Finite Group Databasebeta

← #25000696

Subgroups — #25000696

Order 11008.

344 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 79 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#19133293C212yesmaximal
3#19133106C212yesmaximal
4#19132465C211yesmaximal, characteristic
5C43×#1832C211yesmaximal, characteristic
6#14583456C2212yes—
7#14583195—22no—
8#14583140—22no—
9#14583110—22no—
10#14582956C2212yes—
11#14582646—22no—
12#14582644—22no—
13#14582635—24no—
14C2×C4⋊C8×C43C2211yescharacteristic
15C2×C4⋊C8×C43C2211yescharacteristic
16C43×#376C2211yescharacteristic
17C43×#336—22no—
18C2×Dic172—22no—
19#13063325D412yes—
20#13063325D412yes—
21#13063317—22no—
22#13063304—22no—
23#13063304—22no—
24C4×Dic86—22no—
25C4×Dic86—22no—
26#13063284—22no—
27#13063259—22no—
28C4⋊(C43⋊C8)—22no—
29#13063250—24no—
30C22⋊(C43⋊C8)—22no—
31#13063236—22no—
32C22×C8×C43—21no—
33C22×C8×C43D412yes—
34C2×C42×C43—21no—
35C2×C42×C43C2311yescharacteristic
36C4⋊C8×C43—22no—
37C4⋊C8×C43—22no—
38#95×C43—21no—
39#95×C43D412yes—
40C22×C4×C43—22no—
41C22×C4×C43C2×D411yescharacteristic
42C22×C4×C43C2×D411yescharacteristic
43C22×C4×C43#4111yescharacteristic
44C2×Dic86—22no—
45C2×Dic86—22no—
46C2×C8×C43—22no—
47C2×C8×C43—42no—
48C2×C8×C43—42no—
49C2×C8×C43—41no—
50C42×C43—41no—
51C42×C43—41no—
52C42×C43C2×D412yes—
53C42×C43#4112yes—
54C22⋊Dic43—42no—
55C4⋊Dic43—22no—
56C4⋊Dic43—22no—
57C4⋊Dic43—22no—
58C4⋊Dic43—22no—
59Dic43⋊C4—42no—
60Dic43⋊C4—42no—
61C4×Dic43—42no—
62C2×C43⋊C8—42no—
63Dic172—82no—
64C23×C43#12111yescharacteristic
65C2×C4×C43—22no—
66C2×C4×C43—21no—
67C2×C4×C43—21no—
68C2×C4×C43—41no—
69C2×C4×C43—42no—
70C2×C4×C43—42no—
71C2×C4×C43—42no—
72C2×C4×C43#12011yescharacteristic
73C2×C4×C43#12112yes—
74C2×C4×C43#12312yes—
75C2×C4×C43#12411yescharacteristic
76C2×Dic43—42no—
77C2×Dic43—42no—
78Dic86—42no—
79Dic86—42no—
80Dic86—82no—
81C8×C43—42no—
82C8×C43—81no—
83C43⋊C8—82no—
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—82no—
93C4×C43#45411yescharacteristic
94C4×C43#45511yescharacteristic
95Dic43—82no—
96Dic43—82no—
97#3249—431no—
98#1832D4311yescharacteristic
99#1552—432no—
100#1506—432no—
101#1290—431no—
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#432—432no—
111C2×C4⋊C8C2×D4311yescharacteristic
112C2×C4⋊C8C2×D4311yescharacteristic
113#376C2×D4311yescharacteristic
114#336—22no—
115#332—862no—
116#332—862no—
117#328—864no—
118C43#1051711yescharacteristic, complemented, Sylow
119C2×Q16—862no—
120C22×C8—21no—
121C22×C8C22⋊D4312yes—
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—21no—
131C2×C42C22×D4311yescharacteristic
132#107—862no—
133C4⋊C8—22no—
134C4⋊C8—22no—
135C4⋊C8—862no—
136#103—864no—
137C22⋊C8—862no—
138#97—862no—
139#95—21no—
140#95D17212yes—
141C2×Q8—862no—
142C2×Q8—862no—
143C22×C4—22no—
144C22×C4C2×D17211yescharacteristic
145C22×C4#1062189811yescharacteristic
146C22×C4C2×C22⋊D4311yescharacteristic
147Q16—3442no—
148C2×C8—22no—
149C2×C8—42no—
150C2×C8—42no—
151C2×C8—41no—
152C2×C8—1722no—
153C4⋊C4—862no—
154C4⋊C4—862no—
155C4⋊C4—862no—
156C4⋊C4—862no—
157C4⋊C4—1722no—
158C4⋊C4—1722no—
159C22⋊C4—1722no—
160C42—41no—
161C42—41no—
162C42—1722no—
163C42D4×D4312yes—
164C42#1062190212yes—
165C23#1306329911yescharacteristic
166Q8—3442no—
167Q8—1722no—
168Q8—1722no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—1722no—
177C2×C4—1722no—
178C2×C4#1306329311yescharacteristic
179C2×C4#1306330012yes—
180C2×C4#1306331012yes—
181C2×C4#1306331411yescharacteristic
182C8—42no—
183C8—81no—
184C8—3442no—
185C22—21no—
186C22—21no—
187C22#1458281611yescharacteristic
188C22#1458317412yes—
189C4—21no—
190C4—22no—
191C4—22no—
192C4—82no—
193C4—3442no—
194C4—3442no—
195C4#1458307111yescharacteristic
196C4#1458307611yescharacteristic
197C2—22no—
198C2#1913582411yescharacteristic
199C2#1913586311yescharacteristic
200C2#1913590111yescharacteristic
subgroupG/H
centerC22#14582816
commutator, cosocleC2×C42×C43C23
FrattiniC2×C42C22×D43
FittingC43×#1832C2
socleC22×C43#394
prime radicalC23×C43#121
hypercenter#1832D43
hypocenterC43#10517
LCSG ▷ C2×C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1832

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
#191332932
#191331062
#191324652
C43×#18322
#1051743