Finite Group Databasebeta

← #19136616

Subgroups — #19136616

Order 5504.

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

normal subgroups only

This group has 216 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#14583081C212yesmaximal, complemented
2#14583071C211yesmaximal, characteristic
3#14582698C212yesmaximal, complemented
4#14582696C211yesmaximal, characteristic, complemented
5C43×#563C211yesmaximal, characteristic, complemented
6#13063373C2211yescharacteristic
7#13063356—22no—
8#13063351—21no—
9#13063253—21no—
10#13063253—22no—
11#13063244C2211yescharacteristic
12#13063244C2212yes—
13C4⋊Q8×C43C2212yes—
14#126×C43—22no—
15#125×C43—21no—
16#124×C43C2211yescharacteristic
17#123×C43—21no—
18C22⋊Q8×C43—22no—
19C2×Q8×C43D412yes—
20C2×Q8×C43C2311yescharacteristic
21C2×D4×C43D411yescharacteristic
22C22×C4×C43—21no—
23#10621902—41no—
24Q8×D43—41no—
25#10621898—21no—
26#10621898—22no—
27C4⋊C4×C43—21no—
28C4⋊C4×C43—22no—
29C4⋊C4×C43—21no—
30C4⋊C4×C43—22no—
31C4⋊C4×C43—22no—
32C22⋊C4×C43—22no—
33C22⋊C4×C43—21no—
34C22⋊C4×C43—22no—
35C42×C43D411yescharacteristic
36C42×C43D412yes—
37#10621885—42no—
38#10621884—42no—
39#10621883—41no—
40#10621882—41no—
41#10621877—21no—
42#10621877—22no—
43C23×C43—21no—
44Q8×C43—41no—
45Q8×C43—42no—
46D4×C43—41no—
47C2×C4×C43—21no—
48C2×C4×C43—22no—
49C2×C4×C43—22no—
50C2×C4×C43—81no—
51C2×C4×C43C2×D412yes—
52C2×C4×C43C2×D411yescharacteristic
53C22⋊D43—41no—
54D172—21no—
55D172—22no—
56C4×D43—41no—
57C4×D43—42no—
58Dic86—21no—
59Dic86—22no—
60C43⋊C8—41no—
61C43⋊C8—42no—
62C22×C43—42no—
63C22×C43—41no—
64C22×C43#12011yescharacteristic
65C2×D43—41no—
66C4×C43—21no—
67C4×C43—22no—
68C4×C43—41no—
69C4×C43—42no—
70C4×C43—42no—
71Dic43—41no—
72#2203—431nomaximal, Sylow
73C2×C43—21no—
74C2×C43—81no—
75C2×C43B(4,𝔽2)11yescharacteristic
76D43—81no—
77#563D4311yescharacteristic, complemented
78#456—432no—
79#454—431no—
80#356—432no—
81#355—431no—
82C43#220311yescharacteristic, complemented, Sylow
832−1+4—431no—
84#137—862no—
85AGL(1,ℤ/8)—861no—
86C4⋊Q8C2×D4312yes—
87#126—22no—
88#125—21no—
89#124C2×D4311yescharacteristic
90#123—21no—
91C22⋊Q8—22no—
92#104—861no—
93#104—862no—
94#101—432no—
95#101—431no—
96#41—861no—
97#41—862no—
98#41—1721no—
99C2×Q8—1721no—
100C2×Q8C22⋊D4312yes—
101C2×Q8C22×D4311yescharacteristic
102C2×D4C22⋊D4311yescharacteristic
103C22×C4—21no—
104Q16—1722no—
105SD16—1721no—
106SD16—1722no—
107D8—1721no—
108M16—861no—
109M16—862no—
110C4⋊C4—21no—
111C4⋊C4—22no—
112C4⋊C4—21no—
113C4⋊C4—22no—
114C4⋊C4—22no—
115C22⋊C4—22no—
116C22⋊C4—21no—
117C22⋊C4—22no—
118C42C22⋊D4311yescharacteristic
119C42C22⋊D4312yes—
120C23—21no—
121Q8—41no—
122Q8—42no—
123Q8—861no—
124Q8—862no—
125D4—41no—
126D4—861no—
127D4—862no—
128D4—1721no—
129C2×C4—21no—
130C2×C4—22no—
131C2×C4—22no—
132C2×C4—81no—
133C2×C4—1721no—
134C2×C4—1722no—
135C2×C4C2×C22⋊D4312yes—
136C2×C4C2×C22⋊D4311yescharacteristic
137C8—1721no—
138C8—1722no—
139C22—42no—
140C22—41no—
141C22—1721no—
142C22#1306329411yescharacteristic
143C4—21no—
144C4—22no—
145C4—41no—
146C4—42no—
147C4—42no—
148C4—1721no—
149C2—21no—
150C2—81no—
151C2—3441no—
152C2#1458308611yescharacteristic
subgroupG/H
centerC2#14583086
commutatorC2×Q8×C43C23
FrattiniC2×Q8C22×D43
FittingC43×#563C2
socleC2×C43B(4,𝔽2)
hypercenter#563D43
hypocenterC43#2203
LCSG ▷ C2×Q8×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×Q8 ◁ #563

Complements

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

NH ≅ G/Ntype
1. #14583081C2semidirect
3. #14582698C2semidirect
4. #14582696C2semidirect
5. C43×#563C2semidirect
77. #563D43semidirect
82. C43#2203semidirect