Finite Group Databasebeta

← #20254003

Subgroups — #20254003

Order 6016.

362 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 115 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#15689738C212yesmaximal, complemented
2#15689520C211yesmaximal, characteristic, complemented
3#15689506C211yesmaximal, characteristic, complemented
4#15689481C212yesmaximal, complemented
5#15689382C211yesmaximal, characteristic, complemented
6#15689373C211yesmaximal, characteristic
7#15689351C212yesmaximal, complemented
8#15689231C211yesmaximal, characteristic, complemented
9C4×#10625335C212yesmaximal, complemented
10#15689080C211yesmaximal, characteristic, complemented
11C47×#442C211yesmaximal, characteristic, complemented
12C2×Dic188C2211yescharacteristic
13C2×#10625335C2212yes—
14C2×#10625324C2211yescharacteristic
15C2×C8×D47C2211yescharacteristic
16#13094023C2212yes—
17#13094017—22no—
18#13094011C2212yes—
19#13094010—22no—
20#13094007—22no—
21#13094004C2212yes—
22#13094003—22no—
23#13093995C2212yes—
24C4×Dic94C2212yes—
25#13093981C2211yescharacteristic
26#13093956C2211yescharacteristic
27#13093955C2212yes—
28#13093949C2212yes—
29#13093947C2212yes—
30#13093945C2212yes—
31#13093934C2211yescharacteristic
32C4×C47⋊C8C2211yescharacteristic
33C8×Dic47C2211yescharacteristic
34C2×D8×C47C2211yescharacteristic
35C4×D4×C47C2212yes—
36#106×C47C2211yescharacteristic
37#102×C47C2212yes—
38#97×C47C2211yescharacteristic
39C2×D4×C47C2312yes—
40C22×C4×C47—22no—
41C2×C22⋊D47—22no—
42C2×C4×D47C2311yescharacteristic
43C2×Dic94—22no—
44C2×Dic94C2312yes—
45D8×C47—22no—
46C2×C8×C47C2311yescharacteristic
47C2×C8×C47C2311yescharacteristic
48C4⋊C4×C47C2312yes—
49C22⋊C4×C47—22no—
50C42×C47C2311yescharacteristic
51C22⋊Dic47—22no—
52C22⋊Dic47—22no—
53C22⋊Dic47—22no—
54#10625335—24no—
55(C2×D47)⋊C4—22no—
56(C2×D47)⋊C4D412yes—
57C4⋊Dic47—22no—
58C4⋊Dic47C2312yes—
59Dic47⋊C4—22no—
60Dic47⋊C4—22no—
61Dic47⋊C4D412yes—
62C4×Dic47—22no—
63C4×Dic47C2311yescharacteristic
64C2×C47⋊C8C2311yescharacteristic
65C2×C47⋊C8C2311yescharacteristic
66Dic188—22no—
67#10625324—22no—
68C8×D47—22no—
69C23×C47—22no—
70C22×D47C2×D411yescharacteristic
71D4×C47—22no—
72D4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—82no—
75C2×C4×C47C2×D412yes—
76C2×C4×C47C2411yescharacteristic
77C22⋊D47—82no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47C2×D412yes—
81C2×Dic47C2×D411yescharacteristic
82C4×D47—21no—
83C4×D47—21no—
84Dic94—22no—
85Dic94—22no—
86Dic94—82no—
87C8×C47—21no—
88C8×C47#4112yes—
89C47⋊C8—21no—
90C47⋊C8#4112yes—
91C22×C47—42no—
92C22×C47—42no—
93C22×C47—42no—
94C22×C47C22×D411yescharacteristic
95C2×D47—21no—
96C2×D47—22no—
97C4×C47—22no—
98C4×C47—42no—
99C4×C47C2×#4111yescharacteristic
100C4×C47C2×#4111yescharacteristic
101Dic47—21no—
102Dic47—22no—
103Dic47—42no—
104Dic47—42no—
105#3173—471nomaximal, Sylow
106C2×C47—82no—
107C2×C47#53211yescharacteristic
108C2×C47#57712yes—
109D47—41no—
110#542—472no—
111#498—471no—
112#495—471no—
113#489—472no—
114#470—471no—
115#469—471no—
116#465—472no—
117#442D4711yescharacteristic, complemented
118#441—471no—
119C4×SD16—472no—
120#405—471no—
121C47#317311yescharacteristic, complemented, Sylow
122C2×Q16—471no—
123C2×SD16—472no—
124C2×D8C2×D4711yescharacteristic
125C2×M16—471no—
126C22×C8—471no—
127C4⋊Q8—472no—
128#126—942no—
129#124—472no—
130#124—942no—
131#123—942no—
132C22⋊Q8—472no—
133C22⋊Q8—942no—
134#121—472no—
135C4×Q8—472no—
136C4×D4C2×D4712yes—
137#117—471no—
138#106—471no—
139#106—472no—
140#106C2×D4711yescharacteristic
141#103—472no—
142#103—472no—
143#102—472no—
144#102C2×D4712yes—
145#97—471no—
146#97C2×D4711yescharacteristic
147C4×C8—471no—
148C4×C8—471no—
149C2×Q8—472no—
150C2×Q8—942no—
151C2×D4—942no—
152C2×D4C22×D4712yes—
153C22×C4—22no—
154C22×C4—471no—
155Q16—942no—
156SD16—944no—
157D8—22no—
158M16—942no—
159C2×C8—471no—
160C2×C8—471no—
161C2×C8—942no—
162C2×C8C22×D4711yescharacteristic
163C2×C8C22×D4711yescharacteristic
164C4⋊C4—472no—
165C4⋊C4—472no—
166C4⋊C4—942no—
167C4⋊C4—942no—
168C4⋊C4—942no—
169C4⋊C4C22×D4712yes—
170C22⋊C4—22no—
171C22⋊C4—472no—
172C22⋊C4—942no—
173C22⋊C4—942no—
174C22⋊C4—942no—
175C22⋊C4—942no—
176C42—471no—
177C42—942no—
178C42C22×D4711yescharacteristic
179C23—22no—
180C23—471no—
181Q8—942no—
182Q8—942no—
183Q8—3762no—
184D4—22no—
185D4—22no—
186D4—3762no—
187C2×C4—22no—
188C2×C4—82no—
189C2×C4—472no—
190C2×C4—471no—
191C2×C4—941no—
192C2×C4—941no—
193C2×C4—942no—
194C2×C4—942no—
195C2×C4D4×D4712yes—
196C2×C4C23×D4711yescharacteristic
197C8—21no—
198C8—472no—
199C8—941no—
200C8#1062535012yes—
201C22—42no—
202C22—42no—
203C22—42no—
204C22—941no—
205C22—942no—
206C22C2×D4×D4711yescharacteristic
207C4—22no—
208C4—42no—
209C4—941no—
210C4—942no—
211C4—1882no—
212C4—1882no—
213C4#41×D4711yescharacteristic
214C4C2×#1062535011yescharacteristic
215C2—82no—
216C2—1881no—
217C2#1568967011yescharacteristic
218C2#1568993312yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#442C2
socleC22×C47C22×D4
hypercenter#442D47
hypocenterC47#3173
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #15689738C2semidirect
2. #15689520C2semidirect
3. #15689506C2semidirect
4. #15689481C2semidirect
5. #15689382C2semidirect
7. #15689351C2semidirect
8. #15689231C2semidirect
9. C4×#10625335C2semidirect
10. #15689080C2semidirect
11. C47×#442C2semidirect
117. #442D47semidirect
121. C47#3173semidirect