Finite Group Databasebeta

← #20243889

Subgroups — #20243889

Order 6016.

332 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 89 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#15689921C211yesmaximal, characteristic
2#15689140C211yesmaximal, characteristic, complemented
3C2×#13093952C211yesmaximal, characteristic, complemented
4#15689096C211yesmaximal, characteristic, complemented
5#15688893C211yesmaximal, characteristic, complemented
6#15688883C211yesmaximal, characteristic, complemented
7C4×#41×C47C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094055—21no—
10#13094054C412yescomplemented
11#13094050—21no—
12#13094049C412yescomplemented
13#13094044—22no—
14C2×#10625329C2211yescharacteristic
15C2×#10625329C2211yescharacteristic
16#13093983C2211yescharacteristic
17#13093952—21no—
18#13093952—21no—
19#13093951—22no—
20#13093938—22no—
21C2×#41×C47C2211yescharacteristic
22C4×Q8×C47—21no—
23C4×D4×C47—21no—
24C4×D4×C47—22no—
25#117×C47—21no—
26#117×C47C2211yescharacteristic
27C2×C42×C47—21no—
28C2×C42×C47C2211yescharacteristic
29#41×C47—21no—
30#41×C47—21no—
31#41×C47C2×C412yes—
32#41×C47D412yes—
33C2×Q8×C47D411yescharacteristic
34C2×D4×C47—21no—
35C2×D4×C47D411yescharacteristic
36C22×C4×C47—21no—
37C22×C4×C47—22no—
38C22×C4×C47—21no—
39C22×C4×C47C2311yescharacteristic
40C2×C22⋊D47—21no—
41#10625350—21no—
42#10625350—21no—
43#10625350—21no—
44#10625350—21no—
45C2×D188C2×C411yescharacteristic, complemented
46C2×C4×D47—21no—
47C2×Dic94C2×C411yescharacteristic, complemented
48C4⋊C4×C47—22no—
49C4⋊C4×C47—21no—
50C22⋊C4×C47—22no—
51C22⋊C4×C47D412yes—
52C42×C47—22no—
53C42×C47—21no—
54C42×C47—21no—
55C42×C47D411yescharacteristic
56C42×C47D411yescharacteristic
57C22⋊Dic47—21no—
58#10625337—22no—
59#10625336—22no—
60#10625335—22no—
61#10625334—22no—
62C4⋊Dic47—21no—
63C4×Dic47—21no—
64#10625329—21no—
65#10625329—21no—
66#10625329—21no—
67#10625329C2×C412yescomplemented
68C2×C47⋊C8—21no—
69C2×C47⋊C8—21no—
70C23×C47—21no—
71C23×C47C2×D411yescharacteristic
72C22×D47—21no—
73Q8×C47—21no—
74Q8×C47C22⋊C412yes—
75D4×C47—22no—
76D4×C47—22no—
77D4×C47—21no—
78D4×C47C22⋊C412yes—
79C2×C4×C47—21no—
80C2×C4×C47—21no—
81C2×C4×C47—22no—
82C2×C4×C47—22no—
83C2×C4×C47—22no—
84C2×C4×C47—21no—
85C2×C4×C47—42no—
86C2×C4×C47—44no—
87C2×C4×C47C22×C411yescharacteristic
88C2×C4×C47C2×D411yescharacteristic
89C2×C4×C47C2×D411yescharacteristic
90C2×C4×C47C2×D411yescharacteristic
91C2×C4×C47#4111yescharacteristic
92C2×C4×C47#4111yescharacteristic
93C22⋊D47—41no—
94C22⋊D47—41no—
95C2×Dic47—21no—
96C2×Dic47—41no—
97D188—21no—
98D188—21no—
99C4×D47—41no—
100C4×D47—41no—
101Dic94—21no—
102Dic94—21no—
103C47⋊C8—22no—
104C47⋊C8—41no—
105C22×C47—22no—
106C22×C47—41no—
107C22×C47—42no—
108C22×C47C4×D411yescharacteristic
109C22×C47#12011yescharacteristic
110C22×C47#12111yescharacteristic
111C2×D47—41no—
112C2×D47—81no—
113C4×C47—22no—
114C4×C47—22no—
115C4×C47—42no—
116C4×C47—41no—
117C4×C47C2×C22⋊C411yescharacteristic
118C4×C47C4×D411yescharacteristic
119C4×C47#12111yescharacteristic
120C4×C47#12311yescharacteristic
121Dic47—41no—
122Dic47—81no—
123#1906—471nomaximal, Sylow
124C2×C47—21no—
125C2×C47—21no—
126C2×C47—21no—
127C2×C47—42no—
128C2×C47#38611yescharacteristic
129D47—81no—
130#575—471no—
131C4×#41D4711yescharacteristic, complemented
132#421—471no—
133C2×#104—471no—
134#410—471no—
135#344—471no—
136#339—471no—
137C47#190611yescharacteristic, complemented, Sylow
138C2×#41—471no—
139C2×#41C2×D4711yescharacteristic
140#137—472no—
141#137—941no—
142AGL(1,ℤ/8)—472no—
143AGL(1,ℤ/8)—941no—
144#135—942no—
145C2×M16—471no—
146C2×M16—471no—
147C4×Q8—21no—
148C4×D4—21no—
149C4×D4—22no—
150#117—21no—
151#117—471no—
152#117C2×D4711yescharacteristic
153C2×C42—21no—
154C2×C42C2×D4711yescharacteristic
155#104—942no—
156#104—941no—
157#104—941no—
158#99—942no—
159#41—21no—
160#41—21no—
161#41—941no—
162#41—941no—
163#41—941no—
164#41—941no—
165#41C4×D4712yes—
166#41D18812yes—
167C2×Q8—471no—
168C2×Q8C22⋊D4711yescharacteristic
169C2×D4—21no—
170C2×D4—471no—
171C2×D4—941no—
172C2×D4C22⋊D4711yescharacteristic
173C22×C4—21no—
174C22×C4—22no—
175C22×C4—21no—
176C22×C4—941no—
177C22×C4C22×D4711yescharacteristic
178Q16—942no—
179SD16—942no—
180SD16—942no—
181D8—942no—
182M16—472no—
183M16—941no—
184M16—941no—
185M16—941no—
186C2×C8—941no—
187C2×C8—941no—
188C4⋊C4—22no—
189C4⋊C4—21no—
190C4⋊C4—941no—
191C22⋊C4—22no—
192C22⋊C4—941no—
193C22⋊C4C22⋊D4712yes—
194C42—22no—
195C42—21no—
196C42—21no—
197C42—941no—
198C42C22⋊D4711yescharacteristic
199C42C22⋊D4711yescharacteristic
200C23—21no—
201C23—941no—
202C23C2×C22⋊D4711yescharacteristic
203Q8—21no—
204Q8—941no—
205Q8—941no—
206Q8(C2×D47)⋊C412yes—
207D4—22no—
208D4—22no—
209D4—21no—
210D4—941no—
211D4—941no—
212D4—1881no—
213D4—1881no—
214D4(C2×D47)⋊C412yes—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—22no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—21no—
221C2×C4—42no—
222C2×C4—44no—
223C2×C4—941no—
224C2×C4—1881no—
225C2×C4—1881no—
226C2×C4—1881no—
227C2×C4C2×C4×D4711yescharacteristic
228C2×C4C2×D18811yescharacteristic
229C2×C4#1062535011yescharacteristic
230C2×C4#1062535011yescharacteristic
231C2×C4C2×C22⋊D4711yescharacteristic
232C2×C4C2×C22⋊D4711yescharacteristic
233C8—942no—
234C8—1881no—
235C22—22no—
236C22—41no—
237C22—42no—
238C22—3761no—
239C22—1881no—
240C22C4×C22⋊D4711yescharacteristic
241C22#1309399311yescharacteristic
242C22#1309399811yescharacteristic
243C4—22no—
244C4—22no—
245C4—42no—
246C4—41no—
247C4—3761no—
248C4—1881no—
249C4C2×(C2×D47)⋊C411yescharacteristic
250C4C4×C22⋊D4711yescharacteristic
251C4#1309399811yescharacteristic
252C4#1309400711yescharacteristic
253C2—21no—
254C2—21no—
255C2—21no—
256C2—42no—
257C2—3761no—
258C2#1568900211yescharacteristic
subgroupG/H
centerC4#13093998
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC4×#41×C47C2
socleC2×C47#386
hypercenterC4×#41D47
hypocenterC47#1906
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ C4×#41

Complements

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

NH ≅ G/Ntype
2. #15689140C2semidirect
3. C2×#13093952C2semidirect
4. #15689096C2semidirect
5. #15688893C2semidirect
6. #15688883C2semidirect
7. C4×#41×C47C2semidirect
10. #13094054C4semidirect
12. #13094049C4semidirect
45. C2×D188C2×C4semidirect
47. C2×Dic94C2×C4semidirect
67. #10625329C2×C4semidirect
131. C4×#41D47semidirect
137. C47#1906semidirect