Finite Group Databasebeta

← #20244367

Subgroups — #20244367

Order 6016.

244 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 83 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#15689676C211yesmaximal, characteristic
2#15689146C211yesmaximal, characteristic
3#15688969C211yesmaximal, characteristic
4#15688884C211yesmaximal, characteristic
5#15688883C211yesmaximal, characteristic
6#15688882C211yesmaximal, characteristic
7C47×#339C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9#13094023C412yescomplemented
10#13094015C412yescomplemented
11#13094001—22no—
12C4×Dic94—22no—
13#13093983C2211yescharacteristic
14C2×C4×Dic47C2211yescharacteristic
15C2×C4×Dic47C2211yescharacteristic
16Dic47⋊C8—22no—
17C47⋊#95—22no—
18C2×M16×C47C2211yescharacteristic
19#117×C47C2211yescharacteristic
20C2×C42×C47C2211yescharacteristic
21C22×C4×C47—21no—
22C22×C4×C47C2311yescharacteristic
23C22×Dic47—21no—
24C22×Dic47D412yes—
25C2×Dic94—22no—
26M16×C47—21no—
27M16×C47—21no—
28C2×C8×C47—21no—
29C4⋊C4×C47C2×C412yes—
30C22⋊C4×C47—21no—
31C42×C47—21no—
32C42×C47—21no—
33C42×C47Q812yescomplemented
34C22⋊Dic47—21no—
35C4⋊Dic47—22no—
36C4⋊Dic47C2×C412yes—
37Dic47⋊C4—22no—
38Dic47⋊C4—22no—
39C4×Dic47—21no—
40C4×Dic47—21no—
41C4×Dic47C2×C411yescharacteristic
42C4×Dic47C2×C411yescharacteristic
43C4×Dic47D412yes—
44C4×Dic47Q812yescomplemented
45#10625329—21no—
46#10625329—21no—
47C2×C47⋊C8—21no—
48C23×C47C2×D411yescharacteristic
49C2×C4×C47—22no—
50C2×C4×C47—22no—
51C2×C4×C47—42no—
52C2×C4×C47C22×C411yescharacteristic
53C2×C4×C47C2×D411yescharacteristic
54C2×C4×C47C2×Q811yescharacteristic
55C2×C4×C47C2×Q811yescharacteristic
56C2×C4×C47#4111yescharacteristic
57C2×C4×C47#4111yescharacteristic
58C2×Dic47—22no—
59C2×Dic47—22no—
60C2×Dic47—42no—
61C2×Dic47—42no—
62C2×Dic47C22⋊C412yes—
63C2×Dic47C22⋊C412yes—
64Dic94—44no—
65C8×C47—41no—
66C47⋊C8—41no—
67C22×C47—22no—
68C22×C47C2×C22⋊C411yescharacteristic
69C22×C47C22⋊Q811yescharacteristic
70C22×C47C22⋊Q811yescharacteristic
71C4×C47—42no—
72C4×C47—42no—
73C4×C47C4×Q811yescharacteristic
74C4×C47C4×Q811yescharacteristic
75C4×C47#12411yescharacteristic
76C4×C47C4⋊Q811yescharacteristic
77Dic47—22no—
78Dic47—22no—
79Dic47—42no—
80Dic47—42no—
81#1995—471nomaximal, Sylow
82C2×C47—21no—
83C2×C47—21no—
84C2×C47#39111yescharacteristic
85C2×C47#42112yes—
86#533—471no—
87#423—471no—
88#376—471no—
89#339—471no—
90#339—471no—
91#339—471no—
92#339D4711yescharacteristic
93C47#199511yescharacteristic, complemented, Sylow
94C2×M16—471no—
95C2×M16C2×D4711yescharacteristic
96C4⋊Q8—472no—
97#125—472no—
98C22⋊Q8—942no—
99C4×Q8—942no—
100#117—471no—
101#117C2×D4711yescharacteristic
102C2×C42—471no—
103C2×C42—471no—
104C2×C42C2×D4711yescharacteristic
105C4⋊C8—942no—
106#95—942no—
107C2×Q8—942no—
108C22×C4—21no—
109C22×C4—472no—
110C22×C4—941no—
111C22×C4C22×D4711yescharacteristic
112M16—21no—
113M16—21no—
114M16—941no—
115M16—941no—
116C2×C8—21no—
117C2×C8—941no—
118C4⋊C4—472no—
119C4⋊C4—942no—
120C4⋊C4—942no—
121C4⋊C4—942no—
122C4⋊C4C4×D4712yes—
123C22⋊C4—21no—
124C22⋊C4—941no—
125C42—21no—
126C42—21no—
127C42—471no—
128C42—471no—
129C42—472no—
130C42—472no—
131C42—941no—
132C42—941no—
133C42Dic9412yescomplemented
134C23D4×D4711yescharacteristic
135Q8—1884no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—472no—
140C2×C4—472no—
141C2×C4—942no—
142C2×C4—942no—
143C2×C4—1882no—
144C2×C4—1882no—
145C2×C4C2×Dic9411yescharacteristic
146C2×C4C2×C4×D4711yescharacteristic
147C2×C4#1062535011yescharacteristic
148C2×C4D4×D4711yescharacteristic
149C2×C4#1062535211yescharacteristic
150C2×C4Q8×D4711yescharacteristic
151C8—41no—
152C8—1881no—
153C22—22no—
154C22C22⋊C4×D4711yescharacteristic
155C22#1309400111yescharacteristic
156C22#1309400211yescharacteristic
157C4—42no—
158C4—42no—
159C4—942no—
160C4—942no—
161C4—1882no—
162C4—1882no—
163C4#1309398911yescharacteristic
164C4C4×Dic9411yescharacteristic
165C4#1309401011yescharacteristic
166C4#1309402311yescharacteristic
167C2—21no—
168C2—21no—
169C2#1568902711yescharacteristic
170C2#1568913812yes—
subgroupG/H
centerC2×C4D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#339C2
socleC22×C47C2×C22⋊C4
hypercenter#339D47
hypocenterC47#1995
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
9. #13094023C4semidirect
10. #13094015C4semidirect
33. C42×C47Q8semidirect
44. C4×Dic47Q8semidirect
93. C47#1995semidirect
133. C42Dic94semidirect