Finite Group Databasebeta

← #15672720

Subgroups — #15672720

Order 2944.

196 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 49 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#13092787C211yesmaximal, characteristic, complemented
2#13092776C212yesmaximal, complemented
3#13092159C211yesmaximal, characteristic, complemented
4#13092157C212yesmaximal, complemented
5C23×#562C211yesmaximal, characteristic
6C23×#125C2211yescharacteristic
7C23×#124C2212yes—
8C23×#123—22no—
9C23×C22⋊Q8—22no—
10C23×#121—22no—
11#10625040C2211yescharacteristic
12#10625017—22no—
13#10625014—22no—
14#10624992—22no—
15#10624985C2211yescharacteristic
16#10624985C2212yes—
17C2×Q8×C23D412yes—
18C2×D4×C23—22no—
19C2×D4×C23D412yes—
20C22×C4×C23—22no—
21C2×Dic46—21no—
22C4⋊C4×C23—22no—
23C4⋊C4×C23—22no—
24C4⋊C4×C23D412yes—
25C22⋊C4×C23—22no—
26C22⋊C4×C23—22no—
27C22⋊C4×C23—22no—
28C42×C23C2311yescharacteristic
29C4⋊Dic23—22no—
30C2×C23⋊C8—21no—
31C2×C23⋊C8—22no—
32C23×C23—22no—
33Q8×C23—42no—
34D4×C23—42no—
35D4×C23—82no—
36C2×C4×C23—22no—
37C2×C4×C23—22no—
38C2×C4×C23—82no—
39C2×C4×C23C2×D412yes—
40C2×C4×C23C2×D411yescharacteristic
41C2×Dic23—41no—
42Dic46—42no—
43C23⋊C8—41no—
44C23⋊C8—42no—
45#1662—231nomaximal, Sylow
46C22×C23—42no—
47C22×C23—42no—
48C22×C23—42no—
49C22×C23#12011yescharacteristic
50C4×C23—21no—
51C4×C23—22no—
52C4×C23—42no—
53C4×C23—42no—
54Dic23—81no—
55#562D2311yescharacteristic
56#491—231no—
57#489—232no—
58#330—231no—
59#329—232no—
60C2×C23—82no—
61C2×C23#45411yescharacteristic
62C2×C23#45512yes—
63C4⋊Q8—231no—
64#125C2×D2311yescharacteristic
65#124C2×D2312yes—
66#123—22no—
67C22⋊Q8—22no—
68#121—22no—
69#103—462no—
70#103—462no—
71#102—462no—
72#97—231no—
73#97—232no—
74C23#166211yescharacteristic, complemented, Sylow
75C2×Q8—461no—
76C2×Q8C22⋊D2312yes—
77C2×D4—22no—
78C2×D4C22⋊D2312yes—
79C22×C4—22no—
80C2×C8—462no—
81C2×C8—461no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—462no—
85C4⋊C4C22⋊D2312yes—
86C22⋊C4—22no—
87C22⋊C4—22no—
88C22⋊C4—22no—
89C42C22×D2311yescharacteristic
90C23—22no—
91Q8—42no—
92Q8—922no—
93D4—42no—
94D4—82no—
95C2×C4—22no—
96C2×C4—22no—
97C2×C4—82no—
98C2×C4—921no—
99C2×C4C2×C22⋊D2311yescharacteristic
100C2×C4C2×C22⋊D2312yes—
101C8—921no—
102C8—922no—
103C22—42no—
104C22—42no—
105C22—42no—
106C22#1062512411yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—42no—
111C4—1841no—
112C2—82no—
113C2#1309259011yescharacteristic
114C2#1309259512yes—
subgroupG/H
centerC22#10625124
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
Fitting, prime radicalC23×#562C2
socleC22×C23#120
hypercenter#562D23
hypocenterC23#1662
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #562

Complements

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

NH ≅ G/Ntype
1. #13092787C2semidirect
2. #13092776C2semidirect
3. #13092159C2semidirect
4. #13092157C2semidirect
74. C23#1662semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#130927872
#130927762
#130921592
#130921572
C23×#5622
#166223