Finite Group Databasebeta

← #16847838

Subgroups — #16847838

Order 3968.

144 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 45 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#14521465C211yesmaximal, characteristic, complemented
2#14521321C211yesmaximal, characteristic, complemented
3#14521316C211yesmaximal, characteristic
4#14520879C211yesmaximal, characteristic, complemented
5#14520865C211yesmaximal, characteristic, complemented
6#14520862C211yesmaximal, characteristic, complemented
7C2×C31×SD32C211yesmaximal, characteristic, complemented
8C2×Q16×C31C2211yescharacteristic
9C2×D8×C31C2211yescharacteristic
10#11758519—21no—
11#11758509—21no—
12#11758478C2211yescharacteristic
13C31×SD32—21no—
14C31×SD32—21no—
15C2×C16×C31C2211yescharacteristic
16#11758424—21no—
17#11758421—21no—
18#11758407C2211yescharacteristic
19#11758407C2211yescharacteristic
20#11758400C2211yescharacteristic
21#11758386—21no—
22C16×D31—21no—
23C2×Q8×C31—21no—
24C2×D4×C31—21no—
25#92495D411yescharacteristic
26Q16×C31—21no—
27Q16×C31—21no—
28D8×C31—21no—
29D8×C31—21no—
30C2×C8×C31C2311yescharacteristic
31#92482—41no—
32#92481—41no—
33#92480—41no—
34#92479—41no—
35#92474—21no—
36#92474—21no—
37#92474D411yescharacteristic
38#92469—21no—
39C8×D31—21no—
40C16×C31D411yescharacteristic
41C16×C31D411yescharacteristic
42C31⋊C16—21no—
43C23×C31—41no—
44Q8×C31—41no—
45Q8×C31—41no—
46D4×C31—41no—
47D4×C31—41no—
48C2×C4×C31—41no—
49C2×C4×C31C2×D411yescharacteristic
50C22⋊D31—21no—
51D124D811yescharacteristic
52C4×D31—21no—
53Dic62D811yescharacteristic
54C8×C31C2×D411yescharacteristic
55C8×C31#4111yescharacteristic
56C31⋊C8—21no—
57C31⋊C8—41no—
58C31⋊C8—41no—
59#2223—311nomaximal, Sylow
60C22×C31—81no—
61C22×C31—161no—
62C22×C31#13511yescharacteristic
63C2×D31—21no—
64C4×C31—81no—
65C4×C31#12111yescharacteristic
66C4×C31C2×D811yescharacteristic
67Dic31—21no—
68C2×SD32D3111yescharacteristic, complemented
69#504—311no—
70#473—311no—
71#472—311no—
72#368—311no—
73#362—311no—
74#361—311no—
75C2×C31—21no—
76C2×C31—161no—
77C2×C31#46611yescharacteristic
78D31—41no—
79#137—621no—
80AGL(1,ℤ/8)—621no—
81C2×Q16C2×D3111yescharacteristic
82C2×D8C2×D3111yescharacteristic
83#131—311no—
84SD32—21no—
85SD32—21no—
86M32—311no—
87M32—621no—
88C2×C16—621no—
89C2×C16C2×D3111yescharacteristic
90#108—311no—
91#108—311no—
92#101—621no—
93#100—621no—
94C31#222311yescharacteristic, complemented, Sylow
95#41—311no—
96C2×Q8—21no—
97C2×D4—21no—
98Q16—21no—
99Q16—21no—
100Q16—1241no—
101SD16—1241no—
102SD16—1241no—
103D8—21no—
104D8—21no—
105D8—1241no—
106M16—311no—
107M16—621no—
108M16—621no—
109M16—621no—
110C2×C8—621no—
111C2×C8C22×D3111yescharacteristic
112C16—621no—
113C16C22⋊D3111yescharacteristic
114C16C22⋊D3111yescharacteristic
115C23—41no—
116Q8—41no—
117Q8—41no—
118Q8—311no—
119D4—41no—
120D4—41no—
121D4—311no—
122D4—621no—
123C2×C4—41no—
124C2×C4—621no—
125C2×C4D4×D3111yescharacteristic
126C8—621no—
127C8—1241no—
128C8—1241no—
129C8#9249711yescharacteristic
130C8C2×C22⋊D3111yescharacteristic
131C22—81no—
132C22—161no—
133C22—621no—
134C22#1175848911yescharacteristic
135C4—81no—
136C4—621no—
137C4D8×D3111yescharacteristic
138C4#1175851511yescharacteristic
139C2—21no—
140C2—161no—
141C2—1241no—
142C2#1452128211yescharacteristic
subgroupG/H
centerC2#14521282
commutator, cosocleC2×C8×C31C23
FrattiniC2×C8C22×D31
FittingC2×C31×SD32C2
socleC2×C31#466
prime radical#14521316C2
hypercenterC2×SD32D31
hypocenterC31#2223
LCSG ▷ C2×C8×C31 ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #14521465C2semidirect
2. #14521321C2semidirect
4. #14520879C2semidirect
5. #14520865C2semidirect
6. #14520862C2semidirect
7. C2×C31×SD32C2semidirect
68. C2×SD32D31semidirect
94. C31#2223semidirect

Maximal subgroups

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

subgroupindex
#145214652
#145213212
#145213162
#145208792
#145208652
#145208622
C2×C31×SD322
#222331