Finite Group Databasebeta

← #35292279

Subgroups — #35292279

Order 21248.

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

normal subgroups only

This group has 138 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×#1708C211yesmaximal, characteristic
4#19127500—21no—
5#19127494—21no—
6#498×C83C411yescharacteristic, complemented
7#492×C83C2211yescharacteristic
8#487×C83—21no—
9#486×C83—21no—
10C82×C83C411yescharacteristic, complemented
11#14581711—41no—
12#14581707—41no—
13C2×SD16×C83—41no—
14C4⋊Q8×C83—21no—
15C4⋊Q8×C83D411yescharacteristic
16#127×C83D411yescharacteristic
17#106×C83—41no—
18#103×C83—42no—
19#102×C83—42no—
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—
29C2×C8×C83—21no—
30C2×C8×C83—22no—
31C4⋊C4×C83—41no—
32C4⋊C4×C83—41no—
33C4⋊C4×C83—41no—
34C42×C83C22⋊C411yescharacteristic
35C23×C83—41no—
36Q8×C83—81no—
37Q8×C83—82no—
38D4×C83—81no—
39D4×C83—82no—
40C2×C4×C83—21no—
41C2×C4×C83—41no—
42C2×C4×C83—81no—
43C2×C4×C83#9911yescharacteristic
44C2×Dic83—161no—
45C8×C83—22no—
46C8×C83—42no—
47C83⋊C8—161no—
48C22×C83—81no—
49C22×C83—161no—
50C22×C83#35311yescharacteristic
51C4×C83—22no—
52C4×C83—21no—
53C4×C83—81no—
54C4×C83—161no—
55Dic83—321no—
56#7536—831nomaximal, Sylow
57C2×C83—21no—
58C2×C83—161no—
59C2×C83#140911yescharacteristic
60#1708D8311yescharacteristic
61#1410—831no—
62#1409—831no—
63C83#753611yescharacteristic, complemented, Sylow
64#498Dic8311yescharacteristic, complemented
65#492C2×D8311yescharacteristic
66#487—21no—
67#486—21no—
68#356—1661no—
69#353—1661no—
70C82Dic8311yescharacteristic, complemented
71C2×SD16—41no—
72C4⋊Q8—21no—
73C4⋊Q8C22⋊D8311yescharacteristic
74#127C22⋊D8311yescharacteristic
75#106—41no—
76#103—42no—
77#102—42no—
78#101—3321no—
79#99—3321no—
80C4×C8—21no—
81C4×C8C2×Dic8311yescharacteristic
82C2×Q8—21no—
83C2×Q8—41no—
84C2×D4—21no—
85C2×D4—41no—
86SD16—82no—
87M16—6641no—
88C2×C8—21no—
89C2×C8—22no—
90C4⋊C4—41no—
91C4⋊C4—41no—
92C4⋊C4—41no—
93C22⋊C4—6641no—
94C42C22⋊Dic8311yescharacteristic
95C23—41no—
96Q8—81no—
97Q8—82no—
98D4—81no—
99D4—82no—
100C2×C4—21no—
101C2×C4—41no—
102C2×C4—81no—
103C2×C4—13281no—
104C2×C4#1458170711yescharacteristic
105C8—22no—
106C8—42no—
107C8—13281no—
108C22—81no—
109C22—161no—
110C22#1912749411yescharacteristic
111C4—22no—
112C4—21no—
113C4—81no—
114C4—161no—
115C4—26561no—
116C2—21no—
117C2—161no—
118C2#2490562811yescharacteristic
subgroupG/H
centerC2#24905628
commutatorC4×C8×C83C2×C4
Frattini#492C2×D83
FittingC83×#1708C2
socleC2×C83#1409
prime radical#127×C83D4
cosocle#492×C83C22
hypercenter#1708D83
hypocenterC83#7536
LCSG ▷ C4×C8×C83 ▷ C42×C83 ▷ C2×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1708

Complements

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

NH ≅ G/Ntype
6. #498×C83C4semidirect
10. C82×C83C4semidirect
63. C83#7536semidirect
64. #498Dic83semidirect
70. C82Dic83semidirect

Maximal subgroups

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

subgroupindex
#249056302
#249056282
C83×#17082
#753683