Finite Group Databasebeta

← #13131244

Subgroups — #13131244

Order 1664.

142 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 142 conjugacy classes of subgroups — too many to draw. Only its 44 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#11719112C211yesmaximal, characteristic
2#11719110C211yesmaximal, characteristic, complemented
3#11718579C211yesmaximal, characteristic
4#11718282C211yesmaximal, characteristic, complemented
5#11718279C211yesmaximal, characteristic
6#11718220C211yesmaximal, characteristic, complemented
7#11718217C211yesmaximal, characteristic, complemented
8Q8×#261—21no—
9#88240—21no—
10#88173C2211yescharacteristic
11Q16×D13C2211yescharacteristic
12#88118—21no—
13#88117—21no—
14#88103C2211yescharacteristic
15#88101C2211yescharacteristic
16#88100C2211yescharacteristic
17#88098C2211yescharacteristic
18C13×Q32C411yescharacteristic, complemented
19#88069C411yescharacteristic, complemented
20#88068C411yescharacteristic, complemented
21#88040C411yescharacteristic, complemented
22#88038C2211yescharacteristic
23#6131—21no—
24Q8×D13—21no—
25C4⋊#261—21no—
26C4⋊#261—41no—
27C4×#261—41no—
28C4×#261D411yescharacteristic
29#6118—21no—
30#6118—41no—
31D13⋊C8—41no—
32D13⋊C8D411yescharacteristic
33C13×Q16C2×C411yescharacteristic
34C13×Q16C2×C411yescharacteristic
35#6107—21no—
36#6106—21no—
37Dic52C2×C411yescharacteristic
38D104C2×C411yescharacteristic
39C8×D13C2311yescharacteristic
40#6092—21no—
41C13×C16C2×C411yescharacteristic
42#6090C2×C411yescharacteristic
43#2180—131nomaximal, Sylow
44C2×#261—21no—
45C2×#261—41no—
46Q8×C13—21no—
47Q8×C13—21no—
48D52—21no—
49D52—41no—
50C4×D13—41no—
51C4×D13—41no—
52C4×D13C2×D411yescharacteristic
53Dic26—21no—
54Dic26—41no—
55#1057—21no—
56#1057—41no—
57C8×C13C22×C411yescharacteristic
58#1055#4111yescharacteristic
59#510—131no—
60#444—131no—
61#441—131no—
62#365—131no—
63#362—131no—
64#360—131no—
65#347—131no—
66C2×D13—41no—
67C2×D13AGL(1,ℤ/8)11yescharacteristic
68#261—41no—
69#261—81no—
70C4×C13—41no—
71C4×C13—41no—
72C4×C13C4×D411yescharacteristic
73Dic13—41no—
74Dic13AGL(1,ℤ/8)11yescharacteristic
75#135—131no—
76C2×Q16—131no—
77#131—261no—
78C4×Q8—261no—
79Q32—131no—
80Q32#26111yescharacteristic, complemented
81SD32—131no—
82SD32—131no—
83M32—131no—
84M32—131no—
85#108—131no—
86#106—131no—
87#104—261no—
88#103—261no—
89#97—131no—
90C2×C13#44211yescharacteristic
91D13—21no—
92D13—81no—
93#41—261no—
94C2×Q8—261no—
95Q16—131no—
96Q16—261no—
97Q16C2×#26111yescharacteristic
98Q16C2×#26111yescharacteristic
99SD16—261no—
100D8—131no—
101M16—261no—
102M16—521no—
103C2×C8—131no—
104C2×C8—131no—
105C2×C8—521no—
106C4⋊C4—261no—
107C4⋊C4—521no—
108C42—131no—
109C42—521no—
110C16—131no—
111C16—261no—
112C16C2×#26111yescharacteristic
113C13#218011yescharacteristic, complemented, Sylow
114Q8—21no—
115Q8—21no—
116Q8—261no—
117Q8—521no—
118D4—261no—
119D4—521no—
120C2×C4—131no—
121C2×C4—261no—
122C2×C4—521no—
123C2×C4—521no—
124C2×C4—521no—
125C8—131no—
126C8—261no—
127C8—521no—
128C8C22×#26111yescharacteristic
129C22—131no—
130C22—521no—
131C4—41no—
132C4—41no—
133C4—131no—
134C4—521no—
135C4—521no—
136C4—1041no—
137C4D4×#26111yescharacteristic
138C2—261no—
139C2—1041no—
140C2#1171910211yescharacteristic
subgroupG/H
centerC2#11719102
commutatorC8×C13C22×C4
FrattiniC8C22×#261
FittingC13×Q32C4
socleC2×C13#442
prime radical#88173C22
cosocleC8×D13C23
hypercenterQ32#261
hypocenterC13#2180
LCSG ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C4 ◁ C8 ◁ Q32

Complements

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

NH ≅ G/Ntype
2. #11719110C2semidirect
4. #11718282C2semidirect
6. #11718220C2semidirect
7. #11718217C2semidirect
18. C13×Q32C4semidirect
19. #88069C4semidirect
20. #88068C4semidirect
21. #88040C4semidirect
80. Q32#261semidirect
113. C13#2180semidirect

Maximal subgroups

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

subgroupindex
#117191122
#117191102
#117185792
#117182822
#117182792
#117182202
#117182172
#218013