Finite Group Databasebeta

← #20243868

Subgroups — #20243868

Order 6016.

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

normal subgroups only

This group has 324 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×#13094049C211yesmaximal, characteristic
2#15689140C211yesmaximal, characteristic, complemented
3#15689129C211yesmaximal, characteristic, complemented
4C2×#13093940C211yesmaximal, characteristic, complemented
5#15688895C211yesmaximal, characteristic, complemented
6C47⋊#338C211yesmaximal, characteristic, complemented
7C47×#568C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9#13094049—22no—
10#13094049—22no—
11C2×#10625336C412yescomplemented
12C2×#10625334C412yescomplemented
13C2×#10625329C2211yescharacteristic
14C2×#10625329C2211yescharacteristic
15#13093983C2211yescharacteristic
16#13093951—22no—
17#13093946—22no—
18#13093940—22no—
19C2×#41×C47C2211yescharacteristic
20#131×C47—22no—
21#131×C47—22no—
22C2×M16×C47—22no—
23C2×M16×C47C2211yescharacteristic
24C2×M16×C47C2211yescharacteristic
25C23×D47—21no—
26#41×C47—21no—
27#41×C47—21no—
28#41×C47D412yes—
29#41×C47D412yes—
30C2×Q8×C47C2×C411yescharacteristic
31C2×D4×C47—21no—
32C2×D4×C47C2×C411yescharacteristic
33C22×C4×C47—21no—
34C22×C4×C47C2311yescharacteristic
35C2×D188—21no—
36C2×D188—21no—
37C2×D188—21no—
38C2×D188—21no—
39C2×D188—21no—
40C2×D188C2×C412yes—
41M16×C47—24no—
42M16×C47—21no—
43M16×C47—21no—
44M16×C47—21no—
45M16×C47D412yes—
46C2×C8×C47—24no—
47C2×C8×C47—21no—
48C2×C8×C47D412yes—
49C22⋊Dic47—21no—
50#10625336—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×C412yes—
60C23×C47—21no—
61C23×C47#4111yescharacteristic
62C22×D47—22no—
63C22×D47—41no—
64C22×D47—41no—
65C22×D47—82no—
66Q8×C47—21no—
67Q8×C47C22⋊C412yes—
68D4×C47—22no—
69D4×C47—22no—
70D4×C47—21no—
71D4×C47C22⋊C412yes—
72C2×C4×C47—21no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47C22×C411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47#4111yescharacteristic
81C2×Dic47—41no—
82D188—22no—
83D188—22no—
84D188—41no—
85D188—41no—
86C8×C47—22no—
87C8×C47—22no—
88C47⋊C8—22no—
89C47⋊C8—41no—
90C22×C47—22no—
91C22×C47—41no—
92C22×C47—81no—
93C22×C47C4×D411yescharacteristic
94C22×C47#12111yescharacteristic
95C22×C47#12311yescharacteristic
96C2×D47—42no—
97C2×D47—82no—
98C2×D47—82no—
99C2×D47—82no—
100C4×C47—22no—
101C4×C47C2×C22⋊C411yescharacteristic
102C4×C47C4×D411yescharacteristic
103C4×C47#12011yescharacteristic
104C4×C47#12111yescharacteristic
105Dic47—81no—
106#1903—471nomaximal, Sylow
107C2×C47—21no—
108C2×C47—21no—
109C2×C47—21no—
110C2×C47—42no—
111C2×C47#38611yescharacteristic
112D47—82no—
113C2×AGL(1,ℤ/8)—471no—
114#568D4711yescharacteristic, complemented
115#421—471no—
116#418—471no—
117C2×#100—471no—
118#344—471no—
119#338—471no—
120C47#190311yescharacteristic, complemented, Sylow
121C2×#41C2×D4711yescharacteristic
122C22×D4—471no—
123AGL(1,ℤ/8)—942no—
124AGL(1,ℤ/8)—942no—
125C2×SD16—472no—
126C2×D8—472no—
127#131—22no—
128#131—22no—
129C2×M16—22no—
130C2×M16—471no—
131C2×M16—471no—
132C2×M16C2×D4711yescharacteristic
133C2×M16C2×D4711yescharacteristic
134#117—471no—
135#104—942no—
136#102—942no—
137#100—942no—
138C24—941no—
139#41—21no—
140#41—21no—
141#41D18812yes—
142#41C22⋊D4712yes—
143C2×Q8C4×D4711yescharacteristic
144C2×D4—21no—
145C2×D4—472no—
146C2×D4—941no—
147C2×D4—941no—
148C2×D4—941no—
149C2×D4—941no—
150C2×D4—941no—
151C2×D4C4×D4711yescharacteristic
152C22×C4—21no—
153C22×C4C22×D4711yescharacteristic
154SD16—944no—
155D8—944no—
156M16—24no—
157M16—21no—
158M16—21no—
159M16—21no—
160M16—941no—
161M16—941no—
162M16—941no—
163M16—941no—
164M16C22⋊D4712yes—
165C2×C8—24no—
166C2×C8—21no—
167C2×C8—472no—
168C2×C8—941no—
169C2×C8C22⋊D4712yes—
170C4⋊C4—941no—
171C22⋊C4—941no—
172C42—941no—
173C23—21no—
174C23—942no—
175C23—3762no—
176C23—1881no—
177C23—1881no—
178C23#1062535011yescharacteristic
179Q8—21no—
180Q8(C2×D47)⋊C412yes—
181D4—22no—
182D4—22no—
183D4—21no—
184D4—942no—
185D4—942no—
186D4—1881no—
187D4—1881no—
188D4(C2×D47)⋊C412yes—
189C2×C4—21no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—1881no—
193C2×C4C2×C4×D4711yescharacteristic
194C2×C4C2×D18811yescharacteristic
195C2×C4#1062535011yescharacteristic
196C2×C4C2×C22⋊D4711yescharacteristic
197C2×C4C2×C22⋊D4711yescharacteristic
198C2×C4C2×C22⋊D4711yescharacteristic
199C8—22no—
200C8—22no—
201C8—942no—
202C8—1881no—
203C22—22no—
204C22—41no—
205C22—81no—
206C22—3762no—
207C22—3762no—
208C22—3762no—
209C22—1882no—
210C22C4×C22⋊D4711yescharacteristic
211C22#1309399811yescharacteristic
212C22#1309400711yescharacteristic
213C4—22no—
214C4—3761no—
215C4C2×(C2×D47)⋊C411yescharacteristic
216C4C4×C22⋊D4711yescharacteristic
217C4#1309399311yescharacteristic
218C4#1309399811yescharacteristic
219C2—21no—
220C2—21no—
221C2—21no—
222C2—42no—
223C2—3762no—
224C2#1568900211yescharacteristic
subgroupG/H
centerC2#15689002
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#568C2
socleC2×C47#386
hypercenter#568D47
hypocenterC47#1903
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #568

Complements

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

NH ≅ G/Ntype
2. #15689140C2semidirect
3. #15689129C2semidirect
4. C2×#13093940C2semidirect
5. #15688895C2semidirect
6. C47⋊#338C2semidirect
7. C47×#568C2semidirect
11. C2×#10625336C4semidirect
12. C2×#10625334C4semidirect
114. #568D47semidirect
120. C47#1903semidirect