Finite Group Databasebeta

← #35292276

Subgroups — #35292276

Order 21248.

150 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 27 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#24905630C211yesmaximal, characteristic
2#24905628C211yesmaximal, characteristic
3C83×#1705C211yesmaximal, characteristic
4#19127500—21no—
5#19127494—21no—
6#498×C83—21no—
7#498×C83C411yescharacteristic, complemented
8#492×C83—21no—
9#492×C83C2211yescharacteristic
10C82×C83C411yescharacteristic, complemented
11#14581711—41no—
12#14581707—41no—
13C2×SD16×C83—41no—
14C2×SD16×C83—42no—
15C4⋊Q8×C83—21no—
16C4⋊Q8×C83D411yescharacteristic
17#127×C83D411yescharacteristic
18#106×C83—42no—
19#106×C83—41no—
20C4×C8×C83—21no—
21C4×C8×C83C2×C411yescharacteristic
22#13050574—81no—
23C22⋊Dic83—81no—
24C2×Q8×C83—21no—
25C2×Q8×C83—41no—
26C2×D4×C83—21no—
27C2×D4×C83—41no—
28SD16×C83—82no—
29SD16×C83—84no—
30C2×C8×C83—22no—
31C2×C8×C83—21no—
32C4⋊C4×C83—41no—
33C4⋊C4×C83—41no—
34C4⋊C4×C83—41no—
35C42×C83C22⋊C411yescharacteristic
36C23×C83—41no—
37Q8×C83—81no—
38Q8×C83—82no—
39D4×C83—81no—
40D4×C83—82no—
41C2×C4×C83—21no—
42C2×C4×C83—41no—
43C2×C4×C83—81no—
44C2×C4×C83#9911yescharacteristic
45C2×Dic83—161no—
46C8×C83—24no—
47C8×C83—22no—
48C83⋊C8—161no—
49C22×C83—81no—
50C22×C83—161no—
51C22×C83#35311yescharacteristic
52C4×C83—22no—
53C4×C83—21no—
54C4×C83—81no—
55C4×C83—161no—
56Dic83—321no—
57#7535—831nomaximal, Sylow
58C2×C83—21no—
59C2×C83—161no—
60C2×C83#140911yescharacteristic
61#1705D8311yescharacteristic
62#1410—831no—
63#1409—831no—
64C83#753511yescharacteristic, complemented, Sylow
65#498—21no—
66#498Dic8311yescharacteristic, complemented
67#492—21no—
68#492C2×D8311yescharacteristic
69#356—1661no—
70#353—1661no—
71C82Dic8311yescharacteristic, complemented
72C2×SD16—41no—
73C2×SD16—42no—
74C4⋊Q8—21no—
75C4⋊Q8C22⋊D8311yescharacteristic
76#127C22⋊D8311yescharacteristic
77#106—42no—
78#106—41no—
79#101—3321no—
80#99—3321no—
81C4×C8—21no—
82C4×C8C2×Dic8311yescharacteristic
83C2×Q8—21no—
84C2×Q8—41no—
85C2×D4—21no—
86C2×D4—41no—
87SD16—82no—
88SD16—84no—
89M16—6641no—
90C2×C8—22no—
91C2×C8—21no—
92C4⋊C4—41no—
93C4⋊C4—41no—
94C4⋊C4—41no—
95C22⋊C4—6641no—
96C42C22⋊Dic8311yescharacteristic
97C23—41no—
98Q8—81no—
99Q8—82no—
100D4—81no—
101D4—82no—
102C2×C4—21no—
103C2×C4—41no—
104C2×C4—81no—
105C2×C4—13281no—
106C2×C4#1458170711yescharacteristic
107C8—24no—
108C8—22no—
109C8—13281no—
110C22—81no—
111C22—161no—
112C22#1912749411yescharacteristic
113C4—22no—
114C4—21no—
115C4—81no—
116C4—161no—
117C4—26561no—
118C2—21no—
119C2—161no—
120C2#2490562811yescharacteristic
subgroupG/H
centerC2#24905628
commutatorC4×C8×C83C2×C4
Frattini#492C2×D83
FittingC83×#1705C2
socleC2×C83#1409
prime radical#127×C83D4
cosocle#492×C83C22
hypercenter#1705D83
hypocenterC83#7535
LCSG ▷ C4×C8×C83 ▷ C42×C83 ▷ C2×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1705

Complements

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

NH ≅ G/Ntype
7. #498×C83C4semidirect
10. C82×C83C4semidirect
64. C83#7535semidirect
66. #498Dic83semidirect
71. C82Dic83semidirect

Maximal subgroups

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

subgroupindex
#249056302
#249056282
C83×#17052
#753583