Finite Group Databasebeta

← #24995980

Subgroups — #24995980

Order 11008.

400 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 115 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#19144918C211yesmaximal, characteristic
2#19134726C211yesmaximal, characteristic, complemented
3#19133160C212yesmaximal, complemented
4#19133156C212yesmaximal
5C43×#1450C211yesmaximal, characteristic, complemented
6#14583456C2211yescharacteristic
7#14583449C2211yescharacteristic
8#14583254—21no—
9#14583254—21no—
10#14583250C412yescomplemented
11#14583246C412yescomplemented
12#14582896—22no—
13#14582765C2212yes—
14#14582662—22no—
15#14582637—24no—
16#14582634—24no—
17C43×#431C2212yes—
18C2×C4×C8×C43C2211yescharacteristic
19C43×#322—21no—
20C82×C43—21no—
21C2×#10621898—21no—
22#13063325C2×C411yescharacteristic
23#13063325C2×C412yes—
24#13063322C2×C411yescharacteristic
25#13063317—21no—
26#13063313—21no—
27#13063304—22no—
28#13063299—22no—
29C4×Dic86—22no—
30C4×D172—22no—
31#13063284—21no—
32C2×C4⋊Dic43—22no—
33#13063250—22no—
34#13063250—22no—
35#13063247—22no—
36#13063247—22no—
37C43⋊#95—22no—
38C43⋊#95—22no—
39C22×C8×C43D412yes—
40C2×C42×C43C2311yescharacteristic
41C4⋊C8×C43—22no—
42C22⋊C8×C43D414yes—
43C4×C8×C43—22no—
44C4×C8×C43C2×C412yes—
45C4×C8×C43D411yescharacteristic
46C4×C8×C43D411yescharacteristic
47C22×C4×C43C2×D412yes—
48C22×C4×C43C2×D411yescharacteristic
49C2×C22⋊D43—41no—
50C22×Dic43—42no—
51#10621898—44no—
52C2×D172—21no—
53C2×D172—22no—
54C2×C4×D43—41no—
55C2×Dic86—21no—
56C2×Dic86—22no—
57C2×C8×C43—24no—
58C2×C8×C43—24no—
59C2×C8×C43C22⋊C412yes—
60C2×C8×C43C22⋊C412yes—
61C42×C43C22×C411yescharacteristic
62C42×C43C2×D411yescharacteristic
63C42×C43#4112yes—
64C22⋊Dic43—41no—
65(C2×D43)⋊C4—42no—
66C4⋊Dic43—22no—
67C4⋊Dic43—22no—
68C4⋊Dic43—22no—
69C4⋊Dic43—44no—
70Dic43⋊C4—42no—
71C4×Dic43—41no—
72C23×C43#12711yescharacteristic
73C22×D43—41no—
74C2×C4×C43—42no—
75C2×C4×C43C2×C22⋊C411yescharacteristic
76C2×C4×C43C4×D412yes—
77C2×C4×C43#12112yes—
78C2×C4×C43#12411yescharacteristic
79C2×C4×C43#13514yes—
80C22⋊D43—82no—
81C2×Dic43—42no—
82C2×Dic43—41no—
83C2×Dic43—84no—
84C2×Dic43—82no—
85D172—42no—
86D172—82no—
87C4×D43—82no—
88Dic86—42no—
89Dic86—82no—
90C8×C43—22no—
91C8×C43—22no—
92C8×C43—44no—
93#9757—431nomaximal, Sylow
94C22×C43—22no—
95C22×C43#39011yescharacteristic
96C22×C43#49512yes—
97C2×D43—81no—
98C2×D43—82no—
99C4×C43—22no—
100C4×C43—22no—
101C4×C43#41612yes—
102C4×C43#48812yes—
103Dic43—81no—
104Dic43—82no—
105Dic43—162no—
106#3131—431no—
107#1835—431no—
108#1518—432no—
109#1517—432no—
110#1450D4311yescharacteristic, complemented
111C2×C43—22no—
112C2×C43#195811yescharacteristic
113C2×C43#197612yes—
114D43—161no—
115#533—431no—
116#532—431no—
117#488—861no—
118#488—861no—
119#487—432no—
120#486—432no—
121#431C2×D4312yes—
122#416—862no—
123C2×C4×C8C2×D4311yescharacteristic
124#382—432no—
125#340—862no—
126#328—864no—
127#327—864no—
128#322—21no—
129C82—21no—
130C43#975711yescharacteristic, complemented, Sylow
131C2×#41—861no—
132C22×C8D17212yes—
133C4⋊Q8—431no—
134C4⋊Q8—432no—
135#127—431no—
136#125—861no—
137#124—861no—
138C22⋊Q8—862no—
139#121—862no—
140C4×Q8—862no—
141C4×D4—862no—
142#117—861no—
143C2×C4⋊C4—862no—
144C2×C42C22×D4311yescharacteristic
145C4⋊C8—22no—
146#103—862no—
147#103—862no—
148#102—862no—
149#102—862no—
150C22⋊C8D17214yes—
151C4×C8—22no—
152C4×C8C4×D4312yes—
153C4×C8C22⋊D4311yescharacteristic
154C4×C8C22⋊D4311yescharacteristic
155#95—862no—
156#95—862no—
157#41—1724no—
158C2×Q8—861no—
159C2×Q8—862no—
160C2×D4—861no—
161C2×D4—862no—
162C2×D4—1721no—
163C22×C4—1722no—
164C22×C4—1721no—
165C22×C4C2×D17212yes—
166C22×C4C2×D17211yescharacteristic
167C2×C8—24no—
168C2×C8—24no—
169C2×C8(C2×D43)⋊C412yes—
170C2×C8(C2×D43)⋊C412yes—
171C4⋊C4—862no—
172C4⋊C4—862no—
173C4⋊C4—862no—
174C4⋊C4—1724no—
175C4⋊C4—1722no—
176C22⋊C4—1721no—
177C22⋊C4—1722no—
178C42—1721no—
179C42C2×C4×D4311yescharacteristic
180C42#1062189812yes—
181C42C2×C22⋊D4311yescharacteristic
182C23—1721no—
183C23#1306332211yescharacteristic
184Q8—3442no—
185Q8—1722no—
186D4—3442no—
187D4—3442no—
188D4—1722no—
189C2×C4—42no—
190C2×C4—3442no—
191C2×C4—3444no—
192C2×C4—3442no—
193C2×C4—1722no—
194C2×C4—1721no—
195C2×C4C2×(C2×D43)⋊C411yescharacteristic
196C2×C4C4×D17212yes—
197C2×C4#1306329912yes—
198C2×C4#1306331311yescharacteristic
199C2×C4#1306334714yes—
200C8—22no—
201C8—22no—
202C8—44no—
203C22—22no—
204C22—3442no—
205C22—3441no—
206C22#1458280111yescharacteristic
207C22#1458328312yes—
208C4—22no—
209C4—22no—
210C4—3442no—
211C4—3441no—
212C4—6882no—
213C4#1458289612yes—
214C4#1458325412yes—
215C2—22no—
216C2—6881no—
217C2#1913540611yescharacteristic
218C2#1913549312yes—
subgroupG/H
centerC22#14582801
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#1450C2
socleC22×C43#390
prime radical#14583449C22
cosocleC2×C42×C43C23
hypercenter#1450D43
hypocenterC43#9757
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1450

Complements

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

NH ≅ G/Ntype
2. #19134726C2semidirect
3. #19133160C2semidirect
5. C43×#1450C2semidirect
10. #14583250C4semidirect
11. #14583246C4semidirect
110. #1450D43semidirect
130. C43#9757semidirect

Maximal subgroups

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

subgroupindex
#191449182
#191347262
#191331602
#191331562
C43×#14502
#975743