Finite Group Databasebeta

← #20243232

Subgroups — #20243232

Order 6016.

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

normal subgroups only

This group has 292 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
1C2×#13094030C211yesmaximal, characteristic
2C2×#13093952C211yesmaximal, characteristic
3#15689120C211yesmaximal, characteristic
4#15689078C211yesmaximal, characteristic, complemented
5#15688888C211yesmaximal, characteristic, complemented
6#15688883C211yesmaximal, characteristic, complemented
7C2×#97×C47C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094030—22no—
10#13094030C414yescomplemented
11C2×#10625329C2211yescharacteristic
12C2×#10625329C2211yescharacteristic
13C2×#10625324—21no—
14C2×C8×D47—21no—
15#13093983C2211yescharacteristic
16#13093952C414yescomplemented
17#13093949C412yescomplemented
18#13093946C412yescomplemented
19#13093934—21no—
20C8×Dic47—21no—
21C22×C8×C47C2211yescharacteristic
22C22×C8×C47C2211yescharacteristic
23C2×C42×C47C2211yescharacteristic
24#97×C47—22no—
25C22×C4×C47—21no—
26C22×C4×C47C2311yescharacteristic
27C2×C22⋊D47—21no—
28#10625350—21no—
29#10625350—21no—
30#10625350C2×C412yes—
31#10625350C2×C412yes—
32C2×D188C2×C411yescharacteristic
33C2×C4×D47—21no—
34C2×Dic94C2×C411yescharacteristic
35C2×C8×C47—21no—
36C2×C8×C47—21no—
37C2×C8×C47C2×C412yes—
38C2×C8×C47C2×C412yes—
39C2×C8×C47D411yescharacteristic
40C2×C8×C47D411yescharacteristic
41C2×C8×C47D412yes—
42C42×C47—21no—
43C42×C47C2×C412yes—
44C22⋊Dic47—21no—
45C4⋊Dic47C2×C412yes—
46C4×Dic47—21no—
47#10625329—21no—
48#10625329—21no—
49#10625329C2×C412yes—
50#10625329C2×C412yes—
51C2×C47⋊C8—21no—
52C2×C47⋊C8—21no—
53#10625324—24no—
54C8×D47—24no—
55C23×C47#4111yescharacteristic
56C22×D47—21no—
57C2×C4×C47—22no—
58C2×C4×C47—42no—
59C2×C4×C47C22×C411yescharacteristic
60C2×C4×C47C22×C411yescharacteristic
61C2×C4×C47C22×C411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47C2×D411yescharacteristic
64C2×C4×C47#4111yescharacteristic
65C22⋊D47—22no—
66C22⋊D47—22no—
67C2×Dic47—21no—
68C2×Dic47—22no—
69D188—21no—
70D188C4212yes—
71C4×D47—22no—
72C4×D47—22no—
73Dic94—21no—
74Dic94C4212yes—
75C8×C47—22no—
76C8×C47C22⋊C412yes—
77C8×C47C22⋊C412yes—
78C47⋊C8—22no—
79C47⋊C8—22no—
80C22×C47—22no—
81C22×C47#11711yescharacteristic
82C22×C47C4×D411yescharacteristic
83C22×C47C4×D411yescharacteristic
84C2×D47—22no—
85C2×D47—42no—
86C4×C47—42no—
87C4×C47C2×C4211yescharacteristic
88C4×C47C2×C22⋊C411yescharacteristic
89C4×C47C4×D411yescharacteristic
90C4×C47C4×D411yescharacteristic
91Dic47—22no—
92Dic47—42no—
93#1765—471nomaximal, Sylow
94C2×C47—21no—
95C2×C47—21no—
96C2×C47C4×C22⋊C411yescharacteristic
97C2×C47#44412yes—
98D47—42no—
99C2×#131—471no—
100C2×#104—471no—
101#416—471no—
102#405—471no—
103C2×#97D4711yescharacteristic, complemented
104#341—471no—
105#339—471no—
106C47#176511yescharacteristic, complemented, Sylow
107C2×#41—471no—
108#131—474no—
109#131—942no—
110C2×M16—471no—
111C2×M16—471no—
112C2×M16—941no—
113C22×C8—941no—
114C22×C8C2×D4711yescharacteristic
115C22×C8C2×D4711yescharacteristic
116#117—471no—
117C2×C42C2×D4711yescharacteristic
118#104—474no—
119#103—472no—
120#102—472no—
121#97—22no—
122#97—941no—
123C4×C8—941no—
124#41—472no—
125#41—472no—
126#41—941no—
127#41—941no—
128C2×Q8—471no—
129C2×D4—471no—
130C2×D4—941no—
131C22×C4—21no—
132C22×C4—941no—
133C22×C4C22×D4711yescharacteristic
134M16—472no—
135M16—472no—
136M16—941no—
137M16—941no—
138M16—944no—
139C2×C8—21no—
140C2×C8—21no—
141C2×C8—941no—
142C2×C8—941no—
143C2×C8—944no—
144C2×C8C4×D4712yes—
145C2×C8C4×D4712yes—
146C2×C8D18811yescharacteristic
147C2×C8D18811yescharacteristic
148C2×C8C22⋊D4712yes—
149C4⋊C4—472no—
150C22⋊C4—941no—
151C42—21no—
152C42—941no—
153C42C4×D4712yes—
154C23—941no—
155C23#1062535011yescharacteristic
156Q8—472no—
157Q8—941no—
158D4—472no—
159D4—942no—
160D4—942no—
161D4—941no—
162C2×C4—22no—
163C2×C4—42no—
164C2×C4—941no—
165C2×C4—942no—
166C2×C4—942no—
167C2×C4—942no—
168C2×C4C2×C4×D4711yescharacteristic
169C2×C4C2×C4×D4711yescharacteristic
170C2×C4C2×C4×D4711yescharacteristic
171C2×C4C2×D18811yescharacteristic
172C2×C4#1062535011yescharacteristic
173C2×C4C2×C22⋊D4711yescharacteristic
174C8—22no—
175C8—942no—
176C8—942no—
177C8(C2×D47)⋊C412yes—
178C8(C2×D47)⋊C412yes—
179C22—22no—
180C22—942no—
181C22—1882no—
182C22#1309398111yescharacteristic
183C22C4×C22⋊D4711yescharacteristic
184C22C4×D18811yescharacteristic
185C4—42no—
186C4—942no—
187C4—1882no—
188C4C42×D4711yescharacteristic
189C4C2×(C2×D47)⋊C411yescharacteristic
190C4C4×C22⋊D4711yescharacteristic
191C4C4×D18811yescharacteristic
192C2—21no—
193C2—21no—
194C2—1882no—
195C2C4×(C2×D47)⋊C411yescharacteristic
196C2#1568924612yes—
subgroupG/H
centerC2×C4C2×D188
commutatorC4×C47C2×C42
FrattiniC22×C4C22×D47
FittingC2×#97×C47C2
socleC22×C47C4×D4
hypercenterC2×#97D47
hypocenterC47#1765
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
4. #15689078C2semidirect
5. #15688888C2semidirect
6. #15688883C2semidirect
7. C2×#97×C47C2semidirect
10. #13094030C4semidirect
16. #13093952C4semidirect
17. #13093949C4semidirect
18. #13093946C4semidirect
103. C2×#97D47semidirect
106. C47#1765semidirect