Finite Group Databasebeta

← #20248638

Subgroups — #20248638

Order 6016.

476 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 476 conjugacy classes of subgroups — too many to draw. Only its 125 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#15689040C211yesmaximal, characteristic
2#15689036C212yesmaximal, complemented
3#15689028C211yesmaximal, characteristic, complemented
4#15689013C212yesmaximal, complemented
5#15689001C212yesmaximal
6#15688990C212yesmaximal, complemented
7#15688985C212yesmaximal, complemented
8#15688970C212yesmaximal, complemented
9C47×#400C211yesmaximal, characteristic, complemented
10C22×Dic94C2211yescharacteristic
11C22×D188C2211yescharacteristic
12C22×C4×D47C2212yes—
13C2×(C2×D47)⋊C4C2212yes—
14C2×(C2×D47)⋊C4C2212yes—
15C2×(C2×D47)⋊C4C2212yes—
16C2×(C2×D47)⋊C4C2212yes—
17C2×(C2×D47)⋊C4C2212yes—
18C2×C4×Dic47C2212yes—
19C2×C4×Dic47C2211yescharacteristic
20C47⋊#95C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2211yescharacteristic
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C2×C4⋊C4×C47C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28#95×C47C2212yes—
29#95×C47C2211yescharacteristic
30#95×C47C2212yes—
31C23×D47C2312yes—
32C22×C4×C47C2311yescharacteristic
33C22×C4×C47C2311yescharacteristic
34C22×C4×C47C2312yes—
35C22×C4×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C22×Dic47C2312yes—
38C22×Dic47C2312yes—
39C22×Dic47C2312yes—
40C2×D188—24no—
41C2×D188—41no—
42C2×C4×D47—24no—
43C2×C4×D47—24no—
44C2×C4×D47—42no—
45C2×Dic94—22no—
46C2×Dic94—41no—
47C2×Dic94—41no—
48C4⋊C4×C47—41no—
49C4⋊C4×C47—41no—
50(C2×D47)⋊C4—24no—
51(C2×D47)⋊C4—24no—
52(C2×D47)⋊C4—24no—
53(C2×D47)⋊C4—42no—
54(C2×D47)⋊C4—42no—
55C4×Dic47—24no—
56C4×Dic47—41no—
57C23×C47C2411yescharacteristic
58C22×D47—22no—
59C22×D47—22no—
60C22×D47—22no—
61C22×D47—22no—
62C22×D47—22no—
63C22×D47—22no—
64C22×D47#4114yes—
65C2×C4×C47—21no—
66C2×C4×C47—21no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—22no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—22no—
75C2×C4×C47—21no—
76C2×C4×C47—21no—
77C2×C4×C47#4112yes—
78C2×Dic47—22no—
79C2×Dic47—22no—
80C2×Dic47—22no—
81C2×Dic47—22no—
82C2×Dic47—22no—
83C2×Dic47—22no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47#4114yes—
87D188—44no—
88C4×D47—48no—
89Dic94—44no—
90C22×C47C2×#4112yes—
91C22×C47C2×#4112yes—
92C22×C47C2×#4111yescharacteristic
93C22×C47H(5,𝔽2)11yescharacteristic
94C22×C47H(5,𝔽2)11yescharacteristic
95C2×D47—24no—
96C2×D47—24no—
97C2×D47—24no—
98C2×D47—42no—
99C2×D47—42no—
100C2×D47—42no—
101C2×D47—42no—
102C4×C47—22no—
103C4×C47—42no—
104C4×C47—41no—
105C4×C47—41no—
106C4×C47—42no—
107Dic47—24no—
108Dic47—42no—
109Dic47—42no—
110#2572—471nomaximal, Sylow
111C2×C47#52912yes—
112C2×C47#53811yescharacteristic
113C2×C47#55112yes—
114C2×C47#55111yescharacteristic
115C2×C47#55511yescharacteristic
116D47—44no—
117#400D4711yescharacteristic, complemented
118#394—471no—
119#393—472no—
120#391—471no—
121#388—472no—
122#386—472no—
123#383—472no—
124#381—472no—
125C4×C22⋊C4—472no—
126C47#257211yescharacteristic, complemented, Sylow
127C22×Q8—471no—
128C22×D4—471no—
129C23×C4—472no—
130C2×C4⋊C4C2×D4711yescharacteristic
131C2×C4⋊C4C2×D4711yescharacteristic
132C2×C22⋊C4—472no—
133C2×C22⋊C4—472no—
134C2×C22⋊C4—472no—
135C2×C22⋊C4—472no—
136C2×C22⋊C4—472no—
137C2×C42—472no—
138C2×C42—471no—
139#95—472no—
140#95—472no—
141#95—472no—
142#95—471no—
143#95—472no—
144#95—472no—
145#95C2×D4712yes—
146#95C2×D4711yescharacteristic
147#95C2×D4712yes—
148C24—472no—
149C2×Q8—942no—
150C2×Q8—1881no—
151C2×Q8—1881no—
152C2×D4—944no—
153C2×D4—1881no—
154C22×C4—472no—
155C22×C4—472no—
156C22×C4—472no—
157C22×C4—944no—
158C22×C4—944no—
159C22×C4—1882no—
160C22×C4C22×D4711yescharacteristic
161C22×C4C22×D4712yes—
162C22×C4C22×D4711yescharacteristic
163C22×C4C22×D4712yes—
164C22×C4C22×D4711yescharacteristic
165C4⋊C4—41no—
166C4⋊C4—41no—
167C22⋊C4—944no—
168C22⋊C4—944no—
169C22⋊C4—944no—
170C22⋊C4—1882no—
171C22⋊C4—1882no—
172C42—944no—
173C42—1881no—
174C23—474no—
175C23—942no—
176C23—942no—
177C23—942no—
178C23—942no—
179C23—942no—
180C23—942no—
181C23C23×D4711yescharacteristic
182Q8—1884no—
183D4—1884no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—21no—
194C2×C4—21no—
195C2×C4—22no—
196C2×C4—474no—
197C2×C4—942no—
198C2×C4—942no—
199C2×C4—942no—
200C2×C4—942no—
201C2×C4—942no—
202C2×C4—942no—
203C2×C4—942no—
204C2×C4—942no—
205C2×C4—1888no—
206C2×C4#1062535412yes—
207C22—944no—
208C22—944no—
209C22—944no—
210C22—1882no—
211C22—1882no—
212C22—1882no—
213C22—1882no—
214C22#41×D4712yes—
215C22#41×D4712yes—
216C22C2×#1062535411yescharacteristic
217C22#1309406911yescharacteristic
218C22#1309407011yescharacteristic
219C4—22no—
220C4—42no—
221C4—41no—
222C4—41no—
223C4—42no—
224C4—944no—
225C4—1882no—
226C4—1882no—
227C2—1884no—
228C2#1568965812yes—
229C2#1568971311yescharacteristic
230C2#1568979812yes—
231C2#1568980111yescharacteristic
232C2#1568983511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#400C2
hypercenter#400D47
hypocenterC47#2572
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #400

Complements

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

NH ≅ G/Ntype
2. #15689036C2semidirect
3. #15689028C2semidirect
4. #15689013C2semidirect
6. #15688990C2semidirect
7. #15688985C2semidirect
8. #15688970C2semidirect
9. C47×#400C2semidirect
117. #400D47semidirect
126. C47#2572semidirect