Finite Group Databasebeta

← #20243719

Subgroups — #20243719

Order 6016.

402 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 101 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
1C22×#10625336C211yesmaximal, characteristic
2C2×#13093986C211yesmaximal, characteristic
3C2×#13093946C211yesmaximal, characteristic
4#15689030C211yesmaximal, characteristic, complemented
5#15688885C211yesmaximal, characteristic, complemented
6#15688877C211yesmaximal, characteristic, complemented
7C2×#103×C47C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9C22×C4×D47—21no—
10C2×#10625336—22no—
11C2×#10625336—22no—
12C2×#10625336C414yescomplemented
13C22×C47⋊C8C2211yescharacteristic
14#13093986—22no—
15#13093986—22no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×(C2×D47)⋊C4—21no—
18C2×C4×Dic47C2211yescharacteristic
19#13093946—22no—
20C47⋊#95—21no—
21C47⋊#95—21no—
22C22×Q8×C47C2211yescharacteristic
23C22×C8×C47C2211yescharacteristic
24C2×C4⋊C4×C47C2211yescharacteristic
25#103×C47—22no—
26C23×D47—21no—
27C2×Q8×C47—21no—
28C2×Q8×C47—21no—
29C2×Q8×C47—21no—
30C2×Q8×C47—21no—
31C2×Q8×C47—21no—
32C2×Q8×C47C2×C412yescomplemented
33C22×C4×C47—21no—
34C22×C4×C47—21no—
35C22×C4×C47C2311yescharacteristic
36C22×Dic47—21no—
37C22×Dic47D411yescharacteristic
38C22×Dic47D411yescharacteristic
39C2×D188—21no—
40C2×D188—21no—
41C2×D188—21no—
42C2×D188C2×C412yes—
43C2×D188D412yes—
44C2×D188D412yes—
45C2×C4×D47—24no—
46C2×C4×D47—42no—
47C2×C4×D47—42no—
48C2×C8×C47—21no—
49C2×C8×C47—21no—
50C2×C8×C47—21no—
51C4⋊C4×C47—21no—
52C4⋊C4×C47D412yes—
53#10625336—28no—
54(C2×D47)⋊C4—24no—
55C4⋊Dic47—21no—
56C4⋊Dic47—21no—
57C4×Dic47—21no—
58C4×Dic47—21no—
59C2×C47⋊C8—21no—
60C2×C47⋊C8—21no—
61C2×C47⋊C8C2×C412yescomplemented
62C23×C47C2×D411yescharacteristic
63C22×D47—22no—
64C22×D47—22no—
65C22×D47—22no—
66C22×D47—41no—
67C22×D47—41no—
68C22×D47—41no—
69C22×D47—41no—
70Q8×C47—22no—
71Q8×C47—22no—
72Q8×C47—41no—
73Q8×C47—41no—
74C2×C4×C47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—41no—
77C2×C4×C47—41no—
78C2×C4×C47—41no—
79C2×C4×C47—41no—
80C2×C4×C47C22×C411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47#4111yescharacteristic
85C2×C4×C47#4111yescharacteristic
86C2×Dic47—21no—
87C2×Dic47—21no—
88C2×Dic47—21no—
89C2×Dic47—21no—
90C2×Dic47—21no—
91C2×Dic47—41no—
92C2×Dic47—41no—
93C2×Dic47—41no—
94C2×Dic47SD1612yescomplemented
95D188—22no—
96D188—22no—
97D188—22no—
98D188C22⋊C414yes—
99C4×D47—48no—
100C8×C47—41no—
101C47⋊C8—22no—
102C22×C47C4×D411yescharacteristic
103C22×C47#12011yescharacteristic
104C22×C47#12111yescharacteristic
105C22×C47C2×SD1611yescharacteristic
106C22×C47#13511yescharacteristic
107C22×C47AGL(1,ℤ/8)11yescharacteristic
108C22×C47#13711yescharacteristic
109C2×D47—24no—
110C2×D47—42no—
111C2×D47—42no—
112C2×D47—42no—
113C2×D47—42no—
114C2×D47—42no—
115C2×D47—42no—
116C4×C47—42no—
117C4×C47—42no—
118C4×C47C2×C22⋊C411yescharacteristic
119C4×C47C4×D411yescharacteristic
120C4×C47#12111yescharacteristic
121C4×C47#12311yescharacteristic
122Dic47—22no—
123Dic47—41no—
124Dic47—81no—
125#1877—471nomaximal, Sylow
126C2×C47#38611yescharacteristic
127C2×C47C4×SD1611yescharacteristic
128C2×C47#44011yescharacteristic
129C2×C47#45011yescharacteristic
130C2×C47#45211yescharacteristic
131C2×C47#46111yescharacteristic
132C2×C47#46311yescharacteristic
133D47—44no—
134C22×SD16—471no—
135C2×C4×D4—471no—
136C2×#103D4711yescharacteristic, complemented
137C2×#102—471no—
138#391—471no—
139#340—471no—
140#336—471no—
141C47#187711yescharacteristic, complemented, Sylow
142C22×Q8C2×D4711yescharacteristic
143C22×D4—471no—
144C23×C4—941no—
145C2×SD16—474no—
146C2×SD16—942no—
147C2×SD16—942no—
148C22×C8—471no—
149C22×C8C2×D4711yescharacteristic
150C4×D4—942no—
151C4×D4—942no—
152C2×C4⋊C4—471no—
153C2×C4⋊C4C2×D4711yescharacteristic
154C2×C22⋊C4—941no—
155C2×C42—471no—
156#103—22no—
157#102—942no—
158#95—941no—
159#95—941no—
160C24—941no—
161C2×Q8—21no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—21no—
166C2×Q8C4×D4712yescomplemented
167C2×D4—472no—
168C2×D4—472no—
169C2×D4—472no—
170C2×D4—941no—
171C2×D4—941no—
172C2×D4—941no—
173C22×C4—21no—
174C22×C4—21no—
175C22×C4—471no—
176C22×C4—471no—
177C22×C4—944no—
178C22×C4—941no—
179C22×C4—1882no—
180C22×C4—1882no—
181C22×C4C22×D4711yescharacteristic
182SD16—948no—
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—21no—
186C2×C8—472no—
187C2×C8—941no—
188C2×C8—941no—
189C4⋊C4—21no—
190C4⋊C4—941no—
191C4⋊C4—941no—
192C4⋊C4C22⋊D4712yes—
193C22⋊C4—944no—
194C42—941no—
195C42—941no—
196C23—942no—
197C23—942no—
198C23—942no—
199C23—1881no—
200C23—1881no—
201C23—1881no—
202C23—1881no—
203C23D4×D4711yescharacteristic
204Q8—22no—
205Q8—22no—
206Q8—41no—
207Q8—41no—
208D4—474no—
209D4—942no—
210D4—942no—
211D4—942no—
212C2×C4—22no—
213C2×C4—22no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—472no—
219C2×C4—941no—
220C2×C4—941no—
221C2×C4—941no—
222C2×C4—941no—
223C2×C4—941no—
224C2×C4—1888no—
225C2×C4—1881no—
226C2×C4—1881no—
227C2×C4—1881no—
228C2×C4C2×C4×D4711yescharacteristic
229C2×C4#1062535011yescharacteristic
230C2×C4D4×D4711yescharacteristic
231C2×C4D4×D4711yescharacteristic
232C2×C4#1062535211yescharacteristic
233C2×C4C2×C22⋊D4711yescharacteristic
234C8—41no—
235C8—942no—
236C22—944no—
237C22—1882no—
238C22—1882no—
239C22—1882no—
240C22—1882no—
241C22—1882no—
242C22—1882no—
243C22(C22⋊D47)⋊C411yescharacteristic
244C22#1309399211yescharacteristic
245C22#1309399711yescharacteristic
246C22SD16×D4711yescharacteristic
247C22#1309404711yescharacteristic
248C22#1309405111yescharacteristic
249C22#1309405611yescharacteristic
250C4—42no—
251C4—42no—
252C4—942no—
253C4—3761no—
254C4—1881no—
255C4C22⋊C4×D4711yescharacteristic
256C4C4×C22⋊D4711yescharacteristic
257C4#1309399511yescharacteristic
258C4#1309400611yescharacteristic
259C2—1884no—
260C2#1568899911yescharacteristic
261C2#1568920811yescharacteristic
262C2#1568922611yescharacteristic
263C2#1568927211yescharacteristic
264C2#1568928411yescharacteristic
265C2#1568932711yescharacteristic
266C2#1568934111yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#103×C47C2
socleC23×C47C2×D4
hypercenterC2×#103D47
hypocenterC47#1877
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
4. #15689030C2semidirect
5. #15688885C2semidirect
6. #15688877C2semidirect
7. C2×#103×C47C2semidirect
12. C2×#10625336C4semidirect
32. C2×Q8×C47C2×C4semidirect
61. C2×C47⋊C8C2×C4semidirect
94. C2×Dic47SD16semidirect
136. C2×#103D47semidirect
141. C47#1877semidirect
166. C2×Q8C4×D47semidirect