Finite Group Databasebeta

← #16844413

Subgroups — #16844413

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#14521597C211yesmaximal, characteristic
2#14521105C211yesmaximal, characteristic, complemented
3#14521101C211yesmaximal, characteristic, complemented
4#14520796C211yesmaximal, characteristic, complemented
5#14520794C211yesmaximal, characteristic, complemented
6#14520793C211yesmaximal, characteristic, complemented
7C31×#331C211yesmaximal, characteristic, complemented
8C2×#92497—21no—
9C31×#127C2211yescharacteristic
10#11758515—21no—
11#11758515C412yes—
12#11758513—21no—
13D4×Dic31—21no—
14D4×Dic31C412yes—
15C42×D31C2211yescharacteristic
16#11758446C2211yescharacteristic
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×D4×C31—21no—
26C2×D4×C31—21no—
27C2×D4×C31C2×C412yes—
28C2×C22⋊D31—22no—
29C22×Dic31—22no—
30#92497—42no—
31#92497—42no—
32C2×C4×D31C2×C411yescharacteristic
33C2×C4×D31D411yescharacteristic
34C2×C4×D31D411yescharacteristic
35C2×Dic62—21no—
36C2×C8×C31—21no—
37C2×C8×C31—21no—
38C42×C31C2311yescharacteristic
39C22⋊Dic31—22no—
40C22⋊Dic31—22no—
41C4⋊Dic31—21no—
42C4⋊Dic31C2×C412yes—
43C4×Dic31C2×C411yescharacteristic
44C4×Dic31D411yescharacteristic
45C4×Dic31D411yescharacteristic
46C2×C31⋊C8—21no—
47C2×C31⋊C8—21no—
48C23×C31—22no—
49C22×D31C22⋊C411yescharacteristic
50D4×C31—42no—
51D4×C31—41no—
52D4×C31—41no—
53D4×C31—41no—
54D4×C31—41no—
55C2×C4×C31C22×C411yescharacteristic
56C2×C4×C31C2×D411yescharacteristic
57C2×C4×C31C2×D411yescharacteristic
58C22⋊D31—44no—
59C2×Dic31—22no—
60C2×Dic31—44no—
61C2×Dic31C22⋊C411yescharacteristic
62C2×Dic31C22⋊C411yescharacteristic
63C2×Dic31C22⋊C411yescharacteristic
64C4×D31—21no—
65C4×D31—21no—
66C4×D31—21no—
67C4×D31—21no—
68C4×D31—41no—
69Dic62—41no—
70Dic62—41no—
71C8×C31—41no—
72C8×C31—41no—
73C31⋊C8—41no—
74C31⋊C8—41no—
75#1553—311nomaximal, Sylow
76C22×C31—42no—
77C22×C31—42no—
78C22×C31—42no—
79C22×C31C2×C22⋊C411yescharacteristic
80C2×D31—21no—
81C2×D31—21no—
82C2×D31—21no—
83C4×C31—21no—
84C4×C31#13511yescharacteristic
85C4×C31#13511yescharacteristic
86C4×C31AGL(1,ℤ/8)11yescharacteristic
87C4×C31AGL(1,ℤ/8)11yescharacteristic
88Dic31—21no—
89Dic31—21no—
90Dic31—21no—
91Dic31—42no—
92#532—311no—
93#432—311no—
94#431—311no—
95#332—311no—
96#332—311no—
97#331—311no—
98#331D3111yescharacteristic, complemented
99C2×C31—82no—
100C2×C31#41311yescharacteristic
101C2×C31#41611yescharacteristic
102C2×C31#41811yescharacteristic
103D31—41no—
104C2×#41—621no—
105C4⋊Q8—311no—
106#127C2×D3111yescharacteristic
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—621no—
125C2×D4—21no—
126C2×D4—21no—
127C2×D4—622no—
128C2×D4C4×D3112yes—
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—312no—
138C4⋊C4—621no—
139C22⋊C4—622no—
140C22⋊C4—622no—
141C42—311no—
142C42—311no—
143C42—311no—
144C42C22×D3111yescharacteristic
145C23—22no—
146C23—311no—
147Q8—1241no—
148Q8—1241no—
149D4—42no—
150D4—41no—
151D4—41no—
152D4—41no—
153D4—41no—
154D4—1244no—
155C2×C4—311no—
156C2×C4—311no—
157C2×C4—311no—
158C2×C4—621no—
159C2×C4—621no—
160C2×C4—621no—
161C2×C4—621no—
162C2×C4—622no—
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—42no—
173C22—42no—
174C22—42no—
175C22—621no—
176C22—621no—
177C22—621no—
178C22C22⋊C4×D3111yescharacteristic
179C4—21no—
180C4—621no—
181C4—621no—
182C4—621no—
183C4—1242no—
184C4#1175848811yescharacteristic
185C4#1175848911yescharacteristic
186C4#1175849111yescharacteristic
187C4#1175849311yescharacteristic
188C2—82no—
189C2—1241no—
190C2#1452103011yescharacteristic
191C2#1452104211yescharacteristic
192C2#1452105211yescharacteristic
subgroupG/H
centerC22C22⋊C4×D31
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC31×#331C2
socleC22×C31C2×C22⋊C4
prime radical#14521597C2
cosocleC42×C31C23
hypercenter#331D31
hypocenterC31#1553
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #331

Complements

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

NH ≅ G/Ntype
2. #14521105C2semidirect
3. #14521101C2semidirect
4. #14520796C2semidirect
5. #14520794C2semidirect
6. #14520793C2semidirect
7. C31×#331C2semidirect
98. #331D31semidirect
121. C31#1553semidirect

Maximal subgroups

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

subgroupindex
#145215972
#145211052
#145211012
#145207962
#145207942
#145207932
C31×#3312
#155331