Finite Group Databasebeta

← #19133636

Subgroups — #19133636

Order 5504.

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

normal subgroups only

This group has 202 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#14583234C212yesmaximal
3#14582635C212yesmaximal
4#14582625C211yesmaximal, characteristic
5C43×#400C211yesmaximal, characteristic
6#13063324—22no—
7#13063316—22no—
8#13063304—21no—
9#13063304C2212yes—
10#13063284—21no—
11#13063258—22no—
12#13063248—22no—
13C22⋊(C43⋊C8)C2212yes—
14C2×C4⋊C4×C43C2211yescharacteristic
15C2×C4⋊C4×C43C2211yescharacteristic
16#95×C43—21no—
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—
28C22⋊Dic43—22no—
29C4⋊Dic43—21no—
30C4⋊Dic43—21no—
31C4⋊Dic43—21no—
32C4⋊Dic43D412yes—
33Dic43⋊C4—22no—
34Dic43⋊C4—22no—
35C4×Dic43—22no—
36C2×C43⋊C8—22no—
37C23×C43C2×D411yescharacteristic
38C2×C4×C43—21no—
39C2×C4×C43—21no—
40C2×C4×C43—21no—
41C2×C4×C43—41no—
42C2×C4×C43—41no—
43C2×C4×C43—41no—
44C2×C4×C43—41no—
45C2×C4×C43—42no—
46C2×C4×C43—41no—
47C2×C4×C43—41no—
48C2×C4×C43Q1612yes—
49C2×C4×C43C2×D412yes—
50C2×Dic43—22no—
51C2×Dic43—22no—
52Dic86—42no—
53Dic86—81no—
54C43⋊C8—42no—
55C22×C43—21no—
56C22×C43—21no—
57C22×C43#12011yescharacteristic
58C22×C43C2×Q1611yescharacteristic
59C22×C43#13711yescharacteristic
60C4×C43—22no—
61C4×C43—22no—
62C4×C43—41no—
63C4×C43—81no—
64C4×C43—81no—
65Dic43—42no—
66Dic43—42no—
67#1617—431nomaximal, Sylow
68C2×C43—21no—
69C2×C43—21no—
70C2×C43#45111yescharacteristic
71C2×C43#45411yescharacteristic
72C2×C43#45811yescharacteristic
73#544—431no—
74#484—432no—
75#400D4311yescharacteristic
76#328—432no—
77#324—431no—
78C43#161711yescharacteristic, complemented, Sylow
79C4⋊Q8—862no—
80#125—862no—
81C22⋊Q8—432no—
82C22⋊Q8—861no—
83#117—861no—
84C2×C4⋊C4C2×D4311yescharacteristic
85C2×C4⋊C4C2×D4311yescharacteristic
86#107—862no—
87#103—862no—
88C22⋊C8—432no—
89#95—21no—
90#95—21no—
91#95C2×D4311yescharacteristic
92C2×Q8—432no—
93C2×Q8—861no—
94C22×C4—21no—
95C22×C4—21no—
96C22×C4C22⋊D4311yescharacteristic
97C22×C4C22⋊D4311yescharacteristic
98C22×C4C22×D4311yescharacteristic
99C2×C8—862no—
100C4⋊C4—22no—
101C4⋊C4—22no—
102C4⋊C4—432no—
103C4⋊C4—861no—
104C4⋊C4—861no—
105C4⋊C4—861no—
106C4⋊C4—862no—
107C4⋊C4—862no—
108C22⋊C4—862no—
109C42—862no—
110C23C2×C22⋊D4311yescharacteristic
111Q8—3441no—
112Q8—1722no—
113C2×C4—21no—
114C2×C4—21no—
115C2×C4—21no—
116C2×C4—41no—
117C2×C4—41no—
118C2×C4—41no—
119C2×C4—41no—
120C2×C4—42no—
121C2×C4—41no—
122C2×C4—41no—
123C2×C4—862no—
124C2×C4—862no—
125C2×C4#1062188512yes—
126C2×C4D4×D4312yes—
127C8—1722no—
128C22—21no—
129C22—21no—
130C22#1306329311yescharacteristic
131C22C2×#1062188511yescharacteristic
132C22#1306335511yescharacteristic
133C4—22no—
134C4—22no—
135C4—41no—
136C4—81no—
137C4—81no—
138C4—1722no—
139C4—1722no—
140C2—21no—
141C2—21no—
142C2#1458305411yescharacteristic
143C2#1458307111yescharacteristic
144C2#1458308811yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#400C2
socleC22×C43#120
hypercenter#400D43
hypocenterC43#1617
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #400

Complements

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

NH ≅ G/Ntype
78. C43#1617semidirect