Finite Group Databasebeta

← #19133566

Subgroups — #19133566

Order 5504.

282 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 53 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#14583480C211yesmaximal, characteristic
2#14583040C212yesmaximal, complemented
3#14582819C211yesmaximal, characteristic, complemented
4#14582634C212yesmaximal, complemented
5C43×#324C211yesmaximal, characteristic, complemented
6C2×#10621898—21no—
7C22×Dic86C2211yescharacteristic
8C2×#10621873—22no—
9#13063305—22no—
10#13063300—22no—
11#13063299—21no—
12#13063299C2212yes—
13C2×Dic43⋊C4—21no—
14#13063250—22no—
15C43⋊#95—21no—
16C43⋊#95C2211yescharacteristic
17C2×C4⋊C4×C43C2211yescharacteristic
18C22⋊C8×C43C2212yes—
19C22×C4×C43D411yescharacteristic
20C22×C4×C43D411yescharacteristic
21C22×C4×C43C2311yescharacteristic
22C2×C22⋊D43—22no—
23C22×Dic43—21no—
24C22×Dic43—21no—
25#10621898—42no—
26#10621898—42no—
27C2×D172—21no—
28C2×D172—21no—
29C2×D172D412yes—
30C2×C4×D43—22no—
31C2×Dic86—22no—
32C2×Dic86—21no—
33C2×Dic86—42no—
34C2×C8×C43—22no—
35C4⋊C4×C43—22no—
36(C2×D43)⋊C4—22no—
37(C2×D43)⋊C4—22no—
38C4⋊Dic43—21no—
39C4⋊Dic43D412yes—
40Dic43⋊C4—42no—
41#10621873—44no—
42C23×C43C2×D411yescharacteristic
43C22×D43—22no—
44C2×C4×C43—21no—
45C2×C4×C43—21no—
46C2×C4×C43—21no—
47C2×C4×C43—41no—
48C2×C4×C43—41no—
49C2×C4×C43SD1612yescomplemented
50C2×C4×C43C2×D412yes—
51C22⋊D43—42no—
52C22⋊D43—42no—
53C2×Dic43—22no—
54C2×Dic43—22no—
55C2×Dic43—22no—
56C2×Dic43—41no—
57C2×Dic43—41no—
58C2×Dic43—41no—
59C2×Dic43—41no—
60D172—42no—
61D172—42no—
62D172—81no—
63C4×D43—44no—
64Dic86—24no—
65Dic86—42no—
66Dic86—42no—
67C8×C43—42no—
68C22×C43—21no—
69C22×C43—21no—
70C22×C43#12011yescharacteristic
71C22×C43C2×SD1611yescharacteristic
72C22×C43AGL(1,ℤ/8)11yescharacteristic
73C2×D43—42no—
74C2×D43—42no—
75C2×D43—42no—
76C4×C43—22no—
77C4×C43—22no—
78C4×C43—41no—
79Dic43—42no—
80Dic43—42no—
81Dic43—42no—
82#1604—431nomaximal, Sylow
83C2×C43—21no—
84C2×C43—21no—
85C2×C43#45011yescharacteristic
86C2×C43#45611yescharacteristic
87C2×C43B(4,𝔽2)11yescharacteristic
88D43—82no—
89#537—431no—
90#448—432no—
91#395—431no—
92#327—432no—
93#324D4311yescharacteristic, complemented
94C43#160411yescharacteristic, complemented, Sylow
95C2×#41—861no—
96C22×Q8—431no—
97C2×SD16—862no—
98C22⋊Q8—862no—
99#121—432no—
100#121—862no—
101#121—861no—
102C2×C4⋊C4—861no—
103C2×C4⋊C4C2×D4311yescharacteristic
104#103—862no—
105C22⋊C8C2×D4312yes—
106#95—431no—
107#95—861no—
108#41—1722no—
109#41—1722no—
110C2×Q8—861no—
111C2×Q8—862no—
112C2×Q8—1722no—
113C2×D4—432no—
114C2×D4—861no—
115C2×D4—861no—
116C2×D4—862no—
117C22×C4—862no—
118C22×C4—861no—
119C22×C4—861no—
120C22×C4D17211yescharacteristic
121C22×C4D17211yescharacteristic
122C22×C4C22×D4311yescharacteristic
123SD16—1724no—
124C2×C8—22no—
125C4⋊C4—22no—
126C4⋊C4—432no—
127C4⋊C4—861no—
128C4⋊C4—1722no—
129C22⋊C4—862no—
130C22⋊C4—862no—
131C23—862no—
132C23C2×D17211yescharacteristic
133Q8—864no—
134Q8—1722no—
135Q8—1722no—
136D4—3441no—
137D4—1722no—
138D4—1722no—
139D4—1722no—
140D4—1722no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—21no—
144C2×C4—41no—
145C2×C4—41no—
146C2×C4—862no—
147C2×C4—862no—
148C2×C4—862no—
149C2×C4—1724no—
150C2×C4—1721no—
151C2×C4—1721no—
152C2×C4—1721no—
153C2×C4—1721no—
154C2×C4#1062187312yescomplemented
155C2×C4D4×D4312yes—
156C8—42no—
157C22—21no—
158C22—21no—
159C22—1722no—
160C22—1722no—
161C22—1722no—
162C22#1306329511yescharacteristic
163C22C2×#1062187311yescharacteristic
164C22#1306335311yescharacteristic
165C4—22no—
166C4—22no—
167C4—41no—
168C4—1722no—
169C4—1722no—
170C4—1722no—
171C2—21no—
172C2—21no—
173C2—3442no—
174C2#1458305211yescharacteristic
175C2#1458308411yescharacteristic
176C2#1458308711yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#324C2
socleC22×C43#120
hypercenter#324D43
hypocenterC43#1604
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #324

Complements

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

NH ≅ G/Ntype
2. #14583040C2semidirect
3. #14582819C2semidirect
4. #14582634C2semidirect
5. C43×#324C2semidirect
49. C2×C4×C43SD16semidirect
93. #324D43semidirect
94. C43#1604semidirect
154. C2×C4#10621873semidirect