Finite Group Databasebeta

← #24905618

Subgroups — #24905618

Order 10624.

106 conjugacy classes of subgroups; only the 23 normal subgroups are shown.

normal subgroups only

This group has 106 conjugacy classes of subgroups — too many to draw. Only its 23 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#19127883C211yesmaximal, characteristic
2#19127500C211yesmaximal, characteristic, complemented
3#333×C83C211yesmaximal, characteristic, complemented
4#14581840C411yescharacteristic
5#14581823—21no—
6#14581720—21no—
7#14581711—21no—
8#14581711C411yescharacteristic
9C4⋊Q8×C83C2211yescharacteristic
10C4⋊C8×C83—21no—
11#13050591—41no—
12#13050590—21no—
13#13050590—41no—
14Q8×D83—41no—
15#13050580—41no—
16#13050577—41no—
17#13050574—21no—
18#13050574—41no—
19C2×Q8×C83C2×C411yescharacteristic
20C2×Q8×C83D411yescharacteristic
21C2×C8×C83—41no—
22C4⋊C4×C83—41no—
23C42×C83D411yescharacteristic
24Q8×C83—41no—
25Q8×C83—41no—
26C2×C4×C83—21no—
27C2×C4×C83—21no—
28C2×C4×C83—21no—
29C2×C4×C83C22⋊C411yescharacteristic
30C22⋊D83—41no—
31D332—21no—
32D332—41no—
33C4×D83—41no—
34C4×D83—42no—
35Dic166—21no—
36Dic166—41no—
37C8×C83—81no—
38C83⋊C8—41no—
39C83⋊C8—81no—
40C22×C83#9911yescharacteristic
41C2×D83—41no—
42C4×C83—21no—
43C4×C83—21no—
44C4×C83—21no—
45C4×C83—41no—
46C4×C83—41no—
47Dic83—41no—
48C2×C83—21no—
49C2×C83AΣL(1,𝔽16)11yescharacteristic
50D83—81no—
51#1405—831nomaximal, Sylow
52C83#140511yescharacteristic, complemented, Sylow
53#456—831no—
54#356—831no—
55#333D8311yescharacteristic, complemented
562−1+4—831no—
57#137—1661no—
58C4⋊Q8C2×D8311yescharacteristic
59C4⋊C8—21no—
60#104—1661no—
61#101—831no—
62#101—1661no—
63#41—3321no—
64#41—3321no—
65#41—1661no—
66C2×Q8—3321no—
67C2×Q8C4×D8311yescharacteristic
68C2×Q8D33211yescharacteristic
69Q16—3321no—
70SD16—3321no—
71M16—3321no—
72M16—1661no—
73C2×C8—41no—
74C4⋊C4—41no—
75C42C22⋊D8311yescharacteristic
76Q8—41no—
77Q8—41no—
78Q8—3321no—
79Q8—1661no—
80D4—3321no—
81D4—3321no—
82D4—1661no—
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—3321no—
87C2×C4—3322no—
88C2×C4(C2×D83)⋊C411yescharacteristic
89C8—81no—
90C8—3321no—
91C8—6641no—
92C22—3321no—
93C22#1458170611yescharacteristic
94C4—21no—
95C4—21no—
96C4—21no—
97C4—41no—
98C4—41no—
99C4—3321no—
100C2—21no—
101C2—6641no—
102C2#1912748911yescharacteristic
subgroupG/H
centerC2#19127489
commutatorC2×Q8×C83C2×C4
FrattiniC4⋊Q8C2×D83
Fitting#333×C83C2
socleC2×C83AΣL(1,𝔽16)
prime radical#14581840C4
cosocleC4⋊Q8×C83C22
hypercenter#333D83
hypocenterC83#1405
LCSG ▷ C2×Q8×C83 ▷ C2×C4×C83 ▷ C22×C83 ▷ C2×C83 ▷ C83
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #19127500C2semidirect
3. #333×C83C2semidirect
52. C83#1405semidirect
55. #333D83semidirect