Finite Group Databasebeta

← #16844218

Subgroups — #16844218

Order 3968.

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

normal subgroups only

This group has 272 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#14521599C211yesmaximal, characteristic
2#14521106C211yesmaximal, characteristic, complemented
3#14520782C214yesmaximal, complemented
4C31×#376C211yesmaximal, characteristic, complemented
5C2×#92495—21no—
6C2×C42×C31—21no—
7C2×C42×C31C2211yescharacteristic
8#11758507—21no—
9#11758507C2212yes—
10#11758452—21no—
11#11758451C411yescharacteristic, complemented
12C4×D124—21no—
13C4×D124C412yescomplemented
14#11758446C411yescharacteristic, complemented
15C31×#95—21no—
16C31×#95C2212yes—
17C22⋊(C31⋊C8)C2212yes—
18C4⋊(C31⋊C8)—21no—
19#11758391—21no—
20C22×C4×C31—22no—
21C22×C4×C31D411yescharacteristic
22C22×C4×C31D411yescharacteristic
23C22×C4×C31C2311yescharacteristic
24C2×C22⋊D31—22no—
25#92495—44no—
26C2×D124—21no—
27C2×D124—21no—
28C2×D124C2×C412yes—
29C2×C4×D31—22no—
30C2×Dic62—21no—
31C42×C31—24no—
32C42×C31C2×C411yescharacteristic
33C42×C31C2×C411yescharacteristic
34C42×C31D411yescharacteristic
35C42×C31D411yescharacteristic
36(C2×D31)⋊C4—22no—
37(C2×D31)⋊C4—22no—
38C4⋊Dic31—21no—
39C4⋊Dic31C2×C412yes—
40C2×C31⋊C8—22no—
41C23×C31C2×D411yescharacteristic
42C22×D31—22no—
43C2×C4×C31—22no—
44C2×C4×C31—22no—
45C2×C4×C31—24no—
46C2×C4×C31—41no—
47C2×C4×C31—42no—
48C2×C4×C31—42no—
49C2×C4×C31C22⋊C411yescharacteristic
50C2×C4×C31C22⋊C411yescharacteristic
51C2×C4×C31C22⋊C411yescharacteristic
52C2×C4×C31C22⋊C411yescharacteristic
53C2×C4×C31C22×C411yescharacteristic
54C2×C4×C31C2×D411yescharacteristic
55C22⋊D31—44no—
56C2×Dic31—22no—
57D124—42no—
58D124—42no—
59D124—42no—
60C4×D31—44no—
61Dic62—42no—
62C31⋊C8—42no—
63#1505—311nomaximal, Sylow
64C22×C31—21no—
65C22×C31—21no—
66C22×C31C2×C22⋊C411yescharacteristic
67C22×C31AGL(1,ℤ/8)12yes—
68C2×D31—42no—
69C2×D31—42no—
70C2×D31—42no—
71C4×C31—21no—
72C4×C31—21no—
73C4×C31—21no—
74C4×C31—21no—
75C4×C31—21no—
76C4×C31—44no—
77C4×C31#10412yes—
78Dic31—42no—
79#532—311no—
80#432—311no—
81#376D3111yescharacteristic, complemented
82#327—314no—
83C2×C31—22no—
84C2×C31#41011yescharacteristic
85C2×C31#41811yescharacteristic
86C2×C31C2×#10411yescharacteristic
87D31—82no—
88C2×#41—621no—
89C4⋊Q8—311no—
90#127—311no—
91#124—621no—
92#121—312no—
93#121—621no—
94C4×D4—312no—
95C4×D4—621no—
96C2×C42—21no—
97C2×C42C2×D3111yescharacteristic
98C4⋊C8—621no—
99C22⋊C8—312no—
100#97—621no—
101#95—21no—
102#95C2×D3112yes—
103C31#150511yescharacteristic, complemented, Sylow
104#41—1244no—
105C2×Q8—621no—
106C2×D4—312no—
107C2×D4—622no—
108C2×D4—621no—
109C2×D4—621no—
110C22×C4—22no—
111C22×C4—622no—
112C22×C4C22⋊D3111yescharacteristic
113C22×C4C22⋊D3111yescharacteristic
114C22×C4C22×D3111yescharacteristic
115C2×C8—622no—
116C4⋊C4—312no—
117C4⋊C4—621no—
118C22⋊C4—622no—
119C22⋊C4—622no—
120C42—24no—
121C42C4×D3111yescharacteristic
122C42C4×D3111yescharacteristic
123C42D12411yescharacteristic
124C42D12411yescharacteristic
125C23—622no—
126C23C2×C22⋊D3111yescharacteristic
127Q8—1242no—
128D4—1242no—
129D4—1242no—
130D4—1244no—
131D4—1242no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—24no—
135C2×C4—41no—
136C2×C4—42no—
137C2×C4—42no—
138C2×C4—622no—
139C2×C4—1244no—
140C2×C4(C2×D31)⋊C411yescharacteristic
141C2×C4(C2×D31)⋊C411yescharacteristic
142C2×C4(C2×D31)⋊C411yescharacteristic
143C2×C4(C2×D31)⋊C411yescharacteristic
144C2×C4C2×C4×D3111yescharacteristic
145C2×C4C2×D12411yescharacteristic
146C8—1242no—
147C22—21no—
148C22—21no—
149C22—1242no—
150C22—1242no—
151C22—1242no—
152C22C2×(C2×D31)⋊C411yescharacteristic
153C22#1175852612yes—
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—21no—
159C4—44no—
160C4—1242no—
161C4#1175839312yes—
162C2—22no—
163C2—2482no—
164C2#1452102211yescharacteristic
165C2#1452105311yescharacteristic
166C2C2×#1175839311yescharacteristic
subgroupG/H
centerC22C2×(C2×D31)⋊C4
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
FittingC31×#376C2
socleC22×C31C2×C22⋊C4
prime radical#14521599C2
cosocleC22×C4×C31C23
hypercenter#376D31
hypocenterC31#1505
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C42 ◁ #376

Complements

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

NH ≅ G/Ntype
2. #14521106C2semidirect
3. #14520782C2semidirect
4. C31×#376C2semidirect
11. #11758451C4semidirect
13. C4×D124C4semidirect
14. #11758446C4semidirect
81. #376D31semidirect
103. C31#1505semidirect

Maximal subgroups

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

subgroupindex
#145215992
#145211062
#145207822
C31×#3762
#150531