Finite Group Databasebeta

← #20243770

Subgroups — #20243770

Order 6016.

332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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#15689889C211yesmaximal, characteristic, complemented
2#15689673C211yesmaximal, characteristic
3#15689141C211yesmaximal, characteristic, complemented
4#15689139C211yesmaximal, characteristic, complemented
5#15689096C211yesmaximal, characteristic, complemented
6#15688883C211yesmaximal, characteristic, complemented
7C47×#339C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9C2×#10625350C2211yescharacteristic
10#13094032—22no—
11#13094030—22no—
12C2×#10625329C2211yescharacteristic
13M16×D47—22no—
14#13094024C411yescharacteristic, complemented
15#13094021C411yescharacteristic, complemented
16#13094012C411yescharacteristic, complemented
17#13094012C411yescharacteristic, complemented
18#13093998—22no—
19C4×D188—22no—
20#13093983C2211yescharacteristic
21#13093952—22no—
22#13093950—22no—
23#13093938—22no—
24C2×M16×C47C2211yescharacteristic
25#117×C47C2211yescharacteristic
26C2×C42×C47C2211yescharacteristic
27C22×C4×C47—21no—
28C22×C4×C47C2311yescharacteristic
29C2×C22⋊D47—21no—
30C2×C22⋊D47D412yes—
31#10625350—21no—
32#10625350—21no—
33#10625350—21no—
34#10625350—21no—
35#10625350—21no—
36#10625350—21no—
37#10625350—21no—
38#10625350—21no—
39C2×D188—22no—
40C2×D188C2×C411yescharacteristic
41C2×D188C2×C411yescharacteristic
42C2×C4×D47—21no—
43C2×C4×D47D412yes—
44C2×Dic94C2×C411yescharacteristic
45C2×Dic94C2×C411yescharacteristic
46M16×C47—21no—
47M16×C47D412yescomplemented
48C2×C8×C47—21no—
49C4⋊C4×C47—21no—
50C22⋊C4×C47—21no—
51C42×C47—21no—
52C42×C47—21no—
53C42×C47C2×C411yescharacteristic
54C42×C47C2×C411yescharacteristic
55C22⋊Dic47—21no—
56(C2×D47)⋊C4—22no—
57(C2×D47)⋊C4—22no—
58C4⋊Dic47—22no—
59C4⋊Dic47—21no—
60C4×Dic47—21no—
61#10625329—21no—
62#10625329D412yescomplemented
63C2×C47⋊C8—21no—
64#10625324—24no—
65C8×D47—24no—
66C23×C47C2×D411yescharacteristic
67C22×D47—21no—
68C22×D47C22⋊C412yes—
69C2×C4×C47—21no—
70C2×C4×C47—21no—
71C2×C4×C47—42no—
72C2×C4×C47—41no—
73C2×C4×C47C22×C411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47#4111yescharacteristic
78C2×C4×C47#4111yescharacteristic
79C22⋊D47—22no—
80C22⋊D47—22no—
81C22⋊D47—41no—
82C22⋊D47—41no—
83C2×Dic47—21no—
84C2×Dic47—41no—
85C2×Dic47C22⋊C412yes—
86D188—21no—
87D188—21no—
88D188—21no—
89D188—21no—
90D188—44no—
91C4×D47—22no—
92C4×D47—22no—
93C4×D47—41no—
94C4×D47—41no—
95Dic94—21no—
96Dic94—21no—
97Dic94—21no—
98Dic94—21no—
99C8×C47—22no—
100C47⋊C8—22no—
101C22×C47—41no—
102C22×C47C2×C22⋊C411yescharacteristic
103C22×C47#12111yescharacteristic
104C22×C47#12111yescharacteristic
105C2×D47—22no—
106C2×D47—42no—
107C2×D47—42no—
108C2×D47—41no—
109C4×C47—22no—
110C4×C47—41no—
111C4×C47—81no—
112C4×C47C4×D411yescharacteristic
113C4×C47C4×D411yescharacteristic
114C4×C47#12011yescharacteristic
115C4×C47#12311yescharacteristic
116Dic47—22no—
117Dic47—41no—
118Dic47—81no—
119#1884—471nomaximal, Sylow
120C2×C47—21no—
121C2×C47—21no—
122C2×C47—21no—
123C2×C47#38611yescharacteristic
124D47—42no—
125D47—81no—
126#568—471no—
127#532—471no—
128#421—471no—
129#421—471no—
130#410—471no—
131#339—471no—
132#339D4711yescharacteristic, complemented
133C47#188411yescharacteristic, complemented, Sylow
134C2×#41—471no—
135C2×#41—471no—
136#131—942no—
137#131—942no—
138C2×M16—471no—
139C2×M16—942no—
140C2×M16C2×D4711yescharacteristic
141C4⋊Q8—471no—
142#127—471no—
143#124—471no—
144#124—471no—
145#121—942no—
146C4×D4—942no—
147#117—471no—
148#117C2×D4711yescharacteristic
149C2×C42C2×D4711yescharacteristic
150#104—942no—
151#104—942no—
152#99—942no—
153#41—941no—
154#41—941no—
155#41—941no—
156#41—941no—
157#41—941no—
158#41—941no—
159#41—941no—
160#41—941no—
161C2×Q8—471no—
162C2×Q8—471no—
163C2×D4—472no—
164C2×D4—471no—
165C2×D4—471no—
166C2×D4—942no—
167C2×D4—941no—
168C22×C4—21no—
169C22×C4—472no—
170C22×C4—941no—
171C22×C4C22×D4711yescharacteristic
172M16—21no—
173M16—472no—
174M16—944no—
175M16—941no—
176M16D18812yescomplemented
177C2×C8—21no—
178C2×C8—944no—
179C2×C8—941no—
180C4⋊C4—21no—
181C4⋊C4—942no—
182C4⋊C4—941no—
183C22⋊C4—21no—
184C22⋊C4—942no—
185C22⋊C4—942no—
186C22⋊C4—941no—
187C42—21no—
188C42—21no—
189C42—941no—
190C42C4×D4711yescharacteristic
191C42C4×D4711yescharacteristic
192C23—472no—
193C23—941no—
194C23D4×D4711yescharacteristic
195Q8—941no—
196Q8—941no—
197Q8—941no—
198Q8—941no—
199D4—942no—
200D4—942no—
201D4—941no—
202D4—941no—
203D4—941no—
204D4—941no—
205D4—1884no—
206D4—1881no—
207D4—1881no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—42no—
211C2×C4—41no—
212C2×C4—472no—
213C2×C4—942no—
214C2×C4—942no—
215C2×C4—941no—
216C2×C4—1881no—
217C2×C4—1881no—
218C2×C4—1881no—
219C2×C4C2×C4×D4711yescharacteristic
220C2×C4C2×D18811yescharacteristic
221C2×C4#1062535011yescharacteristic
222C2×C4D4×D4711yescharacteristic
223C2×C4D4×D4711yescharacteristic
224C2×C4#1062535411yescharacteristic
225C8—22no—
226C8—942no—
227C22—41no—
228C22—942no—
229C22—1882no—
230C22—1882no—
231C22—1881no—
232C22C22⋊C4×D4711yescharacteristic
233C22#1309399711yescharacteristic
234C22#1309399911yescharacteristic
235C4—22no—
236C4—41no—
237C4—81no—
238C4—942no—
239C4—3761no—
240C4—1881no—
241C4#1309398611yescharacteristic
242C4C4×D18811yescharacteristic
243C4#1309399411yescharacteristic
244C4#1309400911yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—3761no—
249C2—1882no—
250C2#1568900111yescharacteristic
subgroupG/H
centerC4#13093994
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#339C2
socleC2×C47#386
hypercenter#339D47
hypocenterC47#1884
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
1. #15689889C2semidirect
3. #15689141C2semidirect
4. #15689139C2semidirect
5. #15689096C2semidirect
6. #15688883C2semidirect
7. C47×#339C2semidirect
14. #13094024C4semidirect
15. #13094021C4semidirect
16. #13094012C4semidirect
17. #13094012C4semidirect
47. M16×C47D4semidirect
62. #10625329D4semidirect
132. #339D47semidirect
133. C47#1884semidirect
176. M16D188semidirect