Subgroups — C₈×#13094004 #26223694

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	C₂×C₄×C₈×D₄₇	C₂	1	1	yes	maximal, characteristic
3	C₄×#13094004	C₂	1	1	yes	maximal, characteristic
4	#20244323	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244107	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243946	C₂	1	2	yes	maximal, complemented
7	#20243567	C₂	1	2	yes	maximal
8	#20243365	C₂	1	1	yes	maximal, characteristic
9	C₈×C₄⋊Dic₄₇	C₂	1	2	yes	maximal, complemented
10	C₈×(C₂×D₄₇)⋊C₄	C₂	1	2	yes	maximal
11	C₈×C₄⋊C₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
13	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
14	C₂×#13094004	C₄	1	1	yes	characteristic
15	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
16	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
17	C₈×Dic₉₄	—	2	4	no	—
18	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	2	yes	—
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×Dic₄₇⋊C₈	C₂²	1	2	yes	—
21	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	2	yes	—
22	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
23	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
24	C₂×C₈×Dic₄₇	C₂²	1	2	yes	—
25	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
26	C₄×C₈×D₄₇	—	2	4	no	—
27	#15689028	C₄	1	1	yes	characteristic
28	#15689022	C₄	1	1	yes	characteristic
29	#15689008	C₄	1	2	yes	—
30	#15688997	C₄	1	2	yes	—
31	#15688980	C₄	1	1	yes	characteristic
32	C₄×C₄⋊Dic₄₇	C₂²	1	2	yes	—
33	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
34	#15688878	C₂²	1	2	yes	—
35	#15688877	C₂²	1	2	yes	—
36	#15688877	C₂²	1	2	yes	—
37	#15688877	C₂²	1	2	yes	—
38	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₄×C₈×C₄₇	C₂²	1	2	yes	—
40	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
41	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
42	C₄₇×#336	C₂²	1	2	yes	—
43	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
44	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
47	C₂²×C₄₇⋊C₈	C₂³	1	2	yes	—
48	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
49	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
50	C₂×C₈×D₄₇	—	2	2	no	—
51	C₂×C₈×D₄₇	—	2	2	no	—
52	C₂×C₈×D₄₇	—	2	2	no	—
53	C₂×C₈×D₄₇	—	2	2	no	—
54	C₂×C₈×D₄₇	—	2	2	no	—
55	C₂×C₈×D₄₇	Q₈	1	4	yes	complemented
56	#13094004	C₈	1	8	yes	direct product factor
57	C₄×Dic₉₄	—	2	2	no	—
58	C₄×Dic₉₄	—	2	2	no	—
59	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
60	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
61	C₂×C₄⋊Dic₄₇	C₂×C₄	1	2	yes	—
62	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
63	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
64	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
65	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂×C₄×Dic₄₇	C₂³	1	2	yes	—
68	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
69	C₄²×D₄₇	—	2	2	no	—
70	C₄²×D₄₇	—	2	2	no	—
71	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
72	C₄⋊(C₄₇⋊C₈)	—	2	4	no	—
73	Dic₄₇⋊C₈	—	2	4	no	—
74	(C₂×D₄₇)⋊C₈	—	2	4	no	—
75	C₄×C₄₇⋊C₈	—	2	2	no	—
76	C₈×Dic₄₇	—	2	4	no	—
77	C₈×Dic₄₇	—	2	2	no	—
78	C₈×Dic₄₇	—	2	2	no	—
79	C₄₇⋊#95	C₂×C₄	1	2	yes	—
80	C₄₇⋊#95	C₂×C₄	1	2	yes	—
81	C₄₇⋊#95	C₂×C₄	1	2	yes	—
82	C₄₇⋊#95	C₂×C₄	1	2	yes	—
83	C₂²×C₈×C₄₇	C₂³	1	2	yes	—
84	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
85	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
86	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
87	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
88	C₂×C₄²×C₄₇	C₂³	1	2	yes	—
89	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
90	C₄⋊C₈×C₄₇	—	2	2	no	—
91	C₄×C₈×C₄₇	—	2	4	no	—
92	C₄×C₈×C₄₇	D₄	1	4	yes	—
93	#95×C₄₇	C₂×C₄	1	2	yes	—
94	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
95	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
96	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
98	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
99	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
100	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
101	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
102	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
103	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
104	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂×C₄×D₄₇	—	2	2	no	—
106	C₂×C₄×D₄₇	—	2	2	no	—
107	C₂×C₄×D₄₇	—	2	2	no	—
108	C₂×C₄×D₄₇	—	2	2	no	—
109	C₂×C₄×D₄₇	—	2	1	no	—
110	C₂×C₄×D₄₇	—	2	1	no	—
111	C₂×C₄×D₄₇	—	2	1	no	—
112	C₂×C₄×D₄₇	—	2	1	no	—
113	C₂×C₄×D₄₇	—	2	2	no	—
114	C₂×C₄×D₄₇	C₂×C₈	1	4	yes	—
115	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
116	C₂×C₄×D₄₇	#41	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	1	no	—
121	C₂×C₈×C₄₇	—	2	1	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	2	2	no	—
124	C₂×C₈×C₄₇	—	2	2	no	—
125	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
128	C₂×C₈×C₄₇	#41	1	2	yes	—
129	C₄⋊C₄×C₄₇	—	2	2	no	—
130	C₄⋊C₄×C₄₇	C₂×C₈	1	4	yes	complemented
131	C₄²×C₄₇	—	2	2	no	—
132	C₄²×C₄₇	—	2	2	no	—
133	C₄²×C₄₇	C₂×D₄	1	2	yes	—
134	C₄²×C₄₇	#41	1	2	yes	—
135	(C₂×D₄₇)⋊C₄	—	2	4	no	—
136	(C₂×D₄₇)⋊C₄	C₂×C₈	1	8	yes	—
137	C₄⋊Dic₄₇	—	2	2	no	—
138	C₄⋊Dic₄₇	—	2	4	no	—
139	C₄⋊Dic₄₇	C₂×C₈	1	8	yes	complemented
140	Dic₄₇⋊C₄	—	2	4	no	—
141	C₄×Dic₄₇	—	2	2	no	—
142	C₄×Dic₄₇	—	2	2	no	—
143	C₄×Dic₄₇	—	2	1	no	—
144	C₄×Dic₄₇	—	2	2	no	—
145	C₄×Dic₄₇	—	2	1	no	—
146	C₄×Dic₄₇	—	2	2	no	—
147	C₂×C₄₇⋊C₈	—	2	1	no	—
148	C₂×C₄₇⋊C₈	—	2	1	no	—
149	C₂×C₄₇⋊C₈	—	2	1	no	—
150	C₂×C₄₇⋊C₈	—	2	1	no	—
151	C₂×C₄₇⋊C₈	—	2	2	no	—
152	C₂×C₄₇⋊C₈	—	2	2	no	—
153	C₂×C₄₇⋊C₈	—	2	2	no	—
154	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
155	C₂×C₄₇⋊C₈	#41	1	2	yes	—
156	C₈×D₄₇	—	2	8	no	—
157	C₈×D₄₇	—	2	8	no	—
158	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
159	C₂²×D₄₇	—	2	1	no	—
160	C₂²×D₄₇	—	2	1	no	—
161	C₂²×D₄₇	—	2	1	no	—
162	C₂²×D₄₇	—	2	1	no	—
163	C₂²×D₄₇	C₄×Q₈	1	2	yes	—
164	C₂²×D₄₇	C₂²×C₈	1	2	yes	—
165	C₂²×D₄₇	#131	1	2	yes	—
166	C₂×C₄×C₄₇	—	2	2	no	—
167	C₂×C₄×C₄₇	—	2	2	no	—
168	C₂×C₄×C₄₇	—	2	1	no	—
169	C₂×C₄×C₄₇	—	2	1	no	—
170	C₂×C₄×C₄₇	—	2	2	no	—
171	C₂×C₄×C₄₇	—	2	2	no	—
172	C₂×C₄×C₄₇	—	2	2	no	—
173	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
174	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
175	C₂×C₄×C₄₇	C₂²×C₈	1	4	yes	—
176	C₂×C₄×C₄₇	C₂²×C₈	1	2	yes	—
177	C₂×C₄×C₄₇	#131	1	2	yes	—
178	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
179	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
180	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
184	C₂×Dic₄₇	—	2	1	no	—
185	C₂×Dic₄₇	—	2	1	no	—
186	C₂×Dic₄₇	—	2	1	no	—
187	C₂×Dic₄₇	—	2	2	no	—
188	C₂×Dic₄₇	—	2	1	no	—
189	C₂×Dic₄₇	—	2	2	no	—
190	C₂×Dic₄₇	—	2	1	no	—
191	C₂×Dic₄₇	—	2	1	no	—
192	C₂×Dic₄₇	—	2	2	no	—
193	C₂×Dic₄₇	—	2	2	no	—
194	C₂×Dic₄₇	—	2	2	no	—
195	C₂×Dic₄₇	C₄×Q₈	1	2	yes	—
196	C₂×Dic₄₇	C₂²×C₈	1	2	yes	—
197	C₂×Dic₄₇	C₂²×C₈	1	4	yes	—
198	C₂×Dic₄₇	#131	1	2	yes	—
199	C₄×D₄₇	—	2	8	no	—
200	C₄×D₄₇	—	2	2	no	—
201	C₄×D₄₇	—	2	2	no	—
202	C₄×D₄₇	—	2	2	no	—
203	C₄×D₄₇	—	2	2	no	—
204	C₄×D₄₇	—	2	8	no	—
205	Dic₉₄	—	2	8	no	—
206	C₈×C₄₇	—	2	2	no	—
207	C₈×C₄₇	—	4	2	no	—
208	C₈×C₄₇	C₂²⋊Q₈	1	4	yes	complemented
209	C₄₇⋊C₈	—	2	2	no	—
210	C₄₇⋊C₈	—	2	2	no	—
211	C₄₇⋊C₈	—	4	2	no	—
212	C₈×C₂²⋊Q₈	—	47	1	no	maximal, Sylow
213	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
214	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
215	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
216	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
217	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
218	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
219	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
220	C₂×D₄₇	—	2	2	no	—
221	C₂×D₄₇	—	2	2	no	—
222	C₂×D₄₇	—	2	2	no	—
223	C₂×D₄₇	—	2	2	no	—
224	C₂×D₄₇	—	2	2	no	—
225	C₂×D₄₇	—	2	2	no	—
226	C₂×D₄₇	C₈×Q₈	1	4	yes	complemented
227	C₄×C₄₇	—	2	2	no	—
228	C₄×C₄₇	—	2	4	no	—
229	C₄×C₄₇	—	4	2	no	—
230	C₄×C₄₇	C₈×D₄	1	4	yes	—
231	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
232	C₄×C₄₇	#525	1	1	yes	characteristic
233	C₄×C₄₇	#529	1	1	yes	characteristic
234	C₄×C₄₇	#533	1	1	yes	characteristic
235	Dic₄₇	—	2	4	no	—
236	Dic₄₇	—	2	2	no	—
237	Dic₄₇	—	2	2	no	—
238	Dic₄₇	—	2	2	no	—
239	Dic₄₇	—	4	2	no	—
240	C₂×C₈×Q₈	—	47	1	no	—
241	C₂²×C₄×C₈	—	47	1	no	—
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	2	no	—
249	C₈×C₄⋊C₄	D₄₇	1	1	yes	characteristic, complemented
250	C₈×C₂²⋊C₄	—	47	2	no	—
251	C₂×C₄₇	C₄×C₂²⋊Q₈	1	1	yes	characteristic
252	C₂×C₄₇	C₂×C₈×D₄	1	1	yes	characteristic
253	C₂×C₄₇	#2929	1	1	yes	characteristic
254	C₂×C₄₇	C₂×C₈×Q₈	1	1	yes	characteristic
255	C₂×C₄₇	#2960	1	1	yes	characteristic
256	C₂×C₄₇	C₈×#41	1	1	yes	characteristic
257	C₂×C₄₇	#2966	1	1	yes	characteristic
258	D₄₇	—	2	4	no	—
259	C₂³×C₈	—	47	1	no	—
260	C₂³×C₈	—	47	1	no	—
261	C₂×C₂²⋊Q₈	—	47	1	no	—
262	C₂×C₄×Q₈	—	47	1	no	—
263	C₂²×C₄²	—	47	1	no	—
264	C₈×Q₈	—	94	4	no	—
265	C₂×C₄⋊C₈	—	47	2	no	—
266	C₂×C₄⋊C₈	—	47	1	no	—
267	C₂×C₄⋊C₈	—	47	2	no	—
268	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
269	C₂×C₂²⋊C₈	—	47	2	no	—
270	C₂×C₄×C₈	—	47	1	no	—
271	C₂×C₄×C₈	—	47	1	no	—
272	C₂×C₄×C₈	—	47	2	no	—
273	C₂×C₄×C₈	—	47	1	no	—
274	C₂×C₄×C₈	—	94	4	no	—
275	C₂×C₄×C₈	C₂×D₄₇	1	2	yes	—
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	2	no	—
283	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
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	C₂×D₄₇	1	2	yes	—
290	C₄₇	C₈×C₂²⋊Q₈	1	1	yes	characteristic, complemented, Sylow
291	C₂²×Q₈	—	47	1	no	—
292	C₂³×C₄	—	47	1	no	—
293	C₂³×C₄	—	47	1	no	—
294	C₂³×C₄	—	47	1	no	—
295	C₂²×C₈	—	47	1	no	—
296	C₂²×C₈	—	47	1	no	—
297	C₂²×C₈	—	47	4	no	—
298	C₂²×C₈	—	47	2	no	—
299	C₂²×C₈	—	94	2	no	—
300	C₂²×C₈	—	94	2	no	—
301	C₂²×C₈	—	94	2	no	—
302	C₂²×C₈	—	94	2	no	—
303	C₂²×C₈	—	94	2	no	—
304	C₂²×C₈	C₂²×D₄₇	1	2	yes	—
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	2	no	—
312	C₂×C₄⋊C₄	—	47	1	no	—
313	C₂×C₄⋊C₄	—	47	2	no	—
314	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
316	C₂×C₂²⋊C₄	—	47	2	no	—
317	C₂×C₂²⋊C₄	—	47	2	no	—
318	C₂×C₄²	—	47	1	no	—
319	C₂×C₄²	—	47	1	no	—
320	C₂×C₄²	—	47	2	no	—
321	C₂×C₄²	—	47	1	no	—
322	C₂×C₄²	—	94	2	no	—
323	C₂×C₄²	—	94	2	no	—
324	C₂×C₄²	C₂²×D₄₇	1	2	yes	—
325	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
326	C₄⋊C₈	—	2	2	no	—
327	C₄⋊C₈	—	94	4	no	—
328	C₄⋊C₈	—	94	4	no	—
329	C₄⋊C₈	—	94	2	no	—
330	C₂²⋊C₈	—	94	4	no	—
331	C₄×C₈	—	2	4	no	—
332	C₄×C₈	—	94	2	no	—
333	C₄×C₈	—	94	2	no	—
334	C₄×C₈	—	94	4	no	—
335	C₄×C₈	—	94	2	no	—
336	C₄×C₈	D₁₈₈	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	C₄×D₄₇	1	2	yes	—
342	C₂⁴	—	47	1	no	—
343	C₂×Q₈	—	47	4	no	—
344	C₂×Q₈	—	94	2	no	—
345	C₂×Q₈	—	94	2	no	—
346	C₂²×C₄	—	47	1	no	—
347	C₂²×C₄	—	47	1	no	—
348	C₂²×C₄	—	47	1	no	—
349	C₂²×C₄	—	47	2	no	—
350	C₂²×C₄	—	47	4	no	—
351	C₂²×C₄	—	47	2	no	—
352	C₂²×C₄	—	47	2	no	—
353	C₂²×C₄	—	47	2	no	—
354	C₂²×C₄	—	94	2	no	—
355	C₂²×C₄	—	94	2	no	—
356	C₂²×C₄	—	94	2	no	—
357	C₂²×C₄	—	94	2	no	—
358	C₂²×C₄	—	94	2	no	—
359	C₂²×C₄	—	94	1	no	—
360	C₂²×C₄	—	94	1	no	—
361	C₂²×C₄	—	94	1	no	—
362	C₂²×C₄	—	94	1	no	—
363	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
364	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
365	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
366	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
367	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
368	C₂×C₈	—	2	1	no	—
369	C₂×C₈	—	2	1	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	2	2	no	—
373	C₂×C₈	—	47	2	no	—
374	C₂×C₈	—	47	2	no	—
375	C₂×C₈	—	94	8	no	—
376	C₂×C₈	—	94	1	no	—
377	C₂×C₈	—	94	1	no	—
378	C₂×C₈	—	94	1	no	—
379	C₂×C₈	—	94	1	no	—
380	C₂×C₈	—	94	8	no	—
381	C₂×C₈	—	94	2	no	—
382	C₂×C₈	—	94	2	no	—
383	C₂×C₈	—	94	2	no	—
384	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
385	C₂×C₈	C₂×D₁₈₈	1	2	yes	—
386	C₂×C₈	#10625352	1	2	yes	—
387	C₂×C₈	Q₈×D₄₇	1	2	yes	—
388	C₄⋊C₄	—	2	2	no	—
389	C₄⋊C₄	—	47	8	no	—
390	C₄⋊C₄	—	94	4	no	—
391	C₄⋊C₄	—	94	4	no	—
392	C₄⋊C₄	—	94	2	no	—
393	C₄⋊C₄	C₈×D₄₇	1	4	yes	complemented
394	C₂²⋊C₄	—	47	8	no	—
395	C₂²⋊C₄	—	94	4	no	—
396	C₄²	—	2	2	no	—
397	C₄²	—	2	2	no	—
398	C₄²	—	94	2	no	—
399	C₄²	—	94	2	no	—
400	C₄²	—	94	1	no	—
401	C₄²	—	94	2	no	—
402	C₄²	—	94	1	no	—
403	C₄²	—	94	2	no	—
404	C₄²	C₂×D₁₈₈	1	2	yes	—
405	C₄²	#10625350	1	2	yes	—
406	C₂³	—	47	2	no	—
407	C₂³	—	47	2	no	—
408	C₂³	—	47	2	no	—
409	C₂³	—	94	1	no	—
410	C₂³	—	94	1	no	—
411	C₂³	—	94	1	no	—
412	C₂³	—	94	1	no	—
413	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
414	Q₈	—	94	8	no	—
415	C₂×C₄	—	2	2	no	—
416	C₂×C₄	—	2	2	no	—
417	C₂×C₄	—	2	1	no	—
418	C₂×C₄	—	2	1	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	47	2	no	—
423	C₂×C₄	—	47	4	no	—
424	C₂×C₄	—	47	2	no	—
425	C₂×C₄	—	47	2	no	—
426	C₂×C₄	—	94	8	no	—
427	C₂×C₄	—	94	1	no	—
428	C₂×C₄	—	94	1	no	—
429	C₂×C₄	—	94	1	no	—
430	C₂×C₄	—	94	2	no	—
431	C₂×C₄	—	94	1	no	—
432	C₂×C₄	—	94	1	no	—
433	C₂×C₄	—	94	1	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	8	no	—
440	C₂×C₄	—	94	2	no	—
441	C₂×C₄	—	94	2	no	—
442	C₂×C₄	—	94	2	no	—
443	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
444	C₂×C₄	C₄×D₁₈₈	1	2	yes	—
445	C₂×C₄	C₂×C₈×D₄₇	1	4	yes	—
446	C₂×C₄	C₂×C₈×D₄₇	1	2	yes	—
447	C₂×C₄	#13094030	1	2	yes	—
448	C₂×C₄	C₂²×D₁₈₈	1	1	yes	characteristic
449	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
450	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
451	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
452	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
453	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
454	C₈	—	2	2	no	—
455	C₈	—	4	2	no	—
456	C₈	—	94	2	no	—
457	C₈	—	94	2	no	—
458	C₈	—	188	2	no	—
459	C₈	#13094004	1	4	yes	direct product factor
460	C₂²	—	47	4	no	—
461	C₂²	—	94	2	no	—
462	C₂²	—	94	2	no	—
463	C₂²	—	94	2	no	—
464	C₂²	—	94	2	no	—
465	C₂²	—	94	2	no	—
466	C₂²	—	94	2	no	—
467	C₂²	C₂×C₄×D₁₈₈	1	1	yes	characteristic
468	C₂²	C₄×Q₈×D₄₇	1	1	yes	characteristic
469	C₂²	C₄×#10625352	1	1	yes	characteristic
470	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
471	C₂²	#131×D₄₇	1	1	yes	characteristic
472	C₂²	#131×D₄₇	1	1	yes	characteristic
473	C₂²	C₂×#13094030	1	1	yes	characteristic
474	C₄	—	2	2	no	—
475	C₄	—	2	4	no	—
476	C₄	—	4	2	no	—
477	C₄	—	94	2	no	—
478	C₄	—	94	4	no	—
479	C₄	—	94	2	no	—
480	C₄	—	94	2	no	—
481	C₄	—	188	2	no	—
482	C₄	C₈×D₁₈₈	1	4	yes	—
483	C₄	C₂×#13094004	1	1	yes	characteristic
484	C₄	#15689635	1	1	yes	characteristic
485	C₄	#15689655	1	1	yes	characteristic
486	C₄	#15689677	1	1	yes	characteristic
487	C₂	—	94	4	no	—
488	C₂	C₄×#13094004	1	1	yes	characteristic
489	C₂	C₂×C₈×D₁₈₈	1	1	yes	characteristic
490	C₂	#20252084	1	1	yes	characteristic
491	C₂	C₈×Q₈×D₄₇	1	1	yes	characteristic
492	C₂	#20252317	1	1	yes	characteristic
493	C₂	C₈×#10625352	1	1	yes	characteristic
494	C₂	#20252360	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
1. C₂×C₈×Dic₉₄	C₂	semidirect
4. #20244323	C₂	semidirect
5. #20244107	C₂	semidirect
6. #20243946	C₂	semidirect
9. C₈×C₄⋊Dic₄₇	C₂	semidirect
11. C₈×C₄⋊C₄×C₄₇	C₂	semidirect
55. C₂×C₈×D₄₇	Q₈	semidirect
56. #13094004	C₈	direct (N × H)
119. C₂×Dic₉₄	C₂×C₈	semidirect
130. C₄⋊C₄×C₄₇	C₂×C₈	semidirect
139. C₄⋊Dic₄₇	C₂×C₈	semidirect
208. C₈×C₄₇	C₂²⋊Q₈	semidirect
226. C₂×D₄₇	C₈×Q₈	semidirect
249. C₈×C₄⋊C₄	D₄₇	semidirect
290. C₄₇	C₈×C₂²⋊Q₈	semidirect
393. C₄⋊C₄	C₈×D₄₇	semidirect
459. C₈	#13094004	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×C₈×Dic₉₄	2
C₂×C₄×C₈×D₄₇	2
C₄×#13094004	2
#20244323	2
#20244107	2
#20243946	2
#20243567	2
#20243365	2
C₈×C₄⋊Dic₄₇	2
C₈×(C₂×D₄₇)⋊C₄	2
C₈×C₄⋊C₄×C₄₇	2
C₈×C₂²⋊Q₈	47

Subgroups — C8×#13094004 #26223694

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₈×#13094004 #26223694