Finite Group Databasebeta

← #20244609

Subgroups — #20244609

Order 6016.

306 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 306 conjugacy classes of subgroups — too many to draw. Only its 71 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
1C2×#13093951C212yesmaximal, complemented
2#15689124C212yesmaximal, complemented
3#15688992C211yesmaximal, characteristic, complemented
4#15688892C211yesmaximal, characteristic, complemented
5C47×#537C211yesmaximal, characteristic
6C2×#10625329C2212yes—
7C2×C4⋊Dic47C2211yescharacteristic
8C2×Dic47⋊C4—22no—
9C2×C4×Dic47C2211yescharacteristic
10#13093951—24no—
11#13093948—22no—
12#13093945—22no—
13C2×#41×C47C2212yes—
14C22⋊Q8×C47—22no—
15#121×C47—22no—
16#121×C47—22no—
17C2×C4⋊C4×C47C2211yescharacteristic
18#41×C47—22no—
19#41×C47—22no—
20#41×C47—22no—
21#41×C47—22no—
22C2×Q8×C47D412yes—
23C2×D4×C47—22no—
24C2×D4×C47—22no—
25C2×D4×C47D412yes—
26C22×C4×C47—22no—
27C22×C4×C47D412yes—
28C22×C4×C47C2311yescharacteristic
29C22×Dic47—21no—
30C22×Dic47—21no—
31C4⋊C4×C47—22no—
32C4⋊C4×C47—22no—
33C22⋊C4×C47—24no—
34C4⋊Dic47—22no—
35Dic47⋊C4—44no—
36C4×Dic47—21no—
37C4×Dic47D412yescomplemented
38#10625329—22no—
39#10625329—22no—
40C2×C47⋊C8—22no—
41C23×C47—22no—
42C23×C47C2×D411yescharacteristic
43Q8×C47—22no—
44Q8×C47—22no—
45D4×C47—22no—
46D4×C47—22no—
47D4×C47—42no—
48D4×C47—42no—
49D4×C47—82no—
50C2×C4×C47—22no—
51C2×C4×C47—22no—
52C2×C4×C47—42no—
53C2×C4×C47—42no—
54C2×C4×C47—42no—
55C2×C4×C47C2×D411yescharacteristic
56C2×C4×C47C2×D412yes—
57C2×C4×C47#4112yes—
58C2×C4×C47#4111yescharacteristic
59C2×Dic47—22no—
60C2×Dic47—22no—
61C2×Dic47—22no—
62C2×Dic47—42no—
63C2×Dic47—41no—
64C47⋊C8—42no—
65C22×C47—21no—
66C22×C47—21no—
67C22×C47—42no—
68C22×C47—42no—
69C22×C47—42no—
70C22×C47#12011yescharacteristic
71C22×C47#12111yescharacteristic
72C22×C47#12411yescharacteristic
73C4×C47—42no—
74C4×C47—42no—
75C4×C47#12112yes—
76C4×C47#12312yes—
77Dic47—24no—
78Dic47—81no—
79#2039—471nomaximal, Sylow
80C2×C47—21no—
81C2×C47—21no—
82C2×C47—82no—
83C2×C47#39411yescharacteristic
84C2×C47#45311yescharacteristic
85C2×C47#45611yescharacteristic
86#537D4711yescharacteristic
87C2×#104—472no—
88#417—472no—
89#384—471no—
90#343—471no—
91C47#203911yescharacteristic, complemented, Sylow
92C2×#41C2×D4712yes—
93C2×M16—472no—
94C22⋊Q8—22no—
95#121—22no—
96#121—22no—
97C2×C4⋊C4—471no—
98C2×C4⋊C4—942no—
99C2×C4⋊C4C2×D4711yescharacteristic
100C2×C42—471no—
101#104—944no—
102#103—942no—
103#102—942no—
104#41—22no—
105#41—22no—
106#41—22no—
107#41—22no—
108C2×Q8C22⋊D4712yes—
109C2×D4—22no—
110C2×D4—22no—
111C2×D4C22⋊D4712yes—
112C22×C4—22no—
113C22×C4—941no—
114C22×C4—941no—
115C22×C4C22⋊D4712yes—
116C22×C4C22×D4711yescharacteristic
117M16—942no—
118M16—942no—
119C2×C8—942no—
120C4⋊C4—22no—
121C4⋊C4—22no—
122C4⋊C4—942no—
123C4⋊C4—1884no—
124C22⋊C4—24no—
125C42—472no—
126C42—941no—
127C23—22no—
128C23C2×C22⋊D4711yescharacteristic
129Q8—22no—
130Q8—22no—
131D4—22no—
132D4—22no—
133D4—42no—
134D4—42no—
135D4—82no—
136C2×C4—22no—
137C2×C4—22no—
138C2×C4—42no—
139C2×C4—42no—
140C2×C4—42no—
141C2×C4—942no—
142C2×C4—942no—
143C2×C4—942no—
144C2×C4—1882no—
145C2×C4—1881no—
146C2×C4D4×D4711yescharacteristic
147C2×C4#1062535212yes—
148C2×C4#1062535211yescharacteristic
149C2×C4C2×C22⋊D4712yes—
150C8—1882no—
151C22—21no—
152C22—21no—
153C22—42no—
154C22—42no—
155C22—42no—
156C22#1309399311yescharacteristic
157C22#1309399511yescharacteristic
158C22#1309401111yescharacteristic
159C4—42no—
160C4—42no—
161C4—944no—
162C4—3761no—
163C4#1309399612yes—
164C4#1309400512yes—
165C2—21no—
166C2—21no—
167C2—82no—
168C2#1568903711yescharacteristic
169C2#1568929111yescharacteristic
170C2#1568930611yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#537C2
socleC22×C47#120
hypercenter#537D47
hypocenterC47#2039
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#13093951C2semidirect
2. #15689124C2semidirect
3. #15688992C2semidirect
4. #15688892C2semidirect
37. C4×Dic47D4semidirect
91. C47#2039semidirect