Finite Group Databasebeta

← #88184⋊C3 #11928295

Subgroups — #88184⋊C3 #11928295

Order 1248.

188 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 188 conjugacy classes of subgroups — too many to draw. Only its 61 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
1C22×C4×C13⋊C3C211yesmaximal, characteristic, complemented
2C2×(C22⋊D13)⋊C3C212yesmaximal, complemented
3C2×C4⋊(D13⋊C3)C211yesmaximal, characteristic, complemented
4#6103⋊C3C212yesmaximal, complemented
5C4⋊(Dic13⋊C3)C211yesmaximal, characteristic, complemented
6#88184C311yesmaximal, characteristic, complemented, Hall
7C23×C13⋊C3C2211yescharacteristic
8C22×D13⋊C3C2212yes—
9C2×C4×C13⋊C3—22no—
10C2×C4×C13⋊C3C2211yescharacteristic
11C2×C4×C13⋊C3C2211yescharacteristic
12(C22⋊D13)⋊C3—24no—
13C2×Dic13⋊C3C2212yes—
14C4⋊(D13⋊C3)—22no—
15C22×C4×C13C2×C311yescharacteristic, complemented
16C2×C22⋊D13C2×C312yescomplemented
17C2×D52C2×C311yescharacteristic, complemented
18#6103C2×C312yescomplemented
19C4⋊Dic13C2×C311yescharacteristic, complemented
20C22×C13⋊C3—21no—
21C22×C13⋊C3—21no—
22C22×C13⋊C3D412yescomplemented
23C22×C13⋊C3C2311yescharacteristic
24C2×D13⋊C3—22no—
25C2×D13⋊C3—22no—
26C2×D13⋊C3—22no—
27C4×C13⋊C3—21no—
28C4×C13⋊C3D412yescomplemented
29Dic13⋊C3—22no—
30C23×C13C22×C311yescharacteristic
31C22×D13C22×C312yes—
32C2×C4×C13—22no—
33C2×C4×C13C22×C311yescharacteristic
34C2×C4×C13C22×C311yescharacteristic
35C22⋊D13—24no—
36C2×Dic13C22×C312yes—
37D52—22no—
38C3×#121—131nomaximal, Hall
39C2×C13⋊C3—22no—
40C2×C13⋊C3C2×D411yescharacteristic
41C2×C13⋊C3C2×D411yescharacteristic
42C2×C13⋊C3#4111yescharacteristic
43D13⋊C3—42no—
44C22×C13—21no—
45C22×C13—21no—
46C22×C13C3×D412yescomplemented
47C22×C13C23×C311yescharacteristic
48C2×D13—22no—
49C2×D13—22no—
50C2×D13—22no—
51C4×C13—21no—
52C4×C13C3×D412yescomplemented
53Dic13—22no—
54C2×C3×D4—131no—
55C2×C3×D4—132no—
56C22×C3×C4—131no—
57C3×C4⋊C4—131no—
58C3×C22⋊C4—132no—
59C13⋊C3#12111yescharacteristic, complemented, Hall
60#121—131noSylow
61C2×C13—22no—
62C2×C13C2×C3×D411yescharacteristic
63C2×C13C2×C3×D411yescharacteristic
64C2×C13C3×#4111yescharacteristic
65D13—42no—
66C23×C3—132no—
67C23×C3—131no—
68C3×D4—262no—
69C3×D4—264no—
70C2×C3×C4—132no—
71C2×C3×C4—131no—
72C2×C3×C4—131no—
73C2×C3×C4—262no—
74C2×D4—132no—
75C2×D4—131no—
76C22×C4D13⋊C311yescharacteristic, complemented
77C4⋊C4—131no—
78C22⋊C4—132no—
79C13C3×#12111yescharacteristic, complemented, Sylow
80C22×C3—132no—
81C22×C3—131no—
82C22×C3—261no—
83C22×C3—261no—
84C22×C3—262no—
85C22×C3—262no—
86C22×C3—262no—
87C3×C4—132no—
88C3×C4—261no—
89C3×C4—262no—
90C23—132no—
91C23C2×D13⋊C311yescharacteristic
92D4—264no—
93D4—262no—
94C2×C4—22no—
95C2×C4—132no—
96C2×C4C2×D13⋊C311yescharacteristic
97C2×C4C2×D13⋊C311yescharacteristic
98C2×C3—131no—
99C2×C3—131no—
100C2×C3—131no—
101C2×C3—262no—
102C2×C3—522no—
103C22—21no—
104C22—21no—
105C22—262no—
106C22—262no—
107C22—262no—
108C22C4⋊(D13⋊C3)12yescomplemented
109C22C22×D13⋊C311yescharacteristic
110C4—21no—
111C4—262no—
112C4(C22⋊D13)⋊C312yescomplemented
113C3—131noSylow
114C2—22no—
115C2—522no—
116C2C2×C4⋊(D13⋊C3)11yescharacteristic
117C2#6127⋊C311yescharacteristic
118C2C2×(C22⋊D13)⋊C311yescharacteristic
subgroupG/H
center, FrattiniC22C22×D13⋊C3
commutator, socle, cosocleC22×C13C23×C3
FittingC22×C4×C13C2×C3
hypercenterC22×C4D13⋊C3
hypocenterC13C3×#121
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×C13⋊C3C2semidirect
2. C2×(C22⋊D13)⋊C3C2semidirect
3. C2×C4⋊(D13⋊C3)C2semidirect
4. #6103⋊C3C2semidirect
5. C4⋊(Dic13⋊C3)C2semidirect
6. #88184C3semidirect
15. C22×C4×C13C2×C3semidirect
16. C2×C22⋊D13C2×C3semidirect
17. C2×D52C2×C3semidirect
18. #6103C2×C3semidirect
19. C4⋊Dic13C2×C3semidirect
22. C22×C13⋊C3D4semidirect
28. C4×C13⋊C3D4semidirect
46. C22×C13C3×D4semidirect
52. C4×C13C3×D4semidirect
59. C13⋊C3#121semidirect
76. C22×C4D13⋊C3semidirect
79. C13C3×#121semidirect
108. C22C4⋊(D13⋊C3)semidirect
112. C4(C22⋊D13)⋊C3semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C13⋊C32
C2×(C22⋊D13)⋊C32
C2×C4⋊(D13⋊C3)2
#6103⋊C32
C4⋊(Dic13⋊C3)2
#881843
C3×#12113