Subgroups — #26369871

Order 12032.

626 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×D₄×D₄₇	C₂	1	1	yes	maximal, characteristic
2	#20245221	C₂	1	1	yes	maximal, characteristic, complemented
3	#20245219	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245213	C₂	1	2	yes	maximal, complemented
5	#20245210	C₂	1	2	yes	maximal, complemented
6	D₄×C₄₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
7	#20245190	C₂	1	1	yes	maximal, characteristic, complemented
8	#20245185	C₂	1	1	yes	maximal, characteristic, complemented
9	#20244997	C₂	1	2	yes	maximal, complemented
10	C₂×(C₂×D₄₇)⋊C₁₆	C₂	1	2	yes	maximal, complemented
11	D₄×C₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₇	C₂²	1	2	yes	—
13	C₄×D₄×D₄₇	C₄	1	1	yes	characteristic
14	C₂×#13093963	C₂²	1	2	yes	complemented
15	C₂×#13093963	C₂²	1	2	yes	complemented
16	C₂²×C₄₇⋊C₁₆	C₂²	1	2	yes	complemented
17	C₈×D₁₈₈	C₂²	1	1	yes	characteristic
18	D₄×C₄₇⋊C₈	C₄	1	1	yes	characteristic
19	#15689188	C₄	1	1	yes	characteristic
20	C₈×C₂²⋊D₄₇	C₂²	1	2	yes	—
21	(C₂²⋊D₄₇)⋊C₈	C₄	1	2	yes	—
22	C₄⋊C₈×D₄₇	C₄	1	1	yes	characteristic
23	C₂²⋊C₈×D₄₇	C₄	1	2	yes	—
24	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
25	C₄⋊(C₄₇⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
26	Dic₄₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
27	Dic₄₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
28	C₂²⋊(C₄₇⋊C₁₆)	C₂²	1	2	yes	complemented
29	(C₂×D₄₇)⋊C₁₆	C₂²	1	1	yes	characteristic
30	(C₂×D₄₇)⋊C₁₆	C₂²	1	2	yes	—
31	(C₂×D₄₇)⋊C₁₆	C₂²	1	1	yes	characteristic
32	(C₂×D₄₇)⋊C₁₆	C₂²	1	2	yes	complemented
33	(C₂×D₄₇)⋊C₁₆	C₂²	1	2	yes	complemented
34	#15688898	C₂²	1	2	yes	complemented
35	C₄×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
36	C₂²×C₁₆×C₄₇	C₂²	1	2	yes	complemented
37	C₈×D₄×C₄₇	C₂²	1	1	yes	characteristic
38	C₄₇×C₄⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
39	C₄₇×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
40	C₄×C₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
41	C₂×D₄×D₄₇	C₈	1	1	yes	characteristic
42	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
43	C₂²×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
44	C₂×C₈×D₄₇	—	4	2	no	—
45	C₂×C₈×D₄₇	—	4	2	no	—
46	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₄₇	C₂×C₄	1	2	yes	—
48	C₂×C₈×D₄₇	C₂×C₄	1	2	yes	—
49	C₂×C₈×D₄₇	C₂³	1	2	yes	—
50	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
51	C₄×D₁₈₈	C₂×C₄	1	1	yes	characteristic
52	D₄×Dic₄₇	C₈	1	1	yes	characteristic
53	#13093986	C₈	1	1	yes	characteristic
54	C₄×C₂²⋊D₄₇	C₂×C₄	1	2	yes	—
55	(C₂²⋊D₄₇)⋊C₄	C₈	1	2	yes	—
56	C₄⋊C₄×D₄₇	C₈	1	1	yes	characteristic
57	C₂²⋊C₄×D₄₇	C₈	1	2	yes	—
58	C₄²×D₄₇	C₂×C₄	1	1	yes	characteristic
59	#13093963	—	4	2	no	—
60	#13093963	—	4	2	no	—
61	C₂×C₄₇⋊C₁₆	—	4	2	no	—
62	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
63	C₂×C₄₇⋊C₁₆	C₂³	1	2	yes	—
64	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
65	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
66	Dic₄₇⋊C₈	C₂×C₄	1	2	yes	—
67	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	2	yes	—
68	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
69	(C₂×D₄₇)⋊C₈	C₂×C₄	1	2	yes	—
70	C₄×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
71	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
72	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
73	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
74	C₄×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
75	C₂×C₁₆×C₄₇	—	4	2	no	—
76	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
77	C₂×C₁₆×C₄₇	C₂³	1	2	yes	—
78	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
79	C₄⋊C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
80	C₂²⋊C₈×C₄₇	C₂×C₄	1	2	yes	—
81	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
82	C₂³×D₄₇	C₂×C₈	1	2	yes	—
83	C₂×D₄×C₄₇	C₂×C₈	1	1	yes	characteristic
84	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
85	C₂×C₂²⋊D₄₇	C₂×C₈	1	2	yes	—
86	C₂²×Dic₄₇	C₂×C₈	1	2	yes	—
87	D₄×D₄₇	—	2	4	no	—
88	C₂×D₁₈₈	C₂×C₈	1	1	yes	characteristic
89	C₂×C₄×D₄₇	—	4	2	no	—
90	C₂×C₄×D₄₇	—	4	2	no	—
91	C₂×C₄×D₄₇	C₂×C₈	1	1	yes	characteristic
92	C₂×C₄×D₄₇	C₂×C₈	1	1	yes	characteristic
93	C₂×C₄×D₄₇	C₂×C₈	1	2	yes	—
94	C₂×C₄×D₄₇	C₂×C₈	1	2	yes	—
95	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
96	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂×C₈×C₄₇	—	2	2	no	—
98	C₂×C₈×C₄₇	—	2	2	no	—
99	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
100	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
102	C₄⋊C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
103	C₂²⋊C₄×C₄₇	C₂×C₈	1	2	yes	—
104	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²⋊Dic₄₇	C₂×C₈	1	2	yes	—
106	(C₂×D₄₇)⋊C₄	C₂×C₈	1	2	yes	—
107	(C₂×D₄₇)⋊C₄	C₂×C₈	1	2	yes	—
108	C₄⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
109	Dic₄₇⋊C₄	C₂×C₈	1	2	yes	—
110	C₄×Dic₄₇	C₂×C₈	1	1	yes	characteristic
111	C₄×Dic₄₇	C₂×C₈	1	1	yes	characteristic
112	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
113	C₂×C₄₇⋊C₈	—	4	2	no	—
114	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
116	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
117	C₈×D₄₇	—	2	2	no	—
118	C₈×D₄₇	—	2	2	no	—
119	C₈×D₄₇	—	2	1	no	—
120	C₈×D₄₇	—	2	1	no	—
121	C₈×D₄₇	—	4	2	no	—
122	C₈×D₄₇	—	4	2	no	—
123	C₈×D₄₇	—	4	1	no	—
124	C₁₆×C₄₇	—	2	1	no	—
125	C₁₆×C₄₇	—	2	2	no	—
126	C₁₆×C₄₇	—	2	1	no	—
127	C₄₇⋊C₁₆	—	2	1	no	—
128	C₄₇⋊C₁₆	—	2	2	no	—
129	C₄₇⋊C₁₆	—	2	1	no	—
130	C₂³×C₄₇	C₂²×C₈	1	2	yes	—
131	C₂²×D₄₇	—	2	4	no	—
132	C₂²×D₄₇	—	2	4	no	—
133	C₂²×D₄₇	—	4	2	no	—
134	C₂²×D₄₇	C₂²×C₈	1	2	yes	—
135	C₂²×D₄₇	C₂²×C₈	1	1	yes	characteristic
136	D₄×C₄₇	M₃₂	1	4	yes	complemented
137	C₂×C₄×C₄₇	—	2	2	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
140	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
141	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
142	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
143	C₂²⋊D₄₇	—	2	4	no	—
144	C₂×Dic₄₇	—	4	2	no	—
145	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
146	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
147	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
148	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
149	D₁₈₈	—	2	2	no	—
150	C₄×D₄₇	—	2	2	no	—
151	C₄×D₄₇	—	2	1	no	—
152	C₄×D₄₇	—	2	2	no	—
153	C₄×D₄₇	—	2	1	no	—
154	C₄×D₄₇	—	2	2	no	—
155	C₄×D₄₇	—	2	2	no	—
156	C₄×D₄₇	—	4	2	no	—
157	C₄×D₄₇	—	4	2	no	—
158	C₈×C₄₇	—	2	2	no	—
159	C₈×C₄₇	—	2	1	no	—
160	C₈×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
161	C₈×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
162	C₄₇⋊C₈	—	2	1	no	—
163	C₄₇⋊C₈	—	2	2	no	—
164	C₄₇⋊C₈	—	2	1	no	—
165	#33488	—	47	1	no	maximal, Sylow
166	C₂²×C₄₇	—	2	2	no	—
167	C₂²×C₄₇	—	2	2	no	—
168	C₂²×C₄₇	C₂×M₃₂	1	4	yes	—
169	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
170	C₂×D₄₇	—	2	1	no	—
171	C₂×D₄₇	—	2	1	no	—
172	C₂×D₄₇	—	2	2	no	—
173	C₂×D₄₇	—	2	2	no	—
174	C₂×D₄₇	—	2	2	no	—
175	C₂×D₄₇	—	4	8	no	—
176	C₂×D₄₇	#504	1	2	yes	—
177	C₄×C₄₇	—	2	1	no	—
178	C₄×C₄₇	—	2	2	no	—
179	C₄×C₄₇	C₂×M₃₂	1	2	yes	—
180	C₄×C₄₇	#518	1	1	yes	characteristic
181	C₄×C₄₇	#568	1	1	yes	characteristic
182	Dic₄₇	—	2	1	no	—
183	Dic₄₇	—	2	1	no	—
184	Dic₄₇	—	2	1	no	—
185	Dic₄₇	—	2	2	no	—
186	C₂×C₈×D₄	—	47	1	no	—
187	#2169	—	47	1	no	—
188	#2169	—	47	1	no	—
189	#2168	—	47	2	no	—
190	#2168	—	47	2	no	—
191	D₄×C₁₆	—	47	1	no	—
192	D₄×C₁₆	D₄₇	1	1	yes	characteristic, complemented
193	#2163	—	47	1	no	—
194	#2162	—	47	1	no	—
195	#2112	—	47	2	no	—
196	C₂×C₂²⋊C₁₆	—	47	2	no	—
197	C₂×C₄₇	—	2	4	no	—
198	C₂×C₄₇	#2972	1	1	yes	characteristic
199	C₂×C₄₇	C₂²×M₃₂	1	1	yes	characteristic
200	C₂×C₄₇	C₂×#504	1	1	yes	characteristic
201	D₄₇	—	2	2	no	—
202	D₄₇	—	4	2	no	—
203	C₂³×C₈	—	47	2	no	—
204	C₂×C₄×D₄	—	47	1	no	—
205	C₂×M₃₂	—	47	2	no	—
206	C₂×M₃₂	—	47	2	no	—
207	C₂²×C₁₆	—	47	2	no	—
208	C₂²×C₁₆	C₂×D₄₇	1	2	yes	complemented
209	C₈×D₄	—	47	2	no	—
210	C₈×D₄	—	47	1	no	—
211	C₈×D₄	—	47	1	no	—
212	C₈×D₄	—	47	2	no	—
213	C₈×D₄	—	47	1	no	—
214	C₈×D₄	C₂×D₄₇	1	1	yes	characteristic
215	C₂×C₄⋊C₈	—	47	1	no	—
216	C₂×C₂²⋊C₈	—	47	2	no	—
217	C₂×C₄×C₈	—	47	1	no	—
218	C₄⋊C₁₆	—	47	1	no	—
219	C₄⋊C₁₆	—	47	1	no	—
220	C₄⋊C₁₆	—	47	1	no	—
221	C₄⋊C₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
222	C₂²⋊C₁₆	—	47	2	no	—
223	C₂²⋊C₁₆	—	47	1	no	—
224	C₂²⋊C₁₆	—	47	2	no	—
225	C₂²⋊C₁₆	—	47	2	no	—
226	C₂²⋊C₁₆	—	47	2	no	—
227	C₂²⋊C₁₆	—	47	1	no	—
228	C₂²⋊C₁₆	C₂×D₄₇	1	2	yes	complemented
229	#346	—	47	2	no	—
230	C₄×C₁₆	—	47	1	no	—
231	C₄×C₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
232	C₄₇	#33488	1	1	yes	characteristic, complemented, Sylow
233	C₂²×D₄	—	47	1	no	—
234	C₂³×C₄	—	47	2	no	—
235	C₂²×C₈	—	47	2	no	—
236	C₂²×C₈	—	47	1	no	—
237	C₂²×C₈	—	47	2	no	—
238	C₂²×C₈	—	47	2	no	—
239	C₂²×C₈	—	47	2	no	—
240	C₂²×C₈	—	47	1	no	—
241	C₂²×C₈	—	188	2	no	—
242	C₂²×C₈	—	188	2	no	—
243	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
244	C₄×D₄	—	47	1	no	—
245	C₄×D₄	—	47	2	no	—
246	C₄×D₄	—	47	1	no	—
247	C₄×D₄	—	47	2	no	—
248	C₄×D₄	—	47	1	no	—
249	C₄×D₄	C₄×D₄₇	1	1	yes	characteristic
250	C₂×C₄⋊C₄	—	47	1	no	—
251	C₂×C₂²⋊C₄	—	47	2	no	—
252	C₂×C₄²	—	47	1	no	—
253	M₃₂	—	188	2	no	—
254	M₃₂	—	188	2	no	—
255	C₂×C₁₆	—	4	2	no	—
256	C₂×C₁₆	—	47	1	no	—
257	C₂×C₁₆	—	47	1	no	—
258	C₂×C₁₆	—	47	2	no	—
259	C₂×C₁₆	—	188	2	no	—
260	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
261	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
262	C₂×C₁₆	C₂²×D₄₇	1	2	yes	—
263	C₄⋊C₈	—	47	2	no	—
264	C₄⋊C₈	—	47	1	no	—
265	C₄⋊C₈	C₄×D₄₇	1	1	yes	characteristic
266	C₂²⋊C₈	—	47	2	no	—
267	C₂²⋊C₈	—	47	2	no	—
268	C₂²⋊C₈	—	47	2	no	—
269	C₂²⋊C₈	C₄×D₄₇	1	2	yes	—
270	C₄×C₈	—	47	1	no	—
271	C₄×C₈	—	47	1	no	—
272	C₄×C₈	—	47	1	no	—
273	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
274	C₂⁴	—	47	2	no	—
275	C₂×D₄	—	47	2	no	—
276	C₂×D₄	—	47	1	no	—
277	C₂×D₄	—	94	4	no	—
278	C₂×D₄	C₈×D₄₇	1	1	yes	characteristic
279	C₂²×C₄	—	47	2	no	—
280	C₂²×C₄	—	47	1	no	—
281	C₂²×C₄	—	47	1	no	—
282	C₂²×C₄	—	47	2	no	—
283	C₂²×C₄	—	47	1	no	—
284	C₂²×C₄	—	47	2	no	—
285	C₂²×C₄	—	47	2	no	—
286	C₂²×C₄	—	188	2	no	—
287	C₂²×C₄	—	188	2	no	—
288	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	2	2	no	—
291	C₂×C₈	—	47	1	no	—
292	C₂×C₈	—	47	1	no	—
293	C₂×C₈	—	47	2	no	—
294	C₂×C₈	—	94	2	no	—
295	C₂×C₈	—	94	1	no	—
296	C₂×C₈	—	94	2	no	—
297	C₂×C₈	—	94	1	no	—
298	C₂×C₈	—	188	1	no	—
299	C₂×C₈	—	188	2	no	—
300	C₂×C₈	—	188	2	no	—
301	C₂×C₈	—	188	2	no	—
302	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
303	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
304	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
305	C₄⋊C₄	—	47	2	no	—
306	C₄⋊C₄	—	47	1	no	—
307	C₄⋊C₄	C₈×D₄₇	1	1	yes	characteristic
308	C₂²⋊C₄	—	47	2	no	—
309	C₂²⋊C₄	—	47	2	no	—
310	C₂²⋊C₄	—	47	2	no	—
311	C₂²⋊C₄	C₈×D₄₇	1	2	yes	—
312	C₄²	—	47	1	no	—
313	C₄²	—	47	1	no	—
314	C₄²	—	47	1	no	—
315	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
316	C₁₆	—	2	1	no	—
317	C₁₆	—	2	2	no	—
318	C₁₆	—	2	1	no	—
319	C₁₆	—	94	1	no	—
320	C₁₆	—	94	1	no	—
321	C₁₆	—	94	2	no	—
322	C₂³	—	47	1	no	—
323	C₂³	—	47	2	no	—
324	C₂³	—	94	4	no	—
325	C₂³	—	94	4	no	—
326	C₂³	—	188	2	no	—
327	C₂³	C₂×C₈×D₄₇	1	2	yes	—
328	D₄	—	94	4	no	—
329	D₄	—	94	2	no	—
330	D₄	#13093963	1	4	yes	complemented
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	47	1	no	—
334	C₂×C₄	—	47	1	no	—
335	C₂×C₄	—	47	1	no	—
336	C₂×C₄	—	47	2	no	—
337	C₂×C₄	—	94	2	no	—
338	C₂×C₄	—	94	2	no	—
339	C₂×C₄	—	94	1	no	—
340	C₂×C₄	—	94	2	no	—
341	C₂×C₄	—	94	1	no	—
342	C₂×C₄	—	94	2	no	—
343	C₂×C₄	—	188	2	no	—
344	C₂×C₄	—	188	2	no	—
345	C₂×C₄	—	188	2	no	—
346	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
347	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
348	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
349	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
350	C₈	—	2	2	no	—
351	C₈	—	2	1	no	—
352	C₈	—	94	2	no	—
353	C₈	—	94	1	no	—
354	C₈	—	94	1	no	—
355	C₈	#13094069	1	1	yes	characteristic
356	C₈	#13094070	1	1	yes	characteristic
357	C₂²	—	2	2	no	—
358	C₂²	—	2	2	no	—
359	C₂²	—	47	2	no	—
360	C₂²	—	94	1	no	—
361	C₂²	—	94	1	no	—
362	C₂²	—	94	2	no	—
363	C₂²	—	94	2	no	—
364	C₂²	—	94	2	no	—
365	C₂²	—	188	8	no	—
366	C₂²	C₂×#13093963	1	4	yes	—
367	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
368	C₄	—	2	1	no	—
369	C₄	—	2	2	no	—
370	C₄	—	94	1	no	—
371	C₄	—	94	1	no	—
372	C₄	—	94	1	no	—
373	C₄	—	94	2	no	—
374	C₄	C₂×#13093963	1	2	yes	—
375	C₄	#15689595	1	1	yes	characteristic
376	C₄	#15689888	1	1	yes	characteristic
377	C₂	—	2	4	no	—
378	C₂	—	94	2	no	—
379	C₂	—	188	2	no	—
380	C₂	#20252409	1	1	yes	characteristic
381	C₂	C₂²×#13093963	1	1	yes	characteristic
382	C₂	#504×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₄₇
commutator, socle	C₂²×C₄₇	C₂³×C₈
Fitting	D₄×C₁₆×C₄₇	C₂
prime radical	C₂×D₄×D₄₇	C₈
cosocle	C₂×C₈×C₄₇	C₂⁴
hypercenter	D₄×C₁₆	D₄₇
hypocenter	C₄₇	#33488
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ D₄×C₁₆

Complements

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

N	H ≅ G/N	type
2. #20245221	C₂	semidirect
3. #20245219	C₂	semidirect
4. #20245213	C₂	semidirect
5. #20245210	C₂	semidirect
6. D₄×C₄₇⋊C₁₆	C₂	semidirect
7. #20245190	C₂	semidirect
8. #20245185	C₂	semidirect
9. #20244997	C₂	semidirect
10. C₂×(C₂×D₄₇)⋊C₁₆	C₂	semidirect
11. D₄×C₁₆×C₄₇	C₂	semidirect
14. C₂×#13093963	C₂²	semidirect
15. C₂×#13093963	C₂²	semidirect
16. C₂²×C₄₇⋊C₁₆	C₂²	semidirect
25. C₄⋊(C₄₇⋊C₁₆)	C₂²	semidirect
26. Dic₄₇⋊C₁₆	C₂²	semidirect
27. Dic₄₇⋊C₁₆	C₂²	semidirect
28. C₂²⋊(C₄₇⋊C₁₆)	C₂²	semidirect
32. (C₂×D₄₇)⋊C₁₆	C₂²	semidirect
33. (C₂×D₄₇)⋊C₁₆	C₂²	semidirect
34. #15688898	C₂²	semidirect
35. C₄×C₄₇⋊C₁₆	C₂²	semidirect
36. C₂²×C₁₆×C₄₇	C₂²	semidirect
38. C₄₇×C₄⋊C₁₆	C₂²	semidirect
39. C₄₇×C₂²⋊C₁₆	C₂²	semidirect
40. C₄×C₁₆×C₄₇	C₂²	semidirect
136. D₄×C₄₇	M₃₂	semidirect
192. D₄×C₁₆	D₄₇	semidirect
208. C₂²×C₁₆	C₂×D₄₇	semidirect
221. C₄⋊C₁₆	C₂×D₄₇	semidirect
228. C₂²⋊C₁₆	C₂×D₄₇	semidirect
231. C₄×C₁₆	C₂×D₄₇	semidirect
232. C₄₇	#33488	semidirect
330. D₄	#13093963	semidirect

Maximal subgroups

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

subgroup	index
C₈×D₄×D₄₇	2
#20245221	2
#20245219	2
#20245213	2
#20245210	2
D₄×C₄₇⋊C₁₆	2
#20245190	2
#20245185	2
#20244997	2
C₂×(C₂×D₄₇)⋊C₁₆	2
D₄×C₁₆×C₄₇	2
#33488	47