Finite Group Databasebeta

← #20254559

Subgroups — #20254559

Order 6016.

334 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 113 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#15689659C211yesmaximal, characteristic
2C2×#13094015C211yesmaximal, characteristic, complemented
3#15689523C212yesmaximal, complemented
4#15689479C212yesmaximal, complemented
5#15689456C211yesmaximal, characteristic, complemented
6#15689442C211yesmaximal, characteristic
7#15689436C211yesmaximal, characteristic
8#15689428C212yesmaximal, complemented
9#15689422C212yesmaximal, complemented
10#15689173C211yesmaximal, characteristic, complemented
11C47×#483C211yesmaximal, characteristic, complemented
12#13094019—21no—
13#13094015—21no—
14#13094015—21no—
15#13094015C2212yes—
16#13094015C2211yescharacteristic
17#13094015C2212yes—
18#13094013C2211yescharacteristic
19#13094008—21no—
20#13093998C2211yescharacteristic
21Q8×Dic47C2211yescharacteristic
22#13093986C2211yescharacteristic
23(C22⋊D47)⋊C4—21no—
24#13093982—21no—
25C2×C4⋊Dic47—21no—
26C2×C4⋊Dic47C2211yescharacteristic
27C2×Dic47⋊C4—21no—
28C2×C4×Dic47C2211yescharacteristic
29#13093957C2212yes—
30#13093957C2212yes—
31#13093956C2212yes—
32Dic47⋊C8C2212yes—
33#13093948C2212yes—
34#13093946C2212yes—
35#13093944C2212yes—
36C22⋊(C47⋊C8)C2211yescharacteristic
37C8×Dic47C2212yes—
38C22⋊Q8×C47C2211yescharacteristic
39C2×C4⋊C4×C47C2211yescharacteristic
40#106×C47C2212yes—
41#103×C47C2212yes—
42C22⋊C8×C47C2211yescharacteristic
43C2×Q8×C47C2311yescharacteristic
44C22×C4×C47—21no—
45C22×C4×C47C2311yescharacteristic
46C2×C22⋊D47—21no—
47C22×Dic47—21no—
48C22×Dic47D411yescharacteristic
49C22×Dic47D411yescharacteristic
50C2×D188C2311yescharacteristic
51C2×C4×D47—21no—
52C2×C8×C47C2312yes—
53C4⋊C4×C47—21no—
54C4⋊C4×C47—21no—
55C4⋊C4×C47C2312yes—
56C4⋊C4×C47C2311yescharacteristic
57C22⋊C4×C47—21no—
58(C2×D47)⋊C4—21no—
59(C2×D47)⋊C4—21no—
60(C2×D47)⋊C4—21no—
61(C2×D47)⋊C4—21no—
62C4⋊Dic47—21no—
63C4⋊Dic47—22no—
64C4⋊Dic47—22no—
65C4⋊Dic47—21no—
66C4⋊Dic47—21no—
67C4⋊Dic47C2312yes—
68C4⋊Dic47C2311yescharacteristic
69Dic47⋊C4—22no—
70Dic47⋊C4—22no—
71Dic47⋊C4—21no—
72C4×Dic47—21no—
73C4×Dic47D411yescharacteristic
74C4×Dic47D411yescharacteristic
75C4×Dic47C2311yescharacteristic
76C4×Dic47C2311yescharacteristic
77C2×C47⋊C8C2312yes—
78C23×C47C2×D411yescharacteristic
79C22×D47—21no—
80Q8×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—21no—
83C2×C4×C47—22no—
84C2×C4×C47—21no—
85C2×C4×C47—42no—
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2411yescharacteristic
88C22⋊D47—42no—
89C2×Dic47—22no—
90C2×Dic47—21no—
91C2×Dic47—22no—
92C2×Dic47—41no—
93C2×Dic47—42no—
94C2×Dic47C2×D411yescharacteristic
95C2×Dic47C2×D411yescharacteristic
96C2×Dic47C2×D411yescharacteristic
97C2×Dic47C2×D411yescharacteristic
98D188—22no—
99C4×D47—42no—
100C8×C47—22no—
101C47⋊C8—22no—
102C22×C47—21no—
103C22×C47—21no—
104C22×C47#13512yes—
105C22×C47C22×D411yescharacteristic
106C2×D47—41no—
107C2×D47—41no—
108C2×D47—41no—
109C4×C47—21no—
110C4×C47—41no—
111C4×C47—42no—
112C4×C47—41no—
113C4×C472−1+412yes—
114Dic47—21no—
115Dic47—21no—
116Dic47—21no—
117Dic47—21no—
118Dic47—41no—
119Dic47—42no—
120#3232—471nomaximal, Sylow
121C2×C47—22no—
122C2×C47#53611yescharacteristic
123C2×C47C2×#13511yescharacteristic
124C2×C47#57511yescharacteristic
125D47—81no—
126#529—471no—
127C2×#125—471no—
128#499—472no—
129#488—472no—
130#484—471no—
131#483D4711yescharacteristic, complemented
132#481—471no—
133#480—471no—
134#479—472no—
135#478—472no—
136#431—471no—
137C47#323211yescharacteristic, complemented, Sylow
138#126—941no—
139#125—472no—
140#125—472no—
141#125—471no—
142#125—941no—
143#125—941no—
144#124—471no—
145#123—941no—
146C22⋊Q8C2×D4711yescharacteristic
147#121—471no—
148C4×Q8—471no—
149C4×D4—471no—
150C4×D4—941no—
151#117—941no—
152C2×C4⋊C4—471no—
153C2×C4⋊C4—941no—
154C2×C4⋊C4—941no—
155C2×C4⋊C4C2×D4711yescharacteristic
156C2×C42—471no—
157#107—472no—
158#107—472no—
159#106—472no—
160#106C2×D4712yes—
161C4⋊C8—472no—
162#103—472no—
163#103C2×D4712yes—
164#102—472no—
165#102—472no—
166C22⋊C8—471no—
167C22⋊C8C2×D4711yescharacteristic
168C4×C8—472no—
169C2×Q8C22×D4711yescharacteristic
170C2×D4—471no—
171C2×D4—941no—
172C22×C4—21no—
173C22×C4—471no—
174C22×C4—471no—
175C22×C4—941no—
176C22×C4—941no—
177C22×C4C22×D4711yescharacteristic
178C2×C8—472no—
179C2×C8C22×D4712yes—
180C4⋊C4—21no—
181C4⋊C4—21no—
182C4⋊C4—472no—
183C4⋊C4—471no—
184C4⋊C4—942no—
185C4⋊C4—942no—
186C4⋊C4—941no—
187C4⋊C4—942no—
188C4⋊C4—942no—
189C4⋊C4—941no—
190C4⋊C4—941no—
191C4⋊C4—941no—
192C4⋊C4C22×D4712yes—
193C4⋊C4C22×D4711yescharacteristic
194C22⋊C4—21no—
195C22⋊C4—941no—
196C22⋊C4—941no—
197C22⋊C4—941no—
198C22⋊C4—941no—
199C42—471no—
200C42—471no—
201C42—471no—
202C42—471no—
203C42—941no—
204C23—941no—
205C23D4×D4711yescharacteristic
206Q8—22no—
207D4—942no—
208D4—1882no—
209C2×C4—22no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—22no—
213C2×C4—42no—
214C2×C4—471no—
215C2×C4—471no—
216C2×C4—471no—
217C2×C4—471no—
218C2×C4—942no—
219C2×C4—941no—
220C2×C4—942no—
221C2×C4—1882no—
222C2×C4—1881no—
223C2×C4—1882no—
224C2×C4D4×D4711yescharacteristic
225C2×C4C23×D4711yescharacteristic
226C8—22no—
227C8—942no—
228C22—21no—
229C22—21no—
230C22—1881no—
231C22—1881no—
232C22—1881no—
233C22#1309404512yes—
234C22C2×D4×D4711yescharacteristic
235C4—21no—
236C4—42no—
237C4—41no—
238C4—41no—
239C4—941no—
240C4—941no—
241C4—941no—
242C4—941no—
243C4—1881no—
244C4—1882no—
245C4#1309407112yes—
246C2—22no—
247C2—3761no—
248C2#1568969511yescharacteristic
249C2C2×#1309404511yescharacteristic
250C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#483C2
socleC22×C47C22×D4
hypercenter#483D47
hypocenterC47#3232
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
2. C2×#13094015C2semidirect
3. #15689523C2semidirect
4. #15689479C2semidirect
5. #15689456C2semidirect
8. #15689428C2semidirect
9. #15689422C2semidirect
10. #15689173C2semidirect
11. C47×#483C2semidirect
131. #483D47semidirect
137. C47#3232semidirect