Finite Group Databasebeta

← #16844810

Subgroups — #16844810

Order 3968.

210 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 210 conjugacy classes of subgroups — too many to draw. Only its 57 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#14521778C211yesmaximal, characteristic, complemented
2#14521396C211yesmaximal, characteristic
3#14521250C211yesmaximal, characteristic
4#14521249C211yesmaximal, characteristic
5#14520796C211yesmaximal, characteristic, complemented
6#14520781C211yesmaximal, characteristic, complemented
7C31×Q8⋊C8C211yesmaximal, characteristic, complemented
8C4×Q8×C31C2211yescharacteristic
9Q8×Dic31—21no—
10C2×#92481—21no—
11C2×#92470—21no—
12#11758467—21no—
13#11758467—22no—
14#11758451C2211yescharacteristic
15#11758446—21no—
16#11758446C2211yescharacteristic
17C4×Dic62—21no—
18C4×Dic62C2211yescharacteristic
19C31×C4⋊C8C2211yescharacteristic
20C4×C8×C31C2211yescharacteristic
21#11758409—22no—
22#11758409—21no—
23#11758397—21no—
24C4⋊(C31⋊C8)C2211yescharacteristic
25C2×Q8×C31D411yescharacteristic
26C2×D124—21no—
27C2×D124—21no—
28C2×D124—21no—
29C2×Dic62—21no—
30C2×Dic62D411yescharacteristic
31C2×C8×C31—21no—
32C2×C8×C31—21no—
33C4⋊C4×C31—21no—
34C4⋊C4×C31D411yescharacteristic
35C42×C31—21no—
36C42×C31C2311yescharacteristic
37#92481—42no—
38C4⋊Dic31—22no—
39C4⋊Dic31—22no—
40C4⋊Dic31—21no—
41C4⋊Dic31D411yescharacteristic
42C4⋊Dic31D412yes—
43Dic31⋊C4—22no—
44Dic31⋊C4—21no—
45C4×Dic31—22no—
46C4×Dic31—21no—
47C2×C31⋊C8—21no—
48#92470—42no—
49C22×D31—41no—
50Q8×C31—21no—
51Q8×C31SD1612yescomplemented
52C2×C4×C31—21no—
53C2×C4×C31—21no—
54C2×C4×C31C2×D411yescharacteristic
55C2×C4×C31C2×D411yescharacteristic
56C2×C4×C31C2×D411yescharacteristic
57C2×Dic31—21no—
58C2×Dic31—21no—
59C2×Dic31—22no—
60D124—42no—
61D124—41no—
62D124—41no—
63D124—41no—
64D124—41no—
65Dic62—21no—
66Dic62—21no—
67Dic62—41no—
68Dic62—41no—
69C8×C31—41no—
70C8×C31—41no—
71C31⋊C8—41no—
72#1626—311nomaximal, Sylow
73C22×C31#12011yescharacteristic
74C2×D31—81no—
75C2×D31—81no—
76C2×D31—81no—
77C4×C31—22no—
78C4×C31—21no—
79C4×C31—41no—
80C4×C31C2×SD1611yescharacteristic
81C4×C31#13511yescharacteristic
82C4×C31AGL(1,ℤ/8)11yescharacteristic
83C4×C31#13711yescharacteristic
84Dic31—41no—
85Dic31—42no—
86Dic31—41no—
87#557—311no—
88#486—311no—
89#460—311no—
90#460—311no—
91#332—311no—
92Q8⋊C8—311no—
93Q8⋊C8D3111yescharacteristic, complemented
94C2×C31#44811yescharacteristic
95C2×C31#44911yescharacteristic
96C2×C31#45411yescharacteristic
97D31—161no—
98C2×SD16—621no—
99C2×SD16—621no—
100C4⋊Q8—311no—
101C4⋊Q8—621no—
102#127—311no—
103#125—622no—
104#125—621no—
105C4×Q8—311no—
106C4×Q8—621no—
107C4×Q8—621no—
108C4×Q8C2×D3111yescharacteristic
109C4⋊C8—311no—
110C4⋊C8C2×D3111yescharacteristic
111#102—621no—
112#102—622no—
113#102—621no—
114C4×C8C2×D3111yescharacteristic
115C31#162611yescharacteristic, complemented, Sylow
116C2×Q8—311no—
117C2×Q8—621no—
118C2×Q8D12411yescharacteristic
119C2×D4—621no—
120C2×D4—621no—
121C2×D4—621no—
122SD16—1242no—
123SD16—1242no—
124C2×C8—21no—
125C2×C8—21no—
126C2×C8—621no—
127C4⋊C4—21no—
128C4⋊C4—311no—
129C4⋊C4—312no—
130C4⋊C4—622no—
131C4⋊C4—622no—
132C4⋊C4—622no—
133C4⋊C4—621no—
134C4⋊C4—621no—
135C4⋊C4D12411yescharacteristic
136C42—21no—
137C42—622no—
138C42—621no—
139C42C22×D3111yescharacteristic
140C23—1241no—
141Q8—21no—
142Q8—621no—
143Q8—621no—
144Q8—1241no—
145Q8—1241no—
146Q8#9247012yescomplemented
147D4—1242no—
148D4—1241no—
149D4—1241no—
150D4—1241no—
151D4—1241no—
152C2×C4—21no—
153C2×C4—21no—
154C2×C4—621no—
155C2×C4—622no—
156C2×C4—621no—
157C2×C4C2×D12411yescharacteristic
158C2×C4D4×D3111yescharacteristic
159C2×C4D4×D3111yescharacteristic
160C8—41no—
161C8—41no—
162C8—1241no—
163C22—2481no—
164C22—2481no—
165C22—2481no—
166C22#1175845911yescharacteristic
167C4—22no—
168C4—21no—
169C4—41no—
170C4—1241no—
171C4—1242no—
172C4—1241no—
173C4C2×#9247011yescharacteristic
174C4#1175848611yescharacteristic
175C4#1175849111yescharacteristic
176C4#1175849611yescharacteristic
177C2—4961no—
178C2#1452119011yescharacteristic
179C2#1452119711yescharacteristic
180C2#1452122311yescharacteristic
subgroupG/H
centerC22#11758459
commutator, cosocleC42×C31C23
FrattiniC42C22×D31
FittingC31×Q8⋊C8C2
socleC22×C31#120
prime radical#11758451C22
hypercenterQ8⋊C8D31
hypocenterC31#1626
LCSG ▷ C42×C31 ▷ C22×C31 ▷ C31
UCSC1 ◁ C22 ◁ C42 ◁ Q8⋊C8

Complements

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

NH ≅ G/Ntype
1. #14521778C2semidirect
5. #14520796C2semidirect
6. #14520781C2semidirect
7. C31×Q8⋊C8C2semidirect
51. Q8×C31SD16semidirect
93. Q8⋊C8D31semidirect
115. C31#1626semidirect
146. Q8#92470semidirect

Maximal subgroups

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

subgroupindex
#145217782
#145213962
#145212502
#145212492
#145207962
#145207812
C31×Q8⋊C82
#162631