Finite Group Databasebeta

← #19136615

Subgroups — #19136615

Order 5504.

216 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 41 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#14583649C211yesmaximal, characteristic, complemented
2#14583082C212yesmaximal, complemented
3#14582697C212yesmaximal, complemented
4#14582696C211yesmaximal, characteristic, complemented
5C43×#454C211yesmaximal, characteristic
6#13063355—22no—
7#13063323C2212yes—
8#13063318—22no—
9#13063317—21no—
10#13063306—21no—
11#13063302—22no—
12#13063252—22no—
13#13063244C2212yes—
142−1+4×C43C2211yescharacteristic
15AGL(1,ℤ/8)×C43—21no—
16#124×C43C2211yescharacteristic
17#104×C43—21no—
18#101×C43C2211yescharacteristic
19#41×C43—21no—
20#41×C43—22no—
21#41×C43—41no—
22C2×Q8×C43—41no—
23C2×Q8×C43C2311yescharacteristic
24C2×D4×C43D411yescharacteristic
25C22×Dic43—21no—
26C2×Dic86D412yes—
27SD16×C43—41no—
28D8×C43—41no—
29M16×C43—21no—
30C22⋊C4×C43—22no—
31C42×C43D411yescharacteristic
32C22⋊Dic43—22no—
33C22⋊Dic43—21no—
34#10621885—42no—
35#10621883—42no—
36C4⋊Dic43—21no—
37C4⋊Dic43—21no—
38Dic43⋊C4—22no—
39Dic43⋊C4—22no—
40Dic43⋊C4—22no—
41C4×Dic43D412yes—
42#10621877—22no—
43C23×C43—21no—
44Q8×C43—22no—
45Q8×C43—21no—
46Q8×C43—41no—
47D4×C43—22no—
48D4×C43—21no—
49D4×C43—41no—
50D4×C43—41no—
51C2×C4×C43—21no—
52C2×C4×C43—42no—
53C2×C4×C43—41no—
54C2×C4×C43C2×D412yes—
55C2×C4×C43C2×D411yescharacteristic
56C2×Dic43—22no—
57C2×Dic43—22no—
58C2×Dic43—81no—
59Dic86—42no—
60C8×C43—41no—
61C43⋊C8—42no—
62C22×C43—42no—
63C22×C43—41no—
64C22×C43—41no—
65C22×C43#12011yescharacteristic
66C4×C43—22no—
67C4×C43—21no—
68C4×C43—41no—
69C4×C43—41no—
70Dic43—42no—
71Dic43—42no—
72#2203—431nomaximal, Sylow
73C2×C43—21no—
74C2×C43—81no—
75C2×C43—81no—
76C2×C43B(4,𝔽2)11yescharacteristic
77#563—431no—
78#456—432no—
79#454D4311yescharacteristic
80#356—432no—
81#355—431no—
82C43#220311yescharacteristic, complemented, Sylow
832−1+4C2×D4311yescharacteristic
84#137—862no—
85AGL(1,ℤ/8)—21no—
86C4⋊Q8—432no—
87#126—862no—
88#125—861no—
89#124C2×D4311yescharacteristic
90#123—861no—
91C22⋊Q8—862no—
92#104—21no—
93#104—862no—
94#101—432no—
95#101C2×D4311yescharacteristic
96#41—22no—
97#41—21no—
98#41—41no—
99C2×Q8—41no—
100C2×Q8—432no—
101C2×Q8C22×D4311yescharacteristic
102C2×D4C22⋊D4311yescharacteristic
103C22×C4—861no—
104Q16—1722no—
105SD16—41no—
106SD16—1722no—
107D8—41no—
108M16—21no—
109M16—862no—
110C4⋊C4—861no—
111C4⋊C4—862no—
112C4⋊C4—861no—
113C4⋊C4—862no—
114C4⋊C4—862no—
115C22⋊C4—22no—
116C22⋊C4—862no—
117C22⋊C4—861no—
118C42—432no—
119C42C22⋊D4311yescharacteristic
120C23—21no—
121Q8—21no—
122Q8—22no—
123Q8—41no—
124Q8—1722no—
125D4—21no—
126D4—22no—
127D4—41no—
128D4—41no—
129C2×C4—21no—
130C2×C4—41no—
131C2×C4—42no—
132C2×C4—862no—
133C2×C4—862no—
134C2×C4—3441no—
135C2×C4D4×D4312yes—
136C2×C4C2×C22⋊D4311yescharacteristic
137C8—41no—
138C8—1722no—
139C22—42no—
140C22—41no—
141C22—41no—
142C22#1306329311yescharacteristic
143C4—21no—
144C4—22no—
145C4—41no—
146C4—41no—
147C4—1722no—
148C4—1722no—
149C2—21no—
150C2—81no—
151C2—81no—
152C2#1458308511yescharacteristic
subgroupG/H
centerC2#14583085
commutatorC2×Q8×C43C23
FrattiniC2×Q8C22×D43
FittingC43×#454C2
socleC2×C43B(4,𝔽2)
hypercenter#454D43
hypocenterC43#2203
LCSG ▷ C2×Q8×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #454

Complements

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

NH ≅ G/Ntype
1. #14583649C2semidirect
2. #14583082C2semidirect
3. #14582697C2semidirect
4. #14582696C2semidirect
82. C43#2203semidirect