Finite Group Databasebeta

← #19133534

Subgroups — #19133534

Order 5504.

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

normal subgroups only

This group has 266 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#14583530C211yesmaximal, characteristic, complemented
2#14583050C212yesmaximal
3#14582635C212yesmaximal, complemented
4#14582625C211yesmaximal, characteristic, complemented
5C43×#394C211yesmaximal, characteristic
6C2×#10621883—22no—
7#13063324—22no—
8#13063316—22no—
9#13063304—21no—
10#13063304C2212yes—
11#13063284—21no—
12#13063246—22no—
13C22⋊(C43⋊C8)C2212yes—
14C22×D4×C43C2211yescharacteristic
15C2×C4⋊C4×C43C2211yescharacteristic
16C2×C22⋊C4×C43—21no—
17C2×C22⋊C4×C43—21no—
18#95×C43C2211yescharacteristic
19C24×C43—21no—
20C2×D4×C43—22no—
21C2×D4×C43—42no—
22C22×C4×C43—21no—
23C22×C4×C43D411yescharacteristic
24C22×C4×C43D411yescharacteristic
25C22×C4×C43C2311yescharacteristic
26C2×Dic86—21no—
27C2×Dic86D412yes—
28C4⋊C4×C43—22no—
29C22⋊C4×C43—42no—
30C22⋊C4×C43—42no—
31C22⋊Dic43—22no—
32#10621883—44no—
33C4⋊Dic43—21no—
34C4⋊Dic43—21no—
35C4⋊Dic43—21no—
36C4⋊Dic43D412yes—
37Dic43⋊C4—22no—
38Dic43⋊C4—22no—
39C4×Dic43—22no—
40C2×C43⋊C8—22no—
41C23×C43—22no—
42C23×C43—41no—
43C23×C43—41no—
44C23×C43—41no—
45C23×C43—41no—
46C23×C43—41no—
47C23×C43—41no—
48C23×C43C2×D411yescharacteristic
49D4×C43—24no—
50D4×C43—42no—
51C2×C4×C43—21no—
52C2×C4×C43—21no—
53C2×C4×C43—21no—
54C2×C4×C43—41no—
55C2×C4×C43—41no—
56C2×C4×C43—41no—
57C2×C4×C43—41no—
58C2×C4×C43—41no—
59C2×C4×C43SD1612yescomplemented
60C2×C4×C43C2×D412yes—
61C2×Dic43—22no—
62C2×Dic43—22no—
63Dic86—42no—
64Dic86—81no—
65C43⋊C8—42no—
66C22×C43—21no—
67C22×C43—21no—
68C22×C43—42no—
69C22×C43—42no—
70C22×C43—42no—
71C22×C43—81no—
72C22×C43—81no—
73C22×C43—81no—
74C22×C43—81no—
75C22×C43#12011yescharacteristic
76C22×C43C2×SD1611yescharacteristic
77C22×C43#13711yescharacteristic
78C4×C43—22no—
79C4×C43—22no—
80C4×C43—41no—
81C4×C43—81no—
82Dic43—42no—
83Dic43—42no—
84#1599—431nomaximal, Sylow
85C2×C43—21no—
86C2×C43—21no—
87C2×C43—82no—
88C2×C43#44811yescharacteristic
89C2×C43#45411yescharacteristic
90C2×C43B(4,𝔽2)11yescharacteristic
91#544—431no—
92#450—432no—
93#394D4311yescharacteristic
94#328—432no—
95#324—431no—
96C43#159911yescharacteristic, complemented, Sylow
97C22×D4C2×D4311yescharacteristic
98C2×SD16—862no—
99C4⋊Q8—862no—
100#125—862no—
101C22⋊Q8—432no—
102C22⋊Q8—861no—
103#117—861no—
104C2×C4⋊C4C2×D4311yescharacteristic
105C2×C22⋊C4—21no—
106C2×C22⋊C4—21no—
107#102—862no—
108C22⋊C8—432no—
109#95C2×D4311yescharacteristic
110C24—21no—
111C2×Q8—432no—
112C2×Q8—861no—
113C2×D4—22no—
114C2×D4—42no—
115C22×C4—21no—
116C22×C4C22⋊D4311yescharacteristic
117C22×C4C22⋊D4311yescharacteristic
118C22×C4C22×D4311yescharacteristic
119SD16—1724no—
120C2×C8—862no—
121C4⋊C4—22no—
122C4⋊C4—432no—
123C4⋊C4—861no—
124C4⋊C4—861no—
125C4⋊C4—861no—
126C4⋊C4—862no—
127C4⋊C4—862no—
128C22⋊C4—42no—
129C22⋊C4—42no—
130C22⋊C4—862no—
131C42—862no—
132C23—22no—
133C23—41no—
134C23—41no—
135C23—41no—
136C23—41no—
137C23—41no—
138C23—41no—
139C23C2×C22⋊D4311yescharacteristic
140Q8—3441no—
141Q8—1722no—
142D4—24no—
143D4—42no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—21no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—862no—
153C2×C4—862no—
154C2×C4#1062188312yescomplemented
155C2×C4D4×D4312yes—
156C8—1722no—
157C22—21no—
158C22—21no—
159C22—42no—
160C22—42no—
161C22—42no—
162C22—81no—
163C22—81no—
164C22—81no—
165C22—81no—
166C22#1306329311yescharacteristic
167C22C2×#1062188311yescharacteristic
168C22#1306335511yescharacteristic
169C4—22no—
170C4—22no—
171C4—41no—
172C4—81no—
173C4—1722no—
174C4—1722no—
175C2—21no—
176C2—21no—
177C2—82no—
178C2#1458303711yescharacteristic
179C2#1458307111yescharacteristic
180C2#1458308511yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#394C2
socleC22×C43#120
hypercenter#394D43
hypocenterC43#1599
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #394

Complements

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

NH ≅ G/Ntype
1. #14583530C2semidirect
3. #14582635C2semidirect
4. #14582625C2semidirect
59. C2×C4×C43SD16semidirect
96. C43#1599semidirect
154. C2×C4#10621883semidirect