Finite Group Databasebeta

← #19136618

Subgroups — #19136618

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#14583084C212yesmaximal, complemented
3#14583071C211yesmaximal, characteristic
4#14582697C212yesmaximal, complemented
5C43×#355C211yesmaximal, characteristic, complemented
6#13063373C2211yescharacteristic
7#13063358—22no—
8#13063351—21no—
9#13063323C2212yes—
10#13063318—22no—
11#13063317—21no—
12#13063306—21no—
13#13063302—22no—
14#13063253—21no—
15#13063251—22no—
16#13063244C2211yescharacteristic
17#124×C43C2211yescharacteristic
18#101×C43C2212yes—
19C2×Q8×C43C2311yescharacteristic
20C2×D4×C43D411yescharacteristic
21C22×Dic43—21no—
22#10621902—41no—
23Q8×D43—41no—
24#10621898—22no—
25#10621898—21no—
26C2×Dic86D412yes—
27M16×C43—22no—
28C22⋊C4×C43—22no—
29C42×C43D411yescharacteristic
30C22⋊Dic43—22no—
31C22⋊Dic43—21no—
32#10621883—41no—
33#10621882—41no—
34C4⋊Dic43—21no—
35C4⋊Dic43—21no—
36Dic43⋊C4—22no—
37Dic43⋊C4—22no—
38Dic43⋊C4—22no—
39C4×Dic43D412yes—
40#10621877—21no—
41Dic172—42no—
42#10621873—42no—
43C23×C43—21no—
44Q8×C43—41no—
45D4×C43—41no—
46C2×C4×C43—21no—
47C2×C4×C43C2×D411yescharacteristic
48C2×C4×C43C2×D412yes—
49C22⋊D43—41no—
50C2×Dic43—22no—
51C2×Dic43—22no—
52C2×Dic43—81no—
53D172—22no—
54D172—21no—
55C4×D43—41no—
56C4×D43—42no—
57Dic86—22no—
58Dic86—21no—
59Dic86—42no—
60C8×C43—42no—
61C43⋊C8—41no—
62C22×C43—42no—
63C22×C43—41no—
64C22×C43#12011yescharacteristic
65C2×D43—41no—
66C4×C43—21no—
67C4×C43—22no—
68C4×C43—41no—
69Dic43—42no—
70Dic43—41no—
71Dic43—42no—
72#2203—431nomaximal, Sylow
73C2×C43—21no—
74C2×C43—81no—
75C2×C43B(4,𝔽2)11yescharacteristic
76D43—81no—
77#563—431no—
78#456—432no—
79#454—431no—
80#356—432no—
81#355D4311yescharacteristic, complemented
82C43#220311yescharacteristic, complemented, Sylow
832−1+4—431no—
84#137—862no—
85AGL(1,ℤ/8)—861no—
86C4⋊Q8—432no—
87#126—862no—
88#125—861no—
89#124C2×D4311yescharacteristic
90#123—861no—
91C22⋊Q8—862no—
92#104—862no—
93#104—861no—
94#101—431no—
95#101C2×D4312yes—
96#41—861no—
97#41—862no—
98#41—1721no—
99C2×Q8—432no—
100C2×Q8—1721no—
101C2×Q8C22×D4311yescharacteristic
102C2×D4D17211yescharacteristic
103C22×C4—861no—
104Q16—1722no—
105SD16—1722no—
106SD16—1721no—
107D8—1721no—
108M16—22no—
109M16—861no—
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—
119C42D17211yescharacteristic
120C23—21no—
121Q8—41no—
122Q8—861no—
123Q8—862no—
124Q8—1722no—
125D4—41no—
126D4—861no—
127D4—862no—
128D4—1721no—
129C2×C4—21no—
130C2×C4—862no—
131C2×C4—862no—
132C2×C4—3441no—
133C2×C4—1722no—
134C2×C4—1721no—
135C2×C4C2×D17211yescharacteristic
136C2×C4D4×D4312yes—
137C8—42no—
138C8—1721no—
139C22—42no—
140C22—41no—
141C22—1721no—
142C22#1306329511yescharacteristic
143C4—22no—
144C4—21no—
145C4—41no—
146C4—1722no—
147C4—1722no—
148C4—1721no—
149C2—21no—
150C2—81no—
151C2—3441no—
152C2#1458308711yescharacteristic
subgroupG/H
centerC2#14583087
commutatorC2×Q8×C43C23
FrattiniC2×Q8C22×D43
FittingC43×#355C2
socleC2×C43B(4,𝔽2)
hypercenter#355D43
hypocenterC43#2203
LCSG ▷ C2×Q8×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #355

Complements

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

NH ≅ G/Ntype
1. #14583649C2semidirect
2. #14583084C2semidirect
4. #14582697C2semidirect
5. C43×#355C2semidirect
81. #355D43semidirect
82. C43#2203semidirect