Finite Group Databasebeta

← #25010878

Subgroups — #25010878

Order 11008.

228 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 228 conjugacy classes of subgroups — too many to draw. Only its 67 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#19136503C211yesmaximal, characteristic, complemented
2#19133962C211yesmaximal, characteristic, complemented
3#19133952C211yesmaximal, characteristic
4#19132667C211yesmaximal, characteristic, complemented
5#19132644C211yesmaximal, characteristic, complemented
6#19132641C211yesmaximal, characteristic
7C43×#2248C211yesmaximal, characteristic
8#14583181—21no—
9#14583096—21no—
10C8×Dic86C2211yescharacteristic
11C4⋊(C43⋊C16)C2211yescharacteristic
12Dic43⋊C16—21no—
13#14582674—21no—
14#14582652C2211yescharacteristic
15#14582652C2211yescharacteristic
16#14582645—21no—
17#14582643—21no—
18C2×SD32×C43—21no—
19C2×SD32×C43—21no—
20C43×#494C2211yescharacteristic
21C43×#493C2211yescharacteristic
22C4×C16×C43C2211yescharacteristic
23C2×#10621883—41no—
24C4×Dic86D411yescharacteristic
25C2×C43⋊C16—21no—
26#13063256—41no—
27C4⋊(C43⋊C8)—21no—
28C4⋊(C43⋊C8)—21no—
29C4⋊(C43⋊C8)D411yescharacteristic
30Dic43⋊C8—21no—
31#13063248—41no—
32#13063246—41no—
33C8×Dic43—21no—
34C2×Q16×C43—21no—
35C2×Q16×C43—21no—
36C2×D8×C43—21no—
37C2×D8×C43—21no—
38C4⋊Q8×C43—21no—
39#127×C43—21no—
40SD32×C43—42no—
41SD32×C43—42no—
42C2×C16×C43D411yescharacteristic
43C2×C16×C43D411yescharacteristic
44C4×C8×C43C2311yescharacteristic
45C2×Q8×C43—41no—
46C2×D4×C43—41no—
47C2×D4×C43—41no—
48C2×D4×C43—41no—
49C2×Dic86D811yescharacteristic
50Q16×C43—41no—
51Q16×C43—41no—
52Q16×C43—81no—
53D8×C43—41no—
54D8×C43—41no—
55D8×C43—81no—
56C2×C8×C43C2×D411yescharacteristic
57C2×C8×C43#4111yescharacteristic
58C4⋊C4×C43—41no—
59C4⋊C4×C43—41no—
60C42×C43C2×D411yescharacteristic
61#10621883—82no—
62C4⋊Dic43D811yescharacteristic
63Dic43⋊C4—21no—
64C4×Dic43—21no—
65C2×C43⋊C8—21no—
66C2×C43⋊C8—41no—
67C2×C43⋊C8—41no—
68C16×C43—21no—
69C16×C43SD1612yescomplemented
70C43⋊C16—41no—
71C23×C43—81no—
72Q8×C43—81no—
73Q8×C43—81no—
74D4×C43—81no—
75D4×C43—81no—
76D4×C43—81no—
77D4×C43—81no—
78D4×C43—161no—
79C2×C4×C43—81no—
80C2×C4×C43#12111yescharacteristic
81C2×C4×C43C2×D811yescharacteristic
82C2×C4×C43#13511yescharacteristic
83C2×Dic43—21no—
84C2×Dic43—21no—
85Dic86—21no—
86Dic86—21no—
87C8×C43—21no—
88C8×C43C2×SD1611yescharacteristic
89C8×C43AGL(1,ℤ/8)11yescharacteristic
90C43⋊C8—41no—
91C43⋊C8—81no—
92C43⋊C8—81no—
93#12444—431nomaximal, Sylow
94C22×C43—161no—
95C22×C43—161no—
96C22×C43—161no—
97C22×C43#46611yescharacteristic
98C4×C43—21no—
99C4×C43—161no—
100C4×C43#46011yescharacteristic
101C4×C43#47211yescharacteristic
102C4×C43#50911yescharacteristic
103C4×C43#51011yescharacteristic
104Dic43—41no—
105Dic43—41no—
106#2248D4311yescharacteristic
107#2183—431no—
108#1670—431no—
109#1668—431no—
110#1371—431no—
111#1362—431no—
112#1361—431no—
113C2×C43—321no—
114C2×C43#166811yescharacteristic
115C2×C43#222011yescharacteristic
116C2×C43#222311yescharacteristic
117C2×SD32—21no—
118C2×SD32—21no—
119#494C2×D4311yescharacteristic
120#493C2×D4311yescharacteristic
121#475—861no—
122#460—861no—
123C8×Q8—431no—
124C4⋊C16—431no—
125C4⋊C16—861no—
126#346—861no—
127C4×C16C2×D4311yescharacteristic
128#335—431no—
129#335—431no—
130#332—861no—
131#331—861no—
132C43#1244411yescharacteristic, complemented, Sylow
133C2×Q16—21no—
134C2×Q16—21no—
135C2×SD16—1721no—
136C2×D8—21no—
137C2×D8—21no—
138C4⋊Q8—21no—
139#127—21no—
140C4×Q8—431no—
141SD32—42no—
142SD32—42no—
143C2×C16—861no—
144C2×C16C22⋊D4311yescharacteristic
145C2×C16C22⋊D4311yescharacteristic
146#106—1721no—
147C4⋊C8—431no—
148C4⋊C8—861no—
149C4⋊C8—861no—
150C4⋊C8—861no—
151#103—1721no—
152#102—1721no—
153C4×C8—861no—
154C4×C8C22×D4311yescharacteristic
155C2×Q8—41no—
156C2×Q8—431no—
157C2×D4—41no—
158C2×D4—41no—
159C2×D4—41no—
160Q16—41no—
161Q16—41no—
162Q16—81no—
163SD16—3442no—
164D8—41no—
165D8—41no—
166D8—81no—
167C2×C8—861no—
168C2×C8—1721no—
169C2×C8—1721no—
170C2×C8#1062190011yescharacteristic
171C2×C8C2×C22⋊D4311yescharacteristic
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—431no—
175C4⋊C4—861no—
176C42—861no—
177C42D4×D4311yescharacteristic
178C16—21no—
179C16—1721no—
180C16#1062188312yescomplemented
181C23—81no—
182Q8—81no—
183Q8—81no—
184Q8—861no—
185Q8—861no—
186D4—81no—
187D4—81no—
188D4—81no—
189D4—81no—
190D4—161no—
191C2×C4—81no—
192C2×C4—861no—
193C2×C4—861no—
194C2×C4#1306329611yescharacteristic
195C2×C4D8×D4311yescharacteristic
196C2×C4#1306334411yescharacteristic
197C8—21no—
198C8—3441no—
199C8—3441no—
200C8—1721no—
201C8C2×#1062188311yescharacteristic
202C8#1306335111yescharacteristic
203C22—161no—
204C22—161no—
205C22—161no—
206C22#1458313211yescharacteristic
207C4—21no—
208C4—161no—
209C4—1721no—
210C4—1721no—
211C4#1458309611yescharacteristic
212C4#1458316611yescharacteristic
213C4#1458333611yescharacteristic
214C4#1458333811yescharacteristic
215C2—321no—
216C2#1913395211yescharacteristic
217C2#1913670511yescharacteristic
218C2#1913672211yescharacteristic
subgroupG/H
centerC22#14583132
commutator, cosocleC4×C8×C43C23
FrattiniC4×C8C22×D43
FittingC43×#2248C2
socleC22×C43#466
prime radicalC43×#493C22
hypercenter#2248D43
hypocenterC43#12444
LCSG ▷ C4×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #2248

Complements

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

NH ≅ G/Ntype
1. #19136503C2semidirect
2. #19133962C2semidirect
4. #19132667C2semidirect
5. #19132644C2semidirect
69. C16×C43SD16semidirect
132. C43#12444semidirect
180. C16#10621883semidirect

Maximal subgroups

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

subgroupindex
#191365032
#191339622
#191339522
#191326672
#191326442
#191326412
C43×#22482
#1244443