Finite Group Databasebeta

← #20254114

Subgroups — #20254114

Order 6016.

370 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 117 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#15689652C212yesmaximal, complemented
2#15689525C211yesmaximal, characteristic, complemented
3#15689477C212yesmaximal, complemented
4#15689378C211yesmaximal, characteristic, complemented
5#15689373C211yesmaximal, characteristic
6#15689366C212yesmaximal, complemented
7#15689235C211yesmaximal, characteristic, complemented
8#15689230C211yesmaximal, characteristic, complemented
9#15689224C212yesmaximal, complemented
10C4×#10625324C211yesmaximal, characteristic, complemented
11C47×#495C211yesmaximal, characteristic, complemented
12C2×#10625324C2211yescharacteristic
13C2×#10625324C2211yescharacteristic
14#13094017—22no—
15#13094016C2212yes—
16#13094006—22no—
17#13094000C2212yes—
18#13093995C2212yes—
19Q8×Dic47C2212yes—
20D4×Dic47C2212yes—
21(C22⋊D47)⋊C4—22no—
22#13093980—22no—
23C42×D47C2211yescharacteristic
24#13093958C2212yes—
25#13093956C2211yescharacteristic
26#13093956C2211yescharacteristic
27#13093948C2212yes—
28#13093948C2212yes—
29#13093945C2212yes—
30#13093945C2212yes—
31#13093934C2211yescharacteristic
32#13093934C2211yescharacteristic
33C4×C47⋊C8C2211yescharacteristic
34C2×Q16×C47C2211yescharacteristic
35C2×SD16×C47C2212yes—
36C2×D8×C47C2211yescharacteristic
37#124×C47C2212yes—
38C4×C8×C47C2211yescharacteristic
39C2×Q8×C47C2312yes—
40C2×D4×C47C2312yes—
41C2×C22⋊D47—22no—
42C22×Dic47—22no—
43C2×C4×D47D412yes—
44C2×C4×D47C2311yescharacteristic
45Q16×C47—22no—
46SD16×C47—24no—
47D8×C47—22no—
48C2×C8×C47C2311yescharacteristic
49C2×C8×C47C2311yescharacteristic
50C22⋊C4×C47—22no—
51C22⋊C4×C47—22no—
52C42×C47C2311yescharacteristic
53C22⋊Dic47—22no—
54C22⋊Dic47—22no—
55(C2×D47)⋊C4—22no—
56C4⋊Dic47—22no—
57C4⋊Dic47C2312yes—
58C4⋊Dic47C2312yes—
59Dic47⋊C4—22no—
60Dic47⋊C4—22no—
61Dic47⋊C4—22no—
62C4×Dic47—22no—
63C4×Dic47D412yes—
64C4×Dic47C2311yescharacteristic
65C2×C47⋊C8C2311yescharacteristic
66C2×C47⋊C8C2311yescharacteristic
67#10625324—22no—
68#10625324—22no—
69C23×C47—22no—
70C22×D47C2×D411yescharacteristic
71Q8×C47—22no—
72Q8×C47—22no—
73D4×C47—22no—
74D4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47C2×D412yes—
77C2×C4×C47C2411yescharacteristic
78C22⋊D47—44no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—44no—
82C2×Dic47C2×D412yes—
83C2×Dic47C2×D411yescharacteristic
84C4×D47—21no—
85C4×D47—21no—
86C4×D47—42no—
87C8×C47#4112yes—
88C8×C47#4112yes—
89C47⋊C8—21no—
90C47⋊C8—21no—
91C22×C47—42no—
92C22×C47—42no—
93C22×C47—42no—
94C22×C47C22×D411yescharacteristic
95C2×D47—21no—
96C2×D47—22no—
97C4×C47—22no—
98C4×C47—42no—
99C4×C47C2×#4111yescharacteristic
100C4×C47C2×#4111yescharacteristic
101Dic47—21no—
102Dic47—22no—
103Dic47—42no—
104Dic47—42no—
105#3183—471nomaximal, Sylow
106C2×C47—82no—
107C2×C47#53211yescharacteristic
108C2×C47#57512yes—
109D47—41no—
110#529—472no—
111#499—471no—
112#495D4711yescharacteristic, complemented
113#488—472no—
114#470—471no—
115#469—471no—
116#468—472no—
117#442—471no—
118#441—471no—
119#440—472no—
120C4×M16—471no—
121C47#318311yescharacteristic, complemented, Sylow
122C2×Q16C2×D4711yescharacteristic
123C2×SD16C2×D4712yes—
124C2×D8C2×D4711yescharacteristic
125C2×M16—471no—
126C2×M16—471no—
127#126—942no—
128#125—472no—
129#124C2×D4712yes—
130#123—942no—
131C22⋊Q8—472no—
132#121—472no—
133C4×Q8—472no—
134C4×D4—472no—
135C4×D4—942no—
136#117—942no—
137C2×C42—471no—
138#107—472no—
139#106—471no—
140#106—471no—
141#103—472no—
142#103—472no—
143#102—472no—
144#102—472no—
145#97—471no—
146#97—471no—
147C4×C8—471no—
148C4×C8C2×D4711yescharacteristic
149C2×Q8C22×D4712yes—
150C2×D4—942no—
151C2×D4C22×D4712yes—
152C22×C4—471no—
153C22×C4—472no—
154C22×C4—942no—
155Q16—22no—
156SD16—24no—
157D8—22no—
158M16—942no—
159M16—942no—
160C2×C8—471no—
161C2×C8—471no—
162C2×C8C22×D4711yescharacteristic
163C2×C8C22×D4711yescharacteristic
164C4⋊C4—472no—
165C4⋊C4—472no—
166C4⋊C4—942no—
167C4⋊C4—942no—
168C4⋊C4—942no—
169C4⋊C4—942no—
170C22⋊C4—22no—
171C22⋊C4—22no—
172C22⋊C4—942no—
173C22⋊C4—942no—
174C22⋊C4—942no—
175C42—472no—
176C42—471no—
177C42—942no—
178C42C22×D4711yescharacteristic
179C23—22no—
180C23—471no—
181Q8—22no—
182Q8—22no—
183D4—22no—
184D4—22no—
185D4—1884no—
186C2×C4—22no—
187C2×C4—472no—
188C2×C4—471no—
189C2×C4—941no—
190C2×C4—941no—
191C2×C4—942no—
192C2×C4—942no—
193C2×C4—1882no—
194C2×C4—1884no—
195C2×C4D4×D4712yes—
196C2×C4C23×D4711yescharacteristic
197C8—941no—
198C8—941no—
199C8#1062535212yes—
200C8#1062535212yes—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—942no—
205C22—941no—
206C22C2×D4×D4711yescharacteristic
207C4—22no—
208C4—42no—
209C4—942no—
210C4—941no—
211C4—1882no—
212C4—1882no—
213C4C2×#1062535211yescharacteristic
214C4C2×#1062535211yescharacteristic
215C2—82no—
216C2—1881no—
217C2#1568967111yescharacteristic
218C2#1568992012yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#495C2
socleC22×C47C22×D4
hypercenter#495D47
hypocenterC47#3183
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #15689652C2semidirect
2. #15689525C2semidirect
3. #15689477C2semidirect
4. #15689378C2semidirect
6. #15689366C2semidirect
7. #15689235C2semidirect
8. #15689230C2semidirect
9. #15689224C2semidirect
10. C4×#10625324C2semidirect
11. C47×#495C2semidirect
112. #495D47semidirect
121. C47#3183semidirect