Finite Group Databasebeta

← #20243617

Subgroups — #20243617

Order 6016.

302 conjugacy classes of subgroups; only the 83 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 83 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#15689604C211yesmaximal, characteristic
2#15689165C211yesmaximal, characteristic, complemented
3C2×#13093950C211yesmaximal, characteristic
4#15689125C211yesmaximal, characteristic
5#15688992C211yesmaximal, characteristic, complemented
6#15688884C211yesmaximal, characteristic, complemented
7C47×#343C211yesmaximal, characteristic, complemented
8C2×#10625350C2211yescharacteristic
9#13093989—21no—
10#13093986—21no—
11C4×C22⋊D47—22no—
12#13093983C2211yescharacteristic
13#13093982—21no—
14C2×C4⋊Dic47C2211yescharacteristic
15C2×Dic47⋊C4—22no—
16C4⋊C4×D47—21no—
17C2×C4×Dic47C2211yescharacteristic
18#13093958—21no—
19#13093956—21no—
20#13093950C414yescomplemented
21#13093949—21no—
22#13093946—21no—
23C2×M16×C47C2211yescharacteristic
24C2×M16×C47C2211yescharacteristic
25C2×C4⋊C4×C47C2211yescharacteristic
26C22×C4×C47D412yes—
27C22×C4×C47C2311yescharacteristic
28C2×C22⋊D47—21no—
29C22×Dic47—21no—
30C22×Dic47—21no—
31#10625350—21no—
32#10625350—21no—
33#10625350C2×C412yes—
34#10625350Q812yes—
35C2×D188D411yescharacteristic
36C2×C4×D47—21no—
37C2×C4×D47—22no—
38C2×Dic94D411yescharacteristic
39M16×C47—21no—
40M16×C47—21no—
41M16×C47—21no—
42M16×C47C2×C412yescomplemented
43C2×C8×C47—21no—
44C2×C8×C47—21no—
45C4⋊C4×C47—21no—
46C4⋊C4×C47—21no—
47C22⋊Dic47—21no—
48(C2×D47)⋊C4—22no—
49C4⋊Dic47—21no—
50C4⋊Dic47—21no—
51C4⋊Dic47D411yescharacteristic
52C4⋊Dic47D411yescharacteristic
53Dic47⋊C4—22no—
54Dic47⋊C4—44no—
55C4×Dic47—22no—
56C4×Dic47—21no—
57C4×Dic47—21no—
58C4×Dic47C2×C412yescomplemented
59C23×C47C2×D411yescharacteristic
60C22×D47—21no—
61C2×C4×C47—22no—
62C2×C4×C47—42no—
63C2×C4×C47C22×C411yescharacteristic
64C2×C4×C47C2×D411yescharacteristic
65C2×C4×C47C2×D411yescharacteristic
66C2×C4×C47C2×Q811yescharacteristic
67C2×C4×C47#4111yescharacteristic
68C2×C4×C47#4111yescharacteristic
69C22⋊D47—22no—
70C22⋊D47—22no—
71C2×Dic47—22no—
72C2×Dic47—22no—
73C2×Dic47—22no—
74C2×Dic47—21no—
75C2×Dic47—21no—
76C2×Dic47—21no—
77C2×Dic47—42no—
78C2×Dic47—41no—
79D188—21no—
80D188C4⋊C412yescomplemented
81C4×D47—22no—
82C4×D47—22no—
83C4×D47—82no—
84Dic94—21no—
85Dic94C4⋊C412yescomplemented
86C8×C47—22no—
87C8×C47—41no—
88C22×C47—21no—
89C22×C47—21no—
90C22×C47C4×D411yescharacteristic
91C22×C47#12011yescharacteristic
92C22×C47C22⋊Q811yescharacteristic
93C2×D47—22no—
94C2×D47—41no—
95C2×D47—41no—
96C4×C47—42no—
97C4×C47C2×C4⋊C411yescharacteristic
98C4×C47C4×D411yescharacteristic
99C4×C47C22⋊Q811yescharacteristic
100C4×C47#12311yescharacteristic
101Dic47—24no—
102Dic47—22no—
103Dic47—41no—
104Dic47—41no—
105Dic47—81no—
106#1859—471nomaximal, Sylow
107C2×C47—21no—
108C2×C47—21no—
109C2×C47#38511yescharacteristic
110C2×C47#45311yescharacteristic
111C2×C47#45611yescharacteristic
112D47—42no—
113#520—471no—
114#428—471no—
115C2×#104—471no—
116#417—471no—
117#384—471no—
118#343D4711yescharacteristic, complemented
119#339—471no—
120C47#185911yescharacteristic, complemented, Sylow
121C2×#41—471no—
122C2×M16C2×D4711yescharacteristic
123C2×M16C2×D4711yescharacteristic
124C4×Q8—941no—
125C4×D4—941no—
126C4×D4—942no—
127#117—471no—
128#117—941no—
129C2×C4⋊C4—471no—
130C2×C4⋊C4—941no—
131C2×C4⋊C4—942no—
132C2×C4⋊C4C2×D4711yescharacteristic
133C2×C42—471no—
134#107—941no—
135#106—941no—
136#104—474no—
137#103—941no—
138#102—941no—
139#41—472no—
140#41—472no—
141#41—941no—
142#41—941no—
143C2×Q8—471no—
144C2×D4—471no—
145C2×D4—941no—
146C22×C4—942no—
147C22×C4—941no—
148C22×C4—941no—
149C22×C4—941no—
150C22×C4D18812yes—
151C22×C4C22×D4711yescharacteristic
152M16—21no—
153M16—21no—
154M16—21no—
155M16C4×D4712yescomplemented
156C2×C8—21no—
157C2×C8—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—471no—
161C4⋊C4—471no—
162C4⋊C4—942no—
163C4⋊C4—941no—
164C4⋊C4—941no—
165C4⋊C4—1884no—
166C22⋊C4—942no—
167C22⋊C4—941no—
168C42—472no—
169C42—942no—
170C42—941no—
171C42—941no—
172C23—941no—
173C23C2×D18811yescharacteristic
174Q8—472no—
175Q8—941no—
176D4—472no—
177D4—942no—
178D4—942no—
179D4—941no—
180C2×C4—22no—
181C2×C4—42no—
182C2×C4—942no—
183C2×C4—942no—
184C2×C4—942no—
185C2×C4—941no—
186C2×C4—942no—
187C2×C4—942no—
188C2×C4—941no—
189C2×C4—941no—
190C2×C4—3762no—
191C2×C4—1882no—
192C2×C4—1881no—
193C2×C4C2×C4×D4711yescharacteristic
194C2×C4#1062535011yescharacteristic
195C2×C4D4×D4711yescharacteristic
196C2×C4D4×D4711yescharacteristic
197C2×C4#1062535211yescharacteristic
198C2×C4Q8×D4711yescharacteristic
199C8—22no—
200C8—41no—
201C22—21no—
202C22—21no—
203C22—942no—
204C22—1881no—
205C22—1881no—
206C22C4×D18811yescharacteristic
207C22#1309399411yescharacteristic
208C22#1309400411yescharacteristic
209C4—42no—
210C4—944no—
211C4—942no—
212C4—3761no—
213C4—1881no—
214C4—1881no—
215C4C4⋊C4×D4711yescharacteristic
216C4(C22⋊D47)⋊C411yescharacteristic
217C4#1309400211yescharacteristic
218C4#1309400611yescharacteristic
219C2—21no—
220C2—21no—
221C2—1882no—
222C2#1568899711yescharacteristic
223C2#1568929311yescharacteristic
224C2#1568930811yescharacteristic
subgroupG/H
centerC22#13093994
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#343C2
socleC22×C47#120
hypercenter#343D47
hypocenterC47#1859
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #343

Complements

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

NH ≅ G/Ntype
2. #15689165C2semidirect
5. #15688992C2semidirect
6. #15688884C2semidirect
7. C47×#343C2semidirect
20. #13093950C4semidirect
42. M16×C47C2×C4semidirect
58. C4×Dic47C2×C4semidirect
80. D188C4⋊C4semidirect
85. Dic94C4⋊C4semidirect
118. #343D47semidirect
120. C47#1859semidirect
155. M16C4×D47semidirect