Subgroups — #26220751

Order 12032.

1162 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689677	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689148	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689080	C₂	1	1	yes	maximal, characteristic
4	#20244328	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244326	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244326	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244325	C₂	1	1	yes	maximal, characteristic, complemented
8	#20244323	C₂	1	1	yes	maximal, characteristic, complemented
9	#20244322	C₂	1	1	yes	maximal, characteristic, complemented
10	#20244322	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243083	C₂	1	1	yes	maximal, characteristic
12	#20243083	C₂	1	1	yes	maximal, characteristic
13	#20243080	C₂	1	1	yes	maximal, characteristic
14	#336×D₄₇	C₂	1	1	yes	maximal, characteristic
15	C₄₇×#1985	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#10625324	C₂²	1	1	yes	characteristic
17	C₂²×#10625324	C₂²	1	1	yes	characteristic
18	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
20	#15689677	—	2	4	no	—
21	#15689677	—	2	4	no	—
22	C₂×#13094023	C₄	1	1	yes	characteristic
23	C₂×#13094022	C₄	1	1	yes	characteristic
24	C₂×#13094014	C₄	1	1	yes	characteristic
25	C₂×#13094014	C₄	1	1	yes	characteristic
26	C₂×#13094004	C₄	1	1	yes	characteristic
27	C₂×#13094002	C₄	1	1	yes	characteristic
28	C₂×#13094002	C₄	1	1	yes	characteristic
29	C₂×#13094000	C₄	1	1	yes	characteristic
30	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
31	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
32	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
33	C₂×#13093981	C₂²	1	1	yes	characteristic
34	C₂×#13093981	C₂²	1	1	yes	characteristic
35	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
36	#15689148	—	2	4	no	—
37	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
38	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
40	#15689080	—	2	4	no	—
41	C₂×#13093934	C₂²	1	1	yes	characteristic
42	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
44	#15688878	C₂²	1	1	yes	characteristic
45	#15688878	C₂²	1	1	yes	characteristic
46	#15688878	C₂²	1	1	yes	characteristic
47	#15688878	C₂²	1	1	yes	characteristic
48	#15688877	C₂²	1	1	yes	characteristic
49	#15688877	C₂²	1	1	yes	characteristic
50	#15688877	C₂²	1	1	yes	characteristic
51	#15688877	C₂²	1	1	yes	characteristic
52	#15688877	C₂²	1	1	yes	characteristic
53	#15688877	C₂²	1	1	yes	characteristic
54	#15688877	C₂²	1	1	yes	characteristic
55	#15688877	C₂²	1	1	yes	characteristic
56	C₂×C₄×Q₈×C₄₇	C₂²	1	1	yes	characteristic
57	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
58	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
59	C₄₇×#336	C₂²	1	1	yes	characteristic
60	C₄₇×#336	C₂²	1	1	yes	characteristic
61	C₄₇×#336	C₂²	1	1	yes	characteristic
62	C₄₇×#336	C₂²	1	1	yes	characteristic
63	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
64	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
65	C₂²×Dic₉₄	C₂×C₄	1	1	yes	characteristic
66	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
67	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
68	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
69	C₂×#10625324	—	2	2	no	—
70	C₂×#10625324	—	2	2	no	—
71	C₂×#10625324	—	2	2	no	—
72	C₂×#10625324	—	2	2	no	—
73	C₂×#10625324	—	2	2	no	—
74	C₂×#10625324	Q₈	1	4	yes	complemented
75	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
76	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
77	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
78	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
79	C₂×C₈×D₄₇	—	2	2	no	—
80	C₂×C₈×D₄₇	—	2	2	no	—
81	C₂×C₈×D₄₇	—	2	2	no	—
82	C₂×C₈×D₄₇	—	2	2	no	—
83	C₂×C₈×D₄₇	—	2	2	no	—
84	C₂×C₈×D₄₇	Q₈	1	4	yes	complemented
85	#13094023	—	2	4	no	—
86	#13094022	—	2	4	no	—
87	#13094014	—	2	4	no	—
88	#13094014	—	2	4	no	—
89	#13094004	—	2	4	no	—
90	#13094002	—	2	4	no	—
91	#13094002	—	2	4	no	—
92	#13094000	—	2	4	no	—
93	C₄×Dic₉₄	—	2	2	no	—
94	C₄×Dic₉₄	—	2	2	no	—
95	C₄×Dic₉₄	—	2	2	no	—
96	C₄×Dic₉₄	—	2	2	no	—
97	C₄×Dic₉₄	—	2	2	no	—
98	C₄×Dic₉₄	—	2	2	no	—
99	#13093981	—	2	2	no	—
100	#13093981	—	2	2	no	—
101	#13093981	D₄	1	4	yes	—
102	#13093981	D₄	1	4	yes	—
103	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
104	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
105	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
106	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
107	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
109	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
110	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
111	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
112	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
113	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
114	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
115	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
116	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
117	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
118	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
119	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
120	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
121	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
122	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
123	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
124	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
125	C₄²×D₄₇	—	2	2	no	—
126	C₄²×D₄₇	—	2	2	no	—
127	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
128	Dic₄₇⋊C₈	—	2	2	no	—
129	Dic₄₇⋊C₈	—	2	2	no	—
130	#13093934	—	2	2	no	—
131	C₄×C₄₇⋊C₈	—	2	2	no	—
132	C₈×Dic₄₇	—	2	2	no	—
133	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
134	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
135	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
136	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
137	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
138	C₄×Q₈×C₄₇	—	2	2	no	—
139	C₄×Q₈×C₄₇	—	2	2	no	—
140	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
141	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
142	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
143	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
144	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
145	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
146	C₄⋊C₈×C₄₇	—	2	2	no	—
147	#97×C₄₇	—	2	2	no	—
148	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
149	C₂×Q₈×C₄₇	—	2	2	no	—
150	C₂×Q₈×C₄₇	—	2	2	no	—
151	C₂×Q₈×C₄₇	—	4	1	no	—
152	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
155	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
156	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
158	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
159	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
160	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
161	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
162	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
163	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
164	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
165	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₄×D₄₇	—	2	2	no	—
167	C₂×C₄×D₄₇	—	2	2	no	—
168	C₂×C₄×D₄₇	—	2	2	no	—
169	C₂×C₄×D₄₇	—	2	2	no	—
170	C₂×C₄×D₄₇	—	4	1	no	—
171	C₂×C₄×D₄₇	—	4	1	no	—
172	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
173	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
174	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
175	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
176	C₂×C₄×D₄₇	#41	1	2	yes	—
177	C₂×C₄×D₄₇	#41	1	2	yes	—
178	C₂×Dic₉₄	—	2	2	no	—
179	C₂×Dic₉₄	—	2	2	no	—
180	C₂×Dic₉₄	—	2	2	no	—
181	C₂×Dic₉₄	—	2	2	no	—
182	C₂×Dic₉₄	—	2	2	no	—
183	C₂×Dic₉₄	—	2	2	no	—
184	C₂×Dic₉₄	—	4	1	no	—
185	C₂×Dic₉₄	—	4	1	no	—
186	C₂×Dic₉₄	—	4	1	no	—
187	C₂×C₈×C₄₇	—	2	1	no	—
188	C₂×C₈×C₄₇	—	2	1	no	—
189	C₂×C₈×C₄₇	—	2	1	no	—
190	C₂×C₈×C₄₇	—	2	1	no	—
191	C₂×C₈×C₄₇	—	2	1	no	—
192	C₂×C₈×C₄₇	—	2	1	no	—
193	C₂×C₈×C₄₇	—	2	1	no	—
194	C₂×C₈×C₄₇	—	2	1	no	—
195	C₂×C₈×C₄₇	—	2	1	no	—
196	C₂×C₈×C₄₇	—	2	1	no	—
197	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
198	C₂×C₈×C₄₇	C₂×Q₈	1	2	yes	—
199	C₄⋊C₄×C₄₇	—	2	2	no	—
200	C₄⋊C₄×C₄₇	—	2	2	no	—
201	C₄⋊C₄×C₄₇	—	2	2	no	—
202	C₄²×C₄₇	—	2	1	no	—
203	C₄²×C₄₇	—	2	1	no	—
204	C₄²×C₄₇	—	2	1	no	—
205	C₄²×C₄₇	—	2	1	no	—
206	C₄²×C₄₇	C₂×D₄	1	2	yes	—
207	C₄²×C₄₇	C₂×D₄	1	2	yes	—
208	(C₂×D₄₇)⋊C₄	—	2	2	no	—
209	(C₂×D₄₇)⋊C₄	—	2	2	no	—
210	(C₂×D₄₇)⋊C₄	C₂²⋊C₄	1	4	yes	—
211	(C₂×D₄₇)⋊C₄	C₂²⋊C₄	1	4	yes	—
212	C₄⋊Dic₄₇	—	2	2	no	—
213	C₄⋊Dic₄₇	—	2	2	no	—
214	C₄⋊Dic₄₇	—	2	2	no	—
215	Dic₄₇⋊C₄	—	2	2	no	—
216	Dic₄₇⋊C₄	—	2	2	no	—
217	Dic₄₇⋊C₄	—	2	2	no	—
218	Dic₄₇⋊C₄	—	2	2	no	—
219	Dic₄₇⋊C₄	—	2	2	no	—
220	Dic₄₇⋊C₄	—	2	2	no	—
221	Dic₄₇⋊C₄	—	2	2	no	—
222	Dic₄₇⋊C₄	—	2	2	no	—
223	Dic₄₇⋊C₄	C₂²⋊C₄	1	4	yes	—
224	Dic₄₇⋊C₄	C₂²⋊C₄	1	4	yes	—
225	C₄×Dic₄₇	—	2	1	no	—
226	C₄×Dic₄₇	—	2	1	no	—
227	C₄×Dic₄₇	—	2	1	no	—
228	C₄×Dic₄₇	—	2	1	no	—
229	C₄×Dic₄₇	—	2	2	no	—
230	C₄×Dic₄₇	—	2	2	no	—
231	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
232	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
233	C₂×C₄₇⋊C₈	—	2	1	no	—
234	C₂×C₄₇⋊C₈	—	2	1	no	—
235	C₂×C₄₇⋊C₈	—	2	1	no	—
236	C₂×C₄₇⋊C₈	—	2	1	no	—
237	C₂×C₄₇⋊C₈	—	2	1	no	—
238	C₂×C₄₇⋊C₈	—	2	1	no	—
239	C₂×C₄₇⋊C₈	—	2	1	no	—
240	C₂×C₄₇⋊C₈	—	2	1	no	—
241	C₂×C₄₇⋊C₈	—	2	1	no	—
242	C₂×C₄₇⋊C₈	—	2	1	no	—
243	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
244	C₂×C₄₇⋊C₈	C₂×Q₈	1	2	yes	—
245	#10625324	—	2	8	no	—
246	#10625324	—	4	4	no	—
247	C₈×D₄₇	—	2	8	no	—
248	C₈×D₄₇	—	4	4	no	—
249	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
250	C₂²×D₄₇	—	2	1	no	—
251	C₂²×D₄₇	—	2	1	no	—
252	C₂²×D₄₇	—	2	1	no	—
253	C₂²×D₄₇	—	2	1	no	—
254	C₂²×D₄₇	C₂×C₂²⋊C₄	1	2	yes	—
255	C₂²×D₄₇	C₄×Q₈	1	2	yes	—
256	C₂²×D₄₇	C₄×Q₈	1	2	yes	—
257	Q₈×C₄₇	—	4	4	no	—
258	C₂×C₄×C₄₇	—	2	1	no	—
259	C₂×C₄×C₄₇	—	2	1	no	—
260	C₂×C₄×C₄₇	—	2	1	no	—
261	C₂×C₄×C₄₇	—	2	1	no	—
262	C₂×C₄×C₄₇	—	2	1	no	—
263	C₂×C₄×C₄₇	—	2	1	no	—
264	C₂×C₄×C₄₇	—	2	1	no	—
265	C₂×C₄×C₄₇	—	2	1	no	—
266	C₂×C₄×C₄₇	—	2	1	no	—
267	C₂×C₄×C₄₇	—	2	1	no	—
268	C₂×C₄×C₄₇	—	2	1	no	—
269	C₂×C₄×C₄₇	—	2	1	no	—
270	C₂×C₄×C₄₇	—	2	1	no	—
271	C₂×C₄×C₄₇	—	2	1	no	—
272	C₂×C₄×C₄₇	—	2	1	no	—
273	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
274	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
275	C₂×C₄×C₄₇	#131	1	2	yes	—
276	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
277	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
278	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
279	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
280	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
281	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
282	C₂×Dic₄₇	—	2	1	no	—
283	C₂×Dic₄₇	—	2	1	no	—
284	C₂×Dic₄₇	—	2	1	no	—
285	C₂×Dic₄₇	—	2	1	no	—
286	C₂×Dic₄₇	—	2	1	no	—
287	C₂×Dic₄₇	—	2	1	no	—
288	C₂×Dic₄₇	—	2	1	no	—
289	C₂×Dic₄₇	—	2	1	no	—
290	C₂×Dic₄₇	—	2	1	no	—
291	C₂×Dic₄₇	—	2	1	no	—
292	C₂×Dic₄₇	—	2	1	no	—
293	C₂×Dic₄₇	—	2	1	no	—
294	C₂×Dic₄₇	—	2	1	no	—
295	C₂×Dic₄₇	—	2	1	no	—
296	C₂×Dic₄₇	—	2	1	no	—
297	C₂×Dic₄₇	C₂×C₂²⋊C₄	1	2	yes	—
298	C₂×Dic₄₇	C₂×C₂²⋊C₄	1	2	yes	—
299	C₂×Dic₄₇	C₂×C₂²⋊C₄	1	2	yes	—
300	C₂×Dic₄₇	C₄×Q₈	1	2	yes	—
301	C₂×Dic₄₇	C₄×Q₈	1	2	yes	—
302	C₂×Dic₄₇	#131	1	2	yes	—
303	C₄×D₄₇	—	4	4	no	—
304	C₄×D₄₇	—	4	4	no	—
305	C₄×D₄₇	C₂²⋊Q₈	1	4	yes	—
306	C₄×D₄₇	C₂²⋊Q₈	1	4	yes	—
307	C₄×D₄₇	#124	1	4	yes	—
308	C₄×D₄₇	C₄⋊Q₈	1	4	yes	—
309	Dic₉₄	—	4	4	no	—
310	Dic₉₄	—	4	4	no	—
311	Dic₉₄	—	4	4	no	—
312	C₈×C₄₇	—	2	2	no	—
313	C₈×C₄₇	—	2	2	no	—
314	C₈×C₄₇	—	4	1	no	—
315	C₈×C₄₇	—	4	1	no	—
316	C₄₇⋊C₈	—	2	2	no	—
317	C₄₇⋊C₈	—	2	2	no	—
318	C₄₇⋊C₈	—	4	1	no	—
319	C₄₇⋊C₈	—	4	1	no	—
320	#21304	—	47	1	no	maximal, Sylow
321	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
322	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
323	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
324	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
325	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
326	C₂²×C₄₇	#568	1	1	yes	characteristic
327	C₂²×C₄₇	#568	1	1	yes	characteristic
328	C₂×D₄₇	—	2	2	no	—
329	C₂×D₄₇	—	2	2	no	—
330	C₂×D₄₇	—	2	2	no	—
331	C₂×D₄₇	—	2	2	no	—
332	C₂×D₄₇	—	2	2	no	—
333	C₂×D₄₇	—	2	2	no	—
334	C₂×D₄₇	#391	1	4	yes	—
335	C₄×C₄₇	—	2	2	no	—
336	C₄×C₄₇	—	2	2	no	—
337	C₄×C₄₇	—	2	2	no	—
338	C₄×C₄₇	—	4	1	no	—
339	C₄×C₄₇	—	4	1	no	—
340	C₄×C₄₇	—	4	1	no	—
341	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
342	C₄×C₄₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
343	C₄×C₄₇	C₂×#124	1	1	yes	characteristic
344	C₄×C₄₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
345	Dic₄₇	—	2	2	no	—
346	Dic₄₇	—	2	2	no	—
347	Dic₄₇	—	2	2	no	—
348	Dic₄₇	—	4	1	no	—
349	Dic₄₇	—	4	1	no	—
350	Dic₄₇	—	4	1	no	—
351	Dic₄₇	#391	1	4	yes	—
352	C₂×#533	—	47	1	no	—
353	C₂×#424	—	47	1	no	—
354	C₂×#405	—	47	1	no	—
355	#1985	—	47	1	no	—
356	#1985	—	47	1	no	—
357	#1985	—	47	1	no	—
358	#1985	D₄₇	1	1	yes	characteristic, complemented
359	#1984	—	47	1	no	—
360	#1984	—	47	1	no	—
361	#1984	—	47	1	no	—
362	#1984	—	47	1	no	—
363	#1729	—	47	1	no	—
364	#1729	—	47	1	no	—
365	#1728	—	47	1	no	—
366	C₂×#336	—	47	1	no	—
367	C₂×C₄₇	C₂×#391	1	1	yes	characteristic
368	C₂×C₄₇	#2880	1	1	yes	characteristic
369	C₂×C₄₇	#2880	1	1	yes	characteristic
370	C₂×C₄₇	#2960	1	1	yes	characteristic
371	C₂×C₄₇	#2961	1	1	yes	characteristic
372	C₂×C₄₇	#2962	1	1	yes	characteristic
373	C₂×C₄₇	#2962	1	1	yes	characteristic
374	D₄₇	—	2	4	no	—
375	C₂²×M₁₆	—	47	1	no	—
376	C₂²×M₁₆	—	47	1	no	—
377	C₂³×C₈	—	47	1	no	—
378	C₂³×C₈	—	47	1	no	—
379	#533	—	94	4	no	—
380	#533	—	94	4	no	—
381	C₂×C₄⋊Q₈	—	47	1	no	—
382	C₂×C₄⋊Q₈	—	47	1	no	—
383	C₂×#125	—	47	1	no	—
384	C₂×#125	—	47	1	no	—
385	C₂×C₂²⋊Q₈	—	47	1	no	—
386	C₂×C₂²⋊Q₈	—	47	1	no	—
387	C₂×C₂²⋊Q₈	—	47	1	no	—
388	C₂×C₂²⋊Q₈	—	47	1	no	—
389	C₂×C₄×Q₈	—	47	1	no	—
390	C₂×C₄×Q₈	—	47	1	no	—
391	C₂×C₄×Q₈	—	47	1	no	—
392	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
393	C₂×#117	—	47	1	no	—
394	C₂×#117	—	47	1	no	—
395	C₂²×C₄²	—	47	1	no	—
396	#424	—	94	4	no	—
397	C₂×C₄⋊C₈	—	47	1	no	—
398	C₂×C₄⋊C₈	—	47	1	no	—
399	C₂×C₄⋊C₈	—	47	1	no	—
400	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
401	#405	—	94	4	no	—
402	C₂×#97	—	47	1	no	—
403	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
404	C₂×C₄×C₈	—	47	1	no	—
405	C₂×C₄×C₈	—	47	1	no	—
406	#336	—	47	1	no	—
407	#336	—	47	1	no	—
408	#336	—	47	1	no	—
409	#336	—	47	1	no	—
410	#336	—	47	1	no	—
411	#336	—	47	1	no	—
412	#336	—	47	1	no	—
413	#336	—	47	1	no	—
414	#336	—	47	1	no	—
415	#336	—	47	1	no	—
416	#336	—	47	1	no	—
417	#336	—	47	1	no	—
418	#336	C₂×D₄₇	1	1	yes	characteristic
419	#336	C₂×D₄₇	1	1	yes	characteristic
420	#336	C₂×D₄₇	1	1	yes	characteristic
421	#336	C₂×D₄₇	1	1	yes	characteristic
422	C₄₇	#21304	1	1	yes	characteristic, complemented, Sylow
423	C₂²×Q₈	—	47	1	no	—
424	C₂²×Q₈	—	47	1	no	—
425	C₂²×Q₈	—	47	1	no	—
426	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
427	C₂³×C₄	—	47	1	no	—
428	C₂³×C₄	—	47	1	no	—
429	C₂³×C₄	—	47	1	no	—
430	C₂×M₁₆	—	47	4	no	—
431	C₂×M₁₆	—	94	2	no	—
432	C₂×M₁₆	—	94	2	no	—
433	C₂×M₁₆	—	94	2	no	—
434	C₂×M₁₆	—	94	2	no	—
435	C₂×M₁₆	—	94	2	no	—
436	C₂²×C₈	—	47	1	no	—
437	C₂²×C₈	—	47	1	no	—
438	C₂²×C₈	—	47	4	no	—
439	C₂²×C₈	—	47	1	no	—
440	C₂²×C₈	—	47	1	no	—
441	C₂²×C₈	—	94	2	no	—
442	C₂²×C₈	—	94	2	no	—
443	C₂²×C₈	—	94	2	no	—
444	C₂²×C₈	—	94	2	no	—
445	C₂²×C₈	—	94	2	no	—
446	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
447	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
448	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
449	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
450	C₄⋊Q₈	—	94	4	no	—
451	C₄⋊Q₈	—	94	4	no	—
452	#125	—	94	4	no	—
453	#125	—	94	4	no	—
454	C₂²⋊Q₈	—	94	4	no	—
455	C₂²⋊Q₈	—	94	4	no	—
456	C₂²⋊Q₈	—	94	4	no	—
457	C₂²⋊Q₈	—	94	4	no	—
458	C₄×Q₈	—	2	2	no	—
459	C₄×Q₈	—	2	2	no	—
460	C₄×Q₈	—	94	2	no	—
461	C₄×Q₈	—	94	2	no	—
462	C₄×Q₈	—	94	2	no	—
463	C₄×Q₈	—	94	2	no	—
464	C₄×Q₈	—	94	2	no	—
465	C₄×Q₈	—	94	2	no	—
466	#117	—	47	4	no	—
467	#117	—	47	4	no	—
468	#117	—	94	2	no	—
469	#117	—	94	2	no	—
470	C₂×C₄⋊C₄	—	47	1	no	—
471	C₂×C₄⋊C₄	—	47	1	no	—
472	C₂×C₄⋊C₄	—	47	1	no	—
473	C₂×C₄⋊C₄	—	47	1	no	—
474	C₂×C₄⋊C₄	—	47	1	no	—
475	C₂×C₄⋊C₄	—	47	1	no	—
476	C₂×C₄⋊C₄	—	47	1	no	—
477	C₂×C₄⋊C₄	—	47	1	no	—
478	C₂×C₄⋊C₄	—	47	1	no	—
479	C₂×C₄⋊C₄	—	47	1	no	—
480	C₂×C₄⋊C₄	—	47	1	no	—
481	C₂×C₄⋊C₄	—	47	1	no	—
482	C₂×C₄⋊C₄	—	47	1	no	—
483	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
484	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
485	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
486	C₂×C₂²⋊C₄	—	47	1	no	—
487	C₂×C₂²⋊C₄	—	47	1	no	—
488	C₂×C₂²⋊C₄	—	47	1	no	—
489	C₂×C₂²⋊C₄	—	47	1	no	—
490	C₂×C₄²	—	47	1	no	—
491	C₂×C₄²	—	47	1	no	—
492	C₂×C₄²	—	47	1	no	—
493	C₂×C₄²	—	47	1	no	—
494	C₂×C₄²	—	47	1	no	—
495	C₂×C₄²	—	94	2	no	—
496	C₂×C₄²	—	94	2	no	—
497	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
498	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
499	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
500	C₄⋊C₈	—	2	2	no	—
501	C₄⋊C₈	—	94	2	no	—
502	C₄⋊C₈	—	94	2	no	—
503	C₄⋊C₈	—	94	2	no	—
504	#97	—	2	2	no	—
505	#97	—	94	2	no	—
506	C₄×C₈	—	94	2	no	—
507	C₄×C₈	—	94	2	no	—
508	C₂⁴	—	47	1	no	—
509	C₂×Q₈	—	2	2	no	—
510	C₂×Q₈	—	2	2	no	—
511	C₂×Q₈	—	4	1	no	—
512	C₂×Q₈	—	94	2	no	—
513	C₂×Q₈	—	94	2	no	—
514	C₂×Q₈	—	94	2	no	—
515	C₂×Q₈	—	94	2	no	—
516	C₂×Q₈	—	94	2	no	—
517	C₂×Q₈	—	94	2	no	—
518	C₂×Q₈	—	188	1	no	—
519	C₂×Q₈	—	188	1	no	—
520	C₂×Q₈	—	188	1	no	—
521	C₂²×C₄	—	47	1	no	—
522	C₂²×C₄	—	47	2	no	—
523	C₂²×C₄	—	47	2	no	—
524	C₂²×C₄	—	47	2	no	—
525	C₂²×C₄	—	47	2	no	—
526	C₂²×C₄	—	47	2	no	—
527	C₂²×C₄	—	47	2	no	—
528	C₂²×C₄	—	47	1	no	—
529	C₂²×C₄	—	47	1	no	—
530	C₂²×C₄	—	47	1	no	—
531	C₂²×C₄	—	47	1	no	—
532	C₂²×C₄	—	47	1	no	—
533	C₂²×C₄	—	47	1	no	—
534	C₂²×C₄	—	94	2	no	—
535	C₂²×C₄	—	94	2	no	—
536	C₂²×C₄	—	94	2	no	—
537	C₂²×C₄	—	94	2	no	—
538	C₂²×C₄	—	188	1	no	—
539	C₂²×C₄	—	188	1	no	—
540	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
541	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
542	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
543	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
544	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
545	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
546	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
547	M₁₆	—	94	8	no	—
548	M₁₆	—	188	4	no	—
549	C₂×C₈	—	2	1	no	—
550	C₂×C₈	—	2	1	no	—
551	C₂×C₈	—	2	1	no	—
552	C₂×C₈	—	2	1	no	—
553	C₂×C₈	—	2	1	no	—
554	C₂×C₈	—	2	1	no	—
555	C₂×C₈	—	2	1	no	—
556	C₂×C₈	—	2	1	no	—
557	C₂×C₈	—	2	1	no	—
558	C₂×C₈	—	2	1	no	—
559	C₂×C₈	—	47	2	no	—
560	C₂×C₈	—	47	2	no	—
561	C₂×C₈	—	94	8	no	—
562	C₂×C₈	—	94	1	no	—
563	C₂×C₈	—	94	1	no	—
564	C₂×C₈	—	94	1	no	—
565	C₂×C₈	—	94	1	no	—
566	C₂×C₈	—	94	1	no	—
567	C₂×C₈	—	94	1	no	—
568	C₂×C₈	—	94	1	no	—
569	C₂×C₈	—	94	1	no	—
570	C₂×C₈	—	94	1	no	—
571	C₂×C₈	—	94	1	no	—
572	C₂×C₈	—	188	4	no	—
573	C₂×C₈	Q₈×D₄₇	1	2	yes	—
574	C₂×C₈	Q₈×D₄₇	1	2	yes	—
575	C₄⋊C₄	—	2	2	no	—
576	C₄⋊C₄	—	2	2	no	—
577	C₄⋊C₄	—	2	2	no	—
578	C₄⋊C₄	—	47	4	no	—
579	C₄⋊C₄	—	47	4	no	—
580	C₄⋊C₄	—	94	2	no	—
581	C₄⋊C₄	—	94	2	no	—
582	C₄⋊C₄	—	94	2	no	—
583	C₄⋊C₄	—	94	2	no	—
584	C₄⋊C₄	—	94	2	no	—
585	C₄⋊C₄	—	94	2	no	—
586	C₄⋊C₄	—	94	2	no	—
587	C₄⋊C₄	—	94	2	no	—
588	C₄⋊C₄	—	94	2	no	—
589	C₄⋊C₄	—	94	2	no	—
590	C₄⋊C₄	—	94	2	no	—
591	C₂²⋊C₄	—	47	4	no	—
592	C₂²⋊C₄	—	47	4	no	—
593	C₂²⋊C₄	—	94	2	no	—
594	C₂²⋊C₄	—	94	2	no	—
595	C₄²	—	2	1	no	—
596	C₄²	—	2	1	no	—
597	C₄²	—	2	1	no	—
598	C₄²	—	2	1	no	—
599	C₄²	—	47	2	no	—
600	C₄²	—	47	2	no	—
601	C₄²	—	94	2	no	—
602	C₄²	—	94	2	no	—
603	C₄²	—	94	1	no	—
604	C₄²	—	94	1	no	—
605	C₄²	—	94	1	no	—
606	C₄²	—	94	1	no	—
607	C₄²	D₄×D₄₇	1	2	yes	—
608	C₄²	D₄×D₄₇	1	2	yes	—
609	C₂³	—	47	2	no	—
610	C₂³	—	47	2	no	—
611	C₂³	—	47	2	no	—
612	C₂³	—	94	1	no	—
613	C₂³	—	94	1	no	—
614	C₂³	—	94	1	no	—
615	C₂³	—	94	1	no	—
616	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
617	Q₈	—	4	4	no	—
618	Q₈	—	188	4	no	—
619	Q₈	—	188	4	no	—
620	Q₈	—	188	4	no	—
621	C₂×C₄	—	2	1	no	—
622	C₂×C₄	—	2	1	no	—
623	C₂×C₄	—	2	1	no	—
624	C₂×C₄	—	2	1	no	—
625	C₂×C₄	—	2	1	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	1	no	—
628	C₂×C₄	—	2	1	no	—
629	C₂×C₄	—	2	1	no	—
630	C₂×C₄	—	2	1	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	2	1	no	—
633	C₂×C₄	—	2	1	no	—
634	C₂×C₄	—	2	1	no	—
635	C₂×C₄	—	2	1	no	—
636	C₂×C₄	—	47	2	no	—
637	C₂×C₄	—	47	2	no	—
638	C₂×C₄	—	47	2	no	—
639	C₂×C₄	—	47	4	no	—
640	C₂×C₄	—	47	4	no	—
641	C₂×C₄	—	47	4	no	—
642	C₂×C₄	—	47	4	no	—
643	C₂×C₄	—	47	2	no	—
644	C₂×C₄	—	47	2	no	—
645	C₂×C₄	—	47	2	no	—
646	C₂×C₄	—	94	1	no	—
647	C₂×C₄	—	94	1	no	—
648	C₂×C₄	—	94	1	no	—
649	C₂×C₄	—	94	1	no	—
650	C₂×C₄	—	94	1	no	—
651	C₂×C₄	—	94	1	no	—
652	C₂×C₄	—	94	1	no	—
653	C₂×C₄	—	94	1	no	—
654	C₂×C₄	—	94	1	no	—
655	C₂×C₄	—	94	1	no	—
656	C₂×C₄	—	94	1	no	—
657	C₂×C₄	—	94	1	no	—
658	C₂×C₄	—	94	1	no	—
659	C₂×C₄	—	94	1	no	—
660	C₂×C₄	—	94	1	no	—
661	C₂×C₄	—	188	4	no	—
662	C₂×C₄	—	188	4	no	—
663	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
664	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
665	C₂×C₄	#13094032	1	2	yes	—
666	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
667	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
668	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
669	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
670	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
671	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
672	C₈	—	2	2	no	—
673	C₈	—	2	2	no	—
674	C₈	—	4	1	no	—
675	C₈	—	4	1	no	—
676	C₈	—	94	2	no	—
677	C₈	—	94	2	no	—
678	C₈	—	188	1	no	—
679	C₈	—	188	1	no	—
680	C₂²	—	47	4	no	—
681	C₂²	—	94	2	no	—
682	C₂²	—	94	2	no	—
683	C₂²	—	94	2	no	—
684	C₂²	—	94	2	no	—
685	C₂²	—	94	2	no	—
686	C₂²	—	94	2	no	—
687	C₂²	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
688	C₂²	C₄×Q₈×D₄₇	1	1	yes	characteristic
689	C₂²	C₄×Q₈×D₄₇	1	1	yes	characteristic
690	C₂²	#131×D₄₇	1	1	yes	characteristic
691	C₂²	C₂×#13094032	1	1	yes	characteristic
692	C₂²	#15689888	1	1	yes	characteristic
693	C₂²	#15689889	1	1	yes	characteristic
694	C₄	—	2	2	no	—
695	C₄	—	2	2	no	—
696	C₄	—	2	2	no	—
697	C₄	—	4	1	no	—
698	C₄	—	4	1	no	—
699	C₄	—	4	1	no	—
700	C₄	—	47	4	no	—
701	C₄	—	94	2	no	—
702	C₄	—	94	2	no	—
703	C₄	—	94	2	no	—
704	C₄	—	188	1	no	—
705	C₄	—	188	1	no	—
706	C₄	—	188	1	no	—
707	C₄	C₂²⋊Q₈×D₄₇	1	1	yes	characteristic
708	C₄	C₂²⋊Q₈×D₄₇	1	1	yes	characteristic
709	C₄	#124×D₄₇	1	1	yes	characteristic
710	C₄	C₄⋊Q₈×D₄₇	1	1	yes	characteristic
711	C₂	—	94	4	no	—
712	C₂	#391×D₄₇	1	1	yes	characteristic
713	C₂	#20251836	1	1	yes	characteristic
714	C₂	#20251838	1	1	yes	characteristic
715	C₂	#20252319	1	1	yes	characteristic
716	C₂	#20252324	1	1	yes	characteristic
717	C₂	#20252333	1	1	yes	characteristic
718	C₂	#20252336	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1985	C₂
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1985	D₄₇
hypocenter	C₄₇	#21304
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1985

Complements

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

N	H ≅ G/N	type
4. #20244328	C₂	semidirect
5. #20244326	C₂	semidirect
6. #20244326	C₂	semidirect
7. #20244325	C₂	semidirect
8. #20244323	C₂	semidirect
9. #20244322	C₂	semidirect
10. #20244322	C₂	semidirect
15. C₄₇×#1985	C₂	semidirect
74. C₂×#10625324	Q₈	semidirect
84. C₂×C₈×D₄₇	Q₈	semidirect
358. #1985	D₄₇	semidirect
422. C₄₇	#21304	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689677	2
C₂×#15689148	2
C₂×#15689080	2
#20244328	2
#20244326	2
#20244325	2
#20244323	2
#20244322	2
#20243083	2
#20243080	2
#336×D₄₇	2
C₄₇×#1985	2
#21304	47