Subgroups — #26234363

Order 12032.

964 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×#15689195	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689151	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15689149	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245853	C₂	1	1	yes	maximal, characteristic
5	#20244111	C₂	1	1	yes	maximal, characteristic, complemented
6	#20244109	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243571	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243570	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243566	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243565	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243539	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243370	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243370	C₂	1	1	yes	maximal, characteristic, complemented
14	#20243242	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×C₄₇×#435	C₂	1	1	yes	maximal, characteristic
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
18	C₂×#13093983	C₂²	1	1	yes	characteristic
19	C₂×#13093983	C₂²	1	1	yes	characteristic
20	#15689195	—	2	4	no	—
21	#15689151	—	2	4	no	—
22	#15689149	—	2	4	no	—
23	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
24	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
31	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
32	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
33	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
34	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
35	C₂×C₂²⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
36	C₂×#13093935	C₂²	1	1	yes	characteristic
37	#15689026	C₄	1	1	yes	characteristic
38	#15689026	C₄	1	1	yes	characteristic
39	#15689022	C₄	1	1	yes	characteristic
40	#15689022	C₄	1	1	yes	characteristic
41	#15689016	C₄	1	1	yes	characteristic
42	#15689016	C₄	1	1	yes	characteristic
43	#15689016	C₄	1	1	yes	characteristic
44	#15689016	C₄	1	1	yes	characteristic
45	C₄×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
47	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
48	C₄²×Dic₄₇	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	C₂²×M₁₆×C₄₇	C₂²	1	1	yes	characteristic
56	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
57	C₂×C₄×D₄×C₄₇	C₂²	1	1	yes	characteristic
58	C₄₇×#435	—	2	4	no	—
59	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
60	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
61	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
62	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
63	C₂×#10625329	—	2	2	no	—
64	C₂×#10625329	—	2	2	no	—
65	C₂×#10625329	—	4	1	no	—
66	C₂²×C₄₇⋊C₈	—	2	2	no	—
67	C₂²×C₄₇⋊C₈	—	2	2	no	—
68	C₂²×C₄₇⋊C₈	—	4	1	no	—
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	#13093983	—	2	2	no	—
74	#13093983	—	2	2	no	—
75	#13093983	—	2	2	no	—
76	#13093983	—	2	2	no	—
77	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
78	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
79	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
80	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
81	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
82	C₂×C₄⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
83	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
84	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
85	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
86	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
87	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
88	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
89	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
90	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
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×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
95	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
96	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
97	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
98	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
99	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
100	Dic₄₇⋊C₈	—	2	2	no	—
101	Dic₄₇⋊C₈	—	2	2	no	—
102	Dic₄₇⋊C₈	—	2	2	no	—
103	Dic₄₇⋊C₈	—	2	2	no	—
104	Dic₄₇⋊C₈	—	2	2	no	—
105	Dic₄₇⋊C₈	—	2	2	no	—
106	Dic₄₇⋊C₈	—	2	2	no	—
107	Dic₄₇⋊C₈	—	4	1	no	—
108	Dic₄₇⋊C₈	—	4	1	no	—
109	Dic₄₇⋊C₈	D₄	1	4	yes	complemented
110	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
111	C₂²⋊(C₄₇⋊C₈)	—	2	2	no	—
112	#13093935	—	2	2	no	—
113	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
114	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
115	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
116	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
117	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
118	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
119	C₂²×D₄×C₄₇	C₂×C₄	1	1	yes	characteristic
120	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
121	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
122	C₂×M₁₆×C₄₇	—	2	2	no	—
123	C₂×M₁₆×C₄₇	—	2	2	no	—
124	C₂×M₁₆×C₄₇	—	4	1	no	—
125	C₂²×C₈×C₄₇	—	2	2	no	—
126	C₂²×C₈×C₄₇	—	2	2	no	—
127	C₂²×C₈×C₄₇	—	4	1	no	—
128	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
129	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
130	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
131	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
132	C₄×D₄×C₄₇	D₄	1	4	yes	—
133	C₄×D₄×C₄₇	Q₈	1	4	yes	—
134	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
135	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
136	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
137	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
138	C₄⋊C₈×C₄₇	—	2	2	no	—
139	C₂²⋊C₈×C₄₇	—	2	2	no	—
140	C₂²⋊C₈×C₄₇	—	2	2	no	—
141	#97×C₄₇	—	2	2	no	—
142	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
143	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
144	C₂×D₄×C₄₇	—	4	1	no	—
145	C₂×D₄×C₄₇	—	4	1	no	—
146	C₂×D₄×C₄₇	C₄⋊C₄	1	4	yes	—
147	C₂²×C₄×C₄₇	—	2	1	no	—
148	C₂²×C₄×C₄₇	—	2	1	no	—
149	C₂²×C₄×C₄₇	—	2	1	no	—
150	C₂²×C₄×C₄₇	—	2	1	no	—
151	C₂²×C₄×C₄₇	—	2	1	no	—
152	C₂²×C₄×C₄₇	—	2	1	no	—
153	C₂²×C₄×C₄₇	—	2	1	no	—
154	C₂²×C₄×C₄₇	—	2	1	no	—
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	C₂²×C₄	1	1	yes	characteristic
159	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
160	C₂²×C₄×C₄₇	C₂×D₄	1	2	yes	—
161	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
162	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
163	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
164	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
165	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
166	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
167	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
168	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
169	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
170	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
171	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
172	M₁₆×C₄₇	—	4	4	no	—
173	C₂×C₈×C₄₇	—	2	1	no	—
174	C₂×C₈×C₄₇	—	2	1	no	—
175	C₂×C₈×C₄₇	—	2	1	no	—
176	C₂×C₈×C₄₇	—	2	1	no	—
177	C₂×C₈×C₄₇	—	2	1	no	—
178	C₂×C₈×C₄₇	—	2	1	no	—
179	C₂×C₈×C₄₇	—	2	1	no	—
180	C₂×C₈×C₄₇	—	2	1	no	—
181	C₂×C₈×C₄₇	—	2	1	no	—
182	C₂×C₈×C₄₇	—	2	1	no	—
183	C₂×C₈×C₄₇	—	2	1	no	—
184	C₂×C₈×C₄₇	—	4	4	no	—
185	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
186	C₄⋊C₄×C₄₇	C₄⋊C₄	1	4	yes	—
187	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	4	yes	—
188	C₂²⋊C₄×C₄₇	C₄⋊C₄	1	4	yes	—
189	C₄²×C₄₇	C₂×D₄	1	2	yes	—
190	C₄²×C₄₇	C₂×Q₈	1	2	yes	—
191	C₂²⋊Dic₄₇	—	2	2	no	—
192	C₂²⋊Dic₄₇	—	2	2	no	—
193	C₂²⋊Dic₄₇	—	2	2	no	—
194	C₂²⋊Dic₄₇	—	2	2	no	—
195	C₂²⋊Dic₄₇	—	2	2	no	—
196	C₂²⋊Dic₄₇	—	2	2	no	—
197	C₂²⋊Dic₄₇	—	4	1	no	—
198	C₂²⋊Dic₄₇	—	4	1	no	—
199	C₄⋊Dic₄₇	—	2	2	no	—
200	C₄⋊Dic₄₇	—	2	2	no	—
201	C₄⋊Dic₄₇	—	2	2	no	—
202	C₄⋊Dic₄₇	—	2	2	no	—
203	C₄⋊Dic₄₇	—	4	1	no	—
204	C₄⋊Dic₄₇	—	4	1	no	—
205	C₄×Dic₄₇	—	2	1	no	—
206	C₄×Dic₄₇	—	2	1	no	—
207	C₄×Dic₄₇	—	2	1	no	—
208	C₄×Dic₄₇	—	2	1	no	—
209	C₄×Dic₄₇	—	2	1	no	—
210	C₄×Dic₄₇	—	2	1	no	—
211	C₄×Dic₄₇	—	2	2	no	—
212	C₄×Dic₄₇	—	4	1	no	—
213	C₄×Dic₄₇	—	4	1	no	—
214	C₄×Dic₄₇	—	4	1	no	—
215	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
216	C₄×Dic₄₇	#41	1	2	yes	—
217	#10625329	—	4	4	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	—	4	4	no	—
230	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
231	C₂³×C₄₇	—	2	1	no	—
232	C₂³×C₄₇	—	2	1	no	—
233	C₂³×C₄₇	—	2	1	no	—
234	C₂³×C₄₇	—	2	1	no	—
235	C₂³×C₄₇	—	2	1	no	—
236	C₂³×C₄₇	—	2	1	no	—
237	C₂³×C₄₇	—	2	1	no	—
238	C₂³×C₄₇	—	2	1	no	—
239	C₂³×C₄₇	—	2	1	no	—
240	C₂³×C₄₇	—	2	1	no	—
241	C₂³×C₄₇	—	2	1	no	—
242	C₂³×C₄₇	—	2	1	no	—
243	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
244	C₂³×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
245	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
246	D₄×C₄₇	—	4	4	no	—
247	C₂×C₄×C₄₇	—	2	1	no	—
248	C₂×C₄×C₄₇	—	2	1	no	—
249	C₂×C₄×C₄₇	—	2	1	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	2	no	—
256	C₂×C₄×C₄₇	—	2	2	no	—
257	C₂×C₄×C₄₇	—	2	2	no	—
258	C₂×C₄×C₄₇	—	2	2	no	—
259	C₂×C₄×C₄₇	—	2	2	no	—
260	C₂×C₄×C₄₇	—	2	2	no	—
261	C₂×C₄×C₄₇	—	2	2	no	—
262	C₂×C₄×C₄₇	—	2	2	no	—
263	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
264	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
265	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
266	C₂×C₄×C₄₇	C₂×C₄⋊C₄	1	2	yes	—
267	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
268	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
269	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
270	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
271	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
272	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
273	C₂×Dic₄₇	—	2	1	no	—
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	—	2	1	no	—
291	C₂×Dic₄₇	—	2	1	no	—
292	C₂×Dic₄₇	—	2	1	no	—
293	C₂×Dic₄₇	—	2	1	no	—
294	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
295	C₂×Dic₄₇	C₄×D₄	1	2	yes	—
296	C₂×Dic₄₇	#131	1	2	yes	—
297	C₈×C₄₇	—	2	2	no	—
298	C₈×C₄₇	—	4	1	no	—
299	C₈×C₄₇	—	4	1	no	—
300	C₈×C₄₇	—	4	1	no	—
301	C₄₇⋊C₈	—	2	2	no	—
302	C₄₇⋊C₈	—	4	1	no	—
303	C₄₇⋊C₈	—	4	1	no	—
304	C₄₇⋊C₈	—	4	1	no	—
305	#22652	—	47	1	no	maximal, Sylow
306	C₂²×C₄₇	—	2	2	no	—
307	C₂²×C₄₇	—	2	2	no	—
308	C₂²×C₄₇	—	2	2	no	—
309	C₂²×C₄₇	—	2	2	no	—
310	C₂²×C₄₇	—	2	2	no	—
311	C₂²×C₄₇	—	2	2	no	—
312	C₂²×C₄₇	—	4	1	no	—
313	C₂²×C₄₇	—	4	1	no	—
314	C₂²×C₄₇	—	4	1	no	—
315	C₂²×C₄₇	—	4	1	no	—
316	C₂²×C₄₇	—	4	1	no	—
317	C₂²×C₄₇	—	4	1	no	—
318	C₂²×C₄₇	—	4	1	no	—
319	C₂²×C₄₇	—	4	1	no	—
320	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
321	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
322	C₂²×C₄₇	#520	1	1	yes	characteristic
323	C₂²×C₄₇	C₂×#131	1	1	yes	characteristic
324	C₂²×C₄₇	#568	1	1	yes	characteristic
325	C₂²×C₄₇	#568	1	1	yes	characteristic
326	C₂²×C₄₇	#568	1	1	yes	characteristic
327	C₄×C₄₇	—	2	2	no	—
328	C₄×C₄₇	—	2	2	no	—
329	C₄×C₄₇	—	2	2	no	—
330	C₄×C₄₇	—	2	2	no	—
331	C₄×C₄₇	D₄²	1	1	yes	characteristic
332	C₄×C₄₇	#547	1	1	yes	characteristic
333	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
334	C₄×C₄₇	#554	1	1	yes	characteristic
335	Dic₄₇	—	2	2	no	—
336	Dic₄₇	—	2	2	no	—
337	Dic₄₇	—	2	2	no	—
338	Dic₄₇	—	4	1	no	—
339	Dic₄₇	—	4	1	no	—
340	Dic₄₇	—	4	1	no	—
341	Dic₄₇	—	4	1	no	—
342	Dic₄₇	—	4	1	no	—
343	C₂×#435	—	47	1	no	—
344	C₂×#435	D₄₇	1	1	yes	characteristic
345	C₂×#424	—	47	1	no	—
346	C₂×#424	—	47	1	no	—
347	#2293	—	47	1	no	—
348	#1940	—	47	1	no	—
349	#1940	—	47	1	no	—
350	#1851	—	47	1	no	—
351	#1851	—	47	1	no	—
352	#1850	—	47	1	no	—
353	#1850	—	47	1	no	—
354	#1842	—	47	1	no	—
355	#1798	—	47	1	no	—
356	#1798	—	47	1	no	—
357	#1767	—	47	1	no	—
358	C₂×C₄₇	—	4	2	no	—
359	C₂×C₄₇	—	4	2	no	—
360	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
361	C₂×C₄₇	#2905	1	1	yes	characteristic
362	C₂×C₄₇	#2906	1	1	yes	characteristic
363	C₂×C₄₇	#2932	1	1	yes	characteristic
364	C₂×C₄₇	#2935	1	1	yes	characteristic
365	C₂×C₄₇	#2992	1	1	yes	characteristic
366	C₂×C₄₇	#2995	1	1	yes	characteristic
367	C₂²×M₁₆	—	47	1	no	—
368	C₂²×M₁₆	C₂×D₄₇	1	1	yes	characteristic
369	C₂³×C₈	—	47	1	no	—
370	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
371	C₂×C₄×D₄	C₂×D₄₇	1	1	yes	characteristic
372	C₂×#117	—	47	1	no	—
373	C₂×#117	—	47	1	no	—
374	#435	—	2	4	no	—
375	#435	—	94	4	no	—
376	#424	—	94	4	no	—
377	#424	—	94	4	no	—
378	C₂×C₄⋊C₈	—	47	1	no	—
379	C₂×C₄⋊C₈	—	47	1	no	—
380	C₂×C₄⋊C₈	—	47	1	no	—
381	C₂×C₄⋊C₈	—	47	1	no	—
382	C₂×C₄⋊C₈	—	47	1	no	—
383	C₂×C₄⋊C₈	—	47	1	no	—
384	C₂×C₄⋊C₈	—	47	1	no	—
385	C₂×C₄⋊C₈	—	47	1	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	C₂×D₄₇	1	1	yes	characteristic
390	C₂×C₂²⋊C₈	—	47	1	no	—
391	C₂×C₂²⋊C₈	—	47	1	no	—
392	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
393	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
394	C₂×#97	—	47	1	no	—
395	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
396	#390	—	47	1	no	—
397	#390	—	47	1	no	—
398	#389	—	47	1	no	—
399	#389	—	47	1	no	—
400	#388	—	47	1	no	—
401	#388	—	47	1	no	—
402	#388	—	47	1	no	—
403	#388	—	47	1	no	—
404	C₄×C₄⋊C₄	—	47	1	no	—
405	C₄×C₂²⋊C₄	—	47	1	no	—
406	C₄×C₂²⋊C₄	—	47	1	no	—
407	C₄³	—	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	C₄₇	#22652	1	1	yes	characteristic, complemented, Sylow
415	C₂²×D₄	C₄×D₄₇	1	1	yes	characteristic
416	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
417	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
418	C₂×M₁₆	—	2	2	no	—
419	C₂×M₁₆	—	2	2	no	—
420	C₂×M₁₆	—	4	1	no	—
421	C₂×M₁₆	—	94	2	no	—
422	C₂×M₁₆	—	94	2	no	—
423	C₂×M₁₆	—	188	1	no	—
424	C₂²×C₈	—	2	2	no	—
425	C₂²×C₈	—	2	2	no	—
426	C₂²×C₈	—	4	1	no	—
427	C₂²×C₈	—	47	1	no	—
428	C₂²×C₈	—	47	1	no	—
429	C₂²×C₈	—	47	1	no	—
430	C₂²×C₈	—	47	1	no	—
431	C₂²×C₈	—	94	2	no	—
432	C₂²×C₈	—	94	2	no	—
433	C₂²×C₈	—	188	1	no	—
434	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
435	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
436	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
437	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
438	C₄×D₄	Dic₉₄	1	4	yes	—
439	C₄×D₄	C₂²⋊D₄₇	1	4	yes	—
440	#117	—	94	2	no	—
441	#117	—	94	2	no	—
442	#117	—	94	2	no	—
443	#117	—	94	2	no	—
444	C₂×C₄⋊C₄	—	47	1	no	—
445	C₂×C₄⋊C₄	—	47	1	no	—
446	C₂×C₄⋊C₄	—	47	1	no	—
447	C₂×C₄⋊C₄	—	47	1	no	—
448	C₂×C₄⋊C₄	—	47	1	no	—
449	C₂×C₄⋊C₄	—	47	1	no	—
450	C₂×C₄⋊C₄	C₄×D₄₇	1	1	yes	characteristic
451	C₂×C₂²⋊C₄	—	47	1	no	—
452	C₂×C₂²⋊C₄	—	47	1	no	—
453	C₂×C₂²⋊C₄	—	47	1	no	—
454	C₂×C₂²⋊C₄	—	47	1	no	—
455	C₂×C₂²⋊C₄	—	47	1	no	—
456	C₂×C₂²⋊C₄	—	47	1	no	—
457	C₂×C₂²⋊C₄	—	47	1	no	—
458	C₂×C₂²⋊C₄	—	47	1	no	—
459	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
460	C₂×C₂²⋊C₄	C₄×D₄₇	1	1	yes	characteristic
461	C₂×C₄²	—	47	1	no	—
462	C₂×C₄²	—	47	1	no	—
463	C₂×C₄²	—	47	1	no	—
464	C₂×C₄²	—	47	1	no	—
465	C₂×C₄²	—	47	1	no	—
466	C₂×C₄²	—	47	1	no	—
467	C₂×C₄²	—	47	1	no	—
468	C₂×C₄²	—	47	1	no	—
469	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
470	C₄⋊C₈	—	2	2	no	—
471	C₄⋊C₈	—	47	4	no	—
472	C₄⋊C₈	—	94	2	no	—
473	C₄⋊C₈	—	94	2	no	—
474	C₄⋊C₈	—	94	2	no	—
475	C₄⋊C₈	—	94	2	no	—
476	C₄⋊C₈	—	94	2	no	—
477	C₄⋊C₈	—	94	2	no	—
478	C₄⋊C₈	—	94	2	no	—
479	C₄⋊C₈	—	94	2	no	—
480	C₄⋊C₈	—	188	1	no	—
481	C₄⋊C₈	—	188	1	no	—
482	C₂²⋊C₈	—	2	2	no	—
483	C₂²⋊C₈	—	2	2	no	—
484	C₂²⋊C₈	—	94	2	no	—
485	C₂²⋊C₈	—	94	2	no	—
486	#97	—	2	2	no	—
487	#97	—	94	2	no	—
488	#95	—	47	1	no	—
489	#95	—	47	1	no	—
490	#95	—	47	1	no	—
491	#95	—	47	1	no	—
492	#95	—	47	1	no	—
493	#95	—	47	1	no	—
494	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
495	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
496	C₂×D₄	—	4	1	no	—
497	C₂×D₄	—	4	1	no	—
498	C₂×D₄	Dic₄₇⋊C₄	1	4	yes	—
499	C₂²×C₄	—	2	1	no	—
500	C₂²×C₄	—	2	1	no	—
501	C₂²×C₄	—	2	1	no	—
502	C₂²×C₄	—	2	1	no	—
503	C₂²×C₄	—	2	1	no	—
504	C₂²×C₄	—	2	1	no	—
505	C₂²×C₄	—	2	1	no	—
506	C₂²×C₄	—	2	1	no	—
507	C₂²×C₄	—	47	1	no	—
508	C₂²×C₄	—	47	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	1	no	—
515	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
516	C₂²×C₄	C₂×Dic₉₄	1	2	yes	—
517	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
518	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
519	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
520	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
521	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
522	C₂²×C₄	C₂×C₂²⋊D₄₇	1	2	yes	—
523	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
524	M₁₆	—	4	4	no	—
525	M₁₆	—	188	4	no	—
526	C₂×C₈	—	2	1	no	—
527	C₂×C₈	—	2	1	no	—
528	C₂×C₈	—	2	1	no	—
529	C₂×C₈	—	2	1	no	—
530	C₂×C₈	—	2	1	no	—
531	C₂×C₈	—	2	1	no	—
532	C₂×C₈	—	2	1	no	—
533	C₂×C₈	—	2	1	no	—
534	C₂×C₈	—	2	1	no	—
535	C₂×C₈	—	2	1	no	—
536	C₂×C₈	—	2	1	no	—
537	C₂×C₈	—	4	4	no	—
538	C₂×C₈	—	47	2	no	—
539	C₂×C₈	—	94	1	no	—
540	C₂×C₈	—	94	1	no	—
541	C₂×C₈	—	94	1	no	—
542	C₂×C₈	—	94	1	no	—
543	C₂×C₈	—	94	1	no	—
544	C₂×C₈	—	94	1	no	—
545	C₂×C₈	—	94	1	no	—
546	C₂×C₈	—	94	1	no	—
547	C₂×C₈	—	94	1	no	—
548	C₂×C₈	—	94	1	no	—
549	C₂×C₈	—	94	1	no	—
550	C₂×C₈	—	188	4	no	—
551	C₂×C₈	D₄×D₄₇	1	2	yes	—
552	C₄⋊C₄	—	94	2	no	—
553	C₄⋊C₄	—	94	2	no	—
554	C₄⋊C₄	—	94	2	no	—
555	C₄⋊C₄	—	94	2	no	—
556	C₄⋊C₄	—	188	1	no	—
557	C₄⋊C₄	—	188	1	no	—
558	C₄⋊C₄	Dic₄₇⋊C₄	1	4	yes	—
559	C₂²⋊C₄	—	94	2	no	—
560	C₂²⋊C₄	—	94	2	no	—
561	C₂²⋊C₄	—	94	2	no	—
562	C₂²⋊C₄	—	94	2	no	—
563	C₂²⋊C₄	—	94	2	no	—
564	C₂²⋊C₄	—	94	2	no	—
565	C₂²⋊C₄	—	188	1	no	—
566	C₂²⋊C₄	—	188	1	no	—
567	C₂²⋊C₄	Dic₄₇⋊C₄	1	4	yes	—
568	C₂²⋊C₄	Dic₄₇⋊C₄	1	4	yes	—
569	C₄²	—	47	2	no	—
570	C₄²	—	47	2	no	—
571	C₄²	—	94	2	no	—
572	C₄²	—	94	1	no	—
573	C₄²	—	94	1	no	—
574	C₄²	—	94	1	no	—
575	C₄²	—	94	1	no	—
576	C₄²	—	94	1	no	—
577	C₄²	—	94	1	no	—
578	C₄²	—	188	1	no	—
579	C₄²	—	188	1	no	—
580	C₄²	—	188	1	no	—
581	C₄²	C₂×Dic₉₄	1	2	yes	—
582	C₄²	C₂×C₂²⋊D₄₇	1	2	yes	—
583	C₂³	—	2	1	no	—
584	C₂³	—	2	1	no	—
585	C₂³	—	2	1	no	—
586	C₂³	—	2	1	no	—
587	C₂³	—	2	1	no	—
588	C₂³	—	2	1	no	—
589	C₂³	—	2	1	no	—
590	C₂³	—	2	1	no	—
591	C₂³	—	2	1	no	—
592	C₂³	—	2	1	no	—
593	C₂³	—	2	1	no	—
594	C₂³	—	2	1	no	—
595	C₂³	C₂×Dic₄₇⋊C₄	1	2	yes	—
596	C₂³	C₂×Dic₄₇⋊C₄	1	2	yes	—
597	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
598	D₄	—	4	4	no	—
599	C₂×C₄	—	2	1	no	—
600	C₂×C₄	—	2	1	no	—
601	C₂×C₄	—	2	1	no	—
602	C₂×C₄	—	2	1	no	—
603	C₂×C₄	—	2	1	no	—
604	C₂×C₄	—	2	1	no	—
605	C₂×C₄	—	2	1	no	—
606	C₂×C₄	—	2	1	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	no	—
609	C₂×C₄	—	2	2	no	—
610	C₂×C₄	—	2	2	no	—
611	C₂×C₄	—	2	2	no	—
612	C₂×C₄	—	2	2	no	—
613	C₂×C₄	—	2	2	no	—
614	C₂×C₄	—	2	2	no	—
615	C₂×C₄	—	47	2	no	—
616	C₂×C₄	—	47	2	no	—
617	C₂×C₄	—	47	2	no	—
618	C₂×C₄	—	94	1	no	—
619	C₂×C₄	—	94	1	no	—
620	C₂×C₄	—	94	1	no	—
621	C₂×C₄	—	94	1	no	—
622	C₂×C₄	—	94	1	no	—
623	C₂×C₄	—	94	1	no	—
624	C₂×C₄	—	94	1	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	1	no	—
636	C₂×C₄	—	94	1	no	—
637	C₂×C₄	—	94	1	no	—
638	C₂×C₄	—	94	1	no	—
639	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
640	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
641	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
642	C₂×C₄	C₂×Dic₄₇⋊C₄	1	2	yes	—
643	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
644	C₂×C₄	C₂²×C₂²⋊D₄₇	1	1	yes	characteristic
645	C₂×C₄	C₂²×Dic₉₄	1	1	yes	characteristic
646	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
647	C₂×C₄	#13094069	1	1	yes	characteristic
648	C₂×C₄	#13094071	1	1	yes	characteristic
649	C₈	—	2	2	no	—
650	C₈	—	4	1	no	—
651	C₈	—	4	1	no	—
652	C₈	—	4	1	no	—
653	C₈	—	94	2	no	—
654	C₈	—	188	1	no	—
655	C₈	—	188	1	no	—
656	C₈	—	188	1	no	—
657	C₂²	—	2	2	no	—
658	C₂²	—	2	2	no	—
659	C₂²	—	2	2	no	—
660	C₂²	—	2	2	no	—
661	C₂²	—	2	2	no	—
662	C₂²	—	2	2	no	—
663	C₂²	—	4	1	no	—
664	C₂²	—	4	1	no	—
665	C₂²	—	4	1	no	—
666	C₂²	—	4	1	no	—
667	C₂²	—	4	1	no	—
668	C₂²	—	4	1	no	—
669	C₂²	—	4	1	no	—
670	C₂²	—	4	1	no	—
671	C₂²	C₂²×Dic₄₇⋊C₄	1	1	yes	characteristic
672	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
673	C₂²	#15689602	1	1	yes	characteristic
674	C₂²	#131×D₄₇	1	1	yes	characteristic
675	C₂²	#15689888	1	1	yes	characteristic
676	C₂²	#15689889	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	—	2	2	no	—
682	C₄	—	94	2	no	—
683	C₄	—	94	2	no	—
684	C₄	—	94	2	no	—
685	C₄	—	188	1	no	—
686	C₄	—	188	1	no	—
687	C₄	—	188	1	no	—
688	C₄	—	188	1	no	—
689	C₄	—	188	1	no	—
690	C₄	D₄×C₂²⋊D₄₇	1	1	yes	characteristic
691	C₄	#15689772	1	1	yes	characteristic
692	C₄	D₄×Dic₉₄	1	1	yes	characteristic
693	C₄	#15689832	1	1	yes	characteristic
694	C₂	—	4	2	no	—
695	C₂	—	4	2	no	—
696	C₂	D₄×Dic₄₇⋊C₄	1	1	yes	characteristic
697	C₂	#20251951	1	1	yes	characteristic
698	C₂	#20251954	1	1	yes	characteristic
699	C₂	#20252102	1	1	yes	characteristic
700	C₂	#20252129	1	1	yes	characteristic
701	C₂	#20252523	1	1	yes	characteristic
702	C₂	#20252554	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₂×C₄₇×#435	C₂
prime radical	C₂²×D₄×C₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	C₂×#435	D₄₇
hypocenter	C₄₇	#22652
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×#435

Complements

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

N	H ≅ G/N	type
2. C₂×#15689151	C₂	semidirect
3. C₂×#15689149	C₂	semidirect
5. #20244111	C₂	semidirect
6. #20244109	C₂	semidirect
7. #20243571	C₂	semidirect
8. #20243570	C₂	semidirect
9. #20243566	C₂	semidirect
10. #20243565	C₂	semidirect
11. #20243539	C₂	semidirect
12. #20243370	C₂	semidirect
13. #20243370	C₂	semidirect
14. #20243242	C₂	semidirect
109. Dic₄₇⋊C₈	D₄	semidirect
414. C₄₇	#22652	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689195	2
C₂×#15689151	2
C₂×#15689149	2
#20245853	2
#20244111	2
#20244109	2
#20243571	2
#20243570	2
#20243566	2
#20243565	2
#20243539	2
#20243370	2
#20243242	2
C₂×C₄₇×#435	2
#22652	47