Finite Group Databasebeta

← #20243694

Subgroups — #20243694

Order 6016.

404 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 404 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C2×#13094004C211yesmaximal, characteristic
2C2×C4⋊C4×D47C211yesmaximal, characteristic
3C2×#13093949C211yesmaximal, characteristic, complemented
4C2×#13093947C211yesmaximal, characteristic, complemented
5C2×(C2×D47)⋊C8C211yesmaximal, characteristic
6#15688885C211yesmaximal, characteristic, complemented
7C47×#340C211yesmaximal, characteristic, complemented
8C22×Dic94C2211yescharacteristic
9C22×C4×D47—21no—
10C22×C4×D47C2211yescharacteristic
11C22×C47⋊C8C2211yescharacteristic
12#13094004—22no—
13#13094004C414yescomplemented
14C2×C4⋊Dic47—21no—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×Dic47⋊C4—21no—
17C4⋊C4×D47—22no—
18C4⋊C4×D47—22no—
19C2×(C2×D47)⋊C4—21no—
20#13093949—22no—
21#13093947—22no—
22(C2×D47)⋊C8—22no—
23C22×C8×C47C2211yescharacteristic
24C2×C4⋊C4×C47C2211yescharacteristic
25C2×C4⋊C4×C47C2211yescharacteristic
26C23×D47D411yescharacteristic
27C22×C4×C47—21no—
28C22×C4×C47—21no—
29C22×C4×C47C2311yescharacteristic
30C22×Dic47—21no—
31C22×Dic47—21no—
32C22×Dic47D411yescharacteristic
33C2×C4×D47—21no—
34C2×C4×D47—21no—
35C2×C4×D47—21no—
36C2×C4×D47—21no—
37C2×C4×D47—24no—
38C2×C4×D47—42no—
39C2×C4×D47—42no—
40C2×C4×D47C2×C412yes—
41C2×C4×D47D412yes—
42C2×Dic94—21no—
43C2×Dic94—21no—
44C2×Dic94—21no—
45C2×Dic94—21no—
46C2×Dic94—21no—
47C2×Dic94C2×C412yescomplemented
48C2×C8×C47—21no—
49C2×C8×C47—21no—
50C2×C8×C47—21no—
51C4⋊C4×C47—21no—
52C4⋊C4×C47—21no—
53C4⋊C4×C47C2×C412yescomplemented
54C4⋊C4×C47D412yes—
55(C2×D47)⋊C4—24no—
56C4⋊Dic47—21no—
57C4⋊Dic47—24no—
58C4⋊Dic47D412yes—
59Dic47⋊C4—24no—
60C2×C47⋊C8—21no—
61C2×C47⋊C8—21no—
62C2×C47⋊C8—21no—
63C23×C47C2×D411yescharacteristic
64C22×D47—21no—
65C22×D47—21no—
66C22×D47—21no—
67C22×D47—21no—
68C22×D47C22⋊C412yes—
69C22×D47SD1612yes—
70C22×D47Q1612yes—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—41no—
74C2×C4×C47—41no—
75C2×C4×C47—41no—
76C2×C4×C47—41no—
77C2×C4×C47C22×C411yescharacteristic
78C2×C4×C47C2×D411yescharacteristic
79C2×C4×C47C2×D411yescharacteristic
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47#4111yescharacteristic
82C2×C4×C47#4111yescharacteristic
83C2×Dic47—21no—
84C2×Dic47—21no—
85C2×Dic47—22no—
86C2×Dic47—22no—
87C2×Dic47—41no—
88C2×Dic47—41no—
89C2×Dic47—41no—
90C2×Dic47—41no—
91C2×Dic47C22⋊C412yes—
92C4×D47—22no—
93C4×D47—22no—
94C4×D47—22no—
95C4×D47—22no—
96C4×D47—48no—
97Dic94—22no—
98Dic94—22no—
99Dic94—41no—
100Dic94—41no—
101C8×C47—41no—
102C47⋊C8—41no—
103C22×C47C2×C22⋊C411yescharacteristic
104C22×C47#12011yescharacteristic
105C22×C47#12311yescharacteristic
106C22×C47C2×SD1611yescharacteristic
107C22×C47C2×Q1611yescharacteristic
108C22×C47AGL(1,ℤ/8)11yescharacteristic
109C22×C47#13711yescharacteristic
110C2×D47—22no—
111C2×D47—22no—
112C2×D47—22no—
113C2×D47—22no—
114C2×D47—22no—
115C2×D47—22no—
116C2×D47#10314yescomplemented
117C4×C47—42no—
118C4×C47—42no—
119C4×C47C4×D411yescharacteristic
120C4×C47C4×D411yescharacteristic
121C4×C47#12111yescharacteristic
122C4×C47#12111yescharacteristic
123Dic47—22no—
124Dic47—42no—
125Dic47—42no—
126#1872—471nomaximal, Sylow
127C2×C47#38611yescharacteristic
128C2×C47C2×#10311yescharacteristic
129C2×C47#41711yescharacteristic
130C2×C47#45011yescharacteristic
131C2×C47#45111yescharacteristic
132C2×C47#48311yescharacteristic
133C2×C47#48411yescharacteristic
134D47—24no—
135C2×C22⋊Q8—471no—
136C22×C4⋊C4—471no—
137C2×#103—471no—
138C2×#103—471no—
139C2×C22⋊C8—471no—
140#340—471no—
141#340D4711yescharacteristic, complemented
142C47#187211yescharacteristic, complemented, Sylow
143C22×Q8—471no—
144C23×C4—471no—
145C23×C4—941no—
146C22×C8—471no—
147C22×C8C2×D4711yescharacteristic
148C22⋊Q8—474no—
149C22⋊Q8—942no—
150C2×C4⋊C4—471no—
151C2×C4⋊C4—942no—
152C2×C4⋊C4—941no—
153C2×C4⋊C4—941no—
154C2×C4⋊C4—942no—
155C2×C4⋊C4C2×D4711yescharacteristic
156C2×C4⋊C4C2×D4711yescharacteristic
157C2×C22⋊C4—941no—
158#103—942no—
159#103—942no—
160C22⋊C8—942no—
161C24—471no—
162C2×Q8—472no—
163C2×Q8—941no—
164C2×Q8—941no—
165C2×Q8—941no—
166C2×Q8—941no—
167C2×Q8—941no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—471no—
171C22×C4—472no—
172C22×C4—472no—
173C22×C4—944no—
174C22×C4—941no—
175C22×C4—941no—
176C22×C4—941no—
177C22×C4—941no—
178C22×C4—941no—
179C22×C4—941no—
180C22×C4—1882no—
181C22×C4—1882no—
182C22×C4C22×D4711yescharacteristic
183C2×C8—21no—
184C2×C8—21no—
185C2×C8—21no—
186C2×C8—941no—
187C2×C8—941no—
188C2×C8—941no—
189C4⋊C4—21no—
190C4⋊C4—21no—
191C4⋊C4—472no—
192C4⋊C4—944no—
193C4⋊C4—944no—
194C4⋊C4—941no—
195C4⋊C4C4×D4712yescomplemented
196C4⋊C4D18812yes—
197C22⋊C4—944no—
198C23—472no—
199C23—472no—
200C23—472no—
201C23—941no—
202C23—941no—
203C23—941no—
204C23—941no—
205C23D4×D4711yescharacteristic
206Q8—942no—
207Q8—942no—
208Q8—1881no—
209Q8—1881no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—41no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—41no—
216C2×C4—472no—
217C2×C4—941no—
218C2×C4—941no—
219C2×C4—942no—
220C2×C4—942no—
221C2×C4—942no—
222C2×C4—942no—
223C2×C4—942no—
224C2×C4—942no—
225C2×C4—1888no—
226C2×C4—1881no—
227C2×C4—1881no—
228C2×C4—1881no—
229C2×C4—1881no—
230C2×C4C2×C4×D4711yescharacteristic
231C2×C4C2×D18811yescharacteristic
232C2×C4#1062535011yescharacteristic
233C2×C4D4×D4711yescharacteristic
234C2×C4D4×D4711yescharacteristic
235C2×C4#1062535411yescharacteristic
236C8—41no—
237C8—1881no—
238C22—474no—
239C22—942no—
240C22—942no—
241C22—942no—
242C22—942no—
243C22—942no—
244C22—942no—
245C22C22⋊C4×D4711yescharacteristic
246C22#1309399411yescharacteristic
247C22#1309400911yescharacteristic
248C22SD16×D4711yescharacteristic
249C22Q16×D4711yescharacteristic
250C22#1309404811yescharacteristic
251C22#1309405311yescharacteristic
252C4—42no—
253C4—42no—
254C4—942no—
255C4—1882no—
256C4—1882no—
257C4#1309398611yescharacteristic
258C4C4×D18811yescharacteristic
259C4#1309399711yescharacteristic
260C4#1309399911yescharacteristic
261C2—944no—
262C2#1568900111yescharacteristic
263C2#103×D4711yescharacteristic
264C2#1568912111yescharacteristic
265C2#1568927511yescharacteristic
266C2#1568928011yescharacteristic
267C2#1568945511yescharacteristic
268C2#1568946011yescharacteristic
subgroupG/H
centerC23D4×D47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#340C2
socleC23×C47C2×D4
hypercenter#340D47
hypocenterC47#1872
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
3. C2×#13093949C2semidirect
4. C2×#13093947C2semidirect
6. #15688885C2semidirect
7. C47×#340C2semidirect
13. #13094004C4semidirect
47. C2×Dic94C2×C4semidirect
53. C4⋊C4×C47C2×C4semidirect
116. C2×D47#103semidirect
141. #340D47semidirect
142. C47#1872semidirect
195. C4⋊C4C4×D47semidirect