Finite Group Databasebeta

← #15675520

Subgroups — #15675520

Order 2944.

140 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 140 conjugacy classes of subgroups — too many to draw. Only its 47 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×#10625011C211yesmaximal, characteristic, complemented
2#13092834C211yesmaximal, characteristic
3#13092692C211yesmaximal, characteristic
4#13092246C211yesmaximal, characteristic, complemented
5#13092233C211yesmaximal, characteristic, complemented
6#13092232C211yesmaximal, characteristic, complemented
7C23×#473C211yesmaximal, characteristic
8C23×#137—21no—
9C2×Q16×C23C2211yescharacteristic
10C23×#131C2211yescharacteristic
11#10625122—21no—
12C2×Dic92C2211yescharacteristic
13C23×#108C2211yescharacteristic
14C23×#101—21no—
15#10625011—21no—
16#10625011—21no—
17#10625006—21no—
18#10625001C2211yescharacteristic
19#10624994—21no—
20#10624994C2211yescharacteristic
21C2×C23⋊C16—21no—
22C2×C23⋊C16C2211yescharacteristic
23#41×C23D411yescharacteristic
24C2×Q8×C23—21no—
25C2×Dic46—21no—
26Q16×C23—21no—
27Q16×C23—21no—
28Q16×C23—41no—
29SD16×C23—41no—
30M16×C23—21no—
31M16×C23—21no—
32M16×C23D411yescharacteristic
33C2×C8×C23—21no—
34C2×C8×C23C2311yescharacteristic
35#67275—41no—
36#67273—41no—
37#67267—21no—
38Dic92—21no—
39Dic92—21no—
40C23⋊C16—21no—
41C23⋊C16D411yescharacteristic
42C23⋊C16D411yescharacteristic
43Q8×C23—41no—
44Q8×C23—41no—
45Q8×C23D811yescharacteristic
46D4×C23—21no—
47D4×C23D811yescharacteristic
48C2×C4×C23—21no—
49C2×C4×C23—41no—
50C2×C4×C23C2×D411yescharacteristic
51C2×Dic23—41no—
52Dic46—41no—
53Dic46—41no—
54C8×C23—21no—
55C8×C23—41no—
56C8×C23C2×D411yescharacteristic
57C8×C23#4111yescharacteristic
58C23⋊C8—41no—
59#2222—231nomaximal, Sylow
60C22×C23—21no—
61C22×C23#13511yescharacteristic
62C4×C23—21no—
63C4×C23—81no—
64C4×C23#12111yescharacteristic
65C4×C23C2×D811yescharacteristic
66Dic23—81no—
67C2×Q32—231no—
68#504—231no—
69#473—231no—
70#473D2311yescharacteristic
71#368—231no—
72#362—231no—
73#362—231no—
74C2×C23—21no—
75C2×C23—41no—
76C2×C23#46611yescharacteristic
77#137—21no—
78#137—461no—
79C2×Q16—231no—
80C2×Q16C2×D2311yescharacteristic
81#131C2×D2311yescharacteristic
82Q32—461no—
83Q32—461no—
84M32—231no—
85M32—461no—
86C2×C16—231no—
87C2×C16—461no—
88#108—231no—
89#108C2×D2311yescharacteristic
90#101—21no—
91#101—461no—
92C23#222211yescharacteristic, complemented, Sylow
93#41C22⋊D2311yescharacteristic
94C2×Q8—21no—
95C2×Q8—461no—
96Q16—21no—
97Q16—21no—
98Q16—41no—
99Q16—461no—
100Q16—461no—
101Q16—921no—
102SD16—41no—
103SD16—921no—
104M16—21no—
105M16—21no—
106M16—461no—
107M16C22⋊D2311yescharacteristic
108C2×C8—21no—
109C2×C8C22×D2311yescharacteristic
110C16—231no—
111C16—231no—
112C16—461no—
113Q8—41no—
114Q8—41no—
115Q8—921no—
116Q8—921no—
117Q8#6727211yescharacteristic
118D4—21no—
119D4#6727211yescharacteristic
120C2×C4—21no—
121C2×C4—41no—
122C2×C4—921no—
123C2×C4C2×C22⋊D2311yescharacteristic
124C8—21no—
125C8—41no—
126C8—921no—
127C8D4×D2311yescharacteristic
128C8#6729011yescharacteristic
129C22—21no—
130C22#1062512111yescharacteristic
131C4—21no—
132C4—81no—
133C4—1841no—
134C4C2×#6727211yescharacteristic
135C4#1062511011yescharacteristic
136C2—21no—
137C2—41no—
138C2#1309265111yescharacteristic
subgroupG/H
centerC2#13092651
commutator, cosocleC2×C8×C23C23
FrattiniC2×C8C22×D23
FittingC23×#473C2
socleC2×C23#466
prime radical#41×C23D4
hypercenter#473D23
hypocenterC23#2222
LCSG ▷ C2×C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ #131 ◁ #473

Complements

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

NH ≅ G/Ntype
1. C2×#10625011C2semidirect
4. #13092246C2semidirect
5. #13092233C2semidirect
6. #13092232C2semidirect
92. C23#2222semidirect

Maximal subgroups

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

subgroupindex
C2×#106250112
#130928342
#130926922
#130922462
#130922332
#130922322
C23×#4732
#222223