Finite Group Databasebeta

← #25000697

Subgroups — #25000697

Order 11008.

344 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 77 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#19145940C211yesmaximal, characteristic
2#19134714C211yesmaximal, characteristic
3#19133296C212yesmaximal
4#19133108C212yesmaximal
5C43×#1290C211yesmaximal, characteristic
6#14583456C2212yes—
7#14583195—22no—
8#14583140—22no—
9#14583110—22no—
10C2×C4⋊(C43⋊C8)C2211yescharacteristic
11#14582745C2211yescharacteristic
12#14582653—22no—
13#14582646—22no—
14#14582644—22no—
15#14582637—24no—
16C43×#432C2212yes—
17C2×C4⋊C8×C43C2211yescharacteristic
18C2×Dic172—22no—
19C22×C43⋊C8—21no—
20#13063325D412yes—
21#13063325D412yes—
22#13063317—22no—
23#13063304—22no—
24#13063304—22no—
25C4×Dic86—22no—
26C4×Dic86—22no—
27#13063284—22no—
28C2×C4×Dic43—21no—
29#13063259—22no—
30C4⋊(C43⋊C8)—22no—
31#13063250—24no—
32C43⋊#95—21no—
33C43⋊#95D412yes—
34C22×C8×C43D412yes—
35C2×C42×C43C2311yescharacteristic
36C4⋊C8×C43—22no—
37C4⋊C8×C43—22no—
38C22⋊C8×C43—22no—
39#97×C43—22no—
40C22×C4×C43C2×D411yescharacteristic
41C22×C4×C43C2×D411yescharacteristic
42C22×C4×C43#4111yescharacteristic
43C22×Dic43—22no—
44C2×Dic86—22no—
45C2×Dic86—22no—
46C2×C8×C43—22no—
47C2×C8×C43—42no—
48C2×C8×C43—42no—
49C42×C43C2×D412yes—
50C42×C43#4112yes—
51C22⋊Dic43—42no—
52C4⋊Dic43—22no—
53C4⋊Dic43—22no—
54C4⋊Dic43—22no—
55C4⋊Dic43—22no—
56Dic43⋊C4—42no—
57Dic43⋊C4—42no—
58C4×Dic43—41no—
59C4×Dic43—41no—
60C4×Dic43—42no—
61C2×C43⋊C8—42no—
62C2×C43⋊C8—41no—
63Dic172—82no—
64C23×C43#12111yescharacteristic
65C2×C4×C43—22no—
66C2×C4×C43—21no—
67C2×C4×C43—21no—
68C2×C4×C43—41no—
69C2×C4×C43#12011yescharacteristic
70C2×C4×C43#12112yes—
71C2×C4×C43#12312yes—
72C2×C4×C43#12411yescharacteristic
73C2×Dic43—42no—
74C2×Dic43—42no—
75C2×Dic43—42no—
76C2×Dic43—42no—
77C2×Dic43—42no—
78Dic86—42no—
79Dic86—42no—
80Dic86—82no—
81C8×C43—42no—
82C8×C43—82no—
83C43⋊C8—81no—
84#10517—431nomaximal, Sylow
85C22×C43—21no—
86C22×C43—21no—
87C22×C43#39411yescharacteristic
88C22×C43#47312yes—
89C4×C43—22no—
90C4×C43—21no—
91C4×C43—22no—
92C4×C43#45411yescharacteristic
93C4×C43#45511yescharacteristic
94Dic43—82no—
95Dic43—82no—
96Dic43—82no—
97#3249—431no—
98#1832—431no—
99#1552—432no—
100#1506—432no—
101#1290D4311yescharacteristic
102C2×C43—22no—
103C2×C43#204011yescharacteristic
104C2×C43#204711yescharacteristic
105C2×C43#205311yescharacteristic
106#533—432no—
107#477—862no—
108#467—862no—
109#462—862no—
110#432C2×D4312yes—
111C2×C4⋊C8—431no—
112C2×C4⋊C8C2×D4311yescharacteristic
113#376—431no—
114#336—862no—
115#332—862no—
116#332—862no—
117#328—864no—
118C43#1051711yescharacteristic, complemented, Sylow
119C2×Q16—862no—
120C22×C8—861no—
121C22×C8D17212yes—
122C4⋊Q8—432no—
123C4⋊Q8—432no—
124#125—862no—
125C22⋊Q8—862no—
126C22⋊Q8—862no—
127C4×Q8—862no—
128C4×Q8—862no—
129#117—862no—
130C2×C42—861no—
131C2×C42C22×D4311yescharacteristic
132#107—862no—
133C4⋊C8—22no—
134C4⋊C8—22no—
135C4⋊C8—862no—
136#103—864no—
137C22⋊C8—22no—
138#97—22no—
139#95—432no—
140#95—861no—
141C2×Q8—862no—
142C2×Q8—862no—
143C22×C4—862no—
144C22×C4C2×D17211yescharacteristic
145C22×C4D4×D4311yescharacteristic
146C22×C4#1062190211yescharacteristic
147Q16—3442no—
148C2×C8—22no—
149C2×C8—42no—
150C2×C8—42no—
151C2×C8—1722no—
152C2×C8—1721no—
153C4⋊C4—862no—
154C4⋊C4—862no—
155C4⋊C4—862no—
156C4⋊C4—862no—
157C4⋊C4—1722no—
158C4⋊C4—1722no—
159C22⋊C4—1722no—
160C42—1721no—
161C42—1721no—
162C42—1722no—
163C42#1062189812yes—
164C42D4×D4312yes—
165C23#1306330011yescharacteristic
166Q8—3442no—
167Q8—1722no—
168Q8—1722no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—1722no—
174C2×C4—1722no—
175C2×C4—1722no—
176C2×C4—1722no—
177C2×C4—1722no—
178C2×C4#1306329511yescharacteristic
179C2×C4#1306329812yes—
180C2×C4#1306331012yes—
181C2×C4#1306331311yescharacteristic
182C8—42no—
183C8—82no—
184C8—3441no—
185C22—21no—
186C22—21no—
187C22#1458281711yescharacteristic
188C22#1458317512yes—
189C4—21no—
190C4—22no—
191C4—22no—
192C4—3442no—
193C4—3442no—
194C4—3442no—
195C4#1458307411yescharacteristic
196C4#1458307911yescharacteristic
197C2—22no—
198C2#1913582511yescharacteristic
199C2#1913586411yescharacteristic
200C2#1913590211yescharacteristic
subgroupG/H
centerC22#14582817
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1290C2
socleC22×C43#394
prime radicalC23×C43#121
hypercenter#1290D43
hypocenterC43#10517
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

Complements

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

NH ≅ G/Ntype
118. C43#10517semidirect

Maximal subgroups

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

subgroupindex
#191459402
#191347142
#191332962
#191331082
C43×#12902
#1051743