Finite Group Databasebeta

← #19134820

Subgroups — #19134820

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#14583380C211yesmaximal, characteristic
2#14582939C211yesmaximal, characteristic, complemented
3C2×#13063253C211yesmaximal, characteristic
4#14582898C211yesmaximal, characteristic
5#14582668C211yesmaximal, characteristic, complemented
6#14582659C211yesmaximal, characteristic, complemented
7C43×#384C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9C2×#10621877C2211yescharacteristic
10C2×#10621877C2211yescharacteristic
11#13063290—21no—
12#13063287—21no—
13C4×C22⋊D43—22no—
14#13063284C2211yescharacteristic
15#13063283—21no—
16C4⋊C4×D43—21no—
17#13063258—21no—
18#13063256—21no—
19#13063253C414yescomplemented
20#13063248—21no—
21#13063245—21no—
22C2×C4⋊C4×C43—22no—
23C2×C4⋊C4×C43C2211yescharacteristic
24C2×C4⋊C4×C43C2211yescharacteristic
25C2×C42×C43C2211yescharacteristic
26C22×C4×C43—21no—
27C22×C4×C43—21no—
28C22×C4×C43D412yes—
29C22×C4×C43C2311yescharacteristic
30C2×C22⋊D43—21no—
31#10621898—21no—
32#10621898—21no—
33#10621898C2×C412yes—
34#10621898Q812yes—
35C2×D172D411yescharacteristic
36C2×C4×D43—21no—
37C2×C4×D43—22no—
38C2×Dic86D411yescharacteristic
39C4⋊C4×C43—21no—
40C4⋊C4×C43—21no—
41C4⋊C4×C43—21no—
42C4⋊C4×C43—21no—
43C4⋊C4×C43—44no—
44C42×C43—21no—
45C42×C43C2×C412yescomplemented
46C22⋊Dic43—21no—
47(C2×D43)⋊C4—22no—
48C4⋊Dic43D411yescharacteristic
49C4⋊Dic43D411yescharacteristic
50Dic43⋊C4—22no—
51C4×Dic43—22no—
52C4×Dic43—21no—
53#10621877—21no—
54#10621877—21no—
55#10621877—21no—
56#10621877C2×C412yescomplemented
57C2×C43⋊C8—21no—
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—22no—
65C2×C4×C43—42no—
66C2×C4×C43—42no—
67C2×C4×C43—41no—
68C2×C4×C43C22×C411yescharacteristic
69C2×C4×C43C2×D411yescharacteristic
70C2×C4×C43C2×D411yescharacteristic
71C2×C4×C43C2×Q811yescharacteristic
72C2×C4×C43#4111yescharacteristic
73C2×C4×C43#4111yescharacteristic
74C22⋊D43—22no—
75C22⋊D43—22no—
76C2×Dic43—21no—
77C2×Dic43—21no—
78C2×Dic43—21no—
79D172—21no—
80D172C4⋊C412yescomplemented
81C4×D43—22no—
82C4×D43—22no—
83C4×D43—82no—
84Dic86—21no—
85Dic86C4⋊C412yescomplemented
86C43⋊C8—22no—
87C43⋊C8—41no—
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—42no—
98C4×C43—81no—
99C4×C43C2×C4⋊C411yescharacteristic
100C4×C43C4×D411yescharacteristic
101C4×C43C22⋊Q811yescharacteristic
102C4×C43#12311yescharacteristic
103Dic43—22no—
104Dic43—41no—
105Dic43—41no—
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#384D4311yescharacteristic, complemented
118#343—431no—
119#339—431no—
120C43#185911yescharacteristic, complemented, Sylow
121C2×#41—431no—
122C2×M16—431no—
123C2×M16—431no—
124C4×Q8—861no—
125C4×D4—861no—
126C4×D4—862no—
127#117—431no—
128#117—861no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—861no—
131C2×C4⋊C4C2×D4311yescharacteristic
132C2×C4⋊C4C2×D4311yescharacteristic
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—21no—
148C22×C4—862no—
149C22×C4—861no—
150C22×C4C22⋊D4312yes—
151C22×C4C22×D4311yescharacteristic
152M16—432no—
153M16—861no—
154M16—861no—
155M16—861no—
156C2×C8—861no—
157C2×C8—861no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—21no—
161C4⋊C4—21no—
162C4⋊C4—44no—
163C4⋊C4—431no—
164C4⋊C4—431no—
165C4⋊C4—862no—
166C22⋊C4—862no—
167C22⋊C4—861no—
168C42—21no—
169C42—862no—
170C42—861no—
171C42C4×D4312yescomplemented
172C23—861no—
173C23C2×C22⋊D4311yescharacteristic
174Q8—432no—
175Q8—861no—
176D4—432no—
177D4—862no—
178D4—862no—
179D4—861no—
180C2×C4—22no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—22no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—41no—
187C2×C4—861no—
188C2×C4—862no—
189C2×C4—862no—
190C2×C4—861no—
191C2×C4—861no—
192C2×C4—3442no—
193C2×C4C2×C4×D4311yescharacteristic
194C2×C4#1062189811yescharacteristic
195C2×C4D4×D4311yescharacteristic
196C2×C4D4×D4311yescharacteristic
197C2×C4Q8×D4311yescharacteristic
198C2×C4#1062190211yescharacteristic
199C8—862no—
200C8—1721no—
201C22—21no—
202C22—21no—
203C22—862no—
204C22—1721no—
205C22—1721no—
206C22C4×C22⋊D4311yescharacteristic
207C22#1306329311yescharacteristic
208C22#1306330111yescharacteristic
209C4—24no—
210C4—42no—
211C4—81no—
212C4—862no—
213C4—1721no—
214C4—1721no—
215C4C4⋊C4×D4311yescharacteristic
216C4#1306328711yescharacteristic
217C4#1306330311yescharacteristic
218C4#1306331011yescharacteristic
219C2—21no—
220C2—21no—
221C2—1722no—
222C2#1458277011yescharacteristic
223C2#1458306611yescharacteristic
224C2#1458308111yescharacteristic
subgroupG/H
centerC22#13063293
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#384C2
socleC22×C43#120
hypercenter#384D43
hypocenterC43#1859
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #384

Complements

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

NH ≅ G/Ntype
2. #14582939C2semidirect
5. #14582668C2semidirect
6. #14582659C2semidirect
7. C43×#384C2semidirect
19. #13063253C4semidirect
45. C42×C43C2×C4semidirect
56. #10621877C2×C4semidirect
80. D172C4⋊C4semidirect
85. Dic86C4⋊C4semidirect
117. #384D43semidirect
120. C43#1859semidirect
171. C42C4×D43semidirect