Finite Group Databasebeta

← #20243448

Subgroups — #20243448

Order 6016.

264 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 93 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×#13094030C211yesmaximal, characteristic
2C2×#13093960C211yesmaximal, characteristic, complemented
3#15689122C212yesmaximal
4#15688892C212yesmaximal, complemented
5C2×#106×C47C211yesmaximal, characteristic, complemented
6C2×#10625350C2211yescharacteristic
7#13094030—22no—
8#13094030C414yescomplemented
9C2×#10625329C2212yes—
10C2×#10625329C2211yescharacteristic
11C2×#10625324—21no—
12C2×C8×D47—21no—
13#13093960—22no—
14#13093947—22no—
15#13093944—22no—
16C22×C8×C47C2211yescharacteristic
17C2×C4⋊C4×C47C2212yes—
18#106×C47—21no—
19#106×C47—21no—
20C22×C4×C47—22no—
21C22×C4×C47C2311yescharacteristic
22C2×C22⋊D47—21no—
23#10625350—21no—
24#10625350—21no—
25#10625350C2×C412yes—
26#10625350Q812yes—
27C2×D188D411yescharacteristic
28C2×C4×D47—21no—
29C2×Dic94D411yescharacteristic
30C2×C8×C47C2×C412yes—
31C2×C8×C47D412yes—
32C2×C8×C47D411yescharacteristic
33C2×C8×C47D411yescharacteristic
34C4⋊C4×C47—22no—
35C4⋊C4×C47—22no—
36#10625329—21no—
37#10625329—22no—
38#10625329—22no—
39#10625329C2×C412yes—
40C2×C47⋊C8—21no—
41C2×C47⋊C8—22no—
42#10625324—24no—
43C8×D47—24no—
44C23×C47#4111yescharacteristic
45C22×D47—21no—
46C2×C4×C47—42no—
47C2×C4×C47—82no—
48C2×C4×C47C22×C411yescharacteristic
49C2×C4×C47C2×D411yescharacteristic
50C2×C4×C47C2×D411yescharacteristic
51C2×C4×C47C2×D411yescharacteristic
52C2×C4×C47C2×Q811yescharacteristic
53C2×C4×C47#4111yescharacteristic
54C22⋊D47—22no—
55C22⋊D47—22no—
56C2×Dic47—21no—
57D188—21no—
58D188C4⋊C412yes—
59C4×D47—22no—
60C4×D47—22no—
61Dic94—21no—
62Dic94C4⋊C412yes—
63C8×C47C22⋊C412yes—
64C8×C47C22⋊C412yes—
65C47⋊C8—22no—
66C47⋊C8—42no—
67C22×C47—22no—
68C22×C47#11711yescharacteristic
69C22×C47#12111yescharacteristic
70C22×C47C22⋊Q811yescharacteristic
71C2×D47—22no—
72C2×D47—42no—
73C4×C47—82no—
74C4×C47C2×C22⋊C411yescharacteristic
75C4×C47C2×C4⋊C411yescharacteristic
76C4×C47#12111yescharacteristic
77C4×C47C22⋊Q811yescharacteristic
78Dic47—22no—
79#1815—471nomaximal, Sylow
80C2×C47—21no—
81C2×C47—21no—
82C2×C47#38011yescharacteristic
83C2×C47#47112yes—
84D47—42no—
85C2×#131—471no—
86C2×#108—471no—
87C2×#106D4711yescharacteristic, complemented
88#417—472no—
89#343—472no—
90C47#181511yescharacteristic, complemented, Sylow
91C2×#41—471no—
92#131—474no—
93#131—942no—
94C2×M16—471no—
95C2×M16—472no—
96C2×M16—941no—
97C22×C8—941no—
98C22×C8C2×D4711yescharacteristic
99C2×C4⋊C4C2×D4712yes—
100#108—942no—
101#106—21no—
102#106—21no—
103#103—942no—
104#102—942no—
105#41—472no—
106#41—472no—
107#41—941no—
108#41—941no—
109C2×Q8—471no—
110C2×D4—471no—
111C2×D4—941no—
112C22×C4—22no—
113C22×C4—941no—
114C22×C4C22×D4711yescharacteristic
115M16—472no—
116M16—941no—
117M16—944no—
118M16—942no—
119M16—942no—
120C2×C8—941no—
121C2×C8—944no—
122C2×C8—942no—
123C2×C8C4×D4712yes—
124C2×C8D18812yes—
125C2×C8C22⋊D4711yescharacteristic
126C2×C8C22⋊D4711yescharacteristic
127C4⋊C4—22no—
128C4⋊C4—22no—
129C23—941no—
130C23#1062535211yescharacteristic
131Q8—472no—
132Q8—941no—
133D4—472no—
134D4—942no—
135D4—942no—
136D4—941no—
137C2×C4—42no—
138C2×C4—82no—
139C2×C4—941no—
140C2×C4—942no—
141C2×C4—942no—
142C2×C4C2×C4×D4711yescharacteristic
143C2×C4C2×D18811yescharacteristic
144C2×C4D4×D4711yescharacteristic
145C2×C4Q8×D4711yescharacteristic
146C2×C4#1062535411yescharacteristic
147C2×C4C2×C22⋊D4711yescharacteristic
148C8—942no—
149C8—1882no—
150C8(C2×D47)⋊C412yes—
151C8(C2×D47)⋊C412yes—
152C22—22no—
153C22—942no—
154C22—1882no—
155C22#1309398211yescharacteristic
156C22#1309399511yescharacteristic
157C22#1309400411yescharacteristic
158C4—82no—
159C4—942no—
160C4C2×(C2×D47)⋊C411yescharacteristic
161C4C4⋊C4×D4711yescharacteristic
162C4#1309399911yescharacteristic
163C4#1309400011yescharacteristic
164C2—21no—
165C2—21no—
166C2—1882no—
167C2#1568898011yescharacteristic
168C2#1568938312yes—
subgroupG/H
centerC22#13093995
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#106×C47C2
socleC22×C47#121
hypercenterC2×#106D47
hypocenterC47#1815
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
2. C2×#13093960C2semidirect
4. #15688892C2semidirect
5. C2×#106×C47C2semidirect
8. #13094030C4semidirect
87. C2×#106D47semidirect
90. C47#1815semidirect