Finite Group Databasebeta

← #20244334

Subgroups — #20244334

Order 6016.

292 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 107 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×#13094023C211yesmaximal, characteristic
2C2×Dic47⋊C8C211yesmaximal, characteristic
3C4⋊C4×Dic47C211yesmaximal, characteristic
4#15688886C211yesmaximal, characteristic
5#15688885C211yesmaximal, characteristic
6#15688885C211yesmaximal, characteristic
7C47×#340C211yesmaximal, characteristic
8C22×Dic94—21no—
9C22×C47⋊C8C2211yescharacteristic
10#13094023—22no—
11#13094023C414yescomplemented
12C2×C4⋊Dic47C2211yescharacteristic
13C2×C4⋊Dic47C2211yescharacteristic
14C2×Dic47⋊C4—21no—
15C2×C4×Dic47—21no—
16C2×C4×Dic47C2211yescharacteristic
17Dic47⋊C8—22no—
18C47⋊#95—21no—
19C22×C8×C47C2211yescharacteristic
20C2×C4⋊C4×C47C2211yescharacteristic
21C2×C4⋊C4×C47C2211yescharacteristic
22C22×C4×C47—21no—
23C22×C4×C47—21no—
24C22×C4×C47C2311yescharacteristic
25C22×Dic47—21no—
26C22×Dic47—21no—
27C22×Dic47D411yescharacteristic
28C22×Dic47D411yescharacteristic
29C2×Dic94—24no—
30C2×Dic94—42no—
31C2×Dic94—42no—
32C2×C8×C47—21no—
33C2×C8×C47—21no—
34C2×C8×C47—21no—
35C4⋊C4×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47C2×C412yes—
38C4⋊C4×C47Q812yescomplemented
39C4⋊Dic47—21no—
40C4⋊Dic47—21no—
41C4⋊Dic47C2×C412yes—
42C4⋊Dic47Q812yescomplemented
43Dic47⋊C4—24no—
44C4×Dic47—42no—
45C4×Dic47C2×C412yes—
46C4×Dic47D412yes—
47C2×C47⋊C8—21no—
48C2×C47⋊C8—21no—
49C2×C47⋊C8—21no—
50C23×C47C2×D411yescharacteristic
51C2×C4×C47—22no—
52C2×C4×C47—22no—
53C2×C4×C47—41no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47—41no—
57C2×C4×C47C22×C411yescharacteristic
58C2×C4×C47C2×D411yescharacteristic
59C2×C4×C47C2×Q811yescharacteristic
60C2×C4×C47C2×Q811yescharacteristic
61C2×C4×C47#4111yescharacteristic
62C2×C4×C47#4111yescharacteristic
63C2×Dic47—21no—
64C2×Dic47—21no—
65C2×Dic47—22no—
66C2×Dic47—22no—
67C2×Dic47—41no—
68C2×Dic47—41no—
69C2×Dic47—41no—
70C2×Dic47—41no—
71C2×Dic47C22⋊C412yes—
72C2×Dic47C22⋊C412yes—
73C2×Dic47SD1612yes—
74C2×Dic47Q1612yes—
75Dic94—48no—
76C8×C47—41no—
77C47⋊C8—41no—
78C22×C47C2×C22⋊C411yescharacteristic
79C22×C47C22⋊Q811yescharacteristic
80C22×C47C22⋊Q811yescharacteristic
81C22×C47C2×SD1611yescharacteristic
82C22×C47C2×Q1611yescharacteristic
83C22×C47AGL(1,ℤ/8)11yescharacteristic
84C22×C47AGL(1,ℤ/8)11yescharacteristic
85C4×C47—42no—
86C4×C47—42no—
87C4×C47C4×Q811yescharacteristic
88C4×C47C4×Q811yescharacteristic
89C4×C47#12411yescharacteristic
90C4×C47C4⋊Q811yescharacteristic
91Dic47—22no—
92Dic47—42no—
93Dic47—42no—
94Dic47#10314yes—
95#1987—471nomaximal, Sylow
96C2×C47#39111yescharacteristic
97C2×C47C2×#10311yescharacteristic
98C2×C47#41811yescharacteristic
99C2×C47#47611yescharacteristic
100C2×C47#47611yescharacteristic
101C2×C47#47711yescharacteristic
102C2×C47#47711yescharacteristic
103C2×C4⋊Q8—471no—
104C2×C4⋊C8—471no—
105C4×C4⋊C4—471no—
106#340—471no—
107#340—471no—
108#340—471no—
109#340D4711yescharacteristic
110C47#198711yescharacteristic, complemented, Sylow
111C22×Q8—941no—
112C22×C8—471no—
113C22×C8C2×D4711yescharacteristic
114C4⋊Q8—474no—
115C4⋊Q8—942no—
116C2×C4⋊C4—471no—
117C2×C4⋊C4—471no—
118C2×C4⋊C4—941no—
119C2×C4⋊C4C2×D4711yescharacteristic
120C2×C4⋊C4C2×D4711yescharacteristic
121C2×C42—471no—
122C2×C42—941no—
123C4⋊C8—942no—
124#95—941no—
125C2×Q8—944no—
126C2×Q8—1882no—
127C2×Q8—1882no—
128C22×C4—21no—
129C22×C4—21no—
130C22×C4—471no—
131C22×C4—471no—
132C22×C4—941no—
133C22×C4—941no—
134C22×C4C22×D4711yescharacteristic
135C2×C8—21no—
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—941no—
139C2×C8—941no—
140C2×C8—941no—
141C4⋊C4—21no—
142C4⋊C4—21no—
143C4⋊C4—472no—
144C4⋊C4—472no—
145C4⋊C4—944no—
146C4⋊C4—941no—
147C4⋊C4—941no—
148C4⋊C4Dic9412yescomplemented
149C4⋊C4C4×D4712yes—
150C42—472no—
151C42—472no—
152C42—1882no—
153C23D4×D4711yescharacteristic
154Q8—1888no—
155C2×C4—22no—
156C2×C4—22no—
157C2×C4—41no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—472no—
162C2×C4—472no—
163C2×C4—472no—
164C2×C4—472no—
165C2×C4—941no—
166C2×C4—941no—
167C2×C4—942no—
168C2×C4—942no—
169C2×C4—1881no—
170C2×C4—1881no—
171C2×C4—1881no—
172C2×C4—1881no—
173C2×C4C2×Dic9411yescharacteristic
174C2×C4C2×C4×D4711yescharacteristic
175C2×C4#1062535011yescharacteristic
176C2×C4D4×D4711yescharacteristic
177C2×C4#1062535211yescharacteristic
178C2×C4Q8×D4711yescharacteristic
179C8—41no—
180C8—1881no—
181C22C22⋊C4×D4711yescharacteristic
182C22#1309400111yescharacteristic
183C22#1309400211yescharacteristic
184C22SD16×D4711yescharacteristic
185C22Q16×D4711yescharacteristic
186C22#1309404811yescharacteristic
187C22#1309405111yescharacteristic
188C4—42no—
189C4—42no—
190C4—474no—
191C4—942no—
192C4—1882no—
193C4—1882no—
194C4#1309398911yescharacteristic
195C4C4×Dic9411yescharacteristic
196C4#1309401011yescharacteristic
197C4#1309402311yescharacteristic
198C2#1568902711yescharacteristic
199C2#103×D4711yescharacteristic
200C2#1568912611yescharacteristic
201C2#1568941111yescharacteristic
202C2#1568941211yescharacteristic
203C2#1568941611yescharacteristic
204C2#1568941711yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#340C2
socleC23×C47C2×D4
hypercenter#340D47
hypocenterC47#1987
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
11. #13094023C4semidirect
38. C4⋊C4×C47Q8semidirect
42. C4⋊Dic47Q8semidirect
110. C47#1987semidirect
148. C4⋊C4Dic94semidirect