Finite Group Databasebeta

← #16844042

Subgroups — #16844042

Order 3968.

252 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C2×#11758454C211yesmaximal, characteristic
2#14521103C212yesmaximal, complemented
3#14520774C212yesmaximal, complemented
4#14520773C211yesmaximal, characteristic
5C31×#323C211yesmaximal, characteristic
6C23×Dic31C411yescharacteristic
7C2×C22⋊C4×C31C2211yescharacteristic
8C2×C22⋊Dic31C411yescharacteristic
9C2×Dic31⋊C4C411yescharacteristic
10C2×Dic31⋊C4C2211yescharacteristic
11C2×C4×Dic31C411yescharacteristic
12C2×C4×Dic31C2211yescharacteristic
13#11758454—22no—
14#11758454—22no—
15C31×C22⋊C8C2212yes—
16C22⋊(C31⋊C8)C2212yes—
17#11758403—22no—
18Dic31⋊C8—22no—
19C24×C31C2×C411yescharacteristic
20C22×C4×C31C2×C411yescharacteristic
21C22×C4×C31C2311yescharacteristic
22C22×Dic31—22no—
23C22×Dic31—21no—
24C22×Dic31—21no—
25C22×Dic31—22no—
26C22×Dic31C2×C411yescharacteristic
27C22×Dic31C2×C411yescharacteristic
28C22×Dic31C2×C411yescharacteristic
29C22×Dic31C2×C411yescharacteristic
30C2×C8×C31—22no—
31C22⋊C4×C31—22no—
32C22⋊Dic31—22no—
33Dic31⋊C4—22no—
34Dic31⋊C4—22no—
35C4×Dic31—21no—
36C4×Dic31—21no—
37C4×Dic31D412yes—
38C4×Dic31D412yes—
39C2×C31⋊C8—22no—
40C23×C31—21no—
41C23×C31—21no—
42C23×C31—41no—
43C23×C31—41no—
44C23×C31M1612yes—
45C23×C31C22×C411yescharacteristic
46C2×C4×C31—21no—
47C2×C4×C31—41no—
48C2×C4×C31—41no—
49C2×C4×C31C2×D412yes—
50C2×Dic31—24no—
51C2×Dic31—24no—
52C2×Dic31—21no—
53C2×Dic31—21no—
54C2×Dic31—21no—
55C2×Dic31—21no—
56C2×Dic31—21no—
57C2×Dic31—41no—
58C2×Dic31—41no—
59C2×Dic31C22⋊C411yescharacteristic
60C2×Dic31C22⋊C411yescharacteristic
61C2×Dic31C22⋊C412yes—
62C2×Dic31M1612yes—
63C8×C31—42no—
64C31⋊C8—42no—
65#1464—311nomaximal, Sylow
66C22×C31—21no—
67C22×C31—21no—
68C22×C31—22no—
69C22×C31—42no—
70C22×C31—42no—
71C22×C31—41no—
72C22×C31—41no—
73C22×C31C2×C22⋊C411yescharacteristic
74C22×C31C2×M1611yescharacteristic
75C22×C31C2×M1611yescharacteristic
76C4×C31—22no—
77C4×C31—41no—
78Dic31—21no—
79Dic31—21no—
80Dic31—22no—
81Dic31—22no—
82Dic31—41no—
83C2×#117—311no—
84#432—312no—
85#324—312no—
86#323—311no—
87#323D3111yescharacteristic
88C2×C31—21no—
89C2×C31—21no—
90C2×C31—42no—
91C2×C31#40711yescharacteristic
92C2×C31#41011yescharacteristic
93C2×C31#41311yescharacteristic
94C23×C4—311no—
95#117—622no—
96#117—622no—
97C2×C4⋊C4—311no—
98C2×C4⋊C4—311no—
99C2×C22⋊C4—311no—
100C2×C22⋊C4C2×D3111yescharacteristic
101C2×C42—311no—
102C2×C42—311no—
103C4⋊C8—622no—
104C22⋊C8—312no—
105C22⋊C8C2×D3112yes—
106#97—622no—
107C31#146411yescharacteristic, complemented, Sylow
108C24C4×D3111yescharacteristic
109C22×C4—311no—
110C22×C4—311no—
111C22×C4—311no—
112C22×C4—311no—
113C22×C4—621no—
114C22×C4—621no—
115C22×C4—622no—
116C22×C4—622no—
117C22×C4C4×D3111yescharacteristic
118C22×C4C22×D3111yescharacteristic
119C2×C8—22no—
120C2×C8—622no—
121C4⋊C4—622no—
122C4⋊C4—622no—
123C22⋊C4—22no—
124C22⋊C4—622no—
125C42—312no—
126C42—312no—
127C42—621no—
128C42—621no—
129C23—21no—
130C23—21no—
131C23—41no—
132C23—41no—
133C23#9246912yes—
134C23C2×C4×D3111yescharacteristic
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—41no—
138C2×C4—311no—
139C2×C4—311no—
140C2×C4—312no—
141C2×C4—312no—
142C2×C4—624no—
143C2×C4—624no—
144C2×C4—621no—
145C2×C4—621no—
146C2×C4—621no—
147C2×C4—621no—
148C2×C4—621no—
149C2×C4—1241no—
150C2×C4—1241no—
151C2×C4D4×D3112yes—
152C8—42no—
153C8—1242no—
154C22—21no—
155C22—21no—
156C22—22no—
157C22—42no—
158C22—42no—
159C22—41no—
160C22—41no—
161C22C22⋊C4×D3111yescharacteristic
162C22C2×#9246911yescharacteristic
163C22M16×D3111yescharacteristic
164C4—22no—
165C4—41no—
166C4—621no—
167C4—621no—
168C4—622no—
169C4—622no—
170C4—1241no—
171C2—21no—
172C2—21no—
173C2—42no—
174C2#1452101111yescharacteristic
175C2#1452102111yescharacteristic
176C2#1452103011yescharacteristic
subgroupG/H
centerC22C22⋊C4×D31
commutatorC23×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#323C2
socleC22×C31C2×C22⋊C4
prime radicalC24×C31C2×C4
cosocleC22×C4×C31C23
hypercenter#323D31
hypocenterC31#1464
LCSG ▷ C23×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

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

NH ≅ G/Ntype
2. #14521103C2semidirect
3. #14520774C2semidirect
107. C31#1464semidirect

Maximal subgroups

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

subgroupindex
C2×#117584542
#145211032
#145207742
#145207732
C31×#3232
#146431