Finite Group Databasebeta

← #20242368

Subgroups — #20242368

Order 6016.

260 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 53 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#15689278C211yesmaximal, characteristic, complemented
2#15689261C211yesmaximal, characteristic, complemented
3#15689035C211yesmaximal, characteristic, complemented
4#15688860C211yesmaximal, characteristic, complemented
5#15688857C211yesmaximal, characteristic, complemented
6#15688847C211yesmaximal, characteristic, complemented
7C47×#538C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C2×#10625337—21no—
10C2×#10625335—21no—
11C2×C22⋊Dic47—21no—
12#13093947—21no—
13#13093947—21no—
14C22⋊(C47⋊C8)C2211yescharacteristic
15C22⋊(C47⋊C8)C2211yescharacteristic
16C47⋊#95—21no—
17C47⋊#95C2211yescharacteristic
18#126×C47—21no—
19#124×C47—21no—
20#123×C47—21no—
21C22⋊Q8×C47C2211yescharacteristic
22#121×C47—21no—
23#121×C47C2211yescharacteristic
24#120×C47—21no—
25C4×D4×C47—21no—
26C2×C22⋊C4×C47C2211yescharacteristic
27C24×C47D411yescharacteristic
28C2×Q8×C47D411yescharacteristic
29C2×D4×C47—21no—
30C2×D4×C47—21no—
31C2×D4×C47—21no—
32C2×D4×C47D411yescharacteristic
33C22×C4×C47—21no—
34C22×C4×C47D411yescharacteristic
35C22×C4×C47C2311yescharacteristic
36C22×Dic47—21no—
37C22×Dic47—21no—
38C2×Dic94—21no—
39C2×Dic94—21no—
40C2×Dic94—42no—
41C4⋊C4×C47—21no—
42C4⋊C4×C47—21no—
43C4⋊C4×C47D411yescharacteristic
44C4⋊C4×C47D411yescharacteristic
45C22⋊C4×C47—21no—
46C22⋊C4×C47—21no—
47C22⋊C4×C47—21no—
48C22⋊C4×C47—21no—
49C22⋊C4×C47—21no—
50C22⋊C4×C47—21no—
51C22⋊C4×C47—21no—
52C42×C47—21no—
53C22⋊Dic47—42no—
54#10625337—42no—
55#10625335—42no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C23×C47—21no—
59C23×C47—21no—
60C23×C47—21no—
61C23×C47—21no—
62C23×C47—41no—
63C23×C47—41no—
64C23×C47C2×D411yescharacteristic
65Q8×C47—41no—
66D4×C47—41no—
67D4×C47—41no—
68D4×C47—41no—
69D4×C47—81no—
70D4×C47—81no—
71C2×C4×C47—21no—
72C2×C4×C47—21no—
73C2×C4×C47—21no—
74C2×C4×C47—21no—
75C2×C4×C47—41no—
76C2×C4×C47—41no—
77C2×C4×C47—81no—
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×Dic47—22no—
81C2×Dic47—41no—
82C2×Dic47—41no—
83C2×Dic47—41no—
84C2×Dic47—41no—
85C2×Dic47—41no—
86Dic94—22no—
87Dic94—22no—
88Dic94—41no—
89Dic94—41no—
90C47⋊C8—41no—
91C47⋊C8—41no—
92C22×C47—21no—
93C22×C47—21no—
94C22×C47—42no—
95C22×C47—41no—
96C22×C47—41no—
97C22×C47—41no—
98C22×C47—41no—
99C22×C47—41no—
100C22×C47—41no—
101C22×C47—81no—
102C22×C47#12011yescharacteristic
103C22×C47#13511yescharacteristic
104C22×C47#13711yescharacteristic
105C4×C47—21no—
106C4×C47—21no—
107C4×C47—41no—
108C4×C47—41no—
109C4×C47—41no—
110C4×C47—41no—
111Dic47—42no—
112Dic47—81no—
113#1606—471nomaximal, Sylow
114C2×C47—21no—
115C2×C47—21no—
116C2×C47—81no—
117C2×C47—81no—
118C2×C47#45211yescharacteristic
119C2×C47#45511yescharacteristic
120C2×C47B(4,𝔽2)11yescharacteristic
121#538D4711yescharacteristic
122#451—471no—
123#448—471no—
124#393—471no—
125#328—471no—
126#327—471no—
127#323—471no—
128C47#160611yescharacteristic, complemented, Sylow
129C22×Q8—471no—
130C2×Q16—941no—
131C2×SD16—941no—
132#126—21no—
133#124—21no—
134#123—21no—
135C22⋊Q8C2×D4711yescharacteristic
136#121—21no—
137#121C2×D4711yescharacteristic
138#120—21no—
139C4×D4—21no—
140C2×C22⋊C4—941no—
141C2×C22⋊C4C2×D4711yescharacteristic
142#103—941no—
143#103—941no—
144C22⋊C8—471no—
145C22⋊C8—471no—
146#95—471no—
147#95—941no—
148C24C22⋊D4711yescharacteristic
149C2×Q8—941no—
150C2×Q8—941no—
151C2×Q8—1882no—
152C2×Q8C22⋊D4711yescharacteristic
153C2×D4—21no—
154C2×D4—21no—
155C2×D4—21no—
156C2×D4C22⋊D4711yescharacteristic
157C22×C4—21no—
158C22×C4—941no—
159C22×C4—941no—
160C22×C4C22⋊D4711yescharacteristic
161C22×C4C22×D4711yescharacteristic
162Q16—1882no—
163SD16—1882no—
164C2×C8—941no—
165C2×C8—941no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4C22⋊D4711yescharacteristic
169C4⋊C4C22⋊D4711yescharacteristic
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—21no—
173C22⋊C4—21no—
174C22⋊C4—21no—
175C22⋊C4—21no—
176C22⋊C4—21no—
177C22⋊C4—1882no—
178C42—21no—
179C23—21no—
180C23—21no—
181C23—21no—
182C23—21no—
183C23—41no—
184C23—41no—
185C23C2×C22⋊D4711yescharacteristic
186Q8—41no—
187Q8—942no—
188Q8—942no—
189Q8—1881no—
190Q8—1881no—
191D4—41no—
192D4—41no—
193D4—41no—
194D4—81no—
195D4—81no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—81no—
203C2×C4—942no—
204C2×C4—1881no—
205C2×C4—1881no—
206C2×C4—1881no—
207C2×C4—1881no—
208C2×C4—1881no—
209C2×C4C2×C22⋊D4711yescharacteristic
210C2×C4C2×C22⋊D4711yescharacteristic
211C8—1881no—
212C8—1881no—
213C22—21no—
214C22—21no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22—41no—
219C22—41no—
220C22—41no—
221C22—41no—
222C22—81no—
223C22#1309399311yescharacteristic
224C22#1309404411yescharacteristic
225C22#1309405411yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—41no—
230C4—41no—
231C4—41no—
232C4—3761no—
233C4—1882no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—81no—
238C2#1568928511yescharacteristic
239C2#1568930111yescharacteristic
240C2#1568931011yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#538C2
socleC22×C47#120
hypercenter#538D47
hypocenterC47#1606
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #538

Complements

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

NH ≅ G/Ntype
1. #15689278C2semidirect
2. #15689261C2semidirect
3. #15689035C2semidirect
4. #15688860C2semidirect
5. #15688857C2semidirect
6. #15688847C2semidirect
128. C47#1606semidirect