Finite Group Databasebeta

← #19133602

Subgroups — #19133602

Order 5504.

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

normal subgroups only

This group has 210 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
2#14583229C212yesmaximal
3#14582635C212yesmaximal
4#14582625C211yesmaximal, characteristic
5C43×#398C211yesmaximal, characteristic
6#13063324—22no—
7#13063316—22no—
8#13063304—21no—
9#13063304C2212yes—
10#13063284—21no—
11#13063256—22no—
12#13063248—22no—
13C22⋊(C43⋊C8)C2212yes—
14C2×C4⋊C4×C43—21no—
15C2×C4⋊C4×C43C2211yescharacteristic
16C2×C4⋊C4×C43C2211yescharacteristic
17#95×C43—21no—
18#95×C43C2211yescharacteristic
19C22×C4×C43—21no—
20C22×C4×C43—21no—
21C22×C4×C43D411yescharacteristic
22C22×C4×C43D411yescharacteristic
23C22×C4×C43C2311yescharacteristic
24C2×Dic86—21no—
25C2×Dic86D412yes—
26C4⋊C4×C43—22no—
27C4⋊C4×C43—22no—
28C4⋊C4×C43—42no—
29C22⋊Dic43—22no—
30C4⋊Dic43—21no—
31C4⋊Dic43—21no—
32C4⋊Dic43—21no—
33C4⋊Dic43D412yes—
34Dic43⋊C4—22no—
35Dic43⋊C4—22no—
36C4×Dic43—22no—
37C2×C43⋊C8—22no—
38C23×C43C2×D411yescharacteristic
39C2×C4×C43—21no—
40C2×C4×C43—21no—
41C2×C4×C43—22no—
42C2×C4×C43—21no—
43C2×C4×C43—41no—
44C2×C4×C43—41no—
45C2×C4×C43—41no—
46C2×C4×C43—41no—
47C2×C4×C43—41no—
48C2×C4×C43—41no—
49C2×C4×C43—41no—
50C2×C4×C43SD1612yes—
51C2×C4×C43C2×D412yes—
52C2×Dic43—22no—
53C2×Dic43—22no—
54Dic86—42no—
55Dic86—81no—
56C43⋊C8—42no—
57C22×C43—21no—
58C22×C43—21no—
59C22×C43#12011yescharacteristic
60C22×C43C2×SD1611yescharacteristic
61C22×C43#13711yescharacteristic
62C4×C43—22no—
63C4×C43—22no—
64C4×C43—42no—
65C4×C43—41no—
66C4×C43—81no—
67Dic43—42no—
68Dic43—42no—
69#1611—431nomaximal, Sylow
70C2×C43—21no—
71C2×C43—21no—
72C2×C43#44811yescharacteristic
73C2×C43#45611yescharacteristic
74C2×C43#45811yescharacteristic
75#544—431no—
76#483—432no—
77#398D4311yescharacteristic
78#328—432no—
79#324—431no—
80C43#161111yescharacteristic, complemented, Sylow
81C4⋊Q8—862no—
82#125—862no—
83C22⋊Q8—432no—
84C22⋊Q8—861no—
85#117—861no—
86C2×C4⋊C4—21no—
87C2×C4⋊C4C2×D4311yescharacteristic
88C2×C4⋊C4C2×D4311yescharacteristic
89#106—862no—
90#103—862no—
91C22⋊C8—432no—
92#95—21no—
93#95C2×D4311yescharacteristic
94C2×Q8—432no—
95C2×Q8—861no—
96C22×C4—21no—
97C22×C4—21no—
98C22×C4C22⋊D4311yescharacteristic
99C22×C4C22⋊D4311yescharacteristic
100C22×C4C22×D4311yescharacteristic
101C2×C8—862no—
102C4⋊C4—22no—
103C4⋊C4—22no—
104C4⋊C4—42no—
105C4⋊C4—432no—
106C4⋊C4—861no—
107C4⋊C4—861no—
108C4⋊C4—861no—
109C4⋊C4—862no—
110C4⋊C4—862no—
111C22⋊C4—862no—
112C42—862no—
113C23C2×C22⋊D4311yescharacteristic
114Q8—3441no—
115Q8—1722no—
116C2×C4—21no—
117C2×C4—21no—
118C2×C4—22no—
119C2×C4—21no—
120C2×C4—41no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—41no—
124C2×C4—41no—
125C2×C4—41no—
126C2×C4—41no—
127C2×C4—862no—
128C2×C4—862no—
129C2×C4#1062188312yes—
130C2×C4D4×D4312yes—
131C8—1722no—
132C22—21no—
133C22—21no—
134C22#1306329311yescharacteristic
135C22C2×#1062188311yescharacteristic
136C22#1306335511yescharacteristic
137C4—22no—
138C4—22no—
139C4—42no—
140C4—41no—
141C4—81no—
142C4—1722no—
143C4—1722no—
144C2—21no—
145C2—21no—
146C2#1458303711yescharacteristic
147C2#1458308111yescharacteristic
148C2#1458308811yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#398C2
socleC22×C43#120
hypercenter#398D43
hypocenterC43#1611
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #398

Complements

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

NH ≅ G/Ntype
80. C43#1611semidirect