Finite Group Databasebeta

← #19135119

Subgroups — #19135119

Order 5504.

344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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#14583665C211yesmaximal, characteristic, complemented
2#14583466C211yesmaximal, characteristic
3#14582904C211yesmaximal, characteristic, complemented
4#14582872C211yesmaximal, characteristic, complemented
5#14582656C211yesmaximal, characteristic, complemented
6#14582655C211yesmaximal, characteristic, complemented
7C43×#418C211yesmaximal, characteristic, complemented
8C2×#10621898C2211yescharacteristic
9#13063333—22no—
10#13063331—22no—
11C2×#10621877C2211yescharacteristic
12M16×D43—22no—
13#13063321C412yescomplemented
14#13063312C412yescomplemented
15#13063296—22no—
16#13063294—22no—
17#13063284C2211yescharacteristic
18#13063284C2211yescharacteristic
19#13063246—22no—
20#13063239—22no—
21C22×D4×C43C2211yescharacteristic
22C2×M16×C43C2211yescharacteristic
23#117×C43C2211yescharacteristic
24#102×C43—22no—
25C24×C43—21no—
26C2×D4×C43—21no—
27C2×D4×C43—21no—
28C2×D4×C43—21no—
29C2×D4×C43—21no—
30C2×D4×C43—21no—
31C2×D4×C43C2×C412yes—
32C22×C4×C43C2311yescharacteristic
33C2×C22⋊D43—24no—
34C2×C22⋊D43D412yes—
35#10621898—21no—
36#10621898—21no—
37#10621898—21no—
38#10621898—21no—
39C2×D172C2×C411yescharacteristic
40C2×C4×D43D412yes—
41C2×Dic86C2×C411yescharacteristic
42M16×C43—21no—
43M16×C43—21no—
44C2×C8×C43D412yescomplemented
45C4⋊C4×C43—21no—
46C22⋊C4×C43—21no—
47C42×C43—21no—
48C22⋊Dic43—24no—
49C22⋊Dic43—21no—
50C22⋊Dic43—21no—
51C4⋊Dic43—21no—
52C4⋊Dic43—21no—
53C4×Dic43—21no—
54C4×Dic43C2×C412yes—
55#10621877—21no—
56#10621877—21no—
57C2×C43⋊C8D412yescomplemented
58#10621872—24no—
59C8×D43—24no—
60C23×C43—22no—
61C23×C43—41no—
62C23×C43—41no—
63C23×C43—82no—
64C23×C43C2×D411yescharacteristic
65C22×D43C22⋊C412yes—
66D4×C43—22no—
67D4×C43—22no—
68D4×C43—41no—
69D4×C43—41no—
70C2×C4×C43—41no—
71C2×C4×C43C22×C411yescharacteristic
72C2×C4×C43C2×D411yescharacteristic
73C2×C4×C43C2×D411yescharacteristic
74C2×C4×C43C2×D411yescharacteristic
75C2×C4×C43#4111yescharacteristic
76C2×C4×C43#4111yescharacteristic
77C22⋊D43—22no—
78C22⋊D43—22no—
79C22⋊D43—84no—
80C2×Dic43—22no—
81C2×Dic43—41no—
82C2×Dic43C22⋊C412yes—
83D172—21no—
84D172—21no—
85C4×D43—22no—
86C4×D43—22no—
87Dic86—21no—
88Dic86—21no—
89C8×C43—22no—
90C43⋊C8—22no—
91C22×C43—41no—
92C22×C43—44no—
93C22×C43—42no—
94C22×C43—82no—
95C22×C43—82no—
96C22×C43C2×C22⋊C411yescharacteristic
97C22×C43#12111yescharacteristic
98C22×C43#12111yescharacteristic
99C2×D43—22no—
100C2×D43—42no—
101C4×C43—81no—
102C4×C43C4×D411yescharacteristic
103C4×C43C4×D411yescharacteristic
104C4×C43#12011yescharacteristic
105C4×C43#12311yescharacteristic
106Dic43—22no—
107Dic43—42no—
108Dic43—81no—
109#1910—431nomaximal, Sylow
110C2×C43—21no—
111C2×C43—21no—
112C2×C43—21no—
113C2×C43—82no—
114C2×C43#38611yescharacteristic
115D43—42no—
116#568—431no—
117#535—431no—
118#418—431no—
119#418D4311yescharacteristic, complemented
120#410—431no—
121H(3,ℤ/4)—431no—
122H(3,ℤ/4)—431no—
123C43#191011yescharacteristic, complemented, Sylow
124C2×#41—431no—
125C22×D4C2×D4311yescharacteristic
126#131—862no—
127#131—862no—
128C2×M16—431no—
129C2×M16—862no—
130C2×M16C2×D4311yescharacteristic
131#127—432no—
132#124—432no—
133#121—862no—
134#120—862no—
135#117—431no—
136#117—431no—
137#117C2×D4311yescharacteristic
138#102—22no—
139#102—862no—
140#99—862no—
141C24—21no—
142#41—861no—
143#41—861no—
144#41—861no—
145#41—861no—
146C2×Q8—431no—
147C2×D4—21no—
148C2×D4—21no—
149C2×D4—21no—
150C2×D4—21no—
151C2×D4—21no—
152C2×D4—432no—
153C2×D4—431no—
154C2×D4—864no—
155C2×D4C4×D4312yes—
156C22×C4—432no—
157C22×C4C22×D4311yescharacteristic
158M16—21no—
159M16—21no—
160M16—864no—
161M16—861no—
162M16—861no—
163C2×C8—432no—
164C2×C8—864no—
165C2×C8C22⋊D4312yescomplemented
166C4⋊C4—21no—
167C4⋊C4—861no—
168C4⋊C4—861no—
169C22⋊C4—21no—
170C22⋊C4—864no—
171C22⋊C4—861no—
172C22⋊C4—861no—
173C42—21no—
174C42—432no—
175C42—861no—
176C23—22no—
177C23—41no—
178C23—41no—
179C23—82no—
180C23—432no—
181C23D4×D4311yescharacteristic
182Q8—861no—
183Q8—861no—
184D4—22no—
185D4—22no—
186D4—41no—
187D4—41no—
188D4—862no—
189D4—862no—
190D4—861no—
191D4—861no—
192D4—3444no—
193C2×C4—41no—
194C2×C4—432no—
195C2×C4—862no—
196C2×C4—862no—
197C2×C4—862no—
198C2×C4—1721no—
199C2×C4C2×C4×D4311yescharacteristic
200C2×C4#1062189811yescharacteristic
201C2×C4D4×D4311yescharacteristic
202C2×C4D4×D4311yescharacteristic
203C2×C4#1062190011yescharacteristic
204C2×C4C2×C22⋊D4311yescharacteristic
205C8—22no—
206C8—862no—
207C22—41no—
208C22—44no—
209C22—42no—
210C22—82no—
211C22—82no—
212C22—862no—
213C22—1722no—
214C22C22⋊C4×D4311yescharacteristic
215C22#1306329611yescharacteristic
216C22#1306329811yescharacteristic
217C4—81no—
218C4—862no—
219C4—3441no—
220C4—1722no—
221C4(C22⋊D43)⋊C411yescharacteristic
222C4C4×C22⋊D4311yescharacteristic
223C4#1306329311yescharacteristic
224C4#1306330711yescharacteristic
225C2—21no—
226C2—21no—
227C2—21no—
228C2—82no—
229C2—1722no—
230C2#1458277511yescharacteristic
subgroupG/H
centerC2#14582775
commutatorC2×C4×C43C22×C4
FrattiniC22×C4C22×D43
FittingC43×#418C2
socleC2×C43#386
hypercenter#418D43
hypocenterC43#1910
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #418

Complements

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

NH ≅ G/Ntype
1. #14583665C2semidirect
3. #14582904C2semidirect
4. #14582872C2semidirect
5. #14582656C2semidirect
6. #14582655C2semidirect
7. C43×#418C2semidirect
13. #13063321C4semidirect
14. #13063312C4semidirect
44. C2×C8×C43D4semidirect
57. C2×C43⋊C8D4semidirect
119. #418D43semidirect
123. C43#1910semidirect
165. C2×C8C22⋊D43semidirect