Finite Group Databasebeta

← #19136591

Subgroups — #19136591

Order 5504.

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

normal subgroups only

This group has 246 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#14583088C212yesmaximal, complemented
2#14583066C211yesmaximal, characteristic
3#14582692C211yesmaximal, characteristic, complemented
4#14582689C212yesmaximal, complemented
5C43×#559C211yesmaximal, characteristic, complemented
6#13063370C2211yescharacteristic
7#13063351—21no—
8#13063308—22no—
9#13063253—21no—
10#13063242C2211yescharacteristic
11#13063240C2212yes—
12#13063239—22no—
13#127×C43C2211yescharacteristic
14#124×C43—22no—
15#123×C43—21no—
16#123×C43C2212yes—
17C4×Q8×C43—21no—
18C4×D4×C43—22no—
19C2×Q8×C43—21no—
20C2×D4×C43—22no—
21C2×D4×C43D411yescharacteristic
22C2×D4×C43C2311yescharacteristic
23C22×C4×C43—21no—
24C22×C4×C43D412yes—
25C2×C22⋊D43—22no—
26#10621900—41no—
27D4×D43—41no—
28#10621898—21no—
29C4⋊C4×C43—21no—
30C4⋊C4×C43—22no—
31C22⋊C4×C43—22no—
32C22⋊C4×C43—21no—
33C22⋊C4×C43—22no—
34C22⋊C4×C43D412yes—
35C42×C43—22no—
36C42×C43D411yescharacteristic
37C22⋊Dic43—22no—
38#10621883—41no—
39#10621882—41no—
40(C2×D43)⋊C4—42no—
41Dic43⋊C4—42no—
42#10621877—21no—
43C23×C43—21no—
44C23×C43C2×D412yes—
45C22×D43—22no—
46Q8×C43—42no—
47D4×C43—41no—
48D4×C43—41no—
49D4×C43—44no—
50C2×C4×C43—21no—
51C2×C4×C43—22no—
52C2×C4×C43—22no—
53C2×C4×C43—42no—
54C2×C4×C43—81no—
55C2×C4×C43C2×D411yescharacteristic
56C22⋊D43—42no—
57C22⋊D43—41no—
58C2×Dic43—22no—
59C2×Dic43—42no—
60D172—21no—
61C4×D43—41no—
62Dic86—21no—
63C43⋊C8—41no—
64C22×C43—22no—
65C22×C43—42no—
66C22×C43—42no—
67C22×C43—41no—
68C22×C43#12011yescharacteristic
69C2×D43—41no—
70C2×D43—82no—
71C4×C43—22no—
72C4×C43—21no—
73C4×C43—42no—
74C4×C43—42no—
75Dic43—41no—
76Dic43—82no—
77#2198—431nomaximal, Sylow
78C2×C43—21no—
79C2×C43—42no—
80C2×C43—81no—
81C2×C43B(4,𝔽2)11yescharacteristic
82D43—81no—
83#559D4311yescharacteristic, complemented
84#458—432no—
85#453—431no—
86#353—431no—
87#352—432no—
88C43#219811yescharacteristic, complemented, Sylow
89H(5,𝔽2)—431no—
90AGL(1,ℤ/8)—861no—
91#127C2×D4311yescharacteristic
92#124—22no—
93#123—21no—
94#123—862no—
95#123C2×D4312yes—
96C4×Q8—21no—
97C4×D4—22no—
98#104—861no—
99#100—431no—
100#99—432no—
101#99—862no—
102#41—861no—
103#41—1721no—
104C2×Q8—21no—
105C2×D4—22no—
106C2×D4—862no—
107C2×D4—1721no—
108C2×D4C22⋊D4311yescharacteristic
109C2×D4C22×D4311yescharacteristic
110C22×C4—21no—
111C22×C4C22⋊D4312yes—
112SD16—1721no—
113D8—1721no—
114M16—861no—
115C4⋊C4—21no—
116C4⋊C4—22no—
117C4⋊C4—1722no—
118C22⋊C4—22no—
119C22⋊C4—21no—
120C22⋊C4—22no—
121C22⋊C4—862no—
122C22⋊C4—1722no—
123C22⋊C4C22⋊D4312yes—
124C42—22no—
125C42C22⋊D4311yescharacteristic
126C23—21no—
127C23—862no—
128C23C2×C22⋊D4312yes—
129Q8—42no—
130Q8—861no—
131D4—41no—
132D4—41no—
133D4—44no—
134D4—861no—
135D4—1722no—
136D4—1721no—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—22no—
140C2×C4—42no—
141C2×C4—81no—
142C2×C4—862no—
143C2×C4—1721no—
144C2×C4—1722no—
145C2×C4C2×C22⋊D4311yescharacteristic
146C8—1721no—
147C22—22no—
148C22—42no—
149C22—42no—
150C22—41no—
151C22—3442no—
152C22—1721no—
153C22#1306329411yescharacteristic
154C4—22no—
155C4—21no—
156C4—42no—
157C4—42no—
158C4—3442no—
159C4—1721no—
160C2—21no—
161C2—42no—
162C2—81no—
163C2—3441no—
164C2#1458308611yescharacteristic
subgroupG/H
centerC2#14583086
commutatorC2×D4×C43C23
FrattiniC2×D4C22×D43
FittingC43×#559C2
socleC2×C43B(4,𝔽2)
hypercenter#559D43
hypocenterC43#2198
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #559

Complements

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

NH ≅ G/Ntype
1. #14583088C2semidirect
3. #14582692C2semidirect
4. #14582689C2semidirect
5. C43×#559C2semidirect
83. #559D43semidirect
88. C43#2198semidirect