Finite Group Databasebeta

← #20241931

Subgroups — #20241931

Order 6016.

286 conjugacy classes of subgroups; only the 81 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 81 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
2#15688983C211yesmaximal, characteristic, complemented
3#15688860C212yesmaximal, complemented
4#15688857C212yesmaximal, complemented
5C47×#525C211yesmaximal, characteristic
6C2×#10625329—21no—
7C2×C4⋊Dic47—21no—
8C2×C22⋊Dic47—21no—
9C22⋊(C47⋊C8)—21no—
10C22⋊(C47⋊C8)C2212yes—
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
26C2×D4×C47—21no—
27C2×D4×C47—21no—
28C2×D4×C47—21no—
29C2×D4×C47C2×C411yescharacteristic
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—22no—
39C4⋊C4×C47—21no—
40C4⋊C4×C47—21no—
41C4⋊C4×C47C2×C411yescharacteristic
42C4⋊C4×C47C2×C411yescharacteristic
43C22⋊C4×C47—21no—
44C22⋊C4×C47—21no—
45C22⋊C4×C47—21no—
46C22⋊C4×C47—21no—
47C22⋊C4×C47—21no—
48C42×C47—21no—
49C22⋊Dic47—42no—
50C4⋊Dic47—42no—
51#10625329—42no—
52C2×C47⋊C8—22no—
53C23×C47—21no—
54C23×C47—21no—
55C23×C47—21no—
56C23×C47—41no—
57C23×C47—41no—
58C23×C47C22⋊C411yescharacteristic
59C23×C47C22⋊C411yescharacteristic
60C23×C47C2×D411yescharacteristic
61Q8×C47—41no—
62D4×C47—41no—
63D4×C47—42no—
64D4×C47—42no—
65D4×C47—41no—
66D4×C47—41no—
67C2×C4×C47—22no—
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—42no—
77C2×C4×C47C22⋊C411yescharacteristic
78C2×C4×C47C22⋊C411yescharacteristic
79C2×C4×C47C22×C411yescharacteristic
80C2×C4×C47C2×D411yescharacteristic
81C2×Dic47—42no—
82C2×Dic47—42no—
83C2×Dic47—42no—
84C47⋊C8—42no—
85C22×C47—21no—
86C22×C47—21no—
87C22×C47—21no—
88C22×C47—21no—
89C22×C47—21no—
90C22×C47—21no—
91C22×C47—21no—
92C22×C47—21no—
93C22×C47—42no—
94C22×C47—42no—
95C22×C47—41no—
96C22×C47—41no—
97C22×C47—41no—
98C22×C47C2×C22⋊C411yescharacteristic
99C22×C47AGL(1,ℤ/8)11yescharacteristic
100C22×C47#13711yescharacteristic
101C4×C47—21no—
102C4×C47—21no—
103C4×C47—21no—
104C4×C47—41no—
105C4×C47—41no—
106C4×C47—41no—
107C4×C47#9912yes—
108Dic47—82no—
109#1513—471nomaximal, Sylow
110C2×C47—21no—
111C2×C47—21no—
112C2×C47—41no—
113C2×C47—41no—
114C2×C47—81no—
115C2×C47C2×#9911yescharacteristic
116C2×C47#41711yescharacteristic
117C2×C47#42111yescharacteristic
118#525D4711yescharacteristic
119#407—471no—
120#380—471no—
121#328—472no—
122#327—472no—
123C47#151311yescharacteristic, complemented, Sylow
124C2×#41Dic4711yescharacteristic, complemented
125C23×C4C2×D4711yescharacteristic
126C2×M16—941no—
127#123—21no—
128C22⋊Q8Dic4711yescharacteristic, complemented
129C22⋊Q8C2×D4711yescharacteristic
130#121Dic4711yescharacteristic, complemented
131#121C2×D4711yescharacteristic
132#120—21no—
133C4×D4—21no—
134C4×D4—21no—
135#117Dic4711yescharacteristic, complemented
136C2×C4⋊C4—941no—
137C2×C22⋊C4—941no—
138C22⋊C8—472no—
139C22⋊C8—941no—
140#95—472no—
141C24C22⋊D4711yescharacteristic
142#41—42no—
143C2×Q8C2×Dic4711yescharacteristic
144C2×D4—21no—
145C2×D4—21no—
146C2×D4—21no—
147C2×D4C2×Dic4711yescharacteristic
148C22×C4—21no—
149C22×C4—42no—
150C22×C4—942no—
151C22×C4C2×Dic4711yescharacteristic
152C22×C4C2×Dic4711yescharacteristic
153C22×C4C22⋊D4711yescharacteristic
154C22×C4C22⋊D4711yescharacteristic
155C22×C4C22⋊D4711yescharacteristic
156C22×C4C22×D4711yescharacteristic
157M16—1882no—
158C2×C8—942no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—1882no—
162C4⋊C4C2×Dic4711yescharacteristic
163C4⋊C4C2×Dic4711yescharacteristic
164C22⋊C4—21no—
165C22⋊C4—21no—
166C22⋊C4—21no—
167C22⋊C4—21no—
168C22⋊C4—21no—
169C22⋊C4—1882no—
170C42—21no—
171C23—21no—
172C23—21no—
173C23—21no—
174C23—41no—
175C23—41no—
176C23C22⋊Dic4711yescharacteristic
177C23C22⋊Dic4711yescharacteristic
178C23C2×C22⋊D4711yescharacteristic
179Q8—41no—
180D4—41no—
181D4—42no—
182D4—42no—
183D4—41no—
184D4—41no—
185C2×C4—22no—
186C2×C4—22no—
187C2×C4—22no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—42no—
195C2×C4—1882no—
196C2×C4—1882no—
197C2×C4—1882no—
198C2×C4C22⋊Dic4711yescharacteristic
199C2×C4C22⋊Dic4711yescharacteristic
200C2×C4C22×Dic4711yescharacteristic
201C2×C4C2×C22⋊D4711yescharacteristic
202C8—1882no—
203C22—21no—
204C22—21no—
205C22—21no—
206C22—21no—
207C22—21no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—42no—
212C22—42no—
213C22—41no—
214C22—41no—
215C22—41no—
216C22C2×C22⋊Dic4711yescharacteristic
217C22#1309404911yescharacteristic
218C22#1309405411yescharacteristic
219C4—21no—
220C4—21no—
221C4—21no—
222C4—41no—
223C4—41no—
224C4—41no—
225C4—3762no—
226C4#1309393912yes—
227C2—21no—
228C2—21no—
229C2—41no—
230C2—41no—
231C2—81no—
232C2C2×#1309393911yescharacteristic
233C2#1568912411yescharacteristic
234C2#1568914011yescharacteristic
subgroupG/H
centerC22C2×C22⋊Dic47
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#525C2
socleC22×C47C2×C22⋊C4
hypercenter#525D47
hypocenterC47#1513
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. #15688983C2semidirect
3. #15688860C2semidirect
4. #15688857C2semidirect
12. C2×#41×C47C4semidirect
15. C22⋊Q8×C47C4semidirect
17. #121×C47C4semidirect
22. #117×C47C4semidirect
123. C47#1513semidirect
124. C2×#41Dic47semidirect
128. C22⋊Q8Dic47semidirect
130. #121Dic47semidirect
135. #117Dic47semidirect