Finite Group Databasebeta

← #20248285

Subgroups — #20248285

Order 6016.

732 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 732 conjugacy classes of subgroups — too many to draw. Only its 169 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×#13093995C212yesmaximal, complemented
2C2×C4×D188C211yesmaximal, characteristic, complemented
3#15689048C212yesmaximal, complemented
4#15689032C212yesmaximal, complemented
5#15689002C214yesmaximal, complemented
6#15688989C211yesmaximal, characteristic, complemented
7#15688980C212yesmaximal, complemented
8C2×C4×D4×C47C211yesmaximal, characteristic, complemented
9C22×D188C2211yescharacteristic
10C22×C22⋊D47C2214yes—
11C22×C4×D47C2212yes—
12#13093995—28no—
13C4×D188—24no—
14C2×C4⋊Dic47C2212yes—
15C2×C4⋊Dic47C2211yescharacteristic
16C2×C22⋊Dic47C2214yes—
17C2×(C2×D47)⋊C4C2212yes—
18C2×(C2×D47)⋊C4C2214yes—
19C47⋊#95C2214yes—
20C47⋊#95C2212yes—
21C47⋊#95C2212yes—
22C22×D4×C47C2211yescharacteristic
23C23×C4×C47C2212yes—
24C4×D4×C47—24no—
25C2×C4⋊C4×C47C2211yescharacteristic
26C2×C22⋊C4×C47C2212yes—
27C2×C42×C47C2211yescharacteristic
28C24×C47C2312yes—
29C23×D47C2312yes—
30C2×D4×C47—22no—
31C2×D4×C47—22no—
32C2×D4×C47D414yescomplemented
33C22×C4×C47—24no—
34C22×C4×C47—44no—
35C22×C4×C47C2312yes—
36C22×C4×C47C2311yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C22×C4×C47C2311yescharacteristic
39C2×C22⋊D47—28no—
40C2×C22⋊D47—28no—
41C2×C22⋊D47—44no—
42C22×Dic47C2314yes—
43C22×Dic47C2312yes—
44C2×D188—24no—
45C2×D188—22no—
46C2×C4×D47—24no—
47C2×C4×D47—24no—
48C2×C4×D47—24no—
49C4⋊C4×C47—22no—
50C22⋊C4×C47—24no—
51C42×C47D414yescomplemented
52C22⋊Dic47—28no—
53(C2×D47)⋊C4—24no—
54(C2×D47)⋊C4—44no—
55C4⋊Dic47—22no—
56C4⋊Dic47—24no—
57C23×C47—22no—
58C23×C47—24no—
59C23×C47—22no—
60C23×C47—24no—
61C23×C47C2×D414yes—
62C23×C47C2411yescharacteristic
63C22×D47—22no—
64C22×D47—22no—
65C22×D47—22no—
66C22×D47—22no—
67C22×D47—22no—
68C22×D47—22no—
69C22×D47#4114yes—
70D4×C47—28no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47—22no—
74C2×C4×C47—24no—
75C2×C4×C47—48no—
76C2×C4×C47C2×D412yes—
77C2×C4×C47C2×D412yes—
78C2×C4×C47C2×D412yes—
79C2×C4×C47C2×D412yes—
80C2×C4×C47#4112yes—
81C22⋊D47—416no—
82C2×Dic47—22no—
83C2×Dic47—24no—
84C2×Dic47—22no—
85C2×Dic47—22no—
86C2×Dic47—24no—
87C2×Dic47—24no—
88D188—28no—
89C4×D47—48no—
90C22×C47—24no—
91C22×C47—28no—
92C22×C47—42no—
93C22×C47—42no—
94C22×C47—44no—
95C22×C47C22×D411yescharacteristic
96C22×C47C22×D411yescharacteristic
97C22×C47C2×#4112yes—
98C22×C47C2×#4111yescharacteristic
99C22×C47H(5,𝔽2)12yes—
100C2×D47—24no—
101C2×D47—24no—
102C2×D47—24no—
103C2×D47—42no—
104C2×D47—42no—
105C2×D47—42no—
106C2×D47—42no—
107C4×C47—22no—
108C4×C47—22no—
109C4×C47—42no—
110C4×C47#12114yes—
111Dic47—42no—
112Dic47—44no—
113#2535—471nomaximal, Sylow
114C2×C47—44no—
115C2×C47C2×#12111yescharacteristic
116C2×C47#52511yescharacteristic
117C2×C47#53511yescharacteristic
118C2×C47#54612yes—
119C2×C47#55312yes—
120D47—44no—
121C2×#121—472no—
122C2×C4×D4—471no—
123C2×C4×D4D4711yescharacteristic, complemented
124#397—472no—
125#392—472no—
126#386—474no—
127#382—471no—
128#380—472no—
129C47#253511yescharacteristic, complemented, Sylow
130C22×D4—474no—
131C22×D4—471no—
132C22×D4C2×D4711yescharacteristic
133C23×C4—472no—
134C23×C4C2×D4712yes—
135#121—948no—
136C4×D4—24no—
137C4×D4—944no—
138C2×C4⋊C4—471no—
139C2×C4⋊C4—472no—
140C2×C4⋊C4C2×D4711yescharacteristic
141C2×C22⋊C4—474no—
142C2×C22⋊C4—472no—
143C2×C22⋊C4—474no—
144C2×C22⋊C4C2×D4712yes—
145C2×C42C2×D4711yescharacteristic
146#95—474no—
147#95—472no—
148#95—472no—
149C24—472no—
150C24C22×D4712yes—
151C2×D4—22no—
152C2×D4—22no—
153C2×D4—944no—
154C2×D4—948no—
155C2×D4—948no—
156C2×D4—942no—
157C2×D4—1884no—
158C2×D4D18814yescomplemented
159C22×C4—24no—
160C22×C4—44no—
161C22×C4—474no—
162C22×C4—472no—
163C22×C4—944no—
164C22×C4—944no—
165C22×C4—944no—
166C22×C4C22×D4712yes—
167C22×C4C22×D4711yescharacteristic
168C22×C4C22×D4711yescharacteristic
169C22×C4C22×D4711yescharacteristic
170C4⋊C4—22no—
171C4⋊C4—944no—
172C4⋊C4—942no—
173C22⋊C4—24no—
174C22⋊C4—948no—
175C22⋊C4—944no—
176C22⋊C4—1884no—
177C42C22⋊D4714yescomplemented
178C23—22no—
179C23—24no—
180C23—22no—
181C23—24no—
182C23—474no—
183C23—942no—
184C23—942no—
185C23—942no—
186C23—942no—
187C23—942no—
188C23—942no—
189C23C2×D18814yes—
190C23C23×D4711yescharacteristic
191D4—28no—
192D4—948no—
193D4—18816no—
194C2×C4—22no—
195C2×C4—22no—
196C2×C4—22no—
197C2×C4—24no—
198C2×C4—48no—
199C2×C4—942no—
200C2×C4—942no—
201C2×C4—944no—
202C2×C4—944no—
203C2×C4—942no—
204C2×C4—944no—
205C2×C4—1888no—
206C2×C4C2×D18812yes—
207C2×C4#1062535012yes—
208C2×C4C2×C22⋊D4712yes—
209C2×C4C2×C22⋊D4712yes—
210C2×C4C2×C22⋊D4712yes—
211C22—28no—
212C22—24no—
213C22—44no—
214C22—42no—
215C22—42no—
216C22—944no—
217C22—944no—
218C22—944no—
219C22—1882no—
220C22—1882no—
221C22—1882no—
222C22—1882no—
223C22C22×C22⋊D4711yescharacteristic
224C22C22×D18811yescharacteristic
225C22#41×D4712yes—
226C22C2×#1062535011yescharacteristic
227C22#1309406912yes—
228C4—22no—
229C4—22no—
230C4—42no—
231C4—1884no—
232C4—1882no—
233C4#1309399814yes—
234C2—44no—
235C2—1884no—
236C2C2×#1309399811yescharacteristic
237C2#1568963011yescharacteristic
238C2#1568969011yescharacteristic
239C2#1568976812yes—
240C2#1568982312yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C4×D4×C47C2
hypercenterC2×C4×D4D47
hypocenterC47#2535
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#13093995C2semidirect
2. C2×C4×D188C2semidirect
3. #15689048C2semidirect
4. #15689032C2semidirect
5. #15689002C2semidirect
6. #15688989C2semidirect
7. #15688980C2semidirect
8. C2×C4×D4×C47C2semidirect
32. C2×D4×C47D4semidirect
51. C42×C47D4semidirect
123. C2×C4×D4D47semidirect
129. C47#2535semidirect
158. C2×D4D188semidirect
177. C42C22⋊D47semidirect