Finite Group Databasebeta

← #16844219

Subgroups — #16844219

Order 3968.

272 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 81 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#14521106C211yesmaximal, characteristic, complemented
2#14520895C211yesmaximal, characteristic, complemented
3#14520783C214yesmaximal, complemented
4C31×#532C211yesmaximal, characteristic
5C2×#41×C31—21no—
6C31×C4⋊Q8C411yescharacteristic, complemented
7C31×#127C411yescharacteristic, complemented
8C31×#124—21no—
9C31×#121—21no—
10C31×#121C2212yes—
11C4×D4×C31—21no—
12C4×D4×C31C412yescomplemented
13C2×C42×C31C2211yescharacteristic
14C2×C4×Dic31—21no—
15C31⋊#95—21no—
16C31⋊#95C2212yes—
17C22⋊(C31⋊C8)C2212yes—
18C4⋊(C31⋊C8)—21no—
19#11758391—21no—
20#41×C31—44no—
21C2×Q8×C31—21no—
22C2×D4×C31—22no—
23C2×D4×C31—21no—
24C2×D4×C31—21no—
25C2×D4×C31C2×C412yes—
26C22×C4×C31—22no—
27C22×C4×C31D411yescharacteristic
28C22×C4×C31D411yescharacteristic
29C22×C4×C31C2311yescharacteristic
30C22×Dic31—22no—
31C4⋊C4×C31—21no—
32C4⋊C4×C31C2×C412yes—
33C22⋊C4×C31—22no—
34C22⋊C4×C31—22no—
35C42×C31C2×C411yescharacteristic
36C42×C31C2×C411yescharacteristic
37C42×C31D411yescharacteristic
38C42×C31D411yescharacteristic
39C4×Dic31—24no—
40C2×C31⋊C8—22no—
41C23×C31—22no—
42C23×C31C2×D411yescharacteristic
43Q8×C31—42no—
44D4×C31—42no—
45D4×C31—42no—
46D4×C31—44no—
47D4×C31—42no—
48C2×C4×C31—22no—
49C2×C4×C31—22no—
50C2×C4×C31—22no—
51C2×C4×C31—41no—
52C2×C4×C31—44no—
53C2×C4×C31C22⋊C411yescharacteristic
54C2×C4×C31C22⋊C411yescharacteristic
55C2×C4×C31C22⋊C411yescharacteristic
56C2×C4×C31C22⋊C411yescharacteristic
57C2×C4×C31C22×C411yescharacteristic
58C2×C4×C31C2×D411yescharacteristic
59C2×Dic31—24no—
60C2×Dic31—42no—
61C2×Dic31—42no—
62C31⋊C8—42no—
63#1505—311nomaximal, Sylow
64C22×C31—21no—
65C22×C31—21no—
66C22×C31—42no—
67C22×C31—42no—
68C22×C31—42no—
69C22×C31C2×C22⋊C411yescharacteristic
70C22×C31AGL(1,ℤ/8)12yes—
71C4×C31—21no—
72C4×C31—21no—
73C4×C31—21no—
74C4×C31—21no—
75C4×C31—21no—
76C4×C31—42no—
77C4×C31#10412yes—
78Dic31—44no—
79#532D3111yescharacteristic
80#432—311no—
81#376—311no—
82#327—314no—
83C2×C31—22no—
84C2×C31—82no—
85C2×C31#41011yescharacteristic
86C2×C31#41811yescharacteristic
87C2×C31C2×#10411yescharacteristic
88C2×#41—21no—
89C4⋊Q8Dic3111yescharacteristic, complemented
90#127Dic3111yescharacteristic, complemented
91#124—21no—
92#121—21no—
93#121C2×D3112yes—
94C4×D4—21no—
95C4×D4Dic3112yescomplemented
96C2×C42—621no—
97C2×C42C2×D3111yescharacteristic
98C4⋊C8—621no—
99C22⋊C8—312no—
100#97—621no—
101#95—312no—
102#95—621no—
103C31#150511yescharacteristic, complemented, Sylow
104#41—44no—
105C2×Q8—21no—
106C2×D4—22no—
107C2×D4—21no—
108C2×D4—21no—
109C2×D4C2×Dic3112yes—
110C22×C4—22no—
111C22×C4—622no—
112C22×C4C22⋊D3111yescharacteristic
113C22×C4C22⋊D3111yescharacteristic
114C22×C4C22×D3111yescharacteristic
115C2×C8—622no—
116C4⋊C4—21no—
117C4⋊C4C2×Dic3112yes—
118C22⋊C4—22no—
119C22⋊C4—22no—
120C42—624no—
121C42C2×Dic3111yescharacteristic
122C42C2×Dic3111yescharacteristic
123C42C22⋊D3111yescharacteristic
124C42C22⋊D3111yescharacteristic
125C23—22no—
126C23C2×C22⋊D3111yescharacteristic
127Q8—42no—
128D4—42no—
129D4—42no—
130D4—44no—
131D4—42no—
132C2×C4—22no—
133C2×C4—22no—
134C2×C4—22no—
135C2×C4—41no—
136C2×C4—44no—
137C2×C4—624no—
138C2×C4—1242no—
139C2×C4—1242no—
140C2×C4C22⋊Dic3111yescharacteristic
141C2×C4C22⋊Dic3111yescharacteristic
142C2×C4C22⋊Dic3111yescharacteristic
143C2×C4C22⋊Dic3111yescharacteristic
144C2×C4C22×Dic3111yescharacteristic
145C2×C4C2×C22⋊D3111yescharacteristic
146C8—1242no—
147C22—21no—
148C22—21no—
149C22—42no—
150C22—42no—
151C22—42no—
152C22#1175850912yes—
153C22C2×C22⋊Dic3111yescharacteristic
154C4—21no—
155C4—21no—
156C4—21no—
157C4—21no—
158C4—21no—
159C4—42no—
160C4—1244no—
161C4#1175842512yes—
162C2—22no—
163C2—82no—
164C2#1452102311yescharacteristic
165C2#1452105411yescharacteristic
166C2C2×#1175842511yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic31
commutatorC2×C4×C31C22×C4
FrattiniC22×C4C22×D31
Fitting, prime radicalC31×#532C2
socleC22×C31C2×C22⋊C4
cosocleC22×C4×C31C23
hypercenter#532D31
hypocenterC31#1505
LCSG ▷ C2×C4×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C2×C42 ◁ #532

Complements

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

NH ≅ G/Ntype
1. #14521106C2semidirect
2. #14520895C2semidirect
3. #14520783C2semidirect
6. C31×C4⋊Q8C4semidirect
7. C31×#127C4semidirect
12. C4×D4×C31C4semidirect
89. C4⋊Q8Dic31semidirect
90. #127Dic31semidirect
95. C4×D4Dic31semidirect
103. C31#1505semidirect

Maximal subgroups

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

subgroupindex
#145211062
#145208952
#145207832
C31×#5322
#150531