Subgroups — #26199787

Order 12032.

652 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	#20254700	C₂	1	1	yes	maximal, characteristic
2	#20254315	C₂	1	1	yes	maximal, characteristic
3	#20253935	C₂	1	1	yes	maximal, characteristic, complemented
4	#20252131	C₂	1	1	yes	maximal, characteristic
5	#20242900	C₂	1	2	yes	maximal, complemented
6	#20242890	C₂	1	2	yes	maximal, complemented
7	#20242776	C₂	1	2	yes	maximal, complemented
8	#20242766	C₂	1	2	yes	maximal, complemented
9	#20242141	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15688868	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1542	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094030	—	2	1	no	—
13	#15689673	C₂²	1	1	yes	characteristic
14	C₂×#13094024	C₂²	1	1	yes	characteristic
15	#15689533	—	2	2	no	—
16	#15689526	C₂²	1	2	yes	—
17	#15689519	C₂²	1	2	yes	—
18	#15689496	—	2	1	no	—
19	#15689474	—	2	1	no	—
20	#15689410	C₂²	1	2	yes	—
21	#15689408	—	2	1	no	—
22	#15689354	—	2	2	no	—
23	#15689329	C₂²	1	2	yes	—
24	#15689329	C₂²	1	2	yes	—
25	#15689325	C₂²	1	2	yes	—
26	#15689323	—	2	1	no	—
27	#15689264	—	2	2	no	—
28	#15689200	C₂²	1	2	yes	—
29	#15689193	—	2	2	no	—
30	#15689188	C₂²	1	2	yes	—
31	#15689166	—	2	1	no	—
32	#15689166	—	2	1	no	—
33	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
34	#15689089	—	2	1	no	—
35	C₄×#10625329	C₂²	1	1	yes	characteristic
36	#15688875	C₂²	1	2	yes	—
37	#15688873	C₂²	1	2	yes	—
38	#15688868	C₂²	1	2	yes	—
39	#15688868	C₂²	1	2	yes	—
40	C₄₇×#533	C₂²	1	1	yes	characteristic
41	C₄₇×#431	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
43	C₄₇×#333	C₂²	1	1	yes	characteristic
44	C₄₇×#333	C₂²	1	1	yes	characteristic
45	C₄₇×#332	C₂²	1	1	yes	characteristic
46	C₄₇×#332	C₂²	1	1	yes	characteristic
47	C₂×#10625350	—	2	1	no	—
48	C₂²×Dic₉₄	—	2	1	no	—
49	C₂×#10625325	—	2	2	no	—
50	C₂×#10625325	—	2	2	no	—
51	C₂×#10625336	—	2	2	no	—
52	#13094030	—	4	4	no	—
53	C₂×#10625329	D₄	1	1	yes	characteristic
54	C₂×#10625329	D₄	1	1	yes	characteristic
55	C₂×#10625324	—	2	2	no	—
56	C₂²×C₄₇⋊C₈	—	2	1	no	—
57	C₂×C₈×D₄₇	—	2	2	no	—
58	#13094024	—	2	1	no	—
59	#13094024	—	2	1	no	—
60	#13094024	—	2	1	no	—
61	#13094024	D₄	1	1	yes	characteristic
62	#13094024	C₂³	1	2	yes	—
63	#13094021	D₄	1	1	yes	characteristic
64	#13094012	—	2	1	no	—
65	#13093998	—	2	1	no	—
66	#13093998	D₄	1	2	yes	—
67	C₄×D₁₈₈	—	2	1	no	—
68	C₄×D₁₈₈	C₂³	1	2	yes	—
69	C₂×C₄⋊Dic₄₇	—	2	1	no	—
70	C₂×C₄⋊Dic₄₇	—	2	1	no	—
71	#13093957	—	2	2	no	—
72	#13093957	—	2	2	no	—
73	#13093955	—	2	2	no	—
74	#13093955	—	2	2	no	—
75	#13093955	—	2	2	no	—
76	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
77	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
78	#13093949	—	2	2	no	—
79	#13093949	—	2	2	no	—
80	#13093948	—	2	2	no	—
81	#13093944	—	2	2	no	—
82	(C₂×D₄₇)⋊C₈	—	2	2	no	—
83	(C₂×D₄₇)⋊C₈	—	2	2	no	—
84	#13093935	D₄	1	2	yes	—
85	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
86	C₂²×C₈×C₄₇	—	2	1	no	—
87	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
88	C₄⋊Q₈×C₄₇	C₂³	1	1	yes	characteristic
89	#125×C₄₇	—	2	1	no	—
90	C₂²⋊Q₈×C₄₇	—	2	1	no	—
91	C₂²⋊Q₈×C₄₇	—	2	1	no	—
92	C₄×Q₈×C₄₇	—	2	1	no	—
93	C₄×Q₈×C₄₇	—	2	1	no	—
94	#117×C₄₇	—	2	1	no	—
95	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
96	C₄⋊C₈×C₄₇	—	2	1	no	—
97	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
98	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
99	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
100	C₄⋊C₈×C₄₇	C₂³	1	1	yes	characteristic
101	C₂²⋊C₈×C₄₇	—	2	1	no	—
102	C₄×C₈×C₄₇	—	2	1	no	—
103	C₂×Q₈×C₄₇	—	2	1	no	—
104	C₂×Q₈×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
108	C₂×C₂²⋊D₄₇	—	2	2	no	—
109	C₂²×Dic₄₇	—	4	1	no	—
110	#10625350	—	4	2	no	—
111	#10625350	—	4	2	no	—
112	C₂×D₁₈₈	—	2	1	no	—
113	C₂×D₁₈₈	—	2	1	no	—
114	C₂×D₁₈₈	C₂×D₄	1	2	yes	—
115	C₂×C₄×D₄₇	—	2	2	no	—
116	C₂×Dic₉₄	—	2	1	no	—
117	C₂×Dic₉₄	—	2	2	no	—
118	C₂×Dic₉₄	—	4	1	no	—
119	C₂×Dic₉₄	—	8	1	no	—
120	C₂×Dic₉₄	—	8	1	no	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	—	2	1	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	—	4	2	no	—
126	C₄⋊C₄×C₄₇	—	2	1	no	—
127	C₄⋊C₄×C₄₇	—	2	1	no	—
128	C₄⋊C₄×C₄₇	—	2	1	no	—
129	C₄⋊C₄×C₄₇	—	2	1	no	—
130	C₄⋊C₄×C₄₇	—	4	1	no	—
131	C₄⋊C₄×C₄₇	—	4	1	no	—
132	C₂²⋊C₄×C₄₇	—	4	1	no	—
133	C₄²×C₄₇	—	4	1	no	—
134	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
135	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
136	C₄²×C₄₇	#41	1	1	yes	characteristic
137	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
138	#10625336	—	8	2	no	—
139	(C₂×D₄₇)⋊C₄	—	2	2	no	—
140	(C₂×D₄₇)⋊C₄	—	2	2	no	—
141	C₄⋊Dic₄₇	—	2	1	no	—
142	C₄⋊Dic₄₇	—	2	2	no	—
143	C₄⋊Dic₄₇	—	2	2	no	—
144	C₄⋊Dic₄₇	—	4	1	no	—
145	C₄⋊Dic₄₇	—	4	1	no	—
146	C₄⋊Dic₄₇	C₂×D₄	1	2	yes	—
147	#10625329	—	2	2	no	—
148	#10625329	SD₁₆	1	4	yes	complemented
149	C₂×C₄₇⋊C₈	—	2	2	no	—
150	C₂×C₄₇⋊C₈	—	8	1	no	—
151	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
152	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
153	#10625325	—	8	2	no	—
154	#10625325	—	8	2	no	—
155	#10625324	—	4	4	no	—
156	C₈×D₄₇	—	4	4	no	—
157	C₂³×C₄₇	#121	1	1	yes	characteristic
158	C₂²×D₄₇	—	2	2	no	—
159	Q₈×C₄₇	—	4	1	no	—
160	Q₈×C₄₇	—	4	1	no	—
161	Q₈×C₄₇	—	8	1	no	—
162	C₂×C₄×C₄₇	—	2	1	no	—
163	C₂×C₄×C₄₇	—	2	1	no	—
164	C₂×C₄×C₄₇	—	4	1	no	—
165	C₂×C₄×C₄₇	—	4	1	no	—
166	C₂×C₄×C₄₇	—	4	1	no	—
167	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
168	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
169	C₂×C₄×C₄₇	#121	1	1	yes	characteristic
170	C₂×C₄×C₄₇	C₂×SD₁₆	1	2	yes	—
171	C₂×C₄×C₄₇	#137	1	2	yes	—
172	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
173	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
174	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
175	C₂²⋊D₄₇	—	4	4	no	—
176	C₂×Dic₄₇	—	2	2	no	—
177	C₂×Dic₄₇	—	4	2	no	—
178	C₂×Dic₄₇	—	8	2	no	—
179	D₁₈₈	—	2	2	no	—
180	D₁₈₈	—	2	2	no	—
181	D₁₈₈	—	4	2	no	—
182	D₁₈₈	—	8	1	no	—
183	C₄×D₄₇	—	4	2	no	—
184	C₄×D₄₇	—	4	2	no	—
185	Dic₉₄	—	4	2	no	—
186	Dic₉₄	—	4	2	no	—
187	Dic₉₄	—	4	2	no	—
188	Dic₉₄	—	8	2	no	—
189	C₈×C₄₇	—	4	1	no	—
190	C₈×C₄₇	—	4	1	no	—
191	C₈×C₄₇	—	4	1	no	—
192	C₈×C₄₇	—	4	1	no	—
193	C₄₇⋊C₈	—	2	2	no	—
194	C₄₇⋊C₈	—	4	2	no	—
195	C₄₇⋊C₈	C₂×SD₁₆	1	4	yes	—
196	#19232	—	47	1	no	maximal, Sylow
197	C₂²×C₄₇	—	2	1	no	—
198	C₂²×C₄₇	—	2	1	no	—
199	C₂²×C₄₇	#461	1	2	yes	—
200	C₂²×C₄₇	C₂×#121	1	1	yes	characteristic
201	C₂×D₄₇	—	4	2	no	—
202	C₂×D₄₇	—	4	2	no	—
203	C₂×D₄₇	—	4	2	no	—
204	C₄×C₄₇	—	2	1	no	—
205	C₄×C₄₇	—	2	1	no	—
206	C₄×C₄₇	—	2	1	no	—
207	C₄×C₄₇	—	8	1	no	—
208	C₄×C₄₇	—	8	1	no	—
209	C₄×C₄₇	#461	1	2	yes	—
210	C₄×C₄₇	C₂²×SD₁₆	1	1	yes	characteristic
211	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
212	C₄×C₄₇	#576	1	1	yes	characteristic
213	C₄×C₄₇	#577	1	1	yes	characteristic
214	Dic₄₇	—	4	2	no	—
215	Dic₄₇	—	8	2	no	—
216	#3246	—	47	1	no	—
217	#3206	—	47	1	no	—
218	#3165	—	47	1	no	—
219	#2935	—	47	1	no	—
220	#1693	—	47	2	no	—
221	#1691	—	47	2	no	—
222	#1673	—	47	2	no	—
223	#1671	—	47	2	no	—
224	#1565	—	47	1	no	—
225	#1542	D₄₇	1	1	yes	characteristic, complemented
226	C₂×#332	—	47	1	no	—
227	C₂×C₄₇	—	2	2	no	—
228	C₂×C₄₇	C₂×#461	1	1	yes	characteristic
229	C₂×C₄₇	#3062	1	1	yes	characteristic
230	C₂×C₄₇	#3069	1	1	yes	characteristic
231	D₄₇	—	8	2	no	—
232	C₂×#131	—	94	1	no	—
233	#533	C₂×D₄₇	1	1	yes	characteristic
234	#532	—	47	1	no	—
235	C₂×C₄⋊Q₈	—	47	1	no	—
236	#501	—	94	2	no	—
237	#500	—	47	2	no	—
238	#498	—	47	2	no	—
239	#492	—	94	1	no	—
240	#487	—	94	1	no	—
241	#476	—	47	2	no	—
242	#475	—	94	1	no	—
243	#465	—	94	2	no	—
244	#461	—	47	2	no	—
245	#461	—	47	2	no	—
246	#461	—	47	2	no	—
247	#460	—	94	1	no	—
248	#448	—	94	2	no	—
249	#436	—	47	2	no	—
250	#435	—	94	2	no	—
251	C₈×D₄	—	47	2	no	—
252	#431	C₂×D₄₇	1	1	yes	characteristic
253	#428	—	94	1	no	—
254	#428	—	94	1	no	—
255	C₂×C₄⋊C₈	—	47	1	no	—
256	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
257	#408	—	94	1	no	—
258	C₄×M₁₆	—	47	1	no	—
259	#335	—	47	2	no	—
260	#334	—	47	2	no	—
261	#333	C₂×D₄₇	1	1	yes	characteristic
262	#333	C₂×D₄₇	1	1	yes	characteristic
263	#332	—	47	2	no	—
264	#332	—	47	2	no	—
265	#332	C₂×D₄₇	1	1	yes	characteristic
266	#332	C₂×D₄₇	1	1	yes	characteristic
267	C₄₇	#19232	1	1	yes	characteristic, complemented, Sylow
268	C₂×#41	—	94	1	no	—
269	C₂²×Q₈	—	94	1	no	—
270	C₂×SD₁₆	—	94	2	no	—
271	C₂×SD₁₆	—	94	2	no	—
272	C₂×SD₁₆	—	94	2	no	—
273	#131	—	188	4	no	—
274	C₂×M₁₆	—	47	1	no	—
275	C₂×M₁₆	—	47	1	no	—
276	C₂×M₁₆	—	94	2	no	—
277	C₂²×C₈	—	2	1	no	—
278	C₂²×C₈	—	94	2	no	—
279	C₂²×C₈	—	94	1	no	—
280	C₄⋊Q₈	—	47	1	no	—
281	C₄⋊Q₈	—	47	2	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	1	yes	characteristic
286	C₄⋊Q₈	C₂²×D₄₇	1	1	yes	characteristic
287	#127	—	47	1	no	—
288	#125	—	2	1	no	—
289	#124	—	94	1	no	—
290	C₂²⋊Q₈	—	2	1	no	—
291	C₂²⋊Q₈	—	2	1	no	—
292	#121	—	47	2	no	—
293	#121	—	94	1	no	—
294	C₄×Q₈	—	2	1	no	—
295	C₄×Q₈	—	2	1	no	—
296	C₄×D₄	—	47	2	no	—
297	C₄×D₄	—	94	1	no	—
298	#117	—	2	1	no	—
299	C₂×C₄⋊C₄	—	94	1	no	—
300	C₂×C₄⋊C₄	—	94	1	no	—
301	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
302	#107	—	94	2	no	—
303	#107	—	94	2	no	—
304	#106	—	94	2	no	—
305	#106	—	94	2	no	—
306	#106	—	94	2	no	—
307	C₄⋊C₈	—	2	1	no	—
308	C₄⋊C₈	—	47	2	no	—
309	C₄⋊C₈	—	94	1	no	—
310	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
311	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
312	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
313	C₄⋊C₈	C₂²×D₄₇	1	1	yes	characteristic
314	#103	—	94	2	no	—
315	#103	—	94	2	no	—
316	#103	—	94	2	no	—
317	#102	—	94	2	no	—
318	C₂²⋊C₈	—	2	1	no	—
319	C₂²⋊C₈	—	94	2	no	—
320	C₂²⋊C₈	—	94	2	no	—
321	#97	—	47	2	no	—
322	C₄×C₈	—	2	1	no	—
323	C₄×C₈	—	47	2	no	—
324	#41	—	188	2	no	—
325	#41	—	188	2	no	—
326	C₂×Q₈	—	2	1	no	—
327	C₂×Q₈	—	2	1	no	—
328	C₂×Q₈	—	94	1	no	—
329	C₂×Q₈	—	94	2	no	—
330	C₂×Q₈	—	376	1	no	—
331	C₂×Q₈	—	376	1	no	—
332	C₂×Q₈	—	188	1	no	—
333	C₂×D₄	—	47	2	no	—
334	C₂×D₄	—	94	2	no	—
335	C₂×D₄	—	94	1	no	—
336	C₂×D₄	—	94	1	no	—
337	C₂²×C₄	—	94	2	no	—
338	C₂²×C₄	—	188	1	no	—
339	C₂²×C₄	#10625350	1	1	yes	characteristic
340	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
341	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
342	SD₁₆	—	376	2	no	—
343	SD₁₆	—	376	2	no	—
344	SD₁₆	—	376	2	no	—
345	M₁₆	—	47	4	no	—
346	M₁₆	—	94	2	no	—
347	M₁₆	—	188	4	no	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	1	no	—
350	C₂×C₈	—	2	1	no	—
351	C₂×C₈	—	2	1	no	—
352	C₂×C₈	—	4	2	no	—
353	C₂×C₈	—	47	2	no	—
354	C₂×C₈	—	47	2	no	—
355	C₂×C₈	—	94	2	no	—
356	C₂×C₈	—	376	1	no	—
357	C₂×C₈	—	188	4	no	—
358	C₄⋊C₄	—	2	1	no	—
359	C₄⋊C₄	—	2	1	no	—
360	C₄⋊C₄	—	2	1	no	—
361	C₄⋊C₄	—	2	1	no	—
362	C₄⋊C₄	—	4	1	no	—
363	C₄⋊C₄	—	4	1	no	—
364	C₄⋊C₄	—	47	2	no	—
365	C₄⋊C₄	—	94	1	no	—
366	C₄⋊C₄	—	94	2	no	—
367	C₄⋊C₄	—	94	2	no	—
368	C₄⋊C₄	—	188	1	no	—
369	C₄⋊C₄	—	188	1	no	—
370	C₂²⋊C₄	—	4	1	no	—
371	C₂²⋊C₄	—	94	2	no	—
372	C₂²⋊C₄	—	94	2	no	—
373	C₄²	—	4	1	no	—
374	C₄²	#10625350	1	1	yes	characteristic
375	C₄²	D₄×D₄₇	1	1	yes	characteristic
376	C₄²	D₄×D₄₇	1	1	yes	characteristic
377	C₄²	C₂³×D₄₇	1	1	yes	characteristic
378	C₂³	—	94	2	no	—
379	C₂³	#13093997	1	1	yes	characteristic
380	Q₈	—	4	1	no	—
381	Q₈	—	4	1	no	—
382	Q₈	—	8	1	no	—
383	Q₈	—	376	2	no	—
384	Q₈	—	188	2	no	—
385	Q₈	—	188	2	no	—
386	Q₈	—	188	2	no	—
387	D₄	—	94	2	no	—
388	D₄	—	94	2	no	—
389	D₄	—	376	1	no	—
390	D₄	—	188	4	no	—
391	D₄	—	188	2	no	—
392	C₂×C₄	—	2	1	no	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	4	1	no	—
395	C₂×C₄	—	4	1	no	—
396	C₂×C₄	—	4	1	no	—
397	C₂×C₄	—	94	2	no	—
398	C₂×C₄	—	376	2	no	—
399	C₂×C₄	—	188	2	no	—
400	C₂×C₄	—	188	2	no	—
401	C₂×C₄	—	188	2	no	—
402	C₂×C₄	#13093997	1	1	yes	characteristic
403	C₂×C₄	#13093997	1	1	yes	characteristic
404	C₂×C₄	#13093997	1	1	yes	characteristic
405	C₂×C₄	SD₁₆×D₄₇	1	2	yes	—
406	C₂×C₄	#13094056	1	2	yes	—
407	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
408	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
409	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
410	C₈	—	4	1	no	—
411	C₈	—	4	1	no	—
412	C₈	—	4	1	no	—
413	C₈	—	4	1	no	—
414	C₈	—	47	4	no	—
415	C₈	—	94	2	no	—
416	C₈	—	188	2	no	—
417	C₂²	—	2	1	no	—
418	C₂²	—	2	1	no	—
419	C₂²	—	188	2	no	—
420	C₂²	—	188	2	no	—
421	C₂²	—	188	2	no	—
422	C₂²	#15689327	1	2	yes	—
423	C₂²	C₂×#13093997	1	1	yes	characteristic
424	C₄	—	2	1	no	—
425	C₄	—	2	1	no	—
426	C₄	—	2	1	no	—
427	C₄	—	8	1	no	—
428	C₄	—	8	1	no	—
429	C₄	—	376	2	no	—
430	C₄	—	188	2	no	—
431	C₄	#15689327	1	2	yes	—
432	C₄	C₂×SD₁₆×D₄₇	1	1	yes	characteristic
433	C₄	C₂×#13094056	1	1	yes	characteristic
434	C₄	#15689925	1	1	yes	characteristic
435	C₄	#15689930	1	1	yes	characteristic
436	C₂	—	2	2	no	—
437	C₂	—	376	2	no	—
438	C₂	C₂×#15689327	1	1	yes	characteristic
439	C₂	#20253071	1	1	yes	characteristic
440	C₂	#20253128	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×#13093997
commutator, cosocle	C₄²×C₄₇	C₂⁴
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1542	C₂
socle	C₂²×C₄₇	C₂×#121
prime radical	#15689673	C₂²
hypercenter	#1542	D₄₇
hypocenter	C₄₇	#19232
LCS	G ▷ C₄²×C₄₇ ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ #1542

Complements

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

N	H ≅ G/N	type
3. #20253935	C₂	semidirect
5. #20242900	C₂	semidirect
6. #20242890	C₂	semidirect
7. #20242776	C₂	semidirect
8. #20242766	C₂	semidirect
9. #20242141	C₂	semidirect
10. C₂×#15688868	C₂	semidirect
11. C₄₇×#1542	C₂	semidirect
148. #10625329	SD₁₆	semidirect
225. #1542	D₄₇	semidirect
267. C₄₇	#19232	semidirect

Maximal subgroups

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

subgroup	index
#20254700	2
#20254315	2
#20253935	2
#20252131	2
#20242900	2
#20242890	2
#20242776	2
#20242766	2
#20242141	2
C₂×#15688868	2
C₄₇×#1542	2
#19232	47