Finite Group Databasebeta

← #20254455

Subgroups — #20254455

Order 6016.

396 conjugacy classes of subgroups; only the 109 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 109 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#15689734C211yesmaximal, characteristic, complemented
2#15689691C211yesmaximal, characteristic
3#15689497C211yesmaximal, characteristic, complemented
4#15689488C211yesmaximal, characteristic, complemented
5#15689477C211yesmaximal, characteristic, complemented
6#15689347C212yesmaximal, complemented
7#15689321C212yesmaximal, complemented
8#15689284C212yesmaximal, complemented
9#15689272C212yesmaximal, complemented
10#15689185C211yesmaximal, characteristic, complemented
11C47×#497C211yesmaximal, characteristic, complemented
12C2×#10625354C2211yescharacteristic
13C2×D4×D47C2211yescharacteristic
14C2×#10625336C2212yes—
15C2×#10625336C2212yescomplemented
16#13094021C2211yescharacteristic
17#13094020C2211yescharacteristic
18#13094019—22no—
19#13094016C2211yescharacteristic, complemented
20#13094014—22no—
21#13094013C2211yescharacteristic
22#13094000C2212yes—
23#13093997—22no—
24#13093994—22no—
25Q8×Dic47C2212yescomplemented
26#13093981C2211yescharacteristic
27Dic47⋊C8C2212yescomplemented
28#13093948C2212yescomplemented
29#13093946C2212yes—
30#13093946C2212yescomplemented
31#13093945C2212yes—
32(C2×D47)⋊C8C2212yes—
33C4×C47⋊C8C2211yescharacteristic, complemented
34C2×Q16×C47C2212yescomplemented
35C2×SD16×C47C2212yes—
36C4⋊Q8×C47C2211yescharacteristic, complemented
37#124×C47C2211yescharacteristic
38#97×C47C2211yescharacteristic, complemented
39C23×D47—21no—
40C2×Q8×C47C2311yescharacteristic
41C2×Q8×C47C2312yes—
42C2×D4×C47C2311yescharacteristic
43C2×C22⋊D47—21no—
44C2×C22⋊D47—22no—
45#10625354—42no—
46D4×D47—42no—
47C2×D188—21no—
48C2×D188—22no—
49C2×D188C2311yescharacteristic
50C2×D188C2311yescharacteristic
51C2×C4×D47—21no—
52C2×C4×D47C2311yescharacteristic
53Q16×C47—42no—
54SD16×C47—42no—
55C2×C8×C47C2312yes—
56C4⋊C4×C47—22no—
57C22⋊C4×C47—22no—
58C42×C47C2311yescharacteristic
59#10625336—42no—
60#10625336—42no—
61(C2×D47)⋊C4—22no—
62(C2×D47)⋊C4—22no—
63(C2×D47)⋊C4D412yes—
64C4⋊Dic47—22no—
65C4⋊Dic47C2312yes—
66Dic47⋊C4—22no—
67Dic47⋊C4—22no—
68Dic47⋊C4D412yes—
69C4×Dic47—22no—
70C4×Dic47C2311yescharacteristic
71C2×C47⋊C8C2312yes—
72C23×C47—21no—
73C22×D47—21no—
74C22×D47—21no—
75C22×D47—42no—
76C22×D47—82no—
77C22×D47C2×D411yescharacteristic
78Q8×C47—22no—
79Q8×C47—22no—
80Q8×C47—22no—
81D4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—21no—
84C2×C4×C47C2×D412yes—
85C2×C4×C47C2411yescharacteristic
86C22⋊D47—42no—
87C22⋊D47—82no—
88C2×Dic47—22no—
89C2×Dic47C2×D412yes—
90C2×Dic47C2×D411yescharacteristic
91D188—22no—
92D188—22no—
93D188—42no—
94D188—82no—
95C4×D47—22no—
96C4×D47—42no—
97C8×C47—22no—
98C47⋊C8—22no—
99C22×C47—41no—
100C22×C47—42no—
101C22×C47C22×D411yescharacteristic
102C2×D47—21no—
103C2×D47—22no—
104C2×D47—41no—
105C2×D47—41no—
106C2×D47—42no—
107C2×D47—42no—
108C2×D47—84no—
109C4×C47—22no—
110C4×C47—41no—
111C4×C47—42no—
112C4×C47H(5,𝔽2)12yes—
113Dic47—21no—
114Dic47—22no—
115Dic47—42no—
116#3222—471nomaximal, Sylow
117C2×C47—81no—
118C2×C47#53511yescharacteristic
119C2×C47#57712yes—
120D47—41no—
121D47—81no—
122D47—81no—
123#541—471no—
124#535—471no—
125#497D4711yescharacteristic, complemented
126#492—471no—
127#490—471no—
128#488—471no—
129#464—472no—
130#460—472no—
131#452—472no—
132#450—472no—
133#433—471no—
134C47#322211yescharacteristic, complemented, Sylow
135C2×#41—471no—
136C22×D4—471no—
137C2×Q16C2×D4712yescomplemented
138C2×SD16—472no—
139C2×SD16—472no—
140C2×SD16C2×D4712yes—
141C4⋊Q8C2×D4711yescharacteristic, complemented
142#127—471no—
143#127—471no—
144#126—942no—
145#125—471no—
146#125—942no—
147#124—471no—
148#124C2×D4711yescharacteristic
149C22⋊Q8—472no—
150#121—942no—
151#120—942no—
152C4×Q8—472no—
153#117—471no—
154C4⋊C8—472no—
155#103—472no—
156#102—472no—
157#102—472no—
158#102—472no—
159C22⋊C8—472no—
160#97C2×D4711yescharacteristic, complemented
161C4×C8—471no—
162C24—941no—
163#41—1882no—
164C2×Q8C22×D4711yescharacteristic
165C2×Q8C22×D4712yes—
166C2×D4—471no—
167C2×D4—471no—
168C2×D4—941no—
169C2×D4—942no—
170C2×D4—941no—
171C2×D4—942no—
172C2×D4—1882no—
173C2×D4C22×D4711yescharacteristic
174C22×C4—471no—
175C22×C4—941no—
176Q16—42no—
177SD16—42no—
178SD16—1882no—
179SD16—1882no—
180C2×C8—472no—
181C2×C8C22×D4712yes—
182C4⋊C4—22no—
183C4⋊C4—472no—
184C4⋊C4—472no—
185C4⋊C4—942no—
186C4⋊C4—942no—
187C4⋊C4—942no—
188C22⋊C4—22no—
189C22⋊C4—472no—
190C22⋊C4—942no—
191C22⋊C4—942no—
192C42—471no—
193C42—942no—
194C42C22×D4711yescharacteristic
195C23—21no—
196C23—471no—
197C23—941no—
198C23—941no—
199C23—3762no—
200C23—1882no—
201Q8—22no—
202Q8—22no—
203Q8—22no—
204D4—22no—
205D4—942no—
206D4—942no—
207D4—3762no—
208D4—3762no—
209D4—1882no—
210D4—1882no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—472no—
214C2×C4—471no—
215C2×C4—942no—
216C2×C4—942no—
217C2×C4—1882no—
218C2×C4D4×D4712yes—
219C2×C4C23×D4711yescharacteristic
220C8—22no—
221C8—942no—
222C22—42no—
223C22—41no—
224C22—942no—
225C22—941no—
226C22—3764no—
227C22—1882no—
228C22—1882no—
229C22—1881no—
230C22—1881no—
231C22C2×D4×D4711yescharacteristic
232C4—22no—
233C4—41no—
234C4—42no—
235C4—942no—
236C4—941no—
237C4—1882no—
238C4#1309406912yes—
239C2—81no—
240C2—3761no—
241C2—3761no—
242C2—1881no—
243C2#1568968611yescharacteristic
244C2#1568993212yes—
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#497C2
socleC22×C47C22×D4
hypercenter#497D47
hypocenterC47#3222
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #497

Complements

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

NH ≅ G/Ntype
1. #15689734C2semidirect
3. #15689497C2semidirect
4. #15689488C2semidirect
5. #15689477C2semidirect
6. #15689347C2semidirect
7. #15689321C2semidirect
8. #15689284C2semidirect
9. #15689272C2semidirect
10. #15689185C2semidirect
11. C47×#497C2semidirect
15. C2×#10625336C22semidirect
19. #13094016C22semidirect
25. Q8×Dic47C22semidirect
27. Dic47⋊C8C22semidirect
28. #13093948C22semidirect
30. #13093946C22semidirect
33. C4×C47⋊C8C22semidirect
34. C2×Q16×C47C22semidirect
36. C4⋊Q8×C47C22semidirect
38. #97×C47C22semidirect
125. #497D47semidirect
134. C47#3222semidirect
137. C2×Q16C2×D47semidirect
141. C4⋊Q8C2×D47semidirect
160. #97C2×D47semidirect