Finite Group Databasebeta

← #20244692

Subgroups — #20244692

Order 6016.

264 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 63 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#15689921C211yesmaximal, characteristic
2#15689149C211yesmaximal, characteristic, complemented
3#15689120C211yesmaximal, characteristic, complemented
4#15689097C211yesmaximal, characteristic, complemented
5#15689096C211yesmaximal, characteristic, complemented
6#15688879C211yesmaximal, characteristic, complemented
7C47×#416C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094055—21no—
10#13094054—21no—
11#13094050—21no—
12#13094049—21no—
13#13094044—22no—
14C2×#10625329C2211yescharacteristic
15#13093983C2211yescharacteristic
16#13093983C2211yescharacteristic
17Dic47⋊C8—22no—
18#13093949—21no—
19#13093946—21no—
20#13093939—22no—
21#13093938—22no—
22C2×#41×C47C2211yescharacteristic
23C22×C8×C47C2211yescharacteristic
24#117×C47C2211yescharacteristic
25#103×C47—21no—
26#102×C47—21no—
27#41×C47—21no—
28#41×C47—21no—
29#41×C47—21no—
30#41×C47—21no—
31C2×Q8×C47D411yescharacteristic
32C2×D4×C47—21no—
33C2×D4×C47D411yescharacteristic
34C22×C4×C47—21no—
35C22×C4×C47C2311yescharacteristic
36C2×C22⋊D47—21no—
37#10625350—21no—
38#10625350—21no—
39#10625350—21no—
40#10625350—21no—
41C2×D188D411yescharacteristic
42C2×C4×D47—21no—
43C2×Dic94D411yescharacteristic
44C2×C8×C47—21no—
45C2×C8×C47—21no—
46C2×C8×C47—21no—
47C4⋊C4×C47—21no—
48C22⋊C4×C47—21no—
49C42×C47—21no—
50C22⋊Dic47—21no—
51C22⋊Dic47D412yes—
52#10625337—22no—
53#10625336—22no—
54#10625335—22no—
55#10625334—22no—
56C4⋊Dic47—21no—
57C4⋊Dic47—21no—
58C4×Dic47—21no—
59C4×Dic47—21no—
60#10625329—21no—
61#10625329—21no—
62C2×C47⋊C8D412yes—
63C23×C47—21no—
64C23×C47C2×D411yescharacteristic
65C22×D47—21no—
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—41no—
74C2×C4×C47—41no—
75C2×C4×C47—41no—
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47#4111yescharacteristic
80C2×C4×C47#4111yescharacteristic
81C2×C4×C47#4111yescharacteristic
82C22⋊D47—41no—
83C22⋊D47—41no—
84C2×Dic47—22no—
85C2×Dic47—21no—
86C2×Dic47—41no—
87D188—21no—
88D188—21no—
89C4×D47—41no—
90C4×D47—41no—
91Dic94—21no—
92Dic94—21no—
93C8×C47—41no—
94C47⋊C8—22no—
95C22×C47—41no—
96C22×C47—41no—
97C22×C47—81no—
98C22×C47#12111yescharacteristic
99C22×C47#12111yescharacteristic
100C22×C47#12111yescharacteristic
101C2×D47—41no—
102C2×D47—81no—
103C4×C47—41no—
104C4×C47—81no—
105C4×C47#12011yescharacteristic
106C4×C47#12311yescharacteristic
107C4×C47#12311yescharacteristic
108C4×C47#12411yescharacteristic
109Dic47—42no—
110Dic47—41no—
111Dic47—81no—
112#2053—471nomaximal, Sylow
113C2×C47—21no—
114C2×C47—21no—
115C2×C47—21no—
116C2×C47—81no—
117C2×C47#39411yescharacteristic
118D47—81no—
119#575—471no—
120#424—471no—
121#416—471no—
122#416D4711yescharacteristic, complemented
123#410—471no—
124#410—471no—
125H(3,ℤ/4)—471no—
126C47#205311yescharacteristic, complemented, Sylow
127C2×#41—471no—
128C2×#41C2×D4711yescharacteristic
129#137—941no—
130#137—941no—
131AGL(1,ℤ/8)—941no—
132AGL(1,ℤ/8)—941no—
133#135—942no—
134C2×M16—471no—
135C22×C8C2×D4711yescharacteristic
136#117—471no—
137#117—471no—
138#117C2×D4711yescharacteristic
139C4⋊C8—942no—
140#103—21no—
141#103—941no—
142#102—21no—
143#102—941no—
144#99—942no—
145#99—942no—
146#41—21no—
147#41—21no—
148#41—21no—
149#41—21no—
150#41—941no—
151#41—941no—
152#41—941no—
153#41—941no—
154C2×Q8—471no—
155C2×Q8C22⋊D4711yescharacteristic
156C2×D4—21no—
157C2×D4—471no—
158C2×D4—941no—
159C2×D4C22⋊D4711yescharacteristic
160C22×C4—21no—
161C22×C4—941no—
162C22×C4C22×D4711yescharacteristic
163Q16—942no—
164SD16—942no—
165SD16—942no—
166D8—942no—
167M16—941no—
168M16—941no—
169C2×C8—21no—
170C2×C8—21no—
171C2×C8—21no—
172C2×C8—472no—
173C4⋊C4—21no—
174C4⋊C4—941no—
175C4⋊C4—941no—
176C22⋊C4—21no—
177C22⋊C4—472no—
178C22⋊C4—941no—
179C42—21no—
180C42—941no—
181C42—941no—
182C23—21no—
183C23—941no—
184C23D4×D4711yescharacteristic
185Q8—21no—
186Q8—21no—
187Q8—941no—
188Q8—941no—
189D4—21no—
190D4—21no—
191D4—41no—
192D4—41no—
193D4—941no—
194D4—941no—
195D4—1881no—
196D4—1881no—
197C2×C4—21no—
198C2×C4—41no—
199C2×C4—41no—
200C2×C4—41no—
201C2×C4—942no—
202C2×C4—941no—
203C2×C4—1881no—
204C2×C4—1881no—
205C2×C4—1881no—
206C2×C4#1062535011yescharacteristic
207C2×C4#1062535011yescharacteristic
208C2×C4D4×D4711yescharacteristic
209C2×C4D4×D4711yescharacteristic
210C2×C4#1062535211yescharacteristic
211C2×C4C2×C22⋊D4711yescharacteristic
212C8—41no—
213C8—942no—
214C22—41no—
215C22—41no—
216C22—81no—
217C22—3761no—
218C22—1881no—
219C22#1309399611yescharacteristic
220C22#1309399711yescharacteristic
221C22#1309399711yescharacteristic
222C4—41no—
223C4—81no—
224C4—3761no—
225C4—1882no—
226C4—1881no—
227C4#1309399211yescharacteristic
228C4#1309400611yescharacteristic
229C4#1309400711yescharacteristic
230C4#1309401011yescharacteristic
231C2—21no—
232C2—21no—
233C2—21no—
234C2—81no—
235C2—3761no—
236C2#1568903811yescharacteristic
subgroupG/H
centerC4#13094010
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#416C2
socleC2×C47#394
hypercenter#416D47
hypocenterC47#2053
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. #15689149C2semidirect
3. #15689120C2semidirect
4. #15689097C2semidirect
5. #15689096C2semidirect
6. #15688879C2semidirect
7. C47×#416C2semidirect
122. #416D47semidirect
126. C47#2053semidirect