Finite Group Databasebeta

← #13116187

Subgroups — #13116187

Order 1664.

230 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 75 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#11719205C211yesmaximal, characteristic
2#11718782C212yesmaximal
3#11718638C211yesmaximal, characteristic
4C13×#343C211yesmaximal, characteristic
5#11718147C212yesmaximal
6C2×C13×M16C2212yes—
7C2×C13×C4⋊C4C2211yescharacteristic
8#88180C2212yes—
9C2×C4⋊Dic13C2211yescharacteristic
10#88178—22no—
11C2×C4×Dic13C2211yescharacteristic
12#88144—22no—
13#88142—22no—
14#88071—22no—
15#88058—22no—
16#88057—22no—
17C22×C4×C13D412yes—
18C22×C4×C13C2311yescharacteristic
19C22×Dic13—21no—
20C22×Dic13—21no—
21C2×Dic26—22no—
22C13×M16—22no—
23C13×M16Q814yescomplemented
24C2×C8×C13—22no—
25C13×C4⋊C4—22no—
26C22⋊Dic13—22no—
27C4⋊Dic13—22no—
28C4⋊Dic13—22no—
29C4⋊Dic13D412yes—
30C4⋊Dic13D412yes—
31#6101—24no—
32C4×Dic13—22no—
33C4×Dic13—21no—
34C4×Dic13Q812yescomplemented
35#2061—131nomaximal, Sylow
36C23×C13C2×D411yescharacteristic
37C2×C4×C13—22no—
38C2×C4×C13—42no—
39C2×C4×C13C2×D412yes—
40C2×C4×C13C2×Q812yes—
41C2×C4×C13C2×Q811yescharacteristic
42C2×C4×C13#4111yescharacteristic
43C2×Dic13—22no—
44C2×Dic13—22no—
45C2×Dic13—22no—
46C2×Dic13—41no—
47C2×Dic13—41no—
48C2×Dic13—42no—
49C2×Dic13—41no—
50Dic26—82no—
51C8×C13—24no—
52#544—131no—
53#428—132no—
54#382—131no—
55#343D1311yescharacteristic
56#339—132no—
57C22×C13—21no—
58C22×C13—21no—
59C22×C13#12011yescharacteristic
60C22×C13C22⋊Q811yescharacteristic
61C22×C13C4⋊Q811yescharacteristic
62C4×C13—42no—
63C4×C13C22⋊Q812yes—
64C4×C13C4⋊Q812yes—
65Dic13—42no—
66Dic13—42no—
67Dic13—42no—
68Dic13—81no—
69C2×M16C2×D1312yes—
70C4⋊Q8—262no—
71#125—262no—
72C22⋊Q8—262no—
73#117—132no—
74C2×C4⋊C4—131no—
75C2×C4⋊C4C2×D1311yescharacteristic
76C2×C42—131no—
77#107—262no—
78#106—262no—
79#95—262no—
80C2×C13—21no—
81C2×C13—21no—
82C2×C13#39511yescharacteristic
83C2×C13#45411yescharacteristic
84C2×C13#45511yescharacteristic
85C2×Q8—262no—
86C22×C4—261no—
87C22×C4—261no—
88C22×C4D5212yes—
89C22×C4C22×D1311yescharacteristic
90M16—22no—
91M16Dic2614yescomplemented
92C2×C8—22no—
93C4⋊C4—22no—
94C4⋊C4—132no—
95C4⋊C4—132no—
96C4⋊C4—262no—
97C4⋊C4—264no—
98C4⋊C4—262no—
99C22⋊C4—262no—
100C42—132no—
101C42—262no—
102C42—261no—
103C13#206111yescharacteristic, complemented, Sylow
104C23C2×D5211yescharacteristic
105Q8—1042no—
106C2×C4—22no—
107C2×C4—42no—
108C2×C4—262no—
109C2×C4—262no—
110C2×C4—262no—
111C2×C4—521no—
112C2×C4—521no—
113C2×C4—522no—
114C2×C4—521no—
115C2×C4C2×Dic2612yes—
116C2×C4D4×D1312yes—
117C2×C4#612911yescharacteristic
118C2×C4Q8×D1311yescharacteristic
119C8—24no—
120C22—21no—
121C22—21no—
122C22#8812311yescharacteristic
123C22#8813611yescharacteristic
124C22#8815111yescharacteristic
125C4—42no—
126C4—522no—
127C4—522no—
128C4—522no—
129C4—1041no—
130C4#8813212yes—
131C4#8814212yes—
132C2—21no—
133C2—21no—
134C2#1171831711yescharacteristic
135C2#1171840711yescharacteristic
136C2#1171841411yescharacteristic
subgroupG/H
centerC22#88136
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
FittingC13×#343C2
socleC22×C13#120
prime radicalC23×C13C2×D4
hypercenter#343D13
hypocenterC13#2061
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
23. C13×M16Q8semidirect
34. C4×Dic13Q8semidirect
91. M16Dic26semidirect
103. C13#2061semidirect

Maximal subgroups

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

subgroupindex
#117192052
#117187822
#117186382
C13×#3432
#117181472
#206113