Finite Group Databasebeta

← #20250157

Subgroups — #20250157

Order 6016.

556 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 556 conjugacy classes of subgroups — too many to draw. Only its 129 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×#13094010C212yesmaximal, complemented
2#15689041C212yesmaximal, complemented
3#15689036C212yesmaximal, complemented
4#15689032C211yesmaximal, characteristic
5#15689027C212yesmaximal, complemented
6#15689013C212yesmaximal, complemented
7#15689000C212yesmaximal, complemented
8#15688995C211yesmaximal, characteristic, complemented
9C47×#397C211yesmaximal, characteristic, complemented
10C22×Dic94C2212yes—
11C22×D188C2211yescharacteristic
12C22×C22⋊D47C2212yes—
13C23×Dic47C2211yescharacteristic
14#13094010—28no—
15C2×Dic47⋊C4C2212yes—
16C2×C22⋊Dic47C2211yescharacteristic
17C2×(C2×D47)⋊C4C2212yes—
18C2×(C2×D47)⋊C4C2212yes—
19C2×(C2×D47)⋊C4C2212yes—
20C2×(C2×D47)⋊C4C2212yes—
21C2×(C2×D47)⋊C4C2212yes—
22C2×C4×Dic47C2212yes—
23C47⋊#95C2212yes—
24C47⋊#95C2212yes—
25C47⋊#95C2212yes—
26C47⋊#95C2211yescharacteristic
27C2×C4⋊C4×C47C2211yescharacteristic
28C2×C22⋊C4×C47C2212yes—
29C2×C22⋊C4×C47C2211yescharacteristic
30#95×C47C2212yes—
31#95×C47C2211yescharacteristic
32C24×C47C2311yescharacteristic
33C23×D47C2312yes—
34C22×C4×C47C2311yescharacteristic
35C22×C4×C47C2312yes—
36C22×C4×C47C2312yes—
37C22×C4×C47C2311yescharacteristic
38C2×C22⋊D47—24no—
39C2×C22⋊D47—24no—
40C2×C22⋊D47—42no—
41C22×Dic47—42no—
42C22×Dic47—41no—
43C22×Dic47C2312yes—
44C22×Dic47C2312yes—
45C22×Dic47C2312yes—
46C2×D188—42no—
47C2×D188—41no—
48C2×Dic94—24no—
49C2×Dic94—24no—
50C2×Dic94—42no—
51C4⋊C4×C47—41no—
52C22⋊C4×C47—24no—
53C22⋊C4×C47—41no—
54C22⋊Dic47D414yescomplemented
55(C2×D47)⋊C4—24no—
56(C2×D47)⋊C4—24no—
57(C2×D47)⋊C4—24no—
58(C2×D47)⋊C4—42no—
59(C2×D47)⋊C4—42no—
60Dic47⋊C4—42no—
61C4×Dic47—24no—
62C23×C47—22no—
63C23×C47—21no—
64C23×C47—22no—
65C23×C47—21no—
66C23×C47C2×D412yes—
67C23×C47C2411yescharacteristic
68C22×D47—22no—
69C22×D47—22no—
70C22×D47—22no—
71C22×D47—22no—
72C22×D47—22no—
73C22×D47—22no—
74C22×D47—22no—
75C2×C4×C47—22no—
76C2×C4×C47—22no—
77C2×C4×C47—22no—
78C2×C4×C47—22no—
79C2×C4×C47—22no—
80C2×C4×C47—22no—
81C2×C4×C47—22no—
82C2×C4×C47—21no—
83C2×C4×C47—21no—
84C2×C4×C47—22no—
85C22⋊D47—48no—
86C2×Dic47—22no—
87C2×Dic47—22no—
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—44no—
94C2×Dic47C2×D414yes—
95C2×Dic47#4114yes—
96D188—44no—
97Dic94—48no—
98C22×C47—22no—
99C22×C47—24no—
100C22×C47—42no—
101C22×C47—41no—
102C22×C47—41no—
103C22×C47C22×D411yescharacteristic
104C22×C47C2×#4112yes—
105C22×C47H(5,𝔽2)11yescharacteristic
106C22×C47H(5,𝔽2)12yes—
107C22×C472−1+411yescharacteristic
108C2×D47—42no—
109C2×D47—42no—
110C2×D47—42no—
111C2×D47—42no—
112C2×D47—42no—
113C2×D47—42no—
114C2×D47—42no—
115C4×C47—42no—
116C4×C47—42no—
117C4×C47—41no—
118C4×C47—41no—
119Dic47—24no—
120Dic47—24no—
121Dic47—42no—
122#2712—471nomaximal, Sylow
123C2×C47—42no—
124C2×C47#53711yescharacteristic
125C2×C47#54212yes—
126C2×C47#54612yes—
127C2×C47#55911yescharacteristic
128C2×C47H(3,𝔽4)11yescharacteristic
129D47—82no—
130C2×#124—472no—
131#397D4711yescharacteristic, complemented
132#394—472no—
133#393—472no—
134#392—471no—
135#391—472no—
136#388—472no—
137#386—472no—
138#385—471no—
139C47#271211yescharacteristic, complemented, Sylow
140C22×Q8—472no—
141C22×D4—472no—
142C22×D4—471no—
143C23×C4—471no—
144#124—948no—
145C2×C4⋊C4—472no—
146C2×C4⋊C4C2×D4711yescharacteristic
147C2×C22⋊C4—471no—
148C2×C22⋊C4—472no—
149C2×C22⋊C4—472no—
150C2×C22⋊C4—472no—
151C2×C22⋊C4—472no—
152C2×C22⋊C4—472no—
153C2×C22⋊C4C2×D4712yes—
154C2×C22⋊C4C2×D4711yescharacteristic
155C2×C42—472no—
156#95—472no—
157#95—472no—
158#95—472no—
159#95—471no—
160#95C2×D4712yes—
161#95C2×D4711yescharacteristic
162C24—472no—
163C24C22×D4711yescharacteristic
164C2×Q8—944no—
165C2×Q8—944no—
166C2×Q8—1882no—
167C2×D4—944no—
168C2×D4—944no—
169C2×D4—1881no—
170C2×D4—1882no—
171C2×D4—1882no—
172C22×C4—472no—
173C22×C4—472no—
174C22×C4—472no—
175C22×C4—1881no—
176C22×C4—1882no—
177C22×C4C22×D4711yescharacteristic
178C22×C4C22×D4712yes—
179C22×C4C22×D4711yescharacteristic
180C22×C4C22×D4712yes—
181C4⋊C4—41no—
182C4⋊C4—1882no—
183C22⋊C4—24no—
184C22⋊C4—41no—
185C22⋊C4—474no—
186C22⋊C4—944no—
187C22⋊C4—944no—
188C22⋊C4—944no—
189C22⋊C4—1882no—
190C22⋊C4—1882no—
191C42—944no—
192C23—22no—
193C23—21no—
194C23—22no—
195C23—21no—
196C23—942no—
197C23—942no—
198C23—942no—
199C23—942no—
200C23—942no—
201C23—942no—
202C23—942no—
203C23D4×D4712yes—
204C23C23×D4711yescharacteristic
205Q8—1888no—
206D4—1884no—
207D4—1888no—
208C2×C4—22no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—22no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—22no—
215C2×C4—22no—
216C2×C4—22no—
217C2×C4—22no—
218C2×C4—474no—
219C2×C4—474no—
220C2×C4—942no—
221C2×C4—942no—
222C2×C4—942no—
223C2×C4—942no—
224C2×C4—942no—
225C2×C4—942no—
226C2×C4—942no—
227C2×C4—1884no—
228C22—24no—
229C22—22no—
230C22—42no—
231C22—41no—
232C22—41no—
233C22—1882no—
234C22—1882no—
235C22—1882no—
236C22—1882no—
237C22—1882no—
238C22—1882no—
239C22—1882no—
240C22C2×D4×D4711yescharacteristic
241C22#41×D4712yes—
242C22#1309406911yescharacteristic
243C22#1309407012yes—
244C22#1309407111yescharacteristic
245C4—42no—
246C4—41no—
247C4—41no—
248C4—42no—
249C4—944no—
250C4—944no—
251C4—1882no—
252C2—42no—
253C2—3762no—
254C2#1568970011yescharacteristic
255C2#1568973912yes—
256C2#1568976512yes—
257C2#1568985711yescharacteristic
258C2#1568986511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC47×#397C2
hypercenter#397D47
hypocenterC47#2712
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ #397

Complements

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

NH ≅ G/Ntype
1. C2×#13094010C2semidirect
2. #15689041C2semidirect
3. #15689036C2semidirect
5. #15689027C2semidirect
6. #15689013C2semidirect
7. #15689000C2semidirect
8. #15688995C2semidirect
9. C47×#397C2semidirect
54. C22⋊Dic47D4semidirect
131. #397D47semidirect
139. C47#2712semidirect