Finite Group Databasebeta

← #23765478

Subgroups — #23765478

Order 10112.

150 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 150 conjugacy classes of subgroups — too many to draw. Only its 47 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#19099004C212yesmaximal
2#19098681C211yesmaximal, characteristic
3#19098384C211yesmaximal, characteristic, complemented
4#19098379C212yesmaximal, complemented
5#494×C79C211yesmaximal, characteristic, complemented
6#14579183C2211yescharacteristic
7#14579167—21no—
8#14579107—22no—
9#14579104—22no—
10#14579101C2212yes—
11#14579097C2211yescharacteristic
12#14579089—21no—
13C2×Q16×C79—21no—
14C2×Q16×C79C2212yes—
15C4⋊Q8×C79—21no—
16C4×C8×C79C2211yescharacteristic
17#11929624—21no—
18Dic316D411yescharacteristic
19#11929613—21no—
20D632D411yescharacteristic
21#11929608—21no—
22#11929607—41no—
23C8×D79—41no—
24C79⋊C16—22no—
25C2×Q8×C79—22no—
26Q16×C79—22no—
27Q16×C79—22no—
28Q16×C79—41no—
29Q16×C79—41no—
30C2×C8×C79D411yescharacteristic
31C2×C8×C79C2311yescharacteristic
32C4⋊C4×C79—42no—
33C42×C79D411yescharacteristic
34Q8×C79—42no—
35Q8×C79—42no—
36C2×C4×C79—21no—
37C2×C4×C79—42no—
38C2×C4×C79C2×D411yescharacteristic
39C22⋊D79—41no—
40D316—21no—
41C4×D79—41no—
42Dic158—21no—
43C8×C79D811yescharacteristic
44C8×C79D811yescharacteristic
45C8×C79C2×D411yescharacteristic
46C8×C79#4111yescharacteristic
47C79⋊C8—41no—
48C22×C79AGL(1,ℤ/8)11yescharacteristic
49C2×D79—41no—
50C4×C79—22no—
51C4×C79—82no—
52C4×C79#12111yescharacteristic
53C4×C79C2×D811yescharacteristic
54Dic79—41no—
55C2×C79—21no—
56C2×C79#45911yescharacteristic
57D79—81no—
58#2214—791nomaximal, Sylow
59C79#221411yescharacteristic, complemented, Sylow
60#510—792no—
61#494D7911yescharacteristic, complemented
62#443—791no—
63#364—791no—
64#362—792no—
65#135—791no—
66C2×Q16—21no—
67C2×Q16C2×D7912yes—
68#131—1581no—
69C4⋊Q8—21no—
70Q32—1582no—
71SD32—1582no—
72M32—792no—
73#108—791no—
74#104—1581no—
75C4×C8C2×D7911yescharacteristic
76#41—1581no—
77C2×Q8—22no—
78Q16—22no—
79Q16—22no—
80Q16—41no—
81Q16—41no—
82Q16—791no—
83SD16—1581no—
84D8—791no—
85M16—3161no—
86M16—1581no—
87C2×C8—3161no—
88C2×C8C22⋊D7911yescharacteristic
89C2×C8C22×D7911yescharacteristic
90C4⋊C4—42no—
91C42C22⋊D7911yescharacteristic
92C16—1582no—
93Q8—42no—
94Q8—42no—
95Q8—1581no—
96D4—3161no—
97D4—1581no—
98C2×C4—21no—
99C2×C4—42no—
100C2×C4—3161no—
101C2×C4C2×C22⋊D7911yescharacteristic
102C8—3161no—
103C8#1192960911yescharacteristic
104C8#1192960911yescharacteristic
105C8D4×D7911yescharacteristic
106C8#1192962311yescharacteristic
107C22—3161no—
108C22#1457918711yescharacteristic
109C4—22no—
110C4—82no—
111C4—3161no—
112C4#1457913211yescharacteristic
113C4C2×#1192960911yescharacteristic
114C2—21no—
115C2—6321no—
116C2#1909875511yescharacteristic
subgroupG/H
centerC2#19098755
commutator, cosocleC2×C8×C79C23
FrattiniC2×C8C22×D79
Fitting#494×C79C2
socleC2×C79#459
prime radical#14579183C22
hypercenter#494D79
hypocenterC79#2214
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #494

Complements

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

NH ≅ G/Ntype
3. #19098384C2semidirect
4. #19098379C2semidirect
5. #494×C79C2semidirect
59. C79#2214semidirect
61. #494D79semidirect