Finite Group Databasebeta

← #20247012

Subgroups — #20247012

Order 6016.

836 conjugacy classes of subgroups; only the 185 normal subgroups are shown.

normal subgroups only

This group has 836 conjugacy classes of subgroups — too many to draw. Only its 185 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×#13094022C211yesmaximal, characteristic, complemented
2C2×#13094011C211yesmaximal, characteristic, complemented
3C2×#13094003C211yesmaximal, characteristic, complemented
4#15689037C214yesmaximal, complemented
5#15689030C211yesmaximal, characteristic, complemented
6#15689026C211yesmaximal, characteristic, complemented
7#15688996C214yesmaximal, complemented
8C4×C22⋊Dic47C211yesmaximal, characteristic, complemented
9C22×#41×C47C211yesmaximal, characteristic
10C22×Dic94C2211yescharacteristic
11#13094022—24no—
12#13094011—24no—
13#13094003—24no—
14C2×C4⋊Dic47C2211yescharacteristic
15C2×Dic47⋊C4C2212yes—
16C2×Dic47⋊C4C2214yes—
17C2×C22⋊Dic47C2212yes—
18C2×C22⋊Dic47C2214yes—
19C2×C22⋊Dic47C2214yes—
20C2×C22⋊Dic47C2212yes—
21C2×C4×Dic47C2211yescharacteristic
22C2×C4×Dic47C2211yescharacteristic
23C47⋊#95C2212yes—
24C47⋊#95C2214yes—
25C2×#41×C47—24no—
26C2×#41×C47—24no—
27C2×#41×C47—24no—
28C22×Q8×C47C2211yescharacteristic
29C22×D4×C47C2212yes—
30C22×D4×C47C2211yescharacteristic
31C23×C4×C47C2212yes—
32C23×C4×C47C2211yescharacteristic
33C24×C47C2312yes—
34C24×C47C2311yescharacteristic
35#41×C47—232no—
36C2×Q8×C47—22no—
37C2×Q8×C47—22no—
38C2×Q8×C47D414yes—
39C2×D4×C47—24no—
40C2×D4×C47—24no—
41C2×D4×C47—24no—
42C2×D4×C47—22no—
43C2×D4×C47—22no—
44C2×D4×C47D414yes—
45C22×C4×C47—24no—
46C22×C4×C47—24no—
47C22×C4×C47—24no—
48C22×C4×C47—22no—
49C22×C4×C47—22no—
50C22×C4×C47D414yes—
51C22×C4×C47C2311yescharacteristic
52C22×C4×C47C2312yes—
53C22×C4×C47C2311yescharacteristic
54C22×Dic47C2312yes—
55C22×Dic47C2312yes—
56C22×Dic47C2312yes—
57C22×Dic47C2312yes—
58C2×Dic94—22no—
59C2×Dic94—22no—
60C2×Dic94—22no—
61C22⋊Dic47—24no—
62C22⋊Dic47—28no—
63C22⋊Dic47—24no—
64C22⋊Dic47—28no—
65C4⋊Dic47—22no—
66Dic47⋊C4—24no—
67Dic47⋊C4—28no—
68C4×Dic47—22no—
69C4×Dic47—22no—
70C23×C47—22no—
71C23×C47—21no—
72C23×C47—22no—
73C23×C47—21no—
74C23×C47—22no—
75C23×C47—24no—
76C23×C47—22no—
77C23×C47—24no—
78C23×C47C2×D414yes—
79C23×C47C2×D412yes—
80C23×C47C2411yescharacteristic
81Q8×C47—28no—
82D4×C47—216no—
83D4×C47—28no—
84C2×C4×C47—216no—
85C2×C4×C47—21no—
86C2×C4×C47—21no—
87C2×C4×C47—22no—
88C2×C4×C47—22no—
89C2×C4×C47—28no—
90C2×C4×C47C2×D412yes—
91C2×C4×C47C2×D414yes—
92C2×C4×C47C2×D412yes—
93C2×C4×C47C2×D412yes—
94C2×C4×C47C2×D412yes—
95C2×Dic47—22no—
96C2×Dic47—22no—
97C2×Dic47—22no—
98C2×Dic47—22no—
99C2×Dic47—22no—
100C2×Dic47—22no—
101C2×Dic47—22no—
102C2×Dic47—24no—
103C2×Dic47—22no—
104C2×Dic47—22no—
105C2×Dic47#4114yescomplemented
106Dic94—44no—
107C22×C47—24no—
108C22×C47—22no—
109C22×C47—22no—
110C22×C47—22no—
111C22×C47—28no—
112C22×C47—42no—
113C22×C47—42no—
114C22×C47—42no—
115C22×C47—42no—
116C22×C47—44no—
117C22×C47C22×D411yescharacteristic
118C22×C47C22×D411yescharacteristic
119C22×C47C22×D411yescharacteristic
120C22×C47C2×#4112yes—
121C22×C472−1+412yes—
122C4×C47—22no—
123C4×C47—24no—
124C4×C47#12014yes—
125Dic47—24no—
126Dic47—42no—
127Dic47—42no—
128Dic47—42no—
129#2432—471nomaximal, Sylow
130C2×C47—42no—
131C2×C47—44no—
132C2×C47C2×#12011yescharacteristic
133C2×C47#53211yescharacteristic
134C2×C47#53611yescharacteristic
135C2×C47#54712yes—
136C2×C47#54812yes—
137C22×#41D4711yescharacteristic
138C2×C4⋊Q8—471no—
139C2×#124—471no—
140C2×C22⋊Q8—471no—
141#394—474no—
142#391—471no—
143#390—471no—
144#385—474no—
145C4×C22⋊C4—471no—
146C47#243211yescharacteristic, complemented, Sylow
147C2×#41—24no—
148C2×#41—24no—
149C2×#41—24no—
150C22×Q8—471no—
151C22×Q8C2×D4711yescharacteristic
152C22×D4C2×D4712yes—
153C22×D4C2×D4711yescharacteristic
154C23×C4C2×D4712yes—
155C23×C4C2×D4711yescharacteristic
156C4⋊Q8—944no—
157#124—944no—
158C22⋊Q8—944no—
159C2×C4⋊C4—472no—
160C2×C4⋊C4—471no—
161C2×C4⋊C4—474no—
162C2×C22⋊C4—472no—
163C2×C22⋊C4—474no—
164C2×C22⋊C4—472no—
165C2×C22⋊C4—474no—
166C2×C42—471no—
167C2×C42—471no—
168#95—472no—
169#95—474no—
170C24C22×D4712yes—
171C24C22×D4711yescharacteristic
172#41—232no—
173C2×Q8—22no—
174C2×Q8—22no—
175C2×Q8—942no—
176C2×Q8—942no—
177C2×Q8—942no—
178C2×Q8C22⋊D4714yes—
179C2×D4—24no—
180C2×D4—24no—
181C2×D4—24no—
182C2×D4—22no—
183C2×D4—22no—
184C2×D4C22⋊D4714yes—
185C22×C4—24no—
186C22×C4—24no—
187C22×C4—24no—
188C22×C4—22no—
189C22×C4—22no—
190C22×C4—472no—
191C22×C4—472no—
192C22×C4—472no—
193C22×C4—472no—
194C22×C4C22⋊D4714yes—
195C22×C4C22×D4711yescharacteristic
196C22×C4C22×D4712yes—
197C22×C4C22×D4711yescharacteristic
198C4⋊C4—944no—
199C4⋊C4—948no—
200C4⋊C4—942no—
201C22⋊C4—944no—
202C22⋊C4—948no—
203C22⋊C4—944no—
204C22⋊C4—948no—
205C42—942no—
206C42—942no—
207C23—21no—
208C23—22no—
209C23—21no—
210C23—22no—
211C23—24no—
212C23—22no—
213C23—24no—
214C23—22no—
215C23C2×C22⋊D4714yes—
216C23C2×C22⋊D4712yes—
217C23C23×D4711yescharacteristic
218Q8—28no—
219Q8—1884no—
220D4—216no—
221D4—28no—
222C2×C4—216no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—22no—
227C2×C4—28no—
228C2×C4—474no—
229C2×C4—942no—
230C2×C4—942no—
231C2×C4—942no—
232C2×C4—942no—
233C2×C4—942no—
234C2×C4—942no—
235C2×C4—942no—
236C2×C4—942no—
237C2×C4—944no—
238C2×C4—942no—
239C2×C4C2×C22⋊D4712yes—
240C2×C4C2×C22⋊D4714yes—
241C2×C4C2×C22⋊D4712yes—
242C2×C4C2×C22⋊D4712yes—
243C2×C4C2×C22⋊D4712yes—
244C22—28no—
245C22—24no—
246C22—22no—
247C22—22no—
248C22—22no—
249C22—42no—
250C22—44no—
251C22—42no—
252C22—42no—
253C22—42no—
254C22C22×C22⋊D4711yescharacteristic
255C22C22×C22⋊D4711yescharacteristic
256C22C22×C22⋊D4711yescharacteristic
257C22#41×D4712yes—
258C22#1309407112yes—
259C4—22no—
260C4—24no—
261C4—944no—
262C4—1882no—
263C4—1882no—
264C4—1882no—
265C4#1309399314yes—
266C2—44no—
267C2—42no—
268C2C2×#1309399311yescharacteristic
269C2#1568966911yescharacteristic
270C2#1568969411yescharacteristic
271C2#1568977212yes—
272C2#1568978012yes—
subgroupG/H
center, FrattiniC23C23×D47
commutator, socleC23×C47C24
FittingC22×#41×C47C2
hypercenterC22×#41D47
hypocenterC47#2432
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C2×#13094022C2semidirect
2. C2×#13094011C2semidirect
3. C2×#13094003C2semidirect
4. #15689037C2semidirect
5. #15689030C2semidirect
6. #15689026C2semidirect
7. #15688996C2semidirect
8. C4×C22⋊Dic47C2semidirect
105. C2×Dic47#41semidirect
146. C47#2432semidirect