Finite Group Databasebeta

← #35292230

Subgroups — #35292230

Order 21248.

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

normal subgroups only

This group has 148 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#24906582C211yesmaximal, characteristic
2#24905630C211yesmaximal, characteristic
3C83×#1359C211yesmaximal, characteristic
4#19128437C411yescharacteristic
5#19127993—21no—
6#19127500—21no—
7#19127445C411yescharacteristic
8#19127433—21no—
9#492×C83C2211yescharacteristic
10#364×C83—21no—
11#14581779—41no—
12#14581773—41no—
13C4×Dic166—21no—
14D4×Dic83—41no—
15#14581725—41no—
16C4⋊(C83⋊C8)—21no—
17#14581715—41no—
18#14581711—41no—
19C2×SD16×C83—41no—
20C4⋊Q8×C83D411yescharacteristic
21#127×C83C2×C411yescharacteristic
22M32×C83—41no—
23C4×C8×C83D411yescharacteristic
24C2×Dic166—21no—
25C22×Dic83—41no—
26#13050574—81no—
27C2×C83⋊C8—41no—
28C4⋊Dic83—21no—
29Dic83⋊C4—41no—
30C22⋊Dic83—42no—
31C22⋊Dic83—41no—
32C4×Dic83—41no—
33C2×Q8×C83—21no—
34C2×D4×C83—21no—
35C2×D4×C83—41no—
36SD16×C83—81no—
37SD16×C83—81no—
38C2×C8×C83—21no—
39C4⋊C4×C83—41no—
40C42×C83C22⋊C411yescharacteristic
41C16×C83—81no—
42C23×C83—41no—
43Q8×C83—81no—
44D4×C83—81no—
45D4×C83—81no—
46D4×C83—81no—
47C2×C4×C83—21no—
48C2×C4×C83—41no—
49C2×C4×C83#9911yescharacteristic
50C2×Dic83—41no—
51C2×Dic83—41no—
52C2×Dic83—161no—
53Dic166—41no—
54Dic166—41no—
55C8×C83—21no—
56C8×C83—21no—
57C83⋊C8—81no—
58C83⋊C8—161no—
59C22×C83—82no—
60C22×C83—81no—
61C22×C83AΣL(1,𝔽16)11yescharacteristic
62C4×C83—21no—
63C4×C83—21no—
64C4×C83—21no—
65C4×C83—81no—
66Dic83—81no—
67Dic83—81no—
68#7518—831nomaximal, Sylow
69C2×C83—21no—
70C2×C83—161no—
71C2×C83#140211yescharacteristic
72#1630—831no—
73#1410—831no—
74#1359D8311yescharacteristic
75C83#751811yescharacteristic, complemented, Sylow
76#559—831no—
77#492C2×D8311yescharacteristic
78#477—1661no—
79#364—21no—
80#356—1661no—
81#331—831no—
82Q8⋊C8—1661no—
83C2×SD16—41no—
84C4⋊Q8D33211yescharacteristic
85#127C4×D8311yescharacteristic
86#124—3321no—
87#123—3321no—
88C4×Q8—1661no—
89C4×D4—3321no—
90M32—41no—
91#107—3321no—
92C4⋊C8—1661no—
93#103—3321no—
94#101—3321no—
95C4×C8C22⋊D8311yescharacteristic
96C2×Q8—21no—
97C2×Q8—1661no—
98C2×D4—21no—
99C2×D4—41no—
100C22×C4—3321no—
101SD16—81no—
102SD16—81no—
103M16—6641no—
104C2×C8—21no—
105C2×C8—3321no—
106C4⋊C4—41no—
107C4⋊C4—3321no—
108C4⋊C4—1661no—
109C22⋊C4—3322no—
110C22⋊C4—3321no—
111C42—3321no—
112C42(C2×D83)⋊C411yescharacteristic
113C16—81no—
114C23—41no—
115Q8—81no—
116Q8—3321no—
117Q8—3321no—
118D4—81no—
119D4—81no—
120D4—81no—
121C2×C4—21no—
122C2×C4—41no—
123C2×C4—13281no—
124C2×C4—3321no—
125C2×C4—3321no—
126C2×C4#1458170611yescharacteristic
127C8—21no—
128C8—21no—
129C8—13281no—
130C8—6641no—
131C22—82no—
132C22—81no—
133C22#1912748911yescharacteristic
134C4—21no—
135C4—21no—
136C4—21no—
137C4—81no—
138C4—6641no—
139C4—6641no—
140C2—21no—
141C2—161no—
142C2#2490560911yescharacteristic
subgroupG/H
centerC2#24905609
commutator, prime radical#127×C83C2×C4
Frattini#492C2×D83
FittingC83×#1359C2
socleC2×C83#1402
cosocle#492×C83C22
hypercenter#1359D83
hypocenterC83#7518
LCSG ▷ #127×C83 ▷ C42×C83 ▷ C2×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1359

Complements

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

NH ≅ G/Ntype
75. C83#7518semidirect

Maximal subgroups

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

subgroupindex
#249065822
#249056302
C83×#13592
#751883