Finite Group Databasebeta

← #19133885

Subgroups — #19133885

Order 5504.

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

normal subgroups only

This group has 262 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#14583641C211yesmaximal, characteristic, complemented
2#14583289C211yesmaximal, characteristic, complemented
3#14583288C212yesmaximal, complemented
4#14582638C212yesmaximal, complemented
5C43×#329C211yesmaximal, characteristic, complemented
6C2×#10621873—22no—
7C2×#10621884—21no—
8C2×D344—22no—
9C2×#10621882—21no—
10#13063322C2211yescharacteristic, complemented
11#13063314—21no—
12#13063313C2212yes—
13#13063311—22no—
14#13063295—22no—
15#13063293—21no—
16#13063236C2211yescharacteristic, complemented
17#124×C43C2211yescharacteristic
18#97×C43C2212yescomplemented
19C23×D43—21no—
20C2×Q8×C43D411yescharacteristic
21C2×D4×C43D411yescharacteristic
22C2×C22⋊D43—22no—
23C2×D172—21no—
24C2×D172—21no—
25C2×D172—22no—
26C2×D172D412yes—
27C2×Dic86D412yes—
28C2×C8×C43—22no—
29C22⋊C4×C43—22no—
30C42×C43C2311yescharacteristic
31C22⋊Dic43—21no—
32#10621884—42no—
33#10621882—42no—
34(C2×D43)⋊C4—22no—
35(C2×D43)⋊C4—22no—
36(C2×D43)⋊C4—22no—
37C4×Dic43—21no—
38C2×C43⋊C8—21no—
39D344—44no—
40#10621873—44no—
41C23×C43—21no—
42C22×D43—22no—
43C22×D43—41no—
44C22×D43—82no—
45C22×D43—81no—
46Q8×C43—41no—
47D4×C43—41no—
48C2×C4×C43—21no—
49C2×C4×C43C2×D411yescharacteristic
50C2×C4×C43C2×D412yes—
51C22⋊D43—82no—
52C2×Dic43—22no—
53D172—42no—
54D172—42no—
55D172—42no—
56D172—41no—
57D172—41no—
58D172—81no—
59Dic86—42no—
60C8×C43—24no—
61C43⋊C8—22no—
62C22×C43—42no—
63C22×C43—41no—
64C22×C43#12011yescharacteristic
65C2×D43—42no—
66C2×D43—42no—
67C2×D43—42no—
68C2×D43—84no—
69C2×D43—82no—
70C2×D43—81no—
71C4×C43—21no—
72C4×C43—22no—
73C4×C43—41no—
74Dic43—42no—
75#1655—431nomaximal, Sylow
76C2×C43—81no—
77C2×C43#45312yes—
78C2×C43#45311yescharacteristic
79D43—82no—
80D43—161no—
81H(3,𝔽4)—431no—
82#496—431no—
83#496—432no—
84#329—432no—
85#329D4311yescharacteristic, complemented
86C43#165511yescharacteristic, complemented, Sylow
87C2×SD16—862no—
88C2×SD16—861no—
89C2×D8—862no—
90C2×D8—861no—
91#127—431no—
92#124—432no—
93#124—862no—
94#124—861no—
95#124C2×D4311yescharacteristic
96#120—862no—
97#120—861no—
98#97—431no—
99#97C2×D4312yescomplemented
100C24—861no—
101C2×Q8—432no—
102C2×Q8D17211yescharacteristic
103C2×D4—432no—
104C2×D4—861no—
105C2×D4—862no—
106C2×D4—861no—
107C2×D4—862no—
108C2×D4D17211yescharacteristic
109SD16—1724no—
110SD16—1722no—
111D8—1724no—
112D8—1722no—
113C2×C8—22no—
114C2×C8—861no—
115C22⋊C4—22no—
116C22⋊C4—862no—
117C22⋊C4—861no—
118C22⋊C4—862no—
119C22⋊C4—862no—
120C42—861no—
121C42C22×D4311yescharacteristic
122C23—21no—
123C23—862no—
124C23—3442no—
125C23—3441no—
126C23—1721no—
127Q8—41no—
128Q8—1722no—
129D4—41no—
130D4—3441no—
131D4—3442no—
132D4—1722no—
133D4—1721no—
134D4—1722no—
135D4—1721no—
136D4—1722no—
137C2×C4—21no—
138C2×C4—862no—
139C2×C4C2×D17211yescharacteristic
140C2×C4D4×D4312yes—
141C8—24no—
142C8—862no—
143C22—42no—
144C22—41no—
145C22—3444no—
146C22—3442no—
147C22—3441no—
148C22—1722no—
149C22—1722no—
150C22—1722no—
151C22#1306329511yescharacteristic
152C4—22no—
153C4—21no—
154C4—41no—
155C4—1722no—
156C2—81no—
157C2—3442no—
158C2—6881no—
159C2#1458306812yes—
160C2#1458306911yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#329C2
socleC22×C43#120
hypercenter#329D43
hypocenterC43#1655
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
1. #14583641C2semidirect
2. #14583289C2semidirect
3. #14583288C2semidirect
4. #14582638C2semidirect
5. C43×#329C2semidirect
10. #13063322C22semidirect
16. #13063236C22semidirect
18. #97×C43C22semidirect
85. #329D43semidirect
86. C43#1655semidirect
99. #97C2×D43semidirect