Finite Group Databasebeta

← #15673045

Subgroups — #15673045

Order 2944.

164 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 164 conjugacy classes of subgroups — too many to draw. Only its 57 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#13092820C211yesmaximal, characteristic
2#13092815C211yesmaximal, characteristic
3#13092769C211yesmaximal, characteristic
4#13092769C211yesmaximal, characteristic
5#13092767C211yesmaximal, characteristic
6#13092139C211yesmaximal, characteristic
7C23×#487C211yesmaximal, characteristic
8C23×C4⋊Q8C2211yescharacteristic
9C23×C4⋊Q8C2211yescharacteristic
10#10625040C2211yescharacteristic
11#10625040C2211yescharacteristic
12C23×#103—22no—
13C4×C8×C23C2211yescharacteristic
14#10625017—22no—
15#10624999—22no—
16#10624992—22no—
17#10624992—22no—
18#10624989—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
31C4⋊Dic23—21no—
32C4⋊Dic23—21no—
33C4⋊Dic23—21no—
34C4⋊Dic23—21no—
35C2×C23⋊C8D412yes—
36C2×C23⋊C8D412yes—
37Q8×C23—42no—
38Q8×C23—42no—
39C2×C4×C23—41no—
40C2×C4×C23—41no—
41C2×C4×C23C2×D411yescharacteristic
42C2×C4×C23C2×D411yescharacteristic
43C2×C4×C23C2×D411yescharacteristic
44C2×Dic23—41no—
45C2×Dic23—41no—
46Dic46—42no—
47Dic46—42no—
48C8×C23—22no—
49C23⋊C8—22no—
50C23⋊C8—22no—
51#1718—231nomaximal, Sylow
52C22×C23#12711yescharacteristic
53C4×C23—81no—
54C4×C23—81no—
55C4×C23#13512yes—
56C4×C23#13712yes—
57C4×C23#13712yes—
58Dic23—81no—
59Dic23—81no—
60#500—231no—
61#498—231no—
62#487—231no—
63#487—231no—
64#487—231no—
65#487D2311yescharacteristic
66#322—231no—
67C2×C23#49511yescharacteristic
68C2×C23#49711yescharacteristic
69C2×C23#49711yescharacteristic
70C4⋊Q8—231no—
71C4⋊Q8—231no—
72C4⋊Q8C2×D2311yescharacteristic
73C4⋊Q8C2×D2311yescharacteristic
74#107—462no—
75#106—462no—
76#103—22no—
77#103—462no—
78#103—462no—
79#103—462no—
80C4×C8—231no—
81C4×C8—231no—
82C4×C8C2×D2311yescharacteristic
83C23#171811yescharacteristic, complemented, Sylow
84C2×Q8—21no—
85C2×Q8—21no—
86C2×Q8—461no—
87C2×Q8—461no—
88C2×C8—232no—
89C2×C8—232no—
90C2×C8C22⋊D2312yes—
91C4⋊C4—21no—
92C4⋊C4—21no—
93C4⋊C4—21no—
94C4⋊C4—21no—
95C4⋊C4—461no—
96C4⋊C4—461no—
97C4⋊C4—461no—
98C4⋊C4—461no—
99C42C22×D2311yescharacteristic
100Q8—42no—
101Q8—42no—
102Q8—922no—
103Q8—922no—
104C2×C4—41no—
105C2×C4—41no—
106C2×C4—921no—
107C2×C4—921no—
108C2×C4D4×D2311yescharacteristic
109C2×C4D4×D2311yescharacteristic
110C2×C4C2×C22⋊D2311yescharacteristic
111C8—22no—
112C8—462no—
113C8—462no—
114C22#1062511111yescharacteristic
115C4—81no—
116C4—81no—
117C4—1841no—
118C4—1841no—
119C4#1062508712yes—
120C4#1062508912yes—
121C4#1062512212yes—
122C2#1309279811yescharacteristic
123C2#1309281011yescharacteristic
124C2#1309281211yescharacteristic
subgroupG/H
centerC22#10625111
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#487C2
socle, prime radicalC22×C23#127
hypercenter#487D23
hypocenterC23#1718
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
83. C23#1718semidirect

Maximal subgroups

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

subgroupindex
#130928202
#130928152
#130927692
#130927672
#130921392
C23×#4872
#171823