Finite Group Databasebeta

← #20253051

Subgroups — #20253051

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×#13094046C211yesmaximal, characteristic, complemented
2C2×#13094030C211yesmaximal, characteristic, complemented
3#15689704C212yesmaximal, complemented
4#15689382C212yesmaximal, complemented
5#15689377C212yesmaximal, complemented
6#15689353C214yesmaximal, complemented
7#15689122C212yesmaximal, complemented
8C2×#106×C47C211yesmaximal, characteristic, complemented
9C2×#10625350C2211yescharacteristic
10C2×#10625350C2212yes—
11#13094046—24no—
12C2×Dic188C2211yescharacteristic
13C2×#10625325C2212yes—
14C2×D376C2211yescharacteristic
15#13094030—24no—
16C2×#10625329C2211yescharacteristic
17C2×#10625324C2212yes—
18C2×C8×D47C2212yes—
19#13094004—22no—
20#13094004C2214yes—
21#13093999—22no—
22#13093999C2214yes—
23#13093998—24no—
24#13093947C2214yes—
25#13093944C2214yes—
26C22×C8×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2212yes—
28#106×C47C2212yes—
29#106×C47C2212yes—
30C22×C4×C47—22no—
31C22×C4×C47C2311yescharacteristic
32C2×C22⋊D47—22no—
33C2×C22⋊D47D412yes—
34#10625350—22no—
35#10625350—22no—
36#10625350—24no—
37#10625350—24no—
38C2×D188—24no—
39C2×D188D411yescharacteristic
40C2×D188C2312yes—
41C2×C4×D47—22no—
42C2×C4×D47C2312yes—
43C2×Dic94D411yescharacteristic
44C2×Dic94C2312yes—
45C2×C8×C47D414yescomplemented
46C2×C8×C47C2311yescharacteristic
47C2×C8×C47C2311yescharacteristic
48C4⋊C4×C47—22no—
49C4⋊C4×C47C2314yes—
50(C2×D47)⋊C4—24no—
51(C2×D47)⋊C4—24no—
52C4⋊Dic47—24no—
53#10625329—22no—
54C2×C47⋊C8C2312yes—
55Dic188—22no—
56D376—22no—
57#10625325—24no—
58#10625324—24no—
59C8×D47—24no—
60C23×C47C2×D411yescharacteristic
61C22×D47—22no—
62C22×D47C2×D412yes—
63C2×C4×C47—24no—
64C2×C4×C47—82no—
65C2×C4×C47C2×D412yes—
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47#4112yes—
68C2×C4×C47C2411yescharacteristic
69C22⋊D47—24no—
70C22⋊D47—44no—
71C2×Dic47—22no—
72C2×Dic47C2×D412yes—
73D188—22no—
74D188—22no—
75D188—22no—
76D188—84no—
77C4×D47—22no—
78C4×D47—22no—
79C4×D47—44no—
80Dic94—22no—
81Dic94—22no—
82Dic94—22no—
83C8×C47C2×D412yes—
84C8×C47C2×D412yes—
85C47⋊C8—22no—
86C22×C47—22no—
87C22×C47#12112yes—
88C22×C47C22×D411yescharacteristic
89C2×D47—22no—
90C2×D47—24no—
91C2×D47—42no—
92C2×D47—42no—
93C2×D47—42no—
94C4×C47—44no—
95C4×C47#12112yes—
96C4×C47C22×D411yescharacteristic
97C4×C47C2×#4111yescharacteristic
98Dic47—22no—
99Dic47—42no—
100#3060—471nomaximal, Sylow
101C2×C47—22no—
102C2×C47C2×#12111yescharacteristic
103C2×C47#57712yes—
104D47—42no—
105D47—82no—
106C2×#135—471no—
107C2×#131—471no—
108#537—472no—
109#470—472no—
110#469—472no—
111#465—474no—
112C2×#106D4711yescharacteristic, complemented
113#417—472no—
114C47#306011yescharacteristic, complemented, Sylow
115C2×#41—471no—
116C2×#41—472no—
117#135—944no—
118C2×Q16—471no—
119C2×SD16—472no—
120C2×D8—471no—
121#131—944no—
122C2×M16—471no—
123C2×M16—472no—
124C22×C8—472no—
125C22×C8C2×D4711yescharacteristic
126C22⋊Q8—474no—
127C22⋊Q8—942no—
128#121—474no—
129#121—942no—
130#121—944no—
131C2×C4⋊C4C2×D4712yes—
132#106C2×D4712yes—
133#106C2×D4712yes—
134#103—474no—
135#102—474no—
136#41—942no—
137#41—942no—
138#41—944no—
139#41—944no—
140C2×Q8—471no—
141C2×Q8—472no—
142C2×D4—472no—
143C2×D4—471no—
144C2×D4—472no—
145C2×D4—944no—
146C2×D4—942no—
147C22×C4—22no—
148C22×C4—472no—
149C22×C4—942no—
150C22×C4C22×D4711yescharacteristic
151Q16—942no—
152SD16—944no—
153D8—942no—
154M16—942no—
155M16—944no—
156C2×C8—472no—
157C2×C8—944no—
158C2×C8D18814yescomplemented
159C2×C8C22×D4711yescharacteristic
160C2×C8C22×D4711yescharacteristic
161C4⋊C4—22no—
162C4⋊C4—944no—
163C4⋊C4C22×D4714yes—
164C22⋊C4—944no—
165C22⋊C4—944no—
166C23—472no—
167C23—942no—
168C23D4×D4711yescharacteristic
169Q8—942no—
170Q8—942no—
171Q8—942no—
172D4—944no—
173D4—942no—
174D4—942no—
175D4—942no—
176D4—3764no—
177D4—1884no—
178C2×C4—24no—
179C2×C4—82no—
180C2×C4—472no—
181C2×C4—942no—
182C2×C4—942no—
183C2×C4—942no—
184C2×C4—1884no—
185C2×C4C2×D18812yes—
186C2×C4D4×D4711yescharacteristic
187C2×C4#1062535412yes—
188C2×C4C23×D4711yescharacteristic
189C8—942no—
190C8C2×D18812yes—
191C8C2×D18812yes—
192C22—22no—
193C22—942no—
194C22—944no—
195C22—1882no—
196C22—1882no—
197C22—1882no—
198C22#1309399912yes—
199C22C2×D4×D4711yescharacteristic
200C4—44no—
201C4—942no—
202C4—1882no—
203C4#1309399912yes—
204C4C22×D18811yescharacteristic
205C4C2×#1062535411yescharacteristic
206C2—22no—
207C2—3762no—
208C2—1882no—
209C2C2×#1309399911yescharacteristic
210C2#1568992912yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC2×#106×C47C2
socleC22×C47C22×D4
hypercenterC2×#106D47
hypocenterC47#3060
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#106

Complements

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

NH ≅ G/Ntype
1. C2×#13094046C2semidirect
2. C2×#13094030C2semidirect
3. #15689704C2semidirect
4. #15689382C2semidirect
5. #15689377C2semidirect
6. #15689353C2semidirect
7. #15689122C2semidirect
8. C2×#106×C47C2semidirect
45. C2×C8×C47D4semidirect
112. C2×#106D47semidirect
114. C47#3060semidirect
158. C2×C8D188semidirect