Finite Group Databasebeta

← C11⋊C5×#496 #72248958

Subgroups — C11⋊C5×#496 #72248958

Order 3520.

288 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 288 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C2×SD16×C11⋊C5C212yesmaximal, complemented
2C2×D8×C11⋊C5C212yesmaximal, complemented
3#127×C11⋊C5C211yesmaximal, characteristic, complemented
4#124×C11⋊C5C211yesmaximal, characteristic, complemented
5#97×C11⋊C5C211yesmaximal, characteristic, complemented
6C2×Q8×C11⋊C5C2211yescharacteristic
7C2×D4×C11⋊C5—22no—
8C2×D4×C11⋊C5C2211yescharacteristic
9C2×D4×C11⋊C5C2212yes—
10SD16×C11⋊C5—24no—
11D8×C11⋊C5—24no—
12C2×C8×C11⋊C5C2212yes—
13C22⋊C4×C11⋊C5—22no—
14C42×C11⋊C5C2211yescharacteristic
15C11×#496C511yesmaximal, characteristic, complemented, Hall
16C23×C11⋊C5—21no—
17C23×C11⋊C5—22no—
18Q8×C11⋊C5—22no—
19D4×C11⋊C5—22no—
20D4×C11⋊C5—22no—
21D4×C11⋊C5—22no—
22D4×C11⋊C5—44no—
23C2×C4×C11⋊C5—21no—
24C2×C4×C11⋊C5D412yes—
25C2×C4×C11⋊C5C2311yescharacteristic
26C8×C11⋊C5D414yescomplemented
27C2×C11×SD16C2×C512yescomplemented
28C2×C11×D8C2×C512yescomplemented
29C11×#127C2×C511yescharacteristic, complemented
30C11×#124C2×C511yescharacteristic, complemented
31C11×#97C2×C511yescharacteristic, complemented
32C5×#496—111nomaximal, Hall
33C22×C11⋊C5—41no—
34C22×C11⋊C5—42no—
35C22×C11⋊C5—44no—
36C22×C11⋊C5—42no—
37C22×C11⋊C5C2×D411yescharacteristic
38C4×C11⋊C5—22no—
39C4×C11⋊C5—41no—
40C4×C11⋊C5C2×D412yes—
41C2×Q8×C11C22×C511yescharacteristic
42C2×D4×C11—22no—
43C2×D4×C11C22×C511yescharacteristic
44C2×D4×C11C22×C512yes—
45C11×SD16—24no—
46C11×D8—24no—
47C2×C8×C11C22×C512yes—
48C11×C22⋊C4—22no—
49C42×C11C22×C511yescharacteristic
50C2×C5×SD16—112no—
51C2×C5×D8—112no—
52C5×#127—111no—
53C5×#124—111no—
54C5×#97—111no—
55C2×C11⋊C5—82no—
56C2×C11⋊C5—81no—
57C2×C11⋊C5#12711yescharacteristic
58C2×C11⋊C5AGL(1,ℤ/8)12yes—
59C23×C11—21no—
60C23×C11—22no—
61Q8×C11—22no—
62D4×C11—22no—
63D4×C11—22no—
64D4×C11—22no—
65D4×C11—44no—
66C2×C4×C11—21no—
67C2×C4×C11C5×D412yes—
68C2×C4×C11C23×C511yescharacteristic
69C8×C11C5×D414yescomplemented
70C2×C5×Q8—111no—
71C2×C5×D4—111no—
72C2×C5×D4—112no—
73C2×C5×D4—222no—
74C5×SD16—224no—
75C5×D8—224no—
76C2×C5×C8—112no—
77C5×C22⋊C4—222no—
78C42×C5—111no—
79#496C11⋊C511yescharacteristic, direct product factor, Sylow
80C11⋊C5#49611yescharacteristic, direct product factor, Hall
81C22×C11—41no—
82C22×C11—42no—
83C22×C11—44no—
84C22×C11—42no—
85C22×C11C2×C5×D411yescharacteristic
86C4×C11—22no—
87C4×C11—41no—
88C4×C11C2×C5×D412yes—
89C23×C5—221no—
90C23×C5—222no—
91C5×Q8—222no—
92C5×D4—222no—
93C5×D4—222no—
94C5×D4—222no—
95C5×D4—444no—
96C2×C4×C5—112no—
97C2×C4×C5—111no—
98C2×C4×C5—221no—
99C5×C8—114no—
100C2×SD16C2×C11⋊C512yescomplemented
101C2×D8C2×C11⋊C512yescomplemented
102#127C2×C11⋊C511yescharacteristic, complemented
103#124C2×C11⋊C511yescharacteristic, complemented
104#97C2×C11⋊C511yescharacteristic, complemented
105C2×C11—82no—
106C2×C11—81no—
107C2×C11C5×#12711yescharacteristic
108C2×C11C5×AGL(1,ℤ/8)12yes—
109C22×C5—111no—
110C22×C5—441no—
111C22×C5—442no—
112C22×C5—444no—
113C22×C5—442no—
114C4×C5—112no—
115C4×C5—222no—
116C4×C5—441no—
117C2×Q8C22×C11⋊C511yescharacteristic
118C2×D4—22no—
119C2×D4C22×C11⋊C511yescharacteristic
120C2×D4C22×C11⋊C512yes—
121SD16—24no—
122D8—24no—
123C2×C8C22×C11⋊C512yes—
124C22⋊C4—22no—
125C42C22×C11⋊C511yescharacteristic
126C11C5×#49611yescharacteristic, complemented, Sylow
127C2×C5—111no—
128C2×C5—112no—
129C2×C5—882no—
130C2×C5—881no—
131C23—21no—
132C23—22no—
133Q8—22no—
134D4—22no—
135D4—22no—
136D4—22no—
137D4—44no—
138C2×C4—21no—
139C2×C4D4×C11⋊C512yes—
140C2×C4C23×C11⋊C511yescharacteristic
141C8D4×C11⋊C514yescomplemented
142C5—111noSylow
143C22—41no—
144C22—42no—
145C22—44no—
146C22—42no—
147C22C2×D4×C11⋊C511yescharacteristic
148C4—22no—
149C4—41no—
150C4C2×D4×C11⋊C512yes—
151C2—82no—
152C2—81no—
153C2#127×C11⋊C511yescharacteristic
154C2AGL(1,ℤ/8)×C11⋊C512yes—
subgroupG/H
centerC22C2×D4×C11⋊C5
commutator, cosocleC2×C4×C11C23×C5
FrattiniC2×C4C23×C11⋊C5
FittingC11×#496C5
socleC22×C11C2×C5×D4
hypercenter#496C11⋊C5
hypocenterC11C5×#496
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C42 ◁ #496

Complements

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

NH ≅ G/Ntype
1. C2×SD16×C11⋊C5C2semidirect
2. C2×D8×C11⋊C5C2semidirect
3. #127×C11⋊C5C2semidirect
4. #124×C11⋊C5C2semidirect
5. #97×C11⋊C5C2semidirect
15. C11×#496C5semidirect
26. C8×C11⋊C5D4semidirect
27. C2×C11×SD16C2×C5semidirect
28. C2×C11×D8C2×C5semidirect
29. C11×#127C2×C5semidirect
30. C11×#124C2×C5semidirect
31. C11×#97C2×C5semidirect
69. C8×C11C5×D4semidirect
79. #496C11⋊C5direct (N × H)
80. C11⋊C5#496direct (N × H)
100. C2×SD16C2×C11⋊C5semidirect
101. C2×D8C2×C11⋊C5semidirect
102. #127C2×C11⋊C5semidirect
103. #124C2×C11⋊C5semidirect
104. #97C2×C11⋊C5semidirect
126. C11C5×#496semidirect
141. C8D4×C11⋊C5semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×C11⋊C52
C2×D8×C11⋊C52
#127×C11⋊C52
#124×C11⋊C52
#97×C11⋊C52
C11×#4965
C5×#49611