Finite Group Databasebeta

← #20243621

Subgroups — #20243621

Order 6016.

286 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 93 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#15689166C211yesmaximal, characteristic, complemented
2C2×#13093951C211yesmaximal, characteristic
3#15689124C211yesmaximal, characteristic
4#15688988C211yesmaximal, characteristic, complemented
5#15688892C211yesmaximal, characteristic, complemented
6#15688882C211yesmaximal, characteristic, complemented
7C47×#520C211yesmaximal, characteristic
8C2×#10625329C2211yescharacteristic
9C2×#10625329C2211yescharacteristic
10C2×C4⋊Dic47C2211yescharacteristic
11C2×C4×Dic47C2211yescharacteristic
12#13093957—21no—
13#13093955—21no—
14#13093951C414yescomplemented
15#13093948—21no—
16#13093945—21no—
17C47⋊#95—22no—
18C2×#41×C47C2211yescharacteristic
19C4×Q8×C47—21no—
20C4×D4×C47—21no—
21C4×D4×C47—22no—
22#117×C47—21no—
23#117×C47C2211yescharacteristic
24C2×C4⋊C4×C47—21no—
25C2×C4⋊C4×C47C2211yescharacteristic
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—22no—
35C22×C4×C47D412yes—
36C22×C4×C47C2311yescharacteristic
37C22×Dic47—21no—
38C22×Dic47—21no—
39C4⋊C4×C47—22no—
40C4⋊C4×C47—21no—
41C4⋊C4×C47—21no—
42C4⋊C4×C47D411yescharacteristic
43C4⋊C4×C47D411yescharacteristic
44C22⋊C4×C47—22no—
45C22⋊C4×C47—21no—
46C42×C47—22no—
47C42×C47—21no—
48C4⋊Dic47—21no—
49C4⋊Dic47—21no—
50C4×Dic47—21no—
51C4×Dic47C2×C412yescomplemented
52#10625329—21no—
53#10625329—21no—
54#10625329—21no—
55#10625329C2×C412yescomplemented
56C2×C47⋊C8—21no—
57C2×C47⋊C8—21no—
58C23×C47—21no—
59C23×C47C2×D411yescharacteristic
60Q8×C47—21no—
61Q8×C47C4⋊C412yes—
62D4×C47—22no—
63D4×C47—22no—
64D4×C47—21no—
65D4×C47C4⋊C412yes—
66C2×C4×C47—21no—
67C2×C4×C47—22no—
68C2×C4×C47—22no—
69C2×C4×C47—21no—
70C2×C4×C47—22no—
71C2×C4×C47—21no—
72C2×C4×C47—42no—
73C2×C4×C47—82no—
74C2×C4×C47C22×C411yescharacteristic
75C2×C4×C47C2×D411yescharacteristic
76C2×C4×C47C2×D411yescharacteristic
77C2×C4×C47C2×Q811yescharacteristic
78C2×C4×C47#4111yescharacteristic
79C2×C4×C47#4111yescharacteristic
80C2×Dic47—22no—
81C2×Dic47—41no—
82C2×Dic47—41no—
83C2×Dic47—42no—
84C2×Dic47—41no—
85C47⋊C8—22no—
86C47⋊C8—41no—
87C22×C47—21no—
88C22×C47—21no—
89C22×C47—22no—
90C22×C47—41no—
91C22×C47—41no—
92C22×C47C4×D411yescharacteristic
93C22×C47#12011yescharacteristic
94C22×C47C22⋊Q811yescharacteristic
95C4×C47—22no—
96C4×C47—41no—
97C4×C47—42no—
98C4×C47—41no—
99C4×C47C2×C4⋊C411yescharacteristic
100C4×C47C4×D411yescharacteristic
101C4×C47C22⋊Q811yescharacteristic
102C4×C47#12311yescharacteristic
103Dic47—42no—
104Dic47—81no—
105#1860—471nomaximal, Sylow
106C2×C47—21no—
107C2×C47—21no—
108C2×C47—42no—
109C2×C47#38511yescharacteristic
110C2×C47#45411yescharacteristic
111C2×C47#45511yescharacteristic
112#520D4711yescharacteristic
113#428—471no—
114C2×#104—471no—
115#417—471no—
116#382—471no—
117#343—471no—
118#339—471no—
119C47#186011yescharacteristic, complemented, Sylow
120C2×#41C2×D4711yescharacteristic
121C2×M16—471no—
122C2×M16—471no—
123C4×Q8—21no—
124C4×D4—21no—
125C4×D4—22no—
126#117—21no—
127#117C2×D4711yescharacteristic
128C2×C4⋊C4—21no—
129C2×C4⋊C4—471no—
130C2×C4⋊C4C2×D4711yescharacteristic
131C2×C42—471no—
132#107—941no—
133#106—941no—
134#104—474no—
135#103—941no—
136#102—941no—
137#95—942no—
138#41—21no—
139#41—21no—
140#41Dic9412yes—
141#41C4×D4712yes—
142C2×Q8C22⋊D4711yescharacteristic
143C2×D4—21no—
144C2×D4C22⋊D4711yescharacteristic
145C22×C4—21no—
146C22×C4—22no—
147C22×C4—941no—
148C22×C4—941no—
149C22×C4C22⋊D4712yes—
150C22×C4C22×D4711yescharacteristic
151M16—472no—
152M16—941no—
153M16—941no—
154M16—941no—
155C2×C8—941no—
156C2×C8—941no—
157C4⋊C4—22no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—941no—
161C4⋊C4—941no—
162C4⋊C4C22⋊D4711yescharacteristic
163C4⋊C4C22⋊D4711yescharacteristic
164C22⋊C4—22no—
165C22⋊C4—21no—
166C42—22no—
167C42—21no—
168C42—472no—
169C42—941no—
170C23—21no—
171C23C2×C22⋊D4711yescharacteristic
172Q8—21no—
173Q8Dic47⋊C412yes—
174D4—22no—
175D4—22no—
176D4—21no—
177D4Dic47⋊C412yes—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—22no—
181C2×C4—21no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—42no—
185C2×C4—82no—
186C2×C4—942no—
187C2×C4—1882no—
188C2×C4—1881no—
189C2×C4—1881no—
190C2×C4—1881no—
191C2×C4C2×Dic9411yescharacteristic
192C2×C4C2×C4×D4711yescharacteristic
193C2×C4#1062535011yescharacteristic
194C2×C4#1062535011yescharacteristic
195C2×C4C2×C22⋊D4711yescharacteristic
196C2×C4C2×C22⋊D4711yescharacteristic
197C8—942no—
198C8—1881no—
199C22—21no—
200C22—21no—
201C22—22no—
202C22—41no—
203C22—41no—
204C22C4×C22⋊D4711yescharacteristic
205C22#1309399311yescharacteristic
206C22#1309400311yescharacteristic
207C4—22no—
208C4—41no—
209C4—42no—
210C4—41no—
211C4—3761no—
212C4—1882no—
213C4C2×Dic47⋊C411yescharacteristic
214C4C4×C22⋊D4711yescharacteristic
215C4#1309400311yescharacteristic
216C4#1309400711yescharacteristic
217C2—21no—
218C2—21no—
219C2—42no—
220C2#1568899611yescharacteristic
221C2#1568929611yescharacteristic
222C2#1568930111yescharacteristic
subgroupG/H
centerC22#13093993
commutatorC2×C4×C47C22×C4
FrattiniC22×C4C22×D47
FittingC47×#520C2
socleC22×C47#120
hypercenter#520D47
hypocenterC47#1860
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C22×C4 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #15689166C2semidirect
4. #15688988C2semidirect
5. #15688892C2semidirect
6. #15688882C2semidirect
14. #13093951C4semidirect
51. C4×Dic47C2×C4semidirect
55. #10625329C2×C4semidirect
119. C47#1860semidirect