Finite Group Databasebeta

← #20241892

Subgroups — #20241892

Order 6016.

334 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 85 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#15689087C211yesmaximal, characteristic, complemented
2C2×C47⋊#95C211yesmaximal, characteristic, complemented
3#15688860C212yesmaximal, complemented
4#15688857C212yesmaximal, complemented
5C47×#525C211yesmaximal, characteristic
6C23×Dic47—21no—
7C2×#10625329—21no—
8C22⋊(C47⋊C8)—21no—
9C22⋊(C47⋊C8)C2212yes—
10C47⋊#95—21no—
11C47⋊#95C2212yes—
12C2×#41×C47C411yescharacteristic, complemented
13C23×C4×C47C2211yescharacteristic
14#123×C47—21no—
15C22⋊Q8×C47C411yescharacteristic, complemented
16C22⋊Q8×C47C2211yescharacteristic
17#121×C47C411yescharacteristic, complemented
18#121×C47C2211yescharacteristic
19#120×C47—21no—
20C4×D4×C47—21no—
21C4×D4×C47—21no—
22#117×C47C411yescharacteristic, complemented
23C24×C47D411yescharacteristic
24#41×C47—42no—
25C2×Q8×C47C2×C411yescharacteristic, complemented
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47—21no—
29C2×D4×C47C2×C411yescharacteristic, complemented
30C22×C4×C47—21no—
31C22×C4×C47—42no—
32C22×C4×C47C2×C411yescharacteristic
33C22×C4×C47C2×C411yescharacteristic
34C22×C4×C47D411yescharacteristic
35C22×C4×C47D411yescharacteristic
36C22×C4×C47D411yescharacteristic
37C22×C4×C47C2311yescharacteristic
38C22×Dic47—24no—
39C22×Dic47—22no—
40C22×Dic47—42no—
41C22×Dic47—42no—
42C4⋊C4×C47—21no—
43C4⋊C4×C47—21no—
44C4⋊C4×C47C2×C411yescharacteristic, complemented
45C4⋊C4×C47C2×C411yescharacteristic, complemented
46C22⋊C4×C47—21no—
47C22⋊C4×C47—21no—
48C22⋊C4×C47—21no—
49C22⋊C4×C47—21no—
50C22⋊C4×C47—21no—
51C42×C47—21no—
52#10625329—42no—
53C2×C47⋊C8—22no—
54C23×C47—22no—
55C23×C47—22no—
56C23×C47—21no—
57C23×C47—21no—
58C23×C47—21no—
59C23×C47C22⋊C411yescharacteristic
60C23×C47C22⋊C411yescharacteristic
61C23×C47C2×D411yescharacteristic
62Q8×C47—41no—
63D4×C47—41no—
64D4×C47—42no—
65D4×C47—42no—
66D4×C47—41no—
67D4×C47—41no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—21no—
71C2×C4×C47—21no—
72C2×C4×C47—21no—
73C2×C4×C47—41no—
74C2×C4×C47—41no—
75C2×C4×C47—41no—
76C2×C4×C47—41no—
77C2×C4×C47—42no—
78C2×C4×C47C22⋊C411yescharacteristic
79C2×C4×C47C22⋊C411yescharacteristic
80C2×C4×C47C22×C411yescharacteristic
81C2×C4×C47C2×D411yescharacteristic
82C2×Dic47—24no—
83C2×Dic47—48no—
84C2×Dic47—42no—
85C2×Dic47—42no—
86C47⋊C8—42no—
87C22×C47—24no—
88C22×C47—24no—
89C22×C47—21no—
90C22×C47—21no—
91C22×C47—21no—
92C22×C47—21no—
93C22×C47—21no—
94C22×C47—21no—
95C22×C47—41no—
96C22×C47—41no—
97C22×C47—41no—
98C22×C47#9912yes—
99C22×C47#10412yes—
100C22×C47C2×C22⋊C411yescharacteristic
101C22×C47AGL(1,ℤ/8)11yescharacteristic
102C22×C47#13711yescharacteristic
103C4×C47—21no—
104C4×C47—21no—
105C4×C47—21no—
106C4×C47—21no—
107C4×C47—41no—
108C4×C47—41no—
109C4×C47—41no—
110Dic47—44no—
111#1504—471nomaximal, Sylow
112C2×C47—21no—
113C2×C47—22no—
114C2×C47—22no—
115C2×C47—21no—
116C2×C47—81no—
117C2×C47C2×#9911yescharacteristic
118C2×C47#41711yescharacteristic
119C2×C47C2×#10411yescharacteristic
120#525D4711yescharacteristic
121#407—471no—
122C2×#95—471no—
123#328—472no—
124#327—472no—
125C47#150411yescharacteristic, complemented, Sylow
126C2×#41Dic4711yescharacteristic, complemented
127C23×C4—941no—
128C23×C4C2×D4711yescharacteristic
129C2×M16—941no—
130#123—21no—
131C22⋊Q8Dic4711yescharacteristic, complemented
132C22⋊Q8C2×D4711yescharacteristic
133#121Dic4711yescharacteristic, complemented
134#121C2×D4711yescharacteristic
135#120—21no—
136C4×D4—21no—
137C4×D4—21no—
138#117Dic4711yescharacteristic, complemented
139C22⋊C8—472no—
140C22⋊C8—941no—
141#95—472no—
142#95—941no—
143C24C22⋊D4711yescharacteristic
144#41—42no—
145C2×Q8C2×Dic4711yescharacteristic, complemented
146C2×D4—21no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4C2×Dic4711yescharacteristic, complemented
150C22×C4—21no—
151C22×C4—42no—
152C22×C4—944no—
153C22×C4—942no—
154C22×C4—1882no—
155C22×C4—1882no—
156C22×C4C2×Dic4711yescharacteristic
157C22×C4C2×Dic4711yescharacteristic
158C22×C4C22⋊D4711yescharacteristic
159C22×C4C22⋊D4711yescharacteristic
160C22×C4C22⋊D4711yescharacteristic
161C22×C4C22×D4711yescharacteristic
162M16—1882no—
163C2×C8—942no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4C2×Dic4711yescharacteristic, complemented
167C4⋊C4C2×Dic4711yescharacteristic, complemented
168C22⋊C4—21no—
169C22⋊C4—21no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—21no—
173C42—21no—
174C23—22no—
175C23—22no—
176C23—21no—
177C23—21no—
178C23—21no—
179C23C22⋊Dic4711yescharacteristic
180C23C22⋊Dic4711yescharacteristic
181C23C2×C22⋊D4711yescharacteristic
182Q8—41no—
183D4—41no—
184D4—42no—
185D4—42no—
186D4—41no—
187D4—41no—
188C2×C4—22no—
189C2×C4—22no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—41no—
194C2×C4—41no—
195C2×C4—41no—
196C2×C4—41no—
197C2×C4—42no—
198C2×C4—944no—
199C2×C4—1888no—
200C2×C4—1882no—
201C2×C4—1882no—
202C2×C4C22⋊Dic4711yescharacteristic
203C2×C4C22⋊Dic4711yescharacteristic
204C2×C4C22×Dic4711yescharacteristic
205C2×C4C2×C22⋊D4711yescharacteristic
206C8—1882no—
207C22—24no—
208C22—24no—
209C22—21no—
210C22—21no—
211C22—21no—
212C22—21no—
213C22—21no—
214C22—21no—
215C22—41no—
216C22—41no—
217C22—41no—
218C22#1309393912yes—
219C22#1309395112yes—
220C22C2×C22⋊Dic4711yescharacteristic
221C22#1309404911yescharacteristic
222C22#1309405411yescharacteristic
223C4—21no—
224C4—21no—
225C4—21no—
226C4—21no—
227C4—41no—
228C4—41no—
229C4—41no—
230C4—1884no—
231C2—21no—
232C2—22no—
233C2—22no—
234C2—21no—
235C2—81no—
236C2C2×#1309393911yescharacteristic
237C2#1568912411yescharacteristic
238C2C2×#1309395111yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#525C2
socleC22×C47C2×C22⋊C4
hypercenter#525D47
hypocenterC47#1504
LCSG ▷ C2×C4×C47 ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #525

Complements

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

NH ≅ G/Ntype
1. #15689087C2semidirect
2. C2×C47⋊#95C2semidirect
3. #15688860C2semidirect
4. #15688857C2semidirect
12. C2×#41×C47C4semidirect
15. C22⋊Q8×C47C4semidirect
17. #121×C47C4semidirect
22. #117×C47C4semidirect
25. C2×Q8×C47C2×C4semidirect
29. C2×D4×C47C2×C4semidirect
44. C4⋊C4×C47C2×C4semidirect
45. C4⋊C4×C47C2×C4semidirect
125. C47#1504semidirect
126. C2×#41Dic47semidirect
131. C22⋊Q8Dic47semidirect
133. #121Dic47semidirect
138. #117Dic47semidirect
145. C2×Q8C2×Dic47semidirect
149. C2×D4C2×Dic47semidirect
166. C4⋊C4C2×Dic47semidirect
167. C4⋊C4C2×Dic47semidirect