Finite Group Databasebeta

← #20254401

Subgroups — #20254401

Order 6016.

390 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 390 conjugacy classes of subgroups — too many to draw. Only its 121 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#15689680C211yesmaximal, characteristic, complemented
2#15689673C211yesmaximal, characteristic
3#15689517C212yesmaximal, complemented
4#15689483C212yesmaximal, complemented
5#15689334C212yesmaximal, complemented
6#15689324C212yesmaximal, complemented
7#15689287C214yesmaximal, complemented
8C47×#432C211yesmaximal, characteristic, complemented
9C2×#10625350C2212yes—
10C2×Dic188C2214yes—
11C2×#10625325C2214yes—
12#13094024C2211yescharacteristic
13#13094024C2211yescharacteristic
14#13094024C2211yescharacteristic
15#13094021C2211yescharacteristic
16#13094016—21no—
17#13094012C2212yes—
18#13094003—21no—
19#13094003C2212yes—
20#13093998—21no—
21#13093998—21no—
22C4×Dic94—21no—
23C4×Dic94C2212yes—
24C4×D188—21no—
25C4×D188—21no—
26#13093983—21no—
27#13093949C2214yes—
28#13093946C2214yes—
29C2×C42×C47C2211yescharacteristic
30C4⋊C8×C47C2212yes—
31C22⋊C8×C47C2212yes—
32#97×C47C2212yes—
33C22×C4×C47D411yescharacteristic
34C22×C4×C47D411yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C2×C22⋊D47—22no—
37#10625350—44no—
38C2×D188—21no—
39C2×D188—21no—
40C2×D188C2312yes—
41C2×C4×D47—22no—
42C2×Dic94—21no—
43C2×Dic94C2312yes—
44C2×Dic94C2312yes—
45C2×C8×C47C2314yes—
46C42×C47D411yescharacteristic
47C42×C47D411yescharacteristic
48C42×C47C2311yescharacteristic
49C42×C47C2311yescharacteristic
50C22⋊Dic47—22no—
51(C2×D47)⋊C4—22no—
52(C2×D47)⋊C4—22no—
53C4⋊Dic47—21no—
54C4⋊Dic47—21no—
55C4⋊Dic47—21no—
56C4⋊Dic47—21no—
57C4⋊Dic47—21no—
58C4⋊Dic47C2312yes—
59Dic47⋊C4—22no—
60Dic47⋊C4—22no—
61C4×Dic47—22no—
62Dic188—44no—
63#10625325—44no—
64C23×C47C2×D411yescharacteristic
65C22×D47—22no—
66C2×C4×C47—22no—
67C2×C4×C47—22no—
68C2×C4×C47—41no—
69C2×C4×C47C2×D411yescharacteristic
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2411yescharacteristic
75C22⋊D47—44no—
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—22no—
79D188—24no—
80D188—42no—
81D188—42no—
82C4×D47—44no—
83Dic94—22no—
84Dic94—22no—
85Dic94—24no—
86Dic94—42no—
87C8×C47—24no—
88C22×C47—21no—
89C22×C47—21no—
90C22×C47—21no—
91C22×C47C22×D411yescharacteristic
92C2×D47—42no—
93C2×D47—42no—
94C2×D47—42no—
95C4×C47—21no—
96C4×C47—21no—
97C4×C47—21no—
98C4×C47—21no—
99C4×C47#13712yes—
100C4×C47H(5,𝔽2)12yes—
101Dic47—42no—
102Dic47—42no—
103Dic47—42no—
104#3216—471nomaximal, Sylow
105C2×C47—41no—
106C2×C47#53511yescharacteristic
107C2×C47C2×#13711yescharacteristic
108C2×C47#57511yescharacteristic
109D47—82no—
110#533—471no—
111#532—471no—
112#497—472no—
113#489—472no—
114#462—472no—
115#460—472no—
116#452—474no—
117#432D4711yescharacteristic, complemented
118C47#321611yescharacteristic, complemented, Sylow
119C2×#41—472no—
120C2×Q16—474no—
121C2×SD16—474no—
122C4⋊Q8—471no—
123C4⋊Q8—471no—
124C4⋊Q8—471no—
125#127—471no—
126#125—941no—
127#124—472no—
128C22⋊Q8—472no—
129C22⋊Q8—941no—
130#121—941no—
131#121—941no—
132C4×Q8—472no—
133C4×Q8—941no—
134C4×D4—941no—
135C4×D4—941no—
136#117—941no—
137C2×C42C2×D4711yescharacteristic
138C4⋊C8C2×D4712yes—
139#103—474no—
140#102—474no—
141C22⋊C8C2×D4712yes—
142#97C2×D4712yes—
143#41—1884no—
144C2×Q8—472no—
145C2×Q8—472no—
146C2×Q8—941no—
147C2×D4—472no—
148C2×D4—942no—
149C2×D4—941no—
150C2×D4—941no—
151C22×C4—942no—
152C22×C4D18811yescharacteristic
153C22×C4D18811yescharacteristic
154C22×C4C22×D4711yescharacteristic
155Q16—1884no—
156SD16—1884no—
157C2×C8C22×D4714yes—
158C4⋊C4—472no—
159C4⋊C4—942no—
160C4⋊C4—942no—
161C4⋊C4—941no—
162C4⋊C4—941no—
163C4⋊C4—941no—
164C4⋊C4—941no—
165C4⋊C4—941no—
166C22⋊C4—942no—
167C22⋊C4—942no—
168C22⋊C4—942no—
169C42—942no—
170C42D18811yescharacteristic
171C42D18811yescharacteristic
172C42C22×D4711yescharacteristic
173C42C22×D4711yescharacteristic
174C23—942no—
175C23C2×D18811yescharacteristic
176Q8—942no—
177Q8—942no—
178Q8—944no—
179Q8—1882no—
180D4—944no—
181D4—1882no—
182D4—1884no—
183D4—1882no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—41no—
187C2×C4—942no—
188C2×C4—942no—
189C2×C4—942no—
190C2×C4—1884no—
191C2×C4C2×D18811yescharacteristic
192C2×C4C2×D18811yescharacteristic
193C2×C4C2×D18811yescharacteristic
194C2×C4C2×D18811yescharacteristic
195C2×C4C2×D18811yescharacteristic
196C2×C4C23×D4711yescharacteristic
197C8—24no—
198C22—21no—
199C22—21no—
200C22—21no—
201C22—1882no—
202C22—1882no—
203C22—1882no—
204C22C22×D18811yescharacteristic
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—1882no—
210C4—1882no—
211C4—1882no—
212C4#1309405712yes—
213C4#1309407012yes—
214C2—41no—
215C2—3762no—
216C2#1568969211yescharacteristic
217C2C2×#1309405711yescharacteristic
218C2#1568992311yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#432C2
socleC22×C47C22×D4
hypercenter#432D47
hypocenterC47#3216
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
1. #15689680C2semidirect
3. #15689517C2semidirect
4. #15689483C2semidirect
5. #15689334C2semidirect
6. #15689324C2semidirect
7. #15689287C2semidirect
8. C47×#432C2semidirect
117. #432D47semidirect
118. C47#3216semidirect