Finite Group Databasebeta

← #20243453

Subgroups — #20243453

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×#107×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#107×C47—21no—
19#107×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—21no—
68C22×C47—21no—
69C22×C47#11711yescharacteristic
70C22×C47#12111yescharacteristic
71C22×C47C22⋊Q811yescharacteristic
72C2×D47—22no—
73C2×D47—41no—
74C2×D47—41no—
75C4×C47—82no—
76C4×C47C2×C22⋊C411yescharacteristic
77C4×C47C2×C4⋊C411yescharacteristic
78C4×C47#12111yescharacteristic
79C4×C47C22⋊Q811yescharacteristic
80Dic47—22no—
81#1816—471nomaximal, Sylow
82C2×C47—21no—
83C2×C47—21no—
84C2×C47#38011yescharacteristic
85C2×C47#47211yescharacteristic
86C2×C47#47311yescharacteristic
87D47—42no—
88C2×#131—471no—
89C2×#108—471no—
90C2×#107D4711yescharacteristic, complemented
91#417—472no—
92#343—472no—
93C47#181611yescharacteristic, complemented, Sylow
94C2×#41—471no—
95#131—474no—
96#131—942no—
97C2×M16—471no—
98C2×M16—472no—
99C2×M16—941no—
100C22×C8—941no—
101C22×C8C2×D4711yescharacteristic
102C2×C4⋊C4C2×D4712yes—
103#108—942no—
104#107—21no—
105#107—21no—
106#103—942no—
107#102—942no—
108#41—472no—
109#41—472no—
110#41—941no—
111#41—941no—
112C2×Q8—471no—
113C2×D4—471no—
114C2×D4—941no—
115C22×C4—22no—
116C22×C4—941no—
117C22×C4C22×D4711yescharacteristic
118M16—472no—
119M16—941no—
120M16—944no—
121M16—942no—
122M16—942no—
123C2×C8—941no—
124C2×C8—944no—
125C2×C8—942no—
126C2×C8C4×D4712yes—
127C2×C8D18812yes—
128C2×C8C22⋊D4711yescharacteristic
129C2×C8C22⋊D4711yescharacteristic
130C4⋊C4—22no—
131C4⋊C4—22no—
132C23—941no—
133C23#1062535211yescharacteristic
134Q8—472no—
135Q8—941no—
136D4—472no—
137D4—942no—
138D4—942no—
139D4—941no—
140C2×C4—42no—
141C2×C4—82no—
142C2×C4—941no—
143C2×C4—942no—
144C2×C4—942no—
145C2×C4C2×C4×D4711yescharacteristic
146C2×C4C2×D18811yescharacteristic
147C2×C4D4×D4711yescharacteristic
148C2×C4Q8×D4711yescharacteristic
149C2×C4#1062535411yescharacteristic
150C2×C4C2×C22⋊D4711yescharacteristic
151C8—942no—
152C8—1882no—
153C8(C2×D47)⋊C412yes—
154C8(C2×D47)⋊C412yes—
155C22—21no—
156C22—21no—
157C22—942no—
158C22—1881no—
159C22—1881no—
160C22#1309398211yescharacteristic
161C22#1309399511yescharacteristic
162C22#1309400411yescharacteristic
163C4—82no—
164C4—942no—
165C4C2×(C2×D47)⋊C411yescharacteristic
166C4C4⋊C4×D4711yescharacteristic
167C4#1309399911yescharacteristic
168C4#1309400011yescharacteristic
169C2—21no—
170C2—21no—
171C2—1882no—
172C2#1568898011yescharacteristic
173C2#1568939011yescharacteristic
174C2#1568939511yescharacteristic
subgroupG/H
centerC22#13093995
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#107×C47C2
socleC22×C47#121
hypercenterC2×#107D47
hypocenterC47#1816
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#107

Complements

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

NH ≅ G/Ntype
2. C2×#13093960C2semidirect
4. #15688892C2semidirect
5. C2×#107×C47C2semidirect
8. #13094030C4semidirect
90. C2×#107D47semidirect
93. C47#1816semidirect