Finite Group Databasebeta

← #24999359

Subgroups — #24999359

Order 11008.

516 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 516 conjugacy classes of subgroups — too many to draw. Only its 87 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#19145989C211yesmaximal, characteristic, complemented
2#19145982C212yesmaximal
3#19135572C212yesmaximal, complemented
4C43⋊#1309C211yesmaximal, characteristic, complemented
5C43×#1962C211yesmaximal, characteristic
6#14583456C2212yes—
7#14583191—22no—
8#14583185—22no—
9#14583179—22no—
10#14583157—22no—
11#14583143—24no—
12#14583110—22no—
13#14583104—22no—
14#14583096—22no—
15#14582923C2212yes—
16#14582659—24no—
17C43×#532C2211yescharacteristic
18C43×#423C2211yescharacteristic
19C2×#104×C43—22no—
20C43×C43C2211yescharacteristic
21C2×Dic172—22no—
22C2×#10621883—24no—
23C2×#10621877D414yes—
24#13063325D412yes—
25#13063325D412yes—
26#13063317—22no—
27#13063304—22no—
28#13063304—22no—
29C4×Dic86—22no—
30C4×Dic86—22no—
31#13063284—22no—
32#13063258—24no—
33#13063257—22no—
34C4⋊(C43⋊C8)—22no—
35C4⋊(C43⋊C8)—22no—
36#13063250—24no—
37#13063248—24no—
38#13063246—24no—
39C2×#41×C43—21no—
40C2×M16×C43D412yes—
41C4⋊Q8×C43D411yescharacteristic
42#127×C43D411yescharacteristic
43#124×C43—21no—
44#121×C43—22no—
45C4×D4×C43—22no—
46C2×C42×C43—22no—
47C2×C42×C43—21no—
48C2×C42×C43C2311yescharacteristic
49C4⋊C8×C43—22no—
50#104×C43—44no—
51#41×C43—42no—
52#41×C43—42no—
53C2×Q8×C43—21no—
54C2×D4×C43—22no—
55C2×D4×C43—21no—
56C2×D4×C43—41no—
57C22×C4×C43—41no—
58C22×C4×C43—41no—
59C22×C4×C43C2×D412yes—
60C22×C4×C43C2×D411yescharacteristic
61C2×Dic86—22no—
62C2×Dic86—22no—
63M16×C43—42no—
64C2×C8×C43—22no—
65C4⋊C4×C43—22no—
66C22⋊C4×C43—42no—
67C42×C43—22no—
68C42×C43—24no—
69C42×C43—41no—
70C42×C43—42no—
71C42×C43C2×D411yescharacteristic
72C42×C43C2×D412yes—
73C42×C43#4111yescharacteristic
74C22⋊Dic43—42no—
75#10621883—84no—
76C4⋊Dic43—22no—
77C4⋊Dic43—22no—
78C4⋊Dic43—22no—
79C4⋊Dic43—22no—
80Dic43⋊C4—42no—
81Dic43⋊C4—42no—
82C4×Dic43—42no—
83#10621877—44no—
84C2×C43⋊C8—24no—
85Dic172—82no—
86C23×C43—41no—
87C23×C43#12711yescharacteristic
88Q8×C43—42no—
89D4×C43—42no—
90D4×C43—42no—
91D4×C43—42no—
92D4×C43—82no—
93C2×C4×C43—21no—
94C2×C4×C43—21no—
95C2×C4×C43—22no—
96C2×C4×C43—22no—
97C2×C4×C43—42no—
98C2×C4×C43—44no—
99C2×C4×C43—41no—
100C2×C4×C43—81no—
101C2×C4×C43—81no—
102C2×C4×C43#12011yescharacteristic
103C2×C4×C43#12012yes—
104C2×C4×C43#12112yes—
105C2×C4×C43#12111yescharacteristic
106C2×Dic43—42no—
107C2×Dic43—42no—
108Dic86—42no—
109Dic86—42no—
110Dic86—42no—
111Dic86—42no—
112C8×C43—42no—
113C43⋊C8—44no—
114#10302—431nomaximal, Sylow
115C22×C43—21no—
116C22×C43—22no—
117C22×C43—81no—
118C22×C43—82no—
119C22×C43#39211yescharacteristic
120C4×C43—21no—
121C4×C43—22no—
122C4×C43—44no—
123C4×C43—81no—
124C4×C43#45311yescharacteristic
125C4×C43#45411yescharacteristic
126C4×C43#45512yes—
127C4×C43#45612yes—
128Dic43—82no—
129Dic43—82no—
130#3255—431no—
131#3254—432no—
132#1994—432no—
133#1962D4311yescharacteristic
134#1309—431no—
135C2×C43—41no—
136C2×C43—161no—
137C2×C43#200611yescharacteristic
138C2×C43#200712yes—
139#533—432no—
140#532C2×D4311yescharacteristic
141#477—862no—
142#475—862no—
143#474—862no—
144#470—862no—
145#468—864no—
146#462—862no—
147#461—862no—
148#460—862no—
149#423—432no—
150#423C2×D4311yescharacteristic
151C2×#104—22no—
152C43C2×D4311yescharacteristic
153#339—864no—
154C43#1030211yescharacteristic, complemented, Sylow
155C2×#41—21no—
156C2×Q16—862no—
157C2×SD16—864no—
158C2×M16—434no—
159C2×M16C22⋊D4312yes—
160C4⋊Q8—432no—
161C4⋊Q8—432no—
162C4⋊Q8D17211yescharacteristic
163#127D17211yescharacteristic
164#125—862no—
165#124—21no—
166C22⋊Q8—862no—
167C22⋊Q8—862no—
168#121—22no—
169C4×Q8—862no—
170C4×Q8—862no—
171C4×D4—22no—
172#117—862no—
173C2×C42—22no—
174C2×C42—21no—
175C2×C42C22×D4311yescharacteristic
176#107—864no—
177#106—862no—
178C4⋊C8—22no—
179C4⋊C8—862no—
180C4⋊C8—862no—
181#104—44no—
182#103—864no—
183#103—864no—
184#102—864no—
185#41—42no—
186#41—42no—
187C2×Q8—21no—
188C2×Q8—862no—
189C2×Q8—862no—
190C2×D4—22no—
191C2×D4—21no—
192C2×D4—41no—
193C22×C4—41no—
194C22×C4—41no—
195C22×C4D4×D4312yes—
196C22×C4C2×C22⋊D4311yescharacteristic
197Q16—3442no—
198SD16—3444no—
199M16—42no—
200M16—1724no—
201C2×C8—22no—
202C2×C8—864no—
203C4⋊C4—22no—
204C4⋊C4—862no—
205C4⋊C4—862no—
206C4⋊C4—862no—
207C4⋊C4—862no—
208C4⋊C4—1722no—
209C4⋊C4—1722no—
210C22⋊C4—42no—
211C22⋊C4—1722no—
212C42—22no—
213C42—24no—
214C42—41no—
215C42—42no—
216C42—1722no—
217C42C2×D17211yescharacteristic
218C42#1062189811yescharacteristic
219C42D4×D4312yes—
220C23—41no—
221C23#1306332111yescharacteristic
222Q8—42no—
223Q8—1722no—
224Q8—1722no—
225Q8—1722no—
226Q8—1722no—
227D4—42no—
228D4—42no—
229D4—42no—
230D4—82no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—22no—
235C2×C4—42no—
236C2×C4—44no—
237C2×C4—41no—
238C2×C4—81no—
239C2×C4—81no—
240C2×C4—1722no—
241C2×C4—1722no—
242C2×C4#1306329311yescharacteristic
243C2×C4#1306329512yes—
244C2×C4#1306329812yes—
245C2×C4#1306329911yescharacteristic
246C8—42no—
247C8—1724no—
248C22—21no—
249C22—22no—
250C22—81no—
251C22—82no—
252C22#1458280811yescharacteristic
253C4—21no—
254C4—22no—
255C4—44no—
256C4—81no—
257C4—3442no—
258C4—3442no—
259C4#1458306611yescharacteristic
260C4#1458307111yescharacteristic
261C4#1458307812yes—
262C4#1458308312yes—
263C2—41no—
264C2—161no—
265C2#1913563611yescharacteristic
266C2#1913564312yes—
subgroupG/H
centerC22#14582808
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1962C2
socleC22×C43#392
prime radicalC43×#532C22
hypercenter#1962D43
hypocenterC43#10302
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1962

Complements

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

NH ≅ G/Ntype
1. #19145989C2semidirect
3. #19135572C2semidirect
4. C43⋊#1309C2semidirect
154. C43#10302semidirect

Maximal subgroups

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

subgroupindex
#191459892
#191459822
#191355722
C43⋊#13092
C43×#19622
#1030243