Finite Group Databasebeta

← #20245014

Subgroups — #20245014

Order 6016.

220 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 75 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
1#131×D47C211yesmaximal, characteristic
2C2×#13093963C211yesmaximal, characteristic, complemented
3M32×D47C211yesmaximal, characteristic, complemented
4#15688908C211yesmaximal, characteristic, complemented
5#15688907C211yesmaximal, characteristic, complemented
6#15688906C211yesmaximal, characteristic, complemented
7C47×#350C211yesmaximal, characteristic, complemented
8#41×D47C411yescharacteristic
9#13094032—21no—
10#13094032C411yescharacteristic
11#13094031C411yescharacteristic
12#13094030—21no—
13#13094030C2211yescharacteristic
14M16×D47—21no—
15M16×D47C411yescharacteristic
16C2×C8×D47—21no—
17C2×C8×D47C2211yescharacteristic
18#13093964C2211yescharacteristic, complemented
19#13093963—21no—
20#13093963—21no—
21#13093963—21no—
22C2×C47⋊C16C2211yescharacteristic, complemented
23C16×D47—21no—
24#131×C47C2211yescharacteristic
25M32×C47C2211yescharacteristic, complemented
26C2×C16×C47C2211yescharacteristic, complemented
27#41×C47C2×C411yescharacteristic
28#10625354C811yescharacteristic
29Q8×D47C811yescharacteristic
30#10625352—21no—
31#10625352C811yescharacteristic
32D4×D47—21no—
33D4×D47C811yescharacteristic
34#10625350—21no—
35#10625350C2×C411yescharacteristic
36C2×C4×D47—21no—
37C2×C4×D47C2×C411yescharacteristic
38M16×C47—21no—
39M16×C47C2×C411yescharacteristic
40C2×C8×C47—21no—
41C2×C8×C47C2311yescharacteristic
42#10625329—21no—
43#10625329C2×C411yescharacteristic
44C2×C47⋊C8—21no—
45C2×C47⋊C8C2×C411yescharacteristic
46#10625324—21no—
47#10625324—21no—
48#10625324—21no—
49C8×D47—21no—
50C8×D47—21no—
51C8×D47—21no—
52C8×D47D411yescharacteristic
53C8×D47D411yescharacteristic
54C8×D47D411yescharacteristic
55C8×D47D411yescharacteristic
56C16×C47—21no—
57C16×C47—21no—
58C47⋊C16—21no—
59C47⋊C16—21no—
60C22×D47—21no—
61C22×D47M1611yescharacteristic
62Q8×C47C2×C811yescharacteristic
63D4×C47—21no—
64D4×C47C2×C811yescharacteristic
65C2×C4×C47—21no—
66C2×C4×C47C22×C411yescharacteristic
67C22⋊D47—21no—
68C22⋊D47—21no—
69C22⋊D47—21no—
70C2×Dic47—21no—
71C2×Dic47M1611yescharacteristic
72D188—21no—
73D188C2×C811yescharacteristic
74C4×D47—21no—
75C4×D47—21no—
76C4×D47—21no—
77C4×D47C22⋊C411yescharacteristic
78C4×D47C22⋊C411yescharacteristic
79C4×D47C2×C811yescharacteristic
80C4×D47C2×C811yescharacteristic
81Dic94—21no—
82Dic94C2×C811yescharacteristic
83C8×C47—21no—
84C8×C47C2×D411yescharacteristic
85C8×C47C2×D411yescharacteristic
86C47⋊C8—21no—
87C47⋊C8C22⋊C411yescharacteristic
88C47⋊C8C22⋊C411yescharacteristic
89C22×C47—21no—
90C22×C47C2×M1611yescharacteristic
91C2×D47—21no—
92C2×D47—41no—
93C2×D47—42no—
94C2×D47C22⋊C811yescharacteristic
95C2×D47C22⋊C811yescharacteristic
96C4×C47—21no—
97C4×C47C2×C22⋊C411yescharacteristic
98C4×C47C22×C811yescharacteristic
99Dic47—21no—
100Dic47C22⋊C811yescharacteristic
101Dic47C22⋊C811yescharacteristic
102#2117—471nomaximal, Sylow
103C2×C47—21no—
104C2×C47—41no—
105C2×C47C2×C22⋊C811yescharacteristic
106D47—21no—
107D47—21no—
108D47—41no—
109C2×#131—471no—
110C2×M32—471no—
111C2×M32—471no—
112#350—471no—
113#350—471no—
114#350—471no—
115#350D4711yescharacteristic, complemented
116C47#211711yescharacteristic, complemented, Sylow
117C2×#41—471no—
118#131—471no—
119#131—471no—
120#131—471no—
121#131—941no—
122#131—941no—
123#131C2×D4711yescharacteristic
124C2×M16—471no—
125C2×M16—941no—
126C22×C8—471no—
127C22×C8—941no—
128M32—471no—
129M32—941no—
130M32—941no—
131M32—941no—
132M32C2×D4711yescharacteristic, complemented
133C2×C16—471no—
134C2×C16—941no—
135C2×C16C2×D4711yescharacteristic, complemented
136#41—471no—
137#41—471no—
138#41—471no—
139#41—941no—
140#41—941no—
141#41C4×D4711yescharacteristic
142C2×Q8—471no—
143C2×D4—471no—
144C2×D4—941no—
145C22×C4—471no—
146C22×C4—941no—
147M16—21no—
148M16—471no—
149M16—941no—
150M16—941no—
151M16—941no—
152M16—941no—
153M16C4×D4711yescharacteristic
154C2×C8—21no—
155C2×C8—471no—
156C2×C8—471no—
157C2×C8—471no—
158C2×C8—471no—
159C2×C8—471no—
160C2×C8—941no—
161C2×C8—941no—
162C2×C8—941no—
163C2×C8—941no—
164C2×C8C22×D4711yescharacteristic
165C16—21no—
166C16—21no—
167C16—941no—
168C16—941no—
169C23—471no—
170C23—941no—
171Q8—471no—
172Q8—941no—
173Q8C8×D4711yescharacteristic
174D4—21no—
175D4—471no—
176D4—941no—
177D4—941no—
178D4—941no—
179D4—941no—
180D4C8×D4711yescharacteristic
181C2×C4—21no—
182C2×C4—471no—
183C2×C4—471no—
184C2×C4—471no—
185C2×C4—471no—
186C2×C4—471no—
187C2×C4—941no—
188C2×C4—941no—
189C2×C4—941no—
190C2×C4—941no—
191C2×C4C2×C4×D4711yescharacteristic
192C8—21no—
193C8—471no—
194C8—471no—
195C8—941no—
196C8D4×D4711yescharacteristic
197C8D4×D4711yescharacteristic
198C22—21no—
199C22—471no—
200C22—471no—
201C22—941no—
202C22—1881no—
203C22—1882no—
204C22M16×D4711yescharacteristic
205C4—21no—
206C4—471no—
207C4—471no—
208C4—941no—
209C4C22⋊C4×D4711yescharacteristic
210C4C2×C8×D4711yescharacteristic
211C2—21no—
212C2—41no—
213C2—941no—
214C2—941no—
215C2—1881no—
216C2C22⋊C8×D4711yescharacteristic
subgroupG/H
centerC8D4×D47
commutatorC4×C47C22×C8
FrattiniC2×C8C22×D47
FittingC47×#350C2
socleC2×C47C2×C22⋊C8
hypercenter#350D47
hypocenterC47#2117
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C8 ◁ C2×C8 ◁ #350

Complements

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

NH ≅ G/Ntype
2. C2×#13093963C2semidirect
3. M32×D47C2semidirect
4. #15688908C2semidirect
5. #15688907C2semidirect
6. #15688906C2semidirect
7. C47×#350C2semidirect
18. #13093964C22semidirect
22. C2×C47⋊C16C22semidirect
25. M32×C47C22semidirect
26. C2×C16×C47C22semidirect
115. #350D47semidirect
116. C47#2117semidirect
132. M32C2×D47semidirect
135. C2×C16C2×D47semidirect