Finite Group Databasebeta

← #20244542

Subgroups — #20244542

Order 6016.

282 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 282 conjugacy classes of subgroups — too many to draw. Only its 69 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#15689751C211yesmaximal, characteristic, complemented
2#15689128C211yesmaximal, characteristic
3#15689026C211yesmaximal, characteristic
4#15688891C211yesmaximal, characteristic, complemented
5#15688884C211yesmaximal, characteristic, complemented
6#15688882C211yesmaximal, characteristic, complemented
7C47×#418C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9#13094024—21no—
10#13094023—21no—
11#13094016—21no—
12#13094015—21no—
13#13094001—22no—
14#13093983C2211yescharacteristic
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C22⋊Dic47—22no—
17C2×C4×Dic47C2211yescharacteristic
18#13093945—21no—
19#13093945—21no—
20C22×D4×C47C2211yescharacteristic
21C2×M16×C47C2211yescharacteristic
22#117×C47C2211yescharacteristic
23#102×C47—21no—
24#102×C47—21no—
25C24×C47—21no—
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47—21no—
29C2×D4×C47—21no—
30C2×D4×C47—21no—
31C2×D4×C47Q812yescomplemented
32C22×C4×C47C2311yescharacteristic
33C22×Dic47—21no—
34C22×Dic47D412yes—
35C2×Dic94—22no—
36M16×C47—21no—
37M16×C47—21no—
38C2×C8×C47—21no—
39C4⋊C4×C47D411yescharacteristic
40C4⋊C4×C47D411yescharacteristic
41C22⋊C4×C47—21no—
42C42×C47—21no—
43C22⋊Dic47—21no—
44C22⋊Dic47—44no—
45C4⋊Dic47—22no—
46C4⋊Dic47—21no—
47C4⋊Dic47—21no—
48C4⋊Dic47D411yescharacteristic
49C4⋊Dic47D411yescharacteristic
50Dic47⋊C4—22no—
51Dic47⋊C4—22no—
52C4×Dic47—21no—
53C4×Dic47—21no—
54C4×Dic47—21no—
55#10625329—21no—
56#10625329—21no—
57C2×C47⋊C8—21no—
58C23×C47—22no—
59C23×C47—42no—
60C23×C47—42no—
61C23×C47—41no—
62C23×C47—41no—
63C23×C47C2×D411yescharacteristic
64D4×C47—22no—
65D4×C47—22no—
66D4×C47—41no—
67D4×C47—41no—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47C2×D411yescharacteristic
71C2×C4×C47C2×D411yescharacteristic
72C2×C4×C47C2×Q811yescharacteristic
73C2×C4×C47#4111yescharacteristic
74C2×C4×C47#4111yescharacteristic
75C2×C4×C47#4111yescharacteristic
76C2×Dic47—22no—
77C2×Dic47—21no—
78C2×Dic47—21no—
79C2×Dic47—22no—
80C2×Dic47—41no—
81C2×Dic47—41no—
82C2×Dic47—42no—
83Dic94—82no—
84C8×C47—41no—
85C47⋊C8—41no—
86C22×C47—21no—
87C22×C47—21no—
88C22×C47—44no—
89C22×C47—42no—
90C22×C47—82no—
91C22×C47—81no—
92C22×C47—81no—
93C22×C47#12011yescharacteristic
94C22×C47C22⋊Q811yescharacteristic
95C22×C47#12411yescharacteristic
96C4×C47—41no—
97C4×C47—41no—
98C4×C47C22⋊Q811yescharacteristic
99C4×C47C22⋊Q811yescharacteristic
100C4×C47#12411yescharacteristic
101C4×C47#12411yescharacteristic
102Dic47—42no—
103Dic47—41no—
104Dic47—42no—
105Dic47—41no—
106#2027—471nomaximal, Sylow
107C2×C47—21no—
108C2×C47—21no—
109C2×C47—82no—
110C2×C47#39311yescharacteristic
111C2×C47#45311yescharacteristic
112C2×C47#45411yescharacteristic
113#544—471no—
114#418—471no—
115#418D4711yescharacteristic
116#390—471no—
117#343—471no—
118#339—471no—
119#339—471no—
120C47#202711yescharacteristic, complemented, Sylow
121C22×D4C2×D4711yescharacteristic
122C2×M16—471no—
123C2×M16C2×D4711yescharacteristic
124C4⋊Q8—941no—
125C4⋊Q8—941no—
126#125—941no—
127#125—941no—
128C22⋊Q8—942no—
129#117—471no—
130#117C2×D4711yescharacteristic
131C2×C4⋊C4—471no—
132C2×C22⋊C4—942no—
133C2×C42—471no—
134#102—21no—
135#102—21no—
136#102—941no—
137#102—941no—
138C24—21no—
139C2×Q8—942no—
140C2×D4—21no—
141C2×D4—21no—
142C2×D4—21no—
143C2×D4—21no—
144C2×D4—21no—
145C2×D4Dic9412yescomplemented
146C22×C4—472no—
147C22×C4—941no—
148C22×C4C22×D4711yescharacteristic
149M16—21no—
150M16—21no—
151M16—941no—
152M16—941no—
153C2×C8—21no—
154C2×C8—941no—
155C4⋊C4—471no—
156C4⋊C4—471no—
157C4⋊C4—942no—
158C4⋊C4—942no—
159C4⋊C4—942no—
160C4⋊C4—941no—
161C4⋊C4—941no—
162C4⋊C4C22⋊D4711yescharacteristic
163C4⋊C4C22⋊D4711yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—941no—
166C22⋊C4—1884no—
167C42—21no—
168C42—941no—
169C42—941no—
170C42—941no—
171C23—22no—
172C23—42no—
173C23—42no—
174C23—41no—
175C23—41no—
176C23D4×D4711yescharacteristic
177Q8—3762no—
178D4—22no—
179D4—22no—
180D4—41no—
181D4—41no—
182C2×C4—21no—
183C2×C4—21no—
184C2×C4—942no—
185C2×C4—941no—
186C2×C4—941no—
187C2×C4—942no—
188C2×C4—1881no—
189C2×C4—1881no—
190C2×C4—1882no—
191C2×C4C2×Dic9411yescharacteristic
192C2×C4#1062535011yescharacteristic
193C2×C4D4×D4711yescharacteristic
194C2×C4#1062535211yescharacteristic
195C2×C4#1062535211yescharacteristic
196C2×C4C2×C22⋊D4711yescharacteristic
197C8—41no—
198C8—1881no—
199C22—21no—
200C22—21no—
201C22—44no—
202C22—42no—
203C22—82no—
204C22—81no—
205C22—81no—
206C22#1309399211yescharacteristic
207C22#1309400111yescharacteristic
208C22#1309401011yescharacteristic
209C4—41no—
210C4—41no—
211C4—1882no—
212C4—1882no—
213C4—1881no—
214C4—1881no—
215C4#1309400111yescharacteristic
216C4#1309400311yescharacteristic
217C4#1309401011yescharacteristic
218C4#1309401111yescharacteristic
219C2—21no—
220C2—21no—
221C2—82no—
222C2#1568903511yescharacteristic
223C2#1568928911yescharacteristic
224C2#1568929411yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#418C2
socleC22×C47#120
hypercenter#418D47
hypocenterC47#2027
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #15689751C2semidirect
4. #15688891C2semidirect
5. #15688884C2semidirect
6. #15688882C2semidirect
31. C2×D4×C47Q8semidirect
120. C47#2027semidirect
145. C2×D4Dic94semidirect