Finite Group Databasebeta

← #20242351

Subgroups — #20242351

Order 6016.

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

normal subgroups only

This group has 244 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
3#15689043C211yesmaximal, characteristic, complemented
4#15688860C211yesmaximal, characteristic, complemented
5#15688857C211yesmaximal, characteristic
6#15688849C211yesmaximal, characteristic, complemented
7C47×#539C211yesmaximal, characteristic
8C22×Dic94C2211yescharacteristic
9C2×#10625337—21no—
10C2×#10625335—21no—
11C2×Dic47⋊C4—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#125×C47—21no—
20#123×C47—21no—
21#123×C47—21no—
22C22⋊Q8×C47—21no—
23C22⋊Q8×C47C2211yescharacteristic
24#121×C47C2211yescharacteristic
25C4×D4×C47—21no—
26C2×C4⋊C4×C47C2211yescharacteristic
27C2×Q8×C47D411yescharacteristic
28C2×D4×C47—21no—
29C2×D4×C47D411yescharacteristic
30C22×C4×C47—21no—
31C22×C4×C47D411yescharacteristic
32C22×C4×C47D411yescharacteristic
33C22×C4×C47C2311yescharacteristic
34C22×Dic47—21no—
35C22×Dic47—21no—
36C2×Dic94—21no—
37C2×Dic94—21no—
38C2×Dic94—42no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47—21no—
41C4⋊C4×C47—21no—
42C4⋊C4×C47—21no—
43C4⋊C4×C47—21no—
44C4⋊C4×C47—21no—
45C4⋊C4×C47D411yescharacteristic
46C4⋊C4×C47D411yescharacteristic
47C22⋊C4×C47—21no—
48C22⋊C4×C47—21no—
49C22⋊C4×C47—21no—
50C22⋊C4×C47—21no—
51C22⋊C4×C47—21no—
52C42×C47—21no—
53#10625337—42no—
54#10625335—42no—
55Dic47⋊C4—42no—
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C23×C47—21no—
59C23×C47C2×D411yescharacteristic
60Q8×C47—41no—
61D4×C47—41no—
62D4×C47—41no—
63D4×C47—41no—
64C2×C4×C47—21no—
65C2×C4×C47—21no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—21no—
71C2×C4×C47—41no—
72C2×C4×C47—41no—
73C2×C4×C47—81no—
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×Dic47—22no—
77C2×Dic47—22no—
78C2×Dic47—41no—
79C2×Dic47—41no—
80C2×Dic47—41no—
81C2×Dic47—41no—
82Dic94—22no—
83Dic94—22no—
84Dic94—41no—
85Dic94—41no—
86C47⋊C8—41no—
87C47⋊C8—41no—
88C22×C47—21no—
89C22×C47—21no—
90C22×C47—41no—
91C22×C47—41no—
92C22×C47—41no—
93C22×C47#12011yescharacteristic
94C22×C47#13511yescharacteristic
95C22×C47#13711yescharacteristic
96C4×C47—21no—
97C4×C47—21no—
98C4×C47—41no—
99C4×C47—41no—
100C4×C47—41no—
101C4×C47—41no—
102C4×C47—41no—
103Dic47—42no—
104Dic47—42no—
105#1603—471nomaximal, Sylow
106C2×C47—21no—
107C2×C47—21no—
108C2×C47—81no—
109C2×C47#45211yescharacteristic
110C2×C47#45611yescharacteristic
111C2×C47B(4,𝔽2)11yescharacteristic
112#539D4711yescharacteristic
113#451—471no—
114#448—471no—
115#395—471no—
116#328—471no—
117#327—471no—
118#324—471no—
119C47#160311yescharacteristic, complemented, Sylow
120C22×Q8—471no—
121C2×Q16—941no—
122C2×SD16—941no—
123#126—21no—
124#125—21no—
125#123—21no—
126#123—21no—
127C22⋊Q8—21no—
128C22⋊Q8C2×D4711yescharacteristic
129#121C2×D4711yescharacteristic
130C4×D4—21no—
131C2×C4⋊C4—941no—
132C2×C4⋊C4C2×D4711yescharacteristic
133#103—941no—
134#103—941no—
135C22⋊C8—471no—
136C22⋊C8—471no—
137#95—471no—
138#95—941no—
139C2×Q8—941no—
140C2×Q8—941no—
141C2×Q8—1882no—
142C2×Q8C22⋊D4711yescharacteristic
143C2×D4—21no—
144C2×D4C22⋊D4711yescharacteristic
145C22×C4—21no—
146C22×C4—941no—
147C22×C4—941no—
148C22×C4C22⋊D4711yescharacteristic
149C22×C4C22⋊D4711yescharacteristic
150C22×C4C22×D4711yescharacteristic
151Q16—1882no—
152SD16—1882no—
153C2×C8—941no—
154C2×C8—941no—
155C4⋊C4—21no—
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—1882no—
162C4⋊C4C22⋊D4711yescharacteristic
163C4⋊C4C22⋊D4711yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—21no—
166C22⋊C4—21no—
167C22⋊C4—21no—
168C22⋊C4—21no—
169C42—21no—
170C23—21no—
171C23C2×C22⋊D4711yescharacteristic
172Q8—41no—
173Q8—942no—
174Q8—942no—
175Q8—1881no—
176Q8—1881no—
177D4—41no—
178D4—41no—
179D4—41no—
180C2×C4—21no—
181C2×C4—21no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—81no—
190C2×C4—942no—
191C2×C4—942no—
192C2×C4—1881no—
193C2×C4—1881no—
194C2×C4—1881no—
195C2×C4—1881no—
196C2×C4C2×C22⋊D4711yescharacteristic
197C2×C4C2×C22⋊D4711yescharacteristic
198C8—1881no—
199C8—1881no—
200C22—21no—
201C22—21no—
202C22—41no—
203C22—41no—
204C22—41no—
205C22#1309399311yescharacteristic
206C22#1309404411yescharacteristic
207C22#1309405411yescharacteristic
208C4—21no—
209C4—21no—
210C4—41no—
211C4—41no—
212C4—41no—
213C4—41no—
214C4—41no—
215C4—1882no—
216C4—1882no—
217C2—21no—
218C2—21no—
219C2—81no—
220C2#1568928511yescharacteristic
221C2#1568930611yescharacteristic
222C2#1568931011yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#539C2
socleC22×C47#120
hypercenter#539D47
hypocenterC47#1603
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #539

Complements

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

NH ≅ G/Ntype
1. #15689278C2semidirect
3. #15689043C2semidirect
4. #15688860C2semidirect
6. #15688849C2semidirect
119. C47#1603semidirect