Finite Group Databasebeta

← #20243346

Subgroups — #20243346

Order 6016.

552 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 101 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×#13094072C211yesmaximal, characteristic
2C2×#13093952C212yesmaximal, complemented
3#15689122C212yesmaximal, complemented
4C2×#13093943C211yesmaximal, characteristic, complemented
5C47×#391C211yesmaximal, characteristic, complemented
6#13094072—22no—
7#13094072—24no—
8#13094072C414yescomplemented
9C2×#10625354—22no—
10C2×#10625350—22no—
11C2×#10625350C2212yes—
12C2×Q8×D47—22no—
13C2×#10625329C2212yes—
14#13093952—24no—
15#13093947—22no—
16#13093944—22no—
17#13093943—22no—
18C22×Q8×C47C2211yescharacteristic
19C2×C4⋊C4×C47C2211yescharacteristic
20C2×C42×C47C2211yescharacteristic
21#95×C47—22no—
22C2×Q8×C47—22no—
23C2×Q8×C47—22no—
24C2×Q8×C47C2×C412yes—
25C2×Q8×C47D412yes—
26C22×C4×C47—21no—
27C22×C4×C47—21no—
28C22×C4×C47D412yes—
29C22×C4×C47C2311yescharacteristic
30C2×C22⋊D47—22no—
31#10625354—28no—
32#10625354—28no—
33Q8×D47—28no—
34Q8×D47—28no—
35#10625350—28no—
36#10625350—28no—
37#10625350—22no—
38#10625350—22no—
39#10625350C2×C414yes—
40#10625350D414yes—
41C2×D188—22no—
42C2×D188D412yes—
43C2×C4×D47—24no—
44C2×C4×D47—22no—
45C2×Dic94—22no—
46C2×Dic94D412yes—
47C4⋊C4×C47—22no—
48C42×C47—22no—
49#10625329—22no—
50#10625329—22no—
51C2×C47⋊C8—22no—
52C23×C47C2×D411yescharacteristic
53C22×D47—22no—
54Q8×C47—24no—
55Q8×C47—24no—
56C2×C4×C47—22no—
57C2×C4×C47—22no—
58C2×C4×C47—22no—
59C2×C4×C47—41no—
60C2×C4×C47—41no—
61C2×C4×C47—42no—
62C2×C4×C47—41no—
63C2×C4×C47C22⋊C414yes—
64C2×C4×C47C22×C411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D412yes—
67C2×C4×C47C2×D412yes—
68C22⋊D47—24no—
69C22⋊D47—24no—
70C2×Dic47—22no—
71D188—28no—
72D188—22no—
73D188C22⋊C414yes—
74C4×D47—216no—
75C4×D47—24no—
76C4×D47—24no—
77Dic94—28no—
78Dic94—22no—
79Dic94C22⋊C414yes—
80C47⋊C8—42no—
81C22×C47—21no—
82C22×C47—21no—
83C22×C47C2×C22⋊C411yescharacteristic
84C22×C47#12011yescharacteristic
85C22×C47#12011yescharacteristic
86C2×D47—24no—
87C2×D47—42no—
88C2×D47—42no—
89C4×C47—24no—
90C4×C47—42no—
91C4×C47—81no—
92C4×C47C2×C22⋊C412yes—
93C4×C47#12012yes—
94Dic47—24no—
95#1793—471nomaximal, Sylow
96C2×C47—21no—
97C2×C47—21no—
98C2×C47#37911yescharacteristic
99C2×C47#45411yescharacteristic
100C2×C47#45611yescharacteristic
101D47—44no—
102C2×2−1+4—471no—
103C2×#104—472no—
104#417—472no—
105C2×#101—471no—
106#391D4711yescharacteristic, complemented
107C47#179311yescharacteristic, complemented, Sylow
1082−1+4—474no—
1092−1+4—944no—
1102−1+4—942no—
111C2×#41—472no—
112C2×#41—942no—
113C2×#41—942no—
114C22×Q8—942no—
115C22×Q8C2×D4711yescharacteristic
116C2×M16—472no—
117C2×C4⋊C4C2×D4711yescharacteristic
118C2×C42C2×D4711yescharacteristic
119#104—944no—
120#103—942no—
121#102—942no—
122#101—942no—
123#95—22no—
124#41—474no—
125#41—474no—
126#41—948no—
127#41—948no—
128#41—948no—
129#41—948no—
130#41—942no—
131#41—942no—
132C2×Q8—22no—
133C2×Q8—22no—
134C2×Q8—472no—
135C2×Q8—942no—
136C2×Q8—948no—
137C2×Q8—948no—
138C2×Q8C4×D4712yes—
139C2×Q8D18812yes—
140C2×D4—472no—
141C2×D4—942no—
142C2×D4—942no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—944no—
146C22×C4—942no—
147C22×C4C22⋊D4712yes—
148C22×C4C22×D4711yescharacteristic
149M16—942no—
150M16—942no—
151C2×C8—942no—
152C4⋊C4—22no—
153C42—22no—
154C23—942no—
155C23C2×C22⋊D4711yescharacteristic
156Q8—24no—
157Q8—24no—
158Q8—474no—
159Q8—948no—
160Q8—942no—
161D4—474no—
162D4—948no—
163D4—944no—
164D4—944no—
165D4—942no—
166C2×C4—22no—
167C2×C4—22no—
168C2×C4—22no—
169C2×C4—41no—
170C2×C4—41no—
171C2×C4—42no—
172C2×C4—41no—
173C2×C4—9416no—
174C2×C4—942no—
175C2×C4—944no—
176C2×C4—944no—
177C2×C4(C2×D47)⋊C414yes—
178C2×C4C2×C4×D4711yescharacteristic
179C2×C4C2×D18811yescharacteristic
180C2×C4D4×D4712yes—
181C2×C4D4×D4712yes—
182C8—1882no—
183C22—21no—
184C22—21no—
185C22—944no—
186C22—1882no—
187C22—1882no—
188C22C2×(C2×D47)⋊C411yescharacteristic
189C22#1309399211yescharacteristic
190C22#1309399211yescharacteristic
191C4—24no—
192C4—42no—
193C4—81no—
194C4—944no—
195C4C22⋊C4×D4712yes—
196C4#1309399412yes—
197C2—21no—
198C2—21no—
199C2—1884no—
200C2#1568897811yescharacteristic
201C2#1568929511yescharacteristic
202C2#1568930511yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#391C2
socleC22×C47#120
hypercenter#391D47
hypocenterC47#1793
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #391

Complements

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

NH ≅ G/Ntype
2. C2×#13093952C2semidirect
3. #15689122C2semidirect
4. C2×#13093943C2semidirect
5. C47×#391C2semidirect
8. #13094072C4semidirect
106. #391D47semidirect
107. C47#1793semidirect