Finite Group Databasebeta

← #24994132

Subgroups — #24994132

Order 11008.

534 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 95 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#19144969C211yesmaximal, characteristic
2#19137772C211yesmaximal, characteristic
3#19133147C212yesmaximal, complemented
4#19132461C212yesmaximal, complemented
5C43×#1555C211yesmaximal, characteristic
6#14583456C2211yescharacteristic
7#14583263—22no—
8#14583245C414yescomplemented
9#14582904—22no—
10C4×#10621877C2211yescharacteristic
11#14582779—24no—
12#14582779—22no—
13#14582767C2212yes—
14#14582637—24no—
15C2×#127×C43C2211yescharacteristic
16C43×#432C2212yes—
17C43×#331—22no—
18C23×Dic43—22no—
19C2×#10621877—21no—
20#13063325C2×C412yescomplemented
21#13063317—21no—
22#13063304—22no—
23C4×Dic86—22no—
24#13063284—21no—
25C2×C22⋊Dic43—24no—
26C2×C22⋊Dic43—22no—
27#13063246—28no—
28#13063236—21no—
29C4×C43⋊C8C2×C412yescomplemented
30C43⋊#95—22no—
31C43⋊#95—22no—
32C43⋊#95D414yes—
33C22×D4×C43—22no—
34C22×D4×C43D412yes—
35#127×C43—22no—
36#127×C43C2×C412yes—
37#127×C43D412yes—
38C2×C42×C43C2311yescharacteristic
39C4⋊C8×C43—22no—
40C22⋊C8×C43—22no—
41#97×C43—22no—
42C24×C43—22no—
43C2×D4×C43—24no—
44C2×D4×C43—24no—
45C2×D4×C43—22no—
46C2×D4×C43—42no—
47C2×D4×C43—42no—
48C2×D4×C43—82no—
49C2×D4×C43—82no—
50C2×D4×C43C22⋊C414yes—
51C22×C4×C43C2×D411yescharacteristic
52C22×C4×C43C2×D412yes—
53C22×Dic43—24no—
54C22×Dic43—84no—
55C22×Dic43—82no—
56C2×Dic86—22no—
57C2×C8×C43—42no—
58C42×C43C22×C411yescharacteristic
59C42×C43C2×D411yescharacteristic
60C42×C43#4112yes—
61C22⋊Dic43—41no—
62C22⋊Dic43—84no—
63C22⋊Dic43—82no—
64C4⋊Dic43—22no—
65C4⋊Dic43—22no—
66Dic43⋊C4—42no—
67C4×Dic43—41no—
68#10621877—42no—
69C2×C43⋊C8—22no—
70C23×C43—24no—
71C23×C43—44no—
72C23×C43—44no—
73C23×C43—42no—
74C23×C43—42no—
75C23×C43#12011yescharacteristic
76D4×C43—44no—
77D4×C43—82no—
78D4×C43—84no—
79D4×C43—84no—
80C2×C4×C43—22no—
81C2×C4×C43—42no—
82C2×C4×C43C2×C22⋊C411yescharacteristic
83C2×C4×C43C4×D412yes—
84C2×C4×C43#12112yes—
85C2×C4×C43#12311yescharacteristic
86C2×Dic43—48no—
87C2×Dic43—42no—
88C2×Dic43—44no—
89C2×Dic43—88no—
90Dic86—82no—
91C8×C43—82no—
92C43⋊C8—42no—
93#9425—431nomaximal, Sylow
94C22×C43—22no—
95C22×C43—44no—
96C22×C43—48no—
97C22×C43—82no—
98C22×C43—84no—
99C22×C43—82no—
100C22×C43#38611yescharacteristic
101C22×C43#45512yes—
102C4×C43—21no—
103C4×C43—21no—
104C4×C43—22no—
105C4×C43—22no—
106Dic43—84no—
107Dic43—82no—
108#3138—431no—
109#2380—431no—
110#1555D4311yescharacteristic
111#1515—432no—
112#1288—432no—
113C2×C43—22no—
114C2×C43—84no—
115C2×C43#188511yescharacteristic
116C2×C43#190412yes—
117#533—431no—
118C2×#127C2×D4311yescharacteristic
119#490—862no—
120#486—434no—
121#432C2×D4312yes—
122#418—862no—
123C4×M16—431no—
124#386—864no—
125#386—862no—
126#383—432no—
127#331—22no—
128#328—864no—
129C43#942511yescharacteristic, complemented, Sylow
130C22×D4—22no—
131C22×D4D17212yes—
132C23×C4—862no—
133C2×M16—861no—
134C4⋊Q8—432no—
135#127—22no—
136#127C4×D4312yes—
137#127C22⋊D4312yes—
138#125—861no—
139C22⋊Q8—862no—
140C4×Q8—862no—
141#117—861no—
142C2×C22⋊C4—864no—
143C2×C22⋊C4—862no—
144C2×C42C22×D4311yescharacteristic
145C4⋊C8—22no—
146#102—868no—
147C22⋊C8—22no—
148#97—22no—
149#97—861no—
150C4×C8—432no—
151#95—434no—
152#95—862no—
153#95—862no—
154C24—22no—
155C2×Q8—862no—
156C2×D4—24no—
157C2×D4—24no—
158C2×D4—22no—
159C2×D4—42no—
160C2×D4—42no—
161C2×D4—82no—
162C2×D4—82no—
163C2×D4(C2×D43)⋊C414yes—
164C22×C4—864no—
165C22×C4—3444no—
166C22×C4—3442no—
167C22×C4C2×D17211yescharacteristic
168C22×C4D4×D4312yes—
169M16—1722no—
170C2×C8—42no—
171C2×C8—862no—
172C4⋊C4—862no—
173C4⋊C4—862no—
174C4⋊C4—1722no—
175C22⋊C4—3444no—
176C22⋊C4—3442no—
177C22⋊C4—1721no—
178C42—1721no—
179C42C2×C4×D4311yescharacteristic
180C42#1062190012yes—
181C42C2×C22⋊D4311yescharacteristic
182C23—24no—
183C23—44no—
184C23—44no—
185C23—42no—
186C23—42no—
187C23#1306329511yescharacteristic
188Q8—3442no—
189D4—44no—
190D4—82no—
191D4—84no—
192D4—84no—
193C2×C4—22no—
194C2×C4—42no—
195C2×C4—3448no—
196C2×C4—1728no—
197C2×C4—1724no—
198C2×C4—1722no—
199C2×C4C2×(C2×D43)⋊C411yescharacteristic
200C2×C4(C22⋊D43)⋊C412yes—
201C2×C4#1306329712yes—
202C2×C4#1306330911yescharacteristic
203C8—82no—
204C8—1722no—
205C22—22no—
206C22—44no—
207C22—48no—
208C22—82no—
209C22—82no—
210C22—84no—
211C22#1458277611yescharacteristic
212C22#1458307912yes—
213C4—21no—
214C4—21no—
215C4—22no—
216C4—22no—
217C4—3444no—
218C4—3442no—
219C2—22no—
220C2—84no—
221C2#1913498111yescharacteristic
222C2#1913508012yes—
subgroupG/H
centerC22#14582776
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1555C2
socleC22×C43#386
prime radicalC2×#127×C43C22
cosocleC2×C42×C43C23
hypercenter#1555D43
hypocenterC43#9425
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1555

Complements

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

NH ≅ G/Ntype
3. #19133147C2semidirect
4. #19132461C2semidirect
8. #14583245C4semidirect
20. #13063325C2×C4semidirect
29. C4×C43⋊C8C2×C4semidirect
129. C43#9425semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#191449692
#191377722
#191331472
#191324612
C43×#15552
#942543