Finite Group Databasebeta

← #24994221

Subgroups — #24994221

Order 11008.

434 conjugacy classes of subgroups; only the 99 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 99 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#19145144C211yesmaximal, characteristic
2#19133222C211yesmaximal, characteristic
3#19133106C212yesmaximal
4#19132488C212yesmaximal
5C43×#2371C211yesmaximal, characteristic
6#14583456C2211yescharacteristic
7#14583309C414yescomplemented
8#14583298—22no—
9#14582956C2212yes—
10#14582939—22no—
11C4×#10621877C2211yescharacteristic
12#14582641—22no—
13#14582635—22no—
14#14582635—22no—
15C2×#125×C43C2211yescharacteristic
16C43×#387—22no—
17C43×#387—22no—
18C4×C4⋊C4×C43—22no—
19C43×#376C2212yes—
20C2×#10621877—21no—
21#13063325C2×C412yes—
22#13063317—21no—
23#13063304—22no—
24C4×Dic86—22no—
25#13063284—21no—
26#13063258—24no—
27#13063256—24no—
28C4⋊(C43⋊C8)—22no—
29C22⋊(C43⋊C8)—22no—
30#13063236—22no—
31#13063236C2×C412yes—
32C4×C43⋊C8—21no—
33#125×C43—22no—
34#125×C43C2×C412yes—
35#125×C43D412yes—
36C2×C4⋊C4×C43—22no—
37C2×C4⋊C4×C43—22no—
38C2×C4⋊C4×C43D412yes—
39C2×C42×C43—22no—
40C2×C42×C43—22no—
41C2×C42×C43C2311yescharacteristic
42#95×C43—22no—
43#95×C43—22no—
44#95×C43—22no—
45#95×C43D412yes—
46#95×C43D412yes—
47C22×C4×C43—22no—
48C22×C4×C43—22no—
49C22×C4×C43—22no—
50C22×C4×C43C2×D411yescharacteristic
51C22×C4×C43C2×D412yes—
52C2×Dic86—22no—
53C4⋊C4×C43—24no—
54C4⋊C4×C43—24no—
55C4⋊C4×C43—22no—
56C4⋊C4×C43—44no—
57C4⋊C4×C43C22⋊C414yes—
58C42×C43—44no—
59C42×C43—44no—
60C42×C43C22×C411yescharacteristic
61C42×C43C2×D411yescharacteristic
62C42×C43#4112yes—
63C22⋊Dic43—41no—
64C4⋊Dic43—22no—
65C4⋊Dic43—22no—
66Dic43⋊C4—42no—
67C4×Dic43—41no—
68#10621877—24no—
69C2×C43⋊C8—22no—
70C2×C43⋊C8—42no—
71C23×C43#12011yescharacteristic
72C2×C4×C43—22no—
73C2×C4×C43—24no—
74C2×C4×C43—24no—
75C2×C4×C43—42no—
76C2×C4×C43—42no—
77C2×C4×C43—42no—
78C2×C4×C43—42no—
79C2×C4×C43—42no—
80C2×C4×C43—42no—
81C2×C4×C43—42no—
82C2×C4×C43—42no—
83C2×C4×C43C2×C22⋊C411yescharacteristic
84C2×C4×C43C4×D412yes—
85C2×C4×C43#12112yes—
86C2×C4×C43#12311yescharacteristic
87C2×Dic43—42no—
88Dic86—82no—
89C43⋊C8—24no—
90C43⋊C8—82no—
91#9440—431nomaximal, Sylow
92C22×C43—22no—
93C22×C43#38611yescharacteristic
94C22×C43#45612yes—
95C4×C43—21no—
96C4×C43—21no—
97C4×C43—22no—
98C4×C43—22no—
99C4×C43—44no—
100C4×C43—44no—
101C4×C43—82no—
102Dic43—82no—
103#3166—431no—
104#2371D4311yescharacteristic
105#1534—431no—
106#1506—432no—
107#1300—432no—
108C2×C43—22no—
109C2×C43#188611yescharacteristic
110C2×C43#190612yes—
111#533—431no—
112C2×#125C2×D4311yescharacteristic
113#501—434no—
114#499—862no—
115#432—432no—
116#428—862no—
117C4×M16—431no—
118#387—22no—
119#387—22no—
120C4×C4⋊C4—22no—
121#376C2×D4312yes—
122#330—862no—
123#328—862no—
124#328—862no—
125C43#944011yescharacteristic, complemented, Sylow
126C2×M16—861no—
127C4⋊Q8—432no—
128#125—22no—
129#125—861no—
130#125C4×D4312yes—
131#125D17212yes—
132C22⋊Q8—862no—
133C4×Q8—862no—
134#117—861no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4C22⋊D4312yes—
138C2×C42—22no—
139C2×C42—22no—
140C2×C42C22×D4311yescharacteristic
141#107—864no—
142#106—864no—
143C4⋊C8—862no—
144C22⋊C8—862no—
145#97—432no—
146#97—862no—
147C4×C8—861no—
148#95—22no—
149#95—22no—
150#95—22no—
151#95C22⋊D4312yes—
152#95C22⋊D4312yes—
153C2×Q8—862no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—22no—
157C22×C4C2×C22⋊D4311yescharacteristic
158C22×C4C2×C22⋊D4312yes—
159M16—864no—
160C2×C8—862no—
161C2×C8—1722no—
162C4⋊C4—24no—
163C4⋊C4—24no—
164C4⋊C4—22no—
165C4⋊C4—44no—
166C4⋊C4—862no—
167C4⋊C4—862no—
168C4⋊C4—1722no—
169C4⋊C4(C2×D43)⋊C414yes—
170C22⋊C4—1721no—
171C42—44no—
172C42—44no—
173C42—1721no—
174C42C2×C4×D4311yescharacteristic
175C42C2×D17211yescharacteristic
176C42#1062189812yes—
177C23#1306329411yescharacteristic
178Q8—3442no—
179C2×C4—22no—
180C2×C4—24no—
181C2×C4—24no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—1722no—
191C2×C4C2×(C2×D43)⋊C411yescharacteristic
192C2×C4C4×C22⋊D4312yes—
193C2×C4#1306329912yes—
194C2×C4#1306330811yescharacteristic
195C8—864no—
196C8—3442no—
197C22—22no—
198C22#1458277811yescharacteristic
199C22#1458308212yes—
200C4—21no—
201C4—21no—
202C4—22no—
203C4—22no—
204C4—44no—
205C4—44no—
206C4—82no—
207C4—3442no—
208C2—22no—
209C2#1913498811yescharacteristic
210C2#1913509612yes—
subgroupG/H
centerC22#14582778
commutatorC42×C43C22×C4
FrattiniC2×C42C22×D43
FittingC43×#2371C2
socleC22×C43#386
prime radicalC23×C43#120
cosocleC2×C42×C43C23
hypercenter#2371D43
hypocenterC43#9440
LCSG ▷ C42×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2371

Complements

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

NH ≅ G/Ntype
7. #14583309C4semidirect
125. C43#9440semidirect

Maximal subgroups

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

subgroupindex
#191451442
#191332222
#191331062
#191324882
C43×#23712
#944043