Finite Group Databasebeta

← #18004987

Subgroups — #18004987

Order 4736.

424 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 424 conjugacy classes of subgroups — too many to draw. Only its 129 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14558079C211yesmaximal, characteristic
2C2×#11924535C211yesmaximal, characteristic, complemented
3#14557894C212yesmaximal, complemented
4#14557891C212yesmaximal, complemented
5#14557882C212yesmaximal, complemented
6#14557878C212yesmaximal, complemented
7#14557535C211yesmaximal, characteristic, complemented
8#14557534C211yesmaximal, characteristic, complemented
9#14557532C211yesmaximal, characteristic, complemented
10M16×Dic37C211yesmaximal, characteristic, complemented
11C37×#417C211yesmaximal, characteristic, complemented
12C2×#10596962C2211yescharacteristic
13C22×Dic74—21no—
14C2×#10596934C2211yescharacteristic
15#11924535—21no—
16#11924535—21no—
17#11924535C2212yes—
18#11924535C2212yes—
19#11924534C2211yescharacteristic
20#11924532C2211yescharacteristic
21#11924525C2211yescharacteristic
22#11924523C2211yescharacteristic
23#11924508—21no—
24#11924508—21no—
25C4×C22⋊D37—21no—
26C4×C22⋊D37—21no—
27C2×C4⋊Dic37C2211yescharacteristic
28C2×#10596936—21no—
29C2×C4×Dic37C2211yescharacteristic
30#11924461C2212yes—
31#11924460C2212yes—
32#11924459C2212yes—
33#11924458C2212yes—
34#11924457C2212yes—
35#11924456C2212yes—
36#11924446C2212yes—
37C8×Dic37C2212yes—
38C2×#41×C37C2211yescharacteristic
39C2×M16×C37C2211yescharacteristic
40C2×C4⋊C4×C37C2211yescharacteristic
41#103×C37C2212yes—
42#102×C37C2212yes—
43#41×C37—22no—
44#41×C37—22no—
45C2×Q8×C37C2311yescharacteristic
46C2×D4×C37—21no—
47C2×D4×C37C2311yescharacteristic
48C22×C4×C37—21no—
49C22×C4×C37—21no—
50C22×C4×C37C2311yescharacteristic
51C2×C22⋊D37—21no—
52C2×C22⋊D37—21no—
53C2×C22⋊D37—21no—
54C22×Dic37—21no—
55C22×Dic37D411yescharacteristic
56C22×Dic37D411yescharacteristic
57#10596962—22no—
58#10596962—22no—
59C2×D148C2311yescharacteristic
60C2×C4×D37—21no—
61C2×Dic74—22no—
62C2×Dic74—22no—
63C2×Dic74—44no—
64C2×Dic74C2311yescharacteristic
65M16×C37—22no—
66C2×C8×C37C2312yes—
67C4⋊C4×C37—21no—
68C4⋊C4×C37C2312yes—
69C22⋊Dic37—21no—
70C22⋊Dic37—21no—
71#10596938—21no—
72#10596938—21no—
73C4⋊Dic37—21no—
74C4⋊Dic37C2312yes—
75#10596936—22no—
76#10596936—22no—
77#10596936—21no—
78#10596936—21no—
79C4×Dic37D411yescharacteristic
80C4×Dic37D411yescharacteristic
81C4×Dic37C2311yescharacteristic
82C4×Dic37C2311yescharacteristic
83#10596934—22no—
84C2×#64436C2312yes—
85C23×C37—21no—
86C23×C37C2×D411yescharacteristic
87C22×D37—21no—
88Q8×C37—21no—
89Q8×C37—21no—
90D4×C37—21no—
91D4×C37—21no—
92D4×C37—42no—
93C2×C4×C37—21no—
94C2×C4×C37—22no—
95C2×C4×C37—42no—
96C2×C4×C37—42no—
97C2×C4×C37C2×D411yescharacteristic
98C2×C4×C37#4112yes—
99C2×C4×C37#4112yes—
100C2×C4×C37C2411yescharacteristic
101C22⋊D37—42no—
102C22⋊D37—42no—
103C22⋊D37—42no—
104C2×Dic37—22no—
105C2×Dic37—22no—
106C2×Dic37—22no—
107C2×Dic37—21no—
108C2×Dic37—42no—
109C2×Dic37C2×D411yescharacteristic
110C2×Dic37C2×D411yescharacteristic
111C2×Dic37C2×D411yescharacteristic
112C2×Dic37C2×D411yescharacteristic
113D148—21no—
114D148—21no—
115C4×D37—42no—
116Dic74—21no—
117Dic74—21no—
118Dic74—44no—
119Dic74—44no—
120C8×C37—22no—
121#64436—22no—
122C22×C37—21no—
123C22×C37—21no—
124C22×C37—41no—
125C22×C37—41no—
126C22×C37—41no—
127C22×C37#12412yes—
128C22×C37C22×D411yescharacteristic
129C2×D37—41no—
130C2×D37—41no—
131C2×D37—41no—
132C4×C37—41no—
133C4×C37—42no—
134C4×C37#12412yes—
135C4×C37C2×#4111yescharacteristic
136C4×C37C2×#4111yescharacteristic
137Dic37—21no—
138Dic37—21no—
139Dic37—41no—
140Dic37—42no—
141Dic37AGL(1,ℤ/8)12yes—
142Dic37#13712yes—
143#3141—371nomaximal, Sylow
144C2×C37—22no—
145C2×C37—81no—
146C2×C37C2×#12411yescharacteristic
147C2×C37C2×AGL(1,ℤ/8)11yescharacteristic
148C2×C37C2×#13711yescharacteristic
149D37—81no—
150#532—371no—
151C2×C4⋊Q8—371no—
152#489—372no—
153#489—372no—
154#487—372no—
155#486—372no—
156#417—371no—
157#417—371no—
158#417—371no—
159#417D3711yescharacteristic, complemented
160C4×M16—371no—
161C37#314111yescharacteristic, complemented, Sylow
162C2×#41—371no—
163C2×#41C2×D3711yescharacteristic
164C22×Q8—741no—
165C2×M16—371no—
166C2×M16C2×D3711yescharacteristic
167C4⋊Q8—372no—
168C4⋊Q8—372no—
169C4⋊Q8—371no—
170C4⋊Q8—741no—
171C4⋊Q8—741no—
172#127—371no—
173#124—371no—
174#124—371no—
175#121—741no—
176#121—741no—
177C4×D4—741no—
178C4×D4—741no—
179C2×C4⋊C4—371no—
180C2×C4⋊C4—741no—
181C2×C4⋊C4C2×D3711yescharacteristic
182C2×C42—371no—
183#103—372no—
184#103—372no—
185#103—372no—
186#103C2×D3712yes—
187#102—372no—
188#102—372no—
189#102—372no—
190#102C2×D3712yes—
191#97—372no—
192C4×C8—372no—
193#41—22no—
194#41—22no—
195#41—742no—
196#41—742no—
197C2×Q8—371no—
198C2×Q8—742no—
199C2×Q8—742no—
200C2×Q8—1484no—
201C2×Q8C22×D3711yescharacteristic
202C2×D4—21no—
203C2×D4—371no—
204C2×D4—741no—
205C2×D4—741no—
206C2×D4—741no—
207C2×D4C22×D3711yescharacteristic
208C22×C4—21no—
209C22×C4—21no—
210C22×C4—371no—
211C22×C4—371no—
212C22×C4—741no—
213C22×C4—741no—
214C22×C4C22×D3711yescharacteristic
215M16—22no—
216M16—742no—
217C2×C8—372no—
218C2×C8C22×D3712yes—
219C4⋊C4—21no—
220C4⋊C4—372no—
221C4⋊C4—742no—
222C4⋊C4—742no—
223C4⋊C4—741no—
224C4⋊C4—741no—
225C4⋊C4—741no—
226C4⋊C4C22×D3712yes—
227C22⋊C4—741no—
228C22⋊C4—741no—
229C22⋊C4—741no—
230C22⋊C4—741no—
231C42—371no—
232C42—371no—
233C42—371no—
234C42—371no—
235C23—21no—
236C23—741no—
237C23D4×D3711yescharacteristic
238Q8—21no—
239Q8—21no—
240Q8—741no—
241Q8—741no—
242Q8—1484no—
243Q8—1484no—
244D4—21no—
245D4—21no—
246D4—42no—
247D4—741no—
248D4—741no—
249D4—1482no—
250D4—1482no—
251D4—1482no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—42no—
255C2×C4—42no—
256C2×C4—371no—
257C2×C4—371no—
258C2×C4—371no—
259C2×C4—371no—
260C2×C4—742no—
261C2×C4—742no—
262C2×C4—741no—
263C2×C4—742no—
264C2×C4—1482no—
265C2×C4—1482no—
266C2×C4#1059696212yes—
267C2×C4D4×D3711yescharacteristic
268C2×C4#1059696412yes—
269C2×C4C23×D3711yescharacteristic
270C8—22no—
271C8—742no—
272C22—21no—
273C22—21no—
274C22—41no—
275C22—41no—
276C22—41no—
277C22—1481no—
278C22—1481no—
279C22—1481no—
280C22#1192452212yes—
281C22C2×D4×D3711yescharacteristic
282C4—41no—
283C4—42no—
284C4—372no—
285C4—372no—
286C4—741no—
287C4—741no—
288C4—1481no—
289C4—1482no—
290C4#1192452212yes—
291C4C2×#1059696411yescharacteristic
292C4C2×#1059696211yescharacteristic
293C2—22no—
294C2—81no—
295C2—2961no—
296C2C2×#1192452211yescharacteristic
297C2AGL(1,ℤ/8)×D3711yescharacteristic
298C2#137×D3711yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#417C2
socleC22×C37C22×D4
prime radical#14558079C2
hypercenter#417D37
hypocenterC37#3141
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #417

Complements

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

NH ≅ G/Ntype
2. C2×#11924535C2semidirect
3. #14557894C2semidirect
4. #14557891C2semidirect
5. #14557882C2semidirect
6. #14557878C2semidirect
7. #14557535C2semidirect
8. #14557534C2semidirect
9. #14557532C2semidirect
10. M16×Dic37C2semidirect
11. C37×#417C2semidirect
159. #417D37semidirect
161. C37#3141semidirect

Maximal subgroups

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

subgroupindex
#145580792
C2×#119245352
#145578942
#145578912
#145578822
#145578782
#145575352
#145575342
#145575322
M16×Dic372
C37×#4172
#314137