Finite Group Databasebeta

← #20252793

Subgroups — #20252793

Order 6016.

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

normal subgroups only

This group has 716 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
1#15689959C211yesmaximal, characteristic
2#15689697C212yesmaximal, complemented
3#15689312C218yesmaximal, complemented
4#15689097C211yesmaximal, characteristic, complemented
5#15689096C212yesmaximal, complemented
6C47×#536C211yesmaximal, characteristic, complemented
7#13094072—21no—
8#13094071—22no—
9#13094070—22no—
10#13094069—21no—
11#13094069C2214yes—
12C2×#10625350—22no—
13C2×#10625350C2212yes—
14#41×D47—24no—
15#13094022—22no—
16#13094013—22no—
17#13094007C2218yescomplemented
18#13094000—24no—
19#13093983C2212yescomplemented
20#13093939C2214yescomplemented
21#13093938C2218yescomplemented
22C2×#41×C47C2211yescharacteristic
23C22×Q8×C47C2211yescharacteristic, complemented
24C4⋊Q8×C47—21no—
25#124×C47—21no—
26#123×C47C2214yescomplemented
27C22⋊Q8×C47—22no—
28#117×C47C2211yescharacteristic, complemented
29#41×C47—22no—
30#41×C47—22no—
31C2×Q8×C47—21no—
32C2×Q8×C47—21no—
33C2×Q8×C47—22no—
34C2×Q8×C47—22no—
35C2×Q8×C47D411yescharacteristic
36C2×D4×C47D411yescharacteristic
37C2×D4×C47C2312yes—
38C22×C4×C47D412yes—
39C22×C4×C47C2312yes—
40C22×C4×C47C2311yescharacteristic
41C2×C22⋊D47—24no—
42C2×C22⋊D47C2314yes—
43#10625354—24no—
44Q8×D47—24no—
45#10625352—24no—
46#10625352—28no—
47D4×D47—24no—
48D4×D47—28no—
49#10625350—24no—
50#10625350—24no—
51#10625350—22no—
52#10625350—22no—
53#10625350—24no—
54#10625350—22no—
55#10625350—22no—
56C2×D188—22no—
57C2×D188D412yes—
58C2×C4×D47—24no—
59C2×C4×D47D414yes—
60C2×Dic94—22no—
61C2×Dic94D412yes—
62C4⋊C4×C47—21no—
63C4⋊C4×C47—24no—
64C22⋊C4×C47—24no—
65C22⋊C4×C47C2312yes—
66C42×C47—21no—
67C22⋊Dic47C2314yes—
68(C2×D47)⋊C4—28no—
69C4⋊Dic47—22no—
70Dic47⋊C4—28no—
71C4×Dic47—22no—
72C23×C47C2×D412yes—
73C23×C47C2411yescharacteristic
74C22×D47—24no—
75C22×D47C2×D414yes—
76Q8×C47—22no—
77Q8×C47—41no—
78Q8×C47—42no—
79Q8×C47—41no—
80D4×C47—24no—
81D4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—24no—
85C2×C4×C47—22no—
86C2×C4×C47—22no—
87C2×C4×C47C2×D412yes—
88C2×C4×C47C2×D412yes—
89C2×C4×C47C2×D412yes—
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47C2×D411yescharacteristic
92C22⋊D47—28no—
93C22⋊D47—24no—
94C22⋊D47—24no—
95C2×Dic47—24no—
96C2×Dic47—24no—
97C2×Dic47C2×D414yes—
98D188—24no—
99D188—22no—
100D188—22no—
101C4×D47—28no—
102C4×D47—24no—
103C4×D47—24no—
104Dic94—24no—
105Dic94—22no—
106Dic94—22no—
107C22×C47—22no—
108C22×C47—41no—
109C22×C47—42no—
110C22×C47C22×D412yes—
111C22×C47C22×D411yescharacteristic
112C2×D47—24no—
113C2×D47—44no—
114C2×D47—84no—
115C4×C47—22no—
116C4×C47—42no—
117C4×C47—42no—
118C4×C47#12011yescharacteristic
119C4×C47#12012yes—
120C4×C47#12011yescharacteristic
121Dic47—24no—
122Dic47—44no—
123#3028—471nomaximal, Sylow
124C2×C47—22no—
125C2×C47—21no—
126C2×C47—42no—
127C2×C47C2×#12011yescharacteristic
128D47—44no—
129#585—471no—
130#536—472no—
131#536D4711yescharacteristic, complemented
132#458—478no—
133#410—471no—
134#410—472no—
135C47#302811yescharacteristic, complemented, Sylow
1362−1+4—942no—
1372−1+4—941no—
138H(5,𝔽2)—474no—
139H(5,𝔽2)—942no—
140H(5,𝔽2)—941no—
141C2×#41—472no—
142C2×#41—944no—
143C2×#41—942no—
144C2×#41C2×D4711yescharacteristic
145C22×Q8C2×D4711yescharacteristic, complemented
146C4⋊Q8—21no—
147C4⋊Q8—942no—
148#124—21no—
149#124—942no—
150#123—478no—
151#123C2×D4714yescomplemented
152C22⋊Q8—22no—
153C22⋊Q8—944no—
154#117—472no—
155#117C2×D4711yescharacteristic, complemented
156#99—474no—
157#99—478no—
158#41—22no—
159#41—22no—
160#41—944no—
161#41—944no—
162#41—948no—
163#41—944no—
164#41—944no—
165#41—942no—
166#41—942no—
167#41—942no—
168#41—942no—
169#41—944no—
170C2×Q8—22no—
171C2×Q8—22no—
172C2×Q8—21no—
173C2×Q8—21no—
174C2×Q8—472no—
175C2×Q8—942no—
176C2×Q8—944no—
177C2×Q8C22⋊D4711yescharacteristic
178C2×D4—474no—
179C2×D4—472no—
180C2×D4—942no—
181C2×D4—948no—
182C2×D4—944no—
183C2×D4—944no—
184C2×D4C22⋊D4711yescharacteristic
185C2×D4C22×D4712yes—
186C22×C4—474no—
187C22×C4—944no—
188C22×C4C22⋊D4712yes—
189C22×C4C22×D4712yes—
190C22×C4C22×D4711yescharacteristic
191C4⋊C4—21no—
192C4⋊C4—24no—
193C4⋊C4—948no—
194C4⋊C4—942no—
195C22⋊C4—24no—
196C22⋊C4—474no—
197C22⋊C4—948no—
198C22⋊C4C22×D4712yes—
199C42—21no—
200C42—942no—
201C23—474no—
202C23—944no—
203C23C2×C22⋊D4712yes—
204C23C23×D4711yescharacteristic
205Q8—22no—
206Q8—41no—
207Q8—41no—
208Q8—42no—
209Q8—944no—
210Q8—942no—
211Q8—942no—
212D4—24no—
213D4—22no—
214D4—944no—
215D4—948no—
216D4—944no—
217D4—944no—
218D4—942no—
219D4—942no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—24no—
223C2×C4—22no—
224C2×C4—22no—
225C2×C4—474no—
226C2×C4—948no—
227C2×C4—944no—
228C2×C4—944no—
229C2×C4—944no—
230C2×C4—944no—
231C2×C4D4×D4712yes—
232C2×C4D4×D4712yes—
233C2×C4C2×C22⋊D4712yes—
234C2×C4C2×C22⋊D4711yescharacteristic
235C2×C4C2×C22⋊D4711yescharacteristic
236C22—22no—
237C22—41no—
238C22—42no—
239C22—944no—
240C22—3764no—
241C22—1884no—
242C22C2×D4×D4712yes—
243C22C22×C22⋊D4711yescharacteristic
244C4—22no—
245C4—42no—
246C4—42no—
247C4—944no—
248C4—1884no—
249C4#1309399211yescharacteristic
250C4#1309399211yescharacteristic
251C4#1309399212yes—
252C2—21no—
253C2—22no—
254C2—42no—
255C2—1884no—
256C2C2×#1309399211yescharacteristic
subgroupG/H
centerC2C2×#13093992
commutatorC23×C47C24
FrattiniC23C23×D47
FittingC47×#536C2
socleC2×C47C2×#120
hypercenter#536D47
hypocenterC47#3028
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2 ◁ C22×C4 ◁ #536

Complements

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

NH ≅ G/Ntype
2. #15689697C2semidirect
3. #15689312C2semidirect
4. #15689097C2semidirect
5. #15689096C2semidirect
6. C47×#536C2semidirect
17. #13094007C22semidirect
19. #13093983C22semidirect
20. #13093939C22semidirect
21. #13093938C22semidirect
23. C22×Q8×C47C22semidirect
26. #123×C47C22semidirect
28. #117×C47C22semidirect
131. #536D47semidirect
135. C47#3028semidirect
145. C22×Q8C2×D47semidirect
151. #123C2×D47semidirect
155. #117C2×D47semidirect