Finite Group Databasebeta

← #16844387

Subgroups — #16844387

Order 3968.

260 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 73 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#14521071C211yesmaximal, characteristic, complemented
3C4⋊C8×D31C211yesmaximal, 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—
11C2×#92469—21no—
12C2×C8×D31—21no—
13#11758472—21no—
14#11758472C412yes—
15#11758470—21no—
16#11758470C412yes—
17#11758451C2211yescharacteristic
18C42×D31C2211yescharacteristic
19C31×C4⋊C8C2211yescharacteristic
20C31×C4⋊C8C2211yescharacteristic
21Dic31⋊C8—21no—
22Dic31⋊C8—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—
48#92469—42no—
49C8×D31—42no—
50C22×D31—22no—
51C22×D31C22⋊C411yescharacteristic
52Q8×C31—41no—
53Q8×C31—41no—
54C2×C4×C31—22no—
55C2×C4×C31C22×C411yescharacteristic
56C2×C4×C31C2×D411yescharacteristic
57C2×C4×C31C2×D411yescharacteristic
58C2×Dic31C22⋊C411yescharacteristic
59C2×Dic31C22⋊C411yescharacteristic
60C2×Dic31C22⋊C411yescharacteristic
61D124—42no—
62D124—44no—
63D124—41no—
64D124—41no—
65D124—41no—
66D124—41no—
67C4×D31—21no—
68C4×D31—21no—
69C4×D31—41no—
70C4×D31—44no—
71C4×D31D812yes—
72C4×D31SD1612yes—
73C8×C31—41no—
74C8×C31—41no—
75C31⋊C8—41no—
76C31⋊C8—41no—
77#1547—311nomaximal, Sylow
78C22×C31C2×C22⋊C411yescharacteristic
79C2×D31—21no—
80C2×D31—21no—
81C2×D31—42no—
82C2×D31—42no—
83C2×D31—42no—
84C2×D31#10212yes—
85C4×C31—21no—
86C4×C31—42no—
87C4×C31C2×D811yescharacteristic
88C4×C31C2×SD1611yescharacteristic
89C4×C31AGL(1,ℤ/8)11yescharacteristic
90C4×C31#13711yescharacteristic
91Dic31—21no—
92Dic31—21no—
93Dic31#10212yes—
94#532—311no—
95#423—311no—
96C2×C4⋊C8—311no—
97#332—311no—
98#332D3111yescharacteristic, complemented
99#331—311no—
100#331—311no—
101C2×C31#41311yescharacteristic
102C2×C31C2×#10211yescharacteristic
103C2×C31#41711yescharacteristic
104D31—22no—
105D31—82no—
106C2×#41—621no—
107C2×M16—621no—
108C22×C8—621no—
109C4⋊Q8C2×D3111yescharacteristic
110#127—311no—
111#124—621no—
112#121—312no—
113#121—621no—
114C4×D4—312no—
115C4×D4—621no—
116C2×C42—311no—
117C4⋊C8—311no—
118C4⋊C8—311no—
119C4⋊C8—621no—
120C4⋊C8—621no—
121C4⋊C8C2×D3111yescharacteristic
122C4⋊C8C2×D3111yescharacteristic
123C31#154711yescharacteristic, complemented, Sylow
124#41—1242no—
125#41—1242no—
126C2×Q8—21no—
127C2×D4—312no—
128C2×D4—622no—
129C2×D4—621no—
130C2×D4—621no—
131C22×C4—311no—
132C22×C4—311no—
133C22×C4—311no—
134C22×C4—622no—
135M16—1242no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—621no—
139C2×C8—621no—
140C2×C8—1242no—
141C4⋊C4—21no—
142C4⋊C4C4×D3112yes—
143C22⋊C4—622no—
144C22⋊C4—622no—
145C42—311no—
146C42—311no—
147C42—311no—
148C42C22×D3111yescharacteristic
149C23—311no—
150C23—622no—
151Q8—41no—
152Q8—41no—
153D4—1242no—
154D4—1244no—
155D4—1241no—
156D4—1241no—
157D4—1241no—
158D4—1241no—
159C2×C4—22no—
160C2×C4—311no—
161C2×C4—312no—
162C2×C4—312no—
163C2×C4—311no—
164C2×C4—311no—
165C2×C4—621no—
166C2×C4—621no—
167C2×C4—1241no—
168C2×C4—1244no—
169C2×C4C2×C4×D3111yescharacteristic
170C2×C4D4×D3111yescharacteristic
171C2×C4D4×D3111yescharacteristic
172C8—41no—
173C8—41no—
174C8—1241no—
175C8—1241no—
176C22—312no—
177C22—621no—
178C22—621no—
179C22—1242no—
180C22—1242no—
181C22—1242no—
182C22C22⋊C4×D3111yescharacteristic
183C4—21no—
184C4—42no—
185C4—312no—
186C4—621no—
187C4—621no—
188C4D8×D3111yescharacteristic
189C4SD16×D3111yescharacteristic
190C4#1175849111yescharacteristic
191C4#1175849511yescharacteristic
192C2—622no—
193C2—2482no—
194C2#1452103211yescharacteristic
195C2#102×D3111yescharacteristic
196C2#1452104911yescharacteristic
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#1547
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. #14521071C2semidirect
3. C4⋊C8×D31C2semidirect
4. #14520795C2semidirect
5. #14520792C2semidirect
6. #14520792C2semidirect
7. C31×#332C2semidirect
98. #332D31semidirect
123. C31#1547semidirect

Maximal subgroups

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

subgroupindex
#145216002
#145210712
C4⋊C8×D312
#145207952
#145207922
C31×#3322
#154731