Finite Group Databasebeta

← #20254119

Subgroups — #20254119

Order 6016.

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

normal subgroups only

This group has 370 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#15689658C212yesmaximal, complemented
2#15689507C211yesmaximal, characteristic, complemented
3#15689480C212yesmaximal, complemented
4#15689382C211yesmaximal, characteristic, complemented
5#15689377C211yesmaximal, characteristic
6#15689370C212yesmaximal, complemented
7#15689234C211yesmaximal, characteristic, complemented
8#15689229C211yesmaximal, characteristic, complemented
9#15689222C212yesmaximal, complemented
10C4×#10625324C211yesmaximal, characteristic, complemented
11C47×#499C211yesmaximal, characteristic, complemented
12C2×Dic188C2211yescharacteristic
13C2×#10625325C2212yes—
14C2×D376C2211yescharacteristic
15C2×#10625324C2211yescharacteristic
16C2×#10625324C2211yescharacteristic
17#13094019—22no—
18#13094012C2212yes—
19#13094009—22no—
20#13094004C2212yes—
21#13093999C2212yes—
22#13093989C2212yes—
23#13093986—22no—
24#13093986C2212yes—
25#13093982—22no—
26C42×D47C2211yescharacteristic
27#13093947C2212yes—
28#13093947C2212yes—
29#13093944C2212yes—
30#13093944C2212yes—
31#13093934C2211yescharacteristic
32#13093934C2211yescharacteristic
33C4×C47⋊C8C2211yescharacteristic
34#125×C47C2212yes—
35#107×C47C2212yes—
36#106×C47C2211yescharacteristic
37#106×C47C2211yescharacteristic
38C4×C8×C47C2211yescharacteristic
39C2×D188—22no—
40C2×D188C2312yes—
41C2×C4×D47—22no—
42C2×C4×D47D412yes—
43C2×C4×D47C2311yescharacteristic
44C2×Dic94C2312yes—
45C2×C8×C47C2311yescharacteristic
46C2×C8×C47C2311yescharacteristic
47C4⋊C4×C47—22no—
48C4⋊C4×C47—22no—
49C4⋊C4×C47C2312yes—
50C4⋊C4×C47C2312yes—
51C42×C47C2311yescharacteristic
52(C2×D47)⋊C4—22no—
53(C2×D47)⋊C4—22no—
54(C2×D47)⋊C4—22no—
55(C2×D47)⋊C4—22no—
56(C2×D47)⋊C4—22no—
57C4⋊Dic47—22no—
58Dic47⋊C4—22no—
59C4×Dic47—22no—
60C4×Dic47D412yes—
61C4×Dic47C2311yescharacteristic
62C2×C47⋊C8C2311yescharacteristic
63C2×C47⋊C8C2311yescharacteristic
64Dic188—22no—
65D376—22no—
66#10625325—24no—
67#10625324—22no—
68#10625324—22no—
69C22×D47—22no—
70C22×D47C2×D411yescharacteristic
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47C2×D412yes—
74C2×C4×C47C2411yescharacteristic
75C2×Dic47—22no—
76C2×Dic47C2×D412yes—
77C2×Dic47C2×D411yescharacteristic
78D188—22no—
79D188—22no—
80D188—44no—
81C4×D47—21no—
82C4×D47—21no—
83C4×D47—42no—
84C4×D47—44no—
85Dic94—22no—
86Dic94—22no—
87C8×C47#4112yes—
88C8×C47#4112yes—
89C47⋊C8—21no—
90C47⋊C8—21no—
91C22×C47C22×D411yescharacteristic
92C2×D47—21no—
93C2×D47—22no—
94C2×D47—42no—
95C2×D47—42no—
96C2×D47—42no—
97C4×C47—22no—
98C4×C47—42no—
99C4×C47—42no—
100C4×C47C2×#4111yescharacteristic
101C4×C47C2×#4111yescharacteristic
102Dic47—21no—
103Dic47—22no—
104Dic47—42no—
105#3183—471nomaximal, Sylow
106C2×C47#53211yescharacteristic
107C2×C47#57512yes—
108D47—41no—
109D47—82no—
110#529—472no—
111#499D4711yescharacteristic, complemented
112#495—471no—
113#488—472no—
114#470—471no—
115#469—471no—
116#468—472no—
117#442—471no—
118#441—471no—
119#440—472no—
120C4×M16—471no—
121C47#318311yescharacteristic, complemented, Sylow
122C2×Q16—471no—
123C2×SD16—472no—
124C2×D8—471no—
125C2×M16—471no—
126C2×M16—471no—
127#126—942no—
128#125C2×D4712yes—
129#124—472no—
130#123—942no—
131C22⋊Q8—472no—
132#121—472no—
133C4×Q8—472no—
134C4×D4—472no—
135C4×D4—942no—
136#117—942no—
137C2×C42—471no—
138#107C2×D4712yes—
139#106C2×D4711yescharacteristic
140#106C2×D4711yescharacteristic
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—472no—
150C2×D4—472no—
151C2×D4—942no—
152C22×C4—471no—
153C22×C4—472no—
154C22×C4—942no—
155Q16—942no—
156SD16—944no—
157D8—942no—
158M16—942no—
159M16—942no—
160C2×C8—471no—
161C2×C8—471no—
162C2×C8C22×D4711yescharacteristic
163C2×C8C22×D4711yescharacteristic
164C4⋊C4—22no—
165C4⋊C4—22no—
166C4⋊C4—942no—
167C4⋊C4—942no—
168C4⋊C4C22×D4712yes—
169C4⋊C4C22×D4712yes—
170C22⋊C4—942no—
171C22⋊C4—942no—
172C22⋊C4—942no—
173C22⋊C4—942no—
174C22⋊C4—942no—
175C42—472no—
176C42—471no—
177C42—942no—
178C42C22×D4711yescharacteristic
179C23—471no—
180C23—942no—
181Q8—942no—
182Q8—942no—
183D4—942no—
184D4—942no—
185D4—1884no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—472no—
189C2×C4—471no—
190C2×C4—941no—
191C2×C4—941no—
192C2×C4—942no—
193C2×C4—1882no—
194C2×C4—1884no—
195C2×C4D4×D4712yes—
196C2×C4C23×D4711yescharacteristic
197C8—941no—
198C8—941no—
199C8#1062535412yes—
200C8#1062535412yes—
201C22—942no—
202C22—941no—
203C22—1882no—
204C22—1882no—
205C22—1882no—
206C22C2×D4×D4711yescharacteristic
207C4—22no—
208C4—42no—
209C4—42no—
210C4—942no—
211C4—941no—
212C4—1882no—
213C4C2×#1062535411yescharacteristic
214C4C2×#1062535411yescharacteristic
215C2—3762no—
216C2—1881no—
217C2#1568967411yescharacteristic
218C2#1568992012yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#499C2
socleC22×C47C22×D4
hypercenter#499D47
hypocenterC47#3183
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
1. #15689658C2semidirect
2. #15689507C2semidirect
3. #15689480C2semidirect
4. #15689382C2semidirect
6. #15689370C2semidirect
7. #15689234C2semidirect
8. #15689229C2semidirect
9. #15689222C2semidirect
10. C4×#10625324C2semidirect
11. C47×#499C2semidirect
111. #499D47semidirect
121. C47#3183semidirect