Finite Group Databasebeta

← #20243616

Subgroups — #20243616

Order 6016.

302 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 97 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#15689606C211yesmaximal, characteristic
2#15689165C211yesmaximal, characteristic, complemented
3#15689124C211yesmaximal, characteristic
4#15688993C211yesmaximal, characteristic, complemented
5#15688891C211yesmaximal, characteristic, complemented
6#15688883C211yesmaximal, characteristic, complemented
7C2×#104×C47C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9Q8×Dic47—21no—
10D4×Dic47—21no—
11D4×Dic47—22no—
12#13093983—21no—
13#13093983C2211yescharacteristic
14C2×C4⋊Dic47—21no—
15C2×C4⋊Dic47—22no—
16C2×C4⋊Dic47C2211yescharacteristic
17C2×C4⋊Dic47C2211yescharacteristic
18#13093958—21no—
19#13093956—21no—
20#13093948—21no—
21#13093945—21no—
22C2×#41×C47C2211yescharacteristic
23C2×M16×C47C2211yescharacteristic
24C2×C42×C47C2211yescharacteristic
25#104×C47C414yescomplemented
26#41×C47—21no—
27#41×C47—21no—
28#41×C47C2×C412yes—
29#41×C47Q812yes—
30C2×Q8×C47D411yescharacteristic
31C2×D4×C47—21no—
32C2×D4×C47D411yescharacteristic
33C22×C4×C47—21no—
34C22×C4×C47—21no—
35C22×C4×C47C2311yescharacteristic
36C22×Dic47—22no—
37C22×Dic47—21no—
38C22×Dic47D412yes—
39M16×C47—21no—
40M16×C47C2×C412yescomplemented
41C2×C8×C47—21no—
42C42×C47—21no—
43C42×C47C2×C412yescomplemented
44C22⋊Dic47—22no—
45C22⋊Dic47—21no—
46C4⋊Dic47—22no—
47C4⋊Dic47—21no—
48C4⋊Dic47—21no—
49C4⋊Dic47—21no—
50C4⋊Dic47—21no—
51C4⋊Dic47—44no—
52C4⋊Dic47D411yescharacteristic
53C4⋊Dic47D411yescharacteristic
54C4×Dic47—22no—
55C4×Dic47—21no—
56#10625329—21no—
57#10625329—21no—
58C2×C47⋊C8—21no—
59C23×C47—21no—
60C23×C47C2×D411yescharacteristic
61Q8×C47—21no—
62Q8×C47C4⋊C412yescomplemented
63D4×C47—22no—
64D4×C47—22no—
65D4×C47—21no—
66D4×C47C4⋊C412yescomplemented
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47—22no—
70C2×C4×C47—21no—
71C2×C4×C47—22no—
72C2×C4×C47—22no—
73C2×C4×C47C22×C411yescharacteristic
74C2×C4×C47C2×D411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×Q811yescharacteristic
77C2×C4×C47#4111yescharacteristic
78C2×C4×C47#4111yescharacteristic
79C2×Dic47—21no—
80C2×Dic47—22no—
81C2×Dic47—21no—
82C2×Dic47—42no—
83C2×Dic47—42no—
84C2×Dic47—41no—
85C2×Dic47—82no—
86C8×C47—22no—
87C47⋊C8—41no—
88C22×C47—21no—
89C22×C47—21no—
90C22×C47—22no—
91C22×C47—41no—
92C22×C47—41no—
93C22×C47C4×D411yescharacteristic
94C22×C47#12011yescharacteristic
95C22×C47C22⋊Q811yescharacteristic
96C4×C47—24no—
97C4×C47—22no—
98C4×C47C2×C4⋊C411yescharacteristic
99C4×C47C4×D411yescharacteristic
100C4×C47C22⋊Q811yescharacteristic
101C4×C47#12311yescharacteristic
102Dic47—42no—
103Dic47—41no—
104Dic47—41no—
105Dic47—81no—
106#1859—471nomaximal, Sylow
107C2×C47—21no—
108C2×C47—21no—
109C2×C47—42no—
110C2×C47#38511yescharacteristic
111C2×C47#45311yescharacteristic
112C2×C47#45611yescharacteristic
113#520—471no—
114#428—471no—
115C2×#104D4711yescharacteristic
116#417—471no—
117#384—471no—
118#343—471no—
119#339—471no—
120C47#185911yescharacteristic, complemented, Sylow
121C2×#41C2×D4711yescharacteristic
122C2×M16—471no—
123C2×M16C2×D4711yescharacteristic
124C4×Q8—941no—
125C4×D4—942no—
126C4×D4—941no—
127#117—471no—
128#117—941no—
129C2×C4⋊C4—471no—
130C2×C4⋊C4—471no—
131C2×C4⋊C4—941no—
132C2×C4⋊C4—942no—
133C2×C42C2×D4711yescharacteristic
134#107—941no—
135#106—941no—
136#104Dic4714yescomplemented
137#103—941no—
138#102—941no—
139#41—21no—
140#41—21no—
141#41Dic9412yes—
142#41C2×Dic4712yes—
143C2×Q8D18811yescharacteristic
144C2×D4—21no—
145C2×D4D18811yescharacteristic
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—472no—
149C22×C4—942no—
150C22×C4—941no—
151C22×C4C22×D4711yescharacteristic
152M16—21no—
153M16—941no—
154M16—941no—
155M16C2×Dic4712yescomplemented
156C2×C8—21no—
157C2×C8—941no—
158C4⋊C4—471no—
159C4⋊C4—471no—
160C4⋊C4—942no—
161C4⋊C4—941no—
162C4⋊C4—941no—
163C4⋊C4—941no—
164C4⋊C4—941no—
165C4⋊C4—1884no—
166C22⋊C4—942no—
167C22⋊C4—941no—
168C42—21no—
169C42—942no—
170C42—941no—
171C42C2×Dic4712yescomplemented
172C23—21no—
173C23D4×D4711yescharacteristic
174Q8—21no—
175Q8C4⋊Dic4712yescomplemented
176D4—22no—
177D4—22no—
178D4—21no—
179D4C4⋊Dic4712yescomplemented
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—22no—
185C2×C4—22no—
186C2×C4—941no—
187C2×C4—941no—
188C2×C4—942no—
189C2×C4—3762no—
190C2×C4—1882no—
191C2×C4—1881no—
192C2×C4—1882no—
193C2×C4C2×Dic9411yescharacteristic
194C2×C4C2×D18811yescharacteristic
195C2×C4D4×D4711yescharacteristic
196C2×C4#1062535211yescharacteristic
197C2×C4#1062535211yescharacteristic
198C2×C4C22×Dic4711yescharacteristic
199C8—22no—
200C8—1881no—
201C22—21no—
202C22—21no—
203C22—22no—
204C22—41no—
205C22—41no—
206C22D4×Dic4711yescharacteristic
207C22#1309399411yescharacteristic
208C22#1309400111yescharacteristic
209C4—24no—
210C4—22no—
211C4—3761no—
212C4—1881no—
213C4—1882no—
214C4—1881no—
215C4C2×C4⋊Dic4711yescharacteristic
216C4D4×Dic4711yescharacteristic
217C4#1309400111yescharacteristic
218C4#1309400811yescharacteristic
219C2—21no—
220C2—21no—
221C2—42no—
222C2#1568899811yescharacteristic
223C2#1568929211yescharacteristic
224C2#1568930711yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC2×#104×C47C2
socleC22×C47#120
hypercenterC2×#104D47
hypocenterC47#1859
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
2. #15689165C2semidirect
4. #15688993C2semidirect
5. #15688891C2semidirect
6. #15688883C2semidirect
25. #104×C47C4semidirect
40. M16×C47C2×C4semidirect
43. C42×C47C2×C4semidirect
62. Q8×C47C4⋊C4semidirect
66. D4×C47C4⋊C4semidirect
120. C47#1859semidirect
136. #104Dic47semidirect
155. M16C2×Dic47semidirect
171. C42C2×Dic47semidirect
175. Q8C4⋊Dic47semidirect
179. D4C4⋊Dic47semidirect