Finite Group Databasebeta

← #20253054

Subgroups — #20253054

Order 6016.

484 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 484 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C2×#13094030C211yesmaximal, characteristic, complemented
2#15689701C212yesmaximal, complemented
3#15689366C214yesmaximal, complemented
4#15689361C212yesmaximal, complemented
5#15689356C212yesmaximal, complemented
6C2×#13093958C211yesmaximal, characteristic, complemented
7#15689124C212yesmaximal, complemented
8C2×#135×C47C211yesmaximal, characteristic, complemented
9C2×#10625350C2211yescharacteristic
10#13094030—24no—
11C2×#10625329C2211yescharacteristic
12C2×#10625324C2212yes—
13C2×C8×D47C2212yes—
14#13094003—22no—
15#13094000C2214yes—
16#13093998—22no—
17#13093996—24no—
18#13093995C2214yes—
19C2×C4⋊Dic47C2212yes—
20#13093958C2212yes—
21#13093958C2212yes—
22#13093948C2214yes—
23#13093945C2214yes—
24C2×#41×C47C2212yes—
25#135×C47—24no—
26C2×Q16×C47C2211yescharacteristic
27C2×SD16×C47C2212yes—
28C2×D8×C47C2211yescharacteristic
29C22×C8×C47C2211yescharacteristic
30#41×C47—24no—
31#41×C47—24no—
32C2×Q8×C47C2312yes—
33C2×D4×C47—22no—
34C2×D4×C47C2312yes—
35C22×C4×C47—22no—
36C22×C4×C47C2311yescharacteristic
37C2×C22⋊D47—24no—
38C2×C22⋊D47D412yes—
39C22×Dic47—22no—
40#10625350—22no—
41#10625350—22no—
42C2×D188D411yescharacteristic
43C2×C4×D47C2312yes—
44C2×Dic94D411yescharacteristic
45Q16×C47—22no—
46SD16×C47—24no—
47D8×C47—22no—
48C2×C8×C47D414yescomplemented
49C2×C8×C47C2311yescharacteristic
50C2×C8×C47C2311yescharacteristic
51C22⋊Dic47—24no—
52(C2×D47)⋊C4—24no—
53C4⋊Dic47—22no—
54C4⋊Dic47C2314yes—
55Dic47⋊C4—24no—
56#10625329—22no—
57C2×C47⋊C8C2312yes—
58#10625324—24no—
59C8×D47—24no—
60C23×C47—22no—
61C23×C47C2×D411yescharacteristic
62C22×D47C2×D412yes—
63Q8×C47—22no—
64Q8×C47—22no—
65D4×C47—22no—
66D4×C47—22no—
67D4×C47—44no—
68C2×C4×C47—22no—
69C2×C4×C47—44no—
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D412yes—
72C2×C4×C47#4112yes—
73C2×C4×C47C2411yescharacteristic
74C22⋊D47—24no—
75C22⋊D47—84no—
76C2×Dic47—24no—
77C2×Dic47—82no—
78C2×Dic47C2×D412yes—
79D188—22no—
80C4×D47—22no—
81C4×D47—22no—
82Dic94—22no—
83C8×C47C2×D412yes—
84C8×C47C2×D412yes—
85C47⋊C8—22no—
86C22×C47—21no—
87C22×C47—21no—
88C22×C47—42no—
89C22×C47—42no—
90C22×C47—42no—
91C22×C47#12112yes—
92C22×C47C22×D411yescharacteristic
93C2×D47—22no—
94C2×D47—22no—
95C2×D47—22no—
96C4×C47—42no—
97C4×C47#12112yes—
98C4×C47C22×D411yescharacteristic
99C4×C47C2×#4111yescharacteristic
100Dic47—22no—
101Dic47—44no—
102#3061—471nomaximal, Sylow
103C2×C47—22no—
104C2×C47—82no—
105C2×C47C2×#12111yescharacteristic
106C2×C47#57611yescharacteristic
107C2×C47#57811yescharacteristic
108D47—42no—
109C2×#135D4711yescharacteristic, complemented
110C2×#131—471no—
111#537—472no—
112#468—474no—
113#467—472no—
114#466—472no—
115C2×#107—471no—
116#417—472no—
117C47#306111yescharacteristic, complemented, Sylow
118C2×#41—471no—
119C2×#41C2×D4712yes—
120#135—24no—
121C2×Q16C2×D4711yescharacteristic
122C2×SD16C2×D4712yes—
123C2×D8C2×D4711yescharacteristic
124#131—944no—
125C2×M16—471no—
126C2×M16—472no—
127C22×C8—472no—
128C22×C8C2×D4711yescharacteristic
129C22⋊Q8—474no—
130C22⋊Q8—942no—
131#121—474no—
132#121—942no—
133#121—944no—
134C2×C4⋊C4—472no—
135#107—472no—
136#107—472no—
137#103—474no—
138#102—474no—
139#41—24no—
140#41—24no—
141#41—942no—
142#41—942no—
143C2×Q8—471no—
144C2×Q8C22×D4712yes—
145C2×D4—22no—
146C2×D4—472no—
147C2×D4—471no—
148C2×D4—944no—
149C2×D4C22×D4712yes—
150C22×C4—22no—
151C22×C4—472no—
152C22×C4—942no—
153C22×C4C22×D4711yescharacteristic
154Q16—22no—
155SD16—24no—
156D8—22no—
157M16—942no—
158M16—944no—
159C2×C8—472no—
160C2×C8—944no—
161C2×C8C22⋊D4714yescomplemented
162C2×C8C22×D4711yescharacteristic
163C2×C8C22×D4711yescharacteristic
164C4⋊C4—474no—
165C4⋊C4—944no—
166C4⋊C4—942no—
167C22⋊C4—944no—
168C22⋊C4—944no—
169C23—22no—
170C23—472no—
171C23D4×D4711yescharacteristic
172Q8—22no—
173Q8—22no—
174Q8—942no—
175D4—22no—
176D4—22no—
177D4—44no—
178D4—944no—
179D4—942no—
180D4—3764no—
181C2×C4—22no—
182C2×C4—44no—
183C2×C4—472no—
184C2×C4—942no—
185C2×C4—942no—
186C2×C4—944no—
187C2×C4—3762no—
188C2×C4D4×D4711yescharacteristic
189C2×C4#1062535212yes—
190C2×C4C2×C22⋊D4712yes—
191C2×C4C23×D4711yescharacteristic
192C8—942no—
193C8C2×C22⋊D4712yes—
194C8C2×C22⋊D4712yes—
195C22—21no—
196C22—21no—
197C22—42no—
198C22—42no—
199C22—42no—
200C22—942no—
201C22—942no—
202C22—942no—
203C22#1309399512yes—
204C22C2×D4×D4711yescharacteristic
205C4—42no—
206C4—942no—
207C4—1884no—
208C4#1309399512yes—
209C4C22×C22⋊D4711yescharacteristic
210C4C2×#1062535211yescharacteristic
211C2—22no—
212C2—82no—
213C2—1882no—
214C2C2×#1309399511yescharacteristic
215C2#1568992511yescharacteristic
216C2#1568993711yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#135×C47C2
socleC22×C47C22×D4
hypercenterC2×#135D47
hypocenterC47#3061
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#135

Complements

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

NH ≅ G/Ntype
1. C2×#13094030C2semidirect
2. #15689701C2semidirect
3. #15689366C2semidirect
4. #15689361C2semidirect
5. #15689356C2semidirect
6. C2×#13093958C2semidirect
7. #15689124C2semidirect
8. C2×#135×C47C2semidirect
48. C2×C8×C47D4semidirect
109. C2×#135D47semidirect
117. C47#3061semidirect
161. C2×C8C22⋊D47semidirect