Finite Group Databasebeta

← #13131236

Subgroups — #13131236

Order 1664.

146 conjugacy classes of subgroups; only the 46 normal subgroups are shown.

normal subgroups only

This group has 146 conjugacy classes of subgroups — too many to draw. Only its 46 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#11719111C211yesmaximal, characteristic, complemented
2#11719103C211yesmaximal, characteristic, complemented
3#11718577C211yesmaximal, characteristic
4#11718281C211yesmaximal, characteristic, complemented
5#11718277C211yesmaximal, characteristic, complemented
6#11718224C211yesmaximal, characteristic, complemented
7C16×#261C211yesmaximal, characteristic, complemented
8#88240—21no—
9#88238—21no—
10#88173C2211yescharacteristic
11#88166C2211yescharacteristic
12#88118—21no—
13#88116—21no—
14#88104C2211yescharacteristic
15#88104C2211yescharacteristic
16C8×#261C2211yescharacteristic
17D13⋊C16C2211yescharacteristic
18C13×SD32C411yescharacteristic, complemented
19#88069C411yescharacteristic, complemented
20#88066C411yescharacteristic, complemented
21#88040C411yescharacteristic, complemented
22C16×D13C2211yescharacteristic
23#6131—21no—
24#6129—21no—
25#6122—41no—
26C2×#1057—41no—
27C4×#261D411yescharacteristic
28#6118—21no—
29#6118—21no—
30#6118—41no—
31D13⋊C8—41no—
32D13⋊C8D411yescharacteristic
33C13×Q16C2×C411yescharacteristic
34C13×D8C2×C411yescharacteristic
35#6106—21no—
36#6105—21no—
37Dic52C2×C411yescharacteristic
38D104C2×C411yescharacteristic
39C8×D13C2311yescharacteristic
40#6092—21no—
41C13×C16C2×C411yescharacteristic
42#6090C2×C411yescharacteristic
43#2178—131nomaximal, Sylow
44C2×#261—21no—
45Q8×C13—21no—
46D4×C13—21no—
47C22⋊D13—41no—
48C2×Dic13—41no—
49D52—21no—
50D52—41no—
51C4×D13—41no—
52C4×D13C2×D411yescharacteristic
53Dic26—21no—
54#1057—41no—
55#1057—41no—
56#1057D811yescharacteristic
57#1057D811yescharacteristic
58C8×C13C22×C411yescharacteristic
59#1055#4111yescharacteristic
60#508—131no—
61#443—131no—
62#443—131no—
63#368—131no—
64#359—131no—
65#359—131no—
66C4×C16—131no—
67C22×C13—41no—
68C2×D13—41no—
69C2×D13#13511yescharacteristic
70#261—22no—
71C4×C13—41no—
72C4×C13C4×D411yescharacteristic
73Dic13—41no—
74Dic13C2×D811yescharacteristic
75#135—131no—
76#135—131no—
77#131—261no—
78#131—261no—
79Q32—131no—
80SD32—131no—
81SD32#26111yescharacteristic, complemented
82D16—131no—
83C2×C16—131no—
84C2×C16—131no—
85#108—131no—
86#108—131no—
87#104—261no—
88#104—261no—
89C4×C8—131no—
90C2×C13—81no—
91C2×C13C4×D811yescharacteristic
92D13—21no—
93D13—81no—
94#41—261no—
95#41—261no—
96Q16—131no—
97Q16C2×#26111yescharacteristic
98SD16—261no—
99SD16—261no—
100D8—131no—
101D8C2×#26111yescharacteristic
102M16—261no—
103M16—261no—
104M16—521no—
105M16—521no—
106C2×C8—131no—
107C2×C8—131no—
108C2×C8—521no—
109C2×C8—521no—
110C42—131no—
111C16—131no—
112C16—261no—
113C16C2×#26111yescharacteristic
114C13#217811yescharacteristic, complemented, Sylow
115Q8—21no—
116Q8—261no—
117D4—21no—
118D4—261no—
119D4—521no—
120D4—521no—
121C2×C4—131no—
122C2×C4—261no—
123C2×C4—521no—
124C2×C4—521no—
125C8—131no—
126C8—131no—
127C8—131no—
128C8—521no—
129C8—521no—
130C8C22×#26111yescharacteristic
131C22—41no—
132C22—131no—
133C22—521no—
134C4—41no—
135C4—131no—
136C4—262no—
137C4—521no—
138C4D4×#26111yescharacteristic
139C2—81no—
140C2—261no—
141C2—1041no—
142C2D8×#26111yescharacteristic
subgroupG/H
centerC2D8×#261
commutatorC8×C13C22×C4
FrattiniC8C22×#261
FittingC13×SD32C4
socleC2×C13C4×D8
prime radical#11718577C2
cosocleC8×D13C23
hypercenterSD32#261
hypocenterC13#2178
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ SD32

Complements

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

NH ≅ G/Ntype
1. #11719111C2semidirect
2. #11719103C2semidirect
4. #11718281C2semidirect
5. #11718277C2semidirect
6. #11718224C2semidirect
7. C16×#261C2semidirect
18. C13×SD32C4semidirect
19. #88069C4semidirect
20. #88066C4semidirect
21. #88040C4semidirect
81. SD32#261semidirect
114. C13#2178semidirect

Maximal subgroups

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

subgroupindex
#117191112
#117191032
#117185772
#117182812
#117182772
#117182242
C16×#2612
#217813