Finite Group Databasebeta

← #15672718

Subgroups — #15672718

Order 2944.

196 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 45 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#13093165C211yesmaximal, characteristic
2#13092779C212yesmaximal, complemented
3#13092159C211yesmaximal, characteristic, complemented
4#13092156C212yesmaximal, complemented
5C23×#491C211yesmaximal, characteristic, complemented
6C23×C4⋊Q8C2211yescharacteristic
7C23×#125C2211yescharacteristic
8#10625067—22no—
9#10625066—22no—
10#10625065—22no—
11#10625046C2212yes—
12C23×#103—22no—
13C23×#97C2211yescharacteristic
14#10624992—22no—
15#10624991—22no—
16#10624985C2212yes—
17C2×Q8×C23—21no—
18C2×D92—22no—
19C2×D92D412yes—
20C2×C4×D23—22no—
21C2×Dic46D412yes—
22C2×C8×C23—21no—
23C4⋊C4×C23—22no—
24C4⋊C4×C23—22no—
25C4⋊C4×C23D412yes—
26C42×C23C2311yescharacteristic
27(C2×D23)⋊C4—22no—
28(C2×D23)⋊C4—22no—
29(C2×D23)⋊C4—22no—
30Dic23⋊C4—22no—
31C2×C23⋊C8—22no—
32C22×D23—22no—
33Q8×C23—42no—
34C2×C4×C23—22no—
35C2×C4×C23—41no—
36C2×C4×C23C2×D412yes—
37C2×C4×C23C2×D411yescharacteristic
38C2×Dic23—22no—
39D92—42no—
40D92—82no—
41C4×D23—82no—
42Dic46—42no—
43C8×C23—41no—
44C23⋊C8—42no—
45#1662—231nomaximal, Sylow
46C22×C23#12011yescharacteristic
47C2×D23—42no—
48C2×D23—42no—
49C2×D23—42no—
50C4×C23—21no—
51C4×C23—22no—
52C4×C23—42no—
53C4×C23—81no—
54Dic23—42no—
55#562—231no—
56#491D2311yescharacteristic, complemented
57#489—232no—
58#330—231no—
59#329—232no—
60C2×C23#45411yescharacteristic
61C2×C23#45512yes—
62D23—82no—
63C4⋊Q8C2×D2311yescharacteristic
64#125C2×D2311yescharacteristic
65#124—232no—
66#123—462no—
67C22⋊Q8—462no—
68#121—462no—
69#103—22no—
70#103—462no—
71#102—462no—
72#97—232no—
73#97C2×D2311yescharacteristic
74C23#166211yescharacteristic, complemented, Sylow
75C2×Q8—21no—
76C2×Q8—232no—
77C2×D4—232no—
78C2×D4—462no—
79C22×C4—462no—
80C2×C8—21no—
81C2×C8—462no—
82C4⋊C4—22no—
83C4⋊C4—22no—
84C4⋊C4—462no—
85C4⋊C4C22⋊D2312yes—
86C22⋊C4—462no—
87C22⋊C4—462no—
88C22⋊C4—462no—
89C42C22×D2311yescharacteristic
90C23—462no—
91Q8—42no—
92Q8—922no—
93D4—922no—
94D4—1842no—
95C2×C4—22no—
96C2×C4—41no—
97C2×C4—462no—
98C2×C4—1842no—
99C2×C4D4×D2312yes—
100C2×C4C2×C22⋊D2311yescharacteristic
101C8—41no—
102C8—922no—
103C22—922no—
104C22—922no—
105C22—922no—
106C22#1062510811yescharacteristic
107C4—21no—
108C4—22no—
109C4—42no—
110C4—81no—
111C4—922no—
112C2—1842no—
113C2#1309258911yescharacteristic
114C2#1309259312yes—
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#491C2
socleC22×C23#120
prime radical#13093165C2
hypercenter#491D23
hypocenterC23#1662
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #13092779C2semidirect
3. #13092159C2semidirect
4. #13092156C2semidirect
5. C23×#491C2semidirect
56. #491D23semidirect
74. C23#1662semidirect

Maximal subgroups

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

subgroupindex
#130931652
#130927792
#130921592
#130921562
C23×#4912
#166223