Finite Group Databasebeta

← #25009961

Subgroups — #25009961

Order 11008.

262 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 59 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#19136812C212yesmaximal
2#19136175C211yesmaximal, characteristic
3#19132589C212yesmaximal
4#19132548C211yesmaximal, characteristic
5C43×#3261C211yesmaximal, characteristic
6#14582948C2211yescharacteristic
7#14582721—22no—
8#14582715—22no—
9#14582681C2212yes—
10#14582669—21no—
11#14582664—21no—
12C43⋊#338C2211yescharacteristic
13C43×#541—21no—
14C43×#479—22no—
15C43×#470C2212yes—
16C43×#467—21no—
17C43×#462—22no—
18C43×#424C2211yescharacteristic
19C2×#10621877—21no—
20C2×#10621877—21no—
21#13063265—22no—
22#13063261—22no—
23C2×Q16×C43—21no—
24C2×Q16×C43D412yes—
25C2×M16×C43C2311yescharacteristic
26C22×C8×C43D411yescharacteristic
27C4⋊Q8×C43—21no—
28#126×C43—42no—
29#125×C43—21no—
30#125×C43—42no—
31C22⋊Q8×C43—22no—
32C4×Q8×C43—22no—
33#117×C43D411yescharacteristic
34#107×C43—21no—
35#106×C43D412yes—
36C4⋊C8×C43—22no—
37#103×C43—22no—
38#103×C43—22no—
39C2×Q8×C43—22no—
40C22×C4×C43C2×D411yescharacteristic
41Q16×C43—42no—
42Q16×C43—81no—
43M16×C43—41no—
44C2×C8×C43—21no—
45C2×C8×C43—41no—
46C2×C8×C43C2×D412yes—
47C4⋊C4×C43—21no—
48C4⋊C4×C43—22no—
49C4⋊C4×C43—42no—
50C4⋊C4×C43—42no—
51C4⋊C4×C43—42no—
52C4⋊C4×C43—42no—
53C22⋊C4×C43—42no—
54C22⋊C4×C43SD1612yes—
55C42×C43—21no—
56C42×C43—42no—
57#10621877—41no—
58#10621877—41no—
59#10621877—41no—
60#10621877—41no—
61C2×C43⋊C8—41no—
62C2×C43⋊C8—41no—
63C43⋊C16—42no—
64C23×C43C2×SD1611yescharacteristic
65Q8×C43—42no—
66Q8×C43—42no—
67C2×C4×C43—21no—
68C2×C4×C43—21no—
69C2×C4×C43—22no—
70C2×C4×C43—42no—
71C2×C4×C43—42no—
72C2×C4×C43#12011yescharacteristic
73C2×C4×C43AGL(1,ℤ/8)11yescharacteristic
74C8×C43—22no—
75C8×C43—41no—
76C43⋊C8—81no—
77C43⋊C8—81no—
78#12305—431nomaximal, Sylow
79C22×C43—21no—
80C22×C43—41no—
81C22×C43#45011yescharacteristic
82C4×C43—21no—
83C4×C43—42no—
84C4×C43—82no—
85C4×C43—82no—
86C4×C43#45411yescharacteristic
87C4×C43#45811yescharacteristic
88#3261D4311yescharacteristic
89#2239—432no—
90#2103—431no—
91#1342—432no—
92#1328—431no—
93C2×C43—21no—
94C2×C43—41no—
95C2×C43#161611yescharacteristic
96#541—21no—
97#479—22no—
98#470C2×D4312yes—
99#467—21no—
100#462—22no—
101#430—431no—
102#424C2×D4311yescharacteristic
103#365—862no—
104#362—862no—
105#349—432no—
106#344—861no—
107#341—861no—
108#338—431no—
109C43#1230511yescharacteristic, complemented, Sylow
110C2×Q16—21no—
111C2×Q16C22⋊D4312yes—
112C2×M16—861no—
113C2×M16—861no—
114C2×M16C22×D4311yescharacteristic
115C22×C8C22⋊D4311yescharacteristic
116C4⋊Q8—21no—
117#126—42no—
118#125—21no—
119#125—42no—
120C22⋊Q8—22no—
121C4×Q8—22no—
122#117C22⋊D4311yescharacteristic
123M32—862no—
124#108—862no—
125#107—21no—
126#106C22⋊D4312yes—
127C4⋊C8—22no—
128#103—22no—
129#103—22no—
130C2×Q8—22no—
131C22×C4C2×C22⋊D4311yescharacteristic
132Q16—42no—
133Q16—81no—
134M16—41no—
135M16—1721no—
136M16—1721no—
137M16—1721no—
138M16—1721no—
139C2×C8—21no—
140C2×C8—41no—
141C2×C8—1721no—
142C2×C8—1721no—
143C2×C8C2×C22⋊D4312yes—
144C4⋊C4—21no—
145C4⋊C4—22no—
146C4⋊C4—42no—
147C4⋊C4—42no—
148C4⋊C4—42no—
149C4⋊C4—42no—
150C22⋊C4—42no—
151C22⋊C4#1062188312yes—
152C42—21no—
153C42—42no—
154C16—1722no—
155C23C2×#1062188311yescharacteristic
156Q8—42no—
157Q8—42no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4#1306329411yescharacteristic
164C2×C4#1306335111yescharacteristic
165C8—22no—
166C8—41no—
167C8—3441no—
168C8—3441no—
169C22—21no—
170C22—41no—
171C22#1458305011yescharacteristic
172C4—21no—
173C4—42no—
174C4—82no—
175C4—82no—
176C4#1458307211yescharacteristic
177C4#1458308911yescharacteristic
178C2—21no—
179C2—41no—
180C2#1913363211yescharacteristic
subgroupG/H
centerC2#19133632
commutator, cosocleC2×M16×C43C23
FrattiniC2×M16C22×D43
FittingC43×#3261C2
socleC2×C43#1616
prime radicalC23×C43C2×SD16
hypercenter#3261D43
hypocenterC43#12305
LCSG ▷ C2×M16×C43 ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3261

Complements

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

NH ≅ G/Ntype
109. C43#12305semidirect

Maximal subgroups

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

subgroupindex
#191368122
#191361752
#191325892
#191325482
C43×#32612
#1230543