Finite Group Databasebeta

← #23761555

Subgroups — #23761555

Order 10112.

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#19098745C211yesmaximal, characteristic
2#19098362C211yesmaximal, characteristic, complemented
3#333×C79C211yesmaximal, characteristic, complemented
4#14579209C411yescharacteristic
5#14579192—21no—
6#14579089—21no—
7#14579080—21no—
8#14579080C411yescharacteristic
9C4⋊Q8×C79C2211yescharacteristic
10C4⋊C8×C79—21no—
11#11929625—41no—
12#11929624—21no—
13#11929624—41no—
14Q8×D79—41no—
15#11929614—41no—
16#11929611—41no—
17#11929608—21no—
18#11929608—41no—
19C2×Q8×C79C2×C411yescharacteristic
20C2×Q8×C79D411yescharacteristic
21C2×C8×C79—41no—
22C4⋊C4×C79—41no—
23C42×C79D411yescharacteristic
24Q8×C79—41no—
25Q8×C79—41no—
26C2×C4×C79—21no—
27C2×C4×C79—21no—
28C2×C4×C79—21no—
29C2×C4×C79C22⋊C411yescharacteristic
30C22⋊D79—41no—
31D316—21no—
32D316—41no—
33C4×D79—41no—
34C4×D79—42no—
35Dic158—21no—
36Dic158—41no—
37C8×C79—81no—
38C79⋊C8—41no—
39C79⋊C8—81no—
40C22×C79#9911yescharacteristic
41C2×D79—41no—
42C4×C79—21no—
43C4×C79—21no—
44C4×C79—21no—
45C4×C79—41no—
46C4×C79—41no—
47Dic79—41no—
48C2×C79—21no—
49C2×C79AΣL(1,𝔽16)11yescharacteristic
50D79—81no—
51#1405—791nomaximal, Sylow
52C79#140511yescharacteristic, complemented, Sylow
53#456—791no—
54#356—791no—
55#333D7911yescharacteristic, complemented
562−1+4—791no—
57#137—1581no—
58C4⋊Q8C2×D7911yescharacteristic
59C4⋊C8—21no—
60#104—1581no—
61#101—791no—
62#101—1581no—
63#41—3161no—
64#41—3161no—
65#41—1581no—
66C2×Q8—3161no—
67C2×Q8C4×D7911yescharacteristic
68C2×Q8D31611yescharacteristic
69Q16—3161no—
70SD16—3161no—
71M16—3161no—
72M16—1581no—
73C2×C8—41no—
74C4⋊C4—41no—
75C42C22⋊D7911yescharacteristic
76Q8—41no—
77Q8—41no—
78Q8—3161no—
79Q8—1581no—
80D4—3161no—
81D4—3161no—
82D4—1581no—
83C2×C4—21no—
84C2×C4—21no—
85C2×C4—21no—
86C2×C4—3161no—
87C2×C4—3162no—
88C2×C4(C2×D79)⋊C411yescharacteristic
89C8—81no—
90C8—3161no—
91C8—6321no—
92C22—3161no—
93C22#1457907511yescharacteristic
94C4—21no—
95C4—21no—
96C4—21no—
97C4—41no—
98C4—41no—
99C4—3161no—
100C2—21no—
101C2—6321no—
102C2#1909835111yescharacteristic
subgroupG/H
centerC2#19098351
commutatorC2×Q8×C79C2×C4
FrattiniC4⋊Q8C2×D79
Fitting#333×C79C2
socleC2×C79AΣL(1,𝔽16)
prime radical#14579209C4
cosocleC4⋊Q8×C79C22
hypercenter#333D79
hypocenterC79#1405
LCSG ▷ C2×Q8×C79 ▷ C2×C4×C79 ▷ C22×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #333

Complements

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

NH ≅ G/Ntype
2. #19098362C2semidirect
3. #333×C79C2semidirect
52. C79#1405semidirect
55. #333D79semidirect