Finite Group Databasebeta

← #20243341

Subgroups — #20243341

Order 6016.

620 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 101 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×#13094069C211yesmaximal, characteristic
2C2×#13093952C212yesmaximal, complemented
3#15689122C212yesmaximal, complemented
4C2×#13093941C211yesmaximal, characteristic, complemented
5C47×#390C211yesmaximal, characteristic, complemented
6#13094069—22no—
7#13094069—24no—
8#13094069C414yescomplemented
9C2×#10625350C2212yes—
10C2×#10625352—22no—
11C22×C22⋊D47—22no—
12C2×D4×D47—22no—
13C2×#10625329C2212yescomplemented
14#13093952—24no—
15#13093947—22no—
16#13093944—22no—
17#13093941—22no—
18C22×D4×C47C2211yescharacteristic
19C2×C4⋊C4×C47C2211yescharacteristic, complemented
20C2×C22⋊C4×C47—22no—
21C2×C42×C47C2211yescharacteristic, complemented
22C24×C47D412yes—
23C23×D47—22no—
24C2×D4×C47—22no—
25C2×D4×C47—22no—
26C2×D4×C47C2×C412yes—
27C2×D4×C47D412yes—
28C22×C4×C47—21no—
29C22×C4×C47—21no—
30C22×C4×C47C2311yescharacteristic
31C2×C22⋊D47—24no—
32C2×C22⋊D47—28no—
33C2×C22⋊D47—28no—
34C2×C22⋊D47—22no—
35C22×Dic47—22no—
36#10625352—28no—
37#10625352—28no—
38D4×D47—28no—
39D4×D47—28no—
40#10625350—22no—
41#10625350—22no—
42#10625350C2×C414yes—
43#10625350D414yes—
44C2×D188D412yes—
45C2×C4×D47—22no—
46C2×Dic94D412yes—
47C4⋊C4×C47—22no—
48C22⋊C4×C47—44no—
49C42×C47—22no—
50#10625329—22no—
51#10625329—22no—
52C2×C47⋊C8—22no—
53C23×C47—22no—
54C23×C47—22no—
55C23×C47—42no—
56C23×C47—42no—
57C23×C47C22⋊C414yes—
58C23×C47C2×D411yescharacteristic
59C22×D47—22no—
60C22×D47—28no—
61C22×D47—82no—
62C22×D47—82no—
63D4×C47—24no—
64D4×C47—24no—
65C2×C4×C47—22no—
66C2×C4×C47—41no—
67C2×C4×C47—41no—
68C2×C4×C47—42no—
69C2×C4×C47—41no—
70C2×C4×C47C22×C411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D412yes—
73C2×C4×C47C2×D412yes—
74C22⋊D47—216no—
75C22⋊D47—24no—
76C22⋊D47—24no—
77C2×Dic47—28no—
78C2×Dic47—22no—
79D188—22no—
80D188C22⋊C414yescomplemented
81C4×D47—24no—
82C4×D47—24no—
83Dic94—22no—
84Dic94C22⋊C414yescomplemented
85C47⋊C8—42no—
86C22×C47—21no—
87C22×C47—21no—
88C22×C47—24no—
89C22×C47—44no—
90C22×C47—42no—
91C22×C47—42no—
92C22×C47—82no—
93C22×C47C2×C22⋊C411yescharacteristic
94C22×C47#12011yescharacteristic
95C22×C47#12011yescharacteristic
96C2×D47—24no—
97C2×D47—42no—
98C2×D47—42no—
99C2×D47—88no—
100C4×C47—42no—
101C4×C47—81no—
102C4×C47C2×C22⋊C412yes—
103C4×C47#12012yes—
104Dic47—24no—
105#1792—471nomaximal, Sylow
106C2×C47—21no—
107C2×C47—21no—
108C2×C47—44no—
109C2×C47#37911yescharacteristic
110C2×C47#45311yescharacteristic
111C2×C47#45511yescharacteristic
112D47—44no—
113C2×H(5,𝔽2)—471no—
114C2×#104—472no—
115#417—472no—
116C2×#100—471no—
117#390D4711yescharacteristic, complemented
118C47#179211yescharacteristic, complemented, Sylow
119H(5,𝔽2)—474no—
120H(5,𝔽2)—944no—
121H(5,𝔽2)—942no—
122C2×#41—472no—
123C2×#41—942no—
124C22×D4—942no—
125C22×D4—942no—
126C22×D4C2×D4711yescharacteristic
127C2×M16—472no—
128C2×C4⋊C4C2×D4711yescharacteristic, complemented
129C2×C22⋊C4—22no—
130C2×C42C2×D4711yescharacteristic, complemented
131#104—944no—
132#103—942no—
133#102—942no—
134#100—942no—
135C24—942no—
136C24C22⋊D4712yes—
137#41—474no—
138#41—474no—
139#41—948no—
140#41—948no—
141#41—942no—
142#41—942no—
143C2×Q8—472no—
144C2×D4—22no—
145C2×D4—22no—
146C2×D4—472no—
147C2×D4—948no—
148C2×D4—948no—
149C2×D4—944no—
150C2×D4—948no—
151C2×D4—948no—
152C2×D4—942no—
153C2×D4C4×D4712yes—
154C2×D4D18812yes—
155C22×C4—21no—
156C22×C4—21no—
157C22×C4—942no—
158C22×C4—942no—
159C22×C4C22×D4711yescharacteristic
160M16—942no—
161M16—942no—
162C2×C8—942no—
163C4⋊C4—22no—
164C22⋊C4—44no—
165C42—22no—
166C23—22no—
167C23—22no—
168C23—42no—
169C23—42no—
170C23—948no—
171C23—942no—
172C23—3762no—
173C23—3762no—
174C23(C2×D47)⋊C414yes—
175C23C2×C22⋊D4711yescharacteristic
176Q8—474no—
177Q8—942no—
178D4—24no—
179D4—24no—
180D4—474no—
181D4—9416no—
182D4—944no—
183D4—944no—
184D4—942no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—42no—
189C2×C4—41no—
190C2×C4—948no—
191C2×C4—942no—
192C2×C4—944no—
193C2×C4—944no—
194C2×C4C2×C4×D4711yescharacteristic
195C2×C4C2×D18811yescharacteristic
196C2×C4D4×D4712yes—
197C2×C4D4×D4712yes—
198C8—1882no—
199C22—21no—
200C22—21no—
201C22—24no—
202C22—44no—
203C22—42no—
204C22—42no—
205C22—82no—
206C22—944no—
207C22—3768no—
208C22—1882no—
209C22—1882no—
210C22C2×(C2×D47)⋊C411yescharacteristic
211C22#1309399211yescharacteristic
212C22#1309399211yescharacteristic
213C4—42no—
214C4—81no—
215C4—944no—
216C4C22⋊C4×D4712yes—
217C4#1309399412yes—
218C2—21no—
219C2—21no—
220C2—44no—
221C2—1884no—
222C2#1568897811yescharacteristic
223C2#1568929011yescharacteristic
224C2#1568930011yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#390C2
socleC22×C47#120
hypercenter#390D47
hypocenterC47#1792
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #390

Complements

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

NH ≅ G/Ntype
2. C2×#13093952C2semidirect
3. #15689122C2semidirect
4. C2×#13093941C2semidirect
5. C47×#390C2semidirect
8. #13094069C4semidirect
13. C2×#10625329C22semidirect
19. C2×C4⋊C4×C47C22semidirect
21. C2×C42×C47C22semidirect
80. D188C22⋊C4semidirect
84. Dic94C22⋊C4semidirect
117. #390D47semidirect
118. C47#1792semidirect
128. C2×C4⋊C4C2×D47semidirect
130. C2×C42C2×D47semidirect