Finite Group Databasebeta

← #15671990

Subgroups — #15671990

Order 2944.

226 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 63 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#13092973C211yesmaximal, characteristic
2#13092369C212yesmaximal
3#13092159C211yesmaximal, characteristic, complemented
4#13092158C212yesmaximal, complemented
5C23×#330C211yesmaximal, characteristic, complemented
6C23×#125C2211yescharacteristic
7C2×#67262—22no—
8#10625067—22no—
9#10625063C412yes—
10#10625059C412yes—
11#10625058—22no—
12C42×D23C2211yescharacteristic
13#10625041C2211yescharacteristic
14C23×#97C2212yes—
15C8×Dic23—22no—
16#10624985C2212yes—
17C2×C4×D23C2×C411yescharacteristic
18C2×C4×D23D412yes—
19C2×Dic46—22no—
20C2×C8×C23—22no—
21C4⋊C4×C23—22no—
22C4⋊C4×C23C2×C412yes—
23C42×C23C2311yescharacteristic
24(C2×D23)⋊C4—22no—
25C4⋊Dic23C2×C412yes—
26Dic23⋊C4—22no—
27Dic23⋊C4—22no—
28C4×Dic23—22no—
29C4×Dic23C2×C411yescharacteristic
30C4×Dic23D412yes—
31C2×C23⋊C8—22no—
32#67262—28no—
33C22×D23C22⋊C411yescharacteristic
34C2×C4×C23—22no—
35C2×C4×C23C22×C411yescharacteristic
36C2×C4×C23C2×D412yes—
37C2×Dic23—22no—
38C2×Dic23C22⋊C411yescharacteristic
39C2×Dic23C22⋊C412yes—
40C4×D23—22no—
41C4×D23—24no—
42Dic46—44no—
43C8×C23—24no—
44C23⋊C8—24no—
45#1526—231nomaximal, Sylow
46C22×C23C2×C22⋊C411yescharacteristic
47C2×D23—21no—
48C2×D23—22no—
49C4×C23—21no—
50C4×C23—22no—
51C4×C23—42no—
52Dic23—42no—
53Dic23#10112yes—
54Dic23#10414yes—
55#533—231no—
56C4×M16—232no—
57#330—231no—
58#330—232no—
59#330D2311yescharacteristic, complemented
60C2×C23C2×#10111yescharacteristic
61C2×C23C2×#10412yes—
62D23—41no—
63C2×M16—462no—
64C4⋊Q8—232no—
65#125—231no—
66#125C2×D2311yescharacteristic
67C22⋊Q8—462no—
68C4×Q8—462no—
69#117—232no—
70C2×C42—231no—
71#97—232no—
72#97C2×D2312yes—
73C4×C8—462no—
74C23#152611yescharacteristic, complemented, Sylow
75C2×Q8—462no—
76C22×C4—231no—
77C22×C4—232no—
78M16—468no—
79C2×C8—22no—
80C2×C8—462no—
81C4⋊C4—22no—
82C4⋊C4—232no—
83C4⋊C4—462no—
84C4⋊C4—462no—
85C4⋊C4C4×D2312yes—
86C22⋊C4—462no—
87C42—231no—
88C42—232no—
89C42—462no—
90C42C22×D2311yescharacteristic
91C23—231no—
92Q8—924no—
93C2×C4—22no—
94C2×C4—231no—
95C2×C4—232no—
96C2×C4—464no—
97C2×C4—462no—
98C2×C4—462no—
99C2×C4C2×C4×D2311yescharacteristic
100C2×C4D4×D2312yes—
101C8—24no—
102C8—464no—
103C22—461no—
104C22—462no—
105C22C22⋊C4×D2311yescharacteristic
106C4—21no—
107C4—22no—
108C4—42no—
109C4—232no—
110C4—234no—
111C4—922no—
112C2—921no—
113C2#101×D2311yescharacteristic
114C2#104×D2312yes—
subgroupG/H
centerC22C22⋊C4×D23
commutatorC2×C4×C23C22×C4
FrattiniC42C22×D23
FittingC23×#330C2
socleC22×C23C2×C22⋊C4
prime radicalC22×D23C22⋊C4
cosocleC42×C23C23
hypercenter#330D23
hypocenterC23#1526
LCSG ▷ C2×C4×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
3. #13092159C2semidirect
4. #13092158C2semidirect
5. C23×#330C2semidirect
59. #330D23semidirect
74. C23#1526semidirect

Maximal subgroups

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

subgroupindex
#130929732
#130923692
#130921592
#130921582
C23×#3302
#152623