Finite Group Databasebeta

← #13130366

Subgroups — #13130366

Order 1664.

228 conjugacy classes of subgroups; only the 60 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 60 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
1D13×C4⋊Q8C211yesmaximal, characteristic
2#11719055C211yesmaximal, characteristic
3#11719055C211yesmaximal, characteristic
4#11718245C214yesmaximal, complemented
5C2×Q8×D13—21no—
6C13×C4⋊Q8C411yescharacteristic
7#88198—21no—
8C4⋊C4×D13—21no—
9C4⋊C4×D13C412yes—
10#88142—21no—
11#88142C2212yes—
12C42×D13C2211yescharacteristic
13#88123C411yescharacteristic
14#88112C2212yes—
15#88112C2212yes—
16#88111—21no—
17#88111—21no—
18#88110—21no—
19#88110—21no—
20C2×Q8×C13—21no—
21Q8×D13—44no—
22C2×C4×D13—22no—
23C2×C4×D13C2×C411yescharacteristic
24C2×C4×D13D411yescharacteristic
25C2×C4×D13D411yescharacteristic
26C2×Dic26—21no—
27C2×Dic26—22no—
28C2×#1057—22no—
29C2×#1057—22no—
30C13×C4⋊C4—21no—
31C13×C4⋊C4C2×C412yes—
32C42×C13C2×C411yescharacteristic
33C4⋊Dic13—21no—
34C4⋊Dic13C2×C412yes—
35#6101—22no—
36#6101—22no—
37C4×Dic13D411yescharacteristic
38C4×Dic13D411yescharacteristic
39C4×Dic13C2311yescharacteristic
40#1556—131nomaximal, Sylow
41C22×D13C22⋊C411yescharacteristic
42Q8×C13—42no—
43C2×C4×C13—22no—
44C2×C4×C13C22⋊C411yescharacteristic
45C2×C4×C13C22⋊C411yescharacteristic
46C2×C4×C13C22×C411yescharacteristic
47C2×Dic13—22no—
48C2×Dic13C22⋊C411yescharacteristic
49C2×Dic13C2×D411yescharacteristic
50C2×Dic13C2×D411yescharacteristic
51C4×D13—22no—
52C4×D13—22no—
53C4×D13—22no—
54C4×D13—44no—
55Dic26—42no—
56Dic26—44no—
57#1057—42no—
58#1057—42no—
59C2×C4⋊Q8—131no—
60#432—131no—
61#432—131no—
62#332—134no—
63C22×C13C2×C22⋊C411yescharacteristic
64C2×D13—21no—
65C2×D13—21no—
66C2×D13#10112yes—
67C4×C13—21no—
68C4×C13—21no—
69C4×C13—21no—
70C4×C13—42no—
71Dic13—21no—
72Dic13—42no—
73Dic13AGL(1,ℤ/8)12yes—
74Dic13#13712yes—
75C22×Q8—261no—
76C4⋊Q8—132no—
77C4⋊Q8—131no—
78C4⋊Q8—261no—
79C4⋊Q8—261no—
80C4⋊Q8#26111yescharacteristic
81C2×C4⋊C4—132no—
82C2×C4⋊C4—261no—
83C2×C42—131no—
84C4⋊C8—132no—
85C4⋊C8—132no—
86C22⋊C8—261no—
87C22⋊C8—261no—
88#97—261no—
89#97—261no—
90C2×C13C2×#10111yescharacteristic
91C2×C13#41811yescharacteristic
92C2×C13#41911yescharacteristic
93D13—22no—
94C2×Q8—21no—
95C2×Q8—262no—
96C2×Q8—261no—
97C2×Q8—524no—
98C22×C4—131no—
99C22×C4—131no—
100C22×C4—131no—
101C22×C4—262no—
102C2×C8—262no—
103C2×C8—262no—
104C4⋊C4—21no—
105C4⋊C4—132no—
106C4⋊C4—262no—
107C4⋊C4—262no—
108C4⋊C4—261no—
109C4⋊C4C2×#26112yes—
110C42—131no—
111C42—131no—
112C42—131no—
113C42C2×#26111yescharacteristic
114C13#155611yescharacteristic, complemented, Sylow
115C23—131no—
116Q8—42no—
117Q8—522no—
118Q8—524no—
119C2×C4—22no—
120C2×C4—131no—
121C2×C4—131no—
122C2×C4—131no—
123C2×C4—262no—
124C2×C4—262no—
125C2×C4—262no—
126C2×C4—262no—
127C2×C4—524no—
128C2×C4C22⋊#26111yescharacteristic
129C2×C4C22⋊#26111yescharacteristic
130C2×C4C22×#26111yescharacteristic
131C8—522no—
132C8—522no—
133C22—132no—
134C22—261no—
135C22—261no—
136C22C2×C22⋊#26111yescharacteristic
137C4—21no—
138C4—21no—
139C4—21no—
140C4—42no—
141C4—132no—
142C4—132no—
143C4—261no—
144C4—522no—
145C2—262no—
146C2#1171913811yescharacteristic
147C2#1171915311yescharacteristic
148C2D13⋊#10111yescharacteristic
subgroupG/H
centerC22C2×C22⋊#261
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×C4⋊Q8C4
socleC22×C13C2×C22⋊C4
prime radicalC22×D13C22⋊C4
cosocleC4×Dic13C23
hypercenterC4⋊Q8#261
hypocenterC13#1556
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
4. #11718245C2semidirect
114. C13#1556semidirect

Maximal subgroups

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

subgroupindex
D13×C4⋊Q82
#117190552
#117182452
#155613