Finite Group Databasebeta

← #20243606

Subgroups — #20243606

Order 6016.

252 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 252 conjugacy classes of subgroups — too many to draw. Only its 79 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#15689889C211yesmaximal, characteristic
2#15689171C211yesmaximal, characteristic, complemented
3#15689105C211yesmaximal, characteristic
4#15689091C211yesmaximal, characteristic
5#15688887C211yesmaximal, characteristic, complemented
6#15688887C211yesmaximal, characteristic, complemented
7C47×#430C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094032—22no—
10#13094030—22no—
11C2×#10625329C2211yescharacteristic
12C2×#10625329C2211yescharacteristic
13M16×D47—22no—
14C22×C47⋊C8C2211yescharacteristic
15#13093959—22no—
16#13093942C412yes—
17#13093940C412yes—
18(C2×D47)⋊C8—22no—
19C2×M16×C47C2211yescharacteristic
20C2×M16×C47C2211yescharacteristic
21C2×M16×C47C2211yescharacteristic
22#108×C47—22no—
23C22×C4×C47C2311yescharacteristic
24C2×C22⋊D47Q812yes—
25#10625350—21no—
26#10625350—21no—
27#10625350—21no—
28#10625350—21no—
29C2×D188C2×C411yescharacteristic
30C2×C4×D47D412yes—
31C2×Dic94C2×C411yescharacteristic
32M16×C47—21no—
33M16×C47—21no—
34M16×C47—21no—
35M16×C47—21no—
36M16×C47C2×C412yes—
37M16×C47D412yes—
38C2×C8×C47—21no—
39C2×C8×C47—21no—
40C2×C8×C47—21no—
41#10625329—21no—
42#10625329—21no—
43#10625329C2×C412yes—
44#10625329D412yes—
45C2×C47⋊C8—21no—
46C2×C47⋊C8—21no—
47C2×C47⋊C8—21no—
48C2×C47⋊C8—21no—
49C2×C47⋊C8—21no—
50#10625324—24no—
51C8×D47—24no—
52C23×C47C2×Q811yescharacteristic
53C22×D47C4⋊C412yes—
54C2×C4×C47C22×C411yescharacteristic
55C2×C4×C47C2×D411yescharacteristic
56C2×C4×C47C2×D411yescharacteristic
57C2×C4×C47C2×D411yescharacteristic
58C2×C4×C47#4111yescharacteristic
59C2×C4×C47#4111yescharacteristic
60C22⋊D47—22no—
61C22⋊D47—22no—
62C2×Dic47C4⋊C412yes—
63D188—21no—
64D188—21no—
65C4×D47—22no—
66C4×D47—22no—
67Dic94—21no—
68Dic94—21no—
69C8×C47—22no—
70C8×C47—22no—
71C8×C47—41no—
72C47⋊C8—22no—
73C47⋊C8—22no—
74C47⋊C8—41no—
75C22×C47—41no—
76C22×C47C2×C4⋊C411yescharacteristic
77C22×C47C22⋊Q811yescharacteristic
78C22×C47C22⋊Q811yescharacteristic
79C2×D47—22no—
80C2×D47—42no—
81C4×C47C4×D411yescharacteristic
82C4×C47C4×D411yescharacteristic
83C4×C47#12011yescharacteristic
84C4×C47#12311yescharacteristic
85Dic47—22no—
86#1858—471nomaximal, Sylow
87C2×C47—21no—
88C2×C47—21no—
89C2×C47—21no—
90C2×C47#38511yescharacteristic
91D47—42no—
92#568—471no—
93#430—471no—
94#430D4711yescharacteristic, complemented
95#413—471no—
96#408—471no—
97#341—471no—
98#341—471no—
99C47#185811yescharacteristic, complemented, Sylow
100C2×#41—471no—
101#131—942no—
102#131—942no—
103C2×M16—471no—
104C2×M16—471no—
105C2×M16—942no—
106C2×M16C2×D4711yescharacteristic
107C2×M16C2×D4711yescharacteristic
108C2×M16C2×D4711yescharacteristic
109C22×C8—471no—
110#108—22no—
111#108—942no—
112#101—472no—
113#100—472no—
114C22⋊C8—942no—
115#41—941no—
116#41—941no—
117#41—941no—
118#41—941no—
119C2×Q8—471no—
120C2×D4—472no—
121C2×D4—471no—
122C22×C4—472no—
123C22×C4C22×D4711yescharacteristic
124M16—21no—
125M16—21no—
126M16—21no—
127M16—21no—
128M16—472no—
129M16—472no—
130M16—944no—
131M16—941no—
132M16—941no—
133M16C4×D4712yes—
134M16C22⋊D4712yes—
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—944no—
139C2×C8—941no—
140C2×C8—941no—
141C2×C8—941no—
142C2×C8—941no—
143C2×C8—941no—
144C23—472no—
145C23Q8×D4711yescharacteristic
146Q8—941no—
147Q8—941no—
148D4—942no—
149D4—942no—
150D4—941no—
151D4—941no—
152C2×C4—472no—
153C2×C4—942no—
154C2×C4—942no—
155C2×C4C2×C4×D4711yescharacteristic
156C2×C4#1062535011yescharacteristic
157C2×C4D4×D4711yescharacteristic
158C2×C4D4×D4711yescharacteristic
159C2×C4#1062535411yescharacteristic
160C2×C4C2×C22⋊D4711yescharacteristic
161C8—22no—
162C8—22no—
163C8—41no—
164C8—942no—
165C8—942no—
166C8—1881no—
167C22—41no—
168C22—942no—
169C22—1882no—
170C22C4⋊C4×D4711yescharacteristic
171C22#1309400011yescharacteristic
172C22#1309400211yescharacteristic
173C4—942no—
174C4C4×C22⋊D4711yescharacteristic
175C4#1309398611yescharacteristic
176C4#1309399211yescharacteristic
177C4#1309400911yescharacteristic
178C2—21no—
179C2—21no—
180C2—21no—
181C2—1882no—
182C2#1568899411yescharacteristic
subgroupG/H
centerC4#13093992
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#430C2
socleC2×C47#385
hypercenter#430D47
hypocenterC47#1858
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #430

Complements

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

NH ≅ G/Ntype
2. #15689171C2semidirect
5. #15688887C2semidirect
6. #15688887C2semidirect
7. C47×#430C2semidirect
94. #430D47semidirect
99. C47#1858semidirect