Finite Group Databasebeta

← #20254595

Subgroups — #20254595

Order 6016.

324 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 324 conjugacy classes of subgroups — too many to draw. Only its 111 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
2#125×D47C211yesmaximal, characteristic
3#15689529C211yesmaximal, characteristic, complemented
4#15689493C211yesmaximal, characteristic, complemented
5#15689492C211yesmaximal, characteristic, complemented
6#15689460C212yesmaximal
7#15689455C212yesmaximal
8#15689433C212yesmaximal, complemented
9#15689429C212yesmaximal, complemented
10#15689178C211yesmaximal, characteristic
11C47×#501C211yesmaximal, characteristic, complemented
12#13094024C2211yescharacteristic
13#13094016C2211yescharacteristic
14#13094015—21no—
15#13094015C2211yescharacteristic
16#13094015C2211yescharacteristic
17#13094014—21no—
18#13094014—21no—
19#13094004C2212yes—
20#13094000—21no—
21Q8×Dic47—21no—
22#13093989C2212yes—
23#13093982—21no—
24C4⋊C4×D47—21no—
25C4⋊C4×D47—21no—
26C4⋊C4×D47C2211yescharacteristic
27C4⋊C4×D47C2211yescharacteristic
28C42×D47C2211yescharacteristic
29#13093957C2212yes—
30#13093955C2212yes—
31Dic47⋊C8C2212yes—
32#13093949C2212yes—
33#13093949C2212yes—
34#13093947C2212yes—
35#13093947C2212yes—
36(C2×D47)⋊C8C2212yes—
37#13093935C2211yescharacteristic
38C4⋊Q8×C47C2211yescharacteristic
39#125×C47C2211yescharacteristic
40#107×C47C2212yes—
41#106×C47C2212yes—
42#97×C47C2211yescharacteristic
43C2×Q8×C47—21no—
44C2×C4×D47—21no—
45C2×C4×D47—21no—
46C2×C4×D47D411yescharacteristic
47C2×C4×D47D411yescharacteristic
48C2×C4×D47C2311yescharacteristic
49C2×Dic94C2312yes—
50C2×C8×C47C2312yes—
51C4⋊C4×C47—21no—
52C4⋊C4×C47—21no—
53C4⋊C4×C47—21no—
54C4⋊C4×C47C2311yescharacteristic
55C4⋊C4×C47C2312yes—
56C4⋊C4×C47C2311yescharacteristic
57C42×C47C2311yescharacteristic
58(C2×D47)⋊C4—22no—
59C4⋊Dic47—21no—
60C4⋊Dic47—21no—
61C4⋊Dic47—21no—
62C4⋊Dic47—21no—
63C4⋊Dic47—22no—
64C4⋊Dic47C2311yescharacteristic
65C4⋊Dic47C2311yescharacteristic
66Dic47⋊C4—21no—
67Dic47⋊C4—21no—
68Dic47⋊C4—21no—
69Dic47⋊C4—21no—
70Dic47⋊C4—21no—
71Dic47⋊C4—21no—
72Dic47⋊C4—22no—
73C4×Dic47—22no—
74C4×Dic47D411yescharacteristic
75C4×Dic47D411yescharacteristic
76C4×Dic47C2311yescharacteristic
77C2×C47⋊C8C2312yes—
78C22×D47C2×D411yescharacteristic
79Q8×C47—42no—
80C2×C4×C47—22no—
81C2×C4×C47—21no—
82C2×C4×C47—21no—
83C2×C4×C47C2×D411yescharacteristic
84C2×C4×C47C2×D411yescharacteristic
85C2×C4×C47C2411yescharacteristic
86C2×Dic47—22no—
87C2×Dic47—21no—
88C2×Dic47—21no—
89C2×Dic47C2×D411yescharacteristic
90C2×Dic47C2×D411yescharacteristic
91C2×Dic47C2×D411yescharacteristic
92C4×D47—22no—
93C4×D47—22no—
94C4×D47—41no—
95C4×D47—42no—
96C4×D47—42no—
97Dic94—24no—
98C8×C47—22no—
99C47⋊C8—22no—
100C22×C47C22×D411yescharacteristic
101C2×D47—21no—
102C2×D47—21no—
103C2×D47#13712yes—
104C4×C47—21no—
105C4×C47—21no—
106C4×C47—41no—
107C4×C47—41no—
108C4×C47—42no—
109C4×C472−1+412yes—
110Dic47—21no—
111Dic47—21no—
112Dic47—21no—
113Dic47—42no—
114Dic47—41no—
115Dic47—41no—
116#3236—471nomaximal, Sylow
117C2×C47#53611yescharacteristic
118C2×C47C2×#13711yescharacteristic
119C2×C47#57511yescharacteristic
120D47—22no—
121#533—471no—
122C2×#125—471no—
123#501—471no—
124#501D4711yescharacteristic, complemented
125#491—471no—
126#491—471no—
127#484—472no—
128#483—472no—
129#479—472no—
130#479—472no—
131#432—471no—
132C47#323611yescharacteristic, complemented, Sylow
133C4⋊Q8—471no—
134C4⋊Q8C2×D4711yescharacteristic
135#125—471no—
136#125—471no—
137#125—471no—
138#125—941no—
139#125—941no—
140#125—941no—
141#125C2×D4711yescharacteristic
142C22⋊Q8—472no—
143C22⋊Q8—941no—
144C4×Q8—472no—
145C4×Q8—941no—
146#117—941no—
147C2×C4⋊C4—471no—
148C2×C4⋊C4—471no—
149C2×C4⋊C4—941no—
150C2×C4⋊C4—941no—
151C2×C42—471no—
152#107—472no—
153#107C2×D4712yes—
154#106—472no—
155#106C2×D4712yes—
156C4⋊C8—472no—
157#103—472no—
158#103—472no—
159#103—472no—
160#103—472no—
161C22⋊C8—472no—
162#97—471no—
163#97C2×D4711yescharacteristic
164C2×Q8—21no—
165C2×Q8—472no—
166C22×C4—471no—
167C22×C4—471no—
168C22×C4—471no—
169C22×C4—941no—
170C22×C4—941no—
171C2×C8—472no—
172C2×C8C22×D4712yes—
173C4⋊C4—21no—
174C4⋊C4—21no—
175C4⋊C4—21no—
176C4⋊C4—471no—
177C4⋊C4—471no—
178C4⋊C4—941no—
179C4⋊C4—941no—
180C4⋊C4—941no—
181C4⋊C4—941no—
182C4⋊C4—942no—
183C4⋊C4—941no—
184C4⋊C4—941no—
185C4⋊C4—942no—
186C4⋊C4—941no—
187C4⋊C4—941no—
188C4⋊C4—941no—
189C4⋊C4—941no—
190C4⋊C4C22×D4711yescharacteristic
191C4⋊C4C22×D4711yescharacteristic
192C4⋊C4C22×D4712yes—
193C22⋊C4—942no—
194C42—471no—
195C42—471no—
196C42—471no—
197C42—942no—
198C42C22×D4711yescharacteristic
199C23—471no—
200Q8—42no—
201Q8—944no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—471no—
206C2×C4—471no—
207C2×C4—471no—
208C2×C4—942no—
209C2×C4—942no—
210C2×C4—942no—
211C2×C4—941no—
212C2×C4—941no—
213C2×C4—1881no—
214C2×C4—1882no—
215C2×C4—1882no—
216C2×C4D4×D4711yescharacteristic
217C2×C4D4×D4711yescharacteristic
218C2×C4C23×D4711yescharacteristic
219C8—22no—
220C8—942no—
221C22—472no—
222C22—941no—
223C22—941no—
224C22C2×D4×D4711yescharacteristic
225C4—21no—
226C4—21no—
227C4—41no—
228C4—41no—
229C4—42no—
230C4—941no—
231C4—941no—
232C4—941no—
233C4—1881no—
234C4—1881no—
235C4—1882no—
236C4#1309407212yes—
237C2—942no—
238C2#1568969811yescharacteristic
239C2#137×D4711yescharacteristic
240C2#1568991911yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#501C2
socleC22×C47C22×D4
hypercenter#501D47
hypocenterC47#3236
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C42 ◁ #501

Complements

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

NH ≅ G/Ntype
3. #15689529C2semidirect
4. #15689493C2semidirect
5. #15689492C2semidirect
8. #15689433C2semidirect
9. #15689429C2semidirect
11. C47×#501C2semidirect
124. #501D47semidirect
132. C47#3236semidirect