Finite Group Databasebeta

← #24994151

Subgroups — #24994151

Order 11008.

620 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 620 conjugacy classes of subgroups — too many to draw. Only its 99 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#19145045C211yesmaximal, characteristic
2#19133309C211yesmaximal, characteristic, complemented
3#19133141C212yesmaximal, complemented
4#19132459C212yesmaximal, complemented
5C43×#2380C211yesmaximal, characteristic, complemented
6C2×#13063351—22no—
7#14583449C2211yescharacteristic
8#14583286—22no—
9#14583275C412yescomplemented
10#14583271C412yescomplemented
11#14582956C2212yes—
12C4×#10621877C2211yescharacteristic
13#14582643—22no—
14#14582632—24no—
15C2×#127×C43C2211yescharacteristic
16C43×#386—22no—
17C43×#386—24no—
18C43×#383C2212yes—
19C2×#10621898—21no—
20#13063351—44no—
21#13063351—44no—
22C2×#10621883—24no—
23C2×#10621882—24no—
24C2×#10621877—21no—
25#13063325C2×C411yescharacteristic, complemented
26#13063322C2×C411yescharacteristic, complemented
27#13063313—21no—
28#13063299—22no—
29C4×D172—22no—
30C4⋊(C43⋊C8)—22no—
31C22⋊(C43⋊C8)—22no—
32#13063236—21no—
33#13063236—22no—
34C4×C43⋊C8C2×C412yescomplemented
35C22×D4×C43—22no—
36C22×D4×C43D412yes—
37C23×C4×C43—22no—
38#127×C43—22no—
39#127×C43C2×C412yes—
40#127×C43D412yes—
41C2×C22⋊C4×C43—24no—
42C2×C22⋊C4×C43—22no—
43C2×C42×C43C2311yescharacteristic
44#95×C43—22no—
45#95×C43—22no—
46#95×C43D414yes—
47C24×C43—22no—
48C2×D4×C43—24no—
49C2×D4×C43—24no—
50C2×D4×C43—22no—
51C2×D4×C43—42no—
52C2×D4×C43—42no—
53C2×D4×C43—82no—
54C2×D4×C43—82no—
55C2×D4×C43C22⋊C414yes—
56C22×C4×C43—24no—
57C22×C4×C43—84no—
58C22×C4×C43—82no—
59C22×C4×C43C2×D411yescharacteristic
60C22×C4×C43C2×D412yes—
61C2×C22⋊D43—41no—
62#10621898—42no—
63#10621898—42no—
64C2×D172—21no—
65C2×D172—22no—
66C2×C4×D43—41no—
67C2×Dic86—21no—
68C22⋊C4×C43—84no—
69C22⋊C4×C43—82no—
70C42×C43C22×C411yescharacteristic
71C42×C43C2×D411yescharacteristic
72C42×C43#4112yes—
73#10621883—48no—
74#10621882—48no—
75(C2×D43)⋊C4—42no—
76C4⋊Dic43—22no—
77#10621877—24no—
78C2×C43⋊C8—22no—
79C2×C43⋊C8—42no—
80C23×C43—24no—
81C23×C43—44no—
82C23×C43—44no—
83C23×C43—42no—
84C23×C43—42no—
85C23×C43#12011yescharacteristic
86C22×D43—41no—
87D4×C43—44no—
88D4×C43—82no—
89D4×C43—84no—
90D4×C43—84no—
91C2×C4×C43—22no—
92C2×C4×C43—42no—
93C2×C4×C43—48no—
94C2×C4×C43—44no—
95C2×C4×C43—88no—
96C2×C4×C43C2×C22⋊C411yescharacteristic
97C2×C4×C43C4×D412yes—
98C2×C4×C43#12112yes—
99C2×C4×C43#12311yescharacteristic
100C22⋊D43—82no—
101C2×Dic43—41no—
102D172—42no—
103D172—82no—
104C4×D43—81no—
105C4×D43—81no—
106Dic86—42no—
107C43⋊C8—24no—
108C43⋊C8—82no—
109#9428—431nomaximal, Sylow
110C22×C43—22no—
111C22×C43—44no—
112C22×C43—48no—
113C22×C43—82no—
114C22×C43—84no—
115C22×C43—82no—
116C22×C43#38611yescharacteristic
117C22×C43#45312yes—
118C2×D43—81no—
119C2×D43—82no—
120C4×C43—21no—
121C4×C43—21no—
122C4×C43—22no—
123C4×C43—22no—
124C4×C43—84no—
125Dic43—81no—
126#3151—431no—
127#2380D4311yescharacteristic, complemented
128#1555—431no—
129#1514—432no—
130#1288—432no—
131C2×C43—22no—
132C2×C43—84no—
133C2×C43#188711yescharacteristic
134C2×C43#190412yes—
135D43—161no—
136C2×AGL(1,ℤ/8)—862no—
137#532—431no—
138C2×#127C2×D4311yescharacteristic
139#496—862no—
140#493—432no—
141#492—432no—
142#432—432no—
143C4×M16—431no—
144#386—22no—
145#386—24no—
146#383C2×D4312yes—
147#331—862no—
148#327—864no—
149C43#942811yescharacteristic, complemented, Sylow
150C2×#41—861no—
151C22×D4—22no—
152C22×D4C22⋊D4312yes—
153C23×C4—22no—
154AGL(1,ℤ/8)—1724no—
155AGL(1,ℤ/8)—1724no—
156C2×SD16—864no—
157C2×D8—864no—
158C2×M16—861no—
159C4⋊Q8—431no—
160#127—22no—
161#127—431no—
162#127C4×D4312yes—
163#127D17212yes—
164#124—861no—
165#121—862no—
166C4×D4—862no—
167C2×C22⋊C4—24no—
168C2×C22⋊C4—22no—
169C2×C42C22×D4311yescharacteristic
170C4⋊C8—862no—
171C22⋊C8—862no—
172#97—861no—
173#97—862no—
174C4×C8—432no—
175#95—22no—
176#95—22no—
177#95C22⋊D4314yes—
178C24—22no—
179#41—1722no—
180#41—1722no—
181C2×Q8—861no—
182C2×D4—24no—
183C2×D4—24no—
184C2×D4—22no—
185C2×D4—42no—
186C2×D4—42no—
187C2×D4—82no—
188C2×D4—82no—
189C2×D4—861no—
190C2×D4—862no—
191C2×D4—1721no—
192C2×D4(C2×D43)⋊C414yes—
193C22×C4—24no—
194C22×C4—84no—
195C22×C4—82no—
196C22×C4—1721no—
197C22×C4C2×C22⋊D4311yescharacteristic
198C22×C4C2×C22⋊D4312yes—
199SD16—1728no—
200D8—1728no—
201M16—864no—
202C2×C8—862no—
203C2×C8—1722no—
204C4⋊C4—862no—
205C22⋊C4—84no—
206C22⋊C4—82no—
207C22⋊C4—1722no—
208C42C2×C4×D4311yescharacteristic
209C42C2×D17211yescharacteristic
210C42#1062189812yes—
211C23—24no—
212C23—44no—
213C23—44no—
214C23—42no—
215C23—42no—
216C23—1721no—
217C23#1306329411yescharacteristic
218Q8—1722no—
219D4—44no—
220D4—82no—
221D4—84no—
222D4—84no—
223D4—3442no—
224D4—3442no—
225D4—1722no—
226C2×C4—22no—
227C2×C4—42no—
228C2×C4—48no—
229C2×C4—44no—
230C2×C4—88no—
231C2×C4—3441no—
232C2×C4—3441no—
233C2×C4—1721no—
234C2×C4C2×(C2×D43)⋊C411yescharacteristic
235C2×C4C4×C22⋊D4312yes—
236C2×C4#1306329912yes—
237C2×C4#1306330811yescharacteristic
238C8—864no—
239C8—3442no—
240C22—22no—
241C22—44no—
242C22—48no—
243C22—82no—
244C22—82no—
245C22—84no—
246C22—3441no—
247C22—3442no—
248C22#1458277811yescharacteristic
249C22#1458306712yes—
250C4—21no—
251C4—21no—
252C4—22no—
253C4—22no—
254C4—84no—
255C4—3441no—
256C2—22no—
257C2—84no—
258C2—6881no—
259C2#1913499311yescharacteristic
260C2#1913508212yes—
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2380C2
socleC22×C43#386
prime radical#19145045C2
cosocleC2×C42×C43C23
hypercenter#2380D43
hypocenterC43#9428
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2380

Complements

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

NH ≅ G/Ntype
2. #19133309C2semidirect
3. #19133141C2semidirect
4. #19132459C2semidirect
5. C43×#2380C2semidirect
9. #14583275C4semidirect
10. #14583271C4semidirect
25. #13063325C2×C4semidirect
26. #13063322C2×C4semidirect
34. C4×C43⋊C8C2×C4semidirect
127. #2380D43semidirect
149. C43#9428semidirect

Maximal subgroups

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

subgroupindex
#191450452
#191333092
#191331412
#191324592
C43×#23802
#942843