Finite Group Databasebeta

← #23765473

Subgroups — #23765473

Order 10112.

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

normal subgroups only

This group has 170 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#19098999C212yesmaximal, complemented
2#19098681C211yesmaximal, characteristic, complemented
3#19098384C211yesmaximal, characteristic, complemented
4#19098376C212yesmaximal, complemented
5#493×C79C211yesmaximal, characteristic, complemented
6#14579183C2211yescharacteristic
7#14579167—21no—
8#14579105—22no—
9#14579102—22no—
10#14579101C2212yes—
11#14579097C2211yescharacteristic
12#14579089—21no—
13C2×D8×C79—21no—
14C2×D8×C79C2212yes—
15#127×C79—21no—
16C4×C8×C79C2211yescharacteristic
17#11929624—21no—
18Dic316D411yescharacteristic, complemented
19#11929613—21no—
20D632D411yescharacteristic, complemented
21#11929608—21no—
22#11929607—41no—
23C8×D79—41no—
24C79⋊C16—22no—
25C2×D4×C79—22no—
26C2×D4×C79—42no—
27D8×C79—22no—
28D8×C79—22no—
29D8×C79—41no—
30D8×C79—41no—
31C2×C8×C79D411yescharacteristic
32C2×C8×C79C2311yescharacteristic
33C42×C79D411yescharacteristic
34C23×C79—42no—
35D4×C79—42no—
36D4×C79—42no—
37D4×C79—84no—
38C2×C4×C79—21no—
39C2×C4×C79C2×D411yescharacteristic
40C22⋊D79—41no—
41D316—21no—
42C4×D79—41no—
43Dic158—21no—
44C8×C79D811yescharacteristic
45C8×C79D811yescharacteristic
46C8×C79C2×D411yescharacteristic
47C8×C79#4111yescharacteristic
48C79⋊C8—41no—
49C22×C79—84no—
50C22×C79—82no—
51C22×C79AGL(1,ℤ/8)11yescharacteristic
52C2×D79—41no—
53C4×C79—22no—
54C4×C79#12111yescharacteristic
55C4×C79C2×D811yescharacteristic
56Dic79—41no—
57C2×C79—21no—
58C2×C79—162no—
59C2×C79#45911yescharacteristic
60D79—81no—
61#2213—791nomaximal, Sylow
62C79#221311yescharacteristic, complemented, Sylow
63#509—792no—
64#493D7911yescharacteristic, complemented
65#443—791no—
66#364—791no—
67#361—792no—
68#135—791no—
69C2×D8—21no—
70C2×D8C2×D7912yes—
71#131—1581no—
72#127—21no—
73SD32—1582no—
74D16—1582no—
75M32—792no—
76#108—791no—
77#104—1581no—
78C4×C8C2×D7911yescharacteristic
79#41—1581no—
80C2×D4—22no—
81C2×D4—42no—
82Q16—791no—
83SD16—1581no—
84D8—22no—
85D8—22no—
86D8—41no—
87D8—41no—
88D8—791no—
89M16—3161no—
90M16—1581no—
91C2×C8—3161no—
92C2×C8C22⋊D7911yescharacteristic
93C2×C8C22×D7911yescharacteristic
94C42C22⋊D7911yescharacteristic
95C16—1582no—
96C23—42no—
97Q8—1581no—
98D4—42no—
99D4—42no—
100D4—84no—
101D4—3161no—
102D4—1581no—
103C2×C4—21no—
104C2×C4—3161no—
105C2×C4C2×C22⋊D7911yescharacteristic
106C8—3161no—
107C8#1192960911yescharacteristic
108C8#1192960911yescharacteristic
109C8D4×D7911yescharacteristic
110C8#1192962311yescharacteristic
111C22—84no—
112C22—82no—
113C22—3161no—
114C22#1457918711yescharacteristic
115C4—22no—
116C4—3161no—
117C4#1457913211yescharacteristic
118C4C2×#1192960911yescharacteristic
119C2—21no—
120C2—162no—
121C2—6321no—
122C2#1909875511yescharacteristic
subgroupG/H
centerC2#19098755
commutator, cosocleC2×C8×C79C23
FrattiniC2×C8C22×D79
Fitting#493×C79C2
socleC2×C79#459
hypercenter#493D79
hypocenterC79#2213
LCSG ▷ C2×C8×C79 ▷ C4×C79 ▷ C2×C79 ▷ C79
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #493

Complements

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

NH ≅ G/Ntype
1. #19098999C2semidirect
2. #19098681C2semidirect
3. #19098384C2semidirect
4. #19098376C2semidirect
5. #493×C79C2semidirect
18. Dic316D4semidirect
20. D632D4semidirect
62. C79#2213semidirect
64. #493D79semidirect