Finite Group Databasebeta

← #25007448

Subgroups — #25007448

Order 11008.

280 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 71 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#19145340C211yesmaximal, characteristic
2#19136407C211yesmaximal, characteristic
3#19132588C212yesmaximal
4#19132582C212yesmaximal
5C43×#1841C211yesmaximal, characteristic
6#14583456—21no—
7#14583297C411yescharacteristic, complemented
8#14583279C411yescharacteristic, complemented
9#14583250—21no—
10#14583157—21no—
11#14583157C2212yes—
12#14583007—21no—
13#14583007C412yescomplemented
14#14582720—21no—
15#14582681C2212yes—
16#14582677—21no—
17C4×M16×C43C2211yescharacteristic
18C43×#344—21no—
19C43×#339—21no—
20C43×#338C2211yescharacteristic
21C43×H(3,ℤ/4)C2211yescharacteristic
22C2×Dic172—21no—
23C2×Dic172C2×C412yes—
24#13063325—21no—
25#13063325—21no—
26#13063317—41no—
27#13063304—22no—
28#13063304—41no—
29C4×Dic86—22no—
30C4×Dic86—41no—
31#13063284—41no—
32#13063265—22no—
33#13063257—21no—
34#13063257C2×C412yes—
35#13063250—22no—
36#13063250—22no—
37C2×M16×C43—21no—
38C2×M16×C43D411yescharacteristic
39C2×M16×C43C2311yescharacteristic
40#117×C43—21no—
41C2×C42×C43D411yescharacteristic
42#97×C43C2×C411yescharacteristic
43#97×C43D411yescharacteristic
44C4×C8×C43C2×C411yescharacteristic
45C4×C8×C43D411yescharacteristic
46C22×C4×C43—21no—
47C22×C4×C43C2×D411yescharacteristic
48C2×Dic86—22no—
49C2×Dic86—41no—
50M16×C43—41no—
51M16×C43—41no—
52M16×C43—41no—
53M16×C43—41no—
54C2×C8×C43—41no—
55C2×C8×C43C22⋊C411yescharacteristic
56C2×C8×C43C22⋊C411yescharacteristic
57C2×C8×C43C22×C411yescharacteristic
58C2×C8×C43C2×D411yescharacteristic
59C4⋊C4×C43—41no—
60C22⋊C4×C43—41no—
61C42×C43—21no—
62C42×C43—41no—
63C42×C43C22⋊C411yescharacteristic
64C42×C43C22⋊C411yescharacteristic
65C22⋊Dic43—42no—
66C4⋊Dic43—22no—
67C4⋊Dic43—41no—
68C4⋊Dic43—41no—
69C4⋊Dic43—41no—
70Dic43⋊C4—42no—
71Dic43⋊C4—42no—
72C4×Dic43—42no—
73Dic172—42no—
74Dic172—42no—
75C43⋊C16—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×C43—42no—
82C2×C4×C43—81no—
83C2×C4×C43C2×C22⋊C411yescharacteristic
84C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
85C2×Dic43—42no—
86C2×Dic43—42no—
87Dic86—42no—
88Dic86—42no—
89Dic86—82no—
90C8×C43—21no—
91C8×C43—21no—
92C8×C43—21no—
93C8×C43—21no—
94C8×C43—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—161no—
103C4×C43#41011yescharacteristic
104C4×C43#42111yescharacteristic
105Dic43—82no—
106Dic43—82no—
107#3185—431no—
108#2165—431no—
109#1841D4311yescharacteristic
110#1342—432no—
111#1340—432no—
112C2×C43—21no—
113C2×C43—41no—
114C2×C43#151411yescharacteristic
115#533—861no—
116#498—431no—
117#494—431no—
118#487—861no—
119#470—432no—
120#470—861no—
121#441—432no—
122#441—861no—
123C4×M16C2×D4311yescharacteristic
124#364—861no—
125#349—432no—
126#347—861no—
127#344—21no—
128#339—21no—
129#338C2×D4311yescharacteristic
130H(3,ℤ/4)C2×D4311yescharacteristic
131C43#1183811yescharacteristic, complemented, Sylow
132C2×Q16—432no—
133C2×Q16—861no—
134C2×M16—21no—
135C2×M16C22⋊D4311yescharacteristic
136C2×M16C22×D4311yescharacteristic
137C4⋊Q8—861no—
138C4⋊Q8—861no—
139#125—1721no—
140C22⋊Q8—862no—
141C22⋊Q8—1721no—
142C4×Q8—862no—
143C4×Q8—1721no—
144#117—21no—
145#117—1721no—
146C2×C42C22⋊D4311yescharacteristic
147M32—862no—
148#106—432no—
149#106—861no—
150#103—862no—
151#103—862no—
152#97C4×D4311yescharacteristic
153#97D17211yescharacteristic
154C4×C8C4×D4311yescharacteristic
155C4×C8D17211yescharacteristic
156C2×Q8—862no—
157C2×Q8—1721no—
158C22×C4—21no—
159C22×C4C2×C22⋊D4311yescharacteristic
160Q16—1722no—
161Q16—1722no—
162M16—41no—
163M16—41no—
164M16—41no—
165M16—41no—
166C2×C8—41no—
167C2×C8(C2×D43)⋊C411yescharacteristic
168C2×C8(C2×D43)⋊C411yescharacteristic
169C2×C8C2×C4×D4311yescharacteristic
170C2×C8C2×D17211yescharacteristic
171C4⋊C4—41no—
172C4⋊C4—862no—
173C4⋊C4—1721no—
174C4⋊C4—1721no—
175C4⋊C4—1722no—
176C4⋊C4—1721no—
177C4⋊C4—1722no—
178C22⋊C4—41no—
179C22⋊C4—1722no—
180C42—21no—
181C42—41no—
182C42—1722no—
183C42(C2×D43)⋊C411yescharacteristic
184C42(C2×D43)⋊C411yescharacteristic
185C16—1722no—
186C23#1306335011yescharacteristic
187Q8—3442no—
188Q8—1722no—
189Q8—1722no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—21no—
193C2×C4—21no—
194C2×C4—42no—
195C2×C4—81no—
196C2×C4—1722no—
197C2×C4—1722no—
198C2×C4C2×(C2×D43)⋊C411yescharacteristic
199C2×C4#1306335011yescharacteristic
200C8—21no—
201C8—21no—
202C8—21no—
203C8—21no—
204C8—81no—
205C22—21no—
206C22—41no—
207C22#1458290311yescharacteristic
208C4—22no—
209C4—21no—
210C4—41no—
211C4—161no—
212C4—3442no—
213C4—3442no—
214C4#1458287211yescharacteristic
215C4#1458291711yescharacteristic
216C2—21no—
217C2—41no—
218C2#1913314111yescharacteristic
subgroupG/H
centerC2#19133141
commutatorC2×C8×C43C22×C4
FrattiniC2×M16C22×D43
FittingC43×#1841C2
socleC2×C43#1514
prime radicalC23×C43AGL(1,ℤ/8)
cosocleC2×M16×C43C23
hypercenter#1841D43
hypocenterC43#11838
LCSG ▷ C2×C8×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×M16 ◁ #1841

Complements

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

NH ≅ G/Ntype
7. #14583297C4semidirect
8. #14583279C4semidirect
13. #14583007C4semidirect
131. C43#11838semidirect

Maximal subgroups

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

subgroupindex
#191453402
#191364072
#191325882
#191325822
C43×#18412
#1183843