Subgroups — C₈×#13094003 #26223692

Order 12032.

990 conjugacy classes of subgroups.

The subgroup lattice has 496 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#13094003	C₂	1	1	yes	maximal, characteristic
3	#20244324	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244106	C₂	1	1	yes	maximal, characteristic, complemented
5	#20243945	C₂	1	2	yes	maximal, complemented
6	#20243566	C₂	1	2	yes	maximal
7	#20243368	C₂	1	1	yes	maximal, characteristic
8	C₈×Dic₄₇⋊C₄	C₂	1	2	yes	maximal, complemented
9	C₈×C₄⋊Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×C₂²⋊Dic₄₇	C₂	1	2	yes	maximal
11	C₂²×C₄×C₈×C₄₇	C₂	1	1	yes	maximal, characteristic
12	C₂×#13094003	C₄	1	1	yes	characteristic
13	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
14	C₈×Dic₉₄	—	2	4	no	—
15	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
17	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
18	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
19	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
20	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
21	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
22	#15689029	C₄	1	1	yes	characteristic
23	#15689021	C₄	1	1	yes	characteristic
24	#15689007	C₄	1	2	yes	—
25	#15688996	C₄	1	2	yes	—
26	#15688983	C₄	1	1	yes	characteristic
27	C₄×Dic₄₇⋊C₄	C₂²	1	2	yes	—
28	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
29	C₄×C₂²⋊Dic₄₇	C₂²	1	2	yes	—
30	#15688878	C₂²	1	2	yes	—
31	#15688877	C₂²	1	2	yes	—
32	#15688877	C₂²	1	2	yes	—
33	#15688877	C₂²	1	2	yes	—
34	#15688877	C₂²	1	2	yes	—
35	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
36	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
37	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
38	C₂×C₄×C₈×C₄₇	—	2	4	no	—
39	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
40	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
43	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
45	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
46	#13094003	C₈	1	8	yes	direct product factor
47	C₄×Dic₉₄	—	2	2	no	—
48	C₄×Dic₉₄	—	2	2	no	—
49	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
52	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
53	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
54	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
55	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
56	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
57	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
58	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
59	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
60	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
61	Dic₄₇⋊C₈	—	2	4	no	—
62	Dic₄₇⋊C₈	—	2	4	no	—
63	C₂²⋊(C₄₇⋊C₈)	—	2	4	no	—
64	C₈×Dic₄₇	—	2	4	no	—
65	C₈×Dic₄₇	—	2	4	no	—
66	C₄₇⋊#95	C₂×C₄	1	2	yes	—
67	C₄₇⋊#95	C₂×C₄	1	2	yes	—
68	C₄₇⋊#95	C₂×C₄	1	2	yes	—
69	C₄₇⋊#95	C₂×C₄	1	2	yes	—
70	C₄₇⋊#95	C₂×C₄	1	2	yes	—
71	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
72	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
73	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
74	C₂²×C₈×C₄₇	—	2	2	no	—
75	C₂²×C₈×C₄₇	—	2	2	no	—
76	C₂²×C₈×C₄₇	—	2	2	no	—
77	C₂²×C₈×C₄₇	—	2	2	no	—
78	C₂²×C₈×C₄₇	—	2	2	no	—
79	C₂²×C₈×C₄₇	Q₈	1	4	yes	complemented
80	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
81	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
82	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
83	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
84	C₂×C₄²×C₄₇	—	2	2	no	—
85	C₂×C₄²×C₄₇	—	2	2	no	—
86	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	C₄×C₈×C₄₇	—	2	2	no	—
91	C₄×C₈×C₄₇	—	2	2	no	—
92	C₄×C₈×C₄₇	—	2	2	no	—
93	C₄×C₈×C₄₇	D₄	1	4	yes	—
94	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	—	2	2	no	—
96	C₂²×C₄×C₄₇	—	2	2	no	—
97	C₂²×C₄×C₄₇	—	2	2	no	—
98	C₂²×C₄×C₄₇	—	2	2	no	—
99	C₂²×C₄×C₄₇	—	2	2	no	—
100	C₂²×C₄×C₄₇	—	2	1	no	—
101	C₂²×C₄×C₄₇	—	2	1	no	—
102	C₂²×C₄×C₄₇	—	2	1	no	—
103	C₂²×C₄×C₄₇	—	2	1	no	—
104	C₂²×C₄×C₄₇	C₂×C₈	1	4	yes	—
105	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
108	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
109	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
110	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
111	C₂²×C₄×C₄₇	#41	1	2	yes	—
112	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
113	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
114	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
115	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
116	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
117	C₂×Dic₉₄	—	2	2	no	—
118	C₂×Dic₉₄	—	2	2	no	—
119	C₂×Dic₉₄	C₂×C₈	1	4	yes	complemented
120	C₂×C₈×C₄₇	—	2	8	no	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	1	no	—
123	C₂×C₈×C₄₇	—	2	1	no	—
124	C₂×C₈×C₄₇	—	2	1	no	—
125	C₂×C₈×C₄₇	—	2	1	no	—
126	C₂×C₈×C₄₇	—	2	1	no	—
127	C₂×C₈×C₄₇	—	2	8	no	—
128	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
129	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
130	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
131	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
132	C₂×C₈×C₄₇	#41	1	2	yes	—
133	C₂×C₈×C₄₇	#41	1	2	yes	—
134	C₄²×C₄₇	—	2	2	no	—
135	C₄²×C₄₇	—	2	2	no	—
136	C₄²×C₄₇	—	2	1	no	—
137	C₄²×C₄₇	—	2	1	no	—
138	C₄²×C₄₇	C₂×D₄	1	2	yes	—
139	C₄²×C₄₇	#41	1	2	yes	—
140	C₂²⋊Dic₄₇	—	2	4	no	—
141	C₂²⋊Dic₄₇	C₂×C₈	1	8	yes	—
142	C₄⋊Dic₄₇	—	2	2	no	—
143	C₄⋊Dic₄₇	—	2	2	no	—
144	C₄⋊Dic₄₇	C₂×C₈	1	4	yes	complemented
145	Dic₄₇⋊C₄	—	2	4	no	—
146	Dic₄₇⋊C₄	—	2	4	no	—
147	Dic₄₇⋊C₄	C₂×C₈	1	8	yes	complemented
148	C₄×Dic₄₇	—	2	2	no	—
149	C₄×Dic₄₇	—	2	2	no	—
150	C₄×Dic₄₇	—	2	2	no	—
151	C₄×Dic₄₇	—	2	2	no	—
152	C₂×C₄₇⋊C₈	—	2	2	no	—
153	C₂×C₄₇⋊C₈	—	2	2	no	—
154	C₂×C₄₇⋊C₈	—	2	2	no	—
155	C₂×C₄₇⋊C₈	—	2	2	no	—
156	C₂×C₄₇⋊C₈	—	2	2	no	—
157	C₂×C₄₇⋊C₈	—	2	2	no	—
158	C₂³×C₄₇	—	2	1	no	—
159	C₂³×C₄₇	—	2	1	no	—
160	C₂³×C₄₇	—	2	1	no	—
161	C₂³×C₄₇	—	2	1	no	—
162	C₂³×C₄₇	C₄×Q₈	1	2	yes	—
163	C₂³×C₄₇	C₂²×C₈	1	2	yes	—
164	C₂³×C₄₇	#131	1	2	yes	—
165	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
166	C₂×C₄×C₄₇	—	2	8	no	—
167	C₂×C₄×C₄₇	—	2	1	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	2	1	no	—
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	2	no	—
176	C₂×C₄×C₄₇	—	2	2	no	—
177	C₂×C₄×C₄₇	—	2	2	no	—
178	C₂×C₄×C₄₇	—	2	2	no	—
179	C₂×C₄×C₄₇	—	2	8	no	—
180	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
181	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
182	C₂×C₄×C₄₇	C₄×Q₈	1	2	yes	—
183	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
184	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
185	C₂×C₄×C₄₇	#131	1	2	yes	—
186	C₂×C₄×C₄₇	#131	1	2	yes	—
187	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
188	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
189	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
190	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
191	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
192	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
193	C₂×Dic₄₇	—	2	2	no	—
194	C₂×Dic₄₇	—	2	2	no	—
195	C₂×Dic₄₇	—	2	2	no	—
196	C₂×Dic₄₇	—	2	2	no	—
197	C₂×Dic₄₇	—	2	2	no	—
198	C₂×Dic₄₇	—	2	2	no	—
199	C₂×Dic₄₇	—	2	2	no	—
200	C₂×Dic₄₇	—	2	2	no	—
201	C₂×Dic₄₇	—	2	2	no	—
202	C₂×Dic₄₇	—	2	2	no	—
203	C₂×Dic₄₇	C₂²×C₈	1	4	yes	—
204	C₂×Dic₄₇	C₂²×C₈	1	4	yes	—
205	Dic₉₄	—	2	8	no	—
206	C₈×C₄₇	—	2	2	no	—
207	C₈×C₄₇	—	2	2	no	—
208	C₈×C₄₇	—	2	2	no	—
209	C₈×C₄₇	C₂²⋊Q₈	1	4	yes	complemented
210	C₄₇⋊C₈	—	4	2	no	—
211	C₄₇⋊C₈	—	4	2	no	—
212	C₈×C₂²⋊Q₈	—	47	1	no	maximal, Sylow
213	C₂²×C₄₇	—	2	2	no	—
214	C₂²×C₄₇	—	2	2	no	—
215	C₂²×C₄₇	—	2	2	no	—
216	C₂²×C₄₇	—	2	2	no	—
217	C₂²×C₄₇	—	2	2	no	—
218	C₂²×C₄₇	—	2	2	no	—
219	C₂²×C₄₇	C₈×Q₈	1	4	yes	complemented
220	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
221	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
222	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
223	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
224	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
225	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
226	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
227	C₄×C₄₇	—	2	2	no	—
228	C₄×C₄₇	—	2	2	no	—
229	C₄×C₄₇	—	2	2	no	—
230	C₄×C₄₇	—	2	2	no	—
231	C₄×C₄₇	C₈×D₄	1	4	yes	—
232	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
233	C₄×C₄₇	#525	1	1	yes	characteristic
234	C₄×C₄₇	#529	1	1	yes	characteristic
235	C₄×C₄₇	#533	1	1	yes	characteristic
236	Dic₄₇	—	2	4	no	—
237	Dic₄₇	—	2	4	no	—
238	Dic₄₇	—	4	2	no	—
239	Dic₄₇	—	4	2	no	—
240	C₂×C₈×Q₈	—	47	1	no	—
241	C₂²×C₄×C₈	D₄₇	1	1	yes	characteristic
242	C₄×C₂²⋊Q₈	—	47	1	no	—
243	#1984	—	47	1	no	—
244	#1939	—	47	1	no	—
245	#1916	—	47	2	no	—
246	#1850	—	47	2	no	—
247	#1797	—	47	1	no	—
248	C₈×C₄⋊C₄	—	47	1	no	—
249	C₈×C₄⋊C₄	—	47	2	no	—
250	C₈×C₂²⋊C₄	—	47	2	no	—
251	C₂×C₄₇	—	2	4	no	—
252	C₂×C₄₇	C₄×C₂²⋊Q₈	1	1	yes	characteristic
253	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
254	C₂×C₄₇	#2929	1	1	yes	characteristic
255	C₂×C₄₇	C₂×C₈×Q₈	1	1	yes	characteristic
256	C₂×C₄₇	#2960	1	1	yes	characteristic
257	C₂×C₄₇	C₈×#41	1	1	yes	characteristic
258	C₂×C₄₇	#2966	1	1	yes	characteristic
259	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
260	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
261	C₂×C₂²⋊Q₈	—	47	1	no	—
262	C₂×C₄×Q₈	—	47	1	no	—
263	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
264	C₈×Q₈	—	94	4	no	—
265	C₂×C₄⋊C₈	—	47	2	no	—
266	C₂×C₄⋊C₈	—	47	2	no	—
267	C₂×C₄⋊C₈	—	47	1	no	—
268	C₂×C₄⋊C₈	—	47	1	no	—
269	C₂×C₂²⋊C₈	—	47	2	no	—
270	C₂×C₄×C₈	—	2	4	no	—
271	C₂×C₄×C₈	—	47	2	no	—
272	C₂×C₄×C₈	—	47	2	no	—
273	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
274	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
275	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
276	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
277	#391	—	47	1	no	—
278	#389	—	47	1	no	—
279	#387	—	47	2	no	—
280	#385	—	47	2	no	—
281	#380	—	47	1	no	—
282	C₄×C₄⋊C₄	—	47	1	no	—
283	C₄×C₄⋊C₄	—	47	2	no	—
284	C₄×C₂²⋊C₄	—	47	2	no	—
285	#336	—	47	2	no	—
286	#336	—	47	2	no	—
287	#336	—	47	2	no	—
288	#336	—	47	2	no	—
289	#336	—	47	2	no	—
290	C₄₇	C₈×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
291	C₂²×Q₈	—	47	1	no	—
292	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
293	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
294	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
295	C₂²×C₈	—	2	2	no	—
296	C₂²×C₈	—	2	2	no	—
297	C₂²×C₈	—	2	2	no	—
298	C₂²×C₈	—	2	2	no	—
299	C₂²×C₈	—	2	2	no	—
300	C₂²×C₈	—	47	2	no	—
301	C₂²×C₈	—	47	2	no	—
302	C₂²×C₈	Dic₉₄	1	4	yes	complemented
303	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
304	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
305	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
306	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
307	C₂²⋊Q₈	—	47	8	no	—
308	C₄×Q₈	—	94	2	no	—
309	C₄×Q₈	—	94	2	no	—
310	C₂×C₄⋊C₄	—	47	2	no	—
311	C₂×C₄⋊C₄	—	47	1	no	—
312	C₂×C₄⋊C₄	—	47	2	no	—
313	C₂×C₄⋊C₄	—	47	1	no	—
314	C₂×C₄⋊C₄	—	47	2	no	—
315	C₂×C₄⋊C₄	—	47	1	no	—
316	C₂×C₂²⋊C₄	—	47	2	no	—
317	C₂×C₂²⋊C₄	—	47	2	no	—
318	C₂×C₄²	—	2	2	no	—
319	C₂×C₄²	—	2	2	no	—
320	C₂×C₄²	—	47	2	no	—
321	C₂×C₄²	—	47	2	no	—
322	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
323	C₂×C₄²	C₄×D₄₇	1	1	yes	characteristic
324	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
325	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
326	C₄⋊C₈	—	94	4	no	—
327	C₄⋊C₈	—	94	4	no	—
328	C₄⋊C₈	—	94	2	no	—
329	C₄⋊C₈	—	94	2	no	—
330	C₂²⋊C₈	—	94	4	no	—
331	C₄×C₈	—	2	2	no	—
332	C₄×C₈	—	2	2	no	—
333	C₄×C₈	—	2	2	no	—
334	C₄×C₈	—	94	4	no	—
335	C₄×C₈	—	94	4	no	—
336	C₄×C₈	C₂²⋊D₄₇	1	4	yes	—
337	#95	—	47	2	no	—
338	#95	—	47	2	no	—
339	#95	—	47	2	no	—
340	#95	—	47	2	no	—
341	#95	—	47	2	no	—
342	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
343	C₂×Q₈	—	47	4	no	—
344	C₂×Q₈	—	94	2	no	—
345	C₂×Q₈	—	94	2	no	—
346	C₂²×C₄	—	2	2	no	—
347	C₂²×C₄	—	2	2	no	—
348	C₂²×C₄	—	2	2	no	—
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	1	no	—
352	C₂²×C₄	—	2	1	no	—
353	C₂²×C₄	—	2	1	no	—
354	C₂²×C₄	—	2	1	no	—
355	C₂²×C₄	—	47	2	no	—
356	C₂²×C₄	—	47	2	no	—
357	C₂²×C₄	—	47	2	no	—
358	C₂²×C₄	—	47	2	no	—
359	C₂²×C₄	C₈×D₄₇	1	4	yes	—
360	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
361	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
362	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
363	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
364	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
365	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
366	C₂²×C₄	#10625350	1	2	yes	—
367	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
368	C₂×C₈	—	2	8	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	1	no	—
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	2	1	no	—
374	C₂×C₈	—	2	1	no	—
375	C₂×C₈	—	2	8	no	—
376	C₂×C₈	—	94	2	no	—
377	C₂×C₈	—	94	2	no	—
378	C₂×C₈	—	94	2	no	—
379	C₂×C₈	—	94	2	no	—
380	C₂×C₈	—	94	2	no	—
381	C₂×C₈	—	94	2	no	—
382	C₂×C₈	C₂×Dic₉₄	1	2	yes	—
383	C₂×C₈	C₂×Dic₉₄	1	2	yes	—
384	C₂×C₈	#10625350	1	2	yes	—
385	C₂×C₈	#10625350	1	2	yes	—
386	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
387	C₂×C₈	C₂×C₂²⋊D₄₇	1	2	yes	—
388	C₄⋊C₄	—	47	8	no	—
389	C₄⋊C₄	—	47	4	no	—
390	C₄⋊C₄	—	94	4	no	—
391	C₄⋊C₄	—	94	2	no	—
392	C₄⋊C₄	—	94	4	no	—
393	C₄⋊C₄	—	94	2	no	—
394	C₂²⋊C₄	—	47	8	no	—
395	C₂²⋊C₄	—	94	4	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	2	1	no	—
399	C₄²	—	2	1	no	—
400	C₄²	—	94	2	no	—
401	C₄²	—	94	2	no	—
402	C₄²	—	94	2	no	—
403	C₄²	—	94	2	no	—
404	C₄²	#10625350	1	2	yes	—
405	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
406	C₂³	—	2	1	no	—
407	C₂³	—	2	1	no	—
408	C₂³	—	2	1	no	—
409	C₂³	—	2	1	no	—
410	C₂³	C₄×Dic₉₄	1	2	yes	—
411	C₂³	C₂×C₈×D₄₇	1	2	yes	—
412	C₂³	#13094030	1	2	yes	—
413	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
414	Q₈	—	94	8	no	—
415	C₂×C₄	—	2	8	no	—
416	C₂×C₄	—	2	1	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	1	no	—
421	C₂×C₄	—	2	1	no	—
422	C₂×C₄	—	2	1	no	—
423	C₂×C₄	—	2	1	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	8	no	—
429	C₂×C₄	—	47	4	no	—
430	C₂×C₄	—	47	4	no	—
431	C₂×C₄	—	94	2	no	—
432	C₂×C₄	—	94	2	no	—
433	C₂×C₄	—	94	2	no	—
434	C₂×C₄	—	94	2	no	—
435	C₂×C₄	—	94	2	no	—
436	C₂×C₄	—	94	2	no	—
437	C₂×C₄	—	94	2	no	—
438	C₂×C₄	—	94	2	no	—
439	C₂×C₄	—	94	2	no	—
440	C₂×C₄	—	94	2	no	—
441	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
442	C₂×C₄	C₄×C₂²⋊D₄₇	1	2	yes	—
443	C₂×C₄	C₄×Dic₉₄	1	2	yes	—
444	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
445	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
446	C₂×C₄	#13094030	1	2	yes	—
447	C₂×C₄	#13094030	1	2	yes	—
448	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
449	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
450	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
451	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
452	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
453	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
454	C₈	—	2	2	no	—
455	C₈	—	2	2	no	—
456	C₈	—	2	2	no	—
457	C₈	—	188	2	no	—
458	C₈	—	188	2	no	—
459	C₈	#13094003	1	4	yes	direct product factor
460	C₂²	—	2	2	no	—
461	C₂²	—	2	2	no	—
462	C₂²	—	2	2	no	—
463	C₂²	—	2	2	no	—
464	C₂²	—	2	2	no	—
465	C₂²	—	2	2	no	—
466	C₂²	C₈×Dic₉₄	1	4	yes	complemented
467	C₂²	C₂×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
468	C₂²	C₂×C₄×Dic₉₄	1	1	yes	characteristic
469	C₂²	C₄×#10625350	1	1	yes	characteristic
470	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
471	C₂²	C₂×#13094030	1	1	yes	characteristic
472	C₂²	C₂×#13094030	1	1	yes	characteristic
473	C₂²	C₂×#13094030	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	2	no	—
478	C₄	—	94	4	no	—
479	C₄	—	94	4	no	—
480	C₄	—	188	2	no	—
481	C₄	—	188	2	no	—
482	C₄	C₈×C₂²⋊D₄₇	1	4	yes	—
483	C₄	C₂×#13094003	1	1	yes	characteristic
484	C₄	#15689634	1	1	yes	characteristic
485	C₄	#15689657	1	1	yes	characteristic
486	C₄	#15689680	1	1	yes	characteristic
487	C₂	—	2	4	no	—
488	C₂	C₄×#13094003	1	1	yes	characteristic
489	C₂	C₂×C₈×C₂²⋊D₄₇	1	1	yes	characteristic
490	C₂	#20252082	1	1	yes	characteristic
491	C₂	C₂×C₈×Dic₉₄	1	1	yes	characteristic
492	C₂	#20252322	1	1	yes	characteristic
493	C₂	C₈×#10625350	1	1	yes	characteristic
494	C₂	#20252363	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×Dic₉₄	C₂	semidirect
3. #20244324	C₂	semidirect
4. #20244106	C₂	semidirect
5. #20243945	C₂	semidirect
8. C₈×Dic₄₇⋊C₄	C₂	semidirect
9. C₈×C₄⋊Dic₄₇	C₂	semidirect
46. #13094003	C₈	direct (N × H)
79. C₂²×C₈×C₄₇	Q₈	semidirect
119. C₂×Dic₉₄	C₂×C₈	semidirect
144. C₄⋊Dic₄₇	C₂×C₈	semidirect
147. Dic₄₇⋊C₄	C₂×C₈	semidirect
209. C₈×C₄₇	C₂²⋊Q₈	semidirect
219. C₂²×C₄₇	C₈×Q₈	semidirect
290. C₄₇	C₈×C₂²⋊Q₈	semidirect
302. C₂²×C₈	Dic₉₄	semidirect
459. C₈	#13094003	direct (N × H)
466. C₂²	C₈×Dic₉₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×Dic₉₄	2
C₄×#13094003	2
#20244324	2
#20244106	2
#20243945	2
#20243566	2
#20243368	2
C₈×Dic₄₇⋊C₄	2
C₈×C₄⋊Dic₄₇	2
C₈×C₂²⋊Dic₄₇	2
C₂²×C₄×C₈×C₄₇	2
C₈×C₂²⋊Q₈	47

Subgroups — C8×#13094003 #26223692

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#13094003 #26223692