Subgroups — #26369869

Order 12032.

626 conjugacy classes of subgroups.

The subgroup lattice has 498 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₈×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic
2	#20245217	C₂	1	2	yes	maximal, complemented
3	#20245216	C₂	1	2	yes	maximal, complemented
4	#20245213	C₂	1	2	yes	maximal, complemented
5	C₁₆×C₂²⋊D₄₇	C₂	1	2	yes	maximal, complemented
6	#20245188	C₂	1	1	yes	maximal, characteristic, complemented
7	#20245184	C₂	1	1	yes	maximal, characteristic, complemented
8	#20244999	C₂	1	1	yes	maximal, characteristic, complemented
9	#20244997	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²⋊C₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄₇×C₂²⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
13	C₂×C₄×C₂²⋊D₄₇	C₄	1	1	yes	characteristic
14	C₂×#13093964	C₂²	1	2	yes	complemented
15	C₂×#13093963	C₂²	1	2	yes	complemented
16	C₂×C₁₆×D₄₇	C₂²	1	2	yes	complemented
17	C₈×C₂²⋊D₄₇	C₄	1	1	yes	characteristic
18	C₈×C₂²⋊D₄₇	C₄	1	1	yes	characteristic
19	C₈×C₂²⋊D₄₇	C₄	1	1	yes	characteristic
20	C₈×C₂²⋊D₄₇	C₄	1	1	yes	characteristic
21	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
22	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
23	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
24	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
25	C₂×Dic₄₇⋊C₈	C₄	1	1	yes	characteristic
26	C₂×C₂²⋊(C₄₇⋊C₈)	C₄	1	1	yes	characteristic
27	C₂×(C₂×D₄₇)⋊C₈	C₄	1	1	yes	characteristic
28	C₂×C₈×Dic₄₇	C₂²	1	1	yes	characteristic
29	Dic₄₇⋊C₁₆	C₂²	1	2	yes	complemented
30	Dic₄₇⋊C₁₆	C₂²	1	2	yes	complemented
31	C₂²⋊(C₄₇⋊C₁₆)	C₂²	1	1	yes	characteristic
32	C₂²⋊(C₄₇⋊C₁₆)	C₂²	1	1	yes	characteristic
33	C₂²⋊(C₄₇⋊C₁₆)	C₂²	1	2	yes	complemented
34	(C₂×D₄₇)⋊C₁₆	C₂²	1	2	yes	complemented
35	(C₂×D₄₇)⋊C₁₆	C₂²	1	2	yes	complemented
36	#15688898	C₂²	1	2	yes	complemented
37	C₁₆×Dic₄₇	C₂²	1	2	yes	complemented
38	C₂³×C₈×C₄₇	C₂²	1	1	yes	characteristic
39	C₂²×C₁₆×C₄₇	C₂²	1	2	yes	complemented
40	C₄₇×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
41	C₄₇×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
42	C₄₇×C₂²⋊C₁₆	C₂²	1	2	yes	complemented
43	C₂²×C₂²⋊D₄₇	C₈	1	1	yes	characteristic
44	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
46	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
47	C₂×C₈×D₄₇	—	4	2	no	—
48	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
49	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
50	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
51	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
52	C₄×C₂²⋊D₄₇	C₈	1	1	yes	characteristic
53	C₄×C₂²⋊D₄₇	C₈	1	1	yes	characteristic
54	C₄×C₂²⋊D₄₇	C₈	1	1	yes	characteristic
55	C₄×C₂²⋊D₄₇	C₈	1	1	yes	characteristic
56	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
57	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
58	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
59	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂×Dic₄₇⋊C₄	C₈	1	1	yes	characteristic
61	C₂×C₂²⋊Dic₄₇	C₈	1	1	yes	characteristic
62	C₂×(C₂×D₄₇)⋊C₄	C₈	1	1	yes	characteristic
63	C₂×C₄×Dic₄₇	C₂×C₄	1	1	yes	characteristic
64	#13093964	—	4	2	no	—
65	#13093963	—	4	2	no	—
66	C₂×C₄₇⋊C₁₆	C₂³	1	2	yes	—
67	C₂×C₄₇⋊C₁₆	C₂³	1	2	yes	—
68	C₁₆×D₄₇	—	4	2	no	—
69	Dic₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
70	Dic₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
71	Dic₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
72	Dic₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
73	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
74	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
75	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
76	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
77	(C₂×D₄₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
78	(C₂×D₄₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
79	(C₂×D₄₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
80	(C₂×D₄₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
81	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
82	C₈×Dic₄₇	C₂×C₄	1	1	yes	characteristic
83	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
84	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
85	C₂³×C₄×C₄₇	C₂×C₄	1	1	yes	characteristic
86	C₂²×C₈×C₄₇	—	4	2	no	—
87	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
88	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
89	C₂²×C₈×C₄₇	C₂×C₄	1	1	yes	characteristic
90	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
92	C₂²×C₈×C₄₇	C₂³	1	1	yes	characteristic
93	C₂×C₁₆×C₄₇	—	4	2	no	—
94	C₂×C₁₆×C₄₇	C₂³	1	2	yes	—
95	C₂×C₁₆×C₄₇	C₂³	1	2	yes	—
96	C₂⁴×C₄₇	C₂×C₈	1	1	yes	characteristic
97	C₂³×D₄₇	C₂×C₈	1	1	yes	characteristic
98	C₂²×C₄×C₄₇	—	4	1	no	—
99	C₂²×C₄×C₄₇	—	4	1	no	—
100	C₂²×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
101	C₂²×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
102	C₂²×C₄×C₄₇	C₂×C₈	1	1	yes	characteristic
103	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
104	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
105	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
106	C₂×C₂²⋊D₄₇	—	2	4	no	—
107	C₂×C₂²⋊D₄₇	C₂×C₈	1	1	yes	characteristic
108	C₂×C₂²⋊D₄₇	C₂×C₈	1	1	yes	characteristic
109	C₂×C₂²⋊D₄₇	C₂×C₈	1	1	yes	characteristic
110	C₂×C₂²⋊D₄₇	C₂×C₈	1	1	yes	characteristic
111	C₂²×Dic₄₇	C₂×C₈	1	1	yes	characteristic
112	C₂²×Dic₄₇	C₂×C₈	1	1	yes	characteristic
113	C₂²×Dic₄₇	C₂×C₈	1	1	yes	characteristic
114	C₂×C₄×D₄₇	—	4	1	no	—
115	C₂×C₄×D₄₇	—	4	1	no	—
116	C₂×C₄×D₄₇	C₂×C₈	1	1	yes	characteristic
117	C₂×C₄×D₄₇	C₂×C₈	1	1	yes	characteristic
118	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
119	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
120	C₂×C₈×C₄₇	—	2	2	no	—
121	C₂×C₈×C₄₇	—	2	2	no	—
122	C₂×C₈×C₄₇	—	2	2	no	—
123	C₂×C₈×C₄₇	—	4	1	no	—
124	C₂×C₈×C₄₇	—	4	1	no	—
125	C₂×C₈×C₄₇	—	4	1	no	—
126	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
127	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
130	C₂²⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
131	C₂²⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
132	C₂²⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
133	C₂²⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
134	(C₂×D₄₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
135	(C₂×D₄₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
136	(C₂×D₄₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
137	(C₂×D₄₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
138	Dic₄₇⋊C₄	C₂×C₈	1	1	yes	characteristic
139	Dic₄₇⋊C₄	C₂×C₈	1	1	yes	characteristic
140	Dic₄₇⋊C₄	C₂×C₈	1	1	yes	characteristic
141	Dic₄₇⋊C₄	C₂×C₈	1	1	yes	characteristic
142	C₄×Dic₄₇	C₂×C₈	1	1	yes	characteristic
143	C₄×Dic₄₇	C₂×C₈	1	1	yes	characteristic
144	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
145	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
146	C₂×C₄₇⋊C₈	—	4	1	no	—
147	C₂×C₄₇⋊C₈	—	4	1	no	—
148	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
149	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
150	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
151	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
152	C₈×D₄₇	—	2	2	no	—
153	C₈×D₄₇	—	2	2	no	—
154	C₈×D₄₇	—	4	1	no	—
155	C₈×D₄₇	—	4	1	no	—
156	C₁₆×C₄₇	—	2	2	no	—
157	C₁₆×C₄₇	—	2	2	no	—
158	C₄₇⋊C₁₆	—	2	2	no	—
159	C₄₇⋊C₁₆	—	2	2	no	—
160	C₂³×C₄₇	—	2	2	no	—
161	C₂³×C₄₇	—	2	2	no	—
162	C₂³×C₄₇	—	4	1	no	—
163	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
164	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
165	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
166	C₂²×D₄₇	—	2	2	no	—
167	C₂²×D₄₇	—	2	2	no	—
168	C₂²×D₄₇	—	4	1	no	—
169	C₂²×D₄₇	C₂²×C₈	1	1	yes	characteristic
170	C₂²×D₄₇	C₂²×C₈	1	1	yes	characteristic
171	C₂×C₄×C₄₇	—	2	1	no	—
172	C₂×C₄×C₄₇	—	2	1	no	—
173	C₂×C₄×C₄₇	—	2	1	no	—
174	C₂×C₄×C₄₇	—	2	1	no	—
175	C₂×C₄×C₄₇	—	2	1	no	—
176	C₂×C₄×C₄₇	—	2	1	no	—
177	C₂×C₄×C₄₇	—	4	1	no	—
178	C₂×C₄×C₄₇	—	4	1	no	—
179	C₂×C₄×C₄₇	—	4	1	no	—
180	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
181	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
182	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
183	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
184	C₂²⋊D₄₇	—	2	2	no	—
185	C₂²⋊D₄₇	—	2	2	no	—
186	C₂²⋊D₄₇	—	2	2	no	—
187	C₂²⋊D₄₇	M₃₂	1	4	yes	complemented
188	C₂×Dic₄₇	—	2	2	no	—
189	C₂×Dic₄₇	—	2	2	no	—
190	C₂×Dic₄₇	—	4	1	no	—
191	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
192	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
193	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
194	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
195	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
196	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
197	C₄×D₄₇	—	2	1	no	—
198	C₄×D₄₇	—	2	1	no	—
199	C₄×D₄₇	—	2	1	no	—
200	C₄×D₄₇	—	2	1	no	—
201	C₄×D₄₇	—	4	1	no	—
202	C₄×D₄₇	—	4	1	no	—
203	C₈×C₄₇	—	2	1	no	—
204	C₈×C₄₇	—	2	1	no	—
205	C₈×C₄₇	—	2	1	no	—
206	C₈×C₄₇	H(5,𝔽₂)	1	2	yes	—
207	C₄₇⋊C₈	—	2	1	no	—
208	C₄₇⋊C₈	—	2	1	no	—
209	C₄₇⋊C₈	—	2	1	no	—
210	C₄₇⋊C₈	—	2	1	no	—
211	#33488	—	47	1	no	maximal, Sylow
212	C₂²×C₄₇	—	2	1	no	—
213	C₂²×C₄₇	—	2	1	no	—
214	C₂²×C₄₇	—	2	1	no	—
215	C₂²×C₄₇	—	2	1	no	—
216	C₂²×C₄₇	—	2	1	no	—
217	C₂²×C₄₇	—	2	1	no	—
218	C₂²×C₄₇	—	2	1	no	—
219	C₂²×C₄₇	—	4	4	no	—
220	C₂²×C₄₇	C₂×M₃₂	1	2	yes	—
221	C₂²×C₄₇	#504	1	2	yes	—
222	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
223	C₂×D₄₇	—	2	1	no	—
224	C₂×D₄₇	—	2	1	no	—
225	C₂×D₄₇	—	2	1	no	—
226	C₂×D₄₇	—	2	1	no	—
227	C₂×D₄₇	—	2	1	no	—
228	C₂×D₄₇	—	4	4	no	—
229	C₂×D₄₇	C₂×M₃₂	1	2	yes	—
230	C₄×C₄₇	—	2	1	no	—
231	C₄×C₄₇	—	2	1	no	—
232	C₄×C₄₇	—	2	1	no	—
233	C₄×C₄₇	#518	1	1	yes	characteristic
234	C₄×C₄₇	#568	1	1	yes	characteristic
235	Dic₄₇	—	2	1	no	—
236	Dic₄₇	—	2	1	no	—
237	Dic₄₇	—	2	1	no	—
238	Dic₄₇	—	2	1	no	—
239	Dic₄₇	—	2	1	no	—
240	Dic₄₇	C₂×M₃₂	1	2	yes	—
241	C₂×C₈×D₄	—	47	1	no	—
242	#2169	—	47	2	no	—
243	#2168	—	47	2	no	—
244	#2168	—	47	2	no	—
245	D₄×C₁₆	—	47	2	no	—
246	#2163	—	47	1	no	—
247	#2162	—	47	1	no	—
248	#2112	—	47	1	no	—
249	#2112	—	47	1	no	—
250	C₂×C₂²⋊C₁₆	—	47	1	no	—
251	C₂×C₂²⋊C₁₆	D₄₇	1	1	yes	characteristic, complemented
252	C₂×C₄₇	—	2	2	no	—
253	C₂×C₄₇	—	2	2	no	—
254	C₂×C₄₇	—	4	1	no	—
255	C₂×C₄₇	#2972	1	1	yes	characteristic
256	C₂×C₄₇	C₂²×M₃₂	1	1	yes	characteristic
257	C₂×C₄₇	C₂×#504	1	1	yes	characteristic
258	D₄₇	—	2	2	no	—
259	D₄₇	—	4	1	no	—
260	C₂³×C₈	—	47	1	no	—
261	C₂³×C₈	C₂×D₄₇	1	1	yes	characteristic
262	C₂×C₄×D₄	—	47	1	no	—
263	C₂×M₃₂	—	47	2	no	—
264	C₂×M₃₂	—	47	2	no	—
265	C₂²×C₁₆	—	47	2	no	—
266	C₂²×C₁₆	C₂×D₄₇	1	2	yes	complemented
267	C₈×D₄	—	47	1	no	—
268	C₈×D₄	—	47	1	no	—
269	C₈×D₄	—	47	1	no	—
270	C₈×D₄	—	47	1	no	—
271	C₈×D₄	—	47	1	no	—
272	C₈×D₄	—	47	1	no	—
273	C₈×D₄	—	47	1	no	—
274	C₈×D₄	—	47	1	no	—
275	C₂×C₄⋊C₈	—	47	1	no	—
276	C₂×C₂²⋊C₈	—	47	1	no	—
277	C₂×C₂²⋊C₈	—	47	1	no	—
278	C₂×C₄×C₈	—	47	1	no	—
279	C₄⋊C₁₆	—	47	2	no	—
280	C₄⋊C₁₆	—	47	2	no	—
281	C₂²⋊C₁₆	—	47	1	no	—
282	C₂²⋊C₁₆	—	47	1	no	—
283	C₂²⋊C₁₆	—	47	2	no	—
284	C₂²⋊C₁₆	—	47	2	no	—
285	C₂²⋊C₁₆	—	47	2	no	—
286	C₂²⋊C₁₆	C₂×D₄₇	1	1	yes	characteristic
287	C₂²⋊C₁₆	C₂×D₄₇	1	1	yes	characteristic
288	C₂²⋊C₁₆	C₂×D₄₇	1	2	yes	complemented
289	#346	—	47	2	no	—
290	C₄×C₁₆	—	47	2	no	—
291	C₄₇	#33488	1	1	yes	characteristic, complemented, Sylow
292	C₂²×D₄	—	47	1	no	—
293	C₂³×C₄	—	47	1	no	—
294	C₂³×C₄	C₄×D₄₇	1	1	yes	characteristic
295	C₂²×C₈	—	4	2	no	—
296	C₂²×C₈	—	47	1	no	—
297	C₂²×C₈	—	47	1	no	—
298	C₂²×C₈	—	47	1	no	—
299	C₂²×C₈	—	47	1	no	—
300	C₂²×C₈	—	47	1	no	—
301	C₂²×C₈	—	47	1	no	—
302	C₂²×C₈	—	188	2	no	—
303	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
304	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
305	C₂²×C₈	C₄×D₄₇	1	1	yes	characteristic
306	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
307	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
308	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
309	C₄×D₄	—	47	1	no	—
310	C₄×D₄	—	47	1	no	—
311	C₄×D₄	—	47	1	no	—
312	C₄×D₄	—	47	1	no	—
313	C₄×D₄	—	47	1	no	—
314	C₄×D₄	—	47	1	no	—
315	C₄×D₄	—	47	1	no	—
316	C₄×D₄	—	47	1	no	—
317	C₂×C₄⋊C₄	—	47	1	no	—
318	C₂×C₂²⋊C₄	—	47	1	no	—
319	C₂×C₂²⋊C₄	—	47	1	no	—
320	C₂×C₄²	—	47	1	no	—
321	M₃₂	—	188	2	no	—
322	M₃₂	—	188	2	no	—
323	C₂×C₁₆	—	4	2	no	—
324	C₂×C₁₆	—	47	2	no	—
325	C₂×C₁₆	—	47	2	no	—
326	C₂×C₁₆	—	188	2	no	—
327	C₂×C₁₆	C₂²×D₄₇	1	2	yes	—
328	C₂×C₁₆	C₂²×D₄₇	1	2	yes	—
329	C₄⋊C₈	—	47	1	no	—
330	C₄⋊C₈	—	47	1	no	—
331	C₄⋊C₈	—	47	1	no	—
332	C₄⋊C₈	—	47	1	no	—
333	C₂²⋊C₈	—	47	1	no	—
334	C₂²⋊C₈	—	47	1	no	—
335	C₂²⋊C₈	—	47	1	no	—
336	C₂²⋊C₈	—	47	1	no	—
337	C₂²⋊C₈	—	47	1	no	—
338	C₂²⋊C₈	—	47	1	no	—
339	C₂²⋊C₈	—	47	1	no	—
340	C₂²⋊C₈	—	47	1	no	—
341	C₄×C₈	—	47	1	no	—
342	C₄×C₈	—	47	1	no	—
343	C₄×C₈	—	47	1	no	—
344	C₄×C₈	—	47	1	no	—
345	C₂⁴	—	47	1	no	—
346	C₂⁴	C₈×D₄₇	1	1	yes	characteristic
347	C₂×D₄	—	47	1	no	—
348	C₂×D₄	—	47	1	no	—
349	C₂×D₄	—	47	1	no	—
350	C₂×D₄	—	47	1	no	—
351	C₂×D₄	—	94	4	no	—
352	C₂²×C₄	—	4	1	no	—
353	C₂²×C₄	—	4	1	no	—
354	C₂²×C₄	—	47	1	no	—
355	C₂²×C₄	—	47	1	no	—
356	C₂²×C₄	—	47	1	no	—
357	C₂²×C₄	—	47	1	no	—
358	C₂²×C₄	—	47	1	no	—
359	C₂²×C₄	—	47	1	no	—
360	C₂²×C₄	—	47	1	no	—
361	C₂²×C₄	—	188	1	no	—
362	C₂²×C₄	—	188	1	no	—
363	C₂²×C₄	C₈×D₄₇	1	1	yes	characteristic
364	C₂²×C₄	C₈×D₄₇	1	1	yes	characteristic
365	C₂²×C₄	C₈×D₄₇	1	1	yes	characteristic
366	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
367	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
368	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
369	C₂×C₈	—	2	2	no	—
370	C₂×C₈	—	2	2	no	—
371	C₂×C₈	—	2	2	no	—
372	C₂×C₈	—	4	1	no	—
373	C₂×C₈	—	4	1	no	—
374	C₂×C₈	—	4	1	no	—
375	C₂×C₈	—	47	1	no	—
376	C₂×C₈	—	47	1	no	—
377	C₂×C₈	—	47	1	no	—
378	C₂×C₈	—	47	1	no	—
379	C₂×C₈	—	94	2	no	—
380	C₂×C₈	—	94	2	no	—
381	C₂×C₈	—	188	1	no	—
382	C₂×C₈	—	188	1	no	—
383	C₂×C₈	—	188	1	no	—
384	C₂×C₈	—	188	1	no	—
385	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
386	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
387	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
388	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
389	C₄⋊C₄	—	47	1	no	—
390	C₄⋊C₄	—	47	1	no	—
391	C₄⋊C₄	—	47	1	no	—
392	C₄⋊C₄	—	47	1	no	—
393	C₂²⋊C₄	—	47	1	no	—
394	C₂²⋊C₄	—	47	1	no	—
395	C₂²⋊C₄	—	47	1	no	—
396	C₂²⋊C₄	—	47	1	no	—
397	C₂²⋊C₄	—	47	1	no	—
398	C₂²⋊C₄	—	47	1	no	—
399	C₂²⋊C₄	—	47	1	no	—
400	C₂²⋊C₄	—	47	1	no	—
401	C₄²	—	47	1	no	—
402	C₄²	—	47	1	no	—
403	C₄²	—	47	1	no	—
404	C₄²	—	47	1	no	—
405	C₁₆	—	2	2	no	—
406	C₁₆	—	2	2	no	—
407	C₁₆	—	94	2	no	—
408	C₁₆	—	94	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	4	1	no	—
412	C₂³	—	47	1	no	—
413	C₂³	—	47	1	no	—
414	C₂³	—	94	2	no	—
415	C₂³	—	94	2	no	—
416	C₂³	—	188	1	no	—
417	C₂³	C₂×C₈×D₄₇	1	1	yes	characteristic
418	C₂³	C₂×C₈×D₄₇	1	1	yes	characteristic
419	C₂³	C₂×C₈×D₄₇	1	1	yes	characteristic
420	D₄	—	47	4	no	—
421	D₄	—	94	2	no	—
422	D₄	—	94	2	no	—
423	D₄	—	94	2	no	—
424	C₂×C₄	—	2	1	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	1	no	—
428	C₂×C₄	—	2	1	no	—
429	C₂×C₄	—	2	1	no	—
430	C₂×C₄	—	4	1	no	—
431	C₂×C₄	—	4	1	no	—
432	C₂×C₄	—	4	1	no	—
433	C₂×C₄	—	47	1	no	—
434	C₂×C₄	—	47	1	no	—
435	C₂×C₄	—	47	1	no	—
436	C₂×C₄	—	47	1	no	—
437	C₂×C₄	—	47	1	no	—
438	C₂×C₄	—	47	1	no	—
439	C₂×C₄	—	94	2	no	—
440	C₂×C₄	—	94	2	no	—
441	C₂×C₄	—	94	1	no	—
442	C₂×C₄	—	94	1	no	—
443	C₂×C₄	—	94	1	no	—
444	C₂×C₄	—	94	1	no	—
445	C₂×C₄	—	188	1	no	—
446	C₂×C₄	—	188	1	no	—
447	C₂×C₄	—	188	1	no	—
448	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
449	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
450	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
451	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
452	C₈	—	2	1	no	—
453	C₈	—	2	1	no	—
454	C₈	—	2	1	no	—
455	C₈	—	94	1	no	—
456	C₈	—	94	1	no	—
457	C₈	—	94	1	no	—
458	C₈	—	94	1	no	—
459	C₈	#13094069	1	2	yes	—
460	C₂²	—	2	1	no	—
461	C₂²	—	2	1	no	—
462	C₂²	—	2	1	no	—
463	C₂²	—	2	1	no	—
464	C₂²	—	2	1	no	—
465	C₂²	—	2	1	no	—
466	C₂²	—	2	1	no	—
467	C₂²	—	4	4	no	—
468	C₂²	—	47	2	no	—
469	C₂²	—	94	1	no	—
470	C₂²	—	94	1	no	—
471	C₂²	—	94	1	no	—
472	C₂²	—	94	1	no	—
473	C₂²	—	94	1	no	—
474	C₂²	—	188	4	no	—
475	C₂²	M₃₂×D₄₇	1	2	yes	—
476	C₂²	#15689539	1	2	yes	—
477	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
478	C₄	—	2	1	no	—
479	C₄	—	2	1	no	—
480	C₄	—	2	1	no	—
481	C₄	—	47	2	no	—
482	C₄	—	94	1	no	—
483	C₄	—	94	1	no	—
484	C₄	—	94	1	no	—
485	C₄	—	94	1	no	—
486	C₄	—	94	1	no	—
487	C₄	#15689596	1	1	yes	characteristic
488	C₄	#15689889	1	1	yes	characteristic
489	C₂	—	2	2	no	—
490	C₂	—	2	2	no	—
491	C₂	—	4	1	no	—
492	C₂	—	94	2	no	—
493	C₂	—	188	1	no	—
494	C₂	#20252410	1	1	yes	characteristic
495	C₂	C₂×M₃₂×D₄₇	1	1	yes	characteristic
496	C₂	C₂×#15689539	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₄₇
commutator, socle	C₂²×C₄₇	C₂³×C₈
Fitting	C₂×C₄₇×C₂²⋊C₁₆	C₂
prime radical	C₂²×C₂²⋊D₄₇	C₈
cosocle	C₂×C₈×C₄₇	C₂⁴
hypercenter	C₂×C₂²⋊C₁₆	D₄₇
hypocenter	C₄₇	#33488
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂×C₂²⋊C₁₆

Complements

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

N	H ≅ G/N	type
2. #20245217	C₂	semidirect
3. #20245216	C₂	semidirect
4. #20245213	C₂	semidirect
5. C₁₆×C₂²⋊D₄₇	C₂	semidirect
6. #20245188	C₂	semidirect
7. #20245184	C₂	semidirect
8. #20244999	C₂	semidirect
9. #20244997	C₂	semidirect
10. C₂²⋊C₁₆×D₄₇	C₂	semidirect
11. C₂×C₄₇×C₂²⋊C₁₆	C₂	semidirect
14. C₂×#13093964	C₂²	semidirect
15. C₂×#13093963	C₂²	semidirect
16. C₂×C₁₆×D₄₇	C₂²	semidirect
29. Dic₄₇⋊C₁₆	C₂²	semidirect
30. Dic₄₇⋊C₁₆	C₂²	semidirect
33. C₂²⋊(C₄₇⋊C₁₆)	C₂²	semidirect
34. (C₂×D₄₇)⋊C₁₆	C₂²	semidirect
35. (C₂×D₄₇)⋊C₁₆	C₂²	semidirect
36. #15688898	C₂²	semidirect
37. C₁₆×Dic₄₇	C₂²	semidirect
39. C₂²×C₁₆×C₄₇	C₂²	semidirect
42. C₄₇×C₂²⋊C₁₆	C₂²	semidirect
187. C₂²⋊D₄₇	M₃₂	semidirect
251. C₂×C₂²⋊C₁₆	D₄₇	semidirect
266. C₂²×C₁₆	C₂×D₄₇	semidirect
288. C₂²⋊C₁₆	C₂×D₄₇	semidirect
291. C₄₇	#33488	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₈×C₂²⋊D₄₇	2
#20245217	2
#20245216	2
#20245213	2
C₁₆×C₂²⋊D₄₇	2
#20245188	2
#20245184	2
#20244999	2
#20244997	2
C₂²⋊C₁₆×D₄₇	2
C₂×C₄₇×C₂²⋊C₁₆	2
#33488	47