Finite Group Databasebeta

← #24989111

Subgroups — #24989111

Order 11008.

690 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 690 conjugacy classes of subgroups — too many to draw. Only its 107 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
1C2×#14583511C211yesmaximal, characteristic
2#19134678C211yesmaximal, characteristic
3#19133127C214yesmaximal
4C43×#1820C211yesmaximal, characteristic
5#14583511—28no—
6C2×#13063325C411yescharacteristic, complemented
7C2×#13063318—22no—
8C2×#13063317C411yescharacteristic, complemented
9C2×#13063315—22no—
10C2×#13063304C2212yes—
11C2×C4×Dic86C412yescomplemented
12#14582863C2212yes—
13#14582668—22no—
14#14582635—28no—
15C2×#117×C43C2211yescharacteristic
16C43×#381C2212yes—
17C43×#342—22no—
18C22×Dic86C2×C412yes—
19C2×#10621877—22no—
20#13063325—24no—
21#13063318—216no—
22#13063317—24no—
23#13063315—216no—
24#13063304—24no—
25#13063304D418yes—
26C4×Dic86—24no—
27C4×Dic86—24no—
28C2×C4⋊Dic43—22no—
29C2×C4⋊Dic43C2×C412yes—
30C2×Dic43⋊C4—22no—
31C2×Dic43⋊C4—22no—
32C2×Dic43⋊C4—22no—
33C2×C22⋊Dic43—22no—
34C2×C4×Dic43—22no—
35C22⋊(C43⋊C8)—24no—
36C23×C4×C43C2311yescharacteristic
37#117×C43—24no—
38C2×C4⋊C4×C43D412yes—
39C2×C22⋊C4×C43—22no—
40C2×C22⋊C4×C43D412yes—
41C2×C42×C43C2×C411yescharacteristic
42C2×C42×C43C2×C411yescharacteristic
43#95×C43—24no—
44C24×C43C2×D411yescharacteristic
45C22×C4×C43—42no—
46C22×C4×C43—42no—
47C22×C4×C43C22⋊C412yes—
48C22×C4×C43C22⋊C412yes—
49C22×C4×C43C22×C411yescharacteristic
50C22×C4×C43C2×D411yescharacteristic
51C22×C4×C43C2×D414yes—
52C22×Dic43—22no—
53C22×Dic43—22no—
54C2×Dic86—22no—
55C2×Dic86—44no—
56C2×Dic86C22⋊C414yes—
57C4⋊C4×C43—24no—
58C22⋊C4×C43—24no—
59C22⋊C4×C43—44no—
60C42×C43—22no—
61C42×C43—22no—
62C22⋊Dic43—28no—
63C4⋊Dic43—28no—
64C4⋊Dic43—22no—
65C4⋊Dic43C22⋊C414yes—
66Dic43⋊C4—28no—
67Dic43⋊C4—28no—
68Dic43⋊C4—28no—
69C4×Dic43—28no—
70#10621877—44no—
71C2×C43⋊C8—42no—
72C23×C43—22no—
73C23×C43—42no—
74C23×C43C2×C22⋊C411yescharacteristic
75C23×C43#12012yes—
76C2×C4×C43—22no—
77C2×C4×C43—22no—
78C2×C4×C43—22no—
79C2×C4×C43—22no—
80C2×C4×C43—44no—
81C2×C4×C43—42no—
82C2×C4×C43—42no—
83C2×C4×C43—82no—
84C2×C4×C43—84no—
85C2×C4×C43C2×C22⋊C412yes—
86C2×C4×C43#12012yes—
87C2×Dic43—24no—
88C2×Dic43—24no—
89C2×Dic43—44no—
90C2×Dic43—44no—
91Dic86—44no—
92Dic86—44no—
93C43⋊C8—82no—
94#8521—431nomaximal, Sylow
95C22×C43—22no—
96C22×C43—24no—
97C22×C43—22no—
98C22×C43—82no—
99C22×C43#37911yescharacteristic
100C22×C43#41012yes—
101C4×C43—22no—
102C4×C43—22no—
103C4×C43—42no—
104C4×C43—42no—
105C4×C43—162no—
106Dic43—44no—
107Dic43—44no—
108C2×#541—431no—
109#1822—431no—
110#1820D4311yescharacteristic
111#1511—434no—
112C2×C43—22no—
113C2×C43—42no—
114C2×C43#178211yescharacteristic
115C2×C43#179612yes—
116#541—868no—
117C2×C4⋊Q8—431no—
118C2×#126—862no—
119C2×#125—431no—
120C2×#125—862no—
121C2×C22⋊Q8—432no—
122C2×C4×Q8—432no—
123C2×#117C2×D4311yescharacteristic
124#407—432no—
125#381C2×D4312yes—
126#343—862no—
127#342—22no—
128#328—868no—
129C43#852111yescharacteristic, complemented, Sylow
130C22×Q8—432no—
131C23×C4C22×D4311yescharacteristic
132C2×M16—862no—
133C4⋊Q8—864no—
134#126—8616no—
135#125—864no—
136#125—8616no—
137C22⋊Q8—438no—
138C22⋊Q8—864no—
139C4×Q8—864no—
140C4×Q8—864no—
141#117—24no—
142C2×C4⋊C4—432no—
143C2×C4⋊C4—862no—
144C2×C4⋊C4—862no—
145C2×C4⋊C4—862no—
146C2×C4⋊C4—862no—
147C2×C4⋊C4D17212yes—
148C2×C22⋊C4—22no—
149C2×C22⋊C4—862no—
150C2×C22⋊C4C22⋊D4312yes—
151C2×C42—862no—
152C2×C42C4×D4311yescharacteristic
153C2×C42C4×D4311yescharacteristic
154C22⋊C8—864no—
155#95—24no—
156C24C2×C22⋊D4311yescharacteristic
157C2×Q8—434no—
158C2×Q8—862no—
159C2×Q8—1724no—
160C22×C4—42no—
161C22×C4—42no—
162C22×C4—862no—
163C22×C4—862no—
164C22×C4(C2×D43)⋊C412yes—
165C22×C4(C2×D43)⋊C412yes—
166C22×C4C2×C4×D4311yescharacteristic
167C22×C4C2×D17211yescharacteristic
168C22×C4D4×D4314yes—
169M16—1724no—
170C2×C8—1722no—
171C4⋊C4—24no—
172C4⋊C4—434no—
173C4⋊C4—868no—
174C4⋊C4—868no—
175C4⋊C4—868no—
176C4⋊C4—862no—
177C4⋊C4—868no—
178C22⋊C4—24no—
179C22⋊C4—44no—
180C22⋊C4—868no—
181C42—22no—
182C42—22no—
183C42—868no—
184C23—22no—
185C23—42no—
186C23C2×(C2×D43)⋊C411yescharacteristic
187C23#1306329312yes—
188Q8—1724no—
189Q8—1724no—
190C2×C4—22no—
191C2×C4—22no—
192C2×C4—22no—
193C2×C4—22no—
194C2×C4—44no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—82no—
198C2×C4—84no—
199C2×C4—864no—
200C2×C4—864no—
201C2×C4—1724no—
202C2×C4—1724no—
203C2×C4C22⋊C4×D4312yes—
204C2×C4#1306329512yes—
205C8—3442no—
206C22—22no—
207C22—22no—
208C22—24no—
209C22—82no—
210C22#1458275411yescharacteristic
211C22#1458287212yes—
212C4—22no—
213C4—22no—
214C4—42no—
215C4—42no—
216C4—162no—
217C4—1724no—
218C4—1724no—
219C2—22no—
220C2—42no—
221C2#1913451211yescharacteristic
222C2#1913456812yes—
subgroupG/H
centerC22#14582754
commutatorC22×C4×C43C22×C4
FrattiniC23×C4C22×D43
FittingC43×#1820C2
socleC22×C43#379
prime radicalC24×C43C2×D4
cosocleC23×C4×C43C23
hypercenter#1820D43
hypocenterC43#8521
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1820

Complements

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

NH ≅ G/Ntype
6. C2×#13063325C4semidirect
8. C2×#13063317C4semidirect
11. C2×C4×Dic86C4semidirect
129. C43#8521semidirect

Maximal subgroups

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

subgroupindex
C2×#145835112
#191346782
#191331272
C43×#18202
#852143