Finite Group Databasebeta

← #23762886

Subgroups — #23762886

Order 10112.

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

normal subgroups only

This group has 166 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#19098840C212yesmaximal
2#19098642C211yesmaximal, characteristic
3#19098314C211yesmaximal, characteristic, complemented
4#19098309C212yesmaximal, complemented
5#494×C79C211yesmaximal, characteristic, complemented
6C2×#11929607—21no—
7C4×D316C2211yescharacteristic
8#14579094—22no—
9C4⋊(C79⋊C8)C2211yescharacteristic
10C4⋊(C79⋊C8)C2212yes—
11#14579081—22no—
12(C2×D79)⋊C8—21no—
13C2×Q16×C79—21no—
14C2×Q16×C79—21no—
15C4⋊Q8×C79C2212yes—
16C4×C8×C79C2211yescharacteristic
17C2×D316D411yescharacteristic
18C2×C4×D79—21no—
19#11929607—42no—
20C2×C79⋊C8—21no—
21C2×C79⋊C8—22no—
22C4⋊Dic79D411yescharacteristic
23(C2×D79)⋊C4—21no—
24C2×Q8×C79—22no—
25Q16×C79—42no—
26Q16×C79—42no—
27C2×C8×C79D411yescharacteristic
28C2×C8×C79D411yescharacteristic
29C4⋊C4×C79—22no—
30C4⋊C4×C79—22no—
31C42×C79C2311yescharacteristic
32C22×D79—21no—
33Q8×C79—42no—
34Q8×C79—42no—
35C2×C4×C79—42no—
36C2×C4×C79C2×D411yescharacteristic
37C2×C4×C79C2×D411yescharacteristic
38C2×C4×C79#4111yescharacteristic
39C2×Dic79—21no—
40D316—22no—
41C4×D79—41no—
42C4×D79—41no—
43C8×C79—21no—
44C8×C79D812yes—
45C79⋊C8—41no—
46C79⋊C8—42no—
47C22×C79#12111yescharacteristic
48C2×D79—41no—
49C2×D79—41no—
50C2×D79—41no—
51C4×C79—21no—
52C4×C79—82no—
53C4×C79C2×D811yescharacteristic
54C4×C79AGL(1,ℤ/8)11yescharacteristic
55C4×C79#13712yes—
56Dic79—41no—
57C2×C79#45911yescharacteristic
58C2×C79#47011yescharacteristic
59C2×C79#47311yescharacteristic
60D79—81no—
61#1689—791nomaximal, Sylow
62C79#168911yescharacteristic, complemented, Sylow
63#494D7911yescharacteristic, complemented
64#474—792no—
65#436—791no—
66#334—791no—
67#332—792no—
68C2×Q16—21no—
69C2×Q16—21no—
70C2×M16—1581no—
71C4⋊Q8C2×D7912yes—
72C4×D4—791no—
73#107—1582no—
74C4⋊C8—791no—
75C4⋊C8—792no—
76#102—1582no—
77C22⋊C8—1581no—
78C4×C8C2×D7911yescharacteristic
79C2×Q8—22no—
80C2×D4—791no—
81C22×C4—1581no—
82Q16—42no—
83Q16—42no—
84M16—3162no—
85C2×C8—1582no—
86C2×C8—1581no—
87C2×C8C22⋊D7911yescharacteristic
88C2×C8C22⋊D7911yescharacteristic
89C4⋊C4—22no—
90C4⋊C4—22no—
91C4⋊C4—791no—
92C22⋊C4—1581no—
93C42C22×D7911yescharacteristic
94C23—1581no—
95Q8—42no—
96Q8—42no—
97D4—1582no—
98C2×C4—42no—
99C2×C4—3161no—
100C2×C4—3161no—
101C2×C4—1581no—
102C2×C4D4×D7911yescharacteristic
103C2×C4C2×C22⋊D7911yescharacteristic
104C2×C4#1192962311yescharacteristic
105C8—21no—
106C8—3161no—
107C8—3162no—
108C8#1192960912yes—
109C22—3161no—
110C22—3161no—
111C22—3161no—
112C22#1457913211yescharacteristic
113C4—21no—
114C4—82no—
115C4—3161no—
116C4C2×#1192960911yescharacteristic
117C4#1457918711yescharacteristic
118C4#1457919312yes—
119C2—6321no—
120C2#1909875511yescharacteristic
121C2#1909881811yescharacteristic
122C2#1909883511yescharacteristic
subgroupG/H
centerC22#14579132
commutator, cosocleC42×C79C23
FrattiniC42C22×D79
Fitting#494×C79C2
socleC22×C79#121
prime radicalC2×D316D4
hypercenter#494D79
hypocenterC79#1689
LCSG ▷ C42×C79 ▷ C22×C79 ▷ C79
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
3. #19098314C2semidirect
4. #19098309C2semidirect
5. #494×C79C2semidirect
62. C79#1689semidirect
63. #494D79semidirect