Subgroups — #26216715

Order 12032.

1070 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689162	C₂	1	2	yes	maximal
2	C₂×#15689158	C₂	1	1	yes	maximal, characteristic
3	C₂×#106×D₄₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#15689077	C₂	1	1	yes	maximal, characteristic
5	#20246009	C₂	1	2	yes	maximal
6	#20243554	C₂	1	2	yes	maximal, complemented
7	#20243553	C₂	1	2	yes	maximal, complemented
8	#20243552	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243549	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243543	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1844	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#10625324	C₂²	1	1	yes	characteristic
13	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
14	C₂×#13093982	C₂²	1	2	yes	—
15	C₂×#13093981	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊C₄×D₄₇	C₂²	1	2	yes	—
17	#15689162	—	2	8	no	—
18	#15689158	—	2	4	no	—
19	C₂×#13093958	C₂²	1	2	yes	—
20	C₂×#13093957	C₂²	1	2	yes	—
21	C₂×#13093957	C₂²	1	2	yes	—
22	C₂×#13093956	C₂²	1	1	yes	characteristic
23	C₂×#13093956	C₂²	1	1	yes	characteristic
24	C₂×#13093955	C₂²	1	2	yes	—
25	C₂×#13093955	C₂²	1	2	yes	—
26	#106×D₄₇	—	2	4	no	—
27	#15689077	C₄	1	8	yes	complemented
28	C₂×#13093935	C₂²	1	1	yes	characteristic
29	C₂×#13093934	C₂²	1	1	yes	characteristic
30	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
31	#15689018	—	2	4	no	—
32	#15688994	—	2	4	no	—
33	#15688992	C₂²	1	2	yes	—
34	#15688989	C₂²	1	2	yes	—
35	#15688988	C₂²	1	2	yes	—
36	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
37	C₂×#106×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×#106×C₄₇	C₂²	1	2	yes	—
39	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₄₇×#384	C₂²	1	2	yes	—
41	C₂²×C₄×D₄₇	—	2	2	no	—
42	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
43	C₂×#10625324	C₂×C₄	1	4	yes	—
44	C₂×#10625324	D₄	1	4	yes	—
45	C₂×#10625324	Q₈	1	4	yes	—
46	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
48	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	—
49	C₂×C₈×D₄₇	D₄	1	4	yes	—
50	C₂×C₈×D₄₇	Q₈	1	4	yes	—
51	#13093982	—	2	4	no	—
52	#13093982	—	2	4	no	—
53	#13093981	C₂×C₄	1	4	yes	—
54	#13093981	Q₈	1	4	yes	—
55	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
56	C₂×C₄⋊Dic₄₇	C₂³	1	2	yes	—
57	C₂×Dic₄₇⋊C₄	—	2	2	no	—
58	C₂×Dic₄₇⋊C₄	—	2	4	no	—
59	C₂×Dic₄₇⋊C₄	D₄	1	2	yes	—
60	C₄⋊C₄×D₄₇	—	2	4	no	—
61	C₄⋊C₄×D₄₇	—	2	4	no	—
62	C₂×(C₂×D₄₇)⋊C₄	—	2	2	no	—
63	C₂×(C₂×D₄₇)⋊C₄	D₄	1	2	yes	—
64	C₂×C₄×Dic₄₇	—	2	2	no	—
65	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
66	#13093958	—	2	4	no	—
67	#13093957	—	2	4	no	—
68	#13093957	—	2	4	no	—
69	#13093956	—	2	2	no	—
70	#13093956	—	2	2	no	—
71	#13093955	—	2	4	no	—
72	#13093955	—	2	4	no	—
73	#13093935	C₂×C₄	1	4	yes	complemented
74	#13093934	C₂×C₄	1	4	yes	complemented
75	C₈×Dic₄₇	C₂×C₄	1	4	yes	complemented
76	C₄₇⋊#95	—	2	4	no	—
77	C₄₇⋊#95	—	2	4	no	—
78	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
79	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
80	C₂×C₄⋊C₄×C₄₇	—	2	4	no	—
81	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
82	C₂×C₄⋊C₄×C₄₇	C₂³	1	2	yes	—
83	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
84	#106×C₄₇	—	2	2	no	—
85	#106×C₄₇	—	2	2	no	—
86	#106×C₄₇	—	2	4	no	—
87	C₄×C₈×C₄₇	C₂×C₄	1	4	yes	complemented
88	C₂³×D₄₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₇	—	2	2	no	—
90	C₂²×C₄×C₄₇	—	2	2	no	—
91	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
93	C₂²×Dic₄₇	—	2	2	no	—
94	C₂²×Dic₄₇	—	2	2	no	—
95	C₂²×Dic₄₇	C₂×D₄	1	2	yes	—
96	C₂²×Dic₄₇	C₂×D₄	1	1	yes	characteristic
97	C₂×C₄×D₄₇	—	4	4	no	—
98	C₂×C₄×D₄₇	—	8	4	no	—
99	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
100	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
101	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
102	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
103	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
104	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
105	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
106	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
107	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
108	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
109	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
110	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
111	C₄⋊C₄×C₄₇	—	2	2	no	—
112	C₄⋊C₄×C₄₇	—	2	2	no	—
113	C₄⋊C₄×C₄₇	—	2	2	no	—
114	C₄⋊C₄×C₄₇	—	2	2	no	—
115	C₄⋊C₄×C₄₇	—	8	4	no	—
116	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
117	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
118	(C₂×D₄₇)⋊C₄	—	4	4	no	—
119	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	8	yes	—
120	C₄⋊Dic₄₇	—	2	2	no	—
121	C₄⋊Dic₄₇	—	2	2	no	—
122	C₄⋊Dic₄₇	—	2	2	no	—
123	C₄⋊Dic₄₇	—	2	2	no	—
124	Dic₄₇⋊C₄	—	4	4	no	—
125	Dic₄₇⋊C₄	—	8	4	no	—
126	Dic₄₇⋊C₄	C₄⋊C₄	1	8	yes	—
127	C₄×Dic₄₇	—	4	4	no	—
128	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
129	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
130	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
131	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
132	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
133	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
134	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
135	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
136	#10625324	C₄⋊C₄	1	16	yes	complemented
137	C₈×D₄₇	C₄⋊C₄	1	16	yes	complemented
138	C₂³×C₄₇	C₂²×D₄	1	1	yes	characteristic
139	C₂²×D₄₇	—	2	4	no	—
140	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
141	C₂²×D₄₇	#127	1	2	yes	—
142	C₂²×D₄₇	C₄⋊Q₈	1	2	yes	—
143	C₂×C₄×C₄₇	—	2	4	no	—
144	C₂×C₄×C₄₇	—	4	2	no	—
145	C₂×C₄×C₄₇	—	4	2	no	—
146	C₂×C₄×C₄₇	—	4	4	no	—
147	C₂×C₄×C₄₇	—	4	4	no	—
148	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
149	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
153	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
155	C₂×Dic₄₇	—	2	4	no	—
156	C₂×Dic₄₇	—	4	2	no	—
157	C₂×Dic₄₇	—	4	2	no	—
158	C₂×Dic₄₇	—	4	4	no	—
159	C₂×Dic₄₇	—	4	4	no	—
160	C₂×Dic₄₇	C₂×C₄⋊C₄	1	4	yes	—
161	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
162	C₂×Dic₄₇	#127	1	2	yes	—
163	C₂×Dic₄₇	C₄⋊Q₈	1	2	yes	—
164	C₄×D₄₇	—	8	8	no	—
165	C₄×D₄₇	C₂×C₄⋊C₄	1	4	yes	—
166	C₄×D₄₇	C₂×C₄⋊C₄	1	4	yes	—
167	C₄×D₄₇	C₄⋊Q₈	1	4	yes	—
168	C₄×D₄₇	C₄⋊Q₈	1	4	yes	—
169	C₈×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
170	C₈×C₄₇	C₂×C₄⋊C₄	1	4	yes	—
171	C₄₇⋊C₈	C₂×C₄⋊C₄	1	4	yes	—
172	C₄₇⋊C₈	C₂×C₄⋊C₄	1	4	yes	—
173	#20802	—	47	1	no	maximal, Sylow
174	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
175	C₂²×C₄₇	C₂×#127	1	1	yes	characteristic
176	C₂²×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
177	C₂²×C₄₇	#577	1	4	yes	—
178	C₂×D₄₇	—	2	4	no	—
179	C₂×D₄₇	—	2	4	no	—
180	C₂×D₄₇	—	2	4	no	—
181	C₂×D₄₇	#384	1	4	yes	—
182	C₄×C₄₇	—	2	4	no	—
183	C₄×C₄₇	—	8	2	no	—
184	C₄×C₄₇	—	8	2	no	—
185	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
186	C₄×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
187	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
188	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
189	Dic₄₇	—	2	4	no	—
190	Dic₄₇	—	8	2	no	—
191	Dic₄₇	—	8	2	no	—
192	Dic₄₇	#384	1	4	yes	—
193	C₂×#428	—	47	2	no	—
194	C₂×#427	—	47	1	no	—
195	C₂²×#106	—	47	1	no	—
196	C₂×#405	—	47	1	no	—
197	#2317	—	47	2	no	—
198	#1847	—	47	2	no	—
199	#1847	—	47	2	no	—
200	#1846	—	47	1	no	—
201	#1846	—	47	1	no	—
202	#1844	—	47	1	no	—
203	#1844	D₄₇	1	1	yes	characteristic, complemented
204	C₂×C₄₇	C₂×#384	1	1	yes	characteristic
205	C₂×C₄₇	#2912	1	2	yes	—
206	C₂×C₄₇	#3154	1	2	yes	—
207	C₂×C₄₇	#3163	1	2	yes	—
208	D₄₇	—	2	4	no	—
209	C₂²×M₁₆	—	47	1	no	—
210	C₂³×C₈	—	47	1	no	—
211	C₂×#117	—	47	1	no	—
212	C₂×#117	—	47	2	no	—
213	C₂²×C₄⋊C₄	—	47	2	no	—
214	#428	—	94	8	no	—
215	#427	—	94	4	no	—
216	C₂×#107	—	47	2	no	—
217	C₂×#107	—	47	2	no	—
218	C₂×#107	—	47	2	no	—
219	C₂×#106	—	47	1	no	—
220	C₂×#106	—	47	1	no	—
221	C₂×#106	—	47	2	no	—
222	C₂×#106	—	47	2	no	—
223	C₂×#106	—	94	4	no	—
224	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
225	C₂×#106	C₂×D₄₇	1	1	yes	characteristic
226	C₂×#106	C₂×D₄₇	1	2	yes	—
227	#405	—	47	8	no	—
228	C₂×#97	—	47	1	no	—
229	C₂×#97	—	47	1	no	—
230	C₂×C₄×C₈	—	47	1	no	—
231	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
232	#389	—	94	4	no	—
233	#385	—	94	4	no	—
234	#384	—	47	2	no	—
235	#384	C₂×D₄₇	1	2	yes	—
236	#382	—	47	2	no	—
237	#382	—	47	2	no	—
238	C₄₇	#20802	1	1	yes	characteristic, complemented, Sylow
239	C₂³×C₄	—	47	1	no	—
240	C₂³×C₄	—	94	2	no	—
241	C₂×M₁₆	—	47	4	no	—
242	C₂×M₁₆	—	47	4	no	—
243	C₂×M₁₆	—	47	4	no	—
244	C₂²×C₈	—	47	1	no	—
245	C₂²×C₈	—	47	1	no	—
246	C₂²×C₈	—	47	4	no	—
247	C₂²×C₈	—	47	4	no	—
248	C₂²×C₈	—	47	4	no	—
249	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
250	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
251	#117	—	47	4	no	—
252	#117	—	47	4	no	—
253	#117	—	94	4	no	—
254	#117	—	94	4	no	—
255	C₂×C₄⋊C₄	—	2	4	no	—
256	C₂×C₄⋊C₄	—	47	2	no	—
257	C₂×C₄⋊C₄	—	47	2	no	—
258	C₂×C₄⋊C₄	—	47	2	no	—
259	C₂×C₄⋊C₄	—	94	4	no	—
260	C₂×C₄⋊C₄	—	94	4	no	—
261	C₂×C₄⋊C₄	—	94	4	no	—
262	C₂×C₄⋊C₄	—	94	2	no	—
263	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
264	C₂×C₄⋊C₄	C₂²×D₄₇	1	2	yes	—
265	C₂×C₂²⋊C₄	—	47	2	no	—
266	C₂×C₂²⋊C₄	—	94	2	no	—
267	C₂×C₄²	—	47	1	no	—
268	C₂×C₄²	—	94	2	no	—
269	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
270	#107	—	94	4	no	—
271	#107	—	94	4	no	—
272	#107	—	94	4	no	—
273	#106	—	2	2	no	—
274	#106	—	2	2	no	—
275	#106	—	2	4	no	—
276	#106	—	94	4	no	—
277	#106	—	94	4	no	—
278	#106	—	94	2	no	—
279	#106	—	94	2	no	—
280	#97	—	47	4	no	—
281	#97	—	47	4	no	—
282	C₄×C₈	—	47	4	no	—
283	C₄×C₈	C₄×D₄₇	1	4	yes	complemented
284	#95	—	94	4	no	—
285	#95	—	94	4	no	—
286	C₂⁴	—	47	1	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	—	2	2	no	—
289	C₂²×C₄	—	47	1	no	—
290	C₂²×C₄	—	47	2	no	—
291	C₂²×C₄	—	47	2	no	—
292	C₂²×C₄	—	47	2	no	—
293	C₂²×C₄	—	47	2	no	—
294	C₂²×C₄	—	47	2	no	—
295	C₂²×C₄	—	47	2	no	—
296	C₂²×C₄	—	47	2	no	—
297	C₂²×C₄	—	94	2	no	—
298	C₂²×C₄	—	94	2	no	—
299	C₂²×C₄	—	376	4	no	—
300	C₂²×C₄	—	188	4	no	—
301	C₂²×C₄	D₄×D₄₇	1	2	yes	—
302	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
303	M₁₆	—	47	16	no	—
304	C₂×C₈	—	47	2	no	—
305	C₂×C₈	—	47	2	no	—
306	C₂×C₈	—	47	2	no	—
307	C₂×C₈	—	47	2	no	—
308	C₂×C₈	—	47	2	no	—
309	C₂×C₈	—	47	2	no	—
310	C₂×C₈	—	47	16	no	—
311	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
312	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
313	C₂×C₈	D₄×D₄₇	1	2	yes	—
314	C₂×C₈	D₄×D₄₇	1	2	yes	—
315	C₂×C₈	Q₈×D₄₇	1	2	yes	—
316	C₂×C₈	Q₈×D₄₇	1	2	yes	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	2	2	no	—
319	C₄⋊C₄	—	2	2	no	—
320	C₄⋊C₄	—	2	2	no	—
321	C₄⋊C₄	—	8	4	no	—
322	C₄⋊C₄	—	47	8	no	—
323	C₄⋊C₄	—	94	2	no	—
324	C₄⋊C₄	—	94	2	no	—
325	C₄⋊C₄	—	94	2	no	—
326	C₄⋊C₄	—	94	2	no	—
327	C₄⋊C₄	—	376	4	no	—
328	C₄⋊C₄	—	188	4	no	—
329	C₂²⋊C₄	—	47	8	no	—
330	C₂²⋊C₄	—	188	4	no	—
331	C₄²	—	47	2	no	—
332	C₄²	—	47	2	no	—
333	C₄²	—	188	4	no	—
334	C₄²	C₂×C₄×D₄₇	1	2	yes	—
335	C₄²	Q₈×D₄₇	1	2	yes	—
336	C₂³	—	47	2	no	—
337	C₂³	—	47	2	no	—
338	C₂³	—	47	2	no	—
339	C₂³	—	94	4	no	—
340	C₂³	C₂×D₄×D₄₇	1	1	yes	characteristic
341	C₂×C₄	—	2	4	no	—
342	C₂×C₄	—	4	2	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	4	no	—
345	C₂×C₄	—	4	4	no	—
346	C₂×C₄	—	47	2	no	—
347	C₂×C₄	—	47	2	no	—
348	C₂×C₄	—	47	2	no	—
349	C₂×C₄	—	47	4	no	—
350	C₂×C₄	—	47	4	no	—
351	C₂×C₄	—	47	4	no	—
352	C₂×C₄	—	47	4	no	—
353	C₂×C₄	—	47	4	no	—
354	C₂×C₄	—	94	4	no	—
355	C₂×C₄	—	376	8	no	—
356	C₂×C₄	—	188	2	no	—
357	C₂×C₄	—	188	2	no	—
358	C₂×C₄	—	188	4	no	—
359	C₂×C₄	—	188	4	no	—
360	C₂×C₄	C₄⋊C₄×D₄₇	1	4	yes	—
361	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
362	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
363	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
364	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
365	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
366	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
367	C₈	—	47	4	no	—
368	C₈	—	47	4	no	—
369	C₈	C₄⋊C₄×D₄₇	1	4	yes	—
370	C₈	C₄⋊C₄×D₄₇	1	4	yes	—
371	C₂²	—	47	4	no	—
372	C₂²	—	94	4	no	—
373	C₂²	—	94	4	no	—
374	C₂²	—	94	4	no	—
375	C₂²	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
376	C₂²	#127×D₄₇	1	1	yes	characteristic
377	C₂²	C₄⋊Q₈×D₄₇	1	1	yes	characteristic
378	C₂²	#15689929	1	4	yes	—
379	C₄	—	2	4	no	—
380	C₄	—	8	2	no	—
381	C₄	—	8	2	no	—
382	C₄	—	47	4	no	—
383	C₄	—	94	4	no	—
384	C₄	—	376	2	no	—
385	C₄	—	376	2	no	—
386	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
387	C₄	C₂×C₄⋊C₄×D₄₇	1	1	yes	characteristic
388	C₄	C₄⋊Q₈×D₄₇	1	1	yes	characteristic
389	C₄	C₄⋊Q₈×D₄₇	1	1	yes	characteristic
390	C₂	—	94	4	no	—
391	C₂	#384×D₄₇	1	1	yes	characteristic
392	C₂	#20251979	1	2	yes	—
393	C₂	#20253857	1	2	yes	—
394	C₂	#20253913	1	2	yes	—

	subgroup	G/H
center	C₂³	C₂×D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₄₇×#1844	C₂
socle	C₂³×C₄₇	C₂²×D₄
prime radical	C₂³×D₄₇	C₂×D₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1844	D₄₇
hypocenter	C₄₇	#20802
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ #1844

Complements

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

N	H ≅ G/N	type
6. #20243554	C₂	semidirect
7. #20243553	C₂	semidirect
8. #20243552	C₂	semidirect
9. #20243549	C₂	semidirect
10. #20243543	C₂	semidirect
11. C₄₇×#1844	C₂	semidirect
27. #15689077	C₄	semidirect
73. #13093935	C₂×C₄	semidirect
74. #13093934	C₂×C₄	semidirect
75. C₈×Dic₄₇	C₂×C₄	semidirect
87. C₄×C₈×C₄₇	C₂×C₄	semidirect
136. #10625324	C₄⋊C₄	semidirect
137. C₈×D₄₇	C₄⋊C₄	semidirect
203. #1844	D₄₇	semidirect
238. C₄₇	#20802	semidirect
283. C₄×C₈	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689162	2
C₂×#15689158	2
C₂×#106×D₄₇	2
C₂×#15689077	2
#20246009	2
#20243554	2
#20243553	2
#20243552	2
#20243549	2
#20243543	2
C₄₇×#1844	2
#20802	47