Finite Group Databasebeta

← #19144914

Subgroups — #19144914

Order 5504.

400 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 125 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#14583454C211yesmaximal, characteristic, complemented
2#14583447C211yesmaximal, characteristic
3#14583252C214yesmaximal, complemented
4#14583251C211yesmaximal, characteristic, complemented
5#14583250C211yesmaximal, characteristic, complemented
6#14583245C211yesmaximal, characteristic, complemented
7#14582892C214yesmaximal, complemented
8C4×C8×D43C211yesmaximal, characteristic, complemented
9C43×#486C211yesmaximal, characteristic, complemented
10C2×#10621900C2212yes—
11C2×C8×D43C2212yes—
12#13063325C2211yescharacteristic
13#13063325C2211yescharacteristic
14#13063316C2212yes—
15#13063312C2212yes—
16#13063305—21no—
17#13063301—21no—
18#13063296—21no—
19#13063296—21no—
20Q8×Dic43—21no—
21#13063290—21no—
22D4×Dic43—21no—
23D4×Dic43—21no—
24#13063283C2212yes—
25C42×D43C2211yescharacteristic
26#13063250C2214yes—
27#13063248C2214yes—
28#13063246C2214yes—
29C4×C43⋊C8C2211yescharacteristic
30C8×Dic43C2212yes—
31C4⋊Q8×C43C2211yescharacteristic
32#127×C43C2211yescharacteristic
33#102×C43C2214yes—
34C4×C8×C43C2211yescharacteristic
35C2×Q8×C43—21no—
36C2×D4×C43—21no—
37C2×D4×C43—21no—
38C2×D4×C43C2312yes—
39C2×C22⋊D43—22no—
40C22×Dic43—22no—
41#10621900—28no—
42C2×C4×D43D411yescharacteristic
43C2×C4×D43D411yescharacteristic
44C2×C4×D43C2311yescharacteristic
45C2×Dic86—21no—
46C2×Dic86C2312yes—
47C2×C8×C43C2312yes—
48C4⋊C4×C43—21no—
49C4⋊C4×C43C2312yes—
50C42×C43C2311yescharacteristic
51C22⋊Dic43—22no—
52C22⋊Dic43—22no—
53(C2×D43)⋊C4—22no—
54C4⋊Dic43—21no—
55C4⋊Dic43—21no—
56C4⋊Dic43—21no—
57C4⋊Dic43—22no—
58C4⋊Dic43C2312yes—
59Dic43⋊C4—22no—
60C4×Dic43—22no—
61C4×Dic43D411yescharacteristic
62C4×Dic43D411yescharacteristic
63C4×Dic43C2311yescharacteristic
64C2×C43⋊C8C2312yes—
65C8×D43—24no—
66C23×C43—22no—
67C22×D43C2×D411yescharacteristic
68Q8×C43—42no—
69D4×C43—24no—
70D4×C43—42no—
71D4×C43—42no—
72C2×C4×C43—22no—
73C2×C4×C43C2×D411yescharacteristic
74C2×C4×C43C2×D411yescharacteristic
75C2×C4×C43C2411yescharacteristic
76C22⋊D43—44no—
77C2×Dic43—22no—
78C2×Dic43—22no—
79C2×Dic43—44no—
80C2×Dic43C2×D411yescharacteristic
81C2×Dic43C2×D411yescharacteristic
82C2×Dic43C2×D411yescharacteristic
83C4×D43—22no—
84C4×D43—22no—
85C4×D43#4114yes—
86Dic86—24no—
87Dic86—42no—
88C8×C43—22no—
89C43⋊C8—22no—
90C22×C43—42no—
91C22×C43—42no—
92C22×C43—42no—
93C22×C43C22×D411yescharacteristic
94C2×D43—21no—
95C2×D43—21no—
96C2×D43#12412yes—
97C4×C43—42no—
98C4×C43#13512yes—
99C4×C43#13512yes—
100C4×C43C2×#4112yes—
101Dic43—21no—
102Dic43—21no—
103Dic43—42no—
104Dic43—42no—
105Dic43#12412yes—
106#3131—431nomaximal, Sylow
107C2×C43—82no—
108C2×C43C2×#12411yescharacteristic
109C2×C43C2×#13511yescharacteristic
110C2×C43C2×#13511yescharacteristic
111D43—22no—
112#533—431no—
113#532—431no—
114#488—434no—
115#487—431no—
116#487—431no—
117#486—431no—
118#486D4311yescharacteristic, complemented
119#416—434no—
120C2×C4×C8—431no—
121C43#313111yescharacteristic, complemented, Sylow
122C2×#41—432no—
123C22×C8—432no—
124C4⋊Q8—431no—
125C4⋊Q8—431no—
126C4⋊Q8C2×D4311yescharacteristic
127#127C2×D4311yescharacteristic
128#125—432no—
129#124—432no—
130C22⋊Q8—861no—
131C22⋊Q8—861no—
132#121—861no—
133#121—861no—
134C4×Q8—861no—
135C4×Q8—861no—
136C4×D4—861no—
137C4×D4—861no—
138#117—432no—
139C2×C42—431no—
140#103—434no—
141#103—434no—
142#102—434no—
143#102C2×D4314yes—
144C4×C8—432no—
145C4×C8—431no—
146C4×C8C2×D4311yescharacteristic
147#41—868no—
148C2×Q8—21no—
149C2×Q8—432no—
150C2×Q8—861no—
151C2×D4—21no—
152C2×D4—21no—
153C2×D4—862no—
154C2×D4C22×D4312yes—
155C22×C4—431no—
156C22×C4—431no—
157C22×C4—431no—
158C22×C4—862no—
159C2×C8—432no—
160C2×C8—864no—
161C2×C8C22×D4312yes—
162C4⋊C4—21no—
163C4⋊C4—432no—
164C4⋊C4—862no—
165C4⋊C4—862no—
166C4⋊C4—861no—
167C4⋊C4—861no—
168C4⋊C4—861no—
169C4⋊C4C22×D4312yes—
170C22⋊C4—862no—
171C22⋊C4—862no—
172C22⋊C4—862no—
173C42—431no—
174C42—431no—
175C42—431no—
176C42—862no—
177C42C22×D4311yescharacteristic
178C23—22no—
179C23—431no—
180Q8—42no—
181Q8—864no—
182Q8—1722no—
183D4—24no—
184D4—42no—
185D4—42no—
186D4—1724no—
187C2×C4—22no—
188C2×C4—431no—
189C2×C4—434no—
190C2×C4—431no—
191C2×C4—431no—
192C2×C4—862no—
193C2×C4—862no—
194C2×C4—862no—
195C2×C4—862no—
196C2×C4—1724no—
197C2×C4D4×D4311yescharacteristic
198C2×C4D4×D4311yescharacteristic
199C2×C4C23×D4311yescharacteristic
200C8—22no—
201C8—862no—
202C22—42no—
203C22—42no—
204C22—42no—
205C22—432no—
206C22—861no—
207C22—861no—
208C22C2×D4×D4311yescharacteristic
209C4—42no—
210C4—432no—
211C4—861no—
212C4—861no—
213C4—1722no—
214C4—1722no—
215C4#1306334412yes—
216C4#1306334612yes—
217C4#41×D4312yes—
218C2—82no—
219C2—862no—
220C2#124×D4311yescharacteristic
221C2C2×#1306334411yescharacteristic
222C2C2×#1306334611yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#486C2
socleC22×C43C22×D4
hypercenter#486D43
hypocenterC43#3131
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
1. #14583454C2semidirect
3. #14583252C2semidirect
4. #14583251C2semidirect
5. #14583250C2semidirect
6. #14583245C2semidirect
7. #14582892C2semidirect
8. C4×C8×D43C2semidirect
9. C43×#486C2semidirect
118. #486D43semidirect
121. C43#3131semidirect