Finite Group Databasebeta

← #19133893

Subgroups — #19133893

Order 5504.

206 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 49 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#14583289C211yesmaximal, characteristic
2#14583265C212yesmaximal, complemented
3#14582641C212yesmaximal, complemented
4#14582639C211yesmaximal, characteristic, complemented
5C43×#563C211yesmaximal, characteristic, complemented
6C2×#10621884—21no—
7C2×#10621882—21no—
8#13063322C2211yescharacteristic
9#13063245—22no—
10#13063245—22no—
11#13063236C2212yes—
12#13063236C2211yescharacteristic
13C4⋊Q8×C43—21no—
14#126×C43—22no—
15#125×C43C2212yes—
16#124×C43C2211yescharacteristic
17#123×C43—21no—
18C22⋊Q8×C43—22no—
19C2×Q8×C43—21no—
20C2×Q8×C43D411yescharacteristic
21C2×D4×C43D411yescharacteristic
22C22×C4×C43—21no—
23C2×D172—22no—
24C2×D172—21no—
25C4⋊C4×C43—22no—
26C4⋊C4×C43—22no—
27C4⋊C4×C43—22no—
28C4⋊C4×C43D412yes—
29C4⋊C4×C43D412yes—
30C22⋊C4×C43—22no—
31C22⋊C4×C43—21no—
32C22⋊C4×C43—22no—
33C42×C43—21no—
34C42×C43C2311yescharacteristic
35#10621884—42no—
36#10621882—42no—
37C2×C43⋊C8—21no—
38C2×C43⋊C8—22no—
39C23×C43—21no—
40C22×D43—41no—
41Q8×C43—41no—
42Q8×C43—81no—
43D4×C43—41no—
44C2×C4×C43—22no—
45C2×C4×C43—21no—
46C2×C4×C43—22no—
47C2×C4×C43—81no—
48C2×C4×C43C2×D412yes—
49C2×C4×C43C2×D411yescharacteristic
50D172—41no—
51D172—41no—
52D172—44no—
53C43⋊C8—22no—
54C43⋊C8—42no—
55C22×C43—41no—
56C22×C43—42no—
57C22×C43#12011yescharacteristic
58C2×D43—81no—
59C2×D43—82no—
60C4×C43—21no—
61C4×C43—22no—
62C4×C43—42no—
63C4×C43—41no—
64C4×C43—42no—
65#1657—431nomaximal, Sylow
66C2×C43—81no—
67C2×C43#45311yescharacteristic
68C2×C43#45412yes—
69D43—161no—
70#563D4311yescharacteristic, complemented
71#496—431no—
72#490—432no—
73#330—432no—
74#329—431no—
75C43#165711yescharacteristic, complemented, Sylow
76C2×SD16—861no—
77C2×D8—861no—
78C4⋊Q8—21no—
79#127—431no—
80#126—22no—
81#125C2×D4312yes—
82#124C2×D4311yescharacteristic
83#123—21no—
84C22⋊Q8—22no—
85#102—862no—
86#102—862no—
87#97—432no—
88#97—431no—
89C2×Q8—21no—
90C2×Q8C22⋊D4311yescharacteristic
91C2×D4—862no—
92C2×D4—861no—
93C2×D4C22⋊D4311yescharacteristic
94C22×C4—21no—
95SD16—1722no—
96D8—1722no—
97C2×C8—861no—
98C2×C8—862no—
99C4⋊C4—22no—
100C4⋊C4—22no—
101C4⋊C4—22no—
102C4⋊C4C22⋊D4312yes—
103C4⋊C4C22⋊D4312yes—
104C22⋊C4—22no—
105C22⋊C4—21no—
106C22⋊C4—22no—
107C42—21no—
108C42C22×D4311yescharacteristic
109C23—21no—
110C23—1721no—
111Q8—41no—
112Q8—81no—
113D4—41no—
114D4—1721no—
115D4—1721no—
116D4—1724no—
117C2×C4—22no—
118C2×C4—21no—
119C2×C4—22no—
120C2×C4—81no—
121C2×C4C2×C22⋊D4312yes—
122C2×C4C2×C22⋊D4311yescharacteristic
123C8—862no—
124C8—1722no—
125C22—41no—
126C22—42no—
127C22—3441no—
128C22—3442no—
129C22#1306329411yescharacteristic
130C4—21no—
131C4—22no—
132C4—42no—
133C4—41no—
134C4—42no—
135C2—81no—
136C2—6881no—
137C2#1458306711yescharacteristic
138C2#1458307212yes—
subgroupG/H
centerC22#13063294
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#563C2
socleC22×C43#120
hypercenter#563D43
hypocenterC43#1657
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #563

Complements

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

NH ≅ G/Ntype
2. #14583265C2semidirect
3. #14582641C2semidirect
4. #14582639C2semidirect
5. C43×#563C2semidirect
70. #563D43semidirect
75. C43#1657semidirect