Finite Group Databasebeta

← #20253515

Subgroups — #20253515

Order 6016.

380 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 119 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#15689675C211yesmaximal, characteristic
2C2×#13093989C211yesmaximal, characteristic
3#15689453C211yesmaximal, characteristic
4#15689407C212yesmaximal, complemented
5#15689332C212yesmaximal, complemented
6#15689281C211yesmaximal, characteristic
7#15689278C211yesmaximal, characteristic
8#15689229C212yesmaximal, complemented
9#15689227C212yesmaximal, complemented
10#15689177C211yesmaximal, characteristic
11C47×#483C211yesmaximal, characteristic
12C22×Dic94C2211yescharacteristic
13C2×Dic188C2212yes—
14C2×#10625337C2212yes—
15#13094023C2211yescharacteristic
16#13094022C2211yescharacteristic
17#13094014—21no—
18#13094003C2211yescharacteristic
19#13094001—21no—
20Q8×Dic47C2211yescharacteristic
21#13093989—21no—
22#13093989—21no—
23#13093989—21no—
24#13093989C2212yes—
25#13093989C2211yescharacteristic
26#13093989C2212yes—
27#13093980—21no—
28C2×Dic47⋊C4—21no—
29C2×C4×Dic47—21no—
30C2×C4×Dic47C2211yescharacteristic
31#13093955C2212yes—
32Dic47⋊C8C2212yes—
33#13093949C2212yes—
34#13093947C2212yes—
35#13093947C2212yes—
36C22⋊(C47⋊C8)C2211yescharacteristic
37#13093934C2212yes—
38C22⋊Q8×C47C2211yescharacteristic
39C2×C4⋊C4×C47C2211yescharacteristic
40#106×C47C2212yes—
41#103×C47C2212yes—
42C22⋊C8×C47C2211yescharacteristic
43C2×Q8×C47C2311yescharacteristic
44C22×C4×C47—21no—
45C22×C4×C47C2311yescharacteristic
46C22×Dic47—21no—
47C22×Dic47D411yescharacteristic
48C22×Dic47D411yescharacteristic
49C2×Dic94—21no—
50C2×Dic94—24no—
51C2×Dic94—21no—
52C2×Dic94C2311yescharacteristic
53C2×Dic94C2312yes—
54C2×C8×C47C2312yes—
55C4⋊C4×C47—21no—
56C4⋊C4×C47—21no—
57C4⋊C4×C47C2312yes—
58C4⋊C4×C47C2311yescharacteristic
59C22⋊C4×C47—21no—
60C22⋊Dic47—21no—
61#10625337—24no—
62C4⋊Dic47—21no—
63C4⋊Dic47C2311yescharacteristic
64Dic47⋊C4—21no—
65Dic47⋊C4—22no—
66Dic47⋊C4—22no—
67Dic47⋊C4—21no—
68Dic47⋊C4—21no—
69Dic47⋊C4—21no—
70Dic47⋊C4—21no—
71C4×Dic47—22no—
72C4×Dic47—22no—
73C4×Dic47—21no—
74C4×Dic47—21no—
75C4×Dic47D411yescharacteristic
76C4×Dic47D411yescharacteristic
77C4×Dic47C2311yescharacteristic
78C4×Dic47C2311yescharacteristic
79C2×C47⋊C8C2312yes—
80Dic188—24no—
81C23×C47C2×D411yescharacteristic
82Q8×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—21no—
86C2×C4×C47—21no—
87C2×C4×C47—42no—
88C2×C4×C47C2×D411yescharacteristic
89C2×C4×C47C2411yescharacteristic
90C2×Dic47—24no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—21no—
95C2×Dic47—21no—
96C2×Dic47C2×D411yescharacteristic
97C2×Dic47C2×D411yescharacteristic
98C2×Dic47C2×D411yescharacteristic
99C2×Dic47C2×D411yescharacteristic
100Dic94—24no—
101Dic94—22no—
102Dic94—22no—
103Dic94—42no—
104Dic94#4114yes—
105C8×C47—22no—
106C47⋊C8—22no—
107C22×C47—21no—
108C22×C47—21no—
109C22×C47#13712yes—
110C22×C47C22×D411yescharacteristic
111C4×C47—21no—
112C4×C47—41no—
113C4×C47—41no—
114C4×C47—42no—
115C4×C47C2×#4112yes—
116Dic47—24no—
117Dic47—21no—
118Dic47—21no—
119Dic47—21no—
120Dic47—41no—
121Dic47—41no—
122Dic47#13712yes—
123#3113—471nomaximal, Sylow
124C2×C47—22no—
125C2×C47#52511yescharacteristic
126C2×C47C2×#13711yescharacteristic
127C2×C47C2×#13711yescharacteristic
128#533—471no—
129C2×C4×Q8—471no—
130#483—471no—
131#483D4711yescharacteristic
132#475—472no—
133#462—472no—
134#451—471no—
135#451—471no—
136#441—472no—
137#441—472no—
138#432—471no—
139C47#311311yescharacteristic, complemented, Sylow
140C22×Q8—471no—
141C2×Q16—472no—
142C2×Q16—472no—
143C4⋊Q8—471no—
144C4⋊Q8—471no—
145#125—941no—
146C22⋊Q8—471no—
147C22⋊Q8—941no—
148C22⋊Q8C2×D4711yescharacteristic
149C4×Q8—471no—
150C4×Q8—472no—
151C4×Q8—472no—
152C4×Q8—471no—
153C4×Q8—941no—
154C4×Q8—941no—
155C4×Q8—941no—
156#117—941no—
157C2×C4⋊C4—941no—
158C2×C4⋊C4C2×D4711yescharacteristic
159C2×C42—471no—
160C2×C42—941no—
161#106—472no—
162#106C2×D4712yes—
163C4⋊C8—472no—
164#103—472no—
165#103—472no—
166#103—472no—
167#103C2×D4712yes—
168C22⋊C8—471no—
169C22⋊C8C2×D4711yescharacteristic
170#97—472no—
171C2×Q8—472no—
172C2×Q8—471no—
173C2×Q8—941no—
174C2×Q8—944no—
175C2×Q8—941no—
176C2×Q8C22×D4711yescharacteristic
177C22×C4—21no—
178C22×C4—471no—
179C22×C4—471no—
180C22×C4—941no—
181C22×C4C22×D4711yescharacteristic
182Q16—944no—
183Q16—944no—
184C2×C8—472no—
185C2×C8C22×D4712yes—
186C4⋊C4—21no—
187C4⋊C4—21no—
188C4⋊C4—471no—
189C4⋊C4—942no—
190C4⋊C4—942no—
191C4⋊C4—941no—
192C4⋊C4—941no—
193C4⋊C4—941no—
194C4⋊C4—941no—
195C4⋊C4—941no—
196C4⋊C4—941no—
197C4⋊C4C22×D4711yescharacteristic
198C4⋊C4C22×D4712yes—
199C22⋊C4—21no—
200C22⋊C4—941no—
201C42—471no—
202C42—471no—
203C42—471no—
204C42—471no—
205C42—942no—
206C42—942no—
207C42—941no—
208C42—941no—
209C23D4×D4711yescharacteristic
210Q8—22no—
211Q8—474no—
212Q8—944no—
213Q8—942no—
214Q8—942no—
215Q8—1882no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—21no—
219C2×C4—21no—
220C2×C4—42no—
221C2×C4—471no—
222C2×C4—471no—
223C2×C4—471no—
224C2×C4—471no—
225C2×C4—942no—
226C2×C4—944no—
227C2×C4—942no—
228C2×C4—942no—
229C2×C4—941no—
230C2×C4—941no—
231C2×C4D4×D4711yescharacteristic
232C2×C4C23×D4711yescharacteristic
233C8—22no—
234C8—942no—
235C22—21no—
236C22—21no—
237C22#1309405312yes—
238C22C2×D4×D4711yescharacteristic
239C4—21no—
240C4—41no—
241C4—41no—
242C4—42no—
243C4—472no—
244C4—944no—
245C4—941no—
246C4—941no—
247C4—941no—
248C4—1881no—
249C4—1881no—
250C4#41×D4712yes—
251C2—22no—
252C2#1568963111yescharacteristic
253C2#137×D4711yescharacteristic
254C2C2×#1309405311yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#483C2
socleC22×C47C22×D4
hypercenter#483D47
hypocenterC47#3113
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #483

Complements

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

NH ≅ G/Ntype
4. #15689407C2semidirect
5. #15689332C2semidirect
8. #15689229C2semidirect
9. #15689227C2semidirect
139. C47#3113semidirect