Subgroups — #26214846

Order 12032.

1006 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689240	C₂	1	1	yes	maximal, characteristic
2	#20252189	C₂	1	1	yes	maximal, characteristic
3	#131×Dic₄₇	C₂	1	2	yes	maximal, complemented
4	#20243296	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243272	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243270	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243230	C₂	1	2	yes	maximal, complemented
8	#20243226	C₂	1	2	yes	maximal, complemented
9	#20243200	C₂	1	2	yes	maximal, complemented
10	#20243076	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×#444	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094031	C₂²	1	2	yes	—
13	#41×Dic₄₇	C₂²	1	2	yes	—
14	#15689240	C₄	1	8	yes	complemented
15	#15689235	C₄	1	2	yes	complemented
16	#15689230	C₄	1	2	yes	complemented
17	#15689224	C₄	1	4	yes	complemented
18	C₂×#13093960	C₂²	1	1	yes	characteristic
19	#15689161	C₂²	1	1	yes	characteristic
20	C₂×#13093951	C₂²	1	2	yes	—
21	#15689119	C₂²	1	2	yes	—
22	#15689081	—	2	2	no	—
23	#15689081	C₂²	1	2	yes	—
24	#15689078	—	2	2	no	—
25	#15689078	C₂²	1	2	yes	—
26	M₁₆×Dic₄₇	—	2	2	no	—
27	M₁₆×Dic₄₇	C₂²	1	2	yes	—
28	C₂×#13093934	C₂²	1	1	yes	characteristic
29	C₂×#13093934	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₄₇	—	2	2	no	—
32	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
34	#15688969	C₂²	1	1	yes	characteristic
35	#15688887	C₂²	1	2	yes	—
36	#15688884	C₂²	1	2	yes	—
37	#15688883	C₂²	1	2	yes	—
38	C₂×#135×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×#131×C₄₇	C₂²	1	2	yes	—
40	C₄₇×#444	C₄	1	8	yes	complemented
41	C₂×#108×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×#104×C₄₇	C₂²	1	2	yes	—
43	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
44	#13094031	—	2	4	no	—
45	#13094031	C₂×C₄	1	8	yes	complemented
46	C₂×#10625329	—	2	2	no	—
47	C₂×#10625329	C₂³	1	2	yes	—
48	C₂²×C₄₇⋊C₈	—	2	2	no	—
49	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
51	Q₈×Dic₄₇	C₂×C₄	1	4	yes	—
52	D₄×Dic₄₇	—	2	4	no	—
53	D₄×Dic₄₇	C₂×C₄	1	4	yes	—
54	#13093983	—	2	2	no	—
55	#13093983	C₂³	1	2	yes	—
56	C₂×C₄×Dic₄₇	—	2	2	no	—
57	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
58	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
59	#13093960	C₂×C₄	1	4	yes	complemented
60	#13093958	C₂×C₄	1	2	yes	—
61	#13093956	C₂×C₄	1	2	yes	—
62	#13093951	C₂×C₄	1	8	yes	complemented
63	#13093948	C₂×C₄	1	4	yes	—
64	#13093945	C₂×C₄	1	4	yes	—
65	#13093934	—	2	2	no	—
66	#13093934	—	2	2	no	—
67	#13093934	—	2	2	no	—
68	#13093934	—	2	2	no	—
69	#13093934	C₂×C₄	1	2	yes	—
70	#13093934	C₂×C₄	1	2	yes	—
71	C₄×C₄₇⋊C₈	—	2	2	no	—
72	C₈×Dic₄₇	—	2	2	no	—
73	C₈×Dic₄₇	—	2	2	no	—
74	C₈×Dic₄₇	—	2	2	no	—
75	C₈×Dic₄₇	C₂×C₄	1	4	yes	complemented
76	C₈×Dic₄₇	D₄	1	2	yes	—
77	C₈×Dic₄₇	D₄	1	2	yes	—
78	C₄₇⋊#95	—	2	2	no	—
79	C₂×#41×C₄₇	C₂³	1	2	yes	—
80	#135×C₄₇	C₂×C₄	1	4	yes	—
81	#135×C₄₇	C₂×C₄	1	4	yes	—
82	C₂×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
83	C₂×SD₁₆×C₄₇	C₂×C₄	1	2	yes	—
84	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic
85	#131×C₄₇	—	2	4	no	—
86	#131×C₄₇	C₂×C₄	1	8	yes	complemented
87	C₂×M₁₆×C₄₇	—	2	2	no	—
88	C₂×M₁₆×C₄₇	C₂³	1	2	yes	—
89	C₂²×C₈×C₄₇	—	2	2	no	—
90	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
93	#108×C₄₇	C₂×C₄	1	4	yes	complemented
94	#104×C₄₇	C₂×C₄	1	8	yes	complemented
95	#97×C₄₇	C₂×C₄	1	4	yes	complemented
96	#41×C₄₇	—	2	2	no	—
97	#41×C₄₇	—	2	2	no	—
98	#41×C₄₇	C₂²×C₄	1	4	yes	—
99	#41×C₄₇	C₂²×C₄	1	4	yes	—
100	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
101	C₂×D₄×C₄₇	—	2	2	no	—
102	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
103	C₂²×C₄×C₄₇	—	2	2	no	—
104	C₂²×C₄×C₄₇	—	2	1	no	—
105	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
106	C₂²×Dic₄₇	—	2	1	no	—
107	C₂²×Dic₄₇	—	2	4	no	—
108	C₂²×Dic₄₇	#41	1	2	yes	—
109	Q₁₆×C₄₇	C₄²	1	4	yes	—
110	SD₁₆×C₄₇	C₄²	1	8	yes	—
111	D₈×C₄₇	C₄²	1	4	yes	—
112	M₁₆×C₄₇	—	2	2	no	—
113	M₁₆×C₄₇	—	2	8	no	—
114	M₁₆×C₄₇	C₂²×C₄	1	4	yes	—
115	C₂×C₈×C₄₇	—	2	2	no	—
116	C₂×C₈×C₄₇	—	2	8	no	—
117	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
118	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
120	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
121	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
122	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
123	C₂×C₈×C₄₇	#41	1	2	yes	—
124	C₄²×C₄₇	—	2	1	no	—
125	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
126	C₂²⋊Dic₄₇	—	2	2	no	—
127	C₂²⋊Dic₄₇	—	2	4	no	—
128	C₄⋊Dic₄₇	—	2	4	no	—
129	C₄⋊Dic₄₇	C₂²×C₄	1	4	yes	—
130	C₄×Dic₄₇	—	2	2	no	—
131	C₄×Dic₄₇	—	2	1	no	—
132	C₄×Dic₄₇	—	2	4	no	—
133	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
134	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
135	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
136	#10625329	—	2	2	no	—
137	#10625329	—	2	8	no	—
138	#10625329	C₂²×C₄	1	4	yes	—
139	C₂×C₄₇⋊C₈	—	2	2	no	—
140	C₂×C₄₇⋊C₈	—	2	1	no	—
141	C₂×C₄₇⋊C₈	—	2	1	no	—
142	C₂×C₄₇⋊C₈	—	2	8	no	—
143	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
144	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
145	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
146	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
147	C₂×C₄₇⋊C₈	#41	1	2	yes	—
148	C₂³×C₄₇	—	2	2	no	—
149	C₂³×C₄₇	C₂×#41	1	1	yes	characteristic
150	Q₈×C₄₇	—	2	2	no	—
151	Q₈×C₄₇	C₂×C₄²	1	4	yes	—
152	D₄×C₄₇	—	2	4	no	—
153	D₄×C₄₇	—	2	4	no	—
154	D₄×C₄₇	—	2	2	no	—
155	D₄×C₄₇	C₂×C₄²	1	4	yes	—
156	C₂×C₄×C₄₇	—	2	2	no	—
157	C₂×C₄×C₄₇	—	2	4	no	—
158	C₂×C₄×C₄₇	—	2	4	no	—
159	C₂×C₄×C₄₇	—	2	2	no	—
160	C₂×C₄×C₄₇	—	4	2	no	—
161	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
162	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
165	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
166	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
167	C₂×Dic₄₇	—	2	4	no	—
168	C₂×Dic₄₇	—	2	2	no	—
169	C₂×Dic₄₇	—	4	2	no	—
170	C₂×Dic₄₇	—	4	8	no	—
171	C₂×Dic₄₇	—	4	2	no	—
172	C₂×Dic₄₇	C₄×D₄	1	4	yes	—
173	C₈×C₄₇	—	2	4	no	—
174	C₈×C₄₇	C₂×C₄²	1	2	yes	—
175	C₈×C₄₇	C₂×C₄²	1	2	yes	—
176	C₈×C₄₇	C₄×D₄	1	4	yes	—
177	C₄₇⋊C₈	—	2	4	no	—
178	C₄₇⋊C₈	—	2	2	no	—
179	C₄₇⋊C₈	C₄×D₄	1	2	yes	—
180	C₄₇⋊C₈	C₄×D₄	1	2	yes	—
181	#20510	—	47	1	no	maximal, Sylow
182	C₂²×C₄₇	—	2	2	no	—
183	C₂²×C₄₇	—	2	4	no	—
184	C₂²×C₄₇	—	4	4	no	—
185	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
186	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
187	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
188	C₄×C₄₇	—	2	4	no	—
189	C₄×C₄₇	—	4	2	no	—
190	C₄×C₄₇	C₂²×C₄²	1	1	yes	characteristic
191	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
192	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
194	Dic₄₇	—	2	4	no	—
195	Dic₄₇	—	4	2	no	—
196	Dic₄₇	—	4	4	no	—
197	C₂×#444	D₄₇	1	1	yes	characteristic
198	C₂×#443	—	47	1	no	—
199	#2943	—	47	1	no	—
200	C₄×#131	—	47	2	no	—
201	#1778	—	47	1	no	—
202	#1773	—	47	1	no	—
203	#1772	—	47	1	no	—
204	#1765	—	47	2	no	—
205	#1764	—	47	2	no	—
206	#1759	—	47	2	no	—
207	#1726	—	47	1	no	—
208	C₂×C₄₇	—	2	1	no	—
209	C₂×C₄₇	—	2	1	no	—
210	C₂×C₄₇	—	4	4	no	—
211	C₂×C₄₇	C₄²×D₄	1	1	yes	characteristic
212	C₂×C₄₇	#2955	1	2	yes	—
213	C₂×#135	C₂×D₄₇	1	1	yes	characteristic
214	C₂×#131	—	47	2	no	—
215	C₂×#131	C₂×D₄₇	1	2	yes	—
216	C₄×#41	—	47	2	no	—
217	#444	Dic₄₇	1	8	yes	complemented
218	#443	—	47	8	no	—
219	#442	—	47	2	no	—
220	#441	—	47	2	no	—
221	#440	—	47	4	no	—
222	C₂×#108	—	47	1	no	—
223	C₂×#108	C₂×D₄₇	1	1	yes	characteristic
224	#427	—	47	1	no	—
225	C₂×#104	—	47	2	no	—
226	C₂×#104	C₂×D₄₇	1	2	yes	—
227	#416	—	47	2	no	—
228	#405	—	47	2	no	—
229	#405	—	47	2	no	—
230	#405	—	94	2	no	—
231	#405	—	94	2	no	—
232	C₄×M₁₆	—	47	2	no	—
233	C₄×M₁₆	—	94	2	no	—
234	C₂×#97	—	47	1	no	—
235	C₂×#97	—	47	1	no	—
236	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
237	C₂×C₄×C₈	—	47	1	no	—
238	C₂×C₄×C₈	—	47	1	no	—
239	C₂×C₄×C₈	—	47	1	no	—
240	C₂×C₄×C₈	—	94	2	no	—
241	#376	—	47	1	no	—
242	#341	—	47	2	no	—
243	#339	—	47	2	no	—
244	#339	—	47	2	no	—
245	C₄₇	#20510	1	1	yes	characteristic, complemented, Sylow
246	C₂×#41	C₂²×D₄₇	1	2	yes	—
247	#135	C₄×D₄₇	1	4	yes	—
248	#135	C₂×Dic₄₇	1	4	yes	—
249	C₂×Q₁₆	C₄×D₄₇	1	1	yes	characteristic
250	C₂×SD₁₆	C₄×D₄₇	1	2	yes	—
251	C₂×D₈	C₄×D₄₇	1	1	yes	characteristic
252	#131	—	2	4	no	—
253	#131	—	47	8	no	—
254	#131	—	94	4	no	—
255	#131	C₂×Dic₄₇	1	8	yes	complemented
256	C₂×M₁₆	—	2	2	no	—
257	C₂×M₁₆	—	47	2	no	—
258	C₂×M₁₆	—	94	2	no	—
259	C₂×M₁₆	C₂²×D₄₇	1	2	yes	—
260	C₂²×C₈	—	2	2	no	—
261	C₂²×C₈	—	47	1	no	—
262	C₂²×C₈	—	47	1	no	—
263	C₂²×C₈	—	94	2	no	—
264	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
265	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
266	C₄×Q₈	—	47	4	no	—
267	C₄×D₄	—	47	4	no	—
268	C₄×D₄	—	94	4	no	—
269	#117	—	47	2	no	—
270	#117	—	94	2	no	—
271	C₂×C₄²	—	47	1	no	—
272	C₂×C₄²	—	47	1	no	—
273	C₂×C₄²	—	94	2	no	—
274	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
275	#108	—	47	4	no	—
276	#108	C₂×Dic₄₇	1	4	yes	complemented
277	#107	—	47	2	no	—
278	#106	—	47	2	no	—
279	#104	—	47	8	no	—
280	#104	C₂×Dic₄₇	1	8	yes	complemented
281	#103	—	47	4	no	—
282	#102	—	47	4	no	—
283	#97	—	47	2	no	—
284	#97	—	47	2	no	—
285	#97	—	94	2	no	—
286	#97	—	94	2	no	—
287	#97	—	94	2	no	—
288	#97	—	94	2	no	—
289	#97	C₂×Dic₄₇	1	4	yes	complemented
290	C₄×C₈	—	47	4	no	—
291	C₄×C₈	—	47	2	no	—
292	C₄×C₈	—	47	2	no	—
293	C₄×C₈	—	94	2	no	—
294	C₄×C₈	—	94	2	no	—
295	C₄×C₈	—	94	2	no	—
296	C₄×C₈	—	94	2	no	—
297	#95	—	94	2	no	—
298	#41	—	2	2	no	—
299	#41	—	2	2	no	—
300	#41	C₂×C₄×D₄₇	1	4	yes	—
301	#41	C₂²×Dic₄₇	1	4	yes	—
302	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
303	C₂×D₄	—	2	2	no	—
304	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	2	1	no	—
307	C₂²×C₄	—	47	2	no	—
308	C₂²×C₄	—	94	4	no	—
309	C₂²×C₄	—	94	1	no	—
310	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
311	Q₁₆	C₄×Dic₄₇	1	4	yes	—
312	SD₁₆	C₄×Dic₄₇	1	8	yes	—
313	D₈	C₄×Dic₄₇	1	4	yes	—
314	M₁₆	—	2	2	no	—
315	M₁₆	—	2	8	no	—
316	M₁₆	—	47	4	no	—
317	M₁₆	—	94	8	no	—
318	M₁₆	—	94	2	no	—
319	M₁₆	C₂²×Dic₄₇	1	4	yes	—
320	C₂×C₈	—	2	2	no	—
321	C₂×C₈	—	2	8	no	—
322	C₂×C₈	—	47	2	no	—
323	C₂×C₈	—	47	1	no	—
324	C₂×C₈	—	47	1	no	—
325	C₂×C₈	—	47	2	no	—
326	C₂×C₈	—	47	2	no	—
327	C₂×C₈	—	94	8	no	—
328	C₂×C₈	—	94	2	no	—
329	C₂×C₈	—	94	1	no	—
330	C₂×C₈	—	94	1	no	—
331	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
332	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
333	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
334	C₂×C₈	D₄×D₄₇	1	2	yes	—
335	C₂×C₈	#10625352	1	2	yes	—
336	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
337	C₂×C₈	C₂²×Dic₄₇	1	2	yes	—
338	C₄⋊C₄	—	47	4	no	—
339	C₄⋊C₄	—	94	4	no	—
340	C₂²⋊C₄	—	94	4	no	—
341	C₂²⋊C₄	—	94	2	no	—
342	C₄²	—	2	1	no	—
343	C₄²	—	47	2	no	—
344	C₄²	—	47	2	no	—
345	C₄²	—	47	2	no	—
346	C₄²	—	94	4	no	—
347	C₄²	—	94	2	no	—
348	C₄²	—	94	1	no	—
349	C₄²	C₂²×Dic₄₇	1	2	yes	—
350	C₂³	—	2	2	no	—
351	C₂³	#41×D₄₇	1	1	yes	characteristic
352	Q₈	—	2	2	no	—
353	Q₈	C₂×C₄×Dic₄₇	1	4	yes	—
354	D₄	—	2	4	no	—
355	D₄	—	2	4	no	—
356	D₄	—	2	2	no	—
357	D₄	C₂×C₄×Dic₄₇	1	4	yes	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	2	4	no	—
360	C₂×C₄	—	2	4	no	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	4	2	no	—
363	C₂×C₄	—	47	4	no	—
364	C₂×C₄	—	94	4	no	—
365	C₂×C₄	—	94	2	no	—
366	C₂×C₄	—	188	2	no	—
367	C₂×C₄	—	188	8	no	—
368	C₂×C₄	—	188	2	no	—
369	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
370	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
371	C₂×C₄	C₂³×Dic₄₇	1	1	yes	characteristic
372	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
373	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
374	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
375	C₈	—	2	4	no	—
376	C₈	—	47	2	no	—
377	C₈	—	47	2	no	—
378	C₈	—	94	4	no	—
379	C₈	—	94	2	no	—
380	C₈	C₂×C₄×Dic₄₇	1	2	yes	—
381	C₈	C₂×C₄×Dic₄₇	1	2	yes	—
382	C₈	D₄×Dic₄₇	1	4	yes	—
383	C₂²	—	2	2	no	—
384	C₂²	—	2	4	no	—
385	C₂²	—	4	4	no	—
386	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
387	C₂²	C₄×#10625352	1	1	yes	characteristic
388	C₂²	#41×Dic₄₇	1	1	yes	characteristic
389	C₄	—	2	4	no	—
390	C₄	—	4	2	no	—
391	C₄	—	94	4	no	—
392	C₄	—	188	2	no	—
393	C₄	—	188	4	no	—
394	C₄	C₂²×C₄×Dic₄₇	1	1	yes	characteristic
395	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
396	C₄	C₂×D₄×Dic₄₇	1	1	yes	characteristic
397	C₄	C₄×#10625352	1	1	yes	characteristic
398	C₂	—	2	1	no	—
399	C₂	—	2	1	no	—
400	C₂	—	4	4	no	—
401	C₂	C₄×D₄×Dic₄₇	1	1	yes	characteristic
402	C₂	#20252288	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₄₇
Fitting	C₂×C₄₇×#444	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#135×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#444	D₄₇
hypocenter	C₄₇	#20510
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#444

Complements

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

N	H ≅ G/N	type
3. #131×Dic₄₇	C₂	semidirect
4. #20243296	C₂	semidirect
5. #20243272	C₂	semidirect
6. #20243270	C₂	semidirect
7. #20243230	C₂	semidirect
8. #20243226	C₂	semidirect
9. #20243200	C₂	semidirect
10. #20243076	C₂	semidirect
14. #15689240	C₄	semidirect
15. #15689235	C₄	semidirect
16. #15689230	C₄	semidirect
17. #15689224	C₄	semidirect
40. C₄₇×#444	C₄	semidirect
45. #13094031	C₂×C₄	semidirect
59. #13093960	C₂×C₄	semidirect
62. #13093951	C₂×C₄	semidirect
75. C₈×Dic₄₇	C₂×C₄	semidirect
86. #131×C₄₇	C₂×C₄	semidirect
93. #108×C₄₇	C₂×C₄	semidirect
94. #104×C₄₇	C₂×C₄	semidirect
95. #97×C₄₇	C₂×C₄	semidirect
217. #444	Dic₄₇	semidirect
245. C₄₇	#20510	semidirect
255. #131	C₂×Dic₄₇	semidirect
276. #108	C₂×Dic₄₇	semidirect
280. #104	C₂×Dic₄₇	semidirect
289. #97	C₂×Dic₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689240	2
#20252189	2
#131×Dic₄₇	2
#20243296	2
#20243272	2
#20243270	2
#20243230	2
#20243226	2
#20243200	2
#20243076	2
C₂×C₄₇×#444	2
#20510	47