Finite Group Databasebeta

← #23762924

Subgroups — #23762924

Order 10112.

154 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 154 conjugacy classes of subgroups — too many to draw. Only its 55 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#19098968C211yesmaximal, characteristic, complemented
2#19098854C212yesmaximal
3#19098642C211yesmaximal, characteristic
4#19098311C212yesmaximal, complemented
5#334×C79C211yesmaximal, characteristic, complemented
6C2×#11929607—21no—
7#14579161C2212yes—
8C4×D316C2211yescharacteristic
9#14579095—21no—
10#14579095—21no—
11#14579093—22no—
12C4⋊(C79⋊C8)C2211yescharacteristic
13#14579083—22no—
14(C2×D79)⋊C8—21no—
15C4⋊C8×C79C2212yes—
16C4×C8×C79C2211yescharacteristic
17C2×Dic158—22no—
18C2×D316D411yescharacteristic
19C2×C4×D79—21no—
20#11929607—42no—
21C2×C79⋊C8—21no—
22C4⋊Dic79—22no—
23C4⋊Dic79—22no—
24C4⋊Dic79D411yescharacteristic
25(C2×D79)⋊C4—21no—
26C2×C8×C79—22no—
27C2×C8×C79D411yescharacteristic
28C2×C8×C79D411yescharacteristic
29C42×C79C2311yescharacteristic
30C22×D79—21no—
31C2×C4×C79C2×D411yescharacteristic
32C2×C4×C79C2×D411yescharacteristic
33C2×C4×C79#4111yescharacteristic
34C2×Dic79—21no—
35C2×Dic79—42no—
36D316—22no—
37C4×D79—41no—
38C4×D79—41no—
39Dic158—82no—
40C8×C79—21no—
41C8×C79—42no—
42C8×C79SD1612yes—
43C79⋊C8—41no—
44C22×C79#12111yescharacteristic
45C2×D79—41no—
46C2×D79—41no—
47C2×D79—41no—
48C4×C79—21no—
49C4×C79C2×SD1611yescharacteristic
50C4×C79#13712yes—
51C4×C79#13711yescharacteristic
52Dic79—41no—
53Dic79—82no—
54C2×C79#46111yescharacteristic
55C2×C79#47011yescharacteristic
56C2×C79#47211yescharacteristic
57D79—81no—
58#1695—791nomaximal, Sylow
59C79#169511yescharacteristic, complemented, Sylow
60#500—791no—
61#476—792no—
62#436—791no—
63#334D7911yescharacteristic, complemented
64#333—792no—
65C2×M16—1581no—
66C4⋊Q8—792no—
67C4×D4—791no—
68#107—1581no—
69#107—1581no—
70#106—1582no—
71C4⋊C8—791no—
72C4⋊C8C2×D7912yes—
73#102—1582no—
74C22⋊C8—1581no—
75C4×C8C2×D7911yescharacteristic
76C2×Q8—1582no—
77C2×D4—791no—
78C22×C4—1581no—
79M16—3162no—
80C2×C8—22no—
81C2×C8—1581no—
82C2×C8D31611yescharacteristic
83C2×C8D31611yescharacteristic
84C4⋊C4—791no—
85C4⋊C4—1582no—
86C4⋊C4—1582no—
87C22⋊C4—1581no—
88C42C22×D7911yescharacteristic
89C23—1581no—
90Q8—6322no—
91D4—1582no—
92C2×C4—3161no—
93C2×C4—3161no—
94C2×C4—3162no—
95C2×C4—1581no—
96C2×C4D4×D7911yescharacteristic
97C2×C4C2×D31611yescharacteristic
98C2×C4#1192962511yescharacteristic
99C8—21no—
100C8—42no—
101C8—3161no—
102C8#1192961312yes—
103C22—3161no—
104C22—3161no—
105C22—3161no—
106C22#1457913611yescharacteristic
107C4—21no—
108C4—3161no—
109C4—6322no—
110C4C2×#1192961311yescharacteristic
111C4#1457919012yes—
112C4#1457919411yescharacteristic
113C2—6321no—
114C2#1909876911yescharacteristic
115C2#1909882211yescharacteristic
116C2#1909883411yescharacteristic
subgroupG/H
centerC22#14579136
commutator, cosocleC42×C79C23
FrattiniC42C22×D79
Fitting#334×C79C2
socleC22×C79#121
prime radicalC2×D316D4
hypercenter#334D79
hypocenterC79#1695
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #334

Complements

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

NH ≅ G/Ntype
1. #19098968C2semidirect
4. #19098311C2semidirect
5. #334×C79C2semidirect
59. C79#1695semidirect
63. #334D79semidirect