Finite Group Databasebeta

← #24997450

Subgroups — #24997450

Order 11008.

566 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 105 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#19144626C212yesmaximal
2#19135427C211yesmaximal, characteristic
3#19133024C212yesmaximal, complemented
4#19132424C211yesmaximal, characteristic, complemented
5C43×#2399C211yesmaximal, characteristic, complemented
6#14583449C2211yescharacteristic
7#14583217—22no—
8#14583184—22no—
9#14583099—22no—
10#14583038—22no—
11C4×#10621884—24no—
12#14582952C2212yes—
13#14582923C2211yescharacteristic
14C2×#13063253—22no—
15Q8⋊(C43⋊C8)—24no—
16C2×C4×Q8×C43C2212yes—
17C43×#398—22no—
18C43×#395—22no—
19C4×C4⋊C4×C43—22no—
20C43×#376C2211yescharacteristic
21C2×#10621898—21no—
22C2×#10621884—24no—
23C2×#10621877—21no—
24#13063325D411yescharacteristic
25#13063322D411yescharacteristic
26#13063313—21no—
27#13063299—22no—
28C4×D172—22no—
29#13063256—24no—
30C4⋊(C43⋊C8)—22no—
31C4⋊(C43⋊C8)—22no—
32#13063253—44no—
33#13063249—24no—
34#13063245—24no—
35C22⋊(C43⋊C8)—22no—
36C4×C43⋊C8D414yes—
37C22×Q8×C43D412yes—
38C4×Q8×C43—22no—
39C4×Q8×C43—22no—
40C4×Q8×C43—22no—
41C4×Q8×C43—22no—
42C2×C4⋊C4×C43—24no—
43C2×C4⋊C4×C43—22no—
44C2×C4⋊C4×C43D412yes—
45C2×C42×C43—22no—
46C2×C42×C43D412yes—
47C2×C42×C43C2311yescharacteristic
48#95×C43—22no—
49#95×C43—22no—
50#95×C43—22no—
51C2×Q8×C43—22no—
52C2×Q8×C43—22no—
53C2×Q8×C43—44no—
54C22×C4×C43—22no—
55C22×C4×C43—22no—
56C22×C4×C43—22no—
57C22×C4×C43C2×D412yes—
58C22×C4×C43C2×D411yescharacteristic
59C2×C22⋊D43—41no—
60#10621898—42no—
61#10621898—42no—
62C2×D172—22no—
63C2×D172—21no—
64C2×C4×D43—41no—
65C2×Dic86—21no—
66C4⋊C4×C43—22no—
67C4⋊C4×C43—22no—
68C4⋊C4×C43—48no—
69C4⋊C4×C43—42no—
70C4⋊C4×C43—42no—
71C42×C43—22no—
72C42×C43—42no—
73C42×C43—42no—
74C42×C43SD1614yescomplemented
75C42×C43C2×D411yescharacteristic
76C42×C43C2×D412yes—
77C42×C43#4111yescharacteristic
78#10621884—48no—
79(C2×D43)⋊C4—42no—
80C4⋊Dic43—22no—
81#10621877—42no—
82C2×C43⋊C8—24no—
83C2×C43⋊C8—41no—
84C23×C43#12011yescharacteristic
85C22×D43—41no—
86Q8×C43—24no—
87Q8×C43—24no—
88Q8×C43—42no—
89Q8×C43—42no—
90C2×C4×C43—24no—
91C2×C4×C43—24no—
92C2×C4×C43—42no—
93C2×C4×C43—44no—
94C2×C4×C43—42no—
95C2×C4×C43—42no—
96C2×C4×C43—44no—
97C2×C4×C43—42no—
98C2×C4×C43#12012yes—
99C2×C4×C43#12111yescharacteristic
100C2×C4×C43#12112yes—
101C2×C4×C43#12711yescharacteristic
102C2×C4×C43C2×SD1612yes—
103C2×C4×C43#13712yes—
104C22⋊D43—82no—
105C2×Dic43—41no—
106D172—44no—
107D172—42no—
108C4×D43—81no—
109C4×D43—81no—
110Dic86—42no—
111C43⋊C8—44no—
112C43⋊C8—81no—
113#10014—431nomaximal, Sylow
114C22×C43—22no—
115C22×C43#39211yescharacteristic
116C22×C43#44812yes—
117C2×D43—82no—
118C2×D43—81no—
119C4×C43—22no—
120C4×C43—22no—
121C4×C43—44no—
122C4×C43—44no—
123C4×C43—82no—
124C4×C43#46112yes—
125C4×C43#49211yescharacteristic
126C4×C43#49711yescharacteristic
127Dic43—81no—
128#3103—432no—
129#2399D4311yescharacteristic, complemented
130#1963—431no—
131#1487—432no—
132#1274—431no—
133C2×C43—22no—
134C2×C43#201012yes—
135C2×C43#201311yescharacteristic
136D43—161no—
137#532—431no—
138C2×C4×Q8C2×D4312yes—
139#481—862no—
140#475—862no—
141#460—862no—
142#448—862no—
143C4×SD16—864no—
144#431—432no—
145#423—431no—
146C2×#104—862no—
147#398—22no—
148#395—22no—
149C4×C4⋊C4—22no—
150#376C2×D4311yescharacteristic
151Q8⋊C8—864no—
152C43#1001411yescharacteristic, complemented, Sylow
153C2×#41—861no—
154C22×Q8C22⋊D4312yes—
155C2×SD16—864no—
156C2×M16—861no—
157C4⋊Q8—431no—
158#127—431no—
159#124—861no—
160#121—862no—
161C4×Q8—22no—
162C4×Q8—22no—
163C4×Q8—22no—
164C4×Q8—22no—
165C4×D4—862no—
166C2×C4⋊C4—24no—
167C2×C4⋊C4—22no—
168C2×C4⋊C4C22⋊D4312yes—
169C2×C42—22no—
170C2×C42C22⋊D4312yes—
171C2×C42C22×D4311yescharacteristic
172#106—864no—
173C4⋊C8—862no—
174C4⋊C8—862no—
175#104—1724no—
176#103—864no—
177#102—864no—
178C22⋊C8—862no—
179C4×C8—434no—
180#95—22no—
181#95—22no—
182#95—22no—
183#41—1722no—
184#41—1722no—
185C2×Q8—22no—
186C2×Q8—22no—
187C2×Q8—44no—
188C2×Q8—861no—
189C2×D4—862no—
190C2×D4—861no—
191C2×D4—1721no—
192C22×C4—22no—
193C22×C4—22no—
194C22×C4—22no—
195C22×C4—1721no—
196C22×C4C2×C22⋊D4312yes—
197C22×C4C2×C22⋊D4311yescharacteristic
198SD16—1728no—
199M16—1722no—
200C2×C8—864no—
201C2×C8—1721no—
202C4⋊C4—22no—
203C4⋊C4—22no—
204C4⋊C4—48no—
205C4⋊C4—42no—
206C4⋊C4—42no—
207C4⋊C4—862no—
208C22⋊C4—1722no—
209C42—22no—
210C42—42no—
211C42—42no—
212C42#1062188414yescomplemented
213C42D4×D4311yescharacteristic
214C42D4×D4312yes—
215C42#1062190011yescharacteristic
216C23—1721no—
217C23#1306329411yescharacteristic
218Q8—24no—
219Q8—24no—
220Q8—42no—
221Q8—42no—
222Q8—1722no—
223D4—3442no—
224D4—1724no—
225D4—1722no—
226C2×C4—24no—
227C2×C4—24no—
228C2×C4—42no—
229C2×C4—44no—
230C2×C4—42no—
231C2×C4—42no—
232C2×C4—44no—
233C2×C4—42no—
234C2×C4—3441no—
235C2×C4—3441no—
236C2×C4—1721no—
237C2×C4#1306329312yes—
238C2×C4#1306329611yescharacteristic
239C2×C4#1306329712yes—
240C2×C4#1306332111yescharacteristic
241C2×C4C2×#1062188412yes—
242C2×C4#1306335612yes—
243C8—3441no—
244C8—1724no—
245C22—22no—
246C22—3442no—
247C22—3441no—
248C22#1458280711yescharacteristic
249C22#1458303812yes—
250C4—22no—
251C4—22no—
252C4—44no—
253C4—44no—
254C4—82no—
255C4—3441no—
256C4#1458310112yes—
257C4#1458327311yescharacteristic
258C4#1458329111yescharacteristic
259C2—22no—
260C2—6881no—
261C2#1913566012yes—
262C2#1913567811yescharacteristic
subgroupG/H
centerC2×C4#13063321
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#2399C2
socleC22×C43#392
prime radical#14583449C22
hypercenter#2399D43
hypocenterC43#10014
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2399

Complements

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

NH ≅ G/Ntype
3. #19133024C2semidirect
4. #19132424C2semidirect
5. C43×#2399C2semidirect
74. C42×C43SD16semidirect
129. #2399D43semidirect
152. C43#10014semidirect
212. C42#10621884semidirect

Maximal subgroups

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

subgroupindex
#191446262
#191354272
#191330242
#191324242
C43×#23992
#1001443