Subgroups — C₂×#20242203 #26185666

Order 12032.

806 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×Q₈×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₄×#10625336	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689188	C₂	1	1	yes	maximal, characteristic
4	#20242203	C₂	1	8	yes	maximal, direct product factor
5	C₂×#15688875	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15688852	C₂	1	1	yes	maximal, characteristic
7	C₂×#15688845	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₄₇×Q₈⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×#10625336	C₄	1	1	yes	characteristic
10	C₂²×C₈×D₄₇	—	2	1	no	—
11	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
12	Q₈×C₄₇⋊C₈	—	2	2	no	—
13	Q₈×C₄₇⋊C₈	C₂²	1	4	yes	complemented
14	C₄×#10625336	C₄	1	4	yes	—
15	C₄×#10625336	C₂²	1	4	yes	—
16	#15689188	—	2	2	no	—
17	#15689188	C₂²	1	4	yes	—
18	C₂×#13093955	C₄	1	1	yes	characteristic
19	C₂×C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
20	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×#13093948	C₄	1	1	yes	characteristic
22	C₂×#13093944	C₄	1	1	yes	characteristic
23	C₂×(C₂×D₄₇)⋊C₈	—	2	1	no	—
24	C₂×C₄×C₄₇⋊C₈	—	2	1	no	—
25	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
27	#15688875	C₂²	1	4	yes	complemented
28	#15688852	C₂²	1	4	yes	—
29	#15688845	C₂²	1	4	yes	complemented
30	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
31	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
33	C₄₇×Q₈⋊C₈	C₂²	1	4	yes	complemented
34	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₄×D₄₇	—	2	1	no	—
36	C₂×#10625336	C₈	1	8	yes	complemented
37	C₂×#10625336	C₂×C₄	1	4	yes	—
38	C₂²×C₄₇⋊C₈	—	2	1	no	—
39	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
40	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
41	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
42	C₂²×C₄₇⋊C₈	D₄	1	1	yes	characteristic
43	C₂×C₈×D₄₇	—	2	4	no	—
44	C₂×C₈×D₄₇	—	4	4	no	—
45	C₄×D₁₈₈	—	2	1	no	—
46	C₄×D₁₈₈	—	2	1	no	—
47	C₄×D₁₈₈	C₂×C₄	1	2	yes	—
48	C₄×D₁₈₈	C₂³	1	2	yes	—
49	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×(C₂×D₄₇)⋊C₄	—	2	1	no	—
51	#13093955	C₂×C₄	1	4	yes	—
52	C₄⋊(C₄₇⋊C₈)	—	2	1	no	—
53	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
54	C₄⋊(C₄₇⋊C₈)	C₂³	1	2	yes	—
55	#13093948	C₂×C₄	1	4	yes	—
56	#13093944	C₂×C₄	1	4	yes	—
57	(C₂×D₄₇)⋊C₈	—	2	4	no	—
58	C₄×C₄₇⋊C₈	—	2	4	no	—
59	C₄×C₄₇⋊C₈	C₂×C₄	1	2	yes	—
60	C₄×C₄₇⋊C₈	D₄	1	2	yes	—
61	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
62	C₄×C₄₇⋊C₈	C₂³	1	2	yes	—
63	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₈×C₄₇	—	2	1	no	—
65	C₂²×C₈×C₄₇	—	2	1	no	—
66	C₄×Q₈×C₄₇	—	2	1	no	—
67	C₄×Q₈×C₄₇	—	2	1	no	—
68	C₄×Q₈×C₄₇	C₂×C₄	1	2	yes	—
69	C₄×Q₈×C₄₇	C₂³	1	2	yes	—
70	C₂×C₄⋊C₄×C₄₇	—	2	1	no	—
71	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂×C₄²×C₄₇	—	2	1	no	—
73	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
74	C₄⋊C₈×C₄₇	—	2	1	no	—
75	C₄⋊C₈×C₄₇	C₂³	1	2	yes	—
76	C₄×C₈×C₄₇	—	2	1	no	—
77	C₄×C₈×C₄₇	C₂³	1	2	yes	—
78	C₂³×D₄₇	—	2	1	no	—
79	C₂×Q₈×C₄₇	—	2	1	no	—
80	C₂×Q₈×C₄₇	—	2	2	no	—
81	C₂×Q₈×C₄₇	C₂×C₈	1	4	yes	complemented
82	C₂×Q₈×C₄₇	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₄₇	—	2	1	no	—
84	C₂²×C₄×C₄₇	—	2	1	no	—
85	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₇	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₇	#41	1	1	yes	characteristic
88	C₂²×Dic₄₇	—	2	1	no	—
89	C₂×D₁₈₈	—	2	1	no	—
90	C₂×D₁₈₈	—	2	2	no	—
91	C₂×D₁₈₈	C₂×C₈	1	4	yes	—
92	C₂×D₁₈₈	C₂²×C₄	1	2	yes	—
93	C₂×C₄×D₄₇	—	2	2	no	—
94	C₂×C₄×D₄₇	—	2	2	no	—
95	C₂×C₄×D₄₇	—	4	2	no	—
96	C₂×C₄×D₄₇	—	4	2	no	—
97	C₂×C₈×C₄₇	—	2	2	no	—
98	C₂×C₈×C₄₇	—	2	2	no	—
99	C₂×C₈×C₄₇	—	4	2	no	—
100	C₂×C₈×C₄₇	—	4	2	no	—
101	C₄⋊C₄×C₄₇	—	2	2	no	—
102	C₄⋊C₄×C₄₇	—	2	1	no	—
103	C₄⋊C₄×C₄₇	—	2	2	no	—
104	C₄⋊C₄×C₄₇	C₂²×C₄	1	2	yes	—
105	C₄²×C₄₇	—	2	2	no	—
106	C₄²×C₄₇	—	2	2	no	—
107	C₄²×C₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₄²×C₄₇	C₂×D₄	1	1	yes	characteristic
109	C₄²×C₄₇	#41	1	1	yes	characteristic
110	C₄²×C₄₇	C₂⁴	1	1	yes	characteristic
111	#10625336	C₂×C₈	1	16	yes	complemented
112	(C₂×D₄₇)⋊C₄	—	2	2	no	—
113	(C₂×D₄₇)⋊C₄	—	2	2	no	—
114	C₄⋊Dic₄₇	—	2	1	no	—
115	C₄⋊Dic₄₇	C₂²×C₄	1	2	yes	—
116	C₂×C₄₇⋊C₈	—	2	2	no	—
117	C₂×C₄₇⋊C₈	—	2	2	no	—
118	C₂×C₄₇⋊C₈	—	2	2	no	—
119	C₂×C₄₇⋊C₈	—	2	2	no	—
120	C₂×C₄₇⋊C₈	—	4	2	no	—
121	C₂×C₄₇⋊C₈	C₂×C₈	1	4	yes	complemented
122	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
123	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
124	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
125	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
126	C₈×D₄₇	—	4	8	no	—
127	C₂³×C₄₇	C₄×D₄	1	1	yes	characteristic
128	C₂²×D₄₇	—	2	2	no	—
129	C₂²×D₄₇	—	2	4	no	—
130	C₂²×D₄₇	—	4	2	no	—
131	C₂²×D₄₇	—	4	2	no	—
132	Q₈×C₄₇	—	2	2	no	—
133	Q₈×C₄₇	—	2	4	no	—
134	Q₈×C₄₇	C₂²×C₈	1	4	yes	complemented
135	C₂×C₄×C₄₇	—	2	2	no	—
136	C₂×C₄×C₄₇	—	2	4	no	—
137	C₂×C₄×C₄₇	—	2	2	no	—
138	C₂×C₄×C₄₇	—	2	2	no	—
139	C₂×C₄×C₄₇	—	4	2	no	—
140	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
142	C₂×C₄×C₄₇	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
144	C₂×C₄×C₄₇	#131	1	2	yes	—
145	C₂×C₄×C₄₇	AGL(1,ℤ/8)	1	2	yes	—
146	C₂×C₄×C₄₇	#137	1	2	yes	—
147	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
148	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
150	C₂×Dic₄₇	—	2	2	no	—
151	C₂×Dic₄₇	—	4	2	no	—
152	D₁₈₈	—	2	2	no	—
153	D₁₈₈	—	2	4	no	—
154	D₁₈₈	C₂²×C₈	1	4	yes	—
155	C₄×D₄₇	—	4	2	no	—
156	C₄×D₄₇	—	4	2	no	—
157	C₄×D₄₇	—	4	4	no	—
158	C₈×C₄₇	—	4	2	no	—
159	C₈×C₄₇	—	4	2	no	—
160	C₄₇⋊C₈	—	2	2	no	—
161	C₄₇⋊C₈	—	2	2	no	—
162	C₄₇⋊C₈	—	2	2	no	—
163	C₄₇⋊C₈	—	4	2	no	—
164	C₄₇⋊C₈	C₂²×C₈	1	4	yes	complemented
165	C₂×SD₁₆⋊C₈	—	47	1	no	maximal, Sylow
166	C₂²×C₄₇	C₈×D₄	1	2	yes	—
167	C₂²×C₄₇	#440	1	2	yes	—
168	C₂²×C₄₇	#444	1	2	yes	—
169	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
170	C₂×D₄₇	—	2	4	no	—
171	C₂×D₄₇	—	4	8	no	—
172	C₂×D₄₇	—	4	2	no	—
173	C₂×D₄₇	—	4	2	no	—
174	C₄×C₄₇	—	2	4	no	—
175	C₄×C₄₇	—	2	1	no	—
176	C₄×C₄₇	—	2	1	no	—
177	C₄×C₄₇	—	4	2	no	—
178	C₄×C₄₇	C₈×D₄	1	2	yes	—
179	C₄×C₄₇	#440	1	2	yes	—
180	C₄×C₄₇	C₂³×C₈	1	1	yes	characteristic
181	C₄×C₄₇	C₂×#131	1	1	yes	characteristic
182	C₄×C₄₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
183	C₄×C₄₇	C₂×#137	1	1	yes	characteristic
184	Dic₄₇	—	4	2	no	—
185	C₂×C₈×Q₈	—	47	1	no	—
186	C₂×C₄×SD₁₆	—	47	1	no	—
187	C₂×C₈×D₄	—	47	1	no	—
188	SD₁₆⋊C₈	—	47	8	no	—
189	C₂×#335	—	47	1	no	—
190	C₂×Q₈⋊C₈	D₄₇	1	1	yes	characteristic, complemented
191	C₂×D₄⋊C₈	—	47	1	no	—
192	C₂×#322	—	47	1	no	—
193	C₂×C₄₇	SD₁₆⋊C₈	1	4	yes	complemented
194	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
195	C₂×C₄₇	C₂×#440	1	1	yes	characteristic
196	C₂×C₄₇	C₂×#444	1	1	yes	characteristic
197	D₄₇	—	4	4	no	—
198	C₂²×SD₁₆	—	47	1	no	—
199	C₂³×C₈	—	94	1	no	—
200	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
201	C₂×C₄×D₄	—	47	1	no	—
202	C₈×Q₈	—	47	4	no	—
203	C₈×Q₈	—	94	2	no	—
204	C₄×SD₁₆	—	47	4	no	—
205	C₄×SD₁₆	—	47	4	no	—
206	C₈×D₄	—	47	4	no	—
207	C₈×D₄	—	94	2	no	—
208	C₂×#106	—	47	1	no	—
209	C₂×C₄⋊C₈	—	47	1	no	—
210	C₂×C₄⋊C₈	—	94	1	no	—
211	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
212	C₂×#103	—	47	1	no	—
213	C₂×#102	—	47	1	no	—
214	C₂×C₂²⋊C₈	—	94	1	no	—
215	C₂×C₄×C₈	—	47	1	no	—
216	C₂×C₄×C₈	—	47	1	no	—
217	C₂×C₄×C₈	—	94	1	no	—
218	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
219	#335	—	47	4	no	—
220	Q₈⋊C₈	C₂×D₄₇	1	4	yes	complemented
221	D₄⋊C₈	—	47	4	no	—
222	#322	—	47	4	no	—
223	C₄₇	C₂×SD₁₆⋊C₈	1	1	yes	characteristic, complemented, Sylow
224	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
225	C₂²×D₄	—	47	1	no	—
226	C₂³×C₄	—	94	1	no	—
227	C₂×SD₁₆	—	47	8	no	—
228	C₂×SD₁₆	—	47	4	no	—
229	C₂²×C₈	—	2	1	no	—
230	C₂²×C₈	—	2	1	no	—
231	C₂²×C₈	—	47	1	no	—
232	C₂²×C₈	—	47	1	no	—
233	C₂²×C₈	—	47	1	no	—
234	C₂²×C₈	—	47	1	no	—
235	C₂²×C₈	—	94	4	no	—
236	C₂²×C₈	—	94	1	no	—
237	C₂²×C₈	—	188	4	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	—	2	1	no	—
240	C₄×Q₈	C₄×D₄₇	1	2	yes	—
241	C₄×Q₈	C₂²×D₄₇	1	2	yes	—
242	C₄×D₄	—	47	2	no	—
243	C₄×D₄	—	47	2	no	—
244	C₄×D₄	—	94	1	no	—
245	C₄×D₄	—	94	1	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	47	1	no	—
248	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
249	C₂×C₂²⋊C₄	—	94	1	no	—
250	C₂×C₄²	—	2	1	no	—
251	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
252	#106	—	47	4	no	—
253	C₄⋊C₈	—	2	1	no	—
254	C₄⋊C₈	—	47	2	no	—
255	C₄⋊C₈	—	94	4	no	—
256	C₄⋊C₈	—	94	1	no	—
257	C₄⋊C₈	C₂²×D₄₇	1	2	yes	—
258	#103	—	47	4	no	—
259	#102	—	47	4	no	—
260	C₂²⋊C₈	—	94	4	no	—
261	C₄×C₈	—	2	1	no	—
262	C₄×C₈	—	47	2	no	—
263	C₄×C₈	—	47	2	no	—
264	C₄×C₈	—	47	2	no	—
265	C₄×C₈	—	47	2	no	—
266	C₄×C₈	—	94	4	no	—
267	C₄×C₈	C₂²×D₄₇	1	2	yes	—
268	C₂⁴	—	94	1	no	—
269	C₂×Q₈	—	2	1	no	—
270	C₂×Q₈	—	2	2	no	—
271	C₂×Q₈	C₈×D₄₇	1	4	yes	complemented
272	C₂×Q₈	C₂×C₄×D₄₇	1	2	yes	—
273	C₂×D₄	—	47	4	no	—
274	C₂×D₄	—	47	2	no	—
275	C₂×D₄	—	94	1	no	—
276	C₂×D₄	—	94	2	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	2	1	no	—
279	C₂²×C₄	—	94	1	no	—
280	C₂²×C₄	—	94	2	no	—
281	C₂²×C₄	—	94	2	no	—
282	C₂²×C₄	—	188	2	no	—
283	C₂²×C₄	—	188	2	no	—
284	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
285	C₂²×C₄	D₄×D₄₇	1	1	yes	characteristic
286	C₂²×C₄	#10625352	1	1	yes	characteristic
287	SD₁₆	—	47	16	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	2	no	—
290	C₂×C₈	—	4	2	no	—
291	C₂×C₈	—	4	2	no	—
292	C₂×C₈	—	47	4	no	—
293	C₂×C₈	—	47	2	no	—
294	C₂×C₈	—	47	2	no	—
295	C₂×C₈	—	47	2	no	—
296	C₂×C₈	—	47	2	no	—
297	C₂×C₈	—	94	2	no	—
298	C₂×C₈	—	94	2	no	—
299	C₂×C₈	—	94	2	no	—
300	C₂×C₈	—	94	2	no	—
301	C₂×C₈	—	188	8	no	—
302	C₂×C₈	—	188	2	no	—
303	C₄⋊C₄	—	2	2	no	—
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	2	2	no	—
306	C₄⋊C₄	—	47	2	no	—
307	C₄⋊C₄	—	94	1	no	—
308	C₄⋊C₄	C₂×C₄×D₄₇	1	2	yes	—
309	C₂²⋊C₄	—	94	2	no	—
310	C₂²⋊C₄	—	94	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	C₂×C₄×D₄₇	1	1	yes	characteristic
314	C₄²	D₄×D₄₇	1	1	yes	characteristic
315	C₄²	#10625352	1	1	yes	characteristic
316	C₄²	C₂³×D₄₇	1	1	yes	characteristic
317	C₂³	—	94	2	no	—
318	C₂³	—	94	4	no	—
319	C₂³	—	188	2	no	—
320	C₂³	—	188	2	no	—
321	C₂³	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
322	Q₈	—	2	2	no	—
323	Q₈	—	2	4	no	—
324	Q₈	C₂×C₈×D₄₇	1	4	yes	complemented
325	D₄	—	47	4	no	—
326	D₄	—	94	2	no	—
327	D₄	—	94	4	no	—
328	C₂×C₄	—	2	2	no	—
329	C₂×C₄	—	2	2	no	—
330	C₂×C₄	—	2	4	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	4	2	no	—
333	C₂×C₄	—	94	2	no	—
334	C₂×C₄	—	188	2	no	—
335	C₂×C₄	—	188	4	no	—
336	C₂×C₄	—	188	2	no	—
337	C₂×C₄	—	188	2	no	—
338	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
339	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
340	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
341	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
342	C₂×C₄	#13094032	1	2	yes	—
343	C₂×C₄	#13094051	1	2	yes	—
344	C₂×C₄	#13094056	1	2	yes	—
345	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
346	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
347	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
348	C₈	—	4	2	no	—
349	C₈	—	4	2	no	—
350	C₈	—	47	4	no	—
351	C₈	—	94	2	no	—
352	C₈	—	94	2	no	—
353	C₈	—	94	2	no	—
354	C₈	—	188	2	no	—
355	C₂²	—	94	4	no	—
356	C₂²	—	188	2	no	—
357	C₂²	—	188	8	no	—
358	C₂²	—	188	2	no	—
359	C₂²	(C₂²⋊D₄₇)⋊C₈	1	2	yes	—
360	C₂²	#15689226	1	2	yes	—
361	C₂²	#15689242	1	2	yes	—
362	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
363	C₄	—	2	1	no	—
364	C₄	—	2	1	no	—
365	C₄	—	2	4	no	—
366	C₄	—	4	2	no	—
367	C₄	—	188	2	no	—
368	C₄	(C₂²⋊D₄₇)⋊C₈	1	2	yes	—
369	C₄	#15689226	1	2	yes	—
370	C₄	C₂²×C₈×D₄₇	1	1	yes	characteristic
371	C₄	C₂×#13094032	1	1	yes	characteristic
372	C₄	C₂×#13094051	1	1	yes	characteristic
373	C₄	C₂×#13094056	1	1	yes	characteristic
374	C₂	—	188	4	no	—
375	C₂	#20242203	1	4	yes	direct product factor
376	C₂	C₂×(C₂²⋊D₄₇)⋊C₈	1	1	yes	characteristic
377	C₂	C₂×#15689226	1	1	yes	characteristic
378	C₂	C₂×#15689242	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	D₄×D₄₇
commutator	C₄×C₄₇	C₂³×C₈
Frattini	C₄²	C₂³×D₄₇
Fitting	C₂×C₄₇×Q₈⋊C₈	C₂
socle	C₂³×C₄₇	C₄×D₄
prime radical	C₂²×D₁₈₈	C₂×C₄
cosocle	C₄²×C₄₇	C₂⁴
hypercenter	C₂×Q₈⋊C₈	D₄₇
hypocenter	C₄₇	C₂×SD₁₆⋊C₈
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×Q₈⋊C₈

Complements

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

N	H ≅ G/N	type
1. C₂×Q₈×C₄₇⋊C₈	C₂	semidirect
4. #20242203	C₂	direct (N × H)
5. C₂×#15688875	C₂	semidirect
7. C₂×#15688845	C₂	semidirect
8. C₂×C₄₇×Q₈⋊C₈	C₂	semidirect
13. Q₈×C₄₇⋊C₈	C₂²	semidirect
27. #15688875	C₂²	semidirect
29. #15688845	C₂²	semidirect
33. C₄₇×Q₈⋊C₈	C₂²	semidirect
36. C₂×#10625336	C₈	semidirect
81. C₂×Q₈×C₄₇	C₂×C₈	semidirect
111. #10625336	C₂×C₈	semidirect
121. C₂×C₄₇⋊C₈	C₂×C₈	semidirect
134. Q₈×C₄₇	C₂²×C₈	semidirect
164. C₄₇⋊C₈	C₂²×C₈	semidirect
190. C₂×Q₈⋊C₈	D₄₇	semidirect
193. C₂×C₄₇	SD₁₆⋊C₈	semidirect
220. Q₈⋊C₈	C₂×D₄₇	semidirect
223. C₄₇	C₂×SD₁₆⋊C₈	semidirect
271. C₂×Q₈	C₈×D₄₇	semidirect
324. Q₈	C₂×C₈×D₄₇	semidirect
375. C₂	#20242203	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×Q₈×C₄₇⋊C₈	2
C₂×C₄×#10625336	2
C₂×#15689188	2
#20242203	2
C₂×#15688875	2
C₂×#15688852	2
C₂×#15688845	2
C₂×C₄₇×Q₈⋊C₈	2
C₂×SD₁₆⋊C₈	47

Subgroups — C2×#20242203 #26185666

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#20242203 #26185666