Finite Group Databasebeta

← #20244429

Subgroups — #20244429

Order 6016.

406 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 73 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×#13094050C212yesmaximal, complemented
2#15689704C211yesmaximal, characteristic, complemented
3C2×#13093952C212yesmaximal, complemented
4#15688892C211yesmaximal, characteristic, complemented
5C47×#390C211yesmaximal, characteristic, complemented
6C2×#10625350C2212yes—
7#13094050—24no—
8#13094050—24no—
9C2×#10625335—22no—
10C2×#10625334—22no—
11C2×#10625329C2212yes—
12#13094004—22no—
13#13093999—22no—
14#13093998—22no—
15#13093952—24no—
16C22×D4×C47C2211yescharacteristic
17C2×C4⋊C4×C47C2211yescharacteristic
18C2×C22⋊C4×C47—22no—
19C2×C42×C47C2211yescharacteristic
20C24×C47—21no—
21C2×D4×C47—22no—
22C2×D4×C47—22no—
23C2×D4×C47—21no—
24C2×D4×C47D412yescomplemented
25C22×C4×C47—21no—
26C22×C4×C47D412yes—
27C22×C4×C47C2311yescharacteristic
28C2×C22⋊D47—22no—
29#10625350—22no—
30#10625350—22no—
31#10625350—22no—
32#10625350—22no—
33C2×D188—22no—
34C2×D188D412yes—
35C2×C4×D47—22no—
36C2×Dic94D412yes—
37C4⋊C4×C47—22no—
38C22⋊C4×C47—44no—
39C42×C47—22no—
40#10625335—28no—
41#10625334—28no—
42(C2×D47)⋊C4—24no—
43C4⋊Dic47—22no—
44#10625329—22no—
45#10625329D414yescomplemented
46C2×C47⋊C8—22no—
47C23×C47—22no—
48C23×C47—42no—
49C23×C47—42no—
50C23×C47—41no—
51C23×C47—41no—
52C23×C47C2×D411yescharacteristic
53C22×D47—22no—
54D4×C47—24no—
55D4×C47—42no—
56C2×C4×C47—22no—
57C2×C4×C47—22no—
58C2×C4×C47—41no—
59C2×C4×C47—41no—
60C2×C4×C47—42no—
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×D412yes—
63C2×C4×C47C2×D412yes—
64C2×C4×C47#4111yescharacteristic
65C22⋊D47—42no—
66C22⋊D47—42no—
67C2×Dic47—22no—
68D188—22no—
69D188—22no—
70D188—82no—
71C4×D47—42no—
72C4×D47—42no—
73Dic94—22no—
74Dic94—22no—
75C47⋊C8—24no—
76C22×C47—21no—
77C22×C47—21no—
78C22×C47—44no—
79C22×C47—42no—
80C22×C47—82no—
81C22×C47—81no—
82C22×C47—81no—
83C22×C47#12011yescharacteristic
84C22×C47#12111yescharacteristic
85C22×C47#12711yescharacteristic
86C2×D47—42no—
87C2×D47—42no—
88C2×D47—42no—
89C4×C47—42no—
90C4×C47—42no—
91C4×C47#12012yes—
92C4×C47#12112yes—
93Dic47—42no—
94#2006—471nomaximal, Sylow
95C2×C47—21no—
96C2×C47—21no—
97C2×C47—82no—
98C2×C47#39211yescharacteristic
99C2×C47#45311yescharacteristic
100C2×C47#45411yescharacteristic
101D47—82no—
102C2×AGL(1,ℤ/8)—472no—
103#537—471no—
104C2×#104—472no—
105#390D4711yescharacteristic, complemented
106#343—471no—
107C47#200611yescharacteristic, complemented, Sylow
108C2×#41—472no—
109C22×D4C2×D4711yescharacteristic
110AGL(1,ℤ/8)—944no—
111AGL(1,ℤ/8)—944no—
112C2×SD16—942no—
113C2×D8—942no—
114C2×M16—472no—
115C22⋊Q8—942no—
116#121—942no—
117#121—942no—
118C2×C4⋊C4C2×D4711yescharacteristic
119C2×C22⋊C4—22no—
120C2×C42C2×D4711yescharacteristic
121#104—944no—
122C24—21no—
123#41—942no—
124#41—942no—
125#41—942no—
126#41—942no—
127C2×Q8—472no—
128C2×D4—21no—
129C2×D4—22no—
130C2×D4—22no—
131C2×D4—472no—
132C2×D4—942no—
133C2×D4—942no—
134C2×D4D18812yescomplemented
135C22×C4—21no—
136C22×C4—942no—
137C22×C4C22⋊D4712yes—
138C22×C4C22×D4711yescharacteristic
139SD16—948no—
140D8—948no—
141M16—474no—
142M16—942no—
143C2×C8—942no—
144C4⋊C4—22no—
145C4⋊C4—942no—
146C22⋊C4—44no—
147C22⋊C4—944no—
148C42—22no—
149C23—22no—
150C23—42no—
151C23—42no—
152C23—41no—
153C23—41no—
154C23—942no—
155C23C2×C22⋊D4711yescharacteristic
156Q8—942no—
157Q8—942no—
158D4—24no—
159D4—42no—
160D4—942no—
161D4—942no—
162D4—3762no—
163D4—1882no—
164D4—1882no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—41no—
168C2×C4—41no—
169C2×C4—42no—
170C2×C4—942no—
171C2×C4—1882no—
172C2×C4—1882no—
173C2×C4C2×D18811yescharacteristic
174C2×C4#1062535011yescharacteristic
175C2×C4D4×D4712yes—
176C2×C4D4×D4712yes—
177C8—944no—
178C22—21no—
179C22—21no—
180C22—44no—
181C22—42no—
182C22—82no—
183C22—81no—
184C22—81no—
185C22—1882no—
186C22—1882no—
187C22—1882no—
188C22#1309399211yescharacteristic
189C22#1309399811yescharacteristic
190C22#1309402011yescharacteristic
191C4—42no—
192C4—42no—
193C4—1882no—
194C4#1309399412yes—
195C4#1309399712yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—3762no—
200C2#1568903211yescharacteristic
201C2#1568929011yescharacteristic
202C2#1568929511yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#390C2
socleC22×C47#120
hypercenter#390D47
hypocenterC47#2006
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
1. C2×#13094050C2semidirect
2. #15689704C2semidirect
3. C2×#13093952C2semidirect
4. #15688892C2semidirect
5. C47×#390C2semidirect
24. C2×D4×C47D4semidirect
45. #10625329D4semidirect
105. #390D47semidirect
107. C47#2006semidirect
134. C2×D4D188semidirect