Finite Group Databasebeta

← #19136541

Subgroups — #19136541

Order 5504.

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

normal subgroups only

This group has 226 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#14583334C212yesmaximal, complemented
2#14583152C211yesmaximal, characteristic, complemented
3#14582709C212yesmaximal, complemented
4#14582681C211yesmaximal, characteristic, complemented
5C43×#575C211yesmaximal, characteristic, complemented
6C2×D344C2211yescharacteristic, complemented
7#13063299—21no—
8#13063268—22no—
9#13063266—22no—
10#13063265C2212yescomplemented
11#13063257C2211yescharacteristic, complemented
12#13063247—21no—
13C2×#41×C43—21no—
14#137×C43—22no—
15AGL(1,ℤ/8)×C43—22no—
16#135×C43—21no—
17#135×C43C2212yes—
18C2×M16×C43C2211yescharacteristic
19#41×C43—22no—
20#41×C43—22no—
21#41×C43—41no—
22#41×C43—41no—
23C2×Q8×C43—21no—
24C2×D4×C43—21no—
25C2×D4×C43—41no—
26C22×C4×C43—41no—
27C22×C4×C43D411yescharacteristic
28C2×C22⋊D43—41no—
29C2×D172—21no—
30Q16×C43—21no—
31Q16×C43D412yescomplemented
32SD16×C43—22no—
33SD16×C43—22no—
34D8×C43—21no—
35D8×C43D412yescomplemented
36M16×C43—22no—
37C2×C8×C43D411yescharacteristic
38C2×C8×C43C2311yescharacteristic
39(C2×D43)⋊C4—41no—
40C4⋊Dic43—21no—
41D344—22no—
42C43⋊C16—22no—
43C23×C43—41no—
44C23×C43D811yescharacteristic
45C22×D43—41no—
46Q8×C43—22no—
47Q8×C43—41no—
48D4×C43—22no—
49D4×C43—41no—
50D4×C43—42no—
51D4×C43—42no—
52C2×C4×C43—21no—
53C2×C4×C43—21no—
54C2×C4×C43—42no—
55C2×C4×C43—41no—
56C2×C4×C43—42no—
57C2×C4×C43D811yescharacteristic
58C2×C4×C43C2×D411yescharacteristic
59C22⋊D43—82no—
60C2×Dic43—41no—
61D172—41no—
62D172—41no—
63C8×C43—21no—
64C8×C43C2×D412yes—
65C22×C43—21no—
66C22×C43—41no—
67C22×C43—42no—
68C22×C43—82no—
69C22×C43C2×D811yescharacteristic
70C2×D43—81no—
71C2×D43—81no—
72C2×D43—81no—
73C4×C43—21no—
74C4×C43—42no—
75C4×C43#12011yescharacteristic
76C4×C43AGL(1,ℤ/8)11yescharacteristic
77Dic43—81no—
78#2190—431nomaximal, Sylow
79C2×C43—21no—
80C2×C43—41no—
81C2×C43—82no—
82C2×C43#44711yescharacteristic
83D43—161no—
84#575D4311yescharacteristic, complemented
85#509—432no—
86#469—431no—
87#360—432no—
88#349—431no—
89C43#219011yescharacteristic, complemented, Sylow
90C2×#41—21no—
91#137—22no—
92AGL(1,ℤ/8)—22no—
93#135—21no—
94#135C2×D4312yes—
95C2×D8—431no—
96C2×M16C2×D4311yescharacteristic
97#121—861no—
98SD32—862no—
99D16—862no—
100M32—432no—
101#106—431no—
102#102—861no—
103#41—22no—
104#41—22no—
105#41—41no—
106#41—41no—
107C2×Q8—21no—
108C2×D4—21no—
109C2×D4—41no—
110C2×D4—861no—
111C2×D4—1721no—
112C22×C4—41no—
113C22×C4C22⋊D4311yescharacteristic
114Q16—21no—
115Q16C22⋊D4312yescomplemented
116SD16—22no—
117SD16—22no—
118D8—21no—
119D8—862no—
120D8C22⋊D4312yescomplemented
121M16—22no—
122C2×C8C22⋊D4311yescharacteristic
123C2×C8C22×D4311yescharacteristic
124C4⋊C4—861no—
125C22⋊C4—1721no—
126C16—862no—
127C23—41no—
128C23—1721no—
129C23#1062188211yescharacteristic
130Q8—22no—
131Q8—41no—
132D4—22no—
133D4—41no—
134D4—42no—
135D4—42no—
136D4—3442no—
137D4—1721no—
138D4—1721no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—42no—
142C2×C4—41no—
143C2×C4—42no—
144C2×C4—1721no—
145C2×C4#1062188211yescharacteristic
146C2×C4C2×C22⋊D4311yescharacteristic
147C8—21no—
148C8C2×C22⋊D4312yes—
149C22—21no—
150C22—41no—
151C22—42no—
152C22—82no—
153C22—3441no—
154C22—3441no—
155C22—3441no—
156C22C2×#1062188211yescharacteristic
157C4—21no—
158C4—42no—
159C4—3441no—
160C4#1306329411yescharacteristic
161C4#1306335111yescharacteristic
162C2—21no—
163C2—41no—
164C2—82no—
165C2—6881no—
166C2#1458303311yescharacteristic
subgroupG/H
centerC2#14583033
commutatorC2×C8×C43C23
FrattiniC2×C8C22×D43
FittingC43×#575C2
socleC2×C43#447
hypercenter#575D43
hypocenterC43#2190
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #14583334C2semidirect
2. #14583152C2semidirect
3. #14582709C2semidirect
4. #14582681C2semidirect
5. C43×#575C2semidirect
6. C2×D344C22semidirect
10. #13063265C22semidirect
11. #13063257C22semidirect
31. Q16×C43D4semidirect
35. D8×C43D4semidirect
84. #575D43semidirect
89. C43#2190semidirect
115. Q16C22⋊D43semidirect
120. D8C22⋊D43semidirect