Finite Group Databasebeta

← #20254005

Subgroups — #20254005

Order 6016.

362 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689744C212yesmaximal, complemented
2#15689521C211yesmaximal, characteristic, complemented
3#15689507C211yesmaximal, characteristic, complemented
4#15689483C212yesmaximal, complemented
5#15689381C211yesmaximal, characteristic, complemented
6#15689376C211yesmaximal, characteristic
7#15689352C212yesmaximal, complemented
8#15689236C211yesmaximal, characteristic, complemented
9#15689231C211yesmaximal, characteristic, complemented
10C4×#10625325C212yesmaximal, complemented
11C47×#405C211yesmaximal, characteristic, complemented
12C2×Dic188C2211yescharacteristic
13C2×#10625325C2212yes—
14C2×D376C2211yescharacteristic
15#13094024C2212yes—
16#13094019—22no—
17#13094012C2212yes—
18#13094010—22no—
19#13094006—22no—
20#13094003C2212yes—
21#13094002—22no—
22#13093998C2212yes—
23C4×Dic94C2212yes—
24C4×D188C2212yes—
25#13093956C2211yescharacteristic
26#13093956C2211yescharacteristic
27#13093956C2212yes—
28#13093949C2212yes—
29#13093949C2212yes—
30#13093946C2212yes—
31#13093946C2212yes—
32C2×M16×C47C2211yescharacteristic
33C22×C8×C47C2211yescharacteristic
34#117×C47C2211yescharacteristic
35#97×C47C2211yescharacteristic
36#97×C47C2211yescharacteristic
37C4×C8×C47C2211yescharacteristic
38C4×C8×C47C2211yescharacteristic
39C22×C4×C47C2311yescharacteristic
40C2×C22⋊D47—22no—
41C2×D188C2312yes—
42C2×C4×D47—22no—
43C2×Dic94—22no—
44C2×Dic94C2312yes—
45M16×C47—22no—
46C2×C8×C47—22no—
47C2×C8×C47C2311yescharacteristic
48C2×C8×C47C2311yescharacteristic
49C2×C8×C47C2311yescharacteristic
50C2×C8×C47C2311yescharacteristic
51C4⋊C4×C47D412yes—
52C22⋊C4×C47D412yes—
53C42×C47C2311yescharacteristic
54C42×C47C2311yescharacteristic
55C22⋊Dic47—22no—
56(C2×D47)⋊C4—22no—
57(C2×D47)⋊C4—22no—
58(C2×D47)⋊C4—22no—
59(C2×D47)⋊C4—22no—
60C4⋊Dic47—22no—
61C4⋊Dic47C2312yes—
62C4⋊Dic47C2312yes—
63Dic47⋊C4—22no—
64Dic47⋊C4—22no—
65C4×Dic47—22no—
66Dic188—22no—
67D376—22no—
68#10625325—24no—
69C23×C47C2×D411yescharacteristic
70C22×D47—22no—
71C2×C4×C47—21no—
72C2×C4×C47—21no—
73C2×C4×C47C2×D412yes—
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D412yes—
76C2×C4×C47C2411yescharacteristic
77C22⋊D47—82no—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81D188—22no—
82D188—22no—
83C4×D47—82no—
84Dic94—22no—
85Dic94—22no—
86Dic94—82no—
87C8×C47—21no—
88C8×C47—21no—
89C8×C47#4112yes—
90C8×C47#4112yes—
91C22×C47—21no—
92C22×C47—22no—
93C22×C47C22×D411yescharacteristic
94C2×D47—42no—
95C2×D47—42no—
96C2×D47—42no—
97C4×C47—21no—
98C4×C47—22no—
99C4×C47—22no—
100C4×C47C2×#4111yescharacteristic
101C4×C47C2×#4111yescharacteristic
102Dic47—42no—
103Dic47—42no—
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#470—471no—
115#469—471no—
116#465—472no—
117#442—471no—
118#441—471no—
119C4×SD16—472no—
120#405D4711yescharacteristic, complemented
121C47#317311yescharacteristic, complemented, Sylow
122C2×Q16—471no—
123C2×SD16—472no—
124C2×D8—471no—
125C2×M16C2×D4711yescharacteristic
126C22×C8C2×D4711yescharacteristic
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×D4—472no—
137#117C2×D4711yescharacteristic
138#106—472no—
139#106—471no—
140#106—471no—
141#103—472no—
142#103—472no—
143#102—472no—
144#102—472no—
145#97C2×D4711yescharacteristic
146#97C2×D4711yescharacteristic
147C4×C8C2×D4711yescharacteristic
148C4×C8C2×D4711yescharacteristic
149C2×Q8—472no—
150C2×Q8—942no—
151C2×D4—472no—
152C2×D4—942no—
153C22×C4—942no—
154C22×C4C22×D4711yescharacteristic
155Q16—942no—
156SD16—944no—
157D8—942no—
158M16—22no—
159C2×C8—22no—
160C2×C8C22×D4711yescharacteristic
161C2×C8C22×D4711yescharacteristic
162C2×C8C22×D4711yescharacteristic
163C2×C8C22×D4711yescharacteristic
164C4⋊C4—472no—
165C4⋊C4—472no—
166C4⋊C4—942no—
167C4⋊C4—942no—
168C4⋊C4—942no—
169C4⋊C4D18812yes—
170C22⋊C4—942no—
171C22⋊C4—942no—
172C22⋊C4—942no—
173C22⋊C4—942no—
174C22⋊C4—942no—
175C22⋊C4D18812yes—
176C42—942no—
177C42C22×D4711yescharacteristic
178C42C22×D4711yescharacteristic
179C23—942no—
180C23C2×D18811yescharacteristic
181Q8—942no—
182Q8—942no—
183Q8—3762no—
184D4—942no—
185D4—942no—
186D4—3762no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—942no—
190C2×C4—942no—
191C2×C4—942no—
192C2×C4—3762no—
193C2×C4C2×D18812yes—
194C2×C4C2×D18812yes—
195C2×C4C2×D18811yescharacteristic
196C2×C4C23×D4711yescharacteristic
197C8—21no—
198C8—21no—
199C8#1062535012yes—
200C8#1062535012yes—
201C22—21no—
202C22—22no—
203C22—1882no—
204C22—1882no—
205C22—1882no—
206C22C22×D18811yescharacteristic
207C4—21no—
208C4—22no—
209C4—22no—
210C4—1882no—
211C4—1882no—
212C4—1882no—
213C4C2×#1062535011yescharacteristic
214C4C2×#1062535011yescharacteristic
215C2—41no—
216C2—3762no—
217C2#1568967311yescharacteristic
218C2#1568993512yes—
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#405C2
socleC22×C47C22×D4
hypercenter#405D47
hypocenterC47#3173
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ #117 ◁ #405

Complements

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

NH ≅ G/Ntype
1. #15689744C2semidirect
2. #15689521C2semidirect
3. #15689507C2semidirect
4. #15689483C2semidirect
5. #15689381C2semidirect
7. #15689352C2semidirect
8. #15689236C2semidirect
9. #15689231C2semidirect
10. C4×#10625325C2semidirect
11. C47×#405C2semidirect
120. #405D47semidirect
121. C47#3173semidirect