Finite Group Databasebeta

← #15673032

Subgroups — #15673032

Order 2944.

176 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 176 conjugacy classes of subgroups — too many to draw. Only its 61 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#13092815C211yesmaximal, characteristic
2#13092813C211yesmaximal, characteristic
3#13092813C211yesmaximal, characteristic
4#13092796C211yesmaximal, characteristic
5#13092769C211yesmaximal, characteristic
6#13092139C211yesmaximal, characteristic
7C23×#487C211yesmaximal, characteristic
8C23×C4⋊Q8C2211yescharacteristic
9C23×C4⋊Q8C2211yescharacteristic
10C2×#67275—22no—
11#10625040C2211yescharacteristic
12#10625040C2211yescharacteristic
13C23×#103—22no—
14C4×C8×C23C2211yescharacteristic
15#10624999—22no—
16#10624992—22no—
17#10624990—22no—
18#10624990—22no—
19C4×C23⋊C8C2211yescharacteristic
20C4×C23⋊C8C2211yescharacteristic
21C2×Q8×C23—21no—
22C2×Q8×C23—21no—
23C2×Dic46—21no—
24C2×Dic46—21no—
25C2×C8×C23D412yes—
26C4⋊C4×C23—21no—
27C4⋊C4×C23—21no—
28C4⋊C4×C23—21no—
29C4⋊C4×C23—21no—
30C42×C23C2311yescharacteristic
31#67275—44no—
32C4⋊Dic23—21no—
33C4⋊Dic23—21no—
34C4⋊Dic23—21no—
35C4⋊Dic23—21no—
36C2×C23⋊C8D412yes—
37C2×C23⋊C8D412yes—
38Q8×C23—42no—
39Q8×C23—42no—
40C2×C4×C23—41no—
41C2×C4×C23—41no—
42C2×C4×C23C2×D411yescharacteristic
43C2×C4×C23C2×D411yescharacteristic
44C2×C4×C23C2×D411yescharacteristic
45C2×Dic23—41no—
46C2×Dic23—41no—
47Dic46—42no—
48Dic46—42no—
49C8×C23—22no—
50C23⋊C8—22no—
51C23⋊C8SD1614yes—
52#1716—231nomaximal, Sylow
53C22×C23#12711yescharacteristic
54C4×C23—81no—
55C4×C23—81no—
56C4×C23C2×SD1612yes—
57C4×C23#13712yes—
58C4×C23#13712yes—
59Dic23—81no—
60Dic23—81no—
61#498—231no—
62#498—231no—
63#498—231no—
64#494—231no—
65#487—231no—
66#487D2311yescharacteristic
67#322—231no—
68C2×C23#49211yescharacteristic
69C2×C23#49711yescharacteristic
70C2×C23#49711yescharacteristic
71C2×Q16—462no—
72C4⋊Q8—231no—
73C4⋊Q8—231no—
74C4⋊Q8C2×D2311yescharacteristic
75C4⋊Q8C2×D2311yescharacteristic
76#106—462no—
77#106—462no—
78#106—462no—
79#103—22no—
80#103—462no—
81C4×C8—231no—
82C4×C8—231no—
83C4×C8C2×D2311yescharacteristic
84C23#171611yescharacteristic, complemented, Sylow
85C2×Q8—21no—
86C2×Q8—21no—
87C2×Q8—461no—
88C2×Q8—461no—
89Q16—924no—
90C2×C8—232no—
91C2×C8—232no—
92C2×C8C22⋊D2312yes—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—21no—
96C4⋊C4—21no—
97C4⋊C4—461no—
98C4⋊C4—461no—
99C4⋊C4—461no—
100C4⋊C4—461no—
101C42C22×D2311yescharacteristic
102Q8—42no—
103Q8—42no—
104Q8—922no—
105Q8—922no—
106C2×C4—41no—
107C2×C4—41no—
108C2×C4—921no—
109C2×C4—921no—
110C2×C4D4×D2311yescharacteristic
111C2×C4D4×D2311yescharacteristic
112C2×C4C2×C22⋊D2311yescharacteristic
113C8—22no—
114C8—234no—
115C8—462no—
116C22#1062511111yescharacteristic
117C4—81no—
118C4—81no—
119C4—1841no—
120C4—1841no—
121C4SD16×D2312yes—
122C4#1062508912yes—
123C4#1062512212yes—
124C2#1309278811yescharacteristic
125C2#1309281011yescharacteristic
126C2#1309281211yescharacteristic
subgroupG/H
centerC22#10625111
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#487C2
socle, prime radicalC22×C23#127
hypercenter#487D23
hypocenterC23#1716
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
84. C23#1716semidirect

Maximal subgroups

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

subgroupindex
#130928152
#130928132
#130927962
#130927692
#130921392
C23×#4872
#171623