Subgroups — #26214680

Order 12032.

1246 conjugacy classes of subgroups.

The subgroup lattice has 598 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689196	C₂	1	1	yes	maximal, characteristic
2	C₂×#15689193	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#10625324	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#97×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×#13093986	C₂	1	1	yes	maximal, characteristic
6	#20243263	C₂	1	1	yes	maximal, characteristic, complemented
7	#20243243	C₂	1	1	yes	maximal, characteristic, complemented
8	#20243173	C₂	1	1	yes	maximal, characteristic, complemented
9	#20243170	C₂	1	1	yes	maximal, characteristic, complemented
10	C₈×(C₂×D₄₇)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
11	#20243158	C₂	1	1	yes	maximal, characteristic, complemented
12	#20243149	C₂	1	1	yes	maximal, characteristic, complemented
13	#20243149	C₂	1	1	yes	maximal, characteristic, complemented
14	#97×Dic₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#1771	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#10625324	C₂²	1	1	yes	characteristic
17	C₂²×#10625324	C₂²	1	1	yes	characteristic
18	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
19	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
20	C₂×C₄×D₁₈₈	C₂²	1	1	yes	characteristic
21	C₂×#13093986	C₄	1	2	yes	—
22	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₄²×D₄₇	C₂²	1	1	yes	characteristic
24	#15689196	C₄	1	8	yes	complemented
25	#15689193	C₄	1	8	yes	complemented
26	C₂×C₄⋊(C₄₇⋊C₈)	C₂²	1	1	yes	characteristic
27	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
28	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
29	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
30	C₂×(C₂×D₄₇)⋊C₈	C₂²	1	1	yes	characteristic
31	C₄×#10625324	—	2	4	no	—
32	C₂×#13093935	C₂²	1	1	yes	characteristic
33	C₂×#13093935	C₂²	1	1	yes	characteristic
34	C₂×#13093934	C₂²	1	1	yes	characteristic
35	C₂×#13093934	C₂²	1	1	yes	characteristic
36	C₂×#13093934	C₂²	1	1	yes	characteristic
37	C₂×#13093934	C₂²	1	1	yes	characteristic
38	#97×D₄₇	—	2	4	no	—
39	C₂×C₄×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
40	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
41	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
42	C₄⋊C₄×Dic₄₇	C₄	1	2	yes	—
43	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
44	C₄×(C₂×D₄₇)⋊C₄	C₂²	1	1	yes	characteristic
45	#15688970	C₄	1	2	yes	—
46	#15688970	C₄	1	2	yes	—
47	C₄²×Dic₄₇	C₂²	1	1	yes	characteristic
48	#15688878	C₂²	1	1	yes	characteristic
49	#15688878	C₂²	1	1	yes	characteristic
50	#15688877	C₂²	1	1	yes	characteristic
51	#15688877	C₂²	1	1	yes	characteristic
52	C₂×C₄⋊C₈×C₄₇	C₂²	1	1	yes	characteristic
53	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
54	C₂×#97×C₄₇	C₂²	1	1	yes	characteristic
55	C₂×C₄×C₈×C₄₇	C₂²	1	1	yes	characteristic
56	C₄×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
57	C₄₇×#336	C₂²	1	1	yes	characteristic
58	C₄₇×#336	C₂²	1	1	yes	characteristic
59	C₂²×D₁₈₈	C₂×C₄	1	1	yes	characteristic
60	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
61	C₂²×C₄×D₄₇	C₂×C₄	1	2	yes	—
62	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
63	C₂²×C₄×D₄₇	C₂³	1	1	yes	characteristic
64	C₂×#10625324	—	2	2	no	—
65	C₂×#10625324	—	2	2	no	—
66	C₂×#10625324	—	2	2	no	—
67	C₂×#10625324	—	2	2	no	—
68	C₂×#10625324	C₂×C₄	1	4	yes	complemented
69	C₂×#10625324	C₂×C₄	1	4	yes	complemented
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	C₂×C₈×D₄₇	—	2	2	no	—
75	C₂×C₈×D₄₇	—	2	2	no	—
76	C₂×C₈×D₄₇	—	2	2	no	—
77	C₂×C₈×D₄₇	—	2	2	no	—
78	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	complemented
79	C₂×C₈×D₄₇	C₂×C₄	1	4	yes	complemented
80	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
81	C₄×D₁₈₈	C₂×C₄	1	4	yes	—
82	#13093986	—	2	8	no	—
83	C₂×C₄⋊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×(C₂×D₄₇)⋊C₄	C₂×C₄	1	1	yes	characteristic
87	C₂×(C₂×D₄₇)⋊C₄	C₂×C₄	1	2	yes	—
88	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
89	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
90	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
91	C₂×C₄×Dic₄₇	C₂×C₄	1	2	yes	—
92	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
93	C₂×C₄×Dic₄₇	C₂³	1	1	yes	characteristic
94	C₄²×D₄₇	—	2	2	no	—
95	C₄²×D₄₇	—	2	2	no	—
96	C₄²×D₄₇	—	2	2	no	—
97	C₄²×D₄₇	—	2	2	no	—
98	C₄⋊(C₄₇⋊C₈)	C₂×C₄	1	4	yes	complemented
99	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	complemented
100	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	complemented
101	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	complemented
102	(C₂×D₄₇)⋊C₈	C₂×C₄	1	4	yes	complemented
103	#13093935	—	2	2	no	—
104	#13093935	C₂×C₄	1	4	yes	complemented
105	#13093934	—	2	2	no	—
106	#13093934	—	2	2	no	—
107	#13093934	—	2	2	no	—
108	#13093934	D₄	1	4	yes	complemented
109	C₄×C₄₇⋊C₈	—	2	2	no	—
110	C₈×Dic₄₇	—	2	2	no	—
111	C₈×Dic₄₇	—	2	2	no	—
112	C₄₇⋊#95	C₂×C₄	1	2	yes	—
113	C₄₇⋊#95	C₂×C₄	1	2	yes	—
114	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
115	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
116	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
117	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
118	C₂×C₄⋊C₄×C₄₇	C₂×C₄	1	2	yes	—
119	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
120	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
121	C₂×C₄²×C₄₇	C₂³	1	1	yes	characteristic
122	C₄⋊C₈×C₄₇	C₂×C₄	1	4	yes	complemented
123	#97×C₄₇	—	2	2	no	—
124	#97×C₄₇	C₂×C₄	1	4	yes	complemented
125	C₄×C₈×C₄₇	—	2	2	no	—
126	#95×C₄₇	C₂×C₄	1	2	yes	—
127	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂³×D₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
130	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
132	C₂²×C₄×C₄₇	C₂²×C₄	1	2	yes	—
133	C₂²×C₄×C₄₇	C₂⁴	1	1	yes	characteristic
134	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
135	C₂²×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
136	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
137	C₂²×Dic₄₇	C₂²×C₄	1	2	yes	—
138	C₂×D₁₈₈	—	2	4	no	—
139	C₂×D₁₈₈	C₄²	1	4	yes	—
140	C₂×C₄×D₄₇	—	2	1	no	—
141	C₂×C₄×D₄₇	—	2	1	no	—
142	C₂×C₄×D₄₇	—	2	1	no	—
143	C₂×C₄×D₄₇	—	2	1	no	—
144	C₂×C₄×D₄₇	—	2	1	no	—
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	4	no	—
149	C₂×C₄×D₄₇	—	2	4	no	—
150	C₂×C₄×D₄₇	—	2	4	no	—
151	C₂×C₄×D₄₇	—	2	4	no	—
152	C₂×C₄×D₄₇	—	4	2	no	—
153	C₂×C₄×D₄₇	—	4	2	no	—
154	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
155	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
156	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
157	C₂×C₄×D₄₇	C₂²×C₄	1	2	yes	—
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	—	2	1	no	—
163	C₂×C₈×C₄₇	—	2	1	no	—
164	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
165	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
166	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
167	C₂×C₈×C₄₇	C₂²×C₄	1	2	yes	—
168	C₂×C₈×C₄₇	C₂×D₄	1	2	yes	—
169	C₂×C₈×C₄₇	#41	1	2	yes	—
170	C₄⋊C₄×C₄₇	—	2	4	no	—
171	C₄²×C₄₇	—	2	1	no	—
172	C₄²×C₄₇	—	2	1	no	—
173	C₄²×C₄₇	—	2	1	no	—
174	C₄²×C₄₇	—	2	1	no	—
175	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
176	C₄²×C₄₇	C₂²×C₄	1	2	yes	—
177	(C₂×D₄₇)⋊C₄	—	2	4	no	—
178	(C₂×D₄₇)⋊C₄	C₄²	1	4	yes	—
179	(C₂×D₄₇)⋊C₄	C₄²	1	4	yes	—
180	(C₂×D₄₇)⋊C₄	M₁₆	1	8	yes	complemented
181	C₄⋊Dic₄₇	C₄²	1	4	yes	—
182	C₄×Dic₄₇	—	2	1	no	—
183	C₄×Dic₄₇	—	2	1	no	—
184	C₄×Dic₄₇	—	2	4	no	—
185	C₄×Dic₄₇	—	2	4	no	—
186	C₄×Dic₄₇	—	2	4	no	—
187	C₄×Dic₄₇	—	4	2	no	—
188	C₄×Dic₄₇	C₂×D₄	1	2	yes	—
189	C₄×Dic₄₇	#41	1	2	yes	—
190	C₂×C₄₇⋊C₈	—	2	1	no	—
191	C₂×C₄₇⋊C₈	—	2	1	no	—
192	C₂×C₄₇⋊C₈	—	2	1	no	—
193	C₂×C₄₇⋊C₈	—	2	1	no	—
194	C₂×C₄₇⋊C₈	—	2	1	no	—
195	C₂×C₄₇⋊C₈	—	2	1	no	—
196	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
197	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
198	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
199	C₂×C₄₇⋊C₈	C₂²×C₄	1	2	yes	—
200	C₂×C₄₇⋊C₈	C₂×D₄	1	2	yes	—
201	C₂×C₄₇⋊C₈	#41	1	2	yes	—
202	#10625324	—	2	8	no	—
203	#10625324	—	2	8	no	—
204	C₈×D₄₇	—	2	8	no	—
205	C₈×D₄₇	—	2	8	no	—
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	1	no	—
211	C₂²×D₄₇	—	2	1	no	—
212	C₂²×D₄₇	—	2	2	no	—
213	C₂²×D₄₇	—	2	2	no	—
214	C₂²×D₄₇	C₂×C₄²	1	2	yes	—
215	C₂²×D₄₇	C₂×C₄²	1	2	yes	—
216	C₂²×D₄₇	C₂×M₁₆	1	4	yes	—
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	—	2	2	no	—
224	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
225	C₂×C₄×C₄₇	C₂×C₄²	1	2	yes	—
226	C₂×C₄×C₄₇	C₂×M₁₆	1	4	yes	—
227	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
228	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
229	C₂×C₄×C₄₇	C₂²×D₄	1	1	yes	characteristic
230	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
231	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
232	C₂×C₄×C₄₇	C₂×#41	1	1	yes	characteristic
233	C₂×Dic₄₇	—	2	1	no	—
234	C₂×Dic₄₇	—	2	1	no	—
235	C₂×Dic₄₇	—	2	2	no	—
236	C₂×Dic₄₇	—	2	1	no	—
237	C₂×Dic₄₇	—	2	1	no	—
238	C₂×Dic₄₇	—	2	2	no	—
239	C₂×Dic₄₇	—	2	2	no	—
240	C₂×Dic₄₇	—	2	2	no	—
241	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
242	C₂×Dic₄₇	C₂×C₄²	1	2	yes	—
243	C₂×Dic₄₇	C₄×D₄	1	4	yes	—
244	C₂×Dic₄₇	C₂×M₁₆	1	4	yes	—
245	D₁₈₈	—	2	8	no	—
246	C₄×D₄₇	—	2	2	no	—
247	C₄×D₄₇	—	2	2	no	—
248	C₄×D₄₇	—	2	2	no	—
249	C₄×D₄₇	—	2	2	no	—
250	C₄×D₄₇	—	2	2	no	—
251	C₄×D₄₇	—	2	2	no	—
252	C₄×D₄₇	—	2	2	no	—
253	C₄×D₄₇	—	2	2	no	—
254	C₄×D₄₇	—	4	8	no	—
255	C₄×D₄₇	—	4	8	no	—
256	C₈×C₄₇	—	2	2	no	—
257	C₈×C₄₇	—	2	2	no	—
258	C₈×C₄₇	—	2	2	no	—
259	C₈×C₄₇	C₄×D₄	1	4	yes	complemented
260	C₄₇⋊C₈	—	2	2	no	—
261	C₄₇⋊C₈	—	2	2	no	—
262	C₄₇⋊C₈	—	2	2	no	—
263	C₄₇⋊C₈	C₄×D₄	1	4	yes	complemented
264	#20491	—	47	1	no	maximal, Sylow
265	C₂²×C₄₇	C₂²×C₄²	1	1	yes	characteristic
266	C₂²×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
267	C₂²×C₄₇	C₄×#41	1	1	yes	characteristic
268	C₂²×C₄₇	C₂²×M₁₆	1	2	yes	—
269	C₂²×C₄₇	#568	1	2	yes	—
270	C₂×D₄₇	—	2	2	no	—
271	C₂×D₄₇	—	2	4	no	—
272	C₂×D₄₇	—	2	4	no	—
273	C₂×D₄₇	—	2	2	no	—
274	C₂×D₄₇	—	2	2	no	—
275	C₂×D₄₇	—	2	2	no	—
276	C₂×D₄₇	—	2	2	no	—
277	C₂×D₄₇	—	4	2	no	—
278	C₂×D₄₇	—	4	2	no	—
279	C₂×D₄₇	C₄×M₁₆	1	4	yes	complemented
280	C₄×C₄₇	—	2	2	no	—
281	C₄×C₄₇	—	2	2	no	—
282	C₄×C₄₇	—	2	4	no	—
283	C₄×C₄₇	—	4	2	no	—
284	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
285	C₄×C₄₇	C₂×C₄×D₄	1	1	yes	characteristic
286	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
287	C₄×C₄₇	C₄×#41	1	1	yes	characteristic
288	Dic₄₇	—	2	4	no	—
289	Dic₄₇	—	2	4	no	—
290	Dic₄₇	—	2	2	no	—
291	Dic₄₇	—	2	2	no	—
292	C₂×#435	—	47	1	no	—
293	C₂×#435	—	47	1	no	—
294	C₂×C₄×M₁₆	—	47	1	no	—
295	C₂²×#97	—	47	1	no	—
296	C₄²×D₄	—	47	1	no	—
297	#1771	—	47	1	no	—
298	#1771	D₄₇	1	1	yes	characteristic, complemented
299	#1767	—	47	1	no	—
300	#1753	—	47	1	no	—
301	#1753	—	47	1	no	—
302	C₈×C₂²⋊C₄	—	47	1	no	—
303	C₈×C₂²⋊C₄	—	47	1	no	—
304	#1749	—	47	1	no	—
305	#1749	—	47	1	no	—
306	C₄×#97	—	47	1	no	—
307	C₂×C₄₇	C₄²×D₄	1	1	yes	characteristic
308	C₂×C₄₇	C₂×C₄×M₁₆	1	1	yes	characteristic
309	C₂×C₄₇	#2875	1	1	yes	characteristic
310	C₂×C₄₇	D₄×M₁₆	1	2	yes	—
311	C₂×C₄₇	#2970	1	2	yes	—
312	D₄₇	—	2	4	no	—
313	D₄₇	—	4	2	no	—
314	C₂²×M₁₆	—	47	1	no	—
315	C₂²×M₁₆	—	47	1	no	—
316	C₂³×C₈	—	47	1	no	—
317	C₂³×C₈	—	47	1	no	—
318	C₂×C₄×D₄	—	47	2	no	—
319	C₂×C₄×D₄	—	47	1	no	—
320	C₂²×C₄²	—	47	1	no	—
321	C₂²×C₄²	—	47	1	no	—
322	#435	—	47	8	no	—
323	#435	—	47	8	no	—
324	C₂×C₄⋊C₈	—	47	1	no	—
325	C₂×C₄⋊C₈	C₂×D₄₇	1	1	yes	characteristic
326	C₂×C₂²⋊C₈	—	47	1	no	—
327	C₂×C₂²⋊C₈	—	47	1	no	—
328	C₂×C₂²⋊C₈	—	47	1	no	—
329	C₂×C₂²⋊C₈	—	47	1	no	—
330	C₄×M₁₆	—	94	4	no	—
331	C₂×#97	—	47	1	no	—
332	C₂×#97	—	47	1	no	—
333	C₂×#97	—	47	1	no	—
334	C₂×#97	—	47	1	no	—
335	C₂×#97	—	47	1	no	—
336	C₂×#97	—	47	1	no	—
337	C₂×#97	—	94	4	no	—
338	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
339	C₂×#97	C₂×D₄₇	1	1	yes	characteristic
340	C₂×C₄×C₈	—	47	1	no	—
341	C₂×C₄×C₈	—	47	1	no	—
342	C₂×C₄×C₈	—	47	1	no	—
343	C₂×C₄×C₈	C₂×D₄₇	1	1	yes	characteristic
344	C₄×C₄⋊C₄	—	47	2	no	—
345	C₄×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
346	C₄×C₂²⋊C₄	—	47	1	no	—
347	C₄×C₂²⋊C₄	—	47	1	no	—
348	C₄×C₂²⋊C₄	—	47	2	no	—
349	C₄×C₂²⋊C₄	—	47	2	no	—
350	C₄³	—	47	1	no	—
351	#336	—	47	1	no	—
352	#336	—	47	1	no	—
353	#336	—	47	1	no	—
354	#336	—	47	1	no	—
355	#336	C₂×D₄₇	1	1	yes	characteristic
356	#336	C₂×D₄₇	1	1	yes	characteristic
357	C₄₇	#20491	1	1	yes	characteristic, complemented, Sylow
358	C₂²×D₄	—	47	1	no	—
359	C₂³×C₄	—	47	1	no	—
360	C₂³×C₄	—	47	1	no	—
361	C₂³×C₄	—	47	2	no	—
362	C₂³×C₄	—	47	2	no	—
363	C₂×M₁₆	—	47	4	no	—
364	C₂×M₁₆	—	47	4	no	—
365	C₂×M₁₆	—	94	2	no	—
366	C₂×M₁₆	—	94	2	no	—
367	C₂×M₁₆	—	94	2	no	—
368	C₂×M₁₆	—	94	2	no	—
369	C₂²×C₈	—	47	1	no	—
370	C₂²×C₈	—	47	1	no	—
371	C₂²×C₈	—	47	1	no	—
372	C₂²×C₈	—	47	1	no	—
373	C₂²×C₈	—	47	4	no	—
374	C₂²×C₈	—	47	4	no	—
375	C₂²×C₈	—	94	2	no	—
376	C₂²×C₈	—	94	2	no	—
377	C₂²×C₈	—	94	2	no	—
378	C₂²×C₈	—	94	2	no	—
379	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
380	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
381	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
382	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
383	C₄×D₄	—	47	4	no	—
384	C₄×D₄	—	47	4	no	—
385	C₄×D₄	—	94	8	no	—
386	C₂×C₄⋊C₄	—	47	1	no	—
387	C₂×C₄⋊C₄	C₄×D₄₇	1	2	yes	—
388	C₂×C₂²⋊C₄	—	47	1	no	—
389	C₂×C₂²⋊C₄	—	47	1	no	—
390	C₂×C₂²⋊C₄	—	47	2	no	—
391	C₂×C₂²⋊C₄	—	47	2	no	—
392	C₂×C₄²	—	47	1	no	—
393	C₂×C₄²	—	47	2	no	—
394	C₂×C₄²	—	47	2	no	—
395	C₂×C₄²	—	47	2	no	—
396	C₂×C₄²	—	47	1	no	—
397	C₂×C₄²	—	47	2	no	—
398	C₂×C₄²	—	94	2	no	—
399	C₂×C₄²	—	94	2	no	—
400	C₂×C₄²	—	94	2	no	—
401	C₂×C₄²	—	94	2	no	—
402	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
403	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
404	C₂×C₄²	C₂²×D₄₇	1	1	yes	characteristic
405	C₄⋊C₈	—	47	4	no	—
406	C₄⋊C₈	C₄×D₄₇	1	4	yes	complemented
407	C₂²⋊C₈	—	47	4	no	—
408	C₂²⋊C₈	—	47	4	no	—
409	C₂²⋊C₈	—	47	4	no	—
410	C₂²⋊C₈	—	47	4	no	—
411	#97	—	2	2	no	—
412	#97	—	47	4	no	—
413	#97	—	47	4	no	—
414	#97	—	94	2	no	—
415	#97	—	94	2	no	—
416	#97	—	94	2	no	—
417	#97	—	94	2	no	—
418	#97	C₄×D₄₇	1	4	yes	complemented
419	C₄×C₈	—	2	2	no	—
420	C₄×C₈	—	94	2	no	—
421	C₄×C₈	—	94	2	no	—
422	C₄×C₈	—	94	2	no	—
423	#95	—	47	2	no	—
424	#95	—	47	2	no	—
425	#95	C₄×D₄₇	1	2	yes	—
426	C₂⁴	—	47	1	no	—
427	C₂⁴	—	47	1	no	—
428	C₂×D₄	—	47	4	no	—
429	C₂×D₄	—	94	4	no	—
430	C₂²×C₄	—	47	2	no	—
431	C₂²×C₄	—	47	1	no	—
432	C₂²×C₄	—	47	1	no	—
433	C₂²×C₄	—	47	2	no	—
434	C₂²×C₄	—	47	2	no	—
435	C₂²×C₄	—	47	2	no	—
436	C₂²×C₄	—	47	2	no	—
437	C₂²×C₄	—	47	2	no	—
438	C₂²×C₄	—	94	4	no	—
439	C₂²×C₄	—	94	4	no	—
440	C₂²×C₄	—	94	4	no	—
441	C₂²×C₄	—	94	1	no	—
442	C₂²×C₄	—	94	1	no	—
443	C₂²×C₄	—	94	1	no	—
444	C₂²×C₄	—	94	1	no	—
445	C₂²×C₄	—	94	1	no	—
446	C₂²×C₄	—	94	1	no	—
447	C₂²×C₄	—	94	1	no	—
448	C₂²×C₄	—	94	1	no	—
449	C₂²×C₄	—	94	4	no	—
450	C₂²×C₄	—	188	2	no	—
451	C₂²×C₄	—	188	2	no	—
452	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
453	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
454	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
455	C₂²×C₄	C₂×C₄×D₄₇	1	2	yes	—
456	C₂²×C₄	C₂³×D₄₇	1	1	yes	characteristic
457	M₁₆	—	94	8	no	—
458	M₁₆	—	94	8	no	—
459	C₂×C₈	—	2	1	no	—
460	C₂×C₈	—	2	1	no	—
461	C₂×C₈	—	2	1	no	—
462	C₂×C₈	—	2	1	no	—
463	C₂×C₈	—	2	1	no	—
464	C₂×C₈	—	2	1	no	—
465	C₂×C₈	—	47	2	no	—
466	C₂×C₈	—	47	2	no	—
467	C₂×C₈	—	47	2	no	—
468	C₂×C₈	—	47	2	no	—
469	C₂×C₈	—	47	2	no	—
470	C₂×C₈	—	47	2	no	—
471	C₂×C₈	—	94	8	no	—
472	C₂×C₈	—	94	1	no	—
473	C₂×C₈	—	94	1	no	—
474	C₂×C₈	—	94	1	no	—
475	C₂×C₈	—	94	1	no	—
476	C₂×C₈	—	94	1	no	—
477	C₂×C₈	—	94	1	no	—
478	C₂×C₈	—	94	8	no	—
479	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
480	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
481	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
482	C₂×C₈	C₂×C₄×D₄₇	1	2	yes	—
483	C₂×C₈	D₄×D₄₇	1	2	yes	—
484	C₂×C₈	#10625354	1	2	yes	—
485	C₄⋊C₄	—	2	4	no	—
486	C₄⋊C₄	—	47	4	no	—
487	C₂²⋊C₄	—	47	4	no	—
488	C₂²⋊C₄	—	47	4	no	—
489	C₂²⋊C₄	—	47	8	no	—
490	C₂²⋊C₄	—	94	4	no	—
491	C₄²	—	2	1	no	—
492	C₄²	—	2	1	no	—
493	C₄²	—	2	1	no	—
494	C₄²	—	2	1	no	—
495	C₄²	—	47	2	no	—
496	C₄²	—	47	2	no	—
497	C₄²	—	94	4	no	—
498	C₄²	—	94	4	no	—
499	C₄²	—	94	4	no	—
500	C₄²	—	94	1	no	—
501	C₄²	—	94	1	no	—
502	C₄²	—	188	2	no	—
503	C₄²	C₂×C₄×D₄₇	1	2	yes	—
504	C₄²	C₂×C₄×D₄₇	1	2	yes	—
505	C₂³	—	47	2	no	—
506	C₂³	—	47	4	no	—
507	C₂³	—	47	2	no	—
508	C₂³	—	94	1	no	—
509	C₂³	—	94	1	no	—
510	C₂³	—	94	2	no	—
511	C₂³	—	94	1	no	—
512	C₂³	—	94	1	no	—
513	C₂³	—	94	2	no	—
514	C₂³	—	94	2	no	—
515	C₂³	C₂²×C₄×D₄₇	1	1	yes	characteristic
516	D₄	—	94	8	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	2	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	2	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	47	2	no	—
525	C₂×C₄	—	47	2	no	—
526	C₂×C₄	—	47	4	no	—
527	C₂×C₄	—	47	4	no	—
528	C₂×C₄	—	94	1	no	—
529	C₂×C₄	—	94	1	no	—
530	C₂×C₄	—	94	2	no	—
531	C₂×C₄	—	94	1	no	—
532	C₂×C₄	—	94	1	no	—
533	C₂×C₄	—	94	2	no	—
534	C₂×C₄	—	94	2	no	—
535	C₂×C₄	—	94	2	no	—
536	C₂×C₄	—	94	2	no	—
537	C₂×C₄	—	94	2	no	—
538	C₂×C₄	—	94	2	no	—
539	C₂×C₄	—	94	2	no	—
540	C₂×C₄	—	94	2	no	—
541	C₂×C₄	—	94	2	no	—
542	C₂×C₄	—	94	2	no	—
543	C₂×C₄	—	94	2	no	—
544	C₂×C₄	—	188	8	no	—
545	C₂×C₄	—	188	8	no	—
546	C₂×C₄	C₄²×D₄₇	1	2	yes	—
547	C₂×C₄	C₄²×D₄₇	1	2	yes	—
548	C₂×C₄	M₁₆×D₄₇	1	4	yes	—
549	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
550	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
551	C₂×C₄	C₂×D₄×D₄₇	1	1	yes	characteristic
552	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
553	C₂×C₄	#41×D₄₇	1	1	yes	characteristic
554	C₂×C₄	C₂×#10625354	1	1	yes	characteristic
555	C₈	—	2	2	no	—
556	C₈	—	2	2	no	—
557	C₈	—	2	2	no	—
558	C₈	—	47	4	no	—
559	C₈	—	94	2	no	—
560	C₈	—	94	2	no	—
561	C₈	—	94	2	no	—
562	C₈	#13093986	1	4	yes	complemented
563	C₂²	—	47	4	no	—
564	C₂²	—	94	2	no	—
565	C₂²	—	94	4	no	—
566	C₂²	—	94	2	no	—
567	C₂²	—	94	4	no	—
568	C₂²	—	94	2	no	—
569	C₂²	—	94	2	no	—
570	C₂²	—	94	2	no	—
571	C₂²	—	188	2	no	—
572	C₂²	—	188	2	no	—
573	C₂²	C₂×C₄²×D₄₇	1	1	yes	characteristic
574	C₂²	C₄×D₄×D₄₇	1	1	yes	characteristic
575	C₂²	C₄×#10625354	1	1	yes	characteristic
576	C₂²	C₂×M₁₆×D₄₇	1	2	yes	—
577	C₂²	#15689888	1	2	yes	—
578	C₄	—	2	2	no	—
579	C₄	—	2	2	no	—
580	C₄	—	2	4	no	—
581	C₄	—	4	2	no	—
582	C₄	—	94	4	no	—
583	C₄	—	94	2	no	—
584	C₄	—	94	2	no	—
585	C₄	—	94	4	no	—
586	C₄	C₄×D₄×D₄₇	1	1	yes	characteristic
587	C₄	C₂×#13093986	1	1	yes	characteristic
588	C₄	#15689591	1	1	yes	characteristic
589	C₄	C₄×#10625354	1	1	yes	characteristic
590	C₂	—	94	4	no	—
591	C₂	—	188	2	no	—
592	C₂	C₄×#13093986	1	1	yes	characteristic
593	C₂	C₄×M₁₆×D₄₇	1	1	yes	characteristic
594	C₂	#20251815	1	1	yes	characteristic
595	C₂	#20252121	1	2	yes	—
596	C₂	#20252401	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₄₇
commutator	C₂²×C₄₇	C₂²×C₄²
Fitting	C₄₇×#1771	C₂
socle	C₂³×C₄₇	C₂³×C₄
prime radical	C₂²×D₁₈₈	C₂×C₄
cosocle	C₂²×C₄×C₄₇	C₂⁴
hypercenter	#1771	D₄₇
hypocenter	C₄₇	#20491
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂²×C₄ ◁ #1771

Complements

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

N	H ≅ G/N	type
3. C₂×C₄×#10625324	C₂	semidirect
4. C₂×#97×D₄₇	C₂	semidirect
6. #20243263	C₂	semidirect
7. #20243243	C₂	semidirect
8. #20243173	C₂	semidirect
9. #20243170	C₂	semidirect
10. C₈×(C₂×D₄₇)⋊C₄	C₂	semidirect
11. #20243158	C₂	semidirect
12. #20243149	C₂	semidirect
13. #20243149	C₂	semidirect
14. #97×Dic₄₇	C₂	semidirect
15. C₄₇×#1771	C₂	semidirect
24. #15689196	C₄	semidirect
25. #15689193	C₄	semidirect
68. C₂×#10625324	C₂×C₄	semidirect
69. C₂×#10625324	C₂×C₄	semidirect
78. C₂×C₈×D₄₇	C₂×C₄	semidirect
79. C₂×C₈×D₄₇	C₂×C₄	semidirect
98. C₄⋊(C₄₇⋊C₈)	C₂×C₄	semidirect
99. (C₂×D₄₇)⋊C₈	C₂×C₄	semidirect
100. (C₂×D₄₇)⋊C₈	C₂×C₄	semidirect
101. (C₂×D₄₇)⋊C₈	C₂×C₄	semidirect
102. (C₂×D₄₇)⋊C₈	C₂×C₄	semidirect
104. #13093935	C₂×C₄	semidirect
108. #13093934	D₄	semidirect
122. C₄⋊C₈×C₄₇	C₂×C₄	semidirect
124. #97×C₄₇	C₂×C₄	semidirect
180. (C₂×D₄₇)⋊C₄	M₁₆	semidirect
259. C₈×C₄₇	C₄×D₄	semidirect
263. C₄₇⋊C₈	C₄×D₄	semidirect
279. C₂×D₄₇	C₄×M₁₆	semidirect
298. #1771	D₄₇	semidirect
357. C₄₇	#20491	semidirect
406. C₄⋊C₈	C₄×D₄₇	semidirect
418. #97	C₄×D₄₇	semidirect
562. C₈	#13093986	semidirect

Maximal subgroups

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

subgroup	index
C₂×#15689196	2
C₂×#15689193	2
C₂×C₄×#10625324	2
C₂×#97×D₄₇	2
C₄×#13093986	2
#20243263	2
#20243243	2
#20243173	2
#20243170	2
C₈×(C₂×D₄₇)⋊C₄	2
#20243158	2
#20243149	2
#97×Dic₄₇	2
C₄₇×#1771	2
#20491	47