Finite Group Databasebeta

← #20254385

Subgroups — #20254385

Order 6016.

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

normal subgroups only

This group has 434 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#15689673C211yesmaximal, characteristic, complemented
2#15689673C211yesmaximal, characteristic, complemented
3#15689512C212yesmaximal, complemented
4#15689483C212yesmaximal, complemented
5#15689329C212yesmaximal, complemented
6#15689319C212yesmaximal, complemented
7#15689270C214yesmaximal, complemented
8C47×#432C211yesmaximal, characteristic, complemented
9C2×#10625350—21no—
10C2×#10625350C2212yes—
11C2×#10625325C2214yes—
12C2×D376C2214yes—
13#13094024C2211yescharacteristic
14#13094024C2211yescharacteristic
15#13094021C2211yescharacteristic
16#13094021C2211yescharacteristic
17#13094012—21no—
18#13094012C2212yes—
19#13093998—21no—
20#13093998—21no—
21#13093998—21no—
22#13093998C2212yes—
23C4×D188—21no—
24C4×D188—21no—
25C4×D188—21no—
26C4×D188C2212yes—
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—
37C2×C22⋊D47—22no—
38#10625350—44no—
39#10625350—44no—
40C2×D188—21no—
41C2×D188—21no—
42C2×D188—21no—
43C2×D188—21no—
44C2×D188C2312yes—
45C2×D188C2312yes—
46C2×C4×D47—22no—
47C2×C4×D47—22no—
48C2×Dic94—21no—
49C2×Dic94C2312yes—
50C2×C8×C47C2314yes—
51C42×C47D411yescharacteristic
52C42×C47D411yescharacteristic
53C42×C47C2311yescharacteristic
54C42×C47C2311yescharacteristic
55(C2×D47)⋊C4—22no—
56(C2×D47)⋊C4—22no—
57(C2×D47)⋊C4—22no—
58(C2×D47)⋊C4—22no—
59C4⋊Dic47—21no—
60C4⋊Dic47—21no—
61C4⋊Dic47—21no—
62C4⋊Dic47C2312yes—
63D376—44no—
64#10625325—44no—
65C23×C47C2×D411yescharacteristic
66C22×D47—22no—
67C22×D47—22no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—41no—
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×D411yescharacteristic
73C2×C4×C47C2×D411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2411yescharacteristic
77C22⋊D47—44no—
78C22⋊D47—44no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81D188—22no—
82D188—22no—
83D188—24no—
84D188—42no—
85D188—42no—
86D188—42no—
87D188—42no—
88C4×D47—44no—
89C4×D47—44no—
90Dic94—24no—
91Dic94—42no—
92C8×C47—24no—
93C22×C47—21no—
94C22×C47—21no—
95C22×C47—21no—
96C22×C47C22×D411yescharacteristic
97C2×D47—42no—
98C2×D47—42no—
99C2×D47—42no—
100C2×D47—42no—
101C2×D47—42no—
102C2×D47—42no—
103C4×C47—21no—
104C4×C47—21no—
105C4×C47—21no—
106C4×C47—21no—
107C4×C47AGL(1,ℤ/8)12yes—
108C4×C47H(5,𝔽2)12yes—
109Dic47—42no—
110Dic47—42no—
111#3214—471nomaximal, Sylow
112C2×C47—41no—
113C2×C47#53511yescharacteristic
114C2×C47C2×AGL(1,ℤ/8)11yescharacteristic
115C2×C47#57511yescharacteristic
116D47—82no—
117D47—82no—
118#532—471no—
119#532—471no—
120#496—472no—
121#489—472no—
122#461—472no—
123#459—472no—
124#449—474no—
125#432D4711yescharacteristic, complemented
126C47#321411yescharacteristic, complemented, Sylow
127C2×#41—472no—
128C2×#41—941no—
129C2×SD16—474no—
130C2×D8—474no—
131C4⋊Q8—471no—
132C4⋊Q8—471no—
133#127—471no—
134#127—471no—
135#124—472no—
136#124—941no—
137#121—472no—
138#121—941no—
139#121—941no—
140#121—941no—
141C4×D4—472no—
142C4×D4—941no—
143C4×D4—941no—
144C4×D4—941no—
145C2×C42C2×D4711yescharacteristic
146C4⋊C8C2×D4712yes—
147#103—474no—
148#102—474no—
149C22⋊C8C2×D4712yes—
150#97C2×D4712yes—
151#41—1884no—
152#41—1884no—
153C2×Q8—472no—
154C2×Q8—941no—
155C2×D4—472no—
156C2×D4—472no—
157C2×D4—942no—
158C2×D4—942no—
159C2×D4—941no—
160C2×D4—941no—
161C2×D4—941no—
162C2×D4—941no—
163C22×C4—942no—
164C22×C4—942no—
165C22×C4D18811yescharacteristic
166C22×C4D18811yescharacteristic
167C22×C4C22×D4711yescharacteristic
168SD16—1884no—
169D8—1884no—
170C2×C8C22×D4714yes—
171C4⋊C4—472no—
172C4⋊C4—941no—
173C4⋊C4—941no—
174C4⋊C4—941no—
175C22⋊C4—942no—
176C22⋊C4—942no—
177C22⋊C4—942no—
178C22⋊C4—942no—
179C42D18811yescharacteristic
180C42D18811yescharacteristic
181C42C22×D4711yescharacteristic
182C42C22×D4711yescharacteristic
183C23—942no—
184C23—942no—
185C23C2×D18811yescharacteristic
186Q8—944no—
187Q8—1882no—
188D4—942no—
189D4—944no—
190D4—942no—
191D4—1882no—
192D4—1882no—
193D4—1882no—
194D4—1884no—
195D4—1884no—
196D4—1882no—
197C2×C4—22no—
198C2×C4—22no—
199C2×C4—41no—
200C2×C4—942no—
201C2×C4—942no—
202C2×C4—1884no—
203C2×C4—1884no—
204C2×C4C2×D18811yescharacteristic
205C2×C4C2×D18811yescharacteristic
206C2×C4C2×D18811yescharacteristic
207C2×C4C2×D18811yescharacteristic
208C2×C4C2×D18811yescharacteristic
209C2×C4C23×D4711yescharacteristic
210C8—24no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—1882no—
215C22—1882no—
216C22—1882no—
217C22—1882no—
218C22—1882no—
219C22—1882no—
220C22C22×D18811yescharacteristic
221C4—21no—
222C4—21no—
223C4—21no—
224C4—21no—
225C4—1882no—
226C4—1882no—
227C4#1309405212yes—
228C4#1309407012yes—
229C2—41no—
230C2—3762no—
231C2—3762no—
232C2#1568969211yescharacteristic
233C2C2×#1309405211yescharacteristic
234C2#1568992311yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#432C2
socleC22×C47C22×D4
hypercenter#432D47
hypocenterC47#3214
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. #15689673C2semidirect
2. #15689673C2semidirect
3. #15689512C2semidirect
4. #15689483C2semidirect
5. #15689329C2semidirect
6. #15689319C2semidirect
7. #15689270C2semidirect
8. C47×#432C2semidirect
125. #432D47semidirect
126. C47#3214semidirect