Finite Group Databasebeta

← #15675558

Subgroups — #15675558

Order 2944.

124 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 124 conjugacy classes of subgroups — too many to draw. Only its 51 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
1C4×Dic92C211yesmaximal, characteristic
2#13092244C211yesmaximal, characteristic
3#13092242C211yesmaximal, characteristic
4C4⋊(C23⋊C16)C211yesmaximal, characteristic
5#13092220C211yesmaximal, characteristic
6#13092220C211yesmaximal, characteristic
7C23×#499C211yesmaximal, characteristic
8C23×#125—21no—
9C2×Dic92C2211yescharacteristic
10C4×Dic46—21no—
11C23×#107C2211yescharacteristic
12C23×#107C2211yescharacteristic
13C23×#106—21no—
14C4×C8×C23C2211yescharacteristic
15#10625000C2211yescharacteristic
16#10624998—21no—
17C2×C23⋊C16C2211yescharacteristic
18C2×C23⋊C16C2211yescharacteristic
19C2×Dic46—21no—
20C2×C8×C23D411yescharacteristic
21C2×C8×C23C2311yescharacteristic
22C4⋊C4×C23—21no—
23C4⋊C4×C23—21no—
24C4⋊C4×C23—41no—
25C4⋊C4×C23—41no—
26C42×C23D411yescharacteristic
27C4⋊Dic23—21no—
28Dic23⋊C4—41no—
29C4×Dic23—41no—
30Dic92—21no—
31Dic92Q812yes—
32C23⋊C16—21no—
33C23⋊C16—21no—
34C2×C4×C23—41no—
35C2×C4×C23—41no—
36C2×C4×C23D811yescharacteristic
37C2×C4×C23D811yescharacteristic
38C2×C4×C23C2×D411yescharacteristic
39C2×Dic23—41no—
40C2×Dic23—41no—
41Dic46—22no—
42Dic46—41no—
43C8×C23—21no—
44C8×C23C2×Q811yescharacteristic
45C8×C23#4111yescharacteristic
46#2229—231nomaximal, Sylow
47C22×C23C2×D811yescharacteristic
48C4×C23—21no—
49C4×C23—21no—
50C4×C23—81no—
51C4×C23—81no—
52C4×C23C22⋊Q811yescharacteristic
53C4×C23#13711yescharacteristic
54Dic23—42no—
55Dic23—81no—
56#499D2311yescharacteristic
57C4×Q16—231no—
58#367—231no—
59#366—231no—
60C4⋊C16—231no—
61#358—231no—
62#358—231no—
63C2×C23#47411yescharacteristic
64C2×C23#50811yescharacteristic
65C2×C23#51011yescharacteristic
66C2×Q16—231no—
67#125—21no—
68C4×Q8—461no—
69C2×C16—231no—
70C2×C16—231no—
71#107—231no—
72#107C2×D2311yescharacteristic
73#107C2×D2311yescharacteristic
74#106—21no—
75#103—461no—
76C4×C8C2×D2311yescharacteristic
77C23#222911yescharacteristic, complemented, Sylow
78C2×Q8—461no—
79Q16—232no—
80Q16—461no—
81C2×C8C22⋊D2311yescharacteristic
82C2×C8C22×D2311yescharacteristic
83C4⋊C4—21no—
84C4⋊C4—21no—
85C4⋊C4—41no—
86C4⋊C4—41no—
87C4⋊C4—461no—
88C4⋊C4—921no—
89C42—921no—
90C42C22⋊D2311yescharacteristic
91C16—461no—
92C16—461no—
93Q8—462no—
94Q8—921no—
95C2×C4—41no—
96C2×C4—41no—
97C2×C4—921no—
98C2×C4—921no—
99C2×C4#6727211yescharacteristic
100C2×C4#6727211yescharacteristic
101C2×C4C2×C22⋊D2311yescharacteristic
102C8—21no—
103C8Q8×D2311yescharacteristic
104C8#6729211yescharacteristic
105C22C2×#6727211yescharacteristic
106C4—21no—
107C4—21no—
108C4—81no—
109C4—81no—
110C4—922no—
111C4—1841no—
112C4#1062511311yescharacteristic
113C4#1062511711yescharacteristic
114C2#1309269411yescharacteristic
115C2#1309284711yescharacteristic
116C2#1309285711yescharacteristic
subgroupG/H
centerC22C2×#67272
commutator, cosocleC2×C8×C23C23
FrattiniC2×C8C22×D23
FittingC23×#499C2
socle, prime radicalC22×C23C2×D8
hypercenter#499D23
hypocenterC23#2229
LCSG ▷ C2×C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #499

Complements

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

NH ≅ G/Ntype
77. C23#2229semidirect

Maximal subgroups

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

subgroupindex
C4×Dic922
#130922442
#130922422
C4⋊(C23⋊C16)2
#130922202
C23×#4992
#222923