Finite Group Databasebeta

← #20243872

Subgroups — #20243872

Order 6016.

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

normal subgroups only

This group has 346 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
1C2×#13094049C211yesmaximal, characteristic
2#15689597C211yesmaximal, characteristic, complemented
3#15689129C211yesmaximal, characteristic, complemented
4#15689097C211yesmaximal, characteristic, complemented
5#15688895C211yesmaximal, characteristic, complemented
6#15688879C211yesmaximal, characteristic, complemented
7C47×#421C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9#13094049—22no—
10#13094049—22no—
11C2×#10625336C412yescomplemented
12C2×#10625334C412yescomplemented
13C2×#10625329C2211yescharacteristic
14C4×D188—22no—
15#13093986—22no—
16#13093983C2211yescharacteristic
17#13093983C2211yescharacteristic
18C22⋊C4×D47—22no—
19#13093946—22no—
20#13093939—22no—
21C2×#41×C47C2211yescharacteristic
22C2×M16×C47C2211yescharacteristic
23#117×C47C2211yescharacteristic
24#104×C47—22no—
25C23×D47—21no—
26#41×C47—21no—
27#41×C47—21no—
28#41×C47—21no—
29#41×C47—21no—
30C2×Q8×C47C2×C411yescharacteristic, complemented
31C2×D4×C47—21no—
32C2×D4×C47C2×C411yescharacteristic, complemented
33C22×C4×C47—21no—
34C22×C4×C47C2311yescharacteristic
35C2×D188—21no—
36C2×D188—21no—
37C2×D188—21no—
38C2×D188C2×C412yes—
39C2×D188D412yes—
40C2×D188D412yes—
41C2×C4×D47—24no—
42M16×C47—21no—
43M16×C47—21no—
44C2×C8×C47—21no—
45C4⋊C4×C47—21no—
46C22⋊C4×C47—21no—
47C42×C47D412yes—
48C22⋊Dic47—21no—
49C22⋊Dic47D412yes—
50#10625336—24no—
51#10625334—24no—
52(C2×D47)⋊C4—24no—
53C4⋊Dic47—21no—
54C4⋊Dic47—21no—
55C4×Dic47—21no—
56C4×Dic47—21no—
57#10625329—21no—
58#10625329—21no—
59C2×C47⋊C8C2×C412yescomplemented
60C23×C47—21no—
61C23×C47C2×D411yescharacteristic
62C22×D47—22no—
63C22×D47—22no—
64C22×D47—22no—
65C22×D47—82no—
66Q8×C47—21no—
67Q8×C47—21no—
68D4×C47—21no—
69D4×C47—21no—
70D4×C47—41no—
71D4×C47—41no—
72C2×C4×C47—21no—
73C2×C4×C47—22no—
74C2×C4×C47—41no—
75C2×C4×C47—41no—
76C2×C4×C47C22×C411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47#4111yescharacteristic
81C2×C4×C47#4111yescharacteristic
82C2×Dic47—22no—
83C2×Dic47—41no—
84D188—22no—
85D188—22no—
86D188—22no—
87D188C22⋊C414yes—
88C4×D47—84no—
89C8×C47—41no—
90C47⋊C8—22no—
91C22×C47—41no—
92C22×C47—41no—
93C22×C47—81no—
94C22×C47C4×D411yescharacteristic
95C22×C47#12011yescharacteristic
96C22×C47#12111yescharacteristic
97C2×D47—24no—
98C2×D47—44no—
99C2×D47—82no—
100C2×D47—82no—
101C4×C47—42no—
102C4×C47—41no—
103C4×C47C2×C22⋊C411yescharacteristic
104C4×C47C4×D411yescharacteristic
105C4×C47#12111yescharacteristic
106C4×C47#12311yescharacteristic
107Dic47—42no—
108Dic47—81no—
109#1904—471nomaximal, Sylow
110C2×C47—21no—
111C2×C47—21no—
112C2×C47—21no—
113C2×C47—81no—
114C2×C47#38611yescharacteristic
115D47—44no—
116C2×AGL(1,ℤ/8)—471no—
117#518—471no—
118#421D4711yescharacteristic, complemented
119#418—471no—
120#410—471no—
121#344—471no—
122H(3,ℤ/4)—471no—
123C47#190411yescharacteristic, complemented, Sylow
124C2×#41C2×D4711yescharacteristic
125C22×D4—471no—
126AGL(1,ℤ/8)—942no—
127AGL(1,ℤ/8)—942no—
128C2×SD16—472no—
129C2×D8—472no—
130C2×M16—471no—
131C2×M16C2×D4711yescharacteristic
132C4×D4—942no—
133C4×D4—942no—
134#117—471no—
135#117—471no—
136#117C2×D4711yescharacteristic
137C2×C22⋊C4—942no—
138#104—22no—
139#102—942no—
140#99—942no—
141C24—941no—
142#41—21no—
143#41—21no—
144#41—21no—
145#41—21no—
146C2×Q8C4×D4711yescharacteristic, complemented
147C2×D4—21no—
148C2×D4—472no—
149C2×D4—472no—
150C2×D4—472no—
151C2×D4—941no—
152C2×D4—941no—
153C2×D4—941no—
154C2×D4C4×D4711yescharacteristic, complemented
155C22×C4—21no—
156C22×C4—944no—
157C22×C4C22×D4711yescharacteristic
158SD16—944no—
159D8—944no—
160M16—21no—
161M16—21no—
162M16—941no—
163M16—941no—
164C2×C8—21no—
165C2×C8—472no—
166C4⋊C4—21no—
167C4⋊C4—941no—
168C4⋊C4—941no—
169C22⋊C4—21no—
170C22⋊C4—472no—
171C22⋊C4—944no—
172C22⋊C4—941no—
173C42—941no—
174C42—941no—
175C42C22⋊D4712yes—
176C23—21no—
177C23—942no—
178C23—942no—
179C23—942no—
180C23—3762no—
181C23D4×D4711yescharacteristic
182Q8—21no—
183Q8—21no—
184D4—21no—
185D4—21no—
186D4—41no—
187D4—41no—
188D4—474no—
189D4—942no—
190D4—942no—
191D4—942no—
192C2×C4—21no—
193C2×C4—22no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—942no—
197C2×C4—3764no—
198C2×C4—1881no—
199C2×C4C2×C4×D4711yescharacteristic
200C2×C4#1062535011yescharacteristic
201C2×C4D4×D4711yescharacteristic
202C2×C4D4×D4711yescharacteristic
203C2×C4#1062535211yescharacteristic
204C2×C4C2×C22⋊D4711yescharacteristic
205C8—41no—
206C8—942no—
207C22—41no—
208C22—41no—
209C22—81no—
210C22—944no—
211C22—3762no—
212C22—3762no—
213C22—1884no—
214C22(C22⋊D47)⋊C411yescharacteristic
215C22#1309399211yescharacteristic
216C22#1309399711yescharacteristic
217C4—42no—
218C4—41no—
219C4—3761no—
220C4—1882no—
221C4C22⋊C4×D4711yescharacteristic
222C4C4×C22⋊D4711yescharacteristic
223C4#1309399511yescharacteristic
224C4#1309400611yescharacteristic
225C2—21no—
226C2—21no—
227C2—21no—
228C2—81no—
229C2—1884no—
230C2#1568899911yescharacteristic
subgroupG/H
centerC2#15688999
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#421C2
socleC2×C47#386
hypercenter#421D47
hypocenterC47#1904
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
2. #15689597C2semidirect
3. #15689129C2semidirect
4. #15689097C2semidirect
5. #15688895C2semidirect
6. #15688879C2semidirect
7. C47×#421C2semidirect
11. C2×#10625336C4semidirect
12. C2×#10625334C4semidirect
30. C2×Q8×C47C2×C4semidirect
32. C2×D4×C47C2×C4semidirect
59. C2×C47⋊C8C2×C4semidirect
118. #421D47semidirect
123. C47#1904semidirect
146. C2×Q8C4×D47semidirect
154. C2×D4C4×D47semidirect