Finite Group Databasebeta

← #20244402

Subgroups — #20244402

Order 6016.

478 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 478 conjugacy classes of subgroups — too many to draw. Only its 73 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
3C2×#13094021C211yesmaximal, characteristic, complemented
4#15689129C211yesmaximal, characteristic, complemented
5C2×#13093940C211yesmaximal, characteristic, complemented
6#15688883C211yesmaximal, characteristic, complemented
7C2×#104×C47C211yesmaximal, characteristic, complemented
8C22×D188—22no—
9C22×D188C2211yescharacteristic
10C22×D188C2211yescharacteristic
11#13094049—22no—
12#13094049—22no—
13C2×#10625336—21no—
14C2×#10625334—21no—
15C2×#10625329C2211yescharacteristic
16#13094021—22no—
17#13094021—22no—
18#13094020—21no—
19#13094013—21no—
20#13093998—22no—
21#13093992—22no—
22#13093983C2211yescharacteristic
23#13093946—22no—
24#13093940—22no—
25C2×#41×C47C2211yescharacteristic
26C2×M16×C47C2211yescharacteristic
27C2×C42×C47C2211yescharacteristic
28#104×C47—22no—
29C23×D47—21no—
30C23×D47D412yes—
31#41×C47—21no—
32#41×C47—21no—
33#41×C47—21no—
34#41×C47—21no—
35C2×Q8×C47D411yescharacteristic, complemented
36C2×D4×C47—21no—
37C2×D4×C47D411yescharacteristic, complemented
38C22×C4×C47—21no—
39C22×C4×C47—21no—
40C22×C4×C47C2311yescharacteristic
41C2×C22⋊D47—24no—
42C2×D188—21no—
43C2×D188—21no—
44C2×D188—21no—
45C2×D188—21no—
46C2×D188—28no—
47C2×D188—21no—
48C2×D188—21no—
49C2×D188—21no—
50C2×D188—21no—
51C2×D188—21no—
52C2×D188—21no—
53C2×D188—21no—
54C2×D188—48no—
55C2×D188D412yescomplemented
56M16×C47—21no—
57M16×C47—21no—
58C2×C8×C47—21no—
59C42×C47—21no—
60C42×C47D412yescomplemented
61C22⋊Dic47—21no—
62#10625336—24no—
63#10625334—24no—
64(C2×D47)⋊C4—24no—
65C4⋊Dic47D412yescomplemented
66C4×Dic47—21no—
67#10625329—21no—
68#10625329D412yescomplemented
69C2×C47⋊C8—21no—
70C23×C47—21no—
71C23×C47C2×D411yescharacteristic
72C22×D47—22no—
73C22×D47—22no—
74C22×D47—22no—
75C22×D47—22no—
76C22×D47—44no—
77C22×D47—44no—
78C22×D47—41no—
79C22×D47—41no—
80Q8×C47—21no—
81Q8×C47—21no—
82D4×C47—21no—
83D4×C47—21no—
84D4×C47—41no—
85D4×C47—41no—
86C2×C4×C47—24no—
87C2×C4×C47—22no—
88C2×C4×C47—21no—
89C2×C4×C47—41no—
90C2×C4×C47—41no—
91C2×C4×C47C2×D411yescharacteristic
92C2×C4×C47C2×D411yescharacteristic
93C2×C4×C47C2×D411yescharacteristic
94C2×C4×C47C2×D411yescharacteristic
95C2×C4×C47C2×D411yescharacteristic
96C2×C4×C47#4111yescharacteristic
97C22⋊D47—84no—
98C2×Dic47—22no—
99D188—22no—
100D188—22no—
101D188—416no—
102D188—41no—
103D188—41no—
104D188—41no—
105D188—41no—
106D188—41no—
107D188—41no—
108C8×C47—41no—
109C47⋊C8—22no—
110C22×C47—22no—
111C22×C47—41no—
112C22×C47—42no—
113C22×C47#12011yescharacteristic
114C22×C47#12011yescharacteristic
115C22×C47#12111yescharacteristic
116C2×D47—44no—
117C2×D47—44no—
118C2×D47—42no—
119C2×D47—42no—
120C2×D47—44no—
121C2×D47—82no—
122C2×D47—82no—
123C2×D47—82no—
124C4×C47—24no—
125C4×C47—41no—
126C4×C47#12011yescharacteristic
127C4×C47#12111yescharacteristic
128C4×C47#12111yescharacteristic
129C4×C47#12711yescharacteristic
130Dic47—42no—
131#2002—471nomaximal, Sylow
132C2×C47—21no—
133C2×C47—21no—
134C2×C47—81no—
135C2×C47#39211yescharacteristic
136C2×C47#45312yes—
137D47—82no—
138D47—82no—
139C2×AGL(1,ℤ/8)—471no—
140#535—471no—
141C2×#127—471no—
142C2×#104D4711yescharacteristic, complemented
143#418—471no—
144C2×#100—471no—
145#339—471no—
146C47#200211yescharacteristic, complemented, Sylow
147C2×#41C2×D4711yescharacteristic
148C22×D4—471no—
149C22×D4—471no—
150C22×D4—942no—
151AGL(1,ℤ/8)—942no—
152AGL(1,ℤ/8)—942no—
153C2×SD16—941no—
154C2×D8—941no—
155C2×M16—471no—
156C2×M16C2×D4711yescharacteristic
157#127—942no—
158#127—941no—
159#127—942no—
160#124—941no—
161#121—942no—
162#120—942no—
163#117—471no—
164C2×C42C2×D4711yescharacteristic
165#104—22no—
166#102—942no—
167#100—942no—
168C24—472no—
169C24—941no—
170#41—21no—
171#41—21no—
172#41—21no—
173#41—21no—
174C2×Q8D18811yescharacteristic, complemented
175C2×D4—21no—
176C2×D4—472no—
177C2×D4—948no—
178C2×D4—944no—
179C2×D4—941no—
180C2×D4—941no—
181C2×D4—941no—
182C2×D4—941no—
183C2×D4—941no—
184C2×D4—941no—
185C2×D4—941no—
186C2×D4—941no—
187C2×D4—941no—
188C2×D4—941no—
189C2×D4—941no—
190C2×D4—1888no—
191C2×D4D18811yescharacteristic, complemented
192C22×C4—21no—
193C22×C4—21no—
194C22×C4C22×D4711yescharacteristic
195SD16—944no—
196D8—944no—
197M16—21no—
198M16—21no—
199M16—472no—
200M16—941no—
201C2×C8—21no—
202C2×C8—941no—
203C4⋊C4—472no—
204C22⋊C4—944no—
205C22⋊C4—941no—
206C42—21no—
207C42—941no—
208C42C22⋊D4712yescomplemented
209C23—21no—
210C23—942no—
211C23—942no—
212C23—942no—
213C23—942no—
214C23—1884no—
215C23—1884no—
216C23—1881no—
217C23—1881no—
218C23D4×D4711yescharacteristic
219Q8—21no—
220Q8—21no—
221D4—21no—
222D4—21no—
223D4—41no—
224D4—41no—
225D4—942no—
226D4—942no—
227D4—3764no—
228D4—18816no—
229D4—1881no—
230D4—1881no—
231D4—1881no—
232D4—1881no—
233D4—1881no—
234D4—1881no—
235C2×C4—24no—
236C2×C4—22no—
237C2×C4—21no—
238C2×C4—41no—
239C2×C4—41no—
240C2×C4—942no—
241C2×C4C2×D18811yescharacteristic
242C2×C4#1062535011yescharacteristic
243C2×C4D4×D4711yescharacteristic
244C2×C4D4×D4711yescharacteristic
245C2×C4D4×D4711yescharacteristic
246C2×C4C2×C22⋊D4711yescharacteristic
247C8—41no—
248C8—942no—
249C22—22no—
250C22—41no—
251C22—42no—
252C22—3762no—
253C22—3762no—
254C22—3762no—
255C22—1884no—
256C22—1884no—
257C22—1882no—
258C22—1882no—
259C22—1884no—
260C22#1309399211yescharacteristic
261C22#1309399411yescharacteristic
262C22#1309399711yescharacteristic
263C4—24no—
264C4—41no—
265C4—1882no—
266C4#1309399411yescharacteristic
267C4#1309399711yescharacteristic
268C4#1309399811yescharacteristic
269C4#1309402011yescharacteristic
270C2—21no—
271C2—21no—
272C2—81no—
273C2—3762no—
274C2—3762no—
275C2#1568903211yescharacteristic
276C2#1568929212yes—
subgroupG/H
centerC22#13093994
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC2×#104×C47C2
socleC22×C47#120
hypercenterC2×#104D47
hypocenterC47#2002
LCSG ▷ C22×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
1. C2×#13094049C2semidirect
2. #15689687C2semidirect
3. C2×#13094021C2semidirect
4. #15689129C2semidirect
5. C2×#13093940C2semidirect
6. #15688883C2semidirect
7. C2×#104×C47C2semidirect
35. C2×Q8×C47D4semidirect
37. C2×D4×C47D4semidirect
55. C2×D188D4semidirect
60. C42×C47D4semidirect
65. C4⋊Dic47D4semidirect
68. #10625329D4semidirect
142. C2×#104D47semidirect
146. C47#2002semidirect
174. C2×Q8D188semidirect
191. C2×D4D188semidirect
208. C42C22⋊D47semidirect