Subgroups — #26204287

Order 12032.

754 conjugacy classes of subgroups.

The subgroup lattice has 442 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20254315	C₂	1	1	yes	maximal, characteristic, complemented
2	#20253963	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689526	C₂	1	1	yes	maximal, characteristic, complemented
4	#20253784	C₂	1	1	yes	maximal, characteristic, complemented
5	#20253781	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243043	C₂	1	2	yes	maximal, complemented
7	#20243039	C₂	1	2	yes	maximal, complemented
8	#20242996	C₂	1	2	yes	maximal, complemented
9	#20242978	C₂	1	2	yes	maximal, complemented
10	#20241669	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#3206	C₂	1	1	yes	maximal, characteristic, complemented
12	#15689673	C₂²	1	1	yes	characteristic
13	C₂×#13094024	C₂²	1	1	yes	characteristic
14	#15689526	—	2	2	no	—
15	#15689526	C₂²	1	1	yes	characteristic
16	#15689526	C₂²	1	2	yes	—
17	#15689526	C₂²	1	2	yes	—
18	#15689499	C₂²	1	1	yes	characteristic
19	#15689496	C₂²	1	2	yes	—
20	#15689485	—	2	2	no	—
21	#15689482	—	2	2	no	—
22	#15689475	C₂²	1	2	yes	—
23	#15689474	C₂²	1	2	yes	—
24	#15689473	C₂²	1	2	yes	—
25	#15689471	C₂²	1	1	yes	characteristic
26	#15689471	C₂²	1	2	yes	—
27	#15689469	C₂²	1	1	yes	characteristic
28	#15689469	C₂²	1	2	yes	—
29	#15689357	—	2	2	no	—
30	#15689329	—	2	2	no	—
31	#15689264	—	2	2	no	—
32	C₄×#10625334	—	2	2	no	—
33	C₂×#13093957	—	2	2	no	—
34	#15689124	—	2	2	no	—
35	#15689122	—	2	2	no	—
36	C₄×#10625329	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
38	#15688845	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×#492	C₂²	1	2	yes	—
43	C₄₇×#487	C₂²	1	2	yes	—
44	C₄₇×#461	—	2	2	no	—
45	C₄₇×#448	—	2	2	no	—
46	C₄₇×#431	C₂²	1	1	yes	characteristic
47	C₂×#10625350	—	2	1	no	—
48	C₂²×Dic₉₄	—	2	1	no	—
49	C₂×#10625325	—	2	4	no	—
50	C₂×#10625334	—	2	2	no	—
51	C₂×#10625329	D₄	1	2	yes	—
52	C₂²×C₄₇⋊C₈	D₄	1	2	yes	—
53	#13094024	—	2	1	no	—
54	#13094024	—	2	1	no	—
55	#13094024	—	2	1	no	—
56	#13094024	C₂³	1	2	yes	—
57	#13094024	C₂³	1	1	yes	characteristic
58	#13094021	C₂³	1	1	yes	characteristic
59	#13094012	—	2	1	no	—
60	#13093998	—	2	1	no	—
61	#13093998	—	2	1	no	—
62	C₄×D₁₈₈	—	2	1	no	—
63	C₄×D₁₈₈	—	2	1	no	—
64	C₂×C₄⋊Dic₄₇	—	2	1	no	—
65	C₂×C₄⋊Dic₄₇	—	2	1	no	—
66	#13093957	—	2	4	no	—
67	#13093957	—	2	4	no	—
68	#13093957	—	2	2	no	—
69	#13093949	—	2	4	no	—
70	#13093948	—	2	4	no	—
71	#13093947	—	2	4	no	—
72	#13093945	—	2	4	no	—
73	#13093945	—	2	2	no	—
74	#13093944	—	2	4	no	—
75	#13093944	—	2	2	no	—
76	#13093935	D₄	1	2	yes	—
77	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
78	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
79	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
80	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
81	C₂×#41×C₄₇	—	2	1	no	—
82	C₂²×Q₈×C₄₇	—	2	1	no	—
83	C₂×SD₁₆×C₄₇	—	2	4	no	—
84	C₄⋊Q₈×C₄₇	—	2	1	no	—
85	C₄⋊Q₈×C₄₇	—	2	1	no	—
86	C₄⋊Q₈×C₄₇	—	2	1	no	—
87	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
88	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
89	#127×C₄₇	C₂³	1	1	yes	characteristic
90	#124×C₄₇	—	2	1	no	—
91	#121×C₄₇	—	2	1	no	—
92	#121×C₄₇	—	2	1	no	—
93	C₄×D₄×C₄₇	—	2	1	no	—
94	C₄×D₄×C₄₇	—	2	1	no	—
95	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
96	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
97	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₄₇	D₄	1	2	yes	—
99	#103×C₄₇	—	2	4	no	—
100	C₂²⋊C₈×C₄₇	D₄	1	2	yes	—
101	C₄×C₈×C₄₇	C₂³	1	2	yes	—
102	#41×C₄₇	—	4	4	no	—
103	C₂×Q₈×C₄₇	—	2	2	no	—
104	C₂×Q₈×C₄₇	—	2	1	no	—
105	C₂×Q₈×C₄₇	—	4	1	no	—
106	C₂×Q₈×C₄₇	—	8	2	no	—
107	C₂×D₄×C₄₇	—	2	1	no	—
108	C₂×D₄×C₄₇	—	2	1	no	—
109	C₂×D₄×C₄₇	—	2	1	no	—
110	C₂×D₄×C₄₇	—	4	1	no	—
111	C₂²×C₄×C₄₇	—	4	1	no	—
112	C₂²×C₄×C₄₇	—	4	1	no	—
113	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
114	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
116	C₂×C₂²⋊D₄₇	—	4	1	no	—
117	C₂²×Dic₄₇	—	4	1	no	—
118	#10625350	—	4	4	no	—
119	C₂×D₁₈₈	—	2	1	no	—
120	C₂×D₁₈₈	—	2	1	no	—
121	C₂×D₁₈₈	—	2	1	no	—
122	C₂×C₄×D₄₇	—	4	1	no	—
123	C₂×Dic₉₄	—	2	1	no	—
124	C₂×Dic₉₄	—	2	2	no	—
125	C₂×Dic₉₄	—	4	1	no	—
126	C₂×Dic₉₄	—	8	2	no	—
127	SD₁₆×C₄₇	—	8	4	no	—
128	C₂×C₈×C₄₇	C₂×D₄	1	4	yes	—
129	C₄⋊C₄×C₄₇	—	2	1	no	—
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	—	4	1	no	—
134	C₄⋊C₄×C₄₇	—	4	1	no	—
135	C₂²⋊C₄×C₄₇	—	4	1	no	—
136	C₂²⋊C₄×C₄₇	—	4	1	no	—
137	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
139	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
140	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
141	#10625334	—	4	4	no	—
142	(C₂×D₄₇)⋊C₄	—	4	1	no	—
143	(C₂×D₄₇)⋊C₄	—	4	1	no	—
144	C₄⋊Dic₄₇	—	2	2	no	—
145	C₄⋊Dic₄₇	—	2	1	no	—
146	C₄⋊Dic₄₇	—	2	1	no	—
147	C₄⋊Dic₄₇	—	2	2	no	—
148	C₄⋊Dic₄₇	—	4	1	no	—
149	C₄⋊Dic₄₇	—	4	1	no	—
150	#10625329	—	2	4	no	—
151	C₂×C₄₇⋊C₈	—	2	4	no	—
152	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
153	C₂×C₄₇⋊C₈	C₂×D₄	1	4	yes	—
154	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
155	#10625325	—	8	4	no	—
156	C₂³×C₄₇	—	4	1	no	—
157	C₂³×C₄₇	#127	1	1	yes	characteristic
158	C₂²×D₄₇	—	4	1	no	—
159	Q₈×C₄₇	—	4	2	no	—
160	Q₈×C₄₇	—	4	4	no	—
161	Q₈×C₄₇	—	8	2	no	—
162	D₄×C₄₇	—	4	2	no	—
163	D₄×C₄₇	—	4	2	no	—
164	D₄×C₄₇	—	4	2	no	—
165	D₄×C₄₇	—	8	2	no	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	4	1	no	—
169	C₂×C₄×C₄₇	—	4	2	no	—
170	C₂×C₄×C₄₇	—	8	2	no	—
171	C₂×C₄×C₄₇	—	8	2	no	—
172	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
173	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
174	C₂×C₄×C₄₇	#127	1	1	yes	characteristic
175	C₂×C₄×C₄₇	#135	1	4	yes	—
176	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
177	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
178	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
179	C₂²⋊D₄₇	—	8	2	no	—
180	C₂×Dic₄₇	—	4	2	no	—
181	C₂×Dic₄₇	—	4	1	no	—
182	C₂×Dic₄₇	—	8	2	no	—
183	D₁₈₈	—	4	2	no	—
184	D₁₈₈	—	4	2	no	—
185	D₁₈₈	—	4	2	no	—
186	C₄×D₄₇	—	8	2	no	—
187	Dic₉₄	—	4	2	no	—
188	Dic₉₄	—	4	4	no	—
189	Dic₉₄	—	8	2	no	—
190	C₈×C₄₇	—	2	4	no	—
191	C₄₇⋊C₈	—	2	4	no	—
192	C₄₇⋊C₈	—	2	2	no	—
193	C₄₇⋊C₈	#137	1	4	yes	—
194	#19638	—	47	1	no	maximal, Sylow
195	C₂²×C₄₇	—	2	1	no	—
196	C₂²×C₄₇	—	2	1	no	—
197	C₂²×C₄₇	—	8	1	no	—
198	C₂²×C₄₇	—	8	1	no	—
199	C₂²×C₄₇	—	8	1	no	—
200	C₂²×C₄₇	#495	1	2	yes	—
201	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
202	C₂×D₄₇	—	8	1	no	—
203	C₂×D₄₇	—	8	1	no	—
204	C₂×D₄₇	—	8	1	no	—
205	C₄×C₄₇	—	2	1	no	—
206	C₄×C₄₇	—	2	1	no	—
207	C₄×C₄₇	—	8	1	no	—
208	C₄×C₄₇	—	8	2	no	—
209	C₄×C₄₇	#495	1	2	yes	—
210	C₄×C₄₇	C₂×#135	1	2	yes	—
211	C₄×C₄₇	C₂×#137	1	2	yes	—
212	C₄×C₄₇	#576	1	2	yes	—
213	Dic₄₇	—	8	1	no	—
214	Dic₄₇	—	8	2	no	—
215	#3206	—	47	1	no	—
216	#3206	D₄₇	1	1	yes	characteristic, complemented
217	#3169	—	47	1	no	—
218	C₂×#500	—	47	1	no	—
219	#3141	—	47	1	no	—
220	#3141	—	47	1	no	—
221	#1719	—	47	2	no	—
222	#1719	—	47	2	no	—
223	#1710	—	47	2	no	—
224	#1706	—	47	2	no	—
225	C₈×M₁₆	—	47	1	no	—
226	C₂×C₄₇	—	2	2	no	—
227	C₂×C₄₇	—	16	1	no	—
228	C₂×C₄₇	C₂×#495	1	1	yes	characteristic
229	C₂×C₄₇	#3152	1	1	yes	characteristic
230	C₂×C₄₇	#3155	1	1	yes	characteristic
231	D₄₇	—	16	1	no	—
232	#532	—	47	1	no	—
233	#532	C₂×D₄₇	1	1	yes	characteristic
234	C₂×C₄⋊Q₈	—	47	1	no	—
235	C₂×C₄⋊Q₈	C₂×D₄₇	1	1	yes	characteristic
236	#500	—	47	2	no	—
237	#500	—	47	2	no	—
238	#500	—	47	1	no	—
239	#500	—	94	2	no	—
240	#493	—	47	1	no	—
241	#492	—	47	2	no	—
242	#492	C₂×D₄₇	1	2	yes	—
243	#489	—	94	2	no	—
244	#489	—	94	2	no	—
245	#487	—	47	2	no	—
246	#487	—	47	2	no	—
247	#487	—	47	2	no	—
248	#487	C₂×D₄₇	1	2	yes	—
249	#486	—	47	2	no	—
250	#486	—	47	1	no	—
251	#486	—	47	2	no	—
252	#486	—	47	1	no	—
253	#466	—	94	2	no	—
254	#461	—	2	2	no	—
255	#461	—	94	2	no	—
256	#448	—	2	2	no	—
257	#448	—	94	2	no	—
258	C₄×D₈	—	94	2	no	—
259	#431	C₂×D₄₇	1	1	yes	characteristic
260	C₂×#107	—	94	2	no	—
261	#417	—	94	2	no	—
262	#417	—	94	2	no	—
263	C₄×M₁₆	—	47	1	no	—
264	C₂×C₄×C₈	—	47	1	no	—
265	#322	—	47	2	no	—
266	C₈²	—	47	2	no	—
267	C₄₇	#19638	1	1	yes	characteristic, complemented, Sylow
268	C₂×#41	—	2	1	no	—
269	C₂×#41	—	94	1	no	—
270	C₂²×Q₈	—	2	1	no	—
271	C₂²×Q₈	—	94	1	no	—
272	C₂×SD₁₆	—	2	4	no	—
273	C₂×SD₁₆	—	94	4	no	—
274	C₂×D₈	—	94	2	no	—
275	C₂×M₁₆	—	47	2	no	—
276	C₂²×C₈	—	47	2	no	—
277	C₄⋊Q₈	—	2	1	no	—
278	C₄⋊Q₈	—	2	1	no	—
279	C₄⋊Q₈	—	2	1	no	—
280	C₄⋊Q₈	—	47	2	no	—
281	C₄⋊Q₈	—	47	1	no	—
282	C₄⋊Q₈	—	94	1	no	—
283	C₄⋊Q₈	—	94	1	no	—
284	C₄⋊Q₈	—	94	1	no	—
285	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
286	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
287	#127	—	47	1	no	—
288	#127	C₂²×D₄₇	1	1	yes	characteristic
289	#124	—	2	1	no	—
290	#124	—	94	1	no	—
291	#121	—	2	1	no	—
292	#121	—	2	1	no	—
293	#121	—	94	1	no	—
294	#121	—	94	1	no	—
295	C₄×D₄	—	2	1	no	—
296	C₄×D₄	—	2	1	no	—
297	C₄×D₄	—	94	1	no	—
298	C₄×D₄	—	94	1	no	—
299	C₂×C₄⋊C₄	—	2	1	no	—
300	C₂×C₄⋊C₄	—	2	1	no	—
301	C₂×C₄⋊C₄	—	94	1	no	—
302	C₂×C₄⋊C₄	—	94	1	no	—
303	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
304	#107	—	94	4	no	—
305	#107	—	94	4	no	—
306	#107	—	94	2	no	—
307	C₄⋊C₈	C₂²⋊D₄₇	1	2	yes	—
308	#103	—	2	4	no	—
309	#103	—	94	4	no	—
310	#103	—	94	4	no	—
311	#103	—	94	4	no	—
312	#102	—	94	4	no	—
313	#102	—	94	2	no	—
314	#102	—	94	4	no	—
315	#102	—	94	2	no	—
316	C₂²⋊C₈	C₂²⋊D₄₇	1	2	yes	—
317	#97	—	47	2	no	—
318	C₄×C₈	—	47	2	no	—
319	C₄×C₈	—	47	1	no	—
320	C₄×C₈	—	47	2	no	—
321	C₄×C₈	—	47	1	no	—
322	C₄×C₈	C₂²×D₄₇	1	2	yes	—
323	#41	—	4	4	no	—
324	#41	—	188	4	no	—
325	C₂×Q₈	—	2	1	no	—
326	C₂×Q₈	—	2	2	no	—
327	C₂×Q₈	—	4	1	no	—
328	C₂×Q₈	—	8	2	no	—
329	C₂×Q₈	—	94	1	no	—
330	C₂×Q₈	—	94	2	no	—
331	C₂×Q₈	—	376	2	no	—
332	C₂×Q₈	—	188	1	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	2	1	no	—
336	C₂×D₄	—	4	1	no	—
337	C₂×D₄	—	94	1	no	—
338	C₂×D₄	—	94	1	no	—
339	C₂×D₄	—	94	1	no	—
340	C₂×D₄	—	188	1	no	—
341	C₂²×C₄	—	4	1	no	—
342	C₂²×C₄	—	4	1	no	—
343	C₂²×C₄	—	188	1	no	—
344	C₂²×C₄	—	188	1	no	—
345	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
346	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
347	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
348	SD₁₆	—	8	4	no	—
349	SD₁₆	—	376	4	no	—
350	D₈	—	188	4	no	—
351	M₁₆	—	94	4	no	—
352	C₂×C₈	—	47	2	no	—
353	C₂×C₈	—	47	2	no	—
354	C₂×C₈	—	47	4	no	—
355	C₂×C₈	—	94	4	no	—
356	C₂×C₈	C₂×C₂²⋊D₄₇	1	4	yes	—
357	C₄⋊C₄	—	2	2	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	2	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	4	1	no	—
362	C₄⋊C₄	—	4	1	no	—
363	C₄⋊C₄	—	94	2	no	—
364	C₄⋊C₄	—	94	1	no	—
365	C₄⋊C₄	—	94	2	no	—
366	C₄⋊C₄	—	94	1	no	—
367	C₄⋊C₄	—	188	1	no	—
368	C₄⋊C₄	—	188	1	no	—
369	C₂²⋊C₄	—	4	1	no	—
370	C₂²⋊C₄	—	4	1	no	—
371	C₂²⋊C₄	—	188	1	no	—
372	C₂²⋊C₄	—	188	1	no	—
373	C₄²	D₄×D₄₇	1	1	yes	characteristic
374	C₄²	D₄×D₄₇	1	1	yes	characteristic
375	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
376	C₄²	C₂³×D₄₇	1	1	yes	characteristic
377	C₂³	—	4	1	no	—
378	C₂³	—	188	1	no	—
379	C₂³	#13094020	1	1	yes	characteristic
380	Q₈	—	4	2	no	—
381	Q₈	—	4	4	no	—
382	Q₈	—	8	2	no	—
383	Q₈	—	376	2	no	—
384	Q₈	—	188	2	no	—
385	Q₈	—	188	4	no	—
386	D₄	—	4	2	no	—
387	D₄	—	4	2	no	—
388	D₄	—	4	2	no	—
389	D₄	—	8	2	no	—
390	D₄	—	376	2	no	—
391	D₄	—	188	2	no	—
392	D₄	—	188	2	no	—
393	D₄	—	188	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	4	2	no	—
398	C₂×C₄	—	8	2	no	—
399	C₂×C₄	—	8	2	no	—
400	C₂×C₄	—	376	2	no	—
401	C₂×C₄	—	376	2	no	—
402	C₂×C₄	—	188	1	no	—
403	C₂×C₄	—	188	2	no	—
404	C₂×C₄	#13094020	1	1	yes	characteristic
405	C₂×C₄	#13094020	1	1	yes	characteristic
406	C₂×C₄	#13094020	1	1	yes	characteristic
407	C₂×C₄	#13094045	1	4	yes	—
408	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
409	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
410	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
411	C₈	—	2	4	no	—
412	C₈	—	47	4	no	—
413	C₈	—	94	4	no	—
414	C₈	—	94	2	no	—
415	C₂²	—	2	1	no	—
416	C₂²	—	2	1	no	—
417	C₂²	—	8	1	no	—
418	C₂²	—	8	1	no	—
419	C₂²	—	8	1	no	—
420	C₂²	—	376	1	no	—
421	C₂²	—	376	1	no	—
422	C₂²	—	376	1	no	—
423	C₂²	#15689504	1	2	yes	—
424	C₂²	C₂×#13094020	1	1	yes	characteristic
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	8	1	no	—
428	C₄	—	8	2	no	—
429	C₄	—	376	1	no	—
430	C₄	—	376	2	no	—
431	C₄	#15689504	1	2	yes	—
432	C₄	C₂×#13094045	1	2	yes	—
433	C₄	#137×D₄₇	1	2	yes	—
434	C₄	#15689926	1	2	yes	—
435	C₂	—	2	2	no	—
436	C₂	—	16	1	no	—
437	C₂	—	752	1	no	—
438	C₂	C₂×#15689504	1	1	yes	characteristic
439	C₂	#20253843	1	1	yes	characteristic
440	C₂	#20253871	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13094020
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3206	C₂
socle	C₂²×C₄₇	C₂×#127
prime radical	#20253963	C₂
hypercenter	#3206	D₄₇
hypocenter	C₄₇	#19638
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3206

Complements

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

N	H ≅ G/N	type
1. #20254315	C₂	semidirect
3. C₂×#15689526	C₂	semidirect
4. #20253784	C₂	semidirect
5. #20253781	C₂	semidirect
6. #20243043	C₂	semidirect
7. #20243039	C₂	semidirect
8. #20242996	C₂	semidirect
9. #20242978	C₂	semidirect
10. #20241669	C₂	semidirect
11. C₄₇×#3206	C₂	semidirect
216. #3206	D₄₇	semidirect
267. C₄₇	#19638	semidirect

Maximal subgroups

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

subgroup	index
#20254315	2
#20253963	2
C₂×#15689526	2
#20253784	2
#20253781	2
#20243043	2
#20243039	2
#20242996	2
#20242978	2
#20241669	2
C₄₇×#3206	2
#19638	47