Finite Group Databasebeta

← #24994231

Subgroups — #24994231

Order 11008.

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

normal subgroups only

This group has 456 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#19144998C211yesmaximal, characteristic
2#19133222C211yesmaximal, characteristic, complemented
3#19133102C212yesmaximal
4#19132488C212yesmaximal, complemented
5C43×#2371C211yesmaximal, characteristic, complemented
6#14583449C2211yescharacteristic
7#14583269C412yescomplemented
8#14583265C412yescomplemented
9#14583256—22no—
10#14582956C2212yes—
11#14582898—22no—
12C4×#10621877C2211yescharacteristic
13#14582641—22no—
14#14582632—22no—
15#14582632—22no—
16C2×#125×C43C2211yescharacteristic
17C43×#387—22no—
18C43×#387—22no—
19C4×C4⋊C4×C43—22no—
20C43×#376C2212yes—
21C2×#10621898—21no—
22C2×#10621877—21no—
23#13063325C2×C411yescharacteristic
24#13063322C2×C411yescharacteristic
25#13063313—21no—
26#13063299—22no—
27C4×D172—22no—
28C4⋊(C43⋊C8)—22no—
29#13063248—24no—
30#13063245—24no—
31C22⋊(C43⋊C8)—22no—
32#13063236—22no—
33#13063236C2×C412yes—
34C4×C43⋊C8—21no—
35#125×C43—22no—
36#125×C43C2×C412yes—
37#125×C43D412yes—
38C2×C4⋊C4×C43—22no—
39C2×C4⋊C4×C43—22no—
40C2×C4⋊C4×C43D412yes—
41C2×C42×C43—22no—
42C2×C42×C43—22no—
43C2×C42×C43C2311yescharacteristic
44#95×C43—22no—
45#95×C43—22no—
46#95×C43—22no—
47#95×C43D412yes—
48#95×C43D412yes—
49C22×C4×C43—22no—
50C22×C4×C43—22no—
51C22×C4×C43—22no—
52C22×C4×C43C2×D411yescharacteristic
53C22×C4×C43C2×D412yes—
54C2×C22⋊D43—41no—
55#10621898—44no—
56C2×D172—21no—
57C2×D172—22no—
58C2×C4×D43—41no—
59C2×Dic86—21no—
60C4⋊C4×C43—24no—
61C4⋊C4×C43—24no—
62C4⋊C4×C43—22no—
63C4⋊C4×C43—44no—
64C4⋊C4×C43C22⋊C414yes—
65C42×C43—44no—
66C42×C43—44no—
67C42×C43C22×C411yescharacteristic
68C42×C43C2×D411yescharacteristic
69C42×C43#4112yes—
70(C2×D43)⋊C4—42no—
71C4⋊Dic43—22no—
72#10621877—42no—
73C2×C43⋊C8—22no—
74C2×C43⋊C8—42no—
75C23×C43#12011yescharacteristic
76C22×D43—41no—
77C2×C4×C43—22no—
78C2×C4×C43—24no—
79C2×C4×C43—24no—
80C2×C4×C43—42no—
81C2×C4×C43—42no—
82C2×C4×C43—42no—
83C2×C4×C43—42no—
84C2×C4×C43—42no—
85C2×C4×C43—42no—
86C2×C4×C43—42no—
87C2×C4×C43—42no—
88C2×C4×C43C2×C22⋊C411yescharacteristic
89C2×C4×C43C4×D412yes—
90C2×C4×C43#12112yes—
91C2×C4×C43#12311yescharacteristic
92C22⋊D43—82no—
93C2×Dic43—41no—
94D172—42no—
95D172—82no—
96C4×D43—82no—
97Dic86—42no—
98C43⋊C8—42no—
99C43⋊C8—82no—
100#9442—431nomaximal, Sylow
101C22×C43—22no—
102C22×C43#38611yescharacteristic
103C22×C43#45412yes—
104C2×D43—81no—
105C2×D43—82no—
106C4×C43—21no—
107C4×C43—21no—
108C4×C43—22no—
109C4×C43—22no—
110C4×C43—44no—
111C4×C43—44no—
112C4×C43—82no—
113Dic43—81no—
114#3142—431no—
115#2371D4311yescharacteristic, complemented
116#1534—431no—
117#1505—432no—
118#1300—432no—
119C2×C43—22no—
120C2×C43#188811yescharacteristic
121C2×C43#190612yes—
122D43—161no—
123#532—431no—
124C2×#125C2×D4311yescharacteristic
125#491—432no—
126#490—432no—
127#488—862no—
128#432—432no—
129#417—862no—
130C4×M16—431no—
131#387—22no—
132#387—22no—
133C4×C4⋊C4—22no—
134#376C2×D4312yes—
135#330—862no—
136#327—862no—
137#327—862no—
138C43#944211yescharacteristic, complemented, Sylow
139C2×#41—861no—
140C2×M16—861no—
141C4⋊Q8—431no—
142#127—431no—
143#125—22no—
144#125C4×D4312yes—
145#125D17212yes—
146#124—861no—
147#121—862no—
148C4×D4—862no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—22no—
151C2×C4⋊C4C22⋊D4312yes—
152C2×C42—22no—
153C2×C42—22no—
154C2×C42C22×D4311yescharacteristic
155C4⋊C8—862no—
156#103—864no—
157#102—864no—
158C22⋊C8—862no—
159#97—432no—
160#97—862no—
161C4×C8—861no—
162#95—22no—
163#95—22no—
164#95—22no—
165#95C22⋊D4312yes—
166#95C22⋊D4312yes—
167#41—1724no—
168C2×Q8—861no—
169C2×D4—861no—
170C2×D4—862no—
171C2×D4—1721no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—22no—
175C22×C4—1721no—
176C22×C4C2×C22⋊D4311yescharacteristic
177C22×C4C2×C22⋊D4312yes—
178M16—1722no—
179C2×C8—862no—
180C2×C8—1722no—
181C4⋊C4—24no—
182C4⋊C4—24no—
183C4⋊C4—22no—
184C4⋊C4—44no—
185C4⋊C4—862no—
186C4⋊C4(C2×D43)⋊C414yes—
187C22⋊C4—1722no—
188C42—44no—
189C42—44no—
190C42C2×C4×D4311yescharacteristic
191C42C2×D17211yescharacteristic
192C42#1062189812yes—
193C23—1721no—
194C23#1306329411yescharacteristic
195Q8—1722no—
196D4—3442no—
197D4—3442no—
198D4—1722no—
199C2×C4—22no—
200C2×C4—24no—
201C2×C4—24no—
202C2×C4—42no—
203C2×C4—42no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—3442no—
211C2×C4—1721no—
212C2×C4C2×(C2×D43)⋊C411yescharacteristic
213C2×C4C4×C22⋊D4312yes—
214C2×C4#1306329912yes—
215C2×C4#1306330811yescharacteristic
216C8—3442no—
217C8—1722no—
218C22—22no—
219C22—3441no—
220C22—3442no—
221C22#1458277811yescharacteristic
222C22#1458307212yes—
223C4—21no—
224C4—21no—
225C4—22no—
226C4—22no—
227C4—44no—
228C4—44no—
229C4—82no—
230C4—3441no—
231C2—22no—
232C2—6881no—
233C2#1913499811yescharacteristic
234C2#1913509612yes—
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2371C2
socleC22×C43#386
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#2371D43
hypocenterC43#9442
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2371

Complements

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

NH ≅ G/Ntype
2. #19133222C2semidirect
4. #19132488C2semidirect
5. C43×#2371C2semidirect
7. #14583269C4semidirect
8. #14583265C4semidirect
115. #2371D43semidirect
138. C43#9442semidirect

Maximal subgroups

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

subgroupindex
#191449982
#191332222
#191331022
#191324882
C43×#23712
#944243