Finite Group Databasebeta

← #20254002

Subgroups — #20254002

Order 6016.

362 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 117 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#15689742C212yesmaximal, complemented
2#15689521C211yesmaximal, characteristic, complemented
3#15689482C212yesmaximal, complemented
4#15689378C211yesmaximal, characteristic, complemented
5#15689373C211yesmaximal, characteristic
6#15689349C212yesmaximal, complemented
7#15689235C211yesmaximal, characteristic, complemented
8#15689230C211yesmaximal, characteristic, complemented
9SD16×Dic47C212yesmaximal, complemented
10#15689077C211yesmaximal, characteristic, complemented
11C47×#495C211yesmaximal, characteristic, complemented
12C2×#10625324C2211yescharacteristic
13C2×C8×D47C2211yescharacteristic
14#13094024C2212yes—
15#13094017—22no—
16#13094010—22no—
17#13094008—22no—
18#13094001—22no—
19#13094000C2212yes—
20#13093995C2212yes—
21Q8×Dic47C2212yes—
22D4×Dic47C2212yes—
23#13093981C2211yescharacteristic
24#13093956C2211yescharacteristic
25#13093956C2211yescharacteristic
26#13093956C2212yes—
27#13093948C2212yes—
28#13093948C2212yes—
29#13093945C2212yes—
30#13093945C2212yes—
31#13093935C2211yescharacteristic
32#13093934C2211yescharacteristic
33C8×Dic47C2211yescharacteristic
34C2×Q16×C47C2211yescharacteristic
35C2×SD16×C47C2212yes—
36C2×D8×C47C2211yescharacteristic
37#124×C47C2212yes—
38C4×C8×C47C2211yescharacteristic
39C2×Q8×C47C2312yes—
40C2×D4×C47C2312yes—
41C2×C22⋊D47—22no—
42C22×Dic47—22no—
43C2×C4×D47C2311yescharacteristic
44C2×Dic94—22no—
45Q16×C47—22no—
46SD16×C47—24no—
47D8×C47—22no—
48C2×C8×C47C2311yescharacteristic
49C2×C8×C47C2311yescharacteristic
50C22⋊C4×C47—22no—
51C22⋊C4×C47—22no—
52C42×C47C2311yescharacteristic
53C22⋊Dic47—22no—
54C22⋊Dic47—22no—
55(C2×D47)⋊C4—22no—
56(C2×D47)⋊C4D412yes—
57C4⋊Dic47—22no—
58C4⋊Dic47—22no—
59C4⋊Dic47C2312yes—
60C4⋊Dic47C2312yes—
61Dic47⋊C4—22no—
62Dic47⋊C4D412yes—
63C4×Dic47—22no—
64C4×Dic47C2311yescharacteristic
65C2×C47⋊C8C2311yescharacteristic
66C2×C47⋊C8C2311yescharacteristic
67#10625324—22no—
68C8×D47—22no—
69C23×C47—22no—
70C22×D47C2×D411yescharacteristic
71Q8×C47—22no—
72Q8×C47—22no—
73D4×C47—22no—
74D4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47C2×D412yes—
77C2×C4×C47C2411yescharacteristic
78C22⋊D47—82no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—82no—
82C2×Dic47C2×D412yes—
83C2×Dic47C2×D411yescharacteristic
84C4×D47—21no—
85C4×D47—21no—
86Dic94—82no—
87C8×C47#4112yes—
88C8×C47#4112yes—
89C47⋊C8—21no—
90C47⋊C8—21no—
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#495D4711yescharacteristic, complemented
113#489—472no—
114#470—471no—
115#469—471no—
116#465—472no—
117#442—471no—
118#441—471no—
119C4×SD16—472no—
120#405—471no—
121C47#317311yescharacteristic, complemented, Sylow
122C2×Q16C2×D4711yescharacteristic
123C2×SD16C2×D4712yes—
124C2×D8C2×D4711yescharacteristic
125C2×M16—471no—
126C22×C8—471no—
127C4⋊Q8—472no—
128#126—942no—
129#124—942no—
130#124C2×D4712yes—
131#123—942no—
132C22⋊Q8—472no—
133C22⋊Q8—942no—
134#121—472no—
135C4×Q8—472no—
136C4×D4—472no—
137#117—471no—
138#106—472no—
139#106—471no—
140#106—471no—
141#103—472no—
142#103—472no—
143#102—472no—
144#102—472no—
145#97—471no—
146#97—471no—
147C4×C8—471no—
148C4×C8C2×D4711yescharacteristic
149C2×Q8—942no—
150C2×Q8C22×D4712yes—
151C2×D4—942no—
152C2×D4C22×D4712yes—
153C22×C4—471no—
154C22×C4—942no—
155Q16—22no—
156SD16—24no—
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—472no—
167C4⋊C4—942no—
168C4⋊C4—942no—
169C4⋊C4—942no—
170C22⋊C4—22no—
171C22⋊C4—22no—
172C22⋊C4—472no—
173C22⋊C4—942no—
174C22⋊C4—942no—
175C22⋊C4—942no—
176C42—471no—
177C42—942no—
178C42C22×D4711yescharacteristic
179C23—22no—
180C23—471no—
181Q8—22no—
182Q8—22no—
183Q8—3762no—
184D4—22no—
185D4—22no—
186D4—3762no—
187C2×C4—22no—
188C2×C4—472no—
189C2×C4—471no—
190C2×C4—941no—
191C2×C4—941no—
192C2×C4—942no—
193C2×C4—942no—
194C2×C4—3762no—
195C2×C4D4×D4712yes—
196C2×C4C23×D4711yescharacteristic
197C8—941no—
198C8—941no—
199C8#1062535212yes—
200C8#1062535212yes—
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—
213C4C2×#1062535211yescharacteristic
214C4C2×#1062535211yescharacteristic
215C2—82no—
216C2—1881no—
217C2#1568967111yescharacteristic
218C2#1568993012yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#495C2
socleC22×C47C22×D4
hypercenter#495D47
hypocenterC47#3173
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #495

Complements

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

NH ≅ G/Ntype
1. #15689742C2semidirect
2. #15689521C2semidirect
3. #15689482C2semidirect
4. #15689378C2semidirect
6. #15689349C2semidirect
7. #15689235C2semidirect
8. #15689230C2semidirect
9. SD16×Dic47C2semidirect
10. #15689077C2semidirect
11. C47×#495C2semidirect
112. #495D47semidirect
121. C47#3173semidirect