Finite Group Databasebeta

← #24995981

Subgroups — #24995981

Order 11008.

400 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 119 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#19134726C211yesmaximal, characteristic, complemented
2#19133159C212yesmaximal, complemented
3#19133155C212yesmaximal
4#19132878C211yesmaximal, characteristic, complemented
5C43×#3131C211yesmaximal, characteristic
6#14582952C2212yes—
7#14582765C2212yes—
8#14582662—22no—
9#14582636—24no—
10#14582633—24no—
11#14582620—21no—
12C8×C43⋊C8—21no—
13C43×#533C2211yescharacteristic
14C43×#532C2211yescharacteristic
15C43×#488—21no—
16C43×#488—21no—
17C43×#487C412yescomplemented
18C43×#486C412yescomplemented
19C43×#416—22no—
20C2×C4×C8×C43C2211yescharacteristic
21C2×C4⋊Dic43—22no—
22C4⋊(C43⋊C8)—22no—
23C22⋊(C43⋊C8)D414yes—
24C4×C43⋊C8—22no—
25C43⋊#95—22no—
26C43⋊#95—22no—
27C2×#41×C43—21no—
28C22×C8×C43D412yes—
29C4⋊Q8×C43C2×C411yescharacteristic
30C4⋊Q8×C43C2×C412yes—
31#127×C43C2×C411yescharacteristic
32#125×C43—21no—
33#124×C43—21no—
34C22⋊Q8×C43—22no—
35#121×C43—22no—
36C4×Q8×C43—22no—
37C4×D4×C43—22no—
38#117×C43—21no—
39C2×C42×C43C2311yescharacteristic
40#103×C43—22no—
41#103×C43—22no—
42#102×C43—22no—
43#102×C43—22no—
44C4×C8×C43C2×C412yes—
45C4×C8×C43D411yescharacteristic
46C4×C8×C43D411yescharacteristic
47#41×C43—44no—
48C2×Q8×C43—21no—
49C2×Q8×C43—22no—
50C2×D4×C43—21no—
51C2×D4×C43—22no—
52C2×D4×C43—41no—
53C22×C4×C43—41no—
54C22×C4×C43C2×D412yes—
55C22×C4×C43C2×D411yescharacteristic
56C22×Dic43—42no—
57C2×C8×C43—24no—
58C2×C8×C43C22⋊C412yes—
59C2×C8×C43C22⋊C412yes—
60C4⋊C4×C43—22no—
61C4⋊C4×C43—22no—
62C4⋊C4×C43—22no—
63C4⋊C4×C43—42no—
64C22⋊C4×C43—42no—
65C22⋊C4×C43—41no—
66C42×C43—41no—
67C42×C43C22×C411yescharacteristic
68C42×C43C2×D411yescharacteristic
69C42×C43#4112yes—
70C4⋊Dic43—44no—
71C2×C43⋊C8—24no—
72C23×C43—41no—
73C23×C43#12711yescharacteristic
74Q8×C43—42no—
75Q8×C43—82no—
76D4×C43—42no—
77D4×C43—82no—
78D4×C43—82no—
79C2×C4×C43—42no—
80C2×C4×C43—42no—
81C2×C4×C43—41no—
82C2×C4×C43—82no—
83C2×C4×C43C2×C22⋊C411yescharacteristic
84C2×C4×C43C4×D412yes—
85C2×C4×C43#12112yes—
86C2×C4×C43#12411yescharacteristic
87C2×C4×C43#13514yes—
88C2×Dic43—84no—
89C2×Dic43—82no—
90C8×C43—22no—
91C8×C43—22no—
92C43⋊C8—44no—
93#9757—431nomaximal, Sylow
94C22×C43—22no—
95C22×C43—81no—
96C22×C43—82no—
97C22×C43#39011yescharacteristic
98C22×C43#49512yes—
99C4×C43—22no—
100C4×C43—22no—
101C4×C43—81no—
102C4×C43—82no—
103C4×C43#41612yes—
104C4×C43#48812yes—
105Dic43—162no—
106#3131D4311yescharacteristic
107#1835—431no—
108#1518—432no—
109#1517—432no—
110#1450—431no—
111C2×C43—22no—
112C2×C43—161no—
113C2×C43#195811yescharacteristic
114C2×C43#197612yes—
115#533C2×D4311yescharacteristic
116#532C2×D4311yescharacteristic
117#488—21no—
118#488—21no—
119#487Dic4312yescomplemented
120#486Dic4312yescomplemented
121#431—432no—
122#416—22no—
123C2×C4×C8C2×D4311yescharacteristic
124#382—432no—
125#340—862no—
126#328—864no—
127#327—864no—
128#322—861no—
129C82—861no—
130C43#975711yescharacteristic, complemented, Sylow
131C2×#41—21no—
132C22×C8C22⋊D4312yes—
133C4⋊Q8C2×Dic4311yescharacteristic
134C4⋊Q8C2×Dic4312yes—
135#127C2×Dic4311yescharacteristic
136#125—21no—
137#124—21no—
138C22⋊Q8—22no—
139#121—22no—
140C4×Q8—22no—
141C4×D4—22no—
142#117—21no—
143C2×C4⋊C4—862no—
144C2×C42C22×D4311yescharacteristic
145C4⋊C8—862no—
146#103—22no—
147#103—22no—
148#102—22no—
149#102—22no—
150C22⋊C8—434no—
151C4×C8—862no—
152C4×C8C2×Dic4312yes—
153C4×C8C22⋊D4311yescharacteristic
154C4×C8C22⋊D4311yescharacteristic
155#95—862no—
156#95—862no—
157#41—44no—
158C2×Q8—21no—
159C2×Q8—22no—
160C2×D4—21no—
161C2×D4—22no—
162C2×D4—41no—
163C22×C4—41no—
164C22×C4—1722no—
165C22×C4D4×D4312yes—
166C22×C4C2×C22⋊D4311yescharacteristic
167C2×C8—24no—
168C2×C8—864no—
169C2×C8C22⋊Dic4312yes—
170C2×C8C22⋊Dic4312yes—
171C4⋊C4—22no—
172C4⋊C4—22no—
173C4⋊C4—22no—
174C4⋊C4—42no—
175C4⋊C4—1724no—
176C22⋊C4—41no—
177C22⋊C4—42no—
178C42—41no—
179C42#1062190012yes—
180C42C22×Dic4311yescharacteristic
181C42C2×C22⋊D4311yescharacteristic
182C23—41no—
183C23#1306332111yescharacteristic
184Q8—42no—
185Q8—82no—
186D4—42no—
187D4—82no—
188D4—82no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—41no—
192C2×C4—82no—
193C2×C4—3444no—
194C2×C4—3442no—
195C2×C4C2×C22⋊Dic4311yescharacteristic
196C2×C4D4×Dic4312yes—
197C2×C4#1306329612yes—
198C2×C4#1306331211yescharacteristic
199C2×C4#1306334514yes—
200C8—22no—
201C8—22no—
202C8—1724no—
203C22—22no—
204C22—82no—
205C22—81no—
206C22#1458280211yescharacteristic
207C22#1458328112yes—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—81no—
212C4—6882no—
213C4#1458289512yes—
214C4#1458325312yes—
215C2—22no—
216C2—161no—
217C2#1913540711yescharacteristic
218C2#1913549412yes—
subgroupG/H
centerC22#14582802
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#3131C2
socleC22×C43#390
prime radicalC43×#532C22
cosocleC2×C42×C43C23
hypercenter#3131D43
hypocenterC43#9757
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #3131

Complements

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

NH ≅ G/Ntype
1. #19134726C2semidirect
2. #19133159C2semidirect
4. #19132878C2semidirect
17. C43×#487C4semidirect
18. C43×#486C4semidirect
119. #487Dic43semidirect
120. #486Dic43semidirect
130. C43#9757semidirect

Maximal subgroups

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

subgroupindex
#191347262
#191331592
#191331552
#191328782
C43×#31312
#975743