Finite Group Databasebeta

← #25007146

Subgroups — #25007146

Order 11008.

292 conjugacy classes of subgroups; only the 75 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 75 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#19145254C211yesmaximal, characteristic
2#19134350C211yesmaximal, characteristic
3#19132590C212yesmaximal
4#19132584C212yesmaximal
5C43×#2166C211yesmaximal, characteristic
6#14583511—21no—
7#14583301C411yescharacteristic, complemented
8#14583279C411yescharacteristic, complemented
9#14583268—21no—
10#14583157C2212yes—
11#14583140—21no—
12#14583007C412yescomplemented
13C4×Dic172—21no—
14#14582854—21no—
15C43⋊#338C2211yescharacteristic
16#14582656C2211yescharacteristic
17#14582655—21no—
18C43×#405C2211yescharacteristic
19C43×#364—21no—
20C43×#349C2212yes—
21C43×#347—21no—
22C2×Dic172—21no—
23C2×Dic172C2×C412yes—
24C2×#10621877—21no—
25#13063325—21no—
26#13063318—42no—
27#13063317—21no—
28#13063315—42no—
29#13063304—22no—
30C4×Dic86—22no—
31#13063284—21no—
32#13063259—21no—
33#13063257C2×C412yes—
34#13063250—22no—
35#13063250—22no—
36#13063235—22no—
37C8×Dic43—22no—
38C2×M16×C43C2311yescharacteristic
39C22×C8×C43D411yescharacteristic
40#117×C43D411yescharacteristic
41M32×C43—22no—
42#97×C43C2×C411yescharacteristic
43#97×C43D411yescharacteristic
44C4×C8×C43C2×C411yescharacteristic
45C4×C8×C43D411yescharacteristic
46C22×C4×C43C2×D411yescharacteristic
47C2×Dic86—22no—
48M16×C43—41no—
49C2×C8×C43—21no—
50C2×C8×C43—21no—
51C2×C8×C43C22⋊C411yescharacteristic
52C2×C8×C43C22⋊C411yescharacteristic
53C2×C8×C43C22×C411yescharacteristic
54C2×C8×C43C2×D411yescharacteristic
55C4⋊C4×C43—21no—
56C22⋊C4×C43—21no—
57C42×C43C22⋊C411yescharacteristic
58C42×C43C22⋊C411yescharacteristic
59C22⋊Dic43—41no—
60C22⋊Dic43—42no—
61C4⋊Dic43—22no—
62C4⋊Dic43—41no—
63C4⋊Dic43—42no—
64Dic43⋊C4—42no—
65Dic43⋊C4—42no—
66Dic43⋊C4—42no—
67C4×Dic43—22no—
68C4×Dic43—42no—
69#10621877—41no—
70#10621877—41no—
71C2×C43⋊C8—22no—
72Dic172—42no—
73Dic172—41no—
74Dic172—41no—
75C16×C43—42no—
76C23×C43AGL(1,ℤ/8)11yescharacteristic
77C2×C4×C43—21no—
78C2×C4×C43—21no—
79C2×C4×C43—21no—
80C2×C4×C43—21no—
81C2×C4×C43C2×C22⋊C411yescharacteristic
82C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
83C2×Dic43—42no—
84C2×Dic43—42no—
85C2×Dic43—42no—
86Dic86—42no—
87Dic86—42no—
88C8×C43—21no—
89C8×C43—21no—
90C8×C43—21no—
91C8×C43#10411yescharacteristic
92C8×C43#10411yescharacteristic
93C43⋊C8—42no—
94#11771—431nomaximal, Sylow
95C22×C43—21no—
96C22×C43—41no—
97C22×C43#41811yescharacteristic
98C4×C43—21no—
99C4×C43—41no—
100C4×C43—41no—
101C4×C43#41011yescharacteristic
102C4×C43C2×#10411yescharacteristic
103Dic43—82no—
104Dic43—82no—
105Dic43—82no—
106#3177—431no—
107#2166D4311yescharacteristic
108#1747—431no—
109#1342—432no—
110#1340—432no—
111C2×C43—21no—
112C2×C43—41no—
113C2×C43#150511yescharacteristic
114#541—861no—
115#499—431no—
116#494—431no—
117#491—861no—
118#470—432no—
119#467—861no—
120#441—432no—
121C4×Q16—861no—
122#405—861no—
123#405C2×D4311yescharacteristic
124#364—21no—
125#349C2×D4312yes—
126#347—21no—
127#338—431no—
128H(3,ℤ/4)—431no—
129H(3,ℤ/4)—861no—
130C43#1177111yescharacteristic, complemented, Sylow
131C2×Q16—432no—
132C2×Q16—861no—
133C2×M16—861no—
134C2×M16C22×D4311yescharacteristic
135C22×C8D17211yescharacteristic
136C4⋊Q8—861no—
137#126—1722no—
138#125—861no—
139#125—1722no—
140C22⋊Q8—862no—
141C4×Q8—862no—
142#117—861no—
143#117D17211yescharacteristic
144M32—22no—
145#107—861no—
146#106—432no—
147#103—862no—
148#103—862no—
149#97—862no—
150#97C4×D4311yescharacteristic
151#97C22⋊D4311yescharacteristic
152C4×C8—862no—
153C4×C8C4×D4311yescharacteristic
154C4×C8C22⋊D4311yescharacteristic
155C2×Q8—862no—
156C22×C4C2×D17211yescharacteristic
157Q16—1722no—
158Q16—1721no—
159Q16—1721no—
160M16—41no—
161M16—1721no—
162M16—1721no—
163C2×C8—21no—
164C2×C8—21no—
165C2×C8—862no—
166C2×C8(C2×D43)⋊C411yescharacteristic
167C2×C8(C2×D43)⋊C411yescharacteristic
168C2×C8C2×C4×D4311yescharacteristic
169C2×C8C2×C22⋊D4311yescharacteristic
170C4⋊C4—21no—
171C4⋊C4—862no—
172C4⋊C4—1721no—
173C4⋊C4—1722no—
174C4⋊C4—1722no—
175C4⋊C4—1722no—
176C4⋊C4—1722no—
177C22⋊C4—21no—
178C22⋊C4—1721no—
179C22⋊C4—1722no—
180C42—862no—
181C42—1722no—
182C42(C2×D43)⋊C411yescharacteristic
183C42(C2×D43)⋊C411yescharacteristic
184C16—42no—
185C23#1306335311yescharacteristic
186Q8—1722no—
187Q8—1722no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—1722no—
193C2×C4—1722no—
194C2×C4—1722no—
195C2×C4C2×(C2×D43)⋊C411yescharacteristic
196C2×C4#1306335311yescharacteristic
197C8—21no—
198C8—21no—
199C8—21no—
200C8—1722no—
201C8#1306325111yescharacteristic
202C8#1306325111yescharacteristic
203C22—21no—
204C22—41no—
205C22#1458290511yescharacteristic
206C4—21no—
207C4—41no—
208C4—41no—
209C4—3442no—
210C4—3442no—
211C4—3442no—
212C4#1458287211yescharacteristic
213C4C2×#1306325111yescharacteristic
214C2—21no—
215C2—41no—
216C2#1913310411yescharacteristic
subgroupG/H
centerC2#19133104
commutatorC2×C8×C43C22×C4
FrattiniC2×M16C22×D43
FittingC43×#2166C2
socleC2×C43#1505
prime radicalC23×C43AGL(1,ℤ/8)
cosocleC2×M16×C43C23
hypercenter#2166D43
hypocenterC43#11771
LCSG ▷ C2×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ #405 ◁ #2166

Complements

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

NH ≅ G/Ntype
7. #14583301C4semidirect
8. #14583279C4semidirect
12. #14583007C4semidirect
130. C43#11771semidirect

Maximal subgroups

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

subgroupindex
#191452542
#191343502
#191325902
#191325842
C43×#21662
#1177143