Finite Group Databasebeta

← #16844415

Subgroups — #16844415

Order 3968.

242 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 65 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#14521600C211yesmaximal, characteristic
2#14521105C211yesmaximal, characteristic, complemented
3#14521101C211yesmaximal, characteristic, complemented
4#14520795C211yesmaximal, characteristic, complemented
5#14520792C211yesmaximal, characteristic, complemented
6#14520792C211yesmaximal, characteristic, complemented
7C31×#332C211yesmaximal, characteristic, complemented
8C2×#92499—21no—
9C31×C4⋊Q8C2211yescharacteristic
10#11758524—21no—
11#11758472—21no—
12#11758472C412yes—
13#11758470—21no—
14#11758470C412yes—
15#11758451C2211yescharacteristic
16C42×D31C2211yescharacteristic
17C31×C4⋊C8C2211yescharacteristic
18C31×C4⋊C8C2211yescharacteristic
19(C2×D31)⋊C8—21no—
20(C2×D31)⋊C8—21no—
21#11758403—21no—
22C8×Dic31—21no—
23C4⋊(C31⋊C8)C2211yescharacteristic
24C4⋊(C31⋊C8)C2211yescharacteristic
25C2×Q8×C31—21no—
26#92499—42no—
27#92499—42no—
28C2×D124—22no—
29C2×D124—21no—
30C2×D124—21no—
31C2×D124C2×C412yes—
32C2×C4×D31—22no—
33C2×C4×D31C2×C411yescharacteristic
34C2×C4×D31D411yescharacteristic
35C2×C4×D31D411yescharacteristic
36C2×C8×C31—21no—
37C2×C8×C31—21no—
38C4⋊C4×C31—21no—
39C4⋊C4×C31C2×C412yes—
40C42×C31C2311yescharacteristic
41(C2×D31)⋊C4—22no—
42(C2×D31)⋊C4—22no—
43C4×Dic31C2×C411yescharacteristic
44C4×Dic31D411yescharacteristic
45C4×Dic31D411yescharacteristic
46C2×C31⋊C8—21no—
47C2×C31⋊C8—21no—
48C22×D31—22no—
49C22×D31C22⋊C411yescharacteristic
50Q8×C31—41no—
51Q8×C31—41no—
52C2×C4×C31—22no—
53C2×C4×C31C22×C411yescharacteristic
54C2×C4×C31C2×D411yescharacteristic
55C2×C4×C31C2×D411yescharacteristic
56C2×Dic31C22⋊C411yescharacteristic
57C2×Dic31C22⋊C411yescharacteristic
58C2×Dic31C22⋊C411yescharacteristic
59D124—42no—
60D124—44no—
61D124—41no—
62D124—41no—
63D124—41no—
64D124—41no—
65C4×D31—21no—
66C4×D31—21no—
67C4×D31—21no—
68C4×D31—21no—
69C4×D31—41no—
70C4×D31—44no—
71C8×C31—41no—
72C8×C31—41no—
73C31⋊C8—41no—
74C31⋊C8—41no—
75#1553—311nomaximal, Sylow
76C22×C31C2×C22⋊C411yescharacteristic
77C2×D31—21no—
78C2×D31—21no—
79C2×D31—21no—
80C2×D31—42no—
81C2×D31—42no—
82C2×D31—42no—
83C4×C31—21no—
84C4×C31—42no—
85C4×C31#13511yescharacteristic
86C4×C31#13511yescharacteristic
87C4×C31AGL(1,ℤ/8)11yescharacteristic
88C4×C31AGL(1,ℤ/8)11yescharacteristic
89Dic31—21no—
90Dic31—21no—
91Dic31—21no—
92#532—311no—
93#432—311no—
94#431—311no—
95#332—311no—
96#332D3111yescharacteristic, complemented
97#331—311no—
98#331—311no—
99C2×C31#41311yescharacteristic
100C2×C31#41611yescharacteristic
101C2×C31#41811yescharacteristic
102D31—41no—
103D31—82no—
104C2×#41—621no—
105C4⋊Q8C2×D3111yescharacteristic
106#127—311no—
107#124—621no—
108#121—312no—
109#121—621no—
110C4×D4—312no—
111C4×D4—621no—
112C2×C42—311no—
113C4⋊C8—311no—
114C4⋊C8—311no—
115C4⋊C8C2×D3111yescharacteristic
116C4⋊C8C2×D3111yescharacteristic
117C22⋊C8—621no—
118C22⋊C8—621no—
119#97—621no—
120C4×C8—621no—
121C31#155311yescharacteristic, complemented, Sylow
122#41—1242no—
123#41—1242no—
124C2×Q8—21no—
125C2×D4—312no—
126C2×D4—622no—
127C2×D4—621no—
128C2×D4—621no—
129C22×C4—311no—
130C22×C4—311no—
131C22×C4—311no—
132C22×C4—622no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—621no—
136C2×C8—621no—
137C4⋊C4—21no—
138C4⋊C4C4×D3112yes—
139C22⋊C4—622no—
140C22⋊C4—622no—
141C42—311no—
142C42—311no—
143C42—311no—
144C42C22×D3111yescharacteristic
145C23—311no—
146C23—622no—
147Q8—41no—
148Q8—41no—
149D4—1242no—
150D4—1244no—
151D4—1241no—
152D4—1241no—
153D4—1241no—
154D4—1241no—
155C2×C4—22no—
156C2×C4—311no—
157C2×C4—311no—
158C2×C4—311no—
159C2×C4—621no—
160C2×C4—621no—
161C2×C4—621no—
162C2×C4—621no—
163C2×C4—1241no—
164C2×C4—1244no—
165C2×C4C2×C4×D3111yescharacteristic
166C2×C4D4×D3111yescharacteristic
167C2×C4D4×D3111yescharacteristic
168C8—41no—
169C8—41no—
170C8—1241no—
171C8—1241no—
172C22—621no—
173C22—621no—
174C22—621no—
175C22—1242no—
176C22—1242no—
177C22—1242no—
178C22C22⋊C4×D3111yescharacteristic
179C4—21no—
180C4—42no—
181C4—621no—
182C4—621no—
183C4—621no—
184C4#1175848811yescharacteristic
185C4#1175849111yescharacteristic
186C4#1175849311yescharacteristic
187C4#1175849611yescharacteristic
188C2—1241no—
189C2—2482no—
190C2#1452103211yescharacteristic
191C2#1452104411yescharacteristic
192C2#1452105211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D31
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC31×#332C2
socleC22×C31C2×C22⋊C4
prime radical#14521600C2
cosocleC42×C31C23
hypercenter#332D31
hypocenterC31#1553
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
2. #14521105C2semidirect
3. #14521101C2semidirect
4. #14520795C2semidirect
5. #14520792C2semidirect
6. #14520792C2semidirect
7. C31×#332C2semidirect
96. #332D31semidirect
121. C31#1553semidirect

Maximal subgroups

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

subgroupindex
#145216002
#145211052
#145211012
#145207952
#145207922
C31×#3322
#155331