Finite Group Databasebeta

← #25007449

Subgroups — #25007449

Order 11008.

280 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 79 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#19136407C211yesmaximal, characteristic
2#19134744C211yesmaximal, characteristic
3#19132589C212yesmaximal
4#19132583C212yesmaximal
5C43×#3185C211yesmaximal, characteristic
6#14582720—21no—
7#14582681C2212yes—
8#14582677—21no—
9#14582670—21no—
10#14582659—21no—
11C43⋊#338C2211yescharacteristic
12#14582656C2211yescharacteristic
13C43×#533—21no—
14C43×#498C411yescharacteristic, complemented
15C43×#494C411yescharacteristic, complemented
16C43×#487—21no—
17C43×#470—21no—
18C43×#470C2212yes—
19C43×#441—21no—
20C43×#441C412yescomplemented
21C4×M16×C43C2211yescharacteristic
22C2×#10621877—21no—
23#13063284—21no—
24#13063265—22no—
25C2×Q16×C43—21no—
26C2×Q16×C43C2×C412yes—
27C2×M16×C43D411yescharacteristic
28C2×M16×C43C2311yescharacteristic
29C4⋊Q8×C43—21no—
30C4⋊Q8×C43—21no—
31#125×C43—41no—
32C22⋊Q8×C43—22no—
33C22⋊Q8×C43—41no—
34C4×Q8×C43—22no—
35C4×Q8×C43—41no—
36#117×C43—41no—
37C2×C42×C43D411yescharacteristic
38#106×C43—21no—
39#106×C43C2×C412yes—
40#103×C43—22no—
41#103×C43—22no—
42#97×C43C2×C411yescharacteristic
43#97×C43D411yescharacteristic
44C4×C8×C43C2×C411yescharacteristic
45C4×C8×C43D411yescharacteristic
46C2×Q8×C43—22no—
47C2×Q8×C43—41no—
48C22×C4×C43—21no—
49C22×C4×C43C2×D411yescharacteristic
50Q16×C43—42no—
51Q16×C43—42no—
52M16×C43—41no—
53M16×C43—41no—
54C2×C8×C43C22⋊C411yescharacteristic
55C2×C8×C43C22⋊C411yescharacteristic
56C2×C8×C43C22×C411yescharacteristic
57C2×C8×C43C2×D411yescharacteristic
58C4⋊C4×C43—22no—
59C4⋊C4×C43—41no—
60C4⋊C4×C43—41no—
61C4⋊C4×C43—42no—
62C4⋊C4×C43—41no—
63C4⋊C4×C43—42no—
64C22⋊C4×C43—42no—
65C42×C43—21no—
66C42×C43—42no—
67C42×C43C22⋊C411yescharacteristic
68C42×C43C22⋊C411yescharacteristic
69C22⋊Dic43—41no—
70C4⋊Dic43—41no—
71C4×Dic43—41no—
72#10621877—41no—
73#10621877—41no—
74C2×C43⋊C8—41no—
75C43⋊C16—42no—
76C23×C43AGL(1,ℤ/8)11yescharacteristic
77Q8×C43—42no—
78Q8×C43—42no—
79Q8×C43—82no—
80C2×C4×C43—21no—
81C2×C4×C43—21no—
82C2×C4×C43—21no—
83C2×C4×C43—21no—
84C2×C4×C43—42no—
85C2×C4×C43—42no—
86C2×C4×C43—42no—
87C2×C4×C43C2×C22⋊C411yescharacteristic
88C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
89C2×Dic43—81no—
90C8×C43—21no—
91C8×C43—21no—
92C8×C43—21no—
93C8×C43—21no—
94C43⋊C8—81no—
95#11838—431nomaximal, Sylow
96C22×C43—21no—
97C22×C43—41no—
98C22×C43#41811yescharacteristic
99C4×C43—22no—
100C4×C43—21no—
101C4×C43—41no—
102C4×C43—82no—
103C4×C43—82no—
104C4×C43#41011yescharacteristic
105C4×C43#42111yescharacteristic
106Dic43—161no—
107#3185D4311yescharacteristic
108#2165—431no—
109#1841—431no—
110#1342—432no—
111#1340—432no—
112C2×C43—21no—
113C2×C43—41no—
114C2×C43#151411yescharacteristic
115#533—21no—
116#498Dic4311yescharacteristic, complemented
117#494Dic4311yescharacteristic, complemented
118#487—21no—
119#470—21no—
120#470C2×D4312yes—
121#441—21no—
122#441Dic4312yescomplemented
123C4×M16C2×D4311yescharacteristic
124#364—861no—
125#349—432no—
126#347—861no—
127#344—861no—
128#339—861no—
129#338—431no—
130H(3,ℤ/4)—431no—
131C43#1183811yescharacteristic, complemented, Sylow
132C2×Q16—21no—
133C2×Q16C2×Dic4312yes—
134C2×M16—861no—
135C2×M16C22⋊D4311yescharacteristic
136C2×M16C22×D4311yescharacteristic
137C4⋊Q8—21no—
138C4⋊Q8—21no—
139#125—41no—
140C22⋊Q8—22no—
141C22⋊Q8—41no—
142C4×Q8—22no—
143C4×Q8—41no—
144#117—41no—
145#117—861no—
146C2×C42C22⋊D4311yescharacteristic
147M32—862no—
148#106—21no—
149#106C2×Dic4312yes—
150#103—22no—
151#103—22no—
152#97C2×Dic4311yescharacteristic
153#97C22⋊D4311yescharacteristic
154C4×C8C2×Dic4311yescharacteristic
155C4×C8C22⋊D4311yescharacteristic
156C2×Q8—22no—
157C2×Q8—41no—
158C22×C4—21no—
159C22×C4C2×C22⋊D4311yescharacteristic
160Q16—42no—
161Q16—42no—
162M16—41no—
163M16—41no—
164M16—1721no—
165M16—1721no—
166C2×C8—1721no—
167C2×C8C22⋊Dic4311yescharacteristic
168C2×C8C22⋊Dic4311yescharacteristic
169C2×C8C22×Dic4311yescharacteristic
170C2×C8C2×C22⋊D4311yescharacteristic
171C4⋊C4—22no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—42no—
175C4⋊C4—41no—
176C4⋊C4—42no—
177C4⋊C4—1721no—
178C22⋊C4—42no—
179C22⋊C4—1721no—
180C42—21no—
181C42—42no—
182C42—1721no—
183C42C22⋊Dic4311yescharacteristic
184C42C22⋊Dic4311yescharacteristic
185C16—1722no—
186C23#1306335111yescharacteristic
187Q8—42no—
188Q8—42no—
189Q8—82no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—42no—
195C2×C4—42no—
196C2×C4—42no—
197C2×C4—3441no—
198C2×C4C2×C22⋊Dic4311yescharacteristic
199C2×C4#1306335111yescharacteristic
200C8—21no—
201C8—21no—
202C8—21no—
203C8—21no—
204C8—3441no—
205C22—21no—
206C22—41no—
207C22#1458290411yescharacteristic
208C4—22no—
209C4—21no—
210C4—41no—
211C4—82no—
212C4—82no—
213C4—6881no—
214C4#1458287311yescharacteristic
215C4#1458291611yescharacteristic
216C2—21no—
217C2—41no—
218C2#1913314211yescharacteristic
subgroupG/H
centerC2#19133142
commutatorC2×C8×C43C22×C4
FrattiniC2×M16C22×D43
FittingC43×#3185C2
socleC2×C43#1514
prime radicalC23×C43AGL(1,ℤ/8)
cosocleC2×M16×C43C23
hypercenter#3185D43
hypocenterC43#11838
LCSG ▷ C2×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #3185

Complements

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

NH ≅ G/Ntype
14. C43×#498C4semidirect
15. C43×#494C4semidirect
20. C43×#441C4semidirect
116. #498Dic43semidirect
117. #494Dic43semidirect
122. #441Dic43semidirect
131. C43#11838semidirect

Maximal subgroups

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

subgroupindex
#191364072
#191347442
#191325892
#191325832
C43×#31852
#1183843