Finite Group Databasebeta

← #24984424

Subgroups — #24984424

Order 11008.

162 conjugacy classes of subgroups; only the 25 normal subgroups are shown.

normal subgroups only

This group has 162 conjugacy classes of subgroups — too many to draw. Only its 25 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#19133676C211yesmaximal, characteristic
2#19132636C211yesmaximal, characteristic, complemented
3C43×#1409C211yesmaximal, characteristic, complemented
4#14583615C411yescharacteristic, complemented
5#14583091—21no—
6#14582720—21no—
7#14582648C411yescharacteristic, complemented
8#14582628—21no—
9C43×#492C2211yescharacteristic
10C43×#353—21no—
11C2×#10621882—41no—
12#13063314—41no—
13#13063300—41no—
14C4×D172—21no—
15#13063283—41no—
16#13063265—41no—
17C4⋊(C43⋊C8)—21no—
18#13063246—41no—
19C2×SD16×C43—41no—
20C4⋊Q8×C43C2×C411yescharacteristic
21#127×C43D411yescharacteristic
22#99×C43—41no—
23C4×C8×C43D411yescharacteristic
24C2×Q8×C43—21no—
25C2×D4×C43—21no—
26C2×D4×C43—41no—
27C2×D172—21no—
28C2×D172—41no—
29C2×C4×D43—41no—
30SD16×C43—81no—
31SD16×C43—81no—
32C2×C8×C43—21no—
33C4⋊C4×C43—41no—
34C22⋊C4×C43—81no—
35C42×C43C22⋊C411yescharacteristic
36#10621882—82no—
37(C2×D43)⋊C4—42no—
38(C2×D43)⋊C4—41no—
39C4⋊Dic43—21no—
40C4×Dic43—41no—
41C2×C43⋊C8—41no—
42C43⋊C16—81no—
43C23×C43—41no—
44C22×D43—41no—
45Q8×C43—81no—
46D4×C43—81no—
47D4×C43—81no—
48D4×C43—81no—
49C2×C4×C43—21no—
50C2×C4×C43—41no—
51C2×C4×C43—161no—
52C2×C4×C43#9911yescharacteristic
53C2×Dic43—41no—
54D172—41no—
55D172—41no—
56D172—161no—
57C4×D43—81no—
58C4×D43—81no—
59C8×C43—21no—
60C8×C43—21no—
61C43⋊C8—81no—
62#7519—431nomaximal, Sylow
63C22×C43—81no—
64C22×C43—161no—
65C22×C43AΣL(1,𝔽16)11yescharacteristic
66C2×D43—81no—
67C2×D43—81no—
68C2×D43—81no—
69C4×C43—21no—
70C4×C43—21no—
71C4×C43—21no—
72C4×C43—81no—
73C4×C43—321no—
74Dic43—81no—
75#1624—431no—
76#1409D4311yescharacteristic, complemented
77#1359—431no—
78C2×C43—21no—
79C2×C43—161no—
80C2×C43#140211yescharacteristic
81D43—161no—
82#555—431no—
83#492C2×D4311yescharacteristic
84#459—861no—
85#364—861no—
86#353—21no—
87#333—431no—
88D4⋊C8—861no—
89C43#751911yescharacteristic, complemented, Sylow
90C2×SD16—41no—
91C2×D8—1721no—
92C4⋊Q8C4×D4311yescharacteristic
93#127C22⋊D4311yescharacteristic
94#124—1721no—
95#121—1721no—
96C4×D4—861no—
97#117—1721no—
98M32—1721no—
99C4⋊C8—861no—
100#102—1721no—
101#99—41no—
102C4×C8D17211yescharacteristic
103C2×Q8—21no—
104C2×D4—21no—
105C2×D4—41no—
106C2×D4—861no—
107C2×D4—1721no—
108C22×C4—1721no—
109SD16—81no—
110SD16—81no—
111D8—3442no—
112C2×C8—21no—
113C2×C8—1721no—
114C4⋊C4—41no—
115C4⋊C4—861no—
116C22⋊C4—81no—
117C22⋊C4—1722no—
118C22⋊C4—1721no—
119C42—1721no—
120C42(C2×D43)⋊C411yescharacteristic
121C16—3441no—
122C23—41no—
123C23—1721no—
124Q8—81no—
125D4—81no—
126D4—81no—
127D4—81no—
128D4—1721no—
129D4—1721no—
130D4—6881no—
131C2×C4—21no—
132C2×C4—41no—
133C2×C4—161no—
134C2×C4—3441no—
135C2×C4—3441no—
136C2×C4—1721no—
137C2×C4#1306323911yescharacteristic
138C8—21no—
139C8—21no—
140C8—3441no—
141C22—81no—
142C22—161no—
143C22—3441no—
144C22—3441no—
145C22—3441no—
146C22#1458268511yescharacteristic
147C4—21no—
148C4—21no—
149C4—21no—
150C4—81no—
151C4—321no—
152C4—3441no—
153C2—21no—
154C2—161no—
155C2—6881no—
156C2#1913273911yescharacteristic
subgroupG/H
centerC2#19132739
commutatorC4⋊Q8×C43C2×C4
Frattini#492C2×D43
FittingC43×#1409C2
socleC2×C43#1402
prime radical#19133676C2
cosocleC43×#492C22
hypercenter#1409D43
hypocenterC43#7519
LCSG ▷ C4⋊Q8×C43 ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #492 ◁ #1409

Complements

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

NH ≅ G/Ntype
2. #19132636C2semidirect
3. C43×#1409C2semidirect
4. #14583615C4semidirect
7. #14582648C4semidirect
76. #1409D43semidirect
89. C43#7519semidirect

Maximal subgroups

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

subgroupindex
#191336762
#191326362
C43×#14092
#751943