Finite Group Databasebeta

← #20254417

Subgroups — #20254417

Order 6016.

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

normal subgroups only

This group has 386 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
1C2×#13094024C211yesmaximal, characteristic, complemented
2#15689657C211yesmaximal, characteristic
3#15689517C212yesmaximal, complemented
4#15689492C212yesmaximal, complemented
5#15689334C212yesmaximal, complemented
6#15689329C212yesmaximal, complemented
7#15689281C212yesmaximal, complemented
8#15689264C212yesmaximal
9C47×#432C211yesmaximal, characteristic, complemented
10C22×Dic94C2212yes—
11C2×Dic188C2214yes—
12C2×#10625325C2214yes—
13#13094024—21no—
14#13094024—21no—
15#13094024C2212yes—
16#13094024C2212yes—
17#13094018—21no—
18#13094016C2211yescharacteristic
19#13094012C2211yescharacteristic
20#13094007—21no—
21#13094003C2211yescharacteristic
22#13093998C2211yescharacteristic
23C4×Dic94C2211yescharacteristic
24C4×D188C2211yescharacteristic
25C4×C22⋊D47—21no—
26#13093981—21no—
27C2×C4⋊Dic47—21no—
28C2×C4⋊Dic47—21no—
29#13093949C2214yes—
30#13093949C2214yes—
31C2×C42×C47C2211yescharacteristic
32C4⋊C8×C47C2212yes—
33C22⋊C8×C47C2212yes—
34#97×C47C2212yes—
35C22×C4×C47D411yescharacteristic
36C22×C4×C47D411yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C2×C22⋊D47—21no—
39C22×Dic47—22no—
40C2×D188C2311yescharacteristic
41C2×C4×D47—21no—
42C2×Dic94—22no—
43C2×Dic94—44no—
44C2×Dic94C2314yes—
45C2×Dic94C2311yescharacteristic
46C2×C8×C47C2314yes—
47C42×C47D411yescharacteristic
48C42×C47D411yescharacteristic
49C42×C47C2311yescharacteristic
50C42×C47C2311yescharacteristic
51C22⋊Dic47—21no—
52(C2×D47)⋊C4—21no—
53(C2×D47)⋊C4—21no—
54(C2×D47)⋊C4—21no—
55(C2×D47)⋊C4—21no—
56C4⋊Dic47—22no—
57C4⋊Dic47—22no—
58C4⋊Dic47—22no—
59C4⋊Dic47—22no—
60C4⋊Dic47C2311yescharacteristic
61C4⋊Dic47C2311yescharacteristic
62Dic47⋊C4—21no—
63Dic47⋊C4—21no—
64Dic47⋊C4—21no—
65Dic47⋊C4—21no—
66C4×Dic47—21no—
67Dic188—44no—
68#10625325—44no—
69C23×C47C2×D411yescharacteristic
70C22×D47—21no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×D411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2411yescharacteristic
80C22⋊D47—42no—
81C2×Dic47—21no—
82C2×Dic47—21no—
83C2×Dic47—21no—
84C2×Dic47—24no—
85C2×Dic47—44no—
86D188—22no—
87C4×D47—42no—
88Dic94—24no—
89Dic94—22no—
90Dic94—24no—
91Dic94—44no—
92C8×C47—24no—
93C22×C47—21no—
94C22×C47—21no—
95C22×C47#13712yes—
96C22×C47C22×D411yescharacteristic
97C2×D47—41no—
98C2×D47—41no—
99C2×D47—41no—
100C4×C47—21no—
101C4×C47—21no—
102C4×C47—21no—
103C4×C47—21no—
104C4×C47#13712yes—
105C4×C47H(5,𝔽2)12yes—
106Dic47—44no—
107Dic47—41no—
108Dic47—41no—
109Dic47—41no—
110#3218—471nomaximal, Sylow
111C2×C47—22no—
112C2×C47#53511yescharacteristic
113C2×C47C2×#13711yescharacteristic
114C2×C47C2×#13711yescharacteristic
115D47—81no—
116C2×C4⋊Q8—471no—
117#529—471no—
118#497—472no—
119#491—472no—
120#462—472no—
121#461—472no—
122#451—472no—
123#448—472no—
124#432D4711yescharacteristic, complemented
125C47#321811yescharacteristic, complemented, Sylow
126C22×Q8—472no—
127C2×Q16—474no—
128C2×SD16—474no—
129C4⋊Q8—472no—
130C4⋊Q8—472no—
131C4⋊Q8—941no—
132C4⋊Q8—941no—
133#126—941no—
134#125—471no—
135#124—471no—
136#123—941no—
137C22⋊Q8—471no—
138#121—471no—
139C4×Q8—471no—
140C4×D4—471no—
141C4×D4—941no—
142#117—941no—
143C2×C4⋊C4—941no—
144C2×C4⋊C4—941no—
145C2×C42C2×D4711yescharacteristic
146C4⋊C8C2×D4712yes—
147#103—474no—
148#103—474no—
149C22⋊C8C2×D4712yes—
150#97C2×D4712yes—
151C2×Q8—474no—
152C2×Q8—471no—
153C2×Q8—942no—
154C2×Q8—1884no—
155C2×D4—471no—
156C2×D4—941no—
157C22×C4—942no—
158C22×C4—941no—
159C22×C4D18811yescharacteristic
160C22×C4D18811yescharacteristic
161C22×C4C22×D4711yescharacteristic
162Q16—1884no—
163SD16—1884no—
164C2×C8C22×D4714yes—
165C4⋊C4—471no—
166C4⋊C4—471no—
167C4⋊C4—941no—
168C4⋊C4—941no—
169C4⋊C4—941no—
170C4⋊C4—941no—
171C4⋊C4—942no—
172C4⋊C4—942no—
173C4⋊C4—942no—
174C4⋊C4—942no—
175C22⋊C4—941no—
176C22⋊C4—941no—
177C22⋊C4—941no—
178C22⋊C4—941no—
179C22⋊C4—941no—
180C42—941no—
181C42D18811yescharacteristic
182C42D18811yescharacteristic
183C42C22×D4711yescharacteristic
184C42C22×D4711yescharacteristic
185C23—941no—
186C23C2×D18811yescharacteristic
187Q8—944no—
188Q8—942no—
189Q8—944no—
190Q8—1884no—
191D4—942no—
192D4—1882no—
193C2×C4—22no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—941no—
197C2×C4—941no—
198C2×C4—941no—
199C2×C4—944no—
200C2×C4—1884no—
201C2×C4—1882no—
202C2×C4C2×D18811yescharacteristic
203C2×C4C2×D18811yescharacteristic
204C2×C4C2×D18811yescharacteristic
205C2×C4C2×D18811yescharacteristic
206C2×C4C2×D18811yescharacteristic
207C2×C4C23×D4711yescharacteristic
208C8—24no—
209C22—21no—
210C22—21no—
211C22—1881no—
212C22—1881no—
213C22—1881no—
214C22#1309405712yes—
215C22C22×D18811yescharacteristic
216C4—21no—
217C4—21no—
218C4—21no—
219C4—21no—
220C4—1881no—
221C4—1881no—
222C4—1884no—
223C4—1881no—
224C4#1309405712yes—
225C4#1309407012yes—
226C2—22no—
227C2—3761no—
228C2#1568969211yescharacteristic
229C2C2×#1309405711yescharacteristic
230C2C2×#1309405711yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#432C2
socleC22×C47C22×D4
hypercenter#432D47
hypocenterC47#3218
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. C2×#13094024C2semidirect
3. #15689517C2semidirect
4. #15689492C2semidirect
5. #15689334C2semidirect
6. #15689329C2semidirect
7. #15689281C2semidirect
9. C47×#432C2semidirect
124. #432D47semidirect
125. C47#3218semidirect