Finite Group Databasebeta

← #20248965

Subgroups — #20248965

Order 6016.

492 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 492 conjugacy classes of subgroups — too many to draw. Only its 145 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×C4×Dic94C211yesmaximal, characteristic, complemented
2#15689053C211yesmaximal, characteristic, complemented
3#15689048C211yesmaximal, characteristic
4#15689043C211yesmaximal, characteristic, complemented
5#15689035C211yesmaximal, characteristic
6#15689011C212yesmaximal
7#15689007C212yesmaximal, complemented
8#15689004C212yesmaximal, complemented
9#15688996C212yesmaximal
10#15688991C211yesmaximal, characteristic, complemented
11C2×#117×C47C211yesmaximal, characteristic
12C22×Dic94C2211yescharacteristic
13C4×Dic94—24no—
14C2×C4⋊Dic47C2211yescharacteristic
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2212yes—
17C2×Dic47⋊C4C2212yes—
18C2×C22⋊Dic47C2212yes—
19C2×C22⋊Dic47C2212yes—
20C2×C4×Dic47C2212yes—
21C47⋊#95C2212yes—
22C47⋊#95C2212yes—
23C47⋊#95C2211yescharacteristic
24C47⋊#95C2211yescharacteristic
25C47⋊#95C2212yes—
26C47⋊#95C2212yes—
27C47⋊#95C2212yes—
28C47⋊#95C2212yes—
29C23×C4×C47C2211yescharacteristic
30#117×C47—24no—
31C2×C4⋊C4×C47C2211yescharacteristic
32C2×C4⋊C4×C47C2211yescharacteristic
33C2×C22⋊C4×C47C2211yescharacteristic
34C2×C22⋊C4×C47C2211yescharacteristic
35C2×C42×C47C2211yescharacteristic
36C2×C42×C47C2211yescharacteristic
37C24×C47C2311yescharacteristic
38C22×C4×C47—22no—
39C22×C4×C47—22no—
40C22×C4×C47—22no—
41C22×C4×C47C2311yescharacteristic
42C22×C4×C47C2311yescharacteristic
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2311yescharacteristic
45C22×C4×C47C2311yescharacteristic
46C22×C4×C47C2311yescharacteristic
47C22×Dic47C2312yes—
48C22×Dic47C2312yes—
49C22×Dic47C2312yes—
50C22×Dic47C2312yes—
51C2×Dic94—22no—
52C2×Dic94—24no—
53C4⋊C4×C47—22no—
54C4⋊C4×C47—22no—
55C22⋊C4×C47—22no—
56C22⋊C4×C47—22no—
57C42×C47—22no—
58C42×C47D414yes—
59C22⋊Dic47—24no—
60C22⋊Dic47—24no—
61C4⋊Dic47—22no—
62Dic47⋊C4—24no—
63Dic47⋊C4—24no—
64Dic47⋊C4—24no—
65C4×Dic47—24no—
66C23×C47—21no—
67C23×C47—22no—
68C23×C47—21no—
69C23×C47—22no—
70C23×C47#4112yes—
71C23×C47C2411yescharacteristic
72C2×C4×C47—28no—
73C2×C4×C47—21no—
74C2×C4×C47—22no—
75C2×C4×C47—21no—
76C2×C4×C47—21no—
77C2×C4×C47—21no—
78C2×C4×C47—22no—
79C2×C4×C47—21no—
80C2×C4×C47—21no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47C2×D412yes—
84C2×C4×C47C2×D412yes—
85C2×C4×C47C2×D412yes—
86C2×C4×C47#4112yes—
87C2×Dic47—22no—
88C2×Dic47—22no—
89C2×Dic47—22no—
90C2×Dic47—22no—
91C2×Dic47—22no—
92C2×Dic47—22no—
93C2×Dic47—22no—
94C2×Dic47—22no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47#4114yes—
99Dic94—28no—
100C22×C47—22no—
101C22×C47—24no—
102C22×C47—41no—
103C22×C47—41no—
104C22×C47—42no—
105C22×C47C22×D411yescharacteristic
106C22×C47C2×#4112yes—
107C22×C47C2×#4111yescharacteristic
108C22×C47C2×#4111yescharacteristic
109C22×C472−1+412yes—
110C4×C47—22no—
111C4×C47—22no—
112C4×C47—22no—
113C4×C47—22no—
114C4×C47—41no—
115C4×C47—41no—
116Dic47—24no—
117Dic47—42no—
118Dic47—42no—
119Dic47—42no—
120#2599—471nomaximal, Sylow
121C2×C47—42no—
122C2×C47#52511yescharacteristic
123C2×C47#52511yescharacteristic
124C2×C47#53611yescharacteristic
125C2×C47#55212yes—
126C2×C47#55612yes—
127C2×C4×Q8—471no—
128C2×#117D4711yescharacteristic
129#398—471no—
130#397—471no—
131#395—471no—
132#393—471no—
133#388—472no—
134#387—472no—
135#387—472no—
136#385—472no—
137#383—471no—
138C47#259911yescharacteristic, complemented, Sylow
139C22×Q8—471no—
140C23×C4C2×D4711yescharacteristic
141C4×Q8—944no—
142#117—24no—
143C2×C4⋊C4—472no—
144C2×C4⋊C4—471no—
145C2×C4⋊C4—472no—
146C2×C4⋊C4—472no—
147C2×C4⋊C4C2×D4711yescharacteristic
148C2×C4⋊C4C2×D4711yescharacteristic
149C2×C22⋊C4—472no—
150C2×C22⋊C4—472no—
151C2×C22⋊C4C2×D4711yescharacteristic
152C2×C22⋊C4C2×D4711yescharacteristic
153C2×C42—472no—
154C2×C42C2×D4711yescharacteristic
155C2×C42C2×D4711yescharacteristic
156#95—472no—
157#95—472no—
158#95—471no—
159#95—471no—
160#95—472no—
161#95—472no—
162#95—472no—
163#95—472no—
164C24C22×D4711yescharacteristic
165C2×Q8—944no—
166C2×Q8—942no—
167C22×C4—22no—
168C22×C4—22no—
169C22×C4—22no—
170C22×C4—472no—
171C22×C4—472no—
172C22×C4—472no—
173C22×C4—472no—
174C22×C4C22×D4711yescharacteristic
175C22×C4C22×D4711yescharacteristic
176C22×C4C22×D4711yescharacteristic
177C22×C4C22×D4711yescharacteristic
178C22×C4C22×D4711yescharacteristic
179C22×C4C22×D4711yescharacteristic
180C4⋊C4—22no—
181C4⋊C4—22no—
182C4⋊C4—944no—
183C4⋊C4—944no—
184C4⋊C4—944no—
185C4⋊C4—942no—
186C22⋊C4—22no—
187C22⋊C4—22no—
188C22⋊C4—944no—
189C22⋊C4—944no—
190C42—22no—
191C42—944no—
192C42C22⋊D4714yes—
193C23—21no—
194C23—22no—
195C23—21no—
196C23—22no—
197C23#1062535012yes—
198C23C23×D4711yescharacteristic
199Q8—948no—
200C2×C4—28no—
201C2×C4—21no—
202C2×C4—22no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—21no—
206C2×C4—22no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—22no—
210C2×C4—22no—
211C2×C4—474no—
212C2×C4—942no—
213C2×C4—942no—
214C2×C4—942no—
215C2×C4—942no—
216C2×C4—942no—
217C2×C4—942no—
218C2×C4—942no—
219C2×C4—942no—
220C2×C4—942no—
221C2×C4—942no—
222C2×C4—942no—
223C2×C4#1062535012yes—
224C2×C4C2×C22⋊D4712yes—
225C2×C4C2×C22⋊D4712yes—
226C2×C4C2×C22⋊D4712yes—
227C22—24no—
228C22—22no—
229C22—42no—
230C22—41no—
231C22—41no—
232C22C22×C22⋊D4711yescharacteristic
233C22#41×D4712yes—
234C22C2×#1062535011yescharacteristic
235C22C2×#1062535011yescharacteristic
236C22#1309407112yes—
237C4—22no—
238C4—22no—
239C4—22no—
240C4—22no—
241C4—41no—
242C4—41no—
243C4—944no—
244C4—1882no—
245C4—1882no—
246C4—1882no—
247C2—42no—
248C2#1568963011yescharacteristic
249C2#1568963411yescharacteristic
250C2#1568969411yescharacteristic
251C2#1568980612yes—
252C2#1568984112yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×#117×C47C2
hypercenterC2×#117D47
hypocenterC47#2599
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×#117

Complements

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

NH ≅ G/Ntype
1. C2×C4×Dic94C2semidirect
2. #15689053C2semidirect
4. #15689043C2semidirect
7. #15689007C2semidirect
8. #15689004C2semidirect
10. #15688991C2semidirect
138. C47#2599semidirect