Finite Group Databasebeta

← #20243234

Subgroups — #20243234

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×#13093950C211yesmaximal, characteristic
3#15689117C211yesmaximal, characteristic
4C2×#13093934C211yesmaximal, characteristic, complemented
5#15688887C211yesmaximal, characteristic, complemented
6#15688882C211yesmaximal, characteristic, complemented
7C47×#405C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094030—22no—
10#13094030C414yescomplemented
11C2×#10625329C2211yescharacteristic
12C2×#10625324—21no—
13C22×C47⋊C8C2211yescharacteristic
14C2×C8×D47—21no—
15C2×C4×Dic47C2211yescharacteristic
16#13093950C414yescomplemented
17#13093947C412yescomplemented
18#13093944C412yescomplemented
19#13093934—22no—
20C2×M16×C47C2211yescharacteristic
21C22×C8×C47C2211yescharacteristic
22#117×C47C2211yescharacteristic
23#97×C47—21no—
24C4×C8×C47—21no—
25C22×C4×C47C2311yescharacteristic
26C2×C22⋊D47—21no—
27C22×Dic47—21no—
28#10625350—21no—
29#10625350—21no—
30#10625350C2×C412yes—
31#10625350C2×C412yes—
32C2×D188C2×C411yescharacteristic
33C2×C4×D47—21no—
34C2×Dic94C2×C411yescharacteristic
35M16×C47—21no—
36M16×C47C2×C412yes—
37C2×C8×C47—21no—
38C2×C8×C47C2×C412yes—
39C2×C8×C47D412yes—
40C2×C8×C47D411yescharacteristic
41C2×C8×C47D411yescharacteristic
42C4⋊C4×C47C2×C412yes—
43C22⋊C4×C47—21no—
44C42×C47—21no—
45C4×Dic47—21no—
46C4×Dic47C2×C412yes—
47#10625329—21no—
48#10625329C2×C412yes—
49C2×C47⋊C8—21no—
50C2×C47⋊C8—21no—
51C2×C47⋊C8—21no—
52C2×C47⋊C8C2×C412yes—
53#10625324—24no—
54C8×D47—24no—
55C23×C47#4111yescharacteristic
56C22×D47—21no—
57C2×C4×C47—22no—
58C2×C4×C47C22×C411yescharacteristic
59C2×C4×C47C22×C411yescharacteristic
60C2×C4×C47C22×C411yescharacteristic
61C2×C4×C47C2×D411yescharacteristic
62C2×C4×C47C2×D411yescharacteristic
63C2×C4×C47#4111yescharacteristic
64C22⋊D47—22no—
65C22⋊D47—22no—
66C2×Dic47—21no—
67C2×Dic47—22no—
68C2×Dic47—42no—
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#405D4711yescharacteristic, complemented
103C2×#97—471no—
104#341—471no—
105#339—471no—
106C47#176511yescharacteristic, complemented, Sylow
107C2×#41—471no—
108#131—474no—
109#131—942no—
110C2×M16—471no—
111C2×M16—941no—
112C2×M16C2×D4711yescharacteristic
113C22×C8—471no—
114C22×C8—941no—
115C22×C8C2×D4711yescharacteristic
116#117C2×D4711yescharacteristic
117C2×C42—471no—
118#104—474no—
119#103—472no—
120#102—472no—
121#97—21no—
122#97—942no—
123C4×C8—21no—
124#41—472no—
125#41—472no—
126#41—941no—
127#41—941no—
128C2×Q8—471no—
129C2×D4—471no—
130C2×D4—941no—
131C22×C4—941no—
132C22×C4—941no—
133C22×C4C22×D4711yescharacteristic
134M16—21no—
135M16—472no—
136M16—941no—
137M16—944no—
138M16C4×D4712yes—
139C2×C8—21no—
140C2×C8—472no—
141C2×C8—941no—
142C2×C8—941no—
143C2×C8—941no—
144C2×C8—944no—
145C2×C8C4×D4712yes—
146C2×C8D18812yes—
147C2×C8C22⋊D4711yescharacteristic
148C2×C8C22⋊D4711yescharacteristic
149C4⋊C4C4×D4712yes—
150C22⋊C4—21no—
151C42—21no—
152C42—472no—
153C42—941no—
154C23—941no—
155C23#1062535011yescharacteristic
156Q8—472no—
157Q8—941no—
158D4—472no—
159D4—942no—
160D4—942no—
161D4—941no—
162C2×C4—22no—
163C2×C4—941no—
164C2×C4—942no—
165C2×C4—942no—
166C2×C4—942no—
167C2×C4—1882no—
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#1568924312yes—
subgroupG/H
centerC2×C4C2×C22⋊D47
commutatorC4×C47C2×C42
FrattiniC22×C4C22×D47
FittingC47×#405C2
socleC22×C47C4×D4
hypercenter#405D47
hypocenterC47#1765
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #405

Complements

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

NH ≅ G/Ntype
4. C2×#13093934C2semidirect
5. #15688887C2semidirect
6. #15688882C2semidirect
7. C47×#405C2semidirect
10. #13094030C4semidirect
16. #13093950C4semidirect
17. #13093947C4semidirect
18. #13093944C4semidirect
102. #405D47semidirect
106. C47#1765semidirect