Finite Group Databasebeta

← #19134822

Subgroups — #19134822

Order 5504.

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#14583379C211yesmaximal, characteristic
2#14582942C211yesmaximal, characteristic, complemented
3C2×#13063253C211yesmaximal, characteristic
4#14582901C211yesmaximal, characteristic
5#14582769C211yesmaximal, characteristic, complemented
6#14582667C211yesmaximal, characteristic, complemented
7C43×#339C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9C2×#10621877C2211yescharacteristic
10C4×Dic86—21no—
11C4×D172—21no—
12(C22⋊D43)⋊C4—22no—
13#13063283—21no—
14C2×C4⋊Dic43—22no—
15C2×C4⋊Dic43C2211yescharacteristic
16C2×C4⋊Dic43C2211yescharacteristic
17C4⋊C4×D43—21no—
18#13063258—21no—
19#13063256—21no—
20#13063253C414yescomplemented
21#13063250—21no—
22#13063247—21no—
23C2×M16×C43C2211yescharacteristic
24#117×C43C2211yescharacteristic
25C2×C42×C43C2211yescharacteristic
26C22×C4×C43—21no—
27C22×C4×C43C2311yescharacteristic
28C2×C22⋊D43—21no—
29C22×Dic43—21no—
30C22×Dic43D412yes—
31#10621898—21no—
32#10621898—21no—
33#10621898C2×C412yes—
34#10621898Q812yes—
35C2×D172D411yescharacteristic
36C2×C4×D43—21no—
37C2×C4×D43—22no—
38C2×Dic86D411yescharacteristic
39M16×C43—21no—
40M16×C43—21no—
41C2×C8×C43—21no—
42C4⋊C4×C43D411yescharacteristic
43C4⋊C4×C43D411yescharacteristic
44C22⋊C4×C43—21no—
45C42×C43—21no—
46C42×C43—21no—
47C42×C43C2×C412yescomplemented
48(C2×D43)⋊C4—22no—
49C4⋊Dic43—21no—
50C4⋊Dic43—21no—
51C4⋊Dic43—21no—
52C4⋊Dic43—21no—
53C4⋊Dic43—44no—
54Dic43⋊C4—22no—
55C4×Dic43—22no—
56#10621877—21no—
57#10621877C2×C412yescomplemented
58C2×C43⋊C8—21no—
59C23×C43C2×D411yescharacteristic
60C22×D43—21no—
61C2×C4×C43—22no—
62C2×C4×C43—22no—
63C2×C4×C43—22no—
64C2×C4×C43—21no—
65C2×C4×C43—21no—
66C2×C4×C43C22×C411yescharacteristic
67C2×C4×C43C2×D411yescharacteristic
68C2×C4×C43C2×D411yescharacteristic
69C2×C4×C43C2×Q811yescharacteristic
70C2×C4×C43#4111yescharacteristic
71C2×C4×C43#4111yescharacteristic
72C22⋊D43—22no—
73C22⋊D43—22no—
74C2×Dic43—21no—
75C2×Dic43—22no—
76C2×Dic43—42no—
77C2×Dic43—42no—
78C2×Dic43—41no—
79D172—21no—
80D172C4⋊C412yescomplemented
81C4×D43—22no—
82C4×D43—22no—
83C4×D43—82no—
84Dic86—21no—
85Dic86C4⋊C412yescomplemented
86C8×C43—41no—
87C43⋊C8—22no—
88C22×C43—21no—
89C22×C43—21no—
90C22×C43C4×D411yescharacteristic
91C22×C43#12011yescharacteristic
92C22×C43C22⋊Q811yescharacteristic
93C2×D43—22no—
94C2×D43—41no—
95C2×D43—41no—
96C4×C43—24no—
97C4×C43—41no—
98C4×C43—41no—
99C4×C43C2×C4⋊C411yescharacteristic
100C4×C43C4×D411yescharacteristic
101C4×C43C22⋊Q811yescharacteristic
102C4×C43#12311yescharacteristic
103Dic43—22no—
104Dic43—42no—
105Dic43—81no—
106#1859—431nomaximal, Sylow
107C2×C43—21no—
108C2×C43—21no—
109C2×C43#38511yescharacteristic
110C2×C43#45311yescharacteristic
111C2×C43#45611yescharacteristic
112D43—42no—
113#520—431no—
114#428—431no—
115C2×#104—431no—
116#417—431no—
117#384—431no—
118#343—431no—
119#339D4311yescharacteristic, complemented
120C43#185911yescharacteristic, complemented, Sylow
121C2×#41—431no—
122C2×M16—431no—
123C2×M16C2×D4311yescharacteristic
124C4×Q8—861no—
125C4×D4—861no—
126C4×D4—862no—
127#117—861no—
128#117C2×D4311yescharacteristic
129C2×C4⋊C4—431no—
130C2×C4⋊C4—431no—
131C2×C4⋊C4—861no—
132C2×C4⋊C4—862no—
133C2×C42C2×D4311yescharacteristic
134#107—861no—
135#106—861no—
136#104—434no—
137#103—861no—
138#102—861no—
139#41—432no—
140#41—432no—
141#41—861no—
142#41—861no—
143C2×Q8—431no—
144C2×D4—431no—
145C2×D4—861no—
146C22×C4—21no—
147C22×C4—432no—
148C22×C4—862no—
149C22×C4—861no—
150C22×C4—861no—
151C22×C4C22×D4311yescharacteristic
152M16—21no—
153M16—21no—
154M16—432no—
155M16—861no—
156C2×C8—21no—
157C2×C8—861no—
158C4⋊C4—862no—
159C4⋊C4—861no—
160C4⋊C4—861no—
161C4⋊C4—861no—
162C4⋊C4—861no—
163C4⋊C4—1724no—
164C4⋊C4D17211yescharacteristic
165C4⋊C4D17211yescharacteristic
166C22⋊C4—21no—
167C22⋊C4—862no—
168C42—21no—
169C42—21no—
170C42—862no—
171C42C4×D4312yescomplemented
172C23—861no—
173C23D4×D4311yescharacteristic
174Q8—432no—
175Q8—861no—
176D4—432no—
177D4—862no—
178D4—862no—
179D4—861no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—21no—
184C2×C4—21no—
185C2×C4—861no—
186C2×C4—862no—
187C2×C4—862no—
188C2×C4—862no—
189C2×C4—3442no—
190C2×C4—1722no—
191C2×C4—1721no—
192C2×C4—1722no—
193C2×C4C2×C4×D4311yescharacteristic
194C2×C4C2×D17211yescharacteristic
195C2×C4#1062189811yescharacteristic
196C2×C4D4×D4311yescharacteristic
197C2×C4#1062190011yescharacteristic
198C2×C4Q8×D4311yescharacteristic
199C8—41no—
200C8—862no—
201C22—21no—
202C22—21no—
203C22—862no—
204C22—1721no—
205C22—1721no—
206C22(C22⋊D43)⋊C411yescharacteristic
207C22#1306329511yescharacteristic
208C22#1306330311yescharacteristic
209C4—24no—
210C4—41no—
211C4—41no—
212C4—862no—
213C4—3441no—
214C4—1722no—
215C4C4⋊C4×D4311yescharacteristic
216C4C4×D17211yescharacteristic
217C4#1306330511yescharacteristic
218C4#1306330711yescharacteristic
219C2—21no—
220C2—21no—
221C2—1722no—
222C2#1458277311yescharacteristic
223C2#1458306811yescharacteristic
224C2#1458308311yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#339C2
socleC22×C43#120
hypercenter#339D43
hypocenterC43#1859
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #339

Complements

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

NH ≅ G/Ntype
2. #14582942C2semidirect
5. #14582769C2semidirect
6. #14582667C2semidirect
7. C43×#339C2semidirect
20. #13063253C4semidirect
47. C42×C43C2×C4semidirect
57. #10621877C2×C4semidirect
80. D172C4⋊C4semidirect
85. Dic86C4⋊C4semidirect
119. #339D43semidirect
120. C43#1859semidirect
171. C42C4×D43semidirect