Subgroups — C₈×#13094047 #26185656

Order 12032.

750 conjugacy classes of subgroups.

The subgroup lattice has 406 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₈×#10625354	C₂	1	2	yes	maximal, complemented
2	C₄×#13094047	C₂	1	1	yes	maximal, characteristic
3	Q₁₆×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₈×#10625336	C₂	1	2	yes	maximal, complemented
5	#20242185	C₂	1	2	yes	maximal, complemented
6	C₈×D₃₇₆	C₂	1	1	yes	maximal, characteristic, complemented
7	#20242182	C₂	1	1	yes	maximal, characteristic, complemented
8	#20242135	C₂	1	1	yes	maximal, characteristic, complemented
9	#20241769	C₂	1	2	yes	maximal, complemented
10	C₈²×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₈×Q₁₆×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#13094047	C₄	1	1	yes	characteristic
13	C₄×#10625354	C₂²	1	2	yes	—
14	Q₈×C₄₇⋊C₈	C₂²	1	2	yes	—
15	Q₁₆×Dic₄₇	C₄	1	1	yes	characteristic
16	C₄×#10625336	C₂²	1	2	yes	—
17	#15689208	C₄	1	2	yes	—
18	C₄×D₃₇₆	C₂²	1	1	yes	characteristic
19	#15689205	C₄	1	1	yes	characteristic
20	C₈×D₁₈₈	—	2	2	no	—
21	C₈×D₁₈₈	C₂²	1	2	yes	—
22	#15689188	—	2	2	no	—
23	#15689188	C₂²	1	2	yes	—
24	#15689175	—	2	2	no	—
25	#15689175	C₂²	1	2	yes	—
26	#15689160	C₄	1	1	yes	characteristic
27	#15689118	C₄	1	2	yes	—
28	C₄×C₈×D₄₇	—	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	#15688873	C₂²	1	2	yes	—
34	Q₈⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
35	#15688852	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	C₈×Q₈×C₄₇	C₂²	1	2	yes	—
41	C₄×Q₁₆×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#335	C₂²	1	1	yes	characteristic
43	C₄₇×Q₈⋊C₈	C₂²	1	2	yes	—
44	C₈²×C₄₇	C₂²	1	1	yes	characteristic
45	C₂×#10625354	C₂×C₄	1	2	yes	—
46	#13094047	C₈	1	8	yes	direct product factor
47	C₂×#10625336	C₂×C₄	1	2	yes	—
48	C₂×D₃₇₆	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₄₇	—	2	1	no	—
50	C₂×C₈×D₄₇	—	2	2	no	—
51	C₂×C₈×D₄₇	—	2	2	no	—
52	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
55	C₂×C₈×D₄₇	D₄	1	1	yes	characteristic
56	Q₈×Dic₄₇	C₂×C₄	1	2	yes	—
57	C₄×D₁₈₈	—	2	2	no	—
58	C₄×D₁₈₈	C₂³	1	2	yes	—
59	#13093986	—	2	2	no	—
60	#13093986	C₂×C₄	1	2	yes	—
61	#13093982	—	2	2	no	—
62	#13093982	C₂×C₄	1	2	yes	—
63	C₄²×D₄₇	—	2	2	no	—
64	C₄²×D₄₇	C₂³	1	1	yes	characteristic
65	#13093958	C₂×C₄	1	1	yes	characteristic
66	#13093955	C₂×C₄	1	2	yes	—
67	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
68	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
69	#13093948	C₂×C₄	1	2	yes	—
70	#13093946	C₂×C₄	1	2	yes	—
71	#13093944	C₂×C₄	1	2	yes	—
72	(C₂×D₄₇)⋊C₈	—	2	2	no	—
73	(C₂×D₄₇)⋊C₈	—	2	2	no	—
74	(C₂×D₄₇)⋊C₈	—	2	2	no	—
75	C₄×C₄₇⋊C₈	—	2	2	no	—
76	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
77	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
78	C₄×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
79	C₈×Dic₄₇	—	2	2	no	—
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×Q₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
86	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
87	#107×C₄₇	C₂×C₄	1	1	yes	characteristic
88	C₄⋊C₈×C₄₇	—	2	2	no	—
89	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
90	#103×C₄₇	C₂×C₄	1	2	yes	—
91	C₄×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×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
96	#10625354	—	2	4	no	—
97	#10625354	C₂×C₈	1	8	yes	complemented
98	C₂×D₁₈₈	—	2	2	no	—
99	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
100	C₂×C₄×D₄₇	—	2	2	no	—
101	C₂×C₄×D₄₇	—	2	2	no	—
102	C₂×C₄×D₄₇	—	2	2	no	—
103	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂×C₄×D₄₇	C₂×D₄	1	1	yes	characteristic
105	C₂×C₄×D₄₇	#41	1	1	yes	characteristic
106	Q₁₆×C₄₇	C₂×C₈	1	4	yes	complemented
107	C₂×C₈×C₄₇	—	2	1	no	—
108	C₂×C₈×C₄₇	—	2	2	no	—
109	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
111	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
112	C₂×C₈×C₄₇	C₂×D₄	1	1	yes	characteristic
113	C₄⋊C₄×C₄₇	—	2	2	no	—
114	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
115	C₄²×C₄₇	—	2	2	no	—
116	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
117	#10625336	C₂×C₈	1	8	yes	complemented
118	(C₂×D₄₇)⋊C₄	—	2	2	no	—
119	(C₂×D₄₇)⋊C₄	—	2	2	no	—
120	(C₂×D₄₇)⋊C₄	—	2	2	no	—
121	C₄⋊Dic₄₇	—	2	2	no	—
122	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
123	C₄×Dic₄₇	—	2	2	no	—
124	C₄×Dic₄₇	—	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	1	no	—
129	C₂×C₄₇⋊C₈	—	2	2	no	—
130	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
131	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
133	C₂×C₄₇⋊C₈	C₂×D₄	1	1	yes	characteristic
134	D₃₇₆	C₂×C₈	1	4	yes	complemented
135	C₈×D₄₇	—	2	4	no	—
136	C₈×D₄₇	—	2	2	no	—
137	C₈×D₄₇	—	2	2	no	—
138	C₈×D₄₇	—	2	2	no	—
139	C₈×D₄₇	—	4	4	no	—
140	C₈×D₄₇	—	4	4	no	—
141	C₈×D₄₇	C₂×C₈	1	4	yes	complemented
142	C₂²×D₄₇	—	2	2	no	—
143	C₂²×D₄₇	C₄×D₄	1	1	yes	characteristic
144	Q₈×C₄₇	—	2	2	no	—
145	Q₈×C₄₇	C₂²×C₈	1	4	yes	—
146	C₂×C₄×C₄₇	—	2	2	no	—
147	C₂×C₄×C₄₇	—	2	2	no	—
148	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
150	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
151	C₂×Dic₄₇	—	2	2	no	—
152	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
153	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
154	C₂×Dic₄₇	C₄×D₄	1	1	yes	characteristic
155	D₁₈₈	—	2	8	no	—
156	D₁₈₈	—	2	2	no	—
157	D₁₈₈	C₂²×C₈	1	4	yes	—
158	C₄×D₄₇	—	2	1	no	—
159	C₄×D₄₇	—	2	1	no	—
160	C₄×D₄₇	—	2	8	no	—
161	C₄×D₄₇	—	2	2	no	—
162	C₄×D₄₇	—	4	2	no	—
163	C₄×D₄₇	—	4	2	no	—
164	C₄×D₄₇	—	4	4	no	—
165	C₄×D₄₇	C₂²×C₈	1	2	yes	—
166	C₄×D₄₇	#131	1	2	yes	—
167	C₈×C₄₇	—	2	2	no	—
168	C₈×C₄₇	—	2	1	no	—
169	C₈×C₄₇	—	2	1	no	—
170	C₈×C₄₇	—	4	2	no	—
171	C₈×C₄₇	C₂²×C₈	1	2	yes	—
172	C₈×C₄₇	#135	1	2	yes	complemented
173	C₄₇⋊C₈	—	2	2	no	—
174	C₄₇⋊C₈	—	2	1	no	—
175	C₄₇⋊C₈	—	2	1	no	—
176	C₄₇⋊C₈	—	4	2	no	—
177	C₄₇⋊C₈	C₂²×C₈	1	2	yes	—
178	C₄₇⋊C₈	#135	1	2	yes	complemented
179	C₈×#135	—	47	1	no	maximal, Sylow
180	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
181	C₂×D₄₇	—	2	1	no	—
182	C₂×D₄₇	—	2	1	no	—
183	C₂×D₄₇	—	2	4	no	—
184	C₂×D₄₇	—	4	2	no	—
185	C₂×D₄₇	—	4	2	no	—
186	C₂×D₄₇	C₈×D₄	1	2	yes	—
187	C₄×C₄₇	—	2	4	no	—
188	C₄×C₄₇	—	2	1	no	—
189	C₄×C₄₇	—	4	2	no	—
190	C₄×C₄₇	C₂³×C₈	1	1	yes	characteristic
191	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
192	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
193	C₄×C₄₇	C₂×#135	1	1	yes	characteristic
194	Dic₄₇	—	2	1	no	—
195	Dic₄₇	—	4	2	no	—
196	Dic₄₇	C₈×D₄	1	2	yes	—
197	Dic₄₇	#443	1	2	yes	—
198	C₈×#41	—	47	2	no	—
199	C₄×#135	—	47	1	no	—
200	C₈×Q₁₆	—	47	1	no	—
201	C₈×Q₁₆	D₄₇	1	1	yes	characteristic, complemented
202	C₈×SD₁₆	—	47	2	no	—
203	C₈×SD₁₆	—	47	2	no	—
204	C₈×D₈	—	47	1	no	—
205	C₈×D₈	—	47	1	no	—
206	#1564	—	47	1	no	—
207	#1476	—	47	2	no	—
208	C₂×C₈²	—	47	1	no	—
209	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
210	C₂×C₄₇	C₄×#135	1	1	yes	characteristic
211	C₂×C₄₇	C₂×#443	1	1	yes	characteristic
212	D₄₇	—	2	2	no	—
213	D₄₇	—	4	4	no	—
214	C₂×#135	—	47	1	no	—
215	C₄×#41	—	47	2	no	—
216	C₈×Q₈	—	47	2	no	—
217	C₈×Q₈	C₂×D₄₇	1	2	yes	—
218	C₄×Q₁₆	—	47	1	no	—
219	C₄×Q₁₆	C₂×D₄₇	1	1	yes	characteristic
220	C₄×SD₁₆	—	47	2	no	—
221	C₄×SD₁₆	—	47	2	no	—
222	C₄×D₈	—	47	1	no	—
223	C₄×D₈	—	47	1	no	—
224	C₈×D₄	—	47	2	no	—
225	C₈×D₄	—	47	2	no	—
226	C₈×D₄	—	94	2	no	—
227	C₈×D₄	—	94	2	no	—
228	#431	—	47	2	no	—
229	#431	—	94	2	no	—
230	#427	—	47	1	no	—
231	#416	—	47	2	no	—
232	C₂×C₄×C₈	—	47	1	no	—
233	C₂×C₄×C₈	—	47	1	no	—
234	C₂×C₄×C₈	—	47	1	no	—
235	C₂×C₄×C₈	—	94	2	no	—
236	#335	—	47	1	no	—
237	#335	C₂×D₄₇	1	1	yes	characteristic
238	#334	—	47	2	no	—
239	Q₈⋊C₈	—	47	2	no	—
240	Q₈⋊C₈	C₂×D₄₇	1	2	yes	—
241	D₄⋊C₈	—	47	2	no	—
242	D₄⋊C₈	—	47	2	no	—
243	C₈²	—	47	1	no	—
244	C₈²	—	47	1	no	—
245	C₈²	—	47	1	no	—
246	C₈²	C₂×D₄₇	1	1	yes	characteristic
247	C₄₇	C₈×#135	1	1	yes	characteristic, complemented, Sylow
248	C₂×#41	—	47	2	no	—
249	#135	—	47	8	no	—
250	C₂×Q₁₆	C₄×D₄₇	1	1	yes	characteristic
251	C₂×SD₁₆	—	47	2	no	—
252	C₂×D₈	—	47	1	no	—
253	C₂²×C₈	—	47	1	no	—
254	C₂²×C₈	—	47	1	no	—
255	C₂²×C₈	—	47	1	no	—
256	C₂²×C₈	—	47	1	no	—
257	C₂²×C₈	—	94	2	no	—
258	C₂²×C₈	—	94	1	no	—
259	C₂²×C₈	—	94	2	no	—
260	C₄×Q₈	—	47	2	no	—
261	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
262	C₄×D₄	—	47	2	no	—
263	C₄×D₄	—	47	2	no	—
264	C₄×D₄	—	94	2	no	—
265	C₄×D₄	—	94	2	no	—
266	#117	—	47	2	no	—
267	#117	—	94	2	no	—
268	C₂×C₄²	—	47	1	no	—
269	C₂×C₄²	—	94	2	no	—
270	#107	—	47	1	no	—
271	#107	C₄×D₄₇	1	1	yes	characteristic
272	#106	—	47	2	no	—
273	C₄⋊C₈	—	2	2	no	—
274	C₄⋊C₈	—	47	2	no	—
275	C₄⋊C₈	—	94	2	no	—
276	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
277	#103	—	47	2	no	—
278	#103	C₄×D₄₇	1	2	yes	—
279	#102	—	47	2	no	—
280	#102	—	47	2	no	—
281	C₂²⋊C₈	—	94	2	no	—
282	C₂²⋊C₈	—	94	2	no	—
283	C₂²⋊C₈	—	94	2	no	—
284	C₄×C₈	—	2	2	no	—
285	C₄×C₈	—	47	1	no	—
286	C₄×C₈	—	47	1	no	—
287	C₄×C₈	—	47	1	no	—
288	C₄×C₈	—	47	1	no	—
289	C₄×C₈	—	47	1	no	—
290	C₄×C₈	—	47	1	no	—
291	C₄×C₈	—	47	1	no	—
292	C₄×C₈	—	94	2	no	—
293	C₄×C₈	—	94	1	no	—
294	C₄×C₈	—	94	2	no	—
295	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
296	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
297	C₄×C₈	C₂²×D₄₇	1	1	yes	characteristic
298	#41	—	47	8	no	—
299	#41	—	94	4	no	—
300	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
301	C₂×D₄	—	47	2	no	—
302	C₂×D₄	—	94	2	no	—
303	C₂²×C₄	—	47	1	no	—
304	C₂²×C₄	—	47	1	no	—
305	C₂²×C₄	—	47	1	no	—
306	C₂²×C₄	—	94	2	no	—
307	C₂²×C₄	—	94	2	no	—
308	C₂²×C₄	—	94	2	no	—
309	Q₁₆	C₈×D₄₇	1	4	yes	complemented
310	SD₁₆	—	47	8	no	—
311	D₈	—	47	4	no	—
312	C₂×C₈	—	2	1	no	—
313	C₂×C₈	—	2	2	no	—
314	C₂×C₈	—	47	1	no	—
315	C₂×C₈	—	47	1	no	—
316	C₂×C₈	—	47	4	no	—
317	C₂×C₈	—	47	1	no	—
318	C₂×C₈	—	47	1	no	—
319	C₂×C₈	—	94	2	no	—
320	C₂×C₈	—	94	2	no	—
321	C₂×C₈	—	94	4	no	—
322	C₂×C₈	—	94	1	no	—
323	C₂×C₈	—	94	2	no	—
324	C₂×C₈	—	94	2	no	—
325	C₂×C₈	—	188	4	no	—
326	C₂×C₈	—	188	4	no	—
327	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
328	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
329	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
330	C₂×C₈	D₄×D₄₇	1	1	yes	characteristic
331	C₄⋊C₄	—	2	2	no	—
332	C₄⋊C₄	—	47	2	no	—
333	C₄⋊C₄	—	94	2	no	—
334	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
335	C₂²⋊C₄	—	94	2	no	—
336	C₂²⋊C₄	—	94	2	no	—
337	C₂²⋊C₄	—	94	2	no	—
338	C₄²	—	2	2	no	—
339	C₄²	—	47	1	no	—
340	C₄²	—	47	1	no	—
341	C₄²	—	47	1	no	—
342	C₄²	—	94	2	no	—
343	C₄²	—	94	2	no	—
344	C₄²	C₂³×D₄₇	1	1	yes	characteristic
345	C₂³	—	47	1	no	—
346	C₂³	—	94	2	no	—
347	Q₈	—	2	2	no	—
348	Q₈	C₂×C₈×D₄₇	1	4	yes	—
349	D₄	—	47	4	no	—
350	D₄	—	94	8	no	—
351	D₄	—	94	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	47	1	no	—
355	C₂×C₄	—	47	1	no	—
356	C₂×C₄	—	47	2	no	—
357	C₂×C₄	—	47	2	no	—
358	C₂×C₄	—	47	1	no	—
359	C₂×C₄	—	94	2	no	—
360	C₂×C₄	—	94	8	no	—
361	C₂×C₄	—	94	1	no	—
362	C₂×C₄	—	94	1	no	—
363	C₂×C₄	—	94	2	no	—
364	C₂×C₄	—	188	4	no	—
365	C₂×C₄	—	188	2	no	—
366	C₂×C₄	—	188	2	no	—
367	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
368	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
369	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
370	C₈	—	2	2	no	—
371	C₈	—	2	1	no	—
372	C₈	—	2	1	no	—
373	C₈	—	4	2	no	—
374	C₈	—	47	2	no	—
375	C₈	—	47	2	no	—
376	C₈	—	94	2	no	—
377	C₈	—	94	1	no	—
378	C₈	—	94	1	no	—
379	C₈	—	188	2	no	—
380	C₈	C₂×C₈×D₄₇	1	2	yes	—
381	C₈	#13094047	1	2	yes	direct product factor
382	C₂²	—	47	2	no	—
383	C₂²	—	94	1	no	—
384	C₂²	—	94	1	no	—
385	C₂²	—	94	4	no	—
386	C₂²	—	188	2	no	—
387	C₂²	—	188	2	no	—
388	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
389	C₄	—	2	1	no	—
390	C₄	—	2	4	no	—
391	C₄	—	4	2	no	—
392	C₄	—	47	2	no	—
393	C₄	—	47	2	no	—
394	C₄	—	94	1	no	—
395	C₄	—	188	2	no	—
396	C₄	C₂²×C₈×D₄₇	1	1	yes	characteristic
397	C₄	#131×D₄₇	1	1	yes	characteristic
398	C₄	#135×D₄₇	1	1	yes	characteristic
399	C₄	C₂×#13094047	1	1	yes	characteristic
400	C₂	—	94	2	no	—
401	C₂	—	188	4	no	—
402	C₂	C₈×D₄×D₄₇	1	1	yes	characteristic
403	C₂	C₄×#13094047	1	1	yes	characteristic
404	C₂	#443×D₄₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	D₄×D₄₇
commutator	C₄×C₄₇	C₂³×C₈
Frattini	C₄²	C₂³×D₄₇
Fitting	C₈×Q₁₆×C₄₇	C₂
socle	C₂²×C₄₇	C₂×C₄×D₄
prime radical	C₂×#13094047	C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₈×Q₁₆	D₄₇
hypocenter	C₄₇	C₈×#135
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₄×C₈ ◁ C₈×Q₁₆

Complements

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

N	H ≅ G/N	type
1. C₈×#10625354	C₂	semidirect
3. Q₁₆×C₄₇⋊C₈	C₂	semidirect
4. C₈×#10625336	C₂	semidirect
5. #20242185	C₂	semidirect
6. C₈×D₃₇₆	C₂	semidirect
7. #20242182	C₂	semidirect
8. #20242135	C₂	semidirect
9. #20241769	C₂	semidirect
10. C₈²×D₄₇	C₂	semidirect
11. C₈×Q₁₆×C₄₇	C₂	semidirect
46. #13094047	C₈	direct (N × H)
97. #10625354	C₂×C₈	semidirect
106. Q₁₆×C₄₇	C₂×C₈	semidirect
117. #10625336	C₂×C₈	semidirect
134. D₃₇₆	C₂×C₈	semidirect
141. C₈×D₄₇	C₂×C₈	semidirect
172. C₈×C₄₇	#135	semidirect
178. C₄₇⋊C₈	#135	semidirect
201. C₈×Q₁₆	D₄₇	semidirect
247. C₄₇	C₈×#135	semidirect
309. Q₁₆	C₈×D₄₇	semidirect
381. C₈	#13094047	direct (N × H)

Maximal subgroups

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

subgroup	index
C₈×#10625354	2
C₄×#13094047	2
Q₁₆×C₄₇⋊C₈	2
C₈×#10625336	2
#20242185	2
C₈×D₃₇₆	2
#20242182	2
#20242135	2
#20241769	2
C₈²×D₄₇	2
C₈×Q₁₆×C₄₇	2
C₈×#135	47

Subgroups — C8×#13094047 #26185656

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#13094047 #26185656