Finite Group Databasebeta

← #20256046

Subgroups — #20256046

Order 6016.

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

normal subgroups only

This group has 362 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#15689858C211yesmaximal, characteristic, complemented
2#15689830C211yesmaximal, characteristic, complemented
3#15689479C212yesmaximal, complemented
4#15689470C211yesmaximal, characteristic, complemented
5#15689422C212yesmaximal, complemented
6#15689418C211yesmaximal, characteristic, complemented
7#15689340C212yesmaximal, complemented
8#15689318C211yesmaximal, characteristic
9C8×Dic94C211yesmaximal, characteristic, complemented
10#15689203C212yesmaximal, complemented
11C4×SD16×C47C211yesmaximal, characteristic, complemented
12C2×#10625334C2212yes—
13#13094024C2211yescharacteristic
14#13094021C2211yescharacteristic
15#13094015C2212yes—
16#13094013C2212yes—
17#13094012—21no—
18#13094009—22no—
19#13094003—21no—
20#13094001—22no—
21C4×Dic94C2211yescharacteristic
22C4×D188—21no—
23D4×Dic47C2212yes—
24#13093986C2212yes—
25C2×C4⋊Dic47—21no—
26#13093957C2212yes—
27C4⋊(C47⋊C8)C2211yescharacteristic
28Dic47⋊C8C2212yes—
29#13093948C2212yes—
30#13093946C2212yes—
31#13093946C2212yes—
32#13093944C2212yes—
33C8×Dic47C2212yes—
34C2×SD16×C47C2211yescharacteristic
35C4×Q8×C47C2211yescharacteristic
36C4×D4×C47C2211yescharacteristic
37#106×C47C2211yescharacteristic
38#103×C47C2211yescharacteristic
39#102×C47C2211yescharacteristic
40C4×C8×C47C2211yescharacteristic
41C2×Q8×C47C2311yescharacteristic
42C2×D4×C47C2311yescharacteristic
43C22×C4×C47—21no—
44C22×Dic47—22no—
45C2×D188—21no—
46C2×D188—21no—
47C2×D188C2312yes—
48C2×C4×D47—22no—
49C2×Dic94—21no—
50C2×Dic94D411yescharacteristic
51SD16×C47—22no—
52C2×C8×C47C2311yescharacteristic
53C2×C8×C47C2311yescharacteristic
54C4⋊C4×C47—21no—
55C4⋊C4×C47C2311yescharacteristic
56C4⋊C4×C47C2311yescharacteristic
57C22⋊C4×C47—21no—
58C42×C47—21no—
59C42×C47C2311yescharacteristic
60C22⋊Dic47—22no—
61#10625334—24no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4—22no—
64(C2×D47)⋊C4—22no—
65C4⋊Dic47—21no—
66C4⋊Dic47—22no—
67C4⋊Dic47D411yescharacteristic
68C4⋊Dic47C2312yes—
69Dic47⋊C4—22no—
70Dic47⋊C4D412yes—
71C4×Dic47C2312yes—
72C2×C47⋊C8C2312yes—
73C23×C47—21no—
74C22×D47—22no—
75Q8×C47—21no—
76Q8×C47—21no—
77D4×C47—21no—
78D4×C47#4112yes—
79C2×C4×C47—21no—
80C2×C4×C47—21no—
81C2×C4×C47—21no—
82C2×C4×C47—42no—
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2411yescharacteristic
86C2×Dic47—22no—
87C2×Dic47—82no—
88C2×Dic47C2×D412yes—
89C2×Dic47C2×D412yes—
90D188—22no—
91D188—22no—
92D188—42no—
93D188—81no—
94C4×D47—82no—
95Dic94—22no—
96Dic94—81no—
97C8×C47—21no—
98C8×C47—21no—
99C47⋊C8—22no—
100C22×C47—22no—
101C22×C47—41no—
102C22×C47—41no—
103C22×C47C22×D411yescharacteristic
104C2×D47—42no—
105C2×D47—42no—
106C2×D47—42no—
107C4×C47—21no—
108C4×C47—41no—
109C4×C47—41no—
110C4×C47—41no—
111C4×C47#13512yes—
112C4×C47C2×#4111yescharacteristic
113C4×C472−1+411yescharacteristic
114Dic47—22no—
115Dic47—22no—
116Dic47—42no—
117#3361—471nomaximal, Sylow
118C2×C47—42no—
119C2×C47#54811yescharacteristic
120C2×C47C2×#13511yescharacteristic
121C2×C47#57611yescharacteristic
122D47—82no—
123#559—471no—
124#554—471no—
125#488—472no—
126#486—471no—
127#478—472no—
128#477—471no—
129#463—472no—
130#459—471no—
131C8×Q8—471no—
132C4×SD16D4711yescharacteristic, complemented
133C4×D8—472no—
134C47#336111yescharacteristic, complemented, Sylow
135C2×SD16C2×D4711yescharacteristic
136C2×D8—472no—
137C4⋊Q8—471no—
138#127—471no—
139#125—472no—
140#124—472no—
141#124—941no—
142#123—942no—
143C22⋊Q8—942no—
144C22⋊Q8—941no—
145C4×Q8—471no—
146C4×Q8C2×D4711yescharacteristic
147C4×D4—472no—
148C4×D4—472no—
149C4×D4—941no—
150C4×D4C2×D4711yescharacteristic
151C2×C4⋊C4—941no—
152#107—472no—
153#106C2×D4711yescharacteristic
154C4⋊C8—472no—
155C4⋊C8—471no—
156#103—472no—
157#103C2×D4711yescharacteristic
158#102—472no—
159#102—472no—
160#102—472no—
161#102C2×D4711yescharacteristic
162C4×C8—472no—
163C4×C8C2×D4711yescharacteristic
164C2×Q8—471no—
165C2×Q8—941no—
166C2×Q8C22×D4711yescharacteristic
167C2×D4—472no—
168C2×D4—941no—
169C2×D4—941no—
170C2×D4C22×D4711yescharacteristic
171C22×C4—21no—
172C22×C4—942no—
173C22×C4—942no—
174SD16—22no—
175D8—944no—
176C2×C8—472no—
177C2×C8C22×D4711yescharacteristic
178C2×C8C22×D4711yescharacteristic
179C4⋊C4—21no—
180C4⋊C4—472no—
181C4⋊C4—471no—
182C4⋊C4—472no—
183C4⋊C4—942no—
184C4⋊C4—942no—
185C4⋊C4—941no—
186C4⋊C4C22×D4711yescharacteristic
187C4⋊C4C22×D4711yescharacteristic
188C22⋊C4—21no—
189C22⋊C4—942no—
190C22⋊C4—942no—
191C22⋊C4—942no—
192C22⋊C4—942no—
193C42—21no—
194C42—472no—
195C42C22×D4711yescharacteristic
196C23—21no—
197C23—942no—
198Q8—21no—
199Q8—21no—
200Q8—942no—
201Q8—3761no—
202D4—21no—
203D4—942no—
204D4—942no—
205D4—3761no—
206D4—1882no—
207D4#1062535012yes—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—42no—
212C2×C4—472no—
213C2×C4—472no—
214C2×C4—942no—
215C2×C4—3762no—
216C2×C4—3762no—
217C2×C4D4×D4711yescharacteristic
218C2×C4D4×D4711yescharacteristic
219C2×C4C23×D4711yescharacteristic
220C8—21no—
221C8—21no—
222C8—942no—
223C22—22no—
224C22—41no—
225C22—41no—
226C22—1882no—
227C22—1882no—
228C22—1882no—
229C22C2×D4×D4711yescharacteristic
230C4—21no—
231C4—41no—
232C4—41no—
233C4—41no—
234C4—942no—
235C4—942no—
236C4—1882no—
237C4#1309404512yes—
238C4C2×#1062535011yescharacteristic
239C4#1309407111yescharacteristic
240C2—42no—
241C2—3762no—
242C2#1568978211yescharacteristic
243C2C2×#1309404511yescharacteristic
244C2#1568992511yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC4×SD16×C47C2
socleC22×C47C22×D4
hypercenterC4×SD16D47
hypocenterC47#3361
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
1. #15689858C2semidirect
2. #15689830C2semidirect
3. #15689479C2semidirect
4. #15689470C2semidirect
5. #15689422C2semidirect
6. #15689418C2semidirect
7. #15689340C2semidirect
9. C8×Dic94C2semidirect
10. #15689203C2semidirect
11. C4×SD16×C47C2semidirect
132. C4×SD16D47semidirect
134. C47#3361semidirect