Finite Group Databasebeta

← #20242305

Subgroups — #20242305

Order 6016.

368 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 368 conjugacy classes of subgroups — too many to draw. Only its 53 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
1#15689685C211yesmaximal, characteristic, complemented
2#15689257C212yesmaximal, complemented
3#15688856C212yesmaximal, complemented
4#15688847C211yesmaximal, characteristic, complemented
5C47×#392C211yesmaximal, characteristic, complemented
6C22×C22⋊D47—21no—
7C2×#10625334—22no—
8#13094008—22no—
9#13093998—21no—
10#13093998C2212yes—
11#13093994—22no—
12#13093945—22no—
13C22⋊(C47⋊C8)C2212yescomplemented
14C22×D4×C47—21no—
15C22×D4×C47C2211yescharacteristic, complemented
16C2×C22⋊C4×C47—21no—
17C2×C22⋊C4×C47C2211yescharacteristic
18#95×C47C2211yescharacteristic, complemented
19C24×C47—21no—
20C24×C47D411yescharacteristic
21C23×D47—21no—
22C2×D4×C47—22no—
23C2×D4×C47—42no—
24C2×D4×C47—42no—
25C2×D4×C47—42no—
26C2×D4×C47—42no—
27C22×C4×C47—21no—
28C22×C4×C47D411yescharacteristic
29C22×C4×C47C2311yescharacteristic
30C2×C22⋊D47—22no—
31C2×C22⋊D47—22no—
32C2×C22⋊D47—42no—
33C2×C22⋊D47—42no—
34C22×Dic47—21no—
35C2×D188—21no—
36C2×D188D412yescomplemented
37C22⋊C4×C47—22no—
38C22⋊C4×C47—42no—
39#10625334—44no—
40(C2×D47)⋊C4—22no—
41(C2×D47)⋊C4—22no—
42C4⋊Dic47—21no—
43C4⋊Dic47D412yescomplemented
44C2×C47⋊C8—22no—
45C23×C47—21no—
46C23×C47—21no—
47C23×C47—22no—
48C23×C47—41no—
49C23×C47—41no—
50C23×C47—41no—
51C23×C47—41no—
52C23×C47—41no—
53C23×C47—41no—
54C23×C47—41no—
55C23×C47—41no—
56C23×C47D812yescomplemented
57C23×C47C2×D411yescharacteristic
58C22×D47—22no—
59C22×D47—42no—
60C22×D47—81no—
61C22×D47—81no—
62D4×C47—24no—
63D4×C47—42no—
64D4×C47—48no—
65C2×C4×C47—22no—
66C2×C4×C47—21no—
67C2×C4×C47—41no—
68C2×C4×C47—41no—
69C2×C4×C47—41no—
70C2×C4×C47—41no—
71C2×C4×C47C2×D412yes—
72C22⋊D47—44no—
73C22⋊D47—42no—
74C22⋊D47—42no—
75C2×Dic47—22no—
76C2×Dic47—42no—
77D188—42no—
78D188—81no—
79C47⋊C8—42no—
80C22×C47—21no—
81C22×C47—21no—
82C22×C47—22no—
83C22×C47—42no—
84C22×C47—42no—
85C22×C47—42no—
86C22×C47—41no—
87C22×C47—41no—
88C22×C47—42no—
89C22×C47—81no—
90C22×C47—81no—
91C22×C47—81no—
92C22×C47—81no—
93C22×C47—81no—
94C22×C47#12011yescharacteristic
95C22×C47C2×D811yescharacteristic
96C22×C47AGL(1,ℤ/8)11yescharacteristic
97C2×D47—42no—
98C2×D47—42no—
99C2×D47—42no—
100C2×D47—84no—
101C4×C47—22no—
102C4×C47—42no—
103C4×C47—41no—
104Dic47—42no—
105#1595—471nomaximal, Sylow
106C2×C47—21no—
107C2×C47—21no—
108C2×C47—42no—
109C2×C47—82no—
110C2×C47#44711yescharacteristic
111C2×C47#45311yescharacteristic
112C2×C47B(4,𝔽2)11yescharacteristic
113D47—82no—
114#534—471no—
115#447—472no—
116#392D4711yescharacteristic, complemented
117#327—472no—
118#323—471no—
119C47#159511yescharacteristic, complemented, Sylow
120C22×D4—21no—
121C22×D4—941no—
122C22×D4C2×D4711yescharacteristic, complemented
123C2×D8—942no—
124#123—942no—
125#121—472no—
126#121—941no—
127#120—942no—
128C2×C22⋊C4—21no—
129C2×C22⋊C4C2×D4711yescharacteristic
130#102—942no—
131C22⋊C8—472no—
132#95C2×D4711yescharacteristic, complemented
133C24—21no—
134C24—941no—
135C24C22⋊D4711yescharacteristic
136C2×D4—22no—
137C2×D4—42no—
138C2×D4—42no—
139C2×D4—42no—
140C2×D4—42no—
141C2×D4—472no—
142C2×D4—941no—
143C2×D4—942no—
144C2×D4—942no—
145C2×D4—1882no—
146C2×D4—1882no—
147C22×C4—21no—
148C22×C4—941no—
149C22×C4C22⋊D4711yescharacteristic
150C22×C4C22×D4711yescharacteristic
151D8—1884no—
152C2×C8—942no—
153C4⋊C4—472no—
154C4⋊C4—941no—
155C22⋊C4—22no—
156C22⋊C4—42no—
157C22⋊C4—942no—
158C22⋊C4—942no—
159C23—21no—
160C23—21no—
161C23—22no—
162C23—41no—
163C23—41no—
164C23—41no—
165C23—41no—
166C23—41no—
167C23—41no—
168C23—41no—
169C23—41no—
170C23—942no—
171C23—3761no—
172C23—3761no—
173C23—1882no—
174C23#1062533412yescomplemented
175C23C2×C22⋊D4711yescharacteristic
176D4—24no—
177D4—42no—
178D4—48no—
179D4—3761no—
180D4—1882no—
181D4—1884no—
182D4—1882no—
183D4—1882no—
184C2×C4—22no—
185C2×C4—21no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—41no—
190C2×C4—942no—
191C2×C4—1882no—
192C2×C4D4×D4712yes—
193C8—1882no—
194C22—21no—
195C22—21no—
196C22—22no—
197C22—42no—
198C22—42no—
199C22—42no—
200C22—41no—
201C22—41no—
202C22—42no—
203C22—81no—
204C22—81no—
205C22—81no—
206C22—81no—
207C22—81no—
208C22—3764no—
209C22—1882no—
210C22—1882no—
211C22—1882no—
212C22#1309399211yescharacteristic
213C22C2×#1062533411yescharacteristic
214C22#1309404911yescharacteristic
215C4—22no—
216C4—42no—
217C4—41no—
218C4—1882no—
219C2—21no—
220C2—21no—
221C2—42no—
222C2—82no—
223C2—3762no—
224C2#1568925611yescharacteristic
225C2#1568929011yescharacteristic
226C2#1568930911yescharacteristic
subgroupG/H
centerC22#13093992
commutatorC22×C4×C47C23
FrattiniC22×C4C22×D47
FittingC47×#392C2
socleC22×C47#120
hypercenter#392D47
hypocenterC47#1595
LCSG ▷ C22×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #392

Complements

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

NH ≅ G/Ntype
1. #15689685C2semidirect
2. #15689257C2semidirect
3. #15688856C2semidirect
4. #15688847C2semidirect
5. C47×#392C2semidirect
13. C22⋊(C47⋊C8)C22semidirect
15. C22×D4×C47C22semidirect
18. #95×C47C22semidirect
36. C2×D188D4semidirect
43. C4⋊Dic47D4semidirect
56. C23×C47D8semidirect
116. #392D47semidirect
119. C47#1595semidirect
122. C22×D4C2×D47semidirect
132. #95C2×D47semidirect
174. C23#10625334semidirect