Subgroups — #26369881

Order 12032.

574 conjugacy classes of subgroups.

The subgroup lattice has 558 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20252080	C₂	1	1	yes	maximal, characteristic
2	#20245218	C₂	1	1	yes	maximal, characteristic, complemented
3	#20245217	C₂	1	1	yes	maximal, characteristic, complemented
4	#20245216	C₂	1	1	yes	maximal, characteristic, complemented
5	#20245213	C₂	1	1	yes	maximal, characteristic, complemented
6	#20245211	C₂	1	1	yes	maximal, characteristic, complemented
7	#20245210	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₆×C₂²⋊D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
9	(C₂²⋊D₄₇)⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	#20245192	C₂	1	1	yes	maximal, characteristic, complemented
11	#20245192	C₂	1	1	yes	maximal, characteristic, complemented
12	#20245002	C₂	1	1	yes	maximal, characteristic, complemented
13	#20244997	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂²⋊C₁₆×D₄₇	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄₇×#2113	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×C₈×D₄₇	C₂²	1	1	yes	characteristic
17	#15689630	C₄	1	1	yes	characteristic
18	C₂×#13093964	C₂²	1	1	yes	characteristic, complemented
19	C₂×#13093963	C₂²	1	1	yes	characteristic
20	C₂×#13093963	C₂²	1	1	yes	characteristic
21	C₂²×C₄₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₁₆×D₄₇	C₂²	1	1	yes	characteristic
23	C₂×C₁₆×D₄₇	C₂²	1	1	yes	characteristic
24	#15689192	C₄	1	1	yes	characteristic
25	#15689192	C₄	1	1	yes	characteristic
26	#15689192	C₄	1	1	yes	characteristic
27	#15689192	C₄	1	1	yes	characteristic
28	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
29	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
30	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
31	C₈×C₂²⋊D₄₇	C₂²	1	1	yes	characteristic
32	#15689151	C₄	1	1	yes	characteristic
33	#15689090	C₄	1	1	yes	characteristic
34	#15689086	C₄	1	1	yes	characteristic
35	#15689078	C₂²	1	1	yes	characteristic
36	Dic₄₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
37	Dic₄₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
38	Dic₄₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
39	Dic₄₇⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
40	C₂²⋊(C₄₇⋊C₁₆)	C₂²	1	1	yes	characteristic
41	C₂²⋊(C₄₇⋊C₁₆)	C₂²	1	1	yes	characteristic
42	C₂²⋊(C₄₇⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
43	C₂²⋊(C₄₇⋊C₁₆)	C₂²	1	1	yes	characteristic, complemented
44	(C₂×D₄₇)⋊C₁₆	C₂²	1	1	yes	characteristic
45	(C₂×D₄₇)⋊C₁₆	C₂²	1	1	yes	characteristic
46	(C₂×D₄₇)⋊C₁₆	C₂²	1	1	yes	characteristic
47	(C₂×D₄₇)⋊C₁₆	C₂²	1	1	yes	characteristic
48	#15688898	C₂²	1	1	yes	characteristic, complemented
49	#15688898	C₂²	1	1	yes	characteristic, complemented
50	C₁₆×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
51	C₁₆×Dic₄₇	C₂²	1	1	yes	characteristic, complemented
52	C₂×#131×C₄₇	C₂²	1	1	yes	characteristic
53	C₂×M₃₂×C₄₇	C₂²	1	1	yes	characteristic, complemented
54	C₂²×C₁₆×C₄₇	C₂²	1	1	yes	characteristic, complemented
55	C₄₇×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
56	C₄₇×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic
57	C₄₇×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
58	C₄₇×C₂²⋊C₁₆	C₂²	1	1	yes	characteristic, complemented
59	C₂²×C₄×D₄₇	C₂×C₄	1	1	yes	characteristic
60	C₂×#10625329	C₂×C₄	1	1	yes	characteristic
61	C₂²×C₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
62	C₂×C₈×D₄₇	—	4	1	no	—
63	C₂×C₈×D₄₇	—	4	1	no	—
64	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₈×D₄₇	C₂×C₄	1	1	yes	characteristic
66	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
67	C₂×C₈×D₄₇	C₂³	1	1	yes	characteristic
68	#13094005	C₈	1	1	yes	characteristic
69	#13094005	C₈	1	1	yes	characteristic
70	#13094000	C₈	1	1	yes	characteristic
71	#13094000	C₈	1	1	yes	characteristic
72	#13093995	C₈	1	1	yes	characteristic
73	#13093995	C₈	1	1	yes	characteristic
74	#13093992	C₈	1	1	yes	characteristic
75	#13093992	C₈	1	1	yes	characteristic
76	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
77	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
78	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
79	C₄×C₂²⋊D₄₇	C₂×C₄	1	1	yes	characteristic
80	#13093983	C₂×C₄	1	1	yes	characteristic
81	#13093964	—	4	1	no	—
82	#13093963	—	4	1	no	—
83	#13093963	—	4	1	no	—
84	C₂×C₄₇⋊C₁₆	—	4	1	no	—
85	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
86	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
87	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
88	C₂×C₄₇⋊C₁₆	C₂³	1	1	yes	characteristic
89	C₁₆×D₄₇	—	4	1	no	—
90	C₁₆×D₄₇	—	4	1	no	—
91	Dic₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
92	Dic₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
93	Dic₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
94	Dic₄₇⋊C₈	C₂×C₄	1	1	yes	characteristic
95	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
96	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
97	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
98	C₂²⋊(C₄₇⋊C₈)	C₂×C₄	1	1	yes	characteristic
99	(C₂×D₄₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
100	(C₂×D₄₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
101	(C₂×D₄₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
102	(C₂×D₄₇)⋊C₈	C₂×C₄	1	1	yes	characteristic
103	#13093934	C₂×C₄	1	1	yes	characteristic
104	#13093934	C₂×C₄	1	1	yes	characteristic
105	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
106	C₈×Dic₄₇	C₂³	1	1	yes	characteristic
107	C₂×#41×C₄₇	C₂×C₄	1	1	yes	characteristic
108	#131×C₄₇	—	4	1	no	—
109	#131×C₄₇	—	4	1	no	—
110	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
111	C₂×M₁₆×C₄₇	C₂×C₄	1	1	yes	characteristic
112	C₂×M₁₆×C₄₇	C₂×C₄	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	M₃₂×C₄₇	—	4	1	no	—
117	C₂×C₁₆×C₄₇	—	4	1	no	—
118	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
119	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
120	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
121	C₂×C₁₆×C₄₇	C₂³	1	1	yes	characteristic
122	C₂³×D₄₇	C₂×C₈	1	1	yes	characteristic
123	#41×C₄₇	—	4	1	no	—
124	#41×C₄₇	—	4	1	no	—
125	C₂×Q₈×C₄₇	C₂×C₈	1	1	yes	characteristic
126	C₂×D₄×C₄₇	C₂×C₈	1	1	yes	characteristic
127	C₂×D₄×C₄₇	C₂×C₈	1	1	yes	characteristic
128	C₂×D₄×C₄₇	C₂×C₈	1	1	yes	characteristic
129	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
130	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
131	C₂²×C₄×C₄₇	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₂²⋊D₄₇	C₂×C₈	1	1	yes	characteristic
133	C₂×C₂²⋊D₄₇	C₂×C₈	1	1	yes	characteristic
134	C₂×C₂²⋊D₄₇	C₂×C₈	1	1	yes	characteristic
135	C₂×C₂²⋊D₄₇	C₂×C₈	1	1	yes	characteristic
136	C₂²×Dic₄₇	C₂×C₈	1	1	yes	characteristic
137	C₂×C₄×D₄₇	—	4	1	no	—
138	C₂×C₄×D₄₇	—	4	1	no	—
139	C₂×C₄×D₄₇	C₂×C₈	1	1	yes	characteristic
140	C₂×C₄×D₄₇	C₂×C₈	1	1	yes	characteristic
141	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₄×D₄₇	C₂²×C₄	1	1	yes	characteristic
143	M₁₆×C₄₇	—	4	1	no	—
144	M₁₆×C₄₇	—	4	1	no	—
145	M₁₆×C₄₇	—	4	1	no	—
146	C₂×C₈×C₄₇	—	2	1	no	—
147	C₂×C₈×C₄₇	—	2	1	no	—
148	C₂×C₈×C₄₇	—	2	1	no	—
149	C₂×C₈×C₄₇	—	2	1	no	—
150	C₂×C₈×C₄₇	—	2	1	no	—
151	C₂×C₈×C₄₇	—	2	1	no	—
152	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
153	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
154	C₂×C₈×C₄₇	C₂²×C₄	1	1	yes	characteristic
155	C₂×C₈×C₄₇	C₂⁴	1	1	yes	characteristic
156	C₂²⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
157	C₂²⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
158	C₂²⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
159	C₂²⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
160	C₂²⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
161	C₂²⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
162	(C₂×D₄₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
163	(C₂×D₄₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
164	(C₂×D₄₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
165	(C₂×D₄₇)⋊C₄	C₂×C₈	1	1	yes	characteristic
166	C₄⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
167	C₄⋊Dic₄₇	C₂×C₈	1	1	yes	characteristic
168	Dic₄₇⋊C₄	C₂×C₈	1	1	yes	characteristic
169	Dic₄₇⋊C₄	C₂×C₈	1	1	yes	characteristic
170	Dic₄₇⋊C₄	C₂×C₈	1	1	yes	characteristic
171	Dic₄₇⋊C₄	C₂×C₈	1	1	yes	characteristic
172	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
173	C₄×Dic₄₇	C₂²×C₄	1	1	yes	characteristic
174	#10625329	—	4	1	no	—
175	C₂×C₄₇⋊C₈	—	4	1	no	—
176	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
177	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
178	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
179	C₂×C₄₇⋊C₈	C₂²×C₄	1	1	yes	characteristic
180	C₈×D₄₇	—	2	1	no	—
181	C₈×D₄₇	—	2	1	no	—
182	C₈×D₄₇	—	2	1	no	—
183	C₈×D₄₇	—	2	1	no	—
184	C₈×D₄₇	—	4	1	no	—
185	C₈×D₄₇	—	4	1	no	—
186	C₁₆×C₄₇	—	2	1	no	—
187	C₁₆×C₄₇	—	2	1	no	—
188	C₁₆×C₄₇	—	2	1	no	—
189	C₁₆×C₄₇	—	2	1	no	—
190	C₄₇⋊C₁₆	—	2	1	no	—
191	C₄₇⋊C₁₆	—	2	1	no	—
192	C₄₇⋊C₁₆	—	2	1	no	—
193	C₄₇⋊C₁₆	—	2	1	no	—
194	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
195	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
196	C₂³×C₄₇	C₂²×C₈	1	1	yes	characteristic
197	C₂²×D₄₇	—	2	2	no	—
198	C₂²×D₄₇	—	4	1	no	—
199	C₂²×D₄₇	—	4	1	no	—
200	C₂²×D₄₇	C₂²×C₈	1	1	yes	characteristic
201	C₂²×D₄₇	C₂²×C₈	1	1	yes	characteristic
202	Q₈×C₄₇	—	4	1	no	—
203	D₄×C₄₇	—	4	1	no	—
204	D₄×C₄₇	—	4	1	no	—
205	D₄×C₄₇	—	4	1	no	—
206	C₂×C₄×C₄₇	—	2	1	no	—
207	C₂×C₄×C₄₇	—	2	1	no	—
208	C₂×C₄×C₄₇	—	2	1	no	—
209	C₂×C₄×C₄₇	—	2	1	no	—
210	C₂×C₄×C₄₇	—	2	1	no	—
211	C₂×C₄×C₄₇	—	2	1	no	—
212	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
213	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
214	C₂×C₄×C₄₇	C₂²×C₈	1	1	yes	characteristic
215	C₂×C₄×C₄₇	C₂³×C₄	1	1	yes	characteristic
216	C₂²⋊D₄₇	—	2	2	no	—
217	C₂²⋊D₄₇	—	2	2	no	—
218	C₂²⋊D₄₇	—	4	1	no	—
219	C₂²⋊D₄₇	—	4	1	no	—
220	C₂×Dic₄₇	—	4	1	no	—
221	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
222	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
223	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
224	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
225	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
226	C₂×Dic₄₇	C₂²×C₈	1	1	yes	characteristic
227	C₄×D₄₇	—	2	1	no	—
228	C₄×D₄₇	—	2	1	no	—
229	C₄×D₄₇	—	2	1	no	—
230	C₄×D₄₇	—	2	1	no	—
231	C₄×D₄₇	—	4	1	no	—
232	C₄×D₄₇	—	4	1	no	—
233	C₈×C₄₇	—	2	1	no	—
234	C₈×C₄₇	—	2	1	no	—
235	C₈×C₄₇	—	2	1	no	—
236	C₈×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
237	C₈×C₄₇	H(5,𝔽₂)	1	1	yes	characteristic
238	C₄₇⋊C₈	—	2	1	no	—
239	C₄₇⋊C₈	—	2	1	no	—
240	C₄₇⋊C₈	—	2	1	no	—
241	C₄₇⋊C₈	—	2	1	no	—
242	#33490	—	47	1	no	maximal, Sylow
243	C₂²×C₄₇	—	2	1	no	—
244	C₂²×C₄₇	—	2	1	no	—
245	C₂²×C₄₇	—	2	1	no	—
246	C₂²×C₄₇	—	2	1	no	—
247	C₂²×C₄₇	—	2	1	no	—
248	C₂²×C₄₇	—	2	1	no	—
249	C₂²×C₄₇	—	2	1	no	—
250	C₂²×C₄₇	—	2	1	no	—
251	C₂²×C₄₇	—	2	1	no	—
252	C₂²×C₄₇	C₂³×C₈	1	1	yes	characteristic
253	C₂×D₄₇	—	2	1	no	—
254	C₂×D₄₇	—	2	1	no	—
255	C₂×D₄₇	—	2	1	no	—
256	C₂×D₄₇	—	2	1	no	—
257	C₂×D₄₇	—	2	1	no	—
258	C₂×D₄₇	—	4	4	no	—
259	C₂×D₄₇	#504	1	2	yes	—
260	C₄×C₄₇	—	2	1	no	—
261	C₄×C₄₇	—	2	1	no	—
262	C₄×C₄₇	—	2	1	no	—
263	C₄×C₄₇	#518	1	1	yes	characteristic
264	C₄×C₄₇	#568	1	1	yes	characteristic
265	Dic₄₇	—	2	1	no	—
266	Dic₄₇	—	2	1	no	—
267	Dic₄₇	—	2	1	no	—
268	Dic₄₇	—	2	1	no	—
269	Dic₄₇	—	2	1	no	—
270	Dic₄₇	—	2	1	no	—
271	#2929	—	47	1	no	—
272	#2169	—	47	1	no	—
273	#2169	—	47	1	no	—
274	#2168	—	47	1	no	—
275	#2168	—	47	1	no	—
276	#2168	—	47	1	no	—
277	#2168	—	47	1	no	—
278	D₄×C₁₆	—	47	1	no	—
279	D₄×C₁₆	—	47	1	no	—
280	#2164	—	47	1	no	—
281	#2164	—	47	1	no	—
282	#2113	—	47	1	no	—
283	#2113	D₄₇	1	1	yes	characteristic, complemented
284	#2112	—	47	1	no	—
285	C₂×C₂²⋊C₁₆	—	47	1	no	—
286	C₂×C₄₇	—	4	1	no	—
287	C₂×C₄₇	—	4	1	no	—
288	C₂×C₄₇	—	4	1	no	—
289	C₂×C₄₇	#2972	1	1	yes	characteristic
290	C₂×C₄₇	C₂×#504	1	1	yes	characteristic
291	C₂×C₄₇	#3407	1	1	yes	characteristic
292	D₄₇	—	2	2	no	—
293	D₄₇	—	4	1	no	—
294	C₂×#131	C₂×D₄₇	1	1	yes	characteristic
295	C₂³×C₈	—	47	1	no	—
296	#525	—	47	1	no	—
297	C₂×M₃₂	—	47	1	no	—
298	C₂×M₃₂	—	47	1	no	—
299	C₂×M₃₂	—	47	1	no	—
300	C₂×M₃₂	C₂×D₄₇	1	1	yes	characteristic, complemented
301	C₂²×C₁₆	—	47	1	no	—
302	C₂²×C₁₆	—	47	1	no	—
303	C₂²×C₁₆	—	47	1	no	—
304	C₂²×C₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
305	#435	—	47	1	no	—
306	#435	—	47	1	no	—
307	#435	—	47	1	no	—
308	#435	—	47	1	no	—
309	C₈×D₄	—	47	1	no	—
310	C₈×D₄	—	47	1	no	—
311	C₈×D₄	—	47	1	no	—
312	C₈×D₄	—	47	1	no	—
313	#424	—	47	1	no	—
314	#408	—	47	1	no	—
315	#407	—	47	1	no	—
316	#405	—	47	1	no	—
317	C₄⋊C₁₆	—	47	1	no	—
318	C₄⋊C₁₆	—	47	1	no	—
319	C₄⋊C₁₆	—	47	1	no	—
320	C₄⋊C₁₆	—	47	1	no	—
321	C₂²⋊C₁₆	—	47	1	no	—
322	C₂²⋊C₁₆	—	47	1	no	—
323	C₂²⋊C₁₆	—	47	1	no	—
324	C₂²⋊C₁₆	—	47	1	no	—
325	C₂²⋊C₁₆	—	47	1	no	—
326	C₂²⋊C₁₆	—	47	1	no	—
327	C₂²⋊C₁₆	—	47	1	no	—
328	C₂²⋊C₁₆	—	47	1	no	—
329	C₂²⋊C₁₆	C₂×D₄₇	1	1	yes	characteristic
330	C₂²⋊C₁₆	C₂×D₄₇	1	1	yes	characteristic
331	C₂²⋊C₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
332	C₂²⋊C₁₆	C₂×D₄₇	1	1	yes	characteristic, complemented
333	#346	—	47	1	no	—
334	#346	—	47	1	no	—
335	C₄×C₁₆	—	47	1	no	—
336	C₄×C₁₆	—	47	1	no	—
337	C₄₇	#33490	1	1	yes	characteristic, complemented, Sylow
338	C₂×#41	C₄×D₄₇	1	1	yes	characteristic
339	C₂³×C₄	—	47	1	no	—
340	#131	—	4	1	no	—
341	#131	—	4	1	no	—
342	C₂×M₁₆	—	47	1	no	—
343	C₂×M₁₆	C₄×D₄₇	1	1	yes	characteristic
344	C₂×M₁₆	C₄×D₄₇	1	1	yes	characteristic
345	C₂×M₁₆	C₄×D₄₇	1	1	yes	characteristic
346	C₂²×C₈	—	47	1	no	—
347	C₂²×C₈	—	47	1	no	—
348	C₂²×C₈	—	47	1	no	—
349	C₂²×C₈	—	47	1	no	—
350	C₂²×C₈	—	47	1	no	—
351	C₂²×C₈	—	188	1	no	—
352	C₂²×C₈	—	188	1	no	—
353	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
354	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
355	C₂²×C₈	C₂²×D₄₇	1	1	yes	characteristic
356	#123	—	47	1	no	—
357	#123	—	47	1	no	—
358	C₂²⋊Q₈	—	47	1	no	—
359	C₂²⋊Q₈	—	47	1	no	—
360	#121	—	47	1	no	—
361	#121	—	47	1	no	—
362	#120	—	47	1	no	—
363	#120	—	47	1	no	—
364	C₄×D₄	—	47	1	no	—
365	C₄×D₄	—	47	1	no	—
366	C₄×D₄	—	47	1	no	—
367	C₄×D₄	—	47	1	no	—
368	#117	—	47	1	no	—
369	M₃₂	—	4	1	no	—
370	M₃₂	—	188	1	no	—
371	M₃₂	—	188	1	no	—
372	M₃₂	—	188	1	no	—
373	C₂×C₁₆	—	4	1	no	—
374	C₂×C₁₆	—	47	1	no	—
375	C₂×C₁₆	—	47	1	no	—
376	C₂×C₁₆	—	47	1	no	—
377	C₂×C₁₆	—	47	1	no	—
378	C₂×C₁₆	—	188	1	no	—
379	C₂×C₁₆	—	188	1	no	—
380	C₂×C₁₆	—	188	1	no	—
381	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
382	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
383	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
384	C₂×C₁₆	C₂²×D₄₇	1	1	yes	characteristic
385	C₄⋊C₈	—	47	1	no	—
386	C₄⋊C₈	—	47	1	no	—
387	C₄⋊C₈	—	47	1	no	—
388	C₄⋊C₈	—	47	1	no	—
389	C₂²⋊C₈	—	47	1	no	—
390	C₂²⋊C₈	—	47	1	no	—
391	C₂²⋊C₈	—	47	1	no	—
392	C₂²⋊C₈	—	47	1	no	—
393	C₂²⋊C₈	—	47	1	no	—
394	C₂²⋊C₈	—	47	1	no	—
395	C₂²⋊C₈	—	47	1	no	—
396	C₂²⋊C₈	—	47	1	no	—
397	#97	—	47	1	no	—
398	#97	—	47	1	no	—
399	C₄×C₈	—	47	1	no	—
400	C₄×C₈	—	47	1	no	—
401	C₂⁴	—	47	1	no	—
402	#41	—	4	1	no	—
403	#41	—	4	1	no	—
404	C₂×Q₈	C₈×D₄₇	1	1	yes	characteristic
405	C₂×D₄	—	47	1	no	—
406	C₂×D₄	—	47	1	no	—
407	C₂×D₄	—	47	1	no	—
408	C₂×D₄	—	47	1	no	—
409	C₂×D₄	C₈×D₄₇	1	1	yes	characteristic
410	C₂×D₄	C₈×D₄₇	1	1	yes	characteristic
411	C₂×D₄	C₈×D₄₇	1	1	yes	characteristic
412	C₂²×C₄	—	47	1	no	—
413	C₂²×C₄	—	47	1	no	—
414	C₂²×C₄	—	47	1	no	—
415	C₂²×C₄	—	47	1	no	—
416	C₂²×C₄	—	47	1	no	—
417	C₂²×C₄	—	188	1	no	—
418	C₂²×C₄	—	188	1	no	—
419	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
420	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
421	C₂²×C₄	C₂×C₄×D₄₇	1	1	yes	characteristic
422	M₁₆	—	4	1	no	—
423	M₁₆	—	4	1	no	—
424	M₁₆	—	4	1	no	—
425	M₁₆	—	188	1	no	—
426	C₂×C₈	—	2	1	no	—
427	C₂×C₈	—	2	1	no	—
428	C₂×C₈	—	2	1	no	—
429	C₂×C₈	—	2	1	no	—
430	C₂×C₈	—	2	1	no	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	47	1	no	—
433	C₂×C₈	—	47	1	no	—
434	C₂×C₈	—	47	1	no	—
435	C₂×C₈	—	47	1	no	—
436	C₂×C₈	—	94	1	no	—
437	C₂×C₈	—	94	1	no	—
438	C₂×C₈	—	94	1	no	—
439	C₂×C₈	—	94	1	no	—
440	C₂×C₈	—	188	1	no	—
441	C₂×C₈	—	188	1	no	—
442	C₂×C₈	—	188	1	no	—
443	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
444	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
445	C₂×C₈	C₂×C₄×D₄₇	1	1	yes	characteristic
446	C₂×C₈	C₂³×D₄₇	1	1	yes	characteristic
447	C₄⋊C₄	—	47	1	no	—
448	C₄⋊C₄	—	47	1	no	—
449	C₄⋊C₄	—	47	1	no	—
450	C₄⋊C₄	—	47	1	no	—
451	C₄⋊C₄	—	47	1	no	—
452	C₄⋊C₄	—	47	1	no	—
453	C₂²⋊C₄	—	47	1	no	—
454	C₂²⋊C₄	—	47	1	no	—
455	C₂²⋊C₄	—	47	1	no	—
456	C₂²⋊C₄	—	47	1	no	—
457	C₂²⋊C₄	—	47	1	no	—
458	C₂²⋊C₄	—	47	1	no	—
459	C₂²⋊C₄	—	47	1	no	—
460	C₂²⋊C₄	—	47	1	no	—
461	C₂²⋊C₄	—	47	1	no	—
462	C₂²⋊C₄	—	47	1	no	—
463	C₄²	—	47	1	no	—
464	C₄²	—	47	1	no	—
465	C₁₆	—	2	1	no	—
466	C₁₆	—	2	1	no	—
467	C₁₆	—	2	1	no	—
468	C₁₆	—	2	1	no	—
469	C₁₆	—	94	1	no	—
470	C₁₆	—	94	1	no	—
471	C₁₆	—	94	1	no	—
472	C₁₆	—	94	1	no	—
473	C₂³	—	47	1	no	—
474	C₂³	—	47	1	no	—
475	C₂³	—	94	2	no	—
476	C₂³	—	188	1	no	—
477	C₂³	—	188	1	no	—
478	C₂³	C₂×C₈×D₄₇	1	1	yes	characteristic
479	C₂³	C₂×C₈×D₄₇	1	1	yes	characteristic
480	C₂³	C₂×C₈×D₄₇	1	1	yes	characteristic
481	Q₈	—	4	1	no	—
482	D₄	—	4	1	no	—
483	D₄	—	4	1	no	—
484	D₄	—	4	1	no	—
485	D₄	—	94	2	no	—
486	D₄	—	94	2	no	—
487	D₄	—	188	1	no	—
488	D₄	—	188	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	2	1	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	1	no	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	47	1	no	—
496	C₂×C₄	—	47	1	no	—
497	C₂×C₄	—	47	1	no	—
498	C₂×C₄	—	47	1	no	—
499	C₂×C₄	—	47	1	no	—
500	C₂×C₄	—	47	1	no	—
501	C₂×C₄	—	94	1	no	—
502	C₂×C₄	—	94	1	no	—
503	C₂×C₄	—	94	1	no	—
504	C₂×C₄	—	94	1	no	—
505	C₂×C₄	—	188	1	no	—
506	C₂×C₄	—	188	1	no	—
507	C₂×C₄	—	188	1	no	—
508	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
509	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
510	C₂×C₄	C₂×C₈×D₄₇	1	1	yes	characteristic
511	C₂×C₄	C₂²×C₄×D₄₇	1	1	yes	characteristic
512	C₈	—	2	1	no	—
513	C₈	—	2	1	no	—
514	C₈	—	2	1	no	—
515	C₈	—	94	1	no	—
516	C₈	—	94	1	no	—
517	C₈	—	94	1	no	—
518	C₈	—	94	1	no	—
519	C₈	#13094069	1	1	yes	characteristic
520	C₈	#13094069	1	1	yes	characteristic
521	C₂²	—	2	1	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	2	1	no	—
527	C₂²	—	2	1	no	—
528	C₂²	—	2	1	no	—
529	C₂²	—	2	1	no	—
530	C₂²	—	47	2	no	—
531	C₂²	—	94	1	no	—
532	C₂²	—	94	1	no	—
533	C₂²	—	94	1	no	—
534	C₂²	—	94	1	no	—
535	C₂²	—	94	1	no	—
536	C₂²	—	188	4	no	—
537	C₂²	C₂²×C₈×D₄₇	1	1	yes	characteristic
538	C₄	—	2	1	no	—
539	C₄	—	2	1	no	—
540	C₄	—	2	1	no	—
541	C₄	—	94	1	no	—
542	C₄	—	94	1	no	—
543	C₄	—	94	1	no	—
544	C₄	—	94	1	no	—
545	C₄	—	94	1	no	—
546	C₄	—	94	1	no	—
547	C₄	#15689596	1	1	yes	characteristic
548	C₄	#15689889	1	1	yes	characteristic
549	C₂	—	4	1	no	—
550	C₂	—	4	1	no	—
551	C₂	—	4	1	no	—
552	C₂	—	94	2	no	—
553	C₂	—	188	1	no	—
554	C₂	#20252410	1	1	yes	characteristic
555	C₂	#504×D₄₇	1	1	yes	characteristic
556	C₂	#20256489	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂×C₈	C₂³×D₄₇
commutator, socle	C₂²×C₄₇	C₂³×C₈
Fitting	C₄₇×#2113	C₂
prime radical	#15689630	C₄
cosocle	C₂×C₈×C₄₇	C₂⁴
hypercenter	#2113	D₄₇
hypocenter	C₄₇	#33490
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂×C₈ ◁ #2113

Complements

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

N	H ≅ G/N	type
2. #20245218	C₂	semidirect
3. #20245217	C₂	semidirect
4. #20245216	C₂	semidirect
5. #20245213	C₂	semidirect
6. #20245211	C₂	semidirect
7. #20245210	C₂	semidirect
8. C₁₆×C₂²⋊D₄₇	C₂	semidirect
9. (C₂²⋊D₄₇)⋊C₁₆	C₂	semidirect
10. #20245192	C₂	semidirect
11. #20245192	C₂	semidirect
12. #20245002	C₂	semidirect
13. #20244997	C₂	semidirect
14. C₂²⋊C₁₆×D₄₇	C₂	semidirect
15. C₄₇×#2113	C₂	semidirect
18. C₂×#13093964	C₂²	semidirect
21. C₂²×C₄₇⋊C₁₆	C₂²	semidirect
36. Dic₄₇⋊C₁₆	C₂²	semidirect
37. Dic₄₇⋊C₁₆	C₂²	semidirect
38. Dic₄₇⋊C₁₆	C₂²	semidirect
39. Dic₄₇⋊C₁₆	C₂²	semidirect
42. C₂²⋊(C₄₇⋊C₁₆)	C₂²	semidirect
43. C₂²⋊(C₄₇⋊C₁₆)	C₂²	semidirect
48. #15688898	C₂²	semidirect
49. #15688898	C₂²	semidirect
50. C₁₆×Dic₄₇	C₂²	semidirect
51. C₁₆×Dic₄₇	C₂²	semidirect
53. C₂×M₃₂×C₄₇	C₂²	semidirect
54. C₂²×C₁₆×C₄₇	C₂²	semidirect
57. C₄₇×C₂²⋊C₁₆	C₂²	semidirect
58. C₄₇×C₂²⋊C₁₆	C₂²	semidirect
283. #2113	D₄₇	semidirect
300. C₂×M₃₂	C₂×D₄₇	semidirect
304. C₂²×C₁₆	C₂×D₄₇	semidirect
331. C₂²⋊C₁₆	C₂×D₄₇	semidirect
332. C₂²⋊C₁₆	C₂×D₄₇	semidirect
337. C₄₇	#33490	semidirect

Maximal subgroups

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

subgroup	index
#20252080	2
#20245218	2
#20245217	2
#20245216	2
#20245213	2
#20245211	2
#20245210	2
C₁₆×C₂²⋊D₄₇	2
(C₂²⋊D₄₇)⋊C₁₆	2
#20245192	2
#20245002	2
#20244997	2
C₂²⋊C₁₆×D₄₇	2
C₄₇×#2113	2
#33490	47