Finite Group Databasebeta

← #20244430

Subgroups — #20244430

Order 6016.

406 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 406 conjugacy classes of subgroups — too many to draw. Only its 75 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×#13094049C212yesmaximal, complemented
2C2×#13093951C212yesmaximal, complemented
3#15689024C211yesmaximal, characteristic, complemented
4#15688892C211yesmaximal, characteristic, complemented
5C47×#537C211yesmaximal, characteristic, complemented
6C22×D188C2211yescharacteristic
7#13094049—24no—
8#13094049—24no—
9C2×#10625336—22no—
10C2×#10625334—22no—
11C2×#10625329C2212yes—
12C2×(C2×D47)⋊C4—22no—
13C2×C4×Dic47C2211yescharacteristic
14#13093951—24no—
15C2×#41×C47C2212yes—
16C22⋊Q8×C47—22no—
17#121×C47—22no—
18#121×C47—22no—
19C2×C4⋊C4×C47C2211yescharacteristic
20C23×D47—21no—
21#41×C47—22no—
22#41×C47—22no—
23#41×C47—22no—
24#41×C47—22no—
25C2×Q8×C47D412yes—
26C2×D4×C47—22no—
27C2×D4×C47—22no—
28C2×D4×C47D412yes—
29C22×C4×C47—22no—
30C22×C4×C47D412yes—
31C22×C4×C47C2311yescharacteristic
32C22×Dic47—21no—
33C2×D188—22no—
34C2×D188—22no—
35C2×D188—21no—
36C2×D188D412yescomplemented
37C4⋊C4×C47—22no—
38C4⋊C4×C47—22no—
39C22⋊C4×C47—24no—
40#10625336—28no—
41#10625334—28no—
42(C2×D47)⋊C4—44no—
43C4×Dic47—22no—
44#10625329—22no—
45#10625329D414yescomplemented
46C2×C47⋊C8—22no—
47C23×C47—22no—
48C23×C47C2×D411yescharacteristic
49C22×D47—22no—
50C22×D47—42no—
51C22×D47—42no—
52C22×D47—41no—
53C22×D47—41no—
54Q8×C47—22no—
55Q8×C47—22no—
56D4×C47—22no—
57D4×C47—22no—
58D4×C47—42no—
59D4×C47—42no—
60D4×C47—82no—
61C2×C4×C47—22no—
62C2×C4×C47—22no—
63C2×C4×C47—42no—
64C2×C4×C47—42no—
65C2×C4×C47—42no—
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47C2×D412yes—
68C2×C4×C47C2×D412yes—
69C2×C4×C47#4111yescharacteristic
70C2×Dic47—22no—
71C2×Dic47—41no—
72C2×Dic47—41no—
73D188—24no—
74D188—42no—
75C47⋊C8—24no—
76C22×C47—21no—
77C22×C47—21no—
78C22×C47—42no—
79C22×C47—42no—
80C22×C47—42no—
81C22×C47#12011yescharacteristic
82C22×C47#12111yescharacteristic
83C22×C47#12711yescharacteristic
84C2×D47—44no—
85C2×D47—42no—
86C2×D47—82no—
87C2×D47—81no—
88C2×D47—81no—
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#537D4711yescharacteristic, complemented
104C2×#104—472no—
105#390—471no—
106#343—471no—
107C47#200611yescharacteristic, complemented, Sylow
108C2×#41C2×D4712yes—
109C22×D4—471no—
110AGL(1,ℤ/8)—944no—
111AGL(1,ℤ/8)—944no—
112C2×SD16—942no—
113C2×D8—942no—
114C2×M16—472no—
115C22⋊Q8—22no—
116#121—22no—
117#121—22no—
118C2×C4⋊C4C2×D4711yescharacteristic
119C2×C22⋊C4—942no—
120C2×C42—471no—
121#104—944no—
122C24—941no—
123#41—22no—
124#41—22no—
125#41—22no—
126#41—22no—
127C2×Q8C22⋊D4712yes—
128C2×D4—22no—
129C2×D4—22no—
130C2×D4—472no—
131C2×D4—942no—
132C2×D4—941no—
133C2×D4—942no—
134C2×D4C22⋊D4712yes—
135C22×C4—22no—
136C22×C4—941no—
137C22×C4C22⋊D4712yes—
138C22×C4C22×D4711yescharacteristic
139SD16—948no—
140D8—948no—
141M16—474no—
142M16—942no—
143C2×C8—942no—
144C4⋊C4—22no—
145C4⋊C4—22no—
146C22⋊C4—24no—
147C22⋊C4—1884no—
148C42—942no—
149C23—22no—
150C23—942no—
151C23—1882no—
152C23—1882no—
153C23—1881no—
154C23—1881no—
155C23C2×C22⋊D4711yescharacteristic
156Q8—22no—
157Q8—22no—
158D4—22no—
159D4—22no—
160D4—42no—
161D4—42no—
162D4—82no—
163D4—944no—
164D4—1882no—
165C2×C4—22no—
166C2×C4—22no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—942no—
171C2×C4—1881no—
172C2×C4—1881no—
173C2×C4D4×D4711yescharacteristic
174C2×C4D4×D4712yes—
175C2×C4#1062535211yescharacteristic
176C2×C4C2×C22⋊D4712yes—
177C8—944no—
178C22—21no—
179C22—21no—
180C22—42no—
181C22—42no—
182C22—42no—
183C22—3762no—
184C22—3761no—
185C22—3761no—
186C22—1884no—
187C22—1882no—
188C22#1309399311yescharacteristic
189C22#1309399511yescharacteristic
190C22#1309402011yescharacteristic
191C4—42no—
192C4—42no—
193C4—1882no—
194C4#1309399212yes—
195C4#1309399612yes—
196C2—21no—
197C2—21no—
198C2—82no—
199C2—3762no—
200C2#1568903111yescharacteristic
201C2#1568929111yescharacteristic
202C2#1568929611yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#537C2
socleC22×C47#120
hypercenter#537D47
hypocenterC47#2006
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #537

Complements

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

NH ≅ G/Ntype
1. C2×#13094049C2semidirect
2. C2×#13093951C2semidirect
3. #15689024C2semidirect
4. #15688892C2semidirect
5. C47×#537C2semidirect
36. C2×D188D4semidirect
45. #10625329D4semidirect
103. #537D47semidirect
107. C47#2006semidirect