Finite Group Databasebeta

← #35292248

Subgroups — #35292248

Order 21248.

134 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 134 conjugacy classes of subgroups — too many to draw. Only its 25 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#24906764C211yesmaximal, characteristic
2#24905634C211yesmaximal, characteristic
3C83×#1355C211yesmaximal, characteristic
4C83⋊#564C411yescharacteristic, complemented
5#19128065—21no—
6#19127494—21no—
7#19127443C411yescharacteristic, complemented
8#19127442—21no—
9#490×C83C2211yescharacteristic
10#347×C83—21no—
11#14581784—21no—
12#14581783—41no—
13#14581782—41no—
14#14581782—41no—
15#14581713—41no—
16#14581713—41no—
17#14581707—41no—
18#14581703—21no—
19#127×C83D411yescharacteristic
20#125×C83C2×C411yescharacteristic
21M32×C83—41no—
22#102×C83—41no—
23#97×C83D411yescharacteristic
24C2×C83⋊C8—41no—
25C4⋊Dic83—21no—
26C4⋊Dic83—21no—
27C4⋊Dic83—41no—
28Dic83⋊C4—41no—
29Dic83⋊C4—41no—
30Dic83⋊C4—41no—
31Dic83⋊C4—41no—
32C22⋊Dic83—81no—
33C4×Dic83—41no—
34C2×D4×C83—21no—
35C2×D4×C83—41no—
36C2×C8×C83—21no—
37C4⋊C4×C83—21no—
38C4⋊C4×C83—41no—
39C42×C83C22⋊C411yescharacteristic
40C16×C83—42no—
41C23×C83—41no—
42D4×C83—81no—
43D4×C83—82no—
44C2×C4×C83—21no—
45C2×C4×C83—41no—
46C2×C4×C83#9911yescharacteristic
47C2×Dic83—41no—
48C2×Dic83—41no—
49C2×Dic83—161no—
50C8×C83—41no—
51C83⋊C8—81no—
52C22×C83—81no—
53C22×C83—161no—
54C22×C83AΣL(1,𝔽16)11yescharacteristic
55C4×C83—21no—
56C4×C83—41no—
57C4×C83—81no—
58Dic83—81no—
59Dic83—81no—
60Dic83—321no—
61#7524—831nomaximal, Sylow
62C2×C83—21no—
63C2×C83—161no—
64C2×C83#140411yescharacteristic
65#1658—831no—
66#1412—831no—
67#1355D8311yescharacteristic
68C83#752411yescharacteristic, complemented, Sylow
69#564—831no—
70#490—1661no—
71#490C2×D8311yescharacteristic
72#353—1661no—
73#347—21no—
74#330—831no—
75#330—1661no—
76#127D33211yescharacteristic
77#125—3321no—
78#125—3321no—
79#125—3321no—
80#125—1661no—
81#125C4×D8311yescharacteristic
82M32—41no—
83#102—41no—
84#102—3321no—
85#102—3321no—
86#99—3321no—
87#97—1661no—
88#97C22⋊D8311yescharacteristic
89C2×D4—21no—
90C2×D4—41no—
91C2×C8—21no—
92C2×C8—3321no—
93C4⋊C4—21no—
94C4⋊C4—41no—
95C4⋊C4—3321no—
96C4⋊C4—3321no—
97C4⋊C4—3321no—
98C4⋊C4—3321no—
99C4⋊C4—3321no—
100C4⋊C4—1661no—
101C4⋊C4—1661no—
102C22⋊C4—6641no—
103C42—3321no—
104C42(C2×D83)⋊C411yescharacteristic
105C16—42no—
106C23—41no—
107D4—81no—
108D4—82no—
109C2×C4—21no—
110C2×C4—41no—
111C2×C4—13281no—
112C2×C4—3321no—
113C2×C4—3321no—
114C2×C4#1458170611yescharacteristic
115C8—41no—
116C8—6641no—
117C22—81no—
118C22—161no—
119C22#1912748911yescharacteristic
120C4—21no—
121C4—41no—
122C4—81no—
123C4—26561no—
124C4—6641no—
125C4—6641no—
126C2—21no—
127C2—161no—
128C2#2490561511yescharacteristic
subgroupG/H
centerC2#24905615
commutator#125×C83C2×C4
Frattini#490C2×D83
FittingC83×#1355C2
socleC2×C83#1404
prime radical#127×C83D4
cosocle#490×C83C22
hypercenter#1355D83
hypocenterC83#7524
LCSG ▷ #125×C83 ▷ C42×C83 ▷ C2×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #490 ◁ #1355

Complements

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

NH ≅ G/Ntype
4. C83⋊#564C4semidirect
7. #19127443C4semidirect
68. C83#7524semidirect

Maximal subgroups

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

subgroupindex
#249067642
#249056342
C83×#13552
#752483