Finite Group Databasebeta

← #20254115

Subgroups — #20254115

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#15689655C212yesmaximal, complemented
2#15689523C211yesmaximal, characteristic, complemented
3#15689506C211yesmaximal, characteristic, complemented
4#15689476C212yesmaximal, complemented
5#15689382C211yesmaximal, characteristic, complemented
6#15689373C211yesmaximal, characteristic
7#15689368C212yesmaximal, complemented
8#15689231C211yesmaximal, characteristic, complemented
9#15689223C212yesmaximal, complemented
10#15689075C211yesmaximal, characteristic, complemented
11C47×#442C211yesmaximal, characteristic, complemented
12C2×Dic188C2211yescharacteristic
13C2×#10625335C2212yes—
14C2×#10625324C2211yescharacteristic
15C2×#10625324C2211yescharacteristic
16#13094017—22no—
17#13094015C2212yes—
18#13094011C2212yes—
19#13094006—22no—
20#13094004C2212yes—
21#13093995C2212yes—
22C4×Dic94C2212yes—
23C4×C22⋊D47—22no—
24#13093983—22no—
25C42×D47C2211yescharacteristic
26#13093957C2212yes—
27#13093956C2211yescharacteristic
28#13093949C2212yes—
29#13093947C2212yes—
30#13093945C2212yes—
31#13093935C2211yescharacteristic
32C8×Dic47C2211yescharacteristic
33C8×Dic47C2211yescharacteristic
34C2×D8×C47C2211yescharacteristic
35C4×D4×C47C2212yes—
36#106×C47C2211yescharacteristic
37#102×C47C2212yes—
38#97×C47C2211yescharacteristic
39C2×D4×C47C2312yes—
40C22×C4×C47—22no—
41C2×C22⋊D47—22no—
42C2×C4×D47D412yes—
43C2×C4×D47C2311yescharacteristic
44C2×Dic94C2312yes—
45D8×C47—22no—
46C2×C8×C47C2311yescharacteristic
47C2×C8×C47C2311yescharacteristic
48C4⋊C4×C47C2312yes—
49C22⋊C4×C47—22no—
50C42×C47C2311yescharacteristic
51C22⋊Dic47—22no—
52C22⋊Dic47—22no—
53C22⋊Dic47—22no—
54#10625335—24no—
55(C2×D47)⋊C4—22no—
56C4⋊Dic47—22no—
57C4⋊Dic47—22no—
58C4⋊Dic47C2312yes—
59Dic47⋊C4—22no—
60Dic47⋊C4—22no—
61C4×Dic47—22no—
62C4×Dic47D412yes—
63C4×Dic47C2311yescharacteristic
64C2×C47⋊C8C2311yescharacteristic
65C2×C47⋊C8C2311yescharacteristic
66Dic188—22no—
67#10625324—22no—
68#10625324—22no—
69C23×C47—22no—
70C22×D47C2×D411yescharacteristic
71D4×C47—22no—
72D4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—44no—
75C2×C4×C47C2×D412yes—
76C2×C4×C47C2411yescharacteristic
77C22⋊D47—44no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47C2×D411yescharacteristic
81C2×Dic47C2×D412yes—
82C4×D47—21no—
83C4×D47—21no—
84C4×D47—42no—
85Dic94—22no—
86Dic94—22no—
87C8×C47—21no—
88C8×C47#4112yes—
89C47⋊C8—21no—
90C47⋊C8#4112yes—
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#495—471no—
113#488—472no—
114#470—471no—
115#469—471no—
116#468—472no—
117#442D4711yescharacteristic, complemented
118#441—471no—
119#440—472no—
120C4×M16—471no—
121C47#318311yescharacteristic, complemented, Sylow
122C2×Q16—471no—
123C2×SD16—472no—
124C2×D8C2×D4711yescharacteristic
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×Q8—472no—
134C4×D4—942no—
135C4×D4C2×D4712yes—
136#117—942no—
137C2×C42—471no—
138#107—472no—
139#106—471no—
140#106C2×D4711yescharacteristic
141#103—472no—
142#103—472no—
143#102—472no—
144#102C2×D4712yes—
145#97—471no—
146#97C2×D4711yescharacteristic
147C4×C8—471no—
148C4×C8—471no—
149C2×Q8—472no—
150C2×D4—942no—
151C2×D4C22×D4712yes—
152C22×C4—22no—
153C22×C4—471no—
154C22×C4—472no—
155Q16—942no—
156SD16—944no—
157D8—22no—
158M16—942no—
159M16—942no—
160C2×C8—471no—
161C2×C8—471no—
162C2×C8C22×D4711yescharacteristic
163C2×C8C22×D4711yescharacteristic
164C4⋊C4—472no—
165C4⋊C4—942no—
166C4⋊C4—942no—
167C4⋊C4—942no—
168C4⋊C4—942no—
169C4⋊C4C22×D4712yes—
170C22⋊C4—22no—
171C22⋊C4—942no—
172C22⋊C4—942no—
173C22⋊C4—942no—
174C22⋊C4—942no—
175C42—472no—
176C42—471no—
177C42—942no—
178C42C22×D4711yescharacteristic
179C23—22no—
180C23—471no—
181Q8—942no—
182Q8—942no—
183D4—22no—
184D4—22no—
185D4—1884no—
186C2×C4—22no—
187C2×C4—44no—
188C2×C4—472no—
189C2×C4—471no—
190C2×C4—941no—
191C2×C4—941no—
192C2×C4—942no—
193C2×C4—942no—
194C2×C4—1882no—
195C2×C4D4×D4712yes—
196C2×C4C23×D4711yescharacteristic
197C8—21no—
198C8—472no—
199C8—941no—
200C8#1062535012yes—
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—
213C4#41×D4711yescharacteristic
214C4C2×#1062535011yescharacteristic
215C2—82no—
216C2—1881no—
217C2#1568967011yescharacteristic
218C2#1568991912yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#442C2
socleC22×C47C22×D4
hypercenter#442D47
hypocenterC47#3183
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #15689655C2semidirect
2. #15689523C2semidirect
3. #15689506C2semidirect
4. #15689476C2semidirect
5. #15689382C2semidirect
7. #15689368C2semidirect
8. #15689231C2semidirect
9. #15689223C2semidirect
10. #15689075C2semidirect
11. C47×#442C2semidirect
117. #442D47semidirect
121. C47#3183semidirect