Finite Group Databasebeta

← #20245334

Subgroups — #20245334

Order 6016.

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#15689558C212yesmaximal, complemented
2#15689376C211yesmaximal, characteristic, complemented
3#15688933C212yesmaximal, complemented
4#15688905C211yesmaximal, characteristic, complemented
5C47×#575C211yesmaximal, characteristic, complemented
6C2×D376C2211yescharacteristic, complemented
7#13093998—21no—
8#13093967—22no—
9#13093965—22no—
10#13093964C2212yescomplemented
11#13093956C2211yescharacteristic, complemented
12#13093946—21no—
13C2×#41×C47—21no—
14#137×C47—22no—
15AGL(1,ℤ/8)×C47—22no—
16#135×C47—21no—
17#135×C47C2212yes—
18C2×M16×C47C2211yescharacteristic
19#41×C47—22no—
20#41×C47—22no—
21#41×C47—41no—
22#41×C47—41no—
23C2×Q8×C47—21no—
24C2×D4×C47—21no—
25C2×D4×C47—41no—
26C22×C4×C47—41no—
27C22×C4×C47D411yescharacteristic
28C2×C22⋊D47—41no—
29C2×D188—21no—
30Q16×C47—21no—
31Q16×C47D412yescomplemented
32SD16×C47—22no—
33SD16×C47—22no—
34D8×C47—21no—
35D8×C47D412yescomplemented
36M16×C47—22no—
37C2×C8×C47D411yescharacteristic
38C2×C8×C47C2311yescharacteristic
39(C2×D47)⋊C4—41no—
40C4⋊Dic47—21no—
41D376—22no—
42C47⋊C16—22no—
43C23×C47—41no—
44C23×C47D811yescharacteristic
45C22×D47—41no—
46Q8×C47—22no—
47Q8×C47—41no—
48D4×C47—22no—
49D4×C47—41no—
50D4×C47—42no—
51D4×C47—42no—
52C2×C4×C47—21no—
53C2×C4×C47—21no—
54C2×C4×C47—42no—
55C2×C4×C47—41no—
56C2×C4×C47—42no—
57C2×C4×C47D811yescharacteristic
58C2×C4×C47C2×D411yescharacteristic
59C22⋊D47—82no—
60C2×Dic47—41no—
61D188—41no—
62D188—41no—
63C8×C47—21no—
64C8×C47C2×D412yes—
65C22×C47—21no—
66C22×C47—41no—
67C22×C47—42no—
68C22×C47—82no—
69C22×C47C2×D811yescharacteristic
70C2×D47—81no—
71C2×D47—81no—
72C2×D47—81no—
73C4×C47—21no—
74C4×C47—42no—
75C4×C47#12011yescharacteristic
76C4×C47AGL(1,ℤ/8)11yescharacteristic
77Dic47—81no—
78#2190—471nomaximal, Sylow
79C2×C47—21no—
80C2×C47—41no—
81C2×C47—82no—
82C2×C47#44711yescharacteristic
83D47—161no—
84#575D4711yescharacteristic, complemented
85#509—472no—
86#469—471no—
87#360—472no—
88#349—471no—
89C47#219011yescharacteristic, complemented, Sylow
90C2×#41—21no—
91#137—22no—
92AGL(1,ℤ/8)—22no—
93#135—21no—
94#135C2×D4712yes—
95C2×D8—471no—
96C2×M16C2×D4711yescharacteristic
97#121—941no—
98SD32—942no—
99D16—942no—
100M32—472no—
101#106—471no—
102#102—941no—
103#41—22no—
104#41—22no—
105#41—41no—
106#41—41no—
107C2×Q8—21no—
108C2×D4—21no—
109C2×D4—41no—
110C2×D4—941no—
111C2×D4—1881no—
112C22×C4—41no—
113C22×C4C22⋊D4711yescharacteristic
114Q16—21no—
115Q16C22⋊D4712yescomplemented
116SD16—22no—
117SD16—22no—
118D8—21no—
119D8—942no—
120D8C22⋊D4712yescomplemented
121M16—22no—
122C2×C8C22⋊D4711yescharacteristic
123C2×C8C22×D4711yescharacteristic
124C4⋊C4—941no—
125C22⋊C4—1881no—
126C16—942no—
127C23—41no—
128C23—1881no—
129C23#1062533411yescharacteristic
130Q8—22no—
131Q8—41no—
132D4—22no—
133D4—41no—
134D4—42no—
135D4—42no—
136D4—3762no—
137D4—1881no—
138D4—1881no—
139C2×C4—21no—
140C2×C4—21no—
141C2×C4—42no—
142C2×C4—41no—
143C2×C4—42no—
144C2×C4—1881no—
145C2×C4#1062533411yescharacteristic
146C2×C4C2×C22⋊D4711yescharacteristic
147C8—21no—
148C8C2×C22⋊D4712yes—
149C22—21no—
150C22—41no—
151C22—42no—
152C22—82no—
153C22—3761no—
154C22—3761no—
155C22—3761no—
156C22C2×#1062533411yescharacteristic
157C4—21no—
158C4—42no—
159C4—3761no—
160C4#1309399311yescharacteristic
161C4#1309405011yescharacteristic
162C2—21no—
163C2—41no—
164C2—82no—
165C2—7521no—
166C2#1568925711yescharacteristic
subgroupG/H
centerC2#15689257
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#575C2
socleC2×C47#447
hypercenter#575D47
hypocenterC47#2190
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #575

Complements

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

NH ≅ G/Ntype
1. #15689558C2semidirect
2. #15689376C2semidirect
3. #15688933C2semidirect
4. #15688905C2semidirect
5. C47×#575C2semidirect
6. C2×D376C22semidirect
10. #13093964C22semidirect
11. #13093956C22semidirect
31. Q16×C47D4semidirect
35. D8×C47D4semidirect
84. #575D47semidirect
89. C47#2190semidirect
115. Q16C22⋊D47semidirect
120. D8C22⋊D47semidirect