Finite Group Databasebeta

← #20243768

Subgroups — #20243768

Order 6016.

332 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 79 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#15689889C211yesmaximal, characteristic, complemented
2#15689669C211yesmaximal, characteristic
3#15689140C211yesmaximal, characteristic, complemented
4#15689096C211yesmaximal, characteristic, complemented
5#15688884C211yesmaximal, characteristic, complemented
6#15688882C211yesmaximal, characteristic, complemented
7C47×#421C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13094032—22no—
10#13094030—22no—
11C2×#10625329C2211yescharacteristic
12M16×D47—22no—
13#13094022C411yescharacteristic, complemented
14#13094020C411yescharacteristic, complemented
15#13094013C411yescharacteristic, complemented
16#13094011C411yescharacteristic, complemented
17#13093996—22no—
18C4×C22⋊D47—22no—
19#13093983C2211yescharacteristic
20C2×C4×Dic47C2211yescharacteristic
21#13093951—22no—
22#13093938—22no—
23C2×#41×C47C2211yescharacteristic
24C2×M16×C47C2211yescharacteristic
25#117×C47C2211yescharacteristic
26#104×C47—22no—
27#41×C47—21no—
28#41×C47—21no—
29#41×C47—21no—
30#41×C47—21no—
31C2×Q8×C47C2×C411yescharacteristic
32C2×D4×C47—21no—
33C2×D4×C47C2×C411yescharacteristic
34C22×C4×C47—21no—
35C22×C4×C47C2311yescharacteristic
36C2×C22⋊D47—22no—
37C2×C22⋊D47D412yes—
38C22×Dic47—21no—
39#10625350—21no—
40#10625350—21no—
41#10625350—21no—
42#10625350—21no—
43C2×D188C2×C411yescharacteristic
44C2×C4×D47D412yes—
45C2×Dic94C2×C411yescharacteristic
46M16×C47—21no—
47M16×C47D412yescomplemented
48C2×C8×C47—21no—
49C4⋊C4×C47—21no—
50C22⋊C4×C47—21no—
51C42×C47—21no—
52C22⋊Dic47—22no—
53C22⋊Dic47—21no—
54(C2×D47)⋊C4—22no—
55C4⋊Dic47—21no—
56Dic47⋊C4—22no—
57C4×Dic47—21no—
58C4×Dic47—21no—
59C4×Dic47C2×C411yescharacteristic
60C4×Dic47C2×C411yescharacteristic
61#10625329—21no—
62#10625329D412yescomplemented
63C2×C47⋊C8—21no—
64#10625324—24no—
65C8×D47—24no—
66C23×C47—21no—
67C23×C47C2×D411yescharacteristic
68C22×D47C22⋊C412yes—
69Q8×C47—21no—
70Q8×C47—21no—
71D4×C47—21no—
72D4×C47—21no—
73D4×C47—41no—
74D4×C47—41no—
75C2×C4×C47—21no—
76C2×C4×C47—41no—
77C2×C4×C47—41no—
78C2×C4×C47—41no—
79C2×C4×C47C22×C411yescharacteristic
80C2×C4×C47C2×D411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×C4×C47C2×D411yescharacteristic
83C2×C4×C47#4111yescharacteristic
84C2×C4×C47#4111yescharacteristic
85C22⋊D47—22no—
86C22⋊D47—22no—
87C22⋊D47—44no—
88C2×Dic47—21no—
89C2×Dic47—21no—
90C2×Dic47—42no—
91C2×Dic47—41no—
92C2×Dic47C22⋊C412yes—
93D188—21no—
94D188—21no—
95C4×D47—22no—
96C4×D47—22no—
97Dic94—21no—
98Dic94—21no—
99C8×C47—22no—
100C47⋊C8—22no—
101C22×C47—41no—
102C22×C47—42no—
103C22×C47—41no—
104C22×C47C2×C22⋊C411yescharacteristic
105C22×C47#12111yescharacteristic
106C22×C47#12111yescharacteristic
107C2×D47—22no—
108C2×D47—42no—
109C4×C47—41no—
110C4×C47—81no—
111C4×C47C4×D411yescharacteristic
112C4×C47C4×D411yescharacteristic
113C4×C47#12011yescharacteristic
114C4×C47#12311yescharacteristic
115Dic47—22no—
116Dic47—22no—
117Dic47—41no—
118Dic47—81no—
119#1884—471nomaximal, Sylow
120C2×C47—21no—
121C2×C47—21no—
122C2×C47—21no—
123C2×C47—81no—
124C2×C47#38611yescharacteristic
125D47—42no—
126#568—471no—
127#532—471no—
128#421—471no—
129#421D4711yescharacteristic, complemented
130#410—471no—
131#339—471no—
132#339—471no—
133C47#188411yescharacteristic, complemented, Sylow
134C2×#41—471no—
135C2×#41C2×D4711yescharacteristic
136#131—942no—
137#131—942no—
138C2×M16—471no—
139C2×M16—942no—
140C2×M16C2×D4711yescharacteristic
141C4⋊Q8—471no—
142#127—471no—
143#124—471no—
144#124—471no—
145#121—942no—
146C4×D4—942no—
147#117—471no—
148#117C2×D4711yescharacteristic
149C2×C42—471no—
150#104—22no—
151#104—942no—
152#99—942no—
153#41—21no—
154#41—21no—
155#41—21no—
156#41—21no—
157#41—941no—
158#41—941no—
159#41—941no—
160#41—941no—
161C2×Q8—471no—
162C2×Q8C4×D4711yescharacteristic
163C2×D4—21no—
164C2×D4—472no—
165C2×D4—471no—
166C2×D4—942no—
167C2×D4C4×D4711yescharacteristic
168C22×C4—21no—
169C22×C4—472no—
170C22×C4—941no—
171C22×C4C22×D4711yescharacteristic
172M16—21no—
173M16—472no—
174M16—944no—
175M16—941no—
176M16C22⋊D4712yescomplemented
177C2×C8—21no—
178C2×C8—944no—
179C2×C8—941no—
180C4⋊C4—21no—
181C4⋊C4—942no—
182C4⋊C4—941no—
183C22⋊C4—21no—
184C22⋊C4—942no—
185C22⋊C4—942no—
186C22⋊C4—941no—
187C42—21no—
188C42—471no—
189C42—471no—
190C42—941no—
191C42—941no—
192C23—21no—
193C23—472no—
194C23D4×D4711yescharacteristic
195Q8—21no—
196Q8—21no—
197Q8—941no—
198Q8—941no—
199D4—21no—
200D4—21no—
201D4—41no—
202D4—41no—
203D4—942no—
204D4—942no—
205D4—941no—
206D4—941no—
207D4—1884no—
208C2×C4—21no—
209C2×C4—41no—
210C2×C4—41no—
211C2×C4—41no—
212C2×C4—472no—
213C2×C4—941no—
214C2×C4—942no—
215C2×C4—942no—
216C2×C4—941no—
217C2×C4—1882no—
218C2×C4—1881no—
219C2×C4C2×C4×D4711yescharacteristic
220C2×C4#1062535011yescharacteristic
221C2×C4D4×D4711yescharacteristic
222C2×C4D4×D4711yescharacteristic
223C2×C4#1062535211yescharacteristic
224C2×C4C2×C22⋊D4711yescharacteristic
225C8—22no—
226C8—942no—
227C22—41no—
228C22—42no—
229C22—41no—
230C22—942no—
231C22—1882no—
232C22C22⋊C4×D4711yescharacteristic
233C22#1309399511yescharacteristic
234C22#1309399711yescharacteristic
235C4—41no—
236C4—81no—
237C4—942no—
238C4—942no—
239C4—3761no—
240C4—1881no—
241C4(C22⋊D47)⋊C411yescharacteristic
242C4C4×C22⋊D4711yescharacteristic
243C4#1309399211yescharacteristic
244C4#1309400611yescharacteristic
245C2—21no—
246C2—21no—
247C2—21no—
248C2—81no—
249C2—1882no—
250C2#1568899911yescharacteristic
subgroupG/H
centerC4#13093992
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#421C2
socleC2×C47#386
hypercenter#421D47
hypocenterC47#1884
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. #15689889C2semidirect
3. #15689140C2semidirect
4. #15689096C2semidirect
5. #15688884C2semidirect
6. #15688882C2semidirect
7. C47×#421C2semidirect
13. #13094022C4semidirect
14. #13094020C4semidirect
15. #13094013C4semidirect
16. #13094011C4semidirect
47. M16×C47D4semidirect
62. #10625329D4semidirect
129. #421D47semidirect
133. C47#1884semidirect
176. M16C22⋊D47semidirect