Finite Group Databasebeta

← #20254120

Subgroups — #20254120

Order 6016.

370 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 115 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#15689660C212yesmaximal, complemented
2#15689523C211yesmaximal, characteristic, complemented
3#15689508C211yesmaximal, characteristic, complemented
4#15689479C212yesmaximal, complemented
5#15689378C211yesmaximal, characteristic, complemented
6#15689377C211yesmaximal, characteristic
7#15689372C212yesmaximal, complemented
8#15689236C211yesmaximal, characteristic, complemented
9#15689221C212yesmaximal, complemented
10#15689075C211yesmaximal, characteristic, complemented
11C47×#441C211yesmaximal, characteristic, complemented
12C2×#10625336C2212yes—
13C2×D376C2211yescharacteristic
14C2×#10625324C2211yescharacteristic
15C2×#10625324C2211yescharacteristic
16#13094019—22no—
17#13094015C2212yes—
18#13094013C2212yes—
19#13094009—22no—
20#13094000C2212yes—
21#13093999C2212yes—
22C4×D188—22no—
23C4×D188C2212yes—
24#13093981—22no—
25C42×D47C2211yescharacteristic
26#13093957C2212yes—
27#13093956C2211yescharacteristic
28#13093948C2212yes—
29#13093946C2212yes—
30#13093944C2212yes—
31#13093935C2211yescharacteristic
32C8×Dic47C2211yescharacteristic
33C8×Dic47C2211yescharacteristic
34C2×Q16×C47C2211yescharacteristic
35C4×Q8×C47C2212yes—
36#106×C47C2211yescharacteristic
37#103×C47C2212yes—
38#97×C47C2211yescharacteristic
39C2×Q8×C47C2312yes—
40C2×D188—22no—
41C2×D188C2312yes—
42C2×C4×D47—22no—
43C2×C4×D47D412yes—
44C2×C4×D47C2311yescharacteristic
45Q16×C47—22no—
46C2×C8×C47C2311yescharacteristic
47C2×C8×C47C2311yescharacteristic
48C4⋊C4×C47—22no—
49C4⋊C4×C47C2312yes—
50C42×C47—22no—
51C42×C47C2311yescharacteristic
52#10625336—24no—
53(C2×D47)⋊C4—22no—
54(C2×D47)⋊C4—22no—
55(C2×D47)⋊C4—22no—
56(C2×D47)⋊C4—22no—
57(C2×D47)⋊C4—22no—
58C4⋊Dic47—22no—
59C4⋊Dic47C2312yes—
60Dic47⋊C4—22no—
61Dic47⋊C4—22no—
62C4×Dic47D412yes—
63C4×Dic47C2311yescharacteristic
64C2×C47⋊C8C2311yescharacteristic
65C2×C47⋊C8C2311yescharacteristic
66D376—22no—
67#10625324—22no—
68#10625324—22no—
69C22×D47—22no—
70C22×D47C2×D411yescharacteristic
71Q8×C47—22no—
72Q8×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47C2×D412yes—
76C2×C4×C47C2411yescharacteristic
77C2×Dic47—22no—
78C2×Dic47C2×D411yescharacteristic
79C2×Dic47C2×D412yes—
80D188—22no—
81D188—22no—
82D188—44no—
83C4×D47—21no—
84C4×D47—21no—
85C4×D47—42no—
86C4×D47—44no—
87C8×C47—21no—
88C8×C47#4112yes—
89C47⋊C8—21no—
90C47⋊C8#4112yes—
91C22×C47C22×D411yescharacteristic
92C2×D47—21no—
93C2×D47—22no—
94C2×D47—42no—
95C2×D47—42no—
96C2×D47—42no—
97C4×C47—22no—
98C4×C47—42no—
99C4×C47—42no—
100C4×C47C2×#4111yescharacteristic
101C4×C47C2×#4111yescharacteristic
102Dic47—21no—
103Dic47—22no—
104Dic47—42no—
105#3183—471nomaximal, Sylow
106C2×C47#53211yescharacteristic
107C2×C47#57512yes—
108D47—41no—
109D47—82no—
110#529—472no—
111#499—471no—
112#495—471no—
113#488—472no—
114#470—471no—
115#469—471no—
116#468—472no—
117#442—471no—
118#441D4711yescharacteristic, complemented
119#440—472no—
120C4×M16—471no—
121C47#318311yescharacteristic, complemented, Sylow
122C2×Q16C2×D4711yescharacteristic
123C2×SD16—472no—
124C2×D8—471no—
125C2×M16—471no—
126C2×M16—471no—
127#126—942no—
128#125—472no—
129#124—472no—
130#123—942no—
131C22⋊Q8—472no—
132#121—472no—
133C4×Q8C2×D4712yes—
134C4×D4—472no—
135C4×D4—942no—
136#117—942no—
137C2×C42—471no—
138#107—472no—
139#106—471no—
140#106C2×D4711yescharacteristic
141#103—472no—
142#103C2×D4712yes—
143#102—472no—
144#102—472no—
145#97—471no—
146#97C2×D4711yescharacteristic
147C4×C8—471no—
148C4×C8—471no—
149C2×Q8C22×D4712yes—
150C2×D4—472no—
151C2×D4—942no—
152C22×C4—471no—
153C22×C4—472no—
154C22×C4—942no—
155Q16—22no—
156SD16—944no—
157D8—942no—
158M16—942no—
159M16—942no—
160C2×C8—471no—
161C2×C8—471no—
162C2×C8C22×D4711yescharacteristic
163C2×C8C22×D4711yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—472no—
166C4⋊C4—942no—
167C4⋊C4—942no—
168C4⋊C4—942no—
169C4⋊C4C22×D4712yes—
170C22⋊C4—942no—
171C22⋊C4—942no—
172C22⋊C4—942no—
173C22⋊C4—942no—
174C22⋊C4—942no—
175C42—22no—
176C42—472no—
177C42—471no—
178C42C22×D4711yescharacteristic
179C23—471no—
180C23—942no—
181Q8—22no—
182Q8—22no—
183D4—942no—
184D4—942no—
185D4—1884no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—472no—
189C2×C4—471no—
190C2×C4—941no—
191C2×C4—941no—
192C2×C4—942no—
193C2×C4—1882no—
194C2×C4—1884no—
195C2×C4D4×D4712yes—
196C2×C4C23×D4711yescharacteristic
197C8—21no—
198C8—472no—
199C8—941no—
200C8#1062535012yes—
201C22—942no—
202C22—941no—
203C22—1882no—
204C22—1882no—
205C22—1882no—
206C22C2×D4×D4711yescharacteristic
207C4—22no—
208C4—42no—
209C4—42no—
210C4—942no—
211C4—941no—
212C4—1882no—
213C4#41×D4711yescharacteristic
214C4C2×#1062535011yescharacteristic
215C2—3762no—
216C2—1881no—
217C2#1568967011yescharacteristic
218C2#1568992212yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#441C2
socleC22×C47C22×D4
hypercenter#441D47
hypocenterC47#3183
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #441

Complements

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

NH ≅ G/Ntype
1. #15689660C2semidirect
2. #15689523C2semidirect
3. #15689508C2semidirect
4. #15689479C2semidirect
5. #15689378C2semidirect
7. #15689372C2semidirect
8. #15689236C2semidirect
9. #15689221C2semidirect
10. #15689075C2semidirect
11. C47×#441C2semidirect
118. #441D47semidirect
121. C47#3183semidirect