Subgroups — #26234362

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×#15689197	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689191	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689150	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15689148	C₂	1	1	yes	maximal, characteristic, complemented
5	#20245847	C₂	1	1	yes	maximal, characteristic
6	#20244110	C₂	1	1	yes	maximal, characteristic, complemented
7	#20244110	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243572	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243570	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243567	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243565	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243539	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243369	C₂	1	1	yes	maximal, characteristic, complemented
14	#20243243	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#1798	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂²×#10625324	C₂²	1	1	yes	characteristic
18	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
21	C₂×#13093981	C₂²	1	1	yes	characteristic
22	#15689197	—	2	4	no	—
23	#15689191	—	2	4	no	—
24	#15689150	—	2	4	no	—
25	#15689148	—	2	4	no	—
26	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
28	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
29	C₂×C₄⋊(C₄₇⋊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×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
35	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
36	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×#13093934	C₂²	1	1	yes	characteristic
39	C₂×#13093934	C₂²	1	1	yes	characteristic
40	#15689023	C₄	1	1	yes	characteristic
41	#15689023	C₄	1	1	yes	characteristic
42	#15689018	C₄	1	1	yes	characteristic
43	#15689018	C₄	1	1	yes	characteristic
44	#15689017	C₄	1	1	yes	characteristic
45	#15689017	C₄	1	1	yes	characteristic
46	#15689013	C₄	1	1	yes	characteristic
47	#15689013	C₄	1	1	yes	characteristic
48	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
49	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
50	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
51	C₄²×Dic₄₇	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×#117×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	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
60	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
61	C₄₇×#336	C₂²	1	1	yes	characteristic
62	C₄₇×#336	C₂²	1	1	yes	characteristic
63	C₂²×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
64	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
65	C₂×#10625329	—	2	2	no	—
66	C₂×#10625329	—	2	2	no	—
67	C₂×#10625329	—	4	1	no	—
68	C₂×#10625324	—	2	2	no	—
69	C₂×#10625324	—	2	2	no	—
70	C₂×#10625324	—	4	1	no	—
71	C₂²×C₄₇⋊C₈	—	2	2	no	—
72	C₂²×C₄₇⋊C₈	—	2	2	no	—
73	C₂²×C₄₇⋊C₈	—	4	1	no	—
74	C₂²×C₄₇⋊C₈	C₂³	1	1	yes	characteristic
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	C₂×C₈×D₄₇	—	2	2	no	—
79	C₂×C₈×D₄₇	—	2	2	no	—
80	C₂×C₈×D₄₇	—	4	1	no	—
81	C₄×C₂²⋊D₄₇	D₄	1	4	yes	—
82	C₄×C₂²⋊D₄₇	Q₈	1	4	yes	—
83	#13093981	—	2	2	no	—
84	#13093981	—	2	2	no	—
85	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
88	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
89	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
90	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
91	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
92	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
93	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
94	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
95	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
96	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
97	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
98	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
99	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
100	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
101	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
102	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
103	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
104	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
105	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
106	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
107	C₄⋊(C₄₇⋊C₈)	—	2	2	no	—
108	C₄⋊(C₄₇⋊C₈)	D₄	1	4	yes	complemented
109	Dic₄₇⋊C₈	—	2	2	no	—
110	Dic₄₇⋊C₈	—	2	2	no	—
111	Dic₄₇⋊C₈	—	2	2	no	—
112	Dic₄₇⋊C₈	—	2	2	no	—
113	Dic₄₇⋊C₈	—	4	1	no	—
114	Dic₄₇⋊C₈	—	4	1	no	—
115	(C₂×D₄₇)⋊C₈	—	2	2	no	—
116	(C₂×D₄₇)⋊C₈	—	2	2	no	—
117	#13093934	—	2	2	no	—
118	#13093934	—	2	2	no	—
119	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
120	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
121	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
122	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
123	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
124	C₄₇⋊#95	C₂×C₄	1	1	yes	characteristic
125	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
126	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
127	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
128	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
129	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
130	#117×C₄₇	—	2	2	no	—
131	#117×C₄₇	—	2	2	no	—
132	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
133	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
134	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
135	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
136	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
137	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
138	C₄⋊C₈×C₄₇	—	2	2	no	—
139	C₄⋊C₈×C₄₇	—	2	2	no	—
140	C₂²⋊C₈×C₄₇	—	2	2	no	—
141	C₂²⋊C₈×C₄₇	—	2	2	no	—
142	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
143	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
144	C₂²×C₄×C₄₇	—	2	1	no	—
145	C₂²×C₄×C₄₇	—	2	1	no	—
146	C₂²×C₄×C₄₇	—	2	1	no	—
147	C₂²×C₄×C₄₇	—	2	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	C₂×D₄	1	2	yes	—
154	C₂²×C₄×C₄₇	C₂×Q₈	1	2	yes	—
155	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
156	C₂×C₂²⋊D₄₇	—	4	1	no	—
157	C₂×C₂²⋊D₄₇	—	4	1	no	—
158	C₂×C₂²⋊D₄₇	C₄⋊C₄	1	4	yes	—
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	1	no	—
167	C₂×C₄×D₄₇	—	2	1	no	—
168	C₂×C₄×D₄₇	—	2	1	no	—
169	C₂×C₄×D₄₇	—	2	1	no	—
170	C₂×C₄×D₄₇	C₂×D₄	1	2	yes	—
171	C₂×C₄×D₄₇	C₂×Q₈	1	2	yes	—
172	C₂×C₈×C₄₇	—	2	1	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	C₄⋊C₄×C₄₇	—	2	2	no	—
185	C₄⋊C₄×C₄₇	—	2	2	no	—
186	C₂²⋊C₄×C₄₇	—	2	2	no	—
187	C₂²⋊C₄×C₄₇	—	2	2	no	—
188	C₄²×C₄₇	—	2	1	no	—
189	C₄²×C₄₇	—	2	1	no	—
190	C₄²×C₄₇	C₂×D₄	1	2	yes	—
191	C₄²×C₄₇	#41	1	2	yes	—
192	C₂²⋊Dic₄₇	—	2	2	no	—
193	C₂²⋊Dic₄₇	—	4	1	no	—
194	C₂²⋊Dic₄₇	C₄⋊C₄	1	4	yes	—
195	(C₂×D₄₇)⋊C₄	—	2	2	no	—
196	(C₂×D₄₇)⋊C₄	—	2	2	no	—
197	(C₂×D₄₇)⋊C₄	—	2	2	no	—
198	(C₂×D₄₇)⋊C₄	—	4	1	no	—
199	(C₂×D₄₇)⋊C₄	C₄⋊C₄	1	4	yes	—
200	Dic₄₇⋊C₄	—	2	2	no	—
201	Dic₄₇⋊C₄	—	2	2	no	—
202	Dic₄₇⋊C₄	—	4	1	no	—
203	Dic₄₇⋊C₄	—	4	1	no	—
204	Dic₄₇⋊C₄	C₄⋊C₄	1	4	yes	—
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	2	no	—
210	C₄×Dic₄₇	—	4	1	no	—
211	C₄×Dic₄₇	—	4	1	no	—
212	C₄×Dic₄₇	—	4	1	no	—
213	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
214	C₄×Dic₄₇	C₂×Q₈	1	2	yes	—
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	—	4	4	no	—
227	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
228	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
229	#10625324	—	4	4	no	—
230	C₈×D₄₇	—	4	4	no	—
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	C₂×C₄⋊C₄	1	2	yes	—
238	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
239	C₂²×D₄₇	—	2	1	no	—
240	C₂²×D₄₇	—	2	1	no	—
241	C₂²×D₄₇	—	2	1	no	—
242	C₂²×D₄₇	—	2	1	no	—
243	C₂²×D₄₇	—	2	1	no	—
244	C₂²×D₄₇	—	2	1	no	—
245	C₂²×D₄₇	C₂×C₄⋊C₄	1	2	yes	—
246	C₂×C₄×C₄₇	—	2	1	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	2	no	—
253	C₂×C₄×C₄₇	—	2	2	no	—
254	C₂×C₄×C₄₇	—	2	2	no	—
255	C₂×C₄×C₄₇	—	2	2	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	C₂×C₄⋊C₄	1	2	yes	—
263	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
264	C₂×C₄×C₄₇	C₄×D₄	1	2	yes	—
265	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
266	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
267	C₂×C₄×C₄₇	C₂²×Q₈	1	1	yes	characteristic
268	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
269	C₂×C₄×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
270	C₂×C₄×C₄₇	2₋¹⁺⁴	1	1	yes	characteristic
271	C₂²⋊D₄₇	—	4	4	no	—
272	C₂×Dic₄₇	—	2	1	no	—
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	C₂×C₄⋊C₄	1	2	yes	—
290	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
291	C₂×Dic₄₇	C₂×C₄⋊C₄	1	2	yes	—
292	C₂×Dic₄₇	#131	1	2	yes	—
293	C₄×D₄₇	—	2	2	no	—
294	C₄×D₄₇	—	2	2	no	—
295	C₄×D₄₇	—	2	2	no	—
296	C₄×D₄₇	—	2	2	no	—
297	C₈×C₄₇	—	4	1	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	—	2	2	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	—	4	1	no	—
310	C₂²×C₄₇	—	4	1	no	—
311	C₂²×C₄₇	—	4	1	no	—
312	C₂²×C₄₇	—	4	1	no	—
313	C₂²×C₄₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
314	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
315	C₂²×C₄₇	#520	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	D₄²	1	1	yes	characteristic
333	C₄×C₄₇	#547	1	1	yes	characteristic
334	C₄×C₄₇	D₄×Q₈	1	1	yes	characteristic
335	C₄×C₄₇	#554	1	1	yes	characteristic
336	Dic₄₇	—	2	2	no	—
337	Dic₄₇	—	2	2	no	—
338	Dic₄₇	—	2	2	no	—
339	Dic₄₇	—	2	2	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	—	47	1	no	—
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	D₄₇	1	1	yes	characteristic, complemented
357	#1767	—	47	1	no	—
358	C₂×C₄₇	—	4	2	no	—
359	C₂×C₄₇	D₄×C₄⋊C₄	1	1	yes	characteristic
360	C₂×C₄₇	#2905	1	1	yes	characteristic
361	C₂×C₄₇	#2906	1	1	yes	characteristic
362	C₂×C₄₇	#2932	1	1	yes	characteristic
363	C₂×C₄₇	#2935	1	1	yes	characteristic
364	C₂×C₄₇	#2992	1	1	yes	characteristic
365	C₂×C₄₇	#2995	1	1	yes	characteristic
366	D₄₇	—	4	2	no	—
367	C₂²×M₁₆	—	47	1	no	—
368	C₂²×M₁₆	—	47	1	no	—
369	C₂³×C₈	—	47	1	no	—
370	C₂³×C₈	—	47	1	no	—
371	C₂×C₄×D₄	—	47	1	no	—
372	C₂×#117	—	47	1	no	—
373	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
374	#435	—	94	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	C₂×D₄₇	1	1	yes	characteristic
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	—	47	1	no	—
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	C₂×D₄₇	1	1	yes	characteristic
413	#336	C₂×D₄₇	1	1	yes	characteristic
414	C₄₇	#22652	1	1	yes	characteristic, complemented, Sylow
415	C₂²×D₄	—	47	1	no	—
416	C₂³×C₄	—	47	1	no	—
417	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
418	C₂×M₁₆	—	94	2	no	—
419	C₂×M₁₆	—	94	2	no	—
420	C₂×M₁₆	—	94	2	no	—
421	C₂×M₁₆	—	94	2	no	—
422	C₂×M₁₆	—	188	1	no	—
423	C₂×M₁₆	—	188	1	no	—
424	C₂²×C₈	—	47	1	no	—
425	C₂²×C₈	—	47	1	no	—
426	C₂²×C₈	—	47	1	no	—
427	C₂²×C₈	—	47	1	no	—
428	C₂²×C₈	—	94	2	no	—
429	C₂²×C₈	—	94	2	no	—
430	C₂²×C₈	—	94	2	no	—
431	C₂²×C₈	—	94	2	no	—
432	C₂²×C₈	—	188	1	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	—	47	4	no	—
439	C₄×D₄	—	47	4	no	—
440	#117	—	2	2	no	—
441	#117	—	2	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	C₄×D₄₇	1	1	yes	characteristic
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	C₂²×D₄₇	1	1	yes	characteristic
469	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
470	C₄⋊C₈	—	2	2	no	—
471	C₄⋊C₈	—	2	2	no	—
472	C₄⋊C₈	—	47	4	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	—	94	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	—	47	1	no	—
495	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
496	C₂×D₄	—	47	4	no	—
497	C₂×D₄	—	188	1	no	—
498	C₂×D₄	—	188	1	no	—
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	—	47	1	no	—
504	C₂²×C₄	—	47	1	no	—
505	C₂²×C₄	—	47	1	no	—
506	C₂²×C₄	—	47	1	no	—
507	C₂²×C₄	—	47	2	no	—
508	C₂²×C₄	—	47	2	no	—
509	C₂²×C₄	—	47	1	no	—
510	C₂²×C₄	—	47	1	no	—
511	C₂²×C₄	—	47	1	no	—
512	C₂²×C₄	—	94	1	no	—
513	C₂²×C₄	—	94	1	no	—
514	C₂²×C₄	—	94	1	no	—
515	C₂²×C₄	—	94	1	no	—
516	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
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	D₄×D₄₇	1	2	yes	—
522	C₂²×C₄	Q₈×D₄₇	1	2	yes	—
523	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
524	M₁₆	—	188	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	—	2	1	no	—
538	C₂×C₈	—	47	2	no	—
539	C₂×C₈	—	47	2	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	—	188	4	no	—
552	C₄⋊C₄	—	2	2	no	—
553	C₄⋊C₄	—	2	2	no	—
554	C₄⋊C₄	—	47	4	no	—
555	C₄⋊C₄	—	94	2	no	—
556	C₄⋊C₄	—	94	2	no	—
557	C₄⋊C₄	—	188	1	no	—
558	C₄⋊C₄	—	188	1	no	—
559	C₂²⋊C₄	—	2	2	no	—
560	C₂²⋊C₄	—	2	2	no	—
561	C₂²⋊C₄	—	47	4	no	—
562	C₂²⋊C₄	—	47	4	no	—
563	C₂²⋊C₄	—	94	2	no	—
564	C₂²⋊C₄	—	94	2	no	—
565	C₂²⋊C₄	—	94	2	no	—
566	C₂²⋊C₄	—	94	2	no	—
567	C₂²⋊C₄	—	188	1	no	—
568	C₂²⋊C₄	—	188	1	no	—
569	C₄²	—	2	1	no	—
570	C₄²	—	2	1	no	—
571	C₄²	—	47	2	no	—
572	C₄²	—	47	2	no	—
573	C₄²	—	94	2	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	D₄×D₄₇	1	2	yes	—
582	C₄²	#10625352	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	—	47	2	no	—
590	C₂³	—	94	1	no	—
591	C₂³	—	94	1	no	—
592	C₂³	—	94	1	no	—
593	C₂³	—	94	1	no	—
594	C₂³	—	94	1	no	—
595	C₂³	—	94	1	no	—
596	C₂³	C₄⋊C₄×D₄₇	1	2	yes	—
597	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
598	D₄	—	188	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	2	no	—
606	C₂×C₄	—	2	2	no	—
607	C₂×C₄	—	2	2	no	—
608	C₂×C₄	—	2	2	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	—	47	2	no	—
616	C₂×C₄	—	47	2	no	—
617	C₂×C₄	—	47	2	no	—
618	C₂×C₄	—	47	2	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	2	no	—
628	C₂×C₄	—	94	2	no	—
629	C₂×C₄	—	94	2	no	—
630	C₂×C₄	—	94	2	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	—	94	1	no	—
640	C₂×C₄	C₄⋊C₄×D₄₇	1	2	yes	—
641	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
642	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	2	yes	—
643	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
644	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
645	C₂×C₄	C₂×Q₈×D₄₇	1	1	yes	characteristic
646	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
647	C₂×C₄	#13094070	1	1	yes	characteristic
648	C₂×C₄	#13094071	1	1	yes	characteristic
649	C₈	—	4	1	no	—
650	C₈	—	4	1	no	—
651	C₈	—	4	1	no	—
652	C₈	—	4	1	no	—
653	C₈	—	94	2	no	—
654	C₈	—	94	2	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	—	4	1	no	—
661	C₂²	—	4	1	no	—
662	C₂²	—	4	1	no	—
663	C₂²	—	4	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×C₄⋊C₄×D₄₇	1	1	yes	characteristic
672	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
673	C₂²	#15689603	1	1	yes	characteristic
674	C₂²	#131×D₄₇	1	1	yes	characteristic
675	C₂²	#15689888	1	1	yes	characteristic
676	C₂²	#15689888	1	1	yes	characteristic
677	C₂²	#15689888	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	—	94	2	no	—
684	C₄	—	94	2	no	—
685	C₄	—	94	2	no	—
686	C₄	—	94	2	no	—
687	C₄	—	188	1	no	—
688	C₄	—	188	1	no	—
689	C₄	—	188	1	no	—
690	C₄	#15689757	1	1	yes	characteristic
691	C₄	#15689773	1	1	yes	characteristic
692	C₄	#15689786	1	1	yes	characteristic
693	C₄	#15689831	1	1	yes	characteristic
694	C₂	—	4	2	no	—
695	C₂	—	188	2	no	—
696	C₂	#20246284	1	1	yes	characteristic
697	C₂	#20251949	1	1	yes	characteristic
698	C₂	#20251955	1	1	yes	characteristic
699	C₂	#20252103	1	1	yes	characteristic
700	C₂	#20252128	1	1	yes	characteristic
701	C₂	#20252522	1	1	yes	characteristic
702	C₂	#20252553	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator, socle	C₂³×C₄₇	C₂³×C₄
Fitting	C₄₇×#1798	C₂
prime radical	C₂²×C₂²⋊D₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1798	D₄₇
hypocenter	C₄₇	#22652
LCS	G ▷ C₂³×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1798

Complements

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

N	H ≅ G/N	type
3. C₂×#15689150	C₂	semidirect
4. C₂×#15689148	C₂	semidirect
6. #20244110	C₂	semidirect
7. #20244110	C₂	semidirect
8. #20243572	C₂	semidirect
9. #20243570	C₂	semidirect
10. #20243567	C₂	semidirect
11. #20243565	C₂	semidirect
12. #20243539	C₂	semidirect
13. #20243369	C₂	semidirect
14. #20243243	C₂	semidirect
15. C₄₇×#1798	C₂	semidirect
108. C₄⋊(C₄₇⋊C₈)	D₄	semidirect
356. #1798	D₄₇	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×#15689197	2
C₂×#15689191	2
C₂×#15689150	2
C₂×#15689148	2
#20245847	2
#20244110	2
#20243572	2
#20243570	2
#20243567	2
#20243565	2
#20243539	2
#20243369	2
#20243243	2
C₄₇×#1798	2
#22652	47