Finite Group Databasebeta

← #20256041

Subgroups — #20256041

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#15689847C211yesmaximal, characteristic, complemented
2#15689830C211yesmaximal, characteristic, complemented
3#15689479C212yesmaximal, complemented
4#15689473C211yesmaximal, characteristic, complemented
5#15689428C212yesmaximal, complemented
6#15689414C211yesmaximal, characteristic, complemented
7#15689340C212yesmaximal
8#15689247C211yesmaximal, characteristic, complemented
9SD16×Dic47C212yesmaximal, complemented
10C4×#10625334C211yesmaximal, characteristic
11C47×#461C211yesmaximal, characteristic, complemented
12C2×#10625334C2211yescharacteristic
13#13094024C2211yescharacteristic
14#13094019—22no—
15#13094015C2212yes—
16#13094013C2212yes—
17#13094004—21no—
18#13094003—21no—
19#13094001—22no—
20Q8×Dic47C2212yes—
21C4×Dic94C2211yescharacteristic
22C4×D188C2211yescharacteristic
23D4×Dic47C2212yes—
24#13093982—21no—
25C2×C4⋊Dic47—21no—
26#13093957C2211yescharacteristic
27#13093956C2212yes—
28Dic47⋊C8C2212yes—
29#13093948C2212yes—
30#13093948C2212yes—
31#13093946C2212yes—
32#13093945C2211yescharacteristic
33#13093944C2211yescharacteristic
34C4×C47⋊C8C2211yescharacteristic
35C8×Dic47C2212yes—
36C2×SD16×C47C2212yes—
37C4⋊Q8×C47C2211yescharacteristic
38C4×D4×C47C2211yescharacteristic
39C4⋊C8×C47C2211yescharacteristic
40#103×C47C2212yes—
41C2×Q8×C47C2312yes—
42C2×D4×C47C2311yescharacteristic
43C22×C4×C47—21no—
44C22×Dic47—22no—
45C2×D188C2311yescharacteristic
46C2×C4×D47—21no—
47C2×Dic94—21no—
48C2×Dic94D411yescharacteristic
49SD16×C47—24no—
50C2×C8×C47C2312yes—
51C4⋊C4×C47—21no—
52C4⋊C4×C47—21no—
53C4⋊C4×C47C2311yescharacteristic
54C22⋊C4×C47—21no—
55C42×C47C2311yescharacteristic
56C22⋊Dic47—22no—
57#10625334—22no—
58(C2×D47)⋊C4—21no—
59(C2×D47)⋊C4—22no—
60(C2×D47)⋊C4—22no—
61C4⋊Dic47—21no—
62C4⋊Dic47—22no—
63C4⋊Dic47—22no—
64C4⋊Dic47D411yescharacteristic
65C4⋊Dic47C2311yescharacteristic
66C4⋊Dic47C2312yes—
67Dic47⋊C4—22no—
68Dic47⋊C4D412yes—
69C4×Dic47—22no—
70C4×Dic47C2312yes—
71C2×C47⋊C8C2311yescharacteristic
72C2×C47⋊C8C2311yescharacteristic
73C23×C47—21no—
74C22×D47—21no—
75Q8×C47—22no—
76Q8×C47—22no—
77D4×C47—21no—
78D4×C47#4112yes—
79C2×C4×C47—22no—
80C2×C4×C47—21no—
81C2×C4×C47—42no—
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2411yescharacteristic
85C2×Dic47—21no—
86C2×Dic47—22no—
87C2×Dic47—82no—
88C2×Dic47C2×D412yes—
89C2×Dic47C2×D412yes—
90D188—21no—
91D188—21no—
92C4×D47—42no—
93Dic94—22no—
94Dic94—81no—
95C8×C47—22no—
96C47⋊C8—21no—
97C47⋊C8—21no—
98C22×C47—22no—
99C22×C47—41no—
100C22×C47—41no—
101C22×C47C22×D411yescharacteristic
102C2×D47—41no—
103C2×D47—41no—
104C2×D47—41no—
105C4×C47—21no—
106C4×C47—42no—
107C4×C47—41no—
108C4×C47#13512yes—
109C4×C47C2×#4111yescharacteristic
110C4×C472−1+411yescharacteristic
111Dic47—22no—
112Dic47—22no—
113Dic47—41no—
114Dic47—42no—
115#3360—471nomaximal, Sylow
116C2×C47—42no—
117C2×C47#54811yescharacteristic
118C2×C47C2×#13511yescharacteristic
119C2×C47#57711yescharacteristic
120D47—81no—
121#556—471no—
122#554—471no—
123#488—472no—
124#487—471no—
125#479—472no—
126#476—471no—
127#463—472no—
128#461D4711yescharacteristic, complemented
129C8×Q8—471no—
130C4×SD16—472no—
131C4×D8—471no—
132C47#336011yescharacteristic, complemented, Sylow
133C2×SD16C2×D4712yes—
134C2×D8—471no—
135C4⋊Q8—471no—
136C4⋊Q8C2×D4711yescharacteristic
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×D4—471no—
147C4×D4C2×D4711yescharacteristic
148#117—941no—
149C2×C4⋊C4—941no—
150#107—471no—
151#106—472no—
152C4⋊C8—472no—
153C4⋊C8C2×D4711yescharacteristic
154#103—472no—
155#103—472no—
156#103C2×D4712yes—
157#102—471no—
158#102—472no—
159#102—471no—
160C4×C8—472no—
161C4×C8—471no—
162C2×Q8—471no—
163C2×Q8—941no—
164C2×Q8C22×D4712yes—
165C2×D4—471no—
166C2×D4C22×D4711yescharacteristic
167C22×C4—21no—
168C22×C4—942no—
169C22×C4—941no—
170SD16—24no—
171D8—942no—
172C2×C8—471no—
173C2×C8—471no—
174C2×C8C22×D4712yes—
175C4⋊C4—21no—
176C4⋊C4—21no—
177C4⋊C4—472no—
178C4⋊C4—471no—
179C4⋊C4—472no—
180C4⋊C4—471no—
181C4⋊C4—942no—
182C4⋊C4—942no—
183C4⋊C4—942no—
184C4⋊C4—941no—
185C4⋊C4C22×D4711yescharacteristic
186C22⋊C4—21no—
187C22⋊C4—942no—
188C22⋊C4—942no—
189C22⋊C4—942no—
190C22⋊C4—941no—
191C42—472no—
192C42—942no—
193C42C22×D4711yescharacteristic
194C23—21no—
195C23—941no—
196Q8—22no—
197Q8—22no—
198Q8—942no—
199Q8—3761no—
200D4—21no—
201D4—941no—
202D4—941no—
203D4#1062535212yes—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—42no—
207C2×C4—472no—
208C2×C4—472no—
209C2×C4—941no—
210C2×C4—942no—
211C2×C4—3762no—
212C2×C4—1882no—
213C2×C4D4×D4711yescharacteristic
214C2×C4D4×D4711yescharacteristic
215C2×C4C23×D4711yescharacteristic
216C8—22no—
217C8—941no—
218C8—941no—
219C22—22no—
220C22—41no—
221C22—41no—
222C22—1881no—
223C22—1881no—
224C22—1881no—
225C22C2×D4×D4711yescharacteristic
226C4—21no—
227C4—42no—
228C4—41no—
229C4—942no—
230C4—942no—
231C4—1881no—
232C4—1882no—
233C4#1309404512yes—
234C4C2×#1062535211yescharacteristic
235C4#1309407111yescharacteristic
236C2—42no—
237C2—3761no—
238C2#1568977911yescharacteristic
239C2C2×#1309404511yescharacteristic
240C2#1568993211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#461C2
socleC22×C47C22×D4
hypercenter#461D47
hypocenterC47#3360
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #461

Complements

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

NH ≅ G/Ntype
1. #15689847C2semidirect
2. #15689830C2semidirect
3. #15689479C2semidirect
4. #15689473C2semidirect
5. #15689428C2semidirect
6. #15689414C2semidirect
8. #15689247C2semidirect
9. SD16×Dic47C2semidirect
11. C47×#461C2semidirect
128. #461D47semidirect
132. C47#3360semidirect