Finite Group Databasebeta

← #25009093

Subgroups — #25009093

Order 11008.

330 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 330 conjugacy classes of subgroups — too many to draw. Only its 59 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#19136529C212yesmaximal
3#19132612C212yesmaximal
4#19132537C211yesmaximal, characteristic
5C43×#2047C211yesmaximal, characteristic
6#14583511—21no—
7C2×#13063271—22no—
8#14583207—22no—
9#14583157—21no—
10#14583140C2212yes—
11#14583110—22no—
12#14582703—22no—
13C22⋊(C43⋊C16)C2212yes—
14C22×Q16×C43C2211yescharacteristic
15C43×#424C2211yescharacteristic
16C43×#419—21no—
17C2×#101×C43—21no—
18C43×#341C2211yescharacteristic
19C2×Dic172—21no—
20C2×Dic172D412yes—
21#13063325—21no—
22#13063318—42no—
23#13063317—21no—
24#13063315—42no—
25#13063304—22no—
26C4×Dic86—22no—
27#13063271—44no—
28C2×C43⋊C16—22no—
29#13063259D412yes—
30#13063257—21no—
31#13063250—22no—
32#13063250—22no—
33C22×Q8×C43—21no—
34C2×Q16×C43—22no—
35C2×Q16×C43—42no—
36C2×M16×C43—21no—
37C2×M16×C43D411yescharacteristic
38C22×C8×C43C2311yescharacteristic
39#117×C43D411yescharacteristic
40C4⋊C8×C43—22no—
41#103×C43—42no—
42#101×C43—42no—
43C2×Q8×C43—22no—
44C2×Q8×C43—41no—
45C2×Q8×C43—41no—
46C2×Q8×C43—41no—
47C2×Q8×C43—41no—
48C2×Q8×C43—41no—
49C22×C4×C43—41no—
50C22×C4×C43C2×D411yescharacteristic
51C2×Dic86—22no—
52Q16×C43—24no—
53Q16×C43—42no—
54M16×C43—41no—
55M16×C43—41no—
56M16×C43—41no—
57C2×C8×C43—21no—
58C2×C8×C43—41no—
59C2×C8×C43—41no—
60C2×C8×C43C2×D412yes—
61C4⋊C4×C43D812yes—
62C22⋊C4×C43—21no—
63C42×C43—21no—
64C22⋊Dic43—42no—
65C4⋊Dic43—22no—
66C4⋊Dic43—42no—
67Dic43⋊C4—42no—
68Dic43⋊C4—42no—
69Dic43⋊C4—42no—
70C4×Dic43—42no—
71Dic172—42no—
72Dic172—81no—
73C43⋊C16—42no—
74C23×C43AGL(1,ℤ/8)11yescharacteristic
75Q8×C43—42no—
76Q8×C43—42no—
77Q8×C43—81no—
78Q8×C43—81no—
79C2×C4×C43—21no—
80C2×C4×C43—21no—
81C2×C4×C43—22no—
82C2×C4×C43—42no—
83C2×C4×C43—81no—
84C2×C4×C43—81no—
85C2×C4×C43#12011yescharacteristic
86C2×C4×C43C2×D811yescharacteristic
87C2×Dic43—42no—
88C2×Dic43—42no—
89Dic86—42no—
90Dic86—42no—
91C8×C43—22no—
92C8×C43—41no—
93C8×C43—81no—
94#12168—431nomaximal, Sylow
95C22×C43—21no—
96C22×C43—22no—
97C22×C43#44711yescharacteristic
98C4×C43—21no—
99C4×C43—42no—
100C4×C43—82no—
101C4×C43#45411yescharacteristic
102C4×C43B(4,𝔽2)11yescharacteristic
103Dic43—82no—
104Dic43—82no—
105#3261—431no—
106#2188—432no—
107#2047D4311yescharacteristic
108#1350—432no—
109#1323—431no—
110C2×C43—41no—
111C2×C43#159811yescharacteristic
112C2×C43#219512yes—
113C22×Q16C2×D4311yescharacteristic
114#541—861no—
115C2×Q32—862no—
116#479—862no—
117#470—861no—
118#467—432no—
119#462—862no—
120#424C2×D4311yescharacteristic
121#419—21no—
122C2×#101—21no—
123#358—862no—
124C22⋊C16—432no—
125#341C2×D4311yescharacteristic
126C43#1216811yescharacteristic, complemented, Sylow
127C22×Q8—21no—
128C2×Q16—22no—
129C2×Q16—42no—
130C2×Q16—432no—
131C2×Q16—861no—
132C2×M16—21no—
133C2×M16C22⋊D4311yescharacteristic
134C22×C8C22×D4311yescharacteristic
135C4⋊Q8—861no—
136#126—1722no—
137#125—861no—
138#125—1722no—
139C22⋊Q8—862no—
140C4×Q8—862no—
141#117C22⋊D4311yescharacteristic
142Q32—1724no—
143C2×C16—862no—
144#107—432no—
145#106—861no—
146C4⋊C8—22no—
147#103—42no—
148#103—862no—
149#103—862no—
150#101—42no—
151C2×Q8—22no—
152C2×Q8—41no—
153C2×Q8—41no—
154C2×Q8—41no—
155C2×Q8—41no—
156C2×Q8—41no—
157C2×Q8—862no—
158C22×C4—41no—
159C22×C4C2×C22⋊D4311yescharacteristic
160Q16—24no—
161Q16—42no—
162Q16—3441no—
163Q16—1722no—
164M16—41no—
165M16—41no—
166M16—41no—
167C2×C8—21no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8D4×D4312yes—
171C4⋊C4—862no—
172C4⋊C4—1722no—
173C4⋊C4—1722no—
174C4⋊C4—1722no—
175C4⋊C4—1722no—
176C4⋊C4#1062188212yes—
177C22⋊C4—21no—
178C22⋊C4—1722no—
179C42—21no—
180C42—1722no—
181C16—1722no—
182C23#1306335011yescharacteristic
183Q8—42no—
184Q8—42no—
185Q8—81no—
186Q8—81no—
187Q8—1722no—
188Q8—1722no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—22no—
192C2×C4—42no—
193C2×C4—81no—
194C2×C4—81no—
195C2×C4—1722no—
196C2×C4—1722no—
197C2×C4#1306329311yescharacteristic
198C2×C4C2×#1062188211yescharacteristic
199C8—22no—
200C8—41no—
201C8—81no—
202C22—22no—
203C22—21no—
204C22#1458303211yescharacteristic
205C4—21no—
206C4—42no—
207C4—82no—
208C4—3442no—
209C4—3442no—
210C4#1458307111yescharacteristic
211C4#1458308511yescharacteristic
212C2—41no—
213C2#1913352911yescharacteristic
214C2#1913657112yes—
subgroupG/H
centerC22#14583032
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#2047C2
socleC22×C43#447
prime radicalC23×C43AGL(1,ℤ/8)
hypercenter#2047D43
hypocenterC43#12168
LCSG ▷ C22×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #424 ◁ #2047

Complements

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

NH ≅ G/Ntype
126. C43#12168semidirect

Maximal subgroups

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

subgroupindex
#191460492
#191365292
#191326122
#191325372
C43×#20472
#1216843