Finite Group Databasebeta

← #20243896

Subgroups — #20243896

Order 6016.

332 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 93 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#15689124C211yesmaximal, characteristic, complemented
3C2×#13093946C211yesmaximal, characteristic, complemented
4C2×#13093940C211yesmaximal, characteristic, complemented
5#15688891C211yesmaximal, characteristic, complemented
6#15688888C211yesmaximal, characteristic, complemented
7C2×#131×C47C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9#13094049—22no—
10#13094049C414yescomplemented
11C2×#10625336—21no—
12C2×#10625334—21no—
13C2×#10625329C2211yescharacteristic
14C2×#10625329C2211yescharacteristic
15C2×C4⋊Dic47C2211yescharacteristic
16#13093948—21no—
17#13093946—21no—
18#13093946—21no—
19#13093945—21no—
20#13093940—22no—
21C2×#41×C47C2211yescharacteristic
22#131×C47—22no—
23#131×C47—22no—
24C2×M16×C47—21no—
25C2×M16×C47C2211yescharacteristic
26C22×C8×C47—21no—
27C22×C8×C47C2211yescharacteristic
28C23×D47—21no—
29#41×C47—21no—
30#41×C47—21no—
31#41×C47C2×C412yes—
32#41×C47D412yes—
33C2×Q8×C47D411yescharacteristic
34C2×D4×C47—21no—
35C2×D4×C47D411yescharacteristic
36C22×C4×C47—21no—
37C22×C4×C47C2311yescharacteristic
38C22×Dic47—21no—
39C2×D188—21no—
40C2×D188—21no—
41C2×D188—21no—
42C2×D188—21no—
43C2×D188—21no—
44C2×D188C2×C412yes—
45M16×C47—24no—
46M16×C47—21no—
47M16×C47D412yes—
48C2×C8×C47—24no—
49C2×C8×C47—21no—
50C2×C8×C47—21no—
51C2×C8×C47—21no—
52C2×C8×C47D411yescharacteristic
53C2×C8×C47D411yescharacteristic
54#10625336—24no—
55#10625334—24no—
56C4⋊Dic47—21no—
57C4⋊Dic47—21no—
58#10625329—21no—
59#10625329—21no—
60#10625329—21no—
61#10625329C2×C412yes—
62C2×C47⋊C8—21no—
63C2×C47⋊C8—21no—
64C23×C47—21no—
65C23×C47#4111yescharacteristic
66C22×D47—22no—
67C22×D47—41no—
68C22×D47—41no—
69C22×D47—81no—
70C22×D47—81no—
71Q8×C47—21no—
72Q8×C47C22⋊C412yes—
73D4×C47—22no—
74D4×C47—22no—
75D4×C47—21no—
76D4×C47C22⋊C412yes—
77C2×C4×C47—21no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47C22×C411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47#4111yescharacteristic
86C2×Dic47—41no—
87C2×Dic47—81no—
88D188—22no—
89D188—22no—
90D188—41no—
91D188—41no—
92C8×C47—21no—
93C8×C47—22no—
94C8×C47—21no—
95C47⋊C8—22no—
96C47⋊C8—41no—
97C22×C47—21no—
98C22×C47—21no—
99C22×C47—22no—
100C22×C47—41no—
101C22×C47—41no—
102C22×C47C4×D411yescharacteristic
103C22×C47#12111yescharacteristic
104C22×C47#12311yescharacteristic
105C2×D47—42no—
106C2×D47—82no—
107C2×D47—81no—
108C2×D47—81no—
109C2×D47—82no—
110C4×C47—22no—
111C4×C47C2×C22⋊C411yescharacteristic
112C4×C47C4×D411yescharacteristic
113C4×C47#12011yescharacteristic
114C4×C47#12111yescharacteristic
115Dic47—81no—
116#1907—471nomaximal, Sylow
117C2×C47—21no—
118C2×C47—21no—
119C2×C47—42no—
120C2×C47#38611yescharacteristic
121C2×C47#47111yescharacteristic
122C2×C47#47211yescharacteristic
123D47—82no—
124C2×AGL(1,ℤ/8)—471no—
125C2×#131D4711yescharacteristic, complemented
126#417—471no—
127C2×#102—471no—
128C2×#100—471no—
129#343—471no—
130#341—471no—
131C47#190711yescharacteristic, complemented, Sylow
132C2×#41C2×D4711yescharacteristic
133C22×D4—471no—
134AGL(1,ℤ/8)—474no—
135AGL(1,ℤ/8)—942no—
136C2×SD16—941no—
137C2×D8—941no—
138#131—22no—
139#131—22no—
140C2×M16—21no—
141C2×M16—471no—
142C2×M16—471no—
143C2×M16C2×D4711yescharacteristic
144C22×C8—21no—
145C22×C8C2×D4711yescharacteristic
146C2×C4⋊C4—471no—
147#103—941no—
148#102—941no—
149#102—941no—
150#102—941no—
151#100—942no—
152C24—941no—
153#41—21no—
154#41—21no—
155#41C4×D4712yes—
156#41C22⋊D4712yes—
157C2×Q8D18811yescharacteristic
158C2×D4—21no—
159C2×D4—472no—
160C2×D4—941no—
161C2×D4—941no—
162C2×D4—941no—
163C2×D4—941no—
164C2×D4—941no—
165C2×D4D18811yescharacteristic
166C22×C4—21no—
167C22×C4—941no—
168C22×C4C22×D4711yescharacteristic
169SD16—944no—
170D8—944no—
171M16—24no—
172M16—21no—
173M16—472no—
174M16—941no—
175M16—941no—
176M16—941no—
177M16C22⋊D4712yes—
178C2×C8—24no—
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—21no—
182C2×C8—941no—
183C2×C8—941no—
184C2×C8C22⋊D4711yescharacteristic
185C2×C8C22⋊D4711yescharacteristic
186C4⋊C4—941no—
187C4⋊C4—941no—
188C23—21no—
189C23—942no—
190C23—3761no—
191C23—3761no—
192C23—1881no—
193C23—1881no—
194C23#1062535011yescharacteristic
195Q8—21no—
196Q8(C2×D47)⋊C412yes—
197D4—22no—
198D4—22no—
199D4—21no—
200D4—942no—
201D4—942no—
202D4—1881no—
203D4—1881no—
204D4(C2×D47)⋊C412yes—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—22no—
208C2×C4—3761no—
209C2×C4—1881no—
210C2×C4C2×C4×D4711yescharacteristic
211C2×C4C2×D18811yescharacteristic
212C2×C4#1062535011yescharacteristic
213C2×C4C2×C22⋊D4711yescharacteristic
214C2×C4C2×C22⋊D4711yescharacteristic
215C2×C4C2×C22⋊D4711yescharacteristic
216C8—21no—
217C8—22no—
218C8—21no—
219C8—942no—
220C8—1881no—
221C22—21no—
222C22—21no—
223C22—22no—
224C22—41no—
225C22—41no—
226C22—3762no—
227C22—3762no—
228C22—3761no—
229C22—3761no—
230C22—1882no—
231C22C4×C22⋊D4711yescharacteristic
232C22#1309399811yescharacteristic
233C22#1309400711yescharacteristic
234C4—22no—
235C4—3761no—
236C4C2×(C2×D47)⋊C411yescharacteristic
237C4C4×C22⋊D4711yescharacteristic
238C4#1309399311yescharacteristic
239C4#1309399811yescharacteristic
240C2—21no—
241C2—21no—
242C2—42no—
243C2—3762no—
244C2#1568900211yescharacteristic
245C2#1568938611yescharacteristic
246C2#1568939311yescharacteristic
subgroupG/H
centerC22#13093998
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#131×C47C2
socleC22×C47#121
hypercenterC2×#131D47
hypocenterC47#1907
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#131

Complements

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

NH ≅ G/Ntype
2. #15689124C2semidirect
3. C2×#13093946C2semidirect
4. C2×#13093940C2semidirect
5. #15688891C2semidirect
6. #15688888C2semidirect
7. C2×#131×C47C2semidirect
10. #13094049C4semidirect
125. C2×#131D47semidirect
131. C47#1907semidirect