Finite Group Databasebeta

← #15673788

Subgroups — #15673788

Order 2944.

324 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 89 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
1C2×#10625115C211yesmaximal, characteristic
2#13092895C211yesmaximal, characteristic
3#13092427C212yesmaximal
4#13092178C212yesmaximal
5C2×C23×#101C211yesmaximal, characteristic
6C22×Q8×C23C2211yescharacteristic
7C22×Dic46C2211yescharacteristic
8C2×M16×C23C2212yes—
9Q8×Dic23—24no—
10#10625115—22no—
11#10625115C414yescomplemented
12#10625097—22no—
13#10625097C2212yes—
14C2×Dic23⋊C4—22no—
15C2×C4×Dic23C2211yescharacteristic
16C23×#101—22no—
17#10624998—24no—
18C2×Q8×C23—22no—
19C2×Q8×C23—22no—
20C2×Q8×C23C2×C412yes—
21C2×Q8×C23D412yes—
22C22×C4×C23D412yes—
23C22×C4×C23C2311yescharacteristic
24C22×Dic23—21no—
25C22×Dic23—21no—
26C2×Dic46—22no—
27C2×Dic46—22no—
28C2×Dic46—21no—
29C2×Dic46C2×C412yes—
30M16×C23—22no—
31M16×C23—22no—
32C2×C8×C23—22no—
33C22⋊Dic23—22no—
34C4⋊Dic23—24no—
35C4⋊Dic23D414yes—
36Dic23⋊C4—28no—
37C4×Dic23—24no—
38C4×Dic23—21no—
39C4×Dic23—22no—
40C4×Dic23C2×C412yes—
41C23×C23C2×D411yescharacteristic
42Q8×C23—24no—
43Q8×C23—24no—
44C2×C4×C23—22no—
45C2×C4×C23—22no—
46C2×C4×C23C22⋊C414yes—
47C2×C4×C23C22×C411yescharacteristic
48C2×C4×C23C2×D412yes—
49C2×C4×C23C2×D411yescharacteristic
50C2×C4×C23#4112yes—
51C2×Dic23—24no—
52C2×Dic23—22no—
53C2×Dic23—22no—
54C2×Dic23—24no—
55C2×Dic23—41no—
56C2×Dic23—41no—
57Dic46—24no—
58Dic46—42no—
59C8×C23—42no—
60#1886—231nomaximal, Sylow
61C22×C23—22no—
62C22×C23C2×C22⋊C411yescharacteristic
63C22×C23#12011yescharacteristic
64C22×C23#12311yescharacteristic
65C4×C23—24no—
66C4×C23C4×D412yes—
67C4×C23#12112yes—
68Dic23—24no—
69Dic23—42no—
70Dic23—44no—
71C2×C4⋊Q8—231no—
72#519—231no—
73#419—232no—
74C2×#101D2311yescharacteristic
75#339—232no—
76C2×C23—21no—
77C2×C23—21no—
78C2×C23#38611yescharacteristic
79C2×C23#45612yes—
80C22×Q8—231no—
81C22×Q8C2×D2311yescharacteristic
82C2×M16C2×D2312yes—
83C4⋊Q8—234no—
84C4⋊Q8—462no—
85C4×Q8—464no—
86#117—232no—
87#117—462no—
88C2×C4⋊C4—462no—
89C2×C42—231no—
90#103—464no—
91#101—22no—
92C23#188611yescharacteristic, complemented, Sylow
93C2×Q8—22no—
94C2×Q8—22no—
95C2×Q8—232no—
96C2×Q8—461no—
97C2×Q8—462no—
98C2×Q8—462no—
99C2×Q8C4×D2312yes—
100C2×Q8C22⋊D2312yes—
101C22×C4—461no—
102C22×C4—461no—
103C22×C4D9212yes—
104C22×C4C22×D2311yescharacteristic
105M16—22no—
106M16—22no—
107C2×C8—22no—
108C4⋊C4—234no—
109C4⋊C4—464no—
110C4⋊C4—468no—
111C22⋊C4—462no—
112C42—232no—
113C42—464no—
114C42—462no—
115C42—461no—
116C23C2×D9211yescharacteristic
117Q8—24no—
118Q8—24no—
119Q8—464no—
120Q8—922no—
121C2×C4—22no—
122C2×C4—22no—
123C2×C4—464no—
124C2×C4—462no—
125C2×C4—464no—
126C2×C4—462no—
127C2×C4—921no—
128C2×C4—921no—
129C2×C4(C2×D23)⋊C414yes—
130C2×C4C2×C4×D2311yescharacteristic
131C2×C4D4×D2312yes—
132C2×C4#6729012yes—
133C2×C4C2×C22⋊D2311yescharacteristic
134C8—42no—
135C22—22no—
136C22#1062505311yescharacteristic
137C22#1062505711yescharacteristic
138C22C2×(C2×D23)⋊C411yescharacteristic
139C4—24no—
140C4—464no—
141C4—922no—
142C4—924no—
143C4(C22⋊D23)⋊C412yes—
144C4#1062511012yes—
145C2—21no—
146C2—21no—
147C2#1309229411yescharacteristic
148C2#1309260212yes—
subgroupG/H
centerC22#10625053
commutatorC2×C4×C23C22×C4
FrattiniC22×C4C22×D23
FittingC2×C23×#101C2
socleC22×C23#120
prime radicalC23×C23C2×D4
cosocleC22×C4×C23C23
hypercenterC2×#101D23
hypocenterC23#1886
LCSG ▷ C2×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#101

Complements

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

NH ≅ G/Ntype
11. #10625115C4semidirect
92. C23#1886semidirect

Maximal subgroups

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

subgroupindex
C2×#106251152
#130928952
#130924272
#130921782
C2×C23×#1012
#188623