Finite Group Databasebeta

← #35292263

Subgroups — #35292263

Order 21248.

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

normal subgroups only

This group has 152 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#24907068C211yesmaximal, characteristic
2#24905626C211yesmaximal, characteristic
3C83×#1408C211yesmaximal, characteristic
4#19128081C411yescharacteristic, complemented
5#19128047—21no—
6#19128047—21no—
7#19127494—21no—
8C8×C83⋊C8C411yescharacteristic, complemented
9#493×C83C2211yescharacteristic
10#353×C83—21no—
11C2×Dic332—41no—
12#14581792—21no—
13#14581713—42no—
14#14581713—42no—
15#14581707—41no—
16C4×C83⋊C8—21no—
17C2×D8×C83—41no—
18#127×C83D411yescharacteristic
19#127×C83D411yescharacteristic
20#99×C83—41no—
21C4×C8×C83C2×C411yescharacteristic
22C2×Dic166—41no—
23Dic332—82no—
24C2×C83⋊C8—22no—
25C4⋊Dic83—41no—
26C4⋊Dic83—41no—
27C22⋊Dic83—81no—
28C2×D4×C83—21no—
29C2×D4×C83—21no—
30C2×D4×C83—41no—
31C2×D4×C83—41no—
32D8×C83—82no—
33C2×C8×C83—21no—
34C22⋊C4×C83—81no—
35C42×C83C22⋊C411yescharacteristic
36C23×C83—41no—
37C23×C83—41no—
38D4×C83—81no—
39D4×C83—81no—
40D4×C83—82no—
41D4×C83—82no—
42C2×C4×C83—21no—
43C2×C4×C83—161no—
44C2×C4×C83#9911yescharacteristic
45C2×Dic83—81no—
46C2×Dic83—161no—
47Dic166—82no—
48C8×C83—22no—
49C83⋊C8—42no—
50C22×C83—81no—
51C22×C83—81no—
52C22×C83—161no—
53C22×C83—161no—
54C22×C83#35311yescharacteristic
55C4×C83—22no—
56C4×C83—21no—
57C4×C83—321no—
58Dic83—161no—
59Dic83—321no—
60#7530—831nomaximal, Sylow
61C2×C83—21no—
62C2×C83—161no—
63C2×C83—161no—
64C2×C83#140811yescharacteristic
65#1709—831no—
66#1408—831no—
67#1408D8311yescharacteristic
68C83#753011yescharacteristic, complemented, Sylow
69#494—831no—
70#493C2×D8311yescharacteristic
71#486—1661no—
72#486—1661no—
73#353—21no—
74#353—1661no—
75C82—831no—
76C2×Q16—3321no—
77C2×D8—41no—
78C4⋊Q8—1661no—
79#127D33211yescharacteristic
80#127C22⋊D8311yescharacteristic
81#102—3322no—
82#102—3322no—
83#99—41no—
84#99—3321no—
85C4×C8—1661no—
86C4×C8C4×D8311yescharacteristic
87C2×Q8—3321no—
88C2×D4—21no—
89C2×D4—21no—
90C2×D4—41no—
91C2×D4—41no—
92Q16—6642no—
93D8—82no—
94C2×C8—21no—
95C2×C8—1662no—
96C4⋊C4—3321no—
97C4⋊C4—3321no—
98C22⋊C4—81no—
99C22⋊C4—6641no—
100C42(C2×D83)⋊C411yescharacteristic
101C23—41no—
102C23—41no—
103Q8—6642no—
104D4—81no—
105D4—81no—
106D4—82no—
107D4—82no—
108C2×C4—21no—
109C2×C4—161no—
110C2×C4—13281no—
111C2×C4—6641no—
112C2×C4#1458170611yescharacteristic
113C8—22no—
114C8—3322no—
115C22—81no—
116C22—81no—
117C22—161no—
118C22—161no—
119C22#1912749311yescharacteristic
120C4—22no—
121C4—21no—
122C4—321no—
123C4—13281no—
124C4—26561no—
125C2—21no—
126C2—161no—
127C2—161no—
128C2#2490562511yescharacteristic
subgroupG/H
centerC2#24905625
commutatorC4×C8×C83C2×C4
Frattini#493C2×D83
FittingC83×#1408C2
socleC2×C83#1408
prime radical, cosocle#493×C83C22
hypercenter#1408D83
hypocenterC83#7530
LCSG ▷ C4×C8×C83 ▷ C42×C83 ▷ C2×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #493 ◁ #1408

Complements

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

NH ≅ G/Ntype
4. #19128081C4semidirect
8. C8×C83⋊C8C4semidirect
68. C83#7530semidirect

Maximal subgroups

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

subgroupindex
#249070682
#249056262
C83×#14082
#753083