Finite Group Databasebeta

← #24994140

Subgroups — #24994140

Order 11008.

422 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 422 conjugacy classes of subgroups — too many to draw. Only its 103 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#19137776C211yesmaximal, characteristic
2#19133321C211yesmaximal, characteristic
3#19133146C212yesmaximal
4#19132460C212yesmaximal
5C43×#3139C211yesmaximal, characteristic
6#14582956C2212yes—
7#14582806—22no—
8#14582785—24no—
9#14582767C2212yes—
10#14582648—22no—
11#14582636—24no—
12C43×#533C2211yescharacteristic
13C2×C4⋊Q8×C43C2211yescharacteristic
14C43×#491—22no—
15C43×#487C414yescomplemented
16C43×#419—22no—
17C4×M16×C43C2211yescharacteristic
18C2×C4⋊Dic43—22no—
19C2×C4×Dic43—22no—
20C4⋊(C43⋊C8)—22no—
21C22⋊(C43⋊C8)—22no—
22#13063236—22no—
23C43⋊#95—24no—
24C43⋊#95—22no—
25C43⋊#95—22no—
26C43⋊#95D414yes—
27C22×Q8×C43D412yes—
28C2×M16×C43—21no—
29C4⋊Q8×C43—22no—
30C4⋊Q8×C43C2×C412yes—
31C4⋊Q8×C43C2×C412yes—
32C4⋊Q8×C43D412yes—
33#125×C43—21no—
34C22⋊Q8×C43—22no—
35C4×Q8×C43—22no—
36#117×C43—21no—
37C2×C4⋊C4×C43—22no—
38C2×C42×C43C2311yescharacteristic
39#103×C43—28no—
40#97×C43—21no—
41C4×C8×C43C2×C412yes—
42C2×Q8×C43—22no—
43C2×Q8×C43—22no—
44C2×Q8×C43—42no—
45C2×Q8×C43—42no—
46C2×Q8×C43C22⋊C414yes—
47C22×C4×C43—22no—
48C22×C4×C43C2×D412yes—
49C22×C4×C43C2×D411yescharacteristic
50C22×Dic43—24no—
51M16×C43—42no—
52C2×C8×C43—22no—
53C4⋊C4×C43—24no—
54C4⋊C4×C43—24no—
55C4⋊C4×C43—22no—
56C4⋊C4×C43—22no—
57C4⋊C4×C43—42no—
58C22⋊C4×C43—41no—
59C42×C43—41no—
60C42×C43C22×C411yescharacteristic
61C42×C43C2×D411yescharacteristic
62C42×C43#4112yes—
63C4⋊Dic43—82no—
64C4×Dic43—82no—
65C2×C43⋊C8—42no—
66C23×C43#12011yescharacteristic
67Q8×C43—44no—
68Q8×C43—82no—
69Q8×C43—82no—
70C2×C4×C43—22no—
71C2×C4×C43—24no—
72C2×C4×C43—42no—
73C2×C4×C43—42no—
74C2×C4×C43—42no—
75C2×C4×C43—42no—
76C2×C4×C43C2×C22⋊C411yescharacteristic
77C2×C4×C43C4×D412yes—
78C2×C4×C43#12112yes—
79C2×C4×C43#12311yescharacteristic
80C2×Dic43—48no—
81C2×Dic43—44no—
82C8×C43—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—82no—
94Dic43—84no—
95#3139D4311yescharacteristic
96#2381—431no—
97#1558—431no—
98#1515—432no—
99#1288—432no—
100C2×C43—22no—
101C2×C43#188511yescharacteristic
102C2×C43#190512yes—
103#533C2×D4311yescharacteristic
104C2×C4⋊Q8C2×D4311yescharacteristic
105#491—22no—
106#487Dic4314yescomplemented
107#432—432no—
108#419—22no—
109C4×M16C2×D4311yescharacteristic
110#391—862no—
111#387—864no—
112#383—432no—
113#333—862no—
114#328—864no—
115C43#942611yescharacteristic, complemented, Sylow
116C22×Q8C22⋊D4312yes—
117C2×M16—21no—
118C4⋊Q8—22no—
119C4⋊Q8C2×Dic4312yes—
120C4⋊Q8C2×Dic4312yes—
121C4⋊Q8C22⋊D4312yes—
122#125—21no—
123C22⋊Q8—22no—
124C4×Q8—22no—
125#117—21no—
126C2×C4⋊C4—22no—
127C2×C4⋊C4—862no—
128C2×C42—862no—
129C2×C42C22×D4311yescharacteristic
130C4⋊C8—862no—
131#103—28no—
132C22⋊C8—862no—
133#97—21no—
134#97—862no—
135C4×C8C2×Dic4312yes—
136#95—434no—
137#95—864no—
138#95—862no—
139#95—862no—
140C2×Q8—22no—
141C2×Q8—22no—
142C2×Q8—42no—
143C2×Q8—42no—
144C2×Q8C22⋊Dic4314yes—
145C22×C4—22no—
146C22×C4—864no—
147C22×C4D4×D4312yes—
148C22×C4C2×C22⋊D4311yescharacteristic
149M16—42no—
150C2×C8—22no—
151C2×C8—1722no—
152C4⋊C4—24no—
153C4⋊C4—24no—
154C4⋊C4—22no—
155C4⋊C4—22no—
156C4⋊C4—42no—
157C4⋊C4—3442no—
158C22⋊C4—41no—
159C42—41no—
160C42—3442no—
161C42#1062190012yes—
162C42C22×Dic4311yescharacteristic
163C42C2×C22⋊D4311yescharacteristic
164C23#1306329311yescharacteristic
165Q8—44no—
166Q8—82no—
167Q8—82no—
168C2×C4—22no—
169C2×C4—24no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—1728no—
175C2×C4—1724no—
176C2×C4C2×C22⋊Dic4311yescharacteristic
177C2×C4D4×Dic4312yes—
178C2×C4#1306329712yes—
179C2×C4#1306330611yescharacteristic
180C8—42no—
181C8—3442no—
182C22—22no—
183C22#1458277911yescharacteristic
184C22#1458307612yes—
185C4—21no—
186C4—21no—
187C4—22no—
188C4—22no—
189C4—44no—
190C4—82no—
191C4—3444no—
192C2—22no—
193C2#1913498411yescharacteristic
194C2#1913509112yes—
subgroupG/H
centerC22#14582779
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#3139C2
socleC22×C43#386
prime radicalC23×C43#120
cosocleC2×C42×C43C23
hypercenter#3139D43
hypocenterC43#9426
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3139

Complements

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

NH ≅ G/Ntype
15. C43×#487C4semidirect
106. #487Dic43semidirect
115. C43#9426semidirect

Maximal subgroups

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

subgroupindex
#191377762
#191333212
#191331462
#191324602
C43×#31392
#942643