Finite Group Databasebeta

← #20244347

Subgroups — #20244347

Order 6016.

300 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 115 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×C8×Dic47C211yesmaximal, characteristic
3#15688992C211yesmaximal, 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×Dic47⋊C4—21no—
16C2×Dic47⋊C4—21no—
17C2×C4×Dic47C2211yescharacteristic
18C8×Dic47—22no—
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×C47Q812yescomplemented
35C4⋊C4×C47—21no—
36C4⋊C4×C47—21no—
37C4⋊C4×C47—21no—
38C4⋊C4×C47C2×C412yes—
39C4⋊Dic47—21no—
40C4⋊Dic47—21no—
41C4⋊Dic47—21no—
42C4⋊Dic47C2×C412yes—
43Dic47⋊C4—24no—
44Dic47⋊C4—42no—
45Dic47⋊C4—42no—
46C4×Dic47C2×C412yes—
47C4×Dic47D412yes—
48C2×C47⋊C8—21no—
49C2×C47⋊C8—21no—
50C2×C47⋊C8Q812yescomplemented
51C23×C47C2×D411yescharacteristic
52C2×C4×C47—22no—
53C2×C4×C47—41no—
54C2×C4×C47—41no—
55C2×C4×C47—41no—
56C2×C4×C47—41no—
57C2×C4×C47—41no—
58C2×C4×C47C22×C411yescharacteristic
59C2×C4×C47C2×D411yescharacteristic
60C2×C4×C47C2×Q811yescharacteristic
61C2×C4×C47C2×Q811yescharacteristic
62C2×C4×C47#4111yescharacteristic
63C2×C4×C47#4111yescharacteristic
64C2×Dic47—22no—
65C2×Dic47—41no—
66C2×Dic47—41no—
67C2×Dic47—41no—
68C2×Dic47—41no—
69C2×Dic47—41no—
70C2×Dic47C22⋊C412yes—
71C2×Dic47C22⋊C412yes—
72C2×Dic47D812yes—
73C2×Dic47SD1612yes—
74C2×Dic47SD1612yes—
75C2×Dic47Q1612yes—
76Dic94—48no—
77C8×C47—22no—
78C47⋊C8—22no—
79C22×C47C2×C22⋊C411yescharacteristic
80C22×C47#12411yescharacteristic
81C22×C47C4⋊Q811yescharacteristic
82C22×C47C2×D811yescharacteristic
83C22×C47C2×SD1611yescharacteristic
84C22×C47C2×SD1611yescharacteristic
85C22×C47C2×Q1611yescharacteristic
86C4×C47—42no—
87C4×C47—81no—
88C4×C47C4×Q811yescharacteristic
89C4×C47C4×Q811yescharacteristic
90C4×C47C22⋊Q811yescharacteristic
91C4×C47C22⋊Q811yescharacteristic
92Dic47—42no—
93Dic47—81no—
94Dic47#10214yes—
95Dic47#10314yes—
96#1990—471nomaximal, Sylow
97C2×C47#39111yescharacteristic
98C2×C47C2×#10211yescharacteristic
99C2×C47C2×#10311yescharacteristic
100C2×C47#48611yescharacteristic
101C2×C47#48711yescharacteristic
102C2×C47#49811yescharacteristic
103C2×C47#50011yescharacteristic
104C2×C4⋊Q8—471no—
105C2×C4×C8—471no—
106#384—471no—
107#340—471no—
108#340—471no—
109#340—471no—
110#340D4711yescharacteristic
111C47#199011yescharacteristic, complemented, Sylow
112C22×Q8—941no—
113C22×C8—471no—
114C22×C8C2×D4711yescharacteristic
115C4⋊Q8—474no—
116C4⋊Q8—942no—
117C2×C4⋊C4—471no—
118C2×C4⋊C4—471no—
119C2×C4⋊C4—941no—
120C2×C4⋊C4—941no—
121C2×C4⋊C4—941no—
122C2×C4⋊C4C2×D4711yescharacteristic
123C2×C4⋊C4C2×D4711yescharacteristic
124C2×C42—471no—
125C4×C8—942no—
126C2×Q8—944no—
127C2×Q8—1882no—
128C2×Q8—1882no—
129C22×C4—21no—
130C22×C4—21no—
131C22×C4—471no—
132C22×C4—471no—
133C22×C4—941no—
134C22×C4—941no—
135C22×C4C22×D4711yescharacteristic
136C2×C8—21no—
137C2×C8—21no—
138C2×C8—472no—
139C2×C8—941no—
140C2×C8—941no—
141C2×C8Dic9412yescomplemented
142C4⋊C4—21no—
143C4⋊C4—21no—
144C4⋊C4—21no—
145C4⋊C4—472no—
146C4⋊C4—944no—
147C4⋊C4—941no—
148C4⋊C4—941no—
149C4⋊C4—941no—
150C4⋊C4—1882no—
151C4⋊C4—1882no—
152C4⋊C4C4×D4712yes—
153C42—472no—
154C42—472no—
155C23D4×D4711yescharacteristic
156Q8—1888no—
157C2×C4—22no—
158C2×C4—41no—
159C2×C4—41no—
160C2×C4—41no—
161C2×C4—41no—
162C2×C4—41no—
163C2×C4—472no—
164C2×C4—472no—
165C2×C4—472no—
166C2×C4—472no—
167C2×C4—472no—
168C2×C4—472no—
169C2×C4—942no—
170C2×C4—1881no—
171C2×C4—1881no—
172C2×C4—1881no—
173C2×C4—1881no—
174C2×C4—1881no—
175C2×C4C2×Dic9411yescharacteristic
176C2×C4C2×C4×D4711yescharacteristic
177C2×C4#1062535011yescharacteristic
178C2×C4D4×D4711yescharacteristic
179C2×C4#1062535211yescharacteristic
180C2×C4Q8×D4711yescharacteristic
181C8—22no—
182C8—942no—
183C22C22⋊C4×D4711yescharacteristic
184C22#1309401011yescharacteristic
185C22#1309402311yescharacteristic
186C22D8×D4711yescharacteristic
187C22SD16×D4711yescharacteristic
188C22SD16×D4711yescharacteristic
189C22Q16×D4711yescharacteristic
190C4—42no—
191C4—81no—
192C4—474no—
193C4—474no—
194C4—3761no—
195C4—1882no—
196C4#1309398911yescharacteristic
197C4C4×Dic9411yescharacteristic
198C4#1309400111yescharacteristic
199C4#1309400211yescharacteristic
200C2#1568902711yescharacteristic
201C2#102×D4711yescharacteristic
202C2#103×D4711yescharacteristic
203C2#1568946811yescharacteristic
204C2#1568947211yescharacteristic
205C2#1568952011yescharacteristic
206C2#1568952711yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#340C2
socleC23×C47C2×D4
hypercenter#340D47
hypocenterC47#1990
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
34. C2×C8×C47Q8semidirect
50. C2×C47⋊C8Q8semidirect
111. C47#1990semidirect
141. C2×C8Dic94semidirect