Finite Group Databasebeta

← #13131139

Subgroups — #13131139

Order 1664.

230 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 52 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#11719380C211yesmaximal, characteristic
2#11719148C212yesmaximal
3#11718301C212yesmaximal, complemented
4#11718227C212yesmaximal, complemented
5C2×Q8×D13C411yescharacteristic
6C2×#6129C2211yescharacteristic
7C2×#6122—22no—
8C13×#124C411yescharacteristic
9#88198C2211yescharacteristic
10#88190C411yescharacteristic
11#88137—22no—
12#88132—22no—
13#88126C411yescharacteristic
14#88123C2211yescharacteristic
15#88121—22no—
16#88113C2214yes—
17C2×Q8×C13C2×C411yescharacteristic
18C2×D4×C13C2×C411yescharacteristic
19C2×C22⋊D13D412yes—
20C22×Dic13D412yes—
21Q8×D13—42no—
22#6129—42no—
23C2×C4×D13—21no—
24C2×C4×D13C2×C411yescharacteristic
25C2×Dic26—21no—
26C2×Dic26C2×C411yescharacteristic
27C2×Dic26C2311yescharacteristic
28#6122—24no—
29#6122—42no—
30C2×#1057—42no—
31C13×C22⋊C4—22no—
32C42×C13C2×C411yescharacteristic
33C22⋊Dic13—22no—
34#6103—21no—
35C4⋊Dic13—22no—
36#6101—21no—
37#6101—22no—
38C4×Dic13C2×C411yescharacteristic
39#2135—131nomaximal, Sylow
40C23×C13C22⋊C412yes—
41C22×D13C22⋊C411yescharacteristic
42Q8×C13—41no—
43D4×C13—41no—
44C2×C4×C13—21no—
45C2×C4×C13—21no—
46C2×C4×C13C22×C411yescharacteristic
47C22⋊D13—42no—
48C2×Dic13—22no—
49C2×Dic13—22no—
50C2×Dic13—21no—
51C2×Dic13—21no—
52C2×Dic13C22⋊C411yescharacteristic
53C2×Dic13C2×D412yes—
54C4×D13—22no—
55C4×D13—42no—
56Dic26—41no—
57Dic26—42no—
58Dic26—41no—
59#1057—44no—
60#536—131no—
61#413—132no—
62#356—132no—
63#356—132no—
64C22×C13—22no—
65C22×C13—42no—
66C22×C13C2×C22⋊C411yescharacteristic
67C2×D13—21no—
68C2×D13—41no—
69C4×C13—21no—
70C4×C13—41no—
71C4×C13—41no—
72Dic13—22no—
73Dic13—41no—
74Dic13—41no—
75Dic13#9912yes—
76C2×#41—131no—
77C22×Q8—131no—
78C2×M16—262no—
79C4⋊Q8—131no—
80C4⋊Q8—131no—
81#124—131no—
82#124#26111yescharacteristic
83#123—262no—
84C22⋊Q8—262no—
85#117—131no—
86#101—134no—
87#100—262no—
88C2×C13—21no—
89C2×C13—42no—
90C2×C13C2×#9911yescharacteristic
91D13—41no—
92#41—522no—
93C2×Q8—131no—
94C2×Q8—131no—
95C2×Q8—261no—
96C2×Q8—522no—
97C2×Q8C2×#26111yescharacteristic
98C2×D4—132no—
99C2×D4C2×#26111yescharacteristic
100C22×C4—132no—
101C22×C4—131no—
102C22×C4—261no—
103M16—264no—
104M16—522no—
105C2×C8—522no—
106C4⋊C4—261no—
107C4⋊C4—262no—
108C4⋊C4—262no—
109C22⋊C4—22no—
110C22⋊C4—261no—
111C22⋊C4—262no—
112C42—131no—
113C42C2×#26111yescharacteristic
114C13#213511yescharacteristic, complemented, Sylow
115C23—131no—
116C23C22⋊#26112yes—
117Q8—41no—
118Q8—521no—
119Q8—521no—
120Q8—522no—
121D4—41no—
122D4—522no—
123C2×C4—21no—
124C2×C4—21no—
125C2×C4—131no—
126C2×C4—132no—
127C2×C4—262no—
128C2×C4—262no—
129C2×C4—262no—
130C2×C4—261no—
131C2×C4—261no—
132C2×C4—522no—
133C2×C4C22×#26111yescharacteristic
134C8—524no—
135C22—22no—
136C22—42no—
137C22—261no—
138C22—521no—
139C22C2×C22⋊#26111yescharacteristic
140C4—21no—
141C4—41no—
142C4—41no—
143C4—132no—
144C4—262no—
145C4—521no—
146C4—521no—
147C2—21no—
148C2—42no—
149C2—521no—
150C2D13⋊#9911yescharacteristic
subgroupG/H
centerC2D13⋊#99
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
FittingC13×#124C4
socleC2×C13C2×#99
prime radicalC2×#6129C22
cosocleC2×Dic26C23
hypercenter#124#261
hypocenterC13#2135
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #124

Complements

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

NH ≅ G/Ntype
3. #11718301C2semidirect
4. #11718227C2semidirect
114. C13#2135semidirect

Maximal subgroups

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

subgroupindex
#117193802
#117191482
#117183012
#117182272
#213513