Finite Group Databasebeta

← #20247017

Subgroups — #20247017

Order 6016.

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

normal subgroups only

This group has 836 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
1C22×#10625350C211yesmaximal, characteristic
2C2×#13094022C211yesmaximal, characteristic, complemented
3C2×#13094013C211yesmaximal, characteristic, complemented
4#15689038C214yesmaximal, complemented
5#15689028C211yesmaximal, characteristic, complemented
6#15689024C211yesmaximal, characteristic, complemented
7#15688994C214yesmaximal, complemented
8C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
9C2×C22⋊Q8×C47C211yesmaximal, characteristic, complemented
10C2×#10625350—24no—
11C2×#10625350—24no—
12C2×#10625350—24no—
13C22×Dic94C2211yescharacteristic
14C22×D188C2211yescharacteristic
15C22×C22⋊D47C2212yes—
16C22×C4×D47C2212yes—
17#13094022—24no—
18#13094013—24no—
19C2×Dic47⋊C4C2214yes—
20C2×C22⋊Dic47C2212yes—
21C2×(C2×D47)⋊C4C2214yes—
22C2×(C2×D47)⋊C4C2214yes—
23C2×C4×Dic47C2211yescharacteristic
24C2×C4×Dic47C2211yescharacteristic
25C47⋊#95C2212yes—
26C47⋊#95C2214yes—
27C22×Q8×C47C2211yescharacteristic
28C23×C4×C47C2211yescharacteristic
29C22⋊Q8×C47—24no—
30C2×C4⋊C4×C47C2212yes—
31C2×C4⋊C4×C47C2211yescharacteristic
32C2×C22⋊C4×C47C2212yes—
33C24×C47C2311yescharacteristic
34C23×D47C2312yes—
35C2×Q8×C47—22no—
36C2×Q8×C47—22no—
37C2×Q8×C47—22no—
38C22×C4×C47—22no—
39C22×C4×C47—22no—
40C22×C4×C47D414yes—
41C22×C4×C47C2312yes—
42C22×C4×C47C2312yes—
43C22×C4×C47C2311yescharacteristic
44C22×C4×C47C2311yescharacteristic
45C2×C22⋊D47—24no—
46C2×C22⋊D47—24no—
47C2×C22⋊D47—24no—
48C22×Dic47C2312yes—
49C22×Dic47C2312yes—
50C22×Dic47C2312yes—
51#10625350—232no—
52C2×D188—22no—
53C2×D188—22no—
54C2×D188D414yes—
55C2×C4×D47—24no—
56C2×C4×D47—24no—
57C2×C4×D47—24no—
58C2×Dic94—22no—
59C2×Dic94—22no—
60C2×Dic94D414yes—
61C4⋊C4×C47—22no—
62C4⋊C4×C47—24no—
63C22⋊C4×C47—24no—
64C22⋊Dic47—24no—
65(C2×D47)⋊C4—28no—
66(C2×D47)⋊C4—28no—
67Dic47⋊C4—28no—
68C4×Dic47—22no—
69C4×Dic47—22no—
70C23×C47—21no—
71C23×C47—21no—
72C23×C47—22no—
73C23×C47—22no—
74C23×C47C2×D412yes—
75C23×C47C2411yescharacteristic
76C22×D47—22no—
77C22×D47—22no—
78C22×D47—24no—
79C22×D47—24no—
80C22×D47C2×D414yes—
81Q8×C47—44no—
82C2×C4×C47—21no—
83C2×C4×C47—21no—
84C2×C4×C47—28no—
85C2×C4×C47—22no—
86C2×C4×C47—22no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—24no—
90C2×C4×C47C2×D412yes—
91C2×C4×C47C2×D412yes—
92C2×C4×C47C2×D412yes—
93C2×C4×C47C2×D412yes—
94C22⋊D47—216no—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47—22no—
102C2×Dic47C2×D414yes—
103C2×Dic47#4114yescomplemented
104D188—28no—
105C4×D47—216no—
106Dic94—28no—
107C22×C47—22no—
108C22×C47—22no—
109C22×C47—22no—
110C22×C47—42no—
111C22×C47—42no—
112C22×C47C22×D411yescharacteristic
113C22×C47C22×D411yescharacteristic
114C22×C47C22×D411yescharacteristic
115C22×C47C2×#4112yes—
116C22×C472−1+412yes—
117C2×D47—24no—
118C2×D47—28no—
119C2×D47—42no—
120C2×D47—42no—
121C2×D47—44no—
122C4×C47—22no—
123C4×C47—42no—
124C4×C47—42no—
125C4×C47#12014yes—
126Dic47—24no—
127Dic47—24no—
128Dic47—42no—
129#2432—471nomaximal, Sylow
130C2×C47—42no—
131C2×C47C2×#12011yescharacteristic
132C2×C47#53211yescharacteristic
133C2×C47#53611yescharacteristic
134C2×C47#54712yes—
135C2×C47#54812yes—
136D47—44no—
137C22×#41—471no—
138C2×C4⋊Q8—471no—
139C2×#124—471no—
140C2×C22⋊Q8D4711yescharacteristic, complemented
141#394—474no—
142#391—471no—
143#390—471no—
144#385—474no—
145C4×C22⋊C4—471no—
146C47#243211yescharacteristic, complemented, Sylow
147C2×#41—944no—
148C2×#41—944no—
149C2×#41—944no—
150C22×Q8—471no—
151C22×Q8C2×D4711yescharacteristic
152C22×D4—472no—
153C22×D4—471no—
154C23×C4—472no—
155C23×C4C2×D4711yescharacteristic
156C4⋊Q8—944no—
157#124—944no—
158C22⋊Q8—24no—
159C2×C4⋊C4—474no—
160C2×C4⋊C4C2×D4712yes—
161C2×C4⋊C4C2×D4711yescharacteristic
162C2×C22⋊C4—472no—
163C2×C22⋊C4—474no—
164C2×C22⋊C4—474no—
165C2×C22⋊C4C2×D4712yes—
166C2×C42—471no—
167C2×C42—471no—
168#95—472no—
169#95—474no—
170C24—472no—
171C24C22×D4711yescharacteristic
172#41—9432no—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—22no—
176C2×Q8—474no—
177C2×Q8—942no—
178C2×Q8—942no—
179C2×D4—474no—
180C2×D4—944no—
181C2×D4—944no—
182C2×D4—944no—
183C2×D4—942no—
184C2×D4—942no—
185C22×C4—22no—
186C22×C4—22no—
187C22×C4—472no—
188C22×C4—472no—
189C22×C4—472no—
190C22×C4—944no—
191C22×C4—944no—
192C22×C4—944no—
193C22×C4C22⋊D4714yes—
194C22×C4C22×D4712yes—
195C22×C4C22×D4712yes—
196C22×C4C22×D4711yescharacteristic
197C22×C4C22×D4711yescharacteristic
198C4⋊C4—22no—
199C4⋊C4—24no—
200C4⋊C4—948no—
201C22⋊C4—24no—
202C22⋊C4—948no—
203C22⋊C4—948no—
204C22⋊C4—944no—
205C42—942no—
206C42—942no—
207C23—21no—
208C23—21no—
209C23—22no—
210C23—22no—
211C23—474no—
212C23—942no—
213C23—942no—
214C23—944no—
215C23—944no—
216C23C2×C22⋊D4712yes—
217C23C23×D4711yescharacteristic
218Q8—44no—
219Q8—948no—
220D4—9416no—
221D4—948no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—28no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—24no—
230C2×C4—474no—
231C2×C4—474no—
232C2×C4—9416no—
233C2×C4—942no—
234C2×C4—942no—
235C2×C4—942no—
236C2×C4—942no—
237C2×C4—942no—
238C2×C4—942no—
239C2×C4—942no—
240C2×C4D4×D4712yes—
241C2×C4D4×D4712yes—
242C2×C4C2×C22⋊D4712yes—
243C2×C4C2×C22⋊D4712yes—
244C22—22no—
245C22—22no—
246C22—22no—
247C22—42no—
248C22—42no—
249C22—948no—
250C22—944no—
251C22—1884no—
252C22—1882no—
253C22—1882no—
254C22C2×D4×D4711yescharacteristic
255C22C2×D4×D4711yescharacteristic
256C22C22×C22⋊D4711yescharacteristic
257C22#41×D4712yes—
258C22#1309407212yes—
259C4—22no—
260C4—42no—
261C4—42no—
262C4—944no—
263C4—944no—
264C4—1882no—
265C4#1309399214yes—
266C2—42no—
267C2—1884no—
268C2C2×#1309399211yescharacteristic
269C2#1568966911yescharacteristic
270C2#1568969711yescharacteristic
271C2#1568977512yes—
272C2#1568978312yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC2×C22⋊Q8×C47C2
hypercenterC2×C22⋊Q8D47
hypocenterC47#2432
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. C2×#13094022C2semidirect
3. C2×#13094013C2semidirect
4. #15689038C2semidirect
5. #15689028C2semidirect
6. #15689024C2semidirect
7. #15688994C2semidirect
8. C4×C22⋊Dic47C2semidirect
9. C2×C22⋊Q8×C47C2semidirect
103. C2×Dic47#41semidirect
140. C2×C22⋊Q8D47semidirect
146. C47#2432semidirect