Finite Group Databasebeta

← #15672511

Subgroups — #15672511

Order 2944.

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

normal subgroups only

This group has 314 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#13093052C211yesmaximal, characteristic
2#13092704C212yesmaximal, complemented
3#13092161C211yesmaximal, characteristic, complemented
4#13092146C212yesmaximal, complemented
5C23×#492C211yesmaximal, characteristic, complemented
6C2×D4×D23—22no—
7C2×SD16×C23—22no—
8C23×C4⋊Q8C2211yescharacteristic, complemented
9C23×#127C2211yescharacteristic
10#10625109—22no—
11#10625108—22no—
12C4×D92C2212yes—
13C4×C8×C23C2211yescharacteristic, complemented
14#10624991—22no—
15#10624990—22no—
16C4⋊(C23⋊C8)C2212yescomplemented
17C23×D23—22no—
18C2×Q8×C23—21no—
19C2×D4×C23—22no—
20C2×D4×C23D412yes—
21C2×C22⋊D23—24no—
22D4×D23—44no—
23D4×D23—44no—
24C2×D92D412yes—
25C2×C4×D23—22no—
26SD16×C23—44no—
27C2×C8×C23—21no—
28C4⋊C4×C23—22no—
29C42×C23C2311yescharacteristic
30C22⋊Dic23—22no—
31(C2×D23)⋊C4—22no—
32C4⋊Dic23D412yes—
33C2×C23⋊C8—22no—
34C23×C23—22no—
35C22×D23—22no—
36C22×D23—48no—
37C22×D23—82no—
38Q8×C23—42no—
39D4×C23—42no—
40D4×C23—42no—
41D4×C23—42no—
42C2×C4×C23—41no—
43C2×C4×C23C2×D412yes—
44C2×C4×C23C2×D411yescharacteristic
45C22⋊D23—48no—
46C2×Dic23—22no—
47D92—22no—
48D92SD1614yescomplemented
49C4×D23—42no—
50C4×D23—42no—
51C8×C23—22no—
52C23⋊C8—42no—
53#1629—231nomaximal, Sylow
54C22×C23—44no—
55C22×C23—42no—
56C22×C23#12011yescharacteristic
57C2×D23—24no—
58C2×D23—42no—
59C2×D23—42no—
60C2×D23—88no—
61C4×C23—21no—
62C4×C23—81no—
63C4×C23C2×SD1612yes—
64C4×C23AGL(1,ℤ/8)12yes—
65Dic23—42no—
66D42—231no—
67#492D2311yescharacteristic, complemented
68#476—232no—
69#331—231no—
70D4⋊C8—232no—
71C2×C23—82no—
72C2×C23#45012yes—
73C2×C23#45311yescharacteristic
74D23—44no—
75C22×D4—462no—
76C2×SD16—22no—
77C4⋊Q8C2×D2311yescharacteristic, complemented
78#127C2×D2311yescharacteristic
79#121—462no—
80#120—462no—
81C4×D4—232no—
82#106—462no—
83C4⋊C8—232no—
84#102—462no—
85C4×C8C2×D2311yescharacteristic, complemented
86C23#162911yescharacteristic, complemented, Sylow
87C24—462no—
88C2×Q8—21no—
89C2×D4—22no—
90C2×D4—232no—
91C2×D4—464no—
92C2×D4—924no—
93C2×D4—924no—
94C2×D4C22⋊D2312yes—
95C22×C4—462no—
96SD16—44no—
97C2×C8—21no—
98C2×C8—462no—
99C4⋊C4—22no—
100C4⋊C4—232no—
101C22⋊C4—462no—
102C22⋊C4—462no—
103C42C22×D2311yescharacteristic
104C23—22no—
105C23—462no—
106C23—928no—
107C23—1842no—
108Q8—42no—
109D4—42no—
110D4—42no—
111D4—42no—
112D4—234no—
113D4—462no—
114D4—928no—
115C2×C4—41no—
116C2×C4—462no—
117C2×C4—922no—
118C2×C4—922no—
119C2×C4D4×D2312yes—
120C2×C4C2×C22⋊D2311yescharacteristic
121C8—22no—
122C8—922no—
123C22—44no—
124C22—42no—
125C22—464no—
126C22—922no—
127C22—922no—
128C22—1848no—
129C22#1062510811yescharacteristic
130C4—21no—
131C4—81no—
132C4—922no—
133C4SD16×D2312yes—
134C4#1062508512yes—
135C2—82no—
136C2—924no—
137C2#1309256612yes—
138C2#1309258411yescharacteristic
subgroupG/H
centerC22#10625108
commutator, cosocleC42×C23C23
FrattiniC42C22×D23
FittingC23×#492C2
socleC22×C23#120
prime radical#13093052C2
hypercenter#492D23
hypocenterC23#1629
LCSG ▷ C42×C23 ▷ C22×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ #492

Complements

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

NH ≅ G/Ntype
2. #13092704C2semidirect
3. #13092161C2semidirect
4. #13092146C2semidirect
5. C23×#492C2semidirect
8. C23×C4⋊Q8C22semidirect
13. C4×C8×C23C22semidirect
16. C4⋊(C23⋊C8)C22semidirect
48. D92SD16semidirect
67. #492D23semidirect
77. C4⋊Q8C2×D23semidirect
85. C4×C8C2×D23semidirect
86. C23#1629semidirect

Maximal subgroups

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

subgroupindex
#130930522
#130927042
#130921612
#130921462
C23×#4922
#162923