Subgroups — #26214631

Order 12032.

1118 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689198	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689191	C₂	1	1	yes	maximal, characteristic
3	C₂×#15689079	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₄×#10625324	C₂	1	1	yes	maximal, characteristic, complemented
5	#20245825	C₂	1	1	yes	maximal, characteristic
6	#20243259	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243254	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243246	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243174	C₂	1	1	yes	maximal, characteristic, complemented
10	#20243170	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243168	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243167	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243151	C₂	1	1	yes	maximal, characteristic, complemented
14	#20243076	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#1750	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#10625329	C₂²	1	1	yes	characteristic
17	C₂²×#10625324	C₂²	1	1	yes	characteristic
18	C₂²×#10625324	C₂²	1	1	yes	characteristic
19	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₄×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
21	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
22	#15689198	C₄	1	8	yes	complemented
23	#15689191	C₄	1	8	yes	complemented
24	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
25	C₂×Dic₄₇⋊C₈	C₂²	1	1	yes	characteristic
26	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
27	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
28	#15689079	—	2	4	no	—
29	C₄×#10625324	—	2	4	no	—
30	C₂×#13093935	C₂²	1	1	yes	characteristic
31	C₂×#13093935	C₂²	1	1	yes	characteristic
32	C₂×#13093934	C₂²	1	1	yes	characteristic
33	C₂×#13093934	C₂²	1	1	yes	characteristic
34	C₂×#13093934	C₂²	1	1	yes	characteristic
35	C₂×#13093934	C₂²	1	1	yes	characteristic
36	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
37	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
38	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
39	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
40	#15689011	C₄	1	2	yes	—
41	#15689004	C₄	1	2	yes	—
42	#15688999	C₄	1	2	yes	—
43	#15688994	C₄	1	2	yes	—
44	C₄×Dic₄₇⋊C₄	C₂²	1	1	yes	characteristic
45	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
46	C₄×C₂²⋊Dic₄₇	C₂²	1	1	yes	characteristic
47	#15688969	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	C₂×#117×C₄₇	C₂²	1	1	yes	characteristic
53	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
54	C₂×C₂²⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
55	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
56	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
57	C₄₇×#336	C₂²	1	1	yes	characteristic
58	C₄₇×#336	C₂²	1	1	yes	characteristic
59	C₂²×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
61	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
62	C₂×#10625329	—	2	2	no	—
63	C₂×#10625329	—	2	2	no	—
64	C₂×#10625329	C₂×C₄	1	4	yes	complemented
65	C₂×#10625324	—	2	2	no	—
66	C₂×#10625324	—	2	2	no	—
67	C₂×#10625324	—	2	2	no	—
68	C₂×#10625324	—	2	2	no	—
69	C₂×#10625324	C₂×C₄	1	4	yes	—
70	C₂×#10625324	C₂×C₄	1	4	yes	—
71	C₂²×C₄₇⋊C₈	—	2	2	no	—
72	C₂²×C₄₇⋊C₈	—	2	2	no	—
73	C₂²×C₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
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	C₄×C₂²⋊D₄₇	C₂×C₄	1	4	yes	—
79	C₄×C₂²⋊D₄₇	C₂×C₄	1	4	yes	—
80	C₂×Dic₄₇⋊C₄	C₂×C₄	1	2	yes	—
81	C₂×Dic₄₇⋊C₄	C₂×C₄	1	1	yes	characteristic
82	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	2	yes	—
83	C₂×C₂²⋊Dic₄₇	C₂×C₄	1	1	yes	characteristic
84	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
85	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
86	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
87	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
88	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
89	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
90	C₄²×D₄₇	—	2	2	no	—
91	C₄²×D₄₇	—	2	2	no	—
92	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
93	Dic₄₇⋊C₈	C₂×C₄	1	4	yes	complemented
94	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
95	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	—
96	#13093935	—	2	2	no	—
97	#13093935	—	2	2	no	—
98	#13093934	—	2	2	no	—
99	#13093934	—	2	2	no	—
100	#13093934	—	2	2	no	—
101	#13093934	C₂×C₄	1	4	yes	complemented
102	C₄×C₄₇⋊C₈	—	2	2	no	—
103	C₄×C₄₇⋊C₈	D₄	1	4	yes	complemented
104	C₈×Dic₄₇	—	2	2	no	—
105	C₈×Dic₄₇	C₂×C₄	1	4	yes	complemented
106	C₄₇⋊#95	C₂×C₄	1	2	yes	—
107	C₄₇⋊#95	C₂×C₄	1	2	yes	—
108	C₄₇⋊#95	C₂×C₄	1	2	yes	—
109	C₄₇⋊#95	C₂×C₄	1	2	yes	—
110	C₄₇⋊#95	C₂×C₄	1	2	yes	—
111	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
112	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
113	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
114	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
116	#117×C₄₇	—	2	2	no	—
117	#117×C₄₇	—	2	2	no	—
118	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
119	C₂×C₂²⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
120	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
122	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
123	C₂²⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
124	#97×C₄₇	—	2	2	no	—
125	C₄×C₈×C₄₇	—	2	2	no	—
126	C₂⁴×C₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂²×C₄×C₄₇	—	2	1	no	—
129	C₂²×C₄×C₄₇	—	2	1	no	—
130	C₂²×C₄×C₄₇	—	2	1	no	—
131	C₂²×C₄×C₄₇	—	2	1	no	—
132	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
134	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
135	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
136	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
137	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
138	C₂×C₂²⋊D₄₇	—	4	2	no	—
139	C₂×C₂²⋊D₄₇	C₄²	1	4	yes	—
140	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
141	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
142	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
143	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
144	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₄×D₄₇	—	2	1	no	—
146	C₂×C₄×D₄₇	—	2	1	no	—
147	C₂×C₄×D₄₇	—	2	1	no	—
148	C₂×C₄×D₄₇	—	2	1	no	—
149	C₂×C₄×D₄₇	—	2	4	no	—
150	C₂×C₄×D₄₇	—	4	2	no	—
151	C₂×C₄×D₄₇	—	4	2	no	—
152	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
153	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
154	C₂×C₈×C₄₇	—	2	1	no	—
155	C₂×C₈×C₄₇	—	2	1	no	—
156	C₂×C₈×C₄₇	—	2	1	no	—
157	C₂×C₈×C₄₇	—	2	1	no	—
158	C₂×C₈×C₄₇	—	2	1	no	—
159	C₂×C₈×C₄₇	—	2	1	no	—
160	C₂×C₈×C₄₇	—	2	1	no	—
161	C₂×C₈×C₄₇	—	2	1	no	—
162	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
163	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
164	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
165	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
166	C₄⋊C₄×C₄₇	—	2	4	no	—
167	C₂²⋊C₄×C₄₇	—	2	4	no	—
168	C₄²×C₄₇	—	2	1	no	—
169	C₄²×C₄₇	—	2	1	no	—
170	C₄²×C₄₇	C₂×D₄	1	2	yes	—
171	C₄²×C₄₇	#41	1	2	yes	—
172	C₂²⋊Dic₄₇	—	4	2	no	—
173	C₂²⋊Dic₄₇	C₄²	1	4	yes	—
174	(C₂×D₄₇)⋊C₄	—	4	2	no	—
175	(C₂×D₄₇)⋊C₄	C₄²	1	4	yes	—
176	Dic₄₇⋊C₄	—	4	2	no	—
177	Dic₄₇⋊C₄	C₄²	1	4	yes	—
178	C₄×Dic₄₇	—	2	4	no	—
179	C₄×Dic₄₇	—	2	1	no	—
180	C₄×Dic₄₇	—	2	1	no	—
181	C₄×Dic₄₇	—	2	1	no	—
182	C₄×Dic₄₇	—	2	1	no	—
183	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
184	C₄×Dic₄₇	C₂²×C₄	1	2	yes	—
185	#10625329	—	2	8	no	—
186	C₂×C₄₇⋊C₈	—	2	1	no	—
187	C₂×C₄₇⋊C₈	—	2	1	no	—
188	C₂×C₄₇⋊C₈	—	2	1	no	—
189	C₂×C₄₇⋊C₈	—	2	1	no	—
190	C₂×C₄₇⋊C₈	—	2	8	no	—
191	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
192	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
193	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
194	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
195	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
196	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
197	C₂×C₄₇⋊C₈	#41	1	2	yes	—
198	C₂×C₄₇⋊C₈	#41	1	2	yes	—
199	#10625324	—	2	8	no	—
200	#10625324	—	2	8	no	—
201	C₂³×C₄₇	—	2	1	no	—
202	C₂³×C₄₇	—	2	1	no	—
203	C₂³×C₄₇	—	2	2	no	—
204	C₂³×C₄₇	—	2	2	no	—
205	C₂³×C₄₇	C₂×C₄²	1	2	yes	—
206	C₂³×C₄₇	C₂³×C₄	1	1	yes	characteristic
207	C₂²×D₄₇	—	2	1	no	—
208	C₂²×D₄₇	—	2	1	no	—
209	C₂²×D₄₇	—	2	2	no	—
210	C₂²×D₄₇	—	2	2	no	—
211	C₂²×D₄₇	C₂×C₄²	1	2	yes	—
212	C₂×C₄×C₄₇	—	2	1	no	—
213	C₂×C₄×C₄₇	—	2	1	no	—
214	C₂×C₄×C₄₇	—	2	2	no	—
215	C₂×C₄×C₄₇	—	2	2	no	—
216	C₂×C₄×C₄₇	—	2	2	no	—
217	C₂×C₄×C₄₇	—	2	2	no	—
218	C₂×C₄×C₄₇	—	2	2	no	—
219	C₂×C₄×C₄₇	—	2	2	no	—
220	C₂×C₄×C₄₇	—	2	2	no	—
221	C₂×C₄×C₄₇	—	2	2	no	—
222	C₂×C₄×C₄₇	—	2	2	no	—
223	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
224	C₂×C₄×C₄₇	C₄×D₄	1	4	yes	—
225	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
226	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
227	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
229	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
230	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
231	C₂²⋊D₄₇	—	4	4	no	—
232	C₂×Dic₄₇	—	2	1	no	—
233	C₂×Dic₄₇	—	2	1	no	—
234	C₂×Dic₄₇	—	2	2	no	—
235	C₂×Dic₄₇	—	2	2	no	—
236	C₂×Dic₄₇	—	2	2	no	—
237	C₂×Dic₄₇	—	2	2	no	—
238	C₂×Dic₄₇	—	2	2	no	—
239	C₂×Dic₄₇	—	2	2	no	—
240	C₂×Dic₄₇	—	2	2	no	—
241	C₂×Dic₄₇	—	2	2	no	—
242	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
243	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
244	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
245	C₄×D₄₇	—	2	2	no	—
246	C₄×D₄₇	—	2	2	no	—
247	C₄×D₄₇	—	2	2	no	—
248	C₄×D₄₇	—	2	2	no	—
249	C₄×D₄₇	—	4	8	no	—
250	C₈×C₄₇	—	2	2	no	—
251	C₈×C₄₇	—	2	2	no	—
252	C₈×C₄₇	—	2	2	no	—
253	C₈×C₄₇	—	2	2	no	—
254	C₄₇⋊C₈	—	2	2	no	—
255	C₄₇⋊C₈	—	2	2	no	—
256	C₄₇⋊C₈	C₄×D₄	1	4	yes	—
257	C₄₇⋊C₈	C₄×D₄	1	4	yes	—
258	#20487	—	47	1	no	maximal, Sylow
259	C₂²×C₄₇	—	2	2	no	—
260	C₂²×C₄₇	—	2	2	no	—
261	C₂²×C₄₇	—	2	2	no	—
262	C₂²×C₄₇	—	4	2	no	—
263	C₂²×C₄₇	—	4	2	no	—
264	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
265	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
266	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
267	C₂²×C₄₇	#568	1	2	yes	—
268	C₂²×C₄₇	#568	1	2	yes	—
269	C₂×D₄₇	—	2	2	no	—
270	C₂×D₄₇	—	2	2	no	—
271	C₂×D₄₇	—	2	2	no	—
272	C₂×D₄₇	—	4	2	no	—
273	C₂×D₄₇	—	4	2	no	—
274	C₄×C₄₇	—	2	4	no	—
275	C₄×C₄₇	—	2	2	no	—
276	C₄×C₄₇	—	4	2	no	—
277	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
278	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
279	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
280	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
281	Dic₄₇	—	2	2	no	—
282	Dic₄₇	—	2	2	no	—
283	Dic₄₇	—	2	2	no	—
284	Dic₄₇	—	4	2	no	—
285	Dic₄₇	—	4	2	no	—
286	C₂×#436	—	47	1	no	—
287	C₂×#435	—	47	1	no	—
288	C₂×#405	—	47	1	no	—
289	C₂×C₄×M₁₆	—	47	1	no	—
290	#2290	—	47	1	no	—
291	#1771	—	47	1	no	—
292	#1770	—	47	1	no	—
293	#1768	—	47	1	no	—
294	#1753	—	47	1	no	—
295	#1753	—	47	1	no	—
296	#1753	—	47	1	no	—
297	#1752	—	47	1	no	—
298	#1750	D₄₇	1	1	yes	characteristic, complemented
299	#1749	—	47	1	no	—
300	#1726	—	47	1	no	—
301	C₂×C₄₇	—	4	2	no	—
302	C₂×C₄₇	C₄²×D₄	1	1	yes	characteristic
303	C₂×C₄₇	#2873	1	1	yes	characteristic
304	C₂×C₄₇	#2875	1	1	yes	characteristic
305	C₂×C₄₇	#2930	1	2	yes	—
306	C₂×C₄₇	#2967	1	2	yes	—
307	D₄₇	—	4	2	no	—
308	C₂²×M₁₆	—	47	1	no	—
309	C₂²×M₁₆	—	47	1	no	—
310	C₂²×M₁₆	—	47	1	no	—
311	C₂³×C₈	—	47	1	no	—
312	C₂×C₄×D₄	—	47	1	no	—
313	C₂×#117	C₂×D₄₇	1	1	yes	characteristic
314	C₂²×C₄²	—	47	1	no	—
315	#436	—	47	8	no	—
316	#435	—	47	8	no	—
317	C₂×C₄⋊C₈	—	47	1	no	—
318	C₂×C₄⋊C₈	—	47	1	no	—
319	C₂×C₂²⋊C₈	—	47	1	no	—
320	C₂×C₂²⋊C₈	—	47	1	no	—
321	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
322	C₂×C₂²⋊C₈	C₂×D₄₇	1	1	yes	characteristic
323	#405	—	94	4	no	—
324	C₄×M₁₆	—	94	4	no	—
325	C₂×#97	—	47	1	no	—
326	C₂×#97	—	47	1	no	—
327	C₂×#97	—	47	1	no	—
328	C₂×#97	—	47	1	no	—
329	C₂×#97	—	47	1	no	—
330	C₂×#97	—	47	1	no	—
331	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
332	C₂×C₄×C₈	—	47	1	no	—
333	C₂×C₄×C₈	—	47	1	no	—
334	C₂×C₄×C₈	—	47	1	no	—
335	C₂×C₄×C₈	—	47	1	no	—
336	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
337	#388	—	47	2	no	—
338	#387	—	47	2	no	—
339	#386	—	47	2	no	—
340	#385	—	47	2	no	—
341	C₄×C₄⋊C₄	—	47	1	no	—
342	C₄×C₂²⋊C₄	—	47	1	no	—
343	C₄×C₂²⋊C₄	—	47	1	no	—
344	#376	—	47	1	no	—
345	#336	—	47	1	no	—
346	#336	—	47	1	no	—
347	#336	—	47	1	no	—
348	#336	—	47	1	no	—
349	#336	C₂×D₄₇	1	1	yes	characteristic
350	#336	C₂×D₄₇	1	1	yes	characteristic
351	C₄₇	#20487	1	1	yes	characteristic, complemented, Sylow
352	C₂²×D₄	—	47	1	no	—
353	C₂³×C₄	—	47	1	no	—
354	C₂³×C₄	—	47	2	no	—
355	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
356	C₂×M₁₆	—	47	4	no	—
357	C₂×M₁₆	—	47	4	no	—
358	C₂×M₁₆	—	47	4	no	—
359	C₂×M₁₆	—	94	2	no	—
360	C₂×M₁₆	—	94	2	no	—
361	C₂×M₁₆	—	94	2	no	—
362	C₂×M₁₆	—	94	2	no	—
363	C₂×M₁₆	—	94	2	no	—
364	C₂×M₁₆	—	94	2	no	—
365	C₂²×C₈	—	47	1	no	—
366	C₂²×C₈	—	47	1	no	—
367	C₂²×C₈	—	47	4	no	—
368	C₂²×C₈	—	47	1	no	—
369	C₂²×C₈	—	47	1	no	—
370	C₂²×C₈	—	94	2	no	—
371	C₂²×C₈	—	94	2	no	—
372	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
373	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
374	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
375	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
376	C₄×D₄	—	47	4	no	—
377	C₄×D₄	—	47	4	no	—
378	#117	—	2	2	no	—
379	#117	—	2	2	no	—
380	C₂×C₄⋊C₄	—	47	1	no	—
381	C₂×C₄⋊C₄	—	47	2	no	—
382	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
383	C₂×C₂²⋊C₄	—	47	1	no	—
384	C₂×C₂²⋊C₄	—	47	1	no	—
385	C₂×C₂²⋊C₄	—	47	2	no	—
386	C₂×C₂²⋊C₄	—	47	2	no	—
387	C₂×C₂²⋊C₄	C₄×D₄₇	1	2	yes	—
388	C₂×C₄²	—	47	1	no	—
389	C₂×C₄²	—	47	2	no	—
390	C₂×C₄²	—	47	1	no	—
391	C₂×C₄²	—	47	1	no	—
392	C₂×C₄²	—	94	2	no	—
393	C₂×C₄²	—	94	2	no	—
394	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
395	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
396	C₄⋊C₈	—	47	4	no	—
397	C₄⋊C₈	—	47	4	no	—
398	C₂²⋊C₈	—	47	4	no	—
399	C₂²⋊C₈	—	47	4	no	—
400	C₂²⋊C₈	C₄×D₄₇	1	4	yes	complemented
401	C₂²⋊C₈	C₄×D₄₇	1	4	yes	complemented
402	#97	—	2	2	no	—
403	#97	—	47	4	no	—
404	#97	—	94	2	no	—
405	#97	—	94	2	no	—
406	#97	—	94	2	no	—
407	#97	—	94	2	no	—
408	#97	—	94	2	no	—
409	C₄×C₈	—	2	2	no	—
410	C₄×C₈	—	47	4	no	—
411	C₄×C₈	—	47	4	no	—
412	C₄×C₈	—	94	2	no	—
413	C₄×C₈	—	94	2	no	—
414	#95	—	47	2	no	—
415	#95	—	47	2	no	—
416	#95	—	47	2	no	—
417	#95	—	47	2	no	—
418	#95	—	47	2	no	—
419	C₂⁴	—	47	1	no	—
420	C₂⁴	C₂×C₄×D₄₇	1	1	yes	characteristic
421	C₂×D₄	—	47	4	no	—
422	C₂×D₄	—	188	2	no	—
423	C₂²×C₄	—	2	1	no	—
424	C₂²×C₄	—	2	1	no	—
425	C₂²×C₄	—	2	1	no	—
426	C₂²×C₄	—	2	1	no	—
427	C₂²×C₄	—	47	1	no	—
428	C₂²×C₄	—	47	1	no	—
429	C₂²×C₄	—	47	1	no	—
430	C₂²×C₄	—	47	2	no	—
431	C₂²×C₄	—	47	2	no	—
432	C₂²×C₄	—	47	2	no	—
433	C₂²×C₄	—	47	2	no	—
434	C₂²×C₄	—	94	1	no	—
435	C₂²×C₄	—	94	1	no	—
436	C₂²×C₄	—	94	1	no	—
437	C₂²×C₄	—	94	1	no	—
438	C₂²×C₄	—	94	4	no	—
439	C₂²×C₄	—	188	2	no	—
440	C₂²×C₄	—	188	2	no	—
441	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
442	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
443	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
444	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
445	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
446	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
447	M₁₆	—	94	8	no	—
448	M₁₆	—	94	8	no	—
449	M₁₆	—	94	8	no	—
450	C₂×C₈	—	2	1	no	—
451	C₂×C₈	—	2	1	no	—
452	C₂×C₈	—	2	1	no	—
453	C₂×C₈	—	2	1	no	—
454	C₂×C₈	—	2	1	no	—
455	C₂×C₈	—	2	1	no	—
456	C₂×C₈	—	2	1	no	—
457	C₂×C₈	—	2	1	no	—
458	C₂×C₈	—	47	2	no	—
459	C₂×C₈	—	47	2	no	—
460	C₂×C₈	—	47	2	no	—
461	C₂×C₈	—	47	2	no	—
462	C₂×C₈	—	47	2	no	—
463	C₂×C₈	—	47	2	no	—
464	C₂×C₈	—	47	2	no	—
465	C₂×C₈	—	47	2	no	—
466	C₂×C₈	—	94	8	no	—
467	C₂×C₈	—	94	1	no	—
468	C₂×C₈	—	94	1	no	—
469	C₂×C₈	—	94	1	no	—
470	C₂×C₈	—	94	1	no	—
471	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
472	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
473	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
474	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
475	C₄⋊C₄	—	2	4	no	—
476	C₄⋊C₄	—	47	4	no	—
477	C₄⋊C₄	—	188	2	no	—
478	C₂²⋊C₄	—	2	4	no	—
479	C₂²⋊C₄	—	47	4	no	—
480	C₂²⋊C₄	—	47	4	no	—
481	C₂²⋊C₄	—	188	2	no	—
482	C₂²⋊C₄	—	188	2	no	—
483	C₄²	—	2	1	no	—
484	C₄²	—	2	1	no	—
485	C₄²	—	47	2	no	—
486	C₄²	—	47	2	no	—
487	C₄²	—	94	4	no	—
488	C₄²	—	94	1	no	—
489	C₄²	—	94	1	no	—
490	C₄²	—	94	1	no	—
491	C₄²	—	94	1	no	—
492	C₄²	D₄×D₄₇	1	2	yes	—
493	C₄²	#10625352	1	2	yes	—
494	C₂³	—	2	1	no	—
495	C₂³	—	2	1	no	—
496	C₂³	—	2	2	no	—
497	C₂³	—	2	2	no	—
498	C₂³	—	47	2	no	—
499	C₂³	—	94	1	no	—
500	C₂³	—	94	1	no	—
501	C₂³	—	94	2	no	—
502	C₂³	—	94	2	no	—
503	C₂³	C₄²×D₄₇	1	2	yes	—
504	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
505	D₄	—	188	4	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	2	2	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	47	2	no	—
518	C₂×C₄	—	47	2	no	—
519	C₂×C₄	—	47	2	no	—
520	C₂×C₄	—	94	1	no	—
521	C₂×C₄	—	94	1	no	—
522	C₂×C₄	—	94	2	no	—
523	C₂×C₄	—	94	2	no	—
524	C₂×C₄	—	94	2	no	—
525	C₂×C₄	—	94	2	no	—
526	C₂×C₄	—	94	2	no	—
527	C₂×C₄	—	94	2	no	—
528	C₂×C₄	—	94	2	no	—
529	C₂×C₄	—	94	2	no	—
530	C₂×C₄	—	94	2	no	—
531	C₂×C₄	—	94	2	no	—
532	C₂×C₄	—	94	2	no	—
533	C₂×C₄	—	94	2	no	—
534	C₂×C₄	—	188	8	no	—
535	C₂×C₄	C₄²×D₄₇	1	2	yes	—
536	C₂×C₄	(C₂²⋊D₄₇)⋊C₄	1	4	yes	—
537	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
538	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
539	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
540	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
541	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
542	C₂×C₄	C₂×#10625352	1	1	yes	characteristic
543	C₈	—	2	2	no	—
544	C₈	—	2	2	no	—
545	C₈	—	2	2	no	—
546	C₈	—	2	2	no	—
547	C₈	—	47	4	no	—
548	C₈	—	47	4	no	—
549	C₈	—	94	2	no	—
550	C₈	—	94	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	94	2	no	—
557	C₂²	—	94	2	no	—
558	C₂²	—	94	2	no	—
559	C₂²	—	188	2	no	—
560	C₂²	—	188	2	no	—
561	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
562	C₂²	C₂×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
563	C₂²	#15689591	1	1	yes	characteristic
564	C₂²	#15689888	1	2	yes	—
565	C₂²	#15689888	1	2	yes	—
566	C₄	—	2	4	no	—
567	C₄	—	2	2	no	—
568	C₄	—	4	2	no	—
569	C₄	—	94	2	no	—
570	C₄	—	94	2	no	—
571	C₄	—	94	2	no	—
572	C₄	—	188	2	no	—
573	C₄	—	188	2	no	—
574	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
575	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
576	C₄	C₄×#10625352	1	1	yes	characteristic
577	C₄	C₄×#10625352	1	1	yes	characteristic
578	C₂	—	4	2	no	—
579	C₂	—	188	2	no	—
580	C₂	C₄×(C₂²⋊D₄₇)⋊C₄	1	1	yes	characteristic
581	C₂	#20251804	1	1	yes	characteristic
582	C₂	#20251815	1	1	yes	characteristic
583	C₂	#20252094	1	2	yes	—
584	C₂	#20252371	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₄₇×#1750	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×C₂²⋊D₄₇	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1750	D₄₇
hypocenter	C₄₇	#20487
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1750

Complements

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

N	H ≅ G/N	type
3. C₂×#15689079	C₂	semidirect
4. C₂×C₄×#10625324	C₂	semidirect
6. #20243259	C₂	semidirect
7. #20243254	C₂	semidirect
8. #20243246	C₂	semidirect
9. #20243174	C₂	semidirect
10. #20243170	C₂	semidirect
11. #20243168	C₂	semidirect
12. #20243167	C₂	semidirect
13. #20243151	C₂	semidirect
14. #20243076	C₂	semidirect
15. C₄₇×#1750	C₂	semidirect
22. #15689198	C₄	semidirect
23. #15689191	C₄	semidirect
64. C₂×#10625329	C₂×C₄	semidirect
73. C₂²×C₄₇⋊C₈	C₂×C₄	semidirect
92. Dic₄₇⋊C₈	C₂×C₄	semidirect
93. Dic₄₇⋊C₈	C₂×C₄	semidirect
101. #13093934	C₂×C₄	semidirect
103. C₄×C₄₇⋊C₈	D₄	semidirect
105. C₈×Dic₄₇	C₂×C₄	semidirect
122. C₂²⋊C₈×C₄₇	C₂×C₄	semidirect
123. C₂²⋊C₈×C₄₇	C₂×C₄	semidirect
298. #1750	D₄₇	semidirect
351. C₄₇	#20487	semidirect
400. C₂²⋊C₈	C₄×D₄₇	semidirect
401. C₂²⋊C₈	C₄×D₄₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689198	2
C₂×#15689191	2
C₂×#15689079	2
C₂×C₄×#10625324	2
#20245825	2
#20243259	2
#20243254	2
#20243246	2
#20243174	2
#20243170	2
#20243168	2
#20243167	2
#20243151	2
#20243076	2
C₄₇×#1750	2
#20487	47