Finite Group Databasebeta

← #19136607

Subgroups — #19136607

Order 5504.

226 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 226 conjugacy classes of subgroups — too many to draw. Only its 41 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#14583649C211yesmaximal, characteristic, complemented
2#14583089C212yesmaximal
3#14582694C211yesmaximal, characteristic, complemented
4#14582690C212yesmaximal, complemented
5C43×#455C211yesmaximal, characteristic
6#13063323—21no—
7#13063318—22no—
8#13063317—21no—
9#13063306—22no—
10#13063306C2212yes—
11#13063302—22no—
12#13063240—22no—
13#13063240C2212yes—
14H(5,𝔽2)×C43C2211yescharacteristic
15#137×C43—21no—
16#124×C43C2211yescharacteristic
17#104×C43—21no—
18#100×C43C2211yescharacteristic
19#41×C43—21no—
20#41×C43—41no—
21C2×Q8×C43D411yescharacteristic
22C2×D4×C43—22no—
23C2×D4×C43—41no—
24C2×D4×C43C2311yescharacteristic
25C22×Dic43D412yes—
26C2×Dic86—21no—
27Q16×C43—41no—
28SD16×C43—41no—
29M16×C43—21no—
30C22⋊C4×C43—22no—
31C42×C43D411yescharacteristic
32C22⋊Dic43—22no—
33C22⋊Dic43—22no—
34C22⋊Dic43—42no—
35C22⋊Dic43D412yes—
36C4⋊Dic43—21no—
37C4⋊Dic43—21no—
38Dic43⋊C4—22no—
39Dic43⋊C4—22no—
40Dic43⋊C4—22no—
41Dic43⋊C4—42no—
42C4×Dic43—21no—
43C23×C43—22no—
44C23×C43C2×D412yes—
45Q8×C43—21no—
46Q8×C43—41no—
47D4×C43—21no—
48D4×C43—41no—
49D4×C43—42no—
50D4×C43—41no—
51C2×C4×C43—22no—
52C2×C4×C43—21no—
53C2×C4×C43—21no—
54C2×C4×C43—41no—
55C2×C4×C43C2×D411yescharacteristic
56C2×Dic43—22no—
57C2×Dic43—22no—
58C2×Dic43—42no—
59C2×Dic43—42no—
60Dic86—81no—
61C8×C43—41no—
62C22×C43—22no—
63C22×C43—42no—
64C22×C43—41no—
65C22×C43—82no—
66C22×C43#12011yescharacteristic
67C4×C43—21no—
68C4×C43—41no—
69C4×C43—41no—
70C4×C43—41no—
71Dic43—42no—
72Dic43—42no—
73Dic43—82no—
74#2201—431nomaximal, Sylow
75C2×C43—21no—
76C2×C43—42no—
77C2×C43—81no—
78C2×C43B(4,𝔽2)11yescharacteristic
79#563—431no—
80#458—432no—
81#455D4311yescharacteristic
82#354—431no—
83#352—432no—
84C43#220111yescharacteristic, complemented, Sylow
85H(5,𝔽2)C2×D4311yescharacteristic
86#137—21no—
87C4⋊Q8—861no—
88#126—862no—
89#125—861no—
90#124C2×D4311yescharacteristic
91#123—432no—
92#123—862no—
93C22⋊Q8—862no—
94#104—21no—
95#100C2×D4311yescharacteristic
96#99—432no—
97#99—862no—
98#41—21no—
99#41—41no—
100C2×Q8—861no—
101C2×Q8C22⋊D4311yescharacteristic
102C2×D4—22no—
103C2×D4—41no—
104C2×D4C22×D4311yescharacteristic
105C22×C4—432no—
106Q16—41no—
107SD16—41no—
108M16—21no—
109C4⋊C4—861no—
110C4⋊C4—862no—
111C4⋊C4—862no—
112C4⋊C4—861no—
113C4⋊C4—862no—
114C4⋊C4—1722no—
115C22⋊C4—22no—
116C22⋊C4—432no—
117C22⋊C4—862no—
118C22⋊C4—862no—
119C22⋊C4—1722no—
120C42—861no—
121C42C22⋊D4311yescharacteristic
122C23—22no—
123C23D4×D4312yes—
124Q8—21no—
125Q8—41no—
126Q8—3441no—
127D4—21no—
128D4—41no—
129D4—42no—
130D4—41no—
131C2×C4—22no—
132C2×C4—21no—
133C2×C4—21no—
134C2×C4—41no—
135C2×C4—862no—
136C2×C4—862no—
137C2×C4—1722no—
138C2×C4—1722no—
139C2×C4C2×C22⋊D4311yescharacteristic
140C8—41no—
141C22—22no—
142C22—42no—
143C22—41no—
144C22—82no—
145C22#1306329311yescharacteristic
146C4—21no—
147C4—41no—
148C4—41no—
149C4—41no—
150C4—3442no—
151C4—1722no—
152C4—1722no—
153C2—21no—
154C2—42no—
155C2—81no—
156C2#1458308511yescharacteristic
subgroupG/H
centerC2#14583085
commutatorC2×D4×C43C23
FrattiniC2×D4C22×D43
FittingC43×#455C2
socleC2×C43B(4,𝔽2)
hypercenter#455D43
hypocenterC43#2201
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #455

Complements

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

NH ≅ G/Ntype
1. #14583649C2semidirect
3. #14582694C2semidirect
4. #14582690C2semidirect
84. C43#2201semidirect