Finite Group Databasebeta

← #20253190

Subgroups — #20253190

Order 6016.

376 conjugacy classes of subgroups; only the 143 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 143 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#15689676C211yesmaximal, characteristic
2C2×Q8×Dic47C211yesmaximal, characteristic
3#15689432C212yesmaximal, complemented
4#15689428C212yesmaximal, complemented
5#15689416C212yesmaximal, complemented
6#15689406C212yesmaximal, complemented
7#15689166C211yesmaximal, characteristic
8#15689165C211yesmaximal, characteristic
9#15689146C211yesmaximal, characteristic
10#15689132C211yesmaximal, characteristic
11C47×#419C211yesmaximal, characteristic
12C2×#10625329C2211yescharacteristic
13#13094023C2211yescharacteristic
14#13094023C2211yescharacteristic
15#13094015C2211yescharacteristic
16#13094015C2211yescharacteristic
17#13094001—21no—
18#13094001—21no—
19Q8×Dic47—21no—
20Q8×Dic47—21no—
21Q8×Dic47C2212yes—
22Q8×Dic47C2212yes—
23C4×Dic94—21no—
24C4×Dic94—21no—
25#13093983C2211yescharacteristic
26C2×C4⋊Dic47—21no—
27C2×C4⋊Dic47C2211yescharacteristic
28C2×C4×Dic47—21no—
29C2×C4×Dic47C2211yescharacteristic
30#13093958C2212yes—
31#13093957C2212yes—
32#13093956C2212yes—
33#13093955C2212yes—
34Dic47⋊C8C2212yes—
35Dic47⋊C8C2212yes—
36#13093948C2212yes—
37#13093948C2212yes—
38C22×Q8×C47C2211yescharacteristic
39C2×M16×C47C2211yescharacteristic
40#117×C47C2211yescharacteristic
41#103×C47C2212yes—
42#103×C47C2212yes—
43C2×Q8×C47—21no—
44C2×Q8×C47—22no—
45C2×Q8×C47Q814yescomplemented
46C2×Q8×C47C2312yes—
47C22×C4×C47—21no—
48C22×C4×C47C2311yescharacteristic
49C22×Dic47—21no—
50C22×Dic47D411yescharacteristic
51C22×Dic47D411yescharacteristic
52C2×Dic94—21no—
53C2×Dic94—21no—
54M16×C47—22no—
55C2×C8×C47C2312yes—
56C4⋊C4×C47C2311yescharacteristic
57C4⋊C4×C47C2311yescharacteristic
58C22⋊C4×C47—21no—
59C42×C47—21no—
60C22⋊Dic47—21no—
61C4⋊Dic47—21no—
62C4⋊Dic47—22no—
63C4⋊Dic47—22no—
64C4⋊Dic47—21no—
65C4⋊Dic47—21no—
66C4⋊Dic47C2311yescharacteristic
67C4⋊Dic47C2311yescharacteristic
68C4⋊Dic47C2312yes—
69Dic47⋊C4—21no—
70Dic47⋊C4—21no—
71Dic47⋊C4—21no—
72Dic47⋊C4—21no—
73C4×Dic47—21no—
74C4×Dic47—22no—
75C4×Dic47—22no—
76C4×Dic47D411yescharacteristic
77C4×Dic47D411yescharacteristic
78C4×Dic47C2311yescharacteristic
79C4×Dic47C2311yescharacteristic
80#10625329—22no—
81C2×C47⋊C8C2312yes—
82C23×C47C2×D411yescharacteristic
83Q8×C47—24no—
84Q8×C47—22no—
85Q8×C47C2×Q814yes—
86C2×C4×C47—24no—
87C2×C4×C47—22no—
88C2×C4×C47—21no—
89C2×C4×C47—21no—
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47C2×Q812yes—
92C2×C4×C47#4112yes—
93C2×C4×C47C2411yescharacteristic
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—21no—
97C2×Dic47—21no—
98C2×Dic47—41no—
99C2×Dic47—42no—
100C2×Dic47C2×D411yescharacteristic
101C2×Dic47C2×D411yescharacteristic
102C2×Dic47C2×D411yescharacteristic
103C2×Dic47C2×D411yescharacteristic
104Dic94—42no—
105Dic94—42no—
106C8×C47—22no—
107C47⋊C8—22no—
108C22×C47—21no—
109C22×C47—21no—
110C22×C47C22⋊Q812yes—
111C22×C47C22×D411yescharacteristic
112C4×C47—24no—
113C4×C47—41no—
114C4×C47—41no—
115C4×C47C22⋊Q812yes—
116C4×C47C22×Q811yescharacteristic
117C4×C47C2×#4111yescharacteristic
118Dic47—21no—
119Dic47—21no—
120Dic47—21no—
121Dic47—41no—
122Dic47—41no—
123Dic47—42no—
124Dic47#13712yes—
125#3078—471nomaximal, Sylow
126C2×C47—22no—
127C2×C47C2×C22⋊Q811yescharacteristic
128C2×C47C2×#13711yescharacteristic
129C2×C47#57511yescharacteristic
130#533—471no—
131C2×C4×Q8—471no—
132#479—472no—
133#479—472no—
134#477—472no—
135#475—472no—
136#428—471no—
137#428—471no—
138#423—471no—
139#419—471no—
140#419D4711yescharacteristic
141C47#307811yescharacteristic, complemented, Sylow
142C22×Q8C2×D4711yescharacteristic
143C2×M16—471no—
144C2×M16C2×D4711yescharacteristic
145C4⋊Q8—471no—
146C4⋊Q8—471no—
147#125—471no—
148#125—471no—
149C22⋊Q8—941no—
150C22⋊Q8—941no—
151C4×Q8—472no—
152C4×Q8—472no—
153C4×Q8—941no—
154C4×Q8—941no—
155C4×Q8—941no—
156C4×Q8—941no—
157#117—471no—
158#117C2×D4711yescharacteristic
159C2×C4⋊C4—471no—
160C2×C4⋊C4—941no—
161C2×C42—471no—
162C2×C42—941no—
163#107—472no—
164#107—472no—
165#106—472no—
166#106—472no—
167C4⋊C8—472no—
168C4⋊C8—472no—
169#103—472no—
170#103—472no—
171#103C2×D4712yes—
172#103C2×D4712yes—
173C2×Q8—21no—
174C2×Q8—22no—
175C2×Q8—941no—
176C2×Q8—941no—
177C2×Q8Dic9414yescomplemented
178C2×Q8C22×D4712yes—
179C22×C4—21no—
180C22×C4—471no—
181C22×C4—471no—
182C22×C4—941no—
183C22×C4C22×D4711yescharacteristic
184M16—22no—
185M16—942no—
186C2×C8—472no—
187C2×C8C22×D4712yes—
188C4⋊C4—471no—
189C4⋊C4—471no—
190C4⋊C4—472no—
191C4⋊C4—941no—
192C4⋊C4—941no—
193C4⋊C4—941no—
194C4⋊C4—941no—
195C4⋊C4—942no—
196C4⋊C4—942no—
197C4⋊C4—941no—
198C4⋊C4—941no—
199C4⋊C4—941no—
200C4⋊C4C22×D4711yescharacteristic
201C4⋊C4C22×D4711yescharacteristic
202C22⋊C4—21no—
203C22⋊C4—941no—
204C42—21no—
205C42—471no—
206C42—471no—
207C42—471no—
208C42—471no—
209C42—942no—
210C42—942no—
211C42—941no—
212C23D4×D4711yescharacteristic
213Q8—24no—
214Q8—22no—
215Q8—1882no—
216Q8—1882no—
217Q8C2×Dic9414yes—
218C2×C4—24no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—471no—
223C2×C4—471no—
224C2×C4—471no—
225C2×C4—471no—
226C2×C4—942no—
227C2×C4—942no—
228C2×C4—941no—
229C2×C4—941no—
230C2×C4—1881no—
231C2×C4—1882no—
232C2×C4C2×Dic9412yes—
233C2×C4D4×D4711yescharacteristic
234C2×C4#1062535212yes—
235C2×C4C23×D4711yescharacteristic
236C8—22no—
237C8—942no—
238C22—21no—
239C22—21no—
240C22#1309400112yes—
241C22C2×D4×D4711yescharacteristic
242C4—24no—
243C4—41no—
244C4—41no—
245C4—472no—
246C4—941no—
247C4—941no—
248C4—941no—
249C4—1881no—
250C4—1882no—
251C4—1881no—
252C4#1309400112yes—
253C4C22×Dic9411yescharacteristic
254C4C2×#1062535211yescharacteristic
255C2—22no—
256C2C2×#1309400111yescharacteristic
257C2#137×D4711yescharacteristic
258C2#1568992211yescharacteristic
subgroupG/H
centerC22C2×D4×D47
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#419C2
socleC22×C47C22×D4
hypercenter#419D47
hypocenterC47#3078
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #419

Complements

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

NH ≅ G/Ntype
3. #15689432C2semidirect
4. #15689428C2semidirect
5. #15689416C2semidirect
6. #15689406C2semidirect
45. C2×Q8×C47Q8semidirect
141. C47#3078semidirect
177. C2×Q8Dic94semidirect