Finite Group Databasebeta

← #20243762

Subgroups — #20243762

Order 6016.

370 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 370 conjugacy classes of subgroups — too many to draw. Only its 89 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
2#15689606C211yesmaximal, characteristic, complemented
3#15689129C211yesmaximal, characteristic, complemented
4#15689025C211yesmaximal, characteristic, complemented
5#15688891C211yesmaximal, characteristic, complemented
6#15688883C211yesmaximal, characteristic, complemented
7C2×#104×C47C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9#13094049—22no—
10#13094049C414yescomplemented
11C2×#10625336—21no—
12C2×#10625334—21no—
13C2×#10625329C2211yescharacteristic
14Q8×Dic47—21no—
15D4×Dic47—21no—
16D4×Dic47—22no—
17#13093983—21no—
18#13093983C2211yescharacteristic
19C2×C4⋊Dic47—21no—
20C2×C4⋊Dic47C2211yescharacteristic
21C2×(C2×D47)⋊C4—22no—
22#13093946—21no—
23#13093946—21no—
24C2×#41×C47C2211yescharacteristic
25C2×M16×C47C2211yescharacteristic
26C2×C42×C47C2211yescharacteristic
27#104×C47—22no—
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—21no—
38C22×C4×C47C2311yescharacteristic
39C22×Dic47—22no—
40C22×Dic47D412yes—
41C2×D188—21no—
42C2×D188—21no—
43C2×D188—21no—
44C2×D188—21no—
45C2×D188—21no—
46C2×D188C2×C412yescomplemented
47M16×C47—21no—
48M16×C47—21no—
49C2×C8×C47—21no—
50C42×C47—21no—
51C42×C47—21no—
52C22⋊Dic47—22no—
53C22⋊Dic47—21no—
54#10625336—24no—
55#10625334—24no—
56(C2×D47)⋊C4—44no—
57C4⋊Dic47—22no—
58C4⋊Dic47—21no—
59C4⋊Dic47—21no—
60C4⋊Dic47D411yescharacteristic
61C4⋊Dic47D411yescharacteristic
62C4×Dic47—22no—
63C4×Dic47—21no—
64#10625329—21no—
65#10625329C2×C412yescomplemented
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—22no—
84C2×C4×C47—41no—
85C2×C4×C47—41no—
86C2×C4×C47C22×C411yescharacteristic
87C2×C4×C47C2×D411yescharacteristic
88C2×C4×C47C2×D411yescharacteristic
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47#4111yescharacteristic
91C2×C4×C47#4111yescharacteristic
92C2×Dic47—21no—
93C2×Dic47—22no—
94C2×Dic47—21no—
95C2×Dic47—42no—
96C2×Dic47—82no—
97D188—22no—
98D188—22no—
99D188—41no—
100D188—41no—
101C8×C47—41no—
102C47⋊C8—22no—
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×C47C2×C22⋊C411yescharacteristic
119C4×C47C4×D411yescharacteristic
120C4×C47#12111yescharacteristic
121C4×C47#12311yescharacteristic
122Dic47—42no—
123Dic47—41no—
124Dic47—41no—
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#520—471no—
135C2×#104D4711yescharacteristic, complemented
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×M16C2×D4711yescharacteristic
149C4×Q8—941no—
150C4×D4—942no—
151C4×D4—941no—
152#117—471no—
153#117—941no—
154C2×C4⋊C4—471no—
155C2×C4⋊C4—941no—
156C2×C22⋊C4—942no—
157C2×C42C2×D4711yescharacteristic
158#104—22no—
159#102—941no—
160#102—941no—
161C24—941no—
162#41—21no—
163#41—21no—
164#41C4×D4712yes—
165#41C22⋊D4712yes—
166C2×Q8D18811yescharacteristic
167C2×D4—21no—
168C2×D4—472no—
169C2×D4—941no—
170C2×D4—941no—
171C2×D4—941no—
172C2×D4—941no—
173C2×D4—941no—
174C2×D4D18811yescharacteristic
175C22×C4—21no—
176C22×C4—21no—
177C22×C4—472no—
178C22×C4—942no—
179C22×C4C22×D4711yescharacteristic
180SD16—944no—
181D8—944no—
182M16—21no—
183M16—21no—
184M16—472no—
185M16—941no—
186C2×C8—21no—
187C2×C8—941no—
188C4⋊C4—471no—
189C4⋊C4—471no—
190C4⋊C4—942no—
191C4⋊C4—941no—
192C4⋊C4—941no—
193C22⋊C4—942no—
194C22⋊C4—941no—
195C22⋊C4—1884no—
196C42—21no—
197C42—21no—
198C42—942no—
199C42—941no—
200C23—21no—
201C23—942no—
202C23—1882no—
203C23—1882no—
204C23—1881no—
205C23—1881no—
206C23D4×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—22no—
221C2×C4—41no—
222C2×C4—41no—
223C2×C4—941no—
224C2×C4—941no—
225C2×C4—942no—
226C2×C4—3762no—
227C2×C4—1882no—
228C2×C4C2×C4×D4711yescharacteristic
229C2×C4C2×D18811yescharacteristic
230C2×C4D4×D4711yescharacteristic
231C2×C4#1062535211yescharacteristic
232C2×C4#1062535211yescharacteristic
233C2×C4C2×C22⋊D4711yescharacteristic
234C8—41no—
235C8—942no—
236C22—21no—
237C22—21no—
238C22—22no—
239C22—41no—
240C22—41no—
241C22—3762no—
242C22—3761no—
243C22—3761no—
244C22—1884no—
245C22—1882no—
246C22(C22⋊D47)⋊C411yescharacteristic
247C22#1309399411yescharacteristic
248C22#1309399611yescharacteristic
249C4—22no—
250C4—42no—
251C4—1881no—
252C4—1882no—
253C4—1881no—
254C4C2×(C2×D47)⋊C411yescharacteristic
255C4(C22⋊D47)⋊C411yescharacteristic
256C4#1309399611yescharacteristic
257C4#1309400811yescharacteristic
258C2—21no—
259C2—21no—
260C2—42no—
261C2—3762no—
262C2#1568900011yescharacteristic
263C2#1568929211yescharacteristic
264C2#1568929711yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#104×C47C2
socleC22×C47#120
hypercenterC2×#104D47
hypocenterC47#1883
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #15689606C2semidirect
3. #15689129C2semidirect
4. #15689025C2semidirect
5. #15688891C2semidirect
6. #15688883C2semidirect
7. C2×#104×C47C2semidirect
10. #13094049C4semidirect
46. C2×D188C2×C4semidirect
65. #10625329C2×C4semidirect
75. Q8×C47C22⋊C4semidirect
79. D4×C47C22⋊C4semidirect
135. C2×#104D47semidirect
140. C47#1883semidirect
208. Q8(C2×D47)⋊C4semidirect
216. D4(C2×D47)⋊C4semidirect