Finite Group Databasebeta

← #16847777

Subgroups — #16847777

Order 3968.

154 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 47 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#14521490C211yesmaximal, characteristic, complemented
2#14521485C211yesmaximal, characteristic
3#14521167C211yesmaximal, characteristic, complemented
4#14520870C211yesmaximal, characteristic, complemented
5#14520865C211yesmaximal, characteristic, complemented
6#14520862C211yesmaximal, characteristic, complemented
7C31×#495C211yesmaximal, characteristic, complemented
8C2×Q16×C31C2211yescharacteristic
9C2×SD16×C31—21no—
10C2×D8×C31C2211yescharacteristic
11C31×#124—21no—
12#11758481C2211yescharacteristic
13#11758478—21no—
14C4×C8×C31C2211yescharacteristic
15#11758417—21no—
16#11758416—21no—
17#11758415—21no—
18#11758414—21no—
19#11758407C2211yescharacteristic
20#11758400C2211yescharacteristic
21#11758400C2211yescharacteristic
22#11758393—21no—
23C2×Q8×C31—21no—
24C2×D4×C31—21no—
25#92495—21no—
26Q16×C31—21no—
27Q16×C31—21no—
28SD16×C31—41no—
29SD16×C31—41no—
30D8×C31—21no—
31D8×C31—21no—
32C2×C8×C31D411yescharacteristic
33C2×C8×C31C2311yescharacteristic
34C22⋊C4×C31—42no—
35C42×C31D411yescharacteristic
36#92474—21no—
37Dic124D411yescharacteristic
38D248D411yescharacteristic
39#92470—21no—
40#92469—41no—
41C8×D31—41no—
42C31⋊C16—21no—
43C31⋊C16—21no—
44C23×C31—41no—
45Q8×C31—41no—
46Q8×C31—41no—
47D4×C31—41no—
48D4×C31—41no—
49C2×C4×C31—21no—
50C2×C4×C31—41no—
51C2×C4×C31C2×D411yescharacteristic
52C22⋊D31—41no—
53D124—21no—
54C4×D31—41no—
55Dic62—21no—
56C8×C31D811yescharacteristic
57C8×C31D811yescharacteristic
58C8×C31C2×D411yescharacteristic
59C8×C31#4111yescharacteristic
60C31⋊C8—41no—
61#2212—311nomaximal, Sylow
62C22×C31—82no—
63C22×C31—81no—
64C22×C31AGL(1,ℤ/8)11yescharacteristic
65C2×D31—41no—
66C4×C31—41no—
67C4×C31—81no—
68C4×C31#12111yescharacteristic
69C4×C31C2×D811yescharacteristic
70Dic31—41no—
71#510—311no—
72#509—311no—
73#495D3111yescharacteristic, complemented
74#443—311no—
75#364—311no—
76#362—311no—
77#361—311no—
78C2×C31—21no—
79C2×C31—161no—
80C2×C31#45911yescharacteristic
81D31—81no—
82#135—311no—
83C2×Q16C2×D3111yescharacteristic
84C2×SD16—21no—
85C2×D8C2×D3111yescharacteristic
86#131—621no—
87#124—21no—
88Q32—621no—
89SD32—621no—
90SD32—621no—
91D16—621no—
92M32—311no—
93M32—311no—
94#108—311no—
95#104—621no—
96C4×C8C2×D3111yescharacteristic
97C31#221211yescharacteristic, complemented, Sylow
98#41—621no—
99C2×Q8—21no—
100C2×D4—21no—
101Q16—21no—
102Q16—21no—
103Q16—311no—
104SD16—41no—
105SD16—41no—
106SD16—621no—
107D8—21no—
108D8—21no—
109D8—311no—
110M16—621no—
111M16—1241no—
112C2×C8—1241no—
113C2×C8C22⋊D3111yescharacteristic
114C2×C8C22×D3111yescharacteristic
115C22⋊C4—42no—
116C42C22⋊D3111yescharacteristic
117C16—621no—
118C16—621no—
119C23—41no—
120Q8—41no—
121Q8—41no—
122Q8—621no—
123D4—41no—
124D4—41no—
125D4—621no—
126D4—1241no—
127C2×C4—21no—
128C2×C4—41no—
129C2×C4—1241no—
130C2×C4C2×C22⋊D3111yescharacteristic
131C8—1241no—
132C8#9247911yescharacteristic
133C8#9247911yescharacteristic
134C8D4×D3111yescharacteristic
135C8#9249711yescharacteristic
136C22—82no—
137C22—81no—
138C22—1241no—
139C22#1175850911yescharacteristic
140C4—41no—
141C4—81no—
142C4—1241no—
143C4C2×#9247911yescharacteristic
144C4#1175851511yescharacteristic
145C2—21no—
146C2—161no—
147C2—2481no—
148C2#1452124111yescharacteristic
subgroupG/H
centerC2#14521241
commutator, cosocleC2×C8×C31C23
FrattiniC2×C8C22×D31
FittingC31×#495C2
socleC2×C31#459
prime radical#14521485C2
hypercenter#495D31
hypocenterC31#2212
LCSG ▷ C2×C8×C31 ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #14521490C2semidirect
3. #14521167C2semidirect
4. #14520870C2semidirect
5. #14520865C2semidirect
6. #14520862C2semidirect
7. C31×#495C2semidirect
73. #495D31semidirect
97. C31#2212semidirect

Maximal subgroups

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

subgroupindex
#145214902
#145214852
#145211672
#145208702
#145208652
#145208622
C31×#4952
#221231