Finite Group Databasebeta

← #20253730

Subgroups — #20253730

Order 6016.

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

normal subgroups only

This group has 392 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#15689678C211yesmaximal, characteristic, complemented
2#15689672C211yesmaximal, characteristic
3#15689490C212yesmaximal, complemented
4#15689486C212yesmaximal, complemented
5#15689485C211yesmaximal, characteristic, complemented
6#15689483C211yesmaximal, characteristic, complemented
7#15689482C211yesmaximal, characteristic, complemented
8#15689118C212yesmaximal, complemented
9#15689116C212yesmaximal, complemented
10#97×D47C211yesmaximal, characteristic, complemented
11C47×#489C211yesmaximal, characteristic, complemented
12C2×#10625354C2211yescharacteristic
13C2×#10625352C2211yescharacteristic
14C2×C8×D47C2212yes—
15#13094024C2211yescharacteristic
16#13094022C2211yescharacteristic
17#13094020C2211yescharacteristic
18#13094015C2212yes—
19#13094012C2211yescharacteristic
20#13094004—21no—
21#13094000—21no—
22#13093997—21no—
23#13093997—21no—
24Q8×Dic47—21no—
25#13093989—21no—
26(C22⋊D47)⋊C4—21no—
27(C22⋊D47)⋊C4—21no—
28#13093982C2212yes—
29C42×D47C2211yescharacteristic
30#13093949C2212yes—
31#13093948C2212yes—
32#13093947C2212yes—
33#13093946C2212yes—
34#13093945C2212yes—
35#13093944C2212yes—
36#13093935C2211yescharacteristic
37#13093934C2212yes—
38C4⋊Q8×C47C2211yescharacteristic
39#124×C47C2211yescharacteristic
40#103×C47C2212yes—
41#102×C47C2212yes—
42#97×C47C2211yescharacteristic
43C2×Q8×C47—21no—
44C2×Q8×C47C2311yescharacteristic
45C2×D4×C47C2311yescharacteristic
46C2×C22⋊D47—21no—
47C2×C22⋊D47—21no—
48C2×C22⋊D47—21no—
49C22×Dic47—21no—
50#10625354—24no—
51#10625352—24no—
52C2×D188—21no—
53C2×D188C2311yescharacteristic
54C2×C4×D47—21no—
55C2×C4×D47D411yescharacteristic
56C2×C4×D47D411yescharacteristic
57C2×C4×D47C2311yescharacteristic
58C2×Dic94—21no—
59C2×Dic94C2311yescharacteristic
60C2×C8×C47C2312yes—
61C4⋊C4×C47—21no—
62C4⋊C4×C47C2312yes—
63C22⋊C4×C47—21no—
64C22⋊C4×C47—21no—
65C42×C47C2311yescharacteristic
66(C2×D47)⋊C4—22no—
67(C2×D47)⋊C4—21no—
68(C2×D47)⋊C4—21no—
69C4⋊Dic47—21no—
70C4⋊Dic47—22no—
71C4⋊Dic47C2312yes—
72Dic47⋊C4—21no—
73Dic47⋊C4—21no—
74Dic47⋊C4—22no—
75C4×Dic47—22no—
76C4×Dic47D411yescharacteristic
77C4×Dic47D411yescharacteristic
78C4×Dic47C2311yescharacteristic
79C2×C47⋊C8C2312yes—
80C8×D47—24no—
81C23×C47—21no—
82C22×D47—21no—
83C22×D47C2×D411yescharacteristic
84Q8×C47—22no—
85Q8×C47—42no—
86D4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—21no—
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47C2411yescharacteristic
92C22⋊D47—42no—
93C22⋊D47—42no—
94C22⋊D47—42no—
95C2×Dic47—22no—
96C2×Dic47—21no—
97C2×Dic47—42no—
98C2×Dic47C2×D411yescharacteristic
99C2×Dic47C2×D411yescharacteristic
100C2×Dic47C2×D411yescharacteristic
101D188—22no—
102D188—42no—
103C4×D47—41no—
104C4×D47—41no—
105C4×D47—42no—
106C4×D47#4114yes—
107Dic94—22no—
108Dic94—42no—
109C8×C47—22no—
110C47⋊C8—22no—
111C22×C47—41no—
112C22×C47—41no—
113C22×C47—41no—
114C22×C47C22×D411yescharacteristic
115C2×D47—21no—
116C2×D47—21no—
117C2×D47—41no—
118C2×D47—41no—
119C2×D47—41no—
120C2×D47#12412yes—
121C4×C47—21no—
122C4×C47—21no—
123C4×C47—41no—
124C4×C47—42no—
125C4×C47C2×#4112yes—
126Dic47—21no—
127Dic47—21no—
128Dic47—41no—
129Dic47—42no—
130Dic47#12412yes—
131#3135—471nomaximal, Sylow
132C2×C47—81no—
133C2×C47C2×#12411yescharacteristic
134C2×C47#57511yescharacteristic
135C2×C47#57511yescharacteristic
136D47—22no—
137D47—81no—
138#533—471no—
139#532—471no—
140#491—472no—
141#490—472no—
142#489—471no—
143#489—471no—
144#489—471no—
145#489D4711yescharacteristic, complemented
146#416—472no—
147#416—472no—
148C2×#97—471no—
149C47#313511yescharacteristic, complemented, Sylow
150C2×#41—471no—
151C2×#41—471no—
152C22×C8—472no—
153C4⋊Q8—471no—
154C4⋊Q8—471no—
155C4⋊Q8C2×D4711yescharacteristic
156#127—471no—
157#125—472no—
158#124—471no—
159#124C2×D4711yescharacteristic
160C22⋊Q8—941no—
161C22⋊Q8—941no—
162#121—941no—
163#121—941no—
164C4×Q8—941no—
165C4×Q8—941no—
166C4×D4—941no—
167C4×D4—941no—
168#117—472no—
169C2×C42—471no—
170#103—472no—
171#103—472no—
172#103—472no—
173#103C2×D4712yes—
174#102—472no—
175#102—472no—
176#102—472no—
177#102C2×D4712yes—
178#97—472no—
179#97—471no—
180#97C2×D4711yescharacteristic
181#41—944no—
182#41—944no—
183C2×Q8—21no—
184C2×Q8—471no—
185C2×Q8—941no—
186C2×Q8C22×D4711yescharacteristic
187C2×D4—471no—
188C2×D4—941no—
189C2×D4—941no—
190C2×D4—941no—
191C2×D4—941no—
192C2×D4C22×D4711yescharacteristic
193C22×C4—471no—
194C22×C4—471no—
195C22×C4—471no—
196C22×C4—941no—
197C22×C4—941no—
198C2×C8—472no—
199C2×C8—944no—
200C2×C8C22×D4712yes—
201C4⋊C4—21no—
202C4⋊C4—472no—
203C4⋊C4—941no—
204C4⋊C4—941no—
205C4⋊C4—942no—
206C4⋊C4—942no—
207C4⋊C4—941no—
208C4⋊C4C22×D4712yes—
209C22⋊C4—21no—
210C22⋊C4—21no—
211C22⋊C4—942no—
212C22⋊C4—941no—
213C22⋊C4—941no—
214C42—471no—
215C42—471no—
216C42—471no—
217C42—942no—
218C42C22×D4711yescharacteristic
219C23—21no—
220C23—471no—
221C23—941no—
222Q8—22no—
223Q8—42no—
224Q8—942no—
225Q8—1882no—
226D4—22no—
227D4—942no—
228D4—1882no—
229D4—1882no—
230D4—1882no—
231D4—1882no—
232C2×C4—22no—
233C2×C4—21no—
234C2×C4—471no—
235C2×C4—474no—
236C2×C4—471no—
237C2×C4—471no—
238C2×C4—942no—
239C2×C4—941no—
240C2×C4—1881no—
241C2×C4—1881no—
242C2×C4—1882no—
243C2×C4—1882no—
244C2×C4D4×D4711yescharacteristic
245C2×C4D4×D4711yescharacteristic
246C2×C4C23×D4711yescharacteristic
247C8—22no—
248C8—942no—
249C22—41no—
250C22—41no—
251C22—41no—
252C22—472no—
253C22—941no—
254C22—941no—
255C22—1881no—
256C22—1881no—
257C22—1881no—
258C22C2×D4×D4711yescharacteristic
259C4—21no—
260C4—21no—
261C4—41no—
262C4—42no—
263C4—472no—
264C4—941no—
265C4—941no—
266C4—1881no—
267C4—1882no—
268C4#41×D4712yes—
269C2—81no—
270C2—942no—
271C2—3761no—
272C2#124×D4711yescharacteristic
273C2#1568991911yescharacteristic
274C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#489C2
socleC22×C47C22×D4
hypercenter#489D47
hypocenterC47#3135
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
1. #15689678C2semidirect
3. #15689490C2semidirect
4. #15689486C2semidirect
5. #15689485C2semidirect
6. #15689483C2semidirect
7. #15689482C2semidirect
8. #15689118C2semidirect
9. #15689116C2semidirect
10. #97×D47C2semidirect
11. C47×#489C2semidirect
145. #489D47semidirect
149. C47#3135semidirect