Finite Group Databasebeta

← #15674703

Subgroups — #15674703

Order 2944.

264 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 65 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#13093217C211yesmaximal, characteristic
2#13092414C212yesmaximal, complemented
3#13092390C212yesmaximal, complemented
4#13092174C211yesmaximal, characteristic, complemented
5C23×#424C211yesmaximal, characteristic, complemented
6C2×#67288C2212yes—
7C2×M16×C23C2211yescharacteristic
8C22×C8×C23C2211yescharacteristic
9C23×#117C2211yescharacteristic
10#10625097C2212yes—
11#10625080—22no—
12#10625079—22no—
13#10625075—22no—
14C23×C4⋊C8—22no—
15#10625003—22no—
16#10624998—22no—
17#10624988—24no—
18C22×C4×C23C2311yescharacteristic
19C2×C22⋊D23—22no—
20#67288—22no—
21#67288—22no—
22#67288—22no—
23#67288—22no—
24C2×D92D412yes—
25C2×C4×D23—22no—
26C2×Dic46D412yes—
27M16×C23—22no—
28C2×C8×C23—21no—
29C2×C8×C23—22no—
30C2×C8×C23D412yes—
31C4⋊C4×C23—21no—
32C22⋊C4×C23D412yes—
33C42×C23—21no—
34C22⋊Dic23—22no—
35C4⋊Dic23—22no—
36C4×Dic23—22no—
37Dic92—22no—
38D184—22no—
39#67263—24no—
40C23×C23C2×D411yescharacteristic
41C22×D23—22no—
42C2×C4×C23—22no—
43C2×C4×C23C2×D412yes—
44C2×C4×C23C2×D411yescharacteristic
45C2×C4×C23#4111yescharacteristic
46C2×C4×C23#4112yes—
47C22⋊D23—42no—
48C22⋊D23—42no—
49C2×Dic23—22no—
50C2×Dic23—42no—
51D92—22no—
52D92—22no—
53C4×D23—42no—
54C4×D23—42no—
55Dic46—22no—
56Dic46—22no—
57C8×C23—22no—
58C8×C23—41no—
59#2053—231nomaximal, Sylow
60C22×C23—41no—
61C22×C23#12112yes—
62C22×C23#12111yescharacteristic
63C2×D23—42no—
64C2×D23—82no—
65C4×C23—42no—
66C4×C23#12011yescharacteristic
67C4×C23#12312yes—
68C4×C23#12411yescharacteristic
69Dic23—42no—
70Dic23—82no—
71#575—231no—
72#424D2311yescharacteristic, complemented
73#416—232no—
74#410—232no—
75H(3,ℤ/4)—231no—
76C2×C23—22no—
77C2×C23—21no—
78C2×C23#39411yescharacteristic
79D23—82no—
80C2×#41—232no—
81#137—462no—
82AGL(1,ℤ/8)—462no—
83#135—462no—
84C2×M16C2×D2311yescharacteristic
85C22×C8C2×D2311yescharacteristic
86#117—232no—
87#117C2×D2311yescharacteristic
88C4⋊C8—22no—
89#103—462no—
90#102—462no—
91#99—464no—
92C23#205311yescharacteristic, complemented, Sylow
93#41—462no—
94#41—462no—
95#41—462no—
96#41—462no—
97C2×Q8—232no—
98C2×D4—232no—
99C2×D4—462no—
100C22×C4—462no—
101C22×C4C22×D2311yescharacteristic
102Q16—462no—
103SD16—464no—
104D8—462no—
105M16—22no—
106C2×C8—22no—
107C2×C8—21no—
108C2×C8C22⋊D2312yes—
109C4⋊C4—21no—
110C4⋊C4—462no—
111C22⋊C4—462no—
112C22⋊C4D9212yes—
113C42—21no—
114C42—462no—
115C23—462no—
116C23C2×D9211yescharacteristic
117Q8—462no—
118Q8—462no—
119D4—462no—
120D4—462no—
121D4—922no—
122D4—922no—
123C2×C4—22no—
124C2×C4—462no—
125C2×C4—922no—
126C2×C4—922no—
127C2×C4—922no—
128C2×C4#6728811yescharacteristic
129C2×C4D4×D2312yes—
130C2×C4#6729212yes—
131C2×C4C2×C22⋊D2311yescharacteristic
132C8—22no—
133C8—41no—
134C22—41no—
135C22—922no—
136C22—1842no—
137C22#1062506612yes—
138C22#1062510111yescharacteristic
139C4—42no—
140C4—922no—
141C4—1842no—
142C4#1062506512yes—
143C4#1062510811yescharacteristic
144C4#1062511811yescharacteristic
145C2—21no—
146C2—22no—
147C2—1842no—
148C2#1309233411yescharacteristic
subgroupG/H
centerC4#10625118
commutator, cosocleC22×C4×C23C23
FrattiniC22×C4C22×D23
FittingC23×#424C2
socleC2×C23#394
prime radical#13093217C2
hypercenter#424D23
hypocenterC23#2053
LCSG ▷ C22×C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C4 ◁ C22×C4 ◁ #424

Complements

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

NH ≅ G/Ntype
2. #13092414C2semidirect
3. #13092390C2semidirect
4. #13092174C2semidirect
5. C23×#424C2semidirect
72. #424D23semidirect
92. C23#2053semidirect

Maximal subgroups

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

subgroupindex
#130932172
#130924142
#130923902
#130921742
C23×#4242
#205323