Finite Group Databasebeta

← #49142385

Subgroups — #49142385

Order 36544.

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

normal subgroups only

This group has 104 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#32912714C211yesmaximal, characteristic
2#32912702C211yesmaximal, characteristic, complemented
3#32912701C211yesmaximal, characteristic, complemented
4#32912629C211yesmaximal, characteristic, complemented
5#32912622C211yesmaximal, characteristic, complemented
6#32912605C211yesmaximal, characteristic, complemented
7#104×C571C211yesmaximal, characteristic, complemented
8#22603733C2211yescharacteristic
9#22603723C411yescharacteristic, complemented
10#22603721C411yescharacteristic, complemented
11#22603720C411yescharacteristic, complemented
12#22603718C411yescharacteristic, complemented
13#22603717—21no—
14#22603717C2211yescharacteristic
15#22603716—21no—
16C2×C571⋊C8—21no—
17C2×C571⋊C8C2211yescharacteristic
18C2×C571⋊C8C2211yescharacteristic
19C8×D571—21no—
20#41×C571C2211yescharacteristic
21M16×C571C2211yescharacteristic
22C42×C571C2211yescharacteristic
23Dic1142C2×C411yescharacteristic
24D2284C2×C411yescharacteristic
25C22⋊D571—21no—
26C4×D571—21no—
27C571⋊C8—21no—
28C571⋊C8C2×C411yescharacteristic
29C571⋊C8C2×C411yescharacteristic
30C571⋊C8D411yescharacteristic
31C571⋊C8D411yescharacteristic
32Q8×C571C2×C411yescharacteristic
33D4×C571—21no—
34D4×C571C2×C411yescharacteristic
35C2×C4×C571—21no—
36C2×C4×C571—21no—
37C2×C4×C571C2311yescharacteristic
38C8×C571—21no—
39C22×C571—21no—
40C22×C571#4111yescharacteristic
41C2×D571—21no—
42C4×C571—21no—
43C4×C571—41no—
44C4×C571C22×C411yescharacteristic
45C4×C571C2×D411yescharacteristic
46Dic571—21no—
47C2×C571—21no—
48C2×C571—41no—
49C2×C571C4×D411yescharacteristic
50D571—41no—
51C571#44411yescharacteristic, complemented, Sylow
52#444—5711nomaximal, Sylow
53#135—5711no—
54#131—5711no—
55#131—5711no—
56#108—5711no—
57#104—5711no—
58#104D57111yescharacteristic, complemented
59#97—5711no—
60#41—5711no—
61#41C2×D57111yescharacteristic
62Q16—5711no—
63SD16—5711no—
64SD16—5711no—
65D8—5711no—
66M16—5711no—
67M16—11421no—
68M16—11421no—
69M16C2×D57111yescharacteristic
70C2×C8—5711no—
71C2×C8—5711no—
72C2×C8—11421no—
73C2×C8—11421no—
74C42C2×D57111yescharacteristic
75Q8—5711no—
76Q8C4×D57111yescharacteristic
77D4—21no—
78D4—5711no—
79D4—11421no—
80D4C4×D57111yescharacteristic
81C2×C4—21no—
82C2×C4—21no—
83C2×C4—11421no—
84C2×C4C22×D57111yescharacteristic
85C8—21no—
86C8—5711no—
87C8—5711no—
88C8—5711no—
89C8—5711no—
90C8—11421no—
91C22—21no—
92C22—11421no—
93C22#2260373211yescharacteristic
94C4—21no—
95C4—41no—
96C4—11421no—
97C4C2×C4×D57111yescharacteristic
98C4D4×D57111yescharacteristic
99C2—21no—
100C2—41no—
101C2—22841no—
102C2(C22⋊D571)⋊C411yescharacteristic
subgroupG/H
centerC4D4×D571
commutatorC4×C571C22×C4
FrattiniC2×C4C22×D571
Fitting#104×C571C2
socleC2×C571C4×D4
prime radical#32912714C2
cosocleC2×C4×C571C23
hypercenter#104D571
hypocenterC571#444
LCSG ▷ C4×C571 ▷ C2×C571 ▷ C571
UCSC1 ◁ C4 ◁ C2×C4 ◁ #104

Complements

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

NH ≅ G/Ntype
2. #32912702C2semidirect
3. #32912701C2semidirect
4. #32912629C2semidirect
5. #32912622C2semidirect
6. #32912605C2semidirect
7. #104×C571C2semidirect
9. #22603723C4semidirect
10. #22603721C4semidirect
11. #22603720C4semidirect
12. #22603718C4semidirect
51. C571#444semidirect
58. #104D571semidirect

Maximal subgroups

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

subgroupindex
#329127142
#329127022
#329127012
#329126292
#329126222
#329126052
#104×C5712
#444571