Finite Group Databasebeta

← #24991554

Subgroups — #24991554

Order 11008.

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

normal subgroups only

This group has 502 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#19145040C211yesmaximal, characteristic
2#19143666C211yesmaximal, characteristic, complemented
3#19133065C212yesmaximal, complemented
4#19132495C212yesmaximal, complemented
5C43×#1543C211yesmaximal, characteristic, complemented
6C2×#13063345—22no—
7#14583449C2211yescharacteristic
8#14583294C412yes—
9#14583291—21no—
10#14583289C412yes—
11#14583286—21no—
12#14582971—24no—
13#14582956C2212yes—
14#14582866—22no—
15C2×#13063236C2211yescharacteristic
16#14582628—24no—
17C43×#532C2211yescharacteristic
18C43×#431C2212yes—
19C43×#333—21no—
20C43×#331—21no—
21C2×#10621898—21no—
22#13063345—44no—
23#13063345—44no—
24C2×#10621885—22no—
25C2×#10621883—22no—
26C2×#10621884—22no—
27C2×#10621882—22no—
28C2×#10621877—22no—
29C22×C43⋊C8—21no—
30C22×C43⋊C8—22no—
31#13063325C2×C411yescharacteristic
32#13063322C2×C411yescharacteristic
33#13063313—21no—
34#13063299—22no—
35C4×D172—22no—
36C4⋊(C43⋊C8)D414yes—
37C22⋊(C43⋊C8)—24no—
38C22⋊(C43⋊C8)—22no—
39#13063236—21no—
40#13063236—22no—
41#13063236C2×C412yes—
42C2×#41×C43D412yes—
43C4⋊Q8×C43D411yescharacteristic
44#127×C43D411yescharacteristic
45#124×C43C2×C412yes—
46#121×C43—22no—
47C4×D4×C43—22no—
48C2×C42×C43C2311yescharacteristic
49C4⋊C8×C43—22no—
50C22⋊C8×C43—22no—
51C4×C8×C43—22no—
52#41×C43—42no—
53#41×C43—42no—
54C2×Q8×C43C22⋊C412yes—
55C2×D4×C43—22no—
56C2×D4×C43—22no—
57C2×D4×C43C22⋊C412yes—
58C22×C4×C43—22no—
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43#4112yes—
61C2×C22⋊D43—41no—
62#10621898—42no—
63#10621898—42no—
64C2×D172—21no—
65C2×D172—22no—
66C2×C4×D43—41no—
67C2×Dic86—21no—
68C2×C8×C43—42no—
69C4⋊C4×C43—22no—
70C22⋊C4×C43—24no—
71C42×C43C22×C411yescharacteristic
72C42×C43C2×D412yes—
73C42×C43C2×D411yescharacteristic
74#10621885—44no—
75#10621884—44no—
76#10621883—44no—
77#10621882—44no—
78(C2×D43)⋊C4—42no—
79C4⋊Dic43—22no—
80#10621877—82no—
81C2×C43⋊C8—24no—
82C2×C43⋊C8—22no—
83C2×C43⋊C8—24no—
84C2×C43⋊C8—82no—
85C23×C43—22no—
86C23×C43#12311yescharacteristic
87C22×D43—41no—
88Q8×C43—42no—
89D4×C43—42no—
90D4×C43—82no—
91D4×C43—82no—
92C2×C4×C43—22no—
93C2×C4×C43—22no—
94C2×C4×C43—42no—
95C2×C4×C43—42no—
96C2×C4×C43—42no—
97C2×C4×C43C2×C22⋊C411yescharacteristic
98C2×C4×C43C4×D412yes—
99C2×C4×C43#12011yescharacteristic
100C2×C4×C43#12112yes—
101C22⋊D43—81no—
102C22⋊D43—81no—
103C2×Dic43—41no—
104D172—42no—
105D172—44no—
106C4×D43—82no—
107Dic86—42no—
108C8×C43—82no—
109C43⋊C8—24no—
110C43⋊C8—44no—
111#9007—431nomaximal, Sylow
112C22×C43—22no—
113C22×C43—21no—
114C22×C43—44no—
115C22×C43—42no—
116C22×C43#38611yescharacteristic
117C2×D43—82no—
118C2×D43—81no—
119C4×C43—22no—
120C4×C43—22no—
121C4×C43—21no—
122C4×C43—42no—
123C4×C43#45312yes—
124Dic43—81no—
125#3150—431no—
126#2980—431no—
127#1543D4311yescharacteristic, complemented
128#1496—432no—
129#1302—432no—
130C2×C43—41no—
131C2×C43—82no—
132C2×C43#188112yes—
133C2×C43#188711yescharacteristic
134D43—161no—
135C2×#135—862no—
136#532—431no—
137#532C2×D4311yescharacteristic
138#497—432no—
139#497—861no—
140#496—432no—
141#496—861no—
142#435—864no—
143#432—432no—
144#431C2×D4312yes—
145#408—862no—
146C2×#97—431no—
147#333—21no—
148#331—21no—
149D4⋊C8—864no—
150C43#900711yescharacteristic, complemented, Sylow
151C2×#41—861no—
152C2×#41D17212yes—
153#135—1724no—
154#135—1724no—
155C2×Q16—862no—
156C2×SD16—862no—
157C2×SD16—862no—
158C2×D8—862no—
159C2×M16—862no—
160C22×C8—861no—
161C22×C8—862no—
162C4⋊Q8—431no—
163C4⋊Q8C22⋊D4311yescharacteristic
164#127—431no—
165#127C22⋊D4311yescharacteristic
166#124—861no—
167#124C4×D4312yes—
168#121—22no—
169#121—862no—
170C4×D4—22no—
171C4×D4—862no—
172C2×C42C22×D4311yescharacteristic
173C4⋊C8—22no—
174C4⋊C8—434no—
175C22⋊C8—22no—
176C22⋊C8—864no—
177C22⋊C8—862no—
178#97—432no—
179#97—862no—
180#97—861no—
181C4×C8—22no—
182#41—42no—
183#41—42no—
184#41—1722no—
185#41—1722no—
186C2×Q8—861no—
187C2×Q8(C2×D43)⋊C412yes—
188C2×D4—22no—
189C2×D4—22no—
190C2×D4—861no—
191C2×D4—862no—
192C2×D4—1721no—
193C2×D4(C2×D43)⋊C412yes—
194C22×C4—22no—
195C22×C4—1721no—
196C22×C4C2×D17211yescharacteristic
197C22×C4#1062190012yes—
198Q16—1724no—
199SD16—1724no—
200SD16—1724no—
201D8—1724no—
202M16—3442no—
203C2×C8—42no—
204C2×C8—864no—
205C2×C8—862no—
206C2×C8—864no—
207C2×C8—3442no—
208C4⋊C4—22no—
209C4⋊C4—862no—
210C22⋊C4—24no—
211C22⋊C4—1722no—
212C42C2×C4×D4311yescharacteristic
213C42D4×D4312yes—
214C42C2×C22⋊D4311yescharacteristic
215C23—22no—
216C23—1721no—
217C23#1306330911yescharacteristic
218Q8—42no—
219Q8—1722no—
220D4—42no—
221D4—82no—
222D4—82no—
223D4—3441no—
224D4—3441no—
225D4—1722no—
226D4—1724no—
227C2×C4—22no—
228C2×C4—22no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—3442no—
233C2×C4—1721no—
234C2×C4C2×(C2×D43)⋊C411yescharacteristic
235C2×C4(C22⋊D43)⋊C412yes—
236C2×C4#1306329511yescharacteristic
237C2×C4#1306329712yes—
238C8—82no—
239C8—864no—
240C8—1724no—
241C22—21no—
242C22—22no—
243C22—42no—
244C22—44no—
245C22—3441no—
246C22—3442no—
247C22#1458277611yescharacteristic
248C4—21no—
249C4—22no—
250C4—22no—
251C4—42no—
252C4—3441no—
253C4#1458306912yes—
254C2—41no—
255C2—82no—
256C2—6881no—
257C2#1913495512yes—
258C2#1913499111yescharacteristic
subgroupG/H
centerC2×C4#13063295
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1543C2
socleC22×C43#386
prime radical#19145040C2
cosocleC2×C42×C43C23
hypercenter#1543D43
hypocenterC43#9007
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1543

Complements

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

NH ≅ G/Ntype
2. #19143666C2semidirect
3. #19133065C2semidirect
4. #19132495C2semidirect
5. C43×#1543C2semidirect
127. #1543D43semidirect
150. C43#9007semidirect

Maximal subgroups

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

subgroupindex
#191450402
#191436662
#191330652
#191324952
C43×#15432
#900743