Finite Group Databasebeta

← #20253635

Subgroups — #20253635

Order 6016.

394 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 121 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#15689597C211yesmaximal, characteristic
2#15689461C212yesmaximal, complemented
3#15689420C212yesmaximal, complemented
4#15689325C212yesmaximal, complemented
5#15689273C212yesmaximal
6#15689221C212yesmaximal, complemented
7C4×#10625336C212yesmaximal, complemented
8#15689184C211yesmaximal, characteristic, complemented
9C47×#541C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11C2×#10625336C2212yes—
12C2×#10625336C2212yes—
13C4×D188C2212yes—
14C4×D188C2212yes—
15#13093986—22no—
16#13093983C2211yescharacteristic
17C22⋊C4×D47—22no—
18#13093957C2212yescomplemented
19#13093955C2212yescomplemented
20C4⋊(C47⋊C8)C2212yescomplemented
21#13093948C2212yescomplemented
22#13093948C2212yescomplemented
23#13093944C2212yes—
24#13093944C2212yes—
25C22⋊(C47⋊C8)C2212yes—
26#13093935C2211yescharacteristic, complemented
27C4×C47⋊C8C2211yescharacteristic, complemented
28C4⋊Q8×C47C2211yescharacteristic, complemented
29#126×C47—22no—
30#125×C47—22no—
31#125×C47C2211yescharacteristic, complemented
32C22⋊Q8×C47C2212yes—
33C4×Q8×C47C2212yescomplemented
34#117×C47C2211yescharacteristic
35C23×D47—21no—
36C2×Q8×C47C2312yes—
37C22×C4×C47C2311yescharacteristic
38C2×D188—21no—
39C2×D188—24no—
40C2×D188C2312yes—
41C2×C4×D47—22no—
42C2×C4×D47—22no—
43C4⋊C4×C47—22no—
44C4⋊C4×C47—22no—
45C4⋊C4×C47—22no—
46C4⋊C4×C47—22no—
47C4⋊C4×C47D412yes—
48C4⋊C4×C47C2312yes—
49C22⋊C4×C47—22no—
50C22⋊C4×C47D412yes—
51C42×C47—22no—
52C42×C47C2311yescharacteristic
53C42×C47C2311yescharacteristic
54C22⋊Dic47—21no—
55#10625336—24no—
56#10625336—24no—
57(C2×D47)⋊C4—22no—
58(C2×D47)⋊C4—22no—
59C4⋊Dic47C2312yes—
60C4×Dic47—21no—
61C2×C47⋊C8C2312yes—
62C2×C47⋊C8C2312yes—
63C23×C47C2×D411yescharacteristic
64C22×D47—22no—
65C22×D47—24no—
66C22×D47—82no—
67Q8×C47—22no—
68Q8×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D412yes—
74C2×C4×C47C2×D412yes—
75C2×C4×C47C2411yescharacteristic
76C2×Dic47—22no—
77D188—24no—
78D188—22no—
79D188#4114yes—
80C4×D47—82no—
81C4×D47—82no—
82C47⋊C8—22no—
83C47⋊C8—22no—
84C22×C47—21no—
85C22×C47—22no—
86C22×C47C22×D411yescharacteristic
87C2×D47—24no—
88C2×D47—42no—
89C2×D47—42no—
90C2×D47—84no—
91C4×C47—21no—
92C4×C47—22no—
93C4×C47—22no—
94C4×C47—42no—
95C4×C47—42no—
96C4×C47C2×#4112yes—
97Dic47—42no—
98#3123—471nomaximal, Sylow
99C2×C47—41no—
100C2×C47#52511yescharacteristic
101C2×C47#57712yes—
102D47—44no—
103#541D4711yescharacteristic, complemented
104#518—471no—
105#485—472no—
106#478—472no—
107#461—472no—
108#450—472no—
109#440—472no—
110C4×SD16—472no—
111#433—471no—
112C47#312311yescharacteristic, complemented, Sylow
113C22×D4—471no—
114C2×SD16—472no—
115C2×SD16—472no—
116C4⋊Q8C2×D4711yescharacteristic, complemented
117#126—22no—
118#125—22no—
119#125C2×D4711yescharacteristic, complemented
120C22⋊Q8C2×D4712yes—
121C4×Q8C2×D4712yescomplemented
122C4×D4—472no—
123C4×D4—472no—
124C4×D4—942no—
125#117—471no—
126#117C2×D4711yescharacteristic
127C2×C22⋊C4—942no—
128#107—472no—
129#106—472no—
130C4⋊C8—472no—
131#103—472no—
132#103—472no—
133#102—472no—
134#102—472no—
135C22⋊C8—472no—
136#97—471no—
137C4×C8—471no—
138C24—941no—
139C2×Q8C22×D4712yes—
140C2×D4—472no—
141C2×D4—944no—
142C2×D4—941no—
143C22×C4—942no—
144C22×C4—942no—
145C22×C4C22×D4711yescharacteristic
146SD16—944no—
147SD16—944no—
148C2×C8—472no—
149C2×C8—472no—
150C4⋊C4—22no—
151C4⋊C4—22no—
152C4⋊C4—22no—
153C4⋊C4—22no—
154C4⋊C4—472no—
155C4⋊C4C22⋊D4712yes—
156C4⋊C4C22×D4712yes—
157C22⋊C4—22no—
158C22⋊C4—941no—
159C22⋊C4—942no—
160C22⋊C4—942no—
161C22⋊C4C22⋊D4712yes—
162C42—22no—
163C42—941no—
164C42C22×D4711yescharacteristic
165C42C22×D4711yescharacteristic
166C23—944no—
167C23—942no—
168C23—3762no—
169C23C2×C22⋊D4711yescharacteristic
170Q8—22no—
171Q8—22no—
172D4—474no—
173D4—944no—
174D4—942no—
175C2×C4—22no—
176C2×C4—22no—
177C2×C4—22no—
178C2×C4—942no—
179C2×C4—3762no—
180C2×C4—3762no—
181C2×C4C2×C22⋊D4712yes—
182C2×C4C2×C22⋊D4711yescharacteristic
183C2×C4C2×C22⋊D4712yes—
184C2×C4C23×D4711yescharacteristic
185C8—942no—
186C8—942no—
187C22—21no—
188C22—22no—
189C22—944no—
190C22—3764no—
191C22—1882no—
192C22—1882no—
193C22C22×C22⋊D4711yescharacteristic
194C4—21no—
195C4—22no—
196C4—22no—
197C4—42no—
198C4—42no—
199C4—1882no—
200C4#41×D4712yes—
201C2—41no—
202C2—1884no—
203C2#1568963011yescharacteristic
204C2#1568993112yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#541C2
socleC22×C47C22×D4
hypercenter#541D47
hypocenterC47#3123
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #541

Complements

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

NH ≅ G/Ntype
2. #15689461C2semidirect
3. #15689420C2semidirect
4. #15689325C2semidirect
6. #15689221C2semidirect
7. C4×#10625336C2semidirect
8. #15689184C2semidirect
9. C47×#541C2semidirect
18. #13093957C22semidirect
19. #13093955C22semidirect
20. C4⋊(C47⋊C8)C22semidirect
21. #13093948C22semidirect
22. #13093948C22semidirect
26. #13093935C22semidirect
27. C4×C47⋊C8C22semidirect
28. C4⋊Q8×C47C22semidirect
31. #125×C47C22semidirect
33. C4×Q8×C47C22semidirect
103. #541D47semidirect
112. C47#3123semidirect
116. C4⋊Q8C2×D47semidirect
119. #125C2×D47semidirect
121. C4×Q8C2×D47semidirect