Finite Group Databasebeta

← #19136590

Subgroups — #19136590

Order 5504.

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

normal subgroups only

This group has 246 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#14583635C211yesmaximal, characteristic, complemented
2#14583089C212yesmaximal, complemented
3#14582692C211yesmaximal, characteristic, complemented
4#14582690C212yesmaximal, complemented
5C43×#453C211yesmaximal, characteristic
6#13063312—22no—
7#13063306—21no—
8#13063306—22no—
9#13063306C2212yes—
10C4×Dic86—21no—
11D4×Dic43—22no—
12#13063240—22no—
13#13063240C2212yes—
14H(5,𝔽2)×C43C2211yescharacteristic
15AGL(1,ℤ/8)×C43—21no—
16#127×C43C2211yescharacteristic
17#104×C43—21no—
18#100×C43C2211yescharacteristic
19#41×C43—21no—
20#41×C43—41no—
21C2×D4×C43—22no—
22C2×D4×C43—22no—
23C2×D4×C43—41no—
24C2×D4×C43D411yescharacteristic
25C2×D4×C43C2311yescharacteristic
26C22×Dic43—21no—
27C22×Dic43D412yes—
28C2×Dic86—21no—
29SD16×C43—41no—
30D8×C43—41no—
31M16×C43—21no—
32C42×C43D411yescharacteristic
33C22⋊Dic43—22no—
34C22⋊Dic43—21no—
35C22⋊Dic43—22no—
36C22⋊Dic43—22no—
37C22⋊Dic43—42no—
38C22⋊Dic43D412yes—
39C4⋊Dic43—21no—
40Dic43⋊C4—22no—
41Dic43⋊C4—42no—
42C4×Dic43—22no—
43C23×C43—22no—
44C23×C43—21no—
45C23×C43C2×D412yes—
46Q8×C43—21no—
47D4×C43—21no—
48D4×C43—41no—
49D4×C43—41no—
50D4×C43—44no—
51D4×C43—42no—
52D4×C43—41no—
53C2×C4×C43—21no—
54C2×C4×C43—22no—
55C2×C4×C43—41no—
56C2×C4×C43C2×D411yescharacteristic
57C2×Dic43—22no—
58C2×Dic43—22no—
59C2×Dic43—42no—
60C2×Dic43—42no—
61C2×Dic43—81no—
62Dic86—42no—
63C8×C43—41no—
64C22×C43—22no—
65C22×C43—42no—
66C22×C43—42no—
67C22×C43—41no—
68C22×C43—41no—
69C22×C43—82no—
70C22×C43#12011yescharacteristic
71C4×C43—22no—
72C4×C43—21no—
73C4×C43—41no—
74Dic43—42no—
75Dic43—42no—
76Dic43—82no—
77#2198—431nomaximal, Sylow
78C2×C43—21no—
79C2×C43—42no—
80C2×C43—81no—
81C2×C43—81no—
82C2×C43B(4,𝔽2)11yescharacteristic
83#559—431no—
84#458—432no—
85#453D4311yescharacteristic
86#353—431no—
87#352—432no—
88C43#219811yescharacteristic, complemented, Sylow
89H(5,𝔽2)C2×D4311yescharacteristic
90AGL(1,ℤ/8)—21no—
91#127C2×D4311yescharacteristic
92#124—862no—
93#123—432no—
94#123—861no—
95#123—862no—
96C4×Q8—861no—
97C4×D4—862no—
98#104—21no—
99#100C2×D4311yescharacteristic
100#99—432no—
101#99—862no—
102#41—21no—
103#41—41no—
104C2×Q8—861no—
105C2×D4—22no—
106C2×D4—22no—
107C2×D4—41no—
108C2×D4C22⋊D4311yescharacteristic
109C2×D4C22×D4311yescharacteristic
110C22×C4—432no—
111C22×C4—861no—
112SD16—41no—
113D8—41no—
114M16—21no—
115C4⋊C4—861no—
116C4⋊C4—862no—
117C4⋊C4—1722no—
118C22⋊C4—432no—
119C22⋊C4—862no—
120C22⋊C4—861no—
121C22⋊C4—862no—
122C22⋊C4—862no—
123C22⋊C4—1722no—
124C42—862no—
125C42C22⋊D4311yescharacteristic
126C23—22no—
127C23—21no—
128C23D4×D4312yes—
129Q8—21no—
130Q8—1722no—
131D4—21no—
132D4—41no—
133D4—41no—
134D4—44no—
135D4—42no—
136D4—41no—
137C2×C4—21no—
138C2×C4—22no—
139C2×C4—41no—
140C2×C4—862no—
141C2×C4—862no—
142C2×C4—3441no—
143C2×C4—1722no—
144C2×C4—1722no—
145C2×C4C2×C22⋊D4311yescharacteristic
146C8—41no—
147C22—22no—
148C22—42no—
149C22—42no—
150C22—41no—
151C22—41no—
152C22—82no—
153C22#1306329311yescharacteristic
154C4—22no—
155C4—21no—
156C4—41no—
157C4—3442no—
158C4—1722no—
159C4—1722no—
160C2—21no—
161C2—42no—
162C2—81no—
163C2—81no—
164C2#1458308511yescharacteristic
subgroupG/H
centerC2#14583085
commutatorC2×D4×C43C23
FrattiniC2×D4C22×D43
FittingC43×#453C2
socleC2×C43B(4,𝔽2)
hypercenter#453D43
hypocenterC43#2198
LCSG ▷ C2×D4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×D4 ◁ #453

Complements

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

NH ≅ G/Ntype
1. #14583635C2semidirect
2. #14583089C2semidirect
3. #14582692C2semidirect
4. #14582690C2semidirect
88. C43#2198semidirect