Finite Group Databasebeta

← #37526703

Subgroups — #37526703

Order 22976.

104 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 37 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#26040046C211yesmaximal, characteristic, complemented
2#26040041C211yesmaximal, characteristic
3#26040021C211yesmaximal, characteristic, complemented
4#26039951C211yesmaximal, characteristic, complemented
5#26039934C211yesmaximal, characteristic, complemented
6#26039932C211yesmaximal, characteristic, complemented
7C2×SD16×C359C211yesmaximal, characteristic, complemented
8#19153341C2211yescharacteristic
9#19153331—21no—
10#19153329—21no—
11#19153328—21no—
12#19153326—21no—
13#19153325C2211yescharacteristic
14#19153325C2211yescharacteristic
15#19153325C2211yescharacteristic
16#19153324—21no—
17C8×D359—21no—
18C2×Q8×C359C2211yescharacteristic
19C2×D4×C359C2211yescharacteristic
20SD16×C359—21no—
21SD16×C359—21no—
22C2×C8×C359C2211yescharacteristic
23Dic718D411yescharacteristic
24D1436D411yescharacteristic
25C22⋊D359—21no—
26C4×D359—21no—
27C359⋊C8—21no—
28C359⋊C8—21no—
29C359⋊C8—21no—
30C23×C359—21no—
31Q8×C359—21no—
32Q8×C359—21no—
33D4×C359—21no—
34D4×C359—21no—
35C2×C4×C359—21no—
36C2×C4×C359C2311yescharacteristic
37C8×C359D411yescharacteristic
38C8×C359D411yescharacteristic
39C22×C359—41no—
40C22×C359—81no—
41C22×C359#4111yescharacteristic
42C2×D359—21no—
43C4×C359—41no—
44C4×C359C2×D411yescharacteristic
45C4×C359C2×D411yescharacteristic
46Dic359—21no—
47C2×C359—21no—
48C2×C359—81no—
49C2×C359#12111yescharacteristic
50D359—41no—
51C359#47111yescharacteristic, complemented, Sylow
52#471—3591nomaximal, Sylow
53#137—3591no—
54AGL(1,ℤ/8)—3591no—
55C2×SD16D35911yescharacteristic, complemented
56#131—3591no—
57#108—3591no—
58#101—3591no—
59#100—3591no—
60#41—3591no—
61C2×Q8C2×D35911yescharacteristic
62C2×D4C2×D35911yescharacteristic
63Q16—7181no—
64SD16—21no—
65SD16—21no—
66SD16—7181no—
67SD16—7181no—
68D8—7181no—
69M16—3591no—
70M16—3591no—
71M16—3591no—
72M16—7181no—
73C2×C8—7181no—
74C2×C8C2×D35911yescharacteristic
75C23—21no—
76Q8—21no—
77Q8—21no—
78Q8—3591no—
79D4—21no—
80D4—21no—
81D4—3591no—
82D4—7181no—
83C2×C4—21no—
84C2×C4—7181no—
85C2×C4C22×D35911yescharacteristic
86C8—7181no—
87C8—7181no—
88C8—7181no—
89C8C22⋊D35911yescharacteristic
90C8C22⋊D35911yescharacteristic
91C22—41no—
92C22—81no—
93C22—7181no—
94C22#1915334011yescharacteristic
95C4—41no—
96C4—7181no—
97C4D4×D35911yescharacteristic
98C4C2×C22⋊D35911yescharacteristic
99C2—21no—
100C2—81no—
101C2—14361no—
102C2#2603998611yescharacteristic
subgroupG/H
centerC2#26039986
commutator, cosocleC2×C4×C359C23
FrattiniC2×C4C22×D359
FittingC2×SD16×C359C2
socleC2×C359#121
prime radical#26040041C2
hypercenterC2×SD16D359
hypocenterC359#471
LCSG ▷ C2×C4×C359 ▷ C2×C359 ▷ C359
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×SD16

Complements

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

NH ≅ G/Ntype
1. #26040046C2semidirect
3. #26040021C2semidirect
4. #26039951C2semidirect
5. #26039934C2semidirect
6. #26039932C2semidirect
7. C2×SD16×C359C2semidirect
51. C359#471semidirect
55. C2×SD16D359semidirect

Maximal subgroups

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

subgroupindex
#260400462
#260400412
#260400212
#260399512
#260399342
#260399322
C2×SD16×C3592
#471359