Finite Group Databasebeta

← #14558578

Subgroups — #14558578

Order 2368.

104 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 104 conjugacy classes of subgroups — too many to draw. Only its 40 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#11924624C211yesmaximal, characteristic, complemented
2#11924623C211yesmaximal, characteristic, complemented
3#11924607C211yesmaximal, characteristic, complemented
4#11924601C211yesmaximal, characteristic, complemented
5#11924600C211yesmaximal, characteristic, complemented
6#11924590C211yesmaximal, characteristic, complemented
7#11924557C211yesmaximal, characteristic
8#10596966C2211yescharacteristic
9#10596964C2211yescharacteristic
10#10596957—21no—
11C2×#64438—21no—
12C4×#3866C2211yescharacteristic
13#10596953—21no—
14#10596953C2211yescharacteristic
15#10596953C2211yescharacteristic
16D37⋊C8—21no—
17D37⋊C8C2211yescharacteristic
18SD16×C37C411yescharacteristic, complemented
19#10596942C411yescharacteristic, complemented
20#10596939C411yescharacteristic, complemented
21#10596930C411yescharacteristic, complemented
22C8×D37C2211yescharacteristic
23C2×#3866—21no—
24Q8×C37C2×C411yescharacteristic
25D4×C37C2×C411yescharacteristic
26C22⋊D37—21no—
27C2×Dic37—21no—
28D148—21no—
29D148C2×C411yescharacteristic
30C4×D37—21no—
31C4×D37C2311yescharacteristic
32Dic74C2×C411yescharacteristic
33#64438—21no—
34#64438—21no—
35#64438D411yescharacteristic
36#64438D411yescharacteristic
37C8×C37C2×C411yescharacteristic
38#64436C2×C411yescharacteristic
39C22×C37—21no—
40C2×D37—21no—
41C2×D37#4111yescharacteristic
42#3866—41no—
43C4×C37—21no—
44C4×C37C22×C411yescharacteristic
45Dic37—21no—
46Dic37C2×D411yescharacteristic
47C2×C37—41no—
48C2×C37C4×D411yescharacteristic
49D37—21no—
50D37—41no—
51#444—371nomaximal, Sylow
52C37#44411yescharacteristic, complemented, Sylow
53#135—371no—
54#131—371no—
55#131—371no—
56#108—371no—
57#104—371no—
58#104—371no—
59#97—371no—
60#41—371no—
61#41—371no—
62Q16—371no—
63SD16—371no—
64SD16#386611yescharacteristic, complemented
65D8—371no—
66M16—371no—
67M16—371no—
68M16—741no—
69M16—741no—
70C2×C8—371no—
71C2×C8—371no—
72C2×C8—741no—
73C2×C8—741no—
74C42—371no—
75Q8—371no—
76Q8C2×#386611yescharacteristic
77D4—371no—
78D4—741no—
79D4—741no—
80D4C2×#386611yescharacteristic
81C2×C4—371no—
82C2×C4—741no—
83C2×C4—741no—
84C2×C4—741no—
85C8—371no—
86C8—371no—
87C8—371no—
88C8—741no—
89C8—741no—
90C8C2×#386611yescharacteristic
91C22—21no—
92C22—371no—
93C22—741no—
94C4—21no—
95C4—371no—
96C4—741no—
97C4—1481no—
98C4C22×#386611yescharacteristic
99C2—41no—
100C2—741no—
101C2—1481no—
102C2D4×#386611yescharacteristic
subgroupG/H
centerC2D4×#3866
commutatorC4×C37C22×C4
FrattiniC4C22×#3866
FittingSD16×C37C4
socleC2×C37C4×D4
prime radical#11924557C2
cosocleC4×D37C23
hypercenterSD16#3866
hypocenterC37#444
LCSG ▷ C4×C37 ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ C4 ◁ SD16

Complements

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

NH ≅ G/Ntype
1. #11924624C2semidirect
2. #11924623C2semidirect
3. #11924607C2semidirect
4. #11924601C2semidirect
5. #11924600C2semidirect
6. #11924590C2semidirect
18. SD16×C37C4semidirect
19. #10596942C4semidirect
20. #10596939C4semidirect
21. #10596930C4semidirect
52. C37#444semidirect
64. SD16#3866semidirect

Maximal subgroups

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

subgroupindex
#119246242
#119246232
#119246072
#119246012
#119246002
#119245902
#119245572
#44437