Finite Group Databasebeta

← #18004530

Subgroups — #18004530

Order 4736.

414 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 414 conjugacy classes of subgroups — too many to draw. Only its 125 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#14558045C211yesmaximal, characteristic
2C2×#11924494C211yesmaximal, characteristic, complemented
3#14557877C212yesmaximal, complemented
4#14557876C212yesmaximal, complemented
5#14557860C212yesmaximal, complemented
6#14557859C212yesmaximal, complemented
7#14557576C211yesmaximal, characteristic, complemented
8#14557535C211yesmaximal, characteristic, complemented
9#14557532C211yesmaximal, characteristic, complemented
10#14557496C211yesmaximal, characteristic, complemented
11C37×#428C211yesmaximal, characteristic, complemented
12C2×#10596962C2211yescharacteristic
13C22×C4×D37C2211yescharacteristic
14C2×#10596934C2211yescharacteristic
15#11924520—21no—
16#11924516C2211yescharacteristic
17#11924516C2211yescharacteristic
18#11924511C2211yescharacteristic
19#11924511C2211yescharacteristic
20#11924506—21no—
21C4×D148—21no—
22C4×D148—21no—
23#11924494—21no—
24#11924494—21no—
25#11924494C2212yes—
26#11924494C2212yes—
27C2×C4⋊Dic37C2211yescharacteristic
28C2×#10596938—21no—
29C2×C4×Dic37—21no—
30#11924469C2212yescomplemented
31#11924467C2212yescomplemented
32#11924461C2212yescomplemented
33#11924459C2212yescomplemented
34#11924458C2212yescomplemented
35#11924456C2212yescomplemented
36#11924448C2212yes—
37#11924448C2212yes—
38C2×M16×C37C2211yescharacteristic
39#117×C37C2211yescharacteristic
40C2×C4⋊C4×C37C2211yescharacteristic
41#107×C37C2212yescomplemented
42#106×C37C2212yescomplemented
43C23×D37D411yescharacteristic
44C22×C4×C37—21no—
45C22×C4×C37C2311yescharacteristic
46C2×C22⋊D37—21no—
47C22×Dic37—21no—
48C22×Dic37D411yescharacteristic
49#10596962—22no—
50#10596962—22no—
51C2×D148—21no—
52C2×D148—21no—
53C2×D148C2311yescharacteristic
54C2×C4×D37—22no—
55C2×C4×D37—22no—
56C2×C4×D37—21no—
57C2×C4×D37D411yescharacteristic
58C2×C4×D37D411yescharacteristic
59C2×C4×D37C2311yescharacteristic
60C2×C4×D37C2311yescharacteristic
61C2×Dic74C2311yescharacteristic
62M16×C37—22no—
63C2×C8×C37C2312yes—
64C4⋊C4×C37—21no—
65C4⋊C4×C37C2312yes—
66C4⋊C4×C37C2311yescharacteristic
67C4⋊C4×C37C2311yescharacteristic
68C22⋊C4×C37—21no—
69C42×C37—21no—
70#10596938—22no—
71#10596938—22no—
72#10596938—21no—
73#10596938—21no—
74#10596938—21no—
75#10596938—21no—
76C4⋊Dic37—21no—
77C4⋊Dic37—21no—
78C4⋊Dic37—21no—
79C4⋊Dic37C2312yes—
80C4×Dic37—22no—
81C4×Dic37—22no—
82#10596934—22no—
83C2×#64436C2312yes—
84C23×C37C2×D411yescharacteristic
85C22×D37—22no—
86C22×D37—21no—
87C22×D37—41no—
88C22×D37—41no—
89C22×D37C2×D411yescharacteristic
90C22×D37C2×D411yescharacteristic
91C2×C4×C37—22no—
92C2×C4×C37—21no—
93C2×C4×C37—21no—
94C2×C4×C37—42no—
95C2×C4×C37C2×D411yescharacteristic
96C2×C4×C37#4112yes—
97C2×C4×C37#4112yes—
98C2×C4×C37C2411yescharacteristic
99C22⋊D37—42no—
100C2×Dic37—22no—
101C2×Dic37—22no—
102C2×Dic37—21no—
103C2×Dic37—42no—
104C2×Dic37C2×D411yescharacteristic
105C2×Dic37C2×D411yescharacteristic
106D148—21no—
107D148—21no—
108D148—42no—
109D148—42no—
110C4×D37—22no—
111C4×D37—22no—
112C4×D37—21no—
113C4×D37—21no—
114C4×D37—21no—
115C4×D37—21no—
116C4×D37—42no—
117Dic74—21no—
118Dic74—21no—
119C8×C37—22no—
120#64436—22no—
121C22×C37—21no—
122C22×C37—21no—
123C22×C37#12312yes—
124C22×C37C22×D411yescharacteristic
125C2×D37—21no—
126C2×D37—21no—
127C2×D37—21no—
128C2×D37—21no—
129C2×D37—21no—
130C2×D37—21no—
131C2×D37—44no—
132C2×D37—41no—
133C2×D37—41no—
134C2×D37—41no—
135C4×C37—41no—
136C4×C37—41no—
137C4×C37—42no—
138C4×C37#12312yes—
139C4×C37C2×#4111yescharacteristic
140C4×C37C2×#4111yescharacteristic
141Dic37—21no—
142Dic37—21no—
143Dic37—41no—
144Dic37—42no—
145#3093—371nomaximal, Sylow
146C2×C37—22no—
147C2×C37C2×#12311yescharacteristic
148C2×C37#57511yescharacteristic
149C2×C37#57511yescharacteristic
150D37—41no—
151D37—41no—
152D37—81no—
153#525—371no—
154C2×#117—371no—
155#485—372no—
156#485—372no—
157#482—372no—
158#482—372no—
159#428—371no—
160#428D3711yescharacteristic, complemented
161#417—371no—
162#417—371no—
163#407—371no—
164C37#309311yescharacteristic, complemented, Sylow
165C2×#41—371no—
166C23×C4—371no—
167C2×M16—371no—
168C2×M16C2×D3711yescharacteristic
169#123—741no—
170C22⋊Q8—371no—
171C22⋊Q8—371no—
172#121—371no—
173#121—371no—
174#120—741no—
175C4×D4—741no—
176C4×D4—741no—
177#117—372no—
178#117—372no—
179#117—741no—
180#117—741no—
181#117C2×D3711yescharacteristic
182C2×C4⋊C4—371no—
183C2×C4⋊C4C2×D3711yescharacteristic
184C2×C22⋊C4—741no—
185C2×C42—741no—
186#107—372no—
187#107C2×D3712yescomplemented
188#106—372no—
189#106C2×D3712yescomplemented
190#103—372no—
191#103—372no—
192#102—372no—
193#102—372no—
194C22⋊C8—372no—
195C22⋊C8—372no—
196C24—371no—
197#41—742no—
198#41—742no—
199C2×Q8—371no—
200C2×D4—371no—
201C2×D4—741no—
202C2×D4—741no—
203C2×D4—741no—
204C22×C4—21no—
205C22×C4—371no—
206C22×C4—371no—
207C22×C4—371no—
208C22×C4—371no—
209C22×C4—371no—
210C22×C4—742no—
211C22×C4—742no—
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—741no—
222C4⋊C4—741no—
223C4⋊C4—741no—
224C4⋊C4C22×D3712yes—
225C4⋊C4C22×D3711yescharacteristic
226C4⋊C4C22×D3711yescharacteristic
227C22⋊C4—21no—
228C22⋊C4—741no—
229C22⋊C4—741no—
230C22⋊C4—742no—
231C22⋊C4—742no—
232C22⋊C4—741no—
233C22⋊C4—741no—
234C42—21no—
235C42—742no—
236C42—742no—
237C23—371no—
238C23—371no—
239C23—742no—
240C23—741no—
241C23—1481no—
242C23—1481no—
243C23D4×D3711yescharacteristic
244Q8—741no—
245Q8—741no—
246D4—741no—
247D4—741no—
248D4—1482no—
249D4—1482no—
250D4—1482no—
251C2×C4—21no—
252C2×C4—21no—
253C2×C4—22no—
254C2×C4—42no—
255C2×C4—371no—
256C2×C4—371no—
257C2×C4—742no—
258C2×C4—742no—
259C2×C4—742no—
260C2×C4—741no—
261C2×C4—741no—
262C2×C4—741no—
263C2×C4—741no—
264C2×C4—742no—
265C2×C4—741no—
266C2×C4—1482no—
267C2×C4—1482no—
268C2×C4#1059696212yes—
269C2×C4D4×D3711yescharacteristic
270C2×C4#1059696612yes—
271C2×C4C23×D3711yescharacteristic
272C8—22no—
273C8—742no—
274C22—21no—
275C22—21no—
276C22—741no—
277C22—741no—
278C22—741no—
279C22—741no—
280C22—741no—
281C22—741no—
282C22—1484no—
283C22—1481no—
284C22—1481no—
285C22—1481no—
286C22#1192452112yes—
287C22C2×D4×D3711yescharacteristic
288C4—42no—
289C4—41no—
290C4—41no—
291C4—741no—
292C4—741no—
293C4—1481no—
294C4—1482no—
295C4#1192452112yes—
296C4C2×#1059696211yescharacteristic
297C4C2×#1059696611yescharacteristic
298C2—22no—
299C2—2961no—
300C2—1481no—
301C2—1481no—
302C2C2×#1192452111yescharacteristic
303C2#1455832911yescharacteristic
304C2#1455833211yescharacteristic
subgroupG/H
centerC22C2×D4×D37
commutator, cosocleC2×C4×C37C24
FrattiniC2×C4C23×D37
FittingC37×#428C2
socleC22×C37C22×D4
prime radical#14558045C2
hypercenter#428D37
hypocenterC37#3093
LCSG ▷ C2×C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
2. C2×#11924494C2semidirect
3. #14557877C2semidirect
4. #14557876C2semidirect
5. #14557860C2semidirect
6. #14557859C2semidirect
7. #14557576C2semidirect
8. #14557535C2semidirect
9. #14557532C2semidirect
10. #14557496C2semidirect
11. C37×#428C2semidirect
30. #11924469C22semidirect
31. #11924467C22semidirect
32. #11924461C22semidirect
33. #11924459C22semidirect
34. #11924458C22semidirect
35. #11924456C22semidirect
41. #107×C37C22semidirect
42. #106×C37C22semidirect
160. #428D37semidirect
164. C37#3093semidirect
187. #107C2×D37semidirect
189. #106C2×D37semidirect

Maximal subgroups

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

subgroupindex
#145580452
C2×#119244942
#145578772
#145578762
#145578602
#145578592
#145575762
#145575352
#145575322
#145574962
C37×#4282
#309337