Finite Group Databasebeta

← #24994134

Subgroups — #24994134

Order 11008.

534 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 534 conjugacy classes of subgroups — too many to draw. Only its 99 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#19133309C211yesmaximal, characteristic
3#19133145C212yesmaximal, complemented
4#19132459C212yesmaximal, complemented
5C43×#2380C211yesmaximal, characteristic
6#14583456C2211yescharacteristic
7#14583263—22no—
8#14583245C414yescomplemented
9#14582956C2212yes—
10#14582904—22no—
11C4×#10621877C2211yescharacteristic
12#14582643—22no—
13#14582635—24no—
14C2×#127×C43C2211yescharacteristic
15C43×#386—22no—
16C43×#386—24no—
17C43×#383C2212yes—
18C2×#10621877—21no—
19#13063325C2×C412yescomplemented
20#13063317—21no—
21#13063304—22no—
22C4×Dic86—22no—
23#13063284—21no—
24C4⋊(C43⋊C8)—22no—
25#13063246—28no—
26C22⋊(C43⋊C8)—22no—
27#13063236—21no—
28#13063236—22no—
29C4×C43⋊C8C2×C412yescomplemented
30C22×D4×C43—22no—
31C22×D4×C43D412yes—
32C23×C4×C43—22no—
33#127×C43—22no—
34#127×C43C2×C412yes—
35#127×C43D412yes—
36C2×C22⋊C4×C43—24no—
37C2×C22⋊C4×C43—22no—
38C2×C42×C43C2311yescharacteristic
39#95×C43—22no—
40#95×C43—22no—
41#95×C43D414yes—
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×C43—24no—
52C22×C4×C43—84no—
53C22×C4×C43—82no—
54C22×C4×C43C2×D411yescharacteristic
55C22×C4×C43C2×D412yes—
56C2×Dic86—22no—
57C22⋊C4×C43—84no—
58C22⋊C4×C43—82no—
59C42×C43C22×C411yescharacteristic
60C42×C43C2×D411yescharacteristic
61C42×C43#4112yes—
62C22⋊Dic43—41no—
63C4⋊Dic43—22no—
64C4⋊Dic43—22no—
65Dic43⋊C4—42no—
66C4×Dic43—41no—
67#10621877—42no—
68C2×C43⋊C8—22no—
69C2×C43⋊C8—42no—
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×C43—48no—
83C2×C4×C43—44no—
84C2×C4×C43—88no—
85C2×C4×C43C2×C22⋊C411yescharacteristic
86C2×C4×C43C4×D412yes—
87C2×C4×C43#12112yes—
88C2×C4×C43#12311yescharacteristic
89C2×Dic43—42no—
90Dic86—82no—
91C43⋊C8—42no—
92C43⋊C8—82no—
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—
106C4×C43—84no—
107Dic43—82no—
108#3138—431no—
109#2380D4311yescharacteristic
110#1555—431no—
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#432—432no—
122#418—862no—
123C4×M16—431no—
124#386—22no—
125#386—24no—
126#383C2×D4312yes—
127#331—862no—
128#328—864no—
129C43#942511yescharacteristic, complemented, Sylow
130C22×D4—22no—
131C22×D4C22⋊D4312yes—
132C23×C4—22no—
133C2×M16—861no—
134C4⋊Q8—432no—
135#127—22no—
136#127C4×D4312yes—
137#127D17212yes—
138#125—861no—
139C22⋊Q8—862no—
140C4×Q8—862no—
141#117—861no—
142C2×C22⋊C4—24no—
143C2×C22⋊C4—22no—
144C2×C42C22×D4311yescharacteristic
145C4⋊C8—862no—
146#102—868no—
147C22⋊C8—862no—
148#97—861no—
149#97—862no—
150C4×C8—432no—
151#95—22no—
152#95—22no—
153#95C22⋊D4314yes—
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—24no—
165C22×C4—84no—
166C22×C4—82no—
167C22×C4C2×C22⋊D4311yescharacteristic
168C22×C4C2×C22⋊D4312yes—
169M16—1722no—
170C2×C8—862no—
171C2×C8—1722no—
172C4⋊C4—862no—
173C4⋊C4—862no—
174C4⋊C4—1722no—
175C22⋊C4—84no—
176C22⋊C4—82no—
177C22⋊C4—1721no—
178C42—1721no—
179C42C2×C4×D4311yescharacteristic
180C42C2×D17211yescharacteristic
181C42#1062189812yes—
182C23—24no—
183C23—44no—
184C23—44no—
185C23—42no—
186C23—42no—
187C23#1306329411yescharacteristic
188Q8—3442no—
189D4—44no—
190D4—82no—
191D4—84no—
192D4—84no—
193C2×C4—22no—
194C2×C4—42no—
195C2×C4—48no—
196C2×C4—44no—
197C2×C4—88no—
198C2×C4—1722no—
199C2×C4C2×(C2×D43)⋊C411yescharacteristic
200C2×C4C4×C22⋊D4312yes—
201C2×C4#1306329912yes—
202C2×C4#1306330811yescharacteristic
203C8—3442no—
204C8—1722no—
205C22—22no—
206C22—44no—
207C22—48no—
208C22—82no—
209C22—82no—
210C22—84no—
211C22#1458277811yescharacteristic
212C22#1458307712yes—
213C4—21no—
214C4—21no—
215C4—22no—
216C4—22no—
217C4—84no—
218C4—3442no—
219C2—22no—
220C2—84no—
221C2#1913498311yescharacteristic
222C2#1913508212yes—
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2380C2
socleC22×C43#386
prime radicalC2×#127×C43C22
cosocleC2×C42×C43C23
hypercenter#2380D43
hypocenterC43#9425
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2380

Complements

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

NH ≅ G/Ntype
3. #19133145C2semidirect
4. #19132459C2semidirect
8. #14583245C4semidirect
19. #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
#191333092
#191331452
#191324592
C43×#23802
#942543