Finite Group Databasebeta

← #20244623

Subgroups — #20244623

Order 6016.

402 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 91 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×#13094021C211yesmaximal, characteristic
2C2×#13093946C212yesmaximal, complemented
3C2×#13093946C212yesmaximal, complemented
4#15689021C211yesmaximal, characteristic, complemented
5C47×#336C211yesmaximal, characteristic, complemented
6C22×D188—21no—
7C22×D188—21no—
8C22×D188C2212yes—
9#13094021—24no—
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4⋊Dic47C2211yescharacteristic
12C2×Dic47⋊C4—21no—
13#13093946—24no—
14#13093946—24no—
15C47⋊#95—21no—
16C22×C8×C47C2212yes—
17C2×C42×C47C2211yescharacteristic
18C23×D47—22no—
19C22×C4×C47D411yescharacteristic
20C22×C4×C47D411yescharacteristic
21C22×C4×C47C2311yescharacteristic
22C22×Dic47—21no—
23C22×Dic47—21no—
24C2×D188—22no—
25C2×D188—22no—
26C2×D188—22no—
27C2×D188—22no—
28C2×D188—24no—
29C2×D188—24no—
30C2×D188—22no—
31C2×D188—42no—
32C2×D188—42no—
33C2×D188—42no—
34C2×D188—42no—
35C2×D188D414yes—
36C2×C8×C47—22no—
37C2×C8×C47—22no—
38C2×C8×C47—22no—
39C42×C47—22no—
40C4⋊Dic47—21no—
41C4⋊Dic47—22no—
42C4⋊Dic47D412yescomplemented
43Dic47⋊C4—42no—
44C23×C47C2×D411yescharacteristic
45C22×D47—24no—
46C22×D47—42no—
47C22×D47—42no—
48C22×D47—42no—
49C22×D47—42no—
50C22×D47—42no—
51C22×D47—42no—
52C2×C4×C47—21no—
53C2×C4×C47—21no—
54C2×C4×C47—21no—
55C2×C4×C47—21no—
56C2×C4×C47D812yes—
57C2×C4×C47SD1612yes—
58C2×C4×C47C2×D411yescharacteristic
59C2×C4×C47C2×D412yes—
60C2×C4×C47#4112yes—
61C2×C4×C47#4111yescharacteristic
62C2×Dic47—22no—
63C2×Dic47—41no—
64C2×Dic47—41no—
65C2×Dic47—41no—
66C2×Dic47—41no—
67C2×Dic47—41no—
68D188—24no—
69D188—24no—
70D188—48no—
71D188—48no—
72D188—42no—
73D188—42no—
74C8×C47—42no—
75C22×C47#12011yescharacteristic
76C22×C47#12111yescharacteristic
77C22×C47#12411yescharacteristic
78C22×C47C2×D811yescharacteristic
79C22×C47C2×SD1611yescharacteristic
80C22×C47AGL(1,ℤ/8)11yescharacteristic
81C22×C47AGL(1,ℤ/8)11yescharacteristic
82C2×D47—44no—
83C2×D47—44no—
84C2×D47—44no—
85C2×D47—82no—
86C2×D47—82no—
87C2×D47—82no—
88C2×D47—82no—
89C4×C47—22no—
90C4×C47—22no—
91C4×C47#12112yes—
92C4×C47#12312yes—
93Dic47—42no—
94Dic47—81no—
95#2041—471nomaximal, Sylow
96C2×C47#39411yescharacteristic
97C2×C47#44711yescharacteristic
98C2×C47#45011yescharacteristic
99C2×C47#45911yescharacteristic
100C2×C47#46011yescharacteristic
101C2×C47#48611yescharacteristic
102C2×C47#49011yescharacteristic
103D47—84no—
104C2×#127—471no—
105C2×#102—472no—
106C2×#102—472no—
107#389—471no—
108#336D4711yescharacteristic, complemented
109C47#204111yescharacteristic, complemented, Sylow
110C22×D4—472no—
111C22×D4—941no—
112C22×D4—941no—
113C22×C8C2×D4712yes—
114#127—944no—
115C2×C4⋊C4—471no—
116C2×C4⋊C4—471no—
117C2×C4⋊C4—941no—
118C2×C42C2×D4711yescharacteristic
119#102—944no—
120#102—944no—
121#95—941no—
122C24—942no—
123C2×D4—474no—
124C2×D4—944no—
125C2×D4—944no—
126C2×D4—942no—
127C2×D4—942no—
128C2×D4—942no—
129C2×D4—942no—
130C2×D4—942no—
131C2×D4—1882no—
132C2×D4—1882no—
133C2×D4—1882no—
134C2×D4—1882no—
135C22×C4—941no—
136C22×C4—941no—
137C22×C4D18811yescharacteristic
138C22×C4D18811yescharacteristic
139C22×C4C22×D4711yescharacteristic
140C2×C8—22no—
141C2×C8—22no—
142C2×C8—22no—
143C4⋊C4—472no—
144C4⋊C4—941no—
145C4⋊C4—942no—
146C4⋊C4—1882no—
147C42—22no—
148C23—944no—
149C23—1882no—
150C23—1882no—
151C23—1882no—
152C23—1882no—
153C23—1882no—
154C23—1882no—
155C23C2×D18811yescharacteristic
156D4—944no—
157D4—944no—
158D4—1888no—
159D4—1888no—
160D4—1882no—
161D4—1882no—
162C2×C4—21no—
163C2×C4—21no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—942no—
167C2×C4—1881no—
168C2×C4—1881no—
169C2×C4—1881no—
170C2×C4—1881no—
171C2×C4—1881no—
172C2×C4#1062532512yes—
173C2×C4D37612yes—
174C2×C4#1062535012yes—
175C2×C4D4×D4711yescharacteristic
176C2×C4D4×D4712yes—
177C2×C4#1062535411yescharacteristic
178C8—42no—
179C22—3762no—
180C22—3762no—
181C22—3762no—
182C22—3762no—
183C22—1884no—
184C22—1884no—
185C22—1884no—
186C22#1309399411yescharacteristic
187C22#1309399911yescharacteristic
188C22#1309401211yescharacteristic
189C22C2×D37611yescharacteristic
190C22C2×#1062532511yescharacteristic
191C22#1309405211yescharacteristic
192C22#1309405211yescharacteristic
193C4—22no—
194C4—22no—
195C4—3761no—
196C4—1882no—
197C4#1309399712yes—
198C4#1309400912yes—
199C2—3764no—
200C2#1568904111yescharacteristic
201C2#1568925911yescharacteristic
202C2#1568927611yescharacteristic
203C2#1568931911yescharacteristic
204C2#1568932411yescharacteristic
205C2#1568947011yescharacteristic
206C2#1568948811yescharacteristic
subgroupG/H
centerC23C2×D188
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#336C2
socleC23×C47C2×D4
hypercenter#336D47
hypocenterC47#2041
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
2. C2×#13093946C2semidirect
3. C2×#13093946C2semidirect
4. #15689021C2semidirect
5. C47×#336C2semidirect
42. C4⋊Dic47D4semidirect
108. #336D47semidirect
109. C47#2041semidirect