Finite Group Databasebeta

← #20242339

Subgroups — #20242339

Order 6016.

308 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 53 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#15689685C211yesmaximal, characteristic
2#15689262C212yesmaximal, complemented
3#15688856C212yesmaximal, complemented
4#15688847C211yesmaximal, characteristic, complemented
5C47×#393C211yesmaximal, characteristic, complemented
6C22×C22⋊D47—21no—
7C2×#10625336—22no—
8#13094008—22no—
9#13093998—21no—
10#13093998C2212yes—
11#13093994—22no—
12#13093948—22no—
13C22⋊(C47⋊C8)C2212yescomplemented
14C22×Q8×C47C2211yescharacteristic, complemented
15C2×C22⋊C4×C47—21no—
16C2×C22⋊C4×C47C2211yescharacteristic
17#95×C47—21no—
18#95×C47C2211yescharacteristic, complemented
19C24×C47D411yescharacteristic
20C23×D47—21no—
21C2×Q8×C47—22no—
22C2×Q8×C47—42no—
23C22×C4×C47—21no—
24C22×C4×C47—21no—
25C22×C4×C47D411yescharacteristic
26C22×C4×C47C2311yescharacteristic
27C2×C22⋊D47—22no—
28C2×C22⋊D47—22no—
29C2×C22⋊D47—42no—
30C2×C22⋊D47—42no—
31C22×Dic47—21no—
32C2×D188—21no—
33C2×D188D412yes—
34C22⋊C4×C47—22no—
35C22⋊C4×C47—42no—
36#10625336—44no—
37(C2×D47)⋊C4—22no—
38(C2×D47)⋊C4—22no—
39C4⋊Dic47—21no—
40C4⋊Dic47D412yes—
41C2×C47⋊C8—22no—
42C23×C47—21no—
43C23×C47—21no—
44C23×C47—41no—
45C23×C47—41no—
46C23×C47SD1612yescomplemented
47C23×C47C2×D411yescharacteristic
48C22×D47—22no—
49C22×D47—42no—
50C22×D47—81no—
51C22×D47—81no—
52Q8×C47—24no—
53Q8×C47—42no—
54C2×C4×C47—22no—
55C2×C4×C47—21no—
56C2×C4×C47—41no—
57C2×C4×C47—41no—
58C2×C4×C47—41no—
59C2×C4×C47—41no—
60C2×C4×C47—41no—
61C2×C4×C47—41no—
62C2×C4×C47—41no—
63C2×C4×C47C2×D412yes—
64C22⋊D47—44no—
65C22⋊D47—42no—
66C22⋊D47—42no—
67C2×Dic47—22no—
68C2×Dic47—42no—
69D188—42no—
70D188—81no—
71C47⋊C8—42no—
72C22×C47—21no—
73C22×C47—21no—
74C22×C47—22no—
75C22×C47—42no—
76C22×C47—41no—
77C22×C47—41no—
78C22×C47—81no—
79C22×C47#12011yescharacteristic
80C22×C47C2×SD1611yescharacteristic
81C22×C47AGL(1,ℤ/8)11yescharacteristic
82C2×D47—42no—
83C2×D47—42no—
84C2×D47—42no—
85C2×D47—84no—
86C4×C47—22no—
87C4×C47—41no—
88C4×C47—42no—
89C4×C47—81no—
90Dic47—42no—
91#1601—471nomaximal, Sylow
92C2×C47—21no—
93C2×C47—21no—
94C2×C47—42no—
95C2×C47#45011yescharacteristic
96C2×C47#45511yescharacteristic
97C2×C47B(4,𝔽2)11yescharacteristic
98D47—82no—
99#534—471no—
100#448—472no—
101#393D4711yescharacteristic, complemented
102#327—472no—
103#323—471no—
104C47#160111yescharacteristic, complemented, Sylow
105C22×Q8C2×D4711yescharacteristic, complemented
106C22×D4—941no—
107C2×SD16—942no—
108#123—942no—
109#121—472no—
110#121—941no—
111#120—942no—
112C2×C22⋊C4—21no—
113C2×C22⋊C4C2×D4711yescharacteristic
114#103—942no—
115C22⋊C8—472no—
116#95—21no—
117#95C2×D4711yescharacteristic, complemented
118C24—941no—
119C24C22⋊D4711yescharacteristic
120C2×Q8—22no—
121C2×Q8—42no—
122C2×D4—472no—
123C2×D4—941no—
124C2×D4—942no—
125C2×D4—942no—
126C2×D4—1882no—
127C2×D4—1882no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—941no—
131C22×C4C22⋊D4711yescharacteristic
132C22×C4C22×D4711yescharacteristic
133SD16—1884no—
134C2×C8—942no—
135C4⋊C4—472no—
136C4⋊C4—941no—
137C22⋊C4—22no—
138C22⋊C4—42no—
139C22⋊C4—942no—
140C22⋊C4—942no—
141C23—21no—
142C23—21no—
143C23—41no—
144C23—41no—
145C23—942no—
146C23—3761no—
147C23—3761no—
148C23—1882no—
149C23#1062533612yescomplemented
150C23C2×C22⋊D4711yescharacteristic
151Q8—24no—
152Q8—42no—
153D4—3761no—
154D4—1882no—
155D4—1884no—
156D4—1882no—
157D4—1882no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—41no—
164C2×C4—41no—
165C2×C4—41no—
166C2×C4—41no—
167C2×C4—942no—
168C2×C4—1882no—
169C2×C4D4×D4712yes—
170C8—1882no—
171C22—21no—
172C22—21no—
173C22—22no—
174C22—42no—
175C22—41no—
176C22—41no—
177C22—81no—
178C22—3764no—
179C22—1882no—
180C22—1882no—
181C22—1882no—
182C22#1309399211yescharacteristic
183C22C2×#1062533611yescharacteristic
184C22#1309404911yescharacteristic
185C4—22no—
186C4—41no—
187C4—42no—
188C4—81no—
189C4—1882no—
190C2—21no—
191C2—21no—
192C2—42no—
193C2—3762no—
194C2#1568927311yescharacteristic
195C2#1568930011yescharacteristic
196C2#1568930911yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#393C2
socleC22×C47#120
hypercenter#393D47
hypocenterC47#1601
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #393

Complements

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

NH ≅ G/Ntype
2. #15689262C2semidirect
3. #15688856C2semidirect
4. #15688847C2semidirect
5. C47×#393C2semidirect
13. C22⋊(C47⋊C8)C22semidirect
14. C22×Q8×C47C22semidirect
18. #95×C47C22semidirect
46. C23×C47SD16semidirect
101. #393D47semidirect
104. C47#1601semidirect
105. C22×Q8C2×D47semidirect
117. #95C2×D47semidirect
149. C23#10625336semidirect