Subgroups — #26186789

Order 12032.

750 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20253964	C₂	1	1	yes	maximal, characteristic
2	#20252095	C₂	1	2	yes	maximal, complemented
3	#20242273	C₂	1	1	yes	maximal, characteristic, complemented
4	#20242272	C₂	1	1	yes	maximal, characteristic, complemented
5	#20242270	C₂	1	2	yes	maximal, complemented
6	C₈×D₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
7	C₈×#10625334	C₂	1	2	yes	maximal, complemented
8	#20242145	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241837	C₂	1	2	yes	maximal, complemented
10	C₈²×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×D₈×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094030	—	2	2	no	—
13	#15689670	C₂²	1	2	yes	—
14	#15689527	C₄	1	1	yes	characteristic
15	#15689498	C₄	1	1	yes	characteristic
16	#15689468	C₄	1	2	yes	—
17	#15689360	C₄	1	1	yes	characteristic
18	#15689358	C₄	1	2	yes	—
19	#15689356	C₄	1	1	yes	characteristic
20	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
21	C₄×#10625334	C₂²	1	2	yes	—
22	#15689201	C₂²	1	2	yes	—
23	#15689200	C₂²	1	2	yes	—
24	#15689198	—	2	2	no	—
25	C₈×D₁₈₈	C₂²	1	2	yes	—
26	C₈×C₂²⋊D₄₇	—	2	2	no	—
27	#15689145	C₂²	1	2	yes	—
28	#15689088	—	2	2	no	—
29	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
30	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
31	C₄×C₈×D₄₇	C₂²	1	1	yes	characteristic
32	#15688876	C₂²	1	1	yes	characteristic
33	#15688875	C₂²	1	2	yes	—
34	#15688852	C₂²	1	2	yes	—
35	D₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
36	#15688850	C₂²	1	2	yes	—
37	C₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
38	C₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
39	C₈×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
40	C₄×D₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₈×D₄×C₄₇	C₂²	1	2	yes	—
42	C₄₇×#335	C₂²	1	1	yes	characteristic
43	C₄₇×D₄⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₄₇	C₂²	1	1	yes	characteristic
45	C₂×#10625350	—	2	2	no	—
46	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic
47	C₂×#10625334	C₂×C₄	1	2	yes	—
48	#13094030	—	4	8	no	—
49	C₂×#10625329	—	2	2	no	—
50	C₂×#10625324	—	2	2	no	—
51	C₂×#10625324	—	2	2	no	—
52	C₂×C₈×D₄₇	—	2	1	no	—
53	C₂×C₈×D₄₇	—	2	2	no	—
54	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
55	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
57	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
58	#13094023	C₂×C₄	1	2	yes	—
59	#13094020	C₂×C₄	1	2	yes	—
60	#13094010	—	2	2	no	—
61	#13093999	C₂×C₄	1	2	yes	—
62	#13093997	—	2	2	no	—
63	#13093995	C₂×C₄	1	2	yes	—
64	C₄×D₁₈₈	C₂³	1	2	yes	—
65	C₄×C₂²⋊D₄₇	—	2	2	no	—
66	C₄²×D₄₇	C₂³	1	1	yes	characteristic
67	#13093958	C₂×C₄	1	1	yes	characteristic
68	#13093957	C₂×C₄	1	2	yes	—
69	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
70	Dic₄₇⋊C₈	—	2	2	no	—
71	#13093946	C₂×C₄	1	2	yes	—
72	#13093945	C₂×C₄	1	2	yes	—
73	#13093944	C₂×C₄	1	2	yes	—
74	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
75	(C₂×D₄₇)⋊C₈	—	2	2	no	—
76	(C₂×D₄₇)⋊C₈	—	2	2	no	—
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	1	no	—
81	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₄₇	D₄	1	1	yes	characteristic
84	C₈×Dic₄₇	D₄	1	1	yes	characteristic
85	C₂×D₈×C₄₇	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₈×C₄₇	—	2	2	no	—
87	C₄×D₄×C₄₇	C₂³	1	2	yes	—
88	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
89	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
90	#102×C₄₇	C₂×C₄	1	2	yes	—
91	C₂²⋊C₈×C₄₇	—	2	2	no	—
92	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
93	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
94	C₄×C₈×C₄₇	C₂³	1	1	yes	characteristic
95	C₂×D₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂×C₂²⋊D₄₇	—	2	2	no	—
98	C₂×C₂²⋊D₄₇	—	2	2	no	—
99	C₂×C₂²⋊D₄₇	—	2	2	no	—
100	#10625350	—	4	4	no	—
101	#10625350	—	4	4	no	—
102	C₂×D₁₈₈	—	2	2	no	—
103	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
104	C₂×C₄×D₄₇	—	2	2	no	—
105	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
107	C₂×C₄×D₄₇	#41	1	1	yes	characteristic
108	C₂×Dic₉₄	—	2	2	no	—
109	D₈×C₄₇	—	2	2	no	—
110	C₂×C₈×C₄₇	—	2	1	no	—
111	C₂×C₈×C₄₇	—	2	2	no	—
112	C₂×C₈×C₄₇	—	4	4	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	1	yes	characteristic
116	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
117	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
118	C₂²⋊C₄×C₄₇	—	2	2	no	—
119	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
120	C₂²⋊Dic₄₇	—	2	2	no	—
121	#10625334	—	2	4	no	—
122	(C₂×D₄₇)⋊C₄	—	2	2	no	—
123	(C₂×D₄₇)⋊C₄	—	2	2	no	—
124	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
125	Dic₄₇⋊C₄	—	2	2	no	—
126	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₄×Dic₄₇	C₂×D₄	1	1	yes	characteristic
128	C₄×Dic₄₇	#41	1	1	yes	characteristic
129	#10625329	—	4	4	no	—
130	C₂×C₄₇⋊C₈	—	2	1	no	—
131	C₂×C₄₇⋊C₈	—	2	2	no	—
132	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
135	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
136	D₃₇₆	—	2	2	no	—
137	#10625324	—	4	4	no	—
138	#10625324	—	4	4	no	—
139	C₈×D₄₇	—	2	4	no	—
140	C₈×D₄₇	—	2	2	no	—
141	C₈×D₄₇	—	2	2	no	—
142	C₈×D₄₇	—	2	2	no	—
143	C₈×D₄₇	—	4	4	no	—
144	C₈×D₄₇	D₈	1	4	yes	complemented
145	C₂³×C₄₇	—	2	2	no	—
146	C₂²×D₄₇	—	2	2	no	—
147	C₂²×D₄₇	C₄×D₄	1	1	yes	characteristic
148	D₄×C₄₇	—	2	2	no	—
149	D₄×C₄₇	—	2	2	no	—
150	C₂×C₄×C₄₇	—	2	2	no	—
151	C₂×C₄×C₄₇	—	4	2	no	—
152	C₂×C₄×C₄₇	—	4	2	no	—
153	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
155	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
156	C₂²⋊D₄₇	—	4	4	no	—
157	C₂²⋊D₄₇	—	4	4	no	—
158	C₂²⋊D₄₇	—	4	4	no	—
159	C₂×Dic₄₇	—	2	2	no	—
160	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
161	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
162	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
163	D₁₈₈	—	2	2	no	—
164	D₁₈₈	—	2	2	no	—
165	D₁₈₈	—	4	4	no	—
166	C₄×D₄₇	—	2	1	no	—
167	C₄×D₄₇	—	2	1	no	—
168	C₄×D₄₇	—	2	2	no	—
169	C₄×D₄₇	—	4	2	no	—
170	C₄×D₄₇	—	4	2	no	—
171	C₄×D₄₇	C₂×D₈	1	2	yes	—
172	C₄×D₄₇	#135	1	2	yes	—
173	Dic₉₄	—	4	4	no	—
174	C₈×C₄₇	—	2	2	no	—
175	C₈×C₄₇	—	2	1	no	—
176	C₈×C₄₇	—	2	1	no	—
177	C₈×C₄₇	—	4	2	no	—
178	C₈×C₄₇	#131	1	2	yes	complemented
179	C₈×C₄₇	C₂×D₈	1	2	yes	—
180	C₄₇⋊C₈	—	2	2	no	—
181	C₄₇⋊C₈	—	2	1	no	—
182	C₄₇⋊C₈	—	2	1	no	—
183	C₄₇⋊C₈	—	4	2	no	—
184	C₄₇⋊C₈	#131	1	2	yes	complemented
185	C₄₇⋊C₈	C₂×D₈	1	2	yes	—
186	#17956	—	47	1	no	maximal, Sylow
187	C₂²×C₄₇	—	4	2	no	—
188	C₂²×C₄₇	—	4	2	no	—
189	C₂²×C₄₇	—	4	2	no	—
190	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
191	C₂×D₄₇	—	2	1	no	—
192	C₂×D₄₇	—	2	1	no	—
193	C₂×D₄₇	—	4	2	no	—
194	C₂×D₄₇	—	4	2	no	—
195	C₂×D₄₇	—	4	2	no	—
196	C₂×D₄₇	C₄×D₈	1	2	yes	—
197	C₄×C₄₇	—	2	1	no	—
198	C₄×C₄₇	—	4	2	no	—
199	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
200	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
201	C₄×C₄₇	C₂²×D₈	1	1	yes	characteristic
202	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
203	Dic₄₇	—	2	1	no	—
204	Dic₄₇	—	4	2	no	—
205	Dic₄₇	C₄×D₈	1	2	yes	—
206	Dic₄₇	#443	1	2	yes	—
207	#3169	—	47	1	no	—
208	#2931	—	47	2	no	—
209	#1589	—	47	1	no	—
210	#1589	—	47	1	no	—
211	#1589	—	47	2	no	—
212	C₈×D₈	—	47	2	no	—
213	C₈×D₈	—	47	1	no	—
214	C₈×D₈	D₄₇	1	1	yes	characteristic, complemented
215	#1567	—	47	1	no	—
216	#1492	—	47	2	no	—
217	C₂×C₈²	—	47	1	no	—
218	C₂×C₄₇	—	8	2	no	—
219	C₂×C₄₇	#2931	1	1	yes	characteristic
220	C₂×C₄₇	C₂×C₄×D₈	1	1	yes	characteristic
221	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
222	D₄₇	—	2	2	no	—
223	D₄₇	—	8	2	no	—
224	C₂×#131	—	94	2	no	—
225	#532	—	47	2	no	—
226	#500	—	47	1	no	—
227	#493	—	47	1	no	—
228	#486	—	47	2	no	—
229	#466	—	47	1	no	—
230	#466	—	47	1	no	—
231	#466	—	47	2	no	—
232	C₄×D₈	—	47	2	no	—
233	C₄×D₈	—	47	1	no	—
234	C₄×D₈	C₂×D₄₇	1	1	yes	characteristic
235	#436	—	47	2	no	—
236	#436	—	47	2	no	—
237	#436	—	94	2	no	—
238	C₈×D₄	—	47	2	no	—
239	C₈×D₄	—	94	2	no	—
240	C₈×D₄	C₂×D₄₇	1	2	yes	—
241	#423	—	47	2	no	—
242	#408	—	94	2	no	—
243	C₂×C₄×C₈	—	47	1	no	—
244	C₂×C₄×C₈	—	47	1	no	—
245	C₂×C₄×C₈	—	47	1	no	—
246	#335	—	47	2	no	—
247	#335	—	47	1	no	—
248	#335	C₂×D₄₇	1	1	yes	characteristic
249	D₄⋊C₈	—	47	2	no	—
250	D₄⋊C₈	—	47	2	no	—
251	D₄⋊C₈	—	47	2	no	—
252	D₄⋊C₈	C₂×D₄₇	1	2	yes	—
253	C₈²	—	47	1	no	—
254	C₈²	—	47	1	no	—
255	C₈²	—	47	1	no	—
256	C₈²	C₂×D₄₇	1	1	yes	characteristic
257	C₄₇	#17956	1	1	yes	characteristic, complemented, Sylow
258	C₂×#41	—	94	2	no	—
259	C₂×D₈	—	47	2	no	—
260	C₂×D₈	—	47	1	no	—
261	C₂×D₈	C₄×D₄₇	1	1	yes	characteristic
262	#131	—	188	8	no	—
263	C₂×M₁₆	—	94	2	no	—
264	C₂×M₁₆	—	94	2	no	—
265	C₂×M₁₆	—	94	2	no	—
266	C₂²×C₈	—	2	2	no	—
267	C₂²×C₈	—	47	1	no	—
268	C₂²×C₈	—	47	1	no	—
269	C₂²×C₈	—	47	1	no	—
270	C₂²×C₈	—	47	1	no	—
271	C₂²×C₈	—	94	1	no	—
272	C₂²×C₈	—	94	2	no	—
273	C₄⋊Q₈	—	47	2	no	—
274	#127	—	47	2	no	—
275	#124	—	94	2	no	—
276	#121	—	47	2	no	—
277	#121	—	47	2	no	—
278	#121	—	94	2	no	—
279	C₄×D₄	—	47	2	no	—
280	C₄×D₄	—	94	2	no	—
281	C₄×D₄	C₂²×D₄₇	1	2	yes	—
282	C₂×C₄²	—	47	1	no	—
283	#107	—	47	1	no	—
284	#107	—	47	2	no	—
285	#107	C₄×D₄₇	1	1	yes	characteristic
286	C₄⋊C₈	—	47	2	no	—
287	C₄⋊C₈	—	94	2	no	—
288	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
289	#102	—	47	2	no	—
290	#102	—	47	2	no	—
291	#102	—	47	2	no	—
292	#102	C₄×D₄₇	1	2	yes	—
293	C₂²⋊C₈	—	2	2	no	—
294	C₂²⋊C₈	—	94	2	no	—
295	C₂²⋊C₈	—	94	2	no	—
296	C₂²⋊C₈	—	94	2	no	—
297	C₄×C₈	—	47	1	no	—
298	C₄×C₈	—	47	1	no	—
299	C₄×C₈	—	47	1	no	—
300	C₄×C₈	—	47	1	no	—
301	C₄×C₈	—	47	1	no	—
302	C₄×C₈	—	47	1	no	—
303	C₄×C₈	—	47	1	no	—
304	C₄×C₈	—	94	1	no	—
305	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
306	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
307	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
308	#41	—	188	4	no	—
309	#41	—	188	4	no	—
310	C₂×Q₈	—	94	2	no	—
311	C₂×D₄	—	47	2	no	—
312	C₂×D₄	—	94	2	no	—
313	C₂×D₄	—	94	2	no	—
314	C₂×D₄	—	94	2	no	—
315	C₂×D₄	—	94	2	no	—
316	C₂×D₄	C₂×C₄×D₄₇	1	2	yes	—
317	C₂²×C₄	—	2	2	no	—
318	C₂²×C₄	—	47	1	no	—
319	C₂²×C₄	—	47	1	no	—
320	C₂²×C₄	—	47	1	no	—
321	C₂²×C₄	—	94	2	no	—
322	D₈	—	2	2	no	—
323	D₈	—	94	4	no	—
324	D₈	—	94	2	no	—
325	M₁₆	—	188	4	no	—
326	M₁₆	—	188	4	no	—
327	M₁₆	—	188	4	no	—
328	C₂×C₈	—	2	1	no	—
329	C₂×C₈	—	2	2	no	—
330	C₂×C₈	—	4	4	no	—
331	C₂×C₈	—	47	1	no	—
332	C₂×C₈	—	47	1	no	—
333	C₂×C₈	—	47	4	no	—
334	C₂×C₈	—	47	1	no	—
335	C₂×C₈	—	47	1	no	—
336	C₂×C₈	—	94	2	no	—
337	C₂×C₈	—	94	2	no	—
338	C₂×C₈	—	94	4	no	—
339	C₂×C₈	—	94	1	no	—
340	C₂×C₈	—	94	2	no	—
341	C₂×C₈	—	94	2	no	—
342	C₂×C₈	—	188	4	no	—
343	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
344	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
345	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
346	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
347	C₄⋊C₄	—	47	2	no	—
348	C₄⋊C₄	—	94	2	no	—
349	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
350	C₂²⋊C₄	—	2	2	no	—
351	C₂²⋊C₄	—	94	2	no	—
352	C₂²⋊C₄	—	94	2	no	—
353	C₂²⋊C₄	—	94	2	no	—
354	C₄²	—	47	1	no	—
355	C₄²	—	47	1	no	—
356	C₄²	—	47	1	no	—
357	C₄²	C₂³×D₄₇	1	1	yes	characteristic
358	C₂³	—	2	2	no	—
359	C₂³	—	47	1	no	—
360	C₂³	—	94	2	no	—
361	Q₈	—	188	4	no	—
362	D₄	—	2	2	no	—
363	D₄	—	2	2	no	—
364	D₄	—	94	2	no	—
365	D₄	—	94	2	no	—
366	D₄	—	188	4	no	—
367	D₄	—	188	4	no	—
368	D₄	—	188	4	no	—
369	D₄	—	188	4	no	—
370	C₂×C₄	—	2	2	no	—
371	C₂×C₄	—	4	2	no	—
372	C₂×C₄	—	4	2	no	—
373	C₂×C₄	—	47	1	no	—
374	C₂×C₄	—	47	1	no	—
375	C₂×C₄	—	47	2	no	—
376	C₂×C₄	—	47	2	no	—
377	C₂×C₄	—	47	1	no	—
378	C₂×C₄	—	94	2	no	—
379	C₂×C₄	—	94	1	no	—
380	C₂×C₄	—	94	1	no	—
381	C₂×C₄	—	94	2	no	—
382	C₂×C₄	—	188	2	no	—
383	C₂×C₄	—	188	2	no	—
384	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
385	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
386	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	2	1	no	—
389	C₈	—	2	1	no	—
390	C₈	—	4	2	no	—
391	C₈	—	47	2	no	—
392	C₈	—	47	2	no	—
393	C₈	—	94	2	no	—
394	C₈	—	94	1	no	—
395	C₈	—	94	1	no	—
396	C₈	—	188	2	no	—
397	C₈	#13094030	1	2	yes	complemented
398	C₈	D₈×D₄₇	1	2	yes	—
399	C₂²	—	4	2	no	—
400	C₂²	—	4	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	47	2	no	—
403	C₂²	—	94	1	no	—
404	C₂²	—	94	1	no	—
405	C₂²	—	188	2	no	—
406	C₂²	—	188	2	no	—
407	C₂²	—	188	2	no	—
408	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
409	C₄	—	2	1	no	—
410	C₄	—	4	2	no	—
411	C₄	—	47	2	no	—
412	C₄	—	47	2	no	—
413	C₄	—	94	1	no	—
414	C₄	—	188	2	no	—
415	C₄	#131×D₄₇	1	1	yes	characteristic
416	C₄	C₂×#13094030	1	1	yes	characteristic
417	C₄	C₂×D₈×D₄₇	1	1	yes	characteristic
418	C₄	#135×D₄₇	1	1	yes	characteristic
419	C₂	—	8	2	no	—
420	C₂	—	94	2	no	—
421	C₂	—	376	2	no	—
422	C₂	#20252095	1	1	yes	characteristic
423	C₂	C₄×D₈×D₄₇	1	1	yes	characteristic
424	C₂	#443×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₄₇
commutator	C₂×C₄×C₄₇	C₂³×C₄
Frattini	C₄²	C₂³×D₄₇
Fitting	C₈×D₈×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	#20253964	C₂
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₈×D₈	D₄₇
hypocenter	C₄₇	#17956
LCS	G ▷ C₂×C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈×D₈

Complements

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

N	H ≅ G/N	type
2. #20252095	C₂	semidirect
3. #20242273	C₂	semidirect
4. #20242272	C₂	semidirect
5. #20242270	C₂	semidirect
6. C₈×D₃₇₆	C₂	semidirect
7. C₈×#10625334	C₂	semidirect
8. #20242145	C₂	semidirect
9. #20241837	C₂	semidirect
10. C₈²×D₄₇	C₂	semidirect
11. C₈×D₈×C₄₇	C₂	semidirect
144. C₈×D₄₇	D₈	semidirect
178. C₈×C₄₇	#131	semidirect
184. C₄₇⋊C₈	#131	semidirect
214. C₈×D₈	D₄₇	semidirect
257. C₄₇	#17956	semidirect
397. C₈	#13094030	semidirect

Maximal subgroups

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

subgroup	index
#20253964	2
#20252095	2
#20242273	2
#20242272	2
#20242270	2
C₈×D₃₇₆	2
C₈×#10625334	2
#20242145	2
#20241837	2
C₈²×D₄₇	2
C₈×D₈×C₄₇	2
#17956	47