Finite Group Databasebeta

← #35292274

Subgroups — #35292274

Order 21248.

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

normal subgroups only

This group has 128 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#24907094C211yesmaximal, characteristic
2#24905632C211yesmaximal, characteristic
3C83×#1411C211yesmaximal, characteristic
4#19128099C411yescharacteristic
5#19128097—21no—
6#19128053—21no—
7#19127500—21no—
8#19127422C411yescharacteristic
9#494×C83C2211yescharacteristic
10#356×C83—21no—
11#14581792—21no—
12#14581724—41no—
13#14581723—42no—
14#14581715—42no—
15#14581711—41no—
16C4×C83⋊C8—21no—
17C2×Q16×C83—41no—
18C4⋊Q8×C83D411yescharacteristic
19C4⋊Q8×C83D411yescharacteristic
20#101×C83—41no—
21C4×C8×C83C2×C411yescharacteristic
22C2×Dic166—41no—
23#13050574—81no—
24C2×C83⋊C8—22no—
25C4⋊Dic83—41no—
26C4⋊Dic83—41no—
27C2×Q8×C83—21no—
28C2×Q8×C83—21no—
29Q16×C83—82no—
30M16×C83—81no—
31C2×C8×C83—21no—
32C4⋊C4×C83—41no—
33C4⋊C4×C83—41no—
34C42×C83C22⋊C411yescharacteristic
35Q8×C83—81no—
36Q8×C83—81no—
37C2×C4×C83—21no—
38C2×C4×C83—41no—
39C2×C4×C83—41no—
40C2×C4×C83#9911yescharacteristic
41C2×Dic83—81no—
42Dic166—82no—
43C8×C83—22no—
44C8×C83—161no—
45C83⋊C8—42no—
46C83⋊C8—161no—
47C22×C83#35311yescharacteristic
48C4×C83—22no—
49C4×C83—21no—
50C4×C83—81no—
51C4×C83—81no—
52Dic83—161no—
53#7534—831nomaximal, Sylow
54C2×C83—21no—
55C2×C83#140911yescharacteristic
56#1716—831no—
57#1411—831no—
58#1411D8311yescharacteristic
59C83#753411yescharacteristic, complemented, Sylow
60#498—831no—
61#498—1661no—
62#494C2×D8311yescharacteristic
63#487—1661no—
64#356—21no—
65#356—1661no—
66#322—831no—
67C2×Q16—41no—
68C4⋊Q8—1661no—
69C4⋊Q8D33211yescharacteristic
70C4⋊Q8C22⋊D8311yescharacteristic
71#106—3322no—
72#106—3321no—
73#103—3322no—
74#101—41no—
75#101—3321no—
76C4×C8—1661no—
77C4×C8C4×D8311yescharacteristic
78C2×Q8—21no—
79C2×Q8—21no—
80C2×Q8—3321no—
81Q16—82no—
82M16—81no—
83M16—6641no—
84C2×C8—21no—
85C2×C8—1662no—
86C4⋊C4—41no—
87C4⋊C4—41no—
88C4⋊C4—3321no—
89C4⋊C4—3321no—
90C42(C2×D83)⋊C411yescharacteristic
91Q8—81no—
92Q8—81no—
93Q8—6642no—
94C2×C4—21no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—6641no—
98C2×C4#1458170611yescharacteristic
99C8—22no—
100C8—161no—
101C8—13281no—
102C8—3322no—
103C22#1912749311yescharacteristic
104C4—22no—
105C4—21no—
106C4—81no—
107C4—81no—
108C4—13281no—
109C2—21no—
110C2#2490562711yescharacteristic
subgroupG/H
centerC2#24905627
commutatorC4×C8×C83C2×C4
Frattini#494C2×D83
FittingC83×#1411C2
socleC2×C83#1409
prime radicalC22×C83#353
cosocle#494×C83C22
hypercenter#1411D83
hypocenterC83#7534
LCSG ▷ C4×C8×C83 ▷ C42×C83 ▷ C2×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #494 ◁ #1411

Complements

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

NH ≅ G/Ntype
59. C83#7534semidirect

Maximal subgroups

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

subgroupindex
#249070942
#249056322
C83×#14112
#753483