Subgroups — #26185733

Order 12032.

782 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252409	C₂	1	2	yes	maximal, complemented
2	C₄×D₈×D₄₇	C₂	1	1	yes	maximal, characteristic
3	#20242213	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242212	C₂	1	1	yes	maximal, characteristic, complemented
5	#20242211	C₂	1	1	yes	maximal, characteristic, complemented
6	C₈×#10625334	C₂	1	2	yes	maximal, complemented
7	#20242180	C₂	1	2	yes	maximal, complemented
8	#20242133	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241777	C₂	1	2	yes	maximal, complemented
10	#20241673	C₂	1	1	yes	maximal, characteristic, complemented
11	C₄₇×#1580	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×D₈×D₄₇	C₄	1	1	yes	characteristic
13	C₄×D₄×D₄₇	C₂²	1	2	yes	—
14	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
15	D₈×Dic₄₇	C₄	1	1	yes	characteristic
16	#15689205	C₄	1	1	yes	characteristic
17	C₄×#10625334	C₂²	1	2	yes	—
18	#15689203	C₄	1	2	yes	—
19	C₈×D₁₈₈	C₂²	1	2	yes	complemented
20	D₄×C₄₇⋊C₈	C₂²	1	2	yes	complemented
21	#15689188	C₂²	1	2	yes	complemented
22	C₈×C₂²⋊D₄₇	—	2	2	no	—
23	(C₂²⋊D₄₇)⋊C₈	—	2	2	no	—
24	#15689175	C₂²	1	2	yes	—
25	#15689174	C₂²	1	1	yes	characteristic
26	#15689174	C₂²	1	1	yes	characteristic
27	#107×D₄₇	C₄	1	1	yes	characteristic
28	#102×D₄₇	C₄	1	2	yes	—
29	C₂×(C₂×D₄₇)⋊C₈	—	2	2	no	—
30	C₂²⋊C₈×D₄₇	—	2	2	no	—
31	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
32	#15688875	C₂²	1	2	yes	complemented
33	#15688874	C₂²	1	1	yes	characteristic, complemented
34	#15688852	C₂²	1	2	yes	complemented
35	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	complemented
36	#15688850	C₂²	1	2	yes	complemented
37	#15688844	C₂²	1	1	yes	characteristic, complemented
38	C₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
39	C₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic, complemented
40	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₄₇	C₂²	1	2	yes	complemented
42	C₄₇×#334	C₂²	1	1	yes	characteristic, complemented
43	C₄₇×D₄⋊C₈	C₂²	1	2	yes	complemented
44	C₄₇×#322	C₂²	1	1	yes	characteristic, complemented
45	C₂×D₄×D₄₇	C₂×C₄	1	2	yes	—
46	C₂²×C₄×D₄₇	—	2	2	no	—
47	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic
48	C₂×#10625334	C₂×C₄	1	2	yes	—
49	D₈×D₄₇	C₈	1	8	yes	complemented
50	C₂²×C₄₇⋊C₈	—	2	2	no	—
51	C₂×C₈×D₄₇	—	2	2	no	—
52	C₂×C₈×D₄₇	—	2	2	no	—
53	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
55	C₄×D₁₈₈	C₂³	1	2	yes	—
56	D₄×Dic₄₇	C₂×C₄	1	2	yes	—
57	#13093986	C₂×C₄	1	2	yes	—
58	C₄×C₂²⋊D₄₇	—	2	2	no	—
59	(C₂²⋊D₄₇)⋊C₄	—	2	2	no	—
60	C₄⋊C₄×D₄₇	C₂×C₄	1	2	yes	—
61	C₂²⋊C₄×D₄₇	—	2	2	no	—
62	C₄²×D₄₇	C₂³	1	1	yes	characteristic
63	#13093958	C₂×C₄	1	1	yes	characteristic
64	#13093957	C₂×C₄	1	2	yes	—
65	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
66	Dic₄₇⋊C₈	—	2	1	no	—
67	Dic₄₇⋊C₈	D₄	1	2	yes	—
68	#13093946	C₂×C₄	1	2	yes	—
69	#13093945	C₂×C₄	1	2	yes	—
70	#13093944	C₂×C₄	1	2	yes	—
71	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
72	(C₂×D₄₇)⋊C₈	—	2	2	no	—
73	(C₂×D₄₇)⋊C₈	—	2	1	no	—
74	(C₂×D₄₇)⋊C₈	—	2	2	no	—
75	(C₂×D₄₇)⋊C₈	—	2	2	no	—
76	(C₂×D₄₇)⋊C₈	D₄	1	2	yes	—
77	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
78	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
79	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
80	C₈×Dic₄₇	—	2	2	no	—
81	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
83	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic
84	C₂²×C₈×C₄₇	—	2	2	no	—
85	C₄×D₄×C₄₇	C₂³	1	2	yes	—
86	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
87	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
88	#102×C₄₇	C₂×C₄	1	2	yes	—
89	C₂²⋊C₈×C₄₇	—	2	2	no	—
90	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
91	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
92	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
93	C₂³×D₄₇	—	2	2	no	—
94	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂×C₂²⋊D₄₇	—	2	2	no	—
97	C₂²×Dic₄₇	—	2	2	no	—
98	D₄×D₄₇	—	2	4	no	—
99	D₄×D₄₇	C₂×C₈	1	8	yes	complemented
100	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
101	C₂×C₄×D₄₇	—	2	2	no	—
102	C₂×C₄×D₄₇	—	2	2	no	—
103	C₂×C₄×D₄₇	—	2	2	no	—
104	C₂×C₄×D₄₇	—	8	2	no	—
105	C₂×C₄×D₄₇	—	8	2	no	—
106	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
108	C₂×C₄×D₄₇	#41	1	1	yes	characteristic
109	D₈×C₄₇	C₂×C₈	1	4	yes	complemented
110	C₂×C₈×C₄₇	—	2	2	no	—
111	C₂×C₈×C₄₇	—	2	1	no	—
112	C₂×C₈×C₄₇	—	8	2	no	—
113	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
114	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
115	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
116	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
117	C₂²⋊C₄×C₄₇	—	2	2	no	—
118	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
119	C₂²⋊Dic₄₇	—	2	2	no	—
120	#10625334	C₂×C₈	1	8	yes	complemented
121	(C₂×D₄₇)⋊C₄	—	2	2	no	—
122	(C₂×D₄₇)⋊C₄	—	2	2	no	—
123	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
124	Dic₄₇⋊C₄	—	2	2	no	—
125	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
126	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
127	C₄×Dic₄₇	#41	1	1	yes	characteristic
128	C₂×C₄₇⋊C₈	—	2	2	no	—
129	C₂×C₄₇⋊C₈	—	2	1	no	—
130	C₂×C₄₇⋊C₈	—	8	2	no	—
131	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
134	D₃₇₆	C₂×C₈	1	4	yes	complemented
135	C₈×D₄₇	—	2	2	no	—
136	C₈×D₄₇	—	8	2	no	—
137	C₈×D₄₇	—	8	2	no	—
138	C₈×D₄₇	C₂×C₈	1	4	yes	complemented
139	C₂³×C₄₇	—	2	2	no	—
140	C₂²×D₄₇	—	2	2	no	—
141	C₂²×D₄₇	—	2	8	no	—
142	C₂²×D₄₇	—	8	2	no	—
143	C₂²×D₄₇	—	8	2	no	—
144	C₂²×D₄₇	C₄×D₄	1	1	yes	characteristic
145	D₄×C₄₇	—	2	2	no	—
146	D₄×C₄₇	C₂²×C₈	1	4	yes	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	—	4	2	no	—
149	C₂×C₄×C₄₇	—	4	2	no	—
150	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
152	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
153	C₂²⋊D₄₇	—	2	8	no	—
154	C₂×Dic₄₇	—	2	2	no	—
155	C₂×Dic₄₇	—	8	2	no	—
156	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
157	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
158	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
159	D₁₈₈	—	2	2	no	—
160	D₁₈₈	C₂²×C₈	1	4	yes	—
161	C₄×D₄₇	—	2	2	no	—
162	C₄×D₄₇	—	4	1	no	—
163	C₄×D₄₇	—	4	2	no	—
164	C₄×D₄₇	—	4	2	no	—
165	C₄×D₄₇	—	8	2	no	—
166	C₄×D₄₇	—	8	2	no	—
167	C₄×D₄₇	C₂²×C₈	1	2	yes	—
168	C₄×D₄₇	#131	1	2	yes	—
169	C₈×C₄₇	—	2	1	no	—
170	C₈×C₄₇	—	2	2	no	—
171	C₈×C₄₇	—	4	1	no	—
172	C₈×C₄₇	—	4	2	no	—
173	C₈×C₄₇	C₂²×C₈	1	2	yes	—
174	C₄₇⋊C₈	—	2	1	no	—
175	C₄₇⋊C₈	—	2	2	no	—
176	C₄₇⋊C₈	—	4	1	no	—
177	C₄₇⋊C₈	—	4	2	no	—
178	C₄₇⋊C₈	C₂²×C₈	1	2	yes	—
179	#17854	—	47	1	no	maximal, Sylow
180	C₂²×C₄₇	—	2	4	no	—
181	C₂²×C₄₇	—	4	2	no	—
182	C₂²×C₄₇	—	4	2	no	—
183	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
184	C₂×D₄₇	—	2	1	no	—
185	C₂×D₄₇	—	2	1	no	—
186	C₂×D₄₇	—	2	4	no	—
187	C₂×D₄₇	—	4	2	no	—
188	C₂×D₄₇	—	4	2	no	—
189	C₂×D₄₇	—	8	8	no	—
190	C₂×D₄₇	C₈×D₄	1	2	yes	—
191	C₄×C₄₇	—	2	1	no	—
192	C₄×C₄₇	—	4	2	no	—
193	C₄×C₄₇	C₂³×C₈	1	1	yes	characteristic
194	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
195	C₄×C₄₇	#576	1	2	yes	—
196	Dic₄₇	—	2	1	no	—
197	Dic₄₇	—	2	1	no	—
198	Dic₄₇	—	4	2	no	—
199	Dic₄₇	C₈×D₄	1	2	yes	—
200	#2972	—	47	2	no	—
201	C₂×C₄×D₈	—	47	1	no	—
202	#1580	—	47	1	no	—
203	#1580	—	47	1	no	—
204	#1580	—	47	1	no	—
205	#1580	D₄₇	1	1	yes	characteristic, complemented
206	C₈×D₈	—	47	2	no	—
207	C₈×D₈	—	47	2	no	—
208	#1564	—	47	1	no	—
209	#1478	—	47	2	no	—
210	#1450	—	47	1	no	—
211	C₂×C₄₇	—	4	4	no	—
212	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
213	C₂×C₄₇	#2948	1	1	yes	characteristic
214	C₂×C₄₇	#2957	1	1	yes	characteristic
215	D₄₇	—	2	2	no	—
216	D₄₇	—	4	4	no	—
217	C₂²×D₈	—	47	1	no	—
218	C₂×C₄×D₄	—	47	2	no	—
219	C₄×D₈	—	47	1	no	—
220	C₄×D₈	—	47	2	no	—
221	C₄×D₈	—	47	1	no	—
222	C₄×D₈	—	47	2	no	—
223	C₄×D₈	—	47	1	no	—
224	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
225	C₈×D₄	—	47	2	no	—
226	C₈×D₄	—	47	2	no	—
227	C₈×D₄	—	47	2	no	—
228	C₈×D₄	—	94	2	no	—
229	C₈×D₄	—	94	2	no	—
230	C₈×D₄	C₂×D₄₇	1	2	yes	complemented
231	#431	—	47	1	no	—
232	#431	—	47	1	no	—
233	#431	—	47	2	no	—
234	C₂×#107	—	47	1	no	—
235	C₂×#102	—	47	2	no	—
236	C₂×C₂²⋊C₈	—	94	2	no	—
237	C₂×C₂²⋊C₈	—	94	2	no	—
238	C₂×C₄×C₈	—	47	1	no	—
239	#335	—	47	2	no	—
240	#334	—	47	1	no	—
241	#334	C₂×D₄₇	1	1	yes	characteristic, complemented
242	D₄⋊C₈	—	47	2	no	—
243	D₄⋊C₈	—	47	2	no	—
244	D₄⋊C₈	—	47	2	no	—
245	D₄⋊C₈	C₂×D₄₇	1	2	yes	complemented
246	#322	—	47	1	no	—
247	#322	C₂×D₄₇	1	1	yes	characteristic, complemented
248	C₈²	—	47	1	no	—
249	C₈²	—	47	1	no	—
250	C₄₇	#17854	1	1	yes	characteristic, complemented, Sylow
251	C₂²×D₄	—	47	2	no	—
252	C₂³×C₄	—	94	2	no	—
253	C₂×D₈	—	47	2	no	—
254	C₂×D₈	—	47	8	no	—
255	C₂×D₈	—	47	1	no	—
256	C₂×D₈	C₄×D₄₇	1	1	yes	characteristic
257	C₂²×C₈	—	2	2	no	—
258	C₂²×C₈	—	47	1	no	—
259	C₂²×C₈	—	47	1	no	—
260	C₂²×C₈	—	94	2	no	—
261	C₂²×C₈	—	94	2	no	—
262	C₂²×C₈	—	94	2	no	—
263	C₄×D₄	—	47	2	no	—
264	C₄×D₄	—	47	2	no	—
265	C₄×D₄	—	47	2	no	—
266	C₄×D₄	—	94	2	no	—
267	C₄×D₄	—	94	2	no	—
268	C₄×D₄	C₂²×D₄₇	1	2	yes	—
269	C₂×C₄⋊C₄	—	47	2	no	—
270	C₂×C₂²⋊C₄	—	94	2	no	—
271	C₂×C₄²	—	47	1	no	—
272	#107	—	47	1	no	—
273	#107	—	47	2	no	—
274	#107	C₄×D₄₇	1	1	yes	characteristic
275	C₄⋊C₈	—	47	2	no	—
276	C₄⋊C₈	—	47	2	no	—
277	C₄⋊C₈	—	94	1	no	—
278	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
279	#102	—	47	2	no	—
280	#102	—	47	2	no	—
281	#102	—	47	2	no	—
282	#102	C₄×D₄₇	1	2	yes	—
283	C₂²⋊C₈	—	2	2	no	—
284	C₂²⋊C₈	—	47	2	no	—
285	C₂²⋊C₈	—	94	2	no	—
286	C₂²⋊C₈	—	94	2	no	—
287	C₂²⋊C₈	—	94	1	no	—
288	C₂²⋊C₈	—	94	2	no	—
289	C₂²⋊C₈	—	94	2	no	—
290	C₄×C₈	—	47	1	no	—
291	C₄×C₈	—	47	1	no	—
292	C₄×C₈	—	47	1	no	—
293	C₄×C₈	—	47	1	no	—
294	C₄×C₈	—	47	1	no	—
295	C₄×C₈	—	94	2	no	—
296	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
297	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
298	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
299	C₂⁴	—	94	2	no	—
300	C₂×D₄	—	47	8	no	—
301	C₂×D₄	—	47	2	no	—
302	C₂×D₄	—	94	4	no	—
303	C₂×D₄	—	94	2	no	—
304	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
305	C₂²×C₄	—	2	2	no	—
306	C₂²×C₄	—	47	1	no	—
307	C₂²×C₄	—	47	1	no	—
308	C₂²×C₄	—	47	1	no	—
309	C₂²×C₄	—	94	2	no	—
310	C₂²×C₄	—	94	2	no	—
311	C₂²×C₄	—	94	2	no	—
312	C₂²×C₄	—	94	2	no	—
313	C₂²×C₄	—	376	2	no	—
314	C₂²×C₄	—	376	2	no	—
315	D₈	—	47	8	no	—
316	D₈	—	47	4	no	—
317	D₈	C₈×D₄₇	1	4	yes	complemented
318	C₂×C₈	—	2	2	no	—
319	C₂×C₈	—	2	1	no	—
320	C₂×C₈	—	8	2	no	—
321	C₂×C₈	—	47	1	no	—
322	C₂×C₈	—	47	4	no	—
323	C₂×C₈	—	47	1	no	—
324	C₂×C₈	—	47	2	no	—
325	C₂×C₈	—	94	2	no	—
326	C₂×C₈	—	94	2	no	—
327	C₂×C₈	—	94	1	no	—
328	C₂×C₈	—	376	2	no	—
329	C₂×C₈	—	376	2	no	—
330	C₂×C₈	—	376	2	no	—
331	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
332	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
333	C₂×C₈	D₄×D₄₇	1	2	yes	—
334	C₄⋊C₄	—	47	2	no	—
335	C₄⋊C₄	—	94	2	no	—
336	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
337	C₂²⋊C₄	—	2	2	no	—
338	C₂²⋊C₄	—	94	2	no	—
339	C₂²⋊C₄	—	94	2	no	—
340	C₂²⋊C₄	—	94	2	no	—
341	C₄²	—	47	1	no	—
342	C₄²	—	47	1	no	—
343	C₄²	—	47	1	no	—
344	C₄²	C₂³×D₄₇	1	1	yes	characteristic
345	C₂³	—	2	2	no	—
346	C₂³	—	47	1	no	—
347	C₂³	—	94	8	no	—
348	C₂³	—	94	2	no	—
349	C₂³	—	376	2	no	—
350	C₂³	—	376	2	no	—
351	D₄	—	2	2	no	—
352	D₄	—	47	4	no	—
353	D₄	—	94	8	no	—
354	D₄	—	94	2	no	—
355	D₄	C₂×C₈×D₄₇	1	4	yes	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	4	2	no	—
358	C₂×C₄	—	4	2	no	—
359	C₂×C₄	—	47	1	no	—
360	C₂×C₄	—	47	2	no	—
361	C₂×C₄	—	47	2	no	—
362	C₂×C₄	—	47	1	no	—
363	C₂×C₄	—	47	1	no	—
364	C₂×C₄	—	94	2	no	—
365	C₂×C₄	—	94	2	no	—
366	C₂×C₄	—	376	2	no	—
367	C₂×C₄	—	376	2	no	—
368	C₂×C₄	—	376	2	no	—
369	C₂×C₄	—	188	1	no	—
370	C₂×C₄	—	188	2	no	—
371	C₂×C₄	—	188	2	no	—
372	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
373	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
374	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	2	no	—
377	C₈	—	4	1	no	—
378	C₈	—	4	2	no	—
379	C₈	—	47	2	no	—
380	C₈	—	94	1	no	—
381	C₈	—	94	2	no	—
382	C₈	—	188	1	no	—
383	C₈	—	188	2	no	—
384	C₈	C₂×C₈×D₄₇	1	2	yes	—
385	C₂²	—	2	4	no	—
386	C₂²	—	4	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	47	2	no	—
389	C₂²	—	94	1	no	—
390	C₂²	—	94	1	no	—
391	C₂²	—	94	4	no	—
392	C₂²	—	376	8	no	—
393	C₂²	—	188	2	no	—
394	C₂²	—	188	2	no	—
395	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
396	C₄	—	2	1	no	—
397	C₄	—	4	2	no	—
398	C₄	—	47	2	no	—
399	C₄	—	94	1	no	—
400	C₄	—	94	1	no	—
401	C₄	—	188	2	no	—
402	C₄	C₂²×C₈×D₄₇	1	1	yes	characteristic
403	C₄	#131×D₄₇	1	1	yes	characteristic
404	C₄	#15689927	1	2	yes	—
405	C₂	—	4	4	no	—
406	C₂	—	94	2	no	—
407	C₂	—	188	4	no	—
408	C₂	C₈×D₄×D₄₇	1	1	yes	characteristic
409	C₂	#20252237	1	1	yes	characteristic
410	C₂	#20252302	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₄₇
commutator	C₄×C₄₇	C₂³×C₈
Frattini	C₄²	C₂³×D₄₇
Fitting	C₄₇×#1580	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×D₈×D₄₇	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	#1580	D₄₇
hypocenter	C₄₇	#17854
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ #1580

Complements

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

N	H ≅ G/N	type
1. #20252409	C₂	semidirect
3. #20242213	C₂	semidirect
4. #20242212	C₂	semidirect
5. #20242211	C₂	semidirect
6. C₈×#10625334	C₂	semidirect
7. #20242180	C₂	semidirect
8. #20242133	C₂	semidirect
9. #20241777	C₂	semidirect
10. #20241673	C₂	semidirect
11. C₄₇×#1580	C₂	semidirect
19. C₈×D₁₈₈	C₂²	semidirect
20. D₄×C₄₇⋊C₈	C₂²	semidirect
21. #15689188	C₂²	semidirect
32. #15688875	C₂²	semidirect
33. #15688874	C₂²	semidirect
34. #15688852	C₂²	semidirect
35. D₄⋊(C₄₇⋊C₈)	C₂²	semidirect
36. #15688850	C₂²	semidirect
37. #15688844	C₂²	semidirect
38. C₈×C₄₇⋊C₈	C₂²	semidirect
39. C₈×C₄₇⋊C₈	C₂²	semidirect
41. C₈×D₄×C₄₇	C₂²	semidirect
42. C₄₇×#334	C₂²	semidirect
43. C₄₇×D₄⋊C₈	C₂²	semidirect
44. C₄₇×#322	C₂²	semidirect
49. D₈×D₄₇	C₈	semidirect
99. D₄×D₄₇	C₂×C₈	semidirect
109. D₈×C₄₇	C₂×C₈	semidirect
120. #10625334	C₂×C₈	semidirect
134. D₃₇₆	C₂×C₈	semidirect
138. C₈×D₄₇	C₂×C₈	semidirect
205. #1580	D₄₇	semidirect
230. C₈×D₄	C₂×D₄₇	semidirect
241. #334	C₂×D₄₇	semidirect
245. D₄⋊C₈	C₂×D₄₇	semidirect
247. #322	C₂×D₄₇	semidirect
250. C₄₇	#17854	semidirect
317. D₈	C₈×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
#20252409	2
C₄×D₈×D₄₇	2
#20242213	2
#20242212	2
#20242211	2
C₈×#10625334	2
#20242180	2
#20242133	2
#20241777	2
#20241673	2
C₄₇×#1580	2
#17854	47