Finite Group Databasebeta

← #20243662

Subgroups — #20243662

Order 6016.

270 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 83 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×#13093959C211yesmaximal, characteristic, complemented
3C2×#13093950C211yesmaximal, characteristic
4#15689117C211yesmaximal, characteristic
5#15688882C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C47×#424C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094030—22no—
10#13094030—22no—
11C2×#10625329C2211yescharacteristic
12C2×#10625324—21no—
13C22×C47⋊C8C2211yescharacteristic
14C2×C8×D47—21no—
15C2×C4×Dic47C2211yescharacteristic
16#13093959—22no—
17#13093950—22no—
18#13093947C411yescharacteristic, complemented
19#13093947C411yescharacteristic, complemented
20#13093944C411yescharacteristic, complemented
21#13093944C411yescharacteristic, complemented
22C2×M16×C47C2211yescharacteristic
23C22×C8×C47C2211yescharacteristic
24#117×C47C2211yescharacteristic
25C4⋊C8×C47—21no—
26C4⋊C8×C47—21no—
27C22×C4×C47C2311yescharacteristic
28C2×C22⋊D47—21no—
29C22×Dic47—21no—
30#10625350—21no—
31#10625350—21no—
32#10625350D412yes—
33#10625350Q812yes—
34C2×D188C2×C411yescharacteristic
35C2×C4×D47—21no—
36C2×Dic94C2×C411yescharacteristic
37M16×C47—21no—
38M16×C47—21no—
39C2×C8×C47—21no—
40C2×C8×C47—21no—
41C2×C8×C47—21no—
42C2×C8×C47D411yescharacteristic
43C2×C8×C47D411yescharacteristic
44C4⋊C4×C47C2×C411yescharacteristic
45C4⋊C4×C47C2×C411yescharacteristic
46C22⋊C4×C47—21no—
47C42×C47—21no—
48C4×Dic47—21no—
49C4×Dic47—21no—
50#10625329—21no—
51#10625329D412yes—
52C2×C47⋊C8—21no—
53C2×C47⋊C8—21no—
54C2×C47⋊C8—21no—
55C2×C47⋊C8C2×C411yescharacteristic
56C2×C47⋊C8C2×C411yescharacteristic
57#10625324—24no—
58C8×D47—24no—
59C23×C47#4111yescharacteristic
60C22×D47—21no—
61C2×C4×C47—21no—
62C2×C4×C47—21no—
63C2×C4×C47C22×C411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×D411yescharacteristic
67C2×C4×C47C2×Q811yescharacteristic
68C2×C4×C47#4111yescharacteristic
69C22⋊D47—22no—
70C22⋊D47—22no—
71C2×Dic47—21no—
72C2×Dic47—22no—
73C2×Dic47—41no—
74C2×Dic47—41no—
75D188—21no—
76D188C4⋊C412yes—
77C4×D47—22no—
78C4×D47—22no—
79Dic94—21no—
80Dic94C4⋊C412yes—
81C8×C47—21no—
82C8×C47—21no—
83C8×C47—41no—
84C47⋊C8—21no—
85C47⋊C8—21no—
86C47⋊C8—22no—
87C22×C47—21no—
88C22×C47—21no—
89C22×C47C4×D411yescharacteristic
90C22×C47C22⋊Q811yescharacteristic
91C22×C47#12311yescharacteristic
92C2×D47—22no—
93C2×D47—41no—
94C2×D47—41no—
95C4×C47—41no—
96C4×C47—41no—
97C4×C47C2×C4⋊C411yescharacteristic
98C4×C47C4×D411yescharacteristic
99C4×C47#12011yescharacteristic
100C4×C47C22⋊Q811yescharacteristic
101Dic47—22no—
102Dic47—42no—
103#1866—471nomaximal, Sylow
104C2×C47—21no—
105C2×C47—21no—
106C2×C47#38511yescharacteristic
107C2×C47#44311yescharacteristic
108C2×C47#44411yescharacteristic
109D47—42no—
110C2×#131—471no—
111C2×#108—471no—
112#424D4711yescharacteristic, complemented
113C2×#104—471no—
114#416—471no—
115#339—471no—
116#336—471no—
117C47#186611yescharacteristic, complemented, Sylow
118C2×#41—471no—
119#131—942no—
120#131—942no—
121C2×M16—471no—
122C2×M16—941no—
123C2×M16C2×D4711yescharacteristic
124C22×C8—471no—
125C22×C8—941no—
126C22×C8C2×D4711yescharacteristic
127#117C2×D4711yescharacteristic
128C2×C42—471no—
129#108—942no—
130C4⋊C8—21no—
131C4⋊C8—21no—
132#104—942no—
133#103—471no—
134#103—471no—
135#102—471no—
136#102—471no—
137#41—472no—
138#41—472no—
139#41—941no—
140#41—941no—
141C2×Q8—471no—
142C2×D4—471no—
143C2×D4—941no—
144C22×C4—941no—
145C22×C4—941no—
146C22×C4C22×D4711yescharacteristic
147M16—21no—
148M16—21no—
149M16—472no—
150M16—944no—
151M16—941no—
152C2×C8—21no—
153C2×C8—21no—
154C2×C8—21no—
155C2×C8—471no—
156C2×C8—471no—
157C2×C8—944no—
158C2×C8—941no—
159C2×C8—941no—
160C2×C8—941no—
161C2×C8C22⋊D4711yescharacteristic
162C2×C8C22⋊D4711yescharacteristic
163C4⋊C4C4×D4711yescharacteristic
164C4⋊C4C4×D4711yescharacteristic
165C22⋊C4—21no—
166C42—21no—
167C42—941no—
168C42—941no—
169C23—941no—
170C23#1062535011yescharacteristic
171Q8—472no—
172Q8—941no—
173D4—472no—
174D4—942no—
175D4—942no—
176D4—941no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—941no—
180C2×C4—942no—
181C2×C4—942no—
182C2×C4—942no—
183C2×C4—1881no—
184C2×C4—1881no—
185C2×C4C2×C4×D4711yescharacteristic
186C2×C4D4×D4711yescharacteristic
187C2×C4D4×D4711yescharacteristic
188C2×C4Q8×D4711yescharacteristic
189C2×C4#1062535411yescharacteristic
190C2×C4C2×C22⋊D4711yescharacteristic
191C8—21no—
192C8—21no—
193C8—41no—
194C8—941no—
195C8—941no—
196C8—942no—
197C22—21no—
198C22—21no—
199C22—942no—
200C22—1881no—
201C22—1881no—
202C22C4×C22⋊D4711yescharacteristic
203C22#1309400211yescharacteristic
204C22#1309400911yescharacteristic
205C4—41no—
206C4—41no—
207C4—942no—
208C4—1882no—
209C4C4⋊C4×D4711yescharacteristic
210C4#1309398611yescharacteristic
211C4#1309399211yescharacteristic
212C4#1309400011yescharacteristic
213C2—21no—
214C2—21no—
215C2—1882no—
216C2#1568899411yescharacteristic
217C2#1568923811yescharacteristic
218C2#1568924311yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#424C2
socleC22×C47C4×D4
hypercenter#424D47
hypocenterC47#1866
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #424

Complements

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

NH ≅ G/Ntype
2. C2×#13093959C2semidirect
5. #15688882C2semidirect
6. #15688877C2semidirect
7. C47×#424C2semidirect
18. #13093947C4semidirect
19. #13093947C4semidirect
20. #13093944C4semidirect
21. #13093944C4semidirect
112. #424D47semidirect
117. C47#1866semidirect