Finite Group Databasebeta

← #19136620

Subgroups — #19136620

Order 5504.

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

normal subgroups only

This group has 236 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#14583615C211yesmaximal, characteristic, complemented
2#14583072C212yesmaximal, complemented
3#14582698C211yesmaximal, characteristic, complemented
4#14582695C212yesmaximal, complemented
5C43×#456C211yesmaximal, characteristic, complemented
6#13063350—22no—
7#13063314—21no—
8#13063314C2212yes—
9#13063300—22no—
10C4×D172—21no—
11#13063283—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×D172—21no—
26C2×D172—21no—
27C2×D172D412yes—
28C2×C4×D43—22no—
29Q16×C43—41no—
30SD16×C43—41no—
31M16×C43—21no—
32C4⋊C4×C43—22no—
33C42×C43D411yescharacteristic
34#10621884—42no—
35#10621882—42no—
36(C2×D43)⋊C4—22no—
37(C2×D43)⋊C4—22no—
38(C2×D43)⋊C4—22no—
39C4⋊Dic43—21no—
40C4×Dic43—21no—
41C4×Dic43D412yes—
42#10621877—22no—
43C22×D43—22no—
44Q8×C43—22no—
45Q8×C43—21no—
46Q8×C43—41no—
47Q8×C43—41no—
48D4×C43—22no—
49D4×C43—21no—
50D4×C43—41no—
51C2×C4×C43—21no—
52C2×C4×C43—21no—
53C2×C4×C43—42no—
54C2×C4×C43—41no—
55C2×C4×C43C2×D412yes—
56C2×C4×C43C2×D411yescharacteristic
57C2×Dic43—22no—
58D172—42no—
59D172—42no—
60D172—81no—
61C4×D43—44no—
62C8×C43—41no—
63C43⋊C8—42no—
64C22×C43—41no—
65C22×C43#12011yescharacteristic
66C2×D43—42no—
67C2×D43—42no—
68C2×D43—42no—
69C4×C43—22no—
70C4×C43—22no—
71C4×C43—21no—
72C4×C43—41no—
73C4×C43—41no—
74Dic43—42no—
75#2204—431nomaximal, Sylow
76C2×C43—21no—
77C2×C43—81no—
78C2×C43B(4,𝔽2)11yescharacteristic
79D43—82no—
80#555—431no—
81#456D4311yescharacteristic, complemented
82#454—432no—
83#356—431no—
84#355—432no—
85C43#220411yescharacteristic, complemented, Sylow
862−1+4C2×D4311yescharacteristic
87#137—21no—
88AGL(1,ℤ/8)—862no—
89C4⋊Q8C2×D4311yescharacteristic
90#124—432no—
91#124—861no—
92#121—862no—
93C4×D4—861no—
94#117—862no—
95#104—21no—
96#104—862no—
97#101—432no—
98#101C2×D4311yescharacteristic
99#41—22no—
100#41—21no—
101#41—41no—
102C2×Q8—41no—
103C2×Q8C22⋊D4311yescharacteristic
104C2×Q8C22×D4311yescharacteristic
105C2×D4—432no—
106C2×D4—861no—
107C2×D4—861no—
108C22×C4—862no—
109Q16—41no—
110SD16—41no—
111SD16—1722no—
112D8—1722no—
113M16—21no—
114M16—862no—
115C4⋊C4—22no—
116C4⋊C4—861no—
117C22⋊C4—862no—
118C22⋊C4—862no—
119C22⋊C4—862no—
120C42—432no—
121C42—861no—
122C42C22⋊D4311yescharacteristic
123C23—862no—
124Q8—22no—
125Q8—21no—
126Q8—41no—
127Q8—41no—
128D4—22no—
129D4—21no—
130D4—41no—
131D4—3441no—
132D4—1722no—
133D4—1722no—
134C2×C4—21no—
135C2×C4—21no—
136C2×C4—41no—
137C2×C4—42no—
138C2×C4—862no—
139C2×C4—1724no—
140C2×C4D4×D4312yes—
141C2×C4C2×C22⋊D4311yescharacteristic
142C8—41no—
143C8—1722no—
144C22—41no—
145C22—1722no—
146C22—1722no—
147C22—1722no—
148C22#1306329311yescharacteristic
149C4—22no—
150C4—21no—
151C4—22no—
152C4—41no—
153C4—41no—
154C4—1722no—
155C2—21no—
156C2—81no—
157C2—3442no—
158C2#1458308511yescharacteristic
subgroupG/H
centerC2#14583085
commutatorC2×Q8×C43C23
FrattiniC2×Q8C22×D43
FittingC43×#456C2
socleC2×C43B(4,𝔽2)
hypercenter#456D43
hypocenterC43#2204
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. #14583615C2semidirect
2. #14583072C2semidirect
3. #14582698C2semidirect
4. #14582695C2semidirect
5. C43×#456C2semidirect
81. #456D43semidirect
85. C43#2204semidirect