Finite Group Databasebeta

← #20256053

Subgroups — #20256053

Order 6016.

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

normal subgroups only

This group has 362 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
1#15689859C211yesmaximal, characteristic, complemented
2#15689834C211yesmaximal, characteristic, complemented
3#15689476C212yesmaximal, complemented
4#15689425C212yesmaximal, complemented
5#15689415C211yesmaximal, characteristic, complemented
6#15689337C212yesmaximal, complemented
7#15689315C211yesmaximal, characteristic
8C8×Dic94C211yesmaximal, characteristic, complemented
9C4×#10625325C211yesmaximal, characteristic, complemented
10#15689203C212yesmaximal, complemented
11C47×#486C211yesmaximal, characteristic, complemented
12C2×#10625325C2211yescharacteristic
13C2×#10625334C2212yes—
14#13094015C2212yes—
15#13094011—21no—
16#13094011C2212yes—
17#13094005—22no—
18#13094004—21no—
19#13094000—22no—
20C4×Dic94C2211yescharacteristic
21C4×Dic94C2211yescharacteristic
22C4×D188C2211yescharacteristic
23D4×Dic47—21no—
24D4×Dic47C2212yes—
25#13093986C2212yes—
26C4⋊C4×D47—21no—
27#13093957C2212yes—
28#13093956C2211yescharacteristic
29C4⋊(C47⋊C8)C2211yescharacteristic
30Dic47⋊C8C2212yes—
31#13093949C2211yescharacteristic
32#13093947C2212yes—
33#13093946C2211yescharacteristic
34#13093945C2212yes—
35C8×Dic47C2212yes—
36C4⋊Q8×C47C2211yescharacteristic
37#127×C47C2211yescharacteristic
38#102×C47C2212yes—
39#102×C47C2212yes—
40C4×C8×C47C2211yescharacteristic
41C2×Q8×C47—21no—
42C2×D4×C47—21no—
43C2×D4×C47—21no—
44C2×D4×C47C2312yes—
45C22×Dic47—22no—
46C2×D188C2311yescharacteristic
47C2×C4×D47—21no—
48C2×C4×D47—22no—
49C2×Dic94D411yescharacteristic
50C2×Dic94C2311yescharacteristic
51C2×C8×C47C2311yescharacteristic
52C2×C8×C47C2311yescharacteristic
53C4⋊C4×C47—21no—
54C4⋊C4×C47C2312yes—
55C42×C47C2311yescharacteristic
56C22⋊Dic47—22no—
57C22⋊Dic47—22no—
58C22⋊Dic47—22no—
59#10625334—24no—
60(C2×D47)⋊C4—21no—
61(C2×D47)⋊C4—22no—
62C4⋊Dic47—22no—
63C4⋊Dic47D411yescharacteristic
64C4⋊Dic47C2311yescharacteristic
65C4⋊Dic47C2311yescharacteristic
66Dic47⋊C4—21no—
67Dic47⋊C4—22no—
68Dic47⋊C4D412yes—
69C4×Dic47—21no—
70C4×Dic47C2312yes—
71C2×C47⋊C8C2312yes—
72#10625325—22no—
73C23×C47—22no—
74C22×D47—21no—
75Q8×C47—81no—
76D4×C47—22no—
77D4×C47—22no—
78D4×C47—42no—
79D4×C47—81no—
80C2×C4×C47—22no—
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2411yescharacteristic
84C2×Dic47—21no—
85C2×Dic47—21no—
86C2×Dic47—21no—
87C2×Dic47—82no—
88C2×Dic47C2×D412yes—
89C2×Dic47C2×D412yes—
90D188—21no—
91D188#4112yes—
92C4×D47—42no—
93C4×D47—82no—
94Dic94—22no—
95Dic94—21no—
96Dic94—21no—
97C8×C47—21no—
98C8×C47—21no—
99C47⋊C8—22no—
100C22×C47—42no—
101C22×C47—42no—
102C22×C47—42no—
103C22×C47C22×D411yescharacteristic
104C2×D47—22no—
105C2×D47—41no—
106C2×D47—41no—
107C4×C47—21no—
108C4×C47—42no—
109C4×C47#13512yes—
110C4×C47C2×#4111yescharacteristic
111C4×C472−1+411yescharacteristic
112Dic47—22no—
113Dic47—22no—
114Dic47—41no—
115Dic47—41no—
116Dic47—41no—
117#3361—471nomaximal, Sylow
118C2×C47—82no—
119C2×C47#54811yescharacteristic
120C2×C47C2×#13511yescharacteristic
121C2×C47#57611yescharacteristic
122D47—42no—
123#559—471no—
124#554—471no—
125#488—472no—
126#486D4711yescharacteristic, complemented
127#478—472no—
128#477—471no—
129#463—472no—
130#459—471no—
131C8×Q8—471no—
132C4×SD16—471no—
133C4×D8—472no—
134C47#336111yescharacteristic, complemented, Sylow
135C2×SD16—471no—
136C2×D8—472no—
137C4⋊Q8C2×D4711yescharacteristic
138#127C2×D4711yescharacteristic
139#125—472no—
140#124—472no—
141#124—941no—
142#123—942no—
143C22⋊Q8—941no—
144C22⋊Q8—942no—
145C4×Q8—471no—
146C4×Q8—471no—
147C4×D4—472no—
148C4×D4—472no—
149C4×D4—471no—
150C4×D4—941no—
151C2×C4⋊C4—941no—
152#107—472no—
153#106—471no—
154C4⋊C8—472no—
155C4⋊C8—471no—
156#103—471no—
157#103—472no—
158#102—472no—
159#102—471no—
160#102C2×D4712yes—
161#102C2×D4712yes—
162C4×C8—472no—
163C4×C8C2×D4711yescharacteristic
164C2×Q8—21no—
165C2×Q8—471no—
166C2×Q8—471no—
167C2×D4—21no—
168C2×D4—21no—
169C2×D4—471no—
170C2×D4C22×D4712yes—
171C22×C4—942no—
172C22×C4—942no—
173C22×C4—941no—
174SD16—942no—
175D8—944no—
176C2×C8—472no—
177C2×C8C22×D4711yescharacteristic
178C2×C8C22×D4711yescharacteristic
179C4⋊C4—21no—
180C4⋊C4—472no—
181C4⋊C4—471no—
182C4⋊C4—471no—
183C4⋊C4—471no—
184C4⋊C4—942no—
185C4⋊C4—942no—
186C4⋊C4—941no—
187C4⋊C4C22×D4712yes—
188C22⋊C4—942no—
189C22⋊C4—942no—
190C22⋊C4—942no—
191C22⋊C4—942no—
192C22⋊C4—941no—
193C42—472no—
194C42—941no—
195C42C22×D4711yescharacteristic
196C23—22no—
197C23—941no—
198Q8—81no—
199Q8—942no—
200Q8—941no—
201Q8—941no—
202D4—22no—
203D4—22no—
204D4—42no—
205D4—81no—
206D4—472no—
207D4—941no—
208C2×C4—22no—
209C2×C4—472no—
210C2×C4—472no—
211C2×C4—941no—
212C2×C4—941no—
213C2×C4—941no—
214C2×C4—3762no—
215C2×C4—3762no—
216C2×C4—1882no—
217C2×C4D4×D4711yescharacteristic
218C2×C4D4×D4711yescharacteristic
219C2×C4C23×D4711yescharacteristic
220C8—21no—
221C8—21no—
222C8—942no—
223C22—42no—
224C22—42no—
225C22—42no—
226C22—942no—
227C22—1881no—
228C22—1881no—
229C22C2×D4×D4711yescharacteristic
230C4—21no—
231C4—42no—
232C4—942no—
233C4—942no—
234C4—1881no—
235C4—1881no—
236C4—1881no—
237C4#1309404512yes—
238C4#41×D4711yescharacteristic
239C4#1309407111yescharacteristic
240C2—82no—
241C2—1882no—
242C2#1568978111yescharacteristic
243C2C2×#1309404511yescharacteristic
244C2#1568992411yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#486C2
socleC22×C47C22×D4
hypercenter#486D47
hypocenterC47#3361
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #15689859C2semidirect
2. #15689834C2semidirect
3. #15689476C2semidirect
4. #15689425C2semidirect
5. #15689415C2semidirect
6. #15689337C2semidirect
8. C8×Dic94C2semidirect
9. C4×#10625325C2semidirect
10. #15689203C2semidirect
11. C47×#486C2semidirect
126. #486D47semidirect
134. C47#3361semidirect