Finite Group Databasebeta

← #20243875

Subgroups — #20243875

Order 6016.

346 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 346 conjugacy classes of subgroups — too many to draw. Only its 89 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×#13094050C211yesmaximal, characteristic
2#15689141C211yesmaximal, characteristic, complemented
3#15689128C211yesmaximal, characteristic, complemented
4#15689096C211yesmaximal, characteristic, complemented
5#15688893C211yesmaximal, characteristic, complemented
6#15688879C211yesmaximal, characteristic, complemented
7C47×#518C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094050—22no—
10#13094050—22no—
11C2×#10625335C412yescomplemented
12C2×#10625334C412yescomplemented
13C2×#10625329C2211yescharacteristic
14C2×#10625329C2211yescharacteristic
15#13093983C2211yescharacteristic
16#13093952—22no—
17#13093945—22no—
18#13093938—22no—
19C22×D4×C47C2211yescharacteristic
20C4×D4×C47—22no—
21C4×D4×C47—22no—
22#117×C47C2211yescharacteristic
23#117×C47C2211yescharacteristic
24C2×C22⋊C4×C47—22no—
25C24×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47—21no—
29C2×D4×C47C2×C412yes—
30C2×D4×C47D412yes—
31C2×D4×C47D412yes—
32C22×C4×C47—24no—
33C22×C4×C47C2311yescharacteristic
34C2×C22⋊D47—21no—
35#10625350—21no—
36#10625350—21no—
37#10625350—21no—
38#10625350—21no—
39C2×D188C2×C411yescharacteristic, complemented
40C2×C4×D47—21no—
41C2×Dic94C2×C411yescharacteristic, complemented
42C4⋊C4×C47—21no—
43C4⋊C4×C47—21no—
44C22⋊C4×C47—24no—
45C22⋊C4×C47—21no—
46C22⋊C4×C47D412yes—
47C42×C47—21no—
48C42×C47D412yes—
49C22⋊Dic47—21no—
50#10625335—24no—
51#10625334—24no—
52C4⋊Dic47—21no—
53C4×Dic47—21no—
54#10625329—21no—
55#10625329—21no—
56#10625329—21no—
57#10625329—21no—
58C2×C47⋊C8—21no—
59C2×C47⋊C8C2×C412yescomplemented
60C23×C47—22no—
61C23×C47—22no—
62C23×C47—22no—
63C23×C47—82no—
64C23×C47C2×D411yescharacteristic
65C22×D47—21no—
66D4×C47—22no—
67D4×C47—22no—
68D4×C47—22no—
69D4×C47C22⋊C414yes—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—84no—
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—41no—
80C22⋊D47—41no—
81C2×Dic47—21no—
82C2×Dic47—41no—
83D188—21no—
84D188—21no—
85C4×D47—41no—
86C4×D47—41no—
87Dic94—21no—
88Dic94—21no—
89C47⋊C8—22no—
90C47⋊C8—41no—
91C22×C47—24no—
92C22×C47—41no—
93C22×C47—44no—
94C22×C47—82no—
95C22×C47—82no—
96C22×C47C4×D411yescharacteristic
97C22×C47#12011yescharacteristic
98C22×C47#12111yescharacteristic
99C2×D47—41no—
100C2×D47—81no—
101C4×C47—42no—
102C4×C47—42no—
103C4×C47C2×C22⋊C411yescharacteristic
104C4×C47C4×D411yescharacteristic
105C4×C47#12111yescharacteristic
106C4×C47#12311yescharacteristic
107Dic47—41no—
108Dic47—81no—
109#1904—471nomaximal, Sylow
110C2×C47—21no—
111C2×C47—21no—
112C2×C47—21no—
113C2×C47—44no—
114C2×C47#38611yescharacteristic
115D47—81no—
116C2×AGL(1,ℤ/8)—471no—
117#518D4711yescharacteristic, complemented
118#421—471no—
119#418—471no—
120#410—471no—
121#344—471no—
122H(3,ℤ/4)—471no—
123C47#190411yescharacteristic, complemented, Sylow
124C2×#41—471no—
125C22×D4C2×D4711yescharacteristic
126AGL(1,ℤ/8)—942no—
127AGL(1,ℤ/8)—942no—
128C2×SD16—472no—
129C2×D8—472no—
130C2×M16—471no—
131C2×M16—471no—
132C4×D4—22no—
133C4×D4—22no—
134#117—471no—
135#117C2×D4711yescharacteristic
136#117C2×D4711yescharacteristic
137C2×C22⋊C4—22no—
138#104—942no—
139#102—942no—
140#99—942no—
141C24—21no—
142#41—941no—
143#41—941no—
144#41—941no—
145#41—941no—
146C2×Q8—471no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4—471no—
151C2×D4—941no—
152C2×D4C4×D4712yes—
153C2×D4D18812yes—
154C2×D4C22⋊D4712yes—
155C22×C4—24no—
156C22×C4—941no—
157C22×C4C22×D4711yescharacteristic
158SD16—944no—
159D8—944no—
160M16—941no—
161M16—941no—
162M16—941no—
163M16—941no—
164C2×C8—472no—
165C2×C8—941no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—941no—
169C22⋊C4—24no—
170C22⋊C4—21no—
171C22⋊C4—941no—
172C22⋊C4C22⋊D4712yes—
173C42—21no—
174C42—941no—
175C42C22⋊D4712yes—
176C23—22no—
177C23—22no—
178C23—22no—
179C23—82no—
180C23—941no—
181C23C2×C22⋊D4711yescharacteristic
182Q8—941no—
183Q8—941no—
184D4—22no—
185D4—22no—
186D4—22no—
187D4—941no—
188D4—941no—
189D4—1881no—
190D4—1881no—
191D4(C2×D47)⋊C414yes—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—84no—
195C2×C4—941no—
196C2×C4—1881no—
197C2×C4—1881no—
198C2×C4—1881no—
199C2×C4C2×C4×D4711yescharacteristic
200C2×C4C2×D18811yescharacteristic
201C2×C4#1062535011yescharacteristic
202C2×C4#1062535011yescharacteristic
203C2×C4C2×C22⋊D4711yescharacteristic
204C2×C4C2×C22⋊D4711yescharacteristic
205C8—942no—
206C8—1881no—
207C22—24no—
208C22—41no—
209C22—44no—
210C22—82no—
211C22—82no—
212C22—3761no—
213C22—1881no—
214C22C4×C22⋊D4711yescharacteristic
215C22#1309399311yescharacteristic
216C22#1309399811yescharacteristic
217C4—42no—
218C4—42no—
219C4—3761no—
220C4—1881no—
221C4C2×(C2×D47)⋊C411yescharacteristic
222C4C4×C22⋊D4711yescharacteristic
223C4#1309399811yescharacteristic
224C4#1309400711yescharacteristic
225C2—21no—
226C2—21no—
227C2—21no—
228C2—44no—
229C2—3761no—
230C2#1568900211yescharacteristic
subgroupG/H
centerC2#15689002
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#518C2
socleC2×C47#386
hypercenter#518D47
hypocenterC47#1904
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #518

Complements

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

NH ≅ G/Ntype
2. #15689141C2semidirect
3. #15689128C2semidirect
4. #15689096C2semidirect
5. #15688893C2semidirect
6. #15688879C2semidirect
7. C47×#518C2semidirect
11. C2×#10625335C4semidirect
12. C2×#10625334C4semidirect
39. C2×D188C2×C4semidirect
41. C2×Dic94C2×C4semidirect
59. C2×C47⋊C8C2×C4semidirect
117. #518D47semidirect
123. C47#1904semidirect