Finite Group Databasebeta

← #20244438

Subgroups — #20244438

Order 6016.

380 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 380 conjugacy classes of subgroups — too many to draw. Only its 71 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, complemented
2#15689687C211yesmaximal, characteristic, complemented
3#15689140C211yesmaximal, characteristic, complemented
4#15689129C211yesmaximal, characteristic, complemented
5#15689097C211yesmaximal, characteristic, complemented
6#15688894C211yesmaximal, characteristic, complemented
7C47×#575C211yesmaximal, characteristic, complemented
8C22×D188C2211yescharacteristic
9#13094049—22no—
10#13094049—22no—
11C2×#10625336—21no—
12C2×#10625334—21no—
13C2×#10625329C2211yescharacteristic
14#13094020—21no—
15#13094013—21no—
16#13093998—22no—
17#13093992—22no—
18#13093983C2211yescharacteristic
19#13093983C2211yescharacteristic
20#13093951—22no—
21#13093946—22no—
22#13093939—22no—
23C2×#41×C47C2211yescharacteristic
24C2×#41×C47C2211yescharacteristic
25#137×C47—21no—
26#137×C47—21no—
27AGL(1,ℤ/8)×C47—21no—
28AGL(1,ℤ/8)×C47—21no—
29#135×C47—22no—
30C2×M16×C47C2211yescharacteristic
31C23×D47—21no—
32#41×C47—21no—
33#41×C47—21no—
34#41×C47—21no—
35#41×C47—21no—
36#41×C47—21no—
37#41×C47—21no—
38#41×C47—21no—
39#41×C47—21no—
40C2×Q8×C47D411yescharacteristic
41C2×Q8×C47D411yescharacteristic, complemented
42C2×D4×C47—21no—
43C2×D4×C47—21no—
44C2×D4×C47D411yescharacteristic
45C2×D4×C47D411yescharacteristic, complemented
46C22×C4×C47—21no—
47C22×C4×C47—21no—
48C22×C4×C47C2311yescharacteristic
49C2×C22⋊D47—24no—
50C2×D188—21no—
51C2×D188—21no—
52C2×D188—21no—
53C2×D188—21no—
54C2×D188—21no—
55C2×D188D412yes—
56Q16×C47—22no—
57SD16×C47—22no—
58SD16×C47—22no—
59D8×C47—22no—
60M16×C47—21no—
61M16×C47—21no—
62C2×C8×C47D412yescomplemented
63C22⋊Dic47—21no—
64C22⋊Dic47D412yes—
65#10625336—24no—
66#10625334—24no—
67(C2×D47)⋊C4—24no—
68C4⋊Dic47—21no—
69C4⋊Dic47—21no—
70C4×Dic47—21no—
71C4×Dic47—21no—
72#10625329—21no—
73#10625329D412yescomplemented
74C2×C47⋊C8—21no—
75C23×C47—21no—
76C23×C47—21no—
77C23×C47C2×D411yescharacteristic
78C22×D47—22no—
79C22×D47—41no—
80C22×D47—41no—
81C22×D47—82no—
82Q8×C47—21no—
83Q8×C47—21no—
84Q8×C47—21no—
85Q8×C47—21no—
86D4×C47—21no—
87D4×C47—21no—
88D4×C47—21no—
89D4×C47—21no—
90D4×C47—41no—
91D4×C47—41no—
92D4×C47—41no—
93D4×C47—41no—
94C2×C4×C47—21no—
95C2×C4×C47—21no—
96C2×C4×C47—41no—
97C2×C4×C47—41no—
98C2×C4×C47—41no—
99C2×C4×C47—41no—
100C2×C4×C47C2×D411yescharacteristic
101C2×C4×C47C2×D411yescharacteristic
102C2×C4×C47C2×D411yescharacteristic
103C2×C4×C47C2×D411yescharacteristic
104C2×C4×C47C2×D411yescharacteristic
105C2×C4×C47#4111yescharacteristic
106C22⋊D47—84no—
107C2×Dic47—22no—
108C2×Dic47—41no—
109D188—22no—
110D188—22no—
111D188—41no—
112D188—41no—
113C8×C47—22no—
114C47⋊C8—22no—
115C22×C47—41no—
116C22×C47—42no—
117C22×C47—41no—
118C22×C47—41no—
119C22×C47—81no—
120C22×C47#12011yescharacteristic
121C22×C47#12111yescharacteristic
122C22×C47#12711yescharacteristic
123C2×D47—44no—
124C2×D47—42no—
125C2×D47—82no—
126C2×D47—82no—
127C4×C47—41no—
128C4×C47—41no—
129C4×C47#12011yescharacteristic
130C4×C47#12011yescharacteristic
131C4×C47#12111yescharacteristic
132C4×C47#12111yescharacteristic
133Dic47—42no—
134Dic47—81no—
135#2008—471nomaximal, Sylow
136C2×C47—21no—
137C2×C47—21no—
138C2×C47—21no—
139C2×C47—81no—
140C2×C47—81no—
141C2×C47#39211yescharacteristic
142D47—82no—
143#575D4711yescharacteristic, complemented
144C2×AGL(1,ℤ/8)—471no—
145#535—471no—
146#421—471no—
147#418—471no—
148#410—471no—
149#344—471no—
150C47#200811yescharacteristic, complemented, Sylow
151C2×#41C2×D4711yescharacteristic
152C2×#41C2×D4711yescharacteristic
153C22×D4—471no—
154#137—21no—
155#137—21no—
156AGL(1,ℤ/8)—21no—
157AGL(1,ℤ/8)—21no—
158AGL(1,ℤ/8)—942no—
159AGL(1,ℤ/8)—942no—
160#135—22no—
161C2×SD16—941no—
162C2×D8—941no—
163C2×M16—471no—
164C2×M16C2×D4711yescharacteristic
165#127—941no—
166#124—941no—
167#121—942no—
168#120—942no—
169#117—471no—
170#117—471no—
171#104—942no—
172#102—942no—
173#99—942no—
174C24—941no—
175#41—21no—
176#41—21no—
177#41—21no—
178#41—21no—
179#41—21no—
180#41—21no—
181#41—21no—
182#41—21no—
183C2×Q8C22⋊D4711yescharacteristic
184C2×Q8C22⋊D4711yescharacteristic, complemented
185C2×D4—21no—
186C2×D4—21no—
187C2×D4—472no—
188C2×D4—944no—
189C2×D4—941no—
190C2×D4—941no—
191C2×D4—941no—
192C2×D4—941no—
193C2×D4—941no—
194C2×D4C22⋊D4711yescharacteristic
195C2×D4C22⋊D4711yescharacteristic, complemented
196C22×C4—21no—
197C22×C4—21no—
198C22×C4C22×D4711yescharacteristic
199Q16—22no—
200SD16—22no—
201SD16—22no—
202SD16—944no—
203D8—22no—
204D8—944no—
205M16—21no—
206M16—21no—
207M16—472no—
208M16—941no—
209C2×C8—941no—
210C2×C8C22⋊D4712yescomplemented
211C4⋊C4—941no—
212C4⋊C4—941no—
213C22⋊C4—472no—
214C22⋊C4—944no—
215C22⋊C4—941no—
216C42—941no—
217C42—941no—
218C23—21no—
219C23—21no—
220C23—942no—
221C23—3762no—
222C23—1881no—
223C23—1881no—
224C23D4×D4711yescharacteristic
225Q8—21no—
226Q8—21no—
227Q8—21no—
228Q8—21no—
229D4—21no—
230D4—21no—
231D4—21no—
232D4—21no—
233D4—41no—
234D4—41no—
235D4—41no—
236D4—41no—
237D4—942no—
238D4—942no—
239D4—3764no—
240D4—1881no—
241D4—1881no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—41no—
245C2×C4—41no—
246C2×C4—41no—
247C2×C4—41no—
248C2×C4—942no—
249C2×C4—1881no—
250C2×C4D4×D4711yescharacteristic
251C2×C4D4×D4711yescharacteristic
252C2×C4#1062535211yescharacteristic
253C2×C4C2×C22⋊D4711yescharacteristic
254C2×C4C2×C22⋊D4711yescharacteristic
255C2×C4C2×C22⋊D4711yescharacteristic
256C8—22no—
257C8—942no—
258C22—41no—
259C22—42no—
260C22—41no—
261C22—41no—
262C22—81no—
263C22—3762no—
264C22—3762no—
265C22—1884no—
266C22—1882no—
267C22#1309399211yescharacteristic
268C22#1309399611yescharacteristic
269C22#1309402011yescharacteristic
270C4—41no—
271C4—41no—
272C4—3761no—
273C4—1882no—
274C4#1309399211yescharacteristic
275C4#1309399311yescharacteristic
276C4#1309399511yescharacteristic
277C4#1309399611yescharacteristic
278C2—21no—
279C2—21no—
280C2—21no—
281C2—81no—
282C2—81no—
283C2—3762no—
284C2#1568903111yescharacteristic
subgroupG/H
centerC2#15689031
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#575C2
socleC2×C47#392
hypercenter#575D47
hypocenterC47#2008
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #575

Complements

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

NH ≅ G/Ntype
1. C2×#13094049C2semidirect
2. #15689687C2semidirect
3. #15689140C2semidirect
4. #15689129C2semidirect
5. #15689097C2semidirect
6. #15688894C2semidirect
7. C47×#575C2semidirect
41. C2×Q8×C47D4semidirect
45. C2×D4×C47D4semidirect
62. C2×C8×C47D4semidirect
73. #10625329D4semidirect
143. #575D47semidirect
150. C47#2008semidirect
184. C2×Q8C22⋊D47semidirect
195. C2×D4C22⋊D47semidirect
210. C2×C8C22⋊D47semidirect