Finite Group Databasebeta

← #16855810

Subgroups — #16855810

Order 3968.

444 conjugacy classes of subgroups; only the 133 normal subgroups are shown.

normal subgroups only

This group has 444 conjugacy classes of subgroups — too many to draw. Only its 133 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#14521606C211yesmaximal, characteristic, complemented
2#14521384C212yesmaximal, complemented
3#14521329C212yesmaximal, complemented
4#14521254C212yesmaximal, complemented
5#14521200C212yesmaximal
6#14521149C214yesmaximal, complemented
7#14521106C211yesmaximal, characteristic, complemented
8C2×C4×D4×C31C211yesmaximal, characteristic
9C22×D4×C31C2211yescharacteristic
10C23×C4×C31—21no—
11C4×D4×C31—21no—
12C4×D4×C31—21no—
13C4×D4×C31C2212yes—
14C4×D4×C31C2212yes—
15C2×C4⋊C4×C31C2211yescharacteristic
16C2×C22⋊C4×C31—21no—
17C2×C42×C31C2211yescharacteristic
18C2×#92480C2214yes—
19#11758503—21no—
20#11758501—21no—
21#11758501C2212yes—
22#11758447—21no—
23#11758446C2211yescharacteristic, complemented
24#11758446C2211yescharacteristic, complemented
25C4×Dic62—21no—
26C4×Dic62C2212yescomplemented
27#11758420C2214yes—
28C22⋊(C31⋊C8)C2212yes—
29#11758398C2214yescomplemented
30#11758395C2214yescomplemented
31C4⋊(C31⋊C8)C2212yescomplemented
32#11758391C2212yescomplemented
33C24×C31—21no—
34C2×D4×C31—24no—
35C2×D4×C31—21no—
36C2×D4×C31C2312yes—
37C22×C4×C31—21no—
38C22×C4×C31—22no—
39C22×C4×C31—22no—
40C22×C4×C31—44no—
41C22×C4×C31D411yescharacteristic
42C22×C4×C31D411yescharacteristic
43C22×C4×C31C2311yescharacteristic
44C2×Dic62—21no—
45C2×Dic62C2312yes—
46C4⋊C4×C31—21no—
47C4⋊C4×C31C2312yes—
48C22⋊C4×C31—22no—
49C22⋊C4×C31—22no—
50C42×C31D411yescharacteristic
51C42×C31D411yescharacteristic
52C42×C31C2311yescharacteristic
53C42×C31C2311yescharacteristic
54C22⋊Dic31—22no—
55#92480—28no—
56C4⋊Dic31—21no—
57C4⋊Dic31—21no—
58C4⋊Dic31—21no—
59C4⋊Dic31C2312yes—
60Dic31⋊C4—22no—
61Dic31⋊C4—22no—
62C4×Dic31—22no—
63C2×C31⋊C8C2314yes—
64C23×C31—24no—
65C23×C31—22no—
66C23×C31—42no—
67C23×C31—42no—
68C23×C31C2×D411yescharacteristic
69D4×C31—24no—
70D4×C31—22no—
71D4×C31#4114yes—
72C2×C4×C31—22no—
73C2×C4×C31—22no—
74C2×C4×C31—22no—
75C2×C4×C31—22no—
76C2×C4×C31—44no—
77C2×C4×C31—42no—
78C2×C4×C31—44no—
79C2×C4×C31C2×D411yescharacteristic
80C2×C4×C31C2×D411yescharacteristic
81C2×C4×C31C2×D411yescharacteristic
82C2×C4×C31C2×D411yescharacteristic
83C2×C4×C31C2×D411yescharacteristic
84C2×C4×C31C2411yescharacteristic
85C2×Dic31—22no—
86C2×Dic31—22no—
87Dic62—24no—
88Dic62—42no—
89C31⋊C8—24no—
90#3110—311nomaximal, Sylow
91C22×C31—21no—
92C22×C31—21no—
93C22×C31—24no—
94C22×C31—48no—
95C22×C31—42no—
96C22×C31—42no—
97C22×C31#13712yes—
98C22×C31C22×D411yescharacteristic
99C4×C31—21no—
100C4×C31—21no—
101C4×C31—21no—
102C4×C31—21no—
103C4×C31—42no—
104C4×C31AGL(1,ℤ/8)12yes—
105C4×C31C2×#4112yes—
106Dic31—42no—
107Dic31—42no—
108#533—311no—
109C2×C4×D4D3111yescharacteristic
110#484—312no—
111#474—312no—
112#461—312no—
113#450—312no—
114#440—314no—
115#432—311no—
116C2×C31—22no—
117C2×C31—44no—
118C2×C31#52511yescharacteristic
119C2×C31C2×AGL(1,ℤ/8)11yescharacteristic
120C2×C31C2×#13711yescharacteristic
121C22×D4C2×D3111yescharacteristic
122C23×C4—21no—
123C2×SD16—314no—
124C4⋊Q8—311no—
125C4⋊Q8—311no—
126#125—621no—
127C22⋊Q8—312no—
128C22⋊Q8—621no—
129C4×Q8—312no—
130C4×Q8—621no—
131C4×D4—21no—
132C4×D4—21no—
133C4×D4C2×D3112yes—
134C4×D4C2×D3112yes—
135#117—621no—
136C2×C4⋊C4C2×D3111yescharacteristic
137C2×C22⋊C4—21no—
138C2×C42C2×D3111yescharacteristic
139#107—314no—
140C4⋊C8—312no—
141#103—314no—
142#102—314no—
143C22⋊C8—312no—
144#97—312no—
145C31#311011yescharacteristic, complemented, Sylow
146C24—21no—
147C2×Q8—312no—
148C2×Q8—621no—
149C2×D4—24no—
150C2×D4—21no—
151C2×D4C22×D3112yes—
152C22×C4—21no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—44no—
156C22×C4C22⋊D3111yescharacteristic
157C22×C4C22⋊D3111yescharacteristic
158C22×C4C22×D3111yescharacteristic
159SD16—628no—
160C2×C8—314no—
161C4⋊C4—21no—
162C4⋊C4—312no—
163C4⋊C4—622no—
164C4⋊C4—622no—
165C4⋊C4—621no—
166C4⋊C4—621no—
167C4⋊C4—621no—
168C4⋊C4C22×D3112yes—
169C22⋊C4—22no—
170C22⋊C4—22no—
171C22⋊C4—622no—
172C42—622no—
173C42C22⋊D3111yescharacteristic
174C42C22⋊D3111yescharacteristic
175C42C22×D3111yescharacteristic
176C42C22×D3111yescharacteristic
177C23—24no—
178C23—22no—
179C23—42no—
180C23—42no—
181C23C2×C22⋊D3111yescharacteristic
182Q8—624no—
183Q8—1242no—
184D4—24no—
185D4—22no—
186D4#9249514yes—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—44no—
192C2×C4—42no—
193C2×C4—44no—
194C2×C4—622no—
195C2×C4—622no—
196C2×C4C2×C22⋊D3111yescharacteristic
197C2×C4C2×C22⋊D3111yescharacteristic
198C2×C4C2×C22⋊D3111yescharacteristic
199C2×C4C2×C22⋊D3111yescharacteristic
200C2×C4C2×C22⋊D3111yescharacteristic
201C2×C4C23×D3111yescharacteristic
202C8—624no—
203C22—21no—
204C22—21no—
205C22—24no—
206C22—48no—
207C22—42no—
208C22—42no—
209C22#1175852812yes—
210C22C22×C22⋊D3111yescharacteristic
211C4—21no—
212C4—21no—
213C4—21no—
214C4—21no—
215C4—42no—
216C4—1242no—
217C4—1242no—
218C4#1175850912yes—
219C4C2×#9249512yes—
220C2—22no—
221C2—44no—
222C2#1452156011yescharacteristic
223C2C2×#1175850911yescharacteristic
224C2C2×#1175852811yescharacteristic
subgroupG/H
centerC22C22×C22⋊D31
commutator, cosocleC2×C4×C31C24
FrattiniC2×C4C23×D31
FittingC2×C4×D4×C31C2
socleC22×C31C22×D4
prime radicalC22×D4×C31C22
hypercenterC2×C4×D4D31
hypocenterC31#3110
LCSG ▷ C2×C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C42 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. #14521606C2semidirect
2. #14521384C2semidirect
3. #14521329C2semidirect
4. #14521254C2semidirect
6. #14521149C2semidirect
7. #14521106C2semidirect
23. #11758446C22semidirect
24. #11758446C22semidirect
26. C4×Dic62C22semidirect
29. #11758398C22semidirect
30. #11758395C22semidirect
31. C4⋊(C31⋊C8)C22semidirect
32. #11758391C22semidirect
145. C31#3110semidirect

Maximal subgroups

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

subgroupindex
#145216062
#145213842
#145213292
#145212542
#145212002
#145211492
#145211062
C2×C4×D4×C312
#311031