Finite Group Databasebeta

← #13116139

Subgroups — #13116139

Order 1664.

264 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 67 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
1C13×#575C211yesmaximal, characteristic
2#11718901C212yesmaximal, complemented
3#11718894C212yesmaximal, complemented
4#11718780C211yesmaximal, characteristic, complemented
5#11718149C211yesmaximal, characteristic, complemented
6C2×C13×#41C2212yes—
7C13×#137—22no—
8C13×AGL(1,ℤ/8)—22no—
9C13×#135—22no—
10C2×C13×M16C2211yescharacteristic
11#88180C2212yes—
12#88180C2211yescharacteristic
13C22×#1055C2211yescharacteristic
14#88075—22no—
15#88074—24no—
16#88072—22no—
17#88054—22no—
18C13×#41—22no—
19C13×#41—22no—
20C13×#41—22no—
21C13×#41—22no—
22C2×Q8×C13D412yes—
23C2×D4×C13—22no—
24C2×D4×C13D412yes—
25C22×C4×C13—22no—
26C22×C4×C13C2311yescharacteristic
27C13×Q16—22no—
28C13×SD16—24no—
29C13×D8—22no—
30C13×M16—22no—
31C2×C8×C13D412yes—
32C22⋊Dic13—22no—
33C22⋊Dic13D412yes—
34C4⋊Dic13—21no—
35C4⋊Dic13—22no—
36C4×Dic13—21no—
37C4×Dic13—22no—
38C2×#1055—22no—
39C2×#1055—21no—
40#2053—131nomaximal, Sylow
41C23×C13—22no—
42C23×C13C2×D411yescharacteristic
43Q8×C13—22no—
44Q8×C13—22no—
45D4×C13—22no—
46D4×C13—22no—
47D4×C13—42no—
48D4×C13—42no—
49C2×C4×C13—22no—
50C2×C4×C13—42no—
51C2×C4×C13—42no—
52C2×C4×C13C2×D412yes—
53C2×C4×C13C2×D411yescharacteristic
54C2×C4×C13#4111yescharacteristic
55C2×C4×C13#4112yes—
56C2×Dic13—22no—
57C2×Dic13—42no—
58C8×C13—22no—
59#1055—41no—
60#575D1311yescharacteristic
61#424—131no—
62#416—132no—
63#410—132no—
64H(3,ℤ/4)—131no—
65C22×C13—41no—
66C22×C13—42no—
67C22×C13—82no—
68C22×C13#12111yescharacteristic
69C22×C13#12112yes—
70C4×C13—42no—
71C4×C13#12011yescharacteristic
72C4×C13#12312yes—
73C4×C13#12411yescharacteristic
74Dic13—42no—
75Dic13—82no—
76C2×#41C2×D1312yes—
77#137—22no—
78AGL(1,ℤ/8)—22no—
79#135—22no—
80C2×M16C2×D1311yescharacteristic
81C22×C8—131no—
82#117—131no—
83#117—132no—
84C4⋊C8—262no—
85#103—262no—
86#102—262no—
87#99—264no—
88C2×C13—21no—
89C2×C13—22no—
90C2×C13—82no—
91C2×C13#39411yescharacteristic
92#41—22no—
93#41—22no—
94#41—22no—
95#41—22no—
96C2×Q8C22⋊D1312yes—
97C2×D4—22no—
98C2×D4C22⋊D1312yes—
99C22×C4—22no—
100C22×C4C22×D1311yescharacteristic
101Q16—22no—
102SD16—24no—
103D8—22no—
104M16—22no—
105C2×C8—262no—
106C2×C8—261no—
107C2×C8C22⋊D1312yes—
108C4⋊C4—261no—
109C4⋊C4—262no—
110C22⋊C4—132no—
111C22⋊C4—262no—
112C42—261no—
113C42—262no—
114C13#205311yescharacteristic, complemented, Sylow
115C23—22no—
116C23D4×D1311yescharacteristic
117Q8—22no—
118Q8—22no—
119D4—22no—
120D4—22no—
121D4—42no—
122D4—42no—
123C2×C4—22no—
124C2×C4—42no—
125C2×C4—42no—
126C2×C4—262no—
127C2×C4—522no—
128C2×C4#612911yescharacteristic
129C2×C4#612912yes—
130C2×C4C2×C22⋊D1312yes—
131C2×C4C2×C22⋊D1311yescharacteristic
132C8—22no—
133C8—521no—
134C22—41no—
135C22—42no—
136C22—82no—
137C22#8819211yescharacteristic
138C22#8819312yes—
139C4—42no—
140C4—522no—
141C4—1042no—
142C4#8818912yes—
143C4#8819011yescharacteristic
144C4#8820711yescharacteristic
145C2—21no—
146C2—22no—
147C2—82no—
148C2#1171888311yescharacteristic
subgroupG/H
centerC4#88190
commutator, cosocleC22×C4×C13C23
FrattiniC22×C4C22×D13
Fitting, prime radicalC13×#575C2
socleC2×C13#394
hypercenter#575D13
hypocenterC13#2053
LCSG ▷ C22×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C4 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
2. #11718901C2semidirect
3. #11718894C2semidirect
4. #11718780C2semidirect
5. #11718149C2semidirect
114. C13#2053semidirect

Maximal subgroups

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

subgroupindex
C13×#5752
#117189012
#117188942
#117187802
#117181492
#205313