Finite Group Databasebeta

← #20243764

Subgroups — #20243764

Order 6016.

370 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 93 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×#13094049C211yesmaximal, characteristic
2C2×#13093951C211yesmaximal, characteristic, complemented
3#15689127C211yesmaximal, characteristic, complemented
4#15689024C211yesmaximal, characteristic, complemented
5#15688892C211yesmaximal, characteristic, complemented
6#15688882C211yesmaximal, characteristic, complemented
7C47×#520C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9#13094049—22no—
10#13094049C414yescomplemented
11C2×#10625336—21no—
12C2×#10625334—21no—
13C2×#10625329C2211yescharacteristic
14C2×#10625329C2211yescharacteristic
15C2×(C2×D47)⋊C4—22no—
16C2×C4×Dic47C2211yescharacteristic
17#13093951—22no—
18#13093944—21no—
19#13093944—21no—
20C2×#41×C47C2211yescharacteristic
21C4×Q8×C47—21no—
22C4×D4×C47—21no—
23C4×D4×C47—22no—
24#117×C47—21no—
25#117×C47C2211yescharacteristic
26C2×C4⋊C4×C47—21no—
27C2×C4⋊C4×C47C2211yescharacteristic
28C23×D47—21no—
29#41×C47—21no—
30#41×C47—21no—
31#41×C47C2×C412yes—
32#41×C47D412yes—
33C2×Q8×C47D411yescharacteristic
34C2×D4×C47—21no—
35C2×D4×C47D411yescharacteristic
36C22×C4×C47—21no—
37C22×C4×C47—22no—
38C22×C4×C47D412yes—
39C22×C4×C47C2311yescharacteristic
40C22×Dic47—21no—
41C2×D188—21no—
42C2×D188—21no—
43C2×D188—21no—
44C2×D188—21no—
45C2×D188—21no—
46C2×D188C2×C412yescomplemented
47C4⋊C4×C47—22no—
48C4⋊C4×C47—21no—
49C4⋊C4×C47—21no—
50C4⋊C4×C47D411yescharacteristic
51C4⋊C4×C47D411yescharacteristic
52C22⋊C4×C47—22no—
53C22⋊C4×C47—21no—
54C42×C47—22no—
55C42×C47—21no—
56#10625336—24no—
57#10625334—24no—
58(C2×D47)⋊C4—44no—
59C4×Dic47—21no—
60C4×Dic47—21no—
61#10625329—21no—
62#10625329—21no—
63#10625329—21no—
64#10625329C2×C412yescomplemented
65C2×C47⋊C8—21no—
66C2×C47⋊C8—21no—
67C23×C47—21no—
68C23×C47C2×D411yescharacteristic
69C22×D47—22no—
70C22×D47—42no—
71C22×D47—42no—
72C22×D47—41no—
73C22×D47—41no—
74Q8×C47—21no—
75Q8×C47C22⋊C412yescomplemented
76D4×C47—22no—
77D4×C47—22no—
78D4×C47—21no—
79D4×C47C22⋊C412yescomplemented
80C2×C4×C47—21no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—21no—
84C2×C4×C47—22no—
85C2×C4×C47—21no—
86C2×C4×C47—42no—
87C2×C4×C47—82no—
88C2×C4×C47C22×C411yescharacteristic
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47C2×D411yescharacteristic
92C2×C4×C47#4111yescharacteristic
93C2×C4×C47#4111yescharacteristic
94C2×Dic47—22no—
95C2×Dic47—41no—
96C2×Dic47—41no—
97D188—22no—
98D188—22no—
99D188—41no—
100D188—41no—
101C47⋊C8—22no—
102C47⋊C8—41no—
103C22×C47—21no—
104C22×C47—21no—
105C22×C47—22no—
106C22×C47—41no—
107C22×C47—41no—
108C22×C47C4×D411yescharacteristic
109C22×C47#12011yescharacteristic
110C22×C47#12111yescharacteristic
111C2×D47—44no—
112C2×D47—42no—
113C2×D47—82no—
114C2×D47—81no—
115C2×D47—81no—
116C4×C47—22no—
117C4×C47—42no—
118C4×C47—41no—
119C4×C47—41no—
120C4×C47C2×C22⋊C411yescharacteristic
121C4×C47C4×D411yescharacteristic
122C4×C47#12111yescharacteristic
123C4×C47#12311yescharacteristic
124Dic47—42no—
125#1883—471nomaximal, Sylow
126C2×C47—21no—
127C2×C47—21no—
128C2×C47—42no—
129C2×C47#38611yescharacteristic
130C2×C47#45311yescharacteristic
131C2×C47#45411yescharacteristic
132D47—82no—
133C2×AGL(1,ℤ/8)—471no—
134#520D4711yescharacteristic, complemented
135C2×#104—471no—
136#418—471no—
137#390—471no—
138#343—471no—
139#339—471no—
140C47#188311yescharacteristic, complemented, Sylow
141C2×#41C2×D4711yescharacteristic
142C22×D4—471no—
143AGL(1,ℤ/8)—474no—
144AGL(1,ℤ/8)—942no—
145C2×SD16—941no—
146C2×D8—941no—
147C2×M16—471no—
148C2×M16—471no—
149C4×Q8—21no—
150C4×D4—21no—
151C4×D4—22no—
152#117—21no—
153#117C2×D4711yescharacteristic
154C2×C4⋊C4—21no—
155C2×C4⋊C4C2×D4711yescharacteristic
156C2×C22⋊C4—942no—
157C2×C42—471no—
158#104—942no—
159#102—941no—
160#102—941no—
161C24—941no—
162#41—21no—
163#41—21no—
164#41C4×D4712yes—
165#41D18812yes—
166C2×Q8C22⋊D4711yescharacteristic
167C2×D4—21no—
168C2×D4—472no—
169C2×D4—941no—
170C2×D4—941no—
171C2×D4—941no—
172C2×D4—941no—
173C2×D4—941no—
174C2×D4C22⋊D4711yescharacteristic
175C22×C4—21no—
176C22×C4—22no—
177C22×C4—941no—
178C22×C4C22⋊D4712yes—
179C22×C4C22×D4711yescharacteristic
180SD16—944no—
181D8—944no—
182M16—472no—
183M16—941no—
184M16—941no—
185M16—941no—
186C2×C8—941no—
187C2×C8—941no—
188C4⋊C4—22no—
189C4⋊C4—21no—
190C4⋊C4—21no—
191C4⋊C4C22⋊D4711yescharacteristic
192C4⋊C4C22⋊D4711yescharacteristic
193C22⋊C4—22no—
194C22⋊C4—21no—
195C22⋊C4—1884no—
196C42—22no—
197C42—21no—
198C42—941no—
199C42—941no—
200C23—21no—
201C23—942no—
202C23—1882no—
203C23—1882no—
204C23—1881no—
205C23—1881no—
206C23C2×C22⋊D4711yescharacteristic
207Q8—21no—
208Q8(C2×D47)⋊C412yescomplemented
209D4—22no—
210D4—22no—
211D4—21no—
212D4—942no—
213D4—942no—
214D4—1881no—
215D4—1881no—
216D4(C2×D47)⋊C412yescomplemented
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—22no—
222C2×C4—21no—
223C2×C4—42no—
224C2×C4—82no—
225C2×C4—942no—
226C2×C4—1881no—
227C2×C4—1881no—
228C2×C4C2×C4×D4711yescharacteristic
229C2×C4C2×D18811yescharacteristic
230C2×C4#1062535011yescharacteristic
231C2×C4#1062535011yescharacteristic
232C2×C4C2×C22⋊D4711yescharacteristic
233C2×C4C2×C22⋊D4711yescharacteristic
234C8—942no—
235C8—1881no—
236C22—21no—
237C22—21no—
238C22—22no—
239C22—41no—
240C22—41no—
241C22—3762no—
242C22—3761no—
243C22—3761no—
244C22—1884no—
245C22—1882no—
246C22C4×C22⋊D4711yescharacteristic
247C22#1309399311yescharacteristic
248C22#1309399811yescharacteristic
249C4—22no—
250C4—42no—
251C4—41no—
252C4—41no—
253C4—1882no—
254C4C2×(C2×D47)⋊C411yescharacteristic
255C4C4×C22⋊D4711yescharacteristic
256C4#1309399811yescharacteristic
257C4#1309400711yescharacteristic
258C2—21no—
259C2—21no—
260C2—42no—
261C2—3762no—
262C2#1568900211yescharacteristic
263C2#1568929111yescharacteristic
264C2#1568929611yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#520C2
socleC22×C47#120
hypercenter#520D47
hypocenterC47#1883
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #520

Complements

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

NH ≅ G/Ntype
2. C2×#13093951C2semidirect
3. #15689127C2semidirect
4. #15689024C2semidirect
5. #15688892C2semidirect
6. #15688882C2semidirect
7. C47×#520C2semidirect
10. #13094049C4semidirect
46. C2×D188C2×C4semidirect
64. #10625329C2×C4semidirect
75. Q8×C47C22⋊C4semidirect
79. D4×C47C22⋊C4semidirect
134. #520D47semidirect
140. C47#1883semidirect
208. Q8(C2×D47)⋊C4semidirect
216. D4(C2×D47)⋊C4semidirect