Finite Group Databasebeta

← #20243452

Subgroups — #20243452

Order 6016.

264 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 109 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×#13093960C211yesmaximal, characteristic, complemented
2C2×#13093958C211yesmaximal, characteristic, complemented
3#15689124C212yesmaximal
4#15688891C212yesmaximal, complemented
5C2×#131×C47C211yesmaximal, characteristic
6C2×#10625329C2212yes—
7C2×C4⋊Dic47C2212yes—
8#13093960—22no—
9#13093958—21no—
10#13093958—21no—
11#13093948—22no—
12#13093945—22no—
13C2×#41×C47C2211yescharacteristic
14#131×C47—22no—
15#131×C47C414yescomplemented
16C2×M16×C47—21no—
17C2×M16×C47C2211yescharacteristic
18C22×C8×C47—21no—
19C22×C8×C47C2211yescharacteristic
20#41×C47—21no—
21#41×C47—21no—
22#41×C47C2×C412yes—
23#41×C47Q812yes—
24C2×Q8×C47D411yescharacteristic
25C2×D4×C47—21no—
26C2×D4×C47D411yescharacteristic
27C22×C4×C47—21no—
28C22×C4×C47C2311yescharacteristic
29C22×Dic47—22no—
30M16×C47—21no—
31M16×C47—24no—
32M16×C47C2×C412yes—
33C2×C8×C47—21no—
34C2×C8×C47—24no—
35C2×C8×C47C2×C412yes—
36C2×C8×C47D411yescharacteristic
37C2×C8×C47D411yescharacteristic
38C2×C8×C47D412yes—
39C4⋊Dic47—22no—
40C4⋊Dic47—22no—
41#10625329—22no—
42#10625329—22no—
43C2×C47⋊C8—22no—
44C23×C47—21no—
45C23×C47#4111yescharacteristic
46Q8×C47—21no—
47Q8×C47C4⋊C412yes—
48D4×C47—22no—
49D4×C47—22no—
50D4×C47—21no—
51D4×C47C4⋊C412yes—
52C2×C4×C47—21no—
53C2×C4×C47—22no—
54C2×C4×C47—22no—
55C2×C4×C47C22×C411yescharacteristic
56C2×C4×C47C2×D411yescharacteristic
57C2×C4×C47C2×D411yescharacteristic
58C2×C4×C47C2×D411yescharacteristic
59C2×C4×C47C2×Q811yescharacteristic
60C2×C4×C47#4111yescharacteristic
61C2×Dic47—42no—
62C2×Dic47—82no—
63C8×C47—22no—
64C8×C47C22⋊C412yes—
65C8×C47C22⋊C412yes—
66C47⋊C8—42no—
67C22×C47—21no—
68C22×C47—21no—
69C22×C47—22no—
70C22×C47—41no—
71C22×C47—41no—
72C22×C47#11711yescharacteristic
73C22×C47#12111yescharacteristic
74C22×C47C22⋊Q811yescharacteristic
75C4×C47—22no—
76C4×C47C2×C22⋊C411yescharacteristic
77C4×C47C2×C4⋊C411yescharacteristic
78C4×C47#12111yescharacteristic
79C4×C47C22⋊Q811yescharacteristic
80Dic47—82no—
81#1816—471nomaximal, Sylow
82C2×C47—21no—
83C2×C47—21no—
84C2×C47—42no—
85C2×C47#38011yescharacteristic
86C2×C47#47211yescharacteristic
87C2×C47#47311yescharacteristic
88C2×#131D4711yescharacteristic
89C2×#108—471no—
90C2×#107—471no—
91#417—472no—
92#343—472no—
93C47#181611yescharacteristic, complemented, Sylow
94C2×#41C2×D4711yescharacteristic
95#131—22no—
96#131Dic4714yescomplemented
97C2×M16—21no—
98C2×M16—472no—
99C2×M16C2×D4711yescharacteristic
100C22×C8—21no—
101C22×C8C2×D4711yescharacteristic
102C2×C4⋊C4—472no—
103#108—942no—
104#107—941no—
105#107—941no—
106#103—942no—
107#102—942no—
108#41—21no—
109#41—21no—
110#41Dic9412yes—
111#41C2×Dic4712yes—
112C2×Q8D18811yescharacteristic
113C2×D4—21no—
114C2×D4D18811yescharacteristic
115C22×C4—21no—
116C22×C4—942no—
117C22×C4C22×D4711yescharacteristic
118M16—21no—
119M16—24no—
120M16—942no—
121M16—942no—
122M16C2×Dic4712yes—
123C2×C8—21no—
124C2×C8—24no—
125C2×C8—942no—
126C2×C8C2×Dic4712yes—
127C2×C8C22⋊D4711yescharacteristic
128C2×C8C22⋊D4711yescharacteristic
129C2×C8C22⋊D4712yes—
130C4⋊C4—942no—
131C4⋊C4—942no—
132C23—21no—
133C23#1062535011yescharacteristic
134Q8—21no—
135Q8C4⋊Dic4712yes—
136D4—22no—
137D4—22no—
138D4—21no—
139D4C4⋊Dic4712yes—
140C2×C4—21no—
141C2×C4—22no—
142C2×C4—22no—
143C2×C4—3762no—
144C2×C4—1882no—
145C2×C4C2×Dic9411yescharacteristic
146C2×C4C2×D18811yescharacteristic
147C2×C4#1062535011yescharacteristic
148C2×C4C22×Dic4711yescharacteristic
149C2×C4C2×C22⋊D4711yescharacteristic
150C2×C4C2×C22⋊D4711yescharacteristic
151C8—22no—
152C8—1882no—
153C8C22⋊Dic4712yes—
154C8C22⋊Dic4712yes—
155C22—21no—
156C22—21no—
157C22—22no—
158C22—41no—
159C22—41no—
160C22#1309398311yescharacteristic
161C22#1309399811yescharacteristic
162C22#1309400311yescharacteristic
163C4—22no—
164C4—3762no—
165C4C2×C22⋊Dic4711yescharacteristic
166C4C2×C4⋊Dic4711yescharacteristic
167C4#1309399811yescharacteristic
168C4#1309400311yescharacteristic
169C2—21no—
170C2—21no—
171C2—42no—
172C2#1568898311yescharacteristic
173C2#1568939311yescharacteristic
174C2#1568939811yescharacteristic
subgroupG/H
centerC22#13093998
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#131×C47C2
socleC22×C47#121
hypercenterC2×#131D47
hypocenterC47#1816
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
1. C2×#13093960C2semidirect
2. C2×#13093958C2semidirect
4. #15688891C2semidirect
15. #131×C47C4semidirect
93. C47#1816semidirect
96. #131Dic47semidirect