Finite Group Databasebeta

← #20242010

Subgroups — #20242010

Order 6016.

248 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 59 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#124×D47C211yesmaximal, characteristic
2#15689178C212yesmaximal, complemented
3#15688863C211yesmaximal, characteristic, complemented
4#15688862C212yesmaximal, complemented
5C47×#329C211yesmaximal, characteristic, complemented
6C2×Q8×D47C411yescharacteristic
7C2×D4×D47C411yescharacteristic
8#13094013C411yescharacteristic
9#13094012C2211yescharacteristic
10#13094011C411yescharacteristic
11#13094010—22no—
12C22⋊C4×D47—22no—
13C42×D47C2211yescharacteristic
14Dic47⋊C8—22no—
15(C2×D47)⋊C8—22no—
16#13093935C2212yescomplemented
17#124×C47C2211yescharacteristic
18#97×C47C2212yescomplemented
19C23×D47—21no—
20C2×Q8×C47C2×C411yescharacteristic
21C2×D4×C47C2×C411yescharacteristic
22C2×C22⋊D47—21no—
23Q8×D47—42no—
24D4×D47—42no—
25C2×D188C2×C411yescharacteristic
26C2×C4×D47—21no—
27C2×C4×D47C2×C411yescharacteristic
28C2×C4×D47D412yes—
29C2×Dic94—21no—
30C2×Dic94C2×C411yescharacteristic
31C2×C8×C47—22no—
32C22⋊C4×C47—22no—
33C42×C47C2311yescharacteristic
34C22⋊Dic47—22no—
35(C2×D47)⋊C4—22no—
36(C2×D47)⋊C4—22no—
37C4×Dic47C2×C411yescharacteristic
38C4×Dic47D412yes—
39C2×C47⋊C8—22no—
40C23×C47—21no—
41C22×D47—21no—
42C22×D47—44no—
43C22×D47—42no—
44C22×D47C22⋊C411yescharacteristic
45Q8×C47—41no—
46D4×C47—41no—
47C2×C4×C47—21no—
48C2×C4×C47C22×C411yescharacteristic
49C2×C4×C47C2×D412yes—
50C22⋊D47—42no—
51C2×Dic47—21no—
52C2×Dic47C22⋊C412yes—
53C2×Dic47C22⋊C411yescharacteristic
54D188—41no—
55C4×D47—22no—
56C4×D47—42no—
57C4×D47—42no—
58Dic94—42no—
59Dic94—41no—
60C8×C47—42no—
61C47⋊C8—42no—
62C22×C47—41no—
63C22×C47—42no—
64C22×C47C2×C22⋊C411yescharacteristic
65C2×D47—22no—
66C2×D47—41no—
67C2×D47—42no—
68C2×D47—84no—
69C2×D47#10012yes—
70C4×C47—21no—
71C4×C47—22no—
72C4×C47—41no—
73Dic47—21no—
74Dic47—22no—
75Dic47—41no—
76#1533—471nomaximal, Sylow
77C2×C47—81no—
78C2×C47C2×#10011yescharacteristic
79C2×C47#42112yes—
80D47—22no—
81D47—81no—
82C2×#124—471no—
83#432—472no—
84#329—471no—
85#329—472no—
86#329D4711yescharacteristic, complemented
87C47#153311yescharacteristic, complemented, Sylow
88C22×Q8—471no—
89C22×D4—471no—
90#124—471no—
91#124—471no—
92#124—471no—
93#124—942no—
94#124C2×D4711yescharacteristic
95C2×C22⋊C4—942no—
96C2×C42—471no—
97C4⋊C8—942no—
98C22⋊C8—942no—
99#97—472no—
100#97C2×D4712yescomplemented
101C24—941no—
102C2×Q8—471no—
103C2×Q8—941no—
104C2×Q8—1882no—
105C2×Q8C4×D4711yescharacteristic
106C2×D4—471no—
107C2×D4—941no—
108C2×D4—1882no—
109C2×D4C4×D4711yescharacteristic
110C22×C4—471no—
111C22×C4—472no—
112C22×C4—941no—
113C2×C8—22no—
114C2×C8—942no—
115C22⋊C4—22no—
116C22⋊C4—942no—
117C22⋊C4—942no—
118C22⋊C4—942no—
119C42—471no—
120C42—472no—
121C42C22×D4711yescharacteristic
122C23—21no—
123C23—471no—
124C23—941no—
125C23—1882no—
126C23—1884no—
127Q8—41no—
128Q8—1881no—
129Q8—1882no—
130D4—41no—
131D4—1881no—
132D4—1882no—
133C2×C4—21no—
134C2×C4—472no—
135C2×C4—471no—
136C2×C4—942no—
137C2×C4—941no—
138C2×C4—1882no—
139C2×C4—1882no—
140C2×C4C2×C4×D4711yescharacteristic
141C2×C4D4×D4712yes—
142C8—42no—
143C8—1882no—
144C22—41no—
145C22—42no—
146C22—472no—
147C22—942no—
148C22—3764no—
149C22—1881no—
150C22—1882no—
151C22C22⋊C4×D4711yescharacteristic
152C4—21no—
153C4—22no—
154C4—41no—
155C4—941no—
156C4—942no—
157C4—1881no—
158C2—81no—
159C2—942no—
160C2—3761no—
161C2#100×D4711yescharacteristic
162C2#1568913812yes—
subgroupG/H
centerC22C22⋊C4×D47
commutatorC2×C4×C47C22×C4
FrattiniC42C22×D47
FittingC47×#329C2
socleC22×C47C2×C22⋊C4
hypercenter#329D47
hypocenterC47#1533
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #329

Complements

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

NH ≅ G/Ntype
2. #15689178C2semidirect
3. #15688863C2semidirect
4. #15688862C2semidirect
5. C47×#329C2semidirect
16. #13093935C22semidirect
18. #97×C47C22semidirect
86. #329D47semidirect
87. C47#1533semidirect
100. #97C2×D47semidirect