Finite Group Databasebeta

← #20245027

Subgroups — #20245027

Order 6016.

264 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 65 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#15689630C211yesmaximal, characteristic
2#15689107C211yesmaximal, characteristic, complemented
3#15688912C212yesmaximal, complemented
4#15688909C212yesmaximal, complemented
5C47×#410C211yesmaximal, characteristic, complemented
6C22×C4×D47C411yescharacteristic, complemented
7C2×#10625329—21no—
8#13094005C411yescharacteristic, complemented
9#13094005C2211yescharacteristic
10#13094000—21no—
11#13093995—21no—
12#13093992C411yescharacteristic, complemented
13#13093992C2211yescharacteristic
14C4×C22⋊D47—21no—
15C4×C22⋊D47—21no—
16#13093983C411yescharacteristic, complemented
17#13093943—21no—
18#13093941C2212yes—
19C2×#41×C47C2211yescharacteristic
20#117×C47—21no—
21#99×C47—21no—
22#99×C47C2212yes—
23C23×D47C2×C411yescharacteristic
24#41×C47—41no—
25#41×C47—41no—
26C2×Q8×C47D411yescharacteristic
27C2×D4×C47C2×C411yescharacteristic
28C2×D4×C47D411yescharacteristic
29C2×D4×C47C2311yescharacteristic
30C22×C4×C47C2×C411yescharacteristic
31C22×C4×C47D411yescharacteristic
32C22×C4×C47D411yescharacteristic
33C2×C22⋊D47—21no—
34C2×C22⋊D47—21no—
35C22×Dic47C2×C411yescharacteristic
36C2×C4×D47—21no—
37C2×C4×D47—21no—
38C2×C4×D47—41no—
39C2×C4×D47—41no—
40C4⋊C4×C47—41no—
41C22⋊C4×C47—22no—
42C42×C47—41no—
43C22⋊Dic47—21no—
44C22⋊Dic47—21no—
45C22⋊Dic47C2×C411yescharacteristic
46C22⋊Dic47C2×C411yescharacteristic
47(C2×D47)⋊C4—21no—
48(C2×D47)⋊C4—21no—
49C4⋊Dic47—21no—
50Dic47⋊C4—21no—
51Dic47⋊C4—21no—
52C4×Dic47—21no—
53#10625329—22no—
54#10625329—41no—
55C2×C47⋊C8—41no—
56C23×C47C22⋊C411yescharacteristic
57C23×C47C22×C411yescharacteristic
58C23×C47C2×D411yescharacteristic
59C22×D47—21no—
60C22×D47—42no—
61C22×D47—41no—
62Q8×C47—41no—
63D4×C47—41no—
64D4×C47—41no—
65D4×C47—41no—
66C2×C4×C47—21no—
67C2×C4×C47—21no—
68C2×C4×C47—21no—
69C2×C4×C47—21no—
70C2×C4×C47—21no—
71C2×C4×C47—21no—
72C2×C4×C47—42no—
73C2×C4×C47C22⋊C411yescharacteristic
74C2×C4×C47C22⋊C411yescharacteristic
75C2×C4×C47C22⋊C411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C22⋊D47—42no—
78C22⋊D47—42no—
79C2×Dic47—21no—
80C2×Dic47—21no—
81C2×Dic47—21no—
82C2×Dic47—41no—
83C4×D47—42no—
84C4×D47—41no—
85C4×D47—41no—
86C47⋊C8—42no—
87C22×C47—21no—
88C22×C47—21no—
89C22×C47—21no—
90C22×C47—41no—
91C22×C47—41no—
92C22×C47—41no—
93C22×C47C2×C22⋊C411yescharacteristic
94C2×D47—22no—
95C2×D47—41no—
96C2×D47—42no—
97C2×D47—41no—
98C2×D47—42no—
99C4×C47—21no—
100C4×C47—21no—
101C4×C47—21no—
102C4×C47—82no—
103C4×C47#9911yescharacteristic
104C4×C47#9911yescharacteristic
105Dic47—41no—
106Dic47—41no—
107Dic47—41no—
108#2120—471nomaximal, Sylow
109C2×C47—21no—
110C2×C47—41no—
111C2×C47—41no—
112C2×C47—41no—
113C2×C47C2×#9911yescharacteristic
114D47—42no—
115#525—471no—
116#413—471no—
117#410D4711yescharacteristic, complemented
118#352—472no—
119AΣL(1,𝔽16)—472no—
120C47#212011yescharacteristic, complemented, Sylow
121C2×#41C2×D4711yescharacteristic
122C23×C4—471no—
123C2×M16—941no—
124#123—471no—
125#123—471no—
126C22⋊Q8—941no—
127#121—941no—
128#120—471no—
129#120—471no—
130C4×D4—941no—
131C4×D4—941no—
132#117—21no—
133#117—471no—
134#101—941no—
135#100—472no—
136#99—21no—
137#99C2×D4712yes—
138C24—471no—
139#41—41no—
140#41—41no—
141C2×Q8D18811yescharacteristic
142C2×D4—941no—
143C2×D4—941no—
144C2×D4C4×D4711yescharacteristic
145C2×D4C22⋊D4711yescharacteristic
146C2×D4C22×D4711yescharacteristic
147C22×C4—471no—
148C22×C4—941no—
149C22×C4—941no—
150C22×C4—1881no—
151C22×C4—1881no—
152C22×C4C4×D4711yescharacteristic
153C22×C4D18811yescharacteristic
154C22×C4C22⋊D4711yescharacteristic
155M16—942no—
156M16—1881no—
157C2×C8—1881no—
158C4⋊C4—41no—
159C4⋊C4—941no—
160C4⋊C4—941no—
161C4⋊C4—941no—
162C22⋊C4—22no—
163C22⋊C4—471no—
164C22⋊C4—471no—
165C22⋊C4—941no—
166C22⋊C4—941no—
167C22⋊C4—941no—
168C22⋊C4—941no—
169C42—41no—
170C42—941no—
171C23—941no—
172C23—1881no—
173C23—1882no—
174C23(C2×D47)⋊C411yescharacteristic
175C23C2×C4×D4711yescharacteristic
176C23C2×C22⋊D4711yescharacteristic
177Q8—41no—
178D4—41no—
179D4—41no—
180D4—41no—
181D4—1882no—
182D4—1882no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—21no—
186C2×C4—21no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—42no—
190C2×C4—941no—
191C2×C4—941no—
192C2×C4—941no—
193C2×C4—1882no—
194C2×C4—1881no—
195C2×C4—1881no—
196C2×C4—1881no—
197C2×C4(C2×D47)⋊C411yescharacteristic
198C2×C4(C2×D47)⋊C411yescharacteristic
199C2×C4(C2×D47)⋊C411yescharacteristic
200C2×C4C2×D18811yescharacteristic
201C8—1882no—
202C22—21no—
203C22—21no—
204C22—21no—
205C22—41no—
206C22—41no—
207C22—41no—
208C22—942no—
209C22—1881no—
210C22—1882no—
211C22—1882no—
212C22—1881no—
213C22C2×(C2×D47)⋊C411yescharacteristic
214C4—21no—
215C4—21no—
216C4—21no—
217C4—82no—
218C4—1881no—
219C4—1881no—
220C4—1881no—
221C4#1309393811yescharacteristic
222C4#1309393811yescharacteristic
223C2—21no—
224C2—41no—
225C2—41no—
226C2—41no—
227C2—1882no—
228C2C2×#1309393811yescharacteristic
subgroupG/H
centerC4#13093938
commutatorC23×C47C22×C4
FrattiniC2×D4C22×D47
FittingC47×#410C2
socleC2×C47C2×#99
hypercenter#410D47
hypocenterC47#2120
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×#41 ◁ #410

Complements

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

NH ≅ G/Ntype
2. #15689107C2semidirect
3. #15688912C2semidirect
4. #15688909C2semidirect
5. C47×#410C2semidirect
6. C22×C4×D47C4semidirect
8. #13094005C4semidirect
12. #13093992C4semidirect
16. #13093983C4semidirect
117. #410D47semidirect
120. C47#2120semidirect