Finite Group Databasebeta

← #24994139

Subgroups — #24994139

Order 11008.

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

normal subgroups only

This group has 422 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#19144975C211yesmaximal, characteristic
2#19133321C211yesmaximal, characteristic
3#19133145C212yesmaximal
4#19132459C212yesmaximal
5C43×#2381C211yesmaximal, characteristic
6#14583456C2211yescharacteristic
7#14583267—22no—
8#14583249C414yescomplemented
9#14582956C2212yes—
10#14582908—22no—
11C4×#10621877C2211yescharacteristic
12#14582648—22no—
13#14582635—24no—
14C2×C4⋊Q8×C43C2211yescharacteristic
15C43×#391—22no—
16C43×#387—24no—
17C43×#383C2212yes—
18C2×#10621877—21no—
19#13063325C2×C412yes—
20#13063317—21no—
21#13063304—22no—
22C4×Dic86—22no—
23#13063284—21no—
24C4⋊(C43⋊C8)—22no—
25#13063249—28no—
26C22⋊(C43⋊C8)—22no—
27#13063236—21no—
28#13063236—22no—
29C4×C43⋊C8C2×C412yes—
30C22×Q8×C43D412yes—
31C4⋊Q8×C43—22no—
32C4⋊Q8×C43C2×C412yes—
33C4⋊Q8×C43D412yes—
34C2×C4⋊C4×C43—22no—
35C2×C4⋊C4×C43—22no—
36C2×C42×C43—22no—
37C2×C42×C43C2311yescharacteristic
38#95×C43—24no—
39#95×C43—22no—
40#95×C43—22no—
41#95×C43D414yes—
42C2×Q8×C43—22no—
43C2×Q8×C43—42no—
44C2×Q8×C43—42no—
45C2×Q8×C43C22⋊C414yes—
46C22×C4×C43—22no—
47C22×C4×C43—24no—
48C22×C4×C43C2×D411yescharacteristic
49C22×C4×C43C2×D412yes—
50C2×Dic86—22no—
51C4⋊C4×C43—24no—
52C4⋊C4×C43—24no—
53C4⋊C4×C43—82no—
54C42×C43—82no—
55C42×C43C22×C411yescharacteristic
56C42×C43C2×D411yescharacteristic
57C42×C43#4112yes—
58C22⋊Dic43—41no—
59C4⋊Dic43—22no—
60C4⋊Dic43—22no—
61Dic43⋊C4—42no—
62C4×Dic43—41no—
63#10621877—42no—
64C2×C43⋊C8—22no—
65C2×C43⋊C8—42no—
66C23×C43#12011yescharacteristic
67Q8×C43—44no—
68Q8×C43—82no—
69C2×C4×C43—22no—
70C2×C4×C43—24no—
71C2×C4×C43—42no—
72C2×C4×C43—42no—
73C2×C4×C43—42no—
74C2×C4×C43—48no—
75C2×C4×C43—44no—
76C2×C4×C43C2×C22⋊C411yescharacteristic
77C2×C4×C43C4×D412yes—
78C2×C4×C43#12112yes—
79C2×C4×C43#12311yescharacteristic
80C2×Dic43—42no—
81Dic86—82no—
82C43⋊C8—42no—
83C43⋊C8—82no—
84#9426—431nomaximal, Sylow
85C22×C43—22no—
86C22×C43#38611yescharacteristic
87C22×C43#45512yes—
88C4×C43—21no—
89C4×C43—21no—
90C4×C43—22no—
91C4×C43—22no—
92C4×C43—44no—
93C4×C43—84no—
94Dic43—82no—
95#3139—431no—
96#2381D4311yescharacteristic
97#1558—431no—
98#1515—432no—
99#1288—432no—
100C2×C43—22no—
101C2×C43#188511yescharacteristic
102C2×C43#190512yes—
103#533—431no—
104C2×C4⋊Q8C2×D4311yescharacteristic
105#491—862no—
106#487—434no—
107#432—432no—
108#419—862no—
109C4×M16—431no—
110#391—22no—
111#387—24no—
112#383C2×D4312yes—
113#333—862no—
114#328—864no—
115C43#942611yescharacteristic, complemented, Sylow
116C22×Q8C22⋊D4312yes—
117C2×M16—861no—
118C4⋊Q8—22no—
119C4⋊Q8—432no—
120C4⋊Q8C4×D4312yes—
121C4⋊Q8D17212yes—
122#125—861no—
123C22⋊Q8—862no—
124C4×Q8—862no—
125#117—861no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—22no—
128C2×C42—22no—
129C2×C42C22×D4311yescharacteristic
130C4⋊C8—862no—
131#103—868no—
132C22⋊C8—862no—
133#97—861no—
134#97—862no—
135C4×C8—432no—
136#95—24no—
137#95—22no—
138#95—22no—
139#95C22⋊D4314yes—
140C2×Q8—22no—
141C2×Q8—42no—
142C2×Q8—42no—
143C2×Q8—862no—
144C2×Q8(C2×D43)⋊C414yes—
145C22×C4—22no—
146C22×C4—24no—
147C22×C4C2×C22⋊D4311yescharacteristic
148C22×C4C2×C22⋊D4312yes—
149M16—1722no—
150C2×C8—862no—
151C2×C8—1722no—
152C4⋊C4—24no—
153C4⋊C4—24no—
154C4⋊C4—82no—
155C4⋊C4—862no—
156C4⋊C4—862no—
157C4⋊C4—1722no—
158C22⋊C4—1721no—
159C42—82no—
160C42—1721no—
161C42C2×C4×D4311yescharacteristic
162C42C2×D17211yescharacteristic
163C42#1062189812yes—
164C23#1306329411yescharacteristic
165Q8—44no—
166Q8—82no—
167Q8—3442no—
168C2×C4—22no—
169C2×C4—24no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—48no—
174C2×C4—44no—
175C2×C4—1722no—
176C2×C4C2×(C2×D43)⋊C411yescharacteristic
177C2×C4C4×C22⋊D4312yes—
178C2×C4#1306329912yes—
179C2×C4#1306330811yescharacteristic
180C8—3442no—
181C8—1722no—
182C22—22no—
183C22#1458277811yescharacteristic
184C22#1458307712yes—
185C4—21no—
186C4—21no—
187C4—22no—
188C4—22no—
189C4—44no—
190C4—84no—
191C4—3442no—
192C2—22no—
193C2#1913498311yescharacteristic
194C2#1913508912yes—
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2381C2
socleC22×C43#386
prime radicalC23×C43#120
cosocleC2×C42×C43C23
hypercenter#2381D43
hypocenterC43#9426
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2381

Complements

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

NH ≅ G/Ntype
8. #14583249C4semidirect
115. C43#9426semidirect

Maximal subgroups

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

subgroupindex
#191449752
#191333212
#191331452
#191324592
C43×#23812
#942643