Finite Group Databasebeta

← #20244500

Subgroups — #20244500

Order 6016.

362 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 75 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×#13094055C211yesmaximal, characteristic, complemented
2C2×#13094050C211yesmaximal, characteristic
3C2×#13093943C211yesmaximal, characteristic, complemented
4C2×#13093941C211yesmaximal, characteristic, complemented
5#15689089C211yesmaximal, characteristic, complemented
6#15688888C211yesmaximal, characteristic, complemented
7C22×SD16×C47C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094055—22no—
10#13094055—22no—
11#13094050—22no—
12#13094050—22no—
13C2×#10625337—21no—
14C2×#10625335—21no—
15C2×#10625336—21no—
16C2×#10625334—21no—
17C2×#10625329C2211yescharacteristic
18C2×#10625329C2211yescharacteristic
19C2×#10625329C2211yescharacteristic
20#13093943—22no—
21#13093941—22no—
22(C2×D47)⋊C8—22no—
23C22×Q8×C47C2211yescharacteristic
24C22×D4×C47C2211yescharacteristic
25C2×SD16×C47—22no—
26C2×SD16×C47—22no—
27C2×SD16×C47—22no—
28C22×C8×C47C2211yescharacteristic
29C24×C47—21no—
30C2×Q8×C47—21no—
31C2×Q8×C47—21no—
32C2×Q8×C47—21no—
33C2×Q8×C47—21no—
34C2×Q8×C47—21no—
35C2×Q8×C47D412yes—
36C2×D4×C47—21no—
37C2×D4×C47—21no—
38C2×D4×C47—21no—
39C2×D4×C47—21no—
40C2×D4×C47—21no—
41C2×D4×C47D412yes—
42C22×C4×C47—21no—
43C22×C4×C47C2311yescharacteristic
44C2×C22⋊D47—21no—
45#10625350—21no—
46#10625350—21no—
47#10625350—21no—
48#10625350—21no—
49C2×D188D411yescharacteristic
50C2×C4×D47—21no—
51C2×Dic94D411yescharacteristic
52SD16×C47—28no—
53C2×C8×C47—21no—
54C2×C8×C47—21no—
55C2×C8×C47D412yes—
56#10625337—24no—
57#10625336—24no—
58#10625335—24no—
59#10625334—24no—
60#10625329—21no—
61#10625329—21no—
62#10625329—21no—
63#10625329—21no—
64#10625329D412yes—
65#10625329D412yes—
66C2×C47⋊C8—21no—
67C2×C47⋊C8—21no—
68C2×C47⋊C8—21no—
69C23×C47—22no—
70C23×C47—41no—
71C23×C47—41no—
72C23×C47—82no—
73C23×C47#4111yescharacteristic
74C22×D47—21no—
75Q8×C47—22no—
76Q8×C47—22no—
77Q8×C47—41no—
78Q8×C47—41no—
79D4×C47—22no—
80D4×C47—22no—
81D4×C47—41no—
82D4×C47—41no—
83C2×C4×C47—22no—
84C2×C4×C47—41no—
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×C47C2×D411yescharacteristic
92C22⋊D47—41no—
93C22⋊D47—41no—
94C2×Dic47—21no—
95D188—21no—
96D188—21no—
97C4×D47—41no—
98C4×D47—41no—
99Dic94—21no—
100Dic94—21no—
101C8×C47—22no—
102C47⋊C8—22no—
103C47⋊C8—22no—
104C47⋊C8—41no—
105C22×C47—22no—
106C22×C47—42no—
107C22×C47—82no—
108C22×C47—82no—
109C22×C47—82no—
110C22×C47#12111yescharacteristic
111C22×C47#12111yescharacteristic
112C22×C47#12111yescharacteristic
113C2×D47—41no—
114C2×D47—42no—
115C4×C47—42no—
116C4×C47#12011yescharacteristic
117C4×C47#12011yescharacteristic
118C4×C47#12011yescharacteristic
119C4×C47#12711yescharacteristic
120Dic47—41no—
121#2019—471nomaximal, Sylow
122C2×C47—21no—
123C2×C47—21no—
124C2×C47—82no—
125C2×C47#39211yescharacteristic
126C2×C47#47112yes—
127D47—81no—
128C2×#137—471no—
129C2×AGL(1,ℤ/8)—471no—
130C22×SD16D4711yescharacteristic, complemented
131C2×#101—471no—
132C2×#100—471no—
133#408—471no—
134#341—471no—
135C47#201911yescharacteristic, complemented, Sylow
136C2×#41—471no—
137C22×Q8C2×D4711yescharacteristic
138C22×D4C2×D4711yescharacteristic
139#137—942no—
140#137—942no—
141AGL(1,ℤ/8)—942no—
142AGL(1,ℤ/8)—942no—
143C2×Q16—941no—
144C2×SD16—22no—
145C2×SD16—22no—
146C2×SD16—22no—
147C2×SD16—941no—
148C2×SD16—941no—
149C2×D8—941no—
150C2×M16—471no—
151C2×M16—471no—
152C2×M16—471no—
153C22×C8C2×D4711yescharacteristic
154#101—942no—
155#100—942no—
156C22⋊C8—942no—
157C24—21no—
158#41—941no—
159#41—941no—
160#41—941no—
161#41—941no—
162C2×Q8—21no—
163C2×Q8—21no—
164C2×Q8—21no—
165C2×Q8—21no—
166C2×Q8—21no—
167C2×Q8—471no—
168C2×Q8C22⋊D4712yes—
169C2×D4—21no—
170C2×D4—21no—
171C2×D4—21no—
172C2×D4—21no—
173C2×D4—21no—
174C2×D4—471no—
175C2×D4—941no—
176C2×D4C22⋊D4712yes—
177C22×C4—21no—
178C22×C4—941no—
179C22×C4C22×D4711yescharacteristic
180Q16—944no—
181SD16—28no—
182SD16—944no—
183SD16—944no—
184D8—944no—
185M16—472no—
186M16—472no—
187M16—941no—
188M16—941no—
189M16—941no—
190M16—941no—
191C2×C8—21no—
192C2×C8—21no—
193C2×C8—941no—
194C2×C8—941no—
195C2×C8—941no—
196C2×C8C22⋊D4712yes—
197C23—22no—
198C23—41no—
199C23—41no—
200C23—82no—
201C23—941no—
202C23#1062535211yescharacteristic
203Q8—22no—
204Q8—22no—
205Q8—41no—
206Q8—41no—
207Q8—941no—
208Q8—941no—
209D4—22no—
210D4—22no—
211D4—41no—
212D4—41no—
213D4—941no—
214D4—941no—
215D4—1881no—
216D4—1881no—
217C2×C4—22no—
218C2×C4—41no—
219C2×C4—41no—
220C2×C4—941no—
221C2×C4—1881no—
222C2×C4—1881no—
223C2×C4D4×D4711yescharacteristic
224C2×C4D4×D4711yescharacteristic
225C2×C4D4×D4711yescharacteristic
226C2×C4C2×C22⋊D4711yescharacteristic
227C2×C4C2×C22⋊D4711yescharacteristic
228C2×C4C2×C22⋊D4711yescharacteristic
229C8—22no—
230C8—942no—
231C8—942no—
232C8—1881no—
233C22—22no—
234C22—42no—
235C22—82no—
236C22—82no—
237C22—82no—
238C22—1881no—
239C22—1882no—
240C22#1309399511yescharacteristic
241C22#1309399611yescharacteristic
242C22#1309399611yescharacteristic
243C4—42no—
244C4—1881no—
245C4#1309399211yescharacteristic
246C4#1309399211yescharacteristic
247C4#1309399311yescharacteristic
248C4#1309402011yescharacteristic
249C2—21no—
250C2—21no—
251C2—82no—
252C2—3761no—
253C2#1568903111yescharacteristic
254C2#1568938312yes—
subgroupG/H
centerC22#13093995
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC22×SD16×C47C2
socleC22×C47#121
hypercenterC22×SD16D47
hypocenterC47#2019
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#13094055C2semidirect
3. C2×#13093943C2semidirect
4. C2×#13093941C2semidirect
5. #15689089C2semidirect
6. #15688888C2semidirect
7. C22×SD16×C47C2semidirect
130. C22×SD16D47semidirect
135. C47#2019semidirect