Finite Group Databasebeta

← #15675522

Subgroups — #15675522

Order 2944.

140 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 49 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×Dic184C211yesmaximal, characteristic, complemented
2#13092692C212yesmaximal
3#13092247C211yesmaximal, characteristic, complemented
4#13092234C212yesmaximal, complemented
5C23×#504C211yesmaximal, characteristic
6C23×#131C2211yescharacteristic
7#10625122—22no—
8C2×Dic92C2212yes—
9C23×M32—21no—
10C23×M32C2211yescharacteristic
11C2×C16×C23—21no—
12C2×C16×C23C2211yescharacteristic
13#10625006—22no—
14#10625001C2212yes—
15Dic184—21no—
16Dic184—21no—
17#41×C23D411yescharacteristic
18C2×Dic46—22no—
19M16×C23—21no—
20M16×C23D411yescharacteristic
21C2×C8×C23—21no—
22C2×C8×C23C2311yescharacteristic
23#67275—42no—
24#67273—42no—
25#67267—22no—
26Dic92—22no—
27Dic92—22no—
28C16×C23—21no—
29C16×C23D411yescharacteristic
30C16×C23D411yescharacteristic
31Q8×C23D811yescharacteristic
32D4×C23—21no—
33D4×C23D811yescharacteristic
34C2×C4×C23—21no—
35C2×C4×C23C2×D411yescharacteristic
36C2×Dic23—42no—
37Dic46—42no—
38Dic46—42no—
39C8×C23—21no—
40C8×C23C2×D411yescharacteristic
41C8×C23#4111yescharacteristic
42C23⋊C8—42no—
43#2222—231nomaximal, Sylow
44C22×C23—21no—
45C22×C23#13511yescharacteristic
46C4×C23—21no—
47C4×C23#12111yescharacteristic
48C4×C23C2×D811yescharacteristic
49Dic23—82no—
50C2×Q32—231no—
51#504D2311yescharacteristic
52#473—232no—
53#368—231no—
54#362—232no—
55C2×C23—21no—
56C2×C23—41no—
57C2×C23#46611yescharacteristic
58#137—462no—
59C2×Q16—232no—
60#131C2×D2311yescharacteristic
61Q32—461no—
62Q32—461no—
63M32—21no—
64M32C2×D2311yescharacteristic
65C2×C16—21no—
66C2×C16C2×D2311yescharacteristic
67#108—232no—
68#101—462no—
69C23#222211yescharacteristic, complemented, Sylow
70#41D9211yescharacteristic
71C2×Q8—462no—
72Q16—462no—
73Q16—462no—
74Q16—922no—
75SD16—922no—
76M16—21no—
77M16—462no—
78M16D9211yescharacteristic
79C2×C8—21no—
80C2×C8C22×D2311yescharacteristic
81C16—21no—
82C16C22⋊D2311yescharacteristic
83C16C22⋊D2311yescharacteristic
84Q8—922no—
85Q8—922no—
86Q8D18411yescharacteristic
87D4—21no—
88D4D18411yescharacteristic
89C2×C4—21no—
90C2×C4—922no—
91C2×C4C2×D9211yescharacteristic
92C8—21no—
93C8—922no—
94C8#6728811yescharacteristic
95C8C2×C22⋊D2311yescharacteristic
96C22—21no—
97C22#1062507511yescharacteristic
98C4—21no—
99C4—1842no—
100C4C2×D18411yescharacteristic
101C4#1062510111yescharacteristic
102C2—21no—
103C2—41no—
104C2#1309265311yescharacteristic
subgroupG/H
centerC2#13092653
commutator, cosocleC2×C8×C23C23
FrattiniC2×C8C22×D23
FittingC23×#504C2
socleC2×C23#466
prime radical#41×C23D4
hypercenter#504D23
hypocenterC23#2222
LCSG ▷ C2×C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #504

Complements

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

NH ≅ G/Ntype
1. C2×Dic184C2semidirect
3. #13092247C2semidirect
4. #13092234C2semidirect
69. C23#2222semidirect

Maximal subgroups

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

subgroupindex
C2×Dic1842
#130926922
#130922472
#130922342
C23×#5042
#222223