Finite Group Databasebeta

← #16855851

Subgroups — #16855851

Order 3968.

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

normal subgroups only

This group has 450 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#14521583C211yesmaximal, characteristic, complemented
2C2×C4×D124C211yesmaximal, characteristic, complemented
3#14521380C211yesmaximal, characteristic, complemented
4#14521363C211yesmaximal, characteristic, complemented
5#14521350C212yesmaximal, complemented
6#14521265C212yesmaximal, complemented
7#14521202C211yesmaximal, characteristic, complemented
8#14521185C211yesmaximal, characteristic
9#14521162C212yesmaximal, complemented
10#14521151C212yesmaximal, complemented
11C31×#432C211yesmaximal, characteristic, complemented
12C22×D124C2211yescharacteristic
13C22×C4×D31—21no—
14C2×C42×C31C2211yescharacteristic
15#11758507C2211yescharacteristic
16#11758506—21no—
17C4×C22⋊D31—21no—
18C2×(C2×D31)⋊C4—21no—
19C2×C4⋊Dic31C2211yescharacteristic
20#11758501C2211yescharacteristic
21C2×D248C2212yes—
22C2×#92470C2212yes—
23#11758453—21no—
24#11758452C2211yescharacteristic, complemented
25C4×D124—21no—
26C4×D124—21no—
27C4×D124C2212yes—
28C4×D124C2212yes—
29C4×D124C2211yescharacteristic, complemented
30#11758449—21no—
31#11758447C2211yescharacteristic, complemented
32C4×Dic62C2211yescharacteristic, complemented
33C31×C4⋊C8C2212yescomplemented
34C31×C22⋊C8C2211yescharacteristic
35C31×C22⋊C8C2211yescharacteristic
36C31×#97C2212yescomplemented
37#11758409C2212yes—
38#11758409C2212yes—
39#11758409C2212yescomplemented
40#11758406C2212yescomplemented
41#11758405C2212yescomplemented
42#11758404C2212yescomplemented
43C23×D31—21no—
44C22×C4×C31D411yescharacteristic
45C22×C4×C31D411yescharacteristic
46C22×C4×C31C2311yescharacteristic
47C2×C22⋊D31—21no—
48C22×Dic31—21no—
49C2×D124—21no—
50C2×D124—24no—
51C2×D124C2311yescharacteristic
52C2×D124C2312yes—
53C2×C4×D31—21no—
54C2×C4×D31—22no—
55C2×C4×D31—22no—
56C2×C4×D31—44no—
57C2×Dic62C2311yescharacteristic
58C2×C8×C31C2312yes—
59C2×C8×C31C2312yes—
60C42×C31D411yescharacteristic
61C42×C31D411yescharacteristic
62C42×C31C2311yescharacteristic
63C42×C31C2311yescharacteristic
64C22⋊Dic31—21no—
65(C2×D31)⋊C4—21no—
66(C2×D31)⋊C4—21no—
67(C2×D31)⋊C4—22no—
68(C2×D31)⋊C4—22no—
69(C2×D31)⋊C4—21no—
70(C2×D31)⋊C4—21no—
71C4⋊Dic31—21no—
72C4⋊Dic31C2312yes—
73C4⋊Dic31C2311yescharacteristic
74C4⋊Dic31C2311yescharacteristic
75Dic31⋊C4—21no—
76Dic31⋊C4—21no—
77Dic31⋊C4—21no—
78Dic31⋊C4—21no—
79C4×Dic31—21no—
80D248—24no—
81#92470—24no—
82C23×C31C2×D411yescharacteristic
83C22×D31—24no—
84C22×D31—22no—
85C22×D31—21no—
86C22×D31—42no—
87C22×D31—42no—
88C2×C4×C31—22no—
89C2×C4×C31—22no—
90C2×C4×C31—41no—
91C2×C4×C31C2×D411yescharacteristic
92C2×C4×C31C2×D411yescharacteristic
93C2×C4×C31C2×D411yescharacteristic
94C2×C4×C31C2×D411yescharacteristic
95C2×C4×C31C2×D411yescharacteristic
96C2×C4×C31C2411yescharacteristic
97C22⋊D31—42no—
98C2×Dic31—21no—
99C2×Dic31—21no—
100C2×Dic31—21no—
101C2×Dic31—22no—
102C2×Dic31—42no—
103D124—24no—
104D124—22no—
105D124—22no—
106D124#4114yes—
107C4×D31—42no—
108C4×D31—44no—
109C4×D31—44no—
110Dic62—22no—
111C8×C31—22no—
112C8×C31—22no—
113#3114—311nomaximal, Sylow
114C22×C31—21no—
115C22×C31—21no—
116C22×C31AGL(1,ℤ/8)12yes—
117C22×C31C22×D411yescharacteristic
118C2×D31—24no—
119C2×D31—48no—
120C2×D31—42no—
121C2×D31—42no—
122C2×D31—41no—
123C2×D31—41no—
124C2×D31—41no—
125C4×C31—21no—
126C4×C31—21no—
127C4×C31—21no—
128C4×C31—21no—
129C4×C31—21no—
130C4×C31C2×#4112yes—
131Dic31—41no—
132Dic31—42no—
133Dic31—41no—
134Dic31—41no—
135#529—311no—
136C2×C4×D4—311no—
137#483—311no—
138#480—311no—
139#478—312no—
140#463—312no—
141#450—311no—
142#447—311no—
143#442—312no—
144#440—312no—
145#432D3111yescharacteristic, complemented
146C2×C31—22no—
147C2×C31#52511yescharacteristic
148C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
149C2×C31#57511yescharacteristic
150D31—44no—
151D31—81no—
152C22×D4—311no—
153C23×C4—621no—
154C2×SD16—312no—
155C2×D8—312no—
156#126—621no—
157#125—311no—
158#124—311no—
159#123—621no—
160C22⋊Q8—311no—
161#121—311no—
162C4×Q8—311no—
163C4×D4—312no—
164C4×D4—312no—
165C4×D4—311no—
166C4×D4—621no—
167C4×D4—621no—
168C4×D4—621no—
169#117—621no—
170C2×C4⋊C4—311no—
171C2×C22⋊C4—621no—
172C2×C42C2×D3111yescharacteristic
173#107—312no—
174#106—312no—
175C4⋊C8C2×D3112yescomplemented
176#103—312no—
177#102—312no—
178#102—312no—
179#102—312no—
180C22⋊C8C2×D3111yescharacteristic
181C22⋊C8C2×D3111yescharacteristic
182#97C2×D3112yescomplemented
183C31#311411yescharacteristic, complemented, Sylow
184C24—621no—
185C2×Q8—311no—
186C2×D4—312no—
187C2×D4—311no—
188C2×D4—624no—
189C2×D4—621no—
190C2×D4—621no—
191C22×C4—621no—
192C22×C4—621no—
193C22×C4—622no—
194C22×C4—622no—
195C22×C4—1244no—
196C22×C4D12411yescharacteristic
197C22×C4D12411yescharacteristic
198C22×C4C22×D3111yescharacteristic
199SD16—624no—
200D8—624no—
201C2×C8C22×D3112yes—
202C2×C8C22×D3112yes—
203C4⋊C4—311no—
204C4⋊C4—311no—
205C4⋊C4—312no—
206C4⋊C4—621no—
207C4⋊C4—621no—
208C4⋊C4—621no—
209C4⋊C4—621no—
210C4⋊C4—621no—
211C22⋊C4—621no—
212C22⋊C4—622no—
213C22⋊C4—622no—
214C22⋊C4—621no—
215C22⋊C4—621no—
216C22⋊C4—621no—
217C22⋊C4—621no—
218C42—621no—
219C42D12411yescharacteristic
220C42D12411yescharacteristic
221C42C22×D3111yescharacteristic
222C42C22×D3111yescharacteristic
223C23—624no—
224C23—622no—
225C23—621no—
226C23—1242no—
227C23—1242no—
228C23C2×D12411yescharacteristic
229Q8—622no—
230D4—314no—
231D4—624no—
232D4—622no—
233D4—622no—
234D4—1242no—
235C2×C4—22no—
236C2×C4—22no—
237C2×C4—41no—
238C2×C4—621no—
239C2×C4—621no—
240C2×C4—621no—
241C2×C4—622no—
242C2×C4—1242no—
243C2×C4—1244no—
244C2×C4—1244no—
245C2×C4—1242no—
246C2×C4C2×D12411yescharacteristic
247C2×C4C2×D12411yescharacteristic
248C2×C4C2×D12411yescharacteristic
249C2×C4C2×D12411yescharacteristic
250C2×C4C2×D12411yescharacteristic
251C2×C4C23×D3111yescharacteristic
252C8—22no—
253C8—22no—
254C22—21no—
255C22—21no—
256C22—624no—
257C22—1248no—
258C22—1242no—
259C22—1242no—
260C22—1241no—
261C22—1241no—
262C22—1241no—
263C22#1175848512yes—
264C22C22×D12411yescharacteristic
265C4—21no—
266C4—21no—
267C4—21no—
268C4—21no—
269C4—21no—
270C4—1241no—
271C4—1242no—
272C4—1241no—
273C4—1241no—
274C4#41×D3112yes—
275C2—22no—
276C2—1244no—
277C2—2481no—
278C2#1452156111yescharacteristic
279C2C2×#1175848511yescharacteristic
280C2#1452184911yescharacteristic
subgroupG/H
centerC22C22×D124
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC31×#432C2
socleC22×C31C22×D4
prime radical#14521185C2
hypercenter#432D31
hypocenterC31#3114
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #14521583C2semidirect
2. C2×C4×D124C2semidirect
3. #14521380C2semidirect
4. #14521363C2semidirect
5. #14521350C2semidirect
6. #14521265C2semidirect
7. #14521202C2semidirect
9. #14521162C2semidirect
10. #14521151C2semidirect
11. C31×#432C2semidirect
24. #11758452C22semidirect
29. C4×D124C22semidirect
31. #11758447C22semidirect
32. C4×Dic62C22semidirect
33. C31×C4⋊C8C22semidirect
36. C31×#97C22semidirect
39. #11758409C22semidirect
40. #11758406C22semidirect
41. #11758405C22semidirect
42. #11758404C22semidirect
145. #432D31semidirect
175. C4⋊C8C2×D31semidirect
182. #97C2×D31semidirect
183. C31#3114semidirect

Maximal subgroups

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

subgroupindex
#145215832
C2×C4×D1242
#145213802
#145213632
#145213502
#145212652
#145212022
#145211852
#145211622
#145211512
C31×#4322
#311431