Finite Group Databasebeta

← #14558602

Subgroups — #14558602

Order 2368.

294 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 294 conjugacy classes of subgroups — too many to draw. Only its 138 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
1Q8×#3866C212yesmaximal, complemented
2D4×#3866C216yesmaximal, complemented
3#11924615C213yesmaximal, complemented
4C2×C4⋊#3866C213yesmaximal, complemented
5#41×D37C211yesmaximal, characteristic
6C22×#3866C2216yes—
7#41×C37C411yescharacteristic, complemented
8#10596966C411yescharacteristic, complemented
9Q8×D37C2211yescharacteristic
10#10596964C413yescomplemented
11D4×D37C2213yes—
12#10596962C413yescomplemented
13C2×C4×D37C2213yes—
14C22⋊#3866C2216yes—
15C4⋊#3866C2213yes—
16C4⋊#3866C2216yes—
17C4⋊#3866C2211yescharacteristic
18C4×#3866C2216yes—
19C22×D37C2313yes—
20C2×#3866—46no—
21C2×#3866C2312yes—
22C2×#3866C2316yes—
23Q8×C37C2×C411yescharacteristic, complemented
24D4×C37C2×C413yescomplemented
25C2×C4×C37C2×C413yescomplemented
26C22⋊D37C2×C416yescomplemented
27C2×Dic37C2×C413yescomplemented
28D148C2×C413yescomplemented
29C4×D37C2×C413yescomplemented
30C4×D37C2×C413yescomplemented
31C4×D37C2313yes—
32C4×D37C2311yescharacteristic
33Dic74C2×C413yescomplemented
34C22×C37C22×C413yes—
35C2×D37—23no—
36C2×D37—23no—
37C2×D37C22×C413yes—
38C2×D37C2411yescharacteristic
39#3866—26no—
40#3866—22no—
41C4×C37C22×C413yes—
42C4×C37C22×C411yescharacteristic
43Dic37C22×C413yes—
44Dic37C22×C411yescharacteristic
45C2×C37—23no—
46C2×C37C23×C411yescharacteristic
47D37—23no—
48D37H(5,𝔽2)11yescharacteristic
49D372−1+411yescharacteristic
50#520—371nomaximal, Sylow
51C37#52011yescharacteristic, complemented, Sylow
52C2×#41—371no—
53C4×Q8—372no—
54C4×D4—376no—
55#117—373no—
56C2×C4⋊C4—373no—
57#41—371no—
58#41—373no—
59#41—373no—
60#41#386611yescharacteristic, complemented
61C2×Q8—371no—
62C2×D4—373no—
63C22×C4—373no—
64C22×C4—376no—
65C4⋊C4—373no—
66C4⋊C4—376no—
67C4⋊C4—371no—
68C22⋊C4—376no—
69C42—376no—
70C23—373no—
71Q8—373no—
72Q8C2×#386611yescharacteristic, complemented
73D4—376no—
74D4—373no—
75D4C2×#386613yescomplemented
76C2×C4—373no—
77C2×C4—373no—
78C2×C4—371no—
79C2×C4—373no—
80C2×C4—373no—
81C2×C4—372no—
82C2×C4—376no—
83C2×C4—1486no—
84C2×C4C2×#386613yescomplemented
85C22—371no—
86C22—373no—
87C22—743no—
88C22—743no—
89C22C22×#386613yes—
90C4—371no—
91C4—373no—
92C4—746no—
93C4—742no—
94C4C22×#386611yescharacteristic
95C4C22×#386613yes—
96C2—23no—
97C2—371no—
98C2—371no—
99C2—743no—
100C2C23×#386611yescharacteristic
subgroupG/H
center, FrattiniC2C23×#3866
commutator, socleC2×C37C23×C4
Fitting#41×C37C4
prime radical#41×D37C2
cosocleC2×D37C24
hypercenter#41#3866
hypocenterC37#520
LCSG ▷ C2×C37 ▷ C37
UCSC1 ◁ C2 ◁ #41

Complements

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

NH ≅ G/Ntype
1. Q8×#3866C2semidirect
2. D4×#3866C2semidirect
3. #11924615C2semidirect
4. C2×C4⋊#3866C2semidirect
7. #41×C37C4semidirect
8. #10596966C4semidirect
10. #10596964C4semidirect
12. #10596962C4semidirect
23. Q8×C37C2×C4semidirect
24. D4×C37C2×C4semidirect
25. C2×C4×C37C2×C4semidirect
26. C22⋊D37C2×C4semidirect
27. C2×Dic37C2×C4semidirect
28. D148C2×C4semidirect
29. C4×D37C2×C4semidirect
30. C4×D37C2×C4semidirect
33. Dic74C2×C4semidirect
51. C37#520semidirect
60. #41#3866semidirect
72. Q8C2×#3866semidirect
75. D4C2×#3866semidirect
84. C2×C4C2×#3866semidirect

Maximal subgroups

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

subgroupindex
Q8×#38662
D4×#38662
#119246152
C2×C4⋊#38662
#41×D372
#52037