Finite Group Databasebeta

← #15675524

Subgroups — #15675524

Order 2944.

144 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 144 conjugacy classes of subgroups — too many to draw. Only its 45 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#13092833C211yesmaximal, characteristic, complemented
2#13092689C211yesmaximal, characteristic, complemented
3#13092684C211yesmaximal, characteristic
4#13092247C211yesmaximal, characteristic, complemented
5#13092233C211yesmaximal, characteristic, complemented
6#13092230C211yesmaximal, characteristic, complemented
7C2×C23×SD32C211yesmaximal, characteristic, complemented
8C2×Q16×C23C2211yescharacteristic
9C2×D8×C23C2211yescharacteristic
10#10625113—21no—
11#10625103—21no—
12#10625072C2211yescharacteristic
13C23×SD32—21no—
14C23×SD32—21no—
15C2×C16×C23C2211yescharacteristic
16#10625018—21no—
17#10625015—21no—
18#10625001C2211yescharacteristic
19#10625001C2211yescharacteristic
20#10624994C2211yescharacteristic
21#10624980—21no—
22C16×D23—21no—
23C2×Q8×C23—21no—
24C2×D4×C23—21no—
25#67288D411yescharacteristic
26Q16×C23—21no—
27Q16×C23—21no—
28D8×C23—21no—
29D8×C23—21no—
30C2×C8×C23C2311yescharacteristic
31#67275—41no—
32#67274—41no—
33#67273—41no—
34#67272—41no—
35#67267—21no—
36#67267—21no—
37#67267D411yescharacteristic
38#67262—21no—
39C8×D23—21no—
40C16×C23D411yescharacteristic
41C16×C23D411yescharacteristic
42C23⋊C16—21no—
43C23×C23—41no—
44Q8×C23—41no—
45Q8×C23—41no—
46D4×C23—41no—
47D4×C23—41no—
48C2×C4×C23—41no—
49C2×C4×C23C2×D411yescharacteristic
50C22⋊D23—21no—
51D92D811yescharacteristic
52C4×D23—21no—
53Dic46D811yescharacteristic
54C8×C23C2×D411yescharacteristic
55C8×C23#4111yescharacteristic
56C23⋊C8—21no—
57C23⋊C8—41no—
58C23⋊C8—41no—
59#2223—231nomaximal, Sylow
60C22×C23—81no—
61C22×C23—161no—
62C22×C23#13511yescharacteristic
63C2×D23—21no—
64C4×C23—81no—
65C4×C23#12111yescharacteristic
66C4×C23C2×D811yescharacteristic
67Dic23—21no—
68C2×SD32D2311yescharacteristic, complemented
69#504—231no—
70#473—231no—
71#472—231no—
72#368—231no—
73#362—231no—
74#361—231no—
75C2×C23—21no—
76C2×C23—161no—
77C2×C23#46611yescharacteristic
78D23—41no—
79#137—461no—
80AGL(1,ℤ/8)—461no—
81C2×Q16C2×D2311yescharacteristic
82C2×D8C2×D2311yescharacteristic
83#131—231no—
84SD32—21no—
85SD32—21no—
86M32—231no—
87M32—461no—
88C2×C16—461no—
89C2×C16C2×D2311yescharacteristic
90#108—231no—
91#108—231no—
92#101—461no—
93#100—461no—
94C23#222311yescharacteristic, complemented, Sylow
95#41—231no—
96C2×Q8—21no—
97C2×D4—21no—
98Q16—21no—
99Q16—21no—
100Q16—921no—
101SD16—921no—
102SD16—921no—
103D8—21no—
104D8—21no—
105D8—921no—
106M16—231no—
107M16—461no—
108M16—461no—
109M16—461no—
110C2×C8—461no—
111C2×C8C22×D2311yescharacteristic
112C16—461no—
113C16C22⋊D2311yescharacteristic
114C16C22⋊D2311yescharacteristic
115C23—41no—
116Q8—41no—
117Q8—41no—
118Q8—231no—
119D4—41no—
120D4—41no—
121D4—231no—
122D4—461no—
123C2×C4—41no—
124C2×C4—461no—
125C2×C4D4×D2311yescharacteristic
126C8—461no—
127C8—921no—
128C8—921no—
129C8#6729011yescharacteristic
130C8C2×C22⋊D2311yescharacteristic
131C22—81no—
132C22—161no—
133C22—461no—
134C22#1062508311yescharacteristic
135C4—81no—
136C4—461no—
137C4D8×D2311yescharacteristic
138C4#1062510911yescharacteristic
139C2—21no—
140C2—161no—
141C2—921no—
142C2#1309265011yescharacteristic
subgroupG/H
centerC2#13092650
commutator, cosocleC2×C8×C23C23
FrattiniC2×C8C22×D23
FittingC2×C23×SD32C2
socleC2×C23#466
prime radical#13092684C2
hypercenterC2×SD32D23
hypocenterC23#2223
LCSG ▷ C2×C8×C23 ▷ C4×C23 ▷ C2×C23 ▷ C23
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. #13092833C2semidirect
2. #13092689C2semidirect
4. #13092247C2semidirect
5. #13092233C2semidirect
6. #13092230C2semidirect
7. C2×C23×SD32C2semidirect
68. C2×SD32D23semidirect
94. C23#2223semidirect

Maximal subgroups

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

subgroupindex
#130928332
#130926892
#130926842
#130922472
#130922332
#130922302
C2×C23×SD322
#222323