Finite Group Databasebeta

← #20245338

Subgroups — #20245338

Order 6016.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#15689923C211yesmaximal, characteristic
2#15689564C212yesmaximal, complemented
3#15688932C212yesmaximal, complemented
4#15688905C211yesmaximal, characteristic, complemented
5C47×#470C211yesmaximal, characteristic, complemented
6C2×#10625350—21no—
7#13094057—22no—
8#13094052—22no—
9#13094046—21no—
10#13094046C2212yes—
11#13093970—22no—
12#13093967—22no—
13#13093964C2212yescomplemented
14C2×Q16×C47C2211yescharacteristic, complemented
15C2×M16×C47C2211yescharacteristic
16C22⋊Q8×C47—21no—
17#106×C47C2211yescharacteristic, complemented
18#103×C47—21no—
19C2×Q8×C47—21no—
20C22×C4×C47D411yescharacteristic
21C2×C22⋊D47—41no—
22#10625350—22no—
23#10625350—22no—
24#10625350—41no—
25#10625350—41no—
26C2×D188—21no—
27C2×C4×D47—41no—
28C2×Dic94—21no—
29Q16×C47—22no—
30M16×C47—22no—
31C2×C8×C47D411yescharacteristic
32C2×C8×C47C2311yescharacteristic
33C4⋊C4×C47—21no—
34C4⋊C4×C47—41no—
35C22⋊C4×C47—41no—
36Dic188—21no—
37Dic188D412yes—
38D376—21no—
39D376D412yes—
40#10625325—22no—
41#10625325—22no—
42C47⋊C16—22no—
43C23×C47D811yescharacteristic
44C22×D47—41no—
45Q8×C47—41no—
46Q8×C47—41no—
47C2×C4×C47—21no—
48C2×C4×C47—21no—
49C2×C4×C47—41no—
50C2×C4×C47—41no—
51C2×C4×C47D811yescharacteristic
52C2×C4×C47C2×D411yescharacteristic
53C22⋊D47—42no—
54C22⋊D47—42no—
55C2×Dic47—41no—
56D188—22no—
57D188—41no—
58C4×D47—42no—
59C4×D47—42no—
60Dic94—22no—
61Dic94—41no—
62C8×C47—21no—
63C8×C47C2×D412yes—
64C22×C47—21no—
65C22×C47—41no—
66C22×C47C2×D811yescharacteristic
67C2×D47—42no—
68C2×D47—82no—
69C4×C47—21no—
70C4×C47—81no—
71C4×C47—81no—
72C4×C47#12011yescharacteristic
73C4×C47AGL(1,ℤ/8)11yescharacteristic
74Dic47—42no—
75#2191—471nomaximal, Sylow
76C2×C47—21no—
77C2×C47—41no—
78C2×C47#44711yescharacteristic
79D47—82no—
80#575—471no—
81#510—472no—
82#470D4711yescharacteristic, complemented
83#360—472no—
84#349—471no—
85C47#219111yescharacteristic, complemented, Sylow
86C2×#41—941no—
87#137—942no—
88AGL(1,ℤ/8)—942no—
89#135—472no—
90#135—941no—
91C2×Q16C2×D4711yescharacteristic, complemented
92C2×M16C2×D4711yescharacteristic
93C22⋊Q8—21no—
94Q32—942no—
95SD32—942no—
96M32—472no—
97#106C2×D4711yescharacteristic, complemented
98#103—21no—
99#41—942no—
100#41—942no—
101#41—1881no—
102#41—1881no—
103C2×Q8—21no—
104C2×Q8—941no—
105C2×D4—941no—
106C2×D4—1881no—
107C22×C4—1881no—
108C22×C4C22⋊D4711yescharacteristic
109Q16—22no—
110Q16—472no—
111Q16—941no—
112SD16—942no—
113SD16—942no—
114D8—472no—
115D8—941no—
116M16—22no—
117C2×C8C22⋊D4711yescharacteristic
118C2×C8C22×D4711yescharacteristic
119C4⋊C4—21no—
120C4⋊C4—41no—
121C22⋊C4—41no—
122C16—942no—
123C23—1881no—
124C23#1062533411yescharacteristic
125Q8—41no—
126Q8—41no—
127Q8—942no—
128Q8—1881no—
129D4—942no—
130D4—1881no—
131D4—1882no—
132D4—1882no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—41no—
136C2×C4—41no—
137C2×C4—1882no—
138C2×C4—1881no—
139C2×C4—1882no—
140C2×C4#1062533411yescharacteristic
141C2×C4C2×C22⋊D4711yescharacteristic
142C8—21no—
143C8D4×D4712yes—
144C22—21no—
145C22—41no—
146C22—3762no—
147C22—1882no—
148C22C2×#1062533411yescharacteristic
149C4—21no—
150C4—81no—
151C4—81no—
152C4—1882no—
153C4#1309399211yescharacteristic
154C4#1309404911yescharacteristic
155C2—21no—
156C2—41no—
157C2—3762no—
158C2#1568925611yescharacteristic
subgroupG/H
centerC2#15689256
commutatorC2×C8×C47C23
FrattiniC2×C8C22×D47
FittingC47×#470C2
socleC2×C47#447
hypercenter#470D47
hypocenterC47#2191
LCSG ▷ C2×C8×C47 ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #470

Complements

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

NH ≅ G/Ntype
2. #15689564C2semidirect
3. #15688932C2semidirect
4. #15688905C2semidirect
5. C47×#470C2semidirect
13. #13093964C22semidirect
14. C2×Q16×C47C22semidirect
17. #106×C47C22semidirect
82. #470D47semidirect
85. C47#2191semidirect
91. C2×Q16C2×D47semidirect
97. #106C2×D47semidirect