Finite Group Databasebeta

← #13131131

Subgroups — #13131131

Order 1664.

230 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 54 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#11719530C211yesmaximal, characteristic
2C2×#88113C212yesmaximal, complemented
3#11718301C212yesmaximal, complemented
4#11718295C212yesmaximal, complemented
5C2×C13×#41C411yescharacteristic
6C22×Dic26C2211yescharacteristic
7C2×#6122—22no—
8#88198C411yescharacteristic
9#88198C2211yescharacteristic
10#88190C411yescharacteristic
11#88190C2211yescharacteristic
12#88189—22no—
13#88180C411yescharacteristic
14#88178—22no—
15#88113—22no—
16#88113C2214yes—
17C13×#41—42no—
18C2×Q8×C13C2×C411yescharacteristic
19C2×D4×C13—21no—
20C2×D4×C13C2×C411yescharacteristic
21C22×C4×C13—21no—
22C22×C4×C13C2×C411yescharacteristic
23C22×Dic13D412yes—
24C2×Dic26—42no—
25C2×Dic26C2×C411yescharacteristic
26C2×Dic26D412yes—
27C2×Dic26C2311yescharacteristic
28#6122—24no—
29#6122—42no—
30C2×#1057—42no—
31C22⋊Dic13—21no—
32C22⋊Dic13—22no—
33C22⋊Dic13—22no—
34C4⋊Dic13—21no—
35#6101—22no—
36#6101—22no—
37C4×Dic13C2×C411yescharacteristic
38C4×Dic13C2×C411yescharacteristic
39#2133—131nomaximal, Sylow
40C23×C13—21no—
41C23×C13C22⋊C411yescharacteristic
42Q8×C13—41no—
43D4×C13—41no—
44D4×C13—42no—
45C2×C4×C13—22no—
46C2×C4×C13—21no—
47C2×C4×C13—42no—
48C2×C4×C13C22⋊C411yescharacteristic
49C2×C4×C13C22×C411yescharacteristic
50C2×Dic13—22no—
51C2×Dic13—22no—
52C2×Dic13—21no—
53C2×Dic13—21no—
54C2×Dic13C22⋊C412yes—
55C2×Dic13C2×D412yes—
56Dic26—41no—
57Dic26—42no—
58Dic26—41no—
59#1057—44no—
60#536—131no—
61C2×#101—132no—
62#356—132no—
63#355—132no—
64C22×C13—41no—
65C22×C13—42no—
66C22×C13—41no—
67C22×C13#9912yes—
68C22×C13C2×C22⋊C411yescharacteristic
69C4×C13—21no—
70C4×C13—21no—
71C4×C13—41no—
72Dic13—22no—
73Dic13—22no—
74Dic13—41no—
75Dic13—41no—
76C2×#41#26111yescharacteristic
77C22×Q8—131no—
78C2×M16—262no—
79C4⋊Q8—131no—
80C4⋊Q8—131no—
81#124—131no—
82#124—131no—
83#123—262no—
84C22⋊Q8—262no—
85#117—131no—
86#101—134no—
87#101—262no—
88C2×C13—21no—
89C2×C13—22no—
90C2×C13—81no—
91C2×C13C2×#9911yescharacteristic
92#41—42no—
93C2×Q8—132no—
94C2×Q8—131no—
95C2×Q8—131no—
96C2×Q8—522no—
97C2×Q8C2×#26111yescharacteristic
98C2×D4—21no—
99C2×D4C2×#26111yescharacteristic
100C22×C4—21no—
101C22×C4—132no—
102C22×C4C2×#26111yescharacteristic
103M16—264no—
104M16—522no—
105C2×C8—522no—
106C4⋊C4—262no—
107C4⋊C4—262no—
108C4⋊C4—261no—
109C22⋊C4—262no—
110C22⋊C4—262no—
111C22⋊C4—261no—
112C42—131no—
113C42—131no—
114C13#213311yescharacteristic, complemented, Sylow
115C23—21no—
116C23C22⋊#26111yescharacteristic
117Q8—41no—
118Q8—522no—
119Q8—521no—
120Q8—521no—
121D4—41no—
122D4—42no—
123C2×C4—22no—
124C2×C4—21no—
125C2×C4—42no—
126C2×C4—132no—
127C2×C4—132no—
128C2×C4—262no—
129C2×C4—262no—
130C2×C4—261no—
131C2×C4—261no—
132C2×C4C22⋊#26111yescharacteristic
133C2×C4C22×#26111yescharacteristic
134C8—524no—
135C22—41no—
136C22—42no—
137C22—41no—
138C22#8811912yes—
139C22C2×C22⋊#26111yescharacteristic
140C4—21no—
141C4—21no—
142C4—41no—
143C4—262no—
144C4—262no—
145C4—521no—
146C4—521no—
147C2—21no—
148C2—22no—
149C2—81no—
150C2C2×#8811911yescharacteristic
subgroupG/H
centerC2C2×#88119
commutatorC2×C4×C13C22×C4
FrattiniC2×C4C22×#261
Fitting, prime radicalC2×C13×#41C4
socleC2×C13C2×#99
cosocleC2×Dic26C23
hypercenterC2×#41#261
hypocenterC13#2133
LCSG ▷ C2×C4×C13 ▷ C22×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C23 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
2. C2×#88113C2semidirect
3. #11718301C2semidirect
4. #11718295C2semidirect
114. C13#2133semidirect

Maximal subgroups

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

subgroupindex
#117195302
C2×#881132
#117183012
#117182952
#213313