Finite Group Databasebeta

← #16847594

Subgroups — #16847594

Order 3968.

144 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 53 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#14521479C211yesmaximal, characteristic
2#14521166C211yesmaximal, characteristic, complemented
3#14521165C211yesmaximal, characteristic, complemented
4#14520878C211yesmaximal, characteristic, complemented
5#14520857C211yesmaximal, characteristic, complemented
6#14520824C211yesmaximal, characteristic, complemented
7C31×#359C211yesmaximal, characteristic, complemented
8C31×#135C2211yescharacteristic
9#11758525—21no—
10#11758484—21no—
11#11758481C2211yescharacteristic
12C2×C16×C31C2211yescharacteristic
13C31×#108C2211yescharacteristic
14#11758425—21no—
15#11758417C411yescharacteristic, complemented
16#11758416C411yescharacteristic, complemented
17#11758415C411yescharacteristic, complemented
18#11758414C411yescharacteristic, complemented
19#11758413—21no—
20#11758407C2211yescharacteristic
21C8×Dic31C2211yescharacteristic
22C2×C31⋊C16C2211yescharacteristic
23#41×C31—21no—
24#92495—21no—
25Q16×C31C2×C411yescharacteristic
26SD16×C31—21no—
27D8×C31C2×C411yescharacteristic
28M16×C31—21no—
29C2×C8×C31C2311yescharacteristic
30C4×Dic31D411yescharacteristic
31#92474—21no—
32#92474—41no—
33C2×C31⋊C8—41no—
34C2×C31⋊C8D411yescharacteristic
35Dic124C2×C411yescharacteristic
36D248C2×C411yescharacteristic
37#92470—21no—
38#92469—41no—
39C8×D31—41no—
40C16×C31—21no—
41C31⋊C16C2×C411yescharacteristic
42C31⋊C16C2×C411yescharacteristic
43Q8×C31—21no—
44D4×C31—21no—
45D4×C31—41no—
46C2×C4×C31—41no—
47C2×C4×C31C2×D411yescharacteristic
48C22⋊D31—41no—
49C2×Dic31—21no—
50D124—21no—
51C4×D31—41no—
52Dic62—21no—
53C8×C31—41no—
54C8×C31C22×C411yescharacteristic
55C8×C31#4111yescharacteristic
56C31⋊C8—41no—
57C31⋊C8D811yescharacteristic
58C31⋊C8D811yescharacteristic
59#2179—311nomaximal, Sylow
60C22×C31—41no—
61C22×C31#13511yescharacteristic
62C2×D31—41no—
63C4×C31—41no—
64C4×C31C4×D411yescharacteristic
65C4×C31C2×D811yescharacteristic
66Dic31—41no—
67Dic31—41no—
68#508—311no—
69#443—311no—
70#443—311no—
71#368—311no—
72#359—311no—
73#359D3111yescharacteristic, complemented
74#346—311no—
75C2×C31—21no—
76C2×C31—81no—
77C2×C31C4×D811yescharacteristic
78D31—81no—
79#135—311no—
80#135C2×D3111yescharacteristic
81#131—621no—
82#131—621no—
83Q32—311no—
84SD32—311no—
85SD32—311no—
86D16—311no—
87C2×C16—311no—
88C2×C16C2×D3111yescharacteristic
89#108—311no—
90#108C2×D3111yescharacteristic
91#104—621no—
92#104—621no—
93C4×C8—311no—
94C31#217911yescharacteristic, complemented, Sylow
95#41—21no—
96#41—621no—
97Q16—311no—
98Q16C4×D3111yescharacteristic
99SD16—21no—
100SD16—621no—
101D8—311no—
102D8C4×D3111yescharacteristic
103M16—21no—
104M16—621no—
105M16—1241no—
106M16—1241no—
107C2×C8—311no—
108C2×C8—1241no—
109C2×C8—1241no—
110C2×C8C22×D3111yescharacteristic
111C42—311no—
112C16—21no—
113C16—311no—
114C16—311no—
115Q8—21no—
116Q8—621no—
117D4—21no—
118D4—41no—
119D4—621no—
120D4—1241no—
121C2×C4—41no—
122C2×C4—621no—
123C2×C4—1241no—
124C2×C4D4×D3111yescharacteristic
125C8—41no—
126C8—311no—
127C8—311no—
128C8—1241no—
129C8C2×C4×D3111yescharacteristic
130C8#9249711yescharacteristic
131C22—41no—
132C22—1241no—
133C22#1175849311yescharacteristic
134C4—41no—
135C4—1241no—
136C4—1241no—
137C4(C22⋊D31)⋊C411yescharacteristic
138C4D8×D3111yescharacteristic
139C2—21no—
140C2—81no—
141C2—2481no—
142C2#1452112911yescharacteristic
subgroupG/H
centerC4D8×D31
commutatorC8×C31C22×C4
FrattiniC2×C8C22×D31
FittingC31×#359C2
socleC2×C31C4×D8
prime radical#14521479C2
cosocleC2×C8×C31C23
hypercenter#359D31
hypocenterC31#2179
LCSG ▷ C8×C31 ▷ C4×C31 ▷ C2×C31 ▷ C31
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8 ◁ #359

Complements

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

NH ≅ G/Ntype
2. #14521166C2semidirect
3. #14521165C2semidirect
4. #14520878C2semidirect
5. #14520857C2semidirect
6. #14520824C2semidirect
7. C31×#359C2semidirect
15. #11758417C4semidirect
16. #11758416C4semidirect
17. #11758415C4semidirect
18. #11758414C4semidirect
73. #359D31semidirect
94. C31#2179semidirect

Maximal subgroups

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

subgroupindex
#145214792
#145211662
#145211652
#145208782
#145208572
#145208242
C31×#3592
#217931