Finite Group Databasebeta

← #19133890

Subgroups — #19133890

Order 5504.

230 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 45 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#14583647C211yesmaximal, characteristic, complemented
2#14583288C212yesmaximal, complemented
3#14583265C211yesmaximal, characteristic, complemented
4#14582638C212yesmaximal, complemented
5C43×#330C211yesmaximal, characteristic, complemented
6C2×#10621873—22no—
7C2×D344—22no—
8#13063322C2211yescharacteristic
9#13063313C2212yes—
10#13063310—22no—
11#13063303—22no—
12#13063300—22no—
13#13063245—22no—
14#13063236C2211yescharacteristic
15#125×C43C2211yescharacteristic
16#97×C43C2212yes—
17C2×D172—22no—
18C2×D172—21no—
19C2×D172—22no—
20C2×D172D412yes—
21C2×C4×D43—22no—
22C2×Dic86D412yes—
23C2×C8×C43—22no—
24C4⋊C4×C43—22no—
25C4⋊C4×C43D412yes—
26C42×C43C2311yescharacteristic
27(C2×D43)⋊C4—22no—
28(C2×D43)⋊C4—22no—
29(C2×D43)⋊C4—22no—
30Dic43⋊C4—22no—
31C2×C43⋊C8—21no—
32D344—44no—
33#10621873—44no—
34C22×D43—22no—
35C22×D43—41no—
36C2×C4×C43—22no—
37C2×C4×C43C2×D411yescharacteristic
38C2×C4×C43C2×D412yes—
39C2×Dic43—22no—
40D172—42no—
41D172—42no—
42D172—42no—
43D172—42no—
44D172—82no—
45C4×D43—82no—
46Dic86—42no—
47C8×C43—24no—
48C43⋊C8—41no—
49C22×C43#12011yescharacteristic
50C2×D43—42no—
51C2×D43—42no—
52C2×D43—42no—
53C2×D43—82no—
54C2×D43—81no—
55C4×C43—22no—
56C4×C43—21no—
57C4×C43—42no—
58Dic43—42no—
59#1656—431nomaximal, Sylow
60C2×C43#45312yes—
61C2×C43#45411yescharacteristic
62D43—82no—
63D43—161no—
64#562—431no—
65#496—432no—
66#490—431no—
67#330D4311yescharacteristic, complemented
68#329—432no—
69C43#165611yescharacteristic, complemented, Sylow
70C2×SD16—862no—
71C2×D8—862no—
72#127—431no—
73#125C2×D4311yescharacteristic
74#124—432no—
75#123—862no—
76C22⋊Q8—862no—
77#121—862no—
78#102—862no—
79#97—431no—
80#97C2×D4312yes—
81C2×Q8—432no—
82C2×D4—432no—
83C2×D4—862no—
84C2×D4—861no—
85C2×D4—862no—
86C22×C4—862no—
87SD16—1724no—
88D8—1724no—
89C2×C8—22no—
90C2×C8—861no—
91C4⋊C4—22no—
92C4⋊C4—862no—
93C4⋊C4D17212yes—
94C22⋊C4—862no—
95C22⋊C4—862no—
96C22⋊C4—862no—
97C42C22×D4311yescharacteristic
98C23—862no—
99C23—1721no—
100Q8—1722no—
101D4—3442no—
102D4—1722no—
103D4—1722no—
104D4—1722no—
105D4—1722no—
106C2×C4—22no—
107C2×C4—862no—
108C2×C4—3442no—
109C2×C4C2×D17211yescharacteristic
110C2×C4D4×D4312yes—
111C8—24no—
112C8—1721no—
113C22—3442no—
114C22—3441no—
115C22—1722no—
116C22—1722no—
117C22—1722no—
118C22#1306329511yescharacteristic
119C4—22no—
120C4—21no—
121C4—42no—
122C4—1722no—
123C2—3442no—
124C2—6881no—
125C2#1458306812yes—
126C2#1458307411yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#330C2
socleC22×C43#120
hypercenter#330D43
hypocenterC43#1656
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #330

Complements

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

NH ≅ G/Ntype
1. #14583647C2semidirect
2. #14583288C2semidirect
3. #14583265C2semidirect
4. #14582638C2semidirect
5. C43×#330C2semidirect
67. #330D43semidirect
69. C43#1656semidirect