Finite Group Databasebeta

← #24994137

Subgroups — #24994137

Order 11008.

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

normal subgroups only

This group has 422 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#19144975C211yesmaximal, characteristic
2#19137776C211yesmaximal, characteristic
3#19133147C212yesmaximal
4#19132461C212yesmaximal
5C43×#1558C211yesmaximal, characteristic
6#14583456C2211yescharacteristic
7#14583267—22no—
8#14583249C414yescomplemented
9#14582908—22no—
10C4×#10621877C2211yescharacteristic
11#14582806—22no—
12#14582785—24no—
13#14582767C2212yes—
14#14582637—24no—
15C2×C4⋊Q8×C43C2211yescharacteristic
16C43×#432C2212yes—
17C43×#333—22no—
18C2×#10621877—21no—
19#13063325C2×C412yes—
20#13063317—21no—
21#13063304—22no—
22C4×Dic86—22no—
23#13063284—21no—
24C2×C4⋊Dic43—22no—
25C2×C4×Dic43—22no—
26#13063249—28no—
27#13063236—21no—
28C4×C43⋊C8C2×C412yes—
29C43⋊#95—24no—
30C43⋊#95—22no—
31C43⋊#95—22no—
32C43⋊#95D414yes—
33C22×Q8×C43D412yes—
34C4⋊Q8×C43—22no—
35C4⋊Q8×C43C2×C412yes—
36C4⋊Q8×C43D412yes—
37C2×C4⋊C4×C43—22no—
38C2×C42×C43C2311yescharacteristic
39C4⋊C8×C43—22no—
40C22⋊C8×C43—22no—
41#97×C43—22no—
42C2×Q8×C43—22no—
43C2×Q8×C43—42no—
44C2×Q8×C43—42no—
45C2×Q8×C43C22⋊C414yes—
46C22×C4×C43—22no—
47C22×C4×C43C2×D411yescharacteristic
48C22×C4×C43C2×D412yes—
49C22×Dic43—24no—
50C2×Dic86—22no—
51C2×C8×C43—42no—
52C4⋊C4×C43—24no—
53C4⋊C4×C43—24no—
54C42×C43C22×C411yescharacteristic
55C42×C43C2×D411yescharacteristic
56C42×C43#4112yes—
57C22⋊Dic43—41no—
58C4⋊Dic43—22no—
59C4⋊Dic43—22no—
60C4⋊Dic43—82no—
61Dic43⋊C4—42no—
62C4×Dic43—41no—
63C4×Dic43—82no—
64#10621877—42no—
65C2×C43⋊C8—22no—
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×C43C2×C22⋊C411yescharacteristic
75C2×C4×C43C4×D412yes—
76C2×C4×C43#12112yes—
77C2×C4×C43#12311yescharacteristic
78C2×Dic43—48no—
79C2×Dic43—42no—
80C2×Dic43—44no—
81Dic86—82no—
82C8×C43—82no—
83C43⋊C8—42no—
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—
93Dic43—84no—
94Dic43—82no—
95#3139—431no—
96#2381—431no—
97#1558D4311yescharacteristic
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#432C2×D4312yes—
108#419—862no—
109C4×M16—431no—
110#391—862no—
111#387—864no—
112#383—432no—
113#333—22no—
114#328—864no—
115C43#942611yescharacteristic, complemented, Sylow
116C22×Q8D17212yes—
117C2×M16—861no—
118C4⋊Q8—22no—
119C4⋊Q8—432no—
120C4⋊Q8C4×D4312yes—
121C4⋊Q8C22⋊D4312yes—
122#125—861no—
123C22⋊Q8—862no—
124C4×Q8—862no—
125#117—861no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—862no—
128C2×C42—862no—
129C2×C42C22×D4311yescharacteristic
130C4⋊C8—22no—
131#103—868no—
132C22⋊C8—22no—
133#97—22no—
134#97—861no—
135C4×C8—432no—
136#95—434no—
137#95—864no—
138#95—862no—
139#95—862no—
140C2×Q8—22no—
141C2×Q8—42no—
142C2×Q8—42no—
143C2×Q8—862no—
144C2×Q8(C2×D43)⋊C414yes—
145C22×C4—22no—
146C22×C4—864no—
147C22×C4C2×D17211yescharacteristic
148C22×C4D4×D4312yes—
149M16—1722no—
150C2×C8—42no—
151C2×C8—862no—
152C4⋊C4—24no—
153C4⋊C4—24no—
154C4⋊C4—862no—
155C4⋊C4—862no—
156C4⋊C4—3442no—
157C4⋊C4—1722no—
158C22⋊C4—1721no—
159C42—3442no—
160C42—1721no—
161C42C2×C4×D4311yescharacteristic
162C42#1062190012yes—
163C42C2×C22⋊D4311yescharacteristic
164C23#1306329511yescharacteristic
165Q8—44no—
166Q8—82no—
167Q8—3442no—
168C2×C4—22no—
169C2×C4—24no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—1728no—
174C2×C4—1724no—
175C2×C4—1722no—
176C2×C4C2×(C2×D43)⋊C411yescharacteristic
177C2×C4(C22⋊D43)⋊C412yes—
178C2×C4#1306329712yes—
179C2×C4#1306330911yescharacteristic
180C8—82no—
181C8—1722no—
182C22—22no—
183C22#1458277611yescharacteristic
184C22#1458307912yes—
185C4—21no—
186C4—21no—
187C4—22no—
188C4—22no—
189C4—44no—
190C4—3444no—
191C4—3442no—
192C2—22no—
193C2#1913498111yescharacteristic
194C2#1913508712yes—
subgroupG/H
centerC22#14582776
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1558C2
socleC22×C43#386
prime radicalC23×C43#120
cosocleC2×C42×C43C23
hypercenter#1558D43
hypocenterC43#9426
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1558

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
#191377762
#191331472
#191324612
C43×#15582
#942643