Finite Group Databasebeta

← #25251498

Subgroups — #25251498

Order 11008.

566 conjugacy classes of subgroups; only the 167 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 167 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#19143206C211yesmaximal, characteristic, complemented
2#19136807C218yesmaximal, complemented
3#19136367C212yesmaximal, complemented
4C2×#14582712C212yesmaximal, complemented
5#19136216C211yesmaximal, characteristic, complemented
6C43×#3058C211yesmaximal, characteristic
7#14583666—21no—
8C2×#13063265C2212yes—
9#14582948—21no—
10#14582948C2214yescomplemented
11C2×#13063261—22no—
12C2×#13063261C2212yes—
13#14582721C2218yescomplemented
14#14582712C2218yes—
15#14582681C2214yescomplemented
16C22×D8×C43C2211yescharacteristic
17C2×#131×C43C2211yescharacteristic
18C43×#535—21no—
19C43×#469C2214yes—
20C43×#466—22no—
21C43×#427C2211yescharacteristic
22C43×#418—21no—
23#13063332—44no—
24C2×#10621877—24no—
25C2×#10621877—22no—
26#13063265—22no—
27#13063265C2314yes—
28C2×C43⋊C16—22no—
29#13063261—22no—
30#13063261—24no—
31#13063261C2314yes—
32C2×#41×C43D411yescharacteristic
33C22×D4×C43—21no—
34C2×D8×C43—21no—
35C2×D8×C43—22no—
36C2×D8×C43—22no—
37C2×D8×C43C2312yes—
38#131×C43—22no—
39#131×C43—22no—
40C2×M16×C43D411yescharacteristic
41C2×M16×C43C2312yes—
42C22×C8×C43D412yes—
43C22×C8×C43C2311yescharacteristic
44#127×C43—41no—
45#124×C43—41no—
46#121×C43—24no—
47#120×C43—42no—
48#117×C43—21no—
49#107×C43—21no—
50#106×C43C2312yes—
51#102×C43—24no—
52C24×C43—41no—
53#41×C43—22no—
54#41×C43—22no—
55C2×Q8×C43SD1611yescharacteristic
56C2×D4×C43—22no—
57C2×D4×C43—41no—
58C2×D4×C43—44no—
59C2×D4×C43—42no—
60C2×D4×C43—42no—
61C2×D4×C43SD1612yes—
62C2×D4×C43SD1611yescharacteristic
63C22×C4×C43C2×D412yes—
64C22×C4×C43C2×D411yescharacteristic
65D8×C43—24no—
66D8×C43—41no—
67D8×C43—41no—
68M16×C43—22no—
69M16×C43—24no—
70C2×C8×C43—22no—
71C2×C8×C43—22no—
72C2×C8×C43C2×D412yes—
73C2×C8×C43C2×D411yescharacteristic
74C2×C8×C43#4112yes—
75C2×C8×C43#4112yes—
76C2×C8×C43C2411yescharacteristic
77C4⋊C4×C43—22no—
78C22⋊C4×C43—44no—
79C22⋊C4×C43—41no—
80C42×C43—41no—
81#10621877—24no—
82#10621877—44no—
83#10621877—42no—
84C2×C43⋊C8—44no—
85C2×C43⋊C8—42no—
86C43⋊C16—24no—
87C23×C43—42no—
88C23×C43—82no—
89C23×C43—162no—
90C23×C43C2×SD1612yes—
91C23×C43C2×SD1611yescharacteristic
92Q8×C43—22no—
93D4×C43—24no—
94D4×C43—22no—
95D4×C43—42no—
96D4×C43—42no—
97D4×C43—82no—
98D4×C43—164no—
99C2×C4×C43—22no—
100C2×C4×C43—22no—
101C2×C4×C43—42no—
102C2×C4×C43#12312yes—
103C2×C4×C43C2×SD1612yes—
104C2×C4×C43C2×SD1611yescharacteristic
105C2×C4×C43AGL(1,ℤ/8)12yes—
106C2×C4×C43C22×D411yescharacteristic
107C8×C43—22no—
108C8×C43#12311yescharacteristic
109C8×C43#12311yescharacteristic
110C8×C43C2×#4112yes—
111C43⋊C8—44no—
112#33657—431nomaximal, Sylow
113C22×C43—22no—
114C22×C43—41no—
115C22×C43—42no—
116C22×C43—84no—
117C22×C43—82no—
118C22×C43—164no—
119C22×C43#48112yes—
120C22×C43C22×SD1611yescharacteristic
121C4×C43—22no—
122C4×C43—82no—
123C4×C43#48112yes—
124C4×C43C2×#12311yescharacteristic
125C4×C43C2×AGL(1,ℤ/8)11yescharacteristic
126#3058D4311yescharacteristic
127#2916—431no—
128#2238—438no—
129#2155—432no—
130C2×#361—432no—
131#2115—431no—
132C2×C43—21no—
133C2×C43—22no—
134C2×C43—42no—
135C2×C43—162no—
136C2×C43C2×#48111yescharacteristic
137C22×D8C2×D4311yescharacteristic
138#568—861no—
139C2×#131C2×D4311yescharacteristic
140#535—21no—
141C2×M32—432no—
142#469C2×D4314yes—
143#466—22no—
144#430—434no—
145#430—861no—
146C2×#108—432no—
147C2×#108—862no—
148#427C2×D4311yescharacteristic
149#418—21no—
150#365—438no—
151#361—438no—
152#349—434no—
153C43#3365711yescharacteristic, complemented, Sylow
154C2×#41C22⋊D4311yescharacteristic
155C22×D4—21no—
156C2×D8—22no—
157C2×D8—22no—
158C2×D8—21no—
159C2×D8C22×D4312yes—
160#131—22no—
161#131—22no—
162#131—1724no—
163C2×M16—864no—
164C2×M16—862no—
165C2×M16C22⋊D4311yescharacteristic
166C2×M16C22×D4312yes—
167C22×C8C22⋊D4312yes—
168C22×C8C22×D4311yescharacteristic
169#127—41no—
170#124—41no—
171#121—24no—
172#120—42no—
173#117—21no—
174M32—434no—
175M32—862no—
176C2×C16—862no—
177#108—434no—
178#108—862no—
179#108—864no—
180#107—21no—
181#106C22×D4312yes—
182#102—24no—
183C24—41no—
184#41—22no—
185#41—22no—
186C2×Q8#1062188311yescharacteristic
187C2×D4—22no—
188C2×D4—44no—
189C2×D4—42no—
190C2×D4—41no—
191C2×D4—42no—
192C2×D4#1062188312yes—
193C2×D4#1062188311yescharacteristic
194C22×C4C2×C22⋊D4312yes—
195C22×C4C2×C22⋊D4311yescharacteristic
196D8—24no—
197D8—41no—
198D8—41no—
199M16—22no—
200M16—24no—
201M16—864no—
202M16—1724no—
203M16—1722no—
204C2×C8—22no—
205C2×C8—22no—
206C2×C8—1724no—
207C2×C8—1722no—
208C2×C8#1062190012yes—
209C2×C8#1062190012yes—
210C2×C8C2×C22⋊D4312yes—
211C2×C8C2×C22⋊D4311yescharacteristic
212C2×C8C23×D4311yescharacteristic
213C4⋊C4—22no—
214C22⋊C4—41no—
215C22⋊C4—44no—
216C42—41no—
217C16—864no—
218C23—42no—
219C23—82no—
220C23—162no—
221C23C2×#1062188312yes—
222C23C2×#1062188311yescharacteristic
223Q8—22no—
224D4—24no—
225D4—22no—
226D4—42no—
227D4—42no—
228D4—82no—
229D4—164no—
230C2×C4—22no—
231C2×C4—22no—
232C2×C4—42no—
233C2×C4#1306330612yes—
234C2×C4C2×#1062188312yes—
235C2×C4C2×#1062188311yescharacteristic
236C2×C4#1306335012yes—
237C2×C4C22×C22⋊D4311yescharacteristic
238C8—22no—
239C8—1724no—
240C8#1306330611yescharacteristic
241C8#1306330611yescharacteristic
242C8C2×#1062190012yes—
243C22—22no—
244C22—41no—
245C22—42no—
246C22—84no—
247C22—82no—
248C22—164no—
249C22#1458321512yes—
250C22C22×#1062188311yescharacteristic
251C4—22no—
252C4—82no—
253C4#1458321512yes—
254C4C2×#1306330611yescharacteristic
255C4C2×#1306335011yescharacteristic
256C2—21no—
257C2—22no—
258C2—42no—
259C2—162no—
260C2C2×#1458321511yescharacteristic
subgroupG/H
centerC2C2×#14583215
commutator, cosocleC2×C8×C43C24
FrattiniC2×C8C23×D43
Fitting, prime radicalC43×#3058C2
socleC2×C43C2×#481
hypercenter#3058D43
hypocenterC43#33657
LCSG ▷ C2×C8×C43 ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#131 ◁ #3058

Complements

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

NH ≅ G/Ntype
1. #19143206C2semidirect
2. #19136807C2semidirect
3. #19136367C2semidirect
4. C2×#14582712C2semidirect
5. #19136216C2semidirect
10. #14582948C22semidirect
13. #14582721C22semidirect
15. #14582681C22semidirect
153. C43#33657semidirect

Maximal subgroups

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

subgroupindex
#191432062
#191368072
#191363672
C2×#145827122
#191362162
C43×#30582
#3365743