Finite Group Databasebeta

← #20242328

Subgroups — #20242328

Order 6016.

266 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 266 conjugacy classes of subgroups — too many to draw. Only its 57 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#15689273C212yesmaximal
2#15689040C211yesmaximal, characteristic
3#15688860C212yesmaximal, complemented
4#15688849C211yesmaximal, characteristic, complemented
5C47×#544C211yesmaximal, characteristic, complemented
6C22×D188C2211yescharacteristic
7C2×#10625336—22no—
8C2×(C2×D47)⋊C4—21no—
9C2×(C2×D47)⋊C4—21no—
10#13093944—22no—
11C22⋊(C47⋊C8)C2212yes—
12C47⋊#95C2211yescharacteristic
13C4⋊Q8×C47—22no—
14#125×C47—22no—
15C22⋊Q8×C47—21no—
16C22⋊Q8×C47C2212yes—
17#117×C47—21no—
18C2×C4⋊C4×C47C2211yescharacteristic
19C23×D47—21no—
20C2×Q8×C47—21no—
21C2×Q8×C47D412yes—
22C22×C4×C47D411yescharacteristic
23C22×C4×C47D411yescharacteristic
24C22×C4×C47C2311yescharacteristic
25C22×Dic47—21no—
26C2×D188—22no—
27C2×D188—42no—
28C4⋊C4×C47—21no—
29C4⋊C4×C47—21no—
30C4⋊C4×C47—21no—
31C4⋊C4×C47—22no—
32C4⋊C4×C47—22no—
33C4⋊C4×C47—22no—
34C4⋊C4×C47D412yes—
35C22⋊C4×C47—22no—
36C42×C47—22no—
37#10625336—44no—
38(C2×D47)⋊C4—42no—
39(C2×D47)⋊C4—42no—
40C2×C47⋊C8—22no—
41C23×C47C2×D411yescharacteristic
42C22×D47—22no—
43C22×D47—41no—
44C22×D47—41no—
45C22×D47—41no—
46C22×D47—41no—
47C22×D47—41no—
48C22×D47—41no—
49Q8×C47—42no—
50Q8×C47—81no—
51C2×C4×C47—21no—
52C2×C4×C47—21no—
53C2×C4×C47—22no—
54C2×C4×C47—22no—
55C2×C4×C47—21no—
56C2×C4×C47—41no—
57C2×C4×C47—41no—
58C2×C4×C47SD1612yescomplemented
59C2×C4×C47C2×D412yes—
60C2×Dic47—41no—
61C2×Dic47—41no—
62C2×Dic47—41no—
63D188—24no—
64D188—42no—
65C47⋊C8—42no—
66C22×C47—21no—
67C22×C47—21no—
68C22×C47#12011yescharacteristic
69C22×C47C2×SD1611yescharacteristic
70C22×C47#13711yescharacteristic
71C2×D47—42no—
72C2×D47—42no—
73C2×D47—42no—
74C2×D47—81no—
75C2×D47—81no—
76C2×D47—81no—
77C2×D47—81no—
78C4×C47—22no—
79C4×C47—22no—
80C4×C47—42no—
81C4×C47—41no—
82C4×C47—42no—
83Dic47—81no—
84#1599—471nomaximal, Sylow
85C2×C47—21no—
86C2×C47—21no—
87C2×C47#44811yescharacteristic
88C2×C47#45411yescharacteristic
89C2×C47B(4,𝔽2)11yescharacteristic
90D47—82no—
91#544D4711yescharacteristic, complemented
92#450—472no—
93#394—471no—
94#328—472no—
95#324—471no—
96C47#159911yescharacteristic, complemented, Sylow
97C22×D4—471no—
98C2×SD16—942no—
99C4⋊Q8—22no—
100#125—22no—
101C22⋊Q8—21no—
102C22⋊Q8C2×D4712yes—
103#117—21no—
104C2×C4⋊C4C2×D4711yescharacteristic
105C2×C22⋊C4—941no—
106C2×C22⋊C4—941no—
107#102—942no—
108C22⋊C8—472no—
109#95—471no—
110C24—941no—
111C2×Q8—21no—
112C2×Q8C22⋊D4712yes—
113C2×D4—942no—
114C2×D4—1882no—
115C22×C4—941no—
116C22×C4C22⋊D4711yescharacteristic
117C22×C4C22⋊D4711yescharacteristic
118C22×C4C22×D4711yescharacteristic
119SD16—1884no—
120C2×C8—942no—
121C4⋊C4—21no—
122C4⋊C4—21no—
123C4⋊C4—21no—
124C4⋊C4—22no—
125C4⋊C4—22no—
126C4⋊C4—22no—
127C4⋊C4C22⋊D4712yes—
128C22⋊C4—22no—
129C22⋊C4—1882no—
130C22⋊C4—1882no—
131C42—22no—
132C23—942no—
133C23—1881no—
134C23—1881no—
135C23—1881no—
136C23—1881no—
137C23—1881no—
138C23—1881no—
139C23C2×C22⋊D4711yescharacteristic
140Q8—42no—
141Q8—81no—
142D4—944no—
143D4—1882no—
144C2×C4—21no—
145C2×C4—21no—
146C2×C4—22no—
147C2×C4—22no—
148C2×C4—21no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—1881no—
152C2×C4—1881no—
153C2×C4—1881no—
154C2×C4#1062533612yescomplemented
155C2×C4C2×C22⋊D4712yes—
156C8—1882no—
157C22—21no—
158C22—21no—
159C22—3761no—
160C22—3761no—
161C22—3761no—
162C22—3761no—
163C22—1882no—
164C22—1882no—
165C22—1882no—
166C22#1309399311yescharacteristic
167C22C2×#1062533611yescharacteristic
168C22#1309405511yescharacteristic
169C4—22no—
170C4—22no—
171C4—42no—
172C4—41no—
173C4—42no—
174C4—3761no—
175C2—21no—
176C2—21no—
177C2—3762no—
178C2#1568926211yescharacteristic
179C2#1568929611yescharacteristic
180C2#1568931011yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#544C2
socleC22×C47#120
hypercenter#544D47
hypocenterC47#1599
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #544

Complements

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

NH ≅ G/Ntype
3. #15688860C2semidirect
4. #15688849C2semidirect
5. C47×#544C2semidirect
58. C2×C4×C47SD16semidirect
91. #544D47semidirect
96. C47#1599semidirect
154. C2×C4#10625336semidirect