Finite Group Databasebeta

← #25009960

Subgroups — #25009960

Order 11008.

262 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 55 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#19146049C211yesmaximal, characteristic
2#19136814C212yesmaximal
3#19132588C212yesmaximal
4#19132548C211yesmaximal, characteristic
5C43×#2103C211yesmaximal, characteristic
6#14583511—21no—
7#14583207—22no—
8#14583157C2212yes—
9#14583140—21no—
10#14583110—22no—
11#14582723—22no—
12#14582714—22no—
13#14582681C2212yes—
14C43×#430C2211yescharacteristic
15C43×#424C2211yescharacteristic
16C43×#344—21no—
17C43×#341—21no—
18C43×#338C2211yescharacteristic
19C2×Dic172—21no—
20C2×Dic172D412yes—
21#13063325—21no—
22#13063318—42no—
23#13063317—21no—
24#13063315—42no—
25#13063304—22no—
26C4×Dic86—22no—
27#13063265—22no—
28#13063259—21no—
29#13063257D412yes—
30#13063250—22no—
31#13063250—22no—
32C2×M16×C43—21no—
33C2×M16×C43—21no—
34C2×M16×C43C2311yescharacteristic
35C22×C8×C43D411yescharacteristic
36#117×C43D411yescharacteristic
37#108×C43—22no—
38C4⋊C8×C43—22no—
39C22×C4×C43C2×D411yescharacteristic
40C2×Dic86—22no—
41M16×C43—41no—
42M16×C43—41no—
43M16×C43—41no—
44M16×C43—41no—
45M16×C43—41no—
46C2×C8×C43—21no—
47C2×C8×C43—41no—
48C2×C8×C43—41no—
49C2×C8×C43—41no—
50C2×C8×C43C2×D412yes—
51C4⋊C4×C43—21no—
52C22⋊C4×C43SD1612yes—
53C42×C43—21no—
54C22⋊Dic43—42no—
55C4⋊Dic43—22no—
56C4⋊Dic43—42no—
57Dic43⋊C4—42no—
58Dic43⋊C4—42no—
59Dic43⋊C4—42no—
60C4×Dic43—42no—
61Dic172—42no—
62Dic172—81no—
63C43⋊C16—42no—
64C23×C43C2×SD1611yescharacteristic
65C2×C4×C43—21no—
66C2×C4×C43—21no—
67C2×C4×C43—22no—
68C2×C4×C43#12011yescharacteristic
69C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
70C2×Dic43—42no—
71C2×Dic43—42no—
72Dic86—42no—
73Dic86—42no—
74C8×C43—22no—
75C8×C43—41no—
76C8×C43—81no—
77C8×C43—81no—
78#12305—431nomaximal, Sylow
79C22×C43—21no—
80C22×C43—41no—
81C22×C43#45011yescharacteristic
82C4×C43—21no—
83C4×C43—42no—
84C4×C43#45411yescharacteristic
85C4×C43#45811yescharacteristic
86Dic43—82no—
87Dic43—82no—
88#3261—431no—
89#2239—432no—
90#2103D4311yescharacteristic
91#1342—432no—
92#1328—431no—
93C2×C43—21no—
94C2×C43—41no—
95C2×C43#161611yescharacteristic
96#541—861no—
97#479—862no—
98#470—432no—
99#467—861no—
100#462—862no—
101#430C2×D4311yescharacteristic
102#424C2×D4311yescharacteristic
103#365—862no—
104#362—862no—
105#349—432no—
106#344—21no—
107#341—21no—
108#338C2×D4311yescharacteristic
109C43#1230511yescharacteristic, complemented, Sylow
110C2×Q16—432no—
111C2×Q16—861no—
112C2×M16—21no—
113C2×M16—21no—
114C2×M16C22×D4311yescharacteristic
115C22×C8C22⋊D4311yescharacteristic
116C4⋊Q8—861no—
117#126—1722no—
118#125—861no—
119#125—1722no—
120C22⋊Q8—862no—
121C4×Q8—862no—
122#117C22⋊D4311yescharacteristic
123M32—862no—
124#108—22no—
125#107—861no—
126#106—432no—
127C4⋊C8—22no—
128#103—862no—
129#103—862no—
130C2×Q8—862no—
131C22×C4C2×C22⋊D4311yescharacteristic
132Q16—3441no—
133Q16—1722no—
134M16—41no—
135M16—41no—
136M16—41no—
137M16—41no—
138M16—41no—
139C2×C8—21no—
140C2×C8—41no—
141C2×C8—41no—
142C2×C8—41no—
143C2×C8D4×D4312yes—
144C4⋊C4—21no—
145C4⋊C4—862no—
146C4⋊C4—1722no—
147C4⋊C4—1722no—
148C4⋊C4—1722no—
149C4⋊C4—1722no—
150C22⋊C4—1722no—
151C22⋊C4#1062188412yes—
152C42—21no—
153C42—1722no—
154C16—1722no—
155C23C2×#1062188411yescharacteristic
156Q8—1722no—
157Q8—1722no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—1722no—
162C2×C4—1722no—
163C2×C4#1306329311yescharacteristic
164C2×C4#1306335011yescharacteristic
165C8—22no—
166C8—41no—
167C8—81no—
168C8—81no—
169C22—21no—
170C22—41no—
171C22#1458304911yescharacteristic
172C4—21no—
173C4—42no—
174C4—3442no—
175C4—3442no—
176C4#1458307111yescharacteristic
177C4#1458308811yescharacteristic
178C2—21no—
179C2—41no—
180C2#1913363111yescharacteristic
subgroupG/H
centerC2#19133631
commutator, cosocleC2×M16×C43C23
FrattiniC2×M16C22×D43
FittingC43×#2103C2
socleC2×C43#1616
prime radicalC23×C43C2×SD16
hypercenter#2103D43
hypocenterC43#12305
LCSG ▷ C2×M16×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2103

Complements

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

NH ≅ G/Ntype
109. C43#12305semidirect

Maximal subgroups

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

subgroupindex
#191460492
#191368142
#191325882
#191325482
C43×#21032
#1230543