Finite Group Databasebeta

← #19133926

Subgroups — #19133926

Order 5504.

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

normal subgroups only

This group has 184 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#14583653C211yesmaximal, characteristic
2#14583305C211yesmaximal, characteristic, complemented
3#14583261C211yesmaximal, characteristic
4#14582641C211yesmaximal, characteristic, complemented
5#14582640C211yesmaximal, characteristic, complemented
6#14582638C211yesmaximal, characteristic
7C43×#491C211yesmaximal, characteristic, complemented
8#13063324—21no—
9#13063320—21no—
10#13063320—21no—
11#13063317C2211yescharacteristic
12#13063313C2211yescharacteristic
13#13063310—21no—
14#13063305—21no—
15#13063303—21no—
16#13063258—21no—
17#13063256—21no—
18#13063248—21no—
19#13063245—21no—
20#13063236C2211yescharacteristic
21#13063236C2211yescharacteristic
22C4⋊Q8×C43C2211yescharacteristic
23#125×C43C2211yescharacteristic
24#103×C43—21no—
25#103×C43—21no—
26#97×C43C2211yescharacteristic
27C2×Q8×C43—21no—
28C2×D172D411yescharacteristic
29C2×C4×D43—21no—
30C2×Dic86—21no—
31C2×Dic86D411yescharacteristic
32C2×C8×C43—21no—
33C4⋊C4×C43—21no—
34C4⋊C4×C43—21no—
35C4⋊C4×C43—21no—
36C4⋊C4×C43—21no—
37C4⋊C4×C43D411yescharacteristic
38C4⋊C4×C43D411yescharacteristic
39C42×C43C2311yescharacteristic
40(C2×D43)⋊C4—21no—
41(C2×D43)⋊C4—21no—
42(C2×D43)⋊C4—21no—
43(C2×D43)⋊C4—21no—
44(C2×D43)⋊C4—21no—
45C4⋊Dic43—21no—
46C4⋊Dic43D411yescharacteristic
47C4⋊Dic43D411yescharacteristic
48Dic43⋊C4—21no—
49Dic43⋊C4—21no—
50Dic43⋊C4—21no—
51C4×Dic43—21no—
52C2×C43⋊C8—21no—
53C2×C43⋊C8—21no—
54C22×D43—21no—
55Q8×C43—42no—
56C2×C4×C43—21no—
57C2×C4×C43—21no—
58C2×C4×C43—41no—
59C2×C4×C43C2×D411yescharacteristic
60C2×C4×C43C2×D411yescharacteristic
61C2×C4×C43C2×D411yescharacteristic
62C2×Dic43—21no—
63C2×Dic43—21no—
64C2×Dic43—21no—
65D172—41no—
66C4×D43—81no—
67Dic86—41no—
68Dic86—81no—
69C8×C43—41no—
70C43⋊C8—22no—
71C43⋊C8—41no—
72C22×C43#12011yescharacteristic
73C2×D43—41no—
74C2×D43—41no—
75C2×D43—41no—
76C4×C43—21no—
77C4×C43—21no—
78C4×C43—21no—
79C4×C43—41no—
80C4×C43—41no—
81C4×C43—81no—
82Dic43—41no—
83Dic43—41no—
84Dic43—41no—
85#1664—431nomaximal, Sylow
86C2×C43#45411yescharacteristic
87C2×C43#45511yescharacteristic
88C2×C43#45611yescharacteristic
89D43—81no—
90#563—431no—
91#501—431no—
92#491D4311yescharacteristic, complemented
93#489—431no—
94#330—431no—
95#330—431no—
96#329—431no—
97C43#166411yescharacteristic, complemented, Sylow
98C4⋊Q8—861no—
99C4⋊Q8C2×D4311yescharacteristic
100#126—861no—
101#126—861no—
102#125—431no—
103#125C2×D4311yescharacteristic
104#124—431no—
105#123—861no—
106C22⋊Q8—861no—
107C22⋊Q8—861no—
108#107—861no—
109#106—861no—
110#103—21no—
111#103—21no—
112#103—861no—
113#102—861no—
114#97—431no—
115#97—431no—
116#97C2×D4311yescharacteristic
117C2×Q8—21no—
118C2×Q8—431no—
119C2×Q8—861no—
120C2×D4—431no—
121C22×C4—861no—
122C2×C8—21no—
123C2×C8—861no—
124C2×C8—861no—
125C4⋊C4—21no—
126C4⋊C4—21no—
127C4⋊C4—21no—
128C4⋊C4—21no—
129C4⋊C4—431no—
130C4⋊C4—431no—
131C4⋊C4—861no—
132C4⋊C4—861no—
133C4⋊C4—861no—
134C4⋊C4—861no—
135C4⋊C4C22⋊D4311yescharacteristic
136C4⋊C4C22⋊D4311yescharacteristic
137C22⋊C4—861no—
138C22⋊C4—861no—
139C22⋊C4—861no—
140C22⋊C4—861no—
141C22⋊C4—861no—
142C42—861no—
143C42C22×D4311yescharacteristic
144C23—861no—
145Q8—42no—
146Q8—3441no—
147Q8—1721no—
148D4—1721no—
149C2×C4—21no—
150C2×C4—21no—
151C2×C4—41no—
152C2×C4—861no—
153C2×C4—861no—
154C2×C4—861no—
155C2×C4—3441no—
156C2×C4D4×D4311yescharacteristic
157C2×C4D4×D4311yescharacteristic
158C2×C4C2×C22⋊D4311yescharacteristic
159C8—41no—
160C8—862no—
161C8—1721no—
162C22—1721no—
163C22—1721no—
164C22—1721no—
165C22#1306329311yescharacteristic
166C4—21no—
167C4—21no—
168C4—21no—
169C4—41no—
170C4—41no—
171C4—81no—
172C4—1721no—
173C4—1721no—
174C4—1721no—
175C2—3441no—
176C2#1458307111yescharacteristic
177C2#1458307511yescharacteristic
178C2#1458308011yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC42×C43C23
FrattiniC42C22×D43
FittingC43×#491C2
socleC22×C43#120
hypercenter#491D43
hypocenterC43#1664
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. #14583305C2semidirect
4. #14582641C2semidirect
5. #14582640C2semidirect
7. C43×#491C2semidirect
92. #491D43semidirect
97. C43#1664semidirect