Finite Group Databasebeta

← #20254015

Subgroups — #20254015

Order 6016.

362 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 113 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#15689736C211yesmaximal, characteristic, complemented
2#15689727C211yesmaximal, characteristic
3#15689522C211yesmaximal, characteristic, complemented
4#15689495C211yesmaximal, characteristic, complemented
5#15689492C211yesmaximal, characteristic, complemented
6#15689368C212yesmaximal, complemented
7#15689351C212yesmaximal, complemented
8#15689220C212yesmaximal, complemented
9#15689214C212yesmaximal, complemented
10#15689080C211yesmaximal, characteristic, complemented
11C47×#490C211yesmaximal, characteristic, complemented
12C2×#10625335C2212yes—
13C2×#10625335C2212yes—
14C2×#10625324C2211yescharacteristic
15C2×C8×D47C2211yescharacteristic
16#13094024C2211yescharacteristic
17#13094019—22no—
18#13094016C2211yescharacteristic
19#13094015—22no—
20#13094005—22no—
21#13094004C2212yes—
22#13093996—22no—
23#13093995C2212yes—
24#13093989C2212yes—
25D4×Dic47C2212yes—
26#13093981C2211yescharacteristic
27#13093957C2212yes—
28#13093955C2212yes—
29#13093949C2212yes—
30#13093949C2212yes—
31#13093934C2211yescharacteristic
32C4×C47⋊C8C2211yescharacteristic
33C8×Dic47C2211yescharacteristic
34#127×C47C2211yescharacteristic
35#125×C47C2211yescharacteristic
36#102×C47C2212yes—
37#102×C47C2212yes—
38#97×C47C2211yescharacteristic
39C2×D4×C47—22no—
40C2×D4×C47C2312yes—
41C2×C22⋊D47—22no—
42C22×Dic47—22no—
43C2×C4×D47C2311yescharacteristic
44C2×Dic94C2312yes—
45C2×C8×C47C2311yescharacteristic
46C2×C8×C47C2311yescharacteristic
47C4⋊C4×C47—22no—
48C4⋊C4×C47C2312yes—
49C42×C47C2311yescharacteristic
50C22⋊Dic47—22no—
51C22⋊Dic47—22no—
52#10625335—24no—
53#10625335—24no—
54(C2×D47)⋊C4—22no—
55(C2×D47)⋊C4D412yes—
56C4⋊Dic47—22no—
57C4⋊Dic47—22no—
58C4⋊Dic47C2312yes—
59Dic47⋊C4—22no—
60Dic47⋊C4—22no—
61Dic47⋊C4D412yes—
62C4×Dic47—22no—
63C4×Dic47C2311yescharacteristic
64C2×C47⋊C8C2311yescharacteristic
65C2×C47⋊C8C2311yescharacteristic
66#10625324—22no—
67C8×D47—22no—
68C23×C47—22no—
69C22×D47C2×D411yescharacteristic
70D4×C47—22no—
71D4×C47—22no—
72D4×C47—82no—
73C2×C4×C47—22no—
74C2×C4×C47C2×D412yes—
75C2×C4×C47C2411yescharacteristic
76C22⋊D47—82no—
77C2×Dic47—22no—
78C2×Dic47—22no—
79C2×Dic47—82no—
80C2×Dic47C2×D412yes—
81C2×Dic47C2×D411yescharacteristic
82C4×D47—21no—
83C4×D47—21no—
84Dic94—22no—
85Dic94—22no—
86C8×C47—21no—
87C8×C47—21no—
88C47⋊C8#4112yes—
89C47⋊C8#4112yes—
90C22×C47—42no—
91C22×C47—42no—
92C22×C47—42no—
93C22×C47C22×D411yescharacteristic
94C2×D47—21no—
95C2×D47—22no—
96C4×C47—22no—
97C4×C47—42no—
98C4×C47C2×#4111yescharacteristic
99C4×C47C2×#4111yescharacteristic
100Dic47—21no—
101Dic47—22no—
102Dic47—42no—
103Dic47—42no—
104#3174—471nomaximal, Sylow
105C2×C47—82no—
106C2×C47#53211yescharacteristic
107C2×C47#57712yes—
108D47—41no—
109#541—471no—
110#540—471no—
111#499—471no—
112#492—471no—
113#491—471no—
114#490D4711yescharacteristic, complemented
115#468—472no—
116#465—472no—
117#440—472no—
118C4×SD16—472no—
119#405—471no—
120C47#317411yescharacteristic, complemented, Sylow
121C2×SD16—472no—
122C2×SD16—472no—
123C2×M16—471no—
124C22×C8—471no—
125C4⋊Q8—471no—
126#127C2×D4711yescharacteristic
127#126—942no—
128#125—471no—
129#125—942no—
130#125C2×D4711yescharacteristic
131#123—942no—
132C22⋊Q8—472no—
133#121—472no—
134#121—942no—
135C4×Q8—472no—
136C4×D4—472no—
137#117—471no—
138#107—472no—
139#106—472no—
140#103—472no—
141#103—472no—
142#102C2×D4712yes—
143#102C2×D4712yes—
144#97—471no—
145#97C2×D4711yescharacteristic
146C4×C8—471no—
147C4×C8—471no—
148C2×Q8—472no—
149C2×D4—22no—
150C2×D4—942no—
151C2×D4C22×D4712yes—
152C22×C4—471no—
153C22×C4—942no—
154SD16—944no—
155SD16—944no—
156M16—942no—
157C2×C8—471no—
158C2×C8—471no—
159C2×C8—942no—
160C2×C8C22×D4711yescharacteristic
161C2×C8C22×D4711yescharacteristic
162C4⋊C4—22no—
163C4⋊C4—472no—
164C4⋊C4—472no—
165C4⋊C4—942no—
166C4⋊C4—942no—
167C4⋊C4—942no—
168C4⋊C4—942no—
169C4⋊C4C22×D4712yes—
170C22⋊C4—472no—
171C22⋊C4—942no—
172C22⋊C4—942no—
173C22⋊C4—942no—
174C42—471no—
175C42—942no—
176C42C22×D4711yescharacteristic
177C23—22no—
178C23—471no—
179Q8—942no—
180Q8—942no—
181D4—22no—
182D4—22no—
183D4—82no—
184D4—3762no—
185C2×C4—22no—
186C2×C4—472no—
187C2×C4—471no—
188C2×C4—941no—
189C2×C4—941no—
190C2×C4—942no—
191C2×C4—942no—
192C2×C4—3762no—
193C2×C4D4×D4712yes—
194C2×C4C23×D4711yescharacteristic
195C8—21no—
196C8—21no—
197C8—472no—
198C8—472no—
199C22—42no—
200C22—42no—
201C22—42no—
202C22—941no—
203C22—942no—
204C22C2×D4×D4711yescharacteristic
205C4—22no—
206C4—42no—
207C4—941no—
208C4—942no—
209C4—1882no—
210C4—1882no—
211C4#41×D4711yescharacteristic
212C4#41×D4711yescharacteristic
213C2—82no—
214C2—1881no—
215C2#1568967211yescharacteristic
216C2#1568993312yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#490C2
socleC22×C47C22×D4
hypercenter#490D47
hypocenterC47#3174
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #15689736C2semidirect
3. #15689522C2semidirect
4. #15689495C2semidirect
5. #15689492C2semidirect
6. #15689368C2semidirect
7. #15689351C2semidirect
8. #15689220C2semidirect
9. #15689214C2semidirect
10. #15689080C2semidirect
11. C47×#490C2semidirect
114. #490D47semidirect
120. C47#3174semidirect