Subgroups — #26232819

Order 12032.

1036 conjugacy classes of subgroups.

The subgroup lattice has 704 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×#15689253	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689252	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244329	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	#20244326	C₂	1	1	yes	maximal, characteristic, complemented
8	#20244322	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243371	C₂	1	1	yes	maximal, characteristic
10	#20243369	C₂	1	1	yes	maximal, characteristic
11	#20243367	C₂	1	1	yes	maximal, characteristic
12	#20243155	C₂	1	1	yes	maximal, characteristic
13	#20243153	C₂	1	1	yes	maximal, characteristic
14	#20243149	C₂	1	1	yes	maximal, characteristic
15	C₄₇×#1984	C₂	1	1	yes	maximal, characteristic, complemented
16	#15689677	—	2	4	no	—
17	#15689677	—	2	4	no	—
18	C₂×#13094023	C₄	1	1	yes	characteristic
19	C₂×#13094022	C₄	1	1	yes	characteristic
20	C₂×#13094014	C₄	1	1	yes	characteristic
21	C₂×#13094014	C₄	1	1	yes	characteristic
22	C₂×#13094004	C₄	1	1	yes	characteristic
23	C₂×#13094002	C₄	1	1	yes	characteristic
24	C₂×#13094002	C₄	1	1	yes	characteristic
25	C₂×#13094000	C₄	1	1	yes	characteristic
26	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
27	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
28	C₂×C₄×Dic₉₄	C₂²	1	1	yes	characteristic
29	C₂×#13093981	C₂²	1	1	yes	characteristic
30	C₂×#13093981	C₂²	1	1	yes	characteristic
31	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
32	#15689253	—	2	4	no	—
33	#15689252	—	2	4	no	—
34	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
35	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
39	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
41	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
42	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
43	C₂×#13093935	C₂²	1	1	yes	characteristic
44	C₂×#13093934	C₂²	1	1	yes	characteristic
45	C₂×#13093934	C₂²	1	1	yes	characteristic
46	C₂×#13093934	C₂²	1	1	yes	characteristic
47	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
48	#15688878	C₂²	1	1	yes	characteristic
49	#15688878	C₂²	1	1	yes	characteristic
50	#15688878	C₂²	1	1	yes	characteristic
51	#15688878	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×C₄×C₈×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	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
70	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
71	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
72	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
73	#13094023	—	2	4	no	—
74	#13094022	—	2	4	no	—
75	#13094014	—	2	4	no	—
76	#13094014	—	2	4	no	—
77	#13094004	—	2	4	no	—
78	#13094002	—	2	4	no	—
79	#13094002	—	2	4	no	—
80	#13094000	—	2	4	no	—
81	C₄×Dic₉₄	—	2	2	no	—
82	C₄×Dic₉₄	—	2	2	no	—
83	C₄×Dic₉₄	—	2	2	no	—
84	C₄×Dic₉₄	—	2	2	no	—
85	C₄×Dic₉₄	D₄	1	4	yes	—
86	C₄×Dic₉₄	D₄	1	4	yes	—
87	#13093981	—	2	2	no	—
88	#13093981	—	2	2	no	—
89	#13093981	—	2	2	no	—
90	#13093981	—	2	2	no	—
91	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
92	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
93	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
94	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
99	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
100	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
101	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
102	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
103	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
104	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
105	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
106	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
107	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
108	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
109	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
110	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
111	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
112	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
113	C₄²×D₄₇	—	2	2	no	—
114	C₄²×D₄₇	—	2	2	no	—
115	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
116	Dic₄₇⋊C₈	—	2	2	no	—
117	Dic₄₇⋊C₈	—	2	2	no	—
118	Dic₄₇⋊C₈	—	2	2	no	—
119	Dic₄₇⋊C₈	—	2	2	no	—
120	(C₂×D₄₇)⋊C₈	—	2	2	no	—
121	(C₂×D₄₇)⋊C₈	—	2	2	no	—
122	(C₂×D₄₇)⋊C₈	—	2	2	no	—
123	(C₂×D₄₇)⋊C₈	Q₈	1	4	yes	complemented
124	#13093935	—	2	2	no	—
125	#13093934	—	2	2	no	—
126	#13093934	—	2	2	no	—
127	#13093934	—	2	2	no	—
128	C₈×Dic₄₇	—	2	2	no	—
129	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
130	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
132	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
133	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
134	C₄×Q₈×C₄₇	—	2	2	no	—
135	C₄×Q₈×C₄₇	—	2	2	no	—
136	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
137	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
138	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
139	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
140	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
141	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
142	C₄⋊C₈×C₄₇	—	2	2	no	—
143	C₄×C₈×C₄₇	—	2	2	no	—
144	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₂×Q₈×C₄₇	—	2	2	no	—
146	C₂×Q₈×C₄₇	—	2	2	no	—
147	C₂×Q₈×C₄₇	—	4	1	no	—
148	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
149	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
152	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
153	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
154	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
155	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
156	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
157	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
158	C₂²×Dic₄₇	C₂²×C₄	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	C₂×C₄×D₄₇	—	2	1	no	—
163	C₂×C₄×D₄₇	—	2	1	no	—
164	C₂×C₄×D₄₇	—	2	1	no	—
165	C₂×C₄×D₄₇	—	2	1	no	—
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	—	4	1	no	—
170	C₂×C₄×D₄₇	—	4	1	no	—
171	C₂×C₄×D₄₇	—	4	1	no	—
172	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
173	C₂×C₄×D₄₇	#41	1	2	yes	—
174	C₂×Dic₉₄	—	2	2	no	—
175	C₂×Dic₉₄	—	2	2	no	—
176	C₂×Dic₉₄	—	2	2	no	—
177	C₂×Dic₉₄	—	4	1	no	—
178	C₂×Dic₉₄	—	4	1	no	—
179	C₂×Dic₉₄	—	4	1	no	—
180	C₂×Dic₉₄	—	4	1	no	—
181	C₂×Dic₉₄	—	4	1	no	—
182	C₂×Dic₉₄	C₂²⋊C₄	1	4	yes	—
183	C₂×C₈×C₄₇	—	2	1	no	—
184	C₂×C₈×C₄₇	—	2	1	no	—
185	C₂×C₈×C₄₇	—	2	1	no	—
186	C₂×C₈×C₄₇	—	2	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	C₂×Q₈	1	2	yes	—
195	C₄⋊C₄×C₄₇	—	2	2	no	—
196	C₄⋊C₄×C₄₇	—	2	2	no	—
197	C₄⋊C₄×C₄₇	—	2	2	no	—
198	C₄²×C₄₇	—	2	1	no	—
199	C₄²×C₄₇	—	2	1	no	—
200	C₄²×C₄₇	—	2	1	no	—
201	C₄²×C₄₇	—	2	1	no	—
202	C₄²×C₄₇	C₂×D₄	1	2	yes	—
203	C₄²×C₄₇	C₂×D₄	1	2	yes	—
204	(C₂×D₄₇)⋊C₄	—	2	2	no	—
205	(C₂×D₄₇)⋊C₄	—	2	2	no	—
206	(C₂×D₄₇)⋊C₄	—	2	2	no	—
207	(C₂×D₄₇)⋊C₄	—	2	2	no	—
208	C₄⋊Dic₄₇	—	2	2	no	—
209	C₄⋊Dic₄₇	—	2	2	no	—
210	C₄⋊Dic₄₇	C₂²⋊C₄	1	4	yes	—
211	Dic₄₇⋊C₄	—	2	2	no	—
212	Dic₄₇⋊C₄	—	2	2	no	—
213	Dic₄₇⋊C₄	—	2	2	no	—
214	Dic₄₇⋊C₄	—	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	C₂²⋊C₄	1	4	yes	—
220	Dic₄₇⋊C₄	C₂²⋊C₄	1	4	yes	—
221	C₄×Dic₄₇	—	2	1	no	—
222	C₄×Dic₄₇	—	2	1	no	—
223	C₄×Dic₄₇	—	2	2	no	—
224	C₄×Dic₄₇	—	2	2	no	—
225	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
226	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
227	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
228	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
229	C₂×C₄₇⋊C₈	—	2	1	no	—
230	C₂×C₄₇⋊C₈	—	2	1	no	—
231	C₂×C₄₇⋊C₈	—	2	1	no	—
232	C₂×C₄₇⋊C₈	—	2	1	no	—
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	C₂×Q₈	1	2	yes	—
241	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
242	C₂²×D₄₇	—	2	1	no	—
243	C₂²×D₄₇	—	2	1	no	—
244	C₂²×D₄₇	—	2	1	no	—
245	C₂²×D₄₇	—	2	1	no	—
246	C₂²×D₄₇	—	2	1	no	—
247	C₂²×D₄₇	—	2	1	no	—
248	C₂²×D₄₇	C₄×Q₈	1	2	yes	—
249	Q₈×C₄₇	—	4	4	no	—
250	C₂×C₄×C₄₇	—	2	1	no	—
251	C₂×C₄×C₄₇	—	2	1	no	—
252	C₂×C₄×C₄₇	—	2	1	no	—
253	C₂×C₄×C₄₇	—	2	1	no	—
254	C₂×C₄×C₄₇	—	2	1	no	—
255	C₂×C₄×C₄₇	—	2	1	no	—
256	C₂×C₄×C₄₇	—	2	1	no	—
257	C₂×C₄×C₄₇	—	2	1	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	C₂×C₂²⋊C₄	1	2	yes	—
266	C₂×C₄×C₄₇	C₂×C₂²⋊C₄	1	2	yes	—
267	C₂×C₄×C₄₇	#131	1	2	yes	—
268	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
270	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
271	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
272	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
273	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
274	C₂×Dic₄₇	—	2	1	no	—
275	C₂×Dic₄₇	—	2	1	no	—
276	C₂×Dic₄₇	—	2	1	no	—
277	C₂×Dic₄₇	—	2	1	no	—
278	C₂×Dic₄₇	—	2	1	no	—
279	C₂×Dic₄₇	—	2	1	no	—
280	C₂×Dic₄₇	—	2	1	no	—
281	C₂×Dic₄₇	—	2	1	no	—
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	C₂×C₂²⋊C₄	1	2	yes	—
291	C₂×Dic₄₇	C₂×C₂²⋊C₄	1	2	yes	—
292	C₂×Dic₄₇	C₂×C₂²⋊C₄	1	2	yes	—
293	C₂×Dic₄₇	C₂×C₂²⋊C₄	1	2	yes	—
294	C₂×Dic₄₇	C₄×Q₈	1	2	yes	—
295	C₄×D₄₇	—	2	2	no	—
296	C₄×D₄₇	—	2	2	no	—
297	C₄×D₄₇	—	2	2	no	—
298	C₄×D₄₇	—	2	2	no	—
299	C₄×D₄₇	—	4	4	no	—
300	C₄×D₄₇	—	4	4	no	—
301	Dic₉₄	—	4	4	no	—
302	Dic₉₄	—	4	4	no	—
303	Dic₉₄	—	4	4	no	—
304	C₈×C₄₇	—	2	2	no	—
305	C₈×C₄₇	—	4	1	no	—
306	C₈×C₄₇	—	4	1	no	—
307	C₈×C₄₇	—	4	1	no	—
308	C₄₇⋊C₈	—	2	2	no	—
309	C₄₇⋊C₈	—	4	1	no	—
310	C₄₇⋊C₈	—	4	1	no	—
311	C₄₇⋊C₈	—	4	1	no	—
312	#22511	—	47	1	no	maximal, Sylow
313	C₂²×C₄₇	C₂²×C₂²⋊C₄	1	1	yes	characteristic
314	C₂²×C₄₇	C₂×C₄×Q₈	1	1	yes	characteristic
315	C₂²×C₄₇	#519	1	1	yes	characteristic
316	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
317	C₂²×C₄₇	#568	1	1	yes	characteristic
318	C₂²×C₄₇	#568	1	1	yes	characteristic
319	C₂²×C₄₇	#568	1	1	yes	characteristic
320	C₂×D₄₇	—	2	2	no	—
321	C₂×D₄₇	—	2	2	no	—
322	C₂×D₄₇	—	2	2	no	—
323	C₂×D₄₇	—	4	1	no	—
324	C₂×D₄₇	—	4	1	no	—
325	C₂×D₄₇	—	4	1	no	—
326	C₂×D₄₇	—	4	1	no	—
327	C₄×C₄₇	—	2	2	no	—
328	C₄×C₄₇	—	2	2	no	—
329	C₄×C₄₇	—	2	2	no	—
330	C₄×C₄₇	—	4	1	no	—
331	C₄×C₄₇	—	4	1	no	—
332	C₄×C₄₇	—	4	1	no	—
333	C₄×C₄₇	#548	1	1	yes	characteristic
334	C₄×C₄₇	#548	1	1	yes	characteristic
335	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
336	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
337	Dic₄₇	—	2	2	no	—
338	Dic₄₇	—	2	2	no	—
339	Dic₄₇	—	2	2	no	—
340	Dic₄₇	—	2	2	no	—
341	Dic₄₇	—	2	2	no	—
342	Dic₄₇	—	4	1	no	—
343	Dic₄₇	—	4	1	no	—
344	C₂×#533	—	47	1	no	—
345	C₂×#446	—	47	1	no	—
346	C₂×#446	—	47	1	no	—
347	#1985	—	47	1	no	—
348	#1985	—	47	1	no	—
349	#1985	—	47	1	no	—
350	#1985	—	47	1	no	—
351	#1984	—	47	1	no	—
352	#1984	D₄₇	1	1	yes	characteristic, complemented
353	#1798	—	47	1	no	—
354	#1798	—	47	1	no	—
355	#1797	—	47	1	no	—
356	#1750	—	47	1	no	—
357	#1750	—	47	1	no	—
358	#1749	—	47	1	no	—
359	C₂×C₄₇	Q₈×C₂²⋊C₄	1	1	yes	characteristic
360	C₂×C₄₇	#2879	1	1	yes	characteristic
361	C₂×C₄₇	#2880	1	1	yes	characteristic
362	C₂×C₄₇	#2961	1	1	yes	characteristic
363	C₂×C₄₇	#2962	1	1	yes	characteristic
364	C₂×C₄₇	#2985	1	1	yes	characteristic
365	C₂×C₄₇	#2987	1	1	yes	characteristic
366	D₄₇	—	4	2	no	—
367	#533	—	94	4	no	—
368	#533	—	94	4	no	—
369	C₂×C₄⋊Q₈	—	47	1	no	—
370	C₂×C₄⋊Q₈	—	47	1	no	—
371	C₂×#125	—	47	1	no	—
372	C₂×#125	—	47	1	no	—
373	C₂×C₂²⋊Q₈	—	47	1	no	—
374	C₂×C₂²⋊Q₈	—	47	1	no	—
375	C₂×C₂²⋊Q₈	—	47	1	no	—
376	C₂×C₂²⋊Q₈	—	47	1	no	—
377	C₂×C₄×Q₈	—	47	1	no	—
378	C₂×C₄×Q₈	—	47	1	no	—
379	C₂×C₄×Q₈	—	47	1	no	—
380	C₂×C₄×Q₈	C₂×D₄₇	1	1	yes	characteristic
381	C₂×#117	—	47	1	no	—
382	C₂×#117	—	47	1	no	—
383	C₂²×C₄²	—	47	1	no	—
384	#446	—	94	4	no	—
385	#446	—	94	4	no	—
386	C₂×C₄⋊C₈	—	47	1	no	—
387	C₂×C₄⋊C₈	—	47	1	no	—
388	C₂×C₄⋊C₈	—	47	1	no	—
389	C₂×C₄⋊C₈	—	47	1	no	—
390	C₂×C₄⋊C₈	—	47	1	no	—
391	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
392	C₂×C₂²⋊C₈	—	47	1	no	—
393	C₂×C₂²⋊C₈	—	47	1	no	—
394	C₂×C₂²⋊C₈	—	47	1	no	—
395	C₂×C₂²⋊C₈	—	47	1	no	—
396	C₂×#97	—	47	1	no	—
397	C₂×#97	—	47	1	no	—
398	C₂×#97	—	47	1	no	—
399	C₂×#97	—	47	1	no	—
400	C₂×C₄×C₈	—	47	1	no	—
401	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
402	#336	—	47	1	no	—
403	#336	—	47	1	no	—
404	#336	—	47	1	no	—
405	#336	—	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	C₂×D₄₇	1	1	yes	characteristic
411	#336	C₂×D₄₇	1	1	yes	characteristic
412	#336	C₂×D₄₇	1	1	yes	characteristic
413	#336	C₂×D₄₇	1	1	yes	characteristic
414	C₄₇	#22511	1	1	yes	characteristic, complemented, Sylow
415	C₂²×Q₈	—	47	1	no	—
416	C₂²×Q₈	—	47	1	no	—
417	C₂²×Q₈	—	47	1	no	—
418	C₂²×Q₈	C₄×D₄₇	1	1	yes	characteristic
419	C₂³×C₄	—	47	1	no	—
420	C₂³×C₄	—	47	1	no	—
421	C₂³×C₄	—	47	1	no	—
422	C₂²×C₈	—	47	1	no	—
423	C₂²×C₈	—	47	1	no	—
424	C₂²×C₈	—	47	1	no	—
425	C₂²×C₈	—	47	1	no	—
426	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
427	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
428	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
429	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
430	C₄⋊Q₈	—	94	4	no	—
431	C₄⋊Q₈	—	94	4	no	—
432	#125	—	94	4	no	—
433	#125	—	94	4	no	—
434	C₂²⋊Q₈	—	94	4	no	—
435	C₂²⋊Q₈	—	94	4	no	—
436	C₂²⋊Q₈	—	94	4	no	—
437	C₂²⋊Q₈	—	94	4	no	—
438	C₄×Q₈	—	2	2	no	—
439	C₄×Q₈	—	2	2	no	—
440	C₄×Q₈	—	47	4	no	—
441	C₄×Q₈	—	47	4	no	—
442	C₄×Q₈	—	94	2	no	—
443	C₄×Q₈	—	94	2	no	—
444	C₄×Q₈	—	94	2	no	—
445	C₄×Q₈	—	94	2	no	—
446	#117	—	94	2	no	—
447	#117	—	94	2	no	—
448	#117	—	94	2	no	—
449	#117	—	94	2	no	—
450	C₂×C₄⋊C₄	—	47	1	no	—
451	C₂×C₄⋊C₄	—	47	1	no	—
452	C₂×C₄⋊C₄	—	47	1	no	—
453	C₂×C₄⋊C₄	—	47	1	no	—
454	C₂×C₄⋊C₄	—	47	1	no	—
455	C₂×C₄⋊C₄	—	47	1	no	—
456	C₂×C₄⋊C₄	—	47	1	no	—
457	C₂×C₄⋊C₄	—	47	1	no	—
458	C₂×C₄⋊C₄	—	47	1	no	—
459	C₂×C₄⋊C₄	—	47	1	no	—
460	C₂×C₄⋊C₄	—	47	1	no	—
461	C₂×C₄⋊C₄	—	47	1	no	—
462	C₂×C₄⋊C₄	—	47	1	no	—
463	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
464	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
465	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
466	C₂×C₂²⋊C₄	—	47	1	no	—
467	C₂×C₂²⋊C₄	—	47	1	no	—
468	C₂×C₂²⋊C₄	—	47	1	no	—
469	C₂×C₂²⋊C₄	—	47	1	no	—
470	C₂×C₄²	—	47	1	no	—
471	C₂×C₄²	—	47	1	no	—
472	C₂×C₄²	—	47	1	no	—
473	C₂×C₄²	—	47	1	no	—
474	C₂×C₄²	—	47	1	no	—
475	C₂×C₄²	—	94	2	no	—
476	C₂×C₄²	—	94	2	no	—
477	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
478	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
479	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
480	C₄⋊C₈	—	2	2	no	—
481	C₄⋊C₈	—	94	2	no	—
482	C₄⋊C₈	—	94	2	no	—
483	C₄⋊C₈	—	94	2	no	—
484	C₄⋊C₈	—	94	2	no	—
485	C₄⋊C₈	—	94	2	no	—
486	C₂²⋊C₈	—	47	4	no	—
487	C₂²⋊C₈	—	94	2	no	—
488	C₂²⋊C₈	—	94	2	no	—
489	C₂²⋊C₈	—	94	2	no	—
490	#97	—	94	2	no	—
491	#97	—	94	2	no	—
492	#97	—	94	2	no	—
493	#97	—	94	2	no	—
494	C₄×C₈	—	2	2	no	—
495	C₄×C₈	—	94	2	no	—
496	C₂⁴	—	47	1	no	—
497	C₂×Q₈	—	2	2	no	—
498	C₂×Q₈	—	2	2	no	—
499	C₂×Q₈	—	4	1	no	—
500	C₂×Q₈	—	47	4	no	—
501	C₂×Q₈	—	94	2	no	—
502	C₂×Q₈	—	94	2	no	—
503	C₂×Q₈	—	94	2	no	—
504	C₂×Q₈	—	188	1	no	—
505	C₂×Q₈	—	188	1	no	—
506	C₂×Q₈	—	188	1	no	—
507	C₂×Q₈	—	188	1	no	—
508	C₂×Q₈	—	188	1	no	—
509	C₂²×C₄	—	47	1	no	—
510	C₂²×C₄	—	47	1	no	—
511	C₂²×C₄	—	47	1	no	—
512	C₂²×C₄	—	47	1	no	—
513	C₂²×C₄	—	47	1	no	—
514	C₂²×C₄	—	47	2	no	—
515	C₂²×C₄	—	47	2	no	—
516	C₂²×C₄	—	47	1	no	—
517	C₂²×C₄	—	47	1	no	—
518	C₂²×C₄	—	94	2	no	—
519	C₂²×C₄	—	94	2	no	—
520	C₂²×C₄	—	94	1	no	—
521	C₂²×C₄	—	94	1	no	—
522	C₂²×C₄	—	94	1	no	—
523	C₂²×C₄	—	94	1	no	—
524	C₂²×C₄	—	94	2	no	—
525	C₂²×C₄	—	188	1	no	—
526	C₂²×C₄	—	188	1	no	—
527	C₂²×C₄	—	188	1	no	—
528	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
529	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
530	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
531	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
532	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
533	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
534	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	2	1	no	—
538	C₂×C₈	—	2	1	no	—
539	C₂×C₈	—	2	1	no	—
540	C₂×C₈	—	2	1	no	—
541	C₂×C₈	—	2	1	no	—
542	C₂×C₈	—	2	1	no	—
543	C₂×C₈	—	2	1	no	—
544	C₂×C₈	—	2	1	no	—
545	C₂×C₈	—	2	1	no	—
546	C₂×C₈	—	47	2	no	—
547	C₂×C₈	—	94	1	no	—
548	C₂×C₈	—	94	1	no	—
549	C₂×C₈	—	94	1	no	—
550	C₂×C₈	—	94	1	no	—
551	C₂×C₈	—	94	1	no	—
552	C₂×C₈	—	94	1	no	—
553	C₂×C₈	—	94	1	no	—
554	C₂×C₈	—	94	1	no	—
555	C₂×C₈	—	94	1	no	—
556	C₂×C₈	—	94	1	no	—
557	C₂×C₈	—	94	1	no	—
558	C₂×C₈	Q₈×D₄₇	1	2	yes	—
559	C₄⋊C₄	—	2	2	no	—
560	C₄⋊C₄	—	2	2	no	—
561	C₄⋊C₄	—	2	2	no	—
562	C₄⋊C₄	—	47	4	no	—
563	C₄⋊C₄	—	47	4	no	—
564	C₄⋊C₄	—	47	4	no	—
565	C₄⋊C₄	—	94	2	no	—
566	C₄⋊C₄	—	94	2	no	—
567	C₄⋊C₄	—	94	2	no	—
568	C₄⋊C₄	—	94	2	no	—
569	C₄⋊C₄	—	94	2	no	—
570	C₄⋊C₄	—	94	2	no	—
571	C₄⋊C₄	—	94	2	no	—
572	C₄⋊C₄	—	94	2	no	—
573	C₄⋊C₄	—	94	2	no	—
574	C₄⋊C₄	—	94	2	no	—
575	C₂²⋊C₄	—	94	2	no	—
576	C₂²⋊C₄	—	94	2	no	—
577	C₂²⋊C₄	—	94	2	no	—
578	C₂²⋊C₄	—	94	2	no	—
579	C₄²	—	2	1	no	—
580	C₄²	—	2	1	no	—
581	C₄²	—	2	1	no	—
582	C₄²	—	2	1	no	—
583	C₄²	—	47	2	no	—
584	C₄²	—	47	2	no	—
585	C₄²	—	47	2	no	—
586	C₄²	—	47	2	no	—
587	C₄²	—	94	2	no	—
588	C₄²	—	94	2	no	—
589	C₄²	—	94	1	no	—
590	C₄²	—	94	1	no	—
591	C₄²	D₄×D₄₇	1	2	yes	—
592	C₄²	D₄×D₄₇	1	2	yes	—
593	C₂³	—	47	2	no	—
594	C₂³	—	94	1	no	—
595	C₂³	—	94	1	no	—
596	C₂³	—	94	1	no	—
597	C₂³	—	94	1	no	—
598	C₂³	—	94	1	no	—
599	C₂³	—	94	1	no	—
600	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
601	Q₈	—	4	4	no	—
602	Q₈	—	188	4	no	—
603	Q₈	—	188	4	no	—
604	Q₈	—	188	4	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	1	no	—
608	C₂×C₄	—	2	1	no	—
609	C₂×C₄	—	2	1	no	—
610	C₂×C₄	—	2	1	no	—
611	C₂×C₄	—	2	1	no	—
612	C₂×C₄	—	2	1	no	—
613	C₂×C₄	—	2	1	no	—
614	C₂×C₄	—	2	1	no	—
615	C₂×C₄	—	2	1	no	—
616	C₂×C₄	—	2	1	no	—
617	C₂×C₄	—	2	1	no	—
618	C₂×C₄	—	2	1	no	—
619	C₂×C₄	—	2	1	no	—
620	C₂×C₄	—	47	2	no	—
621	C₂×C₄	—	47	2	no	—
622	C₂×C₄	—	47	2	no	—
623	C₂×C₄	—	47	2	no	—
624	C₂×C₄	—	47	2	no	—
625	C₂×C₄	—	94	1	no	—
626	C₂×C₄	—	94	1	no	—
627	C₂×C₄	—	94	1	no	—
628	C₂×C₄	—	94	1	no	—
629	C₂×C₄	—	94	1	no	—
630	C₂×C₄	—	94	1	no	—
631	C₂×C₄	—	94	1	no	—
632	C₂×C₄	—	94	1	no	—
633	C₂×C₄	—	94	1	no	—
634	C₂×C₄	—	94	1	no	—
635	C₂×C₄	—	94	2	no	—
636	C₂×C₄	—	94	2	no	—
637	C₂×C₄	—	94	2	no	—
638	C₂×C₄	—	94	2	no	—
639	C₂×C₄	—	94	1	no	—
640	C₂×C₄	—	94	1	no	—
641	C₂×C₄	—	94	1	no	—
642	C₂×C₄	—	94	1	no	—
643	C₂×C₄	—	94	1	no	—
644	C₂×C₄	—	94	1	no	—
645	C₂×C₄	—	188	4	no	—
646	C₂×C₄	—	188	4	no	—
647	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
648	C₂×C₄	C₂²⋊C₄×D₄₇	1	2	yes	—
649	C₂×C₄	#13094030	1	2	yes	—
650	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
651	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
652	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
653	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
654	C₂×C₄	#13094071	1	1	yes	characteristic
655	C₂×C₄	#13094072	1	1	yes	characteristic
656	C₈	—	2	2	no	—
657	C₈	—	4	1	no	—
658	C₈	—	4	1	no	—
659	C₈	—	4	1	no	—
660	C₈	—	94	2	no	—
661	C₈	—	188	1	no	—
662	C₈	—	188	1	no	—
663	C₈	—	188	1	no	—
664	C₂²	—	94	2	no	—
665	C₂²	—	94	2	no	—
666	C₂²	—	94	2	no	—
667	C₂²	—	188	1	no	—
668	C₂²	—	188	1	no	—
669	C₂²	—	188	1	no	—
670	C₂²	—	188	1	no	—
671	C₂²	C₂×C₂²⋊C₄×D₄₇	1	1	yes	characteristic
672	C₂²	C₄×Q₈×D₄₇	1	1	yes	characteristic
673	C₂²	#15689599	1	1	yes	characteristic
674	C₂²	C₂×#13094030	1	1	yes	characteristic
675	C₂²	#15689888	1	1	yes	characteristic
676	C₂²	#15689888	1	1	yes	characteristic
677	C₂²	#15689889	1	1	yes	characteristic
678	C₄	—	2	2	no	—
679	C₄	—	2	2	no	—
680	C₄	—	2	2	no	—
681	C₄	—	4	1	no	—
682	C₄	—	4	1	no	—
683	C₄	—	4	1	no	—
684	C₄	—	94	2	no	—
685	C₄	—	94	2	no	—
686	C₄	—	94	2	no	—
687	C₄	—	94	2	no	—
688	C₄	—	94	2	no	—
689	C₄	—	188	1	no	—
690	C₄	—	188	1	no	—
691	C₄	#15689781	1	1	yes	characteristic
692	C₄	#15689783	1	1	yes	characteristic
693	C₄	#15689786	1	1	yes	characteristic
694	C₄	#15689788	1	1	yes	characteristic
695	C₂	—	188	2	no	—
696	C₂	#20246222	1	1	yes	characteristic
697	C₂	#20251830	1	1	yes	characteristic
698	C₂	#20251834	1	1	yes	characteristic
699	C₂	#20252324	1	1	yes	characteristic
700	C₂	#20252330	1	1	yes	characteristic
701	C₂	#20252479	1	1	yes	characteristic
702	C₂	#20252491	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1984	C₂
prime radical	C₂³×D₄₇	C₂²×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1984	D₄₇
hypocenter	C₄₇	#22511
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1984

Complements

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

N	H ≅ G/N	type
2. C₂×#15689253	C₂	semidirect
3. C₂×#15689252	C₂	semidirect
4. #20244329	C₂	semidirect
5. #20244326	C₂	semidirect
6. #20244326	C₂	semidirect
7. #20244326	C₂	semidirect
8. #20244322	C₂	semidirect
15. C₄₇×#1984	C₂	semidirect
123. (C₂×D₄₇)⋊C₈	Q₈	semidirect
352. #1984	D₄₇	semidirect
414. C₄₇	#22511	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×#15689253	2
C₂×#15689252	2
#20244329	2
#20244326	2
#20244322	2
#20243371	2
#20243369	2
#20243367	2
#20243155	2
#20243153	2
#20243149	2
C₄₇×#1984	2
#22511	47