Finite Group Databasebeta

← #25009088

Subgroups — #25009088

Order 11008.

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

normal subgroups only

This group has 354 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#19146034C211yesmaximal, characteristic
2#19136512C212yesmaximal, complemented
3#19132609C212yesmaximal, complemented
4#19132537C211yesmaximal, characteristic, complemented
5C43×#2047C211yesmaximal, characteristic, complemented
6#14583504—21no—
7C2×#13063268—22no—
8#14583200—22no—
9#14583152—21no—
10#14583135C2212yes—
11#14583095—22no—
12#14582703—22no—
13C22⋊(C43⋊C16)C2212yes—
14C22×Q16×C43C2211yescharacteristic
15C43×#424C2211yescharacteristic
16C43×#419—21no—
17C2×#101×C43—21no—
18C43×#341C2211yescharacteristic
19C2×D344—21no—
20C2×D344D412yes—
21#13063322—21no—
22#13063317—21no—
23#13063310—42no—
24#13063299—22no—
25#13063298—42no—
26C4×D172—22no—
27#13063268—44no—
28C2×C43⋊C16—22no—
29#13063259D412yes—
30#13063257—21no—
31#13063247—22no—
32#13063247—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×C22⋊D43—42no—
52C2×D172—22no—
53C2×D172—42no—
54C2×C4×D43—42no—
55Q16×C43—24no—
56Q16×C43—42no—
57M16×C43—41no—
58M16×C43—41no—
59M16×C43—41no—
60C2×C8×C43—21no—
61C2×C8×C43—41no—
62C2×C8×C43—41no—
63C2×C8×C43C2×D412yes—
64C4⋊C4×C43D812yes—
65C22⋊C4×C43—21no—
66C42×C43—21no—
67(C2×D43)⋊C4—42no—
68(C2×D43)⋊C4—42no—
69C4⋊Dic43—22no—
70Dic43⋊C4—42no—
71D344—42no—
72D344—81no—
73C43⋊C16—42no—
74C23×C43AGL(1,ℤ/8)11yescharacteristic
75C22×D43—42no—
76Q8×C43—42no—
77Q8×C43—42no—
78Q8×C43—81no—
79Q8×C43—81no—
80C2×C4×C43—21no—
81C2×C4×C43—21no—
82C2×C4×C43—22no—
83C2×C4×C43—42no—
84C2×C4×C43—81no—
85C2×C4×C43—81no—
86C2×C4×C43#12011yescharacteristic
87C2×C4×C43C2×D811yescharacteristic
88C22⋊D43—162no—
89C2×Dic43—42no—
90D172—42no—
91D172—42no—
92D172—162no—
93C4×D43—162no—
94C8×C43—22no—
95C8×C43—41no—
96C8×C43—81no—
97#12167—431nomaximal, Sylow
98C22×C43—21no—
99C22×C43—22no—
100C22×C43#44711yescharacteristic
101C2×D43—82no—
102C2×D43—82no—
103C2×D43—82no—
104C4×C43—21no—
105C4×C43—42no—
106C4×C43—82no—
107C4×C43#45411yescharacteristic
108C4×C43B(4,𝔽2)11yescharacteristic
109Dic43—82no—
110#3259—431no—
111#2185—432no—
112#2047D4311yescharacteristic, complemented
113#1349—432no—
114#1323—431no—
115C2×C43—41no—
116C2×C43#159811yescharacteristic
117C2×C43#219412yes—
118D43—162no—
119C22×Q16C2×D4311yescharacteristic
120#540—861no—
121C2×SD32—862no—
122#478—862no—
123#469—861no—
124#466—432no—
125#459—862no—
126#424C2×D4311yescharacteristic
127#419—21no—
128C2×#101—21no—
129#358—862no—
130C22⋊C16—432no—
131#341C2×D4311yescharacteristic
132C43#1216711yescharacteristic, complemented, Sylow
133C22×Q8—21no—
134C2×Q16—22no—
135C2×Q16—42no—
136C2×D8—432no—
137C2×D8—861no—
138C2×M16—21no—
139C2×M16C22⋊D4311yescharacteristic
140C22×C8C22×D4311yescharacteristic
141#127—861no—
142#125—861no—
143#123—1722no—
144#121—862no—
145#121—1722no—
146C4×D4—862no—
147#117C22⋊D4311yescharacteristic
148SD32—1724no—
149C2×C16—862no—
150#107—432no—
151#106—861no—
152C4⋊C8—22no—
153#103—42no—
154#102—862no—
155#102—862no—
156#101—42no—
157C2×Q8—22no—
158C2×Q8—41no—
159C2×Q8—41no—
160C2×Q8—41no—
161C2×Q8—41no—
162C2×Q8—41no—
163C2×D4—862no—
164C2×D4—1722no—
165C2×D4—1722no—
166C22×C4—41no—
167C22×C4—1722no—
168C22×C4C2×C22⋊D4311yescharacteristic
169Q16—24no—
170Q16—42no—
171D8—3441no—
172D8—1722no—
173M16—41no—
174M16—41no—
175M16—41no—
176C2×C8—21no—
177C2×C8—41no—
178C2×C8—41no—
179C2×C8D4×D4312yes—
180C4⋊C4—862no—
181C4⋊C4—1722no—
182C4⋊C4#1062188212yes—
183C22⋊C4—21no—
184C22⋊C4—1722no—
185C22⋊C4—1722no—
186C42—21no—
187C16—1722no—
188C23—1722no—
189C23#1306335011yescharacteristic
190Q8—42no—
191Q8—42no—
192Q8—81no—
193Q8—81no—
194D4—1722no—
195D4—1722no—
196D4—6882no—
197D4—6882no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—42no—
202C2×C4—81no—
203C2×C4—81no—
204C2×C4—1722no—
205C2×C4—6882no—
206C2×C4#1306329311yescharacteristic
207C2×C4C2×#1062188211yescharacteristic
208C8—22no—
209C8—41no—
210C8—81no—
211C22—22no—
212C22—21no—
213C22—3442no—
214C22—3442no—
215C22—3442no—
216C22#1458303211yescharacteristic
217C4—21no—
218C4—42no—
219C4—82no—
220C4—3442no—
221C4#1458307111yescharacteristic
222C4#1458308511yescharacteristic
223C2—41no—
224C2—6882no—
225C2#1913352911yescharacteristic
226C2#1913656412yes—
subgroupG/H
centerC22#14583032
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
FittingC43×#2047C2
socleC22×C43#447
prime radical#19146034C2
hypercenter#2047D43
hypocenterC43#12167
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
2. #19136512C2semidirect
3. #19132609C2semidirect
4. #19132537C2semidirect
5. C43×#2047C2semidirect
112. #2047D43semidirect
132. C43#12167semidirect

Maximal subgroups

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

subgroupindex
#191460342
#191365122
#191326092
#191325372
C43×#20472
#1216743