semidirect
4. C₂×#15689502	C₂	semidirect
5. #20253782	C₂	semidirect
6. #20243049	C₂	semidirect
7. #20243045	C₂	semidirect
8. #20242992	C₂	semidirect
9. #20242984	C₂	semidirect
10. M₁₆×C₄₇⋊C₈	C₂	semidirect
11. C₄₇×#3141	C₂	semidirect
221. #3141	D₄₇	semidirect
268. C₄₇	#19639	semidirect

Maximal subgroups

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

subgroup	index
#20254516	2
#20254513	2
#20253963	2
C₂×#15689502	2
#20253782	2
#20243049	2
#20243045	2
#20242992	2
#20242984	2
M₁₆×C₄₇⋊C₈	2
C₄₇×#3141	2
#19639	47