Finite Group Databasebeta

← #20254118

Subgroups — #20254118

Order 6016.

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

normal subgroups only

This group has 370 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#15689659C212yesmaximal, complemented
2#15689523C211yesmaximal, characteristic, complemented
3#15689508C211yesmaximal, characteristic, complemented
4#15689479C212yesmaximal, complemented
5#15689376C211yesmaximal, characteristic
6#15689371C212yesmaximal, complemented
7#15689234C211yesmaximal, characteristic, complemented
8#15689230C211yesmaximal, characteristic, complemented
9#15689226C212yesmaximal, complemented
10M16×Dic47C211yesmaximal, characteristic, complemented
11C47×#470C211yesmaximal, characteristic, complemented
12C2×#10625336C2212yes—
13C2×D376C2211yescharacteristic
14C2×#10625329C2211yescharacteristic
15#13094019—22no—
16#13094015C2212yes—
17#13094013C2212yes—
18#13094008—22no—
19#13093998C2212yes—
20Q8×Dic47C2212yes—
21#13093986C2212yes—
22(C22⋊D47)⋊C4—22no—
23#13093982—22no—
24C2×C4×Dic47C2211yescharacteristic
25#13093957C2212yes—
26#13093956C2211yescharacteristic
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—
42C22×Dic47D412yes—
43C2×D188C2312yes—
44C2×C4×D47—22no—
45Q16×C47—22no—
46M16×C47—22no—
47C2×C8×C47C2311yescharacteristic
48C2×C8×C47C2311yescharacteristic
49C4⋊C4×C47—22no—
50C4⋊C4×C47C2312yes—
51C22⋊C4×C47—22no—
52#10625336—24no—
53(C2×D47)⋊C4—22no—
54(C2×D47)⋊C4—22no—
55(C2×D47)⋊C4—22no—
56(C2×D47)⋊C4—22no—
57C4⋊Dic47—22no—
58C4⋊Dic47—22no—
59C4⋊Dic47C2312yes—
60Dic47⋊C4—22no—
61C4×Dic47—22no—
62C4×Dic47D412yes—
63C4×Dic47C2311yescharacteristic
64C4×Dic47C2311yescharacteristic
65#10625329—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—44no—
80C2×Dic47—22no—
81C2×Dic47—42no—
82C2×Dic47C2×D412yes—
83C2×Dic47C2×D412yes—
84D188—22no—
85D188—22no—
86C4×D47—44no—
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#3183—471nomaximal, Sylow
106C2×C47—41no—
107C2×C47#53211yescharacteristic
108C2×C47#57512yes—
109D47—82no—
110#529—472no—
111#499—471no—
112#495—471no—
113#488—472no—
114#470D4711yescharacteristic, complemented
115#469—471no—
116#468—472no—
117#442—471no—
118#441—471no—
119#440—472no—
120C4×M16—471no—
121C47#318311yescharacteristic, complemented, Sylow
122C2×Q16C2×D4711yescharacteristic
123C2×SD16—472no—
124C2×D8—471no—
125C2×M16—471no—
126C2×M16C2×D4711yescharacteristic
127#126—942no—
128#125—472no—
129#124—472no—
130#123—942no—
131C22⋊Q8C2×D4712yes—
132#121—472no—
133C4×Q8—472no—
134C4×D4—472no—
135C4×D4—942no—
136#117—942no—
137C2×C42—471no—
138#107—472no—
139#106—471no—
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×Q8C22×D4712yes—
150C2×D4—472no—
151C2×D4—942no—
152C22×C4—472no—
153C22×C4—942no—
154C22×C4C22×D4711yescharacteristic
155Q16—22no—
156SD16—944no—
157D8—942no—
158M16—22no—
159M16—942no—
160C2×C8—471no—
161C2×C8—471no—
162C2×C8C22×D4711yescharacteristic
163C2×C8C22×D4711yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—472no—
166C4⋊C4—942no—
167C4⋊C4—942no—
168C4⋊C4—942no—
169C4⋊C4C22×D4712yes—
170C22⋊C4—22no—
171C22⋊C4—942no—
172C22⋊C4—942no—
173C22⋊C4—942no—
174C22⋊C4—942no—
175C42—472no—
176C42—471no—
177C42—471no—
178C42—942no—
179C23—942no—
180C23D4×D4711yescharacteristic
181Q8—22no—
182Q8—22no—
183D4—942no—
184D4—942no—
185D4—1884no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—472no—
191C2×C4—472no—
192C2×C4—942no—
193C2×C4—1884no—
194C2×C4—1882no—
195C2×C4D4×D4711yescharacteristic
196C2×C4C23×D4711yescharacteristic
197C8—21no—
198C8—472no—
199C8—941no—
200C8#1062535212yes—
201C22—22no—
202C22—21no—
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#1568992212yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#470C2
socleC22×C47C22×D4
hypercenter#470D47
hypocenterC47#3183
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. #15689659C2semidirect
2. #15689523C2semidirect
3. #15689508C2semidirect
4. #15689479C2semidirect
6. #15689371C2semidirect
7. #15689234C2semidirect
8. #15689230C2semidirect
9. #15689226C2semidirect
10. M16×Dic47C2semidirect
11. C47×#470C2semidirect
114. #470D47semidirect
121. C47#3183semidirect