Finite Group Databasebeta

← #20253561

Subgroups — #20253561

Order 6016.

386 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689657C211yesmaximal, characteristic
2C2×C4×Dic94C211yesmaximal, characteristic, complemented
3#15689459C211yesmaximal, characteristic, complemented
4#15689442C211yesmaximal, characteristic
5#15689431C212yesmaximal, complemented
6#15689346C212yesmaximal, complemented
7#15689281C211yesmaximal, characteristic, complemented
8#15689264C211yesmaximal, characteristic
9#15689231C212yesmaximal, complemented
10#15689225C212yesmaximal, complemented
11C47×#432C211yesmaximal, characteristic, complemented
12C22×Dic94C2211yescharacteristic
13C2×Dic188C2212yes—
14C2×#10625325C2212yes—
15#13094018—21no—
16#13094016C2211yescharacteristic
17#13094012C2211yescharacteristic
18#13094007—21no—
19#13094003C2211yescharacteristic
20#13093998C2211yescharacteristic
21C4×Dic94—21no—
22C4×Dic94—21no—
23C4×Dic94C2212yes—
24C4×Dic94C2211yescharacteristic
25C4×Dic94C2212yes—
26C4×D188C2211yescharacteristic
27C4×C22⋊D47—21no—
28#13093981—21no—
29C2×C4⋊Dic47C2211yescharacteristic
30C2×Dic47⋊C4—21no—
31C2×C4×Dic47—21no—
32#13093958C2212yes—
33#13093956C2212yes—
34#13093949C2212yes—
35#13093949C2212yes—
36#13093949C2212yes—
37#13093946C2212yes—
38C2×C42×C47C2211yescharacteristic
39C4⋊C8×C47C2212yes—
40C22⋊C8×C47C2211yescharacteristic
41C22⋊C8×C47C2211yescharacteristic
42#97×C47C2212yes—
43C22×C4×C47D411yescharacteristic
44C22×C4×C47D411yescharacteristic
45C22×C4×C47C2311yescharacteristic
46C2×C22⋊D47—21no—
47C22×Dic47—21no—
48C22×Dic47—21no—
49C2×D188C2311yescharacteristic
50C2×C4×D47—21no—
51C2×Dic94—21no—
52C2×Dic94—24no—
53C2×Dic94C2311yescharacteristic
54C2×Dic94C2312yes—
55C2×C8×C47C2312yes—
56C2×C8×C47C2312yes—
57C42×C47D411yescharacteristic
58C42×C47D411yescharacteristic
59C42×C47C2311yescharacteristic
60C42×C47C2311yescharacteristic
61C22⋊Dic47—21no—
62(C2×D47)⋊C4—21no—
63(C2×D47)⋊C4—21no—
64(C2×D47)⋊C4—21no—
65(C2×D47)⋊C4—21no—
66C4⋊Dic47—21no—
67C4⋊Dic47C2312yes—
68C4⋊Dic47C2311yescharacteristic
69C4⋊Dic47C2311yescharacteristic
70Dic47⋊C4—22no—
71Dic47⋊C4—22no—
72Dic47⋊C4—21no—
73Dic47⋊C4—21no—
74Dic47⋊C4—21no—
75Dic47⋊C4—21no—
76C4×Dic47—22no—
77C4×Dic47—22no—
78C4×Dic47—21no—
79Dic188—24no—
80#10625325—24no—
81C23×C47C2×D411yescharacteristic
82C22×D47—21no—
83C2×C4×C47—22no—
84C2×C4×C47—22no—
85C2×C4×C47—41no—
86C2×C4×C47C2×D411yescharacteristic
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47C2×D411yescharacteristic
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47C2411yescharacteristic
92C22⋊D47—42no—
93C2×Dic47—24no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—21no—
97C2×Dic47—21no—
98C2×Dic47—21no—
99C2×Dic47—42no—
100D188—22no—
101C4×D47—42no—
102Dic94—24no—
103Dic94—22no—
104Dic94—22no—
105Dic94#4114yes—
106C8×C47—22no—
107C8×C47—22no—
108C22×C47—21no—
109C22×C47—21no—
110C22×C47#13712yes—
111C22×C47C22×D411yescharacteristic
112C2×D47—41no—
113C2×D47—41no—
114C2×D47—41no—
115C4×C47—21no—
116C4×C47—21no—
117C4×C47—21no—
118C4×C47—21no—
119C4×C47—21no—
120C4×C47C2×#4112yes—
121Dic47—24no—
122Dic47—41no—
123Dic47—41no—
124Dic47—41no—
125Dic47—42no—
126#3117—471nomaximal, Sylow
127C2×C47—22no—
128C2×C47#52511yescharacteristic
129C2×C47C2×#13711yescharacteristic
130C2×C47#57511yescharacteristic
131D47—81no—
132#529—471no—
133C2×C4×Q8—471no—
134#484—471no—
135#481—471no—
136#479—472no—
137#464—472no—
138#451—471no—
139#448—471no—
140#441—472no—
141#440—472no—
142#432D4711yescharacteristic, complemented
143C47#311711yescharacteristic, complemented, Sylow
144C22×Q8—471no—
145C2×Q16—472no—
146C2×SD16—472no—
147#126—941no—
148#125—471no—
149#124—471no—
150#123—941no—
151C22⋊Q8—471no—
152#121—471no—
153C4×Q8—472no—
154C4×Q8—472no—
155C4×Q8—471no—
156C4×Q8—941no—
157C4×Q8—941no—
158C4×D4—471no—
159C4×D4—941no—
160#117—941no—
161C2×C4⋊C4—471no—
162C2×C4⋊C4—941no—
163C2×C42—941no—
164C2×C42C2×D4711yescharacteristic
165#107—472no—
166#106—472no—
167C4⋊C8C2×D4712yes—
168#103—472no—
169#103—472no—
170#103—472no—
171#102—472no—
172C22⋊C8C2×D4711yescharacteristic
173C22⋊C8C2×D4711yescharacteristic
174#97C2×D4712yes—
175C2×Q8—472no—
176C2×Q8—471no—
177C2×Q8—944no—
178C2×Q8—941no—
179C2×D4—471no—
180C2×D4—941no—
181C22×C4—941no—
182C22×C4—941no—
183C22×C4—941no—
184C22×C4D18811yescharacteristic
185C22×C4D18811yescharacteristic
186C22×C4C22×D4711yescharacteristic
187Q16—944no—
188SD16—944no—
189C2×C8C22×D4712yes—
190C2×C8C22×D4712yes—
191C4⋊C4—472no—
192C4⋊C4—471no—
193C4⋊C4—471no—
194C4⋊C4—942no—
195C4⋊C4—942no—
196C4⋊C4—941no—
197C4⋊C4—941no—
198C4⋊C4—941no—
199C4⋊C4—941no—
200C4⋊C4—941no—
201C22⋊C4—941no—
202C22⋊C4—941no—
203C22⋊C4—941no—
204C22⋊C4—941no—
205C22⋊C4—941no—
206C42—942no—
207C42—942no—
208C42—941no—
209C42D18811yescharacteristic
210C42D18811yescharacteristic
211C42C22×D4711yescharacteristic
212C42C22×D4711yescharacteristic
213C23—941no—
214C23C2×D18811yescharacteristic
215Q8—474no—
216Q8—944no—
217Q8—942no—
218Q8—942no—
219D4—942no—
220D4—1882no—
221C2×C4—22no—
222C2×C4—22no—
223C2×C4—41no—
224C2×C4—944no—
225C2×C4—942no—
226C2×C4—942no—
227C2×C4—941no—
228C2×C4—941no—
229C2×C4—941no—
230C2×C4—1882no—
231C2×C4—1882no—
232C2×C4C2×D18811yescharacteristic
233C2×C4C2×D18811yescharacteristic
234C2×C4C2×D18811yescharacteristic
235C2×C4C2×D18811yescharacteristic
236C2×C4C2×D18811yescharacteristic
237C2×C4C23×D4711yescharacteristic
238C8—22no—
239C8—22no—
240C22—21no—
241C22—21no—
242C22—1881no—
243C22—1881no—
244C22—1881no—
245C22#1309405712yes—
246C22C22×D18811yescharacteristic
247C4—21no—
248C4—21no—
249C4—21no—
250C4—21no—
251C4—21no—
252C4—944no—
253C4—1881no—
254C4—1881no—
255C4—1882no—
256C4—1881no—
257C4#41×D4712yes—
258C2—22no—
259C2—3761no—
260C2#1568963511yescharacteristic
261C2C2×#1309405711yescharacteristic
262C2#1568992311yescharacteristic
subgroupG/H
centerC22C22×D188
commutatorC2×C4×C47C24
FrattiniC2×C4C23×D47
FittingC47×#432C2
socleC22×C47C22×D4
hypercenter#432D47
hypocenterC47#3117
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×C42 ◁ #432

Complements

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

NH ≅ G/Ntype
2. C2×C4×Dic94C2semidirect
3. #15689459C2semidirect
5. #15689431C2semidirect
6. #15689346C2semidirect
7. #15689281C2semidirect
9. #15689231C2semidirect
10. #15689225C2semidirect
11. C47×#432C2semidirect
142. #432D47semidirect
143. C47#3117semidirect