Finite Group Databasebeta

← #19136611

Subgroups — #19136611

Order 5504.

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

normal subgroups only

This group has 248 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#14583641C211yesmaximal, characteristic, complemented
2#14583072C212yesmaximal, complemented
3#14582696C211yesmaximal, characteristic, complemented
4#14582695C212yesmaximal, complemented
5C43×#454C211yesmaximal, characteristic, complemented
6#13063350—22no—
7#13063314C2212yes—
8#13063313—21no—
9#13063311—22no—
10#13063295—22no—
11#13063293—21no—
12#13063252—22no—
13#13063244C2212yescomplemented
142−1+4×C43C2211yescharacteristic, complemented
15AGL(1,ℤ/8)×C43—21no—
16#124×C43C2211yescharacteristic
17#104×C43—21no—
18#101×C43C2211yescharacteristic, complemented
19C23×D43—21no—
20#41×C43—21no—
21#41×C43—22no—
22#41×C43—41no—
23C2×Q8×C43—41no—
24C2×Q8×C43C2311yescharacteristic
25C2×D4×C43D411yescharacteristic
26C2×C22⋊D43—22no—
27C2×D172—21no—
28C2×D172D412yes—
29C2×Dic86—21no—
30SD16×C43—41no—
31D8×C43—41no—
32M16×C43—21no—
33C22⋊C4×C43—22no—
34C42×C43D411yescharacteristic
35C22⋊Dic43—21no—
36#10621884—42no—
37#10621882—42no—
38(C2×D43)⋊C4—22no—
39(C2×D43)⋊C4—22no—
40(C2×D43)⋊C4—22no—
41C4×Dic43D412yes—
42#10621877—22no—
43C23×C43—21no—
44C22×D43—22no—
45C22×D43—82no—
46C22×D43—81no—
47Q8×C43—22no—
48Q8×C43—21no—
49Q8×C43—41no—
50D4×C43—22no—
51D4×C43—21no—
52D4×C43—41no—
53D4×C43—41no—
54C2×C4×C43—21no—
55C2×C4×C43—42no—
56C2×C4×C43—41no—
57C2×C4×C43C2×D412yes—
58C2×C4×C43C2×D411yescharacteristic
59C22⋊D43—82no—
60C2×Dic43—22no—
61D172—42no—
62D172—81no—
63Dic86—81no—
64C8×C43—41no—
65C43⋊C8—42no—
66C22×C43—42no—
67C22×C43—41no—
68C22×C43—41no—
69C22×C43#12011yescharacteristic
70C2×D43—42no—
71C2×D43—42no—
72C2×D43—42no—
73C2×D43—84no—
74C4×C43—22no—
75C4×C43—21no—
76C4×C43—41no—
77C4×C43—41no—
78Dic43—42no—
79#2202—431nomaximal, Sylow
80C2×C43—21no—
81C2×C43—81no—
82C2×C43—81no—
83C2×C43B(4,𝔽2)11yescharacteristic
84D43—82no—
85H(3,𝔽4)—431no—
86#454—432no—
87#454D4311yescharacteristic, complemented
88#355—431no—
89#355—432no—
90C43#220211yescharacteristic, complemented, Sylow
912−1+4C2×D4311yescharacteristic, complemented
92AGL(1,ℤ/8)—21no—
93AGL(1,ℤ/8)—862no—
94#124—432no—
95#124—862no—
96#124—861no—
97#124C2×D4311yescharacteristic
98#120—862no—
99#120—861no—
100#104—21no—
101#104—862no—
102#101—432no—
103#101C2×D4311yescharacteristic, complemented
104C24—861no—
105#41—22no—
106#41—21no—
107#41—41no—
108C2×Q8—41no—
109C2×Q8—861no—
110C2×Q8C22×D4311yescharacteristic
111C2×D4—432no—
112C2×D4—861no—
113C2×D4—862no—
114C2×D4C22⋊D4311yescharacteristic
115SD16—41no—
116SD16—1722no—
117D8—41no—
118D8—1722no—
119M16—21no—
120M16—862no—
121C22⋊C4—22no—
122C22⋊C4—862no—
123C22⋊C4—861no—
124C22⋊C4—862no—
125C22⋊C4—862no—
126C42—432no—
127C42C22⋊D4311yescharacteristic
128C23—21no—
129C23—862no—
130C23—3442no—
131C23—3441no—
132Q8—21no—
133Q8—22no—
134Q8—41no—
135Q8—3441no—
136D4—21no—
137D4—22no—
138D4—41no—
139D4—41no—
140D4—3441no—
141D4—3442no—
142D4—1722no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—42no—
146C2×C4—862no—
147C2×C4D4×D4312yes—
148C2×C4C2×C22⋊D4311yescharacteristic
149C8—41no—
150C8—1722no—
151C22—42no—
152C22—41no—
153C22—41no—
154C22—3444no—
155C22—1722no—
156C22—1722no—
157C22—1722no—
158C22#1306329311yescharacteristic
159C4—21no—
160C4—22no—
161C4—41no—
162C4—41no—
163C4—1722no—
164C2—21no—
165C2—81no—
166C2—81no—
167C2—3442no—
168C2#1458308511yescharacteristic
subgroupG/H
centerC2#14583085
commutatorC2×Q8×C43C23
FrattiniC2×Q8C22×D43
FittingC43×#454C2
socleC2×C43B(4,𝔽2)
hypercenter#454D43
hypocenterC43#2202
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. #14583641C2semidirect
2. #14583072C2semidirect
3. #14582696C2semidirect
4. #14582695C2semidirect
5. C43×#454C2semidirect
13. #13063244C22semidirect
14. 2−1+4×C43C22semidirect
18. #101×C43C22semidirect
87. #454D43semidirect
90. C43#2202semidirect
91. 2−1+4C2×D43semidirect
103. #101C2×D43semidirect