Finite Group Databasebeta

← #25009958

Subgroups — #25009958

Order 11008.

286 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 55 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#19146034C211yesmaximal, characteristic
2#19136810C212yesmaximal, complemented
3#19136175C211yesmaximal, characteristic, complemented
4#19132587C212yesmaximal, complemented
5C43×#1328C211yesmaximal, characteristic, complemented
6#14583504—21no—
7#14583200—22no—
8#14583152C2212yes—
9#14583135—21no—
10#14583095—22no—
11#14582948C2211yescharacteristic
12#14582722—22no—
13#14582713—22no—
14#14582669—21no—
15#14582664—21no—
16C43⋊#338C2211yescharacteristic
17C43×#424C2211yescharacteristic
18C43×#349C2212yes—
19C2×D344—21no—
20C2×D344D412yes—
21C2×#10621877—21no—
22C2×#10621877—21no—
23#13063322—21no—
24#13063317—21no—
25#13063310—42no—
26#13063299—22no—
27#13063298—42no—
28C4×D172—22no—
29#13063261—22no—
30#13063259—21no—
31#13063257D412yes—
32#13063247—22no—
33#13063247—22no—
34C2×M16×C43C2311yescharacteristic
35C22×C8×C43D411yescharacteristic
36#117×C43D411yescharacteristic
37M32×C43—22no—
38C4⋊C8×C43—22no—
39C22×C4×C43C2×D411yescharacteristic
40C2×C22⋊D43—42no—
41C2×D172—22no—
42C2×D172—42no—
43C2×C4×D43—42no—
44M16×C43—41no—
45C2×C8×C43—21no—
46C2×C8×C43—41no—
47C2×C8×C43C2×D412yes—
48C4⋊C4×C43—21no—
49C22⋊C4×C43SD1612yes—
50C42×C43—21no—
51(C2×D43)⋊C4—42no—
52(C2×D43)⋊C4—42no—
53C4⋊Dic43—22no—
54Dic43⋊C4—42no—
55#10621877—41no—
56#10621877—41no—
57#10621877—41no—
58#10621877—41no—
59C2×C43⋊C8—41no—
60C2×C43⋊C8—41no—
61D344—42no—
62D344—81no—
63C16×C43—42no—
64C23×C43C2×SD1611yescharacteristic
65C22×D43—42no—
66C2×C4×C43—21no—
67C2×C4×C43—21no—
68C2×C4×C43—22no—
69C2×C4×C43#12011yescharacteristic
70C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
71C22⋊D43—162no—
72C2×Dic43—42no—
73D172—42no—
74D172—42no—
75D172—162no—
76C4×D43—162no—
77C8×C43—22no—
78C8×C43—41no—
79C43⋊C8—81no—
80C43⋊C8—81no—
81#12304—431nomaximal, Sylow
82C22×C43—21no—
83C22×C43—41no—
84C22×C43#45011yescharacteristic
85C2×D43—82no—
86C2×D43—82no—
87C2×D43—82no—
88C4×C43—21no—
89C4×C43—42no—
90C4×C43#45411yescharacteristic
91C4×C43#45811yescharacteristic
92Dic43—82no—
93#3259—431no—
94#2238—432no—
95#2103—431no—
96#1341—432no—
97#1328D4311yescharacteristic, complemented
98C2×C43—21no—
99C2×C43—41no—
100C2×C43#161611yescharacteristic
101D43—162no—
102#540—861no—
103#478—862no—
104#469—432no—
105#466—861no—
106#459—862no—
107#430—431no—
108#424C2×D4311yescharacteristic
109#365—862no—
110#361—862no—
111#349C2×D4312yes—
112#344—861no—
113#341—861no—
114#338—431no—
115C43#1230411yescharacteristic, complemented, Sylow
116C2×D8—432no—
117C2×D8—861no—
118C2×M16—861no—
119C2×M16—861no—
120C2×M16C22×D4311yescharacteristic
121C22×C8D17211yescharacteristic
122#127—861no—
123#125—861no—
124#123—1722no—
125#121—862no—
126#121—1722no—
127C4×D4—862no—
128#117D17211yescharacteristic
129M32—22no—
130#108—862no—
131#107—861no—
132#106—432no—
133C4⋊C8—22no—
134#102—862no—
135#102—862no—
136C2×D4—862no—
137C2×D4—1722no—
138C2×D4—1722no—
139C22×C4—1722no—
140C22×C4C2×D17211yescharacteristic
141D8—3441no—
142D8—1722no—
143M16—41no—
144M16—1721no—
145M16—1721no—
146M16—1721no—
147M16—1721no—
148C2×C8—21no—
149C2×C8—41no—
150C2×C8—1721no—
151C2×C8—1721no—
152C2×C8D4×D4312yes—
153C4⋊C4—21no—
154C4⋊C4—862no—
155C4⋊C4—1722no—
156C22⋊C4—1722no—
157C22⋊C4—1722no—
158C22⋊C4#1062187312yes—
159C42—21no—
160C16—42no—
161C23—1722no—
162C23C2×#1062187311yescharacteristic
163D4—1722no—
164D4—1722no—
165D4—6882no—
166D4—6882no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—1722no—
171C2×C4—6882no—
172C2×C4#1306329511yescharacteristic
173C2×C4#1306335311yescharacteristic
174C8—22no—
175C8—41no—
176C8—3441no—
177C8—3441no—
178C22—21no—
179C22—41no—
180C22—3442no—
181C22—3442no—
182C22—3442no—
183C22#1458305211yescharacteristic
184C4—21no—
185C4—42no—
186C4—3442no—
187C4#1458307411yescharacteristic
188C4#1458309011yescharacteristic
189C2—21no—
190C2—41no—
191C2—6882no—
192C2#1913363411yescharacteristic
subgroupG/H
centerC2#19133634
commutator, cosocleC2×M16×C43C23
FrattiniC2×M16C22×D43
FittingC43×#1328C2
socleC2×C43#1616
prime radical#19146034C2
hypercenter#1328D43
hypocenterC43#12304
LCSG ▷ C2×M16×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #1328

Complements

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

NH ≅ G/Ntype
2. #19136810C2semidirect
3. #19136175C2semidirect
4. #19132587C2semidirect
5. C43×#1328C2semidirect
97. #1328D43semidirect
115. C43#12304semidirect

Maximal subgroups

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

subgroupindex
#191460342
#191368102
#191361752
#191325872
C43×#13282
#1230443