Finite Group Databasebeta

← #16844405

Subgroups — #16844405

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
1#14521600C211yesmaximal, characteristic
2#14521105C211yesmaximal, characteristic, complemented
3C4⋊C8×D31C211yesmaximal, characteristic, complemented
4#14520798C211yesmaximal, characteristic, complemented
5#14520792C211yesmaximal, characteristic, complemented
6#14520792C211yesmaximal, characteristic, complemented
7C31×#333C211yesmaximal, characteristic, complemented
8C2×#92499C412yes—
9C31×C4⋊Q8C2211yescharacteristic
10#11758524C412yes—
11C2×C8×D31—21no—
12#11758472—21no—
13#11758472—21no—
14#11758470—21no—
15#11758470—21no—
16#11758451C2211yescharacteristic
17C42×D31C2211yescharacteristic
18C31×C4⋊C8C2211yescharacteristic
19C31×C4⋊C8C2211yescharacteristic
20(C2×D31)⋊C8—21no—
21#11758403—21no—
22Dic31⋊C8—21no—
23C4⋊(C31⋊C8)C2211yescharacteristic
24C4⋊(C31⋊C8)C2211yescharacteristic
25C2×Q8×C31C2×C412yes—
26#92499—44no—
27C2×D124—22no—
28C2×D124—21no—
29C2×D124—21no—
30C2×D124C2×C412yes—
31C2×C4×D31—22no—
32C2×C4×D31C2×C411yescharacteristic
33C2×C4×D31D411yescharacteristic
34C2×C4×D31D411yescharacteristic
35C2×C8×C31—21no—
36C2×C8×C31—21no—
37C4⋊C4×C31—21no—
38C4⋊C4×C31—21no—
39C42×C31C2311yescharacteristic
40(C2×D31)⋊C4—22no—
41(C2×D31)⋊C4—22no—
42C4×Dic31C2×C411yescharacteristic
43C4×Dic31D411yescharacteristic
44C4×Dic31D411yescharacteristic
45C2×C31⋊C8—21no—
46C2×C31⋊C8—21no—
47C8×D31—42no—
48C22×D31—22no—
49C22×D31C22⋊C411yescharacteristic
50Q8×C31—42no—
51C2×C4×C31—22no—
52C2×C4×C31C22×C411yescharacteristic
53C2×C4×C31C2×D411yescharacteristic
54C2×C4×C31C2×D411yescharacteristic
55C2×Dic31C22⋊C411yescharacteristic
56C2×Dic31C22⋊C411yescharacteristic
57C2×Dic31C22⋊C411yescharacteristic
58D124—42no—
59D124—44no—
60D124—41no—
61D124—41no—
62D124—41no—
63D124—41no—
64C4×D31—22no—
65C4×D31—21no—
66C4×D31—21no—
67C4×D31—21no—
68C4×D31—21no—
69C4×D31—44no—
70C8×C31—41no—
71C8×C31—41no—
72C31⋊C8—41no—
73C31⋊C8—41no—
74#1551—311nomaximal, Sylow
75C22×C31C2×C22⋊C411yescharacteristic
76C2×D31—21no—
77C2×D31—21no—
78C2×D31—42no—
79C2×D31—42no—
80C2×D31—42no—
81C2×D31#10012yes—
82C4×C31—21no—
83C4×C31—42no—
84C4×C31#13511yescharacteristic
85C4×C31#13511yescharacteristic
86C4×C31AGL(1,ℤ/8)11yescharacteristic
87C4×C31#13711yescharacteristic
88Dic31—21no—
89Dic31—21no—
90Dic31—21no—
91#532—311no—
92#432—311no—
93C2×C4⋊C8—311no—
94#333—311no—
95#333D3111yescharacteristic, complemented
96#331—311no—
97#331—311no—
98C2×C31C2×#10011yescharacteristic
99C2×C31#41611yescharacteristic
100C2×C31#41711yescharacteristic
101D31—22no—
102D31—82no—
103C2×#41—312no—
104C22×C8—621no—
105C4⋊Q8C2×D3111yescharacteristic
106#127—311no—
107#124—312no—
108#121—621no—
109#121—621no—
110C4×D4—621no—
111C4×D4—621no—
112C2×C42—311no—
113C4⋊C8—311no—
114C4⋊C8—311no—
115C4⋊C8—621no—
116C4⋊C8C2×D3111yescharacteristic
117C4⋊C8C2×D3111yescharacteristic
118C22⋊C8—621no—
119#97—621no—
120C31#155111yescharacteristic, complemented, Sylow
121#41—1244no—
122C2×Q8C4×D3112yes—
123C2×D4—312no—
124C2×D4—622no—
125C2×D4—621no—
126C2×D4—621no—
127C22×C4—311no—
128C22×C4—311no—
129C22×C4—311no—
130C22×C4—622no—
131C2×C8—21no—
132C2×C8—21no—
133C2×C8—621no—
134C2×C8—621no—
135C2×C8—1242no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C22⋊C4—622no—
139C22⋊C4—622no—
140C42—311no—
141C42—311no—
142C42—311no—
143C42C22×D3111yescharacteristic
144C23—311no—
145C23—622no—
146Q8—42no—
147D4—1242no—
148D4—1244no—
149D4—1241no—
150D4—1241no—
151D4—1241no—
152D4—1241no—
153C2×C4—22no—
154C2×C4—311no—
155C2×C4—311no—
156C2×C4—311no—
157C2×C4—622no—
158C2×C4—621no—
159C2×C4—621no—
160C2×C4—621no—
161C2×C4—621no—
162C2×C4—1244no—
163C2×C4C2×C4×D3111yescharacteristic
164C2×C4D4×D3111yescharacteristic
165C2×C4D4×D3111yescharacteristic
166C8—41no—
167C8—41no—
168C8—1241no—
169C8—1241no—
170C22—312no—
171C22—621no—
172C22—621no—
173C22—1242no—
174C22—1242no—
175C22—1242no—
176C22C22⋊C4×D3111yescharacteristic
177C4—21no—
178C4—42no—
179C4—621no—
180C4—621no—
181C4—621no—
182C4#1175849111yescharacteristic
183C4#1175849311yescharacteristic
184C4#1175849511yescharacteristic
185C4#1175849611yescharacteristic
186C2—622no—
187C2—2482no—
188C2#100×D3111yescharacteristic
189C2#1452104411yescharacteristic
190C2#1452104911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D31
commutatorC2×C4×C31C22×C4
FrattiniC42C22×D31
FittingC31×#333C2
socleC22×C31C2×C22⋊C4
prime radical#14521600C2
cosocleC42×C31C23
hypercenter#333D31
hypocenterC31#1551
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #14521105C2semidirect
3. C4⋊C8×D31C2semidirect
4. #14520798C2semidirect
5. #14520792C2semidirect
6. #14520792C2semidirect
7. C31×#333C2semidirect
95. #333D31semidirect
120. C31#1551semidirect

Maximal subgroups

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

subgroupindex
#145216002
#145211052
C4⋊C8×D312
#145207982
#145207922
C31×#3332
#155131