Finite Group Databasebeta

← #20253626

Subgroups — #20253626

Order 6016.

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

normal subgroups only

This group has 418 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, complemented
2#15689444C212yesmaximal, complemented
3#15689420C212yesmaximal, complemented
4#15689315C212yesmaximal, complemented
5#15689256C212yesmaximal, complemented
6#15689233C212yesmaximal, complemented
7C4×#10625334C212yesmaximal, complemented
8#15689184C211yesmaximal, characteristic, complemented
9C47×#540C211yesmaximal, characteristic, complemented
10C22×D188C2211yescharacteristic
11C2×#10625334C2212yes—
12C2×#10625334C2212yes—
13C4×D188C2212yes—
14C4×D188C2212yes—
15#13093986—22no—
16#13093983C2211yescharacteristic
17C22⋊C4×D47—22no—
18#13093957C2212yescomplemented
19#13093955C2212yescomplemented
20C4⋊(C47⋊C8)C2212yescomplemented
21#13093945C2212yescomplemented
22#13093945C2212yescomplemented
23#13093944C2212yes—
24#13093944C2212yes—
25C22⋊(C47⋊C8)C2212yes—
26#13093935C2211yescharacteristic, complemented
27C4×C47⋊C8C2211yescharacteristic, complemented
28#127×C47C2211yescharacteristic, complemented
29#125×C47C2211yescharacteristic, complemented
30#123×C47—22no—
31#121×C47—22no—
32#121×C47C2212yes—
33C4×D4×C47C2212yescomplemented
34#117×C47C2211yescharacteristic
35C23×D47—21no—
36C2×D4×C47—22no—
37C2×D4×C47—22no—
38C2×D4×C47C2312yes—
39C22×C4×C47—22no—
40C22×C4×C47C2311yescharacteristic
41C2×D188—21no—
42C2×D188—24no—
43C2×D188C2312yes—
44C2×C4×D47—22no—
45C2×C4×D47—22no—
46C4⋊C4×C47—22no—
47C4⋊C4×C47D412yes—
48C4⋊C4×C47C2312yes—
49C22⋊C4×C47—22no—
50C22⋊C4×C47—22no—
51C22⋊C4×C47D412yes—
52C42×C47C2311yescharacteristic
53C42×C47C2311yescharacteristic
54C22⋊Dic47—21no—
55#10625334—24no—
56#10625334—24no—
57(C2×D47)⋊C4—22no—
58(C2×D47)⋊C4—22no—
59C4⋊Dic47C2312yes—
60C4×Dic47—21no—
61C2×C47⋊C8C2312yes—
62C2×C47⋊C8C2312yes—
63C23×C47—22no—
64C23×C47C2×D411yescharacteristic
65C22×D47—22no—
66C22×D47—24no—
67C22×D47—82no—
68D4×C47—22no—
69D4×C47—22no—
70D4×C47—82no—
71D4×C47—82no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—82no—
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×D412yes—
77C2×C4×C47C2×D412yes—
78C2×C4×C47C2411yescharacteristic
79C2×Dic47—22no—
80D188—24no—
81D188—22no—
82D188#4114yes—
83C4×D47—82no—
84C4×D47—82no—
85C47⋊C8—22no—
86C47⋊C8—22no—
87C22×C47—21no—
88C22×C47—22no—
89C22×C47—42no—
90C22×C47—42no—
91C22×C47—42no—
92C22×C47C22×D411yescharacteristic
93C2×D47—24no—
94C2×D47—42no—
95C2×D47—42no—
96C2×D47—84no—
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—82no—
106C2×C47#52511yescharacteristic
107C2×C47#57612yes—
108D47—44no—
109#540D4711yescharacteristic, complemented
110#518—471no—
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×D4—471no—
120C2×D8—472no—
121C2×D8—472no—
122#127C2×D4711yescharacteristic, complemented
123#125C2×D4711yescharacteristic, complemented
124#123—22no—
125#121—22no—
126#121C2×D4712yes—
127C4×D4—472no—
128C4×D4—472no—
129C4×D4—942no—
130C4×D4C2×D4712yescomplemented
131#117—471no—
132#117C2×D4711yescharacteristic
133C2×C22⋊C4—942no—
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—941no—
145C2×D4—22no—
146C2×D4—22no—
147C2×D4—472no—
148C2×D4—944no—
149C2×D4—941no—
150C2×D4C22×D4712yes—
151C22×C4—22no—
152C22×C4—942no—
153C22×C4—942no—
154C22×C4C22×D4711yescharacteristic
155D8—944no—
156D8—944no—
157C2×C8—472no—
158C2×C8—472no—
159C4⋊C4—22no—
160C4⋊C4—472no—
161C4⋊C4C22⋊D4712yes—
162C4⋊C4C22×D4712yes—
163C22⋊C4—22no—
164C22⋊C4—22no—
165C22⋊C4—941no—
166C22⋊C4—942no—
167C22⋊C4—942no—
168C22⋊C4C22⋊D4712yes—
169C42—941no—
170C42C22×D4711yescharacteristic
171C42C22×D4711yescharacteristic
172C23—22no—
173C23—944no—
174C23—942no—
175C23—3762no—
176C23C2×C22⋊D4711yescharacteristic
177D4—22no—
178D4—22no—
179D4—82no—
180D4—82no—
181D4—474no—
182D4—944no—
183D4—942no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—82no—
187C2×C4—942no—
188C2×C4—3762no—
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—22no—
198C22—42no—
199C22—42no—
200C22—42no—
201C22—944no—
202C22—3764no—
203C22—1882no—
204C22—1882no—
205C22C22×C22⋊D4711yescharacteristic
206C4—21no—
207C4—22no—
208C4—22no—
209C4—42no—
210C4—1882no—
211C4#41×D4712yes—
212C2—41no—
213C2—82no—
214C2—1884no—
215C2#1568963011yescharacteristic
216C2#1568992612yes—
subgroupG/H
centerC22C22×C22⋊D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#540C2
socleC22×C47C22×D4
hypercenter#540D47
hypocenterC47#3122
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #540

Complements

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

NH ≅ G/Ntype
1. #15689597C2semidirect
2. #15689444C2semidirect
3. #15689420C2semidirect
4. #15689315C2semidirect
5. #15689256C2semidirect
6. #15689233C2semidirect
7. C4×#10625334C2semidirect
8. #15689184C2semidirect
9. C47×#540C2semidirect
18. #13093957C22semidirect
19. #13093955C22semidirect
20. C4⋊(C47⋊C8)C22semidirect
21. #13093945C22semidirect
22. #13093945C22semidirect
26. #13093935C22semidirect
27. C4×C47⋊C8C22semidirect
28. #127×C47C22semidirect
29. #125×C47C22semidirect
33. C4×D4×C47C22semidirect
109. #540D47semidirect
118. C47#3122semidirect
122. #127C2×D47semidirect
123. #125C2×D47semidirect
130. C4×D4C2×D47semidirect