Finite Group Databasebeta

← #25009089

Subgroups — #25009089

Order 11008.

354 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 354 conjugacy classes of subgroups — too many to draw. Only its 63 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#19136511C212yesmaximal, complemented
2#19135863C211yesmaximal, characteristic, complemented
3#19132610C212yesmaximal, complemented
4#19132537C211yesmaximal, characteristic, complemented
5C43×#3259C211yesmaximal, characteristic
6C22×Dic172C2211yescharacteristic
7C2×#13063269—22no—
8#14582907—21no—
9C2×#13063243—21no—
10#14582702—22no—
11C22⋊(C43⋊C16)C2212yes—
12#14582664C2211yescharacteristic
13C43×#540—21no—
14C43×#478—22no—
15C43×#469—21no—
16C43×#466C2212yes—
17C43×#459—22no—
18C43×#424C2211yescharacteristic
19C22×Dic86—21no—
20C2×Dic172—22no—
21C2×Dic172—42no—
22C2×#10621877—21no—
23#13063269—44no—
24C2×C43⋊C16—22no—
25#13063248—42no—
26#13063243—42no—
27C2×D8×C43—21no—
28C2×D8×C43D412yes—
29C2×M16×C43D411yescharacteristic
30C22×C8×C43C2311yescharacteristic
31#127×C43—21no—
32#125×C43—21no—
33#123×C43—42no—
34#121×C43—22no—
35#121×C43—42no—
36C4×D4×C43—22no—
37#117×C43D411yescharacteristic
38#107×C43D412yes—
39#106×C43—21no—
40C4⋊C8×C43—22no—
41#102×C43—22no—
42#102×C43—22no—
43C2×D4×C43—22no—
44C2×D4×C43—42no—
45C2×D4×C43—42no—
46C22×C4×C43—42no—
47C22×C4×C43C2×D411yescharacteristic
48C22×Dic43—41no—
49C2×Dic86—22no—
50C2×Dic86—41no—
51C2×Dic86—41no—
52C2×Dic86—41no—
53C2×Dic86—41no—
54C2×Dic86—41no—
55D8×C43—42no—
56D8×C43—81no—
57M16×C43—41no—
58C2×C8×C43—21no—
59C2×C8×C43—41no—
60C2×C8×C43C2×D412yes—
61C4⋊C4×C43—22no—
62C4⋊C4×C43—42no—
63C4⋊C4×C43D812yes—
64C22⋊C4×C43—21no—
65C22⋊C4×C43—42no—
66C22⋊C4×C43—42no—
67C42×C43—21no—
68#10621877—41no—
69#10621877—41no—
70C2×C43⋊C8—41no—
71Dic172—24no—
72Dic172—42no—
73C43⋊C16—42no—
74C23×C43—42no—
75C23×C43AGL(1,ℤ/8)11yescharacteristic
76D4×C43—42no—
77D4×C43—42no—
78D4×C43—162no—
79D4×C43—162no—
80C2×C4×C43—21no—
81C2×C4×C43—21no—
82C2×C4×C43—22no—
83C2×C4×C43—42no—
84C2×C4×C43—162no—
85C2×C4×C43#12011yescharacteristic
86C2×C4×C43C2×D811yescharacteristic
87C2×Dic43—42no—
88C2×Dic43—81no—
89C2×Dic43—81no—
90Dic86—42no—
91Dic86—42no—
92Dic86—81no—
93Dic86—81no—
94C8×C43—22no—
95C8×C43—41no—
96C43⋊C8—81no—
97#12167—431nomaximal, Sylow
98C22×C43—21no—
99C22×C43—22no—
100C22×C43—82no—
101C22×C43—82no—
102C22×C43—82no—
103C22×C43#44711yescharacteristic
104C4×C43—21no—
105C4×C43—42no—
106C4×C43—82no—
107C4×C43#45411yescharacteristic
108C4×C43B(4,𝔽2)11yescharacteristic
109Dic43—82no—
110#3259D4311yescharacteristic
111#2185—432no—
112#2047—431no—
113#1349—432no—
114#1323—431no—
115C2×C43—41no—
116C2×C43—162no—
117C2×C43#159811yescharacteristic
118C2×C43#219412yes—
119C22×Q16—431no—
120#540—21no—
121C2×SD32—862no—
122#478—22no—
123#469—21no—
124#466C2×D4312yes—
125#459—22no—
126#424C2×D4311yescharacteristic
127#419—861no—
128C2×#101—861no—
129#358—862no—
130C22⋊C16—432no—
131#341—431no—
132C43#1216711yescharacteristic, complemented, Sylow
133C22×Q8—861no—
134C2×Q16—862no—
135C2×Q16—1722no—
136C2×D8—21no—
137C2×D8C22⋊D4312yes—
138C2×M16—861no—
139C2×M16C22⋊D4311yescharacteristic
140C22×C8C22×D4311yescharacteristic
141#127—21no—
142#125—21no—
143#123—42no—
144#121—22no—
145#121—42no—
146C4×D4—22no—
147#117C22⋊D4311yescharacteristic
148SD32—1724no—
149C2×C16—862no—
150#107C22⋊D4312yes—
151#106—21no—
152C4⋊C8—22no—
153#103—1722no—
154#102—22no—
155#102—22no—
156#101—1722no—
157C2×Q8—862no—
158C2×Q8—1721no—
159C2×Q8—1721no—
160C2×Q8—1721no—
161C2×Q8—1721no—
162C2×Q8—1721no—
163C2×D4—22no—
164C2×D4—42no—
165C2×D4—42no—
166C22×C4—42no—
167C22×C4—1721no—
168C22×C4C2×C22⋊D4311yescharacteristic
169Q16—864no—
170Q16—1722no—
171D8—42no—
172D8—81no—
173M16—41no—
174M16—1721no—
175M16—1721no—
176C2×C8—21no—
177C2×C8—41no—
178C2×C8—1721no—
179C2×C8C2×C22⋊D4312yes—
180C4⋊C4—22no—
181C4⋊C4—42no—
182C4⋊C4#1062188212yes—
183C22⋊C4—21no—
184C22⋊C4—42no—
185C22⋊C4—42no—
186C42—21no—
187C16—1722no—
188C23—42no—
189C23#1306335111yescharacteristic
190Q8—3441no—
191Q8—3441no—
192Q8—1722no—
193Q8—1722no—
194D4—42no—
195D4—42no—
196D4—162no—
197D4—162no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—22no—
201C2×C4—42no—
202C2×C4—162no—
203C2×C4—3441no—
204C2×C4—3441no—
205C2×C4—1722no—
206C2×C4#1306329411yescharacteristic
207C2×C4C2×#1062188211yescharacteristic
208C8—22no—
209C8—41no—
210C8—3441no—
211C22—22no—
212C22—21no—
213C22—82no—
214C22—82no—
215C22—82no—
216C22#1458303311yescharacteristic
217C4—21no—
218C4—42no—
219C4—82no—
220C4—3442no—
221C4#1458307211yescharacteristic
222C4#1458308611yescharacteristic
223C2—41no—
224C2—162no—
225C2#1913353011yescharacteristic
226C2#1913656612yes—
subgroupG/H
centerC22#14583033
commutator, cosocleC22×C8×C43C23
FrattiniC22×C8C22×D43
Fitting, prime radicalC43×#3259C2
socleC22×C43#447
hypercenter#3259D43
hypocenterC43#12167
LCSG ▷ C22×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #424 ◁ #3259

Complements

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

NH ≅ G/Ntype
1. #19136511C2semidirect
2. #19135863C2semidirect
3. #19132610C2semidirect
4. #19132537C2semidirect
132. C43#12167semidirect

Maximal subgroups

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

subgroupindex
#191365112
#191358632
#191326102
#191325372
C43×#32592
#1216743