Subgroups — #26200217

Order 12032.

608 conjugacy classes of subgroups.

The subgroup lattice has 430 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253544	C₂	1	2	yes	maximal
2	C₈×#10625350	C₂	1	1	yes	maximal, characteristic
3	#20242789	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242784	C₂	1	1	yes	maximal, characteristic, complemented
5	#20242779	C₂	1	1	yes	maximal, characteristic, complemented
6	#20242774	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242767	C₂	1	2	yes	maximal, complemented
8	#20242760	C₂	1	2	yes	maximal, complemented
9	#20242151	C₂	1	1	yes	maximal, characteristic, complemented
10	#20242098	C₂	1	2	yes	maximal, complemented
11	C₄₇×#3160	C₂	1	1	yes	maximal, characteristic, complemented
12	C₄×#10625350	C₂²	1	1	yes	characteristic
13	#15689461	—	2	2	no	—
14	#15689415	C₂²	1	2	yes	—
15	#15689410	C₂²	1	2	yes	—
16	#15689330	C₂²	1	2	yes	—
17	#15689325	C₂²	1	2	yes	—
18	#15689283	—	2	2	no	—
19	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
20	C₈×Dic₉₄	C₂²	1	1	yes	characteristic
21	#15689228	—	2	2	no	—
22	#15689221	—	2	2	no	—
23	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
24	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
25	C₈×C₂²⋊D₄₇	—	2	1	no	—
26	C₈×C₂²⋊D₄₇	—	2	1	no	—
27	#15689180	C₂²	1	2	yes	—
28	#15689176	C₂²	1	1	yes	characteristic
29	#15689174	—	2	1	no	—
30	C₄×C₈×D₄₇	—	2	1	no	—
31	#15688876	C₂²	1	1	yes	characteristic
32	#15688876	C₂²	1	1	yes	characteristic
33	#15688874	C₂²	1	2	yes	—
34	#15688872	C₂²	1	2	yes	—
35	#15688872	C₂²	1	2	yes	—
36	#15688869	C₂²	1	2	yes	—
37	#15688869	C₂²	1	2	yes	—
38	C₄₇×#533	C₂²	1	2	yes	—
39	C₄₇×#500	C₂²	1	1	yes	characteristic
40	C₄₇×#500	C₂²	1	1	yes	characteristic
41	C₄₇×#499	—	2	1	no	—
42	C₄₇×#499	—	2	1	no	—
43	C₄₇×#498	C₂²	1	2	yes	—
44	C₄₇×#427	—	2	1	no	—
45	C₄₇×#427	—	2	1	no	—
46	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×#10625350	D₄	1	1	yes	characteristic
48	C₂×#10625337	—	2	2	no	—
49	C₂×#10625336	—	2	2	no	—
50	C₂×C₈×D₄₇	—	2	1	no	—
51	C₂×C₈×D₄₇	—	2	1	no	—
52	C₄×Dic₉₄	D₄	1	1	yes	characteristic
53	C₄×Dic₉₄	C₂³	1	1	yes	characteristic
54	C₄×D₁₈₈	D₄	1	1	yes	characteristic
55	C₄×D₁₈₈	C₂³	1	1	yes	characteristic
56	C₄×C₂²⋊D₄₇	—	2	1	no	—
57	C₄×C₂²⋊D₄₇	—	2	1	no	—
58	#13093983	D₄	1	1	yes	characteristic
59	#13093981	—	2	1	no	—
60	C₄²×D₄₇	—	2	1	no	—
61	#13093957	—	2	2	no	—
62	#13093955	—	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	2	yes	—
66	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
67	Dic₄₇⋊C₈	—	2	1	no	—
68	Dic₄₇⋊C₈	—	2	1	no	—
69	#13093948	—	2	2	no	—
70	#13093948	—	2	2	no	—
71	#13093947	—	2	2	no	—
72	#13093944	—	2	2	no	—
73	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
74	C₂²⋊(C₄₇⋊C₈)	—	2	1	no	—
75	(C₂×D₄₇)⋊C₈	—	2	1	no	—
76	(C₂×D₄₇)⋊C₈	—	2	1	no	—
77	#13093935	—	2	2	no	—
78	C₄×C₄₇⋊C₈	—	2	1	no	—
79	C₈×Dic₄₇	—	2	1	no	—
80	C₈×Dic₄₇	—	2	1	no	—
81	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
82	C₂²×C₈×C₄₇	D₄	1	1	yes	characteristic
83	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
84	C₄⋊Q₈×C₄₇	C₂³	1	2	yes	—
85	#125×C₄₇	—	2	2	no	—
86	C₂²⋊Q₈×C₄₇	—	2	2	no	—
87	C₂²⋊Q₈×C₄₇	—	2	2	no	—
88	C₄×Q₈×C₄₇	—	2	2	no	—
89	C₄×Q₈×C₄₇	—	2	2	no	—
90	#117×C₄₇	—	2	2	no	—
91	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
92	#107×C₄₇	—	2	1	no	—
93	#107×C₄₇	—	2	1	no	—
94	#107×C₄₇	—	2	1	no	—
95	#107×C₄₇	—	2	1	no	—
96	#106×C₄₇	—	2	2	no	—
97	#106×C₄₇	—	2	2	no	—
98	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
99	C₄×C₈×C₄₇	D₄	1	1	yes	characteristic
100	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
101	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
102	C₂×Q₈×C₄₇	—	2	2	no	—
103	C₂×Q₈×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
107	C₂×C₂²⋊D₄₇	—	2	1	no	—
108	#10625350	—	2	2	no	—
109	#10625350	—	2	2	no	—
110	C₂×D₁₈₈	C₂×D₄	1	1	yes	characteristic
111	C₂×C₄×D₄₇	—	2	1	no	—
112	C₂×C₄×D₄₇	—	2	1	no	—
113	C₂×C₄×D₄₇	—	2	1	no	—
114	C₂×Dic₉₄	C₂×D₄	1	1	yes	characteristic
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	—	2	2	no	—
117	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
118	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
119	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
120	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
121	C₄⋊C₄×C₄₇	—	2	2	no	—
122	C₄⋊C₄×C₄₇	—	2	2	no	—
123	C₄⋊C₄×C₄₇	—	2	2	no	—
124	C₄⋊C₄×C₄₇	—	2	2	no	—
125	C₄⋊C₄×C₄₇	—	4	2	no	—
126	C₄⋊C₄×C₄₇	—	4	2	no	—
127	C₂²⋊C₄×C₄₇	—	4	2	no	—
128	C₄²×C₄₇	—	4	2	no	—
129	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
130	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
131	C₄²×C₄₇	#41	1	1	yes	characteristic
132	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
133	C₂²⋊Dic₄₇	—	2	1	no	—
134	#10625337	—	4	4	no	—
135	#10625336	—	4	4	no	—
136	(C₂×D₄₇)⋊C₄	—	2	1	no	—
137	(C₂×D₄₇)⋊C₄	—	2	1	no	—
138	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
139	C₄⋊Dic₄₇	C₂×D₄	1	1	yes	characteristic
140	Dic₄₇⋊C₄	—	2	1	no	—
141	Dic₄₇⋊C₄	—	2	1	no	—
142	C₄×Dic₄₇	—	2	1	no	—
143	C₄×Dic₄₇	—	2	1	no	—
144	C₄×Dic₄₇	—	2	1	no	—
145	C₂×C₄₇⋊C₈	—	2	1	no	—
146	C₂×C₄₇⋊C₈	—	2	1	no	—
147	C₂×C₄₇⋊C₈	—	2	2	no	—
148	C₂×C₄₇⋊C₈	—	2	2	no	—
149	C₈×D₄₇	—	4	2	no	—
150	C₈×D₄₇	—	4	2	no	—
151	C₂³×C₄₇	#121	1	1	yes	characteristic
152	C₂²×D₄₇	—	2	1	no	—
153	Q₈×C₄₇	—	4	2	no	—
154	Q₈×C₄₇	—	4	2	no	—
155	Q₈×C₄₇	—	8	2	no	—
156	C₂×C₄×C₄₇	—	2	1	no	—
157	C₂×C₄×C₄₇	—	2	1	no	—
158	C₂×C₄×C₄₇	—	2	1	no	—
159	C₂×C₄×C₄₇	—	2	1	no	—
160	C₂×C₄×C₄₇	—	4	1	no	—
161	C₂×C₄×C₄₇	—	4	2	no	—
162	C₂×C₄×C₄₇	—	4	2	no	—
163	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
164	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
165	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
168	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
169	C₂²⋊D₄₇	—	2	4	no	—
170	C₂×Dic₄₇	—	2	1	no	—
171	C₂×Dic₄₇	—	2	1	no	—
172	C₂×Dic₄₇	—	2	1	no	—
173	D₁₈₈	—	2	1	no	—
174	D₁₈₈	#135	1	2	yes	—
175	C₄×D₄₇	—	2	4	no	—
176	C₄×D₄₇	—	4	2	no	—
177	C₄×D₄₇	—	4	1	no	—
178	C₄×D₄₇	—	4	1	no	—
179	Dic₉₄	—	2	1	no	—
180	Dic₉₄	#135	1	2	yes	—
181	C₈×C₄₇	—	2	1	no	—
182	C₈×C₄₇	—	2	1	no	—
183	C₈×C₄₇	#137	1	2	yes	—
184	C₈×C₄₇	#137	1	2	yes	—
185	C₄₇⋊C₈	—	4	2	no	—
186	C₄₇⋊C₈	—	4	2	no	—
187	C₄₇⋊C₈	—	4	1	no	—
188	C₄₇⋊C₈	—	4	1	no	—
189	#19273	—	47	1	no	maximal, Sylow
190	C₂²×C₄₇	—	2	1	no	—
191	C₂²×C₄₇	—	2	1	no	—
192	C₂²×C₄₇	—	2	1	no	—
193	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
194	C₂×D₄₇	—	2	2	no	—
195	C₂×D₄₇	—	4	1	no	—
196	C₂×D₄₇	—	4	1	no	—
197	C₄×C₄₇	—	2	1	no	—
198	C₄×C₄₇	—	2	1	no	—
199	C₄×C₄₇	—	2	1	no	—
200	C₄×C₄₇	—	2	1	no	—
201	C₄×C₄₇	—	8	2	no	—
202	C₄×C₄₇	—	8	2	no	—
203	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
204	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
205	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
206	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
207	Dic₄₇	—	2	2	no	—
208	Dic₄₇	—	4	1	no	—
209	Dic₄₇	—	4	1	no	—
210	#3160	D₄₇	1	1	yes	characteristic, complemented
211	#3116	—	47	2	no	—
212	C₈×#41	—	47	1	no	—
213	#1676	—	47	1	no	—
214	#1675	—	47	1	no	—
215	#1674	—	47	1	no	—
216	#1673	—	47	1	no	—
217	#1672	—	47	2	no	—
218	#1671	—	47	2	no	—
219	#1568	—	47	1	no	—
220	#1554	—	47	2	no	—
221	C₂×C₄₇	—	4	1	no	—
222	C₂×C₄₇	#3039	1	1	yes	characteristic
223	C₂×C₄₇	#3050	1	1	yes	characteristic
224	C₂×C₄₇	#3067	1	1	yes	characteristic
225	D₄₇	—	4	2	no	—
226	#533	C₂×D₄₇	1	2	yes	—
227	C₄×#41	—	47	1	no	—
228	#500	C₂×D₄₇	1	1	yes	characteristic
229	#500	C₂×D₄₇	1	1	yes	characteristic
230	#499	—	2	1	no	—
231	#499	—	2	1	no	—
232	#498	C₂×D₄₇	1	2	yes	—
233	#485	—	94	2	no	—
234	#477	—	47	2	no	—
235	#476	—	47	2	no	—
236	#462	—	47	2	no	—
237	#461	—	47	2	no	—
238	#452	—	94	2	no	—
239	C₈×Q₈	—	47	1	no	—
240	C₈×Q₈	—	47	1	no	—
241	#441	—	94	2	no	—
242	#440	—	94	2	no	—
243	C₈×D₄	—	47	1	no	—
244	C₈×D₄	—	47	1	no	—
245	C₈×D₄	—	94	1	no	—
246	C₈×D₄	—	94	1	no	—
247	#432	—	47	2	no	—
248	#431	—	47	1	no	—
249	#431	—	94	1	no	—
250	#427	—	2	1	no	—
251	#427	—	2	1	no	—
252	C₂×C₄×C₈	—	94	1	no	—
253	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
254	#335	—	47	1	no	—
255	#335	—	47	1	no	—
256	#334	—	47	2	no	—
257	#333	—	47	2	no	—
258	#333	—	47	2	no	—
259	#332	—	47	2	no	—
260	#332	—	47	2	no	—
261	C₄₇	#19273	1	1	yes	characteristic, complemented, Sylow
262	C₂×#41	—	47	1	no	—
263	C₂×Q₁₆	—	94	2	no	—
264	C₂×SD₁₆	—	94	2	no	—
265	C₂²×C₈	—	94	1	no	—
266	C₂²×C₈	—	94	1	no	—
267	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
268	C₂²×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
269	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
270	C₄⋊Q₈	C₂²×D₄₇	1	2	yes	—
271	#125	—	2	2	no	—
272	C₂²⋊Q₈	—	2	2	no	—
273	C₂²⋊Q₈	—	2	2	no	—
274	C₄×Q₈	—	2	2	no	—
275	C₄×Q₈	—	2	2	no	—
276	C₄×Q₈	—	47	1	no	—
277	C₄×Q₈	—	47	1	no	—
278	C₄×D₄	—	47	1	no	—
279	C₄×D₄	—	47	1	no	—
280	C₄×D₄	—	94	1	no	—
281	C₄×D₄	—	94	1	no	—
282	#117	—	2	2	no	—
283	#117	—	47	1	no	—
284	#117	—	94	1	no	—
285	C₂×C₄²	—	94	1	no	—
286	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
287	#107	—	2	1	no	—
288	#107	—	2	1	no	—
289	#107	—	2	1	no	—
290	#107	—	2	1	no	—
291	#107	—	94	2	no	—
292	#106	—	2	2	no	—
293	#106	—	2	2	no	—
294	#106	—	94	2	no	—
295	C₄⋊C₈	—	47	1	no	—
296	C₄⋊C₈	—	47	1	no	—
297	C₄⋊C₈	—	47	2	no	—
298	C₄⋊C₈	—	47	2	no	—
299	C₄⋊C₈	—	94	1	no	—
300	C₄⋊C₈	—	94	1	no	—
301	#103	—	94	2	no	—
302	#103	—	94	2	no	—
303	#103	—	94	2	no	—
304	#102	—	94	2	no	—
305	C₂²⋊C₈	—	94	2	no	—
306	C₂²⋊C₈	—	94	1	no	—
307	C₂²⋊C₈	—	94	1	no	—
308	C₂²⋊C₈	—	94	1	no	—
309	#97	—	94	2	no	—
310	C₄×C₈	—	94	1	no	—
311	C₄×C₈	—	94	1	no	—
312	C₄×C₈	—	94	1	no	—
313	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
314	C₄×C₈	C₂²⋊D₄₇	1	1	yes	characteristic
315	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
316	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
317	#41	—	94	2	no	—
318	#41	—	94	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	47	1	no	—
322	C₂×D₄	—	47	1	no	—
323	C₂×D₄	—	94	1	no	—
324	C₂²×C₄	—	94	1	no	—
325	C₂²×C₄	—	94	1	no	—
326	C₂²×C₄	—	94	1	no	—
327	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
328	C₂²×C₄	#10625352	1	1	yes	characteristic
329	C₂²×C₄	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
330	Q₁₆	—	188	4	no	—
331	SD₁₆	—	188	4	no	—
332	C₂×C₈	—	2	2	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	94	2	no	—
335	C₂×C₈	—	94	2	no	—
336	C₂×C₈	—	94	1	no	—
337	C₂×C₈	—	94	1	no	—
338	C₂×C₈	—	188	2	no	—
339	C₂×C₈	—	188	2	no	—
340	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
341	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
342	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
343	C₂×C₈	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
344	C₄⋊C₄	—	2	2	no	—
345	C₄⋊C₄	—	2	2	no	—
346	C₄⋊C₄	—	2	2	no	—
347	C₄⋊C₄	—	2	2	no	—
348	C₄⋊C₄	—	4	2	no	—
349	C₄⋊C₄	—	4	2	no	—
350	C₄⋊C₄	—	47	1	no	—
351	C₄⋊C₄	—	47	1	no	—
352	C₄⋊C₄	—	94	1	no	—
353	C₄⋊C₄	—	94	1	no	—
354	C₂²⋊C₄	—	4	2	no	—
355	C₂²⋊C₄	—	94	1	no	—
356	C₂²⋊C₄	—	94	1	no	—
357	C₂²⋊C₄	—	94	1	no	—
358	C₄²	—	4	2	no	—
359	C₄²	—	94	1	no	—
360	C₄²	—	94	1	no	—
361	C₄²	—	94	1	no	—
362	C₄²	D₄×D₄₇	1	1	yes	characteristic
363	C₄²	#10625352	1	1	yes	characteristic
364	C₄²	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
365	C₄²	C₂³×D₄₇	1	1	yes	characteristic
366	C₂³	—	94	1	no	—
367	C₂³	#13093995	1	1	yes	characteristic
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	—	8	2	no	—
371	Q₈	—	47	2	no	—
372	Q₈	—	94	1	no	—
373	D₄	—	47	2	no	—
374	D₄	—	94	4	no	—
375	D₄	—	94	1	no	—
376	C₂×C₄	—	2	1	no	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	4	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	94	4	no	—
384	C₂×C₄	—	94	1	no	—
385	C₂×C₄	—	94	1	no	—
386	C₂×C₄	—	94	1	no	—
387	C₂×C₄	—	188	2	no	—
388	C₂×C₄	—	188	1	no	—
389	C₂×C₄	—	188	1	no	—
390	C₂×C₄	#13093995	1	1	yes	characteristic
391	C₂×C₄	#13093995	1	1	yes	characteristic
392	C₂×C₄	#13093995	1	1	yes	characteristic
393	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
394	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
395	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
396	C₈	—	2	1	no	—
397	C₈	—	2	1	no	—
398	C₈	—	188	2	no	—
399	C₈	—	188	2	no	—
400	C₈	—	188	1	no	—
401	C₈	—	188	1	no	—
402	C₈	#13094055	1	2	yes	—
403	C₈	#13094055	1	2	yes	—
404	C₂²	—	2	1	no	—
405	C₂²	—	2	1	no	—
406	C₂²	—	2	1	no	—
407	C₂²	—	94	2	no	—
408	C₂²	—	188	1	no	—
409	C₂²	—	188	1	no	—
410	C₂²	C₂×#13093995	1	1	yes	characteristic
411	C₄	—	2	1	no	—
412	C₄	—	2	1	no	—
413	C₄	—	2	1	no	—
414	C₄	—	2	1	no	—
415	C₄	—	8	2	no	—
416	C₄	—	8	2	no	—
417	C₄	—	94	2	no	—
418	C₄	—	188	1	no	—
419	C₄	—	188	1	no	—
420	C₄	#135×D₄₇	1	1	yes	characteristic
421	C₄	#135×D₄₇	1	1	yes	characteristic
422	C₄	C₂×#13094055	1	1	yes	characteristic
423	C₄	C₂×#13094055	1	1	yes	characteristic
424	C₂	—	4	1	no	—
425	C₂	—	188	2	no	—
426	C₂	#20252871	1	1	yes	characteristic
427	C₂	#20252965	1	1	yes	characteristic
428	C₂	#20253104	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13093995
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#3160	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	C₂×#10625350	D₄
hypercenter	#3160	D₄₇
hypocenter	C₄₇	#19273
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #3160

Complements

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

N	H ≅ G/N	type
3. #20242789	C₂	semidirect
4. #20242784	C₂	semidirect
5. #20242779	C₂	semidirect
6. #20242774	C₂	semidirect
7. #20242767	C₂	semidirect
8. #20242760	C₂	semidirect
9. #20242151	C₂	semidirect
10. #20242098	C₂	semidirect
11. C₄₇×#3160	C₂	semidirect
210. #3160	D₄₇	semidirect
261. C₄₇	#19273	semidirect

Maximal subgroups

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

subgroup	index
#20253544	2
C₈×#10625350	2
#20242789	2
#20242784	2
#20242779	2
#20242774	2
#20242767	2
#20242760	2
#20242151	2
#20242098	2
C₄₇×#3160	2
#19273	47