Finite Group Databasebeta

← #19133563

Subgroups — #19133563

Order 5504.

282 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 53 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#14583480C211yesmaximal, characteristic
2#14583038C212yesmaximal, complemented
3#14582632C212yesmaximal, complemented
4#14582625C211yesmaximal, characteristic, complemented
5C43×#395C211yesmaximal, characteristic, complemented
6C2×#10621898—21no—
7C2×#10621884—22no—
8#13063305—22no—
9#13063300—22no—
10#13063299—21no—
11#13063299C2212yes—
12#13063249—22no—
13C22⋊(C43⋊C8)C2212yes—
14C22×Q8×C43C2211yescharacteristic
15C2×C4⋊C4×C43—21no—
16C2×C4⋊C4×C43C2211yescharacteristic
17#95×C43—21no—
18#95×C43C2211yescharacteristic
19C2×Q8×C43—22no—
20C2×Q8×C43—42no—
21C22×C4×C43—21no—
22C22×C4×C43—21no—
23C22×C4×C43D411yescharacteristic
24C22×C4×C43D411yescharacteristic
25C22×C4×C43C2311yescharacteristic
26C2×C22⋊D43—22no—
27#10621898—42no—
28#10621898—42no—
29C2×D172—21no—
30C2×D172—21no—
31C2×D172D412yes—
32C2×C4×D43—22no—
33C2×Dic86—21no—
34C4⋊C4×C43—22no—
35C4⋊C4×C43—42no—
36#10621884—44no—
37(C2×D43)⋊C4—22no—
38(C2×D43)⋊C4—22no—
39C4⋊Dic43—21no—
40C4⋊Dic43D412yes—
41C2×C43⋊C8—22no—
42C23×C43C2×D411yescharacteristic
43C22×D43—22no—
44Q8×C43—24no—
45Q8×C43—42no—
46C2×C4×C43—21no—
47C2×C4×C43—21no—
48C2×C4×C43—22no—
49C2×C4×C43—22no—
50C2×C4×C43—21no—
51C2×C4×C43—41no—
52C2×C4×C43—41no—
53C2×C4×C43—41no—
54C2×C4×C43—41no—
55C2×C4×C43—41no—
56C2×C4×C43—41no—
57C2×C4×C43SD1612yescomplemented
58C2×C4×C43C2×D412yes—
59C22⋊D43—42no—
60C22⋊D43—42no—
61C2×Dic43—22no—
62D172—42no—
63D172—42no—
64D172—81no—
65C4×D43—44no—
66Dic86—42no—
67C43⋊C8—42no—
68C22×C43—21no—
69C22×C43—21no—
70C22×C43#12011yescharacteristic
71C22×C43C2×SD1611yescharacteristic
72C22×C43AGL(1,ℤ/8)11yescharacteristic
73C2×D43—42no—
74C2×D43—42no—
75C2×D43—42no—
76C4×C43—22no—
77C4×C43—22no—
78C4×C43—42no—
79C4×C43—41no—
80C4×C43—42no—
81Dic43—42no—
82#1604—431nomaximal, Sylow
83C2×C43—21no—
84C2×C43—21no—
85C2×C43#45011yescharacteristic
86C2×C43#45611yescharacteristic
87C2×C43B(4,𝔽2)11yescharacteristic
88D43—82no—
89#537—431no—
90#448—432no—
91#395D4311yescharacteristic, complemented
92#327—432no—
93#324—431no—
94C43#160411yescharacteristic, complemented, Sylow
95C2×#41—861no—
96C22×Q8C2×D4311yescharacteristic
97C2×SD16—862no—
98C22⋊Q8—862no—
99#121—432no—
100#121—862no—
101#121—861no—
102C2×C4⋊C4—21no—
103C2×C4⋊C4C2×D4311yescharacteristic
104#103—862no—
105C22⋊C8—432no—
106#95—21no—
107#95C2×D4311yescharacteristic
108#41—1722no—
109#41—1722no—
110C2×Q8—22no—
111C2×Q8—42no—
112C2×Q8—861no—
113C2×D4—432no—
114C2×D4—861no—
115C2×D4—861no—
116C2×D4—862no—
117C22×C4—21no—
118C22×C4—21no—
119C22×C4—862no—
120C22×C4C22⋊D4311yescharacteristic
121C22×C4C22⋊D4311yescharacteristic
122C22×C4C22×D4311yescharacteristic
123SD16—1724no—
124C2×C8—862no—
125C4⋊C4—22no—
126C4⋊C4—42no—
127C4⋊C4—432no—
128C4⋊C4—861no—
129C22⋊C4—862no—
130C22⋊C4—862no—
131C23—862no—
132C23C2×C22⋊D4311yescharacteristic
133Q8—24no—
134Q8—42no—
135Q8—1722no—
136D4—3441no—
137D4—1722no—
138D4—1722no—
139D4—1722no—
140D4—1722no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—22no—
144C2×C4—22no—
145C2×C4—21no—
146C2×C4—41no—
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—862no—
153C2×C4—1724no—
154C2×C4#1062188412yescomplemented
155C2×C4D4×D4312yes—
156C8—1722no—
157C22—21no—
158C22—21no—
159C22—1722no—
160C22—1722no—
161C22—1722no—
162C22#1306329311yescharacteristic
163C22C2×#1062188411yescharacteristic
164C22#1306335011yescharacteristic
165C4—22no—
166C4—22no—
167C4—42no—
168C4—42no—
169C4—41no—
170C4—1722no—
171C2—21no—
172C2—21no—
173C2—3442no—
174C2#1458304911yescharacteristic
175C2#1458308111yescharacteristic
176C2#1458308511yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC22×C4×C43C23
FrattiniC22×C4C22×D43
FittingC43×#395C2
socleC22×C43#120
hypercenter#395D43
hypocenterC43#1604
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #395

Complements

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

NH ≅ G/Ntype
2. #14583038C2semidirect
3. #14582632C2semidirect
4. #14582625C2semidirect
5. C43×#395C2semidirect
57. C2×C4×C43SD16semidirect
91. #395D43semidirect
94. C43#1604semidirect
154. C2×C4#10621884semidirect