Subgroups — #26233316

Order 12032.

990 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689184	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15689090	C₂	1	1	yes	maximal, characteristic
3	#20244003	C₂	1	1	yes	maximal, characteristic, complemented
4	#20244003	C₂	1	1	yes	maximal, characteristic, complemented
5	#20244003	C₂	1	1	yes	maximal, characteristic, complemented
6	#20243996	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243573	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243568	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243459	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243368	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243300	C₂	1	1	yes	maximal, characteristic
12	#20243172	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243166	C₂	1	1	yes	maximal, characteristic, complemented
14	#20243150	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#2297	C₂	1	1	yes	maximal, characteristic
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	#15689184	—	2	4	no	—
19	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
21	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
22	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
23	#15689090	—	2	4	no	—
24	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
25	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
26	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
30	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
31	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
32	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
33	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
34	C₂×#13093935	C₂²	1	1	yes	characteristic
35	C₂×#13093935	C₂²	1	1	yes	characteristic
36	C₂×#13093935	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
38	#15688878	C₂²	1	1	yes	characteristic
39	#15688878	C₂²	1	1	yes	characteristic
40	#15688878	C₂²	1	1	yes	characteristic
41	#15688878	C₂²	1	1	yes	characteristic
42	#15688878	C₂²	1	1	yes	characteristic
43	#15688878	C₂²	1	1	yes	characteristic
44	#15688878	C₂²	1	1	yes	characteristic
45	#15688878	C₂²	1	1	yes	characteristic
46	C₂²×#41×C₄₇	C₂²	1	1	yes	characteristic
47	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
48	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
49	C₄₇×#391	C₄	1	1	yes	characteristic
50	C₄₇×#391	C₄	1	1	yes	characteristic
51	C₄₇×#390	C₄	1	1	yes	characteristic
52	C₄₇×#390	C₄	1	1	yes	characteristic
53	C₄₇×#386	C₄	1	1	yes	characteristic
54	C₄₇×#386	C₄	1	1	yes	characteristic
55	C₄₇×#386	C₄	1	1	yes	characteristic
56	C₄₇×#386	C₄	1	1	yes	characteristic
57	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
58	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
59	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
60	C₄×C₂²⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
61	C₂×#10625329	—	2	2	no	—
62	C₂×#10625329	—	2	2	no	—
63	C₂×#10625329	—	4	1	no	—
64	C₂²×C₄₇⋊C₈	—	2	2	no	—
65	C₂²×C₄₇⋊C₈	—	2	2	no	—
66	C₂²×C₄₇⋊C₈	—	4	1	no	—
67	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
68	C₂²×C₄₇⋊C₈	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	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
74	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
75	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
76	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
77	C₄⋊(C₄₇⋊C₈)	—	4	1	no	—
78	C₄⋊(C₄₇⋊C₈)	—	4	1	no	—
79	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
80	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
81	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
82	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
83	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
84	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
85	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
86	C₂²⋊(C₄₇⋊C₈)	—	4	1	no	—
87	C₂²⋊(C₄₇⋊C₈)	—	4	1	no	—
88	C₂²⋊(C₄₇⋊C₈)	D₄	1	4	yes	—
89	#13093935	—	2	2	no	—
90	#13093935	—	4	1	no	—
91	#13093935	—	4	1	no	—
92	C₄×C₄₇⋊C₈	—	2	2	no	—
93	C₂×#41×C₄₇	—	2	2	no	—
94	C₂×#41×C₄₇	—	2	2	no	—
95	C₂×#41×C₄₇	—	2	2	no	—
96	C₂×#41×C₄₇	—	2	2	no	—
97	C₂×#41×C₄₇	—	4	1	no	—
98	C₂×#41×C₄₇	—	4	1	no	—
99	C₂²×Q₈×C₄₇	C₂×C₄	1	1	yes	characteristic
100	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
101	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
102	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
103	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
104	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
105	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
106	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
107	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
108	#117×C₄₇	—	2	2	no	—
109	#117×C₄₇	—	2	2	no	—
110	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
111	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
112	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
113	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
114	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
115	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
116	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
117	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
118	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
119	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
120	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
121	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
122	C₂×C₄²×C₄₇	—	4	1	no	—
123	C₂×C₄²×C₄₇	—	4	1	no	—
124	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
125	C₂×C₄²×C₄₇	C₂×C₄	1	1	yes	characteristic
126	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
127	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
128	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
129	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
130	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
131	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
132	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
133	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
134	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
135	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
136	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
137	#95×C₄₇	C₂×C₄	1	1	yes	characteristic
138	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
139	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
140	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
141	#41×C₄₇	—	4	4	no	—
142	#41×C₄₇	—	4	4	no	—
143	#41×C₄₇	—	4	4	no	—
144	#41×C₄₇	—	4	4	no	—
145	C₂×Q₈×C₄₇	—	2	2	no	—
146	C₂×Q₈×C₄₇	—	2	2	no	—
147	C₂×Q₈×C₄₇	—	4	1	no	—
148	C₂×D₄×C₄₇	—	2	2	no	—
149	C₂×D₄×C₄₇	—	2	2	no	—
150	C₂×D₄×C₄₇	—	2	2	no	—
151	C₂×D₄×C₄₇	—	2	2	no	—
152	C₂×D₄×C₄₇	—	2	2	no	—
153	C₂×D₄×C₄₇	—	2	2	no	—
154	C₂×D₄×C₄₇	—	4	1	no	—
155	C₂×D₄×C₄₇	—	4	1	no	—
156	C₂×D₄×C₄₇	—	4	1	no	—
157	C₂²×C₄×C₄₇	—	2	1	no	—
158	C₂²×C₄×C₄₇	—	2	1	no	—
159	C₂²×C₄×C₄₇	—	2	1	no	—
160	C₂²×C₄×C₄₇	—	2	1	no	—
161	C₂²×C₄×C₄₇	—	2	1	no	—
162	C₂²×C₄×C₄₇	—	2	1	no	—
163	C₂²×C₄×C₄₇	—	2	1	no	—
164	C₂²×C₄×C₄₇	—	2	1	no	—
165	C₂²×C₄×C₄₇	—	2	2	no	—
166	C₂²×C₄×C₄₇	—	2	1	no	—
167	C₂²×C₄×C₄₇	—	2	1	no	—
168	C₂²×C₄×C₄₇	—	2	1	no	—
169	C₂²×C₄×C₄₇	—	2	1	no	—
170	C₂²×C₄×C₄₇	—	2	1	no	—
171	C₂²×C₄×C₄₇	—	2	1	no	—
172	C₂²×C₄×C₄₇	—	4	1	no	—
173	C₂²×C₄×C₄₇	—	4	1	no	—
174	C₂²×C₄×C₄₇	—	4	1	no	—
175	C₂²×C₄×C₄₇	—	4	1	no	—
176	C₂²×C₄×C₄₇	—	4	1	no	—
177	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
178	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
179	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
180	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
181	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
182	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
183	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
184	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
185	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
189	C₂²×C₄×C₄₇	#41	1	2	yes	—
190	C₂²×C₄×C₄₇	#41	1	2	yes	—
191	C₂²×C₄×C₄₇	#41	1	2	yes	—
192	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
193	C₄⋊C₄×C₄₇	—	2	2	no	—
194	C₄⋊C₄×C₄₇	—	2	2	no	—
195	C₂²⋊C₄×C₄₇	—	2	2	no	—
196	C₂²⋊C₄×C₄₇	—	2	2	no	—
197	C₂²⋊C₄×C₄₇	—	2	2	no	—
198	C₂²⋊C₄×C₄₇	—	2	2	no	—
199	C₂²⋊C₄×C₄₇	—	4	1	no	—
200	C₂²⋊C₄×C₄₇	—	4	1	no	—
201	C₂²⋊C₄×C₄₇	—	4	1	no	—
202	C₂²⋊C₄×C₄₇	—	4	1	no	—
203	C₂²⋊C₄×C₄₇	—	4	1	no	—
204	C₂²⋊C₄×C₄₇	—	4	1	no	—
205	C₄²×C₄₇	—	2	1	no	—
206	C₄²×C₄₇	—	2	1	no	—
207	C₄²×C₄₇	—	2	1	no	—
208	C₄²×C₄₇	—	2	1	no	—
209	C₄²×C₄₇	—	2	1	no	—
210	C₄²×C₄₇	—	2	1	no	—
211	C₄²×C₄₇	—	2	1	no	—
212	C₄²×C₄₇	—	2	1	no	—
213	C₄²×C₄₇	—	4	1	no	—
214	C₄²×C₄₇	—	4	1	no	—
215	#10625329	—	4	4	no	—
216	C₂×C₄₇⋊C₈	—	2	1	no	—
217	C₂×C₄₇⋊C₈	—	2	1	no	—
218	C₂×C₄₇⋊C₈	—	2	1	no	—
219	C₂×C₄₇⋊C₈	—	2	1	no	—
220	C₂×C₄₇⋊C₈	—	2	1	no	—
221	C₂×C₄₇⋊C₈	—	2	1	no	—
222	C₂×C₄₇⋊C₈	—	2	1	no	—
223	C₂×C₄₇⋊C₈	—	2	1	no	—
224	C₂×C₄₇⋊C₈	—	2	1	no	—
225	C₂×C₄₇⋊C₈	—	2	1	no	—
226	C₂×C₄₇⋊C₈	—	2	1	no	—
227	C₂×C₄₇⋊C₈	—	2	1	no	—
228	C₂×C₄₇⋊C₈	—	2	1	no	—
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	—	4	4	no	—
239	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
240	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
241	C₂³×C₄₇	—	2	1	no	—
242	C₂³×C₄₇	—	2	1	no	—
243	C₂³×C₄₇	—	2	1	no	—
244	C₂³×C₄₇	—	2	1	no	—
245	C₂³×C₄₇	—	2	1	no	—
246	C₂³×C₄₇	—	2	1	no	—
247	C₂³×C₄₇	—	2	1	no	—
248	C₂³×C₄₇	—	2	1	no	—
249	C₂³×C₄₇	—	2	1	no	—
250	C₂³×C₄₇	—	2	1	no	—
251	C₂³×C₄₇	—	2	1	no	—
252	C₂³×C₄₇	—	2	1	no	—
253	C₂³×C₄₇	—	2	1	no	—
254	C₂³×C₄₇	—	2	1	no	—
255	C₂³×C₄₇	—	2	1	no	—
256	C₂³×C₄₇	—	2	1	no	—
257	C₂³×C₄₇	—	2	1	no	—
258	C₂³×C₄₇	—	2	1	no	—
259	C₂³×C₄₇	—	2	1	no	—
260	C₂³×C₄₇	#117	1	2	yes	—
261	C₂³×C₄₇	C₄×D₄	1	2	yes	—
262	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
263	Q₈×C₄₇	—	4	4	no	—
264	D₄×C₄₇	—	4	4	no	—
265	D₄×C₄₇	—	4	4	no	—
266	D₄×C₄₇	—	4	4	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	—	2	2	no	—
274	C₂×C₄×C₄₇	—	2	2	no	—
275	C₂×C₄×C₄₇	—	2	2	no	—
276	C₂×C₄×C₄₇	—	2	2	no	—
277	C₂×C₄×C₄₇	—	2	2	no	—
278	C₂×C₄×C₄₇	—	2	2	no	—
279	C₂×C₄×C₄₇	—	2	2	no	—
280	C₂×C₄×C₄₇	—	2	2	no	—
281	C₂×C₄×C₄₇	—	2	1	no	—
282	C₂×C₄×C₄₇	—	2	1	no	—
283	C₂×C₄×C₄₇	—	2	1	no	—
284	C₂×C₄×C₄₇	—	2	1	no	—
285	C₂×C₄×C₄₇	—	2	1	no	—
286	C₂×C₄×C₄₇	—	2	1	no	—
287	C₂×C₄×C₄₇	—	2	1	no	—
288	C₂×C₄×C₄₇	—	2	1	no	—
289	C₂×C₄×C₄₇	—	2	1	no	—
290	C₂×C₄×C₄₇	—	2	1	no	—
291	C₂×C₄×C₄₇	—	2	1	no	—
292	C₂×C₄×C₄₇	—	2	1	no	—
293	C₂×C₄×C₄₇	—	2	1	no	—
294	C₂×C₄×C₄₇	—	2	1	no	—
295	C₂×C₄×C₄₇	—	2	1	no	—
296	C₂×C₄×C₄₇	—	2	1	no	—
297	C₂×C₄×C₄₇	—	2	1	no	—
298	C₂×C₄×C₄₇	—	2	1	no	—
299	C₂×C₄×C₄₇	—	2	1	no	—
300	C₂×C₄×C₄₇	—	2	1	no	—
301	C₂×C₄×C₄₇	—	2	1	no	—
302	C₂×C₄×C₄₇	—	2	1	no	—
303	C₂×C₄×C₄₇	—	2	1	no	—
304	C₂×C₄×C₄₇	—	2	1	no	—
305	C₂×C₄×C₄₇	—	4	4	no	—
306	C₂×C₄×C₄₇	—	4	4	no	—
307	C₂×C₄×C₄₇	—	4	1	no	—
308	C₂×C₄×C₄₇	—	4	1	no	—
309	C₂×C₄×C₄₇	—	4	1	no	—
310	C₂×C₄×C₄₇	—	4	1	no	—
311	C₂×C₄×C₄₇	#117	1	2	yes	—
312	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
313	C₂×C₄×C₄₇	#131	1	2	yes	—
314	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
315	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
316	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
317	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
318	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
319	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
320	C₄₇⋊C₈	—	2	2	no	—
321	C₄₇⋊C₈	—	2	2	no	—
322	C₄₇⋊C₈	—	4	1	no	—
323	C₄₇⋊C₈	—	4	1	no	—
324	C₄₇⋊C₈	—	4	1	no	—
325	C₄₇⋊C₈	—	4	1	no	—
326	C₄₇⋊C₈	—	4	1	no	—
327	C₄₇⋊C₈	—	4	1	no	—
328	#22561	—	47	1	no	maximal, Sylow
329	C₂²×C₄₇	—	2	2	no	—
330	C₂²×C₄₇	—	2	2	no	—
331	C₂²×C₄₇	—	2	2	no	—
332	C₂²×C₄₇	—	2	2	no	—
333	C₂²×C₄₇	—	2	2	no	—
334	C₂²×C₄₇	—	2	2	no	—
335	C₂²×C₄₇	—	4	1	no	—
336	C₂²×C₄₇	—	4	1	no	—
337	C₂²×C₄₇	—	4	1	no	—
338	C₂²×C₄₇	—	4	1	no	—
339	C₂²×C₄₇	—	4	1	no	—
340	C₂²×C₄₇	—	4	1	no	—
341	C₂²×C₄₇	—	4	1	no	—
342	C₂²×C₄₇	—	4	1	no	—
343	C₂²×C₄₇	—	4	1	no	—
344	C₂²×C₄₇	—	4	1	no	—
345	C₂²×C₄₇	—	4	1	no	—
346	C₂²×C₄₇	—	4	1	no	—
347	C₂²×C₄₇	—	4	1	no	—
348	C₂²×C₄₇	—	4	1	no	—
349	C₂²×C₄₇	—	4	1	no	—
350	C₂²×C₄₇	C₂×#117	1	1	yes	characteristic
351	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
352	C₂²×C₄₇	#518	1	1	yes	characteristic
353	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
354	C₂²×C₄₇	#568	1	1	yes	characteristic
355	C₂²×C₄₇	#568	1	1	yes	characteristic
356	C₂²×C₄₇	#568	1	1	yes	characteristic
357	C₄×C₄₇	—	2	2	no	—
358	C₄×C₄₇	—	2	2	no	—
359	C₄×C₄₇	—	2	2	no	—
360	C₄×C₄₇	—	4	1	no	—
361	C₄×C₄₇	—	4	1	no	—
362	C₄×C₄₇	—	4	1	no	—
363	C₄×C₄₇	—	4	1	no	—
364	C₄×C₄₇	—	4	1	no	—
365	C₄×C₄₇	—	4	1	no	—
366	C₄×C₄₇	—	4	1	no	—
367	C₄×C₄₇	—	4	1	no	—
368	C₄×C₄₇	#546	1	1	yes	characteristic
369	C₄×C₄₇	#546	1	1	yes	characteristic
370	C₄×C₄₇	#551	1	1	yes	characteristic
371	C₄×C₄₇	#551	1	1	yes	characteristic
372	C₂×#433	—	47	1	no	—
373	C₂×#408	—	47	1	no	—
374	#2297	D₄₇	1	1	yes	characteristic
375	#1924	—	47	1	no	—
376	#1924	—	47	1	no	—
377	#1924	—	47	1	no	—
378	#1923	—	47	1	no	—
379	#1851	—	47	1	no	—
380	#1850	—	47	1	no	—
381	#1818	—	47	1	no	—
382	#1797	—	47	1	no	—
383	#1780	—	47	1	no	—
384	#1753	—	47	1	no	—
385	#1752	—	47	1	no	—
386	#1749	—	47	1	no	—
387	C₂×C₄₇	—	4	2	no	—
388	C₂×C₄₇	—	4	2	no	—
389	C₂×C₄₇	—	8	1	no	—
390	C₂×C₄₇	#2342	1	1	yes	characteristic
391	C₂×C₄₇	#2923	1	1	yes	characteristic
392	C₂×C₄₇	#2925	1	1	yes	characteristic
393	C₂×C₄₇	#2932	1	1	yes	characteristic
394	C₂×C₄₇	#2935	1	1	yes	characteristic
395	C₂×C₄₇	#2976	1	1	yes	characteristic
396	C₂×C₄₇	#2978	1	1	yes	characteristic
397	C₂²×#41	C₂×D₄₇	1	1	yes	characteristic
398	C₂²×M₁₆	—	47	1	no	—
399	C₂³×C₈	—	47	1	no	—
400	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
401	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
402	#433	—	94	4	no	—
403	C₂×C₄⋊C₈	—	47	1	no	—
404	C₂×C₄⋊C₈	—	47	1	no	—
405	C₂×C₄⋊C₈	—	47	1	no	—
406	C₂×C₄⋊C₈	—	47	1	no	—
407	#408	—	94	4	no	—
408	C₂×C₂²⋊C₈	—	47	1	no	—
409	C₂×C₂²⋊C₈	—	47	1	no	—
410	C₂×C₂²⋊C₈	—	47	1	no	—
411	C₂×C₂²⋊C₈	—	47	1	no	—
412	C₂×C₂²⋊C₈	—	47	1	no	—
413	C₂×C₂²⋊C₈	—	47	1	no	—
414	C₂×C₂²⋊C₈	—	47	1	no	—
415	C₂×C₂²⋊C₈	—	47	1	no	—
416	C₂×C₂²⋊C₈	—	47	1	no	—
417	C₂×C₂²⋊C₈	—	47	1	no	—
418	C₂×#97	—	47	1	no	—
419	C₂×#97	—	47	1	no	—
420	C₂×#97	—	47	1	no	—
421	C₂×C₄×C₈	—	47	1	no	—
422	#391	Dic₄₇	1	1	yes	characteristic
423	#391	Dic₄₇	1	1	yes	characteristic
424	#390	Dic₄₇	1	1	yes	characteristic
425	#390	Dic₄₇	1	1	yes	characteristic
426	#386	Dic₄₇	1	1	yes	characteristic
427	#386	Dic₄₇	1	1	yes	characteristic
428	#386	Dic₄₇	1	1	yes	characteristic
429	#386	Dic₄₇	1	1	yes	characteristic
430	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
431	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
432	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
433	C₄×C₂²⋊C₄	C₂×D₄₇	1	1	yes	characteristic
434	#336	—	47	1	no	—
435	#336	—	47	1	no	—
436	#336	—	47	1	no	—
437	#336	—	47	1	no	—
438	#336	—	47	1	no	—
439	#336	—	47	1	no	—
440	#336	—	47	1	no	—
441	#336	—	47	1	no	—
442	C₄₇	#22561	1	1	yes	characteristic, complemented, Sylow
443	C₂×#41	—	2	2	no	—
444	C₂×#41	—	2	2	no	—
445	C₂×#41	—	2	2	no	—
446	C₂×#41	—	2	2	no	—
447	C₂×#41	—	4	1	no	—
448	C₂×#41	—	4	1	no	—
449	C₂²×Q₈	C₂×Dic₄₇	1	1	yes	characteristic
450	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
451	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
452	C₂²×D₄	C₂×Dic₄₇	1	1	yes	characteristic
453	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
454	C₂³×C₄	C₂×Dic₄₇	1	1	yes	characteristic
455	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
456	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
457	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
458	C₂×M₁₆	—	94	2	no	—
459	C₂×M₁₆	—	94	2	no	—
460	C₂×M₁₆	—	188	1	no	—
461	C₂²×C₈	—	47	1	no	—
462	C₂²×C₈	—	47	1	no	—
463	C₂²×C₈	—	47	1	no	—
464	C₂²×C₈	—	47	1	no	—
465	C₂²×C₈	—	47	1	no	—
466	C₂²×C₈	—	47	1	no	—
467	C₂²×C₈	—	47	1	no	—
468	C₂²×C₈	—	47	1	no	—
469	C₂²×C₈	—	94	2	no	—
470	C₂²×C₈	—	94	2	no	—
471	C₂²×C₈	—	188	1	no	—
472	#117	—	2	2	no	—
473	#117	—	2	2	no	—
474	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
475	C₂×C₄⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
476	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
477	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
478	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
479	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
480	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
481	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
482	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
483	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
484	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
485	C₂×C₂²⋊C₄	C₂×Dic₄₇	1	1	yes	characteristic
486	C₂×C₄²	—	4	1	no	—
487	C₂×C₄²	—	4	1	no	—
488	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
489	C₂×C₄²	C₂×Dic₄₇	1	1	yes	characteristic
490	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
491	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
492	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
493	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
494	C₄⋊C₈	—	94	2	no	—
495	C₄⋊C₈	—	94	2	no	—
496	C₄⋊C₈	—	188	1	no	—
497	C₄⋊C₈	—	188	1	no	—
498	C₂²⋊C₈	—	47	4	no	—
499	C₂²⋊C₈	—	94	2	no	—
500	C₂²⋊C₈	—	94	2	no	—
501	C₂²⋊C₈	—	94	2	no	—
502	C₂²⋊C₈	—	94	2	no	—
503	C₂²⋊C₈	—	94	2	no	—
504	C₂²⋊C₈	—	94	2	no	—
505	C₂²⋊C₈	—	94	2	no	—
506	C₂²⋊C₈	—	188	1	no	—
507	C₂²⋊C₈	—	188	1	no	—
508	#97	—	94	2	no	—
509	#97	—	188	1	no	—
510	#97	—	188	1	no	—
511	C₄×C₈	—	94	2	no	—
512	#95	C₂×Dic₄₇	1	1	yes	characteristic
513	#95	C₂×Dic₄₇	1	1	yes	characteristic
514	#95	C₂×Dic₄₇	1	1	yes	characteristic
515	#95	C₂×Dic₄₇	1	1	yes	characteristic
516	#95	C₂×Dic₄₇	1	1	yes	characteristic
517	#95	C₂×Dic₄₇	1	1	yes	characteristic
518	#95	C₂×Dic₄₇	1	1	yes	characteristic
519	#95	C₂×Dic₄₇	1	1	yes	characteristic
520	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
521	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
522	C₂⁴	C₂²×Dic₄₇	1	1	yes	characteristic
523	#41	—	4	4	no	—
524	#41	—	4	4	no	—
525	#41	—	4	4	no	—
526	#41	—	4	4	no	—
527	C₂×Q₈	—	2	2	no	—
528	C₂×Q₈	—	2	2	no	—
529	C₂×Q₈	—	4	1	no	—
530	C₂×D₄	—	2	2	no	—
531	C₂×D₄	—	2	2	no	—
532	C₂×D₄	—	2	2	no	—
533	C₂×D₄	—	2	2	no	—
534	C₂×D₄	—	2	2	no	—
535	C₂×D₄	—	2	2	no	—
536	C₂×D₄	—	4	1	no	—
537	C₂×D₄	—	4	1	no	—
538	C₂×D₄	—	4	1	no	—
539	C₂²×C₄	—	2	1	no	—
540	C₂²×C₄	—	2	1	no	—
541	C₂²×C₄	—	2	1	no	—
542	C₂²×C₄	—	2	1	no	—
543	C₂²×C₄	—	2	1	no	—
544	C₂²×C₄	—	2	1	no	—
545	C₂²×C₄	—	2	1	no	—
546	C₂²×C₄	—	2	1	no	—
547	C₂²×C₄	—	2	2	no	—
548	C₂²×C₄	—	2	1	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	—	2	1	no	—
553	C₂²×C₄	—	2	1	no	—
554	C₂²×C₄	—	4	1	no	—
555	C₂²×C₄	—	4	1	no	—
556	C₂²×C₄	—	4	1	no	—
557	C₂²×C₄	—	4	1	no	—
558	C₂²×C₄	—	4	1	no	—
559	C₂²×C₄	#10625350	1	2	yes	—
560	C₂²×C₄	#10625350	1	2	yes	—
561	C₂²×C₄	D₄×D₄₇	1	2	yes	—
562	C₂²×C₄	#10625352	1	2	yes	—
563	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
564	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
565	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
566	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
567	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
568	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
569	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
570	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
571	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
572	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
573	C₂²×C₄	C₂²×Dic₄₇	1	1	yes	characteristic
574	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
575	M₁₆	—	188	4	no	—
576	C₂×C₈	—	47	2	no	—
577	C₂×C₈	—	47	2	no	—
578	C₂×C₈	—	94	1	no	—
579	C₂×C₈	—	94	1	no	—
580	C₂×C₈	—	94	1	no	—
581	C₂×C₈	—	94	1	no	—
582	C₂×C₈	—	94	1	no	—
583	C₂×C₈	—	94	1	no	—
584	C₂×C₈	—	94	1	no	—
585	C₂×C₈	—	94	1	no	—
586	C₂×C₈	—	94	1	no	—
587	C₂×C₈	—	94	1	no	—
588	C₂×C₈	—	94	1	no	—
589	C₂×C₈	—	94	1	no	—
590	C₂×C₈	—	94	1	no	—
591	C₂×C₈	—	94	1	no	—
592	C₂×C₈	—	94	1	no	—
593	C₂×C₈	—	94	1	no	—
594	C₂×C₈	—	94	1	no	—
595	C₂×C₈	—	94	1	no	—
596	C₂×C₈	—	94	1	no	—
597	C₂×C₈	—	94	1	no	—
598	C₂×C₈	—	94	1	no	—
599	C₂×C₈	—	94	1	no	—
600	C₂×C₈	—	188	4	no	—
601	C₄⋊C₄	—	2	2	no	—
602	C₄⋊C₄	—	2	2	no	—
603	C₂²⋊C₄	—	2	2	no	—
604	C₂²⋊C₄	—	2	2	no	—
605	C₂²⋊C₄	—	2	2	no	—
606	C₂²⋊C₄	—	2	2	no	—
607	C₂²⋊C₄	—	4	1	no	—
608	C₂²⋊C₄	—	4	1	no	—
609	C₂²⋊C₄	—	4	1	no	—
610	C₂²⋊C₄	—	4	1	no	—
611	C₂²⋊C₄	—	4	1	no	—
612	C₂²⋊C₄	—	4	1	no	—
613	C₄²	—	2	1	no	—
614	C₄²	—	2	1	no	—
615	C₄²	—	2	1	no	—
616	C₄²	—	2	1	no	—
617	C₄²	—	2	1	no	—
618	C₄²	—	2	1	no	—
619	C₄²	—	2	1	no	—
620	C₄²	—	2	1	no	—
621	C₄²	—	4	1	no	—
622	C₄²	—	4	1	no	—
623	C₂³	—	2	1	no	—
624	C₂³	—	2	1	no	—
625	C₂³	—	2	1	no	—
626	C₂³	—	2	1	no	—
627	C₂³	—	2	1	no	—
628	C₂³	—	2	1	no	—
629	C₂³	—	2	1	no	—
630	C₂³	—	2	1	no	—
631	C₂³	—	2	1	no	—
632	C₂³	—	2	1	no	—
633	C₂³	—	2	1	no	—
634	C₂³	—	2	1	no	—
635	C₂³	—	2	1	no	—
636	C₂³	—	2	1	no	—
637	C₂³	—	2	1	no	—
638	C₂³	—	2	1	no	—
639	C₂³	—	2	1	no	—
640	C₂³	—	2	1	no	—
641	C₂³	—	2	1	no	—
642	C₂³	#13093983	1	2	yes	—
643	C₂³	D₄×Dic₄₇	1	2	yes	—
644	C₂³	C₂³×Dic₄₇	1	1	yes	characteristic
645	Q₈	—	4	4	no	—
646	D₄	—	4	4	no	—
647	D₄	—	4	4	no	—
648	D₄	—	4	4	no	—
649	C₂×C₄	—	2	1	no	—
650	C₂×C₄	—	2	1	no	—
651	C₂×C₄	—	2	1	no	—
652	C₂×C₄	—	2	1	no	—
653	C₂×C₄	—	2	1	no	—
654	C₂×C₄	—	2	1	no	—
655	C₂×C₄	—	2	2	no	—
656	C₂×C₄	—	2	2	no	—
657	C₂×C₄	—	2	2	no	—
658	C₂×C₄	—	2	2	no	—
659	C₂×C₄	—	2	2	no	—
660	C₂×C₄	—	2	2	no	—
661	C₂×C₄	—	2	2	no	—
662	C₂×C₄	—	2	2	no	—
663	C₂×C₄	—	2	1	no	—
664	C₂×C₄	—	2	1	no	—
665	C₂×C₄	—	2	1	no	—
666	C₂×C₄	—	2	1	no	—
667	C₂×C₄	—	2	1	no	—
668	C₂×C₄	—	2	1	no	—
669	C₂×C₄	—	2	1	no	—
670	C₂×C₄	—	2	1	no	—
671	C₂×C₄	—	2	1	no	—
672	C₂×C₄	—	2	1	no	—
673	C₂×C₄	—	2	1	no	—
674	C₂×C₄	—	2	1	no	—
675	C₂×C₄	—	2	1	no	—
676	C₂×C₄	—	2	1	no	—
677	C₂×C₄	—	2	1	no	—
678	C₂×C₄	—	2	1	no	—
679	C₂×C₄	—	2	1	no	—
680	C₂×C₄	—	2	1	no	—
681	C₂×C₄	—	2	1	no	—
682	C₂×C₄	—	2	1	no	—
683	C₂×C₄	—	2	1	no	—
684	C₂×C₄	—	2	1	no	—
685	C₂×C₄	—	2	1	no	—
686	C₂×C₄	—	2	1	no	—
687	C₂×C₄	—	4	4	no	—
688	C₂×C₄	—	4	4	no	—
689	C₂×C₄	—	4	1	no	—
690	C₂×C₄	—	4	1	no	—
691	C₂×C₄	—	4	1	no	—
692	C₂×C₄	—	4	1	no	—
693	C₂×C₄	#13093983	1	2	yes	—
694	C₂×C₄	D₄×Dic₄₇	1	2	yes	—
695	C₂×C₄	#13094031	1	2	yes	—
696	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
697	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
698	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
699	C₂×C₄	C₂×#10625350	1	1	yes	characteristic
700	C₂×C₄	#13094069	1	1	yes	characteristic
701	C₂×C₄	#13094069	1	1	yes	characteristic
702	C₈	—	94	2	no	—
703	C₈	—	94	2	no	—
704	C₈	—	188	1	no	—
705	C₈	—	188	1	no	—
706	C₈	—	188	1	no	—
707	C₈	—	188	1	no	—
708	C₈	—	188	1	no	—
709	C₈	—	188	1	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	2	2	no	—
712	C₂²	—	2	2	no	—
713	C₂²	—	2	2	no	—
714	C₂²	—	2	2	no	—
715	C₂²	—	2	2	no	—
716	C₂²	—	4	1	no	—
717	C₂²	—	4	1	no	—
718	C₂²	—	4	1	no	—
719	C₂²	—	4	1	no	—
720	C₂²	—	4	1	no	—
721	C₂²	—	4	1	no	—
722	C₂²	—	4	1	no	—
723	C₂²	—	4	1	no	—
724	C₂²	—	4	1	no	—
725	C₂²	—	4	1	no	—
726	C₂²	—	4	1	no	—
727	C₂²	—	4	1	no	—
728	C₂²	—	4	1	no	—
729	C₂²	—	4	1	no	—
730	C₂²	—	4	1	no	—
731	C₂²	C₂×#13093983	1	1	yes	characteristic
732	C₂²	C₂×D₄×Dic₄₇	1	1	yes	characteristic
733	C₂²	#15689598	1	1	yes	characteristic
734	C₂²	C₂×#13094031	1	1	yes	characteristic
735	C₂²	#15689890	1	1	yes	characteristic
736	C₂²	#15689890	1	1	yes	characteristic
737	C₂²	#15689890	1	1	yes	characteristic
738	C₄	—	2	2	no	—
739	C₄	—	2	2	no	—
740	C₄	—	2	2	no	—
741	C₄	—	4	1	no	—
742	C₄	—	4	1	no	—
743	C₄	—	4	1	no	—
744	C₄	—	4	1	no	—
745	C₄	—	4	1	no	—
746	C₄	—	4	1	no	—
747	C₄	—	4	1	no	—
748	C₄	—	4	1	no	—
749	C₄	#15689763	1	1	yes	characteristic
750	C₄	#15689763	1	1	yes	characteristic
751	C₄	#15689799	1	1	yes	characteristic
752	C₄	#15689799	1	1	yes	characteristic
753	C₂	—	4	2	no	—
754	C₂	—	4	2	no	—
755	C₂	—	8	1	no	—
756	C₂	#20246237	1	1	yes	characteristic
757	C₂	#20252039	1	1	yes	characteristic
758	C₂	#20252054	1	1	yes	characteristic
759	C₂	#20252106	1	1	yes	characteristic
760	C₂	#20252132	1	1	yes	characteristic
761	C₂	#20252436	1	1	yes	characteristic
762	C₂	#20252450	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#2297	C₂
prime radical	C₂²×#41×C₄₇	C₂²
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#2297	D₄₇
hypocenter	C₄₇	#22561
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #2297

Complements

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

N	H ≅ G/N	type
1. C₂×#15689184	C₂	semidirect
3. #20244003	C₂	semidirect
4. #20244003	C₂	semidirect
5. #20244003	C₂	semidirect
6. #20243996	C₂	semidirect
7. #20243573	C₂	semidirect
8. #20243568	C₂	semidirect
9. #20243459	C₂	semidirect
10. #20243368	C₂	semidirect
12. #20243172	C₂	semidirect
13. #20243166	C₂	semidirect
14. #20243150	C₂	semidirect
442. C₄₇	#22561	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689184	2
C₂×#15689090	2
#20244003	2
#20243996	2
#20243573	2
#20243568	2
#20243459	2
#20243368	2
#20243300	2
#20243172	2
#20243166	2
#20243150	2
C₄₇×#2297	2
#22561	47