Finite Group Databasebeta

← #20256035

Subgroups — #20256035

Order 6016.

350 conjugacy classes of subgroups; only the 117 normal subgroups are shown.

normal subgroups only

This group has 350 conjugacy classes of subgroups — too many to draw. Only its 117 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#15689843C211yesmaximal, characteristic, complemented
2#15689830C211yesmaximal, characteristic, complemented
3#15689476C212yesmaximal, complemented
4#15689474C211yesmaximal, characteristic, complemented
5#15689429C212yesmaximal, complemented
6#15689413C211yesmaximal, characteristic, complemented
7#15689336C212yesmaximal
8#15689328C211yesmaximal, characteristic, complemented
9C8×Dic94C211yesmaximal, characteristic, complemented
10#15689214C212yesmaximal, complemented
11C4×D8×C47C211yesmaximal, characteristic
12C2×#10625335C2212yes—
13#13094024C2211yescharacteristic
14#13094024C2211yescharacteristic
15#13094017—22no—
16#13094015C2212yes—
17#13094011C2212yes—
18#13094003—21no—
19#13094003—21no—
20#13094001—22no—
21C4×Dic94C2211yescharacteristic
22#13093989C2212yes—
23D4×Dic47C2212yes—
24#13093983—21no—
25C2×C4⋊Dic47—21no—
26#13093955C2212yes—
27C4⋊(C47⋊C8)C2211yescharacteristic
28Dic47⋊C8C2212yes—
29#13093949C2212yes—
30#13093949C2212yes—
31#13093947C2212yes—
32#13093945C2212yes—
33C8×Dic47C2212yes—
34C2×D8×C47C2211yescharacteristic
35C4×D4×C47C2211yescharacteristic
36C4×D4×C47C2211yescharacteristic
37#107×C47C2211yescharacteristic
38#102×C47C2211yescharacteristic
39#102×C47C2211yescharacteristic
40C4×C8×C47C2211yescharacteristic
41C2×D4×C47C2311yescharacteristic
42C2×D4×C47C2311yescharacteristic
43C22×C4×C47—21no—
44C22×C4×C47—21no—
45C22×Dic47—22no—
46C2×Dic94—21no—
47C2×Dic94D411yescharacteristic
48C2×Dic94C2312yes—
49D8×C47—22no—
50C2×C8×C47C2311yescharacteristic
51C2×C8×C47C2311yescharacteristic
52C4⋊C4×C47C2311yescharacteristic
53C4⋊C4×C47C2311yescharacteristic
54C22⋊C4×C47—21no—
55C22⋊C4×C47—21no—
56C42×C47C2311yescharacteristic
57C22⋊Dic47—22no—
58C22⋊Dic47—22no—
59C22⋊Dic47—22no—
60#10625335—24no—
61C4⋊Dic47—21no—
62C4⋊Dic47—21no—
63C4⋊Dic47—21no—
64C4⋊Dic47—22no—
65C4⋊Dic47D411yescharacteristic
66C4⋊Dic47C2312yes—
67Dic47⋊C4—22no—
68Dic47⋊C4—22no—
69Dic47⋊C4D412yes—
70C4×Dic47—22no—
71C4×Dic47C2312yes—
72C2×C47⋊C8C2312yes—
73C23×C47—21no—
74C23×C47—21no—
75D4×C47—21no—
76D4×C47—21no—
77D4×C47—21no—
78D4×C47#4112yes—
79C2×C4×C47—21no—
80C2×C4×C47—21no—
81C2×C4×C47—42no—
82C2×C4×C47—42no—
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2411yescharacteristic
86C2×Dic47—22no—
87C2×Dic47—22no—
88C2×Dic47—82no—
89C2×Dic47C2×D412yes—
90C2×Dic47C2×D412yes—
91Dic94—22no—
92Dic94—22no—
93Dic94—22no—
94Dic94—81no—
95C8×C47—21no—
96C8×C47—21no—
97C47⋊C8—22no—
98C22×C47—22no—
99C22×C47—41no—
100C22×C47—41no—
101C22×C47—41no—
102C22×C47—41no—
103C22×C47—41no—
104C22×C47C22×D411yescharacteristic
105C4×C47—21no—
106C4×C47—41no—
107C4×C47—41no—
108C4×C47#13512yes—
109C4×C47C2×#4111yescharacteristic
110C4×C472−1+411yescharacteristic
111Dic47—22no—
112Dic47—22no—
113Dic47—42no—
114Dic47—42no—
115#3360—471nomaximal, Sylow
116C2×C47—42no—
117C2×C47—81no—
118C2×C47#54811yescharacteristic
119C2×C47C2×#13511yescharacteristic
120C2×C47#57711yescharacteristic
121#556—471no—
122#554—471no—
123#488—472no—
124#487—471no—
125#479—472no—
126#476—471no—
127#463—472no—
128#461—471no—
129C8×Q8—471no—
130C4×SD16—472no—
131C4×D8D4711yescharacteristic
132C47#336011yescharacteristic, complemented, Sylow
133C2×SD16—472no—
134C2×D8C2×D4711yescharacteristic
135C4⋊Q8—471no—
136C4⋊Q8—471no—
137#126—942no—
138#125—472no—
139#124—472no—
140C22⋊Q8—942no—
141C22⋊Q8—941no—
142C22⋊Q8—941no—
143C4×Q8—471no—
144C4×Q8—472no—
145C4×D4—472no—
146C4×D4C2×D4711yescharacteristic
147C4×D4C2×D4711yescharacteristic
148#117—941no—
149C2×C4⋊C4—941no—
150#107C2×D4711yescharacteristic
151#106—472no—
152C4⋊C8—472no—
153C4⋊C8—471no—
154#103—472no—
155#103—472no—
156#103—472no—
157#102—472no—
158#102C2×D4711yescharacteristic
159#102C2×D4711yescharacteristic
160C4×C8—472no—
161C4×C8C2×D4711yescharacteristic
162C2×Q8—471no—
163C2×Q8—472no—
164C2×Q8—941no—
165C2×D4C22×D4711yescharacteristic
166C2×D4C22×D4711yescharacteristic
167C22×C4—21no—
168C22×C4—21no—
169C22×C4—942no—
170SD16—944no—
171D8—22no—
172C2×C8—472no—
173C2×C8C22×D4711yescharacteristic
174C2×C8C22×D4711yescharacteristic
175C4⋊C4—472no—
176C4⋊C4—471no—
177C4⋊C4—472no—
178C4⋊C4—942no—
179C4⋊C4—942no—
180C4⋊C4—942no—
181C4⋊C4—941no—
182C4⋊C4—941no—
183C4⋊C4—941no—
184C4⋊C4C22×D4711yescharacteristic
185C4⋊C4C22×D4711yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—21no—
188C22⋊C4—942no—
189C22⋊C4—942no—
190C22⋊C4—942no—
191C42—472no—
192C42—942no—
193C42C22×D4711yescharacteristic
194C23—21no—
195C23—21no—
196Q8—942no—
197Q8—942no—
198Q8—942no—
199Q8—3761no—
200D4—21no—
201D4—21no—
202D4—21no—
203D4#1062535012yes—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—472no—
209C2×C4—472no—
210C2×C4—942no—
211C2×C4—942no—
212C2×C4—3762no—
213C2×C4D4×D4711yescharacteristic
214C2×C4D4×D4711yescharacteristic
215C2×C4C23×D4711yescharacteristic
216C8—21no—
217C8—21no—
218C8—942no—
219C22—22no—
220C22—41no—
221C22—41no—
222C22—41no—
223C22—41no—
224C22—41no—
225C22C2×D4×D4711yescharacteristic
226C4—21no—
227C4—41no—
228C4—41no—
229C4—942no—
230C4—942no—
231C4—1882no—
232C4—1882no—
233C4#1309404312yes—
234C4C2×#1062535011yescharacteristic
235C4#1309407111yescharacteristic
236C2—42no—
237C2—81no—
238C2#1568978211yescharacteristic
239C2C2×#1309404311yescharacteristic
240C2#1568993011yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC4×D8×C47C2
socleC22×C47C22×D4
hypercenterC4×D8D47
hypocenterC47#3360
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×D8

Complements

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

NH ≅ G/Ntype
1. #15689843C2semidirect
2. #15689830C2semidirect
3. #15689476C2semidirect
4. #15689474C2semidirect
5. #15689429C2semidirect
6. #15689413C2semidirect
8. #15689328C2semidirect
9. C8×Dic94C2semidirect
10. #15689214C2semidirect
132. C47#3360semidirect