Finite Group Databasebeta

← #24984436

Subgroups — #24984436

Order 11008.

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

normal subgroups only

This group has 158 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#19133887C211yesmaximal, characteristic
2#19132628C211yesmaximal, characteristic, complemented
3C43×#1412C211yesmaximal, characteristic, complemented
4#14583647C411yescharacteristic, complemented
5#14583286—21no—
6#14582677—21no—
7#14582641C411yescharacteristic, complemented
8#14582638—21no—
9C43×#490C2211yescharacteristic
10C43×#353—21no—
11C2×#10621883—41no—
12C2×#10621882—41no—
13#13063313—21no—
14#13063310—41no—
15#13063303—41no—
16#13063300—41no—
17#13063265—41no—
18#13063236—21no—
19#127×C43D411yescharacteristic
20#125×C43C2×C411yescharacteristic
21#102×C43—41no—
22#99×C43—41no—
23#97×C43D411yescharacteristic
24C2×D4×C43—21no—
25C2×D4×C43—41no—
26C2×D172—21no—
27C2×D172—41no—
28C2×C4×D43—41no—
29C2×Dic86—21no—
30C2×C8×C43—21no—
31C4⋊C4×C43—21no—
32C4⋊C4×C43—41no—
33C22⋊C4×C43—81no—
34C42×C43C22⋊C411yescharacteristic
35#10621883—82no—
36#10621882—82no—
37(C2×D43)⋊C4—41no—
38(C2×D43)⋊C4—41no—
39(C2×D43)⋊C4—41no—
40Dic43⋊C4—41no—
41C2×C43⋊C8—41no—
42C43⋊C16—42no—
43C23×C43—41no—
44C22×D43—41no—
45D4×C43—81no—
46D4×C43—81no—
47D4×C43—81no—
48C2×C4×C43—21no—
49C2×C4×C43—41no—
50C2×C4×C43—161no—
51C2×C4×C43#9911yescharacteristic
52C2×Dic43—41no—
53D172—81no—
54D172—161no—
55C4×D43—161no—
56Dic86—81no—
57C8×C43—41no—
58C43⋊C8—42no—
59#7523—431nomaximal, Sylow
60C22×C43—81no—
61C22×C43—161no—
62C22×C43AΣL(1,𝔽16)11yescharacteristic
63C2×D43—81no—
64C2×D43—81no—
65C2×D43—81no—
66C4×C43—21no—
67C4×C43—41no—
68C4×C43—81no—
69C4×C43—321no—
70Dic43—81no—
71#1656—431no—
72#1412D4311yescharacteristic, complemented
73#1355—431no—
74C2×C43—21no—
75C2×C43—161no—
76C2×C43#140411yescharacteristic
77D43—161no—
78#562—431no—
79#496—861no—
80#490C2×D4311yescharacteristic
81#353—21no—
82#347—861no—
83#330—431no—
84#329—861no—
85C43#752311yescharacteristic, complemented, Sylow
86C2×SD16—1721no—
87C2×D8—1721no—
88#127C22⋊D4311yescharacteristic
89#125C4×D4311yescharacteristic
90#124—861no—
91#123—1721no—
92C22⋊Q8—1721no—
93#121—1721no—
94M32—1721no—
95#102—41no—
96#99—41no—
97#97—861no—
98#97D17211yescharacteristic
99C2×Q8—861no—
100C2×D4—21no—
101C2×D4—41no—
102C2×D4—861no—
103C2×D4—1721no—
104C22×C4—1721no—
105SD16—3442no—
106D8—3442no—
107C2×C8—21no—
108C2×C8—1721no—
109C4⋊C4—21no—
110C4⋊C4—41no—
111C4⋊C4—1721no—
112C22⋊C4—81no—
113C22⋊C4—1721no—
114C22⋊C4—1721no—
115C22⋊C4—1721no—
116C42(C2×D43)⋊C411yescharacteristic
117C16—1722no—
118C23—41no—
119C23—1721no—
120Q8—3441no—
121D4—81no—
122D4—81no—
123D4—81no—
124D4—3441no—
125D4—6881no—
126C2×C4—21no—
127C2×C4—41no—
128C2×C4—161no—
129C2×C4—1721no—
130C2×C4—6881no—
131C2×C4#1306323911yescharacteristic
132C8—41no—
133C8—1722no—
134C22—81no—
135C22—161no—
136C22—3441no—
137C22—3441no—
138C22—3441no—
139C22#1458268511yescharacteristic
140C4—21no—
141C4—41no—
142C4—81no—
143C4—321no—
144C4—3441no—
145C2—21no—
146C2—161no—
147C2—6881no—
148C2#1913274511yescharacteristic
subgroupG/H
centerC2#19132745
commutator#125×C43C2×C4
Frattini#490C2×D43
FittingC43×#1412C2
socleC2×C43#1404
prime radical#19133887C2
cosocleC43×#490C22
hypercenter#1412D43
hypocenterC43#7523
LCSG ▷ #125×C43 ▷ C42×C43 ▷ C2×C4×C43 ▷ C22×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C42 ◁ #490 ◁ #1412

Complements

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

NH ≅ G/Ntype
2. #19132628C2semidirect
3. C43×#1412C2semidirect
4. #14583647C4semidirect
7. #14582641C4semidirect
72. #1412D43semidirect
85. C43#7523semidirect

Maximal subgroups

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

subgroupindex
#191338872
#191326282
C43×#14122
#752343