Finite Group Databasebeta

← #20253631

Subgroups — #20253631

Order 6016.

418 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 418 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689728C211yesmaximal, characteristic, complemented
2#15689447C212yesmaximal, complemented
3#15689423C212yesmaximal, complemented
4#15689318C212yesmaximal, complemented
5#15689257C212yesmaximal, complemented
6#15689233C212yesmaximal, complemented
7C4×#10625334C212yesmaximal, complemented
8#15689184C211yesmaximal, characteristic, complemented
9C47×#518C211yesmaximal, characteristic, complemented
10C2×#10625334C2212yes—
11C2×#10625334C2212yes—
12#13094021C2211yescharacteristic, complemented
13#13094016C2211yescharacteristic, complemented
14#13094009—22no—
15#13093998C2212yes—
16#13093997—22no—
17C4×D188C2212yescomplemented
18#13093957C2212yescomplemented
19#13093955C2212yescomplemented
20C4⋊(C47⋊C8)C2212yescomplemented
21#13093945C2212yes—
22#13093945C2212yes—
23#13093944C2212yescomplemented
24#13093944C2212yescomplemented
25C22⋊(C47⋊C8)C2212yes—
26#13093935C2211yescharacteristic, complemented
27C4×C47⋊C8C2211yescharacteristic, complemented
28C22×D4×C47C2211yescharacteristic
29C4×D4×C47—22no—
30C4×D4×C47C2212yes—
31C4×D4×C47C2212yes—
32#117×C47C2211yescharacteristic
33#117×C47C2211yescharacteristic
34C2×C22⋊C4×C47—22no—
35C24×C47—21no—
36C2×D4×C47—24no—
37C2×D4×C47—21no—
38C2×D4×C47C2312yes—
39C22×C4×C47—22no—
40C22×C4×C47—22no—
41C22×C4×C47C2311yescharacteristic
42C2×C22⋊D47—22no—
43C2×D188—22no—
44C2×D188C2312yes—
45C2×C4×D47—22no—
46C4⋊C4×C47D412yes—
47C4⋊C4×C47C2312yes—
48C22⋊C4×C47—21no—
49C22⋊C4×C47—22no—
50C22⋊C4×C47—22no—
51C22⋊C4×C47D412yes—
52C42×C47—21no—
53C42×C47C2311yescharacteristic
54C42×C47C2311yescharacteristic
55#10625334—24no—
56#10625334—24no—
57(C2×D47)⋊C4—22no—
58(C2×D47)⋊C4—22no—
59C4⋊Dic47C2312yes—
60Dic47⋊C4—22no—
61C2×C47⋊C8C2312yes—
62C2×C47⋊C8C2312yes—
63C23×C47—24no—
64C23×C47—22no—
65C23×C47—82no—
66C23×C47C2×D411yescharacteristic
67C22×D47—22no—
68D4×C47—24no—
69D4×C47—22no—
70D4×C47#4114yes—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—82no—
74C2×C4×C47—82no—
75C2×C4×C47C2×D412yes—
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D412yes—
78C2×C4×C47C2411yescharacteristic
79C22⋊D47—82no—
80C2×Dic47—22no—
81D188—22no—
82D188—22no—
83D188—82no—
84C4×D47—82no—
85C47⋊C8—22no—
86C47⋊C8—22no—
87C22×C47—21no—
88C22×C47—24no—
89C22×C47—22no—
90C22×C47—42no—
91C22×C47—42no—
92C22×C47—84no—
93C22×C47C22×D411yescharacteristic
94C2×D47—42no—
95C2×D47—42no—
96C2×D47—42no—
97C4×C47—21no—
98C4×C47—22no—
99C4×C47—22no—
100C4×C47—42no—
101C4×C47C2×#4112yes—
102Dic47—42no—
103#3122—471nomaximal, Sylow
104C2×C47—41no—
105C2×C47—44no—
106C2×C47#52511yescharacteristic
107C2×C47#57612yes—
108D47—82no—
109#540—471no—
110#518D4711yescharacteristic, complemented
111#482—472no—
112#478—472no—
113#459—472no—
114#447—472no—
115#442—472no—
116C4×D8—472no—
117#433—471no—
118C47#312211yescharacteristic, complemented, Sylow
119C22×D4C2×D4711yescharacteristic
120C2×D8—472no—
121C2×D8—472no—
122#127—471no—
123#125—471no—
124#123—942no—
125#121—472no—
126#121—942no—
127C4×D4—22no—
128C4×D4—472no—
129C4×D4C2×D4712yes—
130C4×D4C2×D4712yes—
131#117C2×D4711yescharacteristic
132#117C2×D4711yescharacteristic
133C2×C22⋊C4—22no—
134#107—472no—
135#106—472no—
136C4⋊C8—472no—
137#102—472no—
138#102—472no—
139#102—472no—
140#102—472no—
141C22⋊C8—472no—
142#97—471no—
143C4×C8—471no—
144C24—21no—
145C2×D4—24no—
146C2×D4—21no—
147C2×D4—472no—
148C2×D4—942no—
149C2×D4—942no—
150C2×D4C22×D4712yes—
151C22×C4—22no—
152C22×C4—22no—
153C22×C4—942no—
154C22×C4C22×D4711yescharacteristic
155D8—944no—
156D8—944no—
157C2×C8—472no—
158C2×C8—472no—
159C4⋊C4—472no—
160C4⋊C4—942no—
161C4⋊C4C22⋊D4712yes—
162C4⋊C4C22×D4712yes—
163C22⋊C4—21no—
164C22⋊C4—22no—
165C22⋊C4—22no—
166C22⋊C4—942no—
167C22⋊C4—942no—
168C22⋊C4C22⋊D4712yes—
169C42—21no—
170C42C22×D4711yescharacteristic
171C42C22×D4711yescharacteristic
172C23—24no—
173C23—22no—
174C23—82no—
175C23—942no—
176C23C2×C22⋊D4711yescharacteristic
177D4—24no—
178D4—22no—
179D4—942no—
180D4—942no—
181D4—3762no—
182D4—3762no—
183D4#1062535014yes—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—82no—
188C2×C4—942no—
189C2×C4—3762no—
190C2×C4C2×C22⋊D4711yescharacteristic
191C2×C4C2×C22⋊D4712yes—
192C2×C4C2×C22⋊D4712yes—
193C2×C4C23×D4711yescharacteristic
194C8—942no—
195C8—942no—
196C22—21no—
197C22—24no—
198C22—22no—
199C22—42no—
200C22—42no—
201C22—84no—
202C22—1882no—
203C22—1882no—
204C22—1882no—
205C22C22×C22⋊D4711yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—1882no—
211C4C2×#1062535012yes—
212C2—41no—
213C2—44no—
214C2—3762no—
215C2#1568963411yescharacteristic
216C2#1568992612yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#518C2
socleC22×C47C22×D4
hypercenter#518D47
hypocenterC47#3122
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #518

Complements

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

NH ≅ G/Ntype
1. #15689728C2semidirect
2. #15689447C2semidirect
3. #15689423C2semidirect
4. #15689318C2semidirect
5. #15689257C2semidirect
6. #15689233C2semidirect
7. C4×#10625334C2semidirect
8. #15689184C2semidirect
9. C47×#518C2semidirect
12. #13094021C22semidirect
13. #13094016C22semidirect
17. C4×D188C22semidirect
18. #13093957C22semidirect
19. #13093955C22semidirect
20. C4⋊(C47⋊C8)C22semidirect
23. #13093944C22semidirect
24. #13093944C22semidirect
26. #13093935C22semidirect
27. C4×C47⋊C8C22semidirect
110. #518D47semidirect
118. C47#3122semidirect