Finite Group Databasebeta

← #24999353

Subgroups — #24999353

Order 11008.

554 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 554 conjugacy classes of subgroups — too many to draw. Only its 89 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#19145982C212yesmaximal, complemented
2#19135571C211yesmaximal, characteristic, complemented
3#19135424C212yesmaximal, complemented
4C43⋊#1309C211yesmaximal, characteristic, complemented
5C43×#3253C211yesmaximal, characteristic
6#14583456C2211yescharacteristic
7#14583191—22no—
8#14583179—22no—
9#14583143—24no—
10#14583104—22no—
11#14583096—22no—
12#14582923C2212yes—
13C2×#13063252—24no—
14C42×Dic43C2211yescharacteristic
15#14582660—22no—
16C43×#532C2212yes—
17C43×#476—22no—
18C43×#469—22no—
19C43×#459—22no—
20C43×#423C2211yescharacteristic
21C2×#10621883—24no—
22C2×#10621877D414yes—
23#13063325D412yes—
24#13063317—21no—
25#13063304—22no—
26C4×Dic86—22no—
27#13063284—21no—
28C2×C4×Dic43—22no—
29C2×C4×Dic43—21no—
30#13063258—24no—
31C4⋊(C43⋊C8)—22no—
32C4⋊(C43⋊C8)—22no—
33#13063252—48no—
34#13063248—24no—
35#13063246—24no—
36C2×#41×C43—22no—
37C2×D8×C43—22no—
38C2×M16×C43D412yes—
39C4⋊Q8×C43D412yes—
40#127×C43D412yes—
41#124×C43—22no—
42#121×C43—22no—
43#121×C43—22no—
44C4×D4×C43—22no—
45C4×D4×C43—22no—
46C2×C42×C43C2311yescharacteristic
47#106×C43—22no—
48C4⋊C8×C43—22no—
49#102×C43—24no—
50#41×C43—44no—
51#41×C43—44no—
52C2×Q8×C43—22no—
53C2×D4×C43—22no—
54C2×D4×C43—22no—
55C2×D4×C43—22no—
56C2×D4×C43—42no—
57C22×C4×C43—42no—
58C22×C4×C43C2×D412yes—
59C22×C4×C43C2×D411yescharacteristic
60C22×Dic43—41no—
61C2×Dic86—22no—
62D8×C43—82no—
63M16×C43—42no—
64C2×C8×C43—22no—
65C4⋊C4×C43—22no—
66C4⋊C4×C43—22no—
67C22⋊C4×C43—42no—
68C22⋊C4×C43—42no—
69C42×C43C2×D411yescharacteristic
70C42×C43C2×D412yes—
71C42×C43#4111yescharacteristic
72C22⋊Dic43—41no—
73#10621883—84no—
74C4⋊Dic43—22no—
75C4⋊Dic43—22no—
76Dic43⋊C4—42no—
77C4×Dic43—24no—
78C4×Dic43—22no—
79C4×Dic43—42no—
80C4×Dic43—41no—
81C4×Dic43—41no—
82#10621877—44no—
83C2×C43⋊C8—24no—
84C23×C43—42no—
85C23×C43#12711yescharacteristic
86Q8×C43—44no—
87D4×C43—44no—
88D4×C43—42no—
89D4×C43—42no—
90D4×C43—42no—
91D4×C43—42no—
92D4×C43—84no—
93C2×C4×C43—22no—
94C2×C4×C43—22no—
95C2×C4×C43—21no—
96C2×C4×C43—21no—
97C2×C4×C43—42no—
98C2×C4×C43—82no—
99C2×C4×C43—82no—
100C2×C4×C43#12012yes—
101C2×C4×C43#12011yescharacteristic
102C2×C4×C43#12111yescharacteristic
103C2×C4×C43#12112yes—
104C2×Dic43—44no—
105C2×Dic43—42no—
106C2×Dic43—42no—
107Dic86—42no—
108Dic86—42no—
109C8×C43—42no—
110C43⋊C8—44no—
111#10301—431nomaximal, Sylow
112C22×C43—22no—
113C22×C43—21no—
114C22×C43—82no—
115C22×C43—82no—
116C22×C43—82no—
117C22×C43#39211yescharacteristic
118C4×C43—22no—
119C4×C43—21no—
120C4×C43—82no—
121C4×C43#45312yes—
122C4×C43#45412yes—
123C4×C43#45511yescharacteristic
124C4×C43#45611yescharacteristic
125Dic43—44no—
126Dic43—82no—
127#3254—432no—
128#3253D4311yescharacteristic
129#1994—431no—
130#1962—432no—
131#1309—431no—
132C2×C43—41no—
133C2×C43—162no—
134C2×C43#200612yes—
135C2×C43#200711yescharacteristic
136#533—431no—
137#532C2×D4312yes—
138#477—862no—
139#476—22no—
140#474—862no—
141#469—22no—
142#468—864no—
143#461—862no—
144#460—862no—
145#459—22no—
146#423—432no—
147#423C2×D4311yescharacteristic
148C2×#104—864no—
149C43—431no—
150#339—862no—
151C43#1030111yescharacteristic, complemented, Sylow
152C2×#41—22no—
153C2×SD16—864no—
154C2×D8—22no—
155C2×M16—434no—
156C2×M16C22⋊D4312yes—
157C4⋊Q8—432no—
158C4⋊Q8C22⋊D4312yes—
159#127C22⋊D4312yes—
160#125—861no—
161#124—22no—
162C22⋊Q8—862no—
163#121—22no—
164#121—22no—
165C4×Q8—862no—
166C4×D4—22no—
167C4×D4—22no—
168#117—861no—
169C2×C42—862no—
170C2×C42—861no—
171C2×C42C22×D4311yescharacteristic
172#107—864no—
173#106—22no—
174C4⋊C8—22no—
175C4⋊C8—862no—
176C4⋊C8—862no—
177#104—1728no—
178#103—864no—
179#102—24no—
180#102—864no—
181#41—44no—
182#41—44no—
183C2×Q8—22no—
184C2×Q8—862no—
185C2×D4—22no—
186C2×D4—22no—
187C2×D4—22no—
188C2×D4—42no—
189C22×C4—42no—
190C22×C4—1721no—
191C22×C4D4×D4312yes—
192C22×C4C2×C22⋊D4311yescharacteristic
193SD16—3444no—
194D8—82no—
195M16—42no—
196M16—1724no—
197C2×C8—22no—
198C2×C8—864no—
199C4⋊C4—22no—
200C4⋊C4—22no—
201C4⋊C4—862no—
202C4⋊C4—862no—
203C4⋊C4—1722no—
204C22⋊C4—42no—
205C22⋊C4—42no—
206C22⋊C4—1721no—
207C42—864no—
208C42—862no—
209C42—1722no—
210C42—1721no—
211C42—1721no—
212C42D4×D4311yescharacteristic
213C42#1062190011yescharacteristic
214C42C2×C22⋊D4312yes—
215C23—42no—
216C23#1306332111yescharacteristic
217Q8—44no—
218Q8—1722no—
219Q8—1722no—
220D4—44no—
221D4—42no—
222D4—42no—
223D4—42no—
224D4—42no—
225D4—84no—
226C2×C4—22no—
227C2×C4—22no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—42no—
231C2×C4—82no—
232C2×C4—82no—
233C2×C4—1722no—
234C2×C4—1724no—
235C2×C4—1722no—
236C2×C4#1306329312yes—
237C2×C4#1306329411yescharacteristic
238C2×C4#1306329611yescharacteristic
239C2×C4#1306329712yes—
240C8—42no—
241C8—1724no—
242C22—22no—
243C22—21no—
244C22—82no—
245C22—82no—
246C22—82no—
247C22#1458280711yescharacteristic
248C4—22no—
249C4—21no—
250C4—82no—
251C4—3442no—
252C4—1724no—
253C4#1458306512yes—
254C4#1458307012yes—
255C4#1458307711yescharacteristic
256C4#1458308211yescharacteristic
257C2—41no—
258C2—162no—
259C2#1913563512yes—
260C2#1913564211yescharacteristic
subgroupG/H
centerC22#14582807
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
Fitting, prime radicalC43×#3253C2
socleC22×C43#392
hypercenter#3253D43
hypocenterC43#10301
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3253

Complements

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

NH ≅ G/Ntype
1. #19145982C2semidirect
2. #19135571C2semidirect
3. #19135424C2semidirect
4. C43⋊#1309C2semidirect
151. C43#10301semidirect

Maximal subgroups

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

subgroupindex
#191459822
#191355712
#191354242
C43⋊#13092
C43×#32532
#1030143