Finite Group Databasebeta

← #24997452

Subgroups — #24997452

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#19144627C212yesmaximal
2#19137888C211yesmaximal, characteristic, complemented
3#19135427C211yesmaximal, characteristic
4#19133025C212yesmaximal, complemented
5C43×#1274C211yesmaximal, characteristic, complemented
6#14583449C2211yescharacteristic
7C2×C4×Dic86C2212yes—
8#14583218—22no—
9#14583185—22no—
10#14583100—22no—
11#14583040—22no—
12C4×#10621873—24no—
13#14582923C2211yescharacteristic
14C2×#13063253—22no—
15#14582831—22no—
16#14582820—22no—
17C4×C4⋊Dic43—22no—
18#14582631—24no—
19C43×#431C2212yes—
20C43×#376C2211yescharacteristic
21C2×#10621898—21no—
22C22×Dic86D412yes—
23C2×#10621873—24no—
24C2×#10621877—21no—
25#13063325D411yescharacteristic
26#13063322D411yescharacteristic
27#13063313—21no—
28#13063299—22no—
29C4×Dic86—22no—
30C4×Dic86—22no—
31C4×Dic86—22no—
32C4×Dic86—22no—
33C4×D172—22no—
34C2×C4⋊Dic43—24no—
35C2×C4⋊Dic43D412yes—
36C2×Dic43⋊C4—22no—
37C2×C4×Dic43—22no—
38#13063257—24no—
39C4⋊(C43⋊C8)—22no—
40#13063253—44no—
41#13063250—24no—
42#13063247—24no—
43C43⋊#95—22no—
44C43⋊#95—22no—
45C2×C42×C43D412yes—
46C2×C42×C43C2311yescharacteristic
47C4⋊C8×C43—22no—
48C22⋊C8×C43—22no—
49C4×C8×C43D414yes—
50#95×C43—22no—
51C22×C4×C43—22no—
52C22×C4×C43C2×D411yescharacteristic
53C22×C4×C43C2×D412yes—
54C2×C22⋊D43—41no—
55C22×Dic43—22no—
56C22×Dic43—22no—
57#10621898—42no—
58#10621898—42no—
59C2×D172—22no—
60C2×D172—21no—
61C2×C4×D43—41no—
62C2×Dic86—22no—
63C2×Dic86—22no—
64C2×Dic86—21no—
65C2×Dic86—44no—
66C2×C8×C43—24no—
67C42×C43—22no—
68C42×C43SD1614yescomplemented
69C42×C43C2×D412yes—
70C42×C43C2×D411yescharacteristic
71C42×C43#4111yescharacteristic
72(C2×D43)⋊C4—42no—
73C4⋊Dic43—22no—
74C4⋊Dic43—22no—
75C4⋊Dic43—22no—
76C4⋊Dic43—48no—
77Dic43⋊C4—42no—
78Dic43⋊C4—42no—
79C4×Dic43—42no—
80C4×Dic43—42no—
81#10621877—42no—
82C2×C43⋊C8—41no—
83#10621873—48no—
84C23×C43#12011yescharacteristic
85C22×D43—41no—
86C2×C4×C43—24no—
87C2×C4×C43—42no—
88C2×C4×C43—44no—
89C2×C4×C43#12012yes—
90C2×C4×C43#12112yes—
91C2×C4×C43#12111yescharacteristic
92C2×C4×C43#12711yescharacteristic
93C2×C4×C43C2×SD1612yes—
94C2×C4×C43#13712yes—
95C22⋊D43—82no—
96C2×Dic43—24no—
97C2×Dic43—42no—
98C2×Dic43—42no—
99C2×Dic43—44no—
100C2×Dic43—42no—
101C2×Dic43—41no—
102D172—44no—
103D172—42no—
104C4×D43—81no—
105C4×D43—81no—
106Dic86—24no—
107Dic86—24no—
108Dic86—42no—
109Dic86—42no—
110Dic86—42no—
111C8×C43—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#46112yes—
123C4×C43#49211yescharacteristic
124C4×C43#49711yescharacteristic
125Dic43—44no—
126Dic43—82no—
127Dic43—81no—
128#3103—432no—
129#2399—431no—
130#1963—431no—
131#1487—432no—
132#1274D4311yescharacteristic, complemented
133C2×C43—22no—
134C2×C43#201012yes—
135C2×C43#201311yescharacteristic
136D43—161no—
137#532—431no—
138C2×C4×Q8—432no—
139#481—862no—
140#475—862no—
141#460—862no—
142#448—862no—
143C4×SD16—864no—
144#431C2×D4312yes—
145#423—431no—
146C2×#104—862no—
147#398—862no—
148#395—862no—
149C4×C4⋊C4—862no—
150#376C2×D4311yescharacteristic
151Q8⋊C8—864no—
152C43#1001411yescharacteristic, complemented, Sylow
153C2×#41—861no—
154C22×Q8—432no—
155C2×SD16—864no—
156C2×M16—861no—
157C4⋊Q8—431no—
158#127—431no—
159#124—861no—
160#121—862no—
161C4×Q8—862no—
162C4×Q8—862no—
163C4×Q8—862no—
164C4×Q8—862no—
165C4×D4—862no—
166C2×C4⋊C4—432no—
167C2×C4⋊C4—864no—
168C2×C4⋊C4—862no—
169C2×C42—862no—
170C2×C42D17212yes—
171C2×C42C22×D4311yescharacteristic
172#106—864no—
173C4⋊C8—22no—
174C4⋊C8—862no—
175#104—1724no—
176#103—864no—
177#102—864no—
178C22⋊C8—22no—
179C4×C8D17214yes—
180#95—22no—
181#95—862no—
182#95—862no—
183#41—1722no—
184#41—1722no—
185C2×Q8—862no—
186C2×Q8—862no—
187C2×Q8—861no—
188C2×Q8—1724no—
189C2×D4—862no—
190C2×D4—861no—
191C2×D4—1721no—
192C22×C4—22no—
193C22×C4—862no—
194C22×C4—862no—
195C22×C4—1721no—
196C22×C4C2×D17211yescharacteristic
197C22×C4D4×D4312yes—
198SD16—1728no—
199M16—1722no—
200C2×C8—24no—
201C2×C8—1721no—
202C4⋊C4—862no—
203C4⋊C4—862no—
204C4⋊C4—862no—
205C4⋊C4—1728no—
206C4⋊C4—1722no—
207C4⋊C4—1722no—
208C22⋊C4—1722no—
209C42—22no—
210C42—1722no—
211C42—1722no—
212C42#1062187314yescomplemented
213C42C2×D17212yes—
214C42D4×D4311yescharacteristic
215C42#1062190211yescharacteristic
216C23—1721no—
217C23#1306329511yescharacteristic
218Q8—864no—
219Q8—864no—
220Q8—1722no—
221Q8—1722no—
222Q8—1722no—
223D4—3442no—
224D4—1724no—
225D4—1722no—
226C2×C4—24no—
227C2×C4—42no—
228C2×C4—44no—
229C2×C4—864no—
230C2×C4—3441no—
231C2×C4—3441no—
232C2×C4—1724no—
233C2×C4—1722no—
234C2×C4—1721no—
235C2×C4—1722no—
236C2×C4—1722no—
237C2×C4#1306329512yes—
238C2×C4#1306330012yes—
239C2×C4#1306330011yescharacteristic
240C2×C4#1306332211yescharacteristic
241C2×C4C2×#1062187312yes—
242C2×C4#1306335812yes—
243C8—44no—
244C8—3441no—
245C22—22no—
246C22—3442no—
247C22—3441no—
248C22#1458280911yescharacteristic
249C22#1458304012yes—
250C4—22no—
251C4—22no—
252C4—44no—
253C4—3442no—
254C4—3441no—
255C4—1724no—
256C4#1458310512yes—
257C4#1458327211yescharacteristic
258C4#1458329311yescharacteristic
259C2—22no—
260C2—6881no—
261C2#1913566312yes—
262C2#1913568011yescharacteristic
subgroupG/H
centerC2×C4#13063322
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1274C2
socleC22×C43#392
prime radical#14583449C22
hypercenter#1274D43
hypocenterC43#10014
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1274

Complements

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

NH ≅ G/Ntype
2. #19137888C2semidirect
4. #19133025C2semidirect
5. C43×#1274C2semidirect
68. C42×C43SD16semidirect
132. #1274D43semidirect
152. C43#10014semidirect
212. C42#10621873semidirect

Maximal subgroups

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

subgroupindex
#191446272
#191378882
#191354272
#191330252
C43×#12742
#1001443