Finite Group Databasebeta

← #19136624

Subgroups — #19136624

Order 5504.

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

normal subgroups only

This group has 224 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#14583629C211yesmaximal, characteristic, complemented
2#14583082C212yesmaximal
3#14582698C211yesmaximal, characteristic, complemented
4#14582697C212yesmaximal, complemented
5C43×#456C211yesmaximal, characteristic
6#13063355—22no—
7#13063324—22no—
8#13063323—21no—
9#13063323C2212yes—
10C4×Dic86—21no—
11#13063290—22no—
12#13063252—22no—
13#13063244C2212yes—
142−1+4×C43C2211yescharacteristic
15#137×C43—21no—
16C4⋊Q8×C43C2211yescharacteristic
17#104×C43—21no—
18#101×C43C2211yescharacteristic
19#41×C43—21no—
20#41×C43—22no—
21#41×C43—41no—
22C2×Q8×C43—41no—
23C2×Q8×C43D411yescharacteristic
24C2×Q8×C43C2311yescharacteristic
25C2×Dic86—21no—
26C2×Dic86—21no—
27C2×Dic86D412yes—
28Q16×C43—41no—
29SD16×C43—41no—
30M16×C43—21no—
31C4⋊C4×C43—22no—
32C42×C43D411yescharacteristic
33#10621885—42no—
34#10621883—42no—
35C4⋊Dic43—21no—
36Dic43⋊C4—22no—
37Dic43⋊C4—22no—
38Dic43⋊C4—22no—
39C4×Dic43—21no—
40C4×Dic43—22no—
41C4×Dic43D412yes—
42#10621877—22no—
43Q8×C43—22no—
44Q8×C43—21no—
45Q8×C43—41no—
46Q8×C43—41no—
47D4×C43—22no—
48D4×C43—21no—
49D4×C43—41no—
50C2×C4×C43—21no—
51C2×C4×C43—21no—
52C2×C4×C43—42no—
53C2×C4×C43—41no—
54C2×C4×C43C2×D412yes—
55C2×C4×C43C2×D411yescharacteristic
56C2×Dic43—22no—
57C2×Dic43—22no—
58Dic86—24no—
59Dic86—42no—
60Dic86—81no—
61C8×C43—41no—
62C43⋊C8—42no—
63C22×C43—41no—
64C22×C43#12011yescharacteristic
65C4×C43—22no—
66C4×C43—22no—
67C4×C43—21no—
68C4×C43—41no—
69C4×C43—41no—
70Dic43—24no—
71Dic43—42no—
72#2205—431nomaximal, Sylow
73C2×C43—21no—
74C2×C43—81no—
75C2×C43B(4,𝔽2)11yescharacteristic
76Q82—431no—
77#456—432no—
78#456D4311yescharacteristic
79#356—431no—
80#356—432no—
81C43#220511yescharacteristic, complemented, Sylow
822−1+4C2×D4311yescharacteristic
83#137—21no—
84#137—862no—
85C4⋊Q8—432no—
86C4⋊Q8—862no—
87C4⋊Q8—861no—
88C4⋊Q8C2×D4311yescharacteristic
89C4×Q8—862no—
90C4×Q8—861no—
91#104—21no—
92#104—862no—
93#101—432no—
94#101C2×D4311yescharacteristic
95#41—22no—
96#41—21no—
97#41—41no—
98C2×Q8—41no—
99C2×Q8—432no—
100C2×Q8—861no—
101C2×Q8—861no—
102C2×Q8C22⋊D4311yescharacteristic
103C2×Q8C22×D4311yescharacteristic
104Q16—41no—
105Q16—1722no—
106SD16—41no—
107SD16—1722no—
108M16—21no—
109M16—862no—
110C4⋊C4—22no—
111C4⋊C4—862no—
112C4⋊C4—861no—
113C4⋊C4—862no—
114C4⋊C4—862no—
115C42—432no—
116C42—862no—
117C42—861no—
118C42C22⋊D4311yescharacteristic
119Q8—21no—
120Q8—22no—
121Q8—41no—
122Q8—41no—
123Q8—864no—
124Q8—3441no—
125Q8—1722no—
126D4—21no—
127D4—22no—
128D4—41no—
129C2×C4—21no—
130C2×C4—21no—
131C2×C4—41no—
132C2×C4—42no—
133C2×C4—862no—
134C2×C4—862no—
135C2×C4D4×D4312yes—
136C2×C4C2×C22⋊D4311yescharacteristic
137C8—41no—
138C8—1722no—
139C22—41no—
140C22#1306329311yescharacteristic
141C4—22no—
142C4—21no—
143C4—22no—
144C4—41no—
145C4—41no—
146C4—864no—
147C4—1722no—
148C2—21no—
149C2—81no—
150C2#1458308511yescharacteristic
subgroupG/H
centerC2#14583085
commutatorC2×Q8×C43C23
FrattiniC2×Q8C22×D43
FittingC43×#456C2
socleC2×C43B(4,𝔽2)
hypercenter#456D43
hypocenterC43#2205
LCSG ▷ C2×Q8×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #456

Complements

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

NH ≅ G/Ntype
1. #14583629C2semidirect
3. #14582698C2semidirect
4. #14582697C2semidirect
81. C43#2205semidirect