Finite Group Databasebeta

← #20254006

Subgroups — #20254006

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#15689746C212yesmaximal, complemented
2#15689520C211yesmaximal, characteristic, complemented
3#15689508C211yesmaximal, characteristic, complemented
4#15689484C212yesmaximal, complemented
5#15689376C211yesmaximal, characteristic
6#15689354C212yesmaximal, complemented
7#15689234C211yesmaximal, characteristic, complemented
8#15689230C211yesmaximal, characteristic, complemented
9#15689208C212yesmaximal, complemented
10#15689081C211yesmaximal, characteristic, complemented
11C47×#470C211yesmaximal, characteristic, complemented
12C2×#10625336C2212yes—
13C2×D376C2211yescharacteristic
14C22×C47⋊C8C2211yescharacteristic
15#13094023C2212yes—
16#13094019—22no—
17#13094013C2212yes—
18#13094010—22no—
19#13094006—22no—
20#13094004—22no—
21#13093998C2212yes—
22Q8×Dic47C2212yes—
23#13093986C2212yes—
24#13093983C2211yescharacteristic
25#13093956C2211yescharacteristic
26#13093955C2212yes—
27#13093948C2212yes—
28#13093946C2212yes—
29#13093944C2212yes—
30#13093934C2211yescharacteristic
31#13093934C2211yescharacteristic
32C8×Dic47C2211yescharacteristic
33C8×Dic47C2211yescharacteristic
34C2×Q16×C47C2211yescharacteristic
35C2×M16×C47C2211yescharacteristic
36C22⋊Q8×C47C2212yes—
37#106×C47C2211yescharacteristic
38#103×C47C2212yes—
39C2×Q8×C47C2312yes—
40C22×C4×C47C2311yescharacteristic
41C2×C22⋊D47—22no—
42C2×D188C2312yes—
43C2×C4×D47—22no—
44C2×Dic94—22no—
45Q16×C47—22no—
46M16×C47—22no—
47C2×C8×C47C2311yescharacteristic
48C2×C8×C47C2311yescharacteristic
49C4⋊C4×C47—22no—
50C4⋊C4×C47C2312yes—
51C22⋊C4×C47—22no—
52C22⋊Dic47D412yes—
53#10625336—24no—
54(C2×D47)⋊C4—22no—
55(C2×D47)⋊C4—22no—
56(C2×D47)⋊C4—22no—
57(C2×D47)⋊C4—22no—
58C4⋊Dic47—22no—
59C4⋊Dic47D412yes—
60C4⋊Dic47C2312yes—
61Dic47⋊C4—22no—
62C4×Dic47—22no—
63C4×Dic47C2311yescharacteristic
64C4×Dic47C2311yescharacteristic
65C2×C47⋊C8—22no—
66C2×C47⋊C8C2311yescharacteristic
67C2×C47⋊C8C2311yescharacteristic
68D376—22no—
69C23×C47C2×D411yescharacteristic
70C22×D47—22no—
71Q8×C47—22no—
72Q8×C47—22no—
73C2×C4×C47—21no—
74C2×C4×C47—21no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2411yescharacteristic
79C22⋊D47—82no—
80C2×Dic47—22no—
81C2×Dic47C2×D412yes—
82C2×Dic47C2×D412yes—
83D188—22no—
84D188—22no—
85C4×D47—82no—
86Dic94—82no—
87C8×C47—21no—
88C8×C47#4112yes—
89C47⋊C8—21no—
90C47⋊C8#4112yes—
91C22×C47—21no—
92C22×C47—22no—
93C22×C47C22×D411yescharacteristic
94C2×D47—42no—
95C2×D47—42no—
96C2×D47—42no—
97C4×C47—21no—
98C4×C47—42no—
99C4×C47—42no—
100C4×C47C2×#4111yescharacteristic
101C4×C47C2×#4111yescharacteristic
102Dic47—22no—
103Dic47—22no—
104Dic47—42no—
105#3173—471nomaximal, Sylow
106C2×C47—41no—
107C2×C47#53211yescharacteristic
108C2×C47#57712yes—
109D47—82no—
110#542—472no—
111#498—471no—
112#495—471no—
113#489—472no—
114#470D4711yescharacteristic, complemented
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×SD16—472no—
124C2×D8—471no—
125C2×M16C2×D4711yescharacteristic
126C22×C8—471no—
127C4⋊Q8—472no—
128#126—942no—
129#124—472no—
130#124—942no—
131#123—942no—
132C22⋊Q8—942no—
133C22⋊Q8C2×D4712yes—
134#121—472no—
135C4×Q8—472no—
136C4×D4—472no—
137#117—471no—
138#106—471no—
139#106—472no—
140#106C2×D4711yescharacteristic
141#103—472no—
142#103C2×D4712yes—
143#102—472no—
144#102—472no—
145#97—471no—
146#97—471no—
147C4×C8—471no—
148C4×C8—471no—
149C2×Q8—942no—
150C2×Q8C22×D4712yes—
151C2×D4—472no—
152C2×D4—942no—
153C22×C4—942no—
154C22×C4C22×D4711yescharacteristic
155Q16—22no—
156SD16—944no—
157D8—942no—
158M16—22no—
159C2×C8—471no—
160C2×C8—471no—
161C2×C8—942no—
162C2×C8C22×D4711yescharacteristic
163C2×C8C22×D4711yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—472no—
166C4⋊C4—472no—
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—471no—
178C42—942no—
179C23—942no—
180C23D4×D4711yescharacteristic
181Q8—22no—
182Q8—22no—
183Q8—3762no—
184D4—942no—
185D4—942no—
186D4—3762no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—472no—
192C2×C4—472no—
193C2×C4—942no—
194C2×C4—3762no—
195C2×C4D4×D4711yescharacteristic
196C2×C4C23×D4711yescharacteristic
197C8—21no—
198C8—472no—
199C8—941no—
200C8#1062535212yes—
201C22—21no—
202C22—22no—
203C22—1882no—
204C22—1882no—
205C22—1882no—
206C22C2×D4×D4711yescharacteristic
207C4—21no—
208C4—42no—
209C4—42no—
210C4—942no—
211C4—942no—
212C4—1882no—
213C4#41×D4711yescharacteristic
214C4C2×#1062535211yescharacteristic
215C2—41no—
216C2—3762no—
217C2#1568966811yescharacteristic
218C2#1568993212yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#470C2
socleC22×C47C22×D4
hypercenter#470D47
hypocenterC47#3173
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #470

Complements

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

NH ≅ G/Ntype
1. #15689746C2semidirect
2. #15689520C2semidirect
3. #15689508C2semidirect
4. #15689484C2semidirect
6. #15689354C2semidirect
7. #15689234C2semidirect
8. #15689230C2semidirect
9. #15689208C2semidirect
10. #15689081C2semidirect
11. C47×#470C2semidirect
114. #470D47semidirect
121. C47#3173semidirect